updated SMT certificates

--- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Sun Dec 19 18:54:29 2010 +0100
+++ b/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Sun Dec 19 18:55:21 2010 +0100
@@ -1,4 +1,4 @@
-2bcca4894d12c21351a258c93ec6b00e790bb1de 7195 0
+b9c818fc8db5c62ae4864b1c933f204656ce6c70 7184 0
 #2 := false
 decl f13 :: (-> S5 S3 Int)
 decl f22 :: S3
@@ -9,883 +9,878 @@
 decl f10 :: S3
 #56 := f10
 #99 := (f13 f14 f10)
-#7797 := (= #99 #174)
-#7825 := (= #174 #99)
-#6086 := (= f22 f10)
-#6088 := (= f10 f22)
+#7788 := (= #99 #174)
+#7816 := (= #174 #99)
+#6077 := (= f22 f10)
+#6079 := (= f10 f22)
 decl f3 :: (-> S2 S3 S1)
 decl ?v1!7 :: (-> S3 S3)
-#6069 := (?v1!7 f22)
+#6060 := (?v1!7 f22)
 decl f15 :: S2
 #104 := f15
-#6081 := (f3 f15 #6069)
+#6072 := (f3 f15 #6060)
 decl f1 :: S1
 #4 := f1
-#6082 := (= f1 #6081)
-#6083 := (not #6082)
+#6073 := (= f1 #6072)
+#6074 := (not #6073)
 #44 := 0::Int
 decl f9 :: (-> S4 Int)
 decl f5 :: (-> S3 S3 S4)
-#6074 := (f5 #6069 f22)
-#6075 := (f9 #6074)
-#1208 := -1::Int
-#6076 := (* -1::Int #6075)
-#6070 := (f13 f14 #6069)
-#6071 := (* -1::Int #6070)
-#6077 := (+ #6071 #6076)
-#6078 := (+ #174 #6077)
-#6079 := (= #6078 0::Int)
-#6080 := (not #6079)
-#6072 := (+ #174 #6071)
-#6073 := (<= #6072 0::Int)
-#6091 := (or #6073 #6080 #6083)
+#6065 := (f5 #6060 f22)
+#6066 := (f9 #6065)
+#1199 := -1::Int
+#6067 := (* -1::Int #6066)
+#6061 := (f13 f14 #6060)
+#6062 := (* -1::Int #6061)
+#6068 := (+ #6062 #6067)
+#6069 := (+ #174 #6068)
+#6070 := (= #6069 0::Int)
+#6071 := (not #6070)
+#6063 := (+ #174 #6062)
+#6064 := (<= #6063 0::Int)
+#6082 := (or #6064 #6071 #6074)
 decl f24 :: (-> S3 Int)
 decl ?v0!15 :: S3
-#2273 := ?v0!15
-#2274 := (f24 ?v0!15)
-#2275 := (>= #2274 0::Int)
-#2276 := (not #2275)
+#2264 := ?v0!15
+#2265 := (f24 ?v0!15)
+#2266 := (>= #2265 0::Int)
+#2267 := (not #2266)
 decl ?v0!20 :: S3
-#2346 := ?v0!20
+#2337 := ?v0!20
 #12 := (:var 0 S3)
-#2350 := (f5 #12 ?v0!20)
-#4454 := (pattern #2350)
-#189 := (f24 #12)
-#4394 := (pattern #189)
+#2341 := (f5 #12 ?v0!20)
+#4445 := (pattern #2341)
+#188 := (f24 #12)
+#4385 := (pattern #188)
 decl f23 :: S2
 #179 := f23
-#199 := (f3 f23 #12)
-#4420 := (pattern #199)
-#2351 := (f9 #2350)
-#2347 := (f24 ?v0!20)
-#2348 := (* -1::Int #2347)
-#2950 := (+ #2348 #2351)
-#2951 := (+ #189 #2950)
-#2954 := (= #2951 0::Int)
-#3516 := (not #2954)
-#2349 := (+ #189 #2348)
-#2354 := (>= #2349 0::Int)
-#807 := (= f1 #199)
-#813 := (not #807)
-#3517 := (or #813 #2354 #3516)
-#4455 := (forall (vars (?v1 S3)) (:pat #4420 #4394 #4454) #3517)
-#4460 := (not #4455)
+#198 := (f3 f23 #12)
+#4411 := (pattern #198)
+#2342 := (f9 #2341)
+#2338 := (f24 ?v0!20)
+#2339 := (* -1::Int #2338)
+#2941 := (+ #2339 #2342)
+#2942 := (+ #188 #2941)
+#2945 := (= #2942 0::Int)
+#3507 := (not #2945)
+#2340 := (+ #188 #2339)
+#2345 := (>= #2340 0::Int)
+#798 := (= f1 #198)
+#804 := (not #798)
+#3508 := (or #804 #2345 #3507)
+#4446 := (forall (vars (?v1 S3)) (:pat #4411 #4385 #4445) #3508)
+#4451 := (not #4446)
 #23 := (:var 1 S3)
 #81 := (f5 #12 #23)
-#4249 := (pattern #81)
-#211 := (f24 #23)
-#1503 := (* -1::Int #211)
-#1504 := (+ #189 #1503)
+#4240 := (pattern #81)
+#210 := (f24 #23)
+#1494 := (* -1::Int #210)
+#1495 := (+ #188 #1494)
 #82 := (f9 #81)
-#1534 := (+ #82 #1504)
-#1532 := (>= #1534 0::Int)
-#1231 := (* -1::Int #82)
+#1525 := (+ #82 #1495)
+#1523 := (>= #1525 0::Int)
+#1222 := (* -1::Int #82)
 decl f8 :: Int
 #45 := f8
-#1234 := (+ f8 #1231)
-#1235 := (<= #1234 0::Int)
-#3508 := (or #813 #1235 #1532)
-#4446 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3508)
-#4451 := (not #4446)
-#2926 := (= f10 ?v0!20)
-#2358 := (+ f8 #2348)
-#2359 := (<= #2358 0::Int)
-#4463 := (or #2359 #2926 #4451 #4460)
-#4466 := (not #4463)
+#1225 := (+ f8 #1222)
+#1226 := (<= #1225 0::Int)
+#3499 := (or #804 #1226 #1523)
+#4437 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3499)
+#4442 := (not #4437)
+#2917 := (= f10 ?v0!20)
+#2349 := (+ f8 #2339)
+#2350 := (<= #2349 0::Int)
+#4454 := (or #2350 #2917 #4442 #4451)
+#4457 := (not #4454)
 decl ?v0!19 :: S3
-#2316 := ?v0!19
+#2307 := ?v0!19
 decl ?v1!18 :: S3
-#2315 := ?v1!18
-#2321 := (f5 ?v1!18 ?v0!19)
-#2322 := (f9 #2321)
-#2325 := (* -1::Int #2322)
-#2319 := (f24 ?v1!18)
-#2912 := (* -1::Int #2319)
-#2913 := (+ #2912 #2325)
-#2317 := (f24 ?v0!19)
-#2914 := (+ #2317 #2913)
-#2915 := (<= #2914 0::Int)
-#2329 := (f3 f23 ?v1!18)
-#2330 := (= f1 #2329)
-#3471 := (not #2330)
-#2326 := (+ f8 #2325)
-#2327 := (<= #2326 0::Int)
-#3486 := (or #2327 #3471 #2915)
-#3491 := (not #3486)
-#4469 := (or #3491 #4466)
-#4472 := (not #4469)
-#4437 := (pattern #189 #211)
-#1502 := (>= #1504 0::Int)
-#208 := (f3 f23 #23)
-#827 := (= f1 #208)
-#3448 := (not #827)
-#3463 := (or #807 #3448 #1502)
-#4438 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4437) #3463)
-#4443 := (not #4438)
-#4475 := (or #4443 #4472)
-#4478 := (not #4475)
+#2306 := ?v1!18
+#2312 := (f5 ?v1!18 ?v0!19)
+#2313 := (f9 #2312)
+#2316 := (* -1::Int #2313)
+#2310 := (f24 ?v1!18)
+#2903 := (* -1::Int #2310)
+#2904 := (+ #2903 #2316)
+#2308 := (f24 ?v0!19)
+#2905 := (+ #2308 #2904)
+#2906 := (<= #2905 0::Int)
+#2320 := (f3 f23 ?v1!18)
+#2321 := (= f1 #2320)
+#3462 := (not #2321)
+#2317 := (+ f8 #2316)
+#2318 := (<= #2317 0::Int)
+#3477 := (or #2318 #3462 #2906)
+#3482 := (not #3477)
+#4460 := (or #3482 #4457)
+#4463 := (not #4460)
+#4428 := (pattern #188 #210)
+#1493 := (>= #1495 0::Int)
+#207 := (f3 f23 #23)
+#818 := (= f1 #207)
+#3439 := (not #818)
+#3454 := (or #798 #3439 #1493)
+#4429 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4428) #3454)
+#4434 := (not #4429)
+#4466 := (or #4434 #4463)
+#4469 := (not #4466)
 decl ?v1!16 :: S3
-#2288 := ?v1!16
-#2292 := (f24 ?v1!16)
-#2886 := (* -1::Int #2292)
+#2279 := ?v1!16
+#2283 := (f24 ?v1!16)
+#2877 := (* -1::Int #2283)
 decl ?v0!17 :: S3
-#2289 := ?v0!17
-#2290 := (f24 ?v0!17)
-#2887 := (+ #2290 #2886)
-#2888 := (<= #2887 0::Int)
-#2297 := (f3 f23 ?v1!16)
-#2298 := (= f1 #2297)
-#2295 := (f3 f23 ?v0!17)
-#2296 := (= f1 #2295)
-#3425 := (not #2296)
-#3440 := (or #3425 #2298 #2888)
-#3445 := (not #3440)
-#4481 := (or #3445 #4478)
-#4484 := (not #4481)
-#1493 := (>= #189 0::Int)
-#4429 := (forall (vars (?v0 S3)) (:pat #4394) #1493)
-#4434 := (not #4429)
-#4487 := (or #4434 #4484)
+#2280 := ?v0!17
+#2281 := (f24 ?v0!17)
+#2878 := (+ #2281 #2877)
+#2879 := (<= #2878 0::Int)
+#2288 := (f3 f23 ?v1!16)
+#2289 := (= f1 #2288)
+#2286 := (f3 f23 ?v0!17)
+#2287 := (= f1 #2286)
+#3416 := (not #2287)
+#3431 := (or #3416 #2289 #2879)
+#3436 := (not #3431)
+#4472 := (or #3436 #4469)
+#4475 := (not #4472)
+#1484 := (>= #188 0::Int)
+#4420 := (forall (vars (?v0 S3)) (:pat #4385) #1484)
+#4425 := (not #4420)
+#4478 := (or #4425 #4475)
 decl f6 :: (-> S4 S3)
 decl f7 :: (-> S4 S3)
-#5995 := (f5 f22 f22)
-#7211 := (f7 #5995)
-#14211 := (f5 #7211 ?v0!20)
-#24392 := (f7 #14211)
-#14774 := (?v1!7 ?v0!20)
-#24669 := (f5 #14774 #24392)
-#25042 := (f6 #24669)
-#26213 := (f3 f15 #25042)
-#26214 := (= f1 #26213)
-#14786 := (f3 f15 #14774)
-#27706 := (= #14786 #26213)
-#27703 := (= #26213 #14786)
-#29051 := (= #25042 #14774)
-#14779 := (f5 #14774 ?v0!20)
-#19038 := (f6 #14779)
-#26818 := (= #19038 #14774)
-#19043 := (= #14774 #19038)
+#5986 := (f5 f22 f22)
+#7202 := (f7 #5986)
+#14202 := (f5 #7202 ?v0!20)
+#24383 := (f7 #14202)
+#14765 := (?v1!7 ?v0!20)
+#24660 := (f5 #14765 #24383)
+#25033 := (f6 #24660)
+#26204 := (f3 f15 #25033)
+#26205 := (= f1 #26204)
+#14777 := (f3 f15 #14765)
+#27697 := (= #14777 #26204)
+#27694 := (= #26204 #14777)
+#29042 := (= #25033 #14765)
+#14770 := (f5 #14765 ?v0!20)
+#19029 := (f6 #14770)
+#26809 := (= #19029 #14765)
+#19034 := (= #14765 #19029)
 #37 := (f5 #23 #12)
-#4193 := (pattern #37)
+#4184 := (pattern #37)
 #41 := (f6 #37)
-#344 := (= #23 #41)
-#4200 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4193) #344)
-#348 := (forall (vars (?v0 S3) (?v1 S3)) #344)
-#4203 := (iff #348 #4200)
-#4201 := (iff #344 #344)
-#4202 := [refl]: #4201
-#4204 := [quant-intro #4202]: #4203
-#1848 := (~ #348 #348)
-#1878 := (~ #344 #344)
-#1879 := [refl]: #1878
-#1849 := [nnf-pos #1879]: #1848
+#343 := (= #23 #41)
+#4191 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #343)
+#347 := (forall (vars (?v0 S3) (?v1 S3)) #343)
+#4194 := (iff #347 #4191)
+#4192 := (iff #343 #343)
+#4193 := [refl]: #4192
+#4195 := [quant-intro #4193]: #4194
+#1839 := (~ #347 #347)
+#1869 := (~ #343 #343)
+#1870 := [refl]: #1869
+#1840 := [nnf-pos #1870]: #1839
 #42 := (= #41 #23)
 #43 := (forall (vars (?v0 S3) (?v1 S3)) #42)
-#349 := (iff #43 #348)
-#346 := (iff #42 #344)
-#347 := [rewrite]: #346
-#350 := [quant-intro #347]: #349
-#343 := [asserted]: #43
-#353 := [mp #343 #350]: #348
-#1880 := [mp~ #353 #1849]: #348
-#4205 := [mp #1880 #4204]: #4200
-#6829 := (not #4200)
-#8630 := (or #6829 #19043)
-#13594 := [quant-inst #14774 #2346]: #8630
-#26774 := [unit-resolution #13594 #4205]: #19043
-#26816 := [symm #26774]: #26818
-#26826 := (= #25042 #19038)
-#26823 := (= #24669 #14779)
-#27255 := (= #24392 ?v0!20)
-#19042 := (f7 #14779)
-#25094 := (= #19042 ?v0!20)
-#19037 := (= ?v0!20 #19042)
+#348 := (iff #43 #347)
+#345 := (iff #42 #343)
+#346 := [rewrite]: #345
+#349 := [quant-intro #346]: #348
+#342 := [asserted]: #43
+#352 := [mp #342 #349]: #347
+#1871 := [mp~ #352 #1840]: #347
+#4196 := [mp #1871 #4195]: #4191
+#6820 := (not #4191)
+#8621 := (or #6820 #19034)
+#13585 := [quant-inst #14765 #2337]: #8621
+#26765 := [unit-resolution #13585 #4196]: #19034
+#26807 := [symm #26765]: #26809
+#26817 := (= #25033 #19029)
+#26814 := (= #24660 #14770)
+#27246 := (= #24383 ?v0!20)
+#19033 := (f7 #14770)
+#25085 := (= #19033 ?v0!20)
+#19028 := (= ?v0!20 #19033)
 #38 := (f7 #37)
-#336 := (= #12 #38)
-#4194 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4193) #336)
-#340 := (forall (vars (?v0 S3) (?v1 S3)) #336)
-#4197 := (iff #340 #4194)
-#4195 := (iff #336 #336)
-#4196 := [refl]: #4195
-#4198 := [quant-intro #4196]: #4197
-#1846 := (~ #340 #340)
-#1875 := (~ #336 #336)
-#1876 := [refl]: #1875
-#1847 := [nnf-pos #1876]: #1846
+#335 := (= #12 #38)
+#4185 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #335)
+#339 := (forall (vars (?v0 S3) (?v1 S3)) #335)
+#4188 := (iff #339 #4185)
+#4186 := (iff #335 #335)
+#4187 := [refl]: #4186
+#4189 := [quant-intro #4187]: #4188
+#1837 := (~ #339 #339)
+#1866 := (~ #335 #335)
+#1867 := [refl]: #1866
+#1838 := [nnf-pos #1867]: #1837
 #39 := (= #38 #12)
 #40 := (forall (vars (?v0 S3) (?v1 S3)) #39)
-#341 := (iff #40 #340)
-#338 := (iff #39 #336)
-#339 := [rewrite]: #338
-#342 := [quant-intro #339]: #341
-#335 := [asserted]: #40
-#345 := [mp #335 #342]: #340
-#1877 := [mp~ #345 #1847]: #340
-#4199 := [mp #1877 #4198]: #4194
-#6824 := (not #4194)
-#19044 := (or #6824 #19037)
-#19045 := [quant-inst #14774 #2346]: #19044
-#25093 := [unit-resolution #19045 #4199]: #19037
-#25095 := [symm #25093]: #25094
-#26795 := (= #24392 #19042)
-#23180 := (f5 #7211 #19042)
-#23299 := (f7 #23180)
-#26807 := (= #23299 #19042)
-#23305 := (= #19042 #23299)
-#26717 := (or #6824 #23305)
-#26720 := [quant-inst #7211 #19042]: #26717
-#26803 := [unit-resolution #26720 #4199]: #23305
-#26808 := [symm #26803]: #26807
-#26804 := (= #24392 #23299)
-#26801 := (= #23299 #24392)
-#26799 := (= #23180 #14211)
-#14131 := (f5 f22 ?v0!20)
-#26773 := (= #14131 #14211)
-#24028 := (= #14211 #14131)
-#7784 := (= #7211 f22)
-#7212 := (= f22 #7211)
-#7263 := (or #6824 #7212)
-#7264 := [quant-inst #170 #170]: #7263
-#7789 := [unit-resolution #7264 #4199]: #7212
-#7790 := [symm #7789]: #7784
-#24029 := [monotonicity #7790]: #24028
-#26715 := [symm #24029]: #26773
-#26777 := (= #23180 #14131)
-#26776 := (= #14131 #23180)
-#26752 := [monotonicity #7789 #25093]: #26776
-#26778 := [symm #26752]: #26777
-#26802 := [trans #26778 #26715]: #26799
-#26805 := [monotonicity #26802]: #26801
-#26806 := [symm #26805]: #26804
-#26822 := [trans #26806 #26808]: #26795
-#26796 := [trans #26822 #25095]: #27255
-#26824 := [monotonicity #26796]: #26823
-#26817 := [monotonicity #26824]: #26826
-#26819 := [trans #26817 #26816]: #29051
-#26814 := [monotonicity #26819]: #27703
-#26828 := [symm #26814]: #27706
-#14787 := (= f1 #14786)
-#14788 := (not #14787)
-#14780 := (f9 #14779)
-#14781 := (* -1::Int #14780)
-#14775 := (f13 f14 #14774)
-#14776 := (* -1::Int #14775)
-#14782 := (+ #14776 #14781)
-#14074 := (f13 f14 ?v0!20)
-#14783 := (+ #14074 #14782)
-#14784 := (= #14783 0::Int)
-#14785 := (not #14784)
-#14777 := (+ #14074 #14776)
-#14778 := (<= #14777 0::Int)
-#14794 := (or #14778 #14785 #14788)
-#14797 := (not #14794)
-#14115 := (* -1::Int #14074)
-#14791 := (+ f8 #14115)
-#14792 := (<= #14791 0::Int)
-#21435 := (not #14792)
-#2360 := (not #2359)
-#19783 := [hypothesis]: #2360
-#14116 := (+ #2347 #14115)
-#19567 := (>= #14116 0::Int)
-#14085 := (= #2347 #14074)
-#14132 := (f9 #14131)
-#14150 := (+ #14115 #14132)
-#14151 := (+ #174 #14150)
-#14152 := (>= #14151 0::Int)
-#14136 := (* -1::Int #14132)
-#14140 := (+ f8 #14136)
-#14141 := (<= #14140 0::Int)
-#14183 := (or #14141 #14152)
-#4490 := (not #4487)
-#1453 := (* -1::Int #174)
-#5913 := (+ #99 #1453)
-#7798 := (<= #5913 0::Int)
-#27734 := (or #6073 #2359)
-#25047 := (= #14774 #25042)
-#23337 := (or #6829 #25047)
-#23338 := [quant-inst #14774 #24392]: #23337
-#28984 := [unit-resolution #23338 #4205]: #25047
-#29062 := [symm #28984]: #29051
-#27698 := [monotonicity #29062]: #27703
-#27718 := [symm #27698]: #27706
-#6118 := (not #6073)
-#10074 := [hypothesis]: #6118
-#23174 := (or #14152 #6073)
-#11114 := (or #2275 #6073)
-#7536 := (f13 f14 ?v0!15)
-#7757 := (>= #7536 0::Int)
+#340 := (iff #40 #339)
+#337 := (iff #39 #335)
+#338 := [rewrite]: #337
+#341 := [quant-intro #338]: #340
+#334 := [asserted]: #40
+#344 := [mp #334 #341]: #339
+#1868 := [mp~ #344 #1838]: #339
+#4190 := [mp #1868 #4189]: #4185
+#6815 := (not #4185)
+#19035 := (or #6815 #19028)
+#19036 := [quant-inst #14765 #2337]: #19035
+#25084 := [unit-resolution #19036 #4190]: #19028
+#25086 := [symm #25084]: #25085
+#26786 := (= #24383 #19033)
+#23171 := (f5 #7202 #19033)
+#23290 := (f7 #23171)
+#26798 := (= #23290 #19033)
+#23296 := (= #19033 #23290)
+#26708 := (or #6815 #23296)
+#26711 := [quant-inst #7202 #19033]: #26708
+#26794 := [unit-resolution #26711 #4190]: #23296
+#26799 := [symm #26794]: #26798
+#26795 := (= #24383 #23290)
+#26792 := (= #23290 #24383)
+#26790 := (= #23171 #14202)
+#14122 := (f5 f22 ?v0!20)
+#26764 := (= #14122 #14202)
+#24019 := (= #14202 #14122)
+#7775 := (= #7202 f22)
+#7203 := (= f22 #7202)
+#7254 := (or #6815 #7203)
+#7255 := [quant-inst #170 #170]: #7254
+#7780 := [unit-resolution #7255 #4190]: #7203
+#7781 := [symm #7780]: #7775
+#24020 := [monotonicity #7781]: #24019
+#26706 := [symm #24020]: #26764
+#26768 := (= #23171 #14122)
+#26767 := (= #14122 #23171)
+#26743 := [monotonicity #7780 #25084]: #26767
+#26769 := [symm #26743]: #26768
+#26793 := [trans #26769 #26706]: #26790
+#26796 := [monotonicity #26793]: #26792
+#26797 := [symm #26796]: #26795
+#26813 := [trans #26797 #26799]: #26786
+#26787 := [trans #26813 #25086]: #27246
+#26815 := [monotonicity #26787]: #26814
+#26808 := [monotonicity #26815]: #26817
+#26810 := [trans #26808 #26807]: #29042
+#26805 := [monotonicity #26810]: #27694
+#26819 := [symm #26805]: #27697
+#14778 := (= f1 #14777)
+#14779 := (not #14778)
+#14771 := (f9 #14770)
+#14772 := (* -1::Int #14771)
+#14766 := (f13 f14 #14765)
+#14767 := (* -1::Int #14766)
+#14773 := (+ #14767 #14772)
+#14065 := (f13 f14 ?v0!20)
+#14774 := (+ #14065 #14773)
+#14775 := (= #14774 0::Int)
+#14776 := (not #14775)
+#14768 := (+ #14065 #14767)
+#14769 := (<= #14768 0::Int)
+#14785 := (or #14769 #14776 #14779)
+#14788 := (not #14785)
+#14106 := (* -1::Int #14065)
+#14782 := (+ f8 #14106)
+#14783 := (<= #14782 0::Int)
+#21426 := (not #14783)
+#2351 := (not #2350)
+#19774 := [hypothesis]: #2351
+#14107 := (+ #2338 #14106)
+#19558 := (>= #14107 0::Int)
+#14076 := (= #2338 #14065)
+#14123 := (f9 #14122)
+#14141 := (+ #14106 #14123)
+#14142 := (+ #174 #14141)
+#14143 := (>= #14142 0::Int)
+#14127 := (* -1::Int #14123)
+#14131 := (+ f8 #14127)
+#14132 := (<= #14131 0::Int)
+#14174 := (or #14132 #14143)
+#4481 := (not #4478)
+#1444 := (* -1::Int #174)
+#5904 := (+ #99 #1444)
+#7789 := (<= #5904 0::Int)
+#27725 := (or #6064 #2350)
+#25038 := (= #14765 #25033)
+#23328 := (or #6820 #25038)
+#23329 := [quant-inst #14765 #24383]: #23328
+#28975 := [unit-resolution #23329 #4196]: #25038
+#29053 := [symm #28975]: #29042
+#27689 := [monotonicity #29053]: #27694
+#27709 := [symm #27689]: #27697
+#6109 := (not #6064)
+#10065 := [hypothesis]: #6109
+#23165 := (or #14143 #6064)
+#11105 := (or #2266 #6064)
+#7527 := (f13 f14 ?v0!15)
+#7748 := (>= #7527 0::Int)
 #101 := (f13 f14 #12)
-#4273 := (pattern #101)
-#1736 := (>= #101 0::Int)
-#4274 := (forall (vars (?v0 S3)) (:pat #4273) #1736)
-#4493 := (or #2276 #4490)
-#4496 := (not #4493)
-#203 := (f24 f10)
-#204 := (= #203 0::Int)
-#1490 := (not #204)
-#4499 := (or #1490 #4496)
-#4502 := (not #4499)
-#4505 := (or #1490 #4502)
-#4508 := (not #4505)
-#793 := (= #101 #189)
-#814 := (or #793 #813)
-#4421 := (forall (vars (?v0 S3)) (:pat #4273 #4394 #4420) #814)
-#4426 := (not #4421)
-#4511 := (or #4426 #4508)
-#4514 := (not #4511)
+#4264 := (pattern #101)
+#1727 := (>= #101 0::Int)
+#4265 := (forall (vars (?v0 S3)) (:pat #4264) #1727)
+#4484 := (or #2267 #4481)
+#4487 := (not #4484)
+#202 := (f24 f10)
+#203 := (= #202 0::Int)
+#1481 := (not #203)
+#4490 := (or #1481 #4487)
+#4493 := (not #4490)
+#4496 := (or #1481 #4493)
+#4499 := (not #4496)
+#784 := (= #101 #188)
+#805 := (or #784 #804)
+#4412 := (forall (vars (?v0 S3)) (:pat #4264 #4385 #4411) #805)
+#4417 := (not #4412)
+#4502 := (or #4417 #4499)
+#4505 := (not #4502)
 decl ?v0!14 :: S3
-#2248 := ?v0!14
-#2253 := (f13 f14 ?v0!14)
-#2252 := (f24 ?v0!14)
-#2858 := (= #2252 #2253)
-#2249 := (f3 f23 ?v0!14)
-#2250 := (= f1 #2249)
-#2251 := (not #2250)
-#2864 := (or #2251 #2858)
-#2869 := (not #2864)
-#4517 := (or #2869 #4514)
-#4520 := (not #4517)
-#1478 := (* -1::Int #189)
-#1479 := (+ #101 #1478)
-#1477 := (>= #1479 0::Int)
-#4412 := (forall (vars (?v0 S3)) (:pat #4273 #4394) #1477)
-#4417 := (not #4412)
-#4523 := (or #4417 #4520)
-#4526 := (not #4523)
+#2239 := ?v0!14
+#2244 := (f13 f14 ?v0!14)
+#2243 := (f24 ?v0!14)
+#2849 := (= #2243 #2244)
+#2240 := (f3 f23 ?v0!14)
+#2241 := (= f1 #2240)
+#2242 := (not #2241)
+#2855 := (or #2242 #2849)
+#2860 := (not #2855)
+#4508 := (or #2860 #4505)
+#4511 := (not #4508)
+#1469 := (* -1::Int #188)
+#1470 := (+ #101 #1469)
+#1468 := (>= #1470 0::Int)
+#4403 := (forall (vars (?v0 S3)) (:pat #4264 #4385) #1468)
+#4408 := (not #4403)
+#4514 := (or #4408 #4511)
+#4517 := (not #4514)
 decl ?v0!13 :: S3
-#2230 := ?v0!13
-#2233 := (f13 f14 ?v0!13)
-#2848 := (* -1::Int #2233)
-#2231 := (f24 ?v0!13)
-#2849 := (+ #2231 #2848)
-#2850 := (<= #2849 0::Int)
-#2855 := (not #2850)
-#4529 := (or #2855 #4526)
-#4532 := (not #4529)
-#183 := (f5 f22 #12)
-#4395 := (pattern #183)
-#184 := (f9 #183)
-#1621 := (+ #184 #1478)
-#1622 := (+ #174 #1621)
-#1623 := (= #1622 0::Int)
-#1447 := (* -1::Int #184)
-#1454 := (+ #1453 #1447)
-#1455 := (+ #101 #1454)
-#1456 := (<= #1455 0::Int)
-#1448 := (+ f8 #1447)
-#1449 := (<= #1448 0::Int)
-#3417 := (or #1449 #1456 #1623)
-#4404 := (forall (vars (?v0 S3)) (:pat #4395 #4273 #4394) #3417)
-#4409 := (not #4404)
-#3397 := (or #1449 #1456)
-#3398 := (not #3397)
-#3401 := (or #793 #3398)
-#4396 := (forall (vars (?v0 S3)) (:pat #4273 #4394 #4395) #3401)
-#4401 := (not #4396)
+#2221 := ?v0!13
+#2224 := (f13 f14 ?v0!13)
+#2839 := (* -1::Int #2224)
+#2222 := (f24 ?v0!13)
+#2840 := (+ #2222 #2839)
+#2841 := (<= #2840 0::Int)
+#2846 := (not #2841)
+#4520 := (or #2846 #4517)
+#4523 := (not #4520)
+#182 := (f5 f22 #12)
+#4386 := (pattern #182)
+#183 := (f9 #182)
+#1612 := (+ #183 #1469)
+#1613 := (+ #174 #1612)
+#1614 := (= #1613 0::Int)
+#1438 := (* -1::Int #183)
+#1445 := (+ #1444 #1438)
+#1446 := (+ #101 #1445)
+#1447 := (<= #1446 0::Int)
+#1439 := (+ f8 #1438)
+#1440 := (<= #1439 0::Int)
+#3408 := (or #1440 #1447 #1614)
+#4395 := (forall (vars (?v0 S3)) (:pat #4386 #4264 #4385) #3408)
+#4400 := (not #4395)
+#3388 := (or #1440 #1447)
+#3389 := (not #3388)
+#3392 := (or #784 #3389)
+#4387 := (forall (vars (?v0 S3)) (:pat #4264 #4385 #4386) #3392)
+#4392 := (not #4387)
 decl ?v0!12 :: S3
-#2206 := ?v0!12
-#2212 := (f3 f15 ?v0!12)
-#2213 := (= f1 #2212)
-#2207 := (f13 f14 ?v0!12)
-#2208 := (* -1::Int #2207)
-#2209 := (+ f8 #2208)
-#2210 := (<= #2209 0::Int)
-#1653 := (+ f8 #1453)
-#1654 := (<= #1653 0::Int)
+#2197 := ?v0!12
+#2203 := (f3 f15 ?v0!12)
+#2204 := (= f1 #2203)
+#2198 := (f13 f14 ?v0!12)
+#2199 := (* -1::Int #2198)
+#2200 := (+ f8 #2199)
+#2201 := (<= #2200 0::Int)
+#1644 := (+ f8 #1444)
+#1645 := (<= #1644 0::Int)
 #105 := (f3 f15 #12)
-#4315 := (pattern #105)
-#1636 := (+ #101 #1453)
-#1635 := (>= #1636 0::Int)
-#533 := (= f1 #105)
-#1642 := (or #533 #1635)
-#4386 := (forall (vars (?v0 S3)) (:pat #4315 #4273) #1642)
-#4391 := (not #4386)
+#4306 := (pattern #105)
+#1627 := (+ #101 #1444)
+#1626 := (>= #1627 0::Int)
+#532 := (= f1 #105)
+#1633 := (or #532 #1626)
+#4377 := (forall (vars (?v0 S3)) (:pat #4306 #4264) #1633)
+#4382 := (not #4377)
+#171 := (f3 f15 f22)
+#753 := (= f1 #171)
 decl f4 :: (-> S2 S3 S1 S2)
-#773 := (f4 f15 f22 f1)
-#776 := (= f23 #773)
-#995 := (not #776)
-#171 := (f3 f15 f22)
-#754 := (= f1 #171)
-#4535 := (or #754 #995 #4391 #1654 #2210 #2213 #4401 #4409 #4532)
-#4538 := (not #4535)
+#180 := (f4 f15 f22 f1)
+#181 := (= f23 #180)
+#986 := (not #181)
+#4526 := (or #986 #753 #4382 #1645 #2201 #2204 #4392 #4400 #4523)
+#4529 := (not #4526)
 decl ?v0!11 :: S3
-#2140 := ?v0!11
+#2131 := ?v0!11
 decl ?v1!10 :: S3
-#2139 := ?v1!10
-#2145 := (f5 ?v1!10 ?v0!11)
-#2146 := (f9 #2145)
-#2153 := (* -1::Int #2146)
+#2130 := ?v1!10
+#2136 := (f5 ?v1!10 ?v0!11)
+#2137 := (f9 #2136)
+#2144 := (* -1::Int #2137)
 decl f19 :: S5
 #137 := f19
-#2143 := (f13 f19 ?v1!10)
-#2149 := (* -1::Int #2143)
-#2805 := (+ #2149 #2153)
-#2141 := (f13 f19 ?v0!11)
-#2806 := (+ #2141 #2805)
-#2807 := (<= #2806 0::Int)
-#2154 := (+ f8 #2153)
-#2155 := (<= #2154 0::Int)
-#2150 := (+ f8 #2149)
-#2151 := (<= #2150 0::Int)
-#3361 := (or #2151 #2155 #2807)
-#3366 := (not #3361)
+#2134 := (f13 f19 ?v1!10)
+#2140 := (* -1::Int #2134)
+#2796 := (+ #2140 #2144)
+#2132 := (f13 f19 ?v0!11)
+#2797 := (+ #2132 #2796)
+#2798 := (<= #2797 0::Int)
+#2145 := (+ f8 #2144)
+#2146 := (<= #2145 0::Int)
+#2141 := (+ f8 #2140)
+#2142 := (<= #2141 0::Int)
+#3352 := (or #2142 #2146 #2798)
+#3357 := (not #3352)
 #145 := (f13 f19 #23)
-#1355 := (* -1::Int #145)
+#1346 := (* -1::Int #145)
 #142 := (f13 f19 #12)
-#1356 := (+ #142 #1355)
-#1362 := (+ #82 #1356)
-#1385 := (>= #1362 0::Int)
-#1342 := (* -1::Int #142)
-#1343 := (+ f8 #1342)
-#1344 := (<= #1343 0::Int)
-#3329 := (or #1235 #1344 #1385)
-#4348 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3329)
-#4353 := (not #4348)
+#1347 := (+ #142 #1346)
+#1353 := (+ #82 #1347)
+#1376 := (>= #1353 0::Int)
+#1333 := (* -1::Int #142)
+#1334 := (+ f8 #1333)
+#1335 := (<= #1334 0::Int)
+#3320 := (or #1226 #1335 #1376)
+#4339 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3320)
+#4344 := (not #4339)
 #157 := (f13 f19 f10)
 #158 := (= #157 0::Int)
-#4356 := (or #158 #4353)
-#4359 := (not #4356)
-#4362 := (or #4359 #3366)
-#4365 := (not #4362)
-#4324 := (pattern #142)
+#4347 := (or #158 #4344)
+#4350 := (not #4347)
+#4353 := (or #4350 #3357)
+#4356 := (not #4353)
+#4315 := (pattern #142)
 decl ?v1!9 :: (-> S3 S3)
-#2116 := (?v1!9 #12)
-#2119 := (f5 #2116 #12)
-#2120 := (f9 #2119)
-#2775 := (* -1::Int #2120)
-#2117 := (f13 f19 #2116)
-#2758 := (* -1::Int #2117)
-#2776 := (+ #2758 #2775)
-#2777 := (+ #142 #2776)
-#2778 := (= #2777 0::Int)
-#3299 := (not #2778)
-#2759 := (+ #142 #2758)
-#2760 := (<= #2759 0::Int)
-#3300 := (or #2760 #3299)
-#3301 := (not #3300)
+#2107 := (?v1!9 #12)
+#2110 := (f5 #2107 #12)
+#2111 := (f9 #2110)
+#2766 := (* -1::Int #2111)
+#2108 := (f13 f19 #2107)
+#2749 := (* -1::Int #2108)
+#2767 := (+ #2749 #2766)
+#2768 := (+ #142 #2767)
+#2769 := (= #2768 0::Int)
+#3290 := (not #2769)
+#2750 := (+ #142 #2749)
+#2751 := (<= #2750 0::Int)
+#3291 := (or #2751 #3290)
+#3292 := (not #3291)
 #57 := (= #12 f10)
-#3307 := (or #57 #1344 #3301)
-#4340 := (forall (vars (?v0 S3)) (:pat #4324) #3307)
-#4345 := (not #4340)
-#4368 := (or #4345 #4365)
-#4371 := (not #4368)
+#3298 := (or #57 #1335 #3292)
+#4331 := (forall (vars (?v0 S3)) (:pat #4315) #3298)
+#4336 := (not #4331)
+#4359 := (or #4336 #4356)
+#4362 := (not #4359)
 decl ?v0!8 :: S3
-#2076 := ?v0!8
-#2080 := (f5 #12 ?v0!8)
-#4325 := (pattern #2080)
-#2081 := (f9 #2080)
-#2077 := (f13 f19 ?v0!8)
-#2078 := (* -1::Int #2077)
-#2728 := (+ #2078 #2081)
-#2729 := (+ #142 #2728)
-#2732 := (= #2729 0::Int)
-#3263 := (not #2732)
-#2079 := (+ #142 #2078)
-#2084 := (>= #2079 0::Int)
-#3264 := (or #2084 #3263)
-#4326 := (forall (vars (?v1 S3)) (:pat #4324 #4325) #3264)
-#4331 := (not #4326)
-#2704 := (= f10 ?v0!8)
-#2088 := (+ f8 #2078)
-#2089 := (<= #2088 0::Int)
-#4334 := (or #2089 #2704 #4331)
-#4337 := (not #4334)
-#4374 := (or #4337 #4371)
-#4377 := (not #4374)
-#1297 := (* -1::Int #101)
-#1298 := (+ f8 #1297)
-#1299 := (<= #1298 0::Int)
-#3249 := (or #533 #1299)
-#4316 := (forall (vars (?v0 S3)) (:pat #4315 #4273) #3249)
-#4321 := (not #4316)
-#624 := (= f14 f19)
-#715 := (not #624)
+#2067 := ?v0!8
+#2071 := (f5 #12 ?v0!8)
+#4316 := (pattern #2071)
+#2072 := (f9 #2071)
+#2068 := (f13 f19 ?v0!8)
+#2069 := (* -1::Int #2068)
+#2719 := (+ #2069 #2072)
+#2720 := (+ #142 #2719)
+#2723 := (= #2720 0::Int)
+#3254 := (not #2723)
+#2070 := (+ #142 #2069)
+#2075 := (>= #2070 0::Int)
+#3255 := (or #2075 #3254)
+#4317 := (forall (vars (?v1 S3)) (:pat #4315 #4316) #3255)
+#4322 := (not #4317)
+#2695 := (= f10 ?v0!8)
+#2079 := (+ f8 #2069)
+#2080 := (<= #2079 0::Int)
+#4325 := (or #2080 #2695 #4322)
+#4328 := (not #4325)
+#4365 := (or #4328 #4362)
+#4368 := (not #4365)
+#1288 := (* -1::Int #101)
+#1289 := (+ f8 #1288)
+#1290 := (<= #1289 0::Int)
+#3240 := (or #532 #1290)
+#4307 := (forall (vars (?v0 S3)) (:pat #4306 #4264) #3240)
+#4312 := (not #4307)
+#623 := (= f14 f19)
+#714 := (not #623)
 decl f16 :: S2
 #132 := f16
-#621 := (= f15 f16)
-#733 := (not #621)
+#620 := (= f15 f16)
+#732 := (not #620)
 decl f21 :: S5
 #140 := f21
 decl f20 :: S5
 #139 := f20
 #141 := (= f20 f21)
-#706 := (not #141)
+#705 := (not #141)
 decl f18 :: S3
 #135 := f18
 decl f17 :: S3
 #134 := f17
 #136 := (= f17 f18)
-#724 := (not #136)
-#4380 := (or #724 #706 #733 #715 #4321 #4377)
-#4383 := (not #4380)
-#4541 := (or #4383 #4538)
-#4544 := (not #4541)
-#2039 := (?v1!7 #12)
-#2040 := (f13 f14 #2039)
-#2663 := (* -1::Int #2040)
-#2678 := (+ #101 #2663)
-#2679 := (<= #2678 0::Int)
-#2044 := (f5 #2039 #12)
-#2045 := (f9 #2044)
-#2664 := (* -1::Int #2045)
-#2665 := (+ #2663 #2664)
-#2666 := (+ #101 #2665)
-#2667 := (= #2666 0::Int)
-#3233 := (not #2667)
-#2048 := (f3 f15 #2039)
-#2049 := (= f1 #2048)
-#3232 := (not #2049)
-#3234 := (or #3232 #3233 #2679)
-#3235 := (not #3234)
-#3241 := (or #57 #1299 #3235)
-#4307 := (forall (vars (?v0 S3)) (:pat #4273) #3241)
-#4312 := (not #4307)
+#723 := (not #136)
+#4371 := (or #723 #705 #732 #714 #4312 #4368)
+#4374 := (not #4371)
+#4532 := (or #4374 #4529)
+#4535 := (not #4532)
+#2030 := (?v1!7 #12)
+#2031 := (f13 f14 #2030)
+#2654 := (* -1::Int #2031)
+#2669 := (+ #101 #2654)
+#2670 := (<= #2669 0::Int)
+#2035 := (f5 #2030 #12)
+#2036 := (f9 #2035)
+#2655 := (* -1::Int #2036)
+#2656 := (+ #2654 #2655)
+#2657 := (+ #101 #2656)
+#2658 := (= #2657 0::Int)
+#3224 := (not #2658)
+#2039 := (f3 f15 #2030)
+#2040 := (= f1 #2039)
+#3223 := (not #2040)
+#3225 := (or #3223 #3224 #2670)
+#3226 := (not #3225)
+#3232 := (or #57 #1290 #3226)
+#4298 := (forall (vars (?v0 S3)) (:pat #4264) #3232)
+#4303 := (not #4298)
 decl f11 :: (-> S3 Int)
 #58 := (f11 #12)
-#4218 := (pattern #58)
+#4209 := (pattern #58)
 decl ?v1!6 :: (-> S3 S3)
-#2011 := (?v1!6 #12)
-#2015 := (f11 #2011)
-#2622 := (* -1::Int #2015)
-#2012 := (f5 #2011 #12)
-#2013 := (f9 #2012)
-#2639 := (* -1::Int #2013)
-#2640 := (+ #2639 #2622)
-#2641 := (+ #58 #2640)
-#2642 := (= #2641 0::Int)
-#3205 := (not #2642)
-#2623 := (+ #58 #2622)
-#2624 := (<= #2623 0::Int)
+#2002 := (?v1!6 #12)
+#2006 := (f11 #2002)
+#2613 := (* -1::Int #2006)
+#2003 := (f5 #2002 #12)
+#2004 := (f9 #2003)
+#2630 := (* -1::Int #2004)
+#2631 := (+ #2630 #2613)
+#2632 := (+ #58 #2631)
+#2633 := (= #2632 0::Int)
+#3196 := (not #2633)
+#2614 := (+ #58 #2613)
+#2615 := (<= #2614 0::Int)
 decl f12 :: (-> S3 S1)
-#2021 := (f12 #2011)
-#2022 := (= f1 #2021)
-#3204 := (not #2022)
-#3206 := (or #3204 #2624 #3205)
-#3207 := (not #3206)
-#1259 := (* -1::Int #58)
-#1260 := (+ f8 #1259)
-#1261 := (<= #1260 0::Int)
-#3213 := (or #57 #1261 #3207)
-#4299 := (forall (vars (?v0 S3)) (:pat #4218) #3213)
-#4304 := (not #4299)
+#2012 := (f12 #2002)
+#2013 := (= f1 #2012)
+#3195 := (not #2013)
+#3197 := (or #3195 #2615 #3196)
+#3198 := (not #3197)
+#1250 := (* -1::Int #58)
+#1251 := (+ f8 #1250)
+#1252 := (<= #1251 0::Int)
+#3204 := (or #57 #1252 #3198)
+#4290 := (forall (vars (?v0 S3)) (:pat #4209) #3204)
+#4295 := (not #4290)
 #108 := (f3 f15 #23)
-#4290 := (pattern #105 #108)
+#4281 := (pattern #105 #108)
 #111 := (f13 f14 #23)
-#1311 := (* -1::Int #111)
-#1312 := (+ #101 #1311)
-#1315 := (>= #1312 0::Int)
-#539 := (= f1 #108)
-#3170 := (not #539)
-#3185 := (or #533 #3170 #1315)
-#4291 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4290) #3185)
-#4296 := (not #4291)
-#1313 := (+ #82 #1312)
-#1708 := (>= #1313 0::Int)
-#536 := (not #533)
-#3162 := (or #536 #1235 #1708)
-#4282 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3162)
+#1302 := (* -1::Int #111)
+#1303 := (+ #101 #1302)
+#1306 := (>= #1303 0::Int)
+#538 := (= f1 #108)
+#3161 := (not #538)
+#3176 := (or #532 #3161 #1306)
+#4282 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4281) #3176)
 #4287 := (not #4282)
-#4279 := (not #4274)
+#1304 := (+ #82 #1303)
+#1699 := (>= #1304 0::Int)
+#535 := (not #532)
+#3153 := (or #535 #1226 #1699)
+#4273 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3153)
+#4278 := (not #4273)
+#4270 := (not #4265)
 #100 := (= #99 0::Int)
-#1747 := (not #100)
-#4547 := (or #1747 #4279 #4287 #4296 #4304 #4312 #4544)
-#4550 := (not #4547)
+#1738 := (not #100)
+#4538 := (or #1738 #4270 #4278 #4287 #4295 #4303 #4535)
+#4541 := (not #4538)
 decl ?v0!5 :: S3
-#1967 := ?v0!5
-#1968 := (f5 #12 ?v0!5)
-#4258 := (pattern #1968)
+#1958 := ?v0!5
+#1959 := (f5 #12 ?v0!5)
+#4249 := (pattern #1959)
 #66 := (f12 #12)
-#4225 := (pattern #66)
-#1970 := (f11 ?v0!5)
-#1971 := (* -1::Int #1970)
-#1969 := (f9 #1968)
-#2590 := (+ #1969 #1971)
-#2591 := (+ #58 #2590)
-#2594 := (= #2591 0::Int)
-#3123 := (not #2594)
-#1975 := (+ #58 #1971)
-#1976 := (>= #1975 0::Int)
-#454 := (= f1 #66)
-#457 := (not #454)
-#3124 := (or #457 #1976 #3123)
-#4259 := (forall (vars (?v1 S3)) (:pat #4225 #4218 #4258) #3124)
-#4264 := (not #4259)
-#2566 := (= f10 ?v0!5)
-#1980 := (+ f8 #1971)
-#1981 := (<= #1980 0::Int)
-#4267 := (or #1981 #2566 #4264)
-#4270 := (not #4267)
-#4553 := (or #4270 #4550)
-#4556 := (not #4553)
-#77 := (f11 #23)
-#1211 := (* -1::Int #77)
-#1232 := (+ #1211 #82)
-#1233 := (+ #58 #1232)
-#1230 := (>= #1233 0::Int)
-#3115 := (or #457 #1230 #1235)
-#4250 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4249) #3115)
+#4216 := (pattern #66)
+#1961 := (f11 ?v0!5)
+#1962 := (* -1::Int #1961)
+#1960 := (f9 #1959)
+#2581 := (+ #1960 #1962)
+#2582 := (+ #58 #2581)
+#2585 := (= #2582 0::Int)
+#3114 := (not #2585)
+#1966 := (+ #58 #1962)
+#1967 := (>= #1966 0::Int)
+#453 := (= f1 #66)
+#456 := (not #453)
+#3115 := (or #456 #1967 #3114)
+#4250 := (forall (vars (?v1 S3)) (:pat #4216 #4209 #4249) #3115)
 #4255 := (not #4250)
-#4559 := (or #4255 #4556)
-#4562 := (not #4559)
+#2557 := (= f10 ?v0!5)
+#1971 := (+ f8 #1962)
+#1972 := (<= #1971 0::Int)
+#4258 := (or #1972 #2557 #4255)
+#4261 := (not #4258)
+#4544 := (or #4261 #4541)
+#4547 := (not #4544)
+#77 := (f11 #23)
+#1202 := (* -1::Int #77)
+#1223 := (+ #1202 #82)
+#1224 := (+ #58 #1223)
+#1221 := (>= #1224 0::Int)
+#3106 := (or #456 #1221 #1226)
+#4241 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3106)
+#4246 := (not #4241)
+#4550 := (or #4246 #4547)
+#4553 := (not #4550)
 decl ?v1!3 :: S3
-#1936 := ?v1!3
-#1951 := (f11 ?v1!3)
+#1927 := ?v1!3
+#1942 := (f11 ?v1!3)
 decl ?v0!4 :: S3
-#1937 := ?v0!4
-#1948 := (f11 ?v0!4)
-#1949 := (* -1::Int #1948)
-#2547 := (+ #1949 #1951)
-#1938 := (f5 ?v1!3 ?v0!4)
-#1939 := (f9 #1938)
-#2548 := (+ #1939 #2547)
-#2551 := (>= #2548 0::Int)
-#1944 := (f12 ?v1!3)
-#1945 := (= f1 #1944)
-#3078 := (not #1945)
+#1928 := ?v0!4
+#1939 := (f11 ?v0!4)
 #1940 := (* -1::Int #1939)
-#1941 := (+ f8 #1940)
-#1942 := (<= #1941 0::Int)
-#3093 := (or #1942 #3078 #2551)
-#5222 := [hypothesis]: #1945
-#4226 := (forall (vars (?v0 S3)) (:pat #4225) #457)
-#460 := (forall (vars (?v0 S3)) #457)
-#4229 := (iff #460 #4226)
-#4227 := (iff #457 #457)
-#4228 := [refl]: #4227
-#4230 := [quant-intro #4228]: #4229
-#1858 := (~ #460 #460)
-#1888 := (~ #457 #457)
-#1889 := [refl]: #1888
-#1859 := [nnf-pos #1889]: #1858
+#2538 := (+ #1940 #1942)
+#1929 := (f5 ?v1!3 ?v0!4)
+#1930 := (f9 #1929)
+#2539 := (+ #1930 #2538)
+#2542 := (>= #2539 0::Int)
+#1935 := (f12 ?v1!3)
+#1936 := (= f1 #1935)
+#3069 := (not #1936)
+#1931 := (* -1::Int #1930)
+#1932 := (+ f8 #1931)
+#1933 := (<= #1932 0::Int)
+#3084 := (or #1933 #3069 #2542)
+#5213 := [hypothesis]: #1936
+#4217 := (forall (vars (?v0 S3)) (:pat #4216) #456)
+#459 := (forall (vars (?v0 S3)) #456)
+#4220 := (iff #459 #4217)
+#4218 := (iff #456 #456)
+#4219 := [refl]: #4218
+#4221 := [quant-intro #4219]: #4220
+#1849 := (~ #459 #459)
+#1879 := (~ #456 #456)
+#1880 := [refl]: #1879
+#1850 := [nnf-pos #1880]: #1849
 #59 := (= #58 0::Int)
 #62 := (not #57)
-#1805 := (or #62 #59)
-#1808 := (forall (vars (?v0 S3)) #1805)
-#1811 := (not #1808)
-#1739 := (forall (vars (?v0 S3)) #1736)
-#1742 := (not #1739)
-#542 := (and #536 #539)
-#548 := (not #542)
-#1725 := (or #548 #1315)
-#1730 := (forall (vars (?v0 S3) (?v1 S3)) #1725)
+#1796 := (or #62 #59)
+#1799 := (forall (vars (?v0 S3)) #1796)
+#1802 := (not #1799)
+#1730 := (forall (vars (?v0 S3)) #1727)
 #1733 := (not #1730)
-#1236 := (not #1235)
-#1700 := (and #533 #1236)
-#1705 := (not #1700)
-#1711 := (or #1705 #1708)
-#1714 := (forall (vars (?v0 S3) (?v1 S3)) #1711)
-#1717 := (not #1714)
-#1647 := (forall (vars (?v0 S3)) #1642)
-#1650 := (not #1647)
-#1457 := (not #1456)
-#1450 := (not #1449)
-#1460 := (and #1450 #1457)
-#1618 := (not #1460)
-#1626 := (or #1618 #1623)
-#1629 := (forall (vars (?v0 S3)) #1626)
-#1632 := (not #1629)
-#1556 := (= #1534 0::Int)
-#1559 := (not #1502)
-#1568 := (and #807 #1559 #1556)
-#1573 := (exists (vars (?v1 S3)) #1568)
-#1545 := (+ f8 #1478)
-#1546 := (<= #1545 0::Int)
-#1547 := (not #1546)
-#1550 := (and #62 #1547)
-#1553 := (not #1550)
-#1576 := (or #1553 #1573)
-#1579 := (forall (vars (?v0 S3)) #1576)
-#1524 := (and #807 #1236)
-#1529 := (not #1524)
-#1536 := (or #1529 #1532)
-#1539 := (forall (vars (?v0 S3) (?v1 S3)) #1536)
-#1542 := (not #1539)
-#1582 := (or #1542 #1579)
-#1585 := (and #1539 #1582)
-#830 := (and #813 #827)
-#836 := (not #830)
-#1510 := (or #836 #1502)
-#1515 := (forall (vars (?v0 S3) (?v1 S3)) #1510)
-#1518 := (not #1515)
-#1588 := (or #1518 #1585)
-#1591 := (and #1515 #1588)
-#1496 := (forall (vars (?v0 S3)) #1493)
-#1499 := (not #1496)
-#1594 := (or #1499 #1591)
-#1597 := (and #1496 #1594)
-#1600 := (or #1490 #1597)
-#1603 := (and #204 #1600)
-#819 := (forall (vars (?v0 S3)) #814)
-#953 := (not #819)
-#1606 := (or #953 #1603)
-#1609 := (and #819 #1606)
-#1482 := (forall (vars (?v0 S3)) #1477)
-#1485 := (not #1482)
-#1612 := (or #1485 #1609)
-#1615 := (and #1482 #1612)
-#1466 := (or #793 #1460)
-#1471 := (forall (vars (?v0 S3)) #1466)
-#1474 := (not #1471)
-#1300 := (not #1299)
-#1419 := (and #536 #1300)
-#1424 := (exists (vars (?v0 S3)) #1419)
-#1665 := (not #1424)
-#1689 := (or #754 #995 #1665 #1474 #1615 #1632 #1650 #1654)
-#1345 := (not #1344)
-#1379 := (and #1236 #1345)
-#1382 := (not #1379)
-#1388 := (or #1382 #1385)
-#1391 := (forall (vars (?v0 S3) (?v1 S3)) #1388)
-#1394 := (not #1391)
-#1402 := (or #158 #1394)
-#1407 := (and #1391 #1402)
-#1360 := (= #1362 0::Int)
-#1354 := (>= #1356 0::Int)
-#1357 := (not #1354)
-#1364 := (and #1357 #1360)
-#1367 := (exists (vars (?v1 S3)) #1364)
-#1348 := (and #62 #1345)
-#1351 := (not #1348)
-#1370 := (or #1351 #1367)
-#1373 := (forall (vars (?v0 S3)) #1370)
-#1376 := (not #1373)
-#1410 := (or #1376 #1407)
-#1413 := (and #1373 #1410)
-#1442 := (or #724 #706 #733 #715 #1413 #1424)
-#1694 := (and #1442 #1689)
-#1316 := (not #1315)
-#1309 := (= #1313 0::Int)
-#1325 := (and #533 #1309 #1316)
-#1330 := (exists (vars (?v1 S3)) #1325)
-#1303 := (and #62 #1300)
-#1306 := (not #1303)
-#1333 := (or #1306 #1330)
-#1336 := (forall (vars (?v0 S3)) #1333)
-#1339 := (not #1336)
-#1271 := (= #1233 0::Int)
-#1212 := (+ #58 #1211)
-#1210 := (>= #1212 0::Int)
-#1274 := (not #1210)
-#1283 := (and #454 #1274 #1271)
-#1288 := (exists (vars (?v1 S3)) #1283)
-#1262 := (not #1261)
-#1265 := (and #62 #1262)
-#1268 := (not #1265)
-#1291 := (or #1268 #1288)
-#1294 := (forall (vars (?v0 S3)) #1291)
-#1750 := (not #1294)
-#1771 := (or #1747 #1750 #1339 #1694 #1717 #1733 #1742)
-#1776 := (and #1294 #1771)
-#1242 := (and #454 #1236)
-#1247 := (not #1242)
-#1250 := (or #1230 #1247)
-#1253 := (forall (vars (?v0 S3) (?v1 S3)) #1250)
-#1256 := (not #1253)
-#1779 := (or #1256 #1776)
-#1782 := (and #1253 #1779)
+#541 := (and #535 #538)
+#547 := (not #541)
+#1716 := (or #547 #1306)
+#1721 := (forall (vars (?v0 S3) (?v1 S3)) #1716)
+#1724 := (not #1721)
+#1227 := (not #1226)
+#1691 := (and #532 #1227)
+#1696 := (not #1691)
+#1702 := (or #1696 #1699)
+#1705 := (forall (vars (?v0 S3) (?v1 S3)) #1702)
+#1708 := (not #1705)
+#1638 := (forall (vars (?v0 S3)) #1633)
+#1641 := (not #1638)
+#1448 := (not #1447)
+#1441 := (not #1440)
+#1451 := (and #1441 #1448)
+#1609 := (not #1451)
+#1617 := (or #1609 #1614)
+#1620 := (forall (vars (?v0 S3)) #1617)
+#1623 := (not #1620)
+#1547 := (= #1525 0::Int)
+#1550 := (not #1493)
+#1559 := (and #798 #1550 #1547)
+#1564 := (exists (vars (?v1 S3)) #1559)
+#1536 := (+ f8 #1469)
+#1537 := (<= #1536 0::Int)
+#1538 := (not #1537)
+#1541 := (and #62 #1538)
+#1544 := (not #1541)
+#1567 := (or #1544 #1564)
+#1570 := (forall (vars (?v0 S3)) #1567)
+#1515 := (and #798 #1227)
+#1520 := (not #1515)
+#1527 := (or #1520 #1523)
+#1530 := (forall (vars (?v0 S3) (?v1 S3)) #1527)
+#1533 := (not #1530)
+#1573 := (or #1533 #1570)
+#1576 := (and #1530 #1573)
+#821 := (and #804 #818)
+#827 := (not #821)
+#1501 := (or #827 #1493)
+#1506 := (forall (vars (?v0 S3) (?v1 S3)) #1501)
+#1509 := (not #1506)
+#1579 := (or #1509 #1576)
+#1582 := (and #1506 #1579)
+#1487 := (forall (vars (?v0 S3)) #1484)
+#1490 := (not #1487)
+#1585 := (or #1490 #1582)
+#1588 := (and #1487 #1585)
+#1591 := (or #1481 #1588)
+#1594 := (and #203 #1591)
+#810 := (forall (vars (?v0 S3)) #805)
+#944 := (not #810)
+#1597 := (or #944 #1594)
+#1600 := (and #810 #1597)
+#1473 := (forall (vars (?v0 S3)) #1468)
+#1476 := (not #1473)
+#1603 := (or #1476 #1600)
+#1606 := (and #1473 #1603)
+#1457 := (or #784 #1451)
+#1462 := (forall (vars (?v0 S3)) #1457)
+#1465 := (not #1462)
+#1291 := (not #1290)
+#1410 := (and #535 #1291)
+#1415 := (exists (vars (?v0 S3)) #1410)
+#1656 := (not #1415)
+#1680 := (or #986 #753 #1656 #1465 #1606 #1623 #1641 #1645)
+#1336 := (not #1335)
+#1370 := (and #1227 #1336)
+#1373 := (not #1370)
+#1379 := (or #1373 #1376)
+#1382 := (forall (vars (?v0 S3) (?v1 S3)) #1379)
+#1385 := (not #1382)
+#1393 := (or #158 #1385)
+#1398 := (and #1382 #1393)
+#1351 := (= #1353 0::Int)
+#1345 := (>= #1347 0::Int)
+#1348 := (not #1345)
+#1355 := (and #1348 #1351)
+#1358 := (exists (vars (?v1 S3)) #1355)
+#1339 := (and #62 #1336)
+#1342 := (not #1339)
+#1361 := (or #1342 #1358)
+#1364 := (forall (vars (?v0 S3)) #1361)
+#1367 := (not #1364)
+#1401 := (or #1367 #1398)
+#1404 := (and #1364 #1401)
+#1433 := (or #723 #705 #732 #714 #1404 #1415)
+#1685 := (and #1433 #1680)
+#1307 := (not #1306)
+#1300 := (= #1304 0::Int)
+#1316 := (and #532 #1300 #1307)
+#1321 := (exists (vars (?v1 S3)) #1316)
+#1294 := (and #62 #1291)
+#1297 := (not #1294)
+#1324 := (or #1297 #1321)
+#1327 := (forall (vars (?v0 S3)) #1324)
+#1330 := (not #1327)
+#1262 := (= #1224 0::Int)
+#1203 := (+ #58 #1202)
+#1201 := (>= #1203 0::Int)
+#1265 := (not #1201)
+#1274 := (and #453 #1265 #1262)
+#1279 := (exists (vars (?v1 S3)) #1274)
+#1253 := (not #1252)
+#1256 := (and #62 #1253)
+#1259 := (not #1256)
+#1282 := (or #1259 #1279)
+#1285 := (forall (vars (?v0 S3)) #1282)
+#1741 := (not #1285)
+#1762 := (or #1738 #1741 #1330 #1685 #1708 #1724 #1733)
+#1767 := (and #1285 #1762)
+#1233 := (and #453 #1227)
+#1238 := (not #1233)
+#1241 := (or #1221 #1238)
+#1244 := (forall (vars (?v0 S3) (?v1 S3)) #1241)
+#1247 := (not #1244)
+#1770 := (or #1247 #1767)
+#1773 := (and #1244 #1770)
 #74 := (f12 #23)
-#466 := (= f1 #74)
-#469 := (and #457 #466)
-#475 := (not #469)
-#1217 := (or #475 #1210)
-#1222 := (forall (vars (?v0 S3) (?v1 S3)) #1217)
-#1225 := (not #1222)
-#1785 := (or #1225 #1782)
-#1788 := (and #1222 #1785)
-#1201 := (>= #58 0::Int)
-#1202 := (forall (vars (?v0 S3)) #1201)
-#1205 := (not #1202)
-#1791 := (or #1205 #1788)
-#1794 := (and #1202 #1791)
+#465 := (= f1 #74)
+#468 := (and #456 #465)
+#474 := (not #468)
+#1208 := (or #474 #1201)
+#1213 := (forall (vars (?v0 S3) (?v1 S3)) #1208)
+#1216 := (not #1213)
+#1776 := (or #1216 #1773)
+#1779 := (and #1213 #1776)
+#1192 := (>= #58 0::Int)
+#1193 := (forall (vars (?v0 S3)) #1192)
+#1196 := (not #1193)
+#1782 := (or #1196 #1779)
+#1785 := (and #1193 #1782)
 #70 := (f11 f10)
 #71 := (= #70 0::Int)
-#1196 := (not #71)
-#1797 := (or #1196 #1794)
-#1800 := (and #71 #1797)
-#1160 := (not #460)
-#440 := (= f8 #58)
-#446 := (or #57 #440)
-#451 := (forall (vars (?v0 S3)) #446)
-#1169 := (not #451)
-#1823 := (or #1169 #1160 #1800 #1811)
-#1828 := (not #1823)
+#1187 := (not #71)
+#1788 := (or #1187 #1785)
+#1791 := (and #71 #1788)
+#1151 := (not #459)
+#439 := (= f8 #58)
+#445 := (or #57 #439)
+#450 := (forall (vars (?v0 S3)) #445)
+#1160 := (not #450)
+#1814 := (or #1160 #1151 #1791 #1802)
+#1819 := (not #1814)
 #1 := true
-#216 := (+ #189 #82)
-#223 := (= #211 #216)
-#200 := (= #199 f1)
-#224 := (and #200 #223)
-#222 := (< #189 #211)
-#225 := (and #222 #224)
-#226 := (exists (vars (?v1 S3)) #225)
-#220 := (< #189 f8)
-#221 := (and #62 #220)
-#227 := (implies #221 #226)
-#228 := (forall (vars (?v0 S3)) #227)
-#229 := (and #228 true)
-#217 := (<= #211 #216)
+#215 := (+ #188 #82)
+#222 := (= #210 #215)
+#199 := (= #198 f1)
+#223 := (and #199 #222)
+#221 := (< #188 #210)
+#224 := (and #221 #223)
+#225 := (exists (vars (?v1 S3)) #224)
+#219 := (< #188 f8)
+#220 := (and #62 #219)
+#226 := (implies #220 #225)
+#227 := (forall (vars (?v0 S3)) #226)
+#228 := (and #227 true)
+#216 := (<= #210 #215)
 #83 := (< #82 f8)
-#215 := (and #200 #83)
-#218 := (implies #215 #217)
-#219 := (forall (vars (?v0 S3) (?v1 S3)) #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 S3) (?v1 S3)) #213)
-#232 := (implies #214 #231)
-#233 := (and #214 #232)
-#205 := (<= 0::Int #189)
-#206 := (forall (vars (?v0 S3)) #205)
-#234 := (implies #206 #233)
-#235 := (and #206 #234)
-#236 := (implies #204 #235)
-#237 := (and #204 #236)
-#194 := (= #189 #101)
-#201 := (implies #200 #194)
-#202 := (forall (vars (?v0 S3)) #201)
-#238 := (implies #202 #237)
-#239 := (and #202 #238)
-#197 := (<= #189 #101)
-#198 := (forall (vars (?v0 S3)) #197)
-#240 := (implies #198 #239)
-#241 := (and #198 #240)
-#186 := (+ #174 #184)
-#187 := (< #186 #101)
-#185 := (< #184 f8)
-#188 := (and #185 #187)
-#193 := (not #188)
-#195 := (implies #193 #194)
-#196 := (forall (vars (?v0 S3)) #195)
-#242 := (implies #196 #241)
-#190 := (= #189 #186)
-#191 := (implies #188 #190)
-#192 := (forall (vars (?v0 S3)) #191)
-#243 := (implies #192 #242)
-decl f2 :: S1
-#5 := f2
-#180 := (ite true f1 f2)
-#181 := (f4 f15 f22 #180)
-#182 := (= f23 #181)
-#244 := (implies #182 #243)
+#214 := (and #199 #83)
+#217 := (implies #214 #216)
+#218 := (forall (vars (?v0 S3) (?v1 S3)) #217)
+#229 := (implies #218 #228)
+#230 := (and #218 #229)
+#211 := (<= #210 #188)
+#208 := (= #207 f1)
+#206 := (not #199)
+#209 := (and #206 #208)
+#212 := (implies #209 #211)
+#213 := (forall (vars (?v0 S3) (?v1 S3)) #212)
+#231 := (implies #213 #230)
+#232 := (and #213 #231)
+#204 := (<= 0::Int #188)
+#205 := (forall (vars (?v0 S3)) #204)
+#233 := (implies #205 #232)
+#234 := (and #205 #233)
+#235 := (implies #203 #234)
+#236 := (and #203 #235)
+#193 := (= #188 #101)
+#200 := (implies #199 #193)
+#201 := (forall (vars (?v0 S3)) #200)
+#237 := (implies #201 #236)
+#238 := (and #201 #237)
+#196 := (<= #188 #101)
+#197 := (forall (vars (?v0 S3)) #196)
+#239 := (implies #197 #238)
+#240 := (and #197 #239)
+#185 := (+ #174 #183)
+#186 := (< #185 #101)
+#184 := (< #183 f8)
+#187 := (and #184 #186)
+#192 := (not #187)
+#194 := (implies #192 #193)
+#195 := (forall (vars (?v0 S3)) #194)
+#241 := (implies #195 #240)
+#189 := (= #188 #185)
+#190 := (implies #187 #189)
+#191 := (forall (vars (?v0 S3)) #190)
+#242 := (implies #191 #241)
+#243 := (implies #181 #242)
 #176 := (<= #174 #101)
 #106 := (= #105 f1)
 #107 := (not #106)
 #177 := (implies #107 #176)
 #178 := (forall (vars (?v0 S3)) #177)
-#245 := (implies #178 #244)
+#244 := (implies #178 #243)
 #175 := (< #174 f8)
-#246 := (implies #175 #245)
+#245 := (implies #175 #244)
 #172 := (= #171 f1)
 #173 := (not #172)
-#247 := (implies #173 #246)
+#246 := (implies #173 #245)
 #120 := (< #101 f8)
 #129 := (and #107 #120)
 #130 := (exists (vars (?v0 S3)) #129)
-#248 := (implies #130 #247)
-#249 := (implies true #248)
+#247 := (implies #130 #246)
+#248 := (implies true #247)
 #159 := (and #158 true)
 #147 := (+ #142 #82)
 #154 := (<= #145 #147)
@@ -913,7 +908,7 @@
 #131 := (not #130)
 #168 := (implies #131 #167)
 #169 := (implies true #168)
-#250 := (and #169 #249)
+#249 := (and #169 #248)
 #116 := (+ #101 #82)
 #123 := (= #111 #116)
 #124 := (and #106 #123)
@@ -923,23 +918,23 @@
 #121 := (and #62 #120)
 #127 := (implies #121 #126)
 #128 := (forall (vars (?v0 S3)) #127)
-#251 := (implies #128 #250)
+#250 := (implies #128 #249)
 #117 := (<= #111 #116)
 #115 := (and #106 #83)
 #118 := (implies #115 #117)
 #119 := (forall (vars (?v0 S3) (?v1 S3)) #118)
-#252 := (implies #119 #251)
+#251 := (implies #119 #250)
 #112 := (<= #111 #101)
 #109 := (= #108 f1)
 #110 := (and #107 #109)
 #113 := (implies #110 #112)
 #114 := (forall (vars (?v0 S3) (?v1 S3)) #113)
-#253 := (implies #114 #252)
+#252 := (implies #114 #251)
 #102 := (<= 0::Int #101)
 #103 := (forall (vars (?v0 S3)) #102)
-#254 := (implies #103 #253)
-#255 := (implies #100 #254)
-#256 := (implies true #255)
+#253 := (implies #103 #252)
+#254 := (implies #100 #253)
+#255 := (implies true #254)
 #85 := (+ #58 #82)
 #92 := (= #77 #85)
 #67 := (= #66 f1)
@@ -951,3880 +946,3874 @@
 #90 := (and #62 #89)
 #96 := (implies #90 #95)
 #97 := (forall (vars (?v0 S3)) #96)
-#257 := (implies #97 #256)
-#258 := (and #97 #257)
+#256 := (implies #97 #255)
+#257 := (and #97 #256)
 #86 := (<= #77 #85)
 #84 := (and #67 #83)
 #87 := (implies #84 #86)
 #88 := (forall (vars (?v0 S3) (?v1 S3)) #87)
-#259 := (implies #88 #258)
-#260 := (and #88 #259)
+#258 := (implies #88 #257)
+#259 := (and #88 #258)
 #78 := (<= #77 #58)
 #75 := (= #74 f1)
 #68 := (not #67)
 #76 := (and #68 #75)
 #79 := (implies #76 #78)
 #80 := (forall (vars (?v0 S3) (?v1 S3)) #79)
-#261 := (implies #80 #260)
-#262 := (and #80 #261)
+#260 := (implies #80 #259)
+#261 := (and #80 #260)
 #72 := (<= 0::Int #58)
 #73 := (forall (vars (?v0 S3)) #72)
-#263 := (implies #73 #262)
-#264 := (and #73 #263)
-#265 := (implies #71 #264)
-#266 := (and #71 #265)
+#262 := (implies #73 #261)
+#263 := (and #73 #262)
+#264 := (implies #71 #263)
+#265 := (and #71 #264)
 #69 := (forall (vars (?v0 S3)) #68)
-#267 := (implies #69 #266)
+#266 := (implies #69 #265)
 #63 := (= #58 f8)
 #64 := (implies #62 #63)
 #65 := (forall (vars (?v0 S3)) #64)
-#268 := (implies #65 #267)
+#267 := (implies #65 #266)
 #60 := (implies #57 #59)
 #61 := (forall (vars (?v0 S3)) #60)
-#269 := (implies #61 #268)
-#270 := (implies true #269)
-#271 := (not #270)
-#1831 := (iff #271 #1828)
-#853 := (+ #82 #189)
-#871 := (= #211 #853)
-#874 := (and #807 #871)
-#877 := (and #222 #874)
-#880 := (exists (vars (?v1 S3)) #877)
-#886 := (not #221)
-#887 := (or #886 #880)
-#892 := (forall (vars (?v0 S3)) #887)
-#856 := (<= #211 #853)
-#848 := (and #83 #807)
-#862 := (not #848)
-#863 := (or #862 #856)
-#868 := (forall (vars (?v0 S3) (?v1 S3)) #863)
-#905 := (not #868)
-#906 := (or #905 #892)
-#911 := (and #868 #906)
-#837 := (or #212 #836)
-#842 := (forall (vars (?v0 S3) (?v1 S3)) #837)
-#917 := (not #842)
-#918 := (or #917 #911)
-#923 := (and #842 #918)
-#929 := (not #206)
-#930 := (or #929 #923)
-#935 := (and #206 #930)
-#822 := (= 0::Int #203)
-#941 := (not #822)
-#942 := (or #941 #935)
-#947 := (and #822 #942)
-#954 := (or #953 #947)
-#959 := (and #819 #954)
-#965 := (not #198)
-#966 := (or #965 #959)
-#971 := (and #198 #966)
-#799 := (or #188 #793)
-#804 := (forall (vars (?v0 S3)) #799)
-#977 := (not #804)
-#978 := (or #977 #971)
-#779 := (= #186 #189)
-#785 := (or #193 #779)
-#790 := (forall (vars (?v0 S3)) #785)
-#986 := (not #790)
+#268 := (implies #61 #267)
+#269 := (implies true #268)
+#270 := (not #269)
+#1822 := (iff #270 #1819)
+#844 := (+ #82 #188)
+#862 := (= #210 #844)
+#865 := (and #798 #862)
+#868 := (and #221 #865)
+#871 := (exists (vars (?v1 S3)) #868)
+#877 := (not #220)
+#878 := (or #877 #871)
+#883 := (forall (vars (?v0 S3)) #878)
+#847 := (<= #210 #844)
+#839 := (and #83 #798)
+#853 := (not #839)
+#854 := (or #853 #847)
+#859 := (forall (vars (?v0 S3) (?v1 S3)) #854)
+#896 := (not #859)
+#897 := (or #896 #883)
+#902 := (and #859 #897)
+#828 := (or #211 #827)
+#833 := (forall (vars (?v0 S3) (?v1 S3)) #828)
+#908 := (not #833)
+#909 := (or #908 #902)
+#914 := (and #833 #909)
+#920 := (not #205)
+#921 := (or #920 #914)
+#926 := (and #205 #921)
+#813 := (= 0::Int #202)
+#932 := (not #813)
+#933 := (or #932 #926)
+#938 := (and #813 #933)
+#945 := (or #944 #938)
+#950 := (and #810 #945)
+#956 := (not #197)
+#957 := (or #956 #950)
+#962 := (and #197 #957)
+#790 := (or #187 #784)
+#795 := (forall (vars (?v0 S3)) #790)
+#968 := (not #795)
+#969 := (or #968 #962)
+#770 := (= #185 #188)
+#776 := (or #192 #770)
+#781 := (forall (vars (?v0 S3)) #776)
+#977 := (not #781)
+#978 := (or #977 #969)
 #987 := (or #986 #978)
+#762 := (or #176 #532)
+#767 := (forall (vars (?v0 S3)) #762)
+#995 := (not #767)
 #996 := (or #995 #987)
-#763 := (or #176 #533)
-#768 := (forall (vars (?v0 S3)) #763)
-#1004 := (not #768)
+#1004 := (not #175)
 #1005 := (or #1004 #996)
-#1013 := (not #175)
-#1014 := (or #1013 #1005)
-#1022 := (or #754 #1014)
-#610 := (and #120 #536)
-#615 := (exists (vars (?v0 S3)) #610)
-#618 := (not #615)
-#1030 := (or #618 #1022)
-#669 := (= 0::Int #157)
-#627 := (+ #82 #142)
-#654 := (<= #145 #627)
-#651 := (and #83 #143)
-#660 := (not #651)
-#661 := (or #660 #654)
-#666 := (forall (vars (?v0 S3) (?v1 S3)) #661)
-#682 := (not #666)
-#683 := (or #682 #669)
-#688 := (and #666 #683)
-#630 := (= #145 #627)
-#633 := (and #146 #630)
-#636 := (exists (vars (?v1 S3)) #633)
-#642 := (not #144)
-#643 := (or #642 #636)
-#648 := (forall (vars (?v0 S3)) #643)
-#694 := (not #648)
-#695 := (or #694 #688)
-#700 := (and #648 #695)
-#707 := (or #706 #700)
-#716 := (or #715 #707)
-#725 := (or #724 #716)
-#734 := (or #733 #725)
-#742 := (or #615 #734)
-#1042 := (and #742 #1030)
-#565 := (+ #82 #101)
-#583 := (= #111 #565)
-#586 := (and #533 #583)
-#589 := (and #122 #586)
-#592 := (exists (vars (?v1 S3)) #589)
-#598 := (not #121)
-#599 := (or #598 #592)
-#604 := (forall (vars (?v0 S3)) #599)
-#1048 := (not #604)
-#1049 := (or #1048 #1042)
-#568 := (<= #111 #565)
-#560 := (and #83 #533)
-#574 := (not #560)
-#575 := (or #574 #568)
-#580 := (forall (vars (?v0 S3) (?v1 S3)) #575)
-#1057 := (not #580)
+#1013 := (or #753 #1005)
+#609 := (and #120 #535)
+#614 := (exists (vars (?v0 S3)) #609)
+#617 := (not #614)
+#1021 := (or #617 #1013)
+#668 := (= 0::Int #157)
+#626 := (+ #82 #142)
+#653 := (<= #145 #626)
+#650 := (and #83 #143)
+#659 := (not #650)
+#660 := (or #659 #653)
+#665 := (forall (vars (?v0 S3) (?v1 S3)) #660)
+#681 := (not #665)
+#682 := (or #681 #668)
+#687 := (and #665 #682)
+#629 := (= #145 #626)
+#632 := (and #146 #629)
+#635 := (exists (vars (?v1 S3)) #632)
+#641 := (not #144)
+#642 := (or #641 #635)
+#647 := (forall (vars (?v0 S3)) #642)
+#693 := (not #647)
+#694 := (or #693 #687)
+#699 := (and #647 #694)
+#706 := (or #705 #699)
+#715 := (or #714 #706)
+#724 := (or #723 #715)
+#733 := (or #732 #724)
+#741 := (or #614 #733)
+#1033 := (and #741 #1021)
+#564 := (+ #82 #101)
+#582 := (= #111 #564)
+#585 := (and #532 #582)
+#588 := (and #122 #585)
+#591 := (exists (vars (?v1 S3)) #588)
+#597 := (not #121)
+#598 := (or #597 #591)
+#603 := (forall (vars (?v0 S3)) #598)
+#1039 := (not #603)
+#1040 := (or #1039 #1033)
+#567 := (<= #111 #564)
+#559 := (and #83 #532)
+#573 := (not #559)
+#574 := (or #573 #567)
+#579 := (forall (vars (?v0 S3) (?v1 S3)) #574)
+#1048 := (not #579)
+#1049 := (or #1048 #1040)
+#548 := (or #112 #547)
+#553 := (forall (vars (?v0 S3) (?v1 S3)) #548)
+#1057 := (not #553)
 #1058 := (or #1057 #1049)
-#549 := (or #112 #548)
-#554 := (forall (vars (?v0 S3) (?v1 S3)) #549)
-#1066 := (not #554)
+#1066 := (not #103)
 #1067 := (or #1066 #1058)
-#1075 := (not #103)
+#529 := (= 0::Int #99)
+#1075 := (not #529)
 #1076 := (or #1075 #1067)
-#530 := (= 0::Int #99)
-#1084 := (not #530)
-#1085 := (or #1084 #1076)
-#507 := (and #92 #454)
-#512 := (and #91 #507)
-#515 := (exists (vars (?v1 S3)) #512)
-#521 := (not #90)
-#522 := (or #521 #515)
-#527 := (forall (vars (?v0 S3)) #522)
-#1100 := (not #527)
-#1101 := (or #1100 #1085)
-#1106 := (and #527 #1101)
-#487 := (and #83 #454)
-#495 := (not #487)
-#496 := (or #86 #495)
-#501 := (forall (vars (?v0 S3) (?v1 S3)) #496)
-#1112 := (not #501)
-#1113 := (or #1112 #1106)
-#1118 := (and #501 #1113)
-#476 := (or #78 #475)
-#481 := (forall (vars (?v0 S3) (?v1 S3)) #476)
-#1124 := (not #481)
-#1125 := (or #1124 #1118)
-#1130 := (and #481 #1125)
-#1136 := (not #73)
-#1137 := (or #1136 #1130)
-#1142 := (and #73 #1137)
-#463 := (= 0::Int #70)
-#1148 := (not #463)
-#1149 := (or #1148 #1142)
-#1154 := (and #463 #1149)
-#1161 := (or #1160 #1154)
+#506 := (and #92 #453)
+#511 := (and #91 #506)
+#514 := (exists (vars (?v1 S3)) #511)
+#520 := (not #90)
+#521 := (or #520 #514)
+#526 := (forall (vars (?v0 S3)) #521)
+#1091 := (not #526)
+#1092 := (or #1091 #1076)
+#1097 := (and #526 #1092)
+#486 := (and #83 #453)
+#494 := (not #486)
+#495 := (or #86 #494)
+#500 := (forall (vars (?v0 S3) (?v1 S3)) #495)
+#1103 := (not #500)
+#1104 := (or #1103 #1097)
+#1109 := (and #500 #1104)
+#475 := (or #78 #474)
+#480 := (forall (vars (?v0 S3) (?v1 S3)) #475)
+#1115 := (not #480)
+#1116 := (or #1115 #1109)
+#1121 := (and #480 #1116)
+#1127 := (not #73)
+#1128 := (or #1127 #1121)
+#1133 := (and #73 #1128)
+#462 := (= 0::Int #70)
+#1139 := (not #462)
+#1140 := (or #1139 #1133)
+#1145 := (and #462 #1140)
+#1152 := (or #1151 #1145)
+#1161 := (or #1160 #1152)
+#425 := (= 0::Int #58)
+#431 := (or #62 #425)
+#436 := (forall (vars (?v0 S3)) #431)
+#1169 := (not #436)
 #1170 := (or #1169 #1161)
-#426 := (= 0::Int #58)
-#432 := (or #62 #426)
-#437 := (forall (vars (?v0 S3)) #432)
-#1178 := (not #437)
-#1179 := (or #1178 #1170)
-#1191 := (not #1179)
-#1829 := (iff #1191 #1828)
-#1826 := (iff #1179 #1823)
-#1814 := (or #1160 #1800)
-#1817 := (or #1169 #1814)
-#1820 := (or #1811 #1817)
-#1824 := (iff #1820 #1823)
-#1825 := [rewrite]: #1824
-#1821 := (iff #1179 #1820)
-#1818 := (iff #1170 #1817)
-#1815 := (iff #1161 #1814)
-#1801 := (iff #1154 #1800)
-#1798 := (iff #1149 #1797)
-#1795 := (iff #1142 #1794)
-#1792 := (iff #1137 #1791)
-#1789 := (iff #1130 #1788)
-#1786 := (iff #1125 #1785)
-#1783 := (iff #1118 #1782)
-#1780 := (iff #1113 #1779)
-#1777 := (iff #1106 #1776)
-#1774 := (iff #1101 #1771)
-#1753 := (or #1339 #1694)
-#1756 := (or #1717 #1753)
-#1759 := (or #1733 #1756)
-#1762 := (or #1742 #1759)
-#1765 := (or #1747 #1762)
-#1768 := (or #1750 #1765)
-#1772 := (iff #1768 #1771)
-#1773 := [rewrite]: #1772
-#1769 := (iff #1101 #1768)
-#1766 := (iff #1085 #1765)
-#1763 := (iff #1076 #1762)
-#1760 := (iff #1067 #1759)
-#1757 := (iff #1058 #1756)
-#1754 := (iff #1049 #1753)
-#1695 := (iff #1042 #1694)
-#1692 := (iff #1030 #1689)
-#1668 := (or #1474 #1615)
-#1671 := (or #1632 #1668)
-#1674 := (or #995 #1671)
-#1677 := (or #1650 #1674)
-#1680 := (or #1654 #1677)
-#1683 := (or #754 #1680)
-#1686 := (or #1665 #1683)
-#1690 := (iff #1686 #1689)
-#1691 := [rewrite]: #1690
-#1687 := (iff #1030 #1686)
-#1684 := (iff #1022 #1683)
-#1681 := (iff #1014 #1680)
-#1678 := (iff #1005 #1677)
-#1675 := (iff #996 #1674)
-#1672 := (iff #987 #1671)
-#1669 := (iff #978 #1668)
-#1616 := (iff #971 #1615)
-#1613 := (iff #966 #1612)
-#1610 := (iff #959 #1609)
-#1607 := (iff #954 #1606)
-#1604 := (iff #947 #1603)
-#1601 := (iff #942 #1600)
-#1598 := (iff #935 #1597)
-#1595 := (iff #930 #1594)
-#1592 := (iff #923 #1591)
-#1589 := (iff #918 #1588)
-#1586 := (iff #911 #1585)
-#1583 := (iff #906 #1582)
-#1580 := (iff #892 #1579)
-#1577 := (iff #887 #1576)
-#1574 := (iff #880 #1573)
-#1571 := (iff #877 #1568)
-#1562 := (and #807 #1556)
-#1565 := (and #1559 #1562)
-#1569 := (iff #1565 #1568)
-#1570 := [rewrite]: #1569
-#1566 := (iff #877 #1565)
-#1563 := (iff #874 #1562)
-#1557 := (iff #871 #1556)
-#1558 := [rewrite]: #1557
-#1564 := [monotonicity #1558]: #1563
-#1560 := (iff #222 #1559)
+#1182 := (not #1170)
+#1820 := (iff #1182 #1819)
+#1817 := (iff #1170 #1814)
+#1805 := (or #1151 #1791)
+#1808 := (or #1160 #1805)
+#1811 := (or #1802 #1808)
+#1815 := (iff #1811 #1814)
+#1816 := [rewrite]: #1815
+#1812 := (iff #1170 #1811)
+#1809 := (iff #1161 #1808)
+#1806 := (iff #1152 #1805)
+#1792 := (iff #1145 #1791)
+#1789 := (iff #1140 #1788)
+#1786 := (iff #1133 #1785)
+#1783 := (iff #1128 #1782)
+#1780 := (iff #1121 #1779)
+#1777 := (iff #1116 #1776)
+#1774 := (iff #1109 #1773)
+#1771 := (iff #1104 #1770)
+#1768 := (iff #1097 #1767)
+#1765 := (iff #1092 #1762)
+#1744 := (or #1330 #1685)
+#1747 := (or #1708 #1744)
+#1750 := (or #1724 #1747)
+#1753 := (or #1733 #1750)
+#1756 := (or #1738 #1753)
+#1759 := (or #1741 #1756)
+#1763 := (iff #1759 #1762)
+#1764 := [rewrite]: #1763
+#1760 := (iff #1092 #1759)
+#1757 := (iff #1076 #1756)
+#1754 := (iff #1067 #1753)
+#1751 := (iff #1058 #1750)
+#1748 := (iff #1049 #1747)
+#1745 := (iff #1040 #1744)
+#1686 := (iff #1033 #1685)
+#1683 := (iff #1021 #1680)
+#1659 := (or #1465 #1606)
+#1662 := (or #1623 #1659)
+#1665 := (or #986 #1662)
+#1668 := (or #1641 #1665)
+#1671 := (or #1645 #1668)
+#1674 := (or #753 #1671)
+#1677 := (or #1656 #1674)
+#1681 := (iff #1677 #1680)
+#1682 := [rewrite]: #1681
+#1678 := (iff #1021 #1677)
+#1675 := (iff #1013 #1674)
+#1672 := (iff #1005 #1671)
+#1669 := (iff #996 #1668)
+#1666 := (iff #987 #1665)
+#1663 := (iff #978 #1662)
+#1660 := (iff #969 #1659)
+#1607 := (iff #962 #1606)
+#1604 := (iff #957 #1603)
+#1601 := (iff #950 #1600)
+#1598 := (iff #945 #1597)
+#1595 := (iff #938 #1594)
+#1592 := (iff #933 #1591)
+#1589 := (iff #926 #1588)
+#1586 := (iff #921 #1585)
+#1583 := (iff #914 #1582)
+#1580 := (iff #909 #1579)
+#1577 := (iff #902 #1576)
+#1574 := (iff #897 #1573)
+#1571 := (iff #883 #1570)
+#1568 := (iff #878 #1567)
+#1565 := (iff #871 #1564)
+#1562 := (iff #868 #1559)
+#1553 := (and #798 #1547)
+#1556 := (and #1550 #1553)
+#1560 := (iff #1556 #1559)
 #1561 := [rewrite]: #1560
-#1567 := [monotonicity #1561 #1564]: #1566
-#1572 := [trans #1567 #1570]: #1571
-#1575 := [quant-intro #1572]: #1574
-#1554 := (iff #886 #1553)
-#1551 := (iff #221 #1550)
-#1548 := (iff #220 #1547)
+#1557 := (iff #868 #1556)
+#1554 := (iff #865 #1553)
+#1548 := (iff #862 #1547)
 #1549 := [rewrite]: #1548
-#1552 := [monotonicity #1549]: #1551
-#1555 := [monotonicity #1552]: #1554
-#1578 := [monotonicity #1555 #1575]: #1577
-#1581 := [quant-intro #1578]: #1580
-#1543 := (iff #905 #1542)
-#1540 := (iff #868 #1539)
-#1537 := (iff #863 #1536)
-#1533 := (iff #856 #1532)
-#1535 := [rewrite]: #1533
-#1530 := (iff #862 #1529)
-#1527 := (iff #848 #1524)
-#1521 := (and #1236 #807)
-#1525 := (iff #1521 #1524)
-#1526 := [rewrite]: #1525
-#1522 := (iff #848 #1521)
-#1237 := (iff #83 #1236)
-#1238 := [rewrite]: #1237
-#1523 := [monotonicity #1238]: #1522
-#1528 := [trans #1523 #1526]: #1527
-#1531 := [monotonicity #1528]: #1530
-#1538 := [monotonicity #1531 #1535]: #1537
-#1541 := [quant-intro #1538]: #1540
-#1544 := [monotonicity #1541]: #1543
-#1584 := [monotonicity #1544 #1581]: #1583
-#1587 := [monotonicity #1541 #1584]: #1586
-#1519 := (iff #917 #1518)
-#1516 := (iff #842 #1515)
-#1513 := (iff #837 #1510)
-#1507 := (or #1502 #836)
-#1511 := (iff #1507 #1510)
-#1512 := [rewrite]: #1511
-#1508 := (iff #837 #1507)
-#1505 := (iff #212 #1502)
-#1506 := [rewrite]: #1505
-#1509 := [monotonicity #1506]: #1508
-#1514 := [trans #1509 #1512]: #1513
-#1517 := [quant-intro #1514]: #1516
-#1520 := [monotonicity #1517]: #1519
-#1590 := [monotonicity #1520 #1587]: #1589
-#1593 := [monotonicity #1517 #1590]: #1592
-#1500 := (iff #929 #1499)
-#1497 := (iff #206 #1496)
-#1494 := (iff #205 #1493)
-#1495 := [rewrite]: #1494
-#1498 := [quant-intro #1495]: #1497
-#1501 := [monotonicity #1498]: #1500
-#1596 := [monotonicity #1501 #1593]: #1595
-#1599 := [monotonicity #1498 #1596]: #1598
-#1491 := (iff #941 #1490)
-#1488 := (iff #822 #204)
-#1489 := [rewrite]: #1488
+#1555 := [monotonicity #1549]: #1554
+#1551 := (iff #221 #1550)
+#1552 := [rewrite]: #1551
+#1558 := [monotonicity #1552 #1555]: #1557
+#1563 := [trans #1558 #1561]: #1562
+#1566 := [quant-intro #1563]: #1565
+#1545 := (iff #877 #1544)
+#1542 := (iff #220 #1541)
+#1539 := (iff #219 #1538)
+#1540 := [rewrite]: #1539
+#1543 := [monotonicity #1540]: #1542
+#1546 := [monotonicity #1543]: #1545
+#1569 := [monotonicity #1546 #1566]: #1568
+#1572 := [quant-intro #1569]: #1571
+#1534 := (iff #896 #1533)
+#1531 := (iff #859 #1530)
+#1528 := (iff #854 #1527)
+#1524 := (iff #847 #1523)
+#1526 := [rewrite]: #1524
+#1521 := (iff #853 #1520)
+#1518 := (iff #839 #1515)
+#1512 := (and #1227 #798)
+#1516 := (iff #1512 #1515)
+#1517 := [rewrite]: #1516
+#1513 := (iff #839 #1512)
+#1228 := (iff #83 #1227)
+#1229 := [rewrite]: #1228
+#1514 := [monotonicity #1229]: #1513
+#1519 := [trans #1514 #1517]: #1518
+#1522 := [monotonicity #1519]: #1521
+#1529 := [monotonicity #1522 #1526]: #1528
+#1532 := [quant-intro #1529]: #1531
+#1535 := [monotonicity #1532]: #1534
+#1575 := [monotonicity #1535 #1572]: #1574
+#1578 := [monotonicity #1532 #1575]: #1577
+#1510 := (iff #908 #1509)
+#1507 := (iff #833 #1506)
+#1504 := (iff #828 #1501)
+#1498 := (or #1493 #827)
+#1502 := (iff #1498 #1501)
+#1503 := [rewrite]: #1502
+#1499 := (iff #828 #1498)
+#1496 := (iff #211 #1493)
+#1497 := [rewrite]: #1496
+#1500 := [monotonicity #1497]: #1499
+#1505 := [trans #1500 #1503]: #1504
+#1508 := [quant-intro #1505]: #1507
+#1511 := [monotonicity #1508]: #1510
+#1581 := [monotonicity #1511 #1578]: #1580
+#1584 := [monotonicity #1508 #1581]: #1583
+#1491 := (iff #920 #1490)
+#1488 := (iff #205 #1487)
+#1485 := (iff #204 #1484)
+#1486 := [rewrite]: #1485
+#1489 := [quant-intro #1486]: #1488
 #1492 := [monotonicity #1489]: #1491
-#1602 := [monotonicity #1492 #1599]: #1601
-#1605 := [monotonicity #1489 #1602]: #1604
-#1608 := [monotonicity #1605]: #1607
-#1611 := [monotonicity #1608]: #1610
-#1486 := (iff #965 #1485)
-#1483 := (iff #198 #1482)
-#1480 := (iff #197 #1477)
-#1481 := [rewrite]: #1480
-#1484 := [quant-intro #1481]: #1483
-#1487 := [monotonicity #1484]: #1486
-#1614 := [monotonicity #1487 #1611]: #1613
-#1617 := [monotonicity #1484 #1614]: #1616
-#1475 := (iff #977 #1474)
-#1472 := (iff #804 #1471)
-#1469 := (iff #799 #1466)
-#1463 := (or #1460 #793)
-#1467 := (iff #1463 #1466)
-#1468 := [rewrite]: #1467
-#1464 := (iff #799 #1463)
-#1461 := (iff #188 #1460)
-#1458 := (iff #187 #1457)
+#1587 := [monotonicity #1492 #1584]: #1586
+#1590 := [monotonicity #1489 #1587]: #1589
+#1482 := (iff #932 #1481)
+#1479 := (iff #813 #203)
+#1480 := [rewrite]: #1479
+#1483 := [monotonicity #1480]: #1482
+#1593 := [monotonicity #1483 #1590]: #1592
+#1596 := [monotonicity #1480 #1593]: #1595
+#1599 := [monotonicity #1596]: #1598
+#1602 := [monotonicity #1599]: #1601
+#1477 := (iff #956 #1476)
+#1474 := (iff #197 #1473)
+#1471 := (iff #196 #1468)
+#1472 := [rewrite]: #1471
+#1475 := [quant-intro #1472]: #1474
+#1478 := [monotonicity #1475]: #1477
+#1605 := [monotonicity #1478 #1602]: #1604
+#1608 := [monotonicity #1475 #1605]: #1607
+#1466 := (iff #968 #1465)
+#1463 := (iff #795 #1462)
+#1460 := (iff #790 #1457)
+#1454 := (or #1451 #784)
+#1458 := (iff #1454 #1457)
 #1459 := [rewrite]: #1458
-#1451 := (iff #185 #1450)
-#1452 := [rewrite]: #1451
-#1462 := [monotonicity #1452 #1459]: #1461
-#1465 := [monotonicity #1462]: #1464
-#1470 := [trans #1465 #1468]: #1469
-#1473 := [quant-intro #1470]: #1472
-#1476 := [monotonicity #1473]: #1475
-#1670 := [monotonicity #1476 #1617]: #1669
-#1633 := (iff #986 #1632)
-#1630 := (iff #790 #1629)
-#1627 := (iff #785 #1626)
-#1624 := (iff #779 #1623)
-#1625 := [rewrite]: #1624
-#1619 := (iff #193 #1618)
-#1620 := [monotonicity #1462]: #1619
-#1628 := [monotonicity #1620 #1625]: #1627
-#1631 := [quant-intro #1628]: #1630
-#1634 := [monotonicity #1631]: #1633
-#1673 := [monotonicity #1634 #1670]: #1672
+#1455 := (iff #790 #1454)
+#1452 := (iff #187 #1451)
+#1449 := (iff #186 #1448)
+#1450 := [rewrite]: #1449
+#1442 := (iff #184 #1441)
+#1443 := [rewrite]: #1442
+#1453 := [monotonicity #1443 #1450]: #1452
+#1456 := [monotonicity #1453]: #1455
+#1461 := [trans #1456 #1459]: #1460
+#1464 := [quant-intro #1461]: #1463
+#1467 := [monotonicity #1464]: #1466
+#1661 := [monotonicity #1467 #1608]: #1660
+#1624 := (iff #977 #1623)
+#1621 := (iff #781 #1620)
+#1618 := (iff #776 #1617)
+#1615 := (iff #770 #1614)
+#1616 := [rewrite]: #1615
+#1610 := (iff #192 #1609)
+#1611 := [monotonicity #1453]: #1610
+#1619 := [monotonicity #1611 #1616]: #1618
+#1622 := [quant-intro #1619]: #1621
+#1625 := [monotonicity #1622]: #1624
+#1664 := [monotonicity #1625 #1661]: #1663
+#1667 := [monotonicity #1664]: #1666
+#1642 := (iff #995 #1641)
+#1639 := (iff #767 #1638)
+#1636 := (iff #762 #1633)
+#1630 := (or #1626 #532)
+#1634 := (iff #1630 #1633)
+#1635 := [rewrite]: #1634
+#1631 := (iff #762 #1630)
+#1628 := (iff #176 #1626)
+#1629 := [rewrite]: #1628
+#1632 := [monotonicity #1629]: #1631
+#1637 := [trans #1632 #1635]: #1636
+#1640 := [quant-intro #1637]: #1639
+#1643 := [monotonicity #1640]: #1642
+#1670 := [monotonicity #1643 #1667]: #1669
+#1654 := (iff #1004 #1645)
+#1646 := (not #1645)
+#1649 := (not #1646)
+#1652 := (iff #1649 #1645)
+#1653 := [rewrite]: #1652
+#1650 := (iff #1004 #1649)
+#1647 := (iff #175 #1646)
+#1648 := [rewrite]: #1647
+#1651 := [monotonicity #1648]: #1650
+#1655 := [trans #1651 #1653]: #1654
+#1673 := [monotonicity #1655 #1670]: #1672
 #1676 := [monotonicity #1673]: #1675
-#1651 := (iff #1004 #1650)
-#1648 := (iff #768 #1647)
-#1645 := (iff #763 #1642)
-#1639 := (or #1635 #533)
-#1643 := (iff #1639 #1642)
-#1644 := [rewrite]: #1643
-#1640 := (iff #763 #1639)
-#1637 := (iff #176 #1635)
-#1638 := [rewrite]: #1637
-#1641 := [monotonicity #1638]: #1640
-#1646 := [trans #1641 #1644]: #1645
-#1649 := [quant-intro #1646]: #1648
-#1652 := [monotonicity #1649]: #1651
-#1679 := [monotonicity #1652 #1676]: #1678
-#1663 := (iff #1013 #1654)
-#1655 := (not #1654)
-#1658 := (not #1655)
-#1661 := (iff #1658 #1654)
-#1662 := [rewrite]: #1661
-#1659 := (iff #1013 #1658)
-#1656 := (iff #175 #1655)
-#1657 := [rewrite]: #1656
-#1660 := [monotonicity #1657]: #1659
-#1664 := [trans #1660 #1662]: #1663
-#1682 := [monotonicity #1664 #1679]: #1681
-#1685 := [monotonicity #1682]: #1684
-#1666 := (iff #618 #1665)
-#1425 := (iff #615 #1424)
-#1422 := (iff #610 #1419)
-#1416 := (and #1300 #536)
-#1420 := (iff #1416 #1419)
-#1421 := [rewrite]: #1420
-#1417 := (iff #610 #1416)
-#1301 := (iff #120 #1300)
-#1302 := [rewrite]: #1301
-#1418 := [monotonicity #1302]: #1417
-#1423 := [trans #1418 #1421]: #1422
-#1426 := [quant-intro #1423]: #1425
-#1667 := [monotonicity #1426]: #1666
-#1688 := [monotonicity #1667 #1685]: #1687
-#1693 := [trans #1688 #1691]: #1692
-#1445 := (iff #742 #1442)
-#1427 := (or #706 #1413)
-#1430 := (or #715 #1427)
-#1433 := (or #724 #1430)
-#1436 := (or #733 #1433)
-#1439 := (or #1424 #1436)
-#1443 := (iff #1439 #1442)
-#1444 := [rewrite]: #1443
-#1440 := (iff #742 #1439)
-#1437 := (iff #734 #1436)
-#1434 := (iff #725 #1433)
-#1431 := (iff #716 #1430)
-#1428 := (iff #707 #1427)
-#1414 := (iff #700 #1413)
-#1411 := (iff #695 #1410)
-#1408 := (iff #688 #1407)
-#1405 := (iff #683 #1402)
-#1399 := (or #1394 #158)
-#1403 := (iff #1399 #1402)
-#1404 := [rewrite]: #1403
-#1400 := (iff #683 #1399)
-#1397 := (iff #669 #158)
-#1398 := [rewrite]: #1397
-#1395 := (iff #682 #1394)
-#1392 := (iff #666 #1391)
-#1389 := (iff #661 #1388)
-#1386 := (iff #654 #1385)
-#1387 := [rewrite]: #1386
-#1383 := (iff #660 #1382)
-#1380 := (iff #651 #1379)
-#1346 := (iff #143 #1345)
-#1347 := [rewrite]: #1346
-#1381 := [monotonicity #1238 #1347]: #1380
-#1384 := [monotonicity #1381]: #1383
-#1390 := [monotonicity #1384 #1387]: #1389
-#1393 := [quant-intro #1390]: #1392
-#1396 := [monotonicity #1393]: #1395
-#1401 := [monotonicity #1396 #1398]: #1400
-#1406 := [trans #1401 #1404]: #1405
-#1409 := [monotonicity #1393 #1406]: #1408
-#1377 := (iff #694 #1376)
-#1374 := (iff #648 #1373)
-#1371 := (iff #643 #1370)
-#1368 := (iff #636 #1367)
-#1365 := (iff #633 #1364)
-#1361 := (iff #630 #1360)
-#1363 := [rewrite]: #1361
-#1358 := (iff #146 #1357)
-#1359 := [rewrite]: #1358
-#1366 := [monotonicity #1359 #1363]: #1365
-#1369 := [quant-intro #1366]: #1368
-#1352 := (iff #642 #1351)
-#1349 := (iff #144 #1348)
-#1350 := [monotonicity #1347]: #1349
-#1353 := [monotonicity #1350]: #1352
-#1372 := [monotonicity #1353 #1369]: #1371
-#1375 := [quant-intro #1372]: #1374
-#1378 := [monotonicity #1375]: #1377
-#1412 := [monotonicity #1378 #1409]: #1411
-#1415 := [monotonicity #1375 #1412]: #1414
-#1429 := [monotonicity #1415]: #1428
-#1432 := [monotonicity #1429]: #1431
-#1435 := [monotonicity #1432]: #1434
-#1438 := [monotonicity #1435]: #1437
-#1441 := [monotonicity #1426 #1438]: #1440
-#1446 := [trans #1441 #1444]: #1445
-#1696 := [monotonicity #1446 #1693]: #1695
-#1340 := (iff #1048 #1339)
-#1337 := (iff #604 #1336)
-#1334 := (iff #599 #1333)
-#1331 := (iff #592 #1330)
-#1328 := (iff #589 #1325)
-#1319 := (and #533 #1309)
-#1322 := (and #1316 #1319)
-#1326 := (iff #1322 #1325)
-#1327 := [rewrite]: #1326
-#1323 := (iff #589 #1322)
-#1320 := (iff #586 #1319)
-#1310 := (iff #583 #1309)
-#1314 := [rewrite]: #1310
-#1321 := [monotonicity #1314]: #1320
-#1317 := (iff #122 #1316)
+#1657 := (iff #617 #1656)
+#1416 := (iff #614 #1415)
+#1413 := (iff #609 #1410)
+#1407 := (and #1291 #535)
+#1411 := (iff #1407 #1410)
+#1412 := [rewrite]: #1411
+#1408 := (iff #609 #1407)
+#1292 := (iff #120 #1291)
+#1293 := [rewrite]: #1292
+#1409 := [monotonicity #1293]: #1408
+#1414 := [trans #1409 #1412]: #1413
+#1417 := [quant-intro #1414]: #1416
+#1658 := [monotonicity #1417]: #1657
+#1679 := [monotonicity #1658 #1676]: #1678
+#1684 := [trans #1679 #1682]: #1683
+#1436 := (iff #741 #1433)
+#1418 := (or #705 #1404)
+#1421 := (or #714 #1418)
+#1424 := (or #723 #1421)
+#1427 := (or #732 #1424)
+#1430 := (or #1415 #1427)
+#1434 := (iff #1430 #1433)
+#1435 := [rewrite]: #1434
+#1431 := (iff #741 #1430)
+#1428 := (iff #733 #1427)
+#1425 := (iff #724 #1424)
+#1422 := (iff #715 #1421)
+#1419 := (iff #706 #1418)
+#1405 := (iff #699 #1404)
+#1402 := (iff #694 #1401)
+#1399 := (iff #687 #1398)
+#1396 := (iff #682 #1393)
+#1390 := (or #1385 #158)
+#1394 := (iff #1390 #1393)
+#1395 := [rewrite]: #1394
+#1391 := (iff #682 #1390)
+#1388 := (iff #668 #158)
+#1389 := [rewrite]: #1388
+#1386 := (iff #681 #1385)
+#1383 := (iff #665 #1382)
+#1380 := (iff #660 #1379)
+#1377 := (iff #653 #1376)
+#1378 := [rewrite]: #1377
+#1374 := (iff #659 #1373)
+#1371 := (iff #650 #1370)
+#1337 := (iff #143 #1336)
+#1338 := [rewrite]: #1337
+#1372 := [monotonicity #1229 #1338]: #1371
+#1375 := [monotonicity #1372]: #1374
+#1381 := [monotonicity #1375 #1378]: #1380
+#1384 := [quant-intro #1381]: #1383
+#1387 := [monotonicity #1384]: #1386
+#1392 := [monotonicity #1387 #1389]: #1391
+#1397 := [trans #1392 #1395]: #1396
+#1400 := [monotonicity #1384 #1397]: #1399
+#1368 := (iff #693 #1367)
+#1365 := (iff #647 #1364)
+#1362 := (iff #642 #1361)
+#1359 := (iff #635 #1358)
+#1356 := (iff #632 #1355)
+#1352 := (iff #629 #1351)
+#1354 := [rewrite]: #1352
+#1349 := (iff #146 #1348)
+#1350 := [rewrite]: #1349
+#1357 := [monotonicity #1350 #1354]: #1356
+#1360 := [quant-intro #1357]: #1359
+#1343 := (iff #641 #1342)
+#1340 := (iff #144 #1339)
+#1341 := [monotonicity #1338]: #1340
+#1344 := [monotonicity #1341]: #1343
+#1363 := [monotonicity #1344 #1360]: #1362
+#1366 := [quant-intro #1363]: #1365
+#1369 := [monotonicity #1366]: #1368
+#1403 := [monotonicity #1369 #1400]: #1402
+#1406 := [monotonicity #1366 #1403]: #1405
+#1420 := [monotonicity #1406]: #1419
+#1423 := [monotonicity #1420]: #1422
+#1426 := [monotonicity #1423]: #1425
+#1429 := [monotonicity #1426]: #1428
+#1432 := [monotonicity #1417 #1429]: #1431
+#1437 := [trans #1432 #1435]: #1436
+#1687 := [monotonicity #1437 #1684]: #1686
+#1331 := (iff #1039 #1330)
+#1328 := (iff #603 #1327)
+#1325 := (iff #598 #1324)
+#1322 := (iff #591 #1321)
+#1319 := (iff #588 #1316)
+#1310 := (and #532 #1300)
+#1313 := (and #1307 #1310)
+#1317 := (iff #1313 #1316)
 #1318 := [rewrite]: #1317
-#1324 := [monotonicity #1318 #1321]: #1323
-#1329 := [trans #1324 #1327]: #1328
-#1332 := [quant-intro #1329]: #1331
-#1307 := (iff #598 #1306)
-#1304 := (iff #121 #1303)
-#1305 := [monotonicity #1302]: #1304
-#1308 := [monotonicity #1305]: #1307
-#1335 := [monotonicity #1308 #1332]: #1334
-#1338 := [quant-intro #1335]: #1337
-#1341 := [monotonicity #1338]: #1340
-#1755 := [monotonicity #1341 #1696]: #1754
-#1718 := (iff #1057 #1717)
-#1715 := (iff #580 #1714)
-#1712 := (iff #575 #1711)
-#1709 := (iff #568 #1708)
-#1710 := [rewrite]: #1709
-#1706 := (iff #574 #1705)
-#1703 := (iff #560 #1700)
-#1697 := (and #1236 #533)
-#1701 := (iff #1697 #1700)
-#1702 := [rewrite]: #1701
-#1698 := (iff #560 #1697)
-#1699 := [monotonicity #1238]: #1698
-#1704 := [trans #1699 #1702]: #1703
-#1707 := [monotonicity #1704]: #1706
-#1713 := [monotonicity #1707 #1710]: #1712
-#1716 := [quant-intro #1713]: #1715
-#1719 := [monotonicity #1716]: #1718
-#1758 := [monotonicity #1719 #1755]: #1757
+#1314 := (iff #588 #1313)
+#1311 := (iff #585 #1310)
+#1301 := (iff #582 #1300)
+#1305 := [rewrite]: #1301
+#1312 := [monotonicity #1305]: #1311
+#1308 := (iff #122 #1307)
+#1309 := [rewrite]: #1308
+#1315 := [monotonicity #1309 #1312]: #1314
+#1320 := [trans #1315 #1318]: #1319
+#1323 := [quant-intro #1320]: #1322
+#1298 := (iff #597 #1297)
+#1295 := (iff #121 #1294)
+#1296 := [monotonicity #1293]: #1295
+#1299 := [monotonicity #1296]: #1298
+#1326 := [monotonicity #1299 #1323]: #1325
+#1329 := [quant-intro #1326]: #1328
+#1332 := [monotonicity #1329]: #1331
+#1746 := [monotonicity #1332 #1687]: #1745
+#1709 := (iff #1048 #1708)
+#1706 := (iff #579 #1705)
+#1703 := (iff #574 #1702)
+#1700 := (iff #567 #1699)
+#1701 := [rewrite]: #1700
+#1697 := (iff #573 #1696)
+#1694 := (iff #559 #1691)
+#1688 := (and #1227 #532)
+#1692 := (iff #1688 #1691)
+#1693 := [rewrite]: #1692
+#1689 := (iff #559 #1688)
+#1690 := [monotonicity #1229]: #1689
+#1695 := [trans #1690 #1693]: #1694
+#1698 := [monotonicity #1695]: #1697
+#1704 := [monotonicity #1698 #1701]: #1703
+#1707 := [quant-intro #1704]: #1706
+#1710 := [monotonicity #1707]: #1709
+#1749 := [monotonicity #1710 #1746]: #1748
+#1725 := (iff #1057 #1724)
+#1722 := (iff #553 #1721)
+#1719 := (iff #548 #1716)
+#1713 := (or #1306 #547)
+#1717 := (iff #1713 #1716)
+#1718 := [rewrite]: #1717
+#1714 := (iff #548 #1713)
+#1711 := (iff #112 #1306)
+#1712 := [rewrite]: #1711
+#1715 := [monotonicity #1712]: #1714
+#1720 := [trans #1715 #1718]: #1719
+#1723 := [quant-intro #1720]: #1722
+#1726 := [monotonicity #1723]: #1725
+#1752 := [monotonicity #1726 #1749]: #1751
 #1734 := (iff #1066 #1733)
-#1731 := (iff #554 #1730)
-#1728 := (iff #549 #1725)
-#1722 := (or #1315 #548)
-#1726 := (iff #1722 #1725)
-#1727 := [rewrite]: #1726
-#1723 := (iff #549 #1722)
-#1720 := (iff #112 #1315)
-#1721 := [rewrite]: #1720
-#1724 := [monotonicity #1721]: #1723
-#1729 := [trans #1724 #1727]: #1728
+#1731 := (iff #103 #1730)
+#1728 := (iff #102 #1727)
+#1729 := [rewrite]: #1728
 #1732 := [quant-intro #1729]: #1731
 #1735 := [monotonicity #1732]: #1734
-#1761 := [monotonicity #1735 #1758]: #1760
-#1743 := (iff #1075 #1742)
-#1740 := (iff #103 #1739)
-#1737 := (iff #102 #1736)
-#1738 := [rewrite]: #1737
-#1741 := [quant-intro #1738]: #1740
-#1744 := [monotonicity #1741]: #1743
-#1764 := [monotonicity #1744 #1761]: #1763
-#1748 := (iff #1084 #1747)
-#1745 := (iff #530 #100)
-#1746 := [rewrite]: #1745
-#1749 := [monotonicity #1746]: #1748
-#1767 := [monotonicity #1749 #1764]: #1766
-#1751 := (iff #1100 #1750)
-#1295 := (iff #527 #1294)
-#1292 := (iff #522 #1291)
-#1289 := (iff #515 #1288)
-#1286 := (iff #512 #1283)
-#1277 := (and #1271 #454)
-#1280 := (and #1274 #1277)
-#1284 := (iff #1280 #1283)
-#1285 := [rewrite]: #1284
-#1281 := (iff #512 #1280)
-#1278 := (iff #507 #1277)
-#1272 := (iff #92 #1271)
-#1273 := [rewrite]: #1272
-#1279 := [monotonicity #1273]: #1278
-#1275 := (iff #91 #1274)
+#1755 := [monotonicity #1735 #1752]: #1754
+#1739 := (iff #1075 #1738)
+#1736 := (iff #529 #100)
+#1737 := [rewrite]: #1736
+#1740 := [monotonicity #1737]: #1739
+#1758 := [monotonicity #1740 #1755]: #1757
+#1742 := (iff #1091 #1741)
+#1286 := (iff #526 #1285)
+#1283 := (iff #521 #1282)
+#1280 := (iff #514 #1279)
+#1277 := (iff #511 #1274)
+#1268 := (and #1262 #453)
+#1271 := (and #1265 #1268)
+#1275 := (iff #1271 #1274)
 #1276 := [rewrite]: #1275
-#1282 := [monotonicity #1276 #1279]: #1281
-#1287 := [trans #1282 #1285]: #1286
-#1290 := [quant-intro #1287]: #1289
-#1269 := (iff #521 #1268)
-#1266 := (iff #90 #1265)
-#1263 := (iff #89 #1262)
+#1272 := (iff #511 #1271)
+#1269 := (iff #506 #1268)
+#1263 := (iff #92 #1262)
 #1264 := [rewrite]: #1263
-#1267 := [monotonicity #1264]: #1266
-#1270 := [monotonicity #1267]: #1269
-#1293 := [monotonicity #1270 #1290]: #1292
-#1296 := [quant-intro #1293]: #1295
-#1752 := [monotonicity #1296]: #1751
-#1770 := [monotonicity #1752 #1767]: #1769
-#1775 := [trans #1770 #1773]: #1774
-#1778 := [monotonicity #1296 #1775]: #1777
-#1257 := (iff #1112 #1256)
-#1254 := (iff #501 #1253)
-#1251 := (iff #496 #1250)
-#1248 := (iff #495 #1247)
-#1245 := (iff #487 #1242)
-#1239 := (and #1236 #454)
-#1243 := (iff #1239 #1242)
-#1244 := [rewrite]: #1243
-#1240 := (iff #487 #1239)
-#1241 := [monotonicity #1238]: #1240
-#1246 := [trans #1241 #1244]: #1245
+#1270 := [monotonicity #1264]: #1269
+#1266 := (iff #91 #1265)
+#1267 := [rewrite]: #1266
+#1273 := [monotonicity #1267 #1270]: #1272
+#1278 := [trans #1273 #1276]: #1277
+#1281 := [quant-intro #1278]: #1280
+#1260 := (iff #520 #1259)
+#1257 := (iff #90 #1256)
+#1254 := (iff #89 #1253)
+#1255 := [rewrite]: #1254
+#1258 := [monotonicity #1255]: #1257
+#1261 := [monotonicity #1258]: #1260
+#1284 := [monotonicity #1261 #1281]: #1283
+#1287 := [quant-intro #1284]: #1286
+#1743 := [monotonicity #1287]: #1742
+#1761 := [monotonicity #1743 #1758]: #1760
+#1766 := [trans #1761 #1764]: #1765
+#1769 := [monotonicity #1287 #1766]: #1768
+#1248 := (iff #1103 #1247)
+#1245 := (iff #500 #1244)
+#1242 := (iff #495 #1241)
+#1239 := (iff #494 #1238)
+#1236 := (iff #486 #1233)
+#1230 := (and #1227 #453)
+#1234 := (iff #1230 #1233)
+#1235 := [rewrite]: #1234
+#1231 := (iff #486 #1230)
+#1232 := [monotonicity #1229]: #1231
+#1237 := [trans #1232 #1235]: #1236
+#1240 := [monotonicity #1237]: #1239
+#1220 := (iff #86 #1221)
+#1219 := [rewrite]: #1220
+#1243 := [monotonicity #1219 #1240]: #1242
+#1246 := [quant-intro #1243]: #1245
 #1249 := [monotonicity #1246]: #1248
-#1229 := (iff #86 #1230)
-#1228 := [rewrite]: #1229
-#1252 := [monotonicity #1228 #1249]: #1251
-#1255 := [quant-intro #1252]: #1254
-#1258 := [monotonicity #1255]: #1257
-#1781 := [monotonicity #1258 #1778]: #1780
-#1784 := [monotonicity #1255 #1781]: #1783
-#1226 := (iff #1124 #1225)
-#1223 := (iff #481 #1222)
-#1220 := (iff #476 #1217)
-#1214 := (or #1210 #475)
-#1218 := (iff #1214 #1217)
-#1219 := [rewrite]: #1218
-#1215 := (iff #476 #1214)
-#1209 := (iff #78 #1210)
-#1213 := [rewrite]: #1209
-#1216 := [monotonicity #1213]: #1215
-#1221 := [trans #1216 #1219]: #1220
-#1224 := [quant-intro #1221]: #1223
-#1227 := [monotonicity #1224]: #1226
-#1787 := [monotonicity #1227 #1784]: #1786
-#1790 := [monotonicity #1224 #1787]: #1789
-#1206 := (iff #1136 #1205)
-#1203 := (iff #73 #1202)
-#1199 := (iff #72 #1201)
-#1200 := [rewrite]: #1199
-#1204 := [quant-intro #1200]: #1203
+#1772 := [monotonicity #1249 #1769]: #1771
+#1775 := [monotonicity #1246 #1772]: #1774
+#1217 := (iff #1115 #1216)
+#1214 := (iff #480 #1213)
+#1211 := (iff #475 #1208)
+#1205 := (or #1201 #474)
+#1209 := (iff #1205 #1208)
+#1210 := [rewrite]: #1209
+#1206 := (iff #475 #1205)
+#1200 := (iff #78 #1201)
+#1204 := [rewrite]: #1200
 #1207 := [monotonicity #1204]: #1206
-#1793 := [monotonicity #1207 #1790]: #1792
-#1796 := [monotonicity #1204 #1793]: #1795
-#1197 := (iff #1148 #1196)
-#1194 := (iff #463 #71)
-#1195 := [rewrite]: #1194
+#1212 := [trans #1207 #1210]: #1211
+#1215 := [quant-intro #1212]: #1214
+#1218 := [monotonicity #1215]: #1217
+#1778 := [monotonicity #1218 #1775]: #1777
+#1781 := [monotonicity #1215 #1778]: #1780
+#1197 := (iff #1127 #1196)
+#1194 := (iff #73 #1193)
+#1190 := (iff #72 #1192)
+#1191 := [rewrite]: #1190
+#1195 := [quant-intro #1191]: #1194
 #1198 := [monotonicity #1195]: #1197
-#1799 := [monotonicity #1198 #1796]: #1798
-#1802 := [monotonicity #1195 #1799]: #1801
-#1816 := [monotonicity #1802]: #1815
-#1819 := [monotonicity #1816]: #1818
-#1812 := (iff #1178 #1811)
-#1809 := (iff #437 #1808)
-#1806 := (iff #432 #1805)
-#1803 := (iff #426 #59)
-#1804 := [rewrite]: #1803
-#1807 := [monotonicity #1804]: #1806
-#1810 := [quant-intro #1807]: #1809
-#1813 := [monotonicity #1810]: #1812
-#1822 := [monotonicity #1813 #1819]: #1821
-#1827 := [trans #1822 #1825]: #1826
-#1830 := [monotonicity #1827]: #1829
-#1192 := (iff #271 #1191)
-#1189 := (iff #270 #1179)
-#1184 := (implies true #1179)
-#1187 := (iff #1184 #1179)
-#1188 := [rewrite]: #1187
-#1185 := (iff #270 #1184)
-#1182 := (iff #269 #1179)
-#1175 := (implies #437 #1170)
-#1180 := (iff #1175 #1179)
-#1181 := [rewrite]: #1180
+#1784 := [monotonicity #1198 #1781]: #1783
+#1787 := [monotonicity #1195 #1784]: #1786
+#1188 := (iff #1139 #1187)
+#1185 := (iff #462 #71)
+#1186 := [rewrite]: #1185
+#1189 := [monotonicity #1186]: #1188
+#1790 := [monotonicity #1189 #1787]: #1789
+#1793 := [monotonicity #1186 #1790]: #1792
+#1807 := [monotonicity #1793]: #1806
+#1810 := [monotonicity #1807]: #1809
+#1803 := (iff #1169 #1802)
+#1800 := (iff #436 #1799)
+#1797 := (iff #431 #1796)
+#1794 := (iff #425 #59)
+#1795 := [rewrite]: #1794
+#1798 := [monotonicity #1795]: #1797
+#1801 := [quant-intro #1798]: #1800
+#1804 := [monotonicity #1801]: #1803
+#1813 := [monotonicity #1804 #1810]: #1812
+#1818 := [trans #1813 #1816]: #1817
+#1821 := [monotonicity #1818]: #1820
+#1183 := (iff #270 #1182)
+#1180 := (iff #269 #1170)
+#1175 := (implies true #1170)
+#1178 := (iff #1175 #1170)
+#1179 := [rewrite]: #1178
 #1176 := (iff #269 #1175)
 #1173 := (iff #268 #1170)
-#1166 := (implies #451 #1161)
+#1166 := (implies #436 #1161)
 #1171 := (iff #1166 #1170)
 #1172 := [rewrite]: #1171
 #1167 := (iff #268 #1166)
 #1164 := (iff #267 #1161)
-#1157 := (implies #460 #1154)
+#1157 := (implies #450 #1152)
 #1162 := (iff #1157 #1161)
 #1163 := [rewrite]: #1162
 #1158 := (iff #267 #1157)
-#1155 := (iff #266 #1154)
-#1152 := (iff #265 #1149)
-#1145 := (implies #463 #1142)
-#1150 := (iff #1145 #1149)
-#1151 := [rewrite]: #1150
+#1155 := (iff #266 #1152)
+#1148 := (implies #459 #1145)
+#1153 := (iff #1148 #1152)
+#1154 := [rewrite]: #1153
+#1149 := (iff #266 #1148)
 #1146 := (iff #265 #1145)
-#1143 := (iff #264 #1142)
-#1140 := (iff #263 #1137)
-#1133 := (implies #73 #1130)
-#1138 := (iff #1133 #1137)
-#1139 := [rewrite]: #1138
+#1143 := (iff #264 #1140)
+#1136 := (implies #462 #1133)
+#1141 := (iff #1136 #1140)
+#1142 := [rewrite]: #1141
+#1137 := (iff #264 #1136)
 #1134 := (iff #263 #1133)
-#1131 := (iff #262 #1130)
-#1128 := (iff #261 #1125)
-#1121 := (implies #481 #1118)
-#1126 := (iff #1121 #1125)
-#1127 := [rewrite]: #1126
+#1131 := (iff #262 #1128)
+#1124 := (implies #73 #1121)
+#1129 := (iff #1124 #1128)
+#1130 := [rewrite]: #1129
+#1125 := (iff #262 #1124)
 #1122 := (iff #261 #1121)
-#1119 := (iff #260 #1118)
-#1116 := (iff #259 #1113)
-#1109 := (implies #501 #1106)
-#1114 := (iff #1109 #1113)
-#1115 := [rewrite]: #1114
+#1119 := (iff #260 #1116)
+#1112 := (implies #480 #1109)
+#1117 := (iff #1112 #1116)
+#1118 := [rewrite]: #1117
+#1113 := (iff #260 #1112)
 #1110 := (iff #259 #1109)
-#1107 := (iff #258 #1106)
-#1104 := (iff #257 #1101)
-#1097 := (implies #527 #1085)
-#1102 := (iff #1097 #1101)
-#1103 := [rewrite]: #1102
+#1107 := (iff #258 #1104)
+#1100 := (implies #500 #1097)
+#1105 := (iff #1100 #1104)
+#1106 := [rewrite]: #1105
+#1101 := (iff #258 #1100)
 #1098 := (iff #257 #1097)
-#1095 := (iff #256 #1085)
-#1090 := (implies true #1085)
-#1093 := (iff #1090 #1085)
+#1095 := (iff #256 #1092)
+#1088 := (implies #526 #1076)
+#1093 := (iff #1088 #1092)
 #1094 := [rewrite]: #1093
-#1091 := (iff #256 #1090)
-#1088 := (iff #255 #1085)
-#1081 := (implies #530 #1076)
-#1086 := (iff #1081 #1085)
-#1087 := [rewrite]: #1086
+#1089 := (iff #256 #1088)
+#1086 := (iff #255 #1076)
+#1081 := (implies true #1076)
+#1084 := (iff #1081 #1076)
+#1085 := [rewrite]: #1084
 #1082 := (iff #255 #1081)
 #1079 := (iff #254 #1076)
-#1072 := (implies #103 #1067)
+#1072 := (implies #529 #1067)
 #1077 := (iff #1072 #1076)
 #1078 := [rewrite]: #1077
 #1073 := (iff #254 #1072)
 #1070 := (iff #253 #1067)
-#1063 := (implies #554 #1058)
+#1063 := (implies #103 #1058)
 #1068 := (iff #1063 #1067)
 #1069 := [rewrite]: #1068
 #1064 := (iff #253 #1063)
 #1061 := (iff #252 #1058)
-#1054 := (implies #580 #1049)
+#1054 := (implies #553 #1049)
 #1059 := (iff #1054 #1058)
 #1060 := [rewrite]: #1059
 #1055 := (iff #252 #1054)
 #1052 := (iff #251 #1049)
-#1045 := (implies #604 #1042)
+#1045 := (implies #579 #1040)
 #1050 := (iff #1045 #1049)
 #1051 := [rewrite]: #1050
 #1046 := (iff #251 #1045)
-#1043 := (iff #250 #1042)
-#1040 := (iff #249 #1030)
-#1035 := (implies true #1030)
-#1038 := (iff #1035 #1030)
-#1039 := [rewrite]: #1038
-#1036 := (iff #249 #1035)
-#1033 := (iff #248 #1030)
-#1027 := (implies #615 #1022)
-#1031 := (iff #1027 #1030)
-#1032 := [rewrite]: #1031
-#1028 := (iff #248 #1027)
-#1025 := (iff #247 #1022)
-#757 := (not #754)
-#1019 := (implies #757 #1014)
-#1023 := (iff #1019 #1022)
-#1024 := [rewrite]: #1023
-#1020 := (iff #247 #1019)
-#1017 := (iff #246 #1014)
-#1010 := (implies #175 #1005)
-#1015 := (iff #1010 #1014)
-#1016 := [rewrite]: #1015
+#1043 := (iff #250 #1040)
+#1036 := (implies #603 #1033)
+#1041 := (iff #1036 #1040)
+#1042 := [rewrite]: #1041
+#1037 := (iff #250 #1036)
+#1034 := (iff #249 #1033)
+#1031 := (iff #248 #1021)
+#1026 := (implies true #1021)
+#1029 := (iff #1026 #1021)
+#1030 := [rewrite]: #1029
+#1027 := (iff #248 #1026)
+#1024 := (iff #247 #1021)
+#1018 := (implies #614 #1013)
+#1022 := (iff #1018 #1021)
+#1023 := [rewrite]: #1022
+#1019 := (iff #247 #1018)
+#1016 := (iff #246 #1013)
+#756 := (not #753)
+#1010 := (implies #756 #1005)
+#1014 := (iff #1010 #1013)
+#1015 := [rewrite]: #1014
 #1011 := (iff #246 #1010)
 #1008 := (iff #245 #1005)
-#1001 := (implies #768 #996)
+#1001 := (implies #175 #996)
 #1006 := (iff #1001 #1005)
 #1007 := [rewrite]: #1006
 #1002 := (iff #245 #1001)
 #999 := (iff #244 #996)
-#992 := (implies #776 #987)
+#992 := (implies #767 #987)
 #997 := (iff #992 #996)
 #998 := [rewrite]: #997
 #993 := (iff #244 #992)
 #990 := (iff #243 #987)
-#983 := (implies #790 #978)
+#983 := (implies #181 #978)
 #988 := (iff #983 #987)
 #989 := [rewrite]: #988
 #984 := (iff #243 #983)
 #981 := (iff #242 #978)
-#974 := (implies #804 #971)
+#974 := (implies #781 #969)
 #979 := (iff #974 #978)
 #980 := [rewrite]: #979
 #975 := (iff #242 #974)
-#972 := (iff #241 #971)
-#969 := (iff #240 #966)
-#962 := (implies #198 #959)
-#967 := (iff #962 #966)
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 #963 := (iff #240 #962)
-#960 := (iff #239 #959)
-#957 := (iff #238 #954)
-#950 := (implies #819 #947)
-#955 := (iff #950 #954)
-#956 := [rewrite]: #955
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+#953 := (implies #197 #950)
+#958 := (iff #953 #957)
+#959 := [rewrite]: #958
+#954 := (iff #239 #953)
 #951 := (iff #238 #950)
-#948 := (iff #237 #947)
-#945 := (iff #236 #942)
-#938 := (implies #822 #935)
-#943 := (iff #938 #942)
-#944 := [rewrite]: #943
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+#941 := (implies #810 #938)
+#946 := (iff #941 #945)
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 #939 := (iff #236 #938)
-#936 := (iff #235 #935)
-#933 := (iff #234 #930)
-#926 := (implies #206 #923)
-#931 := (iff #926 #930)
-#932 := [rewrite]: #931
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+#929 := (implies #813 #926)
+#934 := (iff #929 #933)
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+#930 := (iff #235 #929)
 #927 := (iff #234 #926)
-#924 := (iff #233 #923)
-#921 := (iff #232 #918)
-#914 := (implies #842 #911)
-#919 := (iff #914 #918)
-#920 := [rewrite]: #919
+#924 := (iff #233 #921)
+#917 := (implies #205 #914)
+#922 := (iff #917 #921)
+#923 := [rewrite]: #922
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 #915 := (iff #232 #914)
-#912 := (iff #231 #911)
-#909 := (iff #230 #906)
-#902 := (implies #868 #892)
-#907 := (iff #902 #906)
-#908 := [rewrite]: #907
+#912 := (iff #231 #909)
+#905 := (implies #833 #902)
+#910 := (iff #905 #909)
+#911 := [rewrite]: #910
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 #903 := (iff #230 #902)
-#900 := (iff #229 #892)
-#895 := (and #892 true)
-#898 := (iff #895 #892)
+#900 := (iff #229 #897)
+#893 := (implies #859 #883)
+#898 := (iff #893 #897)
 #899 := [rewrite]: #898
-#896 := (iff #229 #895)
-#893 := (iff #228 #892)
-#890 := (iff #227 #887)
-#883 := (implies #221 #880)
-#888 := (iff #883 #887)
-#889 := [rewrite]: #888
+#894 := (iff #229 #893)
+#891 := (iff #228 #883)
+#886 := (and #883 true)
+#889 := (iff #886 #883)
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 #884 := (iff #227 #883)
-#881 := (iff #226 #880)
-#878 := (iff #225 #877)
-#875 := (iff #224 #874)
-#872 := (iff #223 #871)
-#854 := (= #216 #853)
-#855 := [rewrite]: #854
-#873 := [monotonicity #855]: #872
-#808 := (iff #200 #807)
-#809 := [rewrite]: #808
-#876 := [monotonicity #809 #873]: #875
-#879 := [monotonicity #876]: #878
-#882 := [quant-intro #879]: #881
-#885 := [monotonicity #882]: #884
-#891 := [trans #885 #889]: #890
-#894 := [quant-intro #891]: #893
-#897 := [monotonicity #894]: #896
-#901 := [trans #897 #899]: #900
-#869 := (iff #219 #868)
-#866 := (iff #218 #863)
-#859 := (implies #848 #856)
-#864 := (iff #859 #863)
-#865 := [rewrite]: #864
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+#874 := (implies #220 #871)
+#879 := (iff #874 #878)
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+#875 := (iff #226 #874)
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+#869 := (iff #224 #868)
+#866 := (iff #223 #865)
+#863 := (iff #222 #862)
+#845 := (= #215 #844)
+#846 := [rewrite]: #845
+#864 := [monotonicity #846]: #863
+#799 := (iff #199 #798)
+#800 := [rewrite]: #799
+#867 := [monotonicity #800 #864]: #866
+#870 := [monotonicity #867]: #869
+#873 := [quant-intro #870]: #872
+#876 := [monotonicity #873]: #875
+#882 := [trans #876 #880]: #881
+#885 := [quant-intro #882]: #884
+#888 := [monotonicity #885]: #887
+#892 := [trans #888 #890]: #891
 #860 := (iff #218 #859)
-#857 := (iff #217 #856)
-#858 := [monotonicity #855]: #857
-#851 := (iff #215 #848)
-#845 := (and #807 #83)
-#849 := (iff #845 #848)
-#850 := [rewrite]: #849
-#846 := (iff #215 #845)
-#847 := [monotonicity #809]: #846
-#852 := [trans #847 #850]: #851
-#861 := [monotonicity #852 #858]: #860
-#867 := [trans #861 #865]: #866
-#870 := [quant-intro #867]: #869
-#904 := [monotonicity #870 #901]: #903
-#910 := [trans #904 #908]: #909
-#913 := [monotonicity #870 #910]: #912
-#843 := (iff #214 #842)
-#840 := (iff #213 #837)
-#833 := (implies #830 #212)
-#838 := (iff #833 #837)
-#839 := [rewrite]: #838
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+#855 := (iff #850 #854)
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+#851 := (iff #217 #850)
+#848 := (iff #216 #847)
+#849 := [monotonicity #846]: #848
+#842 := (iff #214 #839)
+#836 := (and #798 #83)
+#840 := (iff #836 #839)
+#841 := [rewrite]: #840
+#837 := (iff #214 #836)
+#838 := [monotonicity #800]: #837
+#843 := [trans #838 #841]: #842
+#852 := [monotonicity #843 #849]: #851
+#858 := [trans #852 #856]: #857
+#861 := [quant-intro #858]: #860
+#895 := [monotonicity #861 #892]: #894
+#901 := [trans #895 #899]: #900
+#904 := [monotonicity #861 #901]: #903
 #834 := (iff #213 #833)
-#831 := (iff #210 #830)
-#828 := (iff #209 #827)
-#829 := [rewrite]: #828
-#825 := (iff #207 #813)
-#826 := [monotonicity #809]: #825
-#832 := [monotonicity #826 #829]: #831
-#835 := [monotonicity #832]: #834
-#841 := [trans #835 #839]: #840
-#844 := [quant-intro #841]: #843
-#916 := [monotonicity #844 #913]: #915
-#922 := [trans #916 #920]: #921
-#925 := [monotonicity #844 #922]: #924
+#831 := (iff #212 #828)
+#824 := (implies #821 #211)
+#829 := (iff #824 #828)
+#830 := [rewrite]: #829
+#825 := (iff #212 #824)
+#822 := (iff #209 #821)
+#819 := (iff #208 #818)
+#820 := [rewrite]: #819
+#816 := (iff #206 #804)
+#817 := [monotonicity #800]: #816
+#823 := [monotonicity #817 #820]: #822
+#826 := [monotonicity #823]: #825
+#832 := [trans #826 #830]: #831
+#835 := [quant-intro #832]: #834
+#907 := [monotonicity #835 #904]: #906
+#913 := [trans #907 #911]: #912
+#916 := [monotonicity #835 #913]: #915
+#919 := [monotonicity #916]: #918
+#925 := [trans #919 #923]: #924
 #928 := [monotonicity #925]: #927
-#934 := [trans #928 #932]: #933
-#937 := [monotonicity #934]: #936
-#823 := (iff #204 #822)
-#824 := [rewrite]: #823
-#940 := [monotonicity #824 #937]: #939
-#946 := [trans #940 #944]: #945
-#949 := [monotonicity #824 #946]: #948
-#820 := (iff #202 #819)
-#817 := (iff #201 #814)
-#810 := (implies #807 #793)
-#815 := (iff #810 #814)
-#816 := [rewrite]: #815
+#814 := (iff #203 #813)
+#815 := [rewrite]: #814
+#931 := [monotonicity #815 #928]: #930
+#937 := [trans #931 #935]: #936
+#940 := [monotonicity #815 #937]: #939
 #811 := (iff #201 #810)
-#794 := (iff #194 #793)
-#795 := [rewrite]: #794
-#812 := [monotonicity #809 #795]: #811
-#818 := [trans #812 #816]: #817
-#821 := [quant-intro #818]: #820
-#952 := [monotonicity #821 #949]: #951
-#958 := [trans #952 #956]: #957
-#961 := [monotonicity #821 #958]: #960
+#808 := (iff #200 #805)
+#801 := (implies #798 #784)
+#806 := (iff #801 #805)
+#807 := [rewrite]: #806
+#802 := (iff #200 #801)
+#785 := (iff #193 #784)
+#786 := [rewrite]: #785
+#803 := [monotonicity #800 #786]: #802
+#809 := [trans #803 #807]: #808
+#812 := [quant-intro #809]: #811
+#943 := [monotonicity #812 #940]: #942
+#949 := [trans #943 #947]: #948
+#952 := [monotonicity #812 #949]: #951
+#955 := [monotonicity #952]: #954
+#961 := [trans #955 #959]: #960
 #964 := [monotonicity #961]: #963
-#970 := [trans #964 #968]: #969
-#973 := [monotonicity #970]: #972
-#805 := (iff #196 #804)
-#802 := (iff #195 #799)
-#796 := (implies #193 #793)
-#800 := (iff #796 #799)
-#801 := [rewrite]: #800
-#797 := (iff #195 #796)
-#798 := [monotonicity #795]: #797
-#803 := [trans #798 #801]: #802
-#806 := [quant-intro #803]: #805
-#976 := [monotonicity #806 #973]: #975
-#982 := [trans #976 #980]: #981
-#791 := (iff #192 #790)
-#788 := (iff #191 #785)
-#782 := (implies #188 #779)
-#786 := (iff #782 #785)
-#787 := [rewrite]: #786
-#783 := (iff #191 #782)
-#780 := (iff #190 #779)
-#781 := [rewrite]: #780
-#784 := [monotonicity #781]: #783
-#789 := [trans #784 #787]: #788
-#792 := [quant-intro #789]: #791
-#985 := [monotonicity #792 #982]: #984
-#991 := [trans #985 #989]: #990
-#777 := (iff #182 #776)
-#774 := (= #181 #773)
-#771 := (= #180 f1)
+#796 := (iff #195 #795)
+#793 := (iff #194 #790)
+#787 := (implies #192 #784)
+#791 := (iff #787 #790)
+#792 := [rewrite]: #791
+#788 := (iff #194 #787)
+#789 := [monotonicity #786]: #788
+#794 := [trans #789 #792]: #793
+#797 := [quant-intro #794]: #796
+#967 := [monotonicity #797 #964]: #966
+#973 := [trans #967 #971]: #972
+#782 := (iff #191 #781)
+#779 := (iff #190 #776)
+#773 := (implies #187 #770)
+#777 := (iff #773 #776)
+#778 := [rewrite]: #777
+#774 := (iff #190 #773)
+#771 := (iff #189 #770)
 #772 := [rewrite]: #771
 #775 := [monotonicity #772]: #774
-#778 := [monotonicity #775]: #777
-#994 := [monotonicity #778 #991]: #993
+#780 := [trans #775 #778]: #779
+#783 := [quant-intro #780]: #782
+#976 := [monotonicity #783 #973]: #975
+#982 := [trans #976 #980]: #981
+#985 := [monotonicity #982]: #984
+#991 := [trans #985 #989]: #990
+#768 := (iff #178 #767)
+#765 := (iff #177 #762)
+#759 := (implies #535 #176)
+#763 := (iff #759 #762)
+#764 := [rewrite]: #763
+#760 := (iff #177 #759)
+#536 := (iff #107 #535)
+#533 := (iff #106 #532)
+#534 := [rewrite]: #533
+#537 := [monotonicity #534]: #536
+#761 := [monotonicity #537]: #760
+#766 := [trans #761 #764]: #765
+#769 := [quant-intro #766]: #768
+#994 := [monotonicity #769 #991]: #993
 #1000 := [trans #994 #998]: #999
-#769 := (iff #178 #768)
-#766 := (iff #177 #763)
-#760 := (implies #536 #176)
-#764 := (iff #760 #763)
-#765 := [rewrite]: #764
-#761 := (iff #177 #760)
-#537 := (iff #107 #536)
-#534 := (iff #106 #533)
-#535 := [rewrite]: #534
-#538 := [monotonicity #535]: #537
-#762 := [monotonicity #538]: #761
-#767 := [trans #762 #765]: #766
-#770 := [quant-intro #767]: #769
-#1003 := [monotonicity #770 #1000]: #1002
+#1003 := [monotonicity #1000]: #1002
 #1009 := [trans #1003 #1007]: #1008
-#1012 := [monotonicity #1009]: #1011
-#1018 := [trans #1012 #1016]: #1017
-#758 := (iff #173 #757)
-#755 := (iff #172 #754)
-#756 := [rewrite]: #755
-#759 := [monotonicity #756]: #758
-#1021 := [monotonicity #759 #1018]: #1020
-#1026 := [trans #1021 #1024]: #1025
-#616 := (iff #130 #615)
-#613 := (iff #129 #610)
-#607 := (and #536 #120)
-#611 := (iff #607 #610)
-#612 := [rewrite]: #611
-#608 := (iff #129 #607)
-#609 := [monotonicity #538]: #608
-#614 := [trans #609 #612]: #613
-#617 := [quant-intro #614]: #616
-#1029 := [monotonicity #617 #1026]: #1028
-#1034 := [trans #1029 #1032]: #1033
-#1037 := [monotonicity #1034]: #1036
-#1041 := [trans #1037 #1039]: #1040
-#752 := (iff #169 #742)
-#747 := (implies true #742)
-#750 := (iff #747 #742)
-#751 := [rewrite]: #750
-#748 := (iff #169 #747)
-#745 := (iff #168 #742)
-#739 := (implies #618 #734)
-#743 := (iff #739 #742)
-#744 := [rewrite]: #743
-#740 := (iff #168 #739)
-#737 := (iff #167 #734)
-#730 := (implies #621 #725)
-#735 := (iff #730 #734)
-#736 := [rewrite]: #735
-#731 := (iff #167 #730)
-#728 := (iff #166 #725)
-#721 := (implies #136 #716)
-#726 := (iff #721 #725)
-#727 := [rewrite]: #726
-#722 := (iff #166 #721)
-#719 := (iff #165 #716)
-#712 := (implies #624 #707)
-#717 := (iff #712 #716)
-#718 := [rewrite]: #717
-#713 := (iff #165 #712)
-#710 := (iff #164 #707)
-#703 := (implies #141 #700)
-#708 := (iff #703 #707)
-#709 := [rewrite]: #708
-#704 := (iff #164 #703)
-#701 := (iff #163 #700)
-#698 := (iff #162 #695)
-#691 := (implies #648 #688)
-#696 := (iff #691 #695)
-#697 := [rewrite]: #696
-#692 := (iff #162 #691)
-#689 := (iff #161 #688)
-#686 := (iff #160 #683)
-#679 := (implies #666 #669)
-#684 := (iff #679 #683)
-#685 := [rewrite]: #684
-#680 := (iff #160 #679)
-#677 := (iff #159 #669)
-#672 := (and #669 true)
-#675 := (iff #672 #669)
-#676 := [rewrite]: #675
-#673 := (iff #159 #672)
-#670 := (iff #158 #669)
-#671 := [rewrite]: #670
-#674 := [monotonicity #671]: #673
-#678 := [trans #674 #676]: #677
-#667 := (iff #156 #666)
-#664 := (iff #155 #661)
-#657 := (implies #651 #654)
-#662 := (iff #657 #661)
-#663 := [rewrite]: #662
-#658 := (iff #155 #657)
-#655 := (iff #154 #654)
-#628 := (= #147 #627)
-#629 := [rewrite]: #628
-#656 := [monotonicity #629]: #655
-#652 := (iff #153 #651)
-#653 := [rewrite]: #652
-#659 := [monotonicity #653 #656]: #658
-#665 := [trans #659 #663]: #664
-#668 := [quant-intro #665]: #667
-#681 := [monotonicity #668 #678]: #680
-#687 := [trans #681 #685]: #686
-#690 := [monotonicity #668 #687]: #689
-#649 := (iff #152 #648)
-#646 := (iff #151 #643)
-#639 := (implies #144 #636)
-#644 := (iff #639 #643)
-#645 := [rewrite]: #644
-#640 := (iff #151 #639)
-#637 := (iff #150 #636)
-#634 := (iff #149 #633)
-#631 := (iff #148 #630)
-#632 := [monotonicity #629]: #631
-#635 := [monotonicity #632]: #634
-#638 := [quant-intro #635]: #637
-#641 := [monotonicity #638]: #640
-#647 := [trans #641 #645]: #646
-#650 := [quant-intro #647]: #649
-#693 := [monotonicity #650 #690]: #692
-#699 := [trans #693 #697]: #698
-#702 := [monotonicity #650 #699]: #701
-#705 := [monotonicity #702]: #704
-#711 := [trans #705 #709]: #710
-#625 := (iff #138 #624)
-#626 := [rewrite]: #625
-#714 := [monotonicity #626 #711]: #713
-#720 := [trans #714 #718]: #719
-#723 := [monotonicity #720]: #722
-#729 := [trans #723 #727]: #728
-#622 := (iff #133 #621)
-#623 := [rewrite]: #622
-#732 := [monotonicity #623 #729]: #731
-#738 := [trans #732 #736]: #737
-#619 := (iff #131 #618)
-#620 := [monotonicity #617]: #619
-#741 := [monotonicity #620 #738]: #740
-#746 := [trans #741 #744]: #745
-#749 := [monotonicity #746]: #748
-#753 := [trans #749 #751]: #752
-#1044 := [monotonicity #753 #1041]: #1043
-#605 := (iff #128 #604)
-#602 := (iff #127 #599)
-#595 := (implies #121 #592)
-#600 := (iff #595 #599)
-#601 := [rewrite]: #600
-#596 := (iff #127 #595)
-#593 := (iff #126 #592)
-#590 := (iff #125 #589)
-#587 := (iff #124 #586)
-#584 := (iff #123 #583)
-#566 := (= #116 #565)
-#567 := [rewrite]: #566
-#585 := [monotonicity #567]: #584
-#588 := [monotonicity #535 #585]: #587
-#591 := [monotonicity #588]: #590
-#594 := [quant-intro #591]: #593
-#597 := [monotonicity #594]: #596
-#603 := [trans #597 #601]: #602
-#606 := [quant-intro #603]: #605
-#1047 := [monotonicity #606 #1044]: #1046
+#757 := (iff #173 #756)
+#754 := (iff #172 #753)
+#755 := [rewrite]: #754
+#758 := [monotonicity #755]: #757
+#1012 := [monotonicity #758 #1009]: #1011
+#1017 := [trans #1012 #1015]: #1016
+#615 := (iff #130 #614)
+#612 := (iff #129 #609)
+#606 := (and #535 #120)
+#610 := (iff #606 #609)
+#611 := [rewrite]: #610
+#607 := (iff #129 #606)
+#608 := [monotonicity #537]: #607
+#613 := [trans #608 #611]: #612
+#616 := [quant-intro #613]: #615
+#1020 := [monotonicity #616 #1017]: #1019
+#1025 := [trans #1020 #1023]: #1024
+#1028 := [monotonicity #1025]: #1027
+#1032 := [trans #1028 #1030]: #1031
+#751 := (iff #169 #741)
+#746 := (implies true #741)
+#749 := (iff #746 #741)
+#750 := [rewrite]: #749
+#747 := (iff #169 #746)
+#744 := (iff #168 #741)
+#738 := (implies #617 #733)
+#742 := (iff #738 #741)
+#743 := [rewrite]: #742
+#739 := (iff #168 #738)
+#736 := (iff #167 #733)
+#729 := (implies #620 #724)
+#734 := (iff #729 #733)
+#735 := [rewrite]: #734
+#730 := (iff #167 #729)
+#727 := (iff #166 #724)
+#720 := (implies #136 #715)
+#725 := (iff #720 #724)
+#726 := [rewrite]: #725
+#721 := (iff #166 #720)
+#718 := (iff #165 #715)
+#711 := (implies #623 #706)
+#716 := (iff #711 #715)
+#717 := [rewrite]: #716
+#712 := (iff #165 #711)
+#709 := (iff #164 #706)
+#702 := (implies #141 #699)
+#707 := (iff #702 #706)
+#708 := [rewrite]: #707
+#703 := (iff #164 #702)
+#700 := (iff #163 #699)
+#697 := (iff #162 #694)
+#690 := (implies #647 #687)
+#695 := (iff #690 #694)
+#696 := [rewrite]: #695
+#691 := (iff #162 #690)
+#688 := (iff #161 #687)
+#685 := (iff #160 #682)
+#678 := (implies #665 #668)
+#683 := (iff #678 #682)
+#684 := [rewrite]: #683
+#679 := (iff #160 #678)
+#676 := (iff #159 #668)
+#671 := (and #668 true)
+#674 := (iff #671 #668)
+#675 := [rewrite]: #674
+#672 := (iff #159 #671)
+#669 := (iff #158 #668)
+#670 := [rewrite]: #669
+#673 := [monotonicity #670]: #672
+#677 := [trans #673 #675]: #676
+#666 := (iff #156 #665)
+#663 := (iff #155 #660)
+#656 := (implies #650 #653)
+#661 := (iff #656 #660)
+#662 := [rewrite]: #661
+#657 := (iff #155 #656)
+#654 := (iff #154 #653)
+#627 := (= #147 #626)
+#628 := [rewrite]: #627
+#655 := [monotonicity #628]: #654
+#651 := (iff #153 #650)
+#652 := [rewrite]: #651
+#658 := [monotonicity #652 #655]: #657
+#664 := [trans #658 #662]: #663
+#667 := [quant-intro #664]: #666
+#680 := [monotonicity #667 #677]: #679
+#686 := [trans #680 #684]: #685
+#689 := [monotonicity #667 #686]: #688
+#648 := (iff #152 #647)
+#645 := (iff #151 #642)
+#638 := (implies #144 #635)
+#643 := (iff #638 #642)
+#644 := [rewrite]: #643
+#639 := (iff #151 #638)
+#636 := (iff #150 #635)
+#633 := (iff #149 #632)
+#630 := (iff #148 #629)
+#631 := [monotonicity #628]: #630
+#634 := [monotonicity #631]: #633
+#637 := [quant-intro #634]: #636
+#640 := [monotonicity #637]: #639
+#646 := [trans #640 #644]: #645
+#649 := [quant-intro #646]: #648
+#692 := [monotonicity #649 #689]: #691
+#698 := [trans #692 #696]: #697
+#701 := [monotonicity #649 #698]: #700
+#704 := [monotonicity #701]: #703
+#710 := [trans #704 #708]: #709
+#624 := (iff #138 #623)
+#625 := [rewrite]: #624
+#713 := [monotonicity #625 #710]: #712
+#719 := [trans #713 #717]: #718
+#722 := [monotonicity #719]: #721
+#728 := [trans #722 #726]: #727
+#621 := (iff #133 #620)
+#622 := [rewrite]: #621
+#731 := [monotonicity #622 #728]: #730
+#737 := [trans #731 #735]: #736
+#618 := (iff #131 #617)
+#619 := [monotonicity #616]: #618
+#740 := [monotonicity #619 #737]: #739
+#745 := [trans #740 #743]: #744
+#748 := [monotonicity #745]: #747
+#752 := [trans #748 #750]: #751
+#1035 := [monotonicity #752 #1032]: #1034
+#604 := (iff #128 #603)
+#601 := (iff #127 #598)
+#594 := (implies #121 #591)
+#599 := (iff #594 #598)
+#600 := [rewrite]: #599
+#595 := (iff #127 #594)
+#592 := (iff #126 #591)
+#589 := (iff #125 #588)
+#586 := (iff #124 #585)
+#583 := (iff #123 #582)
+#565 := (= #116 #564)
+#566 := [rewrite]: #565
+#584 := [monotonicity #566]: #583
+#587 := [monotonicity #534 #584]: #586
+#590 := [monotonicity #587]: #589
+#593 := [quant-intro #590]: #592
+#596 := [monotonicity #593]: #595
+#602 := [trans #596 #600]: #601
+#605 := [quant-intro #602]: #604
+#1038 := [monotonicity #605 #1035]: #1037
+#1044 := [trans #1038 #1042]: #1043
+#580 := (iff #119 #579)
+#577 := (iff #118 #574)
+#570 := (implies #559 #567)
+#575 := (iff #570 #574)
+#576 := [rewrite]: #575
+#571 := (iff #118 #570)
+#568 := (iff #117 #567)
+#569 := [monotonicity #566]: #568
+#562 := (iff #115 #559)
+#556 := (and #532 #83)
+#560 := (iff #556 #559)
+#561 := [rewrite]: #560
+#557 := (iff #115 #556)
+#558 := [monotonicity #534]: #557
+#563 := [trans #558 #561]: #562
+#572 := [monotonicity #563 #569]: #571
+#578 := [trans #572 #576]: #577
+#581 := [quant-intro #578]: #580
+#1047 := [monotonicity #581 #1044]: #1046
 #1053 := [trans #1047 #1051]: #1052
-#581 := (iff #119 #580)
-#578 := (iff #118 #575)
-#571 := (implies #560 #568)
-#576 := (iff #571 #575)
-#577 := [rewrite]: #576
-#572 := (iff #118 #571)
-#569 := (iff #117 #568)
-#570 := [monotonicity #567]: #569
-#563 := (iff #115 #560)
-#557 := (and #533 #83)
-#561 := (iff #557 #560)
-#562 := [rewrite]: #561
-#558 := (iff #115 #557)
-#559 := [monotonicity #535]: #558
-#564 := [trans #559 #562]: #563
-#573 := [monotonicity #564 #570]: #572
-#579 := [trans #573 #577]: #578
-#582 := [quant-intro #579]: #581
-#1056 := [monotonicity #582 #1053]: #1055
+#554 := (iff #114 #553)
+#551 := (iff #113 #548)
+#544 := (implies #541 #112)
+#549 := (iff #544 #548)
+#550 := [rewrite]: #549
+#545 := (iff #113 #544)
+#542 := (iff #110 #541)
+#539 := (iff #109 #538)
+#540 := [rewrite]: #539
+#543 := [monotonicity #537 #540]: #542
+#546 := [monotonicity #543]: #545
+#552 := [trans #546 #550]: #551
+#555 := [quant-intro #552]: #554
+#1056 := [monotonicity #555 #1053]: #1055
 #1062 := [trans #1056 #1060]: #1061
-#555 := (iff #114 #554)
-#552 := (iff #113 #549)
-#545 := (implies #542 #112)
-#550 := (iff #545 #549)
-#551 := [rewrite]: #550
-#546 := (iff #113 #545)
-#543 := (iff #110 #542)
-#540 := (iff #109 #539)
-#541 := [rewrite]: #540
-#544 := [monotonicity #538 #541]: #543
-#547 := [monotonicity #544]: #546
-#553 := [trans #547 #551]: #552
-#556 := [quant-intro #553]: #555
-#1065 := [monotonicity #556 #1062]: #1064
+#1065 := [monotonicity #1062]: #1064
 #1071 := [trans #1065 #1069]: #1070
-#1074 := [monotonicity #1071]: #1073
+#530 := (iff #100 #529)
+#531 := [rewrite]: #530
+#1074 := [monotonicity #531 #1071]: #1073
 #1080 := [trans #1074 #1078]: #1079
-#531 := (iff #100 #530)
-#532 := [rewrite]: #531
-#1083 := [monotonicity #532 #1080]: #1082
-#1089 := [trans #1083 #1087]: #1088
-#1092 := [monotonicity #1089]: #1091
-#1096 := [trans #1092 #1094]: #1095
-#528 := (iff #97 #527)
-#525 := (iff #96 #522)
-#518 := (implies #90 #515)
-#523 := (iff #518 #522)
-#524 := [rewrite]: #523
-#519 := (iff #96 #518)
-#516 := (iff #95 #515)
-#513 := (iff #94 #512)
-#510 := (iff #93 #507)
-#504 := (and #454 #92)
-#508 := (iff #504 #507)
-#509 := [rewrite]: #508
-#505 := (iff #93 #504)
-#455 := (iff #67 #454)
-#456 := [rewrite]: #455
-#506 := [monotonicity #456]: #505
-#511 := [trans #506 #509]: #510
-#514 := [monotonicity #511]: #513
-#517 := [quant-intro #514]: #516
-#520 := [monotonicity #517]: #519
-#526 := [trans #520 #524]: #525
-#529 := [quant-intro #526]: #528
-#1099 := [monotonicity #529 #1096]: #1098
-#1105 := [trans #1099 #1103]: #1104
-#1108 := [monotonicity #529 #1105]: #1107
-#502 := (iff #88 #501)
-#499 := (iff #87 #496)
-#492 := (implies #487 #86)
-#497 := (iff #492 #496)
-#498 := [rewrite]: #497
-#493 := (iff #87 #492)
-#490 := (iff #84 #487)
-#484 := (and #454 #83)
-#488 := (iff #484 #487)
-#489 := [rewrite]: #488
-#485 := (iff #84 #484)
-#486 := [monotonicity #456]: #485
-#491 := [trans #486 #489]: #490
-#494 := [monotonicity #491]: #493
-#500 := [trans #494 #498]: #499
-#503 := [quant-intro #500]: #502
-#1111 := [monotonicity #503 #1108]: #1110
-#1117 := [trans #1111 #1115]: #1116
-#1120 := [monotonicity #503 #1117]: #1119
-#482 := (iff #80 #481)
-#479 := (iff #79 #476)
-#472 := (implies #469 #78)
-#477 := (iff #472 #476)
-#478 := [rewrite]: #477
-#473 := (iff #79 #472)
-#470 := (iff #76 #469)
-#467 := (iff #75 #466)
-#468 := [rewrite]: #467
-#458 := (iff #68 #457)
-#459 := [monotonicity #456]: #458
-#471 := [monotonicity #459 #468]: #470
-#474 := [monotonicity #471]: #473
-#480 := [trans #474 #478]: #479
-#483 := [quant-intro #480]: #482
-#1123 := [monotonicity #483 #1120]: #1122
-#1129 := [trans #1123 #1127]: #1128
-#1132 := [monotonicity #483 #1129]: #1131
+#1083 := [monotonicity #1080]: #1082
+#1087 := [trans #1083 #1085]: #1086
+#527 := (iff #97 #526)
+#524 := (iff #96 #521)
+#517 := (implies #90 #514)
+#522 := (iff #517 #521)
+#523 := [rewrite]: #522
+#518 := (iff #96 #517)
+#515 := (iff #95 #514)
+#512 := (iff #94 #511)
+#509 := (iff #93 #506)
+#503 := (and #453 #92)
+#507 := (iff #503 #506)
+#508 := [rewrite]: #507
+#504 := (iff #93 #503)
+#454 := (iff #67 #453)
+#455 := [rewrite]: #454
+#505 := [monotonicity #455]: #504
+#510 := [trans #505 #508]: #509
+#513 := [monotonicity #510]: #512
+#516 := [quant-intro #513]: #515
+#519 := [monotonicity #516]: #518
+#525 := [trans #519 #523]: #524
+#528 := [quant-intro #525]: #527
+#1090 := [monotonicity #528 #1087]: #1089
+#1096 := [trans #1090 #1094]: #1095
+#1099 := [monotonicity #528 #1096]: #1098
+#501 := (iff #88 #500)
+#498 := (iff #87 #495)
+#491 := (implies #486 #86)
+#496 := (iff #491 #495)
+#497 := [rewrite]: #496
+#492 := (iff #87 #491)
+#489 := (iff #84 #486)
+#483 := (and #453 #83)
+#487 := (iff #483 #486)
+#488 := [rewrite]: #487
+#484 := (iff #84 #483)
+#485 := [monotonicity #455]: #484
+#490 := [trans #485 #488]: #489
+#493 := [monotonicity #490]: #492
+#499 := [trans #493 #497]: #498
+#502 := [quant-intro #499]: #501
+#1102 := [monotonicity #502 #1099]: #1101
+#1108 := [trans #1102 #1106]: #1107
+#1111 := [monotonicity #502 #1108]: #1110
+#481 := (iff #80 #480)
+#478 := (iff #79 #475)
+#471 := (implies #468 #78)
+#476 := (iff #471 #475)
+#477 := [rewrite]: #476
+#472 := (iff #79 #471)
+#469 := (iff #76 #468)
+#466 := (iff #75 #465)
+#467 := [rewrite]: #466
+#457 := (iff #68 #456)
+#458 := [monotonicity #455]: #457
+#470 := [monotonicity #458 #467]: #469
+#473 := [monotonicity #470]: #472
+#479 := [trans #473 #477]: #478
+#482 := [quant-intro #479]: #481
+#1114 := [monotonicity #482 #1111]: #1113
+#1120 := [trans #1114 #1118]: #1119
+#1123 := [monotonicity #482 #1120]: #1122
+#1126 := [monotonicity #1123]: #1125
+#1132 := [trans #1126 #1130]: #1131
 #1135 := [monotonicity #1132]: #1134
-#1141 := [trans #1135 #1139]: #1140
-#1144 := [monotonicity #1141]: #1143
-#464 := (iff #71 #463)
-#465 := [rewrite]: #464
-#1147 := [monotonicity #465 #1144]: #1146
-#1153 := [trans #1147 #1151]: #1152
-#1156 := [monotonicity #465 #1153]: #1155
-#461 := (iff #69 #460)
-#462 := [quant-intro #459]: #461
-#1159 := [monotonicity #462 #1156]: #1158
+#463 := (iff #71 #462)
+#464 := [rewrite]: #463
+#1138 := [monotonicity #464 #1135]: #1137
+#1144 := [trans #1138 #1142]: #1143
+#1147 := [monotonicity #464 #1144]: #1146
+#460 := (iff #69 #459)
+#461 := [quant-intro #458]: #460
+#1150 := [monotonicity #461 #1147]: #1149
+#1156 := [trans #1150 #1154]: #1155
+#451 := (iff #65 #450)
+#448 := (iff #64 #445)
+#442 := (implies #62 #439)
+#446 := (iff #442 #445)
+#447 := [rewrite]: #446
+#443 := (iff #64 #442)
+#440 := (iff #63 #439)
+#441 := [rewrite]: #440
+#444 := [monotonicity #441]: #443
+#449 := [trans #444 #447]: #448
+#452 := [quant-intro #449]: #451
+#1159 := [monotonicity #452 #1156]: #1158
 #1165 := [trans #1159 #1163]: #1164
-#452 := (iff #65 #451)
-#449 := (iff #64 #446)
-#443 := (implies #62 #440)
-#447 := (iff #443 #446)
-#448 := [rewrite]: #447
-#444 := (iff #64 #443)
-#441 := (iff #63 #440)
-#442 := [rewrite]: #441
-#445 := [monotonicity #442]: #444
-#450 := [trans #445 #448]: #449
-#453 := [quant-intro #450]: #452
-#1168 := [monotonicity #453 #1165]: #1167
+#437 := (iff #61 #436)
+#434 := (iff #60 #431)
+#428 := (implies #57 #425)
+#432 := (iff #428 #431)
+#433 := [rewrite]: #432
+#429 := (iff #60 #428)
+#426 := (iff #59 #425)
+#427 := [rewrite]: #426
+#430 := [monotonicity #427]: #429
+#435 := [trans #430 #433]: #434
+#438 := [quant-intro #435]: #437
+#1168 := [monotonicity #438 #1165]: #1167
 #1174 := [trans #1168 #1172]: #1173
-#438 := (iff #61 #437)
-#435 := (iff #60 #432)
-#429 := (implies #57 #426)
-#433 := (iff #429 #432)
-#434 := [rewrite]: #433
-#430 := (iff #60 #429)
-#427 := (iff #59 #426)
-#428 := [rewrite]: #427
-#431 := [monotonicity #428]: #430
-#436 := [trans #431 #434]: #435
-#439 := [quant-intro #436]: #438
-#1177 := [monotonicity #439 #1174]: #1176
-#1183 := [trans #1177 #1181]: #1182
-#1186 := [monotonicity #1183]: #1185
-#1190 := [trans #1186 #1188]: #1189
-#1193 := [monotonicity #1190]: #1192
-#1832 := [trans #1193 #1830]: #1831
-#425 := [asserted]: #271
-#1833 := [mp #425 #1832]: #1828
-#1835 := [not-or-elim #1833]: #460
-#1890 := [mp~ #1835 #1859]: #460
-#4231 := [mp #1890 #4230]: #4226
-#5529 := (not #4226)
-#5530 := (or #5529 #3078)
-#5525 := [quant-inst #1936]: #5530
-#5337 := [unit-resolution #5525 #4231 #5222]: false
-#5345 := [lemma #5337]: #3078
-#3845 := (or #3093 #1945)
-#3849 := [def-axiom]: #3845
-#6495 := [unit-resolution #3849 #5345]: #3093
-#3098 := (not #3093)
-#4565 := (or #3098 #4562)
-#4568 := (not #4565)
-#4240 := (pattern #66 #74)
-#2519 := (not #466)
-#3070 := (or #454 #2519 #1210)
-#4241 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3070)
-#4246 := (not #4241)
-#4571 := (or #4246 #4568)
-#4574 := (not #4571)
+#1177 := [monotonicity #1174]: #1176
+#1181 := [trans #1177 #1179]: #1180
+#1184 := [monotonicity #1181]: #1183
+#1823 := [trans #1184 #1821]: #1822
+#424 := [asserted]: #270
+#1824 := [mp #424 #1823]: #1819
+#1826 := [not-or-elim #1824]: #459
+#1881 := [mp~ #1826 #1850]: #459
+#4222 := [mp #1881 #4221]: #4217
+#5520 := (not #4217)
+#5521 := (or #5520 #3069)
+#5516 := [quant-inst #1927]: #5521
+#5328 := [unit-resolution #5516 #4222 #5213]: false
+#5336 := [lemma #5328]: #3069
+#3836 := (or #3084 #1936)
+#3840 := [def-axiom]: #3836
+#6486 := [unit-resolution #3840 #5336]: #3084
+#3089 := (not #3084)
+#4556 := (or #3089 #4553)
+#4559 := (not #4556)
+#4231 := (pattern #66 #74)
+#2510 := (not #465)
+#3061 := (or #453 #2510 #1201)
+#4232 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4231) #3061)
+#4237 := (not #4232)
+#4562 := (or #4237 #4559)
+#4565 := (not #4562)
 decl ?v1!1 :: S3
-#1909 := ?v1!1
-#1913 := (f11 ?v1!1)
-#2534 := (* -1::Int #1913)
+#1900 := ?v1!1
+#1904 := (f11 ?v1!1)
+#2525 := (* -1::Int #1904)
 decl ?v0!2 :: S3
-#1910 := ?v0!2
-#1911 := (f11 ?v0!2)
-#2535 := (+ #1911 #2534)
-#2536 := (<= #2535 0::Int)
-#1918 := (f12 ?v1!1)
-#1919 := (= f1 #1918)
-#1916 := (f12 ?v0!2)
-#1917 := (= f1 #1916)
-#2054 := (not #1917)
-#2026 := (or #2054 #1919 #2536)
-#1928 := (not #2026)
-#4577 := (or #1928 #4574)
-#4580 := (not #4577)
-#4232 := (forall (vars (?v0 S3)) (:pat #4218) #1201)
-#4237 := (not #4232)
-#4583 := (or #4237 #4580)
-#4586 := (not #4583)
+#1901 := ?v0!2
+#1902 := (f11 ?v0!2)
+#2526 := (+ #1902 #2525)
+#2527 := (<= #2526 0::Int)
+#1909 := (f12 ?v1!1)
+#1910 := (= f1 #1909)
+#1907 := (f12 ?v0!2)
+#1908 := (= f1 #1907)
+#2210 := (not #1908)
+#2119 := (or #2210 #1910 #2527)
+#2018 := (not #2119)
+#4568 := (or #2018 #4565)
+#4571 := (not #4568)
+#4223 := (forall (vars (?v0 S3)) (:pat #4209) #1192)
+#4228 := (not #4223)
+#4574 := (or #4228 #4571)
+#4577 := (not #4574)
 decl ?v0!0 :: S3
-#1894 := ?v0!0
-#1895 := (f11 ?v0!0)
-#1896 := (>= #1895 0::Int)
-#1897 := (not #1896)
-#4589 := (or #1897 #4586)
-#4592 := (not #4589)
-#4595 := (or #1196 #4592)
-#4598 := (not #4595)
-#4605 := (forall (vars (?v0 S3)) (:pat #4218) #1805)
-#4608 := (iff #1808 #4605)
-#4606 := (iff #1805 #1805)
-#4607 := [refl]: #4606
-#4609 := [quant-intro #4607]: #4608
-#1958 := (~ #1808 #1808)
-#1900 := (~ #1805 #1805)
-#1901 := [refl]: #1900
-#1959 := [nnf-pos #1901]: #1958
-#1838 := [not-or-elim #1833]: #1808
-#2053 := [mp~ #1838 #1959]: #1808
-#4610 := [mp #2053 #4609]: #4605
-#5324 := [hypothesis]: #1196
-#4784 := (not #4605)
-#5260 := (or #4784 #71)
-#5144 := (= f10 f10)
-#5145 := (not #5144)
-#5147 := (or #5145 #71)
-#5228 := (or #4784 #5147)
-#5262 := (iff #5228 #5260)
-#5264 := (iff #5260 #5260)
-#5259 := [rewrite]: #5264
-#5233 := (iff #5147 #71)
-#5201 := (or false #71)
-#5229 := (iff #5201 #71)
-#5232 := [rewrite]: #5229
-#5202 := (iff #5147 #5201)
-#5199 := (iff #5145 false)
-#5196 := (not true)
-#5193 := (iff #5196 false)
-#5194 := [rewrite]: #5193
-#5197 := (iff #5145 #5196)
-#5148 := (iff #5144 true)
-#5195 := [rewrite]: #5148
-#5198 := [monotonicity #5195]: #5197
-#5200 := [trans #5198 #5194]: #5199
-#5203 := [monotonicity #5200]: #5202
-#5234 := [trans #5203 #5232]: #5233
-#5263 := [monotonicity #5234]: #5262
-#5269 := [trans #5263 #5259]: #5262
-#5261 := [quant-inst #56]: #5228
-#5295 := [mp #5261 #5269]: #5260
-#5325 := [unit-resolution #5295 #5324 #4610]: false
-#5320 := [lemma #5325]: #71
-#4601 := (or #1196 #4598)
-#3528 := (forall (vars (?v1 S3)) #3517)
-#3535 := (not #3528)
-#3513 := (forall (vars (?v0 S3) (?v1 S3)) #3508)
-#3534 := (not #3513)
-#3536 := (or #2359 #2926 #3534 #3535)
-#3537 := (not #3536)
-#3542 := (or #3491 #3537)
-#3549 := (not #3542)
-#3468 := (forall (vars (?v0 S3) (?v1 S3)) #3463)
-#3548 := (not #3468)
-#3550 := (or #3548 #3549)
-#3551 := (not #3550)
-#3556 := (or #3445 #3551)
-#3562 := (not #3556)
-#3563 := (or #1499 #3562)
-#3564 := (not #3563)
-#3569 := (or #2276 #3564)
-#3575 := (not #3569)
-#3576 := (or #1490 #3575)
-#3577 := (not #3576)
-#3582 := (or #1490 #3577)
-#3588 := (not #3582)
-#3589 := (or #953 #3588)
-#3590 := (not #3589)
-#3595 := (or #2869 #3590)
-#3601 := (not #3595)
-#3602 := (or #1485 #3601)
-#3603 := (not #3602)
-#3608 := (or #2855 #3603)
-#3616 := (not #3608)
-#3422 := (forall (vars (?v0 S3)) #3417)
-#3615 := (not #3422)
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-#3614 := (not #3404)
-#3617 := (or #754 #995 #1650 #1654 #2210 #2213 #3614 #3615 #3616)
-#3618 := (not #3617)
-#3334 := (forall (vars (?v0 S3) (?v1 S3)) #3329)
-#3340 := (not #3334)
-#3341 := (or #158 #3340)
-#3342 := (not #3341)
-#3369 := (or #3342 #3366)
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-#3312 := (forall (vars (?v0 S3)) #3307)
-#3375 := (not #3312)
-#3377 := (or #3375 #3376)
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-#3275 := (forall (vars (?v1 S3)) #3264)
-#3281 := (not #3275)
-#3282 := (or #2089 #2704 #3281)
-#3283 := (not #3282)
-#3383 := (or #3283 #3378)
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-#3260 := (forall (vars (?v0 S3)) #3249)
-#3389 := (not #3260)
-#3391 := (or #724 #706 #733 #715 #3389 #3390)
-#3392 := (not #3391)
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-#3633 := (not #3623)
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-#3632 := (not #3246)
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-#3631 := (not #3218)
-#3190 := (forall (vars (?v0 S3) (?v1 S3)) #3185)
-#3630 := (not #3190)
-#3167 := (forall (vars (?v0 S3) (?v1 S3)) #3162)
-#3629 := (not #3167)
-#3634 := (or #1747 #1742 #3629 #3630 #3631 #3632 #3633)
-#3635 := (not #3634)
-#3135 := (forall (vars (?v1 S3)) #3124)
-#3141 := (not #3135)
-#3142 := (or #1981 #2566 #3141)
-#3143 := (not #3142)
-#3640 := (or #3143 #3635)
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-#3648 := (or #3646 #3647)
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-#4578 := (iff #3668 #4577)
-#4575 := (iff #3663 #4574)
-#4572 := (iff #3662 #4571)
-#4569 := (iff #3661 #4568)
+#1885 := ?v0!0
+#1886 := (f11 ?v0!0)
+#1887 := (>= #1886 0::Int)
+#1888 := (not #1887)
+#4580 := (or #1888 #4577)
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+#4599 := (iff #1799 #4596)
+#4597 := (iff #1796 #1796)
+#4598 := [refl]: #4597
+#4600 := [quant-intro #4598]: #4599
+#2044 := (~ #1799 #1799)
+#1891 := (~ #1796 #1796)
+#1892 := [refl]: #1891
+#2045 := [nnf-pos #1892]: #2044
+#1829 := [not-or-elim #1824]: #1799
+#2209 := [mp~ #1829 #2045]: #1799
+#4601 := [mp #2209 #4600]: #4596
+#5315 := [hypothesis]: #1187
+#4775 := (not #4596)
+#5251 := (or #4775 #71)
+#5135 := (= f10 f10)
+#5136 := (not #5135)
+#5138 := (or #5136 #71)
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+#5250 := [rewrite]: #5255
+#5224 := (iff #5138 #71)
+#5192 := (or false #71)
+#5220 := (iff #5192 #71)
+#5223 := [rewrite]: #5220
+#5193 := (iff #5138 #5192)
+#5190 := (iff #5136 false)
+#5187 := (not true)
+#5184 := (iff #5187 false)
+#5185 := [rewrite]: #5184
+#5188 := (iff #5136 #5187)
+#5139 := (iff #5135 true)
+#5186 := [rewrite]: #5139
+#5189 := [monotonicity #5186]: #5188
+#5191 := [trans #5189 #5185]: #5190
+#5194 := [monotonicity #5191]: #5193
+#5225 := [trans #5194 #5223]: #5224
+#5254 := [monotonicity #5225]: #5253
+#5260 := [trans #5254 #5250]: #5253
+#5252 := [quant-inst #56]: #5219
+#5286 := [mp #5252 #5260]: #5251
+#5316 := [unit-resolution #5286 #5315 #4601]: false
+#5311 := [lemma #5316]: #71
+#4592 := (or #1187 #4589)
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+#3382 := (or #723 #705 #732 #714 #3380 #3381)
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+#3625 := (or #1738 #1733 #3620 #3621 #3622 #3623 #3624)
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 #4566 := (iff #3654 #4565)
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 #4554 := (iff #3640 #4553)
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 #4470 := (iff #3542 #4469)
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-#4456 := (iff #3517 #3517)
-#4457 := [refl]: #4456
-#4459 := [quant-intro #4457]: #4458
-#4462 := [monotonicity #4459]: #4461
-#4452 := (iff #3534 #4451)
-#4449 := (iff #3513 #4446)
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 #4447 := (iff #3508 #3508)
 #4448 := [refl]: #4447
 #4450 := [quant-intro #4448]: #4449
 #4453 := [monotonicity #4450]: #4452
-#4465 := [monotonicity #4453 #4462]: #4464
-#4468 := [monotonicity #4465]: #4467
-#4471 := [monotonicity #4468]: #4470
-#4474 := [monotonicity #4471]: #4473
-#4444 := (iff #3548 #4443)
-#4441 := (iff #3468 #4438)
-#4439 := (iff #3463 #3463)
-#4440 := [refl]: #4439
-#4442 := [quant-intro #4440]: #4441
-#4445 := [monotonicity #4442]: #4444
-#4477 := [monotonicity #4445 #4474]: #4476
-#4480 := [monotonicity #4477]: #4479
-#4483 := [monotonicity #4480]: #4482
-#4486 := [monotonicity #4483]: #4485
-#4435 := (iff #1499 #4434)
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-#4430 := (iff #1493 #1493)
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+#4441 := [quant-intro #4439]: #4440
+#4444 := [monotonicity #4441]: #4443
+#4456 := [monotonicity #4444 #4453]: #4455
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+#4435 := (iff #3539 #4434)
+#4432 := (iff #3459 #4429)
+#4430 := (iff #3454 #3454)
 #4431 := [refl]: #4430
 #4433 := [quant-intro #4431]: #4432
 #4436 := [monotonicity #4433]: #4435
-#4489 := [monotonicity #4436 #4486]: #4488
+#4468 := [monotonicity #4436 #4465]: #4467
+#4471 := [monotonicity #4468]: #4470
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+#4426 := (iff #1490 #4425)
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+#4483 := [monotonicity #4480]: #4482
+#4486 := [monotonicity #4483]: #4485
+#4489 := [monotonicity #4486]: #4488
 #4492 := [monotonicity #4489]: #4491
 #4495 := [monotonicity #4492]: #4494
 #4498 := [monotonicity #4495]: #4497
 #4501 := [monotonicity #4498]: #4500
-#4504 := [monotonicity #4501]: #4503
-#4507 := [monotonicity #4504]: #4506
-#4510 := [monotonicity #4507]: #4509
-#4427 := (iff #953 #4426)
-#4424 := (iff #819 #4421)
-#4422 := (iff #814 #814)
-#4423 := [refl]: #4422
-#4425 := [quant-intro #4423]: #4424
-#4428 := [monotonicity #4425]: #4427
-#4513 := [monotonicity #4428 #4510]: #4512
-#4516 := [monotonicity #4513]: #4515
-#4519 := [monotonicity #4516]: #4518
-#4522 := [monotonicity #4519]: #4521
-#4418 := (iff #1485 #4417)
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-#4413 := (iff #1477 #1477)
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+#4413 := (iff #805 #805)
 #4414 := [refl]: #4413
 #4416 := [quant-intro #4414]: #4415
 #4419 := [monotonicity #4416]: #4418
-#4525 := [monotonicity #4419 #4522]: #4524
-#4528 := [monotonicity #4525]: #4527
+#4504 := [monotonicity #4419 #4501]: #4503
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+#4510 := [monotonicity #4507]: #4509
+#4513 := [monotonicity #4510]: #4512
+#4409 := (iff #1476 #4408)
+#4406 := (iff #1473 #4403)
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+#4519 := [monotonicity #4516]: #4518
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+#4401 := (iff #3606 #4400)
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+#4393 := (iff #3605 #4392)
+#4390 := (iff #3395 #4387)
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+#4394 := [monotonicity #4391]: #4393
+#4383 := (iff #1641 #4382)
+#4380 := (iff #1638 #4377)
+#4378 := (iff #1633 #1633)
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+#4384 := [monotonicity #4381]: #4383
+#4528 := [monotonicity #4384 #4394 #4402 #4525]: #4527
 #4531 := [monotonicity #4528]: #4530
-#4534 := [monotonicity #4531]: #4533
-#4410 := (iff #3615 #4409)
-#4407 := (iff #3422 #4404)
-#4405 := (iff #3417 #3417)
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-#4408 := [quant-intro #4406]: #4407
-#4411 := [monotonicity #4408]: #4410
-#4402 := (iff #3614 #4401)
-#4399 := (iff #3404 #4396)
-#4397 := (iff #3401 #3401)
-#4398 := [refl]: #4397
-#4400 := [quant-intro #4398]: #4399
-#4403 := [monotonicity #4400]: #4402
-#4392 := (iff #1650 #4391)
-#4389 := (iff #1647 #4386)
-#4387 := (iff #1642 #1642)
-#4388 := [refl]: #4387
-#4390 := [quant-intro #4388]: #4389
-#4393 := [monotonicity #4390]: #4392
-#4537 := [monotonicity #4393 #4403 #4411 #4534]: #4536
-#4540 := [monotonicity #4537]: #4539
-#4384 := (iff #3392 #4383)
-#4381 := (iff #3391 #4380)
-#4378 := (iff #3390 #4377)
 #4375 := (iff #3383 #4374)
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-#4360 := (iff #3342 #4359)
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-#4351 := (iff #3334 #4348)
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-#4352 := [quant-intro #4350]: #4351
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+#4341 := [refl]: #4340
+#4343 := [quant-intro #4341]: #4342
+#4346 := [monotonicity #4343]: #4345
+#4349 := [monotonicity #4346]: #4348
+#4352 := [monotonicity #4349]: #4351
 #4355 := [monotonicity #4352]: #4354
 #4358 := [monotonicity #4355]: #4357
-#4361 := [monotonicity #4358]: #4360
+#4337 := (iff #3366 #4336)
+#4334 := (iff #3303 #4331)
+#4332 := (iff #3298 #3298)
+#4333 := [refl]: #4332
+#4335 := [quant-intro #4333]: #4334
+#4338 := [monotonicity #4335]: #4337
+#4361 := [monotonicity #4338 #4358]: #4360
 #4364 := [monotonicity #4361]: #4363
-#4367 := [monotonicity #4364]: #4366
-#4346 := (iff #3375 #4345)
-#4343 := (iff #3312 #4340)
-#4341 := (iff #3307 #3307)
-#4342 := [refl]: #4341
-#4344 := [quant-intro #4342]: #4343
-#4347 := [monotonicity #4344]: #4346
-#4370 := [monotonicity #4347 #4367]: #4369
-#4373 := [monotonicity #4370]: #4372
-#4338 := (iff #3283 #4337)
-#4335 := (iff #3282 #4334)
-#4332 := (iff #3281 #4331)
-#4329 := (iff #3275 #4326)
-#4327 := (iff #3264 #3264)
-#4328 := [refl]: #4327
-#4330 := [quant-intro #4328]: #4329
-#4333 := [monotonicity #4330]: #4332
-#4336 := [monotonicity #4333]: #4335
-#4339 := [monotonicity #4336]: #4338
-#4376 := [monotonicity #4339 #4373]: #4375
-#4379 := [monotonicity #4376]: #4378
-#4322 := (iff #3389 #4321)
-#4319 := (iff #3260 #4316)
-#4317 := (iff #3249 #3249)
-#4318 := [refl]: #4317
-#4320 := [quant-intro #4318]: #4319
-#4323 := [monotonicity #4320]: #4322
-#4382 := [monotonicity #4323 #4379]: #4381
-#4385 := [monotonicity #4382]: #4384
-#4543 := [monotonicity #4385 #4540]: #4542
-#4546 := [monotonicity #4543]: #4545
-#4313 := (iff #3632 #4312)
-#4310 := (iff #3246 #4307)
-#4308 := (iff #3241 #3241)
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+#4318 := (iff #3255 #3255)
+#4319 := [refl]: #4318
+#4321 := [quant-intro #4319]: #4320
+#4324 := [monotonicity #4321]: #4323
+#4327 := [monotonicity #4324]: #4326
+#4330 := [monotonicity #4327]: #4329
+#4367 := [monotonicity #4330 #4364]: #4366
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+#4313 := (iff #3380 #4312)
+#4310 := (iff #3251 #4307)
+#4308 := (iff #3240 #3240)
 #4309 := [refl]: #4308
 #4311 := [quant-intro #4309]: #4310
 #4314 := [monotonicity #4311]: #4313
-#4305 := (iff #3631 #4304)
-#4302 := (iff #3218 #4299)
-#4300 := (iff #3213 #3213)
-#4301 := [refl]: #4300
-#4303 := [quant-intro #4301]: #4302
-#4306 := [monotonicity #4303]: #4305
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-#4292 := (iff #3185 #3185)
-#4293 := [refl]: #4292
-#4295 := [quant-intro #4293]: #4294
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-#4288 := (iff #3629 #4287)
-#4285 := (iff #3167 #4282)
-#4283 := (iff #3162 #3162)
+#4373 := [monotonicity #4314 #4370]: #4372
+#4376 := [monotonicity #4373]: #4375
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+#4291 := (iff #3204 #3204)
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 #4284 := [refl]: #4283
 #4286 := [quant-intro #4284]: #4285
 #4289 := [monotonicity #4286]: #4288
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-#4549 := [monotonicity #4281 #4289 #4298 #4306 #4314 #4546]: #4548
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-#4268 := (iff #3142 #4267)
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-#4262 := (iff #3135 #4259)
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-#4263 := [quant-intro #4261]: #4262
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-#4269 := [monotonicity #4266]: #4268
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 #4272 := [monotonicity #4269]: #4271
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-#4558 := [monotonicity #4555]: #4557
-#4256 := (iff #3646 #4255)
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 #4251 := (iff #3115 #3115)
 #4252 := [refl]: #4251
 #4254 := [quant-intro #4252]: #4253
 #4257 := [monotonicity #4254]: #4256
-#4561 := [monotonicity #4257 #4558]: #4560
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-#4244 := (iff #3075 #4241)
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 #4243 := [refl]: #4242
 #4245 := [quant-intro #4243]: #4244
 #4248 := [monotonicity #4245]: #4247
-#4573 := [monotonicity #4248 #4570]: #4572
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 #4234 := [refl]: #4233
 #4236 := [quant-intro #4234]: #4235
 #4239 := [monotonicity #4236]: #4238
-#4585 := [monotonicity #4239 #4582]: #4584
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 #4588 := [monotonicity #4585]: #4587
 #4591 := [monotonicity #4588]: #4590
 #4594 := [monotonicity #4591]: #4593
-#4597 := [monotonicity #4594]: #4596
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-#3013 := (and #757 #776 #1471 #1629 #1647 #1655 #2211 #2214 #3007)
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-#3024 := (and #100 #1714 #1730 #1739 #2653 #2693 #3018)
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+#3660 := (iff #3032 #3659)
+#3657 := (iff #3029 #3654)
+#3648 := (and #3066 #3645)
+#3655 := (iff #3648 #3654)
+#3656 := [rewrite]: #3655
+#3649 := (iff #3029 #3648)
+#3646 := (iff #3026 #3645)
+#3643 := (iff #3023 #3640)
+#3634 := (and #3111 #3631)
+#3641 := (iff #3634 #3640)
+#3642 := [rewrite]: #3641
+#3635 := (iff #3023 #3634)
+#3632 := (iff #3020 #3631)
+#3629 := (iff #3015 #3626)
+#3617 := (and #100 #3158 #3181 #1730 #3209 #3237 #3614)
+#3627 := (iff #3617 #3626)
+#3628 := [rewrite]: #3627
+#3618 := (iff #3015 #3617)
+#3615 := (iff #3009 #3614)
+#3612 := (iff #3004 #3609)
+#3602 := (and #181 #756 #3395 #3413 #1638 #1646 #2202 #2205 #3599)
+#3610 := (iff #3602 #3609)
+#3611 := [rewrite]: #3610
+#3603 := (iff #3004 #3602)
+#3600 := (iff #2998 #3599)
+#3597 := (iff #2995 #3594)
+#3589 := (and #1473 #3586)
+#3595 := (iff #3589 #3594)
+#3596 := [rewrite]: #3595
+#3590 := (iff #2995 #3589)
+#3587 := (iff #2992 #3586)
+#3584 := (iff #2989 #3581)
+#3576 := (and #810 #3573)
+#3582 := (iff #3576 #3581)
+#3583 := [rewrite]: #3582
+#3577 := (iff #2989 #3576)
+#3574 := (iff #2986 #3573)
+#3571 := (iff #2983 #3568)
+#3563 := (and #203 #3560)
+#3569 := (iff #3563 #3568)
+#3570 := [rewrite]: #3569
+#3564 := (iff #2983 #3563)
+#3561 := (iff #2980 #3560)
+#3558 := (iff #2977 #3555)
+#3550 := (and #1487 #3547)
+#3556 := (iff #3550 #3555)
+#3557 := [rewrite]: #3556
+#3551 := (iff #2977 #3550)
+#3548 := (iff #2974 #3547)
+#3545 := (iff #2971 #3542)
+#3536 := (and #3459 #3533)
+#3543 := (iff #3536 #3542)
+#3544 := [rewrite]: #3543
+#3537 := (iff #2971 #3536)
+#3534 := (iff #2968 #3533)
+#3531 := (iff #2963 #3528)
+#3522 := (and #3504 #2351 #2920 #3519)
+#3529 := (iff #3522 #3528)
+#3530 := [rewrite]: #3529
+#3523 := (iff #2963 #3522)
+#3520 := (iff #2954 #3519)
+#3517 := (iff #2951 #3508)
+#3509 := (not #3508)
+#3512 := (not #3509)
+#3515 := (iff #3512 #3508)
+#3516 := [rewrite]: #3515
+#3513 := (iff #2951 #3512)
+#3510 := (iff #2948 #3509)
+#3511 := [rewrite]: #3510
+#3514 := [monotonicity #3511]: #3513
+#3518 := [trans #3514 #3516]: #3517
+#3521 := [quant-intro #3518]: #3520
+#3505 := (iff #1530 #3504)
+#3502 := (iff #1527 #3499)
+#3485 := (or #804 #1226)
+#3496 := (or #3485 #1523)
+#3500 := (iff #3496 #3499)
+#3501 := [rewrite]: #3500
+#3497 := (iff #1527 #3496)
+#3494 := (iff #1520 #3485)
+#3486 := (not #3485)
+#3489 := (not #3486)
+#3492 := (iff #3489 #3485)
+#3493 := [rewrite]: #3492
+#3490 := (iff #1520 #3489)
+#3487 := (iff #1515 #3486)
 #3488 := [rewrite]: #3487
-#3484 := (iff #2920 #3483)
-#3481 := (iff #2902 #3472)
-#3473 := (not #3472)
-#3476 := (not #3473)
-#3479 := (iff #3476 #3472)
-#3480 := [rewrite]: #3479
-#3477 := (iff #2902 #3476)
-#3474 := (iff #2899 #3473)
-#3475 := [rewrite]: #3474
-#3478 := [monotonicity #3475]: #3477
-#3482 := [trans #3478 #3480]: #3481
-#3485 := [monotonicity #3482]: #3484
-#3490 := [trans #3485 #3488]: #3489
-#3493 := [monotonicity #3490]: #3492
-#3544 := [monotonicity #3493 #3541]: #3543
-#3469 := (iff #1515 #3468)
-#3466 := (iff #1510 #3463)
-#3449 := (or #807 #3448)
-#3460 := (or #3449 #1502)
-#3464 := (iff #3460 #3463)
-#3465 := [rewrite]: #3464
-#3461 := (iff #1510 #3460)
-#3458 := (iff #836 #3449)
-#3450 := (not #3449)
-#3453 := (not #3450)
-#3456 := (iff #3453 #3449)
-#3457 := [rewrite]: #3456
-#3454 := (iff #836 #3453)
-#3451 := (iff #830 #3450)
-#3452 := [rewrite]: #3451
-#3455 := [monotonicity #3452]: #3454
-#3459 := [trans #3455 #3457]: #3458
-#3462 := [monotonicity #3459]: #3461
-#3467 := [trans #3462 #3465]: #3466
-#3470 := [quant-intro #3467]: #3469
-#3547 := [monotonicity #3470 #3544]: #3546
-#3555 := [trans #3547 #3553]: #3554
-#3446 := (iff #2896 #3445)
-#3443 := (iff #2893 #3440)
-#3426 := (or #3425 #2298)
-#3437 := (or #3426 #2888)
-#3441 := (iff #3437 #3440)
-#3442 := [rewrite]: #3441
-#3438 := (iff #2893 #3437)
-#3435 := (iff #2877 #3426)
-#3427 := (not #3426)
-#3430 := (not #3427)
-#3433 := (iff #3430 #3426)
-#3434 := [rewrite]: #3433
-#3431 := (iff #2877 #3430)
-#3428 := (iff #2874 #3427)
-#3429 := [rewrite]: #3428
-#3432 := [monotonicity #3429]: #3431
-#3436 := [trans #3432 #3434]: #3435
-#3439 := [monotonicity #3436]: #3438
-#3444 := [trans #3439 #3442]: #3443
-#3447 := [monotonicity #3444]: #3446
-#3558 := [monotonicity #3447 #3555]: #3557
-#3561 := [monotonicity #3558]: #3560
-#3568 := [trans #3561 #3566]: #3567
-#3571 := [monotonicity #3568]: #3570
-#3574 := [monotonicity #3571]: #3573
-#3581 := [trans #3574 #3579]: #3580
-#3584 := [monotonicity #3581]: #3583
-#3587 := [monotonicity #3584]: #3586
-#3594 := [trans #3587 #3592]: #3593
-#3597 := [monotonicity #3594]: #3596
-#3600 := [monotonicity #3597]: #3599
-#3607 := [trans #3600 #3605]: #3606
-#3610 := [monotonicity #3607]: #3609
-#3423 := (iff #1629 #3422)
-#3420 := (iff #1626 #3417)
-#3414 := (or #3397 #1623)
-#3418 := (iff #3414 #3417)
-#3419 := [rewrite]: #3418
-#3415 := (iff #1626 #3414)
-#3412 := (iff #1618 #3397)
-#3407 := (not #3398)
-#3410 := (iff #3407 #3397)
-#3411 := [rewrite]: #3410
-#3408 := (iff #1618 #3407)
-#3399 := (iff #1460 #3398)
-#3400 := [rewrite]: #3399
-#3409 := [monotonicity #3400]: #3408
-#3413 := [trans #3409 #3411]: #3412
-#3416 := [monotonicity #3413]: #3415
-#3421 := [trans #3416 #3419]: #3420
-#3424 := [quant-intro #3421]: #3423
-#3405 := (iff #1471 #3404)
-#3402 := (iff #1466 #3401)
-#3403 := [monotonicity #3400]: #3402
-#3406 := [quant-intro #3403]: #3405
-#3613 := [monotonicity #3406 #3424 #3610]: #3612
-#3622 := [trans #3613 #3620]: #3621
-#3395 := (iff #2835 #3392)
-#3386 := (and #136 #141 #621 #624 #3260 #3383)
-#3393 := (iff #3386 #3392)
-#3394 := [rewrite]: #3393
-#3387 := (iff #2835 #3386)
-#3384 := (iff #2829 #3383)
-#3381 := (iff #2826 #3378)
-#3372 := (and #3312 #3369)
-#3379 := (iff #3372 #3378)
-#3380 := [rewrite]: #3379
-#3373 := (iff #2826 #3372)
-#3370 := (iff #2821 #3369)
-#3367 := (iff #2815 #3366)
-#3364 := (iff #2812 #3361)
-#3347 := (or #2151 #2155)
-#3358 := (or #3347 #2807)
-#3362 := (iff #3358 #3361)
-#3363 := [rewrite]: #3362
-#3359 := (iff #2812 #3358)
-#3356 := (iff #2795 #3347)
-#3348 := (not #3347)
-#3351 := (not #3348)
-#3354 := (iff #3351 #3347)
-#3355 := [rewrite]: #3354
-#3352 := (iff #2795 #3351)
-#3349 := (iff #2792 #3348)
-#3350 := [rewrite]: #3349
-#3353 := [monotonicity #3350]: #3352
-#3357 := [trans #3353 #3355]: #3356
-#3360 := [monotonicity #3357]: #3359
-#3365 := [trans #3360 #3363]: #3364
-#3368 := [monotonicity #3365]: #3367
-#3345 := (iff #2175 #3342)
-#3337 := (and #2165 #3334)
-#3343 := (iff #3337 #3342)
-#3344 := [rewrite]: #3343
-#3338 := (iff #2175 #3337)
-#3335 := (iff #1391 #3334)
-#3332 := (iff #1388 #3329)
-#3315 := (or #1235 #1344)
-#3326 := (or #3315 #1385)
-#3330 := (iff #3326 #3329)
-#3331 := [rewrite]: #3330
-#3327 := (iff #1388 #3326)
-#3324 := (iff #1382 #3315)
-#3316 := (not #3315)
-#3319 := (not #3316)
-#3322 := (iff #3319 #3315)
-#3323 := [rewrite]: #3322
-#3320 := (iff #1382 #3319)
-#3317 := (iff #1379 #3316)
-#3318 := [rewrite]: #3317
-#3321 := [monotonicity #3318]: #3320
-#3325 := [trans #3321 #3323]: #3324
-#3328 := [monotonicity #3325]: #3327
-#3333 := [trans #3328 #3331]: #3332
-#3336 := [quant-intro #3333]: #3335
-#3339 := [monotonicity #3336]: #3338
-#3346 := [trans #3339 #3344]: #3345
-#3371 := [monotonicity #3346 #3368]: #3370
-#3313 := (iff #2789 #3312)
-#3310 := (iff #2786 #3307)
-#3288 := (or #57 #1344)
-#3304 := (or #3288 #3301)
-#3308 := (iff #3304 #3307)
+#3491 := [monotonicity #3488]: #3490
+#3495 := [trans #3491 #3493]: #3494
+#3498 := [monotonicity #3495]: #3497
+#3503 := [trans #3498 #3501]: #3502
+#3506 := [quant-intro #3503]: #3505
+#3524 := [monotonicity #3506 #3521]: #3523
+#3532 := [trans #3524 #3530]: #3531
+#3483 := (iff #2914 #3482)
+#3480 := (iff #2911 #3477)
+#3463 := (or #2318 #3462)
+#3474 := (or #3463 #2906)
+#3478 := (iff #3474 #3477)
+#3479 := [rewrite]: #3478
+#3475 := (iff #2911 #3474)
+#3472 := (iff #2893 #3463)
+#3464 := (not #3463)
+#3467 := (not #3464)
+#3470 := (iff #3467 #3463)
+#3471 := [rewrite]: #3470
+#3468 := (iff #2893 #3467)
+#3465 := (iff #2890 #3464)
+#3466 := [rewrite]: #3465
+#3469 := [monotonicity #3466]: #3468
+#3473 := [trans #3469 #3471]: #3472
+#3476 := [monotonicity #3473]: #3475
+#3481 := [trans #3476 #3479]: #3480
+#3484 := [monotonicity #3481]: #3483
+#3535 := [monotonicity #3484 #3532]: #3534
+#3460 := (iff #1506 #3459)
+#3457 := (iff #1501 #3454)
+#3440 := (or #798 #3439)
+#3451 := (or #3440 #1493)
+#3455 := (iff #3451 #3454)
+#3456 := [rewrite]: #3455
+#3452 := (iff #1501 #3451)
+#3449 := (iff #827 #3440)
+#3441 := (not #3440)
+#3444 := (not #3441)
+#3447 := (iff #3444 #3440)
+#3448 := [rewrite]: #3447
+#3445 := (iff #827 #3444)
+#3442 := (iff #821 #3441)
+#3443 := [rewrite]: #3442
+#3446 := [monotonicity #3443]: #3445
+#3450 := [trans #3446 #3448]: #3449
+#3453 := [monotonicity #3450]: #3452
+#3458 := [trans #3453 #3456]: #3457
+#3461 := [quant-intro #3458]: #3460
+#3538 := [monotonicity #3461 #3535]: #3537
+#3546 := [trans #3538 #3544]: #3545
+#3437 := (iff #2887 #3436)
+#3434 := (iff #2884 #3431)
+#3417 := (or #3416 #2289)
+#3428 := (or #3417 #2879)
+#3432 := (iff #3428 #3431)
+#3433 := [rewrite]: #3432
+#3429 := (iff #2884 #3428)
+#3426 := (iff #2868 #3417)
+#3418 := (not #3417)
+#3421 := (not #3418)
+#3424 := (iff #3421 #3417)
+#3425 := [rewrite]: #3424
+#3422 := (iff #2868 #3421)
+#3419 := (iff #2865 #3418)
+#3420 := [rewrite]: #3419
+#3423 := [monotonicity #3420]: #3422
+#3427 := [trans #3423 #3425]: #3426
+#3430 := [monotonicity #3427]: #3429
+#3435 := [trans #3430 #3433]: #3434
+#3438 := [monotonicity #3435]: #3437
+#3549 := [monotonicity #3438 #3546]: #3548
+#3552 := [monotonicity #3549]: #3551
+#3559 := [trans #3552 #3557]: #3558
+#3562 := [monotonicity #3559]: #3561
+#3565 := [monotonicity #3562]: #3564
+#3572 := [trans #3565 #3570]: #3571
+#3575 := [monotonicity #3572]: #3574
+#3578 := [monotonicity #3575]: #3577
+#3585 := [trans #3578 #3583]: #3584
+#3588 := [monotonicity #3585]: #3587
+#3591 := [monotonicity #3588]: #3590
+#3598 := [trans #3591 #3596]: #3597
+#3601 := [monotonicity #3598]: #3600
+#3414 := (iff #1620 #3413)
+#3411 := (iff #1617 #3408)
+#3405 := (or #3388 #1614)
+#3409 := (iff #3405 #3408)
+#3410 := [rewrite]: #3409
+#3406 := (iff #1617 #3405)
+#3403 := (iff #1609 #3388)
+#3398 := (not #3389)
+#3401 := (iff #3398 #3388)
+#3402 := [rewrite]: #3401
+#3399 := (iff #1609 #3398)
+#3390 := (iff #1451 #3389)
+#3391 := [rewrite]: #3390
+#3400 := [monotonicity #3391]: #3399
+#3404 := [trans #3400 #3402]: #3403
+#3407 := [monotonicity #3404]: #3406
+#3412 := [trans #3407 #3410]: #3411
+#3415 := [quant-intro #3412]: #3414
+#3396 := (iff #1462 #3395)
+#3393 := (iff #1457 #3392)
+#3394 := [monotonicity #3391]: #3393
+#3397 := [quant-intro #3394]: #3396
+#3604 := [monotonicity #3397 #3415 #3601]: #3603
+#3613 := [trans #3604 #3611]: #3612
+#3386 := (iff #2826 #3383)
+#3377 := (and #136 #141 #620 #623 #3251 #3374)
+#3384 := (iff #3377 #3383)
+#3385 := [rewrite]: #3384
+#3378 := (iff #2826 #3377)
+#3375 := (iff #2820 #3374)
+#3372 := (iff #2817 #3369)
+#3363 := (and #3303 #3360)
+#3370 := (iff #3363 #3369)
+#3371 := [rewrite]: #3370
+#3364 := (iff #2817 #3363)
+#3361 := (iff #2812 #3360)
+#3358 := (iff #2806 #3357)
+#3355 := (iff #2803 #3352)
+#3338 := (or #2142 #2146)
+#3349 := (or #3338 #2798)
+#3353 := (iff #3349 #3352)
+#3354 := [rewrite]: #3353
+#3350 := (iff #2803 #3349)
+#3347 := (iff #2786 #3338)
+#3339 := (not #3338)
+#3342 := (not #3339)
+#3345 := (iff #3342 #3338)
+#3346 := [rewrite]: #3345
+#3343 := (iff #2786 #3342)
+#3340 := (iff #2783 #3339)
+#3341 := [rewrite]: #3340
+#3344 := [monotonicity #3341]: #3343
+#3348 := [trans #3344 #3346]: #3347
+#3351 := [monotonicity #3348]: #3350
+#3356 := [trans #3351 #3354]: #3355
+#3359 := [monotonicity #3356]: #3358
+#3336 := (iff #2166 #3333)
+#3328 := (and #2156 #3325)
+#3334 := (iff #3328 #3333)
+#3335 := [rewrite]: #3334
+#3329 := (iff #2166 #3328)
+#3326 := (iff #1382 #3325)
+#3323 := (iff #1379 #3320)
+#3306 := (or #1226 #1335)
+#3317 := (or #3306 #1376)
+#3321 := (iff #3317 #3320)
+#3322 := [rewrite]: #3321
+#3318 := (iff #1379 #3317)
+#3315 := (iff #1373 #3306)
+#3307 := (not #3306)
+#3310 := (not #3307)
+#3313 := (iff #3310 #3306)
+#3314 := [rewrite]: #3313
+#3311 := (iff #1373 #3310)
+#3308 := (iff #1370 #3307)
 #3309 := [rewrite]: #3308
-#3305 := (iff #2786 #3304)
-#3302 := (iff #2783 #3301)
-#3303 := [rewrite]: #3302
-#3297 := (iff #1351 #3288)
-#3289 := (not #3288)
-#3292 := (not #3289)
-#3295 := (iff #3292 #3288)
-#3296 := [rewrite]: #3295
-#3293 := (iff #1351 #3292)
-#3290 := (iff #1348 #3289)
-#3291 := [rewrite]: #3290
-#3294 := [monotonicity #3291]: #3293
-#3298 := [trans #3294 #3296]: #3297
-#3306 := [monotonicity #3298 #3303]: #3305
-#3311 := [trans #3306 #3309]: #3310
-#3314 := [quant-intro #3311]: #3313
-#3374 := [monotonicity #3314 #3371]: #3373
-#3382 := [trans #3374 #3380]: #3381
-#3286 := (iff #2747 #3283)
-#3278 := (and #2090 #2707 #3275)
-#3284 := (iff #3278 #3283)
-#3285 := [rewrite]: #3284
-#3279 := (iff #2747 #3278)
-#3276 := (iff #2741 #3275)
-#3273 := (iff #2738 #3264)
-#3265 := (not #3264)
-#3268 := (not #3265)
-#3271 := (iff #3268 #3264)
-#3272 := [rewrite]: #3271
-#3269 := (iff #2738 #3268)
-#3266 := (iff #2735 #3265)
-#3267 := [rewrite]: #3266
-#3270 := [monotonicity #3267]: #3269
-#3274 := [trans #3270 #3272]: #3273
-#3277 := [quant-intro #3274]: #3276
-#3280 := [monotonicity #3277]: #3279
-#3287 := [trans #3280 #3285]: #3286
-#3385 := [monotonicity #3287 #3382]: #3384
-#3261 := (iff #2194 #3260)
-#3258 := (iff #2191 #3249)
-#3250 := (not #3249)
-#3253 := (not #3250)
-#3256 := (iff #3253 #3249)
-#3257 := [rewrite]: #3256
-#3254 := (iff #2191 #3253)
-#3251 := (iff #1419 #3250)
-#3252 := [rewrite]: #3251
-#3255 := [monotonicity #3252]: #3254
-#3259 := [trans #3255 #3257]: #3258
-#3262 := [quant-intro #3259]: #3261
-#3388 := [monotonicity #3262 #3385]: #3387
-#3396 := [trans #3388 #3394]: #3395
-#3625 := [monotonicity #3396 #3622]: #3624
-#3247 := (iff #2693 #3246)
-#3244 := (iff #2690 #3241)
-#3221 := (or #57 #1299)
-#3238 := (or #3221 #3235)
-#3242 := (iff #3238 #3241)
+#3312 := [monotonicity #3309]: #3311
+#3316 := [trans #3312 #3314]: #3315
+#3319 := [monotonicity #3316]: #3318
+#3324 := [trans #3319 #3322]: #3323
+#3327 := [quant-intro #3324]: #3326
+#3330 := [monotonicity #3327]: #3329
+#3337 := [trans #3330 #3335]: #3336
+#3362 := [monotonicity #3337 #3359]: #3361
+#3304 := (iff #2780 #3303)
+#3301 := (iff #2777 #3298)
+#3279 := (or #57 #1335)
+#3295 := (or #3279 #3292)
+#3299 := (iff #3295 #3298)
+#3300 := [rewrite]: #3299
+#3296 := (iff #2777 #3295)
+#3293 := (iff #2774 #3292)
+#3294 := [rewrite]: #3293
+#3288 := (iff #1342 #3279)
+#3280 := (not #3279)
+#3283 := (not #3280)
+#3286 := (iff #3283 #3279)
+#3287 := [rewrite]: #3286
+#3284 := (iff #1342 #3283)
+#3281 := (iff #1339 #3280)
+#3282 := [rewrite]: #3281
+#3285 := [monotonicity #3282]: #3284
+#3289 := [trans #3285 #3287]: #3288
+#3297 := [monotonicity #3289 #3294]: #3296
+#3302 := [trans #3297 #3300]: #3301
+#3305 := [quant-intro #3302]: #3304
+#3365 := [monotonicity #3305 #3362]: #3364
+#3373 := [trans #3365 #3371]: #3372
+#3277 := (iff #2738 #3274)
+#3269 := (and #2081 #2698 #3266)
+#3275 := (iff #3269 #3274)
+#3276 := [rewrite]: #3275
+#3270 := (iff #2738 #3269)
+#3267 := (iff #2732 #3266)
+#3264 := (iff #2729 #3255)
+#3256 := (not #3255)
+#3259 := (not #3256)
+#3262 := (iff #3259 #3255)
+#3263 := [rewrite]: #3262
+#3260 := (iff #2729 #3259)
+#3257 := (iff #2726 #3256)
+#3258 := [rewrite]: #3257
+#3261 := [monotonicity #3258]: #3260
+#3265 := [trans #3261 #3263]: #3264
+#3268 := [quant-intro #3265]: #3267
+#3271 := [monotonicity #3268]: #3270
+#3278 := [trans #3271 #3276]: #3277
+#3376 := [monotonicity #3278 #3373]: #3375
+#3252 := (iff #2185 #3251)
+#3249 := (iff #2182 #3240)
+#3241 := (not #3240)
+#3244 := (not #3241)
+#3247 := (iff #3244 #3240)
+#3248 := [rewrite]: #3247
+#3245 := (iff #2182 #3244)
+#3242 := (iff #1410 #3241)
 #3243 := [rewrite]: #3242
-#3239 := (iff #2690 #3238)
-#3236 := (iff #2687 #3235)
-#3237 := [rewrite]: #3236
-#3230 := (iff #1306 #3221)
-#3222 := (not #3221)
-#3225 := (not #3222)
-#3228 := (iff #3225 #3221)
-#3229 := [rewrite]: #3228
-#3226 := (iff #1306 #3225)
-#3223 := (iff #1303 #3222)
-#3224 := [rewrite]: #3223
-#3227 := [monotonicity #3224]: #3226
-#3231 := [trans #3227 #3229]: #3230
-#3240 := [monotonicity #3231 #3237]: #3239
-#3245 := [trans #3240 #3243]: #3244
-#3248 := [quant-intro #3245]: #3247
-#3219 := (iff #2653 #3218)
-#3216 := (iff #2650 #3213)
-#3193 := (or #57 #1261)
-#3210 := (or #3193 #3207)
-#3214 := (iff #3210 #3213)
+#3246 := [monotonicity #3243]: #3245
+#3250 := [trans #3246 #3248]: #3249
+#3253 := [quant-intro #3250]: #3252
+#3379 := [monotonicity #3253 #3376]: #3378
+#3387 := [trans #3379 #3385]: #3386
+#3616 := [monotonicity #3387 #3613]: #3615
+#3238 := (iff #2684 #3237)
+#3235 := (iff #2681 #3232)
+#3212 := (or #57 #1290)
+#3229 := (or #3212 #3226)
+#3233 := (iff #3229 #3232)
+#3234 := [rewrite]: #3233
+#3230 := (iff #2681 #3229)
+#3227 := (iff #2678 #3226)
+#3228 := [rewrite]: #3227
+#3221 := (iff #1297 #3212)
+#3213 := (not #3212)
+#3216 := (not #3213)
+#3219 := (iff #3216 #3212)
+#3220 := [rewrite]: #3219
+#3217 := (iff #1297 #3216)
+#3214 := (iff #1294 #3213)
 #3215 := [rewrite]: #3214
-#3211 := (iff #2650 #3210)
-#3208 := (iff #2647 #3207)
-#3209 := [rewrite]: #3208
-#3202 := (iff #1268 #3193)
-#3194 := (not #3193)
-#3197 := (not #3194)
-#3200 := (iff #3197 #3193)
-#3201 := [rewrite]: #3200
-#3198 := (iff #1268 #3197)
-#3195 := (iff #1265 #3194)
-#3196 := [rewrite]: #3195
-#3199 := [monotonicity #3196]: #3198
-#3203 := [trans #3199 #3201]: #3202
-#3212 := [monotonicity #3203 #3209]: #3211
-#3217 := [trans #3212 #3215]: #3216
-#3220 := [quant-intro #3217]: #3219
-#3191 := (iff #1730 #3190)
-#3188 := (iff #1725 #3185)
-#3171 := (or #533 #3170)
-#3182 := (or #3171 #1315)
-#3186 := (iff #3182 #3185)
+#3218 := [monotonicity #3215]: #3217
+#3222 := [trans #3218 #3220]: #3221
+#3231 := [monotonicity #3222 #3228]: #3230
+#3236 := [trans #3231 #3234]: #3235
+#3239 := [quant-intro #3236]: #3238
+#3210 := (iff #2644 #3209)
+#3207 := (iff #2641 #3204)
+#3184 := (or #57 #1252)
+#3201 := (or #3184 #3198)
+#3205 := (iff #3201 #3204)
+#3206 := [rewrite]: #3205
+#3202 := (iff #2641 #3201)
+#3199 := (iff #2638 #3198)
+#3200 := [rewrite]: #3199
+#3193 := (iff #1259 #3184)
+#3185 := (not #3184)
+#3188 := (not #3185)
+#3191 := (iff #3188 #3184)
+#3192 := [rewrite]: #3191
+#3189 := (iff #1259 #3188)
+#3186 := (iff #1256 #3185)
 #3187 := [rewrite]: #3186
-#3183 := (iff #1725 #3182)
-#3180 := (iff #548 #3171)
-#3172 := (not #3171)
-#3175 := (not #3172)
-#3178 := (iff #3175 #3171)
-#3179 := [rewrite]: #3178
-#3176 := (iff #548 #3175)
-#3173 := (iff #542 #3172)
-#3174 := [rewrite]: #3173
-#3177 := [monotonicity #3174]: #3176
-#3181 := [trans #3177 #3179]: #3180
-#3184 := [monotonicity #3181]: #3183
-#3189 := [trans #3184 #3187]: #3188
-#3192 := [quant-intro #3189]: #3191
-#3168 := (iff #1714 #3167)
-#3165 := (iff #1711 #3162)
-#3148 := (or #536 #1235)
-#3159 := (or #3148 #1708)
-#3163 := (iff #3159 #3162)
-#3164 := [rewrite]: #3163
-#3160 := (iff #1711 #3159)
-#3157 := (iff #1705 #3148)
-#3149 := (not #3148)
-#3152 := (not #3149)
-#3155 := (iff #3152 #3148)
-#3156 := [rewrite]: #3155
-#3153 := (iff #1705 #3152)
-#3150 := (iff #1700 #3149)
-#3151 := [rewrite]: #3150
-#3154 := [monotonicity #3151]: #3153
-#3158 := [trans #3154 #3156]: #3157
-#3161 := [monotonicity #3158]: #3160
-#3166 := [trans #3161 #3164]: #3165
-#3169 := [quant-intro #3166]: #3168
-#3628 := [monotonicity #3169 #3192 #3220 #3248 #3625]: #3627
-#3639 := [trans #3628 #3637]: #3638
-#3146 := (iff #2609 #3143)
-#3138 := (and #1982 #2569 #3135)
-#3144 := (iff #3138 #3143)
-#3145 := [rewrite]: #3144
-#3139 := (iff #2609 #3138)
-#3136 := (iff #2603 #3135)
-#3133 := (iff #2600 #3124)
-#3125 := (not #3124)
-#3128 := (not #3125)
-#3131 := (iff #3128 #3124)
-#3132 := [rewrite]: #3131
-#3129 := (iff #2600 #3128)
-#3126 := (iff #2597 #3125)
-#3127 := [rewrite]: #3126
-#3130 := [monotonicity #3127]: #3129
-#3134 := [trans #3130 #3132]: #3133
-#3137 := [quant-intro #3134]: #3136
-#3140 := [monotonicity #3137]: #3139
-#3147 := [trans #3140 #3145]: #3146
-#3642 := [monotonicity #3147 #3639]: #3641
-#3121 := (iff #1253 #3120)
-#3118 := (iff #1250 #3115)
-#3101 := (or #457 #1235)
-#3112 := (or #1230 #3101)
-#3116 := (iff #3112 #3115)
-#3117 := [rewrite]: #3116
-#3113 := (iff #1250 #3112)
-#3110 := (iff #1247 #3101)
-#3102 := (not #3101)
-#3105 := (not #3102)
-#3108 := (iff #3105 #3101)
-#3109 := [rewrite]: #3108
-#3106 := (iff #1247 #3105)
-#3103 := (iff #1242 #3102)
-#3104 := [rewrite]: #3103
-#3107 := [monotonicity #3104]: #3106
-#3111 := [trans #3107 #3109]: #3110
-#3114 := [monotonicity #3111]: #3113
-#3119 := [trans #3114 #3117]: #3118
-#3122 := [quant-intro #3119]: #3121
-#3645 := [monotonicity #3122 #3642]: #3644
-#3653 := [trans #3645 #3651]: #3652
-#3099 := (iff #2563 #3098)
-#3096 := (iff #2560 #3093)
-#3079 := (or #1942 #3078)
-#3090 := (or #2551 #3079)
-#3094 := (iff #3090 #3093)
+#3190 := [monotonicity #3187]: #3189
+#3194 := [trans #3190 #3192]: #3193
+#3203 := [monotonicity #3194 #3200]: #3202
+#3208 := [trans #3203 #3206]: #3207
+#3211 := [quant-intro #3208]: #3210
+#3182 := (iff #1721 #3181)
+#3179 := (iff #1716 #3176)
+#3162 := (or #532 #3161)
+#3173 := (or #3162 #1306)
+#3177 := (iff #3173 #3176)
+#3178 := [rewrite]: #3177
+#3174 := (iff #1716 #3173)
+#3171 := (iff #547 #3162)
+#3163 := (not #3162)
+#3166 := (not #3163)
+#3169 := (iff #3166 #3162)
+#3170 := [rewrite]: #3169
+#3167 := (iff #547 #3166)
+#3164 := (iff #541 #3163)
+#3165 := [rewrite]: #3164
+#3168 := [monotonicity #3165]: #3167
+#3172 := [trans #3168 #3170]: #3171
+#3175 := [monotonicity #3172]: #3174
+#3180 := [trans #3175 #3178]: #3179
+#3183 := [quant-intro #3180]: #3182
+#3159 := (iff #1705 #3158)
+#3156 := (iff #1702 #3153)
+#3139 := (or #535 #1226)
+#3150 := (or #3139 #1699)
+#3154 := (iff #3150 #3153)
+#3155 := [rewrite]: #3154
+#3151 := (iff #1702 #3150)
+#3148 := (iff #1696 #3139)
+#3140 := (not #3139)
+#3143 := (not #3140)
+#3146 := (iff #3143 #3139)
+#3147 := [rewrite]: #3146
+#3144 := (iff #1696 #3143)
+#3141 := (iff #1691 #3140)
+#3142 := [rewrite]: #3141
+#3145 := [monotonicity #3142]: #3144
+#3149 := [trans #3145 #3147]: #3148
+#3152 := [monotonicity #3149]: #3151
+#3157 := [trans #3152 #3155]: #3156
+#3160 := [quant-intro #3157]: #3159
+#3619 := [monotonicity #3160 #3183 #3211 #3239 #3616]: #3618
+#3630 := [trans #3619 #3628]: #3629
+#3137 := (iff #2600 #3134)
+#3129 := (and #1973 #2560 #3126)
+#3135 := (iff #3129 #3134)
+#3136 := [rewrite]: #3135
+#3130 := (iff #2600 #3129)
+#3127 := (iff #2594 #3126)
+#3124 := (iff #2591 #3115)
+#3116 := (not #3115)
+#3119 := (not #3116)
+#3122 := (iff #3119 #3115)
+#3123 := [rewrite]: #3122
+#3120 := (iff #2591 #3119)
+#3117 := (iff #2588 #3116)
+#3118 := [rewrite]: #3117
+#3121 := [monotonicity #3118]: #3120
+#3125 := [trans #3121 #3123]: #3124
+#3128 := [quant-intro #3125]: #3127
+#3131 := [monotonicity #3128]: #3130
+#3138 := [trans #3131 #3136]: #3137
+#3633 := [monotonicity #3138 #3630]: #3632
+#3112 := (iff #1244 #3111)
+#3109 := (iff #1241 #3106)
+#3092 := (or #456 #1226)
+#3103 := (or #1221 #3092)
+#3107 := (iff #3103 #3106)
+#3108 := [rewrite]: #3107
+#3104 := (iff #1241 #3103)
+#3101 := (iff #1238 #3092)
+#3093 := (not #3092)
+#3096 := (not #3093)
+#3099 := (iff #3096 #3092)
+#3100 := [rewrite]: #3099
+#3097 := (iff #1238 #3096)
+#3094 := (iff #1233 #3093)
 #3095 := [rewrite]: #3094
-#3091 := (iff #2560 #3090)
-#3088 := (iff #2557 #3079)
-#3080 := (not #3079)
-#3083 := (not #3080)
-#3086 := (iff #3083 #3079)
-#3087 := [rewrite]: #3086
-#3084 := (iff #2557 #3083)
-#3081 := (iff #2554 #3080)
-#3082 := [rewrite]: #3081
-#3085 := [monotonicity #3082]: #3084
-#3089 := [trans #3085 #3087]: #3088
-#3092 := [monotonicity #3089]: #3091
-#3097 := [trans #3092 #3095]: #3096
-#3100 := [monotonicity #3097]: #3099
-#3656 := [monotonicity #3100 #3653]: #3655
-#3076 := (iff #1222 #3075)
-#3073 := (iff #1217 #3070)
-#3056 := (or #454 #2519)
-#3067 := (or #3056 #1210)
-#3071 := (iff #3067 #3070)
-#3072 := [rewrite]: #3071
-#3068 := (iff #1217 #3067)
-#3065 := (iff #475 #3056)
-#3057 := (not #3056)
-#3060 := (not #3057)
-#3063 := (iff #3060 #3056)
-#3064 := [rewrite]: #3063
-#3061 := (iff #475 #3060)
-#3058 := (iff #469 #3057)
-#3059 := [rewrite]: #3058
-#3062 := [monotonicity #3059]: #3061
-#3066 := [trans #3062 #3064]: #3065
-#3069 := [monotonicity #3066]: #3068
-#3074 := [trans #3069 #3072]: #3073
-#3077 := [quant-intro #3074]: #3076
-#3659 := [monotonicity #3077 #3656]: #3658
-#3667 := [trans #3659 #3665]: #3666
-#2218 := (iff #2544 #1928)
-#2280 := (iff #2541 #2026)
-#2239 := (or #2054 #1919)
-#2338 := (or #2239 #2536)
-#2027 := (iff #2338 #2026)
-#2279 := [rewrite]: #2027
-#2306 := (iff #2541 #2338)
-#2260 := (iff #2525 #2239)
-#1864 := (not #2239)
-#2128 := (not #1864)
-#2164 := (iff #2128 #2239)
-#2259 := [rewrite]: #2164
-#2129 := (iff #2525 #2128)
-#1865 := (iff #2522 #1864)
-#2240 := [rewrite]: #1865
-#2163 := [monotonicity #2240]: #2129
-#2337 := [trans #2163 #2259]: #2260
-#2307 := [monotonicity #2337]: #2306
-#1927 := [trans #2307 #2279]: #2280
-#2219 := [monotonicity #1927]: #2218
-#3670 := [monotonicity #2219 #3667]: #3669
-#3673 := [monotonicity #3670]: #3672
-#3680 := [trans #3673 #3678]: #3679
-#3683 := [monotonicity #3680]: #3682
-#3686 := [monotonicity #3683]: #3685
-#3693 := [trans #3686 #3691]: #3692
-#3696 := [monotonicity #3693]: #3695
-#2352 := (+ #2351 #2349)
-#2353 := (= #2352 0::Int)
-#2356 := (and #807 #2355 #2353)
-#2373 := (not #2356)
-#2376 := (forall (vars (?v1 S3)) #2373)
-#2361 := (= ?v0!20 f10)
-#2362 := (not #2361)
-#2363 := (and #2362 #2360)
-#2364 := (not #2363)
-#2370 := (not #2364)
-#2380 := (and #2370 #2376)
-#2385 := (and #1539 #2380)
-#2318 := (* -1::Int #2317)
-#2320 := (+ #2319 #2318)
-#2323 := (+ #2322 #2320)
-#2324 := (>= #2323 0::Int)
-#2331 := (and #2330 #2328)
-#2332 := (not #2331)
-#2333 := (or #2332 #2324)
-#2334 := (not #2333)
-#2389 := (or #2334 #2385)
-#2393 := (and #1515 #2389)
-#2291 := (* -1::Int #2290)
-#2293 := (+ #2292 #2291)
-#2294 := (>= #2293 0::Int)
-#2300 := (and #2299 #2296)
-#2301 := (not #2300)
-#2302 := (or #2301 #2294)
-#2303 := (not #2302)
-#2397 := (or #2303 #2393)
-#2401 := (and #1496 #2397)
-#2405 := (or #2276 #2401)
-#2270 := (not #1490)
-#2409 := (and #2270 #2405)
-#2413 := (or #1490 #2409)
-#2417 := (and #819 #2413)
-#2254 := (= #2253 #2252)
-#2255 := (or #2254 #2251)
-#2256 := (not #2255)
-#2421 := (or #2256 #2417)
-#2425 := (and #1482 #2421)
-#2232 := (* -1::Int #2231)
-#2234 := (+ #2233 #2232)
-#2235 := (>= #2234 0::Int)
-#2236 := (not #2235)
-#2429 := (or #2236 #2425)
-#2215 := (and #2214 #2211)
-#2203 := (not #995)
-#2449 := (and #757 #2203 #2215 #1471 #2429 #1629 #1647 #1655)
-#2142 := (* -1::Int #2141)
-#2144 := (+ #2143 #2142)
-#2147 := (+ #2146 #2144)
-#2148 := (>= #2147 0::Int)
-#2157 := (and #2156 #2152)
-#2158 := (not #2157)
-#2159 := (or #2158 #2148)
-#2160 := (not #2159)
-#2179 := (or #2160 #2175)
-#2118 := (+ #2117 #1342)
-#2121 := (+ #2120 #2118)
-#2122 := (= #2121 0::Int)
-#2123 := (>= #2118 0::Int)
-#2124 := (not #2123)
-#2125 := (and #2124 #2122)
-#2130 := (or #1351 #2125)
-#2133 := (forall (vars (?v0 S3)) #2130)
-#2183 := (and #2133 #2179)
-#2082 := (+ #2081 #2079)
-#2083 := (= #2082 0::Int)
-#2086 := (and #2085 #2083)
-#2102 := (not #2086)
-#2105 := (forall (vars (?v1 S3)) #2102)
-#2091 := (= ?v0!8 f10)
-#2092 := (not #2091)
-#2093 := (and #2092 #2090)
-#2094 := (not #2093)
-#2099 := (not #2094)
-#2109 := (and #2099 #2105)
-#2187 := (or #2109 #2183)
-#2073 := (not #715)
-#2070 := (not #733)
-#2067 := (not #706)
-#2064 := (not #724)
-#2197 := (and #2064 #2067 #2070 #2073 #2187 #2194)
-#2453 := (or #2197 #2449)
-#2041 := (+ #2040 #1297)
-#2042 := (>= #2041 0::Int)
-#2043 := (not #2042)
-#2046 := (+ #2045 #2041)
-#2047 := (= #2046 0::Int)
-#2050 := (and #2049 #2047 #2043)
-#2055 := (or #1306 #2050)
-#2058 := (forall (vars (?v0 S3)) #2055)
-#2014 := (+ #1259 #2013)
-#2016 := (+ #2015 #2014)
-#2017 := (= #2016 0::Int)
-#2018 := (+ #2015 #1259)
-#2019 := (>= #2018 0::Int)
-#2020 := (not #2019)
-#2023 := (and #2022 #2020 #2017)
-#2028 := (or #1268 #2023)
-#2031 := (forall (vars (?v0 S3)) #2028)
-#2006 := (not #1747)
-#2478 := (and #2006 #2031 #2058 #2453 #1714 #1730 #1739)
-#1972 := (+ #1971 #1969)
-#1973 := (+ #58 #1972)
-#1974 := (= #1973 0::Int)
-#1978 := (and #454 #1977 #1974)
-#1994 := (not #1978)
-#1997 := (forall (vars (?v1 S3)) #1994)
-#1983 := (= ?v0!5 f10)
-#1984 := (not #1983)
-#1985 := (and #1984 #1982)
-#1986 := (not #1985)
-#1991 := (not #1986)
-#2001 := (and #1991 #1997)
-#2482 := (or #2001 #2478)
-#2486 := (and #1253 #2482)
-#1946 := (and #1945 #1943)
-#1947 := (not #1946)
-#1950 := (+ #1949 #1939)
-#1952 := (+ #1951 #1950)
-#1953 := (>= #1952 0::Int)
-#1954 := (or #1953 #1947)
-#1955 := (not #1954)
-#2490 := (or #1955 #2486)
-#2494 := (and #1222 #2490)
-#1912 := (* -1::Int #1911)
-#1914 := (+ #1913 #1912)
-#1915 := (>= #1914 0::Int)
-#1921 := (and #1920 #1917)
-#1922 := (not #1921)
-#1923 := (or #1922 #1915)
-#1924 := (not #1923)
-#2498 := (or #1924 #2494)
-#2502 := (and #1202 #2498)
-#2506 := (or #1897 #2502)
-#1860 := (not #1196)
-#2510 := (and #1860 #2506)
-#2514 := (or #1196 #2510)
-#3054 := (iff #2514 #3053)
-#3051 := (iff #2510 #3050)
-#3048 := (iff #2506 #3047)
-#3045 := (iff #2502 #3044)
-#3042 := (iff #2498 #3041)
-#3039 := (iff #2494 #3038)
-#3036 := (iff #2490 #3035)
-#3033 := (iff #2486 #3032)
-#3030 := (iff #2482 #3029)
-#3027 := (iff #2478 #3024)
-#3021 := (and #100 #2653 #2693 #3018 #1714 #1730 #1739)
-#3025 := (iff #3021 #3024)
-#3026 := [rewrite]: #3025
-#3022 := (iff #2478 #3021)
-#3019 := (iff #2453 #3018)
-#3016 := (iff #2449 #3013)
-#3010 := (and #757 #776 #2215 #1471 #3007 #1629 #1647 #1655)
-#3014 := (iff #3010 #3013)
-#3015 := [rewrite]: #3014
-#3011 := (iff #2449 #3010)
-#3008 := (iff #2429 #3007)
-#3005 := (iff #2425 #3004)
-#3002 := (iff #2421 #3001)
-#2999 := (iff #2417 #2998)
-#2996 := (iff #2413 #2995)
-#2993 := (iff #2409 #2992)
-#2990 := (iff #2405 #2989)
-#2987 := (iff #2401 #2986)
-#2984 := (iff #2397 #2983)
-#2981 := (iff #2393 #2980)
-#2978 := (iff #2389 #2977)
-#2975 := (iff #2385 #2972)
-#2935 := (and #2360 #2929)
-#2966 := (and #2935 #2963)
-#2969 := (and #1539 #2966)
-#2973 := (iff #2969 #2972)
-#2974 := [rewrite]: #2973
-#2970 := (iff #2385 #2969)
-#2967 := (iff #2380 #2966)
-#2964 := (iff #2376 #2963)
-#2961 := (iff #2373 #2960)
-#2958 := (iff #2356 #2957)
-#2955 := (iff #2353 #2954)
-#2952 := (= #2352 #2951)
-#2953 := [rewrite]: #2952
-#2956 := [monotonicity #2953]: #2955
-#2959 := [monotonicity #2956]: #2958
+#3098 := [monotonicity #3095]: #3097
+#3102 := [trans #3098 #3100]: #3101
+#3105 := [monotonicity #3102]: #3104
+#3110 := [trans #3105 #3108]: #3109
+#3113 := [quant-intro #3110]: #3112
+#3636 := [monotonicity #3113 #3633]: #3635
+#3644 := [trans #3636 #3642]: #3643
+#3090 := (iff #2554 #3089)
+#3087 := (iff #2551 #3084)
+#3070 := (or #1933 #3069)
+#3081 := (or #2542 #3070)
+#3085 := (iff #3081 #3084)
+#3086 := [rewrite]: #3085
+#3082 := (iff #2551 #3081)
+#3079 := (iff #2548 #3070)
+#3071 := (not #3070)
+#3074 := (not #3071)
+#3077 := (iff #3074 #3070)
+#3078 := [rewrite]: #3077
+#3075 := (iff #2548 #3074)
+#3072 := (iff #2545 #3071)
+#3073 := [rewrite]: #3072
+#3076 := [monotonicity #3073]: #3075
+#3080 := [trans #3076 #3078]: #3079
+#3083 := [monotonicity #3080]: #3082
+#3088 := [trans #3083 #3086]: #3087
+#3091 := [monotonicity #3088]: #3090
+#3647 := [monotonicity #3091 #3644]: #3646
+#3067 := (iff #1213 #3066)
+#3064 := (iff #1208 #3061)
+#3047 := (or #453 #2510)
+#3058 := (or #3047 #1201)
+#3062 := (iff #3058 #3061)
+#3063 := [rewrite]: #3062
+#3059 := (iff #1208 #3058)
+#3056 := (iff #474 #3047)
+#3048 := (not #3047)
+#3051 := (not #3048)
+#3054 := (iff #3051 #3047)
+#3055 := [rewrite]: #3054
+#3052 := (iff #474 #3051)
+#3049 := (iff #468 #3048)
+#3050 := [rewrite]: #3049
+#3053 := [monotonicity #3050]: #3052
+#3057 := [trans #3053 #3055]: #3056
+#3060 := [monotonicity #3057]: #3059
+#3065 := [trans #3060 #3063]: #3064
+#3068 := [quant-intro #3065]: #3067
+#3650 := [monotonicity #3068 #3647]: #3649
+#3658 := [trans #3650 #3656]: #3657
+#2250 := (iff #2535 #2018)
+#2329 := (iff #2532 #2119)
+#2297 := (or #2210 #1910)
+#2231 := (or #2297 #2527)
+#2120 := (iff #2231 #2119)
+#2328 := [rewrite]: #2120
+#1918 := (iff #2532 #2231)
+#2271 := (iff #2516 #2297)
+#1855 := (not #2297)
+#2154 := (not #1855)
+#1950 := (iff #2154 #2297)
+#2270 := [rewrite]: #1950
+#2155 := (iff #2516 #2154)
+#1856 := (iff #2513 #1855)
+#2298 := [rewrite]: #1856
+#1949 := [monotonicity #2298]: #2155
+#2230 := [trans #1949 #2270]: #2271
+#1919 := [monotonicity #2230]: #1918
+#2017 := [trans #1919 #2328]: #2329
+#2251 := [monotonicity #2017]: #2250
+#3661 := [monotonicity #2251 #3658]: #3660
+#3664 := [monotonicity #3661]: #3663
+#3671 := [trans #3664 #3669]: #3670
+#3674 := [monotonicity #3671]: #3673
+#3677 := [monotonicity #3674]: #3676
+#3684 := [trans #3677 #3682]: #3683
+#3687 := [monotonicity #3684]: #3686
+#2343 := (+ #2342 #2340)
+#2344 := (= #2343 0::Int)
+#2347 := (and #798 #2346 #2344)
+#2364 := (not #2347)
+#2367 := (forall (vars (?v1 S3)) #2364)
+#2352 := (= ?v0!20 f10)
+#2353 := (not #2352)
+#2354 := (and #2353 #2351)
+#2355 := (not #2354)
+#2361 := (not #2355)
+#2371 := (and #2361 #2367)
+#2376 := (and #1530 #2371)
+#2309 := (* -1::Int #2308)
+#2311 := (+ #2310 #2309)
+#2314 := (+ #2313 #2311)
+#2315 := (>= #2314 0::Int)
+#2322 := (and #2321 #2319)
+#2323 := (not #2322)
+#2324 := (or #2323 #2315)
+#2325 := (not #2324)
+#2380 := (or #2325 #2376)
+#2384 := (and #1506 #2380)
+#2282 := (* -1::Int #2281)
+#2284 := (+ #2283 #2282)
+#2285 := (>= #2284 0::Int)
+#2291 := (and #2290 #2287)
+#2292 := (not #2291)
+#2293 := (or #2292 #2285)
+#2294 := (not #2293)
+#2388 := (or #2294 #2384)
+#2392 := (and #1487 #2388)
+#2396 := (or #2267 #2392)
+#2261 := (not #1481)
+#2400 := (and #2261 #2396)
+#2404 := (or #1481 #2400)
+#2408 := (and #810 #2404)
+#2245 := (= #2244 #2243)
+#2246 := (or #2245 #2242)
+#2247 := (not #2246)
+#2412 := (or #2247 #2408)
+#2416 := (and #1473 #2412)
+#2223 := (* -1::Int #2222)
+#2225 := (+ #2224 #2223)
+#2226 := (>= #2225 0::Int)
+#2227 := (not #2226)
+#2420 := (or #2227 #2416)
+#2206 := (and #2205 #2202)
+#2192 := (not #986)
+#2440 := (and #2192 #756 #2206 #1462 #2420 #1620 #1638 #1646)
+#2133 := (* -1::Int #2132)
+#2135 := (+ #2134 #2133)
+#2138 := (+ #2137 #2135)
+#2139 := (>= #2138 0::Int)
+#2148 := (and #2147 #2143)
+#2149 := (not #2148)
+#2150 := (or #2149 #2139)
+#2151 := (not #2150)
+#2170 := (or #2151 #2166)
+#2109 := (+ #2108 #1333)
+#2112 := (+ #2111 #2109)
+#2113 := (= #2112 0::Int)
+#2114 := (>= #2109 0::Int)
+#2115 := (not #2114)
+#2116 := (and #2115 #2113)
+#2121 := (or #1342 #2116)
+#2124 := (forall (vars (?v0 S3)) #2121)
+#2174 := (and #2124 #2170)
+#2073 := (+ #2072 #2070)
+#2074 := (= #2073 0::Int)
+#2077 := (and #2076 #2074)
+#2093 := (not #2077)
+#2096 := (forall (vars (?v1 S3)) #2093)
+#2082 := (= ?v0!8 f10)
+#2083 := (not #2082)
+#2084 := (and #2083 #2081)
+#2085 := (not #2084)
+#2090 := (not #2085)
+#2100 := (and #2090 #2096)
+#2178 := (or #2100 #2174)
+#2064 := (not #714)
+#2061 := (not #732)
+#2058 := (not #705)
+#2055 := (not #723)
+#2188 := (and #2055 #2058 #2061 #2064 #2178 #2185)
+#2444 := (or #2188 #2440)
+#2032 := (+ #2031 #1288)
+#2033 := (>= #2032 0::Int)
+#2034 := (not #2033)
+#2037 := (+ #2036 #2032)
+#2038 := (= #2037 0::Int)
+#2041 := (and #2040 #2038 #2034)
+#2046 := (or #1297 #2041)
+#2049 := (forall (vars (?v0 S3)) #2046)
+#2005 := (+ #1250 #2004)
+#2007 := (+ #2006 #2005)
+#2008 := (= #2007 0::Int)
+#2009 := (+ #2006 #1250)
+#2010 := (>= #2009 0::Int)
+#2011 := (not #2010)
+#2014 := (and #2013 #2011 #2008)
+#2019 := (or #1259 #2014)
+#2022 := (forall (vars (?v0 S3)) #2019)
+#1997 := (not #1738)
+#2469 := (and #1997 #2022 #2049 #2444 #1705 #1721 #1730)
+#1963 := (+ #1962 #1960)
+#1964 := (+ #58 #1963)
+#1965 := (= #1964 0::Int)
+#1969 := (and #453 #1968 #1965)
+#1985 := (not #1969)
+#1988 := (forall (vars (?v1 S3)) #1985)
+#1974 := (= ?v0!5 f10)
+#1975 := (not #1974)
+#1976 := (and #1975 #1973)
+#1977 := (not #1976)
+#1982 := (not #1977)
+#1992 := (and #1982 #1988)
+#2473 := (or #1992 #2469)
+#2477 := (and #1244 #2473)
+#1937 := (and #1936 #1934)
+#1938 := (not #1937)
+#1941 := (+ #1940 #1930)
+#1943 := (+ #1942 #1941)
+#1944 := (>= #1943 0::Int)
+#1945 := (or #1944 #1938)
+#1946 := (not #1945)
+#2481 := (or #1946 #2477)
+#2485 := (and #1213 #2481)
+#1903 := (* -1::Int #1902)
+#1905 := (+ #1904 #1903)
+#1906 := (>= #1905 0::Int)
+#1912 := (and #1911 #1908)
+#1913 := (not #1912)
+#1914 := (or #1913 #1906)
+#1915 := (not #1914)
+#2489 := (or #1915 #2485)
+#2493 := (and #1193 #2489)
+#2497 := (or #1888 #2493)
+#1851 := (not #1187)
+#2501 := (and #1851 #2497)
+#2505 := (or #1187 #2501)
+#3045 := (iff #2505 #3044)
+#3042 := (iff #2501 #3041)
+#3039 := (iff #2497 #3038)
+#3036 := (iff #2493 #3035)
+#3033 := (iff #2489 #3032)
+#3030 := (iff #2485 #3029)
+#3027 := (iff #2481 #3026)
+#3024 := (iff #2477 #3023)
+#3021 := (iff #2473 #3020)
+#3018 := (iff #2469 #3015)
+#3012 := (and #100 #2644 #2684 #3009 #1705 #1721 #1730)
+#3016 := (iff #3012 #3015)
+#3017 := [rewrite]: #3016
+#3013 := (iff #2469 #3012)
+#3010 := (iff #2444 #3009)
+#3007 := (iff #2440 #3004)
+#3001 := (and #181 #756 #2206 #1462 #2998 #1620 #1638 #1646)
+#3005 := (iff #3001 #3004)
+#3006 := [rewrite]: #3005
+#3002 := (iff #2440 #3001)
+#2999 := (iff #2420 #2998)
+#2996 := (iff #2416 #2995)
+#2993 := (iff #2412 #2992)
+#2990 := (iff #2408 #2989)
+#2987 := (iff #2404 #2986)
+#2984 := (iff #2400 #2983)
+#2981 := (iff #2396 #2980)
+#2978 := (iff #2392 #2977)
+#2975 := (iff #2388 #2974)
+#2972 := (iff #2384 #2971)
+#2969 := (iff #2380 #2968)
+#2966 := (iff #2376 #2963)
+#2926 := (and #2351 #2920)
+#2957 := (and #2926 #2954)
+#2960 := (and #1530 #2957)
+#2964 := (iff #2960 #2963)
+#2965 := [rewrite]: #2964
+#2961 := (iff #2376 #2960)
+#2958 := (iff #2371 #2957)
+#2955 := (iff #2367 #2954)
+#2952 := (iff #2364 #2951)
+#2949 := (iff #2347 #2948)
+#2946 := (iff #2344 #2945)
+#2943 := (= #2343 #2942)
+#2944 := [rewrite]: #2943
+#2947 := [monotonicity #2944]: #2946
+#2950 := [monotonicity #2947]: #2949
+#2953 := [monotonicity #2950]: #2952
+#2956 := [quant-intro #2953]: #2955
+#2939 := (iff #2361 #2926)
+#2931 := (not #2926)
+#2934 := (not #2931)
+#2937 := (iff #2934 #2926)
+#2938 := [rewrite]: #2937
+#2935 := (iff #2361 #2934)
+#2932 := (iff #2355 #2931)
+#2929 := (iff #2354 #2926)
+#2923 := (and #2920 #2351)
+#2927 := (iff #2923 #2926)
+#2928 := [rewrite]: #2927
+#2924 := (iff #2354 #2923)
+#2921 := (iff #2353 #2920)
+#2918 := (iff #2352 #2917)
+#2919 := [rewrite]: #2918
+#2922 := [monotonicity #2919]: #2921
+#2925 := [monotonicity #2922]: #2924
+#2930 := [trans #2925 #2928]: #2929
+#2933 := [monotonicity #2930]: #2932
+#2936 := [monotonicity #2933]: #2935
+#2940 := [trans #2936 #2938]: #2939
+#2959 := [monotonicity #2940 #2956]: #2958
 #2962 := [monotonicity #2959]: #2961
-#2965 := [quant-intro #2962]: #2964
-#2948 := (iff #2370 #2935)
-#2940 := (not #2935)
-#2943 := (not #2940)
-#2946 := (iff #2943 #2935)
-#2947 := [rewrite]: #2946
-#2944 := (iff #2370 #2943)
-#2941 := (iff #2364 #2940)
-#2938 := (iff #2363 #2935)
-#2932 := (and #2929 #2360)
-#2936 := (iff #2932 #2935)
-#2937 := [rewrite]: #2936
-#2933 := (iff #2363 #2932)
-#2930 := (iff #2362 #2929)
-#2927 := (iff #2361 #2926)
-#2928 := [rewrite]: #2927
-#2931 := [monotonicity #2928]: #2930
-#2934 := [monotonicity #2931]: #2933
-#2939 := [trans #2934 #2937]: #2938
-#2942 := [monotonicity #2939]: #2941
-#2945 := [monotonicity #2942]: #2944
-#2949 := [trans #2945 #2947]: #2948
-#2968 := [monotonicity #2949 #2965]: #2967
-#2971 := [monotonicity #2968]: #2970
-#2976 := [trans #2971 #2974]: #2975
-#2924 := (iff #2334 #2923)
-#2921 := (iff #2333 #2920)
-#2918 := (iff #2324 #2915)
-#2905 := (+ #2319 #2322)
-#2906 := (+ #2318 #2905)
-#2909 := (>= #2906 0::Int)
-#2916 := (iff #2909 #2915)
-#2917 := [rewrite]: #2916
-#2910 := (iff #2324 #2909)
-#2907 := (= #2323 #2906)
+#2967 := [trans #2962 #2965]: #2966
+#2915 := (iff #2325 #2914)
+#2912 := (iff #2324 #2911)
+#2909 := (iff #2315 #2906)
+#2896 := (+ #2310 #2313)
+#2897 := (+ #2309 #2896)
+#2900 := (>= #2897 0::Int)
+#2907 := (iff #2900 #2906)
 #2908 := [rewrite]: #2907
-#2911 := [monotonicity #2908]: #2910
-#2919 := [trans #2911 #2917]: #2918
-#2903 := (iff #2332 #2902)
-#2900 := (iff #2331 #2899)
-#2901 := [rewrite]: #2900
-#2904 := [monotonicity #2901]: #2903
-#2922 := [monotonicity #2904 #2919]: #2921
-#2925 := [monotonicity #2922]: #2924
-#2979 := [monotonicity #2925 #2976]: #2978
+#2901 := (iff #2315 #2900)
+#2898 := (= #2314 #2897)
+#2899 := [rewrite]: #2898
+#2902 := [monotonicity #2899]: #2901
+#2910 := [trans #2902 #2908]: #2909
+#2894 := (iff #2323 #2893)
+#2891 := (iff #2322 #2890)
+#2892 := [rewrite]: #2891
+#2895 := [monotonicity #2892]: #2894
+#2913 := [monotonicity #2895 #2910]: #2912
+#2916 := [monotonicity #2913]: #2915
+#2970 := [monotonicity #2916 #2967]: #2969
+#2973 := [monotonicity #2970]: #2972
+#2888 := (iff #2294 #2887)
+#2885 := (iff #2293 #2884)
+#2882 := (iff #2285 #2879)
+#2871 := (+ #2282 #2283)
+#2874 := (>= #2871 0::Int)
+#2880 := (iff #2874 #2879)
+#2881 := [rewrite]: #2880
+#2875 := (iff #2285 #2874)
+#2872 := (= #2284 #2871)
+#2873 := [rewrite]: #2872
+#2876 := [monotonicity #2873]: #2875
+#2883 := [trans #2876 #2881]: #2882
+#2869 := (iff #2292 #2868)
+#2866 := (iff #2291 #2865)
+#2867 := [rewrite]: #2866
+#2870 := [monotonicity #2867]: #2869
+#2886 := [monotonicity #2870 #2883]: #2885
+#2889 := [monotonicity #2886]: #2888
+#2976 := [monotonicity #2889 #2973]: #2975
+#2979 := [monotonicity #2976]: #2978
 #2982 := [monotonicity #2979]: #2981
-#2897 := (iff #2303 #2896)
-#2894 := (iff #2302 #2893)
-#2891 := (iff #2294 #2888)
-#2880 := (+ #2291 #2292)
-#2883 := (>= #2880 0::Int)
-#2889 := (iff #2883 #2888)
-#2890 := [rewrite]: #2889
-#2884 := (iff #2294 #2883)
-#2881 := (= #2293 #2880)
-#2882 := [rewrite]: #2881
-#2885 := [monotonicity #2882]: #2884
-#2892 := [trans #2885 #2890]: #2891
-#2878 := (iff #2301 #2877)
-#2875 := (iff #2300 #2874)
-#2876 := [rewrite]: #2875
-#2879 := [monotonicity #2876]: #2878
-#2895 := [monotonicity #2879 #2892]: #2894
-#2898 := [monotonicity #2895]: #2897
-#2985 := [monotonicity #2898 #2982]: #2984
+#2863 := (iff #2261 #203)
+#2864 := [rewrite]: #2863
+#2985 := [monotonicity #2864 #2982]: #2984
 #2988 := [monotonicity #2985]: #2987
 #2991 := [monotonicity #2988]: #2990
-#2872 := (iff #2270 #204)
-#2873 := [rewrite]: #2872
-#2994 := [monotonicity #2873 #2991]: #2993
+#2861 := (iff #2247 #2860)
+#2858 := (iff #2246 #2855)
+#2852 := (or #2849 #2242)
+#2856 := (iff #2852 #2855)
+#2857 := [rewrite]: #2856
+#2853 := (iff #2246 #2852)
+#2850 := (iff #2245 #2849)
+#2851 := [rewrite]: #2850
+#2854 := [monotonicity #2851]: #2853
+#2859 := [trans #2854 #2857]: #2858
+#2862 := [monotonicity #2859]: #2861
+#2994 := [monotonicity #2862 #2991]: #2993
 #2997 := [monotonicity #2994]: #2996
-#3000 := [monotonicity #2997]: #2999
-#2870 := (iff #2256 #2869)
-#2867 := (iff #2255 #2864)
-#2861 := (or #2858 #2251)
-#2865 := (iff #2861 #2864)
-#2866 := [rewrite]: #2865
-#2862 := (iff #2255 #2861)
-#2859 := (iff #2254 #2858)
-#2860 := [rewrite]: #2859
-#2863 := [monotonicity #2860]: #2862
-#2868 := [trans #2863 #2866]: #2867
-#2871 := [monotonicity #2868]: #2870
-#3003 := [monotonicity #2871 #3000]: #3002
-#3006 := [monotonicity #3003]: #3005
-#2856 := (iff #2236 #2855)
-#2853 := (iff #2235 #2850)
-#2842 := (+ #2232 #2233)
-#2845 := (>= #2842 0::Int)
-#2851 := (iff #2845 #2850)
-#2852 := [rewrite]: #2851
-#2846 := (iff #2235 #2845)
-#2843 := (= #2234 #2842)
-#2844 := [rewrite]: #2843
-#2847 := [monotonicity #2844]: #2846
-#2854 := [trans #2847 #2852]: #2853
-#2857 := [monotonicity #2854]: #2856
-#3009 := [monotonicity #2857 #3006]: #3008
-#2840 := (iff #2203 #776)
-#2841 := [rewrite]: #2840
-#3012 := [monotonicity #2841 #3009]: #3011
-#3017 := [trans #3012 #3015]: #3016
-#2838 := (iff #2197 #2835)
-#2832 := (and #136 #141 #621 #624 #2829 #2194)
-#2836 := (iff #2832 #2835)
-#2837 := [rewrite]: #2836
-#2833 := (iff #2197 #2832)
-#2830 := (iff #2187 #2829)
-#2827 := (iff #2183 #2826)
-#2824 := (iff #2179 #2821)
-#2818 := (or #2815 #2175)
-#2822 := (iff #2818 #2821)
-#2823 := [rewrite]: #2822
-#2819 := (iff #2179 #2818)
-#2816 := (iff #2160 #2815)
-#2813 := (iff #2159 #2812)
-#2810 := (iff #2148 #2807)
-#2798 := (+ #2143 #2146)
-#2799 := (+ #2142 #2798)
-#2802 := (>= #2799 0::Int)
-#2808 := (iff #2802 #2807)
-#2809 := [rewrite]: #2808
-#2803 := (iff #2148 #2802)
-#2800 := (= #2147 #2799)
-#2801 := [rewrite]: #2800
-#2804 := [monotonicity #2801]: #2803
-#2811 := [trans #2804 #2809]: #2810
-#2796 := (iff #2158 #2795)
-#2793 := (iff #2157 #2792)
-#2794 := [rewrite]: #2793
-#2797 := [monotonicity #2794]: #2796
-#2814 := [monotonicity #2797 #2811]: #2813
-#2817 := [monotonicity #2814]: #2816
-#2820 := [monotonicity #2817]: #2819
-#2825 := [trans #2820 #2823]: #2824
-#2790 := (iff #2133 #2789)
-#2787 := (iff #2130 #2786)
-#2784 := (iff #2125 #2783)
-#2781 := (iff #2122 #2778)
-#2768 := (+ #2117 #2120)
-#2769 := (+ #1342 #2768)
-#2772 := (= #2769 0::Int)
-#2779 := (iff #2772 #2778)
-#2780 := [rewrite]: #2779
-#2773 := (iff #2122 #2772)
-#2770 := (= #2121 #2769)
+#2847 := (iff #2227 #2846)
+#2844 := (iff #2226 #2841)
+#2833 := (+ #2223 #2224)
+#2836 := (>= #2833 0::Int)
+#2842 := (iff #2836 #2841)
+#2843 := [rewrite]: #2842
+#2837 := (iff #2226 #2836)
+#2834 := (= #2225 #2833)
+#2835 := [rewrite]: #2834
+#2838 := [monotonicity #2835]: #2837
+#2845 := [trans #2838 #2843]: #2844
+#2848 := [monotonicity #2845]: #2847
+#3000 := [monotonicity #2848 #2997]: #2999
+#2831 := (iff #2192 #181)
+#2832 := [rewrite]: #2831
+#3003 := [monotonicity #2832 #3000]: #3002
+#3008 := [trans #3003 #3006]: #3007
+#2829 := (iff #2188 #2826)
+#2823 := (and #136 #141 #620 #623 #2820 #2185)
+#2827 := (iff #2823 #2826)
+#2828 := [rewrite]: #2827
+#2824 := (iff #2188 #2823)
+#2821 := (iff #2178 #2820)
+#2818 := (iff #2174 #2817)
+#2815 := (iff #2170 #2812)
+#2809 := (or #2806 #2166)
+#2813 := (iff #2809 #2812)
+#2814 := [rewrite]: #2813
+#2810 := (iff #2170 #2809)
+#2807 := (iff #2151 #2806)
+#2804 := (iff #2150 #2803)
+#2801 := (iff #2139 #2798)
+#2789 := (+ #2134 #2137)
+#2790 := (+ #2133 #2789)
+#2793 := (>= #2790 0::Int)
+#2799 := (iff #2793 #2798)
+#2800 := [rewrite]: #2799
+#2794 := (iff #2139 #2793)
+#2791 := (= #2138 #2790)
+#2792 := [rewrite]: #2791
+#2795 := [monotonicity #2792]: #2794
+#2802 := [trans #2795 #2800]: #2801
+#2787 := (iff #2149 #2786)
+#2784 := (iff #2148 #2783)
+#2785 := [rewrite]: #2784
+#2788 := [monotonicity #2785]: #2787
+#2805 := [monotonicity #2788 #2802]: #2804
+#2808 := [monotonicity #2805]: #2807
+#2811 := [monotonicity #2808]: #2810
+#2816 := [trans #2811 #2814]: #2815
+#2781 := (iff #2124 #2780)
+#2778 := (iff #2121 #2777)
+#2775 := (iff #2116 #2774)
+#2772 := (iff #2113 #2769)
+#2759 := (+ #2108 #2111)
+#2760 := (+ #1333 #2759)
+#2763 := (= #2760 0::Int)
+#2770 := (iff #2763 #2769)
 #2771 := [rewrite]: #2770
-#2774 := [monotonicity #2771]: #2773
-#2782 := [trans #2774 #2780]: #2781
-#2766 := (iff #2124 #2765)
-#2763 := (iff #2123 #2760)
-#2752 := (+ #1342 #2117)
-#2755 := (>= #2752 0::Int)
-#2761 := (iff #2755 #2760)
+#2764 := (iff #2113 #2763)
+#2761 := (= #2112 #2760)
 #2762 := [rewrite]: #2761
-#2756 := (iff #2123 #2755)
-#2753 := (= #2118 #2752)
-#2754 := [rewrite]: #2753
-#2757 := [monotonicity #2754]: #2756
-#2764 := [trans #2757 #2762]: #2763
-#2767 := [monotonicity #2764]: #2766
-#2785 := [monotonicity #2767 #2782]: #2784
-#2788 := [monotonicity #2785]: #2787
-#2791 := [quant-intro #2788]: #2790
-#2828 := [monotonicity #2791 #2825]: #2827
-#2750 := (iff #2109 #2747)
-#2713 := (and #2090 #2707)
-#2744 := (and #2713 #2741)
-#2748 := (iff #2744 #2747)
-#2749 := [rewrite]: #2748
-#2745 := (iff #2109 #2744)
-#2742 := (iff #2105 #2741)
-#2739 := (iff #2102 #2738)
-#2736 := (iff #2086 #2735)
-#2733 := (iff #2083 #2732)
-#2730 := (= #2082 #2729)
-#2731 := [rewrite]: #2730
-#2734 := [monotonicity #2731]: #2733
-#2737 := [monotonicity #2734]: #2736
-#2740 := [monotonicity #2737]: #2739
-#2743 := [quant-intro #2740]: #2742
-#2726 := (iff #2099 #2713)
-#2718 := (not #2713)
-#2721 := (not #2718)
-#2724 := (iff #2721 #2713)
-#2725 := [rewrite]: #2724
-#2722 := (iff #2099 #2721)
-#2719 := (iff #2094 #2718)
-#2716 := (iff #2093 #2713)
-#2710 := (and #2707 #2090)
-#2714 := (iff #2710 #2713)
-#2715 := [rewrite]: #2714
-#2711 := (iff #2093 #2710)
-#2708 := (iff #2092 #2707)
-#2705 := (iff #2091 #2704)
+#2765 := [monotonicity #2762]: #2764
+#2773 := [trans #2765 #2771]: #2772
+#2757 := (iff #2115 #2756)
+#2754 := (iff #2114 #2751)
+#2743 := (+ #1333 #2108)
+#2746 := (>= #2743 0::Int)
+#2752 := (iff #2746 #2751)
+#2753 := [rewrite]: #2752
+#2747 := (iff #2114 #2746)
+#2744 := (= #2109 #2743)
+#2745 := [rewrite]: #2744
+#2748 := [monotonicity #2745]: #2747
+#2755 := [trans #2748 #2753]: #2754
+#2758 := [monotonicity #2755]: #2757
+#2776 := [monotonicity #2758 #2773]: #2775
+#2779 := [monotonicity #2776]: #2778
+#2782 := [quant-intro #2779]: #2781
+#2819 := [monotonicity #2782 #2816]: #2818
+#2741 := (iff #2100 #2738)
+#2704 := (and #2081 #2698)
+#2735 := (and #2704 #2732)
+#2739 := (iff #2735 #2738)
+#2740 := [rewrite]: #2739
+#2736 := (iff #2100 #2735)
+#2733 := (iff #2096 #2732)
+#2730 := (iff #2093 #2729)
+#2727 := (iff #2077 #2726)
+#2724 := (iff #2074 #2723)
+#2721 := (= #2073 #2720)
+#2722 := [rewrite]: #2721
+#2725 := [monotonicity #2722]: #2724
+#2728 := [monotonicity #2725]: #2727
+#2731 := [monotonicity #2728]: #2730
+#2734 := [quant-intro #2731]: #2733
+#2717 := (iff #2090 #2704)
+#2709 := (not #2704)
+#2712 := (not #2709)
+#2715 := (iff #2712 #2704)
+#2716 := [rewrite]: #2715
+#2713 := (iff #2090 #2712)
+#2710 := (iff #2085 #2709)
+#2707 := (iff #2084 #2704)
+#2701 := (and #2698 #2081)
+#2705 := (iff #2701 #2704)
 #2706 := [rewrite]: #2705
-#2709 := [monotonicity #2706]: #2708
-#2712 := [monotonicity #2709]: #2711
-#2717 := [trans #2712 #2715]: #2716
-#2720 := [monotonicity #2717]: #2719
-#2723 := [monotonicity #2720]: #2722
-#2727 := [trans #2723 #2725]: #2726
-#2746 := [monotonicity #2727 #2743]: #2745
-#2751 := [trans #2746 #2749]: #2750
-#2831 := [monotonicity #2751 #2828]: #2830
-#2702 := (iff #2073 #624)
-#2703 := [rewrite]: #2702
-#2700 := (iff #2070 #621)
-#2701 := [rewrite]: #2700
-#2698 := (iff #2067 #141)
-#2699 := [rewrite]: #2698
-#2696 := (iff #2064 #136)
+#2702 := (iff #2084 #2701)
+#2699 := (iff #2083 #2698)
+#2696 := (iff #2082 #2695)
 #2697 := [rewrite]: #2696
-#2834 := [monotonicity #2697 #2699 #2701 #2703 #2831]: #2833
-#2839 := [trans #2834 #2837]: #2838
-#3020 := [monotonicity #2839 #3017]: #3019
-#2694 := (iff #2058 #2693)
-#2691 := (iff #2055 #2690)
-#2688 := (iff #2050 #2687)
-#2685 := (iff #2043 #2684)
-#2682 := (iff #2042 #2679)
-#2672 := (+ #1297 #2040)
-#2675 := (>= #2672 0::Int)
-#2680 := (iff #2675 #2679)
-#2681 := [rewrite]: #2680
-#2676 := (iff #2042 #2675)
-#2673 := (= #2041 #2672)
-#2674 := [rewrite]: #2673
+#2700 := [monotonicity #2697]: #2699
+#2703 := [monotonicity #2700]: #2702
+#2708 := [trans #2703 #2706]: #2707
+#2711 := [monotonicity #2708]: #2710
+#2714 := [monotonicity #2711]: #2713
+#2718 := [trans #2714 #2716]: #2717
+#2737 := [monotonicity #2718 #2734]: #2736
+#2742 := [trans #2737 #2740]: #2741
+#2822 := [monotonicity #2742 #2819]: #2821
+#2693 := (iff #2064 #623)
+#2694 := [rewrite]: #2693
+#2691 := (iff #2061 #620)
+#2692 := [rewrite]: #2691
+#2689 := (iff #2058 #141)
+#2690 := [rewrite]: #2689
+#2687 := (iff #2055 #136)
+#2688 := [rewrite]: #2687
+#2825 := [monotonicity #2688 #2690 #2692 #2694 #2822]: #2824
+#2830 := [trans #2825 #2828]: #2829
+#3011 := [monotonicity #2830 #3008]: #3010
+#2685 := (iff #2049 #2684)
+#2682 := (iff #2046 #2681)
+#2679 := (iff #2041 #2678)
+#2676 := (iff #2034 #2675)
+#2673 := (iff #2033 #2670)
+#2663 := (+ #1288 #2031)
+#2666 := (>= #2663 0::Int)
+#2671 := (iff #2666 #2670)
+#2672 := [rewrite]: #2671
+#2667 := (iff #2033 #2666)
+#2664 := (= #2032 #2663)
+#2665 := [rewrite]: #2664
+#2668 := [monotonicity #2665]: #2667
+#2674 := [trans #2668 #2672]: #2673
 #2677 := [monotonicity #2674]: #2676
-#2683 := [trans #2677 #2681]: #2682
-#2686 := [monotonicity #2683]: #2685
-#2670 := (iff #2047 #2667)
-#2656 := (+ #2040 #2045)
-#2657 := (+ #1297 #2656)
-#2660 := (= #2657 0::Int)
-#2668 := (iff #2660 #2667)
-#2669 := [rewrite]: #2668
-#2661 := (iff #2047 #2660)
-#2658 := (= #2046 #2657)
-#2659 := [rewrite]: #2658
-#2662 := [monotonicity #2659]: #2661
-#2671 := [trans #2662 #2669]: #2670
-#2689 := [monotonicity #2671 #2686]: #2688
-#2692 := [monotonicity #2689]: #2691
-#2695 := [quant-intro #2692]: #2694
-#2654 := (iff #2031 #2653)
-#2651 := (iff #2028 #2650)
-#2648 := (iff #2023 #2647)
-#2645 := (iff #2017 #2642)
-#2632 := (+ #2013 #2015)
-#2633 := (+ #1259 #2632)
-#2636 := (= #2633 0::Int)
-#2643 := (iff #2636 #2642)
-#2644 := [rewrite]: #2643
-#2637 := (iff #2017 #2636)
-#2634 := (= #2016 #2633)
+#2661 := (iff #2038 #2658)
+#2647 := (+ #2031 #2036)
+#2648 := (+ #1288 #2647)
+#2651 := (= #2648 0::Int)
+#2659 := (iff #2651 #2658)
+#2660 := [rewrite]: #2659
+#2652 := (iff #2038 #2651)
+#2649 := (= #2037 #2648)
+#2650 := [rewrite]: #2649
+#2653 := [monotonicity #2650]: #2652
+#2662 := [trans #2653 #2660]: #2661
+#2680 := [monotonicity #2662 #2677]: #2679
+#2683 := [monotonicity #2680]: #2682
+#2686 := [quant-intro #2683]: #2685
+#2645 := (iff #2022 #2644)
+#2642 := (iff #2019 #2641)
+#2639 := (iff #2014 #2638)
+#2636 := (iff #2008 #2633)
+#2623 := (+ #2004 #2006)
+#2624 := (+ #1250 #2623)
+#2627 := (= #2624 0::Int)
+#2634 := (iff #2627 #2633)
 #2635 := [rewrite]: #2634
-#2638 := [monotonicity #2635]: #2637
-#2646 := [trans #2638 #2644]: #2645
-#2630 := (iff #2020 #2629)
-#2627 := (iff #2019 #2624)
-#2616 := (+ #1259 #2015)
-#2619 := (>= #2616 0::Int)
-#2625 := (iff #2619 #2624)
+#2628 := (iff #2008 #2627)
+#2625 := (= #2007 #2624)
 #2626 := [rewrite]: #2625
-#2620 := (iff #2019 #2619)
-#2617 := (= #2018 #2616)
-#2618 := [rewrite]: #2617
-#2621 := [monotonicity #2618]: #2620
-#2628 := [trans #2621 #2626]: #2627
-#2631 := [monotonicity #2628]: #2630
-#2649 := [monotonicity #2631 #2646]: #2648
-#2652 := [monotonicity #2649]: #2651
-#2655 := [quant-intro #2652]: #2654
-#2614 := (iff #2006 #100)
-#2615 := [rewrite]: #2614
-#3023 := [monotonicity #2615 #2655 #2695 #3020]: #3022
-#3028 := [trans #3023 #3026]: #3027
-#2612 := (iff #2001 #2609)
-#2575 := (and #1982 #2569)
-#2606 := (and #2575 #2603)
-#2610 := (iff #2606 #2609)
-#2611 := [rewrite]: #2610
-#2607 := (iff #2001 #2606)
-#2604 := (iff #1997 #2603)
-#2601 := (iff #1994 #2600)
-#2598 := (iff #1978 #2597)
-#2595 := (iff #1974 #2594)
-#2592 := (= #1973 #2591)
-#2593 := [rewrite]: #2592
-#2596 := [monotonicity #2593]: #2595
-#2599 := [monotonicity #2596]: #2598
-#2602 := [monotonicity #2599]: #2601
-#2605 := [quant-intro #2602]: #2604
-#2588 := (iff #1991 #2575)
-#2580 := (not #2575)
-#2583 := (not #2580)
-#2586 := (iff #2583 #2575)
-#2587 := [rewrite]: #2586
-#2584 := (iff #1991 #2583)
-#2581 := (iff #1986 #2580)
-#2578 := (iff #1985 #2575)
-#2572 := (and #2569 #1982)
-#2576 := (iff #2572 #2575)
-#2577 := [rewrite]: #2576
-#2573 := (iff #1985 #2572)
-#2570 := (iff #1984 #2569)
-#2567 := (iff #1983 #2566)
+#2629 := [monotonicity #2626]: #2628
+#2637 := [trans #2629 #2635]: #2636
+#2621 := (iff #2011 #2620)
+#2618 := (iff #2010 #2615)
+#2607 := (+ #1250 #2006)
+#2610 := (>= #2607 0::Int)
+#2616 := (iff #2610 #2615)
+#2617 := [rewrite]: #2616
+#2611 := (iff #2010 #2610)
+#2608 := (= #2009 #2607)
+#2609 := [rewrite]: #2608
+#2612 := [monotonicity #2609]: #2611
+#2619 := [trans #2612 #2617]: #2618
+#2622 := [monotonicity #2619]: #2621
+#2640 := [monotonicity #2622 #2637]: #2639
+#2643 := [monotonicity #2640]: #2642
+#2646 := [quant-intro #2643]: #2645
+#2605 := (iff #1997 #100)
+#2606 := [rewrite]: #2605
+#3014 := [monotonicity #2606 #2646 #2686 #3011]: #3013
+#3019 := [trans #3014 #3017]: #3018
+#2603 := (iff #1992 #2600)
+#2566 := (and #1973 #2560)
+#2597 := (and #2566 #2594)
+#2601 := (iff #2597 #2600)
+#2602 := [rewrite]: #2601
+#2598 := (iff #1992 #2597)
+#2595 := (iff #1988 #2594)
+#2592 := (iff #1985 #2591)
+#2589 := (iff #1969 #2588)
+#2586 := (iff #1965 #2585)
+#2583 := (= #1964 #2582)
+#2584 := [rewrite]: #2583
+#2587 := [monotonicity #2584]: #2586
+#2590 := [monotonicity #2587]: #2589
+#2593 := [monotonicity #2590]: #2592
+#2596 := [quant-intro #2593]: #2595
+#2579 := (iff #1982 #2566)
+#2571 := (not #2566)
+#2574 := (not #2571)
+#2577 := (iff #2574 #2566)
+#2578 := [rewrite]: #2577
+#2575 := (iff #1982 #2574)
+#2572 := (iff #1977 #2571)
+#2569 := (iff #1976 #2566)
+#2563 := (and #2560 #1973)
+#2567 := (iff #2563 #2566)
 #2568 := [rewrite]: #2567
-#2571 := [monotonicity #2568]: #2570
-#2574 := [monotonicity #2571]: #2573
-#2579 := [trans #2574 #2577]: #2578
-#2582 := [monotonicity #2579]: #2581
-#2585 := [monotonicity #2582]: #2584
-#2589 := [trans #2585 #2587]: #2588
-#2608 := [monotonicity #2589 #2605]: #2607
-#2613 := [trans #2608 #2611]: #2612
-#3031 := [monotonicity #2613 #3028]: #3030
-#3034 := [monotonicity #3031]: #3033
-#2564 := (iff #1955 #2563)
-#2561 := (iff #1954 #2560)
-#2558 := (iff #1947 #2557)
+#2564 := (iff #1976 #2563)
+#2561 := (iff #1975 #2560)
+#2558 := (iff #1974 #2557)
+#2559 := [rewrite]: #2558
+#2562 := [monotonicity #2559]: #2561
+#2565 := [monotonicity #2562]: #2564
+#2570 := [trans #2565 #2568]: #2569
+#2573 := [monotonicity #2570]: #2572
+#2576 := [monotonicity #2573]: #2575
+#2580 := [trans #2576 #2578]: #2579
+#2599 := [monotonicity #2580 #2596]: #2598
+#2604 := [trans #2599 #2602]: #2603
+#3022 := [monotonicity #2604 #3019]: #3021
+#3025 := [monotonicity #3022]: #3024
 #2555 := (iff #1946 #2554)
-#2556 := [rewrite]: #2555
-#2559 := [monotonicity #2556]: #2558
-#2552 := (iff #1953 #2551)
-#2549 := (= #1952 #2548)
-#2550 := [rewrite]: #2549
-#2553 := [monotonicity #2550]: #2552
-#2562 := [monotonicity #2553 #2559]: #2561
-#2565 := [monotonicity #2562]: #2564
-#3037 := [monotonicity #2565 #3034]: #3036
+#2552 := (iff #1945 #2551)
+#2549 := (iff #1938 #2548)
+#2546 := (iff #1937 #2545)
+#2547 := [rewrite]: #2546
+#2550 := [monotonicity #2547]: #2549
+#2543 := (iff #1944 #2542)
+#2540 := (= #1943 #2539)
+#2541 := [rewrite]: #2540
+#2544 := [monotonicity #2541]: #2543
+#2553 := [monotonicity #2544 #2550]: #2552
+#2556 := [monotonicity #2553]: #2555
+#3028 := [monotonicity #2556 #3025]: #3027
+#3031 := [monotonicity #3028]: #3030
+#2536 := (iff #1915 #2535)
+#2533 := (iff #1914 #2532)
+#2530 := (iff #1906 #2527)
+#2519 := (+ #1903 #1904)
+#2522 := (>= #2519 0::Int)
+#2528 := (iff #2522 #2527)
+#2529 := [rewrite]: #2528
+#2523 := (iff #1906 #2522)
+#2520 := (= #1905 #2519)
+#2521 := [rewrite]: #2520
+#2524 := [monotonicity #2521]: #2523
+#2531 := [trans #2524 #2529]: #2530
+#2517 := (iff #1913 #2516)
+#2514 := (iff #1912 #2513)
+#2515 := [rewrite]: #2514
+#2518 := [monotonicity #2515]: #2517
+#2534 := [monotonicity #2518 #2531]: #2533
+#2537 := [monotonicity #2534]: #2536
+#3034 := [monotonicity #2537 #3031]: #3033
+#3037 := [monotonicity #3034]: #3036
 #3040 := [monotonicity #3037]: #3039
-#2545 := (iff #1924 #2544)
-#2542 := (iff #1923 #2541)
-#2539 := (iff #1915 #2536)
-#2528 := (+ #1912 #1913)
-#2531 := (>= #2528 0::Int)
-#2537 := (iff #2531 #2536)
-#2538 := [rewrite]: #2537
-#2532 := (iff #1915 #2531)
-#2529 := (= #1914 #2528)
-#2530 := [rewrite]: #2529
-#2533 := [monotonicity #2530]: #2532
-#2540 := [trans #2533 #2538]: #2539
-#2526 := (iff #1922 #2525)
-#2523 := (iff #1921 #2522)
-#2524 := [rewrite]: #2523
-#2527 := [monotonicity #2524]: #2526
-#2543 := [monotonicity #2527 #2540]: #2542
-#2546 := [monotonicity #2543]: #2545
-#3043 := [monotonicity #2546 #3040]: #3042
+#2511 := (iff #1851 #71)
+#2512 := [rewrite]: #2511
+#3043 := [monotonicity #2512 #3040]: #3042
 #3046 := [monotonicity #3043]: #3045
-#3049 := [monotonicity #3046]: #3048
-#2520 := (iff #1860 #71)
-#2521 := [rewrite]: #2520
-#3052 := [monotonicity #2521 #3049]: #3051
-#3055 := [monotonicity #3052]: #3054
-#1836 := (not #1800)
-#2515 := (~ #1836 #2514)
-#2511 := (not #1797)
-#2512 := (~ #2511 #2510)
-#2507 := (not #1794)
-#2508 := (~ #2507 #2506)
-#2503 := (not #1791)
-#2504 := (~ #2503 #2502)
-#2499 := (not #1788)
-#2500 := (~ #2499 #2498)
-#2495 := (not #1785)
-#2496 := (~ #2495 #2494)
-#2491 := (not #1782)
-#2492 := (~ #2491 #2490)
-#2487 := (not #1779)
-#2488 := (~ #2487 #2486)
-#2483 := (not #1776)
-#2484 := (~ #2483 #2482)
-#2479 := (not #1771)
-#2480 := (~ #2479 #2478)
-#2475 := (not #1742)
-#2476 := (~ #2475 #1739)
-#2473 := (~ #1739 #1739)
-#2471 := (~ #1736 #1736)
-#2472 := [refl]: #2471
-#2474 := [nnf-pos #2472]: #2473
-#2477 := [nnf-neg #2474]: #2476
-#2468 := (not #1733)
-#2469 := (~ #2468 #1730)
-#2466 := (~ #1730 #1730)
-#2464 := (~ #1725 #1725)
-#2465 := [refl]: #2464
-#2467 := [nnf-pos #2465]: #2466
-#2470 := [nnf-neg #2467]: #2469
-#2461 := (not #1717)
-#2462 := (~ #2461 #1714)
-#2459 := (~ #1714 #1714)
-#2457 := (~ #1711 #1711)
-#2458 := [refl]: #2457
-#2460 := [nnf-pos #2458]: #2459
-#2463 := [nnf-neg #2460]: #2462
-#2454 := (not #1694)
-#2455 := (~ #2454 #2453)
-#2450 := (not #1689)
-#2451 := (~ #2450 #2449)
-#2447 := (~ #1655 #1655)
-#2448 := [refl]: #2447
-#2444 := (not #1650)
-#2445 := (~ #2444 #1647)
-#2442 := (~ #1647 #1647)
-#2440 := (~ #1642 #1642)
-#2441 := [refl]: #2440
-#2443 := [nnf-pos #2441]: #2442
-#2446 := [nnf-neg #2443]: #2445
-#2437 := (not #1632)
-#2438 := (~ #2437 #1629)
-#2435 := (~ #1629 #1629)
-#2433 := (~ #1626 #1626)
-#2434 := [refl]: #2433
-#2436 := [nnf-pos #2434]: #2435
-#2439 := [nnf-neg #2436]: #2438
-#2430 := (not #1615)
-#2431 := (~ #2430 #2429)
-#2426 := (not #1612)
-#2427 := (~ #2426 #2425)
-#2422 := (not #1609)
-#2423 := (~ #2422 #2421)
-#2418 := (not #1606)
-#2419 := (~ #2418 #2417)
-#2414 := (not #1603)
-#2415 := (~ #2414 #2413)
-#2410 := (not #1600)
-#2411 := (~ #2410 #2409)
-#2406 := (not #1597)
-#2407 := (~ #2406 #2405)
-#2402 := (not #1594)
-#2403 := (~ #2402 #2401)
-#2398 := (not #1591)
-#2399 := (~ #2398 #2397)
-#2394 := (not #1588)
-#2395 := (~ #2394 #2393)
-#2390 := (not #1585)
-#2391 := (~ #2390 #2389)
-#2386 := (not #1582)
-#2387 := (~ #2386 #2385)
-#2367 := (not #1579)
-#2383 := (~ #2367 #2380)
-#2357 := (exists (vars (?v1 S3)) #2356)
-#2365 := (or #2364 #2357)
-#2366 := (not #2365)
-#2381 := (~ #2366 #2380)
-#2377 := (not #2357)
+#1827 := (not #1791)
+#2506 := (~ #1827 #2505)
+#2502 := (not #1788)
+#2503 := (~ #2502 #2501)
+#2498 := (not #1785)
+#2499 := (~ #2498 #2497)
+#2494 := (not #1782)
+#2495 := (~ #2494 #2493)
+#2490 := (not #1779)
+#2491 := (~ #2490 #2489)
+#2486 := (not #1776)
+#2487 := (~ #2486 #2485)
+#2482 := (not #1773)
+#2483 := (~ #2482 #2481)
+#2478 := (not #1770)
+#2479 := (~ #2478 #2477)
+#2474 := (not #1767)
+#2475 := (~ #2474 #2473)
+#2470 := (not #1762)
+#2471 := (~ #2470 #2469)
+#2466 := (not #1733)
+#2467 := (~ #2466 #1730)
+#2464 := (~ #1730 #1730)
+#2462 := (~ #1727 #1727)
+#2463 := [refl]: #2462
+#2465 := [nnf-pos #2463]: #2464
+#2468 := [nnf-neg #2465]: #2467
+#2459 := (not #1724)
+#2460 := (~ #2459 #1721)
+#2457 := (~ #1721 #1721)
+#2455 := (~ #1716 #1716)
+#2456 := [refl]: #2455
+#2458 := [nnf-pos #2456]: #2457
+#2461 := [nnf-neg #2458]: #2460
+#2452 := (not #1708)
+#2453 := (~ #2452 #1705)
+#2450 := (~ #1705 #1705)
+#2448 := (~ #1702 #1702)
+#2449 := [refl]: #2448
+#2451 := [nnf-pos #2449]: #2450
+#2454 := [nnf-neg #2451]: #2453
+#2445 := (not #1685)
+#2446 := (~ #2445 #2444)
+#2441 := (not #1680)
+#2442 := (~ #2441 #2440)
+#2438 := (~ #1646 #1646)
+#2439 := [refl]: #2438
+#2435 := (not #1641)
+#2436 := (~ #2435 #1638)
+#2433 := (~ #1638 #1638)
+#2431 := (~ #1633 #1633)
+#2432 := [refl]: #2431
+#2434 := [nnf-pos #2432]: #2433
+#2437 := [nnf-neg #2434]: #2436
+#2428 := (not #1623)
+#2429 := (~ #2428 #1620)
+#2426 := (~ #1620 #1620)
+#2424 := (~ #1617 #1617)
+#2425 := [refl]: #2424
+#2427 := [nnf-pos #2425]: #2426
+#2430 := [nnf-neg #2427]: #2429
+#2421 := (not #1606)
+#2422 := (~ #2421 #2420)
+#2417 := (not #1603)
+#2418 := (~ #2417 #2416)
+#2413 := (not #1600)
+#2414 := (~ #2413 #2412)
+#2409 := (not #1597)
+#2410 := (~ #2409 #2408)
+#2405 := (not #1594)
+#2406 := (~ #2405 #2404)
+#2401 := (not #1591)
+#2402 := (~ #2401 #2400)
+#2397 := (not #1588)
+#2398 := (~ #2397 #2396)
+#2393 := (not #1585)
+#2394 := (~ #2393 #2392)
+#2389 := (not #1582)
+#2390 := (~ #2389 #2388)
+#2385 := (not #1579)
+#2386 := (~ #2385 #2384)
+#2381 := (not #1576)
+#2382 := (~ #2381 #2380)
+#2377 := (not #1573)
 #2378 := (~ #2377 #2376)
-#2374 := (~ #2373 #2373)
-#2375 := [refl]: #2374
-#2379 := [nnf-neg #2375]: #2378
-#2371 := (~ #2370 #2370)
-#2372 := [refl]: #2371
-#2382 := [nnf-neg #2372 #2379]: #2381
-#2368 := (~ #2367 #2366)
-#2369 := [sk]: #2368
-#2384 := [trans #2369 #2382]: #2383
-#2343 := (not #1542)
-#2344 := (~ #2343 #1539)
-#2341 := (~ #1539 #1539)
-#2339 := (~ #1536 #1536)
-#2340 := [refl]: #2339
-#2342 := [nnf-pos #2340]: #2341
-#2345 := [nnf-neg #2342]: #2344
-#2388 := [nnf-neg #2345 #2384]: #2387
-#2335 := (~ #1542 #2334)
-#2336 := [sk]: #2335
-#2392 := [nnf-neg #2336 #2388]: #2391
-#2312 := (not #1518)
-#2313 := (~ #2312 #1515)
-#2310 := (~ #1515 #1515)
-#2308 := (~ #1510 #1510)
-#2309 := [refl]: #2308
-#2311 := [nnf-pos #2309]: #2310
-#2314 := [nnf-neg #2311]: #2313
-#2396 := [nnf-neg #2314 #2392]: #2395
-#2304 := (~ #1518 #2303)
-#2305 := [sk]: #2304
-#2400 := [nnf-neg #2305 #2396]: #2399
-#2285 := (not #1499)
-#2286 := (~ #2285 #1496)
-#2283 := (~ #1496 #1496)
-#2281 := (~ #1493 #1493)
-#2282 := [refl]: #2281
-#2284 := [nnf-pos #2282]: #2283
-#2287 := [nnf-neg #2284]: #2286
-#2404 := [nnf-neg #2287 #2400]: #2403
-#2277 := (~ #1499 #2276)
-#2278 := [sk]: #2277
-#2408 := [nnf-neg #2278 #2404]: #2407
-#2271 := (~ #2270 #2270)
-#2272 := [refl]: #2271
-#2412 := [nnf-neg #2272 #2408]: #2411
-#2268 := (~ #1490 #1490)
-#2269 := [refl]: #2268
-#2416 := [nnf-neg #2269 #2412]: #2415
-#2265 := (not #953)
-#2266 := (~ #2265 #819)
-#2263 := (~ #819 #819)
-#2261 := (~ #814 #814)
-#2262 := [refl]: #2261
-#2264 := [nnf-pos #2262]: #2263
-#2267 := [nnf-neg #2264]: #2266
-#2420 := [nnf-neg #2267 #2416]: #2419
-#2257 := (~ #953 #2256)
-#2258 := [sk]: #2257
-#2424 := [nnf-neg #2258 #2420]: #2423
-#2245 := (not #1485)
-#2246 := (~ #2245 #1482)
-#2243 := (~ #1482 #1482)
-#2241 := (~ #1477 #1477)
-#2242 := [refl]: #2241
-#2244 := [nnf-pos #2242]: #2243
-#2247 := [nnf-neg #2244]: #2246
-#2428 := [nnf-neg #2247 #2424]: #2427
-#2237 := (~ #1485 #2236)
-#2238 := [sk]: #2237
-#2432 := [nnf-neg #2238 #2428]: #2431
-#2227 := (not #1474)
-#2228 := (~ #2227 #1471)
-#2225 := (~ #1471 #1471)
-#2223 := (~ #1466 #1466)
-#2224 := [refl]: #2223
-#2226 := [nnf-pos #2224]: #2225
-#2229 := [nnf-neg #2226]: #2228
-#2220 := (not #1665)
-#2221 := (~ #2220 #2215)
-#2216 := (~ #1424 #2215)
-#2217 := [sk]: #2216
-#2222 := [nnf-neg #2217]: #2221
-#2204 := (~ #2203 #2203)
-#2205 := [refl]: #2204
-#2201 := (~ #757 #757)
-#2202 := [refl]: #2201
-#2452 := [nnf-neg #2202 #2205 #2222 #2229 #2432 #2439 #2446 #2448]: #2451
-#2198 := (not #1442)
-#2199 := (~ #2198 #2197)
-#2195 := (~ #1665 #2194)
-#2192 := (~ #2191 #2191)
-#2193 := [refl]: #2192
-#2196 := [nnf-neg #2193]: #2195
-#2188 := (not #1413)
-#2189 := (~ #2188 #2187)
-#2184 := (not #1410)
-#2185 := (~ #2184 #2183)
-#2180 := (not #1407)
-#2181 := (~ #2180 #2179)
-#2176 := (not #1402)
-#2177 := (~ #2176 #2175)
-#2172 := (not #1394)
-#2173 := (~ #2172 #1391)
-#2170 := (~ #1391 #1391)
-#2168 := (~ #1388 #1388)
-#2169 := [refl]: #2168
-#2171 := [nnf-pos #2169]: #2170
-#2174 := [nnf-neg #2171]: #2173
-#2166 := (~ #2165 #2165)
-#2167 := [refl]: #2166
-#2178 := [nnf-neg #2167 #2174]: #2177
-#2161 := (~ #1394 #2160)
-#2162 := [sk]: #2161
-#2182 := [nnf-neg #2162 #2178]: #2181
-#2136 := (not #1376)
-#2137 := (~ #2136 #2133)
-#2134 := (~ #1373 #2133)
-#2131 := (~ #1370 #2130)
-#2126 := (~ #1367 #2125)
-#2127 := [sk]: #2126
-#2114 := (~ #1351 #1351)
-#2115 := [refl]: #2114
-#2132 := [monotonicity #2115 #2127]: #2131
-#2135 := [nnf-pos #2132]: #2134
-#2138 := [nnf-neg #2135]: #2137
-#2186 := [nnf-neg #2138 #2182]: #2185
-#2112 := (~ #1376 #2109)
-#2087 := (exists (vars (?v1 S3)) #2086)
-#2095 := (or #2094 #2087)
-#2096 := (not #2095)
-#2110 := (~ #2096 #2109)
-#2106 := (not #2087)
-#2107 := (~ #2106 #2105)
-#2103 := (~ #2102 #2102)
-#2104 := [refl]: #2103
-#2108 := [nnf-neg #2104]: #2107
-#2100 := (~ #2099 #2099)
-#2101 := [refl]: #2100
-#2111 := [nnf-neg #2101 #2108]: #2110
-#2097 := (~ #1376 #2096)
-#2098 := [sk]: #2097
-#2113 := [trans #2098 #2111]: #2112
-#2190 := [nnf-neg #2113 #2186]: #2189
-#2074 := (~ #2073 #2073)
-#2075 := [refl]: #2074
-#2071 := (~ #2070 #2070)
-#2072 := [refl]: #2071
-#2068 := (~ #2067 #2067)
-#2069 := [refl]: #2068
+#2358 := (not #1570)
+#2374 := (~ #2358 #2371)
+#2348 := (exists (vars (?v1 S3)) #2347)
+#2356 := (or #2355 #2348)
+#2357 := (not #2356)
+#2372 := (~ #2357 #2371)
+#2368 := (not #2348)
+#2369 := (~ #2368 #2367)
+#2365 := (~ #2364 #2364)
+#2366 := [refl]: #2365
+#2370 := [nnf-neg #2366]: #2369
+#2362 := (~ #2361 #2361)
+#2363 := [refl]: #2362
+#2373 := [nnf-neg #2363 #2370]: #2372
+#2359 := (~ #2358 #2357)
+#2360 := [sk]: #2359
+#2375 := [trans #2360 #2373]: #2374
+#2334 := (not #1533)
+#2335 := (~ #2334 #1530)
+#2332 := (~ #1530 #1530)
+#2330 := (~ #1527 #1527)
+#2331 := [refl]: #2330
+#2333 := [nnf-pos #2331]: #2332
+#2336 := [nnf-neg #2333]: #2335
+#2379 := [nnf-neg #2336 #2375]: #2378
+#2326 := (~ #1533 #2325)
+#2327 := [sk]: #2326
+#2383 := [nnf-neg #2327 #2379]: #2382
+#2303 := (not #1509)
+#2304 := (~ #2303 #1506)
+#2301 := (~ #1506 #1506)
+#2299 := (~ #1501 #1501)
+#2300 := [refl]: #2299
+#2302 := [nnf-pos #2300]: #2301
+#2305 := [nnf-neg #2302]: #2304
+#2387 := [nnf-neg #2305 #2383]: #2386
+#2295 := (~ #1509 #2294)
+#2296 := [sk]: #2295
+#2391 := [nnf-neg #2296 #2387]: #2390
+#2276 := (not #1490)
+#2277 := (~ #2276 #1487)
+#2274 := (~ #1487 #1487)
+#2272 := (~ #1484 #1484)
+#2273 := [refl]: #2272
+#2275 := [nnf-pos #2273]: #2274
+#2278 := [nnf-neg #2275]: #2277
+#2395 := [nnf-neg #2278 #2391]: #2394
+#2268 := (~ #1490 #2267)
+#2269 := [sk]: #2268
+#2399 := [nnf-neg #2269 #2395]: #2398
+#2262 := (~ #2261 #2261)
+#2263 := [refl]: #2262
+#2403 := [nnf-neg #2263 #2399]: #2402
+#2259 := (~ #1481 #1481)
+#2260 := [refl]: #2259
+#2407 := [nnf-neg #2260 #2403]: #2406
+#2256 := (not #944)
+#2257 := (~ #2256 #810)
+#2254 := (~ #810 #810)
+#2252 := (~ #805 #805)
+#2253 := [refl]: #2252
+#2255 := [nnf-pos #2253]: #2254
+#2258 := [nnf-neg #2255]: #2257
+#2411 := [nnf-neg #2258 #2407]: #2410
+#2248 := (~ #944 #2247)
+#2249 := [sk]: #2248
+#2415 := [nnf-neg #2249 #2411]: #2414
+#2236 := (not #1476)
+#2237 := (~ #2236 #1473)
+#2234 := (~ #1473 #1473)
+#2232 := (~ #1468 #1468)
+#2233 := [refl]: #2232
+#2235 := [nnf-pos #2233]: #2234
+#2238 := [nnf-neg #2235]: #2237
+#2419 := [nnf-neg #2238 #2415]: #2418
+#2228 := (~ #1476 #2227)
+#2229 := [sk]: #2228
+#2423 := [nnf-neg #2229 #2419]: #2422
+#2218 := (not #1465)
+#2219 := (~ #2218 #1462)
+#2216 := (~ #1462 #1462)
+#2214 := (~ #1457 #1457)
+#2215 := [refl]: #2214
+#2217 := [nnf-pos #2215]: #2216
+#2220 := [nnf-neg #2217]: #2219
+#2211 := (not #1656)
+#2212 := (~ #2211 #2206)
+#2207 := (~ #1415 #2206)
+#2208 := [sk]: #2207
+#2213 := [nnf-neg #2208]: #2212
+#2195 := (~ #756 #756)
+#2196 := [refl]: #2195
+#2193 := (~ #2192 #2192)
+#2194 := [refl]: #2193
+#2443 := [nnf-neg #2194 #2196 #2213 #2220 #2423 #2430 #2437 #2439]: #2442
+#2189 := (not #1433)
+#2190 := (~ #2189 #2188)
+#2186 := (~ #1656 #2185)
+#2183 := (~ #2182 #2182)
+#2184 := [refl]: #2183
+#2187 := [nnf-neg #2184]: #2186
+#2179 := (not #1404)
+#2180 := (~ #2179 #2178)
+#2175 := (not #1401)
+#2176 := (~ #2175 #2174)
+#2171 := (not #1398)
+#2172 := (~ #2171 #2170)
+#2167 := (not #1393)
+#2168 := (~ #2167 #2166)
+#2163 := (not #1385)
+#2164 := (~ #2163 #1382)
+#2161 := (~ #1382 #1382)
+#2159 := (~ #1379 #1379)
+#2160 := [refl]: #2159
+#2162 := [nnf-pos #2160]: #2161
+#2165 := [nnf-neg #2162]: #2164
+#2157 := (~ #2156 #2156)
+#2158 := [refl]: #2157
+#2169 := [nnf-neg #2158 #2165]: #2168
+#2152 := (~ #1385 #2151)
+#2153 := [sk]: #2152
+#2173 := [nnf-neg #2153 #2169]: #2172
+#2127 := (not #1367)
+#2128 := (~ #2127 #2124)
+#2125 := (~ #1364 #2124)
+#2122 := (~ #1361 #2121)
+#2117 := (~ #1358 #2116)
+#2118 := [sk]: #2117
+#2105 := (~ #1342 #1342)
+#2106 := [refl]: #2105
+#2123 := [monotonicity #2106 #2118]: #2122
+#2126 := [nnf-pos #2123]: #2125
+#2129 := [nnf-neg #2126]: #2128
+#2177 := [nnf-neg #2129 #2173]: #2176
+#2103 := (~ #1367 #2100)
+#2078 := (exists (vars (?v1 S3)) #2077)
+#2086 := (or #2085 #2078)
+#2087 := (not #2086)
+#2101 := (~ #2087 #2100)
+#2097 := (not #2078)
+#2098 := (~ #2097 #2096)
+#2094 := (~ #2093 #2093)
+#2095 := [refl]: #2094
+#2099 := [nnf-neg #2095]: #2098
+#2091 := (~ #2090 #2090)
+#2092 := [refl]: #2091
+#2102 := [nnf-neg #2092 #2099]: #2101
+#2088 := (~ #1367 #2087)
+#2089 := [sk]: #2088
+#2104 := [trans #2089 #2102]: #2103
+#2181 := [nnf-neg #2104 #2177]: #2180
 #2065 := (~ #2064 #2064)
 #2066 := [refl]: #2065
-#2200 := [nnf-neg #2066 #2069 #2072 #2075 #2190 #2196]: #2199
-#2456 := [nnf-neg #2200 #2452]: #2455
-#2061 := (not #1339)
-#2062 := (~ #2061 #2058)
-#2059 := (~ #1336 #2058)
-#2056 := (~ #1333 #2055)
-#2051 := (~ #1330 #2050)
-#2052 := [sk]: #2051
-#2037 := (~ #1306 #1306)
-#2038 := [refl]: #2037
-#2057 := [monotonicity #2038 #2052]: #2056
-#2060 := [nnf-pos #2057]: #2059
-#2063 := [nnf-neg #2060]: #2062
-#2034 := (not #1750)
-#2035 := (~ #2034 #2031)
-#2032 := (~ #1294 #2031)
-#2029 := (~ #1291 #2028)
-#2024 := (~ #1288 #2023)
-#2025 := [sk]: #2024
-#2009 := (~ #1268 #1268)
-#2010 := [refl]: #2009
-#2030 := [monotonicity #2010 #2025]: #2029
-#2033 := [nnf-pos #2030]: #2032
-#2036 := [nnf-neg #2033]: #2035
-#2007 := (~ #2006 #2006)
-#2008 := [refl]: #2007
-#2481 := [nnf-neg #2008 #2036 #2063 #2456 #2463 #2470 #2477]: #2480
-#2004 := (~ #1750 #2001)
-#1979 := (exists (vars (?v1 S3)) #1978)
-#1987 := (or #1986 #1979)
-#1988 := (not #1987)
-#2002 := (~ #1988 #2001)
-#1998 := (not #1979)
-#1999 := (~ #1998 #1997)
-#1995 := (~ #1994 #1994)
-#1996 := [refl]: #1995
-#2000 := [nnf-neg #1996]: #1999
-#1992 := (~ #1991 #1991)
-#1993 := [refl]: #1992
-#2003 := [nnf-neg #1993 #2000]: #2002
-#1989 := (~ #1750 #1988)
-#1990 := [sk]: #1989
-#2005 := [trans #1990 #2003]: #2004
-#2485 := [nnf-neg #2005 #2481]: #2484
-#1964 := (not #1256)
-#1965 := (~ #1964 #1253)
-#1962 := (~ #1253 #1253)
-#1960 := (~ #1250 #1250)
-#1961 := [refl]: #1960
-#1963 := [nnf-pos #1961]: #1962
-#1966 := [nnf-neg #1963]: #1965
-#2489 := [nnf-neg #1966 #2485]: #2488
-#1956 := (~ #1256 #1955)
-#1957 := [sk]: #1956
-#2493 := [nnf-neg #1957 #2489]: #2492
-#1933 := (not #1225)
-#1934 := (~ #1933 #1222)
-#1931 := (~ #1222 #1222)
-#1929 := (~ #1217 #1217)
-#1930 := [refl]: #1929
-#1932 := [nnf-pos #1930]: #1931
-#1935 := [nnf-neg #1932]: #1934
-#2497 := [nnf-neg #1935 #2493]: #2496
-#1925 := (~ #1225 #1924)
-#1926 := [sk]: #1925
-#2501 := [nnf-neg #1926 #2497]: #2500
-#1906 := (not #1205)
-#1907 := (~ #1906 #1202)
-#1904 := (~ #1202 #1202)
-#1902 := (~ #1201 #1201)
-#1903 := [refl]: #1902
-#1905 := [nnf-pos #1903]: #1904
-#1908 := [nnf-neg #1905]: #1907
-#2505 := [nnf-neg #1908 #2501]: #2504
-#1898 := (~ #1205 #1897)
-#1899 := [sk]: #1898
-#2509 := [nnf-neg #1899 #2505]: #2508
-#1861 := (~ #1860 #1860)
-#1893 := [refl]: #1861
-#2513 := [nnf-neg #1893 #2509]: #2512
-#1891 := (~ #1196 #1196)
-#1892 := [refl]: #1891
-#2516 := [nnf-neg #1892 #2513]: #2515
-#1837 := [not-or-elim #1833]: #1836
-#2517 := [mp~ #1837 #2516]: #2514
-#2518 := [mp #2517 #3055]: #3053
-#3697 := [mp #2518 #3696]: #3694
-#4604 := [mp #3697 #4603]: #4601
-#6496 := [unit-resolution #4604 #5320]: #4598
-#3943 := (or #4595 #4589)
-#3944 := [def-axiom]: #3943
-#6497 := [unit-resolution #3944 #6496]: #4589
-#6498 := (or #4592 #4586)
-#5107 := [hypothesis]: #1897
-#5106 := (<= #1895 0::Int)
-#4721 := (or #5106 #1896)
-#5139 := [th-lemma arith farkas 1 1]: #4721
-#5140 := [unit-resolution #5139 #5107]: #5106
-#5099 := (not #5106)
-#5114 := (or #5099 #1896)
-#355 := (<= f8 0::Int)
-#356 := (not #355)
+#2062 := (~ #2061 #2061)
+#2063 := [refl]: #2062
+#2059 := (~ #2058 #2058)
+#2060 := [refl]: #2059
+#2056 := (~ #2055 #2055)
+#2057 := [refl]: #2056
+#2191 := [nnf-neg #2057 #2060 #2063 #2066 #2181 #2187]: #2190
+#2447 := [nnf-neg #2191 #2443]: #2446
+#2052 := (not #1330)
+#2053 := (~ #2052 #2049)
+#2050 := (~ #1327 #2049)
+#2047 := (~ #1324 #2046)
+#2042 := (~ #1321 #2041)
+#2043 := [sk]: #2042
+#2028 := (~ #1297 #1297)
+#2029 := [refl]: #2028
+#2048 := [monotonicity #2029 #2043]: #2047
+#2051 := [nnf-pos #2048]: #2050
+#2054 := [nnf-neg #2051]: #2053
+#2025 := (not #1741)
+#2026 := (~ #2025 #2022)
+#2023 := (~ #1285 #2022)
+#2020 := (~ #1282 #2019)
+#2015 := (~ #1279 #2014)
+#2016 := [sk]: #2015
+#2000 := (~ #1259 #1259)
+#2001 := [refl]: #2000
+#2021 := [monotonicity #2001 #2016]: #2020
+#2024 := [nnf-pos #2021]: #2023
+#2027 := [nnf-neg #2024]: #2026
+#1998 := (~ #1997 #1997)
+#1999 := [refl]: #1998
+#2472 := [nnf-neg #1999 #2027 #2054 #2447 #2454 #2461 #2468]: #2471
+#1995 := (~ #1741 #1992)
+#1970 := (exists (vars (?v1 S3)) #1969)
+#1978 := (or #1977 #1970)
+#1979 := (not #1978)
+#1993 := (~ #1979 #1992)
+#1989 := (not #1970)
+#1990 := (~ #1989 #1988)
+#1986 := (~ #1985 #1985)
+#1987 := [refl]: #1986
+#1991 := [nnf-neg #1987]: #1990
+#1983 := (~ #1982 #1982)
+#1984 := [refl]: #1983
+#1994 := [nnf-neg #1984 #1991]: #1993
+#1980 := (~ #1741 #1979)
+#1981 := [sk]: #1980
+#1996 := [trans #1981 #1994]: #1995
+#2476 := [nnf-neg #1996 #2472]: #2475
+#1955 := (not #1247)
+#1956 := (~ #1955 #1244)
+#1953 := (~ #1244 #1244)
+#1951 := (~ #1241 #1241)
+#1952 := [refl]: #1951
+#1954 := [nnf-pos #1952]: #1953
+#1957 := [nnf-neg #1954]: #1956
+#2480 := [nnf-neg #1957 #2476]: #2479
+#1947 := (~ #1247 #1946)
+#1948 := [sk]: #1947
+#2484 := [nnf-neg #1948 #2480]: #2483
+#1924 := (not #1216)
+#1925 := (~ #1924 #1213)
+#1922 := (~ #1213 #1213)
+#1920 := (~ #1208 #1208)
+#1921 := [refl]: #1920
+#1923 := [nnf-pos #1921]: #1922
+#1926 := [nnf-neg #1923]: #1925
+#2488 := [nnf-neg #1926 #2484]: #2487
+#1916 := (~ #1216 #1915)
+#1917 := [sk]: #1916
+#2492 := [nnf-neg #1917 #2488]: #2491
+#1897 := (not #1196)
+#1898 := (~ #1897 #1193)
+#1895 := (~ #1193 #1193)
+#1893 := (~ #1192 #1192)
+#1894 := [refl]: #1893
+#1896 := [nnf-pos #1894]: #1895
+#1899 := [nnf-neg #1896]: #1898
+#2496 := [nnf-neg #1899 #2492]: #2495
+#1889 := (~ #1196 #1888)
+#1890 := [sk]: #1889
+#2500 := [nnf-neg #1890 #2496]: #2499
+#1852 := (~ #1851 #1851)
+#1884 := [refl]: #1852
+#2504 := [nnf-neg #1884 #2500]: #2503
+#1882 := (~ #1187 #1187)
+#1883 := [refl]: #1882
+#2507 := [nnf-neg #1883 #2504]: #2506
+#1828 := [not-or-elim #1824]: #1827
+#2508 := [mp~ #1828 #2507]: #2505
+#2509 := [mp #2508 #3046]: #3044
+#3688 := [mp #2509 #3687]: #3685
+#4595 := [mp #3688 #4594]: #4592
+#6487 := [unit-resolution #4595 #5311]: #4589
+#3934 := (or #4586 #4580)
+#3935 := [def-axiom]: #3934
+#6488 := [unit-resolution #3935 #6487]: #4580
+#6489 := (or #4583 #4577)
+#5098 := [hypothesis]: #1888
+#5097 := (<= #1886 0::Int)
+#4712 := (or #5097 #1887)
+#5130 := [th-lemma arith farkas 1 1]: #4712
+#5131 := [unit-resolution #5130 #5098]: #5097
+#5090 := (not #5097)
+#5105 := (or #5090 #1887)
+#354 := (<= f8 0::Int)
+#355 := (not #354)
 #46 := (< 0::Int f8)
-#357 := (iff #46 #356)
-#358 := [rewrite]: #357
-#351 := [asserted]: #46
-#359 := [mp #351 #358]: #356
-#4718 := (* -1::Int #1895)
-#4719 := (+ f8 #4718)
-#4720 := (<= #4719 0::Int)
-#3933 := (= f8 #1895)
-#3912 := (= f10 ?v0!0)
-#4911 := (not #3912)
-#4908 := (= #1895 0::Int)
-#5108 := (not #4908)
-#5109 := (or #5108 #1896)
-#5110 := [th-lemma arith triangle-eq]: #5109
-#5090 := [unit-resolution #5110 #5107]: #5108
-#4917 := (or #4784 #4911 #4908)
-#3932 := (= ?v0!0 f10)
-#4909 := (not #3932)
-#4910 := (or #4909 #4908)
-#4648 := (or #4784 #4910)
-#5103 := (iff #4648 #4917)
-#4715 := (or #4911 #4908)
-#4934 := (or #4784 #4715)
-#4980 := (iff #4934 #4917)
-#5102 := [rewrite]: #4980
-#4978 := (iff #4648 #4934)
-#4716 := (iff #4910 #4715)
-#4914 := (iff #4909 #4911)
-#3914 := (iff #3932 #3912)
-#3915 := [rewrite]: #3914
-#4915 := [monotonicity #3915]: #4914
-#4783 := [monotonicity #4915]: #4716
-#4979 := [monotonicity #4783]: #4978
-#5104 := [trans #4979 #5102]: #5103
-#4931 := [quant-inst #1894]: #4648
-#5105 := [mp #4931 #5104]: #4917
-#5091 := [unit-resolution #5105 #4610 #5090]: #4911
-#3927 := (or #3912 #3933)
-#4219 := (forall (vars (?v0 S3)) (:pat #4218) #446)
-#4222 := (iff #451 #4219)
-#4220 := (iff #446 #446)
-#4221 := [refl]: #4220
-#4223 := [quant-intro #4221]: #4222
-#1856 := (~ #451 #451)
-#1885 := (~ #446 #446)
-#1886 := [refl]: #1885
-#1857 := [nnf-pos #1886]: #1856
-#1834 := [not-or-elim #1833]: #451
-#1887 := [mp~ #1834 #1857]: #451
-#4224 := [mp #1887 #4223]: #4219
-#3923 := (not #4219)
-#3916 := (or #3923 #3912 #3933)
-#3922 := (or #3932 #3933)
-#3924 := (or #3923 #3922)
-#4662 := (iff #3924 #3916)
-#3909 := (or #3923 #3927)
-#4646 := (iff #3909 #3916)
-#4661 := [rewrite]: #4646
-#4644 := (iff #3924 #3909)
-#3918 := (iff #3922 #3927)
-#3919 := [monotonicity #3915]: #3918
-#4645 := [monotonicity #3919]: #4644
-#4643 := [trans #4645 #4661]: #4662
-#3907 := [quant-inst #1894]: #3924
-#4717 := [mp #3907 #4643]: #3916
-#5092 := [unit-resolution #4717 #4224]: #3927
-#5093 := [unit-resolution #5092 #5091]: #3933
-#5094 := (not #3933)
-#5089 := (or #5094 #4720)
-#5095 := [th-lemma arith triangle-eq]: #5089
-#5096 := [unit-resolution #5095 #5093]: #4720
-#5097 := [hypothesis]: #5106
-#5098 := [th-lemma arith farkas 1 -1 1 #5097 #5096 #359]: false
-#5115 := [lemma #5098]: #5114
-#5141 := [unit-resolution #5115 #5140 #5107]: false
-#5142 := [lemma #5141]: #1896
-#3938 := (or #4592 #1897 #4586)
-#3939 := [def-axiom]: #3938
-#6499 := [unit-resolution #3939 #5142]: #6498
-#6500 := [unit-resolution #6499 #6497]: #4586
-#3962 := (or #4583 #4577)
-#3963 := [def-axiom]: #3962
-#6501 := [unit-resolution #3963 #6500]: #4577
-#5817 := [hypothesis]: #1917
-#5330 := (or #5529 #2054)
-#5335 := [quant-inst #1910]: #5330
-#5818 := [unit-resolution #5335 #4231 #5817]: false
-#5819 := [lemma #5818]: #2054
-#3755 := (or #2026 #1917)
-#3842 := [def-axiom]: #3755
-#6502 := [unit-resolution #3842 #5819]: #2026
-#3956 := (or #4580 #1928 #4574)
-#3958 := [def-axiom]: #3956
-#6503 := [unit-resolution #3958 #6502 #6501]: #4574
-#3983 := (or #4571 #4565)
-#3984 := [def-axiom]: #3983
-#6504 := [unit-resolution #3984 #6503]: #4565
-#3979 := (or #4568 #3098 #4562)
-#3980 := [def-axiom]: #3979
-#6505 := [unit-resolution #3980 #6504 #6495]: #4562
-#3993 := (or #4559 #4553)
-#4014 := [def-axiom]: #3993
-#6506 := [unit-resolution #4014 #6505]: #4553
-#5790 := (= f8 #1970)
-#5854 := (not #5790)
-#5852 := [hypothesis]: #4270
-#4159 := (or #4267 #1982)
-#3833 := [def-axiom]: #4159
-#5853 := [unit-resolution #3833 #5852]: #1982
-#5855 := (or #5854 #1981)
-#5856 := [th-lemma arith triangle-eq]: #5855
-#5857 := [unit-resolution #5856 #5853]: #5854
-#3834 := (or #4267 #2569)
-#4166 := [def-axiom]: #3834
-#5858 := [unit-resolution #4166 #5852]: #2569
-#5810 := (or #3923 #2566 #5790)
-#5791 := (or #1983 #5790)
-#5805 := (or #3923 #5791)
-#5669 := (iff #5805 #5810)
-#5807 := (or #2566 #5790)
-#5812 := (or #3923 #5807)
-#5815 := (iff #5812 #5810)
-#5668 := [rewrite]: #5815
-#5813 := (iff #5805 #5812)
-#5808 := (iff #5791 #5807)
-#5809 := [monotonicity #2568]: #5808
-#5814 := [monotonicity #5809]: #5813
-#5670 := [trans #5814 #5668]: #5669
-#5811 := [quant-inst #1967]: #5805
-#5475 := [mp #5811 #5670]: #5810
-#5859 := [unit-resolution #5475 #4224 #5858 #5857]: false
-#5860 := [lemma #5859]: #4267
-#4001 := (or #4556 #4270 #4550)
-#4002 := [def-axiom]: #4001
-#6507 := [unit-resolution #4002 #5860 #6506]: #4550
-#4034 := (or #4547 #4274)
-#4030 := [def-axiom]: #4034
-#7121 := [unit-resolution #4030 #6507]: #4274
-#9553 := (or #4279 #7757)
-#9554 := [quant-inst #2273]: #9553
-#9580 := [unit-resolution #9554 #7121]: #7757
-#7570 := (* -1::Int #7536)
-#7571 := (+ #2274 #7570)
-#9581 := (>= #7571 0::Int)
-#7539 := (= #2274 #7536)
-#10087 := [hypothesis]: #2276
-#11985 := (or #7539 #2275 #6073)
-#9988 := (f5 #7211 ?v0!15)
-#9989 := (f9 #9988)
-#9990 := (* -1::Int #9989)
-#7586 := (f5 f22 ?v0!15)
-#7587 := (f9 #7586)
-#10058 := (+ #7587 #9990)
-#10062 := (>= #10058 0::Int)
-#10057 := (= #7587 #9989)
-#10065 := (= #9989 #7587)
-#10063 := (= #9988 #7586)
-#10064 := [monotonicity #7790]: #10063
-#10066 := [monotonicity #10064]: #10065
-#10067 := [symm #10066]: #10057
-#10068 := (not #10057)
-#10069 := (or #10068 #10062)
-#10070 := [th-lemma arith triangle-eq]: #10069
-#10071 := [unit-resolution #10070 #10067]: #10062
-#7968 := (f5 #6069 #7211)
-#8217 := (f6 #7968)
-#9081 := (f13 f14 #8217)
-#9082 := (* -1::Int #9081)
-#9455 := (+ #6070 #9082)
-#9457 := (>= #9455 0::Int)
-#9861 := (= #6070 #9081)
-#8218 := (= #6069 #8217)
-#8389 := (or #6829 #8218)
-#8390 := [quant-inst #6069 #7211]: #8389
-#9280 := [unit-resolution #8390 #4205]: #8218
-#11947 := [monotonicity #9280]: #9861
-#11945 := (not #9861)
-#11948 := (or #11945 #9457)
-#11949 := [th-lemma arith triangle-eq]: #11948
-#11950 := [unit-resolution #11949 #11947]: #9457
-#10866 := (+ #99 #9082)
-#10878 := (<= #10866 0::Int)
-#10875 := (= #99 #9081)
-#11956 := (= #9081 #99)
-#10697 := (= #8217 f10)
-#7317 := (= #6069 f10)
-#7319 := (= f10 #6069)
-#7298 := (?v1!7 #6069)
-#7310 := (f3 f15 #7298)
-#7311 := (= f1 #7310)
-#7312 := (not #7311)
-#7303 := (f5 #7298 #6069)
-#7304 := (f9 #7303)
-#7305 := (* -1::Int #7304)
-#7299 := (f13 f14 #7298)
-#7300 := (* -1::Int #7299)
-#7306 := (+ #7300 #7305)
-#7307 := (+ #6070 #7306)
-#7308 := (= #7307 0::Int)
-#7309 := (not #7308)
-#7301 := (+ #6070 #7300)
-#7302 := (<= #7301 0::Int)
-#7322 := (or #7302 #7309 #7312)
-#9607 := (or #2275 #6073 #7302)
-#8251 := (not #7302)
-#10072 := [hypothesis]: #8251
-#10110 := (or #7539 #2275 #6073 #7302)
-#9125 := (>= #7299 0::Int)
-#9128 := (or #4279 #9125)
-#9299 := [quant-inst #7298]: #9128
-#10073 := [unit-resolution #9299 #7121]: #9125
-#7561 := (* -1::Int #2274)
-#7612 := (+ #7561 #7587)
-#7613 := (+ #174 #7612)
-#9497 := (<= #7613 0::Int)
-#7616 := (= #7613 0::Int)
-#7591 := (* -1::Int #7587)
-#7595 := (+ f8 #7591)
-#7596 := (<= #7595 0::Int)
-#9510 := (not #7596)
-#7605 := (+ #7570 #7587)
-#7606 := (+ #174 #7605)
-#7607 := (>= #7606 0::Int)
-#7638 := (or #7596 #7607)
-#7641 := (not #7638)
-#10075 := (not #7539)
-#10076 := [hypothesis]: #10075
-#7644 := (or #7539 #7641)
-#5788 := (or #4547 #4538)
-#4722 := (?v1!7 ?v0!8)
-#4998 := (f13 f19 #4722)
-#5011 := (* -1::Int #4998)
-#4723 := (f13 f14 #4722)
-#5231 := (+ #4723 #5011)
-#5236 := (>= #5231 0::Int)
-#5230 := (= #4723 #4998)
-#5720 := (= #4998 #4723)
-#5715 := [hypothesis]: #4535
-#5716 := [hypothesis]: #4550
-#4023 := (or #4547 #4541)
-#3991 := [def-axiom]: #4023
-#5717 := [unit-resolution #3991 #5716]: #4541
-#4028 := (or #4544 #4383 #4538)
-#4029 := [def-axiom]: #4028
-#5718 := [unit-resolution #4029 #5717 #5715]: #4383
-#4134 := (or #4380 #624)
-#4135 := [def-axiom]: #4134
-#5719 := [unit-resolution #4135 #5718]: #624
-#5714 := [symm #5719]: #138
-#5721 := [monotonicity #5714]: #5720
-#5722 := [symm #5721]: #5230
-#5723 := (not #5230)
-#5724 := (or #5723 #5236)
-#5737 := [th-lemma arith triangle-eq]: #5724
-#5738 := [unit-resolution #5737 #5722]: #5236
-#4705 := (* -1::Int #4723)
-#4655 := (f13 f14 ?v0!8)
-#4706 := (+ #4655 #4705)
-#4707 := (<= #4706 0::Int)
-#4888 := (not #4707)
-#4714 := (f3 f15 #4722)
-#4785 := (= f1 #4714)
-#4786 := (not #4785)
-#4708 := (f5 #4722 ?v0!8)
-#4709 := (f9 #4708)
-#4704 := (* -1::Int #4709)
-#4790 := (+ #4704 #4705)
-#4791 := (+ #4655 #4790)
-#4773 := (= #4791 0::Int)
-#4776 := (not #4773)
-#4781 := (or #4707 #4776 #4786)
-#4855 := (not #4781)
-#4656 := (* -1::Int #4655)
-#4657 := (+ f8 #4656)
-#4637 := (<= #4657 0::Int)
-#4993 := (not #4637)
-#4136 := (or #4380 #4374)
-#4133 := [def-axiom]: #4136
-#5739 := [unit-resolution #4133 #5718]: #4374
-#4032 := (or #4547 #100)
-#4033 := [def-axiom]: #4032
-#5740 := [unit-resolution #4033 #5716]: #100
-#5741 := (= #157 #99)
-#5736 := [monotonicity #5714]: #5741
-#5742 := [trans #5736 #5740]: #158
-#4146 := (or #4356 #2165)
-#3809 := [def-axiom]: #4146
-#5743 := [unit-resolution #3809 #5742]: #4356
-#4035 := (or #4547 #4282)
-#4015 := [def-axiom]: #4035
-#5744 := [unit-resolution #4015 #5716]: #4282
-#3850 := (or #4380 #4316)
-#4132 := [def-axiom]: #3850
-#5745 := [unit-resolution #4132 #5718]: #4316
-#4976 := (or #3361 #4321 #4287 #715)
-#4949 := [hypothesis]: #3366
-#4149 := (or #3361 #2152)
-#4150 := [def-axiom]: #4149
-#4950 := [unit-resolution #4150 #4949]: #2152
-#4724 := (f13 f14 ?v1!10)
-#4725 := (* -1::Int #4724)
-#4726 := (+ f8 #4725)
-#4727 := (<= #4726 0::Int)
-#4728 := (f3 f15 ?v1!10)
-#4729 := (= f1 #4728)
-#4800 := (not #4729)
-#3837 := (f13 f14 ?v0!11)
-#3838 := (* -1::Int #3837)
-#4802 := (+ #3838 #4724)
-#4803 := (+ #2146 #4802)
-#4806 := (>= #4803 0::Int)
-#4959 := (not #4806)
-#4933 := (+ #2143 #4725)
-#4935 := (>= #4933 0::Int)
-#4932 := (= #2143 #4724)
-#4937 := (= #4724 #2143)
-#4936 := [hypothesis]: #624
-#4938 := [monotonicity #4936]: #4937
-#4939 := [symm #4938]: #4932
-#4940 := (not #4932)
-#4941 := (or #4940 #4935)
-#4942 := [th-lemma arith triangle-eq]: #4941
-#4943 := [unit-resolution #4942 #4939]: #4935
-#4147 := (not #2807)
-#4153 := (or #3361 #4147)
-#3791 := [def-axiom]: #4153
-#4944 := [unit-resolution #3791 #4949]: #4147
-#4926 := (+ #2141 #3838)
-#4930 := (<= #4926 0::Int)
-#4925 := (= #2141 #3837)
-#4947 := (= #3837 #2141)
-#4948 := [monotonicity #4936]: #4947
-#4951 := [symm #4948]: #4925
-#4952 := (not #4925)
-#4953 := (or #4952 #4930)
-#4964 := [th-lemma arith triangle-eq]: #4953
-#4965 := [unit-resolution #4964 #4951]: #4930
-#4961 := (not #4935)
-#4960 := (not #4930)
-#4962 := (or #4959 #4960 #2807 #4961)
-#4954 := [hypothesis]: #4935
-#4955 := [hypothesis]: #4147
-#4956 := [hypothesis]: #4930
-#4957 := [hypothesis]: #4806
-#4958 := [th-lemma arith farkas 1 -1 1 1 #4957 #4956 #4955 #4954]: false
-#4963 := [lemma #4958]: #4962
-#4966 := [unit-resolution #4963 #4965 #4944 #4943]: #4959
-#4969 := (or #4800 #4806)
-#4151 := (or #3361 #2156)
-#4152 := [def-axiom]: #4151
-#4967 := [unit-resolution #4152 #4949]: #2156
-#4968 := [hypothesis]: #4282
-#4817 := (or #4287 #2155 #4800 #4806)
-#4795 := (+ #4724 #3838)
-#4796 := (+ #2146 #4795)
-#4799 := (>= #4796 0::Int)
-#4801 := (or #4800 #2155 #4799)
-#4818 := (or #4287 #4801)
-#4825 := (iff #4818 #4817)
-#4812 := (or #2155 #4800 #4806)
-#4820 := (or #4287 #4812)
-#4823 := (iff #4820 #4817)
-#4824 := [rewrite]: #4823
-#4821 := (iff #4818 #4820)
-#4815 := (iff #4801 #4812)
-#4809 := (or #4800 #2155 #4806)
-#4813 := (iff #4809 #4812)
-#4814 := [rewrite]: #4813
-#4810 := (iff #4801 #4809)
-#4807 := (iff #4799 #4806)
-#4804 := (= #4796 #4803)
+#356 := (iff #46 #355)
+#357 := [rewrite]: #356
+#350 := [asserted]: #46
+#358 := [mp #350 #357]: #355
+#4709 := (* -1::Int #1886)
+#4710 := (+ f8 #4709)
+#4711 := (<= #4710 0::Int)
+#3924 := (= f8 #1886)
+#3903 := (= f10 ?v0!0)
+#4902 := (not #3903)
+#4899 := (= #1886 0::Int)
+#5099 := (not #4899)
+#5100 := (or #5099 #1887)
+#5101 := [th-lemma arith triangle-eq]: #5100
+#5081 := [unit-resolution #5101 #5098]: #5099
+#4908 := (or #4775 #4902 #4899)
+#3923 := (= ?v0!0 f10)
+#4900 := (not #3923)
+#4901 := (or #4900 #4899)
+#4639 := (or #4775 #4901)
+#5094 := (iff #4639 #4908)
+#4706 := (or #4902 #4899)
+#4925 := (or #4775 #4706)
+#4971 := (iff #4925 #4908)
+#5093 := [rewrite]: #4971
+#4969 := (iff #4639 #4925)
+#4707 := (iff #4901 #4706)
+#4905 := (iff #4900 #4902)
+#3905 := (iff #3923 #3903)
+#3906 := [rewrite]: #3905
+#4906 := [monotonicity #3906]: #4905
+#4774 := [monotonicity #4906]: #4707
+#4970 := [monotonicity #4774]: #4969
+#5095 := [trans #4970 #5093]: #5094
+#4922 := [quant-inst #1885]: #4639
+#5096 := [mp #4922 #5095]: #4908
+#5082 := [unit-resolution #5096 #4601 #5081]: #4902
+#3918 := (or #3903 #3924)
+#4210 := (forall (vars (?v0 S3)) (:pat #4209) #445)
+#4213 := (iff #450 #4210)
+#4211 := (iff #445 #445)
+#4212 := [refl]: #4211
+#4214 := [quant-intro #4212]: #4213
+#1847 := (~ #450 #450)
+#1876 := (~ #445 #445)
+#1877 := [refl]: #1876
+#1848 := [nnf-pos #1877]: #1847
+#1825 := [not-or-elim #1824]: #450
+#1878 := [mp~ #1825 #1848]: #450
+#4215 := [mp #1878 #4214]: #4210
+#3914 := (not #4210)
+#3907 := (or #3914 #3903 #3924)
+#3913 := (or #3923 #3924)
+#3915 := (or #3914 #3913)
+#4653 := (iff #3915 #3907)
+#3900 := (or #3914 #3918)
+#4637 := (iff #3900 #3907)
+#4652 := [rewrite]: #4637
+#4635 := (iff #3915 #3900)
+#3909 := (iff #3913 #3918)
+#3910 := [monotonicity #3906]: #3909
+#4636 := [monotonicity #3910]: #4635
+#4634 := [trans #4636 #4652]: #4653
+#3898 := [quant-inst #1885]: #3915
+#4708 := [mp #3898 #4634]: #3907
+#5083 := [unit-resolution #4708 #4215]: #3918
+#5084 := [unit-resolution #5083 #5082]: #3924
+#5085 := (not #3924)
+#5080 := (or #5085 #4711)
+#5086 := [th-lemma arith triangle-eq]: #5080
+#5087 := [unit-resolution #5086 #5084]: #4711
+#5088 := [hypothesis]: #5097
+#5089 := [th-lemma arith farkas 1 -1 1 #5088 #5087 #358]: false
+#5106 := [lemma #5089]: #5105
+#5132 := [unit-resolution #5106 #5131 #5098]: false
+#5133 := [lemma #5132]: #1887
+#3929 := (or #4583 #1888 #4577)
+#3930 := [def-axiom]: #3929
+#6490 := [unit-resolution #3930 #5133]: #6489
+#6491 := [unit-resolution #6490 #6488]: #4577
+#3953 := (or #4574 #4568)
+#3954 := [def-axiom]: #3953
+#6492 := [unit-resolution #3954 #6491]: #4568
+#5808 := [hypothesis]: #1908
+#5321 := (or #5520 #2210)
+#5326 := [quant-inst #1901]: #5321
+#5809 := [unit-resolution #5326 #4222 #5808]: false
+#5810 := [lemma #5809]: #2210
+#3746 := (or #2119 #1908)
+#3833 := [def-axiom]: #3746
+#6493 := [unit-resolution #3833 #5810]: #2119
+#3947 := (or #4571 #2018 #4565)
+#3949 := [def-axiom]: #3947
+#6494 := [unit-resolution #3949 #6493 #6492]: #4565
+#3974 := (or #4562 #4556)
+#3975 := [def-axiom]: #3974
+#6495 := [unit-resolution #3975 #6494]: #4556
+#3970 := (or #4559 #3089 #4553)
+#3971 := [def-axiom]: #3970
+#6496 := [unit-resolution #3971 #6495 #6486]: #4553
+#3984 := (or #4550 #4544)
+#4005 := [def-axiom]: #3984
+#6497 := [unit-resolution #4005 #6496]: #4544
+#5781 := (= f8 #1961)
+#5845 := (not #5781)
+#5843 := [hypothesis]: #4261
+#4150 := (or #4258 #1973)
+#3824 := [def-axiom]: #4150
+#5844 := [unit-resolution #3824 #5843]: #1973
+#5846 := (or #5845 #1972)
+#5847 := [th-lemma arith triangle-eq]: #5846
+#5848 := [unit-resolution #5847 #5844]: #5845
+#3825 := (or #4258 #2560)
+#4157 := [def-axiom]: #3825
+#5849 := [unit-resolution #4157 #5843]: #2560
+#5801 := (or #3914 #2557 #5781)
+#5782 := (or #1974 #5781)
+#5796 := (or #3914 #5782)
+#5660 := (iff #5796 #5801)
+#5798 := (or #2557 #5781)
+#5803 := (or #3914 #5798)
+#5806 := (iff #5803 #5801)
+#5659 := [rewrite]: #5806
+#5804 := (iff #5796 #5803)
+#5799 := (iff #5782 #5798)
+#5800 := [monotonicity #2559]: #5799
+#5805 := [monotonicity #5800]: #5804
+#5661 := [trans #5805 #5659]: #5660
+#5802 := [quant-inst #1958]: #5796
+#5466 := [mp #5802 #5661]: #5801
+#5850 := [unit-resolution #5466 #4215 #5849 #5848]: false
+#5851 := [lemma #5850]: #4258
+#3992 := (or #4547 #4261 #4541)
+#3993 := [def-axiom]: #3992
+#6498 := [unit-resolution #3993 #5851 #6497]: #4541
+#4025 := (or #4538 #4265)
+#4021 := [def-axiom]: #4025
+#7112 := [unit-resolution #4021 #6498]: #4265
+#9544 := (or #4270 #7748)
+#9545 := [quant-inst #2264]: #9544
+#9571 := [unit-resolution #9545 #7112]: #7748
+#7561 := (* -1::Int #7527)
+#7562 := (+ #2265 #7561)
+#9572 := (>= #7562 0::Int)
+#7530 := (= #2265 #7527)
+#10078 := [hypothesis]: #2267
+#11976 := (or #7530 #2266 #6064)
+#9979 := (f5 #7202 ?v0!15)
+#9980 := (f9 #9979)
+#9981 := (* -1::Int #9980)
+#7577 := (f5 f22 ?v0!15)
+#7578 := (f9 #7577)
+#10049 := (+ #7578 #9981)
+#10053 := (>= #10049 0::Int)
+#10048 := (= #7578 #9980)
+#10056 := (= #9980 #7578)
+#10054 := (= #9979 #7577)
+#10055 := [monotonicity #7781]: #10054
+#10057 := [monotonicity #10055]: #10056
+#10058 := [symm #10057]: #10048
+#10059 := (not #10048)
+#10060 := (or #10059 #10053)
+#10061 := [th-lemma arith triangle-eq]: #10060
+#10062 := [unit-resolution #10061 #10058]: #10053
+#7959 := (f5 #6060 #7202)
+#8208 := (f6 #7959)
+#9072 := (f13 f14 #8208)
+#9073 := (* -1::Int #9072)
+#9446 := (+ #6061 #9073)
+#9448 := (>= #9446 0::Int)
+#9852 := (= #6061 #9072)
+#8209 := (= #6060 #8208)
+#8380 := (or #6820 #8209)
+#8381 := [quant-inst #6060 #7202]: #8380
+#9271 := [unit-resolution #8381 #4196]: #8209
+#11938 := [monotonicity #9271]: #9852
+#11936 := (not #9852)
+#11939 := (or #11936 #9448)
+#11940 := [th-lemma arith triangle-eq]: #11939
+#11941 := [unit-resolution #11940 #11938]: #9448
+#10857 := (+ #99 #9073)
+#10869 := (<= #10857 0::Int)
+#10866 := (= #99 #9072)
+#11947 := (= #9072 #99)
+#10688 := (= #8208 f10)
+#7308 := (= #6060 f10)
+#7310 := (= f10 #6060)
+#7289 := (?v1!7 #6060)
+#7301 := (f3 f15 #7289)
+#7302 := (= f1 #7301)
+#7303 := (not #7302)
+#7294 := (f5 #7289 #6060)
+#7295 := (f9 #7294)
+#7296 := (* -1::Int #7295)
+#7290 := (f13 f14 #7289)
+#7291 := (* -1::Int #7290)
+#7297 := (+ #7291 #7296)
+#7298 := (+ #6061 #7297)
+#7299 := (= #7298 0::Int)
+#7300 := (not #7299)
+#7292 := (+ #6061 #7291)
+#7293 := (<= #7292 0::Int)
+#7313 := (or #7293 #7300 #7303)
+#9598 := (or #2266 #6064 #7293)
+#8242 := (not #7293)
+#10063 := [hypothesis]: #8242
+#10101 := (or #7530 #2266 #6064 #7293)
+#9116 := (>= #7290 0::Int)
+#9119 := (or #4270 #9116)
+#9290 := [quant-inst #7289]: #9119
+#10064 := [unit-resolution #9290 #7112]: #9116
+#7552 := (* -1::Int #2265)
+#7603 := (+ #7552 #7578)
+#7604 := (+ #174 #7603)
+#9488 := (<= #7604 0::Int)
+#7607 := (= #7604 0::Int)
+#7582 := (* -1::Int #7578)
+#7586 := (+ f8 #7582)
+#7587 := (<= #7586 0::Int)
+#9501 := (not #7587)
+#7596 := (+ #7561 #7578)
+#7597 := (+ #174 #7596)
+#7598 := (>= #7597 0::Int)
+#7629 := (or #7587 #7598)
+#7632 := (not #7629)
+#10066 := (not #7530)
+#10067 := [hypothesis]: #10066
+#7635 := (or #7530 #7632)
+#5779 := (or #4538 #4529)
+#4713 := (?v1!7 ?v0!8)
+#4989 := (f13 f19 #4713)
+#5002 := (* -1::Int #4989)
+#4714 := (f13 f14 #4713)
+#5222 := (+ #4714 #5002)
+#5227 := (>= #5222 0::Int)
+#5221 := (= #4714 #4989)
+#5711 := (= #4989 #4714)
+#5706 := [hypothesis]: #4526
+#5707 := [hypothesis]: #4541
+#4014 := (or #4538 #4532)
+#3982 := [def-axiom]: #4014
+#5708 := [unit-resolution #3982 #5707]: #4532
+#4019 := (or #4535 #4374 #4529)
+#4020 := [def-axiom]: #4019
+#5709 := [unit-resolution #4020 #5708 #5706]: #4374
+#4125 := (or #4371 #623)
+#4126 := [def-axiom]: #4125
+#5710 := [unit-resolution #4126 #5709]: #623
+#5705 := [symm #5710]: #138
+#5712 := [monotonicity #5705]: #5711
+#5713 := [symm #5712]: #5221
+#5714 := (not #5221)
+#5715 := (or #5714 #5227)
+#5728 := [th-lemma arith triangle-eq]: #5715
+#5729 := [unit-resolution #5728 #5713]: #5227
+#4696 := (* -1::Int #4714)
+#4646 := (f13 f14 ?v0!8)
+#4697 := (+ #4646 #4696)
+#4698 := (<= #4697 0::Int)
+#4879 := (not #4698)
+#4705 := (f3 f15 #4713)
+#4776 := (= f1 #4705)
+#4777 := (not #4776)
+#4699 := (f5 #4713 ?v0!8)
+#4700 := (f9 #4699)
+#4695 := (* -1::Int #4700)
+#4781 := (+ #4695 #4696)
+#4782 := (+ #4646 #4781)
+#4764 := (= #4782 0::Int)
+#4767 := (not #4764)
+#4772 := (or #4698 #4767 #4777)
+#4846 := (not #4772)
+#4647 := (* -1::Int #4646)
+#4648 := (+ f8 #4647)
+#4628 := (<= #4648 0::Int)
+#4984 := (not #4628)
+#4127 := (or #4371 #4365)
+#4124 := [def-axiom]: #4127
+#5730 := [unit-resolution #4124 #5709]: #4365
+#4023 := (or #4538 #100)
+#4024 := [def-axiom]: #4023
+#5731 := [unit-resolution #4024 #5707]: #100
+#5732 := (= #157 #99)
+#5727 := [monotonicity #5705]: #5732
+#5733 := [trans #5727 #5731]: #158
+#4137 := (or #4347 #2156)
+#3800 := [def-axiom]: #4137
+#5734 := [unit-resolution #3800 #5733]: #4347
+#4026 := (or #4538 #4273)
+#4006 := [def-axiom]: #4026
+#5735 := [unit-resolution #4006 #5707]: #4273
+#3841 := (or #4371 #4307)
+#4123 := [def-axiom]: #3841
+#5736 := [unit-resolution #4123 #5709]: #4307
+#4967 := (or #3352 #4312 #4278 #714)
+#4940 := [hypothesis]: #3357
+#4140 := (or #3352 #2143)
+#4141 := [def-axiom]: #4140
+#4941 := [unit-resolution #4141 #4940]: #2143
+#4715 := (f13 f14 ?v1!10)
+#4716 := (* -1::Int #4715)
+#4717 := (+ f8 #4716)
+#4718 := (<= #4717 0::Int)
+#4719 := (f3 f15 ?v1!10)
+#4720 := (= f1 #4719)
+#4791 := (not #4720)
+#3828 := (f13 f14 ?v0!11)
+#3829 := (* -1::Int #3828)
+#4793 := (+ #3829 #4715)
+#4794 := (+ #2137 #4793)
+#4797 := (>= #4794 0::Int)
+#4950 := (not #4797)
+#4924 := (+ #2134 #4716)
+#4926 := (>= #4924 0::Int)
+#4923 := (= #2134 #4715)
+#4928 := (= #4715 #2134)
+#4927 := [hypothesis]: #623
+#4929 := [monotonicity #4927]: #4928
+#4930 := [symm #4929]: #4923
+#4931 := (not #4923)
+#4932 := (or #4931 #4926)
+#4933 := [th-lemma arith triangle-eq]: #4932
+#4934 := [unit-resolution #4933 #4930]: #4926
+#4138 := (not #2798)
+#4144 := (or #3352 #4138)
+#3782 := [def-axiom]: #4144
+#4935 := [unit-resolution #3782 #4940]: #4138
+#4917 := (+ #2132 #3829)
+#4921 := (<= #4917 0::Int)
+#4916 := (= #2132 #3828)
+#4938 := (= #3828 #2132)
+#4939 := [monotonicity #4927]: #4938
+#4942 := [symm #4939]: #4916
+#4943 := (not #4916)
+#4944 := (or #4943 #4921)
+#4955 := [th-lemma arith triangle-eq]: #4944
+#4956 := [unit-resolution #4955 #4942]: #4921
+#4952 := (not #4926)
+#4951 := (not #4921)
+#4953 := (or #4950 #4951 #2798 #4952)
+#4945 := [hypothesis]: #4926
+#4946 := [hypothesis]: #4138
+#4947 := [hypothesis]: #4921
+#4948 := [hypothesis]: #4797
+#4949 := [th-lemma arith farkas 1 -1 1 1 #4948 #4947 #4946 #4945]: false
+#4954 := [lemma #4949]: #4953
+#4957 := [unit-resolution #4954 #4956 #4935 #4934]: #4950
+#4960 := (or #4791 #4797)
+#4142 := (or #3352 #2147)
+#4143 := [def-axiom]: #4142
+#4958 := [unit-resolution #4143 #4940]: #2147
+#4959 := [hypothesis]: #4273
+#4808 := (or #4278 #2146 #4791 #4797)
+#4786 := (+ #4715 #3829)
+#4787 := (+ #2137 #4786)
+#4790 := (>= #4787 0::Int)
+#4792 := (or #4791 #2146 #4790)
+#4809 := (or #4278 #4792)
+#4816 := (iff #4809 #4808)
+#4803 := (or #2146 #4791 #4797)
+#4811 := (or #4278 #4803)
+#4814 := (iff #4811 #4808)
+#4815 := [rewrite]: #4814
+#4812 := (iff #4809 #4811)
+#4806 := (iff #4792 #4803)
+#4800 := (or #4791 #2146 #4797)
+#4804 := (iff #4800 #4803)
 #4805 := [rewrite]: #4804
-#4808 := [monotonicity #4805]: #4807
-#4811 := [monotonicity #4808]: #4810
-#4816 := [trans #4811 #4814]: #4815
-#4822 := [monotonicity #4816]: #4821
-#4826 := [trans #4822 #4824]: #4825
-#4819 := [quant-inst #2140 #2139]: #4818
-#4827 := [mp #4819 #4826]: #4817
-#4970 := [unit-resolution #4827 #4968 #4967]: #4969
-#4971 := [unit-resolution #4970 #4966]: #4800
-#4731 := (or #4727 #4729)
-#4972 := [hypothesis]: #4316
-#4734 := (or #4321 #4727 #4729)
-#4730 := (or #4729 #4727)
-#4735 := (or #4321 #4730)
-#4742 := (iff #4735 #4734)
-#4737 := (or #4321 #4731)
-#4740 := (iff #4737 #4734)
-#4741 := [rewrite]: #4740
-#4738 := (iff #4735 #4737)
-#4732 := (iff #4730 #4731)
-#4733 := [rewrite]: #4732
-#4739 := [monotonicity #4733]: #4738
-#4743 := [trans #4739 #4741]: #4742
-#4736 := [quant-inst #2139]: #4735
-#4744 := [mp #4736 #4743]: #4734
-#4973 := [unit-resolution #4744 #4972]: #4731
-#4974 := [unit-resolution #4973 #4971]: #4727
-#4975 := [th-lemma arith farkas 1 -1 1 #4943 #4974 #4950]: false
-#4977 := [lemma #4975]: #4976
-#5746 := [unit-resolution #4977 #5745 #5744 #5719]: #3361
-#4158 := (or #4365 #4359 #3366)
-#4144 := [def-axiom]: #4158
-#5747 := [unit-resolution #4144 #5746 #5743]: #4365
-#3868 := (or #4368 #4362)
-#3869 := [def-axiom]: #3868
-#5748 := [unit-resolution #3869 #5747]: #4368
-#4138 := (or #4377 #4337 #4371)
-#4142 := [def-axiom]: #4138
-#5749 := [unit-resolution #4142 #5748 #5739]: #4337
-#4170 := (or #4334 #2090)
-#4160 := [def-axiom]: #4170
-#5750 := [unit-resolution #4160 #5749]: #2090
-#4986 := (+ #2077 #4656)
-#4988 := (>= #4986 0::Int)
-#4985 := (= #2077 #4655)
-#5413 := (= #4655 #2077)
-#5751 := [monotonicity #5719]: #5413
-#5752 := [symm #5751]: #4985
-#5416 := (not #4985)
-#5421 := (or #5416 #4988)
-#5422 := [th-lemma arith triangle-eq]: #5421
-#5753 := [unit-resolution #5422 #5752]: #4988
-#4994 := (not #4988)
-#4995 := (or #4993 #4994 #2089)
-#4989 := [hypothesis]: #2090
-#4990 := [hypothesis]: #4637
-#4991 := [hypothesis]: #4988
-#4992 := [th-lemma arith farkas 1 -1 1 #4991 #4990 #4989]: false
-#4996 := [lemma #4992]: #4995
-#5754 := [unit-resolution #4996 #5753 #5750]: #4993
-#5764 := (or #4637 #4855)
-#3820 := (or #4334 #2707)
-#3825 := [def-axiom]: #3820
-#5762 := [unit-resolution #3825 #5749]: #2707
-#4022 := (or #4547 #4307)
-#4017 := [def-axiom]: #4022
-#5763 := [unit-resolution #4017 #5716]: #4307
-#4860 := (or #4312 #2704 #4637 #4855)
-#4710 := (+ #4705 #4704)
-#4711 := (+ #4655 #4710)
-#4712 := (= #4711 0::Int)
-#4713 := (not #4712)
-#4787 := (or #4786 #4713 #4707)
-#4788 := (not #4787)
-#4789 := (or #2091 #4637 #4788)
-#4861 := (or #4312 #4789)
-#4884 := (iff #4861 #4860)
-#4858 := (or #2704 #4637 #4855)
-#4863 := (or #4312 #4858)
-#4882 := (iff #4863 #4860)
-#4883 := [rewrite]: #4882
-#4879 := (iff #4861 #4863)
-#4853 := (iff #4789 #4858)
-#4856 := (iff #4788 #4855)
-#4798 := (iff #4787 #4781)
-#4778 := (or #4786 #4776 #4707)
-#4782 := (iff #4778 #4781)
-#4797 := [rewrite]: #4782
-#4779 := (iff #4787 #4778)
-#4777 := (iff #4713 #4776)
-#4774 := (iff #4712 #4773)
-#4792 := (= #4711 #4791)
-#4793 := [rewrite]: #4792
-#4775 := [monotonicity #4793]: #4774
-#4772 := [monotonicity #4775]: #4777
-#4780 := [monotonicity #4772]: #4779
-#4854 := [trans #4780 #4797]: #4798
-#4857 := [monotonicity #4854]: #4856
-#4859 := [monotonicity #2706 #4857]: #4853
-#4881 := [monotonicity #4859]: #4879
-#4885 := [trans #4881 #4883]: #4884
-#4862 := [quant-inst #2076]: #4861
-#4880 := [mp #4862 #4885]: #4860
-#5765 := [unit-resolution #4880 #5763 #5762]: #5764
-#5766 := [unit-resolution #5765 #5754]: #4855
-#4889 := (or #4781 #4888)
-#4890 := [def-axiom]: #4889
-#5767 := [unit-resolution #4890 #5766]: #4888
-#5012 := (+ #2077 #5011)
-#5013 := (<= #5012 0::Int)
-#5025 := (+ #4704 #5011)
-#5026 := (+ #2077 #5025)
-#5027 := (= #5026 0::Int)
-#5049 := (<= #5026 0::Int)
-#5235 := (<= #5231 0::Int)
-#5768 := (or #5723 #5235)
+#4801 := (iff #4792 #4800)
+#4798 := (iff #4790 #4797)
+#4795 := (= #4787 #4794)
+#4796 := [rewrite]: #4795
+#4799 := [monotonicity #4796]: #4798
+#4802 := [monotonicity #4799]: #4801
+#4807 := [trans #4802 #4805]: #4806
+#4813 := [monotonicity #4807]: #4812
+#4817 := [trans #4813 #4815]: #4816
+#4810 := [quant-inst #2131 #2130]: #4809
+#4818 := [mp #4810 #4817]: #4808
+#4961 := [unit-resolution #4818 #4959 #4958]: #4960
+#4962 := [unit-resolution #4961 #4957]: #4791
+#4722 := (or #4718 #4720)
+#4963 := [hypothesis]: #4307
+#4725 := (or #4312 #4718 #4720)
+#4721 := (or #4720 #4718)
+#4726 := (or #4312 #4721)
+#4733 := (iff #4726 #4725)
+#4728 := (or #4312 #4722)
+#4731 := (iff #4728 #4725)
+#4732 := [rewrite]: #4731
+#4729 := (iff #4726 #4728)
+#4723 := (iff #4721 #4722)
+#4724 := [rewrite]: #4723
+#4730 := [monotonicity #4724]: #4729
+#4734 := [trans #4730 #4732]: #4733
+#4727 := [quant-inst #2130]: #4726
+#4735 := [mp #4727 #4734]: #4725
+#4964 := [unit-resolution #4735 #4963]: #4722
+#4965 := [unit-resolution #4964 #4962]: #4718
+#4966 := [th-lemma arith farkas 1 -1 1 #4934 #4965 #4941]: false
+#4968 := [lemma #4966]: #4967
+#5737 := [unit-resolution #4968 #5736 #5735 #5710]: #3352
+#4149 := (or #4356 #4350 #3357)
+#4135 := [def-axiom]: #4149
+#5738 := [unit-resolution #4135 #5737 #5734]: #4356
+#3859 := (or #4359 #4353)
+#3860 := [def-axiom]: #3859
+#5739 := [unit-resolution #3860 #5738]: #4359
+#4129 := (or #4368 #4328 #4362)
+#4133 := [def-axiom]: #4129
+#5740 := [unit-resolution #4133 #5739 #5730]: #4328
+#4161 := (or #4325 #2081)
+#4151 := [def-axiom]: #4161
+#5741 := [unit-resolution #4151 #5740]: #2081
+#4977 := (+ #2068 #4647)
+#4979 := (>= #4977 0::Int)
+#4976 := (= #2068 #4646)
+#5404 := (= #4646 #2068)
+#5742 := [monotonicity #5710]: #5404
+#5743 := [symm #5742]: #4976
+#5407 := (not #4976)
+#5412 := (or #5407 #4979)
+#5413 := [th-lemma arith triangle-eq]: #5412
+#5744 := [unit-resolution #5413 #5743]: #4979
+#4985 := (not #4979)
+#4986 := (or #4984 #4985 #2080)
+#4980 := [hypothesis]: #2081
+#4981 := [hypothesis]: #4628
+#4982 := [hypothesis]: #4979
+#4983 := [th-lemma arith farkas 1 -1 1 #4982 #4981 #4980]: false
+#4987 := [lemma #4983]: #4986
+#5745 := [unit-resolution #4987 #5744 #5741]: #4984
+#5755 := (or #4628 #4846)
+#3811 := (or #4325 #2698)
+#3816 := [def-axiom]: #3811
+#5753 := [unit-resolution #3816 #5740]: #2698
+#4013 := (or #4538 #4298)
+#4008 := [def-axiom]: #4013
+#5754 := [unit-resolution #4008 #5707]: #4298
+#4851 := (or #4303 #2695 #4628 #4846)
+#4701 := (+ #4696 #4695)
+#4702 := (+ #4646 #4701)
+#4703 := (= #4702 0::Int)
+#4704 := (not #4703)
+#4778 := (or #4777 #4704 #4698)
+#4779 := (not #4778)
+#4780 := (or #2082 #4628 #4779)
+#4852 := (or #4303 #4780)
+#4875 := (iff #4852 #4851)
+#4849 := (or #2695 #4628 #4846)
+#4854 := (or #4303 #4849)
+#4873 := (iff #4854 #4851)
+#4874 := [rewrite]: #4873
+#4870 := (iff #4852 #4854)
+#4844 := (iff #4780 #4849)
+#4847 := (iff #4779 #4846)
+#4789 := (iff #4778 #4772)
+#4769 := (or #4777 #4767 #4698)
+#4773 := (iff #4769 #4772)
+#4788 := [rewrite]: #4773
+#4770 := (iff #4778 #4769)
+#4768 := (iff #4704 #4767)
+#4765 := (iff #4703 #4764)
+#4783 := (= #4702 #4782)
+#4784 := [rewrite]: #4783
+#4766 := [monotonicity #4784]: #4765
+#4763 := [monotonicity #4766]: #4768
+#4771 := [monotonicity #4763]: #4770
+#4845 := [trans #4771 #4788]: #4789
+#4848 := [monotonicity #4845]: #4847
+#4850 := [monotonicity #2697 #4848]: #4844
+#4872 := [monotonicity #4850]: #4870
+#4876 := [trans #4872 #4874]: #4875
+#4853 := [quant-inst #2067]: #4852
+#4871 := [mp #4853 #4876]: #4851
+#5756 := [unit-resolution #4871 #5754 #5753]: #5755
+#5757 := [unit-resolution #5756 #5745]: #4846
+#4880 := (or #4772 #4879)
+#4881 := [def-axiom]: #4880
+#5758 := [unit-resolution #4881 #5757]: #4879
+#5003 := (+ #2068 #5002)
+#5004 := (<= #5003 0::Int)
+#5016 := (+ #4695 #5002)
+#5017 := (+ #2068 #5016)
+#5018 := (= #5017 0::Int)
+#5040 := (<= #5017 0::Int)
+#5226 := (<= #5222 0::Int)
+#5759 := (or #5714 #5226)
+#5760 := [th-lemma arith triangle-eq]: #5759
+#5761 := [unit-resolution #5760 #5713]: #5226
+#4877 := (<= #4782 0::Int)
+#4896 := (or #4772 #4764)
+#4898 := [def-axiom]: #4896
+#5762 := [unit-resolution #4898 #5757]: #4764
+#5763 := (or #4767 #4877)
+#5764 := [th-lemma arith triangle-eq]: #5763
+#5765 := [unit-resolution #5764 #5762]: #4877
+#4978 := (<= #4977 0::Int)
+#5408 := (or #5407 #4978)
+#5409 := [th-lemma arith triangle-eq]: #5408
+#5766 := [unit-resolution #5409 #5743]: #4978
+#5350 := (not #5226)
+#5349 := (not #4877)
+#5348 := (not #4978)
+#5351 := (or #5040 #5348 #5349 #5350)
+#5342 := [hypothesis]: #5226
+#5343 := [hypothesis]: #4877
+#5344 := [hypothesis]: #4978
+#5345 := (not #5040)
+#5346 := [hypothesis]: #5345
+#5347 := [th-lemma arith farkas -1 1 1 1 #5346 #5344 #5343 #5342]: false
+#5352 := [lemma #5347]: #5351
+#5767 := [unit-resolution #5352 #5766 #5765 #5761]: #5040
+#5041 := (>= #5017 0::Int)
+#4878 := (>= #4782 0::Int)
+#5768 := (or #4767 #4878)
 #5769 := [th-lemma arith triangle-eq]: #5768
-#5770 := [unit-resolution #5769 #5722]: #5235
-#4886 := (<= #4791 0::Int)
-#4905 := (or #4781 #4773)
-#4907 := [def-axiom]: #4905
-#5771 := [unit-resolution #4907 #5766]: #4773
-#5772 := (or #4776 #4886)
+#5770 := [unit-resolution #5769 #5762]: #4878
+#5750 := (not #5227)
+#5390 := (not #4878)
+#5751 := (or #5041 #4985 #5390 #5750)
+#5746 := [hypothesis]: #5227
+#5386 := [hypothesis]: #4878
+#5747 := (not #5041)
+#5748 := [hypothesis]: #5747
+#5749 := [th-lemma arith farkas -1 1 1 1 #5748 #4982 #5386 #5746]: false
+#5752 := [lemma #5749]: #5751
+#5771 := [unit-resolution #5752 #5744 #5770 #5729]: #5041
+#5772 := (or #5018 #5345 #5747)
 #5773 := [th-lemma arith triangle-eq]: #5772
-#5774 := [unit-resolution #5773 #5771]: #4886
-#4987 := (<= #4986 0::Int)
-#5417 := (or #5416 #4987)
-#5418 := [th-lemma arith triangle-eq]: #5417
-#5775 := [unit-resolution #5418 #5752]: #4987
-#5359 := (not #5235)
-#5358 := (not #4886)
-#5357 := (not #4987)
-#5360 := (or #5049 #5357 #5358 #5359)
-#5351 := [hypothesis]: #5235
-#5352 := [hypothesis]: #4886
-#5353 := [hypothesis]: #4987
-#5354 := (not #5049)
-#5355 := [hypothesis]: #5354
-#5356 := [th-lemma arith farkas -1 1 1 1 #5355 #5353 #5352 #5351]: false
-#5361 := [lemma #5356]: #5360
-#5776 := [unit-resolution #5361 #5775 #5774 #5770]: #5049
-#5050 := (>= #5026 0::Int)
-#4887 := (>= #4791 0::Int)
-#5777 := (or #4776 #4887)
-#5778 := [th-lemma arith triangle-eq]: #5777
-#5779 := [unit-resolution #5778 #5771]: #4887
-#5759 := (not #5236)
-#5399 := (not #4887)
-#5760 := (or #5050 #4994 #5399 #5759)
-#5755 := [hypothesis]: #5236
-#5395 := [hypothesis]: #4887
-#5756 := (not #5050)
-#5757 := [hypothesis]: #5756
-#5758 := [th-lemma arith farkas -1 1 1 1 #5757 #4991 #5395 #5755]: false
-#5761 := [lemma #5758]: #5760
-#5780 := [unit-resolution #5761 #5753 #5779 #5738]: #5050
-#5781 := (or #5027 #5354 #5756)
-#5782 := [th-lemma arith triangle-eq]: #5781
-#5783 := [unit-resolution #5782 #5780 #5776]: #5027
-#5032 := (not #5027)
-#5035 := (or #5013 #5032)
-#4161 := (or #4334 #4326)
-#3821 := [def-axiom]: #4161
-#5784 := [unit-resolution #3821 #5749]: #4326
-#5038 := (or #4331 #5013 #5032)
-#4997 := (+ #2078 #4709)
-#4999 := (+ #4998 #4997)
-#5000 := (= #4999 0::Int)
-#5001 := (not #5000)
-#5002 := (+ #4998 #2078)
-#5003 := (>= #5002 0::Int)
-#5004 := (or #5003 #5001)
-#5039 := (or #4331 #5004)
-#5046 := (iff #5039 #5038)
-#5041 := (or #4331 #5035)
-#5044 := (iff #5041 #5038)
-#5045 := [rewrite]: #5044
-#5042 := (iff #5039 #5041)
-#5036 := (iff #5004 #5035)
-#5033 := (iff #5001 #5032)
-#5030 := (iff #5000 #5027)
-#5018 := (+ #4709 #4998)
-#5019 := (+ #2078 #5018)
-#5022 := (= #5019 0::Int)
-#5028 := (iff #5022 #5027)
-#5029 := [rewrite]: #5028
-#5023 := (iff #5000 #5022)
-#5020 := (= #4999 #5019)
-#5021 := [rewrite]: #5020
-#5024 := [monotonicity #5021]: #5023
-#5031 := [trans #5024 #5029]: #5030
-#5034 := [monotonicity #5031]: #5033
-#5016 := (iff #5003 #5013)
-#5005 := (+ #2078 #4998)
-#5008 := (>= #5005 0::Int)
-#5014 := (iff #5008 #5013)
-#5015 := [rewrite]: #5014
-#5009 := (iff #5003 #5008)
-#5006 := (= #5002 #5005)
-#5007 := [rewrite]: #5006
-#5010 := [monotonicity #5007]: #5009
-#5017 := [trans #5010 #5015]: #5016
-#5037 := [monotonicity #5017 #5034]: #5036
-#5043 := [monotonicity #5037]: #5042
-#5047 := [trans #5043 #5045]: #5046
-#5040 := [quant-inst #4722]: #5039
-#5048 := [mp #5040 #5047]: #5038
-#5785 := [unit-resolution #5048 #5784]: #5035
-#5786 := [unit-resolution #5785 #5783]: #5013
-#5787 := [th-lemma arith farkas 1 -1 1 1 #5753 #5786 #5767 #5738]: false
-#5789 := [lemma #5787]: #5788
-#6508 := [unit-resolution #5789 #6507]: #4538
-#4044 := (or #4535 #4396)
-#4039 := [def-axiom]: #4044
-#6509 := [unit-resolution #4039 #6508]: #4396
-#9499 := (or #4401 #7539 #7641)
-#7592 := (+ #1453 #7591)
-#7593 := (+ #7536 #7592)
-#7594 := (<= #7593 0::Int)
-#7635 := (or #7596 #7594)
-#7636 := (not #7635)
-#7537 := (= #7536 #2274)
-#7637 := (or #7537 #7636)
-#9500 := (or #4401 #7637)
-#9507 := (iff #9500 #9499)
-#9502 := (or #4401 #7644)
-#9505 := (iff #9502 #9499)
-#9506 := [rewrite]: #9505
-#9503 := (iff #9500 #9502)
-#7645 := (iff #7637 #7644)
-#7642 := (iff #7636 #7641)
-#7639 := (iff #7635 #7638)
-#7610 := (iff #7594 #7607)
-#7598 := (+ #7536 #7591)
-#7599 := (+ #1453 #7598)
-#7602 := (<= #7599 0::Int)
-#7608 := (iff #7602 #7607)
-#7609 := [rewrite]: #7608
-#7603 := (iff #7594 #7602)
-#7600 := (= #7593 #7599)
-#7601 := [rewrite]: #7600
-#7604 := [monotonicity #7601]: #7603
-#7611 := [trans #7604 #7609]: #7610
-#7640 := [monotonicity #7611]: #7639
-#7643 := [monotonicity #7640]: #7642
-#7540 := (iff #7537 #7539)
-#7541 := [rewrite]: #7540
-#7646 := [monotonicity #7541 #7643]: #7645
-#9504 := [monotonicity #7646]: #9503
-#9508 := [trans #9504 #9506]: #9507
-#9501 := [quant-inst #2273]: #9500
-#9509 := [mp #9501 #9508]: #9499
-#10077 := [unit-resolution #9509 #6509]: #7644
-#10078 := [unit-resolution #10077 #10076]: #7641
-#9511 := (or #7638 #9510)
-#9512 := [def-axiom]: #9511
-#10079 := [unit-resolution #9512 #10078]: #9510
-#9513 := (not #7607)
-#9514 := (or #7638 #9513)
-#9515 := [def-axiom]: #9514
-#10080 := [unit-resolution #9515 #10078]: #9513
-#7619 := (or #7596 #7607 #7616)
-#4045 := (or #4535 #4404)
-#4018 := [def-axiom]: #4045
-#6513 := [unit-resolution #4018 #6508]: #4404
-#9486 := (or #4409 #7596 #7607 #7616)
-#7588 := (+ #7587 #7561)
-#7589 := (+ #174 #7588)
-#7590 := (= #7589 0::Int)
-#7597 := (or #7596 #7594 #7590)
-#9487 := (or #4409 #7597)
-#9494 := (iff #9487 #9486)
-#9489 := (or #4409 #7619)
-#9492 := (iff #9489 #9486)
-#9493 := [rewrite]: #9492
-#9490 := (iff #9487 #9489)
-#7620 := (iff #7597 #7619)
-#7617 := (iff #7590 #7616)
-#7614 := (= #7589 #7613)
-#7615 := [rewrite]: #7614
-#7618 := [monotonicity #7615]: #7617
-#7621 := [monotonicity #7611 #7618]: #7620
-#9491 := [monotonicity #7621]: #9490
-#9495 := [trans #9491 #9493]: #9494
-#9488 := [quant-inst #2273]: #9487
-#9496 := [mp #9488 #9495]: #9486
-#10081 := [unit-resolution #9496 #6513]: #7619
-#10082 := [unit-resolution #10081 #10080 #10079]: #7616
-#10083 := (not #7616)
-#10084 := (or #10083 #9497)
-#10085 := [th-lemma arith triangle-eq]: #10084
-#10086 := [unit-resolution #10085 #10082]: #9497
-#10050 := (>= #9989 0::Int)
-#10025 := (<= #9989 0::Int)
-#10026 := (not #10025)
-#9949 := (= ?v0!15 #7211)
-#9968 := (not #9949)
-#7668 := (f3 f15 ?v0!15)
-#7669 := (= f1 #7668)
-#5891 := (f3 #773 f22)
-#5892 := (= f1 #5891)
-#9952 := (ite #9949 #5892 #7669)
-#9967 := (not #9952)
-#8442 := (f4 f15 #7211 #5891)
-#9946 := (f3 #8442 ?v0!15)
-#9947 := (= f1 #9946)
-#9955 := (iff #9947 #9952)
+#5774 := [unit-resolution #5773 #5771 #5767]: #5018
+#5023 := (not #5018)
+#5026 := (or #5004 #5023)
+#4152 := (or #4325 #4317)
+#3812 := [def-axiom]: #4152
+#5775 := [unit-resolution #3812 #5740]: #4317
+#5029 := (or #4322 #5004 #5023)
+#4988 := (+ #2069 #4700)
+#4990 := (+ #4989 #4988)
+#4991 := (= #4990 0::Int)
+#4992 := (not #4991)
+#4993 := (+ #4989 #2069)
+#4994 := (>= #4993 0::Int)
+#4995 := (or #4994 #4992)
+#5030 := (or #4322 #4995)
+#5037 := (iff #5030 #5029)
+#5032 := (or #4322 #5026)
+#5035 := (iff #5032 #5029)
+#5036 := [rewrite]: #5035
+#5033 := (iff #5030 #5032)
+#5027 := (iff #4995 #5026)
+#5024 := (iff #4992 #5023)
+#5021 := (iff #4991 #5018)
+#5009 := (+ #4700 #4989)
+#5010 := (+ #2069 #5009)
+#5013 := (= #5010 0::Int)
+#5019 := (iff #5013 #5018)
+#5020 := [rewrite]: #5019
+#5014 := (iff #4991 #5013)
+#5011 := (= #4990 #5010)
+#5012 := [rewrite]: #5011
+#5015 := [monotonicity #5012]: #5014
+#5022 := [trans #5015 #5020]: #5021
+#5025 := [monotonicity #5022]: #5024
+#5007 := (iff #4994 #5004)
+#4996 := (+ #2069 #4989)
+#4999 := (>= #4996 0::Int)
+#5005 := (iff #4999 #5004)
+#5006 := [rewrite]: #5005
+#5000 := (iff #4994 #4999)
+#4997 := (= #4993 #4996)
+#4998 := [rewrite]: #4997
+#5001 := [monotonicity #4998]: #5000
+#5008 := [trans #5001 #5006]: #5007
+#5028 := [monotonicity #5008 #5025]: #5027
+#5034 := [monotonicity #5028]: #5033
+#5038 := [trans #5034 #5036]: #5037
+#5031 := [quant-inst #4713]: #5030
+#5039 := [mp #5031 #5038]: #5029
+#5776 := [unit-resolution #5039 #5775]: #5026
+#5777 := [unit-resolution #5776 #5774]: #5004
+#5778 := [th-lemma arith farkas 1 -1 1 1 #5744 #5777 #5758 #5729]: false
+#5780 := [lemma #5778]: #5779
+#6499 := [unit-resolution #5780 #6498]: #4529
+#4035 := (or #4526 #4387)
+#4030 := [def-axiom]: #4035
+#6500 := [unit-resolution #4030 #6499]: #4387
+#9490 := (or #4392 #7530 #7632)
+#7583 := (+ #1444 #7582)
+#7584 := (+ #7527 #7583)
+#7585 := (<= #7584 0::Int)
+#7626 := (or #7587 #7585)
+#7627 := (not #7626)
+#7528 := (= #7527 #2265)
+#7628 := (or #7528 #7627)
+#9491 := (or #4392 #7628)
+#9498 := (iff #9491 #9490)
+#9493 := (or #4392 #7635)
+#9496 := (iff #9493 #9490)
+#9497 := [rewrite]: #9496
+#9494 := (iff #9491 #9493)
+#7636 := (iff #7628 #7635)
+#7633 := (iff #7627 #7632)
+#7630 := (iff #7626 #7629)
+#7601 := (iff #7585 #7598)
+#7589 := (+ #7527 #7582)
+#7590 := (+ #1444 #7589)
+#7593 := (<= #7590 0::Int)
+#7599 := (iff #7593 #7598)
+#7600 := [rewrite]: #7599
+#7594 := (iff #7585 #7593)
+#7591 := (= #7584 #7590)
+#7592 := [rewrite]: #7591
+#7595 := [monotonicity #7592]: #7594
+#7602 := [trans #7595 #7600]: #7601
+#7631 := [monotonicity #7602]: #7630
+#7634 := [monotonicity #7631]: #7633
+#7531 := (iff #7528 #7530)
+#7532 := [rewrite]: #7531
+#7637 := [monotonicity #7532 #7634]: #7636
+#9495 := [monotonicity #7637]: #9494
+#9499 := [trans #9495 #9497]: #9498
+#9492 := [quant-inst #2264]: #9491
+#9500 := [mp #9492 #9499]: #9490
+#10068 := [unit-resolution #9500 #6500]: #7635
+#10069 := [unit-resolution #10068 #10067]: #7632
+#9502 := (or #7629 #9501)
+#9503 := [def-axiom]: #9502
+#10070 := [unit-resolution #9503 #10069]: #9501
+#9504 := (not #7598)
+#9505 := (or #7629 #9504)
+#9506 := [def-axiom]: #9505
+#10071 := [unit-resolution #9506 #10069]: #9504
+#7610 := (or #7587 #7598 #7607)
+#4036 := (or #4526 #4395)
+#4009 := [def-axiom]: #4036
+#6504 := [unit-resolution #4009 #6499]: #4395
+#9477 := (or #4400 #7587 #7598 #7607)
+#7579 := (+ #7578 #7552)
+#7580 := (+ #174 #7579)
+#7581 := (= #7580 0::Int)
+#7588 := (or #7587 #7585 #7581)
+#9478 := (or #4400 #7588)
+#9485 := (iff #9478 #9477)
+#9480 := (or #4400 #7610)
+#9483 := (iff #9480 #9477)
+#9484 := [rewrite]: #9483
+#9481 := (iff #9478 #9480)
+#7611 := (iff #7588 #7610)
+#7608 := (iff #7581 #7607)
+#7605 := (= #7580 #7604)
+#7606 := [rewrite]: #7605
+#7609 := [monotonicity #7606]: #7608
+#7612 := [monotonicity #7602 #7609]: #7611
+#9482 := [monotonicity #7612]: #9481
+#9486 := [trans #9482 #9484]: #9485
+#9479 := [quant-inst #2264]: #9478
+#9487 := [mp #9479 #9486]: #9477
+#10072 := [unit-resolution #9487 #6504]: #7610
+#10073 := [unit-resolution #10072 #10071 #10070]: #7607
+#10074 := (not #7607)
+#10075 := (or #10074 #9488)
+#10076 := [th-lemma arith triangle-eq]: #10075
+#10077 := [unit-resolution #10076 #10073]: #9488
+#10041 := (>= #9980 0::Int)
+#10016 := (<= #9980 0::Int)
+#10017 := (not #10016)
+#9940 := (= ?v0!15 #7202)
+#9959 := (not #9940)
+#7659 := (f3 f15 ?v0!15)
+#7660 := (= f1 #7659)
+#5882 := (f3 #180 f22)
+#5883 := (= f1 #5882)
+#9943 := (ite #9940 #5883 #7660)
+#9958 := (not #9943)
+#8433 := (f4 f15 #7202 #5882)
+#9937 := (f3 #8433 ?v0!15)
+#9938 := (= f1 #9937)
+#9946 := (iff #9938 #9943)
 #10 := (:var 1 S1)
 #9 := (:var 2 S3)
 #8 := (:var 3 S2)
 #11 := (f4 #8 #9 #10)
 #13 := (f3 #11 #12)
-#4171 := (pattern #13)
+#4162 := (pattern #13)
 #17 := (f3 #8 #12)
-#301 := (= f1 #17)
-#298 := (= f1 #10)
-#295 := (= #9 #12)
-#304 := (ite #295 #298 #301)
-#292 := (= f1 #13)
-#307 := (iff #292 #304)
-#4172 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) (:pat #4171) #307)
-#310 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #307)
-#4175 := (iff #310 #4172)
-#4173 := (iff #307 #307)
-#4174 := [refl]: #4173
-#4176 := [quant-intro #4174]: #4175
-#1868 := (~ #310 #310)
-#1866 := (~ #307 #307)
-#1867 := [refl]: #1866
-#1869 := [nnf-pos #1867]: #1868
+#300 := (= f1 #17)
+#297 := (= f1 #10)
+#294 := (= #9 #12)
+#303 := (ite #294 #297 #300)
+#291 := (= f1 #13)
+#306 := (iff #291 #303)
+#4163 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) (:pat #4162) #306)
+#309 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #306)
+#4166 := (iff #309 #4163)
+#4164 := (iff #306 #306)
+#4165 := [refl]: #4164
+#4167 := [quant-intro #4165]: #4166
+#1859 := (~ #309 #309)
+#1857 := (~ #306 #306)
+#1858 := [refl]: #1857
+#1860 := [nnf-pos #1858]: #1859
 #18 := (= #17 f1)
 #16 := (= #10 f1)
 #15 := (= #12 #9)
@@ -4832,2365 +4821,2365 @@
 #14 := (= #13 f1)
 #20 := (iff #14 #19)
 #21 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #20)
-#311 := (iff #21 #310)
-#308 := (iff #20 #307)
-#305 := (iff #19 #304)
-#302 := (iff #18 #301)
-#303 := [rewrite]: #302
-#299 := (iff #16 #298)
-#300 := [rewrite]: #299
-#296 := (iff #15 #295)
-#297 := [rewrite]: #296
-#306 := [monotonicity #297 #300 #303]: #305
-#293 := (iff #14 #292)
-#294 := [rewrite]: #293
-#309 := [monotonicity #294 #306]: #308
-#312 := [quant-intro #309]: #311
-#291 := [asserted]: #21
-#315 := [mp #291 #312]: #310
-#1840 := [mp~ #315 #1869]: #310
-#4177 := [mp #1840 #4176]: #4172
-#6290 := (not #4172)
-#9958 := (or #6290 #9955)
-#9944 := (= #7211 ?v0!15)
-#9945 := (ite #9944 #5892 #7669)
-#9948 := (iff #9947 #9945)
-#9959 := (or #6290 #9948)
-#9961 := (iff #9959 #9958)
-#9963 := (iff #9958 #9958)
-#9964 := [rewrite]: #9963
-#9956 := (iff #9948 #9955)
-#9953 := (iff #9945 #9952)
-#9950 := (iff #9944 #9949)
-#9951 := [rewrite]: #9950
-#9954 := [monotonicity #9951]: #9953
-#9957 := [monotonicity #9954]: #9956
-#9962 := [monotonicity #9957]: #9961
-#9965 := [trans #9962 #9964]: #9961
-#9960 := [quant-inst #104 #7211 #5891 #2273]: #9959
-#9966 := [mp #9960 #9965]: #9958
-#10088 := [unit-resolution #9966 #4177]: #9955
-#9981 := (not #9947)
-#7533 := (f3 f23 ?v0!15)
-#7534 := (= f1 #7533)
-#7535 := (not #7534)
-#10097 := (iff #7535 #9981)
-#10095 := (iff #7534 #9947)
-#10093 := (iff #9947 #7534)
-#10091 := (= #9946 #7533)
-#9285 := (= #8442 f23)
-#7004 := (= #773 f23)
-#4053 := (or #4535 #776)
-#4048 := [def-axiom]: #4053
-#6998 := [unit-resolution #4048 #6508]: #776
-#7005 := [symm #6998]: #7004
-#9283 := (= #8442 #773)
-#7000 := (= #5891 f1)
+#310 := (iff #21 #309)
+#307 := (iff #20 #306)
+#304 := (iff #19 #303)
+#301 := (iff #18 #300)
+#302 := [rewrite]: #301
+#298 := (iff #16 #297)
+#299 := [rewrite]: #298
+#295 := (iff #15 #294)
+#296 := [rewrite]: #295
+#305 := [monotonicity #296 #299 #302]: #304
+#292 := (iff #14 #291)
+#293 := [rewrite]: #292
+#308 := [monotonicity #293 #305]: #307
+#311 := [quant-intro #308]: #310
+#290 := [asserted]: #21
+#314 := [mp #290 #311]: #309
+#1831 := [mp~ #314 #1860]: #309
+#4168 := [mp #1831 #4167]: #4163
+#6281 := (not #4163)
+#9949 := (or #6281 #9946)
+#9935 := (= #7202 ?v0!15)
+#9936 := (ite #9935 #5883 #7660)
+#9939 := (iff #9938 #9936)
+#9950 := (or #6281 #9939)
+#9952 := (iff #9950 #9949)
+#9954 := (iff #9949 #9949)
+#9955 := [rewrite]: #9954
+#9947 := (iff #9939 #9946)
+#9944 := (iff #9936 #9943)
+#9941 := (iff #9935 #9940)
+#9942 := [rewrite]: #9941
+#9945 := [monotonicity #9942]: #9944
+#9948 := [monotonicity #9945]: #9947
+#9953 := [monotonicity #9948]: #9952
+#9956 := [trans #9953 #9955]: #9952
+#9951 := [quant-inst #104 #7202 #5882 #2264]: #9950
+#9957 := [mp #9951 #9956]: #9949
+#10079 := [unit-resolution #9957 #4168]: #9946
+#9972 := (not #9938)
+#7524 := (f3 f23 ?v0!15)
+#7525 := (= f1 #7524)
+#7526 := (not #7525)
+#10088 := (iff #7526 #9972)
+#10086 := (iff #7525 #9938)
+#10084 := (iff #9938 #7525)
+#10082 := (= #9937 #7524)
+#9276 := (= #8433 f23)
+#6995 := (= #180 f23)
+#4042 := (or #4526 #181)
+#4043 := [def-axiom]: #4042
+#6989 := [unit-resolution #4043 #6499]: #181
+#6996 := [symm #6989]: #6995
+#9274 := (= #8433 #180)
+#6991 := (= #5882 f1)
 #24 := (:var 0 S1)
 #22 := (:var 2 S2)
 #25 := (f4 #22 #23 #24)
-#4178 := (pattern #25)
-#318 := (= f1 #24)
+#4169 := (pattern #25)
+#317 := (= f1 #24)
 #26 := (f3 #25 #23)
-#314 := (= f1 #26)
-#321 := (iff #314 #318)
-#4179 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) (:pat #4178) #321)
-#324 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #321)
-#4182 := (iff #324 #4179)
-#4180 := (iff #321 #321)
-#4181 := [refl]: #4180
-#4183 := [quant-intro #4181]: #4182
-#1842 := (~ #324 #324)
-#1841 := (~ #321 #321)
-#1870 := [refl]: #1841
-#1843 := [nnf-pos #1870]: #1842
+#313 := (= f1 #26)
+#320 := (iff #313 #317)
+#4170 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) (:pat #4169) #320)
+#323 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #320)
+#4173 := (iff #323 #4170)
+#4171 := (iff #320 #320)
+#4172 := [refl]: #4171
+#4174 := [quant-intro #4172]: #4173
+#1833 := (~ #323 #323)
+#1832 := (~ #320 #320)
+#1861 := [refl]: #1832
+#1834 := [nnf-pos #1861]: #1833
 #28 := (= #24 f1)
 #27 := (= #26 f1)
 #29 := (iff #27 #28)
 #30 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #29)
-#325 := (iff #30 #324)
-#322 := (iff #29 #321)
-#319 := (iff #28 #318)
-#320 := [rewrite]: #319
-#316 := (iff #27 #314)
-#317 := [rewrite]: #316
-#323 := [monotonicity #317 #320]: #322
-#326 := [quant-intro #323]: #325
-#313 := [asserted]: #30
-#329 := [mp #313 #326]: #324
-#1871 := [mp~ #329 #1843]: #324
-#4184 := [mp #1871 #4183]: #4179
-#5903 := (not #4179)
-#5904 := (or #5903 #5892)
-#5890 := (= f1 f1)
-#5893 := (iff #5892 #5890)
-#5905 := (or #5903 #5893)
-#5907 := (iff #5905 #5904)
-#5909 := (iff #5904 #5904)
-#5910 := [rewrite]: #5909
-#5901 := (iff #5893 #5892)
-#5896 := (iff #5892 true)
-#5899 := (iff #5896 #5892)
-#5900 := [rewrite]: #5899
-#5897 := (iff #5893 #5896)
-#5894 := (iff #5890 true)
-#5895 := [rewrite]: #5894
-#5898 := [monotonicity #5895]: #5897
-#5902 := [trans #5898 #5900]: #5901
-#5908 := [monotonicity #5902]: #5907
-#5911 := [trans #5908 #5910]: #5907
-#5906 := [quant-inst #104 #170 #4]: #5905
-#5912 := [mp #5906 #5911]: #5904
-#6999 := [unit-resolution #5912 #4184]: #5892
-#7001 := [symm #6999]: #7000
-#9284 := [monotonicity #7790 #7001]: #9283
-#9286 := [trans #9284 #7005]: #9285
-#10092 := [monotonicity #9286]: #10091
-#10094 := [monotonicity #10092]: #10093
-#10096 := [symm #10094]: #10095
-#10098 := [monotonicity #10096]: #10097
-#7545 := (or #7535 #7539)
-#4019 := (or #4535 #4529)
-#4020 := [def-axiom]: #4019
-#7096 := [unit-resolution #4020 #6508]: #4529
-#6311 := (f5 f22 ?v0!13)
-#6312 := (f9 #6311)
-#6337 := (+ #2232 #6312)
-#6338 := (+ #174 #6337)
-#6359 := (>= #6338 0::Int)
-#6341 := (= #6338 0::Int)
-#6316 := (* -1::Int #6312)
-#6320 := (+ f8 #6316)
-#6321 := (<= #6320 0::Int)
-#6388 := (not #6321)
-#6330 := (+ #2848 #6312)
-#6331 := (+ #174 #6330)
-#6332 := (>= #6331 0::Int)
-#6367 := (or #6321 #6332)
-#6370 := (not #6367)
-#6364 := (= #2231 #2233)
-#6489 := (not #6364)
-#6488 := [hypothesis]: #2855
-#6492 := (or #6489 #2850)
-#6493 := [th-lemma arith triangle-eq]: #6492
-#6494 := [unit-resolution #6493 #6488]: #6489
-#6376 := (or #4401 #6364 #6370)
-#6317 := (+ #1453 #6316)
-#6318 := (+ #2233 #6317)
-#6319 := (<= #6318 0::Int)
-#6360 := (or #6321 #6319)
-#6361 := (not #6360)
-#6362 := (= #2233 #2231)
-#6363 := (or #6362 #6361)
-#6377 := (or #4401 #6363)
-#6384 := (iff #6377 #6376)
-#6373 := (or #6364 #6370)
-#6379 := (or #4401 #6373)
-#6382 := (iff #6379 #6376)
-#6383 := [rewrite]: #6382
-#6380 := (iff #6377 #6379)
-#6374 := (iff #6363 #6373)
-#6371 := (iff #6361 #6370)
-#6368 := (iff #6360 #6367)
-#6335 := (iff #6319 #6332)
-#6323 := (+ #2233 #6316)
-#6324 := (+ #1453 #6323)
-#6327 := (<= #6324 0::Int)
-#6333 := (iff #6327 #6332)
-#6334 := [rewrite]: #6333
-#6328 := (iff #6319 #6327)
-#6325 := (= #6318 #6324)
-#6326 := [rewrite]: #6325
-#6329 := [monotonicity #6326]: #6328
-#6336 := [trans #6329 #6334]: #6335
-#6369 := [monotonicity #6336]: #6368
-#6372 := [monotonicity #6369]: #6371
-#6365 := (iff #6362 #6364)
-#6366 := [rewrite]: #6365
-#6375 := [monotonicity #6366 #6372]: #6374
-#6381 := [monotonicity #6375]: #6380
-#6385 := [trans #6381 #6383]: #6384
-#6378 := [quant-inst #2230]: #6377
-#6386 := [mp #6378 #6385]: #6376
-#6510 := [unit-resolution #6386 #6509 #6494]: #6370
-#6389 := (or #6367 #6388)
-#6390 := [def-axiom]: #6389
-#6511 := [unit-resolution #6390 #6510]: #6388
-#6391 := (not #6332)
-#6392 := (or #6367 #6391)
-#6393 := [def-axiom]: #6392
-#6512 := [unit-resolution #6393 #6510]: #6391
-#6344 := (or #6321 #6332 #6341)
-#6347 := (or #4409 #6321 #6332 #6341)
-#6313 := (+ #6312 #2232)
-#6314 := (+ #174 #6313)
-#6315 := (= #6314 0::Int)
-#6322 := (or #6321 #6319 #6315)
-#6348 := (or #4409 #6322)
-#6355 := (iff #6348 #6347)
-#6350 := (or #4409 #6344)
-#6353 := (iff #6350 #6347)
-#6354 := [rewrite]: #6353
-#6351 := (iff #6348 #6350)
-#6345 := (iff #6322 #6344)
-#6342 := (iff #6315 #6341)
-#6339 := (= #6314 #6338)
-#6340 := [rewrite]: #6339
-#6343 := [monotonicity #6340]: #6342
-#6346 := [monotonicity #6336 #6343]: #6345
-#6352 := [monotonicity #6346]: #6351
-#6356 := [trans #6352 #6354]: #6355
-#6349 := [quant-inst #2230]: #6348
-#6357 := [mp #6349 #6356]: #6347
-#6514 := [unit-resolution #6357 #6513]: #6344
-#6515 := [unit-resolution #6514 #6512 #6511]: #6341
-#6516 := (not #6341)
-#6517 := (or #6516 #6359)
-#6518 := [th-lemma arith triangle-eq]: #6517
-#6519 := [unit-resolution #6518 #6515]: #6359
-#6387 := (>= #2849 0::Int)
-#6520 := (or #6387 #2850)
-#6521 := [th-lemma arith farkas 1 1]: #6520
-#6522 := [unit-resolution #6521 #6488]: #6387
-#6523 := [th-lemma arith farkas 1 -1 1 #6522 #6512 #6519]: false
-#6524 := [lemma #6523]: #2850
-#4049 := (or #4532 #2855 #4526)
-#4050 := [def-axiom]: #4049
-#7097 := [unit-resolution #4050 #6524 #7096]: #4526
-#4064 := (or #4523 #4517)
-#4065 := [def-axiom]: #4064
-#7098 := [unit-resolution #4065 #7097]: #4517
-#6879 := (= #174 #2253)
-#6696 := (= f22 ?v0!14)
-#6526 := (f3 f15 ?v0!14)
-#6527 := (= f1 #6526)
-#6697 := (ite #6696 #5892 #6527)
-#6269 := (f4 f15 f22 #5891)
-#6700 := (f3 #6269 ?v0!14)
-#6701 := (= f1 #6700)
-#6703 := (iff #6697 #6701)
-#6706 := (or #6290 #6703)
-#6702 := (iff #6701 #6697)
-#6707 := (or #6290 #6702)
-#6709 := (iff #6707 #6706)
-#6711 := (iff #6706 #6706)
-#6712 := [rewrite]: #6711
-#6704 := (iff #6702 #6703)
-#6705 := [rewrite]: #6704
-#6710 := [monotonicity #6705]: #6709
-#6713 := [trans #6710 #6712]: #6709
-#6708 := [quant-inst #104 #170 #5891 #2248]: #6707
-#6714 := [mp #6708 #6713]: #6706
-#6996 := [unit-resolution #6714 #4177]: #6703
-#7012 := (= #2249 #6700)
-#7008 := (= #6700 #2249)
-#7006 := (= #6269 f23)
-#7002 := (= #6269 #773)
-#7003 := [monotonicity #7001]: #7002
-#7007 := [trans #7003 #7005]: #7006
-#7009 := [monotonicity #7007]: #7008
-#7013 := [symm #7009]: #7012
-#6994 := [hypothesis]: #2869
-#4127 := (or #2864 #2250)
-#4128 := [def-axiom]: #4127
-#6997 := [unit-resolution #4128 #6994]: #2250
-#7014 := [trans #6997 #7013]: #6701
-#6727 := (not #6701)
-#6726 := (not #6703)
-#6728 := (or #6726 #6697 #6727)
-#6729 := [def-axiom]: #6728
-#7015 := [unit-resolution #6729 #7014 #6996]: #6697
-#6555 := (f5 f22 ?v0!14)
-#6556 := (f9 #6555)
-#6486 := (* -1::Int #2253)
-#6573 := (+ #6486 #6556)
-#6574 := (+ #174 #6573)
-#6575 := (>= #6574 0::Int)
-#6603 := (not #6575)
-#6557 := (* -1::Int #6556)
-#6561 := (+ f8 #6557)
-#6562 := (<= #6561 0::Int)
-#6580 := (or #6562 #6575)
-#6583 := (not #6580)
-#4123 := (not #2858)
-#4124 := (or #2864 #4123)
-#4129 := [def-axiom]: #4124
-#6995 := [unit-resolution #4129 #6994]: #4123
-#6589 := (or #4401 #2858 #6583)
-#6558 := (+ #1453 #6557)
-#6559 := (+ #2253 #6558)
-#6560 := (<= #6559 0::Int)
-#6563 := (or #6562 #6560)
-#6564 := (not #6563)
-#6565 := (or #2254 #6564)
-#6590 := (or #4401 #6565)
-#6597 := (iff #6590 #6589)
-#6586 := (or #2858 #6583)
-#6592 := (or #4401 #6586)
-#6595 := (iff #6592 #6589)
-#6596 := [rewrite]: #6595
-#6593 := (iff #6590 #6592)
-#6587 := (iff #6565 #6586)
-#6584 := (iff #6564 #6583)
-#6581 := (iff #6563 #6580)
-#6578 := (iff #6560 #6575)
-#6566 := (+ #2253 #6557)
-#6567 := (+ #1453 #6566)
-#6570 := (<= #6567 0::Int)
-#6576 := (iff #6570 #6575)
-#6577 := [rewrite]: #6576
-#6571 := (iff #6560 #6570)
-#6568 := (= #6559 #6567)
-#6569 := [rewrite]: #6568
-#6572 := [monotonicity #6569]: #6571
-#6579 := [trans #6572 #6577]: #6578
-#6582 := [monotonicity #6579]: #6581
-#6585 := [monotonicity #6582]: #6584
-#6588 := [monotonicity #2860 #6585]: #6587
-#6594 := [monotonicity #6588]: #6593
-#6598 := [trans #6594 #6596]: #6597
-#6591 := [quant-inst #2248]: #6590
-#6599 := [mp #6591 #6598]: #6589
-#7016 := [unit-resolution #6599 #6509 #6995]: #6583
-#6604 := (or #6580 #6603)
-#6605 := [def-axiom]: #6604
-#7017 := [unit-resolution #6605 #7016]: #6603
-#6715 := (not #6697)
-#6941 := (or #6696 #6575 #6715)
-#6822 := (f6 #6555)
-#6832 := (f13 f14 #6822)
-#6847 := (* -1::Int #6832)
-#6887 := (+ #174 #6847)
-#6889 := (>= #6887 0::Int)
-#6886 := (= #174 #6832)
-#6893 := (= #6832 #174)
-#6891 := (= #6822 f22)
-#6823 := (= f22 #6822)
-#6830 := (or #6829 #6823)
-#6831 := [quant-inst #170 #2248]: #6830
-#6890 := [unit-resolution #6831 #4205]: #6823
-#6892 := [symm #6890]: #6891
-#6894 := [monotonicity #6892]: #6893
-#6895 := [symm #6894]: #6886
-#6896 := (not #6886)
-#6897 := (or #6896 #6889)
-#6898 := [th-lemma arith triangle-eq]: #6897
-#6899 := [unit-resolution #6898 #6895]: #6889
-#6900 := [hypothesis]: #6603
-#6819 := (>= #6556 0::Int)
-#6773 := (<= #6556 0::Int)
-#6774 := (not #6773)
-#6716 := (not #6696)
-#6901 := [hypothesis]: #6716
-#6779 := (or #6696 #6774)
+#324 := (iff #30 #323)
+#321 := (iff #29 #320)
+#318 := (iff #28 #317)
+#319 := [rewrite]: #318
+#315 := (iff #27 #313)
+#316 := [rewrite]: #315
+#322 := [monotonicity #316 #319]: #321
+#325 := [quant-intro #322]: #324
+#312 := [asserted]: #30
+#328 := [mp #312 #325]: #323
+#1862 := [mp~ #328 #1834]: #323
+#4175 := [mp #1862 #4174]: #4170
+#5894 := (not #4170)
+#5895 := (or #5894 #5883)
+#5881 := (= f1 f1)
+#5884 := (iff #5883 #5881)
+#5896 := (or #5894 #5884)
+#5898 := (iff #5896 #5895)
+#5900 := (iff #5895 #5895)
+#5901 := [rewrite]: #5900
+#5892 := (iff #5884 #5883)
+#5887 := (iff #5883 true)
+#5890 := (iff #5887 #5883)
+#5891 := [rewrite]: #5890
+#5888 := (iff #5884 #5887)
+#5885 := (iff #5881 true)
+#5886 := [rewrite]: #5885
+#5889 := [monotonicity #5886]: #5888
+#5893 := [trans #5889 #5891]: #5892
+#5899 := [monotonicity #5893]: #5898
+#5902 := [trans #5899 #5901]: #5898
+#5897 := [quant-inst #104 #170 #4]: #5896
+#5903 := [mp #5897 #5902]: #5895
+#6990 := [unit-resolution #5903 #4175]: #5883
+#6992 := [symm #6990]: #6991
+#9275 := [monotonicity #7781 #6992]: #9274
+#9277 := [trans #9275 #6996]: #9276
+#10083 := [monotonicity #9277]: #10082
+#10085 := [monotonicity #10083]: #10084
+#10087 := [symm #10085]: #10086
+#10089 := [monotonicity #10087]: #10088
+#7536 := (or #7526 #7530)
+#4010 := (or #4526 #4520)
+#4011 := [def-axiom]: #4010
+#7087 := [unit-resolution #4011 #6499]: #4520
+#6302 := (f5 f22 ?v0!13)
+#6303 := (f9 #6302)
+#6328 := (+ #2223 #6303)
+#6329 := (+ #174 #6328)
+#6350 := (>= #6329 0::Int)
+#6332 := (= #6329 0::Int)
+#6307 := (* -1::Int #6303)
+#6311 := (+ f8 #6307)
+#6312 := (<= #6311 0::Int)
+#6379 := (not #6312)
+#6321 := (+ #2839 #6303)
+#6322 := (+ #174 #6321)
+#6323 := (>= #6322 0::Int)
+#6358 := (or #6312 #6323)
+#6361 := (not #6358)
+#6355 := (= #2222 #2224)
+#6480 := (not #6355)
+#6479 := [hypothesis]: #2846
+#6483 := (or #6480 #2841)
+#6484 := [th-lemma arith triangle-eq]: #6483
+#6485 := [unit-resolution #6484 #6479]: #6480
+#6367 := (or #4392 #6355 #6361)
+#6308 := (+ #1444 #6307)
+#6309 := (+ #2224 #6308)
+#6310 := (<= #6309 0::Int)
+#6351 := (or #6312 #6310)
+#6352 := (not #6351)
+#6353 := (= #2224 #2222)
+#6354 := (or #6353 #6352)
+#6368 := (or #4392 #6354)
+#6375 := (iff #6368 #6367)
+#6364 := (or #6355 #6361)
+#6370 := (or #4392 #6364)
+#6373 := (iff #6370 #6367)
+#6374 := [rewrite]: #6373
+#6371 := (iff #6368 #6370)
+#6365 := (iff #6354 #6364)
+#6362 := (iff #6352 #6361)
+#6359 := (iff #6351 #6358)
+#6326 := (iff #6310 #6323)
+#6314 := (+ #2224 #6307)
+#6315 := (+ #1444 #6314)
+#6318 := (<= #6315 0::Int)
+#6324 := (iff #6318 #6323)
+#6325 := [rewrite]: #6324
+#6319 := (iff #6310 #6318)
+#6316 := (= #6309 #6315)
+#6317 := [rewrite]: #6316
+#6320 := [monotonicity #6317]: #6319
+#6327 := [trans #6320 #6325]: #6326
+#6360 := [monotonicity #6327]: #6359
+#6363 := [monotonicity #6360]: #6362
+#6356 := (iff #6353 #6355)
+#6357 := [rewrite]: #6356
+#6366 := [monotonicity #6357 #6363]: #6365
+#6372 := [monotonicity #6366]: #6371
+#6376 := [trans #6372 #6374]: #6375
+#6369 := [quant-inst #2221]: #6368
+#6377 := [mp #6369 #6376]: #6367
+#6501 := [unit-resolution #6377 #6500 #6485]: #6361
+#6380 := (or #6358 #6379)
+#6381 := [def-axiom]: #6380
+#6502 := [unit-resolution #6381 #6501]: #6379
+#6382 := (not #6323)
+#6383 := (or #6358 #6382)
+#6384 := [def-axiom]: #6383
+#6503 := [unit-resolution #6384 #6501]: #6382
+#6335 := (or #6312 #6323 #6332)
+#6338 := (or #4400 #6312 #6323 #6332)
+#6304 := (+ #6303 #2223)
+#6305 := (+ #174 #6304)
+#6306 := (= #6305 0::Int)
+#6313 := (or #6312 #6310 #6306)
+#6339 := (or #4400 #6313)
+#6346 := (iff #6339 #6338)
+#6341 := (or #4400 #6335)
+#6344 := (iff #6341 #6338)
+#6345 := [rewrite]: #6344
+#6342 := (iff #6339 #6341)
+#6336 := (iff #6313 #6335)
+#6333 := (iff #6306 #6332)
+#6330 := (= #6305 #6329)
+#6331 := [rewrite]: #6330
+#6334 := [monotonicity #6331]: #6333
+#6337 := [monotonicity #6327 #6334]: #6336
+#6343 := [monotonicity #6337]: #6342
+#6347 := [trans #6343 #6345]: #6346
+#6340 := [quant-inst #2221]: #6339
+#6348 := [mp #6340 #6347]: #6338
+#6505 := [unit-resolution #6348 #6504]: #6335
+#6506 := [unit-resolution #6505 #6503 #6502]: #6332
+#6507 := (not #6332)
+#6508 := (or #6507 #6350)
+#6509 := [th-lemma arith triangle-eq]: #6508
+#6510 := [unit-resolution #6509 #6506]: #6350
+#6378 := (>= #2840 0::Int)
+#6511 := (or #6378 #2841)
+#6512 := [th-lemma arith farkas 1 1]: #6511
+#6513 := [unit-resolution #6512 #6479]: #6378
+#6514 := [th-lemma arith farkas 1 -1 1 #6513 #6503 #6510]: false
+#6515 := [lemma #6514]: #2841
+#4040 := (or #4523 #2846 #4517)
+#4041 := [def-axiom]: #4040
+#7088 := [unit-resolution #4041 #6515 #7087]: #4517
+#4055 := (or #4514 #4508)
+#4056 := [def-axiom]: #4055
+#7089 := [unit-resolution #4056 #7088]: #4508
+#6870 := (= #174 #2244)
+#6687 := (= f22 ?v0!14)
+#6517 := (f3 f15 ?v0!14)
+#6518 := (= f1 #6517)
+#6688 := (ite #6687 #5883 #6518)
+#6260 := (f4 f15 f22 #5882)
+#6691 := (f3 #6260 ?v0!14)
+#6692 := (= f1 #6691)
+#6694 := (iff #6688 #6692)
+#6697 := (or #6281 #6694)
+#6693 := (iff #6692 #6688)
+#6698 := (or #6281 #6693)
+#6700 := (iff #6698 #6697)
+#6702 := (iff #6697 #6697)
+#6703 := [rewrite]: #6702
+#6695 := (iff #6693 #6694)
+#6696 := [rewrite]: #6695
+#6701 := [monotonicity #6696]: #6700
+#6704 := [trans #6701 #6703]: #6700
+#6699 := [quant-inst #104 #170 #5882 #2239]: #6698
+#6705 := [mp #6699 #6704]: #6697
+#6987 := [unit-resolution #6705 #4168]: #6694
+#7003 := (= #2240 #6691)
+#6999 := (= #6691 #2240)
+#6997 := (= #6260 f23)
+#6993 := (= #6260 #180)
+#6994 := [monotonicity #6992]: #6993
+#6998 := [trans #6994 #6996]: #6997
+#7000 := [monotonicity #6998]: #6999
+#7004 := [symm #7000]: #7003
+#6985 := [hypothesis]: #2860
+#4118 := (or #2855 #2241)
+#4119 := [def-axiom]: #4118
+#6988 := [unit-resolution #4119 #6985]: #2241
+#7005 := [trans #6988 #7004]: #6692
+#6718 := (not #6692)
+#6717 := (not #6694)
+#6719 := (or #6717 #6688 #6718)
+#6720 := [def-axiom]: #6719
+#7006 := [unit-resolution #6720 #7005 #6987]: #6688
+#6546 := (f5 f22 ?v0!14)
+#6547 := (f9 #6546)
+#6477 := (* -1::Int #2244)
+#6564 := (+ #6477 #6547)
+#6565 := (+ #174 #6564)
+#6566 := (>= #6565 0::Int)
+#6594 := (not #6566)
+#6548 := (* -1::Int #6547)
+#6552 := (+ f8 #6548)
+#6553 := (<= #6552 0::Int)
+#6571 := (or #6553 #6566)
+#6574 := (not #6571)
+#4114 := (not #2849)
+#4115 := (or #2855 #4114)
+#4120 := [def-axiom]: #4115
+#6986 := [unit-resolution #4120 #6985]: #4114
+#6580 := (or #4392 #2849 #6574)
+#6549 := (+ #1444 #6548)
+#6550 := (+ #2244 #6549)
+#6551 := (<= #6550 0::Int)
+#6554 := (or #6553 #6551)
+#6555 := (not #6554)
+#6556 := (or #2245 #6555)
+#6581 := (or #4392 #6556)
+#6588 := (iff #6581 #6580)
+#6577 := (or #2849 #6574)
+#6583 := (or #4392 #6577)
+#6586 := (iff #6583 #6580)
+#6587 := [rewrite]: #6586
+#6584 := (iff #6581 #6583)
+#6578 := (iff #6556 #6577)
+#6575 := (iff #6555 #6574)
+#6572 := (iff #6554 #6571)
+#6569 := (iff #6551 #6566)
+#6557 := (+ #2244 #6548)
+#6558 := (+ #1444 #6557)
+#6561 := (<= #6558 0::Int)
+#6567 := (iff #6561 #6566)
+#6568 := [rewrite]: #6567
+#6562 := (iff #6551 #6561)
+#6559 := (= #6550 #6558)
+#6560 := [rewrite]: #6559
+#6563 := [monotonicity #6560]: #6562
+#6570 := [trans #6563 #6568]: #6569
+#6573 := [monotonicity #6570]: #6572
+#6576 := [monotonicity #6573]: #6575
+#6579 := [monotonicity #2851 #6576]: #6578
+#6585 := [monotonicity #6579]: #6584
+#6589 := [trans #6585 #6587]: #6588
+#6582 := [quant-inst #2239]: #6581
+#6590 := [mp #6582 #6589]: #6580
+#7007 := [unit-resolution #6590 #6500 #6986]: #6574
+#6595 := (or #6571 #6594)
+#6596 := [def-axiom]: #6595
+#7008 := [unit-resolution #6596 #7007]: #6594
+#6706 := (not #6688)
+#6932 := (or #6687 #6566 #6706)
+#6813 := (f6 #6546)
+#6823 := (f13 f14 #6813)
+#6838 := (* -1::Int #6823)
+#6878 := (+ #174 #6838)
+#6880 := (>= #6878 0::Int)
+#6877 := (= #174 #6823)
+#6884 := (= #6823 #174)
+#6882 := (= #6813 f22)
+#6814 := (= f22 #6813)
+#6821 := (or #6820 #6814)
+#6822 := [quant-inst #170 #2239]: #6821
+#6881 := [unit-resolution #6822 #4196]: #6814
+#6883 := [symm #6881]: #6882
+#6885 := [monotonicity #6883]: #6884
+#6886 := [symm #6885]: #6877
+#6887 := (not #6877)
+#6888 := (or #6887 #6880)
+#6889 := [th-lemma arith triangle-eq]: #6888
+#6890 := [unit-resolution #6889 #6886]: #6880
+#6891 := [hypothesis]: #6594
+#6810 := (>= #6547 0::Int)
+#6764 := (<= #6547 0::Int)
+#6765 := (not #6764)
+#6707 := (not #6687)
+#6892 := [hypothesis]: #6707
+#6770 := (or #6687 #6765)
 #48 := (f9 #37)
-#407 := (<= #48 0::Int)
-#408 := (not #407)
-#354 := (= #12 #23)
-#414 := (or #354 #408)
-#4212 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4193) #414)
-#419 := (forall (vars (?v0 S3) (?v1 S3)) #414)
-#4215 := (iff #419 #4212)
-#4213 := (iff #414 #414)
-#4214 := [refl]: #4213
-#4216 := [quant-intro #4214]: #4215
-#1854 := (~ #419 #419)
-#1853 := (~ #414 #414)
-#1883 := [refl]: #1853
-#1855 := [nnf-pos #1883]: #1854
+#406 := (<= #48 0::Int)
+#407 := (not #406)
+#353 := (= #12 #23)
+#413 := (or #353 #407)
+#4203 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #413)
+#418 := (forall (vars (?v0 S3) (?v1 S3)) #413)
+#4206 := (iff #418 #4203)
+#4204 := (iff #413 #413)
+#4205 := [refl]: #4204
+#4207 := [quant-intro #4205]: #4206
+#1845 := (~ #418 #418)
+#1844 := (~ #413 #413)
+#1874 := [refl]: #1844
+#1846 := [nnf-pos #1874]: #1845
 #53 := (< 0::Int #48)
 #47 := (= #23 #12)
 #52 := (not #47)
 #54 := (implies #52 #53)
 #55 := (forall (vars (?v0 S3) (?v1 S3)) #54)
-#422 := (iff #55 #419)
-#399 := (or #53 #354)
-#404 := (forall (vars (?v0 S3) (?v1 S3)) #399)
-#420 := (iff #404 #419)
-#417 := (iff #399 #414)
-#411 := (or #408 #354)
-#415 := (iff #411 #414)
-#416 := [rewrite]: #415
-#412 := (iff #399 #411)
-#409 := (iff #53 #408)
-#410 := [rewrite]: #409
-#413 := [monotonicity #410]: #412
-#418 := [trans #413 #416]: #417
-#421 := [quant-intro #418]: #420
-#405 := (iff #55 #404)
-#402 := (iff #54 #399)
-#368 := (not #354)
-#396 := (implies #368 #53)
-#400 := (iff #396 #399)
-#401 := [rewrite]: #400
-#397 := (iff #54 #396)
-#394 := (iff #52 #368)
-#360 := (iff #47 #354)
-#361 := [rewrite]: #360
-#395 := [monotonicity #361]: #394
-#398 := [monotonicity #395]: #397
-#403 := [trans #398 #401]: #402
-#406 := [quant-intro #403]: #405
-#423 := [trans #406 #421]: #422
-#393 := [asserted]: #55
-#424 := [mp #393 #423]: #419
-#1884 := [mp~ #424 #1855]: #419
-#4217 := [mp #1884 #4216]: #4212
-#6782 := (not #4212)
-#6783 := (or #6782 #6696 #6774)
-#6775 := (= ?v0!14 f22)
-#6776 := (or #6775 #6774)
-#6784 := (or #6782 #6776)
-#6791 := (iff #6784 #6783)
-#6786 := (or #6782 #6779)
-#6789 := (iff #6786 #6783)
-#6790 := [rewrite]: #6789
-#6787 := (iff #6784 #6786)
-#6780 := (iff #6776 #6779)
-#6777 := (iff #6775 #6696)
-#6778 := [rewrite]: #6777
-#6781 := [monotonicity #6778]: #6780
-#6788 := [monotonicity #6781]: #6787
-#6792 := [trans #6788 #6790]: #6791
-#6785 := [quant-inst #170 #2248]: #6784
-#6793 := [mp #6785 #6792]: #6783
-#6902 := [unit-resolution #6793 #4217]: #6779
-#6903 := [unit-resolution #6902 #6901]: #6774
-#6904 := (or #6819 #6773)
-#6905 := [th-lemma arith farkas 1 1]: #6904
-#6906 := [unit-resolution #6905 #6903]: #6819
-#6820 := (f7 #6555)
-#6827 := (f13 f14 #6820)
-#6828 := (* -1::Int #6827)
-#6877 := (+ #2253 #6828)
-#6884 := (<= #6877 0::Int)
-#6876 := (= #2253 #6827)
-#6910 := (= #6827 #2253)
-#6908 := (= #6820 ?v0!14)
-#6821 := (= ?v0!14 #6820)
-#6825 := (or #6824 #6821)
-#6826 := [quant-inst #170 #2248]: #6825
-#6907 := [unit-resolution #6826 #4199]: #6821
-#6909 := [symm #6907]: #6908
-#6911 := [monotonicity #6909]: #6910
-#6912 := [symm #6911]: #6876
-#6913 := (not #6876)
-#6914 := (or #6913 #6884)
-#6915 := [th-lemma arith triangle-eq]: #6914
-#6916 := [unit-resolution #6915 #6912]: #6884
-#6848 := (+ #6827 #6847)
-#6849 := (<= #6848 0::Int)
-#6835 := (f3 f15 #6820)
-#6836 := (= f1 #6835)
-#6923 := (= #6526 #6835)
-#6919 := (= #6835 #6526)
-#6920 := [monotonicity #6909]: #6919
-#6924 := [symm #6920]: #6923
-#6917 := [hypothesis]: #6697
-#6719 := (or #6715 #6696 #6527)
-#6720 := [def-axiom]: #6719
-#6918 := [unit-resolution #6720 #6901 #6917]: #6527
-#6925 := [trans #6918 #6924]: #6836
-#6838 := (f3 f15 #6822)
-#6839 := (= f1 #6838)
-#6933 := (not #6839)
-#6934 := (iff #757 #6933)
-#6931 := (iff #754 #6839)
-#6929 := (iff #6839 #754)
-#6927 := (= #6838 #171)
-#6928 := [monotonicity #6892]: #6927
-#6930 := [monotonicity #6928]: #6929
-#6932 := [symm #6930]: #6931
-#6935 := [monotonicity #6932]: #6934
-#4051 := (or #4535 #757)
-#4052 := [def-axiom]: #4051
-#6926 := [unit-resolution #4052 #6508]: #757
-#6936 := [mp #6926 #6935]: #6933
-#6837 := (not #6836)
-#6857 := (or #6837 #6839 #6849)
-#3961 := (or #4547 #4291)
-#4016 := [def-axiom]: #3961
-#6937 := [unit-resolution #4016 #6507]: #4291
-#6862 := (or #4296 #6837 #6839 #6849)
-#6833 := (+ #6832 #6828)
-#6834 := (>= #6833 0::Int)
-#6840 := (or #6839 #6837 #6834)
-#6863 := (or #4296 #6840)
-#6870 := (iff #6863 #6862)
-#6865 := (or #4296 #6857)
-#6868 := (iff #6865 #6862)
-#6869 := [rewrite]: #6868
-#6866 := (iff #6863 #6865)
-#6860 := (iff #6840 #6857)
-#6854 := (or #6839 #6837 #6849)
-#6858 := (iff #6854 #6857)
-#6859 := [rewrite]: #6858
-#6855 := (iff #6840 #6854)
-#6852 := (iff #6834 #6849)
-#6841 := (+ #6828 #6832)
-#6844 := (>= #6841 0::Int)
-#6850 := (iff #6844 #6849)
-#6851 := [rewrite]: #6850
-#6845 := (iff #6834 #6844)
-#6842 := (= #6833 #6841)
-#6843 := [rewrite]: #6842
-#6846 := [monotonicity #6843]: #6845
-#6853 := [trans #6846 #6851]: #6852
-#6856 := [monotonicity #6853]: #6855
-#6861 := [trans #6856 #6859]: #6860
-#6867 := [monotonicity #6861]: #6866
-#6871 := [trans #6867 #6869]: #6870
-#6864 := [quant-inst #6820 #6822]: #6863
-#6872 := [mp #6864 #6871]: #6862
-#6938 := [unit-resolution #6872 #6937]: #6857
-#6939 := [unit-resolution #6938 #6936 #6925]: #6849
-#6940 := [th-lemma arith farkas 1 1 1 -1 1 #6939 #6916 #6906 #6900 #6899]: false
-#6942 := [lemma #6940]: #6941
-#7018 := [unit-resolution #6942 #7017 #7015]: #6696
-#7042 := [monotonicity #7018]: #6879
-#7040 := (= #2252 #174)
-#7038 := (= #174 #2252)
-#6795 := (= #6556 0::Int)
-#6802 := (or #6716 #6795)
+#421 := (iff #55 #418)
+#398 := (or #53 #353)
+#403 := (forall (vars (?v0 S3) (?v1 S3)) #398)
+#419 := (iff #403 #418)
+#416 := (iff #398 #413)
+#410 := (or #407 #353)
+#414 := (iff #410 #413)
+#415 := [rewrite]: #414
+#411 := (iff #398 #410)
+#408 := (iff #53 #407)
+#409 := [rewrite]: #408
+#412 := [monotonicity #409]: #411
+#417 := [trans #412 #415]: #416
+#420 := [quant-intro #417]: #419
+#404 := (iff #55 #403)
+#401 := (iff #54 #398)
+#367 := (not #353)
+#395 := (implies #367 #53)
+#399 := (iff #395 #398)
+#400 := [rewrite]: #399
+#396 := (iff #54 #395)
+#393 := (iff #52 #367)
+#359 := (iff #47 #353)
+#360 := [rewrite]: #359
+#394 := [monotonicity #360]: #393
+#397 := [monotonicity #394]: #396
+#402 := [trans #397 #400]: #401
+#405 := [quant-intro #402]: #404
+#422 := [trans #405 #420]: #421
+#392 := [asserted]: #55
+#423 := [mp #392 #422]: #418
+#1875 := [mp~ #423 #1846]: #418
+#4208 := [mp #1875 #4207]: #4203
+#6773 := (not #4203)
+#6774 := (or #6773 #6687 #6765)
+#6766 := (= ?v0!14 f22)
+#6767 := (or #6766 #6765)
+#6775 := (or #6773 #6767)
+#6782 := (iff #6775 #6774)
+#6777 := (or #6773 #6770)
+#6780 := (iff #6777 #6774)
+#6781 := [rewrite]: #6780
+#6778 := (iff #6775 #6777)
+#6771 := (iff #6767 #6770)
+#6768 := (iff #6766 #6687)
+#6769 := [rewrite]: #6768
+#6772 := [monotonicity #6769]: #6771
+#6779 := [monotonicity #6772]: #6778
+#6783 := [trans #6779 #6781]: #6782
+#6776 := [quant-inst #170 #2239]: #6775
+#6784 := [mp #6776 #6783]: #6774
+#6893 := [unit-resolution #6784 #4208]: #6770
+#6894 := [unit-resolution #6893 #6892]: #6765
+#6895 := (or #6810 #6764)
+#6896 := [th-lemma arith farkas 1 1]: #6895
+#6897 := [unit-resolution #6896 #6894]: #6810
+#6811 := (f7 #6546)
+#6818 := (f13 f14 #6811)
+#6819 := (* -1::Int #6818)
+#6868 := (+ #2244 #6819)
+#6875 := (<= #6868 0::Int)
+#6867 := (= #2244 #6818)
+#6901 := (= #6818 #2244)
+#6899 := (= #6811 ?v0!14)
+#6812 := (= ?v0!14 #6811)
+#6816 := (or #6815 #6812)
+#6817 := [quant-inst #170 #2239]: #6816
+#6898 := [unit-resolution #6817 #4190]: #6812
+#6900 := [symm #6898]: #6899
+#6902 := [monotonicity #6900]: #6901
+#6903 := [symm #6902]: #6867
+#6904 := (not #6867)
+#6905 := (or #6904 #6875)
+#6906 := [th-lemma arith triangle-eq]: #6905
+#6907 := [unit-resolution #6906 #6903]: #6875
+#6839 := (+ #6818 #6838)
+#6840 := (<= #6839 0::Int)
+#6826 := (f3 f15 #6811)
+#6827 := (= f1 #6826)
+#6914 := (= #6517 #6826)
+#6910 := (= #6826 #6517)
+#6911 := [monotonicity #6900]: #6910
+#6915 := [symm #6911]: #6914
+#6908 := [hypothesis]: #6688
+#6710 := (or #6706 #6687 #6518)
+#6711 := [def-axiom]: #6710
+#6909 := [unit-resolution #6711 #6892 #6908]: #6518
+#6916 := [trans #6909 #6915]: #6827
+#6829 := (f3 f15 #6813)
+#6830 := (= f1 #6829)
+#6924 := (not #6830)
+#6925 := (iff #756 #6924)
+#6922 := (iff #753 #6830)
+#6920 := (iff #6830 #753)
+#6918 := (= #6829 #171)
+#6919 := [monotonicity #6883]: #6918
+#6921 := [monotonicity #6919]: #6920
+#6923 := [symm #6921]: #6922
+#6926 := [monotonicity #6923]: #6925
+#4044 := (or #4526 #756)
+#4039 := [def-axiom]: #4044
+#6917 := [unit-resolution #4039 #6499]: #756
+#6927 := [mp #6917 #6926]: #6924
+#6828 := (not #6827)
+#6848 := (or #6828 #6830 #6840)
+#3952 := (or #4538 #4282)
+#4007 := [def-axiom]: #3952
+#6928 := [unit-resolution #4007 #6498]: #4282
+#6853 := (or #4287 #6828 #6830 #6840)
+#6824 := (+ #6823 #6819)
+#6825 := (>= #6824 0::Int)
+#6831 := (or #6830 #6828 #6825)
+#6854 := (or #4287 #6831)
+#6861 := (iff #6854 #6853)
+#6856 := (or #4287 #6848)
+#6859 := (iff #6856 #6853)
+#6860 := [rewrite]: #6859
+#6857 := (iff #6854 #6856)
+#6851 := (iff #6831 #6848)
+#6845 := (or #6830 #6828 #6840)
+#6849 := (iff #6845 #6848)
+#6850 := [rewrite]: #6849
+#6846 := (iff #6831 #6845)
+#6843 := (iff #6825 #6840)
+#6832 := (+ #6819 #6823)
+#6835 := (>= #6832 0::Int)
+#6841 := (iff #6835 #6840)
+#6842 := [rewrite]: #6841
+#6836 := (iff #6825 #6835)
+#6833 := (= #6824 #6832)
+#6834 := [rewrite]: #6833
+#6837 := [monotonicity #6834]: #6836
+#6844 := [trans #6837 #6842]: #6843
+#6847 := [monotonicity #6844]: #6846
+#6852 := [trans #6847 #6850]: #6851
+#6858 := [monotonicity #6852]: #6857
+#6862 := [trans #6858 #6860]: #6861
+#6855 := [quant-inst #6811 #6813]: #6854
+#6863 := [mp #6855 #6862]: #6853
+#6929 := [unit-resolution #6863 #6928]: #6848
+#6930 := [unit-resolution #6929 #6927 #6916]: #6840
+#6931 := [th-lemma arith farkas 1 1 1 -1 1 #6930 #6907 #6897 #6891 #6890]: false
+#6933 := [lemma #6931]: #6932
+#7009 := [unit-resolution #6933 #7008 #7006]: #6687
+#7033 := [monotonicity #7009]: #6870
+#7031 := (= #2243 #174)
+#7029 := (= #174 #2243)
+#6786 := (= #6547 0::Int)
+#6793 := (or #6707 #6786)
 #49 := (= #48 0::Int)
-#382 := (or #49 #368)
-#4206 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4193) #382)
-#387 := (forall (vars (?v0 S3) (?v1 S3)) #382)
-#4209 := (iff #387 #4206)
-#4207 := (iff #382 #382)
-#4208 := [refl]: #4207
-#4210 := [quant-intro #4208]: #4209
-#1850 := (~ #387 #387)
-#1881 := (~ #382 #382)
-#1882 := [refl]: #1881
-#1851 := [nnf-pos #1882]: #1850
+#381 := (or #49 #367)
+#4197 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #381)
+#386 := (forall (vars (?v0 S3) (?v1 S3)) #381)
+#4200 := (iff #386 #4197)
+#4198 := (iff #381 #381)
+#4199 := [refl]: #4198
+#4201 := [quant-intro #4199]: #4200
+#1841 := (~ #386 #386)
+#1872 := (~ #381 #381)
+#1873 := [refl]: #1872
+#1842 := [nnf-pos #1873]: #1841
 #50 := (implies #47 #49)
 #51 := (forall (vars (?v0 S3) (?v1 S3)) #50)
-#390 := (iff #51 #387)
-#362 := (= 0::Int #48)
-#369 := (or #368 #362)
-#374 := (forall (vars (?v0 S3) (?v1 S3)) #369)
-#388 := (iff #374 #387)
-#385 := (iff #369 #382)
-#379 := (or #368 #49)
-#383 := (iff #379 #382)
-#384 := [rewrite]: #383
-#380 := (iff #369 #379)
-#377 := (iff #362 #49)
-#378 := [rewrite]: #377
-#381 := [monotonicity #378]: #380
-#386 := [trans #381 #384]: #385
-#389 := [quant-intro #386]: #388
-#375 := (iff #51 #374)
-#372 := (iff #50 #369)
-#365 := (implies #354 #362)
-#370 := (iff #365 #369)
-#371 := [rewrite]: #370
-#366 := (iff #50 #365)
-#363 := (iff #49 #362)
-#364 := [rewrite]: #363
-#367 := [monotonicity #361 #364]: #366
-#373 := [trans #367 #371]: #372
-#376 := [quant-intro #373]: #375
-#391 := [trans #376 #389]: #390
-#352 := [asserted]: #51
-#392 := [mp #352 #391]: #387
-#1852 := [mp~ #392 #1851]: #387
-#4211 := [mp #1852 #4210]: #4206
-#6807 := (not #4206)
-#6808 := (or #6807 #6716 #6795)
-#6794 := (not #6775)
-#6796 := (or #6795 #6794)
-#6809 := (or #6807 #6796)
-#6816 := (iff #6809 #6808)
-#6811 := (or #6807 #6802)
-#6814 := (iff #6811 #6808)
-#6815 := [rewrite]: #6814
-#6812 := (iff #6809 #6811)
-#6805 := (iff #6796 #6802)
-#6799 := (or #6795 #6716)
-#6803 := (iff #6799 #6802)
-#6804 := [rewrite]: #6803
-#6800 := (iff #6796 #6799)
-#6797 := (iff #6794 #6716)
-#6798 := [monotonicity #6778]: #6797
-#6801 := [monotonicity #6798]: #6800
-#6806 := [trans #6801 #6804]: #6805
-#6813 := [monotonicity #6806]: #6812
-#6817 := [trans #6813 #6815]: #6816
-#6810 := [quant-inst #170 #2248]: #6809
-#6818 := [mp #6810 #6817]: #6808
-#7019 := [unit-resolution #6818 #4211]: #6802
-#7020 := [unit-resolution #7019 #7018]: #6795
-#7021 := (not #6795)
-#7022 := (or #7021 #6773)
-#7023 := [th-lemma arith triangle-eq]: #7022
-#7024 := [unit-resolution #7023 #7020]: #6773
-#7025 := (or #7021 #6819)
-#7026 := [th-lemma arith triangle-eq]: #7025
-#7027 := [unit-resolution #7026 #7020]: #6819
-#6424 := (* -1::Int #2252)
-#6612 := (+ #6424 #6556)
-#6613 := (+ #174 #6612)
-#6633 := (<= #6613 0::Int)
-#6616 := (= #6613 0::Int)
-#6600 := (not #6562)
-#6601 := (or #6580 #6600)
-#6602 := [def-axiom]: #6601
-#7028 := [unit-resolution #6602 #7016]: #6600
-#6619 := (or #6562 #6575 #6616)
-#6622 := (or #4409 #6562 #6575 #6616)
-#6608 := (+ #6556 #6424)
-#6609 := (+ #174 #6608)
-#6610 := (= #6609 0::Int)
-#6611 := (or #6562 #6560 #6610)
-#6623 := (or #4409 #6611)
-#6630 := (iff #6623 #6622)
-#6625 := (or #4409 #6619)
-#6628 := (iff #6625 #6622)
-#6629 := [rewrite]: #6628
-#6626 := (iff #6623 #6625)
-#6620 := (iff #6611 #6619)
-#6617 := (iff #6610 #6616)
-#6614 := (= #6609 #6613)
-#6615 := [rewrite]: #6614
-#6618 := [monotonicity #6615]: #6617
-#6621 := [monotonicity #6579 #6618]: #6620
-#6627 := [monotonicity #6621]: #6626
-#6631 := [trans #6627 #6629]: #6630
-#6624 := [quant-inst #2248]: #6623
-#6632 := [mp #6624 #6631]: #6622
-#7029 := [unit-resolution #6632 #6513]: #6619
-#7030 := [unit-resolution #7029 #7017 #7028]: #6616
-#7031 := (not #6616)
-#7032 := (or #7031 #6633)
-#7033 := [th-lemma arith triangle-eq]: #7032
-#7034 := [unit-resolution #7033 #7030]: #6633
-#6634 := (>= #6613 0::Int)
-#7035 := (or #7031 #6634)
-#7036 := [th-lemma arith triangle-eq]: #7035
-#7037 := [unit-resolution #7036 #7030]: #6634
-#7039 := [th-lemma arith eq-propagate 1 1 -1 -1 #7037 #7034 #7027 #7024]: #7038
-#7041 := [symm #7039]: #7040
-#7043 := [trans #7041 #7042]: #2858
-#7044 := [unit-resolution #6995 #7043]: false
-#7045 := [lemma #7044]: #2864
-#4060 := (or #4520 #2869 #4514)
-#4061 := [def-axiom]: #4060
-#7099 := [unit-resolution #4061 #7045 #7098]: #4514
-#4070 := (or #4511 #4421)
-#4072 := [def-axiom]: #4070
-#7100 := [unit-resolution #4072 #7099]: #4421
-#9466 := (or #4426 #7535 #7539)
-#7538 := (or #7537 #7535)
-#9467 := (or #4426 #7538)
-#9474 := (iff #9467 #9466)
-#9469 := (or #4426 #7545)
-#9472 := (iff #9469 #9466)
-#9473 := [rewrite]: #9472
-#9470 := (iff #9467 #9469)
-#7548 := (iff #7538 #7545)
-#7542 := (or #7539 #7535)
-#7546 := (iff #7542 #7545)
-#7547 := [rewrite]: #7546
-#7543 := (iff #7538 #7542)
-#7544 := [monotonicity #7541]: #7543
-#7549 := [trans #7544 #7547]: #7548
-#9471 := [monotonicity #7549]: #9470
-#9475 := [trans #9471 #9473]: #9474
-#9468 := [quant-inst #2273]: #9467
-#9476 := [mp #9468 #9475]: #9466
-#10089 := [unit-resolution #9476 #7100]: #7545
-#10090 := [unit-resolution #10089 #10076]: #7535
-#10099 := [mp #10090 #10098]: #9981
-#9978 := (not #9955)
-#9979 := (or #9978 #9947 #9967)
-#9980 := [def-axiom]: #9979
-#10100 := [unit-resolution #9980 #10099 #10088]: #9967
-#10101 := (or #9952 #9968)
-#6304 := (not #5892)
-#9973 := (or #9952 #9968 #6304)
-#9974 := [def-axiom]: #9973
-#10102 := [unit-resolution #9974 #6999]: #10101
-#10103 := [unit-resolution #10102 #10100]: #9968
-#10027 := (or #9949 #10026)
-#10030 := (or #6782 #9949 #10026)
-#10031 := (or #6782 #10027)
-#10033 := (iff #10031 #10030)
-#10034 := [rewrite]: #10033
-#10032 := [quant-inst #7211 #2273]: #10031
-#10035 := [mp #10032 #10034]: #10030
-#10104 := [unit-resolution #10035 #4217]: #10027
-#10105 := [unit-resolution #10104 #10103]: #10026
-#10106 := (or #10050 #10025)
-#10107 := [th-lemma arith farkas 1 1]: #10106
-#10108 := [unit-resolution #10107 #10105]: #10050
-#10109 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10108 #10087 #10086 #10074 #10073 #10072 #10071]: false
-#10111 := [lemma #10109]: #10110
-#9586 := [unit-resolution #10111 #10087 #10074 #10072]: #7539
-#9587 := (or #10075 #9581)
-#9588 := [th-lemma arith triangle-eq]: #9587
-#9589 := [unit-resolution #9588 #9586]: #9581
-#9590 := [th-lemma arith farkas -1 1 1 #10087 #9589 #9580]: false
-#9608 := [lemma #9590]: #9607
-#11952 := [unit-resolution #9608 #10087 #10074]: #7302
-#9479 := (or #7322 #8251)
-#9477 := [def-axiom]: #9479
-#11953 := [unit-resolution #9477 #11952]: #7322
-#7325 := (not #7322)
-#12703 := (or #7319 #7325)
-#7315 := (+ f8 #6071)
-#7316 := (<= #7315 0::Int)
-#12697 := (not #7316)
-#12700 := (or #12697 #6073)
-#4036 := (or #4535 #1655)
-#4037 := [def-axiom]: #4036
-#7830 := [unit-resolution #4037 #6508]: #1655
-#12698 := (or #12697 #1654 #6073)
-#12699 := [th-lemma arith assign-bounds 1 1]: #12698
-#12701 := [unit-resolution #12699 #7830]: #12700
-#12702 := [unit-resolution #12701 #10074]: #12697
-#12665 := [unit-resolution #4017 #6507]: #4307
-#9211 := (or #4312 #7316 #7319 #7325)
-#7313 := (or #7312 #7309 #7302)
-#7314 := (not #7313)
-#7318 := (or #7317 #7316 #7314)
-#9448 := (or #4312 #7318)
-#9461 := (iff #9448 #9211)
-#7331 := (or #7316 #7319 #7325)
-#9454 := (or #4312 #7331)
-#9459 := (iff #9454 #9211)
-#9460 := [rewrite]: #9459
-#9456 := (iff #9448 #9454)
-#7334 := (iff #7318 #7331)
-#7328 := (or #7319 #7316 #7325)
-#7332 := (iff #7328 #7331)
-#7333 := [rewrite]: #7332
-#7329 := (iff #7318 #7328)
-#7326 := (iff #7314 #7325)
-#7323 := (iff #7313 #7322)
+#389 := (iff #51 #386)
+#361 := (= 0::Int #48)
+#368 := (or #367 #361)
+#373 := (forall (vars (?v0 S3) (?v1 S3)) #368)
+#387 := (iff #373 #386)
+#384 := (iff #368 #381)
+#378 := (or #367 #49)
+#382 := (iff #378 #381)
+#383 := [rewrite]: #382
+#379 := (iff #368 #378)
+#376 := (iff #361 #49)
+#377 := [rewrite]: #376
+#380 := [monotonicity #377]: #379
+#385 := [trans #380 #383]: #384
+#388 := [quant-intro #385]: #387
+#374 := (iff #51 #373)
+#371 := (iff #50 #368)
+#364 := (implies #353 #361)
+#369 := (iff #364 #368)
+#370 := [rewrite]: #369
+#365 := (iff #50 #364)
+#362 := (iff #49 #361)
+#363 := [rewrite]: #362
+#366 := [monotonicity #360 #363]: #365
+#372 := [trans #366 #370]: #371
+#375 := [quant-intro #372]: #374
+#390 := [trans #375 #388]: #389
+#351 := [asserted]: #51
+#391 := [mp #351 #390]: #386
+#1843 := [mp~ #391 #1842]: #386
+#4202 := [mp #1843 #4201]: #4197
+#6798 := (not #4197)
+#6799 := (or #6798 #6707 #6786)
+#6785 := (not #6766)
+#6787 := (or #6786 #6785)
+#6800 := (or #6798 #6787)
+#6807 := (iff #6800 #6799)
+#6802 := (or #6798 #6793)
+#6805 := (iff #6802 #6799)
+#6806 := [rewrite]: #6805
+#6803 := (iff #6800 #6802)
+#6796 := (iff #6787 #6793)
+#6790 := (or #6786 #6707)
+#6794 := (iff #6790 #6793)
+#6795 := [rewrite]: #6794
+#6791 := (iff #6787 #6790)
+#6788 := (iff #6785 #6707)
+#6789 := [monotonicity #6769]: #6788
+#6792 := [monotonicity #6789]: #6791
+#6797 := [trans #6792 #6795]: #6796
+#6804 := [monotonicity #6797]: #6803
+#6808 := [trans #6804 #6806]: #6807
+#6801 := [quant-inst #170 #2239]: #6800
+#6809 := [mp #6801 #6808]: #6799
+#7010 := [unit-resolution #6809 #4202]: #6793
+#7011 := [unit-resolution #7010 #7009]: #6786
+#7012 := (not #6786)
+#7013 := (or #7012 #6764)
+#7014 := [th-lemma arith triangle-eq]: #7013
+#7015 := [unit-resolution #7014 #7011]: #6764
+#7016 := (or #7012 #6810)
+#7017 := [th-lemma arith triangle-eq]: #7016
+#7018 := [unit-resolution #7017 #7011]: #6810
+#6415 := (* -1::Int #2243)
+#6603 := (+ #6415 #6547)
+#6604 := (+ #174 #6603)
+#6624 := (<= #6604 0::Int)
+#6607 := (= #6604 0::Int)
+#6591 := (not #6553)
+#6592 := (or #6571 #6591)
+#6593 := [def-axiom]: #6592
+#7019 := [unit-resolution #6593 #7007]: #6591
+#6610 := (or #6553 #6566 #6607)
+#6613 := (or #4400 #6553 #6566 #6607)
+#6599 := (+ #6547 #6415)
+#6600 := (+ #174 #6599)
+#6601 := (= #6600 0::Int)
+#6602 := (or #6553 #6551 #6601)
+#6614 := (or #4400 #6602)
+#6621 := (iff #6614 #6613)
+#6616 := (or #4400 #6610)
+#6619 := (iff #6616 #6613)
+#6620 := [rewrite]: #6619
+#6617 := (iff #6614 #6616)
+#6611 := (iff #6602 #6610)
+#6608 := (iff #6601 #6607)
+#6605 := (= #6600 #6604)
+#6606 := [rewrite]: #6605
+#6609 := [monotonicity #6606]: #6608
+#6612 := [monotonicity #6570 #6609]: #6611
+#6618 := [monotonicity #6612]: #6617
+#6622 := [trans #6618 #6620]: #6621
+#6615 := [quant-inst #2239]: #6614
+#6623 := [mp #6615 #6622]: #6613
+#7020 := [unit-resolution #6623 #6504]: #6610
+#7021 := [unit-resolution #7020 #7008 #7019]: #6607
+#7022 := (not #6607)
+#7023 := (or #7022 #6624)
+#7024 := [th-lemma arith triangle-eq]: #7023
+#7025 := [unit-resolution #7024 #7021]: #6624
+#6625 := (>= #6604 0::Int)
+#7026 := (or #7022 #6625)
+#7027 := [th-lemma arith triangle-eq]: #7026
+#7028 := [unit-resolution #7027 #7021]: #6625
+#7030 := [th-lemma arith eq-propagate 1 1 -1 -1 #7028 #7025 #7018 #7015]: #7029
+#7032 := [symm #7030]: #7031
+#7034 := [trans #7032 #7033]: #2849
+#7035 := [unit-resolution #6986 #7034]: false
+#7036 := [lemma #7035]: #2855
+#4051 := (or #4511 #2860 #4505)
+#4052 := [def-axiom]: #4051
+#7090 := [unit-resolution #4052 #7036 #7089]: #4505
+#4061 := (or #4502 #4412)
+#4063 := [def-axiom]: #4061
+#7091 := [unit-resolution #4063 #7090]: #4412
+#9457 := (or #4417 #7526 #7530)
+#7529 := (or #7528 #7526)
+#9458 := (or #4417 #7529)
+#9465 := (iff #9458 #9457)
+#9460 := (or #4417 #7536)
+#9463 := (iff #9460 #9457)
+#9464 := [rewrite]: #9463
+#9461 := (iff #9458 #9460)
+#7539 := (iff #7529 #7536)
+#7533 := (or #7530 #7526)
+#7537 := (iff #7533 #7536)
+#7538 := [rewrite]: #7537
+#7534 := (iff #7529 #7533)
+#7535 := [monotonicity #7532]: #7534
+#7540 := [trans #7535 #7538]: #7539
+#9462 := [monotonicity #7540]: #9461
+#9466 := [trans #9462 #9464]: #9465
+#9459 := [quant-inst #2264]: #9458
+#9467 := [mp #9459 #9466]: #9457
+#10080 := [unit-resolution #9467 #7091]: #7536
+#10081 := [unit-resolution #10080 #10067]: #7526
+#10090 := [mp #10081 #10089]: #9972
+#9969 := (not #9946)
+#9970 := (or #9969 #9938 #9958)
+#9971 := [def-axiom]: #9970
+#10091 := [unit-resolution #9971 #10090 #10079]: #9958
+#10092 := (or #9943 #9959)
+#6295 := (not #5883)
+#9964 := (or #9943 #9959 #6295)
+#9965 := [def-axiom]: #9964
+#10093 := [unit-resolution #9965 #6990]: #10092
+#10094 := [unit-resolution #10093 #10091]: #9959
+#10018 := (or #9940 #10017)
+#10021 := (or #6773 #9940 #10017)
+#10022 := (or #6773 #10018)
+#10024 := (iff #10022 #10021)
+#10025 := [rewrite]: #10024
+#10023 := [quant-inst #7202 #2264]: #10022
+#10026 := [mp #10023 #10025]: #10021
+#10095 := [unit-resolution #10026 #4208]: #10018
+#10096 := [unit-resolution #10095 #10094]: #10017
+#10097 := (or #10041 #10016)
+#10098 := [th-lemma arith farkas 1 1]: #10097
+#10099 := [unit-resolution #10098 #10096]: #10041
+#10100 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10099 #10078 #10077 #10065 #10064 #10063 #10062]: false
+#10102 := [lemma #10100]: #10101
+#9577 := [unit-resolution #10102 #10078 #10065 #10063]: #7530
+#9578 := (or #10066 #9572)
+#9579 := [th-lemma arith triangle-eq]: #9578
+#9580 := [unit-resolution #9579 #9577]: #9572
+#9581 := [th-lemma arith farkas -1 1 1 #10078 #9580 #9571]: false
+#9599 := [lemma #9581]: #9598
+#11943 := [unit-resolution #9599 #10078 #10065]: #7293
+#9470 := (or #7313 #8242)
+#9468 := [def-axiom]: #9470
+#11944 := [unit-resolution #9468 #11943]: #7313
+#7316 := (not #7313)
+#12694 := (or #7310 #7316)
+#7306 := (+ f8 #6062)
+#7307 := (<= #7306 0::Int)
+#12688 := (not #7307)
+#12691 := (or #12688 #6064)
+#4027 := (or #4526 #1646)
+#4028 := [def-axiom]: #4027
+#7821 := [unit-resolution #4028 #6499]: #1646
+#12689 := (or #12688 #1645 #6064)
+#12690 := [th-lemma arith assign-bounds 1 1]: #12689
+#12692 := [unit-resolution #12690 #7821]: #12691
+#12693 := [unit-resolution #12692 #10065]: #12688
+#12656 := [unit-resolution #4008 #6498]: #4298
+#9202 := (or #4303 #7307 #7310 #7316)
+#7304 := (or #7303 #7300 #7293)
+#7305 := (not #7304)
+#7309 := (or #7308 #7307 #7305)
+#9439 := (or #4303 #7309)
+#9452 := (iff #9439 #9202)
+#7322 := (or #7307 #7310 #7316)
+#9445 := (or #4303 #7322)
+#9450 := (iff #9445 #9202)
+#9451 := [rewrite]: #9450
+#9447 := (iff #9439 #9445)
+#7325 := (iff #7309 #7322)
+#7319 := (or #7310 #7307 #7316)
+#7323 := (iff #7319 #7322)
 #7324 := [rewrite]: #7323
-#7327 := [monotonicity #7324]: #7326
-#7320 := (iff #7317 #7319)
-#7321 := [rewrite]: #7320
-#7330 := [monotonicity #7321 #7327]: #7329
-#7335 := [trans #7330 #7333]: #7334
-#9458 := [monotonicity #7335]: #9456
-#9462 := [trans #9458 #9460]: #9461
-#9453 := [quant-inst #6069]: #9448
-#9478 := [mp #9453 #9462]: #9211
-#12704 := [unit-resolution #9478 #12665 #12702]: #12703
-#11951 := [unit-resolution #12704 #11953]: #7319
-#11954 := [symm #11951]: #7317
-#9281 := (= #8217 #6069)
-#9282 := [symm #9280]: #9281
-#11955 := [trans #9282 #11954]: #10697
-#11957 := [monotonicity #11955]: #11956
-#11958 := [symm #11957]: #10875
-#11944 := (not #10875)
-#11959 := (or #11944 #10878)
-#11960 := [th-lemma arith triangle-eq]: #11959
-#11961 := [unit-resolution #11960 #11958]: #10878
-#3917 := (>= #99 0::Int)
-#7123 := [unit-resolution #4033 #6507]: #100
-#6989 := (or #1747 #3917)
-#6990 := [th-lemma arith triangle-eq]: #6989
-#6991 := [unit-resolution #6990 #7123]: #3917
-#11981 := [th-lemma arith farkas 1 1 1 1 1 1 1 1 #10108 #10087 #10086 #10074 #6991 #11961 #11950 #10071]: false
-#11986 := [lemma #11981]: #11985
-#11109 := [unit-resolution #11986 #10087 #10074]: #7539
-#11963 := (not #9581)
-#11917 := [hypothesis]: #11963
-#11918 := [hypothesis]: #7539
-#11919 := [unit-resolution #9588 #11918 #11917]: false
-#11920 := [lemma #11919]: #9587
-#11110 := [unit-resolution #11920 #11109]: #9581
-#11113 := [th-lemma arith farkas -1 1 1 #10087 #11110 #9580]: false
-#11112 := [lemma #11113]: #11114
-#23130 := [unit-resolution #11112 #10074]: #2275
-#4073 := (or #4511 #4505)
-#4074 := [def-axiom]: #4073
-#12708 := [unit-resolution #4074 #7099]: #4505
-#5932 := (= #99 #203)
-#12712 := (iff #5932 #204)
-#12711 := [commutativity]: #1488
-#12709 := (iff #5932 #822)
-#12710 := [monotonicity #7123]: #12709
-#12713 := [trans #12710 #12711]: #12712
-#5916 := (f5 f22 f10)
-#5917 := (f9 #5916)
-#7059 := (<= #5917 0::Int)
-#7060 := (not #7059)
-#6767 := (not #6088)
-#3934 := (f3 f15 f10)
-#3937 := (= f1 #3934)
-#6718 := (ite #6088 #5892 #3937)
-#6766 := (not #6718)
-#6698 := (f3 #6269 f10)
-#6699 := (= f1 #6698)
-#6723 := (iff #6699 #6718)
-#6730 := (or #6290 #6723)
-#6683 := (ite #6086 #5892 #3937)
-#6717 := (iff #6699 #6683)
-#6731 := (or #6290 #6717)
-#6733 := (iff #6731 #6730)
-#6735 := (iff #6730 #6730)
-#6763 := [rewrite]: #6735
-#6724 := (iff #6717 #6723)
-#6721 := (iff #6683 #6718)
-#6089 := (iff #6086 #6088)
-#6090 := [rewrite]: #6089
-#6722 := [monotonicity #6090]: #6721
-#6725 := [monotonicity #6722]: #6724
-#6734 := [monotonicity #6725]: #6733
-#6764 := [trans #6734 #6763]: #6733
-#6732 := [quant-inst #104 #170 #5891 #56]: #6731
-#6765 := [mp #6732 #6764]: #6730
-#7091 := [unit-resolution #6765 #4177]: #6723
-#6983 := (not #6699)
-#6358 := (f3 f23 f10)
-#6476 := (= f1 #6358)
-#6545 := (not #6476)
-#7109 := (iff #6545 #6983)
-#7107 := (iff #6476 #6699)
-#7105 := (iff #6699 #6476)
-#7103 := (= #6698 #6358)
-#7104 := [monotonicity #7007]: #7103
-#7106 := [monotonicity #7104]: #7105
-#7108 := [symm #7106]: #7107
-#7110 := [monotonicity #7108]: #7109
-#7092 := (not #5932)
-#7095 := [hypothesis]: #7092
-#6546 := (or #5932 #6545)
-#6549 := (or #4426 #5932 #6545)
-#6544 := (or #4426 #6546)
-#6551 := (iff #6544 #6549)
-#6552 := [rewrite]: #6551
-#6550 := [quant-inst #56]: #6544
-#6553 := [mp #6550 #6552]: #6549
-#7101 := [unit-resolution #6553 #7100]: #6546
-#7102 := [unit-resolution #7101 #7095]: #6545
-#7111 := [mp #7102 #7110]: #6983
-#6986 := (not #6723)
-#6987 := (or #6986 #6699 #6766)
-#6988 := [def-axiom]: #6987
-#7112 := [unit-resolution #6988 #7111 #7091]: #6766
-#7113 := (or #6718 #6767)
-#6771 := (or #6718 #6767 #6304)
-#6772 := [def-axiom]: #6771
-#7114 := [unit-resolution #6772 #6999]: #7113
-#7115 := [unit-resolution #7114 #7112]: #6767
-#7061 := (or #6088 #7060)
-#7064 := (or #6782 #6088 #7060)
-#7065 := (or #6782 #7061)
-#7067 := (iff #7065 #7064)
-#7068 := [rewrite]: #7067
-#7066 := [quant-inst #170 #56]: #7065
-#7069 := [mp #7066 #7068]: #7064
-#7116 := [unit-resolution #7069 #4217]: #7061
-#7117 := [unit-resolution #7116 #7115]: #7060
-#5924 := (* -1::Int #5917)
-#5925 := (+ #1453 #5924)
-#5926 := (+ #99 #5925)
-#5927 := (<= #5926 0::Int)
-#5954 := (not #5927)
-#5928 := (+ f8 #5924)
-#5929 := (<= #5928 0::Int)
-#5934 := (or #5927 #5929)
-#5937 := (not #5934)
-#5940 := (or #5932 #5937)
-#5943 := (or #4401 #5932 #5937)
-#5930 := (or #5929 #5927)
-#5931 := (not #5930)
-#5933 := (or #5932 #5931)
-#5944 := (or #4401 #5933)
-#5951 := (iff #5944 #5943)
-#5946 := (or #4401 #5940)
-#5949 := (iff #5946 #5943)
-#5950 := [rewrite]: #5949
-#5947 := (iff #5944 #5946)
-#5941 := (iff #5933 #5940)
-#5938 := (iff #5931 #5937)
-#5935 := (iff #5930 #5934)
-#5936 := [rewrite]: #5935
-#5939 := [monotonicity #5936]: #5938
-#5942 := [monotonicity #5939]: #5941
-#5948 := [monotonicity #5942]: #5947
-#5952 := [trans #5948 #5950]: #5951
-#5945 := [quant-inst #56]: #5944
-#5953 := [mp #5945 #5952]: #5943
-#7118 := [unit-resolution #5953 #6509]: #5940
-#7119 := [unit-resolution #7118 #7095]: #5937
-#5955 := (or #5934 #5954)
-#5956 := [def-axiom]: #5955
-#7120 := [unit-resolution #5956 #7119]: #5954
-#6127 := (>= #174 0::Int)
-#6130 := (or #4279 #6127)
-#6131 := [quant-inst #170]: #6130
-#7122 := [unit-resolution #6131 #7121]: #6127
-#3920 := (<= #99 0::Int)
-#7124 := (or #1747 #3920)
-#7125 := [th-lemma arith triangle-eq]: #7124
-#7126 := [unit-resolution #7125 #7123]: #3920
-#7127 := [th-lemma arith farkas 1 1 1 1 #7126 #7122 #7120 #7117]: false
-#7128 := [lemma #7127]: #5932
-#12714 := [mp #7128 #12713]: #204
-#4083 := (or #4508 #1490 #4502)
-#4069 := [def-axiom]: #4083
-#12715 := [unit-resolution #4069 #12714 #12708]: #4502
-#4092 := (or #4499 #4493)
-#4076 := [def-axiom]: #4092
-#12716 := [unit-resolution #4076 #12715]: #4493
-#4089 := (or #4496 #2276 #4490)
-#4090 := [def-axiom]: #4089
-#12717 := [unit-resolution #4090 #12716]: #4493
-#23131 := [unit-resolution #12717 #23130]: #4490
-#4084 := (or #4487 #4481)
-#4086 := [def-axiom]: #4084
-#23139 := [unit-resolution #4086 #23131]: #4481
-#12720 := (or #4484 #4478)
-#10288 := [hypothesis]: #3445
-#3973 := (or #3440 #2299)
-#3974 := [def-axiom]: #3973
-#9758 := [unit-resolution #3974 #10288]: #2299
-#10379 := (or #3440 #2298)
-#10564 := (f5 #7211 ?v1!16)
-#10565 := (f9 #10564)
-#10582 := (* -1::Int #10565)
-#8691 := (f5 f22 ?v1!16)
-#8692 := (f9 #8691)
-#10585 := (+ #8692 #10582)
-#10587 := (>= #10585 0::Int)
-#10581 := (= #8692 #10565)
-#10592 := (= #10565 #8692)
-#10590 := (= #10564 #8691)
-#10591 := [monotonicity #7790]: #10590
-#10593 := [monotonicity #10591]: #10592
-#10594 := [symm #10593]: #10581
-#10595 := (not #10581)
-#10596 := (or #10595 #10587)
-#10597 := [th-lemma arith triangle-eq]: #10596
-#10598 := [unit-resolution #10597 #10594]: #10587
-#6007 := (f24 f22)
-#6048 := (* -1::Int #6007)
-#6417 := (+ #174 #6048)
-#6418 := (>= #6417 0::Int)
-#4062 := (or #4523 #4412)
-#4063 := [def-axiom]: #4062
-#8193 := [unit-resolution #4063 #7097]: #4412
-#6422 := (or #4417 #6418)
-#6423 := [quant-inst #170]: #6422
-#8194 := [unit-resolution #6423 #8193]: #6418
-#4116 := (not #2888)
-#4117 := (or #3440 #4116)
-#4118 := [def-axiom]: #4117
-#10291 := [unit-resolution #4118 #10288]: #4116
-#10223 := (+ #2290 #6048)
-#10224 := (<= #10223 0::Int)
-#10212 := (= #2290 #6007)
-#10480 := (= ?v0!17 f22)
-#8517 := (= ?v0!17 #7211)
-#8510 := (f3 f15 ?v0!17)
-#8511 := (= f1 #8510)
-#8520 := (ite #8517 #5892 #8511)
-#8514 := (f3 #8442 ?v0!17)
-#8515 := (= f1 #8514)
-#8523 := (iff #8515 #8520)
-#9711 := (or #6290 #8523)
-#8512 := (= #7211 ?v0!17)
-#8513 := (ite #8512 #5892 #8511)
-#8516 := (iff #8515 #8513)
-#9706 := (or #6290 #8516)
-#9713 := (iff #9706 #9711)
-#9715 := (iff #9711 #9711)
-#9716 := [rewrite]: #9715
-#8524 := (iff #8516 #8523)
-#8521 := (iff #8513 #8520)
-#8518 := (iff #8512 #8517)
-#8519 := [rewrite]: #8518
-#8522 := [monotonicity #8519]: #8521
-#8525 := [monotonicity #8522]: #8524
-#9714 := [monotonicity #8525]: #9713
-#9722 := [trans #9714 #9716]: #9713
-#9712 := [quant-inst #104 #7211 #5891 #2289]: #9706
-#9723 := [mp #9712 #9722]: #9711
-#10292 := [unit-resolution #9723 #4177]: #8523
-#10321 := (= #2295 #8514)
-#10294 := (= #8514 #2295)
-#10231 := [monotonicity #9286]: #10294
-#10322 := [symm #10231]: #10321
-#4131 := (or #3440 #2296)
-#3972 := [def-axiom]: #4131
-#10293 := [unit-resolution #3972 #10288]: #2296
-#10323 := [trans #10293 #10322]: #8515
-#9732 := (not #8515)
-#9735 := (not #8523)
-#9738 := (or #9735 #9732 #8520)
-#9739 := [def-axiom]: #9738
-#10324 := [unit-resolution #9739 #10323 #10292]: #8520
-#9731 := (not #8511)
-#8485 := (f13 f14 ?v0!17)
-#8567 := (* -1::Int #8485)
-#7513 := (f13 f14 #7211)
-#10486 := (+ #7513 #8567)
-#10487 := (>= #10486 0::Int)
-#10612 := (not #10487)
-#8446 := (= ?v1!16 #7211)
-#9616 := (not #8446)
-#8438 := (f3 f15 ?v1!16)
-#8439 := (= f1 #8438)
-#8449 := (ite #8446 #5892 #8439)
-#9615 := (not #8449)
-#8443 := (f3 #8442 ?v1!16)
-#8444 := (= f1 #8443)
-#8452 := (iff #8444 #8449)
-#9584 := (or #6290 #8452)
-#8440 := (= #7211 ?v1!16)
-#8441 := (ite #8440 #5892 #8439)
-#8445 := (iff #8444 #8441)
-#9585 := (or #6290 #8445)
-#9610 := (iff #9585 #9584)
-#9606 := (iff #9584 #9584)
-#9612 := [rewrite]: #9606
-#8453 := (iff #8445 #8452)
-#8450 := (iff #8441 #8449)
-#8447 := (iff #8440 #8446)
-#8448 := [rewrite]: #8447
-#8451 := [monotonicity #8448]: #8450
-#8454 := [monotonicity #8451]: #8453
-#9611 := [monotonicity #8454]: #9610
-#9613 := [trans #9611 #9612]: #9610
-#9609 := [quant-inst #104 #7211 #5891 #2288]: #9585
-#9614 := [mp #9609 #9613]: #9584
-#10325 := [unit-resolution #9614 #4177]: #8452
-#9648 := (not #8444)
-#10333 := (iff #2299 #9648)
-#10331 := (iff #2298 #8444)
-#10329 := (iff #8444 #2298)
-#10327 := (= #8443 #2297)
-#10328 := [monotonicity #9286]: #10327
-#10330 := [monotonicity #10328]: #10329
-#10332 := [symm #10330]: #10331
-#10334 := [monotonicity #10332]: #10333
-#10326 := [hypothesis]: #2299
-#10335 := [mp #10326 #10334]: #9648
-#9640 := (not #8452)
-#9641 := (or #9640 #8444 #9615)
-#9647 := [def-axiom]: #9641
-#10336 := [unit-resolution #9647 #10335 #10325]: #9615
-#10337 := (or #8449 #9616)
-#9636 := (or #8449 #9616 #6304)
-#9631 := [def-axiom]: #9636
-#10338 := [unit-resolution #9631 #6999]: #10337
-#10339 := [unit-resolution #10338 #10336]: #9616
-#8664 := (f13 f14 ?v1!16)
-#8675 := (* -1::Int #8664)
-#8923 := (+ #174 #8675)
-#8924 := (<= #8923 0::Int)
-#9637 := (not #8439)
-#9638 := (or #8449 #8446 #9637)
-#9639 := [def-axiom]: #9638
-#10308 := [unit-resolution #9639 #10339 #10336]: #9637
-#8929 := (or #8439 #8924)
-#4054 := (or #4535 #4386)
-#4040 := [def-axiom]: #4054
-#10313 := [unit-resolution #4040 #6508]: #4386
-#9984 := (or #4391 #8439 #8924)
-#8912 := (+ #8664 #1453)
-#8913 := (>= #8912 0::Int)
-#8916 := (or #8439 #8913)
-#9985 := (or #4391 #8916)
-#10020 := (iff #9985 #9984)
-#10016 := (or #4391 #8929)
-#10019 := (iff #10016 #9984)
-#10014 := [rewrite]: #10019
-#10017 := (iff #9985 #10016)
-#8930 := (iff #8916 #8929)
-#8927 := (iff #8913 #8924)
-#8917 := (+ #1453 #8664)
-#8920 := (>= #8917 0::Int)
-#8925 := (iff #8920 #8924)
-#8926 := [rewrite]: #8925
-#8921 := (iff #8913 #8920)
-#8918 := (= #8912 #8917)
-#8919 := [rewrite]: #8918
+#7320 := (iff #7309 #7319)
+#7317 := (iff #7305 #7316)
+#7314 := (iff #7304 #7313)
+#7315 := [rewrite]: #7314
+#7318 := [monotonicity #7315]: #7317
+#7311 := (iff #7308 #7310)
+#7312 := [rewrite]: #7311
+#7321 := [monotonicity #7312 #7318]: #7320
+#7326 := [trans #7321 #7324]: #7325
+#9449 := [monotonicity #7326]: #9447
+#9453 := [trans #9449 #9451]: #9452
+#9444 := [quant-inst #6060]: #9439
+#9469 := [mp #9444 #9453]: #9202
+#12695 := [unit-resolution #9469 #12656 #12693]: #12694
+#11942 := [unit-resolution #12695 #11944]: #7310
+#11945 := [symm #11942]: #7308
+#9272 := (= #8208 #6060)
+#9273 := [symm #9271]: #9272
+#11946 := [trans #9273 #11945]: #10688
+#11948 := [monotonicity #11946]: #11947
+#11949 := [symm #11948]: #10866
+#11935 := (not #10866)
+#11950 := (or #11935 #10869)
+#11951 := [th-lemma arith triangle-eq]: #11950
+#11952 := [unit-resolution #11951 #11949]: #10869
+#3908 := (>= #99 0::Int)
+#7114 := [unit-resolution #4024 #6498]: #100
+#6980 := (or #1738 #3908)
+#6981 := [th-lemma arith triangle-eq]: #6980
+#6982 := [unit-resolution #6981 #7114]: #3908
+#11972 := [th-lemma arith farkas 1 1 1 1 1 1 1 1 #10099 #10078 #10077 #10065 #6982 #11952 #11941 #10062]: false
+#11977 := [lemma #11972]: #11976
+#11100 := [unit-resolution #11977 #10078 #10065]: #7530
+#11954 := (not #9572)
+#11908 := [hypothesis]: #11954
+#11909 := [hypothesis]: #7530
+#11910 := [unit-resolution #9579 #11909 #11908]: false
+#11911 := [lemma #11910]: #9578
+#11101 := [unit-resolution #11911 #11100]: #9572
+#11104 := [th-lemma arith farkas -1 1 1 #10078 #11101 #9571]: false
+#11103 := [lemma #11104]: #11105
+#23121 := [unit-resolution #11103 #10065]: #2266
+#4064 := (or #4502 #4496)
+#4065 := [def-axiom]: #4064
+#12699 := [unit-resolution #4065 #7090]: #4496
+#5923 := (= #99 #202)
+#12703 := (iff #5923 #203)
+#12702 := [commutativity]: #1479
+#12700 := (iff #5923 #813)
+#12701 := [monotonicity #7114]: #12700
+#12704 := [trans #12701 #12702]: #12703
+#5907 := (f5 f22 f10)
+#5908 := (f9 #5907)
+#7050 := (<= #5908 0::Int)
+#7051 := (not #7050)
+#6758 := (not #6079)
+#3925 := (f3 f15 f10)
+#3928 := (= f1 #3925)
+#6709 := (ite #6079 #5883 #3928)
+#6757 := (not #6709)
+#6689 := (f3 #6260 f10)
+#6690 := (= f1 #6689)
+#6714 := (iff #6690 #6709)
+#6721 := (or #6281 #6714)
+#6674 := (ite #6077 #5883 #3928)
+#6708 := (iff #6690 #6674)
+#6722 := (or #6281 #6708)
+#6724 := (iff #6722 #6721)
+#6726 := (iff #6721 #6721)
+#6754 := [rewrite]: #6726
+#6715 := (iff #6708 #6714)
+#6712 := (iff #6674 #6709)
+#6080 := (iff #6077 #6079)
+#6081 := [rewrite]: #6080
+#6713 := [monotonicity #6081]: #6712
+#6716 := [monotonicity #6713]: #6715
+#6725 := [monotonicity #6716]: #6724
+#6755 := [trans #6725 #6754]: #6724
+#6723 := [quant-inst #104 #170 #5882 #56]: #6722
+#6756 := [mp #6723 #6755]: #6721
+#7082 := [unit-resolution #6756 #4168]: #6714
+#6974 := (not #6690)
+#6349 := (f3 f23 f10)
+#6467 := (= f1 #6349)
+#6536 := (not #6467)
+#7100 := (iff #6536 #6974)
+#7098 := (iff #6467 #6690)
+#7096 := (iff #6690 #6467)
+#7094 := (= #6689 #6349)
+#7095 := [monotonicity #6998]: #7094
+#7097 := [monotonicity #7095]: #7096
+#7099 := [symm #7097]: #7098
+#7101 := [monotonicity #7099]: #7100
+#7083 := (not #5923)
+#7086 := [hypothesis]: #7083
+#6537 := (or #5923 #6536)
+#6540 := (or #4417 #5923 #6536)
+#6535 := (or #4417 #6537)
+#6542 := (iff #6535 #6540)
+#6543 := [rewrite]: #6542
+#6541 := [quant-inst #56]: #6535
+#6544 := [mp #6541 #6543]: #6540
+#7092 := [unit-resolution #6544 #7091]: #6537
+#7093 := [unit-resolution #7092 #7086]: #6536
+#7102 := [mp #7093 #7101]: #6974
+#6977 := (not #6714)
+#6978 := (or #6977 #6690 #6757)
+#6979 := [def-axiom]: #6978
+#7103 := [unit-resolution #6979 #7102 #7082]: #6757
+#7104 := (or #6709 #6758)
+#6762 := (or #6709 #6758 #6295)
+#6763 := [def-axiom]: #6762
+#7105 := [unit-resolution #6763 #6990]: #7104
+#7106 := [unit-resolution #7105 #7103]: #6758
+#7052 := (or #6079 #7051)
+#7055 := (or #6773 #6079 #7051)
+#7056 := (or #6773 #7052)
+#7058 := (iff #7056 #7055)
+#7059 := [rewrite]: #7058
+#7057 := [quant-inst #170 #56]: #7056
+#7060 := [mp #7057 #7059]: #7055
+#7107 := [unit-resolution #7060 #4208]: #7052
+#7108 := [unit-resolution #7107 #7106]: #7051
+#5915 := (* -1::Int #5908)
+#5916 := (+ #1444 #5915)
+#5917 := (+ #99 #5916)
+#5918 := (<= #5917 0::Int)
+#5945 := (not #5918)
+#5919 := (+ f8 #5915)
+#5920 := (<= #5919 0::Int)
+#5925 := (or #5918 #5920)
+#5928 := (not #5925)
+#5931 := (or #5923 #5928)
+#5934 := (or #4392 #5923 #5928)
+#5921 := (or #5920 #5918)
+#5922 := (not #5921)
+#5924 := (or #5923 #5922)
+#5935 := (or #4392 #5924)
+#5942 := (iff #5935 #5934)
+#5937 := (or #4392 #5931)
+#5940 := (iff #5937 #5934)
+#5941 := [rewrite]: #5940
+#5938 := (iff #5935 #5937)
+#5932 := (iff #5924 #5931)
+#5929 := (iff #5922 #5928)
+#5926 := (iff #5921 #5925)
+#5927 := [rewrite]: #5926
+#5930 := [monotonicity #5927]: #5929
+#5933 := [monotonicity #5930]: #5932
+#5939 := [monotonicity #5933]: #5938
+#5943 := [trans #5939 #5941]: #5942
+#5936 := [quant-inst #56]: #5935
+#5944 := [mp #5936 #5943]: #5934
+#7109 := [unit-resolution #5944 #6500]: #5931
+#7110 := [unit-resolution #7109 #7086]: #5928
+#5946 := (or #5925 #5945)
+#5947 := [def-axiom]: #5946
+#7111 := [unit-resolution #5947 #7110]: #5945
+#6118 := (>= #174 0::Int)
+#6121 := (or #4270 #6118)
+#6122 := [quant-inst #170]: #6121
+#7113 := [unit-resolution #6122 #7112]: #6118
+#3911 := (<= #99 0::Int)
+#7115 := (or #1738 #3911)
+#7116 := [th-lemma arith triangle-eq]: #7115
+#7117 := [unit-resolution #7116 #7114]: #3911
+#7118 := [th-lemma arith farkas 1 1 1 1 #7117 #7113 #7111 #7108]: false
+#7119 := [lemma #7118]: #5923
+#12705 := [mp #7119 #12704]: #203
+#4074 := (or #4499 #1481 #4493)
+#4060 := [def-axiom]: #4074
+#12706 := [unit-resolution #4060 #12705 #12699]: #4493
+#4083 := (or #4490 #4484)
+#4067 := [def-axiom]: #4083
+#12707 := [unit-resolution #4067 #12706]: #4484
+#4080 := (or #4487 #2267 #4481)
+#4081 := [def-axiom]: #4080
+#12708 := [unit-resolution #4081 #12707]: #4484
+#23122 := [unit-resolution #12708 #23121]: #4481
+#4075 := (or #4478 #4472)
+#4077 := [def-axiom]: #4075
+#23130 := [unit-resolution #4077 #23122]: #4472
+#12711 := (or #4475 #4469)
+#10279 := [hypothesis]: #3436
+#3964 := (or #3431 #2290)
+#3965 := [def-axiom]: #3964
+#9749 := [unit-resolution #3965 #10279]: #2290
+#10370 := (or #3431 #2289)
+#10555 := (f5 #7202 ?v1!16)
+#10556 := (f9 #10555)
+#10573 := (* -1::Int #10556)
+#8682 := (f5 f22 ?v1!16)
+#8683 := (f9 #8682)
+#10576 := (+ #8683 #10573)
+#10578 := (>= #10576 0::Int)
+#10572 := (= #8683 #10556)
+#10583 := (= #10556 #8683)
+#10581 := (= #10555 #8682)
+#10582 := [monotonicity #7781]: #10581
+#10584 := [monotonicity #10582]: #10583
+#10585 := [symm #10584]: #10572
+#10586 := (not #10572)
+#10587 := (or #10586 #10578)
+#10588 := [th-lemma arith triangle-eq]: #10587
+#10589 := [unit-resolution #10588 #10585]: #10578
+#5998 := (f24 f22)
+#6039 := (* -1::Int #5998)
+#6408 := (+ #174 #6039)
+#6409 := (>= #6408 0::Int)
+#4053 := (or #4514 #4403)
+#4054 := [def-axiom]: #4053
+#8184 := [unit-resolution #4054 #7088]: #4403
+#6413 := (or #4408 #6409)
+#6414 := [quant-inst #170]: #6413
+#8185 := [unit-resolution #6414 #8184]: #6409
+#4107 := (not #2879)
+#4108 := (or #3431 #4107)
+#4109 := [def-axiom]: #4108
+#10282 := [unit-resolution #4109 #10279]: #4107
+#10214 := (+ #2281 #6039)
+#10215 := (<= #10214 0::Int)
+#10203 := (= #2281 #5998)
+#10471 := (= ?v0!17 f22)
+#8508 := (= ?v0!17 #7202)
+#8501 := (f3 f15 ?v0!17)
+#8502 := (= f1 #8501)
+#8511 := (ite #8508 #5883 #8502)
+#8505 := (f3 #8433 ?v0!17)
+#8506 := (= f1 #8505)
+#8514 := (iff #8506 #8511)
+#9702 := (or #6281 #8514)
+#8503 := (= #7202 ?v0!17)
+#8504 := (ite #8503 #5883 #8502)
+#8507 := (iff #8506 #8504)
+#9697 := (or #6281 #8507)
+#9704 := (iff #9697 #9702)
+#9706 := (iff #9702 #9702)
+#9707 := [rewrite]: #9706
+#8515 := (iff #8507 #8514)
+#8512 := (iff #8504 #8511)
+#8509 := (iff #8503 #8508)
+#8510 := [rewrite]: #8509
+#8513 := [monotonicity #8510]: #8512
+#8516 := [monotonicity #8513]: #8515
+#9705 := [monotonicity #8516]: #9704
+#9713 := [trans #9705 #9707]: #9704
+#9703 := [quant-inst #104 #7202 #5882 #2280]: #9697
+#9714 := [mp #9703 #9713]: #9702
+#10283 := [unit-resolution #9714 #4168]: #8514
+#10312 := (= #2286 #8505)
+#10285 := (= #8505 #2286)
+#10222 := [monotonicity #9277]: #10285
+#10313 := [symm #10222]: #10312
+#4122 := (or #3431 #2287)
+#3963 := [def-axiom]: #4122
+#10284 := [unit-resolution #3963 #10279]: #2287
+#10314 := [trans #10284 #10313]: #8506
+#9723 := (not #8506)
+#9726 := (not #8514)
+#9729 := (or #9726 #9723 #8511)
+#9730 := [def-axiom]: #9729
+#10315 := [unit-resolution #9730 #10314 #10283]: #8511
+#9722 := (not #8502)
+#8476 := (f13 f14 ?v0!17)
+#8558 := (* -1::Int #8476)
+#7504 := (f13 f14 #7202)
+#10477 := (+ #7504 #8558)
+#10478 := (>= #10477 0::Int)
+#10603 := (not #10478)
+#8437 := (= ?v1!16 #7202)
+#9607 := (not #8437)
+#8429 := (f3 f15 ?v1!16)
+#8430 := (= f1 #8429)
+#8440 := (ite #8437 #5883 #8430)
+#9606 := (not #8440)
+#8434 := (f3 #8433 ?v1!16)
+#8435 := (= f1 #8434)
+#8443 := (iff #8435 #8440)
+#9575 := (or #6281 #8443)
+#8431 := (= #7202 ?v1!16)
+#8432 := (ite #8431 #5883 #8430)
+#8436 := (iff #8435 #8432)
+#9576 := (or #6281 #8436)
+#9601 := (iff #9576 #9575)
+#9597 := (iff #9575 #9575)
+#9603 := [rewrite]: #9597
+#8444 := (iff #8436 #8443)
+#8441 := (iff #8432 #8440)
+#8438 := (iff #8431 #8437)
+#8439 := [rewrite]: #8438
+#8442 := [monotonicity #8439]: #8441
+#8445 := [monotonicity #8442]: #8444
+#9602 := [monotonicity #8445]: #9601
+#9604 := [trans #9602 #9603]: #9601
+#9600 := [quant-inst #104 #7202 #5882 #2279]: #9576
+#9605 := [mp #9600 #9604]: #9575
+#10316 := [unit-resolution #9605 #4168]: #8443
+#9639 := (not #8435)
+#10324 := (iff #2290 #9639)
+#10322 := (iff #2289 #8435)
+#10320 := (iff #8435 #2289)
+#10318 := (= #8434 #2288)
+#10319 := [monotonicity #9277]: #10318
+#10321 := [monotonicity #10319]: #10320
+#10323 := [symm #10321]: #10322
+#10325 := [monotonicity #10323]: #10324
+#10317 := [hypothesis]: #2290
+#10326 := [mp #10317 #10325]: #9639
+#9631 := (not #8443)
+#9632 := (or #9631 #8435 #9606)
+#9638 := [def-axiom]: #9632
+#10327 := [unit-resolution #9638 #10326 #10316]: #9606
+#10328 := (or #8440 #9607)
+#9627 := (or #8440 #9607 #6295)
+#9622 := [def-axiom]: #9627
+#10329 := [unit-resolution #9622 #6990]: #10328
+#10330 := [unit-resolution #10329 #10327]: #9607
+#8655 := (f13 f14 ?v1!16)
+#8666 := (* -1::Int #8655)
+#8914 := (+ #174 #8666)
+#8915 := (<= #8914 0::Int)
+#9628 := (not #8430)
+#9629 := (or #8440 #8437 #9628)
+#9630 := [def-axiom]: #9629
+#10299 := [unit-resolution #9630 #10330 #10327]: #9628
+#8920 := (or #8430 #8915)
+#4045 := (or #4526 #4377)
+#4031 := [def-axiom]: #4045
+#10304 := [unit-resolution #4031 #6499]: #4377
+#9975 := (or #4382 #8430 #8915)
+#8903 := (+ #8655 #1444)
+#8904 := (>= #8903 0::Int)
+#8907 := (or #8430 #8904)
+#9976 := (or #4382 #8907)
+#10011 := (iff #9976 #9975)
+#10007 := (or #4382 #8920)
+#10010 := (iff #10007 #9975)
+#10005 := [rewrite]: #10010
+#10008 := (iff #9976 #10007)
+#8921 := (iff #8907 #8920)
+#8918 := (iff #8904 #8915)
+#8908 := (+ #1444 #8655)
+#8911 := (>= #8908 0::Int)
+#8916 := (iff #8911 #8915)
+#8917 := [rewrite]: #8916
+#8912 := (iff #8904 #8911)
+#8909 := (= #8903 #8908)
+#8910 := [rewrite]: #8909
+#8913 := [monotonicity #8910]: #8912
+#8919 := [trans #8913 #8917]: #8918
 #8922 := [monotonicity #8919]: #8921
-#8928 := [trans #8922 #8926]: #8927
-#8931 := [monotonicity #8928]: #8930
-#10018 := [monotonicity #8931]: #10017
-#10021 := [trans #10018 #10014]: #10020
-#10015 := [quant-inst #2288]: #9985
-#10022 := [mp #10015 #10021]: #9984
-#10307 := [unit-resolution #10022 #10313]: #8929
-#10314 := [unit-resolution #10307 #10308]: #8924
-#10586 := (not #8924)
-#10633 := (or #10612 #10586 #2888 #8446)
-#8717 := (+ #2886 #8692)
-#8718 := (+ #174 #8717)
-#8721 := (= #8718 0::Int)
-#10618 := (not #8721)
-#9835 := (<= #8718 0::Int)
-#10611 := (not #9835)
-#10599 := [hypothesis]: #9616
-#10601 := [hypothesis]: #4116
-#10588 := [hypothesis]: #10487
-#10613 := (or #10611 #2888 #10612 #8446)
-#10589 := [hypothesis]: #9835
-#10566 := (<= #10565 0::Int)
-#10567 := (not #10566)
-#10571 := (or #6782 #8446 #10567)
-#10568 := (or #8446 #10567)
-#10572 := (or #6782 #10568)
-#10574 := (iff #10572 #10571)
-#10575 := [rewrite]: #10574
-#10573 := [quant-inst #7211 #2288]: #10572
-#10576 := [mp #10573 #10575]: #10571
-#10600 := [unit-resolution #10576 #4217 #10599]: #10567
-#8568 := (+ #2290 #8567)
-#8569 := (<= #8568 0::Int)
-#9748 := (or #4417 #8569)
-#8557 := (+ #8485 #2291)
-#8558 := (>= #8557 0::Int)
-#9751 := (or #4417 #8558)
-#9766 := (iff #9751 #9748)
-#9768 := (iff #9748 #9748)
-#9769 := [rewrite]: #9768
-#8572 := (iff #8558 #8569)
-#8561 := (+ #2291 #8485)
-#8564 := (>= #8561 0::Int)
-#8570 := (iff #8564 #8569)
-#8571 := [rewrite]: #8570
-#8565 := (iff #8558 #8564)
-#8562 := (= #8557 #8561)
-#8563 := [rewrite]: #8562
-#8566 := [monotonicity #8563]: #8565
-#8573 := [trans #8566 #8571]: #8572
-#9767 := [monotonicity #8573]: #9766
-#9770 := [trans #9767 #9769]: #9766
-#9765 := [quant-inst #2289]: #9751
-#9771 := [mp #9765 #9770]: #9748
-#10602 := [unit-resolution #9771 #8193]: #8569
-#7529 := (* -1::Int #7513)
-#8423 := (+ #174 #7529)
-#8429 := (>= #8423 0::Int)
-#7336 := (= #174 #7513)
-#10603 := (= #7513 #174)
-#10604 := [monotonicity #7790]: #10603
-#10605 := [symm #10604]: #7336
-#10606 := (not #7336)
-#10607 := (or #10606 #8429)
-#10608 := [th-lemma arith triangle-eq]: #10607
-#10609 := [unit-resolution #10608 #10605]: #8429
-#10610 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10609 #10602 #10601 #10600 #10598 #10589 #10588]: false
-#10614 := [lemma #10610]: #10613
-#10617 := [unit-resolution #10614 #10588 #10601 #10599]: #10611
-#10619 := (or #10618 #9835)
-#10620 := [th-lemma arith triangle-eq]: #10619
-#10621 := [unit-resolution #10620 #10617]: #10618
-#8696 := (* -1::Int #8692)
-#8700 := (+ f8 #8696)
-#8701 := (<= #8700 0::Int)
-#9849 := (not #8701)
-#8710 := (+ #8675 #8692)
-#8711 := (+ #174 #8710)
-#8712 := (>= #8711 0::Int)
-#8747 := (or #8701 #8712)
-#8750 := (not #8747)
-#8744 := (= #2292 #8664)
-#10623 := (not #8744)
-#8676 := (+ #2292 #8675)
-#9848 := (>= #8676 0::Int)
-#10584 := (not #9848)
-#10579 := [hypothesis]: #8924
-#10615 := (or #10584 #2888 #10586 #10612)
-#10580 := [hypothesis]: #9848
-#10583 := [th-lemma arith farkas 1 -1 1 1 -1 1 #10609 #10602 #10601 #10580 #10579 #10588]: false
-#10616 := [lemma #10583]: #10615
-#10622 := [unit-resolution #10616 #10588 #10579 #10601]: #10584
-#10624 := (or #10623 #9848)
-#10625 := [th-lemma arith triangle-eq]: #10624
-#10626 := [unit-resolution #10625 #10622]: #10623
-#8753 := (or #8744 #8750)
-#9837 := (or #4401 #8744 #8750)
-#8697 := (+ #1453 #8696)
-#8698 := (+ #8664 #8697)
-#8699 := (<= #8698 0::Int)
-#8740 := (or #8701 #8699)
-#8741 := (not #8740)
-#8742 := (= #8664 #2292)
-#8743 := (or #8742 #8741)
-#9838 := (or #4401 #8743)
-#9845 := (iff #9838 #9837)
-#9839 := (or #4401 #8753)
-#9842 := (iff #9839 #9837)
-#9843 := [rewrite]: #9842
-#9840 := (iff #9838 #9839)
-#8754 := (iff #8743 #8753)
-#8751 := (iff #8741 #8750)
-#8748 := (iff #8740 #8747)
-#8715 := (iff #8699 #8712)
-#8703 := (+ #8664 #8696)
-#8704 := (+ #1453 #8703)
-#8707 := (<= #8704 0::Int)
-#8713 := (iff #8707 #8712)
-#8714 := [rewrite]: #8713
-#8708 := (iff #8699 #8707)
-#8705 := (= #8698 #8704)
-#8706 := [rewrite]: #8705
-#8709 := [monotonicity #8706]: #8708
-#8716 := [trans #8709 #8714]: #8715
-#8749 := [monotonicity #8716]: #8748
-#8752 := [monotonicity #8749]: #8751
-#8745 := (iff #8742 #8744)
-#8746 := [rewrite]: #8745
-#8755 := [monotonicity #8746 #8752]: #8754
-#9841 := [monotonicity #8755]: #9840
-#9846 := [trans #9841 #9843]: #9845
-#9817 := [quant-inst #2288]: #9838
-#9847 := [mp #9817 #9846]: #9837
-#10627 := [unit-resolution #9847 #6509]: #8753
-#10628 := [unit-resolution #10627 #10626]: #8750
-#9844 := (or #8747 #9849)
-#9850 := [def-axiom]: #9844
-#10629 := [unit-resolution #9850 #10628]: #9849
-#9851 := (not #8712)
-#9852 := (or #8747 #9851)
-#9853 := [def-axiom]: #9852
-#10630 := [unit-resolution #9853 #10628]: #9851
-#8724 := (or #8701 #8712 #8721)
-#9823 := (or #4409 #8701 #8712 #8721)
-#8693 := (+ #8692 #2886)
-#8694 := (+ #174 #8693)
-#8695 := (= #8694 0::Int)
-#8702 := (or #8701 #8699 #8695)
-#9824 := (or #4409 #8702)
-#9830 := (iff #9824 #9823)
-#9826 := (or #4409 #8724)
-#9828 := (iff #9826 #9823)
-#9829 := [rewrite]: #9828
-#9821 := (iff #9824 #9826)
-#8725 := (iff #8702 #8724)
-#8722 := (iff #8695 #8721)
-#8719 := (= #8694 #8718)
-#8720 := [rewrite]: #8719
-#8723 := [monotonicity #8720]: #8722
-#8726 := [monotonicity #8716 #8723]: #8725
-#9827 := [monotonicity #8726]: #9821
-#9831 := [trans #9827 #9829]: #9830
-#9825 := [quant-inst #2288]: #9824
-#9834 := [mp #9825 #9831]: #9823
-#10631 := [unit-resolution #9834 #6513]: #8724
-#10632 := [unit-resolution #10631 #10630 #10629 #10621]: false
-#10634 := [lemma #10632]: #10633
-#10315 := [unit-resolution #10634 #10314 #10291 #10339]: #10612
-#10310 := (or #9731 #10487)
-#10295 := [hypothesis]: #10612
-#10297 := [hypothesis]: #8511
-#7515 := (f3 f15 #7211)
-#7516 := (= f1 #7515)
-#10303 := (not #7516)
-#10304 := (iff #757 #10303)
-#10296 := (iff #754 #7516)
-#10300 := (iff #7516 #754)
-#10298 := (= #7515 #171)
-#10299 := [monotonicity #7790]: #10298
-#10301 := [monotonicity #10299]: #10300
-#10302 := [symm #10301]: #10296
-#10305 := [monotonicity #10302]: #10304
-#10306 := [mp #6926 #10305]: #10303
-#10233 := (or #4296 #7516 #9731 #10487)
-#10494 := (or #7516 #9731 #10487)
-#10239 := (or #4296 #10494)
-#10241 := (iff #10239 #10233)
-#10242 := [rewrite]: #10241
-#10240 := [quant-inst #2289 #7211]: #10239
-#10243 := [mp #10240 #10242]: #10233
-#10309 := [unit-resolution #10243 #6937 #10306 #10297 #10295]: false
-#10311 := [lemma #10309]: #10310
-#10316 := [unit-resolution #10311 #10315]: #9731
-#9724 := (not #8520)
-#9727 := (or #9724 #8517 #8511)
-#9728 := [def-axiom]: #9727
-#10317 := [unit-resolution #9728 #10316 #10324]: #8517
-#10318 := [trans #10317 #7790]: #10480
-#10319 := [monotonicity #10318]: #10212
-#10346 := (not #10212)
-#10347 := (or #10346 #10224)
-#10345 := [th-lemma arith triangle-eq]: #10347
-#10348 := [unit-resolution #10345 #10319]: #10224
-#10350 := (not #6418)
-#10349 := (not #10224)
-#10355 := (or #10584 #10349 #2888 #10586 #10350)
-#10356 := [th-lemma arith assign-bounds -1 1 -1 1]: #10355
-#10354 := [unit-resolution #10356 #10291 #8194 #10314 #10348]: #10584
-#10357 := [unit-resolution #10625 #10354]: #10623
-#10358 := [unit-resolution #10627 #10357]: #8750
-#10183 := (or #8747 #8721)
-#10179 := [hypothesis]: #10618
-#10180 := [hypothesis]: #8750
-#10181 := [unit-resolution #9850 #10180]: #9849
-#10176 := [unit-resolution #9853 #10180]: #9851
-#10182 := [unit-resolution #10631 #10176 #10181 #10179]: false
-#10184 := [lemma #10182]: #10183
-#10359 := [unit-resolution #10184 #10358]: #8721
-#10376 := [unit-resolution #10620 #10359]: #9835
-#10377 := [unit-resolution #10576 #4217 #10339]: #10567
-#10378 := [th-lemma arith farkas 1 1 1 1 1 1 #10377 #10376 #10348 #10291 #8194 #10598]: false
-#10380 := [lemma #10378]: #10379
-#9759 := [unit-resolution #10380 #9758 #10288]: false
-#9760 := [lemma #9759]: #3440
-#4106 := (or #4484 #3445 #4478)
-#4093 := [def-axiom]: #4106
-#12721 := [unit-resolution #4093 #9760]: #12720
-#23132 := [unit-resolution #12721 #23139]: #4478
-#4000 := (or #4475 #4469)
-#4008 := [def-axiom]: #4000
-#23133 := [unit-resolution #4008 #23132]: #4469
-#23134 := (or #4472 #4466)
-#14671 := (f5 f22 ?v0!19)
-#14672 := (f9 #14671)
-#14467 := (f13 f14 ?v0!19)
-#14603 := (* -1::Int #14467)
-#14719 := (+ #14603 #14672)
-#14720 := (+ #174 #14719)
-#14721 := (>= #14720 0::Int)
-#14960 := (not #14721)
-#14675 := (* -1::Int #14672)
-#15459 := (+ #2322 #14675)
-#15460 := (>= #15459 0::Int)
-#15458 := (= #2322 #14672)
-#15668 := (= #2321 #14671)
-#15695 := (= ?v1!18 f22)
-#13665 := (= ?v1!18 #7211)
-#13658 := (f3 f15 ?v1!18)
-#13659 := (= f1 #13658)
-#13802 := (not #13659)
-#13798 := (f13 f14 ?v1!18)
-#14923 := (+ #13798 #14603)
-#14924 := (+ #2322 #14923)
-#14919 := (>= #14924 0::Int)
-#15619 := (not #14919)
-#14604 := (+ #2317 #14603)
-#14605 := (<= #14604 0::Int)
-#14818 := (or #4417 #14605)
-#14570 := (+ #14467 #2318)
-#14597 := (>= #14570 0::Int)
-#14819 := (or #4417 #14597)
-#14821 := (iff #14819 #14818)
-#14823 := (iff #14818 #14818)
-#14824 := [rewrite]: #14823
-#14622 := (iff #14597 #14605)
-#14598 := (+ #2318 #14467)
-#14601 := (>= #14598 0::Int)
-#14606 := (iff #14601 #14605)
-#14621 := [rewrite]: #14606
-#14596 := (iff #14597 #14601)
-#14599 := (= #14570 #14598)
-#14600 := [rewrite]: #14599
-#14602 := [monotonicity #14600]: #14596
-#14623 := [trans #14602 #14621]: #14622
-#14822 := [monotonicity #14623]: #14821
-#14772 := [trans #14822 #14824]: #14821
-#14820 := [quant-inst #2316]: #14819
-#14891 := [mp #14820 #14772]: #14818
-#15608 := [unit-resolution #14891 #8193]: #14605
-#4122 := (not #2915)
-#15609 := [hypothesis]: #3491
-#3951 := (or #3486 #4122)
-#3953 := [def-axiom]: #3951
-#15607 := [unit-resolution #3953 #15609]: #4122
-#13815 := (* -1::Int #13798)
-#13816 := (+ #2319 #13815)
-#13544 := (>= #13816 0::Int)
-#13884 := (= #2319 #13798)
-#4121 := (or #3486 #2330)
-#4115 := [def-axiom]: #4121
-#15610 := [unit-resolution #4115 #15609]: #2330
-#13776 := (or #4426 #3471 #13884)
-#13882 := (= #13798 #2319)
-#13752 := (or #13882 #3471)
-#13777 := (or #4426 #13752)
-#13799 := (iff #13777 #13776)
-#13750 := (or #3471 #13884)
-#13791 := (or #4426 #13750)
-#13801 := (iff #13791 #13776)
-#13793 := [rewrite]: #13801
-#13796 := (iff #13777 #13791)
-#13758 := (iff #13752 #13750)
-#13753 := (or #13884 #3471)
-#13756 := (iff #13753 #13750)
-#13757 := [rewrite]: #13756
-#13754 := (iff #13752 #13753)
-#13885 := (iff #13882 #13884)
-#13886 := [rewrite]: #13885
-#13755 := [monotonicity #13886]: #13754
-#13759 := [trans #13755 #13757]: #13758
-#13800 := [monotonicity #13759]: #13796
-#13803 := [trans #13800 #13793]: #13799
-#13795 := [quant-inst #2315]: #13777
-#13804 := [mp #13795 #13803]: #13776
-#15615 := [unit-resolution #13804 #7100 #15610]: #13884
-#15616 := (not #13884)
-#15617 := (or #15616 #13544)
-#15601 := [th-lemma arith triangle-eq]: #15617
-#15618 := [unit-resolution #15601 #15615]: #13544
-#15614 := (not #14605)
-#15611 := (not #13544)
-#15620 := (or #15619 #15611 #15614 #2915)
-#15622 := [th-lemma arith assign-bounds 1 -1 1]: #15620
-#15623 := [unit-resolution #15622 #15618 #15607 #15608]: #15619
-#15628 := (or #13802 #14919)
-#4114 := (or #3486 #2328)
-#4120 := [def-axiom]: #4114
-#15626 := [unit-resolution #4120 #15609]: #2328
-#15627 := [unit-resolution #4015 #6507]: #4282
-#13311 := (or #4287 #2327 #13802 #14919)
-#14925 := (or #13802 #2327 #14919)
-#13540 := (or #4287 #14925)
-#15126 := (iff #13540 #13311)
-#14926 := (or #2327 #13802 #14919)
-#13546 := (or #4287 #14926)
-#15124 := (iff #13546 #13311)
-#15125 := [rewrite]: #15124
-#13648 := (iff #13540 #13546)
-#14927 := (iff #14925 #14926)
-#14928 := [rewrite]: #14927
-#15123 := [monotonicity #14928]: #13648
-#15127 := [trans #15123 #15125]: #15126
-#13543 := [quant-inst #2316 #2315]: #13540
-#15128 := [mp #13543 #15127]: #13311
-#15621 := [unit-resolution #15128 #15627 #15626]: #15628
-#15629 := [unit-resolution #15621 #15623]: #13802
-#13668 := (ite #13665 #5892 #13659)
-#13662 := (f3 #8442 ?v1!18)
-#13663 := (= f1 #13662)
-#13671 := (iff #13663 #13668)
-#15012 := (or #6290 #13671)
-#13660 := (= #7211 ?v1!18)
-#13661 := (ite #13660 #5892 #13659)
-#13664 := (iff #13663 #13661)
-#15017 := (or #6290 #13664)
-#14890 := (iff #15017 #15012)
-#15043 := (iff #15012 #15012)
-#15044 := [rewrite]: #15043
-#13672 := (iff #13664 #13671)
-#13669 := (iff #13661 #13668)
-#13666 := (iff #13660 #13665)
-#13667 := [rewrite]: #13666
-#13670 := [monotonicity #13667]: #13669
-#13673 := [monotonicity #13670]: #13672
-#15019 := [monotonicity #13673]: #14890
-#15060 := [trans #15019 #15044]: #14890
-#15018 := [quant-inst #104 #7211 #5891 #2315]: #15017
-#14889 := [mp #15018 #15060]: #15012
-#15630 := [unit-resolution #14889 #4177]: #13671
-#15690 := (= #2329 #13662)
-#15624 := (= #13662 #2329)
-#15625 := [monotonicity #9286]: #15624
-#15692 := [symm #15625]: #15690
-#15693 := [trans #15610 #15692]: #13663
-#13237 := (not #13663)
-#12830 := (not #13671)
-#12788 := (or #12830 #13237 #13668)
-#13250 := [def-axiom]: #12788
-#15694 := [unit-resolution #13250 #15693 #15630]: #13668
-#15061 := (not #13668)
-#15059 := (or #15061 #13665 #13659)
-#15067 := [def-axiom]: #15059
-#15688 := [unit-resolution #15067 #15694 #15629]: #13665
-#15667 := [trans #15688 #7790]: #15695
-#15666 := [monotonicity #15667]: #15668
-#15670 := [monotonicity #15666]: #15458
-#15672 := (not #15458)
-#15673 := (or #15672 #15460)
-#15674 := [th-lemma arith triangle-eq]: #15673
-#15669 := [unit-resolution #15674 #15670]: #15460
-#15238 := (+ #2319 #6048)
-#15240 := (>= #15238 0::Int)
-#15450 := (= #2319 #6007)
-#15761 := [monotonicity #15667]: #15450
-#15671 := (not #15450)
-#15767 := (or #15671 #15240)
-#15768 := [th-lemma arith triangle-eq]: #15767
-#15769 := [unit-resolution #15768 #15761]: #15240
-#6674 := (<= #6417 0::Int)
-#6008 := (= #174 #6007)
-#6547 := (f3 f23 f22)
-#6548 := (= f1 #6547)
-#8184 := (= #5891 #6547)
-#8182 := (= #6547 #5891)
-#8183 := [monotonicity #6998]: #8182
-#8185 := [symm #8183]: #8184
-#8186 := [trans #6999 #8185]: #6548
-#6554 := (not #6548)
-#6606 := (or #6008 #6554)
-#6687 := (or #4426 #6008 #6554)
-#6688 := (or #4426 #6606)
-#6690 := (iff #6688 #6687)
-#6691 := [rewrite]: #6690
-#6689 := [quant-inst #170]: #6688
-#6692 := [mp #6689 #6691]: #6687
-#8187 := [unit-resolution #6692 #7100]: #6606
-#8188 := [unit-resolution #8187 #8186]: #6008
-#8189 := (not #6008)
-#8190 := (or #8189 #6674)
-#8191 := [th-lemma arith triangle-eq]: #8190
-#8192 := [unit-resolution #8191 #8188]: #6674
-#16339 := (not #15460)
-#12652 := (not #6674)
-#15770 := (not #15240)
-#15766 := (or #14960 #15614 #2915 #15770 #12652 #16339)
-#15774 := [th-lemma arith assign-bounds -1 1 1 -1 1]: #15766
-#15775 := [unit-resolution #15774 #15608 #8192 #15769 #15607 #15669]: #14960
-#14679 := (+ f8 #14675)
-#14731 := (<= #14679 0::Int)
-#15014 := (not #14731)
-#16340 := (or #15014 #16339 #2327)
-#16336 := [hypothesis]: #2328
-#16331 := [hypothesis]: #14731
-#16337 := [hypothesis]: #15460
-#16338 := [th-lemma arith farkas 1 -1 1 #16337 #16331 #16336]: false
-#16341 := [lemma #16338]: #16340
-#15776 := [unit-resolution #16341 #15669 #15626]: #15014
-#14725 := (+ #2318 #14672)
-#14726 := (+ #174 #14725)
-#14743 := (= #14726 0::Int)
-#15811 := (not #14743)
-#14857 := (>= #14726 0::Int)
-#15772 := (not #14857)
-#15793 := (or #15772 #2915 #15770 #12652 #16339)
-#15805 := [th-lemma arith assign-bounds 1 1 -1 1]: #15793
-#15806 := [unit-resolution #15805 #15769 #8192 #15607 #15669]: #15772
-#15812 := (or #15811 #14857)
-#15813 := [th-lemma arith triangle-eq]: #15812
-#15847 := [unit-resolution #15813 #15806]: #15811
-#14768 := (or #14721 #14731 #14743)
-#14892 := (or #4409 #14721 #14731 #14743)
-#14673 := (+ #14672 #2318)
-#14674 := (+ #174 #14673)
-#14669 := (= #14674 0::Int)
-#14676 := (+ #1453 #14675)
-#14677 := (+ #14467 #14676)
-#14678 := (<= #14677 0::Int)
-#14732 := (or #14731 #14678 #14669)
-#14893 := (or #4409 #14732)
-#14860 := (iff #14893 #14892)
-#14895 := (or #4409 #14768)
-#14858 := (iff #14895 #14892)
-#14859 := [rewrite]: #14858
-#14921 := (iff #14893 #14895)
-#14770 := (iff #14732 #14768)
-#14765 := (or #14731 #14721 #14743)
-#14763 := (iff #14765 #14768)
-#14769 := [rewrite]: #14763
-#14766 := (iff #14732 #14765)
-#14744 := (iff #14669 #14743)
-#14727 := (= #14674 #14726)
-#14728 := [rewrite]: #14727
-#14764 := [monotonicity #14728]: #14744
-#14718 := (iff #14678 #14721)
-#14733 := (+ #14467 #14675)
-#14734 := (+ #1453 #14733)
-#14737 := (<= #14734 0::Int)
-#14722 := (iff #14737 #14721)
-#14723 := [rewrite]: #14722
-#14738 := (iff #14678 #14737)
-#14735 := (= #14677 #14734)
-#14736 := [rewrite]: #14735
-#14739 := [monotonicity #14736]: #14738
-#14724 := [trans #14739 #14723]: #14718
-#14767 := [monotonicity #14724 #14764]: #14766
-#14771 := [trans #14767 #14769]: #14770
-#14922 := [monotonicity #14771]: #14921
-#14920 := [trans #14922 #14859]: #14860
-#14894 := [quant-inst #2316]: #14893
-#14861 := [mp #14894 #14920]: #14892
-#15845 := [unit-resolution #14861 #6513]: #14768
-#15846 := [unit-resolution #15845 #15847 #15776 #15775]: false
-#15842 := [lemma #15846]: #3486
-#3989 := (or #4472 #3491 #4466)
-#4004 := [def-axiom]: #3989
-#23149 := [unit-resolution #4004 #15842]: #23134
-#23150 := [unit-resolution #23149 #23133]: #4466
-#4108 := (or #4463 #2360)
-#4110 := [def-axiom]: #4108
-#23151 := [unit-resolution #4110 #23150]: #2360
-#23152 := (= #9081 #6070)
-#23153 := [monotonicity #9282]: #23152
-#23155 := [symm #23153]: #9861
-#23156 := [unit-resolution #11949 #23155]: #9457
-#9818 := (<= #9455 0::Int)
-#23148 := (or #11945 #9818)
-#23154 := [th-lemma arith triangle-eq]: #23148
-#23157 := [unit-resolution #23154 #23155]: #9818
-#23158 := (not #9818)
-#23164 := (or #10878 #23158)
-#7358 := (>= #6070 0::Int)
-#7296 := (not #7358)
-#7297 := [hypothesis]: #7296
-#7978 := (or #4279 #7358)
-#7979 := [quant-inst #6069]: #7978
-#7484 := [unit-resolution #7979 #7121 #7297]: false
-#7488 := [lemma #7484]: #7358
-#7053 := (not #3920)
-#23159 := (or #10878 #7053 #7296 #23158)
-#23161 := [th-lemma arith assign-bounds -1 1 -1]: #23159
-#23165 := [unit-resolution #23161 #7488 #7126]: #23164
-#23163 := [unit-resolution #23165 #23157]: #10878
-#3995 := (or #4463 #4455)
-#3996 := [def-axiom]: #3995
-#23166 := [unit-resolution #3996 #23150]: #4455
-#24105 := (or #14183 #4460)
-#8778 := (f24 #7211)
-#9544 := (* -1::Int #8778)
-#14038 := (+ #2347 #9544)
-#14226 := (<= #14038 0::Int)
-#10164 := (f3 f23 #7211)
-#10165 := (= f1 #10164)
-#11810 := (= #5891 #10164)
-#11803 := (= #10164 #5891)
-#11809 := [monotonicity #6998 #7790]: #11803
-#11811 := [symm #11809]: #11810
-#11812 := [trans #6999 #11811]: #10165
-#14212 := (f9 #14211)
-#14238 := (* -1::Int #14212)
-#14239 := (+ #9544 #14238)
-#14240 := (+ #2347 #14239)
-#14241 := (= #14240 0::Int)
-#15156 := (>= #14240 0::Int)
-#14157 := (+ #2348 #14132)
-#14158 := (+ #174 #14157)
-#14427 := (<= #14158 0::Int)
-#14161 := (= #14158 0::Int)
-#14186 := (not #14183)
-#21311 := [hypothesis]: #14186
-#21316 := (or #14183 #14161)
-#21305 := (not #14161)
-#21306 := [hypothesis]: #21305
-#12472 := (not #14141)
-#12479 := (or #14183 #12472)
-#12480 := [def-axiom]: #12479
-#21312 := [unit-resolution #12480 #21311]: #12472
-#12469 := (not #14152)
-#12478 := (or #14183 #12469)
-#12481 := [def-axiom]: #12478
-#21313 := [unit-resolution #12481 #21311]: #12469
-#14164 := (or #14141 #14152 #14161)
-#12411 := (or #4409 #14141 #14152 #14161)
-#14133 := (+ #14132 #2348)
-#14134 := (+ #174 #14133)
-#14135 := (= #14134 0::Int)
-#14137 := (+ #1453 #14136)
-#14138 := (+ #14074 #14137)
-#14139 := (<= #14138 0::Int)
-#14142 := (or #14141 #14139 #14135)
-#12435 := (or #4409 #14142)
-#12440 := (iff #12435 #12411)
-#12408 := (or #4409 #14164)
-#12439 := (iff #12408 #12411)
-#12434 := [rewrite]: #12439
-#12437 := (iff #12435 #12408)
-#14165 := (iff #14142 #14164)
-#14162 := (iff #14135 #14161)
-#14159 := (= #14134 #14158)
-#14160 := [rewrite]: #14159
-#14163 := [monotonicity #14160]: #14162
-#14155 := (iff #14139 #14152)
-#14143 := (+ #14074 #14136)
-#14144 := (+ #1453 #14143)
-#14147 := (<= #14144 0::Int)
-#14153 := (iff #14147 #14152)
-#14154 := [rewrite]: #14153
-#14148 := (iff #14139 #14147)
-#14145 := (= #14138 #14144)
-#14146 := [rewrite]: #14145
-#14149 := [monotonicity #14146]: #14148
-#14156 := [trans #14149 #14154]: #14155
-#14166 := [monotonicity #14156 #14163]: #14165
-#12438 := [monotonicity #14166]: #12437
-#12442 := [trans #12438 #12434]: #12440
-#12436 := [quant-inst #2346]: #12435
-#12443 := [mp #12436 #12442]: #12411
-#21314 := [unit-resolution #12443 #6513]: #14164
-#21315 := [unit-resolution #21314 #21313 #21312 #21306]: false
-#21317 := [lemma #21315]: #21316
-#24022 := [unit-resolution #21317 #21311]: #14161
-#24023 := (or #21305 #14427)
-#24024 := [th-lemma arith triangle-eq]: #24023
-#24025 := [unit-resolution #24024 #24022]: #14427
-#17684 := (not #14427)
-#24046 := (or #15156 #17684)
-#9545 := (+ #6007 #9544)
-#7445 := (>= #9545 0::Int)
-#9543 := (= #6007 #8778)
-#11874 := (= #8778 #6007)
-#11875 := [monotonicity #7790]: #11874
-#11876 := [symm #11875]: #9543
-#11877 := (not #9543)
-#24020 := (or #11877 #7445)
-#24026 := [th-lemma arith triangle-eq]: #24020
-#24027 := [unit-resolution #24026 #11876]: #7445
-#13353 := (+ #14132 #14238)
-#13586 := (>= #13353 0::Int)
-#7923 := (= #14132 #14212)
-#24030 := (= #14212 #14132)
-#24037 := [monotonicity #24029]: #24030
-#24038 := [symm #24037]: #7923
-#24036 := (not #7923)
-#24039 := (or #24036 #13586)
+#10009 := [monotonicity #8922]: #10008
+#10012 := [trans #10009 #10005]: #10011
+#10006 := [quant-inst #2279]: #9976
+#10013 := [mp #10006 #10012]: #9975
+#10298 := [unit-resolution #10013 #10304]: #8920
+#10305 := [unit-resolution #10298 #10299]: #8915
+#10577 := (not #8915)
+#10624 := (or #10603 #10577 #2879 #8437)
+#8708 := (+ #2877 #8683)
+#8709 := (+ #174 #8708)
+#8712 := (= #8709 0::Int)
+#10609 := (not #8712)
+#9826 := (<= #8709 0::Int)
+#10602 := (not #9826)
+#10590 := [hypothesis]: #9607
+#10592 := [hypothesis]: #4107
+#10579 := [hypothesis]: #10478
+#10604 := (or #10602 #2879 #10603 #8437)
+#10580 := [hypothesis]: #9826
+#10557 := (<= #10556 0::Int)
+#10558 := (not #10557)
+#10562 := (or #6773 #8437 #10558)
+#10559 := (or #8437 #10558)
+#10563 := (or #6773 #10559)
+#10565 := (iff #10563 #10562)
+#10566 := [rewrite]: #10565
+#10564 := [quant-inst #7202 #2279]: #10563
+#10567 := [mp #10564 #10566]: #10562
+#10591 := [unit-resolution #10567 #4208 #10590]: #10558
+#8559 := (+ #2281 #8558)
+#8560 := (<= #8559 0::Int)
+#9739 := (or #4408 #8560)
+#8548 := (+ #8476 #2282)
+#8549 := (>= #8548 0::Int)
+#9742 := (or #4408 #8549)
+#9757 := (iff #9742 #9739)
+#9759 := (iff #9739 #9739)
+#9760 := [rewrite]: #9759
+#8563 := (iff #8549 #8560)
+#8552 := (+ #2282 #8476)
+#8555 := (>= #8552 0::Int)
+#8561 := (iff #8555 #8560)
+#8562 := [rewrite]: #8561
+#8556 := (iff #8549 #8555)
+#8553 := (= #8548 #8552)
+#8554 := [rewrite]: #8553
+#8557 := [monotonicity #8554]: #8556
+#8564 := [trans #8557 #8562]: #8563
+#9758 := [monotonicity #8564]: #9757
+#9761 := [trans #9758 #9760]: #9757
+#9756 := [quant-inst #2280]: #9742
+#9762 := [mp #9756 #9761]: #9739
+#10593 := [unit-resolution #9762 #8184]: #8560
+#7520 := (* -1::Int #7504)
+#8414 := (+ #174 #7520)
+#8420 := (>= #8414 0::Int)
+#7327 := (= #174 #7504)
+#10594 := (= #7504 #174)
+#10595 := [monotonicity #7781]: #10594
+#10596 := [symm #10595]: #7327
+#10597 := (not #7327)
+#10598 := (or #10597 #8420)
+#10599 := [th-lemma arith triangle-eq]: #10598
+#10600 := [unit-resolution #10599 #10596]: #8420
+#10601 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10600 #10593 #10592 #10591 #10589 #10580 #10579]: false
+#10605 := [lemma #10601]: #10604
+#10608 := [unit-resolution #10605 #10579 #10592 #10590]: #10602
+#10610 := (or #10609 #9826)
+#10611 := [th-lemma arith triangle-eq]: #10610
+#10612 := [unit-resolution #10611 #10608]: #10609
+#8687 := (* -1::Int #8683)
+#8691 := (+ f8 #8687)
+#8692 := (<= #8691 0::Int)
+#9840 := (not #8692)
+#8701 := (+ #8666 #8683)
+#8702 := (+ #174 #8701)
+#8703 := (>= #8702 0::Int)
+#8738 := (or #8692 #8703)
+#8741 := (not #8738)
+#8735 := (= #2283 #8655)
+#10614 := (not #8735)
+#8667 := (+ #2283 #8666)
+#9839 := (>= #8667 0::Int)
+#10575 := (not #9839)
+#10570 := [hypothesis]: #8915
+#10606 := (or #10575 #2879 #10577 #10603)
+#10571 := [hypothesis]: #9839
+#10574 := [th-lemma arith farkas 1 -1 1 1 -1 1 #10600 #10593 #10592 #10571 #10570 #10579]: false
+#10607 := [lemma #10574]: #10606
+#10613 := [unit-resolution #10607 #10579 #10570 #10592]: #10575
+#10615 := (or #10614 #9839)
+#10616 := [th-lemma arith triangle-eq]: #10615
+#10617 := [unit-resolution #10616 #10613]: #10614
+#8744 := (or #8735 #8741)
+#9828 := (or #4392 #8735 #8741)
+#8688 := (+ #1444 #8687)
+#8689 := (+ #8655 #8688)
+#8690 := (<= #8689 0::Int)
+#8731 := (or #8692 #8690)
+#8732 := (not #8731)
+#8733 := (= #8655 #2283)
+#8734 := (or #8733 #8732)
+#9829 := (or #4392 #8734)
+#9836 := (iff #9829 #9828)
+#9830 := (or #4392 #8744)
+#9833 := (iff #9830 #9828)
+#9834 := [rewrite]: #9833
+#9831 := (iff #9829 #9830)
+#8745 := (iff #8734 #8744)
+#8742 := (iff #8732 #8741)
+#8739 := (iff #8731 #8738)
+#8706 := (iff #8690 #8703)
+#8694 := (+ #8655 #8687)
+#8695 := (+ #1444 #8694)
+#8698 := (<= #8695 0::Int)
+#8704 := (iff #8698 #8703)
+#8705 := [rewrite]: #8704
+#8699 := (iff #8690 #8698)
+#8696 := (= #8689 #8695)
+#8697 := [rewrite]: #8696
+#8700 := [monotonicity #8697]: #8699
+#8707 := [trans #8700 #8705]: #8706
+#8740 := [monotonicity #8707]: #8739
+#8743 := [monotonicity #8740]: #8742
+#8736 := (iff #8733 #8735)
+#8737 := [rewrite]: #8736
+#8746 := [monotonicity #8737 #8743]: #8745
+#9832 := [monotonicity #8746]: #9831
+#9837 := [trans #9832 #9834]: #9836
+#9808 := [quant-inst #2279]: #9829
+#9838 := [mp #9808 #9837]: #9828
+#10618 := [unit-resolution #9838 #6500]: #8744
+#10619 := [unit-resolution #10618 #10617]: #8741
+#9835 := (or #8738 #9840)
+#9841 := [def-axiom]: #9835
+#10620 := [unit-resolution #9841 #10619]: #9840
+#9842 := (not #8703)
+#9843 := (or #8738 #9842)
+#9844 := [def-axiom]: #9843
+#10621 := [unit-resolution #9844 #10619]: #9842
+#8715 := (or #8692 #8703 #8712)
+#9814 := (or #4400 #8692 #8703 #8712)
+#8684 := (+ #8683 #2877)
+#8685 := (+ #174 #8684)
+#8686 := (= #8685 0::Int)
+#8693 := (or #8692 #8690 #8686)
+#9815 := (or #4400 #8693)
+#9821 := (iff #9815 #9814)
+#9817 := (or #4400 #8715)
+#9819 := (iff #9817 #9814)
+#9820 := [rewrite]: #9819
+#9812 := (iff #9815 #9817)
+#8716 := (iff #8693 #8715)
+#8713 := (iff #8686 #8712)
+#8710 := (= #8685 #8709)
+#8711 := [rewrite]: #8710
+#8714 := [monotonicity #8711]: #8713
+#8717 := [monotonicity #8707 #8714]: #8716
+#9818 := [monotonicity #8717]: #9812
+#9822 := [trans #9818 #9820]: #9821
+#9816 := [quant-inst #2279]: #9815
+#9825 := [mp #9816 #9822]: #9814
+#10622 := [unit-resolution #9825 #6504]: #8715
+#10623 := [unit-resolution #10622 #10621 #10620 #10612]: false
+#10625 := [lemma #10623]: #10624
+#10306 := [unit-resolution #10625 #10305 #10282 #10330]: #10603
+#10301 := (or #9722 #10478)
+#10286 := [hypothesis]: #10603
+#10288 := [hypothesis]: #8502
+#7506 := (f3 f15 #7202)
+#7507 := (= f1 #7506)
+#10294 := (not #7507)
+#10295 := (iff #756 #10294)
+#10287 := (iff #753 #7507)
+#10291 := (iff #7507 #753)
+#10289 := (= #7506 #171)
+#10290 := [monotonicity #7781]: #10289
+#10292 := [monotonicity #10290]: #10291
+#10293 := [symm #10292]: #10287
+#10296 := [monotonicity #10293]: #10295
+#10297 := [mp #6917 #10296]: #10294
+#10224 := (or #4287 #7507 #9722 #10478)
+#10485 := (or #7507 #9722 #10478)
+#10230 := (or #4287 #10485)
+#10232 := (iff #10230 #10224)
+#10233 := [rewrite]: #10232
+#10231 := [quant-inst #2280 #7202]: #10230
+#10234 := [mp #10231 #10233]: #10224
+#10300 := [unit-resolution #10234 #6928 #10297 #10288 #10286]: false
+#10302 := [lemma #10300]: #10301
+#10307 := [unit-resolution #10302 #10306]: #9722
+#9715 := (not #8511)
+#9718 := (or #9715 #8508 #8502)
+#9719 := [def-axiom]: #9718
+#10308 := [unit-resolution #9719 #10307 #10315]: #8508
+#10309 := [trans #10308 #7781]: #10471
+#10310 := [monotonicity #10309]: #10203
+#10337 := (not #10203)
+#10338 := (or #10337 #10215)
+#10336 := [th-lemma arith triangle-eq]: #10338
+#10339 := [unit-resolution #10336 #10310]: #10215
+#10341 := (not #6409)
+#10340 := (not #10215)
+#10346 := (or #10575 #10340 #2879 #10577 #10341)
+#10347 := [th-lemma arith assign-bounds -1 1 -1 1]: #10346
+#10345 := [unit-resolution #10347 #10282 #8185 #10305 #10339]: #10575
+#10348 := [unit-resolution #10616 #10345]: #10614
+#10349 := [unit-resolution #10618 #10348]: #8741
+#10174 := (or #8738 #8712)
+#10170 := [hypothesis]: #10609
+#10171 := [hypothesis]: #8741
+#10172 := [unit-resolution #9841 #10171]: #9840
+#10167 := [unit-resolution #9844 #10171]: #9842
+#10173 := [unit-resolution #10622 #10167 #10172 #10170]: false
+#10175 := [lemma #10173]: #10174
+#10350 := [unit-resolution #10175 #10349]: #8712
+#10367 := [unit-resolution #10611 #10350]: #9826
+#10368 := [unit-resolution #10567 #4208 #10330]: #10558
+#10369 := [th-lemma arith farkas 1 1 1 1 1 1 #10368 #10367 #10339 #10282 #8185 #10589]: false
+#10371 := [lemma #10369]: #10370
+#9750 := [unit-resolution #10371 #9749 #10279]: false
+#9751 := [lemma #9750]: #3431
+#4097 := (or #4475 #3436 #4469)
+#4084 := [def-axiom]: #4097
+#12712 := [unit-resolution #4084 #9751]: #12711
+#23123 := [unit-resolution #12712 #23130]: #4469
+#3991 := (or #4466 #4460)
+#3999 := [def-axiom]: #3991
+#23124 := [unit-resolution #3999 #23123]: #4460
+#23125 := (or #4463 #4457)
+#14662 := (f5 f22 ?v0!19)
+#14663 := (f9 #14662)
+#14458 := (f13 f14 ?v0!19)
+#14594 := (* -1::Int #14458)
+#14710 := (+ #14594 #14663)
+#14711 := (+ #174 #14710)
+#14712 := (>= #14711 0::Int)
+#14951 := (not #14712)
+#14666 := (* -1::Int #14663)
+#15450 := (+ #2313 #14666)
+#15451 := (>= #15450 0::Int)
+#15449 := (= #2313 #14663)
+#15659 := (= #2312 #14662)
+#15686 := (= ?v1!18 f22)
+#13656 := (= ?v1!18 #7202)
+#13649 := (f3 f15 ?v1!18)
+#13650 := (= f1 #13649)
+#13793 := (not #13650)
+#13789 := (f13 f14 ?v1!18)
+#14914 := (+ #13789 #14594)
+#14915 := (+ #2313 #14914)
+#14910 := (>= #14915 0::Int)
+#15610 := (not #14910)
+#14595 := (+ #2308 #14594)
+#14596 := (<= #14595 0::Int)
+#14809 := (or #4408 #14596)
+#14561 := (+ #14458 #2309)
+#14588 := (>= #14561 0::Int)
+#14810 := (or #4408 #14588)
+#14812 := (iff #14810 #14809)
+#14814 := (iff #14809 #14809)
+#14815 := [rewrite]: #14814
+#14613 := (iff #14588 #14596)
+#14589 := (+ #2309 #14458)
+#14592 := (>= #14589 0::Int)
+#14597 := (iff #14592 #14596)
+#14612 := [rewrite]: #14597
+#14587 := (iff #14588 #14592)
+#14590 := (= #14561 #14589)
+#14591 := [rewrite]: #14590
+#14593 := [monotonicity #14591]: #14587
+#14614 := [trans #14593 #14612]: #14613
+#14813 := [monotonicity #14614]: #14812
+#14763 := [trans #14813 #14815]: #14812
+#14811 := [quant-inst #2307]: #14810
+#14882 := [mp #14811 #14763]: #14809
+#15599 := [unit-resolution #14882 #8184]: #14596
+#4113 := (not #2906)
+#15600 := [hypothesis]: #3482
+#3942 := (or #3477 #4113)
+#3944 := [def-axiom]: #3942
+#15598 := [unit-resolution #3944 #15600]: #4113
+#13806 := (* -1::Int #13789)
+#13807 := (+ #2310 #13806)
+#13535 := (>= #13807 0::Int)
+#13875 := (= #2310 #13789)
+#4112 := (or #3477 #2321)
+#4106 := [def-axiom]: #4112
+#15601 := [unit-resolution #4106 #15600]: #2321
+#13767 := (or #4417 #3462 #13875)
+#13873 := (= #13789 #2310)
+#13743 := (or #13873 #3462)
+#13768 := (or #4417 #13743)
+#13790 := (iff #13768 #13767)
+#13741 := (or #3462 #13875)
+#13782 := (or #4417 #13741)
+#13792 := (iff #13782 #13767)
+#13784 := [rewrite]: #13792
+#13787 := (iff #13768 #13782)
+#13749 := (iff #13743 #13741)
+#13744 := (or #13875 #3462)
+#13747 := (iff #13744 #13741)
+#13748 := [rewrite]: #13747
+#13745 := (iff #13743 #13744)
+#13876 := (iff #13873 #13875)
+#13877 := [rewrite]: #13876
+#13746 := [monotonicity #13877]: #13745
+#13750 := [trans #13746 #13748]: #13749
+#13791 := [monotonicity #13750]: #13787
+#13794 := [trans #13791 #13784]: #13790
+#13786 := [quant-inst #2306]: #13768
+#13795 := [mp #13786 #13794]: #13767
+#15606 := [unit-resolution #13795 #7091 #15601]: #13875
+#15607 := (not #13875)
+#15608 := (or #15607 #13535)
+#15592 := [th-lemma arith triangle-eq]: #15608
+#15609 := [unit-resolution #15592 #15606]: #13535
+#15605 := (not #14596)
+#15602 := (not #13535)
+#15611 := (or #15610 #15602 #15605 #2906)
+#15613 := [th-lemma arith assign-bounds 1 -1 1]: #15611
+#15614 := [unit-resolution #15613 #15609 #15598 #15599]: #15610
+#15619 := (or #13793 #14910)
+#4105 := (or #3477 #2319)
+#4111 := [def-axiom]: #4105
+#15617 := [unit-resolution #4111 #15600]: #2319
+#15618 := [unit-resolution #4006 #6498]: #4273
+#13302 := (or #4278 #2318 #13793 #14910)
+#14916 := (or #13793 #2318 #14910)
+#13531 := (or #4278 #14916)
+#15117 := (iff #13531 #13302)
+#14917 := (or #2318 #13793 #14910)
+#13537 := (or #4278 #14917)
+#15115 := (iff #13537 #13302)
+#15116 := [rewrite]: #15115
+#13639 := (iff #13531 #13537)
+#14918 := (iff #14916 #14917)
+#14919 := [rewrite]: #14918
+#15114 := [monotonicity #14919]: #13639
+#15118 := [trans #15114 #15116]: #15117
+#13534 := [quant-inst #2307 #2306]: #13531
+#15119 := [mp #13534 #15118]: #13302
+#15612 := [unit-resolution #15119 #15618 #15617]: #15619
+#15620 := [unit-resolution #15612 #15614]: #13793
+#13659 := (ite #13656 #5883 #13650)
+#13653 := (f3 #8433 ?v1!18)
+#13654 := (= f1 #13653)
+#13662 := (iff #13654 #13659)
+#15003 := (or #6281 #13662)
+#13651 := (= #7202 ?v1!18)
+#13652 := (ite #13651 #5883 #13650)
+#13655 := (iff #13654 #13652)
+#15008 := (or #6281 #13655)
+#14881 := (iff #15008 #15003)
+#15034 := (iff #15003 #15003)
+#15035 := [rewrite]: #15034
+#13663 := (iff #13655 #13662)
+#13660 := (iff #13652 #13659)
+#13657 := (iff #13651 #13656)
+#13658 := [rewrite]: #13657
+#13661 := [monotonicity #13658]: #13660
+#13664 := [monotonicity #13661]: #13663
+#15010 := [monotonicity #13664]: #14881
+#15051 := [trans #15010 #15035]: #14881
+#15009 := [quant-inst #104 #7202 #5882 #2306]: #15008
+#14880 := [mp #15009 #15051]: #15003
+#15621 := [unit-resolution #14880 #4168]: #13662
+#15681 := (= #2320 #13653)
+#15615 := (= #13653 #2320)
+#15616 := [monotonicity #9277]: #15615
+#15683 := [symm #15616]: #15681
+#15684 := [trans #15601 #15683]: #13654
+#13228 := (not #13654)
+#12821 := (not #13662)
+#12779 := (or #12821 #13228 #13659)
+#13241 := [def-axiom]: #12779
+#15685 := [unit-resolution #13241 #15684 #15621]: #13659
+#15052 := (not #13659)
+#15050 := (or #15052 #13656 #13650)
+#15058 := [def-axiom]: #15050
+#15679 := [unit-resolution #15058 #15685 #15620]: #13656
+#15658 := [trans #15679 #7781]: #15686
+#15657 := [monotonicity #15658]: #15659
+#15661 := [monotonicity #15657]: #15449
+#15663 := (not #15449)
+#15664 := (or #15663 #15451)
+#15665 := [th-lemma arith triangle-eq]: #15664
+#15660 := [unit-resolution #15665 #15661]: #15451
+#15229 := (+ #2310 #6039)
+#15231 := (>= #15229 0::Int)
+#15441 := (= #2310 #5998)
+#15752 := [monotonicity #15658]: #15441
+#15662 := (not #15441)
+#15758 := (or #15662 #15231)
+#15759 := [th-lemma arith triangle-eq]: #15758
+#15760 := [unit-resolution #15759 #15752]: #15231
+#6665 := (<= #6408 0::Int)
+#5999 := (= #174 #5998)
+#6538 := (f3 f23 f22)
+#6539 := (= f1 #6538)
+#8175 := (= #5882 #6538)
+#8173 := (= #6538 #5882)
+#8174 := [monotonicity #6989]: #8173
+#8176 := [symm #8174]: #8175
+#8177 := [trans #6990 #8176]: #6539
+#6545 := (not #6539)
+#6597 := (or #5999 #6545)
+#6678 := (or #4417 #5999 #6545)
+#6679 := (or #4417 #6597)
+#6681 := (iff #6679 #6678)
+#6682 := [rewrite]: #6681
+#6680 := [quant-inst #170]: #6679
+#6683 := [mp #6680 #6682]: #6678
+#8178 := [unit-resolution #6683 #7091]: #6597
+#8179 := [unit-resolution #8178 #8177]: #5999
+#8180 := (not #5999)
+#8181 := (or #8180 #6665)
+#8182 := [th-lemma arith triangle-eq]: #8181
+#8183 := [unit-resolution #8182 #8179]: #6665
+#16330 := (not #15451)
+#12643 := (not #6665)
+#15761 := (not #15231)
+#15757 := (or #14951 #15605 #2906 #15761 #12643 #16330)
+#15765 := [th-lemma arith assign-bounds -1 1 1 -1 1]: #15757
+#15766 := [unit-resolution #15765 #15599 #8183 #15760 #15598 #15660]: #14951
+#14670 := (+ f8 #14666)
+#14722 := (<= #14670 0::Int)
+#15005 := (not #14722)
+#16331 := (or #15005 #16330 #2318)
+#16327 := [hypothesis]: #2319
+#16322 := [hypothesis]: #14722
+#16328 := [hypothesis]: #15451
+#16329 := [th-lemma arith farkas 1 -1 1 #16328 #16322 #16327]: false
+#16332 := [lemma #16329]: #16331
+#15767 := [unit-resolution #16332 #15660 #15617]: #15005
+#14716 := (+ #2309 #14663)
+#14717 := (+ #174 #14716)
+#14734 := (= #14717 0::Int)
+#15802 := (not #14734)
+#14848 := (>= #14717 0::Int)
+#15763 := (not #14848)
+#15784 := (or #15763 #2906 #15761 #12643 #16330)
+#15796 := [th-lemma arith assign-bounds 1 1 -1 1]: #15784
+#15797 := [unit-resolution #15796 #15760 #8183 #15598 #15660]: #15763
+#15803 := (or #15802 #14848)
+#15804 := [th-lemma arith triangle-eq]: #15803
+#15838 := [unit-resolution #15804 #15797]: #15802
+#14759 := (or #14712 #14722 #14734)
+#14883 := (or #4400 #14712 #14722 #14734)
+#14664 := (+ #14663 #2309)
+#14665 := (+ #174 #14664)
+#14660 := (= #14665 0::Int)
+#14667 := (+ #1444 #14666)
+#14668 := (+ #14458 #14667)
+#14669 := (<= #14668 0::Int)
+#14723 := (or #14722 #14669 #14660)
+#14884 := (or #4400 #14723)
+#14851 := (iff #14884 #14883)
+#14886 := (or #4400 #14759)
+#14849 := (iff #14886 #14883)
+#14850 := [rewrite]: #14849
+#14912 := (iff #14884 #14886)
+#14761 := (iff #14723 #14759)
+#14756 := (or #14722 #14712 #14734)
+#14754 := (iff #14756 #14759)
+#14760 := [rewrite]: #14754
+#14757 := (iff #14723 #14756)
+#14735 := (iff #14660 #14734)
+#14718 := (= #14665 #14717)
+#14719 := [rewrite]: #14718
+#14755 := [monotonicity #14719]: #14735
+#14709 := (iff #14669 #14712)
+#14724 := (+ #14458 #14666)
+#14725 := (+ #1444 #14724)
+#14728 := (<= #14725 0::Int)
+#14713 := (iff #14728 #14712)
+#14714 := [rewrite]: #14713
+#14729 := (iff #14669 #14728)
+#14726 := (= #14668 #14725)
+#14727 := [rewrite]: #14726
+#14730 := [monotonicity #14727]: #14729
+#14715 := [trans #14730 #14714]: #14709
+#14758 := [monotonicity #14715 #14755]: #14757
+#14762 := [trans #14758 #14760]: #14761
+#14913 := [monotonicity #14762]: #14912
+#14911 := [trans #14913 #14850]: #14851
+#14885 := [quant-inst #2307]: #14884
+#14852 := [mp #14885 #14911]: #14883
+#15836 := [unit-resolution #14852 #6504]: #14759
+#15837 := [unit-resolution #15836 #15838 #15767 #15766]: false
+#15833 := [lemma #15837]: #3477
+#3980 := (or #4463 #3482 #4457)
+#3995 := [def-axiom]: #3980
+#23140 := [unit-resolution #3995 #15833]: #23125
+#23141 := [unit-resolution #23140 #23124]: #4457
+#4099 := (or #4454 #2351)
+#4101 := [def-axiom]: #4099
+#23142 := [unit-resolution #4101 #23141]: #2351
+#23143 := (= #9072 #6061)
+#23144 := [monotonicity #9273]: #23143
+#23146 := [symm #23144]: #9852
+#23147 := [unit-resolution #11940 #23146]: #9448
+#9809 := (<= #9446 0::Int)
+#23139 := (or #11936 #9809)
+#23145 := [th-lemma arith triangle-eq]: #23139
+#23148 := [unit-resolution #23145 #23146]: #9809
+#23149 := (not #9809)
+#23155 := (or #10869 #23149)
+#7349 := (>= #6061 0::Int)
+#7287 := (not #7349)
+#7288 := [hypothesis]: #7287
+#7969 := (or #4270 #7349)
+#7970 := [quant-inst #6060]: #7969
+#7475 := [unit-resolution #7970 #7112 #7288]: false
+#7479 := [lemma #7475]: #7349
+#7044 := (not #3911)
+#23150 := (or #10869 #7044 #7287 #23149)
+#23152 := [th-lemma arith assign-bounds -1 1 -1]: #23150
+#23156 := [unit-resolution #23152 #7479 #7117]: #23155
+#23154 := [unit-resolution #23156 #23148]: #10869
+#3986 := (or #4454 #4446)
+#3987 := [def-axiom]: #3986
+#23157 := [unit-resolution #3987 #23141]: #4446
+#24096 := (or #14174 #4451)
+#8769 := (f24 #7202)
+#9535 := (* -1::Int #8769)
+#14029 := (+ #2338 #9535)
+#14217 := (<= #14029 0::Int)
+#10155 := (f3 f23 #7202)
+#10156 := (= f1 #10155)
+#11801 := (= #5882 #10155)
+#11794 := (= #10155 #5882)
+#11800 := [monotonicity #6989 #7781]: #11794
+#11802 := [symm #11800]: #11801
+#11803 := [trans #6990 #11802]: #10156
+#14203 := (f9 #14202)
+#14229 := (* -1::Int #14203)
+#14230 := (+ #9535 #14229)
+#14231 := (+ #2338 #14230)
+#14232 := (= #14231 0::Int)
+#15147 := (>= #14231 0::Int)
+#14148 := (+ #2339 #14123)
+#14149 := (+ #174 #14148)
+#14418 := (<= #14149 0::Int)
+#14152 := (= #14149 0::Int)
+#14177 := (not #14174)
+#21302 := [hypothesis]: #14177
+#21307 := (or #14174 #14152)
+#21296 := (not #14152)
+#21297 := [hypothesis]: #21296
+#12463 := (not #14132)
+#12470 := (or #14174 #12463)
+#12471 := [def-axiom]: #12470
+#21303 := [unit-resolution #12471 #21302]: #12463
+#12460 := (not #14143)
+#12469 := (or #14174 #12460)
+#12472 := [def-axiom]: #12469
+#21304 := [unit-resolution #12472 #21302]: #12460
+#14155 := (or #14132 #14143 #14152)
+#12402 := (or #4400 #14132 #14143 #14152)
+#14124 := (+ #14123 #2339)
+#14125 := (+ #174 #14124)
+#14126 := (= #14125 0::Int)
+#14128 := (+ #1444 #14127)
+#14129 := (+ #14065 #14128)
+#14130 := (<= #14129 0::Int)
+#14133 := (or #14132 #14130 #14126)
+#12426 := (or #4400 #14133)
+#12431 := (iff #12426 #12402)
+#12399 := (or #4400 #14155)
+#12430 := (iff #12399 #12402)
+#12425 := [rewrite]: #12430
+#12428 := (iff #12426 #12399)
+#14156 := (iff #14133 #14155)
+#14153 := (iff #14126 #14152)
+#14150 := (= #14125 #14149)
+#14151 := [rewrite]: #14150
+#14154 := [monotonicity #14151]: #14153
+#14146 := (iff #14130 #14143)
+#14134 := (+ #14065 #14127)
+#14135 := (+ #1444 #14134)
+#14138 := (<= #14135 0::Int)
+#14144 := (iff #14138 #14143)
+#14145 := [rewrite]: #14144
+#14139 := (iff #14130 #14138)
+#14136 := (= #14129 #14135)
+#14137 := [rewrite]: #14136
+#14140 := [monotonicity #14137]: #14139
+#14147 := [trans #14140 #14145]: #14146
+#14157 := [monotonicity #14147 #14154]: #14156
+#12429 := [monotonicity #14157]: #12428
+#12433 := [trans #12429 #12425]: #12431
+#12427 := [quant-inst #2337]: #12426
+#12434 := [mp #12427 #12433]: #12402
+#21305 := [unit-resolution #12434 #6504]: #14155
+#21306 := [unit-resolution #21305 #21304 #21303 #21297]: false
+#21308 := [lemma #21306]: #21307
+#24013 := [unit-resolution #21308 #21302]: #14152
+#24014 := (or #21296 #14418)
+#24015 := [th-lemma arith triangle-eq]: #24014
+#24016 := [unit-resolution #24015 #24013]: #14418
+#17675 := (not #14418)
+#24037 := (or #15147 #17675)
+#9536 := (+ #5998 #9535)
+#7436 := (>= #9536 0::Int)
+#9534 := (= #5998 #8769)
+#11865 := (= #8769 #5998)
+#11866 := [monotonicity #7781]: #11865
+#11867 := [symm #11866]: #9534
+#11868 := (not #9534)
+#24011 := (or #11868 #7436)
+#24017 := [th-lemma arith triangle-eq]: #24011
+#24018 := [unit-resolution #24017 #11867]: #7436
+#13344 := (+ #14123 #14229)
+#13577 := (>= #13344 0::Int)
+#7914 := (= #14123 #14203)
+#24021 := (= #14203 #14123)
+#24028 := [monotonicity #24020]: #24021
+#24029 := [symm #24028]: #7914
+#24027 := (not #7914)
+#24030 := (or #24027 #13577)
+#24031 := [th-lemma arith triangle-eq]: #24030
+#24032 := [unit-resolution #24031 #24029]: #13577
+#24035 := (not #13577)
+#24034 := (not #7436)
+#24033 := (or #15147 #24034 #10341 #24035 #17675)
+#24036 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24033
+#24038 := [unit-resolution #24036 #24032 #24018 #8185]: #24037
+#24026 := [unit-resolution #24038 #24016]: #15147
+#15125 := (<= #14231 0::Int)
+#14419 := (>= #14149 0::Int)
+#24039 := (or #21296 #14419)
 #24040 := [th-lemma arith triangle-eq]: #24039
-#24041 := [unit-resolution #24040 #24038]: #13586
-#24044 := (not #13586)
-#24043 := (not #7445)
-#24042 := (or #15156 #24043 #10350 #24044 #17684)
-#24045 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24042
-#24047 := [unit-resolution #24045 #24041 #24027 #8194]: #24046
-#24035 := [unit-resolution #24047 #24025]: #15156
-#15134 := (<= #14240 0::Int)
-#14428 := (>= #14158 0::Int)
-#24048 := (or #21305 #14428)
-#24049 := [th-lemma arith triangle-eq]: #24048
-#24050 := [unit-resolution #24049 #24022]: #14428
-#24054 := (not #14428)
-#24058 := (or #15134 #24054)
-#9546 := (<= #9545 0::Int)
-#11878 := (or #11877 #9546)
-#11879 := [th-lemma arith triangle-eq]: #11878
-#11880 := [unit-resolution #11879 #11876]: #9546
-#13354 := (<= #13353 0::Int)
-#24051 := (or #24036 #13354)
-#24034 := [th-lemma arith triangle-eq]: #24051
-#24052 := [unit-resolution #24034 #24038]: #13354
-#24053 := (not #13354)
-#12651 := (not #9546)
-#24055 := (or #15134 #12651 #12652 #24053 #24054)
-#24056 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24055
-#24059 := [unit-resolution #24056 #24052 #11880 #8192]: #24058
-#24060 := [unit-resolution #24059 #24050]: #15134
-#24062 := (not #15156)
-#24061 := (not #15134)
-#24057 := (or #14241 #24061 #24062)
-#24063 := [th-lemma arith triangle-eq]: #24057
-#24064 := [unit-resolution #24063 #24060 #24035]: #14241
-#14246 := (not #14241)
-#10177 := (not #10165)
-#14249 := (or #10177 #14226 #14246)
-#24065 := [hypothesis]: #4455
-#12777 := (or #4460 #10177 #14226 #14246)
-#14213 := (+ #2348 #14212)
-#14214 := (+ #8778 #14213)
-#14215 := (= #14214 0::Int)
-#14216 := (not #14215)
-#14217 := (+ #8778 #2348)
-#14218 := (>= #14217 0::Int)
-#14219 := (or #10177 #14218 #14216)
-#12784 := (or #4460 #14219)
-#12837 := (iff #12784 #12777)
-#12848 := (or #4460 #14249)
-#12871 := (iff #12848 #12777)
-#12877 := [rewrite]: #12871
-#12875 := (iff #12784 #12848)
-#14250 := (iff #14219 #14249)
-#14247 := (iff #14216 #14246)
-#14244 := (iff #14215 #14241)
-#14231 := (+ #8778 #14212)
-#14232 := (+ #2348 #14231)
-#14235 := (= #14232 0::Int)
-#14242 := (iff #14235 #14241)
-#14243 := [rewrite]: #14242
-#14236 := (iff #14215 #14235)
-#14233 := (= #14214 #14232)
+#24041 := [unit-resolution #24040 #24013]: #14419
+#24045 := (not #14419)
+#24049 := (or #15125 #24045)
+#9537 := (<= #9536 0::Int)
+#11869 := (or #11868 #9537)
+#11870 := [th-lemma arith triangle-eq]: #11869
+#11871 := [unit-resolution #11870 #11867]: #9537
+#13345 := (<= #13344 0::Int)
+#24042 := (or #24027 #13345)
+#24025 := [th-lemma arith triangle-eq]: #24042
+#24043 := [unit-resolution #24025 #24029]: #13345
+#24044 := (not #13345)
+#12642 := (not #9537)
+#24046 := (or #15125 #12642 #12643 #24044 #24045)
+#24047 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24046
+#24050 := [unit-resolution #24047 #24043 #11871 #8183]: #24049
+#24051 := [unit-resolution #24050 #24041]: #15125
+#24053 := (not #15147)
+#24052 := (not #15125)
+#24048 := (or #14232 #24052 #24053)
+#24054 := [th-lemma arith triangle-eq]: #24048
+#24055 := [unit-resolution #24054 #24051 #24026]: #14232
+#14237 := (not #14232)
+#10168 := (not #10156)
+#14240 := (or #10168 #14217 #14237)
+#24056 := [hypothesis]: #4446
+#12768 := (or #4451 #10168 #14217 #14237)
+#14204 := (+ #2339 #14203)
+#14205 := (+ #8769 #14204)
+#14206 := (= #14205 0::Int)
+#14207 := (not #14206)
+#14208 := (+ #8769 #2339)
+#14209 := (>= #14208 0::Int)
+#14210 := (or #10168 #14209 #14207)
+#12775 := (or #4451 #14210)
+#12828 := (iff #12775 #12768)
+#12839 := (or #4451 #14240)
+#12862 := (iff #12839 #12768)
+#12868 := [rewrite]: #12862
+#12866 := (iff #12775 #12839)
+#14241 := (iff #14210 #14240)
+#14238 := (iff #14207 #14237)
+#14235 := (iff #14206 #14232)
+#14222 := (+ #8769 #14203)
+#14223 := (+ #2339 #14222)
+#14226 := (= #14223 0::Int)
+#14233 := (iff #14226 #14232)
 #14234 := [rewrite]: #14233
-#14237 := [monotonicity #14234]: #14236
-#14245 := [trans #14237 #14243]: #14244
-#14248 := [monotonicity #14245]: #14247
-#14229 := (iff #14218 #14226)
-#14220 := (+ #2348 #8778)
-#14223 := (>= #14220 0::Int)
-#14227 := (iff #14223 #14226)
-#14228 := [rewrite]: #14227
-#14224 := (iff #14218 #14223)
-#14221 := (= #14217 #14220)
-#14222 := [rewrite]: #14221
-#14225 := [monotonicity #14222]: #14224
-#14230 := [trans #14225 #14228]: #14229
-#14251 := [monotonicity #14230 #14248]: #14250
-#12876 := [monotonicity #14251]: #12875
-#12903 := [trans #12876 #12877]: #12837
-#12841 := [quant-inst #7211]: #12784
-#12904 := [mp #12841 #12903]: #12777
-#24066 := [unit-resolution #12904 #24065]: #14249
-#24067 := [unit-resolution #24066 #24064 #11812]: #14226
-#12487 := (f5 f10 ?v0!20)
-#17155 := (f7 #12487)
-#22316 := (f5 #7211 #17155)
-#22325 := (f9 #22316)
-#22328 := (* -1::Int #22325)
-#22457 := (+ #14132 #22328)
-#17191 := (>= #22457 0::Int)
-#17177 := (= #14132 #22325)
-#24068 := (= #22325 #14132)
-#24072 := (= #22316 #14131)
-#24070 := (= #17155 ?v0!20)
-#17156 := (= ?v0!20 #17155)
-#17179 := (or #6824 #17156)
-#17180 := [quant-inst #56 #2346]: #17179
-#24069 := [unit-resolution #17180 #4199]: #17156
-#24071 := [symm #24069]: #24070
-#24073 := [monotonicity #7790 #24071]: #24072
-#24074 := [monotonicity #24073]: #24068
-#24075 := [symm #24074]: #17177
-#24076 := (not #17177)
-#24077 := (or #24076 #17191)
-#24078 := [th-lemma arith triangle-eq]: #24077
-#24080 := [unit-resolution #24078 #24075]: #17191
-#22384 := (<= #22325 0::Int)
-#22364 := (not #22384)
-#22367 := (= #7211 #17155)
-#22397 := (not #22367)
-#20554 := (f3 f15 #17155)
-#20571 := (= f1 #20554)
-#23981 := (ite #22367 #5892 #20571)
-#24001 := (not #23981)
-#23982 := (f3 #8442 #17155)
-#23987 := (= f1 #23982)
-#23989 := (iff #23981 #23987)
-#23993 := (or #6290 #23989)
-#23988 := (iff #23987 #23981)
-#23994 := (or #6290 #23988)
-#23996 := (iff #23994 #23993)
-#23992 := (iff #23993 #23993)
-#23998 := [rewrite]: #23992
-#23990 := (iff #23988 #23989)
-#23991 := [rewrite]: #23990
-#23997 := [monotonicity #23991]: #23996
-#23999 := [trans #23997 #23998]: #23996
-#23995 := [quant-inst #104 #7211 #5891 #17155]: #23994
-#24000 := [mp #23995 #23999]: #23993
-#24081 := [unit-resolution #24000 #4177]: #23989
-#24013 := (not #23987)
-#10246 := (f3 f23 ?v0!20)
-#10247 := (= f1 #10246)
-#10248 := (not #10247)
-#24094 := (iff #10248 #24013)
-#24092 := (iff #10247 #23987)
-#24089 := (iff #23987 #10247)
-#24087 := (= #23982 #10246)
-#24088 := [monotonicity #9286 #24071]: #24087
-#24091 := [monotonicity #24088]: #24089
-#24093 := [symm #24091]: #24092
-#24095 := [monotonicity #24093]: #24094
-#24708 := (not #14085)
-#21436 := (not #19567)
-#24082 := (or #14152 #21436 #24044 #24061 #24043 #10350)
-#24083 := [th-lemma arith assign-bounds 1 1 1 -1 -1]: #24082
-#24084 := [unit-resolution #24083 #24060 #24041 #21313 #24027 #8194]: #21436
-#24709 := (or #24708 #19567)
-#24696 := [hypothesis]: #21436
-#24697 := [hypothesis]: #14085
-#24710 := [th-lemma arith triangle-eq]: #24709
-#24711 := [unit-resolution #24710 #24697 #24696]: false
-#24712 := [lemma #24711]: #24709
-#24079 := [unit-resolution #24712 #24084]: #24708
-#14091 := (or #10248 #14085)
-#12334 := (or #4426 #10248 #14085)
-#14081 := (= #14074 #2347)
-#14084 := (or #14081 #10248)
-#12374 := (or #4426 #14084)
-#12382 := (iff #12374 #12334)
-#12377 := (or #4426 #14091)
-#12379 := (iff #12377 #12334)
-#12381 := [rewrite]: #12379
-#12378 := (iff #12374 #12377)
-#14094 := (iff #14084 #14091)
-#14088 := (or #14085 #10248)
-#14092 := (iff #14088 #14091)
-#14093 := [rewrite]: #14092
-#14089 := (iff #14084 #14088)
-#14086 := (iff #14081 #14085)
-#14087 := [rewrite]: #14086
-#14090 := [monotonicity #14087]: #14089
-#14095 := [trans #14090 #14093]: #14094
-#12373 := [monotonicity #14095]: #12378
-#12383 := [trans #12373 #12381]: #12382
-#12376 := [quant-inst #2346]: #12374
-#12402 := [mp #12376 #12383]: #12334
-#24085 := [unit-resolution #12402 #7100]: #14091
-#24086 := [unit-resolution #24085 #24079]: #10248
-#24090 := [mp #24086 #24095]: #24013
-#24012 := (not #23989)
-#24015 := (or #24012 #24001 #23987)
-#24016 := [def-axiom]: #24015
-#24096 := [unit-resolution #24016 #24090 #24081]: #24001
-#24097 := (or #23981 #22397)
-#24008 := (or #23981 #22397 #6304)
-#24009 := [def-axiom]: #24008
-#24098 := [unit-resolution #24009 #6999]: #24097
-#24099 := [unit-resolution #24098 #24096]: #22397
-#22369 := (or #22367 #22364)
-#23958 := (or #6782 #22367 #22364)
-#22365 := (= #17155 #7211)
-#22366 := (or #22365 #22364)
-#23959 := (or #6782 #22366)
-#23966 := (iff #23959 #23958)
-#23961 := (or #6782 #22369)
-#23964 := (iff #23961 #23958)
-#23965 := [rewrite]: #23964
-#23962 := (iff #23959 #23961)
-#22370 := (iff #22366 #22369)
-#22368 := (iff #22365 #22367)
-#22363 := [rewrite]: #22368
-#22371 := [monotonicity #22363]: #22370
-#23963 := [monotonicity #22371]: #23962
-#23967 := [trans #23963 #23965]: #23966
-#23960 := [quant-inst #7211 #17155]: #23959
-#23968 := [mp #23960 #23967]: #23958
-#24100 := [unit-resolution #23968 #4217]: #22369
-#24103 := [unit-resolution #24100 #24099]: #22364
-#24104 := [th-lemma arith farkas -1 -1 -1 -1 1 1 #24027 #8194 #24103 #24080 #24025 #24067]: false
-#24106 := [lemma #24104]: #24105
-#23167 := [unit-resolution #24106 #23166]: #14183
-#23147 := [hypothesis]: #12469
-#12482 := (or #14186 #14141 #14152)
-#12483 := [def-axiom]: #12482
-#23160 := [unit-resolution #12483 #23147 #23167]: #14141
-#14189 := (or #14085 #14186)
-#12444 := (or #4401 #14085 #14186)
-#14180 := (or #14141 #14139)
-#14181 := (not #14180)
-#14182 := (or #14081 #14181)
-#12463 := (or #4401 #14182)
-#12468 := (iff #12463 #12444)
-#12441 := (or #4401 #14189)
-#12467 := (iff #12441 #12444)
-#12462 := [rewrite]: #12467
-#12465 := (iff #12463 #12441)
-#14190 := (iff #14182 #14189)
-#14187 := (iff #14181 #14186)
-#14184 := (iff #14180 #14183)
-#14185 := [monotonicity #14156]: #14184
-#14188 := [monotonicity #14185]: #14187
-#14191 := [monotonicity #14087 #14188]: #14190
-#12466 := [monotonicity #14191]: #12465
-#12470 := [trans #12466 #12462]: #12468
-#12464 := [quant-inst #2346]: #12463
-#12471 := [mp #12464 #12470]: #12444
-#23168 := [unit-resolution #12471 #6509]: #14189
-#23146 := [unit-resolution #23168 #23167]: #14085
-#23169 := [unit-resolution #24712 #23146]: #19567
-#23170 := [unit-resolution #24083 #23147 #24041 #23169 #24027 #8194]: #24061
-#23162 := (or #15134 #15156)
-#23171 := [th-lemma arith farkas 1 1]: #23162
-#23172 := [unit-resolution #23171 #23170]: #15156
-#23173 := [th-lemma arith farkas 1 1 1 1 1 1 1 1 1 1 #24052 #23172 #11880 #8192 #23160 #10074 #23163 #23156 #6991 #23151]: false
-#23175 := [lemma #23173]: #23174
-#27691 := [unit-resolution #23175 #10074]: #14152
-#27696 := [unit-resolution #12481 #27691]: #14183
-#27708 := [unit-resolution #12471 #6509 #27696]: #14085
-#27709 := [unit-resolution #24710 #27708]: #19567
-#21437 := (or #21435 #21436 #2359)
-#21430 := [hypothesis]: #19567
-#21431 := [hypothesis]: #14792
-#21434 := [th-lemma arith farkas -1 1 1 #21431 #21430 #19783]: false
-#21438 := [lemma #21434]: #21437
-#27710 := [unit-resolution #21438 #27709 #19783]: #21435
-#4111 := (or #4463 #2929)
-#4109 := [def-axiom]: #4111
-#27711 := [unit-resolution #4109 #23150]: #2929
-#24435 := (or #4312 #2926 #14792 #14797)
-#14789 := (or #14788 #14785 #14778)
-#14790 := (not #14789)
-#14793 := (or #2361 #14792 #14790)
-#24444 := (or #4312 #14793)
-#24450 := (iff #24444 #24435)
-#14800 := (or #2926 #14792 #14797)
-#24441 := (or #4312 #14800)
-#24449 := (iff #24441 #24435)
-#24445 := [rewrite]: #24449
-#24440 := (iff #24444 #24441)
-#14801 := (iff #14793 #14800)
-#14798 := (iff #14790 #14797)
-#14795 := (iff #14789 #14794)
-#14796 := [rewrite]: #14795
-#14799 := [monotonicity #14796]: #14798
-#14802 := [monotonicity #2928 #14799]: #14801
-#24447 := [monotonicity #14802]: #24440
-#24439 := [trans #24447 #24445]: #24450
-#24446 := [quant-inst #2346]: #24444
-#24462 := [mp #24446 #24439]: #24435
-#27713 := [unit-resolution #24462 #12665 #27711 #27710]: #14797
-#24466 := (or #14794 #14787)
-#24452 := [def-axiom]: #24466
-#27678 := [unit-resolution #24452 #27713]: #14787
-#27719 := [trans #27678 #27718]: #26214
-#26242 := (not #26214)
-#15536 := (>= #14783 0::Int)
-#24464 := (or #14794 #14784)
-#24465 := [def-axiom]: #24464
-#27715 := [unit-resolution #24465 #27713]: #14784
-#27716 := (or #14785 #15536)
-#27714 := [th-lemma arith triangle-eq]: #27716
-#27717 := [unit-resolution #27714 #27715]: #15536
-#24448 := (not #14778)
-#24463 := (or #14794 #24448)
-#24442 := [def-axiom]: #24463
-#27699 := [unit-resolution #24442 #27713]: #24448
-#15512 := (<= #14783 0::Int)
-#27697 := (or #14785 #15512)
-#27700 := [th-lemma arith triangle-eq]: #27697
-#27701 := [unit-resolution #27700 #27715]: #15512
-#28964 := (not #15536)
-#29081 := (not #15512)
-#29112 := (or #26242 #29081 #4460 #14778 #21436 #28964)
-#21416 := (f24 #14774)
-#21446 := (* -1::Int #21416)
-#21657 := (+ #14781 #21446)
-#21658 := (+ #2347 #21657)
-#17955 := (<= #21658 0::Int)
-#29064 := (not #17955)
-#18266 := (>= #21658 0::Int)
-#21447 := (+ #14775 #21446)
-#21448 := (>= #21447 0::Int)
-#25332 := (or #4417 #21448)
-#25339 := [quant-inst #14774]: #25332
-#28969 := [unit-resolution #25339 #8193]: #21448
-#28961 := [hypothesis]: #15536
-#28966 := (not #21448)
-#28967 := (or #18266 #28964 #21436 #28966)
-#28963 := [th-lemma arith assign-bounds -1 -1 -1]: #28967
-#28962 := [unit-resolution #28963 #28961 #21430 #28969]: #18266
-#21659 := (= #21658 0::Int)
-#21664 := (not #21659)
-#21644 := (+ #2347 #21446)
-#21645 := (<= #21644 0::Int)
-#28965 := (not #21645)
-#28968 := [hypothesis]: #24448
-#28985 := (or #28965 #14778 #21436 #28966)
-#28999 := [th-lemma arith assign-bounds -1 -1 -1]: #28985
-#29042 := [unit-resolution #28999 #28968 #21430 #28969]: #28965
-#21429 := (f3 f23 #14774)
-#21409 := (= f1 #21429)
-#25158 := (f3 f23 #25042)
-#25147 := (= f1 #25158)
-#29043 := (iff #25147 #21409)
-#29046 := (iff #21409 #25147)
-#29045 := (= #21429 #25158)
-#29000 := [monotonicity #28984]: #29045
-#29041 := [monotonicity #29000]: #29046
-#29049 := [symm #29041]: #29043
-#30426 := (= #7211 #25042)
-#30420 := (ite #30426 #5892 #26214)
-#30488 := [hypothesis]: #26214
-#30492 := (or #30420 #26242)
-#30464 := (not #30420)
-#30484 := [hypothesis]: #30464
-#30465 := (not #30426)
-#30485 := (or #30420 #30465)
-#30470 := (or #30420 #30465 #6304)
-#30471 := [def-axiom]: #30470
-#30486 := [unit-resolution #30471 #6999]: #30485
-#30487 := [unit-resolution #30486 #30484]: #30465
-#30489 := (or #30420 #30426)
-#30472 := (or #30420 #30426 #26242)
-#30473 := [def-axiom]: #30472
-#30490 := [unit-resolution #30473 #30488]: #30489
-#30491 := [unit-resolution #30490 #30487 #30484]: false
-#30493 := [lemma #30491]: #30492
-#28983 := [unit-resolution #30493 #30488]: #30420
-#30259 := (or #25147 #30464)
-#30449 := (f3 #8442 #25042)
-#30254 := (= #30449 #25158)
-#30250 := (= #25158 #30449)
-#18324 := (= f23 #8442)
-#18225 := (= #773 #8442)
-#18326 := [symm #9284]: #18225
-#18323 := [trans #6998 #18326]: #18324
-#30251 := [monotonicity #18323]: #30250
-#30256 := [symm #30251]: #30254
-#30450 := (= f1 #30449)
-#30452 := (iff #30420 #30450)
-#30194 := (or #6290 #30452)
-#30451 := (iff #30450 #30420)
-#30192 := (or #6290 #30451)
-#30199 := (iff #30192 #30194)
-#30201 := (iff #30194 #30194)
-#30190 := [rewrite]: #30201
-#30453 := (iff #30451 #30452)
-#30454 := [rewrite]: #30453
-#30200 := [monotonicity #30454]: #30199
-#30202 := [trans #30200 #30190]: #30199
-#30198 := [quant-inst #104 #7211 #5891 #25042]: #30192
-#30203 := [mp #30198 #30202]: #30194
-#30246 := [unit-resolution #30203 #4177]: #30452
-#30204 := (not #30452)
-#30248 := (or #30204 #30450)
-#30247 := [hypothesis]: #30420
-#30209 := (or #30204 #30464 #30450)
-#30210 := [def-axiom]: #30209
-#30249 := [unit-resolution #30210 #30247]: #30248
-#30240 := [unit-resolution #30249 #30246]: #30450
-#30257 := [trans #30240 #30256]: #25147
-#25159 := (not #25147)
-#30241 := [hypothesis]: #25159
-#30258 := [unit-resolution #30241 #30257]: false
-#30260 := [lemma #30258]: #30259
-#29044 := [unit-resolution #30260 #28983]: #25147
-#29050 := [mp #29044 #29049]: #21409
-#21415 := (not #21409)
-#21667 := (or #21415 #21645 #21664)
-#16840 := (or #4460 #21415 #21645 #21664)
-#21631 := (+ #2348 #14780)
-#21632 := (+ #21416 #21631)
-#21633 := (= #21632 0::Int)
-#21634 := (not #21633)
-#21635 := (+ #21416 #2348)
-#21636 := (>= #21635 0::Int)
-#21637 := (or #21415 #21636 #21634)
-#16841 := (or #4460 #21637)
-#16874 := (iff #16841 #16840)
-#16854 := (or #4460 #21667)
-#16857 := (iff #16854 #16840)
-#16852 := [rewrite]: #16857
-#16855 := (iff #16841 #16854)
-#21668 := (iff #21637 #21667)
-#21665 := (iff #21634 #21664)
-#21662 := (iff #21633 #21659)
-#21650 := (+ #14780 #21416)
-#21651 := (+ #2348 #21650)
-#21654 := (= #21651 0::Int)
-#21660 := (iff #21654 #21659)
-#21661 := [rewrite]: #21660
-#21655 := (iff #21633 #21654)
-#21652 := (= #21632 #21651)
-#21653 := [rewrite]: #21652
-#21656 := [monotonicity #21653]: #21655
-#21663 := [trans #21656 #21661]: #21662
-#21666 := [monotonicity #21663]: #21665
-#21648 := (iff #21636 #21645)
-#21638 := (+ #2348 #21416)
-#21641 := (>= #21638 0::Int)
-#21646 := (iff #21641 #21645)
-#21647 := [rewrite]: #21646
-#21642 := (iff #21636 #21641)
-#21639 := (= #21635 #21638)
-#21640 := [rewrite]: #21639
-#21643 := [monotonicity #21640]: #21642
-#21649 := [trans #21643 #21647]: #21648
-#21669 := [monotonicity #21649 #21666]: #21668
-#16862 := [monotonicity #21669]: #16855
-#16859 := [trans #16862 #16852]: #16874
-#16853 := [quant-inst #14774]: #16841
-#16903 := [mp #16853 #16859]: #16840
-#29061 := [unit-resolution #16903 #24065]: #21667
-#29059 := [unit-resolution #29061 #29050 #29042]: #21664
-#29048 := (not #18266)
-#29060 := (or #21659 #29064 #29048)
-#29063 := [th-lemma arith triangle-eq]: #29060
-#29071 := [unit-resolution #29063 #29059 #28962]: #29064
-#25329 := (<= #21447 0::Int)
-#21417 := (= #14775 #21416)
-#26209 := (f13 f14 #25042)
-#25148 := (f24 #25042)
-#26948 := (= #25148 #26209)
-#29155 := (iff #26948 #21417)
-#29077 := (= #21416 #14775)
-#29069 := (iff #29077 #21417)
-#29154 := [commutativity]: #29069
-#29080 := (iff #26948 #29077)
-#29078 := (= #26209 #14775)
-#29047 := [monotonicity #29062]: #29078
-#29073 := (= #25148 #21416)
-#24500 := (= #21416 #25148)
-#29079 := [monotonicity #28984]: #24500
-#29070 := [symm #29079]: #29073
-#29082 := [monotonicity #29070 #29047]: #29080
-#29153 := [trans #29082 #29154]: #29155
-#26988 := (or #25159 #26948)
-#26991 := (or #4426 #25159 #26948)
-#26982 := (= #26209 #25148)
-#27001 := (or #26982 #25159)
-#27008 := (or #4426 #27001)
-#27013 := (iff #27008 #26991)
-#27010 := (or #4426 #26988)
-#26966 := (iff #27010 #26991)
-#27012 := [rewrite]: #26966
-#27003 := (iff #27008 #27010)
-#27004 := (iff #27001 #26988)
-#26981 := (or #26948 #25159)
-#26989 := (iff #26981 #26988)
-#26990 := [rewrite]: #26989
-#26987 := (iff #27001 #26981)
-#26985 := (iff #26982 #26948)
-#26947 := [rewrite]: #26985
-#26986 := [monotonicity #26947]: #26987
-#27007 := [trans #26986 #26990]: #27004
-#27011 := [monotonicity #27007]: #27003
-#26965 := [trans #27011 #27012]: #27013
-#27009 := [quant-inst #25042]: #27008
-#27015 := [mp #27009 #26965]: #26991
-#29072 := [unit-resolution #27015 #7100]: #26988
-#29068 := [unit-resolution #29072 #29044]: #26948
-#29156 := [mp #29068 #29153]: #21417
-#29157 := (not #21417)
-#29158 := (or #29157 #25329)
-#29118 := [th-lemma arith triangle-eq]: #29158
-#29151 := [unit-resolution #29118 #29156]: #25329
-#14117 := (<= #14116 0::Int)
-#13521 := (or #4417 #14117)
-#14107 := (+ #14074 #2348)
-#14108 := (>= #14107 0::Int)
-#13551 := (or #4417 #14108)
-#13518 := (iff #13551 #13521)
-#13567 := (iff #13521 #13521)
-#13575 := [rewrite]: #13567
-#14120 := (iff #14108 #14117)
-#14109 := (+ #2348 #14074)
-#14112 := (>= #14109 0::Int)
-#14118 := (iff #14112 #14117)
-#14119 := [rewrite]: #14118
-#14113 := (iff #14108 #14112)
-#14110 := (= #14107 #14109)
-#14111 := [rewrite]: #14110
-#14114 := [monotonicity #14111]: #14113
-#14121 := [trans #14114 #14119]: #14120
-#13570 := [monotonicity #14121]: #13518
-#13578 := [trans #13570 #13575]: #13518
-#13561 := [quant-inst #2346]: #13551
-#13576 := [mp #13561 #13578]: #13521
-#29110 := [unit-resolution #13576 #8193]: #14117
-#29159 := [hypothesis]: #15512
-#29109 := [th-lemma arith farkas -1 -1 -1 1 #29159 #29110 #29151 #29071]: false
-#29113 := [lemma #29109]: #29112
-#27702 := [unit-resolution #29113 #27701 #23166 #27699 #27709 #27717]: #26242
-#27720 := [unit-resolution #27702 #27719]: false
-#27735 := [lemma #27720]: #27734
-#26718 := [unit-resolution #27735 #19783]: #6073
-#6119 := (or #6091 #6118)
-#6120 := [def-axiom]: #6119
-#26719 := [unit-resolution #6120 #26718]: #6091
-#6094 := (not #6091)
-#12666 := (or #6088 #6094)
-#6105 := (or #4312 #1654 #6088 #6094)
-#6084 := (or #6083 #6080 #6073)
-#6085 := (not #6084)
-#6087 := (or #6086 #1654 #6085)
-#6106 := (or #4312 #6087)
-#6113 := (iff #6106 #6105)
-#6100 := (or #1654 #6088 #6094)
-#6108 := (or #4312 #6100)
-#6111 := (iff #6108 #6105)
-#6112 := [rewrite]: #6111
-#6109 := (iff #6106 #6108)
-#6103 := (iff #6087 #6100)
-#6097 := (or #6088 #1654 #6094)
-#6101 := (iff #6097 #6100)
-#6102 := [rewrite]: #6101
-#6098 := (iff #6087 #6097)
-#6095 := (iff #6085 #6094)
-#6092 := (iff #6084 #6091)
+#14227 := (iff #14206 #14226)
+#14224 := (= #14205 #14223)
+#14225 := [rewrite]: #14224
+#14228 := [monotonicity #14225]: #14227
+#14236 := [trans #14228 #14234]: #14235
+#14239 := [monotonicity #14236]: #14238
+#14220 := (iff #14209 #14217)
+#14211 := (+ #2339 #8769)
+#14214 := (>= #14211 0::Int)
+#14218 := (iff #14214 #14217)
+#14219 := [rewrite]: #14218
+#14215 := (iff #14209 #14214)
+#14212 := (= #14208 #14211)
+#14213 := [rewrite]: #14212
+#14216 := [monotonicity #14213]: #14215
+#14221 := [trans #14216 #14219]: #14220
+#14242 := [monotonicity #14221 #14239]: #14241
+#12867 := [monotonicity #14242]: #12866
+#12894 := [trans #12867 #12868]: #12828
+#12832 := [quant-inst #7202]: #12775
+#12895 := [mp #12832 #12894]: #12768
+#24057 := [unit-resolution #12895 #24056]: #14240
+#24058 := [unit-resolution #24057 #24055 #11803]: #14217
+#12478 := (f5 f10 ?v0!20)
+#17146 := (f7 #12478)
+#22307 := (f5 #7202 #17146)
+#22316 := (f9 #22307)
+#22319 := (* -1::Int #22316)
+#22448 := (+ #14123 #22319)
+#17182 := (>= #22448 0::Int)
+#17168 := (= #14123 #22316)
+#24059 := (= #22316 #14123)
+#24063 := (= #22307 #14122)
+#24061 := (= #17146 ?v0!20)
+#17147 := (= ?v0!20 #17146)
+#17170 := (or #6815 #17147)
+#17171 := [quant-inst #56 #2337]: #17170
+#24060 := [unit-resolution #17171 #4190]: #17147
+#24062 := [symm #24060]: #24061
+#24064 := [monotonicity #7781 #24062]: #24063
+#24065 := [monotonicity #24064]: #24059
+#24066 := [symm #24065]: #17168
+#24067 := (not #17168)
+#24068 := (or #24067 #17182)
+#24069 := [th-lemma arith triangle-eq]: #24068
+#24071 := [unit-resolution #24069 #24066]: #17182
+#22375 := (<= #22316 0::Int)
+#22355 := (not #22375)
+#22358 := (= #7202 #17146)
+#22388 := (not #22358)
+#20545 := (f3 f15 #17146)
+#20562 := (= f1 #20545)
+#23972 := (ite #22358 #5883 #20562)
+#23992 := (not #23972)
+#23973 := (f3 #8433 #17146)
+#23978 := (= f1 #23973)
+#23980 := (iff #23972 #23978)
+#23984 := (or #6281 #23980)
+#23979 := (iff #23978 #23972)
+#23985 := (or #6281 #23979)
+#23987 := (iff #23985 #23984)
+#23983 := (iff #23984 #23984)
+#23989 := [rewrite]: #23983
+#23981 := (iff #23979 #23980)
+#23982 := [rewrite]: #23981
+#23988 := [monotonicity #23982]: #23987
+#23990 := [trans #23988 #23989]: #23987
+#23986 := [quant-inst #104 #7202 #5882 #17146]: #23985
+#23991 := [mp #23986 #23990]: #23984
+#24072 := [unit-resolution #23991 #4168]: #23980
+#24004 := (not #23978)
+#10237 := (f3 f23 ?v0!20)
+#10238 := (= f1 #10237)
+#10239 := (not #10238)
+#24085 := (iff #10239 #24004)
+#24083 := (iff #10238 #23978)
+#24080 := (iff #23978 #10238)
+#24078 := (= #23973 #10237)
+#24079 := [monotonicity #9277 #24062]: #24078
+#24082 := [monotonicity #24079]: #24080
+#24084 := [symm #24082]: #24083
+#24086 := [monotonicity #24084]: #24085
+#24699 := (not #14076)
+#21427 := (not #19558)
+#24073 := (or #14143 #21427 #24035 #24052 #24034 #10341)
+#24074 := [th-lemma arith assign-bounds 1 1 1 -1 -1]: #24073
+#24075 := [unit-resolution #24074 #24051 #24032 #21304 #24018 #8185]: #21427
+#24700 := (or #24699 #19558)
+#24687 := [hypothesis]: #21427
+#24688 := [hypothesis]: #14076
+#24701 := [th-lemma arith triangle-eq]: #24700
+#24702 := [unit-resolution #24701 #24688 #24687]: false
+#24703 := [lemma #24702]: #24700
+#24070 := [unit-resolution #24703 #24075]: #24699
+#14082 := (or #10239 #14076)
+#12325 := (or #4417 #10239 #14076)
+#14072 := (= #14065 #2338)
+#14075 := (or #14072 #10239)
+#12365 := (or #4417 #14075)
+#12373 := (iff #12365 #12325)
+#12368 := (or #4417 #14082)
+#12370 := (iff #12368 #12325)
+#12372 := [rewrite]: #12370
+#12369 := (iff #12365 #12368)
+#14085 := (iff #14075 #14082)
+#14079 := (or #14076 #10239)
+#14083 := (iff #14079 #14082)
+#14084 := [rewrite]: #14083
+#14080 := (iff #14075 #14079)
+#14077 := (iff #14072 #14076)
+#14078 := [rewrite]: #14077
+#14081 := [monotonicity #14078]: #14080
+#14086 := [trans #14081 #14084]: #14085
+#12364 := [monotonicity #14086]: #12369
+#12374 := [trans #12364 #12372]: #12373
+#12367 := [quant-inst #2337]: #12365
+#12393 := [mp #12367 #12374]: #12325
+#24076 := [unit-resolution #12393 #7091]: #14082
+#24077 := [unit-resolution #24076 #24070]: #10239
+#24081 := [mp #24077 #24086]: #24004
+#24003 := (not #23980)
+#24006 := (or #24003 #23992 #23978)
+#24007 := [def-axiom]: #24006
+#24087 := [unit-resolution #24007 #24081 #24072]: #23992
+#24088 := (or #23972 #22388)
+#23999 := (or #23972 #22388 #6295)
+#24000 := [def-axiom]: #23999
+#24089 := [unit-resolution #24000 #6990]: #24088
+#24090 := [unit-resolution #24089 #24087]: #22388
+#22360 := (or #22358 #22355)
+#23949 := (or #6773 #22358 #22355)
+#22356 := (= #17146 #7202)
+#22357 := (or #22356 #22355)
+#23950 := (or #6773 #22357)
+#23957 := (iff #23950 #23949)
+#23952 := (or #6773 #22360)
+#23955 := (iff #23952 #23949)
+#23956 := [rewrite]: #23955
+#23953 := (iff #23950 #23952)
+#22361 := (iff #22357 #22360)
+#22359 := (iff #22356 #22358)
+#22354 := [rewrite]: #22359
+#22362 := [monotonicity #22354]: #22361
+#23954 := [monotonicity #22362]: #23953
+#23958 := [trans #23954 #23956]: #23957
+#23951 := [quant-inst #7202 #17146]: #23950
+#23959 := [mp #23951 #23958]: #23949
+#24091 := [unit-resolution #23959 #4208]: #22360
+#24094 := [unit-resolution #24091 #24090]: #22355
+#24095 := [th-lemma arith farkas -1 -1 -1 -1 1 1 #24018 #8185 #24094 #24071 #24016 #24058]: false
+#24097 := [lemma #24095]: #24096
+#23158 := [unit-resolution #24097 #23157]: #14174
+#23138 := [hypothesis]: #12460
+#12473 := (or #14177 #14132 #14143)
+#12474 := [def-axiom]: #12473
+#23151 := [unit-resolution #12474 #23138 #23158]: #14132
+#14180 := (or #14076 #14177)
+#12435 := (or #4392 #14076 #14177)
+#14171 := (or #14132 #14130)
+#14172 := (not #14171)
+#14173 := (or #14072 #14172)
+#12454 := (or #4392 #14173)
+#12459 := (iff #12454 #12435)
+#12432 := (or #4392 #14180)
+#12458 := (iff #12432 #12435)
+#12453 := [rewrite]: #12458
+#12456 := (iff #12454 #12432)
+#14181 := (iff #14173 #14180)
+#14178 := (iff #14172 #14177)
+#14175 := (iff #14171 #14174)
+#14176 := [monotonicity #14147]: #14175
+#14179 := [monotonicity #14176]: #14178
+#14182 := [monotonicity #14078 #14179]: #14181
+#12457 := [monotonicity #14182]: #12456
+#12461 := [trans #12457 #12453]: #12459
+#12455 := [quant-inst #2337]: #12454
+#12462 := [mp #12455 #12461]: #12435
+#23159 := [unit-resolution #12462 #6500]: #14180
+#23137 := [unit-resolution #23159 #23158]: #14076
+#23160 := [unit-resolution #24703 #23137]: #19558
+#23161 := [unit-resolution #24074 #23138 #24032 #23160 #24018 #8185]: #24052
+#23153 := (or #15125 #15147)
+#23162 := [th-lemma arith farkas 1 1]: #23153
+#23163 := [unit-resolution #23162 #23161]: #15147
+#23164 := [th-lemma arith farkas 1 1 1 1 1 1 1 1 1 1 #24043 #23163 #11871 #8183 #23151 #10065 #23154 #23147 #6982 #23142]: false
+#23166 := [lemma #23164]: #23165
+#27682 := [unit-resolution #23166 #10065]: #14143
+#27687 := [unit-resolution #12472 #27682]: #14174
+#27699 := [unit-resolution #12462 #6500 #27687]: #14076
+#27700 := [unit-resolution #24701 #27699]: #19558
+#21428 := (or #21426 #21427 #2350)
+#21421 := [hypothesis]: #19558
+#21422 := [hypothesis]: #14783
+#21425 := [th-lemma arith farkas -1 1 1 #21422 #21421 #19774]: false
+#21429 := [lemma #21425]: #21428
+#27701 := [unit-resolution #21429 #27700 #19774]: #21426
+#4102 := (or #4454 #2920)
+#4100 := [def-axiom]: #4102
+#27702 := [unit-resolution #4100 #23141]: #2920
+#24426 := (or #4303 #2917 #14783 #14788)
+#14780 := (or #14779 #14776 #14769)
+#14781 := (not #14780)
+#14784 := (or #2352 #14783 #14781)
+#24435 := (or #4303 #14784)
+#24441 := (iff #24435 #24426)
+#14791 := (or #2917 #14783 #14788)
+#24432 := (or #4303 #14791)
+#24440 := (iff #24432 #24426)
+#24436 := [rewrite]: #24440
+#24431 := (iff #24435 #24432)
+#14792 := (iff #14784 #14791)
+#14789 := (iff #14781 #14788)
+#14786 := (iff #14780 #14785)
+#14787 := [rewrite]: #14786
+#14790 := [monotonicity #14787]: #14789
+#14793 := [monotonicity #2919 #14790]: #14792
+#24438 := [monotonicity #14793]: #24431
+#24430 := [trans #24438 #24436]: #24441
+#24437 := [quant-inst #2337]: #24435
+#24453 := [mp #24437 #24430]: #24426
+#27704 := [unit-resolution #24453 #12656 #27702 #27701]: #14788
+#24457 := (or #14785 #14778)
+#24443 := [def-axiom]: #24457
+#27669 := [unit-resolution #24443 #27704]: #14778
+#27710 := [trans #27669 #27709]: #26205
+#26233 := (not #26205)
+#15527 := (>= #14774 0::Int)
+#24455 := (or #14785 #14775)
+#24456 := [def-axiom]: #24455
+#27706 := [unit-resolution #24456 #27704]: #14775
+#27707 := (or #14776 #15527)
+#27705 := [th-lemma arith triangle-eq]: #27707
+#27708 := [unit-resolution #27705 #27706]: #15527
+#24439 := (not #14769)
+#24454 := (or #14785 #24439)
+#24433 := [def-axiom]: #24454
+#27690 := [unit-resolution #24433 #27704]: #24439
+#15503 := (<= #14774 0::Int)
+#27688 := (or #14776 #15503)
+#27691 := [th-lemma arith triangle-eq]: #27688
+#27692 := [unit-resolution #27691 #27706]: #15503
+#28955 := (not #15527)
+#29072 := (not #15503)
+#29103 := (or #26233 #29072 #4451 #14769 #21427 #28955)
+#21407 := (f24 #14765)
+#21437 := (* -1::Int #21407)
+#21648 := (+ #14772 #21437)
+#21649 := (+ #2338 #21648)
+#17946 := (<= #21649 0::Int)
+#29055 := (not #17946)
+#18257 := (>= #21649 0::Int)
+#21438 := (+ #14766 #21437)
+#21439 := (>= #21438 0::Int)
+#25323 := (or #4408 #21439)
+#25330 := [quant-inst #14765]: #25323
+#28960 := [unit-resolution #25330 #8184]: #21439
+#28952 := [hypothesis]: #15527
+#28957 := (not #21439)
+#28958 := (or #18257 #28955 #21427 #28957)
+#28954 := [th-lemma arith assign-bounds -1 -1 -1]: #28958
+#28953 := [unit-resolution #28954 #28952 #21421 #28960]: #18257
+#21650 := (= #21649 0::Int)
+#21655 := (not #21650)
+#21635 := (+ #2338 #21437)
+#21636 := (<= #21635 0::Int)
+#28956 := (not #21636)
+#28959 := [hypothesis]: #24439
+#28976 := (or #28956 #14769 #21427 #28957)
+#28990 := [th-lemma arith assign-bounds -1 -1 -1]: #28976
+#29033 := [unit-resolution #28990 #28959 #21421 #28960]: #28956
+#21420 := (f3 f23 #14765)
+#21400 := (= f1 #21420)
+#25149 := (f3 f23 #25033)
+#25138 := (= f1 #25149)
+#29034 := (iff #25138 #21400)
+#29037 := (iff #21400 #25138)
+#29036 := (= #21420 #25149)
+#28991 := [monotonicity #28975]: #29036
+#29032 := [monotonicity #28991]: #29037
+#29040 := [symm #29032]: #29034
+#30417 := (= #7202 #25033)
+#30411 := (ite #30417 #5883 #26205)
+#30479 := [hypothesis]: #26205
+#30483 := (or #30411 #26233)
+#30455 := (not #30411)
+#30475 := [hypothesis]: #30455
+#30456 := (not #30417)
+#30476 := (or #30411 #30456)
+#30461 := (or #30411 #30456 #6295)
+#30462 := [def-axiom]: #30461
+#30477 := [unit-resolution #30462 #6990]: #30476
+#30478 := [unit-resolution #30477 #30475]: #30456
+#30480 := (or #30411 #30417)
+#30463 := (or #30411 #30417 #26233)
+#30464 := [def-axiom]: #30463
+#30481 := [unit-resolution #30464 #30479]: #30480
+#30482 := [unit-resolution #30481 #30478 #30475]: false
+#30484 := [lemma #30482]: #30483
+#28974 := [unit-resolution #30484 #30479]: #30411
+#30250 := (or #25138 #30455)
+#30440 := (f3 #8433 #25033)
+#30245 := (= #30440 #25149)
+#30241 := (= #25149 #30440)
+#18315 := (= f23 #8433)
+#18216 := (= #180 #8433)
+#18317 := [symm #9275]: #18216
+#18314 := [trans #6989 #18317]: #18315
+#30242 := [monotonicity #18314]: #30241
+#30247 := [symm #30242]: #30245
+#30441 := (= f1 #30440)
+#30443 := (iff #30411 #30441)
+#30185 := (or #6281 #30443)
+#30442 := (iff #30441 #30411)
+#30183 := (or #6281 #30442)
+#30190 := (iff #30183 #30185)
+#30192 := (iff #30185 #30185)
+#30181 := [rewrite]: #30192
+#30444 := (iff #30442 #30443)
+#30445 := [rewrite]: #30444
+#30191 := [monotonicity #30445]: #30190
+#30193 := [trans #30191 #30181]: #30190
+#30189 := [quant-inst #104 #7202 #5882 #25033]: #30183
+#30194 := [mp #30189 #30193]: #30185
+#30237 := [unit-resolution #30194 #4168]: #30443
+#30195 := (not #30443)
+#30239 := (or #30195 #30441)
+#30238 := [hypothesis]: #30411
+#30200 := (or #30195 #30455 #30441)
+#30201 := [def-axiom]: #30200
+#30240 := [unit-resolution #30201 #30238]: #30239
+#30231 := [unit-resolution #30240 #30237]: #30441
+#30248 := [trans #30231 #30247]: #25138
+#25150 := (not #25138)
+#30232 := [hypothesis]: #25150
+#30249 := [unit-resolution #30232 #30248]: false
+#30251 := [lemma #30249]: #30250
+#29035 := [unit-resolution #30251 #28974]: #25138
+#29041 := [mp #29035 #29040]: #21400
+#21406 := (not #21400)
+#21658 := (or #21406 #21636 #21655)
+#16831 := (or #4451 #21406 #21636 #21655)
+#21622 := (+ #2339 #14771)
+#21623 := (+ #21407 #21622)
+#21624 := (= #21623 0::Int)
+#21625 := (not #21624)
+#21626 := (+ #21407 #2339)
+#21627 := (>= #21626 0::Int)
+#21628 := (or #21406 #21627 #21625)
+#16832 := (or #4451 #21628)
+#16865 := (iff #16832 #16831)
+#16845 := (or #4451 #21658)
+#16848 := (iff #16845 #16831)
+#16843 := [rewrite]: #16848
+#16846 := (iff #16832 #16845)
+#21659 := (iff #21628 #21658)
+#21656 := (iff #21625 #21655)
+#21653 := (iff #21624 #21650)
+#21641 := (+ #14771 #21407)
+#21642 := (+ #2339 #21641)
+#21645 := (= #21642 0::Int)
+#21651 := (iff #21645 #21650)
+#21652 := [rewrite]: #21651
+#21646 := (iff #21624 #21645)
+#21643 := (= #21623 #21642)
+#21644 := [rewrite]: #21643
+#21647 := [monotonicity #21644]: #21646
+#21654 := [trans #21647 #21652]: #21653
+#21657 := [monotonicity #21654]: #21656
+#21639 := (iff #21627 #21636)
+#21629 := (+ #2339 #21407)
+#21632 := (>= #21629 0::Int)
+#21637 := (iff #21632 #21636)
+#21638 := [rewrite]: #21637
+#21633 := (iff #21627 #21632)
+#21630 := (= #21626 #21629)
+#21631 := [rewrite]: #21630
+#21634 := [monotonicity #21631]: #21633
+#21640 := [trans #21634 #21638]: #21639
+#21660 := [monotonicity #21640 #21657]: #21659
+#16853 := [monotonicity #21660]: #16846
+#16850 := [trans #16853 #16843]: #16865
+#16844 := [quant-inst #14765]: #16832
+#16894 := [mp #16844 #16850]: #16831
+#29052 := [unit-resolution #16894 #24056]: #21658
+#29050 := [unit-resolution #29052 #29041 #29033]: #21655
+#29039 := (not #18257)
+#29051 := (or #21650 #29055 #29039)
+#29054 := [th-lemma arith triangle-eq]: #29051
+#29062 := [unit-resolution #29054 #29050 #28953]: #29055
+#25320 := (<= #21438 0::Int)
+#21408 := (= #14766 #21407)
+#26200 := (f13 f14 #25033)
+#25139 := (f24 #25033)
+#26939 := (= #25139 #26200)
+#29146 := (iff #26939 #21408)
+#29068 := (= #21407 #14766)
+#29060 := (iff #29068 #21408)
+#29145 := [commutativity]: #29060
+#29071 := (iff #26939 #29068)
+#29069 := (= #26200 #14766)
+#29038 := [monotonicity #29053]: #29069
+#29064 := (= #25139 #21407)
+#24491 := (= #21407 #25139)
+#29070 := [monotonicity #28975]: #24491
+#29061 := [symm #29070]: #29064
+#29073 := [monotonicity #29061 #29038]: #29071
+#29144 := [trans #29073 #29145]: #29146
+#26979 := (or #25150 #26939)
+#26982 := (or #4417 #25150 #26939)
+#26973 := (= #26200 #25139)
+#26992 := (or #26973 #25150)
+#26999 := (or #4417 #26992)
+#27004 := (iff #26999 #26982)
+#27001 := (or #4417 #26979)
+#26957 := (iff #27001 #26982)
+#27003 := [rewrite]: #26957
+#26994 := (iff #26999 #27001)
+#26995 := (iff #26992 #26979)
+#26972 := (or #26939 #25150)
+#26980 := (iff #26972 #26979)
+#26981 := [rewrite]: #26980
+#26978 := (iff #26992 #26972)
+#26976 := (iff #26973 #26939)
+#26938 := [rewrite]: #26976
+#26977 := [monotonicity #26938]: #26978
+#26998 := [trans #26977 #26981]: #26995
+#27002 := [monotonicity #26998]: #26994
+#26956 := [trans #27002 #27003]: #27004
+#27000 := [quant-inst #25033]: #26999
+#27006 := [mp #27000 #26956]: #26982
+#29063 := [unit-resolution #27006 #7091]: #26979
+#29059 := [unit-resolution #29063 #29035]: #26939
+#29147 := [mp #29059 #29144]: #21408
+#29148 := (not #21408)
+#29149 := (or #29148 #25320)
+#29109 := [th-lemma arith triangle-eq]: #29149
+#29142 := [unit-resolution #29109 #29147]: #25320
+#14108 := (<= #14107 0::Int)
+#13512 := (or #4408 #14108)
+#14098 := (+ #14065 #2339)
+#14099 := (>= #14098 0::Int)
+#13542 := (or #4408 #14099)
+#13509 := (iff #13542 #13512)
+#13558 := (iff #13512 #13512)
+#13566 := [rewrite]: #13558
+#14111 := (iff #14099 #14108)
+#14100 := (+ #2339 #14065)
+#14103 := (>= #14100 0::Int)
+#14109 := (iff #14103 #14108)
+#14110 := [rewrite]: #14109
+#14104 := (iff #14099 #14103)
+#14101 := (= #14098 #14100)
+#14102 := [rewrite]: #14101
+#14105 := [monotonicity #14102]: #14104
+#14112 := [trans #14105 #14110]: #14111
+#13561 := [monotonicity #14112]: #13509
+#13569 := [trans #13561 #13566]: #13509
+#13552 := [quant-inst #2337]: #13542
+#13567 := [mp #13552 #13569]: #13512
+#29101 := [unit-resolution #13567 #8184]: #14108
+#29150 := [hypothesis]: #15503
+#29100 := [th-lemma arith farkas -1 -1 -1 1 #29150 #29101 #29142 #29062]: false
+#29104 := [lemma #29100]: #29103
+#27693 := [unit-resolution #29104 #27692 #23157 #27690 #27700 #27708]: #26233
+#27711 := [unit-resolution #27693 #27710]: false
+#27726 := [lemma #27711]: #27725
+#26709 := [unit-resolution #27726 #19774]: #6064
+#6110 := (or #6082 #6109)
+#6111 := [def-axiom]: #6110
+#26710 := [unit-resolution #6111 #26709]: #6082
+#6085 := (not #6082)
+#12657 := (or #6079 #6085)
+#6096 := (or #4303 #1645 #6079 #6085)
+#6075 := (or #6074 #6071 #6064)
+#6076 := (not #6075)
+#6078 := (or #6077 #1645 #6076)
+#6097 := (or #4303 #6078)
+#6104 := (iff #6097 #6096)
+#6091 := (or #1645 #6079 #6085)
+#6099 := (or #4303 #6091)
+#6102 := (iff #6099 #6096)
+#6103 := [rewrite]: #6102
+#6100 := (iff #6097 #6099)
+#6094 := (iff #6078 #6091)
+#6088 := (or #6079 #1645 #6085)
+#6092 := (iff #6088 #6091)
 #6093 := [rewrite]: #6092
-#6096 := [monotonicity #6093]: #6095
-#6099 := [monotonicity #6090 #6096]: #6098
-#6104 := [trans #6099 #6102]: #6103
-#6110 := [monotonicity #6104]: #6109
-#6114 := [trans #6110 #6112]: #6113
-#6107 := [quant-inst #170]: #6106
-#6115 := [mp #6107 #6114]: #6105
-#12667 := [unit-resolution #6115 #12665 #7830]: #12666
-#26765 := [unit-resolution #12667 #26719]: #6088
-#26766 := [symm #26765]: #6086
-#26762 := [monotonicity #26766]: #7825
-#26769 := [symm #26762]: #7797
-#7792 := (not #7797)
-#7822 := (or #7792 #7798)
-#7828 := [th-lemma arith triangle-eq]: #7822
-#26764 := [unit-resolution #7828 #26769]: #7798
-#9969 := (not #7798)
-#8364 := (or #2275 #9969)
-#9900 := (not #9497)
-#9582 := [hypothesis]: #7798
-#9654 := (or #9900 #2275 #9969)
-#10028 := (= #9989 0::Int)
-#9975 := (not #10028)
-#9785 := (not #10050)
-#9583 := [hypothesis]: #9497
-#6992 := (not #3917)
-#9899 := (not #10062)
-#9972 := (or #9785 #9899 #2275 #9900 #6992 #9969)
-#9892 := [th-lemma arith assign-bounds 1 -1 -1 1 -1]: #9972
-#9898 := [unit-resolution #9892 #9583 #6991 #10071 #10087 #9582]: #9785
-#9859 := (or #9975 #10050)
-#9971 := [th-lemma arith triangle-eq]: #9859
-#9653 := [unit-resolution #9971 #9898]: #9975
-#9970 := (or #10025 #9899 #2275 #9900 #6992 #9969)
-#10041 := [th-lemma arith assign-bounds 1 1 1 1 1]: #9970
-#10042 := [unit-resolution #10041 #9583 #6991 #10087 #10071 #9582]: #10025
-#9863 := [unit-resolution #10035 #4217 #10042]: #9949
-#9528 := (or #6807 #9968 #10028)
-#10029 := (or #10028 #9968)
-#9547 := (or #6807 #10029)
-#9801 := (iff #9547 #9528)
-#10036 := (or #9968 #10028)
-#9498 := (or #6807 #10036)
-#9535 := (iff #9498 #9528)
-#9800 := [rewrite]: #9535
-#9537 := (iff #9547 #9498)
-#10037 := (iff #10029 #10036)
-#10038 := [rewrite]: #10037
-#9541 := [monotonicity #10038]: #9537
-#9802 := [trans #9541 #9800]: #9801
-#9539 := [quant-inst #7211 #2273]: #9547
-#9761 := [mp #9539 #9802]: #9528
-#9862 := [unit-resolution #9761 #4211 #9863 #9653]: false
-#10142 := [lemma #9862]: #9654
-#9534 := [unit-resolution #10142 #10087 #9582]: #9900
-#9538 := [unit-resolution #10085 #9534]: #10083
-#8427 := (or #7638 #7616)
-#9098 := [hypothesis]: #10083
-#8424 := [hypothesis]: #7641
-#8426 := [unit-resolution #9512 #8424]: #9510
-#8466 := [unit-resolution #9515 #8424]: #9513
-#8467 := [unit-resolution #10081 #8466 #8426 #9098]: false
-#9343 := [lemma #8467]: #8427
-#9757 := [unit-resolution #9343 #9538]: #7638
-#9799 := [unit-resolution #10077 #9757]: #7539
-#9755 := [unit-resolution #11920 #9799]: #9581
-#9897 := [th-lemma arith farkas 1 -1 1 #9580 #10087 #9755]: false
-#8322 := [lemma #9897]: #8364
-#26770 := [unit-resolution #8322 #26764]: #2275
-#26768 := [unit-resolution #12717 #26770]: #4490
-#26771 := [unit-resolution #4086 #26768]: #4481
-#26767 := [unit-resolution #12721 #26771]: #4478
-#26772 := [unit-resolution #4008 #26767]: #4469
-#26780 := [unit-resolution #23149 #26772]: #4466
-#26782 := [unit-resolution #3996 #26780]: #4455
-#26779 := [unit-resolution #24106 #26782]: #14183
-#26783 := [unit-resolution #12471 #6509 #26779]: #14085
-#26781 := [unit-resolution #24710 #26783]: #19567
-#26797 := [unit-resolution #21438 #26781 #19783]: #21435
-#26800 := [unit-resolution #4109 #26780]: #2929
-#26792 := [unit-resolution #24462 #12665 #26800 #26797]: #14797
-#26775 := [unit-resolution #24452 #26792]: #14787
-#26834 := [trans #26775 #26828]: #26214
-#26798 := [unit-resolution #24465 #26792]: #14784
-#26793 := [unit-resolution #27700 #26798]: #15512
-#26791 := [unit-resolution #24442 #26792]: #24448
-#26794 := [unit-resolution #27714 #26798]: #15536
-#26790 := [unit-resolution #29113 #26794 #26782 #26791 #26781 #26793]: #26242
-#26829 := [unit-resolution #26790 #26834]: false
-#26830 := [lemma #26829]: #2359
-#8229 := [unit-resolution #4110 #26830]: #4463
-#8233 := [unit-resolution #23149 #8229]: #4472
-#8319 := [unit-resolution #4008 #8233]: #4475
-#8238 := [unit-resolution #12721 #8319]: #4484
-#8242 := [unit-resolution #4086 #8238]: #4487
-#8248 := [unit-resolution #12717 #8242]: #2276
-#8342 := [unit-resolution #11112 #8248]: #6073
-#8367 := [unit-resolution #6120 #8342]: #6091
-#8285 := [unit-resolution #12667 #8367]: #6088
-#8425 := [symm #8285]: #6086
-#8354 := [monotonicity #8425]: #7825
-#8358 := [symm #8354]: #7797
-#8360 := [unit-resolution #8322 #8248]: #9969
-[unit-resolution #7828 #8360 #8358]: false
+#6089 := (iff #6078 #6088)
+#6086 := (iff #6076 #6085)
+#6083 := (iff #6075 #6082)
+#6084 := [rewrite]: #6083
+#6087 := [monotonicity #6084]: #6086
+#6090 := [monotonicity #6081 #6087]: #6089
+#6095 := [trans #6090 #6093]: #6094
+#6101 := [monotonicity #6095]: #6100
+#6105 := [trans #6101 #6103]: #6104
+#6098 := [quant-inst #170]: #6097
+#6106 := [mp #6098 #6105]: #6096
+#12658 := [unit-resolution #6106 #12656 #7821]: #12657
+#26756 := [unit-resolution #12658 #26710]: #6079
+#26757 := [symm #26756]: #6077
+#26753 := [monotonicity #26757]: #7816
+#26760 := [symm #26753]: #7788
+#7783 := (not #7788)
+#7813 := (or #7783 #7789)
+#7819 := [th-lemma arith triangle-eq]: #7813
+#26755 := [unit-resolution #7819 #26760]: #7789
+#9960 := (not #7789)
+#8355 := (or #2266 #9960)
+#9891 := (not #9488)
+#9573 := [hypothesis]: #7789
+#9645 := (or #9891 #2266 #9960)
+#10019 := (= #9980 0::Int)
+#9966 := (not #10019)
+#9776 := (not #10041)
+#9574 := [hypothesis]: #9488
+#6983 := (not #3908)
+#9890 := (not #10053)
+#9963 := (or #9776 #9890 #2266 #9891 #6983 #9960)
+#9883 := [th-lemma arith assign-bounds 1 -1 -1 1 -1]: #9963
+#9889 := [unit-resolution #9883 #9574 #6982 #10062 #10078 #9573]: #9776
+#9850 := (or #9966 #10041)
+#9962 := [th-lemma arith triangle-eq]: #9850
+#9644 := [unit-resolution #9962 #9889]: #9966
+#9961 := (or #10016 #9890 #2266 #9891 #6983 #9960)
+#10032 := [th-lemma arith assign-bounds 1 1 1 1 1]: #9961
+#10033 := [unit-resolution #10032 #9574 #6982 #10078 #10062 #9573]: #10016
+#9854 := [unit-resolution #10026 #4208 #10033]: #9940
+#9519 := (or #6798 #9959 #10019)
+#10020 := (or #10019 #9959)
+#9538 := (or #6798 #10020)
+#9792 := (iff #9538 #9519)
+#10027 := (or #9959 #10019)
+#9489 := (or #6798 #10027)
+#9526 := (iff #9489 #9519)
+#9791 := [rewrite]: #9526
+#9528 := (iff #9538 #9489)
+#10028 := (iff #10020 #10027)
+#10029 := [rewrite]: #10028
+#9532 := [monotonicity #10029]: #9528
+#9793 := [trans #9532 #9791]: #9792
+#9530 := [quant-inst #7202 #2264]: #9538
+#9752 := [mp #9530 #9793]: #9519
+#9853 := [unit-resolution #9752 #4202 #9854 #9644]: false
+#10133 := [lemma #9853]: #9645
+#9525 := [unit-resolution #10133 #10078 #9573]: #9891
+#9529 := [unit-resolution #10076 #9525]: #10074
+#8418 := (or #7629 #7607)
+#9089 := [hypothesis]: #10074
+#8415 := [hypothesis]: #7632
+#8417 := [unit-resolution #9503 #8415]: #9501
+#8457 := [unit-resolution #9506 #8415]: #9504
+#8458 := [unit-resolution #10072 #8457 #8417 #9089]: false
+#9334 := [lemma #8458]: #8418
+#9748 := [unit-resolution #9334 #9529]: #7629
+#9790 := [unit-resolution #10068 #9748]: #7530
+#9746 := [unit-resolution #11911 #9790]: #9572
+#9888 := [th-lemma arith farkas 1 -1 1 #9571 #10078 #9746]: false
+#8313 := [lemma #9888]: #8355
+#26761 := [unit-resolution #8313 #26755]: #2266
+#26759 := [unit-resolution #12708 #26761]: #4481
+#26762 := [unit-resolution #4077 #26759]: #4472
+#26758 := [unit-resolution #12712 #26762]: #4469
+#26763 := [unit-resolution #3999 #26758]: #4460
+#26771 := [unit-resolution #23140 #26763]: #4457
+#26773 := [unit-resolution #3987 #26771]: #4446
+#26770 := [unit-resolution #24097 #26773]: #14174
+#26774 := [unit-resolution #12462 #6500 #26770]: #14076
+#26772 := [unit-resolution #24701 #26774]: #19558
+#26788 := [unit-resolution #21429 #26772 #19774]: #21426
+#26791 := [unit-resolution #4100 #26771]: #2920
+#26783 := [unit-resolution #24453 #12656 #26791 #26788]: #14788
+#26766 := [unit-resolution #24443 #26783]: #14778
+#26825 := [trans #26766 #26819]: #26205
+#26789 := [unit-resolution #24456 #26783]: #14775
+#26784 := [unit-resolution #27691 #26789]: #15503
+#26782 := [unit-resolution #24433 #26783]: #24439
+#26785 := [unit-resolution #27705 #26789]: #15527
+#26781 := [unit-resolution #29104 #26785 #26773 #26782 #26772 #26784]: #26233
+#26820 := [unit-resolution #26781 #26825]: false
+#26821 := [lemma #26820]: #2350
+#8220 := [unit-resolution #4101 #26821]: #4454
+#8224 := [unit-resolution #23140 #8220]: #4463
+#8310 := [unit-resolution #3999 #8224]: #4466
+#8229 := [unit-resolution #12712 #8310]: #4475
+#8233 := [unit-resolution #4077 #8229]: #4478
+#8239 := [unit-resolution #12708 #8233]: #2267
+#8333 := [unit-resolution #11103 #8239]: #6064
+#8358 := [unit-resolution #6111 #8333]: #6082
+#8276 := [unit-resolution #12658 #8358]: #6079
+#8416 := [symm #8276]: #6077
+#8345 := [monotonicity #8416]: #7816
+#8349 := [symm #8345]: #7788
+#8351 := [unit-resolution #8313 #8239]: #9960
+[unit-resolution #7819 #8351 #8349]: false
 unsat

