updated SMT certificates
authorboehmes
Tue, 07 Dec 2010 15:44:38 +0100
changeset 41064 0c447a17770a
parent 41063 0828bfa70b20
child 41065 13424972ade4
updated SMT certificates
src/HOL/Boogie/Examples/Boogie_Dijkstra.certs
src/HOL/Boogie/Examples/Boogie_Max.certs
src/HOL/Boogie/Examples/VCC_Max.certs
src/HOL/Multivariate_Analysis/Integration.certs
src/HOL/SMT_Examples/SMT_Examples.certs
src/HOL/SMT_Examples/SMT_Tests.certs
src/HOL/SMT_Examples/SMT_Word_Examples.certs
--- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Tue Dec 07 15:01:42 2010 +0100
+++ b/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Tue Dec 07 15:44:38 2010 +0100
@@ -1,6890 +1,6866 @@
-6752602a8162146a4b4b0b817f42d730f1852d5d 6889 0
+b3bc982ea5dfc2f7a56401abdc23012a96a9cd57 6865 0
 #2 := false
-decl f11 :: (-> S5 S2 S1)
-decl ?v1!7 :: (-> S2 S2)
-decl ?v0!20 :: S2
-#2295 := ?v0!20
-#6027 := (?v1!7 ?v0!20)
-decl f20 :: S5
-#146 := f20
-#12518 := (f11 f20 #6027)
+decl f13 :: (-> S5 S3 int)
+decl ?v0!20 :: S3
+#2319 := ?v0!20
+decl f14 :: S5
+#98 := f14
+#5756 := (f13 f14 ?v0!20)
+decl f24 :: (-> S3 int)
+#2320 := (f24 ?v0!20)
+#5761 := (= #2320 #5756)
+decl f22 :: S3
+#170 := f22
+#174 := (f13 f14 f22)
+#12275 := (= #174 #5756)
+#10317 := (= #5756 #174)
+#12111 := (= ?v0!20 f22)
+decl f4 :: (-> S2 S3)
+decl f3 :: (-> S3 S3 S2)
+decl f10 :: S3
+#56 := f10
+#4870 := (f3 f22 f10)
+#9390 := (f4 #4870)
+#9999 := (= #9390 f22)
+#9391 := (= f22 #9390)
+#15 := (:var 0 S3)
+#14 := (:var 1 S3)
+#16 := (f3 #14 #15)
+#4152 := (pattern #16)
+#20 := (f4 #16)
+#304 := (= #14 #20)
+#4159 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4152) #304)
+#308 := (forall (vars (?v0 S3) (?v1 S3)) #304)
+#4162 := (iff #308 #4159)
+#4160 := (iff #304 #304)
+#4161 := [refl]: #4160
+#4163 := [quant-intro #4161]: #4162
+#1817 := (~ #308 #308)
+#1845 := (~ #304 #304)
+#1846 := [refl]: #1845
+#1818 := [nnf-pos #1846]: #1817
+#21 := (= #20 #14)
+#22 := (forall (vars (?v0 S3) (?v1 S3)) #21)
+#309 := (iff #22 #308)
+#306 := (iff #21 #304)
+#307 := [rewrite]: #306
+#310 := [quant-intro #307]: #309
+#303 := [asserted]: #22
+#313 := [mp #303 #310]: #308
+#1847 := [mp~ #313 #1818]: #308
+#4164 := [mp #1847 #4163]: #4159
+#9463 := (not #4159)
+#9396 := (or #9463 #9391)
+#9397 := [quant-inst]: #9396
+#9998 := [unit-resolution #9397 #4164]: #9391
+#10000 := [symm #9998]: #9999
+#17237 := (= ?v0!20 #9390)
+#44 := 0::int
+decl f9 :: (-> S2 int)
+#5807 := (f3 f22 ?v0!20)
+#5808 := (f9 #5807)
+#1181 := -1::int
+#2321 := (* -1::int #2320)
+#5833 := (+ #2321 #5808)
+#5834 := (+ #174 #5833)
+#5837 := (= #5834 0::int)
+#5812 := (* -1::int #5808)
+decl f8 :: int
+#45 := f8
+#5816 := (+ f8 #5812)
+#5817 := (<= #5816 0::int)
+#17186 := (not #5817)
+#5791 := (* -1::int #5756)
+#5826 := (+ #5791 #5808)
+#5827 := (+ #174 #5826)
+#5828 := (>= #5827 0::int)
+#5859 := (or #5817 #5828)
+#5862 := (not #5859)
+#22167 := (not #5761)
+#5792 := (+ #2320 #5791)
+#18300 := (>= #5792 0::int)
+#22163 := (not #18300)
+#2331 := (+ f8 #2321)
+#2332 := (<= #2331 0::int)
+#2333 := (not #2332)
+#2323 := (f3 #15 ?v0!20)
+#4427 := (pattern #2323)
+#189 := (f24 #15)
+#4367 := (pattern #189)
+decl f6 :: (-> S4 S3 S1)
+decl f23 :: S4
+#179 := f23
+#199 := (f6 f23 #15)
+#4393 := (pattern #199)
+#2324 := (f9 #2323)
+#2923 := (+ #2321 #2324)
+#2924 := (+ #189 #2923)
+#2927 := (= #2924 0::int)
+#3489 := (not #2927)
+#2322 := (+ #189 #2321)
+#2327 := (>= #2322 0::int)
 decl f1 :: S1
 #4 := f1
-#16616 := (= f1 #12518)
-decl f23 :: (-> S3 S2)
-decl f5 :: (-> S2 S2 S3)
-#6032 := (f5 #6027 ?v0!20)
-#19988 := (f23 #6032)
-decl f21 :: (-> S5 S2 S1 S5)
-decl f19 :: S2
-#137 := f19
-decl f12 :: S5
-#71 := f12
-#147 := (f21 f12 f19 f1)
-#3738 := (f11 #147 f19)
-decl f24 :: (-> S3 S2)
-#4718 := (f5 f19 f19)
-#9605 := (f24 #4718)
-#10278 := (f21 f12 #9605 #3738)
-#30481 := (f11 #10278 #19988)
-#24597 := (= #30481 #12518)
-#24573 := (= #12518 #30481)
-#20012 := (= #6027 #19988)
-#12 := (:var 0 S2)
-#11 := (:var 1 S2)
-#14 := (f5 #11 #12)
-#4135 := (pattern #14)
-#259 := (f23 #14)
-#1779 := (= #11 #259)
-#4555 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4135) #1779)
-#1783 := (forall (vars (?v0 S2) (?v1 S2)) #1779)
-#4558 := (iff #1783 #4555)
-#4556 := (iff #1779 #1779)
-#4557 := [refl]: #4556
-#4559 := [quant-intro #4557]: #4558
-#1822 := (~ #1783 #1783)
-#2078 := (~ #1779 #1779)
-#2228 := [refl]: #2078
-#1823 := [nnf-pos #2228]: #1822
-#260 := (= #259 #11)
-#261 := (forall (vars (?v0 S2) (?v1 S2)) #260)
-#1784 := (iff #261 #1783)
-#1781 := (iff #260 #1779)
-#1782 := [rewrite]: #1781
-#1785 := [quant-intro #1782]: #1784
-#1778 := [asserted]: #261
-#1788 := [mp #1778 #1785]: #1783
-#2229 := [mp~ #1788 #1823]: #1783
-#4560 := [mp #2229 #4559]: #4555
-#9574 := (not #4555)
-#20097 := (or #9574 #20012)
-#16830 := [quant-inst]: #20097
-#30680 := [unit-resolution #16830 #4560]: #20012
-#13558 := (= f20 #10278)
-#13508 := (= #147 #10278)
-#11165 := (= #10278 #147)
-#11163 := (= #3738 f1)
-#3747 := (= f1 #3738)
-#239 := (:var 0 S1)
-#238 := (:var 2 S5)
-#240 := (f21 #238 #11 #239)
-#4541 := (pattern #240)
-#1749 := (= f1 #239)
-#241 := (f11 #240 #11)
-#1746 := (= f1 #241)
-#1752 := (iff #1746 #1749)
-#4542 := (forall (vars (?v0 S5) (?v1 S2) (?v2 S1)) (:pat #4541) #1752)
-#1755 := (forall (vars (?v0 S5) (?v1 S2) (?v2 S1)) #1752)
-#4545 := (iff #1755 #4542)
-#4543 := (iff #1752 #1752)
-#4544 := [refl]: #4543
-#4546 := [quant-intro #4544]: #4545
-#1818 := (~ #1755 #1755)
-#2003 := (~ #1752 #1752)
-#1849 := [refl]: #2003
-#1819 := [nnf-pos #1849]: #1818
-#243 := (= #239 f1)
-#242 := (= #241 f1)
-#244 := (iff #242 #243)
-#245 := (forall (vars (?v0 S5) (?v1 S2) (?v2 S1)) #244)
-#1756 := (iff #245 #1755)
-#1753 := (iff #244 #1752)
-#1750 := (iff #243 #1749)
-#1751 := [rewrite]: #1750
-#1747 := (iff #242 #1746)
-#1748 := [rewrite]: #1747
-#1754 := [monotonicity #1748 #1751]: #1753
-#1757 := [quant-intro #1754]: #1756
-#1745 := [asserted]: #245
-#1760 := [mp #1745 #1757]: #1755
-#1850 := [mp~ #1760 #1819]: #1755
-#4547 := [mp #1850 #4546]: #4542
-#6762 := (not #4542)
-#6880 := (or #6762 #3747)
-#3746 := (= f1 f1)
-#3734 := (iff #3747 #3746)
-#6881 := (or #6762 #3734)
-#6895 := (iff #6881 #6880)
-#7240 := (iff #6880 #6880)
-#7241 := [rewrite]: #7240
-#4575 := (iff #3734 #3747)
-#1 := true
-#3724 := (iff #3747 true)
-#3730 := (iff #3724 #3747)
-#3726 := [rewrite]: #3730
-#3725 := (iff #3734 #3724)
-#3735 := (iff #3746 true)
-#3722 := [rewrite]: #3735
-#3723 := [monotonicity #3722]: #3725
-#4576 := [trans #3723 #3726]: #4575
-#7239 := [monotonicity #4576]: #6895
-#7243 := [trans #7239 #7241]: #6895
-#6896 := [quant-inst]: #6881
-#7244 := [mp #6896 #7243]: #6880
-#11162 := [unit-resolution #7244 #4547]: #3747
-#11164 := [symm #11162]: #11163
-#10825 := (= #9605 f19)
-#9606 := (= f19 #9605)
-#262 := (f24 #14)
-#1787 := (= #12 #262)
-#4561 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4135) #1787)
-#1791 := (forall (vars (?v0 S2) (?v1 S2)) #1787)
-#4564 := (iff #1791 #4561)
-#4562 := (iff #1787 #1787)
-#4563 := [refl]: #4562
-#4565 := [quant-intro #4563]: #4564
-#1824 := (~ #1791 #1791)
-#1876 := (~ #1787 #1787)
-#1877 := [refl]: #1876
-#1825 := [nnf-pos #1877]: #1824
-#263 := (= #262 #12)
-#264 := (forall (vars (?v0 S2) (?v1 S2)) #263)
-#1792 := (iff #264 #1791)
-#1789 := (iff #263 #1787)
-#1790 := [rewrite]: #1789
-#1793 := [quant-intro #1790]: #1792
-#1786 := [asserted]: #264
-#1796 := [mp #1786 #1793]: #1791
-#2188 := [mp~ #1796 #1825]: #1791
-#4566 := [mp #2188 #4565]: #4561
-#7210 := (not #4561)
-#9608 := (or #7210 #9606)
-#9609 := [quant-inst]: #9608
-#10824 := [unit-resolution #9609 #4566]: #9606
-#10826 := [symm #10824]: #10825
-#11166 := [monotonicity #10826 #11164]: #11165
-#13557 := [symm #11166]: #13508
-#148 := (= f20 #147)
-#2299 := (f5 #12 ?v0!20)
-#4384 := (pattern #2299)
-decl f22 :: (-> S2 int)
-#155 := (f22 #12)
-#4324 := (pattern #155)
-#165 := (f11 f20 #12)
-#4350 := (pattern #165)
-#8 := 0::int
-decl f4 :: (-> S3 int)
-#2300 := (f4 #2299)
-#2296 := (f22 ?v0!20)
-#1114 := -1::int
-#2297 := (* -1::int #2296)
-#2899 := (+ #2297 #2300)
-#2900 := (+ #155 #2899)
-#2903 := (= #2900 0::int)
-#3480 := (not #2903)
-#2298 := (+ #155 #2297)
-#2303 := (>= #2298 0::int)
-#713 := (= f1 #165)
-#719 := (not #713)
-#3481 := (or #719 #2303 #3480)
-#4385 := (forall (vars (?v1 S2)) (:pat #4350 #4324 #4384) #3481)
+#780 := (= f1 #199)
+#786 := (not #780)
+#3490 := (or #786 #2327 #3489)
+#4428 := (forall (vars (?v1 S3)) (:pat #4393 #4367 #4427) #3490)
+#4433 := (not #4428)
+#81 := (f3 #15 #14)
+#4222 := (pattern #81)
+#211 := (f24 #14)
+#1476 := (* -1::int #211)
+#1477 := (+ #189 #1476)
+#82 := (f9 #81)
+#1507 := (+ #82 #1477)
+#1505 := (>= #1507 0::int)
+#1204 := (* -1::int #82)
+#1207 := (+ f8 #1204)
+#1208 := (<= #1207 0::int)
+#3481 := (or #786 #1208 #1505)
+#4419 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4222) #3481)
+#4424 := (not #4419)
+#2899 := (= f10 ?v0!20)
+#4436 := (or #2332 #2899 #4424 #4433)
+#4439 := (not #4436)
+decl ?v0!19 :: S3
+#2289 := ?v0!19
+decl ?v1!18 :: S3
+#2288 := ?v1!18
+#2294 := (f3 ?v1!18 ?v0!19)
+#2295 := (f9 #2294)
+#2298 := (* -1::int #2295)
+#2292 := (f24 ?v1!18)
+#2885 := (* -1::int #2292)
+#2886 := (+ #2885 #2298)
+#2290 := (f24 ?v0!19)
+#2887 := (+ #2290 #2886)
+#2888 := (<= #2887 0::int)
+#2302 := (f6 f23 ?v1!18)
+#2303 := (= f1 #2302)
+#3444 := (not #2303)
+#2299 := (+ f8 #2298)
+#2300 := (<= #2299 0::int)
+#3459 := (or #2300 #3444 #2888)
+#3464 := (not #3459)
+#4442 := (or #3464 #4439)
+#4445 := (not #4442)
+#4410 := (pattern #189 #211)
+#1475 := (>= #1477 0::int)
+#208 := (f6 f23 #14)
+#800 := (= f1 #208)
+#3421 := (not #800)
+#3436 := (or #780 #3421 #1475)
+#4411 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4410) #3436)
+#4416 := (not #4411)
+#4448 := (or #4416 #4445)
+#4451 := (not #4448)
+decl ?v1!16 :: S3
+#2261 := ?v1!16
+#2265 := (f24 ?v1!16)
+#2859 := (* -1::int #2265)
+decl ?v0!17 :: S3
+#2262 := ?v0!17
+#2263 := (f24 ?v0!17)
+#2860 := (+ #2263 #2859)
+#2861 := (<= #2860 0::int)
+#2270 := (f6 f23 ?v1!16)
+#2271 := (= f1 #2270)
+#2268 := (f6 f23 ?v0!17)
+#2269 := (= f1 #2268)
+#3398 := (not #2269)
+#3413 := (or #3398 #2271 #2861)
+#12747 := (= ?v1!16 #9390)
+#17719 := (not #12747)
+decl f15 :: S4
+#104 := f15
+#6471 := (f6 f15 ?v1!16)
+#6472 := (= f1 #6471)
+decl f7 :: (-> S4 S3 S1 S4)
+#746 := (f7 f15 f22 f1)
+#3804 := (f6 #746 f22)
+#3805 := (= f1 #3804)
+#12748 := (ite #12747 #3805 #6472)
+#17705 := (not #12748)
+#9617 := (f7 f15 #9390 #3804)
+#12749 := (f6 #9617 ?v1!16)
+#12750 := (= f1 #12749)
+#12752 := (iff #12748 #12750)
+#25 := (:var 1 S1)
+#24 := (:var 2 S3)
+#23 := (:var 3 S4)
+#26 := (f7 #23 #24 #25)
+#27 := (f6 #26 #15)
+#4165 := (pattern #27)
+#31 := (f6 #23 #15)
+#319 := (= f1 #31)
+#316 := (= f1 #25)
+#29 := (= #15 #24)
+#322 := (ite #29 #316 #319)
+#312 := (= f1 #27)
+#325 := (iff #312 #322)
+#4166 := (forall (vars (?v0 S4) (?v1 S3) (?v2 S1) (?v3 S3)) (:pat #4165) #325)
+#328 := (forall (vars (?v0 S4) (?v1 S3) (?v2 S1) (?v3 S3)) #325)
+#4169 := (iff #328 #4166)
+#4167 := (iff #325 #325)
+#4168 := [refl]: #4167
+#4170 := [quant-intro #4168]: #4169
+#1819 := (~ #328 #328)
+#1848 := (~ #325 #325)
+#1849 := [refl]: #1848
+#1820 := [nnf-pos #1849]: #1819
+#32 := (= #31 f1)
+#30 := (= #25 f1)
+#33 := (ite #29 #30 #32)
+#28 := (= #27 f1)
+#34 := (iff #28 #33)
+#35 := (forall (vars (?v0 S4) (?v1 S3) (?v2 S1) (?v3 S3)) #34)
+#329 := (iff #35 #328)
+#326 := (iff #34 #325)
+#323 := (iff #33 #322)
+#320 := (iff #32 #319)
+#321 := [rewrite]: #320
+#317 := (iff #30 #316)
+#318 := [rewrite]: #317
+#324 := [monotonicity #318 #321]: #323
+#314 := (iff #28 #312)
+#315 := [rewrite]: #314
+#327 := [monotonicity #315 #324]: #326
+#330 := [quant-intro #327]: #329
+#311 := [asserted]: #35
+#333 := [mp #311 #330]: #328
+#1850 := [mp~ #333 #1820]: #328
+#4171 := [mp #1850 #4170]: #4166
+#8910 := (not #4166)
+#17716 := (or #8910 #12752)
+#12751 := (iff #12750 #12748)
+#17696 := (or #8910 #12751)
+#17700 := (iff #17696 #17716)
+#17701 := (iff #17716 #17716)
+#17702 := [rewrite]: #17701
+#12753 := (iff #12751 #12752)
+#12754 := [rewrite]: #12753
+#17695 := [monotonicity #12754]: #17700
+#17703 := [trans #17695 #17702]: #17700
+#17699 := [quant-inst]: #17696
+#17704 := [mp #17699 #17703]: #17716
+#19323 := [unit-resolution #17704 #4171]: #12752
+#17728 := (not #12750)
+#2272 := (not #2271)
+#19377 := (iff #2272 #17728)
+#19375 := (iff #2271 #12750)
+#19320 := (iff #12750 #2271)
+#19329 := (= #12749 #2270)
+#10057 := (= #9617 f23)
+#10055 := (= #746 f23)
+#749 := (= f23 #746)
+#3418 := (not #3413)
+#4454 := (or #3418 #4451)
+#4457 := (not #4454)
+#1466 := (>= #189 0::int)
+#4402 := (forall (vars (?v0 S3)) (:pat #4367) #1466)
+#4407 := (not #4402)
+#4460 := (or #4407 #4457)
+#4463 := (not #4460)
+decl ?v0!15 :: S3
+#2246 := ?v0!15
+#2247 := (f24 ?v0!15)
+#2248 := (>= #2247 0::int)
+#2249 := (not #2248)
+#4466 := (or #2249 #4463)
+#4469 := (not #4466)
+#203 := (f24 f10)
+#204 := (= #203 0::int)
+#1463 := (not #204)
+#4472 := (or #1463 #4469)
+#4475 := (not #4472)
+#4478 := (or #1463 #4475)
+#4481 := (not #4478)
+#101 := (f13 f14 #15)
+#4246 := (pattern #101)
+#766 := (= #101 #189)
+#787 := (or #766 #786)
+#4394 := (forall (vars (?v0 S3)) (:pat #4246 #4367 #4393) #787)
+#4399 := (not #4394)
+#4484 := (or #4399 #4481)
+#4487 := (not #4484)
+decl ?v0!14 :: S3
+#2221 := ?v0!14
+#2226 := (f13 f14 ?v0!14)
+#2225 := (f24 ?v0!14)
+#2831 := (= #2225 #2226)
+#2222 := (f6 f23 ?v0!14)
+#2223 := (= f1 #2222)
+#2224 := (not #2223)
+#2837 := (or #2224 #2831)
+#2842 := (not #2837)
+#4490 := (or #2842 #4487)
+#4493 := (not #4490)
+#1451 := (* -1::int #189)
+#1452 := (+ #101 #1451)
+#1450 := (>= #1452 0::int)
+#4385 := (forall (vars (?v0 S3)) (:pat #4246 #4367) #1450)
 #4390 := (not #4385)
-#48 := (f5 #12 #11)
-#4179 := (pattern #48)
-#177 := (f22 #11)
-#1409 := (* -1::int #177)
-#1410 := (+ #155 #1409)
-#49 := (f4 #48)
-#1440 := (+ #49 #1410)
-#1438 := (>= #1440 0::int)
-#1137 := (* -1::int #49)
-decl f3 :: int
-#9 := f3
-#1140 := (+ f3 #1137)
-#1141 := (<= #1140 0::int)
-#3472 := (or #719 #1141 #1438)
-#4376 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4179) #3472)
-#4381 := (not #4376)
-decl f6 :: S2
-#23 := f6
-#2875 := (= f6 ?v0!20)
-#2307 := (+ f3 #2297)
-#2308 := (<= #2307 0::int)
-#4393 := (or #2308 #2875 #4381 #4390)
-#4396 := (not #4393)
-decl ?v0!19 :: S2
-#2265 := ?v0!19
-decl ?v1!18 :: S2
-#2264 := ?v1!18
-#2270 := (f5 ?v1!18 ?v0!19)
-#2271 := (f4 #2270)
-#2274 := (* -1::int #2271)
-#2268 := (f22 ?v1!18)
-#2861 := (* -1::int #2268)
-#2862 := (+ #2861 #2274)
-#2266 := (f22 ?v0!19)
-#2863 := (+ #2266 #2862)
-#2864 := (<= #2863 0::int)
-#2278 := (f11 f20 ?v1!18)
-#2279 := (= f1 #2278)
-#3435 := (not #2279)
-#2275 := (+ f3 #2274)
-#2276 := (<= #2275 0::int)
-#3450 := (or #2276 #3435 #2864)
-#3455 := (not #3450)
-#4399 := (or #3455 #4396)
-#4402 := (not #4399)
-#4367 := (pattern #155 #177)
-#1408 := (>= #1410 0::int)
-#174 := (f11 f20 #11)
-#733 := (= f1 #174)
-#3412 := (not #733)
-#3427 := (or #713 #3412 #1408)
-#4368 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4367) #3427)
-#4373 := (not #4368)
-#4405 := (or #4373 #4402)
-#4408 := (not #4405)
-decl ?v1!16 :: S2
-#2237 := ?v1!16
-#2241 := (f22 ?v1!16)
-#2835 := (* -1::int #2241)
-decl ?v0!17 :: S2
-#2238 := ?v0!17
-#2239 := (f22 ?v0!17)
-#2836 := (+ #2239 #2835)
-#2837 := (<= #2836 0::int)
-#2246 := (f11 f20 ?v1!16)
-#2247 := (= f1 #2246)
-#2244 := (f11 f20 ?v0!17)
-#2245 := (= f1 #2244)
-#3389 := (not #2245)
-#3404 := (or #3389 #2247 #2837)
-#3409 := (not #3404)
-#4411 := (or #3409 #4408)
-#4414 := (not #4411)
-#1399 := (>= #155 0::int)
-#4359 := (forall (vars (?v0 S2)) (:pat #4324) #1399)
+#4496 := (or #4390 #4493)
+#4499 := (not #4496)
+decl ?v0!13 :: S3
+#2203 := ?v0!13
+#2206 := (f13 f14 ?v0!13)
+#2821 := (* -1::int #2206)
+#2204 := (f24 ?v0!13)
+#2822 := (+ #2204 #2821)
+#2823 := (<= #2822 0::int)
+#2828 := (not #2823)
+#4502 := (or #2828 #4499)
+#4505 := (not #4502)
+#183 := (f3 f22 #15)
+#4368 := (pattern #183)
+#184 := (f9 #183)
+#1594 := (+ #184 #1451)
+#1595 := (+ #174 #1594)
+#1596 := (= #1595 0::int)
+#1420 := (* -1::int #184)
+#1426 := (* -1::int #174)
+#1427 := (+ #1426 #1420)
+#1428 := (+ #101 #1427)
+#1429 := (<= #1428 0::int)
+#1421 := (+ f8 #1420)
+#1422 := (<= #1421 0::int)
+#3390 := (or #1422 #1429 #1596)
+#4377 := (forall (vars (?v0 S3)) (:pat #4368 #4246 #4367) #3390)
+#4382 := (not #4377)
+#3370 := (or #1422 #1429)
+#3371 := (not #3370)
+#3374 := (or #766 #3371)
+#4369 := (forall (vars (?v0 S3)) (:pat #4246 #4367 #4368) #3374)
+#4374 := (not #4369)
+decl ?v0!12 :: S3
+#2179 := ?v0!12
+#2185 := (f6 f15 ?v0!12)
+#2186 := (= f1 #2185)
+#2180 := (f13 f14 ?v0!12)
+#2181 := (* -1::int #2180)
+#2182 := (+ f8 #2181)
+#2183 := (<= #2182 0::int)
+#1626 := (+ f8 #1426)
+#1627 := (<= #1626 0::int)
+#105 := (f6 f15 #15)
+#4288 := (pattern #105)
+#1609 := (+ #101 #1426)
+#1608 := (>= #1609 0::int)
+#506 := (= f1 #105)
+#1615 := (or #506 #1608)
+#4359 := (forall (vars (?v0 S3)) (:pat #4288 #4246) #1615)
 #4364 := (not #4359)
-#4417 := (or #4364 #4414)
-#4420 := (not #4417)
-decl ?v0!15 :: S2
-#2222 := ?v0!15
-#2223 := (f22 ?v0!15)
-#2224 := (>= #2223 0::int)
-#2225 := (not #2224)
-#4423 := (or #2225 #4420)
-#4426 := (not #4423)
-#169 := (f22 f6)
-#170 := (= #169 0::int)
-#1396 := (not #170)
-#4429 := (or #1396 #4426)
-#4432 := (not #4429)
-#4435 := (or #1396 #4432)
-#4438 := (not #4435)
-decl f9 :: (-> S4 S2 int)
-decl f10 :: S4
-#65 := f10
-#68 := (f9 f10 #12)
-#4203 := (pattern #68)
-#699 := (= #68 #155)
-#720 := (or #699 #719)
-#4351 := (forall (vars (?v0 S2)) (:pat #4203 #4324 #4350) #720)
-#4356 := (not #4351)
-#4441 := (or #4356 #4438)
-#4444 := (not #4441)
-decl ?v0!14 :: S2
-#2197 := ?v0!14
-#2202 := (f9 f10 ?v0!14)
-#2201 := (f22 ?v0!14)
-#2807 := (= #2201 #2202)
-#2198 := (f11 f20 ?v0!14)
-#2199 := (= f1 #2198)
-#2200 := (not #2199)
-#2813 := (or #2200 #2807)
-#2818 := (not #2813)
-#4447 := (or #2818 #4444)
-#4450 := (not #4447)
-#1384 := (* -1::int #155)
-#1385 := (+ #68 #1384)
-#1383 := (>= #1385 0::int)
-#4342 := (forall (vars (?v0 S2)) (:pat #4203 #4324) #1383)
-#4347 := (not #4342)
-#4453 := (or #4347 #4450)
-#4456 := (not #4453)
-decl ?v0!13 :: S2
-#2179 := ?v0!13
-#2182 := (f9 f10 ?v0!13)
-#2797 := (* -1::int #2182)
-#2180 := (f22 ?v0!13)
-#2798 := (+ #2180 #2797)
-#2799 := (<= #2798 0::int)
-#2804 := (not #2799)
-#4459 := (or #2804 #4456)
-#4462 := (not #4459)
-#149 := (f5 f19 #12)
-#4325 := (pattern #149)
-#150 := (f4 #149)
-#1527 := (+ #150 #1384)
-#141 := (f9 f10 f19)
-#1528 := (+ #141 #1527)
-#1529 := (= #1528 0::int)
-#1353 := (* -1::int #150)
-#1359 := (* -1::int #141)
-#1360 := (+ #1359 #1353)
-#1361 := (+ #68 #1360)
-#1362 := (<= #1361 0::int)
-#1354 := (+ f3 #1353)
-#1355 := (<= #1354 0::int)
-#3381 := (or #1355 #1362 #1529)
-#4334 := (forall (vars (?v0 S2)) (:pat #4325 #4203 #4324) #3381)
-#4339 := (not #4334)
-#3361 := (or #1355 #1362)
-#3362 := (not #3361)
-#3365 := (or #699 #3362)
-#4326 := (forall (vars (?v0 S2)) (:pat #4203 #4324 #4325) #3365)
-#4331 := (not #4326)
-decl ?v0!12 :: S2
-#2155 := ?v0!12
-#2161 := (f11 f12 ?v0!12)
-#2162 := (= f1 #2161)
-#2156 := (f9 f10 ?v0!12)
-#2157 := (* -1::int #2156)
-#2158 := (+ f3 #2157)
-#2159 := (<= #2158 0::int)
-#1559 := (+ f3 #1359)
-#1560 := (<= #1559 0::int)
-#72 := (f11 f12 #12)
-#4245 := (pattern #72)
-#1542 := (+ #68 #1359)
-#1541 := (>= #1542 0::int)
-#447 := (= f1 #72)
-#1548 := (or #447 #1541)
-#4316 := (forall (vars (?v0 S2)) (:pat #4245 #4203) #1548)
-#4321 := (not #4316)
-#138 := (f11 f12 f19)
-#668 := (= f1 #138)
-#901 := (not #148)
-#4465 := (or #901 #668 #4321 #1560 #2159 #2162 #4331 #4339 #4462)
-#4468 := (not #4465)
-decl ?v0!11 :: S2
-#2089 := ?v0!11
-decl ?v1!10 :: S2
-#2088 := ?v1!10
-#2094 := (f5 ?v1!10 ?v0!11)
-#2095 := (f4 #2094)
-#2102 := (* -1::int #2095)
+#968 := (not #749)
+#171 := (f6 f15 f22)
+#727 := (= f1 #171)
+#4508 := (or #727 #968 #4364 #1627 #2183 #2186 #4374 #4382 #4505)
+#4511 := (not #4508)
+decl ?v0!11 :: S3
+#2113 := ?v0!11
+decl ?v1!10 :: S3
+#2112 := ?v1!10
+#2118 := (f3 ?v1!10 ?v0!11)
+#2119 := (f9 #2118)
+#2126 := (* -1::int #2119)
+decl f19 :: S5
+#137 := f19
+#2116 := (f13 f19 ?v1!10)
+#2122 := (* -1::int #2116)
+#2778 := (+ #2122 #2126)
+#2114 := (f13 f19 ?v0!11)
+#2779 := (+ #2114 #2778)
+#2780 := (<= #2779 0::int)
+#2127 := (+ f8 #2126)
+#2128 := (<= #2127 0::int)
+#2123 := (+ f8 #2122)
+#2124 := (<= #2123 0::int)
+#3334 := (or #2124 #2128 #2780)
+#3339 := (not #3334)
+#145 := (f13 f19 #14)
+#1328 := (* -1::int #145)
+#142 := (f13 f19 #15)
+#1329 := (+ #142 #1328)
+#1335 := (+ #82 #1329)
+#1358 := (>= #1335 0::int)
+#1315 := (* -1::int #142)
+#1316 := (+ f8 #1315)
+#1317 := (<= #1316 0::int)
+#3302 := (or #1208 #1317 #1358)
+#4321 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4222) #3302)
+#4326 := (not #4321)
+#157 := (f13 f19 f10)
+#158 := (= #157 0::int)
+#4329 := (or #158 #4326)
+#4332 := (not #4329)
+#4335 := (or #4332 #3339)
+#4338 := (not #4335)
+#4297 := (pattern #142)
+decl ?v1!9 :: (-> S3 S3)
+#2089 := (?v1!9 #15)
+#2092 := (f3 #2089 #15)
+#2093 := (f9 #2092)
+#2748 := (* -1::int #2093)
+#2090 := (f13 f19 #2089)
+#2731 := (* -1::int #2090)
+#2749 := (+ #2731 #2748)
+#2750 := (+ #142 #2749)
+#2751 := (= #2750 0::int)
+#3272 := (not #2751)
+#2732 := (+ #142 #2731)
+#2733 := (<= #2732 0::int)
+#3273 := (or #2733 #3272)
+#3274 := (not #3273)
+#57 := (= #15 f10)
+#3280 := (or #57 #1317 #3274)
+#4313 := (forall (vars (?v0 S3)) (:pat #4297) #3280)
+#4318 := (not #4313)
+#4341 := (or #4318 #4338)
+#4344 := (not #4341)
+decl ?v0!8 :: S3
+#2049 := ?v0!8
+#2053 := (f3 #15 ?v0!8)
+#4298 := (pattern #2053)
+#2054 := (f9 #2053)
+#2050 := (f13 f19 ?v0!8)
+#2051 := (* -1::int #2050)
+#2701 := (+ #2051 #2054)
+#2702 := (+ #142 #2701)
+#2705 := (= #2702 0::int)
+#3236 := (not #2705)
+#2052 := (+ #142 #2051)
+#2057 := (>= #2052 0::int)
+#3237 := (or #2057 #3236)
+#4299 := (forall (vars (?v1 S3)) (:pat #4297 #4298) #3237)
+#4304 := (not #4299)
+#2677 := (= f10 ?v0!8)
+#2061 := (+ f8 #2051)
+#2062 := (<= #2061 0::int)
+#4307 := (or #2062 #2677 #4304)
+#4310 := (not #4307)
+#4347 := (or #4310 #4344)
+#4350 := (not #4347)
+#1270 := (* -1::int #101)
+#1271 := (+ f8 #1270)
+#1272 := (<= #1271 0::int)
+#3222 := (or #506 #1272)
+#4289 := (forall (vars (?v0 S3)) (:pat #4288 #4246) #3222)
+#4294 := (not #4289)
+#597 := (= f14 f19)
+#688 := (not #597)
 decl f16 :: S4
-#104 := f16
-#2092 := (f9 f16 ?v1!10)
-#2098 := (* -1::int #2092)
-#2754 := (+ #2098 #2102)
-#2090 := (f9 f16 ?v0!11)
-#2755 := (+ #2090 #2754)
-#2756 := (<= #2755 0::int)
-#2103 := (+ f3 #2102)
-#2104 := (<= #2103 0::int)
-#2099 := (+ f3 #2098)
-#2100 := (<= #2099 0::int)
-#3325 := (or #2100 #2104 #2756)
-#3330 := (not #3325)
-#112 := (f9 f16 #11)
-#1261 := (* -1::int #112)
-#109 := (f9 f16 #12)
-#1262 := (+ #109 #1261)
-#1268 := (+ #49 #1262)
-#1291 := (>= #1268 0::int)
-#1248 := (* -1::int #109)
-#1249 := (+ f3 #1248)
-#1250 := (<= #1249 0::int)
-#3293 := (or #1141 #1250 #1291)
-#4278 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4179) #3293)
-#4283 := (not #4278)
-#124 := (f9 f16 f6)
-#125 := (= #124 0::int)
-#4286 := (or #125 #4283)
-#4289 := (not #4286)
-#4292 := (or #4289 #3330)
-#4295 := (not #4292)
-#4254 := (pattern #109)
-decl ?v1!9 :: (-> S2 S2)
-#2065 := (?v1!9 #12)
-#2068 := (f5 #2065 #12)
-#2069 := (f4 #2068)
-#2724 := (* -1::int #2069)
-#2066 := (f9 f16 #2065)
-#2707 := (* -1::int #2066)
-#2725 := (+ #2707 #2724)
-#2726 := (+ #109 #2725)
-#2727 := (= #2726 0::int)
-#3263 := (not #2727)
-#2708 := (+ #109 #2707)
-#2709 := (<= #2708 0::int)
-#3264 := (or #2709 #3263)
-#3265 := (not #3264)
-#24 := (= #12 f6)
-#3271 := (or #24 #1250 #3265)
-#4270 := (forall (vars (?v0 S2)) (:pat #4254) #3271)
-#4275 := (not #4270)
-#4298 := (or #4275 #4295)
-#4301 := (not #4298)
-decl ?v0!8 :: S2
-#2025 := ?v0!8
-#2029 := (f5 #12 ?v0!8)
-#4255 := (pattern #2029)
-#2030 := (f4 #2029)
-#2026 := (f9 f16 ?v0!8)
-#2027 := (* -1::int #2026)
-#2677 := (+ #2027 #2030)
-#2678 := (+ #109 #2677)
-#2681 := (= #2678 0::int)
-#3227 := (not #2681)
-#2028 := (+ #109 #2027)
-#2033 := (>= #2028 0::int)
-#3228 := (or #2033 #3227)
-#4256 := (forall (vars (?v1 S2)) (:pat #4254 #4255) #3228)
-#4261 := (not #4256)
-#2653 := (= f6 ?v0!8)
-#2037 := (+ f3 #2027)
-#2038 := (<= #2037 0::int)
-#4264 := (or #2038 #2653 #4261)
-#4267 := (not #4264)
-#4304 := (or #4267 #4301)
-#4307 := (not #4304)
-#1203 := (* -1::int #68)
-#1204 := (+ f3 #1203)
-#1205 := (<= #1204 0::int)
-#3213 := (or #447 #1205)
-#4246 := (forall (vars (?v0 S2)) (:pat #4245 #4203) #3213)
-#4251 := (not #4246)
-#538 := (= f10 f16)
-#629 := (not #538)
-decl f13 :: S5
-#99 := f13
-#535 := (= f12 f13)
-#647 := (not #535)
-decl f18 :: S4
-#107 := f18
-decl f17 :: S4
-#106 := f17
-#108 := (= f17 f18)
-#620 := (not #108)
-decl f15 :: S2
-#102 := f15
-decl f14 :: S2
-#101 := f14
-#103 := (= f14 f15)
-#638 := (not #103)
-#4310 := (or #638 #620 #647 #629 #4251 #4307)
-#4313 := (not #4310)
-#4471 := (or #4313 #4468)
-#4474 := (not #4471)
-#1988 := (?v1!7 #12)
-#1989 := (f9 f10 #1988)
-#2612 := (* -1::int #1989)
-#2627 := (+ #68 #2612)
-#2628 := (<= #2627 0::int)
-#1993 := (f5 #1988 #12)
-#1994 := (f4 #1993)
-#2613 := (* -1::int #1994)
-#2614 := (+ #2612 #2613)
-#2615 := (+ #68 #2614)
-#2616 := (= #2615 0::int)
-#3197 := (not #2616)
-#1997 := (f11 f12 #1988)
-#1998 := (= f1 #1997)
-#3196 := (not #1998)
-#3198 := (or #3196 #3197 #2628)
-#3199 := (not #3198)
-#3205 := (or #24 #1205 #3199)
-#4237 := (forall (vars (?v0 S2)) (:pat #4203) #3205)
-#4242 := (not #4237)
-decl f7 :: (-> S2 int)
-#25 := (f7 #12)
-#4148 := (pattern #25)
-decl ?v1!6 :: (-> S2 S2)
-#1960 := (?v1!6 #12)
-#1964 := (f7 #1960)
-#2571 := (* -1::int #1964)
-#1961 := (f5 #1960 #12)
-#1962 := (f4 #1961)
-#2588 := (* -1::int #1962)
-#2589 := (+ #2588 #2571)
-#2590 := (+ #25 #2589)
-#2591 := (= #2590 0::int)
-#3169 := (not #2591)
-#2572 := (+ #25 #2571)
-#2573 := (<= #2572 0::int)
-decl f8 :: (-> S2 S1)
-#1970 := (f8 #1960)
-#1971 := (= f1 #1970)
-#3168 := (not #1971)
-#3170 := (or #3168 #2573 #3169)
-#3171 := (not #3170)
-#1165 := (* -1::int #25)
-#1166 := (+ f3 #1165)
-#1167 := (<= #1166 0::int)
-#3177 := (or #24 #1167 #3171)
-#4229 := (forall (vars (?v0 S2)) (:pat #4148) #3177)
-#4234 := (not #4229)
-#75 := (f11 f12 #11)
-#4220 := (pattern #72 #75)
-#78 := (f9 f10 #11)
-#1217 := (* -1::int #78)
-#1218 := (+ #68 #1217)
-#1221 := (>= #1218 0::int)
-#453 := (= f1 #75)
-#3134 := (not #453)
-#3149 := (or #447 #3134 #1221)
-#4221 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4220) #3149)
-#4226 := (not #4221)
-#1219 := (+ #49 #1218)
-#1614 := (>= #1219 0::int)
-#450 := (not #447)
-#3126 := (or #450 #1141 #1614)
-#4212 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4179) #3126)
-#4217 := (not #4212)
-#1642 := (>= #68 0::int)
-#4204 := (forall (vars (?v0 S2)) (:pat #4203) #1642)
-#4209 := (not #4204)
-#66 := (f9 f10 f6)
-#67 := (= #66 0::int)
-#1653 := (not #67)
-#4477 := (or #1653 #4209 #4217 #4226 #4234 #4242 #4474)
-#4480 := (not #4477)
-decl ?v0!5 :: S2
-#1916 := ?v0!5
-#1917 := (f5 #12 ?v0!5)
-#4188 := (pattern #1917)
-#33 := (f8 #12)
-#4155 := (pattern #33)
-#1919 := (f7 ?v0!5)
-#1920 := (* -1::int #1919)
-#1918 := (f4 #1917)
-#2539 := (+ #1918 #1920)
-#2540 := (+ #25 #2539)
-#2543 := (= #2540 0::int)
-#3087 := (not #2543)
-#1924 := (+ #25 #1920)
-#1925 := (>= #1924 0::int)
-#368 := (= f1 #33)
-#371 := (not #368)
-#3088 := (or #371 #1925 #3087)
-#4189 := (forall (vars (?v1 S2)) (:pat #4155 #4148 #4188) #3088)
-#4194 := (not #4189)
-#2515 := (= f6 ?v0!5)
-#1929 := (+ f3 #1920)
-#1930 := (<= #1929 0::int)
-#4197 := (or #1930 #2515 #4194)
-#4200 := (not #4197)
-#4483 := (or #4200 #4480)
-#4486 := (not #4483)
-#44 := (f7 #11)
-#1117 := (* -1::int #44)
-#1138 := (+ #1117 #49)
-#1139 := (+ #25 #1138)
-#1136 := (>= #1139 0::int)
-#3079 := (or #371 #1136 #1141)
-#4180 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4179) #3079)
-#4185 := (not #4180)
-#4489 := (or #4185 #4486)
-#4492 := (not #4489)
-decl ?v1!3 :: S2
-#1885 := ?v1!3
-#1900 := (f7 ?v1!3)
-decl ?v0!4 :: S2
-#1886 := ?v0!4
-#1897 := (f7 ?v0!4)
-#1898 := (* -1::int #1897)
-#2496 := (+ #1898 #1900)
-#1887 := (f5 ?v1!3 ?v0!4)
-#1888 := (f4 #1887)
-#2497 := (+ #1888 #2496)
-#2500 := (>= #2497 0::int)
-#1893 := (f8 ?v1!3)
-#1894 := (= f1 #1893)
-#3042 := (not #1894)
-#1889 := (* -1::int #1888)
-#1890 := (+ f3 #1889)
-#1891 := (<= #1890 0::int)
-#3057 := (or #1891 #3042 #2500)
-#3062 := (not #3057)
-#4495 := (or #3062 #4492)
-#4498 := (not #4495)
-#41 := (f8 #11)
-#4170 := (pattern #33 #41)
-#1118 := (+ #25 #1117)
-#1116 := (>= #1118 0::int)
-#380 := (= f1 #41)
-#3019 := (not #380)
-#3034 := (or #368 #3019 #1116)
-#4171 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4170) #3034)
-#4176 := (not #4171)
-#4501 := (or #4176 #4498)
-#4504 := (not #4501)
-decl ?v1!1 :: S2
-#1858 := ?v1!1
-#1862 := (f7 ?v1!1)
-#2483 := (* -1::int #1862)
-decl ?v0!2 :: S2
-#1859 := ?v0!2
-#1860 := (f7 ?v0!2)
-#2484 := (+ #1860 #2483)
-#2485 := (<= #2484 0::int)
-#1867 := (f8 ?v1!1)
-#1868 := (= f1 #1867)
-#1865 := (f8 ?v0!2)
-#1866 := (= f1 #1865)
-#2112 := (not #1866)
-#3011 := (or #2112 #1868 #2485)
-#3016 := (not #3011)
-#4507 := (or #3016 #4504)
-#4510 := (not #4507)
-#1107 := (>= #25 0::int)
-#4162 := (forall (vars (?v0 S2)) (:pat #4148) #1107)
-#4167 := (not #4162)
-#4513 := (or #4167 #4510)
-#4516 := (not #4513)
-decl ?v0!0 :: S2
-#1843 := ?v0!0
-#1844 := (f7 ?v0!0)
-#1845 := (>= #1844 0::int)
-#1846 := (not #1845)
-#4519 := (or #1846 #4516)
-#4522 := (not #4519)
-#37 := (f7 f6)
-#38 := (= #37 0::int)
-#1102 := (not #38)
-#4525 := (or #1102 #4522)
-#4528 := (not #4525)
-#26 := (= #25 0::int)
-#29 := (not #24)
-#1711 := (or #29 #26)
-#4535 := (forall (vars (?v0 S2)) (:pat #4148) #1711)
-#1714 := (forall (vars (?v0 S2)) #1711)
-#4538 := (iff #1714 #4535)
-#4536 := (iff #1711 #1711)
-#4537 := [refl]: #4536
-#4539 := [quant-intro #4537]: #4538
-#2167 := (~ #1714 #1714)
-#2286 := (~ #1711 #1711)
-#2287 := [refl]: #2286
-#2168 := [nnf-pos #2287]: #2167
-#1717 := (not #1714)
-#1645 := (forall (vars (?v0 S2)) #1642)
-#1648 := (not #1645)
-#456 := (and #450 #453)
-#462 := (not #456)
-#1631 := (or #462 #1221)
-#1636 := (forall (vars (?v0 S2) (?v1 S2)) #1631)
-#1639 := (not #1636)
-#1142 := (not #1141)
-#1606 := (and #447 #1142)
-#1611 := (not #1606)
-#1617 := (or #1611 #1614)
-#1620 := (forall (vars (?v0 S2) (?v1 S2)) #1617)
+#132 := f16
+#594 := (= f15 f16)
+#706 := (not #594)
+decl f21 :: S5
+#140 := f21
+decl f20 :: S5
+#139 := f20
+#141 := (= f20 f21)
+#679 := (not #141)
+decl f18 :: S3
+#135 := f18
+decl f17 :: S3
+#134 := f17
+#136 := (= f17 f18)
+#697 := (not #136)
+#4353 := (or #697 #679 #706 #688 #4294 #4350)
+#4356 := (not #4353)
+#4514 := (or #4356 #4511)
+#4517 := (not #4514)
+decl ?v1!7 :: (-> S3 S3)
+#2012 := (?v1!7 #15)
+#2013 := (f13 f14 #2012)
+#2636 := (* -1::int #2013)
+#2651 := (+ #101 #2636)
+#2652 := (<= #2651 0::int)
+#2017 := (f3 #2012 #15)
+#2018 := (f9 #2017)
+#2637 := (* -1::int #2018)
+#2638 := (+ #2636 #2637)
+#2639 := (+ #101 #2638)
+#2640 := (= #2639 0::int)
+#3206 := (not #2640)
+#2021 := (f6 f15 #2012)
+#2022 := (= f1 #2021)
+#3205 := (not #2022)
+#3207 := (or #3205 #3206 #2652)
+#3208 := (not #3207)
+#3214 := (or #57 #1272 #3208)
+#4280 := (forall (vars (?v0 S3)) (:pat #4246) #3214)
+#4285 := (not #4280)
+decl f11 :: (-> S3 int)
+#58 := (f11 #15)
+#4191 := (pattern #58)
+decl ?v1!6 :: (-> S3 S3)
+#1984 := (?v1!6 #15)
+#1988 := (f11 #1984)
+#2595 := (* -1::int #1988)
+#1985 := (f3 #1984 #15)
+#1986 := (f9 #1985)
+#2612 := (* -1::int #1986)
+#2613 := (+ #2612 #2595)
+#2614 := (+ #58 #2613)
+#2615 := (= #2614 0::int)
+#3178 := (not #2615)
+#2596 := (+ #58 #2595)
+#2597 := (<= #2596 0::int)
+decl f12 :: (-> S3 S1)
+#1994 := (f12 #1984)
+#1995 := (= f1 #1994)
+#3177 := (not #1995)
+#3179 := (or #3177 #2597 #3178)
+#3180 := (not #3179)
+#1232 := (* -1::int #58)
+#1233 := (+ f8 #1232)
+#1234 := (<= #1233 0::int)
+#3186 := (or #57 #1234 #3180)
+#4272 := (forall (vars (?v0 S3)) (:pat #4191) #3186)
+#4277 := (not #4272)
+#108 := (f6 f15 #14)
+#4263 := (pattern #105 #108)
+#111 := (f13 f14 #14)
+#1284 := (* -1::int #111)
+#1285 := (+ #101 #1284)
+#1288 := (>= #1285 0::int)
+#512 := (= f1 #108)
+#3143 := (not #512)
+#3158 := (or #506 #3143 #1288)
+#4264 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4263) #3158)
+#4269 := (not #4264)
+#1286 := (+ #82 #1285)
+#1681 := (>= #1286 0::int)
+#509 := (not #506)
+#3135 := (or #509 #1208 #1681)
+#4255 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4222) #3135)
+#4260 := (not #4255)
+#1709 := (>= #101 0::int)
+#4247 := (forall (vars (?v0 S3)) (:pat #4246) #1709)
+#4252 := (not #4247)
+#99 := (f13 f14 f10)
+#100 := (= #99 0::int)
+#1720 := (not #100)
+#4520 := (or #1720 #4252 #4260 #4269 #4277 #4285 #4517)
+#4523 := (not #4520)
+decl ?v0!5 :: S3
+#1940 := ?v0!5
+#1941 := (f3 #15 ?v0!5)
+#4231 := (pattern #1941)
+#66 := (f12 #15)
+#4198 := (pattern #66)
+#1943 := (f11 ?v0!5)
+#1944 := (* -1::int #1943)
+#1942 := (f9 #1941)
+#2563 := (+ #1942 #1944)
+#2564 := (+ #58 #2563)
+#2567 := (= #2564 0::int)
+#3096 := (not #2567)
+#1948 := (+ #58 #1944)
+#1949 := (>= #1948 0::int)
+#427 := (= f1 #66)
+#430 := (not #427)
+#3097 := (or #430 #1949 #3096)
+#4232 := (forall (vars (?v1 S3)) (:pat #4198 #4191 #4231) #3097)
+#4237 := (not #4232)
+#2539 := (= f10 ?v0!5)
+#1953 := (+ f8 #1944)
+#1954 := (<= #1953 0::int)
+#4240 := (or #1954 #2539 #4237)
+#4243 := (not #4240)
+#4526 := (or #4243 #4523)
+#4529 := (not #4526)
+#77 := (f11 #14)
+#1184 := (* -1::int #77)
+#1205 := (+ #1184 #82)
+#1206 := (+ #58 #1205)
+#1203 := (>= #1206 0::int)
+#3088 := (or #430 #1203 #1208)
+#4223 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4222) #3088)
+#4228 := (not #4223)
+#4532 := (or #4228 #4529)
+#4535 := (not #4532)
+decl ?v1!3 :: S3
+#1909 := ?v1!3
+#1924 := (f11 ?v1!3)
+decl ?v0!4 :: S3
+#1910 := ?v0!4
+#1921 := (f11 ?v0!4)
+#1922 := (* -1::int #1921)
+#2520 := (+ #1922 #1924)
+#1911 := (f3 ?v1!3 ?v0!4)
+#1912 := (f9 #1911)
+#2521 := (+ #1912 #2520)
+#2524 := (>= #2521 0::int)
+#1917 := (f12 ?v1!3)
+#1918 := (= f1 #1917)
+#3051 := (not #1918)
+#1913 := (* -1::int #1912)
+#1914 := (+ f8 #1913)
+#1915 := (<= #1914 0::int)
+#3066 := (or #1915 #3051 #2524)
+#3071 := (not #3066)
+#4538 := (or #3071 #4535)
+#4541 := (not #4538)
+#74 := (f12 #14)
+#4213 := (pattern #66 #74)
+#1185 := (+ #58 #1184)
+#1183 := (>= #1185 0::int)
+#439 := (= f1 #74)
+#2492 := (not #439)
+#3043 := (or #427 #2492 #1183)
+#4214 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4213) #3043)
+#4219 := (not #4214)
+#4544 := (or #4219 #4541)
+#4547 := (not #4544)
+decl ?v1!1 :: S3
+#1882 := ?v1!1
+#1886 := (f11 ?v1!1)
+#2507 := (* -1::int #1886)
+decl ?v0!2 :: S3
+#1883 := ?v0!2
+#1884 := (f11 ?v0!2)
+#2508 := (+ #1884 #2507)
+#2509 := (<= #2508 0::int)
+#1891 := (f12 ?v1!1)
+#1892 := (= f1 #1891)
+#1889 := (f12 ?v0!2)
+#1890 := (= f1 #1889)
+#2102 := (not #1890)
+#2212 := (or #2102 #1892 #2509)
+#1874 := (not #2212)
+#4550 := (or #1874 #4547)
+#4553 := (not #4550)
+#1174 := (>= #58 0::int)
+#4205 := (forall (vars (?v0 S3)) (:pat #4191) #1174)
+#4210 := (not #4205)
+#4556 := (or #4210 #4553)
+#4559 := (not #4556)
+decl ?v0!0 :: S3
+#1867 := ?v0!0
+#1868 := (f11 ?v0!0)
+#1869 := (>= #1868 0::int)
+#4624 := (* -1::int #1868)
+#4625 := (+ f8 #4624)
+#4626 := (<= #4625 0::int)
+#3831 := (= f8 #1868)
+#3824 := (= f10 ?v0!0)
+#4613 := (not #3824)
+#4610 := (= #1868 0::int)
+#4706 := (not #4610)
+#1870 := (not #1869)
+#4705 := [hypothesis]: #1870
+#4707 := (or #4706 #1869)
+#4708 := [th-lemma]: #4707
+#4709 := [unit-resolution #4708 #4705]: #4706
+#59 := (= #58 0::int)
+#62 := (not #57)
+#1778 := (or #62 #59)
+#4578 := (forall (vars (?v0 S3)) (:pat #4191) #1778)
+#1781 := (forall (vars (?v0 S3)) #1778)
+#4581 := (iff #1781 #4578)
+#4579 := (iff #1778 #1778)
+#4580 := [refl]: #4579
+#4582 := [quant-intro #4580]: #4581
+#1900 := (~ #1781 #1781)
+#2310 := (~ #1778 #1778)
+#2311 := [refl]: #2310
+#1901 := [nnf-pos #2311]: #1900
+#1784 := (not #1781)
+#1712 := (forall (vars (?v0 S3)) #1709)
+#1715 := (not #1712)
+#515 := (and #509 #512)
+#521 := (not #515)
+#1698 := (or #521 #1288)
+#1703 := (forall (vars (?v0 S3) (?v1 S3)) #1698)
+#1706 := (not #1703)
+#1209 := (not #1208)
+#1673 := (and #506 #1209)
+#1678 := (not #1673)
+#1684 := (or #1678 #1681)
+#1687 := (forall (vars (?v0 S3) (?v1 S3)) #1684)
+#1690 := (not #1687)
+#1620 := (forall (vars (?v0 S3)) #1615)
 #1623 := (not #1620)
-#1553 := (forall (vars (?v0 S2)) #1548)
-#1556 := (not #1553)
-#1363 := (not #1362)
-#1356 := (not #1355)
-#1366 := (and #1356 #1363)
-#1524 := (not #1366)
-#1532 := (or #1524 #1529)
-#1535 := (forall (vars (?v0 S2)) #1532)
-#1538 := (not #1535)
-#1462 := (= #1440 0::int)
-#1465 := (not #1408)
-#1474 := (and #713 #1465 #1462)
-#1479 := (exists (vars (?v1 S2)) #1474)
-#1451 := (+ f3 #1384)
-#1452 := (<= #1451 0::int)
-#1453 := (not #1452)
-#1456 := (and #29 #1453)
-#1459 := (not #1456)
-#1482 := (or #1459 #1479)
-#1485 := (forall (vars (?v0 S2)) #1482)
-#1430 := (and #713 #1142)
-#1435 := (not #1430)
-#1442 := (or #1435 #1438)
-#1445 := (forall (vars (?v0 S2) (?v1 S2)) #1442)
-#1448 := (not #1445)
-#1488 := (or #1448 #1485)
-#1491 := (and #1445 #1488)
-#736 := (and #719 #733)
-#742 := (not #736)
-#1416 := (or #742 #1408)
-#1421 := (forall (vars (?v0 S2) (?v1 S2)) #1416)
-#1424 := (not #1421)
-#1494 := (or #1424 #1491)
-#1497 := (and #1421 #1494)
-#1402 := (forall (vars (?v0 S2)) #1399)
-#1405 := (not #1402)
-#1500 := (or #1405 #1497)
-#1503 := (and #1402 #1500)
-#1506 := (or #1396 #1503)
-#1509 := (and #170 #1506)
-#725 := (forall (vars (?v0 S2)) #720)
-#859 := (not #725)
-#1512 := (or #859 #1509)
-#1515 := (and #725 #1512)
-#1388 := (forall (vars (?v0 S2)) #1383)
-#1391 := (not #1388)
-#1518 := (or #1391 #1515)
-#1521 := (and #1388 #1518)
-#1372 := (or #699 #1366)
-#1377 := (forall (vars (?v0 S2)) #1372)
-#1380 := (not #1377)
-#1206 := (not #1205)
-#1325 := (and #450 #1206)
-#1330 := (exists (vars (?v0 S2)) #1325)
-#1571 := (not #1330)
-#1595 := (or #901 #668 #1571 #1380 #1521 #1538 #1556 #1560)
-#1251 := (not #1250)
-#1285 := (and #1142 #1251)
-#1288 := (not #1285)
-#1294 := (or #1288 #1291)
-#1297 := (forall (vars (?v0 S2) (?v1 S2)) #1294)
-#1300 := (not #1297)
-#1308 := (or #125 #1300)
-#1313 := (and #1297 #1308)
-#1266 := (= #1268 0::int)
-#1260 := (>= #1262 0::int)
-#1263 := (not #1260)
