updated SMT certificates

--- 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)
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-#1471 := (and #1465 #1468)
-#1475 := (iff #1471 #1474)
-#1476 := [rewrite]: #1475
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-#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)
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-#1427 := (and #1142 #713)
-#1431 := (iff #1427 #1430)
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+#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)
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+#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)
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+#1480 := (or #1475 #809)
+#1484 := (iff #1480 #1483)
+#1485 := [rewrite]: #1484
+#1481 := (iff #810 #1480)
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+#1479 := [rewrite]: #1478
+#1482 := [monotonicity #1479]: #1481
+#1487 := [trans #1482 #1485]: #1486
+#1490 := [quant-intro #1487]: #1489
+#1493 := [monotonicity #1490]: #1492
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+#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
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+#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)
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+#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)
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+#1155 := (iff #269 #1152)
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+#1149 := (iff #269 #1148)
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+#1144 := (iff #1139 #1143)
+#1145 := [rewrite]: #1144
+#1140 := (iff #268 #1139)
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+#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)
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+#1119 := (iff #265 #1118)
+#1116 := (iff #264 #1115)
+#1113 := (iff #263 #1110)
+#1106 := (implies #73 #1103)
+#1111 := (iff #1106 #1110)
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+#1107 := (iff #263 #1106)
+#1104 := (iff #262 #1103)
+#1101 := (iff #261 #1098)
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+#1100 := [rewrite]: #1099
+#1095 := (iff #261 #1094)
+#1092 := (iff #260 #1091)
+#1089 := (iff #259 #1086)
+#1082 := (implies #474 #1079)
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+#1080 := (iff #258 #1079)
+#1077 := (iff #257 #1074)
+#1070 := (implies #500 #1058)
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+#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)
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+#1055 := (iff #255 #1054)
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+#1045 := (implies #103 #1040)
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+#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)
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+#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)
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-#4388 := (iff #3492 #4385)
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+#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
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+#1062 := [trans #1056 #1060]: #1061
+#1065 := [monotonicity #1062]: #1064
+#1069 := [trans #1065 #1067]: #1068
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+#429 := [rewrite]: #428
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+#490 := [quant-intro #487]: #489
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+#499 := [trans #493 #497]: #498
+#502 := [quant-intro #499]: #501
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+#473 := [trans #467 #471]: #472
+#476 := [quant-intro #473]: #475
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+#1090 := [trans #1084 #1088]: #1089
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+#455 := (iff #80 #454)
+#452 := (iff #79 #449)
+#445 := (implies #442 #78)
+#450 := (iff #445 #449)
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+#447 := [monotonicity #444]: #446
+#453 := [trans #447 #451]: #452
+#456 := [quant-intro #453]: #455
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+#1102 := [trans #1096 #1100]: #1101