--- a/src/HOL/Boogie/Examples/VCC_Max.certs	Sun Dec 19 18:54:29 2010 +0100
+++ b/src/HOL/Boogie/Examples/VCC_Max.certs	Sun Dec 19 18:55:21 2010 +0100
@@ -1,1510 +1,758 @@
-d334e94512e2be06e90930c75ed763964895b7de 7803 0
+3b08169b1d21e7df09081614598ecffbfc739ade 7774 0
 #2 := false
-decl f121 :: (-> S19 S20 Int)
+#161 := 0::Int
+decl f122 :: (-> S19 S20 Int)
 decl f77 :: (-> S20 Int S18 S20)
 decl f19 :: S18
 #50 := f19
 decl ?v0!14 :: Int
-#18614 := ?v0!14
+#18578 := ?v0!14
 decl f54 :: (-> S18 Int S20)
-decl f298 :: Int
-#3041 := f298
-#3042 := (f54 f19 f298)
-#18619 := (f77 #3042 ?v0!14 f19)
-decl f297 :: S19
-#3039 := f297
-#18620 := (f121 f297 #18619)
-decl f309 :: Int
-#3139 := f309
-#3257 := (f77 #3042 f309 f19)
-#3266 := (f121 f297 #3257)
-#30591 := (= #3266 #18620)
-#30624 := (not #30591)
-#161 := 0::Int
+decl f299 :: Int
+#3041 := f299
+#3042 := (f54 f19 f299)
+#18583 := (f77 #3042 ?v0!14 f19)
+decl f298 :: S19
+#3039 := f298
+#18584 := (f122 f298 #18583)
 #4203 := -1::Int
-#18941 := (* -1::Int #18620)
-#30619 := (+ #3266 #18941)
-#30621 := (>= #30619 0::Int)
-#30631 := (not #30621)
+#18905 := (* -1::Int #18584)
+decl f310 :: Int
+#3139 := f310
+#3257 := (f77 #3042 f310 f19)
+#3266 := (f122 f298 #3257)
+#30336 := (+ #3266 #18905)
+#30338 := (>= #30336 0::Int)
+#30332 := (= #3266 #18584)
+#29868 := (= f310 ?v0!14)
+decl f308 :: Int
+#3131 := f308
+#29822 := (+ f308 #18905)
+#29823 := (>= #29822 0::Int)
+#30220 := (not #29823)
+decl f316 :: Int
+#3275 := f316
+#13534 := (* -1::Int f316)
+#24551 := (+ f308 #13534)
+#24552 := (<= #24551 0::Int)
+#30447 := (+ #3266 #13534)
+#30448 := (<= #30447 0::Int)
+#30446 := (= #3266 f316)
 decl f315 :: Int
-#3275 := f315
-#13570 := (* -1::Int f315)
-#30344 := (+ #3266 #13570)
-#30172 := (<= #30344 0::Int)
-#30343 := (= #3266 f315)
-decl f314 :: Int
-#3268 := f314
-#12601 := (= f314 f315)
-#18942 := (+ f315 #18941)
-#18943 := (>= #18942 0::Int)
-#18928 := (* -1::Int ?v0!14)
-decl f317 :: Int
-#3285 := f317
-#18929 := (+ f317 #18928)
-#18930 := (<= #18929 0::Int)
-#18616 := (>= ?v0!14 0::Int)
-#22396 := (not #18616)
-#7632 := 4294967295::Int
-#18615 := (<= ?v0!14 4294967295::Int)
-#22395 := (not #18615)
-#22411 := (or #22395 #22396 #18930 #18943)
-#22416 := (not #22411)
+#3268 := f315
+#12565 := (= f315 f316)
+#18906 := (+ f316 #18905)
+#18907 := (>= #18906 0::Int)
+#18892 := (* -1::Int ?v0!14)
+decl f318 :: Int
+#3285 := f318
+#18893 := (+ f318 #18892)
+#18894 := (<= #18893 0::Int)
+#18580 := (>= ?v0!14 0::Int)
+#22360 := (not #18580)
+#7596 := 4294967295::Int
+#18579 := (<= ?v0!14 4294967295::Int)
+#22359 := (not #18579)
+#22375 := (or #22359 #22360 #18894 #18907)
+#22380 := (not #22375)
 #202 := (:var 0 Int)
 #3123 := (f77 #3042 #202 f19)
-#23363 := (pattern #3123)
-#15219 := (<= #202 4294967295::Int)
-#19613 := (not #15219)
-#3124 := (f121 f297 #3123)
-#13571 := (+ #3124 #13570)
-#13572 := (<= #13571 0::Int)
-#13551 := (* -1::Int f317)
-#13559 := (+ #202 #13551)
-#13558 := (>= #13559 0::Int)
+#23327 := (pattern #3123)
+#15183 := (<= #202 4294967295::Int)
+#19577 := (not #15183)
+#3124 := (f122 f298 #3123)
+#13535 := (+ #3124 #13534)
+#13536 := (<= #13535 0::Int)
+#13515 := (* -1::Int f318)
+#13523 := (+ #202 #13515)
+#13522 := (>= #13523 0::Int)
 #4202 := (>= #202 0::Int)
-#5124 := (not #4202)
-#22377 := (or #5124 #13558 #13572 #19613)
-#23380 := (forall (vars (?v0 Int)) (:pat #23363) #22377)
-#23385 := (not #23380)
-decl f316 :: Int
-#3277 := f316
-#13592 := (* -1::Int f316)
-decl f296 :: Int
-#3036 := f296
-#13593 := (+ f296 #13592)
-#13594 := (<= #13593 0::Int)
-#3298 := (f77 #3042 f316 f19)
-#3299 := (f121 f297 #3298)
-#12643 := (= f315 #3299)
-#22362 := (not #12643)
-#22363 := (or #22362 #13594)
-#22364 := (not #22363)
-#23388 := (or #22364 #23385)
-#23391 := (not #23388)
-#23394 := (or #23391 #22416)
-#23397 := (not #23394)
-#13552 := (+ f296 #13551)
-#13550 := (>= #13552 0::Int)
-#13555 := (not #13550)
-#23400 := (or #13555 #23397)
-#23403 := (not #23400)
-#23406 := (or #13555 #23403)
-#23409 := (not #23406)
-#15899 := 4294967294::Int
-#15900 := (<= f309 4294967294::Int)
-#18597 := (not #15900)
-#13619 := (+ f309 #13551)
-#13618 := (= #13619 -1::Int)
-#13622 := (not #13618)
+#5104 := (not #4202)
+#22341 := (or #5104 #13522 #13536 #19577)
+#23344 := (forall (vars (?v0 Int)) (:pat #23327) #22341)
+#23349 := (not #23344)
+decl f317 :: Int
+#3277 := f317
+#13556 := (* -1::Int f317)
+decl f297 :: Int
+#3036 := f297
+#13557 := (+ f297 #13556)
+#13558 := (<= #13557 0::Int)
+#3298 := (f77 #3042 f317 f19)
+#3299 := (f122 f298 #3298)
+#12607 := (= f316 #3299)
+#22326 := (not #12607)
+#22327 := (or #22326 #13558)
+#22328 := (not #22327)
+#23352 := (or #22328 #23349)
+#23355 := (not #23352)
+#23358 := (or #23355 #22380)
+#23361 := (not #23358)
+#13516 := (+ f297 #13515)
+#13514 := (>= #13516 0::Int)
+#13519 := (not #13514)
+#23364 := (or #13519 #23361)
+#23367 := (not #23364)
+#23370 := (or #13519 #23367)
+#23373 := (not #23370)
+#15863 := 4294967294::Int
+#15864 := (<= f310 4294967294::Int)
+#18561 := (not #15864)
+#13583 := (+ f310 #13515)
+#13582 := (= #13583 -1::Int)
+#13586 := (not #13582)
 #935 := 2::Int
-#13542 := (>= f317 2::Int)
-#22439 := (not #13542)
-#13534 := (>= f309 -1::Int)
-#18594 := (not #13534)
-#13525 := (>= f316 0::Int)
-#22438 := (not #13525)
-decl f301 :: (-> S19 S17 S17 Int S18 S1)
+#13506 := (>= f318 2::Int)
+#22403 := (not #13506)
+#13498 := (>= f310 -1::Int)
+#18558 := (not #13498)
+#13489 := (>= f317 0::Int)
+#22402 := (not #13489)
+decl f302 :: (-> S19 S17 S17 Int S18 S1)
 decl f16 :: S18
 #46 := f16
-decl f284 :: S17
-#3012 := f284
-decl f280 :: S17
-#3008 := f280
-#3287 := (f301 f297 f280 f284 f317 f16)
+decl f285 :: S17
+#3012 := f285
+decl f281 :: S17
+#3008 := f281
+#3287 := (f302 f298 f281 f285 f318 f16)
 decl f1 :: S1
 #4 := f1
-#12622 := (= f1 #3287)
-#12692 := (not #12622)
-#23412 := (or #12692 #22438 #18594 #22439 #13622 #18597 #23409)
-#23415 := (not #23412)
-#23418 := (or #18594 #18597 #23415)
-#23421 := (not #23418)
+#12586 := (= f1 #3287)
+#12656 := (not #12586)
+#23376 := (or #12656 #22402 #18558 #22403 #13586 #18561 #23373)
+#23379 := (not #23376)
+#23382 := (or #18558 #18561 #23379)
+#23385 := (not #23382)
 #42 := 1::Int
-#13516 := (>= f309 1::Int)
-#13656 := (not #13516)
-#12604 := (= f309 f316)
-#12731 := (not #12604)
-#12740 := (not #12601)
-decl f286 :: S17
-#3014 := f286
-decl f281 :: S17
-#3009 := f281
-#3272 := (f301 f297 f281 f286 f309 f16)
-#12596 := (= f1 #3272)
-#12758 := (not #12596)
-decl f288 :: S17
-#3016 := f288
+#13480 := (>= f310 1::Int)
+#13620 := (not #13480)
+#12568 := (= f310 f317)
+#12695 := (not #12568)
+#12704 := (not #12565)
+decl f287 :: S17
+#3014 := f287
 decl f282 :: S17
-#3010 := f282
-#3270 := (f301 f297 f282 f288 f314 f19)
-#12593 := (= f1 #3270)
-#12767 := (not #12593)
-#12590 := (= #3266 f314)
-#12776 := (not #12590)
+#3009 := f282
+#3272 := (f302 f298 f282 f287 f310 f16)
+#12560 := (= f1 #3272)
+#12722 := (not #12560)
+decl f289 :: S17
+#3016 := f289
+decl f283 :: S17
+#3010 := f283
+#3270 := (f302 f298 f283 f289 f315 f19)
+#12557 := (= f1 #3270)
+#12731 := (not #12557)
+#12554 := (= #3266 f315)
+#12740 := (not #12554)
 decl f79 :: (-> S19 S20 S1)
-#3263 := (f79 f297 #3257)
-#12584 := (= f1 #3263)
-#18565 := (not #12584)
+#3263 := (f79 f298 #3257)
+#12548 := (= f1 #3263)
+#18529 := (not #12548)
 decl f59 :: (-> S20 S18 S1)
 #3258 := (f59 #3257 f19)
-#12575 := (= f1 #3258)
-#18556 := (not #12575)
-#23424 := (or #18556 #18565 #12776 #12767 #12758 #12740 #12731 #13656 #22438 #23421)
-#23427 := (not #23424)
-decl f36 :: (-> S19 S20 S20)
-decl f146 :: (-> S29 S20)
-decl f69 :: (-> S28 S20 S29)
-decl f70 :: (-> S19 S28)
-#3220 := (f70 f297)
-#27834 := (f69 #3220 #3257)
-#28494 := (f146 #27834)
-#28497 := (f36 f297 #28494)
-decl f37 :: S20
-#116 := f37
-#28498 := (= f37 #28497)
-decl f221 :: (-> S19 S20 S1)
-#28495 := (f221 f297 #28494)
-#28496 := (= f1 #28495)
-#28554 := (or #28496 #28498)
-#28557 := (not #28554)
-decl f147 :: (-> S29 S1)
-#28507 := (f147 #27834)
-#28508 := (= f1 #28507)
-#28509 := (not #28508)
-decl f38 :: (-> S19 S20 S1)
-#28504 := (f38 f297 #28494)
-#28505 := (= f1 #28504)
-#28506 := (not #28505)
-#28548 := (or #28506 #28509)
-#28551 := (not #28548)
-decl f23 :: (-> S18 S23)
-decl f24 :: (-> S20 S18)
-#28202 := (f24 #3257)
-#28512 := (f23 #28202)
-decl f25 :: S23
-#67 := f25
-#28530 := (= f25 #28512)
-#28545 := (not #28530)
-#28501 := (f24 #28494)
-#28502 := (f23 #28501)
-#28503 := (= f25 #28502)
-#28563 := (or #28503 #28545 #28551 #28557)
-#28568 := (not #28563)
-#28519 := (f36 f297 #3257)
-#28520 := (= f37 #28519)
-#28517 := (f221 f297 #3257)
-#28518 := (= f1 #28517)
-#28533 := (or #28518 #28520)
-#28536 := (not #28533)
-#28539 := (or #28530 #28536)
-#28542 := (not #28539)
-#28571 := (or #28542 #28568)
-#28574 := (not #28571)
+#12539 := (= f1 #3258)
+#18520 := (not #12539)
+#23388 := (or #18520 #18529 #12740 #12731 #12722 #12704 #12695 #13620 #22402 #23385)
+#23391 := (not #23388)
+#13673 := (* -1::Int #3266)
+#13674 := (+ f308 #13673)
+#13672 := (>= #13674 0::Int)
+#13671 := (not #13672)
+decl f309 :: Int
+#3135 := f309
+#13477 := (>= f309 0::Int)
+#22443 := (not #13477)
+#12806 := (= f309 f317)
+#12812 := (not #12806)
+#12803 := (= f308 f316)
+#12821 := (not #12803)
+#23418 := (or #12821 #12812 #22443 #13620 #22402 #13671 #23385)
+#23421 := (not #23418)
+#28423 := [hypothesis]: #23421
+#24557 := (or #23418 #12803)
+#24558 := [def-axiom]: #24557
+#28430 := [unit-resolution #24558 #28423]: #12803
+#29525 := (or #12821 #24552)
+#29591 := [th-lemma arith triangle-eq]: #29525
+#29590 := [unit-resolution #29591 #28430]: #24552
+#24448 := (not #18907)
+#29594 := (or #23418 #22328)
+#13941 := (* -1::Int f309)
+#13942 := (+ f297 #13941)
+#13943 := (<= #13942 0::Int)
+#13944 := (not #13943)
+decl ?v0!15 :: Int
+#18702 := ?v0!15
+#18707 := (f77 #3042 ?v0!15 f19)
+#18708 := (f122 f298 #18707)
+#19053 := (* -1::Int #18708)
+decl f314 :: Int
+#3166 := f314
+#19054 := (+ f314 #19053)
+#19055 := (>= #19054 0::Int)
+#19040 := (* -1::Int ?v0!15)
+#19041 := (+ f297 #19040)
+#19042 := (<= #19041 0::Int)
+#18704 := (>= ?v0!15 0::Int)
+#22537 := (not #18704)
+#18703 := (<= ?v0!15 4294967295::Int)
+#22536 := (not #18703)
+#22552 := (or #22536 #22537 #19042 #19055)
+#22557 := (not #22552)
+#13406 := (* -1::Int f297)
+#13794 := (+ #202 #13406)
+#13793 := (>= #13794 0::Int)
+#3173 := (= #3124 f314)
+#22510 := (not #3173)
+#22511 := (or #22510 #5104 #13793 #19577)
+#23468 := (forall (vars (?v0 Int)) (:pat #23327) #22511)
+#23473 := (not #23468)
+#13805 := (* -1::Int f314)
+#13806 := (+ #3124 #13805)
+#13807 := (<= #13806 0::Int)
+#22502 := (or #5104 #13793 #13807 #19577)
+#23460 := (forall (vars (?v0 Int)) (:pat #23327) #22502)
+#23465 := (not #23460)
+#23476 := (or #23465 #23473)
+#23479 := (not #23476)
+#23482 := (or #23479 #22557)
+#23485 := (not #23482)
+#13501 := (* -1::Int f310)
+#13764 := (+ f297 #13501)
+#13765 := (<= #13764 0::Int)
+#13766 := (not #13765)
+#12242 := (= f308 f314)
+#12277 := (not #12242)
+decl f313 :: Int
+#3164 := f313
+#12239 := (= f309 f313)
+#12286 := (not #12239)
+decl f312 :: Int
+#3162 := f312
+#12236 := (= f310 f312)
+#12295 := (not #12236)
+decl f311 :: Int
+#3160 := f311
+#12233 := (= f308 f311)
+#12304 := (not #12233)
+#23488 := (or #12304 #12295 #12286 #12277 #22443 #13620 #13766 #23485)
+#23491 := (not #23488)
+#23394 := (or #18520 #18529 #23391)
+#23397 := (not #23394)
 decl f35 :: (-> S19 S20 S1)
-#3260 := (f35 f297 #3257)
-#12578 := (= f1 #3260)
-#18559 := (not #12578)
-#28577 := (or #18559 #28574)
-#28580 := (not #28577)
-#28583 := (iff #12584 #28580)
-#29899 := (not #28583)
-#30296 := [hypothesis]: #29899
-#62 := (:var 0 S20)
-#86 := (:var 1 S19)
-#2438 := (f79 #86 #62)
-#2439 := (pattern #2438)
-#324 := (f70 #86)
-#2441 := (f69 #324 #62)
-#2445 := (f146 #2441)
-#2456 := (f221 #86 #2445)
-#10696 := (= f1 #2456)
-#2454 := (f36 #86 #2445)
-#10693 := (= f37 #2454)
-#10699 := (or #10693 #10696)
-#22070 := (not #10699)
-#2450 := (f24 #2445)
-#2451 := (f23 #2450)
-#10687 := (= f25 #2451)
-#2446 := (f38 #86 #2445)
-#10678 := (= f1 #2446)
-#10681 := (not #10678)
-#2442 := (f147 #2441)
-#10672 := (= f1 #2442)
-#10675 := (not #10672)
-#10684 := (or #10675 #10681)
-#22069 := (not #10684)
-#65 := (f24 #62)
-#66 := (f23 #65)
-#68 := (= #66 f25)
-#91 := (not #68)
-#22071 := (or #91 #22069 #10687 #22070)
-#22072 := (not #22071)
-#2462 := (f221 #86 #62)
-#10711 := (= f1 #2462)
-#182 := (f36 #86 #62)
-#3761 := (= f37 #182)
-#10714 := (or #3761 #10711)
-#22064 := (not #10714)
-#22065 := (or #68 #22064)
-#22066 := (not #22065)
-#22075 := (or #22066 #22072)
-#22081 := (not #22075)
-#186 := (f35 #86 #62)
-#3767 := (= f1 #186)
-#11297 := (not #3767)
-#22082 := (or #11297 #22081)
-#22083 := (not #22082)
-#10668 := (= f1 #2438)
-#22088 := (iff #10668 #22083)
-#22091 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #22088)
-#10690 := (not #10687)
-#10732 := (and #68 #10684 #10690 #10699)
-#10717 := (and #91 #10714)
-#10738 := (or #10717 #10732)
-#10743 := (and #3767 #10738)
-#10746 := (iff #10668 #10743)
-#10749 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #10746)
-#22092 := (iff #10749 #22091)
-#22089 := (iff #10746 #22088)
-#22086 := (iff #10743 #22083)
-#22078 := (and #3767 #22075)
-#22084 := (iff #22078 #22083)
-#22085 := [rewrite]: #22084
-#22079 := (iff #10743 #22078)
-#22076 := (iff #10738 #22075)
-#22073 := (iff #10732 #22072)
-#22074 := [rewrite]: #22073
-#22067 := (iff #10717 #22066)
-#22068 := [rewrite]: #22067
-#22077 := [monotonicity #22068 #22074]: #22076
-#22080 := [monotonicity #22077]: #22079
-#22087 := [trans #22080 #22085]: #22086
-#22090 := [monotonicity #22087]: #22089
-#22093 := [quant-intro #22090]: #22092
-#18014 := (~ #10749 #10749)
-#18012 := (~ #10746 #10746)
-#18013 := [refl]: #18012
-#18015 := [nnf-pos #18013]: #18014
-#2463 := (= #2462 f1)
-#183 := (= #182 f37)
-#2464 := (or #183 #2463)
-#2465 := (and #91 #2464)
-#2457 := (= #2456 f1)
-#2455 := (= #2454 f37)
-#2458 := (or #2455 #2457)
-#2452 := (= #2451 f25)
-#2453 := (not #2452)
-#2459 := (and #2453 #2458)
-#2447 := (= #2446 f1)
-#2448 := (not #2447)
-#2443 := (= #2442 f1)
-#2444 := (not #2443)
-#2449 := (or #2444 #2448)
-#2460 := (and #2449 #2459)
-#2461 := (and #68 #2460)
-#2466 := (or #2461 #2465)
-#187 := (= #186 f1)
-#2467 := (and #187 #2466)
-#2440 := (= #2438 f1)
-#2468 := (iff #2440 #2467)
-#2469 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #2468)
-#10752 := (iff #2469 #10749)
-#10702 := (and #10690 #10699)
-#10705 := (and #10684 #10702)
-#10708 := (and #68 #10705)
-#10720 := (or #10708 #10717)
-#10723 := (and #3767 #10720)
-#10726 := (iff #10668 #10723)
-#10729 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #10726)
-#10750 := (iff #10729 #10749)
-#10747 := (iff #10726 #10746)
-#10744 := (iff #10723 #10743)
-#10741 := (iff #10720 #10738)
-#10735 := (or #10732 #10717)
-#10739 := (iff #10735 #10738)
-#10740 := [rewrite]: #10739
-#10736 := (iff #10720 #10735)
-#10733 := (iff #10708 #10732)
-#10734 := [rewrite]: #10733
-#10737 := [monotonicity #10734]: #10736
-#10742 := [trans #10737 #10740]: #10741
-#10745 := [monotonicity #10742]: #10744
-#10748 := [monotonicity #10745]: #10747
-#10751 := [quant-intro #10748]: #10750
-#10730 := (iff #2469 #10729)
-#10727 := (iff #2468 #10726)
-#10724 := (iff #2467 #10723)
-#10721 := (iff #2466 #10720)
-#10718 := (iff #2465 #10717)
-#10715 := (iff #2464 #10714)
-#10712 := (iff #2463 #10711)
-#10713 := [rewrite]: #10712
-#3762 := (iff #183 #3761)
-#3763 := [rewrite]: #3762
-#10716 := [monotonicity #3763 #10713]: #10715
-#10719 := [monotonicity #10716]: #10718
-#10709 := (iff #2461 #10708)
-#10706 := (iff #2460 #10705)
-#10703 := (iff #2459 #10702)
-#10700 := (iff #2458 #10699)
-#10697 := (iff #2457 #10696)
-#10698 := [rewrite]: #10697
-#10694 := (iff #2455 #10693)
-#10695 := [rewrite]: #10694
-#10701 := [monotonicity #10695 #10698]: #10700
-#10691 := (iff #2453 #10690)
-#10688 := (iff #2452 #10687)
-#10689 := [rewrite]: #10688
-#10692 := [monotonicity #10689]: #10691
-#10704 := [monotonicity #10692 #10701]: #10703
-#10685 := (iff #2449 #10684)
-#10682 := (iff #2448 #10681)
-#10679 := (iff #2447 #10678)
-#10680 := [rewrite]: #10679
-#10683 := [monotonicity #10680]: #10682
-#10676 := (iff #2444 #10675)
-#10673 := (iff #2443 #10672)
-#10674 := [rewrite]: #10673
-#10677 := [monotonicity #10674]: #10676
-#10686 := [monotonicity #10677 #10683]: #10685
-#10707 := [monotonicity #10686 #10704]: #10706
-#10710 := [monotonicity #10707]: #10709
-#10722 := [monotonicity #10710 #10719]: #10721
-#3768 := (iff #187 #3767)
-#3769 := [rewrite]: #3768
-#10725 := [monotonicity #3769 #10722]: #10724
-#10670 := (iff #2440 #10668)
-#10671 := [rewrite]: #10670
-#10728 := [monotonicity #10671 #10725]: #10727
-#10731 := [quant-intro #10728]: #10730
-#10753 := [trans #10731 #10751]: #10752
-#10667 := [asserted]: #2469
-#10754 := [mp #10667 #10753]: #10749
-#18016 := [mp~ #10754 #18015]: #10749
-#22094 := [mp #18016 #22093]: #22091
-#28423 := (not #22091)
-#29896 := (or #28423 #28583)
-#28499 := (or #28498 #28496)
-#28500 := (not #28499)
-#28510 := (or #28509 #28506)
-#28511 := (not #28510)
-#28513 := (= #28512 f25)
-#28514 := (not #28513)
-#28515 := (or #28514 #28511 #28503 #28500)
-#28516 := (not #28515)
-#28521 := (or #28520 #28518)
-#28522 := (not #28521)
-#28523 := (or #28513 #28522)
-#28524 := (not #28523)
-#28525 := (or #28524 #28516)
-#28526 := (not #28525)
-#28527 := (or #18559 #28526)
-#28528 := (not #28527)
-#28529 := (iff #12584 #28528)
-#29897 := (or #28423 #28529)
-#29946 := (iff #29897 #29896)
-#29888 := (iff #29896 #29896)
-#29891 := [rewrite]: #29888
-#28584 := (iff #28529 #28583)
-#28581 := (iff #28528 #28580)
-#28578 := (iff #28527 #28577)
-#28575 := (iff #28526 #28574)
-#28572 := (iff #28525 #28571)
-#28569 := (iff #28516 #28568)
-#28566 := (iff #28515 #28563)
-#28560 := (or #28545 #28551 #28503 #28557)
-#28564 := (iff #28560 #28563)
-#28565 := [rewrite]: #28564
-#28561 := (iff #28515 #28560)
-#28558 := (iff #28500 #28557)
-#28555 := (iff #28499 #28554)
-#28556 := [rewrite]: #28555
-#28559 := [monotonicity #28556]: #28558
-#28552 := (iff #28511 #28551)
-#28549 := (iff #28510 #28548)
-#28550 := [rewrite]: #28549
-#28553 := [monotonicity #28550]: #28552
-#28546 := (iff #28514 #28545)
-#28531 := (iff #28513 #28530)
-#28532 := [rewrite]: #28531
-#28547 := [monotonicity #28532]: #28546
-#28562 := [monotonicity #28547 #28553 #28559]: #28561
-#28567 := [trans #28562 #28565]: #28566
-#28570 := [monotonicity #28567]: #28569
-#28543 := (iff #28524 #28542)
-#28540 := (iff #28523 #28539)
-#28537 := (iff #28522 #28536)
-#28534 := (iff #28521 #28533)
-#28535 := [rewrite]: #28534
-#28538 := [monotonicity #28535]: #28537
-#28541 := [monotonicity #28532 #28538]: #28540
-#28544 := [monotonicity #28541]: #28543
-#28573 := [monotonicity #28544 #28570]: #28572
-#28576 := [monotonicity #28573]: #28575
-#28579 := [monotonicity #28576]: #28578
-#28582 := [monotonicity #28579]: #28581
-#28585 := [monotonicity #28582]: #28584
-#29935 := [monotonicity #28585]: #29946
-#29933 := [trans #29935 #29891]: #29946
-#29945 := [quant-inst #3039 #3257]: #29897
-#29889 := [mp #29945 #29933]: #29896
-#30214 := [unit-resolution #29889 #22094 #30296]: false
-#30215 := [lemma #30214]: #28583
-#30322 := (or #29899 #12584)
-#30167 := [hypothesis]: #28563
-decl f127 :: (-> S20 Int)
-#3043 := (f127 #3042)
-decl f135 :: (-> S18 Int S18)
-#3040 := (f135 f19 f296)
-#3044 := (f54 #3040 #3043)
-#3047 := (f36 f297 #3044)
-#30199 := (= #3047 #28497)
-#30193 := (= #28497 #3047)
-#30284 := (= #28494 #3044)
-decl f154 :: (-> S18 Int)
-#24998 := (f154 #3040)
-decl f155 :: (-> S18 S18)
-#24996 := (f155 #3040)
-#27144 := (f135 #24996 #24998)
-#27145 := (f54 #27144 #3043)
-#28787 := (= #27145 #3044)
-#28807 := (= #27144 #3040)
-#28805 := (= #24998 f296)
-#24999 := (= f296 #24998)
-#369 := (:var 1 S18)
-#1401 := (f135 #369 #202)
-#1638 := (pattern #1401)
-#1649 := (f154 #1401)
-#8444 := (= #202 #1649)
-#8447 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8444)
-#17390 := (~ #8447 #8447)
-#17388 := (~ #8444 #8444)
-#17389 := [refl]: #17388
-#17391 := [nnf-pos #17389]: #17390
-#1650 := (= #1649 #202)
-#1651 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1650)
-#8448 := (iff #1651 #8447)
-#8445 := (iff #1650 #8444)
-#8446 := [rewrite]: #8445
-#8449 := [quant-intro #8446]: #8448
-#8443 := [asserted]: #1651
-#8452 := [mp #8443 #8449]: #8447
-#17392 := [mp~ #8452 #17391]: #8447
-#25005 := (not #8447)
-#25006 := (or #25005 #24999)
-#25007 := [quant-inst #50 #3036]: #25006
-#28406 := [unit-resolution #25007 #17392]: #24999
-#28806 := [symm #28406]: #28805
-#28385 := (= #24996 f19)
-#24997 := (= f19 #24996)
-#1652 := (f155 #1401)
-#8451 := (= #369 #1652)
-#8455 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8451)
-#17395 := (~ #8455 #8455)
-#17393 := (~ #8451 #8451)
-#17394 := [refl]: #17393
-#17396 := [nnf-pos #17394]: #17395
-#1653 := (= #1652 #369)
-#1654 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1653)
-#8456 := (iff #1654 #8455)
-#8453 := (iff #1653 #8451)
-#8454 := [rewrite]: #8453
-#8457 := [quant-intro #8454]: #8456
-#8450 := [asserted]: #1654
-#8460 := [mp #8450 #8457]: #8455
-#17397 := [mp~ #8460 #17396]: #8455
-#25000 := (not #8455)
-#25001 := (or #25000 #24997)
-#25002 := [quant-inst #50 #3036]: #25001
-#28384 := [unit-resolution #25002 #17397]: #24997
-#28386 := [symm #28384]: #28385
-#28808 := [monotonicity #28386 #28806]: #28807
-#28789 := [monotonicity #28808]: #28787
-#30282 := (= #28494 #27145)
-decl f136 :: (-> S20 S20 Int)
-decl f39 :: (-> Int S20)
-decl f40 :: (-> S20 Int)
-#3076 := (f40 #3042)
-#24833 := (f39 #3076)
-#27122 := (f24 #24833)
-#29367 := (f77 #24833 f309 #27122)
-#29368 := (f136 #29367 #24833)
-#29431 := (f77 #27145 #29368 #24996)
-#29452 := (f69 #3220 #29431)
-#29458 := (f146 #29452)
-#30280 := (= #29458 #27145)
-#29459 := (= #27145 #29458)
-#29460 := (not #29459)
-#29456 := (f147 #29452)
-#29457 := (= f1 #29456)
-decl f78 :: (-> S29 S1)
-#29453 := (f78 #29452)
-#29454 := (= f1 #29453)
-#29455 := (not #29454)
-#29449 := (f35 f297 #29431)
-#29450 := (= f1 #29449)
-#29451 := (not #29450)
-#29481 := (or #29451 #29455 #29457 #29460)
-#29484 := (not #29481)
-#29474 := (* -1::Int #29368)
-#29475 := (+ #24998 #29474)
-#29476 := (<= #29475 0::Int)
-#30241 := (not #29476)
-#29583 := (+ f309 #29474)
-#29585 := (>= #29583 0::Int)
-#29369 := (= f309 #29368)
-#55 := (:var 1 S20)
-#1433 := (f24 #55)
-#1434 := (f77 #55 #202 #1433)
-#1435 := (pattern #1434)
-#1436 := (f136 #1434 #55)
-#7824 := (= #202 #1436)
-#7828 := (forall (vars (?v0 S20) (?v1 Int)) (:pat #1435) #7824)
-#17105 := (~ #7828 #7828)
-#17103 := (~ #7824 #7824)
-#17104 := [refl]: #17103
-#17106 := [nnf-pos #17104]: #17105
-#1437 := (= #1436 #202)
-#1438 := (forall (vars (?v0 S20) (?v1 Int)) (:pat #1435) #1437)
-#7829 := (iff #1438 #7828)
-#7826 := (iff #1437 #7824)
-#7827 := [rewrite]: #7826
-#7830 := [quant-intro #7827]: #7829
-#7823 := [asserted]: #1438
-#7833 := [mp #7823 #7830]: #7828
-#17107 := [mp~ #7833 #17106]: #7828
-#27129 := (not #7828)
-#29432 := (or #27129 #29369)
-#29448 := [quant-inst #24833 #3139]: #29432
-#29674 := [unit-resolution #29448 #17107]: #29369
-#29675 := (not #29369)
-#30235 := (or #29675 #29585)
-#30236 := [th-lemma arith triangle-eq]: #30235
-#30237 := [unit-resolution #30236 #29674]: #29585
-#13537 := (* -1::Int f309)
-#13800 := (+ f296 #13537)
-#13801 := (<= #13800 0::Int)
-#13802 := (not #13801)
-#13709 := (* -1::Int #3266)
-decl f307 :: Int
-#3131 := f307
-#13710 := (+ f307 #13709)
-#13708 := (>= #13710 0::Int)
-#13707 := (not #13708)
-decl f308 :: Int
-#3135 := f308
-#13513 := (>= f308 0::Int)
-#22479 := (not #13513)
-#12842 := (= f308 f316)
-#12848 := (not #12842)
-#12839 := (= f307 f315)
-#12857 := (not #12839)
-#23454 := (or #12857 #12848 #22479 #13656 #22438 #13707 #23421)
+#3260 := (f35 f298 #3257)
+#12542 := (= f1 #3260)
+#18523 := (not #12542)
+#23400 := (or #18520 #18523 #23397)
+#23403 := (not #23400)
+#23406 := (or #18520 #18523 #23403)
+#23409 := (not #23406)
+#23412 := (or #22443 #13620 #13672 #23409)
+#23415 := (not #23412)
+#23424 := (or #23415 #23421)
+#23427 := (not #23424)
+#23430 := (or #18520 #18529 #22443 #13620 #23427)
+#23433 := (not #23430)
+#23436 := (or #18520 #18529 #23433)
+#23439 := (not #23436)
+#23442 := (or #18520 #18523 #23439)
+#23445 := (not #23442)
+#23448 := (or #18520 #18523 #23445)
+#23451 := (not #23448)
+#23454 := (or #22443 #13620 #13765 #23451)
 #23457 := (not #23454)
-#23430 := (or #18556 #18565 #23427)
-#23433 := (not #23430)
-#23436 := (or #18556 #18559 #23433)
-#23439 := (not #23436)
-#23442 := (or #18556 #18559 #23439)
-#23445 := (not #23442)
-#23448 := (or #22479 #13656 #13708 #23445)
-#23451 := (not #23448)
-#23460 := (or #23451 #23457)
-#23463 := (not #23460)
-#23466 := (or #18556 #18565 #22479 #13656 #23463)
-#23469 := (not #23466)
-#23472 := (or #18556 #18565 #23469)
-#23475 := (not #23472)
-#23478 := (or #18556 #18559 #23475)
-#23481 := (not #23478)
-#23484 := (or #18556 #18559 #23481)
-#23487 := (not #23484)
-#23490 := (or #22479 #13656 #13801 #23487)
-#23493 := (not #23490)
-decl ?v0!15 :: Int
-#18738 := ?v0!15
-#18743 := (f77 #3042 ?v0!15 f19)
-#18744 := (f121 f297 #18743)
-#19089 := (* -1::Int #18744)
-decl f313 :: Int
-#3166 := f313
-#19090 := (+ f313 #19089)
-#19091 := (>= #19090 0::Int)
-#19076 := (* -1::Int ?v0!15)
-#19077 := (+ f296 #19076)
-#19078 := (<= #19077 0::Int)
-#18740 := (>= ?v0!15 0::Int)
-#22573 := (not #18740)
-#18739 := (<= ?v0!15 4294967295::Int)
-#22572 := (not #18739)
-#22588 := (or #22572 #22573 #19078 #19091)
-#22593 := (not #22588)
-#13442 := (* -1::Int f296)
-#13830 := (+ #202 #13442)
-#13829 := (>= #13830 0::Int)
-#3173 := (= #3124 f313)
-#22546 := (not #3173)
-#22547 := (or #22546 #5124 #13829 #19613)
-#23504 := (forall (vars (?v0 Int)) (:pat #23363) #22547)
-#23509 := (not #23504)
-#13841 := (* -1::Int f313)
-#13842 := (+ #3124 #13841)
-#13843 := (<= #13842 0::Int)
-#22538 := (or #5124 #13829 #13843 #19613)
-#23496 := (forall (vars (?v0 Int)) (:pat #23363) #22538)
-#23501 := (not #23496)
-#23512 := (or #23501 #23509)
-#23515 := (not #23512)
-#23518 := (or #23515 #22593)
-#23521 := (not #23518)
-#12278 := (= f307 f313)
-#12313 := (not #12278)
-decl f312 :: Int
-#3164 := f312
-#12275 := (= f308 f312)
-#12322 := (not #12275)
-decl f311 :: Int
-#3162 := f311
-#12272 := (= f309 f311)
-#12331 := (not #12272)
-decl f310 :: Int
-#3160 := f310
-#12269 := (= f307 f310)
-#12340 := (not #12269)
-#23524 := (or #12340 #12331 #12322 #12313 #22479 #13656 #13802 #23521)
-#23527 := (not #23524)
-#23530 := (or #23493 #23527)
-#23533 := (not #23530)
-#14006 := (* -1::Int f307)
-#14007 := (+ #3124 #14006)
-#14008 := (<= #14007 0::Int)
-#13995 := (+ #202 #13537)
-#13994 := (>= #13995 0::Int)
-#22354 := (or #5124 #13994 #14008 #19613)
-#23372 := (forall (vars (?v0 Int)) (:pat #23363) #22354)
-#23377 := (not #23372)
+#23494 := (or #23457 #23491)
+#23497 := (not #23494)
+#13970 := (* -1::Int f308)
+#13971 := (+ #3124 #13970)
+#13972 := (<= #13971 0::Int)
+#13959 := (+ #202 #13501)
+#13958 := (>= #13959 0::Int)
+#22318 := (or #5104 #13958 #13972 #19577)
+#23336 := (forall (vars (?v0 Int)) (:pat #23327) #22318)
+#23341 := (not #23336)
 #1374 := 255::Int
-#15885 := (<= f307 255::Int)
-#22623 := (not #15885)
-#15868 := (<= f308 4294967295::Int)
-#22622 := (not #15868)
-#15851 := (<= f309 4294967295::Int)
-#22621 := (not #15851)
-#14056 := (>= f307 0::Int)
-#22619 := (not #14056)
-#14034 := (>= f309 0::Int)
-#22618 := (not #14034)
-#14028 := (>= #13800 0::Int)
-#14031 := (not #14028)
-#13977 := (* -1::Int f308)
-#13978 := (+ f296 #13977)
-#13979 := (<= #13978 0::Int)
-#13508 := (<= f296 0::Int)
-decl f302 :: (-> S19 S17 S17 S20 S18 S1)
+#15849 := (<= f308 255::Int)
+#22587 := (not #15849)
+#15832 := (<= f309 4294967295::Int)
+#22586 := (not #15832)
+#15815 := (<= f310 4294967295::Int)
+#22585 := (not #15815)
+#14020 := (>= f308 0::Int)
+#22583 := (not #14020)
+#13998 := (>= f310 0::Int)
+#22582 := (not #13998)
+#13992 := (>= #13764 0::Int)
+#13995 := (not #13992)
+#13472 := (<= f297 0::Int)
+decl f303 :: (-> S19 S17 S17 S20 S18 S1)
 decl f18 :: (-> S18 S18)
 #51 := (f18 f19)
+decl f292 :: S17
+#3019 := f292
+decl f284 :: S17
+#3011 := f284
+#3250 := (f303 f298 f284 f292 #3042 #51)
+#12522 := (= f1 #3250)
+#22581 := (not #12522)
+decl f40 :: (-> S20 Int)
+#3076 := (f40 #3042)
+#3248 := (f302 f298 f284 f292 #3076 #51)
+#12519 := (= f1 #3248)
+#22580 := (not #12519)
 decl f291 :: S17
-#3019 := f291
-decl f283 :: S17
-#3011 := f283
-#3250 := (f302 f297 f283 f291 #3042 #51)
-#12558 := (= f1 #3250)
-#22617 := (not #12558)
-#3248 := (f301 f297 f283 f291 #3076 #51)
-#12555 := (= f1 #3248)
-#22616 := (not #12555)
-decl f290 :: S17
-#3018 := f290
-#3246 := (f301 f297 f283 f290 f296 f16)
-#12552 := (= f1 #3246)
-#13033 := (not #12552)
-#3244 := (f301 f297 f283 f288 f307 f19)
-#12549 := (= f1 #3244)
-#13042 := (not #12549)
-#3242 := (f301 f297 f283 f286 f308 f16)
-#12546 := (= f1 #3242)
-#13051 := (not #12546)
-#3240 := (f301 f297 f283 f284 f309 f16)
-#12543 := (= f1 #3240)
-#13060 := (not #12543)
-decl f189 :: (-> S19 S19 S1)
-#3232 := (f189 f297 f297)
-#12515 := (= f1 #3232)
-#13974 := (not #12515)
-decl f213 :: (-> S17 S19 S1)
-#3157 := (f213 f283 f297)
-#12258 := (= f1 #3157)
-#15299 := (not #12258)
-#3152 := (f77 #3042 f308 f19)
-#3153 := (f121 f297 #3152)
-#12250 := (= f307 #3153)
-#22615 := (not #12250)
+#3018 := f291
+#3246 := (f302 f298 f284 f291 f297 f16)
+#12516 := (= f1 #3246)
+#12997 := (not #12516)
+#3244 := (f302 f298 f284 f289 f308 f19)
+#12513 := (= f1 #3244)
+#13006 := (not #12513)
+#3242 := (f302 f298 f284 f287 f309 f16)
+#12510 := (= f1 #3242)
+#13015 := (not #12510)
+#3240 := (f302 f298 f284 f285 f310 f16)
+#12507 := (= f1 #3240)
+#13024 := (not #12507)
+decl f190 :: (-> S19 S19 S1)
+#3232 := (f190 f298 f298)
+#12479 := (= f1 #3232)
+#13938 := (not #12479)
+decl f214 :: (-> S17 S19 S1)
+#3157 := (f214 f284 f298)
+#12222 := (= f1 #3157)
+#15263 := (not #12222)
+#3152 := (f77 #3042 f309 f19)
+#3153 := (f122 f298 #3152)
+#12214 := (= f308 #3153)
+#22579 := (not #12214)
 #3098 := (f77 #3042 0::Int f19)
-#3108 := (f121 f297 #3098)
-decl f306 :: Int
-#3107 := f306
-#3109 := (= f306 #3108)
-#13267 := (not #3109)
-#23536 := (or #13267 #22615 #15299 #13974 #13060 #13051 #13042 #13033 #22616 #22617 #13508 #22479 #13656 #13979 #14031 #22618 #22619 #22621 #22622 #22623 #23377 #23533)
-#23539 := (not #23536)
-#23542 := (or #13267 #13508 #23539)
-#23545 := (not #23542)
-#13488 := (* -1::Int #3124)
-#13489 := (+ f306 #13488)
-#13487 := (>= #13489 0::Int)
-#13475 := (>= #202 1::Int)
-#22343 := (or #5124 #13475 #13487 #19613)
-#23364 := (forall (vars (?v0 Int)) (:pat #23363) #22343)
-#23369 := (not #23364)
-#23548 := (or #23369 #23545)
-#23551 := (not #23548)
+#3108 := (f122 f298 #3098)
+decl f307 :: Int
+#3107 := f307
+#3109 := (= f307 #3108)
+#13231 := (not #3109)
+#23500 := (or #13231 #22579 #15263 #13938 #13024 #13015 #13006 #12997 #22580 #22581 #13472 #22443 #13620 #13943 #13995 #22582 #22583 #22585 #22586 #22587 #23341 #23497)
+#23503 := (not #23500)
+#23506 := (or #13231 #13472 #23503)
+#23509 := (not #23506)
+#13452 := (* -1::Int #3124)
+#13453 := (+ f307 #13452)
+#13451 := (>= #13453 0::Int)
+#13439 := (>= #202 1::Int)
+#22307 := (or #5104 #13439 #13451 #19577)
+#23328 := (forall (vars (?v0 Int)) (:pat #23327) #22307)
+#23333 := (not #23328)
+#23512 := (or #23333 #23509)
+#23515 := (not #23512)
 decl ?v0!13 :: Int
-#18477 := ?v0!13
-#18487 := (>= ?v0!13 1::Int)
-#18482 := (f77 #3042 ?v0!13 f19)
-#18483 := (f121 f297 #18482)
-#18484 := (* -1::Int #18483)
-#18485 := (+ f306 #18484)
-#18486 := (>= #18485 0::Int)
-#18479 := (>= ?v0!13 0::Int)
-#22317 := (not #18479)
-#18478 := (<= ?v0!13 4294967295::Int)
-#22316 := (not #18478)
-#22332 := (or #22316 #22317 #18486 #18487)
-#22337 := (not #22332)
-#23554 := (or #22337 #23551)
+#18441 := ?v0!13
+#18451 := (>= ?v0!13 1::Int)
+#18446 := (f77 #3042 ?v0!13 f19)
+#18447 := (f122 f298 #18446)
+#18448 := (* -1::Int #18447)
+#18449 := (+ f307 #18448)
+#18450 := (>= #18449 0::Int)
+#18443 := (>= ?v0!13 0::Int)
+#22281 := (not #18443)
+#18442 := (<= ?v0!13 4294967295::Int)
+#22280 := (not #18442)
+#22296 := (or #22280 #22281 #18450 #18451)
+#22301 := (not #22296)
+#23518 := (or #22301 #23515)
+#23521 := (not #23518)
+#13433 := (>= f297 1::Int)
+#13436 := (not #13433)
+#23524 := (or #13436 #23521)
+#23527 := (not #23524)
+#23530 := (or #13436 #23527)
+#23533 := (not #23530)
+decl f286 :: S17
+#3013 := f286
+#3114 := (f302 f298 f286 f285 1::Int f16)
+#12165 := (= f1 #3114)
+#13204 := (not #12165)
+decl f288 :: S17
+#3015 := f288
+#3112 := (f302 f298 f288 f287 0::Int f16)
+#12162 := (= f1 #3112)
+#13213 := (not #12162)
+decl f290 :: S17
+#3017 := f290
+#3110 := (f302 f298 f290 f289 f307 f19)
+#12159 := (= f1 #3110)
+#13222 := (not #12159)
+#3104 := (f79 f298 #3098)
+#12153 := (= f1 #3104)
+#18418 := (not #12153)
+#3099 := (f59 #3098 f19)
+#12144 := (= f1 #3099)
+#18409 := (not #12144)
+#23536 := (or #13231 #18409 #18418 #13222 #13213 #13204 #23533)
+#23539 := (not #23536)
+#23542 := (or #18409 #18418 #23539)
+#23545 := (not #23542)
+#3101 := (f35 f298 #3098)
+#12147 := (= f1 #3101)
+#18412 := (not #12147)
+#23548 := (or #18409 #18412 #23545)
+#23551 := (not #23548)
+#23554 := (or #18409 #18412 #23551)
 #23557 := (not #23554)
-#13469 := (>= f296 1::Int)
-#13472 := (not #13469)
-#23560 := (or #13472 #23557)
+decl f212 :: (-> S19 S20 S20 S31 S1)
+decl f306 :: S31
+#3095 := f306
+decl f128 :: (-> S20 Int)
+#3043 := (f128 #3042)
+decl f136 :: (-> S18 Int S18)
+#3040 := (f136 f19 f297)
+#3044 := (f54 #3040 #3043)
+#3096 := (f212 f298 #3044 #3044 f306)
+#12141 := (= f1 #3096)
+#13264 := (not #12141)
+#23560 := (or #13264 #23557)
 #23563 := (not #23560)
-#23566 := (or #13472 #23563)
-#23569 := (not #23566)
-decl f285 :: S17
-#3013 := f285
-#3114 := (f301 f297 f285 f284 1::Int f16)
-#12201 := (= f1 #3114)
-#13240 := (not #12201)
-decl f287 :: S17
-#3015 := f287
-#3112 := (f301 f297 f287 f286 0::Int f16)
-#12198 := (= f1 #3112)
-#13249 := (not #12198)
-decl f289 :: S17
-#3017 := f289
-#3110 := (f301 f297 f289 f288 f306 f19)
-#12195 := (= f1 #3110)
-#13258 := (not #12195)
-#3104 := (f79 f297 #3098)
-#12189 := (= f1 #3104)
-#18454 := (not #12189)
-#3099 := (f59 #3098 f19)
-#12180 := (= f1 #3099)
-#18445 := (not #12180)
-#23572 := (or #13267 #18445 #18454 #13258 #13249 #13240 #23569)
-#23575 := (not #23572)
-#27039 := (f24 #3098)
-#27040 := (= #24996 #27039)
-#27013 := (f59 #3098 #24996)
-#27014 := (= f1 #27013)
-#27042 := (iff #27014 #27040)
-#275 := (:var 0 S18)
-#2729 := (f59 #55 #275)
-#2730 := (pattern #2729)
-#11369 := (= f1 #2729)
-#9220 := (= #275 #1433)
-#11390 := (iff #9220 #11369)
-#23294 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #11390)
-#11395 := (forall (vars (?v0 S20) (?v1 S18)) #11390)
-#23297 := (iff #11395 #23294)
-#23295 := (iff #11390 #11390)
-#23296 := [refl]: #23295
-#23298 := [quant-intro #23296]: #23297
-#18287 := (~ #11395 #11395)
-#18285 := (~ #11390 #11390)
-#18286 := [refl]: #18285
-#18288 := [nnf-pos #18286]: #18287
-#1939 := (= #1433 #275)
-#2731 := (= #2729 f1)
-#2736 := (iff #2731 #1939)
-#2737 := (forall (vars (?v0 S20) (?v1 S18)) #2736)
-#11396 := (iff #2737 #11395)
-#11393 := (iff #2736 #11390)
-#11386 := (iff #11369 #9220)
-#11391 := (iff #11386 #11390)
-#11392 := [rewrite]: #11391
-#11388 := (iff #2736 #11386)
-#9221 := (iff #1939 #9220)
-#9222 := [rewrite]: #9221
-#11371 := (iff #2731 #11369)
-#11372 := [rewrite]: #11371
-#11389 := [monotonicity #11372 #9222]: #11388
-#11394 := [trans #11389 #11392]: #11393
-#11397 := [quant-intro #11394]: #11396
-#11385 := [asserted]: #2737
-#11400 := [mp #11385 #11397]: #11395
-#18289 := [mp~ #11400 #18288]: #11395
-#23299 := [mp #18289 #23298]: #23294
-#26210 := (not #23294)
-#27513 := (or #26210 #27042)
-#27041 := (iff #27040 #27014)
-#27551 := (or #26210 #27041)
-#27552 := (iff #27551 #27513)
-#27592 := (iff #27513 #27513)
-#27593 := [rewrite]: #27592
-#27043 := (iff #27041 #27042)
-#27044 := [rewrite]: #27043
-#27594 := [monotonicity #27044]: #27552
-#27595 := [trans #27594 #27593]: #27552
-#27546 := [quant-inst #3098 #24996]: #27551
-#27596 := [mp #27546 #27595]: #27513
-#27640 := [unit-resolution #27596 #23299]: #27042
-#25112 := (f24 #3042)
-#27668 := (= #25112 #27039)
-#27682 := (= #27039 #25112)
-#27680 := (= #3098 #3042)
-#27070 := (f127 #24833)
-#27086 := (f54 #24996 #27070)
-#27410 := (= #27086 #3042)
-#27367 := (= #27070 f298)
-#28390 := (= #3043 f298)
-#25116 := (= f298 #3043)
+decl f23 :: (-> S18 S23)
+decl f24 :: (-> S20 S18)
+#24844 := (f128 #3044)
+#26146 := (f54 #3040 #24844)
+#26550 := (f24 #26146)
+#26792 := (f23 #26550)
+decl f25 :: S23
+#67 := f25
+#26795 := (= f25 #26792)
+#26915 := (not #26795)
+#3053 := (f23 #3040)
+#12079 := (= f25 #3053)
+#12082 := (not #12079)
+#26897 := (iff #12082 #26915)
+#26913 := (iff #12079 #26795)
+#26911 := (iff #26795 #12079)
+#26909 := (= #26792 #3053)
+#26875 := (= #26550 #3040)
+#25081 := (f24 #3044)
+#28877 := (= #25081 #3040)
+#25084 := (= #3040 #25081)
+#369 := (:var 1 S18)
 #2761 := (f54 #369 #202)
-#23300 := (pattern #2761)
-#2762 := (f127 #2761)
-#11445 := (= #202 #2762)
-#23301 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #23300) #11445)
-#11449 := (forall (vars (?v0 S18) (?v1 Int)) #11445)
-#23304 := (iff #11449 #23301)
-#23302 := (iff #11445 #11445)
-#23303 := [refl]: #23302
-#23305 := [quant-intro #23303]: #23304
-#18302 := (~ #11449 #11449)
-#18300 := (~ #11445 #11445)
-#18301 := [refl]: #18300
-#18303 := [nnf-pos #18301]: #18302
-#2763 := (= #2762 #202)
-#2764 := (forall (vars (?v0 S18) (?v1 Int)) #2763)
-#11450 := (iff #2764 #11449)
-#11447 := (iff #2763 #11445)
-#11448 := [rewrite]: #11447
-#11451 := [quant-intro #11448]: #11450
-#11444 := [asserted]: #2764
-#11454 := [mp #11444 #11451]: #11449
-#18304 := [mp~ #11454 #18303]: #11449
-#23306 := [mp #18304 #23305]: #23301
-#25070 := (not #23301)
-#25121 := (or #25070 #25116)
-#25122 := [quant-inst #50 #3041]: #25121
-#28389 := [unit-resolution #25122 #23306]: #25116
-#28391 := [symm #28389]: #28390
-#27143 := (= #27070 #3043)
-#27141 := (= #24833 #3042)
-#24834 := (= #3042 #24833)
-#132 := (f40 #62)
-#23211 := (pattern #132)
-#133 := (f39 #132)
-#3682 := (= #62 #133)
-#23212 := (forall (vars (?v0 S20)) (:pat #23211) #3682)
-#3685 := (forall (vars (?v0 S20)) #3682)
-#23213 := (iff #3685 #23212)
-#23215 := (iff #23212 #23212)
-#23216 := [rewrite]: #23215
-#23214 := [rewrite]: #23213
-#23217 := [trans #23214 #23216]: #23213
-#16342 := (~ #3685 #3685)
-#16332 := (~ #3682 #3682)
-#16333 := [refl]: #16332
-#16398 := [nnf-pos #16333]: #16342
-#134 := (= #133 #62)
-#135 := (forall (vars (?v0 S20)) #134)
-#3686 := (iff #135 #3685)
-#3683 := (iff #134 #3682)
-#3684 := [rewrite]: #3683
-#3687 := [quant-intro #3684]: #3686
-#3681 := [asserted]: #135
-#3690 := [mp #3681 #3687]: #3685
-#16399 := [mp~ #3690 #16398]: #3685
-#23218 := [mp #16399 #23217]: #23212
-#24837 := (not #23212)
-#24838 := (or #24837 #24834)
-#24839 := [quant-inst #3042]: #24838
-#27140 := [unit-resolution #24839 #23218]: #24834
-#27142 := [symm #27140]: #27141
-#27275 := [monotonicity #27142]: #27143
-#27368 := [trans #27275 #28391]: #27367
-#27414 := [monotonicity #28386 #27368]: #27410
-#27415 := (= #3098 #27086)
-#27064 := (f77 #24833 0::Int #24996)
-#27089 := (= #27064 #27086)
-#27092 := (not #27089)
-decl f149 :: (-> S20 S20 S1)
-#27065 := (f149 #27064 #24833)
-#27066 := (= f1 #27065)
-#27067 := (not #27066)
-#27098 := (or #27067 #27092)
-#27103 := (not #27098)
-#28651 := [hypothesis]: #27098
-#289 := (:var 1 Int)
-#60 := (:var 2 S20)
-#1622 := (f77 #60 #289 #275)
-#1623 := (pattern #1622)
-#1624 := (f149 #1622 #60)
-#8390 := (= f1 #1624)
-#21232 := (not #8390)
-decl f150 :: (-> S18 Int)
-#1627 := (f150 #275)
-#1628 := (* #289 #1627)
-#1626 := (f127 #60)
-#1629 := (+ #1626 #1628)
-#1630 := (f54 #275 #1629)
-#1631 := (= #1622 #1630)
-#21231 := (not #1631)
-#21233 := (or #21231 #21232)
-#21234 := (not #21233)
-#21237 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #21234)
-#8396 := (and #1631 #8390)
-#8401 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #8396)
-#21238 := (iff #8401 #21237)
-#21235 := (iff #8396 #21234)
-#21236 := [rewrite]: #21235
-#21239 := [quant-intro #21236]: #21238
-#17365 := (~ #8401 #8401)
-#17363 := (~ #8396 #8396)
-#17364 := [refl]: #17363
-#17366 := [nnf-pos #17364]: #17365
-#1625 := (= #1624 f1)
-#1632 := (and #1625 #1631)
-#1633 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #1632)
-#8402 := (iff #1633 #8401)
-#8399 := (iff #1632 #8396)
-#8393 := (and #8390 #1631)
-#8397 := (iff #8393 #8396)
-#8398 := [rewrite]: #8397
-#8394 := (iff #1632 #8393)
-#8391 := (iff #1625 #8390)
-#8392 := [rewrite]: #8391
-#8395 := [monotonicity #8392]: #8394
-#8400 := [trans #8395 #8398]: #8399
-#8403 := [quant-intro #8400]: #8402
-#8389 := [asserted]: #1633
-#8406 := [mp #8389 #8403]: #8401
-#17367 := [mp~ #8406 #17366]: #8401
-#21240 := [mp #17367 #21239]: #21237
-#27721 := (not #21237)
-#27728 := (or #27721 #27103)
-#27068 := (f150 #24996)
-#27069 := (* 0::Int #27068)
-#27071 := (+ #27070 #27069)
-#27072 := (f54 #24996 #27071)
-#27073 := (= #27064 #27072)
-#27074 := (not #27073)
-#27075 := (or #27074 #27067)
-#27076 := (not #27075)
-#27729 := (or #27721 #27076)
-#27730 := (iff #27729 #27728)
-#27736 := (iff #27728 #27728)
-#27737 := [rewrite]: #27736
-#27104 := (iff #27076 #27103)
-#27101 := (iff #27075 #27098)
-#27095 := (or #27092 #27067)
-#27099 := (iff #27095 #27098)
-#27100 := [rewrite]: #27099
-#27096 := (iff #27075 #27095)
-#27093 := (iff #27074 #27092)
-#27090 := (iff #27073 #27089)
-#27087 := (= #27072 #27086)
-#27084 := (= #27071 #27070)
-#27079 := (+ #27070 0::Int)
-#27082 := (= #27079 #27070)
-#27083 := [rewrite]: #27082
-#27080 := (= #27071 #27079)
-#27077 := (= #27069 0::Int)
-#27078 := [rewrite]: #27077
-#27081 := [monotonicity #27078]: #27080
-#27085 := [trans #27081 #27083]: #27084
-#27088 := [monotonicity #27085]: #27087
-#27091 := [monotonicity #27088]: #27090
-#27094 := [monotonicity #27091]: #27093
-#27097 := [monotonicity #27094]: #27096
-#27102 := [trans #27097 #27100]: #27101
-#27105 := [monotonicity #27102]: #27104
-#27731 := [monotonicity #27105]: #27730
-#27745 := [trans #27731 #27737]: #27730
-#27727 := [quant-inst #24833 #161 #24996]: #27729
-#27746 := [mp #27727 #27745]: #27728
-#28652 := [unit-resolution #27746 #21240 #28651]: false
-#28653 := [lemma #28652]: #27103
-#27748 := (or #27098 #27089)
-#27749 := [def-axiom]: #27748
-#27673 := [unit-resolution #27749 #28653]: #27089
-#27371 := (= #3098 #27064)
-#27409 := [monotonicity #27140 #28384]: #27371
-#27674 := [trans #27409 #27673]: #27415
-#27675 := [trans #27674 #27414]: #27680
-#27676 := [monotonicity #27675]: #27682
-#27669 := [symm #27676]: #27668
-#27670 := (= #24996 #25112)
-#25113 := (= f19 #25112)
+#23264 := (pattern #2761)
 #2765 := (f24 #2761)
-#11453 := (= #369 #2765)
-#23307 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #23300) #11453)
-#11457 := (forall (vars (?v0 S18) (?v1 Int)) #11453)
-#23310 := (iff #11457 #23307)
-#23308 := (iff #11453 #11453)
-#23309 := [refl]: #23308
-#23311 := [quant-intro #23309]: #23310
-#18307 := (~ #11457 #11457)
-#18305 := (~ #11453 #11453)
-#18306 := [refl]: #18305
-#18308 := [nnf-pos #18306]: #18307
+#11417 := (= #369 #2765)
+#23271 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #23264) #11417)
+#11421 := (forall (vars (?v0 S18) (?v1 Int)) #11417)
+#23274 := (iff #11421 #23271)
+#23272 := (iff #11417 #11417)
+#23273 := [refl]: #23272
+#23275 := [quant-intro #23273]: #23274
+#18271 := (~ #11421 #11421)
+#18269 := (~ #11417 #11417)
+#18270 := [refl]: #18269
+#18272 := [nnf-pos #18270]: #18271
 #2766 := (= #2765 #369)
 #2767 := (forall (vars (?v0 S18) (?v1 Int)) #2766)
-#11458 := (iff #2767 #11457)
-#11455 := (iff #2766 #11453)
-#11456 := [rewrite]: #11455
-#11459 := [quant-intro #11456]: #11458
-#11452 := [asserted]: #2767
-#11462 := [mp #11452 #11459]: #11457
-#18309 := [mp~ #11462 #18308]: #11457
-#23312 := [mp #18309 #23311]: #23307
-#25064 := (not #23307)
-#25118 := (or #25064 #25113)
-#25119 := [quant-inst #50 #3041]: #25118
-#27139 := [unit-resolution #25119 #23312]: #25113
-#27671 := [trans #28386 #27139]: #27670
-#27672 := [trans #27671 #27669]: #27040
-#27021 := (not #27014)
-#27677 := (iff #18445 #27021)
-#27722 := (iff #12180 #27014)
-#27750 := (iff #27014 #12180)
-#27744 := (= #27013 #3099)
-#27747 := [monotonicity #28386]: #27744
-#27751 := [monotonicity #27747]: #27750
-#27723 := [symm #27751]: #27722
-#27724 := [monotonicity #27723]: #27677
-#27667 := [hypothesis]: #18445
-#27725 := [mp #27667 #27724]: #27021
-#27604 := (not #27040)
-#27597 := (not #27042)
-#27605 := (or #27597 #27014 #27604)
-#27603 := [def-axiom]: #27605
-#27726 := [unit-resolution #27603 #27725 #27672 #27640]: false
-#27642 := [lemma #27726]: #12180
-#28945 := (or #27098 #12189)
-#26985 := (f69 #3220 #3098)
-#27775 := (f146 #26985)
-#27778 := (f36 f297 #27775)
-#27786 := (= f37 #27778)
-#27776 := (f221 f297 #27775)
-#27777 := (= f1 #27776)
-#28363 := (or #27777 #27786)
-#28365 := (not #28363)
-#28146 := (f147 #26985)
-#28147 := (= f1 #28146)
-#28148 := (not #28147)
-#28100 := (f38 f297 #27775)
-#28093 := (= f1 #28100)
-#28145 := (not #28093)
-#28326 := (or #28145 #28148)
-#28340 := (not #28326)
-#27920 := (f23 #27039)
-#28266 := (= f25 #27920)
-#28322 := (not #28266)
-#28095 := (f24 #27775)
-#28096 := (f23 #28095)
-#28097 := (= f25 #28096)
-#28345 := (or #28097 #28322 #28340 #28365)
-#28437 := (not #28345)
-#28209 := (f221 f297 #3098)
-#28207 := (= f1 #28209)
-#28196 := (f36 f297 #3098)
-#28197 := (= f37 #28196)
-#28195 := (or #28197 #28207)
-#28275 := (not #28195)
-#28271 := (or #28275 #28266)
-#28273 := (not #28271)
-#28440 := (or #28273 #28437)
-#28443 := (not #28440)
-#3101 := (f35 f297 #3098)
-#12183 := (= f1 #3101)
-#18448 := (not #12183)
-#28446 := (or #18448 #28443)
-#28377 := (not #28446)
-#28367 := (iff #12189 #28377)
-#28434 := (or #28423 #28367)
-#27787 := (or #27786 #27777)
-#28094 := (not #27787)
-#27921 := (or #28148 #28145)
-#27919 := (not #27921)
-#27931 := (= #27920 f25)
-#27965 := (not #27931)
-#27966 := (or #27965 #27919 #28097 #28094)
-#28208 := (not #27966)
-#28276 := (or #27931 #28275)
-#28274 := (not #28276)
-#28277 := (or #28274 #28208)
-#28278 := (not #28277)
-#28279 := (or #18448 #28278)
-#28264 := (not #28279)
-#28265 := (iff #12189 #28264)
-#28435 := (or #28423 #28265)
-#28448 := (iff #28435 #28434)
-#28450 := (iff #28434 #28434)
-#28451 := [rewrite]: #28450
-#28348 := (iff #28265 #28367)
-#28378 := (iff #28264 #28377)
-#28368 := (iff #28279 #28446)
-#28444 := (iff #28278 #28443)
-#28441 := (iff #28277 #28440)
-#28438 := (iff #28208 #28437)
-#28360 := (iff #27966 #28345)
-#28341 := (or #28322 #28340 #28097 #28365)
-#28346 := (iff #28341 #28345)
-#28347 := [rewrite]: #28346
-#28343 := (iff #27966 #28341)
-#28339 := (iff #28094 #28365)
-#28364 := (iff #27787 #28363)
-#28359 := [rewrite]: #28364
-#28342 := [monotonicity #28359]: #28339
-#28361 := (iff #27919 #28340)
-#28331 := (iff #27921 #28326)
-#28332 := [rewrite]: #28331
-#28362 := [monotonicity #28332]: #28361
-#28281 := (iff #27965 #28322)
-#28267 := (iff #27931 #28266)
-#28268 := [rewrite]: #28267
-#28325 := [monotonicity #28268]: #28281
-#28344 := [monotonicity #28325 #28362 #28342]: #28343
-#28436 := [trans #28344 #28347]: #28360
-#28439 := [monotonicity #28436]: #28438
-#28320 := (iff #28274 #28273)
-#28284 := (iff #28276 #28271)
-#28263 := (or #28266 #28275)
-#28272 := (iff #28263 #28271)
-#28283 := [rewrite]: #28272
-#28269 := (iff #28276 #28263)
-#28270 := [monotonicity #28268]: #28269
-#28282 := [trans #28270 #28283]: #28284
-#28321 := [monotonicity #28282]: #28320
-#28442 := [monotonicity #28321 #28439]: #28441
-#28445 := [monotonicity #28442]: #28444
-#28369 := [monotonicity #28445]: #28368
-#28213 := [monotonicity #28369]: #28378
-#28349 := [monotonicity #28213]: #28348
-#28449 := [monotonicity #28349]: #28448
-#28456 := [trans #28449 #28451]: #28448
-#28447 := [quant-inst #3039 #3098]: #28435
-#28457 := [mp #28447 #28456]: #28434
-#28776 := [unit-resolution #28457 #22094]: #28367
-#28625 := (not #28367)
-#28779 := (or #28625 #28446)
-#28778 := [hypothesis]: #18454
-#28626 := (or #28625 #12189 #28446)
-#28627 := [def-axiom]: #28626
-#28777 := [unit-resolution #28627 #28778]: #28779
-#28780 := [unit-resolution #28777 #28776]: #28446
-#28816 := (or #28377 #28443)
-decl f26 :: (-> S20 S21 S1)
-decl f27 :: (-> S19 S20 S21)
-#24880 := (f127 #3044)
-#26182 := (f54 #3040 #24880)
-#26775 := (f27 f297 #26182)
-#27233 := (f26 #27145 #26775)
-#27234 := (= f1 #27233)
-#26776 := (f26 #26182 #26775)
-#28795 := (= #26776 #27233)
-#28792 := (= #27233 #26776)
-#28790 := (= #27145 #26182)
-#26189 := (= #3044 #26182)
+#11422 := (iff #2767 #11421)
+#11419 := (iff #2766 #11417)
+#11420 := [rewrite]: #11419
+#11423 := [quant-intro #11420]: #11422
+#11416 := [asserted]: #2767
+#11426 := [mp #11416 #11423]: #11421
+#18273 := [mp~ #11426 #18272]: #11421
+#23276 := [mp #18273 #23275]: #23271
+#25028 := (not #23271)
+#25089 := (or #25028 #25084)
+#25090 := [quant-inst #3040 #3043]: #25089
+#28876 := [unit-resolution #25090 #23276]: #25084
+#28878 := [symm #28876]: #28877
+#26873 := (= #26550 #25081)
+#26866 := (= #26146 #3044)
+#26153 := (= #3044 #26146)
 #3049 := (f59 #3044 #3040)
-#12109 := (= f1 #3049)
+#12073 := (= f1 #3049)
 decl f34 :: (-> S18 S1)
 #3056 := (f34 #3040)
-#12121 := (= f1 #3056)
-#3053 := (f23 #3040)
-#12115 := (= f25 #3053)
-#12118 := (not #12115)
-#3051 := (f35 f297 #3044)
-#12112 := (= f1 #3051)
-#12106 := (= f37 #3047)
-#3045 := (f38 f297 #3044)
-#12102 := (= f1 #3045)
-#14228 := (and #12102 #12106 #12109 #12112 #12118 #12121)
-decl f293 :: Int
-#3024 := f293
-#14284 := (* -1::Int f293)
-decl f89 :: Int
-#472 := f89
-#14285 := (+ f89 #14284)
-#14283 := (>= #14285 0::Int)
-#14281 := (>= f293 0::Int)
-#14288 := (and #14281 #14283)
-#14291 := (not #14288)
+#12085 := (= f1 #3056)
+#3051 := (f35 f298 #3044)
+#12076 := (= f1 #3051)
+decl f36 :: (-> S19 S20 S20)
+#3047 := (f36 f298 #3044)
+decl f37 :: S20
+#116 := f37
+#12070 := (= f37 #3047)
+decl f38 :: (-> S19 S20 S1)
+#3045 := (f38 f298 #3044)
+#12066 := (= f1 #3045)
+#14192 := (and #12066 #12070 #12073 #12076 #12082 #12085)
 decl f294 :: Int
-#3028 := f294
-#14270 := (* -1::Int f294)
-decl f87 :: Int
-#452 := f87
-#14271 := (+ f87 #14270)
-#14269 := (>= #14271 0::Int)
-#14267 := (>= f294 0::Int)
-#14274 := (and #14267 #14269)
-#14277 := (not #14274)
+#3024 := f294
+#14248 := (* -1::Int f294)
+decl f90 :: Int
+#472 := f90
+#14249 := (+ f90 #14248)
+#14247 := (>= #14249 0::Int)
+#14245 := (>= f294 0::Int)
+#14252 := (and #14245 #14247)
+#14255 := (not #14252)
 decl f295 :: Int
-#3032 := f295
-#14256 := (* -1::Int f295)
-#14257 := (+ f87 #14256)
-#14255 := (>= #14257 0::Int)
-#14253 := (>= f295 0::Int)
-#14260 := (and #14253 #14255)
-#14263 := (not #14260)
+#3028 := f295
+#14234 := (* -1::Int f295)
+decl f88 :: Int
+#452 := f88
+#14235 := (+ f88 #14234)
+#14233 := (>= #14235 0::Int)
+#14231 := (>= f295 0::Int)
+#14238 := (and #14231 #14233)
+#14241 := (not #14238)
+decl f296 :: Int
+#3032 := f296
+#14220 := (* -1::Int f296)
+#14221 := (+ f88 #14220)
+#14219 := (>= #14221 0::Int)
+#14217 := (>= f296 0::Int)
+#14224 := (and #14217 #14219)
+#14227 := (not #14224)
 #1085 := 1099511627776::Int
-#14241 := (>= f296 1099511627776::Int)
-#14231 := (not #14228)
-decl f299 :: (-> S34 Int)
+#14205 := (>= f297 1099511627776::Int)
+#14195 := (not #14192)
+decl f300 :: (-> S34 Int)
 #3070 := (:var 0 S34)
-#3071 := (f299 #3070)
+#3071 := (f300 #3070)
 #3072 := (pattern #3071)
-decl f300 :: Int
-#3073 := f300
-#14218 := (* -1::Int f300)
-#14219 := (+ #3071 #14218)
-#14217 := (>= #14219 0::Int)
-#14216 := (not #14217)
-#14222 := (forall (vars (?v0 S34)) (:pat #3072) #14216)
-#14225 := (not #14222)
-#13509 := (not #13508)
-#14072 := (and #3109 #13509)
-#14077 := (not #14072)
-#14060 := (+ f89 #14006)
-#14059 := (>= #14060 0::Int)
-#14063 := (and #14056 #14059)
-#14066 := (not #14063)
-#14047 := (+ f87 #13977)
-#14046 := (>= #14047 0::Int)
-#14050 := (and #13513 #14046)
-#14053 := (not #14050)
-#13538 := (+ f87 #13537)
-#14037 := (>= #13538 0::Int)
-#14040 := (and #14034 #14037)
-#14043 := (not #14040)
-#4514 := (* -1::Int f87)
-#4515 := (+ #202 #4514)
-#4516 := (<= #4515 0::Int)
-#4523 := (and #4202 #4516)
-#5738 := (not #4523)
-#14017 := (or #5738 #13994 #14008)
-#14022 := (forall (vars (?v0 Int)) #14017)
-#14025 := (not #14022)
-#13980 := (not #13979)
-#13986 := (and #12250 #13980)
-#13991 := (not #13986)
-#13831 := (not #13829)
-#13869 := (and #3173 #4202 #4516 #13831)
-#13874 := (exists (vars (?v0 Int)) #13869)
-#13852 := (or #5738 #13829 #13843)
-#13857 := (forall (vars (?v0 Int)) #13852)
-#13877 := (not #13857)
-#13883 := (or #13877 #13874)
-#13888 := (and #13857 #13883)
-#13518 := (and #13513 #13516)
-#13521 := (not #13518)
-decl f227 :: S1
-#2541 := f227
-#10960 := (= f1 f227)
-#12374 := (not #10960)
-#13915 := (or #12374 #12340 #12331 #12322 #12313 #13521 #13888)
-#13920 := (and #10960 #13915)
-#13945 := (or #13521 #13802 #13920)
-#13536 := (>= #13538 1::Int)
-#13625 := (and #13534 #13536)
-#13628 := (not #13625)
-#13595 := (not #13594)
-#13601 := (and #12643 #13595)
-#13581 := (or #5738 #13558 #13572)
-#13586 := (forall (vars (?v0 Int)) #13581)
-#13589 := (not #13586)
-#13606 := (or #13589 #13601)
-#13609 := (and #13586 #13606)
-#13612 := (or #13555 #13609)
-#13615 := (and #13550 #13612)
-#13544 := (and #13525 #13542)
-#13547 := (not #13544)
-#13643 := (or #12692 #13547 #13615 #13622 #13628)
-#13651 := (and #13534 #13536 #13643)
-#13527 := (and #13516 #13525)
-#13530 := (not #13527)
-#13762 := (or #12857 #12848 #13521 #13530 #13651 #13707)
-#12587 := (and #12575 #12584)
-#12785 := (not #12587)
-#13683 := (or #12785 #12776 #12767 #12758 #12740 #12731 #13656 #13530 #13651)
-#13691 := (and #12575 #12584 #13683)
-#12581 := (and #12575 #12578)
-#12797 := (not #12581)
-#13696 := (or #12797 #13691)
-#13702 := (and #12575 #12578 #13696)
-#13732 := (or #13521 #13702 #13708)
-#13767 := (and #13732 #13762)
-#13776 := (or #12785 #13521 #13767)
-#13784 := (and #12575 #12584 #13776)
-#13789 := (or #12797 #13784)
-#13795 := (and #12575 #12578 #13789)
-#13824 := (or #13521 #13795 #13801)
-#13950 := (and #13824 #13945)
-#12561 := (and #12555 #12558)
-#13024 := (not #12561)
+decl f301 :: Int
+#3073 := f301
+#14182 := (* -1::Int f301)
+#14183 := (+ #3071 #14182)
+#14181 := (>= #14183 0::Int)
+#14180 := (not #14181)
+#14186 := (forall (vars (?v0 S34)) (:pat #3072) #14180)
+#14189 := (not #14186)
+#13473 := (not #13472)
+#14036 := (and #3109 #13473)
+#14041 := (not #14036)
+#14024 := (+ f90 #13970)
+#14023 := (>= #14024 0::Int)
+#14027 := (and #14020 #14023)
+#14030 := (not #14027)
+#14011 := (+ f88 #13941)
+#14010 := (>= #14011 0::Int)
+#14014 := (and #13477 #14010)
+#14017 := (not #14014)
+#13502 := (+ f88 #13501)
+#14001 := (>= #13502 0::Int)
+#14004 := (and #13998 #14001)
+#14007 := (not #14004)
+#4494 := (* -1::Int f88)
+#4495 := (+ #202 #4494)
+#4496 := (<= #4495 0::Int)
+#4503 := (and #4202 #4496)
+#5712 := (not #4503)
+#13981 := (or #5712 #13958 #13972)
+#13986 := (forall (vars (?v0 Int)) #13981)
+#13989 := (not #13986)
+#13950 := (and #12214 #13944)
+#13955 := (not #13950)
+#13795 := (not #13793)
+#13833 := (and #3173 #4202 #4496 #13795)
+#13838 := (exists (vars (?v0 Int)) #13833)
+#13816 := (or #5712 #13793 #13807)
+#13821 := (forall (vars (?v0 Int)) #13816)
+#13841 := (not #13821)
+#13847 := (or #13841 #13838)
+#13852 := (and #13821 #13847)
+#13482 := (and #13477 #13480)
+#13485 := (not #13482)
+decl f228 :: S1
+#2541 := f228
+#10924 := (= f1 f228)
+#12338 := (not #10924)
+#13879 := (or #12338 #12304 #12295 #12286 #12277 #13485 #13852)
+#13884 := (and #10924 #13879)
+#13909 := (or #13485 #13766 #13884)
+#13500 := (>= #13502 1::Int)
+#13589 := (and #13498 #13500)
+#13592 := (not #13589)
+#13559 := (not #13558)
+#13565 := (and #12607 #13559)
+#13545 := (or #5712 #13522 #13536)
+#13550 := (forall (vars (?v0 Int)) #13545)
+#13553 := (not #13550)
+#13570 := (or #13553 #13565)
+#13573 := (and #13550 #13570)
+#13576 := (or #13519 #13573)
+#13579 := (and #13514 #13576)
+#13508 := (and #13489 #13506)
+#13511 := (not #13508)
+#13607 := (or #12656 #13511 #13579 #13586 #13592)
+#13615 := (and #13498 #13500 #13607)
+#13491 := (and #13480 #13489)
+#13494 := (not #13491)
+#13726 := (or #12821 #12812 #13485 #13494 #13615 #13671)
+#12551 := (and #12539 #12548)
+#12749 := (not #12551)
+#13647 := (or #12749 #12740 #12731 #12722 #12704 #12695 #13620 #13494 #13615)
+#13655 := (and #12539 #12548 #13647)
+#12545 := (and #12539 #12542)
+#12761 := (not #12545)
+#13660 := (or #12761 #13655)
+#13666 := (and #12539 #12542 #13660)
+#13696 := (or #13485 #13666 #13672)
+#13731 := (and #13696 #13726)
+#13740 := (or #12749 #13485 #13731)
+#13748 := (and #12539 #12548 #13740)
+#13753 := (or #12761 #13748)
+#13759 := (and #12539 #12542 #13753)
+#13788 := (or #13485 #13759 #13765)
+#13914 := (and #13788 #13909)
+#12525 := (and #12519 #12522)
+#12988 := (not #12525)
 decl f66 :: (-> S19 S1)
-#3067 := (f66 f297)
-#12145 := (= f1 #3067)
-#12264 := (and #12145 #12258)
-#12402 := (not #12264)
-#14143 := (or #12402 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13950 #13991 #14025 #14031 #14043 #14053 #14066 #14077)
-#14151 := (and #3109 #13509 #14143)
-#13497 := (or #5738 #13475 #13487)
-#13502 := (forall (vars (?v0 Int)) #13497)
-#13505 := (not #13502)
-#14156 := (or #13505 #14151)
-#14159 := (and #13502 #14156)
-#14162 := (or #13472 #14159)
-#14165 := (and #13469 #14162)
-#12192 := (and #12180 #12189)
-#13276 := (not #12192)
-#14186 := (or #13267 #13276 #13258 #13249 #13240 #14165)
-#14194 := (and #12180 #12189 #14186)
-#12186 := (and #12180 #12183)
-#13288 := (not #12186)
-#14199 := (or #13288 #14194)
-#14205 := (and #12180 #12183 #14199)
-decl f211 :: (-> S19 S20 S20 S31 S1)
-decl f305 :: S31
-#3095 := f305
-#3096 := (f211 f297 #3044 #3044 f305)
-#12177 := (= f1 #3096)
-#13300 := (not #12177)
-#14210 := (or #13300 #14205)
-#14213 := (and #12177 #14210)
-#13443 := (+ f87 #13442)
-#13441 := (>= #13443 0::Int)
-#13439 := (>= f296 0::Int)
-#13446 := (and #13439 #13441)
-#13449 := (not #13446)
-decl f304 :: (-> Int S20 S1)
-decl f303 :: Int
-#3084 := f303
-#3087 := (f304 f303 #62)
+#3067 := (f66 f298)
+#12109 := (= f1 #3067)
+#12228 := (and #12109 #12222)
+#12366 := (not #12228)
+#14107 := (or #12366 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #13914 #13955 #13989 #13995 #14007 #14017 #14030 #14041)
+#14115 := (and #3109 #13473 #14107)
+#13461 := (or #5712 #13439 #13451)
+#13466 := (forall (vars (?v0 Int)) #13461)
+#13469 := (not #13466)
+#14120 := (or #13469 #14115)
+#14123 := (and #13466 #14120)
+#14126 := (or #13436 #14123)
+#14129 := (and #13433 #14126)
+#12156 := (and #12144 #12153)
+#13240 := (not #12156)
+#14150 := (or #13231 #13240 #13222 #13213 #13204 #14129)
+#14158 := (and #12144 #12153 #14150)
+#12150 := (and #12144 #12147)
+#13252 := (not #12150)
+#14163 := (or #13252 #14158)
+#14169 := (and #12144 #12147 #14163)
+#14174 := (or #13264 #14169)
+#14177 := (and #12141 #14174)
+#13407 := (+ f88 #13406)
+#13405 := (>= #13407 0::Int)
+#13403 := (>= f297 0::Int)
+#13410 := (and #13403 #13405)
+#13413 := (not #13410)
+decl f305 :: (-> Int S20 S1)
+#62 := (:var 0 S20)
+decl f304 :: Int
+#3084 := f304
+#3087 := (f305 f304 #62)
 #3088 := (pattern #3087)
-#12163 := (= f1 #3087)
-#12169 := (not #12163)
-#12174 := (forall (vars (?v0 S20)) (:pat #3088) #12169)
-#13321 := (not #12174)
-decl f292 :: S17
-#3020 := f292
-#3082 := (f301 f297 f292 f290 f296 f16)
-#12160 := (= f1 #3082)
-#13339 := (not #12160)
-#3079 := (f302 f297 f292 f291 #3042 #51)
-#12154 := (= f1 #3079)
-#3077 := (f301 f297 f292 f291 #3076 #51)
-#12151 := (= f1 #3077)
-#12157 := (and #12151 #12154)
-#13348 := (not #12157)
-#3065 := (f213 f292 f297)
-#12142 := (= f1 #3065)
-#12148 := (and #12142 #12145)
-#13366 := (not #12148)
-decl f214 :: (-> S19 S1)
-#3063 := (f214 f297)
-#12139 := (= f1 #3063)
-#13375 := (not #12139)
-decl f184 :: (-> S19 Int)
-#3085 := (f184 f297)
-#3086 := (= f303 #3085)
-#13330 := (not #3086)
-#14336 := (or #13330 #13375 #13366 #13348 #13339 #13321 #13449 #13508 #14213 #14225 #14231 #14241 #14263 #14277 #14291)
-#14341 := (not #14336)
+#12127 := (= f1 #3087)
+#12133 := (not #12127)
+#12138 := (forall (vars (?v0 S20)) (:pat #3088) #12133)
+#13285 := (not #12138)
+decl f293 :: S17
+#3020 := f293
+#3082 := (f302 f298 f293 f291 f297 f16)
+#12124 := (= f1 #3082)
+#13303 := (not #12124)
+#3079 := (f303 f298 f293 f292 #3042 #51)
+#12118 := (= f1 #3079)
+#3077 := (f302 f298 f293 f292 #3076 #51)
+#12115 := (= f1 #3077)
+#12121 := (and #12115 #12118)
+#13312 := (not #12121)
+#3065 := (f214 f293 f298)
+#12106 := (= f1 #3065)
+#12112 := (and #12106 #12109)
+#13330 := (not #12112)
+decl f215 :: (-> S19 S1)
+#3063 := (f215 f298)
+#12103 := (= f1 #3063)
+#13339 := (not #12103)
+decl f185 :: (-> S19 Int)
+#3085 := (f185 f298)
+#3086 := (= f304 #3085)
+#13294 := (not #3086)
+#14300 := (or #13294 #13339 #13330 #13312 #13303 #13285 #13413 #13472 #14177 #14189 #14195 #14205 #14227 #14241 #14255)
+#14305 := (not #14300)
 #1 := true
-#3168 := (< #202 f296)
+#3168 := (< #202 f297)
 #3174 := (and #3168 #3173)
-#454 := (<= #202 f87)
+#454 := (<= #202 f88)
 #3175 := (and #454 #3174)
 #327 := (<= 0::Int #202)
 #3176 := (and #327 #3175)
 #3177 := (exists (vars (?v0 Int)) #3176)
 #3178 := (and #3177 true)
-#3169 := (<= #3124 f313)
+#3169 := (<= #3124 f314)
 #3170 := (implies #3168 #3169)
 #455 := (and #327 #454)
 #3171 := (implies #455 #3170)
 #3172 := (forall (vars (?v0 Int)) #3171)
 #3179 := (implies #3172 #3178)
 #3180 := (and #3172 #3179)
-#3167 := (= f313 f307)
+#3167 := (= f314 f308)
 #3181 := (implies #3167 #3180)
-#3165 := (= f312 f308)
+#3165 := (= f313 f309)
 #3182 := (implies #3165 #3181)
-#3163 := (= f311 f309)
+#3163 := (= f312 f310)
 #3183 := (implies #3163 #3182)
-#3161 := (= f310 f307)
+#3161 := (= f311 f308)
 #3184 := (implies #3161 #3183)
-#3136 := (<= 0::Int f308)
-#3143 := (<= 1::Int f309)
+#3136 := (<= 0::Int f309)
+#3143 := (<= 1::Int f310)
 #3144 := (and #3143 #3136)
 #3185 := (implies #3144 #3184)
 #3186 := (implies #3144 #3185)
 #3187 := (implies #3144 #3186)
-#2542 := (= f227 f1)
+#2542 := (= f228 f1)
 #3188 := (implies #2542 #3187)
 #3189 := (and #2542 #3188)
 #3190 := (implies #3144 #3189)
 #3191 := (implies #3144 #3190)
 #3348 := (implies #3144 #3191)
 #3349 := (implies #3144 #3348)
-#3347 := (<= f296 f309)
+#3347 := (<= f297 f310)
 #3350 := (implies #3347 #3349)
 #3351 := (implies #3144 #3350)
-#3300 := (= #3299 f315)
-#3297 := (< f316 f296)
+#3300 := (= #3299 f316)
+#3297 := (< f317 f297)
 #3301 := (and #3297 #3300)
 #3302 := (and #3301 true)
-#3293 := (<= #3124 f315)
-#3292 := (< #202 f317)
+#3293 := (<= #3124 f316)
+#3292 := (< #202 f318)
 #3294 := (implies #3292 #3293)
 #3295 := (implies #455 #3294)
 #3296 := (forall (vars (?v0 Int)) #3295)
 #3303 := (implies #3296 #3302)
 #3304 := (and #3296 #3303)
-#3291 := (<= f317 f296)
+#3291 := (<= f318 f297)
 #3305 := (implies #3291 #3304)
 #3306 := (and #3291 #3305)
-#3279 := (<= 0::Int f316)
-#3289 := (<= 2::Int f317)
+#3279 := (<= 0::Int f317)
+#3289 := (<= 2::Int f318)
 #3290 := (and #3289 #3279)
 #3307 := (implies #3290 #3306)
 #3288 := (= #3287 f1)
 #3308 := (implies #3288 #3307)
-#3281 := (+ f309 1::Int)
-#3286 := (= f317 #3281)
+#3281 := (+ f310 1::Int)
+#3286 := (= f318 #3281)
 #3309 := (implies #3286 #3308)
-#3283 := (<= #3281 f87)
+#3283 := (<= #3281 f88)
 #3282 := (<= 0::Int #3281)
 #3284 := (and #3282 #3283)
 #3310 := (implies #3284 #3309)
 #3311 := (and #3284 #3310)
 #3280 := (and #3143 #3279)
 #3312 := (implies #3280 #3311)
-#3329 := (= f316 f308)
+#3329 := (= f317 f309)
 #3330 := (implies #3329 #3312)
-#3328 := (= f315 f307)
+#3328 := (= f316 f308)
 #3331 := (implies #3328 #3330)
 #3332 := (implies #3144 #3331)
 #3333 := (implies #3144 #3332)
 #3334 := (implies #3144 #3333)
-#3327 := (<= #3266 f307)
+#3327 := (<= #3266 f308)
 #3335 := (implies #3327 #3334)
 #3336 := (implies #3144 #3335)
-#3278 := (= f316 f309)
+#3278 := (= f317 f310)
 #3313 := (implies #3278 #3312)
-#3276 := (= f315 f314)
+#3276 := (= f316 f315)
 #3314 := (implies #3276 #3313)
 #3274 := (and #3143 #3143)
 #3315 := (implies #3274 #3314)
@@ -1512,7 +760,7 @@
 #3316 := (implies #3273 #3315)
 #3271 := (= #3270 f1)
 #3317 := (implies #3271 #3316)
-#3269 := (= f314 #3266)
+#3269 := (= f315 #3266)
 #3318 := (implies #3269 #3317)
 #3264 := (= #3263 f1)
 #3259 := (= #3258 f1)
@@ -1525,7 +773,7 @@
 #3322 := (and #3262 #3321)
 #3323 := (implies #3144 #3322)
 #3324 := (implies #3144 #3323)
-#3267 := (< f307 #3266)
+#3267 := (< f308 #3266)
 #3325 := (implies #3267 #3324)
 #3326 := (implies #3144 #3325)
 #3337 := (and #3326 #3336)
@@ -1536,14 +784,16 @@
 #3342 := (and #3262 #3341)
 #3343 := (implies #3144 #3342)
 #3344 := (implies #3144 #3343)
-#3256 := (< f309 f296)
+#3256 := (< f310 f297)
 #3345 := (implies #3256 #3344)
 #3346 := (implies #3144 #3345)
 #3352 := (and #3346 #3351)
 #3353 := (implies #3144 #3352)
 decl f52 :: (-> S19 S27)
-#3197 := (f52 f297)
+#3197 := (f52 f298)
 #3254 := (= #3197 #3197)
+decl f70 :: (-> S19 S28)
+#3220 := (f70 f298)
 #3253 := (= #3220 #3220)
 #3255 := (and #3253 #3254)
 #3354 := (implies #3255 #3353)
@@ -1564,8 +814,8 @@
 #3159 := (and #3158 #3068)
 #3360 := (implies #3159 #3359)
 #3233 := (= #3232 f1)
-decl f183 :: (-> S19 S20 Int)
-#3228 := (f183 f297 #62)
+decl f184 :: (-> S19 S20 Int)
+#3228 := (f184 f298 #62)
 #3229 := (pattern #3228)
 #3230 := (<= #3228 #3228)
 #3231 := (forall (vars (?v0 S20)) (:pat #3229) #3230)
@@ -1573,9 +823,10 @@
 #3227 := (<= #3085 #3085)
 #3235 := (and #3227 #3234)
 #3361 := (implies #3235 #3360)
+decl f69 :: (-> S28 S20 S29)
 #3221 := (f69 #3220 #62)
 #3222 := (pattern #3221)
-#3210 := (f79 f297 #62)
+#3210 := (f79 f298 #62)
 #3211 := (= #3210 f1)
 #3223 := (= #3221 #3221)
 #3224 := (and #3223 #3211)
@@ -1592,7 +843,7 @@
 #3237 := (and #3219 #3236)
 decl f30 :: (-> S24 S20 Int)
 decl f31 :: (-> S19 S24)
-#3207 := (f31 f297)
+#3207 := (f31 f298)
 #3208 := (f30 #3207 #62)
 #3209 := (pattern #3208)
 #3212 := (= #3208 #3208)
@@ -1600,12 +851,12 @@
 #3214 := (implies #3211 #3213)
 #3215 := (forall (vars (?v0 S20)) (:pat #3209) #3214)
 #3238 := (and #3215 #3237)
-decl f272 :: S23
-#2903 := f272
-#3200 := (f36 f297 #62)
+decl f273 :: S23
+#2903 := f273
+#3200 := (f36 f298 #62)
 #3201 := (f24 #3200)
 #3202 := (f23 #3201)
-#3203 := (= #3202 f272)
+#3203 := (= #3202 f273)
 #3204 := (not #3203)
 #3205 := (implies #3204 #3204)
 #3206 := (forall (vars (?v0 S20)) (:pat #3199) #3205)
@@ -1622,43 +873,43 @@
 #3196 := (implies #3144 #3195)
 #3366 := (and #3196 #3365)
 #3367 := (implies #3144 #3366)
-#3154 := (= #3153 f307)
-#3151 := (< f308 f296)
+#3154 := (= #3153 f308)
+#3151 := (< f309 f297)
 #3155 := (and #3151 #3154)
 #3368 := (implies #3155 #3367)
-#3147 := (<= #3124 f307)
-#3146 := (< #202 f309)
+#3147 := (<= #3124 f308)
+#3146 := (< #202 f310)
 #3148 := (implies #3146 #3147)
 #3149 := (implies #455 #3148)
 #3150 := (forall (vars (?v0 Int)) #3149)
 #3369 := (implies #3150 #3368)
-#3145 := (<= f309 f296)
+#3145 := (<= f310 f297)
 #3370 := (implies #3145 #3369)
 #3371 := (implies #3144 #3370)
-#3141 := (<= f309 f87)
-#3140 := (<= 0::Int f309)
+#3141 := (<= f310 f88)
+#3140 := (<= 0::Int f310)
 #3142 := (and #3140 #3141)
 #3372 := (implies #3142 #3371)
-#3137 := (<= f308 f87)
+#3137 := (<= f309 f88)
 #3138 := (and #3136 #3137)
 #3373 := (implies #3138 #3372)
-#3133 := (<= f307 f89)
-#3132 := (<= 0::Int f307)
+#3133 := (<= f308 f90)
+#3132 := (<= 0::Int f308)
 #3134 := (and #3132 #3133)
 #3374 := (implies #3134 #3373)
-#3129 := (= #3108 f306)
-#3038 := (< 0::Int f296)
+#3129 := (= #3108 f307)
+#3038 := (< 0::Int f297)
 #3130 := (and #3038 #3129)
 #3375 := (implies #3130 #3374)
 #3376 := (and #3130 #3375)
-#3125 := (<= #3124 f306)
+#3125 := (<= #3124 f307)
 #3122 := (< #202 1::Int)
 #3126 := (implies #3122 #3125)
 #3127 := (implies #455 #3126)
 #3128 := (forall (vars (?v0 Int)) #3127)
 #3377 := (implies #3128 #3376)
 #3378 := (and #3128 #3377)
-#3121 := (<= 1::Int f296)
+#3121 := (<= 1::Int f297)
 #3379 := (implies #3121 #3378)
 #3380 := (and #3121 #3379)
 #3117 := (<= 0::Int 0::Int)
@@ -1686,8 +937,8 @@
 #3097 := (= #3096 f1)
 #3390 := (implies #3097 #3389)
 #3391 := (and #3097 #3390)
-#3093 := (<= f296 f87)
-#3092 := (<= 0::Int f296)
+#3093 := (<= f297 f88)
+#3092 := (<= 0::Int f297)
 #3094 := (and #3092 #3093)
 #3392 := (implies #3094 #3391)
 #3089 := (= #3087 f1)
@@ -1701,7 +952,7 @@
 #3078 := (= #3077 f1)
 #3081 := (and #3078 #3080)
 #3396 := (implies #3081 #3395)
-#3074 := (< #3071 f300)
+#3074 := (< #3071 f301)
 #3075 := (forall (vars (?v0 S34)) (:pat #3072) #3074)
 #3397 := (implies #3075 #3396)
 #3066 := (= #3065 f1)
@@ -1723,2278 +974,2252 @@
 #3062 := (and #3046 #3061)
 #3400 := (implies #3062 #3399)
 #3401 := (implies #3038 #3400)
-#3037 := (< f296 1099511627776::Int)
+#3037 := (< f297 1099511627776::Int)
 #3402 := (implies #3037 #3401)
-#3034 := (<= f295 f87)
-#3033 := (<= 0::Int f295)
+#3034 := (<= f296 f88)
+#3033 := (<= 0::Int f296)
 #3035 := (and #3033 #3034)
 #3403 := (implies #3035 #3402)
-#3030 := (<= f294 f87)
-#3029 := (<= 0::Int f294)
+#3030 := (<= f295 f88)
+#3029 := (<= 0::Int f295)
 #3031 := (and #3029 #3030)
 #3404 := (implies #3031 #3403)
-#3026 := (<= f293 f89)
-#3025 := (<= 0::Int f293)
+#3026 := (<= f294 f90)
+#3025 := (<= 0::Int f294)
 #3027 := (and #3025 #3026)
 #3405 := (implies #3027 #3404)
 #3406 := (not #3405)
-#14344 := (iff #3406 #14341)
-#12281 := (not #3168)
-#12282 := (or #12281 #3169)
-#5729 := (not #455)
-#12288 := (or #5729 #12282)
-#12293 := (forall (vars (?v0 Int)) #12288)
-#12301 := (not #12293)
-#12302 := (or #3177 #12301)
-#12307 := (and #12293 #12302)
-#12314 := (or #12313 #12307)
-#12323 := (or #12322 #12314)
-#12332 := (or #12331 #12323)
-#12341 := (or #12340 #12332)
-#12232 := (and #3136 #3143)
-#12349 := (not #12232)
-#12350 := (or #12349 #12341)
-#12358 := (or #12349 #12350)
-#12366 := (or #12349 #12358)
-#12375 := (or #12374 #12366)
-#12380 := (and #10960 #12375)
-#12386 := (or #12349 #12380)
-#12394 := (or #12349 #12386)
-#12973 := (or #12349 #12394)
-#12981 := (or #12349 #12973)
-#12989 := (not #3347)
-#12990 := (or #12989 #12981)
-#12998 := (or #12349 #12990)
-#12646 := (and #3297 #12643)
-#12628 := (not #3292)
-#12629 := (or #12628 #3293)
-#12635 := (or #5729 #12629)
-#12640 := (forall (vars (?v0 Int)) #12635)
-#12659 := (not #12640)
-#12660 := (or #12659 #12646)
-#12665 := (and #12640 #12660)
-#12671 := (not #3291)
-#12672 := (or #12671 #12665)
-#12677 := (and #3291 #12672)
-#12625 := (and #3279 #3289)
-#12683 := (not #12625)
-#12684 := (or #12683 #12677)
-#12693 := (or #12692 #12684)
-#12607 := (+ 1::Int f309)
-#12619 := (= f317 #12607)
-#12701 := (not #12619)
-#12702 := (or #12701 #12693)
-#12613 := (<= #12607 f87)
-#12610 := (<= 0::Int #12607)
-#12616 := (and #12610 #12613)
-#12710 := (not #12616)
-#12711 := (or #12710 #12702)
-#12716 := (and #12616 #12711)
-#12722 := (not #3280)
-#12723 := (or #12722 #12716)
-#12849 := (or #12723 #12848)
-#12858 := (or #12857 #12849)
-#12866 := (or #12349 #12858)
-#12874 := (or #12349 #12866)
-#12882 := (or #12349 #12874)
-#12890 := (not #3327)
-#12891 := (or #12890 #12882)
-#12899 := (or #12349 #12891)
+#14308 := (iff #3406 #14305)
+#12245 := (not #3168)
+#12246 := (or #12245 #3169)
+#5703 := (not #455)
+#12252 := (or #5703 #12246)
+#12257 := (forall (vars (?v0 Int)) #12252)
+#12265 := (not #12257)
+#12266 := (or #3177 #12265)
+#12271 := (and #12257 #12266)
+#12278 := (or #12277 #12271)
+#12287 := (or #12286 #12278)
+#12296 := (or #12295 #12287)
+#12305 := (or #12304 #12296)
+#12196 := (and #3136 #3143)
+#12313 := (not #12196)
+#12314 := (or #12313 #12305)
+#12322 := (or #12313 #12314)
+#12330 := (or #12313 #12322)
+#12339 := (or #12338 #12330)
+#12344 := (and #10924 #12339)
+#12350 := (or #12313 #12344)
+#12358 := (or #12313 #12350)
+#12937 := (or #12313 #12358)
+#12945 := (or #12313 #12937)
+#12953 := (not #3347)
+#12954 := (or #12953 #12945)
+#12962 := (or #12313 #12954)
+#12610 := (and #3297 #12607)
+#12592 := (not #3292)
+#12593 := (or #12592 #3293)
+#12599 := (or #5703 #12593)
+#12604 := (forall (vars (?v0 Int)) #12599)
+#12623 := (not #12604)
+#12624 := (or #12623 #12610)
+#12629 := (and #12604 #12624)
+#12635 := (not #3291)
+#12636 := (or #12635 #12629)
+#12641 := (and #3291 #12636)
+#12589 := (and #3279 #3289)
+#12647 := (not #12589)
+#12648 := (or #12647 #12641)
+#12657 := (or #12656 #12648)
+#12571 := (+ 1::Int f310)
+#12583 := (= f318 #12571)
+#12665 := (not #12583)
+#12666 := (or #12665 #12657)
+#12577 := (<= #12571 f88)
+#12574 := (<= 0::Int #12571)
+#12580 := (and #12574 #12577)
+#12674 := (not #12580)
+#12675 := (or #12674 #12666)
+#12680 := (and #12580 #12675)
+#12686 := (not #3280)
+#12687 := (or #12686 #12680)
+#12813 := (or #12687 #12812)
+#12822 := (or #12821 #12813)
+#12830 := (or #12313 #12822)
+#12838 := (or #12313 #12830)
+#12846 := (or #12313 #12838)
+#12854 := (not #3327)
+#12855 := (or #12854 #12846)
+#12863 := (or #12313 #12855)
+#12696 := (or #12695 #12687)
+#12705 := (or #12704 #12696)
+#12713 := (not #3143)
+#12714 := (or #12713 #12705)
+#12723 := (or #12722 #12714)
 #12732 := (or #12731 #12723)
 #12741 := (or #12740 #12732)
-#12749 := (not #3143)
 #12750 := (or #12749 #12741)
-#12759 := (or #12758 #12750)
-#12768 := (or #12767 #12759)
-#12777 := (or #12776 #12768)
-#12786 := (or #12785 #12777)
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+#13898 := (iff #12937 #13897)
+#13895 := (iff #12358 #13894)
+#13892 := (iff #12350 #13891)
+#13885 := (iff #12344 #13884)
+#13882 := (iff #12339 #13879)
+#13855 := (or #12277 #13852)
+#13858 := (or #12286 #13855)
+#13861 := (or #12295 #13858)
+#13864 := (or #12304 #13861)
+#13867 := (or #13485 #13864)
+#13870 := (or #13485 #13867)
+#13873 := (or #13485 #13870)
+#13876 := (or #12338 #13873)
+#13880 := (iff #13876 #13879)
+#13881 := [rewrite]: #13880
+#13877 := (iff #12339 #13876)
+#13874 := (iff #12330 #13873)
+#13871 := (iff #12322 #13870)
+#13868 := (iff #12314 #13867)
+#13865 := (iff #12305 #13864)
+#13862 := (iff #12296 #13861)
+#13859 := (iff #12287 #13858)
+#13856 := (iff #12278 #13855)
+#13853 := (iff #12271 #13852)
+#13850 := (iff #12266 #13847)
+#13844 := (or #13838 #13841)
+#13848 := (iff #13844 #13847)
+#13849 := [rewrite]: #13848
+#13845 := (iff #12266 #13844)
+#13842 := (iff #12265 #13841)
+#13822 := (iff #12257 #13821)
+#13819 := (iff #12252 #13816)
+#13810 := (or #13793 #13807)
+#13813 := (or #5712 #13810)
+#13817 := (iff #13813 #13816)
+#13818 := [rewrite]: #13817
+#13814 := (iff #12252 #13813)
+#13811 := (iff #12246 #13810)
+#13808 := (iff #3169 #13807)
+#13809 := [rewrite]: #13808
+#13803 := (iff #12245 #13793)
+#13798 := (not #13795)
+#13801 := (iff #13798 #13793)
+#13802 := [rewrite]: #13801
+#13799 := (iff #12245 #13798)
+#13796 := (iff #3168 #13795)
+#13797 := [rewrite]: #13796
+#13800 := [monotonicity #13797]: #13799
+#13804 := [trans #13800 #13802]: #13803
+#13812 := [monotonicity #13804 #13809]: #13811
+#5713 := (iff #5703 #5712)
+#4504 := (iff #455 #4503)
+#4497 := (iff #454 #4496)
+#4498 := [rewrite]: #4497
 #4200 := (iff #327 #4202)
 #4201 := [rewrite]: #4200
-#4525 := [monotonicity #4201 #4518]: #4524
-#5740 := [monotonicity #4525]: #5739
-#13851 := [monotonicity #5740 #13848]: #13850
-#13856 := [trans #13851 #13854]: #13855
-#13859 := [quant-intro #13856]: #13858
-#13879 := [monotonicity #13859]: #13878
-#13875 := (iff #3177 #13874)
-#13872 := (iff #3176 #13869)
-#13860 := (and #13831 #3173)
-#13863 := (and #4516 #13860)
-#13866 := (and #4202 #13863)
-#13870 := (iff #13866 #13869)
-#13871 := [rewrite]: #13870
-#13867 := (iff #3176 #13866)
-#13864 := (iff #3175 #13863)
-#13861 := (iff #3174 #13860)
-#13862 := [monotonicity #13833]: #13861
-#13865 := [monotonicity #4518 #13862]: #13864
-#13868 := [monotonicity #4201 #13865]: #13867
-#13873 := [trans #13868 #13871]: #13872
-#13876 := [quant-intro #13873]: #13875
-#13882 := [monotonicity #13876 #13879]: #13881
-#13887 := [trans #13882 #13885]: #13886
-#13890 := [monotonicity #13859 #13887]: #13889
-#13893 := [monotonicity #13890]: #13892
-#13896 := [monotonicity #13893]: #13895
-#13899 := [monotonicity #13896]: #13898
-#13902 := [monotonicity #13899]: #13901
-#13522 := (iff #12349 #13521)
-#13519 := (iff #12232 #13518)
-#13515 := (iff #3143 #13516)
-#13517 := [rewrite]: #13515
-#13512 := (iff #3136 #13513)
-#13514 := [rewrite]: #13512
-#13520 := [monotonicity #13514 #13517]: #13519
-#13523 := [monotonicity #13520]: #13522
-#13905 := [monotonicity #13523 #13902]: #13904
-#13908 := [monotonicity #13523 #13905]: #13907
-#13911 := [monotonicity #13523 #13908]: #13910
-#13914 := [monotonicity #13911]: #13913
-#13919 := [trans #13914 #13917]: #13918
-#13922 := [monotonicity #13919]: #13921
-#13929 := [monotonicity #13523 #13922]: #13928
-#13932 := [monotonicity #13523 #13929]: #13931
-#13935 := [monotonicity #13523 #13932]: #13934
-#13938 := [monotonicity #13523 #13935]: #13937
-#13925 := (iff #12989 #13802)
-#13923 := (iff #3347 #13801)
-#13924 := [rewrite]: #13923
-#13926 := [monotonicity #13924]: #13925
-#13941 := [monotonicity #13926 #13938]: #13940
-#13944 := [monotonicity #13523 #13941]: #13943
-#13949 := [trans #13944 #13947]: #13948
-#13827 := (iff #12965 #13824)
-#13812 := (or #13521 #13795)
-#13815 := (or #13521 #13812)
-#13818 := (or #13801 #13815)
-#13821 := (or #13521 #13818)
-#13825 := (iff #13821 #13824)
-#13826 := [rewrite]: #13825
-#13822 := (iff #12965 #13821)
-#13819 := (iff #12957 #13818)
-#13816 := (iff #12948 #13815)
-#13813 := (iff #12940 #13812)
-#13798 := (iff #12934 #13795)
-#13792 := (and #12581 #13789)
-#13796 := (iff #13792 #13795)
-#13797 := [rewrite]: #13796
-#13793 := (iff #12934 #13792)
-#13790 := (iff #12929 #13789)
-#13787 := (iff #12923 #13784)
-#13781 := (and #12587 #13776)
-#13785 := (iff #13781 #13784)
-#13786 := [rewrite]: #13785
-#13782 := (iff #12923 #13781)
-#13779 := (iff #12918 #13776)
-#13770 := (or #13521 #13767)
-#13773 := (or #12785 #13770)
-#13777 := (iff #13773 #13776)
-#13778 := [rewrite]: #13777
-#13774 := (iff #12918 #13773)
-#13771 := (iff #12910 #13770)
-#13768 := (iff #12904 #13767)
-#13765 := (iff #12899 #13762)
-#13659 := (or #13530 #13651)
-#13741 := (or #13659 #12848)
-#13744 := (or #12857 #13741)
-#13747 := (or #13521 #13744)
-#13750 := (or #13521 #13747)
-#13753 := (or #13521 #13750)
-#13756 := (or #13707 #13753)
-#13759 := (or #13521 #13756)
-#13763 := (iff #13759 #13762)
-#13764 := [rewrite]: #13763
-#13760 := (iff #12899 #13759)
-#13757 := (iff #12891 #13756)
-#13754 := (iff #12882 #13753)
-#13751 := (iff #12874 #13750)
-#13748 := (iff #12866 #13747)
-#13745 := (iff #12858 #13744)
-#13742 := (iff #12849 #13741)
-#13660 := (iff #12723 #13659)
-#13654 := (iff #12716 #13651)
-#13648 := (and #13625 #13643)
-#13652 := (iff #13648 #13651)
-#13653 := [rewrite]: #13652
-#13649 := (iff #12716 #13648)
-#13646 := (iff #12711 #13643)
-#13631 := (or #13547 #13615)
-#13634 := (or #12692 #13631)
-#13637 := (or #13622 #13634)
-#13640 := (or #13628 #13637)
-#13644 := (iff #13640 #13643)
-#13645 := [rewrite]: #13644
-#13641 := (iff #12711 #13640)
-#13638 := (iff #12702 #13637)
-#13635 := (iff #12693 #13634)
-#13632 := (iff #12684 #13631)
-#13616 := (iff #12677 #13615)
-#13613 := (iff #12672 #13612)
-#13610 := (iff #12665 #13609)
-#13607 := (iff #12660 #13606)
-#13604 := (iff #12646 #13601)
-#13598 := (and #13595 #12643)
-#13602 := (iff #13598 #13601)
-#13603 := [rewrite]: #13602
-#13599 := (iff #12646 #13598)
-#13596 := (iff #3297 #13595)
-#13597 := [rewrite]: #13596
-#13600 := [monotonicity #13597]: #13599
-#13605 := [trans #13600 #13603]: #13604
-#13590 := (iff #12659 #13589)
-#13587 := (iff #12640 #13586)
-#13584 := (iff #12635 #13581)
-#13575 := (or #13558 #13572)
-#13578 := (or #5738 #13575)
-#13582 := (iff #13578 #13581)
-#13583 := [rewrite]: #13582
-#13579 := (iff #12635 #13578)
-#13576 := (iff #12629 #13575)
-#13573 := (iff #3293 #13572)
-#13574 := [rewrite]: #13573
-#13568 := (iff #12628 #13558)
-#13560 := (not #13558)
-#13563 := (not #13560)
-#13566 := (iff #13563 #13558)
+#4505 := [monotonicity #4201 #4498]: #4504
+#5714 := [monotonicity #4505]: #5713
+#13815 := [monotonicity #5714 #13812]: #13814
+#13820 := [trans #13815 #13818]: #13819
+#13823 := [quant-intro #13820]: #13822
+#13843 := [monotonicity #13823]: #13842
+#13839 := (iff #3177 #13838)
+#13836 := (iff #3176 #13833)
+#13824 := (and #13795 #3173)
+#13827 := (and #4496 #13824)
+#13830 := (and #4202 #13827)
+#13834 := (iff #13830 #13833)
+#13835 := [rewrite]: #13834
+#13831 := (iff #3176 #13830)
+#13828 := (iff #3175 #13827)
+#13825 := (iff #3174 #13824)
+#13826 := [monotonicity #13797]: #13825
+#13829 := [monotonicity #4498 #13826]: #13828
+#13832 := [monotonicity #4201 #13829]: #13831
+#13837 := [trans #13832 #13835]: #13836
+#13840 := [quant-intro #13837]: #13839
+#13846 := [monotonicity #13840 #13843]: #13845
+#13851 := [trans #13846 #13849]: #13850
+#13854 := [monotonicity #13823 #13851]: #13853
+#13857 := [monotonicity #13854]: #13856
+#13860 := [monotonicity #13857]: #13859
+#13863 := [monotonicity #13860]: #13862
+#13866 := [monotonicity #13863]: #13865
+#13486 := (iff #12313 #13485)
+#13483 := (iff #12196 #13482)
+#13479 := (iff #3143 #13480)
+#13481 := [rewrite]: #13479
+#13476 := (iff #3136 #13477)
+#13478 := [rewrite]: #13476
+#13484 := [monotonicity #13478 #13481]: #13483
+#13487 := [monotonicity #13484]: #13486
+#13869 := [monotonicity #13487 #13866]: #13868
+#13872 := [monotonicity #13487 #13869]: #13871
+#13875 := [monotonicity #13487 #13872]: #13874
+#13878 := [monotonicity #13875]: #13877
+#13883 := [trans #13878 #13881]: #13882
+#13886 := [monotonicity #13883]: #13885
+#13893 := [monotonicity #13487 #13886]: #13892
+#13896 := [monotonicity #13487 #13893]: #13895
+#13899 := [monotonicity #13487 #13896]: #13898
+#13902 := [monotonicity #13487 #13899]: #13901
+#13889 := (iff #12953 #13766)
+#13887 := (iff #3347 #13765)
+#13888 := [rewrite]: #13887
+#13890 := [monotonicity #13888]: #13889
+#13905 := [monotonicity #13890 #13902]: #13904
+#13908 := [monotonicity #13487 #13905]: #13907
+#13913 := [trans #13908 #13911]: #13912
+#13791 := (iff #12929 #13788)
+#13776 := (or #13485 #13759)
+#13779 := (or #13485 #13776)
+#13782 := (or #13765 #13779)
+#13785 := (or #13485 #13782)
+#13789 := (iff #13785 #13788)
+#13790 := [rewrite]: #13789
+#13786 := (iff #12929 #13785)
+#13783 := (iff #12921 #13782)
+#13780 := (iff #12912 #13779)
+#13777 := (iff #12904 #13776)
+#13762 := (iff #12898 #13759)
+#13756 := (and #12545 #13753)
+#13760 := (iff #13756 #13759)
+#13761 := [rewrite]: #13760
+#13757 := (iff #12898 #13756)
+#13754 := (iff #12893 #13753)
+#13751 := (iff #12887 #13748)
+#13745 := (and #12551 #13740)
+#13749 := (iff #13745 #13748)
+#13750 := [rewrite]: #13749
+#13746 := (iff #12887 #13745)
+#13743 := (iff #12882 #13740)
+#13734 := (or #13485 #13731)
+#13737 := (or #12749 #13734)
+#13741 := (iff #13737 #13740)
+#13742 := [rewrite]: #13741
+#13738 := (iff #12882 #13737)
+#13735 := (iff #12874 #13734)
+#13732 := (iff #12868 #13731)
+#13729 := (iff #12863 #13726)
+#13623 := (or #13494 #13615)
+#13705 := (or #13623 #12812)
+#13708 := (or #12821 #13705)
+#13711 := (or #13485 #13708)
+#13714 := (or #13485 #13711)
+#13717 := (or #13485 #13714)
+#13720 := (or #13671 #13717)
+#13723 := (or #13485 #13720)
+#13727 := (iff #13723 #13726)
+#13728 := [rewrite]: #13727
+#13724 := (iff #12863 #13723)
+#13721 := (iff #12855 #13720)
+#13718 := (iff #12846 #13717)
+#13715 := (iff #12838 #13714)
+#13712 := (iff #12830 #13711)
+#13709 := (iff #12822 #13708)
+#13706 := (iff #12813 #13705)
+#13624 := (iff #12687 #13623)
+#13618 := (iff #12680 #13615)
+#13612 := (and #13589 #13607)
+#13616 := (iff #13612 #13615)
+#13617 := [rewrite]: #13616
+#13613 := (iff #12680 #13612)
+#13610 := (iff #12675 #13607)
+#13595 := (or #13511 #13579)
+#13598 := (or #12656 #13595)
+#13601 := (or #13586 #13598)
+#13604 := (or #13592 #13601)
+#13608 := (iff #13604 #13607)
+#13609 := [rewrite]: #13608
+#13605 := (iff #12675 #13604)
+#13602 := (iff #12666 #13601)
+#13599 := (iff #12657 #13598)
+#13596 := (iff #12648 #13595)
+#13580 := (iff #12641 #13579)
+#13577 := (iff #12636 #13576)
+#13574 := (iff #12629 #13573)
+#13571 := (iff #12624 #13570)
+#13568 := (iff #12610 #13565)
+#13562 := (and #13559 #12607)
+#13566 := (iff #13562 #13565)
 #13567 := [rewrite]: #13566
-#13564 := (iff #12628 #13563)
-#13561 := (iff #3292 #13560)
-#13562 := [rewrite]: #13561
-#13565 := [monotonicity #13562]: #13564
-#13569 := [trans #13565 #13567]: #13568
-#13577 := [monotonicity #13569 #13574]: #13576
-#13580 := [monotonicity #5740 #13577]: #13579
-#13585 := [trans #13580 #13583]: #13584
-#13588 := [quant-intro #13585]: #13587
-#13591 := [monotonicity #13588]: #13590
-#13608 := [monotonicity #13591 #13605]: #13607
-#13611 := [monotonicity #13588 #13608]: #13610
-#13556 := (iff #12671 #13555)
-#13553 := (iff #3291 #13550)
-#13554 := [rewrite]: #13553
-#13557 := [monotonicity #13554]: #13556
-#13614 := [monotonicity #13557 #13611]: #13613
-#13617 := [monotonicity #13554 #13614]: #13616
-#13548 := (iff #12683 #13547)
-#13545 := (iff #12625 #13544)
-#13541 := (iff #3289 #13542)
-#13543 := [rewrite]: #13541
-#13524 := (iff #3279 #13525)
-#13526 := [rewrite]: #13524
-#13546 := [monotonicity #13526 #13543]: #13545
-#13549 := [monotonicity #13546]: #13548
-#13633 := [monotonicity #13549 #13617]: #13632
-#13636 := [monotonicity #13633]: #13635
-#13623 := (iff #12701 #13622)
-#13620 := (iff #12619 #13618)
-#13621 := [rewrite]: #13620
-#13624 := [monotonicity #13621]: #13623
-#13639 := [monotonicity #13624 #13636]: #13638
-#13629 := (iff #12710 #13628)
-#13626 := (iff #12616 #13625)
-#13539 := (iff #12613 #13536)
-#13540 := [rewrite]: #13539
-#13533 := (iff #12610 #13534)
-#13535 := [rewrite]: #13533
-#13627 := [monotonicity #13535 #13540]: #13626
-#13630 := [monotonicity #13627]: #13629
-#13642 := [monotonicity #13630 #13639]: #13641
-#13647 := [trans #13642 #13645]: #13646
-#13650 := [monotonicity #13627 #13647]: #13649
-#13655 := [trans #13650 #13653]: #13654
-#13531 := (iff #12722 #13530)
-#13528 := (iff #3280 #13527)
-#13529 := [monotonicity #13517 #13526]: #13528
-#13532 := [monotonicity #13529]: #13531
-#13661 := [monotonicity #13532 #13655]: #13660
-#13743 := [monotonicity #13661]: #13742
-#13746 := [monotonicity #13743]: #13745
-#13749 := [monotonicity #13523 #13746]: #13748
-#13752 := [monotonicity #13523 #13749]: #13751
-#13755 := [monotonicity #13523 #13752]: #13754
-#13739 := (iff #12890 #13707)
-#13737 := (iff #3327 #13708)
-#13738 := [rewrite]: #13737
-#13740 := [monotonicity #13738]: #13739
-#13758 := [monotonicity #13740 #13755]: #13757
-#13761 := [monotonicity #13523 #13758]: #13760
-#13766 := [trans #13761 #13764]: #13765
-#13735 := (iff #12834 #13732)
-#13720 := (or #13521 #13702)
-#13723 := (or #13521 #13720)
-#13726 := (or #13708 #13723)
-#13729 := (or #13521 #13726)
-#13733 := (iff #13729 #13732)
-#13734 := [rewrite]: #13733
-#13730 := (iff #12834 #13729)
-#13727 := (iff #12826 #13726)
-#13724 := (iff #12817 #13723)
-#13721 := (iff #12809 #13720)
-#13705 := (iff #12803 #13702)
-#13699 := (and #12581 #13696)
-#13703 := (iff #13699 #13702)
-#13704 := [rewrite]: #13703
-#13700 := (iff #12803 #13699)
-#13697 := (iff #12798 #13696)
-#13694 := (iff #12791 #13691)
-#13688 := (and #12587 #13683)
-#13692 := (iff #13688 #13691)
-#13693 := [rewrite]: #13692
-#13689 := (iff #12791 #13688)
-#13686 := (iff #12786 #13683)
-#13662 := (or #12731 #13659)
-#13665 := (or #12740 #13662)
-#13668 := (or #13656 #13665)
-#13671 := (or #12758 #13668)
-#13674 := (or #12767 #13671)
-#13677 := (or #12776 #13674)
-#13680 := (or #12785 #13677)
-#13684 := (iff #13680 #13683)
-#13685 := [rewrite]: #13684
-#13681 := (iff #12786 #13680)
-#13678 := (iff #12777 #13677)
-#13675 := (iff #12768 #13674)
-#13672 := (iff #12759 #13671)
-#13669 := (iff #12750 #13668)
-#13666 := (iff #12741 #13665)
-#13663 := (iff #12732 #13662)
-#13664 := [monotonicity #13661]: #13663
-#13667 := [monotonicity #13664]: #13666
-#13657 := (iff #12749 #13656)
-#13658 := [monotonicity #13517]: #13657
-#13670 := [monotonicity #13658 #13667]: #13669
-#13673 := [monotonicity #13670]: #13672
-#13676 := [monotonicity #13673]: #13675
+#13563 := (iff #12610 #13562)
+#13560 := (iff #3297 #13559)
+#13561 := [rewrite]: #13560
+#13564 := [monotonicity #13561]: #13563
+#13569 := [trans #13564 #13567]: #13568
+#13554 := (iff #12623 #13553)
+#13551 := (iff #12604 #13550)
+#13548 := (iff #12599 #13545)
+#13539 := (or #13522 #13536)
+#13542 := (or #5712 #13539)
+#13546 := (iff #13542 #13545)
+#13547 := [rewrite]: #13546
+#13543 := (iff #12599 #13542)
+#13540 := (iff #12593 #13539)
+#13537 := (iff #3293 #13536)
+#13538 := [rewrite]: #13537
+#13532 := (iff #12592 #13522)
+#13524 := (not #13522)
+#13527 := (not #13524)
+#13530 := (iff #13527 #13522)
+#13531 := [rewrite]: #13530
+#13528 := (iff #12592 #13527)
+#13525 := (iff #3292 #13524)
+#13526 := [rewrite]: #13525
+#13529 := [monotonicity #13526]: #13528
+#13533 := [trans #13529 #13531]: #13532
+#13541 := [monotonicity #13533 #13538]: #13540
+#13544 := [monotonicity #5714 #13541]: #13543
+#13549 := [trans #13544 #13547]: #13548
+#13552 := [quant-intro #13549]: #13551
+#13555 := [monotonicity #13552]: #13554
+#13572 := [monotonicity #13555 #13569]: #13571
+#13575 := [monotonicity #13552 #13572]: #13574
+#13520 := (iff #12635 #13519)
+#13517 := (iff #3291 #13514)
+#13518 := [rewrite]: #13517
+#13521 := [monotonicity #13518]: #13520
+#13578 := [monotonicity #13521 #13575]: #13577
+#13581 := [monotonicity #13518 #13578]: #13580
+#13512 := (iff #12647 #13511)
+#13509 := (iff #12589 #13508)
+#13505 := (iff #3289 #13506)
+#13507 := [rewrite]: #13505
+#13488 := (iff #3279 #13489)
+#13490 := [rewrite]: #13488
+#13510 := [monotonicity #13490 #13507]: #13509
+#13513 := [monotonicity #13510]: #13512
+#13597 := [monotonicity #13513 #13581]: #13596
+#13600 := [monotonicity #13597]: #13599
+#13587 := (iff #12665 #13586)
+#13584 := (iff #12583 #13582)
+#13585 := [rewrite]: #13584
+#13588 := [monotonicity #13585]: #13587
+#13603 := [monotonicity #13588 #13600]: #13602
+#13593 := (iff #12674 #13592)
+#13590 := (iff #12580 #13589)
+#13503 := (iff #12577 #13500)
+#13504 := [rewrite]: #13503
+#13497 := (iff #12574 #13498)
+#13499 := [rewrite]: #13497
+#13591 := [monotonicity #13499 #13504]: #13590
+#13594 := [monotonicity #13591]: #13593
+#13606 := [monotonicity #13594 #13603]: #13605
+#13611 := [trans #13606 #13609]: #13610
+#13614 := [monotonicity #13591 #13611]: #13613
+#13619 := [trans #13614 #13617]: #13618
+#13495 := (iff #12686 #13494)
+#13492 := (iff #3280 #13491)
+#13493 := [monotonicity #13481 #13490]: #13492
+#13496 := [monotonicity #13493]: #13495
+#13625 := [monotonicity #13496 #13619]: #13624
+#13707 := [monotonicity #13625]: #13706
+#13710 := [monotonicity #13707]: #13709
+#13713 := [monotonicity #13487 #13710]: #13712
+#13716 := [monotonicity #13487 #13713]: #13715
+#13719 := [monotonicity #13487 #13716]: #13718
+#13703 := (iff #12854 #13671)
+#13701 := (iff #3327 #13672)
+#13702 := [rewrite]: #13701
+#13704 := [monotonicity #13702]: #13703
+#13722 := [monotonicity #13704 #13719]: #13721
+#13725 := [monotonicity #13487 #13722]: #13724
+#13730 := [trans #13725 #13728]: #13729
+#13699 := (iff #12798 #13696)
+#13684 := (or #13485 #13666)
+#13687 := (or #13485 #13684)
+#13690 := (or #13672 #13687)
+#13693 := (or #13485 #13690)
+#13697 := (iff #13693 #13696)
+#13698 := [rewrite]: #13697
+#13694 := (iff #12798 #13693)
+#13691 := (iff #12790 #13690)
+#13688 := (iff #12781 #13687)
+#13685 := (iff #12773 #13684)
+#13669 := (iff #12767 #13666)
+#13663 := (and #12545 #13660)
+#13667 := (iff #13663 #13666)
+#13668 := [rewrite]: #13667
+#13664 := (iff #12767 #13663)
+#13661 := (iff #12762 #13660)
+#13658 := (iff #12755 #13655)
+#13652 := (and #12551 #13647)
+#13656 := (iff #13652 #13655)
+#13657 := [rewrite]: #13656
+#13653 := (iff #12755 #13652)
+#13650 := (iff #12750 #13647)
+#13626 := (or #12695 #13623)
+#13629 := (or #12704 #13626)
+#13632 := (or #13620 #13629)
+#13635 := (or #12722 #13632)
+#13638 := (or #12731 #13635)
+#13641 := (or #12740 #13638)
+#13644 := (or #12749 #13641)
+#13648 := (iff #13644 #13647)
+#13649 := [rewrite]: #13648
+#13645 := (iff #12750 #13644)
+#13642 := (iff #12741 #13641)
+#13639 := (iff #12732 #13638)
+#13636 := (iff #12723 #13635)
+#13633 := (iff #12714 #13632)
+#13630 := (iff #12705 #13629)
+#13627 := (iff #12696 #13626)
+#13628 := [monotonicity #13625]: #13627
+#13631 := [monotonicity #13628]: #13630
+#13621 := (iff #12713 #13620)
+#13622 := [monotonicity #13481]: #13621
+#13634 := [monotonicity #13622 #13631]: #13633
+#13637 := [monotonicity #13634]: #13636
+#13640 := [monotonicity #13637]: #13639
+#13643 := [monotonicity #13640]: #13642
+#13646 := [monotonicity #13643]: #13645
+#13651 := [trans #13646 #13649]: #13650
+#13654 := [monotonicity #13651]: #13653
+#13659 := [trans #13654 #13657]: #13658
+#13662 := [monotonicity #13659]: #13661
+#13665 := [monotonicity #13662]: #13664
+#13670 := [trans #13665 #13668]: #13669
+#13686 := [monotonicity #13487 #13670]: #13685
+#13689 := [monotonicity #13487 #13686]: #13688
+#13682 := (iff #12789 #13672)
+#13677 := (not #13671)
+#13680 := (iff #13677 #13672)
+#13681 := [rewrite]: #13680
+#13678 := (iff #12789 #13677)
+#13675 := (iff #3267 #13671)
+#13676 := [rewrite]: #13675
 #13679 := [monotonicity #13676]: #13678
-#13682 := [monotonicity #13679]: #13681
-#13687 := [trans #13682 #13685]: #13686
-#13690 := [monotonicity #13687]: #13689
-#13695 := [trans #13690 #13693]: #13694
-#13698 := [monotonicity #13695]: #13697
-#13701 := [monotonicity #13698]: #13700
-#13706 := [trans #13701 #13704]: #13705
-#13722 := [monotonicity #13523 #13706]: #13721
-#13725 := [monotonicity #13523 #13722]: #13724
-#13718 := (iff #12825 #13708)
-#13713 := (not #13707)
-#13716 := (iff #13713 #13708)
-#13717 := [rewrite]: #13716
-#13714 := (iff #12825 #13713)
-#13711 := (iff #3267 #13707)
-#13712 := [rewrite]: #13711
-#13715 := [monotonicity #13712]: #13714
-#13719 := [trans #13715 #13717]: #13718
-#13728 := [monotonicity #13719 #13725]: #13727
-#13731 := [monotonicity #13523 #13728]: #13730
-#13736 := [trans #13731 #13734]: #13735
-#13769 := [monotonicity #13736 #13766]: #13768
-#13772 := [monotonicity #13523 #13769]: #13771
-#13775 := [monotonicity #13772]: #13774
-#13780 := [trans #13775 #13778]: #13779
-#13783 := [monotonicity #13780]: #13782
-#13788 := [trans #13783 #13786]: #13787
-#13791 := [monotonicity #13788]: #13790
-#13794 := [monotonicity #13791]: #13793
-#13799 := [trans #13794 #13797]: #13798
-#13814 := [monotonicity #13523 #13799]: #13813
-#13817 := [monotonicity #13523 #13814]: #13816
-#13810 := (iff #12956 #13801)
-#13805 := (not #13802)
-#13808 := (iff #13805 #13801)
-#13809 := [rewrite]: #13808
-#13806 := (iff #12956 #13805)
-#13803 := (iff #3256 #13802)
-#13804 := [rewrite]: #13803
-#13807 := [monotonicity #13804]: #13806
-#13811 := [trans #13807 #13809]: #13810
-#13820 := [monotonicity #13811 #13817]: #13819
-#13823 := [monotonicity #13523 #13820]: #13822
-#13828 := [trans #13823 #13826]: #13827
-#13952 := [monotonicity #13828 #13949]: #13951
-#14082 := [monotonicity #13523 #13952]: #14081
-#14085 := [monotonicity #14082]: #14084
-#14088 := [monotonicity #14085]: #14087
-#14091 := [monotonicity #14088]: #14090
-#14094 := [monotonicity #14091]: #14093
-#14097 := [monotonicity #14094]: #14096
-#14100 := [monotonicity #14097]: #14099
-#13975 := (iff #13077 #13974)
-#13972 := (iff #12521 #12515)
-#13964 := (and true #12515)
-#13967 := (and true #13964)
-#13970 := (iff #13967 #12515)
-#13971 := [rewrite]: #13970
-#13968 := (iff #12521 #13967)
-#13965 := (iff #12518 #13964)
-#13960 := (iff #3231 true)
-#13955 := (forall (vars (?v0 S20)) (:pat #3229) true)
-#13958 := (iff #13955 true)
-#13959 := [elim-unused]: #13958
-#13956 := (iff #3231 #13955)
-#13953 := (iff #3230 true)
-#13954 := [rewrite]: #13953
-#13957 := [quant-intro #13954]: #13956
-#13961 := [trans #13957 #13959]: #13960
-#13966 := [monotonicity #13961]: #13965
-#13962 := (iff #3227 true)
-#13963 := [rewrite]: #13962
-#13969 := [monotonicity #13963 #13966]: #13968
-#13973 := [trans #13969 #13971]: #13972
-#13976 := [monotonicity #13973]: #13975
-#14103 := [monotonicity #13976 #14100]: #14102
-#14106 := [monotonicity #13976 #14103]: #14105
-#14109 := [monotonicity #13523 #14106]: #14108
-#14112 := [monotonicity #13523 #14109]: #14111
-#14115 := [monotonicity #13523 #14112]: #14114
-#14118 := [monotonicity #13523 #14115]: #14117
-#13992 := (iff #13133 #13991)
-#13989 := (iff #12253 #13986)
-#13983 := (and #13980 #12250)
-#13987 := (iff #13983 #13986)
-#13988 := [rewrite]: #13987
-#13984 := (iff #12253 #13983)
-#13981 := (iff #3151 #13980)
-#13982 := [rewrite]: #13981
-#13985 := [monotonicity #13982]: #13984
-#13990 := [trans #13985 #13988]: #13989
-#13993 := [monotonicity #13990]: #13992
-#14121 := [monotonicity #13993 #14118]: #14120
-#14026 := (iff #13142 #14025)
-#14023 := (iff #12247 #14022)
-#14020 := (iff #12242 #14017)
-#14011 := (or #13994 #14008)
-#14014 := (or #5738 #14011)
-#14018 := (iff #14014 #14017)
-#14019 := [rewrite]: #14018
-#14015 := (iff #12242 #14014)
-#14012 := (iff #12236 #14011)
-#14009 := (iff #3147 #14008)
-#14010 := [rewrite]: #14009
-#14004 := (iff #12235 #13994)
-#13996 := (not #13994)
-#13999 := (not #13996)
-#14002 := (iff #13999 #13994)
+#13683 := [trans #13679 #13681]: #13682
+#13692 := [monotonicity #13683 #13689]: #13691
+#13695 := [monotonicity #13487 #13692]: #13694
+#13700 := [trans #13695 #13698]: #13699
+#13733 := [monotonicity #13700 #13730]: #13732
+#13736 := [monotonicity #13487 #13733]: #13735
+#13739 := [monotonicity #13736]: #13738
+#13744 := [trans #13739 #13742]: #13743
+#13747 := [monotonicity #13744]: #13746
+#13752 := [trans #13747 #13750]: #13751
+#13755 := [monotonicity #13752]: #13754
+#13758 := [monotonicity #13755]: #13757
+#13763 := [trans #13758 #13761]: #13762
+#13778 := [monotonicity #13487 #13763]: #13777
+#13781 := [monotonicity #13487 #13778]: #13780
+#13774 := (iff #12920 #13765)
+#13769 := (not #13766)
+#13772 := (iff #13769 #13765)
+#13773 := [rewrite]: #13772
+#13770 := (iff #12920 #13769)
+#13767 := (iff #3256 #13766)
+#13768 := [rewrite]: #13767
+#13771 := [monotonicity #13768]: #13770
+#13775 := [trans #13771 #13773]: #13774
+#13784 := [monotonicity #13775 #13781]: #13783
+#13787 := [monotonicity #13487 #13784]: #13786
+#13792 := [trans #13787 #13790]: #13791
+#13916 := [monotonicity #13792 #13913]: #13915
+#14046 := [monotonicity #13487 #13916]: #14045
+#14049 := [monotonicity #14046]: #14048
+#14052 := [monotonicity #14049]: #14051
+#14055 := [monotonicity #14052]: #14054
+#14058 := [monotonicity #14055]: #14057
+#14061 := [monotonicity #14058]: #14060
+#14064 := [monotonicity #14061]: #14063
+#13939 := (iff #13041 #13938)
+#13936 := (iff #12485 #12479)
+#13928 := (and true #12479)
+#13931 := (and true #13928)
+#13934 := (iff #13931 #12479)
+#13935 := [rewrite]: #13934
+#13932 := (iff #12485 #13931)
+#13929 := (iff #12482 #13928)
+#13924 := (iff #3231 true)
+#13919 := (forall (vars (?v0 S20)) (:pat #3229) true)
+#13922 := (iff #13919 true)
+#13923 := [elim-unused]: #13922
+#13920 := (iff #3231 #13919)
+#13917 := (iff #3230 true)
+#13918 := [rewrite]: #13917
+#13921 := [quant-intro #13918]: #13920
+#13925 := [trans #13921 #13923]: #13924
+#13930 := [monotonicity #13925]: #13929
+#13926 := (iff #3227 true)
+#13927 := [rewrite]: #13926
+#13933 := [monotonicity #13927 #13930]: #13932
+#13937 := [trans #13933 #13935]: #13936
+#13940 := [monotonicity #13937]: #13939
+#14067 := [monotonicity #13940 #14064]: #14066
+#14070 := [monotonicity #13940 #14067]: #14069
+#14073 := [monotonicity #13487 #14070]: #14072
+#14076 := [monotonicity #13487 #14073]: #14075
+#14079 := [monotonicity #13487 #14076]: #14078
+#14082 := [monotonicity #13487 #14079]: #14081
+#13956 := (iff #13097 #13955)
+#13953 := (iff #12217 #13950)
+#13947 := (and #13944 #12214)
+#13951 := (iff #13947 #13950)
+#13952 := [rewrite]: #13951
+#13948 := (iff #12217 #13947)
+#13945 := (iff #3151 #13944)
+#13946 := [rewrite]: #13945
+#13949 := [monotonicity #13946]: #13948
+#13954 := [trans #13949 #13952]: #13953
+#13957 := [monotonicity #13954]: #13956
+#14085 := [monotonicity #13957 #14082]: #14084
+#13990 := (iff #13106 #13989)
+#13987 := (iff #12211 #13986)
+#13984 := (iff #12206 #13981)
+#13975 := (or #13958 #13972)
+#13978 := (or #5712 #13975)
+#13982 := (iff #13978 #13981)
+#13983 := [rewrite]: #13982
+#13979 := (iff #12206 #13978)
+#13976 := (iff #12200 #13975)
+#13973 := (iff #3147 #13972)
+#13974 := [rewrite]: #13973
+#13968 := (iff #12199 #13958)
+#13960 := (not #13958)
+#13963 := (not #13960)
+#13966 := (iff #13963 #13958)
+#13967 := [rewrite]: #13966
+#13964 := (iff #12199 #13963)
+#13961 := (iff #3146 #13960)
+#13962 := [rewrite]: #13961
+#13965 := [monotonicity #13962]: #13964
+#13969 := [trans #13965 #13967]: #13968
+#13977 := [monotonicity #13969 #13974]: #13976
+#13980 := [monotonicity #5714 #13977]: #13979
+#13985 := [trans #13980 #13983]: #13984
+#13988 := [quant-intro #13985]: #13987
+#13991 := [monotonicity #13988]: #13990
+#14088 := [monotonicity #13991 #14085]: #14087
+#13996 := (iff #13115 #13995)
+#13993 := (iff #3145 #13992)
+#13994 := [rewrite]: #13993
+#13997 := [monotonicity #13994]: #13996
+#14091 := [monotonicity #13997 #14088]: #14090
+#14094 := [monotonicity #13487 #14091]: #14093
+#14008 := (iff #13132 #14007)
+#14005 := (iff #3142 #14004)
+#14002 := (iff #3141 #14001)
 #14003 := [rewrite]: #14002
-#14000 := (iff #12235 #13999)
-#13997 := (iff #3146 #13996)
-#13998 := [rewrite]: #13997
-#14001 := [monotonicity #13998]: #14000
-#14005 := [trans #14001 #14003]: #14004
-#14013 := [monotonicity #14005 #14010]: #14012
-#14016 := [monotonicity #5740 #14013]: #14015
-#14021 := [trans #14016 #14019]: #14020
-#14024 := [quant-intro #14021]: #14023
-#14027 := [monotonicity #14024]: #14026
-#14124 := [monotonicity #14027 #14121]: #14123
-#14032 := (iff #13151 #14031)
-#14029 := (iff #3145 #14028)
-#14030 := [rewrite]: #14029
-#14033 := [monotonicity #14030]: #14032
-#14127 := [monotonicity #14033 #14124]: #14126
-#14130 := [monotonicity #13523 #14127]: #14129
-#14044 := (iff #13168 #14043)
-#14041 := (iff #3142 #14040)
-#14038 := (iff #3141 #14037)
-#14039 := [rewrite]: #14038
-#14035 := (iff #3140 #14034)
-#14036 := [rewrite]: #14035
-#14042 := [monotonicity #14036 #14039]: #14041
-#14045 := [monotonicity #14042]: #14044
-#14133 := [monotonicity #14045 #14130]: #14132
-#14054 := (iff #13177 #14053)
-#14051 := (iff #3138 #14050)
-#14048 := (iff #3137 #14046)
-#14049 := [rewrite]: #14048
-#14052 := [monotonicity #13514 #14049]: #14051
-#14055 := [monotonicity #14052]: #14054
-#14136 := [monotonicity #14055 #14133]: #14135
-#14067 := (iff #13186 #14066)
-#14064 := (iff #3134 #14063)
-#14061 := (iff #3133 #14059)
-#14062 := [rewrite]: #14061
-#14057 := (iff #3132 #14056)
-#14058 := [rewrite]: #14057
-#14065 := [monotonicity #14058 #14062]: #14064
-#14068 := [monotonicity #14065]: #14067
-#14139 := [monotonicity #14068 #14136]: #14138
-#14078 := (iff #13195 #14077)
-#14075 := (iff #12229 #14072)
-#14073 := (iff #14069 #14072)
-#14074 := [rewrite]: #14073
-#14070 := (iff #12229 #14069)
-#13510 := (iff #3038 #13509)
-#13511 := [rewrite]: #13510
-#14071 := [monotonicity #13511]: #14070
-#14076 := [trans #14071 #14074]: #14075
-#14079 := [monotonicity #14076]: #14078
-#14142 := [monotonicity #14079 #14139]: #14141
-#14147 := [trans #14142 #14145]: #14146
-#14150 := [monotonicity #14071 #14147]: #14149
-#14155 := [trans #14150 #14153]: #14154
-#13506 := (iff #13207 #13505)
-#13503 := (iff #12224 #13502)
-#13500 := (iff #12219 #13497)
-#13491 := (or #13475 #13487)
-#13494 := (or #5738 #13491)
-#13498 := (iff #13494 #13497)
-#13499 := [rewrite]: #13498
-#13495 := (iff #12219 #13494)
-#13492 := (iff #12213 #13491)
-#13486 := (iff #3125 #13487)
-#13490 := [rewrite]: #13486
-#13484 := (iff #12212 #13475)
-#13476 := (not #13475)
-#13479 := (not #13476)
-#13482 := (iff #13479 #13475)
-#13483 := [rewrite]: #13482
-#13480 := (iff #12212 #13479)
-#13477 := (iff #3122 #13476)
-#13478 := [rewrite]: #13477
-#13481 := [monotonicity #13478]: #13480
-#13485 := [trans #13481 #13483]: #13484
-#13493 := [monotonicity #13485 #13490]: #13492
-#13496 := [monotonicity #5740 #13493]: #13495
-#13501 := [trans #13496 #13499]: #13500
-#13504 := [quant-intro #13501]: #13503
-#13507 := [monotonicity #13504]: #13506
-#14158 := [monotonicity #13507 #14155]: #14157
-#14161 := [monotonicity #13504 #14158]: #14160
-#13473 := (iff #13219 #13472)
-#13470 := (iff #3121 #13469)
-#13471 := [rewrite]: #13470
-#13474 := [monotonicity #13471]: #13473
-#14164 := [monotonicity #13474 #14161]: #14163
-#14167 := [monotonicity #13471 #14164]: #14166
-#13467 := (iff #13231 false)
-#12256 := (iff #3156 false)
-#12257 := [rewrite]: #12256
-#13465 := (iff #13231 #3156)
-#13463 := (iff #12209 true)
-#12568 := (and true true)
-#13458 := (and true #12568)
-#13461 := (iff #13458 true)
-#13462 := [rewrite]: #13461
-#13459 := (iff #12209 #13458)
-#13456 := (iff #12206 #12568)
-#13454 := (iff #3117 true)
-#13455 := [rewrite]: #13454
-#13452 := (iff #3116 true)
-#13453 := [rewrite]: #13452
-#13457 := [monotonicity #13453 #13455]: #13456
-#13460 := [monotonicity #13453 #13457]: #13459
-#13464 := [trans #13460 #13462]: #13463
-#13466 := [monotonicity #13464]: #13465
-#13468 := [trans #13466 #12257]: #13467
-#14170 := [monotonicity #13468 #14167]: #14169
-#14173 := [monotonicity #14170]: #14172
+#13999 := (iff #3140 #13998)
+#14000 := [rewrite]: #13999
+#14006 := [monotonicity #14000 #14003]: #14005
+#14009 := [monotonicity #14006]: #14008
+#14097 := [monotonicity #14009 #14094]: #14096
+#14018 := (iff #13141 #14017)
+#14015 := (iff #3138 #14014)
+#14012 := (iff #3137 #14010)
+#14013 := [rewrite]: #14012
+#14016 := [monotonicity #13478 #14013]: #14015
+#14019 := [monotonicity #14016]: #14018
+#14100 := [monotonicity #14019 #14097]: #14099
+#14031 := (iff #13150 #14030)
+#14028 := (iff #3134 #14027)
+#14025 := (iff #3133 #14023)
+#14026 := [rewrite]: #14025
+#14021 := (iff #3132 #14020)
+#14022 := [rewrite]: #14021
+#14029 := [monotonicity #14022 #14026]: #14028
+#14032 := [monotonicity #14029]: #14031
+#14103 := [monotonicity #14032 #14100]: #14102
+#14042 := (iff #13159 #14041)
+#14039 := (iff #12193 #14036)
+#14037 := (iff #14033 #14036)
+#14038 := [rewrite]: #14037
+#14034 := (iff #12193 #14033)
+#13474 := (iff #3038 #13473)
+#13475 := [rewrite]: #13474
+#14035 := [monotonicity #13475]: #14034
+#14040 := [trans #14035 #14038]: #14039
+#14043 := [monotonicity #14040]: #14042
+#14106 := [monotonicity #14043 #14103]: #14105
+#14111 := [trans #14106 #14109]: #14110
+#14114 := [monotonicity #14035 #14111]: #14113
+#14119 := [trans #14114 #14117]: #14118
+#13470 := (iff #13171 #13469)
+#13467 := (iff #12188 #13466)
+#13464 := (iff #12183 #13461)
+#13455 := (or #13439 #13451)
+#13458 := (or #5712 #13455)
+#13462 := (iff #13458 #13461)
+#13463 := [rewrite]: #13462
+#13459 := (iff #12183 #13458)
+#13456 := (iff #12177 #13455)
+#13450 := (iff #3125 #13451)
+#13454 := [rewrite]: #13450
+#13448 := (iff #12176 #13439)
+#13440 := (not #13439)
+#13443 := (not #13440)
+#13446 := (iff #13443 #13439)
+#13447 := [rewrite]: #13446
+#13444 := (iff #12176 #13443)
+#13441 := (iff #3122 #13440)
+#13442 := [rewrite]: #13441
+#13445 := [monotonicity #13442]: #13444
+#13449 := [trans #13445 #13447]: #13448
+#13457 := [monotonicity #13449 #13454]: #13456
+#13460 := [monotonicity #5714 #13457]: #13459
+#13465 := [trans #13460 #13463]: #13464
+#13468 := [quant-intro #13465]: #13467
+#13471 := [monotonicity #13468]: #13470
+#14122 := [monotonicity #13471 #14119]: #14121
+#14125 := [monotonicity #13468 #14122]: #14124
+#13437 := (iff #13183 #13436)
+#13434 := (iff #3121 #13433)
+#13435 := [rewrite]: #13434
+#13438 := [monotonicity #13435]: #13437
+#14128 := [monotonicity #13438 #14125]: #14127
+#14131 := [monotonicity #13435 #14128]: #14130
+#13431 := (iff #13195 false)
+#12220 := (iff #3156 false)
+#12221 := [rewrite]: #12220
+#13429 := (iff #13195 #3156)
+#13427 := (iff #12173 true)
+#12532 := (and true true)
+#13422 := (and true #12532)
+#13425 := (iff #13422 true)
+#13426 := [rewrite]: #13425
+#13423 := (iff #12173 #13422)
+#13420 := (iff #12170 #12532)
+#13418 := (iff #3117 true)
+#13419 := [rewrite]: #13418
+#13416 := (iff #3116 true)
+#13417 := [rewrite]: #13416
+#13421 := [monotonicity #13417 #13419]: #13420
+#13424 := [monotonicity #13417 #13421]: #13423
+#13428 := [trans #13424 #13426]: #13427
+#13430 := [monotonicity #13428]: #13429
+#13432 := [trans #13430 #12221]: #13431
+#14134 := [monotonicity #13432 #14131]: #14133
+#14137 := [monotonicity #14134]: #14136
+#14140 := [monotonicity #14137]: #14139
+#14143 := [monotonicity #14140]: #14142
+#14146 := [monotonicity #14143]: #14145
+#14149 := [monotonicity #14146]: #14148
+#14154 := [trans #14149 #14152]: #14153
+#14157 := [monotonicity #14154]: #14156
+#14162 := [trans #14157 #14160]: #14161
+#14165 := [monotonicity #14162]: #14164
+#14168 := [monotonicity #14165]: #14167
+#14173 := [trans #14168 #14171]: #14172
 #14176 := [monotonicity #14173]: #14175
 #14179 := [monotonicity #14176]: #14178
-#14182 := [monotonicity #14179]: #14181
-#14185 := [monotonicity #14182]: #14184
-#14190 := [trans #14185 #14188]: #14189
-#14193 := [monotonicity #14190]: #14192
-#14198 := [trans #14193 #14196]: #14197
-#14201 := [monotonicity #14198]: #14200
-#14204 := [monotonicity #14201]: #14203
-#14209 := [trans #14204 #14207]: #14208
-#14212 := [monotonicity #14209]: #14211
-#14215 := [monotonicity #14212]: #14214
-#13450 := (iff #13312 #13449)
-#13447 := (iff #3094 #13446)
-#13444 := (iff #3093 #13441)
-#13445 := [rewrite]: #13444
-#13438 := (iff #3092 #13439)
-#13440 := [rewrite]: #13438
-#13448 := [monotonicity #13440 #13445]: #13447
-#13451 := [monotonicity #13448]: #13450
-#14296 := [monotonicity #13451 #14215]: #14295
-#14299 := [monotonicity #14296]: #14298
-#14302 := [monotonicity #14299]: #14301
-#14305 := [monotonicity #14302]: #14304
-#14308 := [monotonicity #14305]: #14307
-#14226 := (iff #13357 #14225)
-#14223 := (iff #3075 #14222)
-#14220 := (iff #3074 #14216)
-#14221 := [rewrite]: #14220
-#14224 := [quant-intro #14221]: #14223
-#14227 := [monotonicity #14224]: #14226
-#14311 := [monotonicity #14227 #14308]: #14310
-#14314 := [monotonicity #14311]: #14313
-#14317 := [monotonicity #14314]: #14316
-#14232 := (iff #13384 #14231)
-#14229 := (iff #12136 #14228)
-#14230 := [rewrite]: #14229
-#14233 := [monotonicity #14230]: #14232
-#14320 := [monotonicity #14233 #14317]: #14319
-#14239 := (iff #13393 #13508)
-#14234 := (not #13509)
-#14237 := (iff #14234 #13508)
-#14238 := [rewrite]: #14237
-#14235 := (iff #13393 #14234)
-#14236 := [monotonicity #13511]: #14235
-#14240 := [trans #14236 #14238]: #14239
-#14323 := [monotonicity #14240 #14320]: #14322
-#14250 := (iff #13402 #14241)
-#14242 := (not #14241)
-#14245 := (not #14242)
-#14248 := (iff #14245 #14241)
-#14249 := [rewrite]: #14248
-#14246 := (iff #13402 #14245)
-#14243 := (iff #3037 #14242)
-#14244 := [rewrite]: #14243
-#14247 := [monotonicity #14244]: #14246
-#14251 := [trans #14247 #14249]: #14250
-#14326 := [monotonicity #14251 #14323]: #14325
-#14264 := (iff #13411 #14263)
-#14261 := (iff #3035 #14260)
-#14258 := (iff #3034 #14255)
-#14259 := [rewrite]: #14258
-#14252 := (iff #3033 #14253)
-#14254 := [rewrite]: #14252
-#14262 := [monotonicity #14254 #14259]: #14261
-#14265 := [monotonicity #14262]: #14264
-#14329 := [monotonicity #14265 #14326]: #14328
-#14278 := (iff #13420 #14277)
-#14275 := (iff #3031 #14274)
-#14272 := (iff #3030 #14269)
-#14273 := [rewrite]: #14272
-#14266 := (iff #3029 #14267)
-#14268 := [rewrite]: #14266
-#14276 := [monotonicity #14268 #14273]: #14275
-#14279 := [monotonicity #14276]: #14278
-#14332 := [monotonicity #14279 #14329]: #14331
-#14292 := (iff #13429 #14291)
-#14289 := (iff #3027 #14288)
-#14286 := (iff #3026 #14283)
-#14287 := [rewrite]: #14286
-#14280 := (iff #3025 #14281)
-#14282 := [rewrite]: #14280
-#14290 := [monotonicity #14282 #14287]: #14289
-#14293 := [monotonicity #14290]: #14292
-#14335 := [monotonicity #14293 #14332]: #14334
-#14340 := [trans #14335 #14338]: #14339
-#14343 := [monotonicity #14340]: #14342
-#13436 := (iff #3406 #13435)
-#13433 := (iff #3405 #13430)
-#13426 := (implies #3027 #13421)
-#13431 := (iff #13426 #13430)
-#13432 := [rewrite]: #13431
-#13427 := (iff #3405 #13426)
-#13424 := (iff #3404 #13421)
-#13417 := (implies #3031 #13412)
-#13422 := (iff #13417 #13421)
-#13423 := [rewrite]: #13422
-#13418 := (iff #3404 #13417)
-#13415 := (iff #3403 #13412)
-#13408 := (implies #3035 #13403)
-#13413 := (iff #13408 #13412)
-#13414 := [rewrite]: #13413
-#13409 := (iff #3403 #13408)
-#13406 := (iff #3402 #13403)
-#13399 := (implies #3037 #13394)
-#13404 := (iff #13399 #13403)
-#13405 := [rewrite]: #13404
-#13400 := (iff #3402 #13399)
-#13397 := (iff #3401 #13394)
-#13390 := (implies #3038 #13385)
+#13414 := (iff #13276 #13413)
+#13411 := (iff #3094 #13410)
+#13408 := (iff #3093 #13405)
+#13409 := [rewrite]: #13408
+#13402 := (iff #3092 #13403)
+#13404 := [rewrite]: #13402
+#13412 := [monotonicity #13404 #13409]: #13411
+#13415 := [monotonicity #13412]: #13414
+#14260 := [monotonicity #13415 #14179]: #14259
+#14263 := [monotonicity #14260]: #14262
+#14266 := [monotonicity #14263]: #14265
+#14269 := [monotonicity #14266]: #14268
+#14272 := [monotonicity #14269]: #14271
+#14190 := (iff #13321 #14189)
+#14187 := (iff #3075 #14186)
+#14184 := (iff #3074 #14180)
+#14185 := [rewrite]: #14184
+#14188 := [quant-intro #14185]: #14187
+#14191 := [monotonicity #14188]: #14190
+#14275 := [monotonicity #14191 #14272]: #14274
+#14278 := [monotonicity #14275]: #14277
+#14281 := [monotonicity #14278]: #14280
+#14196 := (iff #13348 #14195)
+#14193 := (iff #12100 #14192)
+#14194 := [rewrite]: #14193
+#14197 := [monotonicity #14194]: #14196
+#14284 := [monotonicity #14197 #14281]: #14283
+#14203 := (iff #13357 #13472)
+#14198 := (not #13473)
+#14201 := (iff #14198 #13472)
+#14202 := [rewrite]: #14201
+#14199 := (iff #13357 #14198)
+#14200 := [monotonicity #13475]: #14199
+#14204 := [trans #14200 #14202]: #14203
+#14287 := [monotonicity #14204 #14284]: #14286
+#14214 := (iff #13366 #14205)
+#14206 := (not #14205)
+#14209 := (not #14206)
+#14212 := (iff #14209 #14205)
+#14213 := [rewrite]: #14212
+#14210 := (iff #13366 #14209)
+#14207 := (iff #3037 #14206)
+#14208 := [rewrite]: #14207
+#14211 := [monotonicity #14208]: #14210
+#14215 := [trans #14211 #14213]: #14214
+#14290 := [monotonicity #14215 #14287]: #14289
+#14228 := (iff #13375 #14227)
+#14225 := (iff #3035 #14224)
+#14222 := (iff #3034 #14219)
+#14223 := [rewrite]: #14222
+#14216 := (iff #3033 #14217)
+#14218 := [rewrite]: #14216
+#14226 := [monotonicity #14218 #14223]: #14225
+#14229 := [monotonicity #14226]: #14228
+#14293 := [monotonicity #14229 #14290]: #14292
+#14242 := (iff #13384 #14241)
+#14239 := (iff #3031 #14238)
+#14236 := (iff #3030 #14233)
+#14237 := [rewrite]: #14236
+#14230 := (iff #3029 #14231)
+#14232 := [rewrite]: #14230
+#14240 := [monotonicity #14232 #14237]: #14239
+#14243 := [monotonicity #14240]: #14242
+#14296 := [monotonicity #14243 #14293]: #14295
+#14256 := (iff #13393 #14255)
+#14253 := (iff #3027 #14252)
+#14250 := (iff #3026 #14247)
+#14251 := [rewrite]: #14250
+#14244 := (iff #3025 #14245)
+#14246 := [rewrite]: #14244
+#14254 := [monotonicity #14246 #14251]: #14253
+#14257 := [monotonicity #14254]: #14256
+#14299 := [monotonicity #14257 #14296]: #14298
+#14304 := [trans #14299 #14302]: #14303
+#14307 := [monotonicity #14304]: #14306
+#13400 := (iff #3406 #13399)
+#13397 := (iff #3405 #13394)
+#13390 := (implies #3027 #13385)
 #13395 := (iff #13390 #13394)
 #13396 := [rewrite]: #13395
-#13391 := (iff #3401 #13390)
-#13388 := (iff #3400 #13385)
-#13381 := (implies #12136 #13376)
+#13391 := (iff #3405 #13390)
+#13388 := (iff #3404 #13385)
+#13381 := (implies #3031 #13376)
 #13386 := (iff #13381 #13385)
 #13387 := [rewrite]: #13386
-#13382 := (iff #3400 #13381)
-#13379 := (iff #3399 #13376)
-#13372 := (implies #12139 #13367)
+#13382 := (iff #3404 #13381)
+#13379 := (iff #3403 #13376)
+#13372 := (implies #3035 #13367)
 #13377 := (iff #13372 #13376)
 #13378 := [rewrite]: #13377
-#13373 := (iff #3399 #13372)
-#13370 := (iff #3398 #13367)
-#13363 := (implies #12148 #13358)
+#13373 := (iff #3403 #13372)
+#13370 := (iff #3402 #13367)
+#13363 := (implies #3037 #13358)
 #13368 := (iff #13363 #13367)
 #13369 := [rewrite]: #13368
-#13364 := (iff #3398 #13363)
-#13361 := (iff #3397 #13358)
-#13354 := (implies #3075 #13349)
+#13364 := (iff #3402 #13363)
+#13361 := (iff #3401 #13358)
+#13354 := (implies #3038 #13349)
 #13359 := (iff #13354 #13358)
 #13360 := [rewrite]: #13359
-#13355 := (iff #3397 #13354)
-#13352 := (iff #3396 #13349)
-#13345 := (implies #12157 #13340)
+#13355 := (iff #3401 #13354)
+#13352 := (iff #3400 #13349)
+#13345 := (implies #12100 #13340)
 #13350 := (iff #13345 #13349)
 #13351 := [rewrite]: #13350
-#13346 := (iff #3396 #13345)
-#13343 := (iff #3395 #13340)
-#13336 := (implies #12160 #13331)
+#13346 := (iff #3400 #13345)
+#13343 := (iff #3399 #13340)
+#13336 := (implies #12103 #13331)
 #13341 := (iff #13336 #13340)
 #13342 := [rewrite]: #13341
-#13337 := (iff #3395 #13336)
-#13334 := (iff #3394 #13331)
-#13327 := (implies #3086 #13322)
+#13337 := (iff #3399 #13336)
+#13334 := (iff #3398 #13331)
+#13327 := (implies #12112 #13322)
 #13332 := (iff #13327 #13331)
 #13333 := [rewrite]: #13332
-#13328 := (iff #3394 #13327)
-#13325 := (iff #3393 #13322)
-#13318 := (implies #12174 #13313)
+#13328 := (iff #3398 #13327)
+#13325 := (iff #3397 #13322)
+#13318 := (implies #3075 #13313)
 #13323 := (iff #13318 #13322)
 #13324 := [rewrite]: #13323
-#13319 := (iff #3393 #13318)
-#13316 := (iff #3392 #13313)
-#13309 := (implies #3094 #13306)
+#13319 := (iff #3397 #13318)
+#13316 := (iff #3396 #13313)
+#13309 := (implies #12121 #13304)
 #13314 := (iff #13309 #13313)
 #13315 := [rewrite]: #13314
-#13310 := (iff #3392 #13309)
-#13307 := (iff #3391 #13306)
-#13304 := (iff #3390 #13301)
-#13297 := (implies #12177 #13294)
-#13302 := (iff #13297 #13301)
-#13303 := [rewrite]: #13302
-#13298 := (iff #3390 #13297)
-#13295 := (iff #3389 #13294)
-#13292 := (iff #3388 #13289)
-#13285 := (implies #12186 #13282)
-#13290 := (iff #13285 #13289)
-#13291 := [rewrite]: #13290
-#13286 := (iff #3388 #13285)
-#13283 := (iff #3387 #13282)
-#13280 := (iff #3386 #13277)
-#13273 := (implies #12192 #13268)
+#13310 := (iff #3396 #13309)
+#13307 := (iff #3395 #13304)
+#13300 := (implies #12124 #13295)
+#13305 := (iff #13300 #13304)
+#13306 := [rewrite]: #13305
+#13301 := (iff #3395 #13300)
+#13298 := (iff #3394 #13295)
+#13291 := (implies #3086 #13286)
+#13296 := (iff #13291 #13295)
+#13297 := [rewrite]: #13296
+#13292 := (iff #3394 #13291)
+#13289 := (iff #3393 #13286)
+#13282 := (implies #12138 #13277)
+#13287 := (iff #13282 #13286)
+#13288 := [rewrite]: #13287
+#13283 := (iff #3393 #13282)
+#13280 := (iff #3392 #13277)
+#13273 := (implies #3094 #13270)
 #13278 := (iff #13273 #13277)
 #13279 := [rewrite]: #13278
-#13274 := (iff #3386 #13273)
-#13271 := (iff #3385 #13268)
-#13264 := (implies #3109 #13259)
-#13269 := (iff #13264 #13268)
-#13270 := [rewrite]: #13269
-#13265 := (iff #3385 #13264)
-#13262 := (iff #3384 #13259)
-#13255 := (implies #12195 #13250)
-#13260 := (iff #13255 #13259)
-#13261 := [rewrite]: #13260
-#13256 := (iff #3384 #13255)
-#13253 := (iff #3383 #13250)
-#13246 := (implies #12198 #13241)
-#13251 := (iff #13246 #13250)
-#13252 := [rewrite]: #13251
-#13247 := (iff #3383 #13246)
-#13244 := (iff #3382 #13241)
-#13237 := (implies #12201 #13232)
+#13274 := (iff #3392 #13273)
+#13271 := (iff #3391 #13270)
+#13268 := (iff #3390 #13265)
+#13261 := (implies #12141 #13258)
+#13266 := (iff #13261 #13265)
+#13267 := [rewrite]: #13266
+#13262 := (iff #3390 #13261)
+#13259 := (iff #3389 #13258)
+#13256 := (iff #3388 #13253)
+#13249 := (implies #12150 #13246)
+#13254 := (iff #13249 #13253)
+#13255 := [rewrite]: #13254
+#13250 := (iff #3388 #13249)
+#13247 := (iff #3387 #13246)
+#13244 := (iff #3386 #13241)
+#13237 := (implies #12156 #13232)
 #13242 := (iff #13237 #13241)
 #13243 := [rewrite]: #13242
-#13238 := (iff #3382 #13237)
-#13235 := (iff #3381 #13232)
-#13228 := (implies #12209 #13225)
+#13238 := (iff #3386 #13237)
+#13235 := (iff #3385 #13232)
+#13228 := (implies #3109 #13223)
 #13233 := (iff #13228 #13232)
 #13234 := [rewrite]: #13233
-#13229 := (iff #3381 #13228)
-#13226 := (iff #3380 #13225)
-#13223 := (iff #3379 #13220)
-#13216 := (implies #3121 #13213)
-#13221 := (iff #13216 #13220)
-#13222 := [rewrite]: #13221
-#13217 := (iff #3379 #13216)
-#13214 := (iff #3378 #13213)
-#13211 := (iff #3377 #13208)
-#13204 := (implies #12224 #13201)
-#13209 := (iff #13204 #13208)
-#13210 := [rewrite]: #13209
-#13205 := (iff #3377 #13204)
-#13202 := (iff #3376 #13201)
-#13199 := (iff #3375 #13196)
-#13192 := (implies #12229 #13187)
+#13229 := (iff #3385 #13228)
+#13226 := (iff #3384 #13223)
+#13219 := (implies #12159 #13214)
+#13224 := (iff #13219 #13223)
+#13225 := [rewrite]: #13224
+#13220 := (iff #3384 #13219)
+#13217 := (iff #3383 #13214)
+#13210 := (implies #12162 #13205)
+#13215 := (iff #13210 #13214)
+#13216 := [rewrite]: #13215
+#13211 := (iff #3383 #13210)
+#13208 := (iff #3382 #13205)
+#13201 := (implies #12165 #13196)
+#13206 := (iff #13201 #13205)
+#13207 := [rewrite]: #13206
+#13202 := (iff #3382 #13201)
+#13199 := (iff #3381 #13196)
+#13192 := (implies #12173 #13189)
 #13197 := (iff #13192 #13196)
 #13198 := [rewrite]: #13197
-#13193 := (iff #3375 #13192)
-#13190 := (iff #3374 #13187)
-#13183 := (implies #3134 #13178)
-#13188 := (iff #13183 #13187)
-#13189 := [rewrite]: #13188
-#13184 := (iff #3374 #13183)
-#13181 := (iff #3373 #13178)
-#13174 := (implies #3138 #13169)
-#13179 := (iff #13174 #13178)
-#13180 := [rewrite]: #13179
-#13175 := (iff #3373 #13174)
-#13172 := (iff #3372 #13169)
-#13165 := (implies #3142 #13160)
-#13170 := (iff #13165 #13169)
-#13171 := [rewrite]: #13170
-#13166 := (iff #3372 #13165)
-#13163 := (iff #3371 #13160)
-#13157 := (implies #12232 #13152)
-#13161 := (iff #13157 #13160)
+#13193 := (iff #3381 #13192)
+#13190 := (iff #3380 #13189)
+#13187 := (iff #3379 #13184)
+#13180 := (implies #3121 #13177)
+#13185 := (iff #13180 #13184)
+#13186 := [rewrite]: #13185
+#13181 := (iff #3379 #13180)
+#13178 := (iff #3378 #13177)
+#13175 := (iff #3377 #13172)
+#13168 := (implies #12188 #13165)
+#13173 := (iff #13168 #13172)
+#13174 := [rewrite]: #13173
+#13169 := (iff #3377 #13168)
+#13166 := (iff #3376 #13165)
+#13163 := (iff #3375 #13160)
+#13156 := (implies #12193 #13151)
+#13161 := (iff #13156 #13160)
 #13162 := [rewrite]: #13161
-#13158 := (iff #3371 #13157)
-#13155 := (iff #3370 #13152)
-#13148 := (implies #3145 #13143)
-#13153 := (iff #13148 #13152)
-#13154 := [rewrite]: #13153
-#13149 := (iff #3370 #13148)
-#13146 := (iff #3369 #13143)
-#13139 := (implies #12247 #13134)
-#13144 := (iff #13139 #13143)
-#13145 := [rewrite]: #13144
-#13140 := (iff #3369 #13139)
-#13137 := (iff #3368 #13134)
-#13130 := (implies #12253 #13125)
-#13135 := (iff #13130 #13134)
-#13136 := [rewrite]: #13135
-#13131 := (iff #3368 #13130)
-#13128 := (iff #3367 #13125)
-#13122 := (implies #12232 #13110)
-#13126 := (iff #13122 #13125)
-#13127 := [rewrite]: #13126
-#13123 := (iff #3367 #13122)
-#13120 := (iff #3366 #13110)
-#13115 := (and true #13110)
-#13118 := (iff #13115 #13110)
-#13119 := [rewrite]: #13118
-#13116 := (iff #3366 #13115)
-#13113 := (iff #3365 #13110)
-#13107 := (implies #12232 #13102)
-#13111 := (iff #13107 #13110)
-#13112 := [rewrite]: #13111
-#13108 := (iff #3365 #13107)
-#13105 := (iff #3364 #13102)
-#13099 := (implies #12232 #13094)
-#13103 := (iff #13099 #13102)
-#13104 := [rewrite]: #13103
-#13100 := (iff #3364 #13099)
-#13097 := (iff #3363 #13094)
-#13091 := (implies #12232 #13086)
-#13095 := (iff #13091 #13094)
-#13096 := [rewrite]: #13095
-#13092 := (iff #3363 #13091)
-#13089 := (iff #3362 #13086)
-#13083 := (implies #12521 #13078)
-#13087 := (iff #13083 #13086)
-#13088 := [rewrite]: #13087
-#13084 := (iff #3362 #13083)
-#13081 := (iff #3361 #13078)
-#13074 := (implies #12521 #13069)
-#13079 := (iff #13074 #13078)
-#13080 := [rewrite]: #13079
-#13075 := (iff #3361 #13074)
-#13072 := (iff #3360 #13069)
-#13066 := (implies #12264 #13061)
-#13070 := (iff #13066 #13069)
-#13071 := [rewrite]: #13070
-#13067 := (iff #3360 #13066)
-#13064 := (iff #3359 #13061)
-#13057 := (implies #12543 #13052)
-#13062 := (iff #13057 #13061)
-#13063 := [rewrite]: #13062
-#13058 := (iff #3359 #13057)
-#13055 := (iff #3358 #13052)
-#13048 := (implies #12546 #13043)
-#13053 := (iff #13048 #13052)
-#13054 := [rewrite]: #13053
-#13049 := (iff #3358 #13048)
-#13046 := (iff #3357 #13043)
-#13039 := (implies #12549 #13034)
-#13044 := (iff #13039 #13043)
-#13045 := [rewrite]: #13044
-#13040 := (iff #3357 #13039)
-#13037 := (iff #3356 #13034)
-#13030 := (implies #12552 #13025)
-#13035 := (iff #13030 #13034)
-#13036 := [rewrite]: #13035
-#13031 := (iff #3356 #13030)
-#13028 := (iff #3355 #13025)
-#13021 := (implies #12561 #13009)
+#13157 := (iff #3375 #13156)
+#13154 := (iff #3374 #13151)
+#13147 := (implies #3134 #13142)
+#13152 := (iff #13147 #13151)
+#13153 := [rewrite]: #13152
+#13148 := (iff #3374 #13147)
+#13145 := (iff #3373 #13142)
+#13138 := (implies #3138 #13133)
+#13143 := (iff #13138 #13142)
+#13144 := [rewrite]: #13143
+#13139 := (iff #3373 #13138)
+#13136 := (iff #3372 #13133)
+#13129 := (implies #3142 #13124)
+#13134 := (iff #13129 #13133)
+#13135 := [rewrite]: #13134
+#13130 := (iff #3372 #13129)
+#13127 := (iff #3371 #13124)
+#13121 := (implies #12196 #13116)
+#13125 := (iff #13121 #13124)
+#13126 := [rewrite]: #13125
+#13122 := (iff #3371 #13121)
+#13119 := (iff #3370 #13116)
+#13112 := (implies #3145 #13107)
+#13117 := (iff #13112 #13116)
+#13118 := [rewrite]: #13117
+#13113 := (iff #3370 #13112)
+#13110 := (iff #3369 #13107)
+#13103 := (implies #12211 #13098)
+#13108 := (iff #13103 #13107)
+#13109 := [rewrite]: #13108
+#13104 := (iff #3369 #13103)
+#13101 := (iff #3368 #13098)
+#13094 := (implies #12217 #13089)
+#13099 := (iff #13094 #13098)
+#13100 := [rewrite]: #13099
+#13095 := (iff #3368 #13094)
+#13092 := (iff #3367 #13089)
+#13086 := (implies #12196 #13074)
+#13090 := (iff #13086 #13089)
+#13091 := [rewrite]: #13090
+#13087 := (iff #3367 #13086)
+#13084 := (iff #3366 #13074)
+#13079 := (and true #13074)
+#13082 := (iff #13079 #13074)
+#13083 := [rewrite]: #13082
+#13080 := (iff #3366 #13079)
+#13077 := (iff #3365 #13074)
+#13071 := (implies #12196 #13066)
+#13075 := (iff #13071 #13074)
+#13076 := [rewrite]: #13075
+#13072 := (iff #3365 #13071)
+#13069 := (iff #3364 #13066)
+#13063 := (implies #12196 #13058)
+#13067 := (iff #13063 #13066)
+#13068 := [rewrite]: #13067
+#13064 := (iff #3364 #13063)
+#13061 := (iff #3363 #13058)
+#13055 := (implies #12196 #13050)
+#13059 := (iff #13055 #13058)
+#13060 := [rewrite]: #13059
+#13056 := (iff #3363 #13055)
+#13053 := (iff #3362 #13050)
+#13047 := (implies #12485 #13042)
+#13051 := (iff #13047 #13050)
+#13052 := [rewrite]: #13051
+#13048 := (iff #3362 #13047)
+#13045 := (iff #3361 #13042)
+#13038 := (implies #12485 #13033)
+#13043 := (iff #13038 #13042)
+#13044 := [rewrite]: #13043
+#13039 := (iff #3361 #13038)
+#13036 := (iff #3360 #13033)
+#13030 := (implies #12228 #13025)
+#13034 := (iff #13030 #13033)
+#13035 := [rewrite]: #13034
+#13031 := (iff #3360 #13030)
+#13028 := (iff #3359 #13025)
+#13021 := (implies #12507 #13016)
 #13026 := (iff #13021 #13025)
 #13027 := [rewrite]: #13026
-#13022 := (iff #3355 #13021)
-#13019 := (iff #3354 #13009)
-#13014 := (implies true #13009)
-#13017 := (iff #13014 #13009)
+#13022 := (iff #3359 #13021)
+#13019 := (iff #3358 #13016)
+#13012 := (implies #12510 #13007)
+#13017 := (iff #13012 #13016)
 #13018 := [rewrite]: #13017
-#13015 := (iff #3354 #13014)
-#13012 := (iff #3353 #13009)
-#13006 := (implies #12232 #13003)
-#13010 := (iff #13006 #13009)
-#13011 := [rewrite]: #13010
-#13007 := (iff #3353 #13006)
-#13004 := (iff #3352 #13003)
-#13001 := (iff #3351 #12998)
-#12995 := (implies #12232 #12990)
-#12999 := (iff #12995 #12998)
+#13013 := (iff #3358 #13012)
+#13010 := (iff #3357 #13007)
+#13003 := (implies #12513 #12998)
+#13008 := (iff #13003 #13007)
+#13009 := [rewrite]: #13008
+#13004 := (iff #3357 #13003)
+#13001 := (iff #3356 #12998)
+#12994 := (implies #12516 #12989)
+#12999 := (iff #12994 #12998)
 #13000 := [rewrite]: #12999
-#12996 := (iff #3351 #12995)
-#12993 := (iff #3350 #12990)
-#12986 := (implies #3347 #12981)
-#12991 := (iff #12986 #12990)
-#12992 := [rewrite]: #12991
-#12987 := (iff #3350 #12986)
-#12984 := (iff #3349 #12981)
-#12978 := (implies #12232 #12973)
-#12982 := (iff #12978 #12981)
-#12983 := [rewrite]: #12982
-#12979 := (iff #3349 #12978)
-#12976 := (iff #3348 #12973)
-#12970 := (implies #12232 #12394)
+#12995 := (iff #3356 #12994)
+#12992 := (iff #3355 #12989)
+#12985 := (implies #12525 #12973)
+#12990 := (iff #12985 #12989)
+#12991 := [rewrite]: #12990
+#12986 := (iff #3355 #12985)
+#12983 := (iff #3354 #12973)
+#12978 := (implies true #12973)
+#12981 := (iff #12978 #12973)
+#12982 := [rewrite]: #12981
+#12979 := (iff #3354 #12978)
+#12976 := (iff #3353 #12973)
+#12970 := (implies #12196 #12967)
 #12974 := (iff #12970 #12973)
 #12975 := [rewrite]: #12974
-#12971 := (iff #3348 #12970)
-#12397 := (iff #3191 #12394)
-#12391 := (implies #12232 #12386)
-#12395 := (iff #12391 #12394)
-#12396 := [rewrite]: #12395
-#12392 := (iff #3191 #12391)
-#12389 := (iff #3190 #12386)
-#12383 := (implies #12232 #12380)
-#12387 := (iff #12383 #12386)
-#12388 := [rewrite]: #12387
-#12384 := (iff #3190 #12383)
-#12381 := (iff #3189 #12380)
-#12378 := (iff #3188 #12375)
-#12371 := (implies #10960 #12366)
-#12376 := (iff #12371 #12375)
-#12377 := [rewrite]: #12376
-#12372 := (iff #3188 #12371)
-#12369 := (iff #3187 #12366)
-#12363 := (implies #12232 #12358)
-#12367 := (iff #12363 #12366)
-#12368 := [rewrite]: #12367
-#12364 := (iff #3187 #12363)
-#12361 := (iff #3186 #12358)
-#12355 := (implies #12232 #12350)
+#12971 := (iff #3353 #12970)
+#12968 := (iff #3352 #12967)
+#12965 := (iff #3351 #12962)
+#12959 := (implies #12196 #12954)
+#12963 := (iff #12959 #12962)
+#12964 := [rewrite]: #12963
+#12960 := (iff #3351 #12959)
+#12957 := (iff #3350 #12954)
+#12950 := (implies #3347 #12945)
+#12955 := (iff #12950 #12954)
+#12956 := [rewrite]: #12955
+#12951 := (iff #3350 #12950)
+#12948 := (iff #3349 #12945)
+#12942 := (implies #12196 #12937)
+#12946 := (iff #12942 #12945)
+#12947 := [rewrite]: #12946
+#12943 := (iff #3349 #12942)
+#12940 := (iff #3348 #12937)
+#12934 := (implies #12196 #12358)
+#12938 := (iff #12934 #12937)
+#12939 := [rewrite]: #12938
+#12935 := (iff #3348 #12934)
+#12361 := (iff #3191 #12358)
+#12355 := (implies #12196 #12350)
 #12359 := (iff #12355 #12358)
 #12360 := [rewrite]: #12359
-#12356 := (iff #3186 #12355)
-#12353 := (iff #3185 #12350)
-#12346 := (implies #12232 #12341)
-#12351 := (iff #12346 #12350)
+#12356 := (iff #3191 #12355)
+#12353 := (iff #3190 #12350)
+#12347 := (implies #12196 #12344)
+#12351 := (iff #12347 #12350)
 #12352 := [rewrite]: #12351
-#12347 := (iff #3185 #12346)
-#12344 := (iff #3184 #12341)
-#12337 := (implies #12269 #12332)
-#12342 := (iff #12337 #12341)
-#12343 := [rewrite]: #12342
-#12338 := (iff #3184 #12337)
-#12335 := (iff #3183 #12332)
-#12328 := (implies #12272 #12323)
-#12333 := (iff #12328 #12332)
-#12334 := [rewrite]: #12333
-#12329 := (iff #3183 #12328)
-#12326 := (iff #3182 #12323)
-#12319 := (implies #12275 #12314)
-#12324 := (iff #12319 #12323)
-#12325 := [rewrite]: #12324
-#12320 := (iff #3182 #12319)
-#12317 := (iff #3181 #12314)
-#12310 := (implies #12278 #12307)
+#12348 := (iff #3190 #12347)
+#12345 := (iff #3189 #12344)
+#12342 := (iff #3188 #12339)
+#12335 := (implies #10924 #12330)
+#12340 := (iff #12335 #12339)
+#12341 := [rewrite]: #12340
+#12336 := (iff #3188 #12335)
+#12333 := (iff #3187 #12330)
+#12327 := (implies #12196 #12322)
+#12331 := (iff #12327 #12330)
+#12332 := [rewrite]: #12331
+#12328 := (iff #3187 #12327)
+#12325 := (iff #3186 #12322)
+#12319 := (implies #12196 #12314)
+#12323 := (iff #12319 #12322)
+#12324 := [rewrite]: #12323
+#12320 := (iff #3186 #12319)
+#12317 := (iff #3185 #12314)
+#12310 := (implies #12196 #12305)
 #12315 := (iff #12310 #12314)
 #12316 := [rewrite]: #12315
-#12311 := (iff #3181 #12310)
-#12308 := (iff #3180 #12307)
-#12305 := (iff #3179 #12302)
-#12298 := (implies #12293 #3177)
-#12303 := (iff #12298 #12302)
-#12304 := [rewrite]: #12303
-#12299 := (iff #3179 #12298)
-#12296 := (iff #3178 #3177)
-#12297 := [rewrite]: #12296
-#12294 := (iff #3172 #12293)
-#12291 := (iff #3171 #12288)
-#12285 := (implies #455 #12282)
-#12289 := (iff #12285 #12288)
-#12290 := [rewrite]: #12289
-#12286 := (iff #3171 #12285)
-#12283 := (iff #3170 #12282)
-#12284 := [rewrite]: #12283
-#12287 := [monotonicity #12284]: #12286
-#12292 := [trans #12287 #12290]: #12291
-#12295 := [quant-intro #12292]: #12294
-#12300 := [monotonicity #12295 #12297]: #12299
-#12306 := [trans #12300 #12304]: #12305
-#12309 := [monotonicity #12295 #12306]: #12308
-#12279 := (iff #3167 #12278)
+#12311 := (iff #3185 #12310)
+#12308 := (iff #3184 #12305)
+#12301 := (implies #12233 #12296)
+#12306 := (iff #12301 #12305)
+#12307 := [rewrite]: #12306
+#12302 := (iff #3184 #12301)
+#12299 := (iff #3183 #12296)
+#12292 := (implies #12236 #12287)
+#12297 := (iff #12292 #12296)
+#12298 := [rewrite]: #12297
+#12293 := (iff #3183 #12292)
+#12290 := (iff #3182 #12287)
+#12283 := (implies #12239 #12278)
+#12288 := (iff #12283 #12287)
+#12289 := [rewrite]: #12288
+#12284 := (iff #3182 #12283)
+#12281 := (iff #3181 #12278)
+#12274 := (implies #12242 #12271)
+#12279 := (iff #12274 #12278)
 #12280 := [rewrite]: #12279
-#12312 := [monotonicity #12280 #12309]: #12311
+#12275 := (iff #3181 #12274)
+#12272 := (iff #3180 #12271)
+#12269 := (iff #3179 #12266)
+#12262 := (implies #12257 #3177)
+#12267 := (iff #12262 #12266)
+#12268 := [rewrite]: #12267
+#12263 := (iff #3179 #12262)
+#12260 := (iff #3178 #3177)
+#12261 := [rewrite]: #12260
+#12258 := (iff #3172 #12257)
+#12255 := (iff #3171 #12252)
+#12249 := (implies #455 #12246)
+#12253 := (iff #12249 #12252)
+#12254 := [rewrite]: #12253
+#12250 := (iff #3171 #12249)
+#12247 := (iff #3170 #12246)
+#12248 := [rewrite]: #12247
+#12251 := [monotonicity #12248]: #12250
+#12256 := [trans #12251 #12254]: #12255
+#12259 := [quant-intro #12256]: #12258
+#12264 := [monotonicity #12259 #12261]: #12263
+#12270 := [trans #12264 #12268]: #12269
+#12273 := [monotonicity #12259 #12270]: #12272
+#12243 := (iff #3167 #12242)
+#12244 := [rewrite]: #12243
+#12276 := [monotonicity #12244 #12273]: #12275
+#12282 := [trans #12276 #12280]: #12281
+#12240 := (iff #3165 #12239)
+#12241 := [rewrite]: #12240
+#12285 := [monotonicity #12241 #12282]: #12284
+#12291 := [trans #12285 #12289]: #12290
+#12237 := (iff #3163 #12236)
+#12238 := [rewrite]: #12237
+#12294 := [monotonicity #12238 #12291]: #12293
+#12300 := [trans #12294 #12298]: #12299
+#12234 := (iff #3161 #12233)
+#12235 := [rewrite]: #12234
+#12303 := [monotonicity #12235 #12300]: #12302
+#12309 := [trans #12303 #12307]: #12308
+#12197 := (iff #3144 #12196)
+#12198 := [rewrite]: #12197
+#12312 := [monotonicity #12198 #12309]: #12311
 #12318 := [trans #12312 #12316]: #12317
-#12276 := (iff #3165 #12275)
-#12277 := [rewrite]: #12276
-#12321 := [monotonicity #12277 #12318]: #12320
-#12327 := [trans #12321 #12325]: #12326
-#12273 := (iff #3163 #12272)
-#12274 := [rewrite]: #12273
-#12330 := [monotonicity #12274 #12327]: #12329
-#12336 := [trans #12330 #12334]: #12335
-#12270 := (iff #3161 #12269)
-#12271 := [rewrite]: #12270
-#12339 := [monotonicity #12271 #12336]: #12338
-#12345 := [trans #12339 #12343]: #12344
-#12233 := (iff #3144 #12232)
-#12234 := [rewrite]: #12233
-#12348 := [monotonicity #12234 #12345]: #12347
-#12354 := [trans #12348 #12352]: #12353
-#12357 := [monotonicity #12234 #12354]: #12356
+#12321 := [monotonicity #12198 #12318]: #12320
+#12326 := [trans #12321 #12324]: #12325
+#12329 := [monotonicity #12198 #12326]: #12328
+#12334 := [trans #12329 #12332]: #12333
+#10926 := (iff #2542 #10924)
+#10927 := [rewrite]: #10926
+#12337 := [monotonicity #10927 #12334]: #12336
+#12343 := [trans #12337 #12341]: #12342
+#12346 := [monotonicity #10927 #12343]: #12345
+#12349 := [monotonicity #12198 #12346]: #12348
+#12354 := [trans #12349 #12352]: #12353
+#12357 := [monotonicity #12198 #12354]: #12356
 #12362 := [trans #12357 #12360]: #12361
-#12365 := [monotonicity #12234 #12362]: #12364
-#12370 := [trans #12365 #12368]: #12369
-#10962 := (iff #2542 #10960)
-#10963 := [rewrite]: #10962
-#12373 := [monotonicity #10963 #12370]: #12372
-#12379 := [trans #12373 #12377]: #12378
-#12382 := [monotonicity #10963 #12379]: #12381
-#12385 := [monotonicity #12234 #12382]: #12384
-#12390 := [trans #12385 #12388]: #12389
-#12393 := [monotonicity #12234 #12390]: #12392
-#12398 := [trans #12393 #12396]: #12397
-#12972 := [monotonicity #12234 #12398]: #12971
-#12977 := [trans #12972 #12975]: #12976
-#12980 := [monotonicity #12234 #12977]: #12979
-#12985 := [trans #12980 #12983]: #12984
-#12988 := [monotonicity #12985]: #12987
-#12994 := [trans #12988 #12992]: #12993
-#12997 := [monotonicity #12234 #12994]: #12996
-#13002 := [trans #12997 #13000]: #13001
-#12968 := (iff #3346 #12965)
-#12962 := (implies #12232 #12957)
-#12966 := (iff #12962 #12965)
-#12967 := [rewrite]: #12966
-#12963 := (iff #3346 #12962)
-#12960 := (iff #3345 #12957)
-#12953 := (implies #3256 #12948)
-#12958 := (iff #12953 #12957)
-#12959 := [rewrite]: #12958
-#12954 := (iff #3345 #12953)
-#12951 := (iff #3344 #12948)
-#12945 := (implies #12232 #12940)
-#12949 := (iff #12945 #12948)
-#12950 := [rewrite]: #12949
-#12946 := (iff #3344 #12945)
-#12943 := (iff #3343 #12940)
-#12937 := (implies #12232 #12934)
-#12941 := (iff #12937 #12940)
-#12942 := [rewrite]: #12941
-#12938 := (iff #3343 #12937)
-#12935 := (iff #3342 #12934)
-#12932 := (iff #3341 #12929)
-#12926 := (implies #12581 #12923)
+#12936 := [monotonicity #12198 #12362]: #12935
+#12941 := [trans #12936 #12939]: #12940
+#12944 := [monotonicity #12198 #12941]: #12943
+#12949 := [trans #12944 #12947]: #12948
+#12952 := [monotonicity #12949]: #12951
+#12958 := [trans #12952 #12956]: #12957
+#12961 := [monotonicity #12198 #12958]: #12960
+#12966 := [trans #12961 #12964]: #12965
+#12932 := (iff #3346 #12929)
+#12926 := (implies #12196 #12921)
 #12930 := (iff #12926 #12929)
 #12931 := [rewrite]: #12930
-#12927 := (iff #3341 #12926)
-#12924 := (iff #3340 #12923)
-#12921 := (iff #3339 #12918)
-#12915 := (implies #12587 #12910)
-#12919 := (iff #12915 #12918)
-#12920 := [rewrite]: #12919
-#12916 := (iff #3339 #12915)
-#12913 := (iff #3338 #12910)
-#12907 := (implies #12232 #12904)
-#12911 := (iff #12907 #12910)
-#12912 := [rewrite]: #12911
-#12908 := (iff #3338 #12907)
-#12905 := (iff #3337 #12904)
-#12902 := (iff #3336 #12899)
-#12896 := (implies #12232 #12891)
-#12900 := (iff #12896 #12899)
-#12901 := [rewrite]: #12900
-#12897 := (iff #3336 #12896)
-#12894 := (iff #3335 #12891)
-#12887 := (implies #3327 #12882)
-#12892 := (iff #12887 #12891)
-#12893 := [rewrite]: #12892
-#12888 := (iff #3335 #12887)
-#12885 := (iff #3334 #12882)
-#12879 := (implies #12232 #12874)
+#12927 := (iff #3346 #12926)
+#12924 := (iff #3345 #12921)
+#12917 := (implies #3256 #12912)
+#12922 := (iff #12917 #12921)
+#12923 := [rewrite]: #12922
+#12918 := (iff #3345 #12917)
+#12915 := (iff #3344 #12912)
+#12909 := (implies #12196 #12904)
+#12913 := (iff #12909 #12912)
+#12914 := [rewrite]: #12913
+#12910 := (iff #3344 #12909)
+#12907 := (iff #3343 #12904)
+#12901 := (implies #12196 #12898)
+#12905 := (iff #12901 #12904)
+#12906 := [rewrite]: #12905
+#12902 := (iff #3343 #12901)
+#12899 := (iff #3342 #12898)
+#12896 := (iff #3341 #12893)
+#12890 := (implies #12545 #12887)
+#12894 := (iff #12890 #12893)
+#12895 := [rewrite]: #12894
+#12891 := (iff #3341 #12890)
+#12888 := (iff #3340 #12887)
+#12885 := (iff #3339 #12882)
+#12879 := (implies #12551 #12874)
 #12883 := (iff #12879 #12882)
 #12884 := [rewrite]: #12883
-#12880 := (iff #3334 #12879)
-#12877 := (iff #3333 #12874)
-#12871 := (implies #12232 #12866)
+#12880 := (iff #3339 #12879)
+#12877 := (iff #3338 #12874)
+#12871 := (implies #12196 #12868)
 #12875 := (iff #12871 #12874)
 #12876 := [rewrite]: #12875
-#12872 := (iff #3333 #12871)
-#12869 := (iff #3332 #12866)
-#12863 := (implies #12232 #12858)
-#12867 := (iff #12863 #12866)
-#12868 := [rewrite]: #12867
-#12864 := (iff #3332 #12863)
-#12861 := (iff #3331 #12858)
-#12854 := (implies #12839 #12849)
-#12859 := (iff #12854 #12858)
-#12860 := [rewrite]: #12859
-#12855 := (iff #3331 #12854)
-#12852 := (iff #3330 #12849)
-#12845 := (implies #12842 #12723)
-#12850 := (iff #12845 #12849)
-#12851 := [rewrite]: #12850
-#12846 := (iff #3330 #12845)
-#12726 := (iff #3312 #12723)
-#12719 := (implies #3280 #12716)
+#12872 := (iff #3338 #12871)
+#12869 := (iff #3337 #12868)
+#12866 := (iff #3336 #12863)
+#12860 := (implies #12196 #12855)
+#12864 := (iff #12860 #12863)
+#12865 := [rewrite]: #12864
+#12861 := (iff #3336 #12860)
+#12858 := (iff #3335 #12855)
+#12851 := (implies #3327 #12846)
+#12856 := (iff #12851 #12855)
+#12857 := [rewrite]: #12856
+#12852 := (iff #3335 #12851)
+#12849 := (iff #3334 #12846)
+#12843 := (implies #12196 #12838)
+#12847 := (iff #12843 #12846)
+#12848 := [rewrite]: #12847
+#12844 := (iff #3334 #12843)
+#12841 := (iff #3333 #12838)
+#12835 := (implies #12196 #12830)
+#12839 := (iff #12835 #12838)
+#12840 := [rewrite]: #12839
+#12836 := (iff #3333 #12835)
+#12833 := (iff #3332 #12830)
+#12827 := (implies #12196 #12822)
+#12831 := (iff #12827 #12830)
+#12832 := [rewrite]: #12831
+#12828 := (iff #3332 #12827)
+#12825 := (iff #3331 #12822)
+#12818 := (implies #12803 #12813)
+#12823 := (iff #12818 #12822)
+#12824 := [rewrite]: #12823
+#12819 := (iff #3331 #12818)
+#12816 := (iff #3330 #12813)
+#12809 := (implies #12806 #12687)
+#12814 := (iff #12809 #12813)
+#12815 := [rewrite]: #12814
+#12810 := (iff #3330 #12809)
+#12690 := (iff #3312 #12687)
+#12683 := (implies #3280 #12680)
+#12688 := (iff #12683 #12687)
+#12689 := [rewrite]: #12688
+#12684 := (iff #3312 #12683)
+#12681 := (iff #3311 #12680)
+#12678 := (iff #3310 #12675)
+#12671 := (implies #12580 #12666)
+#12676 := (iff #12671 #12675)
+#12677 := [rewrite]: #12676
+#12672 := (iff #3310 #12671)
+#12669 := (iff #3309 #12666)
+#12662 := (implies #12583 #12657)
+#12667 := (iff #12662 #12666)
+#12668 := [rewrite]: #12667
+#12663 := (iff #3309 #12662)
+#12660 := (iff #3308 #12657)
+#12653 := (implies #12586 #12648)
+#12658 := (iff #12653 #12657)
+#12659 := [rewrite]: #12658
+#12654 := (iff #3308 #12653)
+#12651 := (iff #3307 #12648)
+#12644 := (implies #12589 #12641)
+#12649 := (iff #12644 #12648)
+#12650 := [rewrite]: #12649
+#12645 := (iff #3307 #12644)
+#12642 := (iff #3306 #12641)
+#12639 := (iff #3305 #12636)
+#12632 := (implies #3291 #12629)
+#12637 := (iff #12632 #12636)
+#12638 := [rewrite]: #12637
+#12633 := (iff #3305 #12632)
+#12630 := (iff #3304 #12629)
+#12627 := (iff #3303 #12624)
+#12620 := (implies #12604 #12610)
+#12625 := (iff #12620 #12624)
+#12626 := [rewrite]: #12625
+#12621 := (iff #3303 #12620)
+#12618 := (iff #3302 #12610)
+#12613 := (and #12610 true)
+#12616 := (iff #12613 #12610)
+#12617 := [rewrite]: #12616
+#12614 := (iff #3302 #12613)
+#12611 := (iff #3301 #12610)
+#12608 := (iff #3300 #12607)
+#12609 := [rewrite]: #12608
+#12612 := [monotonicity #12609]: #12611
+#12615 := [monotonicity #12612]: #12614
+#12619 := [trans #12615 #12617]: #12618
+#12605 := (iff #3296 #12604)
+#12602 := (iff #3295 #12599)
+#12596 := (implies #455 #12593)
+#12600 := (iff #12596 #12599)
+#12601 := [rewrite]: #12600
+#12597 := (iff #3295 #12596)
+#12594 := (iff #3294 #12593)
+#12595 := [rewrite]: #12594
+#12598 := [monotonicity #12595]: #12597
+#12603 := [trans #12598 #12601]: #12602
+#12606 := [quant-intro #12603]: #12605
+#12622 := [monotonicity #12606 #12619]: #12621
+#12628 := [trans #12622 #12626]: #12627
+#12631 := [monotonicity #12606 #12628]: #12630
+#12634 := [monotonicity #12631]: #12633
+#12640 := [trans #12634 #12638]: #12639
+#12643 := [monotonicity #12640]: #12642
+#12590 := (iff #3290 #12589)
+#12591 := [rewrite]: #12590
+#12646 := [monotonicity #12591 #12643]: #12645
+#12652 := [trans #12646 #12650]: #12651
+#12587 := (iff #3288 #12586)
+#12588 := [rewrite]: #12587
+#12655 := [monotonicity #12588 #12652]: #12654
+#12661 := [trans #12655 #12659]: #12660
+#12584 := (iff #3286 #12583)
+#12572 := (= #3281 #12571)
+#12573 := [rewrite]: #12572
+#12585 := [monotonicity #12573]: #12584
+#12664 := [monotonicity #12585 #12661]: #12663
+#12670 := [trans #12664 #12668]: #12669
+#12581 := (iff #3284 #12580)
+#12578 := (iff #3283 #12577)
+#12579 := [monotonicity #12573]: #12578
+#12575 := (iff #3282 #12574)
+#12576 := [monotonicity #12573]: #12575
+#12582 := [monotonicity #12576 #12579]: #12581
+#12673 := [monotonicity #12582 #12670]: #12672
+#12679 := [trans #12673 #12677]: #12678
+#12682 := [monotonicity #12582 #12679]: #12681
+#12685 := [monotonicity #12682]: #12684
+#12691 := [trans #12685 #12689]: #12690
+#12807 := (iff #3329 #12806)
+#12808 := [rewrite]: #12807
+#12811 := [monotonicity #12808 #12691]: #12810
+#12817 := [trans #12811 #12815]: #12816
+#12804 := (iff #3328 #12803)
+#12805 := [rewrite]: #12804
+#12820 := [monotonicity #12805 #12817]: #12819
+#12826 := [trans #12820 #12824]: #12825
+#12829 := [monotonicity #12198 #12826]: #12828
+#12834 := [trans #12829 #12832]: #12833
+#12837 := [monotonicity #12198 #12834]: #12836
+#12842 := [trans #12837 #12840]: #12841
+#12845 := [monotonicity #12198 #12842]: #12844
+#12850 := [trans #12845 #12848]: #12849
+#12853 := [monotonicity #12850]: #12852
+#12859 := [trans #12853 #12857]: #12858
+#12862 := [monotonicity #12198 #12859]: #12861
+#12867 := [trans #12862 #12865]: #12866
+#12801 := (iff #3326 #12798)
+#12795 := (implies #12196 #12790)
+#12799 := (iff #12795 #12798)
+#12800 := [rewrite]: #12799
+#12796 := (iff #3326 #12795)
+#12793 := (iff #3325 #12790)
+#12786 := (implies #3267 #12781)
+#12791 := (iff #12786 #12790)
+#12792 := [rewrite]: #12791
+#12787 := (iff #3325 #12786)
+#12784 := (iff #3324 #12781)
+#12778 := (implies #12196 #12773)
+#12782 := (iff #12778 #12781)
+#12783 := [rewrite]: #12782
+#12779 := (iff #3324 #12778)
+#12776 := (iff #3323 #12773)
+#12770 := (implies #12196 #12767)
+#12774 := (iff #12770 #12773)
+#12775 := [rewrite]: #12774
+#12771 := (iff #3323 #12770)
+#12768 := (iff #3322 #12767)
+#12765 := (iff #3321 #12762)
+#12758 := (implies #12545 #12755)
+#12763 := (iff #12758 #12762)
+#12764 := [rewrite]: #12763
+#12759 := (iff #3321 #12758)
+#12756 := (iff #3320 #12755)
+#12753 := (iff #3319 #12750)
+#12746 := (implies #12551 #12741)
+#12751 := (iff #12746 #12750)
+#12752 := [rewrite]: #12751
+#12747 := (iff #3319 #12746)
+#12744 := (iff #3318 #12741)
+#12737 := (implies #12554 #12732)
+#12742 := (iff #12737 #12741)
+#12743 := [rewrite]: #12742
+#12738 := (iff #3318 #12737)
+#12735 := (iff #3317 #12732)
+#12728 := (implies #12557 #12723)
+#12733 := (iff #12728 #12732)
+#12734 := [rewrite]: #12733
+#12729 := (iff #3317 #12728)
+#12726 := (iff #3316 #12723)
+#12719 := (implies #12560 #12714)
 #12724 := (iff #12719 #12723)
 #12725 := [rewrite]: #12724
-#12720 := (iff #3312 #12719)
-#12717 := (iff #3311 #12716)
-#12714 := (iff #3310 #12711)
-#12707 := (implies #12616 #12702)
-#12712 := (iff #12707 #12711)
-#12713 := [rewrite]: #12712
-#12708 := (iff #3310 #12707)
-#12705 := (iff #3309 #12702)
-#12698 := (implies #12619 #12693)
-#12703 := (iff #12698 #12702)
-#12704 := [rewrite]: #12703
-#12699 := (iff #3309 #12698)
-#12696 := (iff #3308 #12693)
-#12689 := (implies #12622 #12684)
-#12694 := (iff #12689 #12693)
-#12695 := [rewrite]: #12694
-#12690 := (iff #3308 #12689)
-#12687 := (iff #3307 #12684)
-#12680 := (implies #12625 #12677)
-#12685 := (iff #12680 #12684)
-#12686 := [rewrite]: #12685
-#12681 := (iff #3307 #12680)
-#12678 := (iff #3306 #12677)
-#12675 := (iff #3305 #12672)
-#12668 := (implies #3291 #12665)
-#12673 := (iff #12668 #12672)
-#12674 := [rewrite]: #12673
-#12669 := (iff #3305 #12668)
-#12666 := (iff #3304 #12665)
-#12663 := (iff #3303 #12660)
-#12656 := (implies #12640 #12646)
-#12661 := (iff #12656 #12660)
-#12662 := [rewrite]: #12661
-#12657 := (iff #3303 #12656)
-#12654 := (iff #3302 #12646)
-#12649 := (and #12646 true)
-#12652 := (iff #12649 #12646)
-#12653 := [rewrite]: #12652
-#12650 := (iff #3302 #12649)
-#12647 := (iff #3301 #12646)
-#12644 := (iff #3300 #12643)
-#12645 := [rewrite]: #12644
-#12648 := [monotonicity #12645]: #12647
-#12651 := [monotonicity #12648]: #12650
-#12655 := [trans #12651 #12653]: #12654
-#12641 := (iff #3296 #12640)
-#12638 := (iff #3295 #12635)
-#12632 := (implies #455 #12629)
-#12636 := (iff #12632 #12635)
-#12637 := [rewrite]: #12636
-#12633 := (iff #3295 #12632)
-#12630 := (iff #3294 #12629)
-#12631 := [rewrite]: #12630
-#12634 := [monotonicity #12631]: #12633
-#12639 := [trans #12634 #12637]: #12638
-#12642 := [quant-intro #12639]: #12641
-#12658 := [monotonicity #12642 #12655]: #12657
-#12664 := [trans #12658 #12662]: #12663
-#12667 := [monotonicity #12642 #12664]: #12666
-#12670 := [monotonicity #12667]: #12669
-#12676 := [trans #12670 #12674]: #12675
-#12679 := [monotonicity #12676]: #12678
-#12626 := (iff #3290 #12625)
-#12627 := [rewrite]: #12626
-#12682 := [monotonicity #12627 #12679]: #12681
-#12688 := [trans #12682 #12686]: #12687
-#12623 := (iff #3288 #12622)
-#12624 := [rewrite]: #12623
-#12691 := [monotonicity #12624 #12688]: #12690
-#12697 := [trans #12691 #12695]: #12696
-#12620 := (iff #3286 #12619)
-#12608 := (= #3281 #12607)
-#12609 := [rewrite]: #12608
-#12621 := [monotonicity #12609]: #12620
-#12700 := [monotonicity #12621 #12697]: #12699
-#12706 := [trans #12700 #12704]: #12705
-#12617 := (iff #3284 #12616)
-#12614 := (iff #3283 #12613)
-#12615 := [monotonicity #12609]: #12614
-#12611 := (iff #3282 #12610)
-#12612 := [monotonicity #12609]: #12611
-#12618 := [monotonicity #12612 #12615]: #12617
-#12709 := [monotonicity #12618 #12706]: #12708
-#12715 := [trans #12709 #12713]: #12714
-#12718 := [monotonicity #12618 #12715]: #12717
-#12721 := [monotonicity #12718]: #12720
+#12720 := (iff #3316 #12719)
+#12717 := (iff #3315 #12714)
+#12710 := (implies #3143 #12705)
+#12715 := (iff #12710 #12714)
+#12716 := [rewrite]: #12715
+#12711 := (iff #3315 #12710)
+#12708 := (iff #3314 #12705)
+#12701 := (implies #12565 #12696)
+#12706 := (iff #12701 #12705)
+#12707 := [rewrite]: #12706
+#12702 := (iff #3314 #12701)
+#12699 := (iff #3313 #12696)
+#12692 := (implies #12568 #12687)
+#12697 := (iff #12692 #12696)
+#12698 := [rewrite]: #12697
+#12693 := (iff #3313 #12692)
+#12569 := (iff #3278 #12568)
+#12570 := [rewrite]: #12569
+#12694 := [monotonicity #12570 #12691]: #12693
+#12700 := [trans #12694 #12698]: #12699
+#12566 := (iff #3276 #12565)
+#12567 := [rewrite]: #12566
+#12703 := [monotonicity #12567 #12700]: #12702
+#12709 := [trans #12703 #12707]: #12708
+#12563 := (iff #3274 #3143)
+#12564 := [rewrite]: #12563
+#12712 := [monotonicity #12564 #12709]: #12711
+#12718 := [trans #12712 #12716]: #12717
+#12561 := (iff #3273 #12560)
+#12562 := [rewrite]: #12561
+#12721 := [monotonicity #12562 #12718]: #12720
 #12727 := [trans #12721 #12725]: #12726
-#12843 := (iff #3329 #12842)
-#12844 := [rewrite]: #12843
-#12847 := [monotonicity #12844 #12727]: #12846
-#12853 := [trans #12847 #12851]: #12852
-#12840 := (iff #3328 #12839)
-#12841 := [rewrite]: #12840
-#12856 := [monotonicity #12841 #12853]: #12855
-#12862 := [trans #12856 #12860]: #12861
-#12865 := [monotonicity #12234 #12862]: #12864
-#12870 := [trans #12865 #12868]: #12869
-#12873 := [monotonicity #12234 #12870]: #12872
+#12558 := (iff #3271 #12557)
+#12559 := [rewrite]: #12558
+#12730 := [monotonicity #12559 #12727]: #12729
+#12736 := [trans #12730 #12734]: #12735
+#12555 := (iff #3269 #12554)
+#12556 := [rewrite]: #12555
+#12739 := [monotonicity #12556 #12736]: #12738
+#12745 := [trans #12739 #12743]: #12744
+#12552 := (iff #3265 #12551)
+#12549 := (iff #3264 #12548)
+#12550 := [rewrite]: #12549
+#12540 := (iff #3259 #12539)
+#12541 := [rewrite]: #12540
+#12553 := [monotonicity #12541 #12550]: #12552
+#12748 := [monotonicity #12553 #12745]: #12747
+#12754 := [trans #12748 #12752]: #12753
+#12757 := [monotonicity #12553 #12754]: #12756
+#12546 := (iff #3262 #12545)
+#12543 := (iff #3261 #12542)
+#12544 := [rewrite]: #12543
+#12547 := [monotonicity #12541 #12544]: #12546
+#12760 := [monotonicity #12547 #12757]: #12759
+#12766 := [trans #12760 #12764]: #12765
+#12769 := [monotonicity #12547 #12766]: #12768
+#12772 := [monotonicity #12198 #12769]: #12771
+#12777 := [trans #12772 #12775]: #12776
+#12780 := [monotonicity #12198 #12777]: #12779
+#12785 := [trans #12780 #12783]: #12784
+#12788 := [monotonicity #12785]: #12787
+#12794 := [trans #12788 #12792]: #12793
+#12797 := [monotonicity #12198 #12794]: #12796
+#12802 := [trans #12797 #12800]: #12801
+#12870 := [monotonicity #12802 #12867]: #12869
+#12873 := [monotonicity #12198 #12870]: #12872
 #12878 := [trans #12873 #12876]: #12877
-#12881 := [monotonicity #12234 #12878]: #12880
+#12881 := [monotonicity #12553 #12878]: #12880
 #12886 := [trans #12881 #12884]: #12885
-#12889 := [monotonicity #12886]: #12888
-#12895 := [trans #12889 #12893]: #12894
-#12898 := [monotonicity #12234 #12895]: #12897
-#12903 := [trans #12898 #12901]: #12902
-#12837 := (iff #3326 #12834)
-#12831 := (implies #12232 #12826)
-#12835 := (iff #12831 #12834)
-#12836 := [rewrite]: #12835
-#12832 := (iff #3326 #12831)
-#12829 := (iff #3325 #12826)
-#12822 := (implies #3267 #12817)
-#12827 := (iff #12822 #12826)
-#12828 := [rewrite]: #12827
-#12823 := (iff #3325 #12822)
-#12820 := (iff #3324 #12817)
-#12814 := (implies #12232 #12809)
-#12818 := (iff #12814 #12817)
-#12819 := [rewrite]: #12818
-#12815 := (iff #3324 #12814)
-#12812 := (iff #3323 #12809)
-#12806 := (implies #12232 #12803)
-#12810 := (iff #12806 #12809)
-#12811 := [rewrite]: #12810
-#12807 := (iff #3323 #12806)
-#12804 := (iff #3322 #12803)
-#12801 := (iff #3321 #12798)
-#12794 := (implies #12581 #12791)
-#12799 := (iff #12794 #12798)
-#12800 := [rewrite]: #12799
-#12795 := (iff #3321 #12794)
-#12792 := (iff #3320 #12791)
-#12789 := (iff #3319 #12786)
-#12782 := (implies #12587 #12777)
-#12787 := (iff #12782 #12786)
-#12788 := [rewrite]: #12787
-#12783 := (iff #3319 #12782)
-#12780 := (iff #3318 #12777)
-#12773 := (implies #12590 #12768)
-#12778 := (iff #12773 #12777)
-#12779 := [rewrite]: #12778
-#12774 := (iff #3318 #12773)
-#12771 := (iff #3317 #12768)
-#12764 := (implies #12593 #12759)
-#12769 := (iff #12764 #12768)
-#12770 := [rewrite]: #12769
-#12765 := (iff #3317 #12764)
-#12762 := (iff #3316 #12759)
-#12755 := (implies #12596 #12750)
-#12760 := (iff #12755 #12759)
-#12761 := [rewrite]: #12760
-#12756 := (iff #3316 #12755)
-#12753 := (iff #3315 #12750)
-#12746 := (implies #3143 #12741)
-#12751 := (iff #12746 #12750)
-#12752 := [rewrite]: #12751
-#12747 := (iff #3315 #12746)
-#12744 := (iff #3314 #12741)
-#12737 := (implies #12601 #12732)
-#12742 := (iff #12737 #12741)
-#12743 := [rewrite]: #12742
-#12738 := (iff #3314 #12737)
-#12735 := (iff #3313 #12732)
-#12728 := (implies #12604 #12723)
-#12733 := (iff #12728 #12732)
-#12734 := [rewrite]: #12733
-#12729 := (iff #3313 #12728)
-#12605 := (iff #3278 #12604)
-#12606 := [rewrite]: #12605
-#12730 := [monotonicity #12606 #12727]: #12729
-#12736 := [trans #12730 #12734]: #12735
-#12602 := (iff #3276 #12601)
-#12603 := [rewrite]: #12602
-#12739 := [monotonicity #12603 #12736]: #12738
-#12745 := [trans #12739 #12743]: #12744
-#12599 := (iff #3274 #3143)
-#12600 := [rewrite]: #12599
-#12748 := [monotonicity #12600 #12745]: #12747
-#12754 := [trans #12748 #12752]: #12753
-#12597 := (iff #3273 #12596)
-#12598 := [rewrite]: #12597
-#12757 := [monotonicity #12598 #12754]: #12756
-#12763 := [trans #12757 #12761]: #12762
-#12594 := (iff #3271 #12593)
-#12595 := [rewrite]: #12594
-#12766 := [monotonicity #12595 #12763]: #12765
-#12772 := [trans #12766 #12770]: #12771
-#12591 := (iff #3269 #12590)
-#12592 := [rewrite]: #12591
-#12775 := [monotonicity #12592 #12772]: #12774
-#12781 := [trans #12775 #12779]: #12780
-#12588 := (iff #3265 #12587)
-#12585 := (iff #3264 #12584)
-#12586 := [rewrite]: #12585
-#12576 := (iff #3259 #12575)
-#12577 := [rewrite]: #12576
-#12589 := [monotonicity #12577 #12586]: #12588
-#12784 := [monotonicity #12589 #12781]: #12783
-#12790 := [trans #12784 #12788]: #12789
-#12793 := [monotonicity #12589 #12790]: #12792
-#12582 := (iff #3262 #12581)
-#12579 := (iff #3261 #12578)
-#12580 := [rewrite]: #12579
-#12583 := [monotonicity #12577 #12580]: #12582
-#12796 := [monotonicity #12583 #12793]: #12795
-#12802 := [trans #12796 #12800]: #12801
-#12805 := [monotonicity #12583 #12802]: #12804
-#12808 := [monotonicity #12234 #12805]: #12807
-#12813 := [trans #12808 #12811]: #12812
-#12816 := [monotonicity #12234 #12813]: #12815
-#12821 := [trans #12816 #12819]: #12820
-#12824 := [monotonicity #12821]: #12823
-#12830 := [trans #12824 #12828]: #12829
-#12833 := [monotonicity #12234 #12830]: #12832
-#12838 := [trans #12833 #12836]: #12837
-#12906 := [monotonicity #12838 #12903]: #12905
-#12909 := [monotonicity #12234 #12906]: #12908
-#12914 := [trans #12909 #12912]: #12913
-#12917 := [monotonicity #12589 #12914]: #12916
-#12922 := [trans #12917 #12920]: #12921
-#12925 := [monotonicity #12589 #12922]: #12924
-#12928 := [monotonicity #12583 #12925]: #12927
+#12889 := [monotonicity #12553 #12886]: #12888
+#12892 := [monotonicity #12547 #12889]: #12891
+#12897 := [trans #12892 #12895]: #12896
+#12900 := [monotonicity #12547 #12897]: #12899
+#12903 := [monotonicity #12198 #12900]: #12902
+#12908 := [trans #12903 #12906]: #12907
+#12911 := [monotonicity #12198 #12908]: #12910
+#12916 := [trans #12911 #12914]: #12915
+#12919 := [monotonicity #12916]: #12918
+#12925 := [trans #12919 #12923]: #12924
+#12928 := [monotonicity #12198 #12925]: #12927
 #12933 := [trans #12928 #12931]: #12932
-#12936 := [monotonicity #12583 #12933]: #12935
-#12939 := [monotonicity #12234 #12936]: #12938
-#12944 := [trans #12939 #12942]: #12943
-#12947 := [monotonicity #12234 #12944]: #12946
-#12952 := [trans #12947 #12950]: #12951
-#12955 := [monotonicity #12952]: #12954
-#12961 := [trans #12955 #12959]: #12960
-#12964 := [monotonicity #12234 #12961]: #12963
-#12969 := [trans #12964 #12967]: #12968
-#13005 := [monotonicity #12969 #13002]: #13004
-#13008 := [monotonicity #12234 #13005]: #13007
-#13013 := [trans #13008 #13011]: #13012
-#12573 := (iff #3255 true)
-#12571 := (iff #12568 true)
-#12572 := [rewrite]: #12571
-#12569 := (iff #3255 #12568)
-#12566 := (iff #3254 true)
-#12567 := [rewrite]: #12566
-#12564 := (iff #3253 true)
-#12565 := [rewrite]: #12564
-#12570 := [monotonicity #12565 #12567]: #12569
-#12574 := [trans #12570 #12572]: #12573
-#13016 := [monotonicity #12574 #13013]: #13015
-#13020 := [trans #13016 #13018]: #13019
-#12562 := (iff #3252 #12561)
-#12559 := (iff #3251 #12558)
-#12560 := [rewrite]: #12559
-#12556 := (iff #3249 #12555)
-#12557 := [rewrite]: #12556
-#12563 := [monotonicity #12557 #12560]: #12562
-#13023 := [monotonicity #12563 #13020]: #13022
+#12969 := [monotonicity #12933 #12966]: #12968
+#12972 := [monotonicity #12198 #12969]: #12971
+#12977 := [trans #12972 #12975]: #12976
+#12537 := (iff #3255 true)
+#12535 := (iff #12532 true)
+#12536 := [rewrite]: #12535
+#12533 := (iff #3255 #12532)
+#12530 := (iff #3254 true)
+#12531 := [rewrite]: #12530
+#12528 := (iff #3253 true)
+#12529 := [rewrite]: #12528
+#12534 := [monotonicity #12529 #12531]: #12533
+#12538 := [trans #12534 #12536]: #12537
+#12980 := [monotonicity #12538 #12977]: #12979
+#12984 := [trans #12980 #12982]: #12983
+#12526 := (iff #3252 #12525)
+#12523 := (iff #3251 #12522)
+#12524 := [rewrite]: #12523
+#12520 := (iff #3249 #12519)
+#12521 := [rewrite]: #12520
+#12527 := [monotonicity #12521 #12524]: #12526
+#12987 := [monotonicity #12527 #12984]: #12986
+#12993 := [trans #12987 #12991]: #12992
+#12517 := (iff #3247 #12516)
+#12518 := [rewrite]: #12517
+#12996 := [monotonicity #12518 #12993]: #12995
+#13002 := [trans #12996 #13000]: #13001
+#12514 := (iff #3245 #12513)
+#12515 := [rewrite]: #12514
+#13005 := [monotonicity #12515 #13002]: #13004
+#13011 := [trans #13005 #13009]: #13010
+#12511 := (iff #3243 #12510)
+#12512 := [rewrite]: #12511
+#13014 := [monotonicity #12512 #13011]: #13013
+#13020 := [trans #13014 #13018]: #13019
+#12508 := (iff #3241 #12507)
+#12509 := [rewrite]: #12508
+#13023 := [monotonicity #12509 #13020]: #13022
 #13029 := [trans #13023 #13027]: #13028
-#12553 := (iff #3247 #12552)
-#12554 := [rewrite]: #12553
-#13032 := [monotonicity #12554 #13029]: #13031
-#13038 := [trans #13032 #13036]: #13037
-#12550 := (iff #3245 #12549)
-#12551 := [rewrite]: #12550
-#13041 := [monotonicity #12551 #13038]: #13040
-#13047 := [trans #13041 #13045]: #13046
-#12547 := (iff #3243 #12546)
-#12548 := [rewrite]: #12547
-#13050 := [monotonicity #12548 #13047]: #13049
-#13056 := [trans #13050 #13054]: #13055
-#12544 := (iff #3241 #12543)
-#12545 := [rewrite]: #12544
-#13059 := [monotonicity #12545 #13056]: #13058
-#13065 := [trans #13059 #13063]: #13064
-#12267 := (iff #3159 #12264)
-#12261 := (and #12258 #12145)
-#12265 := (iff #12261 #12264)
-#12266 := [rewrite]: #12265
-#12262 := (iff #3159 #12261)
-#12146 := (iff #3068 #12145)
-#12147 := [rewrite]: #12146
-#12259 := (iff #3158 #12258)
-#12260 := [rewrite]: #12259
-#12263 := [monotonicity #12260 #12147]: #12262
-#12268 := [trans #12263 #12266]: #12267
-#13068 := [monotonicity #12268 #13065]: #13067
-#13073 := [trans #13068 #13071]: #13072
-#12522 := (iff #3235 #12521)
-#12519 := (iff #3234 #12518)
-#12516 := (iff #3233 #12515)
-#12517 := [rewrite]: #12516
-#12520 := [monotonicity #12517]: #12519
-#12523 := [monotonicity #12520]: #12522
-#13076 := [monotonicity #12523 #13073]: #13075
-#13082 := [trans #13076 #13080]: #13081
-#12541 := (iff #3239 #12521)
-#12524 := (and true #12521)
-#12527 := (iff #12524 #12521)
-#12528 := [rewrite]: #12527
-#12539 := (iff #3239 #12524)
-#12537 := (iff #3238 #12521)
-#12535 := (iff #3238 #12524)
-#12533 := (iff #3237 #12521)
-#12531 := (iff #3237 #12524)
-#12529 := (iff #3236 #12521)
-#12525 := (iff #3236 #12524)
-#12513 := (iff #3226 true)
-#12508 := (forall (vars (?v0 S20)) (:pat #3222) true)
-#12511 := (iff #12508 true)
-#12512 := [elim-unused]: #12511
-#12509 := (iff #3226 #12508)
-#12506 := (iff #3225 true)
-#12458 := (= f1 #3210)
-#12470 := (implies #12458 #12458)
-#12473 := (iff #12470 true)
-#12474 := [rewrite]: #12473
-#12504 := (iff #3225 #12470)
-#12502 := (iff #3224 #12458)
-#12463 := (and true #12458)
-#12466 := (iff #12463 #12458)
-#12467 := [rewrite]: #12466
-#12500 := (iff #3224 #12463)
-#12459 := (iff #3211 #12458)
-#12460 := [rewrite]: #12459
-#12498 := (iff #3223 true)
-#12499 := [rewrite]: #12498
-#12501 := [monotonicity #12499 #12460]: #12500
-#12503 := [trans #12501 #12467]: #12502
-#12505 := [monotonicity #12460 #12503]: #12504
-#12507 := [trans #12505 #12474]: #12506
-#12510 := [quant-intro #12507]: #12509
-#12514 := [trans #12510 #12512]: #12513
-#12526 := [monotonicity #12514 #12523]: #12525
-#12530 := [trans #12526 #12528]: #12529
-#12496 := (iff #3219 true)
-#12451 := (forall (vars (?v0 S20)) (:pat #3199) true)
-#12454 := (iff #12451 true)
-#12455 := [elim-unused]: #12454
-#12494 := (iff #3219 #12451)
-#12492 := (iff #3218 true)
-#12490 := (iff #3218 #12470)
-#12488 := (iff #3217 #12458)
-#12486 := (iff #3217 #12463)
-#12484 := (iff #3216 true)
-#12485 := [rewrite]: #12484
-#12487 := [monotonicity #12485 #12460]: #12486
-#12489 := [trans #12487 #12467]: #12488
-#12491 := [monotonicity #12460 #12489]: #12490
-#12493 := [trans #12491 #12474]: #12492
-#12495 := [quant-intro #12493]: #12494
-#12497 := [trans #12495 #12455]: #12496
-#12532 := [monotonicity #12497 #12530]: #12531
-#12534 := [trans #12532 #12528]: #12533
-#12482 := (iff #3215 true)
-#12477 := (forall (vars (?v0 S20)) (:pat #3209) true)
-#12480 := (iff #12477 true)
-#12481 := [elim-unused]: #12480
-#12478 := (iff #3215 #12477)
-#12475 := (iff #3214 true)
-#12471 := (iff #3214 #12470)
-#12468 := (iff #3213 #12458)
-#12464 := (iff #3213 #12463)
-#12461 := (iff #3212 true)
-#12462 := [rewrite]: #12461
-#12465 := [monotonicity #12462 #12460]: #12464
-#12469 := [trans #12465 #12467]: #12468
-#12472 := [monotonicity #12460 #12469]: #12471
-#12476 := [trans #12472 #12474]: #12475
-#12479 := [quant-intro #12476]: #12478
-#12483 := [trans #12479 #12481]: #12482
-#12536 := [monotonicity #12483 #12534]: #12535
-#12538 := [trans #12536 #12528]: #12537
-#12456 := (iff #3206 true)
-#12452 := (iff #3206 #12451)
-#12449 := (iff #3205 true)
-#12438 := (= f272 #3202)
-#12441 := (not #12438)
-#12444 := (implies #12441 #12441)
-#12447 := (iff #12444 true)
-#12448 := [rewrite]: #12447
-#12445 := (iff #3205 #12444)
-#12442 := (iff #3204 #12441)
-#12439 := (iff #3203 #12438)
-#12440 := [rewrite]: #12439
-#12443 := [monotonicity #12440]: #12442
-#12446 := [monotonicity #12443 #12443]: #12445
-#12450 := [trans #12446 #12448]: #12449
-#12453 := [quant-intro #12450]: #12452
-#12457 := [trans #12453 #12455]: #12456
-#12540 := [monotonicity #12457 #12538]: #12539
-#12542 := [trans #12540 #12528]: #12541
-#13085 := [monotonicity #12542 #13082]: #13084
-#13090 := [trans #13085 #13088]: #13089
-#13093 := [monotonicity #12234 #13090]: #13092
-#13098 := [trans #13093 #13096]: #13097
-#13101 := [monotonicity #12234 #13098]: #13100
-#13106 := [trans #13101 #13104]: #13105
-#13109 := [monotonicity #12234 #13106]: #13108
-#13114 := [trans #13109 #13112]: #13113
-#12436 := (iff #3196 true)
-#12431 := (implies #12232 true)
-#12434 := (iff #12431 true)
-#12435 := [rewrite]: #12434
-#12432 := (iff #3196 #12431)
-#12429 := (iff #3195 true)
-#12403 := (or #12402 #12394)
-#12411 := (or #12349 #12403)
-#12419 := (or #12349 #12411)
-#12424 := (implies false #12419)
-#12427 := (iff #12424 true)
-#12428 := [rewrite]: #12427
-#12425 := (iff #3195 #12424)
-#12422 := (iff #3194 #12419)
-#12416 := (implies #12232 #12411)
-#12420 := (iff #12416 #12419)
-#12421 := [rewrite]: #12420
-#12417 := (iff #3194 #12416)
-#12414 := (iff #3193 #12411)
-#12408 := (implies #12232 #12403)
-#12412 := (iff #12408 #12411)
-#12413 := [rewrite]: #12412
-#12409 := (iff #3193 #12408)
-#12406 := (iff #3192 #12403)
-#12399 := (implies #12264 #12394)
-#12404 := (iff #12399 #12403)
-#12405 := [rewrite]: #12404
-#12400 := (iff #3192 #12399)
-#12401 := [monotonicity #12268 #12398]: #12400
-#12407 := [trans #12401 #12405]: #12406
-#12410 := [monotonicity #12234 #12407]: #12409
-#12415 := [trans #12410 #12413]: #12414
-#12418 := [monotonicity #12234 #12415]: #12417
-#12423 := [trans #12418 #12421]: #12422
-#12426 := [monotonicity #12257 #12423]: #12425
-#12430 := [trans #12426 #12428]: #12429
-#12433 := [monotonicity #12234 #12430]: #12432
-#12437 := [trans #12433 #12435]: #12436
-#13117 := [monotonicity #12437 #13114]: #13116
-#13121 := [trans #13117 #13119]: #13120
-#13124 := [monotonicity #12234 #13121]: #13123
-#13129 := [trans #13124 #13127]: #13128
-#12254 := (iff #3155 #12253)
-#12251 := (iff #3154 #12250)
-#12252 := [rewrite]: #12251
-#12255 := [monotonicity #12252]: #12254
-#13132 := [monotonicity #12255 #13129]: #13131
-#13138 := [trans #13132 #13136]: #13137
-#12248 := (iff #3150 #12247)
-#12245 := (iff #3149 #12242)
-#12239 := (implies #455 #12236)
-#12243 := (iff #12239 #12242)
-#12244 := [rewrite]: #12243
-#12240 := (iff #3149 #12239)
-#12237 := (iff #3148 #12236)
-#12238 := [rewrite]: #12237
-#12241 := [monotonicity #12238]: #12240
-#12246 := [trans #12241 #12244]: #12245
-#12249 := [quant-intro #12246]: #12248
-#13141 := [monotonicity #12249 #13138]: #13140
-#13147 := [trans #13141 #13145]: #13146
-#13150 := [monotonicity #13147]: #13149
-#13156 := [trans #13150 #13154]: #13155
-#13159 := [monotonicity #12234 #13156]: #13158
-#13164 := [trans #13159 #13162]: #13163
-#13167 := [monotonicity #13164]: #13166
-#13173 := [trans #13167 #13171]: #13172
-#13176 := [monotonicity #13173]: #13175
-#13182 := [trans #13176 #13180]: #13181
-#13185 := [monotonicity #13182]: #13184
-#13191 := [trans #13185 #13189]: #13190
-#12230 := (iff #3130 #12229)
-#12227 := (iff #3129 #3109)
-#12228 := [rewrite]: #12227
-#12231 := [monotonicity #12228]: #12230
-#13194 := [monotonicity #12231 #13191]: #13193
+#12231 := (iff #3159 #12228)
+#12225 := (and #12222 #12109)
+#12229 := (iff #12225 #12228)
+#12230 := [rewrite]: #12229
+#12226 := (iff #3159 #12225)
+#12110 := (iff #3068 #12109)
+#12111 := [rewrite]: #12110
+#12223 := (iff #3158 #12222)
+#12224 := [rewrite]: #12223
+#12227 := [monotonicity #12224 #12111]: #12226
+#12232 := [trans #12227 #12230]: #12231
+#13032 := [monotonicity #12232 #13029]: #13031
+#13037 := [trans #13032 #13035]: #13036
+#12486 := (iff #3235 #12485)
+#12483 := (iff #3234 #12482)
+#12480 := (iff #3233 #12479)
+#12481 := [rewrite]: #12480
+#12484 := [monotonicity #12481]: #12483
+#12487 := [monotonicity #12484]: #12486
+#13040 := [monotonicity #12487 #13037]: #13039
+#13046 := [trans #13040 #13044]: #13045
+#12505 := (iff #3239 #12485)
+#12488 := (and true #12485)
+#12491 := (iff #12488 #12485)
+#12492 := [rewrite]: #12491
+#12503 := (iff #3239 #12488)
+#12501 := (iff #3238 #12485)
+#12499 := (iff #3238 #12488)
+#12497 := (iff #3237 #12485)
+#12495 := (iff #3237 #12488)
+#12493 := (iff #3236 #12485)
+#12489 := (iff #3236 #12488)
+#12477 := (iff #3226 true)
+#12472 := (forall (vars (?v0 S20)) (:pat #3222) true)
+#12475 := (iff #12472 true)
+#12476 := [elim-unused]: #12475
+#12473 := (iff #3226 #12472)
+#12470 := (iff #3225 true)
+#12422 := (= f1 #3210)
+#12434 := (implies #12422 #12422)
+#12437 := (iff #12434 true)
+#12438 := [rewrite]: #12437
+#12468 := (iff #3225 #12434)
+#12466 := (iff #3224 #12422)
+#12427 := (and true #12422)
+#12430 := (iff #12427 #12422)
+#12431 := [rewrite]: #12430
+#12464 := (iff #3224 #12427)
+#12423 := (iff #3211 #12422)
+#12424 := [rewrite]: #12423
+#12462 := (iff #3223 true)
+#12463 := [rewrite]: #12462
+#12465 := [monotonicity #12463 #12424]: #12464
+#12467 := [trans #12465 #12431]: #12466
+#12469 := [monotonicity #12424 #12467]: #12468
+#12471 := [trans #12469 #12438]: #12470
+#12474 := [quant-intro #12471]: #12473
+#12478 := [trans #12474 #12476]: #12477
+#12490 := [monotonicity #12478 #12487]: #12489
+#12494 := [trans #12490 #12492]: #12493
+#12460 := (iff #3219 true)
+#12415 := (forall (vars (?v0 S20)) (:pat #3199) true)
+#12418 := (iff #12415 true)
+#12419 := [elim-unused]: #12418
+#12458 := (iff #3219 #12415)
+#12456 := (iff #3218 true)
+#12454 := (iff #3218 #12434)
+#12452 := (iff #3217 #12422)
+#12450 := (iff #3217 #12427)
+#12448 := (iff #3216 true)
+#12449 := [rewrite]: #12448
+#12451 := [monotonicity #12449 #12424]: #12450
+#12453 := [trans #12451 #12431]: #12452
+#12455 := [monotonicity #12424 #12453]: #12454
+#12457 := [trans #12455 #12438]: #12456
+#12459 := [quant-intro #12457]: #12458
+#12461 := [trans #12459 #12419]: #12460
+#12496 := [monotonicity #12461 #12494]: #12495
+#12498 := [trans #12496 #12492]: #12497
+#12446 := (iff #3215 true)
+#12441 := (forall (vars (?v0 S20)) (:pat #3209) true)
+#12444 := (iff #12441 true)
+#12445 := [elim-unused]: #12444
+#12442 := (iff #3215 #12441)
+#12439 := (iff #3214 true)
+#12435 := (iff #3214 #12434)
+#12432 := (iff #3213 #12422)
+#12428 := (iff #3213 #12427)
+#12425 := (iff #3212 true)
+#12426 := [rewrite]: #12425
+#12429 := [monotonicity #12426 #12424]: #12428
+#12433 := [trans #12429 #12431]: #12432
+#12436 := [monotonicity #12424 #12433]: #12435
+#12440 := [trans #12436 #12438]: #12439
+#12443 := [quant-intro #12440]: #12442
+#12447 := [trans #12443 #12445]: #12446
+#12500 := [monotonicity #12447 #12498]: #12499
+#12502 := [trans #12500 #12492]: #12501
+#12420 := (iff #3206 true)
+#12416 := (iff #3206 #12415)
+#12413 := (iff #3205 true)
+#12402 := (= f273 #3202)
+#12405 := (not #12402)
+#12408 := (implies #12405 #12405)
+#12411 := (iff #12408 true)
+#12412 := [rewrite]: #12411
+#12409 := (iff #3205 #12408)
+#12406 := (iff #3204 #12405)
+#12403 := (iff #3203 #12402)
+#12404 := [rewrite]: #12403
+#12407 := [monotonicity #12404]: #12406
+#12410 := [monotonicity #12407 #12407]: #12409
+#12414 := [trans #12410 #12412]: #12413
+#12417 := [quant-intro #12414]: #12416
+#12421 := [trans #12417 #12419]: #12420
+#12504 := [monotonicity #12421 #12502]: #12503
+#12506 := [trans #12504 #12492]: #12505
+#13049 := [monotonicity #12506 #13046]: #13048
+#13054 := [trans #13049 #13052]: #13053
+#13057 := [monotonicity #12198 #13054]: #13056
+#13062 := [trans #13057 #13060]: #13061
+#13065 := [monotonicity #12198 #13062]: #13064
+#13070 := [trans #13065 #13068]: #13069
+#13073 := [monotonicity #12198 #13070]: #13072
+#13078 := [trans #13073 #13076]: #13077
+#12400 := (iff #3196 true)
+#12395 := (implies #12196 true)
+#12398 := (iff #12395 true)
+#12399 := [rewrite]: #12398
+#12396 := (iff #3196 #12395)
+#12393 := (iff #3195 true)
+#12367 := (or #12366 #12358)
+#12375 := (or #12313 #12367)
+#12383 := (or #12313 #12375)
+#12388 := (implies false #12383)
+#12391 := (iff #12388 true)
+#12392 := [rewrite]: #12391
+#12389 := (iff #3195 #12388)
+#12386 := (iff #3194 #12383)
+#12380 := (implies #12196 #12375)
+#12384 := (iff #12380 #12383)
+#12385 := [rewrite]: #12384
+#12381 := (iff #3194 #12380)
+#12378 := (iff #3193 #12375)
+#12372 := (implies #12196 #12367)
+#12376 := (iff #12372 #12375)
+#12377 := [rewrite]: #12376
+#12373 := (iff #3193 #12372)
+#12370 := (iff #3192 #12367)
+#12363 := (implies #12228 #12358)
+#12368 := (iff #12363 #12367)
+#12369 := [rewrite]: #12368
+#12364 := (iff #3192 #12363)
+#12365 := [monotonicity #12232 #12362]: #12364
+#12371 := [trans #12365 #12369]: #12370
+#12374 := [monotonicity #12198 #12371]: #12373
+#12379 := [trans #12374 #12377]: #12378
+#12382 := [monotonicity #12198 #12379]: #12381
+#12387 := [trans #12382 #12385]: #12386
+#12390 := [monotonicity #12221 #12387]: #12389
+#12394 := [trans #12390 #12392]: #12393
+#12397 := [monotonicity #12198 #12394]: #12396
+#12401 := [trans #12397 #12399]: #12400
+#13081 := [monotonicity #12401 #13078]: #13080
+#13085 := [trans #13081 #13083]: #13084
+#13088 := [monotonicity #12198 #13085]: #13087
+#13093 := [trans #13088 #13091]: #13092
+#12218 := (iff #3155 #12217)
+#12215 := (iff #3154 #12214)
+#12216 := [rewrite]: #12215
+#12219 := [monotonicity #12216]: #12218
+#13096 := [monotonicity #12219 #13093]: #13095
+#13102 := [trans #13096 #13100]: #13101
+#12212 := (iff #3150 #12211)
+#12209 := (iff #3149 #12206)
+#12203 := (implies #455 #12200)
+#12207 := (iff #12203 #12206)
+#12208 := [rewrite]: #12207
+#12204 := (iff #3149 #12203)
+#12201 := (iff #3148 #12200)
+#12202 := [rewrite]: #12201
+#12205 := [monotonicity #12202]: #12204
+#12210 := [trans #12205 #12208]: #12209
+#12213 := [quant-intro #12210]: #12212
+#13105 := [monotonicity #12213 #13102]: #13104
+#13111 := [trans #13105 #13109]: #13110
+#13114 := [monotonicity #13111]: #13113
+#13120 := [trans #13114 #13118]: #13119
+#13123 := [monotonicity #12198 #13120]: #13122
+#13128 := [trans #13123 #13126]: #13127
+#13131 := [monotonicity #13128]: #13130
+#13137 := [trans #13131 #13135]: #13136
+#13140 := [monotonicity #13137]: #13139
+#13146 := [trans #13140 #13144]: #13145
+#13149 := [monotonicity #13146]: #13148
+#13155 := [trans #13149 #13153]: #13154
+#12194 := (iff #3130 #12193)
+#12191 := (iff #3129 #3109)
+#12192 := [rewrite]: #12191
+#12195 := [monotonicity #12192]: #12194
+#13158 := [monotonicity #12195 #13155]: #13157
+#13164 := [trans #13158 #13162]: #13163
+#13167 := [monotonicity #12195 #13164]: #13166
+#12189 := (iff #3128 #12188)
+#12186 := (iff #3127 #12183)
+#12180 := (implies #455 #12177)
+#12184 := (iff #12180 #12183)
+#12185 := [rewrite]: #12184
+#12181 := (iff #3127 #12180)
+#12178 := (iff #3126 #12177)
+#12179 := [rewrite]: #12178
+#12182 := [monotonicity #12179]: #12181
+#12187 := [trans #12182 #12185]: #12186
+#12190 := [quant-intro #12187]: #12189
+#13170 := [monotonicity #12190 #13167]: #13169
+#13176 := [trans #13170 #13174]: #13175
+#13179 := [monotonicity #12190 #13176]: #13178
+#13182 := [monotonicity #13179]: #13181
+#13188 := [trans #13182 #13186]: #13187
+#13191 := [monotonicity #13188]: #13190
+#12174 := (iff #3120 #12173)
+#12171 := (iff #3119 #12170)
+#12168 := (iff #3118 #3117)
+#12169 := [rewrite]: #12168
+#12172 := [monotonicity #12169]: #12171
+#12175 := [monotonicity #12172]: #12174
+#13194 := [monotonicity #12175 #13191]: #13193
 #13200 := [trans #13194 #13198]: #13199
-#13203 := [monotonicity #12231 #13200]: #13202
-#12225 := (iff #3128 #12224)
-#12222 := (iff #3127 #12219)
-#12216 := (implies #455 #12213)
-#12220 := (iff #12216 #12219)
-#12221 := [rewrite]: #12220
-#12217 := (iff #3127 #12216)
-#12214 := (iff #3126 #12213)
-#12215 := [rewrite]: #12214
-#12218 := [monotonicity #12215]: #12217
-#12223 := [trans #12218 #12221]: #12222
-#12226 := [quant-intro #12223]: #12225
-#13206 := [monotonicity #12226 #13203]: #13205
-#13212 := [trans #13206 #13210]: #13211
-#13215 := [monotonicity #12226 #13212]: #13214
-#13218 := [monotonicity #13215]: #13217
-#13224 := [trans #13218 #13222]: #13223
-#13227 := [monotonicity #13224]: #13226
-#12210 := (iff #3120 #12209)
-#12207 := (iff #3119 #12206)
-#12204 := (iff #3118 #3117)
-#12205 := [rewrite]: #12204
-#12208 := [monotonicity #12205]: #12207
-#12211 := [monotonicity #12208]: #12210
-#13230 := [monotonicity #12211 #13227]: #13229
+#12166 := (iff #3115 #12165)
+#12167 := [rewrite]: #12166
+#13203 := [monotonicity #12167 #13200]: #13202
+#13209 := [trans #13203 #13207]: #13208
+#12163 := (iff #3113 #12162)
+#12164 := [rewrite]: #12163
+#13212 := [monotonicity #12164 #13209]: #13211
+#13218 := [trans #13212 #13216]: #13217
+#12160 := (iff #3111 #12159)
+#12161 := [rewrite]: #12160
+#13221 := [monotonicity #12161 #13218]: #13220
+#13227 := [trans #13221 #13225]: #13226
+#13230 := [monotonicity #13227]: #13229
 #13236 := [trans #13230 #13234]: #13235
-#12202 := (iff #3115 #12201)
-#12203 := [rewrite]: #12202
-#13239 := [monotonicity #12203 #13236]: #13238
+#12157 := (iff #3106 #12156)
+#12154 := (iff #3105 #12153)
+#12155 := [rewrite]: #12154
+#12145 := (iff #3100 #12144)
+#12146 := [rewrite]: #12145
+#12158 := [monotonicity #12146 #12155]: #12157
+#13239 := [monotonicity #12158 #13236]: #13238
 #13245 := [trans #13239 #13243]: #13244
-#12199 := (iff #3113 #12198)
-#12200 := [rewrite]: #12199
-#13248 := [monotonicity #12200 #13245]: #13247
-#13254 := [trans #13248 #13252]: #13253
-#12196 := (iff #3111 #12195)
-#12197 := [rewrite]: #12196
-#13257 := [monotonicity #12197 #13254]: #13256
-#13263 := [trans #13257 #13261]: #13262
-#13266 := [monotonicity #13263]: #13265
-#13272 := [trans #13266 #13270]: #13271
-#12193 := (iff #3106 #12192)
-#12190 := (iff #3105 #12189)
-#12191 := [rewrite]: #12190
-#12181 := (iff #3100 #12180)
-#12182 := [rewrite]: #12181
-#12194 := [monotonicity #12182 #12191]: #12193
-#13275 := [monotonicity #12194 #13272]: #13274
+#13248 := [monotonicity #12158 #13245]: #13247
+#12151 := (iff #3103 #12150)
+#12148 := (iff #3102 #12147)
+#12149 := [rewrite]: #12148
+#12152 := [monotonicity #12146 #12149]: #12151
+#13251 := [monotonicity #12152 #13248]: #13250
+#13257 := [trans #13251 #13255]: #13256
+#13260 := [monotonicity #12152 #13257]: #13259
+#12142 := (iff #3097 #12141)
+#12143 := [rewrite]: #12142
+#13263 := [monotonicity #12143 #13260]: #13262
+#13269 := [trans #13263 #13267]: #13268
+#13272 := [monotonicity #12143 #13269]: #13271
+#13275 := [monotonicity #13272]: #13274
 #13281 := [trans #13275 #13279]: #13280
-#13284 := [monotonicity #12194 #13281]: #13283
-#12187 := (iff #3103 #12186)
-#12184 := (iff #3102 #12183)
-#12185 := [rewrite]: #12184
-#12188 := [monotonicity #12182 #12185]: #12187
-#13287 := [monotonicity #12188 #13284]: #13286
-#13293 := [trans #13287 #13291]: #13292
-#13296 := [monotonicity #12188 #13293]: #13295
-#12178 := (iff #3097 #12177)
-#12179 := [rewrite]: #12178
-#13299 := [monotonicity #12179 #13296]: #13298
-#13305 := [trans #13299 #13303]: #13304
-#13308 := [monotonicity #12179 #13305]: #13307
-#13311 := [monotonicity #13308]: #13310
+#12139 := (iff #3091 #12138)
+#12136 := (iff #3090 #12133)
+#12130 := (iff #12127 false)
+#12134 := (iff #12130 #12133)
+#12135 := [rewrite]: #12134
+#12131 := (iff #3090 #12130)
+#12128 := (iff #3089 #12127)
+#12129 := [rewrite]: #12128
+#12132 := [monotonicity #12129]: #12131
+#12137 := [trans #12132 #12135]: #12136
+#12140 := [quant-intro #12137]: #12139
+#13284 := [monotonicity #12140 #13281]: #13283
+#13290 := [trans #13284 #13288]: #13289
+#13293 := [monotonicity #13290]: #13292
+#13299 := [trans #13293 #13297]: #13298
+#12125 := (iff #3083 #12124)
+#12126 := [rewrite]: #12125
+#13302 := [monotonicity #12126 #13299]: #13301
+#13308 := [trans #13302 #13306]: #13307
+#12122 := (iff #3081 #12121)
+#12119 := (iff #3080 #12118)
+#12120 := [rewrite]: #12119
+#12116 := (iff #3078 #12115)
+#12117 := [rewrite]: #12116
+#12123 := [monotonicity #12117 #12120]: #12122
+#13311 := [monotonicity #12123 #13308]: #13310
 #13317 := [trans #13311 #13315]: #13316
-#12175 := (iff #3091 #12174)
-#12172 := (iff #3090 #12169)
-#12166 := (iff #12163 false)
-#12170 := (iff #12166 #12169)
-#12171 := [rewrite]: #12170
-#12167 := (iff #3090 #12166)
-#12164 := (iff #3089 #12163)
-#12165 := [rewrite]: #12164
-#12168 := [monotonicity #12165]: #12167
-#12173 := [trans #12168 #12171]: #12172
-#12176 := [quant-intro #12173]: #12175
-#13320 := [monotonicity #12176 #13317]: #13319
+#13320 := [monotonicity #13317]: #13319
 #13326 := [trans #13320 #13324]: #13325
-#13329 := [monotonicity #13326]: #13328
+#12113 := (iff #3069 #12112)
+#12107 := (iff #3066 #12106)
+#12108 := [rewrite]: #12107
+#12114 := [monotonicity #12108 #12111]: #12113
+#13329 := [monotonicity #12114 #13326]: #13328
 #13335 := [trans #13329 #13333]: #13334
-#12161 := (iff #3083 #12160)
-#12162 := [rewrite]: #12161
-#13338 := [monotonicity #12162 #13335]: #13337
+#12104 := (iff #3064 #12103)
+#12105 := [rewrite]: #12104
+#13338 := [monotonicity #12105 #13335]: #13337
 #13344 := [trans #13338 #13342]: #13343
-#12158 := (iff #3081 #12157)
-#12155 := (iff #3080 #12154)
-#12156 := [rewrite]: #12155
-#12152 := (iff #3078 #12151)
-#12153 := [rewrite]: #12152
-#12159 := [monotonicity #12153 #12156]: #12158
-#13347 := [monotonicity #12159 #13344]: #13346
+#12101 := (iff #3062 #12100)
+#12098 := (iff #3061 #12097)
+#12095 := (iff #3060 #12094)
+#12092 := (iff #3059 #12091)
+#12089 := (iff #3058 #12088)
+#12086 := (iff #3057 #12085)
+#12087 := [rewrite]: #12086
+#12083 := (iff #3055 #12082)
+#12080 := (iff #3054 #12079)
+#12081 := [rewrite]: #12080
+#12084 := [monotonicity #12081]: #12083
+#12090 := [monotonicity #12084 #12087]: #12089
+#12077 := (iff #3052 #12076)
+#12078 := [rewrite]: #12077
+#12093 := [monotonicity #12078 #12090]: #12092
+#12074 := (iff #3050 #12073)
+#12075 := [rewrite]: #12074
+#12096 := [monotonicity #12075 #12093]: #12095
+#12071 := (iff #3048 #12070)
+#12072 := [rewrite]: #12071
+#12099 := [monotonicity #12072 #12096]: #12098
+#12068 := (iff #3046 #12066)
+#12069 := [rewrite]: #12068
+#12102 := [monotonicity #12069 #12099]: #12101
+#13347 := [monotonicity #12102 #13344]: #13346
 #13353 := [trans #13347 #13351]: #13352
 #13356 := [monotonicity #13353]: #13355
 #13362 := [trans #13356 #13360]: #13361
-#12149 := (iff #3069 #12148)
-#12143 := (iff #3066 #12142)
-#12144 := [rewrite]: #12143
-#12150 := [monotonicity #12144 #12147]: #12149
-#13365 := [monotonicity #12150 #13362]: #13364
+#13365 := [monotonicity #13362]: #13364
 #13371 := [trans #13365 #13369]: #13370
-#12140 := (iff #3064 #12139)
-#12141 := [rewrite]: #12140
-#13374 := [monotonicity #12141 #13371]: #13373
+#13374 := [monotonicity #13371]: #13373
 #13380 := [trans #13374 #13378]: #13379
-#12137 := (iff #3062 #12136)
-#12134 := (iff #3061 #12133)
-#12131 := (iff #3060 #12130)
-#12128 := (iff #3059 #12127)
-#12125 := (iff #3058 #12124)
-#12122 := (iff #3057 #12121)
-#12123 := [rewrite]: #12122
-#12119 := (iff #3055 #12118)
-#12116 := (iff #3054 #12115)
-#12117 := [rewrite]: #12116
-#12120 := [monotonicity #12117]: #12119
-#12126 := [monotonicity #12120 #12123]: #12125
-#12113 := (iff #3052 #12112)
-#12114 := [rewrite]: #12113
-#12129 := [monotonicity #12114 #12126]: #12128
-#12110 := (iff #3050 #12109)
-#12111 := [rewrite]: #12110
-#12132 := [monotonicity #12111 #12129]: #12131
-#12107 := (iff #3048 #12106)
-#12108 := [rewrite]: #12107
-#12135 := [monotonicity #12108 #12132]: #12134
-#12104 := (iff #3046 #12102)
-#12105 := [rewrite]: #12104
-#12138 := [monotonicity #12105 #12135]: #12137
-#13383 := [monotonicity #12138 #13380]: #13382
+#13383 := [monotonicity #13380]: #13382
 #13389 := [trans #13383 #13387]: #13388
 #13392 := [monotonicity #13389]: #13391
 #13398 := [trans #13392 #13396]: #13397
 #13401 := [monotonicity #13398]: #13400
-#13407 := [trans #13401 #13405]: #13406
-#13410 := [monotonicity #13407]: #13409
-#13416 := [trans #13410 #13414]: #13415
-#13419 := [monotonicity #13416]: #13418
-#13425 := [trans #13419 #13423]: #13424
-#13428 := [monotonicity #13425]: #13427
-#13434 := [trans #13428 #13432]: #13433
-#13437 := [monotonicity #13434]: #13436
-#14345 := [trans #13437 #14343]: #14344
-#12101 := [asserted]: #3406
-#14346 := [mp #12101 #14345]: #14341
-#14364 := [not-or-elim #14346]: #14228
-#14367 := [and-elim #14364]: #12109
-#11376 := (not #11369)
-#1302 := (f127 #55)
+#14309 := [trans #13401 #14307]: #14308
+#12065 := [asserted]: #3406
+#14310 := [mp #12065 #14309]: #14305
+#14328 := [not-or-elim #14310]: #14192
+#14331 := [and-elim #14328]: #12073
+#275 := (:var 0 S18)
+#55 := (:var 1 S20)
+#2729 := (f59 #55 #275)
+#2730 := (pattern #2729)
+#11333 := (= f1 #2729)
+#11340 := (not #11333)
+#1302 := (f128 #55)
 #2732 := (f54 #275 #1302)
 #2733 := (= #55 #2732)
-#11377 := (or #2733 #11376)
-#11382 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #11377)
-#18282 := (~ #11382 #11382)
-#18280 := (~ #11377 #11377)
-#18281 := [refl]: #18280
-#18283 := [nnf-pos #18281]: #18282
+#11341 := (or #2733 #11340)
+#11346 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #11341)
+#18246 := (~ #11346 #11346)
+#18244 := (~ #11341 #11341)
+#18245 := [refl]: #18244
+#18247 := [nnf-pos #18245]: #18246
+#2731 := (= #2729 f1)
 #2734 := (implies #2731 #2733)
 #2735 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #2734)
-#11383 := (iff #2735 #11382)
-#11380 := (iff #2734 #11377)
-#11373 := (implies #11369 #2733)
-#11378 := (iff #11373 #11377)
-#11379 := [rewrite]: #11378
-#11374 := (iff #2734 #11373)
-#11375 := [monotonicity #11372]: #11374
-#11381 := [trans #11375 #11379]: #11380
-#11384 := [quant-intro #11381]: #11383
-#11368 := [asserted]: #2735
-#11387 := [mp #11368 #11384]: #11382
-#18284 := [mp~ #11387 #18283]: #11382
-#26181 := (not #12109)
-#26194 := (not #11382)
-#26195 := (or #26194 #26181 #26189)
-#26190 := (or #26189 #26181)
-#26196 := (or #26194 #26190)
-#26203 := (iff #26196 #26195)
-#26191 := (or #26181 #26189)
-#26198 := (or #26194 #26191)
-#26201 := (iff #26198 #26195)
-#26202 := [rewrite]: #26201
-#26199 := (iff #26196 #26198)
-#26192 := (iff #26190 #26191)
-#26193 := [rewrite]: #26192
-#26200 := [monotonicity #26193]: #26199
-#26204 := [trans #26200 #26202]: #26203
-#26197 := [quant-inst #3044 #3040]: #26196
-#26205 := [mp #26197 #26204]: #26195
-#28848 := [unit-resolution #26205 #18284 #14367]: #26189
-#28791 := [trans #28789 #28848]: #28790
-#28793 := [monotonicity #28791]: #28792
-#28796 := [symm #28793]: #28795
-#26777 := (= f1 #26776)
-decl f64 :: (-> S19 S20 S21)
-#26765 := (f64 f297 #26182)
-#26766 := (f26 #62 #26765)
-#26772 := (pattern #26766)
-decl f208 :: (-> S18 S1)
-#26586 := (f24 #26182)
-#26769 := (f208 #26586)
-#26770 := (= f1 #26769)
-#26767 := (= f1 #26766)
-#26768 := (not #26767)
-decl f158 :: (-> S20 S21 S1)
-decl f203 :: (-> S22 S21)
-decl f22 :: (-> S19 S20 S22)
-#26761 := (f22 f297 #26182)
-#26762 := (f203 #26761)
-#26763 := (f158 #62 #26762)
-#26764 := (= f1 #26763)
-#26782 := (or #26764 #26768 #26770)
-#26785 := (forall (vars (?v3 S20)) (:pat #26772) #26782)
-#26788 := (not #26785)
-#26778 := (not #26777)
-#26626 := (f38 f297 #26182)
-#26627 := (= f1 #26626)
-#26649 := (not #26627)
-#26791 := (or #26649 #26778 #26788)
-#26794 := (not #26791)
-decl f207 :: (-> S19 S20 S20 S1)
-#26714 := (f207 f297 #26182 #26182)
-#26715 := (= f1 #26714)
-#26716 := (f211 f297 #26182 #26182 f305)
-#26717 := (= f1 #26716)
-#26719 := (iff #26715 #26717)
+#11347 := (iff #2735 #11346)
+#11344 := (iff #2734 #11341)
+#11337 := (implies #11333 #2733)
+#11342 := (iff #11337 #11341)
+#11343 := [rewrite]: #11342
+#11338 := (iff #2734 #11337)
+#11335 := (iff #2731 #11333)
+#11336 := [rewrite]: #11335
+#11339 := [monotonicity #11336]: #11338
+#11345 := [trans #11339 #11343]: #11344
+#11348 := [quant-intro #11345]: #11347
+#11332 := [asserted]: #2735
+#11351 := [mp #11332 #11348]: #11346
+#18248 := [mp~ #11351 #18247]: #11346
+#26145 := (not #12073)
+#26158 := (not #11346)
+#26159 := (or #26158 #26145 #26153)
+#26154 := (or #26153 #26145)
+#26160 := (or #26158 #26154)
+#26167 := (iff #26160 #26159)
+#26155 := (or #26145 #26153)
+#26162 := (or #26158 #26155)
+#26165 := (iff #26162 #26159)
+#26166 := [rewrite]: #26165
+#26163 := (iff #26160 #26162)
+#26156 := (iff #26154 #26155)
+#26157 := [rewrite]: #26156
+#26164 := [monotonicity #26157]: #26163
+#26168 := [trans #26164 #26166]: #26167
+#26161 := [quant-inst #3044 #3040]: #26160
+#26169 := [mp #26161 #26168]: #26159
+#28875 := [unit-resolution #26169 #18248 #14331]: #26153
+#26872 := [symm #28875]: #26866
+#26874 := [monotonicity #26872]: #26873
+#26876 := [trans #26874 #28878]: #26875
+#26910 := [monotonicity #26876]: #26909
+#26912 := [monotonicity #26910]: #26911
+#26914 := [symm #26912]: #26913
+#26899 := [monotonicity #26914]: #26897
+#14333 := [and-elim #14328]: #12082
+#26900 := [mp #14333 #26899]: #26915
+decl f208 :: (-> S19 S20 S20 S1)
+#26678 := (f208 f298 #26146 #26146)
+#26679 := (= f1 #26678)
+#26700 := (not #26679)
+#26680 := (f212 f298 #26146 #26146 f306)
+#26681 := (= f1 #26680)
+#26683 := (iff #26679 #26681)
 #2299 := (:var 0 S31)
+#60 := (:var 2 S20)
 #53 := (:var 3 S19)
-#2311 := (f211 #53 #60 #55 #2299)
+#2311 := (f212 #53 #60 #55 #2299)
 #2312 := (pattern #2311)
-#2314 := (f207 #53 #60 #55)
-#10318 := (= f1 #2314)
-#10314 := (= f1 #2311)
-#10321 := (iff #10314 #10318)
-#10324 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20) (?v3 S31)) (:pat #2312) #10321)
-#17924 := (~ #10324 #10324)
-#17922 := (~ #10321 #10321)
-#17923 := [refl]: #17922
-#17925 := [nnf-pos #17923]: #17924
+#2314 := (f208 #53 #60 #55)
+#10282 := (= f1 #2314)
+#10278 := (= f1 #2311)
+#10285 := (iff #10278 #10282)
+#10288 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20) (?v3 S31)) (:pat #2312) #10285)
+#17888 := (~ #10288 #10288)
+#17886 := (~ #10285 #10285)
+#17887 := [refl]: #17886
+#17889 := [nnf-pos #17887]: #17888
 #2315 := (= #2314 f1)
 #2313 := (= #2311 f1)
 #2316 := (iff #2313 #2315)
 #2317 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20) (?v3 S31)) (:pat #2312) #2316)
-#10325 := (iff #2317 #10324)
-#10322 := (iff #2316 #10321)
-#10319 := (iff #2315 #10318)
-#10320 := [rewrite]: #10319
-#10316 := (iff #2313 #10314)
-#10317 := [rewrite]: #10316
-#10323 := [monotonicity #10317 #10320]: #10322
-#10326 := [quant-intro #10323]: #10325
-#10313 := [asserted]: #2317
-#10329 := [mp #10313 #10326]: #10324
-#17926 := [mp~ #10329 #17925]: #10324
-#26731 := (not #10324)
-#26749 := (or #26731 #26719)
-#26718 := (iff #26717 #26715)
-#26734 := (or #26731 #26718)
-#26738 := (iff #26734 #26749)
-#26739 := (iff #26749 #26749)
-#26740 := [rewrite]: #26739
-#26720 := (iff #26718 #26719)
-#26721 := [rewrite]: #26720
-#26735 := [monotonicity #26721]: #26738
-#26741 := [trans #26735 #26740]: #26738
-#26737 := [quant-inst #3039 #26182 #26182 #3095]: #26734
-#26742 := [mp #26737 #26741]: #26749
-#26937 := [unit-resolution #26742 #17926]: #26719
-#28782 := (= #3096 #26716)
-#26939 := (= #26716 #3096)
-#26934 := (= #26182 #3044)
-#26940 := [symm #28848]: #26934
-#26966 := [monotonicity #26940 #26940]: #26939
-#28799 := [symm #26966]: #28782
-#26828 := (f23 #26586)
-#26831 := (= f25 #26828)
-#26933 := (not #26831)
-#26947 := (iff #12118 #26933)
-#26950 := (iff #12115 #26831)
-#26948 := (iff #26831 #12115)
-#26960 := (= #26828 #3053)
-#26943 := (= #26586 #3040)
-#25117 := (f24 #3044)
-#28850 := (= #25117 #3040)
-#25120 := (= #3040 #25117)
-#25125 := (or #25064 #25120)
-#25126 := [quant-inst #3040 #3043]: #25125
-#28849 := [unit-resolution #25126 #23312]: #25120
-#28851 := [symm #28849]: #28850
-#26941 := (= #26586 #25117)
-#26942 := [monotonicity #26940]: #26941
-#26944 := [trans #26942 #28851]: #26943
-#26946 := [monotonicity #26944]: #26960
-#26949 := [monotonicity #26946]: #26948
-#26951 := [symm #26949]: #26950
-#26935 := [monotonicity #26951]: #26947
-#14369 := [and-elim #14364]: #12118
-#26936 := [mp #14369 #26935]: #26933
-#26736 := (not #26715)
-#26733 := (not #26717)
-#26958 := (iff #13300 #26733)
-#26969 := (iff #12177 #26717)
-#26967 := (iff #26717 #12177)
-#26968 := [monotonicity #26966]: #26967
-#26957 := [symm #26968]: #26969
-#26959 := [monotonicity #26957]: #26958
-#26938 := [hypothesis]: #13300
-#26972 := [mp #26938 #26959]: #26733
-#26722 := (not #26719)
-#26753 := (or #26722 #26736 #26717)
-#26754 := [def-axiom]: #26753
-#26974 := [unit-resolution #26754 #26972 #26937]: #26736
-#26820 := (f35 f297 #26182)
-#26821 := (= f1 #26820)
-#26965 := (= #3051 #26820)
-#26975 := (= #26820 #3051)
-#26963 := [monotonicity #26940]: #26975
-#26961 := [symm #26963]: #26965
-#14368 := [and-elim #14364]: #12112
-#26973 := [trans #14368 #26961]: #26821
-#26823 := (f59 #26182 #26586)
-#26824 := (= f1 #26823)
-#26978 := (= #3049 #26823)
-#26976 := (= #26823 #3049)
-#26962 := [monotonicity #26940 #26944]: #26976
-#26979 := [symm #26962]: #26978
-#26980 := [trans #14367 #26979]: #26824
-#26825 := (not #26824)
-#26822 := (not #26821)
-#27030 := (or #26715 #26822 #26825 #26831)
-#26598 := (f36 f297 #26182)
-#26826 := (= f37 #26598)
-#26989 := (= #3047 #26598)
-#26981 := (= #26598 #3047)
-#26987 := [monotonicity #26940]: #26981
-#27001 := [symm #26987]: #26989
-#14366 := [and-elim #14364]: #12106
-#27002 := [trans #14366 #27001]: #26826
-#27008 := (= #3045 #26626)
-#27003 := (= #26626 #3045)
-#27004 := [monotonicity #26940]: #27003
-#27009 := [symm #27004]: #27008
-#14365 := [and-elim #14364]: #12102
-#27010 := [trans #14365 #27009]: #26627
-#26587 := (f34 #26586)
-#26594 := (= f1 #26587)
-#27019 := (= #3056 #26587)
-#26996 := (= #26587 #3056)
-#26997 := [monotonicity #26944]: #26996
-#27020 := [symm #26997]: #27019
-#14370 := [and-elim #14364]: #12121
-#27029 := [trans #14370 #27020]: #26594
-#14349 := [not-or-elim #14346]: #12148
-#14351 := [and-elim #14349]: #12145
-#2270 := (f207 #86 #62 #62)
+#10289 := (iff #2317 #10288)
+#10286 := (iff #2316 #10285)
+#10283 := (iff #2315 #10282)
+#10284 := [rewrite]: #10283
+#10280 := (iff #2313 #10278)
+#10281 := [rewrite]: #10280
+#10287 := [monotonicity #10281 #10284]: #10286
+#10290 := [quant-intro #10287]: #10289
+#10277 := [asserted]: #2317
+#10293 := [mp #10277 #10290]: #10288
+#17890 := [mp~ #10293 #17889]: #10288
+#26698 := (not #10288)
+#26699 := (or #26698 #26683)
+#26682 := (iff #26681 #26679)
+#26701 := (or #26698 #26682)
+#26703 := (iff #26701 #26699)
+#26705 := (iff #26699 #26699)
+#26706 := [rewrite]: #26705
+#26684 := (iff #26682 #26683)
+#26685 := [rewrite]: #26684
+#26704 := [monotonicity #26685]: #26703
+#26686 := [trans #26704 #26706]: #26703
+#26702 := [quant-inst #3039 #26146 #26146 #3095]: #26701
+#26688 := [mp #26702 #26686]: #26699
+#26901 := [unit-resolution #26688 #17890]: #26683
+#26697 := (not #26681)
+#26908 := (iff #13264 #26697)
+#26906 := (iff #12141 #26681)
+#26904 := (iff #26681 #12141)
+#26903 := (= #26680 #3096)
+#26898 := [monotonicity #26872 #26872]: #26903
+#26905 := [monotonicity #26898]: #26904
+#26907 := [symm #26905]: #26906
+#26924 := [monotonicity #26907]: #26908
+#26902 := [hypothesis]: #13264
+#26925 := [mp #26902 #26924]: #26697
+#26689 := (not #26683)
+#26691 := (or #26689 #26700 #26681)
+#26692 := [def-axiom]: #26691
+#26926 := [unit-resolution #26692 #26925 #26901]: #26700
+#26784 := (f35 f298 #26146)
+#26785 := (= f1 #26784)
+#26930 := (= #3051 #26784)
+#26927 := (= #26784 #3051)
+#26928 := [monotonicity #26872]: #26927
+#26931 := [symm #26928]: #26930
+#14332 := [and-elim #14328]: #12076
+#26932 := [trans #14332 #26931]: #26785
+#26787 := (f59 #26146 #26550)
+#26788 := (= f1 #26787)
+#26923 := (= #3049 #26787)
+#26933 := (= #26787 #3049)
+#26921 := [monotonicity #26872 #26876]: #26933
+#26936 := [symm #26921]: #26923
+#26938 := [trans #14331 #26936]: #26788
+#26789 := (not #26788)
+#26786 := (not #26785)
+#26972 := (or #26679 #26786 #26789 #26795)
+#26562 := (f36 f298 #26146)
+#26790 := (= f37 #26562)
+#26941 := (= #3047 #26562)
+#26939 := (= #26562 #3047)
+#26937 := [monotonicity #26872]: #26939
+#26942 := [symm #26937]: #26941
+#14330 := [and-elim #14328]: #12070
+#26943 := [trans #14330 #26942]: #26790
+#26590 := (f38 f298 #26146)
+#26591 := (= f1 #26590)
+#26952 := (= #3045 #26590)
+#26944 := (= #26590 #3045)
+#26945 := [monotonicity #26872]: #26944
+#26953 := [symm #26945]: #26952
+#14329 := [and-elim #14328]: #12066
+#26965 := [trans #14329 #26953]: #26591
+#26551 := (f34 #26550)
+#26558 := (= f1 #26551)
+#26969 := (= #3056 #26551)
+#26966 := (= #26551 #3056)
+#26967 := [monotonicity #26876]: #26966
+#26970 := [symm #26967]: #26969
+#14334 := [and-elim #14328]: #12085
+#26971 := [trans #14334 #26970]: #26558
+#14313 := [not-or-elim #14310]: #12112
+#14315 := [and-elim #14313]: #12109
+#86 := (:var 1 S19)
+#2270 := (f208 #86 #62 #62)
 #2271 := (pattern #2270)
-#10190 := (= f1 #2270)
+#10154 := (= f1 #2270)
 #269 := (f66 #86)
 #4055 := (= f1 #269)
-#19481 := (not #4055)
+#19445 := (not #4055)
+#186 := (f35 #86 #62)
+#3767 := (= f1 #186)
+#11261 := (not #3767)
+#65 := (f24 #62)
 #184 := (f59 #62 #65)
 #3764 := (= f1 #184)
-#19355 := (not #3764)
-#19354 := (not #3761)
+#19319 := (not #3764)
+#182 := (f36 #86 #62)
+#3761 := (= f37 #182)
+#19318 := (not #3761)
 #175 := (f38 #86 #62)
 #3746 := (= f1 #175)
-#10910 := (not #3746)
+#10874 := (not #3746)
 #110 := (f34 #65)
 #3595 := (= f1 #110)
-#10969 := (not #3595)
-#21914 := (or #68 #10969 #10910 #19354 #19355 #11297 #19481 #10190)
-#21919 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #21914)
-#10205 := (and #91 #3595 #3746 #3761 #3764 #3767 #4055)
-#10208 := (not #10205)
-#10214 := (or #10190 #10208)
-#10219 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #10214)
-#21920 := (iff #10219 #21919)
-#21917 := (iff #10214 #21914)
-#21900 := (or #68 #10969 #10910 #19354 #19355 #11297 #19481)
-#21911 := (or #10190 #21900)
-#21915 := (iff #21911 #21914)
-#21916 := [rewrite]: #21915
-#21912 := (iff #10214 #21911)
-#21909 := (iff #10208 #21900)
-#21901 := (not #21900)
-#21904 := (not #21901)
-#21907 := (iff #21904 #21900)
-#21908 := [rewrite]: #21907
-#21905 := (iff #10208 #21904)
-#21902 := (iff #10205 #21901)
-#21903 := [rewrite]: #21902
-#21906 := [monotonicity #21903]: #21905
-#21910 := [trans #21906 #21908]: #21909
-#21913 := [monotonicity #21910]: #21912
-#21918 := [trans #21913 #21916]: #21917
-#21921 := [quant-intro #21918]: #21920
-#17892 := (~ #10219 #10219)
-#17890 := (~ #10214 #10214)
-#17891 := [refl]: #17890
-#17893 := [nnf-pos #17891]: #17892
+#10933 := (not #3595)
+#66 := (f23 #65)
+#68 := (= #66 f25)
+#21878 := (or #68 #10933 #10874 #19318 #19319 #11261 #19445 #10154)
+#21883 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #21878)
+#91 := (not #68)
+#10169 := (and #91 #3595 #3746 #3761 #3764 #3767 #4055)
+#10172 := (not #10169)
+#10178 := (or #10154 #10172)
+#10183 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #10178)
+#21884 := (iff #10183 #21883)
+#21881 := (iff #10178 #21878)
+#21864 := (or #68 #10933 #10874 #19318 #19319 #11261 #19445)
+#21875 := (or #10154 #21864)
+#21879 := (iff #21875 #21878)
+#21880 := [rewrite]: #21879
+#21876 := (iff #10178 #21875)
+#21873 := (iff #10172 #21864)
+#21865 := (not #21864)
+#21868 := (not #21865)
+#21871 := (iff #21868 #21864)
+#21872 := [rewrite]: #21871
+#21869 := (iff #10172 #21868)
+#21866 := (iff #10169 #21865)
+#21867 := [rewrite]: #21866
+#21870 := [monotonicity #21867]: #21869
+#21874 := [trans #21870 #21872]: #21873
+#21877 := [monotonicity #21874]: #21876
+#21882 := [trans #21877 #21880]: #21881
+#21885 := [quant-intro #21882]: #21884
+#17856 := (~ #10183 #10183)
+#17854 := (~ #10178 #10178)
+#17855 := [refl]: #17854
+#17857 := [nnf-pos #17855]: #17856
 #2278 := (= #2270 f1)
 #111 := (= #110 f1)
 #2272 := (and #91 #111)
+#187 := (= #186 f1)
 #2273 := (and #187 #2272)
 #185 := (= #184 f1)
 #2274 := (and #185 #2273)
+#183 := (= #182 f37)
 #2275 := (and #183 #2274)
 #176 := (= #175 f1)
 #2276 := (and #176 #2275)
@@ -4002,186 +3227,2200 @@
 #2277 := (and #271 #2276)
 #2279 := (implies #2277 #2278)
 #2280 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #2279)
-#10222 := (iff #2280 #10219)
-#10171 := (and #91 #3595)
-#10175 := (and #3767 #10171)
-#10178 := (and #3764 #10175)
-#10181 := (and #3761 #10178)
-#10184 := (and #3746 #10181)
-#10187 := (and #4055 #10184)
-#10196 := (not #10187)
-#10197 := (or #10196 #10190)
-#10202 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #10197)
-#10220 := (iff #10202 #10219)
-#10217 := (iff #10197 #10214)
-#10211 := (or #10208 #10190)
-#10215 := (iff #10211 #10214)
-#10216 := [rewrite]: #10215
-#10212 := (iff #10197 #10211)
-#10209 := (iff #10196 #10208)
-#10206 := (iff #10187 #10205)
-#10207 := [rewrite]: #10206
-#10210 := [monotonicity #10207]: #10209
-#10213 := [monotonicity #10210]: #10212
-#10218 := [trans #10213 #10216]: #10217
-#10221 := [quant-intro #10218]: #10220
-#10203 := (iff #2280 #10202)
-#10200 := (iff #2279 #10197)
-#10193 := (implies #10187 #10190)
-#10198 := (iff #10193 #10197)
-#10199 := [rewrite]: #10198
-#10194 := (iff #2279 #10193)
-#10191 := (iff #2278 #10190)
-#10192 := [rewrite]: #10191
-#10188 := (iff #2277 #10187)
-#10185 := (iff #2276 #10184)
-#10182 := (iff #2275 #10181)
-#10179 := (iff #2274 #10178)
-#10176 := (iff #2273 #10175)
-#10173 := (iff #2272 #10171)
+#10186 := (iff #2280 #10183)
+#10135 := (and #91 #3595)
+#10139 := (and #3767 #10135)
+#10142 := (and #3764 #10139)
+#10145 := (and #3761 #10142)
+#10148 := (and #3746 #10145)
+#10151 := (and #4055 #10148)
+#10160 := (not #10151)
+#10161 := (or #10160 #10154)
+#10166 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #10161)
+#10184 := (iff #10166 #10183)
+#10181 := (iff #10161 #10178)
+#10175 := (or #10172 #10154)
+#10179 := (iff #10175 #10178)
+#10180 := [rewrite]: #10179
+#10176 := (iff #10161 #10175)
+#10173 := (iff #10160 #10172)
+#10170 := (iff #10151 #10169)
+#10171 := [rewrite]: #10170
+#10174 := [monotonicity #10171]: #10173
+#10177 := [monotonicity #10174]: #10176
+#10182 := [trans #10177 #10180]: #10181
+#10185 := [quant-intro #10182]: #10184
+#10167 := (iff #2280 #10166)
+#10164 := (iff #2279 #10161)
+#10157 := (implies #10151 #10154)
+#10162 := (iff #10157 #10161)
+#10163 := [rewrite]: #10162
+#10158 := (iff #2279 #10157)
+#10155 := (iff #2278 #10154)
+#10156 := [rewrite]: #10155
+#10152 := (iff #2277 #10151)
+#10149 := (iff #2276 #10148)
+#10146 := (iff #2275 #10145)
+#10143 := (iff #2274 #10142)
+#10140 := (iff #2273 #10139)
+#10137 := (iff #2272 #10135)
 #3596 := (iff #111 #3595)
 #3597 := [rewrite]: #3596
-#10174 := [monotonicity #3597]: #10173
-#10177 := [monotonicity #3769 #10174]: #10176
+#10138 := [monotonicity #3597]: #10137
+#3768 := (iff #187 #3767)
+#3769 := [rewrite]: #3768
+#10141 := [monotonicity #3769 #10138]: #10140
 #3765 := (iff #185 #3764)
 #3766 := [rewrite]: #3765
-#10180 := [monotonicity #3766 #10177]: #10179
-#10183 := [monotonicity #3763 #10180]: #10182
+#10144 := [monotonicity #3766 #10141]: #10143
+#3762 := (iff #183 #3761)
+#3763 := [rewrite]: #3762
+#10147 := [monotonicity #3763 #10144]: #10146
 #3748 := (iff #176 #3746)
 #3749 := [rewrite]: #3748
-#10186 := [monotonicity #3749 #10183]: #10185
+#10150 := [monotonicity #3749 #10147]: #10149
 #4057 := (iff #271 #4055)
 #4058 := [rewrite]: #4057
-#10189 := [monotonicity #4058 #10186]: #10188
-#10195 := [monotonicity #10189 #10192]: #10194
-#10201 := [trans #10195 #10199]: #10200
-#10204 := [quant-intro #10201]: #10203
-#10223 := [trans #10204 #10221]: #10222
-#10170 := [asserted]: #2280
-#10224 := [mp #10170 #10223]: #10219
-#17894 := [mp~ #10224 #17893]: #10219
-#21922 := [mp #17894 #21921]: #21919
-#26827 := (not #26826)
-#26595 := (not #26594)
-#24846 := (not #12145)
-#26800 := (not #21919)
-#26802 := (or #26800 #24846 #26595 #26649 #26715 #26822 #26825 #26827 #26831)
-#26829 := (= #26828 f25)
-#26830 := (or #26829 #26595 #26649 #26827 #26825 #26822 #24846 #26715)
-#26803 := (or #26800 #26830)
-#26843 := (iff #26803 #26802)
-#26837 := (or #24846 #26595 #26649 #26715 #26822 #26825 #26827 #26831)
-#26805 := (or #26800 #26837)
-#26847 := (iff #26805 #26802)
-#26848 := [rewrite]: #26847
-#26844 := (iff #26803 #26805)
-#26840 := (iff #26830 #26837)
-#26834 := (or #26831 #26595 #26649 #26827 #26825 #26822 #24846 #26715)
-#26838 := (iff #26834 #26837)
-#26839 := [rewrite]: #26838
-#26835 := (iff #26830 #26834)
-#26832 := (iff #26829 #26831)
-#26833 := [rewrite]: #26832
-#26836 := [monotonicity #26833]: #26835
-#26841 := [trans #26836 #26839]: #26840
-#26846 := [monotonicity #26841]: #26844
-#26849 := [trans #26846 #26848]: #26843
-#26804 := [quant-inst #3039 #26182]: #26803
-#26845 := [mp #26804 #26849]: #26802
-#27031 := [unit-resolution #26845 #21922 #14351 #27029 #27010 #27002]: #27030
-#27032 := [unit-resolution #27031 #26980 #26973 #26974 #26936]: false
-#27033 := [lemma #27032]: #12177
-#28800 := [trans #27033 #28799]: #26717
-#26724 := (or #26722 #26715 #26733)
-#26751 := [def-axiom]: #26724
-#28801 := [unit-resolution #26751 #28800 #26937]: #26715
-#26797 := (or #26736 #26794)
+#10153 := [monotonicity #4058 #10150]: #10152
+#10159 := [monotonicity #10153 #10156]: #10158
+#10165 := [trans #10159 #10163]: #10164
+#10168 := [quant-intro #10165]: #10167
+#10187 := [trans #10168 #10185]: #10186
+#10134 := [asserted]: #2280
+#10188 := [mp #10134 #10187]: #10183
+#17858 := [mp~ #10188 #17857]: #10183
+#21886 := [mp #17858 #21885]: #21883
+#26791 := (not #26790)
+#26613 := (not #26591)
+#26559 := (not #26558)
+#24810 := (not #12109)
+#26766 := (not #21883)
+#26767 := (or #26766 #24810 #26559 #26613 #26679 #26786 #26789 #26791 #26795)
+#26793 := (= #26792 f25)
+#26794 := (or #26793 #26559 #26613 #26791 #26789 #26786 #24810 #26679)
+#26768 := (or #26766 #26794)
+#26774 := (iff #26768 #26767)
+#26801 := (or #24810 #26559 #26613 #26679 #26786 #26789 #26791 #26795)
+#26770 := (or #26766 #26801)
+#26772 := (iff #26770 #26767)
+#26773 := [rewrite]: #26772
+#26765 := (iff #26768 #26770)
+#26804 := (iff #26794 #26801)
+#26798 := (or #26795 #26559 #26613 #26791 #26789 #26786 #24810 #26679)
+#26802 := (iff #26798 #26801)
+#26803 := [rewrite]: #26802
+#26799 := (iff #26794 #26798)
+#26796 := (iff #26793 #26795)
+#26797 := [rewrite]: #26796
+#26800 := [monotonicity #26797]: #26799
+#26805 := [trans #26800 #26803]: #26804
+#26771 := [monotonicity #26805]: #26765
+#26775 := [trans #26771 #26773]: #26774
+#26769 := [quant-inst #3039 #26146]: #26768
+#26806 := [mp #26769 #26775]: #26767
+#26973 := [unit-resolution #26806 #21886 #14315 #26971 #26965 #26943]: #26972
+#26974 := [unit-resolution #26973 #26938 #26932 #26926 #26900]: false
+#26960 := [lemma #26974]: #12141
+#23566 := (or #13264 #23563)
+#22522 := (forall (vars (?v0 Int)) #22511)
+#22529 := (not #22522)
+#22507 := (forall (vars (?v0 Int)) #22502)
+#22528 := (not #22507)
+#22530 := (or #22528 #22529)
+#22531 := (not #22530)
+#22560 := (or #22531 #22557)
+#22566 := (not #22560)
+#22567 := (or #12304 #12295 #12286 #12277 #22443 #13620 #13766 #22566)
+#22568 := (not #22567)
+#22346 := (forall (vars (?v0 Int)) #22341)
+#22352 := (not #22346)
+#22353 := (or #22328 #22352)
+#22354 := (not #22353)
+#22383 := (or #22354 #22380)
+#22389 := (not #22383)
+#22390 := (or #13519 #22389)
+#22391 := (not #22390)
+#22396 := (or #13519 #22391)
+#22404 := (not #22396)
+#22405 := (or #12656 #22402 #18558 #22403 #13586 #18561 #22404)
+#22406 := (not #22405)
+#22411 := (or #18558 #18561 #22406)
+#22417 := (not #22411)
+#22454 := (or #12821 #12812 #22443 #13620 #22402 #13671 #22417)
+#22455 := (not #22454)
+#22418 := (or #18520 #18529 #12740 #12731 #12722 #12704 #12695 #13620 #22402 #22417)
+#22419 := (not #22418)
+#22424 := (or #18520 #18529 #22419)
+#22430 := (not #22424)
+#22431 := (or #18520 #18523 #22430)
+#22432 := (not #22431)
+#22437 := (or #18520 #18523 #22432)
+#22444 := (not #22437)
+#22445 := (or #22443 #13620 #13672 #22444)
+#22446 := (not #22445)
+#22460 := (or #22446 #22455)
+#22466 := (not #22460)
+#22467 := (or #18520 #18529 #22443 #13620 #22466)
+#22468 := (not #22467)
+#22473 := (or #18520 #18529 #22468)
+#22479 := (not #22473)
+#22480 := (or #18520 #18523 #22479)
+#22481 := (not #22480)
+#22486 := (or #18520 #18523 #22481)
+#22492 := (not #22486)
+#22493 := (or #22443 #13620 #13765 #22492)
+#22494 := (not #22493)
+#22573 := (or #22494 #22568)
+#22588 := (not #22573)
+#22323 := (forall (vars (?v0 Int)) #22318)
+#22584 := (not #22323)
+#22589 := (or #13231 #22579 #15263 #13938 #13024 #13015 #13006 #12997 #22580 #22581 #13472 #22443 #13620 #13943 #13995 #22582 #22583 #22585 #22586 #22587 #22584 #22588)
+#22590 := (not #22589)
+#22595 := (or #13231 #13472 #22590)
+#22602 := (not #22595)
+#22312 := (forall (vars (?v0 Int)) #22307)
+#22601 := (not #22312)
+#22603 := (or #22601 #22602)
+#22604 := (not #22603)
+#22609 := (or #22301 #22604)
+#22615 := (not #22609)
+#22616 := (or #13436 #22615)
+#22617 := (not #22616)
+#22622 := (or #13436 #22617)
+#22628 := (not #22622)
+#22629 := (or #13231 #18409 #18418 #13222 #13213 #13204 #22628)
+#22630 := (not #22629)
+#22635 := (or #18409 #18418 #22630)
+#22641 := (not #22635)
+#22642 := (or #18409 #18412 #22641)
+#22643 := (not #22642)
+#22648 := (or #18409 #18412 #22643)
+#22654 := (not #22648)
+#22655 := (or #13264 #22654)
+#22656 := (not #22655)
+#22661 := (or #13264 #22656)
+#23567 := (iff #22661 #23566)
+#23564 := (iff #22656 #23563)
+#23561 := (iff #22655 #23560)
+#23558 := (iff #22654 #23557)
+#23555 := (iff #22648 #23554)
+#23552 := (iff #22643 #23551)
+#23549 := (iff #22642 #23548)
+#23546 := (iff #22641 #23545)
+#23543 := (iff #22635 #23542)
+#23540 := (iff #22630 #23539)
+#23537 := (iff #22629 #23536)
+#23534 := (iff #22628 #23533)
+#23531 := (iff #22622 #23530)
+#23528 := (iff #22617 #23527)
+#23525 := (iff #22616 #23524)
+#23522 := (iff #22615 #23521)
+#23519 := (iff #22609 #23518)
+#23516 := (iff #22604 #23515)
+#23513 := (iff #22603 #23512)
+#23510 := (iff #22602 #23509)
+#23507 := (iff #22595 #23506)
+#23504 := (iff #22590 #23503)
+#23501 := (iff #22589 #23500)
+#23498 := (iff #22588 #23497)
+#23495 := (iff #22573 #23494)
+#23492 := (iff #22568 #23491)
+#23489 := (iff #22567 #23488)
+#23486 := (iff #22566 #23485)
+#23483 := (iff #22560 #23482)
+#23480 := (iff #22531 #23479)
+#23477 := (iff #22530 #23476)
+#23474 := (iff #22529 #23473)
+#23471 := (iff #22522 #23468)
+#23469 := (iff #22511 #22511)
+#23470 := [refl]: #23469
+#23472 := [quant-intro #23470]: #23471
+#23475 := [monotonicity #23472]: #23474
+#23466 := (iff #22528 #23465)
+#23463 := (iff #22507 #23460)
+#23461 := (iff #22502 #22502)
+#23462 := [refl]: #23461
+#23464 := [quant-intro #23462]: #23463
+#23467 := [monotonicity #23464]: #23466
+#23478 := [monotonicity #23467 #23475]: #23477
+#23481 := [monotonicity #23478]: #23480
+#23484 := [monotonicity #23481]: #23483
+#23487 := [monotonicity #23484]: #23486
+#23490 := [monotonicity #23487]: #23489
+#23493 := [monotonicity #23490]: #23492
+#23458 := (iff #22494 #23457)
+#23455 := (iff #22493 #23454)
+#23452 := (iff #22492 #23451)
+#23449 := (iff #22486 #23448)
+#23446 := (iff #22481 #23445)
+#23443 := (iff #22480 #23442)
+#23440 := (iff #22479 #23439)
+#23437 := (iff #22473 #23436)
+#23434 := (iff #22468 #23433)
+#23431 := (iff #22467 #23430)
+#23428 := (iff #22466 #23427)
+#23425 := (iff #22460 #23424)
+#23422 := (iff #22455 #23421)
+#23419 := (iff #22454 #23418)
+#23386 := (iff #22417 #23385)
+#23383 := (iff #22411 #23382)
+#23380 := (iff #22406 #23379)
+#23377 := (iff #22405 #23376)
+#23374 := (iff #22404 #23373)
+#23371 := (iff #22396 #23370)
+#23368 := (iff #22391 #23367)
+#23365 := (iff #22390 #23364)
+#23362 := (iff #22389 #23361)
+#23359 := (iff #22383 #23358)
+#23356 := (iff #22354 #23355)
+#23353 := (iff #22353 #23352)
+#23350 := (iff #22352 #23349)
+#23347 := (iff #22346 #23344)
+#23345 := (iff #22341 #22341)
+#23346 := [refl]: #23345
+#23348 := [quant-intro #23346]: #23347
+#23351 := [monotonicity #23348]: #23350
+#23354 := [monotonicity #23351]: #23353
+#23357 := [monotonicity #23354]: #23356
+#23360 := [monotonicity #23357]: #23359
+#23363 := [monotonicity #23360]: #23362
+#23366 := [monotonicity #23363]: #23365
+#23369 := [monotonicity #23366]: #23368
+#23372 := [monotonicity #23369]: #23371
+#23375 := [monotonicity #23372]: #23374
+#23378 := [monotonicity #23375]: #23377
+#23381 := [monotonicity #23378]: #23380
+#23384 := [monotonicity #23381]: #23383
+#23387 := [monotonicity #23384]: #23386
+#23420 := [monotonicity #23387]: #23419
+#23423 := [monotonicity #23420]: #23422
+#23416 := (iff #22446 #23415)
+#23413 := (iff #22445 #23412)
+#23410 := (iff #22444 #23409)
+#23407 := (iff #22437 #23406)
+#23404 := (iff #22432 #23403)
+#23401 := (iff #22431 #23400)
+#23398 := (iff #22430 #23397)
+#23395 := (iff #22424 #23394)
+#23392 := (iff #22419 #23391)
+#23389 := (iff #22418 #23388)
+#23390 := [monotonicity #23387]: #23389
+#23393 := [monotonicity #23390]: #23392
+#23396 := [monotonicity #23393]: #23395
+#23399 := [monotonicity #23396]: #23398
+#23402 := [monotonicity #23399]: #23401
+#23405 := [monotonicity #23402]: #23404
+#23408 := [monotonicity #23405]: #23407
+#23411 := [monotonicity #23408]: #23410
+#23414 := [monotonicity #23411]: #23413
+#23417 := [monotonicity #23414]: #23416
+#23426 := [monotonicity #23417 #23423]: #23425
+#23429 := [monotonicity #23426]: #23428
+#23432 := [monotonicity #23429]: #23431
+#23435 := [monotonicity #23432]: #23434
+#23438 := [monotonicity #23435]: #23437
+#23441 := [monotonicity #23438]: #23440
+#23444 := [monotonicity #23441]: #23443
+#23447 := [monotonicity #23444]: #23446
+#23450 := [monotonicity #23447]: #23449
+#23453 := [monotonicity #23450]: #23452
+#23456 := [monotonicity #23453]: #23455
+#23459 := [monotonicity #23456]: #23458
+#23496 := [monotonicity #23459 #23493]: #23495
+#23499 := [monotonicity #23496]: #23498
+#23342 := (iff #22584 #23341)
+#23339 := (iff #22323 #23336)
+#23337 := (iff #22318 #22318)
+#23338 := [refl]: #23337
+#23340 := [quant-intro #23338]: #23339
+#23343 := [monotonicity #23340]: #23342
+#23502 := [monotonicity #23343 #23499]: #23501
+#23505 := [monotonicity #23502]: #23504
+#23508 := [monotonicity #23505]: #23507
+#23511 := [monotonicity #23508]: #23510
+#23334 := (iff #22601 #23333)
+#23331 := (iff #22312 #23328)
+#23329 := (iff #22307 #22307)
+#23330 := [refl]: #23329
+#23332 := [quant-intro #23330]: #23331
+#23335 := [monotonicity #23332]: #23334
+#23514 := [monotonicity #23335 #23511]: #23513
+#23517 := [monotonicity #23514]: #23516
+#23520 := [monotonicity #23517]: #23519
+#23523 := [monotonicity #23520]: #23522
+#23526 := [monotonicity #23523]: #23525
+#23529 := [monotonicity #23526]: #23528
+#23532 := [monotonicity #23529]: #23531
+#23535 := [monotonicity #23532]: #23534
+#23538 := [monotonicity #23535]: #23537
+#23541 := [monotonicity #23538]: #23540
+#23544 := [monotonicity #23541]: #23543
+#23547 := [monotonicity #23544]: #23546
+#23550 := [monotonicity #23547]: #23549
+#23553 := [monotonicity #23550]: #23552
+#23556 := [monotonicity #23553]: #23555
+#23559 := [monotonicity #23556]: #23558
+#23562 := [monotonicity #23559]: #23561
+#23565 := [monotonicity #23562]: #23564
+#23568 := [monotonicity #23565]: #23567
+#19060 := (and #18703 #18704)
+#19063 := (not #19060)
+#19066 := (or #19042 #19055 #19063)
+#19069 := (not #19066)
+#15985 := (and #3173 #4202 #13795 #15183)
+#18726 := (not #15985)
+#18729 := (forall (vars (?v0 Int)) #18726)
+#14426 := (and #4202 #15183)
+#14425 := (not #14426)
+#15971 := (or #13793 #13807 #14425)
+#15976 := (forall (vars (?v0 Int)) #15971)
+#18733 := (and #15976 #18729)
+#19075 := (or #18733 #19069)
+#19083 := (and #12233 #12236 #12239 #12242 #13477 #13480 #13765 #19075)
+#18912 := (and #18579 #18580)
+#18915 := (not #18912)
+#18918 := (or #18894 #18907 #18915)
+#18921 := (not #18918)
+#15872 := (or #13522 #13536 #14425)
+#15877 := (forall (vars (?v0 Int)) #15872)
+#18595 := (not #13565)
+#18605 := (and #18595 #15877)
+#18927 := (or #18605 #18921)
+#18932 := (and #13514 #18927)
+#18935 := (or #13519 #18932)
+#18943 := (and #12586 #13489 #13498 #13506 #13582 #15864 #18935)
+#18948 := (or #18558 #18561 #18943)
+#18988 := (and #12803 #12806 #13477 #13480 #13489 #13672 #18948)
+#18954 := (and #12539 #12548 #12554 #12557 #12560 #12565 #12568 #13480 #13489 #18948)
+#18959 := (or #18520 #18529 #18954)
+#18965 := (and #12539 #12542 #18959)
+#18970 := (or #18520 #18523 #18965)
+#18976 := (and #13477 #13480 #13671 #18970)
+#18993 := (or #18976 #18988)
+#18999 := (and #12539 #12548 #13477 #13480 #18993)
+#19004 := (or #18520 #18529 #18999)
+#19010 := (and #12539 #12542 #19004)
+#19015 := (or #18520 #18523 #19010)
+#19021 := (and #13477 #13480 #13766 #19015)
+#19088 := (or #19021 #19083)
+#15798 := (or #13958 #13972 #14425)
+#15803 := (forall (vars (?v0 Int)) #15798)
+#19094 := (and #3109 #12214 #12222 #12479 #12507 #12510 #12513 #12516 #12519 #12522 #13473 #13477 #13480 #13944 #13992 #13998 #14020 #15803 #15815 #15832 #15849 #19088)
+#19099 := (or #13231 #13472 #19094)
+#15784 := (or #13439 #13451 #14425)
+#15789 := (forall (vars (?v0 Int)) #15784)
+#19102 := (and #15789 #19099)
+#18815 := (and #18442 #18443)
+#18818 := (not #18815)
+#18824 := (or #18450 #18451 #18818)
+#18829 := (not #18824)
+#19105 := (or #18829 #19102)
+#19108 := (and #13433 #19105)
+#19111 := (or #13436 #19108)
+#19117 := (and #3109 #12144 #12153 #12159 #12162 #12165 #19111)
+#19122 := (or #18409 #18418 #19117)
+#19128 := (and #12144 #12147 #19122)
+#19133 := (or #18409 #18412 #19128)
+#19136 := (and #12141 #19133)
+#19139 := (or #13264 #19136)
+#22662 := (iff #19139 #22661)
+#22659 := (iff #19136 #22656)
+#22651 := (and #12141 #22648)
+#22657 := (iff #22651 #22656)
+#22658 := [rewrite]: #22657
+#22652 := (iff #19136 #22651)
+#22649 := (iff #19133 #22648)
+#22646 := (iff #19128 #22643)
+#22638 := (and #12144 #12147 #22635)
+#22644 := (iff #22638 #22643)
+#22645 := [rewrite]: #22644
+#22639 := (iff #19128 #22638)
+#22636 := (iff #19122 #22635)
+#22633 := (iff #19117 #22630)
+#22625 := (and #3109 #12144 #12153 #12159 #12162 #12165 #22622)
+#22631 := (iff #22625 #22630)
+#22632 := [rewrite]: #22631
+#22626 := (iff #19117 #22625)
+#22623 := (iff #19111 #22622)
+#22620 := (iff #19108 #22617)
+#22612 := (and #13433 #22609)
+#22618 := (iff #22612 #22617)
+#22619 := [rewrite]: #22618
+#22613 := (iff #19108 #22612)
+#22610 := (iff #19105 #22609)
+#22607 := (iff #19102 #22604)
+#22598 := (and #22312 #22595)
+#22605 := (iff #22598 #22604)
+#22606 := [rewrite]: #22605
+#22599 := (iff #19102 #22598)
+#22596 := (iff #19099 #22595)
+#22593 := (iff #19094 #22590)
+#22576 := (and #3109 #12214 #12222 #12479 #12507 #12510 #12513 #12516 #12519 #12522 #13473 #13477 #13480 #13944 #13992 #13998 #14020 #22323 #15815 #15832 #15849 #22573)
+#22591 := (iff #22576 #22590)
+#22592 := [rewrite]: #22591
+#22577 := (iff #19094 #22576)
+#22574 := (iff #19088 #22573)
+#22571 := (iff #19083 #22568)
+#22563 := (and #12233 #12236 #12239 #12242 #13477 #13480 #13765 #22560)
+#22569 := (iff #22563 #22568)
+#22570 := [rewrite]: #22569
+#22564 := (iff #19083 #22563)
+#22561 := (iff #19075 #22560)
+#22558 := (iff #19069 #22557)
+#22555 := (iff #19066 #22552)
+#22538 := (or #22536 #22537)
+#22549 := (or #19042 #19055 #22538)
+#22553 := (iff #22549 #22552)
+#22554 := [rewrite]: #22553
+#22550 := (iff #19066 #22549)
+#22547 := (iff #19063 #22538)
+#22539 := (not #22538)
+#22542 := (not #22539)
+#22545 := (iff #22542 #22538)
+#22546 := [rewrite]: #22545
+#22543 := (iff #19063 #22542)
+#22540 := (iff #19060 #22539)
+#22541 := [rewrite]: #22540
+#22544 := [monotonicity #22541]: #22543
+#22548 := [trans #22544 #22546]: #22547
+#22551 := [monotonicity #22548]: #22550
+#22556 := [trans #22551 #22554]: #22555
+#22559 := [monotonicity #22556]: #22558
+#22534 := (iff #18733 #22531)
+#22525 := (and #22507 #22522)
+#22532 := (iff #22525 #22531)
+#22533 := [rewrite]: #22532
+#22526 := (iff #18733 #22525)
+#22523 := (iff #18729 #22522)
+#22520 := (iff #18726 #22511)
+#22512 := (not #22511)
+#22515 := (not #22512)
+#22518 := (iff #22515 #22511)
+#22519 := [rewrite]: #22518
+#22516 := (iff #18726 #22515)
+#22513 := (iff #15985 #22512)
+#22514 := [rewrite]: #22513
+#22517 := [monotonicity #22514]: #22516
+#22521 := [trans #22517 #22519]: #22520
+#22524 := [quant-intro #22521]: #22523
+#22508 := (iff #15976 #22507)
+#22505 := (iff #15971 #22502)
+#20215 := (or #5104 #19577)
+#22499 := (or #13793 #13807 #20215)
+#22503 := (iff #22499 #22502)
+#22504 := [rewrite]: #22503
+#22500 := (iff #15971 #22499)
+#20224 := (iff #14425 #20215)
+#20216 := (not #20215)
+#20219 := (not #20216)
+#20222 := (iff #20219 #20215)
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+#18911 := [trans #18904 #18909]: #18910
+#18897 := (iff #18588 #18894)
+#18886 := (+ #13515 ?v0!14)
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+#18890 := (iff #18588 #18889)
+#18887 := (= #18587 #18886)
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+#18898 := [trans #18891 #18896]: #18897
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+#18931 := [trans #18926 #18929]: #18930
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+#18947 := [trans #18942 #18945]: #18946
+#18950 := [monotonicity #18947]: #18949
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+#18983 := (iff #18655 #12806)
+#18984 := [rewrite]: #18983
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+#18992 := [trans #18987 #18990]: #18991
+#18979 := (iff #18648 #18976)
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+#18962 := (and #12545 #18959)
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+#18951 := (and #12551 #12554 #12557 #12560 #12565 #12568 #13480 #13491 #18948)
+#18955 := (iff #18951 #18954)
+#18956 := [rewrite]: #18955
+#18952 := (iff #18632 #18951)
+#18874 := (iff #18552 #13480)
+#18875 := [rewrite]: #18874
+#18872 := (iff #18549 #12568)
+#18873 := [rewrite]: #18872
+#18870 := (iff #18546 #12565)
+#18871 := [rewrite]: #18870
+#18868 := (iff #18543 #12560)
+#18869 := [rewrite]: #18868
+#18866 := (iff #18540 #12557)
+#18867 := [rewrite]: #18866
+#18864 := (iff #18537 #12554)
+#18865 := [rewrite]: #18864
+#18862 := (iff #18532 #12551)
+#18863 := [rewrite]: #18862
+#18953 := [monotonicity #18863 #18865 #18867 #18869 #18871 #18873 #18875 #18877 #18950]: #18952
+#18958 := [trans #18953 #18956]: #18957
+#18961 := [monotonicity #18958]: #18960
+#18860 := (iff #18526 #12545)
+#18861 := [rewrite]: #18860
+#18964 := [monotonicity #18861 #18961]: #18963
+#18969 := [trans #18964 #18967]: #18968
+#18972 := [monotonicity #18969]: #18971
+#18975 := [monotonicity #18847 #18972]: #18974
+#18980 := [trans #18975 #18978]: #18979
+#18995 := [monotonicity #18980 #18992]: #18994
+#18998 := [monotonicity #18863 #18847 #18995]: #18997
+#19003 := [trans #18998 #19001]: #19002
+#19006 := [monotonicity #19003]: #19005
+#19009 := [monotonicity #18861 #19006]: #19008
+#19014 := [trans #19009 #19012]: #19013
+#19017 := [monotonicity #19014]: #19016
+#19020 := [monotonicity #18847 #19017]: #19019
+#19025 := [trans #19020 #19023]: #19024
+#19090 := [monotonicity #19025 #19087]: #19089
+#18858 := (iff #18515 #15854)
+#18859 := [rewrite]: #18858
+#18856 := (iff #18512 #15837)
+#18857 := [rewrite]: #18856
+#18854 := (iff #18509 #15820)
+#18855 := [rewrite]: #18854
+#18852 := (iff #18499 #14036)
+#18853 := [rewrite]: #18852
+#18850 := (iff #18496 #13992)
+#18851 := [rewrite]: #18850
+#18848 := (iff #18493 #13950)
+#18849 := [rewrite]: #18848
+#18844 := (iff #18487 #12525)
+#18845 := [rewrite]: #18844
+#18842 := (iff #18484 #12516)
+#18843 := [rewrite]: #18842
+#18840 := (iff #18481 #12513)
+#18841 := [rewrite]: #18840
+#18838 := (iff #18478 #12510)
+#18839 := [rewrite]: #18838
+#18836 := (iff #18475 #12507)
+#18837 := [rewrite]: #18836
+#18834 := (iff #18472 #12479)
+#18835 := [rewrite]: #18834
+#18832 := (iff #18469 #12222)
+#18833 := [rewrite]: #18832
+#19093 := [monotonicity #18833 #18835 #18837 #18839 #18841 #18843 #18845 #18847 #18849 #18851 #18853 #18855 #18857 #18859 #19090]: #19092
+#19098 := [trans #19093 #19096]: #19097
+#19101 := [monotonicity #14202 #19098]: #19100
+#19104 := [monotonicity #19101]: #19103
+#18830 := (iff #18453 #18829)
+#18827 := (iff #18452 #18824)
+#18821 := (or #18451 #18450 #18818)
+#18825 := (iff #18821 #18824)
+#18826 := [rewrite]: #18825
+#18822 := (iff #18452 #18821)
+#18819 := (iff #18445 #18818)
+#18816 := (iff #18444 #18815)
+#18817 := [rewrite]: #18816
+#18820 := [monotonicity #18817]: #18819
+#18823 := [monotonicity #18820]: #18822
+#18828 := [trans #18823 #18826]: #18827
+#18831 := [monotonicity #18828]: #18830
+#19107 := [monotonicity #18831 #19104]: #19106
+#18813 := (iff #18438 #13433)
+#18814 := [rewrite]: #18813
+#19110 := [monotonicity #18814 #19107]: #19109
+#19113 := [monotonicity #19110]: #19112
+#18811 := (iff #18433 #12165)
+#18812 := [rewrite]: #18811
+#18809 := (iff #18430 #12162)
+#18810 := [rewrite]: #18809
+#18807 := (iff #18427 #12159)
+#18808 := [rewrite]: #18807
+#18805 := (iff #18424 #12156)
+#18806 := [rewrite]: #18805
+#18803 := (iff #18421 #3109)
+#18804 := [rewrite]: #18803
+#19116 := [monotonicity #18804 #18806 #18808 #18810 #18812 #19113]: #19115
+#19121 := [trans #19116 #19119]: #19120
+#19124 := [monotonicity #19121]: #19123
+#18801 := (iff #18415 #12150)
+#18802 := [rewrite]: #18801
+#19127 := [monotonicity #18802 #19124]: #19126
+#19132 := [trans #19127 #19130]: #19131
+#19135 := [monotonicity #19132]: #19134
+#18799 := (iff #18406 #12141)
+#18800 := [rewrite]: #18799
+#19138 := [monotonicity #18800 #19135]: #19137
+#19141 := [monotonicity #19138]: #19140
+#15990 := (exists (vars (?v0 Int)) #15985)
+#15979 := (not #15976)
+#15993 := (or #15979 #15990)
+#15996 := (and #15976 #15993)
+#15999 := (or #12304 #12295 #12286 #12277 #13485 #13766 #15996)
+#15880 := (not #15877)
+#15886 := (or #13565 #15880)
+#15891 := (and #15877 #15886)
+#15894 := (or #13519 #15891)
+#15897 := (and #13514 #15894)
+#15909 := (or #12656 #13511 #13586 #15897 #15903)
+#15914 := (and #13498 #15864 #15909)
+#15940 := (or #12821 #12812 #13485 #13494 #13671 #15914)
+#15917 := (or #12749 #12740 #12731 #12722 #12704 #12695 #13620 #13494 #15914)
+#15920 := (and #12539 #12548 #15917)
+#15923 := (or #12761 #15920)
+#15926 := (and #12539 #12542 #15923)
+#15932 := (or #13485 #13672 #15926)
+#15945 := (and #15932 #15940)
+#15948 := (or #12749 #13485 #15945)
+#15951 := (and #12539 #12548 #15948)
+#15954 := (or #12761 #15951)
+#15957 := (and #12539 #12542 #15954)
+#15963 := (or #13485 #13765 #15957)
+#16002 := (and #15963 #15999)
+#15806 := (not #15803)
+#16008 := (or #15263 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #13955 #13995 #14041 #15806 #15823 #15840 #15857 #16002)
+#16013 := (and #3109 #13473 #16008)
+#15792 := (not #15789)
+#16016 := (or #15792 #16013)
+#16019 := (and #15789 #16016)
+#16022 := (or #13436 #16019)
+#16025 := (and #13433 #16022)
+#16028 := (or #13231 #13240 #13222 #13213 #13204 #16025)
+#16031 := (and #12144 #12153 #16028)
+#16034 := (or #13252 #16031)
+#16037 := (and #12144 #12147 #16034)
+#16040 := (or #13264 #16037)
+#16043 := (and #12141 #16040)
+#16046 := (not #16043)
+#18794 := (~ #16046 #18793)
+#18790 := (not #16040)
+#18791 := (~ #18790 #18789)
+#18786 := (not #16037)
+#18787 := (~ #18786 #18785)
+#18782 := (not #16034)
+#18783 := (~ #18782 #18781)
+#18778 := (not #16031)
+#18779 := (~ #18778 #18777)
+#18774 := (not #16028)
+#18775 := (~ #18774 #18773)
+#18770 := (not #16025)
+#18771 := (~ #18770 #18769)
+#18766 := (not #16022)
+#18767 := (~ #18766 #18765)
+#18762 := (not #16019)
+#18763 := (~ #18762 #18761)
+#18758 := (not #16016)
+#18759 := (~ #18758 #18757)
+#18754 := (not #16013)
+#18755 := (~ #18754 #18753)
+#18750 := (not #16008)
+#18751 := (~ #18750 #18749)
+#18746 := (not #16002)
+#18747 := (~ #18746 #18745)
+#18742 := (not #15999)
+#18743 := (~ #18742 #18741)
+#18738 := (not #15996)
+#18739 := (~ #18738 #18737)
+#18734 := (not #15993)
+#18735 := (~ #18734 #18733)
+#18730 := (not #15990)
+#18731 := (~ #18730 #18729)
+#18727 := (~ #18726 #18726)
+#18728 := [refl]: #18727
+#18732 := [nnf-neg #18728]: #18731
+#18723 := (not #15979)
+#18724 := (~ #18723 #15976)
+#18721 := (~ #15976 #15976)
+#18719 := (~ #15971 #15971)
+#18720 := [refl]: #18719
+#18722 := [nnf-pos #18720]: #18721
+#18725 := [nnf-neg #18722]: #18724
+#18736 := [nnf-neg #18725 #18732]: #18735
+#18715 := (~ #15979 #18714)
+#18716 := [sk]: #18715
+#18740 := [nnf-neg #18716 #18736]: #18739
+#18700 := (~ #13769 #13769)
+#18701 := [refl]: #18700
+#18491 := (~ #18490 #18490)
+#18492 := [refl]: #18491
+#18698 := (~ #18697 #18697)
+#18699 := [refl]: #18698
+#18695 := (~ #18694 #18694)
+#18696 := [refl]: #18695
+#18692 := (~ #18691 #18691)
+#18693 := [refl]: #18692
+#18689 := (~ #18688 #18688)
+#18690 := [refl]: #18689
+#18744 := [nnf-neg #18690 #18693 #18696 #18699 #18492 #18701 #18740]: #18743
+#18685 := (not #15963)
+#18686 := (~ #18685 #18684)
+#18681 := (not #15957)
+#18682 := (~ #18681 #18680)
+#18677 := (not #15954)
+#18678 := (~ #18677 #18676)
+#18673 := (not #15951)
+#18674 := (~ #18673 #18672)
+#18669 := (not #15948)
+#18670 := (~ #18669 #18668)
+#18665 := (not #15945)
+#18666 := (~ #18665 #18664)
+#18661 := (not #15940)
+#18662 := (~ #18661 #18660)
+#18629 := (not #15914)
+#18630 := (~ #18629 #18628)
+#18625 := (not #15909)
+#18626 := (~ #18625 #18624)
+#18622 := (~ #18621 #18621)
+#18623 := [refl]: #18622
+#18618 := (not #15897)
+#18619 := (~ #18618 #18617)
+#18614 := (not #15894)
+#18615 := (~ #18614 #18613)
+#18610 := (not #15891)
+#18611 := (~ #18610 #18609)
+#18606 := (not #15886)
+#18607 := (~ #18606 #18605)
+#18602 := (not #15880)
+#18603 := (~ #18602 #15877)
+#18600 := (~ #15877 #15877)
+#18598 := (~ #15872 #15872)
+#18599 := [refl]: #18598
+#18601 := [nnf-pos #18599]: #18600
+#18604 := [nnf-neg #18601]: #18603
+#18596 := (~ #18595 #18595)
+#18597 := [refl]: #18596
+#18608 := [nnf-neg #18597 #18604]: #18607
+#18591 := (~ #15880 #18590)
+#18592 := [sk]: #18591
+#18612 := [nnf-neg #18592 #18608]: #18611
+#18576 := (~ #18575 #18575)
+#18577 := [refl]: #18576
+#18616 := [nnf-neg #18577 #18612]: #18615
+#18573 := (~ #13519 #13519)
+#18574 := [refl]: #18573
+#18620 := [nnf-neg #18574 #18616]: #18619
+#18571 := (~ #18570 #18570)
+#18572 := [refl]: #18571
+#18568 := (~ #18567 #18567)
+#18569 := [refl]: #18568
+#18565 := (~ #18564 #18564)
+#18566 := [refl]: #18565
+#18627 := [nnf-neg #18566 #18569 #18572 #18620 #18623]: #18626
+#18562 := (~ #18561 #18561)
+#18563 := [refl]: #18562
+#18559 := (~ #18558 #18558)
+#18560 := [refl]: #18559
+#18631 := [nnf-neg #18560 #18563 #18627]: #18630
+#18658 := (~ #13677 #13677)
+#18659 := [refl]: #18658
+#18556 := (~ #18555 #18555)
+#18557 := [refl]: #18556
+#18656 := (~ #18655 #18655)
+#18657 := [refl]: #18656
+#18653 := (~ #18652 #18652)
+#18654 := [refl]: #18653
+#18663 := [nnf-neg #18654 #18657 #18492 #18557 #18659 #18631]: #18662
+#18649 := (not #15932)
+#18650 := (~ #18649 #18648)
+#18645 := (not #15926)
+#18646 := (~ #18645 #18644)
+#18641 := (not #15923)
+#18642 := (~ #18641 #18640)
+#18637 := (not #15920)
+#18638 := (~ #18637 #18636)
+#18633 := (not #15917)
+#18634 := (~ #18633 #18632)
+#18553 := (~ #18552 #18552)
+#18554 := [refl]: #18553
+#18550 := (~ #18549 #18549)
+#18551 := [refl]: #18550
+#18547 := (~ #18546 #18546)
+#18548 := [refl]: #18547
+#18544 := (~ #18543 #18543)
+#18545 := [refl]: #18544
+#18541 := (~ #18540 #18540)
+#18542 := [refl]: #18541
+#18538 := (~ #18537 #18537)
+#18539 := [refl]: #18538
+#18533 := (~ #18532 #18532)
+#18534 := [refl]: #18533
+#18635 := [nnf-neg #18534 #18539 #18542 #18545 #18548 #18551 #18554 #18557 #18631]: #18634
+#18530 := (~ #18529 #18529)
+#18531 := [refl]: #18530
+#18521 := (~ #18520 #18520)
+#18522 := [refl]: #18521
+#18639 := [nnf-neg #18522 #18531 #18635]: #18638
+#18527 := (~ #18526 #18526)
+#18528 := [refl]: #18527
+#18643 := [nnf-neg #18528 #18639]: #18642
+#18524 := (~ #18523 #18523)
+#18525 := [refl]: #18524
+#18647 := [nnf-neg #18522 #18525 #18643]: #18646
+#18535 := (~ #13671 #13671)
+#18536 := [refl]: #18535
+#18651 := [nnf-neg #18492 #18536 #18647]: #18650
+#18667 := [nnf-neg #18651 #18663]: #18666
+#18671 := [nnf-neg #18534 #18492 #18667]: #18670
+#18675 := [nnf-neg #18522 #18531 #18671]: #18674
+#18679 := [nnf-neg #18528 #18675]: #18678
+#18683 := [nnf-neg #18522 #18525 #18679]: #18682
+#18518 := (~ #13766 #13766)
+#18519 := [refl]: #18518
+#18687 := [nnf-neg #18492 #18519 #18683]: #18686
+#18748 := [nnf-neg #18687 #18744]: #18747
+#18516 := (~ #18515 #18515)
+#18517 := [refl]: #18516
+#18513 := (~ #18512 #18512)
+#18514 := [refl]: #18513
+#18510 := (~ #18509 #18509)
+#18511 := [refl]: #18510
+#18506 := (not #15806)
+#18507 := (~ #18506 #15803)
+#18504 := (~ #15803 #15803)
+#18502 := (~ #15798 #15798)
+#18503 := [refl]: #18502
+#18505 := [nnf-pos #18503]: #18504
+#18508 := [nnf-neg #18505]: #18507
+#18500 := (~ #18499 #18499)
+#18501 := [refl]: #18500
+#18497 := (~ #18496 #18496)
+#18498 := [refl]: #18497
+#18494 := (~ #18493 #18493)
+#18495 := [refl]: #18494
+#18488 := (~ #18487 #18487)
+#18489 := [refl]: #18488
+#18485 := (~ #18484 #18484)
+#18486 := [refl]: #18485
+#18482 := (~ #18481 #18481)
+#18483 := [refl]: #18482
+#18479 := (~ #18478 #18478)
+#18480 := [refl]: #18479
+#18476 := (~ #18475 #18475)
+#18477 := [refl]: #18476
+#18473 := (~ #18472 #18472)
+#18474 := [refl]: #18473
+#18470 := (~ #18469 #18469)
+#18471 := [refl]: #18470
+#18752 := [nnf-neg #18471 #18474 #18477 #18480 #18483 #18486 #18489 #18492 #18495 #18498 #18501 #18508 #18511 #18514 #18517 #18748]: #18751
+#18467 := (~ #14198 #14198)
+#18468 := [refl]: #18467
+#18465 := (~ #13231 #13231)
+#18466 := [refl]: #18465
+#18756 := [nnf-neg #18466 #18468 #18752]: #18755
+#18462 := (not #15792)
+#18463 := (~ #18462 #15789)
+#18460 := (~ #15789 #15789)
+#18458 := (~ #15784 #15784)
+#18459 := [refl]: #18458
+#18461 := [nnf-pos #18459]: #18460
+#18464 := [nnf-neg #18461]: #18463
+#18760 := [nnf-neg #18464 #18756]: #18759
+#18454 := (~ #15792 #18453)
+#18455 := [sk]: #18454
+#18764 := [nnf-neg #18455 #18760]: #18763
+#18439 := (~ #18438 #18438)
+#18440 := [refl]: #18439
+#18768 := [nnf-neg #18440 #18764]: #18767
+#18436 := (~ #13436 #13436)
+#18437 := [refl]: #18436
+#18772 := [nnf-neg #18437 #18768]: #18771
+#18434 := (~ #18433 #18433)
+#18435 := [refl]: #18434
+#18431 := (~ #18430 #18430)
+#18432 := [refl]: #18431
+#18428 := (~ #18427 #18427)
+#18429 := [refl]: #18428
+#18425 := (~ #18424 #18424)
+#18426 := [refl]: #18425
+#18422 := (~ #18421 #18421)
+#18423 := [refl]: #18422
+#18776 := [nnf-neg #18423 #18426 #18429 #18432 #18435 #18772]: #18775
+#18419 := (~ #18418 #18418)
+#18420 := [refl]: #18419
+#18410 := (~ #18409 #18409)
+#18411 := [refl]: #18410
+#18780 := [nnf-neg #18411 #18420 #18776]: #18779
+#18416 := (~ #18415 #18415)
+#18417 := [refl]: #18416
+#18784 := [nnf-neg #18417 #18780]: #18783
+#18413 := (~ #18412 #18412)
+#18414 := [refl]: #18413
+#18788 := [nnf-neg #18411 #18414 #18784]: #18787
+#18407 := (~ #18406 #18406)
+#18408 := [refl]: #18407
+#18792 := [nnf-neg #18408 #18788]: #18791
+#18404 := (~ #13264 #13264)
+#18405 := [refl]: #18404
+#18795 := [nnf-neg #18405 #18792]: #18794
+#15288 := (or #12304 #12295 #12286 #12277 #13485 #13766 #13852)
+#15293 := (and #13788 #15288)
+#15299 := (or #15263 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #13955 #13989 #13995 #14007 #14017 #14030 #14041 #15293)
+#15304 := (and #3109 #13473 #15299)
+#15307 := (or #13469 #15304)
+#15310 := (and #13466 #15307)
+#15313 := (or #13436 #15310)
+#15316 := (and #13433 #15313)
+#15319 := (or #13231 #13240 #13222 #13213 #13204 #15316)
+#15322 := (and #12144 #12153 #15319)
+#15325 := (or #13252 #15322)
+#15328 := (and #12144 #12147 #15325)
+#15331 := (or #13264 #15328)
+#15334 := (and #12141 #15331)
+#15337 := (not #15334)
+#16047 := (iff #15337 #16046)
+#16044 := (iff #15334 #16043)
+#16041 := (iff #15331 #16040)
+#16038 := (iff #15328 #16037)
+#16035 := (iff #15325 #16034)
+#16032 := (iff #15322 #16031)
+#16029 := (iff #15319 #16028)
+#16026 := (iff #15316 #16025)
+#16023 := (iff #15313 #16022)
+#16020 := (iff #15310 #16019)
+#16017 := (iff #15307 #16016)
+#16014 := (iff #15304 #16013)
+#16011 := (iff #15299 #16008)
+#16005 := (or #15263 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #13955 #15806 #13995 #15823 #15840 #15857 #14041 #16002)
+#16009 := (iff #16005 #16008)
+#16010 := [rewrite]: #16009
+#16006 := (iff #15299 #16005)
+#16003 := (iff #15293 #16002)
+#16000 := (iff #15288 #15999)
+#15997 := (iff #13852 #15996)
+#15994 := (iff #13847 #15993)
+#15991 := (iff #13838 #15990)
+#15988 := (iff #13833 #15985)
+#15982 := (and #3173 #4202 #15183 #13795)
+#15986 := (iff #15982 #15985)
+#15987 := [rewrite]: #15986
+#15983 := (iff #13833 #15982)
+#15178 := (iff #4496 #15183)
+#15199 := -4294967295::Int
+#15191 := (+ -4294967295::Int #202)
+#15184 := (<= #15191 0::Int)
+#15180 := (iff #15184 #15183)
+#15181 := [rewrite]: #15180
+#15185 := (iff #4496 #15184)
+#15186 := (= #4495 #15191)
+#15192 := (+ #202 -4294967295::Int)
+#15188 := (= #15192 #15191)
+#15189 := [rewrite]: #15188
+#15193 := (= #4495 #15192)
+#15194 := (= #4494 -4294967295::Int)
+#15200 := (* -1::Int 4294967295::Int)
+#15196 := (= #15200 -4294967295::Int)
+#15197 := [rewrite]: #15196
+#15201 := (= #4494 #15200)
+#7601 := (= f88 4294967295::Int)
+#990 := 65536::Int
+#1365 := (* 65536::Int 65536::Int)
+#1370 := (- #1365 1::Int)
+#1371 := (= f88 #1370)
+#7602 := (iff #1371 #7601)
+#7599 := (= #1370 4294967295::Int)
+#1053 := 4294967296::Int
+#7592 := (- 4294967296::Int 1::Int)
+#7597 := (= #7592 4294967295::Int)
+#7598 := [rewrite]: #7597
+#7594 := (= #1370 #7592)
+#7563 := (= #1365 4294967296::Int)
+#7564 := [rewrite]: #7563
+#7595 := [monotonicity #7564]: #7594
+#7600 := [trans #7595 #7598]: #7599
+#7603 := [monotonicity #7600]: #7602
+#7591 := [asserted]: #1371
+#7606 := [mp #7591 #7603]: #7601
+#15198 := [monotonicity #7606]: #15201
+#15195 := [trans #15198 #15197]: #15194
+#15190 := [monotonicity #15195]: #15193
+#15187 := [trans #15190 #15189]: #15186
+#15182 := [monotonicity #15187]: #15185
+#15179 := [trans #15182 #15181]: #15178
+#15984 := [monotonicity #15179]: #15983
+#15989 := [trans #15984 #15987]: #15988
+#15992 := [quant-intro #15989]: #15991
+#15980 := (iff #13841 #15979)
+#15977 := (iff #13821 #15976)
+#15974 := (iff #13816 #15971)
+#15968 := (or #14425 #13793 #13807)
+#15972 := (iff #15968 #15971)
+#15973 := [rewrite]: #15972
+#15969 := (iff #13816 #15968)
+#14422 := (iff #5712 #14425)
+#14427 := (iff #4503 #14426)
+#14424 := [monotonicity #15179]: #14427
+#14423 := [monotonicity #14424]: #14422
+#15970 := [monotonicity #14423]: #15969
+#15975 := [trans #15970 #15973]: #15974
+#15978 := [quant-intro #15975]: #15977
+#15981 := [monotonicity #15978]: #15980
+#15995 := [monotonicity #15981 #15992]: #15994
+#15998 := [monotonicity #15978 #15995]: #15997
+#16001 := [monotonicity #15998]: #16000
+#15966 := (iff #13788 #15963)
+#15960 := (or #13485 #15957 #13765)
+#15964 := (iff #15960 #15963)
+#15965 := [rewrite]: #15964
+#15961 := (iff #13788 #15960)
+#15958 := (iff #13759 #15957)
+#15955 := (iff #13753 #15954)
+#15952 := (iff #13748 #15951)
+#15949 := (iff #13740 #15948)
+#15946 := (iff #13731 #15945)
+#15943 := (iff #13726 #15940)
+#15937 := (or #12821 #12812 #13485 #13494 #15914 #13671)
+#15941 := (iff #15937 #15940)
+#15942 := [rewrite]: #15941
+#15938 := (iff #13726 #15937)
+#15915 := (iff #13615 #15914)
+#15912 := (iff #13607 #15909)
+#15906 := (or #12656 #13511 #15897 #13586 #15903)
+#15910 := (iff #15906 #15909)
+#15911 := [rewrite]: #15910
+#15907 := (iff #13607 #15906)
+#15904 := (iff #13592 #15903)
+#15901 := (iff #13589 #15900)
+#15867 := (iff #13500 #15864)
+#15809 := (+ 4294967295::Int #13501)
+#15860 := (>= #15809 1::Int)
+#15865 := (iff #15860 #15864)
+#15866 := [rewrite]: #15865
+#15861 := (iff #13500 #15860)
+#15810 := (= #13502 #15809)
+#15811 := [monotonicity #7606]: #15810
+#15862 := [monotonicity #15811]: #15861
+#15868 := [trans #15862 #15866]: #15867
+#15902 := [monotonicity #15868]: #15901
+#15905 := [monotonicity #15902]: #15904
+#15898 := (iff #13579 #15897)
+#15895 := (iff #13576 #15894)
+#15892 := (iff #13573 #15891)
+#15889 := (iff #13570 #15886)
+#15883 := (or #15880 #13565)
+#15887 := (iff #15883 #15886)
+#15888 := [rewrite]: #15887
+#15884 := (iff #13570 #15883)
+#15881 := (iff #13553 #15880)
+#15878 := (iff #13550 #15877)
+#15875 := (iff #13545 #15872)
+#15869 := (or #14425 #13522 #13536)
+#15873 := (iff #15869 #15872)
+#15874 := [rewrite]: #15873
+#15870 := (iff #13545 #15869)
+#15871 := [monotonicity #14423]: #15870
+#15876 := [trans #15871 #15874]: #15875
+#15879 := [quant-intro #15876]: #15878
+#15882 := [monotonicity #15879]: #15881
+#15885 := [monotonicity #15882]: #15884
+#15890 := [trans #15885 #15888]: #15889
+#15893 := [monotonicity #15879 #15890]: #15892
+#15896 := [monotonicity #15893]: #15895
+#15899 := [monotonicity #15896]: #15898
+#15908 := [monotonicity #15899 #15905]: #15907
+#15913 := [trans #15908 #15911]: #15912
+#15916 := [monotonicity #15868 #15913]: #15915
+#15939 := [monotonicity #15916]: #15938
+#15944 := [trans #15939 #15942]: #15943
+#15935 := (iff #13696 #15932)
+#15929 := (or #13485 #15926 #13672)
+#15933 := (iff #15929 #15932)
+#15934 := [rewrite]: #15933
+#15930 := (iff #13696 #15929)
+#15927 := (iff #13666 #15926)
+#15924 := (iff #13660 #15923)
+#15921 := (iff #13655 #15920)
+#15918 := (iff #13647 #15917)
+#15919 := [monotonicity #15916]: #15918
+#15922 := [monotonicity #15919]: #15921
+#15925 := [monotonicity #15922]: #15924
+#15928 := [monotonicity #15925]: #15927
+#15931 := [monotonicity #15928]: #15930
+#15936 := [trans #15931 #15934]: #15935
+#15947 := [monotonicity #15936 #15944]: #15946
+#15950 := [monotonicity #15947]: #15949
+#15953 := [monotonicity #15950]: #15952
+#15956 := [monotonicity #15953]: #15955
+#15959 := [monotonicity #15956]: #15958
+#15962 := [monotonicity #15959]: #15961
+#15967 := [trans #15962 #15965]: #15966
+#16004 := [monotonicity #15967 #16001]: #16003
+#15858 := (iff #14030 #15857)
+#15855 := (iff #14027 #15854)
+#15852 := (iff #14023 #15849)
+#15843 := (+ 255::Int #13970)
+#15846 := (>= #15843 0::Int)
+#15850 := (iff #15846 #15849)
+#15851 := [rewrite]: #15850
+#15847 := (iff #14023 #15846)
+#15844 := (= #14024 #15843)
+#1375 := (= f90 255::Int)
+#7605 := [asserted]: #1375
+#15845 := [monotonicity #7605]: #15844
+#15848 := [monotonicity #15845]: #15847
+#15853 := [trans #15848 #15851]: #15852
+#15856 := [monotonicity #15853]: #15855
+#15859 := [monotonicity #15856]: #15858
+#15841 := (iff #14017 #15840)
+#15838 := (iff #14014 #15837)
+#15835 := (iff #14010 #15832)
+#15826 := (+ 4294967295::Int #13941)
+#15829 := (>= #15826 0::Int)
+#15833 := (iff #15829 #15832)
+#15834 := [rewrite]: #15833
+#15830 := (iff #14010 #15829)
+#15827 := (= #14011 #15826)
+#15828 := [monotonicity #7606]: #15827
+#15831 := [monotonicity #15828]: #15830
+#15836 := [trans #15831 #15834]: #15835
+#15839 := [monotonicity #15836]: #15838
+#15842 := [monotonicity #15839]: #15841
+#15824 := (iff #14007 #15823)
+#15821 := (iff #14004 #15820)
+#15818 := (iff #14001 #15815)
+#15812 := (>= #15809 0::Int)
+#15816 := (iff #15812 #15815)
+#15817 := [rewrite]: #15816
+#15813 := (iff #14001 #15812)
+#15814 := [monotonicity #15811]: #15813
+#15819 := [trans #15814 #15817]: #15818
+#15822 := [monotonicity #15819]: #15821
+#15825 := [monotonicity #15822]: #15824
+#15807 := (iff #13989 #15806)
+#15804 := (iff #13986 #15803)
+#15801 := (iff #13981 #15798)
+#15795 := (or #14425 #13958 #13972)
+#15799 := (iff #15795 #15798)
+#15800 := [rewrite]: #15799
+#15796 := (iff #13981 #15795)
+#15797 := [monotonicity #14423]: #15796
+#15802 := [trans #15797 #15800]: #15801
+#15805 := [quant-intro #15802]: #15804
+#15808 := [monotonicity #15805]: #15807
+#16007 := [monotonicity #15808 #15825 #15842 #15859 #16004]: #16006
+#16012 := [trans #16007 #16010]: #16011
+#16015 := [monotonicity #16012]: #16014
+#15793 := (iff #13469 #15792)
+#15790 := (iff #13466 #15789)
+#15787 := (iff #13461 #15784)
+#15781 := (or #14425 #13439 #13451)
+#15785 := (iff #15781 #15784)
+#15786 := [rewrite]: #15785
+#15782 := (iff #13461 #15781)
+#15783 := [monotonicity #14423]: #15782
+#15788 := [trans #15783 #15786]: #15787
+#15791 := [quant-intro #15788]: #15790
+#15794 := [monotonicity #15791]: #15793
+#16018 := [monotonicity #15794 #16015]: #16017
+#16021 := [monotonicity #15791 #16018]: #16020
+#16024 := [monotonicity #16021]: #16023
+#16027 := [monotonicity #16024]: #16026
+#16030 := [monotonicity #16027]: #16029
+#16033 := [monotonicity #16030]: #16032
+#16036 := [monotonicity #16033]: #16035
+#16039 := [monotonicity #16036]: #16038
+#16042 := [monotonicity #16039]: #16041
+#16045 := [monotonicity #16042]: #16044
+#16048 := [monotonicity #16045]: #16047
+#14325 := (not #14177)
+#15338 := (iff #14325 #15337)
+#15335 := (iff #14177 #15334)
+#15332 := (iff #14174 #15331)
+#15329 := (iff #14169 #15328)
+#15326 := (iff #14163 #15325)
+#15323 := (iff #14158 #15322)
+#15320 := (iff #14150 #15319)
+#15317 := (iff #14129 #15316)
+#15314 := (iff #14126 #15313)
+#15311 := (iff #14123 #15310)
+#15308 := (iff #14120 #15307)
+#15305 := (iff #14115 #15304)
+#15302 := (iff #14107 #15299)
+#15296 := (or #15263 #13938 #13024 #13015 #13006 #12997 #12988 #13485 #15293 #13955 #13989 #13995 #14007 #14017 #14030 #14041)
+#15300 := (iff #15296 #15299)
+#15301 := [rewrite]: #15300
+#15297 := (iff #14107 #15296)
+#15294 := (iff #13914 #15293)
+#15291 := (iff #13909 #15288)
+#15273 := (or #12304 #12295 #12286 #12277 #13485 #13852)
+#15285 := (or #13485 #13766 #15273)
+#15289 := (iff #15285 #15288)
+#15290 := [rewrite]: #15289
+#15286 := (iff #13909 #15285)
+#15283 := (iff #13884 #15273)
+#15278 := (and true #15273)
+#15281 := (iff #15278 #15273)
+#15282 := [rewrite]: #15281
+#15279 := (iff #13884 #15278)
+#15276 := (iff #13879 #15273)
+#15270 := (or false #12304 #12295 #12286 #12277 #13485 #13852)
+#15274 := (iff #15270 #15273)
+#15275 := [rewrite]: #15274
+#15271 := (iff #13879 #15270)
+#15268 := (iff #12338 false)
+#15266 := (iff #12338 #3156)
+#15004 := (iff #10924 true)
+#10923 := [asserted]: #2542
+#10930 := [mp #10923 #10927]: #10924
+#15005 := [iff-true #10930]: #15004
+#15267 := [monotonicity #15005]: #15266
+#15269 := [trans #15267 #12221]: #15268
+#15272 := [monotonicity #15269]: #15271
+#15277 := [trans #15272 #15275]: #15276
+#15280 := [monotonicity #15005 #15277]: #15279
+#15284 := [trans #15280 #15282]: #15283
+#15287 := [monotonicity #15284]: #15286
+#15292 := [trans #15287 #15290]: #15291
+#15295 := [monotonicity #15292]: #15294
+#15264 := (iff #12366 #15263)
+#15261 := (iff #12228 #12222)
+#15256 := (and true #12222)
+#15259 := (iff #15256 #12222)
+#15260 := [rewrite]: #15259
+#15257 := (iff #12228 #15256)
+#15240 := (iff #12109 true)
+#15241 := [iff-true #14315]: #15240
+#15258 := [monotonicity #15241]: #15257
+#15262 := [trans #15258 #15260]: #15261
+#15265 := [monotonicity #15262]: #15264
+#15298 := [monotonicity #15265 #15295]: #15297
+#15303 := [trans #15298 #15301]: #15302
+#15306 := [monotonicity #15303]: #15305
+#15309 := [monotonicity #15306]: #15308
+#15312 := [monotonicity #15309]: #15311
+#15315 := [monotonicity #15312]: #15314
+#15318 := [monotonicity #15315]: #15317
+#15321 := [monotonicity #15318]: #15320
+#15324 := [monotonicity #15321]: #15323
+#15327 := [monotonicity #15324]: #15326
+#15330 := [monotonicity #15327]: #15329
+#15333 := [monotonicity #15330]: #15332
+#15336 := [monotonicity #15333]: #15335
+#15339 := [monotonicity #15336]: #15338
+#14326 := [not-or-elim #14310]: #14325
+#15340 := [mp #14326 #15339]: #15337
+#16049 := [mp #15340 #16048]: #16046
+#18796 := [mp~ #16049 #18795]: #18793
+#18797 := [mp #18796 #19141]: #19139
+#22664 := [mp #18797 #22663]: #22661
+#23569 := [mp #22664 #23568]: #23566
+#29167 := [unit-resolution #23569 #26960]: #23563
+#24793 := (or #23560 #23554)
+#24794 := [def-axiom]: #24793
+#29168 := [unit-resolution #24794 #29167]: #23554
+#27003 := (f24 #3098)
+decl f156 :: (-> S18 S18)
+#24960 := (f156 #3040)
+#27004 := (= #24960 #27003)
+decl f39 :: (-> Int S20)
+#24797 := (f39 #3076)
+#27034 := (f128 #24797)
+decl f81 :: (-> Int Int Int)
+decl f151 :: (-> S18 Int)
+#27032 := (f151 #24960)
+#27033 := (f81 0::Int #27032)
+#27041 := (+ #27033 #27034)
+#27044 := (f54 #24960 #27041)
+#27233 := (f24 #27044)
+#27604 := (= #27233 #27003)
+#27600 := (= #27003 #27233)
+#27572 := (= #3098 #27044)
+#27028 := (f77 #24797 0::Int #24960)
+#27047 := (= #27028 #27044)
+#27050 := (not #27047)
+decl f150 :: (-> S20 S20 S1)
+#27029 := (f150 #27028 #24797)
+#27030 := (= f1 #27029)
+#27031 := (not #27030)
+#27056 := (or #27031 #27050)
+#27061 := (not #27056)
+#289 := (:var 1 Int)
+#1622 := (f77 #60 #289 #275)
+#1623 := (pattern #1622)
+#1624 := (f150 #1622 #60)
+#8354 := (= f1 #1624)
+#21196 := (not #8354)
+#1627 := (f151 #275)
+#1628 := (f81 #289 #1627)
+#1626 := (f128 #60)
+#1629 := (+ #1626 #1628)
+#1630 := (f54 #275 #1629)
+#1631 := (= #1622 #1630)
+#21195 := (not #1631)
+#21197 := (or #21195 #21196)
+#21198 := (not #21197)
+#21201 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #21198)
+#8360 := (and #1631 #8354)
+#8365 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #8360)
+#21202 := (iff #8365 #21201)
+#21199 := (iff #8360 #21198)
+#21200 := [rewrite]: #21199
+#21203 := [quant-intro #21200]: #21202
+#17329 := (~ #8365 #8365)
+#17327 := (~ #8360 #8360)
+#17328 := [refl]: #17327
+#17330 := [nnf-pos #17328]: #17329
+#1625 := (= #1624 f1)
+#1632 := (and #1625 #1631)
+#1633 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #1632)
+#8366 := (iff #1633 #8365)
+#8363 := (iff #1632 #8360)
+#8357 := (and #8354 #1631)
+#8361 := (iff #8357 #8360)
+#8362 := [rewrite]: #8361
+#8358 := (iff #1632 #8357)
+#8355 := (iff #1625 #8354)
+#8356 := [rewrite]: #8355
+#8359 := [monotonicity #8356]: #8358
+#8364 := [trans #8359 #8362]: #8363
+#8367 := [quant-intro #8364]: #8366
+#8353 := [asserted]: #1633
+#8370 := [mp #8353 #8367]: #8365
+#17331 := [mp~ #8370 #17330]: #8365
+#21204 := [mp #17331 #21203]: #21201
+#27451 := (not #21201)
+#27452 := (or #27451 #27061)
+#27035 := (+ #27034 #27033)
+#27036 := (f54 #24960 #27035)
+#27037 := (= #27028 #27036)
+#27038 := (not #27037)
+#27039 := (or #27038 #27031)
+#27040 := (not #27039)
+#27453 := (or #27451 #27040)
+#27449 := (iff #27453 #27452)
+#27456 := (iff #27452 #27452)
+#27457 := [rewrite]: #27456
+#27062 := (iff #27040 #27061)
+#27059 := (iff #27039 #27056)
+#27053 := (or #27050 #27031)
+#27057 := (iff #27053 #27056)
+#27058 := [rewrite]: #27057
+#27054 := (iff #27039 #27053)
+#27051 := (iff #27038 #27050)
+#27048 := (iff #27037 #27047)
+#27045 := (= #27036 #27044)
+#27042 := (= #27035 #27041)
+#27043 := [rewrite]: #27042
+#27046 := [monotonicity #27043]: #27045
+#27049 := [monotonicity #27046]: #27048
+#27052 := [monotonicity #27049]: #27051
+#27055 := [monotonicity #27052]: #27054
+#27060 := [trans #27055 #27058]: #27059
+#27063 := [monotonicity #27060]: #27062
+#27455 := [monotonicity #27063]: #27449
+#27458 := [trans #27455 #27457]: #27449
+#27454 := [quant-inst #24797 #161 #24960]: #27453
+#27459 := [mp #27454 #27458]: #27452
+#27562 := [unit-resolution #27459 #21204]: #27061
+#27468 := (or #27056 #27047)
+#27466 := [def-axiom]: #27468
+#27568 := [unit-resolution #27466 #27562]: #27047
+#27570 := (= #3098 #27028)
+#24961 := (= f19 #24960)
+#1401 := (f136 #369 #202)
+#1638 := (pattern #1401)
+#1652 := (f156 #1401)
+#8415 := (= #369 #1652)
+#8419 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8415)
+#17359 := (~ #8419 #8419)
+#17357 := (~ #8415 #8415)
+#17358 := [refl]: #17357
+#17360 := [nnf-pos #17358]: #17359
+#1653 := (= #1652 #369)
+#1654 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1653)
+#8420 := (iff #1654 #8419)
+#8417 := (iff #1653 #8415)
+#8418 := [rewrite]: #8417
+#8421 := [quant-intro #8418]: #8420
+#8414 := [asserted]: #1654
+#8424 := [mp #8414 #8421]: #8419
+#17361 := [mp~ #8424 #17360]: #8419
+#24964 := (not #8419)
+#24965 := (or #24964 #24961)
+#24966 := [quant-inst #50 #3036]: #24965
+#28486 := [unit-resolution #24966 #17361]: #24961
+#24798 := (= #3042 #24797)
+#132 := (f40 #62)
+#23175 := (pattern #132)
+#133 := (f39 #132)
+#3682 := (= #62 #133)
+#23176 := (forall (vars (?v0 S20)) (:pat #23175) #3682)
+#3685 := (forall (vars (?v0 S20)) #3682)
+#23177 := (iff #3685 #23176)
+#23179 := (iff #23176 #23176)
+#23180 := [rewrite]: #23179
+#23178 := [rewrite]: #23177
+#23181 := [trans #23178 #23180]: #23177
+#16306 := (~ #3685 #3685)
+#16296 := (~ #3682 #3682)
+#16297 := [refl]: #16296
+#16362 := [nnf-pos #16297]: #16306
+#134 := (= #133 #62)
+#135 := (forall (vars (?v0 S20)) #134)
+#3686 := (iff #135 #3685)
+#3683 := (iff #134 #3682)
+#3684 := [rewrite]: #3683
+#3687 := [quant-intro #3684]: #3686
+#3681 := [asserted]: #135
+#3690 := [mp #3681 #3687]: #3685
+#16363 := [mp~ #3690 #16362]: #3685
+#23182 := [mp #16363 #23181]: #23176
+#24801 := (not #23176)
+#24802 := (or #24801 #24798)
+#24803 := [quant-inst #3042]: #24802
+#27569 := [unit-resolution #24803 #23182]: #24798
+#27571 := [monotonicity #27569 #28486]: #27570
+#27599 := [trans #27571 #27568]: #27572
+#27601 := [monotonicity #27599]: #27600
+#27591 := [symm #27601]: #27604
+#27234 := (= #24960 #27233)
+#27497 := (or #25028 #27234)
+#27503 := [quant-inst #24960 #27041]: #27497
+#27567 := [unit-resolution #27503 #23276]: #27234
+#27592 := [trans #27567 #27591]: #27004
+#27413 := (not #27004)
+#26977 := (f59 #3098 #24960)
+#26978 := (= f1 #26977)
+#27006 := (iff #26978 #27004)
+#1433 := (f24 #55)
+#9184 := (= #275 #1433)
+#11354 := (iff #9184 #11333)
+#23258 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #11354)
+#11359 := (forall (vars (?v0 S20) (?v1 S18)) #11354)
+#23261 := (iff #11359 #23258)
+#23259 := (iff #11354 #11354)
+#23260 := [refl]: #23259
+#23262 := [quant-intro #23260]: #23261
+#18251 := (~ #11359 #11359)
+#18249 := (~ #11354 #11354)
+#18250 := [refl]: #18249
+#18252 := [nnf-pos #18250]: #18251
+#1939 := (= #1433 #275)
+#2736 := (iff #2731 #1939)
+#2737 := (forall (vars (?v0 S20) (?v1 S18)) #2736)
+#11360 := (iff #2737 #11359)
+#11357 := (iff #2736 #11354)
+#11350 := (iff #11333 #9184)
+#11355 := (iff #11350 #11354)
+#11356 := [rewrite]: #11355
+#11352 := (iff #2736 #11350)
+#9185 := (iff #1939 #9184)
+#9186 := [rewrite]: #9185
+#11353 := [monotonicity #11336 #9186]: #11352
+#11358 := [trans #11353 #11356]: #11357
+#11361 := [quant-intro #11358]: #11360
+#11349 := [asserted]: #2737
+#11364 := [mp #11349 #11361]: #11359
+#18253 := [mp~ #11364 #18252]: #11359
+#23263 := [mp #18253 #23262]: #23258
+#26174 := (not #23258)
+#27419 := (or #26174 #27006)
+#27005 := (iff #27004 #26978)
+#27420 := (or #26174 #27005)
+#27407 := (iff #27420 #27419)
+#27409 := (iff #27419 #27419)
+#27410 := [rewrite]: #27409
+#27007 := (iff #27005 #27006)
+#27008 := [rewrite]: #27007
+#27408 := [monotonicity #27008]: #27407
+#27411 := [trans #27408 #27410]: #27407
+#27405 := [quant-inst #3098 #24960]: #27420
+#27406 := [mp #27405 #27411]: #27419
+#27530 := [unit-resolution #27406 #23263]: #27006
+#26985 := (not #26978)
+#27563 := (iff #18409 #26985)
+#27535 := (iff #12144 #26978)
+#27533 := (iff #26978 #12144)
+#27526 := (= #26977 #3099)
+#28487 := (= #24960 f19)
+#28488 := [symm #28486]: #28487
+#27532 := [monotonicity #28488]: #27526
+#27534 := [monotonicity #27532]: #27533
+#27536 := [symm #27534]: #27535
+#27564 := [monotonicity #27536]: #27563
+#27531 := [hypothesis]: #18409
+#27565 := [mp #27531 #27564]: #26985
+#27412 := (not #27006)
+#27414 := (or #27412 #26978 #27413)
+#27415 := [def-axiom]: #27414
+#27566 := [unit-resolution #27415 #27565 #27530]: #27413
+#27590 := [unit-resolution #27566 #27592]: false
+#27593 := [lemma #27590]: #12144
+#27181 := (f54 #24960 #3043)
+#27182 := (f77 #27181 0::Int #24960)
+#27186 := (f35 f298 #27182)
+#27187 := (= f1 #27186)
+#27188 := (not #27187)
+#28139 := (iff #18412 #27188)
+#28109 := (iff #12147 #27187)
+#28136 := (iff #27187 #12147)
+#28133 := (= #27186 #3101)
+#27752 := (= #27182 #3098)
+#28494 := (= #27181 #3042)
+#28492 := (= #3043 f299)
+#25080 := (= f299 #3043)
+#2762 := (f128 #2761)
+#11409 := (= #202 #2762)
+#23265 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #23264) #11409)
+#11413 := (forall (vars (?v0 S18) (?v1 Int)) #11409)
+#23268 := (iff #11413 #23265)
+#23266 := (iff #11409 #11409)
+#23267 := [refl]: #23266
+#23269 := [quant-intro #23267]: #23268
+#18266 := (~ #11413 #11413)
+#18264 := (~ #11409 #11409)
+#18265 := [refl]: #18264
+#18267 := [nnf-pos #18265]: #18266
+#2763 := (= #2762 #202)
+#2764 := (forall (vars (?v0 S18) (?v1 Int)) #2763)
+#11414 := (iff #2764 #11413)
+#11411 := (iff #2763 #11409)
+#11412 := [rewrite]: #11411
+#11415 := [quant-intro #11412]: #11414
+#11408 := [asserted]: #2764
+#11418 := [mp #11408 #11415]: #11413
+#18268 := [mp~ #11418 #18267]: #11413
+#23270 := [mp #18268 #23269]: #23265
+#25034 := (not #23265)
+#25085 := (or #25034 #25080)
+#25086 := [quant-inst #50 #3041]: #25085
+#28491 := [unit-resolution #25086 #23270]: #25080
+#28493 := [symm #28491]: #28492
+#28495 := [monotonicity #28488 #28493]: #28494
+#28135 := [monotonicity #28495 #28488]: #27752
+#27928 := [monotonicity #28135]: #28133
+#28137 := [monotonicity #27928]: #28136
+#28138 := [symm #28137]: #28109
+#28111 := [monotonicity #28138]: #28139
+#27751 := [hypothesis]: #18412
+#28112 := [mp #27751 #28111]: #27188
+decl f148 :: (-> S29 S1)
+#27183 := (f69 #3220 #27182)
+#27184 := (f148 #27183)
+#27185 := (= f1 #27184)
+#27198 := (or #27185 #27188)
+#27201 := (not #27198)
+decl f33 :: (-> S18 S1)
+#27194 := (f33 #24960)
+#27195 := (= f1 #27194)
+#2848 := (f33 f19)
+#28526 := (= #2848 #27194)
+#28523 := (= #27194 #2848)
+#28524 := [monotonicity #28488]: #28523
+#28527 := [symm #28524]: #28526
+#11588 := (= f1 #2848)
+#2849 := (= #2848 f1)
+#11590 := (iff #2849 #11588)
+#11591 := [rewrite]: #11590
+#11587 := [asserted]: #2849
+#11594 := [mp #11587 #11591]: #11588
+#28528 := [trans #11594 #28527]: #27195
+#27196 := (not #27195)
+#28357 := (or #27196 #27201)
+decl f26 :: (-> S20 S21 S1)
+decl f27 :: (-> S19 S20 S21)
+#26739 := (f27 f298 #26146)
+decl f155 :: (-> S18 Int)
+#24962 := (f155 #3040)
+#27102 := (f136 #24960 #24962)
+#27103 := (f54 #27102 #3043)
+#27191 := (f26 #27103 #26739)
+#27192 := (= f1 #27191)
+#26740 := (f26 #26146 #26739)
+#28128 := (= #26740 #27191)
+#28366 := (= #27191 #26740)
+#28055 := (= #27103 #26146)
+#28363 := (= #27103 #3044)
+#28152 := (= #27102 #3040)
+#28151 := (= #24962 f297)
+#24963 := (= f297 #24962)
+#1649 := (f155 #1401)
+#8408 := (= #202 #1649)
+#8411 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8408)
+#17354 := (~ #8411 #8411)
+#17352 := (~ #8408 #8408)
+#17353 := [refl]: #17352
+#17355 := [nnf-pos #17353]: #17354
+#1650 := (= #1649 #202)
+#1651 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1650)
+#8412 := (iff #1651 #8411)
+#8409 := (iff #1650 #8408)
+#8410 := [rewrite]: #8409
+#8413 := [quant-intro #8410]: #8412
+#8407 := [asserted]: #1651
+#8416 := [mp #8407 #8413]: #8411
+#17356 := [mp~ #8416 #17355]: #8411
+#24969 := (not #8411)
+#24970 := (or #24969 #24963)
+#24971 := [quant-inst #50 #3036]: #24970
+#28508 := [unit-resolution #24971 #17356]: #24963
+#27929 := [symm #28508]: #28151
+#28153 := [monotonicity #28488 #27929]: #28152
+#28364 := [monotonicity #28153]: #28363
+#28365 := [trans #28364 #28875]: #28055
+#28367 := [monotonicity #28365]: #28366
+#28129 := [symm #28367]: #28128
+#26741 := (= f1 #26740)
+decl f64 :: (-> S19 S20 S21)
+#26729 := (f64 f298 #26146)
+#26730 := (f26 #62 #26729)
+#26736 := (pattern #26730)
+decl f209 :: (-> S18 S1)
+#26733 := (f209 #26550)
+#26734 := (= f1 #26733)
+#26731 := (= f1 #26730)
+#26732 := (not #26731)
+decl f159 :: (-> S20 S21 S1)
+decl f204 :: (-> S22 S21)
+decl f22 :: (-> S19 S20 S22)
+#26725 := (f22 f298 #26146)
+#26726 := (f204 #26725)
+#26727 := (f159 #62 #26726)
+#26728 := (= f1 #26727)
+#26746 := (or #26728 #26732 #26734)
+#26749 := (forall (vars (?v3 S20)) (:pat #26736) #26746)
+#26752 := (not #26749)
+#26742 := (not #26741)
+#26755 := (or #26613 #26742 #26752)
+#26758 := (not #26755)
+#28107 := (= #3096 #26680)
+#28113 := [symm #26898]: #28107
+#28131 := [trans #26960 #28113]: #26681
+#26687 := (or #26689 #26679 #26697)
+#26690 := [def-axiom]: #26687
+#28108 := [unit-resolution #26690 #28131 #26901]: #26679
+#26761 := (or #26700 #26758)
 #54 := (:var 2 S19)
-#2218 := (f207 #54 #55 #62)
+#2218 := (f208 #54 #55 #62)
 #2281 := (pattern #2218)
 #2282 := (f64 #53 #60)
 #2283 := (f26 #62 #2282)
 #2284 := (pattern #2283)
 #2210 := (f22 #53 #55)
-#2290 := (f203 #2210)
-#2291 := (f158 #62 #2290)
-#10238 := (= f1 #2291)
-#10232 := (= f1 #2283)
-#21923 := (not #10232)
+#2290 := (f204 #2210)
+#2291 := (f159 #62 #2290)
+#10202 := (= f1 #2291)
+#10196 := (= f1 #2283)
+#21887 := (not #10196)
 #1425 := (f24 #60)
-#2285 := (f208 #1425)
-#10226 := (= f1 #2285)
-#21938 := (or #10226 #21923 #10238)
-#21943 := (forall (vars (?v3 S20)) (:pat #2284) #21938)
-#21949 := (not #21943)
+#2285 := (f209 #1425)
+#10190 := (= f1 #2285)
+#21902 := (or #10190 #21887 #10202)
+#21907 := (forall (vars (?v3 S20)) (:pat #2284) #21902)
+#21913 := (not #21907)
 #2197 := (f27 #54 #62)
 #2198 := (f26 #55 #2197)
-#9926 := (= f1 #2198)
-#21758 := (not #9926)
+#9890 := (= f1 #2198)
+#21722 := (not #9890)
 #221 := (f38 #54 #55)
 #3873 := (= f1 #221)
-#10576 := (not #3873)
-#21950 := (or #10576 #21758 #21949)
-#21951 := (not #21950)
-#9974 := (= f1 #2218)
-#10262 := (not #9974)
-#21956 := (or #10262 #21951)
-#21959 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #21956)
-#10229 := (not #10226)
-#10235 := (and #10229 #10232)
-#10244 := (not #10235)
-#10245 := (or #10244 #10238)
-#10250 := (forall (vars (?v3 S20)) (:pat #2284) #10245)
-#10271 := (and #3873 #9926 #10250)
-#10274 := (or #10262 #10271)
-#10277 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #10274)
-#21960 := (iff #10277 #21959)
-#21957 := (iff #10274 #21956)
-#21954 := (iff #10271 #21951)
-#21946 := (and #3873 #9926 #21943)
-#21952 := (iff #21946 #21951)
-#21953 := [rewrite]: #21952
-#21947 := (iff #10271 #21946)
-#21944 := (iff #10250 #21943)
-#21941 := (iff #10245 #21938)
-#21924 := (or #10226 #21923)
-#21935 := (or #21924 #10238)
-#21939 := (iff #21935 #21938)
-#21940 := [rewrite]: #21939
-#21936 := (iff #10245 #21935)
-#21933 := (iff #10244 #21924)
-#21925 := (not #21924)
-#21928 := (not #21925)
-#21931 := (iff #21928 #21924)
-#21932 := [rewrite]: #21931
-#21929 := (iff #10244 #21928)
-#21926 := (iff #10235 #21925)
-#21927 := [rewrite]: #21926
-#21930 := [monotonicity #21927]: #21929
-#21934 := [trans #21930 #21932]: #21933
-#21937 := [monotonicity #21934]: #21936
-#21942 := [trans #21937 #21940]: #21941
-#21945 := [quant-intro #21942]: #21944
-#21948 := [monotonicity #21945]: #21947
-#21955 := [trans #21948 #21953]: #21954
-#21958 := [monotonicity #21955]: #21957
-#21961 := [quant-intro #21958]: #21960
-#17909 := (~ #10277 #10277)
-#17907 := (~ #10274 #10274)
-#17905 := (~ #10271 #10271)
-#17903 := (~ #10250 #10250)
-#17901 := (~ #10245 #10245)
-#17902 := [refl]: #17901
-#17904 := [nnf-pos #17902]: #17903
-#17899 := (~ #9926 #9926)
-#17900 := [refl]: #17899
-#17897 := (~ #3873 #3873)
-#17898 := [refl]: #17897
-#17906 := [monotonicity #17898 #17900 #17904]: #17905
-#17895 := (~ #10262 #10262)
-#17896 := [refl]: #17895
-#17908 := [monotonicity #17896 #17906]: #17907
-#17910 := [nnf-pos #17908]: #17909
+#10540 := (not #3873)
+#21914 := (or #10540 #21722 #21913)
+#21915 := (not #21914)
+#9938 := (= f1 #2218)
+#10226 := (not #9938)
+#21920 := (or #10226 #21915)
+#21923 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #21920)
+#10193 := (not #10190)
+#10199 := (and #10193 #10196)
+#10208 := (not #10199)
+#10209 := (or #10208 #10202)
+#10214 := (forall (vars (?v3 S20)) (:pat #2284) #10209)
+#10235 := (and #3873 #9890 #10214)
+#10238 := (or #10226 #10235)
+#10241 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #10238)
+#21924 := (iff #10241 #21923)
+#21921 := (iff #10238 #21920)
+#21918 := (iff #10235 #21915)
+#21910 := (and #3873 #9890 #21907)
+#21916 := (iff #21910 #21915)
+#21917 := [rewrite]: #21916
+#21911 := (iff #10235 #21910)
+#21908 := (iff #10214 #21907)
+#21905 := (iff #10209 #21902)
+#21888 := (or #10190 #21887)
+#21899 := (or #21888 #10202)
+#21903 := (iff #21899 #21902)
+#21904 := [rewrite]: #21903
+#21900 := (iff #10209 #21899)
+#21897 := (iff #10208 #21888)
+#21889 := (not #21888)
+#21892 := (not #21889)
+#21895 := (iff #21892 #21888)
+#21896 := [rewrite]: #21895
+#21893 := (iff #10208 #21892)
+#21890 := (iff #10199 #21889)
+#21891 := [rewrite]: #21890
+#21894 := [monotonicity #21891]: #21893
+#21898 := [trans #21894 #21896]: #21897
+#21901 := [monotonicity #21898]: #21900
+#21906 := [trans #21901 #21904]: #21905
+#21909 := [quant-intro #21906]: #21908
+#21912 := [monotonicity #21909]: #21911
+#21919 := [trans #21912 #21917]: #21918
+#21922 := [monotonicity #21919]: #21921
+#21925 := [quant-intro #21922]: #21924
+#17873 := (~ #10241 #10241)
+#17871 := (~ #10238 #10238)
+#17869 := (~ #10235 #10235)
+#17867 := (~ #10214 #10214)
+#17865 := (~ #10209 #10209)
+#17866 := [refl]: #17865
+#17868 := [nnf-pos #17866]: #17867
+#17863 := (~ #9890 #9890)
+#17864 := [refl]: #17863
+#17861 := (~ #3873 #3873)
+#17862 := [refl]: #17861
+#17870 := [monotonicity #17862 #17864 #17868]: #17869
+#17859 := (~ #10226 #10226)
+#17860 := [refl]: #17859
+#17872 := [monotonicity #17860 #17870]: #17871
+#17874 := [nnf-pos #17872]: #17873
 #2292 := (= #2291 f1)
 #2288 := (= #2283 f1)
 #2286 := (= #2285 f1)
@@ -4196,154 +5435,110 @@
 #2219 := (= #2218 f1)
 #2297 := (implies #2219 #2296)
 #2298 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #2297)
-#10280 := (iff #2298 #10277)
-#10253 := (and #3873 #10250)
-#10256 := (and #9926 #10253)
-#10263 := (or #10262 #10256)
-#10268 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #10263)
-#10278 := (iff #10268 #10277)
-#10275 := (iff #10263 #10274)
-#10272 := (iff #10256 #10271)
-#10273 := [rewrite]: #10272
-#10276 := [monotonicity #10273]: #10275
-#10279 := [quant-intro #10276]: #10278
-#10269 := (iff #2298 #10268)
-#10266 := (iff #2297 #10263)
-#10259 := (implies #9974 #10256)
-#10264 := (iff #10259 #10263)
-#10265 := [rewrite]: #10264
-#10260 := (iff #2297 #10259)
-#10257 := (iff #2296 #10256)
-#10254 := (iff #2295 #10253)
-#10251 := (iff #2294 #10250)
-#10248 := (iff #2293 #10245)
-#10241 := (implies #10235 #10238)
-#10246 := (iff #10241 #10245)
-#10247 := [rewrite]: #10246
-#10242 := (iff #2293 #10241)
-#10239 := (iff #2292 #10238)
-#10240 := [rewrite]: #10239
-#10236 := (iff #2289 #10235)
-#10233 := (iff #2288 #10232)
-#10234 := [rewrite]: #10233
-#10230 := (iff #2287 #10229)
-#10227 := (iff #2286 #10226)
-#10228 := [rewrite]: #10227
-#10231 := [monotonicity #10228]: #10230
-#10237 := [monotonicity #10231 #10234]: #10236
-#10243 := [monotonicity #10237 #10240]: #10242
-#10249 := [trans #10243 #10247]: #10248
-#10252 := [quant-intro #10249]: #10251
+#10244 := (iff #2298 #10241)
+#10217 := (and #3873 #10214)
+#10220 := (and #9890 #10217)
+#10227 := (or #10226 #10220)
+#10232 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #10227)
+#10242 := (iff #10232 #10241)
+#10239 := (iff #10227 #10238)
+#10236 := (iff #10220 #10235)
+#10237 := [rewrite]: #10236
+#10240 := [monotonicity #10237]: #10239
+#10243 := [quant-intro #10240]: #10242
+#10233 := (iff #2298 #10232)
+#10230 := (iff #2297 #10227)
+#10223 := (implies #9938 #10220)
+#10228 := (iff #10223 #10227)
+#10229 := [rewrite]: #10228
+#10224 := (iff #2297 #10223)
+#10221 := (iff #2296 #10220)
+#10218 := (iff #2295 #10217)
+#10215 := (iff #2294 #10214)
+#10212 := (iff #2293 #10209)
+#10205 := (implies #10199 #10202)
+#10210 := (iff #10205 #10209)
+#10211 := [rewrite]: #10210
+#10206 := (iff #2293 #10205)
+#10203 := (iff #2292 #10202)
+#10204 := [rewrite]: #10203
+#10200 := (iff #2289 #10199)
+#10197 := (iff #2288 #10196)
+#10198 := [rewrite]: #10197
+#10194 := (iff #2287 #10193)
+#10191 := (iff #2286 #10190)
+#10192 := [rewrite]: #10191
+#10195 := [monotonicity #10192]: #10194
+#10201 := [monotonicity #10195 #10198]: #10200
+#10207 := [monotonicity #10201 #10204]: #10206
+#10213 := [trans #10207 #10211]: #10212
+#10216 := [quant-intro #10213]: #10215
 #3874 := (iff #225 #3873)
 #3875 := [rewrite]: #3874
-#10255 := [monotonicity #3875 #10252]: #10254
-#9927 := (iff #2203 #9926)
-#9928 := [rewrite]: #9927
-#10258 := [monotonicity #9928 #10255]: #10257
-#9975 := (iff #2219 #9974)
-#9976 := [rewrite]: #9975
-#10261 := [monotonicity #9976 #10258]: #10260
-#10267 := [trans #10261 #10265]: #10266
-#10270 := [quant-intro #10267]: #10269
-#10281 := [trans #10270 #10279]: #10280
-#10225 := [asserted]: #2298
-#10282 := [mp #10225 #10281]: #10277
-#17911 := [mp~ #10282 #17910]: #10277
-#21962 := [mp #17911 #21961]: #21959
-#26806 := (not #21959)
-#26801 := (or #26806 #26736 #26794)
-#26771 := (or #26770 #26768 #26764)
-#26773 := (forall (vars (?v3 S20)) (:pat #26772) #26771)
-#26774 := (not #26773)
-#26779 := (or #26649 #26778 #26774)
-#26780 := (not #26779)
-#26781 := (or #26736 #26780)
-#26758 := (or #26806 #26781)
-#26852 := (iff #26758 #26801)
-#26808 := (or #26806 #26797)
-#26811 := (iff #26808 #26801)
-#26850 := [rewrite]: #26811
-#26809 := (iff #26758 #26808)
-#26798 := (iff #26781 #26797)
-#26795 := (iff #26780 #26794)
-#26792 := (iff #26779 #26791)
-#26789 := (iff #26774 #26788)
-#26786 := (iff #26773 #26785)
-#26783 := (iff #26771 #26782)
-#26784 := [rewrite]: #26783
-#26787 := [quant-intro #26784]: #26786
-#26790 := [monotonicity #26787]: #26789
-#26793 := [monotonicity #26790]: #26792
-#26796 := [monotonicity #26793]: #26795
-#26799 := [monotonicity #26796]: #26798
-#26810 := [monotonicity #26799]: #26809
-#26853 := [trans #26810 #26850]: #26852
-#26807 := [quant-inst #3039 #26182 #26182]: #26758
-#26858 := [mp #26807 #26853]: #26801
-#28802 := [unit-resolution #26858 #21962]: #26797
-#28803 := [unit-resolution #28802 #28801]: #26794
-#26851 := (or #26791 #26777)
-#26863 := [def-axiom]: #26851
-#28804 := [unit-resolution #26863 #28803]: #26777
-#28797 := [trans #28804 #28796]: #27234
-#27235 := (not #27234)
-#27547 := (or #12183 #27235)
-#27223 := (f54 #24996 #3043)
-#27224 := (f77 #27223 0::Int #24996)
-#27228 := (f35 f297 #27224)
-#27229 := (= f1 #27228)
-#27230 := (not #27229)
-#27503 := (iff #18448 #27230)
-#27491 := (iff #12183 #27229)
-#27489 := (iff #27229 #12183)
-#27487 := (= #27228 #3101)
-#27486 := (= #27224 #3098)
-#28392 := (= #27223 #3042)
-#28393 := [monotonicity #28386 #28391]: #28392
-#27481 := [monotonicity #28393 #28386]: #27486
-#27488 := [monotonicity #27481]: #27487
-#27490 := [monotonicity #27488]: #27489
-#27502 := [symm #27490]: #27491
-#27511 := [monotonicity #27502]: #27503
-#27485 := [hypothesis]: #18448
-#27512 := [mp #27485 #27511]: #27230
-#27225 := (f69 #3220 #27224)
-#27226 := (f147 #27225)
-#27227 := (= f1 #27226)
-#27240 := (or #27227 #27230)
-#27243 := (not #27240)
-decl f33 :: (-> S18 S1)
-#27236 := (f33 #24996)
-#27237 := (= f1 #27236)
-#2848 := (f33 f19)
-#28424 := (= #2848 #27236)
-#28421 := (= #27236 #2848)
-#28422 := [monotonicity #28386]: #28421
-#28425 := [symm #28422]: #28424
-#11624 := (= f1 #2848)
-#2849 := (= #2848 f1)
-#11626 := (iff #2849 #11624)
-#11627 := [rewrite]: #11626
-#11623 := [asserted]: #2849
-#11630 := [mp #11623 #11627]: #11624
-#28426 := [trans #11630 #28425]: #27237
-#27238 := (not #27237)
-#27517 := (or #27238 #27243)
-#28427 := [hypothesis]: #27234
-#27181 := (<= #24998 0::Int)
-#27514 := (not #27181)
-#14360 := [not-or-elim #14346]: #13509
-#27164 := (* -1::Int #24998)
-#27273 := (+ f296 #27164)
-#27274 := (<= #27273 0::Int)
-#28407 := (not #24999)
-#28408 := (or #28407 #27274)
-#28409 := [th-lemma arith triangle-eq]: #28408
-#28410 := [unit-resolution #28409 #28406]: #27274
-#28416 := (not #27274)
-#27515 := (or #27514 #13508 #28416)
-#27510 := [th-lemma arith assign-bounds -1 1]: #27515
-#27516 := [unit-resolution #27510 #28410 #14360]: #27514
+#10219 := [monotonicity #3875 #10216]: #10218
+#9891 := (iff #2203 #9890)
+#9892 := [rewrite]: #9891
+#10222 := [monotonicity #9892 #10219]: #10221
+#9939 := (iff #2219 #9938)
+#9940 := [rewrite]: #9939
+#10225 := [monotonicity #9940 #10222]: #10224
+#10231 := [trans #10225 #10229]: #10230
+#10234 := [quant-intro #10231]: #10233
+#10245 := [trans #10234 #10243]: #10244
+#10189 := [asserted]: #2298
+#10246 := [mp #10189 #10245]: #10241
+#17875 := [mp~ #10246 #17874]: #10241
+#21926 := [mp #17875 #21925]: #21923
+#26714 := (not #21923)
+#26720 := (or #26714 #26700 #26758)
+#26735 := (or #26734 #26732 #26728)
+#26737 := (forall (vars (?v3 S20)) (:pat #26736) #26735)
+#26738 := (not #26737)
+#26743 := (or #26613 #26742 #26738)
+#26744 := (not #26743)
+#26745 := (or #26700 #26744)
+#26716 := (or #26714 #26745)
+#26810 := (iff #26716 #26720)
+#26722 := (or #26714 #26761)
+#26776 := (iff #26722 #26720)
+#26808 := [rewrite]: #26776
+#26723 := (iff #26716 #26722)
+#26762 := (iff #26745 #26761)
+#26759 := (iff #26744 #26758)
+#26756 := (iff #26743 #26755)
+#26753 := (iff #26738 #26752)
+#26750 := (iff #26737 #26749)
+#26747 := (iff #26735 #26746)
+#26748 := [rewrite]: #26747
+#26751 := [quant-intro #26748]: #26750
+#26754 := [monotonicity #26751]: #26753
+#26757 := [monotonicity #26754]: #26756
+#26760 := [monotonicity #26757]: #26759
+#26763 := [monotonicity #26760]: #26762
+#26724 := [monotonicity #26763]: #26723
+#26811 := [trans #26724 #26808]: #26810
+#26721 := [quant-inst #3039 #26146 #26146]: #26716
+#26812 := [mp #26721 #26811]: #26720
+#28140 := [unit-resolution #26812 #21926]: #26761
+#28132 := [unit-resolution #28140 #28108]: #26758
+#26809 := (or #26755 #26741)
+#26814 := [def-axiom]: #26809
+#28150 := [unit-resolution #26814 #28132]: #26741
+#28130 := [trans #28150 #28129]: #27192
+#27139 := (<= #24962 0::Int)
+#28353 := (not #27139)
+#14324 := [not-or-elim #14310]: #13473
+#27122 := (* -1::Int #24962)
+#27258 := (+ f297 #27122)
+#27259 := (<= #27258 0::Int)
+#28509 := (not #24963)
+#28510 := (or #28509 #27259)
+#28511 := [th-lemma arith triangle-eq]: #28510
+#28512 := [unit-resolution #28511 #28508]: #27259
+#28518 := (not #27259)
+#28354 := (or #28353 #13472 #28518)
+#28355 := [th-lemma arith assign-bounds -1 1]: #28354
+#28356 := [unit-resolution #28355 #28512 #14324]: #28353
 #279 := (f33 #275)
 #805 := (:var 4 Int)
 #2121 := (f54 #275 #805)
@@ -4353,67 +5548,67 @@
 #1408 := (:var 3 S20)
 #2119 := (f27 #1416 #1408)
 #310 := (:var 2 Int)
-#2117 := (f135 #275 #310)
+#2117 := (f136 #275 #310)
 #2118 := (f54 #2117 #805)
 #2120 := (f26 #2118 #2119)
 #2139 := (pattern #2120 #2138 #279)
 #1590 := (f70 #1416)
 #2136 := (f69 #1590 #2122)
 #2137 := (pattern #2120 #2136 #279)
-#2142 := (f147 #2136)
-#9734 := (= f1 #2142)
+#2142 := (f148 #2136)
+#9698 := (= f1 #2142)
 #2140 := (f35 #1416 #2122)
-#9731 := (= f1 #2140)
-#21668 := (not #9731)
-#21669 := (or #21668 #9734)
-#21670 := (not #21669)
-#9675 := (= f1 #2120)
-#21644 := (not #9675)
+#9695 := (= f1 #2140)
+#21632 := (not #9695)
+#21633 := (or #21632 #9698)
+#21634 := (not #21633)
+#9639 := (= f1 #2120)
+#21608 := (not #9639)
 #2125 := (f66 #1416)
-#9672 := (= f1 #2125)
-#21643 := (not #9672)
+#9636 := (= f1 #2125)
+#21607 := (not #9636)
 #4206 := (* -1::Int #310)
-#6270 := (+ #289 #4206)
-#6867 := (>= #6270 0::Int)
-#4468 := (>= #289 0::Int)
-#19581 := (not #4468)
+#6244 := (+ #289 #4206)
+#6841 := (>= #6244 0::Int)
+#4448 := (>= #289 0::Int)
+#19545 := (not #4448)
 #4084 := (= f1 #279)
-#10461 := (not #4084)
-#21676 := (or #10461 #19581 #6867 #21643 #21644 #21670)
-#21681 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #21676)
-#9737 := (not #9734)
-#9740 := (and #9731 #9737)
-#7934 := (not #6867)
-#9713 := (and #4084 #4468 #7934 #9672 #9675)
-#9718 := (not #9713)
-#9754 := (or #9718 #9740)
-#9757 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #9754)
-#21682 := (iff #9757 #21681)
-#21679 := (iff #9754 #21676)
-#21645 := (or #10461 #19581 #6867 #21643 #21644)
-#21673 := (or #21645 #21670)
-#21677 := (iff #21673 #21676)
-#21678 := [rewrite]: #21677
-#21674 := (iff #9754 #21673)
-#21671 := (iff #9740 #21670)
-#21672 := [rewrite]: #21671
-#21654 := (iff #9718 #21645)
-#21646 := (not #21645)
-#21649 := (not #21646)
-#21652 := (iff #21649 #21645)
-#21653 := [rewrite]: #21652
-#21650 := (iff #9718 #21649)
-#21647 := (iff #9713 #21646)
-#21648 := [rewrite]: #21647
-#21651 := [monotonicity #21648]: #21650
-#21655 := [trans #21651 #21653]: #21654
-#21675 := [monotonicity #21655 #21672]: #21674
-#21680 := [trans #21675 #21678]: #21679
-#21683 := [quant-intro #21680]: #21682
-#17775 := (~ #9757 #9757)
-#17773 := (~ #9754 #9754)
-#17774 := [refl]: #17773
-#17776 := [nnf-pos #17774]: #17775
+#10425 := (not #4084)
+#21640 := (or #10425 #19545 #6841 #21607 #21608 #21634)
+#21645 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #21640)
+#9701 := (not #9698)
+#9704 := (and #9695 #9701)
+#7898 := (not #6841)
+#9677 := (and #4084 #4448 #7898 #9636 #9639)
+#9682 := (not #9677)
+#9718 := (or #9682 #9704)
+#9721 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #9718)
+#21646 := (iff #9721 #21645)
+#21643 := (iff #9718 #21640)
+#21609 := (or #10425 #19545 #6841 #21607 #21608)
+#21637 := (or #21609 #21634)
+#21641 := (iff #21637 #21640)
+#21642 := [rewrite]: #21641
+#21638 := (iff #9718 #21637)
+#21635 := (iff #9704 #21634)
+#21636 := [rewrite]: #21635
+#21618 := (iff #9682 #21609)
+#21610 := (not #21609)
+#21613 := (not #21610)
+#21616 := (iff #21613 #21609)
+#21617 := [rewrite]: #21616
+#21614 := (iff #9682 #21613)
+#21611 := (iff #9677 #21610)
+#21612 := [rewrite]: #21611
+#21615 := [monotonicity #21612]: #21614
+#21619 := [trans #21615 #21617]: #21618
+#21639 := [monotonicity #21619 #21636]: #21638
+#21644 := [trans #21639 #21642]: #21643
+#21647 := [quant-intro #21644]: #21646
+#17739 := (~ #9721 #9721)
+#17737 := (~ #9718 #9718)
+#17738 := [refl]: #17737
+#17740 := [nnf-pos #17738]: #17739
 #2143 := (= #2142 f1)
 #2144 := (not #2143)
 #2141 := (= #2140 f1)
@@ -4429,242 +5624,476 @@
 #2130 := (and #2126 #2129)
 #2146 := (implies #2130 #2145)
 #2147 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #2146)
-#9760 := (iff #2147 #9757)
-#9681 := (and #1478 #9675)
-#9686 := (and #4084 #9681)
-#9689 := (and #9672 #9686)
-#9695 := (not #9689)
-#9746 := (or #9695 #9740)
-#9751 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #9746)
-#9758 := (iff #9751 #9757)
-#9755 := (iff #9746 #9754)
-#9719 := (iff #9695 #9718)
-#9716 := (iff #9689 #9713)
-#7937 := (and #4468 #7934)
-#9704 := (and #7937 #9675)
-#9707 := (and #4084 #9704)
-#9710 := (and #9672 #9707)
-#9714 := (iff #9710 #9713)
-#9715 := [rewrite]: #9714
-#9711 := (iff #9689 #9710)
-#9708 := (iff #9686 #9707)
-#9705 := (iff #9681 #9704)
-#7938 := (iff #1478 #7937)
-#7935 := (iff #1477 #7934)
-#7936 := [rewrite]: #7935
-#4467 := (iff #440 #4468)
-#4469 := [rewrite]: #4467
-#7939 := [monotonicity #4469 #7936]: #7938
-#9706 := [monotonicity #7939]: #9705
-#9709 := [monotonicity #9706]: #9708
-#9712 := [monotonicity #9709]: #9711
-#9717 := [trans #9712 #9715]: #9716
-#9720 := [monotonicity #9717]: #9719
-#9756 := [monotonicity #9720]: #9755
-#9759 := [quant-intro #9756]: #9758
-#9752 := (iff #2147 #9751)
-#9749 := (iff #2146 #9746)
-#9743 := (implies #9689 #9740)
-#9747 := (iff #9743 #9746)
-#9748 := [rewrite]: #9747
-#9744 := (iff #2146 #9743)
-#9741 := (iff #2145 #9740)
-#9738 := (iff #2144 #9737)
-#9735 := (iff #2143 #9734)
-#9736 := [rewrite]: #9735
-#9739 := [monotonicity #9736]: #9738
-#9732 := (iff #2141 #9731)
-#9733 := [rewrite]: #9732
-#9742 := [monotonicity #9733 #9739]: #9741
-#9690 := (iff #2130 #9689)
-#9687 := (iff #2129 #9686)
-#9684 := (iff #2128 #9681)
-#9678 := (and #9675 #1478)
-#9682 := (iff #9678 #9681)
-#9683 := [rewrite]: #9682
-#9679 := (iff #2128 #9678)
-#9676 := (iff #2127 #9675)
-#9677 := [rewrite]: #9676
-#9680 := [monotonicity #9677]: #9679
-#9685 := [trans #9680 #9683]: #9684
+#9724 := (iff #2147 #9721)
+#9645 := (and #1478 #9639)
+#9650 := (and #4084 #9645)
+#9653 := (and #9636 #9650)
+#9659 := (not #9653)
+#9710 := (or #9659 #9704)
+#9715 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #9710)
+#9722 := (iff #9715 #9721)
+#9719 := (iff #9710 #9718)
+#9683 := (iff #9659 #9682)
+#9680 := (iff #9653 #9677)
+#7901 := (and #4448 #7898)
+#9668 := (and #7901 #9639)
+#9671 := (and #4084 #9668)
+#9674 := (and #9636 #9671)
+#9678 := (iff #9674 #9677)
+#9679 := [rewrite]: #9678
+#9675 := (iff #9653 #9674)
+#9672 := (iff #9650 #9671)
+#9669 := (iff #9645 #9668)
+#7902 := (iff #1478 #7901)
+#7899 := (iff #1477 #7898)
+#7900 := [rewrite]: #7899
+#4447 := (iff #440 #4448)
+#4449 := [rewrite]: #4447
+#7903 := [monotonicity #4449 #7900]: #7902
+#9670 := [monotonicity #7903]: #9669
+#9673 := [monotonicity #9670]: #9672
+#9676 := [monotonicity #9673]: #9675
+#9681 := [trans #9676 #9679]: #9680
+#9684 := [monotonicity #9681]: #9683
+#9720 := [monotonicity #9684]: #9719
+#9723 := [quant-intro #9720]: #9722
+#9716 := (iff #2147 #9715)
+#9713 := (iff #2146 #9710)
+#9707 := (implies #9653 #9704)
+#9711 := (iff #9707 #9710)
+#9712 := [rewrite]: #9711
+#9708 := (iff #2146 #9707)
+#9705 := (iff #2145 #9704)
+#9702 := (iff #2144 #9701)
+#9699 := (iff #2143 #9698)
+#9700 := [rewrite]: #9699
+#9703 := [monotonicity #9700]: #9702
+#9696 := (iff #2141 #9695)
+#9697 := [rewrite]: #9696
+#9706 := [monotonicity #9697 #9703]: #9705
+#9654 := (iff #2130 #9653)
+#9651 := (iff #2129 #9650)
+#9648 := (iff #2128 #9645)
+#9642 := (and #9639 #1478)
+#9646 := (iff #9642 #9645)
+#9647 := [rewrite]: #9646
+#9643 := (iff #2128 #9642)
+#9640 := (iff #2127 #9639)
+#9641 := [rewrite]: #9640
+#9644 := [monotonicity #9641]: #9643
+#9649 := [trans #9644 #9647]: #9648
 #4085 := (iff #280 #4084)
 #4086 := [rewrite]: #4085
-#9688 := [monotonicity #4086 #9685]: #9687
-#9673 := (iff #2126 #9672)
-#9674 := [rewrite]: #9673
-#9691 := [monotonicity #9674 #9688]: #9690
-#9745 := [monotonicity #9691 #9742]: #9744
-#9750 := [trans #9745 #9748]: #9749
-#9753 := [quant-intro #9750]: #9752
-#9761 := [trans #9753 #9759]: #9760
-#9730 := [asserted]: #2147
-#9762 := [mp #9730 #9761]: #9757
-#17777 := [mp~ #9762 #17776]: #9757
-#21684 := [mp #17777 #21683]: #21681
-#27254 := (not #21681)
-#27453 := (or #27254 #24846 #27181 #27235 #27238 #27243)
-#27231 := (or #27230 #27227)
-#27232 := (not #27231)
-#27165 := (+ 0::Int #27164)
-#27166 := (>= #27165 0::Int)
-#27167 := (>= 0::Int 0::Int)
-#27168 := (not #27167)
-#27239 := (or #27238 #27168 #27166 #24846 #27235 #27232)
-#27454 := (or #27254 #27239)
-#27466 := (iff #27454 #27453)
-#27249 := (or #24846 #27181 #27235 #27238 #27243)
-#27459 := (or #27254 #27249)
-#27464 := (iff #27459 #27453)
-#27465 := [rewrite]: #27464
-#27460 := (iff #27454 #27459)
-#27252 := (iff #27239 #27249)
-#27246 := (or #27238 false #27181 #24846 #27235 #27243)
-#27250 := (iff #27246 #27249)
-#27251 := [rewrite]: #27250
-#27247 := (iff #27239 #27246)
-#27244 := (iff #27232 #27243)
-#27241 := (iff #27231 #27240)
-#27242 := [rewrite]: #27241
-#27245 := [monotonicity #27242]: #27244
-#27184 := (iff #27166 #27181)
-#27178 := (>= #27164 0::Int)
-#27182 := (iff #27178 #27181)
-#27183 := [rewrite]: #27182
-#27179 := (iff #27166 #27178)
-#27176 := (= #27165 #27164)
-#27177 := [rewrite]: #27176
-#27180 := [monotonicity #27177]: #27179
-#27185 := [trans #27180 #27183]: #27184
-#27174 := (iff #27168 false)
-#27172 := (iff #27168 #3156)
-#27170 := (iff #27167 true)
-#27171 := [rewrite]: #27170
-#27173 := [monotonicity #27171]: #27172
-#27175 := [trans #27173 #12257]: #27174
-#27248 := [monotonicity #27175 #27185 #27245]: #27247
-#27253 := [trans #27248 #27251]: #27252
-#27461 := [monotonicity #27253]: #27460
-#27492 := [trans #27461 #27465]: #27466
-#27455 := [quant-inst #3039 #3043 #26182 #24998 #161 #24996]: #27454
-#27493 := [mp #27455 #27492]: #27453
-#27518 := [unit-resolution #27493 #21684 #14351 #27516 #28427]: #27517
-#27519 := [unit-resolution #27518 #28426]: #27243
-#27497 := (or #27240 #27229)
-#27482 := [def-axiom]: #27497
-#27520 := [unit-resolution #27482 #27519 #27512]: false
-#27548 := [lemma #27520]: #27547
-#28798 := [unit-resolution #27548 #28797]: #12183
-#28623 := (or #28377 #18448 #28443)
-#28624 := [def-axiom]: #28623
-#28817 := [unit-resolution #28624 #28798]: #28816
-#28818 := [unit-resolution #28817 #28780]: #28443
-#28615 := (or #28440 #28345)
-#28616 := [def-axiom]: #28615
-#28819 := [unit-resolution #28616 #28818]: #28345
-#28592 := (not #27227)
-#28835 := (iff #28592 #28148)
-#28832 := (iff #27227 #28147)
-#28814 := (= #27226 #28146)
-#28824 := (= #27225 #26985)
-#28825 := [monotonicity #27481]: #28824
-#28815 := [monotonicity #28825]: #28814
-#28834 := [monotonicity #28815]: #28832
-#28833 := [monotonicity #28834]: #28835
-#28821 := [unit-resolution #27493 #21684 #14351 #27516 #28797]: #27517
-#28822 := [unit-resolution #28821 #28426]: #27243
-#28593 := (or #27240 #28592)
-#28594 := [def-axiom]: #28593
-#28823 := [unit-resolution #28594 #28822]: #28592
-#28836 := [mp #28823 #28833]: #28148
-#28478 := (or #28326 #28147)
-#28484 := [def-axiom]: #28478
-#28837 := [unit-resolution #28484 #28836]: #28326
-#25501 := (f23 f19)
-#28366 := (= #25501 #27920)
-#27753 := (= #27920 #25501)
-#27686 := (= #27039 f19)
-#27684 := (= #25112 f19)
-#27685 := [symm #27139]: #27684
-#27369 := [hypothesis]: #27103
-#27370 := [unit-resolution #27749 #27369]: #27089
-#27416 := [trans #27409 #27370]: #27415
-#27681 := [trans #27416 #27414]: #27680
-#27683 := [monotonicity #27681]: #27682
-#27687 := [trans #27683 #27685]: #27686
-#27754 := [monotonicity #27687]: #27753
-#28467 := [symm #27754]: #28366
-#25502 := (= f25 #25501)
-#25509 := (iff #11624 #25502)
-#2363 := (pattern #279)
-#2902 := (f23 #275)
-#11803 := (= f25 #2902)
-#11807 := (iff #4084 #11803)
-#11810 := (forall (vars (?v0 S18)) (:pat #2363) #11807)
-#18402 := (~ #11810 #11810)
-#18400 := (~ #11807 #11807)
-#18401 := [refl]: #18400
-#18403 := [nnf-pos #18401]: #18402
-#2915 := (= #2902 f25)
-#2916 := (iff #280 #2915)
-#2917 := (forall (vars (?v0 S18)) (:pat #2363) #2916)
-#11811 := (iff #2917 #11810)
-#11808 := (iff #2916 #11807)
-#11805 := (iff #2915 #11803)
-#11806 := [rewrite]: #11805
-#11809 := [monotonicity #4086 #11806]: #11808
-#11812 := [quant-intro #11809]: #11811
-#11802 := [asserted]: #2917
-#11815 := [mp #11802 #11812]: #11810
-#18404 := [mp~ #11815 #18403]: #11810
-#25168 := (not #11810)
-#25512 := (or #25168 #25509)
-#25513 := [quant-inst #50]: #25512
-#28838 := [unit-resolution #25513 #18404]: #25509
-#25514 := (not #25509)
-#28839 := (or #25514 #25502)
-#25518 := (not #11624)
-#25519 := (or #25514 #25518 #25502)
-#25520 := [def-axiom]: #25519
-#28840 := [unit-resolution #25520 #11630]: #28839
-#28841 := [unit-resolution #28840 #28838]: #25502
-#28468 := [trans #28841 #28467]: #28266
-#28602 := (not #28097)
-#28934 := (iff #12118 #28602)
-#28932 := (iff #12115 #28097)
-#28930 := (iff #28097 #12115)
-#28928 := (= #28096 #3053)
-#28926 := (= #28095 #3040)
-#28924 := (= #28095 #25117)
-#28922 := (= #27775 #3044)
-#28920 := (= #27775 #27145)
-#27146 := (f77 #27145 0::Int #24996)
-#27150 := (f69 #3220 #27146)
-#27156 := (f146 #27150)
-#28918 := (= #27156 #27145)
-#27157 := (= #27145 #27156)
-#27158 := (not #27157)
-#27154 := (f147 #27150)
-#27155 := (= f1 #27154)
-#27151 := (f78 #27150)
-#27152 := (= f1 #27151)
-#27153 := (not #27152)
-#27147 := (f35 f297 #27146)
-#27148 := (= f1 #27147)
-#27149 := (not #27148)
-#27186 := (or #27149 #27153 #27155 #27158)
-#27189 := (not #27186)
-#27161 := (f35 f297 #27145)
-#27162 := (= f1 #27161)
-#28492 := (= #3051 #27161)
-#28489 := (= #27161 #3051)
-#28490 := [monotonicity #28789]: #28489
-#28872 := [symm #28490]: #28492
-#28873 := [trans #14368 #28872]: #27162
-#27163 := (not #27162)
-#28859 := (or #27163 #27189)
+#9652 := [monotonicity #4086 #9649]: #9651
+#9637 := (iff #2126 #9636)
+#9638 := [rewrite]: #9637
+#9655 := [monotonicity #9638 #9652]: #9654
+#9709 := [monotonicity #9655 #9706]: #9708
+#9714 := [trans #9709 #9712]: #9713
+#9717 := [quant-intro #9714]: #9716
+#9725 := [trans #9717 #9723]: #9724
+#9694 := [asserted]: #2147
+#9726 := [mp #9694 #9725]: #9721
+#17741 := [mp~ #9726 #17740]: #9721
+#21648 := [mp #17741 #21647]: #21645
+#27193 := (not #27192)
+#27212 := (not #21645)
+#27669 := (or #27212 #24810 #27139 #27193 #27196 #27201)
+#27189 := (or #27188 #27185)
+#27190 := (not #27189)
+#27123 := (+ 0::Int #27122)
+#27124 := (>= #27123 0::Int)
+#27125 := (>= 0::Int 0::Int)
+#27126 := (not #27125)
+#27197 := (or #27196 #27126 #27124 #24810 #27193 #27190)
+#27664 := (or #27212 #27197)
+#27712 := (iff #27664 #27669)
+#27207 := (or #24810 #27139 #27193 #27196 #27201)
+#27671 := (or #27212 #27207)
+#27674 := (iff #27671 #27669)
+#27711 := [rewrite]: #27674
+#27672 := (iff #27664 #27671)
+#27210 := (iff #27197 #27207)
+#27204 := (or #27196 false #27139 #24810 #27193 #27201)
+#27208 := (iff #27204 #27207)
+#27209 := [rewrite]: #27208
+#27205 := (iff #27197 #27204)
+#27202 := (iff #27190 #27201)
+#27199 := (iff #27189 #27198)
+#27200 := [rewrite]: #27199
+#27203 := [monotonicity #27200]: #27202
+#27142 := (iff #27124 #27139)
+#27136 := (>= #27122 0::Int)
+#27140 := (iff #27136 #27139)
+#27141 := [rewrite]: #27140
+#27137 := (iff #27124 #27136)
+#27134 := (= #27123 #27122)
+#27135 := [rewrite]: #27134
+#27138 := [monotonicity #27135]: #27137
+#27143 := [trans #27138 #27141]: #27142
+#27132 := (iff #27126 false)
+#27130 := (iff #27126 #3156)
+#27128 := (iff #27125 true)
+#27129 := [rewrite]: #27128
+#27131 := [monotonicity #27129]: #27130
+#27133 := [trans #27131 #12221]: #27132
+#27206 := [monotonicity #27133 #27143 #27203]: #27205
+#27211 := [trans #27206 #27209]: #27210
+#27673 := [monotonicity #27211]: #27672
+#27713 := [trans #27673 #27711]: #27712
+#27670 := [quant-inst #3039 #3043 #26146 #24962 #161 #24960]: #27664
+#27714 := [mp #27670 #27713]: #27669
+#28373 := [unit-resolution #27714 #21648 #14315 #28356 #28130]: #28357
+#28352 := [unit-resolution #28373 #28528]: #27201
+#27717 := (or #27198 #27187)
+#27718 := [def-axiom]: #27717
+#28371 := [unit-resolution #27718 #28352 #28112]: false
+#28372 := [lemma #28371]: #12147
+#24789 := (or #23557 #18409 #18412 #23551)
+#24790 := [def-axiom]: #24789
+#29169 := [unit-resolution #24790 #28372 #27593 #29168]: #23551
+#24779 := (or #23548 #23542)
+#24780 := [def-axiom]: #24779
+#29170 := [unit-resolution #24780 #29169]: #23542
+decl f147 :: (-> S29 S20)
+#28602 := (f69 #3220 #27044)
+#28603 := (f147 #28602)
+#28607 := (f36 f298 #28603)
+#28608 := (= f37 #28607)
+decl f222 :: (-> S19 S20 S1)
+#28605 := (f222 f298 #28603)
+#28606 := (= f1 #28605)
+#28756 := (or #28606 #28608)
+#28740 := (not #28756)
+#28634 := (f148 #28602)
+#28635 := (= f1 #28634)
+#28636 := (not #28635)
+#28631 := (f38 f298 #28603)
+#28632 := (= f1 #28631)
+#28633 := (not #28632)
+#28750 := (or #28633 #28636)
+#28753 := (not #28750)
+#28639 := (f23 #27233)
+#28647 := (= f25 #28639)
+#28726 := (not #28647)
+#28619 := (f24 #28603)
+#28629 := (f23 #28619)
+#28630 := (= f25 #28629)
+#28745 := (or #28630 #28726 #28753 #28740)
+#28793 := (not #28745)
+#28624 := (f36 f298 #27044)
+#28625 := (= f37 #28624)
+#28623 := (f222 f298 #27044)
+#28616 := (= f1 #28623)
+#28595 := (or #28616 #28625)
+#28597 := (not #28595)
+#28706 := (or #28597 #28647)
+#28704 := (not #28706)
+#28796 := (or #28704 #28793)
+#28779 := (not #28796)
+#28643 := (f35 f298 #27044)
+#28644 := (= f1 #28643)
+#27803 := (= #3101 #28643)
+#27432 := (= #28643 #3101)
+#27430 := (= #27044 #3098)
+#27425 := (= #27028 #3098)
+#27426 := [symm #27571]: #27425
+#27382 := (= #27044 #27028)
+#27383 := [symm #27568]: #27382
+#27431 := [trans #27383 #27426]: #27430
+#27742 := [monotonicity #27431]: #27432
+#28586 := [symm #27742]: #27803
+#28587 := [trans #28372 #28586]: #28644
+#28649 := (not #28644)
+#28782 := (or #28649 #28779)
+#28784 := (not #28782)
+#28652 := (f79 f298 #27044)
+#28648 := (= f1 #28652)
+#28787 := (iff #28648 #28784)
+#2438 := (f79 #86 #62)
+#2439 := (pattern #2438)
+#324 := (f70 #86)
+#2441 := (f69 #324 #62)
+#2445 := (f147 #2441)
+#2456 := (f222 #86 #2445)
+#10660 := (= f1 #2456)
+#2454 := (f36 #86 #2445)
+#10657 := (= f37 #2454)
+#10663 := (or #10657 #10660)
+#22034 := (not #10663)
+#2450 := (f24 #2445)
+#2451 := (f23 #2450)
+#10651 := (= f25 #2451)
+#2446 := (f38 #86 #2445)
+#10642 := (= f1 #2446)
+#10645 := (not #10642)
+#2442 := (f148 #2441)
+#10636 := (= f1 #2442)
+#10639 := (not #10636)
+#10648 := (or #10639 #10645)
+#22033 := (not #10648)
+#22035 := (or #91 #22033 #10651 #22034)
+#22036 := (not #22035)
+#2462 := (f222 #86 #62)
+#10675 := (= f1 #2462)
+#10678 := (or #3761 #10675)
+#22028 := (not #10678)
+#22029 := (or #68 #22028)
+#22030 := (not #22029)
+#22039 := (or #22030 #22036)
+#22045 := (not #22039)
+#22046 := (or #11261 #22045)
+#22047 := (not #22046)
+#10632 := (= f1 #2438)
+#22052 := (iff #10632 #22047)
+#22055 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #22052)
+#10654 := (not #10651)
+#10696 := (and #68 #10648 #10654 #10663)
+#10681 := (and #91 #10678)
+#10702 := (or #10681 #10696)
+#10707 := (and #3767 #10702)
+#10710 := (iff #10632 #10707)
+#10713 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #10710)
+#22056 := (iff #10713 #22055)
+#22053 := (iff #10710 #22052)
+#22050 := (iff #10707 #22047)
+#22042 := (and #3767 #22039)
+#22048 := (iff #22042 #22047)
+#22049 := [rewrite]: #22048
+#22043 := (iff #10707 #22042)
+#22040 := (iff #10702 #22039)
+#22037 := (iff #10696 #22036)
+#22038 := [rewrite]: #22037
+#22031 := (iff #10681 #22030)
+#22032 := [rewrite]: #22031
+#22041 := [monotonicity #22032 #22038]: #22040
+#22044 := [monotonicity #22041]: #22043
+#22051 := [trans #22044 #22049]: #22050
+#22054 := [monotonicity #22051]: #22053
+#22057 := [quant-intro #22054]: #22056
+#17978 := (~ #10713 #10713)
+#17976 := (~ #10710 #10710)
+#17977 := [refl]: #17976
+#17979 := [nnf-pos #17977]: #17978
+#2463 := (= #2462 f1)
+#2464 := (or #183 #2463)
+#2465 := (and #91 #2464)
+#2457 := (= #2456 f1)
+#2455 := (= #2454 f37)
+#2458 := (or #2455 #2457)
+#2452 := (= #2451 f25)
+#2453 := (not #2452)
+#2459 := (and #2453 #2458)
+#2447 := (= #2446 f1)
+#2448 := (not #2447)
+#2443 := (= #2442 f1)
+#2444 := (not #2443)
+#2449 := (or #2444 #2448)
+#2460 := (and #2449 #2459)
+#2461 := (and #68 #2460)
+#2466 := (or #2461 #2465)
+#2467 := (and #187 #2466)
+#2440 := (= #2438 f1)
+#2468 := (iff #2440 #2467)
+#2469 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #2468)
+#10716 := (iff #2469 #10713)
+#10666 := (and #10654 #10663)
+#10669 := (and #10648 #10666)
+#10672 := (and #68 #10669)
+#10684 := (or #10672 #10681)
+#10687 := (and #3767 #10684)
+#10690 := (iff #10632 #10687)
+#10693 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #10690)
+#10714 := (iff #10693 #10713)
+#10711 := (iff #10690 #10710)
+#10708 := (iff #10687 #10707)
+#10705 := (iff #10684 #10702)
+#10699 := (or #10696 #10681)
+#10703 := (iff #10699 #10702)
+#10704 := [rewrite]: #10703
+#10700 := (iff #10684 #10699)
+#10697 := (iff #10672 #10696)
+#10698 := [rewrite]: #10697
+#10701 := [monotonicity #10698]: #10700
+#10706 := [trans #10701 #10704]: #10705
+#10709 := [monotonicity #10706]: #10708
+#10712 := [monotonicity #10709]: #10711
+#10715 := [quant-intro #10712]: #10714
+#10694 := (iff #2469 #10693)
+#10691 := (iff #2468 #10690)
+#10688 := (iff #2467 #10687)
+#10685 := (iff #2466 #10684)
+#10682 := (iff #2465 #10681)
+#10679 := (iff #2464 #10678)
+#10676 := (iff #2463 #10675)
+#10677 := [rewrite]: #10676
+#10680 := [monotonicity #3763 #10677]: #10679
+#10683 := [monotonicity #10680]: #10682
+#10673 := (iff #2461 #10672)
+#10670 := (iff #2460 #10669)
+#10667 := (iff #2459 #10666)
+#10664 := (iff #2458 #10663)
+#10661 := (iff #2457 #10660)
+#10662 := [rewrite]: #10661
+#10658 := (iff #2455 #10657)
+#10659 := [rewrite]: #10658
+#10665 := [monotonicity #10659 #10662]: #10664
+#10655 := (iff #2453 #10654)
+#10652 := (iff #2452 #10651)
+#10653 := [rewrite]: #10652
+#10656 := [monotonicity #10653]: #10655
+#10668 := [monotonicity #10656 #10665]: #10667
+#10649 := (iff #2449 #10648)
+#10646 := (iff #2448 #10645)
+#10643 := (iff #2447 #10642)
+#10644 := [rewrite]: #10643
+#10647 := [monotonicity #10644]: #10646
+#10640 := (iff #2444 #10639)
+#10637 := (iff #2443 #10636)
+#10638 := [rewrite]: #10637
+#10641 := [monotonicity #10638]: #10640
+#10650 := [monotonicity #10641 #10647]: #10649
+#10671 := [monotonicity #10650 #10668]: #10670
+#10674 := [monotonicity #10671]: #10673
+#10686 := [monotonicity #10674 #10683]: #10685
+#10689 := [monotonicity #3769 #10686]: #10688
+#10634 := (iff #2440 #10632)
+#10635 := [rewrite]: #10634
+#10692 := [monotonicity #10635 #10689]: #10691
+#10695 := [quant-intro #10692]: #10694
+#10717 := [trans #10695 #10715]: #10716
+#10631 := [asserted]: #2469
+#10718 := [mp #10631 #10717]: #10713
+#17980 := [mp~ #10718 #17979]: #10713
+#22058 := [mp #17980 #22057]: #22055
+#28805 := (not #22055)
+#28806 := (or #28805 #28787)
+#28609 := (or #28608 #28606)
+#28618 := (not #28609)
+#28637 := (or #28636 #28633)
+#28638 := (not #28637)
+#28617 := (= #28639 f25)
+#28620 := (not #28617)
+#28621 := (or #28620 #28638 #28630 #28618)
+#28622 := (not #28621)
+#28626 := (or #28625 #28616)
+#28627 := (not #28626)
+#28628 := (or #28617 #28627)
+#28640 := (not #28628)
+#28641 := (or #28640 #28622)
+#28642 := (not #28641)
+#28650 := (or #28649 #28642)
+#28651 := (not #28650)
+#28653 := (iff #28648 #28651)
+#28804 := (or #28805 #28653)
+#28808 := (iff #28804 #28806)
+#28826 := (iff #28806 #28806)
+#28827 := [rewrite]: #28826
+#28788 := (iff #28653 #28787)
+#28785 := (iff #28651 #28784)
+#28783 := (iff #28650 #28782)
+#28780 := (iff #28642 #28779)
+#28797 := (iff #28641 #28796)
+#28794 := (iff #28622 #28793)
+#28791 := (iff #28621 #28745)
+#28742 := (or #28726 #28753 #28630 #28740)
+#28746 := (iff #28742 #28745)
+#28747 := [rewrite]: #28746
+#28743 := (iff #28621 #28742)
+#28741 := (iff #28618 #28740)
+#28757 := (iff #28609 #28756)
+#28758 := [rewrite]: #28757
+#28739 := [monotonicity #28758]: #28741
+#28754 := (iff #28638 #28753)
+#28751 := (iff #28637 #28750)
+#28752 := [rewrite]: #28751
+#28755 := [monotonicity #28752]: #28754
+#28748 := (iff #28620 #28726)
+#28654 := (iff #28617 #28647)
+#28593 := [rewrite]: #28654
+#28749 := [monotonicity #28593]: #28748
+#28744 := [monotonicity #28749 #28755 #28739]: #28743
+#28792 := [trans #28744 #28747]: #28791
+#28795 := [monotonicity #28792]: #28794
+#28724 := (iff #28640 #28704)
+#28711 := (iff #28628 #28706)
+#28479 := (or #28647 #28597)
+#28707 := (iff #28479 #28706)
+#28710 := [rewrite]: #28707
+#28480 := (iff #28628 #28479)
+#28598 := (iff #28627 #28597)
+#28596 := (iff #28626 #28595)
+#28594 := [rewrite]: #28596
+#28468 := [monotonicity #28594]: #28598
+#28469 := [monotonicity #28593 #28468]: #28480
+#28703 := [trans #28469 #28710]: #28711
+#28725 := [monotonicity #28703]: #28724
+#28777 := [monotonicity #28725 #28795]: #28797
+#28781 := [monotonicity #28777]: #28780
+#28778 := [monotonicity #28781]: #28783
+#28786 := [monotonicity #28778]: #28785
+#28803 := [monotonicity #28786]: #28788
+#28809 := [monotonicity #28803]: #28808
+#28828 := [trans #28809 #28827]: #28808
+#28807 := [quant-inst #3039 #27044]: #28804
+#28829 := [mp #28807 #28828]: #28806
+#28588 := [unit-resolution #28829 #22058]: #28787
+#27354 := (not #28648)
+#28886 := (iff #18418 #27354)
+#28899 := (iff #12153 #28648)
+#28789 := (iff #28648 #12153)
+#28590 := (= #28652 #3104)
+#28591 := [monotonicity #27431]: #28590
+#28790 := [monotonicity #28591]: #28789
+#28900 := [symm #28790]: #28899
+#28887 := [monotonicity #28900]: #28886
+#28589 := [hypothesis]: #18418
+#28906 := [mp #28589 #28887]: #27354
+#27264 := (not #28787)
+#27352 := (or #27264 #28648 #28782)
+#27353 := [def-axiom]: #27352
+#28907 := [unit-resolution #27353 #28906 #28588]: #28782
+#27262 := (or #28784 #28649 #28779)
+#27263 := [def-axiom]: #27262
+#28908 := [unit-resolution #27263 #28907 #28587]: #28779
+#28841 := (not #28630)
+#29014 := (iff #12082 #28841)
+#29012 := (iff #12079 #28630)
+#29010 := (iff #28630 #12079)
+#29008 := (= #28629 #3053)
+#29006 := (= #28619 #3040)
+#29004 := (= #28619 #25081)
+#29002 := (= #28603 #3044)
+#29000 := (= #28603 #27103)
+#27104 := (f77 #27103 0::Int #24960)
+#27108 := (f69 #3220 #27104)
+#27114 := (f147 #27108)
+#28998 := (= #27114 #27103)
+#27115 := (= #27103 #27114)
+#27116 := (not #27115)
+#27112 := (f148 #27108)
+#27113 := (= f1 #27112)
+decl f78 :: (-> S29 S1)
+#27109 := (f78 #27108)
+#27110 := (= f1 #27109)
+#27111 := (not #27110)
+#27105 := (f35 f298 #27104)
+#27106 := (= f1 #27105)
+#27107 := (not #27106)
+#27144 := (or #27107 #27111 #27113 #27116)
+#27147 := (not #27144)
+#27119 := (f35 f298 #27103)
+#27120 := (= f1 #27119)
+#28912 := (= #3051 #27119)
+#28909 := (= #27119 #3051)
+#28910 := [monotonicity #28364]: #28909
+#28913 := [symm #28910]: #28912
+#28914 := [trans #14332 #28913]: #27120
+#27121 := (not #27120)
+#28915 := (or #27121 #27147)
 #319 := (:var 3 Int)
 #353 := (:var 2 S18)
-#1513 := (f135 #353 #289)
+#1513 := (f136 #353 #289)
 #1514 := (f54 #1513 #319)
 #1510 := (f54 #353 #319)
 #1511 := (f77 #1510 #202 #353)
@@ -4677,60 +6106,60 @@
 #1515 := (pattern #1512 #1514)
 #1521 := (f77 #1514 #202 #353)
 #1530 := (f35 #74 #1521)
-#8095 := (= f1 #1530)
-#21008 := (not #8095)
+#8059 := (= f1 #1530)
+#20972 := (not #8059)
 #1522 := (f69 #1516 #1521)
 #1528 := (f78 #1522)
-#8092 := (= f1 #1528)
-#21007 := (not #8092)
-#1525 := (f147 #1522)
-#8086 := (= f1 #1525)
-#1523 := (f146 #1522)
-#8083 := (= #1514 #1523)
-#21006 := (not #8083)
-#21009 := (or #21006 #8086 #21007 #21008)
-#21010 := (not #21009)
+#8056 := (= f1 #1528)
+#20971 := (not #8056)
+#1525 := (f148 #1522)
+#8050 := (= f1 #1525)
+#1523 := (f147 #1522)
+#8047 := (= #1514 #1523)
+#20970 := (not #8047)
+#20973 := (or #20970 #8050 #20971 #20972)
+#20974 := (not #20973)
 #1519 := (f35 #74 #1514)
-#8080 := (= f1 #1519)
-#8118 := (not #8080)
-#5395 := (* -1::Int #289)
-#6275 := (+ #202 #5395)
-#6276 := (>= #6275 0::Int)
-#21016 := (or #5124 #6276 #8118 #21010)
-#21021 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #21016)
-#8089 := (not #8086)
-#8127 := (and #8083 #8089 #8092 #8095)
-#7779 := (not #6276)
-#7782 := (and #4202 #7779)
-#7785 := (not #7782)
-#8136 := (or #7785 #8118 #8127)
-#8141 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #8136)
-#21022 := (iff #8141 #21021)
-#21019 := (iff #8136 #21016)
-#20891 := (or #5124 #6276)
-#21013 := (or #20891 #8118 #21010)
-#21017 := (iff #21013 #21016)
-#21018 := [rewrite]: #21017
-#21014 := (iff #8136 #21013)
-#21011 := (iff #8127 #21010)
-#21012 := [rewrite]: #21011
-#20900 := (iff #7785 #20891)
-#20892 := (not #20891)
-#20895 := (not #20892)
-#20898 := (iff #20895 #20891)
-#20899 := [rewrite]: #20898
-#20896 := (iff #7785 #20895)
-#20893 := (iff #7782 #20892)
-#20894 := [rewrite]: #20893
-#20897 := [monotonicity #20894]: #20896
-#20901 := [trans #20897 #20899]: #20900
-#21015 := [monotonicity #20901 #21012]: #21014
-#21020 := [trans #21015 #21018]: #21019
-#21023 := [quant-intro #21020]: #21022
-#17140 := (~ #8141 #8141)
-#17138 := (~ #8136 #8136)
-#17139 := [refl]: #17138
-#17141 := [nnf-pos #17139]: #17140
+#8044 := (= f1 #1519)
+#8082 := (not #8044)
+#5372 := (* -1::Int #289)
+#6249 := (+ #202 #5372)
+#6250 := (>= #6249 0::Int)
+#20980 := (or #5104 #6250 #8082 #20974)
+#20985 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #20980)
+#8053 := (not #8050)
+#8091 := (and #8047 #8053 #8056 #8059)
+#7743 := (not #6250)
+#7746 := (and #4202 #7743)
+#7749 := (not #7746)
+#8100 := (or #7749 #8082 #8091)
+#8105 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #8100)
+#20986 := (iff #8105 #20985)
+#20983 := (iff #8100 #20980)
+#20855 := (or #5104 #6250)
+#20977 := (or #20855 #8082 #20974)
+#20981 := (iff #20977 #20980)
+#20982 := [rewrite]: #20981
+#20978 := (iff #8100 #20977)
+#20975 := (iff #8091 #20974)
+#20976 := [rewrite]: #20975
+#20864 := (iff #7749 #20855)
+#20856 := (not #20855)
+#20859 := (not #20856)
+#20862 := (iff #20859 #20855)
+#20863 := [rewrite]: #20862
+#20860 := (iff #7749 #20859)
+#20857 := (iff #7746 #20856)
+#20858 := [rewrite]: #20857
+#20861 := [monotonicity #20858]: #20860
+#20865 := [trans #20861 #20863]: #20864
+#20979 := [monotonicity #20865 #20976]: #20978
+#20984 := [trans #20979 #20982]: #20983
+#20987 := [quant-intro #20984]: #20986
+#17104 := (~ #8105 #8105)
+#17102 := (~ #8100 #8100)
+#17103 := [refl]: #17102
+#17105 := [nnf-pos #17103]: #17104
 #1531 := (= #1530 f1)
 #1529 := (= #1528 f1)
 #1532 := (and #1529 #1531)
@@ -4745,3060 +6174,1602 @@
 #1520 := (= #1519 f1)
 #1536 := (implies #1520 #1535)
 #1537 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #1536)
-#8144 := (iff #1537 #8141)
-#8098 := (and #8092 #8095)
-#8101 := (and #8089 #8098)
-#8104 := (and #8083 #8101)
-#7749 := (not #1415)
-#8110 := (or #7749 #8104)
-#8119 := (or #8118 #8110)
-#8124 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #8119)
-#8142 := (iff #8124 #8141)
-#8139 := (iff #8119 #8136)
-#8130 := (or #7785 #8127)
-#8133 := (or #8118 #8130)
-#8137 := (iff #8133 #8136)
-#8138 := [rewrite]: #8137
-#8134 := (iff #8119 #8133)
-#8131 := (iff #8110 #8130)
-#8128 := (iff #8104 #8127)
-#8129 := [rewrite]: #8128
-#7786 := (iff #7749 #7785)
-#7783 := (iff #1415 #7782)
-#7780 := (iff #1414 #7779)
-#7781 := [rewrite]: #7780
-#7784 := [monotonicity #4201 #7781]: #7783
-#7787 := [monotonicity #7784]: #7786
-#8132 := [monotonicity #7787 #8129]: #8131
-#8135 := [monotonicity #8132]: #8134
-#8140 := [trans #8135 #8138]: #8139
-#8143 := [quant-intro #8140]: #8142
-#8125 := (iff #1537 #8124)
-#8122 := (iff #1536 #8119)
-#8115 := (implies #8080 #8110)
-#8120 := (iff #8115 #8119)
-#8121 := [rewrite]: #8120
-#8116 := (iff #1536 #8115)
-#8113 := (iff #1535 #8110)
-#8107 := (implies #1415 #8104)
-#8111 := (iff #8107 #8110)
-#8112 := [rewrite]: #8111
-#8108 := (iff #1535 #8107)
-#8105 := (iff #1534 #8104)
-#8102 := (iff #1533 #8101)
-#8099 := (iff #1532 #8098)
-#8096 := (iff #1531 #8095)
-#8097 := [rewrite]: #8096
-#8093 := (iff #1529 #8092)
-#8094 := [rewrite]: #8093
-#8100 := [monotonicity #8094 #8097]: #8099
-#8090 := (iff #1527 #8089)
-#8087 := (iff #1526 #8086)
-#8088 := [rewrite]: #8087
-#8091 := [monotonicity #8088]: #8090
-#8103 := [monotonicity #8091 #8100]: #8102
-#8084 := (iff #1524 #8083)
+#8108 := (iff #1537 #8105)
+#8062 := (and #8056 #8059)
+#8065 := (and #8053 #8062)
+#8068 := (and #8047 #8065)
+#7713 := (not #1415)
+#8074 := (or #7713 #8068)
+#8083 := (or #8082 #8074)
+#8088 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #8083)
+#8106 := (iff #8088 #8105)
+#8103 := (iff #8083 #8100)
+#8094 := (or #7749 #8091)
+#8097 := (or #8082 #8094)
+#8101 := (iff #8097 #8100)
+#8102 := [rewrite]: #8101
+#8098 := (iff #8083 #8097)
+#8095 := (iff #8074 #8094)
+#8092 := (iff #8068 #8091)
+#8093 := [rewrite]: #8092
+#7750 := (iff #7713 #7749)
+#7747 := (iff #1415 #7746)
+#7744 := (iff #1414 #7743)
+#7745 := [rewrite]: #7744
+#7748 := [monotonicity #4201 #7745]: #7747
+#7751 := [monotonicity #7748]: #7750
+#8096 := [monotonicity #7751 #8093]: #8095
+#8099 := [monotonicity #8096]: #8098
+#8104 := [trans #8099 #8102]: #8103
+#8107 := [quant-intro #8104]: #8106
+#8089 := (iff #1537 #8088)
+#8086 := (iff #1536 #8083)
+#8079 := (implies #8044 #8074)
+#8084 := (iff #8079 #8083)
 #8085 := [rewrite]: #8084
-#8106 := [monotonicity #8085 #8103]: #8105
-#8109 := [monotonicity #8106]: #8108
-#8114 := [trans #8109 #8112]: #8113
-#8081 := (iff #1520 #8080)
-#8082 := [rewrite]: #8081
-#8117 := [monotonicity #8082 #8114]: #8116
-#8123 := [trans #8117 #8121]: #8122
-#8126 := [quant-intro #8123]: #8125
-#8145 := [trans #8126 #8143]: #8144
-#8079 := [asserted]: #1537
-#8146 := [mp #8079 #8145]: #8141
-#17142 := [mp~ #8146 #17141]: #8141
-#21024 := [mp #17142 #21023]: #21021
-#28639 := (not #21021)
-#28640 := (or #28639 #27163 #27181 #27189)
-#27159 := (or #27158 #27155 #27153 #27149)
-#27160 := (not #27159)
-#27169 := (or #27168 #27166 #27163 #27160)
-#28641 := (or #28639 #27169)
-#28648 := (iff #28641 #28640)
-#27195 := (or #27163 #27181 #27189)
-#28643 := (or #28639 #27195)
-#28646 := (iff #28643 #28640)
-#28647 := [rewrite]: #28646
-#28644 := (iff #28641 #28643)
-#27198 := (iff #27169 #27195)
-#27192 := (or false #27181 #27163 #27189)
-#27196 := (iff #27192 #27195)
-#27197 := [rewrite]: #27196
-#27193 := (iff #27169 #27192)
-#27190 := (iff #27160 #27189)
-#27187 := (iff #27159 #27186)
-#27188 := [rewrite]: #27187
-#27191 := [monotonicity #27188]: #27190
-#27194 := [monotonicity #27175 #27185 #27191]: #27193
-#27199 := [trans #27194 #27197]: #27198
-#28645 := [monotonicity #27199]: #28644
-#28649 := [trans #28645 #28647]: #28648
-#28642 := [quant-inst #3039 #3043 #24996 #24998 #161]: #28641
-#28650 := [mp #28642 #28649]: #28640
-#28860 := [unit-resolution #28650 #21024 #27516]: #28859
-#28879 := [unit-resolution #28860 #28873]: #27189
-#28589 := (or #27186 #27157)
-#28587 := [def-axiom]: #28589
-#28880 := [unit-resolution #28587 #28879]: #27157
-#28919 := [symm #28880]: #28918
-#28916 := (= #27775 #27156)
-#28914 := (= #26985 #27150)
-#28912 := (= #27150 #26985)
-#28910 := (= #27146 #3098)
-#28900 := (= #27064 #3098)
-#28901 := [symm #27409]: #28900
-#28908 := (= #27146 #27064)
-#28898 := (= #27086 #27064)
-#28899 := [symm #27370]: #28898
-#28906 := (= #27146 #27086)
-#28896 := (= #3042 #27086)
-#28897 := [symm #27414]: #28896
-#28904 := (= #27146 #3042)
-#27318 := (f127 #26182)
-#27332 := (f54 #24996 #27318)
-#28894 := (= #27332 #3042)
-#28888 := (= #27318 f298)
-#28886 := (= #27318 #3043)
-#28884 := (= #24880 #3043)
-#25123 := (= #3043 #24880)
-#25128 := (or #25070 #25123)
-#25129 := [quant-inst #3040 #3043]: #25128
-#28881 := [unit-resolution #25129 #23306]: #25123
-#28885 := [symm #28881]: #28884
-#28882 := (= #27318 #24880)
-#28883 := [monotonicity #26940]: #28882
-#28887 := [trans #28883 #28885]: #28886
-#28889 := [trans #28887 #28391]: #28888
-#28895 := [monotonicity #28386 #28889]: #28894
-#28902 := (= #27146 #27332)
-#27314 := (f77 #26182 0::Int #24996)
-#27335 := (= #27314 #27332)
-#27338 := (not #27335)
-#27315 := (f149 #27314 #26182)
-#27316 := (= f1 #27315)
-#27317 := (not #27316)
-#27344 := (or #27317 #27338)
-#27349 := (not #27344)
-#28722 := (or #27721 #27349)
-#27319 := (+ #27318 #27069)
-#27320 := (f54 #24996 #27319)
-#27321 := (= #27314 #27320)
-#27322 := (not #27321)
-#27323 := (or #27322 #27317)
-#27324 := (not #27323)
-#28764 := (or #27721 #27324)
-#28766 := (iff #28764 #28722)
-#28768 := (iff #28722 #28722)
-#28769 := [rewrite]: #28768
-#27350 := (iff #27324 #27349)
-#27347 := (iff #27323 #27344)
-#27341 := (or #27338 #27317)
-#27345 := (iff #27341 #27344)
-#27346 := [rewrite]: #27345
-#27342 := (iff #27323 #27341)
-#27339 := (iff #27322 #27338)
-#27336 := (iff #27321 #27335)
-#27333 := (= #27320 #27332)
-#27330 := (= #27319 #27318)
-#27325 := (+ #27318 0::Int)
-#27328 := (= #27325 #27318)
-#27329 := [rewrite]: #27328
-#27326 := (= #27319 #27325)
-#27327 := [monotonicity #27078]: #27326
-#27331 := [trans #27327 #27329]: #27330
-#27334 := [monotonicity #27331]: #27333
-#27337 := [monotonicity #27334]: #27336
-#27340 := [monotonicity #27337]: #27339
-#27343 := [monotonicity #27340]: #27342
-#27348 := [trans #27343 #27346]: #27347
-#27351 := [monotonicity #27348]: #27350
-#28767 := [monotonicity #27351]: #28766
-#28770 := [trans #28767 #28769]: #28766
-#28765 := [quant-inst #26182 #161 #24996]: #28764
-#28752 := [mp #28765 #28770]: #28722
-#28890 := [unit-resolution #28752 #21240]: #27349
-#28756 := (or #27344 #27335)
-#28757 := [def-axiom]: #28756
-#28891 := [unit-resolution #28757 #28890]: #27335
-#28892 := (= #27146 #27314)
-#28893 := [monotonicity #28791]: #28892
-#28903 := [trans #28893 #28891]: #28902
-#28905 := [trans #28903 #28895]: #28904
-#28907 := [trans #28905 #28897]: #28906
-#28909 := [trans #28907 #28899]: #28908
-#28911 := [trans #28909 #28901]: #28910
-#28913 := [monotonicity #28911]: #28912
-#28915 := [symm #28913]: #28914
-#28917 := [monotonicity #28915]: #28916
-#28921 := [trans #28917 #28919]: #28920
-#28923 := [trans #28921 #28789]: #28922
-#28925 := [monotonicity #28923]: #28924
-#28927 := [trans #28925 #28851]: #28926
-#28929 := [monotonicity #28927]: #28928
-#28931 := [monotonicity #28929]: #28930
-#28933 := [symm #28931]: #28932
-#28935 := [monotonicity #28933]: #28934
-#28936 := [mp #14369 #28935]: #28602
-#28940 := (= #3047 #27778)
-#28937 := (= #27778 #3047)
-#28938 := [monotonicity #28923]: #28937
-#28941 := [symm #28938]: #28940
-#28942 := [trans #14366 #28941]: #27786
-#28597 := (not #27786)
-#28598 := (or #28363 #28597)
-#28599 := [def-axiom]: #28598
-#28943 := [unit-resolution #28599 #28942]: #28363
-#28611 := (or #28437 #28097 #28322 #28340 #28365)
-#28612 := [def-axiom]: #28611
-#28944 := [unit-resolution #28612 #28943 #28936 #28468 #28837 #28819]: false
-#28946 := [lemma #28944]: #28945
-#29128 := [unit-resolution #28946 #28653]: #12189
-#23578 := (or #18445 #18454 #23575)
-#23581 := (not #23578)
-#23584 := (or #18445 #18448 #23581)
-#23587 := (not #23584)
-#23590 := (or #18445 #18448 #23587)
-#23593 := (not #23590)
-#23596 := (or #13300 #23593)
-#23599 := (not #23596)
-#23602 := (or #13300 #23599)
-#22558 := (forall (vars (?v0 Int)) #22547)
-#22565 := (not #22558)
-#22543 := (forall (vars (?v0 Int)) #22538)
-#22564 := (not #22543)
-#22566 := (or #22564 #22565)
-#22567 := (not #22566)
-#22596 := (or #22567 #22593)
-#22602 := (not #22596)
-#22603 := (or #12340 #12331 #12322 #12313 #22479 #13656 #13802 #22602)
-#22604 := (not #22603)
-#22382 := (forall (vars (?v0 Int)) #22377)
-#22388 := (not #22382)
-#22389 := (or #22364 #22388)
-#22390 := (not #22389)
-#22419 := (or #22390 #22416)
-#22425 := (not #22419)
-#22426 := (or #13555 #22425)
-#22427 := (not #22426)
-#22432 := (or #13555 #22427)
-#22440 := (not #22432)
-#22441 := (or #12692 #22438 #18594 #22439 #13622 #18597 #22440)
-#22442 := (not #22441)
-#22447 := (or #18594 #18597 #22442)
-#22453 := (not #22447)
-#22490 := (or #12857 #12848 #22479 #13656 #22438 #13707 #22453)
-#22491 := (not #22490)
-#22454 := (or #18556 #18565 #12776 #12767 #12758 #12740 #12731 #13656 #22438 #22453)
-#22455 := (not #22454)
-#22460 := (or #18556 #18565 #22455)
-#22466 := (not #22460)
-#22467 := (or #18556 #18559 #22466)
-#22468 := (not #22467)
-#22473 := (or #18556 #18559 #22468)
-#22480 := (not #22473)
-#22481 := (or #22479 #13656 #13708 #22480)
-#22482 := (not #22481)
-#22496 := (or #22482 #22491)
-#22502 := (not #22496)
-#22503 := (or #18556 #18565 #22479 #13656 #22502)
-#22504 := (not #22503)
-#22509 := (or #18556 #18565 #22504)
-#22515 := (not #22509)
-#22516 := (or #18556 #18559 #22515)
-#22517 := (not #22516)
-#22522 := (or #18556 #18559 #22517)
-#22528 := (not #22522)
-#22529 := (or #22479 #13656 #13801 #22528)
-#22530 := (not #22529)
-#22609 := (or #22530 #22604)
-#22624 := (not #22609)
-#22359 := (forall (vars (?v0 Int)) #22354)
-#22620 := (not #22359)
-#22625 := (or #13267 #22615 #15299 #13974 #13060 #13051 #13042 #13033 #22616 #22617 #13508 #22479 #13656 #13979 #14031 #22618 #22619 #22621 #22622 #22623 #22620 #22624)
-#22626 := (not #22625)
-#22631 := (or #13267 #13508 #22626)
-#22638 := (not #22631)
-#22348 := (forall (vars (?v0 Int)) #22343)
-#22637 := (not #22348)
-#22639 := (or #22637 #22638)
-#22640 := (not #22639)
-#22645 := (or #22337 #22640)
-#22651 := (not #22645)
-#22652 := (or #13472 #22651)
-#22653 := (not #22652)
-#22658 := (or #13472 #22653)
-#22664 := (not #22658)
-#22665 := (or #13267 #18445 #18454 #13258 #13249 #13240 #22664)
-#22666 := (not #22665)
-#22671 := (or #18445 #18454 #22666)
-#22677 := (not #22671)
-#22678 := (or #18445 #18448 #22677)
-#22679 := (not #22678)
-#22684 := (or #18445 #18448 #22679)
-#22690 := (not #22684)
-#22691 := (or #13300 #22690)
-#22692 := (not #22691)
-#22697 := (or #13300 #22692)
-#23603 := (iff #22697 #23602)
-#23600 := (iff #22692 #23599)
-#23597 := (iff #22691 #23596)
-#23594 := (iff #22690 #23593)
-#23591 := (iff #22684 #23590)
-#23588 := (iff #22679 #23587)
-#23585 := (iff #22678 #23584)
-#23582 := (iff #22677 #23581)
-#23579 := (iff #22671 #23578)
-#23576 := (iff #22666 #23575)
-#23573 := (iff #22665 #23572)
-#23570 := (iff #22664 #23569)
-#23567 := (iff #22658 #23566)
-#23564 := (iff #22653 #23563)
-#23561 := (iff #22652 #23560)
-#23558 := (iff #22651 #23557)
-#23555 := (iff #22645 #23554)
-#23552 := (iff #22640 #23551)
-#23549 := (iff #22639 #23548)
-#23546 := (iff #22638 #23545)
-#23543 := (iff #22631 #23542)
-#23540 := (iff #22626 #23539)
-#23537 := (iff #22625 #23536)
-#23534 := (iff #22624 #23533)
-#23531 := (iff #22609 #23530)
-#23528 := (iff #22604 #23527)
-#23525 := (iff #22603 #23524)
-#23522 := (iff #22602 #23521)
-#23519 := (iff #22596 #23518)
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-#23520 := [monotonicity #23517]: #23519
-#23523 := [monotonicity #23520]: #23522
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-#23488 := (iff #22528 #23487)
-#23485 := (iff #22522 #23484)
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-#23383 := (iff #22382 #23380)
-#23381 := (iff #22377 #22377)
-#23382 := [refl]: #23381
-#23384 := [quant-intro #23382]: #23383
-#23387 := [monotonicity #23384]: #23386
-#23390 := [monotonicity #23387]: #23389
-#23393 := [monotonicity #23390]: #23392
-#23396 := [monotonicity #23393]: #23395
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-#23438 := [monotonicity #23435]: #23437
-#23441 := [monotonicity #23438]: #23440
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-#23447 := [monotonicity #23444]: #23446
-#23450 := [monotonicity #23447]: #23449
-#23453 := [monotonicity #23450]: #23452
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-#23465 := [monotonicity #23462]: #23464
-#23468 := [monotonicity #23465]: #23467
-#23471 := [monotonicity #23468]: #23470
-#23474 := [monotonicity #23471]: #23473
-#23477 := [monotonicity #23474]: #23476
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-#23483 := [monotonicity #23480]: #23482
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-#23378 := (iff #22620 #23377)
-#23375 := (iff #22359 #23372)
-#23373 := (iff #22354 #22354)
-#23374 := [refl]: #23373
-#23376 := [quant-intro #23374]: #23375
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-#23365 := (iff #22343 #22343)
-#23366 := [refl]: #23365
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-#23371 := [monotonicity #23368]: #23370
-#23550 := [monotonicity #23371 #23547]: #23549
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-#23562 := [monotonicity #23559]: #23561
-#23565 := [monotonicity #23562]: #23564
-#23568 := [monotonicity #23565]: #23567
-#23571 := [monotonicity #23568]: #23570
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-#23577 := [monotonicity #23574]: #23576
-#23580 := [monotonicity #23577]: #23579
-#23583 := [monotonicity #23580]: #23582
-#23586 := [monotonicity #23583]: #23585
-#23589 := [monotonicity #23586]: #23588
-#23592 := [monotonicity #23589]: #23591
-#23595 := [monotonicity #23592]: #23594
-#23598 := [monotonicity #23595]: #23597
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-#19096 := (and #18739 #18740)
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-#15913 := (forall (vars (?v0 Int)) #15908)
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-#18979 := (and #12622 #13525 #13534 #13542 #13618 #15900 #18971)
-#18984 := (or #18594 #18597 #18979)
-#19024 := (and #12839 #12842 #13513 #13516 #13525 #13708 #18984)
-#18990 := (and #12575 #12584 #12590 #12593 #12596 #12601 #12604 #13516 #13525 #18984)
-#18995 := (or #18556 #18565 #18990)
-#19001 := (and #12575 #12578 #18995)
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-#19012 := (and #13513 #13516 #13707 #19006)
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-#19046 := (and #12575 #12578 #19040)
-#19051 := (or #18556 #18559 #19046)
-#19057 := (and #13513 #13516 #13802 #19051)
-#19124 := (or #19057 #19119)
-#15834 := (or #13994 #14008 #14461)
-#15839 := (forall (vars (?v0 Int)) #15834)
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-#19135 := (or #13267 #13508 #19130)
-#15820 := (or #13475 #13487 #14461)
-#15825 := (forall (vars (?v0 Int)) #15820)
-#19138 := (and #15825 #19135)
-#18851 := (and #18478 #18479)
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-#18860 := (or #18486 #18487 #18854)
-#18865 := (not #18860)
-#19141 := (or #18865 #19138)
-#19144 := (and #13469 #19141)
-#19147 := (or #13472 #19144)
-#19153 := (and #3109 #12180 #12189 #12195 #12198 #12201 #19147)
-#19158 := (or #18445 #18454 #19153)
-#19164 := (and #12180 #12183 #19158)
-#19169 := (or #18445 #18448 #19164)
-#19172 := (and #12177 #19169)
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-#22698 := (iff #19175 #22697)
-#22695 := (iff #19172 #22692)
-#22687 := (and #12177 #22684)
-#22693 := (iff #22687 #22692)
-#22694 := [rewrite]: #22693
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-#22682 := (iff #19164 #22679)
-#22674 := (and #12180 #12183 #22671)
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-#22675 := (iff #19164 #22674)
-#22672 := (iff #19158 #22671)
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-#22661 := (and #3109 #12180 #12189 #12195 #12198 #12201 #22658)
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-#22648 := (and #13469 #22645)
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-#22612 := (and #3109 #12250 #12258 #12515 #12543 #12546 #12549 #12552 #12555 #12558 #13509 #13513 #13516 #13980 #14028 #14034 #14056 #22359 #15851 #15868 #15885 #22609)
-#22627 := (iff #22612 #22626)
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-#22592 := [trans #22587 #22590]: #22591
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-#22361 := [quant-intro #22358]: #22360
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-#18775 := (~ #18774 #18773)
-#18770 := (not #16029)
-#18771 := (~ #18770 #18769)
-#18766 := (not #16026)
-#18767 := (~ #18766 #18765)
-#18763 := (~ #18762 #18762)
-#18764 := [refl]: #18763
-#18768 := [nnf-neg #18764]: #18767
-#18759 := (not #16015)
-#18760 := (~ #18759 #16012)
-#18757 := (~ #16012 #16012)
-#18755 := (~ #16007 #16007)
-#18756 := [refl]: #18755
-#18758 := [nnf-pos #18756]: #18757
-#18761 := [nnf-neg #18758]: #18760
-#18772 := [nnf-neg #18761 #18768]: #18771
-#18751 := (~ #16015 #18750)
-#18752 := [sk]: #18751
-#18776 := [nnf-neg #18752 #18772]: #18775
-#18736 := (~ #13805 #13805)
-#18737 := [refl]: #18736
-#18527 := (~ #18526 #18526)
-#18528 := [refl]: #18527
-#18734 := (~ #18733 #18733)
-#18735 := [refl]: #18734
-#18731 := (~ #18730 #18730)
-#18732 := [refl]: #18731
-#18728 := (~ #18727 #18727)
-#18729 := [refl]: #18728
-#18725 := (~ #18724 #18724)
-#18726 := [refl]: #18725
-#18780 := [nnf-neg #18726 #18729 #18732 #18735 #18528 #18737 #18776]: #18779
-#18721 := (not #15999)
-#18722 := (~ #18721 #18720)
-#18717 := (not #15993)
-#18718 := (~ #18717 #18716)
-#18713 := (not #15990)
-#18714 := (~ #18713 #18712)
-#18709 := (not #15987)
-#18710 := (~ #18709 #18708)
-#18705 := (not #15984)
-#18706 := (~ #18705 #18704)
-#18701 := (not #15981)
-#18702 := (~ #18701 #18700)
-#18697 := (not #15976)
-#18698 := (~ #18697 #18696)
-#18665 := (not #15950)
-#18666 := (~ #18665 #18664)
-#18661 := (not #15945)
-#18662 := (~ #18661 #18660)
-#18658 := (~ #18657 #18657)
-#18659 := [refl]: #18658
-#18654 := (not #15933)
-#18655 := (~ #18654 #18653)
-#18650 := (not #15930)
-#18651 := (~ #18650 #18649)
-#18646 := (not #15927)
-#18647 := (~ #18646 #18645)
-#18642 := (not #15922)
-#18643 := (~ #18642 #18641)
-#18638 := (not #15916)
-#18639 := (~ #18638 #15913)
-#18636 := (~ #15913 #15913)
-#18634 := (~ #15908 #15908)
-#18635 := [refl]: #18634
-#18637 := [nnf-pos #18635]: #18636
-#18640 := [nnf-neg #18637]: #18639
-#18632 := (~ #18631 #18631)
-#18633 := [refl]: #18632
-#18644 := [nnf-neg #18633 #18640]: #18643
-#18627 := (~ #15916 #18626)
-#18628 := [sk]: #18627
-#18648 := [nnf-neg #18628 #18644]: #18647
-#18612 := (~ #18611 #18611)
-#18613 := [refl]: #18612
-#18652 := [nnf-neg #18613 #18648]: #18651
-#18609 := (~ #13555 #13555)
-#18610 := [refl]: #18609
-#18656 := [nnf-neg #18610 #18652]: #18655
-#18607 := (~ #18606 #18606)
-#18608 := [refl]: #18607
-#18604 := (~ #18603 #18603)
-#18605 := [refl]: #18604
-#18601 := (~ #18600 #18600)
-#18602 := [refl]: #18601
-#18663 := [nnf-neg #18602 #18605 #18608 #18656 #18659]: #18662
-#18598 := (~ #18597 #18597)
-#18599 := [refl]: #18598
-#18595 := (~ #18594 #18594)
-#18596 := [refl]: #18595
-#18667 := [nnf-neg #18596 #18599 #18663]: #18666
-#18694 := (~ #13713 #13713)
-#18695 := [refl]: #18694
-#18592 := (~ #18591 #18591)
-#18593 := [refl]: #18592
-#18692 := (~ #18691 #18691)
-#18693 := [refl]: #18692
-#18689 := (~ #18688 #18688)
-#18690 := [refl]: #18689
-#18699 := [nnf-neg #18690 #18693 #18528 #18593 #18695 #18667]: #18698
-#18685 := (not #15968)
-#18686 := (~ #18685 #18684)
-#18681 := (not #15962)
-#18682 := (~ #18681 #18680)
-#18677 := (not #15959)
-#18678 := (~ #18677 #18676)
-#18673 := (not #15956)
-#18674 := (~ #18673 #18672)
-#18669 := (not #15953)
-#18670 := (~ #18669 #18668)
-#18589 := (~ #18588 #18588)
-#18590 := [refl]: #18589
-#18586 := (~ #18585 #18585)
-#18587 := [refl]: #18586
-#18583 := (~ #18582 #18582)
-#18584 := [refl]: #18583
-#18580 := (~ #18579 #18579)
-#18581 := [refl]: #18580
-#18577 := (~ #18576 #18576)
-#18578 := [refl]: #18577
-#18574 := (~ #18573 #18573)
-#18575 := [refl]: #18574
-#18569 := (~ #18568 #18568)
-#18570 := [refl]: #18569
-#18671 := [nnf-neg #18570 #18575 #18578 #18581 #18584 #18587 #18590 #18593 #18667]: #18670
-#18566 := (~ #18565 #18565)
-#18567 := [refl]: #18566
-#18557 := (~ #18556 #18556)
-#18558 := [refl]: #18557
-#18675 := [nnf-neg #18558 #18567 #18671]: #18674
-#18563 := (~ #18562 #18562)
-#18564 := [refl]: #18563
-#18679 := [nnf-neg #18564 #18675]: #18678
-#18560 := (~ #18559 #18559)
-#18561 := [refl]: #18560
-#18683 := [nnf-neg #18558 #18561 #18679]: #18682
-#18571 := (~ #13707 #13707)
-#18572 := [refl]: #18571
-#18687 := [nnf-neg #18528 #18572 #18683]: #18686
-#18703 := [nnf-neg #18687 #18699]: #18702
-#18707 := [nnf-neg #18570 #18528 #18703]: #18706
-#18711 := [nnf-neg #18558 #18567 #18707]: #18710
-#18715 := [nnf-neg #18564 #18711]: #18714
-#18719 := [nnf-neg #18558 #18561 #18715]: #18718
-#18554 := (~ #13802 #13802)
-#18555 := [refl]: #18554
-#18723 := [nnf-neg #18528 #18555 #18719]: #18722
-#18784 := [nnf-neg #18723 #18780]: #18783
-#18552 := (~ #18551 #18551)
-#18553 := [refl]: #18552
-#18549 := (~ #18548 #18548)
-#18550 := [refl]: #18549
-#18546 := (~ #18545 #18545)
-#18547 := [refl]: #18546
-#18542 := (not #15842)
-#18543 := (~ #18542 #15839)
-#18540 := (~ #15839 #15839)
-#18538 := (~ #15834 #15834)
-#18539 := [refl]: #18538
-#18541 := [nnf-pos #18539]: #18540
-#18544 := [nnf-neg #18541]: #18543
-#18536 := (~ #18535 #18535)
-#18537 := [refl]: #18536
-#18533 := (~ #18532 #18532)
-#18534 := [refl]: #18533
-#18530 := (~ #18529 #18529)
-#18531 := [refl]: #18530
-#18524 := (~ #18523 #18523)
-#18525 := [refl]: #18524
-#18521 := (~ #18520 #18520)
-#18522 := [refl]: #18521
-#18518 := (~ #18517 #18517)
-#18519 := [refl]: #18518
-#18515 := (~ #18514 #18514)
-#18516 := [refl]: #18515
-#18512 := (~ #18511 #18511)
-#18513 := [refl]: #18512
-#18509 := (~ #18508 #18508)
-#18510 := [refl]: #18509
-#18506 := (~ #18505 #18505)
-#18507 := [refl]: #18506
-#18788 := [nnf-neg #18507 #18510 #18513 #18516 #18519 #18522 #18525 #18528 #18531 #18534 #18537 #18544 #18547 #18550 #18553 #18784]: #18787
-#18503 := (~ #14234 #14234)
-#18504 := [refl]: #18503
-#18501 := (~ #13267 #13267)
-#18502 := [refl]: #18501
-#18792 := [nnf-neg #18502 #18504 #18788]: #18791
-#18498 := (not #15828)
-#18499 := (~ #18498 #15825)
-#18496 := (~ #15825 #15825)
-#18494 := (~ #15820 #15820)
-#18495 := [refl]: #18494
-#18497 := [nnf-pos #18495]: #18496
-#18500 := [nnf-neg #18497]: #18499
-#18796 := [nnf-neg #18500 #18792]: #18795
-#18490 := (~ #15828 #18489)
-#18491 := [sk]: #18490
-#18800 := [nnf-neg #18491 #18796]: #18799
-#18475 := (~ #18474 #18474)
-#18476 := [refl]: #18475
-#18804 := [nnf-neg #18476 #18800]: #18803
-#18472 := (~ #13472 #13472)
-#18473 := [refl]: #18472
-#18808 := [nnf-neg #18473 #18804]: #18807
-#18470 := (~ #18469 #18469)
-#18471 := [refl]: #18470
-#18467 := (~ #18466 #18466)
-#18468 := [refl]: #18467
-#18464 := (~ #18463 #18463)
-#18465 := [refl]: #18464
-#18461 := (~ #18460 #18460)
-#18462 := [refl]: #18461
-#18458 := (~ #18457 #18457)
-#18459 := [refl]: #18458
-#18812 := [nnf-neg #18459 #18462 #18465 #18468 #18471 #18808]: #18811
-#18455 := (~ #18454 #18454)
-#18456 := [refl]: #18455
-#18446 := (~ #18445 #18445)
-#18447 := [refl]: #18446
-#18816 := [nnf-neg #18447 #18456 #18812]: #18815
-#18452 := (~ #18451 #18451)
-#18453 := [refl]: #18452
-#18820 := [nnf-neg #18453 #18816]: #18819
-#18449 := (~ #18448 #18448)
-#18450 := [refl]: #18449
-#18824 := [nnf-neg #18447 #18450 #18820]: #18823
-#18443 := (~ #18442 #18442)
-#18444 := [refl]: #18443
-#18828 := [nnf-neg #18444 #18824]: #18827
-#18440 := (~ #13300 #13300)
-#18441 := [refl]: #18440
-#18831 := [nnf-neg #18441 #18828]: #18830
-#15324 := (or #12340 #12331 #12322 #12313 #13521 #13802 #13888)
-#15329 := (and #13824 #15324)
-#15335 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13991 #14025 #14031 #14043 #14053 #14066 #14077 #15329)
-#15340 := (and #3109 #13509 #15335)
-#15343 := (or #13505 #15340)
-#15346 := (and #13502 #15343)
-#15349 := (or #13472 #15346)
-#15352 := (and #13469 #15349)
-#15355 := (or #13267 #13276 #13258 #13249 #13240 #15352)
-#15358 := (and #12180 #12189 #15355)
-#15361 := (or #13288 #15358)
-#15364 := (and #12180 #12183 #15361)
-#15367 := (or #13300 #15364)
-#15370 := (and #12177 #15367)
-#15373 := (not #15370)
-#16083 := (iff #15373 #16082)
-#16080 := (iff #15370 #16079)
-#16077 := (iff #15367 #16076)
-#16074 := (iff #15364 #16073)
-#16071 := (iff #15361 #16070)
-#16068 := (iff #15358 #16067)
-#16065 := (iff #15355 #16064)
-#16062 := (iff #15352 #16061)
-#16059 := (iff #15349 #16058)
-#16056 := (iff #15346 #16055)
-#16053 := (iff #15343 #16052)
-#16050 := (iff #15340 #16049)
-#16047 := (iff #15335 #16044)
-#16041 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13991 #15842 #14031 #15859 #15876 #15893 #14077 #16038)
-#16045 := (iff #16041 #16044)
-#16046 := [rewrite]: #16045
-#16042 := (iff #15335 #16041)
-#16039 := (iff #15329 #16038)
-#16036 := (iff #15324 #16035)
-#16033 := (iff #13888 #16032)
-#16030 := (iff #13883 #16029)
-#16027 := (iff #13874 #16026)
-#16024 := (iff #13869 #16021)
-#16018 := (and #3173 #4202 #15219 #13831)
-#16022 := (iff #16018 #16021)
-#16023 := [rewrite]: #16022
-#16019 := (iff #13869 #16018)
-#15214 := (iff #4516 #15219)
-#15235 := -4294967295::Int
-#15227 := (+ -4294967295::Int #202)
-#15220 := (<= #15227 0::Int)
-#15216 := (iff #15220 #15219)
-#15217 := [rewrite]: #15216
-#15221 := (iff #4516 #15220)
-#15222 := (= #4515 #15227)
-#15228 := (+ #202 -4294967295::Int)
-#15224 := (= #15228 #15227)
-#15225 := [rewrite]: #15224
-#15229 := (= #4515 #15228)
-#15230 := (= #4514 -4294967295::Int)
-#15236 := (* -1::Int 4294967295::Int)
-#15232 := (= #15236 -4294967295::Int)
-#15233 := [rewrite]: #15232
-#15237 := (= #4514 #15236)
-#7637 := (= f87 4294967295::Int)
-#990 := 65536::Int
-#1365 := (* 65536::Int 65536::Int)
-#1370 := (- #1365 1::Int)
-#1371 := (= f87 #1370)
-#7638 := (iff #1371 #7637)
-#7635 := (= #1370 4294967295::Int)
-#1053 := 4294967296::Int
-#7628 := (- 4294967296::Int 1::Int)
-#7633 := (= #7628 4294967295::Int)
-#7634 := [rewrite]: #7633
-#7630 := (= #1370 #7628)
-#7599 := (= #1365 4294967296::Int)
-#7600 := [rewrite]: #7599
-#7631 := [monotonicity #7600]: #7630
-#7636 := [trans #7631 #7634]: #7635
-#7639 := [monotonicity #7636]: #7638
-#7627 := [asserted]: #1371
-#7642 := [mp #7627 #7639]: #7637
-#15234 := [monotonicity #7642]: #15237
-#15231 := [trans #15234 #15233]: #15230
-#15226 := [monotonicity #15231]: #15229
-#15223 := [trans #15226 #15225]: #15222
-#15218 := [monotonicity #15223]: #15221
-#15215 := [trans #15218 #15217]: #15214
-#16020 := [monotonicity #15215]: #16019
-#16025 := [trans #16020 #16023]: #16024
-#16028 := [quant-intro #16025]: #16027
-#16016 := (iff #13877 #16015)
-#16013 := (iff #13857 #16012)
-#16010 := (iff #13852 #16007)
-#16004 := (or #14461 #13829 #13843)
-#16008 := (iff #16004 #16007)
-#16009 := [rewrite]: #16008
-#16005 := (iff #13852 #16004)
-#14458 := (iff #5738 #14461)
-#14463 := (iff #4523 #14462)
-#14460 := [monotonicity #15215]: #14463
-#14459 := [monotonicity #14460]: #14458
-#16006 := [monotonicity #14459]: #16005
-#16011 := [trans #16006 #16009]: #16010
-#16014 := [quant-intro #16011]: #16013
-#16017 := [monotonicity #16014]: #16016
-#16031 := [monotonicity #16017 #16028]: #16030
-#16034 := [monotonicity #16014 #16031]: #16033
-#16037 := [monotonicity #16034]: #16036
-#16002 := (iff #13824 #15999)
-#15996 := (or #13521 #15993 #13801)
-#16000 := (iff #15996 #15999)
-#16001 := [rewrite]: #16000
-#15997 := (iff #13824 #15996)
-#15994 := (iff #13795 #15993)
-#15991 := (iff #13789 #15990)
-#15988 := (iff #13784 #15987)
-#15985 := (iff #13776 #15984)
-#15982 := (iff #13767 #15981)
-#15979 := (iff #13762 #15976)
-#15973 := (or #12857 #12848 #13521 #13530 #15950 #13707)
-#15977 := (iff #15973 #15976)
-#15978 := [rewrite]: #15977
-#15974 := (iff #13762 #15973)
-#15951 := (iff #13651 #15950)
-#15948 := (iff #13643 #15945)
-#15942 := (or #12692 #13547 #15933 #13622 #15939)
-#15946 := (iff #15942 #15945)
-#15947 := [rewrite]: #15946
-#15943 := (iff #13643 #15942)
-#15940 := (iff #13628 #15939)
-#15937 := (iff #13625 #15936)
-#15903 := (iff #13536 #15900)
-#15845 := (+ 4294967295::Int #13537)
-#15896 := (>= #15845 1::Int)
-#15901 := (iff #15896 #15900)
-#15902 := [rewrite]: #15901
-#15897 := (iff #13536 #15896)
-#15846 := (= #13538 #15845)
-#15847 := [monotonicity #7642]: #15846
-#15898 := [monotonicity #15847]: #15897
-#15904 := [trans #15898 #15902]: #15903
-#15938 := [monotonicity #15904]: #15937
-#15941 := [monotonicity #15938]: #15940
-#15934 := (iff #13615 #15933)
-#15931 := (iff #13612 #15930)
-#15928 := (iff #13609 #15927)
-#15925 := (iff #13606 #15922)
-#15919 := (or #15916 #13601)
-#15923 := (iff #15919 #15922)
-#15924 := [rewrite]: #15923
-#15920 := (iff #13606 #15919)
-#15917 := (iff #13589 #15916)
-#15914 := (iff #13586 #15913)
-#15911 := (iff #13581 #15908)
-#15905 := (or #14461 #13558 #13572)
-#15909 := (iff #15905 #15908)
-#15910 := [rewrite]: #15909
-#15906 := (iff #13581 #15905)
-#15907 := [monotonicity #14459]: #15906
-#15912 := [trans #15907 #15910]: #15911
-#15915 := [quant-intro #15912]: #15914
-#15918 := [monotonicity #15915]: #15917
-#15921 := [monotonicity #15918]: #15920
-#15926 := [trans #15921 #15924]: #15925
-#15929 := [monotonicity #15915 #15926]: #15928
-#15932 := [monotonicity #15929]: #15931
-#15935 := [monotonicity #15932]: #15934
-#15944 := [monotonicity #15935 #15941]: #15943
-#15949 := [trans #15944 #15947]: #15948
-#15952 := [monotonicity #15904 #15949]: #15951
-#15975 := [monotonicity #15952]: #15974
-#15980 := [trans #15975 #15978]: #15979
-#15971 := (iff #13732 #15968)
-#15965 := (or #13521 #15962 #13708)
-#15969 := (iff #15965 #15968)
-#15970 := [rewrite]: #15969
-#15966 := (iff #13732 #15965)
-#15963 := (iff #13702 #15962)
-#15960 := (iff #13696 #15959)
-#15957 := (iff #13691 #15956)
-#15954 := (iff #13683 #15953)
-#15955 := [monotonicity #15952]: #15954
-#15958 := [monotonicity #15955]: #15957
-#15961 := [monotonicity #15958]: #15960
-#15964 := [monotonicity #15961]: #15963
-#15967 := [monotonicity #15964]: #15966
-#15972 := [trans #15967 #15970]: #15971
-#15983 := [monotonicity #15972 #15980]: #15982
-#15986 := [monotonicity #15983]: #15985
-#15989 := [monotonicity #15986]: #15988
-#15992 := [monotonicity #15989]: #15991
-#15995 := [monotonicity #15992]: #15994
-#15998 := [monotonicity #15995]: #15997
-#16003 := [trans #15998 #16001]: #16002
-#16040 := [monotonicity #16003 #16037]: #16039
-#15894 := (iff #14066 #15893)
-#15891 := (iff #14063 #15890)
-#15888 := (iff #14059 #15885)
-#15879 := (+ 255::Int #14006)
-#15882 := (>= #15879 0::Int)
-#15886 := (iff #15882 #15885)
-#15887 := [rewrite]: #15886
-#15883 := (iff #14059 #15882)
-#15880 := (= #14060 #15879)
-#1375 := (= f89 255::Int)
-#7641 := [asserted]: #1375
-#15881 := [monotonicity #7641]: #15880
-#15884 := [monotonicity #15881]: #15883
-#15889 := [trans #15884 #15887]: #15888
-#15892 := [monotonicity #15889]: #15891
-#15895 := [monotonicity #15892]: #15894
-#15877 := (iff #14053 #15876)
-#15874 := (iff #14050 #15873)
-#15871 := (iff #14046 #15868)
-#15862 := (+ 4294967295::Int #13977)
-#15865 := (>= #15862 0::Int)
-#15869 := (iff #15865 #15868)
-#15870 := [rewrite]: #15869
-#15866 := (iff #14046 #15865)
-#15863 := (= #14047 #15862)
-#15864 := [monotonicity #7642]: #15863
-#15867 := [monotonicity #15864]: #15866
-#15872 := [trans #15867 #15870]: #15871
-#15875 := [monotonicity #15872]: #15874
-#15878 := [monotonicity #15875]: #15877
-#15860 := (iff #14043 #15859)
-#15857 := (iff #14040 #15856)
-#15854 := (iff #14037 #15851)
-#15848 := (>= #15845 0::Int)
-#15852 := (iff #15848 #15851)
-#15853 := [rewrite]: #15852
-#15849 := (iff #14037 #15848)
-#15850 := [monotonicity #15847]: #15849
-#15855 := [trans #15850 #15853]: #15854
-#15858 := [monotonicity #15855]: #15857
-#15861 := [monotonicity #15858]: #15860
-#15843 := (iff #14025 #15842)
-#15840 := (iff #14022 #15839)
-#15837 := (iff #14017 #15834)
-#15831 := (or #14461 #13994 #14008)
-#15835 := (iff #15831 #15834)
-#15836 := [rewrite]: #15835
-#15832 := (iff #14017 #15831)
-#15833 := [monotonicity #14459]: #15832
-#15838 := [trans #15833 #15836]: #15837
-#15841 := [quant-intro #15838]: #15840
-#15844 := [monotonicity #15841]: #15843
-#16043 := [monotonicity #15844 #15861 #15878 #15895 #16040]: #16042
-#16048 := [trans #16043 #16046]: #16047
-#16051 := [monotonicity #16048]: #16050
-#15829 := (iff #13505 #15828)
-#15826 := (iff #13502 #15825)
-#15823 := (iff #13497 #15820)
-#15817 := (or #14461 #13475 #13487)
-#15821 := (iff #15817 #15820)
-#15822 := [rewrite]: #15821
-#15818 := (iff #13497 #15817)
-#15819 := [monotonicity #14459]: #15818
-#15824 := [trans #15819 #15822]: #15823
-#15827 := [quant-intro #15824]: #15826
-#15830 := [monotonicity #15827]: #15829
-#16054 := [monotonicity #15830 #16051]: #16053
-#16057 := [monotonicity #15827 #16054]: #16056
-#16060 := [monotonicity #16057]: #16059
-#16063 := [monotonicity #16060]: #16062
-#16066 := [monotonicity #16063]: #16065
-#16069 := [monotonicity #16066]: #16068
-#16072 := [monotonicity #16069]: #16071
-#16075 := [monotonicity #16072]: #16074
-#16078 := [monotonicity #16075]: #16077
-#16081 := [monotonicity #16078]: #16080
-#16084 := [monotonicity #16081]: #16083
-#14361 := (not #14213)
-#15374 := (iff #14361 #15373)
-#15371 := (iff #14213 #15370)
-#15368 := (iff #14210 #15367)
-#15365 := (iff #14205 #15364)
-#15362 := (iff #14199 #15361)
-#15359 := (iff #14194 #15358)
-#15356 := (iff #14186 #15355)
-#15353 := (iff #14165 #15352)
-#15350 := (iff #14162 #15349)
-#15347 := (iff #14159 #15346)
-#15344 := (iff #14156 #15343)
-#15341 := (iff #14151 #15340)
-#15338 := (iff #14143 #15335)
-#15332 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #15329 #13991 #14025 #14031 #14043 #14053 #14066 #14077)
-#15336 := (iff #15332 #15335)
-#15337 := [rewrite]: #15336
-#15333 := (iff #14143 #15332)
-#15330 := (iff #13950 #15329)
-#15327 := (iff #13945 #15324)
-#15309 := (or #12340 #12331 #12322 #12313 #13521 #13888)
-#15321 := (or #13521 #13802 #15309)
-#15325 := (iff #15321 #15324)
-#15326 := [rewrite]: #15325
-#15322 := (iff #13945 #15321)
-#15319 := (iff #13920 #15309)
-#15314 := (and true #15309)
-#15317 := (iff #15314 #15309)
-#15318 := [rewrite]: #15317
-#15315 := (iff #13920 #15314)
-#15312 := (iff #13915 #15309)
-#15306 := (or false #12340 #12331 #12322 #12313 #13521 #13888)
-#15310 := (iff #15306 #15309)
-#15311 := [rewrite]: #15310
-#15307 := (iff #13915 #15306)
-#15304 := (iff #12374 false)
-#15302 := (iff #12374 #3156)
-#15040 := (iff #10960 true)
-#10959 := [asserted]: #2542
-#10966 := [mp #10959 #10963]: #10960
-#15041 := [iff-true #10966]: #15040
-#15303 := [monotonicity #15041]: #15302
-#15305 := [trans #15303 #12257]: #15304
-#15308 := [monotonicity #15305]: #15307
-#15313 := [trans #15308 #15311]: #15312
-#15316 := [monotonicity #15041 #15313]: #15315
-#15320 := [trans #15316 #15318]: #15319
-#15323 := [monotonicity #15320]: #15322
-#15328 := [trans #15323 #15326]: #15327
-#15331 := [monotonicity #15328]: #15330
-#15300 := (iff #12402 #15299)
-#15297 := (iff #12264 #12258)
-#15292 := (and true #12258)
-#15295 := (iff #15292 #12258)
-#15296 := [rewrite]: #15295
-#15293 := (iff #12264 #15292)
-#15276 := (iff #12145 true)
-#15277 := [iff-true #14351]: #15276
-#15294 := [monotonicity #15277]: #15293
-#15298 := [trans #15294 #15296]: #15297
-#15301 := [monotonicity #15298]: #15300
-#15334 := [monotonicity #15301 #15331]: #15333
-#15339 := [trans #15334 #15337]: #15338
-#15342 := [monotonicity #15339]: #15341
-#15345 := [monotonicity #15342]: #15344
-#15348 := [monotonicity #15345]: #15347
-#15351 := [monotonicity #15348]: #15350
-#15354 := [monotonicity #15351]: #15353
-#15357 := [monotonicity #15354]: #15356
-#15360 := [monotonicity #15357]: #15359
-#15363 := [monotonicity #15360]: #15362
-#15366 := [monotonicity #15363]: #15365
-#15369 := [monotonicity #15366]: #15368
-#15372 := [monotonicity #15369]: #15371
-#15375 := [monotonicity #15372]: #15374
-#14362 := [not-or-elim #14346]: #14361
-#15376 := [mp #14362 #15375]: #15373
-#16085 := [mp #15376 #16084]: #16082
-#18832 := [mp~ #16085 #18831]: #18829
-#18833 := [mp #18832 #19177]: #19175
-#22700 := [mp #18833 #22699]: #22697
-#23605 := [mp #22700 #23604]: #23602
-#29129 := [unit-resolution #23605 #27033]: #23599
-#24829 := (or #23596 #23590)
-#24830 := [def-axiom]: #24829
-#29130 := [unit-resolution #24830 #29129]: #23590
-#24825 := (or #23593 #18445 #18448 #23587)
-#24826 := [def-axiom]: #24825
-#29134 := [unit-resolution #24826 #27642 #28798 #29130]: #23587
-#24815 := (or #23584 #23578)
-#24816 := [def-axiom]: #24815
-#29135 := [unit-resolution #24816 #29134]: #23578
-#24809 := (or #23581 #18445 #18454 #23575)
-#24810 := [def-axiom]: #24809
-#29136 := [unit-resolution #24810 #29135 #29128 #27642]: #23575
-#24787 := (or #23572 #3109)
-#24788 := [def-axiom]: #24787
-#29137 := [unit-resolution #24788 #29136]: #3109
-#24799 := (or #23572 #23566)
-#24800 := [def-axiom]: #24799
-#29663 := [unit-resolution #24800 #29136]: #23566
-#29664 := (or #23569 #23563)
-#27310 := [hypothesis]: #13472
-#27311 := [th-lemma arith farkas 1 1 #14360 #27310]: false
-#27312 := [lemma #27311]: #13469
-#24785 := (or #23569 #13472 #23563)
-#24786 := [def-axiom]: #24785
-#29665 := [unit-resolution #24786 #27312]: #29664
-#29666 := [unit-resolution #29665 #29663]: #23563
-#24777 := (or #23560 #23554)
-#24778 := [def-axiom]: #24777
-#29667 := [unit-resolution #24778 #29666]: #23554
-#27615 := (* -1::Int #3108)
-#27616 := (+ f306 #27615)
-#27617 := (>= #27616 0::Int)
-#29138 := (or #13267 #27617)
-#29139 := [th-lemma arith triangle-eq]: #29138
-#29140 := [unit-resolution #29139 #29137]: #27617
-#24455 := (not #18486)
-#29141 := [hypothesis]: #22337
-#24456 := (or #22332 #24455)
-#24457 := [def-axiom]: #24456
-#29142 := [unit-resolution #24457 #29141]: #24455
-#29102 := (+ #3108 #18484)
-#29104 := (>= #29102 0::Int)
-#29101 := (= #3108 #18483)
-#29149 := (= #18483 #3108)
-#29147 := (= #18482 #3098)
-#29145 := (= ?v0!13 0::Int)
-#24458 := (not #18487)
-#24459 := (or #22332 #24458)
-#24460 := [def-axiom]: #24459
-#29143 := [unit-resolution #24460 #29141]: #24458
-#24453 := (or #22332 #18479)
-#24454 := [def-axiom]: #24453
-#29144 := [unit-resolution #24454 #29141]: #18479
-#29146 := [th-lemma arith eq-propagate 0 0 #29144 #29143]: #29145
-#29148 := [monotonicity #29146]: #29147
-#29150 := [monotonicity #29148]: #29149
-#29151 := [symm #29150]: #29101
-#29152 := (not #29101)
-#29153 := (or #29152 #29104)
-#29154 := [th-lemma arith triangle-eq]: #29153
-#29155 := [unit-resolution #29154 #29151]: #29104
-#29156 := [th-lemma arith farkas 1 -1 1 #29155 #29142 #29140]: false
-#29157 := [lemma #29156]: #22332
-#24773 := (or #23557 #22337 #23551)
+#8080 := (iff #1536 #8079)
+#8077 := (iff #1535 #8074)
+#8071 := (implies #1415 #8068)
+#8075 := (iff #8071 #8074)
+#8076 := [rewrite]: #8075
+#8072 := (iff #1535 #8071)
+#8069 := (iff #1534 #8068)
+#8066 := (iff #1533 #8065)
+#8063 := (iff #1532 #8062)
+#8060 := (iff #1531 #8059)
+#8061 := [rewrite]: #8060
+#8057 := (iff #1529 #8056)
+#8058 := [rewrite]: #8057
+#8064 := [monotonicity #8058 #8061]: #8063
+#8054 := (iff #1527 #8053)
+#8051 := (iff #1526 #8050)
+#8052 := [rewrite]: #8051
+#8055 := [monotonicity #8052]: #8054
+#8067 := [monotonicity #8055 #8064]: #8066
+#8048 := (iff #1524 #8047)
+#8049 := [rewrite]: #8048
+#8070 := [monotonicity #8049 #8067]: #8069
+#8073 := [monotonicity #8070]: #8072
+#8078 := [trans #8073 #8076]: #8077
+#8045 := (iff #1520 #8044)
+#8046 := [rewrite]: #8045
+#8081 := [monotonicity #8046 #8078]: #8080
+#8087 := [trans #8081 #8085]: #8086
+#8090 := [quant-intro #8087]: #8089
+#8109 := [trans #8090 #8107]: #8108
+#8043 := [asserted]: #1537
+#8110 := [mp #8043 #8109]: #8105
+#17106 := [mp~ #8110 #17105]: #8105
+#20988 := [mp #17106 #20987]: #20985
+#27726 := (not #20985)
+#27734 := (or #27726 #27121 #27139 #27147)
+#27117 := (or #27116 #27113 #27111 #27107)
+#27118 := (not #27117)
+#27127 := (or #27126 #27124 #27121 #27118)
+#27725 := (or #27726 #27127)
+#28114 := (iff #27725 #27734)
+#27153 := (or #27121 #27139 #27147)
+#27733 := (or #27726 #27153)
+#27738 := (iff #27733 #27734)
+#27739 := [rewrite]: #27738
+#27736 := (iff #27725 #27733)
+#27156 := (iff #27127 #27153)
+#27150 := (or false #27139 #27121 #27147)
+#27154 := (iff #27150 #27153)
+#27155 := [rewrite]: #27154
+#27151 := (iff #27127 #27150)
+#27148 := (iff #27118 #27147)
+#27145 := (iff #27117 #27144)
+#27146 := [rewrite]: #27145
+#27149 := [monotonicity #27146]: #27148
+#27152 := [monotonicity #27133 #27143 #27149]: #27151
+#27157 := [trans #27152 #27155]: #27156
+#27737 := [monotonicity #27157]: #27736
+#28134 := [trans #27737 #27739]: #28114
+#27735 := [quant-inst #3039 #3043 #24960 #24962 #161]: #27725
+#27527 := [mp #27735 #28134]: #27734
+#28916 := [unit-resolution #27527 #20988 #28356]: #28915
+#28917 := [unit-resolution #28916 #28914]: #27147
+#28369 := (or #27144 #27115)
+#28110 := [def-axiom]: #28369
+#28918 := [unit-resolution #28110 #28917]: #27115
+#28999 := [symm #28918]: #28998
+#28996 := (= #28603 #27114)
+#28994 := (= #28602 #27108)
+#26949 := (f69 #3220 #3098)
+#28992 := (= #26949 #27108)
+#28990 := (= #27108 #26949)
+#28986 := (= #27104 #3098)
+#26957 := (f128 #3098)
+#26986 := (f54 #24960 #26957)
+#28980 := (= #26986 #3098)
+#26987 := (= #3098 #26986)
+#28920 := (= #3099 #26977)
+#28921 := [symm #27532]: #28920
+#28922 := [trans #27593 #28921]: #26978
+#26989 := (or #26985 #26987)
+#27469 := (or #26158 #26985 #26987)
+#26988 := (or #26987 #26985)
+#27470 := (or #26158 #26988)
+#27635 := (iff #27470 #27469)
+#27506 := (or #26158 #26989)
+#27519 := (iff #27506 #27469)
+#27632 := [rewrite]: #27519
+#27507 := (iff #27470 #27506)
+#26990 := (iff #26988 #26989)
+#26991 := [rewrite]: #26990
+#27518 := [monotonicity #26991]: #27507
+#27636 := [trans #27518 #27632]: #27635
+#27505 := [quant-inst #3098 #24960]: #27470
+#27637 := [mp #27505 #27636]: #27469
+#28923 := [unit-resolution #27637 #18248]: #26989
+#28924 := [unit-resolution #28923 #28922]: #26987
+#28981 := [symm #28924]: #28980
+#28984 := (= #27104 #26986)
+#27307 := (f128 #26146)
+#27314 := (+ #27033 #27307)
+#27317 := (f54 #24960 #27314)
+#28978 := (= #27317 #26986)
+#28972 := (= #27314 #26957)
+#28970 := (= #26957 #27314)
+#28573 := (* -1::Int #27307)
+#28580 := (+ #24844 #28573)
+#28581 := (<= #28580 0::Int)
+#28579 := (= #24844 #27307)
+#28925 := (= #27307 #24844)
+#28926 := [monotonicity #26872]: #28925
+#28927 := [symm #28926]: #28579
+#28928 := (not #28579)
+#28929 := (or #28928 #28581)
+#28930 := [th-lemma arith triangle-eq]: #28929
+#28931 := [unit-resolution #28930 #28927]: #28581
+#28582 := (>= #28580 0::Int)
+#28932 := (or #28928 #28582)
+#28933 := [th-lemma arith triangle-eq]: #28932
+#28934 := [unit-resolution #28933 #28927]: #28582
+#27237 := (f128 #27044)
+#27241 := (* -1::Int #27237)
+#28542 := (+ #26957 #27241)
+#28543 := (<= #28542 0::Int)
+#28541 := (= #26957 #27237)
+#28935 := (= #27237 #26957)
+#28936 := [monotonicity #27431]: #28935
+#28937 := [symm #28936]: #28541
+#28938 := (not #28541)
+#28939 := (or #28938 #28543)
+#28940 := [th-lemma arith triangle-eq]: #28939
+#28941 := [unit-resolution #28940 #28937]: #28543
+#28544 := (>= #28542 0::Int)
+#28942 := (or #28938 #28544)
+#28943 := [th-lemma arith triangle-eq]: #28942
+#28944 := [unit-resolution #28943 #28937]: #28544
+#27710 := (* -1::Int #27034)
+#27716 := (+ #24844 #27710)
+#27719 := (<= #27716 0::Int)
+#27715 := (= #24844 #27034)
+#28952 := (= #3043 #27034)
+#28950 := (= #27034 #3043)
+#28945 := (= #24797 #3042)
+#28946 := [symm #27569]: #28945
+#28951 := [monotonicity #28946]: #28950
+#28953 := [symm #28951]: #28952
+#28948 := (= #24844 #3043)
+#25087 := (= #3043 #24844)
+#25092 := (or #25034 #25087)
+#25093 := [quant-inst #3040 #3043]: #25092
+#28947 := [unit-resolution #25093 #23270]: #25087
+#28949 := [symm #28947]: #28948
+#28954 := [trans #28949 #28953]: #27715
+#28955 := (not #27715)
+#28956 := (or #28955 #27719)
+#28957 := [th-lemma arith triangle-eq]: #28956
+#28958 := [unit-resolution #28957 #28954]: #27719
+#27720 := (>= #27716 0::Int)
+#28959 := (or #28955 #27720)
+#28960 := [th-lemma arith triangle-eq]: #28959
+#28961 := [unit-resolution #28960 #28954]: #27720
+#27242 := (+ #27034 #27241)
+#27243 := (+ #27033 #27242)
+#28409 := (<= #27243 0::Int)
+#27244 := (= #27243 0::Int)
+#28127 := (or #25034 #27244)
+#27238 := (= #27041 #27237)
+#28359 := (or #25034 #27238)
+#28461 := (iff #28359 #28127)
+#28464 := (iff #28127 #28127)
+#28465 := [rewrite]: #28464
+#27245 := (iff #27238 #27244)
+#27246 := [rewrite]: #27245
+#28358 := [monotonicity #27246]: #28461
+#28466 := [trans #28358 #28465]: #28461
+#28463 := [quant-inst #24960 #27041]: #28359
+#28467 := [mp #28463 #28466]: #28127
+#28962 := [unit-resolution #28467 #23270]: #27244
+#28963 := (not #27244)
+#28964 := (or #28963 #28409)
+#28965 := [th-lemma arith triangle-eq]: #28964
+#28966 := [unit-resolution #28965 #28962]: #28409
+#28540 := (>= #27243 0::Int)
+#28967 := (or #28963 #28540)
+#28968 := [th-lemma arith triangle-eq]: #28967
+#28969 := [unit-resolution #28968 #28962]: #28540
+#28971 := [th-lemma arith eq-propagate -1 -1 -1 -1 1 1 1 1 #28969 #28966 #28961 #28958 #28944 #28941 #28934 #28931]: #28970
+#28973 := [symm #28971]: #28972
+#28979 := [monotonicity #28973]: #28978
+#28982 := (= #27104 #27317)
+#27303 := (f77 #26146 0::Int #24960)
+#27320 := (= #27303 #27317)
+#27323 := (not #27320)
+#27304 := (f150 #27303 #26146)
+#27305 := (= f1 #27304)
+#27306 := (not #27305)
+#27329 := (or #27306 #27323)
+#27334 := (not #27329)
+#28552 := (or #27451 #27334)
+#27308 := (+ #27307 #27033)
+#27309 := (f54 #24960 #27308)
+#27310 := (= #27303 #27309)
+#27311 := (not #27310)
+#27312 := (or #27311 #27306)
+#27313 := (not #27312)
+#28553 := (or #27451 #27313)
+#28555 := (iff #28553 #28552)
+#28568 := (iff #28552 #28552)
+#28569 := [rewrite]: #28568
+#27335 := (iff #27313 #27334)
+#27332 := (iff #27312 #27329)
+#27326 := (or #27323 #27306)
+#27330 := (iff #27326 #27329)
+#27331 := [rewrite]: #27330
+#27327 := (iff #27312 #27326)
+#27324 := (iff #27311 #27323)
+#27321 := (iff #27310 #27320)
+#27318 := (= #27309 #27317)
+#27315 := (= #27308 #27314)
+#27316 := [rewrite]: #27315
+#27319 := [monotonicity #27316]: #27318
+#27322 := [monotonicity #27319]: #27321
+#27325 := [monotonicity #27322]: #27324
+#27328 := [monotonicity #27325]: #27327
+#27333 := [trans #27328 #27331]: #27332
+#27336 := [monotonicity #27333]: #27335
+#28556 := [monotonicity #27336]: #28555
+#28570 := [trans #28556 #28569]: #28555
+#28554 := [quant-inst #26146 #161 #24960]: #28553
+#28571 := [mp #28554 #28570]: #28552
+#28974 := [unit-resolution #28571 #21204]: #27334
+#28576 := (or #27329 #27320)
+#28577 := [def-axiom]: #28576
+#28975 := [unit-resolution #28577 #28974]: #27320
+#28976 := (= #27104 #27303)
+#28977 := [monotonicity #28365]: #28976
+#28983 := [trans #28977 #28975]: #28982
+#28985 := [trans #28983 #28979]: #28984
+#28987 := [trans #28985 #28981]: #28986
+#28991 := [monotonicity #28987]: #28990
+#28993 := [symm #28991]: #28992
+#28988 := (= #28602 #26949)
+#28989 := [monotonicity #27431]: #28988
+#28995 := [trans #28989 #28993]: #28994
+#28997 := [monotonicity #28995]: #28996
+#29001 := [trans #28997 #28999]: #29000
+#29003 := [trans #29001 #28364]: #29002
+#29005 := [monotonicity #29003]: #29004
+#29007 := [trans #29005 #28878]: #29006
+#29009 := [monotonicity #29007]: #29008
+#29011 := [monotonicity #29009]: #29010
+#29013 := [symm #29011]: #29012
+#29015 := [monotonicity #29013]: #29014
+#29016 := [mp #14333 #29015]: #28841
+#29020 := (= #3047 #28607)
+#29017 := (= #28607 #3047)
+#29018 := [monotonicity #29003]: #29017
+#29021 := [symm #29018]: #29020
+#29022 := [trans #14330 #29021]: #28608
+#28848 := (not #28608)
+#28849 := (or #28756 #28848)
+#28850 := [def-axiom]: #28849
+#29023 := [unit-resolution #28850 #29022]: #28756
+#25465 := (f23 f19)
+#29036 := (= #25465 #28639)
+#29032 := (= #28639 #25465)
+#29030 := (= #27233 f19)
+#29028 := (= #27233 #24960)
+#29029 := [symm #27567]: #29028
+#29031 := [trans #29029 #28488]: #29030
+#29033 := [monotonicity #29031]: #29032
+#29037 := [symm #29033]: #29036
+#25466 := (= f25 #25465)
+#25473 := (iff #11588 #25466)
+#2363 := (pattern #279)
+#2902 := (f23 #275)
+#11767 := (= f25 #2902)
+#11771 := (iff #4084 #11767)
+#11774 := (forall (vars (?v0 S18)) (:pat #2363) #11771)
+#18366 := (~ #11774 #11774)
+#18364 := (~ #11771 #11771)
+#18365 := [refl]: #18364
+#18367 := [nnf-pos #18365]: #18366
+#2915 := (= #2902 f25)
+#2916 := (iff #280 #2915)
+#2917 := (forall (vars (?v0 S18)) (:pat #2363) #2916)
+#11775 := (iff #2917 #11774)
+#11772 := (iff #2916 #11771)
+#11769 := (iff #2915 #11767)
+#11770 := [rewrite]: #11769
+#11773 := [monotonicity #4086 #11770]: #11772
+#11776 := [quant-intro #11773]: #11775
+#11766 := [asserted]: #2917
+#11779 := [mp #11766 #11776]: #11774
+#18368 := [mp~ #11779 #18367]: #11774
+#25132 := (not #11774)
+#25476 := (or #25132 #25473)
+#25477 := [quant-inst #50]: #25476
+#29024 := [unit-resolution #25477 #18368]: #25473
+#25478 := (not #25473)
+#29025 := (or #25478 #25466)
+#25482 := (not #11588)
+#25483 := (or #25478 #25482 #25466)
+#25484 := [def-axiom]: #25483
+#29026 := [unit-resolution #25484 #11594]: #29025
+#29027 := [unit-resolution #29026 #29024]: #25466
+#29038 := [trans #29027 #29037]: #28647
+#28125 := (not #27185)
+#29056 := (iff #28125 #28636)
+#29054 := (iff #27185 #28635)
+#29052 := (iff #28635 #27185)
+#29050 := (= #28634 #27184)
+#29048 := (= #28602 #27183)
+#29046 := (= #26949 #27183)
+#29044 := (= #27183 #26949)
+#29045 := [monotonicity #28135]: #29044
+#29047 := [symm #29045]: #29046
+#29049 := [trans #28989 #29047]: #29048
+#29051 := [monotonicity #29049]: #29050
+#29053 := [monotonicity #29051]: #29052
+#29055 := [symm #29053]: #29054
+#29057 := [monotonicity #29055]: #29056
+#28141 := (or #27198 #28125)
+#28142 := [def-axiom]: #28141
+#29043 := [unit-resolution #28142 #28352]: #28125
+#29058 := [mp #29043 #29057]: #28636
+#28824 := (or #28750 #28635)
+#28825 := [def-axiom]: #28824
+#29059 := [unit-resolution #28825 #29058]: #28750
+#28866 := (or #28793 #28630 #28726 #28753 #28740)
+#28867 := [def-axiom]: #28866
+#29060 := [unit-resolution #28867 #29059 #29038 #29023 #29016]: #28793
+#27098 := (or #28796 #28745)
+#27099 := [def-axiom]: #27098
+#29061 := [unit-resolution #27099 #29060 #28908]: false
+#29062 := [lemma #29061]: #12153
+#24773 := (or #23545 #18409 #18418 #23539)
 #24774 := [def-axiom]: #24773
-#29668 := [unit-resolution #24774 #29157 #29667]: #23551
-#24765 := (or #23548 #23542)
-#24766 := [def-axiom]: #24765
-#29669 := [unit-resolution #24766 #29668]: #23542
-#29670 := (or #23545 #13267 #23539)
-#24761 := (or #23545 #13267 #13508 #23539)
-#24762 := [def-axiom]: #24761
-#29671 := [unit-resolution #24762 #14360]: #29670
-#29672 := [unit-resolution #29671 #29669 #29137]: #23539
-#24751 := (or #23536 #23530)
+#29171 := [unit-resolution #24774 #29062 #27593 #29170]: #23539
+#24751 := (or #23536 #3109)
 #24752 := [def-axiom]: #24751
-#30100 := [unit-resolution #24752 #29672]: #23530
-#24749 := (or #23536 #23372)
+#29172 := [unit-resolution #24752 #29171]: #3109
+#29126 := (+ #3108 #18448)
+#29128 := (>= #29126 0::Int)
+#29125 := (= #3108 #18447)
+#29159 := (= #18447 #3108)
+#29157 := (= #18446 #3098)
+#29155 := (= ?v0!13 0::Int)
+#24422 := (not #18451)
+#29152 := [hypothesis]: #22301
+#24423 := (or #22296 #24422)
+#24424 := [def-axiom]: #24423
+#29153 := [unit-resolution #24424 #29152]: #24422
+#24417 := (or #22296 #18443)
+#24418 := [def-axiom]: #24417
+#29154 := [unit-resolution #24418 #29152]: #18443
+#29156 := [th-lemma arith eq-propagate 0 0 #29154 #29153]: #29155
+#29158 := [monotonicity #29156]: #29157
+#29160 := [monotonicity #29158]: #29159
+#29161 := [symm #29160]: #29125
+#29162 := (not #29125)
+#29163 := (or #29162 #29128)
+#29164 := [th-lemma arith triangle-eq]: #29163
+#29165 := [unit-resolution #29164 #29161]: #29128
+#24419 := (not #18450)
+#24420 := (or #22296 #24419)
+#24421 := [def-axiom]: #24420
+#29166 := [unit-resolution #24421 #29152]: #24419
+#27612 := (* -1::Int #3108)
+#27613 := (+ f307 #27612)
+#27614 := (>= #27613 0::Int)
+#29173 := (or #13231 #27614)
+#29174 := [th-lemma arith triangle-eq]: #29173
+#29175 := [unit-resolution #29174 #29172]: #27614
+#29176 := [th-lemma arith farkas 1 -1 1 #29175 #29166 #29165]: false
+#29177 := [lemma #29176]: #22296
+#24763 := (or #23536 #23530)
+#24764 := [def-axiom]: #24763
+#29735 := [unit-resolution #24764 #29171]: #23530
+#29073 := [hypothesis]: #13436
+#29074 := [th-lemma arith farkas 1 1 #14324 #29073]: false
+#29075 := [lemma #29074]: #13433
+#24749 := (or #23533 #13436 #23527)
 #24750 := [def-axiom]: #24749
-#30095 := [unit-resolution #24750 #29672]: #23372
-#24711 := (or #23536 #12250)
-#24712 := [def-axiom]: #24711
-#30101 := [unit-resolution #24712 #29672]: #12250
-#24745 := (or #23536 #15868)
-#24746 := [def-axiom]: #24745
-#30102 := [unit-resolution #24746 #29672]: #15868
-#24735 := (or #23536 #13980)
-#24736 := [def-axiom]: #24735
-#30103 := [unit-resolution #24736 #29672]: #13980
-#27607 := (f24 #27086)
-#27608 := (f77 #27086 f308 #27607)
-#27609 := (f136 #27608 #27086)
-#27690 := (>= #27609 0::Int)
-#24731 := (or #23536 #13513)
-#24732 := [def-axiom]: #24731
-#30104 := [unit-resolution #24732 #29672]: #13513
-#27706 := (* -1::Int #27609)
-#27779 := (+ f308 #27706)
-#27780 := (<= #27779 0::Int)
-#27610 := (= f308 #27609)
-#29180 := (f77 #24833 f308 #27122)
-#29181 := (f136 #29180 #24833)
-#30129 := (= #29181 #27609)
-#30127 := (= #27609 #29181)
-#30105 := (= #27086 #24833)
-#30109 := [trans #27414 #27140]: #30105
-#30124 := (= #27608 #29180)
-#30122 := (= #3152 #29180)
-#30120 := (= #29180 #3152)
-#30112 := (= #27122 f19)
-#30110 := (= #27122 #25112)
-#30111 := [monotonicity #27142]: #30110
-#30113 := [trans #30111 #27685]: #30112
-#30121 := [monotonicity #27142 #30113]: #30120
-#30123 := [symm #30121]: #30122
-#30118 := (= #27608 #3152)
-#30116 := (= #27607 f19)
-#30114 := (= #27607 #25112)
-#30115 := [monotonicity #27414]: #30114
-#30117 := [trans #30115 #27685]: #30116
-#30119 := [monotonicity #27414 #30117]: #30118
-#30125 := [trans #30119 #30123]: #30124
-#30128 := [monotonicity #30125 #30109]: #30127
-#30130 := [symm #30128]: #30129
-#29182 := (= f308 #29181)
-#29185 := (or #27129 #29182)
-#29186 := [quant-inst #24833 #3135]: #29185
-#30126 := [unit-resolution #29186 #17107]: #29182
-#30131 := [trans #30126 #30130]: #27610
-#28118 := (not #27610)
-#30132 := (or #28118 #27780)
-#30133 := [th-lemma arith triangle-eq]: #30132
-#30134 := [unit-resolution #30133 #30131]: #27780
-#30135 := (not #27780)
-#30136 := (or #27690 #22479 #30135)
-#30137 := [th-lemma arith assign-bounds -1 1]: #30136
-#30138 := [unit-resolution #30137 #30134 #30104]: #27690
-#27691 := (not #27690)
-#28143 := (or #23524 #27691 #13979 #22622 #22615 #23377)
-#27988 := (f77 #3042 #27609 f19)
-#27989 := (f121 f297 #27988)
-#27992 := (= f313 #27989)
-#28098 := (= #3153 #27989)
-#28111 := (= #27989 #3153)
-#28105 := (= #27988 #3152)
-#28103 := (= #27609 f308)
-#27613 := (or #27129 #27610)
-#27614 := [quant-inst #27086 #3135]: #27613
-#28102 := [unit-resolution #27614 #17107]: #27610
-#28104 := [symm #28102]: #28103
-#28106 := [monotonicity #28104]: #28105
-#28112 := [monotonicity #28106]: #28111
-#28113 := [symm #28112]: #28098
-#28114 := (= f313 #3153)
-#28107 := [hypothesis]: #12250
-#28108 := [hypothesis]: #23527
-#24691 := (or #23524 #12278)
-#24692 := [def-axiom]: #24691
-#28109 := [unit-resolution #24692 #28108]: #12278
-#28110 := [symm #28109]: #3167
-#28115 := [trans #28110 #28107]: #28114
-#28116 := [trans #28115 #28113]: #27992
-#27973 := (<= #27609 4294967295::Int)
-#28117 := [hypothesis]: #15868
-#27781 := (>= #27779 0::Int)
-#28119 := (or #28118 #27781)
-#28120 := [th-lemma arith triangle-eq]: #28119
-#28121 := [unit-resolution #28120 #28102]: #27781
-#28122 := (not #27781)
-#28123 := (or #27973 #22622 #28122)
-#28124 := [th-lemma arith assign-bounds -1 1]: #28123
-#28125 := [unit-resolution #28124 #28121 #28117]: #27973
-#28015 := (+ f296 #27706)
-#28016 := (<= #28015 0::Int)
-#28127 := (not #28016)
-#28126 := [hypothesis]: #13980
-#28128 := (or #28127 #13979 #28122)
-#28129 := [th-lemma arith assign-bounds -1 -1]: #28128
-#28130 := [unit-resolution #28129 #28121 #28126]: #28127
-#27995 := (not #27992)
-#27974 := (not #27973)
-#28140 := (or #27974 #27995 #28016)
-#28131 := [hypothesis]: #27690
-#24699 := (or #23524 #23518)
+#29738 := [unit-resolution #24750 #29075 #29735]: #23527
+#24741 := (or #23524 #23518)
+#24742 := [def-axiom]: #24741
+#29739 := [unit-resolution #24742 #29738]: #23518
+#24737 := (or #23521 #22301 #23515)
+#24738 := [def-axiom]: #24737
+#29740 := [unit-resolution #24738 #29739 #29177]: #23515
+#24729 := (or #23512 #23506)
+#24730 := [def-axiom]: #24729
+#29741 := [unit-resolution #24730 #29740]: #23506
+#29742 := (or #23509 #13231 #23503)
+#24725 := (or #23509 #13231 #13472 #23503)
+#24726 := [def-axiom]: #24725
+#29743 := [unit-resolution #24726 #14324]: #29742
+#29744 := [unit-resolution #29743 #29741 #29172]: #23503
+#24699 := (or #23500 #13944)
 #24700 := [def-axiom]: #24699
-#28132 := [unit-resolution #24700 #28108]: #23518
-#24697 := (or #23524 #13801)
-#24698 := [def-axiom]: #24697
-#28133 := [unit-resolution #24698 #28108]: #13801
-#28039 := [hypothesis]: #23372
-#27785 := (+ f307 #13841)
-#27788 := (<= #27785 0::Int)
-#28134 := (or #12313 #27788)
-#28135 := [th-lemma arith triangle-eq]: #28134
-#28136 := [unit-resolution #28135 #28109]: #27788
-#28044 := (not #27788)
-#28045 := (or #22588 #28044 #23377 #13802)
-#28032 := [hypothesis]: #27788
-#24674 := (not #19091)
-#28033 := [hypothesis]: #22593
-#24675 := (or #22588 #24674)
+#29749 := [unit-resolution #24700 #29744]: #13944
+#24675 := (or #23500 #12214)
 #24676 := [def-axiom]: #24675
-#28034 := [unit-resolution #24676 #28033]: #24674
-#27868 := (+ f307 #19089)
-#27869 := (>= #27868 0::Int)
-#27856 := (+ f309 #19076)
-#27857 := (<= #27856 0::Int)
-#28029 := (not #27857)
-#28023 := [hypothesis]: #13801
-#24671 := (not #19078)
-#24672 := (or #22588 #24671)
-#24673 := [def-axiom]: #24672
-#28035 := [unit-resolution #24673 #28033]: #24671
-#28030 := (or #28029 #19078 #13802)
-#28024 := [hypothesis]: #27857
-#28027 := [hypothesis]: #24671
-#28028 := [th-lemma arith farkas -1 1 1 #28027 #28024 #28023]: false
-#28031 := [lemma #28028]: #28030
-#28036 := [unit-resolution #28031 #28035 #28023]: #28029
-#28040 := (or #27857 #27869)
-#24669 := (or #22588 #18740)
-#24670 := [def-axiom]: #24669
-#28037 := [unit-resolution #24670 #28033]: #18740
-#24667 := (or #22588 #18739)
-#24668 := [def-axiom]: #24667
-#28038 := [unit-resolution #24668 #28033]: #18739
-#27882 := (or #23377 #22572 #22573 #27857 #27869)
-#27845 := (+ #18744 #14006)
-#27846 := (<= #27845 0::Int)
-#27847 := (+ ?v0!15 #13537)
-#27848 := (>= #27847 0::Int)
-#27849 := (or #22573 #27848 #27846 #22572)
-#27883 := (or #23377 #27849)
-#27890 := (iff #27883 #27882)
-#27877 := (or #22572 #22573 #27857 #27869)
-#27885 := (or #23377 #27877)
-#27888 := (iff #27885 #27882)
-#27889 := [rewrite]: #27888
-#27886 := (iff #27883 #27885)
-#27880 := (iff #27849 #27877)
-#27874 := (or #22573 #27857 #27869 #22572)
-#27878 := (iff #27874 #27877)
-#27879 := [rewrite]: #27878
-#27875 := (iff #27849 #27874)
-#27872 := (iff #27846 #27869)
-#27862 := (+ #14006 #18744)
-#27865 := (<= #27862 0::Int)
-#27870 := (iff #27865 #27869)
-#27871 := [rewrite]: #27870
-#27866 := (iff #27846 #27865)
-#27863 := (= #27845 #27862)
-#27864 := [rewrite]: #27863
-#27867 := [monotonicity #27864]: #27866
-#27873 := [trans #27867 #27871]: #27872
-#27860 := (iff #27848 #27857)
-#27850 := (+ #13537 ?v0!15)
-#27853 := (>= #27850 0::Int)
-#27858 := (iff #27853 #27857)
-#27859 := [rewrite]: #27858
-#27854 := (iff #27848 #27853)
-#27851 := (= #27847 #27850)
-#27852 := [rewrite]: #27851
-#27855 := [monotonicity #27852]: #27854
-#27861 := [trans #27855 #27859]: #27860
-#27876 := [monotonicity #27861 #27873]: #27875
-#27881 := [trans #27876 #27879]: #27880
-#27887 := [monotonicity #27881]: #27886
-#27891 := [trans #27887 #27889]: #27890
-#27884 := [quant-inst #18738]: #27883
-#27892 := [mp #27884 #27891]: #27882
-#28041 := [unit-resolution #27892 #28039 #28038 #28037]: #28040
-#28042 := [unit-resolution #28041 #28036]: #27869
-#28043 := [th-lemma arith farkas -1 1 1 #28042 #28034 #28032]: false
-#28046 := [lemma #28043]: #28045
-#28137 := [unit-resolution #28046 #28136 #28039 #28133]: #22588
-#24683 := (or #23521 #23515 #22593)
-#24684 := [def-axiom]: #24683
-#28138 := [unit-resolution #24684 #28137 #28132]: #23515
-#24663 := (or #23512 #23504)
+#29747 := [unit-resolution #24676 #29744]: #12214
+#28447 := (or #23418 #22328 #13943 #22579)
+#28422 := [hypothesis]: #22327
+#28434 := (= #3153 #3299)
+#28432 := (= #3299 #3153)
+#28428 := (= #3298 #3152)
+#24559 := (or #23418 #12806)
+#24560 := [def-axiom]: #24559
+#28426 := [unit-resolution #24560 #28423]: #12806
+#28427 := [symm #28426]: #3329
+#28429 := [monotonicity #28427]: #28428
+#28433 := [monotonicity #28429]: #28432
+#28435 := [symm #28433]: #28434
+#28436 := (= f316 #3153)
+#28062 := [hypothesis]: #12214
+#28431 := [symm #28430]: #3328
+#28437 := [trans #28431 #28062]: #28436
+#28438 := [trans #28437 #28435]: #12607
+#28081 := [hypothesis]: #13944
+#24554 := (+ f309 #13556)
+#24556 := (>= #24554 0::Int)
+#28439 := (or #12812 #24556)
+#28440 := [th-lemma arith triangle-eq]: #28439
+#28441 := [unit-resolution #28440 #28426]: #24556
+#28442 := (not #24556)
+#28443 := (or #13559 #13943 #28442)
+#28444 := [th-lemma arith assign-bounds -1 -1]: #28443
+#28445 := [unit-resolution #28444 #28441 #28081]: #13559
+#24433 := (or #22328 #22326 #13558)
+#24434 := [def-axiom]: #24433
+#28446 := [unit-resolution #24434 #28445 #28438 #28422]: false
+#28448 := [lemma #28446]: #28447
+#29589 := [unit-resolution #28448 #29747 #29749]: #29594
+#29595 := [unit-resolution #29589 #28423]: #22328
+#24435 := (or #23352 #22327)
+#24436 := [def-axiom]: #24435
+#29718 := [unit-resolution #24436 #29595]: #23352
+#24569 := (or #23418 #23382)
+#24570 := [def-axiom]: #24569
+#29771 := [unit-resolution #24570 #28423]: #23382
+#29795 := (or #23385 #23379)
+#24715 := (or #23500 #23494)
+#24716 := [def-axiom]: #24715
+#29745 := [unit-resolution #24716 #29744]: #23494
+#24713 := (or #23500 #23336)
+#24714 := [def-axiom]: #24713
+#29746 := [unit-resolution #24714 #29744]: #23336
+#24709 := (or #23500 #15832)
+#24710 := [def-axiom]: #24709
+#29748 := [unit-resolution #24710 #29744]: #15832
+decl f137 :: (-> S20 S20 Int)
+#27080 := (f24 #24797)
+#27605 := (f77 #24797 f309 #27080)
+#27606 := (f137 #27605 #24797)
+#27679 := (>= #27606 0::Int)
+#24695 := (or #23500 #13477)
+#24696 := [def-axiom]: #24695
+#29750 := [unit-resolution #24696 #29744]: #13477
+#27695 := (* -1::Int #27606)
+#27744 := (+ f309 #27695)
+#27745 := (<= #27744 0::Int)
+#27607 := (= f309 #27606)
+#1434 := (f77 #55 #202 #1433)
+#1435 := (pattern #1434)
+#1436 := (f137 #1434 #55)
+#7788 := (= #202 #1436)
+#7792 := (forall (vars (?v0 S20) (?v1 Int)) (:pat #1435) #7788)
+#17069 := (~ #7792 #7792)
+#17067 := (~ #7788 #7788)
+#17068 := [refl]: #17067
+#17070 := [nnf-pos #17068]: #17069
+#1437 := (= #1436 #202)
+#1438 := (forall (vars (?v0 S20) (?v1 Int)) (:pat #1435) #1437)
+#7793 := (iff #1438 #7792)
+#7790 := (iff #1437 #7788)
+#7791 := [rewrite]: #7790
+#7794 := [quant-intro #7791]: #7793
+#7787 := [asserted]: #1438
+#7797 := [mp #7787 #7794]: #7792
+#17071 := [mp~ #7797 #17070]: #7792
+#27087 := (not #7792)
+#27610 := (or #27087 #27607)
+#27611 := [quant-inst #24797 #3135]: #27610
+#28057 := [unit-resolution #27611 #17071]: #27607
+#28073 := (not #27607)
+#29751 := (or #28073 #27745)
+#29752 := [th-lemma arith triangle-eq]: #29751
+#29753 := [unit-resolution #29752 #28057]: #27745
+#29754 := (not #27745)
+#29755 := (or #27679 #22443 #29754)
+#29756 := [th-lemma arith assign-bounds -1 1]: #29755
+#29757 := [unit-resolution #29756 #29753 #29750]: #27679
+#27680 := (not #27679)
+#28098 := (or #23488 #27680 #13943 #22586 #22579 #23341)
+#27951 := (f77 #3042 #27606 f19)
+#27952 := (f122 f298 #27951)
+#27955 := (= f314 #27952)
+#28053 := (= #3153 #27952)
+#28066 := (= #27952 #3153)
+#28060 := (= #27951 #3152)
+#28058 := (= #27606 f309)
+#28059 := [symm #28057]: #28058
+#28061 := [monotonicity #28059]: #28060
+#28067 := [monotonicity #28061]: #28066
+#28068 := [symm #28067]: #28053
+#28069 := (= f314 #3153)
+#28063 := [hypothesis]: #23491
+#24655 := (or #23488 #12242)
+#24656 := [def-axiom]: #24655
+#28064 := [unit-resolution #24656 #28063]: #12242
+#28065 := [symm #28064]: #3167
+#28070 := [trans #28065 #28062]: #28069
+#28071 := [trans #28070 #28068]: #27955
+#27936 := (<= #27606 4294967295::Int)
+#28072 := [hypothesis]: #15832
+#27746 := (>= #27744 0::Int)
+#28074 := (or #28073 #27746)
+#28075 := [th-lemma arith triangle-eq]: #28074
+#28076 := [unit-resolution #28075 #28057]: #27746
+#28077 := (not #27746)
+#28078 := (or #27936 #22586 #28077)
+#28079 := [th-lemma arith assign-bounds -1 1]: #28078
+#28080 := [unit-resolution #28079 #28076 #28072]: #27936
+#27993 := (+ f297 #27695)
+#27994 := (<= #27993 0::Int)
+#28082 := (not #27994)
+#28083 := (or #28082 #13943 #28077)
+#28084 := [th-lemma arith assign-bounds -1 -1]: #28083
+#28085 := [unit-resolution #28084 #28076 #28081]: #28082
+#27958 := (not #27955)
+#27937 := (not #27936)
+#28095 := (or #27937 #27958 #27994)
+#28086 := [hypothesis]: #27679
+#24663 := (or #23488 #23482)
 #24664 := [def-axiom]: #24663
-#28139 := [unit-resolution #24664 #28138]: #23504
-#28052 := (or #23509 #27691 #27974 #27995 #28016)
-#27979 := (+ #27609 #13442)
-#27980 := (>= #27979 0::Int)
-#27987 := (= #27989 f313)
-#27990 := (not #27987)
-#27991 := (or #27990 #27691 #27980 #27974)
-#28053 := (or #23509 #27991)
-#28060 := (iff #28053 #28052)
-#28047 := (or #27691 #27974 #27995 #28016)
-#28055 := (or #23509 #28047)
-#28058 := (iff #28055 #28052)
-#28059 := [rewrite]: #28058
-#28056 := (iff #28053 #28055)
-#28050 := (iff #27991 #28047)
-#27996 := (or #27995 #27691 #28016 #27974)
-#28048 := (iff #27996 #28047)
-#28049 := [rewrite]: #28048
-#27997 := (iff #27991 #27996)
-#28026 := (iff #27980 #28016)
-#28010 := (+ #13442 #27609)
-#28007 := (>= #28010 0::Int)
-#28017 := (iff #28007 #28016)
-#28025 := [rewrite]: #28017
-#28013 := (iff #27980 #28007)
-#28011 := (= #27979 #28010)
-#28012 := [rewrite]: #28011
-#28014 := [monotonicity #28012]: #28013
-#27928 := [trans #28014 #28025]: #28026
-#28008 := (iff #27990 #27995)
-#27993 := (iff #27987 #27992)
-#27994 := [rewrite]: #27993
-#28009 := [monotonicity #27994]: #28008
-#28020 := [monotonicity #28009 #27928]: #27997
-#28051 := [trans #28020 #28049]: #28050
-#28057 := [monotonicity #28051]: #28056
-#28061 := [trans #28057 #28059]: #28060
-#28054 := [quant-inst #27609]: #28053
-#28062 := [mp #28054 #28061]: #28052
-#28141 := [unit-resolution #28062 #28139 #28131]: #28140
-#28142 := [unit-resolution #28141 #28130 #28125 #28116]: false
-#28144 := [lemma #28142]: #28143
-#30139 := [unit-resolution #28144 #30138 #30103 #30102 #30101 #30095]: #23524
-#24707 := (or #23533 #23493 #23527)
-#24708 := [def-axiom]: #24707
-#30140 := [unit-resolution #24708 #30139 #30100]: #23493
-#24655 := (or #23490 #13802)
-#24656 := [def-axiom]: #24655
-#30141 := [unit-resolution #24656 #30140]: #13802
-#30242 := (not #29585)
-#30243 := (or #30241 #28416 #30242 #13801)
-#30244 := [th-lemma arith assign-bounds 1 -1 -1]: #30243
-#30245 := [unit-resolution #30244 #28410 #30141 #30237]: #30241
-#29465 := (>= #29368 0::Int)
-#24733 := (or #23536 #13516)
-#24734 := [def-axiom]: #24733
-#29673 := [unit-resolution #24734 #29672]: #13516
-#29584 := (<= #29583 0::Int)
-#29676 := (or #29675 #29584)
-#29677 := [th-lemma arith triangle-eq]: #29676
-#29678 := [unit-resolution #29677 #29674]: #29584
-#29466 := (not #29465)
-#29679 := [hypothesis]: #29466
-#29680 := [th-lemma arith farkas 1 1 1 #29679 #29678 #29673]: false
-#29681 := [lemma #29680]: #29465
-#30247 := (or #29466 #29476 #29484)
-#29495 := (or #28639 #27163 #29466 #29476 #29484)
-#29461 := (or #29460 #29457 #29455 #29451)
-#29462 := (not #29461)
-#29463 := (+ #29368 #27164)
-#29464 := (>= #29463 0::Int)
-#29467 := (or #29466 #29464 #27163 #29462)
-#29496 := (or #28639 #29467)
-#29503 := (iff #29496 #29495)
-#29490 := (or #27163 #29466 #29476 #29484)
-#29498 := (or #28639 #29490)
-#29501 := (iff #29498 #29495)
-#29502 := [rewrite]: #29501
-#29499 := (iff #29496 #29498)
-#29493 := (iff #29467 #29490)
-#29487 := (or #29466 #29476 #27163 #29484)
-#29491 := (iff #29487 #29490)
-#29492 := [rewrite]: #29491
-#29488 := (iff #29467 #29487)
-#29485 := (iff #29462 #29484)
-#29482 := (iff #29461 #29481)
+#28087 := [unit-resolution #24664 #28063]: #23482
+#27749 := (+ f308 #13805)
+#27750 := (<= #27749 0::Int)
+#28088 := (or #12277 #27750)
+#28089 := [th-lemma arith triangle-eq]: #28088
+#28090 := [unit-resolution #28089 #28064]: #27750
+#27982 := [hypothesis]: #23336
+#24661 := (or #23488 #13765)
+#24662 := [def-axiom]: #24661
+#28091 := [unit-resolution #24662 #28063]: #13765
+#27973 := (not #27750)
+#27988 := (or #22552 #13766 #23341 #27973)
+#27976 := [hypothesis]: #13765
+#27820 := (+ f310 #19040)
+#27821 := (<= #27820 0::Int)
+#27832 := (+ f308 #19053)
+#27833 := (>= #27832 0::Int)
+#27972 := (not #27833)
+#27966 := [hypothesis]: #27750
+#24638 := (not #19055)
+#27977 := [hypothesis]: #22557
+#24639 := (or #22552 #24638)
+#24640 := [def-axiom]: #24639
+#27978 := [unit-resolution #24640 #27977]: #24638
+#27974 := (or #27972 #19055 #27973)
+#27967 := [hypothesis]: #24638
+#27970 := [hypothesis]: #27833
+#27971 := [th-lemma arith farkas -1 1 1 #27970 #27967 #27966]: false
+#27975 := [lemma #27971]: #27974
+#27979 := [unit-resolution #27975 #27978 #27966]: #27972
+#27983 := (or #27821 #27833)
+#24633 := (or #22552 #18704)
+#24634 := [def-axiom]: #24633
+#27980 := [unit-resolution #24634 #27977]: #18704
+#24631 := (or #22552 #18703)
+#24632 := [def-axiom]: #24631
+#27981 := [unit-resolution #24632 #27977]: #18703
+#27846 := (or #23341 #22536 #22537 #27821 #27833)
+#27809 := (+ #18708 #13970)
+#27810 := (<= #27809 0::Int)
+#27811 := (+ ?v0!15 #13501)
+#27812 := (>= #27811 0::Int)
+#27813 := (or #22537 #27812 #27810 #22536)
+#27847 := (or #23341 #27813)
+#27854 := (iff #27847 #27846)
+#27841 := (or #22536 #22537 #27821 #27833)
+#27849 := (or #23341 #27841)
+#27852 := (iff #27849 #27846)
+#27853 := [rewrite]: #27852
+#27850 := (iff #27847 #27849)
+#27844 := (iff #27813 #27841)
+#27838 := (or #22537 #27821 #27833 #22536)
+#27842 := (iff #27838 #27841)
+#27843 := [rewrite]: #27842
+#27839 := (iff #27813 #27838)
+#27836 := (iff #27810 #27833)
+#27826 := (+ #13970 #18708)
+#27829 := (<= #27826 0::Int)
+#27834 := (iff #27829 #27833)
+#27835 := [rewrite]: #27834
+#27830 := (iff #27810 #27829)
+#27827 := (= #27809 #27826)
+#27828 := [rewrite]: #27827
+#27831 := [monotonicity #27828]: #27830
+#27837 := [trans #27831 #27835]: #27836
+#27824 := (iff #27812 #27821)
+#27814 := (+ #13501 ?v0!15)
+#27817 := (>= #27814 0::Int)
+#27822 := (iff #27817 #27821)
+#27823 := [rewrite]: #27822
+#27818 := (iff #27812 #27817)
+#27815 := (= #27811 #27814)
+#27816 := [rewrite]: #27815
+#27819 := [monotonicity #27816]: #27818
+#27825 := [trans #27819 #27823]: #27824
+#27840 := [monotonicity #27825 #27837]: #27839
+#27845 := [trans #27840 #27843]: #27844
+#27851 := [monotonicity #27845]: #27850
+#27855 := [trans #27851 #27853]: #27854
+#27848 := [quant-inst #18702]: #27847
+#27856 := [mp #27848 #27855]: #27846
+#27984 := [unit-resolution #27856 #27982 #27981 #27980]: #27983
+#27985 := [unit-resolution #27984 #27979]: #27821
+#24635 := (not #19042)
+#24636 := (or #22552 #24635)
+#24637 := [def-axiom]: #24636
+#27986 := [unit-resolution #24637 #27977]: #24635
+#27987 := [th-lemma arith farkas -1 1 1 #27986 #27985 #27976]: false
+#27989 := [lemma #27987]: #27988
+#28092 := [unit-resolution #27989 #28091 #27982 #28090]: #22552
+#24647 := (or #23485 #23479 #22557)
+#24648 := [def-axiom]: #24647
+#28093 := [unit-resolution #24648 #28092 #28087]: #23479
+#24627 := (or #23476 #23468)
+#24628 := [def-axiom]: #24627
+#28094 := [unit-resolution #24628 #28093]: #23468
+#28007 := (or #23473 #27680 #27937 #27958 #27994)
+#27942 := (+ #27606 #13406)
+#27943 := (>= #27942 0::Int)
+#27950 := (= #27952 f314)
+#27953 := (not #27950)
+#27954 := (or #27953 #27680 #27943 #27937)
+#28008 := (or #23473 #27954)
+#28015 := (iff #28008 #28007)
+#28002 := (or #27680 #27937 #27958 #27994)
+#28010 := (or #23473 #28002)
+#28013 := (iff #28010 #28007)
+#28014 := [rewrite]: #28013
+#28011 := (iff #28008 #28010)
+#28005 := (iff #27954 #28002)
+#27999 := (or #27958 #27680 #27994 #27937)
+#28003 := (iff #27999 #28002)
+#28004 := [rewrite]: #28003
+#28000 := (iff #27954 #27999)
+#27997 := (iff #27943 #27994)
+#27959 := (+ #13406 #27606)
+#27990 := (>= #27959 0::Int)
+#27995 := (iff #27990 #27994)
+#27996 := [rewrite]: #27995
+#27991 := (iff #27943 #27990)
+#27960 := (= #27942 #27959)
+#27963 := [rewrite]: #27960
+#27992 := [monotonicity #27963]: #27991
+#27998 := [trans #27992 #27996]: #27997
+#27968 := (iff #27953 #27958)
+#27956 := (iff #27950 #27955)
+#27957 := [rewrite]: #27956
+#27969 := [monotonicity #27957]: #27968
+#28001 := [monotonicity #27969 #27998]: #28000
+#28006 := [trans #28001 #28004]: #28005
+#28012 := [monotonicity #28006]: #28011
+#28016 := [trans #28012 #28014]: #28015
+#28009 := [quant-inst #27606]: #28008
+#28017 := [mp #28009 #28016]: #28007
+#28096 := [unit-resolution #28017 #28094 #28086]: #28095
+#28097 := [unit-resolution #28096 #28085 #28080 #28071]: false
+#28099 := [lemma #28097]: #28098
+#29758 := [unit-resolution #28099 #29757 #29749 #29748 #29747 #29746]: #23488
+#24671 := (or #23497 #23457 #23491)
+#24672 := [def-axiom]: #24671
+#29759 := [unit-resolution #24672 #29758 #29745]: #23457
+#24619 := (or #23454 #13766)
+#24620 := [def-axiom]: #24619
+#29760 := [unit-resolution #24620 #29759]: #13766
+#28712 := (or #15864 #13765)
+#15775 := (<= f297 4294967295::Int)
+#15778 := (iff #13405 #15775)
+#15769 := (+ 4294967295::Int #13406)
+#15772 := (>= #15769 0::Int)
+#15776 := (iff #15772 #15775)
+#15777 := [rewrite]: #15776
+#15773 := (iff #13405 #15772)
+#15770 := (= #13407 #15769)
+#15771 := [monotonicity #7606]: #15770
+#15774 := [monotonicity #15771]: #15773
+#15779 := [trans #15774 #15777]: #15778
+#14321 := [not-or-elim #14310]: #13410
+#14323 := [and-elim #14321]: #13405
+#15780 := [mp #14323 #15779]: #15775
+#28513 := [hypothesis]: #13766
+#28701 := [hypothesis]: #18561
+#28702 := [th-lemma arith farkas -1 -1 1 #28701 #28513 #15780]: false
+#28713 := [lemma #28702]: #28712
+#29775 := [unit-resolution #28713 #29760]: #15864
+#24697 := (or #23500 #13480)
+#24698 := [def-axiom]: #24697
+#29674 := [unit-resolution #24698 #29744]: #13480
+#29789 := (or #13620 #13498)
+#29781 := [th-lemma arith farkas 1 1]: #29789
+#29770 := [unit-resolution #29781 #29674]: #13498
+#24493 := (or #23385 #18558 #18561 #23379)
+#24494 := [def-axiom]: #24493
+#29796 := [unit-resolution #24494 #29770 #29775]: #29795
+#29797 := [unit-resolution #29796 #29771]: #23379
+#24483 := (or #23376 #23370)
+#24484 := [def-axiom]: #24483
+#29798 := [unit-resolution #24484 #29797]: #23370
+#24428 := (>= #13583 -1::Int)
+#24479 := (or #23376 #13582)
+#24480 := [def-axiom]: #24479
+#29788 := [unit-resolution #24480 #29797]: #13582
+#29593 := (or #13586 #24428)
+#29608 := [th-lemma arith triangle-eq]: #29593
+#29883 := [unit-resolution #29608 #29788]: #24428
+#29763 := (not #24428)
+#29764 := (or #13514 #29763)
+#29734 := [hypothesis]: #24428
+#29761 := [hypothesis]: #13519
+#29762 := [th-lemma arith farkas -1 1 1 #29761 #29760 #29734]: false
+#29765 := [lemma #29762]: #29764
+#29611 := [unit-resolution #29765 #29883]: #13514
+#24469 := (or #23373 #13519 #23367)
+#24470 := [def-axiom]: #24469
+#29612 := [unit-resolution #24470 #29611 #29798]: #23367
+#24461 := (or #23364 #23358)
+#24462 := [def-axiom]: #24461
+#29610 := [unit-resolution #24462 #29612]: #23358
+#24457 := (or #23361 #23355 #22380)
+#24458 := [def-axiom]: #24457
+#29766 := [unit-resolution #24458 #29610 #29718]: #22380
+#24449 := (or #22375 #24448)
+#24450 := [def-axiom]: #24449
+#29724 := [unit-resolution #24450 #29766]: #24448
+#30349 := (not #24552)
+#29599 := (or #30220 #18907 #30349)
+#29597 := [th-lemma arith assign-bounds -1 -1]: #29599
+#29598 := [unit-resolution #29597 #29724 #29590]: #30220
+#24443 := (or #22375 #18580)
+#24444 := [def-axiom]: #24443
+#29609 := [unit-resolution #24444 #29766]: #18580
+#24441 := (or #22375 #18579)
+#24442 := [def-axiom]: #24441
+#29607 := [unit-resolution #24442 #29766]: #18579
+#29528 := (not #29868)
+#30337 := (not #30332)
+#30348 := (not #30338)
+#24567 := (or #23418 #13672)
+#24568 := [def-axiom]: #24567
+#29677 := [unit-resolution #24568 #28423]: #13672
+#30350 := (or #30348 #18907 #30349 #13671)
+#30343 := [hypothesis]: #13672
+#30344 := [hypothesis]: #24552
+#30345 := [hypothesis]: #24448
+#30346 := [hypothesis]: #30338
+#30347 := [th-lemma arith farkas 1 -1 -1 1 #30346 #30345 #30344 #30343]: false
+#30351 := [lemma #30347]: #30350
+#29874 := [unit-resolution #30351 #29724 #29590 #29677]: #30348
+#30339 := (or #30337 #30338)
+#30340 := [th-lemma arith triangle-eq]: #30339
+#29875 := [unit-resolution #30340 #29874]: #30337
+#29596 := (or #29528 #30332)
+#30115 := (= #18584 #3266)
+#30117 := (= #18583 #3257)
+#30119 := (= ?v0!14 f310)
+#29952 := [hypothesis]: #29868
+#30116 := [symm #29952]: #30119
+#30118 := [monotonicity #30116]: #30117
+#30110 := [monotonicity #30118]: #30115
+#30120 := [symm #30110]: #30332
+#29943 := [hypothesis]: #30337
+#30077 := [unit-resolution #29943 #30120]: false
+#30080 := [lemma #30077]: #29596
+#29873 := [unit-resolution #30080 #29875]: #29528
+#29810 := (+ f310 #18892)
+#29634 := (>= #29810 0::Int)
+#24445 := (not #18894)
+#24446 := (or #22375 #24445)
+#24447 := [def-axiom]: #24446
+#29887 := [unit-resolution #24447 #29766]: #24445
+#29882 := (or #29634 #18894 #29763)
+#29717 := [th-lemma arith assign-bounds 1 1]: #29882
+#29618 := [unit-resolution #29717 #29887 #29883]: #29634
+#30414 := (not #29634)
+#30418 := (or #30414 #29868 #22359 #22360 #29823)
+#30217 := [hypothesis]: #29528
+#30226 := [hypothesis]: #29634
+#29811 := (<= #29810 0::Int)
+#30221 := [hypothesis]: #30220
+#30222 := [hypothesis]: #18580
+#30238 := [hypothesis]: #18579
+#29699 := (or #23341 #22359 #22360 #29811 #29823)
+#29799 := (+ #18584 #13970)
+#29800 := (<= #29799 0::Int)
+#29801 := (+ ?v0!14 #13501)
+#29802 := (>= #29801 0::Int)
+#29803 := (or #22360 #29802 #29800 #22359)
+#29936 := (or #23341 #29803)
+#30174 := (iff #29936 #29699)
+#29831 := (or #22359 #22360 #29811 #29823)
+#29867 := (or #23341 #29831)
+#30176 := (iff #29867 #29699)
+#30172 := [rewrite]: #30176
+#30161 := (iff #29936 #29867)
+#29834 := (iff #29803 #29831)
+#29828 := (or #22360 #29811 #29823 #22359)
+#29832 := (iff #29828 #29831)
+#29833 := [rewrite]: #29832
+#29829 := (iff #29803 #29828)
+#29826 := (iff #29800 #29823)
+#29816 := (+ #13970 #18584)
+#29819 := (<= #29816 0::Int)
+#29824 := (iff #29819 #29823)
+#29825 := [rewrite]: #29824
+#29820 := (iff #29800 #29819)
+#29817 := (= #29799 #29816)
+#29818 := [rewrite]: #29817
+#29821 := [monotonicity #29818]: #29820
+#29827 := [trans #29821 #29825]: #29826
+#29814 := (iff #29802 #29811)
+#29804 := (+ #13501 ?v0!14)
+#29807 := (>= #29804 0::Int)
+#29812 := (iff #29807 #29811)
+#29813 := [rewrite]: #29812
+#29808 := (iff #29802 #29807)
+#29805 := (= #29801 #29804)
+#29806 := [rewrite]: #29805
+#29809 := [monotonicity #29806]: #29808
+#29815 := [trans #29809 #29813]: #29814
+#29830 := [monotonicity #29815 #29827]: #29829
+#29835 := [trans #29830 #29833]: #29834
+#30170 := [monotonicity #29835]: #30161
+#30177 := [trans #30170 #30172]: #30174
+#29870 := [quant-inst #18578]: #29936
+#30173 := [mp #29870 #30177]: #29699
+#30239 := [unit-resolution #30173 #29746 #30238 #30222 #30221]: #29811
+#30413 := (not #29811)
+#30415 := (or #29868 #30413 #30414)
+#30416 := [th-lemma arith triangle-eq]: #30415
+#30417 := [unit-resolution #30416 #30239 #30226 #30217]: false
+#30419 := [lemma #30417]: #30418
+#29716 := [unit-resolution #30419 #29618 #29873 #29607 #29609 #29598]: false
+#29631 := [lemma #29716]: #23418
+#27798 := (f69 #3220 #3257)
+#28223 := (f147 #27798)
+#28228 := (f36 f298 #28223)
+#28229 := (= f37 #28228)
+#28224 := (f222 f298 #28223)
+#28227 := (= f1 #28224)
+#28285 := (or #28227 #28229)
+#28288 := (not #28285)
+#28238 := (f148 #27798)
+#28239 := (= f1 #28238)
+#28240 := (not #28239)
+#28235 := (f38 f298 #28223)
+#28236 := (= f1 #28235)
+#28237 := (not #28236)
+#28279 := (or #28237 #28240)
+#28282 := (not #28279)
+#28118 := (f24 #3257)
+#28243 := (f23 #28118)
+#28261 := (= f25 #28243)
+#28276 := (not #28261)
+#28232 := (f24 #28223)
+#28233 := (f23 #28232)
+#28234 := (= f25 #28233)
+#28294 := (or #28234 #28276 #28282 #28288)
+#28299 := (not #28294)
+#28250 := (f36 f298 #3257)
+#28251 := (= f37 #28250)
+#28248 := (f222 f298 #3257)
+#28249 := (= f1 #28248)
+#28264 := (or #28249 #28251)
+#28267 := (not #28264)
+#28270 := (or #28261 #28267)
+#28273 := (not #28270)
+#28302 := (or #28273 #28299)
+#28305 := (not #28302)
+#28308 := (or #18523 #28305)
+#28311 := (not #28308)
+#28314 := (iff #12548 #28311)
+#30431 := (not #28314)
+#30440 := [hypothesis]: #30431
+#29632 := (or #28805 #28314)
+#28230 := (or #28229 #28227)
+#28231 := (not #28230)
+#28241 := (or #28240 #28237)
+#28242 := (not #28241)
+#28244 := (= #28243 f25)
+#28245 := (not #28244)
+#28246 := (or #28245 #28242 #28234 #28231)
+#28247 := (not #28246)
+#28252 := (or #28251 #28249)
+#28253 := (not #28252)
+#28254 := (or #28244 #28253)
+#28255 := (not #28254)
+#28256 := (or #28255 #28247)
+#28257 := (not #28256)
+#28258 := (or #18523 #28257)
+#28259 := (not #28258)
+#28260 := (iff #12548 #28259)
+#29633 := (or #28805 #28260)
+#29715 := (iff #29633 #29632)
+#30083 := (iff #29632 #29632)
+#30081 := [rewrite]: #30083
+#28315 := (iff #28260 #28314)
+#28312 := (iff #28259 #28311)
+#28309 := (iff #28258 #28308)
+#28306 := (iff #28257 #28305)
+#28303 := (iff #28256 #28302)
+#28300 := (iff #28247 #28299)
+#28297 := (iff #28246 #28294)
+#28291 := (or #28276 #28282 #28234 #28288)
+#28295 := (iff #28291 #28294)
+#28296 := [rewrite]: #28295
+#28292 := (iff #28246 #28291)
+#28289 := (iff #28231 #28288)
+#28286 := (iff #28230 #28285)
+#28287 := [rewrite]: #28286
+#28290 := [monotonicity #28287]: #28289
+#28283 := (iff #28242 #28282)
+#28280 := (iff #28241 #28279)
+#28281 := [rewrite]: #28280
+#28284 := [monotonicity #28281]: #28283
+#28277 := (iff #28245 #28276)
+#28262 := (iff #28244 #28261)
+#28263 := [rewrite]: #28262
+#28278 := [monotonicity #28263]: #28277
+#28293 := [monotonicity #28278 #28284 #28290]: #28292
+#28298 := [trans #28293 #28296]: #28297
+#28301 := [monotonicity #28298]: #28300
+#28274 := (iff #28255 #28273)
+#28271 := (iff #28254 #28270)
+#28268 := (iff #28253 #28267)
+#28265 := (iff #28252 #28264)
+#28266 := [rewrite]: #28265
+#28269 := [monotonicity #28266]: #28268
+#28272 := [monotonicity #28263 #28269]: #28271
+#28275 := [monotonicity #28272]: #28274
+#28304 := [monotonicity #28275 #28301]: #28303
+#28307 := [monotonicity #28304]: #28306
+#28310 := [monotonicity #28307]: #28309
+#28313 := [monotonicity #28310]: #28312
+#28316 := [monotonicity #28313]: #28315
+#30082 := [monotonicity #28316]: #29715
+#30079 := [trans #30082 #30081]: #29715
+#29714 := [quant-inst #3039 #3257]: #29633
+#29698 := [mp #29714 #30079]: #29632
+#30441 := [unit-resolution #29698 #22058 #30440]: false
+#30442 := [lemma #30441]: #28314
+#30489 := (or #30431 #12548)
+#29869 := [hypothesis]: #28294
+#29937 := (= #3047 #28228)
+#29960 := (= #28228 #3047)
+#30333 := (= #28223 #3044)
+#30330 := (= #28223 #27103)
+#28220 := (f77 #24797 f310 #27080)
+#28221 := (f137 #28220 #24797)
+#28154 := (f77 #27103 #28221 #24960)
+#28159 := (f69 #3220 #28154)
+#28219 := (f147 #28159)
+#30328 := (= #28219 #27103)
+#28206 := (= #27103 #28219)
+#28217 := (f148 #28159)
+#28218 := (= f1 #28217)
+#28214 := (f78 #28159)
+#28215 := (= f1 #28214)
+#28216 := (not #28215)
+#28207 := (not #28206)
+#28149 := (f35 f298 #28154)
+#28157 := (= f1 #28149)
+#28158 := (not #28157)
+#28338 := (or #28158 #28207 #28216 #28218)
+#28341 := (not #28338)
+#28211 := (>= #28221 0::Int)
+#24703 := (or #23500 #13998)
+#24704 := [def-axiom]: #24703
+#30247 := [unit-resolution #24704 #29744]: #13998
+#28331 := (* -1::Int #28221)
+#28472 := (+ f310 #28331)
+#28473 := (<= #28472 0::Int)
+#28222 := (= f310 #28221)
+#28155 := (or #27087 #28222)
+#28156 := [quant-inst #24797 #3139]: #28155
+#28478 := [unit-resolution #28156 #17071]: #28222
+#28481 := (not #28222)
+#28482 := (or #28481 #28473)
+#28483 := [th-lemma arith triangle-eq]: #28482
+#28484 := [unit-resolution #28483 #28478]: #28473
+#30252 := (not #28473)
+#30253 := (or #28211 #22582 #30252)
+#30282 := [th-lemma arith assign-bounds 1 1]: #30253
+#30283 := [unit-resolution #30282 #28484 #30247]: #28211
+#28212 := (not #28211)
+#30281 := (or #28212 #28341)
+#28332 := (+ #24962 #28331)
+#28333 := (<= #28332 0::Int)
+#28517 := (not #28333)
+#28474 := (>= #28472 0::Int)
+#28514 := (or #28481 #28474)
+#28515 := [th-lemma arith triangle-eq]: #28514
+#28516 := [unit-resolution #28515 #28478]: #28474
+#28519 := (not #28474)
+#30285 := (or #28517 #28519 #13765)
+#28520 := (or #28517 #28518 #28519 #13765)
+#28521 := [th-lemma arith assign-bounds 1 -1 -1]: #28520
+#30258 := [unit-resolution #28521 #28512]: #30285
+#30286 := [unit-resolution #30258 #28516 #29760]: #28517
+#29476 := (or #27726 #27121 #28212 #28333 #28341)
+#28205 := (or #28207 #28218 #28216 #28158)
+#28208 := (not #28205)
+#28209 := (+ #28221 #27122)
+#28210 := (>= #28209 0::Int)
+#28213 := (or #28212 #28210 #27121 #28208)
+#29477 := (or #27726 #28213)
+#29484 := (iff #29477 #29476)
+#28347 := (or #27121 #28212 #28333 #28341)
+#29479 := (or #27726 #28347)
+#29482 := (iff #29479 #29476)
 #29483 := [rewrite]: #29482
-#29486 := [monotonicity #29483]: #29485
-#29479 := (iff #29464 #29476)
-#29468 := (+ #27164 #29368)
-#29471 := (>= #29468 0::Int)
-#29477 := (iff #29471 #29476)
-#29478 := [rewrite]: #29477
-#29472 := (iff #29464 #29471)
-#29469 := (= #29463 #29468)
-#29470 := [rewrite]: #29469
-#29473 := [monotonicity #29470]: #29472
-#29480 := [trans #29473 #29478]: #29479
-#29489 := [monotonicity #29480 #29486]: #29488
-#29494 := [trans #29489 #29492]: #29493
-#29500 := [monotonicity #29494]: #29499
-#29504 := [trans #29500 #29502]: #29503
-#29497 := [quant-inst #3039 #3043 #24996 #24998 #29368]: #29496
-#29505 := [mp #29497 #29504]: #29495
-#30248 := [unit-resolution #29505 #21024 #28873]: #30247
-#30249 := [unit-resolution #30248 #29681 #30245]: #29484
-#29513 := (or #29481 #29459)
-#29514 := [def-axiom]: #29513
-#30250 := [unit-resolution #29514 #30249]: #29459
-#30281 := [symm #30250]: #30280
-#30278 := (= #28494 #29458)
-#30276 := (= #27834 #29452)
-#30274 := (= #29452 #27834)
-#30272 := (= #29431 #3257)
-#28088 := (f127 #3257)
-#28199 := (f54 #24996 #28088)
-#30266 := (= #28199 #3257)
-#28200 := (= #3257 #28199)
-#28205 := (f59 #3257 #24996)
-#28206 := (= f1 #28205)
-#30252 := (= #3258 #28205)
-#29418 := (= #28205 #3258)
-#29419 := [monotonicity #28386]: #29418
-#30253 := [symm #29419]: #30252
-#28203 := (= #24996 #28202)
-#28182 := (* f309 #27068)
-#29340 := (+ #27070 #28182)
-#29341 := (f54 #24996 #29340)
-#29371 := (f24 #29341)
-#29443 := (= #29371 #28202)
-#29439 := (= #28202 #29371)
-#29437 := (= #3257 #29341)
-#29336 := (f77 #24833 f309 #24996)
-#29342 := (= #29336 #29341)
-#29343 := (not #29342)
-#29337 := (f149 #29336 #24833)
-#29338 := (= f1 #29337)
-#29339 := (not #29338)
-#29346 := (or #29339 #29343)
-#29349 := (not #29346)
-#29352 := (or #27721 #29349)
-#29344 := (or #29343 #29339)
-#29345 := (not #29344)
-#29353 := (or #27721 #29345)
-#29355 := (iff #29353 #29352)
-#29357 := (iff #29352 #29352)
-#29358 := [rewrite]: #29357
-#29350 := (iff #29345 #29349)
-#29347 := (iff #29344 #29346)
-#29348 := [rewrite]: #29347
-#29351 := [monotonicity #29348]: #29350
-#29356 := [monotonicity #29351]: #29355
-#29359 := [trans #29356 #29358]: #29355
-#29354 := [quant-inst #24833 #3139 #24996]: #29353
-#29360 := [mp #29354 #29359]: #29352
-#29429 := [unit-resolution #29360 #21240]: #29349
-#29363 := (or #29346 #29342)
-#29364 := [def-axiom]: #29363
-#29430 := [unit-resolution #29364 #29429]: #29342
-#29435 := (= #3257 #29336)
-#29433 := (= #29336 #3257)
-#29434 := [monotonicity #27142 #28386]: #29433
-#29436 := [symm #29434]: #29435
-#29438 := [trans #29436 #29430]: #29437
-#29440 := [monotonicity #29438]: #29439
-#29444 := [symm #29440]: #29443
-#29374 := (= #24996 #29371)
-#29379 := (or #25064 #29374)
-#29380 := [quant-inst #24996 #29340]: #29379
-#29428 := [unit-resolution #29380 #23312]: #29374
-#29445 := [trans #29428 #29444]: #28203
-#29320 := (not #28203)
-#28280 := (iff #28203 #28206)
-#29315 := (or #26210 #28280)
-#29316 := [quant-inst #3257 #24996]: #29315
-#29416 := [unit-resolution #29316 #23299]: #28280
-#28198 := (not #28206)
-#29424 := (iff #18556 #28198)
-#29422 := (iff #12575 #28206)
-#29420 := (iff #28206 #12575)
-#29421 := [monotonicity #29419]: #29420
-#29423 := [symm #29421]: #29422
-#29425 := [monotonicity #29423]: #29424
-#29417 := [hypothesis]: #18556
-#29426 := [mp #29417 #29425]: #28198
-#29317 := (not #28280)
-#29321 := (or #29317 #29320 #28206)
-#29322 := [def-axiom]: #29321
-#29427 := [unit-resolution #29322 #29426 #29416]: #29320
-#29446 := [unit-resolution #29427 #29445]: false
-#29447 := [lemma #29446]: #12575
-#30254 := [trans #29447 #30253]: #28206
-#28201 := (or #28200 #28198)
-#29376 := (or #26194 #28200 #28198)
-#29388 := (or #26194 #28201)
-#29387 := (iff #29388 #29376)
-#29390 := [rewrite]: #29387
-#29389 := [quant-inst #3257 #24996]: #29388
-#29391 := [mp #29389 #29390]: #29376
-#30255 := [unit-resolution #29391 #18284]: #28201
-#30256 := [unit-resolution #30255 #30254]: #28200
-#30267 := [symm #30256]: #30266
-#30270 := (= #29431 #28199)
-#29648 := (* #27068 #29368)
-#29651 := (+ #27318 #29648)
-#29654 := (f54 #24996 #29651)
-#30264 := (= #29654 #28199)
-#30258 := (= #29651 #28088)
-#30229 := (= #28088 #29651)
-#30230 := (* -1::Int #29651)
-#30231 := (+ #28088 #30230)
-#30232 := (<= #30231 0::Int)
-#29206 := (* -1::Int #27070)
-#29207 := (+ #24880 #29206)
-#29209 := (>= #29207 0::Int)
-#29205 := (= #24880 #27070)
-#30031 := (= #3043 #27070)
-#29986 := [symm #27275]: #30031
-#29987 := [trans #28885 #29986]: #29205
-#30032 := (not #29205)
-#30000 := (or #30032 #29209)
-#29997 := [th-lemma arith triangle-eq]: #30000
-#29984 := [unit-resolution #29997 #29987]: #29209
-#29700 := (* -1::Int #27318)
-#29701 := (+ #24880 #29700)
-#29702 := (<= #29701 0::Int)
-#29699 := (= #24880 #27318)
-#29989 := [symm #28883]: #29699
-#29990 := (not #29699)
-#29991 := (or #29990 #29702)
-#29992 := [th-lemma arith triangle-eq]: #29991
-#29993 := [unit-resolution #29992 #29989]: #29702
-#29377 := (f127 #29341)
-#29381 := (* -1::Int #29377)
-#29587 := (+ #28088 #29381)
-#29588 := (<= #29587 0::Int)
-#29586 := (= #28088 #29377)
-#30043 := (= #29377 #28088)
-#30035 := (= #29341 #3257)
-#30026 := (= #29341 #29336)
-#30034 := [symm #29430]: #30026
-#30042 := [trans #30034 #29434]: #30035
-#30041 := [monotonicity #30042]: #30043
-#30033 := [symm #30041]: #29586
-#30044 := (not #29586)
-#30045 := (or #30044 #29588)
-#30046 := [th-lemma arith triangle-eq]: #30045
-#30049 := [unit-resolution #30046 #30033]: #29588
-#29382 := (+ #28182 #29381)
-#29383 := (+ #27070 #29382)
-#29571 := (>= #29383 0::Int)
-#29384 := (= #29383 0::Int)
-#29559 := (or #25070 #29384)
-#29378 := (= #29340 #29377)
-#29560 := (or #25070 #29378)
-#29564 := (iff #29560 #29559)
-#29566 := (iff #29559 #29559)
-#29567 := [rewrite]: #29566
-#29385 := (iff #29378 #29384)
-#29386 := [rewrite]: #29385
-#29565 := [monotonicity #29386]: #29564
-#29568 := [trans #29565 #29567]: #29564
-#29563 := [quant-inst #24996 #29340]: #29560
-#29569 := [mp #29563 #29568]: #29559
-#30050 := [unit-resolution #29569 #23306]: #29384
-#30055 := (not #29384)
-#30058 := (or #30055 #29571)
-#30057 := [th-lemma arith triangle-eq]: #30058
-#30059 := [unit-resolution #30057 #30050]: #29571
-#29212 := (>= #27068 1::Int)
-#29210 := (= #27068 1::Int)
-#2998 := (f150 f19)
-#2999 := (= #2998 1::Int)
-#12057 := [asserted]: #2999
-#30060 := (= #27068 #2998)
-#30080 := [monotonicity #28386]: #30060
-#30081 := [trans #30080 #12057]: #29210
-#30082 := (not #29210)
-#30098 := (or #30082 #29212)
-#30099 := [th-lemma arith triangle-eq]: #30098
-#30056 := [unit-resolution #30099 #30081]: #29212
-#29211 := (<= #27068 1::Int)
-#30145 := (or #30082 #29211)
-#30146 := [th-lemma arith triangle-eq]: #30145
-#30147 := [unit-resolution #30146 #30081]: #29211
-#30028 := (not #29584)
-#30027 := (not #29702)
-#29999 := (not #29211)
-#29754 := (not #29212)
-#29998 := (not #29209)
-#29995 := (not #29571)
-#29994 := (not #29588)
-#30029 := (or #30232 #29994 #29995 #29998 #29754 #29999 #29754 #29999 #30027 #30028)
-#30030 := [th-lemma arith assign-bounds -1 1 1 -1 -1 1 1 -1 -1]: #30029
-#30025 := [unit-resolution #30030 #30147 #30056 #30059 #29678 #30049 #29993 #29984]: #30232
-#30233 := (>= #30231 0::Int)
-#29208 := (<= #29207 0::Int)
-#30152 := (or #30032 #29208)
-#30153 := [th-lemma arith triangle-eq]: #30152
-#30154 := [unit-resolution #30153 #29987]: #29208
-#29703 := (>= #29701 0::Int)
-#30155 := (or #29990 #29703)
-#30156 := [th-lemma arith triangle-eq]: #30155
-#30157 := [unit-resolution #30156 #29989]: #29703
-#29589 := (>= #29587 0::Int)
-#30150 := (or #30044 #29589)
-#30151 := [th-lemma arith triangle-eq]: #30150
-#30148 := [unit-resolution #30151 #30033]: #29589
-#29570 := (<= #29383 0::Int)
-#30149 := (or #30055 #29570)
-#30158 := [th-lemma arith triangle-eq]: #30149
-#30159 := [unit-resolution #30158 #30050]: #29570
-#30162 := (not #29703)
-#30161 := (not #29208)
-#29784 := (not #29570)
-#30160 := (not #29589)
-#30163 := (or #30233 #30160 #29784 #30161 #29754 #29999 #29754 #29999 #30162 #30242)
-#30164 := [th-lemma arith assign-bounds -1 1 1 -1 -1 1 1 -1 -1]: #30163
-#30165 := [unit-resolution #30164 #30147 #30056 #30159 #30237 #30148 #30157 #30154]: #30233
-#30169 := (not #30233)
-#30168 := (not #30232)
-#30178 := (or #30229 #30168 #30169)
-#30179 := [th-lemma arith triangle-eq]: #30178
-#30180 := [unit-resolution #30179 #30165 #30025]: #30229
-#30177 := [symm #30180]: #30258
-#30186 := [monotonicity #30177]: #30264
-#30268 := (= #29431 #29654)
-#29637 := (f77 #26182 #29368 #24996)
-#29657 := (= #29637 #29654)
-#29592 := (not #29657)
-#29638 := (f149 #29637 #26182)
-#29639 := (= f1 #29638)
-#29640 := (not #29639)
-#29597 := (or #29640 #29592)
-#29660 := (not #29597)
-#29684 := (or #27721 #29660)
-#29641 := (* #29368 #27068)
-#29642 := (+ #27318 #29641)
-#29643 := (f54 #24996 #29642)
-#29644 := (= #29637 #29643)
-#29645 := (not #29644)
-#29646 := (or #29645 #29640)
-#29647 := (not #29646)
-#29685 := (or #27721 #29647)
-#29687 := (iff #29685 #29684)
-#29689 := (iff #29684 #29684)
-#29690 := [rewrite]: #29689
-#29682 := (iff #29647 #29660)
-#29661 := (iff #29646 #29597)
-#29594 := (or #29592 #29640)
-#29598 := (iff #29594 #29597)
-#29599 := [rewrite]: #29598
-#29595 := (iff #29646 #29594)
-#29593 := (iff #29645 #29592)
-#29658 := (iff #29644 #29657)
-#29655 := (= #29643 #29654)
-#29652 := (= #29642 #29651)
-#29649 := (= #29641 #29648)
-#29650 := [rewrite]: #29649
-#29653 := [monotonicity #29650]: #29652
-#29656 := [monotonicity #29653]: #29655
-#29659 := [monotonicity #29656]: #29658
-#29591 := [monotonicity #29659]: #29593
-#29596 := [monotonicity #29591]: #29595
-#29662 := [trans #29596 #29599]: #29661
-#29683 := [monotonicity #29662]: #29682
-#29688 := [monotonicity #29683]: #29687
-#29691 := [trans #29688 #29690]: #29687
-#29686 := [quant-inst #26182 #29368 #24996]: #29685
-#29692 := [mp #29686 #29691]: #29684
-#30260 := [unit-resolution #29692 #21240]: #29660
-#29695 := (or #29597 #29657)
-#29696 := [def-axiom]: #29695
-#30261 := [unit-resolution #29696 #30260]: #29657
-#30262 := (= #29431 #29637)
-#30263 := [monotonicity #28791]: #30262
-#30269 := [trans #30263 #30261]: #30268
-#30187 := [trans #30269 #30186]: #30270
-#30188 := [trans #30187 #30267]: #30272
-#30189 := [monotonicity #30188]: #30274
-#30190 := [symm #30189]: #30276
-#30185 := [monotonicity #30190]: #30278
-#30191 := [trans #30185 #30281]: #30282
-#30192 := [trans #30191 #28789]: #30284
-#30194 := [monotonicity #30192]: #30193
-#30200 := [symm #30194]: #30199
-#30198 := [trans #14366 #30200]: #28498
-#29947 := (not #28498)
-#29948 := (or #28554 #29947)
-#29934 := [def-axiom]: #29948
-#30201 := [unit-resolution #29934 #30198]: #28554
-#30210 := (= #25501 #28512)
-#30212 := (= #28512 #25501)
-#30205 := (= #28202 f19)
-#30203 := (= #28202 #24996)
-#29392 := (or #29317 #28203 #28198)
-#29393 := [def-axiom]: #29392
-#30202 := [unit-resolution #29393 #30254 #29416]: #28203
-#30204 := [symm #30202]: #30203
-#30211 := [trans #30204 #28386]: #30205
-#30213 := [monotonicity #30211]: #30212
-#30216 := [symm #30213]: #30210
-#30217 := [trans #28841 #30216]: #28530
-#29890 := (not #28503)
-#30239 := (iff #12118 #29890)
-#30251 := (iff #12115 #28503)
-#30224 := (iff #28503 #12115)
-#30222 := (= #28502 #3053)
-#30220 := (= #28501 #3040)
-#30218 := (= #28501 #25117)
-#30219 := [monotonicity #30192]: #30218
-#30221 := [trans #30219 #28851]: #30220
-#30223 := [monotonicity #30221]: #30222
-#30288 := [monotonicity #30223]: #30224
-#30246 := [symm #30288]: #30251
-#30240 := [monotonicity #30246]: #30239
-#30238 := [mp #14369 #30240]: #29890
-#29517 := (f77 #27223 #29368 #24996)
-#29518 := (f69 #3220 #29517)
-#29519 := (f147 #29518)
-#29520 := (= f1 #29519)
-#29552 := (not #29520)
-#30315 := (iff #29552 #28509)
-#30313 := (iff #29520 #28508)
-#30311 := (iff #28508 #29520)
-#30309 := (= #28507 #29519)
-#30307 := (= #27834 #29518)
-#30305 := (= #29518 #27834)
-#30303 := (= #29517 #3257)
-#30301 := (= #29368 f309)
-#30302 := [symm #29674]: #30301
-#30304 := [monotonicity #28393 #30302 #28386]: #30303
-#30306 := [monotonicity #30304]: #30305
-#30308 := [symm #30306]: #30307
-#30310 := [monotonicity #30308]: #30309
-#30312 := [monotonicity #30310]: #30311
-#30314 := [symm #30312]: #30313
-#30316 := [monotonicity #30314]: #30315
-#29521 := (f35 f297 #29517)
-#29522 := (= f1 #29521)
-#29523 := (not #29522)
-#29527 := (or #29520 #29523)
-#29530 := (not #29527)
-#30297 := (or #29466 #29476 #29530)
-#29541 := (or #27254 #24846 #27235 #27238 #29466 #29476 #29530)
-#29524 := (or #29523 #29520)
-#29525 := (not #29524)
-#29526 := (or #27238 #29466 #29464 #24846 #27235 #29525)
-#29542 := (or #27254 #29526)
-#29549 := (iff #29542 #29541)
-#29536 := (or #24846 #27235 #27238 #29466 #29476 #29530)
-#29544 := (or #27254 #29536)
-#29547 := (iff #29544 #29541)
-#29548 := [rewrite]: #29547
-#29545 := (iff #29542 #29544)
-#29539 := (iff #29526 #29536)
-#29533 := (or #27238 #29466 #29476 #24846 #27235 #29530)
-#29537 := (iff #29533 #29536)
-#29538 := [rewrite]: #29537
-#29534 := (iff #29526 #29533)
-#29531 := (iff #29525 #29530)
-#29528 := (iff #29524 #29527)
-#29529 := [rewrite]: #29528
-#29532 := [monotonicity #29529]: #29531
-#29535 := [monotonicity #29480 #29532]: #29534
-#29540 := [trans #29535 #29538]: #29539
-#29546 := [monotonicity #29540]: #29545
-#29550 := [trans #29546 #29548]: #29549
-#29543 := [quant-inst #3039 #3043 #26182 #24998 #29368 #24996]: #29542
-#29551 := [mp #29543 #29550]: #29541
-#30298 := [unit-resolution #29551 #21684 #14351 #28797 #28426]: #30297
-#30299 := [unit-resolution #30298 #29681 #30245]: #29530
-#29553 := (or #29527 #29552)
-#29554 := [def-axiom]: #29553
-#30300 := [unit-resolution #29554 #30299]: #29552
-#30317 := [mp #30300 #30316]: #28509
-#29772 := (or #28548 #28508)
-#29773 := [def-axiom]: #29772
-#30318 := [unit-resolution #29773 #30317]: #28548
-#29907 := (or #28568 #28503 #28545 #28551 #28557)
-#29965 := [def-axiom]: #29907
-#30319 := [unit-resolution #29965 #30318 #30238 #30217 #30201 #30167]: false
-#30320 := [lemma #30319]: #28568
-#29805 := (or #28571 #28563)
-#29738 := [def-axiom]: #29805
-#30175 := [unit-resolution #29738 #30320]: #28571
-#28432 := (or #12578 #13656 #27235 #13801)
-#28375 := [hypothesis]: #13516
-#28210 := (f77 #27086 f309 #27607)
-#28211 := (f136 #28210 #27086)
-#28242 := (* -1::Int #28211)
-#28370 := (+ f309 #28242)
-#28371 := (<= #28370 0::Int)
-#28212 := (= f309 #28211)
-#28215 := (or #27129 #28212)
-#28216 := [quant-inst #27086 #3139]: #28215
-#28376 := [unit-resolution #28216 #17107]: #28212
-#28379 := (not #28212)
-#28380 := (or #28379 #28371)
-#28381 := [th-lemma arith triangle-eq]: #28380
-#28382 := [unit-resolution #28381 #28376]: #28371
-#28233 := (>= #28211 0::Int)
-#28234 := (not #28233)
-#28285 := (f77 #27223 #28211 #24996)
-#28289 := (f35 f297 #28285)
-#28290 := (= f1 #28289)
-#28291 := (not #28290)
-#28286 := (f69 #3220 #28285)
-#28287 := (f147 #28286)
-#28288 := (= f1 #28287)
-#28295 := (or #28288 #28291)
-#28402 := (iff #18559 #28291)
-#28400 := (iff #12578 #28290)
-#28398 := (iff #28290 #12578)
-#28396 := (= #28289 #3260)
-#28394 := (= #28285 #3257)
-#28387 := (= #28211 f309)
-#28388 := [symm #28376]: #28387
-#28395 := [monotonicity #28393 #28388 #28386]: #28394
-#28397 := [monotonicity #28395]: #28396
-#28399 := [monotonicity #28397]: #28398
-#28401 := [symm #28399]: #28400
-#28403 := [monotonicity #28401]: #28402
-#28383 := [hypothesis]: #18559
-#28404 := [mp #28383 #28403]: #28291
-#28323 := (or #28295 #28290)
-#28324 := [def-axiom]: #28323
-#28405 := [unit-resolution #28324 #28404]: #28295
-#28243 := (+ #24998 #28242)
-#28244 := (<= #28243 0::Int)
-#28415 := (not #28244)
-#28411 := [hypothesis]: #13802
-#28372 := (>= #28370 0::Int)
-#28412 := (or #28379 #28372)
-#28413 := [th-lemma arith triangle-eq]: #28412
-#28414 := [unit-resolution #28413 #28376]: #28372
-#28417 := (not #28372)
-#28418 := (or #28415 #28416 #28417 #13801)
-#28419 := [th-lemma arith assign-bounds 1 -1 -1]: #28418
-#28420 := [unit-resolution #28419 #28414 #28411 #28410]: #28415
-#28298 := (not #28295)
-#28428 := (or #28234 #28244 #28298)
-#28309 := (or #27254 #24846 #27235 #27238 #28234 #28244 #28298)
-#28292 := (or #28291 #28288)
-#28293 := (not #28292)
-#28231 := (+ #28211 #27164)
-#28232 := (>= #28231 0::Int)
-#28294 := (or #27238 #28234 #28232 #24846 #27235 #28293)
-#28310 := (or #27254 #28294)
-#28317 := (iff #28310 #28309)
-#28304 := (or #24846 #27235 #27238 #28234 #28244 #28298)
-#28312 := (or #27254 #28304)
-#28315 := (iff #28312 #28309)
-#28316 := [rewrite]: #28315
-#28313 := (iff #28310 #28312)
-#28307 := (iff #28294 #28304)
-#28301 := (or #27238 #28234 #28244 #24846 #27235 #28298)
-#28305 := (iff #28301 #28304)
-#28306 := [rewrite]: #28305
-#28302 := (iff #28294 #28301)
-#28299 := (iff #28293 #28298)
-#28296 := (iff #28292 #28295)
-#28297 := [rewrite]: #28296
-#28300 := [monotonicity #28297]: #28299
-#28247 := (iff #28232 #28244)
-#28236 := (+ #27164 #28211)
-#28239 := (>= #28236 0::Int)
-#28245 := (iff #28239 #28244)
-#28246 := [rewrite]: #28245
-#28240 := (iff #28232 #28239)
-#28237 := (= #28231 #28236)
-#28238 := [rewrite]: #28237
-#28241 := [monotonicity #28238]: #28240
-#28248 := [trans #28241 #28246]: #28247
-#28303 := [monotonicity #28248 #28300]: #28302
-#28308 := [trans #28303 #28306]: #28307
-#28314 := [monotonicity #28308]: #28313
-#28318 := [trans #28314 #28316]: #28317
-#28311 := [quant-inst #3039 #3043 #26182 #24998 #28211 #24996]: #28310
-#28319 := [mp #28311 #28318]: #28309
-#28429 := [unit-resolution #28319 #21684 #14351 #28427 #28426]: #28428
-#28430 := [unit-resolution #28429 #28420 #28405]: #28234
-#28431 := [th-lemma arith farkas 1 1 1 #28430 #28382 #28375]: false
-#28433 := [lemma #28431]: #28432
-#30142 := [unit-resolution #28433 #30141 #28797 #29673]: #12578
-#30170 := (or #28580 #18559 #28574)
-#30171 := [def-axiom]: #30170
-#30321 := [unit-resolution #30171 #30142 #30175]: #28580
-#29900 := (or #29899 #12584 #28577)
-#29898 := [def-axiom]: #29900
-#30323 := [unit-resolution #29898 #30321]: #30322
-#30324 := [unit-resolution #30323 #30215]: #12584
-#30424 := (+ f309 #18928)
-#30620 := (>= #30424 0::Int)
-#30702 := (not #30620)
-#30595 := (= f309 ?v0!14)
-#30648 := (not #30595)
-#30651 := [hypothesis]: #23457
-#24603 := (or #23454 #13708)
+#29480 := (iff #29477 #29479)
+#28350 := (iff #28213 #28347)
+#28344 := (or #28212 #28333 #27121 #28341)
+#28348 := (iff #28344 #28347)
+#28349 := [rewrite]: #28348
+#28345 := (iff #28213 #28344)
+#28342 := (iff #28208 #28341)
+#28339 := (iff #28205 #28338)
+#28340 := [rewrite]: #28339
+#28343 := [monotonicity #28340]: #28342
+#28336 := (iff #28210 #28333)
+#28225 := (+ #27122 #28221)
+#28328 := (>= #28225 0::Int)
+#28334 := (iff #28328 #28333)
+#28335 := [rewrite]: #28334
+#28329 := (iff #28210 #28328)
+#28226 := (= #28209 #28225)
+#28327 := [rewrite]: #28226
+#28330 := [monotonicity #28327]: #28329
+#28337 := [trans #28330 #28335]: #28336
+#28346 := [monotonicity #28337 #28343]: #28345
+#28351 := [trans #28346 #28349]: #28350
+#29481 := [monotonicity #28351]: #29480
+#29485 := [trans #29481 #29483]: #29484
+#29478 := [quant-inst #3039 #3043 #24960 #24962 #28221]: #29477
+#29486 := [mp #29478 #29485]: #29476
+#30287 := [unit-resolution #29486 #20988 #30286 #28914]: #30281
+#30288 := [unit-resolution #30287 #30283]: #28341
+#29489 := (or #28338 #28206)
+#29490 := [def-axiom]: #29489
+#30257 := [unit-resolution #29490 #30288]: #28206
+#30329 := [symm #30257]: #30328
+#30326 := (= #28223 #28219)
+#30324 := (= #27798 #28159)
+#29979 := (= #28159 #27798)
+#29970 := (= #28154 #3257)
+#27807 := (f128 #3257)
+#28101 := (f54 #24960 #27807)
+#30319 := (= #28101 #3257)
+#28102 := (= #3257 #28101)
+#28047 := (f59 #3257 #24960)
+#28042 := (= f1 #28047)
+#30290 := (= #3258 #28047)
+#29430 := (= #28047 #3258)
+#29431 := [monotonicity #28488]: #29430
+#30291 := [symm #29431]: #30290
+#28119 := (= #24960 #28118)
+#28192 := (f81 f310 #27032)
+#28193 := (+ #27034 #28192)
+#28194 := (f54 #24960 #28193)
+#28449 := (f24 #28194)
+#29455 := (= #28449 #28118)
+#29451 := (= #28118 #28449)
+#29449 := (= #3257 #28194)
+#28188 := (f77 #24797 f310 #24960)
+#28195 := (= #28188 #28194)
+#28196 := (not #28195)
+#28189 := (f150 #28188 #24797)
+#28190 := (= f1 #28189)
+#28191 := (not #28190)
+#28199 := (or #28191 #28196)
+#28202 := (not #28199)
+#29398 := (or #27451 #28202)
+#28197 := (or #28196 #28191)
+#28198 := (not #28197)
+#29399 := (or #27451 #28198)
+#29401 := (iff #29399 #29398)
+#29403 := (iff #29398 #29398)
+#29404 := [rewrite]: #29403
+#28203 := (iff #28198 #28202)
+#28200 := (iff #28197 #28199)
+#28201 := [rewrite]: #28200
+#28204 := [monotonicity #28201]: #28203
+#29402 := [monotonicity #28204]: #29401
+#29405 := [trans #29402 #29404]: #29401
+#29400 := [quant-inst #24797 #3139 #24960]: #29399
+#29406 := [mp #29400 #29405]: #29398
+#29441 := [unit-resolution #29406 #21204]: #28202
+#29409 := (or #28199 #28195)
+#29410 := [def-axiom]: #29409
+#29442 := [unit-resolution #29410 #29441]: #28195
+#29447 := (= #3257 #28188)
+#29445 := (= #28188 #3257)
+#29446 := [monotonicity #28946 #28488]: #29445
+#29448 := [symm #29446]: #29447
+#29450 := [trans #29448 #29442]: #29449
+#29452 := [monotonicity #29450]: #29451
+#29456 := [symm #29452]: #29455
+#28450 := (= #24960 #28449)
+#29417 := (or #25028 #28450)
+#29418 := [quant-inst #24960 #28193]: #29417
+#29440 := [unit-resolution #29418 #23276]: #28450
+#29457 := [trans #29440 #29456]: #28119
+#29378 := (not #28119)
+#28121 := (iff #28042 #28119)
+#29368 := (or #26174 #28121)
+#28120 := (iff #28119 #28042)
+#29369 := (or #26174 #28120)
+#29371 := (iff #29369 #29368)
+#29373 := (iff #29368 #29368)
+#29374 := [rewrite]: #29373
+#28122 := (iff #28120 #28121)
+#28123 := [rewrite]: #28122
+#29372 := [monotonicity #28123]: #29371
+#29375 := [trans #29372 #29374]: #29371
+#29370 := [quant-inst #3257 #24960]: #29369
+#29376 := [mp #29370 #29375]: #29368
+#29428 := [unit-resolution #29376 #23263]: #28121
+#28100 := (not #28042)
+#29436 := (iff #18520 #28100)
+#29434 := (iff #12539 #28042)
+#29432 := (iff #28042 #12539)
+#29433 := [monotonicity #29431]: #29432
+#29435 := [symm #29433]: #29434
+#29437 := [monotonicity #29435]: #29436
+#29429 := [hypothesis]: #18520
+#29438 := [mp #29429 #29437]: #28100
+#29377 := (not #28121)
+#29379 := (or #29377 #28042 #29378)
+#29380 := [def-axiom]: #29379
+#29439 := [unit-resolution #29380 #29438 #29428]: #29378
+#29458 := [unit-resolution #29439 #29457]: false
+#29459 := [lemma #29458]: #12539
+#30299 := [trans #29459 #30291]: #28042
+#28104 := (or #28100 #28102)
+#29381 := (or #26158 #28100 #28102)
+#28103 := (or #28102 #28100)
+#29382 := (or #26158 #28103)
+#29424 := (iff #29382 #29381)
+#29413 := (or #26158 #28104)
+#29422 := (iff #29413 #29381)
+#29423 := [rewrite]: #29422
+#29420 := (iff #29382 #29413)
+#28105 := (iff #28103 #28104)
+#28106 := [rewrite]: #28105
+#29421 := [monotonicity #28106]: #29420
+#29425 := [trans #29421 #29423]: #29424
+#29419 := [quant-inst #3257 #24960]: #29382
+#29426 := [mp #29419 #29425]: #29381
+#30300 := [unit-resolution #29426 #18248]: #28104
+#30303 := [unit-resolution #30300 #30299]: #28102
+#30298 := [symm #30303]: #30319
+#30322 := (= #28154 #28101)
+#29661 := (f81 #28221 #27032)
+#29662 := (+ #27307 #29661)
+#29663 := (f54 #24960 #29662)
+#30312 := (= #29663 #28101)
+#30302 := (= #29662 #27807)
+#30237 := (= #27807 #29662)
+#30243 := (* -1::Int #29662)
+#30244 := (+ #27807 #30243)
+#30190 := (<= #30244 0::Int)
+#29586 := (* -1::Int #29661)
+#29526 := (+ #28192 #29586)
+#29527 := (<= #29526 0::Int)
+#29585 := (= #28192 #29661)
+#30240 := (= #29661 #28192)
+#28489 := (= #28221 f310)
+#28490 := [symm #28478]: #28489
+#30230 := [monotonicity #28490]: #30240
+#30355 := [symm #30230]: #29585
+#30289 := (not #29585)
+#30284 := (or #30289 #29527)
+#30363 := [th-lemma arith triangle-eq]: #30284
+#30364 := [unit-resolution #30363 #30355]: #29527
+#28451 := (f128 #28194)
+#28455 := (* -1::Int #28451)
+#29517 := (+ #27807 #28455)
+#29518 := (<= #29517 0::Int)
+#29516 := (= #27807 #28451)
+#30369 := (= #28451 #27807)
+#30367 := (= #28194 #3257)
+#30365 := (= #28194 #28188)
+#30366 := [symm #29442]: #30365
+#30368 := [trans #30366 #29446]: #30367
+#30370 := [monotonicity #30368]: #30369
+#30371 := [symm #30370]: #29516
+#30372 := (not #29516)
+#30373 := (or #30372 #29518)
+#30374 := [th-lemma arith triangle-eq]: #30373
+#30375 := [unit-resolution #30374 #30371]: #29518
+#28456 := (+ #28192 #28455)
+#28457 := (+ #27034 #28456)
+#29515 := (>= #28457 0::Int)
+#28458 := (= #28457 0::Int)
+#29503 := (or #25034 #28458)
+#28452 := (= #28193 #28451)
+#29504 := (or #25034 #28452)
+#29508 := (iff #29504 #29503)
+#29510 := (iff #29503 #29503)
+#29511 := [rewrite]: #29510
+#28459 := (iff #28452 #28458)
+#28460 := [rewrite]: #28459
+#29509 := [monotonicity #28460]: #29508
+#29512 := [trans #29509 #29511]: #29508
+#29507 := [quant-inst #24960 #28193]: #29504
+#29513 := [mp #29507 #29512]: #29503
+#30376 := [unit-resolution #29513 #23270]: #28458
+#30377 := (not #28458)
+#30378 := (or #30377 #29515)
+#30379 := [th-lemma arith triangle-eq]: #30378
+#30380 := [unit-resolution #30379 #30376]: #29515
+#30385 := (not #29527)
+#30384 := (not #28581)
+#30383 := (not #27720)
+#30382 := (not #29515)
+#30381 := (not #29518)
+#30386 := (or #30190 #30381 #30382 #30383 #30384 #30385)
+#30387 := [th-lemma arith assign-bounds -1 1 1 -1 -1]: #30386
+#30388 := [unit-resolution #30387 #28931 #30380 #30375 #30364 #28961]: #30190
+#30245 := (>= #30244 0::Int)
+#29637 := (>= #29526 0::Int)
+#30389 := (or #30289 #29637)
+#30390 := [th-lemma arith triangle-eq]: #30389
+#30391 := [unit-resolution #30390 #30355]: #29637
+#29519 := (>= #29517 0::Int)
+#30392 := (or #30372 #29519)
+#30393 := [th-lemma arith triangle-eq]: #30392
+#30394 := [unit-resolution #30393 #30371]: #29519
+#29514 := (<= #28457 0::Int)
+#30395 := (or #30377 #29514)
+#30396 := [th-lemma arith triangle-eq]: #30395
+#30397 := [unit-resolution #30396 #30376]: #29514
+#30402 := (not #29637)
+#30401 := (not #28582)
+#30400 := (not #27719)
+#30399 := (not #29514)
+#30398 := (not #29519)
+#30403 := (or #30245 #30398 #30399 #30400 #30401 #30402)
+#30404 := [th-lemma arith assign-bounds -1 1 1 -1 -1]: #30403
+#30405 := [unit-resolution #30404 #28934 #30397 #30394 #30391 #28958]: #30245
+#30407 := (not #30245)
+#30406 := (not #30190)
+#30408 := (or #30237 #30406 #30407)
+#30409 := [th-lemma arith triangle-eq]: #30408
+#30410 := [unit-resolution #30409 #30405 #30388]: #30237
+#29871 := [symm #30410]: #30302
+#29864 := [monotonicity #29871]: #30312
+#30320 := (= #28154 #29663)
+#29657 := (f77 #26146 #28221 #24960)
+#29664 := (= #29657 #29663)
+#29665 := (not #29664)
+#29658 := (f150 #29657 #26146)
+#29659 := (= f1 #29658)
+#29660 := (not #29659)
+#29668 := (or #29660 #29665)
+#29671 := (not #29668)
+#29559 := (or #27451 #29671)
+#29666 := (or #29665 #29660)
+#29667 := (not #29666)
+#29560 := (or #27451 #29667)
+#29562 := (iff #29560 #29559)
+#29564 := (iff #29559 #29559)
+#29578 := [rewrite]: #29564
+#29672 := (iff #29667 #29671)
+#29669 := (iff #29666 #29668)
+#29670 := [rewrite]: #29669
+#29673 := [monotonicity #29670]: #29672
+#29563 := [monotonicity #29673]: #29562
+#29579 := [trans #29563 #29578]: #29562
+#29561 := [quant-inst #26146 #28221 #24960]: #29560
+#29577 := [mp #29561 #29579]: #29559
+#30315 := [unit-resolution #29577 #21204]: #29671
+#29581 := (or #29668 #29664)
+#29582 := [def-axiom]: #29581
+#30316 := [unit-resolution #29582 #30315]: #29664
+#30301 := (= #28154 #29657)
+#30317 := [monotonicity #28365]: #30301
+#30321 := [trans #30317 #30316]: #30320
+#29872 := [trans #30321 #29864]: #30322
+#29955 := [trans #29872 #30298]: #29970
+#29956 := [monotonicity #29955]: #29979
+#29957 := [symm #29956]: #30324
+#29958 := [monotonicity #29957]: #30326
+#29959 := [trans #29958 #30329]: #30330
+#29954 := [trans #29959 #28364]: #30333
+#29934 := [monotonicity #29954]: #29960
+#29935 := [symm #29934]: #29937
+#29944 := [trans #14330 #29935]: #28229
+#29725 := (not #28229)
+#29773 := (or #28285 #29725)
+#29774 := [def-axiom]: #29773
+#29951 := [unit-resolution #29774 #29944]: #28285
+#29706 := (= #25465 #28243)
+#29679 := (= #28243 #25465)
+#29938 := (= #28118 f19)
+#29839 := (= #28118 #24960)
+#29427 := (or #29377 #28100 #28119)
+#29453 := [def-axiom]: #29427
+#29953 := [unit-resolution #29453 #30299 #29428]: #28119
+#29681 := [symm #29953]: #29839
+#29682 := [trans #29681 #28488]: #29938
+#29680 := [monotonicity #29682]: #29679
+#30114 := [symm #29680]: #29706
+#29708 := [trans #29027 #30114]: #28261
+#29794 := (not #28234)
+#29837 := (iff #12082 #29794)
+#30112 := (iff #12079 #28234)
+#29876 := (iff #28234 #12079)
+#29843 := (= #28233 #3053)
+#29844 := (= #28232 #3040)
+#29842 := (= #28232 #25081)
+#29707 := [monotonicity #29954]: #29842
+#29845 := [trans #29707 #28878]: #29844
+#29846 := [monotonicity #29845]: #29843
+#29836 := [monotonicity #29846]: #29876
+#30113 := [symm #29836]: #30112
+#29838 := [monotonicity #30113]: #29837
+#30111 := [mp #14333 #29838]: #29794
+#28374 := (f77 #27181 #28221 #24960)
+#28375 := (f69 #3220 #28374)
+#28376 := (f148 #28375)
+#28377 := (= f1 #28376)
+#29498 := (not #28377)
+#30162 := (iff #29498 #28240)
+#30093 := (iff #28377 #28239)
+#30146 := (iff #28239 #28377)
+#30141 := (= #28238 #28376)
+#30156 := (= #27798 #28375)
+#30096 := (= #28375 #27798)
+#28496 := (= #28374 #3257)
+#28497 := [monotonicity #28495 #28490 #28488]: #28496
+#30097 := [monotonicity #28497]: #30096
+#30142 := [symm #30097]: #30156
+#29981 := [monotonicity #30142]: #30141
+#30140 := [monotonicity #29981]: #30146
+#30157 := [symm #30140]: #30093
+#30171 := [monotonicity #30157]: #30162
+#28378 := (f35 f298 #28374)
+#28379 := (= f1 #28378)
+#28380 := (not #28379)
+#28384 := (or #28377 #28380)
+#28317 := (not #28384)
+#30144 := (or #28212 #28317)
+#28415 := (or #27212 #24810 #27193 #27196 #28212 #28333 #28317)
+#28381 := (or #28380 #28377)
+#28382 := (not #28381)
+#28383 := (or #27196 #28212 #28210 #24810 #27193 #28382)
+#28416 := (or #27212 #28383)
+#28407 := (iff #28416 #28415)
+#28323 := (or #24810 #27193 #27196 #28212 #28333 #28317)
+#28418 := (or #27212 #28323)
+#28405 := (iff #28418 #28415)
+#28406 := [rewrite]: #28405
+#28419 := (iff #28416 #28418)
+#28326 := (iff #28383 #28323)
+#28318 := (or #27196 #28212 #28333 #24810 #27193 #28317)
+#28324 := (iff #28318 #28323)
+#28325 := [rewrite]: #28324
+#28321 := (iff #28383 #28318)
+#28319 := (iff #28382 #28317)
+#28385 := (iff #28381 #28384)
+#28386 := [rewrite]: #28385
+#28320 := [monotonicity #28386]: #28319
+#28322 := [monotonicity #28337 #28320]: #28321
+#28414 := [trans #28322 #28325]: #28326
+#28404 := [monotonicity #28414]: #28419
+#28408 := [trans #28404 #28406]: #28407
+#28417 := [quant-inst #3039 #3043 #26146 #24962 #28221 #24960]: #28416
+#28403 := [mp #28417 #28408]: #28415
+#30145 := [unit-resolution #28403 #21648 #14315 #28130 #30286 #28528]: #30144
+#30138 := [unit-resolution #30145 #30283]: #28317
+#29499 := (or #28384 #29498)
+#29500 := [def-axiom]: #29499
+#30095 := [unit-resolution #29500 #30138]: #29498
+#30137 := [mp #30095 #30171]: #28240
+#29767 := (or #28279 #28239)
+#29768 := [def-axiom]: #29767
+#30094 := [unit-resolution #29768 #30137]: #28279
+#29524 := (or #28299 #28234 #28276 #28282 #28288)
+#29592 := [def-axiom]: #29524
+#30092 := [unit-resolution #29592 #30094 #30111 #29708 #29951 #29869]: false
+#30175 := [lemma #30092]: #28299
+#30421 := (or #28302 #28294)
+#30422 := [def-axiom]: #30421
+#30484 := [unit-resolution #30422 #30175]: #28302
+#28534 := (or #12542 #13620 #27193 #13765)
+#28477 := [hypothesis]: #13480
+#28504 := (iff #18523 #28380)
+#28502 := (iff #12542 #28379)
+#28500 := (iff #28379 #12542)
+#28498 := (= #28378 #3260)
+#28499 := [monotonicity #28497]: #28498
+#28501 := [monotonicity #28499]: #28500
+#28503 := [symm #28501]: #28502
+#28505 := [monotonicity #28503]: #28504
+#28485 := [hypothesis]: #18523
+#28506 := [mp #28485 #28505]: #28380
+#28412 := (or #28384 #28379)
+#28413 := [def-axiom]: #28412
+#28507 := [unit-resolution #28413 #28506]: #28384
+#28522 := [unit-resolution #28521 #28516 #28513 #28512]: #28517
+#28530 := (or #28212 #28333 #28317)
+#28529 := [hypothesis]: #27192
+#28531 := [unit-resolution #28403 #21648 #14315 #28529 #28528]: #28530
+#28532 := [unit-resolution #28531 #28522 #28507]: #28212
+#28533 := [th-lemma arith farkas 1 1 1 #28532 #28484 #28477]: false
+#28535 := [lemma #28533]: #28534
+#29600 := [unit-resolution #28535 #29760 #28130 #29674]: #12542
+#30429 := (or #28311 #18523 #28305)
+#30430 := [def-axiom]: #30429
+#30488 := [unit-resolution #30430 #29600 #30484]: #28311
+#30432 := (or #30431 #12548 #28308)
+#30433 := [def-axiom]: #30432
+#30490 := [unit-resolution #30433 #30488]: #30489
+#30491 := [unit-resolution #30490 #30442]: #12548
+#29604 := (or #18529 #23421 #23391)
+#27935 := [hypothesis]: #23418
+#27930 := [hypothesis]: #12548
+#29655 := (or #23406 #18529 #23421)
+#24621 := (or #23454 #23448)
+#24622 := [def-axiom]: #24621
+#29654 := [unit-resolution #24622 #29759]: #23448
+#27883 := (or #23406 #18520 #18529 #23421 #23451)
+#27931 := [hypothesis]: #12539
+#27894 := [hypothesis]: #23448
+#27932 := [hypothesis]: #23409
+#24535 := (or #23406 #12542)
+#24536 := [def-axiom]: #24535
+#27927 := [unit-resolution #24536 #27932]: #12542
+#24613 := (or #23451 #18520 #18523 #23445)
+#24614 := [def-axiom]: #24613
+#27933 := [unit-resolution #24614 #27927 #27894 #27931]: #23445
+#24603 := (or #23442 #23436)
 #24604 := [def-axiom]: #24603
-#30652 := [unit-resolution #24604 #30651]: #13708
-#24587 := (+ f307 #13570)
-#24588 := (<= #24587 0::Int)
-#24593 := (or #23454 #12839)
-#24594 := [def-axiom]: #24593
-#30653 := [unit-resolution #24594 #30651]: #12839
-#30654 := (or #12857 #24588)
-#30655 := [th-lemma arith triangle-eq]: #30654
-#30656 := [unit-resolution #30655 #30653]: #24588
-#24484 := (not #18943)
-#30195 := [hypothesis]: #23421
-#24605 := (or #23454 #23418)
-#24606 := [def-axiom]: #24605
-#30176 := [unit-resolution #24606 #30195]: #23454
-#24549 := (or #23424 #23418)
-#24550 := [def-axiom]: #24549
-#30325 := [unit-resolution #24550 #30195]: #23424
-#30326 := (or #23433 #18565 #23427)
-#24559 := (or #23433 #18556 #18565 #23427)
-#24560 := [def-axiom]: #24559
-#30327 := [unit-resolution #24560 #29447]: #30326
-#30328 := [unit-resolution #30327 #30325 #30324]: #23433
-#29801 := (or #23430 #23457)
-#29776 := [hypothesis]: #23454
-#29777 := [hypothesis]: #23433
-#24555 := (or #23430 #12584)
-#24556 := [def-axiom]: #24555
-#29775 := [unit-resolution #24556 #29777]: #12584
-#29789 := (or #18565 #23469)
-#24657 := (or #23490 #23484)
-#24658 := [def-axiom]: #24657
-#29786 := [unit-resolution #24658 #30140]: #23484
-#27971 := (or #23472 #23487 #18559)
-#27967 := [hypothesis]: #12578
-#27968 := [hypothesis]: #23484
-#27930 := [hypothesis]: #23475
-#24627 := (or #23472 #12575)
-#24628 := [def-axiom]: #24627
-#27969 := [unit-resolution #24628 #27930]: #12575
-#24639 := (or #23478 #23472)
-#24640 := [def-axiom]: #24639
-#27964 := [unit-resolution #24640 #27930]: #23478
-#24649 := (or #23487 #18556 #18559 #23481)
-#24650 := [def-axiom]: #24649
-#27970 := [unit-resolution #24650 #27964 #27969 #27968 #27967]: false
-#27972 := [lemma #27970]: #27971
-#29787 := [unit-resolution #27972 #30142 #29786]: #23472
-#24633 := (or #23475 #18556 #18565 #23469)
-#24634 := [def-axiom]: #24633
-#29788 := [unit-resolution #24634 #29787]: #23472
-#29790 := [unit-resolution #29788 #29447]: #29789
-#29791 := [unit-resolution #29790 #29775]: #23469
-#24623 := (or #23466 #23460)
-#24624 := [def-axiom]: #24623
-#29792 := [unit-resolution #24624 #29791]: #23460
-#24565 := (or #23436 #23430)
-#24566 := [def-axiom]: #24565
-#29793 := [unit-resolution #24566 #29777]: #23436
-#29796 := (or #23445 #23439)
-#29794 := (or #23445 #18556 #23439)
-#24575 := (or #23445 #18556 #18559 #23439)
-#24576 := [def-axiom]: #24575
-#29795 := [unit-resolution #24576 #30142]: #29794
-#29797 := [unit-resolution #29795 #29447]: #29796
-#29798 := [unit-resolution #29797 #29793]: #23445
-#24583 := (or #23448 #23442)
-#24584 := [def-axiom]: #24583
-#29799 := [unit-resolution #24584 #29798]: #23448
-#24613 := (or #23463 #23451 #23457)
-#24614 := [def-axiom]: #24613
-#29800 := [unit-resolution #24614 #29799 #29792 #29776]: false
-#29802 := [lemma #29800]: #29801
-#30329 := [unit-resolution #29802 #30328 #30176]: false
-#30330 := [lemma #30329]: #23418
-#30607 := (or #23421 #23415)
-#15811 := (<= f296 4294967295::Int)
-#15814 := (iff #13441 #15811)
-#15805 := (+ 4294967295::Int #13442)
-#15808 := (>= #15805 0::Int)
-#15812 := (iff #15808 #15811)
-#15813 := [rewrite]: #15812
-#15809 := (iff #13441 #15808)
-#15806 := (= #13443 #15805)
-#15807 := [monotonicity #7642]: #15806
-#15810 := [monotonicity #15807]: #15809
-#15815 := [trans #15810 #15813]: #15814
-#14357 := [not-or-elim #14346]: #13446
-#14359 := [and-elim #14357]: #13441
-#15816 := [mp #14359 #15815]: #15811
-#29996 := [hypothesis]: #18597
-#29985 := [th-lemma arith farkas -1 -1 1 #30141 #29996 #15816]: false
-#29988 := [lemma #29985]: #15900
-#30605 := (or #23421 #18597 #23415)
-#30602 := (or #13656 #13534)
-#30603 := [th-lemma arith farkas 1 1]: #30602
-#30604 := [unit-resolution #30603 #29673]: #13534
-#24529 := (or #23421 #18594 #18597 #23415)
+#27934 := [unit-resolution #24604 #27933]: #23436
+#24547 := (or #23412 #23406)
+#24548 := [def-axiom]: #24547
+#28043 := [unit-resolution #24548 #27932]: #23412
+#24577 := (or #23427 #23415 #23421)
+#24578 := [def-axiom]: #24577
+#28044 := [unit-resolution #24578 #28043 #27935]: #23427
+#24587 := (or #23430 #23424)
+#24588 := [def-axiom]: #24587
+#27884 := [unit-resolution #24588 #28044]: #23430
+#24597 := (or #23439 #18520 #18529 #23433)
+#24598 := [def-axiom]: #24597
+#27885 := [unit-resolution #24598 #27884 #27934 #27931 #27930]: false
+#27895 := [lemma #27885]: #27883
+#29684 := [unit-resolution #27895 #29459 #29654]: #29655
+#29685 := [unit-resolution #29684 #27930 #27935]: #23406
+#29686 := [hypothesis]: #23388
+#29687 := (or #23397 #18529 #23391)
+#24523 := (or #23397 #18520 #18529 #23391)
+#24524 := [def-axiom]: #24523
+#29688 := [unit-resolution #24524 #29459]: #29687
+#29675 := [unit-resolution #29688 #27930 #29686]: #23397
+#24529 := (or #23400 #23394)
 #24530 := [def-axiom]: #24529
-#30606 := [unit-resolution #24530 #30604]: #30605
-#30608 := [unit-resolution #30606 #29988]: #30607
-#30609 := [unit-resolution #30608 #30330]: #23415
-#24519 := (or #23412 #23406)
-#24520 := [def-axiom]: #24519
-#30660 := [unit-resolution #24520 #30609]: #23406
-#24464 := (>= #13619 -1::Int)
-#24515 := (or #23412 #13618)
-#24516 := [def-axiom]: #24515
-#30610 := [unit-resolution #24516 #30609]: #13618
-#30611 := (or #13622 #24464)
-#30612 := [th-lemma arith triangle-eq]: #30611
-#30613 := [unit-resolution #30612 #30610]: #24464
-#29780 := (not #24464)
-#29781 := (or #29780 #13550)
-#29774 := [hypothesis]: #24464
-#29778 := [hypothesis]: #13555
-#29779 := [th-lemma arith farkas -1 1 1 #29778 #30141 #29774]: false
-#29782 := [lemma #29779]: #29781
-#30661 := [unit-resolution #29782 #30613]: #13550
-#24505 := (or #23409 #13555 #23403)
+#29676 := [unit-resolution #24530 #29675]: #23400
+#29601 := (or #23409 #23403)
+#24539 := (or #23409 #18520 #18523 #23403)
+#24540 := [def-axiom]: #24539
+#29602 := [unit-resolution #24540 #29600 #29459]: #29601
+#29603 := [unit-resolution #29602 #29676 #29685]: false
+#29605 := [lemma #29603]: #29604
+#30492 := [unit-resolution #29605 #30491 #29631]: #23391
+#24505 := (or #23388 #12565)
 #24506 := [def-axiom]: #24505
-#30662 := [unit-resolution #24506 #30661 #30660]: #23403
-#24497 := (or #23400 #23394)
-#24498 := [def-axiom]: #24497
-#30663 := [unit-resolution #24498 #30662]: #23394
-#24590 := (+ f308 #13592)
-#24592 := (>= #24590 0::Int)
-#24595 := (or #23454 #12842)
-#24596 := [def-axiom]: #24595
-#30664 := [unit-resolution #24596 #30651]: #12842
-#30665 := (or #12848 #24592)
-#30666 := [th-lemma arith triangle-eq]: #30665
-#30667 := [unit-resolution #30666 #30664]: #24592
-#30668 := (not #24592)
-#30671 := (or #13595 #30668)
-#30669 := (or #13595 #13979 #30668)
-#30670 := [th-lemma arith assign-bounds -1 -1]: #30669
-#30672 := [unit-resolution #30670 #30103]: #30671
-#30673 := [unit-resolution #30672 #30667]: #13595
-#30680 := (= #3153 #3299)
-#30678 := (= #3299 #3153)
-#30675 := (= #3298 #3152)
-#30674 := [symm #30664]: #3329
-#30676 := [monotonicity #30674]: #30675
-#30679 := [monotonicity #30676]: #30678
-#30681 := [symm #30679]: #30680
-#30682 := (= f315 #3153)
-#30677 := [symm #30653]: #3328
-#30683 := [trans #30677 #30101]: #30682
-#30684 := [trans #30683 #30681]: #12643
-#24469 := (or #22364 #22362 #13594)
-#24470 := [def-axiom]: #24469
-#30685 := [unit-resolution #24470 #30684 #30673]: #22364
-#24471 := (or #23388 #22363)
-#24472 := [def-axiom]: #24471
-#30686 := [unit-resolution #24472 #30685]: #23388
-#24493 := (or #23397 #23391 #22416)
-#24494 := [def-axiom]: #24493
-#30687 := [unit-resolution #24494 #30686 #30663]: #22416
-#24485 := (or #22411 #24484)
-#24486 := [def-axiom]: #24485
-#30688 := [unit-resolution #24486 #30687]: #24484
-#30632 := (not #24588)
-#30633 := (or #30631 #18943 #30632 #13707)
-#30626 := [hypothesis]: #13708
-#30627 := [hypothesis]: #24588
-#30628 := [hypothesis]: #24484
-#30629 := [hypothesis]: #30621
-#30630 := [th-lemma arith farkas 1 -1 -1 1 #30629 #30628 #30627 #30626]: false
-#30634 := [lemma #30630]: #30633
-#30689 := [unit-resolution #30634 #30688 #30656 #30652]: #30631
-#30625 := (or #30624 #30621)
-#30635 := [th-lemma arith triangle-eq]: #30625
-#30690 := [unit-resolution #30635 #30689]: #30624
-#30649 := (or #30648 #30591)
-#30644 := (= #18620 #3266)
-#30642 := (= #18619 #3257)
-#30640 := (= ?v0!14 f309)
-#30639 := [hypothesis]: #30595
-#30641 := [symm #30639]: #30640
-#30643 := [monotonicity #30641]: #30642
-#30645 := [monotonicity #30643]: #30644
-#30646 := [symm #30645]: #30591
-#30638 := [hypothesis]: #30624
-#30647 := [unit-resolution #30638 #30646]: false
-#30650 := [lemma #30647]: #30649
-#30691 := [unit-resolution #30650 #30690]: #30648
-#30705 := (or #30595 #30702)
-#30425 := (<= #30424 0::Int)
-#30436 := (+ f307 #18941)
-#30437 := (>= #30436 0::Int)
-#30692 := (not #30437)
-#30693 := (or #30692 #18943 #30632)
-#30694 := [th-lemma arith assign-bounds -1 -1]: #30693
-#30695 := [unit-resolution #30694 #30656 #30688]: #30692
-#30698 := (or #30425 #30437)
-#24479 := (or #22411 #18616)
-#24480 := [def-axiom]: #24479
-#30696 := [unit-resolution #24480 #30687]: #18616
-#24477 := (or #22411 #18615)
-#24478 := [def-axiom]: #24477
-#30697 := [unit-resolution #24478 #30687]: #18615
-#30450 := (or #23377 #22395 #22396 #30425 #30437)
-#30413 := (+ #18620 #14006)
-#30414 := (<= #30413 0::Int)
-#30415 := (+ ?v0!14 #13537)
-#30416 := (>= #30415 0::Int)
-#30417 := (or #22396 #30416 #30414 #22395)
-#30451 := (or #23377 #30417)
-#30458 := (iff #30451 #30450)
-#30445 := (or #22395 #22396 #30425 #30437)
-#30453 := (or #23377 #30445)
-#30456 := (iff #30453 #30450)
-#30457 := [rewrite]: #30456
-#30454 := (iff #30451 #30453)
-#30448 := (iff #30417 #30445)
-#30442 := (or #22396 #30425 #30437 #22395)
-#30446 := (iff #30442 #30445)
-#30447 := [rewrite]: #30446
-#30443 := (iff #30417 #30442)
-#30440 := (iff #30414 #30437)
-#30430 := (+ #14006 #18620)
-#30433 := (<= #30430 0::Int)
-#30438 := (iff #30433 #30437)
-#30439 := [rewrite]: #30438
-#30434 := (iff #30414 #30433)
-#30431 := (= #30413 #30430)
-#30432 := [rewrite]: #30431
-#30435 := [monotonicity #30432]: #30434
-#30441 := [trans #30435 #30439]: #30440
-#30428 := (iff #30416 #30425)
-#30418 := (+ #13537 ?v0!14)
-#30421 := (>= #30418 0::Int)
-#30426 := (iff #30421 #30425)
-#30427 := [rewrite]: #30426
-#30422 := (iff #30416 #30421)
-#30419 := (= #30415 #30418)
-#30420 := [rewrite]: #30419
-#30423 := [monotonicity #30420]: #30422
-#30429 := [trans #30423 #30427]: #30428
-#30444 := [monotonicity #30429 #30441]: #30443
-#30449 := [trans #30444 #30447]: #30448
-#30455 := [monotonicity #30449]: #30454
-#30459 := [trans #30455 #30457]: #30458
-#30452 := [quant-inst #18614]: #30451
-#30460 := [mp #30452 #30459]: #30450
-#30699 := [unit-resolution #30460 #30095 #30697 #30696]: #30698
-#30700 := [unit-resolution #30699 #30695]: #30425
-#30701 := (not #30425)
-#30703 := (or #30595 #30701 #30702)
-#30704 := [th-lemma arith triangle-eq]: #30703
-#30706 := [unit-resolution #30704 #30700]: #30705
-#30707 := [unit-resolution #30706 #30691]: #30702
-#24481 := (not #18930)
-#24482 := (or #22411 #24481)
-#24483 := [def-axiom]: #24482
-#30708 := [unit-resolution #24483 #30687]: #24481
-#30709 := [th-lemma arith farkas -1 -1 1 #30708 #30613 #30707]: false
-#30710 := [lemma #30709]: #23454
-#26725 := [unit-resolution #29802 #30710]: #23430
-#26728 := [unit-resolution #30327 #26725 #30324]: #23427
-#24541 := (or #23424 #12601)
-#24542 := [def-axiom]: #24541
-#30556 := [unit-resolution #24542 #26728]: #12601
-#24535 := (or #23424 #12590)
-#24536 := [def-axiom]: #24535
-#30557 := [unit-resolution #24536 #26728]: #12590
-#30555 := [trans #30557 #30556]: #30343
-#30558 := (not #30343)
-#30559 := (or #30558 #30172)
-#30560 := [th-lemma arith triangle-eq]: #30559
-#30561 := [unit-resolution #30560 #30555]: #30172
-#30340 := (+ f309 #13592)
-#30342 := (>= #30340 0::Int)
-#24543 := (or #23424 #12604)
-#24544 := [def-axiom]: #24543
-#26729 := [unit-resolution #24544 #26728]: #12604
-#26730 := (or #12731 #30342)
-#30377 := [th-lemma arith triangle-eq]: #26730
-#30378 := [unit-resolution #30377 #26729]: #30342
-#30379 := [hypothesis]: #13594
-#30374 := [th-lemma arith farkas -1 1 1 #30379 #30378 #30141]: false
-#30380 := [lemma #30374]: #13595
-#30585 := (or #22364 #13594)
-#30575 := (= #3266 #3299)
-#30577 := (= #3299 #3266)
-#30563 := (= #3298 #3257)
-#30562 := [symm #26729]: #3278
-#30576 := [monotonicity #30562]: #30563
-#30578 := [monotonicity #30576]: #30577
-#30581 := [symm #30578]: #30575
-#30582 := (= f315 #3266)
-#30580 := [symm #30557]: #3269
-#30579 := [symm #30556]: #3276
-#30583 := [trans #30579 #30580]: #30582
-#30584 := [trans #30583 #30581]: #12643
-#30593 := [unit-resolution #24470 #30584]: #30585
-#30594 := [unit-resolution #30593 #30380]: #22364
-#30496 := [unit-resolution #24472 #30594]: #23388
-#30564 := [unit-resolution #24494 #30663]: #23394
-#30565 := [unit-resolution #30564 #30496]: #22416
-#30592 := [unit-resolution #24486 #30565]: #24484
-#30658 := (not #30172)
-#30659 := (or #30631 #18943 #30658)
-#30657 := [th-lemma arith assign-bounds -1 -1]: #30659
-#30711 := [unit-resolution #30657 #30592 #30561]: #30631
-#30712 := [unit-resolution #30635 #30711]: #30624
-#30713 := [unit-resolution #24483 #30565]: #24481
-#30714 := (or #30620 #18930 #29780)
-#30715 := [th-lemma arith assign-bounds -1 -1]: #30714
-#30716 := [unit-resolution #30715 #30713 #30613]: #30620
-#30724 := (or #30692 #18943)
-#30717 := [unit-resolution #29790 #30324]: #23469
-#30718 := [unit-resolution #24624 #30717]: #23460
-#30719 := [unit-resolution #24614 #30710 #30718]: #23451
-#24581 := (or #23448 #13707)
-#24582 := [def-axiom]: #24581
-#30720 := [unit-resolution #24582 #30719]: #13707
-#30721 := (or #24588 #30658 #13708)
-#30722 := [th-lemma arith assign-bounds 1 1]: #30721
-#30723 := [unit-resolution #30722 #30720 #30561]: #24588
-#30725 := [unit-resolution #30694 #30723]: #30724
-#30726 := [unit-resolution #30725 #30592]: #30692
-#30727 := [unit-resolution #24480 #30565]: #18616
-#30728 := [unit-resolution #24478 #30565]: #18615
-#30729 := [unit-resolution #30460 #30095 #30728 #30727 #30726]: #30425
-#30730 := [unit-resolution #30704 #30729 #30716]: #30595
-[unit-resolution #30650 #30730 #30712]: false
+#30493 := [unit-resolution #24506 #30492]: #12565
+#24499 := (or #23388 #12554)
+#24500 := [def-axiom]: #24499
+#30494 := [unit-resolution #24500 #30492]: #12554
+#30495 := [trans #30494 #30493]: #30446
+#30496 := (not #30446)
+#30497 := (or #30496 #30448)
+#30498 := [th-lemma arith triangle-eq]: #30497
+#30499 := [unit-resolution #30498 #30495]: #30448
+#30501 := (or #18529 #23433)
+#28051 := (or #23436 #23451 #18523)
+#28115 := [hypothesis]: #12542
+#28116 := [hypothesis]: #23439
+#24591 := (or #23436 #12539)
+#24592 := [def-axiom]: #24591
+#28050 := [unit-resolution #24592 #28116]: #12539
+#28048 := [unit-resolution #24604 #28116]: #23442
+#28049 := [unit-resolution #24614 #28048 #28050 #27894 #28115]: false
+#28052 := [lemma #28049]: #28051
+#30500 := [unit-resolution #28052 #29600 #29654]: #23436
+#30502 := [unit-resolution #24598 #30500 #29459]: #30501
+#30503 := [unit-resolution #30502 #30491]: #23433
+#30504 := [unit-resolution #24588 #30503]: #23424
+#30505 := [unit-resolution #24578 #30504 #29631]: #23415
+#24545 := (or #23412 #13671)
+#24546 := [def-axiom]: #24545
+#30506 := [unit-resolution #24546 #30505]: #13671
+#30507 := (not #30448)
+#30508 := (or #24552 #30507 #13672)
+#30509 := [th-lemma arith assign-bounds 1 1]: #30508
+#30510 := [unit-resolution #30509 #30506 #30499]: #24552
+#24513 := (or #23388 #23382)
+#24514 := [def-axiom]: #24513
+#30511 := [unit-resolution #24514 #30492]: #23382
+#30512 := [unit-resolution #29796 #30511]: #23379
+#30513 := [unit-resolution #24484 #30512]: #23370
+#30514 := [unit-resolution #24480 #30512]: #13582
+#30515 := [unit-resolution #29608 #30514]: #24428
+#30516 := [unit-resolution #29765 #30515]: #13514
+#30517 := [unit-resolution #24470 #30516 #30513]: #23367
+#30518 := [unit-resolution #24462 #30517]: #23358
+#30527 := (= #3266 #3299)
+#30523 := (= #3299 #3266)
+#30521 := (= #3298 #3257)
+#24507 := (or #23388 #12568)
+#24508 := [def-axiom]: #24507
+#30519 := [unit-resolution #24508 #30492]: #12568
+#30520 := [symm #30519]: #3278
+#30522 := [monotonicity #30520]: #30521
+#30524 := [monotonicity #30522]: #30523
+#30528 := [symm #30524]: #30527
+#30529 := (= f316 #3266)
+#30526 := [symm #30494]: #3269
+#30525 := [symm #30493]: #3276
+#30530 := [trans #30525 #30526]: #30529
+#30531 := [trans #30530 #30528]: #12607
+#30443 := (+ f310 #13556)
+#30445 := (>= #30443 0::Int)
+#30532 := (or #12695 #30445)
+#30533 := [th-lemma arith triangle-eq]: #30532
+#30534 := [unit-resolution #30533 #30519]: #30445
+#30535 := (not #30445)
+#30536 := (or #13559 #13765 #30535)
+#30537 := [th-lemma arith assign-bounds -1 -1]: #30536
+#30538 := [unit-resolution #30537 #29760 #30534]: #13559
+#30539 := [unit-resolution #24434 #30538 #30531]: #22328
+#30540 := [unit-resolution #24436 #30539]: #23352
+#30541 := [unit-resolution #24458 #30540 #30518]: #22380
+#30542 := [unit-resolution #24450 #30541]: #24448
+#30543 := [unit-resolution #29597 #30542 #30510]: #30220
+#30544 := [unit-resolution #24444 #30541]: #18580
+#30545 := [unit-resolution #24442 #30541]: #18579
+#30546 := [unit-resolution #24447 #30541]: #24445
+#30547 := [unit-resolution #29717 #30546 #30515]: #29634
+#30548 := [unit-resolution #30419 #30547 #30545 #30544 #30543]: #29868
+#30549 := [unit-resolution #30080 #30548]: #30332
+#30550 := [unit-resolution #30340 #30549]: #30338
+[th-lemma arith farkas -1 -1 1 #30542 #30499 #30550]: false
 unsat