-#1270 := (and #1263 #1266)
-#1273 := (exists (vars (?v1 S2)) #1270)
-#1254 := (and #29 #1251)
-#1257 := (not #1254)
-#1276 := (or #1257 #1273)
-#1279 := (forall (vars (?v0 S2)) #1276)
-#1282 := (not #1279)
-#1316 := (or #1282 #1313)
-#1319 := (and #1279 #1316)
-#1348 := (or #638 #620 #647 #629 #1319 #1330)
-#1600 := (and #1348 #1595)
-#1222 := (not #1221)
-#1215 := (= #1219 0::int)
-#1231 := (and #447 #1215 #1222)
-#1236 := (exists (vars (?v1 S2)) #1231)
-#1209 := (and #29 #1206)
-#1212 := (not #1209)
-#1239 := (or #1212 #1236)
-#1242 := (forall (vars (?v0 S2)) #1239)
-#1245 := (not #1242)
-#1177 := (= #1139 0::int)
-#1180 := (not #1116)
-#1189 := (and #368 #1180 #1177)
-#1194 := (exists (vars (?v1 S2)) #1189)
-#1168 := (not #1167)
-#1171 := (and #29 #1168)
-#1174 := (not #1171)
-#1197 := (or #1174 #1194)
-#1200 := (forall (vars (?v0 S2)) #1197)
-#1656 := (not #1200)
-#1677 := (or #1653 #1656 #1245 #1600 #1623 #1639 #1648)
-#1682 := (and #1200 #1677)
-#1148 := (and #368 #1142)
-#1153 := (not #1148)
-#1156 := (or #1136 #1153)
-#1159 := (forall (vars (?v0 S2) (?v1 S2)) #1156)
-#1162 := (not #1159)
-#1685 := (or #1162 #1682)
-#1688 := (and #1159 #1685)
-#383 := (and #371 #380)
-#389 := (not #383)
-#1123 := (or #389 #1116)
-#1128 := (forall (vars (?v0 S2) (?v1 S2)) #1123)
-#1131 := (not #1128)
-#1691 := (or #1131 #1688)
-#1694 := (and #1128 #1691)
-#1108 := (forall (vars (?v0 S2)) #1107)
-#1111 := (not #1108)
-#1697 := (or #1111 #1694)
-#1700 := (and #1108 #1697)
-#1703 := (or #1102 #1700)
-#1706 := (and #38 #1703)
-#374 := (forall (vars (?v0 S2)) #371)
-#1066 := (not #374)
-#354 := (= f3 #25)
-#360 := (or #24 #354)
-#365 := (forall (vars (?v0 S2)) #360)
-#1075 := (not #365)
-#1729 := (or #1075 #1066 #1706 #1717)
-#1734 := (not #1729)
-#182 := (+ #155 #49)
-#189 := (= #177 #182)
-#166 := (= #165 f1)
-#190 := (and #166 #189)
-#188 := (< #155 #177)
-#191 := (and #188 #190)
-#192 := (exists (vars (?v1 S2)) #191)
-#186 := (< #155 f3)
-#187 := (and #29 #186)
-#193 := (implies #187 #192)
-#194 := (forall (vars (?v0 S2)) #193)
-#195 := (and #194 true)
-#183 := (<= #177 #182)
-#50 := (< #49 f3)
-#181 := (and #166 #50)
-#184 := (implies #181 #183)
-#185 := (forall (vars (?v0 S2) (?v1 S2)) #184)
-#196 := (implies #185 #195)
-#197 := (and #185 #196)
-#178 := (<= #177 #155)
-#175 := (= #174 f1)
-#173 := (not #166)
-#176 := (and #173 #175)
-#179 := (implies #176 #178)
-#180 := (forall (vars (?v0 S2) (?v1 S2)) #179)
-#198 := (implies #180 #197)
-#199 := (and #180 #198)
-#171 := (<= 0::int #155)
-#172 := (forall (vars (?v0 S2)) #171)
-#200 := (implies #172 #199)
-#201 := (and #172 #200)
-#202 := (implies #170 #201)
-#203 := (and #170 #202)
-#160 := (= #155 #68)
-#167 := (implies #166 #160)
-#168 := (forall (vars (?v0 S2)) #167)
-#204 := (implies #168 #203)
-#205 := (and #168 #204)
-#163 := (<= #155 #68)
-#164 := (forall (vars (?v0 S2)) #163)
-#206 := (implies #164 #205)
-#207 := (and #164 #206)
-#152 := (+ #141 #150)
-#153 := (< #152 #68)
-#151 := (< #150 f3)
-#154 := (and #151 #153)
-#159 := (not #154)
-#161 := (implies #159 #160)
-#162 := (forall (vars (?v0 S2)) #161)
-#208 := (implies #162 #207)
-#156 := (= #155 #152)
-#157 := (implies #154 #156)
-#158 := (forall (vars (?v0 S2)) #157)
-#209 := (implies #158 #208)
-#210 := (implies #148 #209)
-#143 := (<= #141 #68)
-#73 := (= #72 f1)
-#74 := (not #73)
-#144 := (implies #74 #143)
-#145 := (forall (vars (?v0 S2)) #144)
-#211 := (implies #145 #210)
-#142 := (< #141 f3)
-#212 := (implies #142 #211)
-#139 := (= #138 f1)
-#140 := (not #139)
-#213 := (implies #140 #212)
-#87 := (< #68 f3)
-#96 := (and #74 #87)
-#97 := (exists (vars (?v0 S2)) #96)
-#214 := (implies #97 #213)
-#215 := (implies true #214)
-#126 := (and #125 true)
-#114 := (+ #109 #49)
-#121 := (<= #112 #114)
-#110 := (< #109 f3)
-#120 := (and #110 #50)
-#122 := (implies #120 #121)
-#123 := (forall (vars (?v0 S2) (?v1 S2)) #122)
-#127 := (implies #123 #126)
-#128 := (and #123 #127)
-#115 := (= #112 #114)
-#113 := (< #109 #112)
-#116 := (and #113 #115)
-#117 := (exists (vars (?v1 S2)) #116)
-#111 := (and #29 #110)
-#118 := (implies #111 #117)
-#119 := (forall (vars (?v0 S2)) #118)
-#129 := (implies #119 #128)
-#130 := (and #119 #129)
-#131 := (implies #108 #130)
-#105 := (= f16 f10)
-#132 := (implies #105 #131)
-#133 := (implies #103 #132)
-#100 := (= f13 f12)
-#134 := (implies #100 #133)
-#98 := (not #97)
-#135 := (implies #98 #134)
-#136 := (implies true #135)
-#216 := (and #136 #215)
-#83 := (+ #68 #49)
-#90 := (= #78 #83)
-#91 := (and #73 #90)
-#89 := (< #68 #78)
-#92 := (and #89 #91)
-#93 := (exists (vars (?v1 S2)) #92)
-#88 := (and #29 #87)
-#94 := (implies #88 #93)
-#95 := (forall (vars (?v0 S2)) #94)
-#217 := (implies #95 #216)
-#84 := (<= #78 #83)
-#82 := (and #73 #50)
-#85 := (implies #82 #84)
-#86 := (forall (vars (?v0 S2) (?v1 S2)) #85)
-#218 := (implies #86 #217)
-#79 := (<= #78 #68)
-#76 := (= #75 f1)
-#77 := (and #74 #76)
-#80 := (implies #77 #79)
-#81 := (forall (vars (?v0 S2) (?v1 S2)) #80)
-#219 := (implies #81 #218)
-#69 := (<= 0::int #68)
-#70 := (forall (vars (?v0 S2)) #69)
-#220 := (implies #70 #219)
-#221 := (implies #67 #220)
-#222 := (implies true #221)
-#52 := (+ #25 #49)
-#59 := (= #44 #52)
-#34 := (= #33 f1)
-#60 := (and #34 #59)
-#58 := (< #25 #44)
-#61 := (and #58 #60)
-#62 := (exists (vars (?v1 S2)) #61)
-#56 := (< #25 f3)
-#57 := (and #29 #56)
-#63 := (implies #57 #62)
-#64 := (forall (vars (?v0 S2)) #63)
-#223 := (implies #64 #222)
-#224 := (and #64 #223)
-#53 := (<= #44 #52)
-#51 := (and #34 #50)
-#54 := (implies #51 #53)
-#55 := (forall (vars (?v0 S2) (?v1 S2)) #54)
-#225 := (implies #55 #224)
-#226 := (and #55 #225)
-#45 := (<= #44 #25)
-#42 := (= #41 f1)
-#35 := (not #34)
-#43 := (and #35 #42)
-#46 := (implies #43 #45)
-#47 := (forall (vars (?v0 S2) (?v1 S2)) #46)
-#227 := (implies #47 #226)
-#228 := (and #47 #227)
-#39 := (<= 0::int #25)
-#40 := (forall (vars (?v0 S2)) #39)
-#229 := (implies #40 #228)
-#230 := (and #40 #229)
-#231 := (implies #38 #230)
-#232 := (and #38 #231)
-#36 := (forall (vars (?v0 S2)) #35)
-#233 := (implies #36 #232)
-#30 := (= #25 f3)
-#31 := (implies #29 #30)
-#32 := (forall (vars (?v0 S2)) #31)
-#234 := (implies #32 #233)
-#27 := (implies #24 #26)
-#28 := (forall (vars (?v0 S2)) #27)
-#235 := (implies #28 #234)
-#236 := (implies true #235)
-#237 := (not #236)
-#1737 := (iff #237 #1734)
-#759 := (+ #49 #155)
-#777 := (= #177 #759)
-#780 := (and #713 #777)
-#783 := (and #188 #780)
-#786 := (exists (vars (?v1 S2)) #783)
-#792 := (not #187)
-#793 := (or #792 #786)
-#798 := (forall (vars (?v0 S2)) #793)
-#762 := (<= #177 #759)
-#754 := (and #50 #713)
-#768 := (not #754)
-#769 := (or #768 #762)
-#774 := (forall (vars (?v0 S2) (?v1 S2)) #769)
-#811 := (not #774)
-#812 := (or #811 #798)
-#817 := (and #774 #812)
-#743 := (or #178 #742)
-#748 := (forall (vars (?v0 S2) (?v1 S2)) #743)
-#823 := (not #748)
-#824 := (or #823 #817)
-#829 := (and #748 #824)
-#835 := (not #172)
-#836 := (or #835 #829)
-#841 := (and #172 #836)
-#728 := (= 0::int #169)
-#847 := (not #728)
-#848 := (or #847 #841)
-#853 := (and #728 #848)
+#1430 := (not #1429)
+#1423 := (not #1422)
+#1433 := (and #1423 #1430)
+#1591 := (not #1433)
+#1599 := (or #1591 #1596)
+#1602 := (forall (vars (?v0 S3)) #1599)
+#1605 := (not #1602)
+#1529 := (= #1507 0::int)
+#1532 := (not #1475)
+#1541 := (and #780 #1532 #1529)
+#1546 := (exists (vars (?v1 S3)) #1541)
+#1518 := (+ f8 #1451)
+#1519 := (<= #1518 0::int)
+#1520 := (not #1519)
+#1523 := (and #62 #1520)
+#1526 := (not #1523)
+#1549 := (or #1526 #1546)
+#1552 := (forall (vars (?v0 S3)) #1549)
+#1497 := (and #780 #1209)
+#1502 := (not #1497)
+#1509 := (or #1502 #1505)
+#1512 := (forall (vars (?v0 S3) (?v1 S3)) #1509)
+#1515 := (not #1512)
+#1555 := (or #1515 #1552)
+#1558 := (and #1512 #1555)
+#803 := (and #786 #800)
+#809 := (not #803)
+#1483 := (or #809 #1475)
+#1488 := (forall (vars (?v0 S3) (?v1 S3)) #1483)
+#1491 := (not #1488)
+#1561 := (or #1491 #1558)
+#1564 := (and #1488 #1561)
+#1469 := (forall (vars (?v0 S3)) #1466)
+#1472 := (not #1469)
+#1567 := (or #1472 #1564)
+#1570 := (and #1469 #1567)
+#1573 := (or #1463 #1570)
+#1576 := (and #204 #1573)
+#792 := (forall (vars (?v0 S3)) #787)
+#926 := (not #792)
+#1579 := (or #926 #1576)
+#1582 := (and #792 #1579)
+#1455 := (forall (vars (?v0 S3)) #1450)
+#1458 := (not #1455)
+#1585 := (or #1458 #1582)
+#1588 := (and #1455 #1585)
+#1439 := (or #766 #1433)
+#1444 := (forall (vars (?v0 S3)) #1439)
+#1447 := (not #1444)
+#1273 := (not #1272)
+#1392 := (and #509 #1273)
+#1397 := (exists (vars (?v0 S3)) #1392)
+#1638 := (not #1397)
+#1662 := (or #727 #968 #1638 #1447 #1588 #1605 #1623 #1627)
+#1318 := (not #1317)
+#1352 := (and #1209 #1318)
+#1355 := (not #1352)
+#1361 := (or #1355 #1358)
+#1364 := (forall (vars (?v0 S3) (?v1 S3)) #1361)
+#1367 := (not #1364)
+#1375 := (or #158 #1367)
+#1380 := (and #1364 #1375)
+#1333 := (= #1335 0::int)
+#1327 := (>= #1329 0::int)
+#1330 := (not #1327)
+#1337 := (and #1330 #1333)
+#1340 := (exists (vars (?v1 S3)) #1337)
+#1321 := (and #62 #1318)
+#1324 := (not #1321)
+#1343 := (or #1324 #1340)
+#1346 := (forall (vars (?v0 S3)) #1343)
+#1349 := (not #1346)
+#1383 := (or #1349 #1380)
+#1386 := (and #1346 #1383)
+#1415 := (or #697 #679 #706 #688 #1386 #1397)
+#1667 := (and #1415 #1662)
+#1289 := (not #1288)
+#1282 := (= #1286 0::int)
+#1298 := (and #506 #1282 #1289)
+#1303 := (exists (vars (?v1 S3)) #1298)
+#1276 := (and #62 #1273)
+#1279 := (not #1276)
+#1306 := (or #1279 #1303)
+#1309 := (forall (vars (?v0 S3)) #1306)
+#1312 := (not #1309)
+#1244 := (= #1206 0::int)
+#1247 := (not #1183)
+#1256 := (and #427 #1247 #1244)
+#1261 := (exists (vars (?v1 S3)) #1256)
+#1235 := (not #1234)
+#1238 := (and #62 #1235)
+#1241 := (not #1238)
+#1264 := (or #1241 #1261)
+#1267 := (forall (vars (?v0 S3)) #1264)
+#1723 := (not #1267)
+#1744 := (or #1720 #1723 #1312 #1667 #1690 #1706 #1715)
+#1749 := (and #1267 #1744)
+#1215 := (and #427 #1209)
+#1220 := (not #1215)
+#1223 := (or #1203 #1220)
+#1226 := (forall (vars (?v0 S3) (?v1 S3)) #1223)
+#1229 := (not #1226)
+#1752 := (or #1229 #1749)
+#1755 := (and #1226 #1752)
+#442 := (and #430 #439)
+#448 := (not #442)
+#1190 := (or #448 #1183)
+#1195 := (forall (vars (?v0 S3) (?v1 S3)) #1190)
+#1198 := (not #1195)
+#1758 := (or #1198 #1755)
+#1761 := (and #1195 #1758)
+#1175 := (forall (vars (?v0 S3)) #1174)
+#1178 := (not #1175)
+#1764 := (or #1178 #1761)
+#1767 := (and #1175 #1764)
+#70 := (f11 f10)
+#71 := (= #70 0::int)
+#1169 := (not #71)
+#1770 := (or #1169 #1767)
+#1773 := (and #71 #1770)
+#433 := (forall (vars (?v0 S3)) #430)
+#1133 := (not #433)
+#413 := (= f8 #58)
+#419 := (or #57 #413)
+#424 := (forall (vars (?v0 S3)) #419)
+#1142 := (not #424)
+#1796 := (or #1142 #1133 #1773 #1784)
+#1801 := (not #1796)
+#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)
+#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 := (f7 f15 f22 #180)
+#182 := (= f23 #181)
+#244 := (implies #182 #243)
+#176 := (<= #174 #101)
+#106 := (= #105 f1)
+#107 := (not #106)
+#177 := (implies #107 #176)
+#178 := (forall (vars (?v0 S3)) #177)
+#245 := (implies #178 #244)
+#175 := (< #174 f8)
+#246 := (implies #175 #245)
+#172 := (= #171 f1)
+#173 := (not #172)
+#247 := (implies #173 #246)
+#120 := (< #101 f8)
+#129 := (and #107 #120)
+#130 := (exists (vars (?v0 S3)) #129)
+#248 := (implies #130 #247)
+#249 := (implies true #248)
+#159 := (and #158 true)
+#147 := (+ #142 #82)
+#154 := (<= #145 #147)
+#143 := (< #142 f8)
+#153 := (and #143 #83)
+#155 := (implies #153 #154)
+#156 := (forall (vars (?v0 S3) (?v1 S3)) #155)
+#160 := (implies #156 #159)
+#161 := (and #156 #160)
+#148 := (= #145 #147)
+#146 := (< #142 #145)
+#149 := (and #146 #148)
+#150 := (exists (vars (?v1 S3)) #149)
+#144 := (and #62 #143)
+#151 := (implies #144 #150)
+#152 := (forall (vars (?v0 S3)) #151)
+#162 := (implies #152 #161)
+#163 := (and #152 #162)
+#164 := (implies #141 #163)
+#138 := (= f19 f14)
+#165 := (implies #138 #164)
+#166 := (implies #136 #165)
+#133 := (= f16 f15)
+#167 := (implies #133 #166)
+#131 := (not #130)
+#168 := (implies #131 #167)
+#169 := (implies true #168)
+#250 := (and #169 #249)
+#116 := (+ #101 #82)
+#123 := (= #111 #116)
+#124 := (and #106 #123)
+#122 := (< #101 #111)
+#125 := (and #122 #124)
+#126 := (exists (vars (?v1 S3)) #125)
+#121 := (and #62 #120)
+#127 := (implies #121 #126)
+#128 := (forall (vars (?v0 S3)) #127)
+#251 := (implies #128 #250)
+#117 := (<= #111 #116)
+#115 := (and #106 #83)
+#118 := (implies #115 #117)
+#119 := (forall (vars (?v0 S3) (?v1 S3)) #118)
+#252 := (implies #119 #251)
+#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)
+#102 := (<= 0::int #101)
+#103 := (forall (vars (?v0 S3)) #102)
+#254 := (implies #103 #253)
+#255 := (implies #100 #254)
+#256 := (implies true #255)
+#85 := (+ #58 #82)
+#92 := (= #77 #85)
+#67 := (= #66 f1)
+#93 := (and #67 #92)
+#91 := (< #58 #77)
+#94 := (and #91 #93)
+#95 := (exists (vars (?v1 S3)) #94)
+#89 := (< #58 f8)
+#90 := (and #62 #89)
+#96 := (implies #90 #95)
+#97 := (forall (vars (?v0 S3)) #96)
+#257 := (implies #97 #256)
+#258 := (and #97 #257)
+#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)
+#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)
+#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)
+#69 := (forall (vars (?v0 S3)) #68)
+#267 := (implies #69 #266)
+#63 := (= #58 f8)
+#64 := (implies #62 #63)
+#65 := (forall (vars (?v0 S3)) #64)
+#268 := (implies #65 #267)
+#60 := (implies #57 #59)
+#61 := (forall (vars (?v0 S3)) #60)
+#269 := (implies #61 #268)
+#270 := (implies true #269)
+#271 := (not #270)
+#1804 := (iff #271 #1801)
+#826 := (+ #82 #189)
+#844 := (= #211 #826)
+#847 := (and #780 #844)
+#850 := (and #222 #847)
+#853 := (exists (vars (?v1 S3)) #850)
+#859 := (not #221)
 #860 := (or #859 #853)
-#865 := (and #725 #860)
-#871 := (not #164)
-#872 := (or #871 #865)
-#877 := (and #164 #872)
-#705 := (or #154 #699)
-#710 := (forall (vars (?v0 S2)) #705)
-#883 := (not #710)
-#884 := (or #883 #877)
-#685 := (= #152 #155)
-#691 := (or #159 #685)
-#696 := (forall (vars (?v0 S2)) #691)
-#892 := (not #696)
-#893 := (or #892 #884)
-#902 := (or #901 #893)
-#677 := (or #143 #447)
-#682 := (forall (vars (?v0 S2)) #677)
-#910 := (not #682)
-#911 := (or #910 #902)
-#919 := (not #142)
-#920 := (or #919 #911)
-#928 := (or #668 #920)
-#524 := (and #87 #450)
-#529 := (exists (vars (?v0 S2)) #524)
-#532 := (not #529)
-#936 := (or #532 #928)
-#583 := (= 0::int #124)
-#541 := (+ #49 #109)
-#568 := (<= #112 #541)
-#565 := (and #50 #110)
-#574 := (not #565)
-#575 := (or #574 #568)
-#580 := (forall (vars (?v0 S2) (?v1 S2)) #575)
-#596 := (not #580)
-#597 := (or #596 #583)
-#602 := (and #580 #597)
-#544 := (= #112 #541)
-#547 := (and #113 #544)
-#550 := (exists (vars (?v1 S2)) #547)
-#556 := (not #111)
-#557 := (or #556 #550)
-#562 := (forall (vars (?v0 S2)) #557)
-#608 := (not #562)
-#609 := (or #608 #602)
-#614 := (and #562 #609)
-#621 := (or #620 #614)
-#630 := (or #629 #621)
-#639 := (or #638 #630)
-#648 := (or #647 #639)
-#656 := (or #529 #648)
-#948 := (and #656 #936)
-#479 := (+ #49 #68)
-#497 := (= #78 #479)
-#500 := (and #447 #497)
-#503 := (and #89 #500)
-#506 := (exists (vars (?v1 S2)) #503)
-#512 := (not #88)
-#513 := (or #512 #506)
-#518 := (forall (vars (?v0 S2)) #513)
-#954 := (not #518)
-#955 := (or #954 #948)
-#482 := (<= #78 #479)
-#474 := (and #50 #447)
-#488 := (not #474)
-#489 := (or #488 #482)
-#494 := (forall (vars (?v0 S2) (?v1 S2)) #489)
-#963 := (not #494)
-#964 := (or #963 #955)
-#463 := (or #79 #462)
-#468 := (forall (vars (?v0 S2) (?v1 S2)) #463)
-#972 := (not #468)
-#973 := (or #972 #964)
-#981 := (not #70)
-#982 := (or #981 #973)
-#444 := (= 0::int #66)
-#990 := (not #444)
-#991 := (or #990 #982)
-#421 := (and #59 #368)
-#426 := (and #58 #421)
-#429 := (exists (vars (?v1 S2)) #426)
-#435 := (not #57)
-#436 := (or #435 #429)
-#441 := (forall (vars (?v0 S2)) #436)
-#1006 := (not #441)
-#1007 := (or #1006 #991)
-#1012 := (and #441 #1007)
-#401 := (and #50 #368)
-#409 := (not #401)
-#410 := (or #53 #409)
-#415 := (forall (vars (?v0 S2) (?v1 S2)) #410)
-#1018 := (not #415)
-#1019 := (or #1018 #1012)
-#1024 := (and #415 #1019)
-#390 := (or #45 #389)
-#395 := (forall (vars (?v0 S2) (?v1 S2)) #390)
-#1030 := (not #395)
-#1031 := (or #1030 #1024)
-#1036 := (and #395 #1031)
-#1042 := (not #40)
-#1043 := (or #1042 #1036)
-#1048 := (and #40 #1043)
-#377 := (= 0::int #37)
-#1054 := (not #377)
-#1055 := (or #1054 #1048)
-#1060 := (and #377 #1055)
-#1067 := (or #1066 #1060)
-#1076 := (or #1075 #1067)
-#340 := (= 0::int #25)
-#346 := (or #29 #340)
-#351 := (forall (vars (?v0 S2)) #346)
-#1084 := (not #351)
-#1085 := (or #1084 #1076)
-#1097 := (not #1085)
-#1735 := (iff #1097 #1734)
-#1732 := (iff #1085 #1729)
-#1720 := (or #1066 #1706)
-#1723 := (or #1075 #1720)
-#1726 := (or #1717 #1723)
-#1730 := (iff #1726 #1729)
-#1731 := [rewrite]: #1730
-#1727 := (iff #1085 #1726)
-#1724 := (iff #1076 #1723)
-#1721 := (iff #1067 #1720)
-#1707 := (iff #1060 #1706)
-#1704 := (iff #1055 #1703)
-#1701 := (iff #1048 #1700)
-#1698 := (iff #1043 #1697)
-#1695 := (iff #1036 #1694)
-#1692 := (iff #1031 #1691)
-#1689 := (iff #1024 #1688)
-#1686 := (iff #1019 #1685)
-#1683 := (iff #1012 #1682)
-#1680 := (iff #1007 #1677)
-#1659 := (or #1245 #1600)
-#1662 := (or #1623 #1659)
-#1665 := (or #1639 #1662)
-#1668 := (or #1648 #1665)
-#1671 := (or #1653 #1668)
-#1674 := (or #1656 #1671)
-#1678 := (iff #1674 #1677)
-#1679 := [rewrite]: #1678
-#1675 := (iff #1007 #1674)
-#1672 := (iff #991 #1671)
-#1669 := (iff #982 #1668)
-#1666 := (iff #973 #1665)
-#1663 := (iff #964 #1662)
-#1660 := (iff #955 #1659)
-#1601 := (iff #948 #1600)
-#1598 := (iff #936 #1595)
-#1574 := (or #1380 #1521)
-#1577 := (or #1538 #1574)
-#1580 := (or #901 #1577)
-#1583 := (or #1556 #1580)
-#1586 := (or #1560 #1583)
-#1589 := (or #668 #1586)
-#1592 := (or #1571 #1589)
-#1596 := (iff #1592 #1595)
-#1597 := [rewrite]: #1596
-#1593 := (iff #936 #1592)
-#1590 := (iff #928 #1589)
-#1587 := (iff #920 #1586)
-#1584 := (iff #911 #1583)
-#1581 := (iff #902 #1580)
-#1578 := (iff #893 #1577)
-#1575 := (iff #884 #1574)
-#1522 := (iff #877 #1521)
-#1519 := (iff #872 #1518)
-#1516 := (iff #865 #1515)
-#1513 := (iff #860 #1512)
-#1510 := (iff #853 #1509)
-#1507 := (iff #848 #1506)
-#1504 := (iff #841 #1503)
-#1501 := (iff #836 #1500)
-#1498 := (iff #829 #1497)
-#1495 := (iff #824 #1494)
-#1492 := (iff #817 #1491)
-#1489 := (iff #812 #1488)
-#1486 := (iff #798 #1485)
-#1483 := (iff #793 #1482)
-#1480 := (iff #786 #1479)
-#1477 := (iff #783 #1474)
-#1468 := (and #713 #1462)
-#1471 := (and #1465 #1468)
-#1475 := (iff #1471 #1474)
-#1476 := [rewrite]: #1475
-#1472 := (iff #783 #1471)
-#1469 := (iff #780 #1468)
-#1463 := (iff #777 #1462)
-#1464 := [rewrite]: #1463
-#1470 := [monotonicity #1464]: #1469
-#1466 := (iff #188 #1465)
-#1467 := [rewrite]: #1466
-#1473 := [monotonicity #1467 #1470]: #1472
-#1478 := [trans #1473 #1476]: #1477
-#1481 := [quant-intro #1478]: #1480
-#1460 := (iff #792 #1459)
-#1457 := (iff #187 #1456)
-#1454 := (iff #186 #1453)
-#1455 := [rewrite]: #1454
-#1458 := [monotonicity #1455]: #1457
-#1461 := [monotonicity #1458]: #1460
-#1484 := [monotonicity #1461 #1481]: #1483
-#1487 := [quant-intro #1484]: #1486
-#1449 := (iff #811 #1448)
-#1446 := (iff #774 #1445)
-#1443 := (iff #769 #1442)
-#1439 := (iff #762 #1438)
-#1441 := [rewrite]: #1439
-#1436 := (iff #768 #1435)
-#1433 := (iff #754 #1430)
-#1427 := (and #1142 #713)
-#1431 := (iff #1427 #1430)
+#865 := (forall (vars (?v0 S3)) #860)
+#829 := (<= #211 #826)
+#821 := (and #83 #780)
+#835 := (not #821)
+#836 := (or #835 #829)
+#841 := (forall (vars (?v0 S3) (?v1 S3)) #836)
+#878 := (not #841)
+#879 := (or #878 #865)
+#884 := (and #841 #879)
+#810 := (or #212 #809)
+#815 := (forall (vars (?v0 S3) (?v1 S3)) #810)
+#890 := (not #815)
+#891 := (or #890 #884)
+#896 := (and #815 #891)
+#902 := (not #206)
+#903 := (or #902 #896)
+#908 := (and #206 #903)
+#795 := (= 0::int #203)
+#914 := (not #795)
+#915 := (or #914 #908)
+#920 := (and #795 #915)
+#927 := (or #926 #920)
+#932 := (and #792 #927)
+#938 := (not #198)
+#939 := (or #938 #932)
+#944 := (and #198 #939)
+#772 := (or #188 #766)
+#777 := (forall (vars (?v0 S3)) #772)
+#950 := (not #777)
+#951 := (or #950 #944)
+#752 := (= #186 #189)
+#758 := (or #193 #752)
+#763 := (forall (vars (?v0 S3)) #758)
+#959 := (not #763)
+#960 := (or #959 #951)
+#969 := (or #968 #960)
+#736 := (or #176 #506)
+#741 := (forall (vars (?v0 S3)) #736)
+#977 := (not #741)
+#978 := (or #977 #969)
+#986 := (not #175)
+#987 := (or #986 #978)
+#995 := (or #727 #987)
+#583 := (and #120 #509)
+#588 := (exists (vars (?v0 S3)) #583)
+#591 := (not #588)
+#1003 := (or #591 #995)
+#642 := (= 0::int #157)
+#600 := (+ #82 #142)
+#627 := (<= #145 #600)
+#624 := (and #83 #143)
+#633 := (not #624)
+#634 := (or #633 #627)
+#639 := (forall (vars (?v0 S3) (?v1 S3)) #634)
+#655 := (not #639)
+#656 := (or #655 #642)
+#661 := (and #639 #656)
+#603 := (= #145 #600)
+#606 := (and #146 #603)
+#609 := (exists (vars (?v1 S3)) #606)
+#615 := (not #144)
+#616 := (or #615 #609)
+#621 := (forall (vars (?v0 S3)) #616)
+#667 := (not #621)
+#668 := (or #667 #661)
+#673 := (and #621 #668)
+#680 := (or #679 #673)
+#689 := (or #688 #680)
+#698 := (or #697 #689)
+#707 := (or #706 #698)
+#715 := (or #588 #707)
+#1015 := (and #715 #1003)
+#538 := (+ #82 #101)
+#556 := (= #111 #538)
+#559 := (and #506 #556)
+#562 := (and #122 #559)
+#565 := (exists (vars (?v1 S3)) #562)
+#571 := (not #121)
+#572 := (or #571 #565)
+#577 := (forall (vars (?v0 S3)) #572)
+#1021 := (not #577)
+#1022 := (or #1021 #1015)
+#541 := (<= #111 #538)
+#533 := (and #83 #506)
+#547 := (not #533)
+#548 := (or #547 #541)
+#553 := (forall (vars (?v0 S3) (?v1 S3)) #548)
+#1030 := (not #553)
+#1031 := (or #1030 #1022)
+#522 := (or #112 #521)
+#527 := (forall (vars (?v0 S3) (?v1 S3)) #522)
+#1039 := (not #527)
+#1040 := (or #1039 #1031)
+#1048 := (not #103)
+#1049 := (or #1048 #1040)
+#503 := (= 0::int #99)
+#1057 := (not #503)
+#1058 := (or #1057 #1049)
+#480 := (and #92 #427)
+#485 := (and #91 #480)
+#488 := (exists (vars (?v1 S3)) #485)
+#494 := (not #90)
+#495 := (or #494 #488)
+#500 := (forall (vars (?v0 S3)) #495)
+#1073 := (not #500)
+#1074 := (or #1073 #1058)
+#1079 := (and #500 #1074)
+#460 := (and #83 #427)
+#468 := (not #460)
+#469 := (or #86 #468)
+#474 := (forall (vars (?v0 S3) (?v1 S3)) #469)
+#1085 := (not #474)
+#1086 := (or #1085 #1079)
+#1091 := (and #474 #1086)
+#449 := (or #78 #448)
+#454 := (forall (vars (?v0 S3) (?v1 S3)) #449)
+#1097 := (not #454)
+#1098 := (or #1097 #1091)
+#1103 := (and #454 #1098)
+#1109 := (not #73)
+#1110 := (or #1109 #1103)
+#1115 := (and #73 #1110)
+#436 := (= 0::int #70)
+#1121 := (not #436)
+#1122 := (or #1121 #1115)
+#1127 := (and #436 #1122)
+#1134 := (or #1133 #1127)
+#1143 := (or #1142 #1134)
+#399 := (= 0::int #58)
+#405 := (or #62 #399)
+#410 := (forall (vars (?v0 S3)) #405)
+#1151 := (not #410)
+#1152 := (or #1151 #1143)
+#1164 := (not #1152)
+#1802 := (iff #1164 #1801)
+#1799 := (iff #1152 #1796)
+#1787 := (or #1133 #1773)
+#1790 := (or #1142 #1787)
+#1793 := (or #1784 #1790)
+#1797 := (iff #1793 #1796)
+#1798 := [rewrite]: #1797
+#1794 := (iff #1152 #1793)
+#1791 := (iff #1143 #1790)
+#1788 := (iff #1134 #1787)
+#1774 := (iff #1127 #1773)
+#1771 := (iff #1122 #1770)
+#1768 := (iff #1115 #1767)
+#1765 := (iff #1110 #1764)
+#1762 := (iff #1103 #1761)
+#1759 := (iff #1098 #1758)
+#1756 := (iff #1091 #1755)
+#1753 := (iff #1086 #1752)
+#1750 := (iff #1079 #1749)
+#1747 := (iff #1074 #1744)
+#1726 := (or #1312 #1667)
+#1729 := (or #1690 #1726)
+#1732 := (or #1706 #1729)
+#1735 := (or #1715 #1732)
+#1738 := (or #1720 #1735)
+#1741 := (or #1723 #1738)
+#1745 := (iff #1741 #1744)
+#1746 := [rewrite]: #1745
+#1742 := (iff #1074 #1741)
+#1739 := (iff #1058 #1738)
+#1736 := (iff #1049 #1735)
+#1733 := (iff #1040 #1732)
+#1730 := (iff #1031 #1729)
+#1727 := (iff #1022 #1726)
+#1668 := (iff #1015 #1667)
+#1665 := (iff #1003 #1662)
+#1641 := (or #1447 #1588)
+#1644 := (or #1605 #1641)
+#1647 := (or #968 #1644)
+#1650 := (or #1623 #1647)
+#1653 := (or #1627 #1650)
+#1656 := (or #727 #1653)
+#1659 := (or #1638 #1656)
+#1663 := (iff #1659 #1662)
+#1664 := [rewrite]: #1663
+#1660 := (iff #1003 #1659)
+#1657 := (iff #995 #1656)
+#1654 := (iff #987 #1653)
+#1651 := (iff #978 #1650)
+#1648 := (iff #969 #1647)
+#1645 := (iff #960 #1644)
+#1642 := (iff #951 #1641)
+#1589 := (iff #944 #1588)
+#1586 := (iff #939 #1585)
+#1583 := (iff #932 #1582)
+#1580 := (iff #927 #1579)
+#1577 := (iff #920 #1576)
+#1574 := (iff #915 #1573)
+#1571 := (iff #908 #1570)
+#1568 := (iff #903 #1567)
+#1565 := (iff #896 #1564)
+#1562 := (iff #891 #1561)
+#1559 := (iff #884 #1558)
+#1556 := (iff #879 #1555)
+#1553 := (iff #865 #1552)
+#1550 := (iff #860 #1549)
+#1547 := (iff #853 #1546)
+#1544 := (iff #850 #1541)
+#1535 := (and #780 #1529)
+#1538 := (and #1532 #1535)
+#1542 := (iff #1538 #1541)
+#1543 := [rewrite]: #1542
+#1539 := (iff #850 #1538)
+#1536 := (iff #847 #1535)
+#1530 := (iff #844 #1529)
+#1531 := [rewrite]: #1530
+#1537 := [monotonicity #1531]: #1536
+#1533 := (iff #222 #1532)
+#1534 := [rewrite]: #1533
+#1540 := [monotonicity #1534 #1537]: #1539
+#1545 := [trans #1540 #1543]: #1544
+#1548 := [quant-intro #1545]: #1547
+#1527 := (iff #859 #1526)
+#1524 := (iff #221 #1523)
+#1521 := (iff #220 #1520)
+#1522 := [rewrite]: #1521
+#1525 := [monotonicity #1522]: #1524
+#1528 := [monotonicity #1525]: #1527
+#1551 := [monotonicity #1528 #1548]: #1550
+#1554 := [quant-intro #1551]: #1553
+#1516 := (iff #878 #1515)
+#1513 := (iff #841 #1512)
+#1510 := (iff #836 #1509)
+#1506 := (iff #829 #1505)
+#1508 := [rewrite]: #1506
+#1503 := (iff #835 #1502)
+#1500 := (iff #821 #1497)
+#1494 := (and #1209 #780)
+#1498 := (iff #1494 #1497)
+#1499 := [rewrite]: #1498
+#1495 := (iff #821 #1494)
+#1210 := (iff #83 #1209)
+#1211 := [rewrite]: #1210
+#1496 := [monotonicity #1211]: #1495
+#1501 := [trans #1496 #1499]: #1500
+#1504 := [monotonicity #1501]: #1503
+#1511 := [monotonicity #1504 #1508]: #1510
+#1514 := [quant-intro #1511]: #1513
+#1517 := [monotonicity #1514]: #1516
+#1557 := [monotonicity #1517 #1554]: #1556
+#1560 := [monotonicity #1514 #1557]: #1559
+#1492 := (iff #890 #1491)
+#1489 := (iff #815 #1488)
+#1486 := (iff #810 #1483)
+#1480 := (or #1475 #809)
+#1484 := (iff #1480 #1483)
+#1485 := [rewrite]: #1484
+#1481 := (iff #810 #1480)
+#1478 := (iff #212 #1475)
+#1479 := [rewrite]: #1478
+#1482 := [monotonicity #1479]: #1481
+#1487 := [trans #1482 #1485]: #1486
+#1490 := [quant-intro #1487]: #1489
+#1493 := [monotonicity #1490]: #1492
+#1563 := [monotonicity #1493 #1560]: #1562
+#1566 := [monotonicity #1490 #1563]: #1565
+#1473 := (iff #902 #1472)
+#1470 := (iff #206 #1469)
+#1467 := (iff #205 #1466)
+#1468 := [rewrite]: #1467
+#1471 := [quant-intro #1468]: #1470
+#1474 := [monotonicity #1471]: #1473
+#1569 := [monotonicity #1474 #1566]: #1568
+#1572 := [monotonicity #1471 #1569]: #1571
+#1464 := (iff #914 #1463)
+#1461 := (iff #795 #204)
+#1462 := [rewrite]: #1461
+#1465 := [monotonicity #1462]: #1464
+#1575 := [monotonicity #1465 #1572]: #1574
+#1578 := [monotonicity #1462 #1575]: #1577
+#1581 := [monotonicity #1578]: #1580
+#1584 := [monotonicity #1581]: #1583
+#1459 := (iff #938 #1458)
+#1456 := (iff #198 #1455)
+#1453 := (iff #197 #1450)
+#1454 := [rewrite]: #1453
+#1457 := [quant-intro #1454]: #1456
+#1460 := [monotonicity #1457]: #1459
+#1587 := [monotonicity #1460 #1584]: #1586
+#1590 := [monotonicity #1457 #1587]: #1589
+#1448 := (iff #950 #1447)
+#1445 := (iff #777 #1444)
+#1442 := (iff #772 #1439)
+#1436 := (or #1433 #766)
+#1440 := (iff #1436 #1439)
+#1441 := [rewrite]: #1440
+#1437 := (iff #772 #1436)
+#1434 := (iff #188 #1433)
+#1431 := (iff #187 #1430)
 #1432 := [rewrite]: #1431
-#1428 := (iff #754 #1427)
-#1143 := (iff #50 #1142)
-#1144 := [rewrite]: #1143
-#1429 := [monotonicity #1144]: #1428
-#1434 := [trans #1429 #1432]: #1433
-#1437 := [monotonicity #1434]: #1436
-#1444 := [monotonicity #1437 #1441]: #1443
-#1447 := [quant-intro #1444]: #1446
-#1450 := [monotonicity #1447]: #1449
-#1490 := [monotonicity #1450 #1487]: #1489
-#1493 := [monotonicity #1447 #1490]: #1492
-#1425 := (iff #823 #1424)
-#1422 := (iff #748 #1421)
-#1419 := (iff #743 #1416)
-#1413 := (or #1408 #742)
-#1417 := (iff #1413 #1416)
-#1418 := [rewrite]: #1417
-#1414 := (iff #743 #1413)
-#1411 := (iff #178 #1408)
-#1412 := [rewrite]: #1411
-#1415 := [monotonicity #1412]: #1414
-#1420 := [trans #1415 #1418]: #1419
-#1423 := [quant-intro #1420]: #1422
-#1426 := [monotonicity #1423]: #1425
-#1496 := [monotonicity #1426 #1493]: #1495
-#1499 := [monotonicity #1423 #1496]: #1498
-#1406 := (iff #835 #1405)
-#1403 := (iff #172 #1402)
-#1400 := (iff #171 #1399)
-#1401 := [rewrite]: #1400
-#1404 := [quant-intro #1401]: #1403
-#1407 := [monotonicity #1404]: #1406
-#1502 := [monotonicity #1407 #1499]: #1501
-#1505 := [monotonicity #1404 #1502]: #1504
-#1397 := (iff #847 #1396)
-#1394 := (iff #728 #170)
-#1395 := [rewrite]: #1394
-#1398 := [monotonicity #1395]: #1397
-#1508 := [monotonicity #1398 #1505]: #1507
-#1511 := [monotonicity #1395 #1508]: #1510
-#1514 := [monotonicity #1511]: #1513
-#1517 := [monotonicity #1514]: #1516
-#1392 := (iff #871 #1391)
-#1389 := (iff #164 #1388)
-#1386 := (iff #163 #1383)
-#1387 := [rewrite]: #1386
-#1390 := [quant-intro #1387]: #1389
-#1393 := [monotonicity #1390]: #1392
-#1520 := [monotonicity #1393 #1517]: #1519
-#1523 := [monotonicity #1390 #1520]: #1522
-#1381 := (iff #883 #1380)
-#1378 := (iff #710 #1377)
-#1375 := (iff #705 #1372)
-#1369 := (or #1366 #699)
-#1373 := (iff #1369 #1372)
-#1374 := [rewrite]: #1373
-#1370 := (iff #705 #1369)
-#1367 := (iff #154 #1366)
-#1364 := (iff #153 #1363)
-#1365 := [rewrite]: #1364
-#1357 := (iff #151 #1356)
-#1358 := [rewrite]: #1357
-#1368 := [monotonicity #1358 #1365]: #1367
-#1371 := [monotonicity #1368]: #1370
-#1376 := [trans #1371 #1374]: #1375
-#1379 := [quant-intro #1376]: #1378
-#1382 := [monotonicity #1379]: #1381
-#1576 := [monotonicity #1382 #1523]: #1575
-#1539 := (iff #892 #1538)
-#1536 := (iff #696 #1535)
-#1533 := (iff #691 #1532)
-#1530 := (iff #685 #1529)
-#1531 := [rewrite]: #1530
-#1525 := (iff #159 #1524)
-#1526 := [monotonicity #1368]: #1525
-#1534 := [monotonicity #1526 #1531]: #1533
-#1537 := [quant-intro #1534]: #1536
-#1540 := [monotonicity #1537]: #1539
-#1579 := [monotonicity #1540 #1576]: #1578
-#1582 := [monotonicity #1579]: #1581
-#1557 := (iff #910 #1556)
-#1554 := (iff #682 #1553)
-#1551 := (iff #677 #1548)
-#1545 := (or #1541 #447)
-#1549 := (iff #1545 #1548)
-#1550 := [rewrite]: #1549
-#1546 := (iff #677 #1545)
-#1543 := (iff #143 #1541)
-#1544 := [rewrite]: #1543
-#1547 := [monotonicity #1544]: #1546
-#1552 := [trans #1547 #1550]: #1551
-#1555 := [quant-intro #1552]: #1554
-#1558 := [monotonicity #1555]: #1557
-#1585 := [monotonicity #1558 #1582]: #1584
-#1569 := (iff #919 #1560)
-#1561 := (not #1560)
-#1564 := (not #1561)
-#1567 := (iff #1564 #1560)
-#1568 := [rewrite]: #1567
-#1565 := (iff #919 #1564)
-#1562 := (iff #142 #1561)
-#1563 := [rewrite]: #1562
-#1566 := [monotonicity #1563]: #1565
-#1570 := [trans #1566 #1568]: #1569
-#1588 := [monotonicity #1570 #1585]: #1587
-#1591 := [monotonicity #1588]: #1590
-#1572 := (iff #532 #1571)
-#1331 := (iff #529 #1330)
-#1328 := (iff #524 #1325)
-#1322 := (and #1206 #450)
-#1326 := (iff #1322 #1325)
-#1327 := [rewrite]: #1326
-#1323 := (iff #524 #1322)
-#1207 := (iff #87 #1206)
-#1208 := [rewrite]: #1207
-#1324 := [monotonicity #1208]: #1323
-#1329 := [trans #1324 #1327]: #1328
-#1332 := [quant-intro #1329]: #1331
-#1573 := [monotonicity #1332]: #1572
-#1594 := [monotonicity #1573 #1591]: #1593
-#1599 := [trans #1594 #1597]: #1598
-#1351 := (iff #656 #1348)
-#1333 := (or #620 #1319)
-#1336 := (or #629 #1333)
-#1339 := (or #638 #1336)
-#1342 := (or #647 #1339)
-#1345 := (or #1330 #1342)
-#1349 := (iff #1345 #1348)
-#1350 := [rewrite]: #1349
-#1346 := (iff #656 #1345)
-#1343 := (iff #648 #1342)
-#1340 := (iff #639 #1339)
-#1337 := (iff #630 #1336)
-#1334 := (iff #621 #1333)
-#1320 := (iff #614 #1319)
-#1317 := (iff #609 #1316)
-#1314 := (iff #602 #1313)
-#1311 := (iff #597 #1308)
-#1305 := (or #1300 #125)
-#1309 := (iff #1305 #1308)
-#1310 := [rewrite]: #1309
-#1306 := (iff #597 #1305)
-#1303 := (iff #583 #125)
-#1304 := [rewrite]: #1303
-#1301 := (iff #596 #1300)
-#1298 := (iff #580 #1297)
-#1295 := (iff #575 #1294)
-#1292 := (iff #568 #1291)
-#1293 := [rewrite]: #1292
-#1289 := (iff #574 #1288)
-#1286 := (iff #565 #1285)
-#1252 := (iff #110 #1251)
-#1253 := [rewrite]: #1252
-#1287 := [monotonicity #1144 #1253]: #1286
-#1290 := [monotonicity #1287]: #1289
-#1296 := [monotonicity #1290 #1293]: #1295
-#1299 := [quant-intro #1296]: #1298
-#1302 := [monotonicity #1299]: #1301
-#1307 := [monotonicity #1302 #1304]: #1306
-#1312 := [trans #1307 #1310]: #1311
-#1315 := [monotonicity #1299 #1312]: #1314
-#1283 := (iff #608 #1282)
-#1280 := (iff #562 #1279)
-#1277 := (iff #557 #1276)
-#1274 := (iff #550 #1273)
-#1271 := (iff #547 #1270)
-#1267 := (iff #544 #1266)
-#1269 := [rewrite]: #1267
-#1264 := (iff #113 #1263)
-#1265 := [rewrite]: #1264
-#1272 := [monotonicity #1265 #1269]: #1271
-#1275 := [quant-intro #1272]: #1274
-#1258 := (iff #556 #1257)
-#1255 := (iff #111 #1254)
-#1256 := [monotonicity #1253]: #1255
-#1259 := [monotonicity #1256]: #1258
-#1278 := [monotonicity #1259 #1275]: #1277
-#1281 := [quant-intro #1278]: #1280
-#1284 := [monotonicity #1281]: #1283
-#1318 := [monotonicity #1284 #1315]: #1317
-#1321 := [monotonicity #1281 #1318]: #1320
-#1335 := [monotonicity #1321]: #1334
-#1338 := [monotonicity #1335]: #1337
-#1341 := [monotonicity #1338]: #1340
-#1344 := [monotonicity #1341]: #1343
-#1347 := [monotonicity #1332 #1344]: #1346
-#1352 := [trans #1347 #1350]: #1351
-#1602 := [monotonicity #1352 #1599]: #1601
-#1246 := (iff #954 #1245)
-#1243 := (iff #518 #1242)
-#1240 := (iff #513 #1239)
-#1237 := (iff #506 #1236)
-#1234 := (iff #503 #1231)
-#1225 := (and #447 #1215)
-#1228 := (and #1222 #1225)
-#1232 := (iff #1228 #1231)
-#1233 := [rewrite]: #1232
-#1229 := (iff #503 #1228)
-#1226 := (iff #500 #1225)
-#1216 := (iff #497 #1215)
-#1220 := [rewrite]: #1216
-#1227 := [monotonicity #1220]: #1226
-#1223 := (iff #89 #1222)
-#1224 := [rewrite]: #1223
-#1230 := [monotonicity #1224 #1227]: #1229
-#1235 := [trans #1230 #1233]: #1234
-#1238 := [quant-intro #1235]: #1237
-#1213 := (iff #512 #1212)
-#1210 := (iff #88 #1209)
-#1211 := [monotonicity #1208]: #1210
-#1214 := [monotonicity #1211]: #1213
-#1241 := [monotonicity #1214 #1238]: #1240
-#1244 := [quant-intro #1241]: #1243
-#1247 := [monotonicity #1244]: #1246
-#1661 := [monotonicity #1247 #1602]: #1660
-#1624 := (iff #963 #1623)
-#1621 := (iff #494 #1620)
-#1618 := (iff #489 #1617)
-#1615 := (iff #482 #1614)
-#1616 := [rewrite]: #1615
-#1612 := (iff #488 #1611)
-#1609 := (iff #474 #1606)
-#1603 := (and #1142 #447)
-#1607 := (iff #1603 #1606)
-#1608 := [rewrite]: #1607
-#1604 := (iff #474 #1603)
-#1605 := [monotonicity #1144]: #1604
-#1610 := [trans #1605 #1608]: #1609
-#1613 := [monotonicity #1610]: #1612
-#1619 := [monotonicity #1613 #1616]: #1618
+#1424 := (iff #185 #1423)
+#1425 := [rewrite]: #1424
+#1435 := [monotonicity #1425 #1432]: #1434
+#1438 := [monotonicity #1435]: #1437
+#1443 := [trans #1438 #1441]: #1442
+#1446 := [quant-intro #1443]: #1445
+#1449 := [monotonicity #1446]: #1448
+#1643 := [monotonicity #1449 #1590]: #1642
+#1606 := (iff #959 #1605)
+#1603 := (iff #763 #1602)
+#1600 := (iff #758 #1599)
+#1597 := (iff #752 #1596)
+#1598 := [rewrite]: #1597
+#1592 := (iff #193 #1591)
+#1593 := [monotonicity #1435]: #1592
+#1601 := [monotonicity #1593 #1598]: #1600
+#1604 := [quant-intro #1601]: #1603
+#1607 := [monotonicity #1604]: #1606
+#1646 := [monotonicity #1607 #1643]: #1645
+#1649 := [monotonicity #1646]: #1648
+#1624 := (iff #977 #1623)
+#1621 := (iff #741 #1620)
+#1618 := (iff #736 #1615)
+#1612 := (or #1608 #506)
+#1616 := (iff #1612 #1615)
+#1617 := [rewrite]: #1616
+#1613 := (iff #736 #1612)
+#1610 := (iff #176 #1608)
+#1611 := [rewrite]: #1610
+#1614 := [monotonicity #1611]: #1613
+#1619 := [trans #1614 #1617]: #1618
 #1622 := [quant-intro #1619]: #1621
 #1625 := [monotonicity #1622]: #1624
-#1664 := [monotonicity #1625 #1661]: #1663
-#1640 := (iff #972 #1639)
-#1637 := (iff #468 #1636)
-#1634 := (iff #463 #1631)
-#1628 := (or #1221 #462)
-#1632 := (iff #1628 #1631)
-#1633 := [rewrite]: #1632
-#1629 := (iff #463 #1628)
-#1626 := (iff #79 #1221)
-#1627 := [rewrite]: #1626
-#1630 := [monotonicity #1627]: #1629
-#1635 := [trans #1630 #1633]: #1634
-#1638 := [quant-intro #1635]: #1637
-#1641 := [monotonicity #1638]: #1640
-#1667 := [monotonicity #1641 #1664]: #1666
-#1649 := (iff #981 #1648)
-#1646 := (iff #70 #1645)
-#1643 := (iff #69 #1642)
-#1644 := [rewrite]: #1643
-#1647 := [quant-intro #1644]: #1646
-#1650 := [monotonicity #1647]: #1649
-#1670 := [monotonicity #1650 #1667]: #1669
-#1654 := (iff #990 #1653)
-#1651 := (iff #444 #67)
-#1652 := [rewrite]: #1651
-#1655 := [monotonicity #1652]: #1654
-#1673 := [monotonicity #1655 #1670]: #1672
-#1657 := (iff #1006 #1656)
-#1201 := (iff #441 #1200)
-#1198 := (iff #436 #1197)
-#1195 := (iff #429 #1194)
-#1192 := (iff #426 #1189)
-#1183 := (and #1177 #368)
-#1186 := (and #1180 #1183)
-#1190 := (iff #1186 #1189)
-#1191 := [rewrite]: #1190
-#1187 := (iff #426 #1186)
-#1184 := (iff #421 #1183)
-#1178 := (iff #59 #1177)
-#1179 := [rewrite]: #1178
-#1185 := [monotonicity #1179]: #1184
-#1181 := (iff #58 #1180)
-#1182 := [rewrite]: #1181
-#1188 := [monotonicity #1182 #1185]: #1187
-#1193 := [trans #1188 #1191]: #1192
-#1196 := [quant-intro #1193]: #1195
-#1175 := (iff #435 #1174)
-#1172 := (iff #57 #1171)
-#1169 := (iff #56 #1168)
-#1170 := [rewrite]: #1169
-#1173 := [monotonicity #1170]: #1172
-#1176 := [monotonicity #1173]: #1175
-#1199 := [monotonicity #1176 #1196]: #1198
-#1202 := [quant-intro #1199]: #1201
-#1658 := [monotonicity #1202]: #1657
-#1676 := [monotonicity #1658 #1673]: #1675
-#1681 := [trans #1676 #1679]: #1680
-#1684 := [monotonicity #1202 #1681]: #1683
-#1163 := (iff #1018 #1162)
-#1160 := (iff #415 #1159)
-#1157 := (iff #410 #1156)
-#1154 := (iff #409 #1153)
-#1151 := (iff #401 #1148)
-#1145 := (and #1142 #368)
-#1149 := (iff #1145 #1148)
-#1150 := [rewrite]: #1149
-#1146 := (iff #401 #1145)
-#1147 := [monotonicity #1144]: #1146