+#1105 := [monotonicity #456 #1102]: #1104
+#1108 := [monotonicity #1105]: #1107
+#1114 := [trans #1108 #1112]: #1113
+#1117 := [monotonicity #1114]: #1116
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+#438 := [rewrite]: #437
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+#1126 := [trans #1120 #1124]: #1125
+#1129 := [monotonicity #438 #1126]: #1128
+#434 := (iff #69 #433)
+#435 := [quant-intro #432]: #434
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+#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)
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+#406 := (iff #402 #405)
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+#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)
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+#4617 := [monotonicity #4609]: #4616
+#4648 := [monotonicity #4617]: #4647
+#4651 := [trans #4648 #4649]: #4650
+#4645 := [quant-inst]: #4644
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+#1829 := (~ #424 #424)
+#1858 := (~ #419 #419)
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+#1860 := [mp~ #1807 #1830]: #424
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+#4712 := [unit-resolution #4711 #4710]: #3831
+#4713 := (not #3831)
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+#4754 := (or #4618 #71)
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+#4781 := [lemma #4780]: #71
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+#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
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+#4438 := [monotonicity #4426 #4435]: #4437
+#4441 := [monotonicity #4438]: #4440
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+#4417 := (iff #3521 #4416)
+#4414 := (iff #3441 #4411)
+#4412 := (iff #3436 #3436)
+#4413 := [refl]: #4412
+#4415 := [quant-intro #4413]: #4414
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+#4450 := [monotonicity #4418 #4447]: #4449
+#4453 := [monotonicity #4450]: #4452
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+#4408 := (iff #1472 #4407)
+#4405 := (iff #1469 #4402)
+#4403 := (iff #1466 #1466)
+#4404 := [refl]: #4403
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+#4462 := [monotonicity #4409 #4459]: #4461
+#4465 := [monotonicity #4462]: #4464
+#4468 := [monotonicity #4465]: #4467
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+#4397 := (iff #792 #4394)
+#4395 := (iff #787 #787)
+#4396 := [refl]: #4395
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+#4486 := [monotonicity #4401 #4483]: #4485
+#4489 := [monotonicity #4486]: #4488
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+#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
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-#4365 := (iff #1405 #4364)
-#4362 := (iff #1402 #4359)
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 #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
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-#4431 := [monotonicity #4428]: #4430
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-#4440 := [monotonicity #4437]: #4439
-#4357 := (iff #859 #4356)
-#4354 := (iff #725 #4351)
-#4352 := (iff #720 #720)
-#4353 := [refl]: #4352
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-#4443 := [monotonicity #4358 #4440]: #4442
-#4446 := [monotonicity #4443]: #4445
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-#4348 := (iff #1391 #4347)
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-#4343 := (iff #1383 #1383)
-#4344 := [refl]: #4343
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-#4458 := [monotonicity #4455]: #4457
-#4461 := [monotonicity #4458]: #4460
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-#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
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-#4319 := (iff #1553 #4316)
-#4317 := (iff #1548 #1548)
-#4318 := [refl]: #4317
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-#4323 := [monotonicity #4320]: #4322
-#4467 := [monotonicity #4323 #4333 #4341 #4464]: #4466
-#4470 := [monotonicity #4467]: #4469
-#4314 := (iff #3356 #4313)
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-#4306 := [monotonicity #4269 #4303]: #4305