--- a/src/HOL/Multivariate_Analysis/Integration.certs	Sun Dec 19 18:54:29 2010 +0100
+++ b/src/HOL/Multivariate_Analysis/Integration.certs	Sun Dec 19 18:55:21 2010 +0100
@@ -621,18 +621,18 @@
 #427 := [unit-resolution #411 #426]: #395
 [th-lemma arith farkas 2 1 2 3 1 1 #421 #319 #321 #414 #318 #427]: false
 unsat
-f26ffd00d169b6b4684265a03d23c9e0efe94a58 57 0
+76aef63700c44d6a49155f473f80703718124469 57 0
 #2 := false
 #37 := 0::Real
 decl f12 :: (-> S5 Real)
 decl f13 :: (-> S4 S4 S5)
 decl f14 :: (-> S3 S4)
+decl f4 :: S3
+#8 := f4
+#45 := (f14 f4)
 decl f10 :: S3
 #25 := f10
-#45 := (f14 f10)
-decl f4 :: S3
-#8 := f4
-#44 := (f14 f4)
+#44 := (f14 f10)
 #46 := (f13 #44 #45)
 #47 := (f12 #46)
 #258 := (>= #47 0::Real)
@@ -642,11 +642,11 @@
 #134 := [asserted]: #50
 #266 := (or #49 #260)
 #48 := (<= #47 0::Real)
-#114 := [asserted]: #48
+#133 := [asserted]: #48
 #259 := (not #48)
 #264 := (or #49 #259 #260)
 #265 := [th-lemma arith triangle-eq]: #264
-#267 := [unit-resolution #265 #114]: #266
+#267 := [unit-resolution #265 #133]: #266
 #268 := [unit-resolution #267 #134]: #260
 #39 := (:var 0 S4)
 #38 := (:var 1 S4)
@@ -670,8 +670,8 @@
 #135 := (iff #42 #136)
 #137 := [rewrite]: #135
 #140 := [quant-intro #137]: #139
-#113 := [asserted]: #43
-#141 := [mp #113 #140]: #138
+#132 := [asserted]: #43
+#141 := [mp #132 #140]: #138
 #167 := [mp~ #141 #166]: #138
 #257 := [mp #167 #256]: #252
 #261 := (not #252)