-#1152 := [trans #1147 #1150]: #1151
-#1155 := [monotonicity #1152]: #1154
-#1135 := (iff #53 #1136)
-#1134 := [rewrite]: #1135
-#1158 := [monotonicity #1134 #1155]: #1157
-#1161 := [quant-intro #1158]: #1160
-#1164 := [monotonicity #1161]: #1163
-#1687 := [monotonicity #1164 #1684]: #1686
-#1690 := [monotonicity #1161 #1687]: #1689
-#1132 := (iff #1030 #1131)
-#1129 := (iff #395 #1128)
-#1126 := (iff #390 #1123)
-#1120 := (or #1116 #389)
-#1124 := (iff #1120 #1123)
-#1125 := [rewrite]: #1124
-#1121 := (iff #390 #1120)
-#1115 := (iff #45 #1116)
-#1119 := [rewrite]: #1115
-#1122 := [monotonicity #1119]: #1121
-#1127 := [trans #1122 #1125]: #1126
-#1130 := [quant-intro #1127]: #1129
-#1133 := [monotonicity #1130]: #1132
-#1693 := [monotonicity #1133 #1690]: #1692
-#1696 := [monotonicity #1130 #1693]: #1695
-#1112 := (iff #1042 #1111)
-#1109 := (iff #40 #1108)
-#1105 := (iff #39 #1107)
-#1106 := [rewrite]: #1105
-#1110 := [quant-intro #1106]: #1109
-#1113 := [monotonicity #1110]: #1112
-#1699 := [monotonicity #1113 #1696]: #1698
-#1702 := [monotonicity #1110 #1699]: #1701
-#1103 := (iff #1054 #1102)
-#1100 := (iff #377 #38)
-#1101 := [rewrite]: #1100
-#1104 := [monotonicity #1101]: #1103
-#1705 := [monotonicity #1104 #1702]: #1704
-#1708 := [monotonicity #1101 #1705]: #1707
-#1722 := [monotonicity #1708]: #1721
-#1725 := [monotonicity #1722]: #1724
-#1718 := (iff #1084 #1717)
-#1715 := (iff #351 #1714)
-#1712 := (iff #346 #1711)
-#1709 := (iff #340 #26)
-#1710 := [rewrite]: #1709
-#1713 := [monotonicity #1710]: #1712
-#1716 := [quant-intro #1713]: #1715
-#1719 := [monotonicity #1716]: #1718
-#1728 := [monotonicity #1719 #1725]: #1727
-#1733 := [trans #1728 #1731]: #1732
-#1736 := [monotonicity #1733]: #1735
-#1098 := (iff #237 #1097)
-#1095 := (iff #236 #1085)
-#1090 := (implies true #1085)
-#1093 := (iff #1090 #1085)
-#1094 := [rewrite]: #1093
-#1091 := (iff #236 #1090)
-#1088 := (iff #235 #1085)
-#1081 := (implies #351 #1076)
-#1086 := (iff #1081 #1085)
-#1087 := [rewrite]: #1086
-#1082 := (iff #235 #1081)
-#1079 := (iff #234 #1076)
-#1072 := (implies #365 #1067)
-#1077 := (iff #1072 #1076)
-#1078 := [rewrite]: #1077
-#1073 := (iff #234 #1072)
-#1070 := (iff #233 #1067)
-#1063 := (implies #374 #1060)
-#1068 := (iff #1063 #1067)
-#1069 := [rewrite]: #1068
-#1064 := (iff #233 #1063)
-#1061 := (iff #232 #1060)
-#1058 := (iff #231 #1055)
-#1051 := (implies #377 #1048)
-#1056 := (iff #1051 #1055)
-#1057 := [rewrite]: #1056
-#1052 := (iff #231 #1051)
-#1049 := (iff #230 #1048)
-#1046 := (iff #229 #1043)
-#1039 := (implies #40 #1036)
-#1044 := (iff #1039 #1043)
-#1045 := [rewrite]: #1044
-#1040 := (iff #229 #1039)
-#1037 := (iff #228 #1036)
-#1034 := (iff #227 #1031)
-#1027 := (implies #395 #1024)
+#1652 := [monotonicity #1625 #1649]: #1651
+#1636 := (iff #986 #1627)
+#1628 := (not #1627)
+#1631 := (not #1628)
+#1634 := (iff #1631 #1627)
+#1635 := [rewrite]: #1634
+#1632 := (iff #986 #1631)
+#1629 := (iff #175 #1628)
+#1630 := [rewrite]: #1629
+#1633 := [monotonicity #1630]: #1632
+#1637 := [trans #1633 #1635]: #1636
+#1655 := [monotonicity #1637 #1652]: #1654
+#1658 := [monotonicity #1655]: #1657
+#1639 := (iff #591 #1638)
+#1398 := (iff #588 #1397)
+#1395 := (iff #583 #1392)
+#1389 := (and #1273 #509)
+#1393 := (iff #1389 #1392)
+#1394 := [rewrite]: #1393
+#1390 := (iff #583 #1389)
+#1274 := (iff #120 #1273)
+#1275 := [rewrite]: #1274
+#1391 := [monotonicity #1275]: #1390
+#1396 := [trans #1391 #1394]: #1395
+#1399 := [quant-intro #1396]: #1398
+#1640 := [monotonicity #1399]: #1639
+#1661 := [monotonicity #1640 #1658]: #1660
+#1666 := [trans #1661 #1664]: #1665
+#1418 := (iff #715 #1415)
+#1400 := (or #679 #1386)
+#1403 := (or #688 #1400)
+#1406 := (or #697 #1403)
+#1409 := (or #706 #1406)
+#1412 := (or #1397 #1409)
+#1416 := (iff #1412 #1415)
+#1417 := [rewrite]: #1416
+#1413 := (iff #715 #1412)
+#1410 := (iff #707 #1409)
+#1407 := (iff #698 #1406)
+#1404 := (iff #689 #1403)
+#1401 := (iff #680 #1400)
+#1387 := (iff #673 #1386)
+#1384 := (iff #668 #1383)
+#1381 := (iff #661 #1380)
+#1378 := (iff #656 #1375)
+#1372 := (or #1367 #158)
+#1376 := (iff #1372 #1375)
+#1377 := [rewrite]: #1376
+#1373 := (iff #656 #1372)
+#1370 := (iff #642 #158)
+#1371 := [rewrite]: #1370
+#1368 := (iff #655 #1367)
+#1365 := (iff #639 #1364)
+#1362 := (iff #634 #1361)
+#1359 := (iff #627 #1358)
+#1360 := [rewrite]: #1359
+#1356 := (iff #633 #1355)
+#1353 := (iff #624 #1352)
+#1319 := (iff #143 #1318)
+#1320 := [rewrite]: #1319
+#1354 := [monotonicity #1211 #1320]: #1353
+#1357 := [monotonicity #1354]: #1356
+#1363 := [monotonicity #1357 #1360]: #1362
+#1366 := [quant-intro #1363]: #1365
+#1369 := [monotonicity #1366]: #1368
+#1374 := [monotonicity #1369 #1371]: #1373
+#1379 := [trans #1374 #1377]: #1378
+#1382 := [monotonicity #1366 #1379]: #1381
+#1350 := (iff #667 #1349)
+#1347 := (iff #621 #1346)
+#1344 := (iff #616 #1343)
+#1341 := (iff #609 #1340)
+#1338 := (iff #606 #1337)
+#1334 := (iff #603 #1333)
+#1336 := [rewrite]: #1334
+#1331 := (iff #146 #1330)
+#1332 := [rewrite]: #1331
+#1339 := [monotonicity #1332 #1336]: #1338
+#1342 := [quant-intro #1339]: #1341
+#1325 := (iff #615 #1324)
+#1322 := (iff #144 #1321)
+#1323 := [monotonicity #1320]: #1322
+#1326 := [monotonicity #1323]: #1325
+#1345 := [monotonicity #1326 #1342]: #1344
+#1348 := [quant-intro #1345]: #1347
+#1351 := [monotonicity #1348]: #1350
+#1385 := [monotonicity #1351 #1382]: #1384
+#1388 := [monotonicity #1348 #1385]: #1387
+#1402 := [monotonicity #1388]: #1401
+#1405 := [monotonicity #1402]: #1404
+#1408 := [monotonicity #1405]: #1407
+#1411 := [monotonicity #1408]: #1410
+#1414 := [monotonicity #1399 #1411]: #1413
+#1419 := [trans #1414 #1417]: #1418
+#1669 := [monotonicity #1419 #1666]: #1668
+#1313 := (iff #1021 #1312)
+#1310 := (iff #577 #1309)
+#1307 := (iff #572 #1306)
+#1304 := (iff #565 #1303)
+#1301 := (iff #562 #1298)
+#1292 := (and #506 #1282)
+#1295 := (and #1289 #1292)
+#1299 := (iff #1295 #1298)
+#1300 := [rewrite]: #1299
+#1296 := (iff #562 #1295)
+#1293 := (iff #559 #1292)
+#1283 := (iff #556 #1282)
+#1287 := [rewrite]: #1283
+#1294 := [monotonicity #1287]: #1293
+#1290 := (iff #122 #1289)
+#1291 := [rewrite]: #1290
+#1297 := [monotonicity #1291 #1294]: #1296
+#1302 := [trans #1297 #1300]: #1301
+#1305 := [quant-intro #1302]: #1304
+#1280 := (iff #571 #1279)
+#1277 := (iff #121 #1276)
+#1278 := [monotonicity #1275]: #1277
+#1281 := [monotonicity #1278]: #1280
+#1308 := [monotonicity #1281 #1305]: #1307
+#1311 := [quant-intro #1308]: #1310
+#1314 := [monotonicity #1311]: #1313
+#1728 := [monotonicity #1314 #1669]: #1727
+#1691 := (iff #1030 #1690)
+#1688 := (iff #553 #1687)
+#1685 := (iff #548 #1684)
+#1682 := (iff #541 #1681)
+#1683 := [rewrite]: #1682
+#1679 := (iff #547 #1678)
+#1676 := (iff #533 #1673)
+#1670 := (and #1209 #506)
+#1674 := (iff #1670 #1673)
+#1675 := [rewrite]: #1674
+#1671 := (iff #533 #1670)
+#1672 := [monotonicity #1211]: #1671
+#1677 := [trans #1672 #1675]: #1676
+#1680 := [monotonicity #1677]: #1679
+#1686 := [monotonicity #1680 #1683]: #1685
+#1689 := [quant-intro #1686]: #1688
+#1692 := [monotonicity #1689]: #1691
+#1731 := [monotonicity #1692 #1728]: #1730
+#1707 := (iff #1039 #1706)
+#1704 := (iff #527 #1703)
+#1701 := (iff #522 #1698)
+#1695 := (or #1288 #521)
+#1699 := (iff #1695 #1698)
+#1700 := [rewrite]: #1699
+#1696 := (iff #522 #1695)
+#1693 := (iff #112 #1288)
+#1694 := [rewrite]: #1693
+#1697 := [monotonicity #1694]: #1696
+#1702 := [trans #1697 #1700]: #1701
+#1705 := [quant-intro #1702]: #1704
+#1708 := [monotonicity #1705]: #1707
+#1734 := [monotonicity #1708 #1731]: #1733
+#1716 := (iff #1048 #1715)
+#1713 := (iff #103 #1712)
+#1710 := (iff #102 #1709)
+#1711 := [rewrite]: #1710
+#1714 := [quant-intro #1711]: #1713
+#1717 := [monotonicity #1714]: #1716
+#1737 := [monotonicity #1717 #1734]: #1736
+#1721 := (iff #1057 #1720)
+#1718 := (iff #503 #100)
+#1719 := [rewrite]: #1718
+#1722 := [monotonicity #1719]: #1721
+#1740 := [monotonicity #1722 #1737]: #1739
+#1724 := (iff #1073 #1723)
+#1268 := (iff #500 #1267)
+#1265 := (iff #495 #1264)
+#1262 := (iff #488 #1261)
+#1259 := (iff #485 #1256)
+#1250 := (and #1244 #427)
+#1253 := (and #1247 #1250)
+#1257 := (iff #1253 #1256)
+#1258 := [rewrite]: #1257
+#1254 := (iff #485 #1253)
+#1251 := (iff #480 #1250)
+#1245 := (iff #92 #1244)
+#1246 := [rewrite]: #1245
+#1252 := [monotonicity #1246]: #1251
+#1248 := (iff #91 #1247)
+#1249 := [rewrite]: #1248
+#1255 := [monotonicity #1249 #1252]: #1254
+#1260 := [trans #1255 #1258]: #1259
+#1263 := [quant-intro #1260]: #1262
+#1242 := (iff #494 #1241)
+#1239 := (iff #90 #1238)
+#1236 := (iff #89 #1235)
+#1237 := [rewrite]: #1236
+#1240 := [monotonicity #1237]: #1239
+#1243 := [monotonicity #1240]: #1242
+#1266 := [monotonicity #1243 #1263]: #1265
+#1269 := [quant-intro #1266]: #1268
+#1725 := [monotonicity #1269]: #1724
+#1743 := [monotonicity #1725 #1740]: #1742
+#1748 := [trans #1743 #1746]: #1747
+#1751 := [monotonicity #1269 #1748]: #1750
+#1230 := (iff #1085 #1229)
+#1227 := (iff #474 #1226)
+#1224 := (iff #469 #1223)
+#1221 := (iff #468 #1220)
+#1218 := (iff #460 #1215)
+#1212 := (and #1209 #427)
+#1216 := (iff #1212 #1215)
+#1217 := [rewrite]: #1216
+#1213 := (iff #460 #1212)
+#1214 := [monotonicity #1211]: #1213
+#1219 := [trans #1214 #1217]: #1218
+#1222 := [monotonicity #1219]: #1221
+#1202 := (iff #86 #1203)
+#1201 := [rewrite]: #1202
+#1225 := [monotonicity #1201 #1222]: #1224
+#1228 := [quant-intro #1225]: #1227
+#1231 := [monotonicity #1228]: #1230
+#1754 := [monotonicity #1231 #1751]: #1753
+#1757 := [monotonicity #1228 #1754]: #1756
+#1199 := (iff #1097 #1198)
+#1196 := (iff #454 #1195)
+#1193 := (iff #449 #1190)
+#1187 := (or #1183 #448)
+#1191 := (iff #1187 #1190)
+#1192 := [rewrite]: #1191
+#1188 := (iff #449 #1187)
+#1182 := (iff #78 #1183)
+#1186 := [rewrite]: #1182
+#1189 := [monotonicity #1186]: #1188
+#1194 := [trans #1189 #1192]: #1193
+#1197 := [quant-intro #1194]: #1196
+#1200 := [monotonicity #1197]: #1199
+#1760 := [monotonicity #1200 #1757]: #1759
+#1763 := [monotonicity #1197 #1760]: #1762
+#1179 := (iff #1109 #1178)
+#1176 := (iff #73 #1175)
+#1172 := (iff #72 #1174)
+#1173 := [rewrite]: #1172
+#1177 := [quant-intro #1173]: #1176
+#1180 := [monotonicity #1177]: #1179
+#1766 := [monotonicity #1180 #1763]: #1765
+#1769 := [monotonicity #1177 #1766]: #1768
+#1170 := (iff #1121 #1169)
+#1167 := (iff #436 #71)
+#1168 := [rewrite]: #1167
+#1171 := [monotonicity #1168]: #1170
+#1772 := [monotonicity #1171 #1769]: #1771
+#1775 := [monotonicity #1168 #1772]: #1774
+#1789 := [monotonicity #1775]: #1788
+#1792 := [monotonicity #1789]: #1791
+#1785 := (iff #1151 #1784)
+#1782 := (iff #410 #1781)
+#1779 := (iff #405 #1778)
+#1776 := (iff #399 #59)
+#1777 := [rewrite]: #1776
+#1780 := [monotonicity #1777]: #1779
+#1783 := [quant-intro #1780]: #1782
+#1786 := [monotonicity #1783]: #1785
+#1795 := [monotonicity #1786 #1792]: #1794
+#1800 := [trans #1795 #1798]: #1799
+#1803 := [monotonicity #1800]: #1802
+#1165 := (iff #271 #1164)
+#1162 := (iff #270 #1152)
+#1157 := (implies true #1152)
+#1160 := (iff #1157 #1152)
+#1161 := [rewrite]: #1160
+#1158 := (iff #270 #1157)
+#1155 := (iff #269 #1152)
+#1148 := (implies #410 #1143)
+#1153 := (iff #1148 #1152)
+#1154 := [rewrite]: #1153
+#1149 := (iff #269 #1148)
+#1146 := (iff #268 #1143)
+#1139 := (implies #424 #1134)
+#1144 := (iff #1139 #1143)
+#1145 := [rewrite]: #1144
+#1140 := (iff #268 #1139)
+#1137 := (iff #267 #1134)
+#1130 := (implies #433 #1127)
+#1135 := (iff #1130 #1134)
+#1136 := [rewrite]: #1135
+#1131 := (iff #267 #1130)
+#1128 := (iff #266 #1127)
+#1125 := (iff #265 #1122)
+#1118 := (implies #436 #1115)
+#1123 := (iff #1118 #1122)
+#1124 := [rewrite]: #1123
+#1119 := (iff #265 #1118)
+#1116 := (iff #264 #1115)
+#1113 := (iff #263 #1110)
+#1106 := (implies #73 #1103)
+#1111 := (iff #1106 #1110)
+#1112 := [rewrite]: #1111
+#1107 := (iff #263 #1106)
+#1104 := (iff #262 #1103)
+#1101 := (iff #261 #1098)
+#1094 := (implies #454 #1091)
+#1099 := (iff #1094 #1098)
+#1100 := [rewrite]: #1099
+#1095 := (iff #261 #1094)
+#1092 := (iff #260 #1091)
+#1089 := (iff #259 #1086)
+#1082 := (implies #474 #1079)
+#1087 := (iff #1082 #1086)
+#1088 := [rewrite]: #1087
+#1083 := (iff #259 #1082)
+#1080 := (iff #258 #1079)
+#1077 := (iff #257 #1074)
+#1070 := (implies #500 #1058)
+#1075 := (iff #1070 #1074)
+#1076 := [rewrite]: #1075
+#1071 := (iff #257 #1070)
+#1068 := (iff #256 #1058)
+#1063 := (implies true #1058)
+#1066 := (iff #1063 #1058)
+#1067 := [rewrite]: #1066
+#1064 := (iff #256 #1063)
+#1061 := (iff #255 #1058)
+#1054 := (implies #503 #1049)
+#1059 := (iff #1054 #1058)
+#1060 := [rewrite]: #1059
+#1055 := (iff #255 #1054)
+#1052 := (iff #254 #1049)
+#1045 := (implies #103 #1040)
+#1050 := (iff #1045 #1049)
+#1051 := [rewrite]: #1050
+#1046 := (iff #254 #1045)
+#1043 := (iff #253 #1040)
+#1036 := (implies #527 #1031)
+#1041 := (iff #1036 #1040)
+#1042 := [rewrite]: #1041
+#1037 := (iff #253 #1036)
+#1034 := (iff #252 #1031)
+#1027 := (implies #553 #1022)
 #1032 := (iff #1027 #1031)
 #1033 := [rewrite]: #1032
-#1028 := (iff #227 #1027)
-#1025 := (iff #226 #1024)
-#1022 := (iff #225 #1019)
-#1015 := (implies #415 #1012)
-#1020 := (iff #1015 #1019)
-#1021 := [rewrite]: #1020
-#1016 := (iff #225 #1015)
-#1013 := (iff #224 #1012)
-#1010 := (iff #223 #1007)
-#1003 := (implies #441 #991)
-#1008 := (iff #1003 #1007)
-#1009 := [rewrite]: #1008
-#1004 := (iff #223 #1003)
-#1001 := (iff #222 #991)
-#996 := (implies true #991)
-#999 := (iff #996 #991)
-#1000 := [rewrite]: #999
-#997 := (iff #222 #996)
-#994 := (iff #221 #991)
-#987 := (implies #444 #982)
-#992 := (iff #987 #991)
-#993 := [rewrite]: #992
-#988 := (iff #221 #987)
-#985 := (iff #220 #982)
-#978 := (implies #70 #973)
-#983 := (iff #978 #982)
-#984 := [rewrite]: #983
-#979 := (iff #220 #978)
-#976 := (iff #219 #973)
-#969 := (implies #468 #964)
-#974 := (iff #969 #973)
-#975 := [rewrite]: #974
-#970 := (iff #219 #969)
-#967 := (iff #218 #964)
-#960 := (implies #494 #955)
-#965 := (iff #960 #964)
-#966 := [rewrite]: #965
-#961 := (iff #218 #960)
-#958 := (iff #217 #955)
-#951 := (implies #518 #948)
-#956 := (iff #951 #955)
-#957 := [rewrite]: #956
-#952 := (iff #217 #951)
-#949 := (iff #216 #948)
-#946 := (iff #215 #936)
-#941 := (implies true #936)
-#944 := (iff #941 #936)
-#945 := [rewrite]: #944
-#942 := (iff #215 #941)
-#939 := (iff #214 #936)
-#933 := (implies #529 #928)
-#937 := (iff #933 #936)
-#938 := [rewrite]: #937
-#934 := (iff #214 #933)
-#931 := (iff #213 #928)
-#671 := (not #668)
-#925 := (implies #671 #920)
-#929 := (iff #925 #928)
-#930 := [rewrite]: #929
-#926 := (iff #213 #925)
-#923 := (iff #212 #920)
-#916 := (implies #142 #911)
-#921 := (iff #916 #920)
-#922 := [rewrite]: #921
-#917 := (iff #212 #916)
-#914 := (iff #211 #911)
-#907 := (implies #682 #902)
-#912 := (iff #907 #911)
-#913 := [rewrite]: #912
-#908 := (iff #211 #907)
-#905 := (iff #210 #902)
-#898 := (implies #148 #893)
-#903 := (iff #898 #902)
-#904 := [rewrite]: #903
-#899 := (iff #210 #898)
-#896 := (iff #209 #893)
-#889 := (implies #696 #884)
-#894 := (iff #889 #893)
-#895 := [rewrite]: #894
-#890 := (iff #209 #889)
-#887 := (iff #208 #884)
-#880 := (implies #710 #877)
-#885 := (iff #880 #884)
-#886 := [rewrite]: #885
-#881 := (iff #208 #880)
-#878 := (iff #207 #877)
-#875 := (iff #206 #872)
-#868 := (implies #164 #865)
-#873 := (iff #868 #872)
-#874 := [rewrite]: #873
-#869 := (iff #206 #868)
-#866 := (iff #205 #865)
-#863 := (iff #204 #860)
-#856 := (implies #725 #853)
+#1028 := (iff #252 #1027)
+#1025 := (iff #251 #1022)
+#1018 := (implies #577 #1015)
+#1023 := (iff #1018 #1022)
+#1024 := [rewrite]: #1023
+#1019 := (iff #251 #1018)
+#1016 := (iff #250 #1015)
+#1013 := (iff #249 #1003)
+#1008 := (implies true #1003)
+#1011 := (iff #1008 #1003)
+#1012 := [rewrite]: #1011
+#1009 := (iff #249 #1008)
+#1006 := (iff #248 #1003)
+#1000 := (implies #588 #995)
+#1004 := (iff #1000 #1003)
+#1005 := [rewrite]: #1004
+#1001 := (iff #248 #1000)
+#998 := (iff #247 #995)
+#730 := (not #727)
+#992 := (implies #730 #987)
+#996 := (iff #992 #995)
+#997 := [rewrite]: #996
+#993 := (iff #247 #992)
+#990 := (iff #246 #987)
+#983 := (implies #175 #978)
+#988 := (iff #983 #987)
+#989 := [rewrite]: #988
+#984 := (iff #246 #983)
+#981 := (iff #245 #978)
+#974 := (implies #741 #969)
+#979 := (iff #974 #978)
+#980 := [rewrite]: #979
+#975 := (iff #245 #974)
+#972 := (iff #244 #969)
+#965 := (implies #749 #960)
+#970 := (iff #965 #969)
+#971 := [rewrite]: #970
+#966 := (iff #244 #965)
+#963 := (iff #243 #960)
+#956 := (implies #763 #951)
+#961 := (iff #956 #960)
+#962 := [rewrite]: #961
+#957 := (iff #243 #956)
+#954 := (iff #242 #951)
+#947 := (implies #777 #944)
+#952 := (iff #947 #951)
+#953 := [rewrite]: #952
+#948 := (iff #242 #947)
+#945 := (iff #241 #944)
+#942 := (iff #240 #939)
+#935 := (implies #198 #932)
+#940 := (iff #935 #939)
+#941 := [rewrite]: #940
+#936 := (iff #240 #935)
+#933 := (iff #239 #932)
+#930 := (iff #238 #927)
+#923 := (implies #792 #920)
+#928 := (iff #923 #927)
+#929 := [rewrite]: #928
+#924 := (iff #238 #923)
+#921 := (iff #237 #920)
+#918 := (iff #236 #915)
+#911 := (implies #795 #908)
+#916 := (iff #911 #915)
+#917 := [rewrite]: #916
+#912 := (iff #236 #911)
+#909 := (iff #235 #908)
+#906 := (iff #234 #903)
+#899 := (implies #206 #896)
+#904 := (iff #899 #903)
+#905 := [rewrite]: #904
+#900 := (iff #234 #899)
+#897 := (iff #233 #896)
+#894 := (iff #232 #891)
+#887 := (implies #815 #884)
+#892 := (iff #887 #891)
+#893 := [rewrite]: #892
+#888 := (iff #232 #887)
+#885 := (iff #231 #884)
+#882 := (iff #230 #879)
+#875 := (implies #841 #865)
+#880 := (iff #875 #879)
+#881 := [rewrite]: #880
+#876 := (iff #230 #875)
+#873 := (iff #229 #865)
+#868 := (and #865 true)
+#871 := (iff #868 #865)
+#872 := [rewrite]: #871
+#869 := (iff #229 #868)
+#866 := (iff #228 #865)
+#863 := (iff #227 #860)
+#856 := (implies #221 #853)
 #861 := (iff #856 #860)
 #862 := [rewrite]: #861
-#857 := (iff #204 #856)
-#854 := (iff #203 #853)
-#851 := (iff #202 #848)
-#844 := (implies #728 #841)
-#849 := (iff #844 #848)
-#850 := [rewrite]: #849
-#845 := (iff #202 #844)
-#842 := (iff #201 #841)
-#839 := (iff #200 #836)
-#832 := (implies #172 #829)
+#857 := (iff #227 #856)
+#854 := (iff #226 #853)
+#851 := (iff #225 #850)
+#848 := (iff #224 #847)
+#845 := (iff #223 #844)
+#827 := (= #216 #826)
+#828 := [rewrite]: #827
+#846 := [monotonicity #828]: #845
+#781 := (iff #200 #780)
+#782 := [rewrite]: #781
+#849 := [monotonicity #782 #846]: #848
+#852 := [monotonicity #849]: #851
+#855 := [quant-intro #852]: #854
+#858 := [monotonicity #855]: #857
+#864 := [trans #858 #862]: #863
+#867 := [quant-intro #864]: #866
+#870 := [monotonicity #867]: #869
+#874 := [trans #870 #872]: #873
+#842 := (iff #219 #841)
+#839 := (iff #218 #836)
+#832 := (implies #821 #829)
 #837 := (iff #832 #836)
 #838 := [rewrite]: #837
-#833 := (iff #200 #832)
-#830 := (iff #199 #829)
-#827 := (iff #198 #824)
-#820 := (implies #748 #817)
-#825 := (iff #820 #824)
-#826 := [rewrite]: #825
-#821 := (iff #198 #820)
-#818 := (iff #197 #817)
-#815 := (iff #196 #812)
-#808 := (implies #774 #798)
-#813 := (iff #808 #812)
-#814 := [rewrite]: #813
-#809 := (iff #196 #808)
-#806 := (iff #195 #798)
-#801 := (and #798 true)
-#804 := (iff #801 #798)
-#805 := [rewrite]: #804
-#802 := (iff #195 #801)
-#799 := (iff #194 #798)
-#796 := (iff #193 #793)
-#789 := (implies #187 #786)
-#794 := (iff #789 #793)
-#795 := [rewrite]: #794
-#790 := (iff #193 #789)
-#787 := (iff #192 #786)
-#784 := (iff #191 #783)
-#781 := (iff #190 #780)
-#778 := (iff #189 #777)
-#760 := (= #182 #759)
-#761 := [rewrite]: #760
-#779 := [monotonicity #761]: #778
-#714 := (iff #166 #713)
-#715 := [rewrite]: #714
-#782 := [monotonicity #715 #779]: #781
-#785 := [monotonicity #782]: #784
-#788 := [quant-intro #785]: #787
-#791 := [monotonicity #788]: #790
-#797 := [trans #791 #795]: #796
-#800 := [quant-intro #797]: #799
-#803 := [monotonicity #800]: #802
-#807 := [trans #803 #805]: #806
-#775 := (iff #185 #774)
-#772 := (iff #184 #769)
-#765 := (implies #754 #762)
-#770 := (iff #765 #769)
-#771 := [rewrite]: #770
-#766 := (iff #184 #765)
-#763 := (iff #183 #762)
-#764 := [monotonicity #761]: #763
-#757 := (iff #181 #754)
-#751 := (and #713 #50)
-#755 := (iff #751 #754)
-#756 := [rewrite]: #755
-#752 := (iff #181 #751)
-#753 := [monotonicity #715]: #752
-#758 := [trans #753 #756]: #757
-#767 := [monotonicity #758 #764]: #766
-#773 := [trans #767 #771]: #772
-#776 := [quant-intro #773]: #775
-#810 := [monotonicity #776 #807]: #809
-#816 := [trans #810 #814]: #815
-#819 := [monotonicity #776 #816]: #818
-#749 := (iff #180 #748)
-#746 := (iff #179 #743)
-#739 := (implies #736 #178)
-#744 := (iff #739 #743)
-#745 := [rewrite]: #744
-#740 := (iff #179 #739)
-#737 := (iff #176 #736)
-#734 := (iff #175 #733)
-#735 := [rewrite]: #734
-#731 := (iff #173 #719)
-#732 := [monotonicity #715]: #731
-#738 := [monotonicity #732 #735]: #737
-#741 := [monotonicity #738]: #740
-#747 := [trans #741 #745]: #746
-#750 := [quant-intro #747]: #749
-#822 := [monotonicity #750 #819]: #821
-#828 := [trans #822 #826]: #827
-#831 := [monotonicity #750 #828]: #830
-#834 := [monotonicity #831]: #833
+#833 := (iff #218 #832)
+#830 := (iff #217 #829)
+#831 := [monotonicity #828]: #830
+#824 := (iff #215 #821)
+#818 := (and #780 #83)
+#822 := (iff #818 #821)
+#823 := [rewrite]: #822
+#819 := (iff #215 #818)
+#820 := [monotonicity #782]: #819
+#825 := [trans #820 #823]: #824
+#834 := [monotonicity #825 #831]: #833
 #840 := [trans #834 #838]: #839
-#843 := [monotonicity #840]: #842
-#729 := (iff #170 #728)
-#730 := [rewrite]: #729
-#846 := [monotonicity #730 #843]: #845
-#852 := [trans #846 #850]: #851
-#855 := [monotonicity #730 #852]: #854
-#726 := (iff #168 #725)
-#723 := (iff #167 #720)
-#716 := (implies #713 #699)
-#721 := (iff #716 #720)
-#722 := [rewrite]: #721
-#717 := (iff #167 #716)
-#700 := (iff #160 #699)
-#701 := [rewrite]: #700
-#718 := [monotonicity #715 #701]: #717
-#724 := [trans #718 #722]: #723
-#727 := [quant-intro #724]: #726
-#858 := [monotonicity #727 #855]: #857
-#864 := [trans #858 #862]: #863
-#867 := [monotonicity #727 #864]: #866
-#870 := [monotonicity #867]: #869
-#876 := [trans #870 #874]: #875
-#879 := [monotonicity #876]: #878
-#711 := (iff #162 #710)
-#708 := (iff #161 #705)
-#702 := (implies #159 #699)
-#706 := (iff #702 #705)
-#707 := [rewrite]: #706
-#703 := (iff #161 #702)
-#704 := [monotonicity #701]: #703
-#709 := [trans #704 #707]: #708
-#712 := [quant-intro #709]: #711
-#882 := [monotonicity #712 #879]: #881
-#888 := [trans #882 #886]: #887
-#697 := (iff #158 #696)
-#694 := (iff #157 #691)
-#688 := (implies #154 #685)
-#692 := (iff #688 #691)
-#693 := [rewrite]: #692
-#689 := (iff #157 #688)
-#686 := (iff #156 #685)
-#687 := [rewrite]: #686
-#690 := [monotonicity #687]: #689
-#695 := [trans #690 #693]: #694
-#698 := [quant-intro #695]: #697
-#891 := [monotonicity #698 #888]: #890
-#897 := [trans #891 #895]: #896
-#900 := [monotonicity #897]: #899
-#906 := [trans #900 #904]: #905
-#683 := (iff #145 #682)
-#680 := (iff #144 #677)
-#674 := (implies #450 #143)
-#678 := (iff #674 #677)
-#679 := [rewrite]: #678
-#675 := (iff #144 #674)
-#451 := (iff #74 #450)
-#448 := (iff #73 #447)
-#449 := [rewrite]: #448
-#452 := [monotonicity #449]: #451
-#676 := [monotonicity #452]: #675
-#681 := [trans #676 #679]: #680
-#684 := [quant-intro #681]: #683
-#909 := [monotonicity #684 #906]: #908
-#915 := [trans #909 #913]: #914
-#918 := [monotonicity #915]: #917
-#924 := [trans #918 #922]: #923
-#672 := (iff #140 #671)
-#669 := (iff #139 #668)
-#670 := [rewrite]: #669
-#673 := [monotonicity #670]: #672
-#927 := [monotonicity #673 #924]: #926
-#932 := [trans #927 #930]: #931
-#530 := (iff #97 #529)
-#527 := (iff #96 #524)
-#521 := (and #450 #87)
-#525 := (iff #521 #524)
-#526 := [rewrite]: #525
-#522 := (iff #96 #521)
-#523 := [monotonicity #452]: #522
-#528 := [trans #523 #526]: #527
-#531 := [quant-intro #528]: #530
-#935 := [monotonicity #531 #932]: #934
-#940 := [trans #935 #938]: #939
-#943 := [monotonicity #940]: #942
-#947 := [trans #943 #945]: #946
-#666 := (iff #136 #656)
-#661 := (implies true #656)
-#664 := (iff #661 #656)
-#665 := [rewrite]: #664
-#662 := (iff #136 #661)
-#659 := (iff #135 #656)
-#653 := (implies #532 #648)
-#657 := (iff #653 #656)
-#658 := [rewrite]: #657
-#654 := (iff #135 #653)
-#651 := (iff #134 #648)
-#644 := (implies #535 #639)
-#649 := (iff #644 #648)
-#650 := [rewrite]: #649
-#645 := (iff #134 #644)
-#642 := (iff #133 #639)
-#635 := (implies #103 #630)
-#640 := (iff #635 #639)
-#641 := [rewrite]: #640
-#636 := (iff #133 #635)
-#633 := (iff #132 #630)
-#626 := (implies #538 #621)
-#631 := (iff #626 #630)
-#632 := [rewrite]: #631
-#627 := (iff #132 #626)
-#624 := (iff #131 #621)
-#617 := (implies #108 #614)
-#622 := (iff #617 #621)
-#623 := [rewrite]: #622
-#618 := (iff #131 #617)
-#615 := (iff #130 #614)
-#612 := (iff #129 #609)
-#605 := (implies #562 #602)
-#610 := (iff #605 #609)
-#611 := [rewrite]: #610
-#606 := (iff #129 #605)
-#603 := (iff #128 #602)
-#600 := (iff #127 #597)
-#593 := (implies #580 #583)
-#598 := (iff #593 #597)
-#599 := [rewrite]: #598
-#594 := (iff #127 #593)
-#591 := (iff #126 #583)
-#586 := (and #583 true)
-#589 := (iff #586 #583)
-#590 := [rewrite]: #589
-#587 := (iff #126 #586)
-#584 := (iff #125 #583)
-#585 := [rewrite]: #584
-#588 := [monotonicity #585]: #587
-#592 := [trans #588 #590]: #591
-#581 := (iff #123 #580)
-#578 := (iff #122 #575)
-#571 := (implies #565 #568)
-#576 := (iff #571 #575)
-#577 := [rewrite]: #576
-#572 := (iff #122 #571)
-#569 := (iff #121 #568)
-#542 := (= #114 #541)
-#543 := [rewrite]: #542
-#570 := [monotonicity #543]: #569
-#566 := (iff #120 #565)
-#567 := [rewrite]: #566
-#573 := [monotonicity #567 #570]: #572
-#579 := [trans #573 #577]: #578
-#582 := [quant-intro #579]: #581
-#595 := [monotonicity #582 #592]: #594
-#601 := [trans #595 #599]: #600
-#604 := [monotonicity #582 #601]: #603
-#563 := (iff #119 #562)
-#560 := (iff #118 #557)
-#553 := (implies #111 #550)
-#558 := (iff #553 #557)
-#559 := [rewrite]: #558
-#554 := (iff #118 #553)
-#551 := (iff #117 #550)
-#548 := (iff #116 #547)
-#545 := (iff #115 #544)
-#546 := [monotonicity #543]: #545
-#549 := [monotonicity #546]: #548
-#552 := [quant-intro #549]: #551
-#555 := [monotonicity #552]: #554
-#561 := [trans #555 #559]: #560
-#564 := [quant-intro #561]: #563
-#607 := [monotonicity #564 #604]: #606
-#613 := [trans #607 #611]: #612
-#616 := [monotonicity #564 #613]: #615
-#619 := [monotonicity #616]: #618
-#625 := [trans #619 #623]: #624
-#539 := (iff #105 #538)
-#540 := [rewrite]: #539
-#628 := [monotonicity #540 #625]: #627
-#634 := [trans #628 #632]: #633
-#637 := [monotonicity #634]: #636
-#643 := [trans #637 #641]: #642
-#536 := (iff #100 #535)
-#537 := [rewrite]: #536
-#646 := [monotonicity #537 #643]: #645
-#652 := [trans #646 #650]: #651
-#533 := (iff #98 #532)
-#534 := [monotonicity #531]: #533
-#655 := [monotonicity #534 #652]: #654
-#660 := [trans #655 #658]: #659
-#663 := [monotonicity #660]: #662
-#667 := [trans #663 #665]: #666
-#950 := [monotonicity #667 #947]: #949
-#519 := (iff #95 #518)
-#516 := (iff #94 #513)
-#509 := (implies #88 #506)
-#514 := (iff #509 #513)
-#515 := [rewrite]: #514
-#510 := (iff #94 #509)
-#507 := (iff #93 #506)
-#504 := (iff #92 #503)
-#501 := (iff #91 #500)
-#498 := (iff #90 #497)
-#480 := (= #83 #479)
-#481 := [rewrite]: #480
-#499 := [monotonicity #481]: #498
-#502 := [monotonicity #449 #499]: #501
-#505 := [monotonicity #502]: #504
-#508 := [quant-intro #505]: #507
+#843 := [quant-intro #840]: #842
+#877 := [monotonicity #843 #874]: #876
+#883 := [trans #877 #881]: #882
+#886 := [monotonicity #843 #883]: #885
+#816 := (iff #214 #815)
+#813 := (iff #213 #810)
+#806 := (implies #803 #212)
+#811 := (iff #806 #810)
+#812 := [rewrite]: #811
+#807 := (iff #213 #806)
+#804 := (iff #210 #803)
+#801 := (iff #209 #800)
+#802 := [rewrite]: #801
+#798 := (iff #207 #786)
+#799 := [monotonicity #782]: #798
+#805 := [monotonicity #799 #802]: #804
+#808 := [monotonicity #805]: #807
+#814 := [trans #808 #812]: #813
+#817 := [quant-intro #814]: #816
+#889 := [monotonicity #817 #886]: #888
+#895 := [trans #889 #893]: #894
+#898 := [monotonicity #817 #895]: #897
+#901 := [monotonicity #898]: #900
+#907 := [trans #901 #905]: #906
+#910 := [monotonicity #907]: #909
+#796 := (iff #204 #795)
+#797 := [rewrite]: #796
+#913 := [monotonicity #797 #910]: #912
+#919 := [trans #913 #917]: #918
+#922 := [monotonicity #797 #919]: #921
+#793 := (iff #202 #792)
+#790 := (iff #201 #787)
+#783 := (implies #780 #766)
+#788 := (iff #783 #787)
+#789 := [rewrite]: #788
+#784 := (iff #201 #783)
+#767 := (iff #194 #766)
+#768 := [rewrite]: #767
+#785 := [monotonicity #782 #768]: #784
+#791 := [trans #785 #789]: #790
+#794 := [quant-intro #791]: #793
+#925 := [monotonicity #794 #922]: #924
+#931 := [trans #925 #929]: #930
+#934 := [monotonicity #794 #931]: #933
+#937 := [monotonicity #934]: #936
+#943 := [trans #937 #941]: #942
+#946 := [monotonicity #943]: #945
+#778 := (iff #196 #777)
+#775 := (iff #195 #772)
+#769 := (implies #193 #766)
+#773 := (iff #769 #772)
+#774 := [rewrite]: #773
+#770 := (iff #195 #769)
+#771 := [monotonicity #768]: #770
+#776 := [trans #771 #774]: #775
+#779 := [quant-intro #776]: #778
+#949 := [monotonicity #779 #946]: #948
+#955 := [trans #949 #953]: #954
+#764 := (iff #192 #763)
+#761 := (iff #191 #758)
+#755 := (implies #188 #752)
+#759 := (iff #755 #758)
+#760 := [rewrite]: #759
+#756 := (iff #191 #755)
+#753 := (iff #190 #752)
+#754 := [rewrite]: #753
+#757 := [monotonicity #754]: #756
+#762 := [trans #757 #760]: #761
+#765 := [quant-intro #762]: #764
+#958 := [monotonicity #765 #955]: #957
+#964 := [trans #958 #962]: #963
+#750 := (iff #182 #749)
+#747 := (= #181 #746)
+#744 := (= #180 f1)
+#745 := [rewrite]: #744
+#748 := [monotonicity #745]: #747
+#751 := [monotonicity #748]: #750
+#967 := [monotonicity #751 #964]: #966
+#973 := [trans #967 #971]: #972
+#742 := (iff #178 #741)
+#739 := (iff #177 #736)
+#733 := (implies #509 #176)
+#737 := (iff #733 #736)
+#738 := [rewrite]: #737
+#734 := (iff #177 #733)
+#510 := (iff #107 #509)
+#507 := (iff #106 #506)
+#508 := [rewrite]: #507
 #511 := [monotonicity #508]: #510
-#517 := [trans #511 #515]: #516
-#520 := [quant-intro #517]: #519
-#953 := [monotonicity #520 #950]: #952
-#959 := [trans #953 #957]: #958
-#495 := (iff #86 #494)
-#492 := (iff #85 #489)
-#485 := (implies #474 #482)
-#490 := (iff #485 #489)
-#491 := [rewrite]: #490
-#486 := (iff #85 #485)
-#483 := (iff #84 #482)
-#484 := [monotonicity #481]: #483
-#477 := (iff #82 #474)
-#471 := (and #447 #50)
-#475 := (iff #471 #474)
-#476 := [rewrite]: #475
-#472 := (iff #82 #471)
-#473 := [monotonicity #449]: #472
-#478 := [trans #473 #476]: #477
-#487 := [monotonicity #478 #484]: #486
-#493 := [trans #487 #491]: #492
-#496 := [quant-intro #493]: #495
-#962 := [monotonicity #496 #959]: #961
-#968 := [trans #962 #966]: #967
-#469 := (iff #81 #468)
-#466 := (iff #80 #463)
-#459 := (implies #456 #79)
-#464 := (iff #459 #463)
-#465 := [rewrite]: #464
-#460 := (iff #80 #459)
-#457 := (iff #77 #456)
-#454 := (iff #76 #453)
-#455 := [rewrite]: #454
-#458 := [monotonicity #452 #455]: #457
-#461 := [monotonicity #458]: #460
-#467 := [trans #461 #465]: #466
-#470 := [quant-intro #467]: #469
-#971 := [monotonicity #470 #968]: #970
-#977 := [trans #971 #975]: #976
-#980 := [monotonicity #977]: #979
-#986 := [trans #980 #984]: #985
-#445 := (iff #67 #444)
-#446 := [rewrite]: #445
-#989 := [monotonicity #446 #986]: #988
-#995 := [trans #989 #993]: #994
-#998 := [monotonicity #995]: #997
-#1002 := [trans #998 #1000]: #1001
-#442 := (iff #64 #441)
-#439 := (iff #63 #436)
-#432 := (implies #57 #429)
-#437 := (iff #432 #436)
-#438 := [rewrite]: #437
-#433 := (iff #63 #432)
-#430 := (iff #62 #429)
-#427 := (iff #61 #426)
-#424 := (iff #60 #421)
-#418 := (and #368 #59)
-#422 := (iff #418 #421)
-#423 := [rewrite]: #422
-#419 := (iff #60 #418)
-#369 := (iff #34 #368)
-#370 := [rewrite]: #369
-#420 := [monotonicity #370]: #419
-#425 := [trans #420 #423]: #424
-#428 := [monotonicity #425]: #427
-#431 := [quant-intro #428]: #430
-#434 := [monotonicity #431]: #433
-#440 := [trans #434 #438]: #439
-#443 := [quant-intro #440]: #442
-#1005 := [monotonicity #443 #1002]: #1004
-#1011 := [trans #1005 #1009]: #1010
-#1014 := [monotonicity #443 #1011]: #1013
-#416 := (iff #55 #415)
-#413 := (iff #54 #410)
-#406 := (implies #401 #53)
-#411 := (iff #406 #410)
-#412 := [rewrite]: #411
-#407 := (iff #54 #406)
-#404 := (iff #51 #401)
-#398 := (and #368 #50)
-#402 := (iff #398 #401)
-#403 := [rewrite]: #402
-#399 := (iff #51 #398)
-#400 := [monotonicity #370]: #399
-#405 := [trans #400 #403]: #404
-#408 := [monotonicity #405]: #407
-#414 := [trans #408 #412]: #413
-#417 := [quant-intro #414]: #416
-#1017 := [monotonicity #417 #1014]: #1016
-#1023 := [trans #1017 #1021]: #1022
-#1026 := [monotonicity #417 #1023]: #1025
-#396 := (iff #47 #395)
-#393 := (iff #46 #390)
-#386 := (implies #383 #45)
-#391 := (iff #386 #390)
-#392 := [rewrite]: #391
-#387 := (iff #46 #386)
-#384 := (iff #43 #383)
-#381 := (iff #42 #380)
-#382 := [rewrite]: #381
-#372 := (iff #35 #371)
-#373 := [monotonicity #370]: #372
-#385 := [monotonicity #373 #382]: #384
-#388 := [monotonicity #385]: #387
-#394 := [trans #388 #392]: #393
-#397 := [quant-intro #394]: #396
-#1029 := [monotonicity #397 #1026]: #1028
+#735 := [monotonicity #511]: #734
+#740 := [trans #735 #738]: #739
+#743 := [quant-intro #740]: #742
+#976 := [monotonicity #743 #973]: #975
+#982 := [trans #976 #980]: #981
+#985 := [monotonicity #982]: #984
+#991 := [trans #985 #989]: #990
+#731 := (iff #173 #730)
+#728 := (iff #172 #727)
+#729 := [rewrite]: #728
+#732 := [monotonicity #729]: #731
+#994 := [monotonicity #732 #991]: #993
+#999 := [trans #994 #997]: #998
+#589 := (iff #130 #588)
+#586 := (iff #129 #583)
+#580 := (and #509 #120)
+#584 := (iff #580 #583)
+#585 := [rewrite]: #584
+#581 := (iff #129 #580)
+#582 := [monotonicity #511]: #581
+#587 := [trans #582 #585]: #586
+#590 := [quant-intro #587]: #589
+#1002 := [monotonicity #590 #999]: #1001
+#1007 := [trans #1002 #1005]: #1006
+#1010 := [monotonicity #1007]: #1009
+#1014 := [trans #1010 #1012]: #1013
+#725 := (iff #169 #715)
+#720 := (implies true #715)
+#723 := (iff #720 #715)
+#724 := [rewrite]: #723
+#721 := (iff #169 #720)
+#718 := (iff #168 #715)
+#712 := (implies #591 #707)
+#716 := (iff #712 #715)
+#717 := [rewrite]: #716
+#713 := (iff #168 #712)
+#710 := (iff #167 #707)
+#703 := (implies #594 #698)
+#708 := (iff #703 #707)
+#709 := [rewrite]: #708
+#704 := (iff #167 #703)
+#701 := (iff #166 #698)
+#694 := (implies #136 #689)
+#699 := (iff #694 #698)
+#700 := [rewrite]: #699
+#695 := (iff #166 #694)
+#692 := (iff #165 #689)
+#685 := (implies #597 #680)
+#690 := (iff #685 #689)
+#691 := [rewrite]: #690
+#686 := (iff #165 #685)
+#683 := (iff #164 #680)
+#676 := (implies #141 #673)
+#681 := (iff #676 #680)
+#682 := [rewrite]: #681
+#677 := (iff #164 #676)
+#674 := (iff #163 #673)
+#671 := (iff #162 #668)
+#664 := (implies #621 #661)
+#669 := (iff #664 #668)
+#670 := [rewrite]: #669
+#665 := (iff #162 #664)
+#662 := (iff #161 #661)
+#659 := (iff #160 #656)
+#652 := (implies #639 #642)
+#657 := (iff #652 #656)
+#658 := [rewrite]: #657
+#653 := (iff #160 #652)
+#650 := (iff #159 #642)
+#645 := (and #642 true)
+#648 := (iff #645 #642)
+#649 := [rewrite]: #648
+#646 := (iff #159 #645)
+#643 := (iff #158 #642)
+#644 := [rewrite]: #643
+#647 := [monotonicity #644]: #646
+#651 := [trans #647 #649]: #650
+#640 := (iff #156 #639)
+#637 := (iff #155 #634)
+#630 := (implies #624 #627)
+#635 := (iff #630 #634)
+#636 := [rewrite]: #635
+#631 := (iff #155 #630)
+#628 := (iff #154 #627)
+#601 := (= #147 #600)
+#602 := [rewrite]: #601
+#629 := [monotonicity #602]: #628
+#625 := (iff #153 #624)
+#626 := [rewrite]: #625
+#632 := [monotonicity #626 #629]: #631
+#638 := [trans #632 #636]: #637
+#641 := [quant-intro #638]: #640
+#654 := [monotonicity #641 #651]: #653
+#660 := [trans #654 #658]: #659
+#663 := [monotonicity #641 #660]: #662
+#622 := (iff #152 #621)
+#619 := (iff #151 #616)
+#612 := (implies #144 #609)
+#617 := (iff #612 #616)
+#618 := [rewrite]: #617
+#613 := (iff #151 #612)
+#610 := (iff #150 #609)
+#607 := (iff #149 #606)
+#604 := (iff #148 #603)
+#605 := [monotonicity #602]: #604
+#608 := [monotonicity #605]: #607
+#611 := [quant-intro #608]: #610
+#614 := [monotonicity #611]: #613
+#620 := [trans #614 #618]: #619
+#623 := [quant-intro #620]: #622
+#666 := [monotonicity #623 #663]: #665
+#672 := [trans #666 #670]: #671
+#675 := [monotonicity #623 #672]: #674
+#678 := [monotonicity #675]: #677
+#684 := [trans #678 #682]: #683
+#598 := (iff #138 #597)
+#599 := [rewrite]: #598
+#687 := [monotonicity #599 #684]: #686
+#693 := [trans #687 #691]: #692
+#696 := [monotonicity #693]: #695
+#702 := [trans #696 #700]: #701
+#595 := (iff #133 #594)
+#596 := [rewrite]: #595
+#705 := [monotonicity #596 #702]: #704
+#711 := [trans #705 #709]: #710
+#592 := (iff #131 #591)
+#593 := [monotonicity #590]: #592
+#714 := [monotonicity #593 #711]: #713
+#719 := [trans #714 #717]: #718
+#722 := [monotonicity #719]: #721
+#726 := [trans #722 #724]: #725
+#1017 := [monotonicity #726 #1014]: #1016
+#578 := (iff #128 #577)
+#575 := (iff #127 #572)
+#568 := (implies #121 #565)
+#573 := (iff #568 #572)
+#574 := [rewrite]: #573
+#569 := (iff #127 #568)
+#566 := (iff #126 #565)
+#563 := (iff #125 #562)
+#560 := (iff #124 #559)
+#557 := (iff #123 #556)
+#539 := (= #116 #538)
+#540 := [rewrite]: #539
+#558 := [monotonicity #540]: #557
+#561 := [monotonicity #508 #558]: #560
+#564 := [monotonicity #561]: #563
+#567 := [quant-intro #564]: #566
+#570 := [monotonicity #567]: #569
+#576 := [trans #570 #574]: #575
+#579 := [quant-intro #576]: #578
+#1020 := [monotonicity #579 #1017]: #1019
+#1026 := [trans #1020 #1024]: #1025
+#554 := (iff #119 #553)
+#551 := (iff #118 #548)
+#544 := (implies #533 #541)
+#549 := (iff #544 #548)
+#550 := [rewrite]: #549
+#545 := (iff #118 #544)
+#542 := (iff #117 #541)
+#543 := [monotonicity #540]: #542
+#536 := (iff #115 #533)
+#530 := (and #506 #83)
+#534 := (iff #530 #533)
+#535 := [rewrite]: #534
+#531 := (iff #115 #530)
+#532 := [monotonicity #508]: #531
+#537 := [trans #532 #535]: #536
+#546 := [monotonicity #537 #543]: #545