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 #4309 := [monotonicity #4306]: #4308
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-#2304 := (not #2303)
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-#3494 := [quant-intro #3491]: #3493
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+#3427 := (iff #809 #3426)
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+#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)
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-#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)
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-#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)
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-#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)
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-#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)
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+#2353 := (and #2343 #2349)
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+#2291 := (* -1::int #2290)
+#2293 := (+ #2292 #2291)
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+#2297 := (>= #2296 0::int)
+#2304 := (and #2303 #2301)
+#2305 := (not #2304)
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+#2264 := (* -1::int #2263)
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+#2273 := (and #2272 #2269)
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+#2402 := (or #2209 #2398)
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+#2091 := (+ #2090 #1315)
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+#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)
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+#1957 := (not #1956)
+#1958 := (and #1957 #1955)
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+#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
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+#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)
+#348 := (= 0::int #48)
+#359 := (or #52 #348)
+#364 := (forall (vars (?v0 S3) (?v1 S3)) #359)
+#373 := (iff #364 #372)
+#370 := (iff #359 #369)
+#367 := (iff #348 #49)
+#368 := [rewrite]: #367
+#371 := [monotonicity #368]: #370
+#374 := [quant-intro #371]: #373
+#365 := (iff #51 #364)
+#362 := (iff #50 #359)
+#356 := (implies #47 #348)
+#360 := (iff #356 #359)
+#361 := [rewrite]: #360
+#357 := (iff #50 #356)
+#354 := (iff #49 #348)
+#355 := [rewrite]: #354
+#358 := [monotonicity #355]: #357
+#363 := [trans #358 #361]: #362
+#366 := [quant-intro #363]: #365
+#376 := [trans #366 #374]: #375
+#346 := [asserted]: #51
+#377 := [mp #346 #376]: #372
+#1825 := [mp~ #377 #1824]: #372
+#4184 := [mp #1825 #4183]: #4179
+#7268 := (not #4179)
+#9730 := (or #7268 #9634 #9722)
+#9723 := (not #9704)
+#9724 := (or #9723 #9722)
+#9731 := (or #7268 #9724)
+#9738 := (iff #9731 #9730)
+#9733 := (or #7268 #9727)
+#9736 := (iff #9733 #9730)
+#9737 := [rewrite]: #9736
+#9734 := (iff #9731 #9733)
+#9728 := (iff #9724 #9727)
+#9725 := (iff #9723 #9634)
+#9706 := (iff #9704 #9613)
+#9707 := [rewrite]: #9706
+#9726 := [monotonicity #9707]: #9725
+#9729 := [monotonicity #9726]: #9728
+#9735 := [monotonicity #9729]: #9734
+#9739 := [trans #9735 #9737]: #9738
+#9732 := [quant-inst]: #9731
+#9740 := [mp #9732 #9739]: #9730
+#10096 := [unit-resolution #9740 #4184]: #9727
+#10097 := [unit-resolution #10096 #10064]: #9722
+#10098 := (not #9722)
+#10099 := (or #10098 #9702)
+#10100 := [th-lemma]: #10099
+#10101 := [unit-resolution #10100 #10097]: #9702
+#9741 := (>= #9656 0::int)
+#10102 := (or #10098 #9741)
+#10103 := [th-lemma]: #10102
+#10104 := [unit-resolution #10103 #10097]: #9741
+#9274 := (+ #9062 #9218)
+#9275 := (+ #174 #9274)
+#9509 := (<= #9275 0::int)
+#9278 := (= #9275 0::int)
+#9219 := (* -1::int #9218)
+#9223 := (+ f8 #9219)
+#9224 := (<= #9223 0::int)
+#9445 := (not #9224)
+#9235 := (+ #9160 #9218)
+#9236 := (+ #174 #9235)
+#9237 := (>= #9236 0::int)
+#9242 := (or #9224 #9237)
+#9245 := (not #9242)
+#10063 := [hypothesis]: #4096
+#9430 := (or #4374 #2831 #9245)
+#9220 := (+ #1426 #9219)
+#9221 := (+ #2226 #9220)
+#9222 := (<= #9221 0::int)
+#9225 := (or #9224 #9222)
+#9226 := (not #9225)
+#9227 := (or #2227 #9226)