--- a/src/HOL/SMT_Examples/SMT_Examples.certs	Sun Dec 19 18:54:29 2010 +0100
+++ b/src/HOL/SMT_Examples/SMT_Examples.certs	Sun Dec 19 18:55:21 2010 +0100
@@ -146,7 +146,65 @@
 #74 := [and-elim #72]: #43
 [mp #74 #88]: false
 unsat
-b369848437710a3b368c375ee857c21adc3f6e30 1 0
+bc6de36d6c86b416e91711bb23067cc8250ac153 59 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f6 :: S1
+#15 := f6
+#16 := (= f6 f1)
+decl f5 :: S1
+#13 := f5
+#14 := (= f5 f1)
+#17 := (and #14 #16)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#12 := (and #9 #11)
+#18 := (or #12 #17)
+#19 := (implies #18 #18)
+#20 := (not #19)
+#74 := (iff #20 false)
+#1 := true
+#69 := (not true)
+#72 := (iff #69 false)
+#73 := [rewrite]: #72
+#70 := (iff #20 #69)
+#67 := (iff #19 true)
+#53 := (= f1 f6)
+#50 := (= f1 f5)
+#56 := (and #50 #53)
+#44 := (= f1 f4)
+#41 := (= f1 f3)
+#47 := (and #41 #44)
+#59 := (or #47 #56)
+#62 := (implies #59 #59)
+#65 := (iff #62 true)
+#66 := [rewrite]: #65
+#63 := (iff #19 #62)
+#60 := (iff #18 #59)
+#57 := (iff #17 #56)
+#54 := (iff #16 #53)
+#55 := [rewrite]: #54
+#51 := (iff #14 #50)
+#52 := [rewrite]: #51
+#58 := [monotonicity #52 #55]: #57
+#48 := (iff #12 #47)
+#45 := (iff #11 #44)
+#46 := [rewrite]: #45
+#42 := (iff #9 #41)
+#43 := [rewrite]: #42
+#49 := [monotonicity #43 #46]: #48
+#61 := [monotonicity #49 #58]: #60
+#64 := [monotonicity #61 #61]: #63
+#68 := [trans #64 #66]: #67
+#71 := [monotonicity #68]: #70
+#75 := [trans #71 #73]: #74
+#40 := [asserted]: #20
+[mp #40 #75]: false
 unsat
 e334e079d0f61721e404e4ca140ce40c317189ba 94 0
 #2 := false
@@ -3973,59 +4031,48 @@
 #241 := [unit-resolution #190 #240]: #156
 [th-lemma arith farkas -1 -1 1 1 #241 #218 #128 #239]: false
 unsat
-a63737c6fce2a605078af85686032a125631e608 53 0
+c722596cfa285e209992f7087932c1ec15fd226b 42 0
 #2 := false
 decl f3 :: (-> S1 S2)
+decl f1 :: S1
+#4 := f1
+#13 := (f3 f1)
 decl f2 :: S1
 #5 := f2
-decl f1 :: S1
-#4 := f1
-#1 := true
-#13 := (ite true f1 f2)
-#14 := (f3 #13)
 #9 := 3::Int
 #8 := 2::Int
 #10 := (< 2::Int 3::Int)
 #11 := (ite #10 f1 f2)
 #12 := (f3 #11)
-#15 := (= #12 #14)
-#16 := (not #15)
-#69 := (iff #16 false)
-#39 := (f3 f1)
-#42 := (= #12 #39)
-#45 := (not #42)
-#67 := (iff #45 false)
-#62 := (not true)
-#65 := (iff #62 false)
-#66 := [rewrite]: #65
-#63 := (iff #45 #62)
-#60 := (iff #42 true)
-#55 := (= #39 #39)
-#58 := (iff #55 true)
+#14 := (= #12 #13)
+#15 := (not #14)
+#60 := (iff #15 false)
+#1 := true
+#55 := (not true)
+#58 := (iff #55 false)
 #59 := [rewrite]: #58
-#56 := (iff #42 #55)
-#52 := (= #11 f1)
-#37 := (= #13 f1)
-#38 := [rewrite]: #37
-#50 := (= #11 #13)
-#48 := (iff #10 true)
-#49 := [rewrite]: #48
-#51 := [monotonicity #49]: #50
-#53 := [trans #51 #38]: #52
-#54 := [monotonicity #53]: #42
+#56 := (iff #15 #55)
+#53 := (iff #14 true)
+#48 := (= #13 #13)
+#51 := (iff #48 true)
+#52 := [rewrite]: #51
+#49 := (iff #14 #48)
+#45 := (= #11 f1)
+#40 := (ite true f1 f2)
+#43 := (= #40 f1)
+#44 := [rewrite]: #43
+#41 := (= #11 #40)
+#38 := (iff #10 true)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#47 := [monotonicity #46]: #14
+#50 := [monotonicity #47]: #49
+#54 := [trans #50 #52]: #53
 #57 := [monotonicity #54]: #56
 #61 := [trans #57 #59]: #60
-#64 := [monotonicity #61]: #63
-#68 := [trans #64 #66]: #67
-#46 := (iff #16 #45)
-#43 := (iff #15 #42)
-#40 := (= #14 #39)
-#41 := [monotonicity #38]: #40
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#70 := [trans #47 #68]: #69
-#36 := [asserted]: #16
-[mp #36 #70]: false
+#35 := [asserted]: #15
+[mp #35 #61]: false
 unsat
 4d8a8a08b49cb28d987bdc1bcdbb3a144907bf45 54 0
 #2 := false
@@ -4288,7 +4335,7 @@
 #42 := [asserted]: #22
 [mp #42 #79]: false
 unsat
-900d439115908f4ef5998166e284e3a309f354ef 104 0
[phone]b5d95d4c28641909502b0f435784ad24 104 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -7376,698 +7423,425 @@
 #37 := [asserted]: #17
 [mp #37 #73]: false
 unsat
-75da1862a2fd162477f9d85292ff8ab2e18559e4 342 0
+f9ae47f5aef750f37ea2d9309845d7cf08946d8c 211 0
 #2 := false
-#21 := 0::Int
+#12 := 0::Int
 decl f3 :: Int
 #8 := f3
-#419 := (<= f3 0::Int)
-#446 := (>= f3 0::Int)
-#753 := (not #446)
-#409 := (not #419)
-#754 := (or #409 #753)
-#715 := (not #754)
-#11 := 2::Int
-#443 := (mod f3 2::Int)
-#113 := -1::Int
-#444 := (* -1::Int #443)
-decl f4 :: (-> Int Int Int)
-#12 := (f4 f3 2::Int)
-#445 := (+ #12 #444)
-#442 := (= #445 0::Int)
-#705 := (not #442)
-#717 := (>= #445 0::Int)
-#647 := (not #717)
-#654 := [hypothesis]: #717
-#689 := (>= #443 0::Int)
-#1 := true
-#65 := [true-axiom]: true
-#665 := (or false #689)
-#643 := [th-lemma arith]: #665
-#644 := [unit-resolution #643 #65]: #689
-#95 := (>= #12 0::Int)
-#98 := (not #95)
-#9 := 1::Int
-#13 := (* 2::Int #12)
-#14 := (+ #13 1::Int)
-#15 := (+ f3 #14)
-#10 := (+ f3 1::Int)
-#16 := (<= #10 #15)
-#17 := (not #16)
-#103 := (iff #17 #98)
-#77 := (+ f3 #13)
-#78 := (+ 1::Int #77)
-#68 := (+ 1::Int f3)
-#83 := (<= #68 #78)
-#86 := (not #83)
-#101 := (iff #86 #98)
-#93 := (>= #13 0::Int)
-#89 := (not #93)
-#99 := (iff #89 #98)
-#96 := (iff #93 #95)
-#97 := [rewrite]: #96
-#100 := [monotonicity #97]: #99
-#90 := (iff #86 #89)
-#91 := (iff #83 #93)
-#92 := [rewrite]: #91
-#94 := [monotonicity #92]: #90
-#102 := [trans #94 #100]: #101
-#87 := (iff #17 #86)
-#84 := (iff #16 #83)
-#81 := (= #15 #78)
-#71 := (+ 1::Int #13)
-#74 := (+ f3 #71)
-#79 := (= #74 #78)
-#80 := [rewrite]: #79
-#75 := (= #15 #74)
-#72 := (= #14 #71)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#82 := [trans #76 #80]: #81
-#69 := (= #10 #68)
-#70 := [rewrite]: #69
-#85 := [monotonicity #70 #82]: #84
-#88 := [monotonicity #85]: #87
-#104 := [trans #88 #102]: #103
-#67 := [asserted]: #17
-#105 := [mp #67 #104]: #98
-#646 := [th-lemma arith farkas -1 1 1 #105 #644 #654]: false
-#648 := [lemma #646]: #647
-#660 := (or #705 #717)
-#661 := [th-lemma arith triangle-eq]: #660
-#662 := [unit-resolution #661 #648]: #705
-#637 := (or #715 #442)
-#741 := -2::Int
-#439 := (* -1::Int f3)
-#465 := (mod #439 -2::Int)
-#361 := (+ #12 #465)
-#460 := (= #361 0::Int)
-#739 := (ite #754 #442 #460)
-#763 := (= #12 0::Int)
-#764 := (= f3 0::Int)
-#450 := (ite #764 #763 #739)
-#19 := (:var 0 Int)
-#18 := (:var 1 Int)
-#39 := (f4 #18 #19)
-#775 := (pattern #39)
-#117 := (* -1::Int #19)
-#114 := (* -1::Int #18)
-#172 := (mod #114 #117)
-#287 := (+ #39 #172)
-#288 := (= #287 0::Int)
-#40 := (mod #18 #19)
-#284 := (* -1::Int #40)
-#285 := (+ #39 #284)
-#286 := (= #285 0::Int)
-#146 := (>= #18 0::Int)
-#139 := (<= #19 0::Int)
-#231 := (or #139 #146)
-#232 := (not #231)
-#135 := (<= #18 0::Int)
-#229 := (or #135 #139)
-#230 := (not #229)
-#235 := (or #230 #232)
-#289 := (ite #235 #286 #288)
-#283 := (= #39 0::Int)
-#22 := (= #18 0::Int)
-#290 := (ite #22 #283 #289)
-#282 := (= #18 #39)
-#23 := (= #19 0::Int)
-#291 := (ite #23 #282 #290)
-#776 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #775) #291)
-#294 := (forall (vars (?v0 Int) (?v1 Int)) #291)
-#779 := (iff #294 #776)
-#777 := (iff #291 #291)
-#778 := [refl]: #777
-#780 := [quant-intro #778]: #779
-#178 := (* -1::Int #172)
-#251 := (ite #235 #40 #178)
-#254 := (ite #22 0::Int #251)
-#257 := (ite #23 #18 #254)
-#260 := (= #39 #257)
-#263 := (forall (vars (?v0 Int) (?v1 Int)) #260)
-#295 := (iff #263 #294)
-#292 := (iff #260 #291)
-#293 := [rewrite]: #292
-#296 := [quant-intro #293]: #295
-#147 := (not #146)
-#140 := (not #139)
-#150 := (and #140 #147)
+#122 := (<= f3 0::Int)
+#135 := (>= f3 0::Int)
 #136 := (not #135)
-#143 := (and #136 #140)
-#153 := (or #143 #150)
-#198 := (ite #153 #40 #178)
-#201 := (ite #22 0::Int #198)
-#204 := (ite #23 #18 #201)
-#207 := (= #39 #204)
-#210 := (forall (vars (?v0 Int) (?v1 Int)) #207)
-#264 := (iff #210 #263)
-#261 := (iff #207 #260)
-#258 := (= #204 #257)
-#255 := (= #201 #254)
-#252 := (= #198 #251)
-#236 := (iff #153 #235)
-#233 := (iff #150 #232)
-#234 := [rewrite]: #233
-#223 := (iff #143 #230)
-#224 := [rewrite]: #223
-#237 := [monotonicity #224 #234]: #236
-#253 := [monotonicity #237]: #252
-#256 := [monotonicity #253]: #255
-#259 := [monotonicity #256]: #258
-#262 := [monotonicity #259]: #261
-#265 := [quant-intro #262]: #264
-#221 := (~ #210 #210)
-#220 := (~ #207 #207)
-#217 := [refl]: #220
-#222 := [nnf-pos #217]: #221
-#33 := (- #19)
-#32 := (- #18)
-#41 := (mod #32 #33)
-#42 := (- #41)
-#26 := (< 0::Int #19)
-#28 := (< #18 0::Int)
-#29 := (and #28 #26)
-#25 := (< 0::Int #18)
-#27 := (and #25 #26)
-#30 := (or #27 #29)
-#43 := (ite #30 #40 #42)
-#44 := (ite #22 0::Int #43)
-#45 := (ite #23 #18 #44)
-#46 := (= #39 #45)
-#47 := (forall (vars (?v0 Int) (?v1 Int)) #46)
-#213 := (iff #47 #210)
-#107 := (and #26 #28)
-#110 := (or #27 #107)
-#183 := (ite #110 #40 #178)
-#186 := (ite #22 0::Int #183)
-#189 := (ite #23 #18 #186)
-#192 := (= #39 #189)
-#195 := (forall (vars (?v0 Int) (?v1 Int)) #192)
-#211 := (iff #195 #210)
-#208 := (iff #192 #207)
-#205 := (= #189 #204)
-#202 := (= #186 #201)
-#199 := (= #183 #198)
-#154 := (iff #110 #153)
-#151 := (iff #107 #150)
-#148 := (iff #28 #147)
-#149 := [rewrite]: #148
-#141 := (iff #26 #140)
-#142 := [rewrite]: #141
-#152 := [monotonicity #142 #149]: #151
-#144 := (iff #27 #143)
-#137 := (iff #25 #136)
+#123 := (not #122)
+#146 := (or #123 #136)
+#195 := (not #146)
+#69 := -2::Int
+#65 := -1::Int
+#66 := (* -1::Int f3)
+#72 := (mod #66 -2::Int)
+#78 := (* -1::Int #72)
+#11 := 2::Int
+#21 := (mod f3 2::Int)
+#149 := (ite #146 #21 #78)
+#193 := (= #21 #149)
+#284 := (not #193)
+#14 := (= f3 0::Int)
+#152 := (ite #14 0::Int #149)
+#268 := (* -1::Int #152)
+#269 := (+ #21 #268)
+#270 := (<= #269 0::Int)
+#267 := (= #21 #152)
+#192 := (= #149 #152)
+#202 := (not #14)
+#191 := (= #152 0::Int)
+#209 := (not #191)
+#175 := (>= #152 0::Int)
+#178 := (not #175)
+#9 := 1::Int
+#23 := (- 2::Int)
+#22 := (- f3)
+#24 := (mod #22 #23)
+#25 := (- #24)
+#16 := (< 0::Int 2::Int)
+#18 := (< f3 0::Int)
+#19 := (and #18 #16)
+#15 := (< 0::Int f3)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#26 := (ite #20 #21 #25)
+#27 := (ite #14 0::Int #26)
+#13 := (= 2::Int 0::Int)
+#28 := (ite #13 f3 #27)
+#29 := (* 2::Int #28)
+#30 := (+ #29 1::Int)
+#31 := (+ f3 #30)
+#10 := (+ f3 1::Int)
+#32 := (<= #10 #31)
+#33 := (not #32)
+#183 := (iff #33 #178)
+#59 := (and #16 #18)
+#62 := (or #17 #59)
+#83 := (ite #62 #21 #78)
+#86 := (ite #14 0::Int #83)
+#96 := (* 2::Int #86)
+#110 := (+ f3 #96)
+#111 := (+ 1::Int #110)
+#54 := (+ 1::Int f3)
+#116 := (<= #54 #111)
+#119 := (not #116)
+#181 := (iff #119 #178)
+#155 := (* 2::Int #152)
+#168 := (>= #155 0::Int)
+#172 := (not #168)
+#179 := (iff #172 #178)
+#176 := (iff #168 #175)
+#177 := [rewrite]: #176
+#180 := [monotonicity #177]: #179
+#173 := (iff #119 #172)
+#170 := (iff #116 #168)
+#158 := (+ f3 #155)
+#161 := (+ 1::Int #158)
+#164 := (<= #54 #161)
+#167 := (iff #164 #168)
+#169 := [rewrite]: #167
+#165 := (iff #116 #164)
+#162 := (= #111 #161)
+#159 := (= #110 #158)
+#156 := (= #96 #155)
+#153 := (= #86 #152)
+#150 := (= #83 #149)
+#147 := (iff #62 #146)
+#144 := (iff #59 #136)
+#1 := true
+#139 := (and true #136)
+#142 := (iff #139 #136)
+#143 := [rewrite]: #142
+#140 := (iff #59 #139)
+#137 := (iff #18 #136)
 #138 := [rewrite]: #137
-#145 := [monotonicity #138 #142]: #144
-#155 := [monotonicity #145 #152]: #154
-#200 := [monotonicity #155]: #199
-#203 := [monotonicity #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [monotonicity #206]: #208
-#212 := [quant-intro #209]: #211
-#196 := (iff #47 #195)
-#193 := (iff #46 #192)
-#190 := (= #45 #189)
-#187 := (= #44 #186)
-#184 := (= #43 #183)
-#181 := (= #42 #178)
-#175 := (- #172)
-#179 := (= #175 #178)
-#180 := [rewrite]: #179
-#176 := (= #42 #175)
-#173 := (= #41 #172)
-#118 := (= #33 #117)
-#119 := [rewrite]: #118
-#115 := (= #32 #114)
-#116 := [rewrite]: #115
-#174 := [monotonicity #116 #119]: #173
-#177 := [monotonicity #174]: #176
-#182 := [trans #177 #180]: #181
-#111 := (iff #30 #110)
-#108 := (iff #29 #107)
-#109 := [rewrite]: #108
-#112 := [monotonicity #109]: #111
-#185 := [monotonicity #112 #182]: #184
-#188 := [monotonicity #185]: #187
-#191 := [monotonicity #188]: #190
-#194 := [monotonicity #191]: #193
-#197 := [quant-intro #194]: #196
-#214 := [trans #197 #212]: #213
-#171 := [asserted]: #47
-#215 := [mp #171 #214]: #210
-#218 := [mp~ #215 #222]: #210
-#266 := [mp #218 #265]: #263
-#297 := [mp #266 #296]: #294
-#781 := [mp #297 #780]: #776
-#734 := (not #776)
-#723 := (or #734 #450)
-#355 := (* -1::Int 2::Int)
-#440 := (mod #439 #355)
-#441 := (+ #12 #440)
-#432 := (= #441 0::Int)
-#425 := (<= 2::Int 0::Int)
-#760 := (or #425 #446)
-#762 := (not #760)
-#549 := (or #419 #425)
-#756 := (not #549)
-#430 := (or #756 #762)
-#431 := (ite #430 #442 #432)
-#765 := (ite #764 #763 #431)
-#766 := (= f3 #12)
-#761 := (= 2::Int 0::Int)
-#767 := (ite #761 #766 #765)
-#724 := (or #734 #767)
-#720 := (iff #724 #723)
-#726 := (iff #723 #723)
-#727 := [rewrite]: #726
-#733 := (iff #767 #450)
-#453 := (ite false #766 #450)
-#447 := (iff #453 #450)
-#729 := [rewrite]: #447
-#731 := (iff #767 #453)
-#451 := (iff #765 #450)
-#736 := (iff #431 #739)
-#461 := (iff #432 #460)
-#737 := (= #441 #361)
-#466 := (= #440 #465)
-#742 := (= #355 -2::Int)
-#464 := [rewrite]: #742
-#467 := [monotonicity #464]: #466
-#738 := [monotonicity #467]: #737
-#735 := [monotonicity #738]: #461
-#752 := (iff #430 #754)
-#393 := (iff #762 #753)
-#388 := (iff #760 #446)
-#747 := (or false #446)
-#744 := (iff #747 #446)
-#750 := [rewrite]: #744
-#748 := (iff #760 #747)
-#422 := (iff #425 false)
-#758 := [rewrite]: #422
-#749 := [monotonicity #758]: #748
-#751 := [trans #749 #750]: #388
-#394 := [monotonicity #751]: #393
-#745 := (iff #756 #409)
-#407 := (iff #549 #419)
-#418 := (or #419 false)
-#743 := (iff #418 #419)
-#406 := [rewrite]: #743
-#759 := (iff #549 #418)
-#402 := [monotonicity #758]: #759
-#408 := [trans #402 #406]: #407
-#746 := [monotonicity #408]: #745
-#755 := [monotonicity #746 #394]: #752
-#740 := [monotonicity #755 #735]: #736
-#452 := [monotonicity #740]: #451
-#757 := (iff #761 false)
-#417 := [rewrite]: #757
-#732 := [monotonicity #417 #452]: #731
-#730 := [trans #732 #729]: #733
-#721 := [monotonicity #730]: #720
-#722 := [trans #721 #727]: #720
-#725 := [quant-inst #8 #11]: #724
-#728 := [mp #725 #722]: #723
-#663 := [unit-resolution #728 #781]: #450
-#593 := (not #764)
-#592 := (not #450)
-#649 := (or #592 #593)
-#698 := (not #763)
-#664 := (or #698 #95)
-#688 := [th-lemma arith triangle-eq]: #664
-#682 := [unit-resolution #688 #105]: #698
-#552 := (or #592 #593 #763)
-#700 := [def-axiom]: #552
-#650 := [unit-resolution #700 #682]: #649
-#645 := [unit-resolution #650 #663]: #593
-#602 := (or #592 #764 #739)
-#697 := [def-axiom]: #602
-#651 := [unit-resolution #697 #645 #663]: #739
-#719 := (not #739)
-#548 := (or #719 #715 #442)
-#550 := [def-axiom]: #548
-#633 := [unit-resolution #550 #651]: #637
-#634 := [unit-resolution #633 #662]: #715
-#570 := (or #754 #419)
-#571 := [def-axiom]: #570
-#635 := [unit-resolution #571 #634]: #419
-#713 := (or #754 #446)
-#714 := [def-axiom]: #713
-#638 := [unit-resolution #714 #634]: #446
-#639 := (or #764 #409 #753)
-#640 := [th-lemma arith triangle-eq]: #639
-#641 := [unit-resolution #640 #645]: #754
-[unit-resolution #641 #638 #635]: false
-unsat
-3b8dfbe5d2104f714ba2e5d249bcf001c2c84dba 349 0
+#126 := (iff #16 true)
+#127 := [rewrite]: #126
+#141 := [monotonicity #127 #138]: #140
+#145 := [trans #141 #143]: #144
+#133 := (iff #17 #123)
+#128 := (and #123 true)
+#131 := (iff #128 #123)
+#132 := [rewrite]: #131
+#129 := (iff #17 #128)
+#124 := (iff #15 #123)
+#125 := [rewrite]: #124
+#130 := [monotonicity #125 #127]: #129
+#134 := [trans #130 #132]: #133
+#148 := [monotonicity #134 #145]: #147
+#151 := [monotonicity #148]: #150
+#154 := [monotonicity #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [monotonicity #163]: #165
+#171 := [trans #166 #169]: #170
+#174 := [monotonicity #171]: #173
+#182 := [trans #174 #180]: #181
+#120 := (iff #33 #119)
+#117 := (iff #32 #116)
+#114 := (= #31 #111)
+#102 := (+ 1::Int #96)
+#107 := (+ f3 #102)
+#112 := (= #107 #111)
+#113 := [rewrite]: #112
+#108 := (= #31 #107)
+#105 := (= #30 #102)
+#99 := (+ #96 1::Int)
+#103 := (= #99 #102)
+#104 := [rewrite]: #103
+#100 := (= #30 #99)
+#97 := (= #29 #96)
+#94 := (= #28 #86)
+#89 := (ite false f3 #86)
+#92 := (= #89 #86)
+#93 := [rewrite]: #92
+#90 := (= #28 #89)
+#87 := (= #27 #86)
+#84 := (= #26 #83)
+#81 := (= #25 #78)
+#75 := (- #72)
+#79 := (= #75 #78)
+#80 := [rewrite]: #79
+#76 := (= #25 #75)
+#73 := (= #24 #72)
+#70 := (= #23 -2::Int)
+#71 := [rewrite]: #70
+#67 := (= #22 #66)
+#68 := [rewrite]: #67
+#74 := [monotonicity #68 #71]: #73
+#77 := [monotonicity #74]: #76
+#82 := [trans #77 #80]: #81
+#63 := (iff #20 #62)
+#60 := (iff #19 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#85 := [monotonicity #64 #82]: #84
+#88 := [monotonicity #85]: #87
+#57 := (iff #13 false)
+#58 := [rewrite]: #57
+#91 := [monotonicity #58 #88]: #90
+#95 := [trans #91 #93]: #94
+#98 := [monotonicity #95]: #97
+#101 := [monotonicity #98]: #100
+#106 := [trans #101 #104]: #105
+#109 := [monotonicity #106]: #108
+#115 := [trans #109 #113]: #114
+#55 := (= #10 #54)
+#56 := [rewrite]: #55
+#118 := [monotonicity #56 #115]: #117
+#121 := [monotonicity #118]: #120
+#184 := [trans #121 #182]: #183
+#53 := [asserted]: #33
+#185 := [mp #53 #184]: #178
+#208 := [hypothesis]: #191
+#210 := (or #209 #175)
+#211 := [th-lemma arith triangle-eq]: #210
+#212 := [unit-resolution #211 #208 #185]: false
+#213 := [lemma #212]: #209
+#203 := (or #202 #191)
+#204 := [def-axiom]: #203
+#272 := [unit-resolution #204 #213]: #202
+#205 := (or #14 #192)
+#206 := [def-axiom]: #205
+#273 := [unit-resolution #206 #272]: #192
+#274 := [hypothesis]: #193
+#275 := [trans #274 #273]: #267
+#276 := (not #267)
+#277 := (or #276 #270)
+#278 := [th-lemma arith triangle-eq]: #277
+#279 := [unit-resolution #278 #275]: #270
+#239 := (>= #21 0::Int)
+#51 := [true-axiom]: true
+#280 := (or false #239)
+#281 := [th-lemma arith]: #280
+#282 := [unit-resolution #281 #51]: #239
+#283 := [th-lemma arith farkas -1 1 1 #282 #185 #279]: false
+#285 := [lemma #283]: #284
+#198 := (or #195 #193)
+#199 := [def-axiom]: #198
+#262 := [unit-resolution #199 #285]: #195
+#189 := (or #146 #122)
+#190 := [def-axiom]: #189
+#263 := [unit-resolution #190 #262]: #122
+#187 := (or #146 #135)
+#188 := [def-axiom]: #187
+#264 := [unit-resolution #188 #262]: #135
+#265 := (or #14 #123 #136)
+#266 := [th-lemma arith triangle-eq]: #265
+#237 := [unit-resolution #266 #272]: #146
+[unit-resolution #237 #264 #263]: false
+unsat
+a9554a5e9a99c006412b9165d7d1ec39d927f284 207 0
 #2 := false
-#20 := 0::Int
+#10 := 0::Int
 decl f3 :: Int
 #8 := f3
-#438 := (>= f3 0::Int)
-#758 := (<= f3 0::Int)
-#404 := (not #758)
-#747 := (not #438)
-#751 := (or #747 #404)
-#714 := (not #751)
+#112 := (<= f3 0::Int)
+#125 := (>= f3 0::Int)
+#126 := (not #125)
+#113 := (not #112)
+#136 := (or #113 #126)
+#184 := (not #136)
+#65 := -2::Int
+#61 := -1::Int
+#62 := (* -1::Int f3)
+#68 := (mod #62 -2::Int)
+#74 := (* -1::Int #68)
 #9 := 2::Int
-#439 := (mod f3 2::Int)
-#108 := -1::Int
-#440 := (* -1::Int #439)
-decl f4 :: (-> Int Int Int)
-#10 := (f4 f3 2::Int)
-#368 := (+ #10 #440)
-#441 := (= #368 0::Int)
-#587 := (not #441)
-#544 := (<= #368 0::Int)
-#647 := (not #544)
-#655 := (>= #439 2::Int)
-#656 := (not #655)
+#19 := (mod f3 2::Int)
+#139 := (ite #136 #19 #74)
+#182 := (= #19 #139)
+#279 := (not #182)
+#251 := (>= #19 2::Int)
+#252 := (not #251)
 #1 := true
-#64 := [true-axiom]: true
-#643 := (or false #656)
-#644 := [th-lemma arith]: #643
-#645 := [unit-resolution #644 #64]: #656
-#646 := [hypothesis]: #544
-#93 := (>= #10 2::Int)
-#13 := 3::Int
-#14 := (+ f3 3::Int)
-#11 := (+ #10 #10)
-#12 := (+ f3 #11)
-#15 := (< #12 #14)
-#16 := (not #15)
-#98 := (iff #16 #93)
-#73 := (+ 3::Int f3)
-#67 := (* 2::Int #10)
-#70 := (+ f3 #67)
-#76 := (< #70 #73)
-#79 := (not #76)
-#96 := (iff #79 #93)
-#86 := (>= #67 3::Int)
-#94 := (iff #86 #93)
-#95 := [rewrite]: #94
-#91 := (iff #79 #86)
-#84 := (not #86)
-#83 := (not #84)
-#89 := (iff #83 #86)
-#90 := [rewrite]: #89
-#87 := (iff #79 #83)
-#85 := (iff #76 #84)
-#82 := [rewrite]: #85
-#88 := [monotonicity #82]: #87
-#92 := [trans #88 #90]: #91
-#97 := [trans #92 #95]: #96
-#80 := (iff #16 #79)
-#77 := (iff #15 #76)
-#74 := (= #14 #73)
-#75 := [rewrite]: #74
-#71 := (= #12 #70)
-#68 := (= #11 #67)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#78 := [monotonicity #72 #75]: #77
-#81 := [monotonicity #78]: #80
-#99 := [trans #81 #97]: #98
-#66 := [asserted]: #16
-#100 := [mp #66 #99]: #93
-#641 := [th-lemma arith farkas -1 1 1 #100 #646 #645]: false
-#633 := [lemma #641]: #647
-#650 := (or #587 #544)
-#661 := [th-lemma arith triangle-eq]: #650
-#639 := [unit-resolution #661 #633]: #587
-#611 := (or #714 #441)
-#462 := -2::Int
-#435 := (* -1::Int f3)
-#733 := (mod #435 -2::Int)
-#457 := (+ #10 #733)
-#732 := (= #457 0::Int)
-#447 := (ite #751 #441 #732)
-#427 := (= #10 0::Int)
-#759 := (= f3 0::Int)
-#727 := (ite #759 #427 #447)
-#18 := (:var 0 Int)
-#17 := (:var 1 Int)
-#38 := (f4 #17 #18)
-#771 := (pattern #38)
-#112 := (* -1::Int #18)
-#109 := (* -1::Int #17)
-#167 := (mod #109 #112)
-#282 := (+ #38 #167)
-#283 := (= #282 0::Int)
-#39 := (mod #17 #18)
-#279 := (* -1::Int #39)
-#280 := (+ #38 #279)
-#281 := (= #280 0::Int)
-#141 := (>= #17 0::Int)
-#134 := (<= #18 0::Int)
-#226 := (or #134 #141)
-#227 := (not #226)
-#130 := (<= #17 0::Int)
-#224 := (or #130 #134)
-#225 := (not #224)
-#230 := (or #225 #227)
-#284 := (ite #230 #281 #283)
-#278 := (= #38 0::Int)
-#21 := (= #17 0::Int)
-#285 := (ite #21 #278 #284)
-#277 := (= #17 #38)
-#22 := (= #18 0::Int)
-#286 := (ite #22 #277 #285)
-#772 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #771) #286)
-#289 := (forall (vars (?v0 Int) (?v1 Int)) #286)
-#775 := (iff #289 #772)
-#773 := (iff #286 #286)
-#774 := [refl]: #773
-#776 := [quant-intro #774]: #775
-#173 := (* -1::Int #167)
-#246 := (ite #230 #39 #173)
-#249 := (ite #21 0::Int #246)
-#252 := (ite #22 #17 #249)
-#255 := (= #38 #252)
-#258 := (forall (vars (?v0 Int) (?v1 Int)) #255)
-#290 := (iff #258 #289)
-#287 := (iff #255 #286)
-#288 := [rewrite]: #287
-#291 := [quant-intro #288]: #290
-#142 := (not #141)
-#135 := (not #134)
-#145 := (and #135 #142)
-#131 := (not #130)
-#138 := (and #131 #135)
-#148 := (or #138 #145)
-#193 := (ite #148 #39 #173)
-#196 := (ite #21 0::Int #193)
-#199 := (ite #22 #17 #196)
-#202 := (= #38 #199)
-#205 := (forall (vars (?v0 Int) (?v1 Int)) #202)
-#259 := (iff #205 #258)
-#256 := (iff #202 #255)
-#253 := (= #199 #252)
-#250 := (= #196 #249)
-#247 := (= #193 #246)
-#231 := (iff #148 #230)
-#228 := (iff #145 #227)
-#229 := [rewrite]: #228
-#218 := (iff #138 #225)
-#219 := [rewrite]: #218
-#232 := [monotonicity #219 #229]: #231
-#248 := [monotonicity #232]: #247
-#251 := [monotonicity #248]: #250
-#254 := [monotonicity #251]: #253
-#257 := [monotonicity #254]: #256
-#260 := [quant-intro #257]: #259
-#216 := (~ #205 #205)
-#215 := (~ #202 #202)
-#212 := [refl]: #215
-#217 := [nnf-pos #212]: #216
-#32 := (- #18)
-#31 := (- #17)
-#40 := (mod #31 #32)
-#41 := (- #40)
-#25 := (< 0::Int #18)
-#27 := (< #17 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #17)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#42 := (ite #29 #39 #41)
-#43 := (ite #21 0::Int #42)
-#44 := (ite #22 #17 #43)
-#45 := (= #38 #44)
-#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#208 := (iff #46 #205)
-#102 := (and #25 #27)
-#105 := (or #26 #102)
-#178 := (ite #105 #39 #173)
-#181 := (ite #21 0::Int #178)
-#184 := (ite #22 #17 #181)
-#187 := (= #38 #184)
-#190 := (forall (vars (?v0 Int) (?v1 Int)) #187)
-#206 := (iff #190 #205)
-#203 := (iff #187 #202)
-#200 := (= #184 #199)
-#197 := (= #181 #196)
-#194 := (= #178 #193)
-#149 := (iff #105 #148)
-#146 := (iff #102 #145)
-#143 := (iff #27 #142)
-#144 := [rewrite]: #143
-#136 := (iff #25 #135)
-#137 := [rewrite]: #136
-#147 := [monotonicity #137 #144]: #146
-#139 := (iff #26 #138)
-#132 := (iff #24 #131)
+#50 := [true-axiom]: true
+#267 := (or false #252)
+#268 := [th-lemma arith]: #267
+#269 := [unit-resolution #268 #50]: #252
+#12 := (= f3 0::Int)
+#142 := (ite #12 0::Int #139)
+#263 := (* -1::Int #142)
+#264 := (+ #19 #263)
+#266 := (>= #264 0::Int)
+#262 := (= #19 #142)
+#181 := (= #139 #142)
+#191 := (not #12)
+#180 := (= #142 0::Int)
+#204 := (not #180)
+#196 := (<= #142 0::Int)
+#198 := (not #196)
+#167 := (>= #142 2::Int)
+#29 := 3::Int
+#30 := (+ f3 3::Int)
+#21 := (- 2::Int)
+#20 := (- f3)
+#22 := (mod #20 #21)
+#23 := (- #22)
+#14 := (< 0::Int 2::Int)
+#16 := (< f3 0::Int)
+#17 := (and #16 #14)
+#13 := (< 0::Int f3)
+#15 := (and #13 #14)
+#18 := (or #15 #17)
+#24 := (ite #18 #19 #23)
+#25 := (ite #12 0::Int #24)
+#11 := (= 2::Int 0::Int)
+#26 := (ite #11 f3 #25)
+#27 := (+ #26 #26)
+#28 := (+ f3 #27)
+#31 := (< #28 #30)
+#32 := (not #31)
+#172 := (iff #32 #167)
+#103 := (+ 3::Int f3)
+#55 := (and #14 #16)
+#58 := (or #15 #55)
+#79 := (ite #58 #19 #74)
+#82 := (ite #12 0::Int #79)
+#95 := (* 2::Int #82)
+#100 := (+ f3 #95)
+#106 := (< #100 #103)
+#109 := (not #106)
+#170 := (iff #109 #167)
+#145 := (* 2::Int #142)
+#155 := (>= #145 3::Int)
+#168 := (iff #155 #167)
+#169 := [rewrite]: #168
+#165 := (iff #109 #155)
+#154 := (not #155)
+#160 := (not #154)
+#163 := (iff #160 #155)
+#164 := [rewrite]: #163
+#161 := (iff #109 #160)
+#158 := (iff #106 #154)
+#148 := (+ f3 #145)
+#151 := (< #148 #103)
+#156 := (iff #151 #154)
+#157 := [rewrite]: #156
+#152 := (iff #106 #151)
+#149 := (= #100 #148)
+#146 := (= #95 #145)
+#143 := (= #82 #142)
+#140 := (= #79 #139)
+#137 := (iff #58 #136)
+#134 := (iff #55 #126)
+#129 := (and true #126)
+#132 := (iff #129 #126)
 #133 := [rewrite]: #132
-#140 := [monotonicity #133 #137]: #139
-#150 := [monotonicity #140 #147]: #149
-#195 := [monotonicity #150]: #194
-#198 := [monotonicity #195]: #197
-#201 := [monotonicity #198]: #200
-#204 := [monotonicity #201]: #203
-#207 := [quant-intro #204]: #206
-#191 := (iff #46 #190)
-#188 := (iff #45 #187)
-#185 := (= #44 #184)
-#182 := (= #43 #181)
-#179 := (= #42 #178)
-#176 := (= #41 #173)
-#170 := (- #167)
-#174 := (= #170 #173)
-#175 := [rewrite]: #174
-#171 := (= #41 #170)
-#168 := (= #40 #167)
-#113 := (= #32 #112)
-#114 := [rewrite]: #113
-#110 := (= #31 #109)
-#111 := [rewrite]: #110
-#169 := [monotonicity #111 #114]: #168
-#172 := [monotonicity #169]: #171
-#177 := [trans #172 #175]: #176
-#106 := (iff #29 #105)
-#103 := (iff #28 #102)
-#104 := [rewrite]: #103
-#107 := [monotonicity #104]: #106
-#180 := [monotonicity #107 #177]: #179
-#183 := [monotonicity #180]: #182
-#186 := [monotonicity #183]: #185
-#189 := [monotonicity #186]: #188
-#192 := [quant-intro #189]: #191
-#209 := [trans #192 #207]: #208
-#166 := [asserted]: #46
-#210 := [mp #166 #209]: #205
-#213 := [mp~ #210 #217]: #205
-#261 := [mp #213 #260]: #258
-#292 := [mp #261 #291]: #289
-#777 := [mp #292 #776]: #772
-#716 := (not #772)
-#717 := (or #716 #727)
-#350 := (* -1::Int 2::Int)
-#436 := (mod #435 #350)
-#437 := (+ #10 #436)
-#428 := (= #437 0::Int)
-#442 := (<= 2::Int 0::Int)
-#421 := (or #442 #438)
-#756 := (not #421)
-#415 := (or #758 #442)
-#545 := (not #415)
-#752 := (or #545 #756)
-#426 := (ite #752 #441 #428)
-#760 := (ite #759 #427 #426)
-#761 := (= f3 #10)
-#762 := (= 2::Int 0::Int)
-#757 := (ite #762 #761 #760)
-#722 := (or #716 #757)
-#718 := (iff #722 #717)
-#565 := (iff #717 #717)
-#566 := [rewrite]: #565
-#720 := (iff #757 #727)
-#725 := (ite false #761 #727)
-#730 := (iff #725 #727)
-#719 := [rewrite]: #730
-#729 := (iff #757 #725)
-#728 := (iff #760 #727)
-#448 := (iff #426 #447)
-#736 := (iff #428 #732)
-#731 := (= #437 #457)
-#734 := (= #436 #733)
-#463 := (= #350 -2::Int)
-#356 := [rewrite]: #463
-#456 := [monotonicity #356]: #734
-#735 := [monotonicity #456]: #731
-#446 := [monotonicity #735]: #736
-#460 := (iff #752 #751)
-#390 := (or #404 #747)
-#737 := (iff #390 #751)
-#738 := [rewrite]: #737
-#750 := (iff #752 #390)
-#749 := (iff #756 #747)
-#746 := (iff #421 #438)
-#742 := (or false #438)
-#745 := (iff #742 #438)
-#740 := [rewrite]: #745
-#743 := (iff #421 #742)
-#413 := (iff #442 false)
-#418 := [rewrite]: #413
-#744 := [monotonicity #418]: #743
-#384 := [trans #744 #740]: #746
-#389 := [monotonicity #384]: #749
-#405 := (iff #545 #404)
-#402 := (iff #415 #758)
-#754 := (or #758 false)
-#398 := (iff #754 #758)
-#739 := [rewrite]: #398
-#414 := (iff #415 #754)
-#755 := [monotonicity #418]: #414
-#403 := [trans #755 #739]: #402
-#741 := [monotonicity #403]: #405
-#748 := [monotonicity #741 #389]: #750
-#461 := [trans #748 #738]: #460
-#449 := [monotonicity #461 #446]: #448
-#443 := [monotonicity #449]: #728
-#763 := (iff #762 false)
-#753 := [rewrite]: #763
-#726 := [monotonicity #753 #443]: #729
-#721 := [trans #726 #719]: #720
-#724 := [monotonicity #721]: #718
-#567 := [trans #724 #566]: #718
-#723 := [quant-inst #8 #9]: #722
-#709 := [mp #723 #567]: #717
-#640 := [unit-resolution #709 #777]: #727
-#694 := (not #759)
-#693 := (not #727)
-#636 := (or #693 #694)
-#600 := (not #427)
-#710 := (<= #10 0::Int)
-#642 := (not #710)
-#672 := (not #93)
-#673 := (or #642 #672)
-#629 := [th-lemma arith farkas 1 1]: #673
-#630 := [unit-resolution #629 #100]: #642
-#631 := (or #600 #710)
-#634 := [th-lemma arith triangle-eq]: #631
-#635 := [unit-resolution #634 #630]: #600
-#697 := (or #693 #694 #427)
-#582 := [def-axiom]: #697
-#637 := [unit-resolution #582 #635]: #636
-#632 := [unit-resolution #637 #640]: #694
-#597 := (or #693 #759 #447)
-#599 := [def-axiom]: #597
-#638 := [unit-resolution #599 #632 #640]: #447
-#701 := (not #447)
-#703 := (or #701 #714 #441)
-#704 := [def-axiom]: #703
-#612 := [unit-resolution #704 #638]: #611
-#613 := [unit-resolution #612 #639]: #714
-#712 := (or #751 #438)
-#706 := [def-axiom]: #712
-#506 := [unit-resolution #706 #613]: #438
-#707 := (or #751 #758)
-#713 := [def-axiom]: #707
-#617 := [unit-resolution #713 #613]: #758
-#618 := (or #759 #404 #747)
-#619 := [th-lemma arith triangle-eq]: #618
-#624 := [unit-resolution #619 #632]: #390
-[unit-resolution #624 #617 #506]: false
+#130 := (iff #55 #129)
+#127 := (iff #16 #126)
+#128 := [rewrite]: #127
+#116 := (iff #14 true)
+#117 := [rewrite]: #116
+#131 := [monotonicity #117 #128]: #130
+#135 := [trans #131 #133]: #134
+#123 := (iff #15 #113)
+#118 := (and #113 true)
+#121 := (iff #118 #113)
+#122 := [rewrite]: #121
+#119 := (iff #15 #118)
+#114 := (iff #13 #113)
+#115 := [rewrite]: #114
+#120 := [monotonicity #115 #117]: #119
+#124 := [trans #120 #122]: #123
+#138 := [monotonicity #124 #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [monotonicity #147]: #149
+#153 := [monotonicity #150]: #152
+#159 := [trans #153 #157]: #158
+#162 := [monotonicity #159]: #161
+#166 := [trans #162 #164]: #165
+#171 := [trans #166 #169]: #170
+#110 := (iff #32 #109)
+#107 := (iff #31 #106)
+#104 := (= #30 #103)
+#105 := [rewrite]: #104
+#101 := (= #28 #100)
+#98 := (= #27 #95)
+#92 := (+ #82 #82)
+#96 := (= #92 #95)
+#97 := [rewrite]: #96
+#93 := (= #27 #92)
+#90 := (= #26 #82)
+#85 := (ite false f3 #82)
+#88 := (= #85 #82)
+#89 := [rewrite]: #88
+#86 := (= #26 #85)
+#83 := (= #25 #82)
+#80 := (= #24 #79)
+#77 := (= #23 #74)
+#71 := (- #68)
+#75 := (= #71 #74)
+#76 := [rewrite]: #75
+#72 := (= #23 #71)
+#69 := (= #22 #68)
+#66 := (= #21 -2::Int)
+#67 := [rewrite]: #66
+#63 := (= #20 #62)
+#64 := [rewrite]: #63
+#70 := [monotonicity #64 #67]: #69
+#73 := [monotonicity #70]: #72
+#78 := [trans #73 #76]: #77
+#59 := (iff #18 #58)
+#56 := (iff #17 #55)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#81 := [monotonicity #60 #78]: #80
+#84 := [monotonicity #81]: #83
+#53 := (iff #11 false)
+#54 := [rewrite]: #53
+#87 := [monotonicity #54 #84]: #86
+#91 := [trans #87 #89]: #90
+#94 := [monotonicity #91 #91]: #93
+#99 := [trans #94 #97]: #98
+#102 := [monotonicity #99]: #101
+#108 := [monotonicity #102 #105]: #107
+#111 := [monotonicity #108]: #110
+#173 := [trans #111 #171]: #172
+#52 := [asserted]: #32
+#174 := [mp #52 #173]: #167
+#199 := (not #167)
+#200 := (or #198 #199)
+#201 := [th-lemma arith farkas 1 1]: #200
+#202 := [unit-resolution #201 #174]: #198
+#203 := [hypothesis]: #180
+#205 := (or #204 #196)
+#206 := [th-lemma arith triangle-eq]: #205
+#207 := [unit-resolution #206 #203 #202]: false
+#208 := [lemma #207]: #204
+#192 := (or #191 #180)
+#193 := [def-axiom]: #192
+#270 := [unit-resolution #193 #208]: #191
+#194 := (or #12 #181)
+#195 := [def-axiom]: #194
+#271 := [unit-resolution #195 #270]: #181
+#272 := [hypothesis]: #182
+#273 := [trans #272 #271]: #262
+#274 := (not #262)
+#275 := (or #274 #266)
+#276 := [th-lemma arith triangle-eq]: #275
+#277 := [unit-resolution #276 #273]: #266
+#278 := [th-lemma arith farkas -1 -1 1 #174 #277 #269]: false
+#280 := [lemma #278]: #279
+#187 := (or #184 #182)
+#188 := [def-axiom]: #187
+#257 := [unit-resolution #188 #280]: #184
+#178 := (or #136 #112)
+#179 := [def-axiom]: #178
+#258 := [unit-resolution #179 #257]: #112
+#176 := (or #136 #125)
+#177 := [def-axiom]: #176
+#259 := [unit-resolution #177 #257]: #125
+#260 := (or #12 #113 #126)
+#261 := [th-lemma arith triangle-eq]: #260
+#232 := [unit-resolution #261 #270]: #136
+[unit-resolution #232 #259 #258]: false
 unsat
 cfa8a4e8b0964986b89eaf37e6038032e9b8b0d6 101 0
 #2 := false
@@ -8171,936 +7945,783 @@
 #123 := [th-lemma arith triangle-eq]: #122
 [unit-resolution #123 #119 #112 #46]: false
 unsat
-742e212b0179422ed718ceb7818522f48622510c 930 0
+cf727a25fbaea6abf5a0d302bf954b4ffa92b324 777 0
 #2 := false
-#20 := 1::Int
-decl f3 :: (-> Int Int Int)
-#11 := 2::Int
-decl f5 :: Int
-#9 := f5
-#22 := (f3 f5 2::Int)
-#1103 := (<= #22 1::Int)
-#13 := 0::Int
-#574 := (mod f5 2::Int)
-#108 := -1::Int
-#575 := (* -1::Int #574)
-#576 := (+ #22 #575)
-#954 := (<= #576 0::Int)
-#577 := (= #576 0::Int)
-decl f4 :: Int
-#8 := f4
-#10 := (+ f4 f5)
-#461 := (>= #10 0::Int)
-#778 := (= #10 0::Int)
-#458 := (mod #10 2::Int)
-#459 := (* -1::Int #458)
-#12 := (f3 #10 2::Int)
-#460 := (+ #12 #459)
-#457 := (= #460 0::Int)
-#715 := (not #457)
-#720 := (<= #460 0::Int)
-#1107 := [hypothesis]: #457
-#1108 := (or #715 #720)
-#1109 := [th-lemma arith triangle-eq]: #1108
-#1110 := [unit-resolution #1109 #1107]: #720
-#722 := (>= #460 0::Int)
-#1111 := (or #715 #722)
-#1322 := [th-lemma arith triangle-eq]: #1111
-#1323 := [unit-resolution #1322 #1107]: #722
-#1193 := (not #720)
-#1239 := (not #722)
-#1348 := (or #1239 #1193)
-#1112 := (div f5 2::Int)
-#476 := -2::Int
-#1125 := (* -2::Int #1112)
-#1126 := (+ #575 #1125)
-#1127 := (+ f5 #1126)
-#1124 := (= #1127 0::Int)
-#1161 := (not #1124)
-#1276 := [hypothesis]: #1161
+#9 := 0::Int
+#30 := 4::Int
+decl f3 :: Int
+#11 := f3
+#546 := (div f3 4::Int)
+#208 := -4::Int
+#574 := (* -4::Int #546)
+#39 := (mod f3 4::Int)
+#107 := -1::Int
+#573 := (* -1::Int #39)
+#575 := (+ #573 #574)
+#576 := (+ f3 #575)
+#581 := (<= #576 0::Int)
+#572 := (= #576 0::Int)
 #1 := true
-#72 := [true-axiom]: true
-#1154 := (or false #1124)
-#1159 := [th-lemma arith]: #1154
-#1277 := [unit-resolution #1159 #72 #1276]: false
-#1278 := [lemma #1277]: #1124
-#1274 := (or #1161 #1239 #1193)
-#1134 := (>= #574 0::Int)
-#1157 := (or false #1134)
-#1158 := [th-lemma arith]: #1157
-#1151 := [unit-resolution #1158 #72]: #1134
-#1224 := (>= #1127 0::Int)
-#1246 := [hypothesis]: #1124
-#1247 := (or #1161 #1224)
-#1248 := [th-lemma arith triangle-eq]: #1247
-#1249 := [unit-resolution #1248 #1246]: #1224
-#17 := 3::Int
-#15 := 4::Int
-#16 := (f3 f4 4::Int)
-#568 := (>= #16 3::Int)
-#18 := (= #16 3::Int)
-#75 := [asserted]: #18
-#967 := (not #18)
-#993 := (or #967 #568)
-#994 := [th-lemma arith triangle-eq]: #993
-#995 := [unit-resolution #994 #75]: #568
-#865 := (div f4 4::Int)
-#663 := -4::Int
-#881 := (* -4::Int #865)
-#696 := (mod f4 4::Int)
-#698 := (* -1::Int #696)
-#882 := (+ #698 #881)
-#883 := (+ f4 #882)
-#889 := (>= #883 0::Int)
-#880 := (= #883 0::Int)
-#971 := (or false #880)
-#972 := [th-lemma arith]: #971
-#973 := [unit-resolution #972 #72]: #880
-#974 := (not #880)
-#996 := (or #974 #889)
-#997 := [th-lemma arith triangle-eq]: #996
-#998 := [unit-resolution #997 #973]: #889
-#560 := (>= #12 0::Int)
-#14 := (= #12 0::Int)
-#74 := [asserted]: #14
-#622 := (not #14)
-#1230 := (or #622 #560)
-#1231 := [th-lemma arith triangle-eq]: #1230
-#1232 := [unit-resolution #1231 #74]: #560
-#811 := (div #10 2::Int)
-#828 := (* -2::Int #811)
-#829 := (+ #459 #828)
-#830 := (+ f5 #829)
-#831 := (+ f4 #830)
-#1106 := (>= #831 0::Int)
-#826 := (= #831 0::Int)
-#1167 := (or false #826)
-#1168 := [th-lemma arith]: #1167
-#1169 := [unit-resolution #1168 #72]: #826
-#1180 := (not #826)
-#1233 := (or #1180 #1106)
-#1234 := [th-lemma arith triangle-eq]: #1233
-#1235 := [unit-resolution #1234 #1169]: #1106
-#708 := (+ #16 #698)
-#600 := (>= #708 0::Int)
-#709 := (= #708 0::Int)
-#482 := (* -1::Int f4)
-#660 := (mod #482 -4::Int)
-#648 := (+ #16 #660)
-#653 := (= #648 0::Int)
-#710 := (>= f4 0::Int)
-#669 := (not #710)
-#701 := (<= f4 0::Int)
-#670 := (not #701)
-#659 := (or #670 #669)
-#656 := (ite #659 #709 #653)
-#689 := (= f4 0::Int)
-#590 := (not #689)
-#688 := (= #16 0::Int)
-#595 := (not #688)
-#428 := (= 3::Int 0::Int)
-#430 := (iff #428 false)
-#419 := [rewrite]: #430
-#425 := [hypothesis]: #688
-#426 := (= 3::Int #16)
-#427 := [symm #75]: #426
-#429 := [trans #427 #425]: #428
-#431 := [mp #429 #419]: false
-#412 := [lemma #431]: #595
-#1027 := (or #590 #688)
-#630 := (ite #689 #688 #656)
-#27 := (:var 0 Int)
-#26 := (:var 1 Int)
-#46 := (f3 #26 #27)
-#790 := (pattern #46)
-#112 := (* -1::Int #27)
-#109 := (* -1::Int #26)
-#173 := (mod #109 #112)
-#302 := (+ #46 #173)
-#303 := (= #302 0::Int)
-#47 := (mod #26 #27)
-#299 := (* -1::Int #47)
-#300 := (+ #46 #299)
-#301 := (= #300 0::Int)
-#147 := (>= #26 0::Int)
-#140 := (<= #27 0::Int)
-#246 := (or #140 #147)
-#247 := (not #246)
-#136 := (<= #26 0::Int)
-#242 := (or #136 #140)
-#243 := (not #242)
-#250 := (or #243 #247)
-#304 := (ite #250 #301 #303)
-#298 := (= #46 0::Int)
-#29 := (= #26 0::Int)
-#305 := (ite #29 #298 #304)
-#297 := (= #26 #46)
-#30 := (= #27 0::Int)
-#306 := (ite #30 #297 #305)
-#791 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #790) #306)
-#309 := (forall (vars (?v0 Int) (?v1 Int)) #306)
-#794 := (iff #309 #791)
-#792 := (iff #306 #306)
-#793 := [refl]: #792
-#795 := [quant-intro #793]: #794
-#179 := (* -1::Int #173)
-#266 := (ite #250 #47 #179)
-#269 := (ite #29 0::Int #266)
-#272 := (ite #30 #26 #269)
-#275 := (= #46 #272)
-#278 := (forall (vars (?v0 Int) (?v1 Int)) #275)
-#310 := (iff #278 #309)
-#307 := (iff #275 #306)
-#308 := [rewrite]: #307
-#311 := [quant-intro #308]: #310
-#148 := (not #147)
-#141 := (not #140)
-#151 := (and #141 #148)
-#137 := (not #136)
-#144 := (and #137 #141)
-#154 := (or #144 #151)
-#199 := (ite #154 #47 #179)
-#202 := (ite #29 0::Int #199)
-#205 := (ite #30 #26 #202)
-#208 := (= #46 #205)
-#211 := (forall (vars (?v0 Int) (?v1 Int)) #208)
-#279 := (iff #211 #278)
-#276 := (iff #208 #275)
-#273 := (= #205 #272)
-#270 := (= #202 #269)
-#267 := (= #199 #266)
-#251 := (iff #154 #250)
-#248 := (iff #151 #247)
-#249 := [rewrite]: #248
-#244 := (iff #144 #243)
-#245 := [rewrite]: #244
-#252 := [monotonicity #245 #249]: #251
-#268 := [monotonicity #252]: #267
-#271 := [monotonicity #268]: #270
+#93 := [true-axiom]: true
+#721 := (or false #572)
+#722 := [th-lemma arith]: #721
+#723 := [unit-resolution #722 #93]: #572
+#724 := (not #572)
+#725 := (or #724 #581)
+#726 := [th-lemma arith triangle-eq]: #725
+#727 := [unit-resolution #726 #723]: #581
+#582 := (>= #576 0::Int)
+#728 := (or #724 #582)
+#729 := [th-lemma arith triangle-eq]: #728
+#730 := [unit-resolution #729 #723]: #582
+#600 := (>= #39 4::Int)
+#601 := (not #600)
+#731 := (or false #601)
+#732 := [th-lemma arith]: #731
+#733 := [unit-resolution #732 #93]: #601
+#47 := 3::Int
+#613 := (>= #39 3::Int)
+#872 := (= #39 3::Int)
+#108 := (* -1::Int f3)
+#211 := (mod #108 -4::Int)
+#217 := (* -1::Int #211)
+#258 := (>= f3 0::Int)
+#259 := (not #258)
+#245 := (<= f3 0::Int)
+#246 := (not #245)
+#269 := (or #246 #259)
+#272 := (ite #269 #39 #217)
+#32 := (= f3 0::Int)
+#275 := (ite #32 0::Int #272)
+#282 := (= #275 3::Int)
+#41 := (- 4::Int)
+#40 := (- f3)
+#42 := (mod #40 #41)
+#43 := (- #42)
+#34 := (< 0::Int 4::Int)
+#36 := (< f3 0::Int)
+#37 := (and #36 #34)
+#33 := (< 0::Int f3)
+#35 := (and #33 #34)
+#38 := (or #35 #37)
+#44 := (ite #38 #39 #43)
+#45 := (ite #32 0::Int #44)
+#31 := (= 4::Int 0::Int)
+#46 := (ite #31 f3 #45)
+#48 := (= #46 3::Int)
+#286 := (iff #48 #282)
+#200 := (and #34 #36)
+#203 := (or #35 #200)
+#222 := (ite #203 #39 #217)
+#197 := (= 0::Int f3)
+#225 := (ite #197 0::Int #222)
+#238 := (= 3::Int #225)
+#284 := (iff #238 #282)
+#278 := (= 3::Int #275)
+#281 := (iff #278 #282)
+#283 := [rewrite]: #281
+#279 := (iff #238 #278)
+#276 := (= #225 #275)
+#273 := (= #222 #272)
+#270 := (iff #203 #269)
+#267 := (iff #200 #259)
+#262 := (and true #259)
+#265 := (iff #262 #259)
+#266 := [rewrite]: #265
+#263 := (iff #200 #262)
+#260 := (iff #36 #259)
+#261 := [rewrite]: #260
+#249 := (iff #34 true)
+#250 := [rewrite]: #249
+#264 := [monotonicity #250 #261]: #263
+#268 := [trans #264 #266]: #267
+#256 := (iff #35 #246)
+#251 := (and #246 true)
+#254 := (iff #251 #246)
+#255 := [rewrite]: #254
+#252 := (iff #35 #251)
+#247 := (iff #33 #246)
+#248 := [rewrite]: #247
+#253 := [monotonicity #248 #250]: #252
+#257 := [trans #253 #255]: #256
+#271 := [monotonicity #257 #268]: #270
 #274 := [monotonicity #271]: #273
-#277 := [monotonicity #274]: #276
-#280 := [quant-intro #277]: #279
-#221 := (~ #211 #211)
-#223 := (~ #208 #208)
-#220 := [refl]: #223
-#224 := [nnf-pos #220]: #221
-#40 := (- #27)
-#39 := (- #26)
-#48 := (mod #39 #40)
-#49 := (- #48)
-#33 := (< 0::Int #27)
-#35 := (< #26 0::Int)
-#36 := (and #35 #33)
-#32 := (< 0::Int #26)
-#34 := (and #32 #33)
-#37 := (or #34 #36)
-#50 := (ite #37 #47 #49)
-#51 := (ite #29 0::Int #50)
-#52 := (ite #30 #26 #51)
-#53 := (= #46 #52)
-#54 := (forall (vars (?v0 Int) (?v1 Int)) #53)
-#214 := (iff #54 #211)
-#102 := (and #33 #35)
-#105 := (or #34 #102)
-#184 := (ite #105 #47 #179)
-#93 := (= 0::Int #26)
-#187 := (ite #93 0::Int #184)
-#96 := (= 0::Int #27)
-#190 := (ite #96 #26 #187)
-#193 := (= #46 #190)
-#196 := (forall (vars (?v0 Int) (?v1 Int)) #193)
-#212 := (iff #196 #211)
-#209 := (iff #193 #208)
-#206 := (= #190 #205)
-#203 := (= #187 #202)
-#200 := (= #184 #199)
-#155 := (iff #105 #154)
-#152 := (iff #102 #151)
-#149 := (iff #35 #148)
-#150 := [rewrite]: #149
-#142 := (iff #33 #141)
-#143 := [rewrite]: #142
-#153 := [monotonicity #143 #150]: #152
-#145 := (iff #34 #144)
-#138 := (iff #32 #137)
-#139 := [rewrite]: #138
-#146 := [monotonicity #139 #143]: #145
-#156 := [monotonicity #146 #153]: #155
-#201 := [monotonicity #156]: #200
-#130 := (iff #93 #29)
-#131 := [rewrite]: #130
-#204 := [monotonicity #131 #201]: #203
-#132 := (iff #96 #30)
-#133 := [rewrite]: #132
-#207 := [monotonicity #133 #204]: #206
-#210 := [monotonicity #207]: #209
-#213 := [quant-intro #210]: #212
-#197 := (iff #54 #196)
-#194 := (iff #53 #193)
-#191 := (= #52 #190)
-#188 := (= #51 #187)
-#185 := (= #50 #184)
-#182 := (= #49 #179)
-#176 := (- #173)
-#180 := (= #176 #179)
-#181 := [rewrite]: #180
-#177 := (= #49 #176)
-#174 := (= #48 #173)
-#113 := (= #40 #112)
-#114 := [rewrite]: #113
-#110 := (= #39 #109)
-#111 := [rewrite]: #110
-#175 := [monotonicity #111 #114]: #174
-#178 := [monotonicity #175]: #177
-#183 := [trans #178 #181]: #182
-#106 := (iff #37 #105)
-#103 := (iff #36 #102)
-#104 := [rewrite]: #103
-#107 := [monotonicity #104]: #106
-#186 := [monotonicity #107 #183]: #185
-#94 := (iff #29 #93)
-#95 := [rewrite]: #94
-#189 := [monotonicity #95 #186]: #188
-#97 := (iff #30 #96)
-#98 := [rewrite]: #97
-#192 := [monotonicity #98 #189]: #191
-#195 := [monotonicity #192]: #194
-#198 := [quant-intro #195]: #197
-#215 := [trans #198 #213]: #214
-#172 := [asserted]: #54
-#216 := [mp #172 #215]: #211
-#225 := [mp~ #216 #224]: #211
-#281 := [mp #225 #280]: #278
-#312 := [mp #281 #311]: #309
-#796 := [mp #312 #795]: #791
-#584 := (not #791)
-#641 := (or #584 #630)
-#718 := (* -1::Int 4::Int)
-#705 := (mod #482 #718)
-#707 := (+ #16 #705)
-#699 := (= #707 0::Int)
-#706 := (<= 4::Int 0::Int)
-#711 := (or #706 #710)
-#700 := (not #711)
-#702 := (or #701 #706)
-#703 := (not #702)
-#697 := (or #703 #700)
-#704 := (ite #697 #709 #699)
-#691 := (ite #689 #688 #704)
-#692 := (= f4 #16)
-#693 := (= 4::Int 0::Int)
-#694 := (ite #693 #692 #691)
-#644 := (or #584 #694)
-#646 := (iff #644 #641)
-#647 := (iff #641 #641)
-#627 := [rewrite]: #647
-#639 := (iff #694 #630)
-#525 := (ite false #692 #630)
-#638 := (iff #525 #630)
-#643 := [rewrite]: #638
-#636 := (iff #694 #525)
-#631 := (iff #691 #630)
-#651 := (iff #704 #656)
-#654 := (iff #699 #653)
-#649 := (= #707 #648)
-#666 := (= #705 #660)
-#664 := (= #718 -4::Int)
-#665 := [rewrite]: #664
-#652 := [monotonicity #665]: #666
-#650 := [monotonicity #652]: #649
-#655 := [monotonicity #650]: #654
-#661 := (iff #697 #659)
-#680 := (iff #700 #669)
-#678 := (iff #711 #710)
-#673 := (or false #710)
-#676 := (iff #673 #710)
-#677 := [rewrite]: #676
-#674 := (iff #711 #673)
-#681 := (iff #706 false)
-#682 := [rewrite]: #681
-#675 := [monotonicity #682]: #674
-#679 := [trans #675 #677]: #678
-#658 := [monotonicity #679]: #680
-#671 := (iff #703 #670)
-#667 := (iff #702 #701)
-#684 := (or #701 false)
-#683 := (iff #684 #701)
-#687 := [rewrite]: #683
-#685 := (iff #702 #684)
-#686 := [monotonicity #682]: #685
-#668 := [trans #686 #687]: #667
-#672 := [monotonicity #668]: #671
-#662 := [monotonicity #672 #658]: #661
-#657 := [monotonicity #662 #655]: #651
-#632 := [monotonicity #657]: #631
-#690 := (iff #693 false)
-#695 := [rewrite]: #690
-#637 := [monotonicity #695 #632]: #636
-#640 := [trans #637 #643]: #639
-#642 := [monotonicity #640]: #646
-#573 := [trans #642 #627]: #646
-#645 := [quant-inst #8 #15]: #644
-#628 := [mp #645 #573]: #641
-#1048 := [unit-resolution #628 #796]: #630
-#589 := (not #630)
-#591 := (or #589 #590 #688)
-#592 := [def-axiom]: #591
-#1047 := [unit-resolution #592 #1048]: #1027
-#1043 := [unit-resolution #1047 #412]: #590
-#957 := (or #689 #656)
-#593 := (or #589 #689 #656)
-#594 := [def-axiom]: #593
-#964 := [unit-resolution #594 #1048]: #957
-#1033 := [unit-resolution #964 #1043]: #656
-#635 := (not #659)
-#860 := [hypothesis]: #635
-#609 := (or #659 #701)
-#633 := [def-axiom]: #609
-#861 := [unit-resolution #633 #860]: #701
-#634 := (or #659 #710)
-#629 := [def-axiom]: #634
-#862 := [unit-resolution #629 #860]: #710
-#863 := (or #689 #670 #669)
-#864 := [th-lemma arith triangle-eq]: #863
-#913 := [unit-resolution #864 #862 #861 #1043]: false
-#914 := [lemma #913]: #659
-#611 := (not #656)
-#613 := (or #611 #635 #709)
-#614 := [def-axiom]: #613
-#1165 := [unit-resolution #614 #914 #1033]: #709
-#605 := (not #709)
-#1054 := (or #605 #600)
-#1055 := [th-lemma arith triangle-eq]: #1054
-#1236 := [unit-resolution #1055 #1165]: #600
-#1237 := [hypothesis]: #722
-#1170 := (* -1::Int #1112)
-#1035 := (* -2::Int #865)
-#1171 := (+ #1035 #1170)
-#1155 := (* -1::Int #811)
-#1172 := (+ #1155 #1171)
-#1173 := (+ #698 #1172)
-#1174 := (+ #459 #1173)
-#1175 := (+ #16 #1174)
-#1176 := (+ #12 #1175)
-#1177 := (+ f5 #1176)
-#1178 := (+ f4 #1177)
-#1179 := (>= #1178 2::Int)
-#1191 := (not #1179)
-#955 := (>= #576 0::Int)
-#1184 := [hypothesis]: #720
-#1240 := (or #577 #1239 #1193)
-#561 := (<= #16 3::Int)
-#968 := (or #967 #561)
-#966 := [th-lemma arith triangle-eq]: #968
-#970 := [unit-resolution #966 #75]: #561
-#888 := (<= #883 0::Int)
-#975 := (or #974 #888)
-#976 := [th-lemma arith triangle-eq]: #975
-#982 := [unit-resolution #976 #973]: #888
-#580 := (<= f5 0::Int)
-#556 := (= f5 0::Int)
-#1059 := (not #577)
-#1146 := [hypothesis]: #1059
-#1222 := (or #556 #577)
-#376 := (* -1::Int f5)
-#521 := (mod #376 -2::Int)
-#523 := (+ #22 #521)
-#508 := (= #523 0::Int)
-#546 := (not #580)
-#578 := (>= f5 0::Int)
-#526 := (not #578)
-#536 := (or #526 #546)
-#511 := (ite #536 #577 #508)
-#1066 := (not #556)
-#1207 := [hypothesis]: #1066
-#1201 := (or #556 #511)
-#555 := (= #22 0::Int)
-#514 := (ite #556 #555 #511)
-#382 := (or #584 #514)
-#370 := (* -1::Int 2::Int)
-#570 := (mod #376 #370)
-#571 := (+ #22 #570)
-#572 := (= #571 0::Int)
-#440 := (<= 2::Int 0::Int)
-#579 := (or #440 #578)
-#562 := (not #579)
-#550 := (or #580 #440)
-#551 := (not #550)
-#552 := (or #551 #562)
-#553 := (ite #552 #577 #572)
-#557 := (ite #556 #555 #553)
-#400 := (= f5 #22)
-#781 := (= 2::Int 0::Int)
-#558 := (ite #781 #400 #557)
-#383 := (or #584 #558)
-#371 := (iff #383 #382)
-#375 := (iff #382 #382)
-#797 := [rewrite]: #375
-#498 := (iff #558 #514)
-#517 := (ite false #400 #514)
-#495 := (iff #517 #514)
-#497 := [rewrite]: #495
-#506 := (iff #558 #517)
-#515 := (iff #557 #514)
-#512 := (iff #553 #511)
-#509 := (iff #572 #508)
-#505 := (= #571 #523)
-#522 := (= #570 #521)
-#750 := (= #370 -2::Int)
-#754 := [rewrite]: #750
-#520 := [monotonicity #754]: #522
-#507 := [monotonicity #520]: #505
-#510 := [monotonicity #507]: #509
-#533 := (iff #552 #536)
-#531 := (or #546 #526)
-#529 := (iff #531 #536)
-#532 := [rewrite]: #529
-#535 := (iff #552 #531)
-#527 := (iff #562 #526)
-#534 := (iff #579 #578)
-#540 := (or false #578)
-#539 := (iff #540 #578)
-#544 := [rewrite]: #539
-#542 := (iff #579 #540)
-#758 := (iff #440 false)
-#421 := [rewrite]: #758
-#543 := [monotonicity #421]: #542
-#524 := [trans #543 #544]: #534
-#530 := [monotonicity #524]: #527
-#549 := (iff #551 #546)
-#547 := (iff #550 #580)
-#554 := (or #580 false)
-#541 := (iff #554 #580)
-#545 := [rewrite]: #541
-#559 := (iff #550 #554)
-#538 := [monotonicity #421]: #559
-#548 := [trans #538 #545]: #547
-#537 := [monotonicity #548]: #549
-#528 := [monotonicity #537 #530]: #535
-#519 := [trans #528 #532]: #533
-#513 := [monotonicity #519 #510]: #512
-#516 := [monotonicity #513]: #515
-#782 := (iff #781 false)
-#772 := [rewrite]: #782
-#518 := [monotonicity #772 #516]: #506
-#499 := [trans #518 #497]: #498
-#372 := [monotonicity #499]: #371
-#798 := [trans #372 #797]: #371
-#384 := [quant-inst #9 #11]: #383
-#799 := [mp #384 #798]: #382
-#1156 := [unit-resolution #799 #796]: #514
-#1028 := (not #514)
-#1034 := (or #1028 #556 #511)
-#1070 := [def-axiom]: #1034
-#1202 := [unit-resolution #1070 #1156]: #1201
-#1208 := [unit-resolution #1202 #1207]: #511
-#1205 := (or #578 #577)
-#1147 := [hypothesis]: #526
-#388 := (or #536 #578)
-#389 := [def-axiom]: #388
-#1148 := [unit-resolution #389 #1147]: #536
-#1149 := (or #1066 #578)
-#1150 := [th-lemma arith triangle-eq]: #1149
-#1133 := [unit-resolution #1150 #1147]: #1066
-#1203 := [unit-resolution #1202 #1133]: #511
-#917 := (not #536)
-#836 := (not #511)
-#1025 := (or #836 #917 #577)
-#1026 := [def-axiom]: #1025
-#1204 := [unit-resolution #1026 #1203 #1148 #1146]: false
-#1206 := [lemma #1204]: #1205
-#1209 := [unit-resolution #1206 #1146]: #578
-#1217 := (or #556 #546 #526)
-#1218 := [th-lemma arith triangle-eq]: #1217
-#1219 := [unit-resolution #1218 #1207 #1209]: #546
-#915 := (or #536 #580)
-#916 := [def-axiom]: #915
-#1220 := [unit-resolution #916 #1219]: #536
-#1221 := [unit-resolution #1026 #1220 #1208 #1146]: false
-#1223 := [lemma #1221]: #1222
-#1226 := [unit-resolution #1223 #1146]: #556
-#1227 := (or #1066 #580)
-#1228 := [th-lemma arith triangle-eq]: #1227
-#1229 := [unit-resolution #1228 #1226]: #580
-#599 := (<= #12 0::Int)
-#1186 := (or #622 #599)
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-#1188 := [unit-resolution #1187 #74]: #599
-#1105 := (<= #831 0::Int)
-#1181 := (or #1180 #1105)
-#1182 := [th-lemma arith triangle-eq]: #1181
-#1183 := [unit-resolution #1182 #1169]: #1105
-#569 := (<= #708 0::Int)
-#1050 := (or #605 #569)
-#1051 := [th-lemma arith triangle-eq]: #1050
-#1166 := [unit-resolution #1051 #1165]: #569
-#1238 := [th-lemma arith gcd-test -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 #1237 #1184 #1236 #1166 #1235 #1183 #1232 #1188 #1209 #1229 #998 #982 #995 #970]: false
-#1241 := [lemma #1238]: #1240
-#1250 := [unit-resolution #1241 #1237 #1184]: #577
-#1251 := (or #1059 #955)
-#1252 := [th-lemma arith triangle-eq]: #1251
-#1253 := [unit-resolution #1252 #1250]: #955
-#1104 := (>= #22 1::Int)
-#1152 := (not #1104)
-#1254 := (or #1059 #954)
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-#1256 := [unit-resolution #1255 #1250]: #954
-#1140 := (>= #574 2::Int)
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-#1259 := [unit-resolution #1258 #72]: #1141
-#1260 := (not #954)
-#1261 := (or #1103 #1140 #1260)
-#1262 := [th-lemma arith assign-bounds 1 1]: #1261
-#1263 := [unit-resolution #1262 #1259 #1256]: #1103
-#1266 := (not #1103)
-#1269 := (or #1266 #1152)
-#23 := (= #22 1::Int)
-#219 := (not #23)
-#19 := (f3 f4 2::Int)
-#21 := (= #19 1::Int)
-#1097 := (or #635 #21)
-#918 := (div f4 2::Int)
-#1036 := (* -1::Int #918)
-#1037 := (+ #1035 #1036)
-#1038 := (+ #698 #1037)
-#483 := (mod f4 2::Int)
-#484 := (* -1::Int #483)
-#1039 := (+ #484 #1038)
-#1040 := (+ #16 #1039)
-#1041 := (+ f4 #1040)
-#1042 := (>= #1041 2::Int)
-#1030 := (not #1042)
-#1045 := [hypothesis]: #659
-#1049 := [unit-resolution #614 #1045 #1033]: #709
-#1052 := [unit-resolution #1051 #1049]: #569
-#988 := (not #569)
-#1031 := (or #1030 #988)
-#940 := (>= #483 0::Int)
-#1023 := (or false #940)
-#1024 := [th-lemma arith]: #1023
-#1021 := [unit-resolution #1024 #72]: #940
-#983 := [hypothesis]: #569
-#931 := (* -2::Int #918)
-#932 := (+ #484 #931)
-#933 := (+ f4 #932)
-#938 := (<= #933 0::Int)
-#930 := (= #933 0::Int)
-#1011 := (or false #930)
-#1010 := [th-lemma arith]: #1011
-#1009 := [unit-resolution #1010 #72]: #930
-#958 := (not #930)
-#959 := (or #958 #938)
-#965 := [th-lemma arith triangle-eq]: #959
-#963 := [unit-resolution #965 #1009]: #938
-#1022 := [hypothesis]: #1042
-#1029 := [th-lemma arith farkas -1 2 -1 -1 -1 1 #970 #1022 #982 #963 #983 #1021]: false
-#1032 := [lemma #1029]: #1031
-#1053 := [unit-resolution #1032 #1052]: #1030
-#1056 := [unit-resolution #1055 #1049]: #600
-#939 := (>= #933 0::Int)
-#1064 := (or #958 #939)
-#1065 := [th-lemma arith triangle-eq]: #1064
-#1068 := [unit-resolution #1065 #1009]: #939
-#485 := (+ #19 #484)
-#385 := (>= #485 0::Int)
-#477 := (= #485 0::Int)
-#500 := (mod #482 -2::Int)
-#504 := (+ #19 #500)
-#491 := (= #504 0::Int)
-#478 := (ite #659 #477 #491)
-#464 := (= #19 0::Int)
-#420 := (ite #689 #464 #478)
-#411 := (or #584 #420)
-#493 := (mod #482 #370)
-#492 := (+ #19 #493)
-#494 := (= #492 0::Int)
-#469 := (or #440 #710)
-#470 := (not #469)
-#471 := (or #701 #440)
-#463 := (not #471)
-#472 := (or #463 #470)
-#473 := (ite #472 #477 #494)
-#474 := (ite #689 #464 #473)
-#441 := (= f4 #19)
-#443 := (ite #781 #441 #474)
-#386 := (or #584 #443)
-#391 := (iff #386 #411)
-#398 := (iff #411 #411)
-#399 := [rewrite]: #398
-#410 := (iff #443 #420)
-#413 := (ite false #441 #420)
-#406 := (iff #413 #420)
-#407 := [rewrite]: #406
-#416 := (iff #443 #413)
-#414 := (iff #474 #420)
-#488 := (iff #473 #478)
-#486 := (iff #494 #491)
-#489 := (= #492 #504)
-#503 := (= #493 #500)
-#496 := [monotonicity #754]: #503
-#490 := [monotonicity #496]: #489
-#487 := [monotonicity #490]: #486
-#501 := (iff #472 #659)
-#438 := (iff #470 #669)
-#453 := (iff #469 #710)
-#452 := (iff #469 #673)
-#442 := [monotonicity #421]: #452
-#436 := [trans #442 #677]: #453
+#243 := (iff #197 #32)
+#244 := [rewrite]: #243
+#277 := [monotonicity #244 #274]: #276
+#280 := [monotonicity #277]: #279
+#285 := [trans #280 #283]: #284
+#241 := (iff #48 #238)
+#235 := (= #225 3::Int)
+#239 := (iff #235 #238)
+#240 := [rewrite]: #239
+#236 := (iff #48 #235)
+#233 := (= #46 #225)
+#228 := (ite false f3 #225)
+#231 := (= #228 #225)
+#232 := [rewrite]: #231
+#229 := (= #46 #228)
+#226 := (= #45 #225)
+#223 := (= #44 #222)
+#220 := (= #43 #217)
+#214 := (- #211)
+#218 := (= #214 #217)
+#219 := [rewrite]: #218
+#215 := (= #43 #214)
+#212 := (= #42 #211)
+#209 := (= #41 -4::Int)
+#210 := [rewrite]: #209
+#206 := (= #40 #108)
+#207 := [rewrite]: #206
+#213 := [monotonicity #207 #210]: #212
+#216 := [monotonicity #213]: #215
+#221 := [trans #216 #219]: #220
+#204 := (iff #38 #203)
+#201 := (iff #37 #200)
+#202 := [rewrite]: #201
+#205 := [monotonicity #202]: #204
+#224 := [monotonicity #205 #221]: #223
+#198 := (iff #32 #197)
+#199 := [rewrite]: #198
+#227 := [monotonicity #199 #224]: #226
+#195 := (iff #31 false)
+#196 := [rewrite]: #195
+#230 := [monotonicity #196 #227]: #229
+#234 := [trans #230 #232]: #233
+#237 := [monotonicity #234]: #236
+#242 := [trans #237 #240]: #241
+#287 := [trans #242 #285]: #286
+#194 := [asserted]: #48
+#288 := [mp #194 #287]: #282
+#883 := (= #39 #275)
+#495 := (= #272 #275)
+#509 := (not #32)
+#494 := (= #275 0::Int)
+#829 := (not #494)
+#608 := (= 3::Int 0::Int)
+#610 := (iff #608 false)
+#827 := [rewrite]: #610
+#606 := [hypothesis]: #494
+#607 := [symm #288]: #278
+#609 := [trans #607 #606]: #608
+#828 := [mp #609 #827]: false
+#830 := [lemma #828]: #829
+#510 := (or #509 #494)
+#511 := [def-axiom]: #510
+#831 := [unit-resolution #511 #830]: #509
+#512 := (or #32 #495)
+#513 := [def-axiom]: #512
+#881 := [unit-resolution #513 #831]: #495
+#496 := (= #39 #272)
+#502 := (not #269)
+#666 := [hypothesis]: #502
+#498 := (or #269 #245)
+#499 := [def-axiom]: #498
+#667 := [unit-resolution #499 #666]: #245
+#500 := (or #269 #258)
+#501 := [def-axiom]: #500
+#813 := [unit-resolution #501 #666]: #258
+#814 := (or #32 #246 #259)
+#832 := [th-lemma arith triangle-eq]: #814
+#865 := [unit-resolution #832 #813 #667 #831]: false
+#866 := [lemma #865]: #269
+#505 := (or #502 #496)
+#506 := [def-axiom]: #505
+#882 := [unit-resolution #506 #866]: #496
+#884 := [trans #882 #881]: #883
+#885 := [trans #884 #288]: #872
+#886 := (not #872)
+#887 := (or #886 #613)
+#888 := [th-lemma arith triangle-eq]: #887
+#889 := [unit-resolution #888 #885]: #613
+#8 := 2::Int
+decl f4 :: Int
+#12 := f4
+#13 := (+ f3 f4)
+#614 := (div #13 2::Int)
+#113 := -2::Int
+#632 := (* -2::Int #614)
+#21 := (mod #13 2::Int)
+#631 := (* -1::Int #21)
+#633 := (+ #631 #632)
+#634 := (+ f4 #633)
+#635 := (+ f3 #634)
+#639 := (<= #635 0::Int)
+#629 := (= #635 0::Int)
+#735 := (or false #629)
+#736 := [th-lemma arith]: #735
+#737 := [unit-resolution #736 #93]: #629
+#738 := (not #629)
+#739 := (or #738 #639)
+#740 := [th-lemma arith triangle-eq]: #739
+#741 := [unit-resolution #740 #737]: #639
+#640 := (>= #635 0::Int)
+#742 := (or #738 #640)
+#743 := [th-lemma arith triangle-eq]: #742
+#744 := [unit-resolution #743 #737]: #640
+#710 := (<= #21 0::Int)
+#709 := (= #21 0::Int)
+#109 := (* -1::Int f4)
+#110 := (+ #108 #109)
+#116 := (mod #110 -2::Int)
+#122 := (* -1::Int #116)
+#163 := (>= #13 0::Int)
+#164 := (not #163)
+#150 := (<= #13 0::Int)
+#151 := (not #150)
+#174 := (or #151 #164)
+#177 := (ite #174 #21 #122)
+#14 := (= #13 0::Int)
+#180 := (ite #14 0::Int #177)
+#187 := (= #180 0::Int)
+#23 := (- 2::Int)
+#22 := (- #13)
+#24 := (mod #22 #23)
+#25 := (- #24)
+#16 := (< 0::Int 2::Int)
+#18 := (< #13 0::Int)
+#19 := (and #18 #16)
+#15 := (< 0::Int #13)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#26 := (ite #20 #21 #25)
+#27 := (ite #14 0::Int #26)
+#10 := (= 2::Int 0::Int)
+#28 := (ite #10 #13 #27)
+#29 := (= #28 0::Int)
+#191 := (iff #29 #187)
+#101 := (and #16 #18)
+#104 := (or #17 #101)
+#127 := (ite #104 #21 #122)
+#98 := (= 0::Int #13)
+#130 := (ite #98 0::Int #127)
+#143 := (= 0::Int #130)
+#189 := (iff #143 #187)
+#183 := (= 0::Int #180)
+#186 := (iff #183 #187)
+#188 := [rewrite]: #186
+#184 := (iff #143 #183)
+#181 := (= #130 #180)
+#178 := (= #127 #177)
+#175 := (iff #104 #174)
+#172 := (iff #101 #164)
+#167 := (and true #164)
+#170 := (iff #167 #164)
+#171 := [rewrite]: #170
+#168 := (iff #101 #167)
+#165 := (iff #18 #164)
+#166 := [rewrite]: #165
+#154 := (iff #16 true)
+#155 := [rewrite]: #154
+#169 := [monotonicity #155 #166]: #168
+#173 := [trans #169 #171]: #172
+#161 := (iff #17 #151)
+#156 := (and #151 true)
+#159 := (iff #156 #151)
+#160 := [rewrite]: #159
+#157 := (iff #17 #156)
+#152 := (iff #15 #151)
+#153 := [rewrite]: #152
+#158 := [monotonicity #153 #155]: #157
+#162 := [trans #158 #160]: #161
+#176 := [monotonicity #162 #173]: #175
+#179 := [monotonicity #176]: #178
+#148 := (iff #98 #14)
+#149 := [rewrite]: #148
+#182 := [monotonicity #149 #179]: #181
+#185 := [monotonicity #182]: #184
+#190 := [trans #185 #188]: #189
+#146 := (iff #29 #143)
+#140 := (= #130 0::Int)
+#144 := (iff #140 #143)
+#145 := [rewrite]: #144
+#141 := (iff #29 #140)
+#138 := (= #28 #130)
+#133 := (ite false #13 #130)
+#136 := (= #133 #130)
+#137 := [rewrite]: #136
+#134 := (= #28 #133)
+#131 := (= #27 #130)
+#128 := (= #26 #127)
+#125 := (= #25 #122)
+#119 := (- #116)
+#123 := (= #119 #122)
+#124 := [rewrite]: #123
+#120 := (= #25 #119)
+#117 := (= #24 #116)
+#114 := (= #23 -2::Int)
+#115 := [rewrite]: #114
+#111 := (= #22 #110)
+#112 := [rewrite]: #111
+#118 := [monotonicity #112 #115]: #117
+#121 := [monotonicity #118]: #120
+#126 := [trans #121 #124]: #125
+#105 := (iff #20 #104)
+#102 := (iff #19 #101)
+#103 := [rewrite]: #102
+#106 := [monotonicity #103]: #105
+#129 := [monotonicity #106 #126]: #128
+#99 := (iff #14 #98)
+#100 := [rewrite]: #99
+#132 := [monotonicity #100 #129]: #131
+#96 := (iff #10 false)
+#97 := [rewrite]: #96
+#135 := [monotonicity #97 #132]: #134
+#139 := [trans #135 #137]: #138
+#142 := [monotonicity #139]: #141
+#147 := [trans #142 #145]: #146
+#192 := [trans #147 #190]: #191
+#95 := [asserted]: #29
+#193 := [mp #95 #192]: #187
+#757 := (= #21 #180)
+#475 := (= #177 #180)
+#489 := (not #14)
+#423 := (>= f4 0::Int)
+#424 := (not #423)
+#412 := (<= f4 0::Int)
+#413 := (not #412)
+#434 := (or #413 #424)
+#534 := (not #434)
+#58 := 1::Int
+#66 := (mod f4 2::Int)
+#834 := (>= #66 1::Int)
+#837 := (not #834)
+#904 := (= #66 1::Int)
+#957 := (not #904)
+#345 := (mod #109 -2::Int)
+#351 := (* -1::Int #345)
+#437 := (ite #434 #66 #351)
+#60 := (= f4 0::Int)
+#440 := (ite #60 0::Int #437)
+#447 := (= #440 1::Int)
+#468 := (not #447)
+#958 := (iff #468 #957)
+#955 := (iff #447 #904)
+#953 := (iff #904 #447)
+#951 := (= #66 #440)
+#527 := (= #437 #440)
+#541 := (not #60)
+#552 := [hypothesis]: #434
+#895 := (or #541 #534)
+#558 := [hypothesis]: #60
+#553 := (or #541 #412)
+#554 := [th-lemma arith triangle-eq]: #553
+#555 := [unit-resolution #554 #558]: #412
+#559 := (or #541 #423)
+#892 := [th-lemma arith triangle-eq]: #559
+#893 := [unit-resolution #892 #558]: #423
+#535 := (or #534 #413 #424)
+#536 := [def-axiom]: #535
+#894 := [unit-resolution #536 #893 #555 #552]: false
+#896 := [lemma #894]: #895
+#947 := [unit-resolution #896 #552]: #541
+#544 := (or #60 #527)
+#545 := [def-axiom]: #544
+#948 := [unit-resolution #545 #947]: #527
+#528 := (= #66 #437)
+#537 := (or #534 #528)
+#538 := [def-axiom]: #537
+#946 := [unit-resolution #538 #552]: #528
+#952 := [trans #946 #948]: #951
+#954 := [monotonicity #952]: #953
+#956 := [symm #954]: #955
+#959 := [monotonicity #956]: #958
+#299 := (mod #108 -2::Int)
+#305 := (* -1::Int #299)
+#52 := (mod f3 2::Int)
+#396 := (ite #269 #52 #305)
+#399 := (ite #32 0::Int #396)
+#406 := (= #399 1::Int)
+#708 := (>= #52 1::Int)
+#669 := (div f3 2::Int)
+#683 := (* -2::Int #669)
+#682 := (* -1::Int #52)
+#684 := (+ #682 #683)
+#685 := (+ f3 #684)
+#556 := (<= #685 0::Int)
+#681 := (= #685 0::Int)
+#551 := (or false #681)
+#560 := [th-lemma arith]: #551
+#561 := [unit-resolution #560 #93]: #681
+#874 := (not #681)
+#875 := (or #874 #556)
+#876 := [th-lemma arith triangle-eq]: #875
+#877 := [unit-resolution #876 #561]: #556
+#557 := (>= #685 0::Int)
+#878 := (or #874 #557)
+#879 := [th-lemma arith triangle-eq]: #878
+#880 := [unit-resolution #879 #561]: #557
+#716 := (not #708)
+#717 := [hypothesis]: #716
+#692 := (>= #52 0::Int)
+#718 := (or false #692)
+#719 := [th-lemma arith]: #718
+#720 := [unit-resolution #719 #93]: #692
+#890 := [th-lemma arith gcd-test 1/4 1/4 1/4 1/4 -1/4 -1/4 -1/4 -1/4 #889 #733 #730 #727 #720 #717 #880 #877]: false
+#891 := [lemma #890]: #708
+#938 := (or #406 #716)
+#515 := (= #396 #399)
+#524 := (or #32 #515)
+#525 := [def-axiom]: #524
+#936 := [unit-resolution #525 #831]: #515
+#516 := (= #52 #396)
+#518 := (or #502 #516)
+#519 := [def-axiom]: #518
+#937 := [unit-resolution #519 #866]: #516
+#785 := (not #516)
+#784 := (not #515)
+#803 := (or #406 #784 #785 #716)
+#690 := (= #52 1::Int)
+#707 := (<= #52 1::Int)
+#788 := (not #707)
+#789 := [hypothesis]: #788
+#698 := (>= #52 2::Int)
+#699 := (not #698)
+#790 := (or false #699)
+#791 := [th-lemma arith]: #790
+#792 := [unit-resolution #791 #93]: #699
+#793 := [th-lemma arith farkas 1 1 #792 #789]: false
+#794 := [lemma #793]: #707
+#797 := [hypothesis]: #708
+#798 := (or #690 #788 #716)
+#799 := [th-lemma arith triangle-eq]: #798
+#800 := [unit-resolution #799 #797 #794]: #690
+#780 := (= #399 #52)
+#778 := (= #396 #52)
+#774 := [hypothesis]: #516
+#779 := [symm #774]: #778
+#776 := (= #399 #396)
+#775 := [hypothesis]: #515
+#777 := [symm #775]: #776
+#781 := [trans #777 #779]: #780
+#801 := [trans #781 #800]: #406
+#467 := (not #406)
+#796 := [hypothesis]: #467
+#802 := [unit-resolution #796 #801]: false
+#804 := [lemma #802]: #803
+#939 := [unit-resolution #804 #937 #936]: #938
+#944 := [unit-resolution #939 #891]: #406
+#461 := (or #467 #468)
+#451 := (and #406 #447)
+#454 := (not #451)
+#472 := (iff #454 #461)
+#462 := (not #461)
+#463 := (not #462)
+#470 := (iff #463 #461)
+#471 := [rewrite]: #470
+#464 := (iff #454 #463)
+#465 := (iff #451 #462)
+#466 := [rewrite]: #465
+#469 := [monotonicity #466]: #464
+#473 := [trans #469 #471]: #472
+#67 := (- f4)
+#68 := (mod #67 #23)
+#69 := (- #68)
+#63 := (< f4 0::Int)
+#64 := (and #63 #16)
+#61 := (< 0::Int f4)
+#62 := (and #61 #16)
+#65 := (or #62 #64)
+#70 := (ite #65 #66 #69)
+#71 := (ite #60 0::Int #70)
+#72 := (ite #10 f4 #71)
+#73 := (= #72 1::Int)
+#53 := (mod #40 #23)
+#54 := (- #53)
+#50 := (and #36 #16)
+#49 := (and #33 #16)
+#51 := (or #49 #50)
+#55 := (ite #51 #52 #54)
+#56 := (ite #32 0::Int #55)
+#57 := (ite #10 f3 #56)
+#59 := (= #57 1::Int)
+#74 := (and #59 #73)
+#75 := (not #74)
+#457 := (iff #75 #454)
+#337 := (and #16 #63)
+#334 := (and #16 #61)
+#340 := (or #334 #337)
+#356 := (ite #340 #66 #351)
+#331 := (= 0::Int f4)
+#359 := (ite #331 0::Int #356)
+#372 := (= 1::Int #359)
+#293 := (and #16 #36)
+#290 := (and #16 #33)
+#296 := (or #290 #293)
+#310 := (ite #296 #52 #305)
+#313 := (ite #197 0::Int #310)
+#326 := (= 1::Int #313)
+#377 := (and #326 #372)
+#380 := (not #377)
+#455 := (iff #380 #454)
+#452 := (iff #377 #451)
+#449 := (iff #372 #447)
+#443 := (= 1::Int #440)
+#446 := (iff #443 #447)
+#448 := [rewrite]: #446
+#444 := (iff #372 #443)
+#441 := (= #359 #440)
+#438 := (= #356 #437)
+#435 := (iff #340 #434)
+#432 := (iff #337 #424)
+#427 := (and true #424)
+#430 := (iff #427 #424)
+#431 := [rewrite]: #430
+#428 := (iff #337 #427)
+#425 := (iff #63 #424)
+#426 := [rewrite]: #425
+#429 := [monotonicity #155 #426]: #428
+#433 := [trans #429 #431]: #432
+#421 := (iff #334 #413)
+#416 := (and true #413)
+#419 := (iff #416 #413)
+#420 := [rewrite]: #419
+#417 := (iff #334 #416)
+#414 := (iff #61 #413)
+#415 := [rewrite]: #414
+#418 := [monotonicity #155 #415]: #417
+#422 := [trans #418 #420]: #421
+#436 := [monotonicity #422 #433]: #435
 #439 := [monotonicity #436]: #438
-#450 := (iff #463 #670)
-#448 := (iff #471 #701)
-#444 := (iff #471 #684)
-#435 := [monotonicity #421]: #444
-#449 := [trans #435 #687]: #448
-#451 := [monotonicity #449]: #450
-#502 := [monotonicity #451 #439]: #501
-#418 := [monotonicity #502 #487]: #488
-#415 := [monotonicity #418]: #414
-#404 := [monotonicity #772 #415]: #416
-#405 := [trans #404 #407]: #410
-#396 := [monotonicity #405]: #391
-#401 := [trans #396 #399]: #391
-#390 := [quant-inst #8 #11]: #386
-#397 := [mp #390 #401]: #411
-#1069 := [unit-resolution #397 #796]: #420
-#379 := (not #420)
-#1072 := (or #379 #478)
-#373 := (or #379 #689 #478)
-#374 := [def-axiom]: #373
-#1073 := [unit-resolution #374 #1043]: #1072
-#1074 := [unit-resolution #1073 #1069]: #478
-#392 := (not #478)
-#393 := (or #392 #635 #477)
-#394 := [def-axiom]: #393
-#1075 := [unit-resolution #394 #1045 #1074]: #477
-#380 := (not #477)
-#1076 := (or #380 #385)
-#1077 := [th-lemma arith triangle-eq]: #1076
-#1078 := [unit-resolution #1077 #1075]: #385
-#801 := (>= #19 1::Int)
-#1015 := (not #801)
-#800 := (<= #19 1::Int)
-#946 := (>= #483 2::Int)
-#947 := (not #946)
-#1079 := (or false #947)
-#1080 := [th-lemma arith]: #1079
-#1081 := [unit-resolution #1080 #72]: #947
-#402 := (<= #485 0::Int)
-#1082 := (or #380 #402)
-#1083 := [th-lemma arith triangle-eq]: #1082
-#1084 := [unit-resolution #1083 #1075]: #402
-#1085 := (not #402)
-#1086 := (or #800 #946 #1085)
-#1087 := [th-lemma arith assign-bounds 1 1]: #1086
-#1088 := [unit-resolution #1087 #1084 #1081]: #800
-#1090 := (not #800)
-#1093 := (or #1090 #1015)
-#218 := (not #21)
-#1089 := [hypothesis]: #218
-#1091 := (or #21 #1090 #1015)
-#1092 := [th-lemma arith triangle-eq]: #1091
-#1094 := [unit-resolution #1092 #1089]: #1093
-#1095 := [unit-resolution #1094 #1088]: #1015
-#1096 := [th-lemma arith farkas -1/2 -1/2 1/2 -1/2 -1/2 -1/2 1 #995 #998 #1095 #1078 #1068 #1056 #1053]: false
-#1098 := [lemma #1096]: #1097
-#1264 := [unit-resolution #1098 #914]: #21
-#230 := (or #218 #219)
-#24 := (and #21 #23)
-#25 := (not #24)
-#239 := (iff #25 #230)
-#231 := (not #230)
-#234 := (not #231)
-#237 := (iff #234 #230)
-#238 := [rewrite]: #237
-#235 := (iff #25 #234)
-#232 := (iff #24 #231)
-#233 := [rewrite]: #232
-#236 := [monotonicity #233]: #235
-#240 := [trans #236 #238]: #239
-#76 := [asserted]: #25
-#241 := [mp #76 #240]: #230
-#1265 := [unit-resolution #241 #1264]: #219
-#1267 := (or #23 #1266 #1152)
-#1268 := [th-lemma arith triangle-eq]: #1267
-#1270 := [unit-resolution #1268 #1265]: #1269
-#1271 := [unit-resolution #1270 #1263]: #1152
-#1192 := (not #955)
-#1194 := (or #1191 #1192 #1193 #1104)
-#1153 := [hypothesis]: #1152
-#1132 := (<= #1127 0::Int)
-#1160 := [unit-resolution #1159 #72]: #1124
-#1162 := (or #1161 #1132)
-#1163 := [th-lemma arith triangle-eq]: #1162
-#1164 := [unit-resolution #1163 #1160]: #1132
-#1185 := [hypothesis]: #1179
-#1189 := [hypothesis]: #955
-#1190 := [th-lemma arith farkas -1 1 -2 1 1 1 1 1 1 1 #1189 #1188 #1185 #1184 #1183 #1166 #1164 #982 #970 #1153]: false
-#1195 := [lemma #1190]: #1194
-#1272 := [unit-resolution #1195 #1271 #1184 #1253]: #1191
-#1273 := [th-lemma arith farkas -2 1 1 1 1 1 1 1 1 #1272 #1237 #1236 #1235 #1232 #998 #995 #1249 #1151]: false
-#1275 := [lemma #1273]: #1274
-#1349 := [unit-resolution #1275 #1278]: #1348
-#1350 := [unit-resolution #1349 #1323 #1110]: false
-#1351 := [lemma #1350]: #715
-#1281 := (or #778 #457)
-#1225 := [hypothesis]: #715
-#752 := (+ #482 #376)
-#751 := (mod #752 -2::Int)
-#466 := (+ #12 #751)
-#746 := (= #466 0::Int)
-#770 := (not #461)
-#434 := (<= #10 0::Int)
-#764 := (not #434)
-#479 := (or #764 #770)
-#744 := (ite #479 #457 #746)
-#618 := (not #778)
-#802 := [hypothesis]: #618
-#1243 := (or #778 #744)
-#749 := (ite #778 #14 #744)
-#585 := (or #584 #749)
-#454 := (* -1::Int #10)
-#455 := (mod #454 #370)
-#456 := (+ #12 #455)
-#447 := (= #456 0::Int)
-#775 := (or #440 #461)
-#777 := (not #775)
-#564 := (or #434 #440)
-#771 := (not #564)
-#445 := (or #771 #777)
-#446 := (ite #445 #457 #447)
-#779 := (ite #778 #14 #446)
-#780 := (= #10 #12)
-#776 := (ite #781 #780 #779)
-#586 := (or #584 #776)
-#729 := (iff #586 #585)
-#731 := (iff #585 #585)
-#725 := [rewrite]: #731
-#737 := (iff #776 #749)
-#432 := (* -1::Int #12)
-#437 := (+ f5 #432)
-#773 := (+ f4 #437)
-#433 := (= #773 0::Int)
-#740 := (ite false #433 #749)
-#741 := (iff #740 #749)
-#742 := [rewrite]: #741
-#735 := (iff #776 #740)
-#738 := (iff #779 #749)
-#748 := (iff #446 #744)
-#747 := (iff #447 #746)
-#467 := (= #456 #466)
-#755 := (= #455 #751)
-#753 := (= #454 #752)
-#475 := [rewrite]: #753
-#465 := [monotonicity #475 #754]: #755
-#468 := [monotonicity #465]: #467
-#462 := [monotonicity #468]: #747
-#480 := (iff #445 #479)
-#756 := (iff #777 #770)
-#769 := (iff #775 #461)
-#403 := (or false #461)
-#408 := (iff #403 #461)
-#409 := [rewrite]: #408
-#766 := (iff #775 #403)
-#768 := [monotonicity #421]: #766
-#767 := [trans #768 #409]: #769
-#757 := [monotonicity #767]: #756
-#759 := (iff #771 #764)
-#762 := (iff #564 #434)
-#422 := (or #434 false)
-#760 := (iff #422 #434)
-#761 := [rewrite]: #760
-#423 := (iff #564 #422)
-#424 := [monotonicity #421]: #423
-#763 := [trans #424 #761]: #762
-#765 := [monotonicity #763]: #759
-#481 := [monotonicity #765 #757]: #480
-#745 := [monotonicity #481 #462]: #748
-#739 := [monotonicity #745]: #738
-#774 := (iff #780 #433)
-#417 := [rewrite]: #774
-#736 := [monotonicity #772 #417 #739]: #735
-#743 := [trans #736 #742]: #737
-#730 := [monotonicity #743]: #729
-#726 := [trans #730 #725]: #729
-#728 := [quant-inst #10 #11]: #586
-#732 := [mp #728 #726]: #585
-#1242 := [unit-resolution #732 #796]: #749
-#616 := (not #749)
-#620 := (or #616 #778 #744)
-#621 := [def-axiom]: #620
-#1244 := [unit-resolution #621 #1242]: #1243
-#1245 := [unit-resolution #1244 #802]: #744
-#809 := (or #479 #778)
-#565 := (not #479)
-#803 := [hypothesis]: #565
-#733 := (or #479 #434)
-#727 := [def-axiom]: #733
-#804 := [unit-resolution #727 #803]: #434
-#734 := (or #479 #461)
-#563 := [def-axiom]: #734
-#805 := [unit-resolution #563 #803]: #461
-#806 := (or #778 #764 #770)
-#807 := [th-lemma arith triangle-eq]: #806
-#808 := [unit-resolution #807 #805 #804 #802]: false
-#810 := [lemma #808]: #809
-#1279 := [unit-resolution #810 #802]: #479
-#724 := (not #744)
-#606 := (or #724 #565 #457)
-#607 := [def-axiom]: #606
-#1280 := [unit-resolution #607 #1279 #1245 #1225]: false
-#1282 := [lemma #1280]: #1281
-#1352 := [unit-resolution #1282 #1351]: #778
-#1353 := (or #618 #461)
-#1354 := [th-lemma arith triangle-eq]: #1353
-#1355 := [unit-resolution #1354 #1352]: #461
-#1356 := (or #618 #434)
-#1357 := [th-lemma arith triangle-eq]: #1356
-#1358 := [unit-resolution #1357 #1352]: #434
-#1346 := (or #577 #770 #764)
-#1295 := [hypothesis]: #434
-#1327 := (or #526 #764 #701)
-#1005 := [hypothesis]: #670
-#1289 := [hypothesis]: #578
-#1291 := [th-lemma arith farkas -1 1 1 #1295 #1289 #1005]: false
-#1328 := [lemma #1291]: #1327
-#1342 := [unit-resolution #1328 #1209 #1295]: #701
-#1343 := [unit-resolution #864 #1043]: #659
-#1344 := [unit-resolution #1343 #1342]: #669
-#1290 := [hypothesis]: #461
-#1345 := [th-lemma arith farkas -1 1 1 #1290 #1344 #1229]: false
-#1347 := [lemma #1345]: #1346
-#1359 := [unit-resolution #1347 #1358 #1355]: #577
-#1360 := [unit-resolution #1255 #1359]: #954
-#1361 := (or #1103 #1260)
-#1302 := [hypothesis]: #1140
-#1308 := [unit-resolution #1258 #72 #1302]: false
-#1321 := [lemma #1308]: #1141
-#1362 := [unit-resolution #1262 #1321]: #1361
-#1363 := [unit-resolution #1362 #1360]: #1103
-#1303 := (+ #698 #1171)
-#1326 := (+ #575 #1303)
-#1335 := (+ #16 #1326)
-#1336 := (+ f5 #1335)
-#1337 := (+ f4 #1336)
-#1338 := (>= #1337 2::Int)
-#1329 := (not #1338)
-#1330 := (or #1329 #764)
-#1294 := [unit-resolution #1163 #1278]: #1132
-#1310 := [hypothesis]: #1338
-#1309 := [th-lemma arith farkas 2 -1 -1 -1 -1 -1 1 #1310 #1295 #1166 #982 #970 #1294 #1151]: false
-#1331 := [lemma #1309]: #1330
-#1364 := [unit-resolution #1331 #1358]: #1329
-#1365 := [unit-resolution #1252 #1359]: #955
-#1340 := (or #1192 #1338 #770 #1104)
-#1332 := [unit-resolution #1248 #1278]: #1224
-#1325 := [th-lemma arith #1290 #1153 #1189 #1236 #998 #995 #1332]: #1338
-#1324 := [hypothesis]: #1329
-#1339 := [unit-resolution #1324 #1325]: false
-#1341 := [lemma #1339]: #1340
-#1366 := [unit-resolution #1341 #1365 #1355 #1364]: #1104
-[unit-resolution #1270 #1366 #1363]: false
+#410 := (iff #331 #60)
+#411 := [rewrite]: #410
+#442 := [monotonicity #411 #439]: #441
+#445 := [monotonicity #442]: #444
+#450 := [trans #445 #448]: #449
+#408 := (iff #326 #406)
+#402 := (= 1::Int #399)
+#405 := (iff #402 #406)
+#407 := [rewrite]: #405
+#403 := (iff #326 #402)
+#400 := (= #313 #399)
+#397 := (= #310 #396)
+#394 := (iff #296 #269)
+#392 := (iff #293 #259)
+#390 := (iff #293 #262)
+#391 := [monotonicity #155 #261]: #390
+#393 := [trans #391 #266]: #392
+#388 := (iff #290 #246)
+#383 := (and true #246)
+#386 := (iff #383 #246)
+#387 := [rewrite]: #386
+#384 := (iff #290 #383)
+#385 := [monotonicity #155 #248]: #384
+#389 := [trans #385 #387]: #388
+#395 := [monotonicity #389 #393]: #394
+#398 := [monotonicity #395]: #397
+#401 := [monotonicity #244 #398]: #400
+#404 := [monotonicity #401]: #403
+#409 := [trans #404 #407]: #408
+#453 := [monotonicity #409 #450]: #452
+#456 := [monotonicity #453]: #455
+#381 := (iff #75 #380)
+#378 := (iff #74 #377)
+#375 := (iff #73 #372)
+#369 := (= #359 1::Int)
+#373 := (iff #369 #372)
+#374 := [rewrite]: #373
+#370 := (iff #73 #369)
+#367 := (= #72 #359)
+#362 := (ite false f4 #359)
+#365 := (= #362 #359)
+#366 := [rewrite]: #365
+#363 := (= #72 #362)
+#360 := (= #71 #359)
+#357 := (= #70 #356)
+#354 := (= #69 #351)
+#348 := (- #345)
+#352 := (= #348 #351)
+#353 := [rewrite]: #352
+#349 := (= #69 #348)
+#346 := (= #68 #345)
+#343 := (= #67 #109)
+#344 := [rewrite]: #343
+#347 := [monotonicity #344 #115]: #346
+#350 := [monotonicity #347]: #349
+#355 := [trans #350 #353]: #354
+#341 := (iff #65 #340)
+#338 := (iff #64 #337)
+#339 := [rewrite]: #338
+#335 := (iff #62 #334)
+#336 := [rewrite]: #335
+#342 := [monotonicity #336 #339]: #341
+#358 := [monotonicity #342 #355]: #357
+#332 := (iff #60 #331)
+#333 := [rewrite]: #332
+#361 := [monotonicity #333 #358]: #360
+#364 := [monotonicity #97 #361]: #363
+#368 := [trans #364 #366]: #367
+#371 := [monotonicity #368]: #370
+#376 := [trans #371 #374]: #375
+#329 := (iff #59 #326)
+#323 := (= #313 1::Int)
+#327 := (iff #323 #326)
+#328 := [rewrite]: #327
+#324 := (iff #59 #323)
+#321 := (= #57 #313)
+#316 := (ite false f3 #313)
+#319 := (= #316 #313)
+#320 := [rewrite]: #319
+#317 := (= #57 #316)
+#314 := (= #56 #313)
+#311 := (= #55 #310)
+#308 := (= #54 #305)
+#302 := (- #299)
+#306 := (= #302 #305)
+#307 := [rewrite]: #306
+#303 := (= #54 #302)
+#300 := (= #53 #299)
+#301 := [monotonicity #207 #115]: #300
+#304 := [monotonicity #301]: #303
+#309 := [trans #304 #307]: #308
+#297 := (iff #51 #296)
+#294 := (iff #50 #293)
+#295 := [rewrite]: #294
+#291 := (iff #49 #290)
+#292 := [rewrite]: #291
+#298 := [monotonicity #292 #295]: #297
+#312 := [monotonicity #298 #309]: #311
+#315 := [monotonicity #199 #312]: #314
+#318 := [monotonicity #97 #315]: #317
+#322 := [trans #318 #320]: #321
+#325 := [monotonicity #322]: #324
+#330 := [trans #325 #328]: #329
+#379 := [monotonicity #330 #376]: #378
+#382 := [monotonicity #379]: #381
+#458 := [trans #382 #456]: #457
+#289 := [asserted]: #75
+#459 := [mp #289 #458]: #454
+#474 := [mp #459 #473]: #461
+#945 := [unit-resolution #474 #944]: #468
+#960 := [mp #945 #959]: #957
+#963 := (or #904 #837)
+#833 := (<= #66 1::Int)
+#858 := (not #833)
+#859 := [hypothesis]: #858
+#821 := (>= #66 2::Int)
+#822 := (not #821)
+#860 := (or false #822)
+#861 := [th-lemma arith]: #860
+#862 := [unit-resolution #861 #93]: #822
+#863 := [th-lemma arith farkas 1 1 #862 #859]: false
+#864 := [lemma #863]: #833
+#961 := (or #904 #858 #837)
+#962 := [th-lemma arith triangle-eq]: #961
+#964 := [unit-resolution #962 #864]: #963
+#965 := [unit-resolution #964 #960]: #837
+#909 := (or #151 #834)
+#906 := [hypothesis]: #150
+#838 := [hypothesis]: #837
+#931 := (or #163 #834)
+#705 := (div f4 2::Int)
+#806 := (* -2::Int #705)
+#805 := (* -1::Int #66)
+#807 := (+ #805 #806)
+#808 := (+ f4 #807)
+#897 := (<= #808 0::Int)
+#795 := (= #808 0::Int)
+#911 := (or false #795)
+#913 := [th-lemma arith]: #911
+#914 := [unit-resolution #913 #93]: #795
+#915 := (not #795)
+#916 := (or #915 #897)
+#917 := [th-lemma arith triangle-eq]: #916
+#918 := [unit-resolution #917 #914]: #897
+#898 := (>= #808 0::Int)
+#919 := (or #915 #898)
+#920 := [th-lemma arith triangle-eq]: #919
+#921 := [unit-resolution #920 #914]: #898
+#815 := (>= #66 0::Int)
+#839 := (or false #815)
+#840 := [th-lemma arith]: #839
+#841 := [unit-resolution #840 #93]: #815
+#922 := [hypothesis]: #164
+#751 := (or #489 #163)
+#752 := [th-lemma arith triangle-eq]: #751
+#923 := [unit-resolution #752 #922]: #489
+#492 := (or #14 #475)
+#493 := [def-axiom]: #492
+#924 := [unit-resolution #493 #923]: #475
+#476 := (= #21 #177)
+#480 := (or #174 #163)
+#481 := [def-axiom]: #480
+#925 := [unit-resolution #481 #922]: #174
+#482 := (not #174)
+#485 := (or #482 #476)
+#486 := [def-axiom]: #485
+#926 := [unit-resolution #486 #925]: #476
+#927 := [trans #926 #924]: #757
+#928 := [trans #927 #193]: #709
+#760 := (not #709)
+#761 := (or #760 #710)
+#762 := [th-lemma arith triangle-eq]: #761
+#929 := [unit-resolution #762 #928]: #710
+#641 := (>= #21 0::Int)
+#764 := (or false #641)
+#765 := [th-lemma arith]: #764
+#766 := [unit-resolution #765 #93]: #641
+#930 := [th-lemma arith gcd-test 1/2 1/2 1/2 1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 #766 #929 #744 #741 #889 #733 #730 #727 #841 #838 #921 #918]: false
+#932 := [lemma #930]: #931
+#907 := [unit-resolution #932 #838]: #163
+#908 := [th-lemma arith gcd-test 1/2 1/2 1/2 1/2 -1/2 -1/2 1/2 1/2 1/2 1/2 #841 #838 #921 #918 #907 #906 #889 #733 #730 #727]: false
+#910 := [lemma #908]: #909
+#966 := [unit-resolution #910 #965]: #151
+#967 := (or #489 #150)
+#968 := [th-lemma arith triangle-eq]: #967
+#969 := [unit-resolution #968 #966]: #489
+#970 := [unit-resolution #493 #969]: #475
+#478 := (or #174 #150)
+#479 := [def-axiom]: #478
+#971 := [unit-resolution #479 #966]: #174
+#972 := [unit-resolution #486 #971]: #476
+#973 := [trans #972 #970]: #757
+#974 := [trans #973 #193]: #709
+#975 := [unit-resolution #762 #974]: #710
+#976 := [th-lemma arith gcd-test 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 #841 #965 #921 #918 #889 #733 #730 #727 #766 #975 #744 #741]: false
+#977 := [lemma #976]: #534
+#532 := (or #434 #423)
+#533 := [def-axiom]: #532
+#836 := [unit-resolution #533 #977]: #423
+#845 := (or #434 #258)
+#769 := (not #613)
+#770 := (or #434 #769 #258)
+#734 := [hypothesis]: #613
+#745 := [hypothesis]: #259
+#746 := [hypothesis]: #534
+#530 := (or #434 #412)
+#531 := [def-axiom]: #530
+#747 := [unit-resolution #531 #746]: #412
+#748 := (or #164 #258 #413)
+#749 := [th-lemma arith assign-bounds -1 -1]: #748
+#750 := [unit-resolution #749 #747 #745]: #164
+#753 := [unit-resolution #752 #750]: #489
+#754 := [unit-resolution #493 #753]: #475
+#755 := [unit-resolution #481 #750]: #174
+#756 := [unit-resolution #486 #755]: #476
+#758 := [trans #756 #754]: #757
+#759 := [trans #758 #193]: #709
+#763 := [unit-resolution #762 #759]: #710
+#767 := [unit-resolution #533 #746]: #423
+#768 := [th-lemma arith gcd-test -1/2 -1/2 1/2 1/2 1/2 1/2 -1/2 -1/2 -1/2 -1/2 #767 #747 #766 #763 #744 #741 #734 #733 #730 #727]: false
+#771 := [lemma #768]: #770
+#846 := [unit-resolution #771 #889]: #845
+#847 := [unit-resolution #846 #977]: #258
+#503 := (or #502 #246 #259)
+#504 := [def-axiom]: #503
+#844 := [unit-resolution #504 #866]: #269
+#848 := [unit-resolution #844 #847]: #246
+#849 := (or #151 #424 #245)
+#850 := [th-lemma arith assign-bounds -1 -1]: #849
+#851 := [unit-resolution #850 #848 #836]: #151
+#842 := [unit-resolution #968 #851]: #489
+#843 := [unit-resolution #493 #842]: #475
+#852 := [unit-resolution #479 #851]: #174
+#853 := [unit-resolution #486 #852]: #476
+#854 := [trans #853 #843]: #757
+#855 := [trans #854 #193]: #709
+#856 := [unit-resolution #762 #855]: #710
+#857 := [unit-resolution #531 #977]: #412
+[th-lemma arith gcd-test -1/2 -1/2 1/2 1/2 1/2 1/2 -1/2 -1/2 -1/2 -1/2 #836 #857 #766 #856 #744 #741 #889 #733 #730 #727]: false
 unsat
 c04d38458726eb1b2cafd52bd3881d6f8160666f 24 0
 #2 := false
@@ -10440,288 +10061,318 @@
 unsat
 ERROR: line 11 column 83: invalid pattern.
 
-8f616b17d0807409dc26bfdf9593c5fcd06fb7e7 1 0
-unsat
-3eb9cf11ee8774c9212c37c265e7552f3b8f24a9 75 0
-#2 := false
-#10 := 1::Int
-decl f5 :: Int
-#12 := f5
-#16 := (+ f5 1::Int)
-decl f3 :: Int
-#8 := f3
-#17 := (* f3 #16)
-decl f4 :: Int
-#9 := f4
-#15 := (* f3 f4)
-#18 := (+ #15 #17)
-#11 := (+ f4 1::Int)
-#13 := (+ #11 f5)
-#14 := (* f3 #13)
-#19 := (= #14 #18)
-#20 := (not #19)
-#93 := (iff #20 false)
-#1 := true
-#88 := (not true)
-#91 := (iff #88 false)
-#92 := [rewrite]: #91
-#89 := (iff #20 #88)
-#86 := (iff #19 true)
-#56 := (* f3 f5)
-#57 := (+ #15 #56)
-#58 := (+ f3 #57)
-#81 := (= #58 #58)
-#84 := (iff #81 true)
-#85 := [rewrite]: #84
-#82 := (iff #19 #81)
-#79 := (= #18 #58)
-#69 := (+ f3 #56)
-#74 := (+ #15 #69)
-#77 := (= #74 #58)
-#78 := [rewrite]: #77
-#75 := (= #18 #74)
-#72 := (= #17 #69)
-#63 := (+ 1::Int f5)
-#66 := (* f3 #63)
-#70 := (= #66 #69)
-#71 := [rewrite]: #70
-#67 := (= #17 #66)
-#64 := (= #16 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#73 := [trans #68 #71]: #72
-#76 := [monotonicity #73]: #75
-#80 := [trans #76 #78]: #79
-#61 := (= #14 #58)
-#47 := (+ f4 f5)
-#48 := (+ 1::Int #47)
-#53 := (* f3 #48)
-#59 := (= #53 #58)
-#60 := [rewrite]: #59
-#54 := (= #14 #53)
-#51 := (= #13 #48)
-#41 := (+ 1::Int f4)
-#44 := (+ #41 f5)
-#49 := (= #44 #48)
-#50 := [rewrite]: #49
-#45 := (= #13 #44)
-#42 := (= #11 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#52 := [trans #46 #50]: #51
-#55 := [monotonicity #52]: #54
-#62 := [trans #55 #60]: #61
-#83 := [monotonicity #62 #80]: #82
-#87 := [trans #83 #85]: #86
-#90 := [monotonicity #87]: #89
-#94 := [trans #90 #92]: #93
-#40 := [asserted]: #20
-[mp #40 #94]: false
-unsat
-741a564e40e4b6610d1d47bdab19a223e004482a 62 0
+8aba3814871680009d1d0267516334493c303e78 175 0
 #2 := false
-decl f4 :: Real
-#10 := f4
-decl f3 :: Real
-#8 := f3
-#16 := 2::Real
-#17 := (* 2::Real f3)
-#18 := (* #17 f4)
-#9 := 1::Real
-#13 := (- 1::Real f4)
-#14 := (* f3 #13)
-#11 := (+ 1::Real f4)
-#12 := (* f3 #11)
-#15 := (- #12 #14)
-#19 := (= #15 #18)
-#20 := (not #19)
-#81 := (iff #20 false)
-#1 := true
-#76 := (not true)
-#79 := (iff #76 false)
-#80 := [rewrite]: #79
-#77 := (iff #20 #76)
-#74 := (iff #19 true)
-#41 := (* f3 f4)
-#63 := (* 2::Real #41)
-#69 := (= #63 #63)
-#72 := (iff #69 true)
-#73 := [rewrite]: #72
-#70 := (iff #19 #69)
-#67 := (= #18 #63)
-#68 := [rewrite]: #67
-#65 := (= #15 #63)
-#45 := -1::Real
-#53 := (* -1::Real #41)
-#54 := (+ f3 #53)
-#42 := (+ f3 #41)
-#59 := (- #42 #54)
-#62 := (= #59 #63)
-#64 := [rewrite]: #62
-#60 := (= #15 #59)
-#57 := (= #14 #54)
-#46 := (* -1::Real f4)
-#47 := (+ 1::Real #46)
-#50 := (* f3 #47)
-#55 := (= #50 #54)
-#56 := [rewrite]: #55
-#51 := (= #14 #50)
-#48 := (= #13 #47)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#58 := [trans #52 #56]: #57
-#43 := (= #12 #42)
-#44 := [rewrite]: #43
-#61 := [monotonicity #44 #58]: #60
-#66 := [trans #61 #64]: #65
-#71 := [monotonicity #66 #68]: #70
-#75 := [trans #71 #73]: #74
-#78 := [monotonicity #75]: #77
-#82 := [trans #78 #80]: #81
-#40 := [asserted]: #20
-[mp #40 #82]: false
-unsat
-06d1bd5308956fb019ef1c09bf97c6326d872fd6 141 0
-#2 := false
-decl f6 :: Int
-#13 := f6
-decl f7 :: Int
-#17 := f7
-decl f5 :: Int
-#12 := f5
-#28 := (+ f5 f7)
-#29 := (+ #28 f6)
+#8 := 0::Int
 decl f4 :: Int
-#10 := f4
-#9 := 1::Int
-#11 := (+ 1::Int f4)
-#30 := (* #11 #29)
-#25 := (* f7 f4)
-#23 := (* #11 f7)
-#14 := (+ f5 f6)
-#20 := 2::Int
-#21 := (* 2::Int #11)
-#22 := (* #21 #14)
-#24 := (+ #22 #23)
-#26 := (+ #24 #25)
-decl f3 :: Int
-#8 := f3
-#27 := (+ f3 #26)
-#31 := (- #27 #30)
-#18 := (* f4 f7)
-#15 := (* #11 #14)
-#16 := (+ f3 #15)
-#19 := (+ #16 #18)
-#32 := (= #19 #31)
-#33 := (not #32)
-#157 := (iff #33 false)
-#1 := true
-#152 := (not true)
-#155 := (iff #152 false)
-#156 := [rewrite]: #155
-#153 := (iff #33 #152)
-#150 := (iff #32 true)
-#55 := (* f4 f6)
-#54 := (* f4 f5)
+#18 := f4
+#138 := (<= f4 0::Int)
+#139 := (not #138)
+decl f5 :: Int
+#20 := f5
+#134 := (<= f5 0::Int)
+#135 := (not #134)
+decl f3 :: (-> Int Int Int)
+#21 := (f3 f4 f5)
+#123 := (<= #21 0::Int)
+#155 := (or #123 #135 #138)
+#160 := (not #155)
+#23 := (< 0::Int f5)
+#22 := (< 0::Int #21)
+#24 := (implies #22 #23)
+#19 := (< 0::Int f4)
+#25 := (implies #19 #24)
+#26 := (not #25)
+#163 := (iff #26 #160)
+#107 := (not #22)
+#108 := (or #107 #23)
+#114 := (not #19)
+#115 := (or #114 #108)
+#120 := (not #115)
+#161 := (iff #120 #160)
+#158 := (iff #115 #155)
+#149 := (or #123 #135)
+#152 := (or #138 #149)
+#156 := (iff #152 #155)
+#157 := [rewrite]: #156
+#153 := (iff #115 #152)
+#150 := (iff #108 #149)
+#136 := (iff #23 #135)
+#137 := [rewrite]: #136
+#132 := (iff #107 #123)
+#124 := (not #123)
+#127 := (not #124)
+#130 := (iff #127 #123)
+#131 := [rewrite]: #130
+#128 := (iff #107 #127)
+#125 := (iff #22 #124)
+#126 := [rewrite]: #125
+#129 := [monotonicity #126]: #128
+#133 := [trans #129 #131]: #132
+#151 := [monotonicity #133 #137]: #150
+#147 := (iff #114 #138)
+#142 := (not #139)
+#145 := (iff #142 #138)
+#146 := [rewrite]: #145
+#143 := (iff #114 #142)
+#140 := (iff #19 #139)
+#141 := [rewrite]: #140
+#144 := [monotonicity #141]: #143
+#148 := [trans #144 #146]: #147
+#154 := [monotonicity #148 #151]: #153
+#159 := [trans #154 #157]: #158
+#162 := [monotonicity #159]: #161
+#121 := (iff #26 #120)
+#118 := (iff #25 #115)
+#111 := (implies #19 #108)
+#116 := (iff #111 #115)
+#117 := [rewrite]: #116
+#112 := (iff #25 #111)
+#109 := (iff #24 #108)
+#110 := [rewrite]: #109
+#113 := [monotonicity #110]: #112
+#119 := [trans #113 #117]: #118
+#122 := [monotonicity #119]: #121
+#164 := [trans #122 #162]: #163
+#106 := [asserted]: #26
+#165 := [mp #106 #164]: #160
+#168 := [not-or-elim #165]: #139
+#167 := [not-or-elim #165]: #134
+#166 := [not-or-elim #165]: #124
+#10 := (:var 0 Int)
+#9 := (:var 1 Int)
+#11 := (f3 #9 #10)
+#647 := (pattern #11)
+#78 := (<= #11 0::Int)
+#74 := (<= #10 0::Int)
+#75 := (not #74)
+#63 := (<= #9 0::Int)
+#95 := (or #63 #75 #78)
+#648 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #647) #95)
+#100 := (forall (vars (?v0 Int) (?v1 Int)) #95)
+#651 := (iff #100 #648)
+#649 := (iff #95 #95)
+#650 := [refl]: #649
+#652 := [quant-intro #650]: #651
+#182 := (~ #100 #100)
+#180 := (~ #95 #95)
+#181 := [refl]: #180
+#183 := [nnf-pos #181]: #182
+#14 := (< 0::Int #10)
+#13 := (< 0::Int #9)
+#15 := (implies #13 #14)
+#12 := (< 0::Int #11)
+#16 := (implies #12 #15)
+#17 := (forall (vars (?v0 Int) (?v1 Int)) #16)
+#103 := (iff #17 #100)
+#47 := (not #13)
+#48 := (or #47 #14)
+#54 := (not #12)
+#55 := (or #54 #48)
+#60 := (forall (vars (?v0 Int) (?v1 Int)) #55)
+#101 := (iff #60 #100)
+#98 := (iff #55 #95)
+#89 := (or #63 #75)
+#92 := (or #78 #89)
+#96 := (iff #92 #95)
+#97 := [rewrite]: #96
+#93 := (iff #55 #92)
+#90 := (iff #48 #89)
+#76 := (iff #14 #75)
+#77 := [rewrite]: #76
+#72 := (iff #47 #63)
+#64 := (not #63)
+#67 := (not #64)
+#70 := (iff #67 #63)
+#71 := [rewrite]: #70
+#68 := (iff #47 #67)
+#65 := (iff #13 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#73 := [trans #69 #71]: #72
+#91 := [monotonicity #73 #77]: #90
+#87 := (iff #54 #78)
+#79 := (not #78)
+#82 := (not #79)
+#85 := (iff #82 #78)
+#86 := [rewrite]: #85
+#83 := (iff #54 #82)
+#80 := (iff #12 #79)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#88 := [trans #84 #86]: #87
+#94 := [monotonicity #88 #91]: #93
+#99 := [trans #94 #97]: #98
+#102 := [quant-intro #99]: #101
+#61 := (iff #17 #60)
+#58 := (iff #16 #55)
+#51 := (implies #12 #48)
+#56 := (iff #51 #55)
+#57 := [rewrite]: #56
+#52 := (iff #16 #51)
+#49 := (iff #15 #48)
+#50 := [rewrite]: #49
+#53 := [monotonicity #50]: #52
+#59 := [trans #53 #57]: #58
+#62 := [quant-intro #59]: #61
+#104 := [trans #62 #102]: #103
+#46 := [asserted]: #17
+#105 := [mp #46 #104]: #100
+#170 := [mp~ #105 #183]: #100
+#653 := [mp #170 #652]: #648
+#319 := (not #648)
+#310 := (or #319 #123 #135 #138)
+#232 := (or #138 #135 #123)
+#321 := (or #319 #232)
+#639 := (iff #321 #310)
+#250 := (or #319 #155)
+#324 := (iff #250 #310)
+#303 := [rewrite]: #324
+#323 := (iff #321 #250)
+#317 := (iff #232 #155)
+#318 := [rewrite]: #317
+#320 := [monotonicity #318]: #323
+#641 := [trans #320 #303]: #639
+#322 := [quant-inst #18 #20]: #321
+#297 := [mp #322 #641]: #310
+[unit-resolution #297 #653 #166 #167 #168]: false
+unsat
+0db52837dc3c07a6a4d5ca34a945edf7aeac1fdf 136 0
+#2 := false
+#58 := 0::Int
+decl f3 :: (-> Int Int Int)
+decl f6 :: Int
+#22 := f6
+#20 := 1::Int
+#80 := (+ 1::Int f6)
+decl f4 :: Int
+#18 := f4
+#83 := (f3 f4 #80)
+decl f5 :: Int
+#19 := f5
+#71 := (+ f5 f6)
+#72 := (+ 1::Int #71)
+#77 := (f3 f4 #72)
+#53 := -1::Int
+#99 := (* -1::Int #77)
+#100 := (+ #99 #83)
+#25 := (f3 f4 f5)
+#101 := (+ #25 #100)
+#97 := (= #101 0::Int)
+#98 := (not #97)
+#26 := (+ f6 1::Int)
+#27 := (f3 f4 #26)
+#28 := (+ #25 #27)
+#21 := (+ f5 1::Int)
+#23 := (+ #21 f6)
+#24 := (f3 f4 #23)
+#29 := (= #24 #28)
+#30 := (not #29)
+#104 := (iff #30 #98)
+#86 := (+ #25 #83)
+#89 := (= #77 #86)
+#92 := (not #89)
+#102 := (iff #92 #98)
+#96 := (iff #89 #97)
+#95 := [rewrite]: #96
+#103 := [monotonicity #95]: #102
+#93 := (iff #30 #92)
+#90 := (iff #29 #89)
+#87 := (= #28 #86)
+#84 := (= #27 #83)
+#81 := (= #26 #80)
+#82 := [rewrite]: #81
+#85 := [monotonicity #82]: #84
+#88 := [monotonicity #85]: #87
+#78 := (= #24 #77)
+#75 := (= #23 #72)
+#52 := (+ 1::Int f5)
+#68 := (+ #52 f6)
+#73 := (= #68 #72)
+#74 := [rewrite]: #73
+#69 := (= #23 #68)
+#66 := (= #21 #52)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#76 := [trans #70 #74]: #75
+#79 := [monotonicity #76]: #78
+#91 := [monotonicity #79 #88]: #90
+#94 := [monotonicity #91]: #93
+#105 := [trans #94 #103]: #104
+#51 := [asserted]: #30
+#106 := [mp #51 #105]: #98
+#10 := (:var 0 Int)
+#8 := (:var 2 Int)
+#14 := (f3 #8 #10)
+#9 := (:var 1 Int)
+#13 := (f3 #8 #9)
+#582 := (pattern #13 #14)
+#55 := (* -1::Int #14)
+#54 := (* -1::Int #13)
 #56 := (+ #54 #55)
-#67 := (+ #18 #56)
-#68 := (+ f6 #67)
-#69 := (+ f5 #68)
-#70 := (+ f3 #69)
-#144 := (= #70 #70)
-#148 := (iff #144 true)
-#149 := [rewrite]: #148
-#143 := (iff #32 #144)
-#146 := (= #31 #70)
-#131 := (+ f7 #67)
-#132 := (+ f6 #131)
-#133 := (+ f5 #132)
-#85 := (* 2::Int #55)
-#83 := (* 2::Int #54)
-#86 := (+ #83 #85)
-#112 := (* 2::Int #18)
-#113 := (+ #112 #86)
-#114 := (+ f7 #113)
-#84 := (* 2::Int f6)
-#115 := (+ #84 #114)
-#82 := (* 2::Int f5)
-#116 := (+ #82 #115)
-#121 := (+ f3 #116)
-#138 := (- #121 #133)
-#141 := (= #138 #70)
-#147 := [rewrite]: #141
-#139 := (= #31 #138)
-#136 := (= #30 #133)
-#124 := (+ f6 f7)
-#125 := (+ f5 #124)
-#128 := (* #11 #125)
-#134 := (= #128 #133)
-#135 := [rewrite]: #134
-#129 := (= #30 #128)
-#126 := (= #29 #125)
-#127 := [rewrite]: #126
-#130 := [monotonicity #127]: #129
-#137 := [trans #130 #135]: #136
-#122 := (= #27 #121)
-#119 := (= #26 #116)
-#99 := (+ #18 #86)
-#100 := (+ f7 #99)
-#101 := (+ #84 #100)
-#102 := (+ #82 #101)
-#109 := (+ #102 #18)
-#117 := (= #109 #116)
-#118 := [rewrite]: #117
-#110 := (= #26 #109)
-#107 := (= #25 #18)
-#108 := [rewrite]: #107
-#105 := (= #24 #102)
-#93 := (+ f7 #18)
-#87 := (+ #84 #86)
-#88 := (+ #82 #87)
-#96 := (+ #88 #93)
-#103 := (= #96 #102)
-#104 := [rewrite]: #103
-#97 := (= #24 #96)
-#94 := (= #23 #93)
-#95 := [rewrite]: #94
-#91 := (= #22 #88)
-#75 := (* 2::Int f4)
-#76 := (+ 2::Int #75)
-#79 := (* #76 #14)
-#89 := (= #79 #88)
-#90 := [rewrite]: #89
-#80 := (= #22 #79)
-#77 := (= #21 #76)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#92 := [trans #81 #90]: #91
-#98 := [monotonicity #92 #95]: #97
-#106 := [trans #98 #104]: #105
-#111 := [monotonicity #106 #108]: #110
-#120 := [trans #111 #118]: #119
-#123 := [monotonicity #120]: #122
-#140 := [monotonicity #123 #137]: #139
-#145 := [trans #140 #147]: #146
-#73 := (= #19 #70)
-#57 := (+ f6 #56)
-#58 := (+ f5 #57)
-#61 := (+ f3 #58)
-#64 := (+ #61 #18)
-#71 := (= #64 #70)
-#72 := [rewrite]: #71
-#65 := (= #19 #64)
-#62 := (= #16 #61)
-#59 := (= #15 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#66 := [monotonicity #63]: #65
-#74 := [trans #66 #72]: #73
-#142 := [monotonicity #74 #145]: #143
-#151 := [trans #142 #149]: #150
-#154 := [monotonicity #151]: #153
-#158 := [trans #154 #156]: #157
-#53 := [asserted]: #33
-[mp #53 #158]: false
+#11 := (+ #9 #10)
+#12 := (f3 #8 #11)
+#57 := (+ #12 #56)
+#59 := (= #57 0::Int)
+#583 := (forall (vars (?v0 Int) (?v1 Int) (?v2 Int)) (:pat #582) #59)
+#62 := (forall (vars (?v0 Int) (?v1 Int) (?v2 Int)) #59)
+#586 := (iff #62 #583)
+#584 := (iff #59 #59)
+#585 := [refl]: #584
+#587 := [quant-intro #585]: #586
+#116 := (~ #62 #62)
+#114 := (~ #59 #59)
+#115 := [refl]: #114
+#117 := [nnf-pos #115]: #116
+#15 := (+ #13 #14)
+#16 := (= #12 #15)
+#17 := (forall (vars (?v0 Int) (?v1 Int) (?v2 Int)) #16)
+#63 := (iff #17 #62)
+#60 := (iff #16 #59)
+#61 := [rewrite]: #60
+#64 := [quant-intro #61]: #63
+#50 := [asserted]: #17
+#65 := [mp #50 #64]: #62
+#108 := [mp~ #65 #117]: #62
+#588 := [mp #108 #587]: #583
+#560 := (not #583)
+#415 := (or #560 #97)
+#530 := (* -1::Int #83)
+#255 := (* -1::Int #25)
+#524 := (+ #255 #530)
+#525 := (+ f5 #80)
+#531 := (f3 f4 #525)
+#532 := (+ #531 #524)
+#526 := (= #532 0::Int)
+#417 := (or #560 #526)
+#411 := (iff #417 #415)
+#420 := (iff #415 #415)
+#421 := [rewrite]: #420
+#515 := (iff #526 #97)
+#522 := (+ #77 #530)
+#520 := (+ #255 #522)
+#366 := (= #520 0::Int)
+#511 := (iff #366 #97)
+#512 := [rewrite]: #511
+#514 := (iff #526 #366)
+#406 := (= #532 #520)
+#518 := (+ #77 #524)
+#523 := (= #518 #520)
+#405 := [rewrite]: #523
+#519 := (= #532 #518)
+#364 := (= #531 #77)
+#533 := (= #525 #72)
+#362 := [rewrite]: #533
+#365 := [monotonicity #362]: #364
+#521 := [monotonicity #365]: #519
+#407 := [trans #521 #405]: #406
+#416 := [monotonicity #407]: #514
+#400 := [trans #416 #512]: #515
+#419 := [monotonicity #400]: #411
+#422 := [trans #419 #421]: #411
+#418 := [quant-inst #18 #19 #80]: #417
+#423 := [mp #418 #422]: #415
+[unit-resolution #423 #588 #106]: false
 unsat
 13d222fc57300189e3c05b2df538ad53757b2feb 257 0
 #2 := false
@@ -13271,7 +12922,7 @@
 #94 := [not-or-elim #88]: #93
 [mp #94 #115]: false
 unsat
-5187d9076857b0889962948031701fbc3f0e1f5d 151 0
+b9360163b10b7a2a34fb792ababcc1898c7e5b1c 138 0
 #2 := false
 decl f3 :: (-> S2 S2)
 decl f5 :: (-> Int S2)
@@ -13282,146 +12933,133 @@
 #20 := (f6 #19)
 #21 := (f5 #20)
 #22 := (f3 #21)
-#71 := (= #21 #22)
-#117 := (not #71)
+#70 := (= #21 #22)
+#106 := (not #70)
 decl f4 :: (-> S1 S1)
 decl f1 :: S1
 #4 := f1
-#77 := (f4 f1)
-#83 := (= f1 #77)
-#118 := (not #83)
-#590 := [hypothesis]: #118
+#24 := (f4 f1)
+#74 := (= f1 #24)
+#107 := (not #74)
+#579 := [hypothesis]: #107
 #12 := (:var 0 S1)
 #13 := (f4 #12)
-#609 := (pattern #13)
-#61 := (= f1 #12)
-#57 := (= f1 #13)
-#64 := (iff #57 #61)
-#610 := (forall (vars (?v0 S1)) (:pat #609) #64)
-#67 := (forall (vars (?v0 S1)) #64)
-#613 := (iff #67 #610)
-#611 := (iff #64 #64)
-#612 := [refl]: #611
-#614 := [quant-intro #612]: #613
-#105 := (~ #67 #67)
-#104 := (~ #64 #64)
-#115 := [refl]: #104
-#106 := [nnf-pos #115]: #105
+#598 := (pattern #13)
+#60 := (= f1 #12)
+#56 := (= f1 #13)
+#63 := (iff #56 #60)
+#599 := (forall (vars (?v0 S1)) (:pat #598) #63)
+#66 := (forall (vars (?v0 S1)) #63)
+#602 := (iff #66 #599)
+#600 := (iff #63 #63)
+#601 := [refl]: #600
+#603 := [quant-intro #601]: #602
+#94 := (~ #66 #66)
+#93 := (~ #63 #63)
+#104 := [refl]: #93
+#95 := [nnf-pos #104]: #94
 #15 := (= #12 f1)
 #14 := (= #13 f1)
 #16 := (iff #14 #15)
 #17 := (forall (vars (?v0 S1)) #16)
-#68 := (iff #17 #67)
-#65 := (iff #16 #64)
-#62 := (iff #15 #61)
-#63 := [rewrite]: #62
-#59 := (iff #14 #57)
-#60 := [rewrite]: #59
-#66 := [monotonicity #60 #63]: #65
-#69 := [quant-intro #66]: #68
-#56 := [asserted]: #17
-#72 := [mp #56 #69]: #67
-#116 := [mp~ #72 #106]: #67
-#615 := [mp #116 #614]: #610
-#276 := (not #610)
-#204 := (or #276 #83)
-#184 := (= f1 f1)
-#271 := (iff #83 #184)
-#277 := (or #276 #271)
-#278 := (iff #277 #204)
-#594 := (iff #204 #204)
-#596 := [rewrite]: #594
-#264 := (iff #271 #83)
+#67 := (iff #17 #66)
+#64 := (iff #16 #63)
+#61 := (iff #15 #60)
+#62 := [rewrite]: #61
+#58 := (iff #14 #56)
+#59 := [rewrite]: #58
+#65 := [monotonicity #59 #62]: #64
+#68 := [quant-intro #65]: #67
+#55 := [asserted]: #17
+#71 := [mp #55 #68]: #66
+#105 := [mp~ #71 #95]: #66
+#604 := [mp #105 #603]: #599
+#265 := (not #599)
+#193 := (or #265 #74)
+#173 := (= f1 f1)
+#260 := (iff #74 #173)
+#266 := (or #265 #260)
+#267 := (iff #266 #193)
+#583 := (iff #193 #193)
+#585 := [rewrite]: #583
+#253 := (iff #260 #74)
 #1 := true
-#88 := (iff #83 true)
-#91 := (iff #88 #83)
-#92 := [rewrite]: #91
-#186 := (iff #271 #88)
-#185 := (iff #184 true)
-#272 := [rewrite]: #185
-#273 := [monotonicity #272]: #186
-#275 := [trans #273 #92]: #264
-#257 := [monotonicity #275]: #278
-#251 := [trans #257 #596]: #278
-#274 := [quant-inst #4]: #277
-#383 := [mp #274 #251]: #204
-#262 := [unit-resolution #383 #615 #590]: false
-#263 := [lemma #262]: #83
-#107 := (or #117 #118)
-#95 := (and #71 #83)
-#98 := (not #95)
-#124 := (iff #98 #107)
-#108 := (not #107)
-#119 := (not #108)
-#122 := (iff #119 #107)
-#123 := [rewrite]: #122
-#120 := (iff #98 #119)
-#109 := (iff #95 #108)
-#110 := [rewrite]: #109
-#121 := [monotonicity #110]: #120
-#125 := [trans #121 #123]: #124
-decl f2 :: S1
-#5 := f2
-#24 := (ite true f1 f2)
-#25 := (f4 #24)
-#26 := (= #25 f1)
-#27 := (iff #26 true)
+#77 := (iff #74 true)
+#80 := (iff #77 #74)
+#81 := [rewrite]: #80
+#175 := (iff #260 #77)
+#174 := (iff #173 true)
+#261 := [rewrite]: #174
+#262 := [monotonicity #261]: #175
+#264 := [trans #262 #81]: #253
+#246 := [monotonicity #264]: #267
+#240 := [trans #246 #585]: #267
+#263 := [quant-inst #4]: #266
+#372 := [mp #263 #240]: #193
+#251 := [unit-resolution #372 #604 #579]: false
+#252 := [lemma #251]: #74
+#96 := (or #106 #107)
+#84 := (and #70 #74)
+#87 := (not #84)
+#113 := (iff #87 #96)
+#97 := (not #96)
+#108 := (not #97)
+#111 := (iff #108 #96)
+#112 := [rewrite]: #111
+#109 := (iff #87 #108)
+#98 := (iff #84 #97)
+#99 := [rewrite]: #98
+#110 := [monotonicity #99]: #109
+#114 := [trans #110 #112]: #113
+#25 := (= #24 f1)
+#26 := (iff #25 true)
 #23 := (= #22 #21)
-#28 := (and #23 #27)
-#29 := (not #28)
-#99 := (iff #29 #98)
-#96 := (iff #28 #95)
-#93 := (iff #27 #83)
-#89 := (iff #27 #88)
-#86 := (iff #26 #83)
-#80 := (= #77 f1)
-#84 := (iff #80 #83)
-#85 := [rewrite]: #84
-#81 := (iff #26 #80)
-#78 := (= #25 #77)
-#75 := (= #24 f1)
+#27 := (and #23 #26)
+#28 := (not #27)
+#88 := (iff #28 #87)
+#85 := (iff #27 #84)
+#82 := (iff #26 #74)
+#78 := (iff #26 #77)
+#75 := (iff #25 #74)
 #76 := [rewrite]: #75
 #79 := [monotonicity #76]: #78
-#82 := [monotonicity #79]: #81
-#87 := [trans #82 #85]: #86
-#90 := [monotonicity #87]: #89
-#94 := [trans #90 #92]: #93
-#73 := (iff #23 #71)
-#74 := [rewrite]: #73
-#97 := [monotonicity #74 #94]: #96
-#100 := [monotonicity #97]: #99
-#70 := [asserted]: #29
-#103 := [mp #70 #100]: #98
-#126 := [mp #103 #125]: #107
-#597 := [unit-resolution #126 #263]: #117
+#83 := [trans #79 #81]: #82
+#72 := (iff #23 #70)
+#73 := [rewrite]: #72
+#86 := [monotonicity #73 #83]: #85
+#89 := [monotonicity #86]: #88
+#69 := [asserted]: #28
+#92 := [mp #69 #89]: #87
+#115 := [mp #92 #114]: #96
+#586 := [unit-resolution #115 #252]: #106
 #8 := (:var 0 S2)
 #9 := (f3 #8)
-#602 := (pattern #9)
-#50 := (= #8 #9)
-#603 := (forall (vars (?v0 S2)) (:pat #602) #50)
-#53 := (forall (vars (?v0 S2)) #50)
-#606 := (iff #53 #603)
-#604 := (iff #50 #50)
-#605 := [refl]: #604
-#607 := [quant-intro #605]: #606
-#113 := (~ #53 #53)
-#111 := (~ #50 #50)
-#112 := [refl]: #111
-#114 := [nnf-pos #112]: #113
+#591 := (pattern #9)
+#49 := (= #8 #9)
+#592 := (forall (vars (?v0 S2)) (:pat #591) #49)
+#52 := (forall (vars (?v0 S2)) #49)
+#595 := (iff #52 #592)
+#593 := (iff #49 #49)
+#594 := [refl]: #593
+#596 := [quant-intro #594]: #595
+#102 := (~ #52 #52)
+#100 := (~ #49 #49)
+#101 := [refl]: #100
+#103 := [nnf-pos #101]: #102
 #10 := (= #9 #8)
 #11 := (forall (vars (?v0 S2)) #10)
-#54 := (iff #11 #53)
-#51 := (iff #10 #50)
-#52 := [rewrite]: #51
-#55 := [quant-intro #52]: #54
-#49 := [asserted]: #11
-#58 := [mp #49 #55]: #53
-#102 := [mp~ #58 #114]: #53
-#608 := [mp #102 #607]: #603
-#599 := (not #603)
-#600 := (or #599 #71)
-#595 := [quant-inst #21]: #600
-[unit-resolution #595 #608 #597]: false
+#53 := (iff #11 #52)
+#50 := (iff #10 #49)
+#51 := [rewrite]: #50
+#54 := [quant-intro #51]: #53
+#48 := [asserted]: #11
+#57 := [mp #48 #54]: #52
+#91 := [mp~ #57 #103]: #52
+#597 := [mp #91 #596]: #592
+#588 := (not #592)
+#589 := (or #588 #70)
+#584 := [quant-inst #21]: #589
+[unit-resolution #584 #597 #586]: false
 unsat
 81c1cc5fc7edfc96b965f4e15b374acf04ca9046 458 0
 #2 := false
@@ -14296,7 +13934,7 @@
 #105 := [asserted]: #29
 [unit-resolution #105 #402]: false
 unsat
-8f8fbc61d0925864fffd8945e68a0401b7416686 1 0
[phone]fda6e81b23523c37671c2fd01b49 1 0
 unsat
 a7ba12fdd24a1cfe15f53475941aaf6855022b7f 76 0
 #2 := false
@@ -14375,443 +14013,425 @@
 #580 := [quant-inst #107]: #579
 [unit-resolution #580 #971 #391]: false
 unsat
-e4dd068db00f152c179631d20d9af452dbe0f45d 439 0
+24f7b95c280da62e693df186e53d1c34ad016474 421 0
 #2 := false
 decl f19 :: (-> S8 S3)
 decl f22 :: (-> S1 S8)
 decl f1 :: S1
 #4 := f1
-#273 := (f22 f1)
-#276 := (f19 #273)
+#101 := (f22 f1)
+#102 := (f19 #101)
 decl f17 :: (-> S7 S3)
 decl f21 :: (-> Int S7)
 #98 := 3::Int
 #99 := (f21 3::Int)
 #100 := (f17 #99)
-#279 := (= #100 #276)
+#103 := (= #100 #102)
 decl f16 :: (-> S4 S3)
 decl f8 :: (-> S1 S4 S4)
 decl f10 :: S4
 #35 := f10
-#900 := (f8 f1 f10)
-#902 := (f16 #900)
-#656 := (= #902 #276)
-#569 := (= #276 #902)
+#884 := (f8 f1 f10)
+#886 := (f16 #884)
+#640 := (= #886 #102)
+#553 := (= #102 #886)
 #91 := (:var 0 S1)
 #94 := (f8 #91 f10)
-#975 := (pattern #94)
+#959 := (pattern #94)
 #92 := (f22 #91)
-#974 := (pattern #92)
+#958 := (pattern #92)
 #95 := (f16 #94)
 #93 := (f19 #92)
 #96 := (= #93 #95)
-#976 := (forall (vars (?v0 S1)) (:pat #974 #975) #96)
+#960 := (forall (vars (?v0 S1)) (:pat #958 #959) #96)
 #97 := (forall (vars (?v0 S1)) #96)
-#979 := (iff #97 #976)
-#977 := (iff #96 #96)
-#978 := [refl]: #977
-#980 := [quant-intro #978]: #979
-#402 := (~ #97 #97)
-#401 := (~ #96 #96)
-#398 := [refl]: #401
-#403 := [nnf-pos #398]: #402
-#268 := [asserted]: #97
-#399 := [mp~ #268 #403]: #97
-#981 := [mp #399 #980]: #976
-#904 := (not #976)
-#905 := (or #904 #569)
-#906 := [quant-inst #4]: #905
-#674 := [unit-resolution #906 #981]: #569
-#660 := [symm #674]: #656
-#645 := (= #100 #902)
+#963 := (iff #97 #960)
+#961 := (iff #96 #96)
+#962 := [refl]: #961
+#964 := [quant-intro #962]: #963
+#386 := (~ #97 #97)
+#385 := (~ #96 #96)
+#382 := [refl]: #385
+#387 := [nnf-pos #382]: #386
+#267 := [asserted]: #97
+#383 := [mp~ #267 #387]: #97
+#965 := [mp #383 #964]: #960
+#888 := (not #960)
+#889 := (or #888 #553)
+#890 := [quant-inst #4]: #889
+#658 := [unit-resolution #890 #965]: #553
+#644 := [symm #658]: #640
+#629 := (= #100 #886)
 decl f7 :: (-> S4 S3)
-#865 := (f7 #900)
-#860 := (= #865 #902)
+#849 := (f7 #884)
+#844 := (= #849 #886)
 #22 := (:var 0 S4)
 #71 := (f16 #22)
-#959 := (pattern #71)
+#943 := (pattern #71)
 #25 := (f7 #22)
-#958 := (pattern #25)
-#248 := (= #25 #71)
-#960 := (forall (vars (?v0 S4)) (:pat #958 #959) #248)
-#252 := (forall (vars (?v0 S4)) #248)
-#963 := (iff #252 #960)
-#961 := (iff #248 #248)
-#962 := [refl]: #961
-#964 := [quant-intro #962]: #963
-#390 := (~ #252 #252)
-#431 := (~ #248 #248)
-#432 := [refl]: #431
-#391 := [nnf-pos #432]: #390
+#942 := (pattern #25)
+#247 := (= #25 #71)
+#944 := (forall (vars (?v0 S4)) (:pat #942 #943) #247)
+#251 := (forall (vars (?v0 S4)) #247)
+#947 := (iff #251 #944)
+#945 := (iff #247 #247)
+#946 := [refl]: #945
+#948 := [quant-intro #946]: #947
+#374 := (~ #251 #251)
+#415 := (~ #247 #247)
+#416 := [refl]: #415
+#375 := [nnf-pos #416]: #374
 #72 := (= #71 #25)
 #73 := (forall (vars (?v0 S4)) #72)
-#253 := (iff #73 #252)
-#250 := (iff #72 #248)
-#251 := [rewrite]: #250
-#254 := [quant-intro #251]: #253
-#247 := [asserted]: #73
-#257 := [mp #247 #254]: #252
-#433 := [mp~ #257 #391]: #252
-#965 := [mp #433 #964]: #960
-#584 := (not #960)
-#709 := (or #584 #860)
-#710 := [quant-inst #900]: #709
-#671 := [unit-resolution #710 #965]: #860
-#646 := (= #100 #865)
+#252 := (iff #73 #251)
+#249 := (iff #72 #247)
+#250 := [rewrite]: #249
+#253 := [quant-intro #250]: #252
+#246 := [asserted]: #73
+#256 := [mp #246 #253]: #251
+#417 := [mp~ #256 #375]: #251
+#949 := [mp #417 #948]: #944
+#568 := (not #944)
+#693 := (or #568 #844)
+#694 := [quant-inst #884]: #693
+#655 := [unit-resolution #694 #949]: #844
+#630 := (= #100 #849)
 decl f5 :: (-> Int S3)
 decl f6 :: (-> S3 Int)
 #36 := (f7 f10)
-#862 := (f6 #36)
+#846 := (f6 #36)
 #15 := 1::Int
-#868 := (+ 1::Int #862)
-#711 := (f5 #868)
-#854 := (= #711 #865)
+#852 := (+ 1::Int #846)
+#695 := (f5 #852)
+#838 := (= #695 #849)
 #21 := (:var 1 S1)
 #23 := (f8 #21 #22)
-#915 := (pattern #23)
+#899 := (pattern #23)
 #26 := (f6 #25)
-#165 := (+ 1::Int #26)
-#170 := (f5 #165)
+#164 := (+ 1::Int #26)
+#169 := (f5 #164)
 #24 := (f7 #23)
-#173 := (= #24 #170)
-#916 := (forall (vars (?v0 S1) (?v1 S4)) (:pat #915) #173)
-#176 := (forall (vars (?v0 S1) (?v1 S4)) #173)
-#919 := (iff #176 #916)
-#917 := (iff #173 #173)
-#918 := [refl]: #917
-#920 := [quant-intro #918]: #919
-#374 := (~ #176 #176)
-#373 := (~ #173 #173)
-#418 := [refl]: #373
-#375 := [nnf-pos #418]: #374
+#172 := (= #24 #169)
+#900 := (forall (vars (?v0 S1) (?v1 S4)) (:pat #899) #172)
+#175 := (forall (vars (?v0 S1) (?v1 S4)) #172)
+#903 := (iff #175 #900)
+#901 := (iff #172 #172)
+#902 := [refl]: #901
+#904 := [quant-intro #902]: #903
+#358 := (~ #175 #175)
+#357 := (~ #172 #172)
+#402 := [refl]: #357
+#359 := [nnf-pos #402]: #358
 #14 := 0::Int
 #16 := (+ 0::Int 1::Int)
 #27 := (+ #26 #16)
 #28 := (f5 #27)
 #29 := (= #24 #28)
 #30 := (forall (vars (?v0 S1) (?v1 S4)) #29)
-#177 := (iff #30 #176)
-#174 := (iff #29 #173)
-#171 := (= #28 #170)
-#168 := (= #27 #165)
-#161 := (+ #26 1::Int)
-#166 := (= #161 #165)
-#167 := [rewrite]: #166
-#163 := (= #27 #161)
-#141 := (= #16 1::Int)
-#142 := [rewrite]: #141
-#164 := [monotonicity #142]: #163
-#169 := [trans #164 #167]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [quant-intro #175]: #177
-#160 := [asserted]: #30
-#181 := [mp #160 #178]: #176
-#419 := [mp~ #181 #375]: #176
-#921 := [mp #419 #920]: #916
-#850 := (not #916)
-#851 := (or #850 #854)
-#853 := (= #865 #711)
-#857 := (or #850 #853)
-#852 := (iff #857 #851)
-#688 := (iff #851 #851)
-#690 := [rewrite]: #688
-#855 := (iff #853 #854)
-#856 := [rewrite]: #855
-#859 := [monotonicity #856]: #852
-#691 := [trans #859 #690]: #852
-#858 := [quant-inst #4 #35]: #857
-#844 := [mp #858 #691]: #851
-#673 := [unit-resolution #844 #921]: #854
-#658 := (= #100 #711)
+#176 := (iff #30 #175)
+#173 := (iff #29 #172)
+#170 := (= #28 #169)
+#167 := (= #27 #164)
+#160 := (+ #26 1::Int)
+#165 := (= #160 #164)
+#166 := [rewrite]: #165
+#162 := (= #27 #160)
+#140 := (= #16 1::Int)
+#141 := [rewrite]: #140
+#163 := [monotonicity #141]: #162
+#168 := [trans #163 #166]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #171]: #173
+#177 := [quant-intro #174]: #176
+#159 := [asserted]: #30
+#180 := [mp #159 #177]: #175
+#403 := [mp~ #180 #359]: #175
+#905 := [mp #403 #904]: #900
+#834 := (not #900)
+#835 := (or #834 #838)
+#837 := (= #849 #695)
+#841 := (or #834 #837)
+#836 := (iff #841 #835)
+#672 := (iff #835 #835)
+#674 := [rewrite]: #672
+#839 := (iff #837 #838)
+#840 := [rewrite]: #839
+#843 := [monotonicity #840]: #836
+#675 := [trans #843 #674]: #836
+#842 := [quant-inst #4 #35]: #841
+#828 := [mp #842 #675]: #835
+#657 := [unit-resolution #828 #905]: #838
+#642 := (= #100 #695)
 decl f3 :: (-> S2 S3)
 decl f9 :: S2
 #31 := f9
 #32 := (f3 f9)
-#870 := (f6 #32)
-#874 := (+ 1::Int #870)
-#863 := (f5 #874)
-#652 := (= #863 #711)
-#664 := (= #711 #863)
-#670 := (= #868 #874)
-#663 := (= 1::Int #874)
-#703 := (= #874 1::Int)
-#847 := (<= #870 0::Int)
-#845 := (= #870 0::Int)
+#854 := (f6 #32)
+#858 := (+ 1::Int #854)
+#847 := (f5 #858)
+#636 := (= #847 #695)
+#648 := (= #695 #847)
+#654 := (= #852 #858)
+#647 := (= 1::Int #858)
+#687 := (= #858 1::Int)
+#831 := (<= #854 0::Int)
+#829 := (= #854 0::Int)
 #33 := (f5 0::Int)
-#901 := (f6 #33)
-#898 := (= #901 0::Int)
+#885 := (f6 #33)
+#882 := (= #885 0::Int)
 #84 := (:var 0 Int)
-#112 := (f5 #84)
-#990 := (pattern #112)
-#312 := (>= #84 0::Int)
-#313 := (not #312)
-#113 := (f6 #112)
-#294 := (= #84 #113)
-#319 := (or #294 #313)
-#991 := (forall (vars (?v0 Int)) (:pat #990) #319)
-#324 := (forall (vars (?v0 Int)) #319)
-#994 := (iff #324 #991)
-#992 := (iff #319 #319)
-#993 := [refl]: #992
-#995 := [quant-intro #993]: #994
-#408 := (~ #324 #324)
-#407 := (~ #319 #319)
-#394 := [refl]: #407
-#409 := [nnf-pos #394]: #408
-#114 := (= #113 #84)
-#111 := (<= 0::Int #84)
-#115 := (implies #111 #114)
-#116 := (forall (vars (?v0 Int)) #115)
-#327 := (iff #116 #324)
-#301 := (not #111)
-#302 := (or #301 #294)
-#307 := (forall (vars (?v0 Int)) #302)
-#325 := (iff #307 #324)
-#322 := (iff #302 #319)
-#316 := (or #313 #294)
-#320 := (iff #316 #319)
-#321 := [rewrite]: #320
-#317 := (iff #302 #316)
-#314 := (iff #301 #313)
-#310 := (iff #111 #312)
-#311 := [rewrite]: #310
-#315 := [monotonicity #311]: #314
-#318 := [monotonicity #315]: #317
-#323 := [trans #318 #321]: #322
-#326 := [quant-intro #323]: #325
-#308 := (iff #116 #307)
-#305 := (iff #115 #302)
-#298 := (implies #111 #294)
-#303 := (iff #298 #302)
-#304 := [rewrite]: #303
-#299 := (iff #115 #298)
-#296 := (iff #114 #294)
-#297 := [rewrite]: #296
-#300 := [monotonicity #297]: #299
-#306 := [trans #300 #304]: #305
-#309 := [quant-intro #306]: #308
-#328 := [trans #309 #326]: #327
-#293 := [asserted]: #116
-#329 := [mp #293 #328]: #324
-#395 := [mp~ #329 #409]: #324
-#996 := [mp #395 #995]: #991
-#891 := (not #991)
-#893 := (or #891 #898)
-#570 := (>= 0::Int 0::Int)
-#903 := (not #570)
-#907 := (= 0::Int #901)
-#897 := (or #907 #903)
-#532 := (or #891 #897)
-#894 := (iff #532 #893)
-#895 := (iff #893 #893)
-#881 := [rewrite]: #895
-#890 := (iff #897 #898)
-#886 := (or #898 false)
-#889 := (iff #886 #898)
-#884 := [rewrite]: #889
-#887 := (iff #897 #886)
-#548 := (iff #903 false)
+#111 := (f5 #84)
+#974 := (pattern #111)
+#296 := (>= #84 0::Int)
+#297 := (not #296)
+#112 := (f6 #111)
+#278 := (= #84 #112)
+#303 := (or #278 #297)
+#975 := (forall (vars (?v0 Int)) (:pat #974) #303)
+#308 := (forall (vars (?v0 Int)) #303)
+#978 := (iff #308 #975)
+#976 := (iff #303 #303)
+#977 := [refl]: #976
+#979 := [quant-intro #977]: #978
+#392 := (~ #308 #308)
+#391 := (~ #303 #303)
+#378 := [refl]: #391
+#393 := [nnf-pos #378]: #392
+#113 := (= #112 #84)
+#110 := (<= 0::Int #84)
+#114 := (implies #110 #113)
+#115 := (forall (vars (?v0 Int)) #114)
+#311 := (iff #115 #308)
+#285 := (not #110)
+#286 := (or #285 #278)
+#291 := (forall (vars (?v0 Int)) #286)
+#309 := (iff #291 #308)
+#306 := (iff #286 #303)
+#300 := (or #297 #278)
+#304 := (iff #300 #303)
+#305 := [rewrite]: #304
+#301 := (iff #286 #300)
+#298 := (iff #285 #297)
+#294 := (iff #110 #296)
+#295 := [rewrite]: #294
+#299 := [monotonicity #295]: #298
+#302 := [monotonicity #299]: #301
+#307 := [trans #302 #305]: #306
+#310 := [quant-intro #307]: #309
+#292 := (iff #115 #291)
+#289 := (iff #114 #286)
+#282 := (implies #110 #278)
+#287 := (iff #282 #286)
+#288 := [rewrite]: #287
+#283 := (iff #114 #282)
+#280 := (iff #113 #278)
+#281 := [rewrite]: #280
+#284 := [monotonicity #281]: #283
+#290 := [trans #284 #288]: #289
+#293 := [quant-intro #290]: #292
+#312 := [trans #293 #310]: #311
+#277 := [asserted]: #115
+#313 := [mp #277 #312]: #308
+#379 := [mp~ #313 #393]: #308
+#980 := [mp #379 #979]: #975
+#875 := (not #975)
+#877 := (or #875 #882)
+#554 := (>= 0::Int 0::Int)
+#887 := (not #554)
+#891 := (= 0::Int #885)
+#881 := (or #891 #887)
+#516 := (or #875 #881)
+#878 := (iff #516 #877)
+#879 := (iff #877 #877)
+#865 := [rewrite]: #879
+#874 := (iff #881 #882)
+#870 := (or #882 false)
+#873 := (iff #870 #882)
+#868 := [rewrite]: #873
+#871 := (iff #881 #870)
+#532 := (iff #887 false)
 #1 := true
-#541 := (not true)
-#546 := (iff #541 false)
-#547 := [rewrite]: #546
-#883 := (iff #903 #541)
-#557 := (iff #570 true)
-#899 := [rewrite]: #557
-#545 := [monotonicity #899]: #883
-#885 := [trans #545 #547]: #548
-#556 := (iff #907 #898)
-#561 := [rewrite]: #556
-#888 := [monotonicity #561 #885]: #887
-#527 := [trans #888 #884]: #890
-#892 := [monotonicity #527]: #894
-#882 := [trans #892 #881]: #894
-#533 := [quant-inst #14]: #532
-#589 := [mp #533 #882]: #893
-#723 := [unit-resolution #589 #996]: #898
-#685 := (= #870 #901)
+#525 := (not true)
+#530 := (iff #525 false)
+#531 := [rewrite]: #530
+#867 := (iff #887 #525)
+#541 := (iff #554 true)
+#883 := [rewrite]: #541
+#529 := [monotonicity #883]: #867
+#869 := [trans #529 #531]: #532
+#540 := (iff #891 #882)
+#545 := [rewrite]: #540
+#872 := [monotonicity #545 #869]: #871
+#511 := [trans #872 #868]: #874
+#876 := [monotonicity #511]: #878
+#866 := [trans #876 #865]: #878
+#517 := [quant-inst #14]: #516
+#573 := [mp #517 #866]: #877
+#707 := [unit-resolution #573 #980]: #882
+#669 := (= #854 #885)
 #34 := (= #32 #33)
-#179 := [asserted]: #34
-#686 := [monotonicity #179]: #685
-#693 := [trans #686 #723]: #845
-#695 := (not #845)
-#696 := (or #695 #847)
-#697 := [th-lemma arith triangle-eq]: #696
-#699 := [unit-resolution #697 #693]: #847
-#848 := (>= #870 0::Int)
-#700 := (or #695 #848)
-#701 := [th-lemma arith triangle-eq]: #700
-#702 := [unit-resolution #701 #693]: #848
-#704 := [th-lemma arith eq-propagate -1 -1 #702 #699]: #703
-#666 := [symm #704]: #663
-#679 := (= #868 1::Int)
-#849 := (<= #862 0::Int)
-#846 := (= #862 0::Int)
-#705 := (= #862 #901)
+#178 := [asserted]: #34
+#670 := [monotonicity #178]: #669
+#677 := [trans #670 #707]: #829
+#679 := (not #829)
+#680 := (or #679 #831)
+#681 := [th-lemma arith triangle-eq]: #680
+#683 := [unit-resolution #681 #677]: #831
+#832 := (>= #854 0::Int)
+#684 := (or #679 #832)
+#685 := [th-lemma arith triangle-eq]: #684
+#686 := [unit-resolution #685 #677]: #832
+#688 := [th-lemma arith eq-propagate -1 -1 #686 #683]: #687
+#650 := [symm #688]: #647
+#663 := (= #852 1::Int)
+#833 := (<= #846 0::Int)
+#830 := (= #846 0::Int)
+#689 := (= #846 #885)
 #37 := (= #36 #33)
-#182 := (= #33 #36)
-#183 := (iff #37 #182)
-#184 := [rewrite]: #183
-#180 := [asserted]: #37
-#187 := [mp #180 #184]: #182
-#687 := [symm #187]: #37
-#675 := [monotonicity #687]: #705
-#676 := [trans #675 #723]: #846
-#677 := (not #846)
-#678 := (or #677 #849)
-#680 := [th-lemma arith triangle-eq]: #678
-#681 := [unit-resolution #680 #676]: #849
-#731 := (>= #862 0::Int)
-#682 := (or #677 #731)
-#524 := [th-lemma arith triangle-eq]: #682
-#683 := [unit-resolution #524 #676]: #731
-#684 := [th-lemma arith eq-propagate -1 -1 #683 #681]: #679
-#672 := [trans #684 #666]: #670
-#669 := [monotonicity #672]: #664
-#655 := [symm #669]: #652
-#654 := (= #100 #863)
+#181 := (= #33 #36)
+#182 := (iff #37 #181)
+#183 := [rewrite]: #182
+#179 := [asserted]: #37
+#186 := [mp #179 #183]: #181
+#671 := [symm #186]: #37
+#659 := [monotonicity #671]: #689
+#660 := [trans #659 #707]: #830
+#661 := (not #830)
+#662 := (or #661 #833)
+#664 := [th-lemma arith triangle-eq]: #662
+#665 := [unit-resolution #664 #660]: #833
+#715 := (>= #846 0::Int)
+#666 := (or #661 #715)
+#508 := [th-lemma arith triangle-eq]: #666
+#667 := [unit-resolution #508 #660]: #715
+#668 := [th-lemma arith eq-propagate -1 -1 #667 #665]: #663
+#656 := [trans #668 #650]: #654
+#653 := [monotonicity #656]: #648
+#639 := [symm #653]: #636
+#638 := (= #100 #847)
 decl f4 :: (-> Int S2 S2)
-#579 := (f4 3::Int f9)
-#601 := (f3 #579)
-#864 := (= #601 #863)
+#563 := (f4 3::Int f9)
+#585 := (f3 #563)
+#848 := (= #585 #847)
 #9 := (:var 0 S2)
 #8 := (:var 1 Int)
 #10 := (f4 #8 #9)
-#908 := (pattern #10)
+#892 := (pattern #10)
 #12 := (f3 #9)
 #13 := (f6 #12)
-#146 := (+ 1::Int #13)
-#151 := (f5 #146)
+#145 := (+ 1::Int #13)
+#150 := (f5 #145)
 #11 := (f3 #10)
-#154 := (= #11 #151)
-#909 := (forall (vars (?v0 Int) (?v1 S2)) (:pat #908) #154)
-#157 := (forall (vars (?v0 Int) (?v1 S2)) #154)
-#912 := (iff #157 #909)
-#910 := (iff #154 #154)
-#911 := [refl]: #910
-#913 := [quant-intro #911]: #912
-#416 := (~ #157 #157)
-#414 := (~ #154 #154)
-#415 := [refl]: #414
-#417 := [nnf-pos #415]: #416
+#153 := (= #11 #150)
+#893 := (forall (vars (?v0 Int) (?v1 S2)) (:pat #892) #153)
+#156 := (forall (vars (?v0 Int) (?v1 S2)) #153)
+#896 := (iff #156 #893)
+#894 := (iff #153 #153)
+#895 := [refl]: #894
+#897 := [quant-intro #895]: #896
+#400 := (~ #156 #156)
+#398 := (~ #153 #153)
+#399 := [refl]: #398
+#401 := [nnf-pos #399]: #400
 #17 := (+ #13 #16)
 #18 := (f5 #17)
 #19 := (= #11 #18)
 #20 := (forall (vars (?v0 Int) (?v1 S2)) #19)
-#158 := (iff #20 #157)
-#155 := (iff #19 #154)
-#152 := (= #18 #151)
-#149 := (= #17 #146)
-#143 := (+ #13 1::Int)
-#147 := (= #143 #146)
-#148 := [rewrite]: #147
-#144 := (= #17 #143)
-#145 := [monotonicity #142]: #144
-#150 := [trans #145 #148]: #149
-#153 := [monotonicity #150]: #152
-#156 := [monotonicity #153]: #155
-#159 := [quant-intro #156]: #158
-#140 := [asserted]: #20
-#162 := [mp #140 #159]: #157
-#372 := [mp~ #162 #417]: #157
-#914 := [mp #372 #913]: #909
-#861 := (not #909)
-#866 := (or #861 #864)
-#867 := [quant-inst #98 #31]: #866
-#722 := [unit-resolution #867 #914]: #864
-#653 := (= #100 #601)
+#157 := (iff #20 #156)
+#154 := (iff #19 #153)
+#151 := (= #18 #150)
+#148 := (= #17 #145)
+#142 := (+ #13 1::Int)
+#146 := (= #142 #145)
+#147 := [rewrite]: #146
+#143 := (= #17 #142)
+#144 := [monotonicity #141]: #143
+#149 := [trans #144 #147]: #148
+#152 := [monotonicity #149]: #151
+#155 := [monotonicity #152]: #154
+#158 := [quant-intro #155]: #157
+#139 := [asserted]: #20
+#161 := [mp #139 #158]: #156
+#356 := [mp~ #161 #401]: #156
+#898 := [mp #356 #897]: #893
+#845 := (not #893)
+#850 := (or #845 #848)
+#851 := [quant-inst #98 #31]: #850
+#706 := [unit-resolution #851 #898]: #848
+#637 := (= #100 #585)
 decl f15 :: (-> S2 S3)
-#583 := (f15 #579)
-#879 := (= #583 #601)
+#567 := (f15 #563)
+#863 := (= #567 #585)
 #68 := (f15 #9)
-#951 := (pattern #68)
-#950 := (pattern #12)
-#240 := (= #12 #68)
-#952 := (forall (vars (?v0 S2)) (:pat #950 #951) #240)
-#244 := (forall (vars (?v0 S2)) #240)
-#955 := (iff #244 #952)
-#953 := (iff #240 #240)
-#954 := [refl]: #953
-#956 := [quant-intro #954]: #955
-#388 := (~ #244 #244)
-#428 := (~ #240 #240)
-#429 := [refl]: #428
-#389 := [nnf-pos #429]: #388
+#935 := (pattern #68)
+#934 := (pattern #12)
+#239 := (= #12 #68)
+#936 := (forall (vars (?v0 S2)) (:pat #934 #935) #239)
+#243 := (forall (vars (?v0 S2)) #239)
+#939 := (iff #243 #936)
+#937 := (iff #239 #239)
+#938 := [refl]: #937
+#940 := [quant-intro #938]: #939
+#372 := (~ #243 #243)
+#412 := (~ #239 #239)
+#413 := [refl]: #412
+#373 := [nnf-pos #413]: #372
 #69 := (= #68 #12)
 #70 := (forall (vars (?v0 S2)) #69)
-#245 := (iff #70 #244)
-#242 := (iff #69 #240)
-#243 := [rewrite]: #242
-#246 := [quant-intro #243]: #245
-#239 := [asserted]: #70
-#249 := [mp #239 #246]: #244
-#430 := [mp~ #249 #389]: #244
-#957 := [mp #430 #956]: #952
-#580 := (not #952)
-#590 := (or #580 #879)
-#875 := (= #601 #583)
-#591 := (or #580 #875)
-#593 := (iff #591 #590)
-#872 := (iff #590 #590)
-#586 := [rewrite]: #872
-#876 := (iff #875 #879)
-#880 := [rewrite]: #876
-#871 := [monotonicity #880]: #593
-#869 := [trans #871 #586]: #593
-#592 := [quant-inst #579]: #591
-#873 := [mp #592 #869]: #590
-#721 := [unit-resolution #873 #957]: #879
-#564 := (= #100 #583)
+#244 := (iff #70 #243)
+#241 := (iff #69 #239)
+#242 := [rewrite]: #241
+#245 := [quant-intro #242]: #244
+#238 := [asserted]: #70
+#248 := [mp #238 #245]: #243
+#414 := [mp~ #248 #373]: #243
+#941 := [mp #414 #940]: #936
+#564 := (not #936)
+#574 := (or #564 #863)
+#859 := (= #585 #567)
+#575 := (or #564 #859)
+#577 := (iff #575 #574)
+#856 := (iff #574 #574)
+#570 := [rewrite]: #856
+#860 := (iff #859 #863)
+#864 := [rewrite]: #860
+#855 := [monotonicity #864]: #577
+#853 := [trans #855 #570]: #577
+#576 := [quant-inst #563]: #575
+#857 := [mp #576 #853]: #574
+#705 := [unit-resolution #857 #941]: #863
+#548 := (= #100 #567)
 #87 := (f4 #84 f9)
-#967 := (pattern #87)
+#951 := (pattern #87)
 #85 := (f21 #84)
-#966 := (pattern #85)
+#950 := (pattern #85)
 #88 := (f15 #87)
 #86 := (f17 #85)
 #89 := (= #86 #88)
-#968 := (forall (vars (?v0 Int)) (:pat #966 #967) #89)
+#952 := (forall (vars (?v0 Int)) (:pat #950 #951) #89)
 #90 := (forall (vars (?v0 Int)) #89)
-#971 := (iff #90 #968)
-#969 := (iff #89 #89)
-#970 := [refl]: #969
-#972 := [quant-intro #970]: #971
-#392 := (~ #90 #90)
-#434 := (~ #89 #89)
-#435 := [refl]: #434
-#393 := [nnf-pos #435]: #392
-#267 := [asserted]: #90
-#400 := [mp~ #267 #393]: #90
-#973 := [mp #400 #972]: #968
-#558 := (not #968)
-#689 := (or #558 #564)
-#896 := [quant-inst #98]: #689
-#662 := [unit-resolution #896 #973]: #564
-#661 := [trans #662 #721]: #653
-#657 := [trans #661 #722]: #654
-#644 := [trans #657 #655]: #658
-#647 := [trans #644 #673]: #646
-#648 := [trans #647 #671]: #645
-#630 := [trans #648 #660]: #279
-#282 := (not #279)
-decl f2 :: S1
-#5 := f2
-#101 := (ite true f1 f2)
-#102 := (f22 #101)
-#103 := (f19 #102)
-#104 := (= #100 #103)
-#105 := (not #104)
-#283 := (iff #105 #282)
-#280 := (iff #104 #279)
-#277 := (= #103 #276)
-#274 := (= #102 #273)
-#271 := (= #101 f1)
-#272 := [rewrite]: #271
-#275 := [monotonicity #272]: #274
-#278 := [monotonicity #275]: #277
-#281 := [monotonicity #278]: #280
-#284 := [monotonicity #281]: #283
-#270 := [asserted]: #105
-#287 := [mp #270 #284]: #282
-[unit-resolution #287 #630]: false
-unsat
+#955 := (iff #90 #952)
+#953 := (iff #89 #89)
+#954 := [refl]: #953
+#956 := [quant-intro #954]: #955
+#376 := (~ #90 #90)
+#418 := (~ #89 #89)
+#419 := [refl]: #418
+#377 := [nnf-pos #419]: #376
+#266 := [asserted]: #90
+#384 := [mp~ #266 #377]: #90
+#957 := [mp #384 #956]: #952
+#542 := (not #952)
+#673 := (or #542 #548)
+#880 := [quant-inst #98]: #673
+#646 := [unit-resolution #880 #957]: #548
+#645 := [trans #646 #705]: #637
+#641 := [trans #645 #706]: #638
+#628 := [trans #641 #639]: #642
+#631 := [trans #628 #657]: #630
+#632 := [trans #631 #655]: #629
+#614 := [trans #632 #644]: #103
+#104 := (not #103)
+#269 := [asserted]: #104
+[unit-resolution #269 #614]: false
+unsat

--- a/src/HOL/SMT_Examples/SMT_Examples.thy	Sun Dec 19 18:54:29 2010 +0100
+++ b/src/HOL/SMT_Examples/SMT_Examples.thy	Sun Dec 19 18:55:21 2010 +0100
@@ -25,7 +25,6 @@
 lemma "(p \<or> q) \<and> \<not>p \<Longrightarrow> q" by smt
 
 lemma "(a \<and> b) \<or> (c \<and> d) \<Longrightarrow> (a \<and> b) \<or> (c \<and> d)"
-  using [[smt_oracle=true]] (* no Z3 proof *)
   by smt
 
 lemma "(p1 \<and> p2) \<or> p3 \<longrightarrow> (p1 \<longrightarrow> (p3 \<and> p2) \<or> (p1 \<and> p3)) \<or> p1" by smt
@@ -400,20 +399,20 @@
 subsection {* Non-linear arithmetic over integers and reals *}
 
 lemma "a > (0::int) \<Longrightarrow> a*b > 0 \<Longrightarrow> b > 0"
-  using [[smt_oracle=true]]  -- {* Isabelle's arithmetic decision procedures
-    are too weak to automatically prove @{thm zero_less_mult_pos}. *}
-  by smt (* FIXME: use z3_rule *)
-
+  using zero_less_mult_pos
+  by smt
 
+lemma  "(a::int) * (x + 1 + y) = a * x + a * (y + 1)"
+  using right_distrib
+  by smt
 