+#552 := [trans #546 #550]: #551
+#555 := [quant-intro #552]: #554
+#1029 := [monotonicity #555 #1026]: #1028
 #1035 := [trans #1029 #1033]: #1034
-#1038 := [monotonicity #397 #1035]: #1037
-#1041 := [monotonicity #1038]: #1040
-#1047 := [trans #1041 #1045]: #1046
-#1050 := [monotonicity #1047]: #1049
-#378 := (iff #38 #377)
-#379 := [rewrite]: #378
-#1053 := [monotonicity #379 #1050]: #1052
-#1059 := [trans #1053 #1057]: #1058
-#1062 := [monotonicity #379 #1059]: #1061
-#375 := (iff #36 #374)
-#376 := [quant-intro #373]: #375
-#1065 := [monotonicity #376 #1062]: #1064
-#1071 := [trans #1065 #1069]: #1070
-#366 := (iff #32 #365)
-#363 := (iff #31 #360)
-#357 := (implies #29 #354)
-#361 := (iff #357 #360)
-#362 := [rewrite]: #361
-#358 := (iff #31 #357)
-#355 := (iff #30 #354)
-#356 := [rewrite]: #355
-#359 := [monotonicity #356]: #358
-#364 := [trans #359 #362]: #363
-#367 := [quant-intro #364]: #366
-#1074 := [monotonicity #367 #1071]: #1073
-#1080 := [trans #1074 #1078]: #1079
-#352 := (iff #28 #351)
-#349 := (iff #27 #346)
-#343 := (implies #24 #340)
-#347 := (iff #343 #346)
-#348 := [rewrite]: #347
-#344 := (iff #27 #343)
-#341 := (iff #26 #340)
-#342 := [rewrite]: #341
-#345 := [monotonicity #342]: #344
-#350 := [trans #345 #348]: #349
-#353 := [quant-intro #350]: #352
-#1083 := [monotonicity #353 #1080]: #1082
-#1089 := [trans #1083 #1087]: #1088
-#1092 := [monotonicity #1089]: #1091
-#1096 := [trans #1092 #1094]: #1095
-#1099 := [monotonicity #1096]: #1098
-#1738 := [trans #1099 #1736]: #1737
-#339 := [asserted]: #237
-#1739 := [mp #339 #1738]: #1734
-#1744 := [not-or-elim #1739]: #1714
-#2002 := [mp~ #1744 #2168]: #1714
-#4540 := [mp #2002 #4539]: #4535
-#4634 := [hypothesis]: #1102
-#4588 := (not #4535)
-#4586 := (or #4588 #38)
-#3871 := (= f6 f6)
-#3836 := (not #3871)
-#3837 := (or #3836 #38)
-#4589 := (or #4588 #3837)
-#4591 := (iff #4589 #4586)
-#4630 := (iff #4586 #4586)
-#4631 := [rewrite]: #4630
-#4587 := (iff #3837 #38)
-#3800 := (or false #38)
-#4577 := (iff #3800 #38)
-#4585 := [rewrite]: #4577
-#3801 := (iff #3837 #3800)
-#3796 := (iff #3836 false)
-#9474 := (not true)
-#9477 := (iff #9474 false)
-#9478 := [rewrite]: #9477
-#3795 := (iff #3836 #9474)
-#3840 := (iff #3871 true)
-#3821 := [rewrite]: #3840
-#3835 := [monotonicity #3821]: #3795
-#3787 := [trans #3835 #9478]: #3796
-#3793 := [monotonicity #3787]: #3801
-#4578 := [trans #3793 #4585]: #4587
-#3911 := [monotonicity #4578]: #4591
-#4632 := [trans #3911 #4631]: #4591
-#4590 := [quant-inst]: #4589
-#4633 := [mp #4590 #4632]: #4586
-#4635 := [unit-resolution #4633 #4634 #4540]: false
-#4636 := [lemma #4635]: #38
-#4531 := (or #1102 #4528)
-#3492 := (forall (vars (?v1 S2)) #3481)
-#3499 := (not #3492)
-#3477 := (forall (vars (?v0 S2) (?v1 S2)) #3472)
-#3498 := (not #3477)
-#3500 := (or #2308 #2875 #3498 #3499)
-#3501 := (not #3500)
-#3506 := (or #3455 #3501)
-#3513 := (not #3506)
-#3432 := (forall (vars (?v0 S2) (?v1 S2)) #3427)
-#3512 := (not #3432)
-#3514 := (or #3512 #3513)
-#3515 := (not #3514)
-#3520 := (or #3409 #3515)
-#3526 := (not #3520)
-#3527 := (or #1405 #3526)
-#3528 := (not #3527)
-#3533 := (or #2225 #3528)
-#3539 := (not #3533)
-#3540 := (or #1396 #3539)
-#3541 := (not #3540)
-#3546 := (or #1396 #3541)
-#3552 := (not #3546)
-#3553 := (or #859 #3552)
-#3554 := (not #3553)
-#3559 := (or #2818 #3554)
-#3565 := (not #3559)
-#3566 := (or #1391 #3565)
-#3567 := (not #3566)
-#3572 := (or #2804 #3567)
-#3580 := (not #3572)
-#3386 := (forall (vars (?v0 S2)) #3381)
-#3579 := (not #3386)
-#3368 := (forall (vars (?v0 S2)) #3365)
-#3578 := (not #3368)
-#3581 := (or #901 #668 #1556 #1560 #2159 #2162 #3578 #3579 #3580)
-#3582 := (not #3581)
-#3298 := (forall (vars (?v0 S2) (?v1 S2)) #3293)
-#3304 := (not #3298)
-#3305 := (or #125 #3304)
-#3306 := (not #3305)
-#3333 := (or #3306 #3330)
-#3340 := (not #3333)
-#3276 := (forall (vars (?v0 S2)) #3271)
-#3339 := (not #3276)
-#3341 := (or #3339 #3340)
-#3342 := (not #3341)
-#3239 := (forall (vars (?v1 S2)) #3228)
-#3245 := (not #3239)
-#3246 := (or #2038 #2653 #3245)
-#3247 := (not #3246)
-#3347 := (or #3247 #3342)
-#3354 := (not #3347)
-#3224 := (forall (vars (?v0 S2)) #3213)
-#3353 := (not #3224)
-#3355 := (or #638 #620 #647 #629 #3353 #3354)
-#3356 := (not #3355)
-#3587 := (or #3356 #3582)
-#3597 := (not #3587)
-#3210 := (forall (vars (?v0 S2)) #3205)
-#3596 := (not #3210)
-#3182 := (forall (vars (?v0 S2)) #3177)
-#3595 := (not #3182)
-#3154 := (forall (vars (?v0 S2) (?v1 S2)) #3149)
-#3594 := (not #3154)
-#3131 := (forall (vars (?v0 S2) (?v1 S2)) #3126)
-#3593 := (not #3131)
-#3598 := (or #1653 #1648 #3593 #3594 #3595 #3596 #3597)
-#3599 := (not #3598)
-#3099 := (forall (vars (?v1 S2)) #3088)
-#3105 := (not #3099)
-#3106 := (or #1930 #2515 #3105)
-#3107 := (not #3106)
-#3604 := (or #3107 #3599)
-#3611 := (not #3604)
-#3084 := (forall (vars (?v0 S2) (?v1 S2)) #3079)
-#3610 := (not #3084)
-#3612 := (or #3610 #3611)
-#3613 := (not #3612)
-#3618 := (or #3062 #3613)
-#3625 := (not #3618)
-#3039 := (forall (vars (?v0 S2) (?v1 S2)) #3034)
-#3624 := (not #3039)
-#3626 := (or #3624 #3625)
-#3627 := (not #3626)
-#3632 := (or #3016 #3627)
-#3638 := (not #3632)
-#3639 := (or #1111 #3638)
-#3640 := (not #3639)
-#3645 := (or #1846 #3640)
-#3651 := (not #3645)
-#3652 := (or #1102 #3651)
-#3653 := (not #3652)
-#3658 := (or #1102 #3653)
-#4532 := (iff #3658 #4531)
-#4529 := (iff #3653 #4528)
-#4526 := (iff #3652 #4525)
-#4523 := (iff #3651 #4522)
-#4520 := (iff #3645 #4519)
-#4517 := (iff #3640 #4516)
-#4514 := (iff #3639 #4513)
-#4511 := (iff #3638 #4510)
-#4508 := (iff #3632 #4507)
-#4505 := (iff #3627 #4504)
-#4502 := (iff #3626 #4501)
-#4499 := (iff #3625 #4498)
-#4496 := (iff #3618 #4495)
-#4493 := (iff #3613 #4492)
-#4490 := (iff #3612 #4489)
-#4487 := (iff #3611 #4486)
-#4484 := (iff #3604 #4483)
-#4481 := (iff #3599 #4480)
-#4478 := (iff #3598 #4477)
-#4475 := (iff #3597 #4474)
-#4472 := (iff #3587 #4471)
-#4469 := (iff #3582 #4468)
-#4466 := (iff #3581 #4465)
-#4463 := (iff #3580 #4462)
-#4460 := (iff #3572 #4459)
-#4457 := (iff #3567 #4456)
-#4454 := (iff #3566 #4453)
-#4451 := (iff #3565 #4450)
-#4448 := (iff #3559 #4447)
-#4445 := (iff #3554 #4444)
-#4442 := (iff #3553 #4441)
-#4439 := (iff #3552 #4438)
-#4436 := (iff #3546 #4435)
-#4433 := (iff #3541 #4432)
-#4430 := (iff #3540 #4429)
-#4427 := (iff #3539 #4426)
-#4424 := (iff #3533 #4423)
-#4421 := (iff #3528 #4420)
-#4418 := (iff #3527 #4417)
-#4415 := (iff #3526 #4414)
-#4412 := (iff #3520 #4411)
-#4409 := (iff #3515 #4408)
-#4406 := (iff #3514 #4405)
-#4403 := (iff #3513 #4402)
-#4400 := (iff #3506 #4399)
-#4397 := (iff #3501 #4396)
-#4394 := (iff #3500 #4393)
-#4391 := (iff #3499 #4390)
-#4388 := (iff #3492 #4385)
-#4386 := (iff #3481 #3481)
+#528 := (iff #114 #527)
+#525 := (iff #113 #522)
+#518 := (implies #515 #112)
+#523 := (iff #518 #522)
+#524 := [rewrite]: #523
+#519 := (iff #113 #518)
+#516 := (iff #110 #515)
+#513 := (iff #109 #512)
+#514 := [rewrite]: #513
+#517 := [monotonicity #511 #514]: #516
+#520 := [monotonicity #517]: #519
+#526 := [trans #520 #524]: #525
+#529 := [quant-intro #526]: #528
+#1038 := [monotonicity #529 #1035]: #1037
+#1044 := [trans #1038 #1042]: #1043
+#1047 := [monotonicity #1044]: #1046
+#1053 := [trans #1047 #1051]: #1052
+#504 := (iff #100 #503)
+#505 := [rewrite]: #504
+#1056 := [monotonicity #505 #1053]: #1055
+#1062 := [trans #1056 #1060]: #1061
+#1065 := [monotonicity #1062]: #1064
+#1069 := [trans #1065 #1067]: #1068
+#501 := (iff #97 #500)
+#498 := (iff #96 #495)
+#491 := (implies #90 #488)
+#496 := (iff #491 #495)
+#497 := [rewrite]: #496
+#492 := (iff #96 #491)
+#489 := (iff #95 #488)
+#486 := (iff #94 #485)
+#483 := (iff #93 #480)
+#477 := (and #427 #92)
+#481 := (iff #477 #480)
+#482 := [rewrite]: #481
+#478 := (iff #93 #477)
+#428 := (iff #67 #427)
+#429 := [rewrite]: #428
+#479 := [monotonicity #429]: #478
+#484 := [trans #479 #482]: #483
+#487 := [monotonicity #484]: #486
+#490 := [quant-intro #487]: #489
+#493 := [monotonicity #490]: #492
+#499 := [trans #493 #497]: #498
+#502 := [quant-intro #499]: #501
+#1072 := [monotonicity #502 #1069]: #1071
+#1078 := [trans #1072 #1076]: #1077
+#1081 := [monotonicity #502 #1078]: #1080
+#475 := (iff #88 #474)
+#472 := (iff #87 #469)
+#465 := (implies #460 #86)
+#470 := (iff #465 #469)
+#471 := [rewrite]: #470
+#466 := (iff #87 #465)
+#463 := (iff #84 #460)
+#457 := (and #427 #83)
+#461 := (iff #457 #460)
+#462 := [rewrite]: #461
+#458 := (iff #84 #457)
+#459 := [monotonicity #429]: #458
+#464 := [trans #459 #462]: #463
+#467 := [monotonicity #464]: #466
+#473 := [trans #467 #471]: #472
+#476 := [quant-intro #473]: #475
+#1084 := [monotonicity #476 #1081]: #1083
+#1090 := [trans #1084 #1088]: #1089
+#1093 := [monotonicity #476 #1090]: #1092
+#455 := (iff #80 #454)
+#452 := (iff #79 #449)
+#445 := (implies #442 #78)
+#450 := (iff #445 #449)
+#451 := [rewrite]: #450
+#446 := (iff #79 #445)
+#443 := (iff #76 #442)
+#440 := (iff #75 #439)
+#441 := [rewrite]: #440
+#431 := (iff #68 #430)
+#432 := [monotonicity #429]: #431
+#444 := [monotonicity #432 #441]: #443
+#447 := [monotonicity #444]: #446
+#453 := [trans #447 #451]: #452
+#456 := [quant-intro #453]: #455
+#1096 := [monotonicity #456 #1093]: #1095
+#1102 := [trans #1096 #1100]: #1101
+#1105 := [monotonicity #456 #1102]: #1104
+#1108 := [monotonicity #1105]: #1107
+#1114 := [trans #1108 #1112]: #1113
+#1117 := [monotonicity #1114]: #1116
+#437 := (iff #71 #436)
+#438 := [rewrite]: #437
+#1120 := [monotonicity #438 #1117]: #1119
+#1126 := [trans #1120 #1124]: #1125
+#1129 := [monotonicity #438 #1126]: #1128
+#434 := (iff #69 #433)
+#435 := [quant-intro #432]: #434
+#1132 := [monotonicity #435 #1129]: #1131
+#1138 := [trans #1132 #1136]: #1137
+#425 := (iff #65 #424)
+#422 := (iff #64 #419)
+#416 := (implies #62 #413)
+#420 := (iff #416 #419)
+#421 := [rewrite]: #420
+#417 := (iff #64 #416)
+#414 := (iff #63 #413)
+#415 := [rewrite]: #414
+#418 := [monotonicity #415]: #417
+#423 := [trans #418 #421]: #422
+#426 := [quant-intro #423]: #425
+#1141 := [monotonicity #426 #1138]: #1140
+#1147 := [trans #1141 #1145]: #1146
+#411 := (iff #61 #410)
+#408 := (iff #60 #405)
+#402 := (implies #57 #399)
+#406 := (iff #402 #405)
+#407 := [rewrite]: #406
+#403 := (iff #60 #402)
+#400 := (iff #59 #399)
+#401 := [rewrite]: #400
+#404 := [monotonicity #401]: #403
+#409 := [trans #404 #407]: #408
+#412 := [quant-intro #409]: #411
+#1150 := [monotonicity #412 #1147]: #1149
+#1156 := [trans #1150 #1154]: #1155
+#1159 := [monotonicity #1156]: #1158
+#1163 := [trans #1159 #1161]: #1162
+#1166 := [monotonicity #1163]: #1165
+#1805 := [trans #1166 #1803]: #1804
+#398 := [asserted]: #271
+#1806 := [mp #398 #1805]: #1801
+#1811 := [not-or-elim #1806]: #1781
+#2101 := [mp~ #1811 #1901]: #1781
+#4583 := [mp #2101 #4582]: #4578
+#4618 := (not #4578)
+#4619 := (or #4618 #4613 #4610)
+#3857 := (= ?v0!0 f10)
+#4611 := (not #3857)
+#4612 := (or #4611 #4610)
+#4644 := (or #4618 #4612)
+#4650 := (iff #4644 #4619)
+#4615 := (or #4613 #4610)
+#4646 := (or #4618 #4615)
+#4643 := (iff #4646 #4619)
+#4649 := [rewrite]: #4643
+#4647 := (iff #4644 #4646)
+#4616 := (iff #4612 #4615)
+#4614 := (iff #4611 #4613)
+#3839 := (iff #3857 #3824)
+#3833 := [rewrite]: #3839
+#4609 := [monotonicity #3833]: #4614
+#4617 := [monotonicity #4609]: #4616
+#4648 := [monotonicity #4617]: #4647
+#4651 := [trans #4648 #4649]: #4650
+#4645 := [quant-inst]: #4644
+#4652 := [mp #4645 #4651]: #4619
+#4710 := [unit-resolution #4652 #4583 #4709]: #4613
+#3834 := (or #3824 #3831)
+#4192 := (forall (vars (?v0 S3)) (:pat #4191) #419)
+#4195 := (iff #424 #4192)
+#4193 := (iff #419 #419)
+#4194 := [refl]: #4193
+#4196 := [quant-intro #4194]: #4195
+#1829 := (~ #424 #424)
+#1858 := (~ #419 #419)
+#1859 := [refl]: #1858
+#1830 := [nnf-pos #1859]: #1829
+#1807 := [not-or-elim #1806]: #424
+#1860 := [mp~ #1807 #1830]: #424
+#4197 := [mp #1860 #4196]: #4192
+#3753 := (not #4192)
+#3749 := (or #3753 #3824 #3831)
+#3832 := (or #3857 #3831)
+#3754 := (or #3753 #3832)
+#4621 := (iff #3754 #3749)
+#3747 := (or #3753 #3834)
+#3737 := (iff #3747 #3749)
+#4620 := [rewrite]: #3737
+#3756 := (iff #3754 #3747)
+#3745 := (iff #3832 #3834)
+#3750 := [monotonicity #3833]: #3745
+#3740 := [monotonicity #3750]: #3756
+#4622 := [trans #3740 #4620]: #4621
+#3755 := [quant-inst]: #3754
+#4623 := [mp #3755 #4622]: #3749
+#4711 := [unit-resolution #4623 #4197]: #3834
+#4712 := [unit-resolution #4711 #4710]: #3831
+#4713 := (not #3831)
+#4693 := (or #4713 #4626)
+#4694 := [th-lemma]: #4693
+#4695 := [unit-resolution #4694 #4712]: #4626
+#4653 := (<= #1868 0::int)
+#4696 := (or #4653 #1869)
+#4697 := [th-lemma]: #4696
+#4692 := [unit-resolution #4697 #4705]: #4653
+#349 := (<= f8 0::int)
+#350 := (not #349)
+#46 := (< 0::int f8)
+#351 := (iff #46 #350)
+#352 := [rewrite]: #351
+#345 := [asserted]: #46
+#353 := [mp #345 #352]: #350
+#4698 := [th-lemma #353 #4692 #4695]: false
+#4699 := [lemma #4698]: #1869
+#4562 := (or #1870 #4559)
+#4565 := (not #4562)
+#4568 := (or #1169 #4565)
+#4571 := (not #4568)
+#4779 := [hypothesis]: #1169
+#4754 := (or #4618 #71)
+#3830 := (= f10 f10)
+#4627 := (not #3830)
+#4700 := (or #4627 #71)
+#4749 := (or #4618 #4700)
+#4756 := (iff #4749 #4754)
+#4758 := (iff #4754 #4754)
+#4759 := [rewrite]: #4758
+#4752 := (iff #4700 #71)
+#4765 := (or false #71)
+#4750 := (iff #4765 #71)
+#4751 := [rewrite]: #4750
+#4766 := (iff #4700 #4765)
+#4763 := (iff #4627 false)
+#4717 := (not true)
+#4761 := (iff #4717 false)
+#4762 := [rewrite]: #4761
+#4718 := (iff #4627 #4717)
+#4701 := (iff #3830 true)
+#4702 := [rewrite]: #4701
+#4760 := [monotonicity #4702]: #4718
+#4764 := [trans #4760 #4762]: #4763
+#4767 := [monotonicity #4764]: #4766
+#4753 := [trans #4767 #4751]: #4752
+#4757 := [monotonicity #4753]: #4756
+#4777 := [trans #4757 #4759]: #4756
+#4755 := [quant-inst]: #4749
+#4778 := [mp #4755 #4777]: #4754
+#4780 := [unit-resolution #4778 #4779 #4583]: false
+#4781 := [lemma #4780]: #71
+#4574 := (or #1169 #4571)
+#3501 := (forall (vars (?v1 S3)) #3490)
+#3508 := (not #3501)
+#3486 := (forall (vars (?v0 S3) (?v1 S3)) #3481)
+#3507 := (not #3486)
+#3509 := (or #2332 #2899 #3507 #3508)
+#3510 := (not #3509)
+#3515 := (or #3464 #3510)
+#3522 := (not #3515)
+#3441 := (forall (vars (?v0 S3) (?v1 S3)) #3436)
+#3521 := (not #3441)
+#3523 := (or #3521 #3522)
+#3524 := (not #3523)
+#3529 := (or #3418 #3524)
+#3535 := (not #3529)
+#3536 := (or #1472 #3535)
+#3537 := (not #3536)
+#3542 := (or #2249 #3537)
+#3548 := (not #3542)
+#3549 := (or #1463 #3548)
+#3550 := (not #3549)
+#3555 := (or #1463 #3550)
+#3561 := (not #3555)
+#3562 := (or #926 #3561)
+#3563 := (not #3562)
+#3568 := (or #2842 #3563)
+#3574 := (not #3568)
+#3575 := (or #1458 #3574)
+#3576 := (not #3575)
+#3581 := (or #2828 #3576)
+#3589 := (not #3581)
+#3395 := (forall (vars (?v0 S3)) #3390)
+#3588 := (not #3395)
+#3377 := (forall (vars (?v0 S3)) #3374)
+#3587 := (not #3377)
+#3590 := (or #727 #968 #1623 #1627 #2183 #2186 #3587 #3588 #3589)
+#3591 := (not #3590)
+#3307 := (forall (vars (?v0 S3) (?v1 S3)) #3302)
+#3313 := (not #3307)
+#3314 := (or #158 #3313)
+#3315 := (not #3314)
+#3342 := (or #3315 #3339)
+#3349 := (not #3342)
+#3285 := (forall (vars (?v0 S3)) #3280)
+#3348 := (not #3285)
+#3350 := (or #3348 #3349)
+#3351 := (not #3350)
+#3248 := (forall (vars (?v1 S3)) #3237)
+#3254 := (not #3248)
+#3255 := (or #2062 #2677 #3254)
+#3256 := (not #3255)
+#3356 := (or #3256 #3351)
+#3363 := (not #3356)
+#3233 := (forall (vars (?v0 S3)) #3222)
+#3362 := (not #3233)
+#3364 := (or #697 #679 #706 #688 #3362 #3363)
+#3365 := (not #3364)
+#3596 := (or #3365 #3591)
+#3606 := (not #3596)
+#3219 := (forall (vars (?v0 S3)) #3214)
+#3605 := (not #3219)
+#3191 := (forall (vars (?v0 S3)) #3186)
+#3604 := (not #3191)
+#3163 := (forall (vars (?v0 S3) (?v1 S3)) #3158)
+#3603 := (not #3163)
+#3140 := (forall (vars (?v0 S3) (?v1 S3)) #3135)
+#3602 := (not #3140)
+#3607 := (or #1720 #1715 #3602 #3603 #3604 #3605 #3606)
+#3608 := (not #3607)
+#3108 := (forall (vars (?v1 S3)) #3097)
+#3114 := (not #3108)
+#3115 := (or #1954 #2539 #3114)
+#3116 := (not #3115)
+#3613 := (or #3116 #3608)
+#3620 := (not #3613)
+#3093 := (forall (vars (?v0 S3) (?v1 S3)) #3088)
+#3619 := (not #3093)
+#3621 := (or #3619 #3620)
+#3622 := (not #3621)
+#3627 := (or #3071 #3622)
+#3634 := (not #3627)
+#3048 := (forall (vars (?v0 S3) (?v1 S3)) #3043)
+#3633 := (not #3048)
+#3635 := (or #3633 #3634)
+#3636 := (not #3635)
+#3641 := (or #1874 #3636)
+#3647 := (not #3641)
+#3648 := (or #1178 #3647)
+#3649 := (not #3648)
+#3654 := (or #1870 #3649)
+#3660 := (not #3654)
+#3661 := (or #1169 #3660)
+#3662 := (not #3661)
+#3667 := (or #1169 #3662)
+#4575 := (iff #3667 #4574)
+#4572 := (iff #3662 #4571)
+#4569 := (iff #3661 #4568)
+#4566 := (iff #3660 #4565)
+#4563 := (iff #3654 #4562)
+#4560 := (iff #3649 #4559)
+#4557 := (iff #3648 #4556)
+#4554 := (iff #3647 #4553)
+#4551 := (iff #3641 #4550)
+#4548 := (iff #3636 #4547)
+#4545 := (iff #3635 #4544)
+#4542 := (iff #3634 #4541)
+#4539 := (iff #3627 #4538)
+#4536 := (iff #3622 #4535)
+#4533 := (iff #3621 #4532)
+#4530 := (iff #3620 #4529)
+#4527 := (iff #3613 #4526)
+#4524 := (iff #3608 #4523)
+#4521 := (iff #3607 #4520)
+#4518 := (iff #3606 #4517)
+#4515 := (iff #3596 #4514)
+#4512 := (iff #3591 #4511)
+#4509 := (iff #3590 #4508)
+#4506 := (iff #3589 #4505)
+#4503 := (iff #3581 #4502)
+#4500 := (iff #3576 #4499)
+#4497 := (iff #3575 #4496)
+#4494 := (iff #3574 #4493)
+#4491 := (iff #3568 #4490)
+#4488 := (iff #3563 #4487)
+#4485 := (iff #3562 #4484)
+#4482 := (iff #3561 #4481)
+#4479 := (iff #3555 #4478)
+#4476 := (iff #3550 #4475)
+#4473 := (iff #3549 #4472)
+#4470 := (iff #3548 #4469)
+#4467 := (iff #3542 #4466)
+#4464 := (iff #3537 #4463)
+#4461 := (iff #3536 #4460)
+#4458 := (iff #3535 #4457)
+#4455 := (iff #3529 #4454)
+#4452 := (iff #3524 #4451)
+#4449 := (iff #3523 #4448)
+#4446 := (iff #3522 #4445)
+#4443 := (iff #3515 #4442)
+#4440 := (iff #3510 #4439)
+#4437 := (iff #3509 #4436)
+#4434 := (iff #3508 #4433)
+#4431 := (iff #3501 #4428)
+#4429 := (iff #3490 #3490)
+#4430 := [refl]: #4429
+#4432 := [quant-intro #4430]: #4431
+#4435 := [monotonicity #4432]: #4434
+#4425 := (iff #3507 #4424)
+#4422 := (iff #3486 #4419)
+#4420 := (iff #3481 #3481)
+#4421 := [refl]: #4420
+#4423 := [quant-intro #4421]: #4422
+#4426 := [monotonicity #4423]: #4425
+#4438 := [monotonicity #4426 #4435]: #4437
+#4441 := [monotonicity #4438]: #4440
+#4444 := [monotonicity #4441]: #4443
+#4447 := [monotonicity #4444]: #4446
+#4417 := (iff #3521 #4416)
+#4414 := (iff #3441 #4411)
+#4412 := (iff #3436 #3436)
+#4413 := [refl]: #4412
+#4415 := [quant-intro #4413]: #4414
+#4418 := [monotonicity #4415]: #4417
+#4450 := [monotonicity #4418 #4447]: #4449
+#4453 := [monotonicity #4450]: #4452
+#4456 := [monotonicity #4453]: #4455
+#4459 := [monotonicity #4456]: #4458
+#4408 := (iff #1472 #4407)
+#4405 := (iff #1469 #4402)
+#4403 := (iff #1466 #1466)
+#4404 := [refl]: #4403
+#4406 := [quant-intro #4404]: #4405
+#4409 := [monotonicity #4406]: #4408
+#4462 := [monotonicity #4409 #4459]: #4461
+#4465 := [monotonicity #4462]: #4464
+#4468 := [monotonicity #4465]: #4467
+#4471 := [monotonicity #4468]: #4470
+#4474 := [monotonicity #4471]: #4473
+#4477 := [monotonicity #4474]: #4476
+#4480 := [monotonicity #4477]: #4479
+#4483 := [monotonicity #4480]: #4482
+#4400 := (iff #926 #4399)
+#4397 := (iff #792 #4394)
+#4395 := (iff #787 #787)
+#4396 := [refl]: #4395
+#4398 := [quant-intro #4396]: #4397
+#4401 := [monotonicity #4398]: #4400
+#4486 := [monotonicity #4401 #4483]: #4485
+#4489 := [monotonicity #4486]: #4488
+#4492 := [monotonicity #4489]: #4491
+#4495 := [monotonicity #4492]: #4494
+#4391 := (iff #1458 #4390)
+#4388 := (iff #1455 #4385)
+#4386 := (iff #1450 #1450)
 #4387 := [refl]: #4386
 #4389 := [quant-intro #4387]: #4388
 #4392 := [monotonicity #4389]: #4391
-#4382 := (iff #3498 #4381)
-#4379 := (iff #3477 #4376)
-#4377 := (iff #3472 #3472)
-#4378 := [refl]: #4377
-#4380 := [quant-intro #4378]: #4379
-#4383 := [monotonicity #4380]: #4382
-#4395 := [monotonicity #4383 #4392]: #4394
-#4398 := [monotonicity #4395]: #4397
-#4401 := [monotonicity #4398]: #4400
-#4404 := [monotonicity #4401]: #4403
-#4374 := (iff #3512 #4373)
-#4371 := (iff #3432 #4368)
-#4369 := (iff #3427 #3427)
-#4370 := [refl]: #4369
-#4372 := [quant-intro #4370]: #4371
-#4375 := [monotonicity #4372]: #4374
-#4407 := [monotonicity #4375 #4404]: #4406
-#4410 := [monotonicity #4407]: #4409
-#4413 := [monotonicity #4410]: #4412
-#4416 := [monotonicity #4413]: #4415
-#4365 := (iff #1405 #4364)
-#4362 := (iff #1402 #4359)
-#4360 := (iff #1399 #1399)
+#4498 := [monotonicity #4392 #4495]: #4497
+#4501 := [monotonicity #4498]: #4500
+#4504 := [monotonicity #4501]: #4503
+#4507 := [monotonicity #4504]: #4506
+#4383 := (iff #3588 #4382)
+#4380 := (iff #3395 #4377)
+#4378 := (iff #3390 #3390)
+#4379 := [refl]: #4378
+#4381 := [quant-intro #4379]: #4380
+#4384 := [monotonicity #4381]: #4383
+#4375 := (iff #3587 #4374)
+#4372 := (iff #3377 #4369)
+#4370 := (iff #3374 #3374)
+#4371 := [refl]: #4370
+#4373 := [quant-intro #4371]: #4372
+#4376 := [monotonicity #4373]: #4375
+#4365 := (iff #1623 #4364)
+#4362 := (iff #1620 #4359)
+#4360 := (iff #1615 #1615)
 #4361 := [refl]: #4360
 #4363 := [quant-intro #4361]: #4362
 #4366 := [monotonicity #4363]: #4365
-#4419 := [monotonicity #4366 #4416]: #4418
-#4422 := [monotonicity #4419]: #4421
-#4425 := [monotonicity #4422]: #4424
-#4428 := [monotonicity #4425]: #4427
-#4431 := [monotonicity #4428]: #4430
-#4434 := [monotonicity #4431]: #4433
-#4437 := [monotonicity #4434]: #4436
-#4440 := [monotonicity #4437]: #4439
-#4357 := (iff #859 #4356)
-#4354 := (iff #725 #4351)
-#4352 := (iff #720 #720)
-#4353 := [refl]: #4352
-#4355 := [quant-intro #4353]: #4354
-#4358 := [monotonicity #4355]: #4357
-#4443 := [monotonicity #4358 #4440]: #4442
-#4446 := [monotonicity #4443]: #4445
-#4449 := [monotonicity #4446]: #4448
-#4452 := [monotonicity #4449]: #4451
-#4348 := (iff #1391 #4347)
-#4345 := (iff #1388 #4342)
-#4343 := (iff #1383 #1383)
-#4344 := [refl]: #4343
-#4346 := [quant-intro #4344]: #4345
-#4349 := [monotonicity #4346]: #4348
-#4455 := [monotonicity #4349 #4452]: #4454
-#4458 := [monotonicity #4455]: #4457
-#4461 := [monotonicity #4458]: #4460
-#4464 := [monotonicity #4461]: #4463
-#4340 := (iff #3579 #4339)
-#4337 := (iff #3386 #4334)
-#4335 := (iff #3381 #3381)
-#4336 := [refl]: #4335
-#4338 := [quant-intro #4336]: #4337
-#4341 := [monotonicity #4338]: #4340
-#4332 := (iff #3578 #4331)
-#4329 := (iff #3368 #4326)
-#4327 := (iff #3365 #3365)
-#4328 := [refl]: #4327
-#4330 := [quant-intro #4328]: #4329
-#4333 := [monotonicity #4330]: #4332
-#4322 := (iff #1556 #4321)
-#4319 := (iff #1553 #4316)
-#4317 := (iff #1548 #1548)
-#4318 := [refl]: #4317
-#4320 := [quant-intro #4318]: #4319
-#4323 := [monotonicity #4320]: #4322
-#4467 := [monotonicity #4323 #4333 #4341 #4464]: #4466
-#4470 := [monotonicity #4467]: #4469
-#4314 := (iff #3356 #4313)
-#4311 := (iff #3355 #4310)
-#4308 := (iff #3354 #4307)
-#4305 := (iff #3347 #4304)
-#4302 := (iff #3342 #4301)
-#4299 := (iff #3341 #4298)
-#4296 := (iff #3340 #4295)
-#4293 := (iff #3333 #4292)
-#4290 := (iff #3306 #4289)
-#4287 := (iff #3305 #4286)
-#4284 := (iff #3304 #4283)
-#4281 := (iff #3298 #4278)
-#4279 := (iff #3293 #3293)
-#4280 := [refl]: #4279
-#4282 := [quant-intro #4280]: #4281
-#4285 := [monotonicity #4282]: #4284
-#4288 := [monotonicity #4285]: #4287
-#4291 := [monotonicity #4288]: #4290
-#4294 := [monotonicity #4291]: #4293
-#4297 := [monotonicity #4294]: #4296
-#4276 := (iff #3339 #4275)
-#4273 := (iff #3276 #4270)
-#4271 := (iff #3271 #3271)
-#4272 := [refl]: #4271
-#4274 := [quant-intro #4272]: #4273
-#4277 := [monotonicity #4274]: #4276
-#4300 := [monotonicity #4277 #4297]: #4299
-#4303 := [monotonicity #4300]: #4302
-#4268 := (iff #3247 #4267)
-#4265 := (iff #3246 #4264)
-#4262 := (iff #3245 #4261)
-#4259 := (iff #3239 #4256)
-#4257 := (iff #3228 #3228)
-#4258 := [refl]: #4257
-#4260 := [quant-intro #4258]: #4259
-#4263 := [monotonicity #4260]: #4262
-#4266 := [monotonicity #4263]: #4265
-#4269 := [monotonicity #4266]: #4268
-#4306 := [monotonicity #4269 #4303]: #4305
+#4510 := [monotonicity #4366 #4376 #4384 #4507]: #4509
+#4513 := [monotonicity #4510]: #4512
+#4357 := (iff #3365 #4356)
+#4354 := (iff #3364 #4353)
+#4351 := (iff #3363 #4350)
+#4348 := (iff #3356 #4347)
+#4345 := (iff #3351 #4344)
+#4342 := (iff #3350 #4341)
+#4339 := (iff #3349 #4338)
+#4336 := (iff #3342 #4335)
+#4333 := (iff #3315 #4332)
+#4330 := (iff #3314 #4329)
+#4327 := (iff #3313 #4326)
+#4324 := (iff #3307 #4321)
+#4322 := (iff #3302 #3302)
+#4323 := [refl]: #4322
+#4325 := [quant-intro #4323]: #4324
+#4328 := [monotonicity #4325]: #4327
+#4331 := [monotonicity #4328]: #4330
+#4334 := [monotonicity #4331]: #4333
+#4337 := [monotonicity #4334]: #4336
+#4340 := [monotonicity #4337]: #4339
+#4319 := (iff #3348 #4318)
+#4316 := (iff #3285 #4313)
+#4314 := (iff #3280 #3280)
+#4315 := [refl]: #4314
+#4317 := [quant-intro #4315]: #4316
+#4320 := [monotonicity #4317]: #4319
+#4343 := [monotonicity #4320 #4340]: #4342
+#4346 := [monotonicity #4343]: #4345
+#4311 := (iff #3256 #4310)
+#4308 := (iff #3255 #4307)
+#4305 := (iff #3254 #4304)
+#4302 := (iff #3248 #4299)
+#4300 := (iff #3237 #3237)
+#4301 := [refl]: #4300
+#4303 := [quant-intro #4301]: #4302
+#4306 := [monotonicity #4303]: #4305
 #4309 := [monotonicity #4306]: #4308
-#4252 := (iff #3353 #4251)
-#4249 := (iff #3224 #4246)
-#4247 := (iff #3213 #3213)
-#4248 := [refl]: #4247
-#4250 := [quant-intro #4248]: #4249
-#4253 := [monotonicity #4250]: #4252
-#4312 := [monotonicity #4253 #4309]: #4311
-#4315 := [monotonicity #4312]: #4314
-#4473 := [monotonicity #4315 #4470]: #4472
-#4476 := [monotonicity #4473]: #4475
-#4243 := (iff #3596 #4242)
-#4240 := (iff #3210 #4237)
-#4238 := (iff #3205 #3205)
-#4239 := [refl]: #4238
-#4241 := [quant-intro #4239]: #4240
-#4244 := [monotonicity #4241]: #4243
-#4235 := (iff #3595 #4234)
-#4232 := (iff #3182 #4229)
-#4230 := (iff #3177 #3177)
-#4231 := [refl]: #4230
-#4233 := [quant-intro #4231]: #4232
-#4236 := [monotonicity #4233]: #4235
-#4227 := (iff #3594 #4226)
-#4224 := (iff #3154 #4221)
-#4222 := (iff #3149 #3149)
-#4223 := [refl]: #4222
-#4225 := [quant-intro #4223]: #4224
-#4228 := [monotonicity #4225]: #4227
-#4218 := (iff #3593 #4217)
-#4215 := (iff #3131 #4212)
-#4213 := (iff #3126 #3126)
-#4214 := [refl]: #4213
-#4216 := [quant-intro #4214]: #4215
-#4219 := [monotonicity #4216]: #4218
-#4210 := (iff #1648 #4209)
-#4207 := (iff #1645 #4204)
-#4205 := (iff #1642 #1642)
-#4206 := [refl]: #4205
-#4208 := [quant-intro #4206]: #4207
-#4211 := [monotonicity #4208]: #4210
-#4479 := [monotonicity #4211 #4219 #4228 #4236 #4244 #4476]: #4478
-#4482 := [monotonicity #4479]: #4481
-#4201 := (iff #3107 #4200)
-#4198 := (iff #3106 #4197)
-#4195 := (iff #3105 #4194)
-#4192 := (iff #3099 #4189)
-#4190 := (iff #3088 #3088)
-#4191 := [refl]: #4190
-#4193 := [quant-intro #4191]: #4192
-#4196 := [monotonicity #4193]: #4195
-#4199 := [monotonicity #4196]: #4198
-#4202 := [monotonicity #4199]: #4201
-#4485 := [monotonicity #4202 #4482]: #4484
-#4488 := [monotonicity #4485]: #4487
-#4186 := (iff #3610 #4185)
-#4183 := (iff #3084 #4180)
-#4181 := (iff #3079 #3079)
-#4182 := [refl]: #4181
-#4184 := [quant-intro #4182]: #4183
-#4187 := [monotonicity #4184]: #4186
-#4491 := [monotonicity #4187 #4488]: #4490
-#4494 := [monotonicity #4491]: #4493
-#4497 := [monotonicity #4494]: #4496
-#4500 := [monotonicity #4497]: #4499
-#4177 := (iff #3624 #4176)
-#4174 := (iff #3039 #4171)
-#4172 := (iff #3034 #3034)
-#4173 := [refl]: #4172
-#4175 := [quant-intro #4173]: #4174
-#4178 := [monotonicity #4175]: #4177
-#4503 := [monotonicity #4178 #4500]: #4502
-#4506 := [monotonicity #4503]: #4505
-#4509 := [monotonicity #4506]: #4508
-#4512 := [monotonicity #4509]: #4511
-#4168 := (iff #1111 #4167)
-#4165 := (iff #1108 #4162)
-#4163 := (iff #1107 #1107)
-#4164 := [refl]: #4163
-#4166 := [quant-intro #4164]: #4165
-#4169 := [monotonicity #4166]: #4168
-#4515 := [monotonicity #4169 #4512]: #4514
-#4518 := [monotonicity #4515]: #4517
-#4521 := [monotonicity #4518]: #4520
-#4524 := [monotonicity #4521]: #4523
-#4527 := [monotonicity #4524]: #4526
-#4530 := [monotonicity #4527]: #4529
-#4533 := [monotonicity #4530]: #4532
-#2304 := (not #2303)
-#2906 := (and #713 #2304 #2903)
-#2909 := (not #2906)
-#2912 := (forall (vars (?v1 S2)) #2909)
-#2878 := (not #2875)
-#2309 := (not #2308)
-#2921 := (and #1445 #2309 #2878 #2912)
-#2277 := (not #2276)
-#2848 := (and #2277 #2279)
-#2851 := (not #2848)
-#2869 := (or #2851 #2864)
-#2872 := (not #2869)
-#2926 := (or #2872 #2921)
-#2929 := (and #1421 #2926)
-#2248 := (not #2247)
-#2823 := (and #2245 #2248)
-#2826 := (not #2823)
-#2842 := (or #2826 #2837)
-#2845 := (not #2842)
-#2932 := (or #2845 #2929)
-#2935 := (and #1402 #2932)
-#2938 := (or #2225 #2935)
-#2941 := (and #170 #2938)
-#2944 := (or #1396 #2941)
-#2947 := (and #725 #2944)
-#2950 := (or #2818 #2947)
-#2953 := (and #1388 #2950)
-#2956 := (or #2804 #2953)
-#2163 := (not #2162)
-#2160 := (not #2159)
-#2962 := (and #148 #671 #1377 #1535 #1553 #1561 #2160 #2163 #2956)
-#2105 := (not #2104)
-#2101 := (not #2100)
-#2741 := (and #2101 #2105)
-#2744 := (not #2741)
-#2761 := (or #2744 #2756)
-#2764 := (not #2761)
-#2114 := (not #125)
-#2124 := (and #2114 #1297)
-#2770 := (or #2124 #2764)
-#2714 := (not #2709)
-#2732 := (and #2714 #2727)
-#2735 := (or #1257 #2732)
-#2738 := (forall (vars (?v0 S2)) #2735)
-#2775 := (and #2738 #2770)
-#2034 := (not #2033)
-#2684 := (and #2034 #2681)
-#2687 := (not #2684)
-#2690 := (forall (vars (?v1 S2)) #2687)
-#2656 := (not #2653)
-#2039 := (not #2038)
-#2696 := (and #2039 #2656 #2690)
-#2778 := (or #2696 #2775)
-#2140 := (not #1325)
-#2143 := (forall (vars (?v0 S2)) #2140)
-#2784 := (and #103 #108 #535 #538 #2143 #2778)
-#2967 := (or #2784 #2962)
-#2633 := (not #2628)
-#2636 := (and #1998 #2616 #2633)
-#2639 := (or #1212 #2636)
-#2642 := (forall (vars (?v0 S2)) #2639)
-#2578 := (not #2573)
-#2596 := (and #1971 #2578 #2591)
-#2599 := (or #1174 #2596)
-#2602 := (forall (vars (?v0 S2)) #2599)
-#2973 := (and #67 #1620 #1636 #1645 #2602 #2642 #2967)
-#1926 := (not #1925)
-#2546 := (and #368 #1926 #2543)
-#2549 := (not #2546)
-#2552 := (forall (vars (?v1 S2)) #2549)
-#2518 := (not #2515)
-#1931 := (not #1930)
-#2558 := (and #1931 #2518 #2552)
-#2978 := (or #2558 #2973)
-#2981 := (and #1159 #2978)
-#1892 := (not #1891)
-#2503 := (and #1892 #1894)
-#2506 := (not #2503)
-#2509 := (or #2500 #2506)
-#2512 := (not #2509)
-#2984 := (or #2512 #2981)
-#2987 := (and #1128 #2984)
-#1869 := (not #1868)
-#2471 := (and #1866 #1869)
-#2474 := (not #2471)
-#2490 := (or #2474 #2485)
-#2493 := (not #2490)
-#2990 := (or #2493 #2987)
-#2993 := (and #1108 #2990)
-#2996 := (or #1846 #2993)
-#2999 := (and #38 #2996)
-#3002 := (or #1102 #2999)
-#3659 := (iff #3002 #3658)
-#3656 := (iff #2999 #3653)
-#3648 := (and #38 #3645)
-#3654 := (iff #3648 #3653)
-#3655 := [rewrite]: #3654
-#3649 := (iff #2999 #3648)
-#3646 := (iff #2996 #3645)
-#3643 := (iff #2993 #3640)
-#3635 := (and #1108 #3632)
-#3641 := (iff #3635 #3640)
-#3642 := [rewrite]: #3641
-#3636 := (iff #2993 #3635)
-#3633 := (iff #2990 #3632)
-#3630 := (iff #2987 #3627)
-#3621 := (and #3039 #3618)
-#3628 := (iff #3621 #3627)
-#3629 := [rewrite]: #3628
-#3622 := (iff #2987 #3621)
-#3619 := (iff #2984 #3618)
-#3616 := (iff #2981 #3613)
-#3607 := (and #3084 #3604)
-#3614 := (iff #3607 #3613)
-#3615 := [rewrite]: #3614
-#3608 := (iff #2981 #3607)
-#3605 := (iff #2978 #3604)
-#3602 := (iff #2973 #3599)
-#3590 := (and #67 #3131 #3154 #1645 #3182 #3210 #3587)
-#3600 := (iff #3590 #3599)
-#3601 := [rewrite]: #3600
-#3591 := (iff #2973 #3590)
-#3588 := (iff #2967 #3587)
-#3585 := (iff #2962 #3582)
-#3575 := (and #148 #671 #3368 #3386 #1553 #1561 #2160 #2163 #3572)
-#3583 := (iff #3575 #3582)
-#3584 := [rewrite]: #3583
-#3576 := (iff #2962 #3575)
-#3573 := (iff #2956 #3572)
-#3570 := (iff #2953 #3567)
-#3562 := (and #1388 #3559)
-#3568 := (iff #3562 #3567)
-#3569 := [rewrite]: #3568
-#3563 := (iff #2953 #3562)
-#3560 := (iff #2950 #3559)
-#3557 := (iff #2947 #3554)
-#3549 := (and #725 #3546)
-#3555 := (iff #3549 #3554)
-#3556 := [rewrite]: #3555
-#3550 := (iff #2947 #3549)
-#3547 := (iff #2944 #3546)
-#3544 := (iff #2941 #3541)
-#3536 := (and #170 #3533)
-#3542 := (iff #3536 #3541)
-#3543 := [rewrite]: #3542
-#3537 := (iff #2941 #3536)
-#3534 := (iff #2938 #3533)
-#3531 := (iff #2935 #3528)
-#3523 := (and #1402 #3520)
-#3529 := (iff #3523 #3528)
-#3530 := [rewrite]: #3529
-#3524 := (iff #2935 #3523)
-#3521 := (iff #2932 #3520)
-#3518 := (iff #2929 #3515)
-#3509 := (and #3432 #3506)
-#3516 := (iff #3509 #3515)
-#3517 := [rewrite]: #3516
-#3510 := (iff #2929 #3509)
-#3507 := (iff #2926 #3506)
-#3504 := (iff #2921 #3501)
-#3495 := (and #3477 #2309 #2878 #3492)
-#3502 := (iff #3495 #3501)
-#3503 := [rewrite]: #3502
-#3496 := (iff #2921 #3495)
-#3493 := (iff #2912 #3492)
-#3490 := (iff #2909 #3481)
-#3482 := (not #3481)
-#3485 := (not #3482)
-#3488 := (iff #3485 #3481)
-#3489 := [rewrite]: #3488
-#3486 := (iff #2909 #3485)
-#3483 := (iff #2906 #3482)
-#3484 := [rewrite]: #3483
-#3487 := [monotonicity #3484]: #3486
-#3491 := [trans #3487 #3489]: #3490
-#3494 := [quant-intro #3491]: #3493
-#3478 := (iff #1445 #3477)
-#3475 := (iff #1442 #3472)
-#3458 := (or #719 #1141)
-#3469 := (or #3458 #1438)
-#3473 := (iff #3469 #3472)
-#3474 := [rewrite]: #3473
-#3470 := (iff #1442 #3469)
-#3467 := (iff #1435 #3458)
-#3459 := (not #3458)
-#3462 := (not #3459)
-#3465 := (iff #3462 #3458)
-#3466 := [rewrite]: #3465
-#3463 := (iff #1435 #3462)
-#3460 := (iff #1430 #3459)
+#4312 := [monotonicity #4309]: #4311
+#4349 := [monotonicity #4312 #4346]: #4348
+#4352 := [monotonicity #4349]: #4351
+#4295 := (iff #3362 #4294)
+#4292 := (iff #3233 #4289)
+#4290 := (iff #3222 #3222)
+#4291 := [refl]: #4290
+#4293 := [quant-intro #4291]: #4292
+#4296 := [monotonicity #4293]: #4295
+#4355 := [monotonicity #4296 #4352]: #4354
+#4358 := [monotonicity #4355]: #4357
+#4516 := [monotonicity #4358 #4513]: #4515
+#4519 := [monotonicity #4516]: #4518
+#4286 := (iff #3605 #4285)
+#4283 := (iff #3219 #4280)
+#4281 := (iff #3214 #3214)
+#4282 := [refl]: #4281
+#4284 := [quant-intro #4282]: #4283
+#4287 := [monotonicity #4284]: #4286
+#4278 := (iff #3604 #4277)
+#4275 := (iff #3191 #4272)
+#4273 := (iff #3186 #3186)
+#4274 := [refl]: #4273
+#4276 := [quant-intro #4274]: #4275
+#4279 := [monotonicity #4276]: #4278
+#4270 := (iff #3603 #4269)
+#4267 := (iff #3163 #4264)
+#4265 := (iff #3158 #3158)
+#4266 := [refl]: #4265
+#4268 := [quant-intro #4266]: #4267
+#4271 := [monotonicity #4268]: #4270
+#4261 := (iff #3602 #4260)
+#4258 := (iff #3140 #4255)
+#4256 := (iff #3135 #3135)
+#4257 := [refl]: #4256
+#4259 := [quant-intro #4257]: #4258
+#4262 := [monotonicity #4259]: #4261
+#4253 := (iff #1715 #4252)
+#4250 := (iff #1712 #4247)
+#4248 := (iff #1709 #1709)
+#4249 := [refl]: #4248
+#4251 := [quant-intro #4249]: #4250
+#4254 := [monotonicity #4251]: #4253
+#4522 := [monotonicity #4254 #4262 #4271 #4279 #4287 #4519]: #4521
+#4525 := [monotonicity #4522]: #4524
+#4244 := (iff #3116 #4243)
+#4241 := (iff #3115 #4240)
+#4238 := (iff #3114 #4237)
+#4235 := (iff #3108 #4232)
+#4233 := (iff #3097 #3097)
+#4234 := [refl]: #4233
+#4236 := [quant-intro #4234]: #4235
+#4239 := [monotonicity #4236]: #4238
+#4242 := [monotonicity #4239]: #4241
+#4245 := [monotonicity #4242]: #4244
+#4528 := [monotonicity #4245 #4525]: #4527
+#4531 := [monotonicity #4528]: #4530
+#4229 := (iff #3619 #4228)
+#4226 := (iff #3093 #4223)
+#4224 := (iff #3088 #3088)
+#4225 := [refl]: #4224
+#4227 := [quant-intro #4225]: #4226
+#4230 := [monotonicity #4227]: #4229
+#4534 := [monotonicity #4230 #4531]: #4533
+#4537 := [monotonicity #4534]: #4536
+#4540 := [monotonicity #4537]: #4539
+#4543 := [monotonicity #4540]: #4542
+#4220 := (iff #3633 #4219)
+#4217 := (iff #3048 #4214)
+#4215 := (iff #3043 #3043)
+#4216 := [refl]: #4215
+#4218 := [quant-intro #4216]: #4217
+#4221 := [monotonicity #4218]: #4220
+#4546 := [monotonicity #4221 #4543]: #4545
+#4549 := [monotonicity #4546]: #4548
+#4552 := [monotonicity #4549]: #4551
+#4555 := [monotonicity #4552]: #4554
+#4211 := (iff #1178 #4210)
+#4208 := (iff #1175 #4205)
+#4206 := (iff #1174 #1174)
+#4207 := [refl]: #4206
+#4209 := [quant-intro #4207]: #4208
+#4212 := [monotonicity #4209]: #4211
+#4558 := [monotonicity #4212 #4555]: #4557
+#4561 := [monotonicity #4558]: #4560
+#4564 := [monotonicity #4561]: #4563
+#4567 := [monotonicity #4564]: #4566
+#4570 := [monotonicity #4567]: #4569
+#4573 := [monotonicity #4570]: #4572
+#4576 := [monotonicity #4573]: #4575
+#2328 := (not #2327)
+#2930 := (and #780 #2328 #2927)
+#2933 := (not #2930)
+#2936 := (forall (vars (?v1 S3)) #2933)
+#2902 := (not #2899)
+#2945 := (and #1512 #2333 #2902 #2936)
+#2301 := (not #2300)
+#2872 := (and #2301 #2303)
+#2875 := (not #2872)
+#2893 := (or #2875 #2888)
+#2896 := (not #2893)
+#2950 := (or #2896 #2945)
+#2953 := (and #1488 #2950)
+#2847 := (and #2269 #2272)
+#2850 := (not #2847)
+#2866 := (or #2850 #2861)
+#2869 := (not #2866)
+#2956 := (or #2869 #2953)
+#2959 := (and #1469 #2956)
+#2962 := (or #2249 #2959)
+#2965 := (and #204 #2962)
+#2968 := (or #1463 #2965)
+#2971 := (and #792 #2968)
+#2974 := (or #2842 #2971)
+#2977 := (and #1455 #2974)
+#2980 := (or #2828 #2977)
+#2187 := (not #2186)
+#2184 := (not #2183)
+#2986 := (and #730 #749 #1444 #1602 #1620 #1628 #2184 #2187 #2980)
+#2129 := (not #2128)
+#2125 := (not #2124)
+#2765 := (and #2125 #2129)
+#2768 := (not #2765)
+#2785 := (or #2768 #2780)
+#2788 := (not #2785)
+#2138 := (not #158)
+#2148 := (and #2138 #1364)
+#2794 := (or #2148 #2788)
+#2738 := (not #2733)
+#2756 := (and #2738 #2751)
+#2759 := (or #1324 #2756)
+#2762 := (forall (vars (?v0 S3)) #2759)
+#2799 := (and #2762 #2794)
+#2058 := (not #2057)
+#2708 := (and #2058 #2705)
+#2711 := (not #2708)
+#2714 := (forall (vars (?v1 S3)) #2711)
+#2680 := (not #2677)
+#2063 := (not #2062)
+#2720 := (and #2063 #2680 #2714)
+#2802 := (or #2720 #2799)
+#2164 := (not #1392)
+#2167 := (forall (vars (?v0 S3)) #2164)
+#2808 := (and #136 #141 #594 #597 #2167 #2802)
+#2991 := (or #2808 #2986)
+#2657 := (not #2652)
+#2660 := (and #2022 #2640 #2657)
+#2663 := (or #1279 #2660)