+#9431 := (or #4374 #9227)
+#9443 := (iff #9431 #9430)
+#9248 := (or #2831 #9245)
+#9432 := (or #4374 #9248)
+#9435 := (iff #9432 #9430)
+#9436 := [rewrite]: #9435
+#9433 := (iff #9431 #9432)
+#9249 := (iff #9227 #9248)
+#9246 := (iff #9226 #9245)
+#9243 := (iff #9225 #9242)
+#9240 := (iff #9222 #9237)
+#9228 := (+ #2226 #9219)
+#9229 := (+ #1426 #9228)
+#9232 := (<= #9229 0::int)
+#9238 := (iff #9232 #9237)
+#9239 := [rewrite]: #9238
+#9233 := (iff #9222 #9232)
+#9230 := (= #9221 #9229)
+#9231 := [rewrite]: #9230
+#9234 := [monotonicity #9231]: #9233
+#9241 := [trans #9234 #9239]: #9240
+#9244 := [monotonicity #9241]: #9243
+#9247 := [monotonicity #9244]: #9246
+#9250 := [monotonicity #2833 #9247]: #9249
+#9434 := [monotonicity #9250]: #9433
+#9444 := [trans #9434 #9436]: #9443
+#9426 := [quant-inst]: #9431
+#9442 := [mp #9426 #9444]: #9430
+#10105 := [unit-resolution #9442 #9177 #10063]: #9245
+#9446 := (or #9242 #9445)
+#9447 := [def-axiom]: #9446
+#10106 := [unit-resolution #9447 #10105]: #9445
+#9451 := (not #9237)
+#9452 := (or #9242 #9451)
+#9450 := [def-axiom]: #9452
+#10107 := [unit-resolution #9450 #10105]: #9451
+#9281 := (or #9224 #9237 #9278)
+#9455 := (or #4382 #9224 #9237 #9278)
+#9270 := (+ #9218 #9062)
+#9271 := (+ #174 #9270)
+#9272 := (= #9271 0::int)
+#9273 := (or #9224 #9222 #9272)
+#9459 := (or #4382 #9273)
+#9501 := (iff #9459 #9455)
+#9502 := (or #4382 #9281)
+#9505 := (iff #9502 #9455)
+#9506 := [rewrite]: #9505
+#9503 := (iff #9459 #9502)
+#9282 := (iff #9273 #9281)
+#9279 := (iff #9272 #9278)
+#9276 := (= #9271 #9275)
+#9277 := [rewrite]: #9276
+#9280 := [monotonicity #9277]: #9279
+#9283 := [monotonicity #9241 #9280]: #9282
+#9504 := [monotonicity #9283]: #9503
+#9507 := [trans #9504 #9506]: #9501
+#9460 := [quant-inst]: #9459
+#9508 := [mp #9460 #9507]: #9455
+#10108 := [unit-resolution #9508 #9181]: #9281
+#10109 := [unit-resolution #10108 #10107 #10106]: #9278
+#10110 := (not #9278)
+#10111 := (or #10110 #9509)
+#10112 := [th-lemma]: #10111
+#10113 := [unit-resolution #10112 #10109]: #9509
+#9510 := (>= #9275 0::int)
+#10114 := (or #10110 #9510)
+#10115 := [th-lemma]: #10114
+#10116 := [unit-resolution #10115 #10109]: #9510
+#10118 := [th-lemma #10116 #10113 #10104 #10101 #10095 #10092]: #10117
+#10121 := [trans #10118 #10072]: #4728
+#10080 := (not #4728)
+#10081 := (iff #4096 #10080)
+#10078 := (iff #2831 #4728)
+#10073 := (= #4727 #174)
+#10076 := (iff #10073 #4728)
+#10077 := [commutativity]: #10076
+#10074 := (iff #2831 #10073)
+#10066 := (= #2226 #174)
+#9358 := (= ?v0!14 f22)
+#10065 := [trans #10064 #10000]: #9358
+#10067 := [monotonicity #10065]: #10066
+#10075 := [monotonicity #10072 #10067]: #10074
+#10079 := [trans #10075 #10077]: #10078
+#10082 := [monotonicity #10079]: #10081
+#10083 := [mp #10063 #10082]: #10080
+#10122 := [unit-resolution #10083 #10121]: false
+#10124 := [lemma #10122]: #10123
+#9896 := [unit-resolution #10124 #9878]: #9634
+#9633 := (not #9614)
+#9637 := (or #9633 #9613 #9171)
+#9638 := [def-axiom]: #9637
+#9897 := [unit-resolution #9638 #9896 #9893]: #9171
+#9968 := [trans #9897 #9967]: #9904
+#9905 := (not #9904)
+#9923 := (or #4269 #9749 #9905 #9915)
+#9899 := (* -1::int #9898)
+#9901 := (+ #9900 #9899)
+#9902 := (>= #9901 0::int)
+#9906 := (or #9749 #9905 #9902)
+#9924 := (or #4269 #9906)
+#9931 := (iff #9924 #9923)
+#9920 := (or #9749 #9905 #9915)
+#9926 := (or #4269 #9920)
+#9929 := (iff #9926 #9923)
+#9930 := [rewrite]: #9929
+#9927 := (iff #9924 #9926)
+#9921 := (iff #9906 #9920)
+#9918 := (iff #9902 #9915)
+#9907 := (+ #9899 #9900)
+#9910 := (>= #9907 0::int)
+#9916 := (iff #9910 #9915)
+#9917 := [rewrite]: #9916
+#9911 := (iff #9902 #9910)
+#9908 := (= #9901 #9907)
+#9909 := [rewrite]: #9908
+#9912 := [monotonicity #9909]: #9911
+#9919 := [trans #9912 #9917]: #9918
+#9922 := [monotonicity #9919]: #9921
+#9928 := [monotonicity #9922]: #9927
+#9932 := [trans #9928 #9930]: #9931
+#9925 := [quant-inst]: #9924
+#9933 := [mp #9925 #9932]: #9923
+#9970 := [unit-resolution #9933 #10011 #9968]: #9969
+#9971 := [unit-resolution #9970 #10010]: #9915
+#9973 := (+ #2226 #9899)
+#9974 := (<= #9973 0::int)
+#9972 := (= #2226 #9898)