-lemma  "(a::int) * (x + 1 + y) = a * x + a * (y + 1)" by smt
-
-lemma "((x::real) * (1 + y) - x * (1 - y)) = (2 * x * y)" by smt
+lemma "((x::real) * (1 + y) - x * (1 - y)) = (2 * x * y)"
+  sorry (* FIXME: Z3 could solve this directly *)
 
 lemma
   "(U::int) + (1 + p) * (b + e) + p * d =
    U + (2 * (1 + p) * (b + e) + (1 + p) * d + d * p) - (1 + p) * (b + d + e)"
-  by smt
+  sorry (* FIXME: Z3 could solve this directly *)
 
 
 subsection {* Linear arithmetic for natural numbers *}

--- a/src/HOL/SMT_Examples/SMT_Tests.certs	Sun Dec 19 18:54:29 2010 +0100
+++ b/src/HOL/SMT_Examples/SMT_Tests.certs	Sun Dec 19 18:55:21 2010 +0100
@@ -12789,9503 +12789,4479 @@
 #53 := [asserted]: #16
 [mp #53 #71]: false
 unsat
-6610e16f7eb0fe91ddb9c3e14cbb3397d007ccfb 260 0
+611c41109aa958be031117f9c38a7deb95b567a0 72 0
 #2 := false
 decl f3 :: (-> Int S2)
 #8 := 0::Int
-#11 := (f3 0::Int)
-decl f4 :: (-> Int Int Int)
-#9 := (f4 0::Int 0::Int)
-#10 := (f3 #9)
-#12 := (= #10 #11)
-#798 := (= #9 0::Int)
-#19 := (:var 0 Int)
-#30 := (:var 1 Int)
-#31 := (f4 #30 #19)
-#877 := (pattern #31)
-#179 := -1::Int
-#183 := (* -1::Int #19)
-#180 := (* -1::Int #30)
-#186 := (div #180 #183)
-#358 := (* -1::Int #186)
-#359 := (+ #31 #358)
-#360 := (= #359 0::Int)
-#41 := (div #30 #19)
-#355 := (* -1::Int #41)
-#356 := (+ #31 #355)
-#357 := (= #356 0::Int)
-#218 := (>= #30 0::Int)
-#211 := (<= #19 0::Int)
-#318 := (or #211 #218)
-#319 := (not #318)
-#207 := (<= #30 0::Int)
-#316 := (or #207 #211)
-#317 := (not #316)
-#322 := (or #317 #319)
-#361 := (ite #322 #357 #360)
-#354 := (= #31 0::Int)
-#33 := (= #19 0::Int)
-#32 := (= #30 0::Int)
-#34 := (or #32 #33)
-#362 := (ite #34 #354 #361)
-#878 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #877) #362)
-#365 := (forall (vars (?v0 Int) (?v1 Int)) #362)
-#881 := (iff #365 #878)
-#879 := (iff #362 #362)
-#880 := [refl]: #879
-#882 := [quant-intro #880]: #881
-#325 := (ite #322 #41 #186)
-#328 := (ite #34 0::Int #325)
-#331 := (= #31 #328)
-#334 := (forall (vars (?v0 Int) (?v1 Int)) #331)
-#366 := (iff #334 #365)
-#363 := (iff #331 #362)
-#364 := [rewrite]: #363
-#367 := [quant-intro #364]: #366
-#219 := (not #218)
-#212 := (not #211)
-#222 := (and #212 #219)
-#208 := (not #207)
-#215 := (and #208 #212)
-#225 := (or #215 #222)
-#228 := (ite #225 #41 #186)
-#231 := (ite #34 0::Int #228)
-#234 := (= #31 #231)
-#237 := (forall (vars (?v0 Int) (?v1 Int)) #234)
-#335 := (iff #237 #334)
-#332 := (iff #234 #331)
-#329 := (= #231 #328)
-#326 := (= #228 #325)
-#323 := (iff #225 #322)
-#320 := (iff #222 #319)
-#321 := [rewrite]: #320
-#301 := (iff #215 #317)
-#302 := [rewrite]: #301
-#324 := [monotonicity #302 #321]: #323
-#327 := [monotonicity #324]: #326
-#330 := [monotonicity #327]: #329
-#333 := [monotonicity #330]: #332
-#336 := [quant-intro #333]: #335
-#297 := (~ #237 #237)
-#310 := (~ #234 #234)
-#311 := [refl]: #310
-#298 := [nnf-pos #311]: #297
-#43 := (- #19)
-#42 := (- #30)
-#44 := (div #42 #43)
-#36 := (< 0::Int #19)
-#38 := (< #30 0::Int)
-#39 := (and #38 #36)
-#35 := (< 0::Int #30)
-#37 := (and #35 #36)
-#40 := (or #37 #39)
-#45 := (ite #40 #41 #44)
-#46 := (ite #34 0::Int #45)
-#47 := (= #31 #46)
-#48 := (forall (vars (?v0 Int) (?v1 Int)) #47)
-#240 := (iff #48 #237)
-#173 := (and #36 #38)
-#176 := (or #37 #173)
-#189 := (ite #176 #41 #186)
-#167 := (= 0::Int #19)
-#164 := (= 0::Int #30)
-#170 := (or #164 #167)
-#192 := (ite #170 0::Int #189)
-#195 := (= #31 #192)
-#198 := (forall (vars (?v0 Int) (?v1 Int)) #195)
-#238 := (iff #198 #237)
-#235 := (iff #195 #234)
-#232 := (= #192 #231)
-#229 := (= #189 #228)
-#226 := (iff #176 #225)
-#223 := (iff #173 #222)
-#220 := (iff #38 #219)
-#221 := [rewrite]: #220
-#213 := (iff #36 #212)
-#214 := [rewrite]: #213
-#224 := [monotonicity #214 #221]: #223
-#216 := (iff #37 #215)
-#209 := (iff #35 #208)
-#210 := [rewrite]: #209
-#217 := [monotonicity #210 #214]: #216
-#227 := [monotonicity #217 #224]: #226
-#230 := [monotonicity #227]: #229
-#205 := (iff #170 #34)
-#203 := (iff #167 #33)
-#204 := [rewrite]: #203
-#201 := (iff #164 #32)
-#202 := [rewrite]: #201
-#206 := [monotonicity #202 #204]: #205
-#233 := [monotonicity #206 #230]: #232
-#236 := [monotonicity #233]: #235
-#239 := [quant-intro #236]: #238
-#199 := (iff #48 #198)
-#196 := (iff #47 #195)
-#193 := (= #46 #192)
-#190 := (= #45 #189)
-#187 := (= #44 #186)
-#184 := (= #43 #183)
-#185 := [rewrite]: #184
-#181 := (= #42 #180)
-#182 := [rewrite]: #181
-#188 := [monotonicity #182 #185]: #187
-#177 := (iff #40 #176)
-#174 := (iff #39 #173)
-#175 := [rewrite]: #174
-#178 := [monotonicity #175]: #177
-#191 := [monotonicity #178 #188]: #190
-#171 := (iff #34 #170)
-#168 := (iff #33 #167)
-#169 := [rewrite]: #168
-#165 := (iff #32 #164)
-#166 := [rewrite]: #165
-#172 := [monotonicity #166 #169]: #171
-#194 := [monotonicity #172 #191]: #193
-#197 := [monotonicity #194]: #196
-#200 := [quant-intro #197]: #199
-#241 := [trans #200 #239]: #240
-#163 := [asserted]: #48
-#242 := [mp #163 #241]: #237
-#312 := [mp~ #242 #298]: #237
-#337 := [mp #312 #336]: #334
-#368 := [mp #337 #367]: #365
-#883 := [mp #368 #882]: #878
-#755 := (not #878)
-#757 := (or #755 #798)
-#811 := (* -1::Int 0::Int)
-#812 := (div #811 #811)
-#813 := (* -1::Int #812)
-#808 := (+ #9 #813)
-#809 := (= #808 0::Int)
-#814 := (div 0::Int 0::Int)
-#815 := (* -1::Int #814)
-#810 := (+ #9 #815)
-#816 := (= #810 0::Int)
-#833 := (>= 0::Int 0::Int)
-#657 := (<= 0::Int 0::Int)
-#658 := (or #657 #833)
-#659 := (not #658)
-#801 := (or #657 #657)
-#802 := (not #801)
-#803 := (or #802 #659)
-#804 := (ite #803 #816 #809)
-#799 := (= 0::Int 0::Int)
-#805 := (or #799 #799)
-#806 := (ite #805 #798 #804)
-#758 := (or #755 #806)
-#756 := (iff #758 #757)
-#740 := (iff #757 #757)
-#741 := [rewrite]: #740
-#768 := (iff #806 #798)
-#1 := true
-#764 := (ite true #798 #816)
-#767 := (iff #764 #798)
-#763 := [rewrite]: #767
-#765 := (iff #806 #764)
-#761 := (iff #804 #816)
-#774 := (ite false #816 #816)
-#770 := (iff #774 #816)
-#777 := [rewrite]: #770
-#775 := (iff #804 #774)
-#784 := (iff #809 #816)
-#783 := (= #808 #810)
-#781 := (= #813 #815)
-#769 := (= #812 #814)
-#780 := (= #811 0::Int)
-#772 := [rewrite]: #780
-#771 := [monotonicity #772 #772]: #769
-#782 := [monotonicity #771]: #781
-#779 := [monotonicity #782]: #783
-#773 := [monotonicity #779]: #784
-#791 := (iff #803 false)
-#695 := (or false false)
-#790 := (iff #695 false)
-#787 := [rewrite]: #790
-#696 := (iff #803 #695)
-#693 := (iff #659 false)
-#481 := (not true)
-#840 := (iff #481 false)
-#843 := [rewrite]: #840
-#692 := (iff #659 #481)
-#689 := (iff #658 true)
-#636 := (or true true)
-#792 := (iff #636 true)
-#793 := [rewrite]: #792
-#789 := (iff #658 #636)
-#839 := (iff #833 true)
-#841 := [rewrite]: #839
-#794 := (iff #657 true)
-#797 := [rewrite]: #794
-#674 := [monotonicity #797 #841]: #789
-#691 := [trans #674 #793]: #689
-#685 := [monotonicity #691]: #692
-#694 := [trans #685 #843]: #693
-#785 := (iff #802 false)
-#788 := (iff #802 #481)
-#681 := (iff #801 true)
-#679 := (iff #801 #636)
-#680 := [monotonicity #797 #797]: #679
-#640 := [trans #680 #793]: #681
-#690 := [monotonicity #640]: #788
-#786 := [trans #690 #843]: #785
-#697 := [monotonicity #786 #694]: #696
-#778 := [trans #697 #787]: #791
-#776 := [monotonicity #778 #773]: #775
-#762 := [trans #776 #777]: #761
-#795 := (iff #805 true)
-#638 := (iff #805 #636)
-#800 := (iff #799 true)
-#807 := [rewrite]: #800
-#639 := [monotonicity #807 #807]: #638
-#796 := [trans #639 #793]: #795
-#766 := [monotonicity #796 #762]: #765
-#754 := [trans #766 #763]: #768
-#760 := [monotonicity #754]: #756
-#743 := [trans #760 #741]: #756
-#759 := [quant-inst #8 #8]: #758
-#744 := [mp #759 #743]: #757
-#746 := [unit-resolution #744 #883]: #798
-#747 := [monotonicity #746]: #12
-#13 := (not #12)
-#77 := [asserted]: #13
-[unit-resolution #77 #747]: false
-unsat
-3797d02b9c4cbb9f278d97dba12e1e356411933c 275 0
+#20 := (f3 0::Int)
+#15 := (- 0::Int)
+#16 := (div #15 #15)
+#14 := (div 0::Int 0::Int)
+#11 := (< 0::Int 0::Int)
+#12 := (and #11 #11)
+#13 := (or #12 #12)
+#17 := (ite #13 #14 #16)
+#9 := (= 0::Int 0::Int)
+#10 := (or #9 #9)
+#18 := (ite #10 0::Int #17)
+#19 := (f3 #18)
+#21 := (= #19 #20)
+#22 := (not #21)
+#108 := (iff #22 false)
+#1 := true
+#103 := (not true)
+#106 := (iff #103 false)
+#107 := [rewrite]: #106
+#104 := (iff #22 #103)
+#101 := (iff #21 true)
+#96 := (= #20 #20)
+#99 := (iff #96 true)
+#100 := [rewrite]: #99
+#97 := (iff #21 #96)
+#93 := (= #18 0::Int)
+#88 := (ite true 0::Int #14)
+#91 := (= #88 0::Int)
+#92 := [rewrite]: #91
+#89 := (= #18 #88)
+#86 := (= #17 #14)
+#81 := (ite #11 #14 #14)
+#84 := (= #81 #14)
+#85 := [rewrite]: #84
+#82 := (= #17 #81)
+#79 := (= #16 #14)
+#77 := (= #15 0::Int)
+#78 := [rewrite]: #77
+#80 := [monotonicity #78 #78]: #79
+#75 := (iff #13 #11)
+#70 := (or #11 #11)
+#73 := (iff #70 #11)
+#74 := [rewrite]: #73
+#71 := (iff #13 #70)
+#68 := (iff #12 #11)
+#69 := [rewrite]: #68
+#72 := [monotonicity #69 #69]: #71
+#76 := [trans #72 #74]: #75
+#83 := [monotonicity #76 #80]: #82
+#87 := [trans #83 #85]: #86
+#66 := (iff #10 true)
+#61 := (or true true)
+#64 := (iff #61 true)
+#65 := [rewrite]: #64
+#62 := (iff #10 #61)
+#59 := (iff #9 true)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60 #60]: #62
+#67 := [trans #63 #65]: #66
+#90 := [monotonicity #67 #87]: #89
+#94 := [trans #90 #92]: #93
+#95 := [monotonicity #94]: #21
+#98 := [monotonicity #95]: #97
+#102 := [trans #98 #100]: #101
+#105 := [monotonicity #102]: #104
+#109 := [trans #105 #107]: #108
+#58 := [asserted]: #22
+[mp #58 #109]: false
+unsat
+a1635dd4dd56e9245fc52a441cde335332b960ef 79 0
 #2 := false
 decl f3 :: (-> Int S2)
 #10 := 0::Int
-#13 := (f3 0::Int)
-decl f4 :: (-> Int Int Int)
-decl f5 :: (-> S2 Int)
-decl f6 :: S2
-#8 := f6
-#9 := (f5 f6)
-#11 := (f4 #9 0::Int)
-#12 := (f3 #11)
-#14 := (= #12 #13)
-#641 := (= #11 0::Int)
-#21 := (:var 0 Int)
-#32 := (:var 1 Int)
-#33 := (f4 #32 #21)
-#879 := (pattern #33)
-#181 := -1::Int
-#185 := (* -1::Int #21)
-#182 := (* -1::Int #32)
-#188 := (div #182 #185)
-#360 := (* -1::Int #188)
-#361 := (+ #33 #360)
-#362 := (= #361 0::Int)
-#43 := (div #32 #21)
-#357 := (* -1::Int #43)
-#358 := (+ #33 #357)
-#359 := (= #358 0::Int)
-#220 := (>= #32 0::Int)
-#213 := (<= #21 0::Int)
-#320 := (or #213 #220)
-#321 := (not #320)
-#209 := (<= #32 0::Int)
-#318 := (or #209 #213)
-#319 := (not #318)
-#324 := (or #319 #321)
-#363 := (ite #324 #359 #362)
-#356 := (= #33 0::Int)
-#35 := (= #21 0::Int)
-#34 := (= #32 0::Int)
-#36 := (or #34 #35)
-#364 := (ite #36 #356 #363)
-#880 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #879) #364)
-#367 := (forall (vars (?v0 Int) (?v1 Int)) #364)
-#883 := (iff #367 #880)
-#881 := (iff #364 #364)
-#882 := [refl]: #881
-#884 := [quant-intro #882]: #883
-#327 := (ite #324 #43 #188)
-#330 := (ite #36 0::Int #327)
-#333 := (= #33 #330)
-#336 := (forall (vars (?v0 Int) (?v1 Int)) #333)
-#368 := (iff #336 #367)
-#365 := (iff #333 #364)
-#366 := [rewrite]: #365
-#369 := [quant-intro #366]: #368
-#221 := (not #220)
-#214 := (not #213)
-#224 := (and #214 #221)
-#210 := (not #209)
-#217 := (and #210 #214)
-#227 := (or #217 #224)
-#230 := (ite #227 #43 #188)
-#233 := (ite #36 0::Int #230)
-#236 := (= #33 #233)
-#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
-#337 := (iff #239 #336)
-#334 := (iff #236 #333)
-#331 := (= #233 #330)
-#328 := (= #230 #327)
-#325 := (iff #227 #324)
-#322 := (iff #224 #321)
-#323 := [rewrite]: #322
-#303 := (iff #217 #319)
-#304 := [rewrite]: #303
-#326 := [monotonicity #304 #323]: #325
-#329 := [monotonicity #326]: #328
-#332 := [monotonicity #329]: #331
-#335 := [monotonicity #332]: #334
-#338 := [quant-intro #335]: #337
-#299 := (~ #239 #239)
-#312 := (~ #236 #236)
-#313 := [refl]: #312
-#300 := [nnf-pos #313]: #299
-#45 := (- #21)
-#44 := (- #32)
-#46 := (div #44 #45)
-#38 := (< 0::Int #21)
-#40 := (< #32 0::Int)
-#41 := (and #40 #38)
-#37 := (< 0::Int #32)
-#39 := (and #37 #38)
-#42 := (or #39 #41)
-#47 := (ite #42 #43 #46)
-#48 := (ite #36 0::Int #47)
-#49 := (= #33 #48)
-#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
-#242 := (iff #50 #239)
-#175 := (and #38 #40)
-#178 := (or #39 #175)
-#191 := (ite #178 #43 #188)
-#169 := (= 0::Int #21)
-#166 := (= 0::Int #32)
-#172 := (or #166 #169)
-#194 := (ite #172 0::Int #191)
-#197 := (= #33 #194)
-#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
-#240 := (iff #200 #239)
-#237 := (iff #197 #236)
-#234 := (= #194 #233)
-#231 := (= #191 #230)
-#228 := (iff #178 #227)
-#225 := (iff #175 #224)
-#222 := (iff #40 #221)
-#223 := [rewrite]: #222
-#215 := (iff #38 #214)
-#216 := [rewrite]: #215
-#226 := [monotonicity #216 #223]: #225
-#218 := (iff #39 #217)
-#211 := (iff #37 #210)
-#212 := [rewrite]: #211
-#219 := [monotonicity #212 #216]: #218
-#229 := [monotonicity #219 #226]: #228
-#232 := [monotonicity #229]: #231
-#207 := (iff #172 #36)
-#205 := (iff #169 #35)
-#206 := [rewrite]: #205
-#203 := (iff #166 #34)
-#204 := [rewrite]: #203
-#208 := [monotonicity #204 #206]: #207
-#235 := [monotonicity #208 #232]: #234
-#238 := [monotonicity #235]: #237
-#241 := [quant-intro #238]: #240
-#201 := (iff #50 #200)
-#198 := (iff #49 #197)
-#195 := (= #48 #194)
-#192 := (= #47 #191)
-#189 := (= #46 #188)
-#186 := (= #45 #185)
-#187 := [rewrite]: #186
-#183 := (= #44 #182)
-#184 := [rewrite]: #183
-#190 := [monotonicity #184 #187]: #189
-#179 := (iff #42 #178)
-#176 := (iff #41 #175)
-#177 := [rewrite]: #176
-#180 := [monotonicity #177]: #179
-#193 := [monotonicity #180 #190]: #192
-#173 := (iff #36 #172)
-#170 := (iff #35 #169)
-#171 := [rewrite]: #170
-#167 := (iff #34 #166)
-#168 := [rewrite]: #167
-#174 := [monotonicity #168 #171]: #173
-#196 := [monotonicity #174 #193]: #195
-#199 := [monotonicity #196]: #198
-#202 := [quant-intro #199]: #201
-#243 := [trans #202 #241]: #242
-#165 := [asserted]: #50
-#244 := [mp #165 #243]: #239
-#314 := [mp~ #244 #300]: #239
-#339 := [mp #314 #338]: #336
-#370 := [mp #339 #369]: #367
-#885 := [mp #370 #884]: #880
-#755 := (not #880)
-#733 := (or #755 #641)
-#816 := (* -1::Int 0::Int)
-#817 := (* -1::Int #9)
-#812 := (div #817 #816)
-#818 := (* -1::Int #812)
-#659 := (+ #11 #818)
-#660 := (= #659 0::Int)
-#661 := (div #9 0::Int)
-#803 := (* -1::Int #661)
-#804 := (+ #11 #803)
-#805 := (= #804 0::Int)
-#806 := (>= #9 0::Int)
-#800 := (<= 0::Int 0::Int)
-#801 := (or #800 #806)
-#807 := (not #801)
-#808 := (<= #9 0::Int)
-#802 := (or #808 #800)
-#809 := (not #802)
-#638 := (or #809 #807)
-#640 := (ite #638 #805 #660)
-#794 := (= 0::Int 0::Int)
-#795 := (= #9 0::Int)
-#797 := (or #795 #794)
-#798 := (ite #797 #641 #640)
-#734 := (or #755 #798)
-#737 := (iff #734 #733)
-#739 := (iff #733 #733)
-#740 := [rewrite]: #739
-#754 := (iff #798 #641)
-#766 := (div #817 0::Int)
-#769 := (* -1::Int #766)
-#756 := (+ #11 #769)
-#760 := (= #756 0::Int)
-#1 := true
-#749 := (ite true #641 #760)
-#752 := (iff #749 #641)
-#753 := [rewrite]: #752
-#750 := (iff #798 #749)
-#747 := (iff #640 #760)
-#762 := (ite false #805 #760)
-#745 := (iff #762 #760)
-#746 := [rewrite]: #745
-#742 := (iff #640 #762)
-#761 := (iff #660 #760)
-#757 := (= #659 #756)
-#765 := (= #818 #769)
-#767 := (= #812 #766)
-#763 := (= #816 0::Int)
-#764 := [rewrite]: #763
-#768 := [monotonicity #764]: #767
-#770 := [monotonicity #768]: #765
-#759 := [monotonicity #770]: #757
-#758 := [monotonicity #759]: #761
-#772 := (iff #638 false)
-#786 := (or false false)
-#777 := (iff #786 false)
-#778 := [rewrite]: #777
-#775 := (iff #638 #786)
-#785 := (iff #807 false)
-#831 := (not true)
-#555 := (iff #831 false)
-#556 := [rewrite]: #555
-#783 := (iff #807 #831)
-#771 := (iff #801 true)
-#789 := (or true #806)
-#782 := (iff #789 true)
-#774 := [rewrite]: #782
-#793 := (iff #801 #789)
-#788 := (iff #800 true)
-#791 := [rewrite]: #788
-#780 := [monotonicity #791]: #793
-#773 := [trans #780 #774]: #771
-#784 := [monotonicity #773]: #783
-#781 := [trans #784 #556]: #785
-#699 := (iff #809 false)
-#697 := (iff #809 #831)
-#695 := (iff #802 true)
-#676 := (or #808 true)
-#694 := (iff #676 true)
-#687 := [rewrite]: #694
-#691 := (iff #802 #676)
-#693 := [monotonicity #791]: #691
-#696 := [trans #693 #687]: #695
-#698 := [monotonicity #696]: #697
-#792 := [trans #698 #556]: #699
-#776 := [monotonicity #792 #781]: #775
-#779 := [trans #776 #778]: #772
-#743 := [monotonicity #779 #758]: #742
-#748 := [trans #743 #746]: #747
-#692 := (iff #797 true)
-#681 := (or #795 true)
-#642 := (iff #681 true)
-#790 := [rewrite]: #642
-#682 := (iff #797 #681)
-#796 := (iff #794 true)
-#799 := [rewrite]: #796
-#683 := [monotonicity #799]: #682
-#787 := [trans #683 #790]: #692
-#751 := [monotonicity #787 #748]: #750
-#744 := [trans #751 #753]: #754
-#738 := [monotonicity #744]: #737
-#735 := [trans #738 #740]: #737
-#736 := [quant-inst #9 #10]: #734
-#741 := [mp #736 #735]: #733
-#723 := [unit-resolution #741 #885]: #641
-#724 := [monotonicity #723]: #14
-#15 := (not #14)
-#79 := [asserted]: #15
-[unit-resolution #79 #724]: false
-unsat
-589d59789d263d5382384d3b16ffc9ff725b6206 297 0
+#27 := (f3 0::Int)
+#22 := (- 0::Int)
+decl f4 :: (-> S2 Int)
+decl f5 :: S2
+#8 := f5
+#9 := (f4 f5)
+#21 := (- #9)
+#23 := (div #21 #22)
+#20 := (div #9 0::Int)
+#15 := (< 0::Int 0::Int)
+#17 := (< #9 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int #9)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#24 := (ite #19 #20 #23)
+#12 := (= 0::Int 0::Int)
+#11 := (= #9 0::Int)
+#13 := (or #11 #12)
+#25 := (ite #13 0::Int #24)
+#26 := (f3 #25)
+#28 := (= #26 #27)
+#29 := (not #28)
+#113 := (iff #29 false)
+#1 := true
+#108 := (not true)
+#111 := (iff #108 false)
+#112 := [rewrite]: #111
+#109 := (iff #29 #108)
+#106 := (iff #28 true)
+#101 := (= #27 #27)
+#104 := (iff #101 true)
+#105 := [rewrite]: #104
+#102 := (iff #28 #101)
+#98 := (= #25 0::Int)
+#81 := -1::Int
+#82 := (* -1::Int #9)
+#87 := (div #82 0::Int)
+#75 := (and #15 #17)
+#78 := (or #16 #75)
+#90 := (ite #78 #20 #87)
+#93 := (ite true 0::Int #90)
+#96 := (= #93 0::Int)
+#97 := [rewrite]: #96
+#94 := (= #25 #93)
+#91 := (= #24 #90)
+#88 := (= #23 #87)
+#85 := (= #22 0::Int)
+#86 := [rewrite]: #85
+#83 := (= #21 #82)
+#84 := [rewrite]: #83
+#89 := [monotonicity #84 #86]: #88
+#79 := (iff #19 #78)
+#76 := (iff #18 #75)
+#77 := [rewrite]: #76
+#80 := [monotonicity #77]: #79
+#92 := [monotonicity #80 #89]: #91
+#73 := (iff #13 true)
+#68 := (or #11 true)
+#71 := (iff #68 true)
+#72 := [rewrite]: #71
+#69 := (iff #13 #68)
+#66 := (iff #12 true)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#74 := [trans #70 #72]: #73
+#95 := [monotonicity #74 #92]: #94
+#99 := [trans #95 #97]: #98
+#100 := [monotonicity #99]: #28
+#103 := [monotonicity #100]: #102
+#107 := [trans #103 #105]: #106
+#110 := [monotonicity #107]: #109
+#114 := [trans #110 #112]: #113
+#65 := [asserted]: #29
+[mp #65 #114]: false
+unsat
+e01bd2bd51de7fe522eece30b6126b14fb1617b9 81 0
 #2 := false
 decl f3 :: (-> Int S2)
 #8 := 0::Int
-#12 := (f3 0::Int)
-decl f4 :: (-> Int Int Int)
-#9 := 1::Int
-#10 := (f4 0::Int 1::Int)
-#11 := (f3 #10)
-#13 := (= #11 #12)
-#806 := (= #10 0::Int)
-#20 := (:var 0 Int)
-#31 := (:var 1 Int)
-#32 := (f4 #31 #20)
-#877 := (pattern #32)
-#180 := -1::Int
-#184 := (* -1::Int #20)
-#181 := (* -1::Int #31)
-#187 := (div #181 #184)
-#359 := (* -1::Int #187)
-#360 := (+ #32 #359)
-#361 := (= #360 0::Int)
-#42 := (div #31 #20)
-#356 := (* -1::Int #42)
-#357 := (+ #32 #356)
-#358 := (= #357 0::Int)
-#219 := (>= #31 0::Int)
-#212 := (<= #20 0::Int)
-#319 := (or #212 #219)
-#320 := (not #319)
-#208 := (<= #31 0::Int)
-#317 := (or #208 #212)
-#318 := (not #317)
-#323 := (or #318 #320)
-#362 := (ite #323 #358 #361)
-#355 := (= #32 0::Int)
-#34 := (= #20 0::Int)
-#33 := (= #31 0::Int)
-#35 := (or #33 #34)
-#363 := (ite #35 #355 #362)
-#878 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #877) #363)
-#366 := (forall (vars (?v0 Int) (?v1 Int)) #363)
-#881 := (iff #366 #878)
-#879 := (iff #363 #363)
-#880 := [refl]: #879
-#882 := [quant-intro #880]: #881
-#326 := (ite #323 #42 #187)
-#329 := (ite #35 0::Int #326)
-#332 := (= #32 #329)
-#335 := (forall (vars (?v0 Int) (?v1 Int)) #332)
-#367 := (iff #335 #366)
-#364 := (iff #332 #363)
-#365 := [rewrite]: #364
-#368 := [quant-intro #365]: #367
-#220 := (not #219)
-#213 := (not #212)
-#223 := (and #213 #220)
-#209 := (not #208)
-#216 := (and #209 #213)
-#226 := (or #216 #223)
-#229 := (ite #226 #42 #187)
-#232 := (ite #35 0::Int #229)
-#235 := (= #32 #232)
-#238 := (forall (vars (?v0 Int) (?v1 Int)) #235)
-#336 := (iff #238 #335)
-#333 := (iff #235 #332)
-#330 := (= #232 #329)
-#327 := (= #229 #326)
-#324 := (iff #226 #323)
-#321 := (iff #223 #320)
-#322 := [rewrite]: #321
-#302 := (iff #216 #318)
-#303 := [rewrite]: #302
-#325 := [monotonicity #303 #322]: #324
-#328 := [monotonicity #325]: #327
-#331 := [monotonicity #328]: #330
-#334 := [monotonicity #331]: #333
-#337 := [quant-intro #334]: #336
-#298 := (~ #238 #238)
-#311 := (~ #235 #235)
-#312 := [refl]: #311
-#299 := [nnf-pos #312]: #298
-#44 := (- #20)
-#43 := (- #31)
-#45 := (div #43 #44)
-#37 := (< 0::Int #20)
-#39 := (< #31 0::Int)
-#40 := (and #39 #37)
-#36 := (< 0::Int #31)
-#38 := (and #36 #37)
-#41 := (or #38 #40)
-#46 := (ite #41 #42 #45)
-#47 := (ite #35 0::Int #46)
-#48 := (= #32 #47)
-#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
-#241 := (iff #49 #238)
-#174 := (and #37 #39)
-#177 := (or #38 #174)
-#190 := (ite #177 #42 #187)
-#168 := (= 0::Int #20)
-#165 := (= 0::Int #31)
-#171 := (or #165 #168)
-#193 := (ite #171 0::Int #190)
-#196 := (= #32 #193)
-#199 := (forall (vars (?v0 Int) (?v1 Int)) #196)
-#239 := (iff #199 #238)
-#236 := (iff #196 #235)
-#233 := (= #193 #232)
-#230 := (= #190 #229)
-#227 := (iff #177 #226)
-#224 := (iff #174 #223)
-#221 := (iff #39 #220)
-#222 := [rewrite]: #221
-#214 := (iff #37 #213)
-#215 := [rewrite]: #214
-#225 := [monotonicity #215 #222]: #224
-#217 := (iff #38 #216)
-#210 := (iff #36 #209)
-#211 := [rewrite]: #210
-#218 := [monotonicity #211 #215]: #217
-#228 := [monotonicity #218 #225]: #227
-#231 := [monotonicity #228]: #230
-#206 := (iff #171 #35)
-#204 := (iff #168 #34)
-#205 := [rewrite]: #204
-#202 := (iff #165 #33)
-#203 := [rewrite]: #202
-#207 := [monotonicity #203 #205]: #206
-#234 := [monotonicity #207 #231]: #233
-#237 := [monotonicity #234]: #236
-#240 := [quant-intro #237]: #239
-#200 := (iff #49 #199)
-#197 := (iff #48 #196)
-#194 := (= #47 #193)
-#191 := (= #46 #190)
-#188 := (= #45 #187)
-#185 := (= #44 #184)
-#186 := [rewrite]: #185
-#182 := (= #43 #181)
-#183 := [rewrite]: #182
-#189 := [monotonicity #183 #186]: #188
-#178 := (iff #41 #177)
-#175 := (iff #40 #174)
-#176 := [rewrite]: #175
-#179 := [monotonicity #176]: #178
-#192 := [monotonicity #179 #189]: #191
-#172 := (iff #35 #171)
-#169 := (iff #34 #168)
-#170 := [rewrite]: #169
-#166 := (iff #33 #165)
-#167 := [rewrite]: #166
-#173 := [monotonicity #167 #170]: #172
-#195 := [monotonicity #173 #192]: #194
-#198 := [monotonicity #195]: #197
-#201 := [quant-intro #198]: #200
-#242 := [trans #201 #240]: #241
-#164 := [asserted]: #49
-#243 := [mp #164 #242]: #238
-#313 := [mp~ #243 #299]: #238
-#338 := [mp #313 #337]: #335
-#369 := [mp #338 #368]: #366
-#883 := [mp #369 #882]: #878
-#724 := (not #878)
-#730 := (or #724 #806)
-#812 := (* -1::Int 1::Int)
-#813 := (* -1::Int 0::Int)
-#808 := (div #813 #812)
-#809 := (* -1::Int #808)
-#814 := (+ #10 #809)
-#815 := (= #814 0::Int)
-#810 := (div 0::Int 1::Int)
-#816 := (* -1::Int #810)
-#657 := (+ #10 #816)
-#658 := (= #657 0::Int)
-#834 := (>= 0::Int 0::Int)
-#659 := (<= 1::Int 0::Int)
-#801 := (or #659 #834)
-#802 := (not #801)
-#803 := (<= 0::Int 0::Int)
-#804 := (or #803 #659)
-#798 := (not #804)
-#799 := (or #798 #802)
-#805 := (ite #799 #658 #815)
-#800 := (= 1::Int 0::Int)
-#807 := (= 0::Int 0::Int)
-#636 := (or #807 #800)
-#638 := (ite #636 #806 #805)
-#703 := (or #724 #638)
-#705 := (iff #703 #730)
-#709 := (iff #730 #730)
-#710 := [rewrite]: #709
-#728 := (iff #638 #806)
-#1 := true
-#721 := (ite true #806 #806)
-#726 := (iff #721 #806)
-#727 := [rewrite]: #726
-#722 := (iff #638 #721)
-#739 := (iff #805 #806)
-#735 := (ite false #806 #806)
-#738 := (iff #735 #806)
-#733 := [rewrite]: #738
-#736 := (iff #805 #735)
-#732 := (iff #815 #806)
-#753 := (= #814 #10)
-#766 := (+ #10 0::Int)
-#768 := (= #766 #10)
-#754 := [rewrite]: #768
-#752 := (= #814 #766)
-#750 := (= #809 0::Int)
-#761 := (= #813 0::Int)
-#762 := [rewrite]: #761
-#748 := (= #809 #813)
-#746 := (= #808 0::Int)
-#740 := (div 0::Int -1::Int)
-#744 := (= #740 0::Int)
-#745 := [rewrite]: #744
-#741 := (= #808 #740)
-#756 := (= #812 -1::Int)
-#760 := [rewrite]: #756
-#743 := [monotonicity #762 #760]: #741
-#747 := [trans #743 #745]: #746
-#749 := [monotonicity #747]: #748
-#751 := [trans #749 #762]: #750
-#742 := [monotonicity #751]: #752
-#731 := [trans #742 #754]: #753
-#734 := [monotonicity #731]: #732
-#758 := (iff #658 #806)
-#755 := (= #657 #10)
-#767 := (= #657 #766)
-#764 := (= #816 0::Int)
-#770 := (= #816 #813)
-#775 := (= #810 0::Int)
-#776 := [rewrite]: #775
-#777 := [monotonicity #776]: #770
-#765 := [trans #777 #762]: #764
-#763 := [monotonicity #765]: #767
-#757 := [trans #763 #754]: #755
-#759 := [monotonicity #757]: #758
-#773 := (iff #799 false)
-#781 := (or false false)
-#779 := (iff #781 false)
-#784 := [rewrite]: #779
-#782 := (iff #799 #781)
-#769 := (iff #802 false)
-#482 := (not true)
-#843 := (iff #482 false)
-#829 := [rewrite]: #843
-#780 := (iff #802 #482)
-#791 := (iff #801 true)
-#695 := (or false true)
-#790 := (iff #695 true)
-#787 := [rewrite]: #790
-#696 := (iff #801 #695)
-#841 := (iff #834 true)
-#481 := [rewrite]: #841
-#785 := (iff #659 false)
-#786 := [rewrite]: #785
-#697 := [monotonicity #786 #481]: #696
-#778 := [trans #697 #787]: #791
-#772 := [monotonicity #778]: #780
-#771 := [trans #772 #829]: #769
-#693 := (iff #798 false)
-#692 := (iff #798 #482)
-#689 := (iff #804 true)
-#796 := (or true false)
-#679 := (iff #796 true)
-#680 := [rewrite]: #679
-#789 := (iff #804 #796)
-#788 := (iff #803 true)
-#690 := [rewrite]: #788
-#674 := [monotonicity #690 #786]: #789
-#691 := [trans #674 #680]: #689
-#685 := [monotonicity #691]: #692
-#694 := [trans #685 #829]: #693
-#783 := [monotonicity #694 #771]: #782
-#774 := [trans #783 #784]: #773
-#737 := [monotonicity #774 #759 #734]: #736
-#725 := [trans #737 #733]: #739
-#681 := (iff #636 true)
-#794 := (iff #636 #796)
-#793 := (iff #800 false)
-#795 := [rewrite]: #793
-#639 := (iff #807 true)
-#792 := [rewrite]: #639
-#797 := [monotonicity #792 #795]: #794
-#640 := [trans #797 #680]: #681
-#723 := [monotonicity #640 #725]: #722
-#729 := [trans #723 #727]: #728
-#598 := [monotonicity #729]: #705
-#711 := [trans #598 #710]: #705
-#704 := [quant-inst #8 #9]: #703
-#716 := [mp #704 #711]: #730
-#713 := [unit-resolution #716 #883]: #806
-#714 := [monotonicity #713]: #13
-#14 := (not #13)
-#78 := [asserted]: #14
-[unit-resolution #78 #714]: false
-unsat
-009cf27bd16a3881b93b6b7959195f72499a5829 300 0
+#24 := (f3 0::Int)
+#10 := 1::Int
+#19 := (- 1::Int)
+#18 := (- 0::Int)
+#20 := (div #18 #19)
+#17 := (div 0::Int 1::Int)
+#14 := (< 0::Int 1::Int)
+#13 := (< 0::Int 0::Int)
+#15 := (and #13 #14)
+#16 := (or #15 #15)
+#21 := (ite #16 #17 #20)
+#11 := (= 1::Int 0::Int)
+#9 := (= 0::Int 0::Int)
+#12 := (or #9 #11)
+#22 := (ite #12 0::Int #21)
+#23 := (f3 #22)
+#25 := (= #23 #24)
+#26 := (not #25)
+#117 := (iff #26 false)
+#1 := true
+#112 := (not true)
+#115 := (iff #112 false)
+#116 := [rewrite]: #115
+#113 := (iff #26 #112)
+#110 := (iff #25 true)
+#105 := (= #24 #24)
+#108 := (iff #105 true)
+#109 := [rewrite]: #108
+#106 := (iff #25 #105)
+#102 := (= #22 0::Int)
+#97 := (ite true 0::Int 0::Int)
+#100 := (= #97 0::Int)
+#101 := [rewrite]: #100
+#98 := (= #22 #97)
+#95 := (= #21 0::Int)
+#90 := (ite #15 0::Int 0::Int)
+#93 := (= #90 0::Int)
+#94 := [rewrite]: #93
+#91 := (= #21 #90)
+#88 := (= #20 0::Int)
+#80 := -1::Int
+#83 := (div 0::Int -1::Int)
+#86 := (= #83 0::Int)
+#87 := [rewrite]: #86
+#84 := (= #20 #83)
+#81 := (= #19 -1::Int)
+#82 := [rewrite]: #81
+#78 := (= #18 0::Int)
+#79 := [rewrite]: #78
+#85 := [monotonicity #79 #82]: #84
+#89 := [trans #85 #87]: #88
+#76 := (= #17 0::Int)
+#77 := [rewrite]: #76
+#74 := (iff #16 #15)
+#75 := [rewrite]: #74
+#92 := [monotonicity #75 #77 #89]: #91
+#96 := [trans #92 #94]: #95
+#72 := (iff #12 true)
+#67 := (or true false)
+#70 := (iff #67 true)
+#71 := [rewrite]: #70
+#68 := (iff #12 #67)
+#65 := (iff #11 false)
+#66 := [rewrite]: #65
+#63 := (iff #9 true)
+#64 := [rewrite]: #63
+#69 := [monotonicity #64 #66]: #68
+#73 := [trans #69 #71]: #72
+#99 := [monotonicity #73 #96]: #98
+#103 := [trans #99 #101]: #102
+#104 := [monotonicity #103]: #25
+#107 := [monotonicity #104]: #106
+#111 := [trans #107 #109]: #110
+#114 := [monotonicity #111]: #113
+#118 := [trans #114 #116]: #117
+#62 := [asserted]: #26
+[mp #62 #118]: false
+unsat
+4d757130b0dc28fe958cf4c129cd34caadcedd08 82 0
 #2 := false
 decl f3 :: (-> Int S2)
 #8 := 1::Int
-#11 := (f3 1::Int)
-decl f4 :: (-> Int Int Int)
-#9 := (f4 1::Int 1::Int)
-#10 := (f3 #9)
-#12 := (= #10 #11)
-#759 := (= #9 1::Int)
-#20 := (:var 0 Int)
-#31 := (:var 1 Int)
-#32 := (f4 #31 #20)
-#877 := (pattern #32)
-#19 := 0::Int
-#180 := -1::Int
-#184 := (* -1::Int #20)
-#181 := (* -1::Int #31)
-#187 := (div #181 #184)
-#359 := (* -1::Int #187)
-#360 := (+ #32 #359)
-#361 := (= #360 0::Int)
-#42 := (div #31 #20)
-#356 := (* -1::Int #42)
-#357 := (+ #32 #356)
-#358 := (= #357 0::Int)
-#219 := (>= #31 0::Int)
-#212 := (<= #20 0::Int)
-#319 := (or #212 #219)
-#320 := (not #319)
-#208 := (<= #31 0::Int)
-#317 := (or #208 #212)
-#318 := (not #317)
-#323 := (or #318 #320)
-#362 := (ite #323 #358 #361)
-#355 := (= #32 0::Int)
-#34 := (= #20 0::Int)
-#33 := (= #31 0::Int)
-#35 := (or #33 #34)
-#363 := (ite #35 #355 #362)
-#878 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #877) #363)
-#366 := (forall (vars (?v0 Int) (?v1 Int)) #363)
-#881 := (iff #366 #878)
-#879 := (iff #363 #363)
-#880 := [refl]: #879
-#882 := [quant-intro #880]: #881
-#326 := (ite #323 #42 #187)
-#329 := (ite #35 0::Int #326)
-#332 := (= #32 #329)
-#335 := (forall (vars (?v0 Int) (?v1 Int)) #332)
-#367 := (iff #335 #366)
-#364 := (iff #332 #363)
-#365 := [rewrite]: #364
-#368 := [quant-intro #365]: #367
-#220 := (not #219)
-#213 := (not #212)
-#223 := (and #213 #220)
-#209 := (not #208)
-#216 := (and #209 #213)
-#226 := (or #216 #223)
-#229 := (ite #226 #42 #187)
-#232 := (ite #35 0::Int #229)
-#235 := (= #32 #232)
-#238 := (forall (vars (?v0 Int) (?v1 Int)) #235)
-#336 := (iff #238 #335)
-#333 := (iff #235 #332)
-#330 := (= #232 #329)
-#327 := (= #229 #326)
-#324 := (iff #226 #323)
-#321 := (iff #223 #320)
-#322 := [rewrite]: #321
-#302 := (iff #216 #318)
-#303 := [rewrite]: #302
-#325 := [monotonicity #303 #322]: #324
-#328 := [monotonicity #325]: #327
-#331 := [monotonicity #328]: #330
-#334 := [monotonicity #331]: #333
-#337 := [quant-intro #334]: #336
-#298 := (~ #238 #238)
-#311 := (~ #235 #235)
-#312 := [refl]: #311
-#299 := [nnf-pos #312]: #298
-#44 := (- #20)
-#43 := (- #31)
-#45 := (div #43 #44)
-#37 := (< 0::Int #20)
-#39 := (< #31 0::Int)
-#40 := (and #39 #37)
-#36 := (< 0::Int #31)
-#38 := (and #36 #37)
-#41 := (or #38 #40)
-#46 := (ite #41 #42 #45)
-#47 := (ite #35 0::Int #46)
-#48 := (= #32 #47)
-#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
-#241 := (iff #49 #238)
-#174 := (and #37 #39)
-#177 := (or #38 #174)
-#190 := (ite #177 #42 #187)
-#168 := (= 0::Int #20)
-#165 := (= 0::Int #31)
-#171 := (or #165 #168)
-#193 := (ite #171 0::Int #190)
-#196 := (= #32 #193)
-#199 := (forall (vars (?v0 Int) (?v1 Int)) #196)
-#239 := (iff #199 #238)
-#236 := (iff #196 #235)
-#233 := (= #193 #232)
-#230 := (= #190 #229)
-#227 := (iff #177 #226)
-#224 := (iff #174 #223)
-#221 := (iff #39 #220)
-#222 := [rewrite]: #221
-#214 := (iff #37 #213)
-#215 := [rewrite]: #214
-#225 := [monotonicity #215 #222]: #224
-#217 := (iff #38 #216)
-#210 := (iff #36 #209)
-#211 := [rewrite]: #210
-#218 := [monotonicity #211 #215]: #217
-#228 := [monotonicity #218 #225]: #227
-#231 := [monotonicity #228]: #230
-#206 := (iff #171 #35)
-#204 := (iff #168 #34)
-#205 := [rewrite]: #204
-#202 := (iff #165 #33)
-#203 := [rewrite]: #202
-#207 := [monotonicity #203 #205]: #206
-#234 := [monotonicity #207 #231]: #233
-#237 := [monotonicity #234]: #236
-#240 := [quant-intro #237]: #239
-#200 := (iff #49 #199)
-#197 := (iff #48 #196)
-#194 := (= #47 #193)
-#191 := (= #46 #190)
-#188 := (= #45 #187)
-#185 := (= #44 #184)
-#186 := [rewrite]: #185
-#182 := (= #43 #181)
-#183 := [rewrite]: #182
-#189 := [monotonicity #183 #186]: #188
-#178 := (iff #41 #177)
-#175 := (iff #40 #174)
-#176 := [rewrite]: #175
-#179 := [monotonicity #176]: #178
-#192 := [monotonicity #179 #189]: #191
-#172 := (iff #35 #171)
-#169 := (iff #34 #168)
-#170 := [rewrite]: #169
-#166 := (iff #33 #165)
-#167 := [rewrite]: #166
-#173 := [monotonicity #167 #170]: #172
-#195 := [monotonicity #173 #192]: #194
-#198 := [monotonicity #195]: #197
-#201 := [quant-intro #198]: #200
-#242 := [trans #201 #240]: #241
-#164 := [asserted]: #49
-#243 := [mp #164 #242]: #238
-#313 := [mp~ #243 #299]: #238
-#338 := [mp #313 #337]: #335
-#369 := [mp #338 #368]: #366
-#883 := [mp #369 #882]: #878
-#705 := (not #878)
-#598 := (or #705 #759)
-#813 := (* -1::Int 1::Int)
-#808 := (div #813 #813)
-#809 := (* -1::Int #808)
-#814 := (+ #9 #809)
-#815 := (= #814 0::Int)
-#810 := (div 1::Int 1::Int)
-#816 := (* -1::Int #810)
-#657 := (+ #9 #816)
-#658 := (= #657 0::Int)
-#834 := (>= 1::Int 0::Int)
-#659 := (<= 1::Int 0::Int)
-#801 := (or #659 #834)
-#802 := (not #801)
-#803 := (or #659 #659)
-#804 := (not #803)
-#798 := (or #804 #802)
-#799 := (ite #798 #658 #815)
-#805 := (= #9 0::Int)
-#806 := (= 1::Int 0::Int)
-#800 := (or #806 #806)
-#807 := (ite #800 #805 #799)
-#709 := (or #705 #807)
-#711 := (iff #709 #598)
-#712 := (iff #598 #598)
-#713 := [rewrite]: #712
-#703 := (iff #807 #759)
-#727 := (ite false #805 #759)
-#724 := (iff #727 #759)
-#730 := [rewrite]: #724
-#728 := (iff #807 #727)
-#723 := (iff #799 #759)
-#1 := true
-#733 := (ite true #759 #759)
-#721 := (iff #733 #759)
-#722 := [rewrite]: #721
-#739 := (iff #799 #733)
-#737 := (iff #815 #759)
-#766 := (+ -1::Int #9)
-#755 := (= #766 0::Int)
-#756 := (iff #755 #759)
-#760 := [rewrite]: #756
-#735 := (iff #815 #755)
-#732 := (= #814 #766)
-#762 := (+ #9 -1::Int)
-#767 := (= #762 #766)
-#763 := [rewrite]: #767
-#753 := (= #814 #762)
-#752 := (= #809 -1::Int)
-#776 := (= #813 -1::Int)
-#770 := [rewrite]: #776
-#750 := (= #809 #813)
-#748 := (= #808 1::Int)
-#743 := (div -1::Int -1::Int)
-#746 := (= #743 1::Int)
-#747 := [rewrite]: #746
-#744 := (= #808 #743)
-#745 := [monotonicity #770 #770]: #744
-#749 := [trans #745 #747]: #748
-#751 := [monotonicity #749]: #750
-#742 := [trans #751 #770]: #752
-#731 := [monotonicity #742]: #753
-#734 := [trans #731 #763]: #732
-#736 := [monotonicity #734]: #735
-#738 := [trans #736 #760]: #737
-#740 := (iff #658 #759)
-#757 := (iff #658 #755)
-#768 := (= #657 #766)
-#764 := (= #657 #762)
-#777 := (= #816 -1::Int)
-#774 := (= #816 #813)
-#784 := (= #810 1::Int)
-#773 := [rewrite]: #784
-#775 := [monotonicity #773]: #774
-#761 := [trans #775 #770]: #777
-#765 := [monotonicity #761]: #764
-#754 := [trans #765 #763]: #768
-#758 := [monotonicity #754]: #757
-#741 := [trans #758 #760]: #740
-#783 := (iff #798 true)
-#772 := (or true false)
-#781 := (iff #772 true)
-#782 := [rewrite]: #781
-#769 := (iff #798 #772)
-#778 := (iff #802 false)
-#482 := (not true)
-#843 := (iff #482 false)
-#829 := [rewrite]: #843
-#787 := (iff #802 #482)
-#697 := (iff #801 true)
-#685 := (or false true)
-#695 := (iff #685 true)
-#696 := [rewrite]: #695
-#693 := (iff #801 #685)
-#841 := (iff #834 true)
-#481 := [rewrite]: #841
-#679 := (iff #659 false)
-#680 := [rewrite]: #679
-#694 := [monotonicity #680 #481]: #693
-#790 := [trans #694 #696]: #697
-#791 := [monotonicity #790]: #787
-#780 := [trans #791 #829]: #778
-#691 := (iff #804 true)
-#785 := (not false)
-#674 := (iff #785 true)
-#689 := [rewrite]: #674
-#786 := (iff #804 #785)
-#788 := (iff #803 false)
-#639 := (or false false)
-#795 := (iff #639 false)
-#796 := [rewrite]: #795
-#681 := (iff #803 #639)
-#640 := [monotonicity #680 #680]: #681
-#690 := [trans #640 #796]: #788
-#789 := [monotonicity #690]: #786
-#692 := [trans #789 #689]: #691
-#771 := [monotonicity #692 #780]: #769
-#779 := [trans #771 #782]: #783
-#725 := [monotonicity #779 #741 #738]: #739
-#726 := [trans #725 #722]: #723
-#794 := (iff #800 false)
-#792 := (iff #800 #639)
-#636 := (iff #806 false)
-#638 := [rewrite]: #636
-#793 := [monotonicity #638 #638]: #792
-#797 := [trans #793 #796]: #794
-#729 := [monotonicity #797 #726]: #728
-#704 := [trans #729 #730]: #703
-#716 := [monotonicity #704]: #711
-#714 := [trans #716 #713]: #711
-#710 := [quant-inst #8 #8]: #709
-#717 := [mp #710 #714]: #598
-#715 := [unit-resolution #717 #883]: #759
-#720 := [monotonicity #715]: #12
-#13 := (not #12)
-#78 := [asserted]: #13
-[unit-resolution #78 #720]: false
-unsat
-ec9d2fe48d42e5d40fd0739c3491a43f0bf8c69d 311 0
+#23 := (f3 1::Int)
+#18 := (- 1::Int)
+#19 := (div #18 #18)
+#17 := (div 1::Int 1::Int)
+#9 := 0::Int
+#12 := (< 0::Int 1::Int)
+#14 := (< 1::Int 0::Int)
+#15 := (and #14 #12)
+#13 := (and #12 #12)
+#16 := (or #13 #15)
+#20 := (ite #16 #17 #19)
+#10 := (= 1::Int 0::Int)
+#11 := (or #10 #10)
+#21 := (ite #11 0::Int #20)
+#22 := (f3 #21)
+#24 := (= #22 #23)
+#25 := (not #24)
+#118 := (iff #25 false)
+#1 := true
+#113 := (not true)
+#116 := (iff #113 false)
+#117 := [rewrite]: #116
+#114 := (iff #25 #113)
+#111 := (iff #24 true)
+#106 := (= #23 #23)
+#109 := (iff #106 true)
+#110 := [rewrite]: #109
+#107 := (iff #24 #106)
+#103 := (= #21 1::Int)
+#98 := (ite false 0::Int 1::Int)
+#101 := (= #98 1::Int)
+#102 := [rewrite]: #101
+#99 := (= #21 #98)
+#96 := (= #20 1::Int)
+#73 := (and #12 #14)
+#76 := (or #12 #73)
+#91 := (ite #76 1::Int 1::Int)
+#94 := (= #91 1::Int)
+#95 := [rewrite]: #94
+#92 := (= #20 #91)
+#89 := (= #19 1::Int)
+#81 := -1::Int
+#84 := (div -1::Int -1::Int)
+#87 := (= #84 1::Int)
+#88 := [rewrite]: #87
+#85 := (= #19 #84)
+#82 := (= #18 -1::Int)
+#83 := [rewrite]: #82
+#86 := [monotonicity #83 #83]: #85
+#90 := [trans #86 #88]: #89
+#79 := (= #17 1::Int)
+#80 := [rewrite]: #79
+#77 := (iff #16 #76)
+#74 := (iff #15 #73)
+#75 := [rewrite]: #74
+#71 := (iff #13 #12)
+#72 := [rewrite]: #71
+#78 := [monotonicity #72 #75]: #77
+#93 := [monotonicity #78 #80 #90]: #92
+#97 := [trans #93 #95]: #96
+#69 := (iff #11 false)
+#64 := (or false false)
+#67 := (iff #64 false)
+#68 := [rewrite]: #67
+#65 := (iff #11 #64)
+#62 := (iff #10 false)
+#63 := [rewrite]: #62
+#66 := [monotonicity #63 #63]: #65
+#70 := [trans #66 #68]: #69
+#100 := [monotonicity #70 #97]: #99
+#104 := [trans #100 #102]: #103
+#105 := [monotonicity #104]: #24
+#108 := [monotonicity #105]: #107
+#112 := [trans #108 #110]: #111
+#115 := [monotonicity #112]: #114
+#119 := [trans #115 #117]: #118
+#61 := [asserted]: #25
+[mp #61 #119]: false
+unsat
+5e55bd29247a2ea10048c10929dae98ba0bdec4e 89 0
 #2 := false
 decl f3 :: (-> Int S2)
 #8 := 3::Int
-#12 := (f3 3::Int)
-decl f4 :: (-> Int Int Int)
-#9 := 1::Int
-#10 := (f4 3::Int 1::Int)
-#11 := (f3 #10)
-#13 := (= #11 #12)
-#747 := (= #10 3::Int)
-#21 := (:var 0 Int)
-#32 := (:var 1 Int)
-#33 := (f4 #32 #21)
-#878 := (pattern #33)
-#20 := 0::Int
-#181 := -1::Int
-#185 := (* -1::Int #21)
-#182 := (* -1::Int #32)
-#188 := (div #182 #185)
-#360 := (* -1::Int #188)
-#361 := (+ #33 #360)
-#362 := (= #361 0::Int)
-#43 := (div #32 #21)
-#357 := (* -1::Int #43)
-#358 := (+ #33 #357)
-#359 := (= #358 0::Int)
-#220 := (>= #32 0::Int)
-#213 := (<= #21 0::Int)
-#320 := (or #213 #220)
-#321 := (not #320)
-#209 := (<= #32 0::Int)
-#318 := (or #209 #213)
-#319 := (not #318)
-#324 := (or #319 #321)
-#363 := (ite #324 #359 #362)
-#356 := (= #33 0::Int)
-#35 := (= #21 0::Int)
-#34 := (= #32 0::Int)
-#36 := (or #34 #35)
-#364 := (ite #36 #356 #363)
-#879 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #878) #364)
-#367 := (forall (vars (?v0 Int) (?v1 Int)) #364)
-#882 := (iff #367 #879)
-#880 := (iff #364 #364)
-#881 := [refl]: #880
-#883 := [quant-intro #881]: #882
-#327 := (ite #324 #43 #188)
-#330 := (ite #36 0::Int #327)
-#333 := (= #33 #330)
-#336 := (forall (vars (?v0 Int) (?v1 Int)) #333)
-#368 := (iff #336 #367)
-#365 := (iff #333 #364)
-#366 := [rewrite]: #365
-#369 := [quant-intro #366]: #368
-#221 := (not #220)
-#214 := (not #213)
-#224 := (and #214 #221)
-#210 := (not #209)
-#217 := (and #210 #214)
-#227 := (or #217 #224)
-#230 := (ite #227 #43 #188)
-#233 := (ite #36 0::Int #230)
-#236 := (= #33 #233)
-#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
-#337 := (iff #239 #336)
-#334 := (iff #236 #333)
-#331 := (= #233 #330)
-#328 := (= #230 #327)
-#325 := (iff #227 #324)
-#322 := (iff #224 #321)
-#323 := [rewrite]: #322
-#303 := (iff #217 #319)
-#304 := [rewrite]: #303
-#326 := [monotonicity #304 #323]: #325
-#329 := [monotonicity #326]: #328
-#332 := [monotonicity #329]: #331
-#335 := [monotonicity #332]: #334
-#338 := [quant-intro #335]: #337
-#299 := (~ #239 #239)
-#312 := (~ #236 #236)
-#313 := [refl]: #312
-#300 := [nnf-pos #313]: #299
-#45 := (- #21)
-#44 := (- #32)
-#46 := (div #44 #45)
-#38 := (< 0::Int #21)
-#40 := (< #32 0::Int)
-#41 := (and #40 #38)
-#37 := (< 0::Int #32)
-#39 := (and #37 #38)
-#42 := (or #39 #41)
-#47 := (ite #42 #43 #46)
-#48 := (ite #36 0::Int #47)
-#49 := (= #33 #48)
-#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
-#242 := (iff #50 #239)
-#175 := (and #38 #40)
-#178 := (or #39 #175)
-#191 := (ite #178 #43 #188)
-#169 := (= 0::Int #21)
-#166 := (= 0::Int #32)
-#172 := (or #166 #169)
-#194 := (ite #172 0::Int #191)
-#197 := (= #33 #194)
-#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
-#240 := (iff #200 #239)
-#237 := (iff #197 #236)
-#234 := (= #194 #233)
-#231 := (= #191 #230)
-#228 := (iff #178 #227)
-#225 := (iff #175 #224)
-#222 := (iff #40 #221)
-#223 := [rewrite]: #222
-#215 := (iff #38 #214)
-#216 := [rewrite]: #215
-#226 := [monotonicity #216 #223]: #225
-#218 := (iff #39 #217)
-#211 := (iff #37 #210)
-#212 := [rewrite]: #211
-#219 := [monotonicity #212 #216]: #218
-#229 := [monotonicity #219 #226]: #228
-#232 := [monotonicity #229]: #231
-#207 := (iff #172 #36)
-#205 := (iff #169 #35)
-#206 := [rewrite]: #205
-#203 := (iff #166 #34)
-#204 := [rewrite]: #203
-#208 := [monotonicity #204 #206]: #207
-#235 := [monotonicity #208 #232]: #234
-#238 := [monotonicity #235]: #237
-#241 := [quant-intro #238]: #240
-#201 := (iff #50 #200)
-#198 := (iff #49 #197)
-#195 := (= #48 #194)
-#192 := (= #47 #191)
-#189 := (= #46 #188)
-#186 := (= #45 #185)
-#187 := [rewrite]: #186
-#183 := (= #44 #182)
-#184 := [rewrite]: #183
-#190 := [monotonicity #184 #187]: #189
-#179 := (iff #42 #178)
-#176 := (iff #41 #175)
-#177 := [rewrite]: #176
-#180 := [monotonicity #177]: #179
-#193 := [monotonicity #180 #190]: #192
-#173 := (iff #36 #172)
-#170 := (iff #35 #169)
-#171 := [rewrite]: #170
-#167 := (iff #34 #166)
-#168 := [rewrite]: #167
-#174 := [monotonicity #168 #171]: #173
-#196 := [monotonicity #174 #193]: #195
-#199 := [monotonicity #196]: #198
-#202 := [quant-intro #199]: #201
-#243 := [trans #202 #241]: #242
-#165 := [asserted]: #50
-#244 := [mp #165 #243]: #239
-#314 := [mp~ #244 #300]: #239
-#339 := [mp #314 #338]: #336
-#370 := [mp #339 #369]: #367
-#884 := [mp #370 #883]: #879
-#719 := (not #879)
-#720 := (or #719 #747)
-#814 := (* -1::Int 1::Int)
-#809 := (* -1::Int 3::Int)
-#810 := (div #809 #814)
-#815 := (* -1::Int #810)
-#816 := (+ #10 #815)
-#811 := (= #816 0::Int)
-#817 := (div 3::Int 1::Int)
-#658 := (* -1::Int #817)
-#659 := (+ #10 #658)
-#660 := (= #659 0::Int)
-#835 := (>= 3::Int 0::Int)
-#802 := (<= 1::Int 0::Int)
-#803 := (or #802 #835)
-#804 := (not #803)
-#805 := (<= 3::Int 0::Int)
-#799 := (or #805 #802)
-#800 := (not #799)
-#806 := (or #800 #804)
-#807 := (ite #806 #660 #811)
-#801 := (= #10 0::Int)
-#808 := (= 1::Int 0::Int)
-#637 := (= 3::Int 0::Int)
-#639 := (or #637 #808)
-#640 := (ite #639 #801 #807)
-#716 := (or #719 #640)
-#701 := (iff #716 #720)
-#702 := (iff #720 #720)
-#683 := [rewrite]: #702
-#715 := (iff #640 #747)
-#711 := (ite false #801 #747)
-#713 := (iff #711 #747)
-#714 := [rewrite]: #713
-#712 := (iff #640 #711)
-#599 := (iff #807 #747)
-#1 := true
-#725 := (ite true #747 #747)
-#705 := (iff #725 #747)
-#706 := [rewrite]: #705
-#731 := (iff #807 #725)
-#729 := (iff #811 #747)
-#767 := -3::Int
-#760 := (+ -3::Int #10)
-#744 := (= #760 0::Int)
-#748 := (iff #744 #747)
-#749 := [rewrite]: #748
-#727 := (iff #811 #744)
-#723 := (= #816 #760)
-#756 := (+ #10 -3::Int)
-#757 := (= #756 #760)
-#761 := [rewrite]: #757
-#726 := (= #816 #756)
-#734 := (= #815 -3::Int)
-#768 := (= #809 -3::Int)
-#764 := [rewrite]: #768
-#738 := (= #815 #809)
-#736 := (= #810 3::Int)
-#743 := (div -3::Int -1::Int)
-#733 := (= #743 3::Int)
-#735 := [rewrite]: #733
-#754 := (= #810 #743)
-#752 := (= #814 -1::Int)
-#753 := [rewrite]: #752
-#732 := [monotonicity #764 #753]: #754
-#737 := [trans #732 #735]: #736
-#739 := [monotonicity #737]: #738
-#740 := [trans #739 #764]: #734
-#722 := [monotonicity #740]: #726
-#724 := [trans #722 #761]: #723
-#728 := [monotonicity #724]: #727
-#730 := [trans #728 #749]: #729
-#750 := (iff #660 #747)
-#745 := (iff #660 #744)
-#741 := (= #659 #760)
-#758 := (= #659 #756)
-#769 := (= #658 -3::Int)
-#765 := (= #658 #809)
-#762 := (= #817 3::Int)
-#763 := [rewrite]: #762
-#766 := [monotonicity #763]: #765
-#755 := [trans #766 #764]: #769
-#759 := [monotonicity #755]: #758
-#742 := [trans #759 #761]: #741
-#746 := [monotonicity #742]: #745
-#751 := [trans #746 #749]: #750
-#771 := (iff #806 true)
-#785 := (or true false)
-#776 := (iff #785 true)
-#777 := [rewrite]: #776
-#774 := (iff #806 #785)
-#784 := (iff #804 false)
-#483 := (not true)
-#844 := (iff #483 false)
-#830 := [rewrite]: #844
-#782 := (iff #804 #483)
-#770 := (iff #803 true)
-#788 := (or false true)
-#781 := (iff #788 true)
-#773 := [rewrite]: #781
-#792 := (iff #803 #788)
-#842 := (iff #835 true)
-#482 := [rewrite]: #842
-#787 := (iff #802 false)
-#790 := [rewrite]: #787
-#779 := [monotonicity #790 #482]: #792
-#772 := [trans #779 #773]: #770
-#783 := [monotonicity #772]: #782
-#780 := [trans #783 #830]: #784
-#698 := (iff #800 true)
-#686 := (not false)
-#696 := (iff #686 true)
-#697 := [rewrite]: #696
-#694 := (iff #800 #686)
-#692 := (iff #799 false)
-#795 := (or false false)
-#681 := (iff #795 false)
-#682 := [rewrite]: #681
-#675 := (iff #799 #795)
-#691 := (iff #805 false)
-#786 := [rewrite]: #691
-#690 := [monotonicity #786 #790]: #675
-#693 := [trans #690 #682]: #692
-#695 := [monotonicity #693]: #694
-#791 := [trans #695 #697]: #698
-#775 := [monotonicity #791 #780]: #774
-#778 := [trans #775 #777]: #771
-#704 := [monotonicity #778 #751 #730]: #731
-#710 := [trans #704 #706]: #599
-#641 := (iff #639 false)
-#798 := (iff #639 #795)
-#796 := (iff #808 false)
-#797 := [rewrite]: #796
-#793 := (iff #637 false)
-#794 := [rewrite]: #793
-#680 := [monotonicity #794 #797]: #798
-#789 := [trans #680 #682]: #641
-#717 := [monotonicity #789 #710]: #712
-#718 := [trans #717 #714]: #715
-#647 := [monotonicity #718]: #701
-#707 := [trans #647 #683]: #701
-#721 := [quant-inst #8 #9]: #716
-#708 := [mp #721 #707]: #720
-#677 := [unit-resolution #708 #884]: #747
-#684 := [monotonicity #677]: #13
-#14 := (not #13)
-#79 := [asserted]: #14
-[unit-resolution #79 #684]: false
-unsat
-3563b0bf363f404d85eb515efc0ea6c63953194a 378 0
-#2 := false
-decl f3 :: (-> Int S2)
-decl f4 :: (-> Int Int Int)
-#10 := 1::Int
-decl f5 :: (-> S2 Int)
-decl f6 :: S2
-#8 := f6
-#9 := (f5 f6)
-#11 := (f4 #9 1::Int)
-#12 := (f3 #11)
-#80 := (= f6 #12)
-#451 := (f3 #9)
-#669 := (= #451 #12)
-#663 := (= #12 #451)
-#731 := (= #11 #9)
-#845 := (div #9 1::Int)
-#660 := (= #845 #9)
-#598 := (= #9 #845)
-#20 := 0::Int
-#188 := -1::Int
-#840 := (* -1::Int #845)
-#632 := (+ #9 #840)
-#638 := (<= #632 0::Int)
-#631 := (= #632 0::Int)
-#1 := true
-#77 := [true-axiom]: true
-#588 := (or false #631)
-#589 := [th-lemma arith]: #588
-#590 := [unit-resolution #589 #77]: #631
-#591 := (not #631)
-#592 := (or #591 #638)
-#593 := [th-lemma arith triangle-eq]: #592
-#594 := [unit-resolution #593 #590]: #638
-#481 := (>= #632 0::Int)
-#595 := (or #591 #481)
-#596 := [th-lemma arith triangle-eq]: #595
-#597 := [unit-resolution #596 #590]: #481
-#587 := [th-lemma arith eq-propagate 1 1 #597 #594]: #598
-#578 := [symm #587]: #660
-#604 := (= #11 #845)
-#846 := (+ #11 #840)
-#790 := (<= #846 0::Int)
-#484 := (= #846 0::Int)
-#562 := (= #9 0::Int)
-#776 := (not #562)
-#715 := (= 0::Int #9)
-#654 := [hypothesis]: #562
-#730 := [symm #654]: #715
-#560 := (= #11 0::Int)
-#709 := (or #776 #560)
-#514 := (* -1::Int #9)
-#644 := (div #514 -1::Int)
-#800 := (* -1::Int #644)
-#804 := (+ #11 #800)
-#687 := (= #804 0::Int)
-#850 := (<= #9 0::Int)
-#830 := (not #850)
-#847 := (>= #9 0::Int)
-#665 := (not #847)
-#812 := (or #665 #830)
-#648 := (ite #812 #484 #687)
-#793 := (ite #562 #560 #648)
-#21 := (:var 0 Int)
-#32 := (:var 1 Int)
-#33 := (f4 #32 #21)
-#885 := (pattern #33)
-#192 := (* -1::Int #21)
-#189 := (* -1::Int #32)
-#195 := (div #189 #192)
-#367 := (* -1::Int #195)
-#368 := (+ #33 #367)
-#369 := (= #368 0::Int)
-#43 := (div #32 #21)
-#364 := (* -1::Int #43)
-#365 := (+ #33 #364)
-#366 := (= #365 0::Int)
-#227 := (>= #32 0::Int)
-#220 := (<= #21 0::Int)
-#327 := (or #220 #227)
-#328 := (not #327)
-#216 := (<= #32 0::Int)
-#325 := (or #216 #220)
-#326 := (not #325)
-#331 := (or #326 #328)
-#370 := (ite #331 #366 #369)
-#363 := (= #33 0::Int)
-#35 := (= #21 0::Int)
-#34 := (= #32 0::Int)
-#36 := (or #34 #35)
-#371 := (ite #36 #363 #370)
-#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #371)
-#374 := (forall (vars (?v0 Int) (?v1 Int)) #371)
-#889 := (iff #374 #886)
-#887 := (iff #371 #371)
-#888 := [refl]: #887
-#890 := [quant-intro #888]: #889
-#334 := (ite #331 #43 #195)
-#337 := (ite #36 0::Int #334)
-#340 := (= #33 #337)
-#343 := (forall (vars (?v0 Int) (?v1 Int)) #340)
-#375 := (iff #343 #374)
-#372 := (iff #340 #371)
-#373 := [rewrite]: #372
-#376 := [quant-intro #373]: #375
-#228 := (not #227)
-#221 := (not #220)
-#231 := (and #221 #228)
-#217 := (not #216)
-#224 := (and #217 #221)
-#234 := (or #224 #231)
-#237 := (ite #234 #43 #195)
-#240 := (ite #36 0::Int #237)
-#243 := (= #33 #240)
-#246 := (forall (vars (?v0 Int) (?v1 Int)) #243)
-#344 := (iff #246 #343)
-#341 := (iff #243 #340)
-#338 := (= #240 #337)
-#335 := (= #237 #334)
-#332 := (iff #234 #331)
-#329 := (iff #231 #328)
-#330 := [rewrite]: #329
-#310 := (iff #224 #326)
-#311 := [rewrite]: #310
-#333 := [monotonicity #311 #330]: #332
-#336 := [monotonicity #333]: #335
-#339 := [monotonicity #336]: #338
-#342 := [monotonicity #339]: #341
-#345 := [quant-intro #342]: #344
-#306 := (~ #246 #246)
-#319 := (~ #243 #243)
-#320 := [refl]: #319
-#307 := [nnf-pos #320]: #306
-#45 := (- #21)
-#44 := (- #32)
-#46 := (div #44 #45)
-#38 := (< 0::Int #21)
-#40 := (< #32 0::Int)
-#41 := (and #40 #38)
-#37 := (< 0::Int #32)
-#39 := (and #37 #38)
-#42 := (or #39 #41)
-#47 := (ite #42 #43 #46)
-#48 := (ite #36 0::Int #47)
-#49 := (= #33 #48)
-#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
-#249 := (iff #50 #246)
-#182 := (and #38 #40)
-#185 := (or #39 #182)
-#198 := (ite #185 #43 #195)
-#176 := (= 0::Int #21)
-#173 := (= 0::Int #32)
-#179 := (or #173 #176)
-#201 := (ite #179 0::Int #198)
-#204 := (= #33 #201)
-#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
-#247 := (iff #207 #246)
-#244 := (iff #204 #243)
-#241 := (= #201 #240)
-#238 := (= #198 #237)
-#235 := (iff #185 #234)
-#232 := (iff #182 #231)
-#229 := (iff #40 #228)
-#230 := [rewrite]: #229
-#222 := (iff #38 #221)
-#223 := [rewrite]: #222
-#233 := [monotonicity #223 #230]: #232
-#225 := (iff #39 #224)
-#218 := (iff #37 #217)
-#219 := [rewrite]: #218
-#226 := [monotonicity #219 #223]: #225
-#236 := [monotonicity #226 #233]: #235
-#239 := [monotonicity #236]: #238
-#214 := (iff #179 #36)
-#212 := (iff #176 #35)
-#213 := [rewrite]: #212
-#210 := (iff #173 #34)
-#211 := [rewrite]: #210
-#215 := [monotonicity #211 #213]: #214
-#242 := [monotonicity #215 #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [quant-intro #245]: #247
-#208 := (iff #50 #207)
-#205 := (iff #49 #204)
-#202 := (= #48 #201)
-#199 := (= #47 #198)
-#196 := (= #46 #195)
-#193 := (= #45 #192)
-#194 := [rewrite]: #193
-#190 := (= #44 #189)
-#191 := [rewrite]: #190
-#197 := [monotonicity #191 #194]: #196
-#186 := (iff #42 #185)
-#183 := (iff #41 #182)
-#184 := [rewrite]: #183
-#187 := [monotonicity #184]: #186
-#200 := [monotonicity #187 #197]: #199
-#180 := (iff #36 #179)
-#177 := (iff #35 #176)
-#178 := [rewrite]: #177
-#174 := (iff #34 #173)
-#175 := [rewrite]: #174
-#181 := [monotonicity #175 #178]: #180
-#203 := [monotonicity #181 #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [quant-intro #206]: #208
-#250 := [trans #209 #248]: #249
-#172 := [asserted]: #50
-#251 := [mp #172 #250]: #246
-#321 := [mp~ #251 #307]: #246
-#346 := [mp #321 #345]: #343
-#377 := [mp #346 #376]: #374
-#891 := [mp #377 #890]: #886
-#682 := (not #886)
-#697 := (or #682 #793)
-#854 := (* -1::Int 1::Int)
-#841 := (div #514 #854)
-#842 := (* -1::Int #841)
-#843 := (+ #11 #842)
-#844 := (= #843 0::Int)
-#849 := (<= 1::Int 0::Int)
-#489 := (or #849 #847)
-#490 := (not #489)
-#848 := (or #850 #849)
-#851 := (not #848)
-#837 := (or #851 #490)
-#838 := (ite #837 #484 #844)
-#561 := (= 1::Int 0::Int)
-#563 := (or #562 #561)
-#457 := (ite #563 #560 #838)
-#699 := (or #682 #457)
-#693 := (iff #699 #697)
-#702 := (iff #697 #697)
-#703 := [rewrite]: #702
-#794 := (iff #457 #793)
-#796 := (iff #838 #648)
-#688 := (iff #844 #687)
-#802 := (= #843 #804)
-#801 := (= #842 #800)
-#646 := (= #841 #644)
-#808 := (= #854 -1::Int)
-#815 := [rewrite]: #808
-#647 := [monotonicity #815]: #646
-#803 := [monotonicity #647]: #801
-#805 := [monotonicity #803]: #802
-#689 := [monotonicity #805]: #688
-#813 := (iff #837 #812)
-#809 := (or #830 #665)
-#806 := (iff #809 #812)
-#807 := [rewrite]: #806
-#810 := (iff #837 #809)
-#666 := (iff #490 #665)
-#818 := (iff #489 #847)
-#821 := (or false #847)
-#822 := (iff #821 #847)
-#823 := [rewrite]: #822
-#816 := (iff #489 #821)
-#547 := (iff #849 false)
-#548 := [rewrite]: #547
-#817 := [monotonicity #548]: #816
-#824 := [trans #817 #823]: #818
-#667 := [monotonicity #824]: #666
-#819 := (iff #851 #830)
-#829 := (iff #848 #850)
-#549 := (or #850 false)
-#543 := (iff #549 #850)
-#825 := [rewrite]: #543
-#827 := (iff #848 #549)
-#828 := [monotonicity #548]: #827
-#826 := [trans #828 #825]: #829
-#820 := [monotonicity #826]: #819
-#811 := [monotonicity #820 #667]: #810
-#814 := [trans #811 #807]: #813
-#698 := [monotonicity #814 #689]: #796
-#836 := (iff #563 #562)
-#556 := (or #562 false)
-#835 := (iff #556 #562)
-#832 := [rewrite]: #835
-#557 := (iff #563 #556)
-#833 := (iff #561 false)
-#834 := [rewrite]: #833
-#831 := [monotonicity #834]: #557
-#546 := [trans #831 #832]: #836
-#797 := [monotonicity #546 #698]: #794
-#701 := [monotonicity #797]: #693
-#704 := [trans #701 #703]: #693
-#700 := [quant-inst #9 #10]: #699
-#705 := [mp #700 #704]: #697
-#684 := [unit-resolution #705 #891]: #793
-#771 := (not #793)
-#762 := (or #771 #776 #560)
-#763 := [def-axiom]: #762
-#690 := [unit-resolution #763 #684]: #709
-#714 := [unit-resolution #690 #654]: #560
-#707 := [trans #714 #730]: #731
-#668 := [monotonicity #707]: #663
-#670 := [symm #668]: #669
-#535 := (= f6 #451)
-#15 := (:var 0 S2)
-#16 := (f5 #15)
-#864 := (pattern #16)
-#17 := (f3 #16)
-#87 := (= #15 #17)
-#865 := (forall (vars (?v0 S2)) (:pat #864) #87)
-#91 := (forall (vars (?v0 S2)) #87)
-#866 := (iff #91 #865)
-#868 := (iff #865 #865)
-#869 := [rewrite]: #868
-#867 := [rewrite]: #866
-#870 := [trans #867 #869]: #866
-#314 := (~ #91 #91)
-#312 := (~ #87 #87)
-#313 := [refl]: #312
-#315 := [nnf-pos #313]: #314
-#18 := (= #17 #15)
-#19 := (forall (vars (?v0 S2)) #18)
-#92 := (iff #19 #91)
-#89 := (iff #18 #87)
+#27 := (f3 3::Int)
+#11 := 1::Int
+#22 := (- 1::Int)
+#21 := (- 3::Int)
+#23 := (div #21 #22)
+#20 := (div 3::Int 1::Int)
+#9 := 0::Int
+#15 := (< 0::Int 1::Int)
+#17 := (< 3::Int 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int 3::Int)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#24 := (ite #19 #20 #23)
+#12 := (= 1::Int 0::Int)
+#10 := (= 3::Int 0::Int)
+#13 := (or #10 #12)
+#25 := (ite #13 0::Int #24)
+#26 := (f3 #25)
+#28 := (= #26 #27)
+#29 := (not #28)
+#125 := (iff #29 false)
+#1 := true
+#120 := (not true)
+#123 := (iff #120 false)
+#124 := [rewrite]: #123
+#121 := (iff #29 #120)
+#118 := (iff #28 true)
+#113 := (= #27 #27)
+#116 := (iff #113 true)
+#117 := [rewrite]: #116
+#114 := (iff #28 #113)
+#110 := (= #25 3::Int)
+#105 := (ite false 0::Int 3::Int)
+#108 := (= #105 3::Int)
+#109 := [rewrite]: #108
+#106 := (= #25 #105)
+#103 := (= #24 3::Int)
+#77 := (and #15 #17)
+#80 := (or #16 #77)
+#98 := (ite #80 3::Int 3::Int)
+#101 := (= #98 3::Int)
+#102 := [rewrite]: #101
+#99 := (= #24 #98)
+#96 := (= #23 3::Int)
+#88 := -1::Int
+#85 := -3::Int
+#91 := (div -3::Int -1::Int)
+#94 := (= #91 3::Int)
+#95 := [rewrite]: #94
+#92 := (= #23 #91)
+#89 := (= #22 -1::Int)
 #90 := [rewrite]: #89
-#93 := [quant-intro #90]: #92
-#86 := [asserted]: #19
-#96 := [mp #86 #93]: #91
-#300 := [mp~ #96 #315]: #91
-#871 := [mp #300 #870]: #865
-#528 := (not #865)
-#539 := (or #528 #535)
-#540 := [quant-inst #8]: #539
-#662 := [unit-resolution #540 #871]: #535
-#671 := [trans #662 #670]: #80
-#83 := (not #80)
-#13 := (= #12 f6)
-#14 := (not #13)
-#84 := (iff #14 #83)
-#81 := (iff #13 #80)
-#82 := [rewrite]: #81
-#85 := [monotonicity #82]: #84
-#79 := [asserted]: #14
-#88 := [mp #79 #85]: #83
-#672 := [unit-resolution #88 #671]: false
-#673 := [lemma #672]: #776
-#706 := (or #562 #484)
-#780 := (not #812)
-#769 := (not #484)
-#710 := [hypothesis]: #769
-#716 := [hypothesis]: #776
-#691 := (or #562 #648)
-#765 := (or #771 #562 #648)
-#766 := [def-axiom]: #765
-#650 := [unit-resolution #766 #684]: #691
-#681 := [unit-resolution #650 #716]: #648
-#782 := (not #648)
-#783 := (or #782 #780 #484)
-#784 := [def-axiom]: #783
-#683 := [unit-resolution #784 #681 #710]: #780
-#786 := (or #812 #850)
-#788 := [def-axiom]: #786
-#685 := [unit-resolution #788 #683]: #850
-#795 := (or #812 #847)
-#799 := [def-axiom]: #795
-#692 := [unit-resolution #799 #683]: #847
-#694 := (or #562 #830 #665)
-#695 := [th-lemma arith triangle-eq]: #694
-#696 := [unit-resolution #695 #716 #692 #685]: false
-#686 := [lemma #696]: #706
-#610 := [unit-resolution #686 #673]: #484
-#613 := (or #769 #790)
-#614 := [th-lemma arith triangle-eq]: #613
-#600 := [unit-resolution #614 #610]: #790
-#791 := (>= #846 0::Int)
-#602 := (or #769 #791)
-#603 := [th-lemma arith triangle-eq]: #602
-#601 := [unit-resolution #603 #610]: #791
-#586 := [th-lemma arith eq-propagate 1 1 #601 #600]: #604
-#579 := [trans #586 #578]: #731
-#580 := [monotonicity #579]: #663
-#581 := [symm #580]: #669
-#582 := [trans #662 #581]: #80
-[unit-resolution #88 #582]: false
-unsat
-84bb282eead031ef4ff9718b6ca086d90bb4eefb 298 0
-#2 := false
-decl f3 :: (-> Int S2)
-#8 := 0::Int
-#12 := (f3 0::Int)
-decl f4 :: (-> Int Int Int)
-#9 := 3::Int
-#10 := (f4 0::Int 3::Int)
-#11 := (f3 #10)
-#13 := (= #11 #12)
-#806 := (= #10 0::Int)
-#20 := (:var 0 Int)
-#31 := (:var 1 Int)
-#32 := (f4 #31 #20)
-#878 := (pattern #32)
-#180 := -1::Int
-#184 := (* -1::Int #20)
-#181 := (* -1::Int #31)
-#187 := (div #181 #184)
-#359 := (* -1::Int #187)
-#360 := (+ #32 #359)
-#361 := (= #360 0::Int)
-#42 := (div #31 #20)
-#356 := (* -1::Int #42)
-#357 := (+ #32 #356)
-#358 := (= #357 0::Int)
-#219 := (>= #31 0::Int)
-#212 := (<= #20 0::Int)
-#319 := (or #212 #219)
-#320 := (not #319)
-#208 := (<= #31 0::Int)
-#317 := (or #208 #212)
-#318 := (not #317)
-#323 := (or #318 #320)
-#362 := (ite #323 #358 #361)
-#355 := (= #32 0::Int)
-#34 := (= #20 0::Int)
-#33 := (= #31 0::Int)
-#35 := (or #33 #34)
-#363 := (ite #35 #355 #362)
-#879 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #878) #363)
-#366 := (forall (vars (?v0 Int) (?v1 Int)) #363)
-#882 := (iff #366 #879)
-#880 := (iff #363 #363)
-#881 := [refl]: #880
-#883 := [quant-intro #881]: #882
-#326 := (ite #323 #42 #187)
-#329 := (ite #35 0::Int #326)
-#332 := (= #32 #329)
-#335 := (forall (vars (?v0 Int) (?v1 Int)) #332)
-#367 := (iff #335 #366)
-#364 := (iff #332 #363)
-#365 := [rewrite]: #364
-#368 := [quant-intro #365]: #367
-#220 := (not #219)
-#213 := (not #212)
-#223 := (and #213 #220)
-#209 := (not #208)
-#216 := (and #209 #213)
-#226 := (or #216 #223)
-#229 := (ite #226 #42 #187)
-#232 := (ite #35 0::Int #229)
-#235 := (= #32 #232)
-#238 := (forall (vars (?v0 Int) (?v1 Int)) #235)
-#336 := (iff #238 #335)
-#333 := (iff #235 #332)
-#330 := (= #232 #329)
-#327 := (= #229 #326)
-#324 := (iff #226 #323)
-#321 := (iff #223 #320)
-#322 := [rewrite]: #321
-#302 := (iff #216 #318)
-#303 := [rewrite]: #302
-#325 := [monotonicity #303 #322]: #324
-#328 := [monotonicity #325]: #327
-#331 := [monotonicity #328]: #330
-#334 := [monotonicity #331]: #333
-#337 := [quant-intro #334]: #336
-#298 := (~ #238 #238)
-#311 := (~ #235 #235)
-#312 := [refl]: #311
-#299 := [nnf-pos #312]: #298
-#44 := (- #20)
-#43 := (- #31)
-#45 := (div #43 #44)
-#37 := (< 0::Int #20)
-#39 := (< #31 0::Int)
-#40 := (and #39 #37)
-#36 := (< 0::Int #31)
-#38 := (and #36 #37)
-#41 := (or #38 #40)
-#46 := (ite #41 #42 #45)
-#47 := (ite #35 0::Int #46)
-#48 := (= #32 #47)
-#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
-#241 := (iff #49 #238)
-#174 := (and #37 #39)
-#177 := (or #38 #174)
-#190 := (ite #177 #42 #187)
-#168 := (= 0::Int #20)
-#165 := (= 0::Int #31)
-#171 := (or #165 #168)
-#193 := (ite #171 0::Int #190)
-#196 := (= #32 #193)
-#199 := (forall (vars (?v0 Int) (?v1 Int)) #196)
-#239 := (iff #199 #238)
-#236 := (iff #196 #235)
-#233 := (= #193 #232)
-#230 := (= #190 #229)
-#227 := (iff #177 #226)
-#224 := (iff #174 #223)
-#221 := (iff #39 #220)
-#222 := [rewrite]: #221
-#214 := (iff #37 #213)
-#215 := [rewrite]: #214
-#225 := [monotonicity #215 #222]: #224
-#217 := (iff #38 #216)
-#210 := (iff #36 #209)
-#211 := [rewrite]: #210
-#218 := [monotonicity #211 #215]: #217
-#228 := [monotonicity #218 #225]: #227
-#231 := [monotonicity #228]: #230
-#206 := (iff #171 #35)
-#204 := (iff #168 #34)
-#205 := [rewrite]: #204
-#202 := (iff #165 #33)
-#203 := [rewrite]: #202
-#207 := [monotonicity #203 #205]: #206
-#234 := [monotonicity #207 #231]: #233
-#237 := [monotonicity #234]: #236
-#240 := [quant-intro #237]: #239
-#200 := (iff #49 #199)
-#197 := (iff #48 #196)
-#194 := (= #47 #193)
-#191 := (= #46 #190)
-#188 := (= #45 #187)
-#185 := (= #44 #184)
-#186 := [rewrite]: #185
-#182 := (= #43 #181)
-#183 := [rewrite]: #182
-#189 := [monotonicity #183 #186]: #188
-#178 := (iff #41 #177)
-#175 := (iff #40 #174)
-#176 := [rewrite]: #175
-#179 := [monotonicity #176]: #178
-#192 := [monotonicity #179 #189]: #191
-#172 := (iff #35 #171)
-#169 := (iff #34 #168)
-#170 := [rewrite]: #169
-#166 := (iff #33 #165)
-#167 := [rewrite]: #166
-#173 := [monotonicity #167 #170]: #172
-#195 := [monotonicity #173 #192]: #194
-#198 := [monotonicity #195]: #197
-#201 := [quant-intro #198]: #200
-#242 := [trans #201 #240]: #241
-#164 := [asserted]: #49
-#243 := [mp #164 #242]: #238
-#313 := [mp~ #243 #299]: #238
-#338 := [mp #313 #337]: #335
-#369 := [mp #338 #368]: #366
-#884 := [mp #369 #883]: #879
-#725 := (not #879)
-#731 := (or #725 #806)
-#812 := (* -1::Int 3::Int)
-#813 := (* -1::Int 0::Int)
-#814 := (div #813 #812)
-#809 := (* -1::Int #814)
-#810 := (+ #10 #809)
-#815 := (= #810 0::Int)
-#816 := (div 0::Int 3::Int)
-#811 := (* -1::Int #816)
-#817 := (+ #10 #811)
-#658 := (= #817 0::Int)
-#834 := (>= 0::Int 0::Int)
-#659 := (<= 3::Int 0::Int)
-#660 := (or #659 #834)
-#802 := (not #660)
-#803 := (<= 0::Int 0::Int)
-#804 := (or #803 #659)
-#805 := (not #804)
-#799 := (or #805 #802)
-#800 := (ite #799 #658 #815)
-#807 := (= 3::Int 0::Int)
-#801 := (= 0::Int 0::Int)
-#808 := (or #801 #807)
-#637 := (ite #808 #806 #800)
-#704 := (or #725 #637)
-#706 := (iff #704 #731)
-#710 := (iff #731 #731)
-#711 := [rewrite]: #710
-#729 := (iff #637 #806)
-#1 := true
-#722 := (ite true #806 #806)
-#727 := (iff #722 #806)
-#728 := [rewrite]: #727
-#723 := (iff #637 #722)
-#740 := (iff #800 #806)
-#736 := (ite false #806 #806)
-#739 := (iff #736 #806)
-#734 := [rewrite]: #739
-#737 := (iff #800 #736)
-#733 := (iff #815 #806)
-#754 := (= #810 #10)
-#766 := (+ #10 0::Int)
-#764 := (= #766 #10)
-#769 := [rewrite]: #764
-#753 := (= #810 #766)
-#751 := (= #809 0::Int)
-#778 := (= #813 0::Int)
-#762 := [rewrite]: #778
-#749 := (= #809 #813)
-#747 := (= #814 0::Int)
-#760 := -3::Int
-#741 := (div 0::Int -3::Int)
-#745 := (= #741 0::Int)
-#746 := [rewrite]: #745
-#742 := (= #814 #741)
-#757 := (= #812 -3::Int)
-#761 := [rewrite]: #757
-#744 := [monotonicity #762 #761]: #742
-#748 := [trans #744 #746]: #747
-#750 := [monotonicity #748]: #749
-#752 := [trans #750 #762]: #751
-#743 := [monotonicity #752]: #753
-#732 := [trans #743 #769]: #754
-#735 := [monotonicity #732]: #733
-#758 := (iff #658 #806)
-#755 := (= #817 #10)
-#767 := (= #817 #766)
-#763 := (= #811 0::Int)
-#777 := (= #811 #813)
-#775 := (= #816 0::Int)
-#776 := [rewrite]: #775
-#771 := [monotonicity #776]: #777
-#765 := [trans #771 #762]: #763
-#768 := [monotonicity #765]: #767
-#756 := [trans #768 #769]: #755
-#759 := [monotonicity #756]: #758
-#785 := (iff #799 false)
-#772 := (or false false)
-#784 := (iff #772 false)
-#780 := [rewrite]: #784
-#782 := (iff #799 #772)
-#773 := (iff #802 false)
-#482 := (not true)
-#841 := (iff #482 false)
-#844 := [rewrite]: #841
-#779 := (iff #802 #482)
-#788 := (iff #660 true)
-#695 := (or false true)
-#698 := (iff #695 true)
-#791 := [rewrite]: #698
-#696 := (iff #660 #695)
-#840 := (iff #834 true)
-#842 := [rewrite]: #840
-#691 := (iff #659 false)
-#786 := [rewrite]: #691
-#697 := [monotonicity #786 #842]: #696
-#792 := [trans #697 #791]: #788
-#781 := [monotonicity #792]: #779
-#770 := [trans #781 #844]: #773
-#686 := (iff #805 false)
-#692 := (iff #805 #482)
-#675 := (iff #804 true)
-#796 := (or true false)
-#798 := (iff #796 true)
-#680 := [rewrite]: #798
-#787 := (iff #804 #796)
-#641 := (iff #803 true)
-#789 := [rewrite]: #641
-#790 := [monotonicity #789 #786]: #787
-#690 := [trans #790 #680]: #675
-#693 := [monotonicity #690]: #692
-#694 := [trans #693 #844]: #686
-#783 := [monotonicity #694 #770]: #782
-#774 := [trans #783 #780]: #785
-#738 := [monotonicity #774 #759 #735]: #737
-#726 := [trans #738 #734]: #740
-#681 := (iff #808 true)
-#797 := (iff #808 #796)
-#793 := (iff #807 false)
-#794 := [rewrite]: #793
-#639 := (iff #801 true)
-#640 := [rewrite]: #639
-#795 := [monotonicity #640 #794]: #797
-#682 := [trans #795 #680]: #681
-#724 := [monotonicity #682 #726]: #723
-#730 := [trans #724 #728]: #729
-#599 := [monotonicity #730]: #706
-#712 := [trans #599 #711]: #706
-#705 := [quant-inst #8 #9]: #704
-#717 := [mp #705 #712]: #731
-#714 := [unit-resolution #717 #884]: #806
-#715 := [monotonicity #714]: #13
-#14 := (not #13)
-#78 := [asserted]: #14
-[unit-resolution #78 #715]: false
-unsat
-753372d6275197bbef48a8ecc32b53d9fd3d1075 315 0
-#2 := false
-decl f3 :: (-> Int S2)
-#12 := 0::Int
-#13 := (f3 0::Int)
-decl f4 :: (-> Int Int Int)
-#9 := 3::Int
-#8 := 1::Int
-#10 := (f4 1::Int 3::Int)
-#11 := (f3 #10)
-#14 := (= #11 #13)
-#801 := (= #10 0::Int)
-#21 := (:var 0 Int)
-#32 := (:var 1 Int)
-#33 := (f4 #32 #21)
-#878 := (pattern #33)
-#181 := -1::Int
-#185 := (* -1::Int #21)
-#182 := (* -1::Int #32)
-#188 := (div #182 #185)
-#360 := (* -1::Int #188)
-#361 := (+ #33 #360)
-#362 := (= #361 0::Int)
-#43 := (div #32 #21)
-#357 := (* -1::Int #43)
-#358 := (+ #33 #357)
-#359 := (= #358 0::Int)
-#220 := (>= #32 0::Int)
-#213 := (<= #21 0::Int)
-#320 := (or #213 #220)
-#321 := (not #320)
-#209 := (<= #32 0::Int)
-#318 := (or #209 #213)
-#319 := (not #318)
-#324 := (or #319 #321)
-#363 := (ite #324 #359 #362)
-#356 := (= #33 0::Int)
-#35 := (= #21 0::Int)
-#34 := (= #32 0::Int)
-#36 := (or #34 #35)
-#364 := (ite #36 #356 #363)
-#879 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #878) #364)
-#367 := (forall (vars (?v0 Int) (?v1 Int)) #364)
-#882 := (iff #367 #879)
-#880 := (iff #364 #364)
-#881 := [refl]: #880
-#883 := [quant-intro #881]: #882
-#327 := (ite #324 #43 #188)
-#330 := (ite #36 0::Int #327)
-#333 := (= #33 #330)
-#336 := (forall (vars (?v0 Int) (?v1 Int)) #333)
-#368 := (iff #336 #367)
-#365 := (iff #333 #364)
-#366 := [rewrite]: #365
-#369 := [quant-intro #366]: #368
-#221 := (not #220)
-#214 := (not #213)
-#224 := (and #214 #221)
-#210 := (not #209)
-#217 := (and #210 #214)
-#227 := (or #217 #224)
-#230 := (ite #227 #43 #188)
-#233 := (ite #36 0::Int #230)
-#236 := (= #33 #233)
-#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
-#337 := (iff #239 #336)
-#334 := (iff #236 #333)
-#331 := (= #233 #330)
-#328 := (= #230 #327)
-#325 := (iff #227 #324)
-#322 := (iff #224 #321)
-#323 := [rewrite]: #322
-#303 := (iff #217 #319)
-#304 := [rewrite]: #303
-#326 := [monotonicity #304 #323]: #325
-#329 := [monotonicity #326]: #328
-#332 := [monotonicity #329]: #331
-#335 := [monotonicity #332]: #334
-#338 := [quant-intro #335]: #337
-#299 := (~ #239 #239)
-#312 := (~ #236 #236)
-#313 := [refl]: #312
-#300 := [nnf-pos #313]: #299
-#45 := (- #21)
-#44 := (- #32)
-#46 := (div #44 #45)
-#38 := (< 0::Int #21)
-#40 := (< #32 0::Int)
-#41 := (and #40 #38)
-#37 := (< 0::Int #32)
-#39 := (and #37 #38)
-#42 := (or #39 #41)
-#47 := (ite #42 #43 #46)
-#48 := (ite #36 0::Int #47)
-#49 := (= #33 #48)
-#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
-#242 := (iff #50 #239)
-#175 := (and #38 #40)
-#178 := (or #39 #175)
-#191 := (ite #178 #43 #188)
-#169 := (= 0::Int #21)
-#166 := (= 0::Int #32)
-#172 := (or #166 #169)
-#194 := (ite #172 0::Int #191)
-#197 := (= #33 #194)
-#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
-#240 := (iff #200 #239)
-#237 := (iff #197 #236)
-#234 := (= #194 #233)
-#231 := (= #191 #230)
-#228 := (iff #178 #227)
-#225 := (iff #175 #224)
-#222 := (iff #40 #221)
-#223 := [rewrite]: #222
-#215 := (iff #38 #214)
-#216 := [rewrite]: #215
-#226 := [monotonicity #216 #223]: #225
-#218 := (iff #39 #217)
-#211 := (iff #37 #210)
-#212 := [rewrite]: #211
-#219 := [monotonicity #212 #216]: #218
-#229 := [monotonicity #219 #226]: #228
-#232 := [monotonicity #229]: #231
-#207 := (iff #172 #36)
-#205 := (iff #169 #35)
-#206 := [rewrite]: #205
-#203 := (iff #166 #34)
-#204 := [rewrite]: #203
-#208 := [monotonicity #204 #206]: #207
-#235 := [monotonicity #208 #232]: #234
-#238 := [monotonicity #235]: #237
-#241 := [quant-intro #238]: #240
-#201 := (iff #50 #200)
-#198 := (iff #49 #197)
-#195 := (= #48 #194)
-#192 := (= #47 #191)
-#189 := (= #46 #188)
-#186 := (= #45 #185)
-#187 := [rewrite]: #186
-#183 := (= #44 #182)
-#184 := [rewrite]: #183
-#190 := [monotonicity #184 #187]: #189
-#179 := (iff #42 #178)
-#176 := (iff #41 #175)
-#177 := [rewrite]: #176
-#180 := [monotonicity #177]: #179
-#193 := [monotonicity #180 #190]: #192
-#173 := (iff #36 #172)
-#170 := (iff #35 #169)
-#171 := [rewrite]: #170
-#167 := (iff #34 #166)
-#168 := [rewrite]: #167
-#174 := [monotonicity #168 #171]: #173
-#196 := [monotonicity #174 #193]: #195
-#199 := [monotonicity #196]: #198
-#202 := [quant-intro #199]: #201
-#243 := [trans #202 #241]: #242
-#165 := [asserted]: #50
-#244 := [mp #165 #243]: #239
-#314 := [mp~ #244 #300]: #239
-#339 := [mp #314 #338]: #336
-#370 := [mp #339 #369]: #367
-#884 := [mp #370 #883]: #879
-#702 := (not #879)
-#683 := (or #702 #801)
-#813 := (* -1::Int 3::Int)
-#814 := (* -1::Int 1::Int)
-#809 := (div #814 #813)
-#810 := (* -1::Int #809)
-#815 := (+ #10 #810)
-#816 := (= #815 0::Int)
-#811 := (div 1::Int 3::Int)
-#817 := (* -1::Int #811)
-#658 := (+ #10 #817)
-#659 := (= #658 0::Int)
-#660 := (>= 1::Int 0::Int)
-#802 := (<= 3::Int 0::Int)
-#803 := (or #802 #660)
-#804 := (not #803)
-#805 := (<= 1::Int 0::Int)
-#799 := (or #805 #802)
-#800 := (not #799)
-#806 := (or #800 #804)
-#807 := (ite #806 #659 #816)
-#808 := (= 3::Int 0::Int)
-#637 := (= 1::Int 0::Int)
-#639 := (or #637 #808)
-#640 := (ite #639 #801 #807)
-#707 := (or #702 #640)
-#703 := (iff #707 #683)
-#677 := (iff #683 #683)
-#684 := [rewrite]: #677
-#701 := (iff #640 #801)
-#718 := (ite false #801 #801)
-#716 := (iff #718 #801)
-#721 := [rewrite]: #716
-#719 := (iff #640 #718)
-#714 := (iff #807 #801)
-#731 := (= #10 1::Int)
-#1 := true
-#710 := (ite true #801 #731)
-#717 := (iff #710 #801)
-#713 := [rewrite]: #717
-#711 := (iff #807 #710)
-#706 := (iff #816 #731)
-#722 := (+ -1::Int #10)
-#729 := (= #722 0::Int)
-#704 := (iff #729 #731)
-#705 := [rewrite]: #704
-#730 := (iff #816 #729)
-#727 := (= #815 #722)
-#734 := (+ #10 -1::Int)
-#723 := (= #734 #722)
-#724 := [rewrite]: #723
-#740 := (= #815 #734)
-#738 := (= #810 -1::Int)
-#747 := (= #814 -1::Int)
-#748 := [rewrite]: #747
-#736 := (= #810 #814)
-#733 := (= #809 1::Int)
-#749 := -3::Int
-#752 := (div -1::Int -3::Int)
-#754 := (= #752 1::Int)
-#732 := [rewrite]: #754
-#753 := (= #809 #752)
-#750 := (= #813 -3::Int)
-#751 := [rewrite]: #750
-#743 := [monotonicity #748 #751]: #753
-#735 := [trans #743 #732]: #733
-#737 := [monotonicity #735]: #736
-#739 := [trans #737 #748]: #738
-#726 := [monotonicity #739]: #740
-#728 := [trans #726 #724]: #727
-#725 := [monotonicity #728]: #730
-#599 := [trans #725 #705]: #706
-#745 := (iff #659 #801)
-#742 := (= #658 #10)
-#759 := (+ #10 0::Int)
-#761 := (= #759 #10)
-#741 := [rewrite]: #761
-#760 := (= #658 #759)
-#756 := (= #817 0::Int)
-#767 := (* -1::Int 0::Int)
-#769 := (= #767 0::Int)
-#755 := [rewrite]: #769
-#768 := (= #817 #767)
-#765 := (= #811 0::Int)
-#766 := [rewrite]: #765
-#764 := [monotonicity #766]: #768
-#758 := [trans #764 #755]: #756
-#757 := [monotonicity #758]: #760
-#744 := [trans #757 #741]: #742
-#746 := [monotonicity #744]: #745
-#762 := (iff #806 true)
-#775 := (or true false)
-#771 := (iff #775 true)
-#778 := [rewrite]: #771
-#776 := (iff #806 #775)
-#785 := (iff #804 false)
-#483 := (not true)
-#844 := (iff #483 false)
-#830 := [rewrite]: #844
-#784 := (iff #804 #483)
-#782 := (iff #803 true)
-#779 := (or false true)
-#770 := (iff #779 true)
-#772 := [rewrite]: #770
-#781 := (iff #803 #779)
-#788 := (iff #660 true)
-#792 := [rewrite]: #788
-#787 := (iff #802 false)
-#790 := [rewrite]: #787
-#773 := [monotonicity #790 #792]: #781
-#783 := [trans #773 #772]: #782
-#780 := [monotonicity #783]: #784
-#774 := [trans #780 #830]: #785
-#698 := (iff #800 true)
-#686 := (not false)
-#696 := (iff #686 true)
-#697 := [rewrite]: #696
-#694 := (iff #800 #686)
-#692 := (iff #799 false)
-#795 := (or false false)
-#681 := (iff #795 false)
-#682 := [rewrite]: #681
-#675 := (iff #799 #795)
-#691 := (iff #805 false)
-#786 := [rewrite]: #691
-#690 := [monotonicity #786 #790]: #675
-#693 := [trans #690 #682]: #692
-#695 := [monotonicity #693]: #694
-#791 := [trans #695 #697]: #698
-#777 := [monotonicity #791 #774]: #776
-#763 := [trans #777 #778]: #762
-#712 := [monotonicity #763 #746 #599]: #711
-#715 := [trans #712 #713]: #714
-#641 := (iff #639 false)
-#798 := (iff #639 #795)
-#796 := (iff #808 false)
-#797 := [rewrite]: #796
-#793 := (iff #637 false)
-#794 := [rewrite]: #793
-#680 := [monotonicity #794 #797]: #798
-#789 := [trans #680 #682]: #641
-#720 := [monotonicity #789 #715]: #719
-#647 := [trans #720 #721]: #701
-#709 := [monotonicity #647]: #703
-#643 := [trans #709 #684]: #703
-#708 := [quant-inst #8 #9]: #707
-#674 := [mp #708 #643]: #683
-#678 := [unit-resolution #674 #884]: #801
-#685 := [monotonicity #678]: #14
-#15 := (not #14)
-#79 := [asserted]: #15
-[unit-resolution #79 #685]: false
-unsat
-c4211064b5728b62240cb2d0bc31b06836a1e3c1 305 0
-#2 := false
-decl f3 :: (-> Int S2)
-#11 := 1::Int
-#12 := (f3 1::Int)
-decl f4 :: (-> Int Int Int)
-#8 := 3::Int
-#9 := (f4 3::Int 3::Int)
-#10 := (f3 #9)
-#13 := (= #10 #12)
-#742 := (= #9 1::Int)
-#21 := (:var 0 Int)
-#32 := (:var 1 Int)
-#33 := (f4 #32 #21)
-#878 := (pattern #33)
-#20 := 0::Int
-#181 := -1::Int
-#185 := (* -1::Int #21)
-#182 := (* -1::Int #32)
-#188 := (div #182 #185)
-#360 := (* -1::Int #188)
-#361 := (+ #33 #360)
-#362 := (= #361 0::Int)
-#43 := (div #32 #21)
-#357 := (* -1::Int #43)
-#358 := (+ #33 #357)
-#359 := (= #358 0::Int)
-#220 := (>= #32 0::Int)
-#213 := (<= #21 0::Int)
-#320 := (or #213 #220)
-#321 := (not #320)
-#209 := (<= #32 0::Int)
-#318 := (or #209 #213)
-#319 := (not #318)
-#324 := (or #319 #321)
-#363 := (ite #324 #359 #362)
-#356 := (= #33 0::Int)
-#35 := (= #21 0::Int)
-#34 := (= #32 0::Int)
-#36 := (or #34 #35)
-#364 := (ite #36 #356 #363)
-#879 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #878) #364)
-#367 := (forall (vars (?v0 Int) (?v1 Int)) #364)
-#882 := (iff #367 #879)
-#880 := (iff #364 #364)
-#881 := [refl]: #880
-#883 := [quant-intro #881]: #882
-#327 := (ite #324 #43 #188)
-#330 := (ite #36 0::Int #327)
-#333 := (= #33 #330)
-#336 := (forall (vars (?v0 Int) (?v1 Int)) #333)
-#368 := (iff #336 #367)
-#365 := (iff #333 #364)
-#366 := [rewrite]: #365
-#369 := [quant-intro #366]: #368
-#221 := (not #220)
-#214 := (not #213)
-#224 := (and #214 #221)
-#210 := (not #209)
-#217 := (and #210 #214)
-#227 := (or #217 #224)
-#230 := (ite #227 #43 #188)
-#233 := (ite #36 0::Int #230)
-#236 := (= #33 #233)
-#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
-#337 := (iff #239 #336)
-#334 := (iff #236 #333)
-#331 := (= #233 #330)
-#328 := (= #230 #327)
-#325 := (iff #227 #324)
-#322 := (iff #224 #321)
-#323 := [rewrite]: #322
-#303 := (iff #217 #319)
-#304 := [rewrite]: #303
-#326 := [monotonicity #304 #323]: #325
-#329 := [monotonicity #326]: #328
-#332 := [monotonicity #329]: #331
-#335 := [monotonicity #332]: #334
-#338 := [quant-intro #335]: #337
-#299 := (~ #239 #239)
-#312 := (~ #236 #236)
-#313 := [refl]: #312
-#300 := [nnf-pos #313]: #299
-#45 := (- #21)
-#44 := (- #32)
-#46 := (div #44 #45)
-#38 := (< 0::Int #21)
-#40 := (< #32 0::Int)
-#41 := (and #40 #38)
-#37 := (< 0::Int #32)
-#39 := (and #37 #38)
-#42 := (or #39 #41)
-#47 := (ite #42 #43 #46)
-#48 := (ite #36 0::Int #47)
-#49 := (= #33 #48)
-#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
-#242 := (iff #50 #239)
-#175 := (and #38 #40)
-#178 := (or #39 #175)
-#191 := (ite #178 #43 #188)
-#169 := (= 0::Int #21)
-#166 := (= 0::Int #32)
-#172 := (or #166 #169)
-#194 := (ite #172 0::Int #191)
-#197 := (= #33 #194)
-#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
-#240 := (iff #200 #239)
-#237 := (iff #197 #236)
-#234 := (= #194 #233)
-#231 := (= #191 #230)
-#228 := (iff #178 #227)
-#225 := (iff #175 #224)
-#222 := (iff #40 #221)
-#223 := [rewrite]: #222
-#215 := (iff #38 #214)
-#216 := [rewrite]: #215
-#226 := [monotonicity #216 #223]: #225
-#218 := (iff #39 #217)
-#211 := (iff #37 #210)
-#212 := [rewrite]: #211
-#219 := [monotonicity #212 #216]: #218
-#229 := [monotonicity #219 #226]: #228
-#232 := [monotonicity #229]: #231
-#207 := (iff #172 #36)
-#205 := (iff #169 #35)
-#206 := [rewrite]: #205
-#203 := (iff #166 #34)
-#204 := [rewrite]: #203
-#208 := [monotonicity #204 #206]: #207
-#235 := [monotonicity #208 #232]: #234
-#238 := [monotonicity #235]: #237
-#241 := [quant-intro #238]: #240
-#201 := (iff #50 #200)
-#198 := (iff #49 #197)
-#195 := (= #48 #194)
-#192 := (= #47 #191)
-#189 := (= #46 #188)
-#186 := (= #45 #185)
-#187 := [rewrite]: #186
-#183 := (= #44 #182)
-#184 := [rewrite]: #183
-#190 := [monotonicity #184 #187]: #189
-#179 := (iff #42 #178)
-#176 := (iff #41 #175)
-#177 := [rewrite]: #176
-#180 := [monotonicity #177]: #179
-#193 := [monotonicity #180 #190]: #192
-#173 := (iff #36 #172)
-#170 := (iff #35 #169)
-#171 := [rewrite]: #170
-#167 := (iff #34 #166)
-#168 := [rewrite]: #167
-#174 := [monotonicity #168 #171]: #173
-#196 := [monotonicity #174 #193]: #195
-#199 := [monotonicity #196]: #198
-#202 := [quant-intro #199]: #201
-#243 := [trans #202 #241]: #242
-#165 := [asserted]: #50
-#244 := [mp #165 #243]: #239
-#314 := [mp~ #244 #300]: #239
-#339 := [mp #314 #338]: #336
-#370 := [mp #339 #369]: #367
-#884 := [mp #370 #883]: #879
-#714 := (not #879)
-#715 := (or #714 #742)
-#814 := (* -1::Int 3::Int)
-#809 := (div #814 #814)
-#810 := (* -1::Int #809)
-#815 := (+ #9 #810)
-#816 := (= #815 0::Int)
-#811 := (div 3::Int 3::Int)
-#817 := (* -1::Int #811)
-#658 := (+ #9 #817)
-#659 := (= #658 0::Int)
-#660 := (>= 3::Int 0::Int)
-#802 := (<= 3::Int 0::Int)
-#803 := (or #802 #660)
-#804 := (not #803)
-#805 := (or #802 #802)
-#799 := (not #805)
-#800 := (or #799 #804)
-#806 := (ite #800 #659 #816)
-#807 := (= #9 0::Int)
-#801 := (= 3::Int 0::Int)
-#808 := (or #801 #801)
-#637 := (ite #808 #807 #806)
-#718 := (or #714 #637)
-#720 := (iff #718 #715)
-#721 := (iff #715 #715)
-#701 := [rewrite]: #721
-#717 := (iff #637 #742)
-#706 := (ite false #807 #742)
-#711 := (iff #706 #742)
-#712 := [rewrite]: #711
-#599 := (iff #637 #706)
-#704 := (iff #806 #742)
-#1 := true
-#728 := (ite true #742 #742)
-#725 := (iff #728 #742)
-#731 := [rewrite]: #725
-#729 := (iff #806 #728)
-#724 := (iff #816 #742)
-#755 := (+ -1::Int #9)
-#757 := (= #755 0::Int)
-#744 := (iff #757 #742)
-#745 := [rewrite]: #744
-#722 := (iff #816 #757)
-#740 := (= #815 #755)
-#768 := (+ #9 -1::Int)
-#756 := (= #768 #755)
-#758 := [rewrite]: #756
-#739 := (= #815 #768)
-#737 := (= #810 -1::Int)
-#771 := (* -1::Int 1::Int)
-#763 := (= #771 -1::Int)
-#765 := [rewrite]: #763
-#735 := (= #810 #771)
-#732 := (= #809 1::Int)
-#748 := -3::Int
-#751 := (div -3::Int -3::Int)
-#743 := (= #751 1::Int)
-#754 := [rewrite]: #743
-#752 := (= #809 #751)
-#749 := (= #814 -3::Int)
-#750 := [rewrite]: #749
-#753 := [monotonicity #750 #750]: #752
-#733 := [trans #753 #754]: #732
-#736 := [monotonicity #733]: #735
-#738 := [trans #736 #765]: #737
-#734 := [monotonicity #738]: #739
-#726 := [trans #734 #758]: #740
-#723 := [monotonicity #726]: #722
-#727 := [trans #723 #745]: #724
-#746 := (iff #659 #742)
-#761 := (iff #659 #757)
-#759 := (= #658 #755)
-#764 := (= #658 #768)
-#766 := (= #817 -1::Int)
-#778 := (= #817 #771)
-#776 := (= #811 1::Int)
-#777 := [rewrite]: #776
-#762 := [monotonicity #777]: #778
-#767 := [trans #762 #765]: #766
-#769 := [monotonicity #767]: #764
-#760 := [trans #769 #758]: #759
-#741 := [monotonicity #760]: #761
-#747 := [trans #741 #745]: #746
-#774 := (iff #800 true)
-#782 := (or true false)
-#780 := (iff #782 true)
-#785 := [rewrite]: #780
-#783 := (iff #800 #782)
-#770 := (iff #804 false)
-#483 := (not true)
-#844 := (iff #483 false)
-#830 := [rewrite]: #844
-#781 := (iff #804 #483)
-#792 := (iff #803 true)
-#696 := (or false true)
-#791 := (iff #696 true)
-#788 := [rewrite]: #791
-#697 := (iff #803 #696)
-#694 := (iff #660 true)
-#695 := [rewrite]: #694
-#681 := (iff #802 false)
-#682 := [rewrite]: #681
-#698 := [monotonicity #682 #695]: #697
-#779 := [trans #698 #788]: #792
-#773 := [monotonicity #779]: #781
-#772 := [trans #773 #830]: #770
-#693 := (iff #799 true)
-#787 := (not false)
-#690 := (iff #787 true)
-#692 := [rewrite]: #690
-#790 := (iff #799 #787)
-#691 := (iff #805 false)
-#793 := (or false false)
-#797 := (iff #793 false)
-#795 := [rewrite]: #797
-#641 := (iff #805 #793)
-#789 := [monotonicity #682 #682]: #641
-#786 := [trans #789 #795]: #691
-#675 := [monotonicity #786]: #790
-#686 := [trans #675 #692]: #693
-#784 := [monotonicity #686 #772]: #783
-#775 := [trans #784 #785]: #774
-#730 := [monotonicity #775 #747 #727]: #729
-#705 := [trans #730 #731]: #704
-#798 := (iff #808 false)
-#794 := (iff #808 #793)
-#639 := (iff #801 false)
-#640 := [rewrite]: #639
-#796 := [monotonicity #640 #640]: #794
-#680 := [trans #796 #795]: #798
-#710 := [monotonicity #680 #705]: #599
-#713 := [trans #710 #712]: #717
-#716 := [monotonicity #713]: #720
-#647 := [trans #716 #701]: #720
-#719 := [quant-inst #8 #8]: #718
-#702 := [mp #719 #647]: #715
-#708 := [unit-resolution #702 #884]: #742
-#703 := [monotonicity #708]: #13
-#14 := (not #13)
-#79 := [asserted]: #14
-[unit-resolution #79 #703]: false
-unsat
-c8c3466ffe36eb7d0f579df3f5c17ffb47bc161f 459 0
-#2 := false
-#19 := 0::Int
-#10 := 3::Int
+#86 := (= #21 -3::Int)
+#87 := [rewrite]: #86
+#93 := [monotonicity #87 #90]: #92
+#97 := [trans #93 #95]: #96
+#83 := (= #20 3::Int)
+#84 := [rewrite]: #83
+#81 := (iff #19 #80)
+#78 := (iff #18 #77)
+#79 := [rewrite]: #78
+#82 := [monotonicity #79]: #81
+#100 := [monotonicity #82 #84 #97]: #99
+#104 := [trans #100 #102]: #103
+#75 := (iff #13 false)
+#70 := (or false false)
+#73 := (iff #70 false)
+#74 := [rewrite]: #73
+#71 := (iff #13 #70)
+#68 := (iff #12 false)
+#69 := [rewrite]: #68
+#66 := (iff #10 false)
+#67 := [rewrite]: #66
+#72 := [monotonicity #67 #69]: #71
+#76 := [trans #72 #74]: #75
+#107 := [monotonicity #76 #104]: #106
+#111 := [trans #107 #109]: #110
+#112 := [monotonicity #111]: #28
+#115 := [monotonicity #112]: #114
+#119 := [trans #115 #117]: #118
+#122 := [monotonicity #119]: #121
+#126 := [trans #122 #124]: #125
+#65 := [asserted]: #29
+[mp #65 #126]: false
+unsat
+541d6fe80b1182e33d84e37f649671b9536f0b45 313 0
+#2 := false
+decl f3 :: (-> Int S2)
+#81 := -1::Int
 decl f4 :: (-> S2 Int)
 decl f5 :: S2
 #8 := f5
 #9 := (f4 f5)
-#807 := (mod #9 3::Int)
-#81 := -1::Int
-#753 := (* -1::Int #807)
-#523 := (div #9 3::Int)
-#549 := -3::Int
-#751 := (* -3::Int #523)
-#754 := (+ #751 #753)
-#755 := (+ #9 #754)
-#750 := (= #755 0::Int)
-#1 := true
-#76 := [true-axiom]: true
-#719 := (or false #750)
-#720 := [th-lemma arith]: #719
-#721 := [unit-resolution #720 #76]: #750
-#759 := (>= #755 0::Int)
-#662 := (not #759)
-#760 := (>= #807 0::Int)
-#664 := (or false #760)
-#665 := [th-lemma arith]: #664
-#670 := [unit-resolution #665 #76]: #760
-decl f3 :: (-> Int Int Int)
-#11 := (f3 #9 3::Int)
-#84 := (* -1::Int #11)
-#85 := (+ #9 #84)
-#83 := (>= #85 0::Int)
-#87 := (not #83)
-#12 := (<= #11 #9)
-#13 := (not #12)
-#88 := (iff #13 #87)
-#82 := (iff #12 #83)
-#86 := [rewrite]: #82
-#89 := [monotonicity #86]: #88
-#78 := [asserted]: #13
-#90 := [mp #78 #89]: #87
-#858 := (* -1::Int #523)
-#860 := (+ #11 #858)
-#689 := (<= #860 0::Int)
-#517 := (= #860 0::Int)
-#539 := (* -1::Int #9)
-#829 := (div #539 -3::Int)
-#827 := (* -1::Int #829)
-#832 := (+ #11 #827)
-#823 := (= #832 0::Int)
-#861 := (<= #9 0::Int)
-#491 := (not #861)
-#647 := (>= #9 0::Int)
-#565 := (not #647)
-#833 := (or #565 #491)
-#824 := (ite #833 #517 #823)
-#515 := (= #9 0::Int)
-#706 := (not #515)
-#817 := (<= #11 0::Int)
-#865 := (= #11 0::Int)
-#740 := [hypothesis]: #515
-#713 := (or #706 #865)
-#826 := (ite #515 #865 #824)
-#20 := (:var 0 Int)
-#31 := (:var 1 Int)
-#32 := (f3 #31 #20)
-#887 := (pattern #32)
-#193 := (* -1::Int #20)
-#190 := (* -1::Int #31)
-#196 := (div #190 #193)
-#368 := (* -1::Int #196)
-#369 := (+ #32 #368)
-#370 := (= #369 0::Int)
-#42 := (div #31 #20)
-#365 := (* -1::Int #42)
-#366 := (+ #32 #365)
-#367 := (= #366 0::Int)
-#228 := (>= #31 0::Int)
-#221 := (<= #20 0::Int)
-#328 := (or #221 #228)
-#329 := (not #328)
-#217 := (<= #31 0::Int)
-#326 := (or #217 #221)
-#327 := (not #326)
-#332 := (or #327 #329)
-#371 := (ite #332 #367 #370)
-#364 := (= #32 0::Int)
-#34 := (= #20 0::Int)
-#33 := (= #31 0::Int)
-#35 := (or #33 #34)
-#372 := (ite #35 #364 #371)
-#888 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #887) #372)
-#375 := (forall (vars (?v0 Int) (?v1 Int)) #372)
-#891 := (iff #375 #888)
-#889 := (iff #372 #372)
-#890 := [refl]: #889
-#892 := [quant-intro #890]: #891
-#335 := (ite #332 #42 #196)
-#338 := (ite #35 0::Int #335)
-#341 := (= #32 #338)
-#344 := (forall (vars (?v0 Int) (?v1 Int)) #341)
-#376 := (iff #344 #375)
-#373 := (iff #341 #372)
-#374 := [rewrite]: #373
-#377 := [quant-intro #374]: #376
-#229 := (not #228)
-#222 := (not #221)
-#232 := (and #222 #229)
-#218 := (not #217)
-#225 := (and #218 #222)
-#235 := (or #225 #232)
-#238 := (ite #235 #42 #196)
-#241 := (ite #35 0::Int #238)
-#244 := (= #32 #241)
-#247 := (forall (vars (?v0 Int) (?v1 Int)) #244)
-#345 := (iff #247 #344)
-#342 := (iff #244 #341)
-#339 := (= #241 #338)
-#336 := (= #238 #335)
-#333 := (iff #235 #332)
-#330 := (iff #232 #329)
-#331 := [rewrite]: #330
-#311 := (iff #225 #327)
-#312 := [rewrite]: #311
-#334 := [monotonicity #312 #331]: #333
-#337 := [monotonicity #334]: #336
-#340 := [monotonicity #337]: #339
-#343 := [monotonicity #340]: #342
-#346 := [quant-intro #343]: #345
-#307 := (~ #247 #247)
-#320 := (~ #244 #244)
-#321 := [refl]: #320
-#308 := [nnf-pos #321]: #307
-#44 := (- #20)
-#43 := (- #31)
-#45 := (div #43 #44)
-#37 := (< 0::Int #20)
-#39 := (< #31 0::Int)
-#40 := (and #39 #37)
-#36 := (< 0::Int #31)
-#38 := (and #36 #37)
-#41 := (or #38 #40)
-#46 := (ite #41 #42 #45)
-#47 := (ite #35 0::Int #46)
-#48 := (= #32 #47)
-#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
-#250 := (iff #49 #247)
-#184 := (and #37 #39)
-#187 := (or #38 #184)
-#199 := (ite #187 #42 #196)
-#178 := (= 0::Int #20)
-#175 := (= 0::Int #31)
-#181 := (or #175 #178)
-#202 := (ite #181 0::Int #199)
-#205 := (= #32 #202)
-#208 := (forall (vars (?v0 Int) (?v1 Int)) #205)
-#248 := (iff #208 #247)
-#245 := (iff #205 #244)
-#242 := (= #202 #241)
-#239 := (= #199 #238)
-#236 := (iff #187 #235)
-#233 := (iff #184 #232)
-#230 := (iff #39 #229)
-#231 := [rewrite]: #230
-#223 := (iff #37 #222)
-#224 := [rewrite]: #223
-#234 := [monotonicity #224 #231]: #233
-#226 := (iff #38 #225)
-#219 := (iff #36 #218)
-#220 := [rewrite]: #219
-#227 := [monotonicity #220 #224]: #226
-#237 := [monotonicity #227 #234]: #236
-#240 := [monotonicity #237]: #239
-#215 := (iff #181 #35)
-#213 := (iff #178 #34)
-#214 := [rewrite]: #213
-#211 := (iff #175 #33)
-#212 := [rewrite]: #211
-#216 := [monotonicity #212 #214]: #215
-#243 := [monotonicity #216 #240]: #242
-#246 := [monotonicity #243]: #245
-#249 := [quant-intro #246]: #248
-#209 := (iff #49 #208)
-#206 := (iff #48 #205)
-#203 := (= #47 #202)
-#200 := (= #46 #199)
-#197 := (= #45 #196)
-#194 := (= #44 #193)
-#195 := [rewrite]: #194
-#191 := (= #43 #190)
-#192 := [rewrite]: #191
-#198 := [monotonicity #192 #195]: #197
-#188 := (iff #41 #187)
-#185 := (iff #40 #184)
-#186 := [rewrite]: #185
-#189 := [monotonicity #186]: #188
-#201 := [monotonicity #189 #198]: #200
-#182 := (iff #35 #181)
-#179 := (iff #34 #178)
-#180 := [rewrite]: #179
-#176 := (iff #33 #175)
-#177 := [rewrite]: #176
-#183 := [monotonicity #177 #180]: #182
-#204 := [monotonicity #183 #201]: #203
-#207 := [monotonicity #204]: #206
-#210 := [quant-intro #207]: #209
-#251 := [trans #210 #249]: #250
-#174 := [asserted]: #49
-#252 := [mp #174 #251]: #247
-#322 := [mp~ #252 #308]: #247
-#347 := [mp #322 #346]: #344
-#378 := [mp #347 #377]: #375
-#893 := [mp #378 #892]: #888
-#669 := (not #888)
-#811 := (or #669 #826)
-#538 := (* -1::Int 3::Int)
-#470 := (div #539 #538)
-#543 := (* -1::Int #470)
-#540 := (+ #11 #543)
-#544 := (= #540 0::Int)
-#854 := (<= 3::Int 0::Int)
-#528 := (or #854 #647)
-#529 := (not #528)
-#862 := (or #861 #854)
-#863 := (not #862)
-#864 := (or #863 #529)
-#859 := (ite #864 #517 #544)
-#855 := (= 3::Int 0::Int)
-#520 := (or #515 #855)
-#856 := (ite #520 #865 #859)
-#812 := (or #669 #856)
-#814 := (iff #812 #811)
-#809 := (iff #811 #811)
-#815 := [rewrite]: #809
-#667 := (iff #856 #826)
-#825 := (iff #859 #824)
-#818 := (iff #544 #823)
-#821 := (= #540 #832)
-#831 := (= #543 #827)
-#830 := (= #470 #829)
-#550 := (= #538 -3::Int)
-#551 := [rewrite]: #550
-#545 := [monotonicity #551]: #830
-#828 := [monotonicity #545]: #831
-#822 := [monotonicity #828]: #821
-#819 := [monotonicity #822]: #818
-#838 := (iff #864 #833)
-#836 := (or #491 #565)
-#837 := (iff #836 #833)
-#834 := [rewrite]: #837
-#558 := (iff #864 #836)
-#458 := (iff #529 #565)
-#563 := (iff #528 #647)
-#850 := (or false #647)
-#840 := (iff #850 #647)
-#562 := [rewrite]: #840
-#853 := (iff #528 #850)
-#844 := (iff #854 false)
-#845 := [rewrite]: #844
-#839 := [monotonicity #845]: #853
-#564 := [trans #839 #562]: #563
-#835 := [monotonicity #564]: #458
-#492 := (iff #863 #491)
-#849 := (iff #862 #861)
-#846 := (or #861 false)
-#848 := (iff #846 #861)
-#486 := [rewrite]: #848
-#847 := (iff #862 #846)
-#842 := [monotonicity #845]: #847
-#851 := [trans #842 #486]: #849
-#852 := [monotonicity #851]: #492
-#559 := [monotonicity #852 #835]: #558
-#548 := [trans #559 #834]: #838
-#820 := [monotonicity #548 #819]: #825
-#507 := (iff #520 #515)
-#500 := (or #515 false)
-#505 := (iff #500 #515)
-#506 := [rewrite]: #505
-#841 := (iff #520 #500)
-#516 := (iff #855 false)
-#857 := [rewrite]: #516
-#504 := [monotonicity #857]: #841
-#843 := [trans #504 #506]: #507
-#668 := [monotonicity #843 #820]: #667
-#808 := [monotonicity #668]: #814
-#816 := [trans #808 #815]: #814
-#813 := [quant-inst #9 #10]: #812
-#810 := [mp #813 #816]: #811
-#728 := [unit-resolution #810 #893]: #826
-#705 := (not #826)
-#707 := (or #705 #706 #865)
-#800 := [def-axiom]: #707
-#714 := [unit-resolution #800 #728]: #713
-#715 := [unit-resolution #714 #740]: #865
-#788 := (not #865)
-#608 := (or #788 #817)
-#758 := [th-lemma arith triangle-eq]: #608
-#674 := [unit-resolution #758 #715]: #817
-#675 := (or #706 #647)
-#676 := [th-lemma arith triangle-eq]: #675
-#677 := [unit-resolution #676 #740]: #647
-#678 := [th-lemma arith farkas -1 1 1 #677 #90 #674]: false
-#679 := [lemma #678]: #706
-#729 := (or #515 #824)
-#797 := (or #705 #515 #824)
-#801 := [def-axiom]: #797
-#725 := [unit-resolution #801 #728]: #729
-#651 := [unit-resolution #725 #679]: #824
-decl f6 :: (-> Int S2)
-#452 := (f6 #9)
-#791 := (f4 #452)
-#792 := (= #791 0::Int)
-#696 := (not #792)
-#697 := (iff #706 #696)
-#687 := (iff #515 #792)
-#683 := (iff #792 #515)
-#693 := (= #791 #9)
-#718 := (= #452 f5)
-#537 := (= f5 #452)
-#14 := (:var 0 S2)
-#15 := (f4 #14)
-#866 := (pattern #15)
-#16 := (f6 #15)
-#80 := (= #14 #16)
-#867 := (forall (vars (?v0 S2)) (:pat #866) #80)
-#93 := (forall (vars (?v0 S2)) #80)
-#868 := (iff #93 #867)
-#870 := (iff #867 #867)
-#871 := [rewrite]: #870
-#869 := [rewrite]: #868
-#872 := [trans #869 #871]: #868
-#315 := (~ #93 #93)
-#313 := (~ #80 #80)
-#314 := [refl]: #313
-#316 := [nnf-pos #314]: #315
-#17 := (= #16 #14)
-#18 := (forall (vars (?v0 S2)) #17)
-#94 := (iff #18 #93)
-#91 := (iff #17 #80)
-#92 := [rewrite]: #91
-#95 := [quant-intro #92]: #94
-#79 := [asserted]: #18
-#98 := [mp #79 #95]: #93
-#301 := [mp~ #98 #316]: #93
-#873 := [mp #301 #872]: #867
-#530 := (not #867)
-#541 := (or #530 #537)
-#542 := [quant-inst #8]: #541
-#712 := [unit-resolution #542 #873]: #537
-#686 := [symm #712]: #718
-#652 := [monotonicity #686]: #693
-#685 := [monotonicity #652]: #683
-#694 := [symm #685]: #687
-#698 := [monotonicity #694]: #697
-#653 := [mp #679 #698]: #696
-#789 := (or #647 #792)
-#22 := (f6 #20)
-#874 := (pattern #22)
-#114 := (>= #20 0::Int)
-#23 := (f4 #22)
-#28 := (= #23 0::Int)
-#163 := (or #28 #114)
-#881 := (forall (vars (?v0 Int)) (:pat #874) #163)
-#168 := (forall (vars (?v0 Int)) #163)
-#884 := (iff #168 #881)
-#882 := (iff #163 #163)
-#883 := [refl]: #882
-#885 := [quant-intro #883]: #884
-#305 := (~ #168 #168)
-#317 := (~ #163 #163)
-#318 := [refl]: #317
-#306 := [nnf-pos #318]: #305
-#27 := (< #20 0::Int)
-#29 := (implies #27 #28)
-#30 := (forall (vars (?v0 Int)) #29)
-#171 := (iff #30 #168)
-#134 := (= 0::Int #23)
-#140 := (not #27)
-#141 := (or #140 #134)
-#146 := (forall (vars (?v0 Int)) #141)
-#169 := (iff #146 #168)
-#166 := (iff #141 #163)
-#160 := (or #114 #28)
-#164 := (iff #160 #163)
-#165 := [rewrite]: #164
-#161 := (iff #141 #160)
-#158 := (iff #134 #28)
-#159 := [rewrite]: #158
-#156 := (iff #140 #114)
-#116 := (not #114)
-#151 := (not #116)
-#154 := (iff #151 #114)
-#155 := [rewrite]: #154
-#152 := (iff #140 #151)
-#149 := (iff #27 #116)
-#150 := [rewrite]: #149
-#153 := [monotonicity #150]: #152
-#157 := [trans #153 #155]: #156
-#162 := [monotonicity #157 #159]: #161
-#167 := [trans #162 #165]: #166
-#170 := [quant-intro #167]: #169
-#147 := (iff #30 #146)
-#144 := (iff #29 #141)
-#137 := (implies #27 #134)
-#142 := (iff #137 #141)
-#143 := [rewrite]: #142
-#138 := (iff #29 #137)
-#135 := (iff #28 #134)
-#136 := [rewrite]: #135
-#139 := [monotonicity #136]: #138
-#145 := [trans #139 #143]: #144
-#148 := [quant-intro #145]: #147
-#172 := [trans #148 #170]: #171
-#133 := [asserted]: #30
-#173 := [mp #133 #172]: #168
-#319 := [mp~ #173 #306]: #168
-#886 := [mp #319 #885]: #881
-#784 := (not #881)
-#785 := (or #784 #647 #792)
-#793 := (or #792 #647)
-#786 := (or #784 #793)
-#776 := (iff #786 #785)
-#787 := (or #784 #789)
-#774 := (iff #787 #785)
-#775 := [rewrite]: #774
-#771 := (iff #786 #787)
-#794 := (iff #793 #789)
-#783 := [rewrite]: #794
-#772 := [monotonicity #783]: #771
-#777 := [trans #772 #775]: #776
-#780 := [quant-inst #9]: #786
-#773 := [mp #780 #777]: #785
-#688 := [unit-resolution #773 #886]: #789
-#654 := [unit-resolution #688 #653]: #647
-#655 := (or #515 #491 #565)
-#657 := [th-lemma arith triangle-eq]: #655
-#658 := [unit-resolution #657 #654 #679]: #491
-#802 := (or #833 #861)
-#803 := [def-axiom]: #802
-#659 := [unit-resolution #803 #658]: #833
-#805 := (not #833)
-#700 := (not #824)
-#795 := (or #700 #805 #517)
-#796 := [def-axiom]: #795
-#660 := [unit-resolution #796 #659 #651]: #517
-#699 := (not #517)
-#692 := (or #699 #689)
-#716 := [th-lemma arith triangle-eq]: #692
-#661 := [unit-resolution #716 #660]: #689
-#663 := (not #689)
-#645 := (not #760)
-#633 := (or #662 #565 #645 #663 #83)
-#634 := [th-lemma arith assign-bounds 2 1 3 3]: #633
-#635 := [unit-resolution #634 #654 #661 #90 #670]: #662
-#726 := (not #750)
-#722 := (or #726 #759)
-#723 := [th-lemma arith triangle-eq]: #722
-[unit-resolution #723 #635 #721]: false
-unsat
-f4adf2827c5540d070c2e622505c61938b50a2ed 636 0
-#2 := false
-decl f3 :: (-> Int S2)
-decl f4 :: (-> Int Int Int)
-#10 := 3::Int
-decl f5 :: (-> S2 Int)
-decl f6 :: S2
-#8 := f6
-#9 := (f5 f6)
-#11 := (f4 #9 3::Int)
-#12 := (f3 #11)
-#83 := (= f6 #12)
-#14 := 0::Int
-#15 := (f3 0::Int)
-#932 := (= #15 #12)
-#930 := (= #12 #15)
-#819 := (= #11 0::Int)
-#822 := (= #9 0::Int)
-#867 := (f5 #15)
-#866 := (= #867 0::Int)
-#24 := (:var 0 Int)
-#26 := (f3 #24)
-#890 := (pattern #26)
-#130 := (>= #24 0::Int)
-#131 := (not #130)
-#27 := (f5 #26)
-#112 := (= #24 #27)
-#137 := (or #112 #131)
-#891 := (forall (vars (?v0 Int)) (:pat #890) #137)
-#142 := (forall (vars (?v0 Int)) #137)
-#894 := (iff #142 #891)
-#892 := (iff #137 #137)
-#893 := [refl]: #892
-#895 := [quant-intro #893]: #894
-#319 := (~ #142 #142)
-#318 := (~ #137 #137)
-#315 := [refl]: #318
-#320 := [nnf-pos #315]: #319
-#28 := (= #27 #24)
-#25 := (<= 0::Int #24)
-#29 := (implies #25 #28)
-#30 := (forall (vars (?v0 Int)) #29)
-#145 := (iff #30 #142)
-#119 := (not #25)
-#120 := (or #119 #112)
-#125 := (forall (vars (?v0 Int)) #120)
-#143 := (iff #125 #142)
-#140 := (iff #120 #137)
-#134 := (or #131 #112)
-#138 := (iff #134 #137)
-#139 := [rewrite]: #138
-#135 := (iff #120 #134)
-#132 := (iff #119 #131)
-#128 := (iff #25 #130)
-#129 := [rewrite]: #128
-#133 := [monotonicity #129]: #132
-#136 := [monotonicity #133]: #135
-#141 := [trans #136 #139]: #140
-#144 := [quant-intro #141]: #143
-#126 := (iff #30 #125)
-#123 := (iff #29 #120)
-#116 := (implies #25 #112)
-#121 := (iff #116 #120)
-#122 := [rewrite]: #121
-#117 := (iff #29 #116)
-#114 := (iff #28 #112)
+#82 := (* -1::Int #9)
+#87 := (div #82 -1::Int)
+#12 := 1::Int
+#21 := (div #9 1::Int)
+#10 := 0::Int
+#123 := (>= #9 0::Int)
+#124 := (not #123)
+#110 := (<= #9 0::Int)
+#111 := (not #110)
+#134 := (or #111 #124)
+#137 := (ite #134 #21 #87)
+#11 := (= #9 0::Int)
+#140 := (ite #11 0::Int #137)
+#143 := (f3 #140)
+#146 := (= f5 #143)
+#725 := (f3 #9)
+#688 := (= #725 #143)
+#691 := (= #143 #725)
+#411 := (= #140 #9)
+#602 := (= #9 #140)
+#510 := (* -1::Int #21)
+#663 := (+ #9 #510)
+#668 := (<= #663 0::Int)
+#509 := (= #663 0::Int)
+#1 := true
+#63 := [true-axiom]: true
+#653 := (or false #509)
+#654 := [th-lemma arith]: #653
+#650 := [unit-resolution #654 #63]: #509
+#655 := (not #509)
+#644 := (or #655 #668)
+#645 := [th-lemma arith triangle-eq]: #644
+#646 := [unit-resolution #645 #650]: #668
+#550 := (>= #663 0::Int)
+#647 := (or #655 #550)
+#641 := [th-lemma arith triangle-eq]: #647
+#648 := [unit-resolution #641 #650]: #550
+#643 := (* -1::Int #140)
+#640 := (+ #21 #643)
+#642 := (<= #640 0::Int)
+#651 := (= #21 #140)
+#398 := (= #137 #140)
+#389 := (not #11)
+#409 := (= 0::Int #9)
+#695 := [hypothesis]: #11
+#410 := [symm #695]: #409
+#313 := (= #140 0::Int)
+#390 := (or #389 #313)
+#722 := [def-axiom]: #390
+#699 := [unit-resolution #722 #695]: #313
+#412 := [trans #699 #410]: #411
+#406 := [monotonicity #412]: #691
+#692 := [symm #406]: #688
+#720 := (= f5 #725)
+#30 := (:var 0 S2)
+#31 := (f4 #30)
+#727 := (pattern #31)
+#32 := (f3 #31)
+#156 := (= #30 #32)
+#728 := (forall (vars (?v0 S2)) (:pat #727) #156)
+#159 := (forall (vars (?v0 S2)) #156)
+#729 := (iff #159 #728)
+#731 := (iff #728 #728)
+#732 := [rewrite]: #731
+#730 := [rewrite]: #729
+#733 := [trans #730 #732]: #729
+#253 := (~ #159 #159)
+#251 := (~ #156 #156)
+#252 := [refl]: #251
+#254 := [nnf-pos #252]: #253
+#33 := (= #32 #30)
+#34 := (forall (vars (?v0 S2)) #33)
+#160 := (iff #34 #159)
+#157 := (iff #33 #156)
+#158 := [rewrite]: #157
+#161 := [quant-intro #158]: #160
+#155 := [asserted]: #34
+#164 := [mp #155 #161]: #159
+#243 := [mp~ #164 #254]: #159
+#734 := [mp #243 #733]: #728
+#376 := (not #728)
+#381 := (or #376 #720)
+#717 := [quant-inst #8]: #381
+#690 := [unit-resolution #717 #734]: #720
+#689 := [trans #690 #692]: #146
+#149 := (not #146)
+#23 := (- 1::Int)
+#22 := (- #9)
+#24 := (div #22 #23)
+#16 := (< 0::Int 1::Int)
+#18 := (< #9 0::Int)
+#19 := (and #18 #16)
+#15 := (< 0::Int #9)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#13 := (= 1::Int 0::Int)
+#14 := (or #11 #13)
+#26 := (ite #14 0::Int #25)
+#27 := (f3 #26)
+#28 := (= #27 f5)
+#29 := (not #28)
+#152 := (iff #29 #149)
+#75 := (and #16 #18)
+#78 := (or #17 #75)
+#90 := (ite #78 #21 #87)
+#93 := (ite #11 0::Int #90)
+#96 := (f3 #93)
+#102 := (= f5 #96)
+#107 := (not #102)
+#150 := (iff #107 #149)
+#147 := (iff #102 #146)
+#144 := (= #96 #143)
+#141 := (= #93 #140)
+#138 := (= #90 #137)
+#135 := (iff #78 #134)
+#132 := (iff #75 #124)
+#127 := (and true #124)
+#130 := (iff #127 #124)
+#131 := [rewrite]: #130
+#128 := (iff #75 #127)
+#125 := (iff #18 #124)
+#126 := [rewrite]: #125
+#114 := (iff #16 true)
 #115 := [rewrite]: #114
-#118 := [monotonicity #115]: #117
-#124 := [trans #118 #122]: #123
-#127 := [quant-intro #124]: #126
-#146 := [trans #127 #144]: #145
-#111 := [asserted]: #30
-#147 := [mp #111 #146]: #142
-#316 := [mp~ #147 #320]: #142
-#896 := [mp #316 #895]: #891
-#880 := (not #891)
-#565 := (or #880 #866)
-#502 := (>= 0::Int 0::Int)
-#865 := (not #502)
-#507 := (= 0::Int #867)
-#508 := (or #507 #865)
-#566 := (or #880 #508)
-#845 := (iff #566 #565)
-#561 := (iff #565 #565)
-#843 := [rewrite]: #561
-#854 := (iff #508 #866)
-#574 := (or #866 false)
-#853 := (iff #574 #866)
-#850 := [rewrite]: #853
-#575 := (iff #508 #574)
-#851 := (iff #865 false)
-#1 := true
-#578 := (not true)
-#581 := (iff #578 false)
-#474 := [rewrite]: #581
-#579 := (iff #865 #578)
-#855 := (iff #502 true)
-#856 := [rewrite]: #855
-#580 := [monotonicity #856]: #579
-#852 := [trans #580 #474]: #851
-#868 := (iff #507 #866)
-#869 := [rewrite]: #868
-#849 := [monotonicity #869 #852]: #575
-#564 := [trans #849 #850]: #854
-#846 := [monotonicity #564]: #845
-#847 := [trans #846 #843]: #845
-#567 := [quant-inst #14]: #566
-#844 := [mp #567 #847]: #565
-#923 := [unit-resolution #844 #896]: #866
-#926 := (= #9 #867)
-#16 := (= f6 #15)
-#560 := (f3 #9)
-#918 := (= #560 #15)
-#473 := (= #15 #560)
-#471 := (= 0::Int #9)
-#544 := (f5 #12)
-#626 := (= #544 #9)
-#497 := (= #9 #544)
-#97 := (not #16)
-#570 := [hypothesis]: #97
-#555 := (or #83 #16)
-#98 := (iff #83 #97)
-#13 := (= #12 f6)
-#17 := (iff #13 #16)
-#18 := (not #17)
-#101 := (iff #18 #98)
-#89 := (iff #16 #83)
-#94 := (not #89)
-#99 := (iff #94 #98)
-#100 := [rewrite]: #99
-#95 := (iff #18 #94)
-#92 := (iff #17 #89)
-#86 := (iff #83 #16)
-#90 := (iff #86 #89)
-#91 := [rewrite]: #90
-#87 := (iff #17 #86)
-#84 := (iff #13 #83)
-#85 := [rewrite]: #84
-#88 := [monotonicity #85]: #87
-#93 := [trans #88 #91]: #92
-#96 := [monotonicity #93]: #95
-#102 := [trans #96 #100]: #101
-#82 := [asserted]: #18
-#105 := [mp #82 #102]: #98
-#468 := (not #98)
-#553 := (or #83 #16 #468)
-#554 := [def-axiom]: #553
-#546 := [unit-resolution #554 #105]: #555
-#562 := [unit-resolution #546 #570]: #83
-#498 := [monotonicity #562]: #497
-#477 := [symm #498]: #626
-#482 := (= 0::Int #544)
-#545 := (= #11 #544)
-#874 := (>= #11 0::Int)
-#557 := (not #83)
-#628 := (or #874 #557)
-#878 := (= #544 0::Int)
-#630 := (iff #878 #822)
-#623 := [hypothesis]: #83
-#625 := [symm #623]: #13
-#629 := [monotonicity #625]: #626
-#634 := [monotonicity #629]: #630
-#876 := (not #874)
-#647 := [hypothesis]: #876
-#532 := (or #874 #878)
-#32 := (= #27 0::Int)
-#178 := (or #32 #130)
-#897 := (forall (vars (?v0 Int)) (:pat #890) #178)
-#183 := (forall (vars (?v0 Int)) #178)
-#900 := (iff #183 #897)
-#898 := (iff #178 #178)
-#899 := [refl]: #898
-#901 := [quant-intro #899]: #900
-#321 := (~ #183 #183)
-#333 := (~ #178 #178)
-#334 := [refl]: #333
-#322 := [nnf-pos #334]: #321
-#31 := (< #24 0::Int)
-#33 := (implies #31 #32)
-#34 := (forall (vars (?v0 Int)) #33)
-#186 := (iff #34 #183)
-#149 := (= 0::Int #27)
-#155 := (not #31)
-#156 := (or #155 #149)
-#161 := (forall (vars (?v0 Int)) #156)
-#184 := (iff #161 #183)
-#181 := (iff #156 #178)
-#175 := (or #130 #32)
-#179 := (iff #175 #178)
-#180 := [rewrite]: #179
-#176 := (iff #156 #175)
-#173 := (iff #149 #32)
-#174 := [rewrite]: #173
-#171 := (iff #155 #130)
-#166 := (not #131)
-#169 := (iff #166 #130)
-#170 := [rewrite]: #169
-#167 := (iff #155 #166)
-#164 := (iff #31 #131)
-#165 := [rewrite]: #164
-#168 := [monotonicity #165]: #167
-#172 := [trans #168 #170]: #171
-#177 := [monotonicity #172 #174]: #176
-#182 := [trans #177 #180]: #181
-#185 := [quant-intro #182]: #184
-#162 := (iff #34 #161)
-#159 := (iff #33 #156)
-#152 := (implies #31 #149)
-#157 := (iff #152 #156)
-#158 := [rewrite]: #157
-#153 := (iff #33 #152)
-#150 := (iff #32 #149)
-#151 := [rewrite]: #150
-#154 := [monotonicity #151]: #153
-#160 := [trans #154 #158]: #159
-#163 := [quant-intro #160]: #162
-#187 := [trans #163 #185]: #186
-#148 := [asserted]: #34
-#188 := [mp #148 #187]: #183
-#335 := [mp~ #188 #322]: #183
-#902 := [mp #335 #901]: #897
-#857 := (not #897)
-#520 := (or #857 #874 #878)
-#879 := (or #878 #874)
-#521 := (or #857 #879)
-#863 := (iff #521 #520)
-#523 := (or #857 #532)
-#861 := (iff #523 #520)
-#862 := [rewrite]: #861
-#859 := (iff #521 #523)
-#873 := (iff #879 #532)
-#516 := [rewrite]: #873
-#860 := [monotonicity #516]: #859
-#858 := [trans #860 #862]: #863
-#522 := [quant-inst #11]: #521
-#864 := [mp #522 #858]: #520
-#643 := [unit-resolution #864 #902]: #532
-#633 := [unit-resolution #643 #647]: #878
-#627 := [mp #633 #634]: #822
-#740 := (not #822)
-#746 := (not #819)
-#645 := (or #746 #874)
-#648 := [th-lemma arith triangle-eq]: #645
-#636 := [unit-resolution #648 #647]: #746
-#641 := (or #740 #819)
-#788 := -3::Int
-#205 := -1::Int
-#842 := (* -1::Int #9)
-#792 := (div #842 -3::Int)
-#794 := (* -1::Int #792)
-#783 := (+ #11 #794)
-#782 := (= #783 0::Int)
-#828 := (div #9 3::Int)
-#829 := (* -1::Int #828)
-#830 := (+ #11 #829)
-#824 := (= #830 0::Int)
-#833 := (<= #9 0::Int)
-#723 := (not #833)
-#825 := (>= #9 0::Int)
-#808 := (not #825)
-#801 := (or #808 #723)
-#767 := (ite #801 #824 #782)
-#771 := (ite #822 #819 #767)
-#35 := (:var 1 Int)
-#36 := (f4 #35 #24)
-#903 := (pattern #36)
-#209 := (* -1::Int #24)
-#206 := (* -1::Int #35)
-#212 := (div #206 #209)
-#384 := (* -1::Int #212)
-#385 := (+ #36 #384)
-#386 := (= #385 0::Int)
-#46 := (div #35 #24)
-#381 := (* -1::Int #46)
-#382 := (+ #36 #381)
-#383 := (= #382 0::Int)
-#244 := (>= #35 0::Int)
-#237 := (<= #24 0::Int)
-#344 := (or #237 #244)
-#345 := (not #344)
-#233 := (<= #35 0::Int)
-#342 := (or #233 #237)
-#343 := (not #342)
-#348 := (or #343 #345)
-#387 := (ite #348 #383 #386)
-#380 := (= #36 0::Int)
-#38 := (= #24 0::Int)
-#37 := (= #35 0::Int)
-#39 := (or #37 #38)
-#388 := (ite #39 #380 #387)
-#904 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #903) #388)
-#391 := (forall (vars (?v0 Int) (?v1 Int)) #388)
-#907 := (iff #391 #904)
-#905 := (iff #388 #388)
-#906 := [refl]: #905
-#908 := [quant-intro #906]: #907
-#351 := (ite #348 #46 #212)
-#354 := (ite #39 0::Int #351)
-#357 := (= #36 #354)
-#360 := (forall (vars (?v0 Int) (?v1 Int)) #357)
-#392 := (iff #360 #391)
-#389 := (iff #357 #388)
-#390 := [rewrite]: #389
-#393 := [quant-intro #390]: #392
-#245 := (not #244)
-#238 := (not #237)
-#248 := (and #238 #245)
-#234 := (not #233)
-#241 := (and #234 #238)
-#251 := (or #241 #248)
-#254 := (ite #251 #46 #212)
-#257 := (ite #39 0::Int #254)
-#260 := (= #36 #257)
-#263 := (forall (vars (?v0 Int) (?v1 Int)) #260)
-#361 := (iff #263 #360)
-#358 := (iff #260 #357)
-#355 := (= #257 #354)
-#352 := (= #254 #351)
-#349 := (iff #251 #348)
-#346 := (iff #248 #345)
-#347 := [rewrite]: #346
-#327 := (iff #241 #343)
-#328 := [rewrite]: #327
-#350 := [monotonicity #328 #347]: #349
-#353 := [monotonicity #350]: #352
-#356 := [monotonicity #353]: #355
-#359 := [monotonicity #356]: #358
-#362 := [quant-intro #359]: #361
-#323 := (~ #263 #263)
-#336 := (~ #260 #260)
-#337 := [refl]: #336
-#324 := [nnf-pos #337]: #323
-#48 := (- #24)
-#47 := (- #35)
-#49 := (div #47 #48)
-#41 := (< 0::Int #24)
-#43 := (< #35 0::Int)
-#44 := (and #43 #41)
-#40 := (< 0::Int #35)
-#42 := (and #40 #41)
-#45 := (or #42 #44)
-#50 := (ite #45 #46 #49)
-#51 := (ite #39 0::Int #50)
-#52 := (= #36 #51)
-#53 := (forall (vars (?v0 Int) (?v1 Int)) #52)
-#266 := (iff #53 #263)
-#199 := (and #41 #43)
-#202 := (or #42 #199)
-#215 := (ite #202 #46 #212)
-#193 := (= 0::Int #24)
-#190 := (= 0::Int #35)
-#196 := (or #190 #193)
-#218 := (ite #196 0::Int #215)
-#221 := (= #36 #218)
-#224 := (forall (vars (?v0 Int) (?v1 Int)) #221)
-#264 := (iff #224 #263)
-#261 := (iff #221 #260)
-#258 := (= #218 #257)
-#255 := (= #215 #254)
-#252 := (iff #202 #251)
-#249 := (iff #199 #248)
-#246 := (iff #43 #245)
-#247 := [rewrite]: #246
-#239 := (iff #41 #238)
-#240 := [rewrite]: #239
-#250 := [monotonicity #240 #247]: #249
-#242 := (iff #42 #241)
-#235 := (iff #40 #234)
-#236 := [rewrite]: #235
-#243 := [monotonicity #236 #240]: #242
-#253 := [monotonicity #243 #250]: #252
-#256 := [monotonicity #253]: #255
-#231 := (iff #196 #39)
-#229 := (iff #193 #38)
-#230 := [rewrite]: #229
-#227 := (iff #190 #37)
-#228 := [rewrite]: #227
-#232 := [monotonicity #228 #230]: #231
-#259 := [monotonicity #232 #256]: #258
-#262 := [monotonicity #259]: #261
-#265 := [quant-intro #262]: #264
-#225 := (iff #53 #224)
-#222 := (iff #52 #221)
-#219 := (= #51 #218)
-#216 := (= #50 #215)
-#213 := (= #49 #212)
-#210 := (= #48 #209)
-#211 := [rewrite]: #210
-#207 := (= #47 #206)
-#208 := [rewrite]: #207
-#214 := [monotonicity #208 #211]: #213
-#203 := (iff #45 #202)
-#200 := (iff #44 #199)
-#201 := [rewrite]: #200
-#204 := [monotonicity #201]: #203
-#217 := [monotonicity #204 #214]: #216
-#197 := (iff #39 #196)
-#194 := (iff #38 #193)
-#195 := [rewrite]: #194
-#191 := (iff #37 #190)
-#192 := [rewrite]: #191
-#198 := [monotonicity #192 #195]: #197
-#220 := [monotonicity #198 #217]: #219
-#223 := [monotonicity #220]: #222
-#226 := [quant-intro #223]: #225
-#267 := [trans #226 #265]: #266
-#189 := [asserted]: #53
-#268 := [mp #189 #267]: #263
-#338 := [mp~ #268 #324]: #263
-#363 := [mp #338 #362]: #360
-#394 := [mp #363 #393]: #391
-#909 := [mp #394 #908]: #904
-#774 := (not #904)
-#775 := (or #774 #771)
-#836 := (* -1::Int 3::Int)
-#683 := (div #842 #836)
-#684 := (* -1::Int #683)
-#685 := (+ #11 #684)
-#827 := (= #685 0::Int)
-#831 := (<= 3::Int 0::Int)
-#832 := (or #831 #825)
-#826 := (not #832)
-#662 := (or #833 #831)
-#664 := (not #662)
-#665 := (or #664 #826)
-#818 := (ite #665 #824 #827)
-#821 := (= 3::Int 0::Int)
-#820 := (or #822 #821)
-#823 := (ite #820 #819 #818)
-#776 := (or #774 #823)
-#778 := (iff #776 #775)
-#779 := (iff #775 #775)
-#757 := [rewrite]: #779
-#772 := (iff #823 #771)
-#769 := (iff #818 #767)
-#786 := (iff #827 #782)
-#784 := (= #685 #783)
-#780 := (= #684 #794)
-#793 := (= #683 #792)
-#790 := (= #836 -3::Int)
-#791 := [rewrite]: #790
-#789 := [monotonicity #791]: #793
-#781 := [monotonicity #789]: #780
-#785 := [monotonicity #781]: #784
-#766 := [monotonicity #785]: #786
-#803 := (iff #665 #801)
-#810 := (or #723 #808)
-#802 := (iff #810 #801)
-#796 := [rewrite]: #802
-#799 := (iff #665 #810)
-#809 := (iff #826 #808)
-#797 := (iff #832 #825)
-#817 := (or false #825)
-#798 := (iff #817 #825)
-#795 := [rewrite]: #798
-#804 := (iff #832 #817)
-#700 := (iff #831 false)
-#715 := [rewrite]: #700
-#806 := [monotonicity #715]: #804
-#807 := [trans #806 #795]: #797
-#805 := [monotonicity #807]: #809
-#816 := (iff #664 #723)
-#721 := (iff #662 #833)
-#717 := (or #833 false)
-#719 := (iff #717 #833)
-#720 := [rewrite]: #719
-#718 := (iff #662 #717)
-#711 := [monotonicity #715]: #718
-#722 := [trans #711 #720]: #721
-#813 := [monotonicity #722]: #816
-#800 := [monotonicity #813 #805]: #799
-#787 := [trans #800 #796]: #803
-#770 := [monotonicity #787 #766]: #769
-#812 := (iff #820 #822)
-#707 := (or #822 false)
-#716 := (iff #707 #822)
-#811 := [rewrite]: #716
-#666 := (iff #820 #707)
-#705 := (iff #821 false)
-#706 := [rewrite]: #705
-#814 := [monotonicity #706]: #666
-#815 := [trans #814 #811]: #812
-#773 := [monotonicity #815 #770]: #772
-#768 := [monotonicity #773]: #778
-#758 := [trans #768 #757]: #778
-#777 := [quant-inst #9 #10]: #776
-#760 := [mp #777 #758]: #775
-#639 := [unit-resolution #760 #909]: #771
-#739 := (not #771)
-#743 := (or #739 #740 #819)
-#744 := [def-axiom]: #743
-#642 := [unit-resolution #744 #639]: #641
-#638 := [unit-resolution #642 #636]: #740
-#635 := [unit-resolution #638 #627]: false
-#631 := [lemma #635]: #628
-#571 := [unit-resolution #631 #562]: #874
-#877 := (or #545 #876)
-#875 := (or #880 #545 #876)
-#881 := (or #880 #877)
-#531 := (iff #881 #875)
-#536 := [rewrite]: #531
-#871 := [quant-inst #11]: #881
-#872 := [mp #871 #536]: #875
-#572 := [unit-resolution #872 #896]: #877
-#563 := [unit-resolution #572 #571]: #545
-#480 := (= 0::Int #11)
-#637 := (* -1::Int #11)
-#640 := (+ #9 #637)
-#646 := (>= #640 0::Int)
-#658 := (= #9 #11)
-#500 := (= #544 #11)
-#496 := [symm #563]: #500
-#501 := [trans #498 #496]: #658
-#483 := (not #658)
-#487 := (or #483 #646)
-#488 := [th-lemma arith triangle-eq]: #487
-#491 := [unit-resolution #488 #501]: #646
-#492 := (not #646)
-#493 := (or #825 #876 #492)
-#485 := [th-lemma arith assign-bounds 1 1]: #493
-#494 := [unit-resolution #485 #571 #491]: #825
-#644 := (<= #640 0::Int)
-#478 := (or #483 #644)
-#475 := [th-lemma arith triangle-eq]: #478
-#476 := [unit-resolution #475 #501]: #644
-#512 := (not #644)
-#489 := (or #819 #512 #808 #876)
-#613 := (* -3::Int #828)
-#748 := (mod #9 3::Int)
-#612 := (* -1::Int #748)
-#614 := (+ #612 #613)
-#615 := (+ #9 #614)
-#611 := (= #615 0::Int)
-#80 := [true-axiom]: true
-#573 := (or false #611)
-#540 := [th-lemma arith]: #573
-#542 := [unit-resolution #540 #80]: #611
-#597 := (>= #615 0::Int)
-#513 := (not #597)
-#598 := (>= #748 0::Int)
-#543 := (or false #598)
-#534 := [th-lemma arith]: #543
-#547 := [unit-resolution #534 #80]: #598
-#761 := (<= #11 0::Int)
-#550 := (not #761)
-#548 := [hypothesis]: #874
-#549 := [hypothesis]: #746
-#551 := (or #819 #550 #876)
-#541 := [th-lemma arith triangle-eq]: #551
-#552 := [unit-resolution #541 #549 #548]: #550
-#535 := [hypothesis]: #644
-#749 := (<= #830 0::Int)
-#537 := [unit-resolution #642 #549]: #740
-#538 := (or #822 #767)
-#745 := (or #739 #822 #767)
-#741 := [def-axiom]: #745
-#517 := [unit-resolution #741 #639]: #538
-#519 := [unit-resolution #517 #537]: #767
-#524 := [hypothesis]: #825
-#525 := (or #822 #723 #808)
-#526 := [th-lemma arith triangle-eq]: #525
-#527 := [unit-resolution #526 #537 #524]: #723
-#764 := (or #801 #833)
-#759 := [def-axiom]: #764
-#528 := [unit-resolution #759 #527]: #801
-#765 := (not #801)
-#750 := (not #767)
-#756 := (or #750 #765 #824)
-#729 := [def-axiom]: #756
-#529 := [unit-resolution #729 #528 #519]: #824
-#624 := (not #824)
-#518 := (or #624 #749)
-#530 := [th-lemma arith triangle-eq]: #518
-#511 := [unit-resolution #530 #529]: #749
-#515 := (not #749)
-#514 := (not #598)
-#503 := (or #513 #514 #761 #512 #515)
-#505 := [th-lemma arith assign-bounds 1 2 1 3]: #503
-#506 := [unit-resolution #505 #511 #535 #552 #547]: #513
-#509 := (not #611)
-#504 := (or #509 #597)
-#510 := [th-lemma arith triangle-eq]: #504
-#484 := [unit-resolution #510 #506 #542]: false
-#490 := [lemma #484]: #489
-#479 := [unit-resolution #490 #476 #494 #571]: #819
-#481 := [symm #479]: #480
-#469 := [trans #481 #563]: #482
-#472 := [trans #469 #477]: #471
-#917 := [monotonicity #472]: #473
-#919 := [symm #917]: #918
-#539 := (= f6 #560)
-#19 := (:var 0 S2)
-#20 := (f5 #19)
-#882 := (pattern #20)
-#21 := (f3 #20)
-#104 := (= #19 #21)
-#883 := (forall (vars (?v0 S2)) (:pat #882) #104)
-#108 := (forall (vars (?v0 S2)) #104)
-#884 := (iff #108 #883)
-#886 := (iff #883 #883)
-#887 := [rewrite]: #886
-#885 := [rewrite]: #884
-#888 := [trans #885 #887]: #884
-#331 := (~ #108 #108)
-#329 := (~ #104 #104)
-#330 := [refl]: #329
-#332 := [nnf-pos #330]: #331
-#22 := (= #21 #19)
-#23 := (forall (vars (?v0 S2)) #22)
-#109 := (iff #23 #108)
-#106 := (iff #22 #104)
-#107 := [rewrite]: #106
-#110 := [quant-intro #107]: #109
-#103 := [asserted]: #23
-#113 := [mp #103 #110]: #108
-#317 := [mp~ #113 #332]: #108
-#889 := [mp #317 #888]: #883
-#533 := (not #883)
-#663 := (or #533 #539)
-#870 := [quant-inst #8]: #663
-#470 := [unit-resolution #870 #889]: #539
-#920 := [trans #470 #919]: #16
-#921 := [unit-resolution #570 #920]: false
-#922 := [lemma #921]: #16
-#927 := [monotonicity #922]: #926
-#928 := [trans #927 #923]: #822
-#929 := [unit-resolution #642 #928]: #819
-#931 := [monotonicity #929]: #930
-#933 := [symm #931]: #932
-#934 := [trans #922 #933]: #83
-#559 := (or #557 #97)
-#558 := (or #557 #97 #468)
-#486 := [def-axiom]: #558
-#556 := [unit-resolution #486 #105]: #559
-#495 := [unit-resolution #556 #922]: #557
-[unit-resolution #495 #934]: false
-unsat
-2e39fe3f9575e15a240203df63c5032154a66535 279 0
+#129 := [monotonicity #115 #126]: #128
+#133 := [trans #129 #131]: #132
+#121 := (iff #17 #111)
+#116 := (and #111 true)
+#119 := (iff #116 #111)
+#120 := [rewrite]: #119
+#117 := (iff #17 #116)
+#112 := (iff #15 #111)
+#113 := [rewrite]: #112
+#118 := [monotonicity #113 #115]: #117
+#122 := [trans #118 #120]: #121
+#136 := [monotonicity #122 #133]: #135
+#139 := [monotonicity #136]: #138
+#142 := [monotonicity #139]: #141
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#151 := [monotonicity #148]: #150
+#108 := (iff #29 #107)
+#105 := (iff #28 #102)
+#99 := (= #96 f5)
+#103 := (iff #99 #102)
+#104 := [rewrite]: #103
+#100 := (iff #28 #99)
+#97 := (= #27 #96)
+#94 := (= #26 #93)
+#91 := (= #25 #90)
+#88 := (= #24 #87)
+#85 := (= #23 -1::Int)
+#86 := [rewrite]: #85
+#83 := (= #22 #82)
+#84 := [rewrite]: #83
+#89 := [monotonicity #84 #86]: #88
+#79 := (iff #20 #78)
+#76 := (iff #19 #75)
+#77 := [rewrite]: #76
+#80 := [monotonicity #77]: #79
+#92 := [monotonicity #80 #89]: #91
+#73 := (iff #14 #11)
+#68 := (or #11 false)
+#71 := (iff #68 #11)
+#72 := [rewrite]: #71
+#69 := (iff #14 #68)
+#66 := (iff #13 false)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#74 := [trans #70 #72]: #73
+#95 := [monotonicity #74 #92]: #94
+#98 := [monotonicity #95]: #97
+#101 := [monotonicity #98]: #100
+#106 := [trans #101 #104]: #105
+#109 := [monotonicity #106]: #108
+#153 := [trans #109 #151]: #152
+#65 := [asserted]: #29
+#154 := [mp #65 #153]: #149
+#693 := [unit-resolution #154 #689]: false
+#682 := [lemma #693]: #389
+#723 := (or #11 #398)
+#724 := [def-axiom]: #723
+#632 := [unit-resolution #724 #682]: #398
+#314 := (= #21 #137)
+#708 := (f4 #725)
+#703 := (= #708 0::Int)
+#626 := (not #703)
+#628 := (iff #389 #626)
+#639 := (iff #11 #703)
+#638 := (iff #703 #11)
+#636 := (= #708 #9)
+#633 := (= #725 f5)
+#635 := [symm #690]: #633
+#637 := [monotonicity #635]: #636
+#634 := [monotonicity #637]: #638
+#625 := [symm #634]: #639
+#629 := [monotonicity #625]: #628
+#630 := [mp #682 #629]: #626
+#714 := (or #123 #703)
+#35 := (:var 0 Int)
+#37 := (f3 #35)
+#735 := (pattern #37)
+#180 := (>= #35 0::Int)
+#38 := (f4 #37)
+#43 := (= #38 0::Int)
+#229 := (or #43 #180)
+#742 := (forall (vars (?v0 Int)) (:pat #735) #229)
+#234 := (forall (vars (?v0 Int)) #229)
+#745 := (iff #234 #742)
+#743 := (iff #229 #229)
+#744 := [refl]: #743
+#746 := [quant-intro #744]: #745
+#247 := (~ #234 #234)
+#255 := (~ #229 #229)
+#256 := [refl]: #255
+#248 := [nnf-pos #256]: #247
+#42 := (< #35 0::Int)
+#44 := (implies #42 #43)
+#45 := (forall (vars (?v0 Int)) #44)
+#237 := (iff #45 #234)
+#200 := (= 0::Int #38)
+#206 := (not #42)
+#207 := (or #206 #200)
+#212 := (forall (vars (?v0 Int)) #207)
+#235 := (iff #212 #234)
+#232 := (iff #207 #229)
+#226 := (or #180 #43)
+#230 := (iff #226 #229)
+#231 := [rewrite]: #230
+#227 := (iff #207 #226)
+#224 := (iff #200 #43)
+#225 := [rewrite]: #224
+#222 := (iff #206 #180)
+#182 := (not #180)
+#217 := (not #182)
+#220 := (iff #217 #180)
+#221 := [rewrite]: #220
+#218 := (iff #206 #217)
+#215 := (iff #42 #182)
+#216 := [rewrite]: #215
+#219 := [monotonicity #216]: #218
+#223 := [trans #219 #221]: #222
+#228 := [monotonicity #223 #225]: #227
+#233 := [trans #228 #231]: #232
+#236 := [quant-intro #233]: #235
+#213 := (iff #45 #212)
+#210 := (iff #44 #207)
+#203 := (implies #42 #200)
+#208 := (iff #203 #207)
+#209 := [rewrite]: #208
+#204 := (iff #44 #203)
+#201 := (iff #43 #200)
+#202 := [rewrite]: #201
+#205 := [monotonicity #202]: #204
+#211 := [trans #205 #209]: #210
+#214 := [quant-intro #211]: #213
+#238 := [trans #214 #236]: #237
+#199 := [asserted]: #45
+#239 := [mp #199 #238]: #234
+#257 := [mp~ #239 #248]: #234
+#747 := [mp #257 #746]: #742
+#709 := (not #742)
+#423 := (or #709 #123 #703)
+#711 := (or #703 #123)
+#424 := (or #709 #711)
+#420 := (iff #424 #423)
+#426 := (or #709 #714)
+#697 := (iff #426 #423)
+#419 := [rewrite]: #697
+#320 := (iff #424 #426)
+#700 := (iff #711 #714)
+#701 := [rewrite]: #700
+#696 := [monotonicity #701]: #320
+#694 := [trans #696 #419]: #420
+#425 := [quant-inst #9]: #424
+#698 := [mp #425 #694]: #423
+#627 := [unit-resolution #698 #747]: #714
+#631 := [unit-resolution #627 #630]: #123
+#611 := (or #11 #111 #124)
+#612 := [th-lemma arith triangle-eq]: #611
+#614 := [unit-resolution #612 #682]: #134
+#615 := [unit-resolution #614 #631]: #111
+#400 := (or #134 #110)
+#391 := [def-axiom]: #400
+#616 := [unit-resolution #391 #615]: #134
+#404 := (not #134)
+#721 := (or #404 #314)
+#378 := [def-axiom]: #721
+#617 := [unit-resolution #378 #616]: #314
+#618 := [trans #617 #632]: #651
+#619 := (not #651)
+#620 := (or #619 #642)
+#621 := [th-lemma arith triangle-eq]: #620
+#622 := [unit-resolution #621 #618]: #642
+#652 := (>= #640 0::Int)
+#623 := (or #619 #652)
+#613 := [th-lemma arith triangle-eq]: #623
+#624 := [unit-resolution #613 #618]: #652
+#603 := [th-lemma arith eq-propagate 1 1 1 1 #624 #622 #648 #646]: #602
+#605 := [symm #603]: #411
+#606 := [monotonicity #605]: #691
+#607 := [symm #606]: #688
+#608 := [trans #690 #607]: #146
+[unit-resolution #154 #608]: false
+unsat
+527e5e3123950986e94b94da9ebd83dc07302cc9 81 0
 #2 := false
 decl f3 :: (-> Int S2)
 #8 := 0::Int
-#11 := (f3 0::Int)
-decl f4 :: (-> Int Int Int)
-#9 := (f4 0::Int 0::Int)
-#10 := (f3 #9)
-#12 := (= #10 #11)
-#804 := (= #9 0::Int)
-#19 := (:var 0 Int)
-#30 := (:var 1 Int)
-#49 := (f4 #30 #19)
-#884 := (pattern #49)
-#179 := -1::Int
-#183 := (* -1::Int #19)
-#180 := (* -1::Int #30)
-#244 := (mod #180 #183)
-#374 := (+ #49 #244)
-#375 := (= #374 0::Int)
-#50 := (mod #30 #19)
-#371 := (* -1::Int #50)
-#372 := (+ #49 #371)
-#373 := (= #372 0::Int)
-#218 := (>= #30 0::Int)
-#211 := (<= #19 0::Int)
-#318 := (or #211 #218)
-#319 := (not #318)
-#207 := (<= #30 0::Int)
-#316 := (or #207 #211)
-#317 := (not #316)
-#322 := (or #317 #319)
-#376 := (ite #322 #373 #375)
-#370 := (= #49 0::Int)
-#32 := (= #30 0::Int)
-#377 := (ite #32 #370 #376)
-#369 := (= #30 #49)
-#33 := (= #19 0::Int)
-#378 := (ite #33 #369 #377)
-#885 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #884) #378)
-#381 := (forall (vars (?v0 Int) (?v1 Int)) #378)
-#888 := (iff #381 #885)
-#886 := (iff #378 #378)
-#887 := [refl]: #886
-#889 := [quant-intro #887]: #888
-#250 := (* -1::Int #244)
-#338 := (ite #322 #50 #250)
-#341 := (ite #32 0::Int #338)
-#344 := (ite #33 #30 #341)
-#347 := (= #49 #344)
-#350 := (forall (vars (?v0 Int) (?v1 Int)) #347)
-#382 := (iff #350 #381)
-#379 := (iff #347 #378)
-#380 := [rewrite]: #379
-#383 := [quant-intro #380]: #382
-#219 := (not #218)
-#212 := (not #211)
-#222 := (and #212 #219)
-#208 := (not #207)
-#215 := (and #208 #212)
-#225 := (or #215 #222)
-#270 := (ite #225 #50 #250)
-#273 := (ite #32 0::Int #270)
-#276 := (ite #33 #30 #273)
-#279 := (= #49 #276)
-#282 := (forall (vars (?v0 Int) (?v1 Int)) #279)
-#351 := (iff #282 #350)
-#348 := (iff #279 #347)
-#345 := (= #276 #344)
-#342 := (= #273 #341)
-#339 := (= #270 #338)
-#323 := (iff #225 #322)
-#320 := (iff #222 #319)
-#321 := [rewrite]: #320
-#301 := (iff #215 #317)
-#302 := [rewrite]: #301
-#324 := [monotonicity #302 #321]: #323
-#340 := [monotonicity #324]: #339
-#343 := [monotonicity #340]: #342
-#346 := [monotonicity #343]: #345
-#349 := [monotonicity #346]: #348
-#352 := [quant-intro #349]: #351
-#299 := (~ #282 #282)
-#313 := (~ #279 #279)
-#314 := [refl]: #313
-#300 := [nnf-pos #314]: #299
-#43 := (- #19)
-#42 := (- #30)
-#51 := (mod #42 #43)
-#52 := (- #51)
-#36 := (< 0::Int #19)
-#38 := (< #30 0::Int)
-#39 := (and #38 #36)
-#35 := (< 0::Int #30)
-#37 := (and #35 #36)
-#40 := (or #37 #39)
-#53 := (ite #40 #50 #52)
-#54 := (ite #32 0::Int #53)
-#55 := (ite #33 #30 #54)
-#56 := (= #49 #55)
-#57 := (forall (vars (?v0 Int) (?v1 Int)) #56)
-#285 := (iff #57 #282)
-#173 := (and #36 #38)
-#176 := (or #37 #173)
-#255 := (ite #176 #50 #250)
-#164 := (= 0::Int #30)
-#258 := (ite #164 0::Int #255)
-#167 := (= 0::Int #19)
-#261 := (ite #167 #30 #258)
-#264 := (= #49 #261)
-#267 := (forall (vars (?v0 Int) (?v1 Int)) #264)
-#283 := (iff #267 #282)
-#280 := (iff #264 #279)
-#277 := (= #261 #276)
-#274 := (= #258 #273)
-#271 := (= #255 #270)
-#226 := (iff #176 #225)
-#223 := (iff #173 #222)
-#220 := (iff #38 #219)
-#221 := [rewrite]: #220
-#213 := (iff #36 #212)
-#214 := [rewrite]: #213
-#224 := [monotonicity #214 #221]: #223
-#216 := (iff #37 #215)
-#209 := (iff #35 #208)
-#210 := [rewrite]: #209
-#217 := [monotonicity #210 #214]: #216
-#227 := [monotonicity #217 #224]: #226
-#272 := [monotonicity #227]: #271
-#201 := (iff #164 #32)
-#202 := [rewrite]: #201
-#275 := [monotonicity #202 #272]: #274
-#203 := (iff #167 #33)
-#204 := [rewrite]: #203
-#278 := [monotonicity #204 #275]: #277
-#281 := [monotonicity #278]: #280
-#284 := [quant-intro #281]: #283
-#268 := (iff #57 #267)
-#265 := (iff #56 #264)
-#262 := (= #55 #261)
-#259 := (= #54 #258)
-#256 := (= #53 #255)
-#253 := (= #52 #250)
-#247 := (- #244)
-#251 := (= #247 #250)
-#252 := [rewrite]: #251
-#248 := (= #52 #247)
-#245 := (= #51 #244)
-#184 := (= #43 #183)
-#185 := [rewrite]: #184
-#181 := (= #42 #180)
-#182 := [rewrite]: #181
-#246 := [monotonicity #182 #185]: #245
-#249 := [monotonicity #246]: #248
-#254 := [trans #249 #252]: #253
-#177 := (iff #40 #176)
-#174 := (iff #39 #173)
-#175 := [rewrite]: #174
-#178 := [monotonicity #175]: #177
-#257 := [monotonicity #178 #254]: #256
-#165 := (iff #32 #164)
-#166 := [rewrite]: #165
-#260 := [monotonicity #166 #257]: #259
-#168 := (iff #33 #167)
-#169 := [rewrite]: #168
-#263 := [monotonicity #169 #260]: #262
-#266 := [monotonicity #263]: #265
-#269 := [quant-intro #266]: #268
-#286 := [trans #269 #284]: #285
-#243 := [asserted]: #57
-#287 := [mp #243 #286]: #282
-#315 := [mp~ #287 #300]: #282
-#353 := [mp #315 #352]: #350
-#384 := [mp #353 #383]: #381
-#890 := [mp #384 #889]: #885
-#760 := (not #885)
-#740 := (or #760 #804)
-#811 := (* -1::Int 0::Int)
-#812 := (mod #811 #811)
-#813 := (+ #9 #812)
-#808 := (= #813 0::Int)
-#809 := (mod 0::Int 0::Int)
-#814 := (* -1::Int #809)
-#815 := (+ #9 #814)
-#810 := (= #815 0::Int)
-#833 := (>= 0::Int 0::Int)
-#816 := (<= 0::Int 0::Int)
-#657 := (or #816 #833)
-#658 := (not #657)
-#659 := (or #816 #816)
-#801 := (not #659)
-#802 := (or #801 #658)
-#803 := (ite #802 #810 #808)
-#798 := (= 0::Int 0::Int)
-#799 := (ite #798 #804 #803)
-#805 := (= 0::Int #9)
-#806 := (ite #798 #805 #799)
-#741 := (or #760 #806)
-#744 := (iff #741 #740)
-#746 := (iff #740 #740)
-#747 := [rewrite]: #746
-#759 := (iff #806 #804)
-#1 := true
-#768 := (ite true #804 #804)
-#757 := (iff #768 #804)
-#758 := [rewrite]: #757
-#754 := (iff #806 #768)
-#767 := (iff #799 #804)
-#769 := (+ #9 #809)
-#782 := (= #769 0::Int)
-#761 := (ite true #804 #782)
-#765 := (iff #761 #804)
-#766 := [rewrite]: #765
-#762 := (iff #799 #761)
-#770 := (iff #803 #782)
-#784 := (ite false #810 #782)
-#775 := (iff #784 #782)
-#776 := [rewrite]: #775
-#773 := (iff #803 #784)
-#783 := (iff #808 #782)
-#771 := (= #813 #769)
-#780 := (= #812 #809)
-#791 := (= #811 0::Int)
-#778 := [rewrite]: #791
-#772 := [monotonicity #778 #778]: #780
-#781 := [monotonicity #772]: #771
-#779 := [monotonicity #781]: #783
-#790 := (iff #802 false)
-#693 := (or false false)
-#696 := (iff #693 false)
-#697 := [rewrite]: #696
-#694 := (iff #802 #693)
-#692 := (iff #658 false)
-#481 := (not true)
-#840 := (iff #481 false)
-#843 := [rewrite]: #840
-#689 := (iff #658 #481)
-#789 := (iff #657 true)
-#793 := (or true true)
-#794 := (iff #793 true)
-#797 := [rewrite]: #794
-#785 := (iff #657 #793)
-#839 := (iff #833 true)
-#841 := [rewrite]: #839
-#639 := (iff #816 true)
-#792 := [rewrite]: #639
-#786 := [monotonicity #792 #841]: #785
-#674 := [trans #786 #797]: #789
-#691 := [monotonicity #674]: #689
-#685 := [trans #691 #843]: #692
-#788 := (iff #801 false)
-#681 := (iff #801 #481)
-#679 := (iff #659 true)
-#795 := (iff #659 #793)
-#796 := [monotonicity #792 #792]: #795
-#680 := [trans #796 #797]: #679
-#640 := [monotonicity #680]: #681
-#690 := [trans #640 #843]: #788
-#695 := [monotonicity #690 #685]: #694
-#787 := [trans #695 #697]: #790
-#774 := [monotonicity #787 #779]: #773
-#777 := [trans #774 #776]: #770
-#800 := (iff #798 true)
-#807 := [rewrite]: #800
-#764 := [monotonicity #807 #777]: #762
-#763 := [trans #764 #766]: #767
-#636 := (iff #805 #804)
-#638 := [rewrite]: #636
-#755 := [monotonicity #807 #638 #763]: #754
-#756 := [trans #755 #758]: #759
-#745 := [monotonicity #756]: #744
-#748 := [trans #745 #747]: #744
-#743 := [quant-inst #8 #8]: #741
-#749 := [mp #743 #748]: #740
-#751 := [unit-resolution #749 #890]: #804
-#752 := [monotonicity #751]: #12
-#13 := (not #12)
-#77 := [asserted]: #13
-[unit-resolution #77 #752]: false
-unsat
-eaf623ea6157604982b5732ebda9f473145c7bd3 326 0
-#2 := false
-decl f3 :: (-> Int S2)
-decl f4 :: (-> Int Int Int)
-#10 := 0::Int
-decl f5 :: (-> S2 Int)
-decl f6 :: S2
-#8 := f6
-#9 := (f5 f6)
-#11 := (f4 #9 0::Int)
-#12 := (f3 #11)
-#79 := (= f6 #12)
-#450 := (f3 #9)
-#785 := (= #450 #12)
-#784 := (= #12 #450)
-#781 := (= #11 #9)
-#831 := (= #9 #11)
-#20 := (:var 0 Int)
-#31 := (:var 1 Int)
-#50 := (f4 #31 #20)
-#892 := (pattern #50)
-#187 := -1::Int
-#191 := (* -1::Int #20)
-#188 := (* -1::Int #31)
-#252 := (mod #188 #191)
-#382 := (+ #50 #252)
-#383 := (= #382 0::Int)
-#51 := (mod #31 #20)
-#379 := (* -1::Int #51)
-#380 := (+ #50 #379)
-#381 := (= #380 0::Int)
-#226 := (>= #31 0::Int)
-#219 := (<= #20 0::Int)
-#326 := (or #219 #226)
-#327 := (not #326)
-#215 := (<= #31 0::Int)
-#324 := (or #215 #219)
-#325 := (not #324)
-#330 := (or #325 #327)
-#384 := (ite #330 #381 #383)
-#378 := (= #50 0::Int)
-#33 := (= #31 0::Int)
-#385 := (ite #33 #378 #384)
-#377 := (= #31 #50)
-#34 := (= #20 0::Int)
-#386 := (ite #34 #377 #385)
-#893 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #892) #386)
-#389 := (forall (vars (?v0 Int) (?v1 Int)) #386)
-#896 := (iff #389 #893)
-#894 := (iff #386 #386)
-#895 := [refl]: #894
-#897 := [quant-intro #895]: #896
-#258 := (* -1::Int #252)
-#346 := (ite #330 #51 #258)
-#349 := (ite #33 0::Int #346)
-#352 := (ite #34 #31 #349)
-#355 := (= #50 #352)
-#358 := (forall (vars (?v0 Int) (?v1 Int)) #355)
-#390 := (iff #358 #389)
-#387 := (iff #355 #386)
-#388 := [rewrite]: #387
-#391 := [quant-intro #388]: #390
-#227 := (not #226)
-#220 := (not #219)
-#230 := (and #220 #227)
-#216 := (not #215)
-#223 := (and #216 #220)
-#233 := (or #223 #230)
-#278 := (ite #233 #51 #258)
-#281 := (ite #33 0::Int #278)
-#284 := (ite #34 #31 #281)
-#287 := (= #50 #284)
-#290 := (forall (vars (?v0 Int) (?v1 Int)) #287)
-#359 := (iff #290 #358)
-#356 := (iff #287 #355)
-#353 := (= #284 #352)
-#350 := (= #281 #349)
-#347 := (= #278 #346)
-#331 := (iff #233 #330)
-#328 := (iff #230 #327)
-#329 := [rewrite]: #328
-#309 := (iff #223 #325)
-#310 := [rewrite]: #309
-#332 := [monotonicity #310 #329]: #331
-#348 := [monotonicity #332]: #347
-#351 := [monotonicity #348]: #350
-#354 := [monotonicity #351]: #353
-#357 := [monotonicity #354]: #356
-#360 := [quant-intro #357]: #359
-#307 := (~ #290 #290)
-#321 := (~ #287 #287)
-#322 := [refl]: #321
-#308 := [nnf-pos #322]: #307
-#44 := (- #20)
-#43 := (- #31)
-#52 := (mod #43 #44)
-#53 := (- #52)
-#37 := (< 0::Int #20)
-#39 := (< #31 0::Int)
-#40 := (and #39 #37)
-#36 := (< 0::Int #31)
-#38 := (and #36 #37)
-#41 := (or #38 #40)
-#54 := (ite #41 #51 #53)
-#55 := (ite #33 0::Int #54)
-#56 := (ite #34 #31 #55)
-#57 := (= #50 #56)
-#58 := (forall (vars (?v0 Int) (?v1 Int)) #57)
-#293 := (iff #58 #290)
-#181 := (and #37 #39)
-#184 := (or #38 #181)
-#263 := (ite #184 #51 #258)
-#172 := (= 0::Int #31)
-#266 := (ite #172 0::Int #263)
-#175 := (= 0::Int #20)
-#269 := (ite #175 #31 #266)
-#272 := (= #50 #269)
-#275 := (forall (vars (?v0 Int) (?v1 Int)) #272)
-#291 := (iff #275 #290)
-#288 := (iff #272 #287)
-#285 := (= #269 #284)
-#282 := (= #266 #281)
-#279 := (= #263 #278)
-#234 := (iff #184 #233)
-#231 := (iff #181 #230)
-#228 := (iff #39 #227)
-#229 := [rewrite]: #228
-#221 := (iff #37 #220)
-#222 := [rewrite]: #221
-#232 := [monotonicity #222 #229]: #231
-#224 := (iff #38 #223)
-#217 := (iff #36 #216)
-#218 := [rewrite]: #217
-#225 := [monotonicity #218 #222]: #224
-#235 := [monotonicity #225 #232]: #234
-#280 := [monotonicity #235]: #279
-#209 := (iff #172 #33)
-#210 := [rewrite]: #209
-#283 := [monotonicity #210 #280]: #282
-#211 := (iff #175 #34)
-#212 := [rewrite]: #211
-#286 := [monotonicity #212 #283]: #285
-#289 := [monotonicity #286]: #288
-#292 := [quant-intro #289]: #291
-#276 := (iff #58 #275)
-#273 := (iff #57 #272)
-#270 := (= #56 #269)
-#267 := (= #55 #266)
-#264 := (= #54 #263)
-#261 := (= #53 #258)
-#255 := (- #252)
-#259 := (= #255 #258)
-#260 := [rewrite]: #259
-#256 := (= #53 #255)
-#253 := (= #52 #252)
-#192 := (= #44 #191)
-#193 := [rewrite]: #192
-#189 := (= #43 #188)
-#190 := [rewrite]: #189
-#254 := [monotonicity #190 #193]: #253
-#257 := [monotonicity #254]: #256
-#262 := [trans #257 #260]: #261
-#185 := (iff #41 #184)
-#182 := (iff #40 #181)
-#183 := [rewrite]: #182
-#186 := [monotonicity #183]: #185
-#265 := [monotonicity #186 #262]: #264
-#173 := (iff #33 #172)
-#174 := [rewrite]: #173
-#268 := [monotonicity #174 #265]: #267
-#176 := (iff #34 #175)
-#177 := [rewrite]: #176
-#271 := [monotonicity #177 #268]: #270
-#274 := [monotonicity #271]: #273
-#277 := [quant-intro #274]: #276
-#294 := [trans #277 #292]: #293
-#251 := [asserted]: #58
-#295 := [mp #251 #294]: #290
-#323 := [mp~ #295 #308]: #290
-#361 := [mp #323 #360]: #358
-#392 := [mp #361 #391]: #389
-#898 := [mp #392 #897]: #893
-#799 := (not #893)
-#786 := (or #799 #831)
-#840 := (* -1::Int 0::Int)
-#846 := (* -1::Int #9)
-#484 := (mod #846 #840)
-#847 := (+ #11 #484)
-#849 := (= #847 0::Int)
-#489 := (mod #9 0::Int)
-#490 := (* -1::Int #489)
-#850 := (+ #11 #490)
-#848 := (= #850 0::Int)
-#851 := (>= #9 0::Int)
-#837 := (<= 0::Int 0::Int)
-#838 := (or #837 #851)
-#560 := (not #838)
-#561 := (<= #9 0::Int)
-#562 := (or #561 #837)
-#563 := (not #562)
-#456 := (or #563 #560)
-#833 := (ite #456 #848 #849)
-#834 := (= #11 0::Int)
-#556 := (= #9 0::Int)
-#557 := (ite #556 #834 #833)
-#835 := (= 0::Int 0::Int)
-#832 := (ite #835 #831 #557)
-#788 := (or #799 #832)
-#777 := (iff #788 #786)
-#789 := (iff #786 #786)
-#790 := [rewrite]: #789
-#798 := (iff #832 #831)
-#801 := (mod #846 0::Int)
-#802 := (+ #11 #801)
-#688 := (= #802 0::Int)
-#699 := (ite #556 #834 #688)
-#1 := true
-#701 := (ite true #831 #699)
-#704 := (iff #701 #831)
-#705 := [rewrite]: #704
-#702 := (iff #832 #701)
-#700 := (iff #557 #699)
-#682 := (iff #833 #688)
-#796 := (ite false #848 #688)
-#794 := (iff #796 #688)
-#797 := [rewrite]: #794
-#698 := (iff #833 #796)
-#689 := (iff #849 #688)
-#805 := (= #847 #802)
-#803 := (= #484 #801)
-#647 := (= #840 0::Int)
-#800 := [rewrite]: #647
-#804 := [monotonicity #800]: #803
-#687 := [monotonicity #804]: #805
-#648 := [monotonicity #687]: #689
-#644 := (iff #456 false)
-#807 := (or false false)
-#808 := (iff #807 false)
-#815 := [rewrite]: #808
-#813 := (iff #456 #807)
-#812 := (iff #560 false)
-#830 := (not true)
-#821 := (iff #830 false)
-#816 := [rewrite]: #821
-#810 := (iff #560 #830)
-#667 := (iff #838 true)
-#823 := (or true #851)
-#665 := (iff #823 true)
-#666 := [rewrite]: #665
-#818 := (iff #838 #823)
-#547 := (iff #837 true)
-#548 := [rewrite]: #547
-#824 := [monotonicity #548]: #818
-#809 := [trans #824 #666]: #667
-#811 := [monotonicity #809]: #810
-#806 := [trans #811 #816]: #812
-#817 := (iff #563 false)
-#819 := (iff #563 #830)
-#829 := (iff #562 true)
-#549 := (or #561 true)
-#543 := (iff #549 true)
-#825 := [rewrite]: #543
-#827 := (iff #562 #549)
-#828 := [monotonicity #548]: #827
-#826 := [trans #828 #825]: #829
-#820 := [monotonicity #826]: #819
-#822 := [trans #820 #816]: #817
-#814 := [monotonicity #822 #806]: #813
-#646 := [trans #814 #815]: #644
-#793 := [monotonicity #646 #648]: #698
-#697 := [trans #793 #797]: #682
-#693 := [monotonicity #697]: #700
-#836 := (iff #835 true)
-#546 := [rewrite]: #836
-#703 := [monotonicity #546 #693]: #702
-#795 := [trans #703 #705]: #798
-#779 := [monotonicity #795]: #777
-#791 := [trans #779 #790]: #777
-#780 := [quant-inst #9 #10]: #788
-#787 := [mp #780 #791]: #786
-#792 := [unit-resolution #787 #898]: #831
-#782 := [symm #792]: #781
-#778 := [monotonicity #782]: #784
-#769 := [symm #778]: #785
-#535 := (= f6 #450)
-#15 := (:var 0 S2)
-#16 := (f5 #15)
-#864 := (pattern #16)
-#17 := (f3 #16)
-#86 := (= #15 #17)
-#865 := (forall (vars (?v0 S2)) (:pat #864) #86)
-#90 := (forall (vars (?v0 S2)) #86)
-#866 := (iff #90 #865)
-#868 := (iff #865 #865)
-#869 := [rewrite]: #868
-#867 := [rewrite]: #866
-#870 := [trans #867 #869]: #866
-#313 := (~ #90 #90)
-#311 := (~ #86 #86)
-#312 := [refl]: #311
-#314 := [nnf-pos #312]: #313
-#18 := (= #17 #15)
-#19 := (forall (vars (?v0 S2)) #18)
-#91 := (iff #19 #90)
-#88 := (iff #18 #86)
-#89 := [rewrite]: #88
-#92 := [quant-intro #89]: #91
-#85 := [asserted]: #19
-#95 := [mp #85 #92]: #90
-#299 := [mp~ #95 #314]: #90
-#871 := [mp #299 #870]: #865
-#528 := (not #865)
-#539 := (or #528 #535)
-#540 := [quant-inst #8]: #539
-#783 := [unit-resolution #540 #871]: #535
-#770 := [trans #783 #769]: #79
-#82 := (not #79)
-#13 := (= #12 f6)
-#14 := (not #13)
-#83 := (iff #14 #82)
-#80 := (iff #13 #79)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#78 := [asserted]: #14
-#87 := [mp #78 #84]: #82
-[unit-resolution #87 #770]: false
-unsat
-acd2d715307b02a82f8d3d25d1935b122a84c3b3 309 0
-#2 := false
-decl f3 :: (-> Int S2)
-#8 := 0::Int
-#12 := (f3 0::Int)
-decl f4 :: (-> Int Int Int)
-#9 := 1::Int
-#10 := (f4 0::Int 1::Int)
-#11 := (f3 #10)
-#13 := (= #11 #12)
-#805 := (= #10 0::Int)
-#20 := (:var 0 Int)
-#31 := (:var 1 Int)
-#50 := (f4 #31 #20)
-#884 := (pattern #50)
-#180 := -1::Int
-#184 := (* -1::Int #20)
-#181 := (* -1::Int #31)
-#245 := (mod #181 #184)
-#375 := (+ #50 #245)
-#376 := (= #375 0::Int)
-#51 := (mod #31 #20)
-#372 := (* -1::Int #51)
-#373 := (+ #50 #372)
-#374 := (= #373 0::Int)
-#219 := (>= #31 0::Int)
-#212 := (<= #20 0::Int)
-#319 := (or #212 #219)
-#320 := (not #319)
-#208 := (<= #31 0::Int)
-#317 := (or #208 #212)
-#318 := (not #317)
-#323 := (or #318 #320)
-#377 := (ite #323 #374 #376)
-#371 := (= #50 0::Int)
-#33 := (= #31 0::Int)
-#378 := (ite #33 #371 #377)
-#370 := (= #31 #50)
-#34 := (= #20 0::Int)
-#379 := (ite #34 #370 #378)
-#885 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #884) #379)
-#382 := (forall (vars (?v0 Int) (?v1 Int)) #379)
-#888 := (iff #382 #885)
-#886 := (iff #379 #379)
-#887 := [refl]: #886
-#889 := [quant-intro #887]: #888
-#251 := (* -1::Int #245)
-#339 := (ite #323 #51 #251)
-#342 := (ite #33 0::Int #339)
-#345 := (ite #34 #31 #342)
-#348 := (= #50 #345)
-#351 := (forall (vars (?v0 Int) (?v1 Int)) #348)
-#383 := (iff #351 #382)
-#380 := (iff #348 #379)
-#381 := [rewrite]: #380
-#384 := [quant-intro #381]: #383
-#220 := (not #219)
-#213 := (not #212)
-#223 := (and #213 #220)
-#209 := (not #208)
-#216 := (and #209 #213)
-#226 := (or #216 #223)
-#271 := (ite #226 #51 #251)
-#274 := (ite #33 0::Int #271)
-#277 := (ite #34 #31 #274)
-#280 := (= #50 #277)
-#283 := (forall (vars (?v0 Int) (?v1 Int)) #280)
-#352 := (iff #283 #351)
-#349 := (iff #280 #348)
-#346 := (= #277 #345)
-#343 := (= #274 #342)
-#340 := (= #271 #339)
-#324 := (iff #226 #323)
-#321 := (iff #223 #320)
-#322 := [rewrite]: #321
-#302 := (iff #216 #318)
-#303 := [rewrite]: #302
-#325 := [monotonicity #303 #322]: #324
-#341 := [monotonicity #325]: #340
-#344 := [monotonicity #341]: #343
-#347 := [monotonicity #344]: #346
-#350 := [monotonicity #347]: #349
-#353 := [quant-intro #350]: #352
-#300 := (~ #283 #283)
-#314 := (~ #280 #280)
-#315 := [refl]: #314
-#301 := [nnf-pos #315]: #300
-#44 := (- #20)
-#43 := (- #31)
-#52 := (mod #43 #44)
-#53 := (- #52)
-#37 := (< 0::Int #20)
-#39 := (< #31 0::Int)
-#40 := (and #39 #37)
-#36 := (< 0::Int #31)
-#38 := (and #36 #37)
-#41 := (or #38 #40)
-#54 := (ite #41 #51 #53)
-#55 := (ite #33 0::Int #54)
-#56 := (ite #34 #31 #55)
-#57 := (= #50 #56)
-#58 := (forall (vars (?v0 Int) (?v1 Int)) #57)
-#286 := (iff #58 #283)
-#174 := (and #37 #39)
-#177 := (or #38 #174)
-#256 := (ite #177 #51 #251)
-#165 := (= 0::Int #31)
-#259 := (ite #165 0::Int #256)
-#168 := (= 0::Int #20)
-#262 := (ite #168 #31 #259)
-#265 := (= #50 #262)
-#268 := (forall (vars (?v0 Int) (?v1 Int)) #265)
-#284 := (iff #268 #283)
-#281 := (iff #265 #280)
-#278 := (= #262 #277)
-#275 := (= #259 #274)
-#272 := (= #256 #271)
-#227 := (iff #177 #226)
-#224 := (iff #174 #223)
-#221 := (iff #39 #220)
-#222 := [rewrite]: #221
-#214 := (iff #37 #213)
-#215 := [rewrite]: #214
-#225 := [monotonicity #215 #222]: #224
-#217 := (iff #38 #216)
-#210 := (iff #36 #209)
-#211 := [rewrite]: #210
-#218 := [monotonicity #211 #215]: #217
-#228 := [monotonicity #218 #225]: #227
-#273 := [monotonicity #228]: #272
-#202 := (iff #165 #33)
-#203 := [rewrite]: #202
-#276 := [monotonicity #203 #273]: #275
-#204 := (iff #168 #34)
-#205 := [rewrite]: #204
-#279 := [monotonicity #205 #276]: #278
-#282 := [monotonicity #279]: #281
-#285 := [quant-intro #282]: #284
-#269 := (iff #58 #268)
-#266 := (iff #57 #265)
-#263 := (= #56 #262)
-#260 := (= #55 #259)
-#257 := (= #54 #256)
-#254 := (= #53 #251)
-#248 := (- #245)
-#252 := (= #248 #251)
-#253 := [rewrite]: #252
-#249 := (= #53 #248)
-#246 := (= #52 #245)
-#185 := (= #44 #184)
-#186 := [rewrite]: #185
-#182 := (= #43 #181)
-#183 := [rewrite]: #182
-#247 := [monotonicity #183 #186]: #246
-#250 := [monotonicity #247]: #249
-#255 := [trans #250 #253]: #254
-#178 := (iff #41 #177)
-#175 := (iff #40 #174)
-#176 := [rewrite]: #175
-#179 := [monotonicity #176]: #178
-#258 := [monotonicity #179 #255]: #257
-#166 := (iff #33 #165)
-#167 := [rewrite]: #166
-#261 := [monotonicity #167 #258]: #260
-#169 := (iff #34 #168)
-#170 := [rewrite]: #169
-#264 := [monotonicity #170 #261]: #263
-#267 := [monotonicity #264]: #266
-#270 := [quant-intro #267]: #269
-#287 := [trans #270 #285]: #286
-#244 := [asserted]: #58
-#288 := [mp #244 #287]: #283
-#316 := [mp~ #288 #301]: #283
-#354 := [mp #316 #353]: #351
-#385 := [mp #354 #384]: #382
-#890 := [mp #385 #889]: #885
-#728 := (not #885)
-#729 := (or #728 #805)
-#812 := (* -1::Int 1::Int)
-#813 := (* -1::Int 0::Int)
-#808 := (mod #813 #812)
-#809 := (+ #10 #808)
-#814 := (= #809 0::Int)
-#815 := (mod 0::Int 1::Int)
-#810 := (* -1::Int #815)
-#816 := (+ #10 #810)
-#657 := (= #816 0::Int)
-#834 := (>= 0::Int 0::Int)
-#658 := (<= 1::Int 0::Int)
-#659 := (or #658 #834)
-#801 := (not #659)
-#802 := (<= 0::Int 0::Int)
-#803 := (or #802 #658)
-#804 := (not #803)
-#798 := (or #804 #801)
-#799 := (ite #798 #657 #814)
-#806 := (= 0::Int 0::Int)
-#800 := (ite #806 #805 #799)
-#807 := (= 0::Int #10)
-#636 := (= 1::Int 0::Int)
-#638 := (ite #636 #807 #800)
-#724 := (or #728 #638)
-#703 := (iff #724 #729)
-#705 := (iff #729 #729)
-#598 := [rewrite]: #705
-#726 := (iff #638 #805)
-#752 := (ite false #805 #805)
-#731 := (iff #752 #805)
-#732 := [rewrite]: #731
-#722 := (iff #638 #752)
-#725 := (iff #800 #805)
-#1 := true
-#736 := (ite true #805 #805)
-#733 := (iff #736 #805)
-#739 := [rewrite]: #733
-#737 := (iff #800 #736)
-#734 := (iff #799 #805)
-#742 := (iff #799 #752)
-#750 := (iff #814 #805)
-#748 := (= #809 #10)
-#764 := (+ #10 0::Int)
-#767 := (= #764 #10)
-#763 := [rewrite]: #767
-#746 := (= #809 #764)
-#744 := (= #808 0::Int)
-#756 := (mod 0::Int -1::Int)
-#741 := (= #756 0::Int)
-#743 := [rewrite]: #741
-#760 := (= #808 #756)
-#758 := (= #812 -1::Int)
-#759 := [rewrite]: #758
-#770 := (= #813 0::Int)
-#777 := [rewrite]: #770
-#740 := [monotonicity #777 #759]: #760
-#745 := [trans #740 #743]: #744
-#747 := [monotonicity #745]: #746
-#749 := [trans #747 #763]: #748
-#751 := [monotonicity #749]: #750
-#755 := (iff #657 #805)
-#768 := (= #816 #10)
-#765 := (= #816 #764)
-#761 := (= #810 0::Int)
-#775 := (= #810 #813)
-#773 := (= #815 0::Int)
-#774 := [rewrite]: #773
-#776 := [monotonicity #774]: #775
-#762 := [trans #776 #777]: #761
-#766 := [monotonicity #762]: #765
-#754 := [trans #766 #763]: #768
-#757 := [monotonicity #754]: #755
-#779 := (iff #798 false)
-#769 := (or false false)
-#782 := (iff #769 false)
-#783 := [rewrite]: #782
-#771 := (iff #798 #769)
-#780 := (iff #801 false)
-#482 := (not true)
-#843 := (iff #482 false)
-#829 := [rewrite]: #843
-#791 := (iff #801 #482)
-#790 := (iff #659 true)
-#693 := (or false true)
-#696 := (iff #693 true)
-#697 := [rewrite]: #696
-#694 := (iff #659 #693)
-#841 := (iff #834 true)
-#481 := [rewrite]: #841
-#680 := (iff #658 false)
-#681 := [rewrite]: #680
-#695 := [monotonicity #681 #481]: #694
-#787 := [trans #695 #697]: #790
-#778 := [monotonicity #787]: #791
-#772 := [trans #778 #829]: #780
-#692 := (iff #804 false)
-#689 := (iff #804 #482)
-#789 := (iff #803 true)
-#640 := (or true false)
-#785 := (iff #640 true)
-#786 := [rewrite]: #785
-#788 := (iff #803 #640)
-#797 := (iff #802 true)
-#679 := [rewrite]: #797
-#690 := [monotonicity #679 #681]: #788
-#674 := [trans #690 #786]: #789
-#691 := [monotonicity #674]: #689
-#685 := [trans #691 #829]: #692
-#781 := [monotonicity #685 #772]: #771
-#784 := [trans #781 #783]: #779
-#753 := [monotonicity #784 #757 #751]: #742
-#735 := [trans #753 #732]: #734
-#796 := (iff #806 true)
-#794 := [rewrite]: #796
-#738 := [monotonicity #794 #735]: #737
-#721 := [trans #738 #739]: #725
-#793 := (iff #807 #805)
-#795 := [rewrite]: #793
-#639 := (iff #636 false)
-#792 := [rewrite]: #639
-#723 := [monotonicity #792 #795 #721]: #722
-#727 := [trans #723 #732]: #726
-#704 := [monotonicity #727]: #703
-#709 := [trans #704 #598]: #703
-#730 := [quant-inst #8 #9]: #724
-#710 := [mp #730 #709]: #729
-#716 := [unit-resolution #710 #890]: #805
-#712 := [monotonicity #716]: #13
-#14 := (not #13)
-#78 := [asserted]: #14
-[unit-resolution #78 #712]: false
-unsat
-a77f50b29c69935853b053858b12886e75a3e1af 310 0
-#2 := false
-decl f3 :: (-> Int S2)
-#11 := 0::Int
-#12 := (f3 0::Int)
-decl f4 :: (-> Int Int Int)
+#24 := (f3 0::Int)
+#10 := 3::Int
+#19 := (- 3::Int)
+#18 := (- 0::Int)
+#20 := (div #18 #19)
+#17 := (div 0::Int 3::Int)
+#14 := (< 0::Int 3::Int)
+#13 := (< 0::Int 0::Int)
+#15 := (and #13 #14)
+#16 := (or #15 #15)
+#21 := (ite #16 #17 #20)
+#11 := (= 3::Int 0::Int)
+#9 := (= 0::Int 0::Int)
+#12 := (or #9 #11)
+#22 := (ite #12 0::Int #21)
+#23 := (f3 #22)
+#25 := (= #23 #24)
+#26 := (not #25)
+#117 := (iff #26 false)
+#1 := true
+#112 := (not true)
+#115 := (iff #112 false)
+#116 := [rewrite]: #115
+#113 := (iff #26 #112)
+#110 := (iff #25 true)
+#105 := (= #24 #24)
+#108 := (iff #105 true)
+#109 := [rewrite]: #108
+#106 := (iff #25 #105)
+#102 := (= #22 0::Int)
+#97 := (ite true 0::Int 0::Int)
+#100 := (= #97 0::Int)
+#101 := [rewrite]: #100
+#98 := (= #22 #97)
+#95 := (= #21 0::Int)
+#90 := (ite #15 0::Int 0::Int)
+#93 := (= #90 0::Int)
+#94 := [rewrite]: #93
+#91 := (= #21 #90)
+#88 := (= #20 0::Int)
+#80 := -3::Int
+#83 := (div 0::Int -3::Int)
+#86 := (= #83 0::Int)
+#87 := [rewrite]: #86
+#84 := (= #20 #83)
+#81 := (= #19 -3::Int)
+#82 := [rewrite]: #81
+#78 := (= #18 0::Int)
+#79 := [rewrite]: #78
+#85 := [monotonicity #79 #82]: #84
+#89 := [trans #85 #87]: #88
+#76 := (= #17 0::Int)
+#77 := [rewrite]: #76
+#74 := (iff #16 #15)
+#75 := [rewrite]: #74
+#92 := [monotonicity #75 #77 #89]: #91
+#96 := [trans #92 #94]: #95
+#72 := (iff #12 true)
+#67 := (or true false)
+#70 := (iff #67 true)
+#71 := [rewrite]: #70
+#68 := (iff #12 #67)
+#65 := (iff #11 false)
+#66 := [rewrite]: #65
+#63 := (iff #9 true)
+#64 := [rewrite]: #63
+#69 := [monotonicity #64 #66]: #68
+#73 := [trans #69 #71]: #72
+#99 := [monotonicity #73 #96]: #98
+#103 := [trans #99 #101]: #102
+#104 := [monotonicity #103]: #25
+#107 := [monotonicity #104]: #106
+#111 := [trans #107 #109]: #110
+#114 := [monotonicity #111]: #113
+#118 := [trans #114 #116]: #117
+#62 := [asserted]: #26
+[mp #62 #118]: false
+unsat
+b6bcc3a997f628b30a8c56db4557945cb134a0bb 135 0
+#2 := false
+decl f3 :: (-> Int S2)
+#9 := 0::Int
+#27 := (f3 0::Int)
+#11 := 3::Int
+#22 := (- 3::Int)
 #8 := 1::Int
-#9 := (f4 1::Int 1::Int)
-#10 := (f3 #9)
-#13 := (= #10 #12)
-#799 := (= #9 0::Int)
-#20 := (:var 0 Int)
-#31 := (:var 1 Int)
-#50 := (f4 #31 #20)
-#884 := (pattern #50)
-#180 := -1::Int
-#184 := (* -1::Int #20)
-#181 := (* -1::Int #31)
-#245 := (mod #181 #184)
-#375 := (+ #50 #245)
-#376 := (= #375 0::Int)
-#51 := (mod #31 #20)
-#372 := (* -1::Int #51)
-#373 := (+ #50 #372)
-#374 := (= #373 0::Int)
-#219 := (>= #31 0::Int)
-#212 := (<= #20 0::Int)
-#319 := (or #212 #219)
-#320 := (not #319)
-#208 := (<= #31 0::Int)
-#317 := (or #208 #212)
-#318 := (not #317)
-#323 := (or #318 #320)
-#377 := (ite #323 #374 #376)
-#371 := (= #50 0::Int)
-#33 := (= #31 0::Int)
-#378 := (ite #33 #371 #377)
-#370 := (= #31 #50)
-#34 := (= #20 0::Int)
-#379 := (ite #34 #370 #378)
-#885 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #884) #379)
-#382 := (forall (vars (?v0 Int) (?v1 Int)) #379)
-#888 := (iff #382 #885)
-#886 := (iff #379 #379)
-#887 := [refl]: #886
-#889 := [quant-intro #887]: #888
-#251 := (* -1::Int #245)
-#339 := (ite #323 #51 #251)
-#342 := (ite #33 0::Int #339)
-#345 := (ite #34 #31 #342)
-#348 := (= #50 #345)
-#351 := (forall (vars (?v0 Int) (?v1 Int)) #348)
-#383 := (iff #351 #382)
-#380 := (iff #348 #379)
-#381 := [rewrite]: #380
-#384 := [quant-intro #381]: #383
-#220 := (not #219)
-#213 := (not #212)
-#223 := (and #213 #220)
-#209 := (not #208)
-#216 := (and #209 #213)
-#226 := (or #216 #223)
-#271 := (ite #226 #51 #251)
-#274 := (ite #33 0::Int #271)
-#277 := (ite #34 #31 #274)
-#280 := (= #50 #277)
-#283 := (forall (vars (?v0 Int) (?v1 Int)) #280)
-#352 := (iff #283 #351)
-#349 := (iff #280 #348)
-#346 := (= #277 #345)
-#343 := (= #274 #342)
-#340 := (= #271 #339)
-#324 := (iff #226 #323)
-#321 := (iff #223 #320)
-#322 := [rewrite]: #321
-#302 := (iff #216 #318)
-#303 := [rewrite]: #302
-#325 := [monotonicity #303 #322]: #324
-#341 := [monotonicity #325]: #340
-#344 := [monotonicity #341]: #343
-#347 := [monotonicity #344]: #346
-#350 := [monotonicity #347]: #349
-#353 := [quant-intro #350]: #352
-#300 := (~ #283 #283)
-#314 := (~ #280 #280)
-#315 := [refl]: #314
-#301 := [nnf-pos #315]: #300
-#44 := (- #20)
-#43 := (- #31)
-#52 := (mod #43 #44)
-#53 := (- #52)
-#37 := (< 0::Int #20)
-#39 := (< #31 0::Int)
-#40 := (and #39 #37)
-#36 := (< 0::Int #31)
-#38 := (and #36 #37)
-#41 := (or #38 #40)
-#54 := (ite #41 #51 #53)
-#55 := (ite #33 0::Int #54)
-#56 := (ite #34 #31 #55)
-#57 := (= #50 #56)
-#58 := (forall (vars (?v0 Int) (?v1 Int)) #57)
-#286 := (iff #58 #283)
-#174 := (and #37 #39)
-#177 := (or #38 #174)
-#256 := (ite #177 #51 #251)
-#165 := (= 0::Int #31)
-#259 := (ite #165 0::Int #256)
-#168 := (= 0::Int #20)
-#262 := (ite #168 #31 #259)
-#265 := (= #50 #262)
-#268 := (forall (vars (?v0 Int) (?v1 Int)) #265)
-#284 := (iff #268 #283)
-#281 := (iff #265 #280)
-#278 := (= #262 #277)
-#275 := (= #259 #274)
-#272 := (= #256 #271)
-#227 := (iff #177 #226)
-#224 := (iff #174 #223)
-#221 := (iff #39 #220)
-#222 := [rewrite]: #221
-#214 := (iff #37 #213)
-#215 := [rewrite]: #214
-#225 := [monotonicity #215 #222]: #224
-#217 := (iff #38 #216)
-#210 := (iff #36 #209)
-#211 := [rewrite]: #210
-#218 := [monotonicity #211 #215]: #217
-#228 := [monotonicity #218 #225]: #227
-#273 := [monotonicity #228]: #272
-#202 := (iff #165 #33)
-#203 := [rewrite]: #202
-#276 := [monotonicity #203 #273]: #275
-#204 := (iff #168 #34)
-#205 := [rewrite]: #204
-#279 := [monotonicity #205 #276]: #278
-#282 := [monotonicity #279]: #281
-#285 := [quant-intro #282]: #284
-#269 := (iff #58 #268)
-#266 := (iff #57 #265)
-#263 := (= #56 #262)
-#260 := (= #55 #259)
-#257 := (= #54 #256)
-#254 := (= #53 #251)
-#248 := (- #245)
-#252 := (= #248 #251)
-#253 := [rewrite]: #252
-#249 := (= #53 #248)
-#246 := (= #52 #245)
-#185 := (= #44 #184)
-#186 := [rewrite]: #185
-#182 := (= #43 #181)
-#183 := [rewrite]: #182
-#247 := [monotonicity #183 #186]: #246
-#250 := [monotonicity #247]: #249
-#255 := [trans #250 #253]: #254
-#178 := (iff #41 #177)
-#175 := (iff #40 #174)
-#176 := [rewrite]: #175
-#179 := [monotonicity #176]: #178
-#258 := [monotonicity #179 #255]: #257
-#166 := (iff #33 #165)
-#167 := [rewrite]: #166
-#261 := [monotonicity #167 #258]: #260
-#169 := (iff #34 #168)
-#170 := [rewrite]: #169
-#264 := [monotonicity #170 #261]: #263
-#267 := [monotonicity #264]: #266
-#270 := [quant-intro #267]: #269
-#287 := [trans #270 #285]: #286
-#244 := [asserted]: #58
-#288 := [mp #244 #287]: #283
-#316 := [mp~ #288 #301]: #283
-#354 := [mp #316 #353]: #351
-#385 := [mp #354 #384]: #382
-#890 := [mp #385 #889]: #885
-#703 := (not #885)
-#704 := (or #703 #799)
-#812 := (* -1::Int 1::Int)
-#813 := (mod #812 #812)
-#808 := (+ #9 #813)
-#809 := (= #808 0::Int)
-#814 := (mod 1::Int 1::Int)
-#815 := (* -1::Int #814)
-#810 := (+ #9 #815)
-#816 := (= #810 0::Int)
-#657 := (>= 1::Int 0::Int)
-#658 := (<= 1::Int 0::Int)
-#659 := (or #658 #657)
-#801 := (not #659)
-#802 := (or #658 #658)
-#803 := (not #802)
-#804 := (or #803 #801)
-#798 := (ite #804 #816 #809)
-#805 := (= 1::Int 0::Int)
-#806 := (ite #805 #799 #798)
-#800 := (= 1::Int #9)
-#807 := (ite #805 #800 #806)
-#705 := (or #703 #807)
-#709 := (iff #705 #704)
-#711 := (iff #704 #704)
-#716 := [rewrite]: #711
-#724 := (iff #807 #799)
-#792 := (= #9 1::Int)
-#723 := (ite false #792 #799)
-#728 := (iff #723 #799)
-#729 := [rewrite]: #728
-#726 := (iff #807 #723)
-#721 := (iff #806 #799)
-#737 := (ite false #799 #799)
-#739 := (iff #737 #799)
-#725 := [rewrite]: #739
-#738 := (iff #806 #737)
-#735 := (iff #798 #799)
-#1 := true
-#742 := (ite true #799 #799)
-#732 := (iff #742 #799)
-#734 := [rewrite]: #732
-#753 := (iff #798 #742)
-#751 := (iff #809 #799)
-#749 := (= #808 #9)
-#765 := (+ #9 0::Int)
-#763 := (= #765 #9)
-#768 := [rewrite]: #763
-#747 := (= #808 #765)
-#745 := (= #813 0::Int)
-#760 := (mod -1::Int -1::Int)
-#743 := (= #760 0::Int)
-#744 := [rewrite]: #743
-#740 := (= #813 #760)
-#759 := (= #812 -1::Int)
-#756 := [rewrite]: #759
-#741 := [monotonicity #756 #756]: #740
-#746 := [trans #741 #744]: #745
-#748 := [monotonicity #746]: #747
-#750 := [trans #748 #768]: #749
-#752 := [monotonicity #750]: #751
-#757 := (iff #816 #799)
-#754 := (= #810 #9)
-#766 := (= #810 #765)
-#762 := (= #815 0::Int)
-#775 := (* -1::Int 0::Int)
-#777 := (= #775 0::Int)
-#761 := [rewrite]: #777
-#776 := (= #815 #775)
-#773 := (= #814 0::Int)
-#774 := [rewrite]: #773
-#770 := [monotonicity #774]: #776
-#764 := [trans #770 #761]: #762
-#767 := [monotonicity #764]: #766
-#755 := [trans #767 #768]: #754
-#758 := [monotonicity #755]: #757
-#779 := (iff #804 true)
-#769 := (or true false)
-#782 := (iff #769 true)
-#783 := [rewrite]: #782
-#771 := (iff #804 #769)
-#780 := (iff #801 false)
-#482 := (not true)
-#843 := (iff #482 false)
-#829 := [rewrite]: #843
-#791 := (iff #801 #482)
-#790 := (iff #659 true)
-#693 := (or false true)
-#696 := (iff #693 true)
-#697 := [rewrite]: #696
-#694 := (iff #659 #693)
-#692 := (iff #657 true)
-#685 := [rewrite]: #692
-#795 := (iff #658 false)
-#796 := [rewrite]: #795
-#695 := [monotonicity #796 #685]: #694
-#787 := [trans #695 #697]: #790
-#778 := [monotonicity #787]: #791
-#772 := [trans #778 #829]: #780
-#689 := (iff #803 true)
-#690 := (not false)
-#789 := (iff #690 true)
-#674 := [rewrite]: #789
-#785 := (iff #803 #690)
-#640 := (iff #802 false)
-#794 := (or false false)
-#680 := (iff #794 false)
-#681 := [rewrite]: #680
-#797 := (iff #802 #794)
-#679 := [monotonicity #796 #796]: #797
-#788 := [trans #679 #681]: #640
-#786 := [monotonicity #788]: #785
-#691 := [trans #786 #674]: #689
-#781 := [monotonicity #691 #772]: #771
-#784 := [trans #781 #783]: #779
-#731 := [monotonicity #784 #758 #752]: #753
-#736 := [trans #731 #734]: #735
-#636 := (iff #805 false)
-#638 := [rewrite]: #636
-#733 := [monotonicity #638 #736]: #738
-#722 := [trans #733 #725]: #721
-#639 := (iff #800 #792)
-#793 := [rewrite]: #639
-#727 := [monotonicity #638 #793 #722]: #726
-#730 := [trans #727 #729]: #724
-#710 := [monotonicity #730]: #709
-#712 := [trans #710 #716]: #709
-#598 := [quant-inst #8 #8]: #705
-#713 := [mp #598 #712]: #704
-#717 := [unit-resolution #713 #890]: #799
-#718 := [monotonicity #717]: #13
-#14 := (not #13)
-#78 := [asserted]: #14
-[unit-resolution #78 #718]: false
-unsat
-0b8020dc224bc16c2ca4d4c9672c839314b04736 321 0
-#2 := false
-decl f3 :: (-> Int S2)
-#12 := 0::Int
-#13 := (f3 0::Int)
-decl f4 :: (-> Int Int Int)
-#9 := 1::Int
-#8 := 3::Int
-#10 := (f4 3::Int 1::Int)
-#11 := (f3 #10)
-#14 := (= #11 #13)
-#807 := (= #10 0::Int)
-#21 := (:var 0 Int)
-#32 := (:var 1 Int)
-#51 := (f4 #32 #21)
-#885 := (pattern #51)
-#181 := -1::Int
-#185 := (* -1::Int #21)
-#182 := (* -1::Int #32)
-#246 := (mod #182 #185)
-#376 := (+ #51 #246)
-#377 := (= #376 0::Int)
-#52 := (mod #32 #21)
-#373 := (* -1::Int #52)
-#374 := (+ #51 #373)
-#375 := (= #374 0::Int)
-#220 := (>= #32 0::Int)
-#213 := (<= #21 0::Int)
-#320 := (or #213 #220)
-#321 := (not #320)
-#209 := (<= #32 0::Int)
-#318 := (or #209 #213)
-#319 := (not #318)
-#324 := (or #319 #321)
-#378 := (ite #324 #375 #377)
-#372 := (= #51 0::Int)
-#34 := (= #32 0::Int)
-#379 := (ite #34 #372 #378)
-#371 := (= #32 #51)
-#35 := (= #21 0::Int)
-#380 := (ite #35 #371 #379)
-#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #380)
-#383 := (forall (vars (?v0 Int) (?v1 Int)) #380)
-#889 := (iff #383 #886)
-#887 := (iff #380 #380)
-#888 := [refl]: #887
-#890 := [quant-intro #888]: #889
-#252 := (* -1::Int #246)
-#340 := (ite #324 #52 #252)
-#343 := (ite #34 0::Int #340)
-#346 := (ite #35 #32 #343)
-#349 := (= #51 #346)
-#352 := (forall (vars (?v0 Int) (?v1 Int)) #349)
-#384 := (iff #352 #383)
-#381 := (iff #349 #380)
-#382 := [rewrite]: #381
-#385 := [quant-intro #382]: #384
-#221 := (not #220)
-#214 := (not #213)
-#224 := (and #214 #221)
-#210 := (not #209)
-#217 := (and #210 #214)
-#227 := (or #217 #224)
-#272 := (ite #227 #52 #252)
-#275 := (ite #34 0::Int #272)
-#278 := (ite #35 #32 #275)
-#281 := (= #51 #278)
-#284 := (forall (vars (?v0 Int) (?v1 Int)) #281)
-#353 := (iff #284 #352)
-#350 := (iff #281 #349)
-#347 := (= #278 #346)
-#344 := (= #275 #343)
-#341 := (= #272 #340)
-#325 := (iff #227 #324)
-#322 := (iff #224 #321)
-#323 := [rewrite]: #322
-#303 := (iff #217 #319)
-#304 := [rewrite]: #303
-#326 := [monotonicity #304 #323]: #325
-#342 := [monotonicity #326]: #341
-#345 := [monotonicity #342]: #344
-#348 := [monotonicity #345]: #347
-#351 := [monotonicity #348]: #350
-#354 := [quant-intro #351]: #353
-#301 := (~ #284 #284)
-#315 := (~ #281 #281)
-#316 := [refl]: #315
-#302 := [nnf-pos #316]: #301
-#45 := (- #21)
-#44 := (- #32)
-#53 := (mod #44 #45)
-#54 := (- #53)
-#38 := (< 0::Int #21)
-#40 := (< #32 0::Int)
-#41 := (and #40 #38)
-#37 := (< 0::Int #32)
-#39 := (and #37 #38)
-#42 := (or #39 #41)
-#55 := (ite #42 #52 #54)
-#56 := (ite #34 0::Int #55)
-#57 := (ite #35 #32 #56)
-#58 := (= #51 #57)
-#59 := (forall (vars (?v0 Int) (?v1 Int)) #58)
-#287 := (iff #59 #284)
-#175 := (and #38 #40)
-#178 := (or #39 #175)
-#257 := (ite #178 #52 #252)
-#166 := (= 0::Int #32)
-#260 := (ite #166 0::Int #257)
-#169 := (= 0::Int #21)
-#263 := (ite #169 #32 #260)
-#266 := (= #51 #263)
-#269 := (forall (vars (?v0 Int) (?v1 Int)) #266)
-#285 := (iff #269 #284)
-#282 := (iff #266 #281)
-#279 := (= #263 #278)
-#276 := (= #260 #275)
-#273 := (= #257 #272)
-#228 := (iff #178 #227)
-#225 := (iff #175 #224)
-#222 := (iff #40 #221)
-#223 := [rewrite]: #222
-#215 := (iff #38 #214)
-#216 := [rewrite]: #215
-#226 := [monotonicity #216 #223]: #225
-#218 := (iff #39 #217)
-#211 := (iff #37 #210)
-#212 := [rewrite]: #211
-#219 := [monotonicity #212 #216]: #218
-#229 := [monotonicity #219 #226]: #228
-#274 := [monotonicity #229]: #273
-#203 := (iff #166 #34)
-#204 := [rewrite]: #203
-#277 := [monotonicity #204 #274]: #276
-#205 := (iff #169 #35)
-#206 := [rewrite]: #205
-#280 := [monotonicity #206 #277]: #279
-#283 := [monotonicity #280]: #282
-#286 := [quant-intro #283]: #285
-#270 := (iff #59 #269)
-#267 := (iff #58 #266)
-#264 := (= #57 #263)
-#261 := (= #56 #260)
-#258 := (= #55 #257)
-#255 := (= #54 #252)
-#249 := (- #246)
-#253 := (= #249 #252)
-#254 := [rewrite]: #253
-#250 := (= #54 #249)
-#247 := (= #53 #246)
-#186 := (= #45 #185)
-#187 := [rewrite]: #186
-#183 := (= #44 #182)
-#184 := [rewrite]: #183
-#248 := [monotonicity #184 #187]: #247
-#251 := [monotonicity #248]: #250
-#256 := [trans #251 #254]: #255
-#179 := (iff #42 #178)
-#176 := (iff #41 #175)
-#177 := [rewrite]: #176
-#180 := [monotonicity #177]: #179
-#259 := [monotonicity #180 #256]: #258
-#167 := (iff #34 #166)
+#21 := (- 1::Int)
+#23 := (div #21 #22)
+#20 := (div 1::Int 3::Int)
+#15 := (< 0::Int 3::Int)
+#17 := (< 1::Int 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int 1::Int)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#24 := (ite #19 #20 #23)
+#12 := (= 3::Int 0::Int)
+#10 := (= 1::Int 0::Int)
+#13 := (or #10 #12)
+#25 := (ite #13 0::Int #24)
+#26 := (f3 #25)
+#28 := (= #26 #27)
+#29 := (not #28)
+#171 := (iff #29 false)
+#77 := (and #15 #17)
+#80 := (or #16 #77)
+#98 := (ite #80 0::Int 1::Int)
+#108 := (f3 #98)
+#114 := (= #27 #108)
+#119 := (not #114)
+#169 := (iff #119 false)
+#1 := true
+#164 := (not true)
+#167 := (iff #164 false)
 #168 := [rewrite]: #167
-#262 := [monotonicity #168 #259]: #261
-#170 := (iff #35 #169)
-#171 := [rewrite]: #170
-#265 := [monotonicity #171 #262]: #264
-#268 := [monotonicity #265]: #267
-#271 := [quant-intro #268]: #270
-#288 := [trans #271 #286]: #287
-#245 := [asserted]: #59
-#289 := [mp #245 #288]: #284
-#317 := [mp~ #289 #302]: #284
-#355 := [mp #317 #354]: #352
-#386 := [mp #355 #385]: #383
-#891 := [mp #386 #890]: #886
-#715 := (not #886)
-#718 := (or #715 #807)
-#813 := (* -1::Int 1::Int)
-#814 := (* -1::Int 3::Int)
-#809 := (mod #814 #813)
-#810 := (+ #10 #809)
-#815 := (= #810 0::Int)
-#816 := (mod 3::Int 1::Int)
-#811 := (* -1::Int #816)
-#817 := (+ #10 #811)
-#658 := (= #817 0::Int)
-#659 := (>= 3::Int 0::Int)
-#660 := (<= 1::Int 0::Int)
-#802 := (or #660 #659)
-#803 := (not #802)
-#804 := (<= 3::Int 0::Int)
-#805 := (or #804 #660)
-#799 := (not #805)
-#800 := (or #799 #803)
-#806 := (ite #800 #658 #815)
-#801 := (= 3::Int 0::Int)
-#808 := (ite #801 #807 #806)
-#637 := (= 3::Int #10)
-#639 := (= 1::Int 0::Int)
-#640 := (ite #639 #637 #808)
-#719 := (or #715 #640)
-#716 := (iff #719 #718)
-#701 := (iff #718 #718)
-#647 := [rewrite]: #701
-#713 := (iff #640 #807)
-#797 := (= #10 3::Int)
-#599 := (ite false #797 #807)
-#712 := (iff #599 #807)
-#717 := [rewrite]: #712
-#710 := (iff #640 #599)
-#705 := (iff #808 #807)
-#729 := (ite false #807 #807)
-#731 := (iff #729 #807)
-#704 := [rewrite]: #731
-#730 := (iff #808 #729)
-#727 := (iff #806 #807)
-#1 := true
-#740 := (ite true #807 #807)
-#723 := (iff #740 #807)
-#724 := [rewrite]: #723
-#726 := (iff #806 #740)
-#739 := (iff #815 #807)
-#737 := (= #810 #10)
-#758 := (+ #10 0::Int)
-#757 := (= #758 #10)
-#761 := [rewrite]: #757
-#735 := (= #810 #758)
-#732 := (= #809 0::Int)
-#746 := -3::Int
-#751 := (mod -3::Int -1::Int)
-#743 := (= #751 0::Int)
-#754 := [rewrite]: #743
-#752 := (= #809 #751)
-#749 := (= #813 -1::Int)
-#750 := [rewrite]: #749
-#747 := (= #814 -3::Int)
-#748 := [rewrite]: #747
-#753 := [monotonicity #748 #750]: #752
-#733 := [trans #753 #754]: #732
-#736 := [monotonicity #733]: #735
-#738 := [trans #736 #761]: #737
-#734 := [monotonicity #738]: #739
-#744 := (iff #658 #807)
-#741 := (= #817 #10)
-#759 := (= #817 #758)
-#755 := (= #811 0::Int)
-#766 := (* -1::Int 0::Int)
-#764 := (= #766 0::Int)
-#769 := [rewrite]: #764
-#767 := (= #811 #766)
-#763 := (= #816 0::Int)
-#765 := [rewrite]: #763
-#768 := [monotonicity #765]: #767
-#756 := [trans #768 #769]: #755
-#760 := [monotonicity #756]: #759
-#742 := [trans #760 #761]: #741
-#745 := [monotonicity #742]: #744
-#778 := (iff #800 true)
-#774 := (or true false)
-#777 := (iff #774 true)
-#771 := [rewrite]: #777
-#775 := (iff #800 #774)
-#780 := (iff #803 false)
-#483 := (not true)
-#844 := (iff #483 false)
-#830 := [rewrite]: #844
-#783 := (iff #803 #483)
-#772 := (iff #802 true)
-#792 := (or false true)
-#773 := (iff #792 true)
-#770 := [rewrite]: #773
-#779 := (iff #802 #792)
-#791 := (iff #659 true)
-#788 := [rewrite]: #791
-#641 := (iff #660 false)
-#789 := [rewrite]: #641
-#781 := [monotonicity #789 #788]: #779
-#782 := [trans #781 #770]: #772
-#784 := [monotonicity #782]: #783
-#785 := [trans #784 #830]: #780
-#697 := (iff #799 true)
-#693 := (not false)
-#695 := (iff #693 true)
-#696 := [rewrite]: #695
-#686 := (iff #799 #693)
-#690 := (iff #805 false)
-#691 := (or false false)
-#790 := (iff #691 false)
-#675 := [rewrite]: #790
-#786 := (iff #805 #691)
-#681 := (iff #804 false)
-#682 := [rewrite]: #681
-#787 := [monotonicity #682 #789]: #786
-#692 := [trans #787 #675]: #690
-#694 := [monotonicity #692]: #686
-#698 := [trans #694 #696]: #697
-#776 := [monotonicity #698 #785]: #775
-#762 := [trans #776 #771]: #778
-#722 := [monotonicity #762 #745 #734]: #726
-#728 := [trans #722 #724]: #727
-#798 := (iff #801 false)
-#680 := [rewrite]: #798
-#725 := [monotonicity #680 #728]: #730
-#706 := [trans #725 #704]: #705
-#796 := (iff #637 #797)
-#795 := [rewrite]: #796
-#793 := (iff #639 false)
-#794 := [rewrite]: #793
-#711 := [monotonicity #794 #795 #706]: #710
-#714 := [trans #711 #717]: #713
-#721 := [monotonicity #714]: #716
-#702 := [trans #721 #647]: #716
-#720 := [quant-inst #8 #9]: #719
-#683 := [mp #720 #702]: #718
-#708 := [unit-resolution #683 #891]: #807
-#703 := [monotonicity #708]: #14
-#15 := (not #14)
-#79 := [asserted]: #15
-[unit-resolution #79 #703]: false
-unsat
-beef9b82cbe8a31ac2e4568749757bdaef5ecf77 324 0
-#2 := false
-#13 := 0::Int
-decl f5 :: (-> S2 Int)
-decl f6 :: S2
-#8 := f6
-#9 := (f5 f6)
-#812 := (>= #9 0::Int)
-#694 := (not #812)
-#801 := (= #9 0::Int)
-#661 := (<= #9 0::Int)
-#683 := (not #661)
-#755 := (or #683 #801 #694)
-#712 := (not #755)
-decl f4 :: (-> Int Int Int)
-#10 := 1::Int
-#11 := (f4 #9 1::Int)
-#800 := (= #11 0::Int)
-#702 := (not #800)
-decl f3 :: (-> Int S2)
-#14 := (f3 0::Int)
-#12 := (f3 #11)
-#15 := (= #12 #14)
-#685 := [hypothesis]: #800
-#644 := [monotonicity #685]: #15
-#16 := (not #15)
-#80 := [asserted]: #16
-#690 := [unit-resolution #80 #644]: false
-#700 := [lemma #690]: #702
-#701 := (or #712 #800)
-#182 := -1::Int
-#824 := (* -1::Int #9)
-#763 := (mod #824 -1::Int)
-#767 := (+ #11 #763)
-#765 := (= #767 0::Int)
-#736 := (ite #755 #800 #765)
-#22 := (:var 0 Int)
-#33 := (:var 1 Int)
-#52 := (f4 #33 #22)
-#886 := (pattern #52)
-#186 := (* -1::Int #22)
-#183 := (* -1::Int #33)
-#247 := (mod #183 #186)
-#377 := (+ #52 #247)
-#378 := (= #377 0::Int)
-#53 := (mod #33 #22)
-#374 := (* -1::Int #53)
-#375 := (+ #52 #374)
-#376 := (= #375 0::Int)
-#221 := (>= #33 0::Int)
-#214 := (<= #22 0::Int)
-#321 := (or #214 #221)
-#322 := (not #321)
-#210 := (<= #33 0::Int)
-#319 := (or #210 #214)
-#320 := (not #319)
-#325 := (or #320 #322)
-#379 := (ite #325 #376 #378)
-#373 := (= #52 0::Int)
-#35 := (= #33 0::Int)
-#380 := (ite #35 #373 #379)
-#372 := (= #33 #52)
-#36 := (= #22 0::Int)
-#381 := (ite #36 #372 #380)
-#887 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #886) #381)
-#384 := (forall (vars (?v0 Int) (?v1 Int)) #381)
-#890 := (iff #384 #887)
-#888 := (iff #381 #381)
-#889 := [refl]: #888
-#891 := [quant-intro #889]: #890
-#253 := (* -1::Int #247)
-#341 := (ite #325 #53 #253)
-#344 := (ite #35 0::Int #341)
-#347 := (ite #36 #33 #344)
-#350 := (= #52 #347)
-#353 := (forall (vars (?v0 Int) (?v1 Int)) #350)
-#385 := (iff #353 #384)
-#382 := (iff #350 #381)
-#383 := [rewrite]: #382
-#386 := [quant-intro #383]: #385
-#222 := (not #221)
-#215 := (not #214)
-#225 := (and #215 #222)
-#211 := (not #210)
-#218 := (and #211 #215)
-#228 := (or #218 #225)
-#273 := (ite #228 #53 #253)
-#276 := (ite #35 0::Int #273)
-#279 := (ite #36 #33 #276)
-#282 := (= #52 #279)
-#285 := (forall (vars (?v0 Int) (?v1 Int)) #282)
-#354 := (iff #285 #353)
-#351 := (iff #282 #350)
-#348 := (= #279 #347)
-#345 := (= #276 #344)
-#342 := (= #273 #341)
-#326 := (iff #228 #325)
-#323 := (iff #225 #322)
-#324 := [rewrite]: #323
-#304 := (iff #218 #320)
-#305 := [rewrite]: #304
-#327 := [monotonicity #305 #324]: #326
-#343 := [monotonicity #327]: #342
-#346 := [monotonicity #343]: #345
-#349 := [monotonicity #346]: #348
-#352 := [monotonicity #349]: #351
-#355 := [quant-intro #352]: #354
-#302 := (~ #285 #285)
-#316 := (~ #282 #282)
-#317 := [refl]: #316
-#303 := [nnf-pos #317]: #302
-#46 := (- #22)
-#45 := (- #33)
-#54 := (mod #45 #46)
-#55 := (- #54)
-#39 := (< 0::Int #22)
-#41 := (< #33 0::Int)
-#42 := (and #41 #39)
-#38 := (< 0::Int #33)
-#40 := (and #38 #39)
-#43 := (or #40 #42)
-#56 := (ite #43 #53 #55)
-#57 := (ite #35 0::Int #56)
-#58 := (ite #36 #33 #57)
-#59 := (= #52 #58)
-#60 := (forall (vars (?v0 Int) (?v1 Int)) #59)
-#288 := (iff #60 #285)
-#176 := (and #39 #41)
-#179 := (or #40 #176)
-#258 := (ite #179 #53 #253)
-#167 := (= 0::Int #33)
-#261 := (ite #167 0::Int #258)
-#170 := (= 0::Int #22)
-#264 := (ite #170 #33 #261)
-#267 := (= #52 #264)
-#270 := (forall (vars (?v0 Int) (?v1 Int)) #267)
-#286 := (iff #270 #285)
-#283 := (iff #267 #282)
-#280 := (= #264 #279)
-#277 := (= #261 #276)
-#274 := (= #258 #273)
-#229 := (iff #179 #228)
-#226 := (iff #176 #225)
-#223 := (iff #41 #222)
-#224 := [rewrite]: #223
-#216 := (iff #39 #215)
+#165 := (iff #119 #164)
+#162 := (iff #114 true)
+#157 := (= #27 #27)
+#160 := (iff #157 true)
+#161 := [rewrite]: #160
+#158 := (iff #114 #157)
+#111 := (= #108 #27)
+#154 := (= #98 0::Int)
+#149 := (ite true 0::Int 1::Int)
+#152 := (= #149 0::Int)
+#153 := [rewrite]: #152
+#150 := (= #98 #149)
+#147 := (iff #80 true)
+#142 := (or true false)
+#145 := (iff #142 true)
+#146 := [rewrite]: #145
+#143 := (iff #80 #142)
+#140 := (iff #77 false)
+#135 := (and true false)
+#138 := (iff #135 false)
+#139 := [rewrite]: #138
+#136 := (iff #77 #135)
+#133 := (iff #17 false)
+#134 := [rewrite]: #133
+#124 := (iff #15 true)
+#125 := [rewrite]: #124
+#137 := [monotonicity #125 #134]: #136
+#141 := [trans #137 #139]: #140
+#131 := (iff #16 true)
+#126 := (and true true)
+#129 := (iff #126 true)
+#130 := [rewrite]: #129
+#127 := (iff #16 #126)
+#122 := (iff #14 true)
+#123 := [rewrite]: #122
+#128 := [monotonicity #123 #125]: #127
+#132 := [trans #128 #130]: #131
+#144 := [monotonicity #132 #141]: #143
+#148 := [trans #144 #146]: #147
+#151 := [monotonicity #148]: #150
+#155 := [trans #151 #153]: #154
+#156 := [monotonicity #155]: #111
+#159 := [monotonicity #156]: #158
+#163 := [trans #159 #161]: #162
+#166 := [monotonicity #163]: #165
+#170 := [trans #166 #168]: #169
+#120 := (iff #29 #119)
+#117 := (iff #28 #114)
+#115 := (iff #111 #114)
+#116 := [rewrite]: #115
+#112 := (iff #28 #111)
+#109 := (= #26 #108)
+#106 := (= #25 #98)
+#101 := (ite false 0::Int #98)
+#104 := (= #101 #98)
+#105 := [rewrite]: #104
+#102 := (= #25 #101)
+#99 := (= #24 #98)
+#96 := (= #23 1::Int)
+#88 := -3::Int
+#85 := -1::Int
+#91 := (div -1::Int -3::Int)
+#94 := (= #91 1::Int)
+#95 := [rewrite]: #94
+#92 := (= #23 #91)
+#89 := (= #22 -3::Int)
+#90 := [rewrite]: #89
+#86 := (= #21 -1::Int)
+#87 := [rewrite]: #86
+#93 := [monotonicity #87 #90]: #92
+#97 := [trans #93 #95]: #96
+#83 := (= #20 0::Int)
+#84 := [rewrite]: #83
+#81 := (iff #19 #80)
+#78 := (iff #18 #77)
+#79 := [rewrite]: #78
+#82 := [monotonicity #79]: #81
+#100 := [monotonicity #82 #84 #97]: #99
+#75 := (iff #13 false)
+#70 := (or false false)
+#73 := (iff #70 false)
+#74 := [rewrite]: #73
+#71 := (iff #13 #70)
+#68 := (iff #12 false)
+#69 := [rewrite]: #68
+#66 := (iff #10 false)
+#67 := [rewrite]: #66
+#72 := [monotonicity #67 #69]: #71
+#76 := [trans #72 #74]: #75
+#103 := [monotonicity #76 #100]: #102
+#107 := [trans #103 #105]: #106
+#110 := [monotonicity #107]: #109
+#113 := [monotonicity #110]: #112
+#118 := [trans #113 #116]: #117
+#121 := [monotonicity #118]: #120
+#172 := [trans #121 #170]: #171
+#65 := [asserted]: #29
+[mp #65 #172]: false
+unsat
+ec979d4232e8803cddce0557ed6997ff67bffe05 83 0
+#2 := false
+decl f3 :: (-> Int S2)
+#23 := 1::Int
+#24 := (f3 1::Int)
+#8 := 3::Int
+#18 := (- 3::Int)
+#19 := (div #18 #18)
+#17 := (div 3::Int 3::Int)
+#9 := 0::Int
+#12 := (< 0::Int 3::Int)
+#14 := (< 3::Int 0::Int)
+#15 := (and #14 #12)
+#13 := (and #12 #12)
+#16 := (or #13 #15)
+#20 := (ite #16 #17 #19)
+#10 := (= 3::Int 0::Int)
+#11 := (or #10 #10)
+#21 := (ite #11 0::Int #20)
+#22 := (f3 #21)
+#25 := (= #22 #24)
+#26 := (not #25)
+#119 := (iff #26 false)
+#1 := true
+#114 := (not true)
+#117 := (iff #114 false)
+#118 := [rewrite]: #117
+#115 := (iff #26 #114)
+#112 := (iff #25 true)
+#107 := (= #24 #24)
+#110 := (iff #107 true)
+#111 := [rewrite]: #110
+#108 := (iff #25 #107)
+#104 := (= #21 1::Int)
+#99 := (ite false 0::Int 1::Int)
+#102 := (= #99 1::Int)
+#103 := [rewrite]: #102
+#100 := (= #21 #99)
+#97 := (= #20 1::Int)
+#74 := (and #12 #14)
+#77 := (or #12 #74)
+#92 := (ite #77 1::Int 1::Int)
+#95 := (= #92 1::Int)
+#96 := [rewrite]: #95
+#93 := (= #20 #92)
+#90 := (= #19 1::Int)
+#82 := -3::Int
+#85 := (div -3::Int -3::Int)
+#88 := (= #85 1::Int)
+#89 := [rewrite]: #88
+#86 := (= #19 #85)
+#83 := (= #18 -3::Int)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84 #84]: #86
+#91 := [trans #87 #89]: #90
+#80 := (= #17 1::Int)
+#81 := [rewrite]: #80
+#78 := (iff #16 #77)
+#75 := (iff #15 #74)
+#76 := [rewrite]: #75
+#72 := (iff #13 #12)
+#73 := [rewrite]: #72
+#79 := [monotonicity #73 #76]: #78
+#94 := [monotonicity #79 #81 #91]: #93
+#98 := [trans #94 #96]: #97
+#70 := (iff #11 false)
+#65 := (or false false)
+#68 := (iff #65 false)
+#69 := [rewrite]: #68
+#66 := (iff #11 #65)
+#63 := (iff #10 false)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64 #64]: #66
+#71 := [trans #67 #69]: #70
+#101 := [monotonicity #71 #98]: #100
+#105 := [trans #101 #103]: #104
+#106 := [monotonicity #105]: #25
+#109 := [monotonicity #106]: #108
+#113 := [trans #109 #111]: #112
+#116 := [monotonicity #113]: #115
+#120 := [trans #116 #118]: #119
+#62 := [asserted]: #26
+[mp #62 #120]: false
+unsat
+7e6d147ebdbd2ef1c1366775850a7558514783c8 299 0
+#2 := false
+#10 := 0::Int
+#12 := 3::Int
+decl f3 :: (-> S2 Int)
+decl f4 :: S2
+#8 := f4
+#9 := (f3 f4)
+#402 := (mod #9 3::Int)
+#403 := (>= #402 0::Int)
+#1 := true
+#62 := [true-axiom]: true
+#663 := (or false #403)
+#664 := [th-lemma arith]: #663
+#662 := [unit-resolution #664 #62]: #403
+#84 := -3::Int
+#80 := -1::Int
+#81 := (* -1::Int #9)
+#87 := (div #81 -3::Int)
+#21 := (div #9 3::Int)
+#115 := (>= #9 0::Int)
+#116 := (not #115)
+#102 := (<= #9 0::Int)
+#103 := (not #102)
+#126 := (or #103 #116)
+#129 := (ite #126 #21 #87)
+#11 := (= #9 0::Int)
+#132 := (ite #11 0::Int #129)
+#139 := (* -1::Int #132)
+#140 := (+ #9 #139)
+#138 := (>= #140 0::Int)
+#145 := (not #138)
+#23 := (- 3::Int)
+#22 := (- #9)
+#24 := (div #22 #23)
+#16 := (< 0::Int 3::Int)
+#18 := (< #9 0::Int)
+#19 := (and #18 #16)
+#15 := (< 0::Int #9)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#13 := (= 3::Int 0::Int)
+#14 := (or #11 #13)
+#26 := (ite #14 0::Int #25)
+#27 := (<= #26 #9)
+#28 := (not #27)
+#148 := (iff #28 #145)
+#74 := (and #16 #18)
+#77 := (or #17 #74)
+#90 := (ite #77 #21 #87)
+#93 := (ite #11 0::Int #90)
+#96 := (<= #93 #9)
+#99 := (not #96)
+#146 := (iff #99 #145)
+#143 := (iff #96 #138)
+#135 := (<= #132 #9)
+#141 := (iff #135 #138)
+#142 := [rewrite]: #141
+#136 := (iff #96 #135)
+#133 := (= #93 #132)
+#130 := (= #90 #129)
+#127 := (iff #77 #126)
+#124 := (iff #74 #116)
+#119 := (and true #116)
+#122 := (iff #119 #116)
+#123 := [rewrite]: #122
+#120 := (iff #74 #119)
+#117 := (iff #18 #116)
+#118 := [rewrite]: #117
+#106 := (iff #16 true)
+#107 := [rewrite]: #106
+#121 := [monotonicity #107 #118]: #120
+#125 := [trans #121 #123]: #124
+#113 := (iff #17 #103)
+#108 := (and #103 true)
+#111 := (iff #108 #103)
+#112 := [rewrite]: #111
+#109 := (iff #17 #108)
+#104 := (iff #15 #103)
+#105 := [rewrite]: #104
+#110 := [monotonicity #105 #107]: #109
+#114 := [trans #110 #112]: #113
+#128 := [monotonicity #114 #125]: #127
+#131 := [monotonicity #128]: #130
+#134 := [monotonicity #131]: #133
+#137 := [monotonicity #134]: #136
+#144 := [trans #137 #142]: #143
+#147 := [monotonicity #144]: #146
+#100 := (iff #28 #99)
+#97 := (iff #27 #96)
+#94 := (= #26 #93)
+#91 := (= #25 #90)
+#88 := (= #24 #87)
+#85 := (= #23 -3::Int)
+#86 := [rewrite]: #85
+#82 := (= #22 #81)
+#83 := [rewrite]: #82
+#89 := [monotonicity #83 #86]: #88
+#78 := (iff #20 #77)
+#75 := (iff #19 #74)
+#76 := [rewrite]: #75
+#79 := [monotonicity #76]: #78
+#92 := [monotonicity #79 #89]: #91
+#72 := (iff #14 #11)
+#67 := (or #11 false)
+#70 := (iff #67 #11)
+#71 := [rewrite]: #70
+#68 := (iff #14 #67)
+#65 := (iff #13 false)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#73 := [trans #69 #71]: #72
+#95 := [monotonicity #73 #92]: #94
+#98 := [monotonicity #95]: #97
+#101 := [monotonicity #98]: #100
+#149 := [trans #101 #147]: #148
+#64 := [asserted]: #28
+#150 := [mp #64 #149]: #145
+#507 := (+ #21 #139)
+#661 := (>= #507 0::Int)
+#506 := (= #21 #132)
+#395 := (= #129 #132)
+#712 := (not #11)
+#344 := (<= #132 0::Int)
+#309 := (= #132 0::Int)
+#709 := [hypothesis]: #11
+#386 := (or #712 #309)
+#387 := [def-axiom]: #386
+#349 := [unit-resolution #387 #709]: #309
+#350 := (not #309)
+#710 := (or #350 #344)
+#708 := [th-lemma arith triangle-eq]: #710
+#711 := [unit-resolution #708 #349]: #344
+#697 := (or #712 #115)
+#698 := [th-lemma arith triangle-eq]: #697
+#420 := [unit-resolution #698 #709]: #115
+#421 := [th-lemma arith farkas -1 1 1 #420 #150 #711]: false
+#422 := [lemma #421]: #712
+#719 := (or #11 #395)
+#720 := [def-axiom]: #719
+#665 := [unit-resolution #720 #422]: #395
+#310 := (= #21 #129)
+decl f5 :: (-> Int S2)
+#721 := (f5 #9)
+#717 := (f3 #721)
+#723 := (= #717 0::Int)
+#542 := (not #723)
+#557 := (iff #712 #542)
+#654 := (iff #11 #723)
+#558 := (iff #723 #11)
+#508 := (= #717 #9)
+#548 := (= #721 f4)
+#722 := (= f4 #721)
+#29 := (:var 0 S2)
+#30 := (f3 #29)
+#724 := (pattern #30)
+#31 := (f5 #30)
+#152 := (= #29 #31)
+#725 := (forall (vars (?v0 S2)) (:pat #724) #152)
+#155 := (forall (vars (?v0 S2)) #152)
+#726 := (iff #155 #725)
+#728 := (iff #725 #725)
+#729 := [rewrite]: #728
+#727 := [rewrite]: #726
+#730 := [trans #727 #729]: #726
+#249 := (~ #155 #155)
+#247 := (~ #152 #152)
+#248 := [refl]: #247
+#250 := [nnf-pos #248]: #249
+#32 := (= #31 #29)
+#33 := (forall (vars (?v0 S2)) #32)
+#156 := (iff #33 #155)
+#153 := (iff #32 #152)
+#154 := [rewrite]: #153
+#157 := [quant-intro #154]: #156
+#151 := [asserted]: #33
+#160 := [mp #151 #157]: #155
+#239 := [mp~ #160 #250]: #155
+#731 := [mp #239 #730]: #725
+#713 := (not #725)
+#373 := (or #713 #722)
+#378 := [quant-inst #8]: #373
+#547 := [unit-resolution #378 #731]: #722
+#549 := [symm #547]: #548
+#656 := [monotonicity #549]: #508
+#653 := [monotonicity #656]: #558
+#657 := [symm #653]: #654
+#559 := [monotonicity #657]: #557
+#560 := [mp #422 #559]: #542
+#374 := (or #115 #723)
+#34 := (:var 0 Int)
+#36 := (f5 #34)
+#732 := (pattern #36)
+#176 := (>= #34 0::Int)
+#37 := (f3 #36)
+#42 := (= #37 0::Int)
+#225 := (or #42 #176)
+#739 := (forall (vars (?v0 Int)) (:pat #732) #225)
+#230 := (forall (vars (?v0 Int)) #225)
+#742 := (iff #230 #739)
+#740 := (iff #225 #225)
+#741 := [refl]: #740
+#743 := [quant-intro #741]: #742
+#243 := (~ #230 #230)
+#251 := (~ #225 #225)
+#252 := [refl]: #251
+#244 := [nnf-pos #252]: #243
+#41 := (< #34 0::Int)
+#43 := (implies #41 #42)
+#44 := (forall (vars (?v0 Int)) #43)
+#233 := (iff #44 #230)
+#196 := (= 0::Int #37)
+#202 := (not #41)
+#203 := (or #202 #196)
+#208 := (forall (vars (?v0 Int)) #203)
+#231 := (iff #208 #230)
+#228 := (iff #203 #225)
+#222 := (or #176 #42)
+#226 := (iff #222 #225)
+#227 := [rewrite]: #226
+#223 := (iff #203 #222)
+#220 := (iff #196 #42)
+#221 := [rewrite]: #220
+#218 := (iff #202 #176)
+#178 := (not #176)
+#213 := (not #178)
+#216 := (iff #213 #176)
 #217 := [rewrite]: #216
-#227 := [monotonicity #217 #224]: #226
-#219 := (iff #40 #218)
-#212 := (iff #38 #211)
-#213 := [rewrite]: #212
-#220 := [monotonicity #213 #217]: #219
-#230 := [monotonicity #220 #227]: #229
-#275 := [monotonicity #230]: #274
-#204 := (iff #167 #35)
+#214 := (iff #202 #213)
+#211 := (iff #41 #178)
+#212 := [rewrite]: #211
+#215 := [monotonicity #212]: #214
+#219 := [trans #215 #217]: #218
+#224 := [monotonicity #219 #221]: #223
+#229 := [trans #224 #227]: #228
+#232 := [quant-intro #229]: #231
+#209 := (iff #44 #208)
+#206 := (iff #43 #203)
+#199 := (implies #41 #196)
+#204 := (iff #199 #203)
 #205 := [rewrite]: #204
-#278 := [monotonicity #205 #275]: #277
-#206 := (iff #170 #36)
-#207 := [rewrite]: #206
-#281 := [monotonicity #207 #278]: #280
-#284 := [monotonicity #281]: #283
-#287 := [quant-intro #284]: #286
-#271 := (iff #60 #270)
-#268 := (iff #59 #267)
-#265 := (= #58 #264)
-#262 := (= #57 #261)
-#259 := (= #56 #258)
-#256 := (= #55 #253)
-#250 := (- #247)
-#254 := (= #250 #253)
-#255 := [rewrite]: #254
-#251 := (= #55 #250)
-#248 := (= #54 #247)
-#187 := (= #46 #186)
-#188 := [rewrite]: #187
-#184 := (= #45 #183)
-#185 := [rewrite]: #184
-#249 := [monotonicity #185 #188]: #248
-#252 := [monotonicity #249]: #251
-#257 := [trans #252 #255]: #256
-#180 := (iff #43 #179)
-#177 := (iff #42 #176)
-#178 := [rewrite]: #177
-#181 := [monotonicity #178]: #180
-#260 := [monotonicity #181 #257]: #259
-#168 := (iff #35 #167)
-#169 := [rewrite]: #168
-#263 := [monotonicity #169 #260]: #262
-#171 := (iff #36 #170)
+#200 := (iff #43 #199)
+#197 := (iff #42 #196)
+#198 := [rewrite]: #197
+#201 := [monotonicity #198]: #200
+#207 := [trans #201 #205]: #206
+#210 := [quant-intro #207]: #209
+#234 := [trans #210 #232]: #233
+#195 := [asserted]: #44
+#235 := [mp #195 #234]: #230
+#253 := [mp~ #235 #244]: #230
+#744 := [mp #253 #743]: #739
+#699 := (not #739)
+#362 := (or #699 #115 #723)
+#714 := (or #723 #115)
+#363 := (or #699 #714)
+#705 := (iff #363 #362)
+#365 := (or #699 #374)
+#703 := (iff #365 #362)
+#704 := [rewrite]: #703
+#701 := (iff #363 #365)
+#715 := (iff #714 #374)
+#358 := [rewrite]: #715
+#702 := [monotonicity #358]: #701
+#700 := [trans #702 #704]: #705
+#364 := [quant-inst #9]: #363
+#706 := [mp #364 #700]: #362
+#553 := [unit-resolution #706 #744]: #374
+#561 := [unit-resolution #553 #560]: #115
+#562 := (or #11 #103 #116)
+#563 := [th-lemma arith triangle-eq]: #562
+#564 := [unit-resolution #563 #561 #422]: #103
+#397 := (or #126 #102)
+#388 := [def-axiom]: #397
+#565 := [unit-resolution #388 #564]: #126
+#328 := (not #126)
+#716 := (or #328 #310)
+#718 := [def-axiom]: #716
+#658 := [unit-resolution #718 #565]: #310
+#655 := [trans #658 #665]: #506
+#659 := (not #506)
+#646 := (or #659 #661)
+#648 := [th-lemma arith triangle-eq]: #646
+#640 := [unit-resolution #648 #655]: #661
+#696 := (* -1::Int #402)
+#692 := (* -3::Int #21)
+#406 := (+ #692 #696)
+#407 := (+ #9 #406)
+#688 := (>= #407 0::Int)
+#695 := (= #407 0::Int)
+#637 := (or false #695)
+#639 := [th-lemma arith]: #637
+#649 := [unit-resolution #639 #62]: #695
+#650 := (not #695)
+#651 := (or #650 #688)
+#647 := [th-lemma arith triangle-eq]: #651
+#652 := [unit-resolution #647 #649]: #688
+[th-lemma arith farkas 2 1 3 3 1 #561 #652 #640 #150 #662]: false
+unsat
+73ec717ba0bbdd95adecb13ea22d00aede55f061 489 0
+#2 := false
+decl f3 :: (-> Int S2)
+#10 := 0::Int
+#29 := (f3 0::Int)
+decl f5 :: S2
+#8 := f5
+#30 := (= f5 #29)
+decl f4 :: (-> S2 Int)
+#9 := (f4 f5)
+#385 := (f3 #9)
+#662 := (= #385 #29)
+#631 := (= #29 #385)
+#629 := (= 0::Int #9)
+#11 := (= #9 0::Int)
+#12 := 3::Int
+#429 := (mod #9 3::Int)
+#663 := (>= #429 0::Int)
+#1 := true
+#66 := [true-axiom]: true
+#624 := (or false #663)
+#619 := [th-lemma arith]: #624
+#625 := [unit-resolution #619 #66]: #663
+#88 := -3::Int
+#84 := -1::Int
+#85 := (* -1::Int #9)
+#91 := (div #85 -3::Int)
+#21 := (div #9 3::Int)
+#141 := (>= #9 0::Int)
+#142 := (not #141)
+#128 := (<= #9 0::Int)
+#129 := (not #128)
+#152 := (or #129 #142)
+#155 := (ite #152 #21 #91)
+#158 := (ite #11 0::Int #155)
+#628 := (* -1::Int #158)
+#634 := (+ #9 #628)
+#620 := (<= #634 0::Int)
+#633 := (= #9 #158)
+#161 := (f3 #158)
+#708 := (f4 #161)
+#577 := (= #708 #158)
+#703 := (= #158 #708)
+#706 := (>= #158 0::Int)
+#709 := (= #708 0::Int)
+#608 := (not #709)
+#739 := (not #11)
+#609 := (iff #739 #608)
+#611 := (iff #11 #709)
+#605 := (iff #709 #11)
+#493 := (= #708 #9)
+#598 := (= #161 f5)
+#164 := (= f5 #161)
+#664 := (= #29 #161)
+#675 := (= #161 #29)
+#336 := (= #158 0::Int)
+#729 := (f4 #29)
+#727 := (= #729 0::Int)
+#38 := (:var 0 Int)
+#40 := (f3 #38)
+#759 := (pattern #40)
+#203 := (>= #38 0::Int)
+#205 := (not #203)
+#41 := (f4 #40)
+#186 := (= #38 #41)
+#211 := (or #186 #205)
+#760 := (forall (vars (?v0 Int)) (:pat #759) #211)
+#216 := (forall (vars (?v0 Int)) #211)
+#763 := (iff #216 #760)
+#761 := (iff #211 #211)
+#762 := [refl]: #761
+#764 := [quant-intro #762]: #763
+#268 := (~ #216 #216)
+#267 := (~ #211 #211)
+#264 := [refl]: #267
+#269 := [nnf-pos #264]: #268
+#42 := (= #41 #38)
+#39 := (<= 0::Int #38)
+#43 := (implies #39 #42)
+#44 := (forall (vars (?v0 Int)) #43)
+#219 := (iff #44 #216)
+#193 := (not #39)
+#194 := (or #193 #186)
+#199 := (forall (vars (?v0 Int)) #194)
+#217 := (iff #199 #216)
+#214 := (iff #194 #211)
+#208 := (or #205 #186)
+#212 := (iff #208 #211)
+#213 := [rewrite]: #212
+#209 := (iff #194 #208)
+#206 := (iff #193 #205)
+#202 := (iff #39 #203)
+#204 := [rewrite]: #202
+#207 := [monotonicity #204]: #206
+#210 := [monotonicity #207]: #209
+#215 := [trans #210 #213]: #214
+#218 := [quant-intro #215]: #217
+#200 := (iff #44 #199)
+#197 := (iff #43 #194)
+#190 := (implies #39 #186)
+#195 := (iff #190 #194)
+#196 := [rewrite]: #195
+#191 := (iff #43 #190)
+#188 := (iff #42 #186)
+#189 := [rewrite]: #188
+#192 := [monotonicity #189]: #191
+#198 := [trans #192 #196]: #197
+#201 := [quant-intro #198]: #200
+#220 := [trans #201 #218]: #219
+#185 := [asserted]: #44
+#221 := [mp #185 #220]: #216
+#265 := [mp~ #221 #269]: #216
+#765 := [mp #265 #764]: #760
+#721 := (not #760)
+#443 := (or #721 #727)
+#389 := (>= 0::Int 0::Int)
+#390 := (not #389)
+#730 := (= 0::Int #729)
+#731 := (or #730 #390)
+#444 := (or #721 #731)
+#722 := (iff #444 #443)
+#723 := (iff #443 #443)
+#433 := [rewrite]: #723
+#343 := (iff #731 #727)
+#725 := (or #727 false)
+#449 := (iff #725 #727)
+#450 := [rewrite]: #449
+#447 := (iff #731 #725)
+#738 := (iff #390 false)
+#736 := (not true)
+#737 := (iff #736 false)
+#735 := [rewrite]: #737
+#376 := (iff #390 #736)
+#371 := (iff #389 true)
+#734 := [rewrite]: #371
+#377 := [monotonicity #734]: #376
+#724 := [trans #377 #735]: #738
+#732 := (iff #730 #727)
+#733 := [rewrite]: #732
+#448 := [monotonicity #733 #724]: #447
+#720 := [trans #448 #450]: #343
+#719 := [monotonicity #720]: #722
+#434 := [trans #719 #433]: #722
+#718 := [quant-inst #10]: #444
+#435 := [mp #718 #434]: #443
+#590 := [unit-resolution #435 #765]: #727
+#685 := (= #9 #729)
+#748 := (not #164)
+#588 := [hypothesis]: #748
+#401 := (or #30 #164)
+#122 := (not #30)
+#170 := (iff #122 #164)
+#23 := (- 3::Int)
+#22 := (- #9)
+#24 := (div #22 #23)
+#16 := (< 0::Int 3::Int)
+#18 := (< #9 0::Int)
+#19 := (and #18 #16)
+#15 := (< 0::Int #9)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#13 := (= 3::Int 0::Int)
+#14 := (or #11 #13)
+#26 := (ite #14 0::Int #25)
+#27 := (f3 #26)
+#28 := (= #27 f5)
+#31 := (iff #28 #30)
+#32 := (not #31)
+#175 := (iff #32 #170)
+#78 := (and #16 #18)
+#81 := (or #17 #78)
+#94 := (ite #81 #21 #91)
+#97 := (ite #11 0::Int #94)
+#100 := (f3 #97)
+#106 := (= f5 #100)
+#123 := (iff #106 #122)
+#173 := (iff #123 #170)
+#167 := (iff #164 #122)
+#171 := (iff #167 #170)
 #172 := [rewrite]: #171
-#266 := [monotonicity #172 #263]: #265
-#269 := [monotonicity #266]: #268
-#272 := [quant-intro #269]: #271
-#289 := [trans #272 #287]: #288
-#246 := [asserted]: #60
-#290 := [mp #246 #289]: #285
-#318 := [mp~ #290 #303]: #285
-#356 := [mp #318 #355]: #353
-#387 := [mp #356 #386]: #384
-#892 := [mp #387 #891]: #887
-#735 := (not #887)
-#741 := (or #735 #736)
-#820 := (* -1::Int 1::Int)
-#813 := (mod #824 #820)
-#814 := (+ #11 #813)
-#815 := (= #814 0::Int)
-#810 := (mod #9 1::Int)
-#811 := (* -1::Int #810)
-#816 := (+ #11 #811)
-#817 := (= #816 0::Int)
-#818 := (<= 1::Int 0::Int)
-#659 := (or #818 #812)
-#660 := (not #659)
-#803 := (or #661 #818)
-#804 := (not #803)
-#805 := (or #804 #660)
-#806 := (ite #805 #817 #815)
-#807 := (ite #801 #800 #806)
-#808 := (= #9 #11)
-#802 := (= 1::Int 0::Int)
-#809 := (ite #802 #808 #807)
-#727 := (or #735 #809)
-#724 := (iff #727 #741)
-#728 := (iff #741 #741)
-#729 := [rewrite]: #728
-#739 := (iff #809 #736)
-#696 := (or #683 #694)
-#742 := (or #696 #801)
-#743 := (ite #742 #800 #765)
-#737 := (iff #743 #736)
-#733 := (iff #742 #755)
-#734 := [rewrite]: #733
-#738 := [monotonicity #734]: #737
-#754 := (iff #809 #743)
-#749 := (ite false #808 #743)
-#752 := (iff #749 #743)
-#753 := [rewrite]: #752
-#750 := (iff #809 #749)
-#747 := (iff #807 #743)
-#757 := (ite #696 #800 #765)
-#761 := (ite #801 #800 #757)
-#745 := (iff #761 #743)
-#746 := [rewrite]: #745
-#758 := (iff #807 #761)
-#759 := (iff #806 #757)
-#770 := (iff #815 #765)
-#768 := (= #814 #767)
-#764 := (= #813 #763)
-#772 := (= #820 -1::Int)
-#779 := [rewrite]: #772
-#766 := [monotonicity #779]: #764
-#769 := [monotonicity #766]: #768
-#756 := [monotonicity #769]: #770
-#777 := (iff #817 #800)
-#775 := (= #816 #11)
-#783 := (+ #11 0::Int)
-#781 := (= #783 #11)
-#786 := [rewrite]: #781
-#784 := (= #816 #783)
-#771 := (= #811 0::Int)
-#789 := (* -1::Int 0::Int)
-#782 := (= #789 0::Int)
-#774 := [rewrite]: #782
-#793 := (= #811 #789)
-#699 := (= #810 0::Int)
-#792 := [rewrite]: #699
-#780 := [monotonicity #792]: #793
-#773 := [trans #780 #774]: #771
-#785 := [monotonicity #773]: #784
-#776 := [trans #785 #786]: #775
-#778 := [monotonicity #776]: #777
-#697 := (iff #805 #696)
-#687 := (iff #660 #694)
-#691 := (iff #659 #812)
-#692 := (or false #812)
-#791 := (iff #692 #812)
-#676 := [rewrite]: #791
-#787 := (iff #659 #692)
-#641 := (iff #818 false)
-#794 := [rewrite]: #641
-#788 := [monotonicity #794]: #787
-#693 := [trans #788 #676]: #691
-#695 := [monotonicity #693]: #687
-#642 := (iff #804 #683)
-#681 := (iff #803 #661)
-#795 := (or #661 false)
-#796 := (iff #795 #661)
-#799 := [rewrite]: #796
-#797 := (iff #803 #795)
-#798 := [monotonicity #794]: #797
-#682 := [trans #798 #799]: #681
-#790 := [monotonicity #682]: #642
-#698 := [monotonicity #790 #695]: #697
-#760 := [monotonicity #698 #778 #756]: #759
-#762 := [monotonicity #760]: #758
-#748 := [trans #762 #746]: #747
-#638 := (iff #802 false)
-#640 := [rewrite]: #638
-#751 := [monotonicity #640 #748]: #750
-#744 := [trans #751 #753]: #754
-#740 := [trans #744 #738]: #739
-#725 := [monotonicity #740]: #724
-#730 := [trans #725 #729]: #724
-#723 := [quant-inst #9 #10]: #727
-#731 := [mp #723 #730]: #741
-#680 := [unit-resolution #731 #892]: #736
-#719 := (not #736)
-#720 := (or #719 #712 #800)
-#721 := [def-axiom]: #720
-#656 := [unit-resolution #721 #680]: #701
-#657 := [unit-resolution #656 #700]: #712
-#600 := (or #755 #812)
-#711 := [def-axiom]: #600
-#662 := [unit-resolution #711 #657]: #812
-#726 := (or #755 #661)
-#732 := [def-axiom]: #726
-#663 := [unit-resolution #732 #657]: #661
-#705 := (not #801)
-#706 := (or #755 #705)
-#707 := [def-axiom]: #706
-#664 := [unit-resolution #707 #657]: #705
-#665 := (or #801 #683 #694)
-#666 := [th-lemma arith triangle-eq]: #665
-[unit-resolution #666 #664 #663 #662]: false
-unsat
-9fbefb874a9c8d1ffb3917c9db0286d637e8beaf 310 0
+#168 := (iff #123 #167)
+#165 := (iff #106 #164)
+#162 := (= #100 #161)
+#159 := (= #97 #158)
+#156 := (= #94 #155)
+#153 := (iff #81 #152)
+#150 := (iff #78 #142)
+#145 := (and true #142)
+#148 := (iff #145 #142)
+#149 := [rewrite]: #148
+#146 := (iff #78 #145)
+#143 := (iff #18 #142)
+#144 := [rewrite]: #143
+#132 := (iff #16 true)
+#133 := [rewrite]: #132
+#147 := [monotonicity #133 #144]: #146
+#151 := [trans #147 #149]: #150
+#139 := (iff #17 #129)
+#134 := (and #129 true)
+#137 := (iff #134 #129)
+#138 := [rewrite]: #137
+#135 := (iff #17 #134)
+#130 := (iff #15 #129)
+#131 := [rewrite]: #130
+#136 := [monotonicity #131 #133]: #135
+#140 := [trans #136 #138]: #139
+#154 := [monotonicity #140 #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [monotonicity #163]: #165
+#169 := [monotonicity #166]: #168
+#174 := [trans #169 #172]: #173
+#126 := (iff #32 #123)
+#114 := (iff #30 #106)
+#119 := (not #114)
+#124 := (iff #119 #123)
+#125 := [rewrite]: #124
+#120 := (iff #32 #119)
+#117 := (iff #31 #114)
+#111 := (iff #106 #30)
+#115 := (iff #111 #114)
+#116 := [rewrite]: #115
+#112 := (iff #31 #111)
+#109 := (iff #28 #106)
+#103 := (= #100 f5)
+#107 := (iff #103 #106)
+#108 := [rewrite]: #107
+#104 := (iff #28 #103)
+#101 := (= #27 #100)
+#98 := (= #26 #97)
+#95 := (= #25 #94)
+#92 := (= #24 #91)
+#89 := (= #23 -3::Int)
+#90 := [rewrite]: #89
+#86 := (= #22 #85)
+#87 := [rewrite]: #86
+#93 := [monotonicity #87 #90]: #92
+#82 := (iff #20 #81)
+#79 := (iff #19 #78)
+#80 := [rewrite]: #79
+#83 := [monotonicity #80]: #82
+#96 := [monotonicity #83 #93]: #95
+#76 := (iff #14 #11)
+#71 := (or #11 false)
+#74 := (iff #71 #11)
+#75 := [rewrite]: #74
+#72 := (iff #14 #71)
+#69 := (iff #13 false)
+#70 := [rewrite]: #69
+#73 := [monotonicity #70]: #72
+#77 := [trans #73 #75]: #76
+#99 := [monotonicity #77 #96]: #98
+#102 := [monotonicity #99]: #101
+#105 := [monotonicity #102]: #104
+#110 := [trans #105 #108]: #109
+#113 := [monotonicity #110]: #112
+#118 := [trans #113 #116]: #117
+#121 := [monotonicity #118]: #120
+#127 := [trans #121 #125]: #126
+#176 := [trans #127 #174]: #175
+#68 := [asserted]: #32
+#177 := [mp #68 #176]: #170
+#749 := (not #170)
+#405 := (or #30 #164 #749)
+#741 := [def-axiom]: #405
+#742 := [unit-resolution #741 #177]: #401
+#589 := [unit-resolution #742 #588]: #30
+#682 := [monotonicity #589]: #685
+#686 := [trans #682 #590]: #11
+#413 := (or #739 #336)
+#414 := [def-axiom]: #413
+#673 := [unit-resolution #414 #686]: #336
+#667 := [monotonicity #673]: #675
+#666 := [symm #667]: #664
+#676 := [trans #589 #666]: #164
+#677 := [unit-resolution #588 #676]: false
+#678 := [lemma #677]: #164
+#599 := [symm #678]: #598
+#604 := [monotonicity #599]: #493
+#606 := [monotonicity #604]: #605
+#607 := [symm #606]: #611
+#612 := [monotonicity #607]: #609
+#600 := [hypothesis]: #739
+#613 := [mp #600 #612]: #608
+#697 := (or #706 #709)
+#46 := (= #41 0::Int)
+#252 := (or #46 #203)
+#766 := (forall (vars (?v0 Int)) (:pat #759) #252)
+#257 := (forall (vars (?v0 Int)) #252)
+#769 := (iff #257 #766)
+#767 := (iff #252 #252)
+#768 := [refl]: #767
+#770 := [quant-intro #768]: #769
+#270 := (~ #257 #257)
+#278 := (~ #252 #252)
+#279 := [refl]: #278
+#271 := [nnf-pos #279]: #270
+#45 := (< #38 0::Int)
+#47 := (implies #45 #46)
+#48 := (forall (vars (?v0 Int)) #47)
+#260 := (iff #48 #257)
+#223 := (= 0::Int #41)
+#229 := (not #45)
+#230 := (or #229 #223)
+#235 := (forall (vars (?v0 Int)) #230)
+#258 := (iff #235 #257)
+#255 := (iff #230 #252)
+#249 := (or #203 #46)
+#253 := (iff #249 #252)
+#254 := [rewrite]: #253
+#250 := (iff #230 #249)
+#247 := (iff #223 #46)
+#248 := [rewrite]: #247
+#245 := (iff #229 #203)
+#240 := (not #205)
+#243 := (iff #240 #203)
+#244 := [rewrite]: #243
+#241 := (iff #229 #240)
+#238 := (iff #45 #205)
+#239 := [rewrite]: #238
+#242 := [monotonicity #239]: #241
+#246 := [trans #242 #244]: #245
+#251 := [monotonicity #246 #248]: #250
+#256 := [trans #251 #254]: #255
+#259 := [quant-intro #256]: #258
+#236 := (iff #48 #235)
+#233 := (iff #47 #230)
+#226 := (implies #45 #223)
+#231 := (iff #226 #230)
+#232 := [rewrite]: #231
+#227 := (iff #47 #226)
+#224 := (iff #46 #223)
+#225 := [rewrite]: #224
+#228 := [monotonicity #225]: #227
+#234 := [trans #228 #232]: #233
+#237 := [quant-intro #234]: #236
+#261 := [trans #237 #259]: #260
+#222 := [asserted]: #48
+#262 := [mp #222 #261]: #257
+#280 := [mp~ #262 #271]: #257
+#771 := [mp #280 #770]: #766
+#693 := (not #766)
+#694 := (or #693 #706 #709)
+#710 := (or #709 #706)
+#700 := (or #693 #710)
+#687 := (iff #700 #694)
+#695 := (or #693 #697)
+#533 := (iff #695 #694)
+#534 := [rewrite]: #533
+#702 := (iff #700 #695)
+#698 := (iff #710 #697)
+#699 := [rewrite]: #698
+#531 := [monotonicity #699]: #702
+#688 := [trans #531 #534]: #687
+#701 := [quant-inst #158]: #700
+#690 := [mp #701 #688]: #694
+#614 := [unit-resolution #690 #771]: #697
+#610 := [unit-resolution #614 #613]: #706
+#707 := (not #706)
+#704 := (or #703 #707)
+#705 := (or #721 #703 #707)
+#711 := (or #721 #704)
+#553 := (iff #711 #705)
+#554 := [rewrite]: #553
+#552 := [quant-inst #158]: #711
+#696 := [mp #552 #554]: #705
+#615 := [unit-resolution #696 #765]: #704
+#595 := [unit-resolution #615 #610]: #703
+#601 := [symm #595]: #577
+#541 := (= #9 #708)
+#596 := [symm #604]: #541
+#602 := [trans #596 #601]: #633
+#597 := (not #633)
+#603 := (or #597 #620)
+#571 := [th-lemma arith triangle-eq]: #603
+#578 := [unit-resolution #571 #602]: #620
+#618 := (+ #21 #628)
+#622 := (>= #618 0::Int)
+#617 := (= #21 #158)
+#422 := (= #155 #158)
+#746 := (or #11 #422)
+#747 := [def-axiom]: #746
+#537 := [unit-resolution #747 #600]: #422
+#337 := (= #21 #155)
+#691 := (f4 #385)
+#689 := (= #691 0::Int)
+#594 := (not #689)
+#549 := (iff #739 #594)
+#593 := (iff #11 #689)
+#582 := (iff #689 #11)
+#579 := (= #691 #9)
+#570 := (= #385 f5)
+#726 := (= f5 #385)
+#33 := (:var 0 S2)
+#34 := (f4 #33)
+#751 := (pattern #34)
+#35 := (f3 #34)
+#179 := (= #33 #35)
+#752 := (forall (vars (?v0 S2)) (:pat #751) #179)
+#182 := (forall (vars (?v0 S2)) #179)
+#753 := (iff #182 #752)
+#755 := (iff #752 #752)
+#756 := [rewrite]: #755
+#754 := [rewrite]: #753
+#757 := [trans #754 #756]: #753
+#276 := (~ #182 #182)
+#274 := (~ #179 #179)
+#275 := [refl]: #274
+#277 := [nnf-pos #275]: #276
+#36 := (= #35 #33)
+#37 := (forall (vars (?v0 S2)) #36)
+#183 := (iff #37 #182)
+#180 := (iff #36 #179)
+#181 := [rewrite]: #180
+#184 := [quant-intro #181]: #183
+#178 := [asserted]: #37
+#187 := [mp #178 #184]: #182
+#266 := [mp~ #187 #277]: #182
+#758 := [mp #266 #757]: #752
+#391 := (not #752)
+#392 := (or #391 #726)
+#728 := [quant-inst #8]: #392
+#568 := [unit-resolution #728 #758]: #726
+#572 := [symm #568]: #570
+#581 := [monotonicity #572]: #579
+#583 := [monotonicity #581]: #582
+#573 := [symm #583]: #593
+#550 := [monotonicity #573]: #549
+#555 := [mp #600 #550]: #594
+#574 := (or #141 #689)
+#535 := (or #693 #141 #689)
+#692 := (or #689 #141)
+#683 := (or #693 #692)
+#586 := (iff #683 #535)
+#680 := (or #693 #574)
+#569 := (iff #680 #535)
+#584 := [rewrite]: #569
+#681 := (iff #683 #680)
+#575 := (iff #692 #574)
+#576 := [rewrite]: #575
+#684 := [monotonicity #576]: #681
+#587 := [trans #684 #584]: #586
+#585 := [quant-inst #9]: #683
+#580 := [mp #585 #587]: #535
+#556 := [unit-resolution #580 #771]: #574
+#557 := [unit-resolution #556 #555]: #141
+#558 := (or #11 #129 #142)
+#559 := [th-lemma arith triangle-eq]: #558
+#560 := [unit-resolution #559 #600]: #152
+#561 := [unit-resolution #560 #557]: #129
+#424 := (or #152 #128)
+#415 := [def-axiom]: #424
+#562 := [unit-resolution #415 #561]: #152
+#355 := (not #152)
+#743 := (or #355 #337)
+#745 := [def-axiom]: #743
+#563 := [unit-resolution #745 #562]: #337
+#564 := [trans #563 #537]: #617
+#565 := (not #617)
+#566 := (or #565 #622)
+#551 := [th-lemma arith triangle-eq]: #566
+#567 := [unit-resolution #551 #564]: #622
+#656 := (* -1::Int #429)
+#672 := (* -3::Int #21)
+#657 := (+ #672 #656)
+#659 := (+ #9 #657)
+#658 := (>= #659 0::Int)
+#665 := (= #659 0::Int)
+#528 := (or false #665)
+#529 := [th-lemma arith]: #528
+#536 := [unit-resolution #529 #66]: #665
+#538 := (not #665)
+#539 := (or #538 #658)
+#540 := [th-lemma arith triangle-eq]: #539
+#542 := [unit-resolution #540 #536]: #658
+#543 := [th-lemma arith farkas 2 1 3 3 1 #561 #542 #567 #578 #625]: false
+#544 := [lemma #543]: #11
+#630 := [symm #544]: #629
+#632 := [monotonicity #630]: #631
+#616 := [symm #632]: #662
+#621 := [trans #568 #616]: #30
+#740 := (or #122 #748)
+#744 := (or #122 #748 #749)
+#750 := [def-axiom]: #744
+#400 := [unit-resolution #750 #177]: #740
+#627 := [unit-resolution #400 #678]: #122
+[unit-resolution #627 #621]: false
+unsat
+1f21dc1a1f14ef0634d3f8992746cd150b8c3799 78 0
 #2 := false
 decl f3 :: (-> Int S2)
 #8 := 0::Int
-#12 := (f3 0::Int)
-decl f4 :: (-> Int Int Int)
-#9 := 3::Int
-#10 := (f4 0::Int 3::Int)
-#11 := (f3 #10)
-#13 := (= #11 #12)
-#800 := (= #10 0::Int)
-#20 := (:var 0 Int)
-#31 := (:var 1 Int)
-#50 := (f4 #31 #20)
-#885 := (pattern #50)
-#180 := -1::Int
-#184 := (* -1::Int #20)
-#181 := (* -1::Int #31)
-#245 := (mod #181 #184)
-#375 := (+ #50 #245)
-#376 := (= #375 0::Int)
-#51 := (mod #31 #20)
-#372 := (* -1::Int #51)
-#373 := (+ #50 #372)
-#374 := (= #373 0::Int)
-#219 := (>= #31 0::Int)
-#212 := (<= #20 0::Int)
-#319 := (or #212 #219)
-#320 := (not #319)
-#208 := (<= #31 0::Int)
-#317 := (or #208 #212)
-#318 := (not #317)
-#323 := (or #318 #320)
-#377 := (ite #323 #374 #376)
-#371 := (= #50 0::Int)
-#33 := (= #31 0::Int)
-#378 := (ite #33 #371 #377)
-#370 := (= #31 #50)
-#34 := (= #20 0::Int)
-#379 := (ite #34 #370 #378)
-#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #379)
-#382 := (forall (vars (?v0 Int) (?v1 Int)) #379)
-#889 := (iff #382 #886)
-#887 := (iff #379 #379)
-#888 := [refl]: #887
-#890 := [quant-intro #888]: #889
-#251 := (* -1::Int #245)
-#339 := (ite #323 #51 #251)
-#342 := (ite #33 0::Int #339)
-#345 := (ite #34 #31 #342)
-#348 := (= #50 #345)
-#351 := (forall (vars (?v0 Int) (?v1 Int)) #348)
-#383 := (iff #351 #382)
-#380 := (iff #348 #379)
-#381 := [rewrite]: #380
-#384 := [quant-intro #381]: #383
-#220 := (not #219)
-#213 := (not #212)
-#223 := (and #213 #220)
-#209 := (not #208)
-#216 := (and #209 #213)
-#226 := (or #216 #223)
-#271 := (ite #226 #51 #251)
-#274 := (ite #33 0::Int #271)
-#277 := (ite #34 #31 #274)
-#280 := (= #50 #277)
-#283 := (forall (vars (?v0 Int) (?v1 Int)) #280)
-#352 := (iff #283 #351)
-#349 := (iff #280 #348)
-#346 := (= #277 #345)
-#343 := (= #274 #342)
-#340 := (= #271 #339)
-#324 := (iff #226 #323)
-#321 := (iff #223 #320)
-#322 := [rewrite]: #321
-#302 := (iff #216 #318)
-#303 := [rewrite]: #302
-#325 := [monotonicity #303 #322]: #324
-#341 := [monotonicity #325]: #340
-#344 := [monotonicity #341]: #343
-#347 := [monotonicity #344]: #346
-#350 := [monotonicity #347]: #349
-#353 := [quant-intro #350]: #352
-#300 := (~ #283 #283)
-#314 := (~ #280 #280)
-#315 := [refl]: #314
-#301 := [nnf-pos #315]: #300
-#44 := (- #20)
-#43 := (- #31)
-#52 := (mod #43 #44)
-#53 := (- #52)
-#37 := (< 0::Int #20)
-#39 := (< #31 0::Int)
-#40 := (and #39 #37)
-#36 := (< 0::Int #31)
-#38 := (and #36 #37)
-#41 := (or #38 #40)
-#54 := (ite #41 #51 #53)
-#55 := (ite #33 0::Int #54)
-#56 := (ite #34 #31 #55)
-#57 := (= #50 #56)
-#58 := (forall (vars (?v0 Int) (?v1 Int)) #57)
-#286 := (iff #58 #283)
-#174 := (and #37 #39)
-#177 := (or #38 #174)
-#256 := (ite #177 #51 #251)
-#165 := (= 0::Int #31)
-#259 := (ite #165 0::Int #256)
-#168 := (= 0::Int #20)
-#262 := (ite #168 #31 #259)
-#265 := (= #50 #262)
-#268 := (forall (vars (?v0 Int) (?v1 Int)) #265)
-#284 := (iff #268 #283)
-#281 := (iff #265 #280)
-#278 := (= #262 #277)
-#275 := (= #259 #274)
-#272 := (= #256 #271)
-#227 := (iff #177 #226)
-#224 := (iff #174 #223)
-#221 := (iff #39 #220)
-#222 := [rewrite]: #221
-#214 := (iff #37 #213)
-#215 := [rewrite]: #214
-#225 := [monotonicity #215 #222]: #224
-#217 := (iff #38 #216)
-#210 := (iff #36 #209)
-#211 := [rewrite]: #210
-#218 := [monotonicity #211 #215]: #217
-#228 := [monotonicity #218 #225]: #227
-#273 := [monotonicity #228]: #272
-#202 := (iff #165 #33)
-#203 := [rewrite]: #202
-#276 := [monotonicity #203 #273]: #275
-#204 := (iff #168 #34)
-#205 := [rewrite]: #204
-#279 := [monotonicity #205 #276]: #278
-#282 := [monotonicity #279]: #281
-#285 := [quant-intro #282]: #284
-#269 := (iff #58 #268)
-#266 := (iff #57 #265)
-#263 := (= #56 #262)
-#260 := (= #55 #259)
-#257 := (= #54 #256)
-#254 := (= #53 #251)
-#248 := (- #245)
-#252 := (= #248 #251)
-#253 := [rewrite]: #252
-#249 := (= #53 #248)
-#246 := (= #52 #245)
-#185 := (= #44 #184)
-#186 := [rewrite]: #185
-#182 := (= #43 #181)
-#183 := [rewrite]: #182
-#247 := [monotonicity #183 #186]: #246
-#250 := [monotonicity #247]: #249
-#255 := [trans #250 #253]: #254
-#178 := (iff #41 #177)
-#175 := (iff #40 #174)
-#176 := [rewrite]: #175
-#179 := [monotonicity #176]: #178
-#258 := [monotonicity #179 #255]: #257
-#166 := (iff #33 #165)
-#167 := [rewrite]: #166
-#261 := [monotonicity #167 #258]: #260
-#169 := (iff #34 #168)
-#170 := [rewrite]: #169
-#264 := [monotonicity #170 #261]: #263
-#267 := [monotonicity #264]: #266
-#270 := [quant-intro #267]: #269
-#287 := [trans #270 #285]: #286
-#244 := [asserted]: #58
-#288 := [mp #244 #287]: #283
-#316 := [mp~ #288 #301]: #283
-#354 := [mp #316 #353]: #351
-#385 := [mp #354 #384]: #382
-#891 := [mp #385 #890]: #886
-#729 := (not #886)
-#730 := (or #729 #800)
-#812 := (* -1::Int 3::Int)
-#813 := (* -1::Int 0::Int)
-#814 := (mod #813 #812)
-#809 := (+ #10 #814)
-#810 := (= #809 0::Int)
-#815 := (mod 0::Int 3::Int)
-#816 := (* -1::Int #815)
-#811 := (+ #10 #816)
-#817 := (= #811 0::Int)
-#834 := (>= 0::Int 0::Int)
-#658 := (<= 3::Int 0::Int)
-#659 := (or #658 #834)
-#660 := (not #659)
-#802 := (<= 0::Int 0::Int)
-#803 := (or #802 #658)
-#804 := (not #803)
-#805 := (or #804 #660)
-#799 := (ite #805 #817 #810)
-#806 := (= 0::Int 0::Int)
-#807 := (ite #806 #800 #799)
-#801 := (= 0::Int #10)
-#808 := (= 3::Int 0::Int)
-#637 := (ite #808 #801 #807)
-#725 := (or #729 #637)
-#704 := (iff #725 #730)
-#706 := (iff #730 #730)
-#599 := [rewrite]: #706
-#727 := (iff #637 #800)
-#753 := (ite false #800 #800)
-#732 := (iff #753 #800)
-#733 := [rewrite]: #732
-#723 := (iff #637 #753)
-#726 := (iff #807 #800)
-#1 := true
-#737 := (ite true #800 #800)
-#734 := (iff #737 #800)
-#740 := [rewrite]: #734
-#738 := (iff #807 #737)
-#735 := (iff #799 #800)
-#743 := (iff #799 #753)
-#751 := (iff #810 #800)
-#749 := (= #809 #10)
-#763 := (+ #10 0::Int)
-#767 := (= #763 #10)
-#768 := [rewrite]: #767
-#747 := (= #809 #763)
-#745 := (= #814 0::Int)
-#758 := -3::Int
-#757 := (mod 0::Int -3::Int)
-#742 := (= #757 0::Int)
-#744 := [rewrite]: #742
-#761 := (= #814 #757)
-#759 := (= #812 -3::Int)
-#760 := [rewrite]: #759
-#777 := (= #813 0::Int)
-#771 := [rewrite]: #777
-#741 := [monotonicity #771 #760]: #761
-#746 := [trans #741 #744]: #745
-#748 := [monotonicity #746]: #747
-#750 := [trans #748 #768]: #749
-#752 := [monotonicity #750]: #751
-#755 := (iff #817 #800)
-#764 := (= #811 #10)
-#765 := (= #811 #763)
-#778 := (= #816 0::Int)
-#775 := (= #816 #813)
-#785 := (= #815 0::Int)
-#774 := [rewrite]: #785
-#776 := [monotonicity #774]: #775
-#762 := [trans #776 #771]: #778
-#766 := [monotonicity #762]: #765
-#769 := [trans #766 #768]: #764
-#756 := [monotonicity #769]: #755
-#784 := (iff #805 false)
-#773 := (or false false)
-#782 := (iff #773 false)
-#783 := [rewrite]: #782
-#770 := (iff #805 #773)
-#779 := (iff #660 false)
-#482 := (not true)
-#841 := (iff #482 false)
-#844 := [rewrite]: #841
-#788 := (iff #660 #482)
-#698 := (iff #659 true)
-#686 := (or false true)
-#696 := (iff #686 true)
-#697 := [rewrite]: #696
-#694 := (iff #659 #686)
-#840 := (iff #834 true)
-#842 := [rewrite]: #840
-#680 := (iff #658 false)
-#681 := [rewrite]: #680
-#695 := [monotonicity #681 #842]: #694
-#791 := [trans #695 #697]: #698
-#792 := [monotonicity #791]: #788
-#781 := [trans #792 #844]: #779
-#692 := (iff #804 false)
-#675 := (iff #804 #482)
-#787 := (iff #803 true)
-#682 := (or true false)
-#691 := (iff #682 true)
-#786 := [rewrite]: #691
-#641 := (iff #803 #682)
-#795 := (iff #802 true)
-#798 := [rewrite]: #795
-#789 := [monotonicity #798 #681]: #641
-#790 := [trans #789 #786]: #787
-#690 := [monotonicity #790]: #675
-#693 := [trans #690 #844]: #692
-#772 := [monotonicity #693 #781]: #770
-#780 := [trans #772 #783]: #784
-#754 := [monotonicity #780 #756 #752]: #743
-#736 := [trans #754 #733]: #735
-#796 := (iff #806 true)
-#797 := [rewrite]: #796
-#739 := [monotonicity #797 #736]: #738
-#722 := [trans #739 #740]: #726
-#793 := (iff #801 #800)
-#794 := [rewrite]: #793
-#639 := (iff #808 false)
-#640 := [rewrite]: #639
-#724 := [monotonicity #640 #794 #722]: #723
-#728 := [trans #724 #733]: #727
-#705 := [monotonicity #728]: #704
-#710 := [trans #705 #599]: #704
-#731 := [quant-inst #8 #9]: #725
-#711 := [mp #731 #710]: #730
-#717 := [unit-resolution #711 #891]: #800
-#713 := [monotonicity #717]: #13
-#14 := (not #13)
-#78 := [asserted]: #14
-[unit-resolution #78 #713]: false
-unsat
-e4bde0ae05cc3d53da641b07fe2928d0ca73206a 336 0
-#2 := false
-decl f3 :: (-> Int S2)
+#21 := (f3 0::Int)
+#14 := (- 0::Int)
+#15 := (mod #14 #14)
+#16 := (- #15)
+#13 := (mod 0::Int 0::Int)
+#10 := (< 0::Int 0::Int)
+#11 := (and #10 #10)
+#12 := (or #11 #11)
+#17 := (ite #12 #13 #16)
+#9 := (= 0::Int 0::Int)
+#18 := (ite #9 0::Int #17)
+#19 := (ite #9 0::Int #18)
+#20 := (f3 #19)
+#22 := (= #20 #21)
+#23 := (not #22)
+#114 := (iff #23 false)
+#1 := true
+#109 := (not true)
+#112 := (iff #109 false)
+#113 := [rewrite]: #112
+#110 := (iff #23 #109)
+#107 := (iff #22 true)
+#102 := (= #21 #21)
+#105 := (iff #102 true)
+#106 := [rewrite]: #105
+#103 := (iff #22 #102)
+#99 := (= #19 0::Int)
+#94 := (ite true 0::Int 0::Int)
+#97 := (= #94 0::Int)
+#98 := [rewrite]: #97
+#95 := (= #19 #94)
+#92 := (= #18 0::Int)
+#78 := -1::Int
+#79 := (* -1::Int #13)
+#84 := (ite #10 #13 #79)
+#87 := (ite true 0::Int #84)
+#90 := (= #87 0::Int)
+#91 := [rewrite]: #90
+#88 := (= #18 #87)
+#85 := (= #17 #84)
+#82 := (= #16 #79)
+#75 := (- #13)
+#80 := (= #75 #79)
+#81 := [rewrite]: #80
+#76 := (= #16 #75)
+#73 := (= #15 #13)
+#71 := (= #14 0::Int)
+#72 := [rewrite]: #71
+#74 := [monotonicity #72 #72]: #73
+#77 := [monotonicity #74]: #76
+#83 := [trans #77 #81]: #82
+#69 := (iff #12 #10)
+#64 := (or #10 #10)
+#67 := (iff #64 #10)
+#68 := [rewrite]: #67
+#65 := (iff #12 #64)
+#62 := (iff #11 #10)
+#63 := [rewrite]: #62
+#66 := [monotonicity #63 #63]: #65
+#70 := [trans #66 #68]: #69
+#86 := [monotonicity #70 #83]: #85
+#60 := (iff #9 true)
+#61 := [rewrite]: #60
+#89 := [monotonicity #61 #86]: #88
+#93 := [trans #89 #91]: #92
+#96 := [monotonicity #61 #93]: #95
+#100 := [trans #96 #98]: #99
+#101 := [monotonicity #100]: #22
+#104 := [monotonicity #101]: #103
+#108 := [trans #104 #106]: #107
+#111 := [monotonicity #108]: #110
+#115 := [trans #111 #113]: #114
+#59 := [asserted]: #23
+[mp #59 #115]: false
+unsat
+18c694d062a2e495b90f6c40f36cef6e909d6c58 115 0
+#2 := false
+decl f4 :: (-> S2 Int)
+#30 := (:var 0 S2)
+#31 := (f4 #30)
+#695 := (pattern #31)
+decl f3 :: (-> Int S2)
+#32 := (f3 #31)
+#122 := (= #30 #32)
+#696 := (forall (vars (?v0 S2)) (:pat #695) #122)
+#126 := (forall (vars (?v0 S2)) #122)
+#697 := (iff #126 #696)
+#699 := (iff #696 #696)
+#700 := [rewrite]: #699
+#698 := [rewrite]: #697
+#701 := [trans #698 #700]: #697
+#220 := (~ #126 #126)
+#218 := (~ #122 #122)
+#219 := [refl]: #218
+#221 := [nnf-pos #219]: #220
+#33 := (= #32 #30)
+#34 := (forall (vars (?v0 S2)) #33)
+#127 := (iff #34 #126)
+#124 := (iff #33 #122)
+#125 := [rewrite]: #124
+#128 := [quant-intro #125]: #127
+#121 := [asserted]: #34
+#131 := [mp #121 #128]: #126
+#210 := [mp~ #131 #221]: #126
+#702 := [mp #210 #701]: #696
+decl f5 :: S2
+#10 := f5
+#11 := (f4 f5)
+#107 := (f3 #11)
+#113 := (= f5 #107)
+#118 := (not #113)
+#8 := 0::Int
+#21 := (- 0::Int)
+#20 := (- #11)
+#22 := (mod #20 #21)
+#23 := (- #22)
+#19 := (mod #11 0::Int)
+#14 := (< 0::Int 0::Int)
+#16 := (< #11 0::Int)
+#17 := (and #16 #14)
+#13 := (< 0::Int #11)
+#15 := (and #13 #14)
+#18 := (or #15 #17)
+#24 := (ite #18 #19 #23)
+#12 := (= #11 0::Int)
+#25 := (ite #12 0::Int #24)
+#9 := (= 0::Int 0::Int)
+#26 := (ite #9 #11 #25)
+#27 := (f3 #26)
+#28 := (= #27 f5)
+#29 := (not #28)
+#119 := (iff #29 #118)
+#116 := (iff #28 #113)
+#110 := (= #107 f5)
+#114 := (iff #110 #113)
+#115 := [rewrite]: #114
+#111 := (iff #28 #110)
+#108 := (= #27 #107)
+#105 := (= #26 #11)
+#77 := -1::Int
+#78 := (* -1::Int #11)
+#83 := (mod #78 0::Int)
+#89 := (* -1::Int #83)
+#71 := (and #14 #16)
+#74 := (or #15 #71)
+#94 := (ite #74 #19 #89)
+#68 := (= 0::Int #11)
+#97 := (ite #68 0::Int #94)
+#1 := true
+#100 := (ite true #11 #97)
+#103 := (= #100 #11)
+#104 := [rewrite]: #103
+#101 := (= #26 #100)
+#98 := (= #25 #97)
+#95 := (= #24 #94)
+#92 := (= #23 #89)
+#86 := (- #83)
+#90 := (= #86 #89)
+#91 := [rewrite]: #90
+#87 := (= #23 #86)
+#84 := (= #22 #83)
+#81 := (= #21 0::Int)
+#82 := [rewrite]: #81
+#79 := (= #20 #78)
+#80 := [rewrite]: #79
+#85 := [monotonicity #80 #82]: #84
+#88 := [monotonicity #85]: #87
+#93 := [trans #88 #91]: #92
+#75 := (iff #18 #74)
+#72 := (iff #17 #71)
+#73 := [rewrite]: #72
+#76 := [monotonicity #73]: #75
+#96 := [monotonicity #76 #93]: #95
+#69 := (iff #12 #68)
+#70 := [rewrite]: #69
+#99 := [monotonicity #70 #96]: #98
+#66 := (iff #9 true)
+#67 := [rewrite]: #66
+#102 := [monotonicity #67 #99]: #101
+#106 := [trans #102 #104]: #105
+#109 := [monotonicity #106]: #108
+#112 := [monotonicity #109]: #111
+#117 := [trans #112 #115]: #116
+#120 := [monotonicity #117]: #119
+#65 := [asserted]: #29
+#123 := [mp #65 #120]: #118
+#281 := (not #696)
+#367 := (or #281 #113)
+#368 := [quant-inst #10]: #367
+[unit-resolution #368 #123 #702]: false
+unsat
+2713378ea3e2d16536aee750f4c4dea73990d05c 86 0
+#2 := false
+decl f3 :: (-> Int S2)
+#9 := 0::Int
+#25 := (f3 0::Int)
 #8 := 1::Int
-#12 := (f3 1::Int)
-decl f4 :: (-> Int Int Int)
-#9 := 3::Int
-#10 := (f4 1::Int 3::Int)
-#11 := (f3 #10)
-#13 := (= #11 #12)
-#797 := (= #10 1::Int)
-#21 := (:var 0 Int)
-#32 := (:var 1 Int)
-#51 := (f4 #32 #21)
-#885 := (pattern #51)
-#20 := 0::Int
-#181 := -1::Int
-#185 := (* -1::Int #21)
-#182 := (* -1::Int #32)
-#246 := (mod #182 #185)
-#376 := (+ #51 #246)
-#377 := (= #376 0::Int)
-#52 := (mod #32 #21)
-#373 := (* -1::Int #52)
-#374 := (+ #51 #373)
-#375 := (= #374 0::Int)
-#220 := (>= #32 0::Int)
-#213 := (<= #21 0::Int)
-#320 := (or #213 #220)
-#321 := (not #320)
-#209 := (<= #32 0::Int)
-#318 := (or #209 #213)
-#319 := (not #318)
-#324 := (or #319 #321)
-#378 := (ite #324 #375 #377)
-#372 := (= #51 0::Int)
-#34 := (= #32 0::Int)
-#379 := (ite #34 #372 #378)
-#371 := (= #32 #51)
-#35 := (= #21 0::Int)
-#380 := (ite #35 #371 #379)
-#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #380)
-#383 := (forall (vars (?v0 Int) (?v1 Int)) #380)
-#889 := (iff #383 #886)
-#887 := (iff #380 #380)
-#888 := [refl]: #887
-#890 := [quant-intro #888]: #889
-#252 := (* -1::Int #246)
-#340 := (ite #324 #52 #252)
-#343 := (ite #34 0::Int #340)
-#346 := (ite #35 #32 #343)
-#349 := (= #51 #346)
-#352 := (forall (vars (?v0 Int) (?v1 Int)) #349)
-#384 := (iff #352 #383)
-#381 := (iff #349 #380)
-#382 := [rewrite]: #381
-#385 := [quant-intro #382]: #384
-#221 := (not #220)
-#214 := (not #213)
-#224 := (and #214 #221)
-#210 := (not #209)
-#217 := (and #210 #214)
-#227 := (or #217 #224)
-#272 := (ite #227 #52 #252)
-#275 := (ite #34 0::Int #272)
-#278 := (ite #35 #32 #275)
-#281 := (= #51 #278)
-#284 := (forall (vars (?v0 Int) (?v1 Int)) #281)
-#353 := (iff #284 #352)
-#350 := (iff #281 #349)
-#347 := (= #278 #346)
-#344 := (= #275 #343)
-#341 := (= #272 #340)
-#325 := (iff #227 #324)
-#322 := (iff #224 #321)
-#323 := [rewrite]: #322
-#303 := (iff #217 #319)
-#304 := [rewrite]: #303
-#326 := [monotonicity #304 #323]: #325
-#342 := [monotonicity #326]: #341
-#345 := [monotonicity #342]: #344
-#348 := [monotonicity #345]: #347
-#351 := [monotonicity #348]: #350
-#354 := [quant-intro #351]: #353
-#301 := (~ #284 #284)
-#315 := (~ #281 #281)
-#316 := [refl]: #315
-#302 := [nnf-pos #316]: #301
-#45 := (- #21)
-#44 := (- #32)
-#53 := (mod #44 #45)
-#54 := (- #53)
-#38 := (< 0::Int #21)
-#40 := (< #32 0::Int)
-#41 := (and #40 #38)
-#37 := (< 0::Int #32)
-#39 := (and #37 #38)
-#42 := (or #39 #41)
-#55 := (ite #42 #52 #54)
-#56 := (ite #34 0::Int #55)
-#57 := (ite #35 #32 #56)
-#58 := (= #51 #57)
-#59 := (forall (vars (?v0 Int) (?v1 Int)) #58)
-#287 := (iff #59 #284)
-#175 := (and #38 #40)
-#178 := (or #39 #175)
-#257 := (ite #178 #52 #252)
-#166 := (= 0::Int #32)
-#260 := (ite #166 0::Int #257)
-#169 := (= 0::Int #21)
-#263 := (ite #169 #32 #260)
-#266 := (= #51 #263)
-#269 := (forall (vars (?v0 Int) (?v1 Int)) #266)
-#285 := (iff #269 #284)
-#282 := (iff #266 #281)
-#279 := (= #263 #278)
-#276 := (= #260 #275)
-#273 := (= #257 #272)
-#228 := (iff #178 #227)
-#225 := (iff #175 #224)
-#222 := (iff #40 #221)
-#223 := [rewrite]: #222
-#215 := (iff #38 #214)
-#216 := [rewrite]: #215
-#226 := [monotonicity #216 #223]: #225
-#218 := (iff #39 #217)
-#211 := (iff #37 #210)
-#212 := [rewrite]: #211
-#219 := [monotonicity #212 #216]: #218
-#229 := [monotonicity #219 #226]: #228
-#274 := [monotonicity #229]: #273
-#203 := (iff #166 #34)
-#204 := [rewrite]: #203
-#277 := [monotonicity #204 #274]: #276
-#205 := (iff #169 #35)
-#206 := [rewrite]: #205
-#280 := [monotonicity #206 #277]: #279
-#283 := [monotonicity #280]: #282
-#286 := [quant-intro #283]: #285
-#270 := (iff #59 #269)
-#267 := (iff #58 #266)
-#264 := (= #57 #263)
-#261 := (= #56 #260)
-#258 := (= #55 #257)
-#255 := (= #54 #252)
-#249 := (- #246)
-#253 := (= #249 #252)
-#254 := [rewrite]: #253
-#250 := (= #54 #249)
-#247 := (= #53 #246)
-#186 := (= #45 #185)
-#187 := [rewrite]: #186
-#183 := (= #44 #182)
-#184 := [rewrite]: #183
-#248 := [monotonicity #184 #187]: #247
-#251 := [monotonicity #248]: #250
-#256 := [trans #251 #254]: #255
-#179 := (iff #42 #178)
-#176 := (iff #41 #175)
-#177 := [rewrite]: #176
-#180 := [monotonicity #177]: #179
-#259 := [monotonicity #180 #256]: #258
-#167 := (iff #34 #166)
-#168 := [rewrite]: #167
-#262 := [monotonicity #168 #259]: #261
-#170 := (iff #35 #169)
-#171 := [rewrite]: #170
-#265 := [monotonicity #171 #262]: #264
-#268 := [monotonicity #265]: #267
-#271 := [quant-intro #268]: #270
-#288 := [trans #271 #286]: #287
-#245 := [asserted]: #59
-#289 := [mp #245 #288]: #284
-#317 := [mp~ #289 #302]: #284
-#355 := [mp #317 #354]: #352
-#386 := [mp #355 #385]: #383
-#891 := [mp #386 #890]: #886
-#709 := (not #886)
-#677 := (or #709 #797)
-#814 := (* -1::Int 3::Int)
-#809 := (* -1::Int 1::Int)
-#810 := (mod #809 #814)
-#815 := (+ #10 #810)
-#816 := (= #815 0::Int)
-#811 := (mod 1::Int 3::Int)
-#817 := (* -1::Int #811)
-#658 := (+ #10 #817)
-#659 := (= #658 0::Int)
-#835 := (>= 1::Int 0::Int)
-#660 := (<= 3::Int 0::Int)
-#802 := (or #660 #835)
-#803 := (not #802)
-#804 := (<= 1::Int 0::Int)
-#805 := (or #804 #660)
-#799 := (not #805)
-#800 := (or #799 #803)
-#806 := (ite #800 #659 #816)
-#807 := (= #10 0::Int)
-#801 := (= 1::Int 0::Int)
-#808 := (ite #801 #807 #806)
-#637 := (= 1::Int #10)
-#639 := (= 3::Int 0::Int)
-#640 := (ite #639 #637 #808)
-#684 := (or #709 #640)
-#674 := (iff #684 #677)
-#678 := (iff #677 #677)
-#685 := [rewrite]: #678
-#708 := (iff #640 #797)
-#701 := (ite false #797 #797)
-#683 := (iff #701 #797)
-#707 := [rewrite]: #683
-#647 := (iff #640 #701)
-#716 := (iff #808 #797)
-#714 := (ite false #807 #797)
-#719 := (iff #714 #797)
-#720 := [rewrite]: #719
-#715 := (iff #808 #714)
-#717 := (iff #806 #797)
-#729 := -2::Int
-#730 := (= #10 -2::Int)
-#1 := true
-#706 := (ite true #797 #730)
-#711 := (iff #706 #797)
-#712 := [rewrite]: #711
-#599 := (iff #806 #706)
-#704 := (iff #816 #730)
-#754 := 2::Int
-#734 := (+ 2::Int #10)
-#724 := (= #734 0::Int)
-#725 := (iff #724 #730)
-#731 := [rewrite]: #725
-#727 := (iff #816 #724)
-#722 := (= #815 #734)
-#737 := (+ #10 2::Int)
-#740 := (= #737 #734)
-#726 := [rewrite]: #740
-#738 := (= #815 #737)
-#735 := (= #810 2::Int)
-#749 := -3::Int
-#752 := (mod -1::Int -3::Int)
-#732 := (= #752 2::Int)
-#733 := [rewrite]: #732
-#753 := (= #810 #752)
-#750 := (= #814 -3::Int)
-#751 := [rewrite]: #750
-#766 := (= #809 -1::Int)
-#767 := [rewrite]: #766
-#743 := [monotonicity #767 #751]: #753
-#736 := [trans #743 #733]: #735
-#739 := [monotonicity #736]: #738
-#723 := [trans #739 #726]: #722
-#728 := [monotonicity #723]: #727
-#705 := [trans #728 #731]: #704
-#747 := (iff #659 #797)
-#758 := (+ -1::Int #10)
-#741 := (= #758 0::Int)
-#745 := (iff #741 #797)
-#746 := [rewrite]: #745
-#742 := (iff #659 #741)
-#757 := (= #658 #758)
-#769 := (+ #10 -1::Int)
-#759 := (= #769 #758)
-#760 := [rewrite]: #759
-#755 := (= #658 #769)
-#768 := (= #817 -1::Int)
-#763 := (= #817 #809)
-#778 := (= #811 1::Int)
-#762 := [rewrite]: #778
-#765 := [monotonicity #762]: #763
-#764 := [trans #765 #767]: #768
-#756 := [monotonicity #764]: #755
-#761 := [trans #756 #760]: #757
-#744 := [monotonicity #761]: #742
-#748 := [trans #744 #746]: #747
-#777 := (iff #800 true)
-#780 := (or true false)
-#775 := (iff #780 true)
-#776 := [rewrite]: #775
-#785 := (iff #800 #780)
-#783 := (iff #803 false)
-#483 := (not true)
-#844 := (iff #483 false)
-#830 := [rewrite]: #844
-#772 := (iff #803 #483)
-#773 := (iff #802 true)
-#791 := (or false true)
-#779 := (iff #791 true)
-#781 := [rewrite]: #779
-#788 := (iff #802 #791)
-#842 := (iff #835 true)
-#482 := [rewrite]: #842
-#641 := (iff #660 false)
-#789 := [rewrite]: #641
-#792 := [monotonicity #789 #482]: #788
-#770 := [trans #792 #781]: #773
-#782 := [monotonicity #770]: #772
-#784 := [trans #782 #830]: #783
-#697 := (iff #799 true)
-#693 := (not false)
-#695 := (iff #693 true)
-#696 := [rewrite]: #695
-#686 := (iff #799 #693)
-#690 := (iff #805 false)
-#691 := (or false false)
-#790 := (iff #691 false)
-#675 := [rewrite]: #790
-#786 := (iff #805 #691)
-#681 := (iff #804 false)
-#682 := [rewrite]: #681
-#787 := [monotonicity #682 #789]: #786
-#692 := [trans #787 #675]: #690
-#694 := [monotonicity #692]: #686
-#698 := [trans #694 #696]: #697
-#774 := [monotonicity #698 #784]: #785
-#771 := [trans #774 #776]: #777
-#710 := [monotonicity #771 #748 #705]: #599
-#713 := [trans #710 #712]: #717
-#798 := (iff #801 false)
-#680 := [rewrite]: #798
-#718 := [monotonicity #680 #713]: #715
-#721 := [trans #718 #720]: #716
-#796 := (iff #637 #797)
-#795 := [rewrite]: #796
-#793 := (iff #639 false)
-#794 := [rewrite]: #793
-#702 := [monotonicity #794 #795 #721]: #647
-#703 := [trans #702 #707]: #708
-#676 := [monotonicity #703]: #674
-#687 := [trans #676 #685]: #674
-#643 := [quant-inst #8 #9]: #684
-#688 := [mp #643 #687]: #677
-#679 := [unit-resolution #688 #891]: #797
-#700 := [monotonicity #679]: #13
-#14 := (not #13)
-#79 := [asserted]: #14
-[unit-resolution #79 #700]: false
-unsat
-1120ebc08fbef118a46bc94c7a17d1ff3c4dbb08 311 0
-#2 := false
-decl f3 :: (-> Int S2)
-#11 := 0::Int
-#12 := (f3 0::Int)
-decl f4 :: (-> Int Int Int)
-#8 := 3::Int
-#9 := (f4 3::Int 3::Int)
-#10 := (f3 #9)
-#13 := (= #10 #12)
-#799 := (= #9 0::Int)
-#20 := (:var 0 Int)
-#31 := (:var 1 Int)
-#50 := (f4 #31 #20)
-#885 := (pattern #50)
-#180 := -1::Int
-#184 := (* -1::Int #20)
-#181 := (* -1::Int #31)
-#245 := (mod #181 #184)
-#375 := (+ #50 #245)
-#376 := (= #375 0::Int)
-#51 := (mod #31 #20)
-#372 := (* -1::Int #51)
-#373 := (+ #50 #372)
-#374 := (= #373 0::Int)
-#219 := (>= #31 0::Int)
-#212 := (<= #20 0::Int)
-#319 := (or #212 #219)
-#320 := (not #319)
-#208 := (<= #31 0::Int)
-#317 := (or #208 #212)
-#318 := (not #317)
-#323 := (or #318 #320)
-#377 := (ite #323 #374 #376)
-#371 := (= #50 0::Int)
-#33 := (= #31 0::Int)
-#378 := (ite #33 #371 #377)
-#370 := (= #31 #50)
-#34 := (= #20 0::Int)
-#379 := (ite #34 #370 #378)
-#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #379)
-#382 := (forall (vars (?v0 Int) (?v1 Int)) #379)
-#889 := (iff #382 #886)
-#887 := (iff #379 #379)
-#888 := [refl]: #887
-#890 := [quant-intro #888]: #889
-#251 := (* -1::Int #245)
-#339 := (ite #323 #51 #251)
-#342 := (ite #33 0::Int #339)
-#345 := (ite #34 #31 #342)
-#348 := (= #50 #345)
-#351 := (forall (vars (?v0 Int) (?v1 Int)) #348)
-#383 := (iff #351 #382)
-#380 := (iff #348 #379)
-#381 := [rewrite]: #380
-#384 := [quant-intro #381]: #383
-#220 := (not #219)
-#213 := (not #212)
-#223 := (and #213 #220)
-#209 := (not #208)
-#216 := (and #209 #213)
-#226 := (or #216 #223)
-#271 := (ite #226 #51 #251)
-#274 := (ite #33 0::Int #271)
-#277 := (ite #34 #31 #274)
-#280 := (= #50 #277)
-#283 := (forall (vars (?v0 Int) (?v1 Int)) #280)
-#352 := (iff #283 #351)
-#349 := (iff #280 #348)
-#346 := (= #277 #345)
-#343 := (= #274 #342)
-#340 := (= #271 #339)
-#324 := (iff #226 #323)
-#321 := (iff #223 #320)
-#322 := [rewrite]: #321
-#302 := (iff #216 #318)
-#303 := [rewrite]: #302
-#325 := [monotonicity #303 #322]: #324
-#341 := [monotonicity #325]: #340
-#344 := [monotonicity #341]: #343
-#347 := [monotonicity #344]: #346
-#350 := [monotonicity #347]: #349
-#353 := [quant-intro #350]: #352
-#300 := (~ #283 #283)
-#314 := (~ #280 #280)
-#315 := [refl]: #314
-#301 := [nnf-pos #315]: #300
-#44 := (- #20)
-#43 := (- #31)
-#52 := (mod #43 #44)
-#53 := (- #52)
-#37 := (< 0::Int #20)
-#39 := (< #31 0::Int)
-#40 := (and #39 #37)
-#36 := (< 0::Int #31)
-#38 := (and #36 #37)
-#41 := (or #38 #40)
-#54 := (ite #41 #51 #53)
-#55 := (ite #33 0::Int #54)
-#56 := (ite #34 #31 #55)
-#57 := (= #50 #56)
-#58 := (forall (vars (?v0 Int) (?v1 Int)) #57)
-#286 := (iff #58 #283)
-#174 := (and #37 #39)
-#177 := (or #38 #174)
-#256 := (ite #177 #51 #251)
-#165 := (= 0::Int #31)
-#259 := (ite #165 0::Int #256)
-#168 := (= 0::Int #20)
-#262 := (ite #168 #31 #259)
-#265 := (= #50 #262)
-#268 := (forall (vars (?v0 Int) (?v1 Int)) #265)
-#284 := (iff #268 #283)
-#281 := (iff #265 #280)
-#278 := (= #262 #277)
-#275 := (= #259 #274)
-#272 := (= #256 #271)
-#227 := (iff #177 #226)
-#224 := (iff #174 #223)
-#221 := (iff #39 #220)
-#222 := [rewrite]: #221
-#214 := (iff #37 #213)
-#215 := [rewrite]: #214
-#225 := [monotonicity #215 #222]: #224
-#217 := (iff #38 #216)
-#210 := (iff #36 #209)
-#211 := [rewrite]: #210
-#218 := [monotonicity #211 #215]: #217
-#228 := [monotonicity #218 #225]: #227
-#273 := [monotonicity #228]: #272
-#202 := (iff #165 #33)
-#203 := [rewrite]: #202
-#276 := [monotonicity #203 #273]: #275
-#204 := (iff #168 #34)
-#205 := [rewrite]: #204
-#279 := [monotonicity #205 #276]: #278
-#282 := [monotonicity #279]: #281
-#285 := [quant-intro #282]: #284
-#269 := (iff #58 #268)
-#266 := (iff #57 #265)
-#263 := (= #56 #262)
-#260 := (= #55 #259)
-#257 := (= #54 #256)
-#254 := (= #53 #251)
-#248 := (- #245)
-#252 := (= #248 #251)
-#253 := [rewrite]: #252
-#249 := (= #53 #248)
-#246 := (= #52 #245)
-#185 := (= #44 #184)
-#186 := [rewrite]: #185
-#182 := (= #43 #181)
-#183 := [rewrite]: #182
-#247 := [monotonicity #183 #186]: #246
-#250 := [monotonicity #247]: #249
-#255 := [trans #250 #253]: #254
-#178 := (iff #41 #177)
-#175 := (iff #40 #174)
-#176 := [rewrite]: #175
-#179 := [monotonicity #176]: #178
-#258 := [monotonicity #179 #255]: #257
-#166 := (iff #33 #165)
-#167 := [rewrite]: #166
-#261 := [monotonicity #167 #258]: #260
-#169 := (iff #34 #168)
-#170 := [rewrite]: #169
-#264 := [monotonicity #170 #261]: #263
-#267 := [monotonicity #264]: #266
-#270 := [quant-intro #267]: #269
-#287 := [trans #270 #285]: #286
-#244 := [asserted]: #58
-#288 := [mp #244 #287]: #283
-#316 := [mp~ #288 #301]: #283
-#354 := [mp #316 #353]: #351
-#385 := [mp #354 #384]: #382
-#891 := [mp #385 #890]: #886
-#704 := (not #886)
-#705 := (or #704 #799)
-#812 := (* -1::Int 3::Int)
-#813 := (mod #812 #812)
-#814 := (+ #9 #813)
-#809 := (= #814 0::Int)
-#810 := (mod 3::Int 3::Int)
-#815 := (* -1::Int #810)
-#816 := (+ #9 #815)
-#811 := (= #816 0::Int)
-#817 := (>= 3::Int 0::Int)
-#658 := (<= 3::Int 0::Int)
-#659 := (or #658 #817)
-#660 := (not #659)
-#802 := (or #658 #658)
-#803 := (not #802)
-#804 := (or #803 #660)
-#805 := (ite #804 #811 #809)
-#800 := (= 3::Int 0::Int)
-#806 := (ite #800 #799 #805)
-#807 := (= 3::Int #9)
-#801 := (ite #800 #807 #806)
-#706 := (or #704 #801)
-#710 := (iff #706 #705)
-#712 := (iff #705 #705)
-#717 := [rewrite]: #712
-#725 := (iff #801 #799)
-#640 := (= #9 3::Int)
-#724 := (ite false #640 #799)
-#729 := (iff #724 #799)
-#730 := [rewrite]: #729
-#727 := (iff #801 #724)
-#722 := (iff #806 #799)
-#738 := (ite false #799 #799)
-#740 := (iff #738 #799)
-#726 := [rewrite]: #740
-#739 := (iff #806 #738)
-#736 := (iff #805 #799)
-#1 := true
-#743 := (ite true #799 #799)
-#733 := (iff #743 #799)
-#735 := [rewrite]: #733
-#754 := (iff #805 #743)
-#752 := (iff #809 #799)
-#750 := (= #814 #9)
-#765 := (+ #9 0::Int)
-#768 := (= #765 #9)
-#764 := [rewrite]: #768
-#748 := (= #814 #765)
-#746 := (= #813 0::Int)
-#759 := -3::Int
-#761 := (mod -3::Int -3::Int)
-#744 := (= #761 0::Int)
-#745 := [rewrite]: #744
-#741 := (= #813 #761)
-#760 := (= #812 -3::Int)
-#757 := [rewrite]: #760
-#742 := [monotonicity #757 #757]: #741
-#747 := [trans #742 #745]: #746
-#749 := [monotonicity #747]: #748
-#751 := [trans #749 #764]: #750
-#753 := [monotonicity #751]: #752
-#756 := (iff #811 #799)
-#769 := (= #816 #9)
-#766 := (= #816 #765)
-#762 := (= #815 0::Int)
-#775 := (* -1::Int 0::Int)
-#771 := (= #775 0::Int)
-#778 := [rewrite]: #771
-#776 := (= #815 #775)
-#785 := (= #810 0::Int)
-#774 := [rewrite]: #785
-#777 := [monotonicity #774]: #776
-#763 := [trans #777 #778]: #762
-#767 := [monotonicity #763]: #766
-#755 := [trans #767 #764]: #769
-#758 := [monotonicity #755]: #756
-#784 := (iff #804 true)
-#773 := (or true false)
-#782 := (iff #773 true)
-#783 := [rewrite]: #782
-#770 := (iff #804 #773)
-#779 := (iff #660 false)
-#482 := (not true)
-#841 := (iff #482 false)
-#844 := [rewrite]: #841
-#788 := (iff #660 #482)
-#698 := (iff #659 true)
-#686 := (or false true)
-#696 := (iff #686 true)
-#697 := [rewrite]: #696
-#694 := (iff #659 #686)
-#692 := (iff #817 true)
-#693 := [rewrite]: #692
-#794 := (iff #658 false)
-#796 := [rewrite]: #794
-#695 := [monotonicity #796 #693]: #694
-#791 := [trans #695 #697]: #698
-#792 := [monotonicity #791]: #788
-#781 := [trans #792 #844]: #779
-#675 := (iff #803 true)
-#789 := (not false)
-#787 := (iff #789 true)
-#790 := [rewrite]: #787
-#691 := (iff #803 #789)
-#682 := (iff #802 false)
-#797 := (or false false)
-#680 := (iff #797 false)
-#681 := [rewrite]: #680
-#795 := (iff #802 #797)
-#798 := [monotonicity #796 #796]: #795
-#641 := [trans #798 #681]: #682
-#786 := [monotonicity #641]: #691
-#690 := [trans #786 #790]: #675
-#772 := [monotonicity #690 #781]: #770
-#780 := [trans #772 #783]: #784
-#732 := [monotonicity #780 #758 #753]: #754
-#737 := [trans #732 #735]: #736
-#808 := (iff #800 false)
-#637 := [rewrite]: #808
-#734 := [monotonicity #637 #737]: #739
-#723 := [trans #734 #726]: #722
-#639 := (iff #807 #640)
-#793 := [rewrite]: #639
-#728 := [monotonicity #637 #793 #723]: #727
-#731 := [trans #728 #730]: #725
-#711 := [monotonicity #731]: #710
-#713 := [trans #711 #717]: #710
-#599 := [quant-inst #8 #8]: #706
-#714 := [mp #599 #713]: #705
-#718 := [unit-resolution #714 #891]: #799
-#719 := [monotonicity #718]: #13
-#14 := (not #13)
-#78 := [asserted]: #14
-[unit-resolution #78 #719]: false
-unsat
-f05688f0b5f9f483f17f9e461ed5ff3d814bfbb3 452 0
-#2 := false
-#10 := 3::Int
-decl f4 :: (-> S2 Int)
-decl f5 :: S2
-#8 := f5
-#9 := (f4 f5)
-#547 := (mod #9 3::Int)
-#741 := (>= #547 3::Int)
-#742 := (not #741)
-#1 := true
-#76 := [true-axiom]: true
-#729 := (or false #742)
-#725 := [th-lemma arith]: #729
-#726 := [unit-resolution #725 #76]: #742
-#19 := 0::Int
-#192 := -1::Int
-#526 := (* -1::Int #547)
-decl f3 :: (-> Int Int Int)
-#11 := (f3 #9 3::Int)
-#861 := (+ #11 #526)
-#808 := (<= #861 0::Int)
-#863 := (= #861 0::Int)
-#561 := -3::Int
-#542 := (* -1::Int #9)
-#840 := (mod #542 -3::Int)
-#551 := (+ #11 #840)
-#554 := (= #551 0::Int)
-#532 := (<= #9 0::Int)
-#849 := (not #532)
-#520 := (>= #9 0::Int)
-#853 := (not #520)
-#567 := (or #853 #849)
-#548 := (ite #567 #863 #554)
-#862 := (= #11 0::Int)
-#868 := (= #9 0::Int)
-#831 := (ite #868 #862 #548)
-#20 := (:var 0 Int)
-#31 := (:var 1 Int)
-#50 := (f3 #31 #20)
-#897 := (pattern #50)
-#196 := (* -1::Int #20)
-#193 := (* -1::Int #31)
-#257 := (mod #193 #196)
-#387 := (+ #50 #257)
-#388 := (= #387 0::Int)
-#51 := (mod #31 #20)
-#384 := (* -1::Int #51)
-#385 := (+ #50 #384)
-#386 := (= #385 0::Int)
-#231 := (>= #31 0::Int)
-#224 := (<= #20 0::Int)
-#331 := (or #224 #231)
-#332 := (not #331)
-#220 := (<= #31 0::Int)
-#329 := (or #220 #224)
-#330 := (not #329)
-#335 := (or #330 #332)
-#389 := (ite #335 #386 #388)
-#383 := (= #50 0::Int)
-#33 := (= #31 0::Int)
-#390 := (ite #33 #383 #389)
-#382 := (= #31 #50)
-#34 := (= #20 0::Int)
-#391 := (ite #34 #382 #390)
-#898 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #897) #391)
-#394 := (forall (vars (?v0 Int) (?v1 Int)) #391)
-#901 := (iff #394 #898)
-#899 := (iff #391 #391)
-#900 := [refl]: #899
-#902 := [quant-intro #900]: #901
-#263 := (* -1::Int #257)
-#351 := (ite #335 #51 #263)
-#354 := (ite #33 0::Int #351)
-#357 := (ite #34 #31 #354)
-#360 := (= #50 #357)
-#363 := (forall (vars (?v0 Int) (?v1 Int)) #360)
-#395 := (iff #363 #394)
-#392 := (iff #360 #391)
-#393 := [rewrite]: #392
-#396 := [quant-intro #393]: #395
-#232 := (not #231)
-#225 := (not #224)
-#235 := (and #225 #232)
-#221 := (not #220)
-#228 := (and #221 #225)
-#238 := (or #228 #235)
-#283 := (ite #238 #51 #263)
-#286 := (ite #33 0::Int #283)
-#289 := (ite #34 #31 #286)
-#292 := (= #50 #289)
-#295 := (forall (vars (?v0 Int) (?v1 Int)) #292)
-#364 := (iff #295 #363)
-#361 := (iff #292 #360)
-#358 := (= #289 #357)
-#355 := (= #286 #354)
-#352 := (= #283 #351)
-#336 := (iff #238 #335)
-#333 := (iff #235 #332)
-#334 := [rewrite]: #333
-#314 := (iff #228 #330)
-#315 := [rewrite]: #314
-#337 := [monotonicity #315 #334]: #336
-#353 := [monotonicity #337]: #352
-#356 := [monotonicity #353]: #355
-#359 := [monotonicity #356]: #358
-#362 := [monotonicity #359]: #361
-#365 := [quant-intro #362]: #364
-#312 := (~ #295 #295)
-#326 := (~ #292 #292)
-#327 := [refl]: #326
-#313 := [nnf-pos #327]: #312
-#44 := (- #20)
-#43 := (- #31)
-#52 := (mod #43 #44)
-#53 := (- #52)
-#37 := (< 0::Int #20)
-#39 := (< #31 0::Int)
-#40 := (and #39 #37)
-#36 := (< 0::Int #31)
-#38 := (and #36 #37)
-#41 := (or #38 #40)
-#54 := (ite #41 #51 #53)
-#55 := (ite #33 0::Int #54)
-#56 := (ite #34 #31 #55)
-#57 := (= #50 #56)
-#58 := (forall (vars (?v0 Int) (?v1 Int)) #57)
-#298 := (iff #58 #295)
-#186 := (and #37 #39)
-#189 := (or #38 #186)
-#268 := (ite #189 #51 #263)
-#177 := (= 0::Int #31)
-#271 := (ite #177 0::Int #268)
-#180 := (= 0::Int #20)
-#274 := (ite #180 #31 #271)
-#277 := (= #50 #274)
-#280 := (forall (vars (?v0 Int) (?v1 Int)) #277)
-#296 := (iff #280 #295)
-#293 := (iff #277 #292)
-#290 := (= #274 #289)
-#287 := (= #271 #286)
-#284 := (= #268 #283)
-#239 := (iff #189 #238)
-#236 := (iff #186 #235)
-#233 := (iff #39 #232)
-#234 := [rewrite]: #233
-#226 := (iff #37 #225)
-#227 := [rewrite]: #226
-#237 := [monotonicity #227 #234]: #236
-#229 := (iff #38 #228)
-#222 := (iff #36 #221)
-#223 := [rewrite]: #222
-#230 := [monotonicity #223 #227]: #229
-#240 := [monotonicity #230 #237]: #239
-#285 := [monotonicity #240]: #284
-#214 := (iff #177 #33)
-#215 := [rewrite]: #214
-#288 := [monotonicity #215 #285]: #287
-#216 := (iff #180 #34)
-#217 := [rewrite]: #216
-#291 := [monotonicity #217 #288]: #290
-#294 := [monotonicity #291]: #293
-#297 := [quant-intro #294]: #296
-#281 := (iff #58 #280)
-#278 := (iff #57 #277)
-#275 := (= #56 #274)
-#272 := (= #55 #271)
-#269 := (= #54 #268)
-#266 := (= #53 #263)
-#260 := (- #257)
-#264 := (= #260 #263)
-#265 := [rewrite]: #264
-#261 := (= #53 #260)
-#258 := (= #52 #257)
-#197 := (= #44 #196)
-#198 := [rewrite]: #197
-#194 := (= #43 #193)
-#195 := [rewrite]: #194
-#259 := [monotonicity #195 #198]: #258
-#262 := [monotonicity #259]: #261
-#267 := [trans #262 #265]: #266
-#190 := (iff #41 #189)
-#187 := (iff #40 #186)
-#188 := [rewrite]: #187
-#191 := [monotonicity #188]: #190
-#270 := [monotonicity #191 #267]: #269
-#178 := (iff #33 #177)
-#179 := [rewrite]: #178
-#273 := [monotonicity #179 #270]: #272
-#181 := (iff #34 #180)
-#182 := [rewrite]: #181
-#276 := [monotonicity #182 #273]: #275
-#279 := [monotonicity #276]: #278
-#282 := [quant-intro #279]: #281
-#299 := [trans #282 #297]: #298
-#256 := [asserted]: #58
-#300 := [mp #256 #299]: #295
-#328 := [mp~ #300 #313]: #295
-#366 := [mp #328 #365]: #363
-#397 := [mp #366 #396]: #394
-#903 := [mp #397 #902]: #898
-#829 := (not #898)
-#670 := (or #829 #831)
-#541 := (* -1::Int 3::Int)
-#473 := (mod #542 #541)
-#546 := (+ #11 #473)
-#543 := (= #546 0::Int)
-#650 := (<= 3::Int 0::Int)
-#857 := (or #650 #520)
-#531 := (not #857)
-#864 := (or #532 #650)
-#865 := (not #864)
-#866 := (or #865 #531)
-#867 := (ite #866 #863 #543)
-#858 := (ite #868 #862 #867)
-#518 := (= #9 #11)
-#523 := (= 3::Int 0::Int)
-#859 := (ite #523 #518 #858)
-#671 := (or #829 #859)
-#814 := (iff #671 #670)
-#816 := (iff #670 #670)
-#817 := [rewrite]: #816
-#828 := (iff #859 #831)
-#825 := (ite false #518 #831)
-#822 := (iff #825 #831)
-#827 := [rewrite]: #822
-#826 := (iff #859 #825)
-#835 := (iff #858 #831)
-#830 := (iff #867 #548)
-#832 := (iff #543 #554)
-#552 := (= #546 #551)
-#837 := (= #473 #840)
-#562 := (= #541 -3::Int)
-#836 := [rewrite]: #562
-#841 := [monotonicity #836]: #837
-#553 := [monotonicity #841]: #552
-#833 := [monotonicity #553]: #832
-#838 := (iff #866 #567)
-#843 := (or #849 #853)
-#568 := (iff #843 #567)
-#461 := [rewrite]: #568
-#565 := (iff #866 #843)
-#856 := (iff #531 #853)
-#495 := (iff #857 #520)
-#851 := (or false #520)
-#854 := (iff #851 #520)
-#494 := [rewrite]: #854
-#489 := (iff #857 #851)
-#503 := (iff #650 false)
-#844 := [rewrite]: #503
-#852 := [monotonicity #844]: #489
-#855 := [trans #852 #494]: #495
-#842 := [monotonicity #855]: #856
-#850 := (iff #865 #849)
-#847 := (iff #864 #532)
-#507 := (or #532 false)
-#510 := (iff #507 #532)
-#846 := [rewrite]: #510
-#508 := (iff #864 #507)
-#509 := [monotonicity #844]: #508
-#848 := [trans #509 #846]: #847
-#845 := [monotonicity #848]: #850
-#566 := [monotonicity #845 #842]: #565
-#839 := [trans #566 #461]: #838
-#834 := [monotonicity #839 #833]: #830
-#824 := [monotonicity #834]: #835
-#519 := (iff #523 false)
-#860 := [rewrite]: #519
-#821 := [monotonicity #860 #824]: #826
-#823 := [trans #821 #827]: #828
-#815 := [monotonicity #823]: #814
-#811 := [trans #815 #817]: #814
-#672 := [quant-inst #9 #10]: #671
-#812 := [mp #672 #811]: #670
-#727 := [unit-resolution #812 #903]: #831
-#705 := (not #868)
-#704 := (not #831)
-#714 := (or #704 #705)
-#709 := (not #862)
-#818 := (<= #11 0::Int)
-#730 := (not #818)
-#83 := (>= #11 3::Int)
-#12 := (< #11 3::Int)
-#13 := (not #12)
-#90 := (iff #13 #83)
-#81 := (not #83)
-#85 := (not #81)
-#88 := (iff #85 #83)
+#18 := (- 1::Int)
+#17 := (- 0::Int)
+#19 := (mod #17 #18)
+#20 := (- #19)
+#16 := (mod 0::Int 1::Int)
+#13 := (< 0::Int 1::Int)
+#12 := (< 0::Int 0::Int)
+#14 := (and #12 #13)
+#15 := (or #14 #14)
+#21 := (ite #15 #16 #20)
+#11 := (= 0::Int 0::Int)
+#22 := (ite #11 0::Int #21)
+#10 := (= 1::Int 0::Int)
+#23 := (ite #10 0::Int #22)
+#24 := (f3 #23)
+#26 := (= #24 #25)
+#27 := (not #26)
+#122 := (iff #27 false)
+#1 := true
+#117 := (not true)
+#120 := (iff #117 false)
+#121 := [rewrite]: #120
+#118 := (iff #27 #117)
+#115 := (iff #26 true)
+#110 := (= #25 #25)
+#113 := (iff #110 true)
+#114 := [rewrite]: #113
+#111 := (iff #26 #110)
+#107 := (= #23 0::Int)
+#102 := (ite false 0::Int 0::Int)
+#105 := (= #102 0::Int)
+#106 := [rewrite]: #105
+#103 := (= #23 #102)
+#100 := (= #22 0::Int)
+#95 := (ite true 0::Int 0::Int)
+#98 := (= #95 0::Int)
+#99 := [rewrite]: #98
+#96 := (= #22 #95)
+#93 := (= #21 0::Int)
+#88 := (ite #14 0::Int 0::Int)
+#91 := (= #88 0::Int)
+#92 := [rewrite]: #91
+#89 := (= #21 #88)
+#86 := (= #20 0::Int)
+#72 := (= #17 0::Int)
+#73 := [rewrite]: #72
+#84 := (= #20 #17)
+#82 := (= #19 0::Int)
+#74 := -1::Int
+#77 := (mod 0::Int -1::Int)
+#80 := (= #77 0::Int)
+#81 := [rewrite]: #80
+#78 := (= #19 #77)
+#75 := (= #18 -1::Int)
+#76 := [rewrite]: #75
+#79 := [monotonicity #73 #76]: #78
+#83 := [trans #79 #81]: #82
+#85 := [monotonicity #83]: #84
+#87 := [trans #85 #73]: #86
+#70 := (= #16 0::Int)
+#71 := [rewrite]: #70
+#68 := (iff #15 #14)
+#69 := [rewrite]: #68
+#90 := [monotonicity #69 #71 #87]: #89
+#94 := [trans #90 #92]: #93
+#66 := (iff #11 true)
+#67 := [rewrite]: #66
+#97 := [monotonicity #67 #94]: #96
+#101 := [trans #97 #99]: #100
+#64 := (iff #10 false)
+#65 := [rewrite]: #64
+#104 := [monotonicity #65 #101]: #103
+#108 := [trans #104 #106]: #107
+#109 := [monotonicity #108]: #26
+#112 := [monotonicity #109]: #111
+#116 := [trans #112 #114]: #115
+#119 := [monotonicity #116]: #118
+#123 := [trans #119 #121]: #122
+#63 := [asserted]: #27
+[mp #63 #123]: false
+unsat
+a1075089dc52af4042f6a4669e72797d6209efe9 90 0
+#2 := false
+decl f3 :: (-> Int S2)
+#9 := 0::Int
+#24 := (f3 0::Int)
+#8 := 1::Int
+#17 := (- 1::Int)
+#18 := (mod #17 #17)
+#19 := (- #18)
+#16 := (mod 1::Int 1::Int)
+#11 := (< 0::Int 1::Int)
+#13 := (< 1::Int 0::Int)
+#14 := (and #13 #11)
+#12 := (and #11 #11)
+#15 := (or #12 #14)
+#20 := (ite #15 #16 #19)
+#10 := (= 1::Int 0::Int)
+#21 := (ite #10 0::Int #20)
+#22 := (ite #10 1::Int #21)
+#23 := (f3 #22)
+#25 := (= #23 #24)
+#26 := (not #25)
+#126 := (iff #26 false)
+#1 := true
+#121 := (not true)
+#124 := (iff #121 false)
+#125 := [rewrite]: #124
+#122 := (iff #26 #121)
+#119 := (iff #25 true)
+#114 := (= #24 #24)
+#117 := (iff #114 true)
+#118 := [rewrite]: #117
+#115 := (iff #25 #114)
+#111 := (= #22 0::Int)
+#106 := (ite false 1::Int 0::Int)
+#109 := (= #106 0::Int)
+#110 := [rewrite]: #109
+#107 := (= #22 #106)
+#104 := (= #21 0::Int)
+#99 := (ite false 0::Int 0::Int)
+#102 := (= #99 0::Int)
+#103 := [rewrite]: #102
+#100 := (= #21 #99)
+#97 := (= #20 0::Int)
+#67 := (and #11 #13)
+#70 := (or #11 #67)
+#92 := (ite #70 0::Int 0::Int)
+#95 := (= #92 0::Int)
+#96 := [rewrite]: #95
+#93 := (= #20 #92)
+#90 := (= #19 0::Int)
+#85 := (- 0::Int)
+#88 := (= #85 0::Int)
 #89 := [rewrite]: #88
-#86 := (iff #13 #85)
-#82 := (iff #12 #81)
-#84 := [rewrite]: #82
+#86 := (= #19 #85)
+#83 := (= #18 0::Int)
+#75 := -1::Int
+#78 := (mod -1::Int -1::Int)
+#81 := (= #78 0::Int)
+#82 := [rewrite]: #81
+#79 := (= #18 #78)
+#76 := (= #17 -1::Int)
+#77 := [rewrite]: #76
+#80 := [monotonicity #77 #77]: #79
+#84 := [trans #80 #82]: #83
 #87 := [monotonicity #84]: #86
 #91 := [trans #87 #89]: #90
-#78 := [asserted]: #13
-#92 := [mp #78 #91]: #83
-#731 := (or #730 #81)
-#732 := [th-lemma arith farkas 1 1]: #731
-#728 := [unit-resolution #732 #92]: #730
-#733 := (or #709 #818)
-#713 := [th-lemma arith triangle-eq]: #733
-#659 := [unit-resolution #713 #728]: #709
-#698 := (or #704 #705 #862)
-#706 := [def-axiom]: #698
-#695 := [unit-resolution #706 #659]: #714
-#719 := [unit-resolution #695 #727]: #705
-#707 := (or #704 #868 #548)
-#708 := [def-axiom]: #707
-#720 := [unit-resolution #708 #719 #727]: #548
-decl f6 :: (-> Int S2)
-#455 := (f6 #9)
-#791 := (f4 #455)
-#793 := (= #791 0::Int)
-#699 := (not #793)
-#700 := (iff #705 #699)
-#690 := (iff #868 #793)
-#686 := (iff #793 #868)
-#696 := (= #791 #9)
-#721 := (= #455 f5)
-#540 := (= f5 #455)
-#14 := (:var 0 S2)
-#15 := (f4 #14)
-#869 := (pattern #15)
-#16 := (f6 #15)
-#80 := (= #14 #16)
-#870 := (forall (vars (?v0 S2)) (:pat #869) #80)
-#95 := (forall (vars (?v0 S2)) #80)
-#871 := (iff #95 #870)
-#873 := (iff #870 #870)
-#874 := [rewrite]: #873
-#872 := [rewrite]: #871
-#875 := [trans #872 #874]: #871
-#318 := (~ #95 #95)
-#316 := (~ #80 #80)
-#317 := [refl]: #316
-#319 := [nnf-pos #317]: #318
-#17 := (= #16 #14)
-#18 := (forall (vars (?v0 S2)) #17)
-#96 := (iff #18 #95)
-#93 := (iff #17 #80)
-#94 := [rewrite]: #93
-#97 := [quant-intro #94]: #96
-#79 := [asserted]: #18
-#100 := [mp #79 #97]: #95
-#304 := [mp~ #100 #319]: #95
-#876 := [mp #304 #875]: #870
-#533 := (not #870)
-#544 := (or #533 #540)
-#545 := [quant-inst #8]: #544
-#715 := [unit-resolution #545 #876]: #540
-#689 := [symm #715]: #721
-#655 := [monotonicity #689]: #696
-#688 := [monotonicity #655]: #686
-#697 := [symm #688]: #690
-#701 := [monotonicity #697]: #700
-#711 := [mp #719 #701]: #699
-#782 := (or #520 #793)
-#22 := (f6 #20)
-#877 := (pattern #22)
-#117 := (>= #20 0::Int)
-#23 := (f4 #22)
-#28 := (= #23 0::Int)
-#165 := (or #28 #117)
-#884 := (forall (vars (?v0 Int)) (:pat #877) #165)
-#170 := (forall (vars (?v0 Int)) #165)
-#887 := (iff #170 #884)
-#885 := (iff #165 #165)
-#886 := [refl]: #885
-#888 := [quant-intro #886]: #887
-#308 := (~ #170 #170)
-#320 := (~ #165 #165)
-#321 := [refl]: #320
-#309 := [nnf-pos #321]: #308
-#27 := (< #20 0::Int)
-#29 := (implies #27 #28)
-#30 := (forall (vars (?v0 Int)) #29)
-#173 := (iff #30 #170)
-#136 := (= 0::Int #23)
-#142 := (not #27)
-#143 := (or #142 #136)
-#148 := (forall (vars (?v0 Int)) #143)
-#171 := (iff #148 #170)
-#168 := (iff #143 #165)
-#162 := (or #117 #28)
-#166 := (iff #162 #165)
-#167 := [rewrite]: #166
-#163 := (iff #143 #162)
-#160 := (iff #136 #28)
-#161 := [rewrite]: #160
-#158 := (iff #142 #117)
-#118 := (not #117)
-#153 := (not #118)
-#156 := (iff #153 #117)
-#157 := [rewrite]: #156
-#154 := (iff #142 #153)
-#151 := (iff #27 #118)
+#73 := (= #16 0::Int)
+#74 := [rewrite]: #73
+#71 := (iff #15 #70)
+#68 := (iff #14 #67)
+#69 := [rewrite]: #68
+#65 := (iff #12 #11)
+#66 := [rewrite]: #65
+#72 := [monotonicity #66 #69]: #71
+#94 := [monotonicity #72 #74 #91]: #93
+#98 := [trans #94 #96]: #97
+#63 := (iff #10 false)
+#64 := [rewrite]: #63
+#101 := [monotonicity #64 #98]: #100
+#105 := [trans #101 #103]: #104
+#108 := [monotonicity #64 #105]: #107
+#112 := [trans #108 #110]: #111
+#113 := [monotonicity #112]: #25
+#116 := [monotonicity #113]: #115
+#120 := [trans #116 #118]: #119
+#123 := [monotonicity #120]: #122
+#127 := [trans #123 #125]: #126
+#62 := [asserted]: #26
+[mp #62 #127]: false
+unsat
+63c9d4e9b322eec0fd3bd7dd16ba42cd509506b7 97 0
+#2 := false
+decl f3 :: (-> Int S2)
+#9 := 0::Int
+#28 := (f3 0::Int)
+#8 := 1::Int
+#21 := (- 1::Int)
+#11 := 3::Int
+#20 := (- 3::Int)
+#22 := (mod #20 #21)
+#23 := (- #22)
+#19 := (mod 3::Int 1::Int)
+#14 := (< 0::Int 1::Int)
+#16 := (< 3::Int 0::Int)
+#17 := (and #16 #14)
+#13 := (< 0::Int 3::Int)
+#15 := (and #13 #14)
+#18 := (or #15 #17)
+#24 := (ite #18 #19 #23)
+#12 := (= 3::Int 0::Int)
+#25 := (ite #12 0::Int #24)
+#10 := (= 1::Int 0::Int)
+#26 := (ite #10 3::Int #25)
+#27 := (f3 #26)
+#29 := (= #27 #28)
+#30 := (not #29)
+#133 := (iff #30 false)
+#1 := true
+#128 := (not true)
+#131 := (iff #128 false)
+#132 := [rewrite]: #131
+#129 := (iff #30 #128)
+#126 := (iff #29 true)
+#121 := (= #28 #28)
+#124 := (iff #121 true)
+#125 := [rewrite]: #124
+#122 := (iff #29 #121)
+#118 := (= #26 0::Int)
+#113 := (ite false 3::Int 0::Int)
+#116 := (= #113 0::Int)
+#117 := [rewrite]: #116
+#114 := (= #26 #113)
+#111 := (= #25 0::Int)
+#106 := (ite false 0::Int 0::Int)
+#109 := (= #106 0::Int)
+#110 := [rewrite]: #109
+#107 := (= #25 #106)
+#104 := (= #24 0::Int)
+#71 := (and #14 #16)
+#74 := (or #15 #71)
+#99 := (ite #74 0::Int 0::Int)
+#102 := (= #99 0::Int)
+#103 := [rewrite]: #102
+#100 := (= #24 #99)
+#97 := (= #23 0::Int)
+#92 := (- 0::Int)
+#95 := (= #92 0::Int)
+#96 := [rewrite]: #95
+#93 := (= #23 #92)
+#90 := (= #22 0::Int)
+#82 := -1::Int
+#79 := -3::Int
+#85 := (mod -3::Int -1::Int)
+#88 := (= #85 0::Int)
+#89 := [rewrite]: #88
+#86 := (= #22 #85)
+#83 := (= #21 -1::Int)
+#84 := [rewrite]: #83
+#80 := (= #20 -3::Int)
+#81 := [rewrite]: #80
+#87 := [monotonicity #81 #84]: #86
+#91 := [trans #87 #89]: #90
+#94 := [monotonicity #91]: #93
+#98 := [trans #94 #96]: #97
+#77 := (= #19 0::Int)
+#78 := [rewrite]: #77
+#75 := (iff #18 #74)
+#72 := (iff #17 #71)
+#73 := [rewrite]: #72
+#76 := [monotonicity #73]: #75
+#101 := [monotonicity #76 #78 #98]: #100
+#105 := [trans #101 #103]: #104
+#69 := (iff #12 false)
+#70 := [rewrite]: #69
+#108 := [monotonicity #70 #105]: #107
+#112 := [trans #108 #110]: #111
+#67 := (iff #10 false)
+#68 := [rewrite]: #67
+#115 := [monotonicity #68 #112]: #114
+#119 := [trans #115 #117]: #118
+#120 := [monotonicity #119]: #29
+#123 := [monotonicity #120]: #122
+#127 := [trans #123 #125]: #126
+#130 := [monotonicity #127]: #129
+#134 := [trans #130 #132]: #133
+#66 := [asserted]: #30
+[mp #66 #134]: false
+unsat
+baacef3aba2d9193028d7d390c9e488f80e40513 170 0
+#2 := false
+#9 := 0::Int
+decl f4 :: (-> S2 Int)
+decl f5 :: S2
+#11 := f5
+#12 := (f4 f5)
+#144 := (>= #12 0::Int)
+#145 := (not #144)
+#131 := (<= #12 0::Int)
+#132 := (not #131)
+#13 := (= #12 0::Int)
+#163 := (or #13 #132 #145)
+#429 := (not #163)
+#81 := -1::Int
+#82 := (* -1::Int #12)
+#87 := (mod #82 -1::Int)
+#93 := (* -1::Int #87)
+#168 := (ite #163 0::Int #93)
+#341 := (= #168 0::Int)
+#706 := (not #341)
+decl f3 :: (-> Int S2)
+#171 := (f3 #168)
+#29 := (f3 0::Int)
+#174 := (= #29 #171)
+#698 := (= #171 #29)
+#697 := [hypothesis]: #341
+#704 := [monotonicity #697]: #698
+#705 := [symm #704]: #174
+#177 := (not #174)
+#8 := 1::Int
+#22 := (- 1::Int)
+#21 := (- #12)
+#23 := (mod #21 #22)
+#24 := (- #23)
+#20 := (mod #12 1::Int)
+#15 := (< 0::Int 1::Int)
+#17 := (< #12 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int #12)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#25 := (ite #19 #20 #24)
+#26 := (ite #13 0::Int #25)
+#10 := (= 1::Int 0::Int)
+#27 := (ite #10 #12 #26)
+#28 := (f3 #27)
+#30 := (= #28 #29)
+#31 := (not #30)
+#180 := (iff #31 #177)
+#73 := (and #15 #17)
+#76 := (or #16 #73)
+#70 := (= 0::Int #12)
+#104 := (or #70 #76)
+#105 := (ite #104 0::Int #93)
+#117 := (f3 #105)
+#123 := (= #29 #117)
+#128 := (not #123)
+#178 := (iff #128 #177)
+#175 := (iff #123 #174)
+#172 := (= #117 #171)
+#169 := (= #105 #168)
+#166 := (iff #104 #163)
+#157 := (or #132 #145)
+#160 := (or #13 #157)
+#164 := (iff #160 #163)
+#165 := [rewrite]: #164
+#161 := (iff #104 #160)
+#158 := (iff #76 #157)
+#153 := (iff #73 #145)
+#1 := true
+#148 := (and true #145)
+#151 := (iff #148 #145)
 #152 := [rewrite]: #151
-#155 := [monotonicity #152]: #154
-#159 := [trans #155 #157]: #158
-#164 := [monotonicity #159 #161]: #163
-#169 := [trans #164 #167]: #168
-#172 := [quant-intro #169]: #171
-#149 := (iff #30 #148)
-#146 := (iff #29 #143)
-#139 := (implies #27 #136)
-#144 := (iff #139 #143)
-#145 := [rewrite]: #144
-#140 := (iff #29 #139)
-#137 := (iff #28 #136)
-#138 := [rewrite]: #137
-#141 := [monotonicity #138]: #140
-#147 := [trans #141 #145]: #146
-#150 := [quant-intro #147]: #149
-#174 := [trans #150 #172]: #173
-#135 := [asserted]: #30
-#175 := [mp #135 #174]: #170
-#322 := [mp~ #175 #309]: #170
-#889 := [mp #322 #888]: #884
-#795 := (not #884)
-#796 := (or #795 #520 #793)
-#785 := (or #793 #520)
-#792 := (or #795 #785)
-#790 := (iff #792 #796)
-#786 := (or #795 #782)
-#789 := (iff #786 #796)
-#783 := [rewrite]: #789
-#787 := (iff #792 #786)
-#784 := (iff #785 #782)
-#794 := [rewrite]: #784
-#788 := [monotonicity #794]: #787
-#774 := [trans #788 #783]: #790
-#797 := [quant-inst #9]: #792
-#775 := [mp #797 #774]: #796
-#691 := [unit-resolution #775 #889]: #782
-#712 := [unit-resolution #691 #711]: #520
-#667 := (or #868 #849 #853)
-#668 := [th-lemma arith triangle-eq]: #667
-#673 := [unit-resolution #668 #719]: #843
-#674 := [unit-resolution #673 #712]: #849
-#649 := (or #567 #532)
-#651 := [def-axiom]: #649
-#675 := [unit-resolution #651 #674]: #567
-#652 := (not #567)
-#692 := (not #548)
-#693 := (or #692 #652 #863)
-#694 := [def-axiom]: #693
-#676 := [unit-resolution #694 #675 #720]: #863
-#703 := (not #863)
-#677 := (or #703 #808)
-#678 := [th-lemma arith triangle-eq]: #677
-#679 := [unit-resolution #678 #676]: #808
-[th-lemma arith farkas -1 1 1 #92 #679 #726]: false
-unsat
-318d5be50bbd50da7b7b7962a11c2c98ae8be85c 662 0
-#2 := false
-#10 := 3::Int
-decl f5 :: (-> S2 Int)
-decl f6 :: S2
-#8 := f6
-#9 := (f5 f6)
-#883 := (mod #9 3::Int)
-#706 := (>= #883 3::Int)
-#707 := (not #706)
-#1 := true
-#79 := [true-axiom]: true
-#666 := (or false #707)
-#667 := [th-lemma arith]: #666
-#669 := [unit-resolution #667 #79]: #707
-#104 := (>= #9 3::Int)
-#102 := (not #104)
-#619 := [hypothesis]: #102
-#22 := 0::Int
-#220 := -1::Int
-#881 := (* -1::Int #883)
-decl f4 :: (-> Int Int Int)
-#11 := (f4 #9 3::Int)
-#884 := (+ #11 #881)
-#824 := (<= #884 0::Int)
-#870 := (= #884 0::Int)
-#864 := (= #9 0::Int)
-#809 := (not #864)
-decl f3 :: (-> Int S2)
-#12 := (f3 #11)
-#82 := (= f6 #12)
-#572 := (not #82)
-#574 := (or #572 #104)
-#113 := (iff #82 #104)
-#14 := (< #9 3::Int)
-#13 := (= #12 f6)
-#15 := (iff #13 #14)
-#16 := (not #15)
-#116 := (iff #16 #113)
-#96 := (not #14)
-#97 := (iff #82 #96)
-#114 := (iff #97 #113)
-#111 := (iff #96 #104)
-#106 := (not #102)
-#109 := (iff #106 #104)
-#110 := [rewrite]: #109
-#107 := (iff #96 #106)
-#103 := (iff #14 #102)
-#105 := [rewrite]: #103
-#108 := [monotonicity #105]: #107
-#112 := [trans #108 #110]: #111
-#115 := [monotonicity #112]: #114
-#100 := (iff #16 #97)
-#88 := (iff #14 #82)
-#93 := (not #88)
-#98 := (iff #93 #97)
+#149 := (iff #73 #148)
+#146 := (iff #17 #145)
+#147 := [rewrite]: #146
+#135 := (iff #15 true)
+#136 := [rewrite]: #135
+#150 := [monotonicity #136 #147]: #149
+#154 := [trans #150 #152]: #153
+#142 := (iff #16 #132)
+#137 := (and #132 true)
+#140 := (iff #137 #132)
+#141 := [rewrite]: #140
+#138 := (iff #16 #137)
+#133 := (iff #14 #132)
+#134 := [rewrite]: #133
+#139 := [monotonicity #134 #136]: #138
+#143 := [trans #139 #141]: #142
+#159 := [monotonicity #143 #154]: #158
+#155 := (iff #70 #13)
+#156 := [rewrite]: #155
+#162 := [monotonicity #156 #159]: #161
+#167 := [trans #162 #165]: #166
+#170 := [monotonicity #167]: #169
+#173 := [monotonicity #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [monotonicity #176]: #178
+#129 := (iff #31 #128)
+#126 := (iff #30 #123)
+#120 := (= #117 #29)
+#124 := (iff #120 #123)
+#125 := [rewrite]: #124
+#121 := (iff #30 #120)
+#118 := (= #28 #117)
+#115 := (= #27 #105)
+#110 := (ite false #12 #105)
+#113 := (= #110 #105)
+#114 := [rewrite]: #113
+#111 := (= #27 #110)
+#108 := (= #26 #105)
+#98 := (ite #76 0::Int #93)
+#101 := (ite #70 0::Int #98)
+#106 := (= #101 #105)
+#107 := [rewrite]: #106
+#102 := (= #26 #101)
+#99 := (= #25 #98)
+#96 := (= #24 #93)
+#90 := (- #87)
+#94 := (= #90 #93)
+#95 := [rewrite]: #94
+#91 := (= #24 #90)
+#88 := (= #23 #87)
+#85 := (= #22 -1::Int)
+#86 := [rewrite]: #85
+#83 := (= #21 #82)
+#84 := [rewrite]: #83
+#89 := [monotonicity #84 #86]: #88
+#92 := [monotonicity #89]: #91
+#97 := [trans #92 #95]: #96
+#79 := (= #20 0::Int)
+#80 := [rewrite]: #79
+#77 := (iff #19 #76)
+#74 := (iff #18 #73)
+#75 := [rewrite]: #74
+#78 := [monotonicity #75]: #77
+#100 := [monotonicity #78 #80 #97]: #99
+#71 := (iff #13 #70)
+#72 := [rewrite]: #71
+#103 := [monotonicity #72 #100]: #102
+#109 := [trans #103 #107]: #108
+#68 := (iff #10 false)
+#69 := [rewrite]: #68
+#112 := [monotonicity #69 #109]: #111
+#116 := [trans #112 #114]: #115
+#119 := [monotonicity #116]: #118
+#122 := [monotonicity #119]: #121
+#127 := [trans #122 #125]: #126
+#130 := [monotonicity #127]: #129
+#181 := [trans #130 #179]: #180
+#67 := [asserted]: #31
+#182 := [mp #67 #181]: #177
+#699 := [unit-resolution #182 #705]: false
+#535 := [lemma #699]: #706
+#747 := (or #429 #341)
+#749 := [def-axiom]: #747
+#658 := [unit-resolution #749 #535]: #429
+#431 := (or #163 #144)
+#432 := [def-axiom]: #431
+#655 := [unit-resolution #432 #658]: #144
+#419 := (or #163 #131)
+#430 := [def-axiom]: #419
+#659 := [unit-resolution #430 #658]: #131
+#342 := (not #13)
+#427 := (or #163 #342)
+#428 := [def-axiom]: #427
+#639 := [unit-resolution #428 #658]: #342
+#640 := [th-lemma arith triangle-eq]: #163
+[unit-resolution #640 #639 #659 #655]: false
+unsat
+52940ae1c337d10436c752f28c341997638bfaa6 86 0
+#2 := false
+decl f3 :: (-> Int S2)
+#9 := 0::Int
+#25 := (f3 0::Int)
+#8 := 3::Int
+#18 := (- 3::Int)
+#17 := (- 0::Int)
+#19 := (mod #17 #18)
+#20 := (- #19)
+#16 := (mod 0::Int 3::Int)
+#13 := (< 0::Int 3::Int)
+#12 := (< 0::Int 0::Int)
+#14 := (and #12 #13)
+#15 := (or #14 #14)
+#21 := (ite #15 #16 #20)
+#11 := (= 0::Int 0::Int)
+#22 := (ite #11 0::Int #21)
+#10 := (= 3::Int 0::Int)
+#23 := (ite #10 0::Int #22)
+#24 := (f3 #23)
+#26 := (= #24 #25)
+#27 := (not #26)
+#122 := (iff #27 false)
+#1 := true
+#117 := (not true)
+#120 := (iff #117 false)
+#121 := [rewrite]: #120
+#118 := (iff #27 #117)
+#115 := (iff #26 true)
+#110 := (= #25 #25)
+#113 := (iff #110 true)
+#114 := [rewrite]: #113
+#111 := (iff #26 #110)
+#107 := (= #23 0::Int)
+#102 := (ite false 0::Int 0::Int)
+#105 := (= #102 0::Int)
+#106 := [rewrite]: #105
+#103 := (= #23 #102)
+#100 := (= #22 0::Int)
+#95 := (ite true 0::Int 0::Int)
+#98 := (= #95 0::Int)
 #99 := [rewrite]: #98
-#94 := (iff #16 #93)
-#91 := (iff #15 #88)
-#85 := (iff #82 #14)
-#89 := (iff #85 #88)
+#96 := (= #22 #95)
+#93 := (= #21 0::Int)
+#88 := (ite #14 0::Int 0::Int)
+#91 := (= #88 0::Int)
+#92 := [rewrite]: #91
+#89 := (= #21 #88)
+#86 := (= #20 0::Int)
+#72 := (= #17 0::Int)
+#73 := [rewrite]: #72
+#84 := (= #20 #17)
+#82 := (= #19 0::Int)
+#74 := -3::Int
+#77 := (mod 0::Int -3::Int)
+#80 := (= #77 0::Int)
+#81 := [rewrite]: #80
+#78 := (= #19 #77)
+#75 := (= #18 -3::Int)
+#76 := [rewrite]: #75
+#79 := [monotonicity #73 #76]: #78
+#83 := [trans #79 #81]: #82
+#85 := [monotonicity #83]: #84
+#87 := [trans #85 #73]: #86
+#70 := (= #16 0::Int)
+#71 := [rewrite]: #70
+#68 := (iff #15 #14)
+#69 := [rewrite]: #68
+#90 := [monotonicity #69 #71 #87]: #89
+#94 := [trans #90 #92]: #93
+#66 := (iff #11 true)
+#67 := [rewrite]: #66
+#97 := [monotonicity #67 #94]: #96
+#101 := [trans #97 #99]: #100
+#64 := (iff #10 false)
+#65 := [rewrite]: #64
+#104 := [monotonicity #65 #101]: #103
+#108 := [trans #104 #106]: #107
+#109 := [monotonicity #108]: #26
+#112 := [monotonicity #109]: #111
+#116 := [trans #112 #114]: #115
+#119 := [monotonicity #116]: #118
+#123 := [trans #119 #121]: #122
+#63 := [asserted]: #27
+[mp #63 #123]: false
+unsat
+eea72e0b08b81263eac13f5c3a2599d4713d6590 145 0
+#2 := false
+decl f3 :: (-> Int S2)
+#11 := 1::Int
+#28 := (f3 1::Int)
+#8 := 3::Int
+#21 := (- 3::Int)
+#20 := (- 1::Int)
+#22 := (mod #20 #21)
+#23 := (- #22)
+#19 := (mod 1::Int 3::Int)
+#9 := 0::Int
+#14 := (< 0::Int 3::Int)
+#16 := (< 1::Int 0::Int)
+#17 := (and #16 #14)
+#13 := (< 0::Int 1::Int)
+#15 := (and #13 #14)
+#18 := (or #15 #17)
+#24 := (ite #18 #19 #23)
+#12 := (= 1::Int 0::Int)
+#25 := (ite #12 0::Int #24)
+#10 := (= 3::Int 0::Int)
+#26 := (ite #10 1::Int #25)
+#27 := (f3 #26)
+#29 := (= #27 #28)
+#30 := (not #29)
+#181 := (iff #30 false)
+#96 := -2::Int
+#71 := (and #14 #16)
+#74 := (or #15 #71)
+#101 := (ite #74 1::Int -2::Int)
+#118 := (f3 #101)
+#124 := (= #28 #118)
+#129 := (not #124)
+#179 := (iff #129 false)
+#1 := true
+#174 := (not true)
+#177 := (iff #174 false)
+#178 := [rewrite]: #177
+#175 := (iff #129 #174)
+#172 := (iff #124 true)
+#167 := (= #28 #28)
+#170 := (iff #167 true)
+#171 := [rewrite]: #170
+#168 := (iff #124 #167)
+#121 := (= #118 #28)
+#164 := (= #101 1::Int)
+#159 := (ite true 1::Int -2::Int)
+#162 := (= #159 1::Int)
+#163 := [rewrite]: #162
+#160 := (= #101 #159)
+#157 := (iff #74 true)
+#152 := (or true false)
+#155 := (iff #152 true)
+#156 := [rewrite]: #155
+#153 := (iff #74 #152)
+#150 := (iff #71 false)
+#145 := (and true false)
+#148 := (iff #145 false)
+#149 := [rewrite]: #148
+#146 := (iff #71 #145)
+#143 := (iff #16 false)
+#144 := [rewrite]: #143
+#134 := (iff #14 true)
+#135 := [rewrite]: #134
+#147 := [monotonicity #135 #144]: #146
+#151 := [trans #147 #149]: #150
+#141 := (iff #15 true)
+#136 := (and true true)
+#139 := (iff #136 true)
+#140 := [rewrite]: #139
+#137 := (iff #15 #136)
+#132 := (iff #13 true)
+#133 := [rewrite]: #132
+#138 := [monotonicity #133 #135]: #137
+#142 := [trans #138 #140]: #141
+#154 := [monotonicity #142 #151]: #153
+#158 := [trans #154 #156]: #157
+#161 := [monotonicity #158]: #160
+#165 := [trans #161 #163]: #164
+#166 := [monotonicity #165]: #121
+#169 := [monotonicity #166]: #168
+#173 := [trans #169 #171]: #172
+#176 := [monotonicity #173]: #175
+#180 := [trans #176 #178]: #179
+#130 := (iff #30 #129)
+#127 := (iff #29 #124)
+#125 := (iff #121 #124)
+#126 := [rewrite]: #125
+#122 := (iff #29 #121)
+#119 := (= #27 #118)
+#116 := (= #26 #101)
+#111 := (ite false 1::Int #101)
+#114 := (= #111 #101)
+#115 := [rewrite]: #114
+#112 := (= #26 #111)
+#109 := (= #25 #101)
+#104 := (ite false 0::Int #101)
+#107 := (= #104 #101)
+#108 := [rewrite]: #107
+#105 := (= #25 #104)
+#102 := (= #24 #101)
+#99 := (= #23 -2::Int)
+#88 := 2::Int
+#93 := (- 2::Int)
+#97 := (= #93 -2::Int)
+#98 := [rewrite]: #97
+#94 := (= #23 #93)
+#91 := (= #22 2::Int)
+#82 := -3::Int
+#79 := -1::Int
+#85 := (mod -1::Int -3::Int)
+#89 := (= #85 2::Int)
 #90 := [rewrite]: #89
-#86 := (iff #15 #85)
-#83 := (iff #13 #82)
+#86 := (= #22 #85)
+#83 := (= #21 -3::Int)
 #84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
+#80 := (= #20 -1::Int)
+#81 := [rewrite]: #80
+#87 := [monotonicity #81 #84]: #86
 #92 := [trans #87 #90]: #91
 #95 := [monotonicity #92]: #94
-#101 := [trans #95 #99]: #100
-#117 := [trans #101 #115]: #116
-#81 := [asserted]: #16
-#118 := [mp #81 #117]: #113
-#483 := (not #113)
-#573 := (or #572 #104 #483)
-#501 := [def-axiom]: #573
-#571 := [unit-resolution #501 #118]: #574
-#636 := [unit-resolution #571 #619]: #572
-#753 := (or #809 #82)
-#575 := (f3 #9)
-#750 := (= #575 #12)
-#746 := (= #12 #575)
-#771 := (= #11 #9)
-#770 := (= 0::Int #9)
-#764 := [hypothesis]: #864
-#765 := [symm #764]: #770
-#590 := (= #11 0::Int)
-#767 := (or #809 #590)
-#840 := -3::Int
-#880 := (* -1::Int #9)
-#841 := (mod #880 -3::Int)
-#679 := (+ #11 #841)
-#834 := (= #679 0::Int)
-#871 := (>= #9 0::Int)
-#700 := (not #871)
-#596 := (<= #9 0::Int)
-#853 := (not #596)
-#844 := (or #853 #700)
-#835 := (ite #844 #870 #834)
-#721 := (ite #864 #590 #835)
-#23 := (:var 0 Int)
-#34 := (:var 1 Int)
-#53 := (f4 #34 #23)
-#925 := (pattern #53)
-#224 := (* -1::Int #23)
-#221 := (* -1::Int #34)
-#285 := (mod #221 #224)
-#415 := (+ #53 #285)
-#416 := (= #415 0::Int)
-#54 := (mod #34 #23)
-#412 := (* -1::Int #54)
-#413 := (+ #53 #412)
-#414 := (= #413 0::Int)
-#259 := (>= #34 0::Int)
-#252 := (<= #23 0::Int)
-#359 := (or #252 #259)
-#360 := (not #359)
-#248 := (<= #34 0::Int)
-#357 := (or #248 #252)
-#358 := (not #357)
-#363 := (or #358 #360)
-#417 := (ite #363 #414 #416)
-#411 := (= #53 0::Int)
-#36 := (= #34 0::Int)
-#418 := (ite #36 #411 #417)
-#410 := (= #34 #53)
-#37 := (= #23 0::Int)
-#419 := (ite #37 #410 #418)
-#926 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #925) #419)
-#422 := (forall (vars (?v0 Int) (?v1 Int)) #419)
-#929 := (iff #422 #926)
-#927 := (iff #419 #419)
-#928 := [refl]: #927
-#930 := [quant-intro #928]: #929
-#291 := (* -1::Int #285)
-#379 := (ite #363 #54 #291)
-#382 := (ite #36 0::Int #379)
-#385 := (ite #37 #34 #382)
-#388 := (= #53 #385)
-#391 := (forall (vars (?v0 Int) (?v1 Int)) #388)
-#423 := (iff #391 #422)
-#420 := (iff #388 #419)
-#421 := [rewrite]: #420
-#424 := [quant-intro #421]: #423
-#260 := (not #259)
-#253 := (not #252)
-#263 := (and #253 #260)
-#249 := (not #248)
-#256 := (and #249 #253)
-#266 := (or #256 #263)
-#311 := (ite #266 #54 #291)
-#314 := (ite #36 0::Int #311)
-#317 := (ite #37 #34 #314)
-#320 := (= #53 #317)
-#323 := (forall (vars (?v0 Int) (?v1 Int)) #320)
-#392 := (iff #323 #391)
-#389 := (iff #320 #388)
-#386 := (= #317 #385)
-#383 := (= #314 #382)
-#380 := (= #311 #379)
-#364 := (iff #266 #363)
-#361 := (iff #263 #360)
-#362 := [rewrite]: #361
-#342 := (iff #256 #358)
-#343 := [rewrite]: #342
-#365 := [monotonicity #343 #362]: #364
-#381 := [monotonicity #365]: #380
-#384 := [monotonicity #381]: #383
-#387 := [monotonicity #384]: #386
-#390 := [monotonicity #387]: #389
-#393 := [quant-intro #390]: #392
-#340 := (~ #323 #323)
-#354 := (~ #320 #320)
-#355 := [refl]: #354
-#341 := [nnf-pos #355]: #340
-#47 := (- #23)
-#46 := (- #34)
-#55 := (mod #46 #47)
-#56 := (- #55)
-#40 := (< 0::Int #23)
-#42 := (< #34 0::Int)
-#43 := (and #42 #40)
-#39 := (< 0::Int #34)
-#41 := (and #39 #40)
-#44 := (or #41 #43)
-#57 := (ite #44 #54 #56)
-#58 := (ite #36 0::Int #57)
-#59 := (ite #37 #34 #58)
-#60 := (= #53 #59)
-#61 := (forall (vars (?v0 Int) (?v1 Int)) #60)
-#326 := (iff #61 #323)
-#214 := (and #40 #42)
-#217 := (or #41 #214)
-#296 := (ite #217 #54 #291)
-#205 := (= 0::Int #34)
-#299 := (ite #205 0::Int #296)
-#208 := (= 0::Int #23)
-#302 := (ite #208 #34 #299)
-#305 := (= #53 #302)
-#308 := (forall (vars (?v0 Int) (?v1 Int)) #305)
-#324 := (iff #308 #323)
-#321 := (iff #305 #320)
-#318 := (= #302 #317)
-#315 := (= #299 #314)
-#312 := (= #296 #311)
-#267 := (iff #217 #266)
-#264 := (iff #214 #263)
-#261 := (iff #42 #260)
-#262 := [rewrite]: #261
-#254 := (iff #40 #253)
-#255 := [rewrite]: #254
-#265 := [monotonicity #255 #262]: #264
-#257 := (iff #41 #256)
-#250 := (iff #39 #249)
+#100 := [trans #95 #98]: #99
+#77 := (= #19 1::Int)
+#78 := [rewrite]: #77
+#75 := (iff #18 #74)
+#72 := (iff #17 #71)
+#73 := [rewrite]: #72
+#76 := [monotonicity #73]: #75
+#103 := [monotonicity #76 #78 #100]: #102
+#69 := (iff #12 false)
+#70 := [rewrite]: #69
+#106 := [monotonicity #70 #103]: #105
+#110 := [trans #106 #108]: #109
+#67 := (iff #10 false)
+#68 := [rewrite]: #67
+#113 := [monotonicity #68 #110]: #112
+#117 := [trans #113 #115]: #116
+#120 := [monotonicity #117]: #119
+#123 := [monotonicity #120]: #122
+#128 := [trans #123 #126]: #127
+#131 := [monotonicity #128]: #130
+#182 := [trans #131 #180]: #181
+#66 := [asserted]: #30
+[mp #66 #182]: false
+unsat
+3921706a8683868f2784292da2026eadf56bd286 90 0
+#2 := false
+decl f3 :: (-> Int S2)
+#9 := 0::Int
+#24 := (f3 0::Int)
+#8 := 3::Int
+#17 := (- 3::Int)
+#18 := (mod #17 #17)
+#19 := (- #18)
+#16 := (mod 3::Int 3::Int)
+#11 := (< 0::Int 3::Int)
+#13 := (< 3::Int 0::Int)
+#14 := (and #13 #11)
+#12 := (and #11 #11)
+#15 := (or #12 #14)
+#20 := (ite #15 #16 #19)
+#10 := (= 3::Int 0::Int)
+#21 := (ite #10 0::Int #20)
+#22 := (ite #10 3::Int #21)
+#23 := (f3 #22)
+#25 := (= #23 #24)
+#26 := (not #25)
+#126 := (iff #26 false)
+#1 := true
+#121 := (not true)
+#124 := (iff #121 false)
+#125 := [rewrite]: #124
+#122 := (iff #26 #121)
+#119 := (iff #25 true)
+#114 := (= #24 #24)
+#117 := (iff #114 true)
+#118 := [rewrite]: #117
+#115 := (iff #25 #114)
+#111 := (= #22 0::Int)
+#106 := (ite false 3::Int 0::Int)
+#109 := (= #106 0::Int)
+#110 := [rewrite]: #109
+#107 := (= #22 #106)
+#104 := (= #21 0::Int)
+#99 := (ite false 0::Int 0::Int)
+#102 := (= #99 0::Int)
+#103 := [rewrite]: #102
+#100 := (= #21 #99)
+#97 := (= #20 0::Int)
+#67 := (and #11 #13)
+#70 := (or #11 #67)
+#92 := (ite #70 0::Int 0::Int)
+#95 := (= #92 0::Int)
+#96 := [rewrite]: #95
+#93 := (= #20 #92)
+#90 := (= #19 0::Int)
+#85 := (- 0::Int)
+#88 := (= #85 0::Int)
+#89 := [rewrite]: #88
+#86 := (= #19 #85)
+#83 := (= #18 0::Int)
+#75 := -3::Int
+#78 := (mod -3::Int -3::Int)
+#81 := (= #78 0::Int)
+#82 := [rewrite]: #81
+#79 := (= #18 #78)
+#76 := (= #17 -3::Int)
+#77 := [rewrite]: #76
+#80 := [monotonicity #77 #77]: #79
+#84 := [trans #80 #82]: #83
+#87 := [monotonicity #84]: #86
+#91 := [trans #87 #89]: #90
+#73 := (= #16 0::Int)
+#74 := [rewrite]: #73
+#71 := (iff #15 #70)
+#68 := (iff #14 #67)
+#69 := [rewrite]: #68
+#65 := (iff #12 #11)
+#66 := [rewrite]: #65
+#72 := [monotonicity #66 #69]: #71
+#94 := [monotonicity #72 #74 #91]: #93
+#98 := [trans #94 #96]: #97
+#63 := (iff #10 false)
+#64 := [rewrite]: #63
+#101 := [monotonicity #64 #98]: #100
+#105 := [trans #101 #103]: #104
+#108 := [monotonicity #64 #105]: #107
+#112 := [trans #108 #110]: #111
+#113 := [monotonicity #112]: #25
+#116 := [monotonicity #113]: #115
+#120 := [trans #116 #118]: #119
+#123 := [monotonicity #120]: #122
+#127 := [trans #123 #125]: #126
+#62 := [asserted]: #26
+[mp #62 #127]: false
+unsat
+514d90db39c84cc7bf19d9cbc0eb437cde0db30b 305 0
+#2 := false
+#8 := 3::Int
+decl f3 :: (-> S2 Int)
+decl f4 :: S2
+#11 := f4
+#12 := (f3 f4)
+#20 := (mod #12 3::Int)
+#690 := (>= #20 3::Int)
+#691 := (not #690)
+#1 := true
+#63 := [true-axiom]: true
+#525 := (or false #691)
+#673 := [th-lemma arith]: #525
+#575 := [unit-resolution #673 #63]: #691
+#9 := 0::Int
+#81 := -3::Int
+#77 := -1::Int
+#78 := (* -1::Int #12)
+#84 := (mod #78 -3::Int)
+#90 := (* -1::Int #84)
+#129 := (>= #12 0::Int)
+#130 := (not #129)
+#116 := (<= #12 0::Int)
+#117 := (not #116)
+#140 := (or #117 #130)
+#143 := (ite #140 #20 #90)
+#13 := (= #12 0::Int)
+#146 := (ite #13 0::Int #143)
+#682 := (* -1::Int #146)
+#564 := (+ #20 #682)
+#566 := (>= #564 0::Int)
+#679 := (= #20 #146)
+#412 := (= #143 #146)
+#392 := (not #13)
+#326 := (= #146 0::Int)
+#727 := (not #326)
+#717 := (<= #146 0::Int)
+#361 := (not #717)
+#153 := (>= #146 3::Int)
+#22 := (- 3::Int)
+#21 := (- #12)
+#23 := (mod #21 #22)
+#24 := (- #23)
+#15 := (< 0::Int 3::Int)
+#17 := (< #12 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int #12)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#25 := (ite #19 #20 #24)
+#26 := (ite #13 0::Int #25)
+#10 := (= 3::Int 0::Int)
+#27 := (ite #10 #12 #26)
+#28 := (< #27 3::Int)
+#29 := (not #28)
+#165 := (iff #29 #153)
+#71 := (and #15 #17)
+#74 := (or #16 #71)
+#95 := (ite #74 #20 #90)
+#68 := (= 0::Int #12)
+#98 := (ite #68 0::Int #95)
+#108 := (< #98 3::Int)
+#111 := (not #108)
+#163 := (iff #111 #153)
+#152 := (not #153)
+#158 := (not #152)
+#161 := (iff #158 #153)
+#162 := [rewrite]: #161
+#159 := (iff #111 #158)
+#156 := (iff #108 #152)
+#149 := (< #146 3::Int)
+#154 := (iff #149 #152)
+#155 := [rewrite]: #154
+#150 := (iff #108 #149)
+#147 := (= #98 #146)
+#144 := (= #95 #143)
+#141 := (iff #74 #140)
+#138 := (iff #71 #130)
+#133 := (and true #130)
+#136 := (iff #133 #130)
+#137 := [rewrite]: #136
+#134 := (iff #71 #133)
+#131 := (iff #17 #130)
+#132 := [rewrite]: #131
+#120 := (iff #15 true)
+#121 := [rewrite]: #120
+#135 := [monotonicity #121 #132]: #134
+#139 := [trans #135 #137]: #138
+#127 := (iff #16 #117)
+#122 := (and #117 true)
+#125 := (iff #122 #117)
+#126 := [rewrite]: #125
+#123 := (iff #16 #122)
+#118 := (iff #14 #117)
+#119 := [rewrite]: #118
+#124 := [monotonicity #119 #121]: #123
+#128 := [trans #124 #126]: #127
+#142 := [monotonicity #128 #139]: #141
+#145 := [monotonicity #142]: #144
+#114 := (iff #68 #13)
+#115 := [rewrite]: #114
+#148 := [monotonicity #115 #145]: #147
+#151 := [monotonicity #148]: #150
+#157 := [trans #151 #155]: #156
+#160 := [monotonicity #157]: #159
+#164 := [trans #160 #162]: #163
+#112 := (iff #29 #111)
+#109 := (iff #28 #108)
+#106 := (= #27 #98)
+#101 := (ite false #12 #98)
+#104 := (= #101 #98)
+#105 := [rewrite]: #104
+#102 := (= #27 #101)
+#99 := (= #26 #98)
+#96 := (= #25 #95)
+#93 := (= #24 #90)
+#87 := (- #84)
+#91 := (= #87 #90)
+#92 := [rewrite]: #91
+#88 := (= #24 #87)
+#85 := (= #23 #84)
+#82 := (= #22 -3::Int)
+#83 := [rewrite]: #82
+#79 := (= #21 #78)
+#80 := [rewrite]: #79
+#86 := [monotonicity #80 #83]: #85
+#89 := [monotonicity #86]: #88
+#94 := [trans #89 #92]: #93
+#75 := (iff #19 #74)
+#72 := (iff #18 #71)
+#73 := [rewrite]: #72
+#76 := [monotonicity #73]: #75
+#97 := [monotonicity #76 #94]: #96
+#69 := (iff #13 #68)
+#70 := [rewrite]: #69
+#100 := [monotonicity #70 #97]: #99
+#66 := (iff #10 false)
+#67 := [rewrite]: #66
+#103 := [monotonicity #67 #100]: #102
+#107 := [trans #103 #105]: #106
+#110 := [monotonicity #107]: #109
+#113 := [monotonicity #110]: #112
+#166 := [trans #113 #164]: #165
+#65 := [asserted]: #29
+#167 := [mp #65 #166]: #153
+#724 := (or #361 #152)
+#726 := [th-lemma arith farkas 1 1]: #724
+#366 := [unit-resolution #726 #167]: #361
+#367 := [hypothesis]: #326
+#725 := (or #727 #717)
+#728 := [th-lemma arith triangle-eq]: #725
+#714 := [unit-resolution #728 #367 #366]: false
+#715 := [lemma #714]: #727
+#522 := (or #392 #326)
+#729 := [def-axiom]: #522
+#670 := [unit-resolution #729 #715]: #392
+#403 := (or #13 #412)
+#404 := [def-axiom]: #403
+#671 := [unit-resolution #404 #670]: #412
+#327 := (= #20 #143)
+decl f5 :: (-> Int S2)
+#736 := (f5 #12)
+#738 := (f3 #736)
+#739 := (= #738 0::Int)
+#581 := (not #739)
+#582 := (iff #392 #581)
+#579 := (iff #13 #739)
+#570 := (iff #739 #13)
+#576 := (= #738 #12)
+#559 := (= #736 f4)
+#737 := (= f4 #736)
+#30 := (:var 0 S2)
+#31 := (f3 #30)
+#741 := (pattern #31)
+#32 := (f5 #31)
+#169 := (= #30 #32)
+#742 := (forall (vars (?v0 S2)) (:pat #741) #169)
+#172 := (forall (vars (?v0 S2)) #169)
+#743 := (iff #172 #742)
+#745 := (iff #742 #742)
+#746 := [rewrite]: #745
+#744 := [rewrite]: #743
+#747 := [trans #744 #746]: #743
+#266 := (~ #172 #172)
+#264 := (~ #169 #169)
+#265 := [refl]: #264
+#267 := [nnf-pos #265]: #266
+#33 := (= #32 #30)
+#34 := (forall (vars (?v0 S2)) #33)
+#173 := (iff #34 #172)
+#170 := (iff #33 #169)
+#171 := [rewrite]: #170
+#174 := [quant-intro #171]: #173
+#168 := [asserted]: #34
+#177 := [mp #168 #174]: #172
+#256 := [mp~ #177 #267]: #172
+#748 := [mp #256 #747]: #742
+#734 := (not #742)
+#740 := (or #734 #737)
+#730 := [quant-inst #11]: #740
+#674 := [unit-resolution #730 #748]: #737
+#574 := [symm #674]: #559
+#577 := [monotonicity #574]: #576
+#578 := [monotonicity #577]: #570
+#580 := [symm #578]: #579
+#675 := [monotonicity #580]: #582
+#672 := [mp #670 #675]: #581
+#395 := (or #129 #739)
+#35 := (:var 0 Int)
+#37 := (f5 #35)
+#749 := (pattern #37)
+#193 := (>= #35 0::Int)
+#38 := (f3 #37)
+#43 := (= #38 0::Int)
+#242 := (or #43 #193)
+#756 := (forall (vars (?v0 Int)) (:pat #749) #242)
+#247 := (forall (vars (?v0 Int)) #242)
+#759 := (iff #247 #756)
+#757 := (iff #242 #242)
+#758 := [refl]: #757
+#760 := [quant-intro #758]: #759
+#260 := (~ #247 #247)
+#268 := (~ #242 #242)
+#269 := [refl]: #268
+#261 := [nnf-pos #269]: #260
+#42 := (< #35 0::Int)
+#44 := (implies #42 #43)
+#45 := (forall (vars (?v0 Int)) #44)
+#250 := (iff #45 #247)
+#213 := (= 0::Int #38)
+#219 := (not #42)
+#220 := (or #219 #213)
+#225 := (forall (vars (?v0 Int)) #220)
+#248 := (iff #225 #247)
+#245 := (iff #220 #242)
+#239 := (or #193 #43)
+#243 := (iff #239 #242)
+#244 := [rewrite]: #243
+#240 := (iff #220 #239)
+#237 := (iff #213 #43)
+#238 := [rewrite]: #237
+#235 := (iff #219 #193)
+#195 := (not #193)
+#230 := (not #195)
+#233 := (iff #230 #193)
+#234 := [rewrite]: #233
+#231 := (iff #219 #230)
+#228 := (iff #42 #195)
+#229 := [rewrite]: #228
+#232 := [monotonicity #229]: #231
+#236 := [trans #232 #234]: #235
+#241 := [monotonicity #236 #238]: #240
+#246 := [trans #241 #244]: #245
+#249 := [quant-intro #246]: #248
+#226 := (iff #45 #225)
+#223 := (iff #44 #220)
+#216 := (implies #42 #213)
+#221 := (iff #216 #220)
+#222 := [rewrite]: #221
+#217 := (iff #44 #216)
+#214 := (iff #43 #213)
+#215 := [rewrite]: #214
+#218 := [monotonicity #215]: #217
+#224 := [trans #218 #222]: #223
+#227 := [quant-intro #224]: #226
+#251 := [trans #227 #249]: #250
+#212 := [asserted]: #45
+#252 := [mp #212 #251]: #247
+#270 := [mp~ #252 #261]: #247
+#761 := [mp #270 #760]: #756
+#732 := (not #756)
+#375 := (or #732 #129 #739)
+#390 := (or #739 #129)
+#716 := (or #732 #390)
+#720 := (iff #716 #375)
+#380 := (or #732 #395)
+#718 := (iff #380 #375)
+#719 := [rewrite]: #718
+#381 := (iff #716 #380)
+#731 := (iff #390 #395)
+#391 := [rewrite]: #731
+#382 := [monotonicity #391]: #381
+#721 := [trans #382 #719]: #720
+#379 := [quant-inst #12]: #716
+#722 := [mp #379 #721]: #375
+#676 := [unit-resolution #722 #761]: #395
+#663 := [unit-resolution #676 #672]: #129
+#665 := (or #13 #117 #130)
+#657 := [th-lemma arith triangle-eq]: #665
+#654 := [unit-resolution #657 #670]: #140
+#656 := [unit-resolution #654 #663]: #117
+#414 := (or #140 #116)
+#405 := [def-axiom]: #414
+#666 := [unit-resolution #405 #656]: #140
+#345 := (not #140)
+#419 := (or #345 #327)
+#398 := [def-axiom]: #419
+#667 := [unit-resolution #398 #666]: #327
+#668 := [trans #667 #671]: #679
+#664 := (not #679)
+#669 := (or #664 #566)
+#658 := [th-lemma arith triangle-eq]: #669
+#659 := [unit-resolution #658 #668]: #566
+[th-lemma arith farkas -1 -1 1 #167 #659 #575]: false
+unsat
+2855a1e15b1d7788a0afdba64d4d2bd112ea0f3b 560 0
+#2 := false
+#9 := 0::Int
+decl f4 :: (-> S2 Int)
+decl f5 :: S2
+#11 := f5
+#12 := (f4 f5)
+#141 := (<= #12 0::Int)
+#142 := (not #141)
+#8 := 3::Int
+#180 := (>= #12 3::Int)
+#654 := 1::Int
+#706 := (div #12 3::Int)
+#555 := -2::Int
+#565 := (* -2::Int #706)
+#20 := (mod #12 3::Int)
+#80 := -1::Int
+#603 := (* -1::Int #20)
+#566 := (+ #603 #565)
+#549 := (+ #12 #566)
+#567 := (>= #549 1::Int)
+#84 := -3::Int
+#605 := (* -3::Int #706)
+#606 := (+ #603 #605)
+#599 := (+ #12 #606)
+#704 := (>= #599 0::Int)
+#588 := (= #599 0::Int)
+#1 := true
+#66 := [true-axiom]: true
+#629 := (or false #588)
+#634 := [th-lemma arith]: #629
+#614 := [unit-resolution #634 #66]: #588
+#560 := (not #588)
+#582 := (or #560 #704)
+#583 := [th-lemma arith triangle-eq]: #582
+#584 := [unit-resolution #583 #614]: #704
+#658 := (+ #12 #603)
+#659 := (<= #658 0::Int)
+#540 := (not #659)
+#657 := (= #12 #20)
+#627 := (not #657)
+decl f3 :: (-> Int S2)
+#81 := (* -1::Int #12)
+#87 := (mod #81 -3::Int)
+#93 := (* -1::Int #87)
+#154 := (>= #12 0::Int)
+#155 := (not #154)
+#165 := (or #142 #155)
+#168 := (ite #165 #20 #93)
+#13 := (= #12 0::Int)
+#171 := (ite #13 0::Int #168)
+#174 := (f3 #171)
+#177 := (= f5 #174)
+#769 := (not #177)
+#181 := (not #180)
+#548 := [hypothesis]: #181
+#424 := (or #769 #180)
+#191 := (iff #177 #180)
+#30 := (< #12 3::Int)
+#22 := (- 3::Int)
+#21 := (- #12)
+#23 := (mod #21 #22)
+#24 := (- #23)
+#15 := (< 0::Int 3::Int)
+#17 := (< #12 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int #12)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#25 := (ite #19 #20 #24)
+#26 := (ite #13 0::Int #25)
+#10 := (= 3::Int 0::Int)
+#27 := (ite #10 #12 #26)
+#28 := (f3 #27)
+#29 := (= #28 f5)
+#31 := (iff #29 #30)
+#32 := (not #31)
+#194 := (iff #32 #191)
+#133 := (not #30)
+#74 := (and #15 #17)
+#77 := (or #16 #74)
+#98 := (ite #77 #20 #93)
+#71 := (= 0::Int #12)
+#101 := (ite #71 0::Int #98)
+#111 := (f3 #101)
+#117 := (= f5 #111)
+#134 := (iff #117 #133)
+#192 := (iff #134 #191)
+#189 := (iff #133 #180)
+#184 := (not #181)
+#187 := (iff #184 #180)
+#188 := [rewrite]: #187
+#185 := (iff #133 #184)
+#182 := (iff #30 #181)
+#183 := [rewrite]: #182
+#186 := [monotonicity #183]: #185
+#190 := [trans #186 #188]: #189
+#178 := (iff #117 #177)
+#175 := (= #111 #174)
+#172 := (= #101 #171)
+#169 := (= #98 #168)
+#166 := (iff #77 #165)
+#163 := (iff #74 #155)
+#158 := (and true #155)
+#161 := (iff #158 #155)
+#162 := [rewrite]: #161
+#159 := (iff #74 #158)
+#156 := (iff #17 #155)
+#157 := [rewrite]: #156
+#145 := (iff #15 true)
+#146 := [rewrite]: #145
+#160 := [monotonicity #146 #157]: #159
+#164 := [trans #160 #162]: #163
+#152 := (iff #16 #142)
+#147 := (and #142 true)
+#150 := (iff #147 #142)
+#151 := [rewrite]: #150
+#148 := (iff #16 #147)
+#143 := (iff #14 #142)
+#144 := [rewrite]: #143
+#149 := [monotonicity #144 #146]: #148
+#153 := [trans #149 #151]: #152
+#167 := [monotonicity #153 #164]: #166
+#170 := [monotonicity #167]: #169
+#139 := (iff #71 #13)
+#140 := [rewrite]: #139
+#173 := [monotonicity #140 #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [monotonicity #176]: #178
+#193 := [monotonicity #179 #190]: #192
+#137 := (iff #32 #134)
+#125 := (iff #30 #117)
+#130 := (not #125)
+#135 := (iff #130 #134)
+#136 := [rewrite]: #135
+#131 := (iff #32 #130)
+#128 := (iff #31 #125)
+#122 := (iff #117 #30)
+#126 := (iff #122 #125)
+#127 := [rewrite]: #126
+#123 := (iff #31 #122)
+#120 := (iff #29 #117)
+#114 := (= #111 f5)
+#118 := (iff #114 #117)
+#119 := [rewrite]: #118
+#115 := (iff #29 #114)
+#112 := (= #28 #111)
+#109 := (= #27 #101)
+#104 := (ite false #12 #101)
+#107 := (= #104 #101)
+#108 := [rewrite]: #107
+#105 := (= #27 #104)
+#102 := (= #26 #101)
+#99 := (= #25 #98)
+#96 := (= #24 #93)
+#90 := (- #87)
+#94 := (= #90 #93)
+#95 := [rewrite]: #94
+#91 := (= #24 #90)
+#88 := (= #23 #87)
+#85 := (= #22 -3::Int)
+#86 := [rewrite]: #85
+#82 := (= #21 #81)
+#83 := [rewrite]: #82
+#89 := [monotonicity #83 #86]: #88
+#92 := [monotonicity #89]: #91
+#97 := [trans #92 #95]: #96
+#78 := (iff #19 #77)
+#75 := (iff #18 #74)
+#76 := [rewrite]: #75
+#79 := [monotonicity #76]: #78
+#100 := [monotonicity #79 #97]: #99
+#72 := (iff #13 #71)
+#73 := [rewrite]: #72
+#103 := [monotonicity #73 #100]: #102
+#69 := (iff #10 false)
+#70 := [rewrite]: #69
+#106 := [monotonicity #70 #103]: #105
+#110 := [trans #106 #108]: #109
+#113 := [monotonicity #110]: #112
+#116 := [monotonicity #113]: #115
+#121 := [trans #116 #119]: #120
+#124 := [monotonicity #121]: #123
+#129 := [trans #124 #127]: #128
+#132 := [monotonicity #129]: #131
+#138 := [trans #132 #136]: #137
+#195 := [trans #138 #193]: #194
+#68 := [asserted]: #32
+#196 := [mp #68 #195]: #191
+#765 := (not #191)
+#759 := (or #769 #180 #765)
+#419 := [def-axiom]: #759
+#760 := [unit-resolution #419 #196]: #424
+#528 := [unit-resolution #760 #548]: #769
+#628 := (or #627 #177)
+#420 := (f3 #12)
+#720 := (= #420 #174)
+#713 := (= #174 #420)
+#717 := (= #171 #12)
+#617 := (= #20 #12)
+#641 := [hypothesis]: #657
+#618 := [symm #641]: #617
+#619 := (= #171 #20)
+#638 := (= #168 #20)
+#356 := (= #20 #168)
+#733 := (f4 #420)
+#734 := (= #733 0::Int)
+#648 := (not #734)
+#421 := (not #13)
+#649 := (iff #421 #648)
+#645 := (iff #13 #734)
+#656 := (iff #734 #13)
+#665 := (= #733 #12)
+#663 := (= #420 f5)
+#761 := (= f5 #420)
+#33 := (:var 0 S2)
+#34 := (f4 #33)
+#770 := (pattern #34)
+#35 := (f3 #34)
+#198 := (= #33 #35)
+#771 := (forall (vars (?v0 S2)) (:pat #770) #198)
+#201 := (forall (vars (?v0 S2)) #198)
+#772 := (iff #201 #771)
+#774 := (iff #771 #771)
+#775 := [rewrite]: #774
+#773 := [rewrite]: #772
+#776 := [trans #773 #775]: #772
+#295 := (~ #201 #201)
+#293 := (~ #198 #198)
+#294 := [refl]: #293
+#296 := [nnf-pos #294]: #295
+#36 := (= #35 #33)
+#37 := (forall (vars (?v0 S2)) #36)
+#202 := (iff #37 #201)
+#199 := (iff #36 #198)
+#200 := [rewrite]: #199
+#203 := [quant-intro #200]: #202
+#197 := [asserted]: #37
+#206 := [mp #197 #203]: #201
+#285 := [mp~ #206 #296]: #201
+#777 := [mp #285 #776]: #771
+#408 := (not #771)
+#409 := (or #408 #761)
+#410 := [quant-inst #11]: #409
+#712 := [unit-resolution #410 #777]: #761
+#664 := [symm #712]: #663
+#666 := [monotonicity #664]: #665
+#667 := [monotonicity #666]: #656
+#646 := [symm #667]: #645
+#650 := [monotonicity #646]: #649
+#572 := [hypothesis]: #769
+#552 := (or #421 #177)
+#573 := [hypothesis]: #13
+#716 := [symm #573]: #71
+#355 := (= #171 0::Int)
+#551 := (or #421 #355)
+#758 := [def-axiom]: #551
+#715 := [unit-resolution #758 #573]: #355
+#718 := [trans #715 #716]: #717
+#719 := [monotonicity #718]: #713
+#714 := [symm #719]: #720
+#721 := [trans #712 #714]: #177
+#550 := [unit-resolution #572 #721]: false
+#553 := [lemma #550]: #552
+#661 := [unit-resolution #553 #572]: #421
+#651 := [mp #661 #650]: #648
+#731 := (or #154 #734)
+#38 := (:var 0 Int)
+#40 := (f3 #38)
+#778 := (pattern #40)
+#222 := (>= #38 0::Int)
+#41 := (f4 #40)
+#46 := (= #41 0::Int)
+#271 := (or #46 #222)
+#785 := (forall (vars (?v0 Int)) (:pat #778) #271)
+#276 := (forall (vars (?v0 Int)) #271)
+#788 := (iff #276 #785)
+#786 := (iff #271 #271)
+#787 := [refl]: #786
+#789 := [quant-intro #787]: #788
+#289 := (~ #276 #276)
+#297 := (~ #271 #271)
+#298 := [refl]: #297
+#290 := [nnf-pos #298]: #289
+#45 := (< #38 0::Int)
+#47 := (implies #45 #46)
+#48 := (forall (vars (?v0 Int)) #47)
+#279 := (iff #48 #276)
+#242 := (= 0::Int #41)
+#248 := (not #45)
+#249 := (or #248 #242)
+#254 := (forall (vars (?v0 Int)) #249)
+#277 := (iff #254 #276)
+#274 := (iff #249 #271)
+#268 := (or #222 #46)
+#272 := (iff #268 #271)
+#273 := [rewrite]: #272
+#269 := (iff #249 #268)
+#266 := (iff #242 #46)
+#267 := [rewrite]: #266
+#264 := (iff #248 #222)
+#224 := (not #222)
+#259 := (not #224)
+#262 := (iff #259 #222)
+#263 := [rewrite]: #262
+#260 := (iff #248 #259)
+#257 := (iff #45 #224)
+#258 := [rewrite]: #257
+#261 := [monotonicity #258]: #260
+#265 := [trans #261 #263]: #264
+#270 := [monotonicity #265 #267]: #269
+#275 := [trans #270 #273]: #274
+#278 := [quant-intro #275]: #277
+#255 := (iff #48 #254)
+#252 := (iff #47 #249)
+#245 := (implies #45 #242)
+#250 := (iff #245 #249)
 #251 := [rewrite]: #250
-#258 := [monotonicity #251 #255]: #257
-#268 := [monotonicity #258 #265]: #267
-#313 := [monotonicity #268]: #312
-#242 := (iff #205 #36)
-#243 := [rewrite]: #242
-#316 := [monotonicity #243 #313]: #315
-#244 := (iff #208 #37)
-#245 := [rewrite]: #244
-#319 := [monotonicity #245 #316]: #318
-#322 := [monotonicity #319]: #321
-#325 := [quant-intro #322]: #324
-#309 := (iff #61 #308)
-#306 := (iff #60 #305)
-#303 := (= #59 #302)
-#300 := (= #58 #299)
-#297 := (= #57 #296)
-#294 := (= #56 #291)
-#288 := (- #285)
-#292 := (= #288 #291)
-#293 := [rewrite]: #292
-#289 := (= #56 #288)
-#286 := (= #55 #285)
-#225 := (= #47 #224)
-#226 := [rewrite]: #225
-#222 := (= #46 #221)
-#223 := [rewrite]: #222
-#287 := [monotonicity #223 #226]: #286
-#290 := [monotonicity #287]: #289
-#295 := [trans #290 #293]: #294
-#218 := (iff #44 #217)
-#215 := (iff #43 #214)
-#216 := [rewrite]: #215
-#219 := [monotonicity #216]: #218
-#298 := [monotonicity #219 #295]: #297
-#206 := (iff #36 #205)
-#207 := [rewrite]: #206
-#301 := [monotonicity #207 #298]: #300
-#209 := (iff #37 #208)
-#210 := [rewrite]: #209
-#304 := [monotonicity #210 #301]: #303
-#307 := [monotonicity #304]: #306
-#310 := [quant-intro #307]: #309
-#327 := [trans #310 #325]: #326
-#284 := [asserted]: #61
-#328 := [mp #284 #327]: #323
-#356 := [mp~ #328 #341]: #323
-#394 := [mp #356 #393]: #391
-#425 := [mp #394 #424]: #422
-#931 := [mp #425 #930]: #926
-#732 := (not #926)
-#733 := (or #732 #721)
-#517 := (* -1::Int 3::Int)
-#882 := (mod #880 #517)
-#522 := (+ #11 #882)
-#523 := (= #522 0::Int)
-#593 := (<= 3::Int 0::Int)
-#594 := (or #593 #871)
-#595 := (not #594)
-#489 := (or #596 #593)
-#866 := (not #489)
-#867 := (or #866 #595)
-#589 := (ite #867 #870 #523)
-#868 := (ite #864 #590 #589)
-#865 := (= #9 #11)
-#869 := (= 3::Int 0::Int)
-#579 := (ite #869 #865 #868)
-#726 := (or #732 #579)
-#735 := (iff #726 #733)
-#737 := (iff #733 #733)
-#738 := [rewrite]: #737
-#715 := (iff #579 #721)
-#829 := (ite false #865 #721)
-#827 := (iff #829 #721)
-#830 := [rewrite]: #827
-#731 := (iff #579 #829)
-#722 := (iff #868 #721)
-#838 := (iff #589 #835)
-#836 := (iff #523 #834)
-#680 := (= #522 #679)
-#848 := (= #882 #841)
-#846 := (= #517 -3::Int)
-#847 := [rewrite]: #846
-#677 := [monotonicity #847]: #848
-#833 := [monotonicity #677]: #680
-#837 := [monotonicity #833]: #836
-#845 := (iff #867 #844)
-#842 := (iff #595 #700)
-#698 := (iff #594 #871)
-#850 := (or false #871)
-#851 := (iff #850 #871)
-#857 := [rewrite]: #851
-#855 := (iff #594 #850)
-#582 := (iff #593 false)
-#860 := [rewrite]: #582
-#856 := [monotonicity #860]: #855
-#699 := [trans #856 #857]: #698
-#843 := [monotonicity #699]: #842
-#854 := (iff #866 #853)
-#863 := (iff #489 #596)
-#861 := (or #596 false)
-#862 := (iff #861 #596)
-#859 := [rewrite]: #862
-#576 := (iff #489 #861)
-#858 := [monotonicity #860]: #576
-#852 := [trans #858 #859]: #863
-#849 := [monotonicity #852]: #854
-#839 := [monotonicity #849 #843]: #845
-#720 := [monotonicity #839 #837]: #838
-#681 := [monotonicity #720]: #722
-#580 := (iff #869 false)
-#581 := [rewrite]: #580
-#826 := [monotonicity #581 #681]: #731
-#730 := [trans #826 #830]: #715
-#736 := [monotonicity #730]: #735
-#831 := [trans #736 #738]: #735
-#734 := [quant-inst #9 #10]: #726
-#828 := [mp #734 #831]: #733
-#794 := [unit-resolution #828 #931]: #721
-#804 := (not #721)
-#795 := (or #804 #809 #590)
-#796 := [def-axiom]: #795
-#768 := [unit-resolution #796 #794]: #767
-#769 := [unit-resolution #768 #764]: #590
-#744 := [trans #769 #765]: #771
-#639 := [monotonicity #744]: #746
-#751 := [symm #639]: #750
-#554 := (= f6 #575)
-#17 := (:var 0 S2)
-#18 := (f5 #17)
-#897 := (pattern #18)
-#19 := (f3 #18)
-#120 := (= #17 #19)
-#898 := (forall (vars (?v0 S2)) (:pat #897) #120)
-#123 := (forall (vars (?v0 S2)) #120)
-#899 := (iff #123 #898)
-#901 := (iff #898 #898)
-#902 := [rewrite]: #901
-#900 := [rewrite]: #899
-#903 := [trans #900 #902]: #899
-#346 := (~ #123 #123)
-#344 := (~ #120 #120)
-#345 := [refl]: #344
-#347 := [nnf-pos #345]: #346
-#20 := (= #19 #17)
-#21 := (forall (vars (?v0 S2)) #20)
-#124 := (iff #21 #123)
-#121 := (iff #20 #120)
-#122 := [rewrite]: #121
-#125 := [quant-intro #122]: #124
-#119 := [asserted]: #21
-#128 := [mp #119 #125]: #123
-#332 := [mp~ #128 #347]: #123
-#904 := [mp #332 #903]: #898
-#548 := (not #898)
-#678 := (or #548 #554)
-#885 := [quant-inst #8]: #678
-#745 := [unit-resolution #885 #904]: #554
-#752 := [trans #745 #751]: #82
-#763 := [hypothesis]: #572
-#757 := [unit-resolution #763 #752]: false
-#754 := [lemma #757]: #753
-#634 := [unit-resolution #754 #636]: #809
-#766 := (or #864 #870)
-#787 := [hypothesis]: #809
-#812 := (not #844)
-#802 := (not #870)
-#788 := [hypothesis]: #802
-#772 := (or #864 #835)
-#798 := (or #804 #864 #835)
-#799 := [def-axiom]: #798
-#773 := [unit-resolution #799 #794]: #772
-#775 := [unit-resolution #773 #787]: #835
-#815 := (not #835)
-#816 := (or #815 #812 #870)
-#817 := [def-axiom]: #816
-#776 := [unit-resolution #817 #775 #788]: #812
-#819 := (or #844 #596)
-#821 := [def-axiom]: #819
-#777 := [unit-resolution #821 #776]: #596
-#813 := (or #844 #871)
-#810 := [def-axiom]: #813
-#778 := [unit-resolution #810 #776]: #871
-#779 := (or #864 #853 #700)
-#774 := [th-lemma arith triangle-eq]: #779
-#780 := [unit-resolution #774 #778 #777 #787]: false
-#762 := [lemma #780]: #766
-#623 := [unit-resolution #762 #634]: #870
-#624 := (or #802 #824)
-#625 := [th-lemma arith triangle-eq]: #624
-#626 := [unit-resolution #625 #623]: #824
-#755 := (div #9 3::Int)
-#747 := (* -3::Int #755)
-#748 := (+ #747 #881)
-#743 := (+ #9 #748)
-#724 := (<= #743 0::Int)
-#723 := (= #743 0::Int)
-#670 := (or false #723)
-#671 := [th-lemma arith]: #670
-#514 := [unit-resolution #671 #79]: #723
-#672 := (not #723)
-#668 := (or #672 #724)
-#673 := [th-lemma arith triangle-eq]: #668
-#652 := [unit-resolution #673 #514]: #724
-#630 := 1::Int
-#621 := -2::Int
-#627 := (* -2::Int #755)
-#628 := (+ #627 #881)
-#629 := (+ #9 #628)
-#631 := (>= #629 1::Int)
-#682 := (* -1::Int #11)
-#684 := (+ #9 #682)
-#685 := (<= #684 0::Int)
-#614 := (not #685)
-#676 := (not #865)
-#694 := (or #676 #82)
-#688 := [hypothesis]: #865
-#689 := [symm #688]: #771
-#690 := [monotonicity #689]: #746
-#691 := [symm #690]: #750
-#692 := [trans #745 #691]: #82
-#693 := [unit-resolution #763 #692]: false
-#664 := [lemma #693]: #694
-#608 := [unit-resolution #664 #636]: #676
-#686 := (>= #684 0::Int)
-#665 := (>= #755 0::Int)
-#784 := (f5 #575)
-#785 := (= #784 0::Int)
-#600 := (not #785)
-#601 := (iff #809 #600)
-#599 := (iff #864 #785)
-#597 := (iff #785 #864)
-#604 := (= #784 #9)
-#607 := (= #575 f6)
-#606 := [symm #745]: #607
-#605 := [monotonicity #606]: #604
-#598 := [monotonicity #605]: #597
-#591 := [symm #598]: #599
-#592 := [monotonicity #591]: #601
-#602 := [mp #634 #592]: #600
-#786 := (or #785 #871)
-#25 := (f3 #23)
-#905 := (pattern #25)
-#145 := (>= #23 0::Int)
-#26 := (f5 #25)
-#31 := (= #26 0::Int)
-#193 := (or #31 #145)
-#912 := (forall (vars (?v0 Int)) (:pat #905) #193)
-#198 := (forall (vars (?v0 Int)) #193)
-#915 := (iff #198 #912)
-#913 := (iff #193 #193)
-#914 := [refl]: #913
-#916 := [quant-intro #914]: #915
-#336 := (~ #198 #198)
-#348 := (~ #193 #193)
-#349 := [refl]: #348
-#337 := [nnf-pos #349]: #336
-#30 := (< #23 0::Int)
-#32 := (implies #30 #31)
-#33 := (forall (vars (?v0 Int)) #32)
-#201 := (iff #33 #198)
-#164 := (= 0::Int #26)
-#170 := (not #30)
-#171 := (or #170 #164)
-#176 := (forall (vars (?v0 Int)) #171)
-#199 := (iff #176 #198)
-#196 := (iff #171 #193)
-#190 := (or #145 #31)
-#194 := (iff #190 #193)
-#195 := [rewrite]: #194
-#191 := (iff #171 #190)
-#188 := (iff #164 #31)
-#189 := [rewrite]: #188
-#186 := (iff #170 #145)
-#146 := (not #145)
-#181 := (not #146)
-#184 := (iff #181 #145)
-#185 := [rewrite]: #184
-#182 := (iff #170 #181)
-#179 := (iff #30 #146)
-#180 := [rewrite]: #179
-#183 := [monotonicity #180]: #182
-#187 := [trans #183 #185]: #186
-#192 := [monotonicity #187 #189]: #191
-#197 := [trans #192 #195]: #196
-#200 := [quant-intro #197]: #199
-#177 := (iff #33 #176)
-#174 := (iff #32 #171)
-#167 := (implies #30 #164)
-#172 := (iff #167 #171)
-#173 := [rewrite]: #172
-#168 := (iff #32 #167)
-#165 := (iff #31 #164)
-#166 := [rewrite]: #165
-#169 := [monotonicity #166]: #168
-#175 := [trans #169 #173]: #174
-#178 := [quant-intro #175]: #177
-#202 := [trans #178 #200]: #201
-#163 := [asserted]: #33
-#203 := [mp #163 #202]: #198
-#350 := [mp~ #203 #337]: #198
-#917 := [mp #350 #916]: #912
-#872 := (not #912)
-#789 := (or #872 #785 #871)
-#790 := (or #872 #786)
-#792 := (iff #790 #789)
-#793 := [rewrite]: #792
-#791 := [quant-inst #9]: #790
-#783 := [mp #791 #793]: #789
-#583 := [unit-resolution #783 #917]: #786
-#584 := [unit-resolution #583 #602]: #871
-#660 := (or #665 #700)
-#655 := (not #665)
-#659 := [hypothesis]: #655
-#661 := [hypothesis]: #871
-#662 := [th-lemma arith farkas 1 3 1 1 #661 #659 #652 #669]: false
-#663 := [lemma #662]: #660
-#585 := [unit-resolution #663 #584]: #665
-#648 := (not #824)
-#633 := (or #686 #648 #655)
-#656 := (not #686)
-#657 := [hypothesis]: #656
-#683 := (>= #743 0::Int)
-#642 := (or #672 #683)
-#650 := [th-lemma arith triangle-eq]: #642
-#643 := [unit-resolution #650 #514]: #683
-#646 := [hypothesis]: #665
-#654 := [hypothesis]: #824
-#647 := [th-lemma arith farkas 1 -3 -1 1 #654 #646 #643 #657]: false
-#635 := [lemma #647]: #633
-#577 := [unit-resolution #635 #626 #585]: #686
-#586 := (or #865 #614 #656)
-#587 := [th-lemma arith triangle-eq]: #586
-#578 := [unit-resolution #587 #577 #608]: #614
-#820 := (>= #884 0::Int)
-#588 := (or #802 #820)
-#555 := [th-lemma arith triangle-eq]: #588
-#557 := [unit-resolution #555 #623]: #820
-#610 := (not #820)
-#618 := (or #631 #610 #685)
-#609 := (not #631)
-#613 := [hypothesis]: #609
-#615 := [hypothesis]: #614
-#616 := [hypothesis]: #820
-#617 := [th-lemma arith farkas -2/3 -1/3 -1/3 1 #643 #616 #615 #613]: false
-#603 := [lemma #617]: #618
-#558 := [unit-resolution #603 #557 #578]: #631
-#889 := (>= #11 0::Int)
-#714 := (>= #883 0::Int)
-#549 := (or false #714)
-#562 := [th-lemma arith]: #549
-#563 := [unit-resolution #562 #79]: #714
-#564 := (not #714)
-#565 := (or #889 #564 #610)
-#566 := [th-lemma arith assign-bounds 1 1]: #565
-#556 := [unit-resolution #566 #557 #563]: #889
-#567 := [th-lemma arith farkas -1 -3 2 1 1 #556 #558 #652 #626 #619]: false
-#550 := [lemma #567]: #104
-#559 := (f5 #12)
-#560 := (= #11 #559)
-#521 := (iff #560 #865)
-#518 := (iff #771 #865)
-#520 := [commutativity]: #518
-#527 := (iff #560 #771)
-#528 := (= #559 #9)
-#570 := (or #82 #102)
-#568 := (or #82 #102 #483)
-#569 := [def-axiom]: #568
-#561 := [unit-resolution #569 #118]: #570
-#545 := [unit-resolution #561 #550]: #82
-#526 := [symm #545]: #13
-#529 := [monotonicity #526]: #528
-#530 := [monotonicity #529]: #527
-#524 := [trans #530 #520]: #521
-#552 := (or #853 #102)
-#553 := [th-lemma arith farkas 1 1]: #552
-#532 := [unit-resolution #553 #550]: #853
-#534 := (or #809 #596)
-#539 := [th-lemma arith triangle-eq]: #534
-#540 := [unit-resolution #539 #532]: #809
-#541 := [unit-resolution #762 #540]: #870
-#542 := [unit-resolution #555 #541]: #820
-#543 := [unit-resolution #566 #542 #563]: #889
-#891 := (not #889)
-#892 := (or #560 #891)
-#127 := (= #23 #26)
-#152 := (or #127 #146)
-#906 := (forall (vars (?v0 Int)) (:pat #905) #152)
-#157 := (forall (vars (?v0 Int)) #152)
-#909 := (iff #157 #906)
-#907 := (iff #152 #152)
-#908 := [refl]: #907
-#910 := [quant-intro #908]: #909
-#334 := (~ #157 #157)
-#333 := (~ #152 #152)
-#330 := [refl]: #333
-#335 := [nnf-pos #330]: #334
-#27 := (= #26 #23)
-#24 := (<= 0::Int #23)
-#28 := (implies #24 #27)
-#29 := (forall (vars (?v0 Int)) #28)
-#160 := (iff #29 #157)
-#134 := (not #24)
-#135 := (or #134 #127)
-#140 := (forall (vars (?v0 Int)) #135)
-#158 := (iff #140 #157)
-#155 := (iff #135 #152)
-#149 := (or #146 #127)
-#153 := (iff #149 #152)
-#154 := [rewrite]: #153
-#150 := (iff #135 #149)
-#147 := (iff #134 #146)
-#143 := (iff #24 #145)
-#144 := [rewrite]: #143
-#148 := [monotonicity #144]: #147
+#246 := (iff #47 #245)
+#243 := (iff #46 #242)
+#244 := [rewrite]: #243
+#247 := [monotonicity #244]: #246
+#253 := [trans #247 #251]: #252
+#256 := [quant-intro #253]: #255
+#280 := [trans #256 #278]: #279
+#241 := [asserted]: #48
+#281 := [mp #241 #280]: #276
+#299 := [mp~ #281 #290]: #276
+#790 := [mp #299 #789]: #785
+#739 := (not #785)
+#736 := (or #739 #154 #734)
+#449 := (or #734 #154)
+#725 := (or #739 #449)
+#724 := (iff #725 #736)
+#727 := (or #739 #731)
+#728 := (iff #727 #736)
+#729 := [rewrite]: #728
+#722 := (iff #725 #727)
+#735 := (iff #449 #731)
+#732 := [rewrite]: #735
+#723 := [monotonicity #732]: #722
+#730 := [trans #723 #729]: #724
+#726 := [quant-inst #12]: #725
+#571 := [mp #726 #730]: #736
+#652 := [unit-resolution #571 #790]: #731
+#647 := [unit-resolution #652 #651]: #154
+#653 := (or #13 #142 #155)
+#639 := [th-lemma arith triangle-eq]: #653
+#635 := [unit-resolution #639 #661]: #165
+#636 := [unit-resolution #635 #647]: #142
+#443 := (or #165 #141)
+#434 := [def-axiom]: #443
+#637 := [unit-resolution #434 #636]: #165
+#374 := (not #165)
+#448 := (or #374 #356)
+#427 := [def-axiom]: #448
+#640 := [unit-resolution #427 #637]: #356
+#644 := [symm #640]: #638
+#642 := (= #171 #168)
+#441 := (= #168 #171)
+#432 := (or #13 #441)
+#433 := [def-axiom]: #432
+#662 := [unit-resolution #433 #661]: #441
+#643 := [symm #662]: #642
+#512 := [trans #643 #644]: #619
+#623 := [trans #512 #618]: #717
+#624 := [monotonicity #623]: #713
+#625 := [symm #624]: #720
+#630 := [trans #712 #625]: #177
+#626 := [unit-resolution #572 #630]: false
+#631 := [lemma #626]: #628
+#546 := [unit-resolution #631 #528]: #627
+#660 := (>= #658 0::Int)
+#578 := (* -1::Int #706)
+#579 := (+ #603 #578)
+#580 := (+ #12 #579)
+#581 := (>= #580 0::Int)
+#545 := [unit-resolution #553 #528]: #421
+#541 := [mp #545 #650]: #648
+#532 := [unit-resolution #652 #541]: #154
+#534 := [unit-resolution #639 #545]: #165
+#535 := [unit-resolution #534 #532]: #142
+#570 := (or #581 #141)
+#574 := (not #581)
+#577 := [hypothesis]: #574
+#691 := (>= #20 3::Int)
+#675 := (not #691)
+#616 := (or false #675)
+#622 := [th-lemma arith]: #616
+#590 := [unit-resolution #622 #66]: #675
+#632 := [hypothesis]: #142
+#585 := [th-lemma arith farkas -2/3 2/3 -1/3 1 #632 #590 #584 #577]: false
+#586 := [lemma #585]: #570
+#533 := [unit-resolution #586 #535]: #581
+#575 := (or #574 #660)
+#568 := (not #660)
+#569 := [hypothesis]: #568
+#611 := (<= #599 0::Int)
+#615 := (or #560 #611)
+#596 := [th-lemma arith triangle-eq]: #615
+#620 := [unit-resolution #596 #614]: #611
+#592 := [hypothesis]: #581
+#613 := [th-lemma arith farkas -3/2 1/2 1 #592 #620 #569]: false
+#576 := [lemma #613]: #575
+#536 := [unit-resolution #576 #533]: #660
+#524 := (or #657 #540 #568)
+#527 := [th-lemma arith triangle-eq]: #524
+#529 := [unit-resolution #527 #536 #546]: #540
+#530 := [th-lemma arith #529 #584]: #567
+#562 := (not #567)
+#563 := (or #562 #180)
+#701 := (>= #20 0::Int)
+#558 := (or false #701)
+#559 := [th-lemma arith]: #558
+#557 := [unit-resolution #559 #66]: #701
+#547 := [hypothesis]: #567
+#561 := [th-lemma arith farkas -1 3 -2 1 #548 #547 #620 #557]: false
+#564 := [lemma #561]: #563
+#525 := [unit-resolution #564 #548]: #562
+#526 := [unit-resolution #525 #530]: false
+#531 := [lemma #526]: #180
+#501 := (or #181 #142)
+#502 := [th-lemma arith farkas 1 1]: #501
+#503 := [unit-resolution #502 #531]: #142
+#411 := (f4 #174)
+#747 := (= #171 #411)
+#491 := (not #747)
+#476 := (iff #627 #491)
+#490 := (iff #657 #747)
+#485 := (= #411 #171)
+#488 := (iff #485 #747)
+#489 := [commutativity]: #488
+#486 := (iff #657 #485)
+#671 := (= #20 #171)
+#521 := [hypothesis]: #421
+#500 := [unit-resolution #433 #521]: #441
+#504 := [unit-resolution #434 #503]: #165
+#493 := [unit-resolution #427 #504]: #356
+#505 := [trans #493 #500]: #671
+#482 := (= #12 #411)
+#517 := (= #411 #12)
+#513 := (= #174 f5)
+#768 := (or #177 #181)
+#766 := (or #177 #181 #765)
+#767 := [def-axiom]: #766
+#763 := [unit-resolution #767 #196]: #768
+#511 := [unit-resolution #763 #531]: #177
+#514 := [symm #511]: #513
+#518 := [monotonicity #514]: #517
+#484 := [symm #518]: #482
+#487 := [monotonicity #484 #505]: #486
+#483 := [trans #487 #489]: #490
+#477 := [monotonicity #483]: #476
+#494 := (or #540 #181 #691)
+#495 := [th-lemma arith assign-bounds -1 1]: #494
+#496 := [unit-resolution #495 #590 #531]: #540
+#497 := (or #627 #659)
+#498 := [th-lemma arith triangle-eq]: #497
+#499 := [unit-resolution #498 #496]: #627
+#478 := [mp #499 #477]: #491
+#404 := (>= #171 0::Int)
+#466 := (= #411 0::Int)
+#519 := (not #466)
+#520 := (iff #421 #519)
+#523 := (iff #13 #466)
+#522 := (iff #466 #13)
+#515 := [monotonicity #518]: #522
+#516 := [symm #515]: #523
+#506 := [monotonicity #516]: #520
+#508 := [mp #521 #506]: #519
+#468 := (or #404 #466)
+#740 := (or #739 #404 #466)
+#467 := (or #466 #404)
+#462 := (or #739 #467)
+#453 := (iff #462 #740)
+#737 := (or #739 #468)
+#742 := (iff #737 #740)
+#452 := [rewrite]: #742
+#741 := (iff #462 #737)
+#469 := (iff #467 #468)
+#362 := [rewrite]: #469
+#738 := [monotonicity #362]: #741
+#454 := [trans #738 #452]: #453
+#463 := [quant-inst #171]: #462
+#455 := [mp #463 #454]: #740
+#509 := [unit-resolution #455 #790]: #468
+#507 := [unit-resolution #509 #508]: #404
+#745 := (not #404)
+#749 := (or #745 #747)
+#205 := (= #38 #41)
+#230 := (or #205 #224)
+#779 := (forall (vars (?v0 Int)) (:pat #778) #230)
+#235 := (forall (vars (?v0 Int)) #230)
+#782 := (iff #235 #779)
+#780 := (iff #230 #230)
+#781 := [refl]: #780
+#783 := [quant-intro #781]: #782
+#287 := (~ #235 #235)
+#286 := (~ #230 #230)
+#283 := [refl]: #286
+#288 := [nnf-pos #283]: #287
+#42 := (= #41 #38)
+#39 := (<= 0::Int #38)
+#43 := (implies #39 #42)
+#44 := (forall (vars (?v0 Int)) #43)
+#238 := (iff #44 #235)
+#212 := (not #39)
+#213 := (or #212 #205)
+#218 := (forall (vars (?v0 Int)) #213)
+#236 := (iff #218 #235)
+#233 := (iff #213 #230)
+#227 := (or #224 #205)
+#231 := (iff #227 #230)
+#232 := [rewrite]: #231
+#228 := (iff #213 #227)
+#225 := (iff #212 #224)
+#221 := (iff #39 #222)
+#223 := [rewrite]: #221
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#234 := [trans #229 #232]: #233
+#237 := [quant-intro #234]: #236
+#219 := (iff #44 #218)
+#216 := (iff #43 #213)
+#209 := (implies #39 #205)
+#214 := (iff #209 #213)
+#215 := [rewrite]: #214
+#210 := (iff #43 #209)
+#207 := (iff #42 #205)
+#208 := [rewrite]: #207
+#211 := [monotonicity #208]: #210
+#217 := [trans #211 #215]: #216
+#220 := [quant-intro #217]: #219
+#239 := [trans #220 #237]: #238
+#204 := [asserted]: #44
+#240 := [mp #204 #239]: #235
+#284 := [mp~ #240 #288]: #235
+#784 := [mp #284 #783]: #779
+#746 := (not #779)
+#752 := (or #746 #745 #747)
+#748 := (or #747 #745)
+#390 := (or #746 #748)
+#757 := (iff #390 #752)
+#755 := (or #746 #749)
+#756 := (iff #755 #752)
+#754 := [rewrite]: #756
+#395 := (iff #390 #755)
+#750 := (iff #748 #749)
+#751 := [rewrite]: #750
+#396 := [monotonicity #751]: #395
+#743 := [trans #396 #754]: #757
+#753 := [quant-inst #171]: #390
+#744 := [mp #753 #743]: #752
+#510 := [unit-resolution #744 #784]: #749
+#492 := [unit-resolution #510 #507]: #747
+#480 := [unit-resolution #492 #478]: false
+#479 := [lemma #480]: #13
+#681 := (or #421 #141)
+#677 := [th-lemma arith triangle-eq]: #681
+[unit-resolution #677 #479 #503]: false
+unsat
+a73683b8b391e3ad74189bec3a2bead06af3f8bd 414 0
+#2 := false
+#10 := 0::Int
+decl f5 :: (-> S2 Int)
+decl f3 :: S2
+#8 := f3
+#9 := (f5 f3)
+#168 := (>= #9 0::Int)
+#169 := (not #168)
+#155 := (<= #9 0::Int)
+#156 := (not #155)
+#11 := (= #9 0::Int)
+#191 := (or #11 #156 #169)
+#776 := (not #191)
+decl f4 :: (-> Int S2)
+#89 := -1::Int
+#90 := (* -1::Int #9)
+#113 := (mod #90 -1::Int)
+#119 := (* -1::Int #113)
+#196 := (ite #191 0::Int #119)
+#95 := (div #90 -1::Int)
+#12 := 1::Int
+#21 := (div #9 1::Int)
+#179 := (or #156 #169)
+#182 := (ite #179 #21 #95)
+#185 := (ite #11 0::Int #182)
+#199 := (+ #185 #196)
+#202 := (f4 #199)
+#205 := (= f3 #202)
+#426 := (f4 #9)
+#715 := (= #426 #202)
+#718 := (= #202 #426)
+#610 := (= #199 #9)
+#628 := (= #185 #9)
+#614 := (= #9 #185)
+#706 := (* -1::Int #21)
+#700 := (+ #9 #706)
+#695 := (<= #700 0::Int)
+#705 := (= #700 0::Int)
+#1 := true
+#71 := [true-axiom]: true
+#665 := (or false #705)
+#666 := [th-lemma arith]: #665
+#667 := [unit-resolution #666 #71]: #705
+#668 := (not #705)
+#663 := (or #668 #695)
+#669 := [th-lemma arith triangle-eq]: #663
+#655 := [unit-resolution #669 #667]: #695
+#696 := (>= #700 0::Int)
+#651 := (or #668 #696)
+#652 := [th-lemma arith triangle-eq]: #651
+#653 := [unit-resolution #652 #667]: #696
+#683 := (* -1::Int #185)
+#661 := (+ #21 #683)
+#662 := (<= #661 0::Int)
+#672 := (= #21 #185)
+#457 := (= #182 #185)
+#567 := (not #11)
+#735 := (<= #196 0::Int)
+#782 := (= #196 0::Int)
+#656 := [hypothesis]: #191
+#420 := (or #776 #782)
+#761 := [def-axiom]: #420
+#657 := [unit-resolution #761 #656]: #782
+#658 := (not #782)
+#659 := (or #658 #735)
+#654 := [th-lemma arith triangle-eq]: #659
+#660 := [unit-resolution #654 #657]: #735
+#736 := (>= #196 0::Int)
+#633 := (or #658 #736)
+#634 := [th-lemma arith triangle-eq]: #633
+#635 := [unit-resolution #634 #657]: #736
+#621 := (not #735)
+#619 := (not #736)
+#622 := (or #567 #619 #621)
+#726 := (= 0::Int #9)
+#730 := [hypothesis]: #11
+#724 := [symm #730]: #726
+#727 := (= #199 0::Int)
+#372 := (= #185 0::Int)
+#774 := (or #567 #372)
+#448 := [def-axiom]: #774
+#737 := [unit-resolution #448 #730]: #372
+#723 := (= #199 #185)
+#569 := (= #185 #199)
+#566 := [hypothesis]: #735
+#568 := [hypothesis]: #736
+#722 := [th-lemma arith eq-propagate -1 -1 #568 #566]: #569
+#725 := [symm #722]: #723
+#609 := [trans #725 #737]: #727
+#611 := [trans #609 #724]: #610
+#620 := [monotonicity #611]: #718
+#716 := [symm #620]: #715
+#427 := (= f3 #426)
+#38 := (:var 0 S2)
+#39 := (f5 #38)
+#786 := (pattern #39)
+#40 := (f4 #39)
+#215 := (= #38 #40)
+#787 := (forall (vars (?v0 S2)) (:pat #786) #215)
+#218 := (forall (vars (?v0 S2)) #215)
+#788 := (iff #218 #787)
+#790 := (iff #787 #787)
+#791 := [rewrite]: #790
+#789 := [rewrite]: #788
+#792 := [trans #789 #791]: #788
+#312 := (~ #218 #218)
+#310 := (~ #215 #215)
+#311 := [refl]: #310
+#313 := [nnf-pos #311]: #312
+#41 := (= #40 #38)
+#42 := (forall (vars (?v0 S2)) #41)
+#219 := (iff #42 #218)
+#216 := (iff #41 #215)
+#217 := [rewrite]: #216
+#220 := [quant-intro #217]: #219
+#214 := [asserted]: #42
+#223 := [mp #214 #220]: #218
+#302 := [mp~ #223 #313]: #218
+#793 := [mp #302 #792]: #787
+#765 := (not #787)
+#766 := (or #765 #427)
+#767 := [quant-inst #8]: #766
+#570 := [unit-resolution #767 #793]: #427
+#719 := [trans #570 #716]: #205
+#208 := (not #205)
+#23 := (- 1::Int)
+#22 := (- #9)
+#29 := (mod #22 #23)
+#30 := (- #29)
+#28 := (mod #9 1::Int)
+#16 := (< 0::Int 1::Int)
+#18 := (< #9 0::Int)
+#19 := (and #18 #16)
+#15 := (< 0::Int #9)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#31 := (ite #20 #28 #30)
+#32 := (ite #11 0::Int #31)
+#13 := (= 1::Int 0::Int)
+#33 := (ite #13 #9 #32)
+#24 := (div #22 #23)
+#25 := (ite #20 #21 #24)
+#14 := (or #11 #13)
+#26 := (ite #14 0::Int #25)
+#27 := (* #26 1::Int)
+#34 := (+ #27 #33)
+#35 := (f4 #34)
+#36 := (= f3 #35)
+#37 := (not #36)
+#211 := (iff #37 #208)
+#83 := (and #16 #18)
+#86 := (or #17 #83)
+#130 := (or #11 #86)
+#131 := (ite #130 0::Int #119)
+#98 := (ite #86 #21 #95)
+#101 := (ite #11 0::Int #98)
+#143 := (+ #101 #131)
+#146 := (f4 #143)
+#149 := (= f3 #146)
+#152 := (not #149)
+#209 := (iff #152 #208)
+#206 := (iff #149 #205)
+#203 := (= #146 #202)
+#200 := (= #143 #199)
+#197 := (= #131 #196)
+#194 := (iff #130 #191)
+#188 := (or #11 #179)
+#192 := (iff #188 #191)
+#193 := [rewrite]: #192
+#189 := (iff #130 #188)
+#180 := (iff #86 #179)
+#177 := (iff #83 #169)
+#172 := (and true #169)
+#175 := (iff #172 #169)
+#176 := [rewrite]: #175
+#173 := (iff #83 #172)
+#170 := (iff #18 #169)
+#171 := [rewrite]: #170
+#159 := (iff #16 true)
+#160 := [rewrite]: #159
+#174 := [monotonicity #160 #171]: #173
+#178 := [trans #174 #176]: #177
+#166 := (iff #17 #156)
+#161 := (and #156 true)
+#164 := (iff #161 #156)
+#165 := [rewrite]: #164
+#162 := (iff #17 #161)
+#157 := (iff #15 #156)
+#158 := [rewrite]: #157
+#163 := [monotonicity #158 #160]: #162
+#167 := [trans #163 #165]: #166
+#181 := [monotonicity #167 #178]: #180
+#190 := [monotonicity #181]: #189
+#195 := [trans #190 #193]: #194
+#198 := [monotonicity #195]: #197
+#186 := (= #101 #185)
+#183 := (= #98 #182)
+#184 := [monotonicity #181]: #183
+#187 := [monotonicity #184]: #186
+#201 := [monotonicity #187 #198]: #200
+#204 := [monotonicity #201]: #203
+#207 := [monotonicity #204]: #206
+#210 := [monotonicity #207]: #209
+#153 := (iff #37 #152)
+#150 := (iff #36 #149)
+#147 := (= #35 #146)
+#144 := (= #34 #143)
+#141 := (= #33 #131)
+#136 := (ite false #9 #131)
+#139 := (= #136 #131)
+#140 := [rewrite]: #139
+#137 := (= #33 #136)
+#134 := (= #32 #131)
+#124 := (ite #86 0::Int #119)
+#127 := (ite #11 0::Int #124)
+#132 := (= #127 #131)
+#133 := [rewrite]: #132
+#128 := (= #32 #127)
+#125 := (= #31 #124)
+#122 := (= #30 #119)
+#116 := (- #113)
+#120 := (= #116 #119)
+#121 := [rewrite]: #120
+#117 := (= #30 #116)
+#114 := (= #29 #113)
+#93 := (= #23 -1::Int)
+#94 := [rewrite]: #93
+#91 := (= #22 #90)
+#92 := [rewrite]: #91
+#115 := [monotonicity #92 #94]: #114
+#118 := [monotonicity #115]: #117
+#123 := [trans #118 #121]: #122
+#111 := (= #28 0::Int)
+#112 := [rewrite]: #111
+#87 := (iff #20 #86)
+#84 := (iff #19 #83)
+#85 := [rewrite]: #84
+#88 := [monotonicity #85]: #87
+#126 := [monotonicity #88 #112 #123]: #125
+#129 := [monotonicity #126]: #128
+#135 := [trans #129 #133]: #134
+#74 := (iff #13 false)
+#75 := [rewrite]: #74
+#138 := [monotonicity #75 #135]: #137
+#142 := [trans #138 #140]: #141
+#109 := (= #27 #101)
+#104 := (* #101 1::Int)
+#107 := (= #104 #101)
+#108 := [rewrite]: #107
+#105 := (= #27 #104)
+#102 := (= #26 #101)
+#99 := (= #25 #98)
+#96 := (= #24 #95)
+#97 := [monotonicity #92 #94]: #96
+#100 := [monotonicity #88 #97]: #99
+#81 := (iff #14 #11)
+#76 := (or #11 false)
+#79 := (iff #76 #11)
+#80 := [rewrite]: #79
+#77 := (iff #14 #76)
+#78 := [monotonicity #75]: #77
+#82 := [trans #78 #80]: #81
+#103 := [monotonicity #82 #100]: #102
+#106 := [monotonicity #103]: #105
+#110 := [trans #106 #108]: #109
+#145 := [monotonicity #110 #142]: #144
+#148 := [monotonicity #145]: #147
 #151 := [monotonicity #148]: #150
-#156 := [trans #151 #154]: #155
-#159 := [quant-intro #156]: #158
-#141 := (iff #29 #140)
-#138 := (iff #28 #135)
-#131 := (implies #24 #127)
-#136 := (iff #131 #135)
-#137 := [rewrite]: #136
-#132 := (iff #28 #131)
-#129 := (iff #27 #127)
-#130 := [rewrite]: #129
-#133 := [monotonicity #130]: #132
-#139 := [trans #133 #137]: #138
-#142 := [quant-intro #139]: #141
-#161 := [trans #142 #159]: #160
-#126 := [asserted]: #29
-#162 := [mp #126 #161]: #157
-#331 := [mp~ #162 #335]: #157
-#911 := [mp #331 #910]: #906
-#895 := (not #906)
-#890 := (or #895 #560 #891)
-#896 := (or #895 #892)
-#546 := (iff #896 #890)
-#551 := [rewrite]: #546
-#886 := [quant-inst #11]: #896
-#887 := [mp #886 #551]: #890
-#544 := [unit-resolution #887 #911]: #892
-#533 := [unit-resolution #544 #543]: #560
-#519 := [mp #533 #524]: #865
-#525 := (or #676 #685)
-#499 := [th-lemma arith triangle-eq]: #525
-#504 := [unit-resolution #499 #519]: #685
-#505 := [unit-resolution #625 #541]: #824
-[th-lemma arith farkas 1 1 -1 1 #505 #504 #550 #669]: false
-unsat
-bf4ed7a0c67dc55dd17034c099d4eaab353230e6 827 0
+#154 := [monotonicity #151]: #153
+#212 := [trans #154 #210]: #211
+#73 := [asserted]: #37
+#213 := [mp #73 #212]: #208
+#604 := [unit-resolution #213 #719]: false
+#615 := [lemma #604]: #622
+#528 := [unit-resolution #615 #635 #660]: #567
+#449 := (or #11 #457)
+#781 := [def-axiom]: #449
+#639 := [unit-resolution #781 #528]: #457
+#373 := (= #21 #182)
+#471 := (f5 #426)
+#749 := (= #471 0::Int)
+#649 := (not #749)
+#645 := (iff #567 #649)
+#647 := (iff #11 #749)
+#643 := (iff #749 #11)
+#646 := (= #471 #9)
+#640 := (= #426 f3)
+#641 := [symm #570]: #640
+#642 := [monotonicity #641]: #646
+#644 := [monotonicity #642]: #643
+#648 := [symm #644]: #647
+#650 := [monotonicity #648]: #645
+#630 := [mp #528 #650]: #649
+#739 := (or #168 #749)
+#43 := (:var 0 Int)
+#45 := (f4 #43)
+#794 := (pattern #45)
+#239 := (>= #43 0::Int)
+#46 := (f5 #45)
+#51 := (= #46 0::Int)
+#288 := (or #51 #239)
+#801 := (forall (vars (?v0 Int)) (:pat #794) #288)
+#293 := (forall (vars (?v0 Int)) #288)
+#804 := (iff #293 #801)
+#802 := (iff #288 #288)
+#803 := [refl]: #802
+#805 := [quant-intro #803]: #804
+#306 := (~ #293 #293)
+#314 := (~ #288 #288)
+#315 := [refl]: #314
+#307 := [nnf-pos #315]: #306
+#50 := (< #43 0::Int)
+#52 := (implies #50 #51)
+#53 := (forall (vars (?v0 Int)) #52)
+#296 := (iff #53 #293)
+#259 := (= 0::Int #46)
+#265 := (not #50)
+#266 := (or #265 #259)
+#271 := (forall (vars (?v0 Int)) #266)
+#294 := (iff #271 #293)
+#291 := (iff #266 #288)
+#285 := (or #239 #51)
+#289 := (iff #285 #288)
+#290 := [rewrite]: #289
+#286 := (iff #266 #285)
+#283 := (iff #259 #51)
+#284 := [rewrite]: #283
+#281 := (iff #265 #239)
+#241 := (not #239)
+#276 := (not #241)
+#279 := (iff #276 #239)
+#280 := [rewrite]: #279
+#277 := (iff #265 #276)
+#274 := (iff #50 #241)
+#275 := [rewrite]: #274
+#278 := [monotonicity #275]: #277
+#282 := [trans #278 #280]: #281
+#287 := [monotonicity #282 #284]: #286
+#292 := [trans #287 #290]: #291
+#295 := [quant-intro #292]: #294
+#272 := (iff #53 #271)
+#269 := (iff #52 #266)
+#262 := (implies #50 #259)
+#267 := (iff #262 #266)
+#268 := [rewrite]: #267
+#263 := (iff #52 #262)
+#260 := (iff #51 #259)
+#261 := [rewrite]: #260
+#264 := [monotonicity #261]: #263
+#270 := [trans #264 #268]: #269
+#273 := [quant-intro #270]: #272
+#297 := [trans #273 #295]: #296
+#258 := [asserted]: #53
+#298 := [mp #258 #297]: #293
+#316 := [mp~ #298 #307]: #293
+#806 := [mp #316 #805]: #801
+#750 := (not #801)
+#740 := (or #750 #168 #749)
+#738 := (or #749 #168)
+#746 := (or #750 #738)
+#734 := (iff #746 #740)
+#588 := (or #750 #739)
+#732 := (iff #588 #740)
+#733 := [rewrite]: #732
+#589 := (iff #746 #588)
+#744 := (iff #738 #739)
+#745 := [rewrite]: #744
+#731 := [monotonicity #745]: #589
+#728 := [trans #731 #733]: #734
+#587 := [quant-inst #9]: #746
+#729 := [mp #587 #728]: #740
+#576 := [unit-resolution #729 #806]: #739
+#631 := [unit-resolution #576 #630]: #168
+#436 := (or #776 #11 #156 #169)
+#777 := [def-axiom]: #436
+#612 := [unit-resolution #777 #631 #528 #656]: #156
+#459 := (or #179 #155)
+#450 := [def-axiom]: #459
+#636 := [unit-resolution #450 #612]: #179
+#463 := (not #179)
+#443 := (or #463 #373)
+#778 := [def-axiom]: #443
+#637 := [unit-resolution #778 #636]: #373
+#632 := [trans #637 #639]: #672
+#638 := (not #672)
+#606 := (or #638 #662)
+#613 := [th-lemma arith triangle-eq]: #606
+#572 := [unit-resolution #613 #632]: #662
+#664 := (>= #661 0::Int)
+#603 := (or #638 #664)
+#605 := [th-lemma arith triangle-eq]: #603
+#607 := [unit-resolution #605 #632]: #664
+#616 := [th-lemma arith eq-propagate 1 1 1 1 #607 #572 #653 #655]: #614
+#608 := [symm #616]: #628
+#617 := [th-lemma arith eq-propagate -1 -1 #635 #660]: #569
+#618 := [symm #617]: #723
+#629 := [trans #618 #608]: #610
+#584 := [monotonicity #629]: #718
+#585 := [symm #584]: #715
+#590 := [trans #570 #585]: #205
+#591 := [unit-resolution #213 #590]: false
+#592 := [lemma #591]: #776
+#435 := (or #191 #168)
+#440 := [def-axiom]: #435
+#533 := [unit-resolution #440 #592]: #168
+#785 := (or #191 #155)
+#775 := [def-axiom]: #785
+#534 := [unit-resolution #775 #592]: #155
+#784 := (or #191 #567)
+#779 := [def-axiom]: #784
+#538 := [unit-resolution #779 #592]: #567
+#531 := [th-lemma arith triangle-eq]: #191
+[unit-resolution #531 #538 #534 #533]: false
+unsat
+9915a65ab7888a474bcd2f001f0a80c1938cedba 411 0
 #2 := false
 decl f4 :: (-> Int S2)
-decl f7 :: (-> Int Int Int)
-#10 := 1::Int
-decl f6 :: (-> S2 Int)
+#93 := -3::Int
+decl f5 :: (-> S2 Int)
 decl f3 :: S2
 #8 := f3
-#9 := (f6 f3)
-#13 := (f7 #9 1::Int)
-decl f5 :: (-> Int Int Int)
-#11 := (f5 #9 1::Int)
-#85 := (+ #11 #13)
-#88 := (f4 #85)
-#91 := (= f3 #88)
-#552 := (f6 #88)
-#470 := (f4 #552)
-#983 := (= #470 #88)
-#473 := (= #88 #470)
-#18 := (:var 0 S2)
-#19 := (f6 #18)
-#875 := (pattern #19)
-#20 := (f4 #19)
-#98 := (= #18 #20)
-#876 := (forall (vars (?v0 S2)) (:pat #875) #98)
-#102 := (forall (vars (?v0 S2)) #98)
-#877 := (iff #102 #876)
-#879 := (iff #876 #876)
-#880 := [rewrite]: #879
-#878 := [rewrite]: #877
-#881 := [trans #878 #880]: #877
-#325 := (~ #102 #102)
-#323 := (~ #98 #98)
-#324 := [refl]: #323
-#326 := [nnf-pos #324]: #325
-#21 := (= #20 #18)
-#22 := (forall (vars (?v0 S2)) #21)
-#103 := (iff #22 #102)
-#100 := (iff #21 #98)
-#101 := [rewrite]: #100
-#104 := [quant-intro #101]: #103
-#97 := [asserted]: #22
-#107 := [mp #97 #104]: #102
-#311 := [mp~ #107 #326]: #102
-#882 := [mp #311 #881]: #876
-#539 := (not #876)
-#931 := (or #539 #473)
-#932 := [quant-inst #88]: #931
-#978 := [unit-resolution #932 #882]: #473
-#984 := [symm #978]: #983
-#985 := (= f3 #470)
-#462 := (f4 #9)
-#981 := (= #462 #470)
-#979 := (= #470 #462)
-#976 := (= #552 #9)
-#23 := 0::Int
-#974 := (= 0::Int #9)
-#847 := (= #9 0::Int)
-#935 := (= #462 #88)
-#933 := (= #9 #85)
-#916 := (= #11 #85)
-#670 := (<= #13 0::Int)
-#757 := (= #13 0::Int)
-#844 := (<= #9 0::Int)
-#676 := (not #844)
-#572 := (>= #9 0::Int)
-#825 := (not #572)
-#718 := (or #825 #676 #847)
-#494 := [hypothesis]: #825
-#630 := (f6 #462)
-#633 := (= #630 0::Int)
-#510 := (iff #633 #847)
-#530 := (= #630 #9)
-#480 := (= #9 #630)
-#546 := (= f3 #462)
-#550 := (or #539 #546)
-#551 := [quant-inst #8]: #550
-#534 := [unit-resolution #551 #882]: #546
-#481 := [monotonicity #534]: #480
-#484 := [symm #481]: #530
-#485 := [monotonicity #484]: #510
-#639 := (or #572 #633)
-#24 := (:var 0 Int)
-#26 := (f4 #24)
-#883 := (pattern #26)
-#124 := (>= #24 0::Int)
-#27 := (f6 #26)
-#32 := (= #27 0::Int)
-#172 := (or #32 #124)
-#890 := (forall (vars (?v0 Int)) (:pat #883) #172)
-#177 := (forall (vars (?v0 Int)) #172)
-#893 := (iff #177 #890)
-#891 := (iff #172 #172)
-#892 := [refl]: #891
-#894 := [quant-intro #892]: #893
-#315 := (~ #177 #177)
-#327 := (~ #172 #172)
-#328 := [refl]: #327
-#316 := [nnf-pos #328]: #315
-#31 := (< #24 0::Int)
-#33 := (implies #31 #32)
-#34 := (forall (vars (?v0 Int)) #33)
-#180 := (iff #34 #177)
-#143 := (= 0::Int #27)
-#149 := (not #31)
-#150 := (or #149 #143)
-#155 := (forall (vars (?v0 Int)) #150)
-#178 := (iff #155 #177)
-#175 := (iff #150 #172)
-#169 := (or #124 #32)
-#173 := (iff #169 #172)
-#174 := [rewrite]: #173
-#170 := (iff #150 #169)
-#167 := (iff #143 #32)
-#168 := [rewrite]: #167
-#165 := (iff #149 #124)
-#125 := (not #124)
-#160 := (not #125)
-#163 := (iff #160 #124)
-#164 := [rewrite]: #163
-#161 := (iff #149 #160)
-#158 := (iff #31 #125)
+#9 := (f5 f3)
+#89 := -1::Int
+#90 := (* -1::Int #9)
+#113 := (mod #90 -3::Int)
+#119 := (* -1::Int #113)
+#12 := 3::Int
+#28 := (mod #9 3::Int)
+#10 := 0::Int
+#162 := (>= #9 0::Int)
+#163 := (not #162)
+#149 := (<= #9 0::Int)
+#150 := (not #149)
+#173 := (or #150 #163)
+#185 := (ite #173 #28 #119)
+#11 := (= #9 0::Int)
+#188 := (ite #11 0::Int #185)
+#96 := (div #90 -3::Int)
+#21 := (div #9 3::Int)
+#176 := (ite #173 #21 #96)
+#179 := (ite #11 0::Int #176)
+#182 := (* 3::Int #179)
+#191 := (+ #182 #188)
+#194 := (f4 #191)
+#197 := (= f3 #194)
+#413 := (f4 #9)
+#714 := (= #413 #194)
+#713 := (= #194 #413)
+#618 := (= #191 #9)
+#579 := (= #9 #191)
+#693 := (* -1::Int #28)
+#699 := (* -3::Int #21)
+#700 := (+ #699 #693)
+#684 := (+ #9 #700)
+#688 := (<= #684 0::Int)
+#698 := (= #684 0::Int)
+#1 := true
+#71 := [true-axiom]: true
+#630 := (or false #698)
+#625 := [th-lemma arith]: #630
+#631 := [unit-resolution #625 #71]: #698
+#599 := (not #698)
+#606 := (or #599 #688)
+#565 := [th-lemma arith triangle-eq]: #606
+#596 := [unit-resolution #565 #631]: #688
+#689 := (>= #684 0::Int)
+#584 := (or #599 #689)
+#585 := [th-lemma arith triangle-eq]: #584
+#588 := [unit-resolution #585 #631]: #689
+#660 := (* -1::Int #179)
+#661 := (+ #21 #660)
+#656 := (<= #661 0::Int)
+#659 := (= #21 #179)
+#450 := (= #176 #179)
+#430 := (not #11)
+#616 := (= 0::Int #9)
+#716 := [hypothesis]: #11
+#617 := [symm #716]: #616
+#615 := (= #191 0::Int)
+#562 := (<= #188 0::Int)
+#774 := (= #188 0::Int)
+#433 := (or #430 #774)
+#769 := [def-axiom]: #433
+#718 := [unit-resolution #769 #716]: #774
+#719 := (not #774)
+#717 := (or #719 #562)
+#720 := [th-lemma arith triangle-eq]: #717
+#602 := [unit-resolution #720 #718]: #562
+#715 := (>= #188 0::Int)
+#603 := (or #719 #715)
+#604 := [th-lemma arith triangle-eq]: #603
+#563 := [unit-resolution #604 #718]: #715
+#559 := (<= #179 0::Int)
+#364 := (= #179 0::Int)
+#560 := (or #430 #364)
+#767 := [def-axiom]: #560
+#711 := [unit-resolution #767 #716]: #364
+#613 := (not #364)
+#708 := (or #613 #559)
+#709 := [th-lemma arith triangle-eq]: #708
+#712 := [unit-resolution #709 #711]: #559
+#561 := (>= #179 0::Int)
+#597 := (or #613 #561)
+#612 := [th-lemma arith triangle-eq]: #597
+#614 := [unit-resolution #612 #711]: #561
+#608 := [th-lemma arith eq-propagate -3 -3 -1 -1 #614 #712 #563 #602]: #615
+#619 := [trans #608 #617]: #618
+#710 := [monotonicity #619]: #713
+#701 := [symm #710]: #714
+#754 := (= f3 #413)
+#38 := (:var 0 S2)
+#39 := (f5 #38)
+#779 := (pattern #39)
+#40 := (f4 #39)
+#207 := (= #38 #40)
+#780 := (forall (vars (?v0 S2)) (:pat #779) #207)
+#210 := (forall (vars (?v0 S2)) #207)
+#781 := (iff #210 #780)
+#783 := (iff #780 #780)
+#784 := [rewrite]: #783
+#782 := [rewrite]: #781
+#785 := [trans #782 #784]: #781
+#304 := (~ #210 #210)
+#302 := (~ #207 #207)
+#303 := [refl]: #302
+#305 := [nnf-pos #303]: #304
+#41 := (= #40 #38)
+#42 := (forall (vars (?v0 S2)) #41)
+#211 := (iff #42 #210)
+#208 := (iff #41 #207)
+#209 := [rewrite]: #208
+#212 := [quant-intro #209]: #211
+#206 := [asserted]: #42
+#215 := [mp #206 #212]: #210
+#294 := [mp~ #215 #305]: #210
+#786 := [mp #294 #785]: #780
+#419 := (not #780)
+#420 := (or #419 #754)
+#756 := [quant-inst #8]: #420
+#620 := [unit-resolution #756 #786]: #754
+#703 := [trans #620 #701]: #197
+#200 := (not #197)
+#23 := (- 3::Int)
+#22 := (- #9)
+#29 := (mod #22 #23)
+#30 := (- #29)
+#16 := (< 0::Int 3::Int)
+#18 := (< #9 0::Int)
+#19 := (and #18 #16)
+#15 := (< 0::Int #9)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#31 := (ite #20 #28 #30)
+#32 := (ite #11 0::Int #31)
+#13 := (= 3::Int 0::Int)
+#33 := (ite #13 #9 #32)
+#24 := (div #22 #23)
+#25 := (ite #20 #21 #24)
+#14 := (or #11 #13)
+#26 := (ite #14 0::Int #25)
+#27 := (* #26 3::Int)
+#34 := (+ #27 #33)
+#35 := (f4 #34)
+#36 := (= f3 #35)
+#37 := (not #36)
+#203 := (iff #37 #200)
+#83 := (and #16 #18)
+#86 := (or #17 #83)
+#124 := (ite #86 #28 #119)
+#127 := (ite #11 0::Int #124)
+#99 := (ite #86 #21 #96)
+#102 := (ite #11 0::Int #99)
+#108 := (* 3::Int #102)
+#137 := (+ #108 #127)
+#140 := (f4 #137)
+#143 := (= f3 #140)
+#146 := (not #143)
+#201 := (iff #146 #200)
+#198 := (iff #143 #197)
+#195 := (= #140 #194)
+#192 := (= #137 #191)
+#189 := (= #127 #188)
+#186 := (= #124 #185)
+#174 := (iff #86 #173)
+#171 := (iff #83 #163)
+#166 := (and true #163)
+#169 := (iff #166 #163)
+#170 := [rewrite]: #169
+#167 := (iff #83 #166)
+#164 := (iff #18 #163)
+#165 := [rewrite]: #164
+#153 := (iff #16 true)
+#154 := [rewrite]: #153
+#168 := [monotonicity #154 #165]: #167
+#172 := [trans #168 #170]: #171
+#160 := (iff #17 #150)
+#155 := (and #150 true)
+#158 := (iff #155 #150)
 #159 := [rewrite]: #158
-#162 := [monotonicity #159]: #161
-#166 := [trans #162 #164]: #165
-#171 := [monotonicity #166 #168]: #170
-#176 := [trans #171 #174]: #175
-#179 := [quant-intro #176]: #178
-#156 := (iff #34 #155)
-#153 := (iff #33 #150)
-#146 := (implies #31 #143)
-#151 := (iff #146 #150)
+#156 := (iff #17 #155)
+#151 := (iff #15 #150)
 #152 := [rewrite]: #151
-#147 := (iff #33 #146)
-#144 := (iff #32 #143)
-#145 := [rewrite]: #144
-#148 := [monotonicity #145]: #147
-#154 := [trans #148 #152]: #153
-#157 := [quant-intro #154]: #156
-#181 := [trans #157 #179]: #180
-#142 := [asserted]: #34
-#182 := [mp #142 #181]: #177
-#329 := [mp~ #182 #316]: #177
-#895 := [mp #329 #894]: #890
-#853 := (not #890)
-#641 := (or #853 #572 #633)
-#637 := (or #633 #572)
-#629 := (or #853 #637)
-#616 := (iff #629 #641)
-#634 := (or #853 #639)
-#636 := (iff #634 #641)
-#626 := [rewrite]: #636
-#635 := (iff #629 #634)
-#640 := (iff #637 #639)
-#638 := [rewrite]: #640
-#631 := [monotonicity #638]: #635
-#618 := [trans #631 #626]: #616
-#632 := [quant-inst #9]: #629
-#619 := [mp #632 #618]: #641
-#511 := [unit-resolution #619 #895]: #639
-#477 := [unit-resolution #511 #494]: #633
-#486 := [mp #477 #485]: #847
-#763 := (not #847)
-#479 := (or #763 #572)
-#487 := [th-lemma arith triangle-eq]: #479
-#472 := [unit-resolution #487 #486 #494]: false
-#469 := [lemma #472]: #572
-#474 := [hypothesis]: #763
-#504 := (or #847 #676 #825)
-#506 := [th-lemma arith triangle-eq]: #504
-#475 := [unit-resolution #506 #474 #469]: #676
-#662 := (or #718 #844)
-#663 := [def-axiom]: #662
-#463 := [unit-resolution #663 #475]: #718
-#667 := (not #718)
-#466 := (or #667 #757)
-#199 := -1::Int
-#852 := (* -1::Int #9)
-#784 := (mod #852 -1::Int)
-#736 := (+ #13 #784)
-#734 := (= #736 0::Int)
-#679 := (ite #718 #757 #734)
-#35 := (:var 1 Int)
-#54 := (f7 #35 #24)
-#903 := (pattern #54)
-#203 := (* -1::Int #24)
-#200 := (* -1::Int #35)
-#264 := (mod #200 #203)
-#394 := (+ #54 #264)
-#395 := (= #394 0::Int)
-#55 := (mod #35 #24)
-#391 := (* -1::Int #55)
-#392 := (+ #54 #391)
-#393 := (= #392 0::Int)
-#238 := (>= #35 0::Int)
-#231 := (<= #24 0::Int)
-#338 := (or #231 #238)
-#339 := (not #338)
-#227 := (<= #35 0::Int)
-#336 := (or #227 #231)
-#337 := (not #336)
-#342 := (or #337 #339)
-#396 := (ite #342 #393 #395)
-#390 := (= #54 0::Int)
-#37 := (= #35 0::Int)
-#397 := (ite #37 #390 #396)
-#389 := (= #35 #54)
-#38 := (= #24 0::Int)
-#398 := (ite #38 #389 #397)
-#904 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #903) #398)
-#401 := (forall (vars (?v0 Int) (?v1 Int)) #398)
-#907 := (iff #401 #904)
-#905 := (iff #398 #398)
-#906 := [refl]: #905
-#908 := [quant-intro #906]: #907
-#270 := (* -1::Int #264)
-#358 := (ite #342 #55 #270)
-#361 := (ite #37 0::Int #358)
-#364 := (ite #38 #35 #361)
-#367 := (= #54 #364)
-#370 := (forall (vars (?v0 Int) (?v1 Int)) #367)
-#402 := (iff #370 #401)
-#399 := (iff #367 #398)
-#400 := [rewrite]: #399
-#403 := [quant-intro #400]: #402
-#239 := (not #238)
-#232 := (not #231)
-#242 := (and #232 #239)
-#228 := (not #227)
-#235 := (and #228 #232)
-#245 := (or #235 #242)
-#290 := (ite #245 #55 #270)
-#293 := (ite #37 0::Int #290)
-#296 := (ite #38 #35 #293)
-#299 := (= #54 #296)
-#302 := (forall (vars (?v0 Int) (?v1 Int)) #299)
-#371 := (iff #302 #370)
-#368 := (iff #299 #367)
-#365 := (= #296 #364)
-#362 := (= #293 #361)
-#359 := (= #290 #358)
-#343 := (iff #245 #342)
-#340 := (iff #242 #339)
-#341 := [rewrite]: #340
-#321 := (iff #235 #337)
-#322 := [rewrite]: #321
-#344 := [monotonicity #322 #341]: #343
-#360 := [monotonicity #344]: #359
-#363 := [monotonicity #360]: #362
-#366 := [monotonicity #363]: #365
-#369 := [monotonicity #366]: #368
-#372 := [quant-intro #369]: #371
-#319 := (~ #302 #302)
-#333 := (~ #299 #299)
-#334 := [refl]: #333
-#320 := [nnf-pos #334]: #319
-#48 := (- #24)
-#47 := (- #35)
-#56 := (mod #47 #48)
-#57 := (- #56)
-#41 := (< 0::Int #24)
-#43 := (< #35 0::Int)
-#44 := (and #43 #41)
-#40 := (< 0::Int #35)
-#42 := (and #40 #41)
-#45 := (or #42 #44)
-#58 := (ite #45 #55 #57)
-#59 := (ite #37 0::Int #58)
-#60 := (ite #38 #35 #59)
-#61 := (= #54 #60)
-#62 := (forall (vars (?v0 Int) (?v1 Int)) #61)
-#305 := (iff #62 #302)
-#193 := (and #41 #43)
-#196 := (or #42 #193)
-#275 := (ite #196 #55 #270)
-#184 := (= 0::Int #35)
-#278 := (ite #184 0::Int #275)
-#187 := (= 0::Int #24)
-#281 := (ite #187 #35 #278)
-#284 := (= #54 #281)
-#287 := (forall (vars (?v0 Int) (?v1 Int)) #284)
-#303 := (iff #287 #302)
-#300 := (iff #284 #299)
-#297 := (= #281 #296)
-#294 := (= #278 #293)
-#291 := (= #275 #290)
-#246 := (iff #196 #245)
-#243 := (iff #193 #242)
-#240 := (iff #43 #239)
-#241 := [rewrite]: #240
-#233 := (iff #41 #232)
-#234 := [rewrite]: #233
-#244 := [monotonicity #234 #241]: #243
-#236 := (iff #42 #235)
-#229 := (iff #40 #228)
-#230 := [rewrite]: #229
-#237 := [monotonicity #230 #234]: #236
-#247 := [monotonicity #237 #244]: #246
-#292 := [monotonicity #247]: #291
-#221 := (iff #184 #37)
-#222 := [rewrite]: #221
-#295 := [monotonicity #222 #292]: #294
-#223 := (iff #187 #38)
-#224 := [rewrite]: #223
-#298 := [monotonicity #224 #295]: #297
-#301 := [monotonicity #298]: #300
-#304 := [quant-intro #301]: #303
-#288 := (iff #62 #287)
-#285 := (iff #61 #284)
-#282 := (= #60 #281)
-#279 := (= #59 #278)
-#276 := (= #58 #275)
-#273 := (= #57 #270)
-#267 := (- #264)
-#271 := (= #267 #270)
-#272 := [rewrite]: #271
-#268 := (= #57 #267)
-#265 := (= #56 #264)
-#204 := (= #48 #203)
-#205 := [rewrite]: #204
-#201 := (= #47 #200)
-#202 := [rewrite]: #201
-#266 := [monotonicity #202 #205]: #265
-#269 := [monotonicity #266]: #268
-#274 := [trans #269 #272]: #273
-#197 := (iff #45 #196)
-#194 := (iff #44 #193)
-#195 := [rewrite]: #194
-#198 := [monotonicity #195]: #197
-#277 := [monotonicity #198 #274]: #276
-#185 := (iff #37 #184)
-#186 := [rewrite]: #185
-#280 := [monotonicity #186 #277]: #279
-#188 := (iff #38 #187)
-#189 := [rewrite]: #188
-#283 := [monotonicity #189 #280]: #282
-#286 := [monotonicity #283]: #285
-#289 := [quant-intro #286]: #288
-#306 := [trans #289 #304]: #305
-#263 := [asserted]: #62
-#307 := [mp #263 #306]: #302
-#335 := [mp~ #307 #320]: #302
-#373 := [mp #335 #372]: #370
-#404 := [mp #373 #403]: #401
-#909 := [mp #404 #908]: #904
-#684 := (not #904)
-#685 := (or #684 #679)
-#516 := (* -1::Int 1::Int)
-#772 := (mod #852 #516)
-#750 := (+ #13 #772)
-#751 := (= #750 0::Int)
-#780 := (mod #9 1::Int)
-#753 := (* -1::Int #780)
-#754 := (+ #13 #753)
-#755 := (= #754 0::Int)
-#573 := (<= 1::Int 0::Int)
-#574 := (or #573 #572)
-#468 := (not #574)
-#845 := (or #844 #573)
-#567 := (not #845)
-#568 := (or #567 #468)
-#756 := (ite #568 #755 #751)
-#752 := (ite #847 #757 #756)
-#758 := (= #9 #13)
-#843 := (= 1::Int 0::Int)
-#744 := (ite #843 #758 #752)
-#686 := (or #684 #744)
-#688 := (iff #686 #685)
-#690 := (iff #685 #685)
-#675 := [rewrite]: #690
-#682 := (iff #744 #679)
-#811 := (or #825 #676)
-#727 := (or #811 #847)
-#695 := (ite #727 #757 #734)
-#680 := (iff #695 #679)
-#673 := (iff #727 #718)
-#674 := [rewrite]: #673
-#681 := [monotonicity #674]: #680
-#717 := (iff #744 #695)
-#696 := (ite false #758 #695)
-#706 := (iff #696 #695)
-#707 := [rewrite]: #706
-#703 := (iff #744 #696)
-#692 := (iff #752 #695)
-#665 := (ite #811 #757 #734)
-#725 := (ite #847 #757 #665)
-#702 := (iff #725 #695)
-#661 := [rewrite]: #702
-#726 := (iff #752 #725)
-#720 := (iff #756 #665)