+#2666 := (forall (vars (?v0 S3)) #2663)
+#2602 := (not #2597)
+#2620 := (and #1995 #2602 #2615)
+#2623 := (or #1241 #2620)
+#2626 := (forall (vars (?v0 S3)) #2623)
+#2997 := (and #100 #1687 #1703 #1712 #2626 #2666 #2991)
+#1950 := (not #1949)
+#2570 := (and #427 #1950 #2567)
+#2573 := (not #2570)
+#2576 := (forall (vars (?v1 S3)) #2573)
+#2542 := (not #2539)
+#1955 := (not #1954)
+#2582 := (and #1955 #2542 #2576)
+#3002 := (or #2582 #2997)
+#3005 := (and #1226 #3002)
+#1916 := (not #1915)
+#2527 := (and #1916 #1918)
+#2530 := (not #2527)
+#2533 := (or #2524 #2530)
+#2536 := (not #2533)
+#3008 := (or #2536 #3005)
+#3011 := (and #1195 #3008)
+#1893 := (not #1892)
+#2495 := (and #1890 #1893)
+#2498 := (not #2495)
+#2514 := (or #2498 #2509)
+#2517 := (not #2514)
+#3014 := (or #2517 #3011)
+#3017 := (and #1175 #3014)
+#3020 := (or #1870 #3017)
+#3023 := (and #71 #3020)
+#3026 := (or #1169 #3023)
+#3668 := (iff #3026 #3667)
+#3665 := (iff #3023 #3662)
+#3657 := (and #71 #3654)
+#3663 := (iff #3657 #3662)
+#3664 := [rewrite]: #3663
+#3658 := (iff #3023 #3657)
+#3655 := (iff #3020 #3654)
+#3652 := (iff #3017 #3649)
+#3644 := (and #1175 #3641)
+#3650 := (iff #3644 #3649)
+#3651 := [rewrite]: #3650
+#3645 := (iff #3017 #3644)
+#3642 := (iff #3014 #3641)
+#3639 := (iff #3011 #3636)
+#3630 := (and #3048 #3627)
+#3637 := (iff #3630 #3636)
+#3638 := [rewrite]: #3637
+#3631 := (iff #3011 #3630)
+#3628 := (iff #3008 #3627)
+#3625 := (iff #3005 #3622)
+#3616 := (and #3093 #3613)
+#3623 := (iff #3616 #3622)
+#3624 := [rewrite]: #3623
+#3617 := (iff #3005 #3616)
+#3614 := (iff #3002 #3613)
+#3611 := (iff #2997 #3608)
+#3599 := (and #100 #3140 #3163 #1712 #3191 #3219 #3596)
+#3609 := (iff #3599 #3608)
+#3610 := [rewrite]: #3609
+#3600 := (iff #2997 #3599)
+#3597 := (iff #2991 #3596)
+#3594 := (iff #2986 #3591)
+#3584 := (and #730 #749 #3377 #3395 #1620 #1628 #2184 #2187 #3581)
+#3592 := (iff #3584 #3591)
+#3593 := [rewrite]: #3592
+#3585 := (iff #2986 #3584)
+#3582 := (iff #2980 #3581)
+#3579 := (iff #2977 #3576)
+#3571 := (and #1455 #3568)
+#3577 := (iff #3571 #3576)
+#3578 := [rewrite]: #3577
+#3572 := (iff #2977 #3571)
+#3569 := (iff #2974 #3568)
+#3566 := (iff #2971 #3563)
+#3558 := (and #792 #3555)
+#3564 := (iff #3558 #3563)
+#3565 := [rewrite]: #3564
+#3559 := (iff #2971 #3558)
+#3556 := (iff #2968 #3555)
+#3553 := (iff #2965 #3550)
+#3545 := (and #204 #3542)
+#3551 := (iff #3545 #3550)
+#3552 := [rewrite]: #3551
+#3546 := (iff #2965 #3545)
+#3543 := (iff #2962 #3542)
+#3540 := (iff #2959 #3537)
+#3532 := (and #1469 #3529)
+#3538 := (iff #3532 #3537)
+#3539 := [rewrite]: #3538
+#3533 := (iff #2959 #3532)
+#3530 := (iff #2956 #3529)
+#3527 := (iff #2953 #3524)
+#3518 := (and #3441 #3515)
+#3525 := (iff #3518 #3524)
+#3526 := [rewrite]: #3525
+#3519 := (iff #2953 #3518)
+#3516 := (iff #2950 #3515)
+#3513 := (iff #2945 #3510)
+#3504 := (and #3486 #2333 #2902 #3501)
+#3511 := (iff #3504 #3510)
+#3512 := [rewrite]: #3511
+#3505 := (iff #2945 #3504)
+#3502 := (iff #2936 #3501)
+#3499 := (iff #2933 #3490)
+#3491 := (not #3490)
+#3494 := (not #3491)
+#3497 := (iff #3494 #3490)
+#3498 := [rewrite]: #3497
+#3495 := (iff #2933 #3494)
+#3492 := (iff #2930 #3491)
+#3493 := [rewrite]: #3492
+#3496 := [monotonicity #3493]: #3495
+#3500 := [trans #3496 #3498]: #3499
+#3503 := [quant-intro #3500]: #3502
+#3487 := (iff #1512 #3486)
+#3484 := (iff #1509 #3481)
+#3467 := (or #786 #1208)
+#3478 := (or #3467 #1505)
+#3482 := (iff #3478 #3481)
+#3483 := [rewrite]: #3482
+#3479 := (iff #1509 #3478)
+#3476 := (iff #1502 #3467)
+#3468 := (not #3467)
+#3471 := (not #3468)
+#3474 := (iff #3471 #3467)
+#3475 := [rewrite]: #3474
+#3472 := (iff #1502 #3471)
+#3469 := (iff #1497 #3468)
+#3470 := [rewrite]: #3469
+#3473 := [monotonicity #3470]: #3472
+#3477 := [trans #3473 #3475]: #3476
+#3480 := [monotonicity #3477]: #3479
+#3485 := [trans #3480 #3483]: #3484
+#3488 := [quant-intro #3485]: #3487
+#3506 := [monotonicity #3488 #3503]: #3505
+#3514 := [trans #3506 #3512]: #3513
+#3465 := (iff #2896 #3464)
+#3462 := (iff #2893 #3459)
+#3445 := (or #2300 #3444)
+#3456 := (or #3445 #2888)
+#3460 := (iff #3456 #3459)
 #3461 := [rewrite]: #3460
-#3464 := [monotonicity #3461]: #3463
-#3468 := [trans #3464 #3466]: #3467
-#3471 := [monotonicity #3468]: #3470
-#3476 := [trans #3471 #3474]: #3475
-#3479 := [quant-intro #3476]: #3478
-#3497 := [monotonicity #3479 #3494]: #3496
-#3505 := [trans #3497 #3503]: #3504
-#3456 := (iff #2872 #3455)
-#3453 := (iff #2869 #3450)
-#3436 := (or #2276 #3435)
-#3447 := (or #3436 #2864)
-#3451 := (iff #3447 #3450)
-#3452 := [rewrite]: #3451
-#3448 := (iff #2869 #3447)
-#3445 := (iff #2851 #3436)
-#3437 := (not #3436)
-#3440 := (not #3437)
-#3443 := (iff #3440 #3436)
-#3444 := [rewrite]: #3443
-#3441 := (iff #2851 #3440)
-#3438 := (iff #2848 #3437)
-#3439 := [rewrite]: #3438
-#3442 := [monotonicity #3439]: #3441
-#3446 := [trans #3442 #3444]: #3445
-#3449 := [monotonicity #3446]: #3448
-#3454 := [trans #3449 #3452]: #3453
-#3457 := [monotonicity #3454]: #3456
-#3508 := [monotonicity #3457 #3505]: #3507
-#3433 := (iff #1421 #3432)
-#3430 := (iff #1416 #3427)
-#3413 := (or #713 #3412)
-#3424 := (or #3413 #1408)
-#3428 := (iff #3424 #3427)
-#3429 := [rewrite]: #3428
-#3425 := (iff #1416 #3424)
-#3422 := (iff #742 #3413)
-#3414 := (not #3413)
-#3417 := (not #3414)
-#3420 := (iff #3417 #3413)
-#3421 := [rewrite]: #3420
-#3418 := (iff #742 #3417)
-#3415 := (iff #736 #3414)
-#3416 := [rewrite]: #3415
-#3419 := [monotonicity #3416]: #3418
-#3423 := [trans #3419 #3421]: #3422
-#3426 := [monotonicity #3423]: #3425
-#3431 := [trans #3426 #3429]: #3430
-#3434 := [quant-intro #3431]: #3433
-#3511 := [monotonicity #3434 #3508]: #3510
-#3519 := [trans #3511 #3517]: #3518
-#3410 := (iff #2845 #3409)
-#3407 := (iff #2842 #3404)
-#3390 := (or #3389 #2247)
-#3401 := (or #3390 #2837)
-#3405 := (iff #3401 #3404)
-#3406 := [rewrite]: #3405
-#3402 := (iff #2842 #3401)
-#3399 := (iff #2826 #3390)
-#3391 := (not #3390)
-#3394 := (not #3391)
-#3397 := (iff #3394 #3390)
-#3398 := [rewrite]: #3397
-#3395 := (iff #2826 #3394)
-#3392 := (iff #2823 #3391)
-#3393 := [rewrite]: #3392
-#3396 := [monotonicity #3393]: #3395
-#3400 := [trans #3396 #3398]: #3399
-#3403 := [monotonicity #3400]: #3402
-#3408 := [trans #3403 #3406]: #3407
-#3411 := [monotonicity #3408]: #3410
-#3522 := [monotonicity #3411 #3519]: #3521
-#3525 := [monotonicity #3522]: #3524
-#3532 := [trans #3525 #3530]: #3531
-#3535 := [monotonicity #3532]: #3534
-#3538 := [monotonicity #3535]: #3537
-#3545 := [trans #3538 #3543]: #3544
-#3548 := [monotonicity #3545]: #3547
-#3551 := [monotonicity #3548]: #3550
-#3558 := [trans #3551 #3556]: #3557
-#3561 := [monotonicity #3558]: #3560
-#3564 := [monotonicity #3561]: #3563
-#3571 := [trans #3564 #3569]: #3570
-#3574 := [monotonicity #3571]: #3573
-#3387 := (iff #1535 #3386)
-#3384 := (iff #1532 #3381)
-#3378 := (or #3361 #1529)
-#3382 := (iff #3378 #3381)
-#3383 := [rewrite]: #3382
-#3379 := (iff #1532 #3378)
-#3376 := (iff #1524 #3361)
-#3371 := (not #3362)
-#3374 := (iff #3371 #3361)
-#3375 := [rewrite]: #3374
-#3372 := (iff #1524 #3371)
-#3363 := (iff #1366 #3362)
-#3364 := [rewrite]: #3363
-#3373 := [monotonicity #3364]: #3372
-#3377 := [trans #3373 #3375]: #3376
-#3380 := [monotonicity #3377]: #3379
-#3385 := [trans #3380 #3383]: #3384
-#3388 := [quant-intro #3385]: #3387
-#3369 := (iff #1377 #3368)
-#3366 := (iff #1372 #3365)
-#3367 := [monotonicity #3364]: #3366
-#3370 := [quant-intro #3367]: #3369
-#3577 := [monotonicity #3370 #3388 #3574]: #3576
-#3586 := [trans #3577 #3584]: #3585
-#3359 := (iff #2784 #3356)
-#3350 := (and #103 #108 #535 #538 #3224 #3347)
-#3357 := (iff #3350 #3356)
-#3358 := [rewrite]: #3357
-#3351 := (iff #2784 #3350)
-#3348 := (iff #2778 #3347)
-#3345 := (iff #2775 #3342)
-#3336 := (and #3276 #3333)
-#3343 := (iff #3336 #3342)
-#3344 := [rewrite]: #3343
-#3337 := (iff #2775 #3336)
-#3334 := (iff #2770 #3333)
-#3331 := (iff #2764 #3330)
-#3328 := (iff #2761 #3325)
-#3311 := (or #2100 #2104)
-#3322 := (or #3311 #2756)
-#3326 := (iff #3322 #3325)
-#3327 := [rewrite]: #3326
-#3323 := (iff #2761 #3322)
-#3320 := (iff #2744 #3311)
-#3312 := (not #3311)
-#3315 := (not #3312)
-#3318 := (iff #3315 #3311)
-#3319 := [rewrite]: #3318
-#3316 := (iff #2744 #3315)
-#3313 := (iff #2741 #3312)
-#3314 := [rewrite]: #3313
-#3317 := [monotonicity #3314]: #3316
-#3321 := [trans #3317 #3319]: #3320
-#3324 := [monotonicity #3321]: #3323
-#3329 := [trans #3324 #3327]: #3328
-#3332 := [monotonicity #3329]: #3331
-#3309 := (iff #2124 #3306)
-#3301 := (and #2114 #3298)
-#3307 := (iff #3301 #3306)
-#3308 := [rewrite]: #3307
-#3302 := (iff #2124 #3301)
-#3299 := (iff #1297 #3298)
-#3296 := (iff #1294 #3293)
-#3279 := (or #1141 #1250)
-#3290 := (or #3279 #1291)
-#3294 := (iff #3290 #3293)
-#3295 := [rewrite]: #3294
-#3291 := (iff #1294 #3290)
-#3288 := (iff #1288 #3279)
-#3280 := (not #3279)
-#3283 := (not #3280)
-#3286 := (iff #3283 #3279)
-#3287 := [rewrite]: #3286
-#3284 := (iff #1288 #3283)
-#3281 := (iff #1285 #3280)
+#3457 := (iff #2893 #3456)
+#3454 := (iff #2875 #3445)
+#3446 := (not #3445)
+#3449 := (not #3446)
+#3452 := (iff #3449 #3445)
+#3453 := [rewrite]: #3452
+#3450 := (iff #2875 #3449)
+#3447 := (iff #2872 #3446)
+#3448 := [rewrite]: #3447
+#3451 := [monotonicity #3448]: #3450
+#3455 := [trans #3451 #3453]: #3454
+#3458 := [monotonicity #3455]: #3457
+#3463 := [trans #3458 #3461]: #3462
+#3466 := [monotonicity #3463]: #3465
+#3517 := [monotonicity #3466 #3514]: #3516
+#3442 := (iff #1488 #3441)
+#3439 := (iff #1483 #3436)
+#3422 := (or #780 #3421)
+#3433 := (or #3422 #1475)
+#3437 := (iff #3433 #3436)
+#3438 := [rewrite]: #3437
+#3434 := (iff #1483 #3433)
+#3431 := (iff #809 #3422)
+#3423 := (not #3422)
+#3426 := (not #3423)
+#3429 := (iff #3426 #3422)
+#3430 := [rewrite]: #3429
+#3427 := (iff #809 #3426)
+#3424 := (iff #803 #3423)
+#3425 := [rewrite]: #3424
+#3428 := [monotonicity #3425]: #3427
+#3432 := [trans #3428 #3430]: #3431
+#3435 := [monotonicity #3432]: #3434
+#3440 := [trans #3435 #3438]: #3439
+#3443 := [quant-intro #3440]: #3442
+#3520 := [monotonicity #3443 #3517]: #3519
+#3528 := [trans #3520 #3526]: #3527
+#3419 := (iff #2869 #3418)
+#3416 := (iff #2866 #3413)
+#3399 := (or #3398 #2271)
+#3410 := (or #3399 #2861)
+#3414 := (iff #3410 #3413)
+#3415 := [rewrite]: #3414
+#3411 := (iff #2866 #3410)
+#3408 := (iff #2850 #3399)
+#3400 := (not #3399)
+#3403 := (not #3400)
+#3406 := (iff #3403 #3399)
+#3407 := [rewrite]: #3406
+#3404 := (iff #2850 #3403)
+#3401 := (iff #2847 #3400)
+#3402 := [rewrite]: #3401
+#3405 := [monotonicity #3402]: #3404
+#3409 := [trans #3405 #3407]: #3408
+#3412 := [monotonicity #3409]: #3411
+#3417 := [trans #3412 #3415]: #3416
+#3420 := [monotonicity #3417]: #3419
+#3531 := [monotonicity #3420 #3528]: #3530
+#3534 := [monotonicity #3531]: #3533
+#3541 := [trans #3534 #3539]: #3540
+#3544 := [monotonicity #3541]: #3543
+#3547 := [monotonicity #3544]: #3546
+#3554 := [trans #3547 #3552]: #3553
+#3557 := [monotonicity #3554]: #3556
+#3560 := [monotonicity #3557]: #3559
+#3567 := [trans #3560 #3565]: #3566
+#3570 := [monotonicity #3567]: #3569
+#3573 := [monotonicity #3570]: #3572
+#3580 := [trans #3573 #3578]: #3579
+#3583 := [monotonicity #3580]: #3582
+#3396 := (iff #1602 #3395)
+#3393 := (iff #1599 #3390)
+#3387 := (or #3370 #1596)
+#3391 := (iff #3387 #3390)
+#3392 := [rewrite]: #3391
+#3388 := (iff #1599 #3387)
+#3385 := (iff #1591 #3370)
+#3380 := (not #3371)
+#3383 := (iff #3380 #3370)
+#3384 := [rewrite]: #3383
+#3381 := (iff #1591 #3380)
+#3372 := (iff #1433 #3371)
+#3373 := [rewrite]: #3372
+#3382 := [monotonicity #3373]: #3381
+#3386 := [trans #3382 #3384]: #3385
+#3389 := [monotonicity #3386]: #3388
+#3394 := [trans #3389 #3392]: #3393
+#3397 := [quant-intro #3394]: #3396
+#3378 := (iff #1444 #3377)
+#3375 := (iff #1439 #3374)
+#3376 := [monotonicity #3373]: #3375
+#3379 := [quant-intro #3376]: #3378
+#3586 := [monotonicity #3379 #3397 #3583]: #3585
+#3595 := [trans #3586 #3593]: #3594
+#3368 := (iff #2808 #3365)
+#3359 := (and #136 #141 #594 #597 #3233 #3356)
+#3366 := (iff #3359 #3365)
+#3367 := [rewrite]: #3366
+#3360 := (iff #2808 #3359)
+#3357 := (iff #2802 #3356)
+#3354 := (iff #2799 #3351)
+#3345 := (and #3285 #3342)
+#3352 := (iff #3345 #3351)
+#3353 := [rewrite]: #3352
+#3346 := (iff #2799 #3345)
+#3343 := (iff #2794 #3342)
+#3340 := (iff #2788 #3339)
+#3337 := (iff #2785 #3334)
+#3320 := (or #2124 #2128)
+#3331 := (or #3320 #2780)
+#3335 := (iff #3331 #3334)
+#3336 := [rewrite]: #3335
+#3332 := (iff #2785 #3331)
+#3329 := (iff #2768 #3320)
+#3321 := (not #3320)
+#3324 := (not #3321)
+#3327 := (iff #3324 #3320)
+#3328 := [rewrite]: #3327
+#3325 := (iff #2768 #3324)
+#3322 := (iff #2765 #3321)
+#3323 := [rewrite]: #3322
+#3326 := [monotonicity #3323]: #3325
+#3330 := [trans #3326 #3328]: #3329
+#3333 := [monotonicity #3330]: #3332
+#3338 := [trans #3333 #3336]: #3337
+#3341 := [monotonicity #3338]: #3340
+#3318 := (iff #2148 #3315)
+#3310 := (and #2138 #3307)
+#3316 := (iff #3310 #3315)
+#3317 := [rewrite]: #3316
+#3311 := (iff #2148 #3310)
+#3308 := (iff #1364 #3307)
+#3305 := (iff #1361 #3302)
+#3288 := (or #1208 #1317)
+#3299 := (or #3288 #1358)
+#3303 := (iff #3299 #3302)
+#3304 := [rewrite]: #3303
+#3300 := (iff #1361 #3299)
+#3297 := (iff #1355 #3288)
+#3289 := (not #3288)
+#3292 := (not #3289)
+#3295 := (iff #3292 #3288)
+#3296 := [rewrite]: #3295
+#3293 := (iff #1355 #3292)
+#3290 := (iff #1352 #3289)
+#3291 := [rewrite]: #3290
+#3294 := [monotonicity #3291]: #3293
+#3298 := [trans #3294 #3296]: #3297
+#3301 := [monotonicity #3298]: #3300
+#3306 := [trans #3301 #3304]: #3305
+#3309 := [quant-intro #3306]: #3308
+#3312 := [monotonicity #3309]: #3311
+#3319 := [trans #3312 #3317]: #3318
+#3344 := [monotonicity #3319 #3341]: #3343
+#3286 := (iff #2762 #3285)
+#3283 := (iff #2759 #3280)
+#3261 := (or #57 #1317)
+#3277 := (or #3261 #3274)
+#3281 := (iff #3277 #3280)
 #3282 := [rewrite]: #3281
-#3285 := [monotonicity #3282]: #3284
-#3289 := [trans #3285 #3287]: #3288
-#3292 := [monotonicity #3289]: #3291
-#3297 := [trans #3292 #3295]: #3296
-#3300 := [quant-intro #3297]: #3299
-#3303 := [monotonicity #3300]: #3302
-#3310 := [trans #3303 #3308]: #3309
-#3335 := [monotonicity #3310 #3332]: #3334
-#3277 := (iff #2738 #3276)
-#3274 := (iff #2735 #3271)
-#3252 := (or #24 #1250)
-#3268 := (or #3252 #3265)
-#3272 := (iff #3268 #3271)
-#3273 := [rewrite]: #3272
-#3269 := (iff #2735 #3268)
-#3266 := (iff #2732 #3265)
-#3267 := [rewrite]: #3266
-#3261 := (iff #1257 #3252)
-#3253 := (not #3252)
-#3256 := (not #3253)
-#3259 := (iff #3256 #3252)
-#3260 := [rewrite]: #3259
-#3257 := (iff #1257 #3256)
-#3254 := (iff #1254 #3253)
-#3255 := [rewrite]: #3254
-#3258 := [monotonicity #3255]: #3257
-#3262 := [trans #3258 #3260]: #3261
-#3270 := [monotonicity #3262 #3267]: #3269
-#3275 := [trans #3270 #3273]: #3274
-#3278 := [quant-intro #3275]: #3277
-#3338 := [monotonicity #3278 #3335]: #3337
-#3346 := [trans #3338 #3344]: #3345
-#3250 := (iff #2696 #3247)
-#3242 := (and #2039 #2656 #3239)
-#3248 := (iff #3242 #3247)
-#3249 := [rewrite]: #3248
-#3243 := (iff #2696 #3242)
-#3240 := (iff #2690 #3239)
-#3237 := (iff #2687 #3228)
-#3229 := (not #3228)
-#3232 := (not #3229)
-#3235 := (iff #3232 #3228)
-#3236 := [rewrite]: #3235
-#3233 := (iff #2687 #3232)
-#3230 := (iff #2684 #3229)
-#3231 := [rewrite]: #3230
-#3234 := [monotonicity #3231]: #3233
-#3238 := [trans #3234 #3236]: #3237
-#3241 := [quant-intro #3238]: #3240
-#3244 := [monotonicity #3241]: #3243
-#3251 := [trans #3244 #3249]: #3250
-#3349 := [monotonicity #3251 #3346]: #3348
-#3225 := (iff #2143 #3224)
-#3222 := (iff #2140 #3213)
-#3214 := (not #3213)
-#3217 := (not #3214)
-#3220 := (iff #3217 #3213)
-#3221 := [rewrite]: #3220
-#3218 := (iff #2140 #3217)
-#3215 := (iff #1325 #3214)
+#3278 := (iff #2759 #3277)
+#3275 := (iff #2756 #3274)
+#3276 := [rewrite]: #3275
+#3270 := (iff #1324 #3261)
+#3262 := (not #3261)
+#3265 := (not #3262)
+#3268 := (iff #3265 #3261)
+#3269 := [rewrite]: #3268
+#3266 := (iff #1324 #3265)
+#3263 := (iff #1321 #3262)
+#3264 := [rewrite]: #3263
+#3267 := [monotonicity #3264]: #3266
+#3271 := [trans #3267 #3269]: #3270
+#3279 := [monotonicity #3271 #3276]: #3278
+#3284 := [trans #3279 #3282]: #3283
+#3287 := [quant-intro #3284]: #3286
+#3347 := [monotonicity #3287 #3344]: #3346
+#3355 := [trans #3347 #3353]: #3354
+#3259 := (iff #2720 #3256)
+#3251 := (and #2063 #2680 #3248)
+#3257 := (iff #3251 #3256)
+#3258 := [rewrite]: #3257
+#3252 := (iff #2720 #3251)
+#3249 := (iff #2714 #3248)
+#3246 := (iff #2711 #3237)
+#3238 := (not #3237)
+#3241 := (not #3238)
+#3244 := (iff #3241 #3237)
+#3245 := [rewrite]: #3244
+#3242 := (iff #2711 #3241)
+#3239 := (iff #2708 #3238)
+#3240 := [rewrite]: #3239
+#3243 := [monotonicity #3240]: #3242
+#3247 := [trans #3243 #3245]: #3246
+#3250 := [quant-intro #3247]: #3249
+#3253 := [monotonicity #3250]: #3252
+#3260 := [trans #3253 #3258]: #3259
+#3358 := [monotonicity #3260 #3355]: #3357
+#3234 := (iff #2167 #3233)
+#3231 := (iff #2164 #3222)
+#3223 := (not #3222)
+#3226 := (not #3223)
+#3229 := (iff #3226 #3222)
+#3230 := [rewrite]: #3229
+#3227 := (iff #2164 #3226)
+#3224 := (iff #1392 #3223)
+#3225 := [rewrite]: #3224
+#3228 := [monotonicity #3225]: #3227
+#3232 := [trans #3228 #3230]: #3231
+#3235 := [quant-intro #3232]: #3234
+#3361 := [monotonicity #3235 #3358]: #3360
+#3369 := [trans #3361 #3367]: #3368
+#3598 := [monotonicity #3369 #3595]: #3597
+#3220 := (iff #2666 #3219)
+#3217 := (iff #2663 #3214)
+#3194 := (or #57 #1272)
+#3211 := (or #3194 #3208)
+#3215 := (iff #3211 #3214)
 #3216 := [rewrite]: #3215
-#3219 := [monotonicity #3216]: #3218
-#3223 := [trans #3219 #3221]: #3222
-#3226 := [quant-intro #3223]: #3225
-#3352 := [monotonicity #3226 #3349]: #3351
-#3360 := [trans #3352 #3358]: #3359
-#3589 := [monotonicity #3360 #3586]: #3588
-#3211 := (iff #2642 #3210)
-#3208 := (iff #2639 #3205)
-#3185 := (or #24 #1205)
-#3202 := (or #3185 #3199)
-#3206 := (iff #3202 #3205)
-#3207 := [rewrite]: #3206
-#3203 := (iff #2639 #3202)
-#3200 := (iff #2636 #3199)
-#3201 := [rewrite]: #3200
-#3194 := (iff #1212 #3185)
-#3186 := (not #3185)
-#3189 := (not #3186)
-#3192 := (iff #3189 #3185)
-#3193 := [rewrite]: #3192
-#3190 := (iff #1212 #3189)
-#3187 := (iff #1209 #3186)
+#3212 := (iff #2663 #3211)
+#3209 := (iff #2660 #3208)
+#3210 := [rewrite]: #3209
+#3203 := (iff #1279 #3194)
+#3195 := (not #3194)
+#3198 := (not #3195)
+#3201 := (iff #3198 #3194)
+#3202 := [rewrite]: #3201
+#3199 := (iff #1279 #3198)
+#3196 := (iff #1276 #3195)
+#3197 := [rewrite]: #3196
+#3200 := [monotonicity #3197]: #3199
+#3204 := [trans #3200 #3202]: #3203
+#3213 := [monotonicity #3204 #3210]: #3212
+#3218 := [trans #3213 #3216]: #3217
+#3221 := [quant-intro #3218]: #3220
+#3192 := (iff #2626 #3191)
+#3189 := (iff #2623 #3186)
+#3166 := (or #57 #1234)
+#3183 := (or #3166 #3180)
+#3187 := (iff #3183 #3186)
 #3188 := [rewrite]: #3187
-#3191 := [monotonicity #3188]: #3190
-#3195 := [trans #3191 #3193]: #3194
-#3204 := [monotonicity #3195 #3201]: #3203
-#3209 := [trans #3204 #3207]: #3208
-#3212 := [quant-intro #3209]: #3211
-#3183 := (iff #2602 #3182)
-#3180 := (iff #2599 #3177)
-#3157 := (or #24 #1167)
-#3174 := (or #3157 #3171)
-#3178 := (iff #3174 #3177)
-#3179 := [rewrite]: #3178
-#3175 := (iff #2599 #3174)
-#3172 := (iff #2596 #3171)
-#3173 := [rewrite]: #3172
-#3166 := (iff #1174 #3157)
-#3158 := (not #3157)
-#3161 := (not #3158)
-#3164 := (iff #3161 #3157)
-#3165 := [rewrite]: #3164
-#3162 := (iff #1174 #3161)
-#3159 := (iff #1171 #3158)
+#3184 := (iff #2623 #3183)
+#3181 := (iff #2620 #3180)
+#3182 := [rewrite]: #3181
+#3175 := (iff #1241 #3166)
+#3167 := (not #3166)
+#3170 := (not #3167)
+#3173 := (iff #3170 #3166)
+#3174 := [rewrite]: #3173
+#3171 := (iff #1241 #3170)
+#3168 := (iff #1238 #3167)
+#3169 := [rewrite]: #3168
+#3172 := [monotonicity #3169]: #3171
+#3176 := [trans #3172 #3174]: #3175
+#3185 := [monotonicity #3176 #3182]: #3184
+#3190 := [trans #3185 #3188]: #3189
+#3193 := [quant-intro #3190]: #3192
+#3164 := (iff #1703 #3163)
+#3161 := (iff #1698 #3158)
+#3144 := (or #506 #3143)
+#3155 := (or #3144 #1288)
+#3159 := (iff #3155 #3158)
 #3160 := [rewrite]: #3159
-#3163 := [monotonicity #3160]: #3162
-#3167 := [trans #3163 #3165]: #3166
-#3176 := [monotonicity #3167 #3173]: #3175
-#3181 := [trans #3176 #3179]: #3180
-#3184 := [quant-intro #3181]: #3183
-#3155 := (iff #1636 #3154)
-#3152 := (iff #1631 #3149)
-#3135 := (or #447 #3134)
-#3146 := (or #3135 #1221)
-#3150 := (iff #3146 #3149)
-#3151 := [rewrite]: #3150
-#3147 := (iff #1631 #3146)
-#3144 := (iff #462 #3135)
-#3136 := (not #3135)
-#3139 := (not #3136)
-#3142 := (iff #3139 #3135)
-#3143 := [rewrite]: #3142
-#3140 := (iff #462 #3139)
-#3137 := (iff #456 #3136)
-#3138 := [rewrite]: #3137
-#3141 := [monotonicity #3138]: #3140
-#3145 := [trans #3141 #3143]: #3144
-#3148 := [monotonicity #3145]: #3147
-#3153 := [trans #3148 #3151]: #3152
-#3156 := [quant-intro #3153]: #3155
-#3132 := (iff #1620 #3131)
-#3129 := (iff #1617 #3126)
-#3112 := (or #450 #1141)
-#3123 := (or #3112 #1614)
-#3127 := (iff #3123 #3126)
-#3128 := [rewrite]: #3127
-#3124 := (iff #1617 #3123)
-#3121 := (iff #1611 #3112)
-#3113 := (not #3112)
-#3116 := (not #3113)
-#3119 := (iff #3116 #3112)
-#3120 := [rewrite]: #3119
-#3117 := (iff #1611 #3116)
-#3114 := (iff #1606 #3113)
-#3115 := [rewrite]: #3114
-#3118 := [monotonicity #3115]: #3117
-#3122 := [trans #3118 #3120]: #3121
-#3125 := [monotonicity #3122]: #3124
-#3130 := [trans #3125 #3128]: #3129
-#3133 := [quant-intro #3130]: #3132
-#3592 := [monotonicity #3133 #3156 #3184 #3212 #3589]: #3591
-#3603 := [trans #3592 #3601]: #3602
-#3110 := (iff #2558 #3107)
-#3102 := (and #1931 #2518 #3099)
-#3108 := (iff #3102 #3107)
-#3109 := [rewrite]: #3108
-#3103 := (iff #2558 #3102)
-#3100 := (iff #2552 #3099)
-#3097 := (iff #2549 #3088)
-#3089 := (not #3088)
-#3092 := (not #3089)
-#3095 := (iff #3092 #3088)
-#3096 := [rewrite]: #3095
-#3093 := (iff #2549 #3092)
-#3090 := (iff #2546 #3089)
-#3091 := [rewrite]: #3090
-#3094 := [monotonicity #3091]: #3093
-#3098 := [trans #3094 #3096]: #3097
-#3101 := [quant-intro #3098]: #3100
-#3104 := [monotonicity #3101]: #3103
-#3111 := [trans #3104 #3109]: #3110
-#3606 := [monotonicity #3111 #3603]: #3605
-#3085 := (iff #1159 #3084)
-#3082 := (iff #1156 #3079)
-#3065 := (or #371 #1141)
-#3076 := (or #1136 #3065)
-#3080 := (iff #3076 #3079)
-#3081 := [rewrite]: #3080
-#3077 := (iff #1156 #3076)
-#3074 := (iff #1153 #3065)
-#3066 := (not #3065)
-#3069 := (not #3066)
-#3072 := (iff #3069 #3065)
-#3073 := [rewrite]: #3072
-#3070 := (iff #1153 #3069)
-#3067 := (iff #1148 #3066)
+#3156 := (iff #1698 #3155)
+#3153 := (iff #521 #3144)
+#3145 := (not #3144)
+#3148 := (not #3145)
+#3151 := (iff #3148 #3144)
+#3152 := [rewrite]: #3151
+#3149 := (iff #521 #3148)
+#3146 := (iff #515 #3145)
+#3147 := [rewrite]: #3146
+#3150 := [monotonicity #3147]: #3149
+#3154 := [trans #3150 #3152]: #3153
+#3157 := [monotonicity #3154]: #3156
+#3162 := [trans #3157 #3160]: #3161
+#3165 := [quant-intro #3162]: #3164
+#3141 := (iff #1687 #3140)
+#3138 := (iff #1684 #3135)
+#3121 := (or #509 #1208)
+#3132 := (or #3121 #1681)
+#3136 := (iff #3132 #3135)
+#3137 := [rewrite]: #3136
+#3133 := (iff #1684 #3132)
+#3130 := (iff #1678 #3121)
+#3122 := (not #3121)
+#3125 := (not #3122)
+#3128 := (iff #3125 #3121)
+#3129 := [rewrite]: #3128
+#3126 := (iff #1678 #3125)
+#3123 := (iff #1673 #3122)
+#3124 := [rewrite]: #3123
+#3127 := [monotonicity #3124]: #3126
+#3131 := [trans #3127 #3129]: #3130
+#3134 := [monotonicity #3131]: #3133
+#3139 := [trans #3134 #3137]: #3138
+#3142 := [quant-intro #3139]: #3141
+#3601 := [monotonicity #3142 #3165 #3193 #3221 #3598]: #3600
+#3612 := [trans #3601 #3610]: #3611
+#3119 := (iff #2582 #3116)
+#3111 := (and #1955 #2542 #3108)
+#3117 := (iff #3111 #3116)
+#3118 := [rewrite]: #3117
+#3112 := (iff #2582 #3111)
+#3109 := (iff #2576 #3108)
+#3106 := (iff #2573 #3097)
+#3098 := (not #3097)
+#3101 := (not #3098)
+#3104 := (iff #3101 #3097)
+#3105 := [rewrite]: #3104
+#3102 := (iff #2573 #3101)
+#3099 := (iff #2570 #3098)
+#3100 := [rewrite]: #3099
+#3103 := [monotonicity #3100]: #3102
+#3107 := [trans #3103 #3105]: #3106
+#3110 := [quant-intro #3107]: #3109
+#3113 := [monotonicity #3110]: #3112
+#3120 := [trans #3113 #3118]: #3119
+#3615 := [monotonicity #3120 #3612]: #3614
+#3094 := (iff #1226 #3093)
+#3091 := (iff #1223 #3088)
+#3074 := (or #430 #1208)
+#3085 := (or #1203 #3074)
+#3089 := (iff #3085 #3088)
+#3090 := [rewrite]: #3089
+#3086 := (iff #1223 #3085)
+#3083 := (iff #1220 #3074)
+#3075 := (not #3074)
+#3078 := (not #3075)
+#3081 := (iff #3078 #3074)
+#3082 := [rewrite]: #3081
+#3079 := (iff #1220 #3078)
+#3076 := (iff #1215 #3075)
+#3077 := [rewrite]: #3076
+#3080 := [monotonicity #3077]: #3079
+#3084 := [trans #3080 #3082]: #3083
+#3087 := [monotonicity #3084]: #3086
+#3092 := [trans #3087 #3090]: #3091
+#3095 := [quant-intro #3092]: #3094
+#3618 := [monotonicity #3095 #3615]: #3617
+#3626 := [trans #3618 #3624]: #3625
+#3072 := (iff #2536 #3071)
+#3069 := (iff #2533 #3066)
+#3052 := (or #1915 #3051)
+#3063 := (or #2524 #3052)
+#3067 := (iff #3063 #3066)
 #3068 := [rewrite]: #3067
-#3071 := [monotonicity #3068]: #3070
-#3075 := [trans #3071 #3073]: #3074
-#3078 := [monotonicity #3075]: #3077
-#3083 := [trans #3078 #3081]: #3082
-#3086 := [quant-intro #3083]: #3085
-#3609 := [monotonicity #3086 #3606]: #3608
-#3617 := [trans #3609 #3615]: #3616
-#3063 := (iff #2512 #3062)
-#3060 := (iff #2509 #3057)
-#3043 := (or #1891 #3042)
-#3054 := (or #2500 #3043)
-#3058 := (iff #3054 #3057)
-#3059 := [rewrite]: #3058
-#3055 := (iff #2509 #3054)
-#3052 := (iff #2506 #3043)
-#3044 := (not #3043)
-#3047 := (not #3044)
-#3050 := (iff #3047 #3043)
-#3051 := [rewrite]: #3050
-#3048 := (iff #2506 #3047)
-#3045 := (iff #2503 #3044)
-#3046 := [rewrite]: #3045
-#3049 := [monotonicity #3046]: #3048
-#3053 := [trans #3049 #3051]: #3052
-#3056 := [monotonicity #3053]: #3055
-#3061 := [trans #3056 #3059]: #3060
-#3064 := [monotonicity #3061]: #3063
-#3620 := [monotonicity #3064 #3617]: #3619
-#3040 := (iff #1128 #3039)
-#3037 := (iff #1123 #3034)
-#3020 := (or #368 #3019)
-#3031 := (or #3020 #1116)
-#3035 := (iff #3031 #3034)
-#3036 := [rewrite]: #3035
-#3032 := (iff #1123 #3031)
-#3029 := (iff #389 #3020)
-#3021 := (not #3020)
-#3024 := (not #3021)
-#3027 := (iff #3024 #3020)
-#3028 := [rewrite]: #3027
-#3025 := (iff #389 #3024)
-#3022 := (iff #383 #3021)
-#3023 := [rewrite]: #3022
-#3026 := [monotonicity #3023]: #3025
-#3030 := [trans #3026 #3028]: #3029
-#3033 := [monotonicity #3030]: #3032
-#3038 := [trans #3033 #3036]: #3037
-#3041 := [quant-intro #3038]: #3040
-#3623 := [monotonicity #3041 #3620]: #3622
-#3631 := [trans #3623 #3629]: #3630
-#3017 := (iff #2493 #3016)
-#3014 := (iff #2490 #3011)
-#2113 := (or #2112 #1868)
-#3008 := (or #2113 #2485)
-#3012 := (iff #3008 #3011)
-#3013 := [rewrite]: #3012
-#3009 := (iff #2490 #3008)
-#3006 := (iff #2474 #2113)
-#1828 := (not #2113)
-#1976 := (not #1828)
-#2468 := (iff #1976 #2113)
-#3005 := [rewrite]: #2468
-#2208 := (iff #2474 #1976)
-#1829 := (iff #2471 #1828)
-#1975 := [rewrite]: #1829
-#2209 := [monotonicity #1975]: #2208
-#3007 := [trans #2209 #3005]: #3006
-#3010 := [monotonicity #3007]: #3009
-#3015 := [trans #3010 #3013]: #3014
-#3018 := [monotonicity #3015]: #3017
-#3634 := [monotonicity #3018 #3631]: #3633
-#3637 := [monotonicity #3634]: #3636
-#3644 := [trans #3637 #3642]: #3643
-#3647 := [monotonicity #3644]: #3646
-#3650 := [monotonicity #3647]: #3649
-#3657 := [trans #3650 #3655]: #3656
-#3660 := [monotonicity #3657]: #3659
-#2301 := (+ #2300 #2298)
-#2302 := (= #2301 0::int)
-#2305 := (and #713 #2304 #2302)
-#2322 := (not #2305)
-#2325 := (forall (vars (?v1 S2)) #2322)
-#2310 := (= ?v0!20 f6)
-#2311 := (not #2310)
-#2312 := (and #2311 #2309)
-#2313 := (not #2312)
-#2319 := (not #2313)
-#2329 := (and #2319 #2325)
-#2334 := (and #1445 #2329)
-#2267 := (* -1::int #2266)
-#2269 := (+ #2268 #2267)
-#2272 := (+ #2271 #2269)
-#2273 := (>= #2272 0::int)
-#2280 := (and #2279 #2277)
-#2281 := (not #2280)
-#2282 := (or #2281 #2273)
-#2283 := (not #2282)
-#2338 := (or #2283 #2334)
-#2342 := (and #1421 #2338)
-#2240 := (* -1::int #2239)
-#2242 := (+ #2241 #2240)
-#2243 := (>= #2242 0::int)
-#2249 := (and #2248 #2245)
-#2250 := (not #2249)
-#2251 := (or #2250 #2243)
-#2252 := (not #2251)
-#2346 := (or #2252 #2342)
-#2350 := (and #1402 #2346)
-#2354 := (or #2225 #2350)
-#2219 := (not #1396)
-#2358 := (and #2219 #2354)
-#2362 := (or #1396 #2358)
-#2366 := (and #725 #2362)
-#2203 := (= #2202 #2201)
-#2204 := (or #2203 #2200)
-#2205 := (not #2204)
-#2370 := (or #2205 #2366)
-#2374 := (and #1388 #2370)
-#2181 := (* -1::int #2180)
-#2183 := (+ #2182 #2181)
-#2184 := (>= #2183 0::int)
-#2185 := (not #2184)
-#2378 := (or #2185 #2374)
-#2164 := (and #2163 #2160)
-#2150 := (not #901)
-#2398 := (and #2150 #671 #2164 #1377 #2378 #1535 #1553 #1561)
-#2091 := (* -1::int #2090)
-#2093 := (+ #2092 #2091)
-#2096 := (+ #2095 #2093)
-#2097 := (>= #2096 0::int)
-#2106 := (and #2105 #2101)
-#2107 := (not #2106)
-#2108 := (or #2107 #2097)
-#2109 := (not #2108)
-#2128 := (or #2109 #2124)
-#2067 := (+ #2066 #1248)
-#2070 := (+ #2069 #2067)
-#2071 := (= #2070 0::int)
-#2072 := (>= #2067 0::int)
-#2073 := (not #2072)
-#2074 := (and #2073 #2071)
-#2079 := (or #1257 #2074)
-#2082 := (forall (vars (?v0 S2)) #2079)
-#2132 := (and #2082 #2128)
-#2031 := (+ #2030 #2028)
-#2032 := (= #2031 0::int)
-#2035 := (and #2034 #2032)
-#2051 := (not #2035)
-#2054 := (forall (vars (?v1 S2)) #2051)
-#2040 := (= ?v0!8 f6)
-#2041 := (not #2040)
-#2042 := (and #2041 #2039)
-#2043 := (not #2042)
-#2048 := (not #2043)
-#2058 := (and #2048 #2054)
-#2136 := (or #2058 #2132)
-#2022 := (not #629)
-#2019 := (not #647)
-#2016 := (not #620)
-#2013 := (not #638)
-#2146 := (and #2013 #2016 #2019 #2022 #2136 #2143)
-#2402 := (or #2146 #2398)
-#1990 := (+ #1989 #1203)
-#1991 := (>= #1990 0::int)
-#1992 := (not #1991)
-#1995 := (+ #1994 #1990)
-#1996 := (= #1995 0::int)
-#1999 := (and #1998 #1996 #1992)
-#2004 := (or #1212 #1999)
-#2007 := (forall (vars (?v0 S2)) #2004)
-#1963 := (+ #1165 #1962)
-#1965 := (+ #1964 #1963)
-#1966 := (= #1965 0::int)
-#1967 := (+ #1964 #1165)
-#1968 := (>= #1967 0::int)
-#1969 := (not #1968)
-#1972 := (and #1971 #1969 #1966)
-#1977 := (or #1174 #1972)
-#1980 := (forall (vars (?v0 S2)) #1977)
-#1955 := (not #1653)
-#2427 := (and #1955 #1980 #2007 #2402 #1620 #1636 #1645)
-#1921 := (+ #1920 #1918)
-#1922 := (+ #25 #1921)
-#1923 := (= #1922 0::int)
-#1927 := (and #368 #1926 #1923)
-#1943 := (not #1927)
-#1946 := (forall (vars (?v1 S2)) #1943)
-#1932 := (= ?v0!5 f6)
-#1933 := (not #1932)
-#1934 := (and #1933 #1931)
-#1935 := (not #1934)
-#1940 := (not #1935)
-#1950 := (and #1940 #1946)
-#2431 := (or #1950 #2427)
-#2435 := (and #1159 #2431)
-#1895 := (and #1894 #1892)
-#1896 := (not #1895)
-#1899 := (+ #1898 #1888)
-#1901 := (+ #1900 #1899)
-#1902 := (>= #1901 0::int)
-#1903 := (or #1902 #1896)
-#1904 := (not #1903)
-#2439 := (or #1904 #2435)
-#2443 := (and #1128 #2439)
-#1861 := (* -1::int #1860)
-#1863 := (+ #1862 #1861)
-#1864 := (>= #1863 0::int)
-#1870 := (and #1869 #1866)
-#1871 := (not #1870)
-#1872 := (or #1871 #1864)
-#1873 := (not #1872)
-#2447 := (or #1873 #2443)
-#2451 := (and #1108 #2447)
-#2455 := (or #1846 #2451)
-#1814 := (not #1102)
-#2459 := (and #1814 #2455)
-#2463 := (or #1102 #2459)
-#3003 := (iff #2463 #3002)
-#3000 := (iff #2459 #2999)
-#2997 := (iff #2455 #2996)
-#2994 := (iff #2451 #2993)
-#2991 := (iff #2447 #2990)
-#2988 := (iff #2443 #2987)
-#2985 := (iff #2439 #2984)
-#2982 := (iff #2435 #2981)
-#2979 := (iff #2431 #2978)
-#2976 := (iff #2427 #2973)
-#2970 := (and #67 #2602 #2642 #2967 #1620 #1636 #1645)
-#2974 := (iff #2970 #2973)
-#2975 := [rewrite]: #2974
-#2971 := (iff #2427 #2970)
-#2968 := (iff #2402 #2967)
-#2965 := (iff #2398 #2962)
-#2959 := (and #148 #671 #2164 #1377 #2956 #1535 #1553 #1561)
-#2963 := (iff #2959 #2962)
-#2964 := [rewrite]: #2963
-#2960 := (iff #2398 #2959)
-#2957 := (iff #2378 #2956)
-#2954 := (iff #2374 #2953)
-#2951 := (iff #2370 #2950)
-#2948 := (iff #2366 #2947)
-#2945 := (iff #2362 #2944)
-#2942 := (iff #2358 #2941)
-#2939 := (iff #2354 #2938)
-#2936 := (iff #2350 #2935)
-#2933 := (iff #2346 #2932)
-#2930 := (iff #2342 #2929)
-#2927 := (iff #2338 #2926)
-#2924 := (iff #2334 #2921)
-#2884 := (and #2309 #2878)
-#2915 := (and #2884 #2912)
-#2918 := (and #1445 #2915)
-#2922 := (iff #2918 #2921)
-#2923 := [rewrite]: #2922
-#2919 := (iff #2334 #2918)
-#2916 := (iff #2329 #2915)
-#2913 := (iff #2325 #2912)
-#2910 := (iff #2322 #2909)
-#2907 := (iff #2305 #2906)
-#2904 := (iff #2302 #2903)
-#2901 := (= #2301 #2900)
-#2902 := [rewrite]: #2901
-#2905 := [monotonicity #2902]: #2904
-#2908 := [monotonicity #2905]: #2907
-#2911 := [monotonicity #2908]: #2910
-#2914 := [quant-intro #2911]: #2913
-#2897 := (iff #2319 #2884)
-#2889 := (not #2884)
-#2892 := (not #2889)
-#2895 := (iff #2892 #2884)
-#2896 := [rewrite]: #2895
-#2893 := (iff #2319 #2892)
-#2890 := (iff #2313 #2889)
-#2887 := (iff #2312 #2884)
-#2881 := (and #2878 #2309)
-#2885 := (iff #2881 #2884)
-#2886 := [rewrite]: #2885
-#2882 := (iff #2312 #2881)
-#2879 := (iff #2311 #2878)
-#2876 := (iff #2310 #2875)
-#2877 := [rewrite]: #2876
-#2880 := [monotonicity #2877]: #2879
-#2883 := [monotonicity #2880]: #2882
-#2888 := [trans #2883 #2886]: #2887
-#2891 := [monotonicity #2888]: #2890
-#2894 := [monotonicity #2891]: #2893
-#2898 := [trans #2894 #2896]: #2897
-#2917 := [monotonicity #2898 #2914]: #2916
-#2920 := [monotonicity #2917]: #2919
-#2925 := [trans #2920 #2923]: #2924
-#2873 := (iff #2283 #2872)
-#2870 := (iff #2282 #2869)
-#2867 := (iff #2273 #2864)
-#2854 := (+ #2268 #2271)
-#2855 := (+ #2267 #2854)
-#2858 := (>= #2855 0::int)
-#2865 := (iff #2858 #2864)
-#2866 := [rewrite]: #2865
-#2859 := (iff #2273 #2858)
-#2856 := (= #2272 #2855)
-#2857 := [rewrite]: #2856
-#2860 := [monotonicity #2857]: #2859
-#2868 := [trans #2860 #2866]: #2867
-#2852 := (iff #2281 #2851)
-#2849 := (iff #2280 #2848)
-#2850 := [rewrite]: #2849
-#2853 := [monotonicity #2850]: #2852
-#2871 := [monotonicity #2853 #2868]: #2870
-#2874 := [monotonicity #2871]: #2873
-#2928 := [monotonicity #2874 #2925]: #2927
-#2931 := [monotonicity #2928]: #2930
-#2846 := (iff #2252 #2845)
-#2843 := (iff #2251 #2842)
-#2840 := (iff #2243 #2837)
-#2829 := (+ #2240 #2241)
-#2832 := (>= #2829 0::int)
-#2838 := (iff #2832 #2837)
+#3064 := (iff #2533 #3063)
+#3061 := (iff #2530 #3052)
+#3053 := (not #3052)
+#3056 := (not #3053)
+#3059 := (iff #3056 #3052)
+#3060 := [rewrite]: #3059
+#3057 := (iff #2530 #3056)
+#3054 := (iff #2527 #3053)
+#3055 := [rewrite]: #3054
+#3058 := [monotonicity #3055]: #3057
+#3062 := [trans #3058 #3060]: #3061
+#3065 := [monotonicity #3062]: #3064
+#3070 := [trans #3065 #3068]: #3069
+#3073 := [monotonicity #3070]: #3072
+#3629 := [monotonicity #3073 #3626]: #3628
+#3049 := (iff #1195 #3048)
+#3046 := (iff #1190 #3043)
+#3029 := (or #427 #2492)
+#3040 := (or #3029 #1183)
+#3044 := (iff #3040 #3043)
+#3045 := [rewrite]: #3044
+#3041 := (iff #1190 #3040)
+#3038 := (iff #448 #3029)
+#3030 := (not #3029)
+#3033 := (not #3030)
+#3036 := (iff #3033 #3029)
+#3037 := [rewrite]: #3036
+#3034 := (iff #448 #3033)
+#3031 := (iff #442 #3030)
+#3032 := [rewrite]: #3031
+#3035 := [monotonicity #3032]: #3034
+#3039 := [trans #3035 #3037]: #3038
+#3042 := [monotonicity #3039]: #3041
+#3047 := [trans #3042 #3045]: #3046
+#3050 := [quant-intro #3047]: #3049
+#3632 := [monotonicity #3050 #3629]: #3631
+#3640 := [trans #3632 #3638]: #3639
+#2191 := (iff #2517 #1874)
+#2137 := (iff #2514 #2212)
+#2232 := (or #2102 #1892)
+#2280 := (or #2232 #2509)
+#2213 := (iff #2280 #2212)
+#2136 := [rewrite]: #2213
+#1931 := (iff #2514 #2280)
+#2000 := (iff #2498 #2232)
+#1837 := (not #2232)
+#2252 := (not #1837)
+#2027 := (iff #2252 #2232)
+#1999 := [rewrite]: #2027
+#2253 := (iff #2498 #2252)
+#1838 := (iff #2495 #1837)
+#2233 := [rewrite]: #1838
+#2026 := [monotonicity #2233]: #2253
+#2279 := [trans #2026 #1999]: #2000
+#1932 := [monotonicity #2279]: #1931
+#1873 := [trans #1932 #2136]: #2137
+#2192 := [monotonicity #1873]: #2191
+#3643 := [monotonicity #2192 #3640]: #3642
+#3646 := [monotonicity #3643]: #3645
+#3653 := [trans #3646 #3651]: #3652
+#3656 := [monotonicity #3653]: #3655
+#3659 := [monotonicity #3656]: #3658
+#3666 := [trans #3659 #3664]: #3665
+#3669 := [monotonicity #3666]: #3668
+#2325 := (+ #2324 #2322)
+#2326 := (= #2325 0::int)
+#2329 := (and #780 #2328 #2326)
+#2346 := (not #2329)
+#2349 := (forall (vars (?v1 S3)) #2346)
+#2334 := (= ?v0!20 f10)
+#2335 := (not #2334)
+#2336 := (and #2335 #2333)
+#2337 := (not #2336)
+#2343 := (not #2337)
+#2353 := (and #2343 #2349)
+#2358 := (and #1512 #2353)
+#2291 := (* -1::int #2290)
+#2293 := (+ #2292 #2291)
+#2296 := (+ #2295 #2293)
+#2297 := (>= #2296 0::int)
+#2304 := (and #2303 #2301)
+#2305 := (not #2304)
+#2306 := (or #2305 #2297)
+#2307 := (not #2306)
+#2362 := (or #2307 #2358)
+#2366 := (and #1488 #2362)
+#2264 := (* -1::int #2263)
+#2266 := (+ #2265 #2264)
+#2267 := (>= #2266 0::int)
+#2273 := (and #2272 #2269)
+#2274 := (not #2273)
+#2275 := (or #2274 #2267)
+#2276 := (not #2275)
+#2370 := (or #2276 #2366)
+#2374 := (and #1469 #2370)
+#2378 := (or #2249 #2374)
+#2243 := (not #1463)
+#2382 := (and #2243 #2378)
+#2386 := (or #1463 #2382)
+#2390 := (and #792 #2386)
+#2227 := (= #2226 #2225)
+#2228 := (or #2227 #2224)
+#2229 := (not #2228)
+#2394 := (or #2229 #2390)
+#2398 := (and #1455 #2394)
+#2205 := (* -1::int #2204)
+#2207 := (+ #2206 #2205)
+#2208 := (>= #2207 0::int)
+#2209 := (not #2208)
+#2402 := (or #2209 #2398)
+#2188 := (and #2187 #2184)
+#2176 := (not #968)
+#2422 := (and #730 #2176 #2188 #1444 #2402 #1602 #1620 #1628)
+#2115 := (* -1::int #2114)
+#2117 := (+ #2116 #2115)
+#2120 := (+ #2119 #2117)
+#2121 := (>= #2120 0::int)
+#2130 := (and #2129 #2125)
+#2131 := (not #2130)
+#2132 := (or #2131 #2121)
+#2133 := (not #2132)
+#2152 := (or #2133 #2148)
+#2091 := (+ #2090 #1315)
+#2094 := (+ #2093 #2091)
+#2095 := (= #2094 0::int)
+#2096 := (>= #2091 0::int)
+#2097 := (not #2096)
+#2098 := (and #2097 #2095)
+#2103 := (or #1324 #2098)
+#2106 := (forall (vars (?v0 S3)) #2103)
+#2156 := (and #2106 #2152)
+#2055 := (+ #2054 #2052)
+#2056 := (= #2055 0::int)
+#2059 := (and #2058 #2056)