+#9989 := (= #9898 #2226)
+#9990 := [monotonicity #9988]: #9989
+#9991 := [symm #9990]: #9972
+#9992 := (not #9972)
+#9993 := (or #9992 #9974)
+#9994 := [th-lemma]: #9993
+#9995 := [unit-resolution #9994 #9991]: #9974
+#9975 := (= #9656 #9218)
+#9978 := [monotonicity #10085]: #9975
+#9980 := [symm #9978]: #9797
+#9981 := [unit-resolution #10094 #9980]: #9800
+#9703 := (not #9702)
+#9708 := (or #9613 #9703)
+#9711 := (or #7251 #9613 #9703)
+#9705 := (or #9704 #9703)
+#9712 := (or #7251 #9705)
+#9719 := (iff #9712 #9711)
+#9714 := (or #7251 #9708)
+#9717 := (iff #9714 #9711)
+#9718 := [rewrite]: #9717
+#9715 := (iff #9712 #9714)
+#9709 := (iff #9705 #9708)
+#9710 := [monotonicity #9707]: #9709
+#9716 := [monotonicity #9710]: #9715
+#9720 := [trans #9716 #9718]: #9719
+#9713 := [quant-inst]: #9712
+#9721 := [mp #9713 #9720]: #9711
+#9982 := [unit-resolution #9721 #4190]: #9708
+#9983 := [unit-resolution #9982 #9896]: #9703
+#10025 := (or #9741 #9702)
+#10026 := [th-lemma]: #10025
+#10027 := [unit-resolution #10026 #9983]: #9741
+#10028 := [unit-resolution #9442 #9177 #9878]: #9245
+#10029 := [unit-resolution #9447 #10028]: #9445
+#10119 := [unit-resolution #9450 #10028]: #9451
+#10120 := [unit-resolution #10108 #10119 #10029]: #9278
+#10125 := [unit-resolution #10112 #10120]: #9509
+#10126 := [th-lemma #10125 #10027 #9981 #9995 #10020 #9971 #9882]: false
+#10127 := [lemma #10126]: #2837
+#4033 := (or #4493 #2842 #4487)
+#4034 := [def-axiom]: #4033
+#11608 := [unit-resolution #4034 #10127 #11607]: #4487
+#4043 := (or #4484 #4394)
+#4045 := [def-axiom]: #4043
+#11609 := [unit-resolution #4045 #11608]: #4394
+#11327 := (or #4399 #5061 #9640)
+#9639 := (or #9636 #5061)
+#11310 := (or #4399 #9639)
+#11316 := (iff #11310 #11327)
+#9650 := (or #5061 #9640)
+#11312 := (or #4399 #9650)
+#11309 := (iff #11312 #11327)
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+#11313 := (iff #11310 #11312)
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+#9643 := (or #9640 #5061)
+#9651 := (iff #9643 #9650)
+#9652 := [rewrite]: #9651
+#9648 := (iff #9639 #9643)
+#9649 := [monotonicity #9642]: #9648
+#9692 := [trans #9649 #9652]: #9653
+#11314 := [monotonicity #9692]: #11313
+#11317 := [trans #11314 #11315]: #11316
+#11311 := [quant-inst]: #11310
+#11318 := [mp #11311 #11317]: #11327
+#11017 := [unit-resolution #11318 #11609 #10958]: #5061
+#11018 := [mp #11017 #12535]: #11887
+#11886 := (not #11990)
+#12268 := (or #11886 #11979 #11993)
+#12269 := [def-axiom]: #12268
+#11019 := [unit-resolution #12269 #11018 #12658]: #11979
+#12684 := (or #11981 #12147)
+#11974 := (or #11981 #12147 #8905)
+#11980 := [def-axiom]: #11974
+#12685 := [unit-resolution #11980 #9891]: #12684
+#11123 := [unit-resolution #12685 #11019]: #12147
+#12128 := (or #12119 #12122)
+#12203 := (or #7251 #12119 #12122)
+#12120 := (= #9390 ?v0!15)
+#12121 := (or #12120 #12119)
+#12206 := (or #7251 #12121)
+#12072 := (iff #12206 #12203)
+#12067 := (or #7251 #12128)
+#12070 := (iff #12067 #12203)
+#12071 := [rewrite]: #12070
+#12068 := (iff #12206 #12067)
+#12131 := (iff #12121 #12128)
+#12125 := (or #12122 #12119)
+#12129 := (iff #12125 #12128)
+#12130 := [rewrite]: #12129
+#12126 := (iff #12121 #12125)
+#12123 := (iff #12120 #12122)
+#12124 := [rewrite]: #12123
+#12127 := [monotonicity #12124]: #12126
+#12132 := [trans #12127 #12130]: #12131
+#12069 := [monotonicity #12132]: #12068
+#12073 := [trans #12069 #12071]: #12072
+#12207 := [quant-inst]: #12206
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+#12282 := [unit-resolution #12074 #4190]: #12128
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+#11122 := (or #12114 #12118)
+#11125 := [th-lemma]: #11122
+#11126 := [unit-resolution #11125 #11124]: #12114
+#11116 := [th-lemma #11126 #12336 #12327 #11016 #9587]: false
+#11127 := [lemma #11116]: #2248
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+#14728 := (iff #4912 #204)
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+#14713 := (iff #4912 #795)
+#14723 := [monotonicity #6916]: #14713
+#14722 := [trans #14723 #14726]: #14728
+#4871 := (f9 #4870)
+#4875 := (* -1::int #4871)
+#4879 := (+ f8 #4875)
+#4880 := (<= #4879 0::int)
+#4876 := (+ #1426 #4875)