-#739 := (iff #751 #734)
-#737 := (= #750 #736)
-#732 := (= #772 #784)
-#816 := (= #516 -1::Int)
-#698 := [rewrite]: #816
-#733 := [monotonicity #698]: #732
-#738 := [monotonicity #733]: #737
-#719 := [monotonicity #738]: #739
-#735 := (iff #755 #757)
-#729 := (= #754 #13)
-#722 := (+ #13 0::Int)
-#617 := (= #722 #13)
-#728 := [rewrite]: #617
-#723 := (= #754 #722)
-#743 := (= #753 0::Int)
-#742 := (* -1::Int 0::Int)
-#747 := (= #742 0::Int)
-#748 := [rewrite]: #747
-#745 := (= #753 #742)
-#740 := (= #780 0::Int)
-#741 := [rewrite]: #740
-#746 := [monotonicity #741]: #745
-#749 := [trans #746 #748]: #743
-#724 := [monotonicity #749]: #723
-#730 := [trans #724 #728]: #729
-#731 := [monotonicity #730]: #735
-#815 := (iff #568 #811)
-#655 := (or #676 #825)
-#812 := (iff #655 #811)
-#814 := [rewrite]: #812
-#657 := (iff #568 #655)
-#819 := (iff #468 #825)
-#818 := (iff #574 #572)
-#820 := (or false #572)
-#823 := (iff #820 #572)
-#817 := [rewrite]: #823
-#821 := (iff #574 #820)
-#830 := (iff #573 false)
-#831 := [rewrite]: #830
-#822 := [monotonicity #831]: #821
-#824 := [trans #822 #817]: #818
-#826 := [monotonicity #824]: #819
-#677 := (iff #567 #676)
-#829 := (iff #845 #844)
-#832 := (or #844 false)
-#833 := (iff #832 #844)
-#834 := [rewrite]: #833
-#827 := (iff #845 #832)
-#828 := [monotonicity #831]: #827
-#835 := [trans #828 #834]: #829
-#678 := [monotonicity #835]: #677
-#658 := [monotonicity #678 #826]: #657
-#813 := [trans #658 #814]: #815
-#701 := [monotonicity #813 #731 #719]: #720
-#721 := [monotonicity #701]: #726
-#694 := [trans #721 #661]: #692
-#559 := (iff #843 false)
-#560 := [rewrite]: #559
-#705 := [monotonicity #560 #694]: #703
-#697 := [trans #705 #707]: #717
-#683 := [trans #697 #681]: #682
-#689 := [monotonicity #683]: #688
-#691 := [trans #689 #675]: #688
-#687 := [quant-inst #9 #10]: #686
-#652 := [mp #687 #691]: #685
-#465 := [unit-resolution #652 #909]: #679
-#642 := (not #679)
-#643 := (or #642 #667 #757)
-#644 := [def-axiom]: #643
-#464 := [unit-resolution #644 #465]: #466
-#467 := [unit-resolution #464 #463]: #757
-#648 := (not #757)
-#910 := (or #648 #670)
-#911 := [th-lemma arith triangle-eq]: #910
-#912 := [unit-resolution #911 #467]: #670
-#671 := (>= #13 0::Int)
-#913 := (or #648 #671)
-#914 := [th-lemma arith triangle-eq]: #913
-#915 := [unit-resolution #914 #467]: #671
-#917 := [th-lemma arith eq-propagate -1 -1 #915 #912]: #916
-#929 := (= #9 #11)
-#862 := (div #9 1::Int)
-#848 := (* -1::Int #862)
-#849 := (+ #11 #848)
-#781 := (<= #849 0::Int)
-#571 := (= #849 0::Int)
-#793 := (or #811 #844)
-#794 := [def-axiom]: #793
-#918 := [unit-resolution #794 #475]: #811
-#699 := (div #852 -1::Int)
-#807 := (* -1::Int #699)
-#805 := (+ #11 #807)
-#708 := (= #805 0::Int)
-#704 := (ite #811 #571 #708)
-#542 := (or #847 #704)
-#846 := (= #11 0::Int)
-#714 := (ite #847 #846 #704)
-#36 := (f5 #35 #24)
-#896 := (pattern #36)
-#206 := (div #200 #203)
-#378 := (* -1::Int #206)
-#379 := (+ #36 #378)
-#380 := (= #379 0::Int)
-#46 := (div #35 #24)
-#375 := (* -1::Int #46)
-#376 := (+ #36 #375)
-#377 := (= #376 0::Int)
-#381 := (ite #342 #377 #380)
-#374 := (= #36 0::Int)
-#39 := (or #37 #38)
-#382 := (ite #39 #374 #381)
-#897 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #896) #382)
-#385 := (forall (vars (?v0 Int) (?v1 Int)) #382)
-#900 := (iff #385 #897)
-#898 := (iff #382 #382)
-#899 := [refl]: #898
-#901 := [quant-intro #899]: #900
-#345 := (ite #342 #46 #206)
-#348 := (ite #39 0::Int #345)
-#351 := (= #36 #348)
-#354 := (forall (vars (?v0 Int) (?v1 Int)) #351)
-#386 := (iff #354 #385)
-#383 := (iff #351 #382)
-#384 := [rewrite]: #383
-#387 := [quant-intro #384]: #386
-#248 := (ite #245 #46 #206)
-#251 := (ite #39 0::Int #248)
-#254 := (= #36 #251)
-#257 := (forall (vars (?v0 Int) (?v1 Int)) #254)
-#355 := (iff #257 #354)
-#352 := (iff #254 #351)
-#349 := (= #251 #348)
-#346 := (= #248 #345)
-#347 := [monotonicity #344]: #346
-#350 := [monotonicity #347]: #349
-#353 := [monotonicity #350]: #352
-#356 := [quant-intro #353]: #355
-#317 := (~ #257 #257)
-#330 := (~ #254 #254)
-#331 := [refl]: #330
-#318 := [nnf-pos #331]: #317
-#49 := (div #47 #48)
-#50 := (ite #45 #46 #49)
-#51 := (ite #39 0::Int #50)
-#52 := (= #36 #51)
-#53 := (forall (vars (?v0 Int) (?v1 Int)) #52)
-#260 := (iff #53 #257)
-#209 := (ite #196 #46 #206)
-#190 := (or #184 #187)
-#212 := (ite #190 0::Int #209)
-#215 := (= #36 #212)
-#218 := (forall (vars (?v0 Int) (?v1 Int)) #215)
-#258 := (iff #218 #257)
-#255 := (iff #215 #254)
-#252 := (= #212 #251)
-#249 := (= #209 #248)
-#250 := [monotonicity #247]: #249
-#225 := (iff #190 #39)
-#226 := [monotonicity #222 #224]: #225
-#253 := [monotonicity #226 #250]: #252
-#256 := [monotonicity #253]: #255
-#259 := [quant-intro #256]: #258
-#219 := (iff #53 #218)
-#216 := (iff #52 #215)
-#213 := (= #51 #212)
-#210 := (= #50 #209)
-#207 := (= #49 #206)
-#208 := [monotonicity #202 #205]: #207
-#211 := [monotonicity #198 #208]: #210
-#191 := (iff #39 #190)
-#192 := [monotonicity #186 #189]: #191
-#214 := [monotonicity #192 #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [quant-intro #217]: #219
-#261 := [trans #220 #259]: #260
-#183 := [asserted]: #53
-#262 := [mp #183 #261]: #257
-#332 := [mp~ #262 #318]: #257
-#357 := [mp #332 #356]: #354
-#388 := [mp #357 #387]: #385
-#902 := [mp #388 #901]: #897
-#809 := (not #897)
-#806 := (or #809 #714)
-#500 := (div #852 #516)
-#501 := (* -1::Int #500)
-#861 := (+ #11 #501)
-#859 := (= #861 0::Int)
-#842 := (ite #568 #571 #859)
-#557 := (or #847 #843)
-#558 := (ite #557 #846 #842)
-#810 := (or #809 #558)
-#799 := (iff #810 #806)
-#788 := (iff #806 #806)
-#790 := [rewrite]: #788
-#715 := (iff #558 #714)
-#712 := (iff #842 #704)
-#710 := (iff #859 #708)
-#808 := (= #861 #805)
-#709 := (= #501 #807)
-#700 := (= #500 #699)
-#659 := [monotonicity #698]: #700
-#804 := [monotonicity #659]: #709
-#693 := [monotonicity #804]: #808
-#711 := [monotonicity #693]: #710
-#713 := [monotonicity #813 #711]: #712
-#837 := (iff #557 #847)
-#838 := (or #847 false)
-#836 := (iff #838 #847)
-#840 := [rewrite]: #836
-#839 := (iff #557 #838)
-#554 := [monotonicity #560]: #839
-#841 := [trans #554 #840]: #837
-#716 := [monotonicity #841 #713]: #715
-#791 := [monotonicity #716]: #799
-#800 := [trans #791 #790]: #799
-#797 := [quant-inst #9 #10]: #810
-#801 := [mp #797 #800]: #806
-#536 := [unit-resolution #801 #902]: #714
-#762 := (not #714)
-#766 := (or #762 #847 #704)
-#767 := [def-axiom]: #766
-#543 := [unit-resolution #767 #536]: #542
-#919 := [unit-resolution #543 #474]: #704
-#795 := (not #811)
-#782 := (not #704)
-#787 := (or #782 #795 #571)
-#773 := [def-axiom]: #787
-#920 := [unit-resolution #773 #919 #918]: #571
-#777 := (not #571)
-#921 := (or #777 #781)
-#922 := [th-lemma arith triangle-eq]: #921
-#923 := [unit-resolution #922 #920]: #781
-#783 := (>= #849 0::Int)
-#498 := (or #777 #783)
-#499 := [th-lemma arith triangle-eq]: #498
-#924 := [unit-resolution #499 #920]: #783
-#606 := (+ #9 #848)
-#610 := (<= #606 0::Int)
-#605 := (= #606 0::Int)
-#1 := true
-#80 := [true-axiom]: true
-#563 := (or false #605)
-#555 := [th-lemma arith]: #563
-#564 := [unit-resolution #555 #80]: #605
-#488 := (not #605)
-#490 := (or #488 #610)
-#491 := [th-lemma arith triangle-eq]: #490
-#925 := [unit-resolution #491 #564]: #610
-#587 := (>= #606 0::Int)
-#926 := (or #488 #587)
-#927 := [th-lemma arith triangle-eq]: #926
-#928 := [unit-resolution #927 #564]: #587
-#930 := [th-lemma arith eq-propagate 1 1 -1 -1 #928 #925 #924 #923]: #929
-#934 := [trans #930 #917]: #933
-#936 := [monotonicity #934]: #935
-#937 := [trans #534 #936]: #91
-#94 := (not #91)
-#12 := (* #11 1::Int)
-#14 := (+ #12 #13)
-#15 := (f4 #14)
-#16 := (= f3 #15)
-#17 := (not #16)
-#95 := (iff #17 #94)
-#92 := (iff #16 #91)
-#89 := (= #15 #88)
-#86 := (= #14 #85)
-#83 := (= #12 #11)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#90 := [monotonicity #87]: #89
-#93 := [monotonicity #90]: #92
-#96 := [monotonicity #93]: #95
-#82 := [asserted]: #17
-#99 := [mp #82 #96]: #94
-#938 := [unit-resolution #99 #937]: false
-#939 := [lemma #938]: #847
-#975 := [symm #939]: #974
-#514 := (= #552 0::Int)
-#860 := (>= #552 0::Int)
-#664 := (or #718 #763)
-#666 := [def-axiom]: #664
-#471 := [unit-resolution #666 #939]: #718
-#476 := [unit-resolution #464 #471]: #757
-#940 := [unit-resolution #914 #476]: #671
-#798 := (>= #11 0::Int)
-#497 := (not #610)
-#565 := (not #798)
-#556 := [hypothesis]: #565
-#768 := (not #846)
-#566 := (or #768 #798)
-#533 := [th-lemma arith triangle-eq]: #566
-#535 := [unit-resolution #533 #556]: #768
-#527 := (or #763 #846)
-#764 := (or #762 #763 #846)
-#765 := [def-axiom]: #764
-#540 := [unit-resolution #765 #536]: #527
-#541 := [unit-resolution #540 #535]: #763
-#544 := [unit-resolution #543 #541]: #704
-#519 := (not #633)
-#520 := (iff #763 #519)
-#517 := (iff #847 #633)
-#545 := (= #462 f3)
-#528 := [symm #534]: #545
-#531 := [monotonicity #528]: #530
-#512 := [monotonicity #531]: #510
-#518 := [symm #512]: #517
-#521 := [monotonicity #518]: #520
-#522 := [mp #541 #521]: #519
-#523 := [unit-resolution #511 #522]: #572
-#507 := [unit-resolution #506 #541]: #655
-#505 := [unit-resolution #507 #523]: #676
-#508 := [unit-resolution #794 #505]: #811
-#496 := [unit-resolution #773 #508 #544]: #571
-#502 := [unit-resolution #499 #496]: #783
-#503 := (not #783)
-#478 := (or #497 #825 #798 #503)
-#482 := [th-lemma arith assign-bounds 1 1 -1]: #478
-#483 := [unit-resolution #482 #523 #502 #556]: #497
-#493 := [unit-resolution #491 #483 #564]: false
-#489 := [lemma #493]: #798
-#532 := (* -1::Int #552)
-#867 := (+ #13 #532)
-#869 := (+ #11 #867)
-#850 := (<= #869 0::Int)
-#526 := (= #869 0::Int)
-#547 := (>= #85 0::Int)
-#941 := (not #671)
-#942 := (or #547 #565 #941)
-#943 := [th-lemma arith assign-bounds -1 -1]: #942
-#944 := [unit-resolution #943 #940 #489]: #547
-#548 := (not #547)
-#537 := (or #526 #548)
-#106 := (= #24 #27)
-#131 := (or #106 #125)
-#884 := (forall (vars (?v0 Int)) (:pat #883) #131)
-#136 := (forall (vars (?v0 Int)) #131)
-#887 := (iff #136 #884)
-#885 := (iff #131 #131)
-#886 := [refl]: #885
-#888 := [quant-intro #886]: #887
-#313 := (~ #136 #136)
-#312 := (~ #131 #131)
-#309 := [refl]: #312
-#314 := [nnf-pos #309]: #313
-#28 := (= #27 #24)
-#25 := (<= 0::Int #24)
-#29 := (implies #25 #28)
-#30 := (forall (vars (?v0 Int)) #29)
-#139 := (iff #30 #136)
-#113 := (not #25)
-#114 := (or #113 #106)
-#119 := (forall (vars (?v0 Int)) #114)
-#137 := (iff #119 #136)
-#134 := (iff #114 #131)
-#128 := (or #125 #106)
-#132 := (iff #128 #131)
-#133 := [rewrite]: #132
-#129 := (iff #114 #128)
-#126 := (iff #113 #125)
-#122 := (iff #25 #124)
-#123 := [rewrite]: #122
-#127 := [monotonicity #123]: #126
-#130 := [monotonicity #127]: #129
-#135 := [trans #130 #133]: #134
-#138 := [quant-intro #135]: #137
-#120 := (iff #30 #119)
-#117 := (iff #29 #114)
-#110 := (implies #25 #106)
-#115 := (iff #110 #114)
-#116 := [rewrite]: #115
-#111 := (iff #29 #110)
-#108 := (iff #28 #106)
-#109 := [rewrite]: #108
-#112 := [monotonicity #109]: #111
-#118 := [trans #112 #116]: #117
-#121 := [quant-intro #118]: #120
-#140 := [trans #121 #138]: #139
-#105 := [asserted]: #30
-#141 := [mp #105 #140]: #136
-#310 := [mp~ #141 #314]: #136
-#889 := [mp #310 #888]: #884
-#871 := (not #884)
-#872 := (or #871 #526 #548)
-#549 := (= #85 #552)
-#553 := (or #549 #548)
-#873 := (or #871 #553)
-#525 := (iff #873 #872)
-#874 := (or #871 #537)
-#529 := (iff #874 #872)
-#865 := [rewrite]: #529
-#864 := (iff #873 #874)
-#538 := (iff #553 #537)
-#656 := (iff #549 #526)
-#863 := [rewrite]: #656
-#870 := [monotonicity #863]: #538
-#524 := [monotonicity #870]: #864
-#866 := [trans #524 #865]: #525
-#868 := [quant-inst #85]: #873
-#509 := [mp #868 #866]: #872
-#945 := [unit-resolution #509 #889]: #537
-#946 := [unit-resolution #945 #944]: #526
-#947 := (not #526)
-#948 := (or #947 #850)
-#949 := [th-lemma arith triangle-eq]: #948
-#950 := [unit-resolution #949 #946]: #850
-#951 := (not #850)
-#952 := (or #860 #941 #951 #565)
-#953 := [th-lemma arith assign-bounds -1 1 -1]: #952
-#954 := [unit-resolution #953 #950 #489 #940]: #860
-#858 := (<= #552 0::Int)
-#955 := [unit-resolution #911 #476]: #670
-#802 := (<= #11 0::Int)
-#956 := [unit-resolution #540 #939]: #846
-#957 := (or #768 #802)
-#958 := [th-lemma arith triangle-eq]: #957
-#959 := [unit-resolution #958 #956]: #802
-#513 := (>= #869 0::Int)
-#960 := (or #947 #513)
-#961 := [th-lemma arith triangle-eq]: #960
-#962 := [unit-resolution #961 #946]: #513
-#965 := (not #802)
-#964 := (not #513)
-#963 := (not #670)
-#966 := (or #858 #963 #964 #965)
-#967 := [th-lemma arith assign-bounds -1 1 -1]: #966
-#968 := [unit-resolution #967 #962 #959 #955]: #858
-#970 := (not #860)
-#969 := (not #858)
-#971 := (or #514 #969 #970)
-#972 := [th-lemma arith triangle-eq]: #971
-#973 := [unit-resolution #972 #968 #954]: #514
-#977 := [trans #973 #975]: #976
-#980 := [monotonicity #977]: #979
-#982 := [symm #980]: #981
-#986 := [trans #534 #982]: #985
-#987 := [trans #986 #984]: #91
-[unit-resolution #99 #987]: false
-unsat
-14ea837cc40eb6dd6a11b7a7e54b897ec75d15ed 873 0
-#2 := false
-decl f4 :: (-> Int S2)
-decl f7 :: (-> Int Int Int)
-#10 := 3::Int
-decl f6 :: (-> S2 Int)
-decl f3 :: S2
-#8 := f3
-#9 := (f6 f3)
-#13 := (f7 #9 3::Int)
-decl f5 :: (-> Int Int Int)
-#11 := (f5 #9 3::Int)
-#83 := (* 3::Int #11)
-#86 := (+ #83 #13)
-#89 := (f4 #86)
-#92 := (= f3 #89)
-#463 := (f4 #9)
-#1031 := (= #463 #89)
-#1029 := (= #89 #463)
-#1027 := (= #86 #9)
-#23 := 0::Int
-#1023 := (= 0::Int #9)
-#832 := (= #9 0::Int)
-#481 := (f6 #89)
-#554 := (= #86 #481)
-#943 := (not #554)
-#844 := (div #9 3::Int)
-#200 := -1::Int
-#848 := (* -1::Int #844)
-#845 := (+ #11 #848)
-#781 := (<= #845 0::Int)
-#849 := (= #845 0::Int)
-#840 := (<= #9 0::Int)
-#828 := (not #840)
-#559 := (>= #9 0::Int)
-#700 := (not #559)
-#806 := (or #700 #828)
-#594 := [hypothesis]: #700
-#671 := (f6 #463)
-#672 := (= #671 0::Int)
-#535 := (iff #672 #832)
-#558 := (= #671 #9)
-#596 := (= #9 #671)
-#548 := (= f3 #463)
-#18 := (:var 0 S2)
-#19 := (f6 #18)
-#877 := (pattern #19)
-#20 := (f4 #19)
-#99 := (= #18 #20)
-#878 := (forall (vars (?v0 S2)) (:pat #877) #99)
-#103 := (forall (vars (?v0 S2)) #99)
-#879 := (iff #103 #878)
-#881 := (iff #878 #878)
-#882 := [rewrite]: #881
-#880 := [rewrite]: #879
-#883 := [trans #880 #882]: #879
-#326 := (~ #103 #103)
-#324 := (~ #99 #99)
-#325 := [refl]: #324
-#327 := [nnf-pos #325]: #326
-#21 := (= #20 #18)
-#22 := (forall (vars (?v0 S2)) #21)
-#104 := (iff #22 #103)
-#101 := (iff #21 #99)
-#102 := [rewrite]: #101
-#105 := [quant-intro #102]: #104
-#98 := [asserted]: #22
-#108 := [mp #98 #105]: #103
-#312 := [mp~ #108 #327]: #103
-#884 := [mp #312 #883]: #878
-#541 := (not #878)
-#552 := (or #541 #548)
-#553 := [quant-inst #8]: #552
-#557 := [unit-resolution #553 #884]: #548
-#597 := [monotonicity #557]: #596
-#590 := [symm #597]: #558
-#498 := [monotonicity #590]: #535
-#656 := (or #559 #672)
-#24 := (:var 0 Int)
-#26 := (f4 #24)
-#885 := (pattern #26)
-#125 := (>= #24 0::Int)
-#27 := (f6 #26)
-#32 := (= #27 0::Int)
-#173 := (or #32 #125)
-#892 := (forall (vars (?v0 Int)) (:pat #885) #173)
-#178 := (forall (vars (?v0 Int)) #173)
-#895 := (iff #178 #892)
-#893 := (iff #173 #173)
-#894 := [refl]: #893
-#896 := [quant-intro #894]: #895
-#316 := (~ #178 #178)
-#328 := (~ #173 #173)
-#329 := [refl]: #328
-#317 := [nnf-pos #329]: #316
-#31 := (< #24 0::Int)
-#33 := (implies #31 #32)
-#34 := (forall (vars (?v0 Int)) #33)
-#181 := (iff #34 #178)
-#144 := (= 0::Int #27)
-#150 := (not #31)
-#151 := (or #150 #144)
-#156 := (forall (vars (?v0 Int)) #151)
-#179 := (iff #156 #178)
-#176 := (iff #151 #173)
-#170 := (or #125 #32)
-#174 := (iff #170 #173)
-#175 := [rewrite]: #174
-#171 := (iff #151 #170)
-#168 := (iff #144 #32)
-#169 := [rewrite]: #168
-#166 := (iff #150 #125)
-#126 := (not #125)
-#161 := (not #126)
-#164 := (iff #161 #125)
-#165 := [rewrite]: #164
-#162 := (iff #150 #161)
-#159 := (iff #31 #126)
-#160 := [rewrite]: #159
-#163 := [monotonicity #160]: #162
-#167 := [trans #163 #165]: #166
-#172 := [monotonicity #167 #169]: #171
-#177 := [trans #172 #175]: #176
-#180 := [quant-intro #177]: #179
-#157 := (iff #34 #156)
-#154 := (iff #33 #151)
-#147 := (implies #31 #144)
-#152 := (iff #147 #151)
-#153 := [rewrite]: #152
-#148 := (iff #33 #147)
-#145 := (iff #32 #144)
-#146 := [rewrite]: #145
-#149 := [monotonicity #146]: #148
-#155 := [trans #149 #153]: #154
-#158 := [quant-intro #155]: #157
-#182 := [trans #158 #180]: #181
-#143 := [asserted]: #34
-#183 := [mp #143 #182]: #178
-#330 := [mp~ #183 #317]: #178
-#897 := [mp #330 #896]: #892
-#859 := (not #892)
-#645 := (or #859 #559 #672)
-#673 := (or #672 #559)
-#646 := (or #859 #673)
-#648 := (iff #646 #645)
-#649 := (or #859 #656)
-#494 := (iff #649 #645)
-#652 := [rewrite]: #494
-#650 := (iff #646 #649)
-#674 := (iff #673 #656)
-#644 := [rewrite]: #674
-#651 := [monotonicity #644]: #650
-#653 := [trans #651 #652]: #648
-#647 := [quant-inst #9]: #646
-#632 := [mp #647 #653]: #645
-#546 := [unit-resolution #632 #897]: #656
-#595 := [unit-resolution #546 #594]: #672
-#500 := [mp #595 #498]: #832
-#755 := (not #832)
-#501 := (or #755 #559)
-#504 := [th-lemma arith triangle-eq]: #501
-#499 := [unit-resolution #504 #500 #594]: false
-#505 := [lemma #499]: #559
-#480 := [hypothesis]: #755
-#547 := (or #832 #828 #700)
-#530 := [th-lemma arith triangle-eq]: #547
-#489 := [unit-resolution #530 #480 #505]: #828
-#775 := (or #806 #840)
-#776 := [def-axiom]: #775
-#488 := [unit-resolution #776 #489]: #806
-#712 := -3::Int
-#469 := (* -1::Int #9)
-#714 := (div #469 -3::Int)
-#717 := (* -1::Int #714)
-#808 := (+ #11 #717)
-#801 := (= #808 0::Int)
-#792 := (ite #806 #849 #801)
-#563 := (or #832 #792)
-#839 := (= #11 0::Int)
-#804 := (ite #832 #839 #792)
-#35 := (:var 1 Int)
-#36 := (f5 #35 #24)
-#898 := (pattern #36)
-#204 := (* -1::Int #24)
-#201 := (* -1::Int #35)
-#207 := (div #201 #204)
-#379 := (* -1::Int #207)
-#380 := (+ #36 #379)
-#381 := (= #380 0::Int)
-#46 := (div #35 #24)
-#376 := (* -1::Int #46)
-#377 := (+ #36 #376)
-#378 := (= #377 0::Int)
-#239 := (>= #35 0::Int)
-#232 := (<= #24 0::Int)
-#339 := (or #232 #239)
-#340 := (not #339)
-#228 := (<= #35 0::Int)
-#337 := (or #228 #232)
-#338 := (not #337)
-#343 := (or #338 #340)
-#382 := (ite #343 #378 #381)
-#375 := (= #36 0::Int)
-#38 := (= #24 0::Int)
-#37 := (= #35 0::Int)
-#39 := (or #37 #38)
-#383 := (ite #39 #375 #382)
-#899 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #898) #383)
-#386 := (forall (vars (?v0 Int) (?v1 Int)) #383)
-#902 := (iff #386 #899)
-#900 := (iff #383 #383)
-#901 := [refl]: #900
-#903 := [quant-intro #901]: #902
-#346 := (ite #343 #46 #207)
-#349 := (ite #39 0::Int #346)
-#352 := (= #36 #349)
-#355 := (forall (vars (?v0 Int) (?v1 Int)) #352)
-#387 := (iff #355 #386)
-#384 := (iff #352 #383)
-#385 := [rewrite]: #384
-#388 := [quant-intro #385]: #387
-#240 := (not #239)
-#233 := (not #232)
-#243 := (and #233 #240)
-#229 := (not #228)
-#236 := (and #229 #233)
-#246 := (or #236 #243)
-#249 := (ite #246 #46 #207)
-#252 := (ite #39 0::Int #249)
-#255 := (= #36 #252)
-#258 := (forall (vars (?v0 Int) (?v1 Int)) #255)
-#356 := (iff #258 #355)
-#353 := (iff #255 #352)
-#350 := (= #252 #349)
-#347 := (= #249 #346)
-#344 := (iff #246 #343)
-#341 := (iff #243 #340)
-#342 := [rewrite]: #341
-#322 := (iff #236 #338)
-#323 := [rewrite]: #322
-#345 := [monotonicity #323 #342]: #344
-#348 := [monotonicity #345]: #347
-#351 := [monotonicity #348]: #350
-#354 := [monotonicity #351]: #353
-#357 := [quant-intro #354]: #356
-#318 := (~ #258 #258)
-#331 := (~ #255 #255)
-#332 := [refl]: #331
-#319 := [nnf-pos #332]: #318
-#48 := (- #24)
-#47 := (- #35)
-#49 := (div #47 #48)
-#41 := (< 0::Int #24)
-#43 := (< #35 0::Int)
-#44 := (and #43 #41)
-#40 := (< 0::Int #35)
-#42 := (and #40 #41)
-#45 := (or #42 #44)
-#50 := (ite #45 #46 #49)
-#51 := (ite #39 0::Int #50)
-#52 := (= #36 #51)
-#53 := (forall (vars (?v0 Int) (?v1 Int)) #52)
-#261 := (iff #53 #258)
-#194 := (and #41 #43)
-#197 := (or #42 #194)
-#210 := (ite #197 #46 #207)
-#188 := (= 0::Int #24)
-#185 := (= 0::Int #35)
-#191 := (or #185 #188)
-#213 := (ite #191 0::Int #210)
-#216 := (= #36 #213)
-#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
-#259 := (iff #219 #258)
-#256 := (iff #216 #255)
-#253 := (= #213 #252)
-#250 := (= #210 #249)
-#247 := (iff #197 #246)
-#244 := (iff #194 #243)
-#241 := (iff #43 #240)
-#242 := [rewrite]: #241
-#234 := (iff #41 #233)
-#235 := [rewrite]: #234
-#245 := [monotonicity #235 #242]: #244
-#237 := (iff #42 #236)
-#230 := (iff #40 #229)
-#231 := [rewrite]: #230
-#238 := [monotonicity #231 #235]: #237
-#248 := [monotonicity #238 #245]: #247
-#251 := [monotonicity #248]: #250
-#226 := (iff #191 #39)
-#224 := (iff #188 #38)
-#225 := [rewrite]: #224
-#222 := (iff #185 #37)
-#223 := [rewrite]: #222
-#227 := [monotonicity #223 #225]: #226
-#254 := [monotonicity #227 #251]: #253
-#257 := [monotonicity #254]: #256
-#260 := [quant-intro #257]: #259
-#220 := (iff #53 #219)
-#217 := (iff #52 #216)
-#214 := (= #51 #213)
-#211 := (= #50 #210)
-#208 := (= #49 #207)
-#205 := (= #48 #204)
-#206 := [rewrite]: #205
-#202 := (= #47 #201)
-#203 := [rewrite]: #202
-#209 := [monotonicity #203 #206]: #208
-#198 := (iff #45 #197)
-#195 := (iff #44 #194)
-#196 := [rewrite]: #195
+#157 := [monotonicity #152 #154]: #156
+#161 := [trans #157 #159]: #160
+#175 := [monotonicity #161 #172]: #174
+#187 := [monotonicity #175]: #186
+#190 := [monotonicity #187]: #189
+#183 := (= #108 #182)
+#180 := (= #102 #179)
+#177 := (= #99 #176)
+#178 := [monotonicity #175]: #177
+#181 := [monotonicity #178]: #180
+#184 := [monotonicity #181]: #183
+#193 := [monotonicity #184 #190]: #192
+#196 := [monotonicity #193]: #195
 #199 := [monotonicity #196]: #198
-#212 := [monotonicity #199 #209]: #211
-#192 := (iff #39 #191)
-#189 := (iff #38 #188)
-#190 := [rewrite]: #189
-#186 := (iff #37 #185)
-#187 := [rewrite]: #186
-#193 := [monotonicity #187 #190]: #192
-#215 := [monotonicity #193 #212]: #214
-#218 := [monotonicity #215]: #217
-#221 := [quant-intro #218]: #220
-#262 := [trans #221 #260]: #261
-#184 := [asserted]: #53
-#263 := [mp #184 #262]: #258
-#333 := [mp~ #263 #319]: #258
-#358 := [mp #333 #357]: #355
-#389 := [mp #358 #388]: #386
-#904 := [mp #389 #903]: #899
-#794 := (not #899)
-#795 := (or #794 #804)
-#576 := (* -1::Int 3::Int)
-#846 := (div #469 #576)
-#847 := (* -1::Int #846)
-#569 := (+ #11 #847)
-#570 := (= #569 0::Int)
-#560 := (<= 3::Int 0::Int)
-#561 := (or #560 #559)
-#562 := (not #561)
-#841 := (or #840 #560)
-#556 := (not #841)
-#838 := (or #556 #562)
-#842 := (ite #838 #849 #570)
-#843 := (= 3::Int 0::Int)
-#833 := (or #832 #843)
-#834 := (ite #833 #839 #842)
-#796 := (or #794 #834)
-#791 := (iff #796 #795)
-#782 := (iff #795 #795)
-#783 := [rewrite]: #782
-#800 := (iff #834 #804)
-#802 := (iff #842 #792)
-#793 := (iff #570 #801)
-#812 := (= #569 #808)
-#718 := (= #847 #717)
-#715 := (= #846 #714)
-#713 := (= #576 -3::Int)
-#706 := [rewrite]: #713
-#716 := [monotonicity #706]: #715
-#811 := [monotonicity #716]: #718
-#799 := [monotonicity #811]: #812
-#790 := [monotonicity #799]: #793
-#695 := (iff #838 #806)
-#661 := (or #828 #700)
-#807 := (iff #661 #806)
-#810 := [rewrite]: #807
-#809 := (iff #838 #661)
-#701 := (iff #562 #700)
-#815 := (iff #561 #559)
-#660 := (or false #559)
-#816 := (iff #660 #559)
-#817 := [rewrite]: #816
-#813 := (iff #561 #660)
-#822 := (iff #560 false)
-#823 := [rewrite]: #822
-#814 := [monotonicity #823]: #813
-#818 := [trans #814 #817]: #815
-#702 := [monotonicity #818]: #701
-#657 := (iff #556 #828)
-#827 := (iff #841 #840)
-#824 := (or #840 false)
-#820 := (iff #824 #840)
-#826 := [rewrite]: #820
-#825 := (iff #841 #824)
-#819 := [monotonicity #823]: #825
-#821 := [trans #819 #826]: #827
-#659 := [monotonicity #821]: #657
-#711 := [monotonicity #659 #702]: #809
-#710 := [trans #711 #810]: #695
-#803 := [monotonicity #710 #790]: #802
-#679 := (iff #833 #832)
-#835 := (or #832 false)
-#837 := (iff #835 #832)
-#678 := [rewrite]: #837
-#836 := (iff #833 #835)
-#829 := (iff #843 false)
-#830 := [rewrite]: #829
-#831 := [monotonicity #830]: #836
-#680 := [trans #831 #678]: #679
-#805 := [monotonicity #680 #803]: #800
-#798 := [monotonicity #805]: #791
-#785 := [trans #798 #783]: #791
-#797 := [quant-inst #9 #10]: #796
-#786 := [mp #797 #785]: #795
-#580 := [unit-resolution #786 #904]: #804
-#753 := (not #804)
-#758 := (or #753 #832 #792)
-#759 := [def-axiom]: #758
-#564 := [unit-resolution #759 #580]: #563
-#473 := [unit-resolution #564 #480]: #792
-#778 := (not #806)
-#766 := (not #792)
-#767 := (or #766 #778 #849)
-#768 := [def-axiom]: #767
-#470 := [unit-resolution #768 #473 #488]: #849
-#771 := (not #849)
-#471 := (or #771 #781)
-#946 := [th-lemma arith triangle-eq]: #471
-#947 := [unit-resolution #946 #470]: #781
-#777 := (mod #9 3::Int)
-#749 := (* -1::Int #777)
-#750 := (+ #13 #749)
-#675 := (<= #750 0::Int)
-#745 := (= #750 0::Int)
-#762 := (mod #469 -3::Int)
-#732 := (+ #13 #762)
-#734 := (= #732 0::Int)
-#739 := (ite #806 #745 #734)
-#949 := (or #832 #739)
-#724 := (= #13 0::Int)
-#741 := (ite #832 #724 #739)
-#54 := (f7 #35 #24)
-#905 := (pattern #54)
-#265 := (mod #201 #204)
-#395 := (+ #54 #265)
-#396 := (= #395 0::Int)
-#55 := (mod #35 #24)
-#392 := (* -1::Int #55)
-#393 := (+ #54 #392)
-#394 := (= #393 0::Int)
-#397 := (ite #343 #394 #396)
-#391 := (= #54 0::Int)
-#398 := (ite #37 #391 #397)
-#390 := (= #35 #54)
-#399 := (ite #38 #390 #398)
-#906 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #905) #399)
-#402 := (forall (vars (?v0 Int) (?v1 Int)) #399)
-#909 := (iff #402 #906)
-#907 := (iff #399 #399)
-#908 := [refl]: #907
-#910 := [quant-intro #908]: #909
-#271 := (* -1::Int #265)
-#359 := (ite #343 #55 #271)
-#362 := (ite #37 0::Int #359)
-#365 := (ite #38 #35 #362)
-#368 := (= #54 #365)
-#371 := (forall (vars (?v0 Int) (?v1 Int)) #368)
-#403 := (iff #371 #402)
-#400 := (iff #368 #399)
-#401 := [rewrite]: #400
-#404 := [quant-intro #401]: #403
-#291 := (ite #246 #55 #271)
-#294 := (ite #37 0::Int #291)
-#297 := (ite #38 #35 #294)
-#300 := (= #54 #297)
-#303 := (forall (vars (?v0 Int) (?v1 Int)) #300)
-#372 := (iff #303 #371)
-#369 := (iff #300 #368)
-#366 := (= #297 #365)
-#363 := (= #294 #362)
-#360 := (= #291 #359)
-#361 := [monotonicity #345]: #360
-#364 := [monotonicity #361]: #363
-#367 := [monotonicity #364]: #366
-#370 := [monotonicity #367]: #369
-#373 := [quant-intro #370]: #372
-#320 := (~ #303 #303)
-#334 := (~ #300 #300)
-#335 := [refl]: #334
-#321 := [nnf-pos #335]: #320
-#56 := (mod #47 #48)
-#57 := (- #56)
-#58 := (ite #45 #55 #57)
-#59 := (ite #37 0::Int #58)
-#60 := (ite #38 #35 #59)
-#61 := (= #54 #60)
-#62 := (forall (vars (?v0 Int) (?v1 Int)) #61)
-#306 := (iff #62 #303)
-#276 := (ite #197 #55 #271)
-#279 := (ite #185 0::Int #276)
-#282 := (ite #188 #35 #279)
-#285 := (= #54 #282)
-#288 := (forall (vars (?v0 Int) (?v1 Int)) #285)
-#304 := (iff #288 #303)
-#301 := (iff #285 #300)
-#298 := (= #282 #297)
-#295 := (= #279 #294)
-#292 := (= #276 #291)
-#293 := [monotonicity #248]: #292
-#296 := [monotonicity #223 #293]: #295
-#299 := [monotonicity #225 #296]: #298
-#302 := [monotonicity #299]: #301
-#305 := [quant-intro #302]: #304
-#289 := (iff #62 #288)
-#286 := (iff #61 #285)
-#283 := (= #60 #282)
-#280 := (= #59 #279)
-#277 := (= #58 #276)
-#274 := (= #57 #271)
-#268 := (- #265)
-#272 := (= #268 #271)
-#273 := [rewrite]: #272
-#269 := (= #57 #268)
-#266 := (= #56 #265)
-#267 := [monotonicity #203 #206]: #266
-#270 := [monotonicity #267]: #269
-#275 := [trans #270 #273]: #274
-#278 := [monotonicity #199 #275]: #277
-#281 := [monotonicity #187 #278]: #280
-#284 := [monotonicity #190 #281]: #283
-#287 := [monotonicity #284]: #286
-#290 := [quant-intro #287]: #289
-#307 := [trans #290 #305]: #306
-#264 := [asserted]: #62
-#308 := [mp #264 #307]: #303
-#336 := [mp~ #308 #321]: #303
-#374 := [mp #336 #373]: #371
-#405 := [mp #374 #404]: #402
-#911 := [mp #405 #910]: #906
-#704 := (not #906)
-#663 := (or #704 #741)
-#744 := (mod #469 #576)
-#747 := (+ #13 #744)
-#748 := (= #747 0::Int)
-#751 := (ite #838 #745 #748)
-#725 := (ite #832 #724 #751)
-#726 := (= #9 #13)
-#619 := (ite #843 #726 #725)
-#694 := (or #704 #619)
-#698 := (iff #694 #663)
-#707 := (iff #663 #663)
-#708 := [rewrite]: #707
-#729 := (iff #619 #741)
-#722 := (ite false #726 #741)
-#728 := (iff #722 #741)
-#723 := [rewrite]: #728
-#703 := (iff #619 #722)
-#721 := (iff #725 #741)
-#740 := (iff #751 #739)
-#735 := (iff #748 #734)
-#737 := (= #747 #732)
-#730 := (= #744 #762)
-#731 := [monotonicity #706]: #730
-#733 := [monotonicity #731]: #737
-#738 := [monotonicity #733]: #735
-#736 := [monotonicity #710 #738]: #740
-#667 := [monotonicity #736]: #721
-#727 := [monotonicity #830 #667]: #703
-#697 := [trans #727 #723]: #729
-#705 := [monotonicity #697]: #698
-#709 := [trans #705 #708]: #698
-#696 := [quant-inst #9 #10]: #694
-#719 := [mp #696 #709]: #663
-#948 := [unit-resolution #719 #911]: #741
-#693 := (not #741)
-#662 := (or #693 #832 #739)
-#664 := [def-axiom]: #662
-#950 := [unit-resolution #664 #948]: #949
-#951 := [unit-resolution #950 #480]: #739
-#683 := (not #739)
-#684 := (or #683 #778 #745)
-#685 := [def-axiom]: #684
-#952 := [unit-resolution #685 #951 #488]: #745
-#688 := (not #745)
-#953 := (or #688 #675)
-#954 := [th-lemma arith triangle-eq]: #953
-#955 := [unit-resolution #954 #952]: #675
-#761 := (>= #845 0::Int)
-#519 := (or #771 #761)
-#520 := [th-lemma arith triangle-eq]: #519
-#956 := [unit-resolution #520 #470]: #761
-#676 := (>= #750 0::Int)
-#957 := (or #688 #676)
-#958 := [th-lemma arith triangle-eq]: #957
-#959 := [unit-resolution #958 #952]: #676
-#916 := (not #781)
-#917 := (not #675)
-#523 := (not #761)
-#924 := (not #676)
-#944 := (or #943 #924 #523 #917 #916)
-#493 := (f4 #481)
-#937 := (= #493 #89)
-#495 := (= #89 #493)
-#478 := (or #541 #495)
-#482 := [quant-inst #89]: #478
-#466 := [unit-resolution #482 #884]: #495
-#938 := [symm #466]: #937
-#939 := (= f3 #493)
-#935 := (= #463 #493)
-#933 := (= #9 #481)
-#467 := [hypothesis]: #554
-#475 := (= #9 #86)
-#476 := (* -1::Int #86)
-#472 := (+ #9 #476)
-#464 := (>= #472 0::Int)
-#465 := [hypothesis]: #781
-#621 := (* -3::Int #844)
-#624 := (+ #749 #621)
-#625 := (+ #9 #624)
-#627 := (>= #625 0::Int)
-#620 := (= #625 0::Int)
-#1 := true
-#80 := [true-axiom]: true
-#598 := (or false #620)
-#583 := [th-lemma arith]: #598
-#584 := [unit-resolution #583 #80]: #620
-#506 := (not #620)
-#468 := (or #506 #627)
-#912 := [th-lemma arith triangle-eq]: #468
-#913 := [unit-resolution #912 #584]: #627
-#914 := [hypothesis]: #675
-#915 := (not #627)
-#918 := (or #464 #915 #916 #917)
-#919 := [th-lemma arith assign-bounds -1 3 1]: #918
-#920 := [unit-resolution #919 #914 #913 #465]: #464
-#477 := (<= #472 0::Int)
-#921 := [hypothesis]: #761
-#626 := (<= #625 0::Int)
-#508 := (or #506 #626)
-#509 := [th-lemma arith triangle-eq]: #508
-#922 := [unit-resolution #509 #584]: #626
-#923 := [hypothesis]: #676
-#522 := (not #626)
-#925 := (or #477 #522 #523 #924)
-#926 := [th-lemma arith assign-bounds -1 3 1]: #925
-#927 := [unit-resolution #926 #923 #922 #921]: #477
-#929 := (not #464)
-#928 := (not #477)
-#930 := (or #475 #928 #929)
-#931 := [th-lemma arith triangle-eq]: #930
-#932 := [unit-resolution #931 #927 #920]: #475
-#934 := [trans #932 #467]: #933
-#936 := [monotonicity #934]: #935
-#940 := [trans #557 #936]: #939
-#941 := [trans #940 #938]: #92
-#95 := (not #92)
-#12 := (* #11 3::Int)
-#14 := (+ #12 #13)
-#15 := (f4 #14)
-#16 := (= f3 #15)
-#17 := (not #16)
-#96 := (iff #17 #95)
-#93 := (iff #16 #92)
-#90 := (= #15 #89)
-#87 := (= #14 #86)
-#84 := (= #12 #83)
+#202 := [monotonicity #199]: #201
+#147 := (iff #37 #146)
+#144 := (iff #36 #143)
+#141 := (= #35 #140)
+#138 := (= #34 #137)
+#135 := (= #33 #127)
+#130 := (ite false #9 #127)
+#133 := (= #130 #127)
+#134 := [rewrite]: #133
+#131 := (= #33 #130)
+#128 := (= #32 #127)
+#125 := (= #31 #124)
+#122 := (= #30 #119)
+#116 := (- #113)
+#120 := (= #116 #119)
+#121 := [rewrite]: #120
+#117 := (= #30 #116)
+#114 := (= #29 #113)
+#94 := (= #23 -3::Int)
+#95 := [rewrite]: #94
+#91 := (= #22 #90)
+#92 := [rewrite]: #91
+#115 := [monotonicity #92 #95]: #114
+#118 := [monotonicity #115]: #117
+#123 := [trans #118 #121]: #122
+#87 := (iff #20 #86)
+#84 := (iff #19 #83)
 #85 := [rewrite]: #84
 #88 := [monotonicity #85]: #87
-#91 := [monotonicity #88]: #90
-#94 := [monotonicity #91]: #93
-#97 := [monotonicity #94]: #96
-#82 := [asserted]: #17
-#100 := [mp #82 #97]: #95
-#942 := [unit-resolution #100 #941]: false
-#945 := [lemma #942]: #944
-#960 := [unit-resolution #945 #959 #956 #955 #947]: #943
-#555 := (* -1::Int #481)
-#486 := (+ #86 #555)
-#487 := (<= #486 0::Int)
-#534 := (+ #13 #555)
-#869 := (+ #83 #534)
-#518 := (<= #869 0::Int)
-#871 := (= #869 0::Int)
-#549 := (>= #86 0::Int)
-#788 := (>= #11 0::Int)
-#600 := (>= #777 3::Int)
-#612 := (not #600)
-#585 := (or false #612)
-#587 := [th-lemma arith]: #585
-#586 := [unit-resolution #587 #80]: #612
-#588 := (not #788)
-#577 := [hypothesis]: #588
-#754 := (not #839)
-#578 := (or #754 #788)
-#579 := [th-lemma arith triangle-eq]: #578
-#571 := [unit-resolution #579 #577]: #754
-#581 := (or #755 #839)
-#756 := (or #753 #755 #839)
-#757 := [def-axiom]: #756
-#572 := [unit-resolution #757 #580]: #581
-#582 := [unit-resolution #572 #571]: #755
-#565 := [unit-resolution #564 #582]: #792
-#542 := (not #672)
-#543 := (iff #755 #542)
-#538 := (iff #832 #672)
-#566 := (= #463 f3)
-#567 := [symm #557]: #566
-#568 := [monotonicity #567]: #558
-#537 := [monotonicity #568]: #535
-#529 := [symm #537]: #538
-#544 := [monotonicity #529]: #543
-#545 := [mp #582 #544]: #542
-#536 := [unit-resolution #546 #545]: #559
-#532 := [unit-resolution #530 #582]: #661
-#533 := [unit-resolution #532 #536]: #828
-#512 := [unit-resolution #776 #533]: #806
-#514 := [unit-resolution #768 #512 #565]: #849
-#521 := [unit-resolution #520 #514]: #761
-#524 := (or #522 #700 #600 #788 #523)
-#513 := [th-lemma arith assign-bounds 1 1 3 -3]: #524
-#525 := [unit-resolution #513 #536 #521 #577 #586]: #522
-#507 := [unit-resolution #509 #525 #584]: false
-#510 := [lemma #507]: #788
-#720 := (>= #13 0::Int)
-#613 := (>= #777 0::Int)
-#961 := (or false #613)
-#962 := [th-lemma arith]: #961
-#963 := [unit-resolution #962 #80]: #613
-#964 := (not #613)
-#965 := (or #720 #964 #924)
-#966 := [th-lemma arith assign-bounds 1 1]: #965
-#967 := [unit-resolution #966 #959 #963]: #720
-#968 := (not #720)
-#969 := (or #549 #968 #588)
-#970 := [th-lemma arith assign-bounds 1 3]: #969
-#971 := [unit-resolution #970 #967 #510]: #549
-#550 := (not #549)
-#872 := (or #550 #871)
-#107 := (= #24 #27)
-#132 := (or #107 #126)
-#886 := (forall (vars (?v0 Int)) (:pat #885) #132)
-#137 := (forall (vars (?v0 Int)) #132)
-#889 := (iff #137 #886)
-#887 := (iff #132 #132)
-#888 := [refl]: #887
-#890 := [quant-intro #888]: #889
-#314 := (~ #137 #137)
-#313 := (~ #132 #132)
-#310 := [refl]: #313
-#315 := [nnf-pos #310]: #314
-#28 := (= #27 #24)
-#25 := (<= 0::Int #24)
-#29 := (implies #25 #28)
-#30 := (forall (vars (?v0 Int)) #29)
-#140 := (iff #30 #137)
-#114 := (not #25)
-#115 := (or #114 #107)
-#120 := (forall (vars (?v0 Int)) #115)
-#138 := (iff #120 #137)
-#135 := (iff #115 #132)
-#129 := (or #126 #107)
-#133 := (iff #129 #132)
-#134 := [rewrite]: #133
-#130 := (iff #115 #129)
-#127 := (iff #114 #126)
-#123 := (iff #25 #125)
-#124 := [rewrite]: #123
-#128 := [monotonicity #124]: #127
-#131 := [monotonicity #128]: #130
-#136 := [trans #131 #134]: #135
-#139 := [quant-intro #136]: #138
-#121 := (iff #30 #120)
-#118 := (iff #29 #115)
-#111 := (implies #25 #107)
-#116 := (iff #111 #115)
-#117 := [rewrite]: #116
-#112 := (iff #29 #111)
-#109 := (iff #28 #107)
+#126 := [monotonicity #88 #123]: #125
+#129 := [monotonicity #126]: #128
+#74 := (iff #13 false)
+#75 := [rewrite]: #74
+#132 := [monotonicity #75 #129]: #131
+#136 := [trans #132 #134]: #135
+#111 := (= #27 #108)
+#105 := (* #102 3::Int)
+#109 := (= #105 #108)
 #110 := [rewrite]: #109
-#113 := [monotonicity #110]: #112
-#119 := [trans #113 #117]: #118
-#122 := [quant-intro #119]: #121
-#141 := [trans #122 #139]: #140
-#106 := [asserted]: #30
-#142 := [mp #106 #141]: #137
-#311 := [mp~ #142 #315]: #137
-#891 := [mp #311 #890]: #886
-#876 := (not #886)
-#866 := (or #876 #550 #871)
-#551 := (or #554 #550)
-#526 := (or #876 #551)
-#515 := (iff #526 #866)
-#867 := (or #876 #872)
-#511 := (iff #867 #866)
-#852 := [rewrite]: #511
-#527 := (iff #526 #867)
-#875 := (iff #551 #872)
-#865 := (or #871 #550)
-#873 := (iff #865 #872)
-#874 := [rewrite]: #873
-#539 := (iff #551 #865)
-#528 := (iff #554 #871)
-#658 := [rewrite]: #528
-#540 := [monotonicity #658]: #539
-#870 := [trans #540 #874]: #875
-#868 := [monotonicity #870]: #527
-#516 := [trans #868 #852]: #515
-#531 := [quant-inst #86]: #526
-#517 := [mp #531 #516]: #866
-#972 := [unit-resolution #517 #891]: #872
-#973 := [unit-resolution #972 #971]: #871
-#974 := (not #871)
-#975 := (or #974 #518)
-#976 := [th-lemma arith triangle-eq]: #975
-#977 := [unit-resolution #976 #973]: #518
-#978 := (not #518)
-#979 := (or #487 #978)
-#980 := [th-lemma arith assign-bounds -1]: #979
-#981 := [unit-resolution #980 #977]: #487
-#474 := (>= #486 0::Int)
-#854 := (>= #869 0::Int)
-#982 := (or #974 #854)
-#983 := [th-lemma arith triangle-eq]: #982
-#984 := [unit-resolution #983 #973]: #854
-#985 := (not #854)
-#986 := (or #474 #985)
-#987 := [th-lemma arith assign-bounds -1]: #986
-#988 := [unit-resolution #987 #984]: #474
-#990 := (not #474)
-#989 := (not #487)
-#991 := (or #554 #989 #990)
-#992 := [th-lemma arith triangle-eq]: #991
-#993 := [unit-resolution #992 #988 #981 #960]: false
-#994 := [lemma #993]: #832
-#1024 := [symm #994]: #1023
-#1025 := (= #86 0::Int)
-#855 := (= #481 0::Int)
-#575 := (>= #481 0::Int)
-#479 := (or #755 #724)
-#654 := (or #693 #755 #724)
-#655 := [def-axiom]: #654
-#484 := [unit-resolution #655 #948]: #479
-#485 := [unit-resolution #484 #994]: #724
-#665 := (not #724)
-#490 := (or #665 #720)
-#492 := [th-lemma arith triangle-eq]: #490
-#995 := [unit-resolution #492 #485]: #720
-#996 := [unit-resolution #970 #995 #510]: #549
-#997 := [unit-resolution #972 #996]: #871
-#998 := [unit-resolution #976 #997]: #518
-#999 := (or #575 #968 #978 #588)
-#1000 := [th-lemma arith assign-bounds 1 1 3]: #999
-#1001 := [unit-resolution #1000 #998 #510 #995]: #575
-#574 := (<= #481 0::Int)
-#699 := (<= #13 0::Int)
-#1002 := (or #665 #699)
-#1003 := [th-lemma arith triangle-eq]: #1002
-#1004 := [unit-resolution #1003 #485]: #699
-#787 := (<= #11 0::Int)
-#1005 := [unit-resolution #572 #994]: #839
-#1006 := (or #754 #787)
-#1007 := [th-lemma arith triangle-eq]: #1006
-#1008 := [unit-resolution #1007 #1005]: #787
-#1009 := [unit-resolution #983 #997]: #854
-#1011 := (not #787)
-#1010 := (not #699)
-#1012 := (or #574 #1010 #985 #1011)
-#1013 := [th-lemma arith assign-bounds -1 1 -3]: #1012
-#1014 := [unit-resolution #1013 #1009 #1008 #1004]: #574
-#1016 := (not #575)
-#1015 := (not #574)
-#1017 := (or #855 #1015 #1016)
-#1018 := [th-lemma arith triangle-eq]: #1017
-#1019 := [unit-resolution #1018 #1014 #1001]: #855
-#1020 := [unit-resolution #980 #998]: #487
-#1021 := [unit-resolution #987 #1009]: #474
-#1022 := [unit-resolution #992 #1021 #1020]: #554
-#1026 := [trans #1022 #1019]: #1025
-#1028 := [trans #1026 #1024]: #1027
-#1030 := [monotonicity #1028]: #1029
-#1032 := [symm #1030]: #1031
-#1033 := [trans #557 #1032]: #92
-[unit-resolution #100 #1033]: false
+#106 := (= #27 #105)
+#103 := (= #26 #102)
+#100 := (= #25 #99)
+#97 := (= #24 #96)
+#98 := [monotonicity #92 #95]: #97
+#101 := [monotonicity #88 #98]: #100
+#81 := (iff #14 #11)
+#76 := (or #11 false)
+#79 := (iff #76 #11)
+#80 := [rewrite]: #79
+#77 := (iff #14 #76)
+#78 := [monotonicity #75]: #77
+#82 := [trans #78 #80]: #81
+#104 := [monotonicity #82 #101]: #103
+#107 := [monotonicity #104]: #106
+#112 := [trans #107 #110]: #111
+#139 := [monotonicity #112 #136]: #138
+#142 := [monotonicity #139]: #141
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#204 := [trans #148 #202]: #203
+#73 := [asserted]: #37
+#205 := [mp #73 #204]: #200
+#695 := [unit-resolution #205 #703]: false
+#692 := [lemma #695]: #430
+#441 := (or #11 #450)
+#442 := [def-axiom]: #441
+#598 := [unit-resolution #442 #692]: #450
+#365 := (= #21 #176)
+#737 := (f5 #413)
+#738 := (= #737 0::Int)
+#632 := (not #738)
+#633 := (iff #430 #632)
+#628 := (iff #11 #738)
+#626 := (iff #738 #11)
+#647 := (= #737 #9)
+#651 := (= #413 f3)
+#652 := [symm #620]: #651
+#653 := [monotonicity #652]: #647
+#627 := [monotonicity #653]: #626
+#521 := [symm #627]: #628
+#634 := [monotonicity #521]: #633
+#639 := [mp #692 #634]: #632
+#739 := (or #162 #738)
+#43 := (:var 0 Int)
+#45 := (f4 #43)
+#787 := (pattern #45)
+#231 := (>= #43 0::Int)
+#46 := (f5 #45)
+#51 := (= #46 0::Int)
+#280 := (or #51 #231)
+#794 := (forall (vars (?v0 Int)) (:pat #787) #280)
+#285 := (forall (vars (?v0 Int)) #280)
+#797 := (iff #285 #794)
+#795 := (iff #280 #280)
+#796 := [refl]: #795
+#798 := [quant-intro #796]: #797
+#298 := (~ #285 #285)
+#306 := (~ #280 #280)
+#307 := [refl]: #306
+#299 := [nnf-pos #307]: #298
+#50 := (< #43 0::Int)
+#52 := (implies #50 #51)
+#53 := (forall (vars (?v0 Int)) #52)
+#288 := (iff #53 #285)
+#251 := (= 0::Int #46)
+#257 := (not #50)
+#258 := (or #257 #251)
+#263 := (forall (vars (?v0 Int)) #258)
+#286 := (iff #263 #285)
+#283 := (iff #258 #280)
+#277 := (or #231 #51)
+#281 := (iff #277 #280)
+#282 := [rewrite]: #281
+#278 := (iff #258 #277)
+#275 := (iff #251 #51)
+#276 := [rewrite]: #275
+#273 := (iff #257 #231)
+#233 := (not #231)
+#268 := (not #233)
+#271 := (iff #268 #231)
+#272 := [rewrite]: #271
+#269 := (iff #257 #268)
+#266 := (iff #50 #233)
+#267 := [rewrite]: #266
+#270 := [monotonicity #267]: #269
+#274 := [trans #270 #272]: #273
+#279 := [monotonicity #274 #276]: #278
+#284 := [trans #279 #282]: #283
+#287 := [quant-intro #284]: #286
+#264 := (iff #53 #263)
+#261 := (iff #52 #258)
+#254 := (implies #50 #251)
+#259 := (iff #254 #258)
+#260 := [rewrite]: #259
+#255 := (iff #52 #254)
+#252 := (iff #51 #251)
+#253 := [rewrite]: #252
+#256 := [monotonicity #253]: #255
+#262 := [trans #256 #260]: #261
+#265 := [quant-intro #262]: #264
+#289 := [trans #265 #287]: #288
+#250 := [asserted]: #53
+#290 := [mp #250 #289]: #285
+#308 := [mp~ #290 #299]: #285
+#799 := [mp #308 #798]: #794
+#463 := (not #794)
+#582 := (or #463 #162 #738)
+#733 := (or #738 #162)
+#724 := (or #463 #733)
+#729 := (iff #724 #582)
+#726 := (or #463 #739)
+#722 := (iff #726 #582)
+#728 := [rewrite]: #722
+#727 := (iff #724 #726)
+#580 := (iff #733 #739)
+#581 := [rewrite]: #580
+#721 := [monotonicity #581]: #727
+#723 := [trans #721 #728]: #729
+#725 := [quant-inst #9]: #724
+#730 := [mp #725 #723]: #582
+#635 := [unit-resolution #730 #799]: #739
+#636 := [unit-resolution #635 #639]: #162
+#637 := (or #11 #150 #163)
+#640 := [th-lemma arith triangle-eq]: #637
+#641 := [unit-resolution #640 #692]: #173
+#642 := [unit-resolution #641 #636]: #150
+#452 := (or #173 #149)
+#443 := [def-axiom]: #452
+#638 := [unit-resolution #443 #642]: #173
+#383 := (not #173)
+#457 := (or #383 #365)
+#436 := [def-axiom]: #457
+#600 := [unit-resolution #436 #638]: #365
+#607 := [trans #600 #598]: #659
+#609 := (not #659)
+#610 := (or #609 #656)
+#611 := [th-lemma arith triangle-eq]: #610
+#621 := [unit-resolution #611 #607]: #656
+#662 := (>= #661 0::Int)
+#589 := (or #609 #662)
+#590 := [th-lemma arith triangle-eq]: #589
+#591 := [unit-resolution #590 #607]: #662
+#644 := (* -1::Int #188)
+#645 := (+ #28 #644)
+#646 := (<= #645 0::Int)
+#648 := (= #28 #188)
+#775 := (= #185 #188)
+#429 := (or #11 #775)
+#770 := [def-axiom]: #429
+#650 := [unit-resolution #770 #692]: #775
+#776 := (= #28 #185)
+#772 := (or #383 #776)
+#778 := [def-axiom]: #772
+#643 := [unit-resolution #778 #638]: #776
+#623 := [trans #643 #650]: #648
+#569 := (not #648)
+#624 := (or #569 #646)
+#605 := [th-lemma arith triangle-eq]: #624
+#629 := [unit-resolution #605 #623]: #646
+#649 := (>= #645 0::Int)
+#592 := (or #569 #649)
+#593 := [th-lemma arith triangle-eq]: #592
+#594 := [unit-resolution #593 #623]: #649
+#595 := [th-lemma arith eq-propagate 1 1 3 3 1 1 #594 #629 #591 #621 #588 #596]: #579
+#556 := [symm #595]: #618
+#557 := [monotonicity #556]: #713
+#564 := [symm #557]: #714
+#566 := [trans #620 #564]: #197
+[unit-resolution #205 #566]: false
 unsat
 34a7ceb02d535a80474ebf3499258caaaf0b3c6d 74 0
 #2 := false
@@ -26439,16909 +21415,6734 @@
 #33 := [asserted]: #13
 [mp #33 #49]: false
 unsat
-9ce15ee2c485c15c28a4c003e8c335d04c1523a1 254 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#13 := (:var 0 Int)
-#12 := (:var 1 Int)
-#14 := (f3 #12 #13)
-#749 := (pattern #14)
+c3a19f1e9eadfa9e1e60ed3204d9afca1d3962d0 64 0
+#2 := false
 #8 := 0::Int
-#87 := -1::Int
-#91 := (* -1::Int #13)
-#88 := (* -1::Int #12)
-#94 := (div #88 #91)
-#251 := (* -1::Int #94)
-#252 := (+ #14 #251)
-#253 := (= #252 0::Int)
-#24 := (div #12 #13)
-#248 := (* -1::Int #24)
-#249 := (+ #14 #248)
-#250 := (= #249 0::Int)
-#126 := (>= #12 0::Int)
-#119 := (<= #13 0::Int)
-#211 := (or #119 #126)
-#212 := (not #211)
-#115 := (<= #12 0::Int)
-#209 := (or #115 #119)
-#210 := (not #209)
-#215 := (or #210 #212)
-#254 := (ite #215 #250 #253)
-#247 := (= #14 0::Int)
-#16 := (= #13 0::Int)
-#15 := (= #12 0::Int)
-#17 := (or #15 #16)
-#255 := (ite #17 #247 #254)
-#750 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #749) #255)
-#258 := (forall (vars (?v0 Int) (?v1 Int)) #255)
-#753 := (iff #258 #750)
-#751 := (iff #255 #255)
-#752 := [refl]: #751
-#754 := [quant-intro #752]: #753
-#218 := (ite #215 #24 #94)
-#221 := (ite #17 0::Int #218)
-#224 := (= #14 #221)
-#227 := (forall (vars (?v0 Int) (?v1 Int)) #224)
-#259 := (iff #227 #258)
-#256 := (iff #224 #255)
-#257 := [rewrite]: #256
-#260 := [quant-intro #257]: #259
-#127 := (not #126)
-#120 := (not #119)
-#130 := (and #120 #127)
-#116 := (not #115)
-#123 := (and #116 #120)
-#133 := (or #123 #130)
-#136 := (ite #133 #24 #94)
-#139 := (ite #17 0::Int #136)
-#142 := (= #14 #139)
-#145 := (forall (vars (?v0 Int) (?v1 Int)) #142)
-#228 := (iff #145 #227)
-#225 := (iff #142 #224)
-#222 := (= #139 #221)
-#219 := (= #136 #218)
-#216 := (iff #133 #215)
-#213 := (iff #130 #212)
-#214 := [rewrite]: #213
-#203 := (iff #123 #210)
-#204 := [rewrite]: #203
-#217 := [monotonicity #204 #214]: #216
-#220 := [monotonicity #217]: #219
-#223 := [monotonicity #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [quant-intro #226]: #228
-#207 := (~ #145 #145)
-#205 := (~ #142 #142)
-#206 := [refl]: #205
-#208 := [nnf-pos #206]: #207
-#26 := (- #13)
-#25 := (- #12)
-#27 := (div #25 #26)
-#19 := (< 0::Int #13)
-#21 := (< #12 0::Int)
-#22 := (and #21 #19)
-#18 := (< 0::Int #12)
-#20 := (and #18 #19)
-#23 := (or #20 #22)
-#28 := (ite #23 #24 #27)
-#29 := (ite #17 0::Int #28)
-#30 := (= #14 #29)
-#31 := (forall (vars (?v0 Int) (?v1 Int)) #30)
-#148 := (iff #31 #145)
-#81 := (and #19 #21)
-#84 := (or #20 #81)
-#97 := (ite #84 #24 #94)
-#75 := (= 0::Int #13)
-#72 := (= 0::Int #12)
-#78 := (or #72 #75)
-#100 := (ite #78 0::Int #97)
-#103 := (= #14 #100)
-#106 := (forall (vars (?v0 Int) (?v1 Int)) #103)
-#146 := (iff #106 #145)
-#143 := (iff #103 #142)
-#140 := (= #100 #139)
-#137 := (= #97 #136)
-#134 := (iff #84 #133)
-#131 := (iff #81 #130)
-#128 := (iff #21 #127)
-#129 := [rewrite]: #128
-#121 := (iff #19 #120)
-#122 := [rewrite]: #121
-#132 := [monotonicity #122 #129]: #131
-#124 := (iff #20 #123)
-#117 := (iff #18 #116)
-#118 := [rewrite]: #117
-#125 := [monotonicity #118 #122]: #124
-#135 := [monotonicity #125 #132]: #134
-#138 := [monotonicity #135]: #137
-#113 := (iff #78 #17)
-#111 := (iff #75 #16)
-#112 := [rewrite]: #111
-#109 := (iff #72 #15)
-#110 := [rewrite]: #109
-#114 := [monotonicity #110 #112]: #113
-#141 := [monotonicity #114 #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [quant-intro #144]: #146
-#107 := (iff #31 #106)
-#104 := (iff #30 #103)
-#101 := (= #29 #100)
-#98 := (= #28 #97)
-#95 := (= #27 #94)
-#92 := (= #26 #91)
-#93 := [rewrite]: #92
-#89 := (= #25 #88)
-#90 := [rewrite]: #89
-#96 := [monotonicity #90 #93]: #95
-#85 := (iff #23 #84)
-#82 := (iff #22 #81)
-#83 := [rewrite]: #82
-#86 := [monotonicity #83]: #85
-#99 := [monotonicity #86 #96]: #98
-#79 := (iff #17 #78)
-#76 := (iff #16 #75)
-#77 := [rewrite]: #76
-#73 := (iff #15 #72)
+#15 := (- 0::Int)
+#16 := (div #15 #15)
+#14 := (div 0::Int 0::Int)
+#11 := (< 0::Int 0::Int)
+#12 := (and #11 #11)
+#13 := (or #12 #12)
+#17 := (ite #13 #14 #16)
+#9 := (= 0::Int 0::Int)
+#10 := (or #9 #9)
+#18 := (ite #10 0::Int #17)
+#19 := (= #18 0::Int)
+#20 := (not #19)
+#85 := (iff #20 false)
+#1 := true
+#80 := (not true)
+#83 := (iff #80 false)
+#84 := [rewrite]: #83
+#81 := (iff #20 #80)
+#78 := (iff #19 true)
+#41 := (iff #9 true)
+#42 := [rewrite]: #41
+#76 := (iff #19 #9)
+#70 := (ite true 0::Int #14)
+#73 := (= #70 0::Int)
 #74 := [rewrite]: #73
-#80 := [monotonicity #74 #77]: #79
-#102 := [monotonicity #80 #99]: #101
-#105 := [monotonicity #102]: #104
-#108 := [quant-intro #105]: #107
-#149 := [trans #108 #147]: #148
-#71 := [asserted]: #31
-#150 := [mp #71 #149]: #145
-#199 := [mp~ #150 #208]: #145
-#230 := [mp #199 #229]: #227
-#261 := [mp #230 #260]: #258
-#755 := [mp #261 #754]: #750
-#9 := (f3 0::Int 0::Int)
-#10 := (= #9 0::Int)
-#11 := (not #10)
-#60 := [asserted]: #11
-#707 := (not #750)
-#708 := (or #707 #10)
-#335 := (* -1::Int 0::Int)
-#420 := (div #335 #335)
-#421 := (* -1::Int #420)
-#422 := (+ #9 #421)
-#413 := (= #422 0::Int)
-#424 := (div 0::Int 0::Int)
-#425 := (* -1::Int #424)
-#353 := (+ #9 #425)
-#426 := (= #353 0::Int)
-#423 := (>= 0::Int 0::Int)
-#427 := (<= 0::Int 0::Int)
-#406 := (or #427 #423)
-#741 := (not #406)
-#743 := (or #427 #427)
-#400 := (not #743)
-#530 := (or #400 #741)
-#737 := (ite #530 #426 #413)
-#411 := (= 0::Int 0::Int)
-#412 := (or #411 #411)
-#744 := (ite #412 #10 #737)
-#703 := (or #707 #744)
-#550 := (iff #703 #708)
-#552 := (iff #708 #708)
-#694 := [rewrite]: #552
-#701 := (iff #744 #10)
-#1 := true
-#711 := (ite true #10 #426)
-#705 := (iff #711 #10)
-#706 := [rewrite]: #705
-#715 := (iff #744 #711)
-#710 := (iff #737 #426)
-#433 := (ite false #426 #426)
-#713 := (iff #433 #426)
-#428 := [rewrite]: #713
-#434 := (iff #737 #433)
-#431 := (iff #413 #426)
-#717 := (= #422 #353)
-#716 := (= #421 #425)
-#441 := (= #420 #424)
-#718 := (= #335 0::Int)
-#719 := [rewrite]: #718
-#442 := [monotonicity #719 #719]: #441
-#720 := [monotonicity #442]: #716
-#721 := [monotonicity #720]: #717
-#432 := [monotonicity #721]: #431
-#448 := (iff #530 false)
-#722 := (or false false)
-#446 := (iff #722 false)
-#447 := [rewrite]: #446
-#723 := (iff #530 #722)
-#733 := (iff #741 false)
-#389 := (not true)
-#727 := (iff #389 false)
-#728 := [rewrite]: #727
-#375 := (iff #741 #389)
-#734 := (iff #406 true)
-#747 := (or true true)
-#738 := (iff #747 true)
-#398 := [rewrite]: #738
-#369 := (iff #406 #747)
-#725 := (iff #423 true)
-#731 := [rewrite]: #725
-#399 := (iff #427 true)
-#740 := [rewrite]: #399
-#732 := [monotonicity #740 #731]: #369
-#374 := [trans #732 #398]: #734
-#735 := [monotonicity #374]: #375
-#736 := [trans #735 #728]: #733
-#729 := (iff #400 false)
-#390 := (iff #400 #389)
-#387 := (iff #743 true)
-#383 := (iff #743 #747)
-#724 := [monotonicity #740 #740]: #383
-#388 := [trans #724 #398]: #387
-#726 := [monotonicity #388]: #390
-#730 := [trans #726 #728]: #729
-#445 := [monotonicity #730 #736]: #723
-#341 := [trans #445 #447]: #448
-#712 := [monotonicity #341 #432]: #434
-#714 := [trans #712 #428]: #710
-#403 := (iff #412 true)
-#742 := (iff #412 #747)
-#745 := (iff #411 true)
-#746 := [rewrite]: #745
-#748 := [monotonicity #746 #746]: #742
-#739 := [trans #748 #398]: #403
-#704 := [monotonicity #739 #714]: #715
-#702 := [trans #704 #706]: #701
-#551 := [monotonicity #702]: #550
-#695 := [trans #551 #694]: #550
-#709 := [quant-inst #8 #8]: #703
-#696 := [mp #709 #695]: #708
-[unit-resolution #696 #60 #755]: false
-unsat
-8c864635f2131bf56f7aae6736c04969e8015d95 267 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#14 := (:var 0 Int)
-#13 := (:var 1 Int)
-#15 := (f3 #13 #14)
-#750 := (pattern #15)
-#9 := 0::Int
-#88 := -1::Int
-#92 := (* -1::Int #14)
-#89 := (* -1::Int #13)
-#95 := (div #89 #92)
-#252 := (* -1::Int #95)
-#253 := (+ #15 #252)
-#254 := (= #253 0::Int)
-#25 := (div #13 #14)
-#249 := (* -1::Int #25)
-#250 := (+ #15 #249)
-#251 := (= #250 0::Int)
-#127 := (>= #13 0::Int)
-#120 := (<= #14 0::Int)
-#212 := (or #120 #127)
-#213 := (not #212)
-#116 := (<= #13 0::Int)
-#210 := (or #116 #120)
-#211 := (not #210)
-#216 := (or #211 #213)
-#255 := (ite #216 #251 #254)
-#248 := (= #15 0::Int)
-#17 := (= #14 0::Int)
-#16 := (= #13 0::Int)
-#18 := (or #16 #17)
-#256 := (ite #18 #248 #255)
-#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #256)
-#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
-#754 := (iff #259 #751)
-#752 := (iff #256 #256)
-#753 := [refl]: #752
-#755 := [quant-intro #753]: #754
-#219 := (ite #216 #25 #95)
-#222 := (ite #18 0::Int #219)
-#225 := (= #15 #222)
-#228 := (forall (vars (?v0 Int) (?v1 Int)) #225)
-#260 := (iff #228 #259)
-#257 := (iff #225 #256)
-#258 := [rewrite]: #257
-#261 := [quant-intro #258]: #260
-#128 := (not #127)
-#121 := (not #120)
-#131 := (and #121 #128)
-#117 := (not #116)
-#124 := (and #117 #121)
-#134 := (or #124 #131)
-#137 := (ite #134 #25 #95)
-#140 := (ite #18 0::Int #137)
-#143 := (= #15 #140)
-#146 := (forall (vars (?v0 Int) (?v1 Int)) #143)
-#229 := (iff #146 #228)
-#226 := (iff #143 #225)
-#223 := (= #140 #222)
-#220 := (= #137 #219)
-#217 := (iff #134 #216)
-#214 := (iff #131 #213)
-#215 := [rewrite]: #214
-#204 := (iff #124 #211)
-#205 := [rewrite]: #204
-#218 := [monotonicity #205 #215]: #217
-#221 := [monotonicity #218]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [quant-intro #227]: #229
-#208 := (~ #146 #146)
-#206 := (~ #143 #143)
-#207 := [refl]: #206
-#209 := [nnf-pos #207]: #208
-#27 := (- #14)
-#26 := (- #13)
-#28 := (div #26 #27)
-#20 := (< 0::Int #14)
-#22 := (< #13 0::Int)
-#23 := (and #22 #20)
-#19 := (< 0::Int #13)
-#21 := (and #19 #20)
-#24 := (or #21 #23)
-#29 := (ite #24 #25 #28)
-#30 := (ite #18 0::Int #29)
-#31 := (= #15 #30)
-#32 := (forall (vars (?v0 Int) (?v1 Int)) #31)
-#149 := (iff #32 #146)
-#82 := (and #20 #22)
-#85 := (or #21 #82)
-#98 := (ite #85 #25 #95)
-#76 := (= 0::Int #14)
-#73 := (= 0::Int #13)
-#79 := (or #73 #76)
-#101 := (ite #79 0::Int #98)
-#104 := (= #15 #101)
-#107 := (forall (vars (?v0 Int) (?v1 Int)) #104)
-#147 := (iff #107 #146)
-#144 := (iff #104 #143)
-#141 := (= #101 #140)
-#138 := (= #98 #137)
-#135 := (iff #85 #134)
-#132 := (iff #82 #131)
-#129 := (iff #22 #128)
-#130 := [rewrite]: #129
-#122 := (iff #20 #121)
-#123 := [rewrite]: #122
-#133 := [monotonicity #123 #130]: #132
-#125 := (iff #21 #124)
-#118 := (iff #19 #117)
-#119 := [rewrite]: #118
-#126 := [monotonicity #119 #123]: #125
-#136 := [monotonicity #126 #133]: #135
-#139 := [monotonicity #136]: #138
-#114 := (iff #79 #18)
-#112 := (iff #76 #17)
-#113 := [rewrite]: #112
-#110 := (iff #73 #16)
-#111 := [rewrite]: #110
-#115 := [monotonicity #111 #113]: #114
-#142 := [monotonicity #115 #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [quant-intro #145]: #147
-#108 := (iff #32 #107)
-#105 := (iff #31 #104)
-#102 := (= #30 #101)
-#99 := (= #29 #98)
-#96 := (= #28 #95)
-#93 := (= #27 #92)
-#94 := [rewrite]: #93
-#90 := (= #26 #89)
-#91 := [rewrite]: #90
-#97 := [monotonicity #91 #94]: #96
-#86 := (iff #24 #85)
-#83 := (iff #23 #82)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#100 := [monotonicity #87 #97]: #99
-#80 := (iff #18 #79)
-#77 := (iff #17 #76)
+#71 := (= #18 #70)
+#68 := (= #17 #14)
+#63 := (ite #11 #14 #14)
+#66 := (= #63 #14)
+#67 := [rewrite]: #66
+#64 := (= #17 #63)
+#61 := (= #16 #14)
+#59 := (= #15 0::Int)
+#60 := [rewrite]: #59
+#62 := [monotonicity #60 #60]: #61
+#57 := (iff #13 #11)
+#52 := (or #11 #11)
+#55 := (iff #52 #11)
+#56 := [rewrite]: #55
+#53 := (iff #13 #52)
+#50 := (iff #12 #11)
+#51 := [rewrite]: #50
+#54 := [monotonicity #51 #51]: #53
+#58 := [trans #54 #56]: #57
+#65 := [monotonicity #58 #62]: #64
+#69 := [trans #65 #67]: #68
+#48 := (iff #10 true)
+#43 := (or true true)
+#46 := (iff #43 true)
+#47 := [rewrite]: #46
+#44 := (iff #10 #43)
+#45 := [monotonicity #42 #42]: #44
+#49 := [trans #45 #47]: #48
+#72 := [monotonicity #49 #69]: #71
+#75 := [trans #72 #74]: #19
+#77 := [monotonicity #75]: #76
+#79 := [trans #77 #42]: #78
+#82 := [monotonicity #79]: #81
+#86 := [trans #82 #84]: #85
+#40 := [asserted]: #20
+[mp #40 #86]: false
+unsat
+c39d13f4d2f865f3613c6b94cb5e51281b48ea9a 69 0
+#2 := false
+#9 := 0::Int
+#21 := (- 0::Int)
+decl f3 :: Int
+#8 := f3
+#20 := (- f3)
+#22 := (div #20 #21)
+#19 := (div f3 0::Int)
+#14 := (< 0::Int 0::Int)
+#16 := (< f3 0::Int)
+#17 := (and #16 #14)
+#13 := (< 0::Int f3)
+#15 := (and #13 #14)
+#18 := (or #15 #17)
+#23 := (ite #18 #19 #22)
+#11 := (= 0::Int 0::Int)
+#10 := (= f3 0::Int)
+#12 := (or #10 #11)
+#24 := (ite #12 0::Int #23)
+#25 := (= #24 0::Int)
+#26 := (not #25)
+#89 := (iff #26 false)
+#1 := true
+#84 := (not true)
+#87 := (iff #84 false)
+#88 := [rewrite]: #87
+#85 := (iff #26 #84)
+#82 := (iff #25 true)
+#47 := (iff #11 true)
+#48 := [rewrite]: #47
+#80 := (iff #25 #11)
+#62 := -1::Int
+#63 := (* -1::Int f3)
+#68 := (div #63 0::Int)
+#56 := (and #14 #16)
+#59 := (or #15 #56)
+#71 := (ite #59 #19 #68)
+#74 := (ite true 0::Int #71)
+#77 := (= #74 0::Int)
 #78 := [rewrite]: #77
-#74 := (iff #16 #73)
-#75 := [rewrite]: #74
-#81 := [monotonicity #75 #78]: #80
-#103 := [monotonicity #81 #100]: #102
-#106 := [monotonicity #103]: #105
-#109 := [quant-intro #106]: #108
-#150 := [trans #109 #148]: #149
-#72 := [asserted]: #32
-#151 := [mp #72 #150]: #146
-#200 := [mp~ #151 #209]: #146
-#231 := [mp #200 #230]: #228
-#262 := [mp #231 #261]: #259
-#756 := [mp #262 #755]: #751
-decl f4 :: Int
-#8 := f4
-#10 := (f3 f4 0::Int)
-#11 := (= #10 0::Int)
-#12 := (not #11)
-#61 := [asserted]: #12
-#692 := (not #751)
-#693 := (or #692 #11)
-#336 := (* -1::Int 0::Int)
-#421 := (* -1::Int f4)
-#422 := (div #421 #336)
-#423 := (* -1::Int #422)
-#414 := (+ #10 #423)
-#425 := (= #414 0::Int)
-#426 := (div f4 0::Int)
-#354 := (* -1::Int #426)
-#427 := (+ #10 #354)
-#424 := (= #427 0::Int)
-#428 := (>= f4 0::Int)
-#407 := (<= 0::Int 0::Int)
-#742 := (or #407 #428)
-#744 := (not #742)
-#401 := (<= f4 0::Int)
-#531 := (or #401 #407)
-#738 := (not #531)
-#412 := (or #738 #744)
-#413 := (ite #412 #424 #425)
-#745 := (= 0::Int 0::Int)
-#746 := (= f4 0::Int)
-#747 := (or #746 #745)
-#748 := (ite #747 #11 #413)
-#699 := (or #692 #748)
-#694 := (iff #699 #693)
-#530 := (iff #693 #693)
-#532 := [rewrite]: #530
-#697 := (iff #748 #11)
-#433 := (div #421 0::Int)
-#713 := (* -1::Int #433)
-#711 := (+ #10 #713)
-#716 := (= #711 0::Int)
-#1 := true
-#551 := (ite true #11 #716)
-#695 := (iff #551 #11)
-#696 := [rewrite]: #695
-#552 := (iff #748 #551)
-#704 := (iff #413 #716)
-#707 := (ite false #424 #716)
-#708 := (iff #707 #716)
-#709 := [rewrite]: #708
-#702 := (iff #413 #707)
-#705 := (iff #425 #716)
-#715 := (= #414 #711)
-#714 := (= #423 #713)
-#434 := (= #422 #433)
-#722 := (= #336 0::Int)
-#432 := [rewrite]: #722
-#435 := [monotonicity #432]: #434
-#429 := [monotonicity #435]: #714
-#712 := [monotonicity #429]: #715
-#706 := [monotonicity #712]: #705
-#721 := (iff #412 false)
-#719 := (or false false)
-#443 := (iff #719 false)
-#717 := [rewrite]: #443
-#720 := (iff #412 #719)
-#449 := (iff #744 false)
-#731 := (not true)
-#370 := (iff #731 false)
-#733 := [rewrite]: #370
-#447 := (iff #744 #731)
-#724 := (iff #742 true)
-#376 := (or true #428)
-#737 := (iff #376 true)
-#723 := [rewrite]: #737
-#736 := (iff #742 #376)
-#725 := (iff #407 true)
-#388 := [rewrite]: #725
-#734 := [monotonicity #388]: #736
-#446 := [trans #734 #723]: #724
-#448 := [monotonicity #446]: #447
-#342 := [trans #448 #733]: #449
-#735 := (iff #738 false)
-#726 := (iff #738 #731)
-#729 := (iff #531 true)
-#389 := (or #401 true)
-#727 := (iff #389 true)
-#728 := [rewrite]: #727
-#390 := (iff #531 #389)
-#391 := [monotonicity #388]: #390
-#730 := [trans #391 #728]: #729
-#732 := [monotonicity #730]: #726
-#375 := [trans #732 #733]: #735
-#442 := [monotonicity #375 #342]: #720
-#718 := [trans #442 #717]: #721
-#703 := [monotonicity #718 #706]: #702
-#710 := [trans #703 #709]: #704
-#741 := (iff #747 true)
-#739 := (or #746 true)
-#740 := (iff #739 true)
-#400 := [rewrite]: #740
-#399 := (iff #747 #739)
-#743 := (iff #745 true)
-#749 := [rewrite]: #743
-#404 := [monotonicity #749]: #399
-#384 := [trans #404 #400]: #741
-#553 := [monotonicity #384 #710]: #552
-#698 := [trans #553 #696]: #697
-#701 := [monotonicity #698]: #694
-#533 := [trans #701 #532]: #694
-#700 := [quant-inst #8 #9]: #699
-#686 := [mp #700 #533]: #693
-[unit-resolution #686 #61 #756]: false
-unsat
-5b04feaa787b42fcdecf376c99ee15421d3ebc84 291 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#14 := (:var 0 Int)
-#13 := (:var 1 Int)
-#15 := (f3 #13 #14)
-#749 := (pattern #15)
+#75 := (= #24 #74)
+#72 := (= #23 #71)
+#69 := (= #22 #68)
+#66 := (= #21 0::Int)
+#67 := [rewrite]: #66
+#64 := (= #20 #63)
+#65 := [rewrite]: #64
+#70 := [monotonicity #65 #67]: #69
+#60 := (iff #18 #59)
+#57 := (iff #17 #56)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#73 := [monotonicity #61 #70]: #72
+#54 := (iff #12 true)
+#49 := (or #10 true)
+#52 := (iff #49 true)
+#53 := [rewrite]: #52
+#50 := (iff #12 #49)
+#51 := [monotonicity #48]: #50
+#55 := [trans #51 #53]: #54
+#76 := [monotonicity #55 #73]: #75
+#79 := [trans #76 #78]: #25
+#81 := [monotonicity #79]: #80
+#83 := [trans #81 #48]: #82
+#86 := [monotonicity #83]: #85
+#90 := [trans #86 #88]: #89
+#46 := [asserted]: #26
+[mp #46 #90]: false
+unsat
+bea53353954aa4070bfc4dfeef54e3441dcd8b82 73 0
+#2 := false
 #8 := 0::Int
-#88 := -1::Int
-#92 := (* -1::Int #14)
-#89 := (* -1::Int #13)
-#95 := (div #89 #92)
-#252 := (* -1::Int #95)
-#253 := (+ #15 #252)
-#254 := (= #253 0::Int)
-#25 := (div #13 #14)
-#249 := (* -1::Int #25)
-#250 := (+ #15 #249)
-#251 := (= #250 0::Int)
-#127 := (>= #13 0::Int)
-#120 := (<= #14 0::Int)
-#212 := (or #120 #127)
-#213 := (not #212)
-#116 := (<= #13 0::Int)
-#210 := (or #116 #120)
-#211 := (not #210)
-#216 := (or #211 #213)
-#255 := (ite #216 #251 #254)
-#248 := (= #15 0::Int)
-#17 := (= #14 0::Int)
-#16 := (= #13 0::Int)
-#18 := (or #16 #17)
-#256 := (ite #18 #248 #255)
-#750 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #749) #256)
-#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
-#753 := (iff #259 #750)
-#751 := (iff #256 #256)
-#752 := [refl]: #751
-#754 := [quant-intro #752]: #753
-#219 := (ite #216 #25 #95)
-#222 := (ite #18 0::Int #219)
-#225 := (= #15 #222)
-#228 := (forall (vars (?v0 Int) (?v1 Int)) #225)
-#260 := (iff #228 #259)
-#257 := (iff #225 #256)
-#258 := [rewrite]: #257
-#261 := [quant-intro #258]: #260
-#128 := (not #127)
-#121 := (not #120)
-#131 := (and #121 #128)
-#117 := (not #116)
-#124 := (and #117 #121)
-#134 := (or #124 #131)
-#137 := (ite #134 #25 #95)
-#140 := (ite #18 0::Int #137)
-#143 := (= #15 #140)
-#146 := (forall (vars (?v0 Int) (?v1 Int)) #143)
-#229 := (iff #146 #228)
-#226 := (iff #143 #225)
-#223 := (= #140 #222)
-#220 := (= #137 #219)
-#217 := (iff #134 #216)
-#214 := (iff #131 #213)
-#215 := [rewrite]: #214
-#204 := (iff #124 #211)
-#205 := [rewrite]: #204
-#218 := [monotonicity #205 #215]: #217
-#221 := [monotonicity #218]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [quant-intro #227]: #229
-#208 := (~ #146 #146)
-#206 := (~ #143 #143)
-#207 := [refl]: #206
-#209 := [nnf-pos #207]: #208
-#27 := (- #14)
-#26 := (- #13)
-#28 := (div #26 #27)
-#20 := (< 0::Int #14)
-#22 := (< #13 0::Int)
-#23 := (and #22 #20)
-#19 := (< 0::Int #13)
-#21 := (and #19 #20)
-#24 := (or #21 #23)
-#29 := (ite #24 #25 #28)
-#30 := (ite #18 0::Int #29)
-#31 := (= #15 #30)
-#32 := (forall (vars (?v0 Int) (?v1 Int)) #31)
-#149 := (iff #32 #146)
-#82 := (and #20 #22)
-#85 := (or #21 #82)
-#98 := (ite #85 #25 #95)
-#76 := (= 0::Int #14)
-#73 := (= 0::Int #13)
-#79 := (or #73 #76)
-#101 := (ite #79 0::Int #98)
-#104 := (= #15 #101)
-#107 := (forall (vars (?v0 Int) (?v1 Int)) #104)
-#147 := (iff #107 #146)
-#144 := (iff #104 #143)
-#141 := (= #101 #140)
-#138 := (= #98 #137)
-#135 := (iff #85 #134)
-#132 := (iff #82 #131)
-#129 := (iff #22 #128)
-#130 := [rewrite]: #129
-#122 := (iff #20 #121)
-#123 := [rewrite]: #122
-#133 := [monotonicity #123 #130]: #132
-#125 := (iff #21 #124)
-#118 := (iff #19 #117)
-#119 := [rewrite]: #118
-#126 := [monotonicity #119 #123]: #125
-#136 := [monotonicity #126 #133]: #135
-#139 := [monotonicity #136]: #138
-#114 := (iff #79 #18)
-#112 := (iff #76 #17)
-#113 := [rewrite]: #112
-#110 := (iff #73 #16)
-#111 := [rewrite]: #110
-#115 := [monotonicity #111 #113]: #114
-#142 := [monotonicity #115 #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [quant-intro #145]: #147
-#108 := (iff #32 #107)
-#105 := (iff #31 #104)
-#102 := (= #30 #101)
-#99 := (= #29 #98)
-#96 := (= #28 #95)
-#93 := (= #27 #92)
-#94 := [rewrite]: #93
-#90 := (= #26 #89)
-#91 := [rewrite]: #90
-#97 := [monotonicity #91 #94]: #96
-#86 := (iff #24 #85)
-#83 := (iff #23 #82)
+#10 := 1::Int
+#19 := (- 1::Int)
+#18 := (- 0::Int)
+#20 := (div #18 #19)
+#17 := (div 0::Int 1::Int)
+#14 := (< 0::Int 1::Int)
+#13 := (< 0::Int 0::Int)
+#15 := (and #13 #14)
+#16 := (or #15 #15)
+#21 := (ite #16 #17 #20)
+#11 := (= 1::Int 0::Int)
+#9 := (= 0::Int 0::Int)
+#12 := (or #9 #11)
+#22 := (ite #12 0::Int #21)
+#23 := (= #22 0::Int)
+#24 := (not #23)
+#94 := (iff #24 false)
+#1 := true
+#89 := (not true)
+#92 := (iff #89 false)
+#93 := [rewrite]: #92
+#90 := (iff #24 #89)
+#87 := (iff #23 true)
+#45 := (iff #9 true)
+#46 := [rewrite]: #45
+#85 := (iff #23 #9)
+#79 := (ite true 0::Int 0::Int)
+#82 := (= #79 0::Int)
+#83 := [rewrite]: #82
+#80 := (= #22 #79)
+#77 := (= #21 0::Int)
+#72 := (ite #15 0::Int 0::Int)
+#75 := (= #72 0::Int)
+#76 := [rewrite]: #75
+#73 := (= #21 #72)
+#70 := (= #20 0::Int)
+#62 := -1::Int
+#65 := (div 0::Int -1::Int)
+#68 := (= #65 0::Int)
+#69 := [rewrite]: #68
+#66 := (= #20 #65)
+#63 := (= #19 -1::Int)
+#64 := [rewrite]: #63
+#60 := (= #18 0::Int)
+#61 := [rewrite]: #60
+#67 := [monotonicity #61 #64]: #66
+#71 := [trans #67 #69]: #70
+#58 := (= #17 0::Int)
+#59 := [rewrite]: #58
+#56 := (iff #16 #15)
+#57 := [rewrite]: #56
+#74 := [monotonicity #57 #59 #71]: #73
+#78 := [trans #74 #76]: #77
+#54 := (iff #12 true)
+#49 := (or true false)
+#52 := (iff #49 true)
+#53 := [rewrite]: #52
+#50 := (iff #12 #49)
+#47 := (iff #11 false)
+#48 := [rewrite]: #47
+#51 := [monotonicity #46 #48]: #50
+#55 := [trans #51 #53]: #54
+#81 := [monotonicity #55 #78]: #80
+#84 := [trans #81 #83]: #23
+#86 := [monotonicity #84]: #85
+#88 := [trans #86 #46]: #87
+#91 := [monotonicity #88]: #90
+#95 := [trans #91 #93]: #94
+#44 := [asserted]: #24
+[mp #44 #95]: false
+unsat
+9f6a38ce629880be5bf8c7f73c6606884657520c 77 0
+#2 := false
+#8 := 1::Int
+#18 := (- 1::Int)
+#19 := (div #18 #18)
+#17 := (div 1::Int 1::Int)
+#9 := 0::Int
+#12 := (< 0::Int 1::Int)
+#14 := (< 1::Int 0::Int)
+#15 := (and #14 #12)
+#13 := (and #12 #12)
+#16 := (or #13 #15)
+#20 := (ite #16 #17 #19)
+#10 := (= 1::Int 0::Int)
+#11 := (or #10 #10)
+#21 := (ite #11 0::Int #20)
+#22 := (= #21 1::Int)
+#23 := (not #22)
+#98 := (iff #23 false)
+#1 := true
+#93 := (not true)
+#96 := (iff #93 false)
+#97 := [rewrite]: #96
+#94 := (iff #23 #93)
+#91 := (iff #22 true)
+#86 := (= 1::Int 1::Int)
+#89 := (iff #86 true)
+#90 := [rewrite]: #89
+#87 := (iff #22 #86)
+#80 := (ite false 0::Int 1::Int)
+#83 := (= #80 1::Int)
 #84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#100 := [monotonicity #87 #97]: #99
-#80 := (iff #18 #79)
-#77 := (iff #17 #76)
-#78 := [rewrite]: #77
-#74 := (iff #16 #73)
-#75 := [rewrite]: #74
-#81 := [monotonicity #75 #78]: #80
-#103 := [monotonicity #81 #100]: #102
-#106 := [monotonicity #103]: #105
-#109 := [quant-intro #106]: #108
-#150 := [trans #109 #148]: #149
-#72 := [asserted]: #32
-#151 := [mp #72 #150]: #146
-#200 := [mp~ #151 #209]: #146
-#231 := [mp #200 #230]: #228
-#262 := [mp #231 #261]: #259
-#755 := [mp #262 #754]: #750
-#9 := 1::Int
-#10 := (f3 0::Int 1::Int)
-#11 := (= #10 0::Int)
-#12 := (not #11)
-#61 := [asserted]: #12
-#584 := (not #750)
-#585 := (or #584 #11)
-#336 := (* -1::Int 1::Int)
-#420 := (* -1::Int 0::Int)
-#421 := (div #420 #336)
-#422 := (* -1::Int #421)
-#413 := (+ #10 #422)
-#424 := (= #413 0::Int)
-#425 := (div 0::Int 1::Int)
-#426 := (* -1::Int #425)
-#423 := (+ #10 #426)
-#427 := (= #423 0::Int)
-#406 := (>= 0::Int 0::Int)
-#741 := (<= 1::Int 0::Int)
-#743 := (or #741 #406)
-#400 := (not #743)
-#530 := (<= 0::Int 0::Int)
-#737 := (or #530 #741)
-#411 := (not #737)
-#412 := (or #411 #400)
-#744 := (ite #412 #427 #424)
-#745 := (= 1::Int 0::Int)
-#746 := (= 0::Int 0::Int)
-#747 := (or #746 #745)
-#742 := (ite #747 #11 #744)
-#578 := (or #584 #742)
-#587 := (iff #578 #585)
-#589 := (iff #585 #585)
-#590 := [rewrite]: #589
-#567 := (iff #742 #11)
-#1 := true
-#681 := (ite true #11 #11)
-#679 := (iff #681 #11)
-#682 := [rewrite]: #679
-#583 := (iff #742 #681)
-#574 := (iff #744 #11)
-#689 := (ite false #11 #11)
-#572 := (iff #689 #11)
-#573 := [rewrite]: #572
-#687 := (iff #744 #689)
-#686 := (iff #424 #11)
-#532 := (= #413 #10)
-#704 := (+ #10 0::Int)
-#701 := (= #704 #10)
-#702 := [rewrite]: #701
-#529 := (= #413 #704)
-#693 := (= #422 0::Int)
-#710 := (= #420 0::Int)
-#714 := [rewrite]: #710
-#698 := (= #422 #420)
-#691 := (= #421 0::Int)
-#552 := (div 0::Int -1::Int)
-#696 := (= #552 0::Int)
-#697 := [rewrite]: #696
-#694 := (= #421 #552)
-#550 := (= #336 -1::Int)
-#551 := [rewrite]: #550
-#695 := [monotonicity #714 #551]: #694
-#692 := [trans #695 #697]: #691
-#699 := [monotonicity #692]: #698
-#700 := [trans #699 #714]: #693
-#531 := [monotonicity #700]: #529
-#685 := [trans #531 #702]: #532
-#688 := [monotonicity #685]: #686
-#703 := (iff #427 #11)
-#707 := (= #423 #10)
-#705 := (= #423 #704)
-#711 := (= #426 0::Int)
-#713 := (= #426 #420)
-#434 := (= #425 0::Int)
-#712 := [rewrite]: #434
-#428 := [monotonicity #712]: #713
-#715 := [trans #428 #714]: #711
-#706 := [monotonicity #715]: #705
-#708 := [trans #706 #702]: #707
-#709 := [monotonicity #708]: #703
-#432 := (iff #412 false)
-#716 := (or false false)
-#721 := (iff #716 false)
-#431 := [rewrite]: #721
-#720 := (iff #412 #716)
-#441 := (iff #400 false)
-#731 := (not true)
-#734 := (iff #731 false)
-#374 := [rewrite]: #734
-#718 := (iff #400 #731)
-#448 := (iff #743 true)
-#722 := (or false true)
-#446 := (iff #722 true)
-#447 := [rewrite]: #446
-#723 := (iff #743 #722)
-#733 := (iff #406 true)
-#736 := [rewrite]: #733
-#726 := (iff #741 false)
-#727 := [rewrite]: #726
-#445 := [monotonicity #727 #736]: #723
-#342 := [trans #445 #447]: #448
-#719 := [monotonicity #342]: #718
-#442 := [trans #719 #374]: #441
-#375 := (iff #411 false)
-#369 := (iff #411 #731)
-#730 := (iff #737 true)
-#739 := (or true false)
-#383 := (iff #739 true)
-#724 := [rewrite]: #383
-#728 := (iff #737 #739)
-#389 := (iff #530 true)
-#390 := [rewrite]: #389
-#729 := [monotonicity #390 #727]: #728
-#725 := [trans #729 #724]: #730
-#732 := [monotonicity #725]: #369
-#735 := [trans #732 #374]: #375
-#717 := [monotonicity #735 #442]: #720
-#433 := [trans #717 #431]: #432
-#690 := [monotonicity #433 #709 #688]: #687
-#533 := [trans #690 #573]: #574
-#387 := (iff #747 true)
-#399 := (iff #747 #739)
-#398 := (iff #745 false)
-#403 := [rewrite]: #398
-#748 := (iff #746 true)
-#738 := [rewrite]: #748
-#740 := [monotonicity #738 #403]: #399
-#388 := [trans #740 #724]: #387
-#678 := [monotonicity #388 #533]: #583
-#582 := [trans #678 #682]: #567
-#588 := [monotonicity #582]: #587
-#683 := [trans #588 #590]: #587
-#586 := [quant-inst #8 #9]: #578
-#680 := [mp #586 #683]: #585
-[unit-resolution #680 #61 #755]: false
-unsat
-ca32959e06f9134641deb61724af7aaee2701280 279 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#13 := (:var 0 Int)
-#12 := (:var 1 Int)
-#14 := (f3 #12 #13)
-#734 := (pattern #14)
-#15 := 0::Int
-#79 := -1::Int
-#83 := (* -1::Int #13)
-#80 := (* -1::Int #12)
-#86 := (div #80 #83)
-#237 := (* -1::Int #86)
-#238 := (+ #14 #237)
-#239 := (= #238 0::Int)
-#25 := (div #12 #13)
-#234 := (* -1::Int #25)
-#235 := (+ #14 #234)
-#236 := (= #235 0::Int)
-#112 := (>= #12 0::Int)
-#105 := (<= #13 0::Int)
-#197 := (or #105 #112)
-#198 := (not #197)
-#101 := (<= #12 0::Int)
-#195 := (or #101 #105)
-#196 := (not #195)
-#201 := (or #196 #198)
-#240 := (ite #201 #236 #239)
-#233 := (= #14 0::Int)
-#17 := (= #13 0::Int)
-#16 := (= #12 0::Int)
-#18 := (or #16 #17)
-#241 := (ite #18 #233 #240)
-#735 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #734) #241)
-#244 := (forall (vars (?v0 Int) (?v1 Int)) #241)
-#738 := (iff #244 #735)
-#736 := (iff #241 #241)
-#737 := [refl]: #736
-#739 := [quant-intro #737]: #738
-#204 := (ite #201 #25 #86)
-#207 := (ite #18 0::Int #204)
-#210 := (= #14 #207)
-#213 := (forall (vars (?v0 Int) (?v1 Int)) #210)
-#245 := (iff #213 #244)
-#242 := (iff #210 #241)
-#243 := [rewrite]: #242
-#246 := [quant-intro #243]: #245
-#113 := (not #112)
-#106 := (not #105)
-#116 := (and #106 #113)
-#102 := (not #101)
-#109 := (and #102 #106)
-#119 := (or #109 #116)
-#122 := (ite #119 #25 #86)
-#125 := (ite #18 0::Int #122)
-#128 := (= #14 #125)
-#131 := (forall (vars (?v0 Int) (?v1 Int)) #128)
-#214 := (iff #131 #213)
-#211 := (iff #128 #210)
-#208 := (= #125 #207)
-#205 := (= #122 #204)
-#202 := (iff #119 #201)
-#199 := (iff #116 #198)
-#200 := [rewrite]: #199
-#189 := (iff #109 #196)
-#190 := [rewrite]: #189
-#203 := [monotonicity #190 #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [monotonicity #206]: #208
-#212 := [monotonicity #209]: #211
-#215 := [quant-intro #212]: #214
-#193 := (~ #131 #131)
-#191 := (~ #128 #128)
-#192 := [refl]: #191
-#194 := [nnf-pos #192]: #193
-#27 := (- #13)
-#26 := (- #12)
-#28 := (div #26 #27)
-#20 := (< 0::Int #13)
-#22 := (< #12 0::Int)
-#23 := (and #22 #20)
-#19 := (< 0::Int #12)
-#21 := (and #19 #20)
-#24 := (or #21 #23)
-#29 := (ite #24 #25 #28)
-#30 := (ite #18 0::Int #29)
-#31 := (= #14 #30)
-#32 := (forall (vars (?v0 Int) (?v1 Int)) #31)
-#134 := (iff #32 #131)
-#73 := (and #20 #22)
-#76 := (or #21 #73)
-#89 := (ite #76 #25 #86)
-#92 := (ite #18 0::Int #89)
-#95 := (= #14 #92)
-#98 := (forall (vars (?v0 Int) (?v1 Int)) #95)
-#132 := (iff #98 #131)
-#129 := (iff #95 #128)
-#126 := (= #92 #125)
-#123 := (= #89 #122)
-#120 := (iff #76 #119)
-#117 := (iff #73 #116)
-#114 := (iff #22 #113)
-#115 := [rewrite]: #114
-#107 := (iff #20 #106)
-#108 := [rewrite]: #107
-#118 := [monotonicity #108 #115]: #117
-#110 := (iff #21 #109)
-#103 := (iff #19 #102)
+#81 := (= #21 #80)
+#78 := (= #20 1::Int)
+#55 := (and #12 #14)
+#58 := (or #12 #55)
+#73 := (ite #58 1::Int 1::Int)
+#76 := (= #73 1::Int)
+#77 := [rewrite]: #76
+#74 := (= #20 #73)
+#71 := (= #19 1::Int)
+#63 := -1::Int
+#66 := (div -1::Int -1::Int)
+#69 := (= #66 1::Int)
+#70 := [rewrite]: #69
+#67 := (= #19 #66)
+#64 := (= #18 -1::Int)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65 #65]: #67
+#72 := [trans #68 #70]: #71
+#61 := (= #17 1::Int)
+#62 := [rewrite]: #61
+#59 := (iff #16 #58)
+#56 := (iff #15 #55)
+#57 := [rewrite]: #56
+#53 := (iff #13 #12)
+#54 := [rewrite]: #53
+#60 := [monotonicity #54 #57]: #59
+#75 := [monotonicity #60 #62 #72]: #74
+#79 := [trans #75 #77]: #78
+#51 := (iff #11 false)
+#46 := (or false false)
+#49 := (iff #46 false)
+#50 := [rewrite]: #49
+#47 := (iff #11 #46)
+#44 := (iff #10 false)
+#45 := [rewrite]: #44
+#48 := [monotonicity #45 #45]: #47
+#52 := [trans #48 #50]: #51
+#82 := [monotonicity #52 #79]: #81
+#85 := [trans #82 #84]: #22
+#88 := [monotonicity #85]: #87
+#92 := [trans #88 #90]: #91
+#95 := [monotonicity #92]: #94
+#99 := [trans #95 #97]: #98
+#43 := [asserted]: #23
+[mp #43 #99]: false
+unsat
+519fa461c6409fb549ed180638c452bbb592389a 84 0
+#2 := false
+#8 := 3::Int
+#11 := 1::Int
+#22 := (- 1::Int)
+#21 := (- 3::Int)
+#23 := (div #21 #22)
+#20 := (div 3::Int 1::Int)
+#9 := 0::Int
+#15 := (< 0::Int 1::Int)
+#17 := (< 3::Int 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int 3::Int)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#24 := (ite #19 #20 #23)
+#12 := (= 1::Int 0::Int)
+#10 := (= 3::Int 0::Int)
+#13 := (or #10 #12)
+#25 := (ite #13 0::Int #24)
+#26 := (= #25 3::Int)
+#27 := (not #26)
+#105 := (iff #27 false)
+#1 := true
+#100 := (not true)
+#103 := (iff #100 false)
 #104 := [rewrite]: #103
-#111 := [monotonicity #104 #108]: #110
-#121 := [monotonicity #111 #118]: #120
+#101 := (iff #27 #100)
+#98 := (iff #26 true)
+#93 := (= 3::Int 3::Int)
+#96 := (iff #93 true)
+#97 := [rewrite]: #96
+#94 := (iff #26 #93)
+#87 := (ite false 0::Int 3::Int)
+#90 := (= #87 3::Int)
+#91 := [rewrite]: #90
+#88 := (= #25 #87)
+#85 := (= #24 3::Int)
+#59 := (and #15 #17)
+#62 := (or #16 #59)
+#80 := (ite #62 3::Int 3::Int)
+#83 := (= #80 3::Int)
+#84 := [rewrite]: #83
+#81 := (= #24 #80)
+#78 := (= #23 3::Int)
+#70 := -1::Int
+#67 := -3::Int
+#73 := (div -3::Int -1::Int)
+#76 := (= #73 3::Int)
+#77 := [rewrite]: #76
+#74 := (= #23 #73)
+#71 := (= #22 -1::Int)
+#72 := [rewrite]: #71
+#68 := (= #21 -3::Int)
+#69 := [rewrite]: #68
+#75 := [monotonicity #69 #72]: #74
+#79 := [trans #75 #77]: #78
+#65 := (= #20 3::Int)
+#66 := [rewrite]: #65
+#63 := (iff #19 #62)
+#60 := (iff #18 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#82 := [monotonicity #64 #66 #79]: #81
+#86 := [trans #82 #84]: #85
+#57 := (iff #13 false)
+#52 := (or false false)
+#55 := (iff #52 false)
+#56 := [rewrite]: #55
+#53 := (iff #13 #52)
+#50 := (iff #12 false)
+#51 := [rewrite]: #50
+#48 := (iff #10 false)
+#49 := [rewrite]: #48
+#54 := [monotonicity #49 #51]: #53
+#58 := [trans #54 #56]: #57
+#89 := [monotonicity #58 #86]: #88
+#92 := [trans #89 #91]: #26
+#95 := [monotonicity #92]: #94
+#99 := [trans #95 #97]: #98
+#102 := [monotonicity #99]: #101
+#106 := [trans #102 #104]: #105
+#47 := [asserted]: #27
+[mp #47 #106]: false
+unsat
+8d9d1f916dc7c49723b00373e1ef641d98863a50 174 0
+#2 := false
+#9 := 0::Int
+decl f3 :: Int
+#8 := f3
+#89 := (<= f3 0::Int)
+#102 := (>= f3 0::Int)
+#103 := (not #102)
+#90 := (not #89)
+#113 := (or #90 #103)
+#140 := (not #113)
+#63 := -1::Int
+#64 := (* -1::Int f3)
+#69 := (div #64 -1::Int)
+#11 := 1::Int
+#20 := (div f3 1::Int)
+#116 := (ite #113 #20 #69)
+#138 := (= #20 #116)
+#246 := (not #138)
+#10 := (= f3 0::Int)
+#119 := (ite #10 0::Int #116)
+#122 := (= f3 #119)
+#137 := (= #116 #119)
+#149 := (not #10)
+#136 := (= #119 0::Int)
+#163 := (iff #136 #122)
+#161 := (iff #122 #136)
+#156 := (= 0::Int #119)
+#159 := (iff #156 #136)
+#160 := [commutativity]: #159
+#157 := (iff #122 #156)
+#154 := [hypothesis]: #10
+#158 := [monotonicity #154]: #157
+#162 := [trans #158 #160]: #161
+#164 := [symm #162]: #163
+#150 := (or #149 #136)
+#151 := [def-axiom]: #150
+#155 := [unit-resolution #151 #154]: #136
+#165 := [mp #155 #164]: #122
+#125 := (not #122)
+#22 := (- 1::Int)
+#21 := (- f3)
+#23 := (div #21 #22)
+#15 := (< 0::Int 1::Int)
+#17 := (< f3 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int f3)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#24 := (ite #19 #20 #23)
+#12 := (= 1::Int 0::Int)
+#13 := (or #10 #12)
+#25 := (ite #13 0::Int #24)
+#26 := (= #25 f3)
+#27 := (not #26)
+#128 := (iff #27 #125)
+#57 := (and #15 #17)
+#60 := (or #16 #57)
+#72 := (ite #60 #20 #69)
+#75 := (ite #10 0::Int #72)
+#81 := (= f3 #75)
+#86 := (not #81)
+#126 := (iff #86 #125)
+#123 := (iff #81 #122)
+#120 := (= #75 #119)
+#117 := (= #72 #116)
+#114 := (iff #60 #113)
+#111 := (iff #57 #103)
+#1 := true
+#106 := (and true #103)
+#109 := (iff #106 #103)
+#110 := [rewrite]: #109
+#107 := (iff #57 #106)
+#104 := (iff #17 #103)
+#105 := [rewrite]: #104
+#93 := (iff #15 true)
+#94 := [rewrite]: #93
+#108 := [monotonicity #94 #105]: #107
+#112 := [trans #108 #110]: #111
+#100 := (iff #16 #90)
+#95 := (and #90 true)
+#98 := (iff #95 #90)
+#99 := [rewrite]: #98
+#96 := (iff #16 #95)
+#91 := (iff #14 #90)
+#92 := [rewrite]: #91
+#97 := [monotonicity #92 #94]: #96
+#101 := [trans #97 #99]: #100
+#115 := [monotonicity #101 #112]: #114
+#118 := [monotonicity #115]: #117
+#121 := [monotonicity #118]: #120
 #124 := [monotonicity #121]: #123
 #127 := [monotonicity #124]: #126
-#130 := [monotonicity #127]: #129
-#133 := [quant-intro #130]: #132
-#99 := (iff #32 #98)
-#96 := (iff #31 #95)
-#93 := (= #30 #92)
-#90 := (= #29 #89)
-#87 := (= #28 #86)
-#84 := (= #27 #83)
-#85 := [rewrite]: #84
-#81 := (= #26 #80)
-#82 := [rewrite]: #81
-#88 := [monotonicity #82 #85]: #87
-#77 := (iff #24 #76)
-#74 := (iff #23 #73)
-#75 := [rewrite]: #74
-#78 := [monotonicity #75]: #77
-#91 := [monotonicity #78 #88]: #90
-#94 := [monotonicity #91]: #93
-#97 := [monotonicity #94]: #96
-#100 := [quant-intro #97]: #99
-#135 := [trans #100 #133]: #134
-#72 := [asserted]: #32
-#136 := [mp #72 #135]: #131
-#185 := [mp~ #136 #194]: #131
-#216 := [mp #185 #215]: #213
-#247 := [mp #216 #246]: #244
-#740 := [mp #247 #739]: #735
-#8 := 1::Int
-#9 := (f3 1::Int 1::Int)
-#10 := (= #9 1::Int)
-#11 := (not #10)
-#61 := [asserted]: #11
-#571 := (not #735)
-#572 := (or #571 #10)
-#321 := (* -1::Int 1::Int)
-#405 := (div #321 #321)
-#406 := (* -1::Int #405)
-#407 := (+ #9 #406)
-#398 := (= #407 0::Int)
-#409 := (div 1::Int 1::Int)
-#410 := (* -1::Int #409)
-#411 := (+ #9 #410)
-#408 := (= #411 0::Int)
-#412 := (>= 1::Int 0::Int)
-#391 := (<= 1::Int 0::Int)
-#726 := (or #391 #412)
-#728 := (not #726)
-#385 := (or #391 #391)
-#515 := (not #385)
-#722 := (or #515 #728)
-#396 := (ite #722 #408 #398)
-#397 := (= #9 0::Int)
-#729 := (= 1::Int 0::Int)
-#730 := (or #729 #729)
-#731 := (ite #730 #397 #396)
-#573 := (or #571 #731)
-#575 := (iff #573 #572)
-#665 := (iff #572 #572)
-#669 := [rewrite]: #665
-#570 := (iff #731 #10)
-#664 := (ite false #397 #10)
-#567 := (iff #664 #10)
-#569 := [rewrite]: #567
-#667 := (iff #731 #664)
-#568 := (iff #396 #10)
-#1 := true
-#557 := (ite true #10 #10)
-#518 := (iff #557 #10)
-#666 := [rewrite]: #518
-#558 := (iff #396 #557)
-#672 := (iff #398 #10)
-#689 := (+ -1::Int #9)
-#692 := (= #689 0::Int)
-#694 := (iff #692 #10)
-#535 := [rewrite]: #694
-#673 := (iff #398 #692)
-#670 := (= #407 #689)
-#699 := (+ #9 -1::Int)
-#690 := (= #699 #689)
-#691 := [rewrite]: #690
-#516 := (= #407 #699)
-#685 := (= #406 -1::Int)
-#697 := (= #321 -1::Int)
-#698 := [rewrite]: #697
-#684 := (= #406 #321)
-#677 := (= #405 1::Int)
-#679 := (div -1::Int -1::Int)
-#682 := (= #679 1::Int)
-#676 := [rewrite]: #682
-#680 := (= #405 #679)
-#681 := [monotonicity #698 #698]: #680
-#683 := [trans #681 #676]: #677
-#678 := [monotonicity #683]: #684
-#514 := [trans #678 #698]: #685
-#517 := [monotonicity #514]: #516
-#671 := [trans #517 #691]: #670
-#674 := [monotonicity #671]: #673
-#675 := [trans #674 #535]: #672
-#536 := (iff #408 #10)
-#693 := (iff #408 #692)
-#686 := (= #411 #689)
-#696 := (= #411 #699)
-#413 := (= #410 -1::Int)
-#418 := (= #410 #321)
-#416 := (= #409 1::Int)
-#417 := [rewrite]: #416
-#419 := [monotonicity #417]: #418
-#695 := [trans #419 #698]: #413
-#700 := [monotonicity #695]: #696
-#687 := [trans #700 #691]: #686
-#688 := [monotonicity #687]: #693
-#537 := [trans #688 #535]: #536
-#702 := (iff #722 true)
-#704 := (or true false)
-#701 := (iff #704 true)
-#705 := [rewrite]: #701
-#426 := (iff #722 #704)
-#327 := (iff #728 false)
-#708 := (not true)
-#432 := (iff #708 false)
-#433 := [rewrite]: #432
-#430 := (iff #728 #708)
-#721 := (iff #726 true)
-#719 := (or false true)
-#720 := (iff #719 true)
-#718 := [rewrite]: #720
-#359 := (iff #726 #719)
-#354 := (iff #412 true)
-#717 := [rewrite]: #354
-#368 := (iff #391 false)
-#709 := [rewrite]: #368
-#360 := [monotonicity #709 #717]: #359
-#707 := [trans #360 #718]: #721
-#431 := [monotonicity #707]: #430
-#703 := [trans #431 #433]: #327
-#710 := (iff #515 true)
-#711 := (not false)
-#714 := (iff #711 true)
-#715 := [rewrite]: #714
-#712 := (iff #515 #711)
-#374 := (iff #385 false)
-#733 := (or false false)
-#388 := (iff #733 false)
-#724 := [rewrite]: #388
-#372 := (iff #385 #733)
-#373 := [monotonicity #709 #709]: #372
-#375 := [trans #373 #724]: #374
-#713 := [monotonicity #375]: #712
-#716 := [trans #713 #715]: #710
-#427 := [monotonicity #716 #703]: #426
-#706 := [trans #427 #705]: #702
-#559 := [monotonicity #706 #537 #675]: #558
-#663 := [trans #559 #666]: #568
-#384 := (iff #730 false)
-#723 := (iff #730 #733)
-#732 := (iff #729 false)
-#727 := [rewrite]: #732
-#383 := [monotonicity #727 #727]: #723
-#725 := [trans #383 #724]: #384
-#552 := [monotonicity #725 #663]: #667
-#563 := [trans #552 #569]: #570
-#668 := [monotonicity #563]: #575
-#656 := [trans #668 #669]: #575
-#574 := [quant-inst #8 #8]: #573
-#658 := [mp #574 #656]: #572
-[unit-resolution #658 #61 #740]: false
-unsat
-4e490baf730f7c2e9689bb8a2892f4f8f052ba53 290 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#14 := (:var 0 Int)
-#13 := (:var 1 Int)
-#15 := (f3 #13 #14)
-#735 := (pattern #15)
-#16 := 0::Int
-#80 := -1::Int
-#84 := (* -1::Int #14)
-#81 := (* -1::Int #13)
-#87 := (div #81 #84)
-#238 := (* -1::Int #87)
-#239 := (+ #15 #238)
-#240 := (= #239 0::Int)
-#26 := (div #13 #14)
-#235 := (* -1::Int #26)
-#236 := (+ #15 #235)
-#237 := (= #236 0::Int)
-#113 := (>= #13 0::Int)
-#106 := (<= #14 0::Int)
-#198 := (or #106 #113)
-#199 := (not #198)
-#102 := (<= #13 0::Int)
-#196 := (or #102 #106)
-#197 := (not #196)
-#202 := (or #197 #199)
-#241 := (ite #202 #237 #240)
-#234 := (= #15 0::Int)
-#18 := (= #14 0::Int)
-#17 := (= #13 0::Int)
-#19 := (or #17 #18)
-#242 := (ite #19 #234 #241)
-#736 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #735) #242)
-#245 := (forall (vars (?v0 Int) (?v1 Int)) #242)
-#739 := (iff #245 #736)
-#737 := (iff #242 #242)
-#738 := [refl]: #737
-#740 := [quant-intro #738]: #739
-#205 := (ite #202 #26 #87)
-#208 := (ite #19 0::Int #205)
-#211 := (= #15 #208)
-#214 := (forall (vars (?v0 Int) (?v1 Int)) #211)
-#246 := (iff #214 #245)
-#243 := (iff #211 #242)
-#244 := [rewrite]: #243
-#247 := [quant-intro #244]: #246
-#114 := (not #113)
-#107 := (not #106)
-#117 := (and #107 #114)
-#103 := (not #102)
-#110 := (and #103 #107)
-#120 := (or #110 #117)
-#123 := (ite #120 #26 #87)
-#126 := (ite #19 0::Int #123)
-#129 := (= #15 #126)
-#132 := (forall (vars (?v0 Int) (?v1 Int)) #129)
-#215 := (iff #132 #214)
-#212 := (iff #129 #211)
-#209 := (= #126 #208)
-#206 := (= #123 #205)
-#203 := (iff #120 #202)
-#200 := (iff #117 #199)
-#201 := [rewrite]: #200
-#190 := (iff #110 #197)
-#191 := [rewrite]: #190
-#204 := [monotonicity #191 #201]: #203
-#207 := [monotonicity #204]: #206
-#210 := [monotonicity #207]: #209
-#213 := [monotonicity #210]: #212
-#216 := [quant-intro #213]: #215
-#194 := (~ #132 #132)
-#192 := (~ #129 #129)
-#193 := [refl]: #192
-#195 := [nnf-pos #193]: #194
-#28 := (- #14)
-#27 := (- #13)
-#29 := (div #27 #28)
-#21 := (< 0::Int #14)
-#23 := (< #13 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #13)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#30 := (ite #25 #26 #29)
-#31 := (ite #19 0::Int #30)
-#32 := (= #15 #31)
-#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
-#135 := (iff #33 #132)
-#74 := (and #21 #23)
-#77 := (or #22 #74)
-#90 := (ite #77 #26 #87)
-#93 := (ite #19 0::Int #90)
-#96 := (= #15 #93)
-#99 := (forall (vars (?v0 Int) (?v1 Int)) #96)
-#133 := (iff #99 #132)
-#130 := (iff #96 #129)
-#127 := (= #93 #126)
-#124 := (= #90 #123)
-#121 := (iff #77 #120)
-#118 := (iff #74 #117)
-#115 := (iff #23 #114)
-#116 := [rewrite]: #115
-#108 := (iff #21 #107)
-#109 := [rewrite]: #108
-#119 := [monotonicity #109 #116]: #118
-#111 := (iff #22 #110)
-#104 := (iff #20 #103)
-#105 := [rewrite]: #104
-#112 := [monotonicity #105 #109]: #111
-#122 := [monotonicity #112 #119]: #121
-#125 := [monotonicity #122]: #124
-#128 := [monotonicity #125]: #127
-#131 := [monotonicity #128]: #130
-#134 := [quant-intro #131]: #133
-#100 := (iff #33 #99)
-#97 := (iff #32 #96)
-#94 := (= #31 #93)
-#91 := (= #30 #90)
-#88 := (= #29 #87)
-#85 := (= #28 #84)
-#86 := [rewrite]: #85
-#82 := (= #27 #81)
-#83 := [rewrite]: #82
-#89 := [monotonicity #83 #86]: #88
-#78 := (iff #25 #77)
-#75 := (iff #24 #74)
-#76 := [rewrite]: #75
-#79 := [monotonicity #76]: #78
-#92 := [monotonicity #79 #89]: #91
-#95 := [monotonicity #92]: #94
-#98 := [monotonicity #95]: #97
-#101 := [quant-intro #98]: #100
-#136 := [trans #101 #134]: #135
-#73 := [asserted]: #33
-#137 := [mp #73 #136]: #132
-#186 := [mp~ #137 #195]: #132
-#217 := [mp #186 #216]: #214
-#248 := [mp #217 #247]: #245
-#741 := [mp #248 #740]: #736
-#8 := 3::Int
-#9 := 1::Int
-#10 := (f3 3::Int 1::Int)
-#11 := (= #10 3::Int)
-#12 := (not #11)
-#62 := [asserted]: #12
-#651 := (not #736)
-#648 := (or #651 #11)
-#322 := (* -1::Int 1::Int)
-#406 := (* -1::Int 3::Int)
-#407 := (div #406 #322)
-#408 := (* -1::Int #407)
-#399 := (+ #10 #408)
-#410 := (= #399 0::Int)
-#411 := (div 3::Int 1::Int)
-#412 := (* -1::Int #411)
-#409 := (+ #10 #412)
-#413 := (= #409 0::Int)
-#392 := (>= 3::Int 0::Int)
-#727 := (<= 1::Int 0::Int)
-#729 := (or #727 #392)
-#386 := (not #729)
-#516 := (<= 3::Int 0::Int)
-#723 := (or #516 #727)
-#397 := (not #723)
-#398 := (or #397 #386)
-#730 := (ite #398 #413 #410)
-#731 := (= #10 0::Int)
-#732 := (= 1::Int 0::Int)
-#733 := (= 3::Int 0::Int)
-#728 := (or #733 #732)
-#734 := (ite #728 #731 #730)
-#650 := (or #651 #734)
-#661 := (iff #650 #648)
-#658 := (iff #648 #648)
-#663 := [rewrite]: #658
-#657 := (iff #734 #11)
-#575 := (ite false #731 #11)
-#666 := (iff #575 #11)
-#670 := [rewrite]: #666
-#576 := (iff #734 #575)
-#573 := (iff #730 #11)
-#1 := true
-#568 := (ite true #11 #11)
-#564 := (iff #568 #11)
-#572 := [rewrite]: #564
-#570 := (iff #730 #568)
-#668 := (iff #410 #11)
-#690 := -3::Int
-#695 := (+ -3::Int #10)
-#681 := (= #695 0::Int)
-#677 := (iff #681 #11)
-#678 := [rewrite]: #677
-#664 := (iff #410 #681)
-#667 := (= #399 #695)
-#693 := (+ #10 -3::Int)
-#536 := (= #693 #695)
-#537 := [rewrite]: #536
-#560 := (= #399 #693)
-#558 := (= #408 -3::Int)
-#691 := (= #406 -3::Int)
-#692 := [rewrite]: #691
-#673 := (= #408 #406)
-#674 := (= #407 3::Int)
-#515 := (div -3::Int -1::Int)
-#671 := (= #515 3::Int)
-#672 := [rewrite]: #671
-#517 := (= #407 #515)
-#679 := (= #322 -1::Int)
-#686 := [rewrite]: #679
-#518 := [monotonicity #692 #686]: #517
-#675 := [trans #518 #672]: #674
-#676 := [monotonicity #675]: #673
-#559 := [trans #676 #692]: #558
-#519 := [monotonicity #559]: #560
-#569 := [trans #519 #537]: #667
-#665 := [monotonicity #569]: #664
-#553 := [trans #665 #678]: #668
-#684 := (iff #413 #11)
-#682 := (iff #413 #681)
-#538 := (= #409 #695)
-#694 := (= #409 #693)
-#687 := (= #412 -3::Int)
-#697 := (= #412 #406)
-#696 := (= #411 3::Int)
-#700 := [rewrite]: #696
-#701 := [monotonicity #700]: #697
-#688 := [trans #701 #692]: #687
-#689 := [monotonicity #688]: #694
-#680 := [trans #689 #537]: #538
-#683 := [monotonicity #680]: #682
-#685 := [trans #683 #678]: #684
-#699 := (iff #398 true)
-#417 := (or true false)
-#420 := (iff #417 true)
-#698 := [rewrite]: #420
-#418 := (iff #398 #417)
-#703 := (iff #386 false)
-#705 := (not true)
-#702 := (iff #705 false)
-#706 := [rewrite]: #702
-#427 := (iff #386 #705)
-#328 := (iff #729 true)
-#709 := (or false true)
-#433 := (iff #709 true)
-#434 := [rewrite]: #433
-#431 := (iff #729 #709)
-#722 := (iff #392 true)
-#708 := [rewrite]: #722
-#713 := (iff #727 false)
-#714 := [rewrite]: #713
-#432 := [monotonicity #714 #708]: #431
-#704 := [trans #432 #434]: #328
-#428 := [monotonicity #704]: #427
-#707 := [trans #428 #706]: #703
-#721 := (iff #397 true)
-#355 := (not false)
-#360 := (iff #355 true)
-#361 := [rewrite]: #360
-#718 := (iff #397 #355)
-#711 := (iff #723 false)
-#385 := (or false false)
-#710 := (iff #385 false)
-#373 := [rewrite]: #710
-#715 := (iff #723 #385)
-#376 := (iff #516 false)
-#712 := [rewrite]: #376
-#716 := [monotonicity #712 #714]: #715
-#717 := [trans #716 #373]: #711
-#720 := [monotonicity #717]: #718
-#719 := [trans #720 #361]: #721
-#419 := [monotonicity #719 #707]: #418
-#414 := [trans #419 #698]: #699
-#571 := [monotonicity #414 #685 #553]: #570
-#574 := [trans #571 #572]: #573
-#374 := (iff #728 false)
-#726 := (iff #728 #385)
-#389 := (iff #732 false)
-#725 := [rewrite]: #389
-#724 := (iff #733 false)
-#384 := [rewrite]: #724
-#369 := [monotonicity #384 #725]: #726
-#375 := [trans #369 #373]: #374
-#669 := [monotonicity #375 #574]: #576
-#659 := [trans #669 #670]: #657
-#662 := [monotonicity #659]: #661
-#652 := [trans #662 #663]: #661
-#660 := [quant-inst #8 #9]: #650
-#653 := [mp #660 #652]: #648
-[unit-resolution #653 #62 #741]: false
-unsat
-3af8b375b2f7758b71c609be3059c3c3f068c4d0 327 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#9 := 1::Int
-decl f4 :: Int
-#8 := f4
-#10 := (f3 f4 1::Int)
-#63 := (= f4 #10)
-#16 := 0::Int
-#728 := (= #10 0::Int)
-#543 := (iff #728 #63)
-#541 := (iff #63 #728)
-#536 := (= 0::Int #10)
-#539 := (iff #536 #728)
-#540 := [commutativity]: #539
-#537 := (iff #63 #536)
-#730 := (= f4 0::Int)
-#408 := (div f4 1::Int)
-#77 := -1::Int
-#409 := (* -1::Int #408)
-#406 := (+ #10 #409)
-#410 := (= #406 0::Int)
-#516 := (not #410)
-#552 := (= #408 #10)
-#590 := (= #10 #408)
-#515 := (<= #406 0::Int)
-#474 := [hypothesis]: #410
-#585 := (or #516 #515)
-#586 := [th-lemma arith triangle-eq]: #585
-#587 := [unit-resolution #586 #474]: #515
-#668 := (>= #406 0::Int)
-#592 := (or #516 #668)
-#588 := [th-lemma arith triangle-eq]: #592
-#589 := [unit-resolution #588 #474]: #668
-#593 := [th-lemma arith eq-propagate 1 1 #589 #587]: #590
-#559 := [symm #593]: #552
-#578 := (= f4 #408)
-#621 := (+ f4 #409)
-#626 := (<= #621 0::Int)
-#620 := (= #621 0::Int)
-#1 := true
-#60 := [true-axiom]: true
-#594 := (or false #620)
-#595 := [th-lemma arith]: #594
-#591 := [unit-resolution #595 #60]: #620
-#596 := (not #620)
-#576 := (or #596 #626)
-#522 := [th-lemma arith triangle-eq]: #576
-#577 := [unit-resolution #522 #591]: #626
-#627 := (>= #621 0::Int)
-#558 := (or #596 #627)
-#582 := [th-lemma arith triangle-eq]: #558
-#583 := [unit-resolution #582 #591]: #627
-#584 := [th-lemma arith eq-propagate 1 1 #583 #577]: #578
-#518 := [trans #584 #559]: #63
-#66 := (not #63)
-#11 := (= #10 f4)
-#12 := (not #11)
-#67 := (iff #12 #66)
-#64 := (iff #11 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#62 := [asserted]: #12
-#71 := [mp #62 #68]: #66
-#549 := [unit-resolution #71 #518]: false
-#551 := [lemma #549]: #516
-#403 := (* -1::Int f4)
-#704 := (div #403 -1::Int)
-#416 := (* -1::Int #704)
-#696 := (+ #10 #416)
-#697 := (= #696 0::Int)
-#513 := (<= f4 0::Int)
-#714 := (not #513)
-#389 := (>= f4 0::Int)
-#706 := (not #389)
-#701 := (or #706 #714)
-#687 := (ite #701 #410 #697)
-#565 := (not #730)
-#657 := [hypothesis]: #565
-#560 := (or #730 #687)
-#684 := (ite #730 #728 #687)
-#14 := (:var 0 Int)
-#13 := (:var 1 Int)
-#15 := (f3 #13 #14)
-#732 := (pattern #15)
-#81 := (* -1::Int #14)
-#78 := (* -1::Int #13)
-#84 := (div #78 #81)
-#235 := (* -1::Int #84)
-#236 := (+ #15 #235)
-#237 := (= #236 0::Int)
-#26 := (div #13 #14)
-#232 := (* -1::Int #26)
-#233 := (+ #15 #232)
-#234 := (= #233 0::Int)
-#110 := (>= #13 0::Int)
-#103 := (<= #14 0::Int)
-#195 := (or #103 #110)
-#196 := (not #195)
-#99 := (<= #13 0::Int)
-#193 := (or #99 #103)
-#194 := (not #193)
-#199 := (or #194 #196)
-#238 := (ite #199 #234 #237)
-#231 := (= #15 0::Int)
-#18 := (= #14 0::Int)
-#17 := (= #13 0::Int)
-#19 := (or #17 #18)
-#239 := (ite #19 #231 #238)
-#733 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #732) #239)
-#242 := (forall (vars (?v0 Int) (?v1 Int)) #239)
-#736 := (iff #242 #733)
-#734 := (iff #239 #239)
-#735 := [refl]: #734
-#737 := [quant-intro #735]: #736
-#202 := (ite #199 #26 #84)
-#205 := (ite #19 0::Int #202)
-#208 := (= #15 #205)
-#211 := (forall (vars (?v0 Int) (?v1 Int)) #208)
-#243 := (iff #211 #242)
-#240 := (iff #208 #239)
-#241 := [rewrite]: #240
-#244 := [quant-intro #241]: #243
-#111 := (not #110)
-#104 := (not #103)
-#114 := (and #104 #111)
-#100 := (not #99)
-#107 := (and #100 #104)
-#117 := (or #107 #114)
-#120 := (ite #117 #26 #84)
-#123 := (ite #19 0::Int #120)
-#126 := (= #15 #123)
-#129 := (forall (vars (?v0 Int) (?v1 Int)) #126)
-#212 := (iff #129 #211)
-#209 := (iff #126 #208)
-#206 := (= #123 #205)
-#203 := (= #120 #202)
-#200 := (iff #117 #199)
-#197 := (iff #114 #196)
-#198 := [rewrite]: #197
-#187 := (iff #107 #194)
-#188 := [rewrite]: #187
-#201 := [monotonicity #188 #198]: #200
-#204 := [monotonicity #201]: #203
-#207 := [monotonicity #204]: #206
-#210 := [monotonicity #207]: #209
-#213 := [quant-intro #210]: #212
-#191 := (~ #129 #129)
-#189 := (~ #126 #126)
-#190 := [refl]: #189
-#192 := [nnf-pos #190]: #191
-#28 := (- #14)
-#27 := (- #13)
-#29 := (div #27 #28)
-#21 := (< 0::Int #14)
-#23 := (< #13 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #13)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#30 := (ite #25 #26 #29)
-#31 := (ite #19 0::Int #30)
-#32 := (= #15 #31)
-#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
-#132 := (iff #33 #129)
-#70 := (and #21 #23)
-#74 := (or #22 #70)
-#87 := (ite #74 #26 #84)
-#90 := (ite #19 0::Int #87)
-#93 := (= #15 #90)
-#96 := (forall (vars (?v0 Int) (?v1 Int)) #93)
-#130 := (iff #96 #129)
-#127 := (iff #93 #126)
-#124 := (= #90 #123)
-#121 := (= #87 #120)
-#118 := (iff #74 #117)
-#115 := (iff #70 #114)
-#112 := (iff #23 #111)
-#113 := [rewrite]: #112
-#105 := (iff #21 #104)
-#106 := [rewrite]: #105
-#116 := [monotonicity #106 #113]: #115
-#108 := (iff #22 #107)
-#101 := (iff #20 #100)
-#102 := [rewrite]: #101
-#109 := [monotonicity #102 #106]: #108
-#119 := [monotonicity #109 #116]: #118
-#122 := [monotonicity #119]: #121
-#125 := [monotonicity #122]: #124
-#128 := [monotonicity #125]: #127
-#131 := [quant-intro #128]: #130
-#97 := (iff #33 #96)
-#94 := (iff #32 #93)
-#91 := (= #31 #90)
-#88 := (= #30 #87)
-#85 := (= #29 #84)
-#82 := (= #28 #81)
+#87 := (iff #27 #86)
+#84 := (iff #26 #81)
+#78 := (= #75 f3)
+#82 := (iff #78 #81)
 #83 := [rewrite]: #82
-#79 := (= #27 #78)
-#80 := [rewrite]: #79
-#86 := [monotonicity #80 #83]: #85
-#75 := (iff #25 #74)
-#72 := (iff #24 #70)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#89 := [monotonicity #76 #86]: #88
-#92 := [monotonicity #89]: #91
-#95 := [monotonicity #92]: #94
-#98 := [quant-intro #95]: #97
-#133 := [trans #98 #131]: #132
-#69 := [asserted]: #33
-#134 := [mp #69 #133]: #129
-#183 := [mp~ #134 #192]: #129
-#214 := [mp #183 #213]: #211
-#245 := [mp #214 #244]: #242
-#738 := [mp #245 #737]: #733
-#691 := (not #733)
-#686 := (or #691 #684)
-#319 := (* -1::Int 1::Int)
-#404 := (div #403 #319)
-#405 := (* -1::Int #404)
-#396 := (+ #10 #405)
-#407 := (= #396 0::Int)
-#724 := (<= 1::Int 0::Int)
-#726 := (or #724 #389)
-#383 := (not #726)
-#720 := (or #513 #724)
-#394 := (not #720)
-#395 := (or #394 #383)
-#727 := (ite #395 #410 #407)
-#729 := (= 1::Int 0::Int)
-#725 := (or #730 #729)
-#731 := (ite #725 #728 #727)
-#692 := (or #691 #731)
-#534 := (iff #692 #686)
-#677 := (iff #686 #686)
-#678 := [rewrite]: #677
-#685 := (iff #731 #684)
-#688 := (iff #727 #687)
-#694 := (iff #407 #697)
-#411 := (= #396 #696)
-#417 := (= #405 #416)
-#414 := (= #404 #704)
-#703 := (= #319 -1::Int)
-#700 := [rewrite]: #703
-#415 := [monotonicity #700]: #414
-#695 := [monotonicity #415]: #417
-#693 := [monotonicity #695]: #411
-#698 := [monotonicity #693]: #694
-#425 := (iff #395 #701)
-#430 := (or #714 #706)
-#702 := (iff #430 #701)
-#424 := [rewrite]: #702
-#431 := (iff #395 #430)
-#428 := (iff #383 #706)
-#719 := (iff #726 #389)
-#717 := (or false #389)
-#718 := (iff #717 #389)
-#716 := [rewrite]: #718
-#357 := (iff #726 #717)
-#371 := (iff #724 false)
-#372 := [rewrite]: #371
-#358 := [monotonicity #372]: #357
-#705 := [trans #358 #716]: #719
-#429 := [monotonicity #705]: #428
-#352 := (iff #394 #714)
-#713 := (iff #720 #513)
-#373 := (or #513 false)
-#711 := (iff #373 #513)
-#712 := [rewrite]: #711
-#709 := (iff #720 #373)
-#710 := [monotonicity #372]: #709
-#708 := [trans #710 #712]: #713
-#715 := [monotonicity #708]: #352
-#325 := [monotonicity #715 #429]: #431
-#699 := [trans #325 #424]: #425
-#689 := [monotonicity #699 #698]: #688
-#707 := (iff #725 #730)
-#386 := (or #730 false)
-#723 := (iff #386 #730)
-#366 := [rewrite]: #723
-#722 := (iff #725 #386)
-#721 := (iff #729 false)
-#381 := [rewrite]: #721
-#382 := [monotonicity #381]: #722
-#370 := [trans #382 #366]: #707
-#690 := [monotonicity #370 #689]: #685
-#535 := [monotonicity #690]: #534
-#679 := [trans #535 #678]: #534
-#533 := [quant-inst #8 #9]: #692
-#680 := [mp #533 #679]: #686
-#553 := [unit-resolution #680 #738]: #684
-#550 := (not #684)
-#561 := (or #550 #730 #687)
-#569 := [def-axiom]: #561
-#562 := [unit-resolution #569 #553]: #560
-#563 := [unit-resolution #562 #657]: #687
-#649 := (or #701 #730)
-#676 := (not #701)
-#648 := [hypothesis]: #676
-#674 := (or #701 #389)
-#675 := [def-axiom]: #674
-#645 := [unit-resolution #675 #648]: #389
-#681 := (or #701 #513)
-#682 := [def-axiom]: #681
-#647 := [unit-resolution #682 #648]: #513
-#658 := (or #730 #714 #706)
-#659 := [th-lemma arith triangle-eq]: #658
-#655 := [unit-resolution #659 #657]: #430
-#660 := [unit-resolution #655 #647 #645]: false
-#650 := [lemma #660]: #649
-#564 := [unit-resolution #650 #657]: #701
-#670 := (not #687)
-#673 := (or #670 #676 #410)
-#555 := [def-axiom]: #673
-#574 := [unit-resolution #555 #564 #563 #551]: false
-#554 := [lemma #574]: #730
-#538 := [monotonicity #554]: #537
-#542 := [trans #538 #540]: #541
-#544 := [symm #542]: #543
-#575 := (or #565 #728)
-#567 := (or #550 #565 #728)
-#568 := [def-axiom]: #567
-#530 := [unit-resolution #568 #553]: #575
-#531 := [unit-resolution #530 #554]: #728
-#545 := [mp #531 #544]: #63
-[unit-resolution #71 #545]: false
-unsat
-6a8ee4256f7c15262363d462bd2dccb9364bb175 316 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#15 := (:var 0 Int)
-#14 := (:var 1 Int)
-#16 := (f3 #14 #15)
-#764 := (pattern #16)
+#79 := (iff #26 #78)
+#76 := (= #25 #75)
+#73 := (= #24 #72)
+#70 := (= #23 #69)
+#67 := (= #22 -1::Int)
+#68 := [rewrite]: #67
+#65 := (= #21 #64)
+#66 := [rewrite]: #65
+#71 := [monotonicity #66 #68]: #70
+#61 := (iff #19 #60)
+#58 := (iff #18 #57)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#74 := [monotonicity #62 #71]: #73
+#55 := (iff #13 #10)
+#50 := (or #10 false)
+#53 := (iff #50 #10)
+#54 := [rewrite]: #53
+#51 := (iff #13 #50)
+#48 := (iff #12 false)
+#49 := [rewrite]: #48
+#52 := [monotonicity #49]: #51
+#56 := [trans #52 #54]: #55
+#77 := [monotonicity #56 #74]: #76
+#80 := [monotonicity #77]: #79
+#85 := [trans #80 #83]: #84
+#88 := [monotonicity #85]: #87
+#129 := [trans #88 #127]: #128
+#47 := [asserted]: #27
+#130 := [mp #47 #129]: #125
+#166 := [unit-resolution #130 #165]: false
+#167 := [lemma #166]: #149
+#152 := (or #10 #137)
+#153 := [def-axiom]: #152
+#225 := [unit-resolution #153 #167]: #137
+#242 := (= f3 #116)
+#226 := [hypothesis]: #138
+#224 := (= f3 #20)
+#191 := (* -1::Int #20)
+#192 := (+ f3 #191)
+#197 := (<= #192 0::Int)
+#190 := (= #192 0::Int)
+#45 := [true-axiom]: true
+#227 := (or false #190)
+#228 := [th-lemma arith]: #227
+#229 := [unit-resolution #228 #45]: #190
+#230 := (not #190)
+#231 := (or #230 #197)
+#232 := [th-lemma arith triangle-eq]: #231
+#233 := [unit-resolution #232 #229]: #197
+#198 := (>= #192 0::Int)
+#234 := (or #230 #198)
+#235 := [th-lemma arith triangle-eq]: #234
+#236 := [unit-resolution #235 #229]: #198
+#238 := (not #198)
+#237 := (not #197)
+#239 := (or #224 #237 #238)
+#240 := [th-lemma arith triangle-eq]: #239
+#241 := [unit-resolution #240 #236 #233]: #224
+#243 := [trans #241 #226]: #242
+#244 := [trans #243 #225]: #122
+#245 := [unit-resolution #130 #244]: false
+#247 := [lemma #245]: #246
+#145 := (or #140 #138)
+#146 := [def-axiom]: #145
+#221 := [unit-resolution #146 #247]: #140
+#134 := (or #113 #89)
+#135 := [def-axiom]: #134
+#222 := [unit-resolution #135 #221]: #89
+#132 := (or #113 #102)
+#133 := [def-axiom]: #132
+#223 := [unit-resolution #133 #221]: #102
+#248 := (or #10 #90 #103)
+#249 := [th-lemma arith triangle-eq]: #248
+#250 := [unit-resolution #249 #167]: #113
+[unit-resolution #250 #223 #222]: false
+unsat
+7116e1ffcf5d8f75fc236e1967d4dc10ce43d95d 102 0
+#2 := false
 #8 := 0::Int
-#63 := -1::Int
-#107 := (* -1::Int #15)
-#104 := (* -1::Int #14)
-#110 := (div #104 #107)
-#267 := (* -1::Int #110)
-#268 := (+ #16 #267)
-#269 := (= #268 0::Int)
-#26 := (div #14 #15)
-#264 := (* -1::Int #26)
-#265 := (+ #16 #264)
-#266 := (= #265 0::Int)
-#142 := (>= #14 0::Int)
-#135 := (<= #15 0::Int)
-#227 := (or #135 #142)
-#228 := (not #227)
-#131 := (<= #14 0::Int)
-#225 := (or #131 #135)
-#226 := (not #225)
-#231 := (or #226 #228)
-#270 := (ite #231 #266 #269)
-#263 := (= #16 0::Int)
-#18 := (= #15 0::Int)
-#17 := (= #14 0::Int)
-#19 := (or #17 #18)
-#271 := (ite #19 #263 #270)
-#765 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #764) #271)
-#274 := (forall (vars (?v0 Int) (?v1 Int)) #271)
-#768 := (iff #274 #765)
-#766 := (iff #271 #271)
-#767 := [refl]: #766
-#769 := [quant-intro #767]: #768
-#234 := (ite #231 #26 #110)
-#237 := (ite #19 0::Int #234)
-#240 := (= #16 #237)
-#243 := (forall (vars (?v0 Int) (?v1 Int)) #240)
-#275 := (iff #243 #274)
-#272 := (iff #240 #271)
-#273 := [rewrite]: #272
-#276 := [quant-intro #273]: #275
-#143 := (not #142)
-#136 := (not #135)
-#146 := (and #136 #143)
-#132 := (not #131)
-#139 := (and #132 #136)
-#149 := (or #139 #146)
-#152 := (ite #149 #26 #110)
-#155 := (ite #19 0::Int #152)
-#158 := (= #16 #155)
-#161 := (forall (vars (?v0 Int) (?v1 Int)) #158)
-#244 := (iff #161 #243)
-#241 := (iff #158 #240)
-#238 := (= #155 #237)
-#235 := (= #152 #234)
-#232 := (iff #149 #231)
-#229 := (iff #146 #228)
-#230 := [rewrite]: #229
-#219 := (iff #139 #226)
-#220 := [rewrite]: #219
-#233 := [monotonicity #220 #230]: #232
-#236 := [monotonicity #233]: #235
-#239 := [monotonicity #236]: #238
-#242 := [monotonicity #239]: #241
-#245 := [quant-intro #242]: #244
-#223 := (~ #161 #161)
-#221 := (~ #158 #158)
-#222 := [refl]: #221
-#224 := [nnf-pos #222]: #223
-#28 := (- #15)
-#27 := (- #14)
-#29 := (div #27 #28)
-#21 := (< 0::Int #15)
-#23 := (< #14 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #14)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#30 := (ite #25 #26 #29)
-#31 := (ite #19 0::Int #30)
-#32 := (= #16 #31)
-#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
-#164 := (iff #33 #161)
-#98 := (and #21 #23)
-#101 := (or #22 #98)
-#113 := (ite #101 #26 #110)
-#92 := (= 0::Int #15)
-#89 := (= 0::Int #14)
-#95 := (or #89 #92)
-#116 := (ite #95 0::Int #113)
-#119 := (= #16 #116)
-#122 := (forall (vars (?v0 Int) (?v1 Int)) #119)
-#162 := (iff #122 #161)
-#159 := (iff #119 #158)
-#156 := (= #116 #155)
-#153 := (= #113 #152)
-#150 := (iff #101 #149)
-#147 := (iff #98 #146)
-#144 := (iff #23 #143)
-#145 := [rewrite]: #144
-#137 := (iff #21 #136)
-#138 := [rewrite]: #137
-#148 := [monotonicity #138 #145]: #147
-#140 := (iff #22 #139)
-#133 := (iff #20 #132)
-#134 := [rewrite]: #133
-#141 := [monotonicity #134 #138]: #140
-#151 := [monotonicity #141 #148]: #150
-#154 := [monotonicity #151]: #153
-#129 := (iff #95 #19)
-#127 := (iff #92 #18)
-#128 := [rewrite]: #127
-#125 := (iff #89 #17)
-#126 := [rewrite]: #125
-#130 := [monotonicity #126 #128]: #129
-#157 := [monotonicity #130 #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [quant-intro #160]: #162
-#123 := (iff #33 #122)
-#120 := (iff #32 #119)
-#117 := (= #31 #116)
-#114 := (= #30 #113)
-#111 := (= #29 #110)
-#108 := (= #28 #107)
-#109 := [rewrite]: #108
-#105 := (= #27 #104)
-#106 := [rewrite]: #105
-#112 := [monotonicity #106 #109]: #111
-#102 := (iff #25 #101)
-#99 := (iff #24 #98)
-#100 := [rewrite]: #99
-#103 := [monotonicity #100]: #102
-#115 := [monotonicity #103 #112]: #114
-#96 := (iff #19 #95)
-#93 := (iff #18 #92)
-#94 := [rewrite]: #93
-#90 := (iff #17 #89)
-#91 := [rewrite]: #90
-#97 := [monotonicity #91 #94]: #96
-#118 := [monotonicity #97 #115]: #117
-#121 := [monotonicity #118]: #120
-#124 := [quant-intro #121]: #123
-#165 := [trans #124 #163]: #164
-#88 := [asserted]: #33
-#166 := [mp #88 #165]: #161
-#215 := [mp~ #166 #224]: #161
-#246 := [mp #215 #245]: #243
-#277 := [mp #246 #276]: #274
-#770 := [mp #277 #769]: #765
-#66 := (f3 0::Int -1::Int)
-#69 := (= #66 0::Int)
-#82 := (not #69)
-#9 := 1::Int
-#10 := (- 1::Int)
-#11 := (f3 0::Int #10)
+#10 := 1::Int
+#11 := (- 1::Int)
+#20 := (- #11)
+#19 := (- 0::Int)
+#21 := (div #19 #20)
+#18 := (div 0::Int #11)
+#15 := (< 0::Int #11)
+#14 := (< 0::Int 0::Int)
+#16 := (and #14 #15)
+#17 := (or #16 #16)
+#22 := (ite #17 #18 #21)
 #12 := (= #11 0::Int)
-#13 := (not #12)
-#85 := (iff #13 #82)
-#72 := (= 0::Int #66)
-#77 := (not #72)
-#83 := (iff #77 #82)
-#80 := (iff #72 #69)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#78 := (iff #13 #77)
-#75 := (iff #12 #72)
-#73 := (iff #69 #72)
-#74 := [rewrite]: #73
-#70 := (iff #12 #69)
-#67 := (= #11 #66)
-#64 := (= #10 -1::Int)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#71 := [monotonicity #68]: #70
-#76 := [trans #71 #74]: #75
-#79 := [monotonicity #76]: #78
-#86 := [trans #79 #84]: #85
-#62 := [asserted]: #13
-#87 := [mp #62 #86]: #82
-#599 := (not #765)
-#600 := (or #599 #69)
-#351 := (* -1::Int -1::Int)
-#435 := (* -1::Int 0::Int)
-#436 := (div #435 #351)
-#437 := (* -1::Int #436)
-#428 := (+ #66 #437)
-#439 := (= #428 0::Int)
-#440 := (div 0::Int -1::Int)
-#441 := (* -1::Int #440)
-#438 := (+ #66 #441)
-#442 := (= #438 0::Int)
-#421 := (>= 0::Int 0::Int)
-#756 := (<= -1::Int 0::Int)
-#758 := (or #756 #421)
-#415 := (not #758)
-#545 := (<= 0::Int 0::Int)
-#752 := (or #545 #756)
-#426 := (not #752)
-#427 := (or #426 #415)
-#759 := (ite #427 #442 #439)
-#760 := (= -1::Int 0::Int)
-#761 := (= 0::Int 0::Int)
-#762 := (or #761 #760)
-#757 := (ite #762 #69 #759)
-#593 := (or #599 #757)
-#602 := (iff #593 #600)
-#604 := (iff #600 #600)
-#605 := [rewrite]: #604
-#582 := (iff #757 #69)
-#1 := true
-#696 := (ite true #69 #69)
-#694 := (iff #696 #69)
-#697 := [rewrite]: #694
-#598 := (iff #757 #696)
-#589 := (iff #759 #69)
-#704 := (ite false #69 #69)
-#587 := (iff #704 #69)
-#588 := [rewrite]: #587
-#702 := (iff #759 #704)
-#701 := (iff #439 #69)
-#547 := (= #428 #66)
-#719 := (+ #66 0::Int)
-#716 := (= #719 #66)
-#717 := [rewrite]: #716
-#544 := (= #428 #719)
-#708 := (= #437 0::Int)
-#725 := (= #435 0::Int)
-#729 := [rewrite]: #725
-#713 := (= #437 #435)
-#706 := (= #436 0::Int)
-#567 := (div 0::Int 1::Int)
-#711 := (= #567 0::Int)
-#712 := [rewrite]: #711
-#709 := (= #436 #567)
-#565 := (= #351 1::Int)
-#566 := [rewrite]: #565
-#710 := [monotonicity #729 #566]: #709
-#707 := [trans #710 #712]: #706
-#714 := [monotonicity #707]: #713
-#715 := [trans #714 #729]: #708
-#546 := [monotonicity #715]: #544
-#700 := [trans #546 #717]: #547
-#703 := [monotonicity #700]: #701
-#718 := (iff #442 #69)
-#722 := (= #438 #66)
-#720 := (= #438 #719)
-#726 := (= #441 0::Int)
-#728 := (= #441 #435)
-#449 := (= #440 0::Int)
-#727 := [rewrite]: #449
-#443 := [monotonicity #727]: #728
-#730 := [trans #443 #729]: #726
-#721 := [monotonicity #730]: #720
-#723 := [trans #721 #717]: #722
-#724 := [monotonicity #723]: #718
-#447 := (iff #427 false)
-#731 := (or false false)
-#736 := (iff #731 false)
-#446 := [rewrite]: #736
-#735 := (iff #427 #731)
-#456 := (iff #415 false)
-#749 := (not true)
-#750 := (iff #749 false)
-#748 := [rewrite]: #750
-#733 := (iff #415 #749)
-#463 := (iff #758 true)
-#743 := (or true true)
-#740 := (iff #743 true)
-#746 := [rewrite]: #740
-#461 := (iff #758 #743)
-#738 := (iff #421 true)
-#460 := [rewrite]: #738
-#741 := (iff #756 true)
-#742 := [rewrite]: #741
-#462 := [monotonicity #742 #460]: #461
-#357 := [trans #462 #746]: #463
-#734 := [monotonicity #357]: #733
-#457 := [trans #734 #748]: #456
-#751 := (iff #426 false)
-#389 := (iff #426 #749)
-#384 := (iff #752 true)
-#744 := (iff #752 #743)
-#404 := (iff #545 true)
-#405 := [rewrite]: #404
-#745 := [monotonicity #405 #742]: #744
-#747 := [trans #745 #746]: #384
-#390 := [monotonicity #747]: #389
-#737 := [trans #390 #748]: #751
-#732 := [monotonicity #737 #457]: #735
-#448 := [trans #732 #446]: #447
-#705 := [monotonicity #448 #724 #703]: #702
-#548 := [trans #705 #588]: #589
-#402 := (iff #762 true)
-#754 := (or true false)
-#398 := (iff #754 true)
-#739 := [rewrite]: #398
-#414 := (iff #762 #754)
-#413 := (iff #760 false)
-#418 := [rewrite]: #413
-#763 := (iff #761 true)
-#753 := [rewrite]: #763
-#755 := [monotonicity #753 #418]: #414
-#403 := [trans #755 #739]: #402
-#693 := [monotonicity #403 #548]: #598
-#597 := [trans #693 #697]: #582
-#603 := [monotonicity #597]: #602
-#698 := [trans #603 #605]: #602
-#601 := [quant-inst #8 #63]: #593
-#695 := [mp #601 #698]: #600
-[unit-resolution #695 #87 #770]: false
-unsat
-beaa0a62fe76b86ad510bf8c2d69fe2ce8dbdc5f 310 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#14 := (:var 0 Int)
-#13 := (:var 1 Int)
-#15 := (f3 #13 #14)
-#749 := (pattern #15)
-#16 := 0::Int
-#63 := -1::Int
-#98 := (* -1::Int #14)
-#95 := (* -1::Int #13)
-#101 := (div #95 #98)
-#252 := (* -1::Int #101)
-#253 := (+ #15 #252)
-#254 := (= #253 0::Int)
-#26 := (div #13 #14)
-#249 := (* -1::Int #26)
-#250 := (+ #15 #249)
-#251 := (= #250 0::Int)
-#127 := (>= #13 0::Int)
-#120 := (<= #14 0::Int)
-#212 := (or #120 #127)
-#213 := (not #212)
-#116 := (<= #13 0::Int)
-#210 := (or #116 #120)
-#211 := (not #210)
-#216 := (or #211 #213)
-#255 := (ite #216 #251 #254)
-#248 := (= #15 0::Int)
-#18 := (= #14 0::Int)
-#17 := (= #13 0::Int)
-#19 := (or #17 #18)
-#256 := (ite #19 #248 #255)
-#750 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #749) #256)
-#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
-#753 := (iff #259 #750)
-#751 := (iff #256 #256)
-#752 := [refl]: #751
-#754 := [quant-intro #752]: #753
-#219 := (ite #216 #26 #101)
-#222 := (ite #19 0::Int #219)
-#225 := (= #15 #222)
-#228 := (forall (vars (?v0 Int) (?v1 Int)) #225)
-#260 := (iff #228 #259)
-#257 := (iff #225 #256)
-#258 := [rewrite]: #257
-#261 := [quant-intro #258]: #260
-#128 := (not #127)
-#121 := (not #120)
-#131 := (and #121 #128)
-#117 := (not #116)
-#124 := (and #117 #121)
-#134 := (or #124 #131)
-#137 := (ite #134 #26 #101)
-#140 := (ite #19 0::Int #137)
-#143 := (= #15 #140)
-#146 := (forall (vars (?v0 Int) (?v1 Int)) #143)
-#229 := (iff #146 #228)
-#226 := (iff #143 #225)
-#223 := (= #140 #222)
-#220 := (= #137 #219)
-#217 := (iff #134 #216)
-#214 := (iff #131 #213)
-#215 := [rewrite]: #214
-#204 := (iff #124 #211)
-#205 := [rewrite]: #204
-#218 := [monotonicity #205 #215]: #217
-#221 := [monotonicity #218]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [quant-intro #227]: #229
-#208 := (~ #146 #146)
-#206 := (~ #143 #143)
-#207 := [refl]: #206
-#209 := [nnf-pos #207]: #208
-#28 := (- #14)
-#27 := (- #13)
-#29 := (div #27 #28)
-#21 := (< 0::Int #14)
-#23 := (< #13 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #13)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#30 := (ite #25 #26 #29)
-#31 := (ite #19 0::Int #30)
-#32 := (= #15 #31)
-#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
-#149 := (iff #33 #146)
-#89 := (and #21 #23)
-#92 := (or #22 #89)
-#104 := (ite #92 #26 #101)
-#107 := (ite #19 0::Int #104)
-#110 := (= #15 #107)
-#113 := (forall (vars (?v0 Int) (?v1 Int)) #110)
-#147 := (iff #113 #146)
-#144 := (iff #110 #143)
-#141 := (= #107 #140)
-#138 := (= #104 #137)
-#135 := (iff #92 #134)
-#132 := (iff #89 #131)
-#129 := (iff #23 #128)
-#130 := [rewrite]: #129
-#122 := (iff #21 #121)
-#123 := [rewrite]: #122
-#133 := [monotonicity #123 #130]: #132
-#125 := (iff #22 #124)
-#118 := (iff #20 #117)
-#119 := [rewrite]: #118
-#126 := [monotonicity #119 #123]: #125
-#136 := [monotonicity #126 #133]: #135
-#139 := [monotonicity #136]: #138
-#142 := [monotonicity #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [quant-intro #145]: #147
-#114 := (iff #33 #113)
-#111 := (iff #32 #110)
-#108 := (= #31 #107)
-#105 := (= #30 #104)
-#102 := (= #29 #101)
-#99 := (= #28 #98)
-#100 := [rewrite]: #99
-#96 := (= #27 #95)
-#97 := [rewrite]: #96
-#103 := [monotonicity #97 #100]: #102
-#93 := (iff #25 #92)
-#90 := (iff #24 #89)
+#9 := (= 0::Int 0::Int)
+#13 := (or #9 #12)
+#23 := (ite #13 0::Int #22)
+#24 := (= #23 0::Int)
+#25 := (not #24)
+#123 := (iff #25 false)
+#1 := true
+#118 := (not true)
+#121 := (iff #118 false)
+#122 := [rewrite]: #121
+#119 := (iff #25 #118)
+#116 := (iff #24 true)
+#46 := (iff #9 true)
+#47 := [rewrite]: #46
+#114 := (iff #24 #9)
+#108 := (ite true 0::Int 0::Int)
+#111 := (= #108 0::Int)
+#112 := [rewrite]: #111
+#109 := (= #23 #108)
+#106 := (= #22 0::Int)
+#48 := -1::Int
+#65 := (< 0::Int -1::Int)
+#68 := (and #14 #65)
+#101 := (ite #68 0::Int 0::Int)
+#104 := (= #101 0::Int)
+#105 := [rewrite]: #104
+#102 := (= #22 #101)
+#99 := (= #21 0::Int)
+#94 := (div 0::Int 1::Int)
+#97 := (= #94 0::Int)
+#98 := [rewrite]: #97
+#95 := (= #21 #94)
+#92 := (= #20 1::Int)
+#87 := (- -1::Int)
+#90 := (= #87 1::Int)
 #91 := [rewrite]: #90
-#94 := [monotonicity #91]: #93
-#106 := [monotonicity #94 #103]: #105
-#109 := [monotonicity #106]: #108
-#112 := [monotonicity #109]: #111
-#115 := [quant-intro #112]: #114
-#150 := [trans #115 #148]: #149
-#88 := [asserted]: #33
-#151 := [mp #88 #150]: #146
-#200 := [mp~ #151 #209]: #146
-#231 := [mp #200 #230]: #228
-#262 := [mp #231 #261]: #259
-#755 := [mp #262 #754]: #750
-#8 := 1::Int
-#66 := (f3 1::Int -1::Int)
-#69 := (= #66 -1::Int)
-#82 := (not #69)
-#9 := (- 1::Int)
-#10 := (f3 1::Int #9)
-#11 := (= #10 #9)
-#12 := (not #11)
-#85 := (iff #12 #82)
-#72 := (= -1::Int #66)
-#77 := (not #72)
-#83 := (iff #77 #82)
-#80 := (iff #72 #69)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#78 := (iff #12 #77)
-#75 := (iff #11 #72)
-#73 := (iff #69 #72)
-#74 := [rewrite]: #73
-#70 := (iff #11 #69)
-#64 := (= #9 -1::Int)
-#65 := [rewrite]: #64
-#67 := (= #10 #66)
-#68 := [monotonicity #65]: #67
-#71 := [monotonicity #68 #65]: #70
-#76 := [trans #71 #74]: #75
-#79 := [monotonicity #76]: #78
-#86 := [trans #79 #84]: #85
-#62 := [asserted]: #12
-#87 := [mp #62 #86]: #82
-#680 := (not #750)
-#684 := (or #680 #69)
-#336 := (* -1::Int -1::Int)
-#420 := (* -1::Int 1::Int)
-#421 := (div #420 #336)
-#422 := (* -1::Int #421)
-#413 := (+ #66 #422)
-#424 := (= #413 0::Int)
-#425 := (div 1::Int -1::Int)
-#426 := (* -1::Int #425)
-#423 := (+ #66 #426)
-#427 := (= #423 0::Int)
-#406 := (>= 1::Int 0::Int)
-#741 := (<= -1::Int 0::Int)
-#743 := (or #741 #406)
-#400 := (not #743)
-#530 := (<= 1::Int 0::Int)
-#737 := (or #530 #741)
-#411 := (not #737)
-#412 := (or #411 #400)
-#744 := (ite #412 #427 #424)
-#745 := (= #66 0::Int)
-#746 := (= -1::Int 0::Int)
-#747 := (= 1::Int 0::Int)
-#742 := (or #747 #746)
-#748 := (ite #742 #745 #744)
-#671 := (or #680 #748)
-#665 := (iff #671 #684)
-#664 := (iff #684 #684)
-#674 := [rewrite]: #664
-#590 := (iff #748 #69)
-#578 := (ite false #745 #69)
-#588 := (iff #578 #69)
-#589 := [rewrite]: #588
-#586 := (iff #748 #578)
-#584 := (iff #744 #69)
-#678 := (ite false #69 #69)
-#567 := (iff #678 #69)
-#582 := [rewrite]: #567
-#679 := (iff #744 #678)
-#681 := (iff #424 #69)
-#702 := (+ 1::Int #66)
-#550 := (= #702 0::Int)
-#694 := (iff #550 #69)
-#695 := [rewrite]: #694
-#574 := (iff #424 #550)
-#572 := (= #413 #702)
-#705 := (+ #66 1::Int)
-#707 := (= #705 #702)
-#708 := [rewrite]: #707
-#687 := (= #413 #705)
-#688 := (= #422 1::Int)
-#714 := (= #336 1::Int)
-#711 := [rewrite]: #714
-#685 := (= #422 #336)
-#531 := (= #421 -1::Int)
-#698 := (div -1::Int 1::Int)
-#700 := (= #698 -1::Int)
-#529 := [rewrite]: #700
-#699 := (= #421 #698)
-#691 := (= #420 -1::Int)
-#692 := [rewrite]: #691
-#693 := [monotonicity #692 #711]: #699
-#532 := [trans #693 #529]: #531
-#686 := [monotonicity #532]: #685
-#689 := [trans #686 #711]: #688
-#690 := [monotonicity #689]: #687
-#573 := [trans #690 #708]: #572
-#533 := [monotonicity #573]: #574
-#583 := [trans #533 #695]: #681
-#696 := (iff #427 #69)
-#551 := (iff #427 #550)
-#703 := (= #423 #702)
-#706 := (= #423 #705)
-#715 := (= #426 1::Int)
-#428 := (= #426 #336)
-#712 := (= #425 -1::Int)
-#713 := [rewrite]: #712
-#710 := [monotonicity #713]: #428
-#704 := [trans #710 #711]: #715
-#701 := [monotonicity #704]: #706
-#709 := [trans #701 #708]: #703
-#552 := [monotonicity #709]: #551
-#697 := [trans #552 #695]: #696
-#433 := (iff #412 false)
-#399 := (or false false)
-#724 := (iff #399 false)
-#387 := [rewrite]: #724
-#431 := (iff #412 #399)
-#717 := (iff #400 false)
-#1 := true
-#374 := (not true)
-#733 := (iff #374 false)
-#736 := [rewrite]: #733
-#716 := (iff #400 #374)
-#441 := (iff #743 true)
-#447 := (or true true)
-#718 := (iff #447 true)
-#719 := [rewrite]: #718
-#448 := (iff #743 #447)
-#445 := (iff #406 true)
-#446 := [rewrite]: #445
-#727 := (iff #741 true)
-#728 := [rewrite]: #727
-#342 := [monotonicity #728 #446]: #448
-#442 := [trans #342 #719]: #441
-#720 := [monotonicity #442]: #716
-#721 := [trans #720 #736]: #717
-#722 := (iff #411 false)
-#375 := (iff #411 #374)
-#732 := (iff #737 true)
-#729 := (or false true)
-#731 := (iff #729 true)
-#369 := [rewrite]: #731
-#730 := (iff #737 #729)
-#390 := (iff #530 false)
-#726 := [rewrite]: #390
-#725 := [monotonicity #726 #728]: #730
-#734 := [trans #725 #369]: #732
-#735 := [monotonicity #734]: #375
-#723 := [trans #735 #736]: #722
-#432 := [monotonicity #723 #721]: #431
-#434 := [trans #432 #387]: #433
-#682 := [monotonicity #434 #697 #583]: #679
-#585 := [trans #682 #582]: #584
-#388 := (iff #742 false)
-#740 := (iff #742 #399)
-#403 := (iff #746 false)
-#739 := [rewrite]: #403
-#738 := (iff #747 false)
-#398 := [rewrite]: #738
-#383 := [monotonicity #398 #739]: #740
-#389 := [trans #383 #387]: #388
-#587 := [monotonicity #389 #585]: #586
-#683 := [trans #587 #589]: #590
-#662 := [monotonicity #683]: #665
-#675 := [trans #662 #674]: #665
-#673 := [quant-inst #8 #63]: #671
-#676 := [mp #673 #675]: #684
-[unit-resolution #676 #87 #755]: false
-unsat
-d7870bb48e209893f272c06c1d45c5a7c1765225 306 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#16 := (:var 0 Int)
-#15 := (:var 1 Int)
-#17 := (f3 #15 #16)
-#742 := (pattern #17)
-#18 := 0::Int
-#65 := -1::Int
-#91 := (* -1::Int #16)
-#88 := (* -1::Int #15)
-#94 := (div #88 #91)
-#245 := (* -1::Int #94)
-#246 := (+ #17 #245)
-#247 := (= #246 0::Int)
-#28 := (div #15 #16)
-#242 := (* -1::Int #28)
-#243 := (+ #17 #242)
-#244 := (= #243 0::Int)
-#120 := (>= #15 0::Int)
-#113 := (<= #16 0::Int)
-#205 := (or #113 #120)
-#206 := (not #205)
-#109 := (<= #15 0::Int)
-#203 := (or #109 #113)
-#204 := (not #203)
-#209 := (or #204 #206)
-#248 := (ite #209 #244 #247)
-#241 := (= #17 0::Int)
-#20 := (= #16 0::Int)
-#19 := (= #15 0::Int)
-#21 := (or #19 #20)
-#249 := (ite #21 #241 #248)
-#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #249)
-#252 := (forall (vars (?v0 Int) (?v1 Int)) #249)
-#746 := (iff #252 #743)
-#744 := (iff #249 #249)
-#745 := [refl]: #744
-#747 := [quant-intro #745]: #746
-#212 := (ite #209 #28 #94)
-#215 := (ite #21 0::Int #212)
-#218 := (= #17 #215)
-#221 := (forall (vars (?v0 Int) (?v1 Int)) #218)
-#253 := (iff #221 #252)
-#250 := (iff #218 #249)
-#251 := [rewrite]: #250
-#254 := [quant-intro #251]: #253
-#121 := (not #120)
-#114 := (not #113)
-#124 := (and #114 #121)
-#110 := (not #109)
-#117 := (and #110 #114)
-#127 := (or #117 #124)
-#130 := (ite #127 #28 #94)
-#133 := (ite #21 0::Int #130)
-#136 := (= #17 #133)
-#139 := (forall (vars (?v0 Int) (?v1 Int)) #136)
-#222 := (iff #139 #221)
-#219 := (iff #136 #218)
-#216 := (= #133 #215)
-#213 := (= #130 #212)
-#210 := (iff #127 #209)
-#207 := (iff #124 #206)
-#208 := [rewrite]: #207
-#197 := (iff #117 #204)
-#198 := [rewrite]: #197
-#211 := [monotonicity #198 #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [monotonicity #217]: #219
-#223 := [quant-intro #220]: #222
-#201 := (~ #139 #139)
-#199 := (~ #136 #136)
-#200 := [refl]: #199
-#202 := [nnf-pos #200]: #201
-#30 := (- #16)
-#29 := (- #15)
-#31 := (div #29 #30)
-#23 := (< 0::Int #16)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#32 := (ite #27 #28 #31)
-#33 := (ite #21 0::Int #32)
-#34 := (= #17 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#142 := (iff #35 #139)
-#81 := (and #23 #25)
-#85 := (or #24 #81)
-#97 := (ite #85 #28 #94)
-#100 := (ite #21 0::Int #97)
-#103 := (= #17 #100)
-#106 := (forall (vars (?v0 Int) (?v1 Int)) #103)
-#140 := (iff #106 #139)
-#137 := (iff #103 #136)
-#134 := (= #100 #133)
-#131 := (= #97 #130)
-#128 := (iff #85 #127)
-#125 := (iff #81 #124)
-#122 := (iff #25 #121)
-#123 := [rewrite]: #122
-#115 := (iff #23 #114)
-#116 := [rewrite]: #115
-#126 := [monotonicity #116 #123]: #125
-#118 := (iff #24 #117)
-#111 := (iff #22 #110)
-#112 := [rewrite]: #111
-#119 := [monotonicity #112 #116]: #118
-#129 := [monotonicity #119 #126]: #128
-#132 := [monotonicity #129]: #131
-#135 := [monotonicity #132]: #134
-#138 := [monotonicity #135]: #137
-#141 := [quant-intro #138]: #140
-#107 := (iff #35 #106)
-#104 := (iff #34 #103)
-#101 := (= #33 #100)
-#98 := (= #32 #97)
-#95 := (= #31 #94)
-#92 := (= #30 #91)
-#93 := [rewrite]: #92
-#89 := (= #29 #88)
-#90 := [rewrite]: #89
-#96 := [monotonicity #90 #93]: #95
-#86 := (iff #27 #85)
-#83 := (iff #26 #81)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#99 := [monotonicity #87 #96]: #98
-#102 := [monotonicity #99]: #101
-#105 := [monotonicity #102]: #104
-#108 := [quant-intro #105]: #107
-#143 := [trans #108 #141]: #142
-#80 := [asserted]: #35
-#144 := [mp #80 #143]: #139
-#193 := [mp~ #144 #202]: #139
-#224 := [mp #193 #223]: #221
-#255 := [mp #224 #254]: #252
-#748 := [mp #255 #747]: #743
-#71 := -3::Int
-#8 := 3::Int
-#68 := (f3 3::Int -1::Int)
-#74 := (= #68 -3::Int)
-#77 := (not #74)
-#12 := (- 3::Int)
-#9 := 1::Int
-#10 := (- 1::Int)
-#11 := (f3 3::Int #10)
-#13 := (= #11 #12)
-#14 := (not #13)
-#78 := (iff #14 #77)
-#75 := (iff #13 #74)
-#72 := (= #12 -3::Int)
-#73 := [rewrite]: #72
-#69 := (= #11 #68)
-#66 := (= #10 -1::Int)
-#67 := [rewrite]: #66
+#88 := (= #20 #87)
+#49 := (= #11 -1::Int)
+#50 := [rewrite]: #49
+#89 := [monotonicity #50]: #88
+#93 := [trans #89 #91]: #92
+#85 := (= #19 0::Int)
+#86 := [rewrite]: #85
+#96 := [monotonicity #86 #93]: #95
+#100 := [trans #96 #98]: #99
+#83 := (= #18 0::Int)
+#78 := (div 0::Int -1::Int)
+#81 := (= #78 0::Int)
+#82 := [rewrite]: #81
+#79 := (= #18 #78)
+#80 := [monotonicity #50]: #79
+#84 := [trans #80 #82]: #83
+#76 := (iff #17 #68)
+#71 := (or #68 #68)
+#74 := (iff #71 #68)
+#75 := [rewrite]: #74
+#72 := (iff #17 #71)
+#69 := (iff #16 #68)
+#66 := (iff #15 #65)
+#67 := [monotonicity #50]: #66
 #70 := [monotonicity #67]: #69
-#76 := [monotonicity #70 #73]: #75
-#79 := [monotonicity #76]: #78
-#64 := [asserted]: #14
-#82 := [mp #64 #79]: #77
-#666 := (not #743)
-#658 := (or #666 #74)
-#329 := (* -1::Int -1::Int)
-#413 := (* -1::Int 3::Int)
-#414 := (div #413 #329)
-#415 := (* -1::Int #414)
-#406 := (+ #68 #415)
-#417 := (= #406 0::Int)
-#418 := (div 3::Int -1::Int)
-#419 := (* -1::Int #418)
-#416 := (+ #68 #419)
-#420 := (= #416 0::Int)
-#399 := (>= 3::Int 0::Int)
-#734 := (<= -1::Int 0::Int)
-#736 := (or #734 #399)
-#393 := (not #736)
-#523 := (<= 3::Int 0::Int)
-#730 := (or #523 #734)
-#404 := (not #730)
-#405 := (or #404 #393)
-#737 := (ite #405 #420 #417)
-#738 := (= #68 0::Int)
-#739 := (= -1::Int 0::Int)
-#740 := (= 3::Int 0::Int)
-#735 := (or #740 #739)
-#741 := (ite #735 #738 #737)
-#655 := (or #666 #741)
-#667 := (iff #655 #658)
-#669 := (iff #658 #658)
-#665 := [rewrite]: #669
-#677 := (iff #741 #74)
-#581 := (ite false #738 #74)
-#676 := (iff #581 #74)
-#673 := [rewrite]: #676
-#582 := (iff #741 #581)
-#579 := (iff #737 #74)
-#560 := (ite false #74 #74)
-#578 := (iff #560 #74)
-#571 := [rewrite]: #578
-#575 := (iff #737 #560)
-#672 := (iff #417 #74)
-#700 := (+ 3::Int #68)
-#544 := (= #700 0::Int)
-#688 := (iff #544 #74)
-#689 := [rewrite]: #688
-#576 := (iff #417 #544)
-#526 := (= #406 #700)
-#699 := (+ #68 3::Int)
-#701 := (= #699 #700)
-#696 := [rewrite]: #701
-#566 := (= #406 #699)
-#683 := (= #415 3::Int)
-#421 := (* -1::Int -3::Int)
-#704 := (= #421 3::Int)
-#708 := [rewrite]: #704
-#682 := (= #415 #421)
-#679 := (= #414 -3::Int)
-#693 := (div -3::Int 1::Int)
-#525 := (= #693 -3::Int)
-#678 := [rewrite]: #525
-#522 := (= #414 #693)
-#692 := (= #329 1::Int)
-#686 := [rewrite]: #692
-#685 := (= #413 -3::Int)
-#691 := [rewrite]: #685
-#524 := [monotonicity #691 #686]: #522
-#681 := [trans #524 #678]: #679
-#680 := [monotonicity #681]: #682
-#565 := [trans #680 #708]: #683
-#567 := [monotonicity #565]: #566
-#674 := [trans #567 #696]: #526
-#671 := [monotonicity #674]: #576
-#675 := [trans #671 #689]: #672
-#690 := (iff #420 #74)
-#545 := (iff #420 #544)
-#702 := (= #416 #700)
-#694 := (= #416 #699)
-#697 := (= #419 3::Int)
-#703 := (= #419 #421)
-#705 := (= #418 -3::Int)
-#706 := [rewrite]: #705
-#707 := [monotonicity #706]: #703
-#698 := [trans #707 #708]: #697
-#695 := [monotonicity #698]: #694
-#543 := [trans #695 #696]: #702
-#687 := [monotonicity #543]: #545
-#684 := [trans #687 #689]: #690
-#426 := (iff #405 false)
-#392 := (or false false)
-#717 := (iff #392 false)
-#380 := [rewrite]: #717
-#424 := (iff #405 #392)
-#710 := (iff #393 false)
-#1 := true
-#367 := (not true)
-#726 := (iff #367 false)
-#729 := [rewrite]: #726
-#709 := (iff #393 #367)
-#434 := (iff #736 true)
-#440 := (or true true)
-#711 := (iff #440 true)
-#712 := [rewrite]: #711
-#441 := (iff #736 #440)
-#438 := (iff #399 true)
-#439 := [rewrite]: #438
-#720 := (iff #734 true)
-#721 := [rewrite]: #720
-#335 := [monotonicity #721 #439]: #441
-#435 := [trans #335 #712]: #434
-#713 := [monotonicity #435]: #709
-#714 := [trans #713 #729]: #710
-#715 := (iff #404 false)
-#368 := (iff #404 #367)
-#725 := (iff #730 true)
-#722 := (or false true)
-#724 := (iff #722 true)
-#362 := [rewrite]: #724
-#723 := (iff #730 #722)
-#383 := (iff #523 false)
-#719 := [rewrite]: #383
-#718 := [monotonicity #719 #721]: #723
-#727 := [trans #718 #362]: #725
-#728 := [monotonicity #727]: #368
-#716 := [trans #728 #729]: #715
-#425 := [monotonicity #716 #714]: #424
-#427 := [trans #425 #380]: #426
-#577 := [monotonicity #427 #684 #675]: #575
-#580 := [trans #577 #571]: #579
-#381 := (iff #735 false)
-#733 := (iff #735 #392)
-#396 := (iff #739 false)
-#732 := [rewrite]: #396
-#731 := (iff #740 false)
-#391 := [rewrite]: #731
-#376 := [monotonicity #391 #732]: #733
-#382 := [trans #376 #380]: #381
-#583 := [monotonicity #382 #580]: #582
-#664 := [trans #583 #673]: #677
-#668 := [monotonicity #664]: #667
-#670 := [trans #668 #665]: #667
-#657 := [quant-inst #8 #65]: #655
-#659 := [mp #657 #670]: #658
-[unit-resolution #659 #82 #748]: false
-unsat
-5ee37b7887579207f198e2d96f811691f176d723 350 0
-#2 := false
-#18 := 0::Int
-#9 := 1::Int
-decl f4 :: Int
-#8 := f4
-#65 := -1::Int
-#71 := (* -1::Int f4)
-#714 := (div #71 1::Int)
-#712 := (* -1::Int #714)
-decl f3 :: (-> Int Int Int)
-#68 := (f3 f4 -1::Int)
-#717 := (+ #68 #712)
-#691 := (<= #717 0::Int)
-#708 := (= #717 0::Int)
-#744 := (= f4 0::Int)
-#574 := (not #744)
-#739 := (<= f4 0::Int)
-#615 := [hypothesis]: #744
-#595 := (or #574 #739)
-#541 := [th-lemma arith triangle-eq]: #595
-#596 := [unit-resolution #541 #615]: #739
-#80 := (+ f4 #68)
-#338 := (<= #80 0::Int)
-#577 := (not #338)
-#422 := (>= #80 0::Int)
-#743 := (>= f4 0::Int)
-#684 := (not #708)
-#689 := (>= #717 0::Int)
-#621 := (not #689)
-#630 := (not #422)
-#631 := [hypothesis]: #630
-#622 := (or #621 #422)
-#629 := [hypothesis]: #689
-#665 := (+ f4 #714)
-#662 := (>= #665 0::Int)
-#672 := (= #665 0::Int)
-#1 := true
-#62 := [true-axiom]: true
-#632 := (or false #672)
-#633 := [th-lemma arith]: #632
-#628 := [unit-resolution #633 #62]: #672
-#634 := (not #672)
-#620 := (or #634 #662)
-#616 := [th-lemma arith triangle-eq]: #620
-#617 := [unit-resolution #616 #628]: #662
-#618 := [th-lemma arith farkas 1 -1 1 #617 #631 #629]: false
-#623 := [lemma #618]: #622
-#661 := [unit-resolution #623 #631]: #621
-#624 := (or #684 #689)
-#619 := [th-lemma arith triangle-eq]: #624
-#625 := [unit-resolution #619 #661]: #684
-#599 := (or #744 #708)
-#748 := (= #68 0::Int)
-#696 := (ite #744 #748 #708)
-#16 := (:var 0 Int)
-#15 := (:var 1 Int)
-#17 := (f3 #15 #16)
-#751 := (pattern #17)
-#100 := (* -1::Int #16)
-#97 := (* -1::Int #15)
-#103 := (div #97 #100)
-#254 := (* -1::Int #103)
-#255 := (+ #17 #254)
-#256 := (= #255 0::Int)
-#28 := (div #15 #16)
-#251 := (* -1::Int #28)
-#252 := (+ #17 #251)
-#253 := (= #252 0::Int)
-#129 := (>= #15 0::Int)
-#122 := (<= #16 0::Int)
-#214 := (or #122 #129)
-#215 := (not #214)
-#118 := (<= #15 0::Int)
-#212 := (or #118 #122)
-#213 := (not #212)
-#218 := (or #213 #215)
-#257 := (ite #218 #253 #256)
-#250 := (= #17 0::Int)
-#20 := (= #16 0::Int)
-#19 := (= #15 0::Int)
-#21 := (or #19 #20)
-#258 := (ite #21 #250 #257)
-#752 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #751) #258)
-#261 := (forall (vars (?v0 Int) (?v1 Int)) #258)
-#755 := (iff #261 #752)
-#753 := (iff #258 #258)
-#754 := [refl]: #753
-#756 := [quant-intro #754]: #755
-#221 := (ite #218 #28 #103)
-#224 := (ite #21 0::Int #221)
-#227 := (= #17 #224)
-#230 := (forall (vars (?v0 Int) (?v1 Int)) #227)
-#262 := (iff #230 #261)
-#259 := (iff #227 #258)
-#260 := [rewrite]: #259
-#263 := [quant-intro #260]: #262
-#130 := (not #129)
-#123 := (not #122)
-#133 := (and #123 #130)
-#119 := (not #118)
-#126 := (and #119 #123)
-#136 := (or #126 #133)
-#139 := (ite #136 #28 #103)
-#142 := (ite #21 0::Int #139)
-#145 := (= #17 #142)
-#148 := (forall (vars (?v0 Int) (?v1 Int)) #145)
-#231 := (iff #148 #230)
-#228 := (iff #145 #227)
-#225 := (= #142 #224)
-#222 := (= #139 #221)
-#219 := (iff #136 #218)
-#216 := (iff #133 #215)
-#217 := [rewrite]: #216
-#206 := (iff #126 #213)
-#207 := [rewrite]: #206
-#220 := [monotonicity #207 #217]: #219
-#223 := [monotonicity #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [quant-intro #229]: #231
-#210 := (~ #148 #148)
-#208 := (~ #145 #145)
-#209 := [refl]: #208
-#211 := [nnf-pos #209]: #210
-#30 := (- #16)
-#29 := (- #15)
-#31 := (div #29 #30)
-#23 := (< 0::Int #16)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#32 := (ite #27 #28 #31)
-#33 := (ite #21 0::Int #32)
-#34 := (= #17 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#151 := (iff #35 #148)
-#91 := (and #23 #25)
-#94 := (or #24 #91)
-#106 := (ite #94 #28 #103)
-#109 := (ite #21 0::Int #106)
-#112 := (= #17 #109)
-#115 := (forall (vars (?v0 Int) (?v1 Int)) #112)
-#149 := (iff #115 #148)
-#146 := (iff #112 #145)
-#143 := (= #109 #142)
-#140 := (= #106 #139)
-#137 := (iff #94 #136)
-#134 := (iff #91 #133)
-#131 := (iff #25 #130)
-#132 := [rewrite]: #131
-#124 := (iff #23 #123)
-#125 := [rewrite]: #124
-#135 := [monotonicity #125 #132]: #134
-#127 := (iff #24 #126)
-#120 := (iff #22 #119)
-#121 := [rewrite]: #120
-#128 := [monotonicity #121 #125]: #127
-#138 := [monotonicity #128 #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [quant-intro #147]: #149
-#116 := (iff #35 #115)
-#113 := (iff #34 #112)
-#110 := (= #33 #109)
-#107 := (= #32 #106)
-#104 := (= #31 #103)
-#101 := (= #30 #100)
-#102 := [rewrite]: #101
-#98 := (= #29 #97)
-#99 := [rewrite]: #98
-#105 := [monotonicity #99 #102]: #104
-#95 := (iff #27 #94)
-#92 := (iff #26 #91)
-#93 := [rewrite]: #92
-#96 := [monotonicity #93]: #95
-#108 := [monotonicity #96 #105]: #107
-#111 := [monotonicity #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [quant-intro #114]: #116
-#152 := [trans #117 #150]: #151
-#90 := [asserted]: #35
-#153 := [mp #90 #152]: #148
-#202 := [mp~ #153 #211]: #148
-#233 := [mp #202 #232]: #230
-#264 := [mp #233 #263]: #261
-#757 := [mp #264 #756]: #752
-#699 := (not #752)
-#693 := (or #699 #696)
-#423 := (* -1::Int -1::Int)
-#424 := (div #71 #423)
-#415 := (* -1::Int #424)
-#426 := (+ #68 #415)
-#427 := (= #426 0::Int)
-#428 := (div f4 -1::Int)
-#425 := (* -1::Int #428)
-#429 := (+ #68 #425)
-#408 := (= #429 0::Int)
-#745 := (<= -1::Int 0::Int)
-#402 := (or #745 #743)
-#532 := (not #402)
-#413 := (or #739 #745)
-#414 := (not #413)
-#746 := (or #414 #532)
-#747 := (ite #746 #408 #427)
-#749 := (= -1::Int 0::Int)
-#750 := (or #744 #749)
-#740 := (ite #750 #748 #747)
-#694 := (or #699 #740)
-#701 := (iff #694 #693)
-#702 := (iff #693 #693)
-#531 := [rewrite]: #702
-#697 := (iff #740 #696)
-#553 := (iff #747 #708)
-#709 := (ite false #408 #708)
-#711 := (iff #709 #708)
-#552 := [rewrite]: #711
-#710 := (iff #747 #709)
-#703 := (iff #427 #708)
-#706 := (= #426 #717)
-#716 := (= #415 #712)
-#715 := (= #424 #714)
-#435 := (= #423 1::Int)
-#436 := [rewrite]: #435
-#430 := [monotonicity #436]: #715
-#713 := [monotonicity #430]: #716
-#707 := [monotonicity #713]: #706
-#704 := [monotonicity #707]: #703
-#433 := (iff #746 false)
-#444 := (or false false)
-#719 := (iff #444 false)
-#723 := [rewrite]: #719
-#718 := (iff #746 #444)
-#721 := (iff #532 false)
-#371 := (not true)
-#376 := (iff #371 false)
-#377 := [rewrite]: #376
-#344 := (iff #532 #371)
-#449 := (iff #402 true)
-#738 := (or true #743)
-#447 := (iff #738 true)
-#448 := [rewrite]: #447
-#724 := (iff #402 #738)
-#391 := (iff #745 true)
-#392 := [rewrite]: #391
-#725 := [monotonicity #392]: #724
-#450 := [trans #725 #448]: #449
-#720 := [monotonicity #450]: #344
-#443 := [trans #720 #377]: #721
-#737 := (iff #414 false)
-#734 := (iff #414 #371)
-#727 := (iff #413 true)
-#728 := (or #739 true)
-#731 := (iff #728 true)
-#732 := [rewrite]: #731
-#729 := (iff #413 #728)
-#730 := [monotonicity #392]: #729
-#733 := [trans #730 #732]: #727
-#736 := [monotonicity #733]: #734
-#735 := [trans #736 #377]: #737
-#722 := [monotonicity #735 #443]: #718
-#434 := [trans #722 #723]: #433
-#705 := [monotonicity #434 #704]: #710
-#554 := [trans #705 #552]: #553
-#389 := (iff #750 #744)
-#741 := (or #744 false)
-#385 := (iff #741 #744)
-#726 := [rewrite]: #385
-#401 := (iff #750 #741)
-#400 := (iff #749 false)
-#405 := [rewrite]: #400
-#742 := [monotonicity #405]: #401
-#390 := [trans #742 #726]: #389
-#698 := [monotonicity #390 #554]: #697
-#695 := [monotonicity #698]: #701
-#533 := [trans #695 #531]: #701
-#700 := [quant-inst #8 #65]: #694
-#534 := [mp #700 #533]: #693
-#598 := [unit-resolution #534 #757]: #696
-#692 := (not #696)
-#535 := (or #692 #744 #708)
-#683 := [def-axiom]: #535
-#600 := [unit-resolution #683 #598]: #599
-#493 := [unit-resolution #600 #625]: #744
-#604 := (or #574 #743)
-#605 := [th-lemma arith triangle-eq]: #604
-#606 := [unit-resolution #605 #493]: #743
-#688 := (>= #68 0::Int)
-#611 := (or #574 #748)
-#575 := (or #692 #574 #748)
-#576 := [def-axiom]: #575
-#607 := [unit-resolution #576 #598]: #611
-#608 := [unit-resolution #607 #493]: #748
-#585 := (not #748)
-#609 := (or #585 #688)
-#612 := [th-lemma arith triangle-eq]: #609
-#613 := [unit-resolution #612 #608]: #688
-#614 := [th-lemma arith farkas 1 -1 1 #613 #631 #606]: false
-#610 := [lemma #614]: #422
-#597 := (or #577 #630)
-#81 := (= #80 0::Int)
-#84 := (not #81)
-#12 := (- f4)
-#10 := (- 1::Int)
-#11 := (f3 f4 #10)
-#13 := (= #11 #12)
-#14 := (not #13)
-#87 := (iff #14 #84)
-#74 := (= #68 #71)
-#77 := (not #74)
-#85 := (iff #77 #84)
-#82 := (iff #74 #81)
-#83 := [rewrite]: #82
-#86 := [monotonicity #83]: #85
-#78 := (iff #14 #77)
-#75 := (iff #13 #74)
-#72 := (= #12 #71)
-#73 := [rewrite]: #72
-#69 := (= #11 #68)
-#66 := (= #10 -1::Int)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#76 := [monotonicity #70 #73]: #75
-#79 := [monotonicity #76]: #78
-#88 := [trans #79 #86]: #87
-#64 := [asserted]: #14
-#89 := [mp #64 #88]: #84
-#601 := (or #81 #577 #630)
-#602 := [th-lemma arith triangle-eq]: #601
-#603 := [unit-resolution #602 #89]: #597
-#571 := [unit-resolution #603 #610]: #577
-#687 := (<= #68 0::Int)
-#578 := [unit-resolution #607 #615]: #748
-#537 := (or #585 #687)
-#568 := [th-lemma arith triangle-eq]: #537
-#570 := [unit-resolution #568 #578]: #687
-#572 := [th-lemma arith farkas 1 -1 1 #570 #571 #596]: false
-#579 := [lemma #572]: #574
-#582 := [unit-resolution #600 #579]: #708
-#583 := (or #684 #691)
-#593 := [th-lemma arith triangle-eq]: #583
-#573 := [unit-resolution #593 #582]: #691
-#581 := (<= #665 0::Int)
-#594 := (or #634 #581)
-#549 := [th-lemma arith triangle-eq]: #594
-#550 := [unit-resolution #549 #628]: #581
-[th-lemma arith farkas 1 -1 1 #550 #571 #573]: false
-unsat
-8db711c99a743e7c5b35063fc01bbf7e9119b29e 292 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#14 := (:var 0 Int)
-#13 := (:var 1 Int)
-#15 := (f3 #13 #14)
-#750 := (pattern #15)
-#8 := 0::Int
-#88 := -1::Int
-#92 := (* -1::Int #14)
-#89 := (* -1::Int #13)
-#95 := (div #89 #92)
-#252 := (* -1::Int #95)
-#253 := (+ #15 #252)
-#254 := (= #253 0::Int)
-#25 := (div #13 #14)
-#249 := (* -1::Int #25)
-#250 := (+ #15 #249)
-#251 := (= #250 0::Int)
-#127 := (>= #13 0::Int)
-#120 := (<= #14 0::Int)
-#212 := (or #120 #127)
-#213 := (not #212)
-#116 := (<= #13 0::Int)
-#210 := (or #116 #120)
-#211 := (not #210)
-#216 := (or #211 #213)
-#255 := (ite #216 #251 #254)
-#248 := (= #15 0::Int)
-#17 := (= #14 0::Int)
-#16 := (= #13 0::Int)
-#18 := (or #16 #17)
-#256 := (ite #18 #248 #255)
-#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #256)
-#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
-#754 := (iff #259 #751)
-#752 := (iff #256 #256)
-#753 := [refl]: #752
-#755 := [quant-intro #753]: #754
-#219 := (ite #216 #25 #95)
-#222 := (ite #18 0::Int #219)
-#225 := (= #15 #222)
-#228 := (forall (vars (?v0 Int) (?v1 Int)) #225)
-#260 := (iff #228 #259)
-#257 := (iff #225 #256)
-#258 := [rewrite]: #257
-#261 := [quant-intro #258]: #260
-#128 := (not #127)
-#121 := (not #120)
-#131 := (and #121 #128)
-#117 := (not #116)
-#124 := (and #117 #121)
-#134 := (or #124 #131)
-#137 := (ite #134 #25 #95)
-#140 := (ite #18 0::Int #137)
-#143 := (= #15 #140)
-#146 := (forall (vars (?v0 Int) (?v1 Int)) #143)
-#229 := (iff #146 #228)
-#226 := (iff #143 #225)
-#223 := (= #140 #222)
-#220 := (= #137 #219)
-#217 := (iff #134 #216)
-#214 := (iff #131 #213)
-#215 := [rewrite]: #214
-#204 := (iff #124 #211)
-#205 := [rewrite]: #204
-#218 := [monotonicity #205 #215]: #217
-#221 := [monotonicity #218]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [quant-intro #227]: #229
-#208 := (~ #146 #146)
-#206 := (~ #143 #143)
-#207 := [refl]: #206
-#209 := [nnf-pos #207]: #208
-#27 := (- #14)
-#26 := (- #13)
-#28 := (div #26 #27)
-#20 := (< 0::Int #14)
-#22 := (< #13 0::Int)
-#23 := (and #22 #20)
-#19 := (< 0::Int #13)
-#21 := (and #19 #20)
-#24 := (or #21 #23)
-#29 := (ite #24 #25 #28)
-#30 := (ite #18 0::Int #29)
-#31 := (= #15 #30)
-#32 := (forall (vars (?v0 Int) (?v1 Int)) #31)
-#149 := (iff #32 #146)
-#82 := (and #20 #22)
-#85 := (or #21 #82)
-#98 := (ite #85 #25 #95)
-#76 := (= 0::Int #14)
-#73 := (= 0::Int #13)
-#79 := (or #73 #76)
-#101 := (ite #79 0::Int #98)
-#104 := (= #15 #101)
-#107 := (forall (vars (?v0 Int) (?v1 Int)) #104)
-#147 := (iff #107 #146)
-#144 := (iff #104 #143)
-#141 := (= #101 #140)
-#138 := (= #98 #137)
-#135 := (iff #85 #134)
-#132 := (iff #82 #131)
-#129 := (iff #22 #128)
-#130 := [rewrite]: #129
-#122 := (iff #20 #121)
-#123 := [rewrite]: #122
-#133 := [monotonicity #123 #130]: #132
-#125 := (iff #21 #124)
-#118 := (iff #19 #117)
-#119 := [rewrite]: #118
-#126 := [monotonicity #119 #123]: #125
-#136 := [monotonicity #126 #133]: #135
-#139 := [monotonicity #136]: #138
-#114 := (iff #79 #18)
-#112 := (iff #76 #17)
-#113 := [rewrite]: #112
-#110 := (iff #73 #16)
-#111 := [rewrite]: #110
-#115 := [monotonicity #111 #113]: #114
-#142 := [monotonicity #115 #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [quant-intro #145]: #147
-#108 := (iff #32 #107)
-#105 := (iff #31 #104)
-#102 := (= #30 #101)
-#99 := (= #29 #98)
-#96 := (= #28 #95)
-#93 := (= #27 #92)
-#94 := [rewrite]: #93
-#90 := (= #26 #89)
-#91 := [rewrite]: #90
-#97 := [monotonicity #91 #94]: #96
-#86 := (iff #24 #85)
-#83 := (iff #23 #82)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#100 := [monotonicity #87 #97]: #99
-#80 := (iff #18 #79)
-#77 := (iff #17 #76)
-#78 := [rewrite]: #77
-#74 := (iff #16 #73)
-#75 := [rewrite]: #74
-#81 := [monotonicity #75 #78]: #80
-#103 := [monotonicity #81 #100]: #102
-#106 := [monotonicity #103]: #105
-#109 := [quant-intro #106]: #108
-#150 := [trans #109 #148]: #149
-#72 := [asserted]: #32
-#151 := [mp #72 #150]: #146
-#200 := [mp~ #151 #209]: #146
-#231 := [mp #200 #230]: #228
-#262 := [mp #231 #261]: #259
-#756 := [mp #262 #755]: #751
-#9 := 3::Int
-#10 := (f3 0::Int 3::Int)
-#11 := (= #10 0::Int)
-#12 := (not #11)
-#61 := [asserted]: #12
-#585 := (not #751)
-#586 := (or #585 #11)
-#336 := (* -1::Int 3::Int)
-#421 := (* -1::Int 0::Int)
-#422 := (div #421 #336)
-#423 := (* -1::Int #422)
-#414 := (+ #10 #423)
-#425 := (= #414 0::Int)
-#426 := (div 0::Int 3::Int)
-#354 := (* -1::Int #426)
-#427 := (+ #10 #354)
-#424 := (= #427 0::Int)
-#428 := (>= 0::Int 0::Int)
-#407 := (<= 3::Int 0::Int)
-#742 := (or #407 #428)
-#744 := (not #742)
-#401 := (<= 0::Int 0::Int)
-#531 := (or #401 #407)
-#738 := (not #531)
-#412 := (or #738 #744)
-#413 := (ite #412 #424 #425)
-#745 := (= 3::Int 0::Int)
-#746 := (= 0::Int 0::Int)
-#747 := (or #746 #745)
-#748 := (ite #747 #11 #413)
-#579 := (or #585 #748)
-#588 := (iff #579 #586)
-#590 := (iff #586 #586)
-#591 := [rewrite]: #590
-#568 := (iff #748 #11)
-#1 := true
-#682 := (ite true #11 #11)
-#680 := (iff #682 #11)
-#683 := [rewrite]: #680
-#584 := (iff #748 #682)
-#575 := (iff #413 #11)
-#690 := (ite false #11 #11)
-#573 := (iff #690 #11)
-#574 := [rewrite]: #573
-#688 := (iff #413 #690)
-#687 := (iff #425 #11)
-#533 := (= #414 #10)
-#716 := (+ #10 0::Int)
-#707 := (= #716 #10)
-#702 := [rewrite]: #707
-#530 := (= #414 #716)
-#694 := (= #423 0::Int)
-#429 := (= #421 0::Int)
-#711 := [rewrite]: #429
-#699 := (= #423 #421)
-#692 := (= #422 0::Int)
-#710 := -3::Int
-#553 := (div 0::Int -3::Int)
-#697 := (= #553 0::Int)
-#698 := [rewrite]: #697
-#695 := (= #422 #553)
-#551 := (= #336 -3::Int)
-#552 := [rewrite]: #551
-#696 := [monotonicity #711 #552]: #695
-#693 := [trans #696 #698]: #692
-#700 := [monotonicity #693]: #699
-#701 := [trans #700 #711]: #694
-#532 := [monotonicity #701]: #530
-#686 := [trans #532 #702]: #533
-#689 := [monotonicity #686]: #687
-#709 := (iff #424 #11)
-#703 := (= #427 #10)
-#705 := (= #427 #716)
-#715 := (= #354 0::Int)
-#713 := (= #354 #421)
-#434 := (= #426 0::Int)
-#435 := [rewrite]: #434
-#714 := [monotonicity #435]: #713
-#712 := [trans #714 #711]: #715
-#706 := [monotonicity #712]: #705
-#708 := [trans #706 #702]: #703
-#704 := [monotonicity #708]: #709
-#432 := (iff #412 false)
-#443 := (or false false)
-#718 := (iff #443 false)
-#722 := [rewrite]: #718
-#717 := (iff #412 #443)
-#720 := (iff #744 false)
-#726 := (not true)
-#733 := (iff #726 false)
-#735 := [rewrite]: #733
-#342 := (iff #744 #726)
-#448 := (iff #742 true)
-#737 := (or false true)
-#446 := (iff #737 true)
-#447 := [rewrite]: #446
-#723 := (iff #742 #737)
-#736 := (iff #428 true)
-#734 := [rewrite]: #736
-#391 := (iff #407 false)
-#727 := [rewrite]: #391
-#724 := [monotonicity #727 #734]: #723
-#449 := [trans #724 #447]: #448
-#719 := [monotonicity #449]: #342
-#442 := [trans #719 #735]: #720
-#375 := (iff #738 false)
-#732 := (iff #738 #726)
-#730 := (iff #531 true)
-#404 := (or true false)
-#741 := (iff #404 true)
-#384 := [rewrite]: #741
-#728 := (iff #531 #404)
-#389 := (iff #401 true)
-#390 := [rewrite]: #389
-#729 := [monotonicity #390 #727]: #728
-#731 := [trans #729 #384]: #730
-#370 := [monotonicity #731]: #732
-#376 := [trans #370 #735]: #375
-#721 := [monotonicity #376 #442]: #717
-#433 := [trans #721 #722]: #432
-#691 := [monotonicity #433 #704 #689]: #688
-#534 := [trans #691 #574]: #575
-#725 := (iff #747 true)
-#740 := (iff #747 #404)
-#739 := (iff #745 false)
-#399 := [rewrite]: #739
-#743 := (iff #746 true)
-#749 := [rewrite]: #743
-#400 := [monotonicity #749 #399]: #740
-#388 := [trans #400 #384]: #725
-#679 := [monotonicity #388 #534]: #584
-#583 := [trans #679 #683]: #568
-#589 := [monotonicity #583]: #588
-#684 := [trans #589 #591]: #588
-#587 := [quant-inst #8 #9]: #579
-#681 := [mp #587 #684]: #586
-[unit-resolution #681 #61 #756]: false
-unsat
-6aeb136b7e9b0d9bd350f376d5db91cb7cdd5fa1 317 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#15 := (:var 0 Int)
-#14 := (:var 1 Int)
-#16 := (f3 #14 #15)
-#766 := (pattern #16)
-#8 := 0::Int
-#104 := -1::Int
-#108 := (* -1::Int #15)
-#105 := (* -1::Int #14)
-#111 := (div #105 #108)
-#268 := (* -1::Int #111)
-#269 := (+ #16 #268)
-#270 := (= #269 0::Int)
-#26 := (div #14 #15)
-#265 := (* -1::Int #26)
-#266 := (+ #16 #265)
-#267 := (= #266 0::Int)
-#143 := (>= #14 0::Int)
-#136 := (<= #15 0::Int)
-#228 := (or #136 #143)
-#229 := (not #228)
-#132 := (<= #14 0::Int)
-#226 := (or #132 #136)
-#227 := (not #226)
-#232 := (or #227 #229)
-#271 := (ite #232 #267 #270)
-#264 := (= #16 0::Int)
-#18 := (= #15 0::Int)
-#17 := (= #14 0::Int)
-#19 := (or #17 #18)
-#272 := (ite #19 #264 #271)
-#767 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #766) #272)
-#275 := (forall (vars (?v0 Int) (?v1 Int)) #272)
-#770 := (iff #275 #767)
-#768 := (iff #272 #272)
-#769 := [refl]: #768
-#771 := [quant-intro #769]: #770
-#235 := (ite #232 #26 #111)
-#238 := (ite #19 0::Int #235)
-#241 := (= #16 #238)
-#244 := (forall (vars (?v0 Int) (?v1 Int)) #241)
-#276 := (iff #244 #275)
-#273 := (iff #241 #272)
-#274 := [rewrite]: #273
-#277 := [quant-intro #274]: #276
-#144 := (not #143)
-#137 := (not #136)
-#147 := (and #137 #144)
-#133 := (not #132)
-#140 := (and #133 #137)
-#150 := (or #140 #147)
-#153 := (ite #150 #26 #111)
-#156 := (ite #19 0::Int #153)
-#159 := (= #16 #156)
-#162 := (forall (vars (?v0 Int) (?v1 Int)) #159)
-#245 := (iff #162 #244)
-#242 := (iff #159 #241)
-#239 := (= #156 #238)
-#236 := (= #153 #235)
-#233 := (iff #150 #232)
-#230 := (iff #147 #229)
-#231 := [rewrite]: #230
-#220 := (iff #140 #227)
-#221 := [rewrite]: #220
-#234 := [monotonicity #221 #231]: #233
-#237 := [monotonicity #234]: #236
-#240 := [monotonicity #237]: #239
-#243 := [monotonicity #240]: #242
-#246 := [quant-intro #243]: #245
-#224 := (~ #162 #162)
-#222 := (~ #159 #159)
-#223 := [refl]: #222
-#225 := [nnf-pos #223]: #224
-#28 := (- #15)
-#27 := (- #14)
-#29 := (div #27 #28)
-#21 := (< 0::Int #15)
-#23 := (< #14 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #14)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#30 := (ite #25 #26 #29)
-#31 := (ite #19 0::Int #30)
-#32 := (= #16 #31)
-#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
-#165 := (iff #33 #162)
-#98 := (and #21 #23)
-#101 := (or #22 #98)
-#114 := (ite #101 #26 #111)
-#92 := (= 0::Int #15)
-#89 := (= 0::Int #14)
-#95 := (or #89 #92)
-#117 := (ite #95 0::Int #114)
-#120 := (= #16 #117)
-#123 := (forall (vars (?v0 Int) (?v1 Int)) #120)
-#163 := (iff #123 #162)
-#160 := (iff #120 #159)
-#157 := (= #117 #156)
-#154 := (= #114 #153)
-#151 := (iff #101 #150)
-#148 := (iff #98 #147)
-#145 := (iff #23 #144)
-#146 := [rewrite]: #145
-#138 := (iff #21 #137)
-#139 := [rewrite]: #138
-#149 := [monotonicity #139 #146]: #148
-#141 := (iff #22 #140)
-#134 := (iff #20 #133)
-#135 := [rewrite]: #134
-#142 := [monotonicity #135 #139]: #141
-#152 := [monotonicity #142 #149]: #151
-#155 := [monotonicity #152]: #154
-#130 := (iff #95 #19)
-#128 := (iff #92 #18)
-#129 := [rewrite]: #128
-#126 := (iff #89 #17)
-#127 := [rewrite]: #126
-#131 := [monotonicity #127 #129]: #130
-#158 := [monotonicity #131 #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [quant-intro #161]: #163
-#124 := (iff #33 #123)
-#121 := (iff #32 #120)
-#118 := (= #31 #117)
-#115 := (= #30 #114)
-#112 := (= #29 #111)
-#109 := (= #28 #108)
-#110 := [rewrite]: #109
-#106 := (= #27 #105)
-#107 := [rewrite]: #106
-#113 := [monotonicity #107 #110]: #112
-#102 := (iff #25 #101)
-#99 := (iff #24 #98)
-#100 := [rewrite]: #99
-#103 := [monotonicity #100]: #102
-#116 := [monotonicity #103 #113]: #115
-#96 := (iff #19 #95)
-#93 := (iff #18 #92)
-#94 := [rewrite]: #93
-#90 := (iff #17 #89)
-#91 := [rewrite]: #90
-#97 := [monotonicity #91 #94]: #96
-#119 := [monotonicity #97 #116]: #118
-#122 := [monotonicity #119]: #121
-#125 := [quant-intro #122]: #124
-#166 := [trans #125 #164]: #165
-#88 := [asserted]: #33
-#167 := [mp #88 #166]: #162
-#216 := [mp~ #167 #225]: #162
-#247 := [mp #216 #246]: #244
-#278 := [mp #247 #277]: #275
-#772 := [mp #278 #771]: #767
-#63 := -3::Int
-#66 := (f3 0::Int -3::Int)
-#69 := (= #66 0::Int)
-#82 := (not #69)
-#9 := 3::Int
-#10 := (- 3::Int)
-#11 := (f3 0::Int #10)
+#73 := [monotonicity #70 #70]: #72
+#77 := [trans #73 #75]: #76
+#103 := [monotonicity #77 #84 #100]: #102
+#107 := [trans #103 #105]: #106
+#63 := (iff #13 true)
+#58 := (or true false)
+#61 := (iff #58 true)
+#62 := [rewrite]: #61
+#59 := (iff #13 #58)
+#56 := (iff #12 false)
+#51 := (= -1::Int 0::Int)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #12 #51)
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#60 := [monotonicity #47 #57]: #59
+#64 := [trans #60 #62]: #63
+#110 := [monotonicity #64 #107]: #109
+#113 := [trans #110 #112]: #24
+#115 := [monotonicity #113]: #114
+#117 := [trans #115 #47]: #116
+#120 := [monotonicity #117]: #119
+#124 := [trans #120 #122]: #123
+#45 := [asserted]: #25
+[mp #45 #124]: false
+unsat
+5c9ec68cb5c6bc2336555bc99c13f0ecae2167b7 104 0
+#2 := false
+#8 := 1::Int
+#11 := (- 1::Int)
+#21 := (- #11)
+#22 := (div #11 #21)
+#20 := (div 1::Int #11)
+#9 := 0::Int
+#15 := (< 0::Int #11)
+#17 := (< 1::Int 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int 1::Int)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#23 := (ite #19 #20 #22)
 #12 := (= #11 0::Int)
-#13 := (not #12)
-#85 := (iff #13 #82)
-#72 := (= 0::Int #66)
-#77 := (not #72)
-#83 := (iff #77 #82)
-#80 := (iff #72 #69)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#78 := (iff #13 #77)
-#75 := (iff #12 #72)
-#73 := (iff #69 #72)
-#74 := [rewrite]: #73
-#70 := (iff #12 #69)
-#67 := (= #11 #66)
-#64 := (= #10 -3::Int)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#71 := [monotonicity #68]: #70
-#76 := [trans #71 #74]: #75
-#79 := [monotonicity #76]: #78
-#86 := [trans #79 #84]: #85
-#62 := [asserted]: #13
-#87 := [mp #62 #86]: #82
-#599 := (not #767)
-#601 := (or #599 #69)
-#352 := (* -1::Int -3::Int)
-#437 := (* -1::Int 0::Int)
-#438 := (div #437 #352)
-#439 := (* -1::Int #438)
-#430 := (+ #66 #439)
-#441 := (= #430 0::Int)
-#442 := (div 0::Int -3::Int)
-#370 := (* -1::Int #442)
-#443 := (+ #66 #370)
-#440 := (= #443 0::Int)
-#444 := (>= 0::Int 0::Int)
-#423 := (<= -3::Int 0::Int)
-#758 := (or #423 #444)
-#760 := (not #758)
-#417 := (<= 0::Int 0::Int)
-#547 := (or #417 #423)
-#754 := (not #547)
-#428 := (or #754 #760)
-#429 := (ite #428 #440 #441)
-#761 := (= -3::Int 0::Int)
-#762 := (= 0::Int 0::Int)
-#763 := (or #762 #761)
-#764 := (ite #763 #69 #429)
-#602 := (or #599 #764)
-#603 := (iff #602 #601)
-#605 := (iff #601 #601)
-#606 := [rewrite]: #605
-#699 := (iff #764 #69)
-#1 := true
-#550 := (ite true #69 #69)
-#695 := (iff #550 #69)
-#696 := [rewrite]: #695
-#698 := (iff #764 #550)
-#590 := (iff #429 #69)
-#705 := (ite false #69 #69)
-#707 := (iff #705 #69)
-#589 := [rewrite]: #707
-#706 := (iff #429 #705)
-#702 := (iff #441 #69)
-#548 := (= #430 #66)
-#732 := (+ #66 0::Int)
-#723 := (= #732 #66)
-#718 := [rewrite]: #723
-#717 := (= #430 #732)
-#716 := (= #439 0::Int)
-#445 := (= #437 0::Int)
-#727 := [rewrite]: #445
-#709 := (= #439 #437)
-#714 := (= #438 0::Int)
-#568 := (div 0::Int 3::Int)
-#712 := (= #568 0::Int)
-#713 := [rewrite]: #712
-#569 := (= #438 #568)
-#726 := (= #352 3::Int)
-#567 := [rewrite]: #726
-#711 := [monotonicity #727 #567]: #569
-#708 := [trans #711 #713]: #714
-#715 := [monotonicity #708]: #709
-#710 := [trans #715 #727]: #716
-#546 := [monotonicity #710]: #717
-#549 := [trans #546 #718]: #548
-#703 := [monotonicity #549]: #702
-#725 := (iff #440 #69)
-#719 := (= #443 #66)
-#721 := (= #443 #732)
-#731 := (= #370 0::Int)
-#729 := (= #370 #437)
-#450 := (= #442 0::Int)
-#451 := [rewrite]: #450
-#730 := [monotonicity #451]: #729
-#728 := [trans #730 #727]: #731
-#722 := [monotonicity #728]: #721
-#724 := [trans #722 #718]: #719
-#720 := [monotonicity #724]: #725
-#448 := (iff #428 false)
-#459 := (or false false)
-#734 := (iff #459 false)
-#738 := [rewrite]: #734
-#733 := (iff #428 #459)
-#736 := (iff #760 false)
-#749 := (not true)
-#392 := (iff #749 false)
-#752 := [rewrite]: #392
-#358 := (iff #760 #749)
-#464 := (iff #758 true)
-#744 := (or true true)
-#747 := (iff #744 true)
-#742 := [rewrite]: #747
-#462 := (iff #758 #744)
-#739 := (iff #444 true)
-#740 := [rewrite]: #739
-#407 := (iff #423 true)
-#743 := [rewrite]: #407
-#463 := [monotonicity #743 #740]: #462
-#465 := [trans #463 #742]: #464
-#735 := [monotonicity #465]: #358
-#458 := [trans #735 #752]: #736
-#750 := (iff #754 false)
-#751 := (iff #754 #749)
-#748 := (iff #547 true)
-#745 := (iff #547 #744)
-#405 := (iff #417 true)
-#406 := [rewrite]: #405
-#746 := [monotonicity #406 #743]: #745
-#386 := [trans #746 #742]: #748
-#391 := [monotonicity #386]: #751
-#753 := [trans #391 #752]: #750
-#737 := [monotonicity #753 #458]: #733
-#449 := [trans #737 #738]: #448
-#704 := [monotonicity #449 #720 #703]: #706
-#591 := [trans #704 #589]: #590
-#741 := (iff #763 true)
-#420 := (or true false)
-#757 := (iff #420 true)
-#400 := [rewrite]: #757
-#756 := (iff #763 #420)
-#755 := (iff #761 false)
-#415 := [rewrite]: #755
-#759 := (iff #762 true)
-#765 := [rewrite]: #759
-#416 := [monotonicity #765 #415]: #756
-#404 := [trans #416 #400]: #741
-#600 := [monotonicity #404 #591]: #698
-#584 := [trans #600 #696]: #699
-#604 := [monotonicity #584]: #603
-#607 := [trans #604 #606]: #603
-#595 := [quant-inst #8 #63]: #602
-#700 := [mp #595 #607]: #601
-[unit-resolution #700 #87 #772]: false
-unsat
-a6a62a3b765435aa1a5f654ae0aa2e6502518a55 309 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#15 := (:var 0 Int)
-#14 := (:var 1 Int)
-#16 := (f3 #14 #15)
-#740 := (pattern #16)
-#11 := 0::Int
-#79 := -1::Int
-#83 := (* -1::Int #15)
-#80 := (* -1::Int #14)
-#86 := (div #80 #83)
-#243 := (* -1::Int #86)
-#244 := (+ #16 #243)
-#245 := (= #244 0::Int)
-#26 := (div #14 #15)
-#240 := (* -1::Int #26)
-#241 := (+ #16 #240)
-#242 := (= #241 0::Int)
-#118 := (>= #14 0::Int)
-#111 := (<= #15 0::Int)
-#203 := (or #111 #118)
-#204 := (not #203)
-#107 := (<= #14 0::Int)
-#201 := (or #107 #111)
-#202 := (not #201)
-#207 := (or #202 #204)
-#246 := (ite #207 #242 #245)
-#239 := (= #16 0::Int)
-#18 := (= #15 0::Int)
-#17 := (= #14 0::Int)
-#19 := (or #17 #18)
-#247 := (ite #19 #239 #246)
-#741 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #740) #247)
-#250 := (forall (vars (?v0 Int) (?v1 Int)) #247)
-#744 := (iff #250 #741)
-#742 := (iff #247 #247)
-#743 := [refl]: #742
-#745 := [quant-intro #743]: #744
-#210 := (ite #207 #26 #86)
-#213 := (ite #19 0::Int #210)
-#216 := (= #16 #213)
-#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
-#251 := (iff #219 #250)
-#248 := (iff #216 #247)
-#249 := [rewrite]: #248
-#252 := [quant-intro #249]: #251
-#119 := (not #118)
-#112 := (not #111)
-#122 := (and #112 #119)
-#108 := (not #107)
-#115 := (and #108 #112)
-#125 := (or #115 #122)
-#128 := (ite #125 #26 #86)
-#131 := (ite #19 0::Int #128)
-#134 := (= #16 #131)
-#137 := (forall (vars (?v0 Int) (?v1 Int)) #134)
-#220 := (iff #137 #219)
-#217 := (iff #134 #216)
-#214 := (= #131 #213)
-#211 := (= #128 #210)
-#208 := (iff #125 #207)
-#205 := (iff #122 #204)
-#206 := [rewrite]: #205
-#195 := (iff #115 #202)
-#196 := [rewrite]: #195
-#209 := [monotonicity #196 #206]: #208
-#212 := [monotonicity #209]: #211
-#215 := [monotonicity #212]: #214
-#218 := [monotonicity #215]: #217
-#221 := [quant-intro #218]: #220
-#199 := (~ #137 #137)
-#197 := (~ #134 #134)
-#198 := [refl]: #197
-#200 := [nnf-pos #198]: #199
-#28 := (- #15)
-#27 := (- #14)
-#29 := (div #27 #28)
-#21 := (< 0::Int #15)
-#23 := (< #14 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #14)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#30 := (ite #25 #26 #29)
-#31 := (ite #19 0::Int #30)
-#32 := (= #16 #31)
-#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
-#140 := (iff #33 #137)
-#73 := (and #21 #23)
-#76 := (or #22 #73)
-#89 := (ite #76 #26 #86)
-#67 := (= 0::Int #15)
-#64 := (= 0::Int #14)
-#70 := (or #64 #67)
-#92 := (ite #70 0::Int #89)
-#95 := (= #16 #92)
-#98 := (forall (vars (?v0 Int) (?v1 Int)) #95)
-#138 := (iff #98 #137)
-#135 := (iff #95 #134)
-#132 := (= #92 #131)
-#129 := (= #89 #128)
-#126 := (iff #76 #125)
-#123 := (iff #73 #122)
-#120 := (iff #23 #119)
-#121 := [rewrite]: #120
-#113 := (iff #21 #112)
-#114 := [rewrite]: #113
-#124 := [monotonicity #114 #121]: #123
-#116 := (iff #22 #115)
-#109 := (iff #20 #108)
+#10 := (= 1::Int 0::Int)
+#13 := (or #10 #12)
+#24 := (ite #13 0::Int #23)
+#25 := (= #24 #11)
+#26 := (not #25)
+#125 := (iff #26 false)
+#1 := true
+#120 := (not true)
+#123 := (iff #120 false)
+#124 := [rewrite]: #123
+#121 := (iff #26 #120)
+#118 := (iff #25 true)
+#49 := -1::Int
+#113 := (= -1::Int -1::Int)
+#116 := (iff #113 true)
+#117 := [rewrite]: #116
+#114 := (iff #25 #113)
+#50 := (= #11 -1::Int)
+#51 := [rewrite]: #50
+#111 := (= #24 -1::Int)
+#106 := (ite false 0::Int -1::Int)
+#109 := (= #106 -1::Int)
 #110 := [rewrite]: #109
-#117 := [monotonicity #110 #114]: #116
-#127 := [monotonicity #117 #124]: #126
-#130 := [monotonicity #127]: #129
-#105 := (iff #70 #19)
-#103 := (iff #67 #18)
-#104 := [rewrite]: #103
-#101 := (iff #64 #17)
-#102 := [rewrite]: #101
-#106 := [monotonicity #102 #104]: #105
-#133 := [monotonicity #106 #130]: #132
-#136 := [monotonicity #133]: #135
-#139 := [quant-intro #136]: #138
-#99 := (iff #33 #98)
-#96 := (iff #32 #95)
-#93 := (= #31 #92)
-#90 := (= #30 #89)
-#87 := (= #29 #86)
-#84 := (= #28 #83)
-#85 := [rewrite]: #84
-#81 := (= #27 #80)
+#107 := (= #24 #106)
+#104 := (= #23 -1::Int)
+#66 := (< 0::Int -1::Int)
+#72 := (and #17 #66)
+#69 := (and #14 #66)
+#75 := (or #69 #72)
+#99 := (ite #75 -1::Int -1::Int)
+#102 := (= #99 -1::Int)
+#103 := [rewrite]: #102
+#100 := (= #23 #99)
+#97 := (= #22 -1::Int)
+#92 := (div -1::Int 1::Int)
+#95 := (= #92 -1::Int)
+#96 := [rewrite]: #95
+#93 := (= #22 #92)
+#90 := (= #21 1::Int)
+#85 := (- -1::Int)
+#88 := (= #85 1::Int)
+#89 := [rewrite]: #88
+#86 := (= #21 #85)
+#87 := [monotonicity #51]: #86
+#91 := [trans #87 #89]: #90
+#94 := [monotonicity #51 #91]: #93
+#98 := [trans #94 #96]: #97
+#83 := (= #20 -1::Int)
+#78 := (div 1::Int -1::Int)
+#81 := (= #78 -1::Int)
 #82 := [rewrite]: #81
-#88 := [monotonicity #82 #85]: #87
-#77 := (iff #25 #76)
-#74 := (iff #24 #73)
-#75 := [rewrite]: #74
-#78 := [monotonicity #75]: #77
-#91 := [monotonicity #78 #88]: #90
-#71 := (iff #19 #70)
-#68 := (iff #18 #67)
-#69 := [rewrite]: #68
-#65 := (iff #17 #64)
-#66 := [rewrite]: #65
-#72 := [monotonicity #66 #69]: #71
-#94 := [monotonicity #72 #91]: #93
-#97 := [monotonicity #94]: #96
-#100 := [quant-intro #97]: #99
-#141 := [trans #100 #139]: #140
-#63 := [asserted]: #33
-#142 := [mp #63 #141]: #137
-#191 := [mp~ #142 #200]: #137
-#222 := [mp #191 #221]: #219
-#253 := [mp #222 #252]: #250
-#746 := [mp #253 #745]: #741
-#9 := 3::Int
-#8 := 1::Int
-#10 := (f3 1::Int 3::Int)
-#12 := (= #10 0::Int)
-#13 := (not #12)
-#62 := [asserted]: #13
-#666 := (not #741)
-#667 := (or #666 #12)
-#327 := (* -1::Int 3::Int)
-#411 := (* -1::Int 1::Int)
-#412 := (div #411 #327)
-#413 := (* -1::Int #412)
-#404 := (+ #10 #413)
-#415 := (= #404 0::Int)
-#416 := (div 1::Int 3::Int)
-#417 := (* -1::Int #416)
-#414 := (+ #10 #417)
-#418 := (= #414 0::Int)
-#397 := (>= 1::Int 0::Int)
-#732 := (<= 3::Int 0::Int)
-#734 := (or #732 #397)
-#391 := (not #734)
-#521 := (<= 1::Int 0::Int)
-#728 := (or #521 #732)
-#402 := (not #728)
-#403 := (or #402 #391)
-#735 := (ite #403 #418 #415)
-#736 := (= 3::Int 0::Int)
-#737 := (= 1::Int 0::Int)
-#738 := (or #737 #736)
-#733 := (ite #738 #12 #735)
-#663 := (or #666 #733)
-#657 := (iff #663 #667)
-#659 := (iff #667 #667)
-#660 := [rewrite]: #659
-#655 := (iff #733 #12)
-#675 := (ite false #12 #12)
-#656 := (iff #675 #12)
-#653 := [rewrite]: #656
-#662 := (iff #733 #675)
-#674 := (iff #735 #12)
-#558 := (= #10 1::Int)
-#1 := true
-#577 := (ite true #12 #558)
-#580 := (iff #577 #12)
-#581 := [rewrite]: #580
-#578 := (iff #735 #577)
-#576 := (iff #415 #558)
-#564 := (+ -1::Int #10)
-#669 := (= #564 0::Int)
-#573 := (iff #669 #558)
-#575 := [rewrite]: #573
-#670 := (iff #415 #669)
-#672 := (= #404 #564)
-#678 := (+ #10 -1::Int)
-#565 := (= #678 #564)
-#524 := [rewrite]: #565
-#681 := (= #404 #678)
-#679 := (= #413 -1::Int)
-#686 := (= #411 -1::Int)
-#687 := [rewrite]: #686
-#676 := (= #413 #411)
-#522 := (= #412 1::Int)
-#688 := -3::Int
-#689 := (div -1::Int -3::Int)
-#691 := (= #689 1::Int)
-#520 := [rewrite]: #691
-#690 := (= #412 #689)
-#682 := (= #327 -3::Int)
-#683 := [rewrite]: #682
-#684 := [monotonicity #687 #683]: #690
-#523 := [trans #684 #520]: #522
-#677 := [monotonicity #523]: #676
-#680 := [trans #677 #687]: #679
-#563 := [monotonicity #680]: #681
-#574 := [trans #563 #524]: #672
-#673 := [monotonicity #574]: #670
-#569 := [trans #673 #575]: #576
-#543 := (iff #418 #12)
-#541 := (= #414 #10)
-#693 := (+ #10 0::Int)
-#694 := (= #693 #10)
-#700 := [rewrite]: #694
-#698 := (= #414 #693)
-#697 := (= #417 0::Int)
-#705 := (* -1::Int 0::Int)
-#695 := (= #705 0::Int)
-#696 := [rewrite]: #695
-#702 := (= #417 #705)
-#419 := (= #416 0::Int)
-#701 := [rewrite]: #419
-#706 := [monotonicity #701]: #702
-#692 := [trans #706 #696]: #697
-#699 := [monotonicity #692]: #698
-#542 := [trans #699 #700]: #541
-#685 := [monotonicity #542]: #543
-#703 := (iff #403 true)
-#712 := (or true false)
-#424 := (iff #712 true)
-#425 := [rewrite]: #424
-#422 := (iff #403 #712)
-#711 := (iff #391 false)
-#709 := (not true)
-#433 := (iff #709 false)
-#707 := [rewrite]: #433
-#710 := (iff #391 #709)
-#439 := (iff #734 true)
-#713 := (or false true)
-#437 := (iff #713 true)
-#438 := [rewrite]: #437
-#714 := (iff #734 #713)
-#724 := (iff #397 true)
-#727 := [rewrite]: #724
-#717 := (iff #732 false)
-#718 := [rewrite]: #717
-#436 := [monotonicity #718 #727]: #714
-#333 := [trans #436 #438]: #439
-#432 := [monotonicity #333]: #710
-#708 := [trans #432 #707]: #711
-#366 := (iff #402 true)
-#722 := (not false)
-#725 := (iff #722 true)
-#365 := [rewrite]: #725
-#360 := (iff #402 #722)
-#721 := (iff #728 false)
-#730 := (or false false)
-#374 := (iff #730 false)
-#715 := [rewrite]: #374
-#719 := (iff #728 #730)
-#380 := (iff #521 false)
-#381 := [rewrite]: #380
-#720 := [monotonicity #381 #718]: #719
-#716 := [trans #720 #715]: #721
-#723 := [monotonicity #716]: #360
-#726 := [trans #723 #365]: #366
-#423 := [monotonicity #726 #708]: #422
-#704 := [trans #423 #425]: #703
-#579 := [monotonicity #704 #685 #569]: #578
-#671 := [trans #579 #581]: #674
-#378 := (iff #738 false)
-#390 := (iff #738 #730)
-#389 := (iff #736 false)
-#394 := [rewrite]: #389
-#739 := (iff #737 false)
-#729 := [rewrite]: #739
-#731 := [monotonicity #729 #394]: #390
-#379 := [trans #731 #715]: #378
-#664 := [monotonicity #379 #671]: #662
-#665 := [trans #664 #653]: #655
-#658 := [monotonicity #665]: #657
-#654 := [trans #658 #660]: #657
-#668 := [quant-inst #8 #9]: #663
-#661 := [mp #668 #654]: #667
-[unit-resolution #661 #62 #746]: false
-unsat
-e8bc05d54be641b4942beaff512e603a9cfaa4dd 284 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#14 := (:var 0 Int)
-#13 := (:var 1 Int)
-#15 := (f3 #13 #14)
-#725 := (pattern #15)
-#16 := 0::Int
-#70 := -1::Int
-#74 := (* -1::Int #14)
-#71 := (* -1::Int #13)
-#77 := (div #71 #74)
-#228 := (* -1::Int #77)
-#229 := (+ #15 #228)
-#230 := (= #229 0::Int)
-#26 := (div #13 #14)
-#225 := (* -1::Int #26)
-#226 := (+ #15 #225)
-#227 := (= #226 0::Int)
-#103 := (>= #13 0::Int)
-#96 := (<= #14 0::Int)
-#188 := (or #96 #103)
-#189 := (not #188)
-#92 := (<= #13 0::Int)
-#186 := (or #92 #96)
-#187 := (not #186)
-#192 := (or #187 #189)
-#231 := (ite #192 #227 #230)
-#224 := (= #15 0::Int)
-#18 := (= #14 0::Int)
-#17 := (= #13 0::Int)
-#19 := (or #17 #18)
-#232 := (ite #19 #224 #231)
-#726 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #725) #232)
-#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
-#729 := (iff #235 #726)
-#727 := (iff #232 #232)
-#728 := [refl]: #727
-#730 := [quant-intro #728]: #729
-#195 := (ite #192 #26 #77)
-#198 := (ite #19 0::Int #195)
-#201 := (= #15 #198)
-#204 := (forall (vars (?v0 Int) (?v1 Int)) #201)
-#236 := (iff #204 #235)
-#233 := (iff #201 #232)
-#234 := [rewrite]: #233
-#237 := [quant-intro #234]: #236
-#104 := (not #103)
-#97 := (not #96)
-#107 := (and #97 #104)
-#93 := (not #92)
-#100 := (and #93 #97)
-#110 := (or #100 #107)
-#113 := (ite #110 #26 #77)
-#116 := (ite #19 0::Int #113)
-#119 := (= #15 #116)
-#122 := (forall (vars (?v0 Int) (?v1 Int)) #119)
-#205 := (iff #122 #204)
-#202 := (iff #119 #201)
-#199 := (= #116 #198)
-#196 := (= #113 #195)
-#193 := (iff #110 #192)
-#190 := (iff #107 #189)
-#191 := [rewrite]: #190
-#180 := (iff #100 #187)
-#181 := [rewrite]: #180
-#194 := [monotonicity #181 #191]: #193
-#197 := [monotonicity #194]: #196
-#200 := [monotonicity #197]: #199
-#203 := [monotonicity #200]: #202
-#206 := [quant-intro #203]: #205
-#184 := (~ #122 #122)
-#182 := (~ #119 #119)
-#183 := [refl]: #182
-#185 := [nnf-pos #183]: #184
-#28 := (- #14)
-#27 := (- #13)
-#29 := (div #27 #28)
-#21 := (< 0::Int #14)
-#23 := (< #13 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #13)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#30 := (ite #25 #26 #29)
-#31 := (ite #19 0::Int #30)
-#32 := (= #15 #31)
-#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
-#125 := (iff #33 #122)
-#64 := (and #21 #23)
-#67 := (or #22 #64)
-#80 := (ite #67 #26 #77)
-#83 := (ite #19 0::Int #80)
-#86 := (= #15 #83)
-#89 := (forall (vars (?v0 Int) (?v1 Int)) #86)
-#123 := (iff #89 #122)
-#120 := (iff #86 #119)
-#117 := (= #83 #116)
-#114 := (= #80 #113)
-#111 := (iff #67 #110)
-#108 := (iff #64 #107)
-#105 := (iff #23 #104)
-#106 := [rewrite]: #105
-#98 := (iff #21 #97)
-#99 := [rewrite]: #98
-#109 := [monotonicity #99 #106]: #108
-#101 := (iff #22 #100)
-#94 := (iff #20 #93)
-#95 := [rewrite]: #94
-#102 := [monotonicity #95 #99]: #101
-#112 := [monotonicity #102 #109]: #111
-#115 := [monotonicity #112]: #114
-#118 := [monotonicity #115]: #117
-#121 := [monotonicity #118]: #120
-#124 := [quant-intro #121]: #123
-#90 := (iff #33 #89)
-#87 := (iff #32 #86)
-#84 := (= #31 #83)
-#81 := (= #30 #80)
-#78 := (= #29 #77)
-#75 := (= #28 #74)
-#76 := [rewrite]: #75
-#72 := (= #27 #71)
-#73 := [rewrite]: #72
-#79 := [monotonicity #73 #76]: #78
-#68 := (iff #25 #67)
-#65 := (iff #24 #64)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#82 := [monotonicity #69 #79]: #81
-#85 := [monotonicity #82]: #84
-#88 := [monotonicity #85]: #87
-#91 := [quant-intro #88]: #90
-#126 := [trans #91 #124]: #125
-#63 := [asserted]: #33
-#127 := [mp #63 #126]: #122
-#176 := [mp~ #127 #185]: #122
-#207 := [mp #176 #206]: #204
-#238 := [mp #207 #237]: #235
-#731 := [mp #238 #730]: #726
-#10 := 1::Int
-#8 := 3::Int
-#9 := (f3 3::Int 3::Int)
-#11 := (= #9 1::Int)
-#12 := (not #11)
-#62 := [asserted]: #12
-#566 := (not #726)
-#659 := (or #566 #11)
-#312 := (* -1::Int 3::Int)
-#396 := (div #312 #312)
-#397 := (* -1::Int #396)
-#398 := (+ #9 #397)
-#389 := (= #398 0::Int)
-#400 := (div 3::Int 3::Int)
-#401 := (* -1::Int #400)
-#402 := (+ #9 #401)
-#399 := (= #402 0::Int)
-#403 := (>= 3::Int 0::Int)
-#382 := (<= 3::Int 0::Int)
-#717 := (or #382 #403)
-#719 := (not #717)
-#376 := (or #382 #382)
-#506 := (not #376)
-#713 := (or #506 #719)
-#387 := (ite #713 #399 #389)
-#388 := (= #9 0::Int)
-#720 := (= 3::Int 0::Int)
-#721 := (or #720 #720)
-#722 := (ite #721 #388 #387)
-#656 := (or #566 #722)
-#647 := (iff #656 #659)
-#641 := (iff #659 #659)
-#638 := [rewrite]: #641
-#564 := (iff #722 #11)
-#560 := (ite false #388 #11)
-#562 := (iff #560 #11)
-#563 := [rewrite]: #562
-#561 := (iff #722 #560)
-#543 := (iff #387 #11)
-#1 := true
-#657 := (ite true #11 #11)
-#655 := (iff #657 #11)
-#658 := [rewrite]: #655
-#559 := (iff #387 #657)
-#550 := (iff #389 #11)
-#681 := (+ -1::Int #9)
-#684 := (= #681 0::Int)
-#526 := (iff #684 #11)
-#527 := [rewrite]: #526
-#548 := (iff #389 #684)
-#663 := (= #398 #681)
-#687 := (+ #9 -1::Int)
-#682 := (= #687 #681)
-#677 := [rewrite]: #682
-#664 := (= #398 #687)
-#661 := (= #397 -1::Int)
-#409 := (* -1::Int 1::Int)
-#689 := (= #409 -1::Int)
-#404 := [rewrite]: #689
-#507 := (= #397 #409)
-#676 := (= #396 1::Int)
-#671 := -3::Int
-#667 := (div -3::Int -3::Int)
-#675 := (= #667 1::Int)
-#669 := [rewrite]: #675
-#668 := (= #396 #667)
-#672 := (= #312 -3::Int)
-#673 := [rewrite]: #672
-#674 := [monotonicity #673 #673]: #668
-#505 := [trans #674 #669]: #676
-#508 := [monotonicity #505]: #507
-#662 := [trans #508 #404]: #661
-#665 := [monotonicity #662]: #664
-#666 := [trans #665 #677]: #663
-#549 := [monotonicity #666]: #548
-#509 := [trans #549 #527]: #550
-#528 := (iff #399 #11)
-#679 := (iff #399 #684)
-#678 := (= #402 #681)
-#691 := (= #402 #687)
-#686 := (= #401 -1::Int)
-#410 := (= #401 #409)
-#407 := (= #400 1::Int)
-#408 := [rewrite]: #407
-#688 := [monotonicity #408]: #410
-#690 := [trans #688 #404]: #686
-#680 := [monotonicity #690]: #691
-#683 := [trans #680 #677]: #678
-#685 := [monotonicity #683]: #679
-#670 := [trans #685 #527]: #528
-#693 := (iff #713 true)
-#695 := (or true false)
-#692 := (iff #695 true)
-#696 := [rewrite]: #692
-#417 := (iff #713 #695)
-#318 := (iff #719 false)
-#699 := (not true)
-#423 := (iff #699 false)
-#424 := [rewrite]: #423
-#421 := (iff #719 #699)
-#712 := (iff #717 true)
-#710 := (or false true)
-#711 := (iff #710 true)
-#709 := [rewrite]: #711
-#350 := (iff #717 #710)
-#345 := (iff #403 true)
-#708 := [rewrite]: #345
-#359 := (iff #382 false)
-#700 := [rewrite]: #359
-#351 := [monotonicity #700 #708]: #350
-#698 := [trans #351 #709]: #712
-#422 := [monotonicity #698]: #421
-#694 := [trans #422 #424]: #318
-#701 := (iff #506 true)
-#702 := (not false)
-#705 := (iff #702 true)
-#706 := [rewrite]: #705
-#703 := (iff #506 #702)
-#365 := (iff #376 false)
-#724 := (or false false)
-#379 := (iff #724 false)
-#715 := [rewrite]: #379
-#363 := (iff #376 #724)
-#364 := [monotonicity #700 #700]: #363
-#366 := [trans #364 #715]: #365
-#704 := [monotonicity #366]: #703
-#707 := [trans #704 #706]: #701
-#418 := [monotonicity #707 #694]: #417
-#697 := [trans #418 #696]: #693
-#654 := [monotonicity #697 #670 #509]: #559
-#558 := [trans #654 #658]: #543
-#375 := (iff #721 false)
-#714 := (iff #721 #724)
-#723 := (iff #720 false)
-#718 := [rewrite]: #723
-#374 := [monotonicity #718 #718]: #714
-#716 := [trans #374 #715]: #375
-#554 := [monotonicity #716 #558]: #561
-#565 := [trans #554 #563]: #564
-#649 := [monotonicity #565]: #647
-#640 := [trans #649 #638]: #647
-#660 := [quant-inst #8 #8]: #656
-#650 := [mp #660 #640]: #659
-[unit-resolution #650 #62 #731]: false
-unsat
-e5eddbef23d1553e8639810f42b39c3055238ad5 308 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#15 := (:var 0 Int)
-#14 := (:var 1 Int)
-#16 := (f3 #14 #15)
-#726 := (pattern #16)
-#17 := 0::Int
-#71 := -1::Int
-#75 := (* -1::Int #15)
-#72 := (* -1::Int #14)
-#78 := (div #72 #75)
-#229 := (* -1::Int #78)
-#230 := (+ #16 #229)
-#231 := (= #230 0::Int)
-#27 := (div #14 #15)
-#226 := (* -1::Int #27)
-#227 := (+ #16 #226)
-#228 := (= #227 0::Int)
-#104 := (>= #14 0::Int)
-#97 := (<= #15 0::Int)
-#189 := (or #97 #104)
-#190 := (not #189)
-#93 := (<= #14 0::Int)
-#187 := (or #93 #97)
-#188 := (not #187)
-#193 := (or #188 #190)
-#232 := (ite #193 #228 #231)
-#225 := (= #16 0::Int)
-#19 := (= #15 0::Int)
-#18 := (= #14 0::Int)
-#20 := (or #18 #19)
-#233 := (ite #20 #225 #232)
-#727 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #726) #233)
-#236 := (forall (vars (?v0 Int) (?v1 Int)) #233)
-#730 := (iff #236 #727)
-#728 := (iff #233 #233)
-#729 := [refl]: #728
-#731 := [quant-intro #729]: #730
-#196 := (ite #193 #27 #78)
-#199 := (ite #20 0::Int #196)
-#202 := (= #16 #199)
-#205 := (forall (vars (?v0 Int) (?v1 Int)) #202)
-#237 := (iff #205 #236)
-#234 := (iff #202 #233)
-#235 := [rewrite]: #234
-#238 := [quant-intro #235]: #237
-#105 := (not #104)
-#98 := (not #97)
-#108 := (and #98 #105)
-#94 := (not #93)
-#101 := (and #94 #98)
-#111 := (or #101 #108)
-#114 := (ite #111 #27 #78)
-#117 := (ite #20 0::Int #114)
-#120 := (= #16 #117)
-#123 := (forall (vars (?v0 Int) (?v1 Int)) #120)
-#206 := (iff #123 #205)
-#203 := (iff #120 #202)
-#200 := (= #117 #199)
-#197 := (= #114 #196)
-#194 := (iff #111 #193)
-#191 := (iff #108 #190)
-#192 := [rewrite]: #191
-#181 := (iff #101 #188)
-#182 := [rewrite]: #181
-#195 := [monotonicity #182 #192]: #194
-#198 := [monotonicity #195]: #197
-#201 := [monotonicity #198]: #200
-#204 := [monotonicity #201]: #203
-#207 := [quant-intro #204]: #206
-#185 := (~ #123 #123)
-#183 := (~ #120 #120)
-#184 := [refl]: #183
-#186 := [nnf-pos #184]: #185
-#29 := (- #15)
-#28 := (- #14)
-#30 := (div #28 #29)
-#22 := (< 0::Int #15)
-#24 := (< #14 0::Int)
-#25 := (and #24 #22)
-#21 := (< 0::Int #14)
-#23 := (and #21 #22)
-#26 := (or #23 #25)
-#31 := (ite #26 #27 #30)
-#32 := (ite #20 0::Int #31)
-#33 := (= #16 #32)
-#34 := (forall (vars (?v0 Int) (?v1 Int)) #33)
-#126 := (iff #34 #123)
-#65 := (and #22 #24)
-#68 := (or #23 #65)
-#81 := (ite #68 #27 #78)
-#84 := (ite #20 0::Int #81)
-#87 := (= #16 #84)
-#90 := (forall (vars (?v0 Int) (?v1 Int)) #87)
-#124 := (iff #90 #123)
-#121 := (iff #87 #120)
-#118 := (= #84 #117)
-#115 := (= #81 #114)
-#112 := (iff #68 #111)
-#109 := (iff #65 #108)
-#106 := (iff #24 #105)
-#107 := [rewrite]: #106
-#99 := (iff #22 #98)
-#100 := [rewrite]: #99
-#110 := [monotonicity #100 #107]: #109
-#102 := (iff #23 #101)
-#95 := (iff #21 #94)
-#96 := [rewrite]: #95
-#103 := [monotonicity #96 #100]: #102
-#113 := [monotonicity #103 #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [monotonicity #116]: #118
+#79 := (= #20 #78)
+#80 := [monotonicity #51]: #79
+#84 := [trans #80 #82]: #83
+#76 := (iff #19 #75)
+#73 := (iff #18 #72)
+#67 := (iff #15 #66)
+#68 := [monotonicity #51]: #67
+#74 := [monotonicity #68]: #73
+#70 := (iff #16 #69)
+#71 := [monotonicity #68]: #70
+#77 := [monotonicity #71 #74]: #76
+#101 := [monotonicity #77 #84 #98]: #100
+#105 := [trans #101 #103]: #104
+#64 := (iff #13 false)
+#59 := (or false false)
+#62 := (iff #59 false)
+#63 := [rewrite]: #62
+#60 := (iff #13 #59)
+#57 := (iff #12 false)
+#52 := (= -1::Int 0::Int)
+#55 := (iff #52 false)
+#56 := [rewrite]: #55
+#53 := (iff #12 #52)
+#54 := [monotonicity #51]: #53
+#58 := [trans #54 #56]: #57
+#47 := (iff #10 false)
+#48 := [rewrite]: #47
+#61 := [monotonicity #48 #58]: #60
+#65 := [trans #61 #63]: #64
+#108 := [monotonicity #65 #105]: #107
+#112 := [trans #108 #110]: #111
+#115 := [monotonicity #112 #51]: #114
+#119 := [trans #115 #117]: #118
 #122 := [monotonicity #119]: #121
-#125 := [quant-intro #122]: #124
-#91 := (iff #34 #90)
-#88 := (iff #33 #87)
-#85 := (= #32 #84)
-#82 := (= #31 #81)
-#79 := (= #30 #78)
-#76 := (= #29 #75)
-#77 := [rewrite]: #76
-#73 := (= #28 #72)
-#74 := [rewrite]: #73
-#80 := [monotonicity #74 #77]: #79
-#69 := (iff #26 #68)
-#66 := (iff #25 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#83 := [monotonicity #70 #80]: #82
-#86 := [monotonicity #83]: #85
-#89 := [monotonicity #86]: #88
-#92 := [quant-intro #89]: #91
-#127 := [trans #92 #125]: #126
-#64 := [asserted]: #34
-#128 := [mp #64 #127]: #123
-#177 := [mp~ #128 #186]: #123
-#208 := [mp #177 #207]: #205
-#239 := [mp #208 #238]: #236
-#732 := [mp #239 #731]: #727
-#11 := 1::Int
-#9 := 3::Int
-#8 := 5::Int
-#10 := (f3 5::Int 3::Int)
-#12 := (= #10 1::Int)
-#13 := (not #12)
-#63 := [asserted]: #13
-#635 := (not #727)
-#636 := (or #635 #12)
-#313 := (* -1::Int 3::Int)
-#397 := (* -1::Int 5::Int)
-#398 := (div #397 #313)
-#399 := (* -1::Int #398)
-#390 := (+ #10 #399)
-#401 := (= #390 0::Int)
-#402 := (div 5::Int 3::Int)
-#403 := (* -1::Int #402)
-#400 := (+ #10 #403)
-#404 := (= #400 0::Int)
-#383 := (>= 5::Int 0::Int)
-#718 := (<= 3::Int 0::Int)
-#720 := (or #718 #383)
-#377 := (not #720)
-#507 := (<= 5::Int 0::Int)
-#714 := (or #507 #718)
-#388 := (not #714)
-#389 := (or #388 #377)
-#721 := (ite #389 #404 #401)
-#722 := (= #10 0::Int)
-#723 := (= 3::Int 0::Int)
-#724 := (= 5::Int 0::Int)
-#719 := (or #724 #723)
-#725 := (ite #719 #722 #721)
-#637 := (or #635 #725)
-#638 := (iff #637 #636)
-#625 := (iff #636 #636)
-#627 := [rewrite]: #625
-#632 := (iff #725 #12)
-#645 := (ite false #722 #12)
-#647 := (iff #645 #12)
-#631 := [rewrite]: #647
-#646 := (iff #725 #645)
-#643 := (iff #721 #12)
-#664 := 2::Int
-#648 := (= #10 2::Int)
-#1 := true
-#651 := (ite true #12 #648)
-#649 := (iff #651 #12)
-#654 := [rewrite]: #649
-#652 := (iff #721 #651)
-#639 := (iff #401 #648)
-#655 := -2::Int
-#563 := (+ -2::Int #10)
-#660 := (= #563 0::Int)
-#650 := (iff #660 #648)
-#642 := [rewrite]: #650
-#657 := (iff #401 #660)
-#566 := (= #390 #563)
-#561 := (+ #10 -2::Int)
-#564 := (= #561 #563)
-#565 := [rewrite]: #564
-#562 := (= #390 #561)
-#544 := (= #399 -2::Int)
-#510 := (* -1::Int 2::Int)
-#656 := (= #510 -2::Int)
-#659 := [rewrite]: #656
-#658 := (= #399 #510)
-#550 := (= #398 2::Int)
-#508 := -3::Int
-#670 := -5::Int
-#663 := (div -5::Int -3::Int)
-#667 := (= #663 2::Int)
-#549 := [rewrite]: #667
-#665 := (= #398 #663)
-#509 := (= #313 -3::Int)
-#662 := [rewrite]: #509
-#677 := (= #397 -5::Int)
-#506 := [rewrite]: #677
-#666 := [monotonicity #506 #662]: #665
-#551 := [trans #666 #549]: #550
-#560 := [monotonicity #551]: #658
-#559 := [trans #560 #659]: #544
-#555 := [monotonicity #559]: #562
-#567 := [trans #555 #565]: #566
-#661 := [monotonicity #567]: #657
-#641 := [trans #661 #642]: #639
-#675 := (iff #404 #12)
-#686 := (+ -1::Int #10)
-#672 := (= #686 0::Int)
-#668 := (iff #672 #12)
-#669 := [rewrite]: #668
-#673 := (iff #404 #672)
-#529 := (= #400 #686)
-#684 := (+ #10 -1::Int)
-#527 := (= #684 #686)
-#528 := [rewrite]: #527
-#685 := (= #400 #684)
-#678 := (= #403 -1::Int)
-#688 := (* -1::Int 1::Int)
-#682 := (= #688 -1::Int)
-#683 := [rewrite]: #682
-#692 := (= #403 #688)
-#687 := (= #402 1::Int)
-#691 := [rewrite]: #687
-#681 := [monotonicity #691]: #692
-#679 := [trans #681 #683]: #678
-#680 := [monotonicity #679]: #685
-#671 := [trans #680 #528]: #529
-#674 := [monotonicity #671]: #673
-#676 := [trans #674 #669]: #675
-#690 := (iff #389 true)
-#408 := (or true false)
-#411 := (iff #408 true)
-#689 := [rewrite]: #411
-#409 := (iff #389 #408)
-#694 := (iff #377 false)
-#696 := (not true)
-#693 := (iff #696 false)
-#697 := [rewrite]: #693
-#418 := (iff #377 #696)
-#319 := (iff #720 true)
-#700 := (or false true)
-#424 := (iff #700 true)
-#425 := [rewrite]: #424
-#422 := (iff #720 #700)
-#713 := (iff #383 true)
-#699 := [rewrite]: #713
-#704 := (iff #718 false)
-#705 := [rewrite]: #704
-#423 := [monotonicity #705 #699]: #422
-#695 := [trans #423 #425]: #319
-#419 := [monotonicity #695]: #418
-#698 := [trans #419 #697]: #694
-#712 := (iff #388 true)
-#346 := (not false)
-#351 := (iff #346 true)
-#352 := [rewrite]: #351
-#709 := (iff #388 #346)
-#702 := (iff #714 false)
-#376 := (or false false)
-#701 := (iff #376 false)
-#364 := [rewrite]: #701
-#706 := (iff #714 #376)
-#367 := (iff #507 false)
-#703 := [rewrite]: #367
-#707 := [monotonicity #703 #705]: #706
-#708 := [trans #707 #364]: #702
-#711 := [monotonicity #708]: #709
-#710 := [trans #711 #352]: #712
-#410 := [monotonicity #710 #698]: #409
-#405 := [trans #410 #689]: #690
-#653 := [monotonicity #405 #676 #641]: #652
-#644 := [trans #653 #654]: #643
-#365 := (iff #719 false)
-#717 := (iff #719 #376)
-#380 := (iff #723 false)
-#716 := [rewrite]: #380
-#715 := (iff #724 false)
-#375 := [rewrite]: #715
-#360 := [monotonicity #375 #716]: #717
-#366 := [trans #360 #364]: #365
-#640 := [monotonicity #366 #644]: #646
-#634 := [trans #640 #631]: #632
-#624 := [monotonicity #634]: #638
-#628 := [trans #624 #627]: #638
-#633 := [quant-inst #8 #9]: #637
-#629 := [mp #633 #628]: #636
-[unit-resolution #629 #63 #732]: false
-unsat
-191c033321d69fed907f76825c4e08dd5071fdbf 307 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#16 := (:var 0 Int)
-#15 := (:var 1 Int)
-#17 := (f3 #15 #16)
-#742 := (pattern #17)
-#18 := 0::Int
-#71 := -1::Int
-#91 := (* -1::Int #16)
-#88 := (* -1::Int #15)
-#94 := (div #88 #91)
-#245 := (* -1::Int #94)
-#246 := (+ #17 #245)
-#247 := (= #246 0::Int)
-#28 := (div #15 #16)
-#242 := (* -1::Int #28)
-#243 := (+ #17 #242)
-#244 := (= #243 0::Int)
-#120 := (>= #15 0::Int)
-#113 := (<= #16 0::Int)
-#205 := (or #113 #120)
-#206 := (not #205)
-#109 := (<= #15 0::Int)
-#203 := (or #109 #113)
-#204 := (not #203)
-#209 := (or #204 #206)
-#248 := (ite #209 #244 #247)
-#241 := (= #17 0::Int)
-#20 := (= #16 0::Int)
-#19 := (= #15 0::Int)
-#21 := (or #19 #20)
-#249 := (ite #21 #241 #248)
-#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #249)
-#252 := (forall (vars (?v0 Int) (?v1 Int)) #249)
-#746 := (iff #252 #743)
-#744 := (iff #249 #249)
-#745 := [refl]: #744
-#747 := [quant-intro #745]: #746
-#212 := (ite #209 #28 #94)
-#215 := (ite #21 0::Int #212)
-#218 := (= #17 #215)
-#221 := (forall (vars (?v0 Int) (?v1 Int)) #218)
-#253 := (iff #221 #252)
-#250 := (iff #218 #249)
-#251 := [rewrite]: #250
-#254 := [quant-intro #251]: #253
-#121 := (not #120)
-#114 := (not #113)
-#124 := (and #114 #121)
-#110 := (not #109)
-#117 := (and #110 #114)
-#127 := (or #117 #124)
-#130 := (ite #127 #28 #94)
-#133 := (ite #21 0::Int #130)
-#136 := (= #17 #133)
-#139 := (forall (vars (?v0 Int) (?v1 Int)) #136)
-#222 := (iff #139 #221)
-#219 := (iff #136 #218)
-#216 := (= #133 #215)
-#213 := (= #130 #212)
-#210 := (iff #127 #209)
-#207 := (iff #124 #206)
-#208 := [rewrite]: #207
-#197 := (iff #117 #204)
-#198 := [rewrite]: #197
-#211 := [monotonicity #198 #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [monotonicity #217]: #219
-#223 := [quant-intro #220]: #222
-#201 := (~ #139 #139)
-#199 := (~ #136 #136)
-#200 := [refl]: #199
-#202 := [nnf-pos #200]: #201
-#30 := (- #16)
-#29 := (- #15)
-#31 := (div #29 #30)
-#23 := (< 0::Int #16)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#32 := (ite #27 #28 #31)
-#33 := (ite #21 0::Int #32)
-#34 := (= #17 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#142 := (iff #35 #139)
-#81 := (and #23 #25)
-#85 := (or #24 #81)
-#97 := (ite #85 #28 #94)
-#100 := (ite #21 0::Int #97)
-#103 := (= #17 #100)
-#106 := (forall (vars (?v0 Int) (?v1 Int)) #103)
-#140 := (iff #106 #139)
-#137 := (iff #103 #136)
-#134 := (= #100 #133)
-#131 := (= #97 #130)
-#128 := (iff #85 #127)
-#125 := (iff #81 #124)
-#122 := (iff #25 #121)
-#123 := [rewrite]: #122
-#115 := (iff #23 #114)
-#116 := [rewrite]: #115
-#126 := [monotonicity #116 #123]: #125
-#118 := (iff #24 #117)
-#111 := (iff #22 #110)
-#112 := [rewrite]: #111
-#119 := [monotonicity #112 #116]: #118
-#129 := [monotonicity #119 #126]: #128
-#132 := [monotonicity #129]: #131
-#135 := [monotonicity #132]: #134
-#138 := [monotonicity #135]: #137
-#141 := [quant-intro #138]: #140
-#107 := (iff #35 #106)
-#104 := (iff #34 #103)
-#101 := (= #33 #100)
-#98 := (= #32 #97)
-#95 := (= #31 #94)
-#92 := (= #30 #91)
-#93 := [rewrite]: #92
-#89 := (= #29 #88)
-#90 := [rewrite]: #89
-#96 := [monotonicity #90 #93]: #95
-#86 := (iff #27 #85)
-#83 := (iff #26 #81)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#99 := [monotonicity #87 #96]: #98
-#102 := [monotonicity #99]: #101
-#105 := [monotonicity #102]: #104
-#108 := [quant-intro #105]: #107
-#143 := [trans #108 #141]: #142
-#80 := [asserted]: #35
-#144 := [mp #80 #143]: #139
-#193 := [mp~ #144 #202]: #139
-#224 := [mp #193 #223]: #221
-#255 := [mp #224 #254]: #252
-#748 := [mp #255 #747]: #743
-#65 := -3::Int
-#8 := 1::Int
-#68 := (f3 1::Int -3::Int)
-#74 := (= #68 -1::Int)
-#77 := (not #74)
-#12 := (- 1::Int)
-#9 := 3::Int
-#10 := (- 3::Int)
-#11 := (f3 1::Int #10)
-#13 := (= #11 #12)
-#14 := (not #13)
-#78 := (iff #14 #77)
-#75 := (iff #13 #74)
-#72 := (= #12 -1::Int)
-#73 := [rewrite]: #72
-#69 := (= #11 #68)
-#66 := (= #10 -3::Int)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#76 := [monotonicity #70 #73]: #75
-#79 := [monotonicity #76]: #78
-#64 := [asserted]: #14
-#82 := [mp #64 #79]: #77
-#658 := (not #743)
-#655 := (or #658 #74)
-#329 := (* -1::Int -3::Int)
-#413 := (* -1::Int 1::Int)
-#414 := (div #413 #329)
-#415 := (* -1::Int #414)
-#406 := (+ #68 #415)
-#417 := (= #406 0::Int)
-#418 := (div 1::Int -3::Int)
-#419 := (* -1::Int #418)
-#416 := (+ #68 #419)
-#420 := (= #416 0::Int)
-#399 := (>= 1::Int 0::Int)
-#734 := (<= -3::Int 0::Int)
-#736 := (or #734 #399)
-#393 := (not #736)
-#523 := (<= 1::Int 0::Int)
-#730 := (or #523 #734)
-#404 := (not #730)
-#405 := (or #404 #393)
-#737 := (ite #405 #420 #417)
-#738 := (= #68 0::Int)
-#739 := (= -3::Int 0::Int)
-#740 := (= 1::Int 0::Int)
-#735 := (or #740 #739)
-#741 := (ite #735 #738 #737)
-#657 := (or #658 #741)
-#668 := (iff #657 #655)
-#665 := (iff #655 #655)
-#670 := [rewrite]: #665
-#664 := (iff #741 #74)
-#571 := (ite false #738 #74)
-#581 := (iff #571 #74)
-#582 := [rewrite]: #581
-#673 := (iff #741 #571)
-#583 := (iff #737 #74)
-#579 := (iff #737 #571)
-#577 := (iff #417 #74)
-#566 := (+ 1::Int #68)
-#671 := (= #566 0::Int)
-#560 := (iff #671 #74)
-#575 := [rewrite]: #560
-#672 := (iff #417 #671)
-#674 := (= #406 #566)
-#680 := (+ #68 1::Int)
-#567 := (= #680 #566)
-#526 := [rewrite]: #567
-#683 := (= #406 #680)
-#681 := (= #415 1::Int)
-#522 := (* -1::Int -1::Int)
-#678 := (= #522 1::Int)
-#679 := [rewrite]: #678
-#524 := (= #415 #522)
-#686 := (= #414 -1::Int)
-#690 := (div -1::Int 3::Int)
-#691 := (= #690 -1::Int)
-#692 := [rewrite]: #691
-#684 := (= #414 #690)
-#688 := (= #329 3::Int)
-#689 := [rewrite]: #688
-#545 := (= #413 -1::Int)
-#687 := [rewrite]: #545
-#685 := [monotonicity #687 #689]: #684
-#693 := [trans #685 #692]: #686
-#525 := [monotonicity #693]: #524
-#682 := [trans #525 #679]: #681
-#565 := [monotonicity #682]: #683
-#576 := [trans #565 #526]: #674
-#675 := [monotonicity #576]: #672
-#578 := [trans #675 #575]: #577
-#543 := (iff #420 #738)
-#696 := (= #416 #68)
-#699 := (+ #68 0::Int)
-#700 := (= #699 #68)
-#701 := [rewrite]: #700
-#694 := (= #416 #699)
-#697 := (= #419 0::Int)
-#421 := (* -1::Int 0::Int)
-#704 := (= #421 0::Int)
-#708 := [rewrite]: #704
-#703 := (= #419 #421)
-#705 := (= #418 0::Int)
-#706 := [rewrite]: #705
-#707 := [monotonicity #706]: #703
-#698 := [trans #707 #708]: #697
-#695 := [monotonicity #698]: #694
-#702 := [trans #695 #701]: #696
-#544 := [monotonicity #702]: #543
-#426 := (iff #405 false)
-#392 := (or false false)
-#717 := (iff #392 false)
-#380 := [rewrite]: #717
-#424 := (iff #405 #392)
-#710 := (iff #393 false)
-#1 := true
-#367 := (not true)
-#726 := (iff #367 false)
-#729 := [rewrite]: #726
-#709 := (iff #393 #367)
-#434 := (iff #736 true)
-#440 := (or true true)
-#711 := (iff #440 true)
-#712 := [rewrite]: #711
-#441 := (iff #736 #440)
-#438 := (iff #399 true)
-#439 := [rewrite]: #438
-#720 := (iff #734 true)
-#721 := [rewrite]: #720
-#335 := [monotonicity #721 #439]: #441
-#435 := [trans #335 #712]: #434
-#713 := [monotonicity #435]: #709
-#714 := [trans #713 #729]: #710
-#715 := (iff #404 false)
-#368 := (iff #404 #367)
-#725 := (iff #730 true)
-#722 := (or false true)
-#724 := (iff #722 true)
-#362 := [rewrite]: #724
-#723 := (iff #730 #722)
-#383 := (iff #523 false)
-#719 := [rewrite]: #383
-#718 := [monotonicity #719 #721]: #723
-#727 := [trans #718 #362]: #725
-#728 := [monotonicity #727]: #368
-#716 := [trans #728 #729]: #715
-#425 := [monotonicity #716 #714]: #424
-#427 := [trans #425 #380]: #426
-#580 := [monotonicity #427 #544 #578]: #579
-#676 := [trans #580 #582]: #583
-#381 := (iff #735 false)
-#733 := (iff #735 #392)
-#396 := (iff #739 false)
-#732 := [rewrite]: #396
-#731 := (iff #740 false)
-#391 := [rewrite]: #731
-#376 := [monotonicity #391 #732]: #733
-#382 := [trans #376 #380]: #381
-#677 := [monotonicity #382 #676]: #673
-#666 := [trans #677 #582]: #664
-#669 := [monotonicity #666]: #668
-#659 := [trans #669 #670]: #668
-#667 := [quant-inst #8 #65]: #657
-#660 := [mp #667 #659]: #655
-[unit-resolution #660 #82 #748]: false
-unsat
-5ac842dfccd0a130b836d32f5bc0e4f0b730d4cf 306 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#16 := (:var 0 Int)
-#15 := (:var 1 Int)
-#17 := (f3 #15 #16)
-#742 := (pattern #17)
-#18 := 0::Int
-#71 := -1::Int
-#91 := (* -1::Int #16)
-#88 := (* -1::Int #15)
-#94 := (div #88 #91)
-#245 := (* -1::Int #94)
-#246 := (+ #17 #245)
-#247 := (= #246 0::Int)
-#28 := (div #15 #16)
-#242 := (* -1::Int #28)
-#243 := (+ #17 #242)
-#244 := (= #243 0::Int)
-#120 := (>= #15 0::Int)
-#113 := (<= #16 0::Int)
-#205 := (or #113 #120)
-#206 := (not #205)
-#109 := (<= #15 0::Int)
-#203 := (or #109 #113)
-#204 := (not #203)
-#209 := (or #204 #206)
-#248 := (ite #209 #244 #247)
-#241 := (= #17 0::Int)
-#20 := (= #16 0::Int)
-#19 := (= #15 0::Int)
-#21 := (or #19 #20)
-#249 := (ite #21 #241 #248)
-#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #249)
-#252 := (forall (vars (?v0 Int) (?v1 Int)) #249)
-#746 := (iff #252 #743)
-#744 := (iff #249 #249)
-#745 := [refl]: #744
-#747 := [quant-intro #745]: #746
-#212 := (ite #209 #28 #94)
-#215 := (ite #21 0::Int #212)
-#218 := (= #17 #215)
-#221 := (forall (vars (?v0 Int) (?v1 Int)) #218)
-#253 := (iff #221 #252)
-#250 := (iff #218 #249)
-#251 := [rewrite]: #250
-#254 := [quant-intro #251]: #253
-#121 := (not #120)
-#114 := (not #113)
-#124 := (and #114 #121)
-#110 := (not #109)
-#117 := (and #110 #114)
-#127 := (or #117 #124)
-#130 := (ite #127 #28 #94)
-#133 := (ite #21 0::Int #130)
-#136 := (= #17 #133)
-#139 := (forall (vars (?v0 Int) (?v1 Int)) #136)
-#222 := (iff #139 #221)
-#219 := (iff #136 #218)
-#216 := (= #133 #215)
-#213 := (= #130 #212)
-#210 := (iff #127 #209)
-#207 := (iff #124 #206)
-#208 := [rewrite]: #207
-#197 := (iff #117 #204)
-#198 := [rewrite]: #197
-#211 := [monotonicity #198 #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [monotonicity #217]: #219
-#223 := [quant-intro #220]: #222
-#201 := (~ #139 #139)
-#199 := (~ #136 #136)
-#200 := [refl]: #199
-#202 := [nnf-pos #200]: #201
-#30 := (- #16)
-#29 := (- #15)
-#31 := (div #29 #30)
-#23 := (< 0::Int #16)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#32 := (ite #27 #28 #31)
-#33 := (ite #21 0::Int #32)
-#34 := (= #17 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#142 := (iff #35 #139)
-#81 := (and #23 #25)
-#85 := (or #24 #81)
-#97 := (ite #85 #28 #94)
-#100 := (ite #21 0::Int #97)
-#103 := (= #17 #100)
-#106 := (forall (vars (?v0 Int) (?v1 Int)) #103)
-#140 := (iff #106 #139)
-#137 := (iff #103 #136)
-#134 := (= #100 #133)
-#131 := (= #97 #130)
-#128 := (iff #85 #127)
-#125 := (iff #81 #124)
-#122 := (iff #25 #121)
-#123 := [rewrite]: #122
-#115 := (iff #23 #114)
-#116 := [rewrite]: #115
-#126 := [monotonicity #116 #123]: #125
-#118 := (iff #24 #117)
-#111 := (iff #22 #110)
-#112 := [rewrite]: #111
-#119 := [monotonicity #112 #116]: #118
-#129 := [monotonicity #119 #126]: #128
-#132 := [monotonicity #129]: #131
-#135 := [monotonicity #132]: #134
-#138 := [monotonicity #135]: #137
-#141 := [quant-intro #138]: #140
-#107 := (iff #35 #106)
-#104 := (iff #34 #103)
-#101 := (= #33 #100)
-#98 := (= #32 #97)
-#95 := (= #31 #94)
-#92 := (= #30 #91)
-#93 := [rewrite]: #92
-#89 := (= #29 #88)
-#90 := [rewrite]: #89
-#96 := [monotonicity #90 #93]: #95
-#86 := (iff #27 #85)
-#83 := (iff #26 #81)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#99 := [monotonicity #87 #96]: #98
-#102 := [monotonicity #99]: #101
-#105 := [monotonicity #102]: #104
-#108 := [quant-intro #105]: #107
-#143 := [trans #108 #141]: #142
-#80 := [asserted]: #35
-#144 := [mp #80 #143]: #139
-#193 := [mp~ #144 #202]: #139
-#224 := [mp #193 #223]: #221
-#255 := [mp #224 #254]: #252
-#748 := [mp #255 #747]: #743
-#65 := -3::Int
+#126 := [trans #122 #124]: #125
+#46 := [asserted]: #26
+[mp #46 #126]: false
+unsat
+a8c1cb5f3abdb5b9970e52ea21ab71e754348560 109 0
+#2 := false
 #8 := 3::Int
-#68 := (f3 3::Int -3::Int)
-#74 := (= #68 -1::Int)
-#77 := (not #74)
+#22 := (- 3::Int)
 #11 := 1::Int
 #12 := (- 1::Int)
-#9 := (- 3::Int)
-#10 := (f3 3::Int #9)
-#13 := (= #10 #12)
-#14 := (not #13)
-#78 := (iff #14 #77)
-#75 := (iff #13 #74)
-#72 := (= #12 -1::Int)
-#73 := [rewrite]: #72
-#69 := (= #10 #68)
-#66 := (= #9 -3::Int)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#76 := [monotonicity #70 #73]: #75
-#79 := [monotonicity #76]: #78
-#64 := [asserted]: #14
-#82 := [mp #64 #79]: #77
-#666 := (not #743)
-#658 := (or #666 #74)
-#329 := (* -1::Int -3::Int)
-#413 := (* -1::Int 3::Int)
-#414 := (div #413 #329)
-#415 := (* -1::Int #414)
-#406 := (+ #68 #415)
-#417 := (= #406 0::Int)
-#418 := (div 3::Int -3::Int)
-#419 := (* -1::Int #418)
-#416 := (+ #68 #419)
-#420 := (= #416 0::Int)
-#399 := (>= 3::Int 0::Int)
-#734 := (<= -3::Int 0::Int)
-#736 := (or #734 #399)
-#393 := (not #736)
-#523 := (<= 3::Int 0::Int)
-#730 := (or #523 #734)
-#404 := (not #730)
-#405 := (or #404 #393)
-#737 := (ite #405 #420 #417)
-#738 := (= #68 0::Int)
-#739 := (= -3::Int 0::Int)
-#740 := (= 3::Int 0::Int)
-#735 := (or #740 #739)
-#741 := (ite #735 #738 #737)
-#655 := (or #666 #741)
-#667 := (iff #655 #658)
-#669 := (iff #658 #658)
-#665 := [rewrite]: #669
-#677 := (iff #741 #74)
-#581 := (ite false #738 #74)
-#676 := (iff #581 #74)
-#673 := [rewrite]: #676
-#582 := (iff #741 #581)
-#579 := (iff #737 #74)
-#560 := (ite false #74 #74)
-#578 := (iff #560 #74)
-#571 := [rewrite]: #578
-#575 := (iff #737 #560)
-#672 := (iff #417 #74)
-#700 := (+ 1::Int #68)
-#544 := (= #700 0::Int)
-#688 := (iff #544 #74)
-#689 := [rewrite]: #688
-#576 := (iff #417 #544)
-#526 := (= #406 #700)
-#699 := (+ #68 1::Int)
-#701 := (= #699 #700)
-#696 := [rewrite]: #701
-#566 := (= #406 #699)
-#683 := (= #415 1::Int)
-#421 := (* -1::Int -1::Int)
-#704 := (= #421 1::Int)
-#708 := [rewrite]: #704
-#682 := (= #415 #421)
-#679 := (= #414 -1::Int)
-#693 := (div -3::Int 3::Int)
-#525 := (= #693 -1::Int)
-#678 := [rewrite]: #525
-#522 := (= #414 #693)
-#692 := (= #329 3::Int)
-#686 := [rewrite]: #692
-#685 := (= #413 -3::Int)
-#691 := [rewrite]: #685
-#524 := [monotonicity #691 #686]: #522
-#681 := [trans #524 #678]: #679
-#680 := [monotonicity #681]: #682
-#565 := [trans #680 #708]: #683
-#567 := [monotonicity #565]: #566
-#674 := [trans #567 #696]: #526
-#671 := [monotonicity #674]: #576
-#675 := [trans #671 #689]: #672
-#690 := (iff #420 #74)
-#545 := (iff #420 #544)
-#702 := (= #416 #700)
-#694 := (= #416 #699)
-#697 := (= #419 1::Int)
-#703 := (= #419 #421)
-#705 := (= #418 -1::Int)
-#706 := [rewrite]: #705
-#707 := [monotonicity #706]: #703
-#698 := [trans #707 #708]: #697
-#695 := [monotonicity #698]: #694
-#543 := [trans #695 #696]: #702
-#687 := [monotonicity #543]: #545
-#684 := [trans #687 #689]: #690
-#426 := (iff #405 false)
-#392 := (or false false)
-#717 := (iff #392 false)
-#380 := [rewrite]: #717
-#424 := (iff #405 #392)
-#710 := (iff #393 false)
-#1 := true
-#367 := (not true)
-#726 := (iff #367 false)
-#729 := [rewrite]: #726
-#709 := (iff #393 #367)
-#434 := (iff #736 true)
-#440 := (or true true)
-#711 := (iff #440 true)
-#712 := [rewrite]: #711
-#441 := (iff #736 #440)
-#438 := (iff #399 true)
-#439 := [rewrite]: #438
-#720 := (iff #734 true)
-#721 := [rewrite]: #720
-#335 := [monotonicity #721 #439]: #441
-#435 := [trans #335 #712]: #434
-#713 := [monotonicity #435]: #709
-#714 := [trans #713 #729]: #710
-#715 := (iff #404 false)
-#368 := (iff #404 #367)
-#725 := (iff #730 true)
-#722 := (or false true)
-#724 := (iff #722 true)
-#362 := [rewrite]: #724
-#723 := (iff #730 #722)
-#383 := (iff #523 false)
-#719 := [rewrite]: #383
-#718 := [monotonicity #719 #721]: #723
-#727 := [trans #718 #362]: #725
-#728 := [monotonicity #727]: #368
-#716 := [trans #728 #729]: #715
-#425 := [monotonicity #716 #714]: #424
-#427 := [trans #425 #380]: #426
-#577 := [monotonicity #427 #684 #675]: #575
-#580 := [trans #577 #571]: #579
-#381 := (iff #735 false)
-#733 := (iff #735 #392)
-#396 := (iff #739 false)
-#732 := [rewrite]: #396
-#731 := (iff #740 false)
-#391 := [rewrite]: #731
-#376 := [monotonicity #391 #732]: #733
-#382 := [trans #376 #380]: #381
-#583 := [monotonicity #382 #580]: #582
-#664 := [trans #583 #673]: #677
-#668 := [monotonicity #664]: #667
-#670 := [trans #668 #665]: #667
-#657 := [quant-inst #8 #65]: #655
-#659 := [mp #657 #670]: #658
-[unit-resolution #659 #82 #748]: false
-unsat
-ff5c5d19f29597667640ddc4ac233d7f220d9f19 321 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#17 := (:var 0 Int)
-#16 := (:var 1 Int)
-#18 := (f3 #16 #17)
-#745 := (pattern #18)
-#19 := 0::Int
-#89 := -1::Int
-#93 := (* -1::Int #17)
-#90 := (* -1::Int #16)
-#96 := (div #90 #93)
-#247 := (* -1::Int #96)
-#248 := (+ #18 #247)
-#249 := (= #248 0::Int)
-#29 := (div #16 #17)
-#244 := (* -1::Int #29)
-#245 := (+ #18 #244)
-#246 := (= #245 0::Int)
-#122 := (>= #16 0::Int)
-#115 := (<= #17 0::Int)
-#207 := (or #115 #122)
-#208 := (not #207)
-#111 := (<= #16 0::Int)
-#205 := (or #111 #115)
-#206 := (not #205)
-#211 := (or #206 #208)
-#250 := (ite #211 #246 #249)
-#243 := (= #18 0::Int)
-#21 := (= #17 0::Int)
-#20 := (= #16 0::Int)
-#22 := (or #20 #21)
-#251 := (ite #22 #243 #250)
-#746 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #745) #251)
-#254 := (forall (vars (?v0 Int) (?v1 Int)) #251)
-#749 := (iff #254 #746)
-#747 := (iff #251 #251)
-#748 := [refl]: #747
-#750 := [quant-intro #748]: #749
-#214 := (ite #211 #29 #96)
-#217 := (ite #22 0::Int #214)
-#220 := (= #18 #217)
-#223 := (forall (vars (?v0 Int) (?v1 Int)) #220)
-#255 := (iff #223 #254)
-#252 := (iff #220 #251)
-#253 := [rewrite]: #252
-#256 := [quant-intro #253]: #255
-#123 := (not #122)
-#116 := (not #115)
-#126 := (and #116 #123)
+#23 := (- #12)
+#24 := (div #22 #23)
+#21 := (div 3::Int #12)
+#9 := 0::Int
+#16 := (< 0::Int #12)
+#18 := (< 3::Int 0::Int)
+#19 := (and #18 #16)
+#15 := (< 0::Int 3::Int)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#13 := (= #12 0::Int)
+#10 := (= 3::Int 0::Int)
+#14 := (or #10 #13)
+#26 := (ite #14 0::Int #25)
+#27 := (= #26 #22)
+#28 := (not #27)
+#130 := (iff #28 false)
+#1 := true
+#125 := (not true)
+#128 := (iff #125 false)
+#129 := [rewrite]: #128
+#126 := (iff #28 #125)
+#123 := (iff #27 true)
+#83 := -3::Int
+#118 := (= -3::Int -3::Int)
+#121 := (iff #118 true)
+#122 := [rewrite]: #121
+#119 := (iff #27 #118)
+#88 := (= #22 -3::Int)
+#89 := [rewrite]: #88
+#116 := (= #26 -3::Int)
+#111 := (ite false 0::Int -3::Int)
+#114 := (= #111 -3::Int)
+#115 := [rewrite]: #114
+#112 := (= #26 #111)
+#109 := (= #25 -3::Int)
+#51 := -1::Int
+#68 := (< 0::Int -1::Int)
+#74 := (and #18 #68)
+#71 := (and #15 #68)
+#77 := (or #71 #74)
+#104 := (ite #77 -3::Int -3::Int)
+#107 := (= #104 -3::Int)
+#108 := [rewrite]: #107
+#105 := (= #25 #104)
+#102 := (= #24 -3::Int)
+#97 := (div -3::Int 1::Int)
+#100 := (= #97 -3::Int)
+#101 := [rewrite]: #100
+#98 := (= #24 #97)
+#95 := (= #23 1::Int)
+#90 := (- -1::Int)
+#93 := (= #90 1::Int)
+#94 := [rewrite]: #93
+#91 := (= #23 #90)
+#52 := (= #12 -1::Int)
+#53 := [rewrite]: #52
+#92 := [monotonicity #53]: #91
+#96 := [trans #92 #94]: #95
+#99 := [monotonicity #89 #96]: #98
+#103 := [trans #99 #101]: #102
+#86 := (= #21 -3::Int)
+#80 := (div 3::Int -1::Int)
+#84 := (= #80 -3::Int)
+#85 := [rewrite]: #84
+#81 := (= #21 #80)
+#82 := [monotonicity #53]: #81
+#87 := [trans #82 #85]: #86
+#78 := (iff #20 #77)
+#75 := (iff #19 #74)
+#69 := (iff #16 #68)
+#70 := [monotonicity #53]: #69
+#76 := [monotonicity #70]: #75
+#72 := (iff #17 #71)
+#73 := [monotonicity #70]: #72
+#79 := [monotonicity #73 #76]: #78
+#106 := [monotonicity #79 #87 #103]: #105
+#110 := [trans #106 #108]: #109
+#66 := (iff #14 false)
+#61 := (or false false)
+#64 := (iff #61 false)
+#65 := [rewrite]: #64
+#62 := (iff #14 #61)
+#59 := (iff #13 false)
+#54 := (= -1::Int 0::Int)
+#57 := (iff #54 false)
+#58 := [rewrite]: #57
+#55 := (iff #13 #54)
+#56 := [monotonicity #53]: #55
+#60 := [trans #56 #58]: #59
+#49 := (iff #10 false)
+#50 := [rewrite]: #49
+#63 := [monotonicity #50 #60]: #62
+#67 := [trans #63 #65]: #66
+#113 := [monotonicity #67 #110]: #112
+#117 := [trans #113 #115]: #116
+#120 := [monotonicity #117 #89]: #119
+#124 := [trans #120 #122]: #123
+#127 := [monotonicity #124]: #126
+#131 := [trans #127 #129]: #130
+#48 := [asserted]: #28
+[mp #48 #131]: false
+unsat
+99124c49e46379cd9d9cbc824f6c48eaad703212 215 0
+#2 := false
+#9 := 0::Int
+#11 := 1::Int
+decl f3 :: Int
+#8 := f3
+#49 := -1::Int
+#81 := (* -1::Int f3)
+#91 := (div #81 1::Int)
+#10 := (= f3 0::Int)
+#149 := (ite #10 0::Int #91)
+#157 := (+ f3 #149)
+#177 := (>= #157 0::Int)
+#274 := (not #177)
+#255 := [hypothesis]: #177
+#176 := (<= #157 0::Int)
+#251 := (* -1::Int #149)
+#252 := (+ #91 #251)
+#254 := (>= #252 0::Int)
+#173 := (= #91 #149)
+#175 := (not #10)
+#156 := (= #157 0::Int)
+#172 := (= #149 0::Int)
+#180 := [hypothesis]: #10
+#170 := (or #175 #172)
+#171 := [def-axiom]: #170
+#181 := [unit-resolution #171 #180]: #172
+#190 := (= #157 #149)
+#188 := (= #149 #157)
+#111 := (<= f3 0::Int)
+#182 := (or #175 #111)
+#183 := [th-lemma arith triangle-eq]: #182
+#184 := [unit-resolution #183 #180]: #111
+#124 := (>= f3 0::Int)
+#185 := (or #175 #124)
+#186 := [th-lemma arith triangle-eq]: #185
+#187 := [unit-resolution #186 #180]: #124
+#189 := [th-lemma arith eq-propagate 1 1 #187 #184]: #188
+#191 := [symm #189]: #190
+#192 := [trans #191 #181]: #156
+#161 := (not #156)
+#22 := (- f3)
+#12 := (- 1::Int)
+#23 := (- #12)
+#24 := (div #22 #23)
+#21 := (div f3 #12)
+#16 := (< 0::Int #12)
+#18 := (< f3 0::Int)
+#19 := (and #18 #16)
+#15 := (< 0::Int f3)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#13 := (= #12 0::Int)
+#14 := (or #10 #13)
+#26 := (ite #14 0::Int #25)
+#27 := (= #26 #22)
+#28 := (not #27)
+#164 := (iff #28 #161)
+#78 := (div f3 -1::Int)
+#66 := (< 0::Int -1::Int)
+#72 := (and #18 #66)
+#69 := (and #15 #66)
+#75 := (or #69 #72)
+#94 := (ite #75 #78 #91)
+#97 := (ite #10 0::Int #94)
+#103 := (= #81 #97)
+#108 := (not #103)
+#162 := (iff #108 #161)
+#159 := (iff #103 #156)
+#152 := (= #81 #149)
+#155 := (iff #152 #156)
+#158 := [rewrite]: #155
+#153 := (iff #103 #152)
+#150 := (= #97 #149)
+#147 := (= #94 #91)
+#142 := (ite false #78 #91)
+#145 := (= #142 #91)
+#146 := [rewrite]: #145
+#143 := (= #94 #142)
+#140 := (iff #75 false)
+#135 := (or false false)
+#138 := (iff #135 false)
+#139 := [rewrite]: #138
+#136 := (iff #75 #135)
+#133 := (iff #72 false)
+#125 := (not #124)
+#128 := (and #125 false)
+#131 := (iff #128 false)
+#132 := [rewrite]: #131
+#129 := (iff #72 #128)
+#115 := (iff #66 false)
+#116 := [rewrite]: #115
+#126 := (iff #18 #125)
+#127 := [rewrite]: #126
+#130 := [monotonicity #127 #116]: #129
+#134 := [trans #130 #132]: #133
+#122 := (iff #69 false)
 #112 := (not #111)
-#119 := (and #112 #116)
-#129 := (or #119 #126)
-#132 := (ite #129 #29 #96)
-#135 := (ite #22 0::Int #132)
-#138 := (= #18 #135)
-#141 := (forall (vars (?v0 Int) (?v1 Int)) #138)
-#224 := (iff #141 #223)
-#221 := (iff #138 #220)
-#218 := (= #135 #217)
-#215 := (= #132 #214)
-#212 := (iff #129 #211)
-#209 := (iff #126 #208)
-#210 := [rewrite]: #209
-#199 := (iff #119 #206)
-#200 := [rewrite]: #199
-#213 := [monotonicity #200 #210]: #212
-#216 := [monotonicity #213]: #215
-#219 := [monotonicity #216]: #218
-#222 := [monotonicity #219]: #221
-#225 := [quant-intro #222]: #224
-#203 := (~ #141 #141)
-#201 := (~ #138 #138)
-#202 := [refl]: #201
-#204 := [nnf-pos #202]: #203
-#31 := (- #17)
-#30 := (- #16)
-#32 := (div #30 #31)
-#24 := (< 0::Int #17)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#33 := (ite #28 #29 #32)
-#34 := (ite #22 0::Int #33)
-#35 := (= #18 #34)
-#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
-#144 := (iff #36 #141)
-#82 := (and #24 #26)
-#86 := (or #25 #82)
-#99 := (ite #86 #29 #96)
-#102 := (ite #22 0::Int #99)
-#105 := (= #18 #102)
-#108 := (forall (vars (?v0 Int) (?v1 Int)) #105)
-#142 := (iff #108 #141)
-#139 := (iff #105 #138)
-#136 := (= #102 #135)
-#133 := (= #99 #132)
-#130 := (iff #86 #129)
-#127 := (iff #82 #126)
-#124 := (iff #26 #123)
-#125 := [rewrite]: #124
-#117 := (iff #24 #116)
-#118 := [rewrite]: #117
-#128 := [monotonicity #118 #125]: #127
-#120 := (iff #25 #119)
-#113 := (iff #23 #112)
+#117 := (and #112 false)
+#120 := (iff #117 false)
+#121 := [rewrite]: #120
+#118 := (iff #69 #117)
+#113 := (iff #15 #112)
 #114 := [rewrite]: #113
-#121 := [monotonicity #114 #118]: #120
-#131 := [monotonicity #121 #128]: #130
-#134 := [monotonicity #131]: #133
-#137 := [monotonicity #134]: #136
-#140 := [monotonicity #137]: #139
-#143 := [quant-intro #140]: #142
-#109 := (iff #36 #108)
-#106 := (iff #35 #105)
-#103 := (= #34 #102)
-#100 := (= #33 #99)
-#97 := (= #32 #96)
-#94 := (= #31 #93)
-#95 := [rewrite]: #94
-#91 := (= #30 #90)
-#92 := [rewrite]: #91
-#98 := [monotonicity #92 #95]: #97
-#87 := (iff #28 #86)
-#84 := (iff #27 #82)
-#85 := [rewrite]: #84
-#88 := [monotonicity #85]: #87
-#101 := [monotonicity #88 #98]: #100
-#104 := [monotonicity #101]: #103
-#107 := [monotonicity #104]: #106
-#110 := [quant-intro #107]: #109
-#145 := [trans #110 #143]: #144
-#81 := [asserted]: #36
-#146 := [mp #81 #145]: #141
-#195 := [mp~ #146 #204]: #141
-#226 := [mp #195 #225]: #223
-#257 := [mp #226 #256]: #254
-#751 := [mp #257 #750]: #746
-#72 := -2::Int
-#66 := -3::Int
-#8 := 5::Int
-#69 := (f3 5::Int -3::Int)
-#75 := (= #69 -2::Int)
-#78 := (not #75)
-#12 := 2::Int
-#13 := (- 2::Int)
-#9 := 3::Int
-#10 := (- 3::Int)
-#11 := (f3 5::Int #10)
-#14 := (= #11 #13)
-#15 := (not #14)
-#79 := (iff #15 #78)
-#76 := (iff #14 #75)
-#73 := (= #13 -2::Int)
-#74 := [rewrite]: #73
-#70 := (= #11 #69)
-#67 := (= #10 -3::Int)
-#68 := [rewrite]: #67
+#119 := [monotonicity #114 #116]: #118
+#123 := [trans #119 #121]: #122
+#137 := [monotonicity #123 #134]: #136
+#141 := [trans #137 #139]: #140
+#144 := [monotonicity #141]: #143
+#148 := [trans #144 #146]: #147
+#151 := [monotonicity #148]: #150
+#154 := [monotonicity #151]: #153
+#160 := [trans #154 #158]: #159
+#163 := [monotonicity #160]: #162
+#109 := (iff #28 #108)
+#106 := (iff #27 #103)
+#100 := (= #97 #81)
+#104 := (iff #100 #103)
+#105 := [rewrite]: #104
+#101 := (iff #27 #100)
+#82 := (= #22 #81)
+#83 := [rewrite]: #82
+#98 := (= #26 #97)
+#95 := (= #25 #94)
+#92 := (= #24 #91)
+#89 := (= #23 1::Int)
+#84 := (- -1::Int)
+#87 := (= #84 1::Int)
+#88 := [rewrite]: #87
+#85 := (= #23 #84)
+#50 := (= #12 -1::Int)
+#51 := [rewrite]: #50
+#86 := [monotonicity #51]: #85
+#90 := [trans #86 #88]: #89
+#93 := [monotonicity #83 #90]: #92
+#79 := (= #21 #78)
+#80 := [monotonicity #51]: #79
+#76 := (iff #20 #75)
+#73 := (iff #19 #72)
+#67 := (iff #16 #66)
+#68 := [monotonicity #51]: #67
+#74 := [monotonicity #68]: #73
+#70 := (iff #17 #69)
 #71 := [monotonicity #68]: #70
 #77 := [monotonicity #71 #74]: #76
-#80 := [monotonicity #77]: #79
-#65 := [asserted]: #15
-#83 := [mp #65 #80]: #78
-#665 := (not #746)
-#659 := (or #665 #75)
-#331 := (* -1::Int -3::Int)
-#416 := (* -1::Int 5::Int)
-#417 := (div #416 #331)
-#418 := (* -1::Int #417)
-#409 := (+ #69 #418)
-#420 := (= #409 0::Int)
-#421 := (div 5::Int -3::Int)
-#349 := (* -1::Int #421)
-#422 := (+ #69 #349)
-#419 := (= #422 0::Int)
-#423 := (>= 5::Int 0::Int)
-#402 := (<= -3::Int 0::Int)
-#737 := (or #402 #423)
-#739 := (not #737)
-#396 := (<= 5::Int 0::Int)
-#526 := (or #396 #402)
-#733 := (not #526)
-#407 := (or #733 #739)
-#408 := (ite #407 #419 #420)
-#740 := (= #69 0::Int)
-#741 := (= -3::Int 0::Int)
-#742 := (= 5::Int 0::Int)
-#743 := (or #742 #741)
-#738 := (ite #743 #740 #408)
-#666 := (or #665 #738)
-#651 := (iff #666 #659)
-#654 := (iff #659 #659)
-#655 := [rewrite]: #654
-#663 := (iff #738 #75)
-#671 := (ite false #740 #75)
-#673 := (iff #671 #75)
-#662 := [rewrite]: #673
-#672 := (iff #738 #671)
-#660 := (iff #408 #75)
-#691 := (= #69 -1::Int)
-#680 := (ite false #691 #75)
-#661 := (iff #680 #75)
-#658 := [rewrite]: #661
-#667 := (iff #408 #680)
-#679 := (iff #420 #75)
-#563 := (+ 2::Int #69)
-#582 := (= #563 0::Int)
-#585 := (iff #582 #75)
-#586 := [rewrite]: #585
-#583 := (iff #420 #582)
-#581 := (= #409 #563)
-#674 := (+ #69 2::Int)
-#578 := (= #674 #563)
-#580 := [rewrite]: #578
-#675 := (= #409 #674)
-#677 := (= #418 2::Int)
-#686 := (* -1::Int -2::Int)
-#570 := (= #686 2::Int)
-#529 := [rewrite]: #570
-#568 := (= #418 #686)
-#685 := (= #417 -2::Int)
-#694 := -5::Int
-#527 := (div -5::Int 3::Int)
-#682 := (= #527 -2::Int)
-#684 := [rewrite]: #682
-#528 := (= #417 #527)
-#696 := (= #331 3::Int)
-#525 := [rewrite]: #696
-#695 := (= #416 -5::Int)
-#689 := [rewrite]: #695
-#681 := [monotonicity #689 #525]: #528
-#683 := [trans #681 #684]: #685
-#569 := [monotonicity #683]: #568
-#579 := [trans #569 #529]: #677
-#678 := [monotonicity #579]: #675
-#574 := [trans #678 #580]: #581
-#584 := [monotonicity #574]: #583
-#676 := [trans #584 #586]: #679
-#687 := (iff #419 #691)
-#710 := 1::Int
-#703 := (+ 1::Int #69)
-#547 := (= #703 0::Int)
-#692 := (iff #547 #691)
-#693 := [rewrite]: #692
-#548 := (iff #419 #547)
-#705 := (= #422 #703)
-#702 := (+ #69 1::Int)
-#704 := (= #702 #703)
-#699 := [rewrite]: #704
-#697 := (= #422 #702)
-#700 := (= #349 1::Int)
-#709 := (* -1::Int -1::Int)
-#707 := (= #709 1::Int)
-#711 := [rewrite]: #707
-#424 := (= #349 #709)
-#430 := (= #421 -1::Int)
-#708 := [rewrite]: #430
-#706 := [monotonicity #708]: #424
-#701 := [trans #706 #711]: #700
-#698 := [monotonicity #701]: #697
-#546 := [trans #698 #699]: #705
-#690 := [monotonicity #546]: #548
-#688 := [trans #690 #693]: #687
-#428 := (iff #407 false)
-#735 := (or false false)
-#379 := (iff #735 false)
-#720 := [rewrite]: #379
-#717 := (iff #407 #735)
-#716 := (iff #739 false)
-#1 := true
-#730 := (not true)
-#731 := (iff #730 false)
-#729 := [rewrite]: #731
-#438 := (iff #739 #730)
-#715 := (iff #737 true)
-#442 := (or true true)
-#337 := (iff #442 true)
-#714 := [rewrite]: #337
-#443 := (iff #737 #442)
-#719 := (iff #423 true)
-#441 := [rewrite]: #719
-#722 := (iff #402 true)
-#723 := [rewrite]: #722
-#444 := [monotonicity #723 #441]: #443
-#437 := [trans #444 #714]: #715
-#712 := [monotonicity #437]: #438
-#713 := [trans #712 #729]: #716
-#732 := (iff #733 false)
-#370 := (iff #733 #730)
-#365 := (iff #526 true)
-#724 := (or false true)
-#721 := (iff #724 true)
-#727 := [rewrite]: #721
-#725 := (iff #526 #724)
-#385 := (iff #396 false)
-#386 := [rewrite]: #385
-#726 := [monotonicity #386 #723]: #725
-#728 := [trans #726 #727]: #365
-#371 := [monotonicity #728]: #370
-#718 := [trans #371 #729]: #732
-#427 := [monotonicity #718 #713]: #717
-#429 := [trans #427 #720]: #428
-#669 := [monotonicity #429 #688 #676]: #667
-#670 := [trans #669 #658]: #660
-#383 := (iff #743 false)
-#395 := (iff #743 #735)
-#394 := (iff #741 false)
-#399 := [rewrite]: #394
-#744 := (iff #742 false)
-#734 := [rewrite]: #744
-#736 := [monotonicity #734 #399]: #395
-#384 := [trans #736 #720]: #383
-#668 := [monotonicity #384 #670]: #672
-#664 := [trans #668 #662]: #663
-#653 := [monotonicity #664]: #651
-#656 := [trans #653 #655]: #651
-#650 := [quant-inst #8 #66]: #666
-#652 := [mp #650 #656]: #659
-[unit-resolution #652 #83 #751]: false
-unsat
-3b09e93d3eb1701446a8a6f0f64071b3ee25d56a 319 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#15 := (:var 0 Int)
-#14 := (:var 1 Int)
-#16 := (f3 #14 #15)
-#750 := (pattern #16)
-#17 := 0::Int
-#64 := -1::Int
-#99 := (* -1::Int #15)
-#96 := (* -1::Int #14)
-#102 := (div #96 #99)
-#253 := (* -1::Int #102)
-#254 := (+ #16 #253)
-#255 := (= #254 0::Int)
-#27 := (div #14 #15)
-#250 := (* -1::Int #27)
-#251 := (+ #16 #250)
-#252 := (= #251 0::Int)
-#128 := (>= #14 0::Int)
-#121 := (<= #15 0::Int)
-#213 := (or #121 #128)
-#214 := (not #213)
-#117 := (<= #14 0::Int)
-#211 := (or #117 #121)
-#212 := (not #211)
-#217 := (or #212 #214)
-#256 := (ite #217 #252 #255)
-#249 := (= #16 0::Int)
-#19 := (= #15 0::Int)
-#18 := (= #14 0::Int)
-#20 := (or #18 #19)
-#257 := (ite #20 #249 #256)
-#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #257)
-#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
-#754 := (iff #260 #751)
-#752 := (iff #257 #257)
-#753 := [refl]: #752
-#755 := [quant-intro #753]: #754
-#220 := (ite #217 #27 #102)
-#223 := (ite #20 0::Int #220)
-#226 := (= #16 #223)
-#229 := (forall (vars (?v0 Int) (?v1 Int)) #226)
-#261 := (iff #229 #260)
-#258 := (iff #226 #257)
-#259 := [rewrite]: #258
-#262 := [quant-intro #259]: #261
-#129 := (not #128)
-#122 := (not #121)
-#132 := (and #122 #129)
-#118 := (not #117)
-#125 := (and #118 #122)
-#135 := (or #125 #132)
-#138 := (ite #135 #27 #102)
-#141 := (ite #20 0::Int #138)
-#144 := (= #16 #141)
-#147 := (forall (vars (?v0 Int) (?v1 Int)) #144)
-#230 := (iff #147 #229)
-#227 := (iff #144 #226)
-#224 := (= #141 #223)
-#221 := (= #138 #220)
-#218 := (iff #135 #217)
-#215 := (iff #132 #214)
-#216 := [rewrite]: #215
-#205 := (iff #125 #212)
-#206 := [rewrite]: #205
-#219 := [monotonicity #206 #216]: #218
-#222 := [monotonicity #219]: #221
-#225 := [monotonicity #222]: #224
-#228 := [monotonicity #225]: #227
-#231 := [quant-intro #228]: #230
-#209 := (~ #147 #147)
-#207 := (~ #144 #144)
-#208 := [refl]: #207
-#210 := [nnf-pos #208]: #209
-#29 := (- #15)
-#28 := (- #14)
-#30 := (div #28 #29)
-#22 := (< 0::Int #15)
-#24 := (< #14 0::Int)
-#25 := (and #24 #22)
-#21 := (< 0::Int #14)
-#23 := (and #21 #22)
-#26 := (or #23 #25)
-#31 := (ite #26 #27 #30)
-#32 := (ite #20 0::Int #31)
-#33 := (= #16 #32)
-#34 := (forall (vars (?v0 Int) (?v1 Int)) #33)
-#150 := (iff #34 #147)
-#90 := (and #22 #24)
-#93 := (or #23 #90)
-#105 := (ite #93 #27 #102)
-#108 := (ite #20 0::Int #105)
-#111 := (= #16 #108)
-#114 := (forall (vars (?v0 Int) (?v1 Int)) #111)
-#148 := (iff #114 #147)
-#145 := (iff #111 #144)
-#142 := (= #108 #141)
-#139 := (= #105 #138)
-#136 := (iff #93 #135)
-#133 := (iff #90 #132)
-#130 := (iff #24 #129)
+#96 := [monotonicity #77 #80 #93]: #95
+#64 := (iff #14 #10)
+#59 := (or #10 false)
+#62 := (iff #59 #10)
+#63 := [rewrite]: #62
+#60 := (iff #14 #59)
+#57 := (iff #13 false)
+#52 := (= -1::Int 0::Int)
+#55 := (iff #52 false)
+#56 := [rewrite]: #55
+#53 := (iff #13 #52)
+#54 := [monotonicity #51]: #53
+#58 := [trans #54 #56]: #57
+#61 := [monotonicity #58]: #60
+#65 := [trans #61 #63]: #64
+#99 := [monotonicity #65 #96]: #98
+#102 := [monotonicity #99 #83]: #101
+#107 := [trans #102 #105]: #106
+#110 := [monotonicity #107]: #109
+#165 := [trans #110 #163]: #164
+#48 := [asserted]: #28
+#166 := [mp #48 #165]: #161
+#193 := [unit-resolution #166 #192]: false
+#194 := [lemma #193]: #175
+#168 := (or #10 #173)
+#169 := [def-axiom]: #168
+#256 := [unit-resolution #169 #194]: #173
+#257 := (not #173)
+#258 := (or #257 #254)
+#259 := [th-lemma arith triangle-eq]: #258
+#260 := [unit-resolution #259 #256]: #254
+#218 := (+ f3 #91)
+#224 := (<= #218 0::Int)
+#219 := (= #218 0::Int)
+#1 := true
+#46 := [true-axiom]: true
+#261 := (or false #219)
+#262 := [th-lemma arith]: #261
+#263 := [unit-resolution #262 #46]: #219
+#264 := (not #219)
+#265 := (or #264 #224)
+#266 := [th-lemma arith triangle-eq]: #265
+#267 := [unit-resolution #266 #263]: #224
+#269 := (not #224)
+#268 := (not #254)
+#270 := (or #176 #268 #269)
+#271 := [th-lemma arith assign-bounds 1 -1]: #270
+#272 := [unit-resolution #271 #267 #260]: #176
+#273 := (not #176)
+#277 := (or #273 #274)
+#275 := (or #156 #273 #274)
+#276 := [th-lemma arith triangle-eq]: #275
+#278 := [unit-resolution #276 #166]: #277
+#279 := [unit-resolution #278 #272 #255]: false
+#280 := [lemma #279]: #274
+#253 := (<= #252 0::Int)
+#281 := (or #257 #253)
+#282 := [th-lemma arith triangle-eq]: #281
+#283 := [unit-resolution #282 #256]: #253
+#225 := (>= #218 0::Int)
+#284 := (or #264 #225)
+#285 := [th-lemma arith triangle-eq]: #284
+#286 := [unit-resolution #285 #263]: #225
+#288 := (not #225)
+#287 := (not #253)
+#289 := (or #177 #287 #288)
+#290 := [th-lemma arith assign-bounds 1 -1]: #289
+#291 := [unit-resolution #290 #286 #283]: #177
+[unit-resolution #291 #280]: false
+unsat
+530d84b9b60629031058dc22de3bbb66e9dd68b7 73 0
+#2 := false
+#8 := 0::Int
+#10 := 3::Int
+#19 := (- 3::Int)
+#18 := (- 0::Int)
+#20 := (div #18 #19)
+#17 := (div 0::Int 3::Int)
+#14 := (< 0::Int 3::Int)
+#13 := (< 0::Int 0::Int)
+#15 := (and #13 #14)
+#16 := (or #15 #15)
+#21 := (ite #16 #17 #20)
+#11 := (= 3::Int 0::Int)
+#9 := (= 0::Int 0::Int)
+#12 := (or #9 #11)
+#22 := (ite #12 0::Int #21)
+#23 := (= #22 0::Int)
+#24 := (not #23)
+#94 := (iff #24 false)
+#1 := true
+#89 := (not true)
+#92 := (iff #89 false)
+#93 := [rewrite]: #92
+#90 := (iff #24 #89)
+#87 := (iff #23 true)
+#45 := (iff #9 true)
+#46 := [rewrite]: #45
+#85 := (iff #23 #9)
+#79 := (ite true 0::Int 0::Int)
+#82 := (= #79 0::Int)
+#83 := [rewrite]: #82
+#80 := (= #22 #79)
+#77 := (= #21 0::Int)
+#72 := (ite #15 0::Int 0::Int)
+#75 := (= #72 0::Int)
+#76 := [rewrite]: #75
+#73 := (= #21 #72)
+#70 := (= #20 0::Int)
+#62 := -3::Int
+#65 := (div 0::Int -3::Int)
+#68 := (= #65 0::Int)
+#69 := [rewrite]: #68
+#66 := (= #20 #65)
+#63 := (= #19 -3::Int)
+#64 := [rewrite]: #63
+#60 := (= #18 0::Int)
+#61 := [rewrite]: #60
+#67 := [monotonicity #61 #64]: #66
+#71 := [trans #67 #69]: #70
+#58 := (= #17 0::Int)
+#59 := [rewrite]: #58
+#56 := (iff #16 #15)
+#57 := [rewrite]: #56
+#74 := [monotonicity #57 #59 #71]: #73
+#78 := [trans #74 #76]: #77
+#54 := (iff #12 true)
+#49 := (or true false)
+#52 := (iff #49 true)
+#53 := [rewrite]: #52
+#50 := (iff #12 #49)
+#47 := (iff #11 false)
+#48 := [rewrite]: #47
+#51 := [monotonicity #46 #48]: #50
+#55 := [trans #51 #53]: #54
+#81 := [monotonicity #55 #78]: #80
+#84 := [trans #81 #83]: #23
+#86 := [monotonicity #84]: #85
+#88 := [trans #86 #46]: #87
+#91 := [monotonicity #88]: #90
+#95 := [trans #91 #93]: #94
+#44 := [asserted]: #24
+[mp #44 #95]: false
+unsat
+99c1933dfc0f818aac1f7a0114d4293293e0a0a1 102 0
+#2 := false
+#8 := 0::Int
+#10 := 3::Int
+#11 := (- 3::Int)
+#20 := (- #11)
+#19 := (- 0::Int)
+#21 := (div #19 #20)
+#18 := (div 0::Int #11)
+#15 := (< 0::Int #11)
+#14 := (< 0::Int 0::Int)
+#16 := (and #14 #15)
+#17 := (or #16 #16)
+#22 := (ite #17 #18 #21)
+#12 := (= #11 0::Int)
+#9 := (= 0::Int 0::Int)
+#13 := (or #9 #12)
+#23 := (ite #13 0::Int #22)
+#24 := (= #23 0::Int)
+#25 := (not #24)
+#123 := (iff #25 false)
+#1 := true
+#118 := (not true)
+#121 := (iff #118 false)
+#122 := [rewrite]: #121
+#119 := (iff #25 #118)
+#116 := (iff #24 true)
+#46 := (iff #9 true)
+#47 := [rewrite]: #46
+#114 := (iff #24 #9)
+#108 := (ite true 0::Int 0::Int)
+#111 := (= #108 0::Int)
+#112 := [rewrite]: #111
+#109 := (= #23 #108)
+#106 := (= #22 0::Int)
+#48 := -3::Int
+#65 := (< 0::Int -3::Int)
+#68 := (and #14 #65)
+#101 := (ite #68 0::Int 0::Int)
+#104 := (= #101 0::Int)
+#105 := [rewrite]: #104
+#102 := (= #22 #101)
+#99 := (= #21 0::Int)
+#94 := (div 0::Int 3::Int)
+#97 := (= #94 0::Int)
+#98 := [rewrite]: #97
+#95 := (= #21 #94)
+#92 := (= #20 3::Int)
+#87 := (- -3::Int)
+#90 := (= #87 3::Int)
+#91 := [rewrite]: #90
+#88 := (= #20 #87)
+#49 := (= #11 -3::Int)
+#50 := [rewrite]: #49
+#89 := [monotonicity #50]: #88
+#93 := [trans #89 #91]: #92
+#85 := (= #19 0::Int)
+#86 := [rewrite]: #85
+#96 := [monotonicity #86 #93]: #95
+#100 := [trans #96 #98]: #99
+#83 := (= #18 0::Int)
+#78 := (div 0::Int -3::Int)
+#81 := (= #78 0::Int)
+#82 := [rewrite]: #81
+#79 := (= #18 #78)
+#80 := [monotonicity #50]: #79
+#84 := [trans #80 #82]: #83
+#76 := (iff #17 #68)
+#71 := (or #68 #68)
+#74 := (iff #71 #68)
+#75 := [rewrite]: #74
+#72 := (iff #17 #71)
+#69 := (iff #16 #68)
+#66 := (iff #15 #65)
+#67 := [monotonicity #50]: #66
+#70 := [monotonicity #67]: #69
+#73 := [monotonicity #70 #70]: #72
+#77 := [trans #73 #75]: #76
+#103 := [monotonicity #77 #84 #100]: #102
+#107 := [trans #103 #105]: #106
+#63 := (iff #13 true)
+#58 := (or true false)
+#61 := (iff #58 true)
+#62 := [rewrite]: #61
+#59 := (iff #13 #58)
+#56 := (iff #12 false)
+#51 := (= -3::Int 0::Int)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #12 #51)
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#60 := [monotonicity #47 #57]: #59
+#64 := [trans #60 #62]: #63
+#110 := [monotonicity #64 #107]: #109
+#113 := [trans #110 #112]: #24
+#115 := [monotonicity #113]: #114
+#117 := [trans #115 #47]: #116
+#120 := [monotonicity #117]: #119
+#124 := [trans #120 #122]: #123
+#45 := [asserted]: #25
+[mp #45 #124]: false
+unsat
+9d138480c7d61fdc258e935f0608d147c435d8d1 113 0
+#2 := false
+#9 := 0::Int
+#11 := 3::Int
+#22 := (- 3::Int)
+#8 := 1::Int
+#21 := (- 1::Int)
+#23 := (div #21 #22)
+#20 := (div 1::Int 3::Int)
+#15 := (< 0::Int 3::Int)
+#17 := (< 1::Int 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int 1::Int)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#24 := (ite #19 #20 #23)
+#12 := (= 3::Int 0::Int)
+#10 := (= 1::Int 0::Int)
+#13 := (or #10 #12)
+#25 := (ite #13 0::Int #24)
+#26 := (= #25 0::Int)
+#27 := (not #26)
+#134 := (iff #27 false)
+#59 := (and #15 #17)
+#62 := (or #16 #59)
+#97 := (not #62)
+#132 := (iff #97 false)
+#1 := true
+#127 := (not true)
+#130 := (iff #127 false)
 #131 := [rewrite]: #130
-#123 := (iff #22 #122)
+#128 := (iff #97 #127)
+#125 := (iff #62 true)
+#120 := (or true false)
+#123 := (iff #120 true)
 #124 := [rewrite]: #123
-#134 := [monotonicity #124 #131]: #133
-#126 := (iff #23 #125)
-#119 := (iff #21 #118)
-#120 := [rewrite]: #119
-#127 := [monotonicity #120 #124]: #126
-#137 := [monotonicity #127 #134]: #136
-#140 := [monotonicity #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [quant-intro #146]: #148
-#115 := (iff #34 #114)
-#112 := (iff #33 #111)
-#109 := (= #32 #108)
-#106 := (= #31 #105)
-#103 := (= #30 #102)
-#100 := (= #29 #99)
+#121 := (iff #62 #120)
+#118 := (iff #59 false)
+#113 := (and true false)
+#116 := (iff #113 false)
+#117 := [rewrite]: #116
+#114 := (iff #59 #113)
+#111 := (iff #17 false)
+#112 := [rewrite]: #111
+#102 := (iff #15 true)
+#103 := [rewrite]: #102
+#115 := [monotonicity #103 #112]: #114
+#119 := [trans #115 #117]: #118
+#109 := (iff #16 true)
+#104 := (and true true)
+#107 := (iff #104 true)
+#108 := [rewrite]: #107
+#105 := (iff #16 #104)
+#100 := (iff #14 true)
 #101 := [rewrite]: #100
-#97 := (= #28 #96)
+#106 := [monotonicity #101 #103]: #105
+#110 := [trans #106 #108]: #109
+#122 := [monotonicity #110 #119]: #121
+#126 := [trans #122 #124]: #125
+#129 := [monotonicity #126]: #128
+#133 := [trans #129 #131]: #132
+#98 := (iff #27 #97)
+#95 := (iff #26 #62)
+#80 := (ite #62 0::Int 1::Int)
+#90 := (= #80 0::Int)
+#93 := (iff #90 #62)
+#94 := [rewrite]: #93
+#91 := (iff #26 #90)
+#88 := (= #25 #80)
+#83 := (ite false 0::Int #80)
+#86 := (= #83 #80)
+#87 := [rewrite]: #86
+#84 := (= #25 #83)
+#81 := (= #24 #80)
+#78 := (= #23 1::Int)
+#70 := -3::Int
+#67 := -1::Int
+#73 := (div -1::Int -3::Int)
+#76 := (= #73 1::Int)
+#77 := [rewrite]: #76
+#74 := (= #23 #73)
+#71 := (= #22 -3::Int)
+#72 := [rewrite]: #71
+#68 := (= #21 -1::Int)
+#69 := [rewrite]: #68
+#75 := [monotonicity #69 #72]: #74
+#79 := [trans #75 #77]: #78
+#65 := (= #20 0::Int)
+#66 := [rewrite]: #65
+#63 := (iff #19 #62)
+#60 := (iff #18 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#82 := [monotonicity #64 #66 #79]: #81
+#57 := (iff #13 false)
+#52 := (or false false)
+#55 := (iff #52 false)
+#56 := [rewrite]: #55
+#53 := (iff #13 #52)
+#50 := (iff #12 false)
+#51 := [rewrite]: #50
+#48 := (iff #10 false)
+#49 := [rewrite]: #48
+#54 := [monotonicity #49 #51]: #53
+#58 := [trans #54 #56]: #57
+#85 := [monotonicity #58 #82]: #84
+#89 := [trans #85 #87]: #88
+#92 := [monotonicity #89]: #91
+#96 := [trans #92 #94]: #95
+#99 := [monotonicity #96]: #98
+#135 := [trans #99 #133]: #134
+#47 := [asserted]: #27
+[mp #47 #135]: false
+unsat
+59082baebee56f4a9740d0c291f81d87438f8452 78 0
+#2 := false
+#22 := 1::Int
+#8 := 3::Int
+#18 := (- 3::Int)
+#19 := (div #18 #18)
+#17 := (div 3::Int 3::Int)
+#9 := 0::Int
+#12 := (< 0::Int 3::Int)
+#14 := (< 3::Int 0::Int)
+#15 := (and #14 #12)
+#13 := (and #12 #12)
+#16 := (or #13 #15)
+#20 := (ite #16 #17 #19)
+#10 := (= 3::Int 0::Int)
+#11 := (or #10 #10)
+#21 := (ite #11 0::Int #20)
+#23 := (= #21 1::Int)
+#24 := (not #23)
+#99 := (iff #24 false)
+#1 := true
+#94 := (not true)
+#97 := (iff #94 false)
 #98 := [rewrite]: #97
-#104 := [monotonicity #98 #101]: #103
-#94 := (iff #26 #93)
-#91 := (iff #25 #90)
+#95 := (iff #24 #94)
+#92 := (iff #23 true)
+#87 := (= 1::Int 1::Int)
+#90 := (iff #87 true)
+#91 := [rewrite]: #90
+#88 := (iff #23 #87)
+#81 := (ite false 0::Int 1::Int)
+#84 := (= #81 1::Int)
+#85 := [rewrite]: #84
+#82 := (= #21 #81)
+#79 := (= #20 1::Int)
+#56 := (and #12 #14)
+#59 := (or #12 #56)
+#74 := (ite #59 1::Int 1::Int)
+#77 := (= #74 1::Int)
+#78 := [rewrite]: #77
+#75 := (= #20 #74)
+#72 := (= #19 1::Int)
+#64 := -3::Int
+#67 := (div -3::Int -3::Int)
+#70 := (= #67 1::Int)
+#71 := [rewrite]: #70
+#68 := (= #19 #67)
+#65 := (= #18 -3::Int)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66 #66]: #68
+#73 := [trans #69 #71]: #72
+#62 := (= #17 1::Int)
+#63 := [rewrite]: #62
+#60 := (iff #16 #59)
+#57 := (iff #15 #56)
+#58 := [rewrite]: #57
+#54 := (iff #13 #12)
+#55 := [rewrite]: #54
+#61 := [monotonicity #55 #58]: #60
+#76 := [monotonicity #61 #63 #73]: #75
+#80 := [trans #76 #78]: #79
+#52 := (iff #11 false)
+#47 := (or false false)
+#50 := (iff #47 false)
+#51 := [rewrite]: #50
+#48 := (iff #11 #47)
+#45 := (iff #10 false)
+#46 := [rewrite]: #45
+#49 := [monotonicity #46 #46]: #48
+#53 := [trans #49 #51]: #52
+#83 := [monotonicity #53 #80]: #82
+#86 := [trans #83 #85]: #23
+#89 := [monotonicity #86]: #88
+#93 := [trans #89 #91]: #92
+#96 := [monotonicity #93]: #95
+#100 := [trans #96 #98]: #99
+#44 := [asserted]: #24
+[mp #44 #100]: false
+unsat
+b2dbf88881de745f35b3193199fcda41f7406d84 115 0
+#2 := false
+#26 := 1::Int
+#11 := 3::Int
+#22 := (- 3::Int)
+#8 := 5::Int
+#21 := (- 5::Int)
+#23 := (div #21 #22)
+#20 := (div 5::Int 3::Int)
+#9 := 0::Int
+#15 := (< 0::Int 3::Int)
+#17 := (< 5::Int 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int 5::Int)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#24 := (ite #19 #20 #23)
+#12 := (= 3::Int 0::Int)
+#10 := (= 5::Int 0::Int)
+#13 := (or #10 #12)
+#25 := (ite #13 0::Int #24)
+#27 := (= #25 1::Int)
+#28 := (not #27)
+#136 := (iff #28 false)
+#60 := (and #15 #17)
+#63 := (or #16 #60)
+#99 := (not #63)
+#134 := (iff #99 false)
+#1 := true
+#129 := (not true)
+#132 := (iff #129 false)
+#133 := [rewrite]: #132
+#130 := (iff #99 #129)
+#127 := (iff #63 true)
+#122 := (or true false)
+#125 := (iff #122 true)
+#126 := [rewrite]: #125
+#123 := (iff #63 #122)
+#120 := (iff #60 false)
+#115 := (and true false)
+#118 := (iff #115 false)
+#119 := [rewrite]: #118
+#116 := (iff #60 #115)
+#113 := (iff #17 false)
+#114 := [rewrite]: #113
+#104 := (iff #15 true)
+#105 := [rewrite]: #104
+#117 := [monotonicity #105 #114]: #116
+#121 := [trans #117 #119]: #120
+#111 := (iff #16 true)
+#106 := (and true true)
+#109 := (iff #106 true)
+#110 := [rewrite]: #109
+#107 := (iff #16 #106)
+#102 := (iff #14 true)
+#103 := [rewrite]: #102
+#108 := [monotonicity #103 #105]: #107
+#112 := [trans #108 #110]: #111
+#124 := [monotonicity #112 #121]: #123
+#128 := [trans #124 #126]: #127
+#131 := [monotonicity #128]: #130
+#135 := [trans #131 #133]: #134
+#100 := (iff #28 #99)
+#97 := (iff #27 #63)
+#77 := 2::Int
+#82 := (ite #63 1::Int 2::Int)
+#92 := (= #82 1::Int)
+#95 := (iff #92 #63)
+#96 := [rewrite]: #95
+#93 := (iff #27 #92)
+#90 := (= #25 #82)
+#85 := (ite false 0::Int #82)
+#88 := (= #85 #82)
+#89 := [rewrite]: #88
+#86 := (= #25 #85)
+#83 := (= #24 #82)
+#80 := (= #23 2::Int)
+#71 := -3::Int
+#68 := -5::Int
+#74 := (div -5::Int -3::Int)
+#78 := (= #74 2::Int)
+#79 := [rewrite]: #78
+#75 := (= #23 #74)
+#72 := (= #22 -3::Int)
+#73 := [rewrite]: #72
+#69 := (= #21 -5::Int)
+#70 := [rewrite]: #69
+#76 := [monotonicity #70 #73]: #75
+#81 := [trans #76 #79]: #80
+#66 := (= #20 1::Int)
+#67 := [rewrite]: #66
+#64 := (iff #19 #63)
+#61 := (iff #18 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#84 := [monotonicity #65 #67 #81]: #83
+#58 := (iff #13 false)
+#53 := (or false false)
+#56 := (iff #53 false)
+#57 := [rewrite]: #56
+#54 := (iff #13 #53)
+#51 := (iff #12 false)
+#52 := [rewrite]: #51
+#49 := (iff #10 false)
+#50 := [rewrite]: #49
+#55 := [monotonicity #50 #52]: #54
+#59 := [trans #55 #57]: #58
+#87 := [monotonicity #59 #84]: #86
+#91 := [trans #87 #89]: #90
+#94 := [monotonicity #91]: #93
+#98 := [trans #94 #96]: #97
+#101 := [monotonicity #98]: #100
+#137 := [trans #101 #135]: #136
+#48 := [asserted]: #28
+[mp #48 #137]: false
+unsat
+e8c50ca8f2d03b633ebd301c60837eeba13d5124 132 0
+#2 := false
+#8 := 1::Int
+#22 := (- 1::Int)
+#11 := 3::Int
+#12 := (- 3::Int)
+#23 := (- #12)
+#24 := (div #22 #23)
+#21 := (div 1::Int #12)
+#9 := 0::Int
+#16 := (< 0::Int #12)
+#18 := (< 1::Int 0::Int)
+#19 := (and #18 #16)
+#15 := (< 0::Int 1::Int)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#13 := (= #12 0::Int)
+#10 := (= 1::Int 0::Int)
+#14 := (or #10 #13)
+#26 := (ite #14 0::Int #25)
+#27 := (= #26 #22)
+#28 := (not #27)
+#153 := (iff #28 false)
+#51 := -3::Int
+#68 := (< 0::Int -3::Int)
+#74 := (and #18 #68)
+#71 := (and #15 #68)
+#77 := (or #71 #74)
+#151 := (iff #77 false)
+#61 := (or false false)
+#64 := (iff #61 false)
+#65 := [rewrite]: #64
+#149 := (iff #77 #61)
+#147 := (iff #74 false)
+#142 := (and false false)
+#145 := (iff #142 false)
+#146 := [rewrite]: #145
+#143 := (iff #74 #142)
+#131 := (iff #68 false)
+#132 := [rewrite]: #131
+#140 := (iff #18 false)
+#141 := [rewrite]: #140
+#144 := [monotonicity #141 #132]: #143
+#148 := [trans #144 #146]: #147
+#138 := (iff #71 false)
+#1 := true
+#133 := (and true false)
+#136 := (iff #133 false)
+#137 := [rewrite]: #136
+#134 := (iff #71 #133)
+#129 := (iff #15 true)
+#130 := [rewrite]: #129
+#135 := [monotonicity #130 #132]: #134
+#139 := [trans #135 #137]: #138
+#150 := [monotonicity #139 #148]: #149
+#152 := [trans #150 #65]: #151
+#127 := (iff #28 #77)
+#117 := (not #77)
+#122 := (not #117)
+#125 := (iff #122 #77)
+#126 := [rewrite]: #125
+#123 := (iff #28 #122)
+#120 := (iff #27 #117)
+#87 := -1::Int
+#104 := (ite #77 0::Int -1::Int)
+#114 := (= #104 -1::Int)
+#118 := (iff #114 #117)
+#119 := [rewrite]: #118
+#115 := (iff #27 #114)
+#88 := (= #22 -1::Int)
+#89 := [rewrite]: #88
+#112 := (= #26 #104)
+#107 := (ite false 0::Int #104)
+#110 := (= #107 #104)
+#111 := [rewrite]: #110
+#108 := (= #26 #107)
+#105 := (= #25 #104)
+#102 := (= #24 -1::Int)
+#97 := (div -1::Int 3::Int)
+#100 := (= #97 -1::Int)
+#101 := [rewrite]: #100
+#98 := (= #24 #97)
+#95 := (= #23 3::Int)
+#90 := (- -3::Int)
+#93 := (= #90 3::Int)
+#94 := [rewrite]: #93
+#91 := (= #23 #90)
+#52 := (= #12 -3::Int)
+#53 := [rewrite]: #52
+#92 := [monotonicity #53]: #91
+#96 := [trans #92 #94]: #95
+#99 := [monotonicity #89 #96]: #98
+#103 := [trans #99 #101]: #102
+#85 := (= #21 0::Int)
+#80 := (div 1::Int -3::Int)
+#83 := (= #80 0::Int)
+#84 := [rewrite]: #83
+#81 := (= #21 #80)
+#82 := [monotonicity #53]: #81
+#86 := [trans #82 #84]: #85
+#78 := (iff #20 #77)
+#75 := (iff #19 #74)
+#69 := (iff #16 #68)
+#70 := [monotonicity #53]: #69
+#76 := [monotonicity #70]: #75
+#72 := (iff #17 #71)
+#73 := [monotonicity #70]: #72
+#79 := [monotonicity #73 #76]: #78
+#106 := [monotonicity #79 #86 #103]: #105
+#66 := (iff #14 false)
+#62 := (iff #14 #61)
+#59 := (iff #13 false)
+#54 := (= -3::Int 0::Int)
+#57 := (iff #54 false)
+#58 := [rewrite]: #57
+#55 := (iff #13 #54)
+#56 := [monotonicity #53]: #55
+#60 := [trans #56 #58]: #59
+#49 := (iff #10 false)
+#50 := [rewrite]: #49
+#63 := [monotonicity #50 #60]: #62
+#67 := [trans #63 #65]: #66
+#109 := [monotonicity #67 #106]: #108
+#113 := [trans #109 #111]: #112
+#116 := [monotonicity #113 #89]: #115
+#121 := [trans #116 #119]: #120
+#124 := [monotonicity #121]: #123
+#128 := [trans #124 #126]: #127
+#154 := [trans #128 #152]: #153
+#48 := [asserted]: #28
+[mp #48 #154]: false
+unsat
+e161cbc5766adb3a07b2f61822dd61195f3dd163 109 0
+#2 := false
+#25 := 1::Int
+#26 := (- 1::Int)
+#8 := 3::Int
+#11 := (- 3::Int)
+#21 := (- #11)
+#22 := (div #11 #21)
+#20 := (div 3::Int #11)
+#9 := 0::Int
+#15 := (< 0::Int #11)
+#17 := (< 3::Int 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int 3::Int)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#23 := (ite #19 #20 #22)
+#12 := (= #11 0::Int)
+#10 := (= 3::Int 0::Int)
+#13 := (or #10 #12)
+#24 := (ite #13 0::Int #23)
+#27 := (= #24 #26)
+#28 := (not #27)
+#130 := (iff #28 false)
+#1 := true
+#125 := (not true)
+#128 := (iff #125 false)
+#129 := [rewrite]: #128
+#126 := (iff #28 #125)
+#123 := (iff #27 true)
+#83 := -1::Int
+#118 := (= -1::Int -1::Int)
+#121 := (iff #118 true)
+#122 := [rewrite]: #121
+#119 := (iff #27 #118)
+#116 := (= #26 -1::Int)
+#117 := [rewrite]: #116
+#114 := (= #24 -1::Int)
+#109 := (ite false 0::Int -1::Int)
+#112 := (= #109 -1::Int)
+#113 := [rewrite]: #112
+#110 := (= #24 #109)
+#107 := (= #23 -1::Int)
+#51 := -3::Int
+#68 := (< 0::Int -3::Int)
+#74 := (and #17 #68)
+#71 := (and #14 #68)
+#77 := (or #71 #74)
+#102 := (ite #77 -1::Int -1::Int)
+#105 := (= #102 -1::Int)
+#106 := [rewrite]: #105
+#103 := (= #23 #102)
+#100 := (= #22 -1::Int)
+#95 := (div -3::Int 3::Int)
+#98 := (= #95 -1::Int)
+#99 := [rewrite]: #98
+#96 := (= #22 #95)
+#93 := (= #21 3::Int)
+#88 := (- -3::Int)
+#91 := (= #88 3::Int)
 #92 := [rewrite]: #91
-#95 := [monotonicity #92]: #94
-#107 := [monotonicity #95 #104]: #106
-#110 := [monotonicity #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [quant-intro #113]: #115
-#151 := [trans #116 #149]: #150
-#89 := [asserted]: #34
-#152 := [mp #89 #151]: #147
-#201 := [mp~ #152 #210]: #147
-#232 := [mp #201 #231]: #229
-#263 := [mp #232 #262]: #260
-#756 := [mp #263 #755]: #751
-#10 := 3::Int
-#67 := (f3 -1::Int 3::Int)
-#70 := (= #67 -1::Int)
-#83 := (not #70)
+#89 := (= #21 #88)
+#52 := (= #11 -3::Int)
+#53 := [rewrite]: #52
+#90 := [monotonicity #53]: #89
+#94 := [trans #90 #92]: #93
+#97 := [monotonicity #53 #94]: #96
+#101 := [trans #97 #99]: #100
+#86 := (= #20 -1::Int)
+#80 := (div 3::Int -3::Int)
+#84 := (= #80 -1::Int)
+#85 := [rewrite]: #84
+#81 := (= #20 #80)
+#82 := [monotonicity #53]: #81
+#87 := [trans #82 #85]: #86
+#78 := (iff #19 #77)
+#75 := (iff #18 #74)
+#69 := (iff #15 #68)
+#70 := [monotonicity #53]: #69
+#76 := [monotonicity #70]: #75
+#72 := (iff #16 #71)
+#73 := [monotonicity #70]: #72
+#79 := [monotonicity #73 #76]: #78
+#104 := [monotonicity #79 #87 #101]: #103
+#108 := [trans #104 #106]: #107
+#66 := (iff #13 false)
+#61 := (or false false)
+#64 := (iff #61 false)
+#65 := [rewrite]: #64
+#62 := (iff #13 #61)
+#59 := (iff #12 false)
+#54 := (= -3::Int 0::Int)
+#57 := (iff #54 false)
+#58 := [rewrite]: #57
+#55 := (iff #12 #54)
+#56 := [monotonicity #53]: #55
+#60 := [trans #56 #58]: #59
+#49 := (iff #10 false)
+#50 := [rewrite]: #49
+#63 := [monotonicity #50 #60]: #62
+#67 := [trans #63 #65]: #66
+#111 := [monotonicity #67 #108]: #110
+#115 := [trans #111 #113]: #114
+#120 := [monotonicity #115 #117]: #119
+#124 := [trans #120 #122]: #123
+#127 := [monotonicity #124]: #126
+#131 := [trans #127 #129]: #130
+#48 := [asserted]: #28
+[mp #48 #131]: false
+unsat
[phone]f93d8549a15817d71271ba90ab0e16ae 138 0
+#2 := false
+#27 := 2::Int
+#28 := (- 2::Int)
+#11 := 3::Int
+#12 := (- 3::Int)
+#23 := (- #12)
+#8 := 5::Int
+#22 := (- 5::Int)
+#24 := (div #22 #23)
+#21 := (div 5::Int #12)
+#9 := 0::Int
+#16 := (< 0::Int #12)
+#18 := (< 5::Int 0::Int)
+#19 := (and #18 #16)
+#15 := (< 0::Int 5::Int)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#13 := (= #12 0::Int)
+#10 := (= 5::Int 0::Int)
+#14 := (or #10 #13)
+#26 := (ite #14 0::Int #25)
+#29 := (= #26 #28)
+#30 := (not #29)
+#159 := (iff #30 false)
+#53 := -3::Int
+#70 := (< 0::Int -3::Int)
+#76 := (and #18 #70)
+#73 := (and #15 #70)
+#79 := (or #73 #76)
+#157 := (iff #79 false)
+#63 := (or false false)
+#66 := (iff #63 false)
+#67 := [rewrite]: #66
+#155 := (iff #79 #63)
+#153 := (iff #76 false)
+#148 := (and false false)
+#151 := (iff #148 false)
+#152 := [rewrite]: #151
+#149 := (iff #76 #148)
+#137 := (iff #70 false)
+#138 := [rewrite]: #137
+#146 := (iff #18 false)
+#147 := [rewrite]: #146
+#150 := [monotonicity #147 #138]: #149
+#154 := [trans #150 #152]: #153
+#144 := (iff #73 false)
+#1 := true
+#139 := (and true false)
+#142 := (iff #139 false)
+#143 := [rewrite]: #142
+#140 := (iff #73 #139)
+#135 := (iff #15 true)
+#136 := [rewrite]: #135
+#141 := [monotonicity #136 #138]: #140
+#145 := [trans #141 #143]: #144
+#156 := [monotonicity #145 #154]: #155
+#158 := [trans #156 #67]: #157
+#133 := (iff #30 #79)
+#123 := (not #79)
+#128 := (not #123)
+#131 := (iff #128 #79)
+#132 := [rewrite]: #131
+#129 := (iff #30 #128)
+#126 := (iff #29 #123)
+#103 := -2::Int
+#85 := -1::Int
+#108 := (ite #79 -1::Int -2::Int)
+#120 := (= #108 -2::Int)
+#124 := (iff #120 #123)
+#125 := [rewrite]: #124
+#121 := (iff #29 #120)
+#118 := (= #28 -2::Int)
+#119 := [rewrite]: #118
+#116 := (= #26 #108)
+#111 := (ite false 0::Int #108)
+#114 := (= #111 #108)
+#115 := [rewrite]: #114
+#112 := (= #26 #111)
+#109 := (= #25 #108)
+#106 := (= #24 -2::Int)
+#90 := -5::Int
+#100 := (div -5::Int 3::Int)
+#104 := (= #100 -2::Int)
+#105 := [rewrite]: #104
+#101 := (= #24 #100)
+#98 := (= #23 3::Int)
+#93 := (- -3::Int)
+#96 := (= #93 3::Int)
+#97 := [rewrite]: #96
+#94 := (= #23 #93)
+#54 := (= #12 -3::Int)
+#55 := [rewrite]: #54
+#95 := [monotonicity #55]: #94
+#99 := [trans #95 #97]: #98
+#91 := (= #22 -5::Int)
+#92 := [rewrite]: #91
+#102 := [monotonicity #92 #99]: #101
+#107 := [trans #102 #105]: #106
+#88 := (= #21 -1::Int)
+#82 := (div 5::Int -3::Int)
+#86 := (= #82 -1::Int)
+#87 := [rewrite]: #86
+#83 := (= #21 #82)
+#84 := [monotonicity #55]: #83
+#89 := [trans #84 #87]: #88
+#80 := (iff #20 #79)
+#77 := (iff #19 #76)
+#71 := (iff #16 #70)
+#72 := [monotonicity #55]: #71
+#78 := [monotonicity #72]: #77
+#74 := (iff #17 #73)
+#75 := [monotonicity #72]: #74
+#81 := [monotonicity #75 #78]: #80
+#110 := [monotonicity #81 #89 #107]: #109
+#68 := (iff #14 false)
+#64 := (iff #14 #63)
+#61 := (iff #13 false)
+#56 := (= -3::Int 0::Int)
+#59 := (iff #56 false)
+#60 := [rewrite]: #59
+#57 := (iff #13 #56)
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#51 := (iff #10 false)
+#52 := [rewrite]: #51
+#65 := [monotonicity #52 #62]: #64
+#69 := [trans #65 #67]: #68
+#113 := [monotonicity #69 #110]: #112
+#117 := [trans #113 #115]: #116
+#122 := [monotonicity #117 #119]: #121
+#127 := [trans #122 #125]: #126
+#130 := [monotonicity #127]: #129
+#134 := [trans #130 #132]: #133
+#160 := [trans #134 #158]: #159
+#50 := [asserted]: #30
+[mp #50 #160]: false
+unsat
+a358eed5b14d12c6db4e25a50a2df755d735c9b5 150 0
+#2 := false
+#8 := 1::Int
+#9 := (- 1::Int)
+#12 := 3::Int
+#23 := (- 3::Int)
+#22 := (- #9)
+#24 := (div #22 #23)
+#21 := (div #9 3::Int)
+#10 := 0::Int
+#16 := (< 0::Int 3::Int)
+#18 := (< #9 0::Int)
+#19 := (and #18 #16)
+#15 := (< 0::Int #9)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#13 := (= 3::Int 0::Int)
+#11 := (= #9 0::Int)
+#14 := (or #11 #13)
+#26 := (ite #14 0::Int #25)
+#27 := (= #26 #9)
+#28 := (not #27)
+#171 := (iff #28 false)
+#49 := -1::Int
+#79 := (< -1::Int 0::Int)
+#85 := (and #16 #79)
+#68 := (< 0::Int -1::Int)
+#74 := (and #16 #68)
+#90 := (or #74 #85)
+#134 := (not #90)
+#169 := (iff #134 false)
+#1 := true
+#164 := (not true)
+#167 := (iff #164 false)
+#168 := [rewrite]: #167
+#165 := (iff #134 #164)
+#162 := (iff #90 true)
+#157 := (or false true)
+#160 := (iff #157 true)
+#161 := [rewrite]: #160
+#158 := (iff #90 #157)
+#155 := (iff #85 true)
+#150 := (and true true)
+#153 := (iff #150 true)
+#154 := [rewrite]: #153
+#151 := (iff #85 #150)
+#148 := (iff #79 true)
+#149 := [rewrite]: #148
+#137 := (iff #16 true)
+#138 := [rewrite]: #137
+#152 := [monotonicity #138 #149]: #151
+#156 := [trans #152 #154]: #155
+#146 := (iff #74 false)
+#141 := (and true false)
+#144 := (iff #141 false)
+#145 := [rewrite]: #144
+#142 := (iff #74 #141)
+#139 := (iff #68 false)
+#140 := [rewrite]: #139
+#143 := [monotonicity #138 #140]: #142
+#147 := [trans #143 #145]: #146
+#159 := [monotonicity #147 #156]: #158
+#163 := [trans #159 #161]: #162
+#166 := [monotonicity #163]: #165
+#170 := [trans #166 #168]: #169
+#135 := (iff #28 #134)
+#132 := (iff #27 #90)
+#117 := (ite #90 -1::Int 0::Int)
+#127 := (= #117 -1::Int)
+#130 := (iff #127 #90)
+#131 := [rewrite]: #130
+#128 := (iff #27 #127)
+#50 := (= #9 -1::Int)
+#51 := [rewrite]: #50
+#125 := (= #26 #117)
+#120 := (ite false 0::Int #117)
+#123 := (= #120 #117)
+#124 := [rewrite]: #123
+#121 := (= #26 #120)
+#118 := (= #25 #117)
+#115 := (= #24 0::Int)
+#107 := -3::Int
+#110 := (div 1::Int -3::Int)
+#113 := (= #110 0::Int)
+#114 := [rewrite]: #113
+#111 := (= #24 #110)
+#108 := (= #23 -3::Int)
+#109 := [rewrite]: #108
+#105 := (= #22 1::Int)
+#100 := (- -1::Int)
+#103 := (= #100 1::Int)
+#104 := [rewrite]: #103
+#101 := (= #22 #100)
+#102 := [monotonicity #51]: #101
+#106 := [trans #102 #104]: #105
+#112 := [monotonicity #106 #109]: #111
+#116 := [trans #112 #114]: #115
+#98 := (= #21 -1::Int)
+#93 := (div -1::Int 3::Int)
+#96 := (= #93 -1::Int)
+#97 := [rewrite]: #96
+#94 := (= #21 #93)
+#95 := [monotonicity #51]: #94
+#99 := [trans #95 #97]: #98
+#91 := (iff #20 #90)
+#88 := (iff #19 #85)
+#82 := (and #79 #16)
+#86 := (iff #82 #85)
+#87 := [rewrite]: #86
+#83 := (iff #19 #82)
+#80 := (iff #18 #79)
+#81 := [monotonicity #51]: #80
+#84 := [monotonicity #81]: #83
+#89 := [trans #84 #87]: #88
+#77 := (iff #17 #74)
+#71 := (and #68 #16)
+#75 := (iff #71 #74)
+#76 := [rewrite]: #75
+#72 := (iff #17 #71)
+#69 := (iff #15 #68)
+#70 := [monotonicity #51]: #69
+#73 := [monotonicity #70]: #72
+#78 := [trans #73 #76]: #77
+#92 := [monotonicity #78 #89]: #91
+#119 := [monotonicity #92 #99 #116]: #118
+#66 := (iff #14 false)
+#61 := (or false false)
+#64 := (iff #61 false)
+#65 := [rewrite]: #64
+#62 := (iff #14 #61)
+#59 := (iff #13 false)
+#60 := [rewrite]: #59
+#57 := (iff #11 false)
+#52 := (= -1::Int 0::Int)
+#55 := (iff #52 false)
+#56 := [rewrite]: #55
+#53 := (iff #11 #52)
+#54 := [monotonicity #51]: #53
+#58 := [trans #54 #56]: #57
+#63 := [monotonicity #58 #60]: #62
+#67 := [trans #63 #65]: #66
+#122 := [monotonicity #67 #119]: #121
+#126 := [trans #122 #124]: #125
+#129 := [monotonicity #126 #51]: #128
+#133 := [trans #129 #131]: #132
+#136 := [monotonicity #133]: #135
+#172 := [trans #136 #170]: #171
+#48 := [asserted]: #28
+[mp #48 #172]: false
+unsat
+282152f210622b67ee14b9ad0372daa57d1c2fe0 122 0
+#2 := false
+#25 := 1::Int
+#26 := (- 1::Int)
+#8 := 3::Int
+#9 := (- 3::Int)
+#21 := (- #9)
+#22 := (div #21 #9)
+#20 := (div #9 3::Int)
+#10 := 0::Int
+#15 := (< 0::Int 3::Int)
+#17 := (< #9 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int #9)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#23 := (ite #19 #20 #22)
+#12 := (= 3::Int 0::Int)
+#11 := (= #9 0::Int)
+#13 := (or #11 #12)
+#24 := (ite #13 0::Int #23)
+#27 := (= #24 #26)
+#28 := (not #27)
+#143 := (iff #28 false)
+#1 := true
+#138 := (not true)
+#141 := (iff #138 false)
+#142 := [rewrite]: #141
+#139 := (iff #28 #138)
+#136 := (iff #27 true)
+#96 := -1::Int
+#131 := (= -1::Int -1::Int)
+#134 := (iff #131 true)
+#135 := [rewrite]: #134
+#132 := (iff #27 #131)
+#129 := (= #26 -1::Int)
+#130 := [rewrite]: #129
+#127 := (= #24 -1::Int)
+#122 := (ite false 0::Int -1::Int)
+#125 := (= #122 -1::Int)
+#126 := [rewrite]: #125
+#123 := (= #24 #122)
+#120 := (= #23 -1::Int)
+#49 := -3::Int
+#79 := (< -3::Int 0::Int)
+#85 := (and #15 #79)
+#68 := (< 0::Int -3::Int)
+#74 := (and #15 #68)
+#90 := (or #74 #85)
+#115 := (ite #90 -1::Int -1::Int)
+#118 := (= #115 -1::Int)
+#119 := [rewrite]: #118
+#116 := (= #23 #115)
+#113 := (= #22 -1::Int)
+#108 := (div 3::Int -3::Int)
+#111 := (= #108 -1::Int)
+#112 := [rewrite]: #111
+#109 := (= #22 #108)
+#50 := (= #9 -3::Int)
+#51 := [rewrite]: #50
+#106 := (= #21 3::Int)
+#101 := (- -3::Int)
+#104 := (= #101 3::Int)
+#105 := [rewrite]: #104
+#102 := (= #21 #101)
+#103 := [monotonicity #51]: #102
+#107 := [trans #103 #105]: #106
+#110 := [monotonicity #107 #51]: #109
+#114 := [trans #110 #112]: #113
+#99 := (= #20 -1::Int)
+#93 := (div -3::Int 3::Int)
+#97 := (= #93 -1::Int)
+#98 := [rewrite]: #97
+#94 := (= #20 #93)
+#95 := [monotonicity #51]: #94
+#100 := [trans #95 #98]: #99
+#91 := (iff #19 #90)
+#88 := (iff #18 #85)
+#82 := (and #79 #15)
+#86 := (iff #82 #85)
+#87 := [rewrite]: #86
+#83 := (iff #18 #82)
+#80 := (iff #17 #79)
+#81 := [monotonicity #51]: #80
+#84 := [monotonicity #81]: #83
+#89 := [trans #84 #87]: #88
+#77 := (iff #16 #74)
+#71 := (and #68 #15)
+#75 := (iff #71 #74)
+#76 := [rewrite]: #75
+#72 := (iff #16 #71)
+#69 := (iff #14 #68)
+#70 := [monotonicity #51]: #69
+#73 := [monotonicity #70]: #72
+#78 := [trans #73 #76]: #77
+#92 := [monotonicity #78 #89]: #91
+#117 := [monotonicity #92 #100 #114]: #116
+#121 := [trans #117 #119]: #120
+#66 := (iff #13 false)
+#61 := (or false false)
+#64 := (iff #61 false)
+#65 := [rewrite]: #64
+#62 := (iff #13 #61)
+#59 := (iff #12 false)
+#60 := [rewrite]: #59
+#57 := (iff #11 false)
+#52 := (= -3::Int 0::Int)
+#55 := (iff #52 false)
+#56 := [rewrite]: #55
+#53 := (iff #11 #52)
+#54 := [monotonicity #51]: #53
+#58 := [trans #54 #56]: #57
+#63 := [monotonicity #58 #60]: #62
+#67 := [trans #63 #65]: #66
+#124 := [monotonicity #67 #121]: #123
+#128 := [trans #124 #126]: #127
+#133 := [monotonicity #128 #130]: #132
+#137 := [trans #133 #135]: #136
+#140 := [monotonicity #137]: #139
+#144 := [trans #140 #142]: #143
+#48 := [asserted]: #28
+[mp #48 #144]: false
+unsat
+09bd21e8184625daa5375adf22f60c439ab0cf17 156 0
+#2 := false
+#27 := 2::Int
+#28 := (- 2::Int)
+#12 := 3::Int
+#23 := (- 3::Int)
+#8 := 5::Int
+#9 := (- 5::Int)
+#22 := (- #9)
+#24 := (div #22 #23)
+#21 := (div #9 3::Int)
+#10 := 0::Int
+#16 := (< 0::Int 3::Int)
+#18 := (< #9 0::Int)
+#19 := (and #18 #16)
+#15 := (< 0::Int #9)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#13 := (= 3::Int 0::Int)
+#11 := (= #9 0::Int)
+#14 := (or #11 #13)
+#26 := (ite #14 0::Int #25)
+#29 := (= #26 #28)
+#30 := (not #29)
+#177 := (iff #30 false)
+#51 := -5::Int
+#81 := (< -5::Int 0::Int)
+#87 := (and #16 #81)
+#70 := (< 0::Int -5::Int)
+#76 := (and #16 #70)
+#92 := (or #76 #87)
+#140 := (not #92)
+#175 := (iff #140 false)
+#1 := true
+#170 := (not true)
+#173 := (iff #170 false)
+#174 := [rewrite]: #173
+#171 := (iff #140 #170)
+#168 := (iff #92 true)
+#163 := (or false true)
+#166 := (iff #163 true)
+#167 := [rewrite]: #166
+#164 := (iff #92 #163)
+#161 := (iff #87 true)
+#156 := (and true true)
+#159 := (iff #156 true)
+#160 := [rewrite]: #159
+#157 := (iff #87 #156)
+#154 := (iff #81 true)
+#155 := [rewrite]: #154
+#143 := (iff #16 true)
+#144 := [rewrite]: #143
+#158 := [monotonicity #144 #155]: #157
+#162 := [trans #158 #160]: #161
+#152 := (iff #76 false)
+#147 := (and true false)
+#150 := (iff #147 false)
+#151 := [rewrite]: #150
+#148 := (iff #76 #147)
+#145 := (iff #70 false)
+#146 := [rewrite]: #145
+#149 := [monotonicity #144 #146]: #148
+#153 := [trans #149 #151]: #152
+#165 := [monotonicity #153 #162]: #164
+#169 := [trans #165 #167]: #168
+#172 := [monotonicity #169]: #171
+#176 := [trans #172 #174]: #175
+#141 := (iff #30 #140)
+#138 := (iff #29 #92)
+#98 := -2::Int
+#116 := -1::Int
+#121 := (ite #92 -2::Int -1::Int)
+#133 := (= #121 -2::Int)
+#136 := (iff #133 #92)
+#137 := [rewrite]: #136
+#134 := (iff #29 #133)
+#131 := (= #28 -2::Int)
+#132 := [rewrite]: #131
+#129 := (= #26 #121)
+#124 := (ite false 0::Int #121)
+#127 := (= #124 #121)
+#128 := [rewrite]: #127
+#125 := (= #26 #124)
+#122 := (= #25 #121)
+#119 := (= #24 -1::Int)
+#110 := -3::Int
+#113 := (div 5::Int -3::Int)
+#117 := (= #113 -1::Int)
+#118 := [rewrite]: #117
+#114 := (= #24 #113)
+#111 := (= #23 -3::Int)
+#112 := [rewrite]: #111
+#108 := (= #22 5::Int)
+#103 := (- -5::Int)
+#106 := (= #103 5::Int)
+#107 := [rewrite]: #106
+#104 := (= #22 #103)
+#52 := (= #9 -5::Int)
+#53 := [rewrite]: #52
+#105 := [monotonicity #53]: #104
+#109 := [trans #105 #107]: #108
+#115 := [monotonicity #109 #112]: #114
+#120 := [trans #115 #118]: #119
+#101 := (= #21 -2::Int)
+#95 := (div -5::Int 3::Int)
+#99 := (= #95 -2::Int)
+#100 := [rewrite]: #99
+#96 := (= #21 #95)
+#97 := [monotonicity #53]: #96
+#102 := [trans #97 #100]: #101
+#93 := (iff #20 #92)
+#90 := (iff #19 #87)
+#84 := (and #81 #16)
+#88 := (iff #84 #87)
+#89 := [rewrite]: #88
+#85 := (iff #19 #84)
+#82 := (iff #18 #81)
+#83 := [monotonicity #53]: #82
+#86 := [monotonicity #83]: #85
+#91 := [trans #86 #89]: #90
+#79 := (iff #17 #76)
+#73 := (and #70 #16)
+#77 := (iff #73 #76)
+#78 := [rewrite]: #77
+#74 := (iff #17 #73)
+#71 := (iff #15 #70)
+#72 := [monotonicity #53]: #71
+#75 := [monotonicity #72]: #74
+#80 := [trans #75 #78]: #79
+#94 := [monotonicity #80 #91]: #93
+#123 := [monotonicity #94 #102 #120]: #122
+#68 := (iff #14 false)
+#63 := (or false false)
+#66 := (iff #63 false)
+#67 := [rewrite]: #66
+#64 := (iff #14 #63)
+#61 := (iff #13 false)
+#62 := [rewrite]: #61
+#59 := (iff #11 false)
+#54 := (= -5::Int 0::Int)
+#57 := (iff #54 false)
+#58 := [rewrite]: #57
+#55 := (iff #11 #54)
+#56 := [monotonicity #53]: #55
+#60 := [trans #56 #58]: #59
+#65 := [monotonicity #60 #62]: #64
+#69 := [trans #65 #67]: #68
+#126 := [monotonicity #69 #123]: #125
+#130 := [trans #126 #128]: #129
+#135 := [monotonicity #130 #132]: #134
+#139 := [trans #135 #137]: #138
+#142 := [monotonicity #139]: #141
+#178 := [trans #142 #176]: #177
+#50 := [asserted]: #30
+[mp #50 #178]: false
+unsat
+75a498a3ae15008c6ba6962bb8ff41e876585e27 156 0
+#2 := false
+#10 := 0::Int
+#12 := 3::Int
+#13 := (- 3::Int)
+#24 := (- #13)
 #8 := 1::Int
 #9 := (- 1::Int)
-#11 := (f3 #9 3::Int)
-#12 := (= #11 #9)
-#13 := (not #12)
-#86 := (iff #13 #83)
-#73 := (= -1::Int #67)
-#78 := (not #73)
-#84 := (iff #78 #83)
-#81 := (iff #73 #70)
-#82 := [rewrite]: #81
-#85 := [monotonicity #82]: #84
-#79 := (iff #13 #78)
-#76 := (iff #12 #73)
-#74 := (iff #70 #73)
-#75 := [rewrite]: #74
-#71 := (iff #12 #70)
-#65 := (= #9 -1::Int)
-#66 := [rewrite]: #65
-#68 := (= #11 #67)
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69 #66]: #71
-#77 := [trans #72 #75]: #76
-#80 := [monotonicity #77]: #79
-#87 := [trans #80 #85]: #86
-#63 := [asserted]: #13
-#88 := [mp #63 #87]: #83
-#676 := (not #751)
-#677 := (or #676 #70)
-#337 := (* -1::Int 3::Int)
-#421 := (* -1::Int -1::Int)
-#422 := (div #421 #337)
-#423 := (* -1::Int #422)
-#414 := (+ #67 #423)
-#425 := (= #414 0::Int)
-#426 := (div -1::Int 3::Int)
-#427 := (* -1::Int #426)
-#424 := (+ #67 #427)
-#428 := (= #424 0::Int)
-#407 := (>= -1::Int 0::Int)
-#742 := (<= 3::Int 0::Int)
-#744 := (or #742 #407)
-#401 := (not #744)
-#531 := (<= -1::Int 0::Int)
-#738 := (or #531 #742)
-#412 := (not #738)
-#413 := (or #412 #401)
-#745 := (ite #413 #428 #425)
-#746 := (= #67 0::Int)
-#747 := (= 3::Int 0::Int)
-#748 := (= -1::Int 0::Int)
-#743 := (or #748 #747)
-#749 := (ite #743 #746 #745)
-#673 := (or #676 #749)
-#667 := (iff #673 #677)
-#669 := (iff #677 #677)
-#670 := [rewrite]: #669
-#665 := (iff #749 #70)
-#685 := (ite false #746 #70)
-#666 := (iff #685 #70)
-#663 := [rewrite]: #666
-#672 := (iff #749 #685)
-#684 := (iff #745 #70)
-#1 := true
-#587 := (ite true #70 #746)
-#590 := (iff #587 #70)
-#591 := [rewrite]: #590
-#588 := (iff #745 #587)
-#586 := (iff #425 #746)
-#583 := (= #414 #67)
-#584 := (+ #67 0::Int)
-#683 := (= #584 #67)
-#568 := [rewrite]: #683
-#679 := (= #414 #584)
-#534 := (= #423 0::Int)
-#688 := (* -1::Int 0::Int)
-#574 := (= #688 0::Int)
-#575 := [rewrite]: #574
-#691 := (= #423 #688)
-#689 := (= #422 0::Int)
-#700 := -3::Int
-#530 := (div 1::Int -3::Int)
-#686 := (= #530 0::Int)
-#687 := [rewrite]: #686
-#532 := (= #422 #530)
-#694 := (= #337 -3::Int)
-#701 := [rewrite]: #694
-#705 := (= #421 1::Int)
-#706 := [rewrite]: #705
-#533 := [monotonicity #706 #701]: #532
-#690 := [trans #533 #687]: #689
-#573 := [monotonicity #690]: #691
-#682 := [trans #573 #575]: #534
-#680 := [monotonicity #682]: #679
-#585 := [trans #680 #568]: #583
-#579 := [monotonicity #585]: #586
-#693 := (iff #428 #70)
-#704 := (+ 1::Int #67)
-#695 := (= #704 0::Int)
-#698 := (iff #695 #70)
-#692 := [rewrite]: #698
-#696 := (iff #428 #695)
-#552 := (= #424 #704)
-#703 := (+ #67 1::Int)
-#710 := (= #703 #704)
-#551 := [rewrite]: #710
-#708 := (= #424 #703)
-#707 := (= #427 1::Int)
-#712 := (= #427 #421)
-#711 := (= #426 -1::Int)
-#715 := [rewrite]: #711
-#716 := [monotonicity #715]: #712
-#702 := [trans #716 #706]: #707
-#709 := [monotonicity #702]: #708
-#553 := [trans #709 #551]: #552
-#697 := [monotonicity #553]: #696
-#699 := [trans #697 #692]: #693
-#714 := (iff #413 true)
-#432 := (or false true)
-#435 := (iff #432 true)
-#713 := [rewrite]: #435
-#433 := (iff #413 #432)
-#718 := (iff #401 true)
-#720 := (not false)
-#717 := (iff #720 true)
-#721 := [rewrite]: #717
-#442 := (iff #401 #720)
-#343 := (iff #744 false)
-#400 := (or false false)
-#725 := (iff #400 false)
-#388 := [rewrite]: #725
-#448 := (iff #744 #400)
-#446 := (iff #407 false)
-#447 := [rewrite]: #446
-#728 := (iff #742 false)
-#729 := [rewrite]: #728
-#449 := [monotonicity #729 #447]: #448
-#719 := [trans #449 #388]: #343
-#443 := [monotonicity #719]: #442
-#722 := [trans #443 #721]: #718
-#723 := (iff #412 false)
-#375 := (not true)
-#734 := (iff #375 false)
-#737 := [rewrite]: #734
-#376 := (iff #412 #375)
-#733 := (iff #738 true)
-#730 := (or true false)
-#732 := (iff #730 true)
-#370 := [rewrite]: #732
-#731 := (iff #738 #730)
-#391 := (iff #531 true)
-#727 := [rewrite]: #391
-#726 := [monotonicity #727 #729]: #731
-#735 := [trans #726 #370]: #733
-#736 := [monotonicity #735]: #376
-#724 := [trans #736 #737]: #723
-#434 := [monotonicity #724 #722]: #433
-#429 := [trans #434 #713]: #714
-#589 := [monotonicity #429 #699 #579]: #588
-#681 := [trans #589 #591]: #684
-#389 := (iff #743 false)
-#741 := (iff #743 #400)
-#404 := (iff #747 false)
-#740 := [rewrite]: #404
-#739 := (iff #748 false)
-#399 := [rewrite]: #739
-#384 := [monotonicity #399 #740]: #741
-#390 := [trans #384 #388]: #389
-#674 := [monotonicity #390 #681]: #672
-#675 := [trans #674 #663]: #665
-#668 := [monotonicity #675]: #667
-#664 := [trans #668 #670]: #667
-#678 := [quant-inst #64 #10]: #673
-#671 := [mp #678 #664]: #677
-[unit-resolution #671 #88 #756]: false
-unsat
-896650ef8f75fd8ef47b1c1a736049dce2114a91 309 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#16 := (:var 0 Int)
-#15 := (:var 1 Int)
-#17 := (f3 #15 #16)
-#742 := (pattern #17)
-#18 := 0::Int
-#71 := -1::Int
-#91 := (* -1::Int #16)
-#88 := (* -1::Int #15)
-#94 := (div #88 #91)
-#245 := (* -1::Int #94)
-#246 := (+ #17 #245)
-#247 := (= #246 0::Int)
-#28 := (div #15 #16)
-#242 := (* -1::Int #28)
-#243 := (+ #17 #242)
-#244 := (= #243 0::Int)
-#120 := (>= #15 0::Int)
-#113 := (<= #16 0::Int)
-#205 := (or #113 #120)
-#206 := (not #205)
-#109 := (<= #15 0::Int)
-#203 := (or #109 #113)
-#204 := (not #203)
-#209 := (or #204 #206)
-#248 := (ite #209 #244 #247)
-#241 := (= #17 0::Int)
-#20 := (= #16 0::Int)
-#19 := (= #15 0::Int)
-#21 := (or #19 #20)
-#249 := (ite #21 #241 #248)
-#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #249)
-#252 := (forall (vars (?v0 Int) (?v1 Int)) #249)
-#746 := (iff #252 #743)
-#744 := (iff #249 #249)
-#745 := [refl]: #744
-#747 := [quant-intro #745]: #746
-#212 := (ite #209 #28 #94)
-#215 := (ite #21 0::Int #212)
-#218 := (= #17 #215)
-#221 := (forall (vars (?v0 Int) (?v1 Int)) #218)
-#253 := (iff #221 #252)
-#250 := (iff #218 #249)
-#251 := [rewrite]: #250
-#254 := [quant-intro #251]: #253
-#121 := (not #120)
-#114 := (not #113)
-#124 := (and #114 #121)
-#110 := (not #109)
-#117 := (and #110 #114)
-#127 := (or #117 #124)
-#130 := (ite #127 #28 #94)
-#133 := (ite #21 0::Int #130)
-#136 := (= #17 #133)
-#139 := (forall (vars (?v0 Int) (?v1 Int)) #136)
-#222 := (iff #139 #221)
-#219 := (iff #136 #218)
-#216 := (= #133 #215)
-#213 := (= #130 #212)
-#210 := (iff #127 #209)
-#207 := (iff #124 #206)
-#208 := [rewrite]: #207
-#197 := (iff #117 #204)
-#198 := [rewrite]: #197
-#211 := [monotonicity #198 #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [monotonicity #217]: #219
-#223 := [quant-intro #220]: #222
-#201 := (~ #139 #139)
-#199 := (~ #136 #136)
-#200 := [refl]: #199
-#202 := [nnf-pos #200]: #201
-#30 := (- #16)
-#29 := (- #15)
-#31 := (div #29 #30)
-#23 := (< 0::Int #16)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#32 := (ite #27 #28 #31)
-#33 := (ite #21 0::Int #32)
-#34 := (= #17 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#142 := (iff #35 #139)
-#81 := (and #23 #25)
-#85 := (or #24 #81)
-#97 := (ite #85 #28 #94)
-#100 := (ite #21 0::Int #97)
-#103 := (= #17 #100)
-#106 := (forall (vars (?v0 Int) (?v1 Int)) #103)
-#140 := (iff #106 #139)
-#137 := (iff #103 #136)
-#134 := (= #100 #133)
-#131 := (= #97 #130)
-#128 := (iff #85 #127)
-#125 := (iff #81 #124)
-#122 := (iff #25 #121)
-#123 := [rewrite]: #122
-#115 := (iff #23 #114)
-#116 := [rewrite]: #115
-#126 := [monotonicity #116 #123]: #125
-#118 := (iff #24 #117)
-#111 := (iff #22 #110)
-#112 := [rewrite]: #111
-#119 := [monotonicity #112 #116]: #118
-#129 := [monotonicity #119 #126]: #128
-#132 := [monotonicity #129]: #131
-#135 := [monotonicity #132]: #134
-#138 := [monotonicity #135]: #137
-#141 := [quant-intro #138]: #140
-#107 := (iff #35 #106)
-#104 := (iff #34 #103)
-#101 := (= #33 #100)
-#98 := (= #32 #97)
-#95 := (= #31 #94)
-#92 := (= #30 #91)
-#93 := [rewrite]: #92
-#89 := (= #29 #88)
-#90 := [rewrite]: #89
-#96 := [monotonicity #90 #93]: #95
-#86 := (iff #27 #85)
-#83 := (iff #26 #81)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#99 := [monotonicity #87 #96]: #98
-#102 := [monotonicity #99]: #101
-#105 := [monotonicity #102]: #104
-#108 := [quant-intro #105]: #107
-#143 := [trans #108 #141]: #142
-#80 := [asserted]: #35
-#144 := [mp #80 #143]: #139
-#193 := [mp~ #144 #202]: #139
-#224 := [mp #193 #223]: #221
-#255 := [mp #224 #254]: #252
-#748 := [mp #255 #747]: #743
+#23 := (- #9)
+#25 := (div #23 #24)
+#22 := (div #9 #13)
+#17 := (< 0::Int #13)
+#19 := (< #9 0::Int)
+#20 := (and #19 #17)
+#16 := (< 0::Int #9)
+#18 := (and #16 #17)
+#21 := (or #18 #20)
+#26 := (ite #21 #22 #25)
+#14 := (= #13 0::Int)
+#11 := (= #9 0::Int)
+#15 := (or #11 #14)
+#27 := (ite #15 0::Int #26)
+#28 := (= #27 0::Int)
+#29 := (not #28)
+#177 := (iff #29 false)
+#50 := -1::Int
+#86 := (< -1::Int 0::Int)
+#60 := -3::Int
+#80 := (< 0::Int -3::Int)
+#92 := (and #80 #86)
+#77 := (< 0::Int -1::Int)
+#83 := (and #77 #80)
+#97 := (or #83 #92)
+#175 := (iff #97 false)
+#70 := (or false false)
+#73 := (iff #70 false)
+#74 := [rewrite]: #73
+#173 := (iff #97 #70)
+#171 := (iff #92 false)
+#1 := true
+#166 := (and false true)
+#169 := (iff #166 false)
+#170 := [rewrite]: #169
+#167 := (iff #92 #166)
+#164 := (iff #86 true)
+#165 := [rewrite]: #164
+#155 := (iff #80 false)
+#156 := [rewrite]: #155
+#168 := [monotonicity #156 #165]: #167
+#172 := [trans #168 #170]: #171
+#162 := (iff #83 false)
+#157 := (and false false)
+#160 := (iff #157 false)
+#161 := [rewrite]: #160
+#158 := (iff #83 #157)
+#153 := (iff #77 false)
+#154 := [rewrite]: #153
+#159 := [monotonicity #154 #156]: #158
+#163 := [trans #159 #161]: #162
+#174 := [monotonicity #163 #172]: #173
+#176 := [trans #174 #74]: #175
+#151 := (iff #29 #97)
+#141 := (not #97)
+#146 := (not #141)
+#149 := (iff #146 #97)
+#150 := [rewrite]: #149
+#147 := (iff #29 #146)
+#144 := (iff #28 #141)
+#128 := (ite #97 1::Int 0::Int)
+#138 := (= #128 0::Int)
+#142 := (iff #138 #141)
+#143 := [rewrite]: #142
+#139 := (iff #28 #138)
+#136 := (= #27 #128)
+#131 := (ite false 0::Int #128)
+#134 := (= #131 #128)
+#135 := [rewrite]: #134
+#132 := (= #27 #131)
+#129 := (= #26 #128)
+#126 := (= #25 0::Int)
+#121 := (div 1::Int 3::Int)
+#124 := (= #121 0::Int)
+#125 := [rewrite]: #124
+#122 := (= #25 #121)
+#119 := (= #24 3::Int)
+#114 := (- -3::Int)
+#117 := (= #114 3::Int)
+#118 := [rewrite]: #117
+#115 := (= #24 #114)
+#61 := (= #13 -3::Int)
+#62 := [rewrite]: #61
+#116 := [monotonicity #62]: #115
+#120 := [trans #116 #118]: #119
+#112 := (= #23 1::Int)
+#107 := (- -1::Int)
+#110 := (= #107 1::Int)
+#111 := [rewrite]: #110
+#108 := (= #23 #107)
+#51 := (= #9 -1::Int)
+#52 := [rewrite]: #51
+#109 := [monotonicity #52]: #108
+#113 := [trans #109 #111]: #112
+#123 := [monotonicity #113 #120]: #122
+#127 := [trans #123 #125]: #126
+#105 := (= #22 1::Int)
+#100 := (div -1::Int -3::Int)
+#103 := (= #100 1::Int)
+#104 := [rewrite]: #103
+#101 := (= #22 #100)
+#102 := [monotonicity #52 #62]: #101
+#106 := [trans #102 #104]: #105
+#98 := (iff #21 #97)
+#95 := (iff #20 #92)
+#89 := (and #86 #80)
+#93 := (iff #89 #92)
+#94 := [rewrite]: #93
+#90 := (iff #20 #89)
+#81 := (iff #17 #80)
+#82 := [monotonicity #62]: #81
+#87 := (iff #19 #86)
+#88 := [monotonicity #52]: #87
+#91 := [monotonicity #88 #82]: #90
+#96 := [trans #91 #94]: #95
+#84 := (iff #18 #83)
+#78 := (iff #16 #77)
+#79 := [monotonicity #52]: #78
+#85 := [monotonicity #79 #82]: #84
+#99 := [monotonicity #85 #96]: #98
+#130 := [monotonicity #99 #106 #127]: #129
+#75 := (iff #15 false)
+#71 := (iff #15 #70)
+#68 := (iff #14 false)
+#63 := (= -3::Int 0::Int)
+#66 := (iff #63 false)
+#67 := [rewrite]: #66
+#64 := (iff #14 #63)
+#65 := [monotonicity #62]: #64
+#69 := [trans #65 #67]: #68
+#58 := (iff #11 false)
+#53 := (= -1::Int 0::Int)
+#56 := (iff #53 false)
+#57 := [rewrite]: #56
+#54 := (iff #11 #53)
+#55 := [monotonicity #52]: #54
+#59 := [trans #55 #57]: #58
+#72 := [monotonicity #59 #69]: #71
+#76 := [trans #72 #74]: #75
+#133 := [monotonicity #76 #130]: #132
+#137 := [trans #133 #135]: #136
+#140 := [monotonicity #137]: #139
+#145 := [trans #140 #143]: #144
+#148 := [monotonicity #145]: #147
+#152 := [trans #148 #150]: #151
+#178 := [trans #152 #176]: #177
+#49 := [asserted]: #29
+[mp #49 #178]: false
+unsat
+b0f55b14153bd1415b180d8eb26a6650d8024f22 112 0
+#2 := false
+#23 := 1::Int
 #8 := 3::Int
-#65 := -3::Int
-#68 := (f3 -3::Int 3::Int)
-#74 := (= #68 -1::Int)
-#77 := (not #74)
-#11 := 1::Int
-#12 := (- 1::Int)
 #9 := (- 3::Int)
-#10 := (f3 #9 3::Int)
-#13 := (= #10 #12)
-#14 := (not #13)
-#78 := (iff #14 #77)
-#75 := (iff #13 #74)
-#72 := (= #12 -1::Int)
-#73 := [rewrite]: #72
-#69 := (= #10 #68)
-#66 := (= #9 -3::Int)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#76 := [monotonicity #70 #73]: #75
-#79 := [monotonicity #76]: #78
-#64 := [asserted]: #14
-#82 := [mp #64 #79]: #77
-#657 := (not #743)
-#667 := (or #657 #74)
-#329 := (* -1::Int 3::Int)
-#413 := (* -1::Int -3::Int)
-#414 := (div #413 #329)
-#415 := (* -1::Int #414)
-#406 := (+ #68 #415)
-#417 := (= #406 0::Int)
-#418 := (div -3::Int 3::Int)
-#419 := (* -1::Int #418)
-#416 := (+ #68 #419)
-#420 := (= #416 0::Int)
-#399 := (>= -3::Int 0::Int)
-#734 := (<= 3::Int 0::Int)
-#736 := (or #734 #399)
-#393 := (not #736)
-#523 := (<= -3::Int 0::Int)
-#730 := (or #523 #734)
-#404 := (not #730)
-#405 := (or #404 #393)
-#737 := (ite #405 #420 #417)
-#738 := (= #68 0::Int)
-#739 := (= 3::Int 0::Int)
-#740 := (= -3::Int 0::Int)
-#735 := (or #740 #739)
-#741 := (ite #735 #738 #737)
-#668 := (or #657 #741)
-#665 := (iff #668 #667)
-#659 := (iff #667 #667)
-#660 := [rewrite]: #659
-#658 := (iff #741 #74)
-#676 := (ite false #738 #74)
-#664 := (iff #676 #74)
-#666 := [rewrite]: #664
-#673 := (iff #741 #676)
-#582 := (iff #737 #74)
-#1 := true
-#578 := (ite true #74 #74)
-#580 := (iff #578 #74)
-#581 := [rewrite]: #580
-#571 := (iff #737 #578)
-#575 := (iff #417 #74)
-#702 := (+ 1::Int #68)
-#688 := (= #702 0::Int)
-#684 := (iff #688 #74)
-#685 := [rewrite]: #684
-#675 := (iff #417 #688)
-#671 := (= #406 #702)
-#700 := (+ #68 1::Int)
-#543 := (= #700 #702)
-#544 := [rewrite]: #543
-#674 := (= #406 #700)
-#567 := (= #415 1::Int)
-#704 := (* -1::Int -1::Int)
-#698 := (= #704 1::Int)
-#699 := [rewrite]: #698
-#565 := (= #415 #704)
-#680 := (= #414 -1::Int)
-#525 := (div 3::Int -3::Int)
-#681 := (= #525 -1::Int)
-#682 := [rewrite]: #681
-#678 := (= #414 #525)
-#522 := (= #329 -3::Int)
-#524 := [rewrite]: #522
-#686 := (= #413 3::Int)
-#693 := [rewrite]: #686
-#679 := [monotonicity #693 #524]: #678
-#683 := [trans #679 #682]: #680
-#566 := [monotonicity #683]: #565
-#526 := [trans #566 #699]: #567
-#576 := [monotonicity #526]: #674
-#672 := [trans #576 #544]: #671
-#560 := [monotonicity #672]: #675
-#577 := [trans #560 #685]: #575
-#691 := (iff #420 #74)
-#689 := (iff #420 #688)
-#545 := (= #416 #702)
-#701 := (= #416 #700)
-#694 := (= #419 1::Int)
-#708 := (= #419 #704)
-#703 := (= #418 -1::Int)
-#707 := [rewrite]: #703
-#697 := [monotonicity #707]: #708
-#695 := [trans #697 #699]: #694
-#696 := [monotonicity #695]: #701
-#687 := [trans #696 #544]: #545
-#690 := [monotonicity #687]: #689
-#692 := [trans #690 #685]: #691
-#706 := (iff #405 true)
-#424 := (or false true)
-#427 := (iff #424 true)
-#705 := [rewrite]: #427
-#425 := (iff #405 #424)
-#710 := (iff #393 true)
-#712 := (not false)
-#709 := (iff #712 true)
-#713 := [rewrite]: #709
-#434 := (iff #393 #712)
-#335 := (iff #736 false)
-#392 := (or false false)
-#717 := (iff #392 false)
-#380 := [rewrite]: #717
-#440 := (iff #736 #392)
-#438 := (iff #399 false)
-#439 := [rewrite]: #438
-#720 := (iff #734 false)
-#721 := [rewrite]: #720
-#441 := [monotonicity #721 #439]: #440
-#711 := [trans #441 #380]: #335
-#435 := [monotonicity #711]: #434
-#714 := [trans #435 #713]: #710
-#715 := (iff #404 false)
-#367 := (not true)
-#726 := (iff #367 false)
-#729 := [rewrite]: #726
-#368 := (iff #404 #367)
-#725 := (iff #730 true)
-#722 := (or true false)
-#724 := (iff #722 true)
-#362 := [rewrite]: #724
-#723 := (iff #730 #722)
-#383 := (iff #523 true)
-#719 := [rewrite]: #383
-#718 := [monotonicity #719 #721]: #723
-#727 := [trans #718 #362]: #725
-#728 := [monotonicity #727]: #368
-#716 := [trans #728 #729]: #715
-#426 := [monotonicity #716 #714]: #425
-#421 := [trans #426 #705]: #706
-#579 := [monotonicity #421 #692 #577]: #571
-#583 := [trans #579 #581]: #582
-#381 := (iff #735 false)
-#733 := (iff #735 #392)
-#396 := (iff #739 false)
-#732 := [rewrite]: #396
-#731 := (iff #740 false)
-#391 := [rewrite]: #731
-#376 := [monotonicity #391 #732]: #733
-#382 := [trans #376 #380]: #381
-#677 := [monotonicity #382 #583]: #673
-#655 := [trans #677 #666]: #658
-#670 := [monotonicity #655]: #665
-#661 := [trans #670 #660]: #665
-#669 := [quant-inst #65 #8]: #668
-#662 := [mp #669 #661]: #667
-[unit-resolution #662 #82 #748]: false
-unsat
-5e9e5ffc31aa8934508da0815460298eed868a8c 324 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#17 := (:var 0 Int)
-#16 := (:var 1 Int)
-#18 := (f3 #16 #17)
-#745 := (pattern #18)
-#19 := 0::Int
-#89 := -1::Int
-#93 := (* -1::Int #17)
-#90 := (* -1::Int #16)
-#96 := (div #90 #93)
-#247 := (* -1::Int #96)
-#248 := (+ #18 #247)
-#249 := (= #248 0::Int)
-#29 := (div #16 #17)
-#244 := (* -1::Int #29)
-#245 := (+ #18 #244)
-#246 := (= #245 0::Int)
-#122 := (>= #16 0::Int)
-#115 := (<= #17 0::Int)
-#207 := (or #115 #122)
-#208 := (not #207)
-#111 := (<= #16 0::Int)
-#205 := (or #111 #115)
-#206 := (not #205)
-#211 := (or #206 #208)
-#250 := (ite #211 #246 #249)
-#243 := (= #18 0::Int)
-#21 := (= #17 0::Int)
-#20 := (= #16 0::Int)
-#22 := (or #20 #21)
-#251 := (ite #22 #243 #250)
-#746 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #745) #251)
-#254 := (forall (vars (?v0 Int) (?v1 Int)) #251)
-#749 := (iff #254 #746)
-#747 := (iff #251 #251)
-#748 := [refl]: #747
-#750 := [quant-intro #748]: #749
-#214 := (ite #211 #29 #96)
-#217 := (ite #22 0::Int #214)
-#220 := (= #18 #217)
-#223 := (forall (vars (?v0 Int) (?v1 Int)) #220)
-#255 := (iff #223 #254)
-#252 := (iff #220 #251)
-#253 := [rewrite]: #252
-#256 := [quant-intro #253]: #255
-#123 := (not #122)
-#116 := (not #115)
-#126 := (and #116 #123)
-#112 := (not #111)
-#119 := (and #112 #116)
-#129 := (or #119 #126)
-#132 := (ite #129 #29 #96)
-#135 := (ite #22 0::Int #132)
-#138 := (= #18 #135)
-#141 := (forall (vars (?v0 Int) (?v1 Int)) #138)
-#224 := (iff #141 #223)
-#221 := (iff #138 #220)
-#218 := (= #135 #217)
-#215 := (= #132 #214)
-#212 := (iff #129 #211)
-#209 := (iff #126 #208)
-#210 := [rewrite]: #209
-#199 := (iff #119 #206)
-#200 := [rewrite]: #199
-#213 := [monotonicity #200 #210]: #212
-#216 := [monotonicity #213]: #215
-#219 := [monotonicity #216]: #218
-#222 := [monotonicity #219]: #221
-#225 := [quant-intro #222]: #224
-#203 := (~ #141 #141)
-#201 := (~ #138 #138)
-#202 := [refl]: #201
-#204 := [nnf-pos #202]: #203
-#31 := (- #17)
-#30 := (- #16)
-#32 := (div #30 #31)
-#24 := (< 0::Int #17)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#33 := (ite #28 #29 #32)
-#34 := (ite #22 0::Int #33)
-#35 := (= #18 #34)
-#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
-#144 := (iff #36 #141)
-#82 := (and #24 #26)
-#86 := (or #25 #82)
-#99 := (ite #86 #29 #96)
-#102 := (ite #22 0::Int #99)
-#105 := (= #18 #102)
-#108 := (forall (vars (?v0 Int) (?v1 Int)) #105)
-#142 := (iff #108 #141)
-#139 := (iff #105 #138)
-#136 := (= #102 #135)
-#133 := (= #99 #132)
-#130 := (iff #86 #129)
-#127 := (iff #82 #126)
-#124 := (iff #26 #123)
+#19 := (- #9)
+#20 := (div #19 #19)
+#18 := (div #9 #9)
+#10 := 0::Int
+#13 := (< 0::Int #9)
+#15 := (< #9 0::Int)
+#16 := (and #15 #13)
+#14 := (and #13 #13)
+#17 := (or #14 #16)
+#21 := (ite #17 #18 #20)
+#11 := (= #9 0::Int)
+#12 := (or #11 #11)
+#22 := (ite #12 0::Int #21)
+#24 := (= #22 1::Int)
+#25 := (not #24)
+#133 := (iff #25 false)
+#1 := true
+#128 := (not true)
+#131 := (iff #128 false)
+#132 := [rewrite]: #131
+#129 := (iff #25 #128)
+#126 := (iff #24 true)
+#121 := (= 1::Int 1::Int)
+#124 := (iff #121 true)
 #125 := [rewrite]: #124
-#117 := (iff #24 #116)
-#118 := [rewrite]: #117
-#128 := [monotonicity #118 #125]: #127
-#120 := (iff #25 #119)
-#113 := (iff #23 #112)
-#114 := [rewrite]: #113
-#121 := [monotonicity #114 #118]: #120
-#131 := [monotonicity #121 #128]: #130
-#134 := [monotonicity #131]: #133
-#137 := [monotonicity #134]: #136
-#140 := [monotonicity #137]: #139
-#143 := [quant-intro #140]: #142
-#109 := (iff #36 #108)
-#106 := (iff #35 #105)
-#103 := (= #34 #102)
-#100 := (= #33 #99)
-#97 := (= #32 #96)
-#94 := (= #31 #93)
-#95 := [rewrite]: #94
-#91 := (= #30 #90)
-#92 := [rewrite]: #91
-#98 := [monotonicity #92 #95]: #97
-#87 := (iff #28 #86)
-#84 := (iff #27 #82)
-#85 := [rewrite]: #84
-#88 := [monotonicity #85]: #87
-#101 := [monotonicity #88 #98]: #100
-#104 := [monotonicity #101]: #103
-#107 := [monotonicity #104]: #106
-#110 := [quant-intro #107]: #109
-#145 := [trans #110 #143]: #144
-#81 := [asserted]: #36
-#146 := [mp #81 #145]: #141
-#195 := [mp~ #146 #204]: #141
-#226 := [mp #195 #225]: #223
-#257 := [mp #226 #256]: #254
-#751 := [mp #257 #750]: #746
-#72 := -2::Int
-#10 := 3::Int
-#66 := -5::Int
-#69 := (f3 -5::Int 3::Int)
-#75 := (= #69 -2::Int)
-#78 := (not #75)
-#12 := 2::Int
-#13 := (- 2::Int)
+#122 := (iff #24 #121)
+#115 := (ite false 0::Int 1::Int)
+#118 := (= #115 1::Int)
+#119 := [rewrite]: #118
+#116 := (= #22 #115)
+#113 := (= #21 1::Int)
+#46 := -3::Int
+#73 := (< -3::Int 0::Int)
+#63 := (< 0::Int -3::Int)
+#79 := (and #63 #73)
+#84 := (or #63 #79)
+#108 := (ite #84 1::Int 1::Int)
+#111 := (= #108 1::Int)
+#112 := [rewrite]: #111
+#109 := (= #21 #108)
+#106 := (= #20 1::Int)
+#101 := (div 3::Int 3::Int)
+#104 := (= #101 1::Int)
+#105 := [rewrite]: #104
+#102 := (= #20 #101)
+#99 := (= #19 3::Int)
+#94 := (- -3::Int)
+#97 := (= #94 3::Int)
+#98 := [rewrite]: #97
+#95 := (= #19 #94)
+#47 := (= #9 -3::Int)
+#48 := [rewrite]: #47
+#96 := [monotonicity #48]: #95
+#100 := [trans #96 #98]: #99
+#103 := [monotonicity #100 #100]: #102
+#107 := [trans #103 #105]: #106
+#92 := (= #18 1::Int)
+#87 := (div -3::Int -3::Int)
+#90 := (= #87 1::Int)
+#91 := [rewrite]: #90
+#88 := (= #18 #87)
+#89 := [monotonicity #48 #48]: #88
+#93 := [trans #89 #91]: #92
+#85 := (iff #17 #84)
+#82 := (iff #16 #79)
+#76 := (and #73 #63)
+#80 := (iff #76 #79)
+#81 := [rewrite]: #80
+#77 := (iff #16 #76)
+#64 := (iff #13 #63)
+#65 := [monotonicity #48]: #64
+#74 := (iff #15 #73)
+#75 := [monotonicity #48]: #74
+#78 := [monotonicity #75 #65]: #77
+#83 := [trans #78 #81]: #82
+#71 := (iff #14 #63)
+#66 := (and #63 #63)
+#69 := (iff #66 #63)
+#70 := [rewrite]: #69
+#67 := (iff #14 #66)
+#68 := [monotonicity #65 #65]: #67
+#72 := [trans #68 #70]: #71
+#86 := [monotonicity #72 #83]: #85
+#110 := [monotonicity #86 #93 #107]: #109
+#114 := [trans #110 #112]: #113
+#61 := (iff #12 false)
+#56 := (or false false)
+#59 := (iff #56 false)
+#60 := [rewrite]: #59
+#57 := (iff #12 #56)
+#54 := (iff #11 false)
+#49 := (= -3::Int 0::Int)
+#52 := (iff #49 false)
+#53 := [rewrite]: #52
+#50 := (iff #11 #49)
+#51 := [monotonicity #48]: #50
+#55 := [trans #51 #53]: #54
+#58 := [monotonicity #55 #55]: #57
+#62 := [trans #58 #60]: #61
+#117 := [monotonicity #62 #114]: #116
+#120 := [trans #117 #119]: #24
+#123 := [monotonicity #120]: #122
+#127 := [trans #123 #125]: #126
+#130 := [monotonicity #127]: #129
+#134 := [trans #130 #132]: #133
+#45 := [asserted]: #25
+[mp #45 #134]: false
+unsat
+cebc167e67bf5c5c55d952431648797ef2d30dde 158 0
+#2 := false
+#28 := 1::Int
+#12 := 3::Int
+#13 := (- 3::Int)
+#24 := (- #13)
 #8 := 5::Int
 #9 := (- 5::Int)
-#11 := (f3 #9 3::Int)
-#14 := (= #11 #13)
-#15 := (not #14)
-#79 := (iff #15 #78)
-#76 := (iff #14 #75)
-#73 := (= #13 -2::Int)
-#74 := [rewrite]: #73
-#70 := (= #11 #69)
-#67 := (= #9 -5::Int)
+#23 := (- #9)
+#25 := (div #23 #24)
+#22 := (div #9 #13)
+#10 := 0::Int
+#17 := (< 0::Int #13)
+#19 := (< #9 0::Int)
+#20 := (and #19 #17)
+#16 := (< 0::Int #9)
+#18 := (and #16 #17)
+#21 := (or #18 #20)
+#26 := (ite #21 #22 #25)
+#14 := (= #13 0::Int)
+#11 := (= #9 0::Int)
+#15 := (or #11 #14)
+#27 := (ite #15 0::Int #26)
+#29 := (= #27 1::Int)
+#30 := (not #29)
+#179 := (iff #30 false)
+#51 := -5::Int
+#87 := (< -5::Int 0::Int)
+#61 := -3::Int
+#81 := (< 0::Int -3::Int)
+#93 := (and #81 #87)
+#78 := (< 0::Int -5::Int)
+#84 := (and #78 #81)
+#98 := (or #84 #93)
+#177 := (iff #98 false)
+#71 := (or false false)
+#74 := (iff #71 false)
+#75 := [rewrite]: #74
+#175 := (iff #98 #71)
+#173 := (iff #93 false)
+#1 := true
+#168 := (and false true)
+#171 := (iff #168 false)
+#172 := [rewrite]: #171
+#169 := (iff #93 #168)
+#166 := (iff #87 true)
+#167 := [rewrite]: #166
+#157 := (iff #81 false)
+#158 := [rewrite]: #157
+#170 := [monotonicity #158 #167]: #169
+#174 := [trans #170 #172]: #173
+#164 := (iff #84 false)
+#159 := (and false false)
+#162 := (iff #159 false)
+#163 := [rewrite]: #162
+#160 := (iff #84 #159)
+#155 := (iff #78 false)
+#156 := [rewrite]: #155
+#161 := [monotonicity #156 #158]: #160
+#165 := [trans #161 #163]: #164
+#176 := [monotonicity #165 #174]: #175
+#178 := [trans #176 #75]: #177
+#153 := (iff #30 #98)
+#143 := (not #98)
+#148 := (not #143)
+#151 := (iff #148 #98)
+#152 := [rewrite]: #151
+#149 := (iff #30 #148)
+#146 := (iff #29 #143)
+#104 := 2::Int
+#130 := (ite #98 2::Int 1::Int)
+#140 := (= #130 1::Int)
+#144 := (iff #140 #143)
+#145 := [rewrite]: #144
+#141 := (iff #29 #140)
+#138 := (= #27 #130)
+#133 := (ite false 0::Int #130)
+#136 := (= #133 #130)
+#137 := [rewrite]: #136
+#134 := (= #27 #133)
+#131 := (= #26 #130)
+#128 := (= #25 1::Int)
+#123 := (div 5::Int 3::Int)
+#126 := (= #123 1::Int)
+#127 := [rewrite]: #126
+#124 := (= #25 #123)
+#121 := (= #24 3::Int)
+#116 := (- -3::Int)
+#119 := (= #116 3::Int)
+#120 := [rewrite]: #119
+#117 := (= #24 #116)
+#62 := (= #13 -3::Int)
+#63 := [rewrite]: #62
+#118 := [monotonicity #63]: #117
+#122 := [trans #118 #120]: #121
+#114 := (= #23 5::Int)
+#109 := (- -5::Int)
+#112 := (= #109 5::Int)
+#113 := [rewrite]: #112
+#110 := (= #23 #109)
+#52 := (= #9 -5::Int)
+#53 := [rewrite]: #52
+#111 := [monotonicity #53]: #110
+#115 := [trans #111 #113]: #114
+#125 := [monotonicity #115 #122]: #124
+#129 := [trans #125 #127]: #128
+#107 := (= #22 2::Int)
+#101 := (div -5::Int -3::Int)
+#105 := (= #101 2::Int)
+#106 := [rewrite]: #105
+#102 := (= #22 #101)
+#103 := [monotonicity #53 #63]: #102
+#108 := [trans #103 #106]: #107
+#99 := (iff #21 #98)
+#96 := (iff #20 #93)
+#90 := (and #87 #81)
+#94 := (iff #90 #93)
+#95 := [rewrite]: #94
+#91 := (iff #20 #90)
+#82 := (iff #17 #81)
+#83 := [monotonicity #63]: #82
+#88 := (iff #19 #87)
+#89 := [monotonicity #53]: #88
+#92 := [monotonicity #89 #83]: #91
+#97 := [trans #92 #95]: #96
+#85 := (iff #18 #84)
+#79 := (iff #16 #78)
+#80 := [monotonicity #53]: #79
+#86 := [monotonicity #80 #83]: #85
+#100 := [monotonicity #86 #97]: #99
+#132 := [monotonicity #100 #108 #129]: #131
+#76 := (iff #15 false)
+#72 := (iff #15 #71)
+#69 := (iff #14 false)
+#64 := (= -3::Int 0::Int)
+#67 := (iff #64 false)
 #68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#77 := [monotonicity #71 #74]: #76
-#80 := [monotonicity #77]: #79
-#65 := [asserted]: #15
-#83 := [mp #65 #80]: #78
-#650 := (not #746)
-#651 := (or #650 #75)
-#331 := (* -1::Int 3::Int)
-#416 := (* -1::Int -5::Int)
-#417 := (div #416 #331)
-#418 := (* -1::Int #417)
-#409 := (+ #69 #418)
-#420 := (= #409 0::Int)
-#421 := (div -5::Int 3::Int)
-#349 := (* -1::Int #421)
-#422 := (+ #69 #349)
-#419 := (= #422 0::Int)
-#423 := (>= -5::Int 0::Int)
-#402 := (<= 3::Int 0::Int)
-#737 := (or #402 #423)
-#739 := (not #737)
-#396 := (<= -5::Int 0::Int)
-#526 := (or #396 #402)
-#733 := (not #526)
-#407 := (or #733 #739)
-#408 := (ite #407 #419 #420)
-#740 := (= #69 0::Int)
-#741 := (= 3::Int 0::Int)
-#742 := (= -5::Int 0::Int)
-#743 := (or #742 #741)
-#738 := (ite #743 #740 #408)
-#653 := (or #650 #738)
-#655 := (iff #653 #651)
-#652 := (iff #651 #651)
-#657 := [rewrite]: #652
-#659 := (iff #738 #75)
-#673 := (ite false #740 #75)
-#664 := (iff #673 #75)
-#665 := [rewrite]: #664
-#662 := (iff #738 #673)
-#672 := (iff #408 #75)
-#679 := (= #69 -1::Int)
-#1 := true
-#661 := (ite true #75 #679)
-#670 := (iff #661 #75)
-#671 := [rewrite]: #670
-#658 := (iff #408 #661)
-#667 := (iff #420 #679)
-#529 := 1::Int
-#580 := (+ 1::Int #69)
-#584 := (= #580 0::Int)
-#676 := (iff #584 #679)
-#680 := [rewrite]: #676
-#585 := (iff #420 #584)
-#582 := (= #409 #580)
-#678 := (+ #69 1::Int)
-#581 := (= #678 #580)
-#574 := [rewrite]: #581
-#563 := (= #409 #678)
-#674 := (= #418 1::Int)
-#568 := (* -1::Int -1::Int)
-#677 := (= #568 1::Int)
-#579 := [rewrite]: #677
-#569 := (= #418 #568)
-#683 := (= #417 -1::Int)
-#696 := -3::Int
-#528 := (div 5::Int -3::Int)
-#684 := (= #528 -1::Int)
-#685 := [rewrite]: #684
-#681 := (= #417 #528)
-#525 := (= #331 -3::Int)
-#527 := [rewrite]: #525
-#695 := (= #416 5::Int)
-#689 := [rewrite]: #695
-#682 := [monotonicity #689 #527]: #681
-#686 := [trans #682 #685]: #683
-#570 := [monotonicity #686]: #569
-#675 := [trans #570 #579]: #674
-#578 := [monotonicity #675]: #563
-#583 := [trans #578 #574]: #582
-#586 := [monotonicity #583]: #585
-#669 := [trans #586 #680]: #667
-#688 := (iff #419 #75)
-#699 := (+ 2::Int #69)
-#690 := (= #699 0::Int)
-#693 := (iff #690 #75)
-#687 := [rewrite]: #693
-#691 := (iff #419 #690)
-#547 := (= #422 #699)
-#698 := (+ #69 2::Int)
-#705 := (= #698 #699)
-#546 := [rewrite]: #705
-#703 := (= #422 #698)
-#702 := (= #349 2::Int)
-#710 := (* -1::Int -2::Int)
-#700 := (= #710 2::Int)
-#701 := [rewrite]: #700
-#707 := (= #349 #710)
-#424 := (= #421 -2::Int)
-#706 := [rewrite]: #424
-#711 := [monotonicity #706]: #707
-#697 := [trans #711 #701]: #702
-#704 := [monotonicity #697]: #703
-#548 := [trans #704 #546]: #547
-#692 := [monotonicity #548]: #691
-#694 := [trans #692 #687]: #688
-#708 := (iff #407 true)
-#717 := (or false true)
-#429 := (iff #717 true)
-#430 := [rewrite]: #429
-#427 := (iff #407 #717)
-#716 := (iff #739 true)
-#714 := (not false)
-#438 := (iff #714 true)
-#712 := [rewrite]: #438
-#715 := (iff #739 #714)
-#444 := (iff #737 false)
-#735 := (or false false)
-#379 := (iff #735 false)
-#720 := [rewrite]: #379
-#442 := (iff #737 #735)
-#719 := (iff #423 false)
-#441 := [rewrite]: #719
-#722 := (iff #402 false)
-#723 := [rewrite]: #722
-#443 := [monotonicity #723 #441]: #442
-#337 := [trans #443 #720]: #444
-#437 := [monotonicity #337]: #715
-#713 := [trans #437 #712]: #716
-#732 := (iff #733 false)
-#730 := (not true)
-#731 := (iff #730 false)
-#729 := [rewrite]: #731
-#370 := (iff #733 #730)
-#365 := (iff #526 true)
-#724 := (or true false)
-#721 := (iff #724 true)
-#727 := [rewrite]: #721
-#725 := (iff #526 #724)
-#385 := (iff #396 true)
-#386 := [rewrite]: #385
-#726 := [monotonicity #386 #723]: #725
-#728 := [trans #726 #727]: #365
-#371 := [monotonicity #728]: #370
-#718 := [trans #371 #729]: #732
-#428 := [monotonicity #718 #713]: #427
-#709 := [trans #428 #430]: #708
-#660 := [monotonicity #709 #694 #669]: #658
-#668 := [trans #660 #671]: #672
-#383 := (iff #743 false)
-#395 := (iff #743 #735)
-#394 := (iff #741 false)
-#399 := [rewrite]: #394
-#744 := (iff #742 false)
-#734 := [rewrite]: #744
-#736 := [monotonicity #734 #399]: #395
-#384 := [trans #736 #720]: #383
-#663 := [monotonicity #384 #668]: #662
-#666 := [trans #663 #665]: #659
-#656 := [monotonicity #666]: #655
-#643 := [trans #656 #657]: #655
-#654 := [quant-inst #66 #10]: #653
-#644 := [mp #654 #643]: #651
-[unit-resolution #644 #83 #751]: false
-unsat
-7de568581f12c6417657495045816e0055a747d5 337 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#17 := (:var 0 Int)
-#16 := (:var 1 Int)
-#18 := (f3 #16 #17)
-#769 := (pattern #18)
-#13 := 0::Int
-#65 := -1::Int
-#112 := (* -1::Int #17)
-#109 := (* -1::Int #16)
-#115 := (div #109 #112)
-#272 := (* -1::Int #115)
-#273 := (+ #18 #272)
-#274 := (= #273 0::Int)
-#28 := (div #16 #17)
-#269 := (* -1::Int #28)
-#270 := (+ #18 #269)
-#271 := (= #270 0::Int)
-#147 := (>= #16 0::Int)
-#140 := (<= #17 0::Int)
-#232 := (or #140 #147)
-#233 := (not #232)
-#136 := (<= #16 0::Int)
-#230 := (or #136 #140)
-#231 := (not #230)
-#236 := (or #231 #233)
-#275 := (ite #236 #271 #274)
-#268 := (= #18 0::Int)
-#20 := (= #17 0::Int)
-#19 := (= #16 0::Int)
-#21 := (or #19 #20)
-#276 := (ite #21 #268 #275)
-#770 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #769) #276)
-#279 := (forall (vars (?v0 Int) (?v1 Int)) #276)
-#773 := (iff #279 #770)
-#771 := (iff #276 #276)
-#772 := [refl]: #771
-#774 := [quant-intro #772]: #773
-#239 := (ite #236 #28 #115)
-#242 := (ite #21 0::Int #239)
-#245 := (= #18 #242)
-#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
-#280 := (iff #248 #279)
-#277 := (iff #245 #276)
-#278 := [rewrite]: #277
-#281 := [quant-intro #278]: #280
-#148 := (not #147)
-#141 := (not #140)
-#151 := (and #141 #148)
-#137 := (not #136)
-#144 := (and #137 #141)
-#154 := (or #144 #151)
-#157 := (ite #154 #28 #115)
-#160 := (ite #21 0::Int #157)
-#163 := (= #18 #160)
-#166 := (forall (vars (?v0 Int) (?v1 Int)) #163)
-#249 := (iff #166 #248)
-#246 := (iff #163 #245)
-#243 := (= #160 #242)
-#240 := (= #157 #239)
-#237 := (iff #154 #236)
-#234 := (iff #151 #233)
-#235 := [rewrite]: #234
-#224 := (iff #144 #231)
-#225 := [rewrite]: #224
-#238 := [monotonicity #225 #235]: #237
-#241 := [monotonicity #238]: #240
-#244 := [monotonicity #241]: #243
-#247 := [monotonicity #244]: #246
-#250 := [quant-intro #247]: #249
-#228 := (~ #166 #166)
-#226 := (~ #163 #163)
-#227 := [refl]: #226
-#229 := [nnf-pos #227]: #228
-#30 := (- #17)
-#29 := (- #16)
-#31 := (div #29 #30)
-#23 := (< 0::Int #17)
-#25 := (< #16 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #16)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#32 := (ite #27 #28 #31)
-#33 := (ite #21 0::Int #32)
-#34 := (= #18 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#169 := (iff #35 #166)
-#103 := (and #23 #25)
-#106 := (or #24 #103)
-#118 := (ite #106 #28 #115)
-#97 := (= 0::Int #17)
-#94 := (= 0::Int #16)
-#100 := (or #94 #97)
-#121 := (ite #100 0::Int #118)
-#124 := (= #18 #121)
-#127 := (forall (vars (?v0 Int) (?v1 Int)) #124)
-#167 := (iff #127 #166)
-#164 := (iff #124 #163)
-#161 := (= #121 #160)
-#158 := (= #118 #157)
-#155 := (iff #106 #154)
-#152 := (iff #103 #151)
-#149 := (iff #25 #148)
-#150 := [rewrite]: #149
-#142 := (iff #23 #141)
+#65 := (iff #14 #64)
+#66 := [monotonicity #63]: #65
+#70 := [trans #66 #68]: #69
+#59 := (iff #11 false)
+#54 := (= -5::Int 0::Int)
+#57 := (iff #54 false)
+#58 := [rewrite]: #57
+#55 := (iff #11 #54)
+#56 := [monotonicity #53]: #55
+#60 := [trans #56 #58]: #59
+#73 := [monotonicity #60 #70]: #72
+#77 := [trans #73 #75]: #76
+#135 := [monotonicity #77 #132]: #134
+#139 := [trans #135 #137]: #138
+#142 := [monotonicity #139]: #141
+#147 := [trans #142 #145]: #146
+#150 := [monotonicity #147]: #149
+#154 := [trans #150 #152]: #153
+#180 := [trans #154 #178]: #179
+#50 := [asserted]: #30
+[mp #50 #180]: false
+unsat
+cb26d273f6e817a53bda9b00a467150cd5bc2594 70 0
+#2 := false
+#8 := 0::Int
+#14 := (- 0::Int)
+#15 := (mod #14 #14)
+#16 := (- #15)
+#13 := (mod 0::Int 0::Int)
+#10 := (< 0::Int 0::Int)
+#11 := (and #10 #10)
+#12 := (or #11 #11)
+#17 := (ite #12 #13 #16)
+#9 := (= 0::Int 0::Int)
+#18 := (ite #9 0::Int #17)
+#19 := (ite #9 0::Int #18)
+#20 := (= #19 0::Int)
+#21 := (not #20)
+#91 := (iff #21 false)
+#1 := true
+#86 := (not true)
+#89 := (iff #86 false)
+#90 := [rewrite]: #89
+#87 := (iff #21 #86)
+#84 := (iff #20 true)
+#42 := (iff #9 true)
+#43 := [rewrite]: #42
+#82 := (iff #20 #9)
+#76 := (ite true 0::Int 0::Int)
+#79 := (= #76 0::Int)
+#80 := [rewrite]: #79
+#77 := (= #19 #76)
+#74 := (= #18 0::Int)
+#60 := -1::Int
+#61 := (* -1::Int #13)
+#66 := (ite #10 #13 #61)
+#69 := (ite true 0::Int #66)
+#72 := (= #69 0::Int)
+#73 := [rewrite]: #72
+#70 := (= #18 #69)
+#67 := (= #17 #66)
+#64 := (= #16 #61)
+#57 := (- #13)
+#62 := (= #57 #61)
+#63 := [rewrite]: #62
+#58 := (= #16 #57)
+#55 := (= #15 #13)
+#53 := (= #14 0::Int)
+#54 := [rewrite]: #53
+#56 := [monotonicity #54 #54]: #55
+#59 := [monotonicity #56]: #58
+#65 := [trans #59 #63]: #64
+#51 := (iff #12 #10)
+#46 := (or #10 #10)
+#49 := (iff #46 #10)
+#50 := [rewrite]: #49
+#47 := (iff #12 #46)
+#44 := (iff #11 #10)
+#45 := [rewrite]: #44
+#48 := [monotonicity #45 #45]: #47
+#52 := [trans #48 #50]: #51
+#68 := [monotonicity #52 #65]: #67
+#71 := [monotonicity #43 #68]: #70
+#75 := [trans #71 #73]: #74
+#78 := [monotonicity #43 #75]: #77
+#81 := [trans #78 #80]: #20
+#83 := [monotonicity #81]: #82
+#85 := [trans #83 #43]: #84
+#88 := [monotonicity #85]: #87
+#92 := [trans #88 #90]: #91
+#41 := [asserted]: #21
+[mp #41 #92]: false
+unsat
+1ec64b4c0435485d0864f4fb378fed079f553a7b 80 0
+#2 := false
+decl f3 :: Int
+#10 := f3
+#8 := 0::Int
+#20 := (- 0::Int)
+#19 := (- f3)
+#21 := (mod #19 #20)
+#22 := (- #21)
+#18 := (mod f3 0::Int)
+#13 := (< 0::Int 0::Int)
+#15 := (< f3 0::Int)
+#16 := (and #15 #13)
+#12 := (< 0::Int f3)
+#14 := (and #12 #13)
+#17 := (or #14 #16)
+#23 := (ite #17 #18 #22)
+#11 := (= f3 0::Int)
+#24 := (ite #11 0::Int #23)
+#9 := (= 0::Int 0::Int)
+#25 := (ite #9 f3 #24)
+#26 := (= #25 f3)
+#27 := (not #26)
+#100 := (iff #27 false)
+#1 := true
+#95 := (not true)
+#98 := (iff #95 false)
+#99 := [rewrite]: #98
+#96 := (iff #27 #95)
+#93 := (iff #26 true)
+#88 := (= f3 f3)
+#91 := (iff #88 true)
+#92 := [rewrite]: #91
+#89 := (iff #26 #88)
+#59 := -1::Int
+#60 := (* -1::Int f3)
+#65 := (mod #60 0::Int)
+#71 := (* -1::Int #65)
+#53 := (and #13 #15)
+#56 := (or #14 #53)
+#76 := (ite #56 #18 #71)
+#50 := (= 0::Int f3)
+#79 := (ite #50 0::Int #76)
+#82 := (ite true f3 #79)
+#85 := (= #82 f3)
+#86 := [rewrite]: #85
+#83 := (= #25 #82)
+#80 := (= #24 #79)
+#77 := (= #23 #76)
+#74 := (= #22 #71)
+#68 := (- #65)
+#72 := (= #68 #71)
+#73 := [rewrite]: #72
+#69 := (= #22 #68)
+#66 := (= #21 #65)
+#63 := (= #20 0::Int)
+#64 := [rewrite]: #63
+#61 := (= #19 #60)
+#62 := [rewrite]: #61
+#67 := [monotonicity #62 #64]: #66
+#70 := [monotonicity #67]: #69
+#75 := [trans #70 #73]: #74
+#57 := (iff #17 #56)
+#54 := (iff #16 #53)
+#55 := [rewrite]: #54
+#58 := [monotonicity #55]: #57
+#78 := [monotonicity #58 #75]: #77
+#51 := (iff #11 #50)
+#52 := [rewrite]: #51
+#81 := [monotonicity #52 #78]: #80
+#48 := (iff #9 true)
+#49 := [rewrite]: #48
+#84 := [monotonicity #49 #81]: #83
+#87 := [trans #84 #86]: #26
+#90 := [monotonicity #87]: #89
+#94 := [trans #90 #92]: #93
+#97 := [monotonicity #94]: #96
+#101 := [trans #97 #99]: #100
+#47 := [asserted]: #27
+[mp #47 #101]: false
+unsat
+57af3178bd4bde4a26173de026e5de08dfc9faa6 78 0
+#2 := false
+#9 := 0::Int
+#8 := 1::Int
+#18 := (- 1::Int)
+#17 := (- 0::Int)
+#19 := (mod #17 #18)
+#20 := (- #19)
+#16 := (mod 0::Int 1::Int)
+#13 := (< 0::Int 1::Int)
+#12 := (< 0::Int 0::Int)
+#14 := (and #12 #13)
+#15 := (or #14 #14)
+#21 := (ite #15 #16 #20)
+#11 := (= 0::Int 0::Int)
+#22 := (ite #11 0::Int #21)
+#10 := (= 1::Int 0::Int)
+#23 := (ite #10 0::Int #22)
+#24 := (= #23 0::Int)
+#25 := (not #24)
+#99 := (iff #25 false)
+#1 := true
+#94 := (not true)
+#97 := (iff #94 false)
+#98 := [rewrite]: #97
+#95 := (iff #25 #94)
+#92 := (iff #24 true)
+#48 := (iff #11 true)
+#49 := [rewrite]: #48
+#90 := (iff #24 #11)
+#84 := (ite false 0::Int 0::Int)
+#87 := (= #84 0::Int)
+#88 := [rewrite]: #87
+#85 := (= #23 #84)
+#82 := (= #22 0::Int)
+#77 := (ite true 0::Int 0::Int)
+#80 := (= #77 0::Int)
+#81 := [rewrite]: #80
+#78 := (= #22 #77)
+#75 := (= #21 0::Int)
+#70 := (ite #14 0::Int 0::Int)
+#73 := (= #70 0::Int)
+#74 := [rewrite]: #73
+#71 := (= #21 #70)
+#68 := (= #20 0::Int)
+#54 := (= #17 0::Int)
+#55 := [rewrite]: #54
+#66 := (= #20 #17)
+#64 := (= #19 0::Int)
+#56 := -1::Int
+#59 := (mod 0::Int -1::Int)
+#62 := (= #59 0::Int)
+#63 := [rewrite]: #62
+#60 := (= #19 #59)
+#57 := (= #18 -1::Int)
+#58 := [rewrite]: #57
+#61 := [monotonicity #55 #58]: #60
+#65 := [trans #61 #63]: #64
+#67 := [monotonicity #65]: #66
+#69 := [trans #67 #55]: #68
+#52 := (= #16 0::Int)
+#53 := [rewrite]: #52
+#50 := (iff #15 #14)
+#51 := [rewrite]: #50
+#72 := [monotonicity #51 #53 #69]: #71
+#76 := [trans #72 #74]: #75
+#79 := [monotonicity #49 #76]: #78
+#83 := [trans #79 #81]: #82
+#46 := (iff #10 false)
+#47 := [rewrite]: #46
+#86 := [monotonicity #47 #83]: #85
+#89 := [trans #86 #88]: #24
+#91 := [monotonicity #89]: #90
+#93 := [trans #91 #49]: #92
+#96 := [monotonicity #93]: #95
+#100 := [trans #96 #98]: #99
+#45 := [asserted]: #25
+[mp #45 #100]: false
+unsat
+1f0751610d262907ec6f1f51ed51a6cd0992f6da 85 0
+#2 := false
+#9 := 0::Int
+#8 := 1::Int
+#17 := (- 1::Int)
+#18 := (mod #17 #17)
+#19 := (- #18)
+#16 := (mod 1::Int 1::Int)
+#11 := (< 0::Int 1::Int)
+#13 := (< 1::Int 0::Int)
+#14 := (and #13 #11)
+#12 := (and #11 #11)
+#15 := (or #12 #14)
+#20 := (ite #15 #16 #19)
+#10 := (= 1::Int 0::Int)
+#21 := (ite #10 0::Int #20)
+#22 := (ite #10 1::Int #21)
+#23 := (= #22 0::Int)
+#24 := (not #23)
+#106 := (iff #24 false)
+#1 := true
+#101 := (not true)
+#104 := (iff #101 false)
+#105 := [rewrite]: #104
+#102 := (iff #24 #101)
+#99 := (iff #23 true)
+#94 := (= 0::Int 0::Int)
+#97 := (iff #94 true)
+#98 := [rewrite]: #97
+#95 := (iff #23 #94)
+#88 := (ite false 1::Int 0::Int)
+#91 := (= #88 0::Int)
+#92 := [rewrite]: #91
+#89 := (= #22 #88)
+#86 := (= #21 0::Int)
+#81 := (ite false 0::Int 0::Int)
+#84 := (= #81 0::Int)
+#85 := [rewrite]: #84
+#82 := (= #21 #81)
+#79 := (= #20 0::Int)
+#49 := (and #11 #13)
+#52 := (or #11 #49)
+#74 := (ite #52 0::Int 0::Int)
+#77 := (= #74 0::Int)
+#78 := [rewrite]: #77
+#75 := (= #20 #74)
+#72 := (= #19 0::Int)
+#67 := (- 0::Int)
+#70 := (= #67 0::Int)
+#71 := [rewrite]: #70
+#68 := (= #19 #67)
+#65 := (= #18 0::Int)
+#57 := -1::Int
+#60 := (mod -1::Int -1::Int)
+#63 := (= #60 0::Int)
+#64 := [rewrite]: #63
+#61 := (= #18 #60)
+#58 := (= #17 -1::Int)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59 #59]: #61
+#66 := [trans #62 #64]: #65
+#69 := [monotonicity #66]: #68
+#73 := [trans #69 #71]: #72
+#55 := (= #16 0::Int)
+#56 := [rewrite]: #55
+#53 := (iff #15 #52)
+#50 := (iff #14 #49)
+#51 := [rewrite]: #50
+#47 := (iff #12 #11)
+#48 := [rewrite]: #47
+#54 := [monotonicity #48 #51]: #53
+#76 := [monotonicity #54 #56 #73]: #75
+#80 := [trans #76 #78]: #79
+#45 := (iff #10 false)
+#46 := [rewrite]: #45
+#83 := [monotonicity #46 #80]: #82
+#87 := [trans #83 #85]: #86
+#90 := [monotonicity #46 #87]: #89
+#93 := [trans #90 #92]: #23
+#96 := [monotonicity #93]: #95
+#100 := [trans #96 #98]: #99
+#103 := [monotonicity #100]: #102
+#107 := [trans #103 #105]: #106
+#44 := [asserted]: #24
+[mp #44 #107]: false
+unsat
+da01481f3f884bcc8fb68943f21adbedb119b252 92 0
+#2 := false
+#9 := 0::Int
+#8 := 1::Int
+#21 := (- 1::Int)
+#11 := 3::Int
+#20 := (- 3::Int)
+#22 := (mod #20 #21)
+#23 := (- #22)
+#19 := (mod 3::Int 1::Int)
+#14 := (< 0::Int 1::Int)
+#16 := (< 3::Int 0::Int)
+#17 := (and #16 #14)
+#13 := (< 0::Int 3::Int)
+#15 := (and #13 #14)
+#18 := (or #15 #17)
+#24 := (ite #18 #19 #23)
+#12 := (= 3::Int 0::Int)
+#25 := (ite #12 0::Int #24)
+#10 := (= 1::Int 0::Int)
+#26 := (ite #10 3::Int #25)
+#27 := (= #26 0::Int)
+#28 := (not #27)
+#113 := (iff #28 false)
+#1 := true
+#108 := (not true)
+#111 := (iff #108 false)
+#112 := [rewrite]: #111
+#109 := (iff #28 #108)
+#106 := (iff #27 true)
+#101 := (= 0::Int 0::Int)
+#104 := (iff #101 true)
+#105 := [rewrite]: #104
+#102 := (iff #27 #101)
+#95 := (ite false 3::Int 0::Int)
+#98 := (= #95 0::Int)
+#99 := [rewrite]: #98
+#96 := (= #26 #95)
+#93 := (= #25 0::Int)
+#88 := (ite false 0::Int 0::Int)
+#91 := (= #88 0::Int)
+#92 := [rewrite]: #91
+#89 := (= #25 #88)
+#86 := (= #24 0::Int)
+#53 := (and #14 #16)
+#56 := (or #15 #53)
+#81 := (ite #56 0::Int 0::Int)
+#84 := (= #81 0::Int)
+#85 := [rewrite]: #84
+#82 := (= #24 #81)
+#79 := (= #23 0::Int)
+#74 := (- 0::Int)
+#77 := (= #74 0::Int)
+#78 := [rewrite]: #77
+#75 := (= #23 #74)
+#72 := (= #22 0::Int)
+#64 := -1::Int
+#61 := -3::Int
+#67 := (mod -3::Int -1::Int)
+#70 := (= #67 0::Int)
+#71 := [rewrite]: #70
+#68 := (= #22 #67)
+#65 := (= #21 -1::Int)
+#66 := [rewrite]: #65
+#62 := (= #20 -3::Int)
+#63 := [rewrite]: #62
+#69 := [monotonicity #63 #66]: #68
+#73 := [trans #69 #71]: #72
+#76 := [monotonicity #73]: #75
+#80 := [trans #76 #78]: #79
+#59 := (= #19 0::Int)
+#60 := [rewrite]: #59
+#57 := (iff #18 #56)
+#54 := (iff #17 #53)
+#55 := [rewrite]: #54
+#58 := [monotonicity #55]: #57
+#83 := [monotonicity #58 #60 #80]: #82
+#87 := [trans #83 #85]: #86
+#51 := (iff #12 false)
+#52 := [rewrite]: #51
+#90 := [monotonicity #52 #87]: #89
+#94 := [trans #90 #92]: #93
+#49 := (iff #10 false)
+#50 := [rewrite]: #49
+#97 := [monotonicity #50 #94]: #96
+#100 := [trans #97 #99]: #27
+#103 := [monotonicity #100]: #102
+#107 := [trans #103 #105]: #106
+#110 := [monotonicity #107]: #109
+#114 := [trans #110 #112]: #113
+#48 := [asserted]: #28
+[mp #48 #114]: false
+unsat
+eb6e7e04e393e3fdf7579776e17a2526d7e7757f 156 0
+#2 := false
+#9 := 0::Int
+decl f3 :: Int
+#11 := f3
+#122 := (>= f3 0::Int)
+#123 := (not #122)
+#109 := (<= f3 0::Int)
+#110 := (not #109)
+#12 := (= f3 0::Int)
+#141 := (or #12 #110 #123)
+#172 := (not #141)
+#62 := -1::Int
+#63 := (* -1::Int f3)
+#68 := (mod #63 -1::Int)
+#74 := (* -1::Int #68)
+#146 := (ite #141 0::Int #74)
+#153 := (= #146 0::Int)
+#157 := (not #153)
+#8 := 1::Int
+#21 := (- 1::Int)
+#20 := (- f3)
+#22 := (mod #20 #21)
+#23 := (- #22)
+#19 := (mod f3 1::Int)
+#14 := (< 0::Int 1::Int)
+#16 := (< f3 0::Int)
+#17 := (and #16 #14)
+#13 := (< 0::Int f3)
+#15 := (and #13 #14)
+#18 := (or #15 #17)
+#24 := (ite #18 #19 #23)
+#25 := (ite #12 0::Int #24)
+#10 := (= 1::Int 0::Int)
+#26 := (ite #10 f3 #25)
+#27 := (= #26 0::Int)
+#28 := (not #27)
+#160 := (iff #28 #157)
+#54 := (and #14 #16)
+#57 := (or #15 #54)
+#51 := (= 0::Int f3)
+#85 := (or #51 #57)
+#86 := (ite #85 0::Int #74)
+#101 := (= 0::Int #86)
+#106 := (not #101)
+#158 := (iff #106 #157)
+#155 := (iff #101 #153)
+#149 := (= 0::Int #146)
+#152 := (iff #149 #153)
+#154 := [rewrite]: #152
+#150 := (iff #101 #149)
+#147 := (= #86 #146)
+#144 := (iff #85 #141)
+#135 := (or #110 #123)
+#138 := (or #12 #135)
+#142 := (iff #138 #141)
 #143 := [rewrite]: #142
-#153 := [monotonicity #143 #150]: #152
-#145 := (iff #24 #144)
-#138 := (iff #22 #137)
-#139 := [rewrite]: #138
-#146 := [monotonicity #139 #143]: #145
-#156 := [monotonicity #146 #153]: #155
-#159 := [monotonicity #156]: #158
-#134 := (iff #100 #21)
-#132 := (iff #97 #20)
-#133 := [rewrite]: #132
-#130 := (iff #94 #19)
-#131 := [rewrite]: #130
-#135 := [monotonicity #131 #133]: #134
-#162 := [monotonicity #135 #159]: #161
-#165 := [monotonicity #162]: #164
-#168 := [quant-intro #165]: #167
-#128 := (iff #35 #127)
-#125 := (iff #34 #124)
-#122 := (= #33 #121)
-#119 := (= #32 #118)
-#116 := (= #31 #115)
-#113 := (= #30 #112)
+#139 := (iff #85 #138)
+#136 := (iff #57 #135)
+#131 := (iff #54 #123)
+#1 := true
+#126 := (and true #123)
+#129 := (iff #126 #123)
+#130 := [rewrite]: #129
+#127 := (iff #54 #126)
+#124 := (iff #16 #123)
+#125 := [rewrite]: #124
+#113 := (iff #14 true)
 #114 := [rewrite]: #113
-#110 := (= #29 #109)
-#111 := [rewrite]: #110
-#117 := [monotonicity #111 #114]: #116
-#107 := (iff #27 #106)
-#104 := (iff #26 #103)
-#105 := [rewrite]: #104
+#128 := [monotonicity #114 #125]: #127
+#132 := [trans #128 #130]: #131
+#120 := (iff #15 #110)
+#115 := (and #110 true)
+#118 := (iff #115 #110)
+#119 := [rewrite]: #118
+#116 := (iff #15 #115)
+#111 := (iff #13 #110)
+#112 := [rewrite]: #111
+#117 := [monotonicity #112 #114]: #116
+#121 := [trans #117 #119]: #120
+#137 := [monotonicity #121 #132]: #136
+#133 := (iff #51 #12)
+#134 := [rewrite]: #133
+#140 := [monotonicity #134 #137]: #139
+#145 := [trans #140 #143]: #144
+#148 := [monotonicity #145]: #147
+#151 := [monotonicity #148]: #150
+#156 := [trans #151 #154]: #155
+#159 := [monotonicity #156]: #158
+#107 := (iff #28 #106)
+#104 := (iff #27 #101)
+#98 := (= #86 0::Int)
+#102 := (iff #98 #101)
+#103 := [rewrite]: #102
+#99 := (iff #27 #98)
+#96 := (= #26 #86)
+#91 := (ite false f3 #86)
+#94 := (= #91 #86)
+#95 := [rewrite]: #94
+#92 := (= #26 #91)
+#89 := (= #25 #86)
+#79 := (ite #57 0::Int #74)
+#82 := (ite #51 0::Int #79)
+#87 := (= #82 #86)
+#88 := [rewrite]: #87
+#83 := (= #25 #82)
+#80 := (= #24 #79)
+#77 := (= #23 #74)
+#71 := (- #68)
+#75 := (= #71 #74)
+#76 := [rewrite]: #75
+#72 := (= #23 #71)
+#69 := (= #22 #68)
+#66 := (= #21 -1::Int)
+#67 := [rewrite]: #66
+#64 := (= #20 #63)
+#65 := [rewrite]: #64
+#70 := [monotonicity #65 #67]: #69
+#73 := [monotonicity #70]: #72
+#78 := [trans #73 #76]: #77
+#60 := (= #19 0::Int)
+#61 := [rewrite]: #60
+#58 := (iff #18 #57)
+#55 := (iff #17 #54)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#81 := [monotonicity #59 #61 #78]: #80
+#52 := (iff #12 #51)
+#53 := [rewrite]: #52
+#84 := [monotonicity #53 #81]: #83
+#90 := [trans #84 #88]: #89
+#49 := (iff #10 false)
+#50 := [rewrite]: #49
+#93 := [monotonicity #50 #90]: #92
+#97 := [trans #93 #95]: #96
+#100 := [monotonicity #97]: #99
+#105 := [trans #100 #103]: #104
 #108 := [monotonicity #105]: #107
-#120 := [monotonicity #108 #117]: #119
-#101 := (iff #21 #100)
-#98 := (iff #20 #97)
-#99 := [rewrite]: #98
-#95 := (iff #19 #94)
-#96 := [rewrite]: #95
-#102 := [monotonicity #96 #99]: #101
-#123 := [monotonicity #102 #120]: #122
-#126 := [monotonicity #123]: #125
-#129 := [quant-intro #126]: #128
-#170 := [trans #129 #168]: #169
-#93 := [asserted]: #35
-#171 := [mp #93 #170]: #166
-#220 := [mp~ #171 #229]: #166
-#251 := [mp #220 #250]: #248
-#282 := [mp #251 #281]: #279
-#775 := [mp #282 #774]: #770
-#68 := -3::Int
-#71 := (f3 -1::Int -3::Int)
-#74 := (= #71 0::Int)
-#87 := (not #74)
-#10 := 3::Int
-#11 := (- 3::Int)
+#161 := [trans #108 #159]: #160
+#48 := [asserted]: #28
+#162 := [mp #48 #161]: #157
+#175 := (or #172 #153)
+#176 := [def-axiom]: #175
+#233 := [unit-resolution #176 #162]: #172
+#164 := (or #141 #122)
+#165 := [def-axiom]: #164
+#234 := [unit-resolution #165 #233]: #122
+#166 := (or #141 #109)
+#167 := [def-axiom]: #166
+#235 := [unit-resolution #167 #233]: #109
+#169 := (not #12)
+#170 := (or #141 #169)
+#171 := [def-axiom]: #170
+#236 := [unit-resolution #171 #233]: #169
+#237 := [th-lemma arith triangle-eq]: #141
+[unit-resolution #237 #236 #235 #234]: false
+unsat
+106013bb1f998104836223245ab92e3b99397a07 107 0
+#2 := false
+#10 := 0::Int
 #8 := 1::Int
 #9 := (- 1::Int)
-#12 := (f3 #9 #11)
-#14 := (= #12 0::Int)
-#15 := (not #14)
-#90 := (iff #15 #87)
-#77 := (= 0::Int #71)
-#82 := (not #77)
-#88 := (iff #82 #87)
-#85 := (iff #77 #74)
-#86 := [rewrite]: #85
-#89 := [monotonicity #86]: #88
-#83 := (iff #15 #82)
-#80 := (iff #14 #77)
-#78 := (iff #74 #77)
-#79 := [rewrite]: #78
-#75 := (iff #14 #74)
-#72 := (= #12 #71)
-#69 := (= #11 -3::Int)
-#70 := [rewrite]: #69
-#66 := (= #9 -1::Int)
-#67 := [rewrite]: #66
+#19 := (- #9)
+#18 := (- 0::Int)
+#20 := (mod #18 #19)
+#21 := (- #20)
+#17 := (mod 0::Int #9)
+#14 := (< 0::Int #9)
+#13 := (< 0::Int 0::Int)
+#15 := (and #13 #14)
+#16 := (or #15 #15)
+#22 := (ite #16 #17 #21)
+#12 := (= 0::Int 0::Int)
+#23 := (ite #12 0::Int #22)
+#11 := (= #9 0::Int)
+#24 := (ite #11 0::Int #23)
+#25 := (= #24 0::Int)
+#26 := (not #25)
+#128 := (iff #26 false)
+#1 := true
+#123 := (not true)
+#126 := (iff #123 false)
+#127 := [rewrite]: #126
+#124 := (iff #26 #123)
+#121 := (iff #25 true)
+#57 := (iff #12 true)
+#58 := [rewrite]: #57
+#119 := (iff #25 #12)
+#113 := (ite false 0::Int 0::Int)
+#116 := (= #113 0::Int)
+#117 := [rewrite]: #116
+#114 := (= #24 #113)
+#111 := (= #23 0::Int)
+#106 := (ite true 0::Int 0::Int)
+#109 := (= #106 0::Int)
+#110 := [rewrite]: #109
+#107 := (= #23 #106)
+#104 := (= #22 0::Int)
+#47 := -1::Int
+#59 := (< 0::Int -1::Int)
+#62 := (and #13 #59)
+#99 := (ite #62 0::Int 0::Int)
+#102 := (= #99 0::Int)
+#103 := [rewrite]: #102
+#100 := (= #22 #99)
+#97 := (= #21 0::Int)
+#79 := (= #18 0::Int)
+#80 := [rewrite]: #79
+#95 := (= #21 #18)
+#93 := (= #20 0::Int)
+#88 := (mod 0::Int 1::Int)
+#91 := (= #88 0::Int)
+#92 := [rewrite]: #91
+#89 := (= #20 #88)
+#86 := (= #19 1::Int)
+#81 := (- -1::Int)
+#84 := (= #81 1::Int)
+#85 := [rewrite]: #84
+#82 := (= #19 #81)
+#48 := (= #9 -1::Int)
+#49 := [rewrite]: #48
+#83 := [monotonicity #49]: #82
+#87 := [trans #83 #85]: #86
+#90 := [monotonicity #80 #87]: #89
+#94 := [trans #90 #92]: #93
+#96 := [monotonicity #94]: #95
+#98 := [trans #96 #80]: #97
+#77 := (= #17 0::Int)
+#72 := (mod 0::Int -1::Int)
+#75 := (= #72 0::Int)
+#76 := [rewrite]: #75
+#73 := (= #17 #72)
+#74 := [monotonicity #49]: #73
+#78 := [trans #74 #76]: #77
+#70 := (iff #16 #62)
+#65 := (or #62 #62)
+#68 := (iff #65 #62)
+#69 := [rewrite]: #68
+#66 := (iff #16 #65)
+#63 := (iff #15 #62)
+#60 := (iff #14 #59)
+#61 := [monotonicity #49]: #60
+#64 := [monotonicity #61]: #63
+#67 := [monotonicity #64 #64]: #66
+#71 := [trans #67 #69]: #70
+#101 := [monotonicity #71 #78 #98]: #100
+#105 := [trans #101 #103]: #104
+#108 := [monotonicity #58 #105]: #107
+#112 := [trans #108 #110]: #111
+#55 := (iff #11 false)
+#50 := (= -1::Int 0::Int)
+#53 := (iff #50 false)
+#54 := [rewrite]: #53
+#51 := (iff #11 #50)
+#52 := [monotonicity #49]: #51
+#56 := [trans #52 #54]: #55
+#115 := [monotonicity #56 #112]: #114
+#118 := [trans #115 #117]: #25
+#120 := [monotonicity #118]: #119
+#122 := [trans #120 #58]: #121
+#125 := [monotonicity #122]: #124
+#129 := [trans #125 #127]: #128
+#46 := [asserted]: #26
+[mp #46 #129]: false
+unsat
+8d5198a1caadbe07ee33787baa9fbc0f66546c9a 111 0
+#2 := false
+#10 := 0::Int
+#8 := 1::Int
+#9 := (- 1::Int)
+#20 := (- #9)
+#21 := (mod #9 #20)
+#22 := (- #21)
+#19 := (mod 1::Int #9)
+#14 := (< 0::Int #9)
+#16 := (< 1::Int 0::Int)
+#17 := (and #16 #14)
+#13 := (< 0::Int 1::Int)
+#15 := (and #13 #14)
+#18 := (or #15 #17)
+#23 := (ite #18 #19 #22)
+#12 := (= 1::Int 0::Int)
+#24 := (ite #12 0::Int #23)
+#11 := (= #9 0::Int)
+#25 := (ite #11 1::Int #24)
+#26 := (= #25 0::Int)
+#27 := (not #26)
+#132 := (iff #27 false)
+#1 := true
+#127 := (not true)
+#130 := (iff #127 false)
+#131 := [rewrite]: #130
+#128 := (iff #27 #127)
+#125 := (iff #26 true)
+#120 := (= 0::Int 0::Int)
+#123 := (iff #120 true)
+#124 := [rewrite]: #123
+#121 := (iff #26 #120)
+#114 := (ite false 1::Int 0::Int)
+#117 := (= #114 0::Int)
+#118 := [rewrite]: #117
+#115 := (= #25 #114)
+#112 := (= #24 0::Int)
+#107 := (ite false 0::Int 0::Int)
+#110 := (= #107 0::Int)
+#111 := [rewrite]: #110
+#108 := (= #24 #107)
+#105 := (= #23 0::Int)
+#48 := -1::Int
+#60 := (< 0::Int -1::Int)
+#66 := (and #16 #60)
+#63 := (and #13 #60)
+#69 := (or #63 #66)
+#100 := (ite #69 0::Int 0::Int)
+#103 := (= #100 0::Int)
+#104 := [rewrite]: #103
+#101 := (= #23 #100)
+#98 := (= #22 0::Int)
+#93 := (- 0::Int)
+#96 := (= #93 0::Int)
+#97 := [rewrite]: #96
+#94 := (= #22 #93)
+#91 := (= #21 0::Int)
+#86 := (mod -1::Int 1::Int)
+#89 := (= #86 0::Int)
+#90 := [rewrite]: #89
+#87 := (= #21 #86)
+#84 := (= #20 1::Int)
+#79 := (- -1::Int)
+#82 := (= #79 1::Int)
+#83 := [rewrite]: #82
+#80 := (= #20 #79)
+#49 := (= #9 -1::Int)
+#50 := [rewrite]: #49
+#81 := [monotonicity #50]: #80
+#85 := [trans #81 #83]: #84
+#88 := [monotonicity #50 #85]: #87
+#92 := [trans #88 #90]: #91
+#95 := [monotonicity #92]: #94
+#99 := [trans #95 #97]: #98
+#77 := (= #19 0::Int)
+#72 := (mod 1::Int -1::Int)
+#75 := (= #72 0::Int)
+#76 := [rewrite]: #75
+#73 := (= #19 #72)
+#74 := [monotonicity #50]: #73
+#78 := [trans #74 #76]: #77
+#70 := (iff #18 #69)
+#67 := (iff #17 #66)
+#61 := (iff #14 #60)
+#62 := [monotonicity #50]: #61
+#68 := [monotonicity #62]: #67
+#64 := (iff #15 #63)
+#65 := [monotonicity #62]: #64
+#71 := [monotonicity #65 #68]: #70
+#102 := [monotonicity #71 #78 #99]: #101
+#106 := [trans #102 #104]: #105
+#58 := (iff #12 false)
+#59 := [rewrite]: #58
+#109 := [monotonicity #59 #106]: #108
+#113 := [trans #109 #111]: #112
+#56 := (iff #11 false)
+#51 := (= -1::Int 0::Int)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #11 #51)
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#116 := [monotonicity #57 #113]: #115
+#119 := [trans #116 #118]: #26
+#122 := [monotonicity #119]: #121
+#126 := [trans #122 #124]: #125
+#129 := [monotonicity #126]: #128
+#133 := [trans #129 #131]: #132
+#47 := [asserted]: #27
+[mp #47 #133]: false
+unsat
+3e5306453747f88fb9407b2be361e50903b04cbd 116 0
+#2 := false
+#10 := 0::Int
+#8 := 1::Int
+#9 := (- 1::Int)
+#22 := (- #9)
+#12 := 3::Int
+#21 := (- 3::Int)
+#23 := (mod #21 #22)
+#24 := (- #23)
+#20 := (mod 3::Int #9)
+#15 := (< 0::Int #9)
+#17 := (< 3::Int 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int 3::Int)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#25 := (ite #19 #20 #24)
+#13 := (= 3::Int 0::Int)
+#26 := (ite #13 0::Int #25)
+#11 := (= #9 0::Int)
+#27 := (ite #11 3::Int #26)
+#28 := (= #27 0::Int)
+#29 := (not #28)
+#137 := (iff #29 false)
+#1 := true
+#132 := (not true)
+#135 := (iff #132 false)
+#136 := [rewrite]: #135
+#133 := (iff #29 #132)
+#130 := (iff #28 true)
+#125 := (= 0::Int 0::Int)
+#128 := (iff #125 true)
+#129 := [rewrite]: #128
+#126 := (iff #28 #125)
+#119 := (ite false 3::Int 0::Int)
+#122 := (= #119 0::Int)
+#123 := [rewrite]: #122
+#120 := (= #27 #119)
+#117 := (= #26 0::Int)
+#112 := (ite false 0::Int 0::Int)
+#115 := (= #112 0::Int)
+#116 := [rewrite]: #115
+#113 := (= #26 #112)
+#110 := (= #25 0::Int)
+#50 := -1::Int
+#62 := (< 0::Int -1::Int)
+#68 := (and #17 #62)
+#65 := (and #14 #62)
+#71 := (or #65 #68)
+#105 := (ite #71 0::Int 0::Int)
+#108 := (= #105 0::Int)
+#109 := [rewrite]: #108
+#106 := (= #25 #105)
+#103 := (= #24 0::Int)
+#98 := (- 0::Int)
+#101 := (= #98 0::Int)
+#102 := [rewrite]: #101
+#99 := (= #24 #98)
+#96 := (= #23 0::Int)
+#81 := -3::Int
+#91 := (mod -3::Int 1::Int)
+#94 := (= #91 0::Int)
+#95 := [rewrite]: #94
+#92 := (= #23 #91)
+#89 := (= #22 1::Int)
+#84 := (- -1::Int)
+#87 := (= #84 1::Int)
+#88 := [rewrite]: #87
+#85 := (= #22 #84)
+#51 := (= #9 -1::Int)
+#52 := [rewrite]: #51
+#86 := [monotonicity #52]: #85
+#90 := [trans #86 #88]: #89
+#82 := (= #21 -3::Int)
+#83 := [rewrite]: #82
+#93 := [monotonicity #83 #90]: #92
+#97 := [trans #93 #95]: #96
+#100 := [monotonicity #97]: #99
+#104 := [trans #100 #102]: #103
+#79 := (= #20 0::Int)
+#74 := (mod 3::Int -1::Int)
+#77 := (= #74 0::Int)
+#78 := [rewrite]: #77
+#75 := (= #20 #74)
+#76 := [monotonicity #52]: #75
+#80 := [trans #76 #78]: #79
+#72 := (iff #19 #71)
+#69 := (iff #18 #68)
+#63 := (iff #15 #62)
+#64 := [monotonicity #52]: #63
+#70 := [monotonicity #64]: #69
+#66 := (iff #16 #65)
+#67 := [monotonicity #64]: #66
 #73 := [monotonicity #67 #70]: #72
-#76 := [monotonicity #73]: #75
-#81 := [trans #76 #79]: #80
-#84 := [monotonicity #81]: #83
-#91 := [trans #84 #89]: #90
-#64 := [asserted]: #15
-#92 := [mp #64 #91]: #87
-#694 := (not #770)
-#695 := (or #694 #74)
-#356 := (* -1::Int -3::Int)
-#440 := (* -1::Int -1::Int)
-#441 := (div #440 #356)
-#442 := (* -1::Int #441)
-#433 := (+ #71 #442)
-#444 := (= #433 0::Int)
-#445 := (div -1::Int -3::Int)
-#446 := (* -1::Int #445)
-#443 := (+ #71 #446)
-#447 := (= #443 0::Int)
-#426 := (>= -1::Int 0::Int)
-#761 := (<= -3::Int 0::Int)
-#763 := (or #761 #426)
-#420 := (not #763)
-#550 := (<= -1::Int 0::Int)
-#757 := (or #550 #761)
-#431 := (not #757)
-#432 := (or #431 #420)
-#764 := (ite #432 #447 #444)
-#765 := (= -3::Int 0::Int)
-#766 := (= -1::Int 0::Int)
-#767 := (or #766 #765)
-#762 := (ite #767 #74 #764)
-#696 := (or #694 #762)
-#697 := (iff #696 #695)
-#687 := (iff #695 #695)
-#688 := [rewrite]: #687
-#682 := (iff #762 #74)
-#700 := (ite false #74 #74)
-#693 := (iff #700 #74)
-#685 := [rewrite]: #693
-#704 := (iff #762 #700)
-#610 := (iff #764 #74)
-#714 := (= #71 1::Int)
-#598 := (ite false #714 #74)
-#608 := (iff #598 #74)
-#609 := [rewrite]: #608
-#606 := (iff #764 #598)
-#604 := (iff #444 #74)
-#587 := (= #433 #71)
-#701 := (+ #71 0::Int)
-#699 := (= #701 #71)
-#702 := [rewrite]: #699
-#603 := (= #433 #701)
-#594 := (= #442 0::Int)
-#709 := (* -1::Int 0::Int)
-#592 := (= #709 0::Int)
-#593 := [rewrite]: #592
-#707 := (= #442 #709)
-#706 := (= #441 0::Int)
-#720 := (div 1::Int 3::Int)
-#552 := (= #720 0::Int)
-#705 := [rewrite]: #552
-#549 := (= #441 #720)
-#719 := (= #356 3::Int)
-#713 := [rewrite]: #719
-#712 := (= #440 1::Int)
-#718 := [rewrite]: #712
-#551 := [monotonicity #718 #713]: #549
-#708 := [trans #551 #705]: #706
-#710 := [monotonicity #708]: #707
-#553 := [trans #710 #593]: #594
-#698 := [monotonicity #553]: #603
-#602 := [trans #698 #702]: #587
-#605 := [monotonicity #602]: #604
-#717 := (iff #447 #714)
-#722 := (+ -1::Int #71)
-#570 := (= #722 0::Int)
-#715 := (iff #570 #714)
-#716 := [rewrite]: #715
-#571 := (iff #447 #570)
-#723 := (= #443 #722)
-#725 := (+ #71 -1::Int)
-#727 := (= #725 #722)
-#728 := [rewrite]: #727
-#726 := (= #443 #725)
-#735 := (= #446 -1::Int)
-#733 := (* -1::Int 1::Int)
-#734 := (= #733 -1::Int)
-#731 := [rewrite]: #734
-#448 := (= #446 #733)
-#454 := (= #445 1::Int)
-#732 := [rewrite]: #454
-#730 := [monotonicity #732]: #448
-#724 := [trans #730 #731]: #735
-#721 := [monotonicity #724]: #726
-#729 := [trans #721 #728]: #723
-#572 := [monotonicity #729]: #571
-#711 := [trans #572 #716]: #717
-#452 := (iff #432 false)
-#759 := (or false false)
-#403 := (iff #759 false)
-#744 := [rewrite]: #403
-#741 := (iff #432 #759)
-#740 := (iff #420 false)
-#1 := true
-#754 := (not true)
-#755 := (iff #754 false)
-#753 := [rewrite]: #755
-#462 := (iff #420 #754)
-#739 := (iff #763 true)
-#466 := (or true false)
-#362 := (iff #466 true)
-#738 := [rewrite]: #362
-#467 := (iff #763 #466)
-#743 := (iff #426 false)
-#465 := [rewrite]: #743
-#746 := (iff #761 true)
-#747 := [rewrite]: #746
-#468 := [monotonicity #747 #465]: #467
-#461 := [trans #468 #738]: #739
-#736 := [monotonicity #461]: #462
-#737 := [trans #736 #753]: #740
-#756 := (iff #431 false)
-#394 := (iff #431 #754)
-#389 := (iff #757 true)
-#748 := (or true true)
-#745 := (iff #748 true)
-#751 := [rewrite]: #745
-#749 := (iff #757 #748)
-#409 := (iff #550 true)
-#410 := [rewrite]: #409
-#750 := [monotonicity #410 #747]: #749
-#752 := [trans #750 #751]: #389
-#395 := [monotonicity #752]: #394
-#742 := [trans #395 #753]: #756
-#451 := [monotonicity #742 #737]: #741
-#453 := [trans #451 #744]: #452
-#607 := [monotonicity #453 #711 #605]: #606
-#703 := [trans #607 #609]: #610
-#407 := (iff #767 false)
-#419 := (iff #767 #759)
-#418 := (iff #765 false)
-#423 := [rewrite]: #418
-#768 := (iff #766 false)
-#758 := [rewrite]: #768
-#760 := [monotonicity #758 #423]: #419
-#408 := [trans #760 #744]: #407
-#691 := [monotonicity #408 #703]: #704
-#684 := [trans #691 #685]: #682
-#686 := [monotonicity #684]: #697
-#689 := [trans #686 #688]: #697
-#692 := [quant-inst #65 #68]: #696
-#683 := [mp #692 #689]: #695
-[unit-resolution #683 #92 #775]: false
-unsat
-67c5769d49bd3d505a24355d203b30bb2a6d4f8d 306 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#15 := (:var 0 Int)
-#14 := (:var 1 Int)
-#16 := (f3 #14 #15)
-#751 := (pattern #16)
-#17 := 0::Int
-#96 := -1::Int
-#100 := (* -1::Int #15)
-#97 := (* -1::Int #14)
-#103 := (div #97 #100)
-#254 := (* -1::Int #103)
-#255 := (+ #16 #254)
-#256 := (= #255 0::Int)
-#27 := (div #14 #15)
-#251 := (* -1::Int #27)
-#252 := (+ #16 #251)
-#253 := (= #252 0::Int)
-#129 := (>= #14 0::Int)
-#122 := (<= #15 0::Int)
-#214 := (or #122 #129)
-#215 := (not #214)
-#118 := (<= #14 0::Int)
-#212 := (or #118 #122)
-#213 := (not #212)
-#218 := (or #213 #215)
-#257 := (ite #218 #253 #256)
-#250 := (= #16 0::Int)
-#19 := (= #15 0::Int)
-#18 := (= #14 0::Int)
-#20 := (or #18 #19)
-#258 := (ite #20 #250 #257)
-#752 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #751) #258)
-#261 := (forall (vars (?v0 Int) (?v1 Int)) #258)
-#755 := (iff #261 #752)
-#753 := (iff #258 #258)
-#754 := [refl]: #753
-#756 := [quant-intro #754]: #755
-#221 := (ite #218 #27 #103)
-#224 := (ite #20 0::Int #221)
-#227 := (= #16 #224)
-#230 := (forall (vars (?v0 Int) (?v1 Int)) #227)
-#262 := (iff #230 #261)
-#259 := (iff #227 #258)
-#260 := [rewrite]: #259
-#263 := [quant-intro #260]: #262
-#130 := (not #129)
-#123 := (not #122)
-#133 := (and #123 #130)
-#119 := (not #118)
-#126 := (and #119 #123)
-#136 := (or #126 #133)
-#139 := (ite #136 #27 #103)
-#142 := (ite #20 0::Int #139)
-#145 := (= #16 #142)
-#148 := (forall (vars (?v0 Int) (?v1 Int)) #145)
-#231 := (iff #148 #230)
-#228 := (iff #145 #227)
-#225 := (= #142 #224)
-#222 := (= #139 #221)
-#219 := (iff #136 #218)
-#216 := (iff #133 #215)
-#217 := [rewrite]: #216
-#206 := (iff #126 #213)
-#207 := [rewrite]: #206
-#220 := [monotonicity #207 #217]: #219
-#223 := [monotonicity #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [quant-intro #229]: #231
-#210 := (~ #148 #148)
-#208 := (~ #145 #145)
-#209 := [refl]: #208
-#211 := [nnf-pos #209]: #210
-#29 := (- #15)
-#28 := (- #14)
-#30 := (div #28 #29)
-#22 := (< 0::Int #15)
-#24 := (< #14 0::Int)
-#25 := (and #24 #22)
-#21 := (< 0::Int #14)
-#23 := (and #21 #22)
-#26 := (or #23 #25)
-#31 := (ite #26 #27 #30)
-#32 := (ite #20 0::Int #31)
-#33 := (= #16 #32)
-#34 := (forall (vars (?v0 Int) (?v1 Int)) #33)
-#151 := (iff #34 #148)
-#90 := (and #22 #24)
-#93 := (or #23 #90)
-#106 := (ite #93 #27 #103)
-#109 := (ite #20 0::Int #106)
-#112 := (= #16 #109)
-#115 := (forall (vars (?v0 Int) (?v1 Int)) #112)
-#149 := (iff #115 #148)
-#146 := (iff #112 #145)
-#143 := (= #109 #142)
-#140 := (= #106 #139)
-#137 := (iff #93 #136)
-#134 := (iff #90 #133)
-#131 := (iff #24 #130)
-#132 := [rewrite]: #131
-#124 := (iff #22 #123)
-#125 := [rewrite]: #124
-#135 := [monotonicity #125 #132]: #134
-#127 := (iff #23 #126)
-#120 := (iff #21 #119)
-#121 := [rewrite]: #120
-#128 := [monotonicity #121 #125]: #127
-#138 := [monotonicity #128 #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [quant-intro #147]: #149
-#116 := (iff #34 #115)
-#113 := (iff #33 #112)
-#110 := (= #32 #109)
-#107 := (= #31 #106)
-#104 := (= #30 #103)
-#101 := (= #29 #100)
-#102 := [rewrite]: #101
-#98 := (= #28 #97)
+#107 := [monotonicity #73 #80 #104]: #106
+#111 := [trans #107 #109]: #110
+#60 := (iff #13 false)
+#61 := [rewrite]: #60
+#114 := [monotonicity #61 #111]: #113
+#118 := [trans #114 #116]: #117
+#58 := (iff #11 false)
+#53 := (= -1::Int 0::Int)
+#56 := (iff #53 false)
+#57 := [rewrite]: #56
+#54 := (iff #11 #53)
+#55 := [monotonicity #52]: #54
+#59 := [trans #55 #57]: #58
+#121 := [monotonicity #59 #118]: #120
+#124 := [trans #121 #123]: #28
+#127 := [monotonicity #124]: #126
+#131 := [trans #127 #129]: #130
+#134 := [monotonicity #131]: #133
+#138 := [trans #134 #136]: #137
+#49 := [asserted]: #29
+[mp #49 #138]: false
+unsat
+56a38afd92c36cbda7ea0320ace529eafcdd0527 180 0
+#2 := false
+#10 := 0::Int
+#8 := 1::Int
+#9 := (- 1::Int)
+#22 := (- #9)
+decl f3 :: Int
+#12 := f3
+#21 := (- f3)
+#23 := (mod #21 #22)
+#24 := (- #23)
+#20 := (mod f3 #9)
+#15 := (< 0::Int #9)
+#17 := (< f3 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int f3)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#25 := (ite #19 #20 #24)
+#13 := (= f3 0::Int)
+#26 := (ite #13 0::Int #25)
+#11 := (= #9 0::Int)
+#27 := (ite #11 f3 #26)
+#28 := (= #27 0::Int)
+#29 := (not #28)
+#200 := (iff #29 false)
+#50 := -1::Int
+#75 := (mod f3 -1::Int)
+#63 := (< 0::Int -1::Int)
+#69 := (and #17 #63)
+#66 := (and #14 #63)
+#72 := (or #66 #69)
+#108 := (not #72)
+#60 := (= 0::Int f3)
+#109 := (or #60 #108)
+#110 := (ite #109 0::Int #75)
+#125 := (= 0::Int #110)
+#130 := (not #125)
+#198 := (iff #130 false)
+#1 := true
+#193 := (not true)
+#196 := (iff #193 false)
+#197 := [rewrite]: #196
+#194 := (iff #130 #193)
+#191 := (iff #125 true)
+#186 := (= 0::Int 0::Int)
+#189 := (iff #186 true)
+#190 := [rewrite]: #189
+#187 := (iff #125 #186)
+#122 := (= #110 0::Int)
+#180 := (ite true 0::Int #75)
+#183 := (= #180 0::Int)
+#184 := [rewrite]: #183
+#181 := (= #110 #180)
+#178 := (iff #109 true)
+#173 := (or #13 true)
+#176 := (iff #173 true)
+#177 := [rewrite]: #176
+#174 := (iff #109 #173)
+#171 := (iff #108 true)
+#166 := (not false)
+#169 := (iff #166 true)
+#170 := [rewrite]: #169
+#167 := (iff #108 #166)
+#164 := (iff #72 false)
+#159 := (or false false)
+#162 := (iff #159 false)
+#163 := [rewrite]: #162
+#160 := (iff #72 #159)
+#157 := (iff #69 false)
+#148 := (>= f3 0::Int)
+#149 := (not #148)
+#152 := (and #149 false)
+#155 := (iff #152 false)
+#156 := [rewrite]: #155
+#153 := (iff #69 #152)
+#139 := (iff #63 false)
+#140 := [rewrite]: #139
+#150 := (iff #17 #149)
+#151 := [rewrite]: #150
+#154 := [monotonicity #151 #140]: #153
+#158 := [trans #154 #156]: #157
+#146 := (iff #66 false)
+#135 := (<= f3 0::Int)
+#136 := (not #135)
+#141 := (and #136 false)
+#144 := (iff #141 false)
+#145 := [rewrite]: #144
+#142 := (iff #66 #141)
+#137 := (iff #14 #136)
+#138 := [rewrite]: #137
+#143 := [monotonicity #138 #140]: #142
+#147 := [trans #143 #145]: #146
+#161 := [monotonicity #147 #158]: #160
+#165 := [trans #161 #163]: #164
+#168 := [monotonicity #165]: #167
+#172 := [trans #168 #170]: #171
+#133 := (iff #60 #13)
+#134 := [rewrite]: #133
+#175 := [monotonicity #134 #172]: #174
+#179 := [trans #175 #177]: #178
+#182 := [monotonicity #179]: #181
+#185 := [trans #182 #184]: #122
+#188 := [monotonicity #185]: #187
+#192 := [trans #188 #190]: #191
+#195 := [monotonicity #192]: #194
+#199 := [trans #195 #197]: #198
+#131 := (iff #29 #130)
+#128 := (iff #28 #125)
+#126 := (iff #122 #125)
+#127 := [rewrite]: #126
+#123 := (iff #28 #122)
+#120 := (= #27 #110)
+#115 := (ite false f3 #110)
+#118 := (= #115 #110)
+#119 := [rewrite]: #118
+#116 := (= #27 #115)
+#113 := (= #26 #110)
+#102 := (ite #72 #75 0::Int)
+#105 := (ite #60 0::Int #102)
+#111 := (= #105 #110)
+#112 := [rewrite]: #111
+#106 := (= #26 #105)
+#103 := (= #25 #102)
+#100 := (= #24 0::Int)
+#95 := (- 0::Int)
+#98 := (= #95 0::Int)
 #99 := [rewrite]: #98
-#105 := [monotonicity #99 #102]: #104
-#94 := (iff #26 #93)
-#91 := (iff #25 #90)
+#96 := (= #24 #95)
+#93 := (= #23 0::Int)
+#78 := (* -1::Int f3)
+#88 := (mod #78 1::Int)
+#91 := (= #88 0::Int)
 #92 := [rewrite]: #91
-#95 := [monotonicity #92]: #94
-#108 := [monotonicity #95 #105]: #107
-#111 := [monotonicity #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [quant-intro #114]: #116
-#152 := [trans #117 #150]: #151
-#89 := [asserted]: #34
-#153 := [mp #89 #152]: #148
-#202 := [mp~ #153 #211]: #148
-#233 := [mp #202 #232]: #230
-#264 := [mp #233 #263]: #261
-#757 := [mp #264 #756]: #752
-#11 := 1::Int
-#64 := -3::Int
-#67 := (f3 -3::Int -3::Int)
-#70 := (= #67 1::Int)
-#83 := (not #70)
+#89 := (= #23 #88)
+#86 := (= #22 1::Int)
+#81 := (- -1::Int)
+#84 := (= #81 1::Int)
+#85 := [rewrite]: #84
+#82 := (= #22 #81)
+#51 := (= #9 -1::Int)
+#52 := [rewrite]: #51
+#83 := [monotonicity #52]: #82
+#87 := [trans #83 #85]: #86
+#79 := (= #21 #78)
+#80 := [rewrite]: #79
+#90 := [monotonicity #80 #87]: #89
+#94 := [trans #90 #92]: #93
+#97 := [monotonicity #94]: #96
+#101 := [trans #97 #99]: #100
+#76 := (= #20 #75)
+#77 := [monotonicity #52]: #76
+#73 := (iff #19 #72)
+#70 := (iff #18 #69)
+#64 := (iff #15 #63)
+#65 := [monotonicity #52]: #64
+#71 := [monotonicity #65]: #70
+#67 := (iff #16 #66)
+#68 := [monotonicity #65]: #67
+#74 := [monotonicity #68 #71]: #73
+#104 := [monotonicity #74 #77 #101]: #103
+#61 := (iff #13 #60)
+#62 := [rewrite]: #61
+#107 := [monotonicity #62 #104]: #106
+#114 := [trans #107 #112]: #113
+#58 := (iff #11 false)
+#53 := (= -1::Int 0::Int)
+#56 := (iff #53 false)
+#57 := [rewrite]: #56
+#54 := (iff #11 #53)
+#55 := [monotonicity #52]: #54
+#59 := [trans #55 #57]: #58
+#117 := [monotonicity #59 #114]: #116
+#121 := [trans #117 #119]: #120
+#124 := [monotonicity #121]: #123
+#129 := [trans #124 #127]: #128
+#132 := [monotonicity #129]: #131
+#201 := [trans #132 #199]: #200
+#49 := [asserted]: #29
+[mp #49 #201]: false
+unsat
+aaecefccca197f785d6ec165e82f88f0ae2f4e23 78 0
+#2 := false
+#9 := 0::Int
+#8 := 3::Int
+#18 := (- 3::Int)
+#17 := (- 0::Int)
+#19 := (mod #17 #18)
+#20 := (- #19)
+#16 := (mod 0::Int 3::Int)
+#13 := (< 0::Int 3::Int)
+#12 := (< 0::Int 0::Int)
+#14 := (and #12 #13)
+#15 := (or #14 #14)
+#21 := (ite #15 #16 #20)
+#11 := (= 0::Int 0::Int)
+#22 := (ite #11 0::Int #21)
+#10 := (= 3::Int 0::Int)
+#23 := (ite #10 0::Int #22)
+#24 := (= #23 0::Int)
+#25 := (not #24)
+#99 := (iff #25 false)
+#1 := true
+#94 := (not true)
+#97 := (iff #94 false)
+#98 := [rewrite]: #97
+#95 := (iff #25 #94)
+#92 := (iff #24 true)
+#48 := (iff #11 true)
+#49 := [rewrite]: #48
+#90 := (iff #24 #11)
+#84 := (ite false 0::Int 0::Int)
+#87 := (= #84 0::Int)
+#88 := [rewrite]: #87
+#85 := (= #23 #84)
+#82 := (= #22 0::Int)
+#77 := (ite true 0::Int 0::Int)
+#80 := (= #77 0::Int)
+#81 := [rewrite]: #80
+#78 := (= #22 #77)
+#75 := (= #21 0::Int)
+#70 := (ite #14 0::Int 0::Int)
+#73 := (= #70 0::Int)
+#74 := [rewrite]: #73
+#71 := (= #21 #70)
+#68 := (= #20 0::Int)
+#54 := (= #17 0::Int)
+#55 := [rewrite]: #54
+#66 := (= #20 #17)
+#64 := (= #19 0::Int)
+#56 := -3::Int
+#59 := (mod 0::Int -3::Int)
+#62 := (= #59 0::Int)
+#63 := [rewrite]: #62
+#60 := (= #19 #59)
+#57 := (= #18 -3::Int)
+#58 := [rewrite]: #57
+#61 := [monotonicity #55 #58]: #60
+#65 := [trans #61 #63]: #64
+#67 := [monotonicity #65]: #66
+#69 := [trans #67 #55]: #68
+#52 := (= #16 0::Int)
+#53 := [rewrite]: #52
+#50 := (iff #15 #14)
+#51 := [rewrite]: #50
+#72 := [monotonicity #51 #53 #69]: #71
+#76 := [trans #72 #74]: #75
+#79 := [monotonicity #49 #76]: #78
+#83 := [trans #79 #81]: #82
+#46 := (iff #10 false)
+#47 := [rewrite]: #46
+#86 := [monotonicity #47 #83]: #85
+#89 := [trans #86 #88]: #24
+#91 := [monotonicity #89]: #90
+#93 := [trans #91 #49]: #92
+#96 := [monotonicity #93]: #95
+#100 := [trans #96 #98]: #99
+#45 := [asserted]: #25
+[mp #45 #100]: false
+unsat
+000d5a08395f518246c54a195994fc62266f45ed 107 0
+#2 := false
+#10 := 0::Int
 #8 := 3::Int
 #9 := (- 3::Int)
-#10 := (f3 #9 #9)
-#12 := (= #10 1::Int)
-#13 := (not #12)
-#86 := (iff #13 #83)
-#73 := (= 1::Int #67)
-#78 := (not #73)
-#84 := (iff #78 #83)
-#81 := (iff #73 #70)
-#82 := [rewrite]: #81
-#85 := [monotonicity #82]: #84
-#79 := (iff #13 #78)
-#76 := (iff #12 #73)
-#74 := (iff #70 #73)
-#75 := [rewrite]: #74
-#71 := (iff #12 #70)
-#68 := (= #10 #67)
-#65 := (= #9 -3::Int)
+#19 := (- #9)
+#18 := (- 0::Int)
+#20 := (mod #18 #19)
+#21 := (- #20)
+#17 := (mod 0::Int #9)
+#14 := (< 0::Int #9)
+#13 := (< 0::Int 0::Int)
+#15 := (and #13 #14)
+#16 := (or #15 #15)
+#22 := (ite #16 #17 #21)
+#12 := (= 0::Int 0::Int)
+#23 := (ite #12 0::Int #22)
+#11 := (= #9 0::Int)
+#24 := (ite #11 0::Int #23)
+#25 := (= #24 0::Int)
+#26 := (not #25)
+#128 := (iff #26 false)
+#1 := true
+#123 := (not true)
+#126 := (iff #123 false)
+#127 := [rewrite]: #126
+#124 := (iff #26 #123)
+#121 := (iff #25 true)
+#57 := (iff #12 true)
+#58 := [rewrite]: #57
+#119 := (iff #25 #12)
+#113 := (ite false 0::Int 0::Int)
+#116 := (= #113 0::Int)
+#117 := [rewrite]: #116
+#114 := (= #24 #113)
+#111 := (= #23 0::Int)
+#106 := (ite true 0::Int 0::Int)
+#109 := (= #106 0::Int)
+#110 := [rewrite]: #109
+#107 := (= #23 #106)
+#104 := (= #22 0::Int)
+#47 := -3::Int
+#59 := (< 0::Int -3::Int)
+#62 := (and #13 #59)
+#99 := (ite #62 0::Int 0::Int)
+#102 := (= #99 0::Int)
+#103 := [rewrite]: #102
+#100 := (= #22 #99)
+#97 := (= #21 0::Int)
+#79 := (= #18 0::Int)
+#80 := [rewrite]: #79
+#95 := (= #21 #18)
+#93 := (= #20 0::Int)
+#88 := (mod 0::Int 3::Int)
+#91 := (= #88 0::Int)
+#92 := [rewrite]: #91
+#89 := (= #20 #88)
+#86 := (= #19 3::Int)
+#81 := (- -3::Int)
+#84 := (= #81 3::Int)
+#85 := [rewrite]: #84
+#82 := (= #19 #81)
+#48 := (= #9 -3::Int)
+#49 := [rewrite]: #48
+#83 := [monotonicity #49]: #82
+#87 := [trans #83 #85]: #86
+#90 := [monotonicity #80 #87]: #89
+#94 := [trans #90 #92]: #93
+#96 := [monotonicity #94]: #95
+#98 := [trans #96 #80]: #97
+#77 := (= #17 0::Int)
+#72 := (mod 0::Int -3::Int)
+#75 := (= #72 0::Int)
+#76 := [rewrite]: #75
+#73 := (= #17 #72)
+#74 := [monotonicity #49]: #73
+#78 := [trans #74 #76]: #77
+#70 := (iff #16 #62)
+#65 := (or #62 #62)
+#68 := (iff #65 #62)
+#69 := [rewrite]: #68
+#66 := (iff #16 #65)
+#63 := (iff #15 #62)
+#60 := (iff #14 #59)
+#61 := [monotonicity #49]: #60
+#64 := [monotonicity #61]: #63
+#67 := [monotonicity #64 #64]: #66
+#71 := [trans #67 #69]: #70
+#101 := [monotonicity #71 #78 #98]: #100
+#105 := [trans #101 #103]: #104
+#108 := [monotonicity #58 #105]: #107
+#112 := [trans #108 #110]: #111
+#55 := (iff #11 false)
+#50 := (= -3::Int 0::Int)
+#53 := (iff #50 false)
+#54 := [rewrite]: #53
+#51 := (iff #11 #50)
+#52 := [monotonicity #49]: #51
+#56 := [trans #52 #54]: #55
+#115 := [monotonicity #56 #112]: #114
+#118 := [trans #115 #117]: #25
+#120 := [monotonicity #118]: #119
+#122 := [trans #120 #58]: #121
+#125 := [monotonicity #122]: #124
+#129 := [trans #125 #127]: #128
+#46 := [asserted]: #26
+[mp #46 #129]: false
+unsat
+54496e8e1bdde41302d50e03b35540e70008eccf 123 0
+#2 := false
+#11 := 1::Int
+#8 := 3::Int
+#21 := (- 3::Int)
+#20 := (- 1::Int)
+#22 := (mod #20 #21)
+#23 := (- #22)
+#19 := (mod 1::Int 3::Int)
+#9 := 0::Int
+#14 := (< 0::Int 3::Int)
+#16 := (< 1::Int 0::Int)
+#17 := (and #16 #14)
+#13 := (< 0::Int 1::Int)
+#15 := (and #13 #14)
+#18 := (or #15 #17)
+#24 := (ite #18 #19 #23)
+#12 := (= 1::Int 0::Int)
+#25 := (ite #12 0::Int #24)
+#10 := (= 3::Int 0::Int)
+#26 := (ite #10 1::Int #25)
+#27 := (= #26 1::Int)
+#28 := (not #27)
+#144 := (iff #28 false)
+#53 := (and #14 #16)
+#56 := (or #15 #53)
+#107 := (not #56)
+#142 := (iff #107 false)
+#1 := true
+#137 := (not true)
+#140 := (iff #137 false)
+#141 := [rewrite]: #140
+#138 := (iff #107 #137)
+#135 := (iff #56 true)
+#130 := (or true false)
+#133 := (iff #130 true)
+#134 := [rewrite]: #133
+#131 := (iff #56 #130)
+#128 := (iff #53 false)
+#123 := (and true false)
+#126 := (iff #123 false)
+#127 := [rewrite]: #126
+#124 := (iff #53 #123)
+#121 := (iff #16 false)
+#122 := [rewrite]: #121
+#112 := (iff #14 true)
+#113 := [rewrite]: #112
+#125 := [monotonicity #113 #122]: #124
+#129 := [trans #125 #127]: #128
+#119 := (iff #15 true)
+#114 := (and true true)
+#117 := (iff #114 true)
+#118 := [rewrite]: #117
+#115 := (iff #15 #114)
+#110 := (iff #13 true)
+#111 := [rewrite]: #110
+#116 := [monotonicity #111 #113]: #115
+#120 := [trans #116 #118]: #119
+#132 := [monotonicity #120 #129]: #131
+#136 := [trans #132 #134]: #135
+#139 := [monotonicity #136]: #138
+#143 := [trans #139 #141]: #142
+#108 := (iff #28 #107)
+#105 := (iff #27 #56)
+#78 := -2::Int
+#83 := (ite #56 1::Int -2::Int)
+#100 := (= #83 1::Int)
+#103 := (iff #100 #56)
+#104 := [rewrite]: #103
+#101 := (iff #27 #100)
+#98 := (= #26 #83)
+#93 := (ite false 1::Int #83)
+#96 := (= #93 #83)
+#97 := [rewrite]: #96
+#94 := (= #26 #93)
+#91 := (= #25 #83)
+#86 := (ite false 0::Int #83)
+#89 := (= #86 #83)
+#90 := [rewrite]: #89
+#87 := (= #25 #86)
+#84 := (= #24 #83)
+#81 := (= #23 -2::Int)
+#70 := 2::Int
+#75 := (- 2::Int)
+#79 := (= #75 -2::Int)
+#80 := [rewrite]: #79
+#76 := (= #23 #75)
+#73 := (= #22 2::Int)
+#64 := -3::Int
+#61 := -1::Int
+#67 := (mod -1::Int -3::Int)
+#71 := (= #67 2::Int)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#65 := (= #21 -3::Int)
 #66 := [rewrite]: #65
-#69 := [monotonicity #66 #66]: #68
-#72 := [monotonicity #69]: #71
-#77 := [trans #72 #75]: #76
-#80 := [monotonicity #77]: #79
-#87 := [trans #80 #85]: #86
-#63 := [asserted]: #13
-#88 := [mp #63 #87]: #83
-#588 := (not #752)
-#589 := (or #588 #70)
-#338 := (* -1::Int -3::Int)
-#422 := (div #338 #338)
-#423 := (* -1::Int #422)
-#424 := (+ #67 #423)
-#415 := (= #424 0::Int)
-#426 := (div -3::Int -3::Int)
-#427 := (* -1::Int #426)
-#428 := (+ #67 #427)
-#425 := (= #428 0::Int)
-#429 := (>= -3::Int 0::Int)
-#408 := (<= -3::Int 0::Int)
-#743 := (or #408 #429)
-#745 := (not #743)
-#402 := (or #408 #408)
-#532 := (not #402)