+#2075 := (not #2059)
+#2078 := (forall (vars (?v1 S3)) #2075)
+#2064 := (= ?v0!8 f10)
+#2065 := (not #2064)
+#2066 := (and #2065 #2063)
+#2067 := (not #2066)
+#2072 := (not #2067)
+#2082 := (and #2072 #2078)
+#2160 := (or #2082 #2156)
+#2046 := (not #688)
+#2043 := (not #706)
+#2040 := (not #679)
+#2037 := (not #697)
+#2170 := (and #2037 #2040 #2043 #2046 #2160 #2167)
+#2426 := (or #2170 #2422)
+#2014 := (+ #2013 #1270)
+#2015 := (>= #2014 0::int)
+#2016 := (not #2015)
+#2019 := (+ #2018 #2014)
+#2020 := (= #2019 0::int)
+#2023 := (and #2022 #2020 #2016)
+#2028 := (or #1279 #2023)
+#2031 := (forall (vars (?v0 S3)) #2028)
+#1987 := (+ #1232 #1986)
+#1989 := (+ #1988 #1987)
+#1990 := (= #1989 0::int)
+#1991 := (+ #1988 #1232)
+#1992 := (>= #1991 0::int)
+#1993 := (not #1992)
+#1996 := (and #1995 #1993 #1990)
+#2001 := (or #1241 #1996)
+#2004 := (forall (vars (?v0 S3)) #2001)
+#1979 := (not #1720)
+#2451 := (and #1979 #2004 #2031 #2426 #1687 #1703 #1712)
+#1945 := (+ #1944 #1942)
+#1946 := (+ #58 #1945)
+#1947 := (= #1946 0::int)
+#1951 := (and #427 #1950 #1947)
+#1967 := (not #1951)
+#1970 := (forall (vars (?v1 S3)) #1967)
+#1956 := (= ?v0!5 f10)
+#1957 := (not #1956)
+#1958 := (and #1957 #1955)
+#1959 := (not #1958)
+#1964 := (not #1959)
+#1974 := (and #1964 #1970)
+#2455 := (or #1974 #2451)
+#2459 := (and #1226 #2455)
+#1919 := (and #1918 #1916)
+#1920 := (not #1919)
+#1923 := (+ #1922 #1912)
+#1925 := (+ #1924 #1923)
+#1926 := (>= #1925 0::int)
+#1927 := (or #1926 #1920)
+#1928 := (not #1927)
+#2463 := (or #1928 #2459)
+#2467 := (and #1195 #2463)
+#1885 := (* -1::int #1884)
+#1887 := (+ #1886 #1885)
+#1888 := (>= #1887 0::int)
+#1894 := (and #1893 #1890)
+#1895 := (not #1894)
+#1896 := (or #1895 #1888)
+#1897 := (not #1896)
+#2471 := (or #1897 #2467)
+#2475 := (and #1175 #2471)
+#2479 := (or #1870 #2475)
+#1833 := (not #1169)
+#2483 := (and #1833 #2479)
+#2487 := (or #1169 #2483)
+#3027 := (iff #2487 #3026)
+#3024 := (iff #2483 #3023)
+#3021 := (iff #2479 #3020)
+#3018 := (iff #2475 #3017)
+#3015 := (iff #2471 #3014)
+#3012 := (iff #2467 #3011)
+#3009 := (iff #2463 #3008)
+#3006 := (iff #2459 #3005)
+#3003 := (iff #2455 #3002)
+#3000 := (iff #2451 #2997)
+#2994 := (and #100 #2626 #2666 #2991 #1687 #1703 #1712)
+#2998 := (iff #2994 #2997)
+#2999 := [rewrite]: #2998
+#2995 := (iff #2451 #2994)
+#2992 := (iff #2426 #2991)
+#2989 := (iff #2422 #2986)
+#2983 := (and #730 #749 #2188 #1444 #2980 #1602 #1620 #1628)
+#2987 := (iff #2983 #2986)
+#2988 := [rewrite]: #2987
+#2984 := (iff #2422 #2983)
+#2981 := (iff #2402 #2980)
+#2978 := (iff #2398 #2977)
+#2975 := (iff #2394 #2974)
+#2972 := (iff #2390 #2971)
+#2969 := (iff #2386 #2968)
+#2966 := (iff #2382 #2965)
+#2963 := (iff #2378 #2962)
+#2960 := (iff #2374 #2959)
+#2957 := (iff #2370 #2956)
+#2954 := (iff #2366 #2953)
+#2951 := (iff #2362 #2950)
+#2948 := (iff #2358 #2945)
+#2908 := (and #2333 #2902)
+#2939 := (and #2908 #2936)
+#2942 := (and #1512 #2939)
+#2946 := (iff #2942 #2945)
+#2947 := [rewrite]: #2946
+#2943 := (iff #2358 #2942)
+#2940 := (iff #2353 #2939)
+#2937 := (iff #2349 #2936)
+#2934 := (iff #2346 #2933)
+#2931 := (iff #2329 #2930)
+#2928 := (iff #2326 #2927)
+#2925 := (= #2325 #2924)
+#2926 := [rewrite]: #2925
+#2929 := [monotonicity #2926]: #2928
+#2932 := [monotonicity #2929]: #2931
+#2935 := [monotonicity #2932]: #2934
+#2938 := [quant-intro #2935]: #2937
+#2921 := (iff #2343 #2908)
+#2913 := (not #2908)
+#2916 := (not #2913)
+#2919 := (iff #2916 #2908)
+#2920 := [rewrite]: #2919
+#2917 := (iff #2343 #2916)
+#2914 := (iff #2337 #2913)
+#2911 := (iff #2336 #2908)
+#2905 := (and #2902 #2333)
+#2909 := (iff #2905 #2908)
+#2910 := [rewrite]: #2909
+#2906 := (iff #2336 #2905)
+#2903 := (iff #2335 #2902)
+#2900 := (iff #2334 #2899)
+#2901 := [rewrite]: #2900
+#2904 := [monotonicity #2901]: #2903
+#2907 := [monotonicity #2904]: #2906
+#2912 := [trans #2907 #2910]: #2911
+#2915 := [monotonicity #2912]: #2914
+#2918 := [monotonicity #2915]: #2917
+#2922 := [trans #2918 #2920]: #2921
+#2941 := [monotonicity #2922 #2938]: #2940
+#2944 := [monotonicity #2941]: #2943
+#2949 := [trans #2944 #2947]: #2948
+#2897 := (iff #2307 #2896)
+#2894 := (iff #2306 #2893)
+#2891 := (iff #2297 #2888)
+#2878 := (+ #2292 #2295)
+#2879 := (+ #2291 #2878)
+#2882 := (>= #2879 0::int)
+#2889 := (iff #2882 #2888)
+#2890 := [rewrite]: #2889
+#2883 := (iff #2297 #2882)
+#2880 := (= #2296 #2879)
+#2881 := [rewrite]: #2880
+#2884 := [monotonicity #2881]: #2883
+#2892 := [trans #2884 #2890]: #2891
+#2876 := (iff #2305 #2875)
+#2873 := (iff #2304 #2872)
+#2874 := [rewrite]: #2873
+#2877 := [monotonicity #2874]: #2876
+#2895 := [monotonicity #2877 #2892]: #2894
+#2898 := [monotonicity #2895]: #2897
+#2952 := [monotonicity #2898 #2949]: #2951
+#2955 := [monotonicity #2952]: #2954
+#2870 := (iff #2276 #2869)
+#2867 := (iff #2275 #2866)
+#2864 := (iff #2267 #2861)
+#2853 := (+ #2264 #2265)
+#2856 := (>= #2853 0::int)
+#2862 := (iff #2856 #2861)
+#2863 := [rewrite]: #2862
+#2857 := (iff #2267 #2856)
+#2854 := (= #2266 #2853)
+#2855 := [rewrite]: #2854
+#2858 := [monotonicity #2855]: #2857
+#2865 := [trans #2858 #2863]: #2864
+#2851 := (iff #2274 #2850)
+#2848 := (iff #2273 #2847)
+#2849 := [rewrite]: #2848
+#2852 := [monotonicity #2849]: #2851
+#2868 := [monotonicity #2852 #2865]: #2867
+#2871 := [monotonicity #2868]: #2870
+#2958 := [monotonicity #2871 #2955]: #2957
+#2961 := [monotonicity #2958]: #2960
+#2964 := [monotonicity #2961]: #2963
+#2845 := (iff #2243 #204)
+#2846 := [rewrite]: #2845
+#2967 := [monotonicity #2846 #2964]: #2966
+#2970 := [monotonicity #2967]: #2969
+#2973 := [monotonicity #2970]: #2972
+#2843 := (iff #2229 #2842)
+#2840 := (iff #2228 #2837)
+#2834 := (or #2831 #2224)
+#2838 := (iff #2834 #2837)
 #2839 := [rewrite]: #2838
-#2833 := (iff #2243 #2832)
-#2830 := (= #2242 #2829)
-#2831 := [rewrite]: #2830
-#2834 := [monotonicity #2831]: #2833
-#2841 := [trans #2834 #2839]: #2840
-#2827 := (iff #2250 #2826)
-#2824 := (iff #2249 #2823)
+#2835 := (iff #2228 #2834)
+#2832 := (iff #2227 #2831)
+#2833 := [rewrite]: #2832
+#2836 := [monotonicity #2833]: #2835
+#2841 := [trans #2836 #2839]: #2840
+#2844 := [monotonicity #2841]: #2843
+#2976 := [monotonicity #2844 #2973]: #2975
+#2979 := [monotonicity #2976]: #2978
+#2829 := (iff #2209 #2828)
+#2826 := (iff #2208 #2823)
+#2815 := (+ #2205 #2206)
+#2818 := (>= #2815 0::int)
+#2824 := (iff #2818 #2823)
 #2825 := [rewrite]: #2824
-#2828 := [monotonicity #2825]: #2827
-#2844 := [monotonicity #2828 #2841]: #2843
-#2847 := [monotonicity #2844]: #2846
-#2934 := [monotonicity #2847 #2931]: #2933
-#2937 := [monotonicity #2934]: #2936
-#2940 := [monotonicity #2937]: #2939
-#2821 := (iff #2219 #170)
-#2822 := [rewrite]: #2821
-#2943 := [monotonicity #2822 #2940]: #2942
-#2946 := [monotonicity #2943]: #2945
-#2949 := [monotonicity #2946]: #2948
-#2819 := (iff #2205 #2818)
-#2816 := (iff #2204 #2813)
-#2810 := (or #2807 #2200)
-#2814 := (iff #2810 #2813)
-#2815 := [rewrite]: #2814
-#2811 := (iff #2204 #2810)
-#2808 := (iff #2203 #2807)
-#2809 := [rewrite]: #2808
-#2812 := [monotonicity #2809]: #2811
-#2817 := [trans #2812 #2815]: #2816
+#2819 := (iff #2208 #2818)
+#2816 := (= #2207 #2815)
+#2817 := [rewrite]: #2816
 #2820 := [monotonicity #2817]: #2819
-#2952 := [monotonicity #2820 #2949]: #2951
-#2955 := [monotonicity #2952]: #2954
-#2805 := (iff #2185 #2804)
-#2802 := (iff #2184 #2799)
-#2791 := (+ #2181 #2182)
-#2794 := (>= #2791 0::int)
-#2800 := (iff #2794 #2799)
-#2801 := [rewrite]: #2800
-#2795 := (iff #2184 #2794)
-#2792 := (= #2183 #2791)
-#2793 := [rewrite]: #2792
-#2796 := [monotonicity #2793]: #2795
-#2803 := [trans #2796 #2801]: #2802
-#2806 := [monotonicity #2803]: #2805
-#2958 := [monotonicity #2806 #2955]: #2957
-#2789 := (iff #2150 #148)
-#2790 := [rewrite]: #2789
-#2961 := [monotonicity #2790 #2958]: #2960
-#2966 := [trans #2961 #2964]: #2965
-#2787 := (iff #2146 #2784)
-#2781 := (and #103 #108 #535 #538 #2778 #2143)
-#2785 := (iff #2781 #2784)
-#2786 := [rewrite]: #2785
-#2782 := (iff #2146 #2781)
-#2779 := (iff #2136 #2778)
-#2776 := (iff #2132 #2775)
-#2773 := (iff #2128 #2770)
-#2767 := (or #2764 #2124)
-#2771 := (iff #2767 #2770)
-#2772 := [rewrite]: #2771
-#2768 := (iff #2128 #2767)
-#2765 := (iff #2109 #2764)
-#2762 := (iff #2108 #2761)
-#2759 := (iff #2097 #2756)
-#2747 := (+ #2092 #2095)
-#2748 := (+ #2091 #2747)
-#2751 := (>= #2748 0::int)
-#2757 := (iff #2751 #2756)
-#2758 := [rewrite]: #2757
-#2752 := (iff #2097 #2751)
-#2749 := (= #2096 #2748)
-#2750 := [rewrite]: #2749
-#2753 := [monotonicity #2750]: #2752
-#2760 := [trans #2753 #2758]: #2759
-#2745 := (iff #2107 #2744)
-#2742 := (iff #2106 #2741)
-#2743 := [rewrite]: #2742
-#2746 := [monotonicity #2743]: #2745
-#2763 := [monotonicity #2746 #2760]: #2762
-#2766 := [monotonicity #2763]: #2765
-#2769 := [monotonicity #2766]: #2768
-#2774 := [trans #2769 #2772]: #2773
-#2739 := (iff #2082 #2738)
-#2736 := (iff #2079 #2735)
-#2733 := (iff #2074 #2732)
-#2730 := (iff #2071 #2727)
-#2717 := (+ #2066 #2069)
-#2718 := (+ #1248 #2717)
-#2721 := (= #2718 0::int)
-#2728 := (iff #2721 #2727)
-#2729 := [rewrite]: #2728
-#2722 := (iff #2071 #2721)
-#2719 := (= #2070 #2718)
-#2720 := [rewrite]: #2719
-#2723 := [monotonicity #2720]: #2722
-#2731 := [trans #2723 #2729]: #2730
-#2715 := (iff #2073 #2714)
-#2712 := (iff #2072 #2709)
-#2701 := (+ #1248 #2066)
-#2704 := (>= #2701 0::int)
-#2710 := (iff #2704 #2709)
-#2711 := [rewrite]: #2710
-#2705 := (iff #2072 #2704)
-#2702 := (= #2067 #2701)
-#2703 := [rewrite]: #2702
-#2706 := [monotonicity #2703]: #2705
-#2713 := [trans #2706 #2711]: #2712
-#2716 := [monotonicity #2713]: #2715
-#2734 := [monotonicity #2716 #2731]: #2733
-#2737 := [monotonicity #2734]: #2736
-#2740 := [quant-intro #2737]: #2739
-#2777 := [monotonicity #2740 #2774]: #2776
-#2699 := (iff #2058 #2696)
-#2662 := (and #2039 #2656)
-#2693 := (and #2662 #2690)
-#2697 := (iff #2693 #2696)
+#2827 := [trans #2820 #2825]: #2826
+#2830 := [monotonicity #2827]: #2829
+#2982 := [monotonicity #2830 #2979]: #2981
+#2813 := (iff #2176 #749)
+#2814 := [rewrite]: #2813
+#2985 := [monotonicity #2814 #2982]: #2984
+#2990 := [trans #2985 #2988]: #2989
+#2811 := (iff #2170 #2808)
+#2805 := (and #136 #141 #594 #597 #2802 #2167)
+#2809 := (iff #2805 #2808)
+#2810 := [rewrite]: #2809
+#2806 := (iff #2170 #2805)
+#2803 := (iff #2160 #2802)
+#2800 := (iff #2156 #2799)
+#2797 := (iff #2152 #2794)
+#2791 := (or #2788 #2148)
+#2795 := (iff #2791 #2794)
+#2796 := [rewrite]: #2795
+#2792 := (iff #2152 #2791)
+#2789 := (iff #2133 #2788)
+#2786 := (iff #2132 #2785)
+#2783 := (iff #2121 #2780)
+#2771 := (+ #2116 #2119)
+#2772 := (+ #2115 #2771)
+#2775 := (>= #2772 0::int)
+#2781 := (iff #2775 #2780)
+#2782 := [rewrite]: #2781
+#2776 := (iff #2121 #2775)
+#2773 := (= #2120 #2772)
+#2774 := [rewrite]: #2773
+#2777 := [monotonicity #2774]: #2776
+#2784 := [trans #2777 #2782]: #2783
+#2769 := (iff #2131 #2768)
+#2766 := (iff #2130 #2765)
+#2767 := [rewrite]: #2766
+#2770 := [monotonicity #2767]: #2769
+#2787 := [monotonicity #2770 #2784]: #2786
+#2790 := [monotonicity #2787]: #2789
+#2793 := [monotonicity #2790]: #2792
+#2798 := [trans #2793 #2796]: #2797
+#2763 := (iff #2106 #2762)
+#2760 := (iff #2103 #2759)
+#2757 := (iff #2098 #2756)
+#2754 := (iff #2095 #2751)
+#2741 := (+ #2090 #2093)
+#2742 := (+ #1315 #2741)
+#2745 := (= #2742 0::int)
+#2752 := (iff #2745 #2751)
+#2753 := [rewrite]: #2752
+#2746 := (iff #2095 #2745)
+#2743 := (= #2094 #2742)
+#2744 := [rewrite]: #2743
+#2747 := [monotonicity #2744]: #2746
+#2755 := [trans #2747 #2753]: #2754
+#2739 := (iff #2097 #2738)
+#2736 := (iff #2096 #2733)
+#2725 := (+ #1315 #2090)
+#2728 := (>= #2725 0::int)
+#2734 := (iff #2728 #2733)
+#2735 := [rewrite]: #2734
+#2729 := (iff #2096 #2728)
+#2726 := (= #2091 #2725)
+#2727 := [rewrite]: #2726
+#2730 := [monotonicity #2727]: #2729
+#2737 := [trans #2730 #2735]: #2736
+#2740 := [monotonicity #2737]: #2739
+#2758 := [monotonicity #2740 #2755]: #2757
+#2761 := [monotonicity #2758]: #2760
+#2764 := [quant-intro #2761]: #2763
+#2801 := [monotonicity #2764 #2798]: #2800
+#2723 := (iff #2082 #2720)
+#2686 := (and #2063 #2680)
+#2717 := (and #2686 #2714)
+#2721 := (iff #2717 #2720)
+#2722 := [rewrite]: #2721
+#2718 := (iff #2082 #2717)
+#2715 := (iff #2078 #2714)
+#2712 := (iff #2075 #2711)
+#2709 := (iff #2059 #2708)
+#2706 := (iff #2056 #2705)
+#2703 := (= #2055 #2702)
+#2704 := [rewrite]: #2703
+#2707 := [monotonicity #2704]: #2706
+#2710 := [monotonicity #2707]: #2709
+#2713 := [monotonicity #2710]: #2712
+#2716 := [quant-intro #2713]: #2715
+#2699 := (iff #2072 #2686)
+#2691 := (not #2686)
+#2694 := (not #2691)
+#2697 := (iff #2694 #2686)
 #2698 := [rewrite]: #2697
-#2694 := (iff #2058 #2693)
-#2691 := (iff #2054 #2690)
-#2688 := (iff #2051 #2687)
-#2685 := (iff #2035 #2684)
-#2682 := (iff #2032 #2681)
-#2679 := (= #2031 #2678)
-#2680 := [rewrite]: #2679
-#2683 := [monotonicity #2680]: #2682
-#2686 := [monotonicity #2683]: #2685
-#2689 := [monotonicity #2686]: #2688
-#2692 := [quant-intro #2689]: #2691
-#2675 := (iff #2048 #2662)
-#2667 := (not #2662)
-#2670 := (not #2667)
-#2673 := (iff #2670 #2662)
+#2695 := (iff #2072 #2694)
+#2692 := (iff #2067 #2691)
+#2689 := (iff #2066 #2686)
+#2683 := (and #2680 #2063)
+#2687 := (iff #2683 #2686)
+#2688 := [rewrite]: #2687
+#2684 := (iff #2066 #2683)
+#2681 := (iff #2065 #2680)
+#2678 := (iff #2064 #2677)
+#2679 := [rewrite]: #2678
+#2682 := [monotonicity #2679]: #2681
+#2685 := [monotonicity #2682]: #2684
+#2690 := [trans #2685 #2688]: #2689
+#2693 := [monotonicity #2690]: #2692
+#2696 := [monotonicity #2693]: #2695
+#2700 := [trans #2696 #2698]: #2699
+#2719 := [monotonicity #2700 #2716]: #2718
+#2724 := [trans #2719 #2722]: #2723
+#2804 := [monotonicity #2724 #2801]: #2803
+#2675 := (iff #2046 #597)
+#2676 := [rewrite]: #2675
+#2673 := (iff #2043 #594)
 #2674 := [rewrite]: #2673
-#2671 := (iff #2048 #2670)
-#2668 := (iff #2043 #2667)
-#2665 := (iff #2042 #2662)
-#2659 := (and #2656 #2039)
-#2663 := (iff #2659 #2662)
-#2664 := [rewrite]: #2663
-#2660 := (iff #2042 #2659)
-#2657 := (iff #2041 #2656)
-#2654 := (iff #2040 #2653)
-#2655 := [rewrite]: #2654
-#2658 := [monotonicity #2655]: #2657
-#2661 := [monotonicity #2658]: #2660
-#2666 := [trans #2661 #2664]: #2665
-#2669 := [monotonicity #2666]: #2668
-#2672 := [monotonicity #2669]: #2671
-#2676 := [trans #2672 #2674]: #2675
-#2695 := [monotonicity #2676 #2692]: #2694
-#2700 := [trans #2695 #2698]: #2699
-#2780 := [monotonicity #2700 #2777]: #2779
-#2651 := (iff #2022 #538)
-#2652 := [rewrite]: #2651
-#2649 := (iff #2019 #535)
-#2650 := [rewrite]: #2649
-#2647 := (iff #2016 #108)
-#2648 := [rewrite]: #2647
-#2645 := (iff #2013 #103)
-#2646 := [rewrite]: #2645
-#2783 := [monotonicity #2646 #2648 #2650 #2652 #2780]: #2782
-#2788 := [trans #2783 #2786]: #2787
-#2969 := [monotonicity #2788 #2966]: #2968
-#2643 := (iff #2007 #2642)
-#2640 := (iff #2004 #2639)
-#2637 := (iff #1999 #2636)
-#2634 := (iff #1992 #2633)
-#2631 := (iff #1991 #2628)
-#2621 := (+ #1203 #1989)
-#2624 := (>= #2621 0::int)
-#2629 := (iff #2624 #2628)
-#2630 := [rewrite]: #2629
-#2625 := (iff #1991 #2624)
-#2622 := (= #1990 #2621)
-#2623 := [rewrite]: #2622
-#2626 := [monotonicity #2623]: #2625
-#2632 := [trans #2626 #2630]: #2631
+#2671 := (iff #2040 #141)
+#2672 := [rewrite]: #2671
+#2669 := (iff #2037 #136)
+#2670 := [rewrite]: #2669
+#2807 := [monotonicity #2670 #2672 #2674 #2676 #2804]: #2806
+#2812 := [trans #2807 #2810]: #2811
+#2993 := [monotonicity #2812 #2990]: #2992
+#2667 := (iff #2031 #2666)
+#2664 := (iff #2028 #2663)
+#2661 := (iff #2023 #2660)
+#2658 := (iff #2016 #2657)
+#2655 := (iff #2015 #2652)
+#2645 := (+ #1270 #2013)
+#2648 := (>= #2645 0::int)
+#2653 := (iff #2648 #2652)
+#2654 := [rewrite]: #2653
+#2649 := (iff #2015 #2648)
+#2646 := (= #2014 #2645)
+#2647 := [rewrite]: #2646
+#2650 := [monotonicity #2647]: #2649
+#2656 := [trans #2650 #2654]: #2655
+#2659 := [monotonicity #2656]: #2658
+#2643 := (iff #2020 #2640)
+#2629 := (+ #2013 #2018)
+#2630 := (+ #1270 #2629)
+#2633 := (= #2630 0::int)
+#2641 := (iff #2633 #2640)
+#2642 := [rewrite]: #2641
+#2634 := (iff #2020 #2633)
+#2631 := (= #2019 #2630)
+#2632 := [rewrite]: #2631
 #2635 := [monotonicity #2632]: #2634
-#2619 := (iff #1996 #2616)
-#2605 := (+ #1989 #1994)
-#2606 := (+ #1203 #2605)
+#2644 := [trans #2635 #2642]: #2643
+#2662 := [monotonicity #2644 #2659]: #2661
+#2665 := [monotonicity #2662]: #2664
+#2668 := [quant-intro #2665]: #2667
+#2627 := (iff #2004 #2626)
+#2624 := (iff #2001 #2623)
+#2621 := (iff #1996 #2620)
+#2618 := (iff #1990 #2615)
+#2605 := (+ #1986 #1988)
+#2606 := (+ #1232 #2605)
 #2609 := (= #2606 0::int)
-#2617 := (iff #2609 #2616)
-#2618 := [rewrite]: #2617
-#2610 := (iff #1996 #2609)
-#2607 := (= #1995 #2606)
+#2616 := (iff #2609 #2615)
+#2617 := [rewrite]: #2616
+#2610 := (iff #1990 #2609)
+#2607 := (= #1989 #2606)
 #2608 := [rewrite]: #2607
 #2611 := [monotonicity #2608]: #2610
-#2620 := [trans #2611 #2618]: #2619
-#2638 := [monotonicity #2620 #2635]: #2637
-#2641 := [monotonicity #2638]: #2640
-#2644 := [quant-intro #2641]: #2643
-#2603 := (iff #1980 #2602)
-#2600 := (iff #1977 #2599)
-#2597 := (iff #1972 #2596)
-#2594 := (iff #1966 #2591)
-#2581 := (+ #1962 #1964)
-#2582 := (+ #1165 #2581)
-#2585 := (= #2582 0::int)
-#2592 := (iff #2585 #2591)
-#2593 := [rewrite]: #2592
-#2586 := (iff #1966 #2585)
-#2583 := (= #1965 #2582)
+#2619 := [trans #2611 #2617]: #2618
+#2603 := (iff #1993 #2602)
+#2600 := (iff #1992 #2597)
+#2589 := (+ #1232 #1988)
+#2592 := (>= #2589 0::int)
+#2598 := (iff #2592 #2597)
+#2599 := [rewrite]: #2598
+#2593 := (iff #1992 #2592)
+#2590 := (= #1991 #2589)
+#2591 := [rewrite]: #2590
+#2594 := [monotonicity #2591]: #2593
+#2601 := [trans #2594 #2599]: #2600
+#2604 := [monotonicity #2601]: #2603
+#2622 := [monotonicity #2604 #2619]: #2621
+#2625 := [monotonicity #2622]: #2624
+#2628 := [quant-intro #2625]: #2627
+#2587 := (iff #1979 #100)
+#2588 := [rewrite]: #2587
+#2996 := [monotonicity #2588 #2628 #2668 #2993]: #2995
+#3001 := [trans #2996 #2999]: #3000
+#2585 := (iff #1974 #2582)
+#2548 := (and #1955 #2542)
+#2579 := (and #2548 #2576)
+#2583 := (iff #2579 #2582)
 #2584 := [rewrite]: #2583
-#2587 := [monotonicity #2584]: #2586
-#2595 := [trans #2587 #2593]: #2594
-#2579 := (iff #1969 #2578)
-#2576 := (iff #1968 #2573)
-#2565 := (+ #1165 #1964)
-#2568 := (>= #2565 0::int)
-#2574 := (iff #2568 #2573)
-#2575 := [rewrite]: #2574
-#2569 := (iff #1968 #2568)
-#2566 := (= #1967 #2565)
-#2567 := [rewrite]: #2566
-#2570 := [monotonicity #2567]: #2569
-#2577 := [trans #2570 #2575]: #2576
-#2580 := [monotonicity #2577]: #2579
-#2598 := [monotonicity #2580 #2595]: #2597
-#2601 := [monotonicity #2598]: #2600
-#2604 := [quant-intro #2601]: #2603
-#2563 := (iff #1955 #67)
-#2564 := [rewrite]: #2563
-#2972 := [monotonicity #2564 #2604 #2644 #2969]: #2971
-#2977 := [trans #2972 #2975]: #2976
-#2561 := (iff #1950 #2558)
-#2524 := (and #1931 #2518)
-#2555 := (and #2524 #2552)
-#2559 := (iff #2555 #2558)
+#2580 := (iff #1974 #2579)
+#2577 := (iff #1970 #2576)
+#2574 := (iff #1967 #2573)
+#2571 := (iff #1951 #2570)
+#2568 := (iff #1947 #2567)
+#2565 := (= #1946 #2564)
+#2566 := [rewrite]: #2565
+#2569 := [monotonicity #2566]: #2568
+#2572 := [monotonicity #2569]: #2571
+#2575 := [monotonicity #2572]: #2574
+#2578 := [quant-intro #2575]: #2577
+#2561 := (iff #1964 #2548)
+#2553 := (not #2548)
+#2556 := (not #2553)
+#2559 := (iff #2556 #2548)
 #2560 := [rewrite]: #2559
-#2556 := (iff #1950 #2555)
-#2553 := (iff #1946 #2552)
-#2550 := (iff #1943 #2549)
-#2547 := (iff #1927 #2546)
-#2544 := (iff #1923 #2543)
-#2541 := (= #1922 #2540)
-#2542 := [rewrite]: #2541
-#2545 := [monotonicity #2542]: #2544
-#2548 := [monotonicity #2545]: #2547
-#2551 := [monotonicity #2548]: #2550
-#2554 := [quant-intro #2551]: #2553
-#2537 := (iff #1940 #2524)
-#2529 := (not #2524)
-#2532 := (not #2529)
-#2535 := (iff #2532 #2524)
-#2536 := [rewrite]: #2535
-#2533 := (iff #1940 #2532)
-#2530 := (iff #1935 #2529)
-#2527 := (iff #1934 #2524)
-#2521 := (and #2518 #1931)
-#2525 := (iff #2521 #2524)
-#2526 := [rewrite]: #2525
-#2522 := (iff #1934 #2521)
-#2519 := (iff #1933 #2518)
-#2516 := (iff #1932 #2515)
-#2517 := [rewrite]: #2516
-#2520 := [monotonicity #2517]: #2519
-#2523 := [monotonicity #2520]: #2522
-#2528 := [trans #2523 #2526]: #2527
-#2531 := [monotonicity #2528]: #2530
-#2534 := [monotonicity #2531]: #2533
-#2538 := [trans #2534 #2536]: #2537
-#2557 := [monotonicity #2538 #2554]: #2556
-#2562 := [trans #2557 #2560]: #2561
-#2980 := [monotonicity #2562 #2977]: #2979
-#2983 := [monotonicity #2980]: #2982
-#2513 := (iff #1904 #2512)
-#2510 := (iff #1903 #2509)
-#2507 := (iff #1896 #2506)
-#2504 := (iff #1895 #2503)
-#2505 := [rewrite]: #2504
-#2508 := [monotonicity #2505]: #2507
-#2501 := (iff #1902 #2500)
-#2498 := (= #1901 #2497)
-#2499 := [rewrite]: #2498
-#2502 := [monotonicity #2499]: #2501
-#2511 := [monotonicity #2502 #2508]: #2510
-#2514 := [monotonicity #2511]: #2513
-#2986 := [monotonicity #2514 #2983]: #2985
-#2989 := [monotonicity #2986]: #2988
-#2494 := (iff #1873 #2493)
-#2491 := (iff #1872 #2490)
-#2488 := (iff #1864 #2485)
-#2477 := (+ #1861 #1862)
-#2480 := (>= #2477 0::int)
-#2486 := (iff #2480 #2485)
-#2487 := [rewrite]: #2486
-#2481 := (iff #1864 #2480)
-#2478 := (= #1863 #2477)
-#2479 := [rewrite]: #2478
-#2482 := [monotonicity #2479]: #2481
-#2489 := [trans #2482 #2487]: #2488
-#2475 := (iff #1871 #2474)
-#2472 := (iff #1870 #2471)
-#2473 := [rewrite]: #2472
-#2476 := [monotonicity #2473]: #2475
-#2492 := [monotonicity #2476 #2489]: #2491
-#2495 := [monotonicity #2492]: #2494
-#2992 := [monotonicity #2495 #2989]: #2991
-#2995 := [monotonicity #2992]: #2994
-#2998 := [monotonicity #2995]: #2997
-#2469 := (iff #1814 #38)
-#2470 := [rewrite]: #2469
-#3001 := [monotonicity #2470 #2998]: #3000
-#3004 := [monotonicity #3001]: #3003
-#1742 := (not #1706)
-#2464 := (~ #1742 #2463)
-#2460 := (not #1703)
+#2557 := (iff #1964 #2556)
+#2554 := (iff #1959 #2553)
+#2551 := (iff #1958 #2548)
+#2545 := (and #2542 #1955)
+#2549 := (iff #2545 #2548)
+#2550 := [rewrite]: #2549
+#2546 := (iff #1958 #2545)
+#2543 := (iff #1957 #2542)
+#2540 := (iff #1956 #2539)
+#2541 := [rewrite]: #2540
+#2544 := [monotonicity #2541]: #2543
+#2547 := [monotonicity #2544]: #2546
+#2552 := [trans #2547 #2550]: #2551
+#2555 := [monotonicity #2552]: #2554
+#2558 := [monotonicity #2555]: #2557
+#2562 := [trans #2558 #2560]: #2561
+#2581 := [monotonicity #2562 #2578]: #2580
+#2586 := [trans #2581 #2584]: #2585
+#3004 := [monotonicity #2586 #3001]: #3003
+#3007 := [monotonicity #3004]: #3006
+#2537 := (iff #1928 #2536)
+#2534 := (iff #1927 #2533)
+#2531 := (iff #1920 #2530)
+#2528 := (iff #1919 #2527)
+#2529 := [rewrite]: #2528
+#2532 := [monotonicity #2529]: #2531
+#2525 := (iff #1926 #2524)
+#2522 := (= #1925 #2521)
+#2523 := [rewrite]: #2522
+#2526 := [monotonicity #2523]: #2525
+#2535 := [monotonicity #2526 #2532]: #2534
+#2538 := [monotonicity #2535]: #2537
+#3010 := [monotonicity #2538 #3007]: #3009
+#3013 := [monotonicity #3010]: #3012
+#2518 := (iff #1897 #2517)
+#2515 := (iff #1896 #2514)
+#2512 := (iff #1888 #2509)
+#2501 := (+ #1885 #1886)
+#2504 := (>= #2501 0::int)
+#2510 := (iff #2504 #2509)
+#2511 := [rewrite]: #2510
+#2505 := (iff #1888 #2504)
+#2502 := (= #1887 #2501)
+#2503 := [rewrite]: #2502
+#2506 := [monotonicity #2503]: #2505
+#2513 := [trans #2506 #2511]: #2512
+#2499 := (iff #1895 #2498)
+#2496 := (iff #1894 #2495)
+#2497 := [rewrite]: #2496
+#2500 := [monotonicity #2497]: #2499
+#2516 := [monotonicity #2500 #2513]: #2515
+#2519 := [monotonicity #2516]: #2518
+#3016 := [monotonicity #2519 #3013]: #3015
+#3019 := [monotonicity #3016]: #3018
+#3022 := [monotonicity #3019]: #3021
+#2493 := (iff #1833 #71)
+#2494 := [rewrite]: #2493
+#3025 := [monotonicity #2494 #3022]: #3024
+#3028 := [monotonicity #3025]: #3027
+#1809 := (not #1773)
+#2488 := (~ #1809 #2487)
+#2484 := (not #1770)
+#2485 := (~ #2484 #2483)
+#2480 := (not #1767)
+#2481 := (~ #2480 #2479)
+#2476 := (not #1764)
+#2477 := (~ #2476 #2475)
+#2472 := (not #1761)
+#2473 := (~ #2472 #2471)
+#2468 := (not #1758)
+#2469 := (~ #2468 #2467)
+#2464 := (not #1755)
+#2465 := (~ #2464 #2463)
+#2460 := (not #1752)
 #2461 := (~ #2460 #2459)
-#2456 := (not #1700)
+#2456 := (not #1749)
 #2457 := (~ #2456 #2455)
-#2452 := (not #1697)
+#2452 := (not #1744)
 #2453 := (~ #2452 #2451)
-#2448 := (not #1694)
-#2449 := (~ #2448 #2447)
-#2444 := (not #1691)
-#2445 := (~ #2444 #2443)
-#2440 := (not #1688)
-#2441 := (~ #2440 #2439)
-#2436 := (not #1685)
-#2437 := (~ #2436 #2435)
-#2432 := (not #1682)
-#2433 := (~ #2432 #2431)
-#2428 := (not #1677)
-#2429 := (~ #2428 #2427)
-#2424 := (not #1648)
-#2425 := (~ #2424 #1645)
-#2422 := (~ #1645 #1645)
-#2420 := (~ #1642 #1642)
+#2448 := (not #1715)
+#2449 := (~ #2448 #1712)
+#2446 := (~ #1712 #1712)
+#2444 := (~ #1709 #1709)
+#2445 := [refl]: #2444
+#2447 := [nnf-pos #2445]: #2446
+#2450 := [nnf-neg #2447]: #2449
+#2441 := (not #1706)
+#2442 := (~ #2441 #1703)
+#2439 := (~ #1703 #1703)
+#2437 := (~ #1698 #1698)
+#2438 := [refl]: #2437
+#2440 := [nnf-pos #2438]: #2439
+#2443 := [nnf-neg #2440]: #2442
+#2434 := (not #1690)
+#2435 := (~ #2434 #1687)
+#2432 := (~ #1687 #1687)
+#2430 := (~ #1684 #1684)
+#2431 := [refl]: #2430
+#2433 := [nnf-pos #2431]: #2432
+#2436 := [nnf-neg #2433]: #2435
+#2427 := (not #1667)
+#2428 := (~ #2427 #2426)
+#2423 := (not #1662)
+#2424 := (~ #2423 #2422)
+#2420 := (~ #1628 #1628)
 #2421 := [refl]: #2420
-#2423 := [nnf-pos #2421]: #2422
-#2426 := [nnf-neg #2423]: #2425
-#2417 := (not #1639)
-#2418 := (~ #2417 #1636)
-#2415 := (~ #1636 #1636)
-#2413 := (~ #1631 #1631)
+#2417 := (not #1623)
+#2418 := (~ #2417 #1620)
+#2415 := (~ #1620 #1620)
+#2413 := (~ #1615 #1615)
 #2414 := [refl]: #2413
 #2416 := [nnf-pos #2414]: #2415
 #2419 := [nnf-neg #2416]: #2418
-#2410 := (not #1623)
-#2411 := (~ #2410 #1620)
-#2408 := (~ #1620 #1620)
-#2406 := (~ #1617 #1617)
+#2410 := (not #1605)
+#2411 := (~ #2410 #1602)
+#2408 := (~ #1602 #1602)
+#2406 := (~ #1599 #1599)
 #2407 := [refl]: #2406
 #2409 := [nnf-pos #2407]: #2408
 #2412 := [nnf-neg #2409]: #2411
-#2403 := (not #1600)
+#2403 := (not #1588)
 #2404 := (~ #2403 #2402)
-#2399 := (not #1595)
+#2399 := (not #1585)
 #2400 := (~ #2399 #2398)
-#2396 := (~ #1561 #1561)
-#2397 := [refl]: #2396
-#2393 := (not #1556)
-#2394 := (~ #2393 #1553)
-#2391 := (~ #1553 #1553)
-#2389 := (~ #1548 #1548)
-#2390 := [refl]: #2389
-#2392 := [nnf-pos #2390]: #2391
-#2395 := [nnf-neg #2392]: #2394
-#2386 := (not #1538)
-#2387 := (~ #2386 #1535)
-#2384 := (~ #1535 #1535)
-#2382 := (~ #1532 #1532)
-#2383 := [refl]: #2382
-#2385 := [nnf-pos #2383]: #2384
-#2388 := [nnf-neg #2385]: #2387
-#2379 := (not #1521)
+#2395 := (not #1582)
+#2396 := (~ #2395 #2394)
+#2391 := (not #1579)
+#2392 := (~ #2391 #2390)
+#2387 := (not #1576)
+#2388 := (~ #2387 #2386)
+#2383 := (not #1573)
+#2384 := (~ #2383 #2382)
+#2379 := (not #1570)
 #2380 := (~ #2379 #2378)
-#2375 := (not #1518)
+#2375 := (not #1567)
 #2376 := (~ #2375 #2374)
-#2371 := (not #1515)
+#2371 := (not #1564)
 #2372 := (~ #2371 #2370)
-#2367 := (not #1512)
+#2367 := (not #1561)
 #2368 := (~ #2367 #2366)
-#2363 := (not #1509)
+#2363 := (not #1558)
 #2364 := (~ #2363 #2362)
-#2359 := (not #1506)
+#2359 := (not #1555)
 #2360 := (~ #2359 #2358)
-#2355 := (not #1503)
-#2356 := (~ #2355 #2354)
-#2351 := (not #1500)
-#2352 := (~ #2351 #2350)
-#2347 := (not #1497)
-#2348 := (~ #2347 #2346)
-#2343 := (not #1494)
-#2344 := (~ #2343 #2342)
-#2339 := (not #1491)
-#2340 := (~ #2339 #2338)
-#2335 := (not #1488)
-#2336 := (~ #2335 #2334)
-#2316 := (not #1485)
-#2332 := (~ #2316 #2329)
-#2306 := (exists (vars (?v1 S2)) #2305)
-#2314 := (or #2313 #2306)
-#2315 := (not #2314)
-#2330 := (~ #2315 #2329)
-#2326 := (not #2306)
-#2327 := (~ #2326 #2325)
-#2323 := (~ #2322 #2322)
-#2324 := [refl]: #2323
-#2328 := [nnf-neg #2324]: #2327
-#2320 := (~ #2319 #2319)
-#2321 := [refl]: #2320
-#2331 := [nnf-neg #2321 #2328]: #2330
-#2317 := (~ #2316 #2315)
-#2318 := [sk]: #2317
-#2333 := [trans #2318 #2331]: #2332
-#2292 := (not #1448)
-#2293 := (~ #2292 #1445)
-#2290 := (~ #1445 #1445)
-#2288 := (~ #1442 #1442)
-#2289 := [refl]: #2288
-#2291 := [nnf-pos #2289]: #2290
-#2294 := [nnf-neg #2291]: #2293
-#2337 := [nnf-neg #2294 #2333]: #2336
-#2284 := (~ #1448 #2283)
-#2285 := [sk]: #2284
-#2341 := [nnf-neg #2285 #2337]: #2340
-#2261 := (not #1424)
-#2262 := (~ #2261 #1421)
-#2259 := (~ #1421 #1421)
-#2257 := (~ #1416 #1416)
-#2258 := [refl]: #2257
-#2260 := [nnf-pos #2258]: #2259
-#2263 := [nnf-neg #2260]: #2262
-#2345 := [nnf-neg #2263 #2341]: #2344
-#2253 := (~ #1424 #2252)
-#2254 := [sk]: #2253
-#2349 := [nnf-neg #2254 #2345]: #2348
-#2234 := (not #1405)
-#2235 := (~ #2234 #1402)
-#2232 := (~ #1402 #1402)
-#2230 := (~ #1399 #1399)
-#2231 := [refl]: #2230
-#2233 := [nnf-pos #2231]: #2232
-#2236 := [nnf-neg #2233]: #2235
-#2353 := [nnf-neg #2236 #2349]: #2352
-#2226 := (~ #1405 #2225)
-#2227 := [sk]: #2226
-#2357 := [nnf-neg #2227 #2353]: #2356
-#2220 := (~ #2219 #2219)
-#2221 := [refl]: #2220
-#2361 := [nnf-neg #2221 #2357]: #2360
-#2217 := (~ #1396 #1396)
-#2218 := [refl]: #2217
-#2365 := [nnf-neg #2218 #2361]: #2364
-#2214 := (not #859)
-#2215 := (~ #2214 #725)
-#2212 := (~ #725 #725)
-#2210 := (~ #720 #720)
-#2211 := [refl]: #2210
-#2213 := [nnf-pos #2211]: #2212
-#2216 := [nnf-neg #2213]: #2215
-#2369 := [nnf-neg #2216 #2365]: #2368
-#2206 := (~ #859 #2205)
-#2207 := [sk]: #2206
-#2373 := [nnf-neg #2207 #2369]: #2372
-#2194 := (not #1391)
-#2195 := (~ #2194 #1388)
-#2192 := (~ #1388 #1388)
-#2190 := (~ #1383 #1383)
-#2191 := [refl]: #2190
-#2193 := [nnf-pos #2191]: #2192
-#2196 := [nnf-neg #2193]: #2195
-#2377 := [nnf-neg #2196 #2373]: #2376
-#2186 := (~ #1391 #2185)
-#2187 := [sk]: #2186
-#2381 := [nnf-neg #2187 #2377]: #2380
-#2176 := (not #1380)
-#2177 := (~ #2176 #1377)
-#2174 := (~ #1377 #1377)
-#2172 := (~ #1372 #1372)
-#2173 := [refl]: #2172
-#2175 := [nnf-pos #2173]: #2174
-#2178 := [nnf-neg #2175]: #2177
-#2169 := (not #1571)
-#2170 := (~ #2169 #2164)
-#2165 := (~ #1330 #2164)
-#2166 := [sk]: #2165
-#2171 := [nnf-neg #2166]: #2170
-#2153 := (~ #671 #671)
-#2154 := [refl]: #2153
-#2151 := (~ #2150 #2150)
-#2152 := [refl]: #2151
-#2401 := [nnf-neg #2152 #2154 #2171 #2178 #2381 #2388 #2395 #2397]: #2400
-#2147 := (not #1348)
-#2148 := (~ #2147 #2146)
-#2144 := (~ #1571 #2143)
-#2141 := (~ #2140 #2140)
+#2340 := (not #1552)
+#2356 := (~ #2340 #2353)
+#2330 := (exists (vars (?v1 S3)) #2329)
+#2338 := (or #2337 #2330)
+#2339 := (not #2338)
+#2354 := (~ #2339 #2353)
+#2350 := (not #2330)
+#2351 := (~ #2350 #2349)
+#2347 := (~ #2346 #2346)
+#2348 := [refl]: #2347
+#2352 := [nnf-neg #2348]: #2351
+#2344 := (~ #2343 #2343)
+#2345 := [refl]: #2344
+#2355 := [nnf-neg #2345 #2352]: #2354
+#2341 := (~ #2340 #2339)
+#2342 := [sk]: #2341
+#2357 := [trans #2342 #2355]: #2356
+#2316 := (not #1515)
+#2317 := (~ #2316 #1512)
+#2314 := (~ #1512 #1512)
+#2312 := (~ #1509 #1509)
+#2313 := [refl]: #2312
+#2315 := [nnf-pos #2313]: #2314
+#2318 := [nnf-neg #2315]: #2317
+#2361 := [nnf-neg #2318 #2357]: #2360
+#2308 := (~ #1515 #2307)
+#2309 := [sk]: #2308
+#2365 := [nnf-neg #2309 #2361]: #2364
+#2285 := (not #1491)
+#2286 := (~ #2285 #1488)
+#2283 := (~ #1488 #1488)
+#2281 := (~ #1483 #1483)
+#2282 := [refl]: #2281
+#2284 := [nnf-pos #2282]: #2283
+#2287 := [nnf-neg #2284]: #2286
+#2369 := [nnf-neg #2287 #2365]: #2368
+#2277 := (~ #1491 #2276)
+#2278 := [sk]: #2277
+#2373 := [nnf-neg #2278 #2369]: #2372
+#2258 := (not #1472)
+#2259 := (~ #2258 #1469)
+#2256 := (~ #1469 #1469)
+#2254 := (~ #1466 #1466)
+#2255 := [refl]: #2254
+#2257 := [nnf-pos #2255]: #2256
+#2260 := [nnf-neg #2257]: #2259
+#2377 := [nnf-neg #2260 #2373]: #2376
+#2250 := (~ #1472 #2249)
+#2251 := [sk]: #2250
+#2381 := [nnf-neg #2251 #2377]: #2380
+#2244 := (~ #2243 #2243)
+#2245 := [refl]: #2244
+#2385 := [nnf-neg #2245 #2381]: #2384
+#2241 := (~ #1463 #1463)
+#2242 := [refl]: #2241
+#2389 := [nnf-neg #2242 #2385]: #2388
+#2238 := (not #926)
+#2239 := (~ #2238 #792)
+#2236 := (~ #792 #792)
+#2234 := (~ #787 #787)
+#2235 := [refl]: #2234
+#2237 := [nnf-pos #2235]: #2236
+#2240 := [nnf-neg #2237]: #2239
+#2393 := [nnf-neg #2240 #2389]: #2392
+#2230 := (~ #926 #2229)
+#2231 := [sk]: #2230
+#2397 := [nnf-neg #2231 #2393]: #2396
+#2218 := (not #1458)
+#2219 := (~ #2218 #1455)
+#2216 := (~ #1455 #1455)
+#2214 := (~ #1450 #1450)
+#2215 := [refl]: #2214
+#2217 := [nnf-pos #2215]: #2216
+#2220 := [nnf-neg #2217]: #2219
+#2401 := [nnf-neg #2220 #2397]: #2400
+#2210 := (~ #1458 #2209)
+#2211 := [sk]: #2210
+#2405 := [nnf-neg #2211 #2401]: #2404
+#2200 := (not #1447)
+#2201 := (~ #2200 #1444)
+#2198 := (~ #1444 #1444)
+#2196 := (~ #1439 #1439)
+#2197 := [refl]: #2196
+#2199 := [nnf-pos #2197]: #2198
+#2202 := [nnf-neg #2199]: #2201
+#2193 := (not #1638)
+#2194 := (~ #2193 #2188)
+#2189 := (~ #1397 #2188)
+#2190 := [sk]: #2189
+#2195 := [nnf-neg #2190]: #2194
+#2177 := (~ #2176 #2176)
+#2178 := [refl]: #2177
+#2174 := (~ #730 #730)
+#2175 := [refl]: #2174
+#2425 := [nnf-neg #2175 #2178 #2195 #2202 #2405 #2412 #2419 #2421]: #2424
+#2171 := (not #1415)
+#2172 := (~ #2171 #2170)
+#2168 := (~ #1638 #2167)
+#2165 := (~ #2164 #2164)
+#2166 := [refl]: #2165
+#2169 := [nnf-neg #2166]: #2168
+#2161 := (not #1386)
+#2162 := (~ #2161 #2160)
+#2157 := (not #1383)
+#2158 := (~ #2157 #2156)
+#2153 := (not #1380)
+#2154 := (~ #2153 #2152)
+#2149 := (not #1375)
+#2150 := (~ #2149 #2148)
+#2145 := (not #1367)
+#2146 := (~ #2145 #1364)
+#2143 := (~ #1364 #1364)
+#2141 := (~ #1361 #1361)
 #2142 := [refl]: #2141
-#2145 := [nnf-neg #2142]: #2144
-#2137 := (not #1319)
-#2138 := (~ #2137 #2136)
-#2133 := (not #1316)
-#2134 := (~ #2133 #2132)
-#2129 := (not #1313)
-#2130 := (~ #2129 #2128)
-#2125 := (not #1308)
-#2126 := (~ #2125 #2124)
-#2121 := (not #1300)
-#2122 := (~ #2121 #1297)
-#2119 := (~ #1297 #1297)
-#2117 := (~ #1294 #1294)
-#2118 := [refl]: #2117
-#2120 := [nnf-pos #2118]: #2119
-#2123 := [nnf-neg #2120]: #2122
-#2115 := (~ #2114 #2114)
-#2116 := [refl]: #2115
-#2127 := [nnf-neg #2116 #2123]: #2126
-#2110 := (~ #1300 #2109)
-#2111 := [sk]: #2110
-#2131 := [nnf-neg #2111 #2127]: #2130
-#2085 := (not #1282)
-#2086 := (~ #2085 #2082)
-#2083 := (~ #1279 #2082)
-#2080 := (~ #1276 #2079)
-#2075 := (~ #1273 #2074)
-#2076 := [sk]: #2075
-#2063 := (~ #1257 #1257)
-#2064 := [refl]: #2063
-#2081 := [monotonicity #2064 #2076]: #2080
-#2084 := [nnf-pos #2081]: #2083
-#2087 := [nnf-neg #2084]: #2086
-#2135 := [nnf-neg #2087 #2131]: #2134
-#2061 := (~ #1282 #2058)
-#2036 := (exists (vars (?v1 S2)) #2035)
-#2044 := (or #2043 #2036)
-#2045 := (not #2044)
-#2059 := (~ #2045 #2058)
-#2055 := (not #2036)
-#2056 := (~ #2055 #2054)
-#2052 := (~ #2051 #2051)
-#2053 := [refl]: #2052
-#2057 := [nnf-neg #2053]: #2056
-#2049 := (~ #2048 #2048)
-#2050 := [refl]: #2049
-#2060 := [nnf-neg #2050 #2057]: #2059
-#2046 := (~ #1282 #2045)
-#2047 := [sk]: #2046
-#2062 := [trans #2047 #2060]: #2061
-#2139 := [nnf-neg #2062 #2135]: #2138
-#2023 := (~ #2022 #2022)
-#2024 := [refl]: #2023
-#2020 := (~ #2019 #2019)
-#2021 := [refl]: #2020
-#2017 := (~ #2016 #2016)
-#2018 := [refl]: #2017
-#2014 := (~ #2013 #2013)
-#2015 := [refl]: #2014
-#2149 := [nnf-neg #2015 #2018 #2021 #2024 #2139 #2145]: #2148
-#2405 := [nnf-neg #2149 #2401]: #2404
-#2010 := (not #1245)
-#2011 := (~ #2010 #2007)
-#2008 := (~ #1242 #2007)
-#2005 := (~ #1239 #2004)
-#2000 := (~ #1236 #1999)
-#2001 := [sk]: #2000
-#1986 := (~ #1212 #1212)
-#1987 := [refl]: #1986
-#2006 := [monotonicity #1987 #2001]: #2005
-#2009 := [nnf-pos #2006]: #2008
-#2012 := [nnf-neg #2009]: #2011
-#1983 := (not #1656)
-#1984 := (~ #1983 #1980)
-#1981 := (~ #1200 #1980)
-#1978 := (~ #1197 #1977)
-#1973 := (~ #1194 #1972)
-#1974 := [sk]: #1973
-#1958 := (~ #1174 #1174)
-#1959 := [refl]: #1958
-#1979 := [monotonicity #1959 #1974]: #1978
-#1982 := [nnf-pos #1979]: #1981
-#1985 := [nnf-neg #1982]: #1984
-#1956 := (~ #1955 #1955)
-#1957 := [refl]: #1956
-#2430 := [nnf-neg #1957 #1985 #2012 #2405 #2412 #2419 #2426]: #2429
-#1953 := (~ #1656 #1950)
-#1928 := (exists (vars (?v1 S2)) #1927)
-#1936 := (or #1935 #1928)
-#1937 := (not #1936)
-#1951 := (~ #1937 #1950)
-#1947 := (not #1928)
-#1948 := (~ #1947 #1946)
-#1944 := (~ #1943 #1943)
-#1945 := [refl]: #1944
-#1949 := [nnf-neg #1945]: #1948
-#1941 := (~ #1940 #1940)
-#1942 := [refl]: #1941
-#1952 := [nnf-neg #1942 #1949]: #1951
-#1938 := (~ #1656 #1937)
-#1939 := [sk]: #1938
-#1954 := [trans #1939 #1952]: #1953
-#2434 := [nnf-neg #1954 #2430]: #2433
-#1913 := (not #1162)
-#1914 := (~ #1913 #1159)
-#1911 := (~ #1159 #1159)
-#1909 := (~ #1156 #1156)
-#1910 := [refl]: #1909
-#1912 := [nnf-pos #1910]: #1911
-#1915 := [nnf-neg #1912]: #1914
-#2438 := [nnf-neg #1915 #2434]: #2437
-#1905 := (~ #1162 #1904)
-#1906 := [sk]: #1905
-#2442 := [nnf-neg #1906 #2438]: #2441
-#1882 := (not #1131)
-#1883 := (~ #1882 #1128)
-#1880 := (~ #1128 #1128)
-#1878 := (~ #1123 #1123)
-#1879 := [refl]: #1878
-#1881 := [nnf-pos #1879]: #1880
-#1884 := [nnf-neg #1881]: #1883
-#2446 := [nnf-neg #1884 #2442]: #2445
-#1874 := (~ #1131 #1873)
-#1875 := [sk]: #1874
-#2450 := [nnf-neg #1875 #2446]: #2449
-#1855 := (not #1111)
-#1856 := (~ #1855 #1108)
-#1853 := (~ #1108 #1108)
-#1851 := (~ #1107 #1107)
+#2144 := [nnf-pos #2142]: #2143
+#2147 := [nnf-neg #2144]: #2146
+#2139 := (~ #2138 #2138)
+#2140 := [refl]: #2139
+#2151 := [nnf-neg #2140 #2147]: #2150
+#2134 := (~ #1367 #2133)
+#2135 := [sk]: #2134
+#2155 := [nnf-neg #2135 #2151]: #2154
+#2109 := (not #1349)
+#2110 := (~ #2109 #2106)
+#2107 := (~ #1346 #2106)
+#2104 := (~ #1343 #2103)
+#2099 := (~ #1340 #2098)
+#2100 := [sk]: #2099
+#2087 := (~ #1324 #1324)
+#2088 := [refl]: #2087
+#2105 := [monotonicity #2088 #2100]: #2104
+#2108 := [nnf-pos #2105]: #2107
+#2111 := [nnf-neg #2108]: #2110
+#2159 := [nnf-neg #2111 #2155]: #2158
+#2085 := (~ #1349 #2082)
+#2060 := (exists (vars (?v1 S3)) #2059)
+#2068 := (or #2067 #2060)
+#2069 := (not #2068)
+#2083 := (~ #2069 #2082)
+#2079 := (not #2060)
+#2080 := (~ #2079 #2078)
+#2076 := (~ #2075 #2075)
+#2077 := [refl]: #2076
+#2081 := [nnf-neg #2077]: #2080
+#2073 := (~ #2072 #2072)
+#2074 := [refl]: #2073
+#2084 := [nnf-neg #2074 #2081]: #2083
+#2070 := (~ #1349 #2069)
+#2071 := [sk]: #2070
+#2086 := [trans #2071 #2084]: #2085
+#2163 := [nnf-neg #2086 #2159]: #2162