-#739 := (or #532 #745)
-#413 := (ite #739 #425 #415)
-#414 := (= #67 0::Int)
-#746 := (= -3::Int 0::Int)
-#747 := (or #746 #746)
-#748 := (ite #747 #414 #413)
-#590 := (or #588 #748)
-#592 := (iff #590 #589)
-#682 := (iff #589 #589)
-#686 := [rewrite]: #682
-#587 := (iff #748 #70)
-#681 := (ite false #414 #70)
-#584 := (iff #681 #70)
-#586 := [rewrite]: #584
-#684 := (iff #748 #681)
-#585 := (iff #413 #70)
-#574 := (ite false #70 #70)
-#535 := (iff #574 #70)
-#683 := [rewrite]: #535
-#575 := (iff #413 #574)
-#689 := (iff #415 #70)
-#713 := (+ -1::Int #67)
-#703 := (= #713 0::Int)
-#710 := (iff #703 #70)
-#705 := [rewrite]: #710
-#690 := (iff #415 #703)
-#687 := (= #424 #713)
-#430 := (+ #67 -1::Int)
-#717 := (= #430 #713)
-#706 := [rewrite]: #717
-#533 := (= #424 #430)
-#702 := (= #423 -1::Int)
-#723 := (* -1::Int 1::Int)
-#435 := (= #723 -1::Int)
-#436 := [rewrite]: #435
-#701 := (= #423 #723)
-#694 := (= #422 1::Int)
-#696 := (div 3::Int 3::Int)
-#699 := (= #696 1::Int)
-#693 := [rewrite]: #699
-#697 := (= #422 #696)
-#553 := (= #338 3::Int)
-#554 := [rewrite]: #553
-#698 := [monotonicity #554 #554]: #697
-#700 := [trans #698 #693]: #694
-#695 := [monotonicity #700]: #701
-#531 := [trans #695 #436]: #702
-#534 := [monotonicity #531]: #533
-#688 := [trans #534 #706]: #687
-#691 := [monotonicity #688]: #690
-#692 := [trans #691 #705]: #689
-#711 := (iff #425 #70)
-#704 := (iff #425 #703)
-#707 := (= #428 #713)
-#712 := (= #428 #430)
-#714 := (= #427 -1::Int)
-#433 := (= #427 #723)
-#722 := (= #426 1::Int)
-#719 := [rewrite]: #722
-#434 := [monotonicity #719]: #433
-#715 := [trans #434 #436]: #714
-#716 := [monotonicity #715]: #712
-#708 := [trans #716 #706]: #707
-#709 := [monotonicity #708]: #704
-#552 := [trans #709 #705]: #711
-#444 := (iff #739 false)
-#750 := (or false false)
-#405 := (iff #750 false)
-#741 := [rewrite]: #405
-#721 := (iff #739 #750)
-#344 := (iff #745 false)
-#1 := true
-#731 := (not true)
-#733 := (iff #731 false)
-#371 := [rewrite]: #733
-#449 := (iff #745 #731)
-#447 := (iff #743 true)
-#737 := (or true false)
-#724 := (iff #737 true)
-#725 := [rewrite]: #724
-#735 := (iff #743 #737)
-#376 := (iff #429 false)
-#377 := [rewrite]: #376
-#385 := (iff #408 true)
-#726 := [rewrite]: #385
-#738 := [monotonicity #726 #377]: #735
-#448 := [trans #738 #725]: #447
-#450 := [monotonicity #448]: #449
-#720 := [trans #450 #371]: #344
-#734 := (iff #532 false)
-#732 := (iff #532 #731)
-#729 := (iff #402 true)
-#389 := (or true true)
-#392 := (iff #389 true)
-#728 := [rewrite]: #392
-#390 := (iff #402 #389)
-#391 := [monotonicity #726 #726]: #390
-#730 := [trans #391 #728]: #729
-#727 := [monotonicity #730]: #732
-#736 := [trans #727 #371]: #734
-#443 := [monotonicity #736 #720]: #721
-#718 := [trans #443 #741]: #444
-#576 := [monotonicity #718 #552 #692]: #575
-#680 := [trans #576 #683]: #585
-#401 := (iff #747 false)
-#740 := (iff #747 #750)
-#749 := (iff #746 false)
-#744 := [rewrite]: #749
-#400 := [monotonicity #744 #744]: #740
-#742 := [trans #400 #741]: #401
-#569 := [monotonicity #742 #680]: #684
-#580 := [trans #569 #586]: #587
-#685 := [monotonicity #580]: #592
-#673 := [trans #685 #686]: #592
-#591 := [quant-inst #64 #64]: #590
-#675 := [mp #591 #673]: #589
-[unit-resolution #675 #88 #757]: false
-unsat
-602bd1c64454e63be2273eaf718ba5b3413f9555 333 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#17 := (:var 0 Int)
-#16 := (:var 1 Int)
-#18 := (f3 #16 #17)
-#756 := (pattern #18)
-#19 := 0::Int
-#101 := -1::Int
-#105 := (* -1::Int #17)
-#102 := (* -1::Int #16)
-#108 := (div #102 #105)
-#259 := (* -1::Int #108)
-#260 := (+ #18 #259)
-#261 := (= #260 0::Int)
-#29 := (div #16 #17)
-#256 := (* -1::Int #29)
-#257 := (+ #18 #256)
-#258 := (= #257 0::Int)
-#134 := (>= #16 0::Int)
-#127 := (<= #17 0::Int)
-#219 := (or #127 #134)
-#220 := (not #219)
-#123 := (<= #16 0::Int)
-#217 := (or #123 #127)
-#218 := (not #217)
-#223 := (or #218 #220)
-#262 := (ite #223 #258 #261)
-#255 := (= #18 0::Int)
-#21 := (= #17 0::Int)
-#20 := (= #16 0::Int)
-#22 := (or #20 #21)
-#263 := (ite #22 #255 #262)
-#757 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #756) #263)
-#266 := (forall (vars (?v0 Int) (?v1 Int)) #263)
-#760 := (iff #266 #757)
-#758 := (iff #263 #263)
-#759 := [refl]: #758
-#761 := [quant-intro #759]: #760
-#226 := (ite #223 #29 #108)
-#229 := (ite #22 0::Int #226)
-#232 := (= #18 #229)
-#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
-#267 := (iff #235 #266)
-#264 := (iff #232 #263)
-#265 := [rewrite]: #264
-#268 := [quant-intro #265]: #267
-#135 := (not #134)
-#128 := (not #127)
-#138 := (and #128 #135)
-#124 := (not #123)
-#131 := (and #124 #128)
-#141 := (or #131 #138)
-#144 := (ite #141 #29 #108)
-#147 := (ite #22 0::Int #144)
-#150 := (= #18 #147)
-#153 := (forall (vars (?v0 Int) (?v1 Int)) #150)
-#236 := (iff #153 #235)
-#233 := (iff #150 #232)
-#230 := (= #147 #229)
-#227 := (= #144 #226)
-#224 := (iff #141 #223)
-#221 := (iff #138 #220)
-#222 := [rewrite]: #221
-#211 := (iff #131 #218)
-#212 := [rewrite]: #211
-#225 := [monotonicity #212 #222]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [quant-intro #234]: #236
-#215 := (~ #153 #153)
-#213 := (~ #150 #150)
-#214 := [refl]: #213
-#216 := [nnf-pos #214]: #215
-#31 := (- #17)
-#30 := (- #16)
-#32 := (div #30 #31)
-#24 := (< 0::Int #17)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#33 := (ite #28 #29 #32)
-#34 := (ite #22 0::Int #33)
-#35 := (= #18 #34)
-#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
-#156 := (iff #36 #153)
-#95 := (and #24 #26)
-#98 := (or #25 #95)
-#111 := (ite #98 #29 #108)
-#114 := (ite #22 0::Int #111)
-#117 := (= #18 #114)
-#120 := (forall (vars (?v0 Int) (?v1 Int)) #117)
-#154 := (iff #120 #153)
-#151 := (iff #117 #150)
-#148 := (= #114 #147)
-#145 := (= #111 #144)
-#142 := (iff #98 #141)
-#139 := (iff #95 #138)
-#136 := (iff #26 #135)
-#137 := [rewrite]: #136
-#129 := (iff #24 #128)
-#130 := [rewrite]: #129
-#140 := [monotonicity #130 #137]: #139
-#132 := (iff #25 #131)
-#125 := (iff #23 #124)
-#126 := [rewrite]: #125
-#133 := [monotonicity #126 #130]: #132
-#143 := [monotonicity #133 #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [monotonicity #149]: #151
-#155 := [quant-intro #152]: #154
-#121 := (iff #36 #120)
-#118 := (iff #35 #117)
-#115 := (= #34 #114)
-#112 := (= #33 #111)
-#109 := (= #32 #108)
-#106 := (= #31 #105)
-#107 := [rewrite]: #106
-#103 := (= #30 #102)
-#104 := [rewrite]: #103
-#110 := [monotonicity #104 #107]: #109
-#99 := (iff #28 #98)
-#96 := (iff #27 #95)
-#97 := [rewrite]: #96
-#100 := [monotonicity #97]: #99
-#113 := [monotonicity #100 #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [monotonicity #116]: #118
-#122 := [quant-intro #119]: #121
-#157 := [trans #122 #155]: #156
-#94 := [asserted]: #36
-#158 := [mp #94 #157]: #153
-#207 := [mp~ #158 #216]: #153
-#238 := [mp #207 #237]: #235
-#269 := [mp #238 #268]: #266
-#762 := [mp #269 #761]: #757
-#13 := 1::Int
-#69 := -3::Int
-#66 := -5::Int
-#72 := (f3 -5::Int -3::Int)
-#75 := (= #72 1::Int)
-#88 := (not #75)
-#10 := 3::Int
-#11 := (- 3::Int)
-#8 := 5::Int
-#9 := (- 5::Int)
-#12 := (f3 #9 #11)
-#14 := (= #12 1::Int)
-#15 := (not #14)
-#91 := (iff #15 #88)
-#78 := (= 1::Int #72)
-#83 := (not #78)
-#89 := (iff #83 #88)
-#86 := (iff #78 #75)
-#87 := [rewrite]: #86
-#90 := [monotonicity #87]: #89
-#84 := (iff #15 #83)
-#81 := (iff #14 #78)
-#79 := (iff #75 #78)
-#80 := [rewrite]: #79
-#76 := (iff #14 #75)
-#73 := (= #12 #72)
-#70 := (= #11 -3::Int)
-#71 := [rewrite]: #70
-#67 := (= #9 -5::Int)
-#68 := [rewrite]: #67
-#74 := [monotonicity #68 #71]: #73
+#62 := (= #20 -1::Int)
+#63 := [rewrite]: #62
+#69 := [monotonicity #63 #66]: #68
+#74 := [trans #69 #72]: #73
 #77 := [monotonicity #74]: #76
 #82 := [trans #77 #80]: #81
-#85 := [monotonicity #82]: #84
-#92 := [trans #85 #90]: #91
-#65 := [asserted]: #15
-#93 := [mp #65 #92]: #88
-#670 := (not #757)
-#677 := (or #670 #75)
-#343 := (* -1::Int -3::Int)
-#427 := (* -1::Int -5::Int)
-#428 := (div #427 #343)
-#429 := (* -1::Int #428)
-#420 := (+ #72 #429)
-#431 := (= #420 0::Int)
-#432 := (div -5::Int -3::Int)
-#433 := (* -1::Int #432)
-#430 := (+ #72 #433)
-#434 := (= #430 0::Int)
-#413 := (>= -5::Int 0::Int)
-#748 := (<= -3::Int 0::Int)
-#750 := (or #748 #413)
-#407 := (not #750)
-#537 := (<= -5::Int 0::Int)
-#744 := (or #537 #748)
-#418 := (not #744)
-#419 := (or #418 #407)
-#751 := (ite #419 #434 #431)
-#752 := (= #72 0::Int)
-#753 := (= -3::Int 0::Int)
-#754 := (= -5::Int 0::Int)
-#749 := (or #754 #753)
-#755 := (ite #749 #752 #751)
-#661 := (or #670 #755)
-#664 := (iff #661 #677)
-#666 := (iff #677 #677)
-#667 := [rewrite]: #666
-#675 := (iff #755 #75)
-#683 := (ite false #752 #75)
-#673 := (iff #683 #75)
-#674 := [rewrite]: #673
-#679 := (iff #755 #683)
-#681 := (iff #751 #75)
-#719 := 2::Int
-#704 := (= #72 2::Int)
-#678 := (ite false #704 #75)
-#669 := (iff #678 #75)
-#671 := [rewrite]: #669
-#680 := (iff #751 #678)
-#687 := (iff #431 #75)
-#589 := (+ -1::Int #72)
-#594 := (= #589 0::Int)
-#597 := (iff #594 #75)
-#690 := [rewrite]: #597
-#595 := (iff #431 #594)
-#585 := (= #420 #589)
-#686 := (+ #72 -1::Int)
-#591 := (= #686 #589)
-#592 := [rewrite]: #591
-#689 := (= #420 #686)
-#590 := (= #429 -1::Int)
-#579 := (* -1::Int 1::Int)
-#540 := (= #579 -1::Int)
-#688 := [rewrite]: #540
-#580 := (= #429 #579)
-#694 := (= #428 1::Int)
-#539 := (div 5::Int 3::Int)
-#695 := (= #539 1::Int)
-#696 := [rewrite]: #695
-#692 := (= #428 #539)
-#536 := (= #343 3::Int)
-#538 := [rewrite]: #536
-#700 := (= #427 5::Int)
-#707 := [rewrite]: #700
-#693 := [monotonicity #707 #538]: #692
-#697 := [trans #693 #696]: #694
-#581 := [monotonicity #697]: #580
-#685 := [trans #581 #688]: #590
-#574 := [monotonicity #685]: #689
-#593 := [trans #574 #592]: #585
-#596 := [monotonicity #593]: #595
-#691 := [trans #596 #690]: #687
-#705 := (iff #434 #704)
-#722 := -2::Int
-#710 := (+ -2::Int #72)
-#701 := (= #710 0::Int)
-#698 := (iff #701 #704)
-#699 := [rewrite]: #698
-#702 := (iff #434 #701)
-#558 := (= #430 #710)
-#709 := (+ #72 -2::Int)
-#716 := (= #709 #710)
-#557 := [rewrite]: #716
-#714 := (= #430 #709)
-#713 := (= #433 -2::Int)
-#717 := (* -1::Int 2::Int)
-#711 := (= #717 -2::Int)
-#712 := [rewrite]: #711
-#721 := (= #433 #717)
-#720 := (= #432 2::Int)
-#435 := [rewrite]: #720
-#718 := [monotonicity #435]: #721
-#708 := [trans #718 #712]: #713
-#715 := [monotonicity #708]: #714
-#559 := [trans #715 #557]: #558
-#703 := [monotonicity #559]: #702
-#706 := [trans #703 #699]: #705
-#440 := (iff #419 false)
-#406 := (or false false)
-#731 := (iff #406 false)
-#394 := [rewrite]: #731
-#438 := (iff #419 #406)
-#724 := (iff #407 false)
-#1 := true
-#381 := (not true)
-#740 := (iff #381 false)
-#743 := [rewrite]: #740
-#723 := (iff #407 #381)
-#448 := (iff #750 true)
-#454 := (or true false)
-#725 := (iff #454 true)
-#726 := [rewrite]: #725
-#455 := (iff #750 #454)
-#452 := (iff #413 false)
-#453 := [rewrite]: #452
-#734 := (iff #748 true)
-#735 := [rewrite]: #734
-#349 := [monotonicity #735 #453]: #455
-#449 := [trans #349 #726]: #448
-#727 := [monotonicity #449]: #723
-#728 := [trans #727 #743]: #724
-#729 := (iff #418 false)
-#382 := (iff #418 #381)
-#739 := (iff #744 true)
-#736 := (or true true)
-#738 := (iff #736 true)
-#376 := [rewrite]: #738
-#737 := (iff #744 #736)
-#397 := (iff #537 true)
-#733 := [rewrite]: #397
-#732 := [monotonicity #733 #735]: #737
-#741 := [trans #732 #376]: #739
-#742 := [monotonicity #741]: #382
-#730 := [trans #742 #743]: #729
-#439 := [monotonicity #730 #728]: #438
-#441 := [trans #439 #394]: #440
-#672 := [monotonicity #441 #706 #691]: #680
-#682 := [trans #672 #671]: #681
-#395 := (iff #749 false)
-#747 := (iff #749 #406)
-#410 := (iff #753 false)
-#746 := [rewrite]: #410
-#745 := (iff #754 false)
-#405 := [rewrite]: #745
-#390 := [monotonicity #405 #746]: #747
-#396 := [trans #390 #394]: #395
-#684 := [monotonicity #396 #682]: #679
-#676 := [trans #684 #674]: #675
-#665 := [monotonicity #676]: #664
-#663 := [trans #665 #667]: #664
-#662 := [quant-inst #66 #69]: #661
-#668 := [mp #662 #663]: #677
-[unit-resolution #668 #93 #762]: false
-unsat
-9d955d673529089780c55958aa0742a5b1471d68 273 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#13 := (:var 0 Int)
-#12 := (:var 1 Int)
-#32 := (f3 #12 #13)
-#756 := (pattern #32)
-#8 := 0::Int
-#87 := -1::Int
-#91 := (* -1::Int #13)
-#88 := (* -1::Int #12)
-#152 := (mod #88 #91)
-#267 := (+ #32 #152)
-#268 := (= #267 0::Int)
-#33 := (mod #12 #13)
-#264 := (* -1::Int #33)
-#265 := (+ #32 #264)
-#266 := (= #265 0::Int)
-#126 := (>= #12 0::Int)
-#119 := (<= #13 0::Int)
-#211 := (or #119 #126)
-#212 := (not #211)
-#115 := (<= #12 0::Int)
-#209 := (or #115 #119)
-#210 := (not #209)
-#215 := (or #210 #212)
-#269 := (ite #215 #266 #268)
-#263 := (= #32 0::Int)
-#15 := (= #12 0::Int)
-#270 := (ite #15 #263 #269)
-#262 := (= #12 #32)
-#16 := (= #13 0::Int)
-#271 := (ite #16 #262 #270)
-#757 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #756) #271)
-#274 := (forall (vars (?v0 Int) (?v1 Int)) #271)
-#760 := (iff #274 #757)
-#758 := (iff #271 #271)
-#759 := [refl]: #758
-#761 := [quant-intro #759]: #760
-#158 := (* -1::Int #152)
-#231 := (ite #215 #33 #158)
-#234 := (ite #15 0::Int #231)
-#237 := (ite #16 #12 #234)
-#240 := (= #32 #237)
-#243 := (forall (vars (?v0 Int) (?v1 Int)) #240)
-#275 := (iff #243 #274)
-#272 := (iff #240 #271)
-#273 := [rewrite]: #272
-#276 := [quant-intro #273]: #275
-#127 := (not #126)
-#120 := (not #119)
-#130 := (and #120 #127)
-#116 := (not #115)
-#123 := (and #116 #120)
-#133 := (or #123 #130)
-#178 := (ite #133 #33 #158)
-#181 := (ite #15 0::Int #178)
-#184 := (ite #16 #12 #181)
-#187 := (= #32 #184)
-#190 := (forall (vars (?v0 Int) (?v1 Int)) #187)
-#244 := (iff #190 #243)
-#241 := (iff #187 #240)
-#238 := (= #184 #237)
-#235 := (= #181 #234)
-#232 := (= #178 #231)
-#216 := (iff #133 #215)
-#213 := (iff #130 #212)
-#214 := [rewrite]: #213
-#203 := (iff #123 #210)
-#204 := [rewrite]: #203
-#217 := [monotonicity #204 #214]: #216
-#233 := [monotonicity #217]: #232
-#236 := [monotonicity #233]: #235
-#239 := [monotonicity #236]: #238
-#242 := [monotonicity #239]: #241
-#245 := [quant-intro #242]: #244
-#201 := (~ #190 #190)
-#200 := (~ #187 #187)
-#197 := [refl]: #200
-#202 := [nnf-pos #197]: #201
-#26 := (- #13)
-#25 := (- #12)
-#34 := (mod #25 #26)
-#35 := (- #34)
-#19 := (< 0::Int #13)
-#21 := (< #12 0::Int)
-#22 := (and #21 #19)
-#18 := (< 0::Int #12)
-#20 := (and #18 #19)
-#23 := (or #20 #22)
-#36 := (ite #23 #33 #35)
-#37 := (ite #15 0::Int #36)
-#38 := (ite #16 #12 #37)
-#39 := (= #32 #38)
-#40 := (forall (vars (?v0 Int) (?v1 Int)) #39)
-#193 := (iff #40 #190)
-#81 := (and #19 #21)
-#84 := (or #20 #81)
-#163 := (ite #84 #33 #158)
-#72 := (= 0::Int #12)
-#166 := (ite #72 0::Int #163)
-#75 := (= 0::Int #13)
-#169 := (ite #75 #12 #166)
-#172 := (= #32 #169)
-#175 := (forall (vars (?v0 Int) (?v1 Int)) #172)
-#191 := (iff #175 #190)
-#188 := (iff #172 #187)
-#185 := (= #169 #184)
-#182 := (= #166 #181)
-#179 := (= #163 #178)
-#134 := (iff #84 #133)
-#131 := (iff #81 #130)
-#128 := (iff #21 #127)
-#129 := [rewrite]: #128
-#121 := (iff #19 #120)
-#122 := [rewrite]: #121
-#132 := [monotonicity #122 #129]: #131
-#124 := (iff #20 #123)
-#117 := (iff #18 #116)
-#118 := [rewrite]: #117
-#125 := [monotonicity #118 #122]: #124
-#135 := [monotonicity #125 #132]: #134
-#180 := [monotonicity #135]: #179
-#109 := (iff #72 #15)
-#110 := [rewrite]: #109
-#183 := [monotonicity #110 #180]: #182
-#111 := (iff #75 #16)
-#112 := [rewrite]: #111
-#186 := [monotonicity #112 #183]: #185
-#189 := [monotonicity #186]: #188
-#192 := [quant-intro #189]: #191
-#176 := (iff #40 #175)
-#173 := (iff #39 #172)
-#170 := (= #38 #169)
-#167 := (= #37 #166)
-#164 := (= #36 #163)
-#161 := (= #35 #158)
-#155 := (- #152)
-#159 := (= #155 #158)
-#160 := [rewrite]: #159
-#156 := (= #35 #155)
-#153 := (= #34 #152)
-#92 := (= #26 #91)
-#93 := [rewrite]: #92
-#89 := (= #25 #88)
-#90 := [rewrite]: #89
-#154 := [monotonicity #90 #93]: #153
-#157 := [monotonicity #154]: #156
-#162 := [trans #157 #160]: #161
-#85 := (iff #23 #84)
-#82 := (iff #22 #81)
-#83 := [rewrite]: #82
-#86 := [monotonicity #83]: #85
-#165 := [monotonicity #86 #162]: #164
-#73 := (iff #15 #72)
-#74 := [rewrite]: #73
-#168 := [monotonicity #74 #165]: #167
-#76 := (iff #16 #75)
-#77 := [rewrite]: #76
-#171 := [monotonicity #77 #168]: #170
-#174 := [monotonicity #171]: #173
-#177 := [quant-intro #174]: #176
-#194 := [trans #177 #192]: #193
-#151 := [asserted]: #40
-#195 := [mp #151 #194]: #190
-#198 := [mp~ #195 #202]: #190
-#246 := [mp #198 #245]: #243
-#277 := [mp #246 #276]: #274
-#762 := [mp #277 #761]: #757
-#9 := (f3 0::Int 0::Int)
-#10 := (= #9 0::Int)
-#11 := (not #10)
-#60 := [asserted]: #11
-#703 := (not #757)
-#709 := (or #703 #10)
-#335 := (* -1::Int 0::Int)
-#420 := (mod #335 #335)
-#421 := (+ #9 #420)
-#422 := (= #421 0::Int)
-#413 := (mod 0::Int 0::Int)
-#424 := (* -1::Int #413)
-#425 := (+ #9 #424)
-#353 := (= #425 0::Int)
-#426 := (>= 0::Int 0::Int)
-#423 := (<= 0::Int 0::Int)
-#427 := (or #423 #426)
-#406 := (not #427)
-#741 := (or #423 #423)
-#743 := (not #741)
-#400 := (or #743 #406)
-#530 := (ite #400 #353 #422)
-#737 := (= 0::Int 0::Int)
-#411 := (ite #737 #10 #530)
-#61 := (= 0::Int #9)
-#412 := (ite #737 #61 #411)
-#550 := (or #703 #412)
-#552 := (iff #550 #709)
-#695 := (iff #709 #709)
-#696 := [rewrite]: #695
-#707 := (iff #412 #10)
-#1 := true
-#704 := (ite true #10 #10)
-#701 := (iff #704 #10)
-#702 := [rewrite]: #701
-#705 := (iff #412 #704)
-#711 := (iff #411 #10)
-#341 := (+ #9 #413)
-#441 := (= #341 0::Int)
-#712 := (ite true #10 #441)
-#710 := (iff #712 #10)
-#714 := [rewrite]: #710
-#713 := (iff #411 #712)
-#433 := (iff #530 #441)
-#720 := (ite false #353 #441)
-#431 := (iff #720 #441)
-#432 := [rewrite]: #431
-#717 := (iff #530 #720)
-#442 := (iff #422 #441)
-#718 := (= #421 #341)
-#447 := (= #420 #413)
-#445 := (= #335 0::Int)
-#446 := [rewrite]: #445
-#448 := [monotonicity #446 #446]: #447
-#719 := [monotonicity #448]: #718
-#716 := [monotonicity #719]: #442
-#722 := (iff #400 false)
-#374 := (or false false)
-#733 := (iff #374 false)
-#736 := [rewrite]: #733
-#375 := (iff #400 #374)
-#732 := (iff #406 false)
-#740 := (not true)
-#387 := (iff #740 false)
-#388 := [rewrite]: #387
-#731 := (iff #406 #740)
-#730 := (iff #427 true)
-#742 := (or true true)
-#398 := (iff #742 true)
-#403 := [rewrite]: #398
-#728 := (iff #427 #742)
-#726 := (iff #426 true)
-#727 := [rewrite]: #726
-#746 := (iff #423 true)
-#747 := [rewrite]: #746
-#729 := [monotonicity #747 #727]: #728
-#725 := [trans #729 #403]: #730
-#369 := [monotonicity #725]: #731
-#734 := [trans #369 #388]: #732
-#389 := (iff #743 false)
-#383 := (iff #743 #740)
-#739 := (iff #741 true)
-#748 := (iff #741 #742)
-#738 := [monotonicity #747 #747]: #748
-#399 := [trans #738 #403]: #739
-#724 := [monotonicity #399]: #383
-#390 := [trans #724 #388]: #389
-#735 := [monotonicity #390 #734]: #375
-#723 := [trans #735 #736]: #722
-#721 := [monotonicity #723 #716]: #717
-#434 := [trans #721 #432]: #433
-#744 := (iff #737 true)
-#745 := [rewrite]: #744
-#428 := [monotonicity #745 #434]: #713
-#715 := [trans #428 #714]: #711
-#67 := (iff #61 #10)
-#68 := [rewrite]: #67
-#706 := [monotonicity #745 #68 #715]: #705
-#708 := [trans #706 #702]: #707
-#694 := [monotonicity #708]: #552
-#697 := [trans #694 #696]: #552
-#551 := [quant-inst #8 #8]: #550
-#691 := [mp #551 #697]: #709
-[unit-resolution #691 #60 #762]: false
-unsat
-ea8997dddba0ea4cee2a7011c7fb001434f88f23 281 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#14 := (:var 0 Int)
-#13 := (:var 1 Int)
-#33 := (f3 #13 #14)
-#754 := (pattern #33)
-#9 := 0::Int
-#85 := -1::Int
-#89 := (* -1::Int #14)
-#86 := (* -1::Int #13)
-#150 := (mod #86 #89)
-#265 := (+ #33 #150)
-#266 := (= #265 0::Int)
-#34 := (mod #13 #14)
-#262 := (* -1::Int #34)
-#263 := (+ #33 #262)
-#264 := (= #263 0::Int)
-#124 := (>= #13 0::Int)
-#117 := (<= #14 0::Int)
-#209 := (or #117 #124)
-#210 := (not #209)
-#113 := (<= #13 0::Int)
-#207 := (or #113 #117)
-#208 := (not #207)
-#213 := (or #208 #210)
-#267 := (ite #213 #264 #266)
-#261 := (= #33 0::Int)
-#16 := (= #13 0::Int)
-#268 := (ite #16 #261 #267)
-#260 := (= #13 #33)
-#17 := (= #14 0::Int)
-#269 := (ite #17 #260 #268)
-#755 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #754) #269)
-#272 := (forall (vars (?v0 Int) (?v1 Int)) #269)
-#758 := (iff #272 #755)
-#756 := (iff #269 #269)
-#757 := [refl]: #756
-#759 := [quant-intro #757]: #758
-#156 := (* -1::Int #150)
-#229 := (ite #213 #34 #156)
-#232 := (ite #16 0::Int #229)
-#235 := (ite #17 #13 #232)
-#238 := (= #33 #235)
-#241 := (forall (vars (?v0 Int) (?v1 Int)) #238)
-#273 := (iff #241 #272)
-#270 := (iff #238 #269)
-#271 := [rewrite]: #270
-#274 := [quant-intro #271]: #273
-#125 := (not #124)
-#118 := (not #117)
-#128 := (and #118 #125)
-#114 := (not #113)
-#121 := (and #114 #118)
-#131 := (or #121 #128)
-#176 := (ite #131 #34 #156)
-#179 := (ite #16 0::Int #176)
-#182 := (ite #17 #13 #179)
-#185 := (= #33 #182)
-#188 := (forall (vars (?v0 Int) (?v1 Int)) #185)
-#242 := (iff #188 #241)
-#239 := (iff #185 #238)
-#236 := (= #182 #235)
-#233 := (= #179 #232)
-#230 := (= #176 #229)
-#214 := (iff #131 #213)
-#211 := (iff #128 #210)
-#212 := [rewrite]: #211
-#201 := (iff #121 #208)
-#202 := [rewrite]: #201
-#215 := [monotonicity #202 #212]: #214
-#231 := [monotonicity #215]: #230
-#234 := [monotonicity #231]: #233
-#237 := [monotonicity #234]: #236
-#240 := [monotonicity #237]: #239
-#243 := [quant-intro #240]: #242
-#199 := (~ #188 #188)
-#198 := (~ #185 #185)
-#195 := [refl]: #198
-#200 := [nnf-pos #195]: #199
-#27 := (- #14)
-#26 := (- #13)
-#35 := (mod #26 #27)
-#36 := (- #35)
-#20 := (< 0::Int #14)
-#22 := (< #13 0::Int)
-#23 := (and #22 #20)
-#19 := (< 0::Int #13)
-#21 := (and #19 #20)
-#24 := (or #21 #23)
-#37 := (ite #24 #34 #36)
-#38 := (ite #16 0::Int #37)
-#39 := (ite #17 #13 #38)
-#40 := (= #33 #39)
-#41 := (forall (vars (?v0 Int) (?v1 Int)) #40)
-#191 := (iff #41 #188)
-#79 := (and #20 #22)
-#82 := (or #21 #79)
-#161 := (ite #82 #34 #156)
-#69 := (= 0::Int #13)
-#164 := (ite #69 0::Int #161)
-#73 := (= 0::Int #14)
-#167 := (ite #73 #13 #164)
-#170 := (= #33 #167)
-#173 := (forall (vars (?v0 Int) (?v1 Int)) #170)
-#189 := (iff #173 #188)
-#186 := (iff #170 #185)
-#183 := (= #167 #182)
-#180 := (= #164 #179)
-#177 := (= #161 #176)
-#132 := (iff #82 #131)
-#129 := (iff #79 #128)
-#126 := (iff #22 #125)
-#127 := [rewrite]: #126
-#119 := (iff #20 #118)
-#120 := [rewrite]: #119
-#130 := [monotonicity #120 #127]: #129
-#122 := (iff #21 #121)
-#115 := (iff #19 #114)
-#116 := [rewrite]: #115
-#123 := [monotonicity #116 #120]: #122
-#133 := [monotonicity #123 #130]: #132
-#178 := [monotonicity #133]: #177
-#107 := (iff #69 #16)
-#108 := [rewrite]: #107
-#181 := [monotonicity #108 #178]: #180
-#109 := (iff #73 #17)
-#110 := [rewrite]: #109
-#184 := [monotonicity #110 #181]: #183
-#187 := [monotonicity #184]: #186
-#190 := [quant-intro #187]: #189
-#174 := (iff #41 #173)
-#171 := (iff #40 #170)
-#168 := (= #39 #167)
-#165 := (= #38 #164)
-#162 := (= #37 #161)
-#159 := (= #36 #156)
-#153 := (- #150)
-#157 := (= #153 #156)
-#158 := [rewrite]: #157
-#154 := (= #36 #153)
-#151 := (= #35 #150)
-#90 := (= #27 #89)
-#91 := [rewrite]: #90
-#87 := (= #26 #86)
-#88 := [rewrite]: #87
-#152 := [monotonicity #88 #91]: #151
-#155 := [monotonicity #152]: #154
-#160 := [trans #155 #158]: #159
-#83 := (iff #24 #82)
-#80 := (iff #23 #79)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#163 := [monotonicity #84 #160]: #162
-#71 := (iff #16 #69)
-#72 := [rewrite]: #71
-#166 := [monotonicity #72 #163]: #165
-#74 := (iff #17 #73)
-#75 := [rewrite]: #74
-#169 := [monotonicity #75 #166]: #168
-#172 := [monotonicity #169]: #171
-#175 := [quant-intro #172]: #174
-#192 := [trans #175 #190]: #191
-#149 := [asserted]: #41
-#193 := [mp #149 #192]: #188
-#196 := [mp~ #193 #200]: #188
-#244 := [mp #196 #243]: #241
-#275 := [mp #244 #274]: #272
-#760 := [mp #275 #759]: #755
-decl f4 :: Int
-#8 := f4
-#10 := (f3 f4 0::Int)
-#62 := (= f4 #10)
-#65 := (not #62)
-#11 := (= #10 f4)
-#12 := (not #11)
-#66 := (iff #12 #65)
-#63 := (iff #11 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#61 := [asserted]: #12
-#70 := [mp #61 #67]: #65
-#548 := (not #755)
-#549 := (or #548 #62)
-#333 := (* -1::Int 0::Int)
-#418 := (* -1::Int f4)
-#419 := (mod #418 #333)
-#420 := (+ #10 #419)
-#411 := (= #420 0::Int)
-#422 := (mod f4 0::Int)
-#423 := (* -1::Int #422)
-#351 := (+ #10 #423)
-#424 := (= #351 0::Int)
-#421 := (>= f4 0::Int)
-#425 := (<= 0::Int 0::Int)
-#404 := (or #425 #421)
-#739 := (not #404)
-#741 := (<= f4 0::Int)
-#398 := (or #741 #425)
-#528 := (not #398)
-#735 := (or #528 #739)
-#409 := (ite #735 #424 #411)
-#410 := (= #10 0::Int)
-#742 := (= f4 0::Int)
-#743 := (ite #742 #410 #409)
-#744 := (= 0::Int 0::Int)
-#745 := (ite #744 #62 #743)
-#550 := (or #548 #745)
-#693 := (iff #550 #549)
-#695 := (iff #549 #549)
-#689 := [rewrite]: #695
-#701 := (iff #745 #62)
-#439 := (mod #418 0::Int)
-#718 := (+ #10 #439)
-#429 := (= #718 0::Int)
-#713 := (ite #742 #410 #429)
-#1 := true
-#704 := (ite true #62 #713)
-#705 := (iff #704 #62)
-#706 := [rewrite]: #705
-#699 := (iff #745 #704)
-#702 := (iff #743 #713)
-#712 := (iff #409 #429)
-#432 := (ite false #424 #429)
-#426 := (iff #432 #429)
-#708 := [rewrite]: #426
-#710 := (iff #409 #432)
-#430 := (iff #411 #429)
-#715 := (= #420 #718)
-#440 := (= #419 #439)
-#716 := (= #333 0::Int)
-#717 := [rewrite]: #716
-#714 := [monotonicity #717]: #440
-#719 := [monotonicity #714]: #715
-#431 := [monotonicity #719]: #430
-#446 := (iff #735 false)
-#720 := (or false false)
-#444 := (iff #720 false)
-#445 := [rewrite]: #444
-#721 := (iff #735 #720)
-#731 := (iff #739 false)
-#386 := (not true)
-#724 := (iff #386 false)
-#725 := [rewrite]: #724
-#373 := (iff #739 #386)
-#732 := (iff #404 true)
-#728 := (or true #421)
-#367 := (iff #728 true)
-#730 := [rewrite]: #367
-#723 := (iff #404 #728)
-#736 := (iff #425 true)
-#396 := [rewrite]: #736
-#729 := [monotonicity #396]: #723
-#372 := [trans #729 #730]: #732
-#733 := [monotonicity #372]: #373
-#734 := [trans #733 #725]: #731
-#726 := (iff #528 false)
-#387 := (iff #528 #386)
-#722 := (iff #398 true)
-#401 := (or #741 true)
-#738 := (iff #401 true)
-#381 := [rewrite]: #738
-#737 := (iff #398 #401)
-#397 := [monotonicity #396]: #737
-#385 := [trans #397 #381]: #722
-#388 := [monotonicity #385]: #387
-#727 := [trans #388 #725]: #726
-#443 := [monotonicity #727 #734]: #721
-#339 := [trans #443 #445]: #446
-#711 := [monotonicity #339 #431]: #710
-#709 := [trans #711 #708]: #712
-#703 := [monotonicity #709]: #702
-#740 := (iff #744 true)
-#746 := [rewrite]: #740
-#700 := [monotonicity #746 #703]: #699
-#707 := [trans #700 #706]: #701
-#694 := [monotonicity #707]: #693
-#690 := [trans #694 #689]: #693
-#692 := [quant-inst #8 #9]: #550
-#696 := [mp #692 #690]: #549
-[unit-resolution #696 #70 #760]: false
-unsat
-b2456294470b5bb8cf71e8629c4adcc89dacf753 303 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#14 := (:var 0 Int)
-#13 := (:var 1 Int)
-#33 := (f3 #13 #14)
-#756 := (pattern #33)
-#8 := 0::Int
-#88 := -1::Int
-#92 := (* -1::Int #14)
-#89 := (* -1::Int #13)
-#153 := (mod #89 #92)
-#268 := (+ #33 #153)
-#269 := (= #268 0::Int)
-#34 := (mod #13 #14)
-#265 := (* -1::Int #34)
-#266 := (+ #33 #265)
-#267 := (= #266 0::Int)
-#127 := (>= #13 0::Int)
-#120 := (<= #14 0::Int)
-#212 := (or #120 #127)
-#213 := (not #212)
-#116 := (<= #13 0::Int)
-#210 := (or #116 #120)
-#211 := (not #210)
-#216 := (or #211 #213)
-#270 := (ite #216 #267 #269)
-#264 := (= #33 0::Int)
-#16 := (= #13 0::Int)
-#271 := (ite #16 #264 #270)
-#263 := (= #13 #33)
-#17 := (= #14 0::Int)
-#272 := (ite #17 #263 #271)
-#757 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #756) #272)
-#275 := (forall (vars (?v0 Int) (?v1 Int)) #272)
-#760 := (iff #275 #757)
-#758 := (iff #272 #272)
-#759 := [refl]: #758
-#761 := [quant-intro #759]: #760
-#159 := (* -1::Int #153)
-#232 := (ite #216 #34 #159)
-#235 := (ite #16 0::Int #232)
-#238 := (ite #17 #13 #235)
-#241 := (= #33 #238)
-#244 := (forall (vars (?v0 Int) (?v1 Int)) #241)
-#276 := (iff #244 #275)
-#273 := (iff #241 #272)
-#274 := [rewrite]: #273
-#277 := [quant-intro #274]: #276
-#128 := (not #127)
-#121 := (not #120)
-#131 := (and #121 #128)
-#117 := (not #116)
-#124 := (and #117 #121)
-#134 := (or #124 #131)
-#179 := (ite #134 #34 #159)
-#182 := (ite #16 0::Int #179)
-#185 := (ite #17 #13 #182)
-#188 := (= #33 #185)
-#191 := (forall (vars (?v0 Int) (?v1 Int)) #188)
-#245 := (iff #191 #244)
-#242 := (iff #188 #241)
-#239 := (= #185 #238)
-#236 := (= #182 #235)
-#233 := (= #179 #232)
-#217 := (iff #134 #216)
-#214 := (iff #131 #213)
-#215 := [rewrite]: #214
-#204 := (iff #124 #211)
-#205 := [rewrite]: #204
-#218 := [monotonicity #205 #215]: #217
-#234 := [monotonicity #218]: #233
-#237 := [monotonicity #234]: #236
-#240 := [monotonicity #237]: #239
-#243 := [monotonicity #240]: #242
-#246 := [quant-intro #243]: #245
-#202 := (~ #191 #191)
-#201 := (~ #188 #188)
-#198 := [refl]: #201
-#203 := [nnf-pos #198]: #202
-#27 := (- #14)
-#26 := (- #13)
-#35 := (mod #26 #27)
-#36 := (- #35)
-#20 := (< 0::Int #14)
-#22 := (< #13 0::Int)
-#23 := (and #22 #20)
-#19 := (< 0::Int #13)
-#21 := (and #19 #20)
-#24 := (or #21 #23)
-#37 := (ite #24 #34 #36)
-#38 := (ite #16 0::Int #37)
-#39 := (ite #17 #13 #38)
-#40 := (= #33 #39)
-#41 := (forall (vars (?v0 Int) (?v1 Int)) #40)
-#194 := (iff #41 #191)
-#82 := (and #20 #22)
-#85 := (or #21 #82)
-#164 := (ite #85 #34 #159)
-#73 := (= 0::Int #13)
-#167 := (ite #73 0::Int #164)
-#76 := (= 0::Int #14)
-#170 := (ite #76 #13 #167)
-#173 := (= #33 #170)
-#176 := (forall (vars (?v0 Int) (?v1 Int)) #173)
-#192 := (iff #176 #191)
-#189 := (iff #173 #188)
-#186 := (= #170 #185)
-#183 := (= #167 #182)
-#180 := (= #164 #179)
-#135 := (iff #85 #134)
-#132 := (iff #82 #131)
-#129 := (iff #22 #128)
-#130 := [rewrite]: #129
-#122 := (iff #20 #121)
-#123 := [rewrite]: #122
-#133 := [monotonicity #123 #130]: #132
-#125 := (iff #21 #124)
-#118 := (iff #19 #117)
-#119 := [rewrite]: #118
-#126 := [monotonicity #119 #123]: #125
-#136 := [monotonicity #126 #133]: #135
-#181 := [monotonicity #136]: #180
-#110 := (iff #73 #16)
-#111 := [rewrite]: #110
-#184 := [monotonicity #111 #181]: #183
-#112 := (iff #76 #17)
-#113 := [rewrite]: #112
-#187 := [monotonicity #113 #184]: #186
-#190 := [monotonicity #187]: #189
-#193 := [quant-intro #190]: #192
-#177 := (iff #41 #176)
-#174 := (iff #40 #173)
-#171 := (= #39 #170)
-#168 := (= #38 #167)
-#165 := (= #37 #164)
-#162 := (= #36 #159)
-#156 := (- #153)
-#160 := (= #156 #159)
-#161 := [rewrite]: #160
-#157 := (= #36 #156)
-#154 := (= #35 #153)
-#93 := (= #27 #92)
-#94 := [rewrite]: #93
-#90 := (= #26 #89)
-#91 := [rewrite]: #90
-#155 := [monotonicity #91 #94]: #154
-#158 := [monotonicity #155]: #157
-#163 := [trans #158 #161]: #162
-#86 := (iff #24 #85)
-#83 := (iff #23 #82)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#166 := [monotonicity #87 #163]: #165
-#74 := (iff #16 #73)
-#75 := [rewrite]: #74
-#169 := [monotonicity #75 #166]: #168
-#77 := (iff #17 #76)
+#59 := (= #19 1::Int)
+#60 := [rewrite]: #59
+#57 := (iff #18 #56)
+#54 := (iff #17 #53)
+#55 := [rewrite]: #54
+#58 := [monotonicity #55]: #57
+#85 := [monotonicity #58 #60 #82]: #84
+#51 := (iff #12 false)
+#52 := [rewrite]: #51
+#88 := [monotonicity #52 #85]: #87
+#92 := [trans #88 #90]: #91
+#49 := (iff #10 false)
+#50 := [rewrite]: #49
+#95 := [monotonicity #50 #92]: #94
+#99 := [trans #95 #97]: #98
+#102 := [monotonicity #99]: #101
+#106 := [trans #102 #104]: #105
+#109 := [monotonicity #106]: #108
+#145 := [trans #109 #143]: #144
+#48 := [asserted]: #28
+[mp #48 #145]: false
+unsat
+2e12b506bd838c7a91cf9b35f04a675da557e17b 85 0
+#2 := false
+#9 := 0::Int
+#8 := 3::Int
+#17 := (- 3::Int)
+#18 := (mod #17 #17)
+#19 := (- #18)
+#16 := (mod 3::Int 3::Int)
+#11 := (< 0::Int 3::Int)
+#13 := (< 3::Int 0::Int)
+#14 := (and #13 #11)
+#12 := (and #11 #11)
+#15 := (or #12 #14)
+#20 := (ite #15 #16 #19)
+#10 := (= 3::Int 0::Int)
+#21 := (ite #10 0::Int #20)
+#22 := (ite #10 3::Int #21)
+#23 := (= #22 0::Int)
+#24 := (not #23)
+#106 := (iff #24 false)
+#1 := true
+#101 := (not true)
+#104 := (iff #101 false)
+#105 := [rewrite]: #104
+#102 := (iff #24 #101)
+#99 := (iff #23 true)
+#94 := (= 0::Int 0::Int)
+#97 := (iff #94 true)
+#98 := [rewrite]: #97
+#95 := (iff #23 #94)
+#88 := (ite false 3::Int 0::Int)
+#91 := (= #88 0::Int)
+#92 := [rewrite]: #91
+#89 := (= #22 #88)
+#86 := (= #21 0::Int)
+#81 := (ite false 0::Int 0::Int)
+#84 := (= #81 0::Int)
+#85 := [rewrite]: #84
+#82 := (= #21 #81)
+#79 := (= #20 0::Int)
+#49 := (and #11 #13)
+#52 := (or #11 #49)
+#74 := (ite #52 0::Int 0::Int)
+#77 := (= #74 0::Int)
 #78 := [rewrite]: #77
-#172 := [monotonicity #78 #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [quant-intro #175]: #177
-#195 := [trans #178 #193]: #194
-#152 := [asserted]: #41
-#196 := [mp #152 #195]: #191
-#199 := [mp~ #196 #203]: #191
-#247 := [mp #199 #246]: #244
-#278 := [mp #247 #277]: #275
-#762 := [mp #278 #761]: #757
-#9 := 1::Int
-#10 := (f3 0::Int 1::Int)
-#11 := (= #10 0::Int)
-#12 := (not #11)
-#61 := [asserted]: #12
-#678 := (not #757)
-#679 := (or #678 #11)
-#336 := (* -1::Int 1::Int)
-#420 := (* -1::Int 0::Int)
-#421 := (mod #420 #336)
-#422 := (+ #10 #421)
-#413 := (= #422 0::Int)
-#424 := (mod 0::Int 1::Int)
-#425 := (* -1::Int #424)
-#426 := (+ #10 #425)
-#423 := (= #426 0::Int)
-#427 := (>= 0::Int 0::Int)
-#406 := (<= 1::Int 0::Int)
-#741 := (or #406 #427)
-#743 := (not #741)
-#400 := (<= 0::Int 0::Int)
-#530 := (or #400 #406)
-#737 := (not #530)
-#411 := (or #737 #743)
-#412 := (ite #411 #423 #413)
-#744 := (= 0::Int 0::Int)
-#745 := (ite #744 #11 #412)
-#62 := (= 0::Int #10)
-#746 := (= 1::Int 0::Int)
-#747 := (ite #746 #62 #745)
-#682 := (or #678 #747)
-#582 := (iff #682 #679)
-#585 := (iff #679 #679)
-#578 := [rewrite]: #585
-#681 := (iff #747 #11)
-#699 := (ite false #11 #11)
-#529 := (iff #699 #11)
-#531 := [rewrite]: #529
-#574 := (iff #747 #699)
-#572 := (iff #745 #11)
-#1 := true
-#686 := (ite true #11 #11)
-#687 := (iff #686 #11)
-#690 := [rewrite]: #687
-#688 := (iff #745 #686)
-#532 := (iff #412 #11)
-#693 := (iff #412 #699)
-#692 := (iff #413 #11)
-#697 := (= #422 #10)
-#428 := (+ #10 0::Int)
-#711 := (= #428 #10)
-#715 := [rewrite]: #711
-#695 := (= #422 #428)
-#552 := (= #421 0::Int)
-#708 := (mod 0::Int -1::Int)
-#550 := (= #708 0::Int)
-#551 := [rewrite]: #550
-#703 := (= #421 #708)
-#702 := (= #336 -1::Int)
-#707 := [rewrite]: #702
-#433 := (= #420 0::Int)
-#434 := [rewrite]: #433
-#709 := [monotonicity #434 #707]: #703
-#694 := [trans #709 #551]: #552
-#696 := [monotonicity #694]: #695
-#691 := [trans #696 #715]: #697
-#698 := [monotonicity #691]: #692
-#706 := (iff #423 #11)
-#704 := (= #426 #10)
-#710 := (= #426 #428)
-#712 := (= #425 0::Int)
-#431 := (= #425 #420)
-#717 := (= #424 0::Int)
-#721 := [rewrite]: #717
-#432 := [monotonicity #721]: #431
-#713 := [trans #432 #434]: #712
-#714 := [monotonicity #713]: #710
-#705 := [trans #714 #715]: #704
-#701 := [monotonicity #705]: #706
-#716 := (iff #411 false)
-#342 := (or false false)
-#441 := (iff #342 false)
-#442 := [rewrite]: #441
-#718 := (iff #411 #342)
-#447 := (iff #743 false)
-#727 := (not true)
-#730 := (iff #727 false)
-#725 := [rewrite]: #730
-#445 := (iff #743 #727)
-#722 := (iff #741 true)
-#374 := (or false true)
-#733 := (iff #374 true)
-#736 := [rewrite]: #733
-#375 := (iff #741 #374)
-#732 := (iff #427 true)
-#734 := [rewrite]: #732
-#399 := (iff #406 false)
-#740 := [rewrite]: #399
-#735 := [monotonicity #740 #734]: #375
-#723 := [trans #735 #736]: #722
-#446 := [monotonicity #723]: #445
-#448 := [trans #446 #725]: #447
-#731 := (iff #737 false)
-#728 := (iff #737 #727)
-#390 := (iff #530 true)
-#383 := (or true false)
-#388 := (iff #383 true)
-#389 := [rewrite]: #388
-#724 := (iff #530 #383)
-#403 := (iff #400 true)
-#739 := [rewrite]: #403
-#387 := [monotonicity #739 #740]: #724
-#726 := [trans #387 #389]: #390
-#729 := [monotonicity #726]: #728
-#369 := [trans #729 #725]: #731
-#719 := [monotonicity #369 #448]: #718
-#720 := [trans #719 #442]: #716
-#700 := [monotonicity #720 #701 #698]: #693
-#685 := [trans #700 #531]: #532
-#738 := (iff #744 true)
-#398 := [rewrite]: #738
-#689 := [monotonicity #398 #685]: #688
-#573 := [trans #689 #690]: #572
-#68 := (iff #62 #11)
-#69 := [rewrite]: #68
-#742 := (iff #746 false)
-#748 := [rewrite]: #742
-#533 := [monotonicity #748 #69 #573]: #574
-#583 := [trans #533 #531]: #681
-#584 := [monotonicity #583]: #582
-#586 := [trans #584 #578]: #582
-#567 := [quant-inst #8 #9]: #682
-#587 := [mp #567 #586]: #679
-[unit-resolution #587 #61 #762]: false
-unsat
-e9db2756594c83e73847951deaad9e2f60acdae2 304 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#14 := (:var 0 Int)
-#13 := (:var 1 Int)
-#33 := (f3 #13 #14)
-#746 := (pattern #33)
-#10 := 0::Int
-#78 := -1::Int
-#82 := (* -1::Int #14)
-#79 := (* -1::Int #13)
-#143 := (mod #79 #82)
-#258 := (+ #33 #143)
-#259 := (= #258 0::Int)
-#34 := (mod #13 #14)
-#255 := (* -1::Int #34)
-#256 := (+ #33 #255)
-#257 := (= #256 0::Int)
-#117 := (>= #13 0::Int)
-#110 := (<= #14 0::Int)
-#202 := (or #110 #117)
-#203 := (not #202)
-#106 := (<= #13 0::Int)
-#200 := (or #106 #110)
-#201 := (not #200)
-#206 := (or #201 #203)
-#260 := (ite #206 #257 #259)
-#254 := (= #33 0::Int)
-#16 := (= #13 0::Int)
-#261 := (ite #16 #254 #260)
-#253 := (= #13 #33)
-#17 := (= #14 0::Int)
-#262 := (ite #17 #253 #261)
-#747 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #746) #262)
-#265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
-#750 := (iff #265 #747)
-#748 := (iff #262 #262)
-#749 := [refl]: #748
-#751 := [quant-intro #749]: #750
-#149 := (* -1::Int #143)
-#222 := (ite #206 #34 #149)
-#225 := (ite #16 0::Int #222)
-#228 := (ite #17 #13 #225)
-#231 := (= #33 #228)
-#234 := (forall (vars (?v0 Int) (?v1 Int)) #231)
-#266 := (iff #234 #265)
-#263 := (iff #231 #262)
-#264 := [rewrite]: #263
-#267 := [quant-intro #264]: #266
-#118 := (not #117)
-#111 := (not #110)
-#121 := (and #111 #118)
-#107 := (not #106)
-#114 := (and #107 #111)
-#124 := (or #114 #121)
-#169 := (ite #124 #34 #149)
-#172 := (ite #16 0::Int #169)
-#175 := (ite #17 #13 #172)
-#178 := (= #33 #175)
-#181 := (forall (vars (?v0 Int) (?v1 Int)) #178)
-#235 := (iff #181 #234)
-#232 := (iff #178 #231)
-#229 := (= #175 #228)
-#226 := (= #172 #225)
-#223 := (= #169 #222)
-#207 := (iff #124 #206)
-#204 := (iff #121 #203)
-#205 := [rewrite]: #204
-#194 := (iff #114 #201)
-#195 := [rewrite]: #194
-#208 := [monotonicity #195 #205]: #207
-#224 := [monotonicity #208]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [quant-intro #233]: #235
-#192 := (~ #181 #181)
-#191 := (~ #178 #178)
-#188 := [refl]: #191
-#193 := [nnf-pos #188]: #192
-#27 := (- #14)
-#26 := (- #13)
-#35 := (mod #26 #27)
-#36 := (- #35)
-#20 := (< 0::Int #14)
-#22 := (< #13 0::Int)
-#23 := (and #22 #20)
-#19 := (< 0::Int #13)
-#21 := (and #19 #20)
-#24 := (or #21 #23)
-#37 := (ite #24 #34 #36)
-#38 := (ite #16 0::Int #37)
-#39 := (ite #17 #13 #38)
-#40 := (= #33 #39)
-#41 := (forall (vars (?v0 Int) (?v1 Int)) #40)
-#184 := (iff #41 #181)
-#72 := (and #20 #22)
-#75 := (or #21 #72)
-#154 := (ite #75 #34 #149)
-#63 := (= 0::Int #13)
-#157 := (ite #63 0::Int #154)
-#66 := (= 0::Int #14)
-#160 := (ite #66 #13 #157)
-#163 := (= #33 #160)
-#166 := (forall (vars (?v0 Int) (?v1 Int)) #163)
-#182 := (iff #166 #181)
-#179 := (iff #163 #178)
-#176 := (= #160 #175)
-#173 := (= #157 #172)
-#170 := (= #154 #169)
-#125 := (iff #75 #124)
-#122 := (iff #72 #121)
-#119 := (iff #22 #118)
-#120 := [rewrite]: #119
-#112 := (iff #20 #111)
-#113 := [rewrite]: #112
-#123 := [monotonicity #113 #120]: #122
-#115 := (iff #21 #114)
-#108 := (iff #19 #107)
-#109 := [rewrite]: #108
-#116 := [monotonicity #109 #113]: #115
-#126 := [monotonicity #116 #123]: #125
-#171 := [monotonicity #126]: #170
-#100 := (iff #63 #16)
-#101 := [rewrite]: #100
-#174 := [monotonicity #101 #171]: #173
-#102 := (iff #66 #17)
-#103 := [rewrite]: #102
-#177 := [monotonicity #103 #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [quant-intro #180]: #182
-#167 := (iff #41 #166)
-#164 := (iff #40 #163)
-#161 := (= #39 #160)
-#158 := (= #38 #157)
-#155 := (= #37 #154)
-#152 := (= #36 #149)
-#146 := (- #143)
-#150 := (= #146 #149)
-#151 := [rewrite]: #150
-#147 := (= #36 #146)
-#144 := (= #35 #143)
-#83 := (= #27 #82)
-#84 := [rewrite]: #83
-#80 := (= #26 #79)
-#81 := [rewrite]: #80
-#145 := [monotonicity #81 #84]: #144
-#148 := [monotonicity #145]: #147
-#153 := [trans #148 #151]: #152
-#76 := (iff #24 #75)
-#73 := (iff #23 #72)
-#74 := [rewrite]: #73
-#77 := [monotonicity #74]: #76
-#156 := [monotonicity #77 #153]: #155
-#64 := (iff #16 #63)
-#65 := [rewrite]: #64
-#159 := [monotonicity #65 #156]: #158
-#67 := (iff #17 #66)
-#68 := [rewrite]: #67
-#162 := [monotonicity #68 #159]: #161
-#165 := [monotonicity #162]: #164
-#168 := [quant-intro #165]: #167
-#185 := [trans #168 #183]: #184
-#142 := [asserted]: #41
-#186 := [mp #142 #185]: #181
-#189 := [mp~ #186 #193]: #181
-#237 := [mp #189 #236]: #234
-#268 := [mp #237 #267]: #265
-#752 := [mp #268 #751]: #747
-#8 := 1::Int
-#9 := (f3 1::Int 1::Int)
-#11 := (= #9 0::Int)
-#12 := (not #11)
-#61 := [asserted]: #12
-#572 := (not #747)
-#574 := (or #572 #11)
-#326 := (* -1::Int 1::Int)
-#410 := (mod #326 #326)
-#411 := (+ #9 #410)
-#412 := (= #411 0::Int)
-#403 := (mod 1::Int 1::Int)
-#414 := (* -1::Int #403)
-#415 := (+ #9 #414)
-#416 := (= #415 0::Int)
-#413 := (>= 1::Int 0::Int)
-#417 := (<= 1::Int 0::Int)
-#396 := (or #417 #413)
-#731 := (not #396)
-#733 := (or #417 #417)
-#390 := (not #733)
-#520 := (or #390 #731)
-#727 := (ite #520 #416 #412)
-#401 := (= 1::Int 0::Int)
-#402 := (ite #401 #11 #727)
-#734 := (= 1::Int #9)
-#735 := (ite #401 #734 #402)
-#575 := (or #572 #735)
-#576 := (iff #575 #574)
-#578 := (iff #574 #574)
-#579 := [rewrite]: #578
-#672 := (iff #735 #11)
-#738 := (= #9 1::Int)
-#523 := (ite false #738 #11)
-#668 := (iff #523 #11)
-#669 := [rewrite]: #668
-#671 := (iff #735 #523)
-#563 := (iff #402 #11)
-#678 := (ite false #11 #11)
-#680 := (iff #678 #11)
-#562 := [rewrite]: #680
-#679 := (iff #402 #678)
-#675 := (iff #727 #11)
-#1 := true
-#683 := (ite true #11 #11)
-#521 := (iff #683 #11)
-#522 := [rewrite]: #521
-#690 := (iff #727 #683)
-#688 := (iff #412 #11)
-#681 := (= #411 #9)
-#700 := (+ #9 0::Int)
-#705 := (= #700 #9)
-#694 := [rewrite]: #705
-#686 := (= #411 #700)
-#684 := (= #410 0::Int)
-#693 := (mod -1::Int -1::Int)
-#541 := (= #693 0::Int)
-#542 := [rewrite]: #541
-#699 := (= #410 #693)
-#697 := (= #326 -1::Int)
-#698 := [rewrite]: #697
-#540 := [monotonicity #698 #698]: #699
-#685 := [trans #540 #542]: #684
-#687 := [monotonicity #685]: #686
-#682 := [trans #687 #694]: #681
-#689 := [monotonicity #682]: #688
-#691 := (iff #416 #11)
-#695 := (= #415 #9)
-#704 := (= #415 #700)
-#703 := (= #414 0::Int)
-#421 := (* -1::Int 0::Int)
-#424 := (= #421 0::Int)
-#702 := [rewrite]: #424
-#422 := (= #414 #421)
-#707 := (= #403 0::Int)
-#711 := [rewrite]: #707
-#423 := [monotonicity #711]: #422
-#418 := [trans #423 #702]: #703
-#701 := [monotonicity #418]: #704
-#696 := [trans #701 #694]: #695
-#692 := [monotonicity #696]: #691
-#706 := (iff #520 true)
-#332 := (or true false)
-#431 := (iff #332 true)
-#432 := [rewrite]: #431
-#708 := (iff #520 #332)
-#437 := (iff #731 false)
-#726 := (not true)
-#435 := (iff #726 false)
-#436 := [rewrite]: #435
-#712 := (iff #731 #726)
-#725 := (iff #396 true)
-#359 := (or false true)
-#364 := (iff #359 true)
-#365 := [rewrite]: #364
-#722 := (iff #396 #359)
-#715 := (iff #413 true)
-#721 := [rewrite]: #715
-#388 := (iff #417 false)
-#393 := [rewrite]: #388
-#724 := [monotonicity #393 #721]: #722
-#723 := [trans #724 #365]: #725
-#713 := [monotonicity #723]: #712
-#438 := [trans #713 #436]: #437
-#719 := (iff #390 true)
-#379 := (not false)
-#717 := (iff #379 true)
-#718 := [rewrite]: #717
-#380 := (iff #390 #379)
-#377 := (iff #733 false)
-#729 := (or false false)
-#373 := (iff #729 false)
-#714 := [rewrite]: #373
-#389 := (iff #733 #729)
-#730 := [monotonicity #393 #393]: #389
-#378 := [trans #730 #714]: #377
-#716 := [monotonicity #378]: #380
-#720 := [trans #716 #718]: #719
-#709 := [monotonicity #720 #438]: #708
-#710 := [trans #709 #432]: #706
-#519 := [monotonicity #710 #692 #689]: #690
-#676 := [trans #519 #522]: #675
-#736 := (iff #401 false)
-#737 := [rewrite]: #736
-#677 := [monotonicity #737 #676]: #679
-#564 := [trans #677 #562]: #563
-#732 := (iff #734 #738)
-#728 := [rewrite]: #732
-#573 := [monotonicity #737 #728 #564]: #671
-#557 := [trans #573 #669]: #672
-#577 := [monotonicity #557]: #576
-#580 := [trans #577 #579]: #576
-#568 := [quant-inst #8 #8]: #575
-#673 := [mp #568 #580]: #574
-[unit-resolution #673 #61 #752]: false
-unsat
-5a27e28e4534905d80bae8170a2a6b87f8d4215e 315 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#15 := (:var 0 Int)
-#14 := (:var 1 Int)
-#34 := (f3 #14 #15)
-#747 := (pattern #34)
-#11 := 0::Int
+#75 := (= #20 #74)
+#72 := (= #19 0::Int)
+#67 := (- 0::Int)
+#70 := (= #67 0::Int)
+#71 := [rewrite]: #70
+#68 := (= #19 #67)
+#65 := (= #18 0::Int)
+#57 := -3::Int
+#60 := (mod -3::Int -3::Int)
+#63 := (= #60 0::Int)
+#64 := [rewrite]: #63
+#61 := (= #18 #60)
+#58 := (= #17 -3::Int)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59 #59]: #61
+#66 := [trans #62 #64]: #65
+#69 := [monotonicity #66]: #68
+#73 := [trans #69 #71]: #72
+#55 := (= #16 0::Int)
+#56 := [rewrite]: #55
+#53 := (iff #15 #52)
+#50 := (iff #14 #49)
+#51 := [rewrite]: #50
+#47 := (iff #12 #11)
+#48 := [rewrite]: #47
+#54 := [monotonicity #48 #51]: #53
+#76 := [monotonicity #54 #56 #73]: #75
+#80 := [trans #76 #78]: #79
+#45 := (iff #10 false)
+#46 := [rewrite]: #45
+#83 := [monotonicity #46 #80]: #82
+#87 := [trans #83 #85]: #86
+#90 := [monotonicity #46 #87]: #89
+#93 := [trans #90 #92]: #23
+#96 := [monotonicity #93]: #95
+#100 := [trans #96 #98]: #99
+#103 := [monotonicity #100]: #102
+#107 := [trans #103 #105]: #106
+#44 := [asserted]: #24
+[mp #44 #107]: false
+unsat
+a185dd1db6f642a5e7d15c4c9072da159f55df2d 124 0
+#2 := false
+#27 := 2::Int
+#8 := 3::Int
+#21 := (- 3::Int)
+#11 := 5::Int
+#20 := (- 5::Int)
+#22 := (mod #20 #21)
+#23 := (- #22)
+#19 := (mod 5::Int 3::Int)
+#9 := 0::Int
+#14 := (< 0::Int 3::Int)
+#16 := (< 5::Int 0::Int)
+#17 := (and #16 #14)
+#13 := (< 0::Int 5::Int)
+#15 := (and #13 #14)
+#18 := (or #15 #17)
+#24 := (ite #18 #19 #23)
+#12 := (= 5::Int 0::Int)
+#25 := (ite #12 0::Int #24)
+#10 := (= 3::Int 0::Int)
+#26 := (ite #10 5::Int #25)
+#28 := (= #26 2::Int)
+#29 := (not #28)
+#145 := (iff #29 false)
+#54 := (and #14 #16)
+#57 := (or #15 #54)
+#108 := (not #57)
+#143 := (iff #108 false)
+#1 := true
+#138 := (not true)
+#141 := (iff #138 false)
+#142 := [rewrite]: #141
+#139 := (iff #108 #138)
+#136 := (iff #57 true)
+#131 := (or true false)
+#134 := (iff #131 true)
+#135 := [rewrite]: #134
+#132 := (iff #57 #131)
+#129 := (iff #54 false)
+#124 := (and true false)
+#127 := (iff #124 false)
+#128 := [rewrite]: #127
+#125 := (iff #54 #124)
+#122 := (iff #16 false)
+#123 := [rewrite]: #122
+#113 := (iff #14 true)
+#114 := [rewrite]: #113
+#126 := [monotonicity #114 #123]: #125
+#130 := [trans #126 #128]: #129
+#120 := (iff #15 true)
+#115 := (and true true)
+#118 := (iff #115 true)
+#119 := [rewrite]: #118
+#116 := (iff #15 #115)
+#111 := (iff #13 true)
+#112 := [rewrite]: #111
+#117 := [monotonicity #112 #114]: #116
+#121 := [trans #117 #119]: #120
+#133 := [monotonicity #121 #130]: #132
+#137 := [trans #133 #135]: #136
+#140 := [monotonicity #137]: #139
+#144 := [trans #140 #142]: #143
+#109 := (iff #29 #108)
+#106 := (iff #28 #57)
 #79 := -1::Int
-#83 := (* -1::Int #15)
-#80 := (* -1::Int #14)
-#144 := (mod #80 #83)
-#259 := (+ #34 #144)
-#260 := (= #259 0::Int)
-#35 := (mod #14 #15)
-#256 := (* -1::Int #35)
-#257 := (+ #34 #256)
-#258 := (= #257 0::Int)
-#118 := (>= #14 0::Int)
-#111 := (<= #15 0::Int)
-#203 := (or #111 #118)
-#204 := (not #203)
-#107 := (<= #14 0::Int)
-#201 := (or #107 #111)
-#202 := (not #201)
-#207 := (or #202 #204)
-#261 := (ite #207 #258 #260)
-#255 := (= #34 0::Int)
-#17 := (= #14 0::Int)
-#262 := (ite #17 #255 #261)
-#254 := (= #14 #34)
-#18 := (= #15 0::Int)
-#263 := (ite #18 #254 #262)
-#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #263)
-#266 := (forall (vars (?v0 Int) (?v1 Int)) #263)
-#751 := (iff #266 #748)
-#749 := (iff #263 #263)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#150 := (* -1::Int #144)
-#223 := (ite #207 #35 #150)
-#226 := (ite #17 0::Int #223)
-#229 := (ite #18 #14 #226)
-#232 := (= #34 #229)
-#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
-#267 := (iff #235 #266)
-#264 := (iff #232 #263)
-#265 := [rewrite]: #264
-#268 := [quant-intro #265]: #267
-#119 := (not #118)
-#112 := (not #111)
-#122 := (and #112 #119)
-#108 := (not #107)
-#115 := (and #108 #112)
-#125 := (or #115 #122)
-#170 := (ite #125 #35 #150)
-#173 := (ite #17 0::Int #170)
-#176 := (ite #18 #14 #173)
-#179 := (= #34 #176)
-#182 := (forall (vars (?v0 Int) (?v1 Int)) #179)
-#236 := (iff #182 #235)
-#233 := (iff #179 #232)
-#230 := (= #176 #229)
-#227 := (= #173 #226)
-#224 := (= #170 #223)
-#208 := (iff #125 #207)
-#205 := (iff #122 #204)
-#206 := [rewrite]: #205
-#195 := (iff #115 #202)
-#196 := [rewrite]: #195
-#209 := [monotonicity #196 #206]: #208
-#225 := [monotonicity #209]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [quant-intro #234]: #236
-#193 := (~ #182 #182)
-#192 := (~ #179 #179)
-#189 := [refl]: #192
-#194 := [nnf-pos #189]: #193
-#28 := (- #15)
-#27 := (- #14)
-#36 := (mod #27 #28)
-#37 := (- #36)
-#21 := (< 0::Int #15)
-#23 := (< #14 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #14)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#38 := (ite #25 #35 #37)
-#39 := (ite #17 0::Int #38)
-#40 := (ite #18 #14 #39)
-#41 := (= #34 #40)
-#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
-#185 := (iff #42 #182)
-#73 := (and #21 #23)
-#76 := (or #22 #73)
-#155 := (ite #76 #35 #150)
-#64 := (= 0::Int #14)
-#158 := (ite #64 0::Int #155)
-#67 := (= 0::Int #15)
-#161 := (ite #67 #14 #158)
-#164 := (= #34 #161)
-#167 := (forall (vars (?v0 Int) (?v1 Int)) #164)
-#183 := (iff #167 #182)
-#180 := (iff #164 #179)
-#177 := (= #161 #176)
-#174 := (= #158 #173)
-#171 := (= #155 #170)
-#126 := (iff #76 #125)
-#123 := (iff #73 #122)
-#120 := (iff #23 #119)
-#121 := [rewrite]: #120
-#113 := (iff #21 #112)
-#114 := [rewrite]: #113
-#124 := [monotonicity #114 #121]: #123
-#116 := (iff #22 #115)
-#109 := (iff #20 #108)
-#110 := [rewrite]: #109
-#117 := [monotonicity #110 #114]: #116
-#127 := [monotonicity #117 #124]: #126
-#172 := [monotonicity #127]: #171
-#101 := (iff #64 #17)
-#102 := [rewrite]: #101
-#175 := [monotonicity #102 #172]: #174
-#103 := (iff #67 #18)
-#104 := [rewrite]: #103
-#178 := [monotonicity #104 #175]: #177
-#181 := [monotonicity #178]: #180
-#184 := [quant-intro #181]: #183
-#168 := (iff #42 #167)
-#165 := (iff #41 #164)
-#162 := (= #40 #161)
-#159 := (= #39 #158)
-#156 := (= #38 #155)
-#153 := (= #37 #150)
-#147 := (- #144)
-#151 := (= #147 #150)
-#152 := [rewrite]: #151
-#148 := (= #37 #147)
-#145 := (= #36 #144)
-#84 := (= #28 #83)
-#85 := [rewrite]: #84
-#81 := (= #27 #80)
-#82 := [rewrite]: #81
-#146 := [monotonicity #82 #85]: #145
-#149 := [monotonicity #146]: #148
-#154 := [trans #149 #152]: #153
-#77 := (iff #25 #76)
-#74 := (iff #24 #73)
-#75 := [rewrite]: #74
-#78 := [monotonicity #75]: #77
-#157 := [monotonicity #78 #154]: #156
-#65 := (iff #17 #64)
-#66 := [rewrite]: #65
-#160 := [monotonicity #66 #157]: #159
-#68 := (iff #18 #67)
-#69 := [rewrite]: #68
-#163 := [monotonicity #69 #160]: #162
-#166 := [monotonicity #163]: #165
-#169 := [quant-intro #166]: #168
-#186 := [trans #169 #184]: #185
-#143 := [asserted]: #42
-#187 := [mp #143 #186]: #182
-#190 := [mp~ #187 #194]: #182
-#238 := [mp #190 #237]: #235
-#269 := [mp #238 #268]: #266
-#753 := [mp #269 #752]: #748
-#9 := 1::Int
-#8 := 3::Int
-#10 := (f3 3::Int 1::Int)
-#12 := (= #10 0::Int)
-#13 := (not #12)
-#62 := [asserted]: #13
-#671 := (not #748)
-#675 := (or #671 #12)
-#327 := (* -1::Int 1::Int)
-#411 := (* -1::Int 3::Int)
-#412 := (mod #411 #327)
-#413 := (+ #10 #412)
-#404 := (= #413 0::Int)
-#415 := (mod 3::Int 1::Int)
-#416 := (* -1::Int #415)
-#417 := (+ #10 #416)
-#414 := (= #417 0::Int)
-#418 := (>= 3::Int 0::Int)
-#397 := (<= 1::Int 0::Int)
-#732 := (or #397 #418)
-#734 := (not #732)
-#391 := (<= 3::Int 0::Int)
-#521 := (or #391 #397)
-#728 := (not #521)
-#402 := (or #728 #734)
-#403 := (ite #402 #414 #404)
-#735 := (= 3::Int 0::Int)
-#736 := (ite #735 #12 #403)
-#737 := (= 3::Int #10)
-#738 := (= 1::Int 0::Int)
-#733 := (ite #738 #737 #736)
-#662 := (or #671 #733)
-#656 := (iff #662 #675)
-#655 := (iff #675 #675)
-#665 := [rewrite]: #655
-#581 := (iff #733 #12)
-#394 := (= #10 3::Int)
-#569 := (ite false #394 #12)
-#579 := (iff #569 #12)
-#580 := [rewrite]: #579
-#577 := (iff #733 #569)
-#575 := (iff #736 #12)
-#669 := (ite false #12 #12)
-#558 := (iff #669 #12)
-#573 := [rewrite]: #558
-#670 := (iff #736 #669)
-#672 := (iff #403 #12)
-#1 := true
-#681 := (ite true #12 #12)
-#565 := (iff #681 #12)
-#524 := [rewrite]: #565
-#563 := (iff #403 #681)
-#680 := (iff #404 #12)
-#677 := (= #413 #10)
-#692 := (+ #10 0::Int)
-#699 := (= #692 #10)
-#694 := [rewrite]: #699
-#523 := (= #413 #692)
-#520 := (= #412 0::Int)
-#685 := -3::Int
-#683 := (mod -3::Int -1::Int)
-#684 := (= #683 0::Int)
-#691 := [rewrite]: #684
-#689 := (= #412 #683)
-#688 := (= #327 -1::Int)
-#682 := [rewrite]: #688
-#686 := (= #411 -3::Int)
-#687 := [rewrite]: #686
-#690 := [monotonicity #687 #682]: #689
-#522 := [trans #690 #691]: #520
-#676 := [monotonicity #522]: #523
-#679 := [trans #676 #694]: #677
-#678 := [monotonicity #679]: #680
-#542 := (iff #414 #12)
-#700 := (= #417 #10)
-#693 := (= #417 #692)
-#696 := (= #416 0::Int)
-#701 := (* -1::Int 0::Int)
-#706 := (= #701 0::Int)
-#695 := [rewrite]: #706
-#705 := (= #416 #701)
-#704 := (= #415 0::Int)
-#419 := [rewrite]: #704
-#702 := [monotonicity #419]: #705
-#697 := [trans #702 #695]: #696
-#698 := [monotonicity #697]: #693
-#541 := [trans #698 #694]: #700
-#543 := [monotonicity #541]: #542
-#425 := (iff #402 true)
-#708 := (or true false)
-#423 := (iff #708 true)
-#424 := [rewrite]: #423
-#712 := (iff #402 #708)
-#707 := (iff #734 false)
-#333 := (not true)
-#432 := (iff #333 false)
-#433 := [rewrite]: #432
-#709 := (iff #734 #333)
-#438 := (iff #732 true)
-#727 := (or false true)
-#436 := (iff #727 true)
-#437 := [rewrite]: #436
-#713 := (iff #732 #727)
-#726 := (iff #418 true)
-#724 := [rewrite]: #726
-#378 := (iff #397 false)
-#379 := [rewrite]: #378
-#714 := [monotonicity #379 #724]: #713
-#439 := [trans #714 #437]: #438
-#710 := [monotonicity #439]: #709
-#711 := [trans #710 #433]: #707
-#365 := (iff #728 true)
-#716 := (not false)
-#723 := (iff #716 true)
-#725 := [rewrite]: #723
-#722 := (iff #728 #716)
-#720 := (iff #521 false)
-#380 := (or false false)
-#718 := (iff #380 false)
-#719 := [rewrite]: #718
-#381 := (iff #521 #380)
-#374 := (iff #391 false)
-#715 := [rewrite]: #374
-#717 := [monotonicity #715 #379]: #381
-#721 := [trans #717 #719]: #720
-#360 := [monotonicity #721]: #722
-#366 := [trans #360 #725]: #365
-#422 := [monotonicity #366 #711]: #712
-#703 := [trans #422 #424]: #425
-#564 := [monotonicity #703 #543 #678]: #563
-#574 := [trans #564 #524]: #672
-#390 := (iff #735 false)
-#731 := [rewrite]: #390
-#673 := [monotonicity #731 #574]: #670
-#576 := [trans #673 #573]: #575
-#389 := (iff #737 #394)
-#730 := [rewrite]: #389
-#739 := (iff #738 false)
-#729 := [rewrite]: #739
-#578 := [monotonicity #729 #730 #576]: #577
-#674 := [trans #578 #580]: #581
-#653 := [monotonicity #674]: #656
-#666 := [trans #653 #665]: #656
-#664 := [quant-inst #8 #9]: #662
-#667 := [mp #664 #666]: #675
-[unit-resolution #667 #62 #753]: false
-unsat
-1b99f23affb0dadf3316102e865176c5efc38d4f 313 0
-#2 := false
-#11 := 0::Int
-decl f4 :: Int
-#8 := f4
-#735 := (= f4 0::Int)
-#576 := (not #735)
-#418 := (>= f4 0::Int)
-#723 := (not #418)
-#391 := (<= f4 0::Int)
-#380 := (not #391)
-#691 := (or #380 #723 #735)
-#578 := (not #691)
-#79 := -1::Int
-#411 := (* -1::Int f4)
-#703 := (mod #411 -1::Int)
-decl f3 :: (-> Int Int Int)
-#9 := 1::Int
-#10 := (f3 f4 1::Int)
-#701 := (+ #10 #703)
-#706 := (= #701 0::Int)
-#12 := (= #10 0::Int)
-#523 := (ite #691 #12 #706)
-#15 := (:var 0 Int)
-#14 := (:var 1 Int)
-#34 := (f3 #14 #15)
-#747 := (pattern #34)
-#83 := (* -1::Int #15)
-#80 := (* -1::Int #14)
-#144 := (mod #80 #83)
-#259 := (+ #34 #144)
-#260 := (= #259 0::Int)
-#35 := (mod #14 #15)
-#256 := (* -1::Int #35)
-#257 := (+ #34 #256)
-#258 := (= #257 0::Int)
-#118 := (>= #14 0::Int)
-#111 := (<= #15 0::Int)
-#203 := (or #111 #118)
-#204 := (not #203)
-#107 := (<= #14 0::Int)
-#201 := (or #107 #111)
-#202 := (not #201)
-#207 := (or #202 #204)
-#261 := (ite #207 #258 #260)
-#255 := (= #34 0::Int)
-#17 := (= #14 0::Int)
-#262 := (ite #17 #255 #261)
-#254 := (= #14 #34)
-#18 := (= #15 0::Int)
-#263 := (ite #18 #254 #262)
-#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #263)
-#266 := (forall (vars (?v0 Int) (?v1 Int)) #263)
-#751 := (iff #266 #748)
-#749 := (iff #263 #263)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#150 := (* -1::Int #144)
-#223 := (ite #207 #35 #150)
-#226 := (ite #17 0::Int #223)
-#229 := (ite #18 #14 #226)
-#232 := (= #34 #229)
-#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
-#267 := (iff #235 #266)
-#264 := (iff #232 #263)
-#265 := [rewrite]: #264
-#268 := [quant-intro #265]: #267
-#119 := (not #118)
-#112 := (not #111)
-#122 := (and #112 #119)
-#108 := (not #107)
-#115 := (and #108 #112)
-#125 := (or #115 #122)
-#170 := (ite #125 #35 #150)
-#173 := (ite #17 0::Int #170)
-#176 := (ite #18 #14 #173)
-#179 := (= #34 #176)
-#182 := (forall (vars (?v0 Int) (?v1 Int)) #179)
-#236 := (iff #182 #235)
-#233 := (iff #179 #232)
-#230 := (= #176 #229)
-#227 := (= #173 #226)
-#224 := (= #170 #223)
-#208 := (iff #125 #207)
-#205 := (iff #122 #204)
-#206 := [rewrite]: #205
-#195 := (iff #115 #202)
-#196 := [rewrite]: #195
-#209 := [monotonicity #196 #206]: #208
-#225 := [monotonicity #209]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [quant-intro #234]: #236
-#193 := (~ #182 #182)
-#192 := (~ #179 #179)
-#189 := [refl]: #192
-#194 := [nnf-pos #189]: #193
-#28 := (- #15)
-#27 := (- #14)
-#36 := (mod #27 #28)
-#37 := (- #36)
-#21 := (< 0::Int #15)
-#23 := (< #14 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #14)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#38 := (ite #25 #35 #37)
-#39 := (ite #17 0::Int #38)
-#40 := (ite #18 #14 #39)
-#41 := (= #34 #40)
-#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
-#185 := (iff #42 #182)
-#73 := (and #21 #23)
-#76 := (or #22 #73)
-#155 := (ite #76 #35 #150)
-#64 := (= 0::Int #14)
-#158 := (ite #64 0::Int #155)
-#67 := (= 0::Int #15)
-#161 := (ite #67 #14 #158)
-#164 := (= #34 #161)
-#167 := (forall (vars (?v0 Int) (?v1 Int)) #164)
-#183 := (iff #167 #182)
-#180 := (iff #164 #179)
-#177 := (= #161 #176)
-#174 := (= #158 #173)
-#171 := (= #155 #170)
-#126 := (iff #76 #125)
-#123 := (iff #73 #122)
-#120 := (iff #23 #119)
-#121 := [rewrite]: #120
-#113 := (iff #21 #112)
-#114 := [rewrite]: #113
-#124 := [monotonicity #114 #121]: #123
-#116 := (iff #22 #115)
-#109 := (iff #20 #108)
-#110 := [rewrite]: #109
-#117 := [monotonicity #110 #114]: #116
-#127 := [monotonicity #117 #124]: #126
-#172 := [monotonicity #127]: #171
-#101 := (iff #64 #17)
-#102 := [rewrite]: #101
-#175 := [monotonicity #102 #172]: #174
-#103 := (iff #67 #18)
-#104 := [rewrite]: #103
-#178 := [monotonicity #104 #175]: #177
-#181 := [monotonicity #178]: #180
-#184 := [quant-intro #181]: #183
-#168 := (iff #42 #167)
-#165 := (iff #41 #164)
-#162 := (= #40 #161)
-#159 := (= #39 #158)
-#156 := (= #38 #155)
-#153 := (= #37 #150)
-#147 := (- #144)
-#151 := (= #147 #150)
-#152 := [rewrite]: #151
-#148 := (= #37 #147)
-#145 := (= #36 #144)
-#84 := (= #28 #83)
-#85 := [rewrite]: #84
-#81 := (= #27 #80)
-#82 := [rewrite]: #81
-#146 := [monotonicity #82 #85]: #145
-#149 := [monotonicity #146]: #148
-#154 := [trans #149 #152]: #153
-#77 := (iff #25 #76)
-#74 := (iff #24 #73)
-#75 := [rewrite]: #74
+#84 := (ite #57 2::Int -1::Int)
+#101 := (= #84 2::Int)
+#104 := (iff #101 #57)
+#105 := [rewrite]: #104
+#102 := (iff #28 #101)
+#99 := (= #26 #84)
+#94 := (ite false 5::Int #84)
+#97 := (= #94 #84)
+#98 := [rewrite]: #97
+#95 := (= #26 #94)
+#92 := (= #25 #84)
+#87 := (ite false 0::Int #84)
+#90 := (= #87 #84)
+#91 := [rewrite]: #90
+#88 := (= #25 #87)
+#85 := (= #24 #84)
+#82 := (= #23 -1::Int)
+#71 := 1::Int
+#76 := (- 1::Int)
+#80 := (= #76 -1::Int)
+#81 := [rewrite]: #80
+#77 := (= #23 #76)
+#74 := (= #22 1::Int)
+#65 := -3::Int
+#62 := -5::Int
+#68 := (mod -5::Int -3::Int)
+#72 := (= #68 1::Int)
+#73 := [rewrite]: #72
+#69 := (= #22 #68)
+#66 := (= #21 -3::Int)
+#67 := [rewrite]: #66
+#63 := (= #20 -5::Int)
+#64 := [rewrite]: #63
+#70 := [monotonicity #64 #67]: #69
+#75 := [trans #70 #73]: #74
 #78 := [monotonicity #75]: #77
-#157 := [monotonicity #78 #154]: #156
-#65 := (iff #17 #64)
-#66 := [rewrite]: #65
-#160 := [monotonicity #66 #157]: #159
-#68 := (iff #18 #67)
-#69 := [rewrite]: #68
-#163 := [monotonicity #69 #160]: #162
-#166 := [monotonicity #163]: #165
-#169 := [quant-intro #166]: #168
-#186 := [trans #169 #184]: #185
-#143 := [asserted]: #42
-#187 := [mp #143 #186]: #182
-#190 := [mp~ #187 #194]: #182
-#238 := [mp #190 #237]: #235
-#269 := [mp #238 #268]: #266
-#753 := [mp #269 #752]: #748
-#678 := (not #748)
-#681 := (or #678 #523)
-#327 := (* -1::Int 1::Int)
-#412 := (mod #411 #327)
-#413 := (+ #10 #412)
-#404 := (= #413 0::Int)
-#415 := (mod f4 1::Int)
-#416 := (* -1::Int #415)
-#417 := (+ #10 #416)
-#414 := (= #417 0::Int)
-#397 := (<= 1::Int 0::Int)
-#732 := (or #397 #418)
-#734 := (not #732)
-#521 := (or #391 #397)
-#728 := (not #521)
-#402 := (or #728 #734)
-#403 := (ite #402 #414 #404)
-#736 := (ite #735 #12 #403)
-#737 := (= f4 #10)
-#738 := (= 1::Int 0::Int)
-#733 := (ite #738 #737 #736)
-#563 := (or #678 #733)
-#565 := (iff #563 #681)
-#672 := (iff #681 #681)
-#574 := [rewrite]: #672
-#679 := (iff #733 #523)
-#366 := (or #380 #723)
-#700 := (or #366 #735)
-#541 := (ite #700 #12 #706)
-#676 := (iff #541 #523)
-#520 := (iff #700 #691)
-#522 := [rewrite]: #520
-#677 := [monotonicity #522]: #676
-#690 := (iff #733 #541)
-#687 := (ite false #737 #541)
-#683 := (iff #687 #541)
-#689 := [rewrite]: #683
-#688 := (iff #733 #687)
-#685 := (iff #736 #541)
-#697 := (ite #366 #12 #706)
-#698 := (ite #735 #12 #697)
-#542 := (iff #698 #541)
-#543 := [rewrite]: #542
-#699 := (iff #736 #698)
-#692 := (iff #403 #697)
-#695 := (iff #404 #706)
-#705 := (= #413 #701)
-#704 := (= #412 #703)
-#424 := (= #327 -1::Int)
-#425 := [rewrite]: #424
-#419 := [monotonicity #425]: #704
-#702 := [monotonicity #419]: #705
-#696 := [monotonicity #702]: #695
-#422 := (iff #414 #12)
-#708 := (= #417 #10)
-#710 := (+ #10 0::Int)
-#707 := (= #710 #10)
-#711 := [rewrite]: #707
-#432 := (= #417 #710)
-#333 := (= #416 0::Int)
-#714 := (* -1::Int 0::Int)
-#438 := (= #714 0::Int)
-#439 := [rewrite]: #438
-#436 := (= #416 #714)
-#727 := (= #415 0::Int)
-#713 := [rewrite]: #727
-#437 := [monotonicity #713]: #436
-#709 := [trans #437 #439]: #333
-#433 := [monotonicity #709]: #432
-#712 := [trans #433 #711]: #708
-#423 := [monotonicity #712]: #422
-#726 := (iff #402 #366)
-#725 := (iff #734 #723)
-#722 := (iff #732 #418)
-#718 := (or false #418)
-#721 := (iff #718 #418)
-#716 := [rewrite]: #721
-#719 := (iff #732 #718)
-#389 := (iff #397 false)
-#394 := [rewrite]: #389
-#720 := [monotonicity #394]: #719
-#360 := [trans #720 #716]: #722
-#365 := [monotonicity #360]: #725
-#381 := (iff #728 #380)
-#378 := (iff #521 #391)
-#730 := (or #391 false)
-#374 := (iff #730 #391)
-#715 := [rewrite]: #374
-#390 := (iff #521 #730)
-#731 := [monotonicity #394]: #390
-#379 := [trans #731 #715]: #378
-#717 := [monotonicity #379]: #381
-#724 := [monotonicity #717 #365]: #726
-#693 := [monotonicity #724 #423 #696]: #692
-#694 := [monotonicity #693]: #699
-#686 := [trans #694 #543]: #685
-#739 := (iff #738 false)
-#729 := [rewrite]: #739
-#682 := [monotonicity #729 #686]: #688
-#684 := [trans #682 #689]: #690
-#680 := [trans #684 #677]: #679
-#524 := [monotonicity #680]: #565
-#669 := [trans #524 #574]: #565
-#564 := [quant-inst #8 #9]: #563
-#670 := [mp #564 #669]: #681
-#663 := [unit-resolution #670 #753]: #523
-#671 := (not #523)
-#668 := (or #671 #578)
-#13 := (not #12)
-#62 := [asserted]: #13
-#675 := (or #671 #578 #12)
-#662 := [def-axiom]: #675
-#657 := [unit-resolution #662 #62]: #668
-#658 := [unit-resolution #657 #663]: #578
-#569 := (or #691 #576)
-#577 := [def-axiom]: #569
-#659 := [unit-resolution #577 #658]: #576
-#673 := (or #691 #391)
-#558 := [def-axiom]: #673
-#660 := [unit-resolution #558 #658]: #391
-#573 := (or #691 #418)
-#575 := [def-axiom]: #573
-#654 := [unit-resolution #575 #658]: #418
-#661 := (or #735 #380 #723)
-#645 := [th-lemma arith triangle-eq]: #661
-[unit-resolution #645 #654 #660 #659]: false
-unsat
-b6f64755653a305b62fdd8df3fd24f1d40f3cc04 322 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#15 := (:var 0 Int)
-#14 := (:var 1 Int)
-#34 := (f3 #14 #15)
-#771 := (pattern #34)
-#8 := 0::Int
-#63 := -1::Int
-#107 := (* -1::Int #15)
-#104 := (* -1::Int #14)
-#168 := (mod #104 #107)
-#283 := (+ #34 #168)
-#284 := (= #283 0::Int)
-#35 := (mod #14 #15)
-#280 := (* -1::Int #35)
-#281 := (+ #34 #280)
-#282 := (= #281 0::Int)
-#142 := (>= #14 0::Int)
-#135 := (<= #15 0::Int)
-#227 := (or #135 #142)
-#228 := (not #227)
-#131 := (<= #14 0::Int)
-#225 := (or #131 #135)
-#226 := (not #225)
-#231 := (or #226 #228)
-#285 := (ite #231 #282 #284)
-#279 := (= #34 0::Int)
-#17 := (= #14 0::Int)
-#286 := (ite #17 #279 #285)
-#278 := (= #14 #34)
-#18 := (= #15 0::Int)
-#287 := (ite #18 #278 #286)
-#772 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #771) #287)
-#290 := (forall (vars (?v0 Int) (?v1 Int)) #287)
-#775 := (iff #290 #772)
-#773 := (iff #287 #287)
-#774 := [refl]: #773
-#776 := [quant-intro #774]: #775
-#174 := (* -1::Int #168)
-#247 := (ite #231 #35 #174)
-#250 := (ite #17 0::Int #247)
-#253 := (ite #18 #14 #250)
-#256 := (= #34 #253)
-#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
-#291 := (iff #259 #290)
-#288 := (iff #256 #287)
-#289 := [rewrite]: #288
-#292 := [quant-intro #289]: #291
-#143 := (not #142)
-#136 := (not #135)
-#146 := (and #136 #143)
-#132 := (not #131)
-#139 := (and #132 #136)
-#149 := (or #139 #146)
-#194 := (ite #149 #35 #174)
-#197 := (ite #17 0::Int #194)
-#200 := (ite #18 #14 #197)
-#203 := (= #34 #200)
-#206 := (forall (vars (?v0 Int) (?v1 Int)) #203)
-#260 := (iff #206 #259)
-#257 := (iff #203 #256)
-#254 := (= #200 #253)
-#251 := (= #197 #250)
-#248 := (= #194 #247)
-#232 := (iff #149 #231)
-#229 := (iff #146 #228)
-#230 := [rewrite]: #229
-#219 := (iff #139 #226)
-#220 := [rewrite]: #219
-#233 := [monotonicity #220 #230]: #232
-#249 := [monotonicity #233]: #248
-#252 := [monotonicity #249]: #251
-#255 := [monotonicity #252]: #254
-#258 := [monotonicity #255]: #257
-#261 := [quant-intro #258]: #260
-#217 := (~ #206 #206)
-#216 := (~ #203 #203)
-#213 := [refl]: #216
-#218 := [nnf-pos #213]: #217
-#28 := (- #15)
-#27 := (- #14)
-#36 := (mod #27 #28)
-#37 := (- #36)
-#21 := (< 0::Int #15)
-#23 := (< #14 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #14)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#38 := (ite #25 #35 #37)
-#39 := (ite #17 0::Int #38)
-#40 := (ite #18 #14 #39)
-#41 := (= #34 #40)
-#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
-#209 := (iff #42 #206)
-#98 := (and #21 #23)
-#101 := (or #22 #98)
-#179 := (ite #101 #35 #174)
-#89 := (= 0::Int #14)
-#182 := (ite #89 0::Int #179)
-#92 := (= 0::Int #15)
-#185 := (ite #92 #14 #182)
-#188 := (= #34 #185)
-#191 := (forall (vars (?v0 Int) (?v1 Int)) #188)
-#207 := (iff #191 #206)
-#204 := (iff #188 #203)
-#201 := (= #185 #200)
-#198 := (= #182 #197)
-#195 := (= #179 #194)
-#150 := (iff #101 #149)
-#147 := (iff #98 #146)
-#144 := (iff #23 #143)
-#145 := [rewrite]: #144
-#137 := (iff #21 #136)
-#138 := [rewrite]: #137
-#148 := [monotonicity #138 #145]: #147
-#140 := (iff #22 #139)
-#133 := (iff #20 #132)
-#134 := [rewrite]: #133
-#141 := [monotonicity #134 #138]: #140
-#151 := [monotonicity #141 #148]: #150
-#196 := [monotonicity #151]: #195
-#125 := (iff #89 #17)
-#126 := [rewrite]: #125
-#199 := [monotonicity #126 #196]: #198
-#127 := (iff #92 #18)
-#128 := [rewrite]: #127
-#202 := [monotonicity #128 #199]: #201
-#205 := [monotonicity #202]: #204
-#208 := [quant-intro #205]: #207
-#192 := (iff #42 #191)
-#189 := (iff #41 #188)
-#186 := (= #40 #185)
-#183 := (= #39 #182)
-#180 := (= #38 #179)
-#177 := (= #37 #174)
-#171 := (- #168)
-#175 := (= #171 #174)
-#176 := [rewrite]: #175
-#172 := (= #37 #171)
-#169 := (= #36 #168)
-#108 := (= #28 #107)
-#109 := [rewrite]: #108
-#105 := (= #27 #104)
-#106 := [rewrite]: #105
-#170 := [monotonicity #106 #109]: #169
-#173 := [monotonicity #170]: #172
-#178 := [trans #173 #176]: #177
-#102 := (iff #25 #101)
-#99 := (iff #24 #98)
-#100 := [rewrite]: #99
+#83 := [trans #78 #81]: #82
+#60 := (= #19 2::Int)
+#61 := [rewrite]: #60
+#58 := (iff #18 #57)
+#55 := (iff #17 #54)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#86 := [monotonicity #59 #61 #83]: #85
+#52 := (iff #12 false)
+#53 := [rewrite]: #52
+#89 := [monotonicity #53 #86]: #88
+#93 := [trans #89 #91]: #92
+#50 := (iff #10 false)
+#51 := [rewrite]: #50
+#96 := [monotonicity #51 #93]: #95
+#100 := [trans #96 #98]: #99
 #103 := [monotonicity #100]: #102
-#181 := [monotonicity #103 #178]: #180
-#90 := (iff #17 #89)
+#107 := [trans #103 #105]: #106
+#110 := [monotonicity #107]: #109
+#146 := [trans #110 #144]: #145
+#49 := [asserted]: #29
+[mp #49 #146]: false
+unsat
+7d327b19e01666c9f9c62ef0af0f737663d19d70 145 0
+#2 := false
+#28 := 2::Int
+#29 := (- 2::Int)
+#8 := 3::Int
+#9 := (- 3::Int)
+#22 := (- #9)
+#12 := 1::Int
+#21 := (- 1::Int)
+#23 := (mod #21 #22)
+#24 := (- #23)
+#20 := (mod 1::Int #9)
+#10 := 0::Int
+#15 := (< 0::Int #9)
+#17 := (< 1::Int 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int 1::Int)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#25 := (ite #19 #20 #24)
+#13 := (= 1::Int 0::Int)
+#26 := (ite #13 0::Int #25)
+#11 := (= #9 0::Int)
+#27 := (ite #11 1::Int #26)
+#30 := (= #27 #29)
+#31 := (not #30)
+#166 := (iff #31 false)
+#52 := -3::Int
+#64 := (< 0::Int -3::Int)
+#70 := (and #17 #64)
+#67 := (and #14 #64)
+#73 := (or #67 #70)
+#164 := (iff #73 false)
+#159 := (or false false)
+#162 := (iff #159 false)
+#163 := [rewrite]: #162
+#160 := (iff #73 #159)
+#157 := (iff #70 false)
+#152 := (and false false)
+#155 := (iff #152 false)
+#156 := [rewrite]: #155
+#153 := (iff #70 #152)
+#141 := (iff #64 false)
+#142 := [rewrite]: #141
+#150 := (iff #17 false)
+#151 := [rewrite]: #150
+#154 := [monotonicity #151 #142]: #153
+#158 := [trans #154 #156]: #157
+#148 := (iff #67 false)
+#1 := true
+#143 := (and true false)
+#146 := (iff #143 false)
+#147 := [rewrite]: #146
+#144 := (iff #67 #143)
+#139 := (iff #14 true)
+#140 := [rewrite]: #139
+#145 := [monotonicity #140 #142]: #144
+#149 := [trans #145 #147]: #148
+#161 := [monotonicity #149 #158]: #160
+#165 := [trans #161 #163]: #164
+#137 := (iff #31 #73)
+#127 := (not #73)
+#132 := (not #127)
+#135 := (iff #132 #73)
+#136 := [rewrite]: #135
+#133 := (iff #31 #132)
+#130 := (iff #30 #127)
+#102 := -2::Int
+#107 := (ite #73 1::Int -2::Int)
+#124 := (= #107 -2::Int)
+#128 := (iff #124 #127)
+#129 := [rewrite]: #128
+#125 := (iff #30 #124)
+#103 := (= #29 -2::Int)
+#104 := [rewrite]: #103
+#122 := (= #27 #107)
+#117 := (ite false 1::Int #107)
+#120 := (= #117 #107)
+#121 := [rewrite]: #120
+#118 := (= #27 #117)
+#115 := (= #26 #107)
+#110 := (ite false 0::Int #107)
+#113 := (= #110 #107)
+#114 := [rewrite]: #113
+#111 := (= #26 #110)
+#108 := (= #25 #107)
+#105 := (= #24 -2::Int)
+#100 := (= #24 #29)
+#98 := (= #23 2::Int)
+#83 := -1::Int
+#93 := (mod -1::Int 3::Int)
+#96 := (= #93 2::Int)
+#97 := [rewrite]: #96
+#94 := (= #23 #93)
+#91 := (= #22 3::Int)
+#86 := (- -3::Int)
+#89 := (= #86 3::Int)
+#90 := [rewrite]: #89
+#87 := (= #22 #86)
+#53 := (= #9 -3::Int)
+#54 := [rewrite]: #53
+#88 := [monotonicity #54]: #87
+#92 := [trans #88 #90]: #91
+#84 := (= #21 -1::Int)
+#85 := [rewrite]: #84
+#95 := [monotonicity #85 #92]: #94
+#99 := [trans #95 #97]: #98
+#101 := [monotonicity #99]: #100
+#106 := [trans #101 #104]: #105
+#81 := (= #20 1::Int)
+#76 := (mod 1::Int -3::Int)
+#79 := (= #76 1::Int)
+#80 := [rewrite]: #79
+#77 := (= #20 #76)
+#78 := [monotonicity #54]: #77
+#82 := [trans #78 #80]: #81
+#74 := (iff #19 #73)
+#71 := (iff #18 #70)
+#65 := (iff #15 #64)
+#66 := [monotonicity #54]: #65
+#72 := [monotonicity #66]: #71
+#68 := (iff #16 #67)
+#69 := [monotonicity #66]: #68
+#75 := [monotonicity #69 #72]: #74
+#109 := [monotonicity #75 #82 #106]: #108
+#62 := (iff #13 false)
+#63 := [rewrite]: #62
+#112 := [monotonicity #63 #109]: #111
+#116 := [trans #112 #114]: #115
+#60 := (iff #11 false)
+#55 := (= -3::Int 0::Int)
+#58 := (iff #55 false)
+#59 := [rewrite]: #58
+#56 := (iff #11 #55)
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#119 := [monotonicity #61 #116]: #118
+#123 := [trans #119 #121]: #122
+#126 := [monotonicity #123 #104]: #125
+#131 := [trans #126 #129]: #130
+#134 := [monotonicity #131]: #133
+#138 := [trans #134 #136]: #137
+#167 := [trans #138 #165]: #166
+#51 := [asserted]: #31
+[mp #51 #167]: false
+unsat
+82d6113024911b407663ddeabeafc31ab21bb4b0 111 0
+#2 := false
+#10 := 0::Int
+#8 := 3::Int
+#9 := (- 3::Int)
+#20 := (- #9)
+#21 := (mod #9 #20)
+#22 := (- #21)
+#19 := (mod 3::Int #9)
+#14 := (< 0::Int #9)
+#16 := (< 3::Int 0::Int)
+#17 := (and #16 #14)
+#13 := (< 0::Int 3::Int)
+#15 := (and #13 #14)
+#18 := (or #15 #17)
+#23 := (ite #18 #19 #22)
+#12 := (= 3::Int 0::Int)
+#24 := (ite #12 0::Int #23)
+#11 := (= #9 0::Int)
+#25 := (ite #11 3::Int #24)
+#26 := (= #25 0::Int)
+#27 := (not #26)
+#132 := (iff #27 false)
+#1 := true
+#127 := (not true)
+#130 := (iff #127 false)
+#131 := [rewrite]: #130
+#128 := (iff #27 #127)
+#125 := (iff #26 true)
+#120 := (= 0::Int 0::Int)
+#123 := (iff #120 true)
+#124 := [rewrite]: #123
+#121 := (iff #26 #120)
+#114 := (ite false 3::Int 0::Int)
+#117 := (= #114 0::Int)
+#118 := [rewrite]: #117
+#115 := (= #25 #114)
+#112 := (= #24 0::Int)
+#107 := (ite false 0::Int 0::Int)
+#110 := (= #107 0::Int)
+#111 := [rewrite]: #110
+#108 := (= #24 #107)
+#105 := (= #23 0::Int)
+#48 := -3::Int
+#60 := (< 0::Int -3::Int)
+#66 := (and #16 #60)
+#63 := (and #13 #60)
+#69 := (or #63 #66)
+#100 := (ite #69 0::Int 0::Int)
+#103 := (= #100 0::Int)
+#104 := [rewrite]: #103
+#101 := (= #23 #100)
+#98 := (= #22 0::Int)
+#93 := (- 0::Int)
+#96 := (= #93 0::Int)
+#97 := [rewrite]: #96
+#94 := (= #22 #93)
+#91 := (= #21 0::Int)
+#86 := (mod -3::Int 3::Int)
+#89 := (= #86 0::Int)
+#90 := [rewrite]: #89
+#87 := (= #21 #86)
+#84 := (= #20 3::Int)
+#79 := (- -3::Int)
+#82 := (= #79 3::Int)
+#83 := [rewrite]: #82
+#80 := (= #20 #79)
+#49 := (= #9 -3::Int)
+#50 := [rewrite]: #49
+#81 := [monotonicity #50]: #80
+#85 := [trans #81 #83]: #84
+#88 := [monotonicity #50 #85]: #87
+#92 := [trans #88 #90]: #91
+#95 := [monotonicity #92]: #94
+#99 := [trans #95 #97]: #98
+#77 := (= #19 0::Int)
+#72 := (mod 3::Int -3::Int)
+#75 := (= #72 0::Int)
+#76 := [rewrite]: #75
+#73 := (= #19 #72)
+#74 := [monotonicity #50]: #73
+#78 := [trans #74 #76]: #77
+#70 := (iff #18 #69)
+#67 := (iff #17 #66)
+#61 := (iff #14 #60)
+#62 := [monotonicity #50]: #61
+#68 := [monotonicity #62]: #67
+#64 := (iff #15 #63)
+#65 := [monotonicity #62]: #64
+#71 := [monotonicity #65 #68]: #70
+#102 := [monotonicity #71 #78 #99]: #101
+#106 := [trans #102 #104]: #105
+#58 := (iff #12 false)
+#59 := [rewrite]: #58
+#109 := [monotonicity #59 #106]: #108
+#113 := [trans #109 #111]: #112
+#56 := (iff #11 false)
+#51 := (= -3::Int 0::Int)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #11 #51)
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#116 := [monotonicity #57 #113]: #115
+#119 := [trans #116 #118]: #26
+#122 := [monotonicity #119]: #121
+#126 := [trans #122 #124]: #125
+#129 := [monotonicity #126]: #128
+#133 := [trans #129 #131]: #132
+#47 := [asserted]: #27
+[mp #47 #133]: false
+unsat
+c4214ad6df5eccc4b53bd004dab0150c7519b10c 146 0
+#2 := false
+#28 := 1::Int
+#29 := (- 1::Int)
+#8 := 3::Int
+#9 := (- 3::Int)
+#22 := (- #9)
+#12 := 5::Int
+#21 := (- 5::Int)
+#23 := (mod #21 #22)
+#24 := (- #23)
+#20 := (mod 5::Int #9)
+#10 := 0::Int
+#15 := (< 0::Int #9)
+#17 := (< 5::Int 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int 5::Int)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#25 := (ite #19 #20 #24)
+#13 := (= 5::Int 0::Int)
+#26 := (ite #13 0::Int #25)
+#11 := (= #9 0::Int)
+#27 := (ite #11 5::Int #26)
+#30 := (= #27 #29)
+#31 := (not #30)
+#167 := (iff #31 false)
+#52 := -3::Int
+#64 := (< 0::Int -3::Int)
+#70 := (and #17 #64)
+#67 := (and #14 #64)
+#73 := (or #67 #70)
+#165 := (iff #73 false)
+#160 := (or false false)
+#163 := (iff #160 false)
+#164 := [rewrite]: #163
+#161 := (iff #73 #160)
+#158 := (iff #70 false)
+#153 := (and false false)
+#156 := (iff #153 false)
+#157 := [rewrite]: #156
+#154 := (iff #70 #153)
+#142 := (iff #64 false)
+#143 := [rewrite]: #142
+#151 := (iff #17 false)
+#152 := [rewrite]: #151
+#155 := [monotonicity #152 #143]: #154
+#159 := [trans #155 #157]: #158
+#149 := (iff #67 false)
+#1 := true
+#144 := (and true false)
+#147 := (iff #144 false)
+#148 := [rewrite]: #147
+#145 := (iff #67 #144)
+#140 := (iff #14 true)
+#141 := [rewrite]: #140
+#146 := [monotonicity #141 #143]: #145
+#150 := [trans #146 #148]: #149
+#162 := [monotonicity #150 #159]: #161
+#166 := [trans #162 #164]: #165
+#138 := (iff #31 #73)
+#128 := (not #73)
+#133 := (not #128)
+#136 := (iff #133 #73)
+#137 := [rewrite]: #136
+#134 := (iff #31 #133)
+#131 := (iff #30 #128)
+#103 := -1::Int
+#79 := 2::Int
+#108 := (ite #73 2::Int -1::Int)
+#125 := (= #108 -1::Int)
+#129 := (iff #125 #128)
+#130 := [rewrite]: #129
+#126 := (iff #30 #125)
+#104 := (= #29 -1::Int)
+#105 := [rewrite]: #104
+#123 := (= #27 #108)
+#118 := (ite false 5::Int #108)
+#121 := (= #118 #108)
+#122 := [rewrite]: #121
+#119 := (= #27 #118)
+#116 := (= #26 #108)
+#111 := (ite false 0::Int #108)
+#114 := (= #111 #108)
+#115 := [rewrite]: #114
+#112 := (= #26 #111)
+#109 := (= #25 #108)
+#106 := (= #24 -1::Int)
+#101 := (= #24 #29)
+#99 := (= #23 1::Int)
+#84 := -5::Int
+#94 := (mod -5::Int 3::Int)
+#97 := (= #94 1::Int)
+#98 := [rewrite]: #97
+#95 := (= #23 #94)
+#92 := (= #22 3::Int)
+#87 := (- -3::Int)
+#90 := (= #87 3::Int)
 #91 := [rewrite]: #90
-#184 := [monotonicity #91 #181]: #183
-#93 := (iff #18 #92)
-#94 := [rewrite]: #93
-#187 := [monotonicity #94 #184]: #186
-#190 := [monotonicity #187]: #189
-#193 := [quant-intro #190]: #192
-#210 := [trans #193 #208]: #209
-#167 := [asserted]: #42
-#211 := [mp #167 #210]: #206
-#214 := [mp~ #211 #218]: #206
-#262 := [mp #214 #261]: #259
-#293 := [mp #262 #292]: #290
-#777 := [mp #293 #776]: #772
-#66 := (f3 0::Int -1::Int)
-#69 := (= #66 0::Int)
-#82 := (not #69)
-#9 := 1::Int
-#10 := (- 1::Int)
-#11 := (f3 0::Int #10)
-#12 := (= #11 0::Int)
-#13 := (not #12)
-#85 := (iff #13 #82)
-#72 := (= 0::Int #66)
-#77 := (not #72)
-#83 := (iff #77 #82)
-#80 := (iff #72 #69)
+#88 := (= #22 #87)
+#53 := (= #9 -3::Int)
+#54 := [rewrite]: #53
+#89 := [monotonicity #54]: #88
+#93 := [trans #89 #91]: #92
+#85 := (= #21 -5::Int)
+#86 := [rewrite]: #85
+#96 := [monotonicity #86 #93]: #95
+#100 := [trans #96 #98]: #99
+#102 := [monotonicity #100]: #101
+#107 := [trans #102 #105]: #106
+#82 := (= #20 2::Int)
+#76 := (mod 5::Int -3::Int)
+#80 := (= #76 2::Int)
 #81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#78 := (iff #13 #77)
-#75 := (iff #12 #72)
-#73 := (iff #69 #72)
-#74 := [rewrite]: #73
-#70 := (iff #12 #69)
-#67 := (= #11 #66)
-#64 := (= #10 -1::Int)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#71 := [monotonicity #68]: #70
-#76 := [trans #71 #74]: #75
-#79 := [monotonicity #76]: #78
-#86 := [trans #79 #84]: #85
-#62 := [asserted]: #13
-#87 := [mp #62 #86]: #82
-#548 := (not #772)
-#696 := (or #548 #69)
-#351 := (* -1::Int -1::Int)
-#435 := (* -1::Int 0::Int)
-#436 := (mod #435 #351)
-#437 := (+ #66 #436)
-#428 := (= #437 0::Int)
-#439 := (mod 0::Int -1::Int)
-#440 := (* -1::Int #439)
-#441 := (+ #66 #440)
-#438 := (= #441 0::Int)
-#442 := (>= 0::Int 0::Int)
-#421 := (<= -1::Int 0::Int)
-#756 := (or #421 #442)
-#758 := (not #756)
-#415 := (<= 0::Int 0::Int)
-#545 := (or #415 #421)
-#752 := (not #545)
-#426 := (or #752 #758)
-#427 := (ite #426 #438 #428)
-#759 := (= 0::Int 0::Int)
-#760 := (ite #759 #69 #427)
-#761 := (= -1::Int 0::Int)
-#762 := (ite #761 #72 #760)
-#598 := (or #548 #762)
-#694 := (iff #598 #696)
-#582 := (iff #696 #696)
-#597 := [rewrite]: #582
-#588 := (iff #762 #69)
-#706 := (ite false #69 #69)
-#714 := (iff #706 #69)
-#708 := [rewrite]: #714
-#705 := (iff #762 #706)
-#704 := (iff #760 #69)
-#1 := true
-#546 := (ite true #69 #69)
-#701 := (iff #546 #69)
-#703 := [rewrite]: #701
-#547 := (iff #760 #546)
-#715 := (iff #427 #69)
-#707 := (iff #427 #706)
-#711 := (iff #428 #69)
-#709 := (= #437 #66)
-#449 := (+ #66 0::Int)
-#443 := (= #449 #66)
-#725 := [rewrite]: #443
-#566 := (= #437 #449)
-#724 := (= #436 0::Int)
-#716 := (mod 0::Int 1::Int)
-#723 := (= #716 0::Int)
-#718 := [rewrite]: #723
-#717 := (= #436 #716)
-#720 := (= #351 1::Int)
-#721 := [rewrite]: #720
-#736 := (= #435 0::Int)
-#446 := [rewrite]: #736
-#722 := [monotonicity #446 #721]: #717
-#565 := [trans #722 #718]: #724
-#567 := [monotonicity #565]: #566
-#710 := [trans #567 #725]: #709
-#712 := [monotonicity #710]: #711
-#730 := (iff #438 #69)
-#729 := (= #441 #66)
-#727 := (= #441 #449)
-#447 := (= #440 0::Int)
-#735 := (= #440 #435)
-#457 := (= #439 0::Int)
-#731 := [rewrite]: #457
-#732 := [monotonicity #731]: #735
-#448 := [trans #732 #446]: #447
-#728 := [monotonicity #448]: #727
-#726 := [trans #728 #725]: #729
-#719 := [monotonicity #726]: #730
-#734 := (iff #426 false)
-#461 := (or false false)
-#357 := (iff #461 false)
-#733 := [rewrite]: #357
-#462 := (iff #426 #461)
-#738 := (iff #758 false)
-#742 := (not true)
-#745 := (iff #742 false)
-#740 := [rewrite]: #745
-#751 := (iff #758 #742)
-#750 := (iff #756 true)
-#398 := (or true true)
-#403 := (iff #398 true)
-#404 := [rewrite]: #403
-#389 := (iff #756 #398)
-#747 := (iff #442 true)
-#749 := [rewrite]: #747
-#414 := (iff #421 true)
-#755 := [rewrite]: #414
-#390 := [monotonicity #755 #749]: #389
-#748 := [trans #390 #404]: #750
-#737 := [monotonicity #748]: #751
-#460 := [trans #737 #740]: #738
-#746 := (iff #752 false)
-#743 := (iff #752 #742)
-#405 := (iff #545 true)
-#739 := (iff #545 #398)
-#418 := (iff #415 true)
-#754 := [rewrite]: #418
-#402 := [monotonicity #754 #755]: #739
-#741 := [trans #402 #404]: #405
-#744 := [monotonicity #741]: #743
-#384 := [trans #744 #740]: #746
-#463 := [monotonicity #384 #460]: #462
-#456 := [trans #463 #733]: #734
-#713 := [monotonicity #456 #719 #712]: #707
-#544 := [trans #713 #708]: #715
-#753 := (iff #759 true)
-#413 := [rewrite]: #753
-#700 := [monotonicity #413 #544]: #547
-#702 := [trans #700 #703]: #704
-#757 := (iff #761 false)
-#763 := [rewrite]: #757
-#587 := [monotonicity #763 #81 #702]: #705
-#589 := [trans #587 #708]: #588
-#697 := [monotonicity #589]: #694
-#599 := [trans #697 #597]: #694
-#693 := [quant-inst #8 #63]: #598
-#600 := [mp #693 #599]: #696
-[unit-resolution #600 #87 #777]: false
-unsat
-7554e53ad4bbf50aa6cebedfca61c8a301b15856 332 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#15 := (:var 0 Int)
-#14 := (:var 1 Int)
-#34 := (f3 #14 #15)
-#771 := (pattern #34)
-#11 := 0::Int
-#63 := -1::Int
-#107 := (* -1::Int #15)
-#104 := (* -1::Int #14)
-#168 := (mod #104 #107)
-#283 := (+ #34 #168)
-#284 := (= #283 0::Int)
-#35 := (mod #14 #15)
-#280 := (* -1::Int #35)
-#281 := (+ #34 #280)
-#282 := (= #281 0::Int)
-#142 := (>= #14 0::Int)
-#135 := (<= #15 0::Int)
-#227 := (or #135 #142)
-#228 := (not #227)
-#131 := (<= #14 0::Int)
-#225 := (or #131 #135)
-#226 := (not #225)
-#231 := (or #226 #228)
-#285 := (ite #231 #282 #284)
-#279 := (= #34 0::Int)
-#17 := (= #14 0::Int)
-#286 := (ite #17 #279 #285)
-#278 := (= #14 #34)
-#18 := (= #15 0::Int)
-#287 := (ite #18 #278 #286)
-#772 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #771) #287)
-#290 := (forall (vars (?v0 Int) (?v1 Int)) #287)
-#775 := (iff #290 #772)
-#773 := (iff #287 #287)
-#774 := [refl]: #773
-#776 := [quant-intro #774]: #775
-#174 := (* -1::Int #168)
-#247 := (ite #231 #35 #174)
-#250 := (ite #17 0::Int #247)
-#253 := (ite #18 #14 #250)
-#256 := (= #34 #253)
-#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
-#291 := (iff #259 #290)
-#288 := (iff #256 #287)
-#289 := [rewrite]: #288
-#292 := [quant-intro #289]: #291
-#143 := (not #142)
-#136 := (not #135)
-#146 := (and #136 #143)
-#132 := (not #131)
-#139 := (and #132 #136)
-#149 := (or #139 #146)
-#194 := (ite #149 #35 #174)
-#197 := (ite #17 0::Int #194)
-#200 := (ite #18 #14 #197)
-#203 := (= #34 #200)
-#206 := (forall (vars (?v0 Int) (?v1 Int)) #203)
-#260 := (iff #206 #259)
-#257 := (iff #203 #256)
-#254 := (= #200 #253)
-#251 := (= #197 #250)
-#248 := (= #194 #247)
-#232 := (iff #149 #231)
-#229 := (iff #146 #228)
-#230 := [rewrite]: #229
-#219 := (iff #139 #226)
-#220 := [rewrite]: #219
-#233 := [monotonicity #220 #230]: #232
-#249 := [monotonicity #233]: #248
-#252 := [monotonicity #249]: #251
-#255 := [monotonicity #252]: #254
-#258 := [monotonicity #255]: #257
-#261 := [quant-intro #258]: #260
-#217 := (~ #206 #206)
-#216 := (~ #203 #203)
-#213 := [refl]: #216
-#218 := [nnf-pos #213]: #217
-#28 := (- #15)
-#27 := (- #14)
-#36 := (mod #27 #28)
-#37 := (- #36)
-#21 := (< 0::Int #15)
-#23 := (< #14 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #14)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#38 := (ite #25 #35 #37)
-#39 := (ite #17 0::Int #38)
-#40 := (ite #18 #14 #39)
-#41 := (= #34 #40)
-#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
-#209 := (iff #42 #206)
-#98 := (and #21 #23)
-#101 := (or #22 #98)
-#179 := (ite #101 #35 #174)
-#89 := (= 0::Int #14)
-#182 := (ite #89 0::Int #179)
-#92 := (= 0::Int #15)
-#185 := (ite #92 #14 #182)
-#188 := (= #34 #185)
-#191 := (forall (vars (?v0 Int) (?v1 Int)) #188)
-#207 := (iff #191 #206)
-#204 := (iff #188 #203)
-#201 := (= #185 #200)
-#198 := (= #182 #197)
-#195 := (= #179 #194)
-#150 := (iff #101 #149)
-#147 := (iff #98 #146)
-#144 := (iff #23 #143)
-#145 := [rewrite]: #144
-#137 := (iff #21 #136)
-#138 := [rewrite]: #137
-#148 := [monotonicity #138 #145]: #147
-#140 := (iff #22 #139)
-#133 := (iff #20 #132)
-#134 := [rewrite]: #133
-#141 := [monotonicity #134 #138]: #140
-#151 := [monotonicity #141 #148]: #150
-#196 := [monotonicity #151]: #195
-#125 := (iff #89 #17)
-#126 := [rewrite]: #125
-#199 := [monotonicity #126 #196]: #198
-#127 := (iff #92 #18)
-#128 := [rewrite]: #127
-#202 := [monotonicity #128 #199]: #201
-#205 := [monotonicity #202]: #204
-#208 := [quant-intro #205]: #207
-#192 := (iff #42 #191)
-#189 := (iff #41 #188)
-#186 := (= #40 #185)
-#183 := (= #39 #182)
-#180 := (= #38 #179)
-#177 := (= #37 #174)
-#171 := (- #168)
-#175 := (= #171 #174)
-#176 := [rewrite]: #175
-#172 := (= #37 #171)
-#169 := (= #36 #168)
-#108 := (= #28 #107)
-#109 := [rewrite]: #108
-#105 := (= #27 #104)
-#106 := [rewrite]: #105
-#170 := [monotonicity #106 #109]: #169
-#173 := [monotonicity #170]: #172
-#178 := [trans #173 #176]: #177
-#102 := (iff #25 #101)
-#99 := (iff #24 #98)
-#100 := [rewrite]: #99
-#103 := [monotonicity #100]: #102
-#181 := [monotonicity #103 #178]: #180
-#90 := (iff #17 #89)
-#91 := [rewrite]: #90
-#184 := [monotonicity #91 #181]: #183
-#93 := (iff #18 #92)
-#94 := [rewrite]: #93
-#187 := [monotonicity #94 #184]: #186
-#190 := [monotonicity #187]: #189
-#193 := [quant-intro #190]: #192
-#210 := [trans #193 #208]: #209
-#167 := [asserted]: #42
-#211 := [mp #167 #210]: #206
-#214 := [mp~ #211 #218]: #206
-#262 := [mp #214 #261]: #259
-#293 := [mp #262 #292]: #290
-#777 := [mp #293 #776]: #772
-#8 := 1::Int
-#66 := (f3 1::Int -1::Int)
-#69 := (= #66 0::Int)
-#82 := (not #69)
-#9 := (- 1::Int)
-#10 := (f3 1::Int #9)
-#12 := (= #10 0::Int)
-#13 := (not #12)
-#85 := (iff #13 #82)
-#72 := (= 0::Int #66)
-#77 := (not #72)
-#83 := (iff #77 #82)
-#80 := (iff #72 #69)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#78 := (iff #13 #77)
-#75 := (iff #12 #72)
-#73 := (iff #69 #72)
-#74 := [rewrite]: #73
-#70 := (iff #12 #69)
-#67 := (= #10 #66)
-#64 := (= #9 -1::Int)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#71 := [monotonicity #68]: #70
-#76 := [trans #71 #74]: #75
-#79 := [monotonicity #76]: #78
-#86 := [trans #79 #84]: #85
-#62 := [asserted]: #13
-#87 := [mp #62 #86]: #82
-#593 := (not #772)
-#601 := (or #593 #69)
-#351 := (* -1::Int -1::Int)
-#435 := (* -1::Int 1::Int)
-#436 := (mod #435 #351)
-#437 := (+ #66 #436)
-#428 := (= #437 0::Int)
-#439 := (mod 1::Int -1::Int)
-#440 := (* -1::Int #439)
-#441 := (+ #66 #440)
-#438 := (= #441 0::Int)
-#442 := (>= 1::Int 0::Int)
-#421 := (<= -1::Int 0::Int)
-#756 := (or #421 #442)
-#758 := (not #756)
-#415 := (<= 1::Int 0::Int)
-#545 := (or #415 #421)
-#752 := (not #545)
-#426 := (or #752 #758)
-#427 := (ite #426 #438 #428)
-#759 := (= 1::Int 0::Int)
-#760 := (ite #759 #69 #427)
-#761 := (= 1::Int #66)
-#762 := (= -1::Int 0::Int)
-#757 := (ite #762 #761 #760)
-#602 := (or #593 #757)
-#604 := (iff #602 #601)
-#698 := (iff #601 #601)
-#695 := [rewrite]: #698
-#599 := (iff #757 #69)
-#418 := (= #66 1::Int)
-#693 := (ite false #418 #69)
-#582 := (iff #693 #69)
-#597 := [rewrite]: #582
-#694 := (iff #757 #693)
-#696 := (iff #760 #69)
-#701 := (ite false #69 #69)
-#702 := (iff #701 #69)
-#705 := [rewrite]: #702
-#589 := (iff #760 #701)
-#587 := (iff #427 #69)
-#703 := (iff #427 #701)
-#547 := (iff #428 #69)
-#544 := (= #437 #66)
-#719 := (+ #66 0::Int)
-#716 := (= #719 #66)
-#717 := [rewrite]: #716
-#708 := (= #437 #719)
-#713 := (= #436 0::Int)
-#710 := (mod -1::Int 1::Int)
-#706 := (= #710 0::Int)
-#707 := [rewrite]: #706
-#711 := (= #436 #710)
-#567 := (= #351 1::Int)
-#709 := [rewrite]: #567
-#565 := (= #435 -1::Int)
-#566 := [rewrite]: #565
-#712 := [monotonicity #566 #709]: #711
-#714 := [trans #712 #707]: #713
-#715 := [monotonicity #714]: #708
-#546 := [trans #715 #717]: #544
-#700 := [monotonicity #546]: #547
-#718 := (iff #438 #69)
-#722 := (= #441 #66)
-#720 := (= #441 #719)
-#726 := (= #440 0::Int)
-#727 := (* -1::Int 0::Int)
-#725 := (= #727 0::Int)
-#729 := [rewrite]: #725
-#728 := (= #440 #727)
-#448 := (= #439 0::Int)
-#449 := [rewrite]: #448
-#443 := [monotonicity #449]: #728
-#730 := [trans #443 #729]: #726
-#721 := [monotonicity #730]: #720
-#723 := [trans #721 #717]: #722
-#724 := [monotonicity #723]: #718
-#446 := (iff #426 false)
-#457 := (or false false)
-#732 := (iff #457 false)
-#736 := [rewrite]: #732
-#731 := (iff #426 #457)
-#734 := (iff #758 false)
-#1 := true
-#740 := (not true)
-#747 := (iff #740 false)
-#749 := [rewrite]: #747
-#357 := (iff #758 #740)
-#462 := (iff #756 true)
-#751 := (or true true)
-#460 := (iff #751 true)
-#461 := [rewrite]: #460
-#737 := (iff #756 #751)
-#750 := (iff #442 true)
-#748 := [rewrite]: #750
-#402 := (iff #421 true)
-#403 := [rewrite]: #402
-#738 := [monotonicity #403 #748]: #737
-#463 := [trans #738 #461]: #462
-#733 := [monotonicity #463]: #357
-#456 := [trans #733 #749]: #734
-#389 := (iff #752 false)
-#746 := (iff #752 #740)
-#744 := (iff #545 true)
-#404 := (or false true)
-#742 := (iff #404 true)
-#743 := [rewrite]: #742
-#405 := (iff #545 #404)
-#398 := (iff #415 false)
-#739 := [rewrite]: #398
-#741 := [monotonicity #739 #403]: #405
-#745 := [trans #741 #743]: #744
-#384 := [monotonicity #745]: #746
-#390 := [trans #384 #749]: #389
-#735 := [monotonicity #390 #456]: #731
-#447 := [trans #735 #736]: #446
-#704 := [monotonicity #447 #724 #700]: #703
-#588 := [trans #704 #705]: #587
-#414 := (iff #759 false)
-#755 := [rewrite]: #414
-#548 := [monotonicity #755 #588]: #589
-#598 := [trans #548 #705]: #696
-#413 := (iff #761 #418)
-#754 := [rewrite]: #413
-#763 := (iff #762 false)
-#753 := [rewrite]: #763
-#697 := [monotonicity #753 #754 #598]: #694
-#600 := [trans #697 #597]: #599
-#605 := [monotonicity #600]: #604
-#699 := [trans #605 #695]: #604
-#603 := [quant-inst #8 #63]: #602
-#686 := [mp #603 #699]: #601
-[unit-resolution #686 #87 #777]: false
-unsat
-768cdc3a48375ab653481018d34501c9146cb16e 334 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#16 := (:var 0 Int)
-#15 := (:var 1 Int)
-#35 := (f3 #15 #16)
-#772 := (pattern #35)
-#12 := 0::Int
-#64 := -1::Int
-#108 := (* -1::Int #16)
-#105 := (* -1::Int #15)
-#169 := (mod #105 #108)
-#284 := (+ #35 #169)
-#285 := (= #284 0::Int)
-#36 := (mod #15 #16)
-#281 := (* -1::Int #36)
-#282 := (+ #35 #281)
-#283 := (= #282 0::Int)
-#143 := (>= #15 0::Int)
-#136 := (<= #16 0::Int)
-#228 := (or #136 #143)
-#229 := (not #228)
-#132 := (<= #15 0::Int)
-#226 := (or #132 #136)
-#227 := (not #226)
-#232 := (or #227 #229)
-#286 := (ite #232 #283 #285)
-#280 := (= #35 0::Int)
-#18 := (= #15 0::Int)
-#287 := (ite #18 #280 #286)
-#279 := (= #15 #35)
-#19 := (= #16 0::Int)
-#288 := (ite #19 #279 #287)
-#773 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #772) #288)
-#291 := (forall (vars (?v0 Int) (?v1 Int)) #288)
-#776 := (iff #291 #773)
-#774 := (iff #288 #288)
-#775 := [refl]: #774
-#777 := [quant-intro #775]: #776
-#175 := (* -1::Int #169)
-#248 := (ite #232 #36 #175)
-#251 := (ite #18 0::Int #248)
-#254 := (ite #19 #15 #251)
-#257 := (= #35 #254)
-#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
-#292 := (iff #260 #291)
-#289 := (iff #257 #288)
-#290 := [rewrite]: #289
-#293 := [quant-intro #290]: #292
-#144 := (not #143)
-#137 := (not #136)
-#147 := (and #137 #144)
-#133 := (not #132)
-#140 := (and #133 #137)
-#150 := (or #140 #147)
-#195 := (ite #150 #36 #175)
-#198 := (ite #18 0::Int #195)
-#201 := (ite #19 #15 #198)
-#204 := (= #35 #201)
-#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
-#261 := (iff #207 #260)
-#258 := (iff #204 #257)
-#255 := (= #201 #254)
-#252 := (= #198 #251)
-#249 := (= #195 #248)
-#233 := (iff #150 #232)
-#230 := (iff #147 #229)
-#231 := [rewrite]: #230
-#220 := (iff #140 #227)
-#221 := [rewrite]: #220
-#234 := [monotonicity #221 #231]: #233
-#250 := [monotonicity #234]: #249
-#253 := [monotonicity #250]: #252
-#256 := [monotonicity #253]: #255
-#259 := [monotonicity #256]: #258
-#262 := [quant-intro #259]: #261
-#218 := (~ #207 #207)
-#217 := (~ #204 #204)
-#214 := [refl]: #217
-#219 := [nnf-pos #214]: #218
-#29 := (- #16)
-#28 := (- #15)
-#37 := (mod #28 #29)
-#38 := (- #37)
-#22 := (< 0::Int #16)
-#24 := (< #15 0::Int)
-#25 := (and #24 #22)
-#21 := (< 0::Int #15)
-#23 := (and #21 #22)
-#26 := (or #23 #25)
-#39 := (ite #26 #36 #38)
-#40 := (ite #18 0::Int #39)
-#41 := (ite #19 #15 #40)
-#42 := (= #35 #41)
-#43 := (forall (vars (?v0 Int) (?v1 Int)) #42)
-#210 := (iff #43 #207)
-#99 := (and #22 #24)
-#102 := (or #23 #99)
-#180 := (ite #102 #36 #175)
-#90 := (= 0::Int #15)
-#183 := (ite #90 0::Int #180)
-#93 := (= 0::Int #16)
-#186 := (ite #93 #15 #183)
-#189 := (= #35 #186)
-#192 := (forall (vars (?v0 Int) (?v1 Int)) #189)
-#208 := (iff #192 #207)
-#205 := (iff #189 #204)
-#202 := (= #186 #201)
-#199 := (= #183 #198)
-#196 := (= #180 #195)
-#151 := (iff #102 #150)
-#148 := (iff #99 #147)
-#145 := (iff #24 #144)
-#146 := [rewrite]: #145
-#138 := (iff #22 #137)
-#139 := [rewrite]: #138
-#149 := [monotonicity #139 #146]: #148
-#141 := (iff #23 #140)
-#134 := (iff #21 #133)
-#135 := [rewrite]: #134
-#142 := [monotonicity #135 #139]: #141
-#152 := [monotonicity #142 #149]: #151
-#197 := [monotonicity #152]: #196
-#126 := (iff #90 #18)
-#127 := [rewrite]: #126
-#200 := [monotonicity #127 #197]: #199
-#128 := (iff #93 #19)
-#129 := [rewrite]: #128
-#203 := [monotonicity #129 #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [quant-intro #206]: #208
-#193 := (iff #43 #192)
-#190 := (iff #42 #189)
-#187 := (= #41 #186)
-#184 := (= #40 #183)
-#181 := (= #39 #180)
-#178 := (= #38 #175)
-#172 := (- #169)
-#176 := (= #172 #175)
-#177 := [rewrite]: #176
-#173 := (= #38 #172)
-#170 := (= #37 #169)
-#109 := (= #29 #108)
-#110 := [rewrite]: #109
-#106 := (= #28 #105)
-#107 := [rewrite]: #106
-#171 := [monotonicity #107 #110]: #170
-#174 := [monotonicity #171]: #173
-#179 := [trans #174 #177]: #178
-#103 := (iff #26 #102)
-#100 := (iff #25 #99)
-#101 := [rewrite]: #100
-#104 := [monotonicity #101]: #103
-#182 := [monotonicity #104 #179]: #181
-#91 := (iff #18 #90)
-#92 := [rewrite]: #91
-#185 := [monotonicity #92 #182]: #184
-#94 := (iff #19 #93)
-#95 := [rewrite]: #94
-#188 := [monotonicity #95 #185]: #187
-#191 := [monotonicity #188]: #190
-#194 := [quant-intro #191]: #193
-#211 := [trans #194 #209]: #210
-#168 := [asserted]: #43
-#212 := [mp #168 #211]: #207
-#215 := [mp~ #212 #219]: #207
-#263 := [mp #215 #262]: #260
-#294 := [mp #263 #293]: #291
-#778 := [mp #294 #777]: #773
+#77 := (= #20 #76)
+#78 := [monotonicity #54]: #77
+#83 := [trans #78 #81]: #82
+#74 := (iff #19 #73)
+#71 := (iff #18 #70)
+#65 := (iff #15 #64)
+#66 := [monotonicity #54]: #65
+#72 := [monotonicity #66]: #71
+#68 := (iff #16 #67)
+#69 := [monotonicity #66]: #68
+#75 := [monotonicity #69 #72]: #74
+#110 := [monotonicity #75 #83 #107]: #109
+#62 := (iff #13 false)
+#63 := [rewrite]: #62
+#113 := [monotonicity #63 #110]: #112
+#117 := [trans #113 #115]: #116
+#60 := (iff #11 false)
+#55 := (= -3::Int 0::Int)
+#58 := (iff #55 false)
+#59 := [rewrite]: #58
+#56 := (iff #11 #55)
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#120 := [monotonicity #61 #117]: #119
+#124 := [trans #120 #122]: #123
+#127 := [monotonicity #124 #105]: #126
+#132 := [trans #127 #130]: #131
+#135 := [monotonicity #132]: #134
+#139 := [trans #135 #137]: #138
+#168 := [trans #139 #166]: #167
+#51 := [asserted]: #31
+[mp #51 #168]: false
+unsat
+fac742ba4b7a09666d1c5cd8a1a25074910c56cc 156 0
+#2 := false
+#28 := 2::Int
 #8 := 3::Int
-#67 := (f3 3::Int -1::Int)
-#70 := (= #67 0::Int)
-#83 := (not #70)
-#9 := 1::Int
-#10 := (- 1::Int)
-#11 := (f3 3::Int #10)
-#13 := (= #11 0::Int)
-#14 := (not #13)
-#86 := (iff #14 #83)
-#73 := (= 0::Int #67)
-#78 := (not #73)
-#84 := (iff #78 #83)
-#81 := (iff #73 #70)
-#82 := [rewrite]: #81
-#85 := [monotonicity #82]: #84
-#79 := (iff #14 #78)
-#76 := (iff #13 #73)
-#74 := (iff #70 #73)
-#75 := [rewrite]: #74
-#71 := (iff #13 #70)
-#68 := (= #11 #67)
-#65 := (= #10 -1::Int)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#77 := [trans #72 #75]: #76
-#80 := [monotonicity #77]: #79
-#87 := [trans #80 #85]: #86
-#63 := [asserted]: #14
-#88 := [mp #63 #87]: #83
-#602 := (not #773)
-#603 := (or #602 #70)
-#352 := (* -1::Int -1::Int)
-#436 := (* -1::Int 3::Int)
-#437 := (mod #436 #352)
-#438 := (+ #67 #437)
-#429 := (= #438 0::Int)
-#440 := (mod 3::Int -1::Int)
-#441 := (* -1::Int #440)
-#442 := (+ #67 #441)
-#439 := (= #442 0::Int)
-#443 := (>= 3::Int 0::Int)
-#422 := (<= -1::Int 0::Int)
-#757 := (or #422 #443)
-#759 := (not #757)
-#416 := (<= 3::Int 0::Int)
-#546 := (or #416 #422)
-#753 := (not #546)
-#427 := (or #753 #759)
-#428 := (ite #427 #439 #429)
-#760 := (= 3::Int 0::Int)
-#761 := (ite #760 #70 #428)
-#762 := (= 3::Int #67)
-#763 := (= -1::Int 0::Int)
-#758 := (ite #763 #762 #761)
-#604 := (or #602 #758)
-#606 := (iff #604 #603)
-#696 := (iff #603 #603)
-#700 := [rewrite]: #696
-#601 := (iff #758 #70)
-#419 := (= #67 3::Int)
-#695 := (ite false #419 #70)
-#598 := (iff #695 #70)
-#600 := [rewrite]: #598
-#698 := (iff #758 #695)
-#599 := (iff #761 #70)
-#704 := (ite false #70 #70)
-#706 := (iff #704 #70)
-#588 := [rewrite]: #706
-#549 := (iff #761 #704)
-#589 := (iff #428 #70)
-#705 := (iff #428 #704)
-#701 := (iff #429 #70)
-#547 := (= #438 #67)
-#720 := (+ #67 0::Int)
-#717 := (= #720 #67)
-#718 := [rewrite]: #717
-#716 := (= #438 #720)
-#715 := (= #437 0::Int)
-#566 := -3::Int
-#712 := (mod -3::Int 1::Int)
-#708 := (= #712 0::Int)
-#714 := [rewrite]: #708
-#713 := (= #437 #712)
-#710 := (= #352 1::Int)
-#711 := [rewrite]: #710
-#567 := (= #436 -3::Int)
-#568 := [rewrite]: #567
-#707 := [monotonicity #568 #711]: #713
-#709 := [trans #707 #714]: #715
-#545 := [monotonicity #709]: #716
-#548 := [trans #545 #718]: #547
-#702 := [monotonicity #548]: #701
-#719 := (iff #439 #70)
-#723 := (= #442 #67)
-#721 := (= #442 #720)
-#727 := (= #441 0::Int)
-#728 := (* -1::Int 0::Int)
-#726 := (= #728 0::Int)
-#730 := [rewrite]: #726
-#729 := (= #441 #728)
-#449 := (= #440 0::Int)
-#450 := [rewrite]: #449
-#444 := [monotonicity #450]: #729
-#731 := [trans #444 #730]: #727
-#722 := [monotonicity #731]: #721
-#724 := [trans #722 #718]: #723
-#725 := [monotonicity #724]: #719
-#447 := (iff #427 false)
-#458 := (or false false)
-#733 := (iff #458 false)
-#737 := [rewrite]: #733
-#732 := (iff #427 #458)
-#735 := (iff #759 false)
-#1 := true
-#741 := (not true)
-#748 := (iff #741 false)
-#750 := [rewrite]: #748
-#358 := (iff #759 #741)
-#463 := (iff #757 true)
-#752 := (or true true)
-#461 := (iff #752 true)
-#462 := [rewrite]: #461
-#738 := (iff #757 #752)
-#751 := (iff #443 true)
-#749 := [rewrite]: #751
-#403 := (iff #422 true)
-#404 := [rewrite]: #403
-#739 := [monotonicity #404 #749]: #738
-#464 := [trans #739 #462]: #463
-#734 := [monotonicity #464]: #358
-#457 := [trans #734 #750]: #735
-#390 := (iff #753 false)
-#747 := (iff #753 #741)
-#745 := (iff #546 true)
-#405 := (or false true)
-#743 := (iff #405 true)
-#744 := [rewrite]: #743
-#406 := (iff #546 #405)
-#399 := (iff #416 false)
-#740 := [rewrite]: #399
-#742 := [monotonicity #740 #404]: #406
-#746 := [trans #742 #744]: #745
-#385 := [monotonicity #746]: #747
-#391 := [trans #385 #750]: #390
-#736 := [monotonicity #391 #457]: #732
-#448 := [trans #736 #737]: #447
-#703 := [monotonicity #448 #725 #702]: #705
-#590 := [trans #703 #588]: #589
-#415 := (iff #760 false)
-#756 := [rewrite]: #415
-#697 := [monotonicity #756 #590]: #549
-#694 := [trans #697 #588]: #599
-#414 := (iff #762 #419)
-#755 := [rewrite]: #414
-#764 := (iff #763 false)
-#754 := [rewrite]: #764
-#583 := [monotonicity #754 #755 #694]: #698
-#594 := [trans #583 #600]: #601
-#699 := [monotonicity #594]: #606
-#687 := [trans #699 #700]: #606
-#605 := [quant-inst #8 #64]: #604
-#689 := [mp #605 #687]: #603
-[unit-resolution #689 #88 #778]: false
-unsat
-d313c8803fd67ab7c81ae803664ddc96f0a1cd58 311 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#16 := (:var 0 Int)
-#15 := (:var 1 Int)
-#35 := (f3 #15 #16)
-#772 := (pattern #35)
-#12 := 0::Int
-#64 := -1::Int
-#108 := (* -1::Int #16)
-#105 := (* -1::Int #15)
-#169 := (mod #105 #108)
-#284 := (+ #35 #169)
-#285 := (= #284 0::Int)
-#36 := (mod #15 #16)
-#281 := (* -1::Int #36)
-#282 := (+ #35 #281)
-#283 := (= #282 0::Int)
-#143 := (>= #15 0::Int)
-#136 := (<= #16 0::Int)
-#228 := (or #136 #143)
-#229 := (not #228)
-#132 := (<= #15 0::Int)
-#226 := (or #132 #136)
-#227 := (not #226)
-#232 := (or #227 #229)
-#286 := (ite #232 #283 #285)
-#280 := (= #35 0::Int)
-#18 := (= #15 0::Int)
-#287 := (ite #18 #280 #286)
-#279 := (= #15 #35)
-#19 := (= #16 0::Int)
-#288 := (ite #19 #279 #287)
-#773 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #772) #288)
-#291 := (forall (vars (?v0 Int) (?v1 Int)) #288)
-#776 := (iff #291 #773)
-#774 := (iff #288 #288)
-#775 := [refl]: #774
-#777 := [quant-intro #775]: #776
-#175 := (* -1::Int #169)
-#248 := (ite #232 #36 #175)
-#251 := (ite #18 0::Int #248)
-#254 := (ite #19 #15 #251)
-#257 := (= #35 #254)
-#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
-#292 := (iff #260 #291)
-#289 := (iff #257 #288)
-#290 := [rewrite]: #289
-#293 := [quant-intro #290]: #292
-#144 := (not #143)
-#137 := (not #136)
-#147 := (and #137 #144)
-#133 := (not #132)
-#140 := (and #133 #137)
-#150 := (or #140 #147)
-#195 := (ite #150 #36 #175)
-#198 := (ite #18 0::Int #195)
-#201 := (ite #19 #15 #198)
-#204 := (= #35 #201)
-#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
-#261 := (iff #207 #260)
-#258 := (iff #204 #257)
-#255 := (= #201 #254)
-#252 := (= #198 #251)
-#249 := (= #195 #248)
-#233 := (iff #150 #232)
-#230 := (iff #147 #229)
-#231 := [rewrite]: #230
-#220 := (iff #140 #227)
-#221 := [rewrite]: #220
-#234 := [monotonicity #221 #231]: #233
-#250 := [monotonicity #234]: #249
-#253 := [monotonicity #250]: #252
-#256 := [monotonicity #253]: #255
-#259 := [monotonicity #256]: #258
-#262 := [quant-intro #259]: #261
-#218 := (~ #207 #207)
-#217 := (~ #204 #204)
-#214 := [refl]: #217
-#219 := [nnf-pos #214]: #218
-#29 := (- #16)
-#28 := (- #15)
-#37 := (mod #28 #29)
-#38 := (- #37)
-#22 := (< 0::Int #16)
-#24 := (< #15 0::Int)
-#25 := (and #24 #22)
-#21 := (< 0::Int #15)
-#23 := (and #21 #22)
-#26 := (or #23 #25)
-#39 := (ite #26 #36 #38)
-#40 := (ite #18 0::Int #39)
-#41 := (ite #19 #15 #40)
-#42 := (= #35 #41)
-#43 := (forall (vars (?v0 Int) (?v1 Int)) #42)
-#210 := (iff #43 #207)
-#99 := (and #22 #24)
-#102 := (or #23 #99)
-#180 := (ite #102 #36 #175)
-#90 := (= 0::Int #15)
-#183 := (ite #90 0::Int #180)
-#93 := (= 0::Int #16)
-#186 := (ite #93 #15 #183)
-#189 := (= #35 #186)
-#192 := (forall (vars (?v0 Int) (?v1 Int)) #189)
-#208 := (iff #192 #207)
-#205 := (iff #189 #204)
-#202 := (= #186 #201)
-#199 := (= #183 #198)
-#196 := (= #180 #195)
-#151 := (iff #102 #150)
-#148 := (iff #99 #147)
-#145 := (iff #24 #144)
+#22 := (- 3::Int)
+#11 := 1::Int
+#12 := (- 1::Int)
+#21 := (- #12)
+#23 := (mod #21 #22)
+#24 := (- #23)
+#20 := (mod #12 3::Int)
+#9 := 0::Int
+#15 := (< 0::Int 3::Int)
+#17 := (< #12 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int #12)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#25 := (ite #19 #20 #24)
+#13 := (= #12 0::Int)
+#26 := (ite #13 0::Int #25)
+#10 := (= 3::Int 0::Int)
+#27 := (ite #10 #12 #26)
+#29 := (= #27 2::Int)
+#30 := (not #29)
+#177 := (iff #30 false)
+#53 := -1::Int
+#74 := (< -1::Int 0::Int)
+#80 := (and #15 #74)
+#63 := (< 0::Int -1::Int)
+#69 := (and #15 #63)
+#85 := (or #69 #80)
+#140 := (not #85)
+#175 := (iff #140 false)
+#1 := true
+#170 := (not true)
+#173 := (iff #170 false)
+#174 := [rewrite]: #173
+#171 := (iff #140 #170)
+#168 := (iff #85 true)
+#163 := (or false true)
+#166 := (iff #163 true)
+#167 := [rewrite]: #166
+#164 := (iff #85 #163)
+#161 := (iff #80 true)
+#156 := (and true true)
+#159 := (iff #156 true)
+#160 := [rewrite]: #159
+#157 := (iff #80 #156)
+#154 := (iff #74 true)
+#155 := [rewrite]: #154
+#143 := (iff #15 true)
+#144 := [rewrite]: #143
+#158 := [monotonicity #144 #155]: #157
+#162 := [trans #158 #160]: #161
+#152 := (iff #69 false)
+#147 := (and true false)
+#150 := (iff #147 false)
+#151 := [rewrite]: #150
+#148 := (iff #69 #147)
+#145 := (iff #63 false)
 #146 := [rewrite]: #145
-#138 := (iff #22 #137)
-#139 := [rewrite]: #138
-#149 := [monotonicity #139 #146]: #148
-#141 := (iff #23 #140)
-#134 := (iff #21 #133)
-#135 := [rewrite]: #134
-#142 := [monotonicity #135 #139]: #141
-#152 := [monotonicity #142 #149]: #151
-#197 := [monotonicity #152]: #196
-#126 := (iff #90 #18)
-#127 := [rewrite]: #126
-#200 := [monotonicity #127 #197]: #199
-#128 := (iff #93 #19)
-#129 := [rewrite]: #128
-#203 := [monotonicity #129 #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [quant-intro #206]: #208
-#193 := (iff #43 #192)
-#190 := (iff #42 #189)
-#187 := (= #41 #186)
-#184 := (= #40 #183)
-#181 := (= #39 #180)
-#178 := (= #38 #175)
-#172 := (- #169)
-#176 := (= #172 #175)
-#177 := [rewrite]: #176
-#173 := (= #38 #172)
-#170 := (= #37 #169)
-#109 := (= #29 #108)
-#110 := [rewrite]: #109
-#106 := (= #28 #105)
-#107 := [rewrite]: #106
-#171 := [monotonicity #107 #110]: #170
-#174 := [monotonicity #171]: #173
-#179 := [trans #174 #177]: #178
-#103 := (iff #26 #102)
-#100 := (iff #25 #99)
-#101 := [rewrite]: #100
-#104 := [monotonicity #101]: #103
-#182 := [monotonicity #104 #179]: #181
-#91 := (iff #18 #90)
+#149 := [monotonicity #144 #146]: #148
+#153 := [trans #149 #151]: #152
+#165 := [monotonicity #153 #162]: #164
+#169 := [trans #165 #167]: #168
+#172 := [monotonicity #169]: #171
+#176 := [trans #172 #174]: #175
+#141 := (iff #30 #140)
+#138 := (iff #29 #85)
+#116 := (ite #85 2::Int -1::Int)
+#133 := (= #116 2::Int)
+#136 := (iff #133 #85)
+#137 := [rewrite]: #136
+#134 := (iff #29 #133)
+#131 := (= #27 #116)
+#126 := (ite false -1::Int #116)
+#129 := (= #126 #116)
+#130 := [rewrite]: #129
+#127 := (= #27 #126)
+#124 := (= #26 #116)
+#119 := (ite false 0::Int #116)
+#122 := (= #119 #116)
+#123 := [rewrite]: #122
+#120 := (= #26 #119)
+#117 := (= #25 #116)
+#114 := (= #24 -1::Int)
+#54 := (= #12 -1::Int)
+#55 := [rewrite]: #54
+#112 := (= #24 #12)
+#110 := (= #23 1::Int)
+#102 := -3::Int
+#105 := (mod 1::Int -3::Int)
+#108 := (= #105 1::Int)
+#109 := [rewrite]: #108
+#106 := (= #23 #105)
+#103 := (= #22 -3::Int)
+#104 := [rewrite]: #103
+#100 := (= #21 1::Int)
+#95 := (- -1::Int)
+#98 := (= #95 1::Int)
+#99 := [rewrite]: #98
+#96 := (= #21 #95)
+#97 := [monotonicity #55]: #96
+#101 := [trans #97 #99]: #100
+#107 := [monotonicity #101 #104]: #106
+#111 := [trans #107 #109]: #110
+#113 := [monotonicity #111]: #112
+#115 := [trans #113 #55]: #114
+#93 := (= #20 2::Int)
+#88 := (mod -1::Int 3::Int)
+#91 := (= #88 2::Int)
 #92 := [rewrite]: #91
-#185 := [monotonicity #92 #182]: #184
-#94 := (iff #19 #93)
-#95 := [rewrite]: #94
-#188 := [monotonicity #95 #185]: #187
-#191 := [monotonicity #188]: #190
-#194 := [quant-intro #191]: #193
-#211 := [trans #194 #209]: #210
-#168 := [asserted]: #43
-#212 := [mp #168 #211]: #207
-#215 := [mp~ #212 #219]: #207
-#263 := [mp #215 #262]: #260
-#294 := [mp #263 #293]: #291
-#778 := [mp #294 #777]: #773
-decl f4 :: Int
-#8 := f4
-#67 := (f3 f4 -1::Int)
-#70 := (= #67 0::Int)
-#83 := (not #70)
-#9 := 1::Int
-#10 := (- 1::Int)
-#11 := (f3 f4 #10)
-#13 := (= #11 0::Int)
-#14 := (not #13)
-#86 := (iff #14 #83)
-#73 := (= 0::Int #67)
-#78 := (not #73)
-#84 := (iff #78 #83)
-#81 := (iff #73 #70)
+#89 := (= #20 #88)
+#90 := [monotonicity #55]: #89
+#94 := [trans #90 #92]: #93
+#86 := (iff #19 #85)
+#83 := (iff #18 #80)
+#77 := (and #74 #15)
+#81 := (iff #77 #80)
 #82 := [rewrite]: #81
-#85 := [monotonicity #82]: #84
-#79 := (iff #14 #78)
-#76 := (iff #13 #73)
-#74 := (iff #70 #73)
-#75 := [rewrite]: #74
-#71 := (iff #13 #70)
-#68 := (= #11 #67)
-#65 := (= #10 -1::Int)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#77 := [trans #72 #75]: #76
-#80 := [monotonicity #77]: #79
-#87 := [trans #80 #85]: #86
-#63 := [asserted]: #14
-#88 := [mp #63 #87]: #83
-#716 := (not #773)
-#545 := (or #716 #70)
-#352 := (* -1::Int -1::Int)
-#436 := (* -1::Int f4)
-#437 := (mod #436 #352)
-#438 := (+ #67 #437)
-#429 := (= #438 0::Int)
-#440 := (mod f4 -1::Int)
-#441 := (* -1::Int #440)
-#442 := (+ #67 #441)
-#439 := (= #442 0::Int)
-#443 := (>= f4 0::Int)
-#422 := (<= -1::Int 0::Int)
-#757 := (or #422 #443)
-#759 := (not #757)
-#416 := (<= f4 0::Int)
-#546 := (or #416 #422)
-#753 := (not #546)
-#427 := (or #753 #759)
-#428 := (ite #427 #439 #429)
-#760 := (= f4 0::Int)
-#761 := (ite #760 #70 #428)
-#762 := (= f4 #67)
-#763 := (= -1::Int 0::Int)
-#758 := (ite #763 #762 #761)
-#547 := (or #716 #758)
-#701 := (iff #547 #545)
-#704 := (iff #545 #545)
-#705 := [rewrite]: #704
-#715 := (iff #758 #70)
-#712 := (ite false #762 #70)
-#708 := (iff #712 #70)
-#714 := [rewrite]: #708
-#713 := (iff #758 #712)
-#710 := (iff #761 #70)
-#719 := (ite #760 #70 #70)
-#567 := (iff #719 #70)
-#568 := [rewrite]: #567
-#725 := (iff #761 #719)
-#723 := (iff #428 #70)
-#720 := (ite false #439 #70)
-#717 := (iff #720 #70)
-#718 := [rewrite]: #717
-#721 := (iff #428 #720)
-#727 := (iff #429 #70)
-#726 := (= #438 #67)
-#449 := (+ #67 0::Int)
-#729 := (= #449 #67)
-#444 := [rewrite]: #729
-#450 := (= #438 #449)
-#447 := (= #437 0::Int)
-#458 := (mod #436 1::Int)
-#733 := (= #458 0::Int)
-#737 := [rewrite]: #733
-#732 := (= #437 #458)
-#735 := (= #352 1::Int)
-#457 := [rewrite]: #735
-#736 := [monotonicity #457]: #732
-#448 := [trans #736 #737]: #447
-#728 := [monotonicity #448]: #450
-#730 := [trans #728 #444]: #726
-#731 := [monotonicity #730]: #727
-#358 := (iff #427 false)
-#739 := (or false false)
-#463 := (iff #739 false)
-#464 := [rewrite]: #463
-#461 := (iff #427 #739)
-#752 := (iff #759 false)
-#1 := true
-#405 := (not true)
-#743 := (iff #405 false)
-#744 := [rewrite]: #743
-#751 := (iff #759 #405)
-#390 := (iff #757 true)
-#741 := (or true #443)
-#748 := (iff #741 true)
-#750 := [rewrite]: #748
-#747 := (iff #757 #741)
-#414 := (iff #422 true)
-#419 := [rewrite]: #414
-#385 := [monotonicity #419]: #747
-#391 := [trans #385 #750]: #390
-#749 := [monotonicity #391]: #751
-#738 := [trans #749 #744]: #752
-#745 := (iff #753 false)
-#406 := (iff #753 #405)
-#403 := (iff #546 true)
-#755 := (or #416 true)
-#399 := (iff #755 true)
-#740 := [rewrite]: #399
-#415 := (iff #546 #755)
-#756 := [monotonicity #419]: #415
-#404 := [trans #756 #740]: #403
-#742 := [monotonicity #404]: #406
-#746 := [trans #742 #744]: #745
-#462 := [monotonicity #746 #738]: #461
-#734 := [trans #462 #464]: #358
-#722 := [monotonicity #734 #731]: #721
-#724 := [trans #722 #718]: #723
-#566 := [monotonicity #724]: #725
-#711 := [trans #566 #568]: #710
-#764 := (iff #763 false)
-#754 := [rewrite]: #764
-#707 := [monotonicity #754 #711]: #713
-#709 := [trans #707 #714]: #715
-#702 := [monotonicity #709]: #701
-#703 := [trans #702 #705]: #701
-#548 := [quant-inst #8 #64]: #547
-#706 := [mp #548 #703]: #545
-[unit-resolution #706 #88 #778]: false
-unsat
-4e6d1a0d0e4d1e5ccd22f2801665c723ffc6cafc 304 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#14 := (:var 0 Int)
-#13 := (:var 1 Int)
-#33 := (f3 #13 #14)
-#757 := (pattern #33)
-#8 := 0::Int
-#88 := -1::Int
-#92 := (* -1::Int #14)
-#89 := (* -1::Int #13)
-#153 := (mod #89 #92)
-#268 := (+ #33 #153)
-#269 := (= #268 0::Int)
-#34 := (mod #13 #14)
-#265 := (* -1::Int #34)
-#266 := (+ #33 #265)
-#267 := (= #266 0::Int)
-#127 := (>= #13 0::Int)
-#120 := (<= #14 0::Int)
-#212 := (or #120 #127)
-#213 := (not #212)
-#116 := (<= #13 0::Int)
-#210 := (or #116 #120)
-#211 := (not #210)
-#216 := (or #211 #213)
-#270 := (ite #216 #267 #269)
-#264 := (= #33 0::Int)
-#16 := (= #13 0::Int)
-#271 := (ite #16 #264 #270)
-#263 := (= #13 #33)
-#17 := (= #14 0::Int)
-#272 := (ite #17 #263 #271)
-#758 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #757) #272)
-#275 := (forall (vars (?v0 Int) (?v1 Int)) #272)
-#761 := (iff #275 #758)
-#759 := (iff #272 #272)
-#760 := [refl]: #759
-#762 := [quant-intro #760]: #761
-#159 := (* -1::Int #153)
-#232 := (ite #216 #34 #159)
-#235 := (ite #16 0::Int #232)
-#238 := (ite #17 #13 #235)
-#241 := (= #33 #238)
-#244 := (forall (vars (?v0 Int) (?v1 Int)) #241)
-#276 := (iff #244 #275)
-#273 := (iff #241 #272)
-#274 := [rewrite]: #273
-#277 := [quant-intro #274]: #276
-#128 := (not #127)
-#121 := (not #120)
-#131 := (and #121 #128)
-#117 := (not #116)
-#124 := (and #117 #121)
-#134 := (or #124 #131)
-#179 := (ite #134 #34 #159)
-#182 := (ite #16 0::Int #179)
-#185 := (ite #17 #13 #182)
-#188 := (= #33 #185)
-#191 := (forall (vars (?v0 Int) (?v1 Int)) #188)
-#245 := (iff #191 #244)
-#242 := (iff #188 #241)
-#239 := (= #185 #238)
-#236 := (= #182 #235)
-#233 := (= #179 #232)
-#217 := (iff #134 #216)
-#214 := (iff #131 #213)
-#215 := [rewrite]: #214
-#204 := (iff #124 #211)
-#205 := [rewrite]: #204
-#218 := [monotonicity #205 #215]: #217
-#234 := [monotonicity #218]: #233
-#237 := [monotonicity #234]: #236
-#240 := [monotonicity #237]: #239
-#243 := [monotonicity #240]: #242
-#246 := [quant-intro #243]: #245
-#202 := (~ #191 #191)
-#201 := (~ #188 #188)
-#198 := [refl]: #201
-#203 := [nnf-pos #198]: #202
-#27 := (- #14)
-#26 := (- #13)
-#35 := (mod #26 #27)
-#36 := (- #35)
-#20 := (< 0::Int #14)
-#22 := (< #13 0::Int)
-#23 := (and #22 #20)
-#19 := (< 0::Int #13)
-#21 := (and #19 #20)
-#24 := (or #21 #23)
-#37 := (ite #24 #34 #36)
-#38 := (ite #16 0::Int #37)
-#39 := (ite #17 #13 #38)
-#40 := (= #33 #39)
-#41 := (forall (vars (?v0 Int) (?v1 Int)) #40)
-#194 := (iff #41 #191)
-#82 := (and #20 #22)
-#85 := (or #21 #82)
-#164 := (ite #85 #34 #159)
-#73 := (= 0::Int #13)
-#167 := (ite #73 0::Int #164)
-#76 := (= 0::Int #14)
-#170 := (ite #76 #13 #167)
-#173 := (= #33 #170)
-#176 := (forall (vars (?v0 Int) (?v1 Int)) #173)
-#192 := (iff #176 #191)
-#189 := (iff #173 #188)
-#186 := (= #170 #185)
-#183 := (= #167 #182)
-#180 := (= #164 #179)
-#135 := (iff #85 #134)
-#132 := (iff #82 #131)
-#129 := (iff #22 #128)
-#130 := [rewrite]: #129
-#122 := (iff #20 #121)
-#123 := [rewrite]: #122
-#133 := [monotonicity #123 #130]: #132
-#125 := (iff #21 #124)
-#118 := (iff #19 #117)
+#78 := (iff #18 #77)
+#75 := (iff #17 #74)
+#76 := [monotonicity #55]: #75
+#79 := [monotonicity #76]: #78
+#84 := [trans #79 #82]: #83
+#72 := (iff #16 #69)
+#66 := (and #63 #15)
+#70 := (iff #66 #69)
+#71 := [rewrite]: #70
+#67 := (iff #16 #66)
+#64 := (iff #14 #63)
+#65 := [monotonicity #55]: #64
+#68 := [monotonicity #65]: #67
+#73 := [trans #68 #71]: #72
+#87 := [monotonicity #73 #84]: #86
+#118 := [monotonicity #87 #94 #115]: #117
+#61 := (iff #13 false)
+#56 := (= -1::Int 0::Int)
+#59 := (iff #56 false)
+#60 := [rewrite]: #59
+#57 := (iff #13 #56)
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#121 := [monotonicity #62 #118]: #120
+#125 := [trans #121 #123]: #124
+#51 := (iff #10 false)
+#52 := [rewrite]: #51
+#128 := [monotonicity #52 #55 #125]: #127
+#132 := [trans #128 #130]: #131
+#135 := [monotonicity #132]: #134
+#139 := [trans #135 #137]: #138
+#142 := [monotonicity #139]: #141
+#178 := [trans #142 #176]: #177
+#50 := [asserted]: #30
+[mp #50 #178]: false
+unsat
+c22b2f1ee044330de34ce6ed88bd5a128a3b12e5 124 0
+#2 := false
+#9 := 0::Int
+#8 := 3::Int
+#11 := (- 3::Int)
+#20 := (- #11)
+#21 := (mod #20 #11)
+#22 := (- #21)
+#19 := (mod #11 3::Int)
+#14 := (< 0::Int 3::Int)
+#16 := (< #11 0::Int)
+#17 := (and #16 #14)
+#13 := (< 0::Int #11)
+#15 := (and #13 #14)
+#18 := (or #15 #17)
+#23 := (ite #18 #19 #22)
+#12 := (= #11 0::Int)
+#24 := (ite #12 0::Int #23)
+#10 := (= 3::Int 0::Int)
+#25 := (ite #10 #11 #24)
+#26 := (= #25 0::Int)
+#27 := (not #26)
+#145 := (iff #27 false)
+#1 := true
+#140 := (not true)
+#143 := (iff #140 false)
+#144 := [rewrite]: #143
+#141 := (iff #27 #140)
+#138 := (iff #26 true)
+#133 := (= 0::Int 0::Int)
+#136 := (iff #133 true)
+#137 := [rewrite]: #136
+#134 := (iff #26 #133)
+#50 := -3::Int
+#127 := (ite false -3::Int 0::Int)
+#130 := (= #127 0::Int)
+#131 := [rewrite]: #130
+#128 := (= #25 #127)
+#125 := (= #24 0::Int)
+#120 := (ite false 0::Int 0::Int)
+#123 := (= #120 0::Int)
+#124 := [rewrite]: #123
+#121 := (= #24 #120)
+#118 := (= #23 0::Int)
+#71 := (< -3::Int 0::Int)
+#77 := (and #14 #71)
+#60 := (< 0::Int -3::Int)
+#66 := (and #14 #60)
+#82 := (or #66 #77)
+#113 := (ite #82 0::Int 0::Int)
+#116 := (= #113 0::Int)
+#117 := [rewrite]: #116
+#114 := (= #23 #113)
+#111 := (= #22 0::Int)
+#106 := (- 0::Int)
+#109 := (= #106 0::Int)
+#110 := [rewrite]: #109
+#107 := (= #22 #106)
+#104 := (= #21 0::Int)
+#99 := (mod 3::Int -3::Int)
+#102 := (= #99 0::Int)
+#103 := [rewrite]: #102
+#100 := (= #21 #99)
+#51 := (= #11 -3::Int)
+#52 := [rewrite]: #51
+#97 := (= #20 3::Int)
+#92 := (- -3::Int)
+#95 := (= #92 3::Int)
+#96 := [rewrite]: #95
+#93 := (= #20 #92)
+#94 := [monotonicity #52]: #93
+#98 := [trans #94 #96]: #97
+#101 := [monotonicity #98 #52]: #100
+#105 := [trans #101 #103]: #104
+#108 := [monotonicity #105]: #107
+#112 := [trans #108 #110]: #111
+#90 := (= #19 0::Int)
+#85 := (mod -3::Int 3::Int)
+#88 := (= #85 0::Int)
+#89 := [rewrite]: #88
+#86 := (= #19 #85)
+#87 := [monotonicity #52]: #86
+#91 := [trans #87 #89]: #90
+#83 := (iff #18 #82)
+#80 := (iff #17 #77)
+#74 := (and #71 #14)
+#78 := (iff #74 #77)
+#79 := [rewrite]: #78
+#75 := (iff #17 #74)
+#72 := (iff #16 #71)
+#73 := [monotonicity #52]: #72
+#76 := [monotonicity #73]: #75
+#81 := [trans #76 #79]: #80
+#69 := (iff #15 #66)
+#63 := (and #60 #14)
+#67 := (iff #63 #66)
+#68 := [rewrite]: #67
+#64 := (iff #15 #63)
+#61 := (iff #13 #60)
+#62 := [monotonicity #52]: #61
+#65 := [monotonicity #62]: #64
+#70 := [trans #65 #68]: #69
+#84 := [monotonicity #70 #81]: #83
+#115 := [monotonicity #84 #91 #112]: #114
+#119 := [trans #115 #117]: #118
+#58 := (iff #12 false)
+#53 := (= -3::Int 0::Int)
+#56 := (iff #53 false)
+#57 := [rewrite]: #56
+#54 := (iff #12 #53)
+#55 := [monotonicity #52]: #54
+#59 := [trans #55 #57]: #58
+#122 := [monotonicity #59 #119]: #121
+#126 := [trans #122 #124]: #125
+#48 := (iff #10 false)
+#49 := [rewrite]: #48
+#129 := [monotonicity #49 #52 #126]: #128
+#132 := [trans #129 #131]: #26
+#135 := [monotonicity #132]: #134
+#139 := [trans #135 #137]: #138
+#142 := [monotonicity #139]: #141
+#146 := [trans #142 #144]: #145
+#47 := [asserted]: #27
+[mp #47 #146]: false
+unsat
+1702a8956e7405182723d9b7e49a559e524180e5 161 0
+#2 := false
+#28 := 1::Int
+#8 := 3::Int
+#22 := (- 3::Int)
+#11 := 5::Int
+#12 := (- 5::Int)
+#21 := (- #12)
+#23 := (mod #21 #22)
+#24 := (- #23)
+#20 := (mod #12 3::Int)
+#9 := 0::Int
+#15 := (< 0::Int 3::Int)
+#17 := (< #12 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int #12)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#25 := (ite #19 #20 #24)
+#13 := (= #12 0::Int)
+#26 := (ite #13 0::Int #25)
+#10 := (= 3::Int 0::Int)
+#27 := (ite #10 #12 #26)
+#29 := (= #27 1::Int)
+#30 := (not #29)
+#182 := (iff #30 false)
+#53 := -5::Int
+#74 := (< -5::Int 0::Int)
+#80 := (and #15 #74)
+#63 := (< 0::Int -5::Int)
+#69 := (and #15 #63)
+#85 := (or #69 #80)
+#145 := (not #85)
+#180 := (iff #145 false)
+#1 := true
+#175 := (not true)
+#178 := (iff #175 false)
+#179 := [rewrite]: #178
+#176 := (iff #145 #175)
+#173 := (iff #85 true)
+#168 := (or false true)
+#171 := (iff #168 true)
+#172 := [rewrite]: #171
+#169 := (iff #85 #168)
+#166 := (iff #80 true)
+#161 := (and true true)
+#164 := (iff #161 true)
+#165 := [rewrite]: #164
+#162 := (iff #80 #161)
+#159 := (iff #74 true)
+#160 := [rewrite]: #159
+#148 := (iff #15 true)
+#149 := [rewrite]: #148
+#163 := [monotonicity #149 #160]: #162
+#167 := [trans #163 #165]: #166
+#157 := (iff #69 false)
+#152 := (and true false)
+#155 := (iff #152 false)
+#156 := [rewrite]: #155
+#153 := (iff #69 #152)
+#150 := (iff #63 false)
+#151 := [rewrite]: #150
+#154 := [monotonicity #149 #151]: #153
+#158 := [trans #154 #156]: #157
+#170 := [monotonicity #158 #167]: #169
+#174 := [trans #170 #172]: #173
+#177 := [monotonicity #174]: #176
+#181 := [trans #177 #179]: #180
+#146 := (iff #30 #145)
+#143 := (iff #29 #85)
+#116 := -2::Int
+#121 := (ite #85 1::Int -2::Int)
+#138 := (= #121 1::Int)
+#141 := (iff #138 #85)
+#142 := [rewrite]: #141
+#139 := (iff #29 #138)
+#136 := (= #27 #121)
+#131 := (ite false -5::Int #121)
+#134 := (= #131 #121)
+#135 := [rewrite]: #134
+#132 := (= #27 #131)
+#129 := (= #26 #121)
+#124 := (ite false 0::Int #121)
+#127 := (= #124 #121)
+#128 := [rewrite]: #127
+#125 := (= #26 #124)
+#122 := (= #25 #121)
+#119 := (= #24 -2::Int)
+#108 := 2::Int
+#113 := (- 2::Int)
+#117 := (= #113 -2::Int)
+#118 := [rewrite]: #117
+#114 := (= #24 #113)
+#111 := (= #23 2::Int)
+#102 := -3::Int
+#105 := (mod 5::Int -3::Int)
+#109 := (= #105 2::Int)
+#110 := [rewrite]: #109
+#106 := (= #23 #105)
+#103 := (= #22 -3::Int)
+#104 := [rewrite]: #103
+#100 := (= #21 5::Int)
+#95 := (- -5::Int)
+#98 := (= #95 5::Int)
+#99 := [rewrite]: #98
+#96 := (= #21 #95)
+#54 := (= #12 -5::Int)
+#55 := [rewrite]: #54
+#97 := [monotonicity #55]: #96
+#101 := [trans #97 #99]: #100
+#107 := [monotonicity #101 #104]: #106
+#112 := [trans #107 #110]: #111
+#115 := [monotonicity #112]: #114
+#120 := [trans #115 #118]: #119
+#93 := (= #20 1::Int)
+#88 := (mod -5::Int 3::Int)
+#91 := (= #88 1::Int)
+#92 := [rewrite]: #91
+#89 := (= #20 #88)
+#90 := [monotonicity #55]: #89
+#94 := [trans #90 #92]: #93
+#86 := (iff #19 #85)
+#83 := (iff #18 #80)
+#77 := (and #74 #15)
+#81 := (iff #77 #80)
+#82 := [rewrite]: #81
+#78 := (iff #18 #77)
+#75 := (iff #17 #74)
+#76 := [monotonicity #55]: #75
+#79 := [monotonicity #76]: #78
+#84 := [trans #79 #82]: #83
+#72 := (iff #16 #69)
+#66 := (and #63 #15)
+#70 := (iff #66 #69)
+#71 := [rewrite]: #70
+#67 := (iff #16 #66)
+#64 := (iff #14 #63)
+#65 := [monotonicity #55]: #64
+#68 := [monotonicity #65]: #67
+#73 := [trans #68 #71]: #72
+#87 := [monotonicity #73 #84]: #86
+#123 := [monotonicity #87 #94 #120]: #122
+#61 := (iff #13 false)
+#56 := (= -5::Int 0::Int)
+#59 := (iff #56 false)
+#60 := [rewrite]: #59
+#57 := (iff #13 #56)
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#126 := [monotonicity #62 #123]: #125
+#130 := [trans #126 #128]: #129
+#51 := (iff #10 false)
+#52 := [rewrite]: #51
+#133 := [monotonicity #52 #55 #130]: #132
+#137 := [trans #133 #135]: #136
+#140 := [monotonicity #137]: #139
+#144 := [trans #140 #142]: #143
+#147 := [monotonicity #144]: #146
+#183 := [trans #147 #181]: #182
+#50 := [asserted]: #30
+[mp #50 #183]: false
+unsat
+1974063c697470ee08048aa93c91e77e8294ad37 165 0
+#2 := false
+#12 := 1::Int
+#13 := (- 1::Int)
+#8 := 3::Int
+#9 := (- 3::Int)
+#23 := (- #9)
+#22 := (- #13)
+#24 := (mod #22 #23)
+#25 := (- #24)
+#21 := (mod #13 #9)
+#10 := 0::Int
+#16 := (< 0::Int #9)
+#18 := (< #13 0::Int)
+#19 := (and #18 #16)
+#15 := (< 0::Int #13)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#26 := (ite #20 #21 #25)
+#14 := (= #13 0::Int)
+#27 := (ite #14 0::Int #26)
+#11 := (= #9 0::Int)
+#28 := (ite #11 #13 #27)
+#29 := (= #28 #13)
+#30 := (not #29)
+#186 := (iff #30 false)
+#61 := -1::Int
+#80 := (< -1::Int 0::Int)
+#51 := -3::Int
+#74 := (< 0::Int -3::Int)
+#86 := (and #74 #80)
+#71 := (< 0::Int -1::Int)
+#77 := (and #71 #74)
+#91 := (or #77 #86)
+#184 := (iff #91 false)
+#179 := (or false false)
+#182 := (iff #179 false)
+#183 := [rewrite]: #182
+#180 := (iff #91 #179)
+#177 := (iff #86 false)
+#1 := true
+#172 := (and false true)
+#175 := (iff #172 false)
+#176 := [rewrite]: #175
+#173 := (iff #86 #172)
+#170 := (iff #80 true)
+#171 := [rewrite]: #170
+#161 := (iff #74 false)
+#162 := [rewrite]: #161
+#174 := [monotonicity #162 #171]: #173
+#178 := [trans #174 #176]: #177
+#168 := (iff #77 false)
+#163 := (and false false)
+#166 := (iff #163 false)
+#167 := [rewrite]: #166
+#164 := (iff #77 #163)
+#159 := (iff #71 false)
+#160 := [rewrite]: #159
+#165 := [monotonicity #160 #162]: #164
+#169 := [trans #165 #167]: #168
+#181 := [monotonicity #169 #178]: #180
+#185 := [trans #181 #183]: #184
+#157 := (iff #30 #91)
+#147 := (not #91)
+#152 := (not #147)
+#155 := (iff #152 #91)
+#156 := [rewrite]: #155
+#153 := (iff #30 #152)
+#150 := (iff #29 #147)
+#97 := 2::Int
+#127 := (ite #91 2::Int -1::Int)
+#144 := (= #127 -1::Int)
+#148 := (iff #144 #147)
+#149 := [rewrite]: #148
+#145 := (iff #29 #144)
+#62 := (= #13 -1::Int)
+#63 := [rewrite]: #62
+#142 := (= #28 #127)
+#137 := (ite false -1::Int #127)
+#140 := (= #137 #127)
+#141 := [rewrite]: #140
+#138 := (= #28 #137)
+#135 := (= #27 #127)
+#130 := (ite false 0::Int #127)
+#133 := (= #130 #127)
+#134 := [rewrite]: #133
+#131 := (= #27 #130)
+#128 := (= #26 #127)
+#125 := (= #25 -1::Int)
+#123 := (= #25 #13)
+#121 := (= #24 1::Int)
+#116 := (mod 1::Int 3::Int)
+#119 := (= #116 1::Int)
+#120 := [rewrite]: #119
+#117 := (= #24 #116)
+#114 := (= #23 3::Int)
+#109 := (- -3::Int)
+#112 := (= #109 3::Int)
+#113 := [rewrite]: #112
+#110 := (= #23 #109)
+#52 := (= #9 -3::Int)
+#53 := [rewrite]: #52
+#111 := [monotonicity #53]: #110
+#115 := [trans #111 #113]: #114
+#107 := (= #22 1::Int)
+#102 := (- -1::Int)
+#105 := (= #102 1::Int)
+#106 := [rewrite]: #105
+#103 := (= #22 #102)
+#104 := [monotonicity #63]: #103
+#108 := [trans #104 #106]: #107
+#118 := [monotonicity #108 #115]: #117
+#122 := [trans #118 #120]: #121
+#124 := [monotonicity #122]: #123
+#126 := [trans #124 #63]: #125
+#100 := (= #21 2::Int)
+#94 := (mod -1::Int -3::Int)
+#98 := (= #94 2::Int)
+#99 := [rewrite]: #98
+#95 := (= #21 #94)
+#96 := [monotonicity #63 #53]: #95
+#101 := [trans #96 #99]: #100
+#92 := (iff #20 #91)
+#89 := (iff #19 #86)
+#83 := (and #80 #74)
+#87 := (iff #83 #86)
+#88 := [rewrite]: #87
+#84 := (iff #19 #83)
+#75 := (iff #16 #74)
+#76 := [monotonicity #53]: #75
+#81 := (iff #18 #80)
+#82 := [monotonicity #63]: #81
+#85 := [monotonicity #82 #76]: #84
+#90 := [trans #85 #88]: #89
+#78 := (iff #17 #77)
+#72 := (iff #15 #71)
+#73 := [monotonicity #63]: #72
+#79 := [monotonicity #73 #76]: #78
+#93 := [monotonicity #79 #90]: #92
+#129 := [monotonicity #93 #101 #126]: #128
+#69 := (iff #14 false)
+#64 := (= -1::Int 0::Int)
+#67 := (iff #64 false)
+#68 := [rewrite]: #67
+#65 := (iff #14 #64)
+#66 := [monotonicity #63]: #65
+#70 := [trans #66 #68]: #69
+#132 := [monotonicity #70 #129]: #131
+#136 := [trans #132 #134]: #135
+#59 := (iff #11 false)
+#54 := (= -3::Int 0::Int)
+#57 := (iff #54 false)
+#58 := [rewrite]: #57
+#55 := (iff #11 #54)
+#56 := [monotonicity #53]: #55
+#60 := [trans #56 #58]: #59
+#139 := [monotonicity #60 #63 #136]: #138
+#143 := [trans #139 #141]: #142
+#146 := [monotonicity #143 #63]: #145
+#151 := [trans #146 #149]: #150
+#154 := [monotonicity #151]: #153
+#158 := [trans #154 #156]: #157
+#187 := [trans #158 #185]: #186
+#50 := [asserted]: #30
+[mp #50 #187]: false
+unsat
+230992a84e85c41a4507e3a0c4b596203478f52c 119 0
+#2 := false
+#10 := 0::Int
+#8 := 3::Int
+#9 := (- 3::Int)
+#18 := (- #9)
+#19 := (mod #18 #18)
+#20 := (- #19)
+#17 := (mod #9 #9)
+#12 := (< 0::Int #9)
+#14 := (< #9 0::Int)
+#15 := (and #14 #12)
+#13 := (and #12 #12)
+#16 := (or #13 #15)
+#21 := (ite #16 #17 #20)
+#11 := (= #9 0::Int)
+#22 := (ite #11 0::Int #21)
+#23 := (ite #11 #9 #22)
+#24 := (= #23 0::Int)
+#25 := (not #24)
+#140 := (iff #25 false)
+#1 := true
+#135 := (not true)
+#138 := (iff #135 false)
+#139 := [rewrite]: #138
+#136 := (iff #25 #135)
+#133 := (iff #24 true)
+#128 := (= 0::Int 0::Int)
+#131 := (iff #128 true)
+#132 := [rewrite]: #131
+#129 := (iff #24 #128)
+#46 := -3::Int
+#122 := (ite false -3::Int 0::Int)
+#125 := (= #122 0::Int)
+#126 := [rewrite]: #125
+#123 := (= #23 #122)
+#120 := (= #22 0::Int)
+#115 := (ite false 0::Int 0::Int)
+#118 := (= #115 0::Int)
 #119 := [rewrite]: #118
-#126 := [monotonicity #119 #123]: #125
-#136 := [monotonicity #126 #133]: #135
-#181 := [monotonicity #136]: #180
-#110 := (iff #73 #16)
-#111 := [rewrite]: #110
-#184 := [monotonicity #111 #181]: #183
-#112 := (iff #76 #17)
-#113 := [rewrite]: #112
-#187 := [monotonicity #113 #184]: #186
-#190 := [monotonicity #187]: #189
-#193 := [quant-intro #190]: #192
-#177 := (iff #41 #176)
-#174 := (iff #40 #173)
-#171 := (= #39 #170)
-#168 := (= #38 #167)
-#165 := (= #37 #164)
-#162 := (= #36 #159)
-#156 := (- #153)
-#160 := (= #156 #159)
-#161 := [rewrite]: #160
-#157 := (= #36 #156)
-#154 := (= #35 #153)
-#93 := (= #27 #92)
-#94 := [rewrite]: #93
-#90 := (= #26 #89)
+#116 := (= #22 #115)
+#113 := (= #21 0::Int)
+#66 := (< -3::Int 0::Int)
+#56 := (< 0::Int -3::Int)
+#72 := (and #56 #66)
+#77 := (or #56 #72)
+#108 := (ite #77 0::Int 0::Int)
+#111 := (= #108 0::Int)
+#112 := [rewrite]: #111
+#109 := (= #21 #108)
+#106 := (= #20 0::Int)
+#101 := (- 0::Int)
+#104 := (= #101 0::Int)
+#105 := [rewrite]: #104
+#102 := (= #20 #101)
+#99 := (= #19 0::Int)
+#94 := (mod 3::Int 3::Int)
+#97 := (= #94 0::Int)
+#98 := [rewrite]: #97
+#95 := (= #19 #94)
+#92 := (= #18 3::Int)
+#87 := (- -3::Int)
+#90 := (= #87 3::Int)
 #91 := [rewrite]: #90
-#155 := [monotonicity #91 #94]: #154
-#158 := [monotonicity #155]: #157
-#163 := [trans #158 #161]: #162
-#86 := (iff #24 #85)
-#83 := (iff #23 #82)
+#88 := (= #18 #87)
+#47 := (= #9 -3::Int)
+#48 := [rewrite]: #47
+#89 := [monotonicity #48]: #88
+#93 := [trans #89 #91]: #92
+#96 := [monotonicity #93 #93]: #95
+#100 := [trans #96 #98]: #99
+#103 := [monotonicity #100]: #102
+#107 := [trans #103 #105]: #106
+#85 := (= #17 0::Int)
+#80 := (mod -3::Int -3::Int)
+#83 := (= #80 0::Int)
 #84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#166 := [monotonicity #87 #163]: #165
-#74 := (iff #16 #73)
-#75 := [rewrite]: #74
-#169 := [monotonicity #75 #166]: #168
-#77 := (iff #17 #76)
-#78 := [rewrite]: #77
-#172 := [monotonicity #78 #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [quant-intro #175]: #177
-#195 := [trans #178 #193]: #194
-#152 := [asserted]: #41
-#196 := [mp #152 #195]: #191
-#199 := [mp~ #196 #203]: #191
-#247 := [mp #199 #246]: #244
-#278 := [mp #247 #277]: #275
-#763 := [mp #278 #762]: #758
-#9 := 3::Int
-#10 := (f3 0::Int 3::Int)
-#11 := (= #10 0::Int)
-#12 := (not #11)
-#61 := [asserted]: #12
-#679 := (not #758)
-#680 := (or #679 #11)
-#336 := (* -1::Int 3::Int)
-#421 := (* -1::Int 0::Int)
-#422 := (mod #421 #336)
-#423 := (+ #10 #422)
-#414 := (= #423 0::Int)
-#425 := (mod 0::Int 3::Int)
-#426 := (* -1::Int #425)
-#354 := (+ #10 #426)
-#427 := (= #354 0::Int)
-#424 := (>= 0::Int 0::Int)
-#428 := (<= 3::Int 0::Int)
-#407 := (or #428 #424)
-#742 := (not #407)
-#744 := (<= 0::Int 0::Int)
-#401 := (or #744 #428)
-#531 := (not #401)
-#738 := (or #531 #742)
-#412 := (ite #738 #427 #414)
-#413 := (= 0::Int 0::Int)
-#745 := (ite #413 #11 #412)
-#62 := (= 0::Int #10)
-#746 := (= 3::Int 0::Int)
-#747 := (ite #746 #62 #745)
-#683 := (or #679 #747)
-#583 := (iff #683 #680)
-#586 := (iff #680 #680)
-#579 := [rewrite]: #586
-#682 := (iff #747 #11)
-#700 := (ite false #11 #11)
-#530 := (iff #700 #11)
-#532 := [rewrite]: #530
-#575 := (iff #747 #700)
-#573 := (iff #745 #11)
-#1 := true
-#687 := (ite true #11 #11)
-#688 := (iff #687 #11)
-#691 := [rewrite]: #688
-#689 := (iff #745 #687)
-#533 := (iff #412 #11)
-#694 := (iff #412 #700)
-#693 := (iff #414 #11)
-#698 := (= #423 #10)
-#714 := (+ #10 0::Int)
-#715 := (= #714 #10)
-#712 := [rewrite]: #715
-#696 := (= #423 #714)
-#553 := (= #422 0::Int)
-#702 := -3::Int
-#709 := (mod 0::Int -3::Int)
-#551 := (= #709 0::Int)
-#552 := [rewrite]: #551
-#704 := (= #422 #709)
-#703 := (= #336 -3::Int)
-#708 := [rewrite]: #703
-#433 := (= #421 0::Int)
-#434 := [rewrite]: #433
-#710 := [monotonicity #434 #708]: #704
-#695 := [trans #710 #552]: #553
-#697 := [monotonicity #695]: #696
-#692 := [trans #697 #712]: #698
-#699 := [monotonicity #692]: #693
-#706 := (iff #427 #11)
-#716 := (= #354 #10)
-#429 := (= #354 #714)
-#435 := (= #426 0::Int)
-#722 := (= #426 #421)
-#721 := (= #425 0::Int)
-#718 := [rewrite]: #721
-#432 := [monotonicity #718]: #722
-#713 := [trans #432 #434]: #435
-#711 := [monotonicity #713]: #429
-#705 := [trans #711 #712]: #716
-#707 := [monotonicity #705]: #706
-#443 := (iff #738 false)
-#449 := (or false false)
-#720 := (iff #449 false)
-#442 := [rewrite]: #720
-#342 := (iff #738 #449)
-#447 := (iff #742 false)
-#727 := (not true)
-#730 := (iff #727 false)
-#731 := [rewrite]: #730
-#724 := (iff #742 #727)
-#737 := (iff #407 true)
-#735 := (or false true)
-#736 := (iff #735 true)
-#734 := [rewrite]: #736
-#375 := (iff #407 #735)
-#370 := (iff #424 true)
-#733 := [rewrite]: #370
-#740 := (iff #428 false)
-#400 := [rewrite]: #740
-#376 := [monotonicity #400 #733]: #375
-#723 := [trans #376 #734]: #737
-#446 := [monotonicity #723]: #724
-#448 := [trans #446 #731]: #447
-#726 := (iff #531 false)
-#728 := (iff #531 #727)
-#390 := (iff #401 true)
-#741 := (or true false)
-#388 := (iff #741 true)
-#389 := [rewrite]: #388
-#384 := (iff #401 #741)
-#399 := (iff #744 true)
-#404 := [rewrite]: #399
-#725 := [monotonicity #404 #400]: #384
-#391 := [trans #725 #389]: #390
-#729 := [monotonicity #391]: #728
-#732 := [trans #729 #731]: #726
-#719 := [monotonicity #732 #448]: #342
-#717 := [trans #719 #442]: #443
-#701 := [monotonicity #717 #707 #699]: #694
-#686 := [trans #701 #532]: #533
-#749 := (iff #413 true)
-#739 := [rewrite]: #749
-#690 := [monotonicity #739 #686]: #689
-#574 := [trans #690 #691]: #573
-#68 := (iff #62 #11)
-#69 := [rewrite]: #68
-#748 := (iff #746 false)
-#743 := [rewrite]: #748
-#534 := [monotonicity #743 #69 #574]: #575
-#584 := [trans #534 #532]: #682
-#585 := [monotonicity #584]: #583
-#587 := [trans #585 #579]: #583
-#568 := [quant-inst #8 #9]: #683
-#588 := [mp #568 #587]: #680
-[unit-resolution #588 #61 #763]: false
-unsat
-8c07fa0d73a756ba84d0fe9fed90f7b86f2beac8 323 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#15 := (:var 0 Int)
-#14 := (:var 1 Int)
-#34 := (f3 #14 #15)
-#773 := (pattern #34)
-#8 := 0::Int
-#104 := -1::Int
-#108 := (* -1::Int #15)
-#105 := (* -1::Int #14)
-#169 := (mod #105 #108)
-#284 := (+ #34 #169)
-#285 := (= #284 0::Int)
-#35 := (mod #14 #15)
-#281 := (* -1::Int #35)
-#282 := (+ #34 #281)
-#283 := (= #282 0::Int)
-#143 := (>= #14 0::Int)
-#136 := (<= #15 0::Int)
-#228 := (or #136 #143)
-#229 := (not #228)
-#132 := (<= #14 0::Int)
-#226 := (or #132 #136)
-#227 := (not #226)
-#232 := (or #227 #229)
-#286 := (ite #232 #283 #285)
-#280 := (= #34 0::Int)
-#17 := (= #14 0::Int)
-#287 := (ite #17 #280 #286)
-#279 := (= #14 #34)
-#18 := (= #15 0::Int)
-#288 := (ite #18 #279 #287)
-#774 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #773) #288)
-#291 := (forall (vars (?v0 Int) (?v1 Int)) #288)
-#777 := (iff #291 #774)
-#775 := (iff #288 #288)
-#776 := [refl]: #775
-#778 := [quant-intro #776]: #777
-#175 := (* -1::Int #169)
-#248 := (ite #232 #35 #175)
-#251 := (ite #17 0::Int #248)
-#254 := (ite #18 #14 #251)
-#257 := (= #34 #254)
-#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
-#292 := (iff #260 #291)
-#289 := (iff #257 #288)
-#290 := [rewrite]: #289
-#293 := [quant-intro #290]: #292
-#144 := (not #143)
-#137 := (not #136)
-#147 := (and #137 #144)
-#133 := (not #132)
-#140 := (and #133 #137)
-#150 := (or #140 #147)
-#195 := (ite #150 #35 #175)
-#198 := (ite #17 0::Int #195)
-#201 := (ite #18 #14 #198)
-#204 := (= #34 #201)
-#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
-#261 := (iff #207 #260)
-#258 := (iff #204 #257)
-#255 := (= #201 #254)
-#252 := (= #198 #251)
-#249 := (= #195 #248)
-#233 := (iff #150 #232)
-#230 := (iff #147 #229)
-#231 := [rewrite]: #230
-#220 := (iff #140 #227)
-#221 := [rewrite]: #220
-#234 := [monotonicity #221 #231]: #233
-#250 := [monotonicity #234]: #249
-#253 := [monotonicity #250]: #252
-#256 := [monotonicity #253]: #255
-#259 := [monotonicity #256]: #258
-#262 := [quant-intro #259]: #261
-#218 := (~ #207 #207)
-#217 := (~ #204 #204)
-#214 := [refl]: #217
-#219 := [nnf-pos #214]: #218
-#28 := (- #15)
-#27 := (- #14)
-#36 := (mod #27 #28)
-#37 := (- #36)
-#21 := (< 0::Int #15)
-#23 := (< #14 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #14)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#38 := (ite #25 #35 #37)
-#39 := (ite #17 0::Int #38)
-#40 := (ite #18 #14 #39)
-#41 := (= #34 #40)
-#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
-#210 := (iff #42 #207)
-#98 := (and #21 #23)
-#101 := (or #22 #98)
-#180 := (ite #101 #35 #175)
-#89 := (= 0::Int #14)
-#183 := (ite #89 0::Int #180)
-#92 := (= 0::Int #15)
-#186 := (ite #92 #14 #183)
-#189 := (= #34 #186)
-#192 := (forall (vars (?v0 Int) (?v1 Int)) #189)
-#208 := (iff #192 #207)
-#205 := (iff #189 #204)
-#202 := (= #186 #201)
-#199 := (= #183 #198)
-#196 := (= #180 #195)
-#151 := (iff #101 #150)
-#148 := (iff #98 #147)
-#145 := (iff #23 #144)
-#146 := [rewrite]: #145
-#138 := (iff #21 #137)
-#139 := [rewrite]: #138
-#149 := [monotonicity #139 #146]: #148
-#141 := (iff #22 #140)
-#134 := (iff #20 #133)
-#135 := [rewrite]: #134
-#142 := [monotonicity #135 #139]: #141
-#152 := [monotonicity #142 #149]: #151
-#197 := [monotonicity #152]: #196
-#126 := (iff #89 #17)
-#127 := [rewrite]: #126
-#200 := [monotonicity #127 #197]: #199
-#128 := (iff #92 #18)
-#129 := [rewrite]: #128
-#203 := [monotonicity #129 #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [quant-intro #206]: #208
-#193 := (iff #42 #192)
-#190 := (iff #41 #189)
-#187 := (= #40 #186)
-#184 := (= #39 #183)
-#181 := (= #38 #180)
-#178 := (= #37 #175)
-#172 := (- #169)
-#176 := (= #172 #175)
-#177 := [rewrite]: #176
-#173 := (= #37 #172)
-#170 := (= #36 #169)
-#109 := (= #28 #108)
-#110 := [rewrite]: #109
-#106 := (= #27 #105)
-#107 := [rewrite]: #106
-#171 := [monotonicity #107 #110]: #170
-#174 := [monotonicity #171]: #173
-#179 := [trans #174 #177]: #178
-#102 := (iff #25 #101)
-#99 := (iff #24 #98)
-#100 := [rewrite]: #99
-#103 := [monotonicity #100]: #102
-#182 := [monotonicity #103 #179]: #181
-#90 := (iff #17 #89)
-#91 := [rewrite]: #90
-#185 := [monotonicity #91 #182]: #184
-#93 := (iff #18 #92)
-#94 := [rewrite]: #93
-#188 := [monotonicity #94 #185]: #187
-#191 := [monotonicity #188]: #190
-#194 := [quant-intro #191]: #193
-#211 := [trans #194 #209]: #210
-#168 := [asserted]: #42
-#212 := [mp #168 #211]: #207
-#215 := [mp~ #212 #219]: #207
-#263 := [mp #215 #262]: #260
-#294 := [mp #263 #293]: #291
-#779 := [mp #294 #778]: #774
-#63 := -3::Int
-#66 := (f3 0::Int -3::Int)
-#69 := (= #66 0::Int)
-#82 := (not #69)
-#9 := 3::Int
-#10 := (- 3::Int)
-#11 := (f3 0::Int #10)
-#12 := (= #11 0::Int)
-#13 := (not #12)
-#85 := (iff #13 #82)
-#72 := (= 0::Int #66)
-#77 := (not #72)
-#83 := (iff #77 #82)
-#80 := (iff #72 #69)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#78 := (iff #13 #77)
-#75 := (iff #12 #72)
+#81 := (= #17 #80)
+#82 := [monotonicity #48 #48]: #81
+#86 := [trans #82 #84]: #85
+#78 := (iff #16 #77)
+#75 := (iff #15 #72)
+#69 := (and #66 #56)
 #73 := (iff #69 #72)
 #74 := [rewrite]: #73
-#70 := (iff #12 #69)
-#67 := (= #11 #66)
-#64 := (= #10 -3::Int)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#71 := [monotonicity #68]: #70
+#70 := (iff #15 #69)
+#57 := (iff #12 #56)
+#58 := [monotonicity #48]: #57
+#67 := (iff #14 #66)
+#68 := [monotonicity #48]: #67
+#71 := [monotonicity #68 #58]: #70
 #76 := [trans #71 #74]: #75
-#79 := [monotonicity #76]: #78
-#86 := [trans #79 #84]: #85
-#62 := [asserted]: #13
-#87 := [mp #62 #86]: #82
-#591 := (not #774)
-#550 := (or #591 #69)
-#352 := (* -1::Int -3::Int)
-#437 := (* -1::Int 0::Int)
-#438 := (mod #437 #352)
-#439 := (+ #66 #438)
-#430 := (= #439 0::Int)
-#441 := (mod 0::Int -3::Int)
-#442 := (* -1::Int #441)
-#370 := (+ #66 #442)
-#443 := (= #370 0::Int)
-#440 := (>= 0::Int 0::Int)
-#444 := (<= -3::Int 0::Int)
-#423 := (or #444 #440)
-#758 := (not #423)
-#760 := (<= 0::Int 0::Int)
-#417 := (or #760 #444)
-#547 := (not #417)
-#754 := (or #547 #758)
-#428 := (ite #754 #443 #430)
-#429 := (= 0::Int 0::Int)
-#761 := (ite #429 #69 #428)
-#762 := (= -3::Int 0::Int)
-#763 := (ite #762 #72 #761)
-#698 := (or #591 #763)
-#695 := (iff #698 #550)
-#699 := (iff #550 #550)
-#584 := [rewrite]: #699
-#589 := (iff #763 #69)
-#714 := (ite false #69 #69)
-#715 := (iff #714 #69)
-#716 := [rewrite]: #715
-#704 := (iff #763 #714)
-#705 := (iff #761 #69)
-#1 := true
-#546 := (ite true #69 #69)
-#702 := (iff #546 #69)
-#703 := [rewrite]: #702
-#548 := (iff #761 #546)
-#710 := (iff #428 #69)
-#708 := (iff #428 #714)
-#712 := (iff #430 #69)
-#569 := (= #439 #66)
-#450 := (+ #66 0::Int)
-#730 := (= #450 #66)
-#445 := [rewrite]: #730
-#567 := (= #439 #450)
-#720 := (= #438 0::Int)
-#723 := (mod 0::Int 3::Int)
-#724 := (= #723 0::Int)
-#725 := [rewrite]: #724
-#718 := (= #438 #723)
-#721 := (= #352 3::Int)
-#722 := [rewrite]: #721
-#734 := (= #437 0::Int)
-#738 := [rewrite]: #734
-#719 := [monotonicity #738 #722]: #718
-#726 := [trans #719 #725]: #720
-#568 := [monotonicity #726]: #567
-#711 := [trans #568 #445]: #569
-#713 := [monotonicity #711]: #712
-#728 := (iff #443 #69)
-#727 := (= #370 #66)
-#451 := (= #370 #450)
-#448 := (= #442 0::Int)
-#733 := (= #442 #437)
-#458 := (= #441 0::Int)
-#459 := [rewrite]: #458
-#737 := [monotonicity #459]: #733
-#449 := [trans #737 #738]: #448
-#729 := [monotonicity #449]: #451
-#731 := [trans #729 #445]: #727
-#732 := [monotonicity #731]: #728
-#735 := (iff #754 false)
-#462 := (or false false)
-#465 := (iff #462 false)
-#358 := [rewrite]: #465
-#463 := (iff #754 #462)
-#739 := (iff #758 false)
-#743 := (not true)
-#746 := (iff #743 false)
-#747 := [rewrite]: #746
-#750 := (iff #758 #743)
-#392 := (iff #423 true)
-#757 := (or true true)
-#404 := (iff #757 true)
-#405 := [rewrite]: #404
-#751 := (iff #423 #757)
-#386 := (iff #440 true)
-#749 := [rewrite]: #386
-#756 := (iff #444 true)
-#416 := [rewrite]: #756
-#391 := [monotonicity #416 #749]: #751
-#752 := [trans #391 #405]: #392
-#753 := [monotonicity #752]: #750
-#740 := [trans #753 #747]: #739
-#742 := (iff #547 false)
-#744 := (iff #547 #743)
-#406 := (iff #417 true)
-#400 := (iff #417 #757)
-#415 := (iff #760 true)
-#420 := [rewrite]: #415
-#741 := [monotonicity #420 #416]: #400
-#407 := [trans #741 #405]: #406
-#745 := [monotonicity #407]: #744
-#748 := [trans #745 #747]: #742
-#464 := [monotonicity #748 #740]: #463
-#736 := [trans #464 #358]: #735
-#709 := [monotonicity #736 #732 #713]: #708
-#717 := [trans #709 #716]: #710
-#765 := (iff #429 true)
-#755 := [rewrite]: #765
-#549 := [monotonicity #755 #717]: #548
-#706 := [trans #549 #703]: #705
-#764 := (iff #762 false)
-#759 := [rewrite]: #764
-#707 := [monotonicity #759 #81 #706]: #704
-#590 := [trans #707 #716]: #589
-#696 := [monotonicity #590]: #695
-#599 := [trans #696 #584]: #695
-#600 := [quant-inst #8 #63]: #698
-#601 := [mp #600 #599]: #550
-[unit-resolution #601 #87 #779]: false
-unsat
-4b125b55545fc1a8ed3851433e86bbecb0071f7b 320 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#14 := (:var 0 Int)
-#13 := (:var 1 Int)
-#34 := (f3 #13 #14)
-#742 := (pattern #34)
-#16 := 0::Int
-#80 := -1::Int
-#84 := (* -1::Int #14)
-#81 := (* -1::Int #13)
-#139 := (mod #81 #84)
-#254 := (+ #34 #139)
-#255 := (= #254 0::Int)
-#35 := (mod #13 #14)
-#251 := (* -1::Int #35)
-#252 := (+ #34 #251)
-#253 := (= #252 0::Int)
-#113 := (>= #13 0::Int)
-#106 := (<= #14 0::Int)
-#198 := (or #106 #113)
-#199 := (not #198)
-#102 := (<= #13 0::Int)
-#196 := (or #102 #106)
-#197 := (not #196)
-#202 := (or #197 #199)
-#256 := (ite #202 #253 #255)
-#250 := (= #34 0::Int)
-#17 := (= #13 0::Int)
-#257 := (ite #17 #250 #256)
-#249 := (= #13 #34)
-#18 := (= #14 0::Int)
-#258 := (ite #18 #249 #257)
-#743 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #742) #258)
-#261 := (forall (vars (?v0 Int) (?v1 Int)) #258)
-#746 := (iff #261 #743)
-#744 := (iff #258 #258)
-#745 := [refl]: #744
-#747 := [quant-intro #745]: #746
-#145 := (* -1::Int #139)
-#218 := (ite #202 #35 #145)
-#221 := (ite #17 0::Int #218)
-#224 := (ite #18 #13 #221)
-#227 := (= #34 #224)
-#230 := (forall (vars (?v0 Int) (?v1 Int)) #227)
-#262 := (iff #230 #261)
-#259 := (iff #227 #258)
-#260 := [rewrite]: #259
-#263 := [quant-intro #260]: #262
-#114 := (not #113)
-#107 := (not #106)
-#117 := (and #107 #114)
-#103 := (not #102)
-#110 := (and #103 #107)
-#120 := (or #110 #117)
-#165 := (ite #120 #35 #145)
-#168 := (ite #17 0::Int #165)
-#171 := (ite #18 #13 #168)
-#174 := (= #34 #171)
-#177 := (forall (vars (?v0 Int) (?v1 Int)) #174)
-#231 := (iff #177 #230)
-#228 := (iff #174 #227)
-#225 := (= #171 #224)
-#222 := (= #168 #221)
-#219 := (= #165 #218)
-#203 := (iff #120 #202)
-#200 := (iff #117 #199)
-#201 := [rewrite]: #200
-#190 := (iff #110 #197)
-#191 := [rewrite]: #190
-#204 := [monotonicity #191 #201]: #203
-#220 := [monotonicity #204]: #219
-#223 := [monotonicity #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [quant-intro #229]: #231
-#188 := (~ #177 #177)
-#187 := (~ #174 #174)
-#184 := [refl]: #187
-#189 := [nnf-pos #184]: #188
-#28 := (- #14)
-#27 := (- #13)
-#36 := (mod #27 #28)
-#37 := (- #36)
-#21 := (< 0::Int #14)
-#23 := (< #13 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #13)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#38 := (ite #25 #35 #37)
-#39 := (ite #17 0::Int #38)
-#40 := (ite #18 #13 #39)
-#41 := (= #34 #40)
-#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
-#180 := (iff #42 #177)
-#74 := (and #21 #23)
-#77 := (or #22 #74)
-#150 := (ite #77 #35 #145)
-#153 := (ite #17 0::Int #150)
-#156 := (ite #18 #13 #153)
-#159 := (= #34 #156)
-#162 := (forall (vars (?v0 Int) (?v1 Int)) #159)
-#178 := (iff #162 #177)
-#175 := (iff #159 #174)
-#172 := (= #156 #171)
-#169 := (= #153 #168)
-#166 := (= #150 #165)
-#121 := (iff #77 #120)
-#118 := (iff #74 #117)
-#115 := (iff #23 #114)
-#116 := [rewrite]: #115
-#108 := (iff #21 #107)
-#109 := [rewrite]: #108
-#119 := [monotonicity #109 #116]: #118
-#111 := (iff #22 #110)
-#104 := (iff #20 #103)
-#105 := [rewrite]: #104
-#112 := [monotonicity #105 #109]: #111
-#122 := [monotonicity #112 #119]: #121
-#167 := [monotonicity #122]: #166
-#170 := [monotonicity #167]: #169
-#173 := [monotonicity #170]: #172
-#176 := [monotonicity #173]: #175
-#179 := [quant-intro #176]: #178
-#163 := (iff #42 #162)
-#160 := (iff #41 #159)
-#157 := (= #40 #156)
-#154 := (= #39 #153)
-#151 := (= #38 #150)
-#148 := (= #37 #145)
-#142 := (- #139)
-#146 := (= #142 #145)
-#147 := [rewrite]: #146
-#143 := (= #37 #142)
-#140 := (= #36 #139)
-#85 := (= #28 #84)
-#86 := [rewrite]: #85
-#82 := (= #27 #81)
-#83 := [rewrite]: #82
-#141 := [monotonicity #83 #86]: #140
-#144 := [monotonicity #141]: #143
-#149 := [trans #144 #147]: #148
-#78 := (iff #25 #77)
-#75 := (iff #24 #74)
-#76 := [rewrite]: #75
-#79 := [monotonicity #76]: #78
-#152 := [monotonicity #79 #149]: #151
-#155 := [monotonicity #152]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [quant-intro #161]: #163
-#181 := [trans #164 #179]: #180
-#138 := [asserted]: #42
-#182 := [mp #138 #181]: #177
-#185 := [mp~ #182 #189]: #177
-#233 := [mp #185 #232]: #230
-#264 := [mp #233 #263]: #261
-#748 := [mp #264 #747]: #743
-#8 := 1::Int
-#9 := 3::Int
-#10 := (f3 1::Int 3::Int)
-#11 := (= #10 1::Int)
-#12 := (not #11)
-#62 := [asserted]: #12
-#652 := (not #743)
-#653 := (or #652 #11)
-#322 := (* -1::Int 3::Int)
-#406 := (* -1::Int 1::Int)
-#407 := (mod #406 #322)
-#408 := (+ #10 #407)
-#399 := (= #408 0::Int)
-#410 := (mod 1::Int 3::Int)
-#411 := (* -1::Int #410)
-#412 := (+ #10 #411)
-#409 := (= #412 0::Int)
-#413 := (>= 1::Int 0::Int)
-#392 := (<= 3::Int 0::Int)
-#727 := (or #392 #413)
-#729 := (not #727)
-#386 := (<= 1::Int 0::Int)
-#516 := (or #386 #392)
-#723 := (not #516)
-#397 := (or #723 #729)
-#398 := (ite #397 #409 #399)
-#730 := (= #10 0::Int)
-#731 := (= 1::Int 0::Int)
-#732 := (ite #731 #730 #398)
-#63 := (= 1::Int #10)
-#733 := (= 3::Int 0::Int)
-#728 := (ite #733 #63 #732)
-#654 := (or #652 #728)
-#649 := (iff #654 #653)
-#640 := (iff #653 #653)
-#641 := [rewrite]: #640
-#658 := (iff #728 #11)
-#648 := (ite false #11 #11)
-#661 := (iff #648 #11)
-#662 := [rewrite]: #661
-#650 := (iff #728 #648)
-#659 := (iff #732 #11)
-#576 := (ite false #730 #11)
-#670 := (iff #576 #11)
-#657 := [rewrite]: #670
-#669 := (iff #732 #576)
-#574 := (iff #398 #11)
-#569 := -2::Int
-#664 := (= #10 -2::Int)
-#1 := true
-#570 := (ite true #11 #664)
-#572 := (iff #570 #11)
-#573 := [rewrite]: #572
-#571 := (iff #398 #570)
-#553 := (iff #399 #664)
-#679 := 2::Int
-#675 := (+ 2::Int #10)
-#560 := (= #675 0::Int)
-#665 := (iff #560 #664)
-#668 := [rewrite]: #665
-#519 := (iff #399 #560)
-#558 := (= #408 #675)
-#671 := (+ #10 2::Int)
-#673 := (= #671 #675)
-#676 := [rewrite]: #673
-#672 := (= #408 #671)
-#517 := (= #407 2::Int)
-#682 := -3::Int
-#678 := (mod -1::Int -3::Int)
-#686 := (= #678 2::Int)
-#515 := [rewrite]: #686
-#684 := (= #407 #678)
-#683 := (= #322 -3::Int)
-#677 := [rewrite]: #683
-#414 := (= #406 -1::Int)
-#696 := [rewrite]: #414
-#685 := [monotonicity #696 #677]: #684
-#518 := [trans #685 #515]: #517
-#674 := [monotonicity #518]: #672
-#559 := [trans #674 #676]: #558
-#667 := [monotonicity #559]: #519
-#568 := [trans #667 #668]: #553
-#680 := (iff #409 #11)
-#692 := (+ -1::Int #10)
-#689 := (= #692 0::Int)
-#537 := (iff #689 #11)
-#538 := [rewrite]: #537
-#695 := (iff #409 #689)
-#693 := (= #412 #692)
-#701 := (+ #10 -1::Int)
-#687 := (= #701 #692)
-#688 := [rewrite]: #687
-#690 := (= #412 #701)
-#700 := (= #411 -1::Int)
-#698 := (= #411 #406)
-#419 := (= #410 1::Int)
-#420 := [rewrite]: #419
-#699 := [monotonicity #420]: #698
-#697 := [trans #699 #696]: #700
-#691 := [monotonicity #697]: #690
-#694 := [trans #691 #688]: #693
-#536 := [monotonicity #694]: #695
-#681 := [trans #536 #538]: #680
-#417 := (iff #397 true)
-#428 := (or true false)
-#703 := (iff #428 true)
-#707 := [rewrite]: #703
-#702 := (iff #397 #428)
-#705 := (iff #729 false)
-#432 := (not true)
-#328 := (iff #432 false)
-#704 := [rewrite]: #328
-#433 := (iff #729 #432)
-#709 := (iff #727 true)
-#361 := (or false true)
-#722 := (iff #361 true)
-#708 := [rewrite]: #722
-#721 := (iff #727 #361)
-#720 := (iff #413 true)
-#360 := [rewrite]: #720
-#726 := (iff #392 false)
-#369 := [rewrite]: #726
-#719 := [monotonicity #369 #360]: #721
-#431 := [trans #719 #708]: #709
-#434 := [monotonicity #431]: #433
-#427 := [trans #434 #704]: #705
-#355 := (iff #723 true)
-#714 := (not false)
-#711 := (iff #714 true)
-#717 := [rewrite]: #711
-#715 := (iff #723 #714)
-#712 := (iff #516 false)
-#710 := (or false false)
-#375 := (iff #710 false)
-#376 := [rewrite]: #375
-#373 := (iff #516 #710)
-#725 := (iff #386 false)
-#385 := [rewrite]: #725
-#374 := [monotonicity #385 #369]: #373
-#713 := [trans #374 #376]: #712
-#716 := [monotonicity #713]: #715
-#718 := [trans #716 #717]: #355
-#706 := [monotonicity #718 #427]: #702
-#418 := [trans #706 #707]: #417
-#564 := [monotonicity #418 #681 #568]: #571
-#575 := [trans #564 #573]: #574
-#384 := (iff #731 false)
-#389 := [rewrite]: #384
-#666 := [monotonicity #389 #575]: #669
-#651 := [trans #666 #657]: #659
-#69 := (iff #63 #11)
+#64 := (iff #13 #56)
+#59 := (and #56 #56)
+#62 := (iff #59 #56)
+#63 := [rewrite]: #62
+#60 := (iff #13 #59)
+#61 := [monotonicity #58 #58]: #60
+#65 := [trans #61 #63]: #64
+#79 := [monotonicity #65 #76]: #78
+#110 := [monotonicity #79 #86 #107]: #109
+#114 := [trans #110 #112]: #113
+#54 := (iff #11 false)
+#49 := (= -3::Int 0::Int)
+#52 := (iff #49 false)
+#53 := [rewrite]: #52
+#50 := (iff #11 #49)
+#51 := [monotonicity #48]: #50
+#55 := [trans #51 #53]: #54
+#117 := [monotonicity #55 #114]: #116
+#121 := [trans #117 #119]: #120
+#124 := [monotonicity #55 #48 #121]: #123
+#127 := [trans #124 #126]: #24
+#130 := [monotonicity #127]: #129
+#134 := [trans #130 #132]: #133
+#137 := [monotonicity #134]: #136
+#141 := [trans #137 #139]: #140
+#45 := [asserted]: #25
+[mp #45 #141]: false
+unsat
+41d81c01f2d4595c3188777c9ff27286d543d121 170 0
+#2 := false
+#29 := 2::Int
+#30 := (- 2::Int)
+#8 := 3::Int
+#9 := (- 3::Int)
+#23 := (- #9)
+#12 := 5::Int
+#13 := (- 5::Int)
+#22 := (- #13)
+#24 := (mod #22 #23)
+#25 := (- #24)
+#21 := (mod #13 #9)
+#10 := 0::Int
+#16 := (< 0::Int #9)
+#18 := (< #13 0::Int)
+#19 := (and #18 #16)
+#15 := (< 0::Int #13)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#26 := (ite #20 #21 #25)
+#14 := (= #13 0::Int)
+#27 := (ite #14 0::Int #26)
+#11 := (= #9 0::Int)
+#28 := (ite #11 #13 #27)
+#31 := (= #28 #30)
+#32 := (not #31)
+#191 := (iff #32 false)
+#63 := -5::Int
+#82 := (< -5::Int 0::Int)
+#53 := -3::Int
+#76 := (< 0::Int -3::Int)
+#88 := (and #76 #82)
+#73 := (< 0::Int -5::Int)
+#79 := (and #73 #76)
+#93 := (or #79 #88)
+#189 := (iff #93 false)
+#184 := (or false false)
+#187 := (iff #184 false)
+#188 := [rewrite]: #187
+#185 := (iff #93 #184)
+#182 := (iff #88 false)
+#1 := true
+#177 := (and false true)
+#180 := (iff #177 false)
+#181 := [rewrite]: #180
+#178 := (iff #88 #177)
+#175 := (iff #82 true)
+#176 := [rewrite]: #175
+#166 := (iff #76 false)
+#167 := [rewrite]: #166
+#179 := [monotonicity #167 #176]: #178
+#183 := [trans #179 #181]: #182
+#173 := (iff #79 false)
+#168 := (and false false)
+#171 := (iff #168 false)
+#172 := [rewrite]: #171
+#169 := (iff #79 #168)
+#164 := (iff #73 false)
+#165 := [rewrite]: #164
+#170 := [monotonicity #165 #167]: #169
+#174 := [trans #170 #172]: #173
+#186 := [monotonicity #174 #183]: #185
+#190 := [trans #186 #188]: #189
+#162 := (iff #32 #93)
+#152 := (not #93)
+#157 := (not #152)
+#160 := (iff #157 #93)
+#161 := [rewrite]: #160
+#158 := (iff #32 #157)
+#155 := (iff #31 #152)
+#127 := -2::Int
+#99 := 1::Int
+#132 := (ite #93 1::Int -2::Int)
+#149 := (= #132 -2::Int)
+#153 := (iff #149 #152)
+#154 := [rewrite]: #153
+#150 := (iff #31 #149)
+#128 := (= #30 -2::Int)
+#129 := [rewrite]: #128
+#147 := (= #28 #132)
+#142 := (ite false -5::Int #132)
+#145 := (= #142 #132)
+#146 := [rewrite]: #145
+#143 := (= #28 #142)
+#140 := (= #27 #132)
+#135 := (ite false 0::Int #132)
+#138 := (= #135 #132)
+#139 := [rewrite]: #138
+#136 := (= #27 #135)
+#133 := (= #26 #132)
+#130 := (= #25 -2::Int)
+#125 := (= #25 #30)
+#123 := (= #24 2::Int)
+#118 := (mod 5::Int 3::Int)
+#121 := (= #118 2::Int)
+#122 := [rewrite]: #121
+#119 := (= #24 #118)
+#116 := (= #23 3::Int)
+#111 := (- -3::Int)
+#114 := (= #111 3::Int)
+#115 := [rewrite]: #114
+#112 := (= #23 #111)
+#54 := (= #9 -3::Int)
+#55 := [rewrite]: #54
+#113 := [monotonicity #55]: #112
+#117 := [trans #113 #115]: #116
+#109 := (= #22 5::Int)
+#104 := (- -5::Int)
+#107 := (= #104 5::Int)
+#108 := [rewrite]: #107
+#105 := (= #22 #104)
+#64 := (= #13 -5::Int)
+#65 := [rewrite]: #64
+#106 := [monotonicity #65]: #105
+#110 := [trans #106 #108]: #109
+#120 := [monotonicity #110 #117]: #119
+#124 := [trans #120 #122]: #123
+#126 := [monotonicity #124]: #125
+#131 := [trans #126 #129]: #130
+#102 := (= #21 1::Int)
+#96 := (mod -5::Int -3::Int)
+#100 := (= #96 1::Int)
+#101 := [rewrite]: #100
+#97 := (= #21 #96)
+#98 := [monotonicity #65 #55]: #97
+#103 := [trans #98 #101]: #102
+#94 := (iff #20 #93)
+#91 := (iff #19 #88)
+#85 := (and #82 #76)
+#89 := (iff #85 #88)
+#90 := [rewrite]: #89
+#86 := (iff #19 #85)
+#77 := (iff #16 #76)
+#78 := [monotonicity #55]: #77
+#83 := (iff #18 #82)
+#84 := [monotonicity #65]: #83
+#87 := [monotonicity #84 #78]: #86
+#92 := [trans #87 #90]: #91
+#80 := (iff #17 #79)
+#74 := (iff #15 #73)
+#75 := [monotonicity #65]: #74
+#81 := [monotonicity #75 #78]: #80
+#95 := [monotonicity #81 #92]: #94
+#134 := [monotonicity #95 #103 #131]: #133
+#71 := (iff #14 false)
+#66 := (= -5::Int 0::Int)
+#69 := (iff #66 false)
 #70 := [rewrite]: #69
-#734 := (iff #733 false)
-#724 := [rewrite]: #734
-#660 := [monotonicity #724 #70 #651]: #650
-#663 := [trans #660 #662]: #658
-#656 := [monotonicity #663]: #649
-#643 := [trans #656 #641]: #649
-#655 := [quant-inst #8 #9]: #654
-#644 := [mp #655 #643]: #653
-[unit-resolution #644 #62 #748]: false
-unsat
-8af900968418033d3c8752b20b45c64c00fb3744 305 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#14 := (:var 0 Int)
-#13 := (:var 1 Int)
-#33 := (f3 #13 #14)
-#747 := (pattern #33)
-#10 := 0::Int
-#78 := -1::Int
-#82 := (* -1::Int #14)
-#79 := (* -1::Int #13)
-#143 := (mod #79 #82)
-#258 := (+ #33 #143)
-#259 := (= #258 0::Int)
-#34 := (mod #13 #14)
-#255 := (* -1::Int #34)
-#256 := (+ #33 #255)
-#257 := (= #256 0::Int)
-#117 := (>= #13 0::Int)
-#110 := (<= #14 0::Int)
-#202 := (or #110 #117)
-#203 := (not #202)
-#106 := (<= #13 0::Int)
-#200 := (or #106 #110)
-#201 := (not #200)
-#206 := (or #201 #203)
-#260 := (ite #206 #257 #259)
-#254 := (= #33 0::Int)
-#16 := (= #13 0::Int)
-#261 := (ite #16 #254 #260)
-#253 := (= #13 #33)
-#17 := (= #14 0::Int)
-#262 := (ite #17 #253 #261)
-#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #262)
-#265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
-#751 := (iff #265 #748)
-#749 := (iff #262 #262)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#149 := (* -1::Int #143)
-#222 := (ite #206 #34 #149)
-#225 := (ite #16 0::Int #222)
-#228 := (ite #17 #13 #225)
-#231 := (= #33 #228)
-#234 := (forall (vars (?v0 Int) (?v1 Int)) #231)
-#266 := (iff #234 #265)
-#263 := (iff #231 #262)
-#264 := [rewrite]: #263
-#267 := [quant-intro #264]: #266
-#118 := (not #117)
-#111 := (not #110)
-#121 := (and #111 #118)
-#107 := (not #106)
-#114 := (and #107 #111)
-#124 := (or #114 #121)
-#169 := (ite #124 #34 #149)
-#172 := (ite #16 0::Int #169)
-#175 := (ite #17 #13 #172)
-#178 := (= #33 #175)
-#181 := (forall (vars (?v0 Int) (?v1 Int)) #178)
-#235 := (iff #181 #234)
-#232 := (iff #178 #231)
-#229 := (= #175 #228)
-#226 := (= #172 #225)
-#223 := (= #169 #222)
-#207 := (iff #124 #206)
-#204 := (iff #121 #203)
-#205 := [rewrite]: #204
-#194 := (iff #114 #201)
-#195 := [rewrite]: #194
-#208 := [monotonicity #195 #205]: #207
-#224 := [monotonicity #208]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [quant-intro #233]: #235
-#192 := (~ #181 #181)
-#191 := (~ #178 #178)
-#188 := [refl]: #191
-#193 := [nnf-pos #188]: #192
-#27 := (- #14)
-#26 := (- #13)
-#35 := (mod #26 #27)
-#36 := (- #35)
-#20 := (< 0::Int #14)
-#22 := (< #13 0::Int)
-#23 := (and #22 #20)
-#19 := (< 0::Int #13)
-#21 := (and #19 #20)
-#24 := (or #21 #23)
-#37 := (ite #24 #34 #36)
-#38 := (ite #16 0::Int #37)
-#39 := (ite #17 #13 #38)
-#40 := (= #33 #39)
-#41 := (forall (vars (?v0 Int) (?v1 Int)) #40)
-#184 := (iff #41 #181)
-#72 := (and #20 #22)
-#75 := (or #21 #72)
-#154 := (ite #75 #34 #149)
-#63 := (= 0::Int #13)
-#157 := (ite #63 0::Int #154)
-#66 := (= 0::Int #14)
-#160 := (ite #66 #13 #157)
-#163 := (= #33 #160)
-#166 := (forall (vars (?v0 Int) (?v1 Int)) #163)
-#182 := (iff #166 #181)
-#179 := (iff #163 #178)
-#176 := (= #160 #175)
-#173 := (= #157 #172)
-#170 := (= #154 #169)
-#125 := (iff #75 #124)
-#122 := (iff #72 #121)
-#119 := (iff #22 #118)
-#120 := [rewrite]: #119
-#112 := (iff #20 #111)
-#113 := [rewrite]: #112
-#123 := [monotonicity #113 #120]: #122
-#115 := (iff #21 #114)
-#108 := (iff #19 #107)
-#109 := [rewrite]: #108
-#116 := [monotonicity #109 #113]: #115
-#126 := [monotonicity #116 #123]: #125
-#171 := [monotonicity #126]: #170
-#100 := (iff #63 #16)
-#101 := [rewrite]: #100
-#174 := [monotonicity #101 #171]: #173
-#102 := (iff #66 #17)
-#103 := [rewrite]: #102
-#177 := [monotonicity #103 #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [quant-intro #180]: #182
-#167 := (iff #41 #166)
-#164 := (iff #40 #163)
-#161 := (= #39 #160)
-#158 := (= #38 #157)
-#155 := (= #37 #154)
-#152 := (= #36 #149)
-#146 := (- #143)
-#150 := (= #146 #149)
-#151 := [rewrite]: #150
-#147 := (= #36 #146)
-#144 := (= #35 #143)
-#83 := (= #27 #82)
-#84 := [rewrite]: #83
-#80 := (= #26 #79)
-#81 := [rewrite]: #80
-#145 := [monotonicity #81 #84]: #144
-#148 := [monotonicity #145]: #147
-#153 := [trans #148 #151]: #152
-#76 := (iff #24 #75)
-#73 := (iff #23 #72)
-#74 := [rewrite]: #73
-#77 := [monotonicity #74]: #76
-#156 := [monotonicity #77 #153]: #155
-#64 := (iff #16 #63)
-#65 := [rewrite]: #64
-#159 := [monotonicity #65 #156]: #158
-#67 := (iff #17 #66)
-#68 := [rewrite]: #67
-#162 := [monotonicity #68 #159]: #161
-#165 := [monotonicity #162]: #164
-#168 := [quant-intro #165]: #167
-#185 := [trans #168 #183]: #184
-#142 := [asserted]: #41
-#186 := [mp #142 #185]: #181
-#189 := [mp~ #186 #193]: #181
-#237 := [mp #189 #236]: #234
-#268 := [mp #237 #267]: #265
-#753 := [mp #268 #752]: #748
+#67 := (iff #14 #66)
+#68 := [monotonicity #65]: #67
+#72 := [trans #68 #70]: #71
+#137 := [monotonicity #72 #134]: #136
+#141 := [trans #137 #139]: #140
+#61 := (iff #11 false)
+#56 := (= -3::Int 0::Int)
+#59 := (iff #56 false)
+#60 := [rewrite]: #59
+#57 := (iff #11 #56)
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#144 := [monotonicity #62 #65 #141]: #143
+#148 := [trans #144 #146]: #147
+#151 := [monotonicity #148 #129]: #150
+#156 := [trans #151 #154]: #155
+#159 := [monotonicity #156]: #158
+#163 := [trans #159 #161]: #162
+#192 := [trans #163 #190]: #191
+#52 := [asserted]: #32
+[mp #52 #192]: false
+unsat
+37d641fb0d3f5af8883d250eb08e7f4e580b8a49 182 0
+#2 := false
+#9 := 0::Int
+decl f3 :: Int
+#11 := f3
+#99 := (<= f3 0::Int)
+#112 := (>= f3 0::Int)
+#113 := (not #112)
+#100 := (not #99)
+#123 := (or #100 #113)
+#160 := (not #123)
+#64 := -3::Int
+#60 := -1::Int
+#61 := (* -1::Int f3)
+#67 := (mod #61 -3::Int)
+#73 := (* -1::Int #67)
 #8 := 3::Int
-#9 := (f3 3::Int 3::Int)
-#11 := (= #9 0::Int)
-#12 := (not #11)
-#61 := [asserted]: #12
-#573 := (not #748)
-#575 := (or #573 #11)
-#326 := (* -1::Int 3::Int)
-#411 := (mod #326 #326)
-#412 := (+ #9 #411)
-#413 := (= #412 0::Int)
-#404 := (mod 3::Int 3::Int)
-#415 := (* -1::Int #404)
-#416 := (+ #9 #415)
-#344 := (= #416 0::Int)
-#417 := (>= 3::Int 0::Int)
-#414 := (<= 3::Int 0::Int)
-#418 := (or #414 #417)
-#397 := (not #418)
-#732 := (or #414 #414)
-#734 := (not #732)
-#391 := (or #734 #397)
-#521 := (ite #391 #344 #413)
-#728 := (= 3::Int 0::Int)
-#402 := (ite #728 #11 #521)
-#403 := (= 3::Int #9)
-#735 := (ite #728 #403 #402)
-#576 := (or #573 #735)
-#577 := (iff #576 #575)
-#579 := (iff #575 #575)
-#580 := [rewrite]: #579
-#673 := (iff #735 #11)
-#733 := (= #9 3::Int)
-#524 := (ite false #733 #11)
-#669 := (iff #524 #11)
-#670 := [rewrite]: #669
-#672 := (iff #735 #524)
-#564 := (iff #402 #11)
-#679 := (ite false #11 #11)
-#681 := (iff #679 #11)
-#563 := [rewrite]: #681
-#680 := (iff #402 #679)
-#676 := (iff #521 #11)
-#1 := true
-#684 := (ite true #11 #11)
-#522 := (iff #684 #11)
-#523 := [rewrite]: #522
-#691 := (iff #521 #684)
-#689 := (iff #413 #11)
-#682 := (= #412 #9)
-#419 := (+ #9 0::Int)
-#702 := (= #419 #9)
-#706 := [rewrite]: #702
-#687 := (= #412 #419)
-#685 := (= #411 0::Int)
-#693 := -3::Int
-#694 := (mod -3::Int -3::Int)
-#542 := (= #694 0::Int)
-#543 := [rewrite]: #542
-#700 := (= #411 #694)
-#698 := (= #326 -3::Int)
-#699 := [rewrite]: #698
-#541 := [monotonicity #699 #699]: #700
-#686 := [trans #541 #543]: #685
-#688 := [monotonicity #686]: #687
-#683 := [trans #688 #706]: #682
-#690 := [monotonicity #683]: #689
-#697 := (iff #344 #11)
-#695 := (= #416 #9)
-#701 := (= #416 #419)
-#703 := (= #415 0::Int)
-#712 := (* -1::Int 0::Int)
-#424 := (= #712 0::Int)
-#425 := [rewrite]: #424
-#422 := (= #415 #712)
-#711 := (= #404 0::Int)
-#708 := [rewrite]: #711
-#423 := [monotonicity #708]: #422
-#704 := [trans #423 #425]: #703
-#705 := [monotonicity #704]: #701
-#696 := [trans #705 #706]: #695
-#692 := [monotonicity #696]: #697
-#433 := (iff #391 true)
-#439 := (or true false)
-#710 := (iff #439 true)
-#432 := [rewrite]: #710
-#332 := (iff #391 #439)
-#437 := (iff #397 false)
-#724 := (not true)
-#714 := (iff #724 false)
-#436 := [rewrite]: #714
-#727 := (iff #397 #724)
-#366 := (iff #418 true)
-#722 := (or false true)
-#725 := (iff #722 true)
-#365 := [rewrite]: #725
-#360 := (iff #418 #722)
-#721 := (iff #417 true)
-#716 := [rewrite]: #721
-#729 := (iff #414 false)
-#389 := [rewrite]: #729
-#723 := [monotonicity #389 #716]: #360
-#726 := [trans #723 #365]: #366
-#713 := [monotonicity #726]: #727
-#438 := [trans #713 #436]: #437
-#719 := (iff #734 true)
-#379 := (not false)
-#717 := (iff #379 true)
-#718 := [rewrite]: #717
-#380 := (iff #734 #379)
-#715 := (iff #732 false)
-#394 := (or false false)
-#731 := (iff #394 false)
-#374 := [rewrite]: #731
-#730 := (iff #732 #394)
-#390 := [monotonicity #389 #389]: #730
-#378 := [trans #390 #374]: #715
-#381 := [monotonicity #378]: #380
-#720 := [trans #381 #718]: #719
-#709 := [monotonicity #720 #438]: #332
-#707 := [trans #709 #432]: #433
-#520 := [monotonicity #707 #692 #690]: #691
-#677 := [trans #520 #523]: #676
-#736 := (iff #728 false)
-#737 := [rewrite]: #736
-#678 := [monotonicity #737 #677]: #680
-#565 := [trans #678 #563]: #564
-#738 := (iff #403 #733)
-#739 := [rewrite]: #738
-#574 := [monotonicity #737 #739 #565]: #672
-#558 := [trans #574 #670]: #673
-#578 := [monotonicity #558]: #577
-#581 := [trans #578 #580]: #577
-#569 := [quant-inst #8 #8]: #576
-#674 := [mp #569 #581]: #575
-[unit-resolution #674 #61 #753]: false
-unsat
-e06ff93350d55c82e0187108fc1a1d48234a7767 326 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#15 := (:var 0 Int)
-#14 := (:var 1 Int)
-#35 := (f3 #14 #15)
-#734 := (pattern #35)
-#17 := 0::Int
-#71 := -1::Int
-#75 := (* -1::Int #15)
-#72 := (* -1::Int #14)
-#130 := (mod #72 #75)
-#245 := (+ #35 #130)
-#246 := (= #245 0::Int)
-#36 := (mod #14 #15)
-#242 := (* -1::Int #36)
-#243 := (+ #35 #242)
-#244 := (= #243 0::Int)
-#104 := (>= #14 0::Int)
-#97 := (<= #15 0::Int)
-#189 := (or #97 #104)
-#190 := (not #189)
-#93 := (<= #14 0::Int)
-#187 := (or #93 #97)
-#188 := (not #187)
-#193 := (or #188 #190)
-#247 := (ite #193 #244 #246)
-#241 := (= #35 0::Int)
-#18 := (= #14 0::Int)
-#248 := (ite #18 #241 #247)
-#240 := (= #14 #35)
-#19 := (= #15 0::Int)
-#249 := (ite #19 #240 #248)
-#735 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #734) #249)
-#252 := (forall (vars (?v0 Int) (?v1 Int)) #249)
-#738 := (iff #252 #735)
-#736 := (iff #249 #249)
-#737 := [refl]: #736
-#739 := [quant-intro #737]: #738
-#136 := (* -1::Int #130)
-#209 := (ite #193 #36 #136)
-#212 := (ite #18 0::Int #209)
-#215 := (ite #19 #14 #212)
-#218 := (= #35 #215)
-#221 := (forall (vars (?v0 Int) (?v1 Int)) #218)
-#253 := (iff #221 #252)
-#250 := (iff #218 #249)
-#251 := [rewrite]: #250
-#254 := [quant-intro #251]: #253
-#105 := (not #104)
-#98 := (not #97)
-#108 := (and #98 #105)
-#94 := (not #93)
-#101 := (and #94 #98)
-#111 := (or #101 #108)
-#156 := (ite #111 #36 #136)
-#159 := (ite #18 0::Int #156)
-#162 := (ite #19 #14 #159)
-#165 := (= #35 #162)
-#168 := (forall (vars (?v0 Int) (?v1 Int)) #165)
-#222 := (iff #168 #221)
-#219 := (iff #165 #218)
-#216 := (= #162 #215)
-#213 := (= #159 #212)
-#210 := (= #156 #209)
-#194 := (iff #111 #193)
-#191 := (iff #108 #190)
-#192 := [rewrite]: #191
-#181 := (iff #101 #188)
-#182 := [rewrite]: #181
-#195 := [monotonicity #182 #192]: #194
-#211 := [monotonicity #195]: #210
-#214 := [monotonicity #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [monotonicity #217]: #219
-#223 := [quant-intro #220]: #222
-#179 := (~ #168 #168)
-#178 := (~ #165 #165)
-#175 := [refl]: #178
-#180 := [nnf-pos #175]: #179
-#29 := (- #15)
-#28 := (- #14)
-#37 := (mod #28 #29)
-#38 := (- #37)
-#22 := (< 0::Int #15)
-#24 := (< #14 0::Int)
-#25 := (and #24 #22)
-#21 := (< 0::Int #14)
-#23 := (and #21 #22)
-#26 := (or #23 #25)
-#39 := (ite #26 #36 #38)
-#40 := (ite #18 0::Int #39)
-#41 := (ite #19 #14 #40)
-#42 := (= #35 #41)
-#43 := (forall (vars (?v0 Int) (?v1 Int)) #42)
-#171 := (iff #43 #168)
-#65 := (and #22 #24)
-#68 := (or #23 #65)
-#141 := (ite #68 #36 #136)
-#144 := (ite #18 0::Int #141)
-#147 := (ite #19 #14 #144)
-#150 := (= #35 #147)
-#153 := (forall (vars (?v0 Int) (?v1 Int)) #150)
-#169 := (iff #153 #168)
-#166 := (iff #150 #165)
-#163 := (= #147 #162)
-#160 := (= #144 #159)
-#157 := (= #141 #156)
-#112 := (iff #68 #111)
-#109 := (iff #65 #108)
-#106 := (iff #24 #105)
+#19 := (mod f3 3::Int)
+#126 := (ite #123 #19 #73)
+#158 := (= #19 #126)
+#254 := (not #158)
+#226 := (>= #19 3::Int)
+#227 := (not #226)
+#1 := true
+#46 := [true-axiom]: true
+#242 := (or false #227)
+#243 := [th-lemma arith]: #242
+#244 := [unit-resolution #243 #46]: #227
+#12 := (= f3 0::Int)
+#129 := (ite #12 0::Int #126)
+#238 := (* -1::Int #129)
+#239 := (+ #19 #238)
+#241 := (>= #239 0::Int)
+#237 := (= #19 #129)
+#157 := (= #126 #129)
+#167 := (not #12)
+#156 := (= #129 0::Int)
+#179 := (not #156)
+#172 := (<= #129 0::Int)
+#174 := (not #172)
+#136 := (>= #129 3::Int)
+#21 := (- 3::Int)
+#20 := (- f3)
+#22 := (mod #20 #21)
+#23 := (- #22)
+#14 := (< 0::Int 3::Int)
+#16 := (< f3 0::Int)
+#17 := (and #16 #14)
+#13 := (< 0::Int f3)
+#15 := (and #13 #14)
+#18 := (or #15 #17)
+#24 := (ite #18 #19 #23)
+#25 := (ite #12 0::Int #24)
+#10 := (= 3::Int 0::Int)
+#26 := (ite #10 f3 #25)
+#27 := (< #26 3::Int)
+#28 := (not #27)
+#148 := (iff #28 #136)
+#54 := (and #14 #16)
+#57 := (or #15 #54)
+#78 := (ite #57 #19 #73)
+#51 := (= 0::Int f3)
+#81 := (ite #51 0::Int #78)
+#91 := (< #81 3::Int)
+#94 := (not #91)
+#146 := (iff #94 #136)
+#135 := (not #136)
+#141 := (not #135)
+#144 := (iff #141 #136)
+#145 := [rewrite]: #144
+#142 := (iff #94 #141)
+#139 := (iff #91 #135)
+#132 := (< #129 3::Int)
+#137 := (iff #132 #135)
+#138 := [rewrite]: #137
+#133 := (iff #91 #132)
+#130 := (= #81 #129)
+#127 := (= #78 #126)
+#124 := (iff #57 #123)
+#121 := (iff #54 #113)
+#116 := (and true #113)
+#119 := (iff #116 #113)
+#120 := [rewrite]: #119
+#117 := (iff #54 #116)
+#114 := (iff #16 #113)
+#115 := [rewrite]: #114
+#103 := (iff #14 true)
+#104 := [rewrite]: #103
+#118 := [monotonicity #104 #115]: #117
+#122 := [trans #118 #120]: #121
+#110 := (iff #15 #100)
+#105 := (and #100 true)
+#108 := (iff #105 #100)
+#109 := [rewrite]: #108
+#106 := (iff #15 #105)
+#101 := (iff #13 #100)
+#102 := [rewrite]: #101
+#107 := [monotonicity #102 #104]: #106
+#111 := [trans #107 #109]: #110
+#125 := [monotonicity #111 #122]: #124
+#128 := [monotonicity #125]: #127
+#97 := (iff #51 #12)
+#98 := [rewrite]: #97
+#131 := [monotonicity #98 #128]: #130
+#134 := [monotonicity #131]: #133
+#140 := [trans #134 #138]: #139
+#143 := [monotonicity #140]: #142
+#147 := [trans #143 #145]: #146
+#95 := (iff #28 #94)
+#92 := (iff #27 #91)
+#89 := (= #26 #81)
+#84 := (ite false f3 #81)
+#87 := (= #84 #81)
+#88 := [rewrite]: #87
+#85 := (= #26 #84)
+#82 := (= #25 #81)
+#79 := (= #24 #78)
+#76 := (= #23 #73)
+#70 := (- #67)
+#74 := (= #70 #73)
+#75 := [rewrite]: #74
+#71 := (= #23 #70)
+#68 := (= #22 #67)
+#65 := (= #21 -3::Int)
+#66 := [rewrite]: #65
+#62 := (= #20 #61)
+#63 := [rewrite]: #62
+#69 := [monotonicity #63 #66]: #68
+#72 := [monotonicity #69]: #71
+#77 := [trans #72 #75]: #76
+#58 := (iff #18 #57)
+#55 := (iff #17 #54)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#80 := [monotonicity #59 #77]: #79
+#52 := (iff #12 #51)
+#53 := [rewrite]: #52
+#83 := [monotonicity #53 #80]: #82
+#49 := (iff #10 false)
+#50 := [rewrite]: #49
+#86 := [monotonicity #50 #83]: #85
+#90 := [trans #86 #88]: #89
+#93 := [monotonicity #90]: #92
+#96 := [monotonicity #93]: #95
+#149 := [trans #96 #147]: #148
+#48 := [asserted]: #28
+#150 := [mp #48 #149]: #136
+#175 := (or #174 #135)
+#176 := [th-lemma arith farkas 1 1]: #175
+#177 := [unit-resolution #176 #150]: #174
+#178 := [hypothesis]: #156
+#180 := (or #179 #172)
+#181 := [th-lemma arith triangle-eq]: #180
+#182 := [unit-resolution #181 #178 #177]: false
+#183 := [lemma #182]: #179
+#168 := (or #167 #156)
+#169 := [def-axiom]: #168
+#245 := [unit-resolution #169 #183]: #167
+#170 := (or #12 #157)
+#171 := [def-axiom]: #170
+#246 := [unit-resolution #171 #245]: #157
+#247 := [hypothesis]: #158
+#248 := [trans #247 #246]: #237
+#249 := (not #237)
+#250 := (or #249 #241)
+#251 := [th-lemma arith triangle-eq]: #250
+#252 := [unit-resolution #251 #248]: #241
+#253 := [th-lemma arith farkas -1 -1 1 #150 #252 #244]: false
+#255 := [lemma #253]: #254
+#163 := (or #160 #158)
+#164 := [def-axiom]: #163
+#232 := [unit-resolution #164 #255]: #160
+#154 := (or #123 #99)
+#155 := [def-axiom]: #154
+#233 := [unit-resolution #155 #232]: #99
+#152 := (or #123 #112)
+#153 := [def-axiom]: #152
+#234 := [unit-resolution #153 #232]: #112
+#235 := (or #12 #100 #113)
+#236 := [th-lemma arith triangle-eq]: #235
+#207 := [unit-resolution #236 #245]: #123
+[unit-resolution #207 #234 #233]: false
+unsat
+fcd3f8cba75d0af01f63efd762505b1dda18b530 187 0
+#2 := false
+#8 := 3::Int
+decl f3 :: Int
+#11 := f3
+#19 := (mod f3 3::Int)
+#233 := (>= #19 3::Int)
+#234 := (not #233)
+#1 := true
+#48 := [true-axiom]: true
+#248 := (or false #234)
+#249 := [th-lemma arith]: #248
+#250 := [unit-resolution #249 #48]: #234
+#9 := 0::Int
+#62 := -1::Int
+#206 := (* -1::Int #19)
+#245 := (+ f3 #206)
+#246 := (<= #245 0::Int)
+#244 := (= f3 #19)
+#66 := -3::Int
+#63 := (* -1::Int f3)
+#69 := (mod #63 -3::Int)
+#75 := (* -1::Int #69)
+#132 := (>= f3 0::Int)
+#133 := (not #132)
+#119 := (<= f3 0::Int)
+#120 := (not #119)
+#143 := (or #120 #133)
+#146 := (ite #143 #19 #75)
+#262 := (= #146 #19)
+#178 := (= #19 #146)
+#113 := (>= f3 3::Int)
+#12 := (= f3 0::Int)
+#149 := (ite #12 0::Int #146)
+#152 := (= f3 #149)
+#155 := (not #152)
+#114 := (not #113)
+#158 := (or #114 #155)
+#161 := (not #158)
+#28 := (< f3 3::Int)
+#21 := (- 3::Int)
+#20 := (- f3)
+#22 := (mod #20 #21)
+#23 := (- #22)
+#14 := (< 0::Int 3::Int)
+#16 := (< f3 0::Int)
+#17 := (and #16 #14)
+#13 := (< 0::Int f3)
+#15 := (and #13 #14)
+#18 := (or #15 #17)
+#24 := (ite #18 #19 #23)
+#25 := (ite #12 0::Int #24)
+#10 := (= 3::Int 0::Int)
+#26 := (ite #10 f3 #25)
+#27 := (= #26 f3)
+#29 := (implies #27 #28)
+#30 := (not #29)
+#164 := (iff #30 #161)
+#56 := (and #14 #16)
+#59 := (or #15 #56)
+#80 := (ite #59 #19 #75)
+#53 := (= 0::Int f3)
+#83 := (ite #53 0::Int #80)
+#96 := (= f3 #83)
+#104 := (not #96)
+#105 := (or #28 #104)
+#110 := (not #105)
+#162 := (iff #110 #161)
+#159 := (iff #105 #158)
+#156 := (iff #104 #155)
+#153 := (iff #96 #152)
+#150 := (= #83 #149)
+#147 := (= #80 #146)
+#144 := (iff #59 #143)
+#141 := (iff #56 #133)
+#136 := (and true #133)
+#139 := (iff #136 #133)
+#140 := [rewrite]: #139
+#137 := (iff #56 #136)
+#134 := (iff #16 #133)
+#135 := [rewrite]: #134
+#123 := (iff #14 true)
+#124 := [rewrite]: #123
+#138 := [monotonicity #124 #135]: #137
+#142 := [trans #138 #140]: #141
+#130 := (iff #15 #120)
+#125 := (and #120 true)
+#128 := (iff #125 #120)
+#129 := [rewrite]: #128
+#126 := (iff #15 #125)
+#121 := (iff #13 #120)
+#122 := [rewrite]: #121
+#127 := [monotonicity #122 #124]: #126
+#131 := [trans #127 #129]: #130
+#145 := [monotonicity #131 #142]: #144
+#148 := [monotonicity #145]: #147
+#117 := (iff #53 #12)
+#118 := [rewrite]: #117
+#151 := [monotonicity #118 #148]: #150
+#154 := [monotonicity #151]: #153
+#157 := [monotonicity #154]: #156
+#115 := (iff #28 #114)
+#116 := [rewrite]: #115
+#160 := [monotonicity #116 #157]: #159
+#163 := [monotonicity #160]: #162
+#111 := (iff #30 #110)
+#108 := (iff #29 #105)
+#101 := (implies #96 #28)
+#106 := (iff #101 #105)
 #107 := [rewrite]: #106
-#99 := (iff #22 #98)
-#100 := [rewrite]: #99
-#110 := [monotonicity #100 #107]: #109
-#102 := (iff #23 #101)
-#95 := (iff #21 #94)
-#96 := [rewrite]: #95
-#103 := [monotonicity #96 #100]: #102
-#113 := [monotonicity #103 #110]: #112
-#158 := [monotonicity #113]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [monotonicity #164]: #166
-#170 := [quant-intro #167]: #169
-#154 := (iff #43 #153)
-#151 := (iff #42 #150)
-#148 := (= #41 #147)
-#145 := (= #40 #144)
-#142 := (= #39 #141)
-#139 := (= #38 #136)
-#133 := (- #130)
-#137 := (= #133 #136)
-#138 := [rewrite]: #137
-#134 := (= #38 #133)
-#131 := (= #37 #130)
-#76 := (= #29 #75)
+#102 := (iff #29 #101)
+#99 := (iff #27 #96)
+#93 := (= #83 f3)
+#97 := (iff #93 #96)
+#98 := [rewrite]: #97
+#94 := (iff #27 #93)
+#91 := (= #26 #83)
+#86 := (ite false f3 #83)
+#89 := (= #86 #83)
+#90 := [rewrite]: #89
+#87 := (= #26 #86)
+#84 := (= #25 #83)
+#81 := (= #24 #80)
+#78 := (= #23 #75)
+#72 := (- #69)
+#76 := (= #72 #75)
 #77 := [rewrite]: #76
-#73 := (= #28 #72)
-#74 := [rewrite]: #73
-#132 := [monotonicity #74 #77]: #131
-#135 := [monotonicity #132]: #134
-#140 := [trans #135 #138]: #139
-#69 := (iff #26 #68)
-#66 := (iff #25 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#143 := [monotonicity #70 #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [monotonicity #149]: #151
-#155 := [quant-intro #152]: #154
-#172 := [trans #155 #170]: #171
-#129 := [asserted]: #43
-#173 := [mp #129 #172]: #168
-#176 := [mp~ #173 #180]: #168
-#224 := [mp #176 #223]: #221
-#255 := [mp #224 #254]: #252
-#740 := [mp #255 #739]: #735
-#11 := 2::Int
-#9 := 3::Int
-#8 := 5::Int
-#10 := (f3 5::Int 3::Int)
-#12 := (= #10 2::Int)
-#13 := (not #12)
-#63 := [asserted]: #13
-#633 := (not #735)
-#635 := (or #633 #12)
-#313 := (* -1::Int 3::Int)
-#398 := (* -1::Int 5::Int)
-#399 := (mod #398 #313)
-#400 := (+ #10 #399)
-#391 := (= #400 0::Int)
-#402 := (mod 5::Int 3::Int)
-#403 := (* -1::Int #402)
-#331 := (+ #10 #403)
-#404 := (= #331 0::Int)
-#401 := (>= 5::Int 0::Int)
-#405 := (<= 3::Int 0::Int)
-#384 := (or #405 #401)
-#719 := (not #384)
-#721 := (<= 5::Int 0::Int)
-#378 := (or #721 #405)
-#508 := (not #378)
-#715 := (or #508 #719)
-#389 := (ite #715 #404 #391)
-#390 := (= #10 0::Int)
-#722 := (= 5::Int 0::Int)
-#723 := (ite #722 #390 #389)
-#724 := (= 5::Int #10)
-#725 := (= 3::Int 0::Int)
-#720 := (ite #725 #724 #723)
-#636 := (or #633 #720)
-#638 := (iff #636 #635)
-#639 := (iff #635 #635)
-#625 := [rewrite]: #639
-#648 := (iff #720 #12)
-#381 := (= #10 5::Int)
-#644 := (ite false #381 #12)
-#647 := (iff #644 #12)
-#641 := [rewrite]: #647
-#645 := (iff #720 #644)
-#650 := (iff #723 #12)
-#640 := (ite false #390 #12)
-#653 := (iff #640 #12)
-#654 := [rewrite]: #653
-#642 := (iff #723 #640)
-#651 := (iff #389 #12)
-#556 := (= #10 -1::Int)
-#1 := true
-#568 := (ite true #12 #556)
-#662 := (iff #568 #12)
-#649 := [rewrite]: #662
-#661 := (iff #389 #568)
-#566 := (iff #391 #556)
-#667 := 1::Int
-#561 := (+ 1::Int #10)
-#560 := (= #561 0::Int)
-#564 := (iff #560 #556)
-#565 := [rewrite]: #564
-#562 := (iff #391 #560)
-#660 := (= #400 #561)
-#552 := (+ #10 1::Int)
-#656 := (= #552 #561)
-#657 := [rewrite]: #656
-#511 := (= #400 #552)
-#550 := (= #399 1::Int)
-#507 := -3::Int
-#677 := -5::Int
-#663 := (mod -5::Int -3::Int)
-#665 := (= #663 1::Int)
-#668 := [rewrite]: #665
-#664 := (= #399 #663)
-#509 := (= #313 -3::Int)
-#510 := [rewrite]: #509
-#671 := (= #398 -5::Int)
-#678 := [rewrite]: #671
-#666 := [monotonicity #678 #510]: #664
-#551 := [trans #666 #668]: #550
-#659 := [monotonicity #551]: #511
-#545 := [trans #659 #657]: #660
-#563 := [monotonicity #545]: #562
-#567 := [trans #563 #565]: #566
-#670 := (iff #404 #12)
-#693 := -2::Int
-#681 := (+ -2::Int #10)
-#672 := (= #681 0::Int)
-#675 := (iff #672 #12)
-#669 := [rewrite]: #675
-#673 := (iff #404 #672)
-#529 := (= #331 #681)
-#680 := (+ #10 -2::Int)
-#687 := (= #680 #681)
-#528 := [rewrite]: #687
-#685 := (= #331 #680)
-#684 := (= #403 -2::Int)
-#688 := (* -1::Int 2::Int)
-#682 := (= #688 -2::Int)
-#683 := [rewrite]: #682
-#692 := (= #403 #688)
-#691 := (= #402 2::Int)
-#406 := [rewrite]: #691
-#689 := [monotonicity #406]: #692
-#679 := [trans #689 #683]: #684
-#686 := [monotonicity #679]: #685
-#530 := [trans #686 #528]: #529
-#674 := [monotonicity #530]: #673
-#676 := [trans #674 #669]: #670
-#412 := (iff #715 true)
-#695 := (or true false)
-#410 := (iff #695 true)
-#411 := [rewrite]: #410
-#699 := (iff #715 #695)
-#694 := (iff #719 false)
-#319 := (not true)
-#419 := (iff #319 false)
-#420 := [rewrite]: #419
-#696 := (iff #719 #319)
-#425 := (iff #384 true)
-#714 := (or false true)
-#423 := (iff #714 true)
-#424 := [rewrite]: #423
-#700 := (iff #384 #714)
-#713 := (iff #401 true)
-#711 := [rewrite]: #713
-#365 := (iff #405 false)
-#366 := [rewrite]: #365
-#701 := [monotonicity #366 #711]: #700
-#426 := [trans #701 #424]: #425
-#697 := [monotonicity #426]: #696
-#698 := [trans #697 #420]: #694
-#352 := (iff #508 true)
-#703 := (not false)
-#710 := (iff #703 true)
-#712 := [rewrite]: #710
-#709 := (iff #508 #703)
-#707 := (iff #378 false)
-#367 := (or false false)
-#705 := (iff #367 false)
-#706 := [rewrite]: #705
-#368 := (iff #378 #367)
-#361 := (iff #721 false)
-#702 := [rewrite]: #361
-#704 := [monotonicity #702 #366]: #368
-#708 := [trans #704 #706]: #707
-#347 := [monotonicity #708]: #709
-#353 := [trans #347 #712]: #352
-#409 := [monotonicity #353 #698]: #699
-#690 := [trans #409 #411]: #412
-#658 := [monotonicity #690 #676 #567]: #661
-#643 := [trans #658 #649]: #651
-#377 := (iff #722 false)
-#718 := [rewrite]: #377
-#652 := [monotonicity #718 #643]: #642
-#655 := [trans #652 #654]: #650
-#376 := (iff #724 #381)
-#717 := [rewrite]: #376
-#726 := (iff #725 false)
-#716 := [rewrite]: #726
-#646 := [monotonicity #716 #717 #655]: #645
-#632 := [trans #646 #641]: #648
-#634 := [monotonicity #632]: #638
-#626 := [trans #634 #625]: #638
-#637 := [quant-inst #8 #9]: #636
-#628 := [mp #637 #626]: #635
-[unit-resolution #628 #63 #740]: false
-unsat
-216c9ba1da8ff35ffdfffd11994f68f93a59b859 330 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#17 := (:var 0 Int)
-#16 := (:var 1 Int)
-#37 := (f3 #16 #17)
-#751 := (pattern #37)
-#19 := 0::Int
-#89 := -1::Int
-#93 := (* -1::Int #17)
-#90 := (* -1::Int #16)
-#148 := (mod #90 #93)
-#263 := (+ #37 #148)
-#264 := (= #263 0::Int)
-#38 := (mod #16 #17)
-#260 := (* -1::Int #38)
-#261 := (+ #37 #260)
-#262 := (= #261 0::Int)
-#122 := (>= #16 0::Int)
-#115 := (<= #17 0::Int)
-#207 := (or #115 #122)
-#208 := (not #207)
-#111 := (<= #16 0::Int)
-#205 := (or #111 #115)
-#206 := (not #205)
-#211 := (or #206 #208)
-#265 := (ite #211 #262 #264)
-#259 := (= #37 0::Int)
-#20 := (= #16 0::Int)
-#266 := (ite #20 #259 #265)
-#258 := (= #16 #37)
-#21 := (= #17 0::Int)
-#267 := (ite #21 #258 #266)
-#752 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #751) #267)
-#270 := (forall (vars (?v0 Int) (?v1 Int)) #267)
-#755 := (iff #270 #752)
-#753 := (iff #267 #267)
-#754 := [refl]: #753
-#756 := [quant-intro #754]: #755
-#154 := (* -1::Int #148)
-#227 := (ite #211 #38 #154)
-#230 := (ite #20 0::Int #227)
-#233 := (ite #21 #16 #230)
-#236 := (= #37 #233)
-#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
-#271 := (iff #239 #270)
-#268 := (iff #236 #267)
-#269 := [rewrite]: #268
-#272 := [quant-intro #269]: #271
-#123 := (not #122)
-#116 := (not #115)
-#126 := (and #116 #123)
-#112 := (not #111)
-#119 := (and #112 #116)
-#129 := (or #119 #126)
-#174 := (ite #129 #38 #154)
-#177 := (ite #20 0::Int #174)
-#180 := (ite #21 #16 #177)
-#183 := (= #37 #180)
-#186 := (forall (vars (?v0 Int) (?v1 Int)) #183)
-#240 := (iff #186 #239)
-#237 := (iff #183 #236)
-#234 := (= #180 #233)
-#231 := (= #177 #230)
-#228 := (= #174 #227)
-#212 := (iff #129 #211)
-#209 := (iff #126 #208)
-#210 := [rewrite]: #209
-#199 := (iff #119 #206)
-#200 := [rewrite]: #199
-#213 := [monotonicity #200 #210]: #212
-#229 := [monotonicity #213]: #228
-#232 := [monotonicity #229]: #231
-#235 := [monotonicity #232]: #234
-#238 := [monotonicity #235]: #237
-#241 := [quant-intro #238]: #240
-#197 := (~ #186 #186)
-#196 := (~ #183 #183)
-#193 := [refl]: #196
-#198 := [nnf-pos #193]: #197
-#31 := (- #17)
-#30 := (- #16)
-#39 := (mod #30 #31)
-#40 := (- #39)
-#24 := (< 0::Int #17)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#41 := (ite #28 #38 #40)
-#42 := (ite #20 0::Int #41)
-#43 := (ite #21 #16 #42)
-#44 := (= #37 #43)
-#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
-#189 := (iff #45 #186)
-#82 := (and #24 #26)
-#86 := (or #25 #82)
-#159 := (ite #86 #38 #154)
-#162 := (ite #20 0::Int #159)
-#165 := (ite #21 #16 #162)
-#168 := (= #37 #165)
-#171 := (forall (vars (?v0 Int) (?v1 Int)) #168)
-#187 := (iff #171 #186)
-#184 := (iff #168 #183)
-#181 := (= #165 #180)
-#178 := (= #162 #177)
-#175 := (= #159 #174)
-#130 := (iff #86 #129)
-#127 := (iff #82 #126)
-#124 := (iff #26 #123)
-#125 := [rewrite]: #124
-#117 := (iff #24 #116)
-#118 := [rewrite]: #117
-#128 := [monotonicity #118 #125]: #127
-#120 := (iff #25 #119)
-#113 := (iff #23 #112)
-#114 := [rewrite]: #113
-#121 := [monotonicity #114 #118]: #120
-#131 := [monotonicity #121 #128]: #130
-#176 := [monotonicity #131]: #175
-#179 := [monotonicity #176]: #178
-#182 := [monotonicity #179]: #181
-#185 := [monotonicity #182]: #184
-#188 := [quant-intro #185]: #187
-#172 := (iff #45 #171)
-#169 := (iff #44 #168)
-#166 := (= #43 #165)
-#163 := (= #42 #162)
-#160 := (= #41 #159)
-#157 := (= #40 #154)
-#151 := (- #148)
-#155 := (= #151 #154)
-#156 := [rewrite]: #155
-#152 := (= #40 #151)
-#149 := (= #39 #148)
-#94 := (= #31 #93)
-#95 := [rewrite]: #94
-#91 := (= #30 #90)
-#92 := [rewrite]: #91
-#150 := [monotonicity #92 #95]: #149
-#153 := [monotonicity #150]: #152
-#158 := [trans #153 #156]: #157
-#87 := (iff #28 #86)
-#84 := (iff #27 #82)
-#85 := [rewrite]: #84
-#88 := [monotonicity #85]: #87
-#161 := [monotonicity #88 #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [monotonicity #164]: #166
-#170 := [monotonicity #167]: #169
-#173 := [quant-intro #170]: #172
-#190 := [trans #173 #188]: #189
-#147 := [asserted]: #45
-#191 := [mp #147 #190]: #186
-#194 := [mp~ #191 #198]: #186
-#242 := [mp #194 #241]: #239
-#273 := [mp #242 #272]: #270
-#757 := [mp #273 #756]: #752
-#72 := -2::Int
-#66 := -3::Int
-#8 := 1::Int
-#69 := (f3 1::Int -3::Int)
-#75 := (= #69 -2::Int)
-#78 := (not #75)
-#12 := 2::Int
-#13 := (- 2::Int)
-#9 := 3::Int
-#10 := (- 3::Int)
-#11 := (f3 1::Int #10)
-#14 := (= #11 #13)
-#15 := (not #14)
-#79 := (iff #15 #78)
-#76 := (iff #14 #75)
-#73 := (= #13 -2::Int)
-#74 := [rewrite]: #73
-#70 := (= #11 #69)
-#67 := (= #10 -3::Int)
+#73 := (= #23 #72)
+#70 := (= #22 #69)
+#67 := (= #21 -3::Int)
 #68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#77 := [monotonicity #71 #74]: #76
-#80 := [monotonicity #77]: #79
-#65 := [asserted]: #15
-#83 := [mp #65 #80]: #78
-#659 := (not #752)
-#669 := (or #659 #75)
-#331 := (* -1::Int -3::Int)
-#415 := (* -1::Int 1::Int)
-#416 := (mod #415 #331)
-#417 := (+ #69 #416)
-#408 := (= #417 0::Int)
-#419 := (mod 1::Int -3::Int)
-#420 := (* -1::Int #419)
-#421 := (+ #69 #420)
-#418 := (= #421 0::Int)
-#422 := (>= 1::Int 0::Int)
-#401 := (<= -3::Int 0::Int)
-#736 := (or #401 #422)
-#738 := (not #736)
-#395 := (<= 1::Int 0::Int)
-#525 := (or #395 #401)
-#732 := (not #525)
-#406 := (or #732 #738)
-#407 := (ite #406 #418 #408)
-#739 := (= #69 0::Int)
-#740 := (= 1::Int 0::Int)
-#741 := (ite #740 #739 #407)
-#742 := (= 1::Int #69)
-#737 := (= -3::Int 0::Int)
-#743 := (ite #737 #742 #741)
-#670 := (or #659 #743)
-#667 := (iff #670 #669)
-#661 := (iff #669 #669)
-#662 := [rewrite]: #661
-#660 := (iff #743 #75)
-#734 := (= #69 1::Int)
-#677 := (ite false #734 #75)
-#579 := (iff #677 #75)
-#580 := [rewrite]: #579
-#666 := (iff #743 #677)
-#675 := (iff #741 #75)
-#582 := (ite false #739 #75)
-#585 := (iff #582 #75)
-#678 := [rewrite]: #585
-#583 := (iff #741 #582)
-#573 := (iff #407 #75)
-#562 := (iff #407 #677)
-#673 := (iff #408 #75)
-#683 := (+ 2::Int #69)
-#568 := (= #683 0::Int)
-#676 := (iff #568 #75)
-#578 := [rewrite]: #676
-#569 := (iff #408 #568)
-#685 := (= #417 #683)
-#527 := (+ #69 2::Int)
-#684 := (= #527 #683)
-#682 := [rewrite]: #684
-#680 := (= #417 #527)
-#524 := (= #416 2::Int)
-#687 := (mod -1::Int 3::Int)
-#688 := (= #687 2::Int)
-#695 := [rewrite]: #688
-#693 := (= #416 #687)
-#692 := (= #331 3::Int)
-#686 := [rewrite]: #692
-#705 := (= #415 -1::Int)
-#709 := [rewrite]: #705
-#694 := [monotonicity #709 #686]: #693
-#526 := [trans #694 #695]: #524
-#681 := [monotonicity #526]: #680
-#567 := [trans #681 #682]: #685
-#528 := [monotonicity #567]: #569
-#674 := [trans #528 #578]: #673
-#690 := (iff #418 #734)
-#696 := (+ -1::Int #69)
-#704 := (= #696 0::Int)
-#547 := (iff #704 #734)
-#689 := [rewrite]: #547
-#545 := (iff #418 #704)
-#703 := (= #421 #696)
-#699 := (+ #69 -1::Int)
-#697 := (= #699 #696)
-#702 := [rewrite]: #697
-#700 := (= #421 #699)
-#706 := (= #420 -1::Int)
-#708 := (= #420 #415)
-#429 := (= #419 1::Int)
-#707 := [rewrite]: #429
-#423 := [monotonicity #707]: #708
-#710 := [trans #423 #709]: #706
-#701 := [monotonicity #710]: #700
-#698 := [trans #701 #702]: #703
-#546 := [monotonicity #698]: #545
-#691 := [trans #546 #689]: #690
-#427 := (iff #406 false)
-#711 := (or false false)
-#716 := (iff #711 false)
-#426 := [rewrite]: #716
-#715 := (iff #406 #711)
-#436 := (iff #738 false)
-#1 := true
-#726 := (not true)
-#729 := (iff #726 false)
-#369 := [rewrite]: #729
-#713 := (iff #738 #726)
-#443 := (iff #736 true)
-#717 := (or true true)
-#441 := (iff #717 true)
-#442 := [rewrite]: #441
-#718 := (iff #736 #717)
-#728 := (iff #422 true)
-#731 := [rewrite]: #728
-#383 := (iff #401 true)
-#384 := [rewrite]: #383
-#440 := [monotonicity #384 #731]: #718
-#337 := [trans #440 #442]: #443
-#714 := [monotonicity #337]: #713
-#437 := [trans #714 #369]: #436
-#370 := (iff #732 false)
-#364 := (iff #732 #726)
-#725 := (iff #525 true)
-#385 := (or false true)
-#723 := (iff #385 true)
-#724 := [rewrite]: #723
-#721 := (iff #525 #385)
-#719 := (iff #395 false)
-#382 := [rewrite]: #719
-#722 := [monotonicity #382 #384]: #721
-#720 := [trans #722 #724]: #725
-#727 := [monotonicity #720]: #364
-#730 := [trans #727 #369]: #370
-#712 := [monotonicity #730 #437]: #715
-#428 := [trans #712 #426]: #427
-#577 := [monotonicity #428 #691 #674]: #562
-#581 := [trans #577 #580]: #573
-#735 := (iff #740 false)
-#378 := [rewrite]: #735
-#584 := [monotonicity #378 #581]: #583
-#679 := [trans #584 #678]: #675
-#398 := (iff #742 #734)
-#394 := [rewrite]: #398
-#733 := (iff #737 false)
-#393 := [rewrite]: #733
-#668 := [monotonicity #393 #394 #679]: #666
-#657 := [trans #668 #580]: #660
-#672 := [monotonicity #657]: #667
-#663 := [trans #672 #662]: #667
-#671 := [quant-inst #8 #66]: #670
-#664 := [mp #671 #663]: #669
-[unit-resolution #664 #83 #757]: false
-unsat
-e4d7746f48f3d604f4d6994a010e44b10b471dbd 333 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#15 := (:var 0 Int)
-#14 := (:var 1 Int)
-#34 := (f3 #14 #15)
-#773 := (pattern #34)
-#11 := 0::Int
-#104 := -1::Int
-#108 := (* -1::Int #15)
-#105 := (* -1::Int #14)
-#169 := (mod #105 #108)
-#284 := (+ #34 #169)
-#285 := (= #284 0::Int)
-#35 := (mod #14 #15)
-#281 := (* -1::Int #35)
-#282 := (+ #34 #281)
-#283 := (= #282 0::Int)
-#143 := (>= #14 0::Int)
-#136 := (<= #15 0::Int)
-#228 := (or #136 #143)
-#229 := (not #228)
-#132 := (<= #14 0::Int)
-#226 := (or #132 #136)
-#227 := (not #226)
-#232 := (or #227 #229)
-#286 := (ite #232 #283 #285)
-#280 := (= #34 0::Int)
-#17 := (= #14 0::Int)
-#287 := (ite #17 #280 #286)
-#279 := (= #14 #34)
-#18 := (= #15 0::Int)
-#288 := (ite #18 #279 #287)
-#774 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #773) #288)
-#291 := (forall (vars (?v0 Int) (?v1 Int)) #288)
-#777 := (iff #291 #774)
-#775 := (iff #288 #288)
-#776 := [refl]: #775
-#778 := [quant-intro #776]: #777
-#175 := (* -1::Int #169)
-#248 := (ite #232 #35 #175)
-#251 := (ite #17 0::Int #248)
-#254 := (ite #18 #14 #251)
-#257 := (= #34 #254)
-#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
-#292 := (iff #260 #291)
-#289 := (iff #257 #288)
-#290 := [rewrite]: #289
-#293 := [quant-intro #290]: #292
-#144 := (not #143)
-#137 := (not #136)
-#147 := (and #137 #144)
-#133 := (not #132)
-#140 := (and #133 #137)
-#150 := (or #140 #147)
-#195 := (ite #150 #35 #175)
-#198 := (ite #17 0::Int #195)
-#201 := (ite #18 #14 #198)
-#204 := (= #34 #201)
-#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
-#261 := (iff #207 #260)
-#258 := (iff #204 #257)
-#255 := (= #201 #254)
-#252 := (= #198 #251)
-#249 := (= #195 #248)
-#233 := (iff #150 #232)
-#230 := (iff #147 #229)
-#231 := [rewrite]: #230
-#220 := (iff #140 #227)
-#221 := [rewrite]: #220
-#234 := [monotonicity #221 #231]: #233
-#250 := [monotonicity #234]: #249
-#253 := [monotonicity #250]: #252
-#256 := [monotonicity #253]: #255
-#259 := [monotonicity #256]: #258
-#262 := [quant-intro #259]: #261
-#218 := (~ #207 #207)
-#217 := (~ #204 #204)
-#214 := [refl]: #217
-#219 := [nnf-pos #214]: #218
-#28 := (- #15)
-#27 := (- #14)
-#36 := (mod #27 #28)
-#37 := (- #36)
-#21 := (< 0::Int #15)
-#23 := (< #14 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #14)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#38 := (ite #25 #35 #37)
-#39 := (ite #17 0::Int #38)
-#40 := (ite #18 #14 #39)
-#41 := (= #34 #40)
-#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
-#210 := (iff #42 #207)
-#98 := (and #21 #23)
-#101 := (or #22 #98)
-#180 := (ite #101 #35 #175)
-#89 := (= 0::Int #14)
-#183 := (ite #89 0::Int #180)
-#92 := (= 0::Int #15)
-#186 := (ite #92 #14 #183)
-#189 := (= #34 #186)
-#192 := (forall (vars (?v0 Int) (?v1 Int)) #189)
-#208 := (iff #192 #207)
-#205 := (iff #189 #204)
-#202 := (= #186 #201)
-#199 := (= #183 #198)
-#196 := (= #180 #195)
-#151 := (iff #101 #150)
-#148 := (iff #98 #147)
-#145 := (iff #23 #144)
-#146 := [rewrite]: #145
-#138 := (iff #21 #137)
-#139 := [rewrite]: #138
-#149 := [monotonicity #139 #146]: #148
-#141 := (iff #22 #140)
-#134 := (iff #20 #133)
-#135 := [rewrite]: #134
-#142 := [monotonicity #135 #139]: #141
-#152 := [monotonicity #142 #149]: #151
-#197 := [monotonicity #152]: #196
-#126 := (iff #89 #17)
-#127 := [rewrite]: #126
-#200 := [monotonicity #127 #197]: #199
-#128 := (iff #92 #18)
-#129 := [rewrite]: #128
-#203 := [monotonicity #129 #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [quant-intro #206]: #208
-#193 := (iff #42 #192)
-#190 := (iff #41 #189)
-#187 := (= #40 #186)
-#184 := (= #39 #183)
-#181 := (= #38 #180)
-#178 := (= #37 #175)
-#172 := (- #169)
-#176 := (= #172 #175)
-#177 := [rewrite]: #176
-#173 := (= #37 #172)
-#170 := (= #36 #169)
-#109 := (= #28 #108)
-#110 := [rewrite]: #109
-#106 := (= #27 #105)
-#107 := [rewrite]: #106
-#171 := [monotonicity #107 #110]: #170
-#174 := [monotonicity #171]: #173
-#179 := [trans #174 #177]: #178
-#102 := (iff #25 #101)
-#99 := (iff #24 #98)
-#100 := [rewrite]: #99
+#64 := (= #20 #63)
+#65 := [rewrite]: #64
+#71 := [monotonicity #65 #68]: #70
+#74 := [monotonicity #71]: #73
+#79 := [trans #74 #77]: #78
+#60 := (iff #18 #59)
+#57 := (iff #17 #56)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#82 := [monotonicity #61 #79]: #81
+#54 := (iff #12 #53)
+#55 := [rewrite]: #54
+#85 := [monotonicity #55 #82]: #84
+#51 := (iff #10 false)
+#52 := [rewrite]: #51
+#88 := [monotonicity #52 #85]: #87
+#92 := [trans #88 #90]: #91
+#95 := [monotonicity #92]: #94
+#100 := [trans #95 #98]: #99
 #103 := [monotonicity #100]: #102
-#182 := [monotonicity #103 #179]: #181
-#90 := (iff #17 #89)
-#91 := [rewrite]: #90
-#185 := [monotonicity #91 #182]: #184
-#93 := (iff #18 #92)
-#94 := [rewrite]: #93
-#188 := [monotonicity #94 #185]: #187
-#191 := [monotonicity #188]: #190
-#194 := [quant-intro #191]: #193
-#211 := [trans #194 #209]: #210
-#168 := [asserted]: #42
-#212 := [mp #168 #211]: #207
-#215 := [mp~ #212 #219]: #207
-#263 := [mp #215 #262]: #260
-#294 := [mp #263 #293]: #291
-#779 := [mp #294 #778]: #774
-#63 := -3::Int
-#8 := 3::Int
-#66 := (f3 3::Int -3::Int)
-#69 := (= #66 0::Int)
-#82 := (not #69)
-#9 := (- 3::Int)
-#10 := (f3 3::Int #9)
-#12 := (= #10 0::Int)
-#13 := (not #12)
-#85 := (iff #13 #82)
-#72 := (= 0::Int #66)
-#77 := (not #72)
-#83 := (iff #77 #82)
-#80 := (iff #72 #69)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#78 := (iff #13 #77)
-#75 := (iff #12 #72)
-#73 := (iff #69 #72)
-#74 := [rewrite]: #73
-#70 := (iff #12 #69)
-#67 := (= #10 #66)
-#64 := (= #9 -3::Int)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#71 := [monotonicity #68]: #70
-#76 := [trans #71 #74]: #75
-#79 := [monotonicity #76]: #78
-#86 := [trans #79 #84]: #85
-#62 := [asserted]: #13
-#87 := [mp #62 #86]: #82
-#602 := (not #774)
-#595 := (or #602 #69)
-#352 := (* -1::Int -3::Int)
-#437 := (* -1::Int 3::Int)
-#438 := (mod #437 #352)
-#439 := (+ #66 #438)
-#430 := (= #439 0::Int)
-#441 := (mod 3::Int -3::Int)
-#442 := (* -1::Int #441)
-#370 := (+ #66 #442)
-#443 := (= #370 0::Int)
-#440 := (>= 3::Int 0::Int)
-#444 := (<= -3::Int 0::Int)
-#423 := (or #444 #440)
-#758 := (not #423)
-#760 := (<= 3::Int 0::Int)
-#417 := (or #760 #444)
-#547 := (not #417)
-#754 := (or #547 #758)
-#428 := (ite #754 #443 #430)
-#429 := (= 3::Int 0::Int)
-#761 := (ite #429 #69 #428)
-#762 := (= 3::Int #66)
-#763 := (= -3::Int 0::Int)
-#764 := (ite #763 #762 #761)
-#603 := (or #602 #764)
-#605 := (iff #603 #595)
-#607 := (iff #595 #595)
-#700 := [rewrite]: #607
-#599 := (iff #764 #69)
-#415 := (= #66 3::Int)
-#600 := (ite false #415 #69)
-#699 := (iff #600 #69)
-#584 := [rewrite]: #699
-#695 := (iff #764 #600)
-#550 := (iff #761 #69)
-#702 := (ite false #69 #69)
-#706 := (iff #702 #69)
-#704 := [rewrite]: #706
-#590 := (iff #761 #702)
-#707 := (iff #428 #69)
-#703 := (iff #428 #702)
-#548 := (iff #430 #69)
-#717 := (= #439 #66)
-#732 := (+ #66 0::Int)
-#723 := (= #732 #66)
-#718 := [rewrite]: #723
-#716 := (= #439 #732)
-#709 := (= #438 0::Int)
-#711 := (mod -3::Int 3::Int)
-#714 := (= #711 0::Int)
-#708 := [rewrite]: #714
-#712 := (= #438 #711)
-#568 := (= #352 3::Int)
-#569 := [rewrite]: #568
-#726 := (= #437 -3::Int)
-#567 := [rewrite]: #726
-#713 := [monotonicity #567 #569]: #712
-#715 := [trans #713 #708]: #709
-#710 := [monotonicity #715]: #716
-#546 := [trans #710 #718]: #717
-#549 := [monotonicity #546]: #548
-#725 := (iff #443 #69)
-#719 := (= #370 #66)
-#721 := (= #370 #732)
-#731 := (= #442 0::Int)
-#451 := (* -1::Int 0::Int)
-#445 := (= #451 0::Int)
-#727 := [rewrite]: #445
-#729 := (= #442 #451)
-#449 := (= #441 0::Int)
-#450 := [rewrite]: #449
-#730 := [monotonicity #450]: #729
-#728 := [trans #730 #727]: #731
-#722 := [monotonicity #728]: #721
-#724 := [trans #722 #718]: #719
-#720 := [monotonicity #724]: #725
-#738 := (iff #754 false)
-#458 := (or false false)
-#737 := (iff #458 false)
-#734 := [rewrite]: #737
-#459 := (iff #754 #458)
-#735 := (iff #758 false)
-#1 := true
-#747 := (not true)
-#386 := (iff #747 false)
-#749 := [rewrite]: #386
-#465 := (iff #758 #747)
-#463 := (iff #423 true)
-#750 := (or true true)
-#740 := (iff #750 true)
-#462 := [rewrite]: #740
-#753 := (iff #423 #750)
-#392 := (iff #440 true)
-#752 := [rewrite]: #392
-#741 := (iff #444 true)
-#404 := [rewrite]: #741
-#739 := [monotonicity #404 #752]: #753
-#464 := [trans #739 #462]: #463
-#358 := [monotonicity #464]: #465
-#736 := [trans #358 #749]: #735
-#751 := (iff #547 false)
-#742 := (iff #547 #747)
-#745 := (iff #417 true)
-#405 := (or false true)
-#743 := (iff #405 true)
-#744 := [rewrite]: #743
-#406 := (iff #417 #405)
-#757 := (iff #760 false)
-#400 := [rewrite]: #757
-#407 := [monotonicity #400 #404]: #406
-#746 := [trans #407 #744]: #745
-#748 := [monotonicity #746]: #742
-#391 := [trans #748 #749]: #751
-#733 := [monotonicity #391 #736]: #459
-#448 := [trans #733 #734]: #738
-#705 := [monotonicity #448 #720 #549]: #703
-#589 := [trans #705 #704]: #707
-#756 := (iff #429 false)
-#416 := [rewrite]: #756
-#591 := [monotonicity #416 #589]: #590
-#698 := [trans #591 #704]: #550
-#755 := (iff #762 #415)
-#420 := [rewrite]: #755
-#759 := (iff #763 false)
-#765 := [rewrite]: #759
-#696 := [monotonicity #765 #420 #698]: #695
-#601 := [trans #696 #584]: #599
-#606 := [monotonicity #601]: #605
-#697 := [trans #606 #700]: #605
-#604 := [quant-inst #8 #63]: #603
-#701 := [mp #604 #697]: #595
-[unit-resolution #701 #87 #779]: false
-unsat
-62dc22cc0a1f11a224be0520d214fcdfef9b8378 339 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#17 := (:var 0 Int)
-#16 := (:var 1 Int)
-#37 := (f3 #16 #17)
-#750 := (pattern #37)
-#19 := 0::Int
-#72 := -1::Int
-#92 := (* -1::Int #17)
-#89 := (* -1::Int #16)
-#147 := (mod #89 #92)
-#262 := (+ #37 #147)
-#263 := (= #262 0::Int)
-#38 := (mod #16 #17)
-#259 := (* -1::Int #38)
-#260 := (+ #37 #259)
-#261 := (= #260 0::Int)
-#121 := (>= #16 0::Int)
-#114 := (<= #17 0::Int)
-#206 := (or #114 #121)
-#207 := (not #206)
-#110 := (<= #16 0::Int)
-#204 := (or #110 #114)
-#205 := (not #204)
-#210 := (or #205 #207)
-#264 := (ite #210 #261 #263)
-#258 := (= #37 0::Int)
-#20 := (= #16 0::Int)
-#265 := (ite #20 #258 #264)
-#257 := (= #16 #37)
-#21 := (= #17 0::Int)
-#266 := (ite #21 #257 #265)
-#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #266)
-#269 := (forall (vars (?v0 Int) (?v1 Int)) #266)
-#754 := (iff #269 #751)
-#752 := (iff #266 #266)
-#753 := [refl]: #752
-#755 := [quant-intro #753]: #754
-#153 := (* -1::Int #147)
-#226 := (ite #210 #38 #153)
-#229 := (ite #20 0::Int #226)
-#232 := (ite #21 #16 #229)
-#235 := (= #37 #232)
-#238 := (forall (vars (?v0 Int) (?v1 Int)) #235)
-#270 := (iff #238 #269)
-#267 := (iff #235 #266)
-#268 := [rewrite]: #267
-#271 := [quant-intro #268]: #270
-#122 := (not #121)
-#115 := (not #114)
-#125 := (and #115 #122)
-#111 := (not #110)
-#118 := (and #111 #115)
-#128 := (or #118 #125)
-#173 := (ite #128 #38 #153)
-#176 := (ite #20 0::Int #173)
-#179 := (ite #21 #16 #176)
-#182 := (= #37 #179)
-#185 := (forall (vars (?v0 Int) (?v1 Int)) #182)
-#239 := (iff #185 #238)
-#236 := (iff #182 #235)
-#233 := (= #179 #232)
-#230 := (= #176 #229)
-#227 := (= #173 #226)
-#211 := (iff #128 #210)
-#208 := (iff #125 #207)
-#209 := [rewrite]: #208
-#198 := (iff #118 #205)
-#199 := [rewrite]: #198
-#212 := [monotonicity #199 #209]: #211
-#228 := [monotonicity #212]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [monotonicity #234]: #236
-#240 := [quant-intro #237]: #239
-#196 := (~ #185 #185)
-#195 := (~ #182 #182)
-#192 := [refl]: #195
-#197 := [nnf-pos #192]: #196
-#31 := (- #17)
-#30 := (- #16)
-#39 := (mod #30 #31)
-#40 := (- #39)
-#24 := (< 0::Int #17)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#41 := (ite #28 #38 #40)
-#42 := (ite #20 0::Int #41)
-#43 := (ite #21 #16 #42)
-#44 := (= #37 #43)
-#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
-#188 := (iff #45 #185)
-#82 := (and #24 #26)
-#86 := (or #25 #82)
-#158 := (ite #86 #38 #153)
-#161 := (ite #20 0::Int #158)
-#164 := (ite #21 #16 #161)
-#167 := (= #37 #164)
-#170 := (forall (vars (?v0 Int) (?v1 Int)) #167)
-#186 := (iff #170 #185)
-#183 := (iff #167 #182)
-#180 := (= #164 #179)
-#177 := (= #161 #176)
-#174 := (= #158 #173)
-#129 := (iff #86 #128)
-#126 := (iff #82 #125)
-#123 := (iff #26 #122)
-#124 := [rewrite]: #123
-#116 := (iff #24 #115)
-#117 := [rewrite]: #116
-#127 := [monotonicity #117 #124]: #126
-#119 := (iff #25 #118)
-#112 := (iff #23 #111)
-#113 := [rewrite]: #112
-#120 := [monotonicity #113 #117]: #119
-#130 := [monotonicity #120 #127]: #129
-#175 := [monotonicity #130]: #174
-#178 := [monotonicity #175]: #177
-#181 := [monotonicity #178]: #180
-#184 := [monotonicity #181]: #183
-#187 := [quant-intro #184]: #186
-#171 := (iff #45 #170)
-#168 := (iff #44 #167)
-#165 := (= #43 #164)
-#162 := (= #42 #161)
-#159 := (= #41 #158)
-#156 := (= #40 #153)
-#150 := (- #147)
-#154 := (= #150 #153)
+#109 := [trans #103 #107]: #108
+#112 := [monotonicity #109]: #111
+#165 := [trans #112 #163]: #164
+#50 := [asserted]: #30
+#166 := [mp #50 #165]: #161
+#167 := [not-or-elim #166]: #113
+#251 := (or #120 #114)
+#252 := [th-lemma arith farkas 1 1]: #251
+#253 := [unit-resolution #252 #167]: #120
+#174 := (or #143 #119)
+#175 := [def-axiom]: #174
+#258 := [unit-resolution #175 #253]: #143
+#170 := (not #143)
+#181 := (or #170 #178)
+#182 := [def-axiom]: #181
+#259 := [unit-resolution #182 #258]: #178
+#263 := [symm #259]: #262
+#264 := (= f3 #146)
+#260 := (= #149 #146)
+#177 := (= #146 #149)
+#185 := (not #12)
+#254 := (or #185 #119)
+#255 := [th-lemma arith triangle-eq]: #254
+#256 := [unit-resolution #255 #253]: #185
+#188 := (or #12 #177)
+#189 := [def-axiom]: #188
+#257 := [unit-resolution #189 #256]: #177
+#261 := [symm #257]: #260
+#168 := [not-or-elim #166]: #152
+#265 := [trans #168 #261]: #264
+#266 := [trans #265 #263]: #244
+#267 := (not #244)
+#268 := (or #267 #246)
+#269 := [th-lemma arith triangle-eq]: #268
+#270 := [unit-resolution #269 #266]: #246
+[th-lemma arith farkas -1 1 1 #167 #270 #250]: false
+unsat
+b0d0143b1d623c3b7e34600e7103453eafcbef9f 326 0
+#2 := false
+#9 := 0::Int
+#71 := -1::Int
+decl f3 :: Int
+#8 := f3
+#72 := (* -1::Int f3)
+#95 := (mod #72 -1::Int)
+#101 := (* -1::Int #95)
+#147 := (>= f3 0::Int)
+#148 := (not #147)
+#134 := (<= f3 0::Int)
+#135 := (not #134)
+#10 := (= f3 0::Int)
+#170 := (or #10 #135 #148)
+#175 := (ite #170 0::Int #101)
+#288 := (<= #175 0::Int)
+#220 := (= #175 0::Int)
+#215 := (not #10)
+#228 := (not #170)
+#375 := [hypothesis]: #228
+#222 := (or #170 #215)
+#223 := [def-axiom]: #222
+#376 := [unit-resolution #223 #375]: #215
+#226 := (or #170 #147)
+#227 := [def-axiom]: #226
+#377 := [unit-resolution #227 #375]: #147
+#378 := (or #10 #148)
+#185 := (* -1::Int #175)
+#77 := (div #72 -1::Int)
+#11 := 1::Int
+#20 := (div f3 1::Int)
+#158 := (or #135 #148)
+#161 := (ite #158 #20 #77)
+#164 := (ite #10 0::Int #161)
+#184 := (* -1::Int #164)
+#186 := (+ #184 #185)
+#187 := (+ f3 #186)
+#236 := (>= #187 0::Int)
+#291 := (+ #20 #184)
+#293 := (>= #291 0::Int)
+#290 := (= #20 #164)
+#205 := (= #161 #164)
+#294 := [hypothesis]: #135
+#295 := (or #215 #134)
+#296 := [th-lemma arith triangle-eq]: #295
+#297 := [unit-resolution #296 #294]: #215
+#218 := (or #10 #205)
+#219 := [def-axiom]: #218
+#298 := [unit-resolution #219 #297]: #205
+#206 := (= #20 #161)
+#202 := (or #158 #134)
+#203 := [def-axiom]: #202
+#299 := [unit-resolution #203 #294]: #158
+#208 := (not #158)
+#211 := (or #208 #206)
+#212 := [def-axiom]: #211
+#300 := [unit-resolution #212 #299]: #206
+#301 := [trans #300 #298]: #290
+#302 := (not #290)
+#303 := (or #302 #293)
+#304 := [th-lemma arith triangle-eq]: #303
+#305 := [unit-resolution #304 #301]: #293
+#224 := (or #170 #134)
+#225 := [def-axiom]: #224
+#306 := [unit-resolution #225 #294]: #170
+#231 := (or #228 #220)
+#232 := [def-axiom]: #231
+#307 := [unit-resolution #232 #306]: #220
+#308 := (not #220)
+#309 := (or #308 #288)
+#310 := [th-lemma arith triangle-eq]: #309
+#311 := [unit-resolution #310 #307]: #288
+#258 := (* -1::Int #20)
+#259 := (+ f3 #258)
+#265 := (>= #259 0::Int)
+#257 := (= #259 0::Int)
+#1 := true
+#53 := [true-axiom]: true
+#312 := (or false #257)
+#313 := [th-lemma arith]: #312
+#314 := [unit-resolution #313 #53]: #257
+#315 := (not #257)
+#316 := (or #315 #265)
+#317 := [th-lemma arith triangle-eq]: #316
+#318 := [unit-resolution #317 #314]: #265
+#321 := (not #265)
+#320 := (not #293)
+#319 := (not #288)
+#322 := (or #236 #319 #320 #321)
+#323 := [th-lemma arith assign-bounds 1 -1 -1]: #322
+#324 := [unit-resolution #323 #318 #311 #305]: #236
+#235 := (<= #187 0::Int)
+#292 := (<= #291 0::Int)
+#325 := (or #302 #292)
+#326 := [th-lemma arith triangle-eq]: #325
+#327 := [unit-resolution #326 #301]: #292
+#289 := (>= #175 0::Int)
+#328 := (or #308 #289)
+#329 := [th-lemma arith triangle-eq]: #328
+#330 := [unit-resolution #329 #307]: #289
+#264 := (<= #259 0::Int)
+#331 := (or #315 #264)
+#332 := [th-lemma arith triangle-eq]: #331
+#333 := [unit-resolution #332 #314]: #264
+#336 := (not #264)
+#335 := (not #292)
+#334 := (not #289)
+#337 := (or #235 #334 #335 #336)
+#338 := [th-lemma arith assign-bounds 1 -1 -1]: #337
+#339 := [unit-resolution #338 #333 #330 #327]: #235
+#341 := (not #236)
+#340 := (not #235)
+#344 := (or #340 #341)
+#188 := (= #187 0::Int)
+#193 := (not #188)
+#22 := (- 1::Int)
+#21 := (- f3)
+#28 := (mod #21 #22)
+#29 := (- #28)
+#27 := (mod f3 1::Int)
+#15 := (< 0::Int 1::Int)
+#17 := (< f3 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int f3)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#30 := (ite #19 #27 #29)
+#31 := (ite #10 0::Int #30)
+#12 := (= 1::Int 0::Int)
+#32 := (ite #12 f3 #31)
+#23 := (div #21 #22)
+#24 := (ite #19 #20 #23)
+#13 := (or #10 #12)
+#25 := (ite #13 0::Int #24)
+#26 := (* #25 1::Int)
+#33 := (+ #26 #32)
+#34 := (= f3 #33)
+#35 := (not #34)
+#196 := (iff #35 #193)
+#65 := (and #15 #17)
+#68 := (or #16 #65)
+#112 := (or #10 #68)
+#113 := (ite #112 0::Int #101)
+#80 := (ite #68 #20 #77)
+#83 := (ite #10 0::Int #80)
+#125 := (+ #83 #113)
+#128 := (= f3 #125)
+#131 := (not #128)
+#194 := (iff #131 #193)
+#191 := (iff #128 #188)
+#178 := (+ #164 #175)
+#181 := (= f3 #178)
+#189 := (iff #181 #188)
+#190 := [rewrite]: #189
+#182 := (iff #128 #181)
+#179 := (= #125 #178)
+#176 := (= #113 #175)
+#173 := (iff #112 #170)
+#167 := (or #10 #158)
+#171 := (iff #167 #170)
+#172 := [rewrite]: #171
+#168 := (iff #112 #167)
+#159 := (iff #68 #158)
+#156 := (iff #65 #148)
+#151 := (and true #148)
+#154 := (iff #151 #148)
 #155 := [rewrite]: #154
-#151 := (= #40 #150)
-#148 := (= #39 #147)
-#93 := (= #31 #92)
-#94 := [rewrite]: #93
-#90 := (= #30 #89)
-#91 := [rewrite]: #90
-#149 := [monotonicity #91 #94]: #148
-#152 := [monotonicity #149]: #151
-#157 := [trans #152 #155]: #156
-#87 := (iff #28 #86)
-#84 := (iff #27 #82)
-#85 := [rewrite]: #84
-#88 := [monotonicity #85]: #87
-#160 := [monotonicity #88 #157]: #159
+#152 := (iff #65 #151)
+#149 := (iff #17 #148)
+#150 := [rewrite]: #149
+#138 := (iff #15 true)
+#139 := [rewrite]: #138
+#153 := [monotonicity #139 #150]: #152
+#157 := [trans #153 #155]: #156
+#145 := (iff #16 #135)
+#140 := (and #135 true)
+#143 := (iff #140 #135)
+#144 := [rewrite]: #143
+#141 := (iff #16 #140)
+#136 := (iff #14 #135)
+#137 := [rewrite]: #136
+#142 := [monotonicity #137 #139]: #141
+#146 := [trans #142 #144]: #145
+#160 := [monotonicity #146 #157]: #159
+#169 := [monotonicity #160]: #168
+#174 := [trans #169 #172]: #173
+#177 := [monotonicity #174]: #176
+#165 := (= #83 #164)
+#162 := (= #80 #161)
 #163 := [monotonicity #160]: #162
 #166 := [monotonicity #163]: #165
-#169 := [monotonicity #166]: #168
-#172 := [quant-intro #169]: #171
-#189 := [trans #172 #187]: #188
-#146 := [asserted]: #45
-#190 := [mp #146 #189]: #185
-#193 := [mp~ #190 #197]: #185
-#241 := [mp #193 #240]: #238
-#272 := [mp #241 #271]: #269
-#756 := [mp #272 #755]: #751
-#66 := -3::Int
-#8 := 5::Int
-#69 := (f3 5::Int -3::Int)
-#75 := (= #69 -1::Int)
-#78 := (not #75)
-#12 := 1::Int
-#13 := (- 1::Int)
-#9 := 3::Int
-#10 := (- 3::Int)
-#11 := (f3 5::Int #10)
-#14 := (= #11 #13)
-#15 := (not #14)
-#79 := (iff #15 #78)
-#76 := (iff #14 #75)
-#73 := (= #13 -1::Int)
-#74 := [rewrite]: #73
-#70 := (= #11 #69)
-#67 := (= #10 -3::Int)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#77 := [monotonicity #71 #74]: #76
-#80 := [monotonicity #77]: #79
-#65 := [asserted]: #15
-#83 := [mp #65 #80]: #78
-#657 := (not #751)
-#664 := (or #657 #75)
-#330 := (* -1::Int -3::Int)
-#414 := (* -1::Int 5::Int)
-#415 := (mod #414 #330)
-#416 := (+ #69 #415)
-#407 := (= #416 0::Int)
-#418 := (mod 5::Int -3::Int)
-#419 := (* -1::Int #418)
-#420 := (+ #69 #419)
-#417 := (= #420 0::Int)
-#421 := (>= 5::Int 0::Int)
-#400 := (<= -3::Int 0::Int)
-#735 := (or #400 #421)
-#737 := (not #735)
-#394 := (<= 5::Int 0::Int)
-#524 := (or #394 #400)
-#731 := (not #524)
-#405 := (or #731 #737)
-#406 := (ite #405 #417 #407)
-#738 := (= #69 0::Int)
-#739 := (= 5::Int 0::Int)
-#740 := (ite #739 #738 #406)
-#741 := (= 5::Int #69)
-#736 := (= -3::Int 0::Int)
-#742 := (ite #736 #741 #740)
-#648 := (or #657 #742)
-#651 := (iff #648 #664)
-#653 := (iff #664 #664)
-#654 := [rewrite]: #653
-#662 := (iff #742 #75)
-#733 := (= #69 5::Int)
-#670 := (ite false #733 #75)
-#660 := (iff #670 #75)
-#661 := [rewrite]: #660
-#666 := (iff #742 #670)
-#668 := (iff #740 #75)
-#665 := (ite false #738 #75)
-#656 := (iff #665 #75)
-#658 := [rewrite]: #656
-#667 := (iff #740 #665)
-#674 := (iff #406 #75)
-#428 := 2::Int
-#690 := (= #69 2::Int)
-#581 := (ite false #690 #75)
-#584 := (iff #581 #75)
-#677 := [rewrite]: #584
-#582 := (iff #406 #581)
-#572 := (iff #407 #75)
-#527 := (+ 1::Int #69)
-#676 := (= #527 0::Int)
-#578 := (iff #676 #75)
-#579 := [rewrite]: #578
-#561 := (iff #407 #676)
-#672 := (= #416 #527)
-#566 := (+ #69 1::Int)
-#675 := (= #566 #527)
-#577 := [rewrite]: #675
-#567 := (= #416 #566)
-#681 := (= #415 1::Int)
-#693 := -5::Int
-#526 := (mod -5::Int 3::Int)
-#682 := (= #526 1::Int)
-#683 := [rewrite]: #682
-#679 := (= #415 #526)
-#523 := (= #330 3::Int)
-#525 := [rewrite]: #523
-#687 := (= #414 -5::Int)
-#694 := [rewrite]: #687
-#680 := [monotonicity #694 #525]: #679
-#684 := [trans #680 #683]: #681
-#568 := [monotonicity #684]: #567
-#673 := [trans #568 #577]: #672
-#576 := [monotonicity #673]: #561
-#580 := [trans #576 #579]: #572
-#686 := (iff #417 #690)
-#705 := -2::Int
-#702 := (+ -2::Int #69)
-#546 := (= #702 0::Int)
-#691 := (iff #546 #690)
-#685 := [rewrite]: #691
-#688 := (iff #417 #546)
-#544 := (= #420 #702)
-#695 := (+ #69 -2::Int)
-#697 := (= #695 #702)
-#703 := [rewrite]: #697
-#696 := (= #420 #695)
-#699 := (= #419 -2::Int)
-#422 := (* -1::Int 2::Int)
-#709 := (= #422 -2::Int)
-#698 := [rewrite]: #709
-#704 := (= #419 #422)
-#706 := (= #418 2::Int)
-#707 := [rewrite]: #706
-#708 := [monotonicity #707]: #704
-#700 := [trans #708 #698]: #699
-#701 := [monotonicity #700]: #696
-#545 := [trans #701 #703]: #544
-#689 := [monotonicity #545]: #688
-#692 := [trans #689 #685]: #686
-#426 := (iff #405 false)
-#710 := (or false false)
-#715 := (iff #710 false)
-#425 := [rewrite]: #715
-#714 := (iff #405 #710)
-#435 := (iff #737 false)
-#1 := true
-#725 := (not true)
-#728 := (iff #725 false)
-#368 := [rewrite]: #728
-#712 := (iff #737 #725)
-#442 := (iff #735 true)
-#716 := (or true true)
-#440 := (iff #716 true)
-#441 := [rewrite]: #440
-#717 := (iff #735 #716)
-#727 := (iff #421 true)
-#730 := [rewrite]: #727
-#382 := (iff #400 true)
-#383 := [rewrite]: #382
-#439 := [monotonicity #383 #730]: #717
-#336 := [trans #439 #441]: #442
-#713 := [monotonicity #336]: #712
-#436 := [trans #713 #368]: #435
-#369 := (iff #731 false)
-#363 := (iff #731 #725)
-#724 := (iff #524 true)
-#384 := (or false true)
-#722 := (iff #384 true)
-#723 := [rewrite]: #722
-#720 := (iff #524 #384)
-#718 := (iff #394 false)
-#381 := [rewrite]: #718
-#721 := [monotonicity #381 #383]: #720
-#719 := [trans #721 #723]: #724
-#726 := [monotonicity #719]: #363
-#729 := [trans #726 #368]: #369
-#711 := [monotonicity #729 #436]: #714
-#427 := [trans #711 #425]: #426
-#583 := [monotonicity #427 #692 #580]: #582
-#678 := [trans #583 #677]: #674
-#734 := (iff #739 false)
-#377 := [rewrite]: #734
-#659 := [monotonicity #377 #678]: #667
-#669 := [trans #659 #658]: #668
-#397 := (iff #741 #733)
-#393 := [rewrite]: #397
-#732 := (iff #736 false)
-#392 := [rewrite]: #732
-#671 := [monotonicity #392 #393 #669]: #666
-#663 := [trans #671 #661]: #662
-#652 := [monotonicity #663]: #651
-#650 := [trans #652 #654]: #651
-#649 := [quant-inst #8 #66]: #648
-#655 := [mp #649 #650]: #664
-[unit-resolution #655 #83 #756]: false
-unsat
-5d7ad299834cafeb0e7528443dd40353cb086137 348 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#16 := (:var 0 Int)
-#15 := (:var 1 Int)
-#36 := (f3 #15 #16)
-#758 := (pattern #36)
-#18 := 0::Int
-#65 := -1::Int
-#100 := (* -1::Int #16)
-#97 := (* -1::Int #15)
-#155 := (mod #97 #100)
-#270 := (+ #36 #155)
-#271 := (= #270 0::Int)
-#37 := (mod #15 #16)
-#267 := (* -1::Int #37)
-#268 := (+ #36 #267)
-#269 := (= #268 0::Int)
-#129 := (>= #15 0::Int)
-#122 := (<= #16 0::Int)
-#214 := (or #122 #129)
-#215 := (not #214)
-#118 := (<= #15 0::Int)
-#212 := (or #118 #122)
-#213 := (not #212)
-#218 := (or #213 #215)
-#272 := (ite #218 #269 #271)
-#266 := (= #36 0::Int)
-#19 := (= #15 0::Int)
-#273 := (ite #19 #266 #272)
-#265 := (= #15 #36)
-#20 := (= #16 0::Int)
-#274 := (ite #20 #265 #273)
-#759 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #758) #274)
-#277 := (forall (vars (?v0 Int) (?v1 Int)) #274)
-#762 := (iff #277 #759)
-#760 := (iff #274 #274)
-#761 := [refl]: #760
-#763 := [quant-intro #761]: #762
-#161 := (* -1::Int #155)
-#234 := (ite #218 #37 #161)
-#237 := (ite #19 0::Int #234)
-#240 := (ite #20 #15 #237)
-#243 := (= #36 #240)
-#246 := (forall (vars (?v0 Int) (?v1 Int)) #243)
-#278 := (iff #246 #277)
-#275 := (iff #243 #274)
-#276 := [rewrite]: #275
-#279 := [quant-intro #276]: #278
-#130 := (not #129)
-#123 := (not #122)
-#133 := (and #123 #130)
-#119 := (not #118)
-#126 := (and #119 #123)
-#136 := (or #126 #133)
-#181 := (ite #136 #37 #161)
-#184 := (ite #19 0::Int #181)
-#187 := (ite #20 #15 #184)
-#190 := (= #36 #187)
-#193 := (forall (vars (?v0 Int) (?v1 Int)) #190)
-#247 := (iff #193 #246)
-#244 := (iff #190 #243)
-#241 := (= #187 #240)
-#238 := (= #184 #237)
-#235 := (= #181 #234)
-#219 := (iff #136 #218)
-#216 := (iff #133 #215)
-#217 := [rewrite]: #216
-#206 := (iff #126 #213)
-#207 := [rewrite]: #206
-#220 := [monotonicity #207 #217]: #219
-#236 := [monotonicity #220]: #235
-#239 := [monotonicity #236]: #238
-#242 := [monotonicity #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [quant-intro #245]: #247
-#204 := (~ #193 #193)
-#203 := (~ #190 #190)
-#200 := [refl]: #203
-#205 := [nnf-pos #200]: #204
-#30 := (- #16)
-#29 := (- #15)
-#38 := (mod #29 #30)
-#39 := (- #38)
-#23 := (< 0::Int #16)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#40 := (ite #27 #37 #39)
-#41 := (ite #19 0::Int #40)
-#42 := (ite #20 #15 #41)
-#43 := (= #36 #42)
-#44 := (forall (vars (?v0 Int) (?v1 Int)) #43)
-#196 := (iff #44 #193)
-#91 := (and #23 #25)
-#94 := (or #24 #91)
-#166 := (ite #94 #37 #161)
-#169 := (ite #19 0::Int #166)
-#172 := (ite #20 #15 #169)
-#175 := (= #36 #172)
-#178 := (forall (vars (?v0 Int) (?v1 Int)) #175)
-#194 := (iff #178 #193)
-#191 := (iff #175 #190)
-#188 := (= #172 #187)
-#185 := (= #169 #184)
-#182 := (= #166 #181)
-#137 := (iff #94 #136)
-#134 := (iff #91 #133)
-#131 := (iff #25 #130)
-#132 := [rewrite]: #131
-#124 := (iff #23 #123)
-#125 := [rewrite]: #124
-#135 := [monotonicity #125 #132]: #134
-#127 := (iff #24 #126)
-#120 := (iff #22 #119)
-#121 := [rewrite]: #120
-#128 := [monotonicity #121 #125]: #127
-#138 := [monotonicity #128 #135]: #137
-#183 := [monotonicity #138]: #182
-#186 := [monotonicity #183]: #185
-#189 := [monotonicity #186]: #188
-#192 := [monotonicity #189]: #191
-#195 := [quant-intro #192]: #194
-#179 := (iff #44 #178)
-#176 := (iff #43 #175)
-#173 := (= #42 #172)
-#170 := (= #41 #169)
-#167 := (= #40 #166)
-#164 := (= #39 #161)
-#158 := (- #155)
-#162 := (= #158 #161)
-#163 := [rewrite]: #162
-#159 := (= #39 #158)
-#156 := (= #38 #155)
-#101 := (= #30 #100)
-#102 := [rewrite]: #101
-#98 := (= #29 #97)
-#99 := [rewrite]: #98
-#157 := [monotonicity #99 #102]: #156
-#160 := [monotonicity #157]: #159
-#165 := [trans #160 #163]: #164
-#95 := (iff #27 #94)
-#92 := (iff #26 #91)
-#93 := [rewrite]: #92
-#96 := [monotonicity #93]: #95
-#168 := [monotonicity #96 #165]: #167
-#171 := [monotonicity #168]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [quant-intro #177]: #179
-#197 := [trans #180 #195]: #196
-#154 := [asserted]: #44
-#198 := [mp #154 #197]: #193
-#201 := [mp~ #198 #205]: #193
-#249 := [mp #201 #248]: #246
-#280 := [mp #249 #279]: #277
-#764 := [mp #280 #763]: #759
-#12 := 2::Int
-#10 := 3::Int
-#68 := (f3 -1::Int 3::Int)
-#71 := (= #68 2::Int)
-#84 := (not #71)
-#8 := 1::Int
-#9 := (- 1::Int)
-#11 := (f3 #9 3::Int)
-#13 := (= #11 2::Int)
-#14 := (not #13)
-#87 := (iff #14 #84)
-#74 := (= 2::Int #68)
-#79 := (not #74)
-#85 := (iff #79 #84)
-#82 := (iff #74 #71)
-#83 := [rewrite]: #82
-#86 := [monotonicity #83]: #85
-#80 := (iff #14 #79)
-#77 := (iff #13 #74)
-#75 := (iff #71 #74)
-#76 := [rewrite]: #75
-#72 := (iff #13 #71)
-#69 := (= #11 #68)
-#66 := (= #9 -1::Int)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#73 := [monotonicity #70]: #72
-#78 := [trans #73 #76]: #77
-#81 := [monotonicity #78]: #80
-#88 := [trans #81 #86]: #87
-#64 := [asserted]: #14
-#89 := [mp #64 #88]: #84
-#672 := (not #759)
-#656 := (or #672 #71)
-#338 := (* -1::Int 3::Int)
-#422 := (* -1::Int -1::Int)
-#423 := (mod #422 #338)
-#424 := (+ #68 #423)
-#415 := (= #424 0::Int)
-#426 := (mod -1::Int 3::Int)
-#427 := (* -1::Int #426)
-#428 := (+ #68 #427)
-#425 := (= #428 0::Int)
-#429 := (>= -1::Int 0::Int)
-#408 := (<= 3::Int 0::Int)
-#743 := (or #408 #429)
-#745 := (not #743)
-#402 := (<= -1::Int 0::Int)
-#532 := (or #402 #408)
-#739 := (not #532)
-#413 := (or #739 #745)
-#414 := (ite #413 #425 #415)
-#746 := (= #68 0::Int)
-#747 := (= -1::Int 0::Int)
-#748 := (ite #747 #746 #414)
-#749 := (= -1::Int #68)
-#744 := (= 3::Int 0::Int)
-#750 := (ite #744 #749 #748)
-#657 := (or #672 #750)
-#660 := (iff #657 #656)
-#662 := (iff #656 #656)
-#658 := [rewrite]: #662
-#671 := (iff #750 #71)
-#741 := (= #68 -1::Int)
-#674 := (ite false #741 #71)
-#669 := (iff #674 #71)
-#670 := [rewrite]: #669
-#679 := (iff #750 #674)
-#677 := (iff #748 #71)
-#675 := (ite false #746 #71)
-#666 := (iff #675 #71)
-#676 := [rewrite]: #666
-#667 := (iff #748 #675)
-#686 := (iff #414 #71)
-#1 := true
-#590 := (ite true #71 #741)
-#685 := (iff #590 #71)
-#682 := [rewrite]: #685
-#591 := (iff #414 #590)
-#588 := (iff #415 #741)
-#683 := (+ 1::Int #68)
-#569 := (= #683 0::Int)
-#587 := (iff #569 #741)
-#580 := [rewrite]: #587
-#584 := (iff #415 #569)
-#681 := (= #424 #683)
-#575 := (+ #68 1::Int)
-#585 := (= #575 #683)
-#680 := [rewrite]: #585
-#576 := (= #424 #575)
-#692 := (= #423 1::Int)
-#531 := -3::Int
-#687 := (mod 1::Int -3::Int)
-#691 := (= #687 1::Int)
-#689 := [rewrite]: #691
-#688 := (= #423 #687)
-#533 := (= #338 -3::Int)
-#534 := [rewrite]: #533
-#695 := (= #422 1::Int)
-#702 := [rewrite]: #695
-#690 := [monotonicity #702 #534]: #688
-#574 := [trans #690 #689]: #692
-#535 := [monotonicity #574]: #576
-#684 := [trans #535 #680]: #681
-#586 := [monotonicity #684]: #584
-#589 := [trans #586 #580]: #588
-#700 := (iff #425 #71)
-#706 := -2::Int
-#711 := (+ -2::Int #68)
-#697 := (= #711 0::Int)
-#693 := (iff #697 #71)
-#694 := [rewrite]: #693
-#698 := (iff #425 #697)
-#554 := (= #428 #711)
-#709 := (+ #68 -2::Int)
-#552 := (= #709 #711)
-#553 := [rewrite]: #552
-#710 := (= #428 #709)
-#703 := (= #427 -2::Int)
-#716 := (* -1::Int 2::Int)
-#707 := (= #716 -2::Int)
-#708 := [rewrite]: #707
-#713 := (= #427 #716)
-#430 := (= #426 2::Int)
-#712 := [rewrite]: #430
-#717 := [monotonicity #712]: #713
-#704 := [trans #717 #708]: #703
-#705 := [monotonicity #704]: #710
-#696 := [trans #705 #553]: #554
-#699 := [monotonicity #696]: #698
-#701 := [trans #699 #694]: #700
-#714 := (iff #413 true)
-#723 := (or false true)
-#435 := (iff #723 true)
-#436 := [rewrite]: #435
-#433 := (iff #413 #723)
-#722 := (iff #745 true)
-#720 := (not false)
-#444 := (iff #720 true)
-#718 := [rewrite]: #444
-#721 := (iff #745 #720)
-#450 := (iff #743 false)
-#724 := (or false false)
-#448 := (iff #724 false)
-#449 := [rewrite]: #448
-#725 := (iff #743 #724)
-#735 := (iff #429 false)
-#738 := [rewrite]: #735
-#390 := (iff #408 false)
-#391 := [rewrite]: #390
-#447 := [monotonicity #391 #738]: #725
-#344 := [trans #447 #449]: #450
-#443 := [monotonicity #344]: #721
-#719 := [trans #443 #718]: #722
-#377 := (iff #739 false)
-#733 := (not true)
-#736 := (iff #733 false)
-#376 := [rewrite]: #736
-#371 := (iff #739 #733)
-#732 := (iff #532 true)
-#392 := (or true false)
-#730 := (iff #392 true)
-#731 := [rewrite]: #730
-#728 := (iff #532 #392)
-#726 := (iff #402 true)
-#389 := [rewrite]: #726
-#729 := [monotonicity #389 #391]: #728
-#727 := [trans #729 #731]: #732
-#734 := [monotonicity #727]: #371
-#737 := [trans #734 #376]: #377
-#434 := [monotonicity #737 #719]: #433
-#715 := [trans #434 #436]: #714
-#592 := [monotonicity #715 #701 #589]: #591
-#673 := [trans #592 #682]: #686
-#742 := (iff #747 false)
-#385 := [rewrite]: #742
-#664 := [monotonicity #385 #673]: #667
-#678 := [trans #664 #676]: #677
-#405 := (iff #749 #741)
-#401 := [rewrite]: #405
-#740 := (iff #744 false)
-#400 := [rewrite]: #740
-#668 := [monotonicity #400 #401 #678]: #679
-#665 := [trans #668 #670]: #671
-#661 := [monotonicity #665]: #660
-#663 := [trans #661 #658]: #660
-#659 := [quant-inst #65 #10]: #657
-#649 := [mp #659 #663]: #656
-[unit-resolution #649 #89 #764]: false
-unsat
-513cb6376361794229c618f4dacebc2dcd3ef34a 339 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#15 := (:var 0 Int)
-#14 := (:var 1 Int)
-#34 := (f3 #14 #15)
-#773 := (pattern #34)
-#11 := 0::Int
-#104 := -1::Int
-#108 := (* -1::Int #15)
-#105 := (* -1::Int #14)
-#169 := (mod #105 #108)
-#284 := (+ #34 #169)
-#285 := (= #284 0::Int)
-#35 := (mod #14 #15)
-#281 := (* -1::Int #35)
-#282 := (+ #34 #281)
-#283 := (= #282 0::Int)
-#143 := (>= #14 0::Int)
-#136 := (<= #15 0::Int)
-#228 := (or #136 #143)
-#229 := (not #228)
-#132 := (<= #14 0::Int)
-#226 := (or #132 #136)
-#227 := (not #226)
-#232 := (or #227 #229)
-#286 := (ite #232 #283 #285)
-#280 := (= #34 0::Int)
-#17 := (= #14 0::Int)
-#287 := (ite #17 #280 #286)
-#279 := (= #14 #34)
-#18 := (= #15 0::Int)
-#288 := (ite #18 #279 #287)
-#774 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #773) #288)
-#291 := (forall (vars (?v0 Int) (?v1 Int)) #288)
-#777 := (iff #291 #774)
-#775 := (iff #288 #288)
-#776 := [refl]: #775
-#778 := [quant-intro #776]: #777
-#175 := (* -1::Int #169)
-#248 := (ite #232 #35 #175)
-#251 := (ite #17 0::Int #248)
-#254 := (ite #18 #14 #251)
-#257 := (= #34 #254)
-#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
-#292 := (iff #260 #291)
-#289 := (iff #257 #288)
-#290 := [rewrite]: #289
-#293 := [quant-intro #290]: #292
-#144 := (not #143)
-#137 := (not #136)
-#147 := (and #137 #144)
-#133 := (not #132)
-#140 := (and #133 #137)
-#150 := (or #140 #147)
-#195 := (ite #150 #35 #175)
-#198 := (ite #17 0::Int #195)
-#201 := (ite #18 #14 #198)
-#204 := (= #34 #201)
-#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
-#261 := (iff #207 #260)
-#258 := (iff #204 #257)
-#255 := (= #201 #254)
-#252 := (= #198 #251)
-#249 := (= #195 #248)
-#233 := (iff #150 #232)
-#230 := (iff #147 #229)
-#231 := [rewrite]: #230
-#220 := (iff #140 #227)
-#221 := [rewrite]: #220
-#234 := [monotonicity #221 #231]: #233
-#250 := [monotonicity #234]: #249
-#253 := [monotonicity #250]: #252
-#256 := [monotonicity #253]: #255
-#259 := [monotonicity #256]: #258
-#262 := [quant-intro #259]: #261
-#218 := (~ #207 #207)
-#217 := (~ #204 #204)
-#214 := [refl]: #217
-#219 := [nnf-pos #214]: #218
-#28 := (- #15)
-#27 := (- #14)
-#36 := (mod #27 #28)
-#37 := (- #36)
-#21 := (< 0::Int #15)
-#23 := (< #14 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #14)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#38 := (ite #25 #35 #37)
-#39 := (ite #17 0::Int #38)
-#40 := (ite #18 #14 #39)
-#41 := (= #34 #40)
-#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
-#210 := (iff #42 #207)
-#98 := (and #21 #23)
-#101 := (or #22 #98)
-#180 := (ite #101 #35 #175)
-#89 := (= 0::Int #14)
-#183 := (ite #89 0::Int #180)
-#92 := (= 0::Int #15)
-#186 := (ite #92 #14 #183)
-#189 := (= #34 #186)
-#192 := (forall (vars (?v0 Int) (?v1 Int)) #189)
-#208 := (iff #192 #207)
-#205 := (iff #189 #204)
-#202 := (= #186 #201)
-#199 := (= #183 #198)
-#196 := (= #180 #195)
-#151 := (iff #101 #150)
-#148 := (iff #98 #147)
-#145 := (iff #23 #144)
-#146 := [rewrite]: #145
-#138 := (iff #21 #137)
-#139 := [rewrite]: #138
-#149 := [monotonicity #139 #146]: #148
-#141 := (iff #22 #140)
-#134 := (iff #20 #133)
-#135 := [rewrite]: #134
-#142 := [monotonicity #135 #139]: #141
-#152 := [monotonicity #142 #149]: #151
-#197 := [monotonicity #152]: #196
-#126 := (iff #89 #17)
-#127 := [rewrite]: #126
-#200 := [monotonicity #127 #197]: #199
-#128 := (iff #92 #18)
-#129 := [rewrite]: #128
-#203 := [monotonicity #129 #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [quant-intro #206]: #208
-#193 := (iff #42 #192)
-#190 := (iff #41 #189)
-#187 := (= #40 #186)
-#184 := (= #39 #183)
-#181 := (= #38 #180)
-#178 := (= #37 #175)
-#172 := (- #169)
-#176 := (= #172 #175)
-#177 := [rewrite]: #176
-#173 := (= #37 #172)
-#170 := (= #36 #169)
-#109 := (= #28 #108)
-#110 := [rewrite]: #109
-#106 := (= #27 #105)
-#107 := [rewrite]: #106
-#171 := [monotonicity #107 #110]: #170
-#174 := [monotonicity #171]: #173
-#179 := [trans #174 #177]: #178
-#102 := (iff #25 #101)
-#99 := (iff #24 #98)
-#100 := [rewrite]: #99
-#103 := [monotonicity #100]: #102
-#182 := [monotonicity #103 #179]: #181
-#90 := (iff #17 #89)
-#91 := [rewrite]: #90
-#185 := [monotonicity #91 #182]: #184
-#93 := (iff #18 #92)
-#94 := [rewrite]: #93
-#188 := [monotonicity #94 #185]: #187
-#191 := [monotonicity #188]: #190
-#194 := [quant-intro #191]: #193
-#211 := [trans #194 #209]: #210
-#168 := [asserted]: #42
-#212 := [mp #168 #211]: #207
-#215 := [mp~ #212 #219]: #207
-#263 := [mp #215 #262]: #260
-#294 := [mp #263 #293]: #291
-#779 := [mp #294 #778]: #774
-#8 := 3::Int
-#63 := -3::Int
-#66 := (f3 -3::Int 3::Int)
-#69 := (= #66 0::Int)
-#82 := (not #69)
-#9 := (- 3::Int)
-#10 := (f3 #9 3::Int)
-#12 := (= #10 0::Int)
-#13 := (not #12)
-#85 := (iff #13 #82)
-#72 := (= 0::Int #66)
-#77 := (not #72)
-#83 := (iff #77 #82)
-#80 := (iff #72 #69)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#78 := (iff #13 #77)
-#75 := (iff #12 #72)
-#73 := (iff #69 #72)
-#74 := [rewrite]: #73
-#70 := (iff #12 #69)
-#67 := (= #10 #66)
-#64 := (= #9 -3::Int)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#71 := [monotonicity #68]: #70
-#76 := [trans #71 #74]: #75
-#79 := [monotonicity #76]: #78
-#86 := [trans #79 #84]: #85
-#62 := [asserted]: #13
-#87 := [mp #62 #86]: #82
-#607 := (not #774)
-#700 := (or #607 #69)
-#352 := (* -1::Int 3::Int)
-#437 := (* -1::Int -3::Int)
-#438 := (mod #437 #352)
-#439 := (+ #66 #438)
-#430 := (= #439 0::Int)
-#441 := (mod -3::Int 3::Int)
-#442 := (* -1::Int #441)
-#370 := (+ #66 #442)
-#443 := (= #370 0::Int)
-#440 := (>= -3::Int 0::Int)
-#444 := (<= 3::Int 0::Int)
-#423 := (or #444 #440)
-#758 := (not #423)
-#760 := (<= -3::Int 0::Int)
-#417 := (or #760 #444)
-#547 := (not #417)
-#754 := (or #547 #758)
-#428 := (ite #754 #443 #430)
-#429 := (= -3::Int 0::Int)
-#761 := (ite #429 #69 #428)
-#762 := (= -3::Int #66)
-#763 := (= 3::Int 0::Int)
-#764 := (ite #763 #762 #761)
-#697 := (or #607 #764)
-#688 := (iff #697 #700)
-#682 := (iff #700 #700)
-#679 := [rewrite]: #682
-#605 := (iff #764 #69)
-#415 := (= #66 -3::Int)
-#601 := (ite false #415 #69)
-#603 := (iff #601 #69)
-#604 := [rewrite]: #603
-#602 := (iff #764 #601)
-#584 := (iff #761 #69)
-#698 := (ite false #69 #69)
-#696 := (iff #698 #69)
-#699 := [rewrite]: #696
-#600 := (iff #761 #698)
-#591 := (iff #428 #69)
-#1 := true
-#706 := (ite true #69 #69)
-#589 := (iff #706 #69)
-#590 := [rewrite]: #589
-#704 := (iff #428 #706)
-#703 := (iff #430 #69)
-#549 := (= #439 #66)
-#723 := (+ #66 0::Int)
-#724 := (= #723 #66)
-#725 := [rewrite]: #724
-#546 := (= #439 #723)
-#710 := (= #438 0::Int)
-#714 := (mod 3::Int -3::Int)
-#715 := (= #714 0::Int)
-#716 := [rewrite]: #715
-#708 := (= #438 #714)
-#712 := (= #352 -3::Int)
-#713 := [rewrite]: #712
-#569 := (= #437 3::Int)
-#711 := [rewrite]: #569
-#709 := [monotonicity #711 #713]: #708
-#717 := [trans #709 #716]: #710
-#548 := [monotonicity #717]: #546
-#702 := [trans #548 #725]: #549
-#705 := [monotonicity #702]: #703
-#567 := (iff #443 #69)
-#720 := (= #370 #66)
-#718 := (= #370 #723)
-#721 := (= #442 0::Int)
-#445 := (* -1::Int 0::Int)
-#728 := (= #445 0::Int)
-#732 := [rewrite]: #728
-#727 := (= #442 #445)
-#729 := (= #441 0::Int)
-#730 := [rewrite]: #729
-#731 := [monotonicity #730]: #727
-#722 := [trans #731 #732]: #721
-#719 := [monotonicity #722]: #718
-#726 := [trans #719 #725]: #720
-#568 := [monotonicity #726]: #567
-#450 := (iff #754 true)
-#737 := (or false true)
-#448 := (iff #737 true)
-#449 := [rewrite]: #448
-#734 := (iff #754 #737)
-#459 := (iff #758 true)
-#465 := (not false)
-#736 := (iff #465 true)
-#458 := [rewrite]: #736
-#358 := (iff #758 #465)
-#463 := (iff #423 false)
-#750 := (or false false)
-#740 := (iff #750 false)
-#462 := [rewrite]: #740
-#753 := (iff #423 #750)
-#392 := (iff #440 false)
-#752 := [rewrite]: #392
-#741 := (iff #444 false)
-#404 := [rewrite]: #741
-#739 := [monotonicity #404 #752]: #753
-#464 := [trans #739 #462]: #463
-#735 := [monotonicity #464]: #358
-#733 := [trans #735 #458]: #459
-#751 := (iff #547 false)
-#747 := (not true)
-#386 := (iff #747 false)
-#749 := [rewrite]: #386
-#742 := (iff #547 #747)
-#745 := (iff #417 true)
-#405 := (or true false)
-#743 := (iff #405 true)
-#744 := [rewrite]: #743
-#406 := (iff #417 #405)
-#757 := (iff #760 true)
-#400 := [rewrite]: #757
-#407 := [monotonicity #400 #404]: #406
-#746 := [trans #407 #744]: #745
-#748 := [monotonicity #746]: #742
-#391 := [trans #748 #749]: #751
-#738 := [monotonicity #391 #733]: #734
-#451 := [trans #738 #449]: #450
-#707 := [monotonicity #451 #568 #705]: #704
-#550 := [trans #707 #590]: #591
-#756 := (iff #429 false)
-#416 := [rewrite]: #756
-#695 := [monotonicity #416 #550]: #600
-#599 := [trans #695 #699]: #584
-#755 := (iff #762 #415)
-#420 := [rewrite]: #755
-#759 := (iff #763 false)
-#765 := [rewrite]: #759
-#595 := [monotonicity #765 #420 #599]: #602
-#606 := [trans #595 #604]: #605
-#690 := [monotonicity #606]: #688
-#681 := [trans #690 #679]: #688
-#701 := [quant-inst #63 #8]: #697
-#691 := [mp #701 #681]: #700
-[unit-resolution #691 #87 #779]: false
-unsat
-117ddb585bc1c6246f02758b44ec466b148da99c 351 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#16 := (:var 0 Int)
-#15 := (:var 1 Int)
-#36 := (f3 #15 #16)
-#759 := (pattern #36)
-#18 := 0::Int
-#97 := -1::Int
-#101 := (* -1::Int #16)
-#98 := (* -1::Int #15)
-#156 := (mod #98 #101)
-#271 := (+ #36 #156)
-#272 := (= #271 0::Int)
-#37 := (mod #15 #16)
-#268 := (* -1::Int #37)
-#269 := (+ #36 #268)
-#270 := (= #269 0::Int)
-#130 := (>= #15 0::Int)
-#123 := (<= #16 0::Int)
-#215 := (or #123 #130)
-#216 := (not #215)
-#119 := (<= #15 0::Int)
-#213 := (or #119 #123)
-#214 := (not #213)
-#219 := (or #214 #216)
-#273 := (ite #219 #270 #272)
-#267 := (= #36 0::Int)
-#19 := (= #15 0::Int)
-#274 := (ite #19 #267 #273)
-#266 := (= #15 #36)
-#20 := (= #16 0::Int)
-#275 := (ite #20 #266 #274)
-#760 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #759) #275)
-#278 := (forall (vars (?v0 Int) (?v1 Int)) #275)
-#763 := (iff #278 #760)
-#761 := (iff #275 #275)
-#762 := [refl]: #761
-#764 := [quant-intro #762]: #763
-#162 := (* -1::Int #156)
-#235 := (ite #219 #37 #162)
-#238 := (ite #19 0::Int #235)
-#241 := (ite #20 #15 #238)
-#244 := (= #36 #241)
-#247 := (forall (vars (?v0 Int) (?v1 Int)) #244)
-#279 := (iff #247 #278)
-#276 := (iff #244 #275)
-#277 := [rewrite]: #276
-#280 := [quant-intro #277]: #279
-#131 := (not #130)
-#124 := (not #123)
-#134 := (and #124 #131)
-#120 := (not #119)
-#127 := (and #120 #124)
-#137 := (or #127 #134)
-#182 := (ite #137 #37 #162)
-#185 := (ite #19 0::Int #182)
-#188 := (ite #20 #15 #185)
-#191 := (= #36 #188)
-#194 := (forall (vars (?v0 Int) (?v1 Int)) #191)
-#248 := (iff #194 #247)
-#245 := (iff #191 #244)
-#242 := (= #188 #241)
-#239 := (= #185 #238)
-#236 := (= #182 #235)
-#220 := (iff #137 #219)
-#217 := (iff #134 #216)
-#218 := [rewrite]: #217
-#207 := (iff #127 #214)
-#208 := [rewrite]: #207
-#221 := [monotonicity #208 #218]: #220
-#237 := [monotonicity #221]: #236
-#240 := [monotonicity #237]: #239
-#243 := [monotonicity #240]: #242
-#246 := [monotonicity #243]: #245
-#249 := [quant-intro #246]: #248
-#205 := (~ #194 #194)
-#204 := (~ #191 #191)
-#201 := [refl]: #204
-#206 := [nnf-pos #201]: #205
-#30 := (- #16)
-#29 := (- #15)
-#38 := (mod #29 #30)
-#39 := (- #38)
-#23 := (< 0::Int #16)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#40 := (ite #27 #37 #39)
-#41 := (ite #19 0::Int #40)
-#42 := (ite #20 #15 #41)
-#43 := (= #36 #42)
-#44 := (forall (vars (?v0 Int) (?v1 Int)) #43)
-#197 := (iff #44 #194)
-#91 := (and #23 #25)
-#94 := (or #24 #91)
-#167 := (ite #94 #37 #162)
-#170 := (ite #19 0::Int #167)
-#173 := (ite #20 #15 #170)
-#176 := (= #36 #173)
-#179 := (forall (vars (?v0 Int) (?v1 Int)) #176)
-#195 := (iff #179 #194)
-#192 := (iff #176 #191)
-#189 := (= #173 #188)
-#186 := (= #170 #185)
-#183 := (= #167 #182)
-#138 := (iff #94 #137)
-#135 := (iff #91 #134)
-#132 := (iff #25 #131)
-#133 := [rewrite]: #132
-#125 := (iff #23 #124)
-#126 := [rewrite]: #125
-#136 := [monotonicity #126 #133]: #135
-#128 := (iff #24 #127)
-#121 := (iff #22 #120)
+#180 := [monotonicity #166 #177]: #179
+#183 := [monotonicity #180]: #182
+#192 := [trans #183 #190]: #191
+#195 := [monotonicity #192]: #194
+#132 := (iff #35 #131)
+#129 := (iff #34 #128)
+#126 := (= #33 #125)
+#123 := (= #32 #113)
+#118 := (ite false f3 #113)
+#121 := (= #118 #113)
 #122 := [rewrite]: #121
-#129 := [monotonicity #122 #126]: #128
-#139 := [monotonicity #129 #136]: #138
-#184 := [monotonicity #139]: #183
-#187 := [monotonicity #184]: #186
-#190 := [monotonicity #187]: #189
-#193 := [monotonicity #190]: #192
-#196 := [quant-intro #193]: #195
-#180 := (iff #44 #179)
-#177 := (iff #43 #176)
-#174 := (= #42 #173)
-#171 := (= #41 #170)
-#168 := (= #40 #167)
-#165 := (= #39 #162)
-#159 := (- #156)
-#163 := (= #159 #162)
-#164 := [rewrite]: #163
-#160 := (= #39 #159)
-#157 := (= #38 #156)
-#102 := (= #30 #101)
+#119 := (= #32 #118)
+#116 := (= #31 #113)
+#106 := (ite #68 0::Int #101)
+#109 := (ite #10 0::Int #106)
+#114 := (= #109 #113)
+#115 := [rewrite]: #114
+#110 := (= #31 #109)
+#107 := (= #30 #106)
+#104 := (= #29 #101)
+#98 := (- #95)
+#102 := (= #98 #101)
 #103 := [rewrite]: #102
 #99 := (= #29 #98)
-#100 := [rewrite]: #99
-#158 := [monotonicity #100 #103]: #157
-#161 := [monotonicity #158]: #160
-#166 := [trans #161 #164]: #165
-#95 := (iff #27 #94)
-#92 := (iff #26 #91)
-#93 := [rewrite]: #92
-#96 := [monotonicity #93]: #95
-#169 := [monotonicity #96 #166]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [quant-intro #178]: #180
-#198 := [trans #181 #196]: #197
-#155 := [asserted]: #44
-#199 := [mp #155 #198]: #194
-#202 := [mp~ #199 #206]: #194
-#250 := [mp #202 #249]: #247
-#281 := [mp #250 #280]: #278
-#765 := [mp #281 #764]: #760
-#12 := 1::Int
-#10 := 3::Int
-#65 := -5::Int
-#68 := (f3 -5::Int 3::Int)
-#71 := (= #68 1::Int)
-#84 := (not #71)
-#8 := 5::Int
-#9 := (- 5::Int)
-#11 := (f3 #9 3::Int)
-#13 := (= #11 1::Int)
-#14 := (not #13)
-#87 := (iff #14 #84)
-#74 := (= 1::Int #68)
-#79 := (not #74)
-#85 := (iff #79 #84)
-#82 := (iff #74 #71)
-#83 := [rewrite]: #82
-#86 := [monotonicity #83]: #85
-#80 := (iff #14 #79)
-#77 := (iff #13 #74)
-#75 := (iff #71 #74)
+#96 := (= #28 #95)
+#75 := (= #22 -1::Int)
 #76 := [rewrite]: #75
-#72 := (iff #13 #71)
-#69 := (= #11 #68)
-#66 := (= #9 -5::Int)
+#73 := (= #21 #72)
+#74 := [rewrite]: #73
+#97 := [monotonicity #74 #76]: #96
+#100 := [monotonicity #97]: #99
+#105 := [trans #100 #103]: #104
+#93 := (= #27 0::Int)
+#94 := [rewrite]: #93
+#69 := (iff #19 #68)
+#66 := (iff #18 #65)
 #67 := [rewrite]: #66
 #70 := [monotonicity #67]: #69
-#73 := [monotonicity #70]: #72
-#78 := [trans #73 #76]: #77
-#81 := [monotonicity #78]: #80
-#88 := [trans #81 #86]: #87
-#64 := [asserted]: #14
-#89 := [mp #64 #88]: #84
-#658 := (not #760)
-#660 := (or #658 #71)
-#339 := (* -1::Int 3::Int)
-#423 := (* -1::Int -5::Int)
-#424 := (mod #423 #339)
-#425 := (+ #68 #424)
-#416 := (= #425 0::Int)
-#427 := (mod -5::Int 3::Int)
-#428 := (* -1::Int #427)
-#429 := (+ #68 #428)
-#426 := (= #429 0::Int)
-#430 := (>= -5::Int 0::Int)
-#409 := (<= 3::Int 0::Int)
-#744 := (or #409 #430)
-#746 := (not #744)
-#403 := (<= -5::Int 0::Int)
-#533 := (or #403 #409)
-#740 := (not #533)
-#414 := (or #740 #746)
-#415 := (ite #414 #426 #416)
-#747 := (= #68 0::Int)
-#748 := (= -5::Int 0::Int)
-#749 := (ite #748 #747 #415)
-#750 := (= -5::Int #68)
-#745 := (= 3::Int 0::Int)
-#751 := (ite #745 #750 #749)
-#661 := (or #658 #751)
-#663 := (iff #661 #660)
-#664 := (iff #660 #660)
-#650 := [rewrite]: #664
-#673 := (iff #751 #71)
-#742 := (= #68 -5::Int)
-#669 := (ite false #742 #71)
-#672 := (iff #669 #71)
-#666 := [rewrite]: #672
-#670 := (iff #751 #669)
-#675 := (iff #749 #71)
-#665 := (ite false #747 #71)
-#678 := (iff #665 #71)
-#679 := [rewrite]: #678
-#667 := (iff #749 #665)
-#676 := (iff #415 #71)
-#588 := -2::Int
-#581 := (= #68 -2::Int)
-#1 := true
-#593 := (ite true #71 #581)
-#687 := (iff #593 #71)
-#674 := [rewrite]: #687
-#686 := (iff #415 #593)
-#591 := (iff #416 #581)
-#691 := 2::Int
-#684 := (+ 2::Int #68)
-#570 := (= #684 0::Int)
-#589 := (iff #570 #581)
-#590 := [rewrite]: #589
-#585 := (iff #416 #570)
-#682 := (= #425 #684)
-#576 := (+ #68 2::Int)
-#586 := (= #576 #684)
-#681 := [rewrite]: #586
-#577 := (= #425 #576)
-#693 := (= #424 2::Int)
-#703 := -3::Int
-#535 := (mod 5::Int -3::Int)
-#692 := (= #535 2::Int)
-#690 := [rewrite]: #692
-#688 := (= #424 #535)
-#532 := (= #339 -3::Int)
-#534 := [rewrite]: #532
-#702 := (= #423 5::Int)
-#696 := [rewrite]: #702
-#689 := [monotonicity #696 #534]: #688
-#575 := [trans #689 #690]: #693
-#536 := [monotonicity #575]: #577
-#685 := [trans #536 #681]: #682
-#587 := [monotonicity #685]: #585
-#592 := [trans #587 #590]: #591
-#695 := (iff #426 #71)
-#706 := (+ -1::Int #68)
-#697 := (= #706 0::Int)
-#700 := (iff #697 #71)
-#694 := [rewrite]: #700
-#698 := (iff #426 #697)
-#554 := (= #429 #706)
-#705 := (+ #68 -1::Int)
-#712 := (= #705 #706)
-#553 := [rewrite]: #712
-#710 := (= #429 #705)
-#709 := (= #428 -1::Int)
-#717 := (* -1::Int 1::Int)
-#707 := (= #717 -1::Int)
-#708 := [rewrite]: #707
-#714 := (= #428 #717)
-#431 := (= #427 1::Int)
-#713 := [rewrite]: #431
-#718 := [monotonicity #713]: #714
-#704 := [trans #718 #708]: #709
-#711 := [monotonicity #704]: #710
-#555 := [trans #711 #553]: #554
-#699 := [monotonicity #555]: #698
-#701 := [trans #699 #694]: #695
-#715 := (iff #414 true)
-#724 := (or false true)
-#436 := (iff #724 true)
-#437 := [rewrite]: #436
-#434 := (iff #414 #724)
-#723 := (iff #746 true)
-#721 := (not false)
-#445 := (iff #721 true)
-#719 := [rewrite]: #445
-#722 := (iff #746 #721)
-#451 := (iff #744 false)
-#725 := (or false false)
-#449 := (iff #725 false)
-#450 := [rewrite]: #449
-#726 := (iff #744 #725)
-#736 := (iff #430 false)
-#739 := [rewrite]: #736
-#391 := (iff #409 false)
-#392 := [rewrite]: #391
-#448 := [monotonicity #392 #739]: #726
-#345 := [trans #448 #450]: #451
-#444 := [monotonicity #345]: #722
-#720 := [trans #444 #719]: #723
-#378 := (iff #740 false)
-#734 := (not true)
-#737 := (iff #734 false)
-#377 := [rewrite]: #737
-#372 := (iff #740 #734)
-#733 := (iff #533 true)
-#393 := (or true false)
-#731 := (iff #393 true)
-#732 := [rewrite]: #731
-#729 := (iff #533 #393)
-#727 := (iff #403 true)
-#390 := [rewrite]: #727
-#730 := [monotonicity #390 #392]: #729
-#728 := [trans #730 #732]: #733
-#735 := [monotonicity #728]: #372
-#738 := [trans #735 #377]: #378
-#435 := [monotonicity #738 #720]: #434
-#716 := [trans #435 #437]: #715
-#683 := [monotonicity #716 #701 #592]: #686
-#668 := [trans #683 #674]: #676
-#743 := (iff #748 false)
-#386 := [rewrite]: #743
-#677 := [monotonicity #386 #668]: #667
-#680 := [trans #677 #679]: #675
-#406 := (iff #750 #742)
-#402 := [rewrite]: #406
-#741 := (iff #745 false)
-#401 := [rewrite]: #741
-#671 := [monotonicity #401 #402 #680]: #670
-#657 := [trans #671 #666]: #673
-#659 := [monotonicity #657]: #663
-#651 := [trans #659 #650]: #663
-#662 := [quant-inst #65 #10]: #661
-#653 := [mp #662 #651]: #660
-[unit-resolution #653 #89 #765]: false
-unsat
-e49f7307606e8c00bbcb83b5fb72cc73d56a411b 345 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#16 := (:var 0 Int)
-#15 := (:var 1 Int)
-#36 := (f3 #15 #16)
-#761 := (pattern #36)
-#18 := 0::Int
-#65 := -1::Int
-#103 := (* -1::Int #16)
-#100 := (* -1::Int #15)
-#158 := (mod #100 #103)
-#273 := (+ #36 #158)
-#274 := (= #273 0::Int)
-#37 := (mod #15 #16)
-#270 := (* -1::Int #37)
-#271 := (+ #36 #270)
-#272 := (= #271 0::Int)
-#132 := (>= #15 0::Int)
-#125 := (<= #16 0::Int)
-#217 := (or #125 #132)
-#218 := (not #217)
-#121 := (<= #15 0::Int)
-#215 := (or #121 #125)
-#216 := (not #215)
-#221 := (or #216 #218)
-#275 := (ite #221 #272 #274)
-#269 := (= #36 0::Int)
-#19 := (= #15 0::Int)
-#276 := (ite #19 #269 #275)
-#268 := (= #15 #36)
-#20 := (= #16 0::Int)
-#277 := (ite #20 #268 #276)
-#762 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #761) #277)
-#280 := (forall (vars (?v0 Int) (?v1 Int)) #277)
-#765 := (iff #280 #762)
-#763 := (iff #277 #277)
-#764 := [refl]: #763
-#766 := [quant-intro #764]: #765
-#164 := (* -1::Int #158)
-#237 := (ite #221 #37 #164)
-#240 := (ite #19 0::Int #237)
-#243 := (ite #20 #15 #240)
-#246 := (= #36 #243)
-#249 := (forall (vars (?v0 Int) (?v1 Int)) #246)
-#281 := (iff #249 #280)
-#278 := (iff #246 #277)
-#279 := [rewrite]: #278
-#282 := [quant-intro #279]: #281
-#133 := (not #132)
-#126 := (not #125)
-#136 := (and #126 #133)
-#122 := (not #121)
-#129 := (and #122 #126)
-#139 := (or #129 #136)
-#184 := (ite #139 #37 #164)
-#187 := (ite #19 0::Int #184)
-#190 := (ite #20 #15 #187)
-#193 := (= #36 #190)
-#196 := (forall (vars (?v0 Int) (?v1 Int)) #193)
-#250 := (iff #196 #249)
-#247 := (iff #193 #246)
-#244 := (= #190 #243)
-#241 := (= #187 #240)
-#238 := (= #184 #237)
-#222 := (iff #139 #221)
-#219 := (iff #136 #218)
-#220 := [rewrite]: #219
-#209 := (iff #129 #216)
-#210 := [rewrite]: #209
-#223 := [monotonicity #210 #220]: #222
-#239 := [monotonicity #223]: #238
-#242 := [monotonicity #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [monotonicity #245]: #247
-#251 := [quant-intro #248]: #250
-#207 := (~ #196 #196)
-#206 := (~ #193 #193)
-#203 := [refl]: #206
-#208 := [nnf-pos #203]: #207
-#30 := (- #16)
-#29 := (- #15)
-#38 := (mod #29 #30)
-#39 := (- #38)
-#23 := (< 0::Int #16)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#40 := (ite #27 #37 #39)
-#41 := (ite #19 0::Int #40)
-#42 := (ite #20 #15 #41)
-#43 := (= #36 #42)
-#44 := (forall (vars (?v0 Int) (?v1 Int)) #43)
-#199 := (iff #44 #196)
-#94 := (and #23 #25)
-#97 := (or #24 #94)
-#169 := (ite #97 #37 #164)
-#172 := (ite #19 0::Int #169)
-#175 := (ite #20 #15 #172)
-#178 := (= #36 #175)
-#181 := (forall (vars (?v0 Int) (?v1 Int)) #178)
-#197 := (iff #181 #196)
-#194 := (iff #178 #193)
-#191 := (= #175 #190)
-#188 := (= #172 #187)
-#185 := (= #169 #184)
-#140 := (iff #97 #139)
-#137 := (iff #94 #136)
-#134 := (iff #25 #133)
-#135 := [rewrite]: #134
-#127 := (iff #23 #126)
-#128 := [rewrite]: #127
-#138 := [monotonicity #128 #135]: #137
-#130 := (iff #24 #129)
-#123 := (iff #22 #122)
-#124 := [rewrite]: #123
-#131 := [monotonicity #124 #128]: #130
-#141 := [monotonicity #131 #138]: #140
-#186 := [monotonicity #141]: #185
-#189 := [monotonicity #186]: #188
-#192 := [monotonicity #189]: #191
-#195 := [monotonicity #192]: #194
-#198 := [quant-intro #195]: #197
-#182 := (iff #44 #181)
-#179 := (iff #43 #178)
-#176 := (= #42 #175)
-#173 := (= #41 #172)
-#170 := (= #40 #169)
-#167 := (= #39 #164)
-#161 := (- #158)
-#165 := (= #161 #164)
-#166 := [rewrite]: #165
-#162 := (= #39 #161)
-#159 := (= #38 #158)
-#104 := (= #30 #103)
-#105 := [rewrite]: #104
-#101 := (= #29 #100)
-#102 := [rewrite]: #101
-#160 := [monotonicity #102 #105]: #159
-#163 := [monotonicity #160]: #162
-#168 := [trans #163 #166]: #167
-#98 := (iff #27 #97)
-#95 := (iff #26 #94)
-#96 := [rewrite]: #95
-#99 := [monotonicity #96]: #98
-#171 := [monotonicity #99 #168]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [quant-intro #180]: #182
-#200 := [trans #183 #198]: #199
-#157 := [asserted]: #44
-#201 := [mp #157 #200]: #196
-#204 := [mp~ #201 #208]: #196
-#252 := [mp #204 #251]: #249
-#283 := [mp #252 #282]: #280
-#767 := [mp #283 #766]: #762
-#68 := -3::Int
-#71 := (f3 -1::Int -3::Int)
-#74 := (= #71 -1::Int)
-#87 := (not #74)
-#8 := 1::Int
-#9 := (- 1::Int)
-#10 := 3::Int
-#11 := (- 3::Int)
-#12 := (f3 #9 #11)
-#13 := (= #12 #9)
-#14 := (not #13)
-#90 := (iff #14 #87)
-#77 := (= -1::Int #71)
-#82 := (not #77)
-#88 := (iff #82 #87)
-#85 := (iff #77 #74)
-#86 := [rewrite]: #85
-#89 := [monotonicity #86]: #88
-#83 := (iff #14 #82)
-#80 := (iff #13 #77)
-#78 := (iff #74 #77)
-#79 := [rewrite]: #78
-#75 := (iff #13 #74)
-#66 := (= #9 -1::Int)
-#67 := [rewrite]: #66
-#72 := (= #12 #71)
-#69 := (= #11 -3::Int)
-#70 := [rewrite]: #69
-#73 := [monotonicity #67 #70]: #72
-#76 := [monotonicity #73 #67]: #75
-#81 := [trans #76 #79]: #80
-#84 := [monotonicity #81]: #83
-#91 := [trans #84 #89]: #90
-#64 := [asserted]: #14
-#92 := [mp #64 #91]: #87
-#682 := (not #762)
-#671 := (or #682 #74)
-#341 := (* -1::Int -3::Int)
-#425 := (* -1::Int -1::Int)
-#426 := (mod #425 #341)
-#427 := (+ #71 #426)
-#418 := (= #427 0::Int)
-#429 := (mod -1::Int -3::Int)
-#430 := (* -1::Int #429)
-#431 := (+ #71 #430)
-#428 := (= #431 0::Int)
-#432 := (>= -1::Int 0::Int)
-#411 := (<= -3::Int 0::Int)
-#746 := (or #411 #432)
-#748 := (not #746)
-#405 := (<= -1::Int 0::Int)
-#535 := (or #405 #411)
-#742 := (not #535)
-#416 := (or #742 #748)
-#417 := (ite #416 #428 #418)
-#749 := (= #71 0::Int)
-#750 := (= -1::Int 0::Int)
-#751 := (ite #750 #749 #417)
-#752 := (= -3::Int 0::Int)
-#747 := (ite #752 #77 #751)
-#672 := (or #682 #747)
-#674 := (iff #672 #671)
-#675 := (iff #671 #671)
-#659 := [rewrite]: #675
-#681 := (iff #747 #74)
-#670 := (ite false #74 #74)
-#679 := (iff #670 #74)
-#680 := [rewrite]: #679
-#667 := (iff #747 #670)
-#676 := (iff #751 #74)
-#594 := (ite false #749 #74)
-#685 := (iff #594 #74)
-#689 := [rewrite]: #685
-#595 := (iff #751 #594)
-#592 := (iff #417 #74)
-#726 := 2::Int
-#556 := (= #71 2::Int)
-#587 := (ite false #556 #74)
-#583 := (iff #587 #74)
-#591 := [rewrite]: #583
-#589 := (iff #417 #587)
-#687 := (iff #418 #74)
-#692 := (+ 1::Int #71)
-#538 := (= #692 0::Int)
-#683 := (iff #538 #74)
-#684 := [rewrite]: #683
-#686 := (iff #418 #538)
-#578 := (= #427 #692)
-#691 := (+ #71 1::Int)
-#695 := (= #691 #692)
-#577 := [rewrite]: #695
-#693 := (= #427 #691)
-#537 := (= #426 1::Int)
-#704 := (mod 1::Int 3::Int)
-#534 := (= #704 1::Int)
-#536 := [rewrite]: #534
-#698 := (= #426 #704)
-#697 := (= #341 3::Int)
-#703 := [rewrite]: #697
-#702 := (= #425 1::Int)
-#696 := [rewrite]: #702
-#705 := [monotonicity #696 #703]: #698
-#690 := [trans #705 #536]: #537
-#694 := [monotonicity #690]: #693
-#579 := [trans #694 #577]: #578
-#588 := [monotonicity #579]: #686
-#572 := [trans #588 #684]: #687
-#700 := (iff #428 #556)
-#718 := -2::Int
-#711 := (+ -2::Int #71)
-#708 := (= #711 0::Int)
-#557 := (iff #708 #556)
-#699 := [rewrite]: #557
-#714 := (iff #428 #708)
-#712 := (= #431 #711)
-#720 := (+ #71 -2::Int)
-#706 := (= #720 #711)
-#707 := [rewrite]: #706
-#709 := (= #431 #720)
-#719 := (= #430 -2::Int)
-#438 := (* -1::Int 2::Int)
-#433 := (= #438 -2::Int)
-#715 := [rewrite]: #433
-#439 := (= #430 #438)
-#436 := (= #429 2::Int)
-#437 := [rewrite]: #436
-#717 := [monotonicity #437]: #439
-#716 := [trans #717 #715]: #719
-#710 := [monotonicity #716]: #709
-#713 := [trans #710 #707]: #712
-#555 := [monotonicity #713]: #714
-#701 := [trans #555 #699]: #700
-#725 := (iff #416 false)
-#723 := (or false false)
-#447 := (iff #723 false)
-#721 := [rewrite]: #447
-#724 := (iff #416 #723)
-#453 := (iff #748 false)
-#1 := true
-#733 := (not true)
-#730 := (iff #733 false)
-#736 := [rewrite]: #730
-#451 := (iff #748 #733)
-#728 := (iff #746 true)
-#380 := (or true false)
-#741 := (iff #380 true)
-#727 := [rewrite]: #741
-#740 := (iff #746 #380)
-#739 := (iff #432 false)
-#379 := [rewrite]: #739
-#745 := (iff #411 true)
-#388 := [rewrite]: #745
-#738 := [monotonicity #388 #379]: #740
-#450 := [trans #738 #727]: #728
-#452 := [monotonicity #450]: #451
-#347 := [trans #452 #736]: #453
-#374 := (iff #742 false)
-#734 := (iff #742 #733)
-#731 := (iff #535 true)
-#729 := (or true true)
-#394 := (iff #729 true)
-#395 := [rewrite]: #394
-#392 := (iff #535 #729)
-#744 := (iff #405 true)
-#404 := [rewrite]: #744
-#393 := [monotonicity #404 #388]: #392
-#732 := [trans #393 #395]: #731
-#735 := [monotonicity #732]: #734
-#737 := [trans #735 #736]: #374
-#446 := [monotonicity #737 #347]: #724
-#722 := [trans #446 #721]: #725
-#590 := [monotonicity #722 #701 #572]: #589
-#593 := [trans #590 #591]: #592
-#403 := (iff #750 false)
-#408 := [rewrite]: #403
-#688 := [monotonicity #408 #593]: #595
-#678 := [trans #688 #689]: #676
-#753 := (iff #752 false)
-#743 := [rewrite]: #753
-#669 := [monotonicity #743 #86 #678]: #667
-#677 := [trans #669 #680]: #681
-#668 := [monotonicity #677]: #674
-#660 := [trans #668 #659]: #674
-#673 := [quant-inst #65 #68]: #672
-#662 := [mp #673 #660]: #671
-[unit-resolution #662 #92 #767]: false
-unsat
-a8f315f795d8dc3da5b76a3fe9d6ebfef481af33 324 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#15 := (:var 0 Int)
-#14 := (:var 1 Int)
-#34 := (f3 #14 #15)
-#773 := (pattern #34)
-#11 := 0::Int
-#104 := -1::Int
-#108 := (* -1::Int #15)
-#105 := (* -1::Int #14)
-#169 := (mod #105 #108)
-#284 := (+ #34 #169)
-#285 := (= #284 0::Int)
-#35 := (mod #14 #15)
-#281 := (* -1::Int #35)
-#282 := (+ #34 #281)
-#283 := (= #282 0::Int)
-#143 := (>= #14 0::Int)
-#136 := (<= #15 0::Int)
-#228 := (or #136 #143)
-#229 := (not #228)
-#132 := (<= #14 0::Int)
-#226 := (or #132 #136)
-#227 := (not #226)
-#232 := (or #227 #229)
-#286 := (ite #232 #283 #285)
-#280 := (= #34 0::Int)
-#17 := (= #14 0::Int)
-#287 := (ite #17 #280 #286)
-#279 := (= #14 #34)
-#18 := (= #15 0::Int)
-#288 := (ite #18 #279 #287)
-#774 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #773) #288)
-#291 := (forall (vars (?v0 Int) (?v1 Int)) #288)
-#777 := (iff #291 #774)
-#775 := (iff #288 #288)
-#776 := [refl]: #775
-#778 := [quant-intro #776]: #777
-#175 := (* -1::Int #169)
-#248 := (ite #232 #35 #175)
-#251 := (ite #17 0::Int #248)
-#254 := (ite #18 #14 #251)
-#257 := (= #34 #254)
-#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
-#292 := (iff #260 #291)
-#289 := (iff #257 #288)
-#290 := [rewrite]: #289
-#293 := [quant-intro #290]: #292
-#144 := (not #143)
-#137 := (not #136)
-#147 := (and #137 #144)
-#133 := (not #132)
-#140 := (and #133 #137)
-#150 := (or #140 #147)
-#195 := (ite #150 #35 #175)
-#198 := (ite #17 0::Int #195)
-#201 := (ite #18 #14 #198)
-#204 := (= #34 #201)
-#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
-#261 := (iff #207 #260)
-#258 := (iff #204 #257)
-#255 := (= #201 #254)
-#252 := (= #198 #251)
-#249 := (= #195 #248)
-#233 := (iff #150 #232)
-#230 := (iff #147 #229)
-#231 := [rewrite]: #230
-#220 := (iff #140 #227)
-#221 := [rewrite]: #220
-#234 := [monotonicity #221 #231]: #233
-#250 := [monotonicity #234]: #249
-#253 := [monotonicity #250]: #252
-#256 := [monotonicity #253]: #255
-#259 := [monotonicity #256]: #258
-#262 := [quant-intro #259]: #261
-#218 := (~ #207 #207)
-#217 := (~ #204 #204)
-#214 := [refl]: #217
-#219 := [nnf-pos #214]: #218
-#28 := (- #15)
-#27 := (- #14)
-#36 := (mod #27 #28)
-#37 := (- #36)
-#21 := (< 0::Int #15)
-#23 := (< #14 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #14)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#38 := (ite #25 #35 #37)
-#39 := (ite #17 0::Int #38)
-#40 := (ite #18 #14 #39)
-#41 := (= #34 #40)
-#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
-#210 := (iff #42 #207)
-#98 := (and #21 #23)
-#101 := (or #22 #98)
-#180 := (ite #101 #35 #175)
-#89 := (= 0::Int #14)
-#183 := (ite #89 0::Int #180)
-#92 := (= 0::Int #15)
-#186 := (ite #92 #14 #183)
-#189 := (= #34 #186)
-#192 := (forall (vars (?v0 Int) (?v1 Int)) #189)
-#208 := (iff #192 #207)
-#205 := (iff #189 #204)
-#202 := (= #186 #201)
-#199 := (= #183 #198)
-#196 := (= #180 #195)
-#151 := (iff #101 #150)
-#148 := (iff #98 #147)
-#145 := (iff #23 #144)
-#146 := [rewrite]: #145
-#138 := (iff #21 #137)
-#139 := [rewrite]: #138
-#149 := [monotonicity #139 #146]: #148
-#141 := (iff #22 #140)
-#134 := (iff #20 #133)
-#135 := [rewrite]: #134
-#142 := [monotonicity #135 #139]: #141
-#152 := [monotonicity #142 #149]: #151
-#197 := [monotonicity #152]: #196
-#126 := (iff #89 #17)
-#127 := [rewrite]: #126
-#200 := [monotonicity #127 #197]: #199
-#128 := (iff #92 #18)
-#129 := [rewrite]: #128
-#203 := [monotonicity #129 #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [quant-intro #206]: #208
-#193 := (iff #42 #192)
-#190 := (iff #41 #189)
-#187 := (= #40 #186)
-#184 := (= #39 #183)
-#181 := (= #38 #180)
-#178 := (= #37 #175)
-#172 := (- #169)
-#176 := (= #172 #175)
-#177 := [rewrite]: #176
-#173 := (= #37 #172)
-#170 := (= #36 #169)
-#109 := (= #28 #108)
-#110 := [rewrite]: #109
-#106 := (= #27 #105)
-#107 := [rewrite]: #106
-#171 := [monotonicity #107 #110]: #170
-#174 := [monotonicity #171]: #173
-#179 := [trans #174 #177]: #178
-#102 := (iff #25 #101)
-#99 := (iff #24 #98)
-#100 := [rewrite]: #99
-#103 := [monotonicity #100]: #102
-#182 := [monotonicity #103 #179]: #181
-#90 := (iff #17 #89)
-#91 := [rewrite]: #90
-#185 := [monotonicity #91 #182]: #184
-#93 := (iff #18 #92)
-#94 := [rewrite]: #93
-#188 := [monotonicity #94 #185]: #187
-#191 := [monotonicity #188]: #190
-#194 := [quant-intro #191]: #193
-#211 := [trans #194 #209]: #210
-#168 := [asserted]: #42
-#212 := [mp #168 #211]: #207
-#215 := [mp~ #212 #219]: #207
-#263 := [mp #215 #262]: #260
-#294 := [mp #263 #293]: #291
-#779 := [mp #294 #778]: #774
-#63 := -3::Int
-#66 := (f3 -3::Int -3::Int)
-#69 := (= #66 0::Int)
-#82 := (not #69)
-#8 := 3::Int
-#9 := (- 3::Int)
-#10 := (f3 #9 #9)
-#12 := (= #10 0::Int)
-#13 := (not #12)
-#85 := (iff #13 #82)
-#72 := (= 0::Int #66)
-#77 := (not #72)
-#83 := (iff #77 #82)
-#80 := (iff #72 #69)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#78 := (iff #13 #77)
-#75 := (iff #12 #72)
-#73 := (iff #69 #72)
-#74 := [rewrite]: #73
-#70 := (iff #12 #69)
-#67 := (= #10 #66)
-#64 := (= #9 -3::Int)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65 #65]: #67
-#71 := [monotonicity #68]: #70
-#76 := [trans #71 #74]: #75
-#79 := [monotonicity #76]: #78
-#86 := [trans #79 #84]: #85
-#62 := [asserted]: #13
-#87 := [mp #62 #86]: #82
-#550 := (not #774)
-#698 := (or #550 #69)
-#352 := (* -1::Int -3::Int)
-#437 := (mod #352 #352)
-#438 := (+ #66 #437)
-#439 := (= #438 0::Int)
-#430 := (mod -3::Int -3::Int)
-#441 := (* -1::Int #430)
-#442 := (+ #66 #441)
-#370 := (= #442 0::Int)
-#443 := (>= -3::Int 0::Int)
-#440 := (<= -3::Int 0::Int)
-#444 := (or #440 #443)
-#423 := (not #444)
-#758 := (or #440 #440)
-#760 := (not #758)
-#417 := (or #760 #423)
-#547 := (ite #417 #370 #439)
-#754 := (= -3::Int 0::Int)
-#428 := (ite #754 #69 #547)
-#429 := (= -3::Int #66)
-#761 := (ite #754 #429 #428)
-#600 := (or #550 #761)
-#696 := (iff #600 #698)
-#584 := (iff #698 #698)
-#599 := [rewrite]: #584
-#590 := (iff #761 #69)
-#759 := (= #66 -3::Int)
-#705 := (ite false #759 #69)
-#707 := (iff #705 #69)
-#589 := [rewrite]: #707
-#706 := (iff #761 #705)
-#702 := (iff #428 #69)
-#708 := (ite false #69 #69)
-#716 := (iff #708 #69)
-#710 := [rewrite]: #716
-#548 := (iff #428 #708)
-#717 := (iff #547 #69)
-#709 := (iff #547 #708)
-#713 := (iff #439 #69)
-#711 := (= #438 #66)
-#451 := (+ #66 0::Int)
-#445 := (= #451 #66)
-#727 := [rewrite]: #445
-#568 := (= #438 #451)
-#726 := (= #437 0::Int)
-#718 := (mod 3::Int 3::Int)
-#725 := (= #718 0::Int)
-#720 := [rewrite]: #725
-#719 := (= #437 #718)
-#722 := (= #352 3::Int)
-#723 := [rewrite]: #722
-#724 := [monotonicity #723 #723]: #719
-#567 := [trans #724 #720]: #726
-#569 := [monotonicity #567]: #568
-#712 := [trans #569 #727]: #711
-#714 := [monotonicity #712]: #713
-#732 := (iff #370 #69)
-#731 := (= #442 #66)
-#729 := (= #442 #451)
-#449 := (= #441 0::Int)
-#733 := (* -1::Int 0::Int)
-#738 := (= #733 0::Int)
-#448 := [rewrite]: #738
-#737 := (= #441 #733)
-#458 := (= #430 0::Int)
-#459 := [rewrite]: #458
-#734 := [monotonicity #459]: #737
-#450 := [trans #734 #448]: #449
-#730 := [monotonicity #450]: #729
-#728 := [trans #730 #727]: #731
-#721 := [monotonicity #728]: #732
-#735 := (iff #417 false)
-#462 := (or false false)
-#465 := (iff #462 false)
-#358 := [rewrite]: #465
-#463 := (iff #417 #462)
-#739 := (iff #423 false)
-#1 := true
-#405 := (not true)
-#743 := (iff #405 false)
-#744 := [rewrite]: #743
-#750 := (iff #423 #405)
-#392 := (iff #444 true)
-#748 := (or true false)
-#751 := (iff #748 true)
-#391 := [rewrite]: #751
-#386 := (iff #444 #748)
-#747 := (iff #443 false)
-#742 := [rewrite]: #747
-#755 := (iff #440 true)
-#415 := [rewrite]: #755
-#749 := [monotonicity #415 #742]: #386
-#752 := [trans #749 #391]: #392
-#753 := [monotonicity #752]: #750
-#740 := [trans #753 #744]: #739
-#745 := (iff #760 false)
-#406 := (iff #760 #405)
-#741 := (iff #758 true)
-#420 := (or true true)
-#757 := (iff #420 true)
-#400 := [rewrite]: #757
-#756 := (iff #758 #420)
-#416 := [monotonicity #415 #415]: #756
-#404 := [trans #416 #400]: #741
-#407 := [monotonicity #404]: #406
-#746 := [trans #407 #744]: #745
-#464 := [monotonicity #746 #740]: #463
-#736 := [trans #464 #358]: #735
-#715 := [monotonicity #736 #721 #714]: #709
-#546 := [trans #715 #710]: #717
-#762 := (iff #754 false)
-#763 := [rewrite]: #762
-#549 := [monotonicity #763 #546]: #548
-#703 := [trans #549 #710]: #702
-#764 := (iff #429 #759)
-#765 := [rewrite]: #764
-#704 := [monotonicity #763 #765 #703]: #706
-#591 := [trans #704 #589]: #590
-#699 := [monotonicity #591]: #696
-#601 := [trans #699 #599]: #696
-#695 := [quant-inst #63 #63]: #600
-#602 := [mp #695 #601]: #698
-[unit-resolution #602 #87 #779]: false
-unsat
-ab60a5d229f921e05cbaa6708d883c31816e3a4a 342 0
-#2 := false
-decl f3 :: (-> Int Int Int)
-#18 := (:var 0 Int)
-#17 := (:var 1 Int)
-#38 := (f3 #17 #18)
-#756 := (pattern #38)
-#20 := 0::Int
-#93 := -1::Int
-#97 := (* -1::Int #18)
-#94 := (* -1::Int #17)
-#152 := (mod #94 #97)
-#267 := (+ #38 #152)
-#268 := (= #267 0::Int)
-#39 := (mod #17 #18)
-#264 := (* -1::Int #39)
-#265 := (+ #38 #264)
-#266 := (= #265 0::Int)
-#126 := (>= #17 0::Int)
-#119 := (<= #18 0::Int)
-#211 := (or #119 #126)
-#212 := (not #211)
-#115 := (<= #17 0::Int)
-#209 := (or #115 #119)
-#210 := (not #209)
-#215 := (or #210 #212)
-#269 := (ite #215 #266 #268)
-#263 := (= #38 0::Int)
-#21 := (= #17 0::Int)
-#270 := (ite #21 #263 #269)
-#262 := (= #17 #38)
-#22 := (= #18 0::Int)
-#271 := (ite #22 #262 #270)
-#757 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #756) #271)
-#274 := (forall (vars (?v0 Int) (?v1 Int)) #271)
-#760 := (iff #274 #757)
-#758 := (iff #271 #271)
-#759 := [refl]: #758
-#761 := [quant-intro #759]: #760
-#158 := (* -1::Int #152)
-#231 := (ite #215 #39 #158)
-#234 := (ite #21 0::Int #231)
-#237 := (ite #22 #17 #234)
-#240 := (= #38 #237)
-#243 := (forall (vars (?v0 Int) (?v1 Int)) #240)
-#275 := (iff #243 #274)
-#272 := (iff #240 #271)
-#273 := [rewrite]: #272
-#276 := [quant-intro #273]: #275
-#127 := (not #126)
-#120 := (not #119)
-#130 := (and #120 #127)
-#116 := (not #115)
-#123 := (and #116 #120)
-#133 := (or #123 #130)
-#178 := (ite #133 #39 #158)
-#181 := (ite #21 0::Int #178)
-#184 := (ite #22 #17 #181)
-#187 := (= #38 #184)
-#190 := (forall (vars (?v0 Int) (?v1 Int)) #187)
-#244 := (iff #190 #243)
-#241 := (iff #187 #240)
-#238 := (= #184 #237)
-#235 := (= #181 #234)
-#232 := (= #178 #231)
-#216 := (iff #133 #215)
-#213 := (iff #130 #212)
-#214 := [rewrite]: #213
-#203 := (iff #123 #210)
-#204 := [rewrite]: #203
-#217 := [monotonicity #204 #214]: #216
-#233 := [monotonicity #217]: #232
-#236 := [monotonicity #233]: #235
-#239 := [monotonicity #236]: #238
-#242 := [monotonicity #239]: #241
-#245 := [quant-intro #242]: #244
-#201 := (~ #190 #190)
-#200 := (~ #187 #187)
-#197 := [refl]: #200
-#202 := [nnf-pos #197]: #201
-#32 := (- #18)
-#31 := (- #17)
-#40 := (mod #31 #32)
-#41 := (- #40)
-#25 := (< 0::Int #18)
-#27 := (< #17 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #17)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#42 := (ite #29 #39 #41)
-#43 := (ite #21 0::Int #42)
-#44 := (ite #22 #17 #43)
-#45 := (= #38 #44)
-#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#193 := (iff #46 #190)
-#86 := (and #25 #27)
-#90 := (or #26 #86)
-#163 := (ite #90 #39 #158)
-#166 := (ite #21 0::Int #163)
-#169 := (ite #22 #17 #166)
-#172 := (= #38 #169)
-#175 := (forall (vars (?v0 Int) (?v1 Int)) #172)
-#191 := (iff #175 #190)
-#188 := (iff #172 #187)
-#185 := (= #169 #184)
-#182 := (= #166 #181)
-#179 := (= #163 #178)
-#134 := (iff #90 #133)
-#131 := (iff #86 #130)
-#128 := (iff #27 #127)
-#129 := [rewrite]: #128
-#121 := (iff #25 #120)
-#122 := [rewrite]: #121
-#132 := [monotonicity #122 #129]: #131
-#124 := (iff #26 #123)
-#117 := (iff #24 #116)
-#118 := [rewrite]: #117
-#125 := [monotonicity #118 #122]: #124
-#135 := [monotonicity #125 #132]: #134
-#180 := [monotonicity #135]: #179
-#183 := [monotonicity #180]: #182
-#186 := [monotonicity #183]: #185
-#189 := [monotonicity #186]: #188
-#192 := [quant-intro #189]: #191
-#176 := (iff #46 #175)
-#173 := (iff #45 #172)
-#170 := (= #44 #169)
-#167 := (= #43 #166)
-#164 := (= #42 #163)
-#161 := (= #41 #158)
-#155 := (- #152)
-#159 := (= #155 #158)
-#160 := [rewrite]: #159
-#156 := (= #41 #155)
-#153 := (= #40 #152)
-#98 := (= #32 #97)
-#99 := [rewrite]: #98
-#95 := (= #31 #94)
-#96 := [rewrite]: #95
-#154 := [monotonicity #96 #99]: #153
-#157 := [monotonicity #154]: #156
-#162 := [trans #157 #160]: #161
-#91 := (iff #29 #90)
-#88 := (iff #28 #86)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#165 := [monotonicity #92 #162]: #164
-#168 := [monotonicity #165]: #167
-#171 := [monotonicity #168]: #170
-#174 := [monotonicity #171]: #173
-#177 := [quant-intro #174]: #176
-#194 := [trans #177 #192]: #193
-#151 := [asserted]: #46
-#195 := [mp #151 #194]: #190
-#198 := [mp~ #195 #202]: #190
-#246 := [mp #198 #245]: #243
-#277 := [mp #246 #276]: #274
-#762 := [mp #277 #761]: #757
-#76 := -2::Int
-#70 := -3::Int
-#67 := -5::Int
-#73 := (f3 -5::Int -3::Int)
-#79 := (= #73 -2::Int)
-#82 := (not #79)
-#13 := 2::Int
-#14 := (- 2::Int)
-#10 := 3::Int
-#11 := (- 3::Int)
-#8 := 5::Int
-#9 := (- 5::Int)
-#12 := (f3 #9 #11)
-#15 := (= #12 #14)
-#16 := (not #15)
-#83 := (iff #16 #82)
-#80 := (iff #15 #79)
-#77 := (= #14 -2::Int)
-#78 := [rewrite]: #77
-#74 := (= #12 #73)
-#71 := (= #11 -3::Int)
-#72 := [rewrite]: #71
-#68 := (= #9 -5::Int)
-#69 := [rewrite]: #68
-#75 := [monotonicity #69 #72]: #74
-#81 := [monotonicity #75 #78]: #80
-#84 := [monotonicity #81]: #83
-#66 := [asserted]: #16
-#87 := [mp #66 #84]: #82
-#667 := (not #757)
-#668 := (or #667 #79)
-#335 := (* -1::Int -3::Int)
-#420 := (* -1::Int -5::Int)
-#421 := (mod #420 #335)
-#422 := (+ #73 #421)
-#413 := (= #422 0::Int)
-#424 := (mod -5::Int -3::Int)
-#425 := (* -1::Int #424)
-#353 := (+ #73 #425)
-#426 := (= #353 0::Int)
-#423 := (>= -5::Int 0::Int)
-#427 := (<= -3::Int 0::Int)
-#406 := (or #427 #423)
-#741 := (not #406)
-#743 := (<= -5::Int 0::Int)
-#400 := (or #743 #427)
-#530 := (not #400)
-#737 := (or #530 #741)
-#411 := (ite #737 #426 #413)
-#412 := (= #73 0::Int)
-#744 := (= -5::Int 0::Int)
-#745 := (ite #744 #412 #411)
-#746 := (= -5::Int #73)
-#747 := (= -3::Int 0::Int)
-#742 := (ite #747 #746 #745)
-#669 := (or #667 #742)
-#670 := (iff #669 #668)
-#655 := (iff #668 #668)
-#657 := [rewrite]: #655
-#677 := (iff #742 #79)
-#403 := (= #73 -5::Int)
-#664 := (ite false #403 #79)
-#676 := (iff #664 #79)
-#672 := [rewrite]: #676
-#674 := (iff #742 #664)
-#665 := (iff #745 #79)
-#683 := (ite false #412 #79)
-#671 := (iff #683 #79)
-#673 := [rewrite]: #671
-#680 := (iff #745 #683)
-#589 := (iff #411 #79)
-#433 := 1::Int
-#694 := (= #73 1::Int)
-#585 := (ite false #694 #79)
-#587 := (iff #585 #79)
-#588 := [rewrite]: #587
-#578 := (iff #411 #585)
-#582 := (iff #413 #79)
-#572 := (+ 2::Int #73)
-#583 := (= #572 0::Int)
-#682 := (iff #583 #79)
-#567 := [rewrite]: #682
-#678 := (iff #413 #583)
-#533 := (= #422 #572)
-#689 := (+ #73 2::Int)
-#573 := (= #689 #572)
-#574 := [rewrite]: #573
-#687 := (= #422 #689)
-#686 := (= #421 2::Int)
-#700 := (mod 5::Int 3::Int)
-#532 := (= #700 2::Int)
-#685 := [rewrite]: #532
-#529 := (= #421 #700)
-#699 := (= #335 3::Int)
-#693 := [rewrite]: #699
-#692 := (= #420 5::Int)
-#698 := [rewrite]: #692
-#531 := [monotonicity #698 #693]: #529
-#688 := [trans #531 #685]: #686
-#690 := [monotonicity #688]: #687
-#681 := [trans #690 #574]: #533
-#679 := [monotonicity #681]: #678
-#584 := [trans #679 #567]: #582
-#697 := (iff #426 #694)
-#702 := (+ -1::Int #73)
-#550 := (= #702 0::Int)
-#695 := (iff #550 #694)
-#696 := [rewrite]: #695
-#551 := (iff #426 #550)
-#703 := (= #353 #702)
-#705 := (+ #73 -1::Int)
-#707 := (= #705 #702)
-#708 := [rewrite]: #707
-#706 := (= #353 #705)
-#715 := (= #425 -1::Int)
-#713 := (* -1::Int 1::Int)
-#714 := (= #713 -1::Int)
-#711 := [rewrite]: #714
-#428 := (= #425 #713)
-#434 := (= #424 1::Int)
-#712 := [rewrite]: #434
-#710 := [monotonicity #712]: #428
-#704 := [trans #710 #711]: #715
-#701 := [monotonicity #704]: #706
-#709 := [trans #701 #708]: #703
-#552 := [monotonicity #709]: #551
-#691 := [trans #552 #696]: #697
-#431 := (iff #737 false)
-#442 := (or false false)
-#717 := (iff #442 false)
-#721 := [rewrite]: #717
-#716 := (iff #737 #442)
-#719 := (iff #741 false)
-#1 := true
-#725 := (not true)
-#732 := (iff #725 false)
-#734 := [rewrite]: #732
-#341 := (iff #741 #725)
-#447 := (iff #406 true)
-#736 := (or true false)
-#445 := (iff #736 true)
-#446 := [rewrite]: #445
-#722 := (iff #406 #736)
-#735 := (iff #423 false)
-#733 := [rewrite]: #735
-#387 := (iff #427 true)
-#388 := [rewrite]: #387
-#723 := [monotonicity #388 #733]: #722
-#448 := [trans #723 #446]: #447
-#718 := [monotonicity #448]: #341
-#441 := [trans #718 #734]: #719
-#374 := (iff #530 false)
-#731 := (iff #530 #725)
-#729 := (iff #400 true)
-#389 := (or true true)
-#727 := (iff #389 true)
-#728 := [rewrite]: #727
-#390 := (iff #400 #389)
-#383 := (iff #743 true)
-#724 := [rewrite]: #383
-#726 := [monotonicity #724 #388]: #390
-#730 := [trans #726 #728]: #729
-#369 := [monotonicity #730]: #731
-#375 := [trans #369 #734]: #374
-#720 := [monotonicity #375 #441]: #716
-#432 := [trans #720 #721]: #431
-#586 := [monotonicity #432 #691 #584]: #578
-#590 := [trans #586 #588]: #589
-#399 := (iff #744 false)
-#740 := [rewrite]: #399
-#684 := [monotonicity #740 #590]: #680
-#662 := [trans #684 #673]: #665
-#398 := (iff #746 #403)
-#739 := [rewrite]: #398
-#748 := (iff #747 false)
-#738 := [rewrite]: #748
-#675 := [monotonicity #738 #739 #662]: #674
-#666 := [trans #675 #672]: #677
-#654 := [monotonicity #666]: #670
-#658 := [trans #654 #657]: #670
-#663 := [quant-inst #67 #70]: #669
-#659 := [mp #663 #658]: #668
-[unit-resolution #659 #87 #762]: false
-unsat
-0c710ae5525793136d2145b7da68378d3667fa91 322 0
-#2 := false
-#16 := 0::Int
-decl f4 :: Int
-#8 := f4
-#412 := (>= f4 0::Int)
-#732 := (<= f4 0::Int)
-#378 := (not #732)
-#721 := (not #412)
-#725 := (or #721 #378)
-#688 := (not #725)
-#9 := 3::Int
-#413 := (mod f4 3::Int)
-#82 := -1::Int
-#414 := (* -1::Int #413)
-decl f3 :: (-> Int Int Int)
-#10 := (f3 f4 3::Int)
-#342 := (+ #10 #414)
-#415 := (= #342 0::Int)
-#561 := (not #415)
-#518 := (<= #342 0::Int)
-#621 := (not #518)
-#629 := (>= #413 3::Int)
-#630 := (not #629)
-#1 := true
-#60 := [true-axiom]: true
-#617 := (or false #630)
-#618 := [th-lemma arith]: #617
-#619 := [unit-resolution #618 #60]: #630
-#620 := [hypothesis]: #518
-#67 := (>= #10 3::Int)
-#11 := (< #10 3::Int)
-#12 := (not #11)
-#74 := (iff #12 #67)
-#65 := (not #67)
-#69 := (not #65)
-#72 := (iff #69 #67)
-#73 := [rewrite]: #72
-#70 := (iff #12 #69)
-#66 := (iff #11 #65)
-#68 := [rewrite]: #66
-#71 := [monotonicity #68]: #70
-#75 := [trans #71 #73]: #74
-#62 := [asserted]: #12
-#76 := [mp #62 #75]: #67
-#615 := [th-lemma arith farkas -1 1 1 #76 #620 #619]: false
-#607 := [lemma #615]: #621
-#624 := (or #561 #518)
-#635 := [th-lemma arith triangle-eq]: #624
-#613 := [unit-resolution #635 #607]: #561
-#612 := (or #688 #415)
-#436 := -3::Int
-#409 := (* -1::Int f4)
-#707 := (mod #409 -3::Int)
-#431 := (+ #10 #707)
-#706 := (= #431 0::Int)
-#421 := (ite #725 #415 #706)
-#401 := (= #10 0::Int)
-#733 := (= f4 0::Int)
-#701 := (ite #733 #401 #421)
-#14 := (:var 0 Int)
-#13 := (:var 1 Int)
-#34 := (f3 #13 #14)
-#745 := (pattern #34)
-#86 := (* -1::Int #14)
-#83 := (* -1::Int #13)
-#141 := (mod #83 #86)
-#256 := (+ #34 #141)
-#257 := (= #256 0::Int)
-#35 := (mod #13 #14)
-#253 := (* -1::Int #35)
-#254 := (+ #34 #253)
-#255 := (= #254 0::Int)
-#115 := (>= #13 0::Int)
-#108 := (<= #14 0::Int)
-#200 := (or #108 #115)
-#201 := (not #200)
-#104 := (<= #13 0::Int)
-#198 := (or #104 #108)
-#199 := (not #198)
-#204 := (or #199 #201)
-#258 := (ite #204 #255 #257)
-#252 := (= #34 0::Int)
-#17 := (= #13 0::Int)
-#259 := (ite #17 #252 #258)
-#251 := (= #13 #34)
-#18 := (= #14 0::Int)
-#260 := (ite #18 #251 #259)
-#746 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #745) #260)
-#263 := (forall (vars (?v0 Int) (?v1 Int)) #260)
-#749 := (iff #263 #746)
-#747 := (iff #260 #260)
-#748 := [refl]: #747
-#750 := [quant-intro #748]: #749
-#147 := (* -1::Int #141)
-#220 := (ite #204 #35 #147)
-#223 := (ite #17 0::Int #220)
-#226 := (ite #18 #13 #223)
-#229 := (= #34 #226)
-#232 := (forall (vars (?v0 Int) (?v1 Int)) #229)
-#264 := (iff #232 #263)
-#261 := (iff #229 #260)
-#262 := [rewrite]: #261
-#265 := [quant-intro #262]: #264
-#116 := (not #115)
-#109 := (not #108)
-#119 := (and #109 #116)
-#105 := (not #104)
-#112 := (and #105 #109)
-#122 := (or #112 #119)
-#167 := (ite #122 #35 #147)
-#170 := (ite #17 0::Int #167)
-#173 := (ite #18 #13 #170)
-#176 := (= #34 #173)
-#179 := (forall (vars (?v0 Int) (?v1 Int)) #176)
-#233 := (iff #179 #232)
-#230 := (iff #176 #229)
-#227 := (= #173 #226)
-#224 := (= #170 #223)
-#221 := (= #167 #220)
-#205 := (iff #122 #204)
-#202 := (iff #119 #201)
-#203 := [rewrite]: #202
-#192 := (iff #112 #199)
-#193 := [rewrite]: #192
-#206 := [monotonicity #193 #203]: #205
-#222 := [monotonicity #206]: #221
-#225 := [monotonicity #222]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [quant-intro #231]: #233
-#190 := (~ #179 #179)
-#189 := (~ #176 #176)
-#186 := [refl]: #189
-#191 := [nnf-pos #186]: #190
-#28 := (- #14)
-#27 := (- #13)
-#36 := (mod #27 #28)
-#37 := (- #36)
-#21 := (< 0::Int #14)
-#23 := (< #13 0::Int)
-#24 := (and #23 #21)
-#20 := (< 0::Int #13)
-#22 := (and #20 #21)
-#25 := (or #22 #24)
-#38 := (ite #25 #35 #37)
-#39 := (ite #17 0::Int #38)
-#40 := (ite #18 #13 #39)
-#41 := (= #34 #40)
-#42 := (forall (vars (?v0 Int) (?v1 Int)) #41)
-#182 := (iff #42 #179)
-#64 := (and #21 #23)
-#79 := (or #22 #64)
-#152 := (ite #79 #35 #147)
-#155 := (ite #17 0::Int #152)
-#158 := (ite #18 #13 #155)
-#161 := (= #34 #158)
-#164 := (forall (vars (?v0 Int) (?v1 Int)) #161)
-#180 := (iff #164 #179)
-#177 := (iff #161 #176)
-#174 := (= #158 #173)
-#171 := (= #155 #170)
-#168 := (= #152 #167)
-#123 := (iff #79 #122)
-#120 := (iff #64 #119)
-#117 := (iff #23 #116)
-#118 := [rewrite]: #117
-#110 := (iff #21 #109)
-#111 := [rewrite]: #110
-#121 := [monotonicity #111 #118]: #120
-#113 := (iff #22 #112)
-#106 := (iff #20 #105)
-#107 := [rewrite]: #106
-#114 := [monotonicity #107 #111]: #113
-#124 := [monotonicity #114 #121]: #123
-#169 := [monotonicity #124]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [quant-intro #178]: #180
-#165 := (iff #42 #164)
-#162 := (iff #41 #161)
-#159 := (= #40 #158)
-#156 := (= #39 #155)
-#153 := (= #38 #152)
-#150 := (= #37 #147)
-#144 := (- #141)
-#148 := (= #144 #147)
+#108 := [monotonicity #70 #94 #105]: #107
+#111 := [monotonicity #108]: #110
+#117 := [trans #111 #115]: #116
+#56 := (iff #12 false)
+#57 := [rewrite]: #56
+#120 := [monotonicity #57 #117]: #119
+#124 := [trans #120 #122]: #123
+#91 := (= #26 #83)
+#86 := (* #83 1::Int)
+#89 := (= #86 #83)
+#90 := [rewrite]: #89
+#87 := (= #26 #86)
+#84 := (= #25 #83)
+#81 := (= #24 #80)
+#78 := (= #23 #77)
+#79 := [monotonicity #74 #76]: #78
+#82 := [monotonicity #70 #79]: #81
+#63 := (iff #13 #10)
+#58 := (or #10 false)
+#61 := (iff #58 #10)
+#62 := [rewrite]: #61
+#59 := (iff #13 #58)
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#85 := [monotonicity #64 #82]: #84
+#88 := [monotonicity #85]: #87
+#92 := [trans #88 #90]: #91
+#127 := [monotonicity #92 #124]: #126
+#130 := [monotonicity #127]: #129
+#133 := [monotonicity #130]: #132
+#197 := [trans #133 #195]: #196
+#55 := [asserted]: #35
+#198 := [mp #55 #197]: #193
+#342 := (or #188 #340 #341)
+#343 := [th-lemma arith triangle-eq]: #342
+#345 := [unit-resolution #343 #198]: #344
+#346 := [unit-resolution #345 #339 #324]: false
+#347 := [lemma #346]: #134
+#363 := [th-lemma arith triangle-eq]: #170
+#379 := [unit-resolution #363 #347]: #378
+#380 := [unit-resolution #379 #377 #376]: false
+#381 := [lemma #380]: #170
+#390 := [unit-resolution #232 #381]: #220
+#391 := [unit-resolution #310 #390]: #288
+#382 := (<= #164 0::Int)
+#204 := (= #164 0::Int)
+#383 := [hypothesis]: #147
+#384 := [unit-resolution #379 #383]: #10
+#216 := (or #215 #204)
+#217 := [def-axiom]: #216
+#385 := [unit-resolution #217 #384]: #204
+#355 := (not #204)
+#386 := (or #355 #382)
+#387 := [th-lemma arith triangle-eq]: #386
+#388 := [unit-resolution #387 #385]: #382
+#359 := [hypothesis]: #340
+#361 := (or #215 #235)
+#350 := [hypothesis]: #10
+#351 := [unit-resolution #223 #350]: #170
+#352 := [unit-resolution #232 #351]: #220
+#353 := [unit-resolution #329 #352]: #289
+#349 := (>= #164 0::Int)
+#354 := [unit-resolution #217 #350]: #204
+#356 := (or #355 #349)
+#357 := [th-lemma arith triangle-eq]: #356
+#358 := [unit-resolution #357 #354]: #349
+#360 := [th-lemma arith farkas 1 1 -1 1 #359 #358 #347 #353]: false
+#362 := [lemma #360]: #361
+#348 := [unit-resolution #362 #359]: #215
+#364 := [unit-resolution #363 #348 #347]: #148
+#365 := [unit-resolution #227 #364]: #170
+#366 := [unit-resolution #232 #365]: #220
+#367 := [unit-resolution #329 #366]: #289
+#368 := [unit-resolution #219 #348]: #205
+#200 := (or #158 #147)
+#201 := [def-axiom]: #200
+#369 := [unit-resolution #201 #364]: #158
+#370 := [unit-resolution #212 #369]: #206
+#371 := [trans #370 #368]: #290
+#372 := [unit-resolution #326 #371]: #292
+#373 := [unit-resolution #338 #333 #372 #359 #367]: false
+#374 := [lemma #373]: #235
+#389 := [unit-resolution #345 #374]: #341
+#392 := [th-lemma arith farkas 1 1 -1 1 #391 #389 #383 #388]: false
+#393 := [lemma #392]: #148
+#394 := (or #215 #147)
+#395 := [th-lemma arith triangle-eq]: #394
+#396 := [unit-resolution #395 #393]: #215
+#397 := [unit-resolution #219 #396]: #205
+#398 := [unit-resolution #201 #393]: #158
+#399 := [unit-resolution #212 #398]: #206
+#400 := [trans #399 #397]: #290
+#401 := [unit-resolution #304 #400]: #293
+#402 := (or #319 #320 #321)
+#403 := [unit-resolution #323 #389]: #402
+[unit-resolution #403 #318 #401 #391]: false
+unsat
+31fe1e25557ea7df409ade184e44a23cd64eda4c 308 0
+#2 := false
+#9 := 0::Int
+#75 := -3::Int
+decl f3 :: Int
+#8 := f3
+#71 := -1::Int
+#72 := (* -1::Int f3)
+#95 := (mod #72 -3::Int)
+#101 := (* -1::Int #95)
+#11 := 3::Int
+#27 := (mod f3 3::Int)
+#141 := (>= f3 0::Int)
+#142 := (not #141)
+#128 := (<= f3 0::Int)
+#129 := (not #128)
+#152 := (or #129 #142)
+#164 := (ite #152 #27 #101)
+#10 := (= f3 0::Int)
+#167 := (ite #10 0::Int #164)
+#177 := (* -1::Int #167)
+#321 := (+ #27 #177)
+#358 := (>= #321 0::Int)
+#320 := (= #27 #167)
+#213 := (= #164 #167)
+#207 := (not #10)
+#78 := (div #72 -3::Int)
+#20 := (div f3 3::Int)
+#155 := (ite #152 #20 #78)
+#158 := (ite #10 0::Int #155)
+#176 := (* -3::Int #158)
+#178 := (+ #176 #177)
+#179 := (+ f3 #178)
+#225 := (>= #179 0::Int)
+#228 := (<= #167 0::Int)
+#212 := (= #167 0::Int)
+#200 := (not #152)
+#230 := [hypothesis]: #200
+#192 := (or #152 #141)
+#193 := [def-axiom]: #192
+#231 := [unit-resolution #193 #230]: #141
+#194 := (or #152 #128)
+#195 := [def-axiom]: #194
+#232 := [unit-resolution #195 #230]: #128
+#233 := (or #10 #129 #142)
+#234 := [th-lemma arith triangle-eq]: #233
+#235 := [unit-resolution #234 #232 #231]: #10
+#220 := (or #207 #212)
+#221 := [def-axiom]: #220
+#236 := [unit-resolution #221 #235]: #212
+#237 := (not #212)
+#238 := (or #237 #228)
+#239 := [th-lemma arith triangle-eq]: #238
+#240 := [unit-resolution #239 #236]: #228
+#226 := (<= #158 0::Int)
+#196 := (= #158 0::Int)
+#208 := (or #207 #196)
+#209 := [def-axiom]: #208
+#241 := [unit-resolution #209 #235]: #196
+#242 := (not #196)
+#243 := (or #242 #226)
+#244 := [th-lemma arith triangle-eq]: #243
+#245 := [unit-resolution #244 #241]: #226
+#247 := (not #228)
+#246 := (not #226)
+#248 := (or #225 #142 #246 #247)
+#249 := [th-lemma arith assign-bounds -1 3 1]: #248
+#250 := [unit-resolution #249 #231 #245 #240]: #225
+#224 := (<= #179 0::Int)
+#229 := (>= #167 0::Int)
+#251 := (or #237 #229)
+#252 := [th-lemma arith triangle-eq]: #251
+#253 := [unit-resolution #252 #236]: #229
+#227 := (>= #158 0::Int)
+#254 := (or #242 #227)
+#255 := [th-lemma arith triangle-eq]: #254
+#256 := [unit-resolution #255 #241]: #227
+#258 := (not #229)
+#257 := (not #227)
+#259 := (or #224 #129 #257 #258)
+#260 := [th-lemma arith assign-bounds -1 3 1]: #259
+#261 := [unit-resolution #260 #232 #256 #253]: #224
+#263 := (not #225)
+#262 := (not #224)
+#266 := (or #262 #263)
+#180 := (= #179 0::Int)
+#185 := (not #180)
+#22 := (- 3::Int)
+#21 := (- f3)
+#28 := (mod #21 #22)
+#29 := (- #28)
+#15 := (< 0::Int 3::Int)
+#17 := (< f3 0::Int)
+#18 := (and #17 #15)
+#14 := (< 0::Int f3)
+#16 := (and #14 #15)
+#19 := (or #16 #18)
+#30 := (ite #19 #27 #29)
+#31 := (ite #10 0::Int #30)
+#12 := (= 3::Int 0::Int)
+#32 := (ite #12 f3 #31)
+#23 := (div #21 #22)
+#24 := (ite #19 #20 #23)
+#13 := (or #10 #12)
+#25 := (ite #13 0::Int #24)
+#26 := (* #25 3::Int)
+#33 := (+ #26 #32)
+#34 := (= f3 #33)
+#35 := (not #34)
+#188 := (iff #35 #185)
+#65 := (and #15 #17)
+#68 := (or #16 #65)
+#106 := (ite #68 #27 #101)
+#109 := (ite #10 0::Int #106)
+#81 := (ite #68 #20 #78)
+#84 := (ite #10 0::Int #81)
+#90 := (* 3::Int #84)
+#119 := (+ #90 #109)
+#122 := (= f3 #119)
+#125 := (not #122)
+#186 := (iff #125 #185)
+#183 := (iff #122 #180)
+#161 := (* 3::Int #158)
+#170 := (+ #161 #167)
+#173 := (= f3 #170)
+#181 := (iff #173 #180)
+#182 := [rewrite]: #181
+#174 := (iff #122 #173)
+#171 := (= #119 #170)
+#168 := (= #109 #167)
+#165 := (= #106 #164)
+#153 := (iff #68 #152)
+#150 := (iff #65 #142)
+#1 := true
+#145 := (and true #142)
+#148 := (iff #145 #142)
 #149 := [rewrite]: #148
-#145 := (= #37 #144)
-#142 := (= #36 #141)
-#87 := (= #28 #86)
-#88 := [rewrite]: #87
-#84 := (= #27 #83)
-#85 := [rewrite]: #84
-#143 := [monotonicity #85 #88]: #142
-#146 := [monotonicity #143]: #145
-#151 := [trans #146 #149]: #150
-#80 := (iff #25 #79)
-#77 := (iff #24 #64)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#154 := [monotonicity #81 #151]: #153
+#146 := (iff #65 #145)
+#143 := (iff #17 #142)
+#144 := [rewrite]: #143
+#132 := (iff #15 true)
+#133 := [rewrite]: #132
+#147 := [monotonicity #133 #144]: #146
+#151 := [trans #147 #149]: #150
+#139 := (iff #16 #129)
+#134 := (and #129 true)
+#137 := (iff #134 #129)
+#138 := [rewrite]: #137
+#135 := (iff #16 #134)
+#130 := (iff #14 #129)
+#131 := [rewrite]: #130
+#136 := [monotonicity #131 #133]: #135
+#140 := [trans #136 #138]: #139
+#154 := [monotonicity #140 #151]: #153
+#166 := [monotonicity #154]: #165
+#169 := [monotonicity #166]: #168
+#162 := (= #90 #161)
+#159 := (= #84 #158)
+#156 := (= #81 #155)
 #157 := [monotonicity #154]: #156
 #160 := [monotonicity #157]: #159
 #163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#183 := [trans #166 #181]: #182
-#140 := [asserted]: #42
-#184 := [mp #140 #183]: #179
-#187 := [mp~ #184 #191]: #179
-#235 := [mp #187 #234]: #232
-#266 := [mp #235 #265]: #263
-#751 := [mp #266 #750]: #746
-#690 := (not #746)
-#691 := (or #690 #701)
-#324 := (* -1::Int 3::Int)
-#410 := (mod #409 #324)
-#411 := (+ #10 #410)
-#402 := (= #411 0::Int)
-#416 := (<= 3::Int 0::Int)
-#395 := (or #416 #412)
-#730 := (not #395)
-#389 := (or #732 #416)
-#519 := (not #389)
-#726 := (or #519 #730)
-#400 := (ite #726 #415 #402)
-#734 := (ite #733 #401 #400)
-#735 := (= f4 #10)
-#736 := (= 3::Int 0::Int)
-#731 := (ite #736 #735 #734)
-#696 := (or #690 #731)
-#692 := (iff #696 #691)
-#539 := (iff #691 #691)
-#540 := [rewrite]: #539
-#694 := (iff #731 #701)
-#699 := (ite false #735 #701)
-#704 := (iff #699 #701)
-#693 := [rewrite]: #704
-#703 := (iff #731 #699)
-#702 := (iff #734 #701)
-#422 := (iff #400 #421)
-#710 := (iff #402 #706)
-#705 := (= #411 #431)
-#708 := (= #410 #707)
-#437 := (= #324 -3::Int)
-#330 := [rewrite]: #437
-#430 := [monotonicity #330]: #708
-#709 := [monotonicity #430]: #705
-#420 := [monotonicity #709]: #710
-#434 := (iff #726 #725)
-#364 := (or #378 #721)
-#711 := (iff #364 #725)
-#712 := [rewrite]: #711
-#724 := (iff #726 #364)
-#723 := (iff #730 #721)
-#720 := (iff #395 #412)
-#716 := (or false #412)
-#719 := (iff #716 #412)
-#714 := [rewrite]: #719
-#717 := (iff #395 #716)
-#387 := (iff #416 false)
-#392 := [rewrite]: #387
-#718 := [monotonicity #392]: #717
-#358 := [trans #718 #714]: #720
-#363 := [monotonicity #358]: #723
-#379 := (iff #519 #378)
-#376 := (iff #389 #732)
-#728 := (or #732 false)
-#372 := (iff #728 #732)
-#713 := [rewrite]: #372
-#388 := (iff #389 #728)
-#729 := [monotonicity #392]: #388
-#377 := [trans #729 #713]: #376
-#715 := [monotonicity #377]: #379
-#722 := [monotonicity #715 #363]: #724
-#435 := [trans #722 #712]: #434
-#423 := [monotonicity #435 #420]: #422
-#417 := [monotonicity #423]: #702
-#737 := (iff #736 false)
-#727 := [rewrite]: #737
-#700 := [monotonicity #727 #417]: #703
-#695 := [trans #700 #693]: #694
-#698 := [monotonicity #695]: #692
-#541 := [trans #698 #540]: #692
-#697 := [quant-inst #8 #9]: #696
-#683 := [mp #697 #541]: #691
-#614 := [unit-resolution #683 #751]: #701
-#668 := (not #733)
-#667 := (not #701)
-#609 := (or #667 #668)
-#574 := (not #401)
-#684 := (<= #10 0::Int)
-#616 := (not #684)
-#646 := (or #616 #65)
-#647 := [th-lemma arith farkas 1 1]: #646
-#603 := [unit-resolution #647 #76]: #616
-#604 := (or #574 #684)
-#605 := [th-lemma arith triangle-eq]: #604
-#608 := [unit-resolution #605 #603]: #574
-#671 := (or #667 #668 #401)
-#556 := [def-axiom]: #671
-#610 := [unit-resolution #556 #608]: #609
-#611 := [unit-resolution #610 #614]: #668
-#571 := (or #667 #733 #421)
-#573 := [def-axiom]: #571
-#606 := [unit-resolution #573 #611 #614]: #421
-#675 := (not #421)
-#677 := (or #675 #688 #415)
-#678 := [def-axiom]: #677
-#585 := [unit-resolution #678 #606]: #612
-#586 := [unit-resolution #585 #613]: #688
-#686 := (or #725 #412)
-#680 := [def-axiom]: #686
-#587 := [unit-resolution #680 #586]: #412
-#681 := (or #725 #732)
-#687 := [def-axiom]: #681
-#480 := [unit-resolution #687 #586]: #732
-#591 := (or #733 #378 #721)
-#592 := [th-lemma arith triangle-eq]: #591
-#593 := [unit-resolution #592 #611]: #364
-[unit-resolution #593 #480 #587]: false
-unsat
-8e1905429e143174e0fcdce59027187ea0e3224c 340 0
-#2 := false
-#9 := 3::Int
-decl f3 :: (-> Int Int Int)
-decl f4 :: Int
-#8 := f4
-#10 := (f3 f4 3::Int)
-#439 := (mod #10 3::Int)
-#655 := (>= #439 3::Int)
-#656 := (not #655)
-#1 := true
-#62 := [true-axiom]: true
-#645 := (or false #656)
-#640 := [th-lemma arith]: #645
-#646 := [unit-resolution #640 #62]: #656
-#18 := 0::Int
-#107 := -1::Int
-#434 := (* -1::Int #10)
-#598 := (+ f4 #434)
-#599 := (<= #598 0::Int)
-#65 := (= f4 #10)
-#82 := (>= f4 3::Int)
-#80 := (not #82)
-#71 := (not #65)
-#87 := (or #71 #80)
-#92 := (not #87)
-#12 := (< f4 3::Int)
-#11 := (= #10 f4)
-#13 := (implies #11 #12)
-#14 := (not #13)
-#95 := (iff #14 #92)
-#72 := (or #12 #71)
-#77 := (not #72)
-#93 := (iff #77 #92)
-#90 := (iff #72 #87)
-#84 := (or #80 #71)
-#88 := (iff #84 #87)
-#89 := [rewrite]: #88
-#85 := (iff #72 #84)
-#81 := (iff #12 #80)
-#83 := [rewrite]: #81
-#86 := [monotonicity #83]: #85
-#91 := [trans #86 #89]: #90
-#94 := [monotonicity #91]: #93
-#78 := (iff #14 #77)
-#75 := (iff #13 #72)
-#68 := (implies #65 #12)
-#73 := (iff #68 #72)
+#172 := [monotonicity #163 #169]: #171
+#175 := [monotonicity #172]: #174
+#184 := [trans #175 #182]: #183
+#187 := [monotonicity #184]: #186
+#126 := (iff #35 #125)
+#123 := (iff #34 #122)
+#120 := (= #33 #119)
+#117 := (= #32 #109)
+#112 := (ite false f3 #109)
+#115 := (= #112 #109)
+#116 := [rewrite]: #115
+#113 := (= #32 #112)
+#110 := (= #31 #109)
+#107 := (= #30 #106)
+#104 := (= #29 #101)
+#98 := (- #95)
+#102 := (= #98 #101)
+#103 := [rewrite]: #102
+#99 := (= #29 #98)
+#96 := (= #28 #95)
+#76 := (= #22 -3::Int)
+#77 := [rewrite]: #76
+#73 := (= #21 #72)
 #74 := [rewrite]: #73
-#69 := (iff #13 #68)
-#66 := (iff #11 #65)
+#97 := [monotonicity #74 #77]: #96
+#100 := [monotonicity #97]: #99
+#105 := [trans #100 #103]: #104
+#69 := (iff #19 #68)
+#66 := (iff #18 #65)
 #67 := [rewrite]: #66
 #70 := [monotonicity #67]: #69
-#76 := [trans #70 #74]: #75
-#79 := [monotonicity #76]: #78
-#96 := [trans #79 #94]: #95
-#64 := [asserted]: #14
-#97 := [mp #64 #96]: #92
-#98 := [not-or-elim #97]: #65
-#632 := (or #71 #599)
-#628 := [th-lemma arith triangle-eq]: #632
-#629 := [unit-resolution #628 #98]: #599
-#99 := [not-or-elim #97]: #82
-#436 := (f3 #10 3::Int)
-#600 := (* -1::Int #436)
-#601 := (+ #10 #600)
-#602 := (<= #601 0::Int)
-#761 := (= #10 #436)
-#633 := (= #436 #10)
-#630 := [symm #98]: #11
-#634 := [monotonicity #630]: #633
-#635 := [symm #634]: #761
-#636 := (not #761)
-#631 := (or #636 #602)
-#637 := [th-lemma arith triangle-eq]: #631
-#610 := [unit-resolution #637 #635]: #602
-#367 := (* -1::Int #439)
-#440 := (+ #436 #367)
-#705 := (<= #440 0::Int)
-#437 := (= #440 0::Int)
-#736 := -3::Int
-#460 := (mod #434 -3::Int)
-#355 := (+ #436 #460)
-#455 := (= #355 0::Int)
-#441 := (>= #10 0::Int)
-#748 := (not #441)
-#414 := (<= #10 0::Int)
-#404 := (not #414)
-#749 := (or #404 #748)
-#734 := (ite #749 #437 #455)
-#758 := (= #436 0::Int)
-#759 := (= #10 0::Int)
-#445 := (ite #759 #758 #734)
-#16 := (:var 0 Int)
-#15 := (:var 1 Int)
-#36 := (f3 #15 #16)
-#770 := (pattern #36)
-#111 := (* -1::Int #16)
-#108 := (* -1::Int #15)
-#166 := (mod #108 #111)
-#281 := (+ #36 #166)
-#282 := (= #281 0::Int)
-#37 := (mod #15 #16)
-#278 := (* -1::Int #37)
-#279 := (+ #36 #278)
-#280 := (= #279 0::Int)
-#140 := (>= #15 0::Int)
-#133 := (<= #16 0::Int)
-#225 := (or #133 #140)
-#226 := (not #225)
-#129 := (<= #15 0::Int)
-#211 := (or #129 #133)
-#212 := (not #211)
-#229 := (or #212 #226)
-#283 := (ite #229 #280 #282)
-#277 := (= #36 0::Int)
-#19 := (= #15 0::Int)
-#284 := (ite #19 #277 #283)
-#276 := (= #15 #36)
-#20 := (= #16 0::Int)
-#285 := (ite #20 #276 #284)
-#771 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #770) #285)
-#288 := (forall (vars (?v0 Int) (?v1 Int)) #285)
-#774 := (iff #288 #771)
-#772 := (iff #285 #285)
-#773 := [refl]: #772
-#775 := [quant-intro #773]: #774
-#172 := (* -1::Int #166)
-#245 := (ite #229 #37 #172)
-#248 := (ite #19 0::Int #245)
-#251 := (ite #20 #15 #248)
-#254 := (= #36 #251)
-#257 := (forall (vars (?v0 Int) (?v1 Int)) #254)
-#289 := (iff #257 #288)
-#286 := (iff #254 #285)
-#287 := [rewrite]: #286
-#290 := [quant-intro #287]: #289
-#141 := (not #140)
-#134 := (not #133)
-#144 := (and #134 #141)
-#130 := (not #129)
-#137 := (and #130 #134)
-#147 := (or #137 #144)
-#192 := (ite #147 #37 #172)
-#195 := (ite #19 0::Int #192)
-#198 := (ite #20 #15 #195)
-#201 := (= #36 #198)
-#204 := (forall (vars (?v0 Int) (?v1 Int)) #201)
-#258 := (iff #204 #257)
-#255 := (iff #201 #254)
-#252 := (= #198 #251)
-#249 := (= #195 #248)
-#246 := (= #192 #245)
-#230 := (iff #147 #229)
-#227 := (iff #144 #226)
-#228 := [rewrite]: #227
-#219 := (iff #137 #212)
-#220 := [rewrite]: #219
-#231 := [monotonicity #220 #228]: #230
-#247 := [monotonicity #231]: #246
-#250 := [monotonicity #247]: #249
-#253 := [monotonicity #250]: #252
-#256 := [monotonicity #253]: #255
-#259 := [quant-intro #256]: #258
-#217 := (~ #204 #204)
-#216 := (~ #201 #201)
-#213 := [refl]: #216
-#218 := [nnf-pos #213]: #217
-#30 := (- #16)
-#29 := (- #15)
-#38 := (mod #29 #30)
-#39 := (- #38)
-#23 := (< 0::Int #16)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#40 := (ite #27 #37 #39)
-#41 := (ite #19 0::Int #40)
-#42 := (ite #20 #15 #41)
-#43 := (= #36 #42)
-#44 := (forall (vars (?v0 Int) (?v1 Int)) #43)
-#207 := (iff #44 #204)
-#101 := (and #23 #25)
-#104 := (or #24 #101)
-#177 := (ite #104 #37 #172)
-#180 := (ite #19 0::Int #177)
-#183 := (ite #20 #15 #180)
-#186 := (= #36 #183)
-#189 := (forall (vars (?v0 Int) (?v1 Int)) #186)
-#205 := (iff #189 #204)
-#202 := (iff #186 #201)
-#199 := (= #183 #198)
-#196 := (= #180 #195)
-#193 := (= #177 #192)
-#148 := (iff #104 #147)
-#145 := (iff #101 #144)
-#142 := (iff #25 #141)
-#143 := [rewrite]: #142
-#135 := (iff #23 #134)
-#136 := [rewrite]: #135
-#146 := [monotonicity #136 #143]: #145
-#138 := (iff #24 #137)
-#131 := (iff #22 #130)
-#132 := [rewrite]: #131
-#139 := [monotonicity #132 #136]: #138
-#149 := [monotonicity #139 #146]: #148
-#194 := [monotonicity #149]: #193
-#197 := [monotonicity #194]: #196
-#200 := [monotonicity #197]: #199
-#203 := [monotonicity #200]: #202
-#206 := [quant-intro #203]: #205
-#190 := (iff #44 #189)
-#187 := (iff #43 #186)
-#184 := (= #42 #183)
-#181 := (= #41 #180)
-#178 := (= #40 #177)
-#175 := (= #39 #172)
-#169 := (- #166)
-#173 := (= #169 #172)
-#174 := [rewrite]: #173
-#170 := (= #39 #169)
-#167 := (= #38 #166)
-#112 := (= #30 #111)
-#113 := [rewrite]: #112
-#109 := (= #29 #108)
-#110 := [rewrite]: #109
-#168 := [monotonicity #110 #113]: #167
-#171 := [monotonicity #168]: #170
-#176 := [trans #171 #174]: #175
-#105 := (iff #27 #104)
-#102 := (iff #26 #101)
-#103 := [rewrite]: #102
-#106 := [monotonicity #103]: #105
-#179 := [monotonicity #106 #176]: #178
-#182 := [monotonicity #179]: #181
-#185 := [monotonicity #182]: #184
-#188 := [monotonicity #185]: #187
-#191 := [quant-intro #188]: #190
-#208 := [trans #191 #206]: #207
-#165 := [asserted]: #44
-#209 := [mp #165 #208]: #204
-#214 := [mp~ #209 #218]: #204
-#260 := [mp #214 #259]: #257
-#291 := [mp #260 #290]: #288
-#776 := [mp #291 #775]: #771
-#729 := (not #771)
-#718 := (or #729 #445)
-#349 := (* -1::Int 3::Int)
-#435 := (mod #434 #349)
-#427 := (+ #436 #435)
-#438 := (= #427 0::Int)
-#420 := (<= 3::Int 0::Int)
-#755 := (or #420 #441)
-#757 := (not #755)
-#544 := (or #414 #420)
-#751 := (not #544)
-#425 := (or #751 #757)
-#426 := (ite #425 #437 #438)
-#760 := (ite #759 #758 #426)
-#756 := (= 3::Int 0::Int)
-#762 := (ite #756 #761 #760)
-#719 := (or #729 #762)
-#715 := (iff #719 #718)
-#721 := (iff #718 #718)
-#722 := [rewrite]: #721
-#728 := (iff #762 #445)
-#448 := (ite false #761 #445)
-#442 := (iff #448 #445)
-#724 := [rewrite]: #442
-#726 := (iff #762 #448)
-#446 := (iff #760 #445)
-#731 := (iff #426 #734)
-#456 := (iff #438 #455)
-#732 := (= #427 #355)
-#461 := (= #435 #460)
-#737 := (= #349 -3::Int)
-#459 := [rewrite]: #737
-#462 := [monotonicity #459]: #461
-#733 := [monotonicity #462]: #732
-#730 := [monotonicity #733]: #456
-#747 := (iff #425 #749)
-#388 := (iff #757 #748)
-#383 := (iff #755 #441)
-#742 := (or false #441)
-#739 := (iff #742 #441)
-#745 := [rewrite]: #739
-#743 := (iff #755 #742)
-#417 := (iff #420 false)
-#753 := [rewrite]: #417
-#744 := [monotonicity #753]: #743
-#746 := [trans #744 #745]: #383
-#389 := [monotonicity #746]: #388
-#740 := (iff #751 #404)
-#402 := (iff #544 #414)
-#413 := (or #414 false)
-#738 := (iff #413 #414)
-#401 := [rewrite]: #738
-#754 := (iff #544 #413)
-#397 := [monotonicity #753]: #754
-#403 := [trans #397 #401]: #402
-#741 := [monotonicity #403]: #740
-#750 := [monotonicity #741 #389]: #747
-#735 := [monotonicity #750 #730]: #731
-#447 := [monotonicity #735]: #446
-#752 := (iff #756 false)
-#412 := [rewrite]: #752
-#727 := [monotonicity #412 #447]: #726
-#725 := [trans #727 #724]: #728
-#716 := [monotonicity #725]: #715
-#717 := [trans #716 #722]: #715
-#720 := [quant-inst #10 #9]: #719
-#723 := [mp #720 #717]: #718
-#611 := [unit-resolution #723 #776]: #445
-#587 := (not #759)
-#612 := (not #599)
-#505 := (or #404 #80 #612)
-#616 := [th-lemma arith assign-bounds 1 1]: #505
-#617 := [unit-resolution #616 #99 #629]: #404
-#618 := (or #587 #414)
-#623 := [th-lemma arith triangle-eq]: #618
-#619 := [unit-resolution #623 #617]: #587
-#586 := (not #445)
-#695 := (or #586 #759 #734)
-#597 := [def-axiom]: #695
-#620 := [unit-resolution #597 #619 #611]: #734
-#564 := (or #749 #414)
-#565 := [def-axiom]: #564
-#621 := [unit-resolution #565 #617]: #749
-#709 := (not #749)
-#707 := (not #734)
-#714 := (or #707 #709 #437)
-#543 := [def-axiom]: #714
-#624 := [unit-resolution #543 #621 #620]: #437
-#699 := (not #437)
-#625 := (or #699 #705)
-#626 := [th-lemma arith triangle-eq]: #625
-#622 := [unit-resolution #626 #624]: #705
-[th-lemma arith farkas 1 1 -1 1 1 #622 #610 #99 #629 #646]: false
-unsat
-554a2c1ef3c9bdd0bc388bdfa3186ab7a764500e 567 0
-#2 := false
-#19 := 0::Int
-decl f5 :: (-> Int Int Int)
-#9 := 1::Int
-decl f3 :: Int
-#8 := f3
-#12 := (f5 f3 1::Int)
-#77 := -1::Int
-#79 := (* -1::Int #12)
-decl f4 :: (-> Int Int Int)
-#10 := (f4 f3 1::Int)
-#78 := (* -1::Int #10)
-#80 := (+ #78 #79)
-#81 := (+ f3 #80)
-#423 := (>= #81 0::Int)
-#596 := (<= #12 0::Int)
-#667 := (= #12 0::Int)
-#751 := (= f3 0::Int)
-#746 := (>= f3 0::Int)
-#449 := (not #746)
-#414 := (<= f3 0::Int)
-#735 := (not #414)
-#635 := (or #735 #449 #751)
-#615 := (not #635)
-#582 := [hypothesis]: #615
-#609 := (or #635 #746)
-#610 := [def-axiom]: #609
-#583 := [unit-resolution #610 #582]: #746
-#612 := (or #635 #414)
-#608 := [def-axiom]: #612
-#584 := [unit-resolution #608 #582]: #414
-#570 := (not #751)
-#613 := (or #635 #570)
-#614 := [def-axiom]: #613
-#594 := [unit-resolution #614 #582]: #570
-#574 := (or #751 #735 #449)
-#595 := [th-lemma arith triangle-eq]: #574
-#550 := [unit-resolution #595 #594 #584 #583]: false
-#551 := [lemma #550]: #635
-#498 := (or #615 #667)
-#425 := (* -1::Int f3)
-#688 := (mod #425 -1::Int)
-#655 := (+ #12 #688)
-#636 := (= #655 0::Int)
-#618 := (ite #635 #667 #636)
-#17 := (:var 0 Int)
-#16 := (:var 1 Int)
-#37 := (f5 #16 #17)
-#759 := (pattern #37)
-#101 := (* -1::Int #17)
-#98 := (* -1::Int #16)
-#156 := (mod #98 #101)
-#271 := (+ #37 #156)
-#272 := (= #271 0::Int)
-#38 := (mod #16 #17)
-#268 := (* -1::Int #38)
-#269 := (+ #37 #268)
-#270 := (= #269 0::Int)
-#130 := (>= #16 0::Int)
-#123 := (<= #17 0::Int)
-#215 := (or #123 #130)
-#216 := (not #215)
-#119 := (<= #16 0::Int)
-#213 := (or #119 #123)
-#214 := (not #213)
-#219 := (or #214 #216)
-#273 := (ite #219 #270 #272)
-#267 := (= #37 0::Int)
-#20 := (= #16 0::Int)
-#274 := (ite #20 #267 #273)
-#266 := (= #16 #37)
-#21 := (= #17 0::Int)
-#275 := (ite #21 #266 #274)
-#760 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #759) #275)
-#278 := (forall (vars (?v0 Int) (?v1 Int)) #275)
-#763 := (iff #278 #760)
-#761 := (iff #275 #275)
-#762 := [refl]: #761
-#764 := [quant-intro #762]: #763
-#162 := (* -1::Int #156)
-#235 := (ite #219 #38 #162)
-#238 := (ite #20 0::Int #235)
-#241 := (ite #21 #16 #238)
-#244 := (= #37 #241)
-#247 := (forall (vars (?v0 Int) (?v1 Int)) #244)
-#279 := (iff #247 #278)
-#276 := (iff #244 #275)
-#277 := [rewrite]: #276
-#280 := [quant-intro #277]: #279
-#131 := (not #130)
-#124 := (not #123)
-#134 := (and #124 #131)
-#120 := (not #119)
-#127 := (and #120 #124)
-#137 := (or #127 #134)
-#182 := (ite #137 #38 #162)
-#185 := (ite #20 0::Int #182)
-#188 := (ite #21 #16 #185)
-#191 := (= #37 #188)
-#194 := (forall (vars (?v0 Int) (?v1 Int)) #191)
-#248 := (iff #194 #247)
-#245 := (iff #191 #244)
-#242 := (= #188 #241)
-#239 := (= #185 #238)
-#236 := (= #182 #235)
-#220 := (iff #137 #219)
-#217 := (iff #134 #216)
-#218 := [rewrite]: #217
-#207 := (iff #127 #214)
-#208 := [rewrite]: #207
-#221 := [monotonicity #208 #218]: #220
-#237 := [monotonicity #221]: #236
-#240 := [monotonicity #237]: #239
-#243 := [monotonicity #240]: #242
-#246 := [monotonicity #243]: #245
-#249 := [quant-intro #246]: #248
-#205 := (~ #194 #194)
-#204 := (~ #191 #191)
-#201 := [refl]: #204
-#206 := [nnf-pos #201]: #205
-#31 := (- #17)
-#30 := (- #16)
-#39 := (mod #30 #31)
-#40 := (- #39)
-#24 := (< 0::Int #17)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#41 := (ite #28 #38 #40)
-#42 := (ite #20 0::Int #41)
-#43 := (ite #21 #16 #42)
-#44 := (= #37 #43)
-#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
-#197 := (iff #45 #194)
-#92 := (and #24 #26)
-#95 := (or #25 #92)
-#167 := (ite #95 #38 #162)
-#170 := (ite #20 0::Int #167)
-#173 := (ite #21 #16 #170)
-#176 := (= #37 #173)
-#179 := (forall (vars (?v0 Int) (?v1 Int)) #176)
-#195 := (iff #179 #194)
-#192 := (iff #176 #191)
-#189 := (= #173 #188)
-#186 := (= #170 #185)
-#183 := (= #167 #182)
-#138 := (iff #95 #137)
-#135 := (iff #92 #134)
-#132 := (iff #26 #131)
-#133 := [rewrite]: #132
-#125 := (iff #24 #124)
-#126 := [rewrite]: #125
-#136 := [monotonicity #126 #133]: #135
-#128 := (iff #25 #127)
-#121 := (iff #23 #120)
-#122 := [rewrite]: #121
-#129 := [monotonicity #122 #126]: #128
-#139 := [monotonicity #129 #136]: #138
-#184 := [monotonicity #139]: #183
-#187 := [monotonicity #184]: #186
-#190 := [monotonicity #187]: #189
-#193 := [monotonicity #190]: #192
-#196 := [quant-intro #193]: #195
-#180 := (iff #45 #179)
-#177 := (iff #44 #176)
-#174 := (= #43 #173)
-#171 := (= #42 #170)
-#168 := (= #41 #167)
-#165 := (= #40 #162)
-#159 := (- #156)
-#163 := (= #159 #162)
-#164 := [rewrite]: #163
-#160 := (= #40 #159)
-#157 := (= #39 #156)
-#102 := (= #31 #101)
-#103 := [rewrite]: #102
-#99 := (= #30 #98)
-#100 := [rewrite]: #99
-#158 := [monotonicity #100 #103]: #157
-#161 := [monotonicity #158]: #160
-#166 := [trans #161 #164]: #165
-#96 := (iff #28 #95)
-#93 := (iff #27 #92)
-#94 := [rewrite]: #93
-#97 := [monotonicity #94]: #96
-#169 := [monotonicity #97 #166]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [quant-intro #178]: #180
-#198 := [trans #181 #196]: #197
-#155 := [asserted]: #45
-#199 := [mp #155 #198]: #194
-#202 := [mp~ #199 #206]: #194
-#250 := [mp #202 #249]: #247
-#281 := [mp #250 #280]: #278
-#765 := [mp #281 #764]: #760
-#625 := (not #760)
-#620 := (or #625 #618)
-#424 := (* -1::Int 1::Int)
-#686 := (mod #425 #424)
-#683 := (+ #12 #686)
-#687 := (= #683 0::Int)
-#532 := (mod f3 1::Int)
-#674 := (* -1::Int #532)
-#676 := (+ #12 #674)
-#668 := (= #676 0::Int)
-#403 := (<= 1::Int 0::Int)
-#533 := (or #403 #746)
-#740 := (not #533)
-#415 := (or #414 #403)
-#747 := (not #415)
-#748 := (or #747 #740)
-#665 := (ite #748 #668 #687)
-#677 := (ite #751 #667 #665)
-#678 := (= f3 #12)
-#745 := (= 1::Int 0::Int)
-#679 := (ite #745 #678 #677)
-#626 := (or #625 #679)
-#600 := (iff #626 #620)
-#494 := (iff #620 #620)
-#605 := [rewrite]: #494
-#623 := (iff #679 #618)
-#345 := (or #735 #449)
-#646 := (or #345 #751)
-#647 := (ite #646 #667 #636)
-#619 := (iff #647 #618)
-#621 := (iff #646 #635)
-#617 := [rewrite]: #621
-#622 := [monotonicity #617]: #619
-#634 := (iff #679 #647)
-#628 := (ite false #678 #647)
-#632 := (iff #628 #647)
-#633 := [rewrite]: #632
-#630 := (iff #679 #628)
-#649 := (iff #677 #647)
-#640 := (ite #345 #667 #636)
-#643 := (ite #751 #667 #640)
-#648 := (iff #643 #647)
-#638 := [rewrite]: #648
-#644 := (iff #677 #643)
-#641 := (iff #665 #640)
-#637 := (iff #687 #636)
-#652 := (= #683 #655)
-#653 := (= #686 #688)
-#444 := (= #424 -1::Int)
-#445 := [rewrite]: #444
-#654 := [monotonicity #445]: #653
-#656 := [monotonicity #654]: #652
-#639 := [monotonicity #656]: #637
-#650 := (iff #668 #667)
-#659 := (= #676 #12)
-#658 := (+ #12 0::Int)
-#662 := (= #658 #12)
-#663 := [rewrite]: #662
-#660 := (= #676 #658)
-#673 := (= #674 0::Int)
-#669 := (* -1::Int 0::Int)
-#672 := (= #669 0::Int)
-#666 := [rewrite]: #672
-#670 := (= #674 #669)
-#675 := (= #532 0::Int)
-#680 := [rewrite]: #675
-#671 := [monotonicity #680]: #670
-#657 := [trans #671 #666]: #673
-#661 := [monotonicity #657]: #660
-#664 := [trans #661 #663]: #659
-#651 := [monotonicity #664]: #650
-#721 := (iff #748 #345)
-#450 := (iff #740 #449)
-#726 := (iff #533 #746)
-#378 := (or false #746)
-#739 := (iff #378 #746)
-#725 := [rewrite]: #739
-#738 := (iff #533 #378)
-#393 := (iff #403 false)
-#729 := [rewrite]: #393
-#736 := [monotonicity #729]: #738
-#448 := [trans #736 #725]: #726
-#451 := [monotonicity #448]: #450
-#737 := (iff #747 #735)
-#734 := (iff #415 #414)
-#730 := (or #414 false)
-#733 := (iff #730 #414)
-#728 := [rewrite]: #733
-#731 := (iff #415 #730)
-#732 := [monotonicity #729]: #731
-#372 := [trans #732 #728]: #734
-#377 := [monotonicity #372]: #737
-#722 := [monotonicity #377 #451]: #721
-#642 := [monotonicity #722 #651 #639]: #641
-#645 := [monotonicity #642]: #644
-#627 := [trans #645 #638]: #649
-#406 := (iff #745 false)
-#742 := [rewrite]: #406
-#631 := [monotonicity #742 #627]: #630
-#629 := [trans #631 #633]: #634
-#624 := [trans #629 #622]: #623
-#601 := [monotonicity #624]: #600
-#606 := [trans #601 #605]: #600
-#599 := [quant-inst #8 #9]: #626
-#607 := [mp #599 #606]: #620
-#505 := [unit-resolution #607 #765]: #618
-#602 := (not #618)
-#603 := (or #602 #615 #667)
-#598 := [def-axiom]: #603
-#501 := [unit-resolution #598 #505]: #498
-#502 := [unit-resolution #501 #551]: #667
-#579 := (not #667)
-#488 := (or #579 #596)
-#490 := [th-lemma arith triangle-eq]: #488
-#491 := [unit-resolution #490 #502]: #596
-#698 := (<= #10 0::Int)
-#750 := (= #10 0::Int)
-#453 := [hypothesis]: #570
-#702 := (not #345)
-#426 := (div f3 1::Int)
-#430 := (* -1::Int #426)
-#409 := (+ #10 #430)
-#744 := (= #409 0::Int)
-#577 := (not #744)
-#544 := (+ f3 #430)
-#549 := (>= #544 0::Int)
-#543 := (= #544 0::Int)
-#1 := true
-#63 := [true-axiom]: true
-#493 := (or false #543)
-#495 := [th-lemma arith]: #493
-#496 := [unit-resolution #495 #63]: #543
-#499 := (not #543)
-#500 := (or #499 #549)
-#504 := [th-lemma arith triangle-eq]: #500
-#497 := [unit-resolution #504 #496]: #549
-#534 := (<= #409 0::Int)
-#489 := [hypothesis]: #744
-#492 := (or #577 #534)
-#474 := [th-lemma arith triangle-eq]: #492
-#476 := [unit-resolution #474 #489]: #534
-#479 := (not #549)
-#478 := (not #534)
-#477 := (not #596)
-#480 := (or #423 #477 #478 #479)
-#481 := [th-lemma arith assign-bounds 1 1 -1]: #480
-#482 := [unit-resolution #481 #476 #491 #497]: #423
-#339 := (<= #81 0::Int)
-#531 := (<= #544 0::Int)
-#483 := (or #499 #531)
-#484 := [th-lemma arith triangle-eq]: #483
-#485 := [unit-resolution #484 #496]: #531
-#542 := (>= #12 0::Int)
-#486 := (or #579 #542)
-#475 := [th-lemma arith triangle-eq]: #486
-#487 := [unit-resolution #475 #502]: #542
-#535 := (>= #409 0::Int)
-#464 := (or #577 #535)
-#466 := [th-lemma arith triangle-eq]: #464
-#467 := [unit-resolution #466 #489]: #535
-#470 := (not #531)
-#469 := (not #535)
-#468 := (not #542)
-#471 := (or #339 #468 #469 #470)
-#472 := [th-lemma arith assign-bounds 1 1 -1]: #471
-#465 := [unit-resolution #472 #467 #487 #485]: #339
-#458 := (not #423)
-#473 := (not #339)
-#462 := (or #473 #458)
-#82 := (= #81 0::Int)
-#85 := (not #82)
-#11 := (* #10 1::Int)
-#13 := (+ #11 #12)
-#14 := (= f3 #13)
-#15 := (not #14)
-#88 := (iff #15 #85)
-#68 := (+ #10 #12)
-#71 := (= f3 #68)
-#74 := (not #71)
-#86 := (iff #74 #85)
-#83 := (iff #71 #82)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#75 := (iff #15 #74)
-#72 := (iff #14 #71)
-#69 := (= #13 #68)
-#66 := (= #11 #10)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73]: #75
-#89 := [trans #76 #87]: #88
-#65 := [asserted]: #15
-#90 := [mp #65 #89]: #85
-#459 := (or #82 #473 #458)
-#460 := [th-lemma arith triangle-eq]: #459
-#461 := [unit-resolution #460 #90]: #462
-#463 := [unit-resolution #461 #465 #482]: false
-#452 := [lemma #463]: #577
-#719 := (div #425 -1::Int)
-#724 := (* -1::Int #719)
-#436 := (+ #10 #724)
-#716 := (= #436 0::Int)
-#717 := (ite #345 #744 #716)
-#446 := (or #751 #717)
-#707 := (ite #751 #750 #717)
-#18 := (f4 #16 #17)
-#752 := (pattern #18)
-#104 := (div #98 #101)
-#255 := (* -1::Int #104)
-#256 := (+ #18 #255)
-#257 := (= #256 0::Int)
-#29 := (div #16 #17)
-#252 := (* -1::Int #29)
-#253 := (+ #18 #252)
-#254 := (= #253 0::Int)
-#258 := (ite #219 #254 #257)
-#251 := (= #18 0::Int)
-#22 := (or #20 #21)
-#259 := (ite #22 #251 #258)
-#753 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #752) #259)
-#262 := (forall (vars (?v0 Int) (?v1 Int)) #259)
-#756 := (iff #262 #753)
-#754 := (iff #259 #259)
-#755 := [refl]: #754
-#757 := [quant-intro #755]: #756
-#222 := (ite #219 #29 #104)
-#225 := (ite #22 0::Int #222)
-#228 := (= #18 #225)
-#231 := (forall (vars (?v0 Int) (?v1 Int)) #228)
-#263 := (iff #231 #262)
-#260 := (iff #228 #259)
-#261 := [rewrite]: #260
-#264 := [quant-intro #261]: #263
-#140 := (ite #137 #29 #104)
-#143 := (ite #22 0::Int #140)
-#146 := (= #18 #143)
-#149 := (forall (vars (?v0 Int) (?v1 Int)) #146)
-#232 := (iff #149 #231)
-#229 := (iff #146 #228)
-#226 := (= #143 #225)
-#223 := (= #140 #222)
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [quant-intro #230]: #232
-#211 := (~ #149 #149)
-#209 := (~ #146 #146)
-#210 := [refl]: #209
-#212 := [nnf-pos #210]: #211
-#32 := (div #30 #31)
-#33 := (ite #28 #29 #32)
-#34 := (ite #22 0::Int #33)
-#35 := (= #18 #34)
-#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
-#152 := (iff #36 #149)
-#107 := (ite #95 #29 #104)
-#110 := (ite #22 0::Int #107)
-#113 := (= #18 #110)
-#116 := (forall (vars (?v0 Int) (?v1 Int)) #113)
-#150 := (iff #116 #149)
-#147 := (iff #113 #146)
-#144 := (= #110 #143)
-#141 := (= #107 #140)
-#142 := [monotonicity #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [monotonicity #145]: #147
-#151 := [quant-intro #148]: #150
-#117 := (iff #36 #116)
-#114 := (iff #35 #113)
-#111 := (= #34 #110)
-#108 := (= #33 #107)
-#105 := (= #32 #104)
-#106 := [monotonicity #100 #103]: #105
-#109 := [monotonicity #97 #106]: #108
-#112 := [monotonicity #109]: #111
-#115 := [monotonicity #112]: #114
-#118 := [quant-intro #115]: #117
-#153 := [trans #118 #151]: #152
-#91 := [asserted]: #36
-#154 := [mp #91 #153]: #149
-#203 := [mp~ #154 #212]: #149
-#234 := [mp #203 #233]: #231
-#265 := [mp #234 #264]: #262
-#758 := [mp #265 #757]: #753
-#704 := (not #753)
-#705 := (or #704 #707)
-#416 := (div #425 #424)
-#427 := (* -1::Int #416)
-#428 := (+ #10 #427)
-#429 := (= #428 0::Int)
-#749 := (ite #748 #744 #429)
-#741 := (or #751 #745)
-#401 := (ite #741 #750 #749)
-#710 := (or #704 #401)
-#706 := (iff #710 #705)
-#553 := (iff #705 #705)
-#554 := [rewrite]: #553
-#708 := (iff #401 #707)
-#714 := (iff #749 #717)
-#431 := (iff #429 #716)
-#437 := (= #428 #436)
-#434 := (= #427 #724)
-#723 := (= #416 #719)
-#720 := [monotonicity #445]: #723
-#435 := [monotonicity #720]: #434
-#715 := [monotonicity #435]: #437
-#713 := [monotonicity #715]: #431
-#718 := [monotonicity #722 #713]: #714
-#391 := (iff #741 #751)
-#402 := (or #751 false)
-#727 := (iff #402 #751)
-#390 := [rewrite]: #727
-#743 := (iff #741 #402)
-#386 := [monotonicity #742]: #743
-#392 := [trans #386 #390]: #391
-#709 := [monotonicity #392 #718]: #708
-#712 := [monotonicity #709]: #706
-#555 := [trans #712 #554]: #706
-#711 := [quant-inst #8 #9]: #710
-#697 := [mp #711 #555]: #705
-#454 := [unit-resolution #697 #758]: #707
-#685 := (not #707)
-#588 := (or #685 #751 #717)
-#581 := [def-axiom]: #588
-#455 := [unit-resolution #581 #454]: #446
-#456 := [unit-resolution #455 #453]: #717
-#692 := (not #717)
-#690 := (or #692 #702 #744)
-#693 := [def-axiom]: #690
-#447 := [unit-resolution #693 #456 #452]: #702
-#700 := (or #345 #414)
-#694 := [def-axiom]: #700
-#457 := [unit-resolution #694 #447]: #414
-#695 := (or #345 #746)
-#701 := [def-axiom]: #695
-#438 := [unit-resolution #701 #447]: #746
-#439 := [unit-resolution #595 #438 #457 #453]: false
-#440 := [lemma #439]: #751
-#432 := (or #570 #750)
-#585 := (or #685 #570 #750)
-#587 := [def-axiom]: #585
-#441 := [unit-resolution #587 #454]: #432
-#442 := [unit-resolution #441 #440]: #750
-#589 := (not #750)
-#433 := (or #589 #698)
-#443 := [th-lemma arith triangle-eq]: #433
-#410 := [unit-resolution #443 #442]: #698
-#412 := (or #570 #746)
-#413 := [th-lemma arith triangle-eq]: #412
-#404 := [unit-resolution #413 #440]: #746
-#417 := (not #698)
-#418 := (or #423 #417 #477 #449)
-#419 := [th-lemma arith assign-bounds 1 1 -1]: #418
-#420 := [unit-resolution #419 #404 #410 #491]: #423
-#699 := (>= #10 0::Int)
-#421 := (or #589 #699)
-#411 := [th-lemma arith triangle-eq]: #421
-#422 := [unit-resolution #411 #442]: #699
-#405 := (or #570 #414)
-#407 := [th-lemma arith triangle-eq]: #405
-#408 := [unit-resolution #407 #440]: #414
-#387 := (not #699)
-#389 := (or #339 #387 #468 #735)
-#394 := [th-lemma arith assign-bounds 1 1 -1]: #389
-#395 := [unit-resolution #394 #408 #422 #487]: #339
-[unit-resolution #461 #395 #420]: false
-unsat
-b7566ab9692699d99b59e9354d5e78d5af5e3d40 544 0
-#2 := false
-#19 := 0::Int
-decl f4 :: (-> Int Int Int)
-#9 := 3::Int
-decl f3 :: Int
-#8 := f3
-#10 := (f4 f3 3::Int)
-#701 := (>= #10 0::Int)
-#752 := (= #10 0::Int)
-#748 := (= f3 0::Int)
-#688 := (not #748)
-#560 := [hypothesis]: #688
-#743 := (<= f3 0::Int)
-#747 := (>= f3 0::Int)
-#451 := (not #747)
-#375 := (not #743)
-#454 := (or #375 #451)
-#704 := (not #454)
-#78 := -3::Int
-#80 := -1::Int
-#428 := (* -1::Int f3)
-#448 := (div #428 -3::Int)
-#723 := (* -1::Int #448)
-#438 := (+ #10 #723)
-#718 := (= #438 0::Int)
-#432 := (div f3 3::Int)
-#429 := (* -1::Int #432)
-#433 := (+ #10 #429)
-#412 := (= #433 0::Int)
-#716 := (ite #454 #412 #718)
-#562 := (or #748 #716)
-#721 := (ite #748 #752 #716)
-#17 := (:var 0 Int)
-#16 := (:var 1 Int)
-#18 := (f4 #16 #17)
-#755 := (pattern #18)
-#103 := (* -1::Int #17)
-#100 := (* -1::Int #16)
-#106 := (div #100 #103)
-#257 := (* -1::Int #106)
-#258 := (+ #18 #257)
-#259 := (= #258 0::Int)
-#29 := (div #16 #17)
-#254 := (* -1::Int #29)
-#255 := (+ #18 #254)
-#256 := (= #255 0::Int)
-#132 := (>= #16 0::Int)
-#125 := (<= #17 0::Int)
-#217 := (or #125 #132)
-#218 := (not #217)
-#121 := (<= #16 0::Int)
-#215 := (or #121 #125)
-#216 := (not #215)
-#221 := (or #216 #218)
-#260 := (ite #221 #256 #259)
-#253 := (= #18 0::Int)
-#21 := (= #17 0::Int)
-#20 := (= #16 0::Int)
-#22 := (or #20 #21)
-#261 := (ite #22 #253 #260)
-#756 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #755) #261)
-#264 := (forall (vars (?v0 Int) (?v1 Int)) #261)
-#759 := (iff #264 #756)
-#757 := (iff #261 #261)
-#758 := [refl]: #757
-#760 := [quant-intro #758]: #759
-#224 := (ite #221 #29 #106)
-#227 := (ite #22 0::Int #224)
-#230 := (= #18 #227)
-#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
-#265 := (iff #233 #264)
-#262 := (iff #230 #261)
-#263 := [rewrite]: #262
-#266 := [quant-intro #263]: #265
-#133 := (not #132)
-#126 := (not #125)
-#136 := (and #126 #133)
-#122 := (not #121)
-#129 := (and #122 #126)
-#139 := (or #129 #136)
-#142 := (ite #139 #29 #106)
-#145 := (ite #22 0::Int #142)
-#148 := (= #18 #145)
-#151 := (forall (vars (?v0 Int) (?v1 Int)) #148)
-#234 := (iff #151 #233)
-#231 := (iff #148 #230)
-#228 := (= #145 #227)
-#225 := (= #142 #224)
-#222 := (iff #139 #221)
-#219 := (iff #136 #218)
-#220 := [rewrite]: #219
-#209 := (iff #129 #216)
-#210 := [rewrite]: #209
-#223 := [monotonicity #210 #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [monotonicity #229]: #231
-#235 := [quant-intro #232]: #234
-#213 := (~ #151 #151)
-#211 := (~ #148 #148)
-#212 := [refl]: #211
-#214 := [nnf-pos #212]: #213
-#31 := (- #17)
-#30 := (- #16)
-#32 := (div #30 #31)
-#24 := (< 0::Int #17)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#33 := (ite #28 #29 #32)
-#34 := (ite #22 0::Int #33)
-#35 := (= #18 #34)
-#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
-#154 := (iff #36 #151)
-#94 := (and #24 #26)
-#97 := (or #25 #94)
-#109 := (ite #97 #29 #106)
-#112 := (ite #22 0::Int #109)
-#115 := (= #18 #112)
-#118 := (forall (vars (?v0 Int) (?v1 Int)) #115)
-#152 := (iff #118 #151)
-#149 := (iff #115 #148)
-#146 := (= #112 #145)
-#143 := (= #109 #142)
-#140 := (iff #97 #139)
-#137 := (iff #94 #136)
-#134 := (iff #26 #133)
-#135 := [rewrite]: #134
-#127 := (iff #24 #126)
-#128 := [rewrite]: #127
-#138 := [monotonicity #128 #135]: #137
-#130 := (iff #25 #129)
-#123 := (iff #23 #122)
-#124 := [rewrite]: #123
-#131 := [monotonicity #124 #128]: #130
-#141 := [monotonicity #131 #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [monotonicity #147]: #149
-#153 := [quant-intro #150]: #152
-#119 := (iff #36 #118)
-#116 := (iff #35 #115)
-#113 := (= #34 #112)
-#110 := (= #33 #109)
-#107 := (= #32 #106)
-#104 := (= #31 #103)
-#105 := [rewrite]: #104
-#101 := (= #30 #100)
-#102 := [rewrite]: #101
-#108 := [monotonicity #102 #105]: #107
-#98 := (iff #28 #97)
-#95 := (iff #27 #94)
-#96 := [rewrite]: #95
-#99 := [monotonicity #96]: #98
-#111 := [monotonicity #99 #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [quant-intro #117]: #119
-#155 := [trans #120 #153]: #154
-#93 := [asserted]: #36
-#156 := [mp #93 #155]: #151
-#205 := [mp~ #156 #214]: #151
-#236 := [mp #205 #235]: #233
-#267 := [mp #236 #266]: #264
-#761 := [mp #267 #760]: #756
-#712 := (not #756)
-#707 := (or #712 #721)
-#427 := (* -1::Int 3::Int)
-#419 := (div #428 #427)
-#430 := (* -1::Int #419)
-#431 := (+ #10 #430)
-#359 := (= #431 0::Int)
-#749 := (<= 3::Int 0::Int)
-#406 := (or #749 #747)
-#536 := (not #406)
-#417 := (or #743 #749)
-#418 := (not #417)
-#750 := (or #418 #536)
-#751 := (ite #750 #412 #359)
-#753 := (= 3::Int 0::Int)
-#754 := (or #748 #753)
-#744 := (ite #754 #752 #751)
-#708 := (or #712 #744)
-#714 := (iff #708 #707)
-#715 := (iff #707 #707)
-#556 := [rewrite]: #715
-#710 := (iff #744 #721)
-#720 := (iff #751 #716)
-#719 := (iff #359 #718)
-#439 := (= #431 #438)
-#727 := (= #430 #723)
-#722 := (= #419 #448)
-#725 := (= #427 -3::Int)
-#447 := [rewrite]: #725
-#726 := [monotonicity #447]: #722
-#437 := [monotonicity #726]: #727
-#440 := [monotonicity #437]: #439
-#434 := [monotonicity #440]: #719
-#347 := (iff #750 #454)
-#452 := (iff #536 #451)
-#728 := (iff #406 #747)
-#380 := (or false #747)
-#739 := (iff #380 #747)
-#742 := [rewrite]: #739
-#381 := (iff #406 #380)
-#395 := (iff #749 false)
-#396 := [rewrite]: #395
-#741 := [monotonicity #396]: #381
-#729 := [trans #741 #742]: #728
-#453 := [monotonicity #729]: #452
-#738 := (iff #418 #375)
-#731 := (iff #417 #743)
-#732 := (or #743 false)
-#735 := (iff #732 #743)
-#736 := [rewrite]: #735
-#733 := (iff #417 #732)
-#734 := [monotonicity #396]: #733
-#737 := [trans #734 #736]: #731
-#740 := [monotonicity #737]: #738
-#724 := [monotonicity #740 #453]: #347
-#717 := [monotonicity #724 #434]: #720
-#393 := (iff #754 #748)
-#745 := (or #748 false)
-#389 := (iff #745 #748)
-#730 := [rewrite]: #389
-#405 := (iff #754 #745)
-#404 := (iff #753 false)
-#409 := [rewrite]: #404
-#746 := [monotonicity #409]: #405
-#394 := [trans #746 #730]: #393
-#711 := [monotonicity #394 #717]: #710
-#709 := [monotonicity #711]: #714
-#557 := [trans #709 #556]: #714
-#713 := [quant-inst #8 #9]: #708
-#558 := [mp #713 #557]: #707
-#561 := [unit-resolution #558 #761]: #721
-#685 := (not #721)
-#590 := (or #685 #748 #716)
-#591 := [def-axiom]: #590
-#563 := [unit-resolution #591 #561]: #562
-#564 := [unit-resolution #563 #560]: #716
-#538 := (mod #428 -3::Int)
-decl f5 :: (-> Int Int Int)
-#12 := (f5 f3 3::Int)
-#683 := (+ #12 #538)
-#674 := (= #683 0::Int)
-#706 := (mod f3 3::Int)
-#690 := (* -1::Int #706)
-#677 := (+ #12 #690)
-#679 := (= #677 0::Int)
-#676 := (ite #454 #679 #674)
-#523 := (or #748 #676)
-#668 := (= #12 0::Int)
-#663 := (ite #748 #668 #676)
-#37 := (f5 #16 #17)
-#762 := (pattern #37)
-#158 := (mod #100 #103)
-#273 := (+ #37 #158)
-#274 := (= #273 0::Int)
-#38 := (mod #16 #17)
-#270 := (* -1::Int #38)
-#271 := (+ #37 #270)
-#272 := (= #271 0::Int)
-#275 := (ite #221 #272 #274)
-#269 := (= #37 0::Int)
-#276 := (ite #20 #269 #275)
-#268 := (= #16 #37)
-#277 := (ite #21 #268 #276)
-#763 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #762) #277)
-#280 := (forall (vars (?v0 Int) (?v1 Int)) #277)
-#766 := (iff #280 #763)
-#764 := (iff #277 #277)
-#765 := [refl]: #764
-#767 := [quant-intro #765]: #766
-#164 := (* -1::Int #158)
-#237 := (ite #221 #38 #164)
-#240 := (ite #20 0::Int #237)
-#243 := (ite #21 #16 #240)
-#246 := (= #37 #243)
-#249 := (forall (vars (?v0 Int) (?v1 Int)) #246)
-#281 := (iff #249 #280)
-#278 := (iff #246 #277)
-#279 := [rewrite]: #278
-#282 := [quant-intro #279]: #281
-#184 := (ite #139 #38 #164)
-#187 := (ite #20 0::Int #184)
-#190 := (ite #21 #16 #187)
-#193 := (= #37 #190)
-#196 := (forall (vars (?v0 Int) (?v1 Int)) #193)
-#250 := (iff #196 #249)
-#247 := (iff #193 #246)
-#244 := (= #190 #243)
-#241 := (= #187 #240)
-#238 := (= #184 #237)
-#239 := [monotonicity #223]: #238
-#242 := [monotonicity #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [monotonicity #245]: #247
-#251 := [quant-intro #248]: #250
-#207 := (~ #196 #196)
-#206 := (~ #193 #193)
-#203 := [refl]: #206
-#208 := [nnf-pos #203]: #207
-#39 := (mod #30 #31)
-#40 := (- #39)
-#41 := (ite #28 #38 #40)
-#42 := (ite #20 0::Int #41)
-#43 := (ite #21 #16 #42)
-#44 := (= #37 #43)
-#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
-#199 := (iff #45 #196)
-#169 := (ite #97 #38 #164)
-#172 := (ite #20 0::Int #169)
-#175 := (ite #21 #16 #172)
-#178 := (= #37 #175)
-#181 := (forall (vars (?v0 Int) (?v1 Int)) #178)
-#197 := (iff #181 #196)
-#194 := (iff #178 #193)
-#191 := (= #175 #190)
-#188 := (= #172 #187)
-#185 := (= #169 #184)
-#186 := [monotonicity #141]: #185
-#189 := [monotonicity #186]: #188
-#192 := [monotonicity #189]: #191
-#195 := [monotonicity #192]: #194
-#198 := [quant-intro #195]: #197
-#182 := (iff #45 #181)
-#179 := (iff #44 #178)
-#176 := (= #43 #175)
-#173 := (= #42 #172)
-#170 := (= #41 #169)
-#167 := (= #40 #164)
-#161 := (- #158)
-#165 := (= #161 #164)
-#166 := [rewrite]: #165
-#162 := (= #40 #161)
-#159 := (= #39 #158)
-#160 := [monotonicity #102 #105]: #159
-#163 := [monotonicity #160]: #162
-#168 := [trans #163 #166]: #167
-#171 := [monotonicity #99 #168]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [quant-intro #180]: #182
-#200 := [trans #183 #198]: #199
-#157 := [asserted]: #45
-#201 := [mp #157 #200]: #196
-#204 := [mp~ #201 #208]: #196
-#252 := [mp #204 #251]: #249
-#283 := [mp #252 #282]: #280
-#768 := [mp #283 #767]: #763
-#658 := (not #763)
-#655 := (or #658 #663)
-#596 := (mod #428 #427)
-#689 := (+ #12 #596)
-#686 := (= #689 0::Int)
-#671 := (ite #750 #679 #686)
-#670 := (ite #748 #668 #671)
-#680 := (= f3 #12)
-#681 := (ite #753 #680 #670)
-#659 := (or #658 #681)
-#640 := (iff #659 #655)
-#643 := (iff #655 #655)
-#644 := [rewrite]: #643
-#656 := (iff #681 #663)
-#666 := (ite false #680 #663)
-#653 := (iff #666 #663)
-#654 := [rewrite]: #653
-#662 := (iff #681 #666)
-#664 := (iff #670 #663)
-#660 := (iff #671 #676)
-#675 := (iff #686 #674)
-#672 := (= #689 #683)
-#682 := (= #596 #538)
-#678 := [monotonicity #447]: #682
-#673 := [monotonicity #678]: #672
-#669 := [monotonicity #673]: #675
-#661 := [monotonicity #724 #669]: #660
-#665 := [monotonicity #661]: #664
-#667 := [monotonicity #409 #665]: #662
-#657 := [trans #667 #654]: #656
-#642 := [monotonicity #657]: #640
-#645 := [trans #642 #644]: #640
-#639 := [quant-inst #8 #9]: #659
-#646 := [mp #639 #645]: #655
-#619 := [unit-resolution #646 #768]: #663
-#620 := (not #663)
-#625 := (or #620 #748 #676)
-#626 := [def-axiom]: #625
-#524 := [unit-resolution #626 #619]: #523
-#525 := [unit-resolution #524 #560]: #676
-#694 := (not #716)
-#652 := (not #676)
-#489 := (or #704 #652 #694)
-#650 := (>= #677 0::Int)
-#565 := [hypothesis]: #676
-#566 := [hypothesis]: #454
-#630 := (or #652 #704 #679)
-#631 := [def-axiom]: #630
-#567 := [unit-resolution #631 #566 #565]: #679
-#635 := (not #679)
-#491 := (or #635 #650)
-#493 := [th-lemma arith triangle-eq]: #491
-#494 := [unit-resolution #493 #567]: #650
-#537 := (>= #433 0::Int)
-#547 := [hypothesis]: #716
-#695 := (or #694 #704 #412)
-#693 := [def-axiom]: #695
-#548 := [unit-resolution #693 #566 #547]: #412
-#579 := (not #412)
-#492 := (or #579 #537)
-#495 := [th-lemma arith triangle-eq]: #492
-#477 := [unit-resolution #495 #548]: #537
-#81 := (* -1::Int #12)
-#79 := (* -3::Int #10)
-#82 := (+ #79 #81)
-#83 := (+ f3 #82)
-#341 := (<= #83 0::Int)
-#479 := (not #341)
-#426 := (>= #83 0::Int)
-#555 := (not #426)
-#571 := [hypothesis]: #555
-#531 := (or #748 #426)
-#552 := (or #704 #426 #652 #694)
-#649 := (<= #677 0::Int)
-#568 := (or #635 #649)
-#569 := [th-lemma arith triangle-eq]: #568
-#570 := [unit-resolution #569 #567]: #649
-#613 := (* -3::Int #432)
-#616 := (+ #613 #690)
-#617 := (+ f3 #616)
-#599 := (>= #617 0::Int)
-#612 := (= #617 0::Int)
-#1 := true
-#63 := [true-axiom]: true
-#532 := (or false #612)
-#533 := [th-lemma arith]: #532
-#540 := [unit-resolution #533 #63]: #612
-#542 := (not #612)
-#543 := (or #542 #599)
-#544 := [th-lemma arith triangle-eq]: #543
-#546 := [unit-resolution #544 #540]: #599
-#535 := (<= #433 0::Int)
-#549 := (or #579 #535)
-#550 := [th-lemma arith triangle-eq]: #549
-#551 := [unit-resolution #550 #548]: #535
-#534 := [th-lemma arith farkas 3 -1 1 1 #551 #546 #571 #570]: false
-#522 := [lemma #534]: #552
-#527 := [unit-resolution #522 #525 #571 #564]: #704
-#702 := (or #454 #743)
-#703 := [def-axiom]: #702
-#528 := [unit-resolution #703 #527]: #743
-#697 := (or #454 #747)
-#698 := [def-axiom]: #697
-#529 := [unit-resolution #698 #527]: #747
-#372 := (or #748 #375 #451)
-#530 := [th-lemma arith triangle-eq]: #372
-#526 := [unit-resolution #530 #529 #528 #560]: false
-#510 := [lemma #526]: #531
-#513 := [unit-resolution #510 #571]: #748
-#517 := (or #688 #747)
-#519 := [th-lemma arith triangle-eq]: #517
-#520 := [unit-resolution #519 #513]: #747
-#647 := (<= #12 0::Int)
-#518 := (or #688 #668)
-#621 := (or #620 #688 #668)
-#622 := [def-axiom]: #621
-#521 := [unit-resolution #622 #619]: #518
-#509 := [unit-resolution #521 #513]: #668
-#627 := (not #668)
-#512 := (or #627 #647)
-#514 := [th-lemma arith triangle-eq]: #512
-#515 := [unit-resolution #514 #509]: #647
-#700 := (<= #10 0::Int)
-#511 := (or #688 #752)
-#573 := (or #685 #688 #752)
-#588 := [def-axiom]: #573
-#516 := [unit-resolution #588 #561]: #511
-#506 := [unit-resolution #516 #513]: #752
-#584 := (not #752)
-#496 := (or #584 #700)
-#498 := [th-lemma arith triangle-eq]: #496
-#499 := [unit-resolution #498 #506]: #700
-#502 := [th-lemma arith farkas -3 -1 -1 1 #499 #515 #571 #520]: false
-#503 := [lemma #502]: #426
-#482 := (or #479 #555)
-#84 := (= #83 0::Int)
-#87 := (not #84)
-#11 := (* #10 3::Int)
-#13 := (+ #11 #12)
-#14 := (= f3 #13)
-#15 := (not #14)
-#90 := (iff #15 #87)
-#66 := (* 3::Int #10)
-#69 := (+ #66 #12)
-#72 := (= f3 #69)
-#75 := (not #72)
-#88 := (iff #75 #87)
-#85 := (iff #72 #84)
-#86 := [rewrite]: #85
+#108 := [monotonicity #70 #105]: #107
+#111 := [monotonicity #108]: #110
+#56 := (iff #12 false)
+#57 := [rewrite]: #56
+#114 := [monotonicity #57 #111]: #113
+#118 := [trans #114 #116]: #117
+#93 := (= #26 #90)
+#87 := (* #84 3::Int)
+#91 := (= #87 #90)
+#92 := [rewrite]: #91
+#88 := (= #26 #87)
+#85 := (= #25 #84)
+#82 := (= #24 #81)
+#79 := (= #23 #78)
+#80 := [monotonicity #74 #77]: #79
+#83 := [monotonicity #70 #80]: #82
+#63 := (iff #13 #10)
+#58 := (or #10 false)
+#61 := (iff #58 #10)
+#62 := [rewrite]: #61
+#59 := (iff #13 #58)
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#86 := [monotonicity #64 #83]: #85
 #89 := [monotonicity #86]: #88
-#76 := (iff #15 #75)
-#73 := (iff #14 #72)
-#70 := (= #13 #69)
-#67 := (= #11 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#74 := [monotonicity #71]: #73
-#77 := [monotonicity #74]: #76
-#91 := [trans #77 #89]: #90
-#65 := [asserted]: #15
-#92 := [mp #65 #91]: #87
-#480 := (or #84 #479 #555)
-#481 := [th-lemma arith triangle-eq]: #480
-#483 := [unit-resolution #481 #92]: #482
-#484 := [unit-resolution #483 #503]: #479
-#507 := (<= #617 0::Int)
-#485 := (or #542 #507)
-#486 := [th-lemma arith triangle-eq]: #485
-#487 := [unit-resolution #486 #540]: #507
-#488 := [th-lemma arith farkas -1 1 3 1 #487 #484 #477 #494]: false
-#478 := [lemma #488]: #489
-#500 := [unit-resolution #478 #525 #564]: #704
-#508 := [unit-resolution #703 #500]: #743
-#501 := [unit-resolution #698 #500]: #747
-#504 := [unit-resolution #530 #501 #508 #560]: false
-#505 := [lemma #504]: #748
-#490 := [unit-resolution #516 #505]: #752
-#467 := (or #584 #701)
-#469 := [th-lemma arith triangle-eq]: #467
-#470 := [unit-resolution #469 #490]: #701
-#648 := (>= #12 0::Int)
-#471 := [unit-resolution #521 #505]: #668
-#472 := (or #627 #648)
-#473 := [th-lemma arith triangle-eq]: #472
-#474 := [unit-resolution #473 #471]: #648
-#475 := (or #688 #743)
-#468 := [th-lemma arith triangle-eq]: #475
-#476 := [unit-resolution #468 #505]: #743
-[th-lemma arith farkas -1/3 1/3 1/3 1 #476 #474 #484 #470]: false
+#94 := [trans #89 #92]: #93
+#121 := [monotonicity #94 #118]: #120
+#124 := [monotonicity #121]: #123
+#127 := [monotonicity #124]: #126
+#189 := [trans #127 #187]: #188
+#55 := [asserted]: #35
+#190 := [mp #55 #189]: #185
+#264 := (or #180 #262 #263)
+#265 := [th-lemma arith triangle-eq]: #264
+#267 := [unit-resolution #265 #190]: #266
+#268 := [unit-resolution #267 #261 #250]: false
+#269 := [lemma #268]: #152
+#310 := [hypothesis]: #10
+#311 := (or #207 #128)
+#312 := [th-lemma arith triangle-eq]: #311
+#313 := [unit-resolution #312 #310]: #128
+#314 := (or #207 #141)
+#286 := [th-lemma arith triangle-eq]: #314
+#319 := [unit-resolution #286 #310]: #141
+#201 := (or #200 #129 #142)
+#202 := [def-axiom]: #201
+#323 := [unit-resolution #202 #319 #313 #269]: false
+#350 := [lemma #323]: #207
+#222 := (or #10 #213)
+#223 := [def-axiom]: #222
+#359 := [unit-resolution #223 #350]: #213
+#214 := (= #27 #164)
+#216 := (or #200 #214)
+#217 := [def-axiom]: #216
+#326 := [unit-resolution #217 #269]: #214
+#360 := [trans #326 #359]: #320
+#328 := (not #320)
+#361 := (or #328 #358)
+#362 := [th-lemma arith triangle-eq]: #361
+#363 := [unit-resolution #362 #360]: #358
+#280 := (* -1::Int #27)
+#279 := (* -3::Int #20)
+#281 := (+ #279 #280)
+#282 := (+ f3 #281)
+#351 := (>= #282 0::Int)
+#278 := (= #282 0::Int)
+#53 := [true-axiom]: true
+#332 := (or false #278)
+#333 := [th-lemma arith]: #332
+#334 := [unit-resolution #333 #53]: #278
+#335 := (not #278)
+#364 := (or #335 #351)
+#365 := [th-lemma arith triangle-eq]: #364
+#366 := [unit-resolution #365 #334]: #351
+#348 := (or #10 #224)
+#322 := (<= #321 0::Int)
+#324 := [hypothesis]: #207
+#325 := [unit-resolution #223 #324]: #213
+#327 := [trans #326 #325]: #320
+#329 := (or #328 #322)
+#330 := [th-lemma arith triangle-eq]: #329
+#331 := [unit-resolution #330 #327]: #322
+#285 := (<= #282 0::Int)
+#336 := (or #335 #285)
+#337 := [th-lemma arith triangle-eq]: #336
+#338 := [unit-resolution #337 #334]: #285
+#339 := [hypothesis]: #262
+#316 := (* -1::Int #158)
+#317 := (+ #20 #316)
+#318 := (<= #317 0::Int)
+#315 := (= #20 #158)
+#197 := (= #155 #158)
+#210 := (or #10 #197)
+#211 := [def-axiom]: #210
+#340 := [unit-resolution #211 #324]: #197
+#198 := (= #20 #155)
+#203 := (or #200 #198)
+#204 := [def-axiom]: #203
+#341 := [unit-resolution #204 #269]: #198
+#342 := [trans #341 #340]: #315
+#343 := (not #315)
+#344 := (or #343 #318)
+#345 := [th-lemma arith triangle-eq]: #344
+#346 := [unit-resolution #345 #342]: #318
+#347 := [th-lemma arith farkas 3 -1 1 1 #346 #339 #338 #331]: false
+#349 := [lemma #347]: #348
+#367 := [unit-resolution #349 #350]: #224
+#368 := [unit-resolution #267 #367]: #263
+#357 := (>= #317 0::Int)
+#369 := [unit-resolution #211 #350]: #197
+#370 := [trans #341 #369]: #315
+#371 := (or #343 #357)
+#372 := [th-lemma arith triangle-eq]: #371
+#373 := [unit-resolution #372 #370]: #357
+[th-lemma arith farkas 3 -1 1 1 #373 #368 #366 #363]: false
 unsat
 cacbb4776a876130daed2cf13657b41ab1c7df25 75 0
 #2 := false