+#2047 := (~ #2046 #2046)
+#2048 := [refl]: #2047
+#2044 := (~ #2043 #2043)
+#2045 := [refl]: #2044
+#2041 := (~ #2040 #2040)
+#2042 := [refl]: #2041
+#2038 := (~ #2037 #2037)
+#2039 := [refl]: #2038
+#2173 := [nnf-neg #2039 #2042 #2045 #2048 #2163 #2169]: #2172
+#2429 := [nnf-neg #2173 #2425]: #2428
+#2034 := (not #1312)
+#2035 := (~ #2034 #2031)
+#2032 := (~ #1309 #2031)
+#2029 := (~ #1306 #2028)
+#2024 := (~ #1303 #2023)
+#2025 := [sk]: #2024
+#2010 := (~ #1279 #1279)
+#2011 := [refl]: #2010
+#2030 := [monotonicity #2011 #2025]: #2029
+#2033 := [nnf-pos #2030]: #2032
+#2036 := [nnf-neg #2033]: #2035
+#2007 := (not #1723)
+#2008 := (~ #2007 #2004)
+#2005 := (~ #1267 #2004)
+#2002 := (~ #1264 #2001)
+#1997 := (~ #1261 #1996)
+#1998 := [sk]: #1997
+#1982 := (~ #1241 #1241)
+#1983 := [refl]: #1982
+#2003 := [monotonicity #1983 #1998]: #2002
+#2006 := [nnf-pos #2003]: #2005
+#2009 := [nnf-neg #2006]: #2008
+#1980 := (~ #1979 #1979)
+#1981 := [refl]: #1980
+#2454 := [nnf-neg #1981 #2009 #2036 #2429 #2436 #2443 #2450]: #2453
+#1977 := (~ #1723 #1974)
+#1952 := (exists (vars (?v1 S3)) #1951)
+#1960 := (or #1959 #1952)
+#1961 := (not #1960)
+#1975 := (~ #1961 #1974)
+#1971 := (not #1952)
+#1972 := (~ #1971 #1970)
+#1968 := (~ #1967 #1967)
+#1969 := [refl]: #1968
+#1973 := [nnf-neg #1969]: #1972
+#1965 := (~ #1964 #1964)
+#1966 := [refl]: #1965
+#1976 := [nnf-neg #1966 #1973]: #1975
+#1962 := (~ #1723 #1961)
+#1963 := [sk]: #1962
+#1978 := [trans #1963 #1976]: #1977
+#2458 := [nnf-neg #1978 #2454]: #2457
+#1937 := (not #1229)
+#1938 := (~ #1937 #1226)
+#1935 := (~ #1226 #1226)
+#1933 := (~ #1223 #1223)
+#1934 := [refl]: #1933
+#1936 := [nnf-pos #1934]: #1935
+#1939 := [nnf-neg #1936]: #1938
+#2462 := [nnf-neg #1939 #2458]: #2461
+#1929 := (~ #1229 #1928)
+#1930 := [sk]: #1929
+#2466 := [nnf-neg #1930 #2462]: #2465
+#1906 := (not #1198)
+#1907 := (~ #1906 #1195)
+#1904 := (~ #1195 #1195)
+#1902 := (~ #1190 #1190)
+#1903 := [refl]: #1902
+#1905 := [nnf-pos #1903]: #1904
+#1908 := [nnf-neg #1905]: #1907
+#2470 := [nnf-neg #1908 #2466]: #2469
+#1898 := (~ #1198 #1897)
+#1899 := [sk]: #1898
+#2474 := [nnf-neg #1899 #2470]: #2473
+#1879 := (not #1178)
+#1880 := (~ #1879 #1175)
+#1877 := (~ #1175 #1175)
+#1875 := (~ #1174 #1174)
+#1876 := [refl]: #1875
+#1878 := [nnf-pos #1876]: #1877
+#1881 := [nnf-neg #1878]: #1880
+#2478 := [nnf-neg #1881 #2474]: #2477
+#1871 := (~ #1178 #1870)
+#1872 := [sk]: #1871
+#2482 := [nnf-neg #1872 #2478]: #2481
+#1834 := (~ #1833 #1833)
+#1866 := [refl]: #1834
+#2486 := [nnf-neg #1866 #2482]: #2485
+#1864 := (~ #1169 #1169)
+#1865 := [refl]: #1864
+#2489 := [nnf-neg #1865 #2486]: #2488
+#1810 := [not-or-elim #1806]: #1809
+#2490 := [mp~ #1810 #2489]: #2487
+#2491 := [mp #2490 #3028]: #3026
+#3670 := [mp #2491 #3669]: #3667
+#4577 := [mp #3670 #4576]: #4574
+#6875 := [unit-resolution #4577 #4781]: #4571
+#3916 := (or #4568 #4562)
+#3917 := [def-axiom]: #3916
+#6876 := [unit-resolution #3917 #6875]: #4562
+#3911 := (or #4565 #1870 #4559)
+#3912 := [def-axiom]: #3911
+#6877 := [unit-resolution #3912 #6876 #4699]: #4559
+#3935 := (or #4556 #4550)
+#3936 := [def-axiom]: #3935
+#6878 := [unit-resolution #3936 #6877]: #4550
+#6894 := (or #4553 #4547)
+#3768 := [hypothesis]: #1890
+#4199 := (forall (vars (?v0 S3)) (:pat #4198) #430)
+#4202 := (iff #433 #4199)
+#4200 := (iff #430 #430)
+#4201 := [refl]: #4200
+#4203 := [quant-intro #4201]: #4202
+#1831 := (~ #433 #433)
+#1861 := (~ #430 #430)
+#1862 := [refl]: #1861
+#1832 := [nnf-pos #1862]: #1831
+#1808 := [not-or-elim #1806]: #433
+#1863 := [mp~ #1808 #1832]: #433
+#4204 := [mp #1863 #4203]: #4199
+#3920 := (not #4199)
+#3899 := (or #3920 #2102)
+#3902 := [quant-inst]: #3899
+#3771 := [unit-resolution #3902 #4204 #3768]: false
+#3746 := [lemma #3771]: #2102
+#3728 := (or #2212 #1890)
+#3815 := [def-axiom]: #3728
+#6893 := [unit-resolution #3815 #3746]: #2212
+#3929 := (or #4553 #1874 #4547)
+#3931 := [def-axiom]: #3929
+#6892 := [unit-resolution #3931 #6893]: #6894
+#6895 := [unit-resolution #6892 #6878]: #4547
+#3956 := (or #4544 #4538)
+#3957 := [def-axiom]: #3956
+#6896 := [unit-resolution #3957 #6895]: #4538
+#5104 := [hypothesis]: #1918
+#4786 := (or #3920 #3051)
+#4838 := [quant-inst]: #4786
+#5105 := [unit-resolution #4838 #4204 #5104]: false
+#5108 := [lemma #5105]: #3051
+#3818 := (or #3066 #1918)
+#3822 := [def-axiom]: #3818
+#6897 := [unit-resolution #3822 #5108]: #3066
+#3952 := (or #4541 #3071 #4535)
+#3953 := [def-axiom]: #3952
+#6913 := [unit-resolution #3953 #6897 #6896]: #4535
+#3966 := (or #4532 #4526)
+#3987 := [def-axiom]: #3966
+#6914 := [unit-resolution #3987 #6913]: #4526
+#4969 := (= f8 #1943)
+#5130 := (not #4969)
+#5128 := [hypothesis]: #4243
+#4132 := (or #4240 #1955)
+#3806 := [def-axiom]: #4132
+#5129 := [unit-resolution #3806 #5128]: #1955
+#5138 := (or #5130 #1954)
+#5139 := [th-lemma]: #5138
+#5140 := [unit-resolution #5139 #5129]: #5130
+#3807 := (or #4240 #2542)
+#4139 := [def-axiom]: #3807
+#5141 := [unit-resolution #4139 #5128]: #2542
+#5017 := (or #3753 #2539 #4969)
+#4972 := (or #1956 #4969)
+#5005 := (or #3753 #4972)
+#5041 := (iff #5005 #5017)
+#5009 := (or #2539 #4969)
+#5018 := (or #3753 #5009)
+#5026 := (iff #5018 #5017)
+#5040 := [rewrite]: #5026
+#5019 := (iff #5005 #5018)
+#5010 := (iff #4972 #5009)
+#5016 := [monotonicity #2541]: #5010
+#5020 := [monotonicity #5016]: #5019
+#5067 := [trans #5020 #5040]: #5041
+#5015 := [quant-inst]: #5005
+#5068 := [mp #5015 #5067]: #5017
+#5142 := [unit-resolution #5068 #4197 #5141 #5140]: false
+#5137 := [lemma #5142]: #4240
+#3974 := (or #4529 #4243 #4523)
+#3975 := [def-axiom]: #3974
+#6915 := [unit-resolution #3975 #5137 #6914]: #4523
+#3996 := (or #4520 #4514)
+#3964 := [def-axiom]: #3996
+#9175 := [unit-resolution #3964 #6915]: #4514
+#7369 := (f13 f14 ?v1!10)
+#7370 := (* -1::int #7369)
+#7673 := (+ f8 #7370)
+#7674 := (<= #7673 0::int)
+#9078 := (not #7674)
+#4005 := (or #4520 #100)
+#4006 := [def-axiom]: #4005
+#6916 := [unit-resolution #4006 #6915]: #100
+#8585 := (= #157 #99)
+#8582 := [hypothesis]: #4356
+#4107 := (or #4353 #597)
+#4108 := [def-axiom]: #4107
+#8584 := [unit-resolution #4108 #8582]: #597
+#8579 := [symm #8584]: #138
+#8586 := [monotonicity #8579]: #8585
+#8587 := [trans #8586 #6916]: #158
+#4119 := (or #4329 #2138)
+#3782 := [def-axiom]: #4119
+#8583 := [unit-resolution #3782 #8587]: #4329
+#4109 := (or #4353 #4347)
+#4106 := [def-axiom]: #4109
+#8563 := [unit-resolution #4106 #8582]: #4347
+#7933 := (or #4307 #688)
+#5246 := (?v1!7 ?v0!8)
+#5479 := (f13 f19 #5246)
+#5621 := (* -1::int #5479)
+#5247 := (f13 f14 #5246)
+#6754 := (+ #5247 #5621)
+#6761 := (>= #6754 0::int)
+#6753 := (= #5247 #5479)
+#7687 := (= #5479 #5247)
+#7713 := [hypothesis]: #597
+#7714 := [symm #7713]: #138
+#7688 := [monotonicity #7714]: #7687
+#7686 := [symm #7688]: #6753
+#7712 := (not #6753)
+#7689 := (or #7712 #6761)
+#7690 := [th-lemma]: #7689
+#7691 := [unit-resolution #7690 #7686]: #6761
+#5272 := (* -1::int #5247)
+#5187 := (f13 f14 ?v0!8)
+#5273 := (+ #5187 #5272)
+#5274 := (<= #5273 0::int)
+#5368 := (not #5274)
+#5281 := (f6 f15 #5246)
+#5306 := (= f1 #5281)
+#5307 := (not #5306)
+#5275 := (f3 #5246 ?v0!8)
+#5276 := (f9 #5275)
+#5271 := (* -1::int #5276)
+#5277 := (+ #5272 #5271)
+#5278 := (+ #5187 #5277)
+#5279 := (= #5278 0::int)
+#5280 := (not #5279)
+#5305 := (or #5274 #5280 #5307)
+#5313 := (not #5305)
+#5209 := (* -1::int #5187)
+#5210 := (+ f8 #5209)
+#5211 := (<= #5210 0::int)
+#5516 := (not #5211)
+#7692 := [hypothesis]: #4310
+#4143 := (or #4307 #2063)
+#4133 := [def-axiom]: #4143
+#7693 := [unit-resolution #4133 #7692]: #2063
+#5506 := (+ #2050 #5209)
+#5508 := (>= #5506 0::int)
+#5503 := (= #2050 #5187)
+#7743 := (= #5187 #2050)
+#7744 := [monotonicity #7713]: #7743
+#7745 := [symm #7744]: #5503
+#7746 := (not #5503)
+#7747 := (or #7746 #5508)
+#7742 := [th-lemma]: #7747
+#7748 := [unit-resolution #7742 #7745]: #5508
+#5517 := (not #5508)
+#5478 := (or #5516 #5517 #2062)
+#5513 := [hypothesis]: #2063
+#5514 := [hypothesis]: #5211
+#5512 := [hypothesis]: #5508
+#5515 := [th-lemma #5512 #5514 #5513]: false
+#5476 := [lemma #5515]: #5478
+#7749 := [unit-resolution #5476 #7748 #7693]: #5516
+#7752 := (or #5211 #5313)
+#3793 := (or #4307 #2680)
+#3798 := [def-axiom]: #3793
+#7750 := [unit-resolution #3798 #7692]: #2680
+#3995 := (or #4520 #4280)
+#3990 := [def-axiom]: #3995
+#7751 := [unit-resolution #3990 #6915]: #4280
+#5338 := (or #4285 #2677 #5211 #5313)
+#5308 := (or #5307 #5280 #5274)
+#5309 := (not #5308)
+#5310 := (or #2064 #5211 #5309)
+#5339 := (or #4285 #5310)
+#5369 := (iff #5339 #5338)
+#5335 := (or #2677 #5211 #5313)
+#5340 := (or #4285 #5335)
+#5343 := (iff #5340 #5338)
+#5344 := [rewrite]: #5343
+#5341 := (iff #5339 #5340)
+#5336 := (iff #5310 #5335)
+#5314 := (iff #5309 #5313)
+#5311 := (iff #5308 #5305)
+#5312 := [rewrite]: #5311
+#5315 := [monotonicity #5312]: #5314
+#5337 := [monotonicity #2679 #5315]: #5336
+#5342 := [monotonicity #5337]: #5341
+#5370 := [trans #5342 #5344]: #5369
+#5334 := [quant-inst]: #5339
+#5371 := [mp #5334 #5370]: #5338
+#7724 := [unit-resolution #5371 #7751 #7750]: #7752
+#7725 := [unit-resolution #7724 #7749]: #5313
+#5374 := (or #5305 #5368)
+#5375 := [def-axiom]: #5374
+#7723 := [unit-resolution #5375 #7725]: #5368
+#5622 := (+ #2050 #5621)
+#5646 := (<= #5622 0::int)
+#5843 := (+ #5271 #5621)
+#5780 := (+ #2050 #5843)
+#5781 := (= #5780 0::int)
+#6116 := (>= #5780 0::int)
+#5373 := (>= #5278 0::int)
+#5376 := (or #5305 #5279)
+#5377 := [def-axiom]: #5376
+#7726 := [unit-resolution #5377 #7725]: #5279
+#7727 := (or #5280 #5373)
+#7728 := [th-lemma]: #7727
+#7729 := [unit-resolution #7728 #7726]: #5373
+#6983 := (not #6761)
+#6982 := (not #5373)
+#6978 := (or #6116 #5517 #6982 #6983)
+#6954 := [hypothesis]: #6761
+#6955 := [hypothesis]: #5373
+#6979 := (not #6116)
+#6980 := [hypothesis]: #6979
+#6981 := [th-lemma #6980 #5512 #6955 #6954]: false
+#6984 := [lemma #6981]: #6978
+#7730 := [unit-resolution #6984 #7748 #7729 #7691]: #6116
+#6115 := (<= #5780 0::int)
+#6758 := (<= #6754 0::int)
+#7778 := (or #7712 #6758)
+#7779 := [th-lemma]: #7778
+#7777 := [unit-resolution #7779 #7686]: #6758
+#5372 := (<= #5278 0::int)
+#7780 := (or #5280 #5372)
+#7781 := [th-lemma]: #7780
+#7782 := [unit-resolution #7781 #7726]: #5372
+#5507 := (<= #5506 0::int)
+#7783 := (or #7746 #5507)
+#7784 := [th-lemma]: #7783
+#7785 := [unit-resolution #7784 #7745]: #5507
+#7793 := (not #6758)
+#7792 := (not #5372)
+#7791 := (not #5507)
+#7794 := (or #6115 #7791 #7792 #7793)
+#7731 := [hypothesis]: #6758
+#7786 := [hypothesis]: #5372
+#7787 := [hypothesis]: #5507
+#7788 := (not #6115)
+#7789 := [hypothesis]: #7788
+#7790 := [th-lemma #7789 #7787 #7786 #7731]: false
+#7795 := [lemma #7790]: #7794
+#7878 := [unit-resolution #7795 #7785 #7782 #7777]: #6115
+#7884 := (or #5781 #7788 #6979)
+#7885 := [th-lemma]: #7884
+#7929 := [unit-resolution #7885 #7878 #7730]: #5781
+#5798 := (not #5781)
+#5803 := (or #5646 #5798)
+#4134 := (or #4307 #4299)
+#3794 := [def-axiom]: #4134
+#7930 := [unit-resolution #3794 #7692]: #4299
+#6150 := (or #4304 #5646 #5798)
+#5477 := (+ #2051 #5276)
+#5480 := (+ #5479 #5477)
+#5481 := (= #5480 0::int)
+#5486 := (not #5481)
+#5487 := (+ #5479 #2051)
+#5485 := (>= #5487 0::int)
+#5616 := (or #5485 #5486)
+#6151 := (or #4304 #5616)
+#6113 := (iff #6151 #6150)
+#6153 := (or #4304 #5803)
+#6156 := (iff #6153 #6150)
+#6157 := [rewrite]: #6156
+#6154 := (iff #6151 #6153)
+#5804 := (iff #5616 #5803)
+#5801 := (iff #5486 #5798)
+#5800 := (iff #5481 #5781)
+#5686 := (+ #5276 #5479)
+#5687 := (+ #2051 #5686)
+#5713 := (= #5687 0::int)
+#5782 := (iff #5713 #5781)
+#5799 := [rewrite]: #5782
+#5714 := (iff #5481 #5713)
+#5688 := (= #5480 #5687)
+#5712 := [rewrite]: #5688
+#5848 := [monotonicity #5712]: #5714
+#5779 := [trans #5848 #5799]: #5800
+#5802 := [monotonicity #5779]: #5801
+#5685 := (iff #5485 #5646)
+#5617 := (+ #2051 #5479)
+#5619 := (>= #5617 0::int)
+#5647 := (iff #5619 #5646)
+#5684 := [rewrite]: #5647
+#5615 := (iff #5485 #5619)
+#5612 := (= #5487 #5617)
+#5618 := [rewrite]: #5612
+#5620 := [monotonicity #5618]: #5615
+#5678 := [trans #5620 #5684]: #5685
+#6149 := [monotonicity #5678 #5802]: #5804
+#6155 := [monotonicity #6149]: #6154
+#6114 := [trans #6155 #6157]: #6113
+#6152 := [quant-inst]: #6151
+#6112 := [mp #6152 #6114]: #6150
+#7877 := [unit-resolution #6112 #7930]: #5803
+#7931 := [unit-resolution #7877 #7929]: #5646
+#7932 := [th-lemma #7748 #7931 #7723 #7691]: false
+#7934 := [lemma #7932]: #7933
+#8564 := [unit-resolution #7934 #8584]: #4307
+#4111 := (or #4350 #4310 #4344)
+#4115 := [def-axiom]: #4111
+#8571 := [unit-resolution #4115 #8564 #8563]: #4344
+#3841 := (or #4341 #4335)
+#3842 := [def-axiom]: #3841
+#8559 := [unit-resolution #3842 #8571]: #4335
+#4131 := (or #4338 #4332 #3339)
+#4117 := [def-axiom]: #4131
+#8565 := [unit-resolution #4117 #8559 #8583]: #3339
+#4122 := (or #3334 #2125)
+#4123 := [def-axiom]: #4122
+#8562 := [unit-resolution #4123 #8565]: #2125
+#8472 := (+ #2116 #7370)
+#8485 := (>= #8472 0::int)
+#8471 := (= #2116 #7369)
+#8566 := (= #7369 #2116)
+#8567 := [monotonicity #8584]: #8566
+#8556 := [symm #8567]: #8471
+#8568 := (not #8471)
+#8569 := (or #8568 #8485)
+#8154 := [th-lemma]: #8569
+#8155 := [unit-resolution #8154 #8556]: #8485
+#9079 := (not #8485)
+#9080 := (or #9078 #9079 #2124)
+#9074 := [hypothesis]: #2125
+#9075 := [hypothesis]: #8485
+#9076 := [hypothesis]: #7674
+#9077 := [th-lemma #9076 #9075 #9074]: false
+#9081 := [lemma #9077]: #9080
+#8434 := [unit-resolution #9081 #8155 #8562]: #9078
+#7677 := (f6 f15 ?v1!10)
+#7650 := (= f1 #7677)
+#8152 := (not #7650)
+#6421 := (f13 f14 ?v0!11)
+#6419 := (* -1::int #6421)
+#8184 := (+ #6419 #7369)
+#8185 := (+ #2119 #8184)
+#8193 := (>= #8185 0::int)
+#8633 := (not #8193)
+#8428 := (+ #2114 #6419)
+#8466 := (<= #8428 0::int)
+#8423 := (= #2114 #6421)
+#8435 := (= #6421 #2114)
+#8557 := [monotonicity #8584]: #8435
+#8558 := [symm #8557]: #8423
+#8570 := (not #8423)
+#8601 := (or #8570 #8466)
+#8602 := [th-lemma]: #8601
+#8631 := [unit-resolution #8602 #8558]: #8466
+#4120 := (not #2780)
+#4126 := (or #3334 #4120)
+#3764 := [def-axiom]: #4126
+#8632 := [unit-resolution #3764 #8565]: #4120
+#8635 := (not #8466)
+#7962 := (or #8633 #8635 #2780 #9079)
+#8625 := [th-lemma]: #7962
+#7963 := [unit-resolution #8625 #8632 #8631 #8155]: #8633
+#8014 := (or #8152 #8193)
+#4124 := (or #3334 #2129)
+#4125 := [def-axiom]: #4124
+#8013 := [unit-resolution #4125 #8565]: #2129
+#4008 := (or #4520 #4255)
+#3988 := [def-axiom]: #4008
+#6949 := [unit-resolution #3988 #6915]: #4255
+#8192 := (or #4260 #2128 #8152 #8193)
+#8153 := (+ #7369 #6419)
+#8173 := (+ #2119 #8153)
+#8176 := (>= #8173 0::int)
+#8177 := (or #8152 #2128 #8176)
+#8195 := (or #4260 #8177)
+#8204 := (iff #8195 #8192)
+#8236 := (or #2128 #8152 #8193)
+#8197 := (or #4260 #8236)
+#8203 := (iff #8197 #8192)
+#8201 := [rewrite]: #8203
+#8187 := (iff #8195 #8197)
+#8238 := (iff #8177 #8236)
+#8233 := (or #8152 #2128 #8193)
+#8237 := (iff #8233 #8236)
+#8232 := [rewrite]: #8237
+#8234 := (iff #8177 #8233)
+#8194 := (iff #8176 #8193)
+#8183 := (= #8173 #8185)
+#8186 := [rewrite]: #8183
+#8206 := [monotonicity #8186]: #8194
+#8235 := [monotonicity #8206]: #8234
+#8188 := [trans #8235 #8232]: #8238
+#8202 := [monotonicity #8188]: #8187
+#8205 := [trans #8202 #8201]: #8204
+#8196 := [quant-inst]: #8195
+#8240 := [mp #8196 #8205]: #8192
+#8634 := [unit-resolution #8240 #6949 #8013]: #8014
+#8143 := [unit-resolution #8634 #7963]: #8152
+#7651 := (or #7650 #7674)
+#3823 := (or #4353 #4289)
+#4105 := [def-axiom]: #3823
+#8638 := [unit-resolution #4105 #8582]: #4289
+#7655 := (or #4294 #7650 #7674)
+#7656 := (or #4294 #7651)
+#7695 := (iff #7656 #7655)
+#7935 := [rewrite]: #7695
+#7657 := [quant-inst]: #7656
+#7927 := [mp #7657 #7935]: #7655
+#8639 := [unit-resolution #7927 #8638]: #7651
+#8719 := [unit-resolution #8639 #8143 #8434]: false
+#8745 := [lemma #8719]: #4353
+#4001 := (or #4517 #4356 #4511)
+#4002 := [def-axiom]: #4001
+#9176 := [unit-resolution #4002 #8745 #9175]: #4511
+#4026 := (or #4508 #749)
+#4021 := [def-axiom]: #4026
+#9890 := [unit-resolution #4021 #9176]: #749
+#10056 := [symm #9890]: #10055
+#10053 := (= #9617 #746)
+#9894 := (= #3804 f1)
+#37 := (:var 0 S1)
+#36 := (:var 2 S4)
+#38 := (f7 #36 #14 #37)
+#4172 := (pattern #38)
+#336 := (= f1 #37)
+#39 := (f6 #38 #14)
+#332 := (= f1 #39)
+#339 := (iff #332 #336)
+#4173 := (forall (vars (?v0 S4) (?v1 S3) (?v2 S1)) (:pat #4172) #339)
+#342 := (forall (vars (?v0 S4) (?v1 S3) (?v2 S1)) #339)
+#4176 := (iff #342 #4173)
+#4174 := (iff #339 #339)
+#4175 := [refl]: #4174
+#4177 := [quant-intro #4175]: #4176
+#1821 := (~ #342 #342)
+#1851 := (~ #339 #339)
 #1852 := [refl]: #1851
-#1854 := [nnf-pos #1852]: #1853
-#1857 := [nnf-neg #1854]: #1856
-#2454 := [nnf-neg #1857 #2450]: #2453
-#1847 := (~ #1111 #1846)
-#1848 := [sk]: #1847
-#2458 := [nnf-neg #1848 #2454]: #2457
-#1815 := (~ #1814 #1814)
-#1842 := [refl]: #1815
-#2462 := [nnf-neg #1842 #2458]: #2461
-#1840 := (~ #1102 #1102)
-#1841 := [refl]: #1840
-#2465 := [nnf-neg #1841 #2462]: #2464
-#1743 := [not-or-elim #1739]: #1742
-#2466 := [mp~ #1743 #2465]: #2463
-#2467 := [mp #2466 #3004]: #3002
-#3661 := [mp #2467 #3660]: #3658
-#4534 := [mp #3661 #4533]: #4531
-#6983 := [unit-resolution #4534 #4636]: #4528
-#3907 := (or #4525 #4519)
-#3908 := [def-axiom]: #3907
-#6984 := [unit-resolution #3908 #6983]: #4519
-#290 := (<= f3 0::int)
-#291 := (not #290)
-#10 := (< 0::int f3)
-#292 := (iff #10 #291)
-#293 := [rewrite]: #292
-#287 := [asserted]: #10
-#294 := [mp #287 #293]: #291
-#4697 := (* -1::int #1844)
-#4698 := (+ f3 #4697)
-#4699 := (<= #4698 0::int)
-#4625 := (= f3 #1844)
-#4628 := (= f6 ?v0!0)
-#4703 := (not #4628)
-#4695 := (= #1844 0::int)
-#4845 := (not #4695)
-#4844 := [hypothesis]: #1846
-#4846 := (or #4845 #1845)
-#4847 := [th-lemma]: #4846
-#4848 := [unit-resolution #4847 #4844]: #4845
-#4770 := (or #4588 #4703 #4695)
-#4626 := (= ?v0!0 f6)
-#4701 := (not #4626)
-#4702 := (or #4701 #4695)
-#4753 := (or #4588 #4702)
-#4759 := (iff #4753 #4770)
-#4720 := (or #4703 #4695)
-#4755 := (or #4588 #4720)
-#4752 := (iff #4755 #4770)
-#4758 := [rewrite]: #4752
-#4756 := (iff #4753 #4755)
-#4721 := (iff #4702 #4720)
-#4704 := (iff #4701 #4703)
-#4629 := (iff #4626 #4628)
-#4647 := [rewrite]: #4629
-#4705 := [monotonicity #4647]: #4704
-#4769 := [monotonicity #4705]: #4721
-#4757 := [monotonicity #4769]: #4756
-#4760 := [trans #4757 #4758]: #4759
-#4754 := [quant-inst]: #4753
-#4761 := [mp #4754 #4760]: #4770
-#4849 := [unit-resolution #4761 #4540 #4848]: #4703
-#4651 := (or #4625 #4628)
-#4149 := (forall (vars (?v0 S2)) (:pat #4148) #360)
-#4152 := (iff #365 #4149)
-#4150 := (iff #360 #360)
-#4151 := [refl]: #4150
-#4153 := [quant-intro #4151]: #4152
-#1810 := (~ #365 #365)
-#1834 := (~ #360 #360)
-#1835 := [refl]: #1834
-#1811 := [nnf-pos #1835]: #1810
-#1740 := [not-or-elim #1739]: #365
-#1836 := [mp~ #1740 #1811]: #365
-#4154 := [mp #1836 #4153]: #4149
-#4655 := (not #4149)
-#4656 := (or #4655 #4625 #4628)
-#4627 := (or #4626 #4625)
-#4708 := (or #4655 #4627)
-#4715 := (iff #4708 #4656)
-#4710 := (or #4655 #4651)
-#4713 := (iff #4710 #4656)
-#4714 := [rewrite]: #4713
-#4711 := (iff #4708 #4710)
-#4653 := (iff #4627 #4651)
-#4648 := (or #4628 #4625)
-#4646 := (iff #4648 #4651)
-#4652 := [rewrite]: #4646
-#4649 := (iff #4627 #4648)
-#4650 := [monotonicity #4647]: #4649
-#4654 := [trans #4650 #4652]: #4653
-#4712 := [monotonicity #4654]: #4711
-#4716 := [trans #4712 #4714]: #4715
-#4709 := [quant-inst]: #4708
-#4696 := [mp #4709 #4716]: #4656
-#4853 := [unit-resolution #4696 #4154]: #4651
-#4854 := [unit-resolution #4853 #4849]: #4625
-#4901 := (not #4625)
-#4902 := (or #4901 #4699)
-#4903 := [th-lemma]: #4902
-#4904 := [unit-resolution #4903 #4854]: #4699
-#4762 := (<= #1844 0::int)
-#4905 := (or #4762 #1845)
-#4900 := [th-lemma]: #4905
-#4906 := [unit-resolution #4900 #4844]: #4762
-#4907 := [th-lemma #4906 #4904 #294]: false
-#4908 := [lemma #4907]: #1845
-#3902 := (or #4522 #1846 #4516)
-#3903 := [def-axiom]: #3902
-#6955 := [unit-resolution #3903 #4908 #6984]: #4516
-#3926 := (or #4513 #4507)
-#3927 := [def-axiom]: #3926
-#6985 := [unit-resolution #3927 #6955]: #4507
-#5112 := [hypothesis]: #1866
-#4156 := (forall (vars (?v0 S2)) (:pat #4155) #371)
-#4159 := (iff #374 #4156)
-#4157 := (iff #371 #371)
-#4158 := [refl]: #4157
-#4160 := [quant-intro #4158]: #4159
-#1812 := (~ #374 #374)
-#1837 := (~ #371 #371)
-#1838 := [refl]: #1837
-#1813 := [nnf-pos #1838]: #1812
-#1741 := [not-or-elim #1739]: #374
-#1839 := [mp~ #1741 #1813]: #374
-#4161 := [mp #1839 #4160]: #4156
-#3899 := (not #4156)
-#4942 := (or #3899 #2112)
-#4943 := [quant-inst]: #4942
-#5113 := [unit-resolution #4943 #4161 #5112]: false
-#5125 := [lemma #5113]: #2112
-#3719 := (or #3011 #1866)
-#3806 := [def-axiom]: #3719
-#6986 := [unit-resolution #3806 #5125]: #3011
-#3920 := (or #4510 #3016 #4504)
-#3922 := [def-axiom]: #3920
-#6981 := [unit-resolution #3922 #6986 #6985]: #4504
-#3947 := (or #4501 #4495)
-#3948 := [def-axiom]: #3947
-#6987 := [unit-resolution #3948 #6981]: #4495
-#6988 := (or #4498 #4492)
-#4583 := [hypothesis]: #1894
-#3900 := (or #3899 #3042)
-#3898 := [quant-inst]: #3900
-#4584 := [unit-resolution #3898 #4161 #4583]: false
-#4592 := [lemma #4584]: #3042
-#3809 := (or #3057 #1894)
-#3813 := [def-axiom]: #3809
-#6954 := [unit-resolution #3813 #4592]: #3057
-#3943 := (or #4498 #3062 #4492)
-#3944 := [def-axiom]: #3943
-#6989 := [unit-resolution #3944 #6954]: #6988
-#6990 := [unit-resolution #6989 #6987]: #4492
-#3957 := (or #4489 #4483)
-#3978 := [def-axiom]: #3957
-#6991 := [unit-resolution #3978 #6990]: #4483
-#5069 := (= f3 #1919)
-#5212 := (not #5069)
-#5185 := [hypothesis]: #4200
-#4123 := (or #4197 #1931)
-#3797 := [def-axiom]: #4123
-#5190 := [unit-resolution #3797 #5185]: #1931
-#5213 := (or #5212 #1930)
-#5178 := [th-lemma]: #5213
-#5214 := [unit-resolution #5178 #5190]: #5212
-#3798 := (or #4197 #2518)
-#4130 := [def-axiom]: #3798
-#5215 := [unit-resolution #4130 #5185]: #2518
-#5107 := (or #4655 #2515 #5069)
-#5070 := (or #1932 #5069)
-#5094 := (or #4655 #5070)
-#4988 := (iff #5094 #5107)
-#5096 := (or #2515 #5069)
-#5103 := (or #4655 #5096)
-#5110 := (iff #5103 #5107)
-#4987 := [rewrite]: #5110
-#5104 := (iff #5094 #5103)
-#5105 := (iff #5070 #5096)
-#5106 := [monotonicity #2517]: #5105
-#5109 := [monotonicity #5106]: #5104
-#4989 := [trans #5109 #4987]: #4988
-#5108 := [quant-inst]: #5094
-#5008 := [mp #5108 #4989]: #5107
-#5216 := [unit-resolution #5008 #4154 #5215 #5214]: false
-#5211 := [lemma #5216]: #4197
-#3965 := (or #4486 #4200 #4480)
-#3966 := [def-axiom]: #3965
-#6995 := [unit-resolution #3966 #5211 #6991]: #4480
-#3987 := (or #4477 #4471)
-#3955 := [def-axiom]: #3987
-#9540 := [unit-resolution #3955 #6995]: #4471
-#6497 := [hypothesis]: #4313
-#4098 := (or #4310 #538)
-#4099 := [def-axiom]: #4098
-#6498 := [unit-resolution #4099 #6497]: #538
-#4100 := (or #4310 #4304)
-#4097 := [def-axiom]: #4100
-#6538 := [unit-resolution #4097 #6497]: #4304
-#3996 := (or #4477 #67)
-#3997 := [def-axiom]: #3996
-#6994 := [unit-resolution #3997 #6995]: #67
-#6569 := (= #124 #66)
-#6495 := [symm #6498]: #105
-#6570 := [monotonicity #6495]: #6569
-#6364 := [trans #6570 #6994]: #125
-#4110 := (or #4286 #2114)
-#3773 := [def-axiom]: #4110
-#6366 := [unit-resolution #3773 #6364]: #4286
-#3814 := (or #4310 #4246)
-#4096 := [def-axiom]: #3814
-#6387 := [unit-resolution #4096 #6497]: #4246
-#8856 := (or #3325 #4251 #629)
-#8080 := (f9 f10 ?v1!10)
-#8078 := (* -1::int #8080)
-#8081 := (+ f3 #8078)
-#8135 := (<= #8081 0::int)
-#9265 := (not #8135)
-#8756 := [hypothesis]: #3330
-#4113 := (or #3325 #2101)
-#4114 := [def-axiom]: #4113
-#8751 := [unit-resolution #4114 #8756]: #2101
-#8701 := (+ #2092 #8078)
-#8703 := (>= #8701 0::int)
-#8700 := (= #2092 #8080)
-#8757 := (= #8080 #2092)
-#8129 := [hypothesis]: #538
-#8758 := [monotonicity #8129]: #8757
-#8759 := [symm #8758]: #8700
-#8760 := (not #8700)
-#8761 := (or #8760 #8703)
-#8744 := [th-lemma]: #8761
-#8745 := [unit-resolution #8744 #8759]: #8703
-#9266 := (not #8703)
-#9310 := (or #9265 #9266 #2100)
-#9256 := [hypothesis]: #2101
-#9262 := [hypothesis]: #8703
-#9263 := [hypothesis]: #8135
-#9264 := [th-lemma #9263 #9262 #9256]: false
-#9311 := [lemma #9264]: #9310
-#8740 := [unit-resolution #9311 #8745 #8751]: #9265
-#8136 := (f11 f12 ?v1!10)
-#6426 := (= f1 #8136)
-#8482 := (not #6426)
-#6573 := (f9 f10 ?v0!11)
-#6574 := (* -1::int #6573)
-#8484 := (+ #6574 #8080)
-#8479 := (+ #2095 #8484)
-#8487 := (>= #8479 0::int)
-#8775 := (not #8487)
-#8680 := (+ #2090 #6574)
-#8698 := (<= #8680 0::int)
-#8679 := (= #2090 #6573)
-#8746 := (= #6573 #2090)
-#8747 := [monotonicity #8129]: #8746
-#8743 := [symm #8747]: #8679
-#8748 := (not #8679)
-#8749 := (or #8748 #8698)
-#8750 := [th-lemma]: #8749
-#8752 := [unit-resolution #8750 #8743]: #8698
-#4111 := (not #2756)
-#4117 := (or #3325 #4111)
-#3755 := [def-axiom]: #4117
-#8753 := [unit-resolution #3755 #8756]: #4111
-#8776 := (not #8698)
-#8779 := (or #8775 #8776 #2756 #9266)
-#8780 := [th-lemma]: #8779
-#8781 := [unit-resolution #8780 #8753 #8752 #8745]: #8775
-#8782 := (or #8482 #8487)
-#4115 := (or #3325 #2105)
-#4116 := [def-axiom]: #4115
-#8774 := [unit-resolution #4116 #8756]: #2105
-#3999 := (or #4477 #4212)
-#3979 := [def-axiom]: #3999
-#7050 := [unit-resolution #3979 #6995]: #4212
-#8513 := (or #4217 #2104 #8482 #8487)
-#8454 := (+ #8080 #6574)
-#8455 := (+ #2095 #8454)
-#8481 := (>= #8455 0::int)
-#8483 := (or #8482 #2104 #8481)
-#8514 := (or #4217 #8483)
-#8520 := (iff #8514 #8513)
-#8498 := (or #2104 #8482 #8487)
-#8510 := (or #4217 #8498)
-#8518 := (iff #8510 #8513)
-#8519 := [rewrite]: #8518
-#8516 := (iff #8514 #8510)
-#8511 := (iff #8483 #8498)
-#8496 := (or #8482 #2104 #8487)
-#8499 := (iff #8496 #8498)
-#8500 := [rewrite]: #8499
-#8497 := (iff #8483 #8496)
-#8488 := (iff #8481 #8487)
-#8485 := (= #8455 #8479)
-#8486 := [rewrite]: #8485
-#8489 := [monotonicity #8486]: #8488
-#8495 := [monotonicity #8489]: #8497
-#8512 := [trans #8495 #8500]: #8511
-#8517 := [monotonicity #8512]: #8516
-#8544 := [trans #8517 #8519]: #8520
-#8515 := [quant-inst]: #8514
-#8545 := [mp #8515 #8544]: #8513
-#8783 := [unit-resolution #8545 #7050 #8774]: #8782
-#8778 := [unit-resolution #8783 #8781]: #8482
-#6427 := (or #6426 #8135)
-#7034 := [hypothesis]: #4246
-#6917 := (or #4251 #6426 #8135)
-#6918 := (or #4251 #6427)
-#7082 := (iff #6918 #6917)
-#7258 := [rewrite]: #7082
-#6919 := [quant-inst]: #6918
-#7256 := [mp #6919 #7258]: #6917
-#8784 := [unit-resolution #7256 #7034]: #6427
-#8785 := [unit-resolution #8784 #8778 #8740]: false
-#8859 := [lemma #8785]: #8856
-#6404 := [unit-resolution #8859 #6387 #6498]: #3325
-#4122 := (or #4295 #4289 #3330)
-#4108 := [def-axiom]: #4122
-#6405 := [unit-resolution #4108 #6404 #6366]: #4295
-#3832 := (or #4298 #4292)
-#3833 := [def-axiom]: #3832
-#6412 := [unit-resolution #3833 #6405]: #4298
-#4102 := (or #4307 #4267 #4301)
-#4106 := [def-axiom]: #4102
-#6363 := [unit-resolution #4106 #6412 #6538]: #4267
-#4134 := (or #4264 #2039)
-#4124 := [def-axiom]: #4134
-#6406 := [unit-resolution #4124 #6363]: #2039
-#8285 := (or #4264 #629 #2038)
-#5344 := (?v1!7 ?v0!8)
-#5850 := (f9 f16 #5344)
-#5807 := (* -1::int #5850)
-#6152 := (+ #2026 #5807)
-#6153 := (<= #6152 0::int)
-#8215 := (not #6153)
-#5345 := (f9 f10 #5344)
-#6786 := (+ #5345 #5807)
-#6788 := (>= #6786 0::int)
-#6784 := (= #5345 #5850)
-#8131 := (= #5850 #5345)
-#8130 := [symm #8129]: #105
-#8132 := [monotonicity #8130]: #8131
-#8147 := [symm #8132]: #6784
-#8148 := (not #6784)
-#8173 := (or #8148 #6788)
-#8174 := [th-lemma]: #8173
-#8175 := [unit-resolution #8174 #8147]: #6788
-#5346 := (* -1::int #5345)
-#5282 := (f9 f10 ?v0!8)
-#5347 := (+ #5282 #5346)
-#5373 := (<= #5347 0::int)
-#5405 := (not #5373)
-#5379 := (f11 f12 #5344)
-#5380 := (= f1 #5379)
-#5381 := (not #5380)
-#5374 := (f5 #5344 ?v0!8)
-#5375 := (f4 #5374)
-#5376 := (* -1::int #5375)
-#5371 := (+ #5346 #5376)
-#5372 := (+ #5282 #5371)
-#5377 := (= #5372 0::int)
-#5378 := (not #5377)
-#5435 := (or #5373 #5378 #5381)
-#5438 := (not #5435)
-#5283 := (* -1::int #5282)
-#5284 := (+ f3 #5283)
-#5310 := (<= #5284 0::int)
-#5809 := (not #5310)
-#5691 := [hypothesis]: #2039
-#5625 := (+ #2026 #5283)
-#5690 := (>= #5625 0::int)
-#5681 := (= #2026 #5282)
-#8176 := (= #5282 #2026)
-#8177 := [monotonicity #8129]: #8176
-#8172 := [symm #8177]: #5681
-#8178 := (not #5681)
-#8179 := (or #8178 #5690)
-#8180 := [th-lemma]: #8179
-#8181 := [unit-resolution #8180 #8172]: #5690
-#5847 := (not #5690)
-#5848 := (or #5809 #5847 #2038)
-#5715 := [hypothesis]: #5310
-#5716 := [hypothesis]: #5690
-#5808 := [th-lemma #5716 #5715 #5691]: false
-#5849 := [lemma #5808]: #5848
-#8182 := [unit-resolution #5849 #8181 #5691]: #5809
-#8212 := (or #5310 #5438)
-#8209 := [hypothesis]: #4267
-#3784 := (or #4264 #2656)
-#3789 := [def-axiom]: #3784
-#8210 := [unit-resolution #3789 #8209]: #2656
-#3986 := (or #4477 #4237)
-#3981 := [def-axiom]: #3986
-#8211 := [unit-resolution #3981 #6995]: #4237
-#5443 := (or #4242 #2653 #5310 #5438)
-#5409 := (or #5381 #5378 #5373)
-#5410 := (not #5409)
-#5434 := (or #2040 #5310 #5410)
-#5491 := (or #4242 #5434)
-#5501 := (iff #5491 #5443)
-#5440 := (or #2653 #5310 #5438)
-#5493 := (or #4242 #5440)
-#5497 := (iff #5493 #5443)
-#5500 := [rewrite]: #5497
-#5498 := (iff #5491 #5493)
-#5441 := (iff #5434 #5440)
-#5433 := (iff #5410 #5438)
-#5436 := (iff #5409 #5435)
-#5437 := [rewrite]: #5436
-#5439 := [monotonicity #5437]: #5433
-#5442 := [monotonicity #2655 #5439]: #5441
-#5499 := [monotonicity #5442]: #5498
-#5402 := [trans #5499 #5500]: #5501
-#5492 := [quant-inst]: #5491
-#5403 := [mp #5492 #5402]: #5443
-#8213 := [unit-resolution #5403 #8211 #8210]: #8212
-#8208 := [unit-resolution #8213 #8182]: #5438
-#5400 := (or #5435 #5405)
-#5406 := [def-axiom]: #5400
-#8214 := [unit-resolution #5406 #8208]: #5405
-#8216 := (not #6788)
-#8217 := (or #8215 #5847 #5373 #8216)
-#8218 := [th-lemma]: #8217
-#8223 := [unit-resolution #8218 #8181 #8214 #8175]: #8215
-#5875 := (+ #5376 #5807)
-#5879 := (+ #2026 #5875)
-#5880 := (= #5879 0::int)
-#6187 := (>= #5879 0::int)
-#5404 := (>= #5372 0::int)
-#5407 := (or #5435 #5377)
-#5408 := [def-axiom]: #5407
-#8224 := [unit-resolution #5408 #8208]: #5377
-#8227 := (or #5378 #5404)
-#8228 := [th-lemma]: #8227
-#8246 := [unit-resolution #8228 #8224]: #5404
-#7153 := (not #5404)
-#8247 := (or #6187 #5847 #7153 #8216)
-#8248 := [th-lemma]: #8247
-#8249 := [unit-resolution #8248 #8181 #8246 #8175]: #6187
-#6211 := (<= #5879 0::int)
-#6785 := (<= #6786 0::int)
-#8250 := (or #8148 #6785)
-#8245 := [th-lemma]: #8250
-#8251 := [unit-resolution #8245 #8147]: #6785
-#5401 := (<= #5372 0::int)
-#8252 := (or #5378 #5401)
-#8253 := [th-lemma]: #8252
-#8254 := [unit-resolution #8253 #8224]: #5401
-#5689 := (<= #5625 0::int)
-#8255 := (or #8178 #5689)
-#8264 := [th-lemma]: #8255
-#8265 := [unit-resolution #8264 #8172]: #5689
-#8268 := (not #6785)
-#8267 := (not #5401)
-#8266 := (not #5689)
-#8263 := (or #6211 #8266 #8267 #8268)
-#8269 := [th-lemma]: #8263
-#8270 := [unit-resolution #8269 #8265 #8254 #8251]: #6211
-#8272 := (not #6187)
-#8271 := (not #6211)
-#8273 := (or #5880 #8271 #8272)
-#8286 := [th-lemma]: #8273
-#8287 := [unit-resolution #8286 #8270 #8249]: #5880
-#6115 := (not #5880)
-#6146 := (or #6115 #6153)
-#4125 := (or #4264 #4256)
-#3785 := [def-axiom]: #4125
-#8288 := [unit-resolution #3785 #8209]: #4256
-#6327 := (or #4261 #6115 #6153)
-#5717 := (+ #2027 #5375)
-#5851 := (+ #5850 #5717)
-#5846 := (= #5851 0::int)
-#5783 := (not #5846)
-#5784 := (+ #5850 #2027)
-#5802 := (>= #5784 0::int)
-#5803 := (or #5802 #5783)
-#6328 := (or #4261 #5803)
-#6189 := (iff #6328 #6327)
-#6308 := (or #4261 #6146)
-#6311 := (iff #6308 #6327)
-#6312 := [rewrite]: #6311
-#6309 := (iff #6328 #6308)
-#6149 := (iff #5803 #6146)
-#6105 := (or #6153 #6115)
-#6147 := (iff #6105 #6146)
-#6148 := [rewrite]: #6147
-#6116 := (iff #5803 #6105)
-#6118 := (iff #5783 #6115)
-#5929 := (iff #5846 #5880)
-#6158 := (+ #5375 #5850)
-#6159 := (+ #2027 #6158)
-#5877 := (= #6159 0::int)
-#5881 := (iff #5877 #5880)
-#5928 := [rewrite]: #5881
-#5878 := (iff #5846 #5877)
-#5876 := (= #5851 #6159)
-#5871 := [rewrite]: #5876
-#5874 := [monotonicity #5871]: #5878
-#6117 := [trans #5874 #5928]: #5929
-#6119 := [monotonicity #6117]: #6118
-#6156 := (iff #5802 #6153)
-#5785 := (+ #2027 #5850)
-#5804 := (>= #5785 0::int)
-#6154 := (iff #5804 #6153)
-#6155 := [rewrite]: #6154
-#5805 := (iff #5802 #5804)
-#5782 := (= #5784 #5785)
-#5801 := [rewrite]: #5782
-#5806 := [monotonicity #5801]: #5805
-#6157 := [trans #5806 #6155]: #6156
-#6120 := [monotonicity #6157 #6119]: #6116
-#6326 := [trans #6120 #6148]: #6149
-#6310 := [monotonicity #6326]: #6309
-#6190 := [trans #6310 #6312]: #6189
-#6323 := [quant-inst]: #6328
-#6210 := [mp #6323 #6190]: #6327
-#8289 := [unit-resolution #6210 #8288]: #6146
-#8290 := [unit-resolution #8289 #8287 #8223]: false
-#8291 := [lemma #8290]: #8285
-#6402 := [unit-resolution #8291 #6406 #6363 #6498]: false
-#6403 := [lemma #6402]: #4310
-#3992 := (or #4474 #4313 #4468)
+#1822 := [nnf-pos #1852]: #1821
+#41 := (= #37 f1)
+#40 := (= #39 f1)
+#42 := (iff #40 #41)
+#43 := (forall (vars (?v0 S4) (?v1 S3) (?v2 S1)) #42)
+#343 := (iff #43 #342)
+#340 := (iff #42 #339)
+#337 := (iff #41 #336)
+#338 := [rewrite]: #337
+#334 := (iff #40 #332)
+#335 := [rewrite]: #334
+#341 := [monotonicity #335 #338]: #340
+#344 := [quant-intro #341]: #343
+#331 := [asserted]: #43
+#347 := [mp #331 #344]: #342
+#1853 := [mp~ #347 #1822]: #342
+#4178 := [mp #1853 #4177]: #4173
+#6420 := (not #4173)
+#6343 := (or #6420 #3805)
+#3865 := (= f1 f1)
+#3796 := (iff #3805 #3865)
+#6344 := (or #6420 #3796)
+#6353 := (iff #6344 #6343)
+#6377 := (iff #6343 #6343)
+#6335 := [rewrite]: #6377
+#3758 := (iff #3796 #3805)
+#3752 := (iff #3805 true)
+#3760 := (iff #3752 #3805)
+#3762 := [rewrite]: #3760
+#3757 := (iff #3796 #3752)
+#3765 := (iff #3865 true)
+#3751 := [rewrite]: #3765
+#3759 := [monotonicity #3751]: #3757
+#3763 := [trans #3759 #3762]: #3758
+#6351 := [monotonicity #3763]: #6353
+#6352 := [trans #6351 #6335]: #6353
+#6345 := [quant-inst]: #6344
+#6354 := [mp #6345 #6352]: #6343
+#9891 := [unit-resolution #6354 #4178]: #3805
+#9895 := [symm #9891]: #9894
+#10054 := [monotonicity #10000 #9895]: #10053
+#10052 := [trans #10054 #10056]: #10057
+#19330 := [monotonicity #10052]: #19329
+#19374 := [monotonicity #19330]: #19320
+#19376 := [symm #19374]: #19375
+#19378 := [monotonicity #19376]: #19377
+#6733 := [hypothesis]: #3418
+#3946 := (or #3413 #2272)
+#3947 := [def-axiom]: #3946
+#6735 := [unit-resolution #3947 #6733]: #2272
+#19380 := [mp #6735 #19378]: #17728
+#17727 := (not #12752)
+#17744 := (or #17727 #17705 #12750)
+#17745 := [def-axiom]: #17744
+#19381 := [unit-resolution #17745 #19380 #19323]: #17705
+#19364 := (or #12748 #17719)
+#8905 := (not #3805)
+#17723 := (or #12748 #17719 #8905)
+#17724 := [def-axiom]: #17723
+#19365 := [unit-resolution #17724 #9891]: #19364
+#19366 := [unit-resolution #19365 #19381]: #17719
+#13908 := (f3 #9390 ?v1!16)
+#13909 := (f9 #13908)
+#15031 := (<= #13909 0::int)
+#4727 := (f24 f22)
+#4768 := (* -1::int #4727)
+#6371 := (+ #2263 #4768)
+#15115 := (<= #6371 0::int)
+#19756 := (= #2263 #4727)
+#6427 := (= ?v0!17 f22)
+#12797 := (= ?v0!17 #9390)
+#4089 := (not #2861)
+#4090 := (or #3413 #4089)
+#4091 := [def-axiom]: #4090
+#6734 := [unit-resolution #4091 #6733]: #4089
+#19453 := (or #3413 #2861 #12797)
+#6647 := (f3 f22 ?v1!16)
+#6648 := (f9 #6647)
+#6673 := (+ #2859 #6648)
+#6674 := (+ #174 #6673)
+#17846 := (<= #6674 0::int)
+#6677 := (= #6674 0::int)
+#6652 := (* -1::int #6648)
+#6656 := (+ f8 #6652)
+#6657 := (<= #6656 0::int)
+#17887 := (not #6657)
+#6614 := (f13 f14 ?v1!16)
+#6631 := (* -1::int #6614)
+#6666 := (+ #6631 #6648)
+#6667 := (+ #174 #6666)
+#6668 := (>= #6667 0::int)
+#6703 := (or #6657 #6668)
+#6706 := (not #6703)
+#6700 := (= #2265 #6614)
+#19461 := (not #6700)
+#6632 := (+ #2265 #6631)
+#11013 := (>= #6632 0::int)
+#19369 := (not #11013)
+#9900 := (f13 f14 #9390)
+#9913 := (* -1::int #9900)
+#6383 := (f13 f14 ?v0!17)
+#13991 := (+ #6383 #9913)
+#13992 := (<= #13991 0::int)
+#6417 := (f6 f15 ?v0!17)
+#6418 := (= f1 #6417)
+#12815 := (not #12797)
+#19268 := [hypothesis]: #12815
+#12798 := (ite #12797 #3805 #6418)
+#12799 := (f6 #9617 ?v0!17)
+#12800 := (= f1 #12799)
+#12802 := (iff #12798 #12800)
+#17740 := (or #8910 #12802)
+#12801 := (iff #12800 #12798)
+#17754 := (or #8910 #12801)
+#17760 := (iff #17754 #17740)
+#17759 := (iff #17740 #17740)
+#17762 := [rewrite]: #17759
+#12803 := (iff #12801 #12802)
+#12804 := [rewrite]: #12803
+#17761 := [monotonicity #12804]: #17760
+#17763 := [trans #17761 #17762]: #17760
+#17755 := [quant-inst]: #17754
+#17764 := [mp #17755 #17763]: #17740
+#19269 := [unit-resolution #17764 #4171]: #12802
+#19273 := (= #2268 #12799)
+#19243 := (= #12799 #2268)
+#19270 := [monotonicity #10052]: #19243
+#19274 := [symm #19270]: #19273
+#4104 := (or #3413 #2269)
+#3945 := [def-axiom]: #4104
+#6736 := [unit-resolution #3945 #6733]: #2269
+#19267 := [trans #6736 #19274]: #12800
+#17770 := (not #12800)
+#17769 := (not #12802)
+#17768 := (or #17769 #12798 #17770)
+#17771 := [def-axiom]: #17768
+#19275 := [unit-resolution #17771 #19267 #19269]: #12798
+#10331 := (not #12798)
+#10328 := (or #10331 #12797 #6418)
+#10334 := [def-axiom]: #10328
+#19276 := [unit-resolution #10334 #19275 #19268]: #6418
+#10397 := (not #6418)
+#19277 := (or #10397 #13992)
+#9748 := (f6 f15 #9390)
+#9749 := (= f1 #9748)
+#10007 := (not #9749)
+#10001 := (= #9748 #171)
+#15180 := (= #171 #9748)
+#15178 := [monotonicity #9998]: #15180
+#15241 := [symm #15178]: #10001
+#15173 := [hypothesis]: #9749
+#15242 := [trans #15173 #15241]: #727
+#4024 := (or #4508 #730)
+#4025 := [def-axiom]: #4024
+#9997 := [unit-resolution #4025 #9176]: #730
+#15244 := [unit-resolution #9997 #15242]: false
+#15245 := [lemma #15244]: #10007
+#3934 := (or #4520 #4264)
+#3989 := [def-axiom]: #3934
+#10011 := [unit-resolution #3989 #6915]: #4264
+#17998 := (or #4269 #10397 #9749 #13992)
+#5555 := (* -1::int #6383)
+#13962 := (+ #9900 #5555)
+#13987 := (>= #13962 0::int)
+#13988 := (or #9749 #10397 #13987)
+#18048 := (or #4269 #13988)
+#18136 := (iff #18048 #17998)
+#14164 := (or #10397 #9749 #13992)
+#18077 := (or #4269 #14164)
+#18088 := (iff #18077 #17998)
+#18089 := [rewrite]: #18088
+#18075 := (iff #18048 #18077)
+#14190 := (iff #13988 #14164)
+#14053 := (or #9749 #10397 #13992)
+#14159 := (iff #14053 #14164)
+#14165 := [rewrite]: #14159
+#14059 := (iff #13988 #14053)
+#14022 := (iff #13987 #13992)
+#13989 := (+ #5555 #9900)
+#13985 := (>= #13989 0::int)
+#13955 := (iff #13985 #13992)
+#13993 := [rewrite]: #13955
+#13961 := (iff #13987 #13985)
+#13990 := (= #13962 #13989)
+#13956 := [rewrite]: #13990
+#13986 := [monotonicity #13956]: #13961
+#14024 := [trans #13986 #13993]: #14022
+#14163 := [monotonicity #14024]: #14059
+#14162 := [trans #14163 #14165]: #14190
+#18087 := [monotonicity #14162]: #18075
+#18145 := [trans #18087 #18089]: #18136
+#18076 := [quant-inst]: #18048
+#18146 := [mp #18076 #18145]: #17998
+#19321 := [unit-resolution #18146 #10011 #15245]: #19277
+#19322 := [unit-resolution #19321 #19276]: #13992
+#14769 := [hypothesis]: #4089
+#5655 := (+ #2263 #5555)
+#5679 := (<= #5655 0::int)
+#4703 := (f3 f22 ?v0!13)
+#4704 := (f9 #4703)
+#8773 := (+ #2205 #4704)
+#8976 := (+ #174 #8773)
+#9034 := (>= #8976 0::int)
+#8979 := (= #8976 0::int)
+#8480 := (+ #2821 #4704)
+#8753 := (+ #174 #8480)
+#8754 := (>= #8753 0::int)
+#8906 := (not #8754)
+#8760 := (* -1::int #4704)
+#8764 := (+ f8 #8760)
+#8765 := (<= #8764 0::int)
+#9049 := (or #8754 #8765)
+#9059 := (not #9049)
+#9038 := (= #2204 #2206)
+#9169 := (not #9038)
+#9168 := [hypothesis]: #2828
+#9172 := (or #9169 #2823)
+#9173 := [th-lemma]: #9172
+#9174 := [unit-resolution #9173 #9168]: #9169
+#4017 := (or #4508 #4369)
+#4012 := [def-axiom]: #4017
+#9177 := [unit-resolution #4012 #9176]: #4369
+#8837 := (or #4374 #9038 #9059)
+#8761 := (+ #1426 #8760)
+#8762 := (+ #2206 #8761)
+#8763 := (<= #8762 0::int)
+#9029 := (or #8765 #8763)
+#9035 := (not #9029)
+#9036 := (= #2206 #2204)
+#9037 := (or #9036 #9035)
+#8840 := (or #4374 #9037)
+#8830 := (iff #8840 #8837)
+#8150 := (or #9038 #9059)
+#8845 := (or #4374 #8150)
+#8849 := (iff #8845 #8837)
+#8850 := [rewrite]: #8849
+#8843 := (iff #8840 #8845)
+#8151 := (iff #9037 #8150)
+#8580 := (iff #9035 #9059)
+#9055 := (iff #9029 #9049)
+#9047 := (or #8765 #8754)
+#9050 := (iff #9047 #9049)
+#9054 := [rewrite]: #9050
+#9045 := (iff #9029 #9047)
+#8757 := (iff #8763 #8754)
+#8767 := (+ #2206 #8760)
+#8768 := (+ #1426 #8767)
+#8483 := (<= #8768 0::int)
+#8755 := (iff #8483 #8754)
+#8756 := [rewrite]: #8755
+#8720 := (iff #8763 #8483)
+#8481 := (= #8762 #8768)
+#8482 := [rewrite]: #8481
+#8721 := [monotonicity #8482]: #8720
+#8772 := [trans #8721 #8756]: #8757
+#9048 := [monotonicity #8772]: #9045
+#9058 := [trans #9048 #9054]: #9055
+#8581 := [monotonicity #9058]: #8580
+#9039 := (iff #9036 #9038)
+#9046 := [rewrite]: #9039
+#8834 := [monotonicity #9046 #8581]: #8151
+#8847 := [monotonicity #8834]: #8843
+#8851 := [trans #8847 #8850]: #8830
+#8844 := [quant-inst]: #8840
+#8829 := [mp #8844 #8851]: #8837
+#9178 := [unit-resolution #8829 #9177 #9174]: #9059
+#8907 := (or #9049 #8906)
+#8758 := [def-axiom]: #8907
+#9179 := [unit-resolution #8758 #9178]: #8906
+#8759 := (not #8765)
+#9056 := (or #9049 #8759)
+#9061 := [def-axiom]: #9056
+#9180 := [unit-resolution #9061 #9178]: #8759
+#8984 := (or #8754 #8765 #8979)
+#4018 := (or #4508 #4377)
+#3991 := [def-axiom]: #4018
+#9181 := [unit-resolution #3991 #9176]: #4377
+#9015 := (or #4382 #8754 #8765 #8979)
+#4787 := (+ #4704 #2205)
+#4788 := (+ #174 #4787)
+#4836 := (= #4788 0::int)
+#8766 := (or #8765 #8763 #4836)
+#9016 := (or #4382 #8766)
+#9030 := (iff #9016 #9015)
+#9017 := (or #4382 #8984)
+#9020 := (iff #9017 #9015)
+#9021 := [rewrite]: #9020
+#9018 := (iff #9016 #9017)
+#9013 := (iff #8766 #8984)
+#8981 := (or #8765 #8754 #8979)
+#8985 := (iff #8981 #8984)
+#9012 := [rewrite]: #8985
+#8982 := (iff #8766 #8981)
+#8980 := (iff #4836 #8979)
+#8977 := (= #4788 #8976)
+#8978 := [rewrite]: #8977
+#8975 := [monotonicity #8978]: #8980
+#8983 := [monotonicity #8772 #8975]: #8982
+#9014 := [trans #8983 #9012]: #9013
+#9019 := [monotonicity #9014]: #9018
+#9031 := [trans #9019 #9021]: #9030
+#9011 := [quant-inst]: #9016
+#9032 := [mp #9011 #9031]: #9015
+#9182 := [unit-resolution #9032 #9181]: #8984
+#9183 := [unit-resolution #9182 #9180 #9179]: #8979
+#9184 := (not #8979)
+#9185 := (or #9184 #9034)
+#9186 := [th-lemma]: #9185
+#9187 := [unit-resolution #9186 #9183]: #9034
+#8854 := (>= #2822 0::int)
+#9188 := (or #8854 #2823)
+#9189 := [th-lemma]: #9188
+#9190 := [unit-resolution #9189 #9168]: #8854
+#9191 := [th-lemma #9190 #9179 #9187]: false
+#9192 := [lemma #9191]: #2823
+#3992 := (or #4508 #4502)
 #3993 := [def-axiom]: #3992
-#9541 := [unit-resolution #3993 #6403 #9540]: #4468
-#4015 := (or #4465 #148)
-#4016 := [def-axiom]: #4015
-#11161 := [unit-resolution #4016 #9541]: #148
-#13559 := [trans #11161 #13557]: #13558
-#24553 := [monotonicity #13559 #30680]: #24573
-#24598 := [symm #24553]: #24597
-#30482 := (= f1 #30481)
-#24659 := (f11 f12 #19988)
-#24663 := (= f1 #24659)
-#30484 := (= #9605 #19988)
-#30487 := (ite #30484 #3747 #24663)
-#30490 := (iff #30482 #30487)
-#248 := (:var 1 S1)
-#247 := (:var 2 S2)
-#246 := (:var 3 S5)
-#249 := (f21 #246 #247 #248)
-#250 := (f11 #249 #12)
-#4548 := (pattern #250)
-#254 := (f11 #246 #12)
-#1766 := (= f1 #254)
-#1763 := (= f1 #248)
-#252 := (= #12 #247)
-#1769 := (ite #252 #1763 #1766)
-#1759 := (= f1 #250)
-#1772 := (iff #1759 #1769)
-#4549 := (forall (vars (?v0 S5) (?v1 S2) (?v2 S1) (?v3 S2)) (:pat #4548) #1772)
-#1775 := (forall (vars (?v0 S5) (?v1 S2) (?v2 S1) (?v3 S2)) #1772)
-#4552 := (iff #1775 #4549)
-#4550 := (iff #1772 #1772)
-#4551 := [refl]: #4550
-#4553 := [quant-intro #4551]: #4552
-#1820 := (~ #1775 #1775)
-#1907 := (~ #1772 #1772)
-#1908 := [refl]: #1907
-#1821 := [nnf-pos #1908]: #1820
-#255 := (= #254 f1)
-#253 := (= #248 f1)
-#256 := (ite #252 #253 #255)
-#251 := (= #250 f1)
-#257 := (iff #251 #256)
-#258 := (forall (vars (?v0 S5) (?v1 S2) (?v2 S1) (?v3 S2)) #257)
-#1776 := (iff #258 #1775)
-#1773 := (iff #257 #1772)
-#1770 := (iff #256 #1769)
-#1767 := (iff #255 #1766)
-#1768 := [rewrite]: #1767
-#1764 := (iff #253 #1763)
-#1765 := [rewrite]: #1764
-#1771 := [monotonicity #1765 #1768]: #1770
-#1761 := (iff #251 #1759)
-#1762 := [rewrite]: #1761
-#1774 := [monotonicity #1762 #1771]: #1773
-#1777 := [quant-intro #1774]: #1776
-#1758 := [asserted]: #258
-#1780 := [mp #1758 #1777]: #1775
-#2077 := [mp~ #1780 #1821]: #1775
-#4554 := [mp #2077 #4553]: #4549
-#8843 := (not #4549)
-#24530 := (or #8843 #30490)
-#30477 := (= #19988 #9605)
-#30478 := (ite #30477 #3747 #24663)
-#30483 := (iff #30482 #30478)
-#24540 := (or #8843 #30483)
-#24451 := (iff #24540 #24530)
-#24524 := (iff #24530 #24530)
-#24546 := [rewrite]: #24524
-#30491 := (iff #30483 #30490)
-#30488 := (iff #30478 #30487)
-#30485 := (iff #30477 #30484)
-#30486 := [rewrite]: #30485
-#30489 := [monotonicity #30486]: #30488
-#30492 := [monotonicity #30489]: #30491
-#24497 := [monotonicity #30492]: #24451
-#24549 := [trans #24497 #24546]: #24451
-#24501 := [quant-inst]: #24540
-#24537 := [mp #24501 #24549]: #24530
-#24564 := [unit-resolution #24537 #4554]: #30490
-#24485 := (not #30490)
-#24569 := (or #24485 #30482)
-#30502 := (not #30487)
-#30665 := [hypothesis]: #30502
-#30503 := (not #30484)
-#30666 := (or #30487 #30503)
-#8984 := (not #3747)
-#30508 := (or #30487 #30503 #8984)
-#30509 := [def-axiom]: #30508
-#30673 := [unit-resolution #30509 #11162]: #30666
-#30674 := [unit-resolution #30673 #30665]: #30503
-#30690 := (or #30487 #30484)
-#6039 := (f11 f12 #6027)
-#30687 := (= #6039 #24659)
-#30683 := (= #24659 #6039)
-#30681 := (= #19988 #6027)
-#30682 := [symm #30680]: #30681
-#30684 := [monotonicity #30682]: #30683
-#30688 := [symm #30684]: #30687
-#6040 := (= f1 #6039)
-#6041 := (not #6040)
-#6033 := (f4 #6032)
-#6034 := (* -1::int #6033)
-#6028 := (f9 f10 #6027)
-#6029 := (* -1::int #6028)
-#6035 := (+ #6029 #6034)
-#5759 := (f9 f10 ?v0!20)
-#6036 := (+ #5759 #6035)
-#6037 := (= #6036 0::int)
-#6038 := (not #6037)
-#6030 := (+ #5759 #6029)
-#6031 := (<= #6030 0::int)
-#6047 := (or #6031 #6038 #6041)
-#6050 := (not #6047)
-#5794 := (* -1::int #5759)
-#6044 := (+ f3 #5794)
-#6045 := (<= #6044 0::int)
-#27050 := (not #6045)
-#5034 := (>= #169 0::int)
-#4872 := (* -1::int #169)
-#4937 := (+ #66 #4872)
-#8861 := (<= #4937 0::int)
-#4915 := (= #66 #169)
-#4873 := (f5 f19 f6)
-#4874 := (f4 #4873)
-#4878 := (* -1::int #4874)
-#4882 := (+ f3 #4878)
-#4883 := (<= #4882 0::int)
-#4879 := (+ #1359 #4878)
-#4880 := (+ #66 #4879)
-#4881 := (<= #4880 0::int)
-#4917 := (or #4881 #4883)
-#4719 := (f4 #4718)
-#9807 := (+ #4719 #4878)
-#9787 := (<= #9807 0::int)
-#10503 := (f5 #9605 f6)
-#10504 := (f4 #10503)
-#18022 := (>= #10504 0::int)
-#10553 := (= #10504 0::int)
-#18544 := (not #10553)
-#18543 := (not #18022)
-#18541 := [hypothesis]: #18543
-#18545 := (or #18544 #18022)
-#18546 := [th-lemma]: #18545
-#18551 := [unit-resolution #18546 #18541]: #18544
-#10558 := (= f6 #9605)
-#10583 := (<= #10504 0::int)
-#18552 := (or #18022 #10583)
-#18550 := [th-lemma]: #18552
-#18553 := [unit-resolution #18550 #18541]: #10583
-#10585 := (not #10583)
-#10587 := (or #10558 #10585)
-#15 := (f4 #14)
-#326 := (<= #15 0::int)
-#327 := (not #326)
-#13 := (= #11 #12)
-#330 := (or #13 #327)
-#4142 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4135) #330)
-#333 := (forall (vars (?v0 S2) (?v1 S2)) #330)
-#4145 := (iff #333 #4142)
-#4143 := (iff #330 #330)
-#4144 := [refl]: #4143
-#4146 := [quant-intro #4144]: #4145
-#1808 := (~ #333 #333)
-#1807 := (~ #330 #330)
-#1805 := [refl]: #1807
-#1809 := [nnf-pos #1805]: #1808
-#20 := (< 0::int #15)
-#19 := (not #13)
-#21 := (implies #19 #20)
-#22 := (forall (vars (?v0 S2) (?v1 S2)) #21)
-#336 := (iff #22 #333)
-#320 := (or #13 #20)
-#323 := (forall (vars (?v0 S2) (?v1 S2)) #320)
-#334 := (iff #323 #333)
-#331 := (iff #320 #330)
-#328 := (iff #20 #327)
-#329 := [rewrite]: #328
-#332 := [monotonicity #329]: #331
-#335 := [quant-intro #332]: #334
-#324 := (iff #22 #323)
-#321 := (iff #21 #320)
-#322 := [rewrite]: #321
-#325 := [quant-intro #322]: #324
-#337 := [trans #325 #335]: #336
-#319 := [asserted]: #22
-#338 := [mp #319 #337]: #333
-#1802 := [mp~ #338 #1809]: #333
-#4147 := [mp #1802 #4146]: #4142
-#7253 := (not #4142)
-#18023 := (or #7253 #10558 #10585)
-#10552 := (= #9605 f6)
-#10586 := (or #10552 #10585)
-#18024 := (or #7253 #10586)
-#18000 := (iff #18024 #18023)
-#18026 := (or #7253 #10587)
-#18001 := (iff #18026 #18023)
-#18002 := [rewrite]: #18001
-#18027 := (iff #18024 #18026)
-#10588 := (iff #10586 #10587)
-#10559 := (iff #10552 #10558)
-#10560 := [rewrite]: #10559
-#10589 := [monotonicity #10560]: #10588
-#18028 := [monotonicity #10589]: #18027
-#18003 := [trans #18028 #18002]: #18000
-#18025 := [quant-inst]: #18024
-#18004 := [mp #18025 #18003]: #18023
-#18554 := [unit-resolution #18004 #4147]: #10587
-#18555 := [unit-resolution #18554 #18553]: #10558
-#10561 := (not #10558)
-#10567 := (or #10553 #10561)
-#16 := (= #15 0::int)
-#310 := (or #19 #16)
-#4136 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4135) #310)
-#313 := (forall (vars (?v0 S2) (?v1 S2)) #310)
-#4139 := (iff #313 #4136)
-#4137 := (iff #310 #310)
-#4138 := [refl]: #4137
-#4140 := [quant-intro #4138]: #4139
-#1832 := (~ #313 #313)
-#1830 := (~ #310 #310)
-#1831 := [refl]: #1830
-#1833 := [nnf-pos #1831]: #1832
-#17 := (implies #13 #16)
-#18 := (forall (vars (?v0 S2) (?v1 S2)) #17)
-#316 := (iff #18 #313)
-#289 := (= 0::int #15)
-#300 := (or #19 #289)
-#305 := (forall (vars (?v0 S2) (?v1 S2)) #300)
-#314 := (iff #305 #313)
-#311 := (iff #300 #310)
-#308 := (iff #289 #16)
-#309 := [rewrite]: #308
-#312 := [monotonicity #309]: #311
-#315 := [quant-intro #312]: #314
-#306 := (iff #18 #305)
-#303 := (iff #17 #300)
-#297 := (implies #13 #289)
-#301 := (iff #297 #300)
-#302 := [rewrite]: #301
-#298 := (iff #17 #297)
-#295 := (iff #16 #289)
-#296 := [rewrite]: #295
-#299 := [monotonicity #296]: #298
-#304 := [trans #299 #302]: #303
-#307 := [quant-intro #304]: #306
-#317 := [trans #307 #315]: #316
-#288 := [asserted]: #18
-#318 := [mp #288 #317]: #313
-#1806 := [mp~ #318 #1833]: #313
-#4141 := [mp #1806 #4140]: #4136
-#7236 := (not #4136)
-#18009 := (or #7236 #10553 #10561)
-#10556 := (not #10552)
-#10557 := (or #10556 #10553)
-#18010 := (or #7236 #10557)
-#18019 := (iff #18010 #18009)
-#18014 := (or #7236 #10567)
-#18017 := (iff #18014 #18009)
-#18018 := [rewrite]: #18017
-#18015 := (iff #18010 #18014)
-#10570 := (iff #10557 #10567)
-#10564 := (or #10561 #10553)
-#10568 := (iff #10564 #10567)
-#10569 := [rewrite]: #10568
-#10565 := (iff #10557 #10564)
-#10562 := (iff #10556 #10561)
-#10563 := [monotonicity #10560]: #10562
-#10566 := [monotonicity #10563]: #10565
-#10571 := [trans #10566 #10569]: #10570
-#18016 := [monotonicity #10571]: #18015
-#18020 := [trans #18016 #18018]: #18019
-#18013 := [quant-inst]: #18010
-#18021 := [mp #18013 #18020]: #18009
-#18557 := [unit-resolution #18021 #4141]: #10567
-#18558 := [unit-resolution #18557 #18555 #18551]: false
-#18556 := [lemma #18558]: #18022
-#9716 := (<= #4719 0::int)
-#9610 := (= #4719 0::int)
-#9657 := (or #7236 #9610)
-#4948 := (= f19 f19)
-#9611 := (not #4948)
-#9628 := (or #9611 #9610)
-#9663 := (or #7236 #9628)
-#9665 := (iff #9663 #9657)
-#9667 := (iff #9657 #9657)
-#9713 := [rewrite]: #9667
-#9661 := (iff #9628 #9610)
-#9635 := (or false #9610)
-#9659 := (iff #9635 #9610)
-#9660 := [rewrite]: #9659
-#9636 := (iff #9628 #9635)
-#9633 := (iff #9611 false)
-#9631 := (iff #9611 #9474)
-#4954 := (iff #4948 true)
-#4955 := [rewrite]: #4954
-#9632 := [monotonicity #4955]: #9631
-#9634 := [trans #9632 #9478]: #9633
-#9658 := [monotonicity #9634]: #9636
-#9662 := [trans #9658 #9660]: #9661
-#9666 := [monotonicity #9662]: #9665
-#9714 := [trans #9666 #9713]: #9665
-#9664 := [quant-inst]: #9663
-#9715 := [mp #9664 #9714]: #9657
-#21178 := [unit-resolution #9715 #4141]: #9610
-#21179 := (not #9610)
-#21176 := (or #21179 #9716)
-#21189 := [th-lemma]: #21176
-#21190 := [unit-resolution #21189 #21178]: #9716
-#10505 := (* -1::int #10504)
-#10602 := (+ #4874 #10505)
-#9802 := (>= #10602 0::int)
-#9801 := (= #4874 #10504)
-#21192 := (= #10504 #4874)
-#21191 := (= #10503 #4873)
-#21181 := [monotonicity #10826]: #21191
-#21193 := [monotonicity #21181]: #21192
-#21187 := [symm #21193]: #9801
-#21188 := (not #9801)
-#21180 := (or #21188 #9802)
-#21194 := [th-lemma]: #21180
-#21195 := [unit-resolution #21194 #21187]: #9802
-#21197 := (not #9716)
-#21196 := (not #9802)
-#21214 := (or #9787 #18543 #21196 #21197)
-#21217 := [th-lemma]: #21214
-#21218 := [unit-resolution #21217 #21195 #21190 #18556]: #9787
-#21202 := (not #9787)
-#21205 := (or #4881 #21202)
-#4851 := (+ #66 #1359)
-#9804 := (<= #4851 0::int)
-#3888 := (<= #66 0::int)
-#6997 := (or #1653 #3888)
-#6998 := [th-lemma]: #6997
-#6999 := [unit-resolution #6998 #6994]: #3888
-#4850 := (>= #141 0::int)
-#3998 := (or #4477 #4204)
-#3994 := [def-axiom]: #3998
-#7124 := [unit-resolution #3994 #6995]: #4204
-#8670 := (or #4209 #4850)
-#8671 := [quant-inst]: #8670
-#13339 := [unit-resolution #8671 #7124]: #4850
-#8050 := (not #3888)
-#21216 := (not #4850)
-#21219 := (or #9804 #21216 #8050)
-#21220 := [th-lemma]: #21219
-#21222 := [unit-resolution #21220 #13339 #6999]: #9804
-#21210 := (not #9804)
-#21199 := (or #4881 #21210 #21202)
-#4738 := (>= #4719 0::int)
-#9568 := (f23 #4873)
-#10325 := (f5 #9568 #9568)
-#10326 := (f4 #10325)
-#10327 := (* -1::int #10326)
-#10391 := (+ #4719 #10327)
-#10393 := (>= #10391 0::int)
-#10390 := (= #4719 #10326)
-#10399 := (= #4718 #10325)
-#10397 := (= #10325 #4718)
-#10395 := (= #9568 f19)
-#9569 := (= f19 #9568)
-#9575 := (or #9574 #9569)
-#9576 := [quant-inst]: #9575
-#10394 := [unit-resolution #9576 #4560]: #9569
-#10396 := [symm #10394]: #10395
-#10398 := [monotonicity #10396 #10396]: #10397
-#10400 := [symm #10398]: #10399
-#10401 := [monotonicity #10400]: #10390
-#10402 := (not #10390)
-#10403 := (or #10402 #10393)
-#10404 := [th-lemma]: #10403
-#10405 := [unit-resolution #10404 #10401]: #10393
-#10336 := (>= #10326 0::int)
-#10364 := (= #10326 0::int)
-#10380 := (or #7236 #10364)
-#9942 := (= #9568 #9568)
-#10365 := (not #9942)
-#10368 := (or #10365 #10364)
-#10381 := (or #7236 #10368)
-#10383 := (iff #10381 #10380)
-#10385 := (iff #10380 #10380)
-#10386 := [rewrite]: #10385
-#10378 := (iff #10368 #10364)
-#10373 := (or false #10364)
-#10376 := (iff #10373 #10364)
-#10377 := [rewrite]: #10376
-#10374 := (iff #10368 #10373)
-#10371 := (iff #10365 false)
-#10369 := (iff #10365 #9474)
-#9947 := (iff #9942 true)
-#9948 := [rewrite]: #9947
-#10370 := [monotonicity #9948]: #10369
-#10372 := [trans #10370 #9478]: #10371
-#10375 := [monotonicity #10372]: #10374
-#10379 := [trans #10375 #10377]: #10378
-#10384 := [monotonicity #10379]: #10383
-#10387 := [trans #10384 #10386]: #10383
-#10382 := [quant-inst]: #10381
-#10388 := [mp #10382 #10387]: #10380
-#10406 := [unit-resolution #10388 #4141]: #10364
-#10407 := (not #10364)
-#10408 := (or #10407 #10336)
-#10409 := [th-lemma]: #10408
-#10410 := [unit-resolution #10409 #10406]: #10336
-#4766 := (not #4738)
-#10411 := [hypothesis]: #4766
-#10412 := [th-lemma #10411 #10410 #10405]: false
-#10413 := [lemma #10412]: #4738
-#21203 := (or #4881 #21210 #4766 #21202)
-#21204 := [th-lemma]: #21203
-#21215 := [unit-resolution #21204 #10413]: #21199
-#21201 := [unit-resolution #21215 #21222]: #21205
-#21206 := [unit-resolution #21201 #21218]: #4881
-#8866 := (not #4881)
-#8867 := (or #4917 #8866)
-#8865 := [def-axiom]: #8867
-#21207 := [unit-resolution #8865 #21206]: #4917
-#4920 := (not #4917)
-#4923 := (or #4915 #4920)
-#4008 := (or #4465 #4326)
-#4003 := [def-axiom]: #4008
-#9542 := [unit-resolution #4003 #9541]: #4326
-#6425 := (or #4331 #4915 #4920)
-#4913 := (or #4883 #4881)
-#4914 := (not #4913)
-#4916 := (or #4915 #4914)
-#6496 := (or #4331 #4916)
-#8699 := (iff #6496 #6425)
-#6879 := (or #4331 #4923)
-#8405 := (iff #6879 #6425)
-#8677 := [rewrite]: #8405
-#7530 := (iff #6496 #6879)
-#4924 := (iff #4916 #4923)
-#4921 := (iff #4914 #4920)
-#4918 := (iff #4913 #4917)
-#4919 := [rewrite]: #4918
+#9862 := [unit-resolution #3993 #9176]: #4502
+#4022 := (or #4505 #2828 #4499)
+#4023 := [def-axiom]: #4022
+#9863 := [unit-resolution #4023 #9862]: #4502
+#9864 := [unit-resolution #9863 #9192]: #4499
+#4035 := (or #4496 #4385)
+#4036 := [def-axiom]: #4035
+#9875 := [unit-resolution #4036 #9864]: #4385
+#10532 := (or #4390 #5679)
+#5648 := (+ #6383 #2264)
+#5649 := (>= #5648 0::int)
+#10662 := (or #4390 #5649)
+#10664 := (iff #10662 #10532)
+#10736 := (iff #10532 #10532)
+#10742 := [rewrite]: #10736
+#5682 := (iff #5649 #5679)
+#5650 := (+ #2264 #6383)
+#5652 := (>= #5650 0::int)
+#5680 := (iff #5652 #5679)
+#5681 := [rewrite]: #5680
+#5653 := (iff #5649 #5652)
+#5645 := (= #5648 #5650)
+#5651 := [rewrite]: #5645
+#5654 := [monotonicity #5651]: #5653
+#5683 := [trans #5654 #5681]: #5682
+#10741 := [monotonicity #5683]: #10664
+#10928 := [trans #10741 #10742]: #10664
+#10663 := [quant-inst]: #10662
+#10929 := [mp #10663 #10928]: #10532
+#14768 := [unit-resolution #10929 #9875]: #5679
+#9977 := (+ #174 #9913)
+#9979 := (>= #9977 0::int)
+#9976 := (= #174 #9900)
+#10014 := (= #9900 #174)
+#10015 := [monotonicity #10000]: #10014
+#10016 := [symm #10015]: #9976
+#10017 := (not #9976)
+#10018 := (or #10017 #9979)
+#10019 := [th-lemma]: #10018
+#10020 := [unit-resolution #10019 #10016]: #9979
+#6447 := (+ #174 #6631)
+#6448 := (<= #6447 0::int)
+#17717 := (not #6472)
+#17725 := (or #12748 #12747 #17717)
+#17726 := [def-axiom]: #17725
+#19379 := [unit-resolution #17726 #19366 #19381]: #17717
+#6502 := (or #6448 #6472)
+#4027 := (or #4508 #4359)
+#4013 := [def-axiom]: #4027
+#19367 := [unit-resolution #4013 #9176]: #4359
+#18388 := (or #4364 #6448 #6472)
+#6468 := (+ #6614 #1426)
+#6469 := (>= #6468 0::int)
+#6470 := (or #6472 #6469)
+#18421 := (or #4364 #6470)
+#18436 := (iff #18421 #18388)
+#18424 := (or #4364 #6502)
+#18434 := (iff #18424 #18388)
+#18435 := [rewrite]: #18434
+#18420 := (iff #18421 #18424)
+#6505 := (iff #6470 #6502)
+#6499 := (or #6472 #6448)
+#6503 := (iff #6499 #6502)
+#6504 := [rewrite]: #6503
+#6500 := (iff #6470 #6499)
+#6497 := (iff #6469 #6448)
+#6442 := (+ #1426 #6614)
+#6444 := (>= #6442 0::int)
+#6449 := (iff #6444 #6448)
+#6496 := [rewrite]: #6449
+#6445 := (iff #6469 #6444)
+#6443 := (= #6468 #6442)
+#6441 := [rewrite]: #6443
+#6446 := [monotonicity #6441]: #6445
+#6498 := [trans #6446 #6496]: #6497
+#6501 := [monotonicity #6498]: #6500
+#6506 := [trans #6501 #6504]: #6505
+#18433 := [monotonicity #6506]: #18420
+#18437 := [trans #18433 #18435]: #18436
+#18423 := [quant-inst]: #18421
+#18488 := [mp #18423 #18437]: #18388
+#19368 := [unit-resolution #18488 #19367]: #6502
+#19363 := [unit-resolution #19368 #19379]: #6448
+#19373 := (not #5679)
+#16162 := (not #9979)
+#14775 := (not #13992)
+#19370 := (not #6448)
+#19397 := (or #19369 #19370 #2861 #14775 #16162 #19373)
+#19406 := [th-lemma]: #19397
+#19460 := [unit-resolution #19406 #19363 #10020 #14768 #14769 #19322]: #19369
+#19462 := (or #19461 #11013)
+#19463 := [th-lemma]: #19462
+#19464 := [unit-resolution #19463 #19460]: #19461
+#6709 := (or #6700 #6706)
+#17854 := (or #4374 #6700 #6706)
+#6653 := (+ #1426 #6652)
+#6654 := (+ #6614 #6653)
+#6655 := (<= #6654 0::int)
+#6696 := (or #6657 #6655)
+#6697 := (not #6696)
+#6698 := (= #6614 #2265)
+#6699 := (or #6698 #6697)
+#17855 := (or #4374 #6699)
+#17861 := (iff #17855 #17854)
+#17857 := (or #4374 #6709)
+#17852 := (iff #17857 #17854)
+#17858 := [rewrite]: #17852
+#17859 := (iff #17855 #17857)
+#6710 := (iff #6699 #6709)
+#6707 := (iff #6697 #6706)
+#6704 := (iff #6696 #6703)
+#6671 := (iff #6655 #6668)
+#6659 := (+ #6614 #6652)
+#6660 := (+ #1426 #6659)
+#6663 := (<= #6660 0::int)
+#6669 := (iff #6663 #6668)
+#6670 := [rewrite]: #6669
+#6664 := (iff #6655 #6663)
+#6661 := (= #6654 #6660)
+#6662 := [rewrite]: #6661
+#6665 := [monotonicity #6662]: #6664
+#6672 := [trans #6665 #6670]: #6671
+#6705 := [monotonicity #6672]: #6704
+#6708 := [monotonicity #6705]: #6707
+#6701 := (iff #6698 #6700)
+#6702 := [rewrite]: #6701
+#6711 := [monotonicity #6702 #6708]: #6710
+#17860 := [monotonicity #6711]: #17859
+#17862 := [trans #17860 #17858]: #17861
+#17856 := [quant-inst]: #17855
+#17863 := [mp #17856 #17862]: #17854
+#19465 := [unit-resolution #17863 #9177]: #6709
+#19466 := [unit-resolution #19465 #19464]: #6706
+#17892 := (or #6703 #17887)
+#17893 := [def-axiom]: #17892
+#19372 := [unit-resolution #17893 #19466]: #17887
+#17886 := (not #6668)
+#17894 := (or #6703 #17886)
+#17895 := [def-axiom]: #17894
+#19398 := [unit-resolution #17895 #19466]: #17886
+#6680 := (or #6657 #6668 #6677)
+#17831 := (or #4382 #6657 #6668 #6677)
+#6649 := (+ #6648 #2859)
+#6650 := (+ #174 #6649)
+#6651 := (= #6650 0::int)
+#6658 := (or #6657 #6655 #6651)
+#17837 := (or #4382 #6658)
+#17839 := (iff #17837 #17831)
+#17840 := (or #4382 #6680)
+#17842 := (iff #17840 #17831)
+#17843 := [rewrite]: #17842
+#17841 := (iff #17837 #17840)
+#6681 := (iff #6658 #6680)
+#6678 := (iff #6651 #6677)
+#6675 := (= #6650 #6674)
+#6676 := [rewrite]: #6675
+#6679 := [monotonicity #6676]: #6678
+#6682 := [monotonicity #6672 #6679]: #6681
+#17836 := [monotonicity #6682]: #17841
+#17844 := [trans #17836 #17843]: #17839
+#17838 := [quant-inst]: #17837
+#17845 := [mp #17838 #17844]: #17831
+#19399 := [unit-resolution #17845 #9181]: #6680
+#19400 := [unit-resolution #19399 #19398 #19372]: #6677
+#19401 := (not #6677)
+#19371 := (or #19401 #17846)
+#19396 := [th-lemma]: #19371
+#19402 := [unit-resolution #19396 #19400]: #17846
+#13911 := (* -1::int #13909)
+#19208 := (+ #6648 #13911)
+#19242 := (>= #19208 0::int)
+#19207 := (= #6648 #13909)
+#19405 := (= #13909 #6648)
+#19403 := (= #13908 #6647)
+#19404 := [monotonicity #10000]: #19403
+#19468 := [monotonicity #19404]: #19405
+#19448 := [symm #19468]: #19207
+#19449 := (not #19207)
+#19450 := (or #19449 #19242)
+#19451 := [th-lemma]: #19450
+#19467 := [unit-resolution #19451 #19448]: #19242
+#14985 := (not #15031)
+#48 := (f9 #16)
+#385 := (<= #48 0::int)
+#386 := (not #385)
+#47 := (= #14 #15)
+#389 := (or #47 #386)
+#4185 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4152) #389)
+#392 := (forall (vars (?v0 S3) (?v1 S3)) #389)
+#4188 := (iff #392 #4185)
+#4186 := (iff #389 #389)
+#4187 := [refl]: #4186
+#4189 := [quant-intro #4187]: #4188
+#1827 := (~ #392 #392)
+#1826 := (~ #389 #389)
+#1856 := [refl]: #1826
+#1828 := [nnf-pos #1856]: #1827
+#53 := (< 0::int #48)
+#52 := (not #47)
+#54 := (implies #52 #53)
+#55 := (forall (vars (?v0 S3) (?v1 S3)) #54)
+#395 := (iff #55 #392)
+#379 := (or #47 #53)
+#382 := (forall (vars (?v0 S3) (?v1 S3)) #379)
+#393 := (iff #382 #392)
+#390 := (iff #379 #389)
+#387 := (iff #53 #386)
+#388 := [rewrite]: #387
+#391 := [monotonicity #388]: #390
+#394 := [quant-intro #391]: #393
+#383 := (iff #55 #382)
+#380 := (iff #54 #379)
+#381 := [rewrite]: #380
+#384 := [quant-intro #381]: #383
+#396 := [trans #384 #394]: #395
+#378 := [asserted]: #55
+#397 := [mp #378 #396]: #392
+#1857 := [mp~ #397 #1828]: #392
+#4190 := [mp #1857 #4189]: #4185
+#7251 := (not #4185)
+#19173 := (or #7251 #12747 #14985)
+#14988 := (= #9390 ?v1!16)
+#14971 := (or #14988 #14985)
+#19200 := (or #7251 #14971)
+#19199 := (iff #19200 #19173)
+#14997 := (or #12747 #14985)
+#19201 := (or #7251 #14997)
+#19204 := (iff #19201 #19173)
+#19164 := [rewrite]: #19204
+#19202 := (iff #19200 #19201)
+#14947 := (iff #14971 #14997)
+#15036 := (iff #14988 #12747)
+#14996 := [rewrite]: #15036
+#14948 := [monotonicity #14996]: #14947
+#19203 := [monotonicity #14948]: #19202
+#19205 := [trans #19203 #19164]: #19199
+#19165 := [quant-inst]: #19200
+#19206 := [mp #19165 #19205]: #19173
+#19452 := [unit-resolution #19206 #4190 #19366]: #14985
+#19447 := [th-lemma #19452 #19467 #14769 #19322 #10020 #14768 #19402]: false
+#19454 := [lemma #19447]: #19453
+#20115 := [unit-resolution #19454 #6733 #6734]: #12797
+#20130 := [trans #20115 #10000]: #6427
+#20125 := [monotonicity #20130]: #19756
+#20170 := (not #19756)
+#20172 := (or #20170 #15115)
+#20173 := [th-lemma]: #20172
+#20171 := [unit-resolution #20173 #20125]: #15115
+#6304 := (>= #2860 0::int)
+#20149 := (or #6304 #2861)
+#20147 := [th-lemma]: #20149
+#20164 := [unit-resolution #20147 #6734]: #6304
+#4989 := (+ #174 #4768)
+#4990 := (>= #4989 0::int)
+#9099 := (or #4390 #4990)
+#9100 := [quant-inst]: #9099
+#11587 := [unit-resolution #9100 #9875]: #4990
+#11593 := (not #4990)
+#15239 := (not #15115)
+#20174 := (or #19369 #19370 #2861 #15239 #11593)
+#20148 := [th-lemma]: #20174
+#20150 := [unit-resolution #20148 #19363 #11587 #6734 #20171]: #19369
+#20176 := [unit-resolution #19463 #20150]: #19461
+#20175 := [unit-resolution #19465 #20176]: #6706
+#20151 := [unit-resolution #17893 #20175]: #17887
+#20204 := [unit-resolution #17895 #20175]: #17886
+#20196 := [unit-resolution #19399 #20204 #20151]: #6677
+#20202 := [unit-resolution #19396 #20196]: #17846
+#20199 := (not #17846)
+#20205 := (not #6304)
+#20209 := (or #15239 #20205 #20199 #15031)
+#20210 := (not #19242)
+#20208 := (or #15239 #11593 #20205 #20199 #15031 #20210)
+#20227 := [th-lemma]: #20208
+#20228 := [unit-resolution #20227 #19467 #11587]: #20209
+#20230 := [unit-resolution #20228 #20202 #20164 #20171]: #15031
+#20316 := [unit-resolution #19206 #4190 #20230 #19366]: false
+#20314 := [lemma #20316]: #3413
+#4847 := (>= #174 0::int)
+#4007 := (or #4520 #4247)
+#4003 := [def-axiom]: #4007
+#7021 := [unit-resolution #4003 #6915]: #4247
+#8746 := (or #4252 #4847)
+#8747 := [quant-inst]: #8746
+#9587 := [unit-resolution #8747 #7021]: #4847
+#9855 := (f3 f22 ?v0!15)
+#9834 := (f9 #9855)
+#5056 := (* -1::int #2247)
+#10134 := (+ #5056 #9834)
+#10135 := (+ #174 #10134)
+#11414 := (<= #10135 0::int)
+#10138 := (= #10135 0::int)
+#9346 := (f13 f14 ?v0!15)
+#9790 := (* -1::int #9346)
+#10061 := (+ #9790 #9834)
+#10128 := (+ #174 #10061)
+#10129 := (>= #10128 0::int)
+#9859 := (* -1::int #9834)
+#9793 := (+ f8 #9859)
+#9794 := (<= #9793 0::int)
+#10160 := (or #9794 #10129)
+#10163 := (not #10160)
+#9640 := (= #2247 #9346)
+#11751 := (not #9640)
+#9791 := (+ #2247 #9790)
+#11668 := (>= #9791 0::int)
+#11694 := (not #11668)
+#12327 := [hypothesis]: #2249
+#11670 := (or #11694 #2248)
+#10279 := (>= #9346 0::int)
+#11526 := (or #4252 #10279)
+#11530 := [quant-inst]: #11526
+#11678 := [unit-resolution #11530 #7021]: #10279
+#11677 := [hypothesis]: #11668
+#11693 := [th-lemma #12327 #11677 #11678]: false
+#11743 := [lemma #11693]: #11670
+#12659 := [unit-resolution #11743 #12327]: #11694
+#11795 := (or #11751 #11668)
+#11736 := [th-lemma]: #11795
+#10958 := [unit-resolution #11736 #12659]: #11751
+#11395 := (or #4374 #9640 #10163)
+#9854 := (+ #1426 #9859)
+#9565 := (+ #9346 #9854)
+#9566 := (<= #9565 0::int)
+#10157 := (or #9794 #9566)
+#10158 := (not #10157)
+#9636 := (= #9346 #2247)
+#10159 := (or #9636 #10158)
+#11396 := (or #4374 #10159)
+#11402 := (iff #11396 #11395)
+#10166 := (or #9640 #10163)
+#11398 := (or #4374 #10166)
+#11400 := (iff #11398 #11395)
+#11401 := [rewrite]: #11400
+#11393 := (iff #11396 #11398)
+#10167 := (iff #10159 #10166)
+#10164 := (iff #10158 #10163)
+#10161 := (iff #10157 #10160)
+#10132 := (iff #9566 #10129)
+#9796 := (+ #9346 #9859)
+#9801 := (+ #1426 #9796)
+#9965 := (<= #9801 0::int)
+#10130 := (iff #9965 #10129)
+#10131 := [rewrite]: #10130
+#9966 := (iff #9566 #9965)
+#9860 := (= #9565 #9801)
+#9861 := [rewrite]: #9860
+#10060 := [monotonicity #9861]: #9966
+#10133 := [trans #10060 #10131]: #10132
+#10162 := [monotonicity #10133]: #10161
+#10165 := [monotonicity #10162]: #10164
+#9641 := (iff #9636 #9640)
+#9642 := [rewrite]: #9641
+#10168 := [monotonicity #9642 #10165]: #10167
+#11399 := [monotonicity #10168]: #11393
+#11403 := [trans #11399 #11401]: #11402
+#11397 := [quant-inst]: #11396
+#11418 := [mp #11397 #11403]: #11395
+#11014 := [unit-resolution #11418 #9177 #10958]: #10163
+#12676 := (or #10160 #10138)
+#12669 := (not #10138)
+#12670 := [hypothesis]: #12669
+#11419 := (not #9794)
+#12671 := [hypothesis]: #10163
+#11437 := (or #10160 #11419)
+#11438 := [def-axiom]: #11437
+#12672 := [unit-resolution #11438 #12671]: #11419
+#11439 := (not #10129)
+#11440 := (or #10160 #11439)
+#11441 := [def-axiom]: #11440
+#12673 := [unit-resolution #11441 #12671]: #11439
+#10141 := (or #9794 #10129 #10138)
+#11350 := (or #4382 #9794 #10129 #10138)
+#9856 := (+ #9834 #5056)
+#9857 := (+ #174 #9856)
+#9858 := (= #9857 0::int)
+#9795 := (or #9794 #9566 #9858)
+#11351 := (or #4382 #9795)
+#11411 := (iff #11351 #11350)
+#11406 := (or #4382 #10141)
+#11409 := (iff #11406 #11350)
+#11410 := [rewrite]: #11409
+#11407 := (iff #11351 #11406)
+#10142 := (iff #9795 #10141)
+#10139 := (iff #9858 #10138)
+#10136 := (= #9857 #10135)
+#10137 := [rewrite]: #10136
+#10140 := [monotonicity #10137]: #10139
+#10143 := [monotonicity #10133 #10140]: #10142
+#11408 := [monotonicity #10143]: #11407
+#11412 := [trans #11408 #11410]: #11411
+#11352 := [quant-inst]: #11351
+#11413 := [mp #11352 #11412]: #11350
+#12674 := [unit-resolution #11413 #9181]: #10141
+#12675 := [unit-resolution #12674 #12673 #12672 #12670]: false
+#12677 := [lemma #12675]: #12676
+#11015 := [unit-resolution #12677 #11014]: #10138
+#12619 := (or #12669 #11414)
+#12620 := [th-lemma]: #12619
+#11016 := [unit-resolution #12620 #11015]: #11414
+#12116 := (f3 #9390 ?v0!15)
+#12117 := (f9 #12116)
+#12164 := (* -1::int #12117)
+#12177 := (+ #9834 #12164)
+#12244 := (>= #12177 0::int)
+#12115 := (= #9834 #12117)
+#12330 := (= #12117 #9834)
+#12328 := (= #12116 #9855)
+#12329 := [monotonicity #10000]: #12328
+#12331 := [monotonicity #12329]: #12330
+#12332 := [symm #12331]: #12115
+#12333 := (not #12115)
+#12334 := (or #12333 #12244)
+#12335 := [th-lemma]: #12334
+#12336 := [unit-resolution #12335 #12332]: #12244
+#12114 := (>= #12117 0::int)
+#12118 := (<= #12117 0::int)
+#12119 := (not #12118)
+#12122 := (= ?v0!15 #9390)
+#12147 := (not #12122)
+#10190 := (f6 f15 ?v0!15)
+#10191 := (= f1 #10190)
+#11981 := (ite #12122 #3805 #10191)
+#11979 := (not #11981)
+#11984 := (f6 #9617 ?v0!15)
+#11993 := (= f1 #11984)
+#11990 := (iff #11981 #11993)
+#11964 := (or #8910 #11990)
+#11994 := (iff #11993 #11981)
+#11965 := (or #8910 #11994)
+#11975 := (iff #11965 #11964)
+#11963 := (iff #11964 #11964)
+#11977 := [rewrite]: #11963
+#11995 := (iff #11994 #11990)
+#12004 := [rewrite]: #11995
+#11976 := [monotonicity #12004]: #11975
+#11978 := [trans #11976 #11977]: #11975
+#11956 := [quant-inst]: #11965
+#11966 := [mp #11956 #11978]: #11964
+#12658 := [unit-resolution #11966 #4171]: #11990
+#11887 := (not #11993)
+#5059 := (f6 f23 ?v0!15)
+#5060 := (= f1 #5059)
+#5061 := (not #5060)
+#12523 := (iff #5061 #11887)
+#12461 := (iff #5060 #11993)
+#12457 := (iff #11993 #5060)
+#12449 := (= #11984 #5059)
+#12456 := [monotonicity #10052]: #12449
+#12460 := [monotonicity #12456]: #12457
+#12522 := [symm #12460]: #12461
+#12535 := [monotonicity #12522]: #12523
+#4037 := (or #4496 #4490)
+#4038 := [def-axiom]: #4037
+#11607 := [unit-resolution #4038 #9864]: #4490
+#9160 := (* -1::int #2226)
+#9161 := (+ #2225 #9160)
+#9654 := (>= #9161 0::int)
+#9874 := (not #9654)
+#9162 := (<= #9161 0::int)
+#9394 := (or #4390 #9162)
+#9062 := (* -1::int #2225)
+#9064 := (+ #2226 #9062)
+#9102 := (>= #9064 0::int)
+#9395 := (or #4390 #9102)
+#9399 := (iff #9395 #9394)
+#9401 := (iff #9394 #9394)
+#9402 := [rewrite]: #9401
+#9165 := (iff #9102 #9162)
+#9103 := (+ #9062 #2226)
+#9106 := (>= #9103 0::int)
+#9163 := (iff #9106 #9162)
+#9164 := [rewrite]: #9163
+#9158 := (iff #9102 #9106)
+#9104 := (= #9064 #9103)
+#9105 := [rewrite]: #9104
+#9159 := [monotonicity #9105]: #9158
+#9166 := [trans #9159 #9164]: #9165
+#9400 := [monotonicity #9166]: #9399
+#9403 := [trans #9400 #9402]: #9399
+#9398 := [quant-inst]: #9395
+#9375 := [mp #9398 #9403]: #9394
+#9876 := [unit-resolution #9375 #9875]: #9162
+#4096 := (not #2831)
+#9877 := [hypothesis]: #2842
+#4097 := (or #2837 #4096)
+#4102 := [def-axiom]: #4097
+#9878 := [unit-resolution #4102 #9877]: #4096
+#9879 := (not #9162)
+#9880 := (or #2831 #9879 #9874)
+#9881 := [th-lemma]: #9880
+#9882 := [unit-resolution #9881 #9878 #9876]: #9874
+decl f5 :: (-> S2 S3)
+#9655 := (f3 #9390 ?v0!14)
+#9742 := (f5 #9655)
+#9898 := (f13 f14 #9742)
+#9914 := (+ #9898 #9913)
+#9915 := (<= #9914 0::int)
+#10008 := (iff #730 #10007)
+#10005 := (iff #727 #9749)
+#10003 := (iff #9749 #727)
+#10002 := [monotonicity #10000]: #10001
+#10004 := [monotonicity #10002]: #10003
+#10006 := [symm #10004]: #10005
+#10009 := [monotonicity #10006]: #10008
+#10010 := [mp #9997 #10009]: #10007
+#9969 := (or #9749 #9915)
+#9903 := (f6 f15 #9742)
+#9904 := (= f1 #9903)
+#9170 := (f6 f15 ?v0!14)
+#9961 := (= #9170 #9903)
+#9963 := (= #9903 #9170)
+#9987 := (= #9742 ?v0!14)
+#9743 := (= ?v0!14 #9742)
+#17 := (f5 #16)
+#296 := (= #15 #17)
+#4153 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4152) #296)
+#300 := (forall (vars (?v0 S3) (?v1 S3)) #296)
+#4156 := (iff #300 #4153)
+#4154 := (iff #296 #296)
+#4155 := [refl]: #4154
+#4157 := [quant-intro #4155]: #4156
+#1815 := (~ #300 #300)
+#1812 := (~ #296 #296)
+#1843 := [refl]: #1812
+#1816 := [nnf-pos #1843]: #1815
+#18 := (= #17 #15)
+#19 := (forall (vars (?v0 S3) (?v1 S3)) #18)
+#301 := (iff #19 #300)
+#298 := (iff #18 #296)
+#299 := [rewrite]: #298
+#302 := [quant-intro #299]: #301
+#295 := [asserted]: #19
+#305 := [mp #295 #302]: #300
+#1844 := [mp~ #305 #1816]: #300
+#4158 := [mp #1844 #4157]: #4153
+#6745 := (not #4153)
+#9746 := (or #6745 #9743)
+#9747 := [quant-inst]: #9746
+#9986 := [unit-resolution #9747 #4158]: #9743
+#9988 := [symm #9986]: #9987
+#9964 := [monotonicity #9988]: #9963
+#9967 := [symm #9964]: #9961
+#9171 := (= f1 #9170)
+#9613 := (= ?v0!14 #9390)
+#9614 := (ite #9613 #3805 #9171)
+#9618 := (f6 #9617 ?v0!14)
+#9619 := (= f1 #9618)
+#9621 := (iff #9614 #9619)
+#9624 := (or #8910 #9621)
+#9620 := (iff #9619 #9614)
+#9625 := (or #8910 #9620)
+#9627 := (iff #9625 #9624)
+#9629 := (iff #9624 #9624)
+#9630 := [rewrite]: #9629
+#9622 := (iff #9620 #9621)
+#9623 := [rewrite]: #9622
+#9628 := [monotonicity #9623]: #9627
+#9631 := [trans #9628 #9630]: #9627
+#9626 := [quant-inst]: #9625
+#9632 := [mp #9626 #9631]: #9624
+#9883 := [unit-resolution #9632 #4171]: #9621
+#10062 := (= #2222 #9618)
+#10058 := (= #9618 #2222)
+#10059 := [monotonicity #10052]: #10058
+#9885 := [symm #10059]: #10062
+#4100 := (or #2837 #2223)
+#4101 := [def-axiom]: #4100
+#9884 := [unit-resolution #4101 #9877]: #2223
+#9892 := [trans #9884 #9885]: #9619
+#9645 := (not #9619)
+#9644 := (not #9621)
+#9646 := (or #9644 #9614 #9645)
+#9647 := [def-axiom]: #9646
+#9893 := [unit-resolution #9647 #9892 #9883]: #9614
+#9634 := (not #9613)
+#10123 := (or #9634 #2831)
+#4728 := (= #174 #4727)
+#9962 := (= #2225 #4727)
+#10070 := (= #4727 #2225)
+#9365 := (= f22 ?v0!14)
+#9704 := (= #9390 ?v0!14)
+#10064 := [hypothesis]: #9613
+#10068 := [symm #10064]: #9704
+#10069 := [trans #9998 #10068]: #9365
+#10071 := [monotonicity #10069]: #10070
+#10072 := [symm #10071]: #9962
+#10117 := (= #174 #2225)
+#9656 := (f9 #9655)
+#9657 := (* -1::int #9656)
+#9217 := (f3 f22 ?v0!14)
+#9218 := (f9 #9217)
+#9798 := (+ #9218 #9657)
+#9799 := (<= #9798 0::int)
+#9797 := (= #9218 #9656)
+#10086 := (= #9217 #9655)
+#10084 := (= #9655 #9217)
+#10085 := [monotonicity #10000]: #10084
+#10087 := [symm #10085]: #10086
+#10088 := [monotonicity #10087]: #9797
+#10089 := (not #9797)
+#10090 := (or #10089 #9799)
+#10091 := [th-lemma]: #10090
+#10092 := [unit-resolution #10091 #10088]: #9799
+#9800 := (>= #9798 0::int)
+#10093 := (or #10089 #9800)
+#10094 := [th-lemma]: #10093
+#10095 := [unit-resolution #10094 #10088]: #9800
+#9702 := (<= #9656 0::int)
+#9722 := (= #9656 0::int)
+#9727 := (or #9634 #9722)
+#49 := (= #48 0::int)
+#369 := (or #52 #49)
+#4179 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4152) #369)
+#372 := (forall (vars (?v0 S3) (?v1 S3)) #369)
+#4182 := (iff #372 #4179)
+#4180 := (iff #369 #369)
+#4181 := [refl]: #4180
+#4183 := [quant-intro #4181]: #4182
+#1823 := (~ #372 #372)
+#1854 := (~ #369 #369)
+#1855 := [refl]: #1854
+#1824 := [nnf-pos #1855]: #1823
+#50 := (implies #47 #49)
+#51 := (forall (vars (?v0 S3) (?v1 S3)) #50)
+#375 := (iff #51 #372)