--- a/src/HOL/SMT_Examples/SMT_Word_Examples.certs	Sun Dec 19 18:54:29 2010 +0100
+++ b/src/HOL/SMT_Examples/SMT_Word_Examples.certs	Sun Dec 19 18:55:21 2010 +0100
@@ -36,6 +36,12 @@
 unsat
 64c9fe73f7ca3832f4daec3b66d94e4f6c730fa5 1 0
 unsat
+d8e56ac599bc3827a065804e88fc36c63a5afcfb 1 0
+unsat
+a3340f8171cd0db9c0dd45f33a3cb1a42e793eee 1 0
+unsat
+a8dd16a0d6a6514edcc3baafb20317536ccd338c 1 0
+unsat
 d5adb105f62510f5a3181800d02bb2208b8170d6 1 0
 unsat
 f9ac14ab5e87743181fef8830f46edfda6007e6e 1 0
@@ -46,5 +52,5 @@
 unsat
 56db2066218af38e5a0015563c6a360d4cba04a7 1 0
 unsat
-e8d71df84f80ee07d30baf7a7df718db9a4df777 1 0
+3bf2dcb45282e43fa4ebfc5c17aaa663f9ce6a76 1 0
 unsat

--- a/src/HOL/SMT_Examples/SMT_Word_Examples.thy	Sun Dec 19 18:54:29 2010 +0100
+++ b/src/HOL/SMT_Examples/SMT_Word_Examples.thy	Sun Dec 19 18:55:21 2010 +0100
@@ -66,11 +66,11 @@
 
 lemma "scast (0b1010 :: 4 word) = (0b111010 :: 6 word)" by smt
 
-lemma "0b10011 << 2 = (0b1001100::8 word)" sorry (* FIXME *)
+lemma "0b10011 << 2 = (0b1001100::8 word)" by smt
 
-lemma "0b11001 >> 2 = (0b110::8 word)" sorry (* FIXME *)
+lemma "0b11001 >> 2 = (0b110::8 word)" by smt
 
-lemma "0b10011 >>> 2 = (0b100::8 word)" sorry (* FIXME *)
+lemma "0b10011 >>> 2 = (0b100::8 word)" by smt
 
 lemma "word_rotr 2 0b0110 = (0b1001::4 word)" by smt