+#4877 := (+ #99 #4876)
+#4878 := (<= #4877 0::int)
+#4914 := (or #4878 #4880)
+#9457 := (f4 #9217)
+#9516 := (= f10 #9457)
+#9461 := (f3 #9457 f10)
+#9462 := (f9 #9461)
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+#9466 := (* -1::int #9462)
+#9572 := (+ #4871 #9466)
+#9574 := (>= #9572 0::int)
+#9571 := (= #4871 #9462)
+#9580 := (= #9462 #4871)
+#9578 := (= #9461 #4870)
+#9576 := (= #9457 f22)
+#9458 := (= f22 #9457)
+#9464 := (or #9463 #9458)
+#9465 := [quant-inst]: #9464
+#9575 := [unit-resolution #9465 #4164]: #9458
+#9577 := [symm #9575]: #9576
+#9579 := [monotonicity #9577]: #9578
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+#9582 := [symm #9581]: #9571
+#9583 := (not #9571)
+#9584 := (or #9583 #9574)
+#9585 := [th-lemma]: #9584
+#9586 := [unit-resolution #9585 #9582]: #9574
+#4973 := (<= #99 0::int)
+#6917 := (or #1720 #4973)
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+#6918 := [unit-resolution #6912 #6916]: #4973
+#8831 := (not #4878)
+#9588 := [hypothesis]: #8831
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+#6920 := (not #4973)
+#9589 := (not #9574)
+#9591 := (or #9512 #9589 #6920 #9590 #4878)
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+#9593 := [unit-resolution #9592 #9588 #9587 #6918 #9586]: #9512
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+#9514 := (= #9457 f10)
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+#9523 := (iff #9519 #9522)
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+#9521 := [monotonicity #9518]: #9520
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+#9529 := [quant-inst]: #9528
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+#9594 := [unit-resolution #9537 #4190]: #9522
+#9595 := [unit-resolution #9594 #9593]: #9516
+#9538 := (= #9462 0::int)
+#9600 := (not #9538)
+#9558 := (>= #9462 0::int)
+#9596 := (not #9558)
+#9597 := (or #9596 #9589 #6920 #9590 #4878)
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+#9599 := [unit-resolution #9598 #9588 #9587 #6918 #9586]: #9596
+#9601 := (or #9600 #9558)
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+#9603 := [unit-resolution #9602 #9599]: #9600
+#9541 := (not #9516)
+#9544 := (or #9541 #9538)
+#9547 := (or #7268 #9541 #9538)
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+#9549 := [quant-inst]: #9548
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+#9604 := [unit-resolution #9557 #4184]: #9544
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+#9606 := [lemma #9605]: #4878
+#8838 := (or #4914 #8831)
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+#4917 := (not #4914)
+#4920 := (or #4912 #4917)
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+#8828 := (iff #8811 #8815)
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+#4915 := (iff #4910 #4914)
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 #4922 := [monotonicity #4919]: #4921
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-#8404 := [monotonicity #4925]: #7530
-#8702 := [trans #8404 #8677]: #8699
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-#21208 := [unit-resolution #8860 #9542]: #4923
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-#21235 := (not #4915)
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-#23937 := (or #5034 #23935 #23936)
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-#23979 := [unit-resolution #23978 #21238]: #5034
-#23983 := (not #5034)
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-#4939 := (>= #4937 0::int)
-#9072 := (f5 f19 ?v0!13)
-#9073 := (f4 #9072)
-#9196 := (+ #2181 #9073)
-#9197 := (+ #141 #9196)
-#9308 := (>= #9197 0::int)
-#9223 := (= #9197 0::int)
-#9059 := (* -1::int #9073)
-#9079 := (+ f3 #9059)
-#9080 := (<= #9079 0::int)
-#9458 := (not #9080)
-#9160 := (+ #2797 #9073)
-#9156 := (+ #141 #9160)
-#9161 := (>= #9156 0::int)
-#9328 := (or #9080 #9161)
-#9324 := (not #9328)
-#9317 := (= #2180 #2182)
-#9534 := (not #9317)
-#9533 := [hypothesis]: #2804
-#9537 := (or #9534 #2799)
-#9538 := [th-lemma]: #9537
-#9539 := [unit-resolution #9538 #9533]: #9534
-#9351 := (or #4331 #9317 #9324)
-#9071 := (+ #1359 #9059)
-#9077 := (+ #2182 #9071)
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-#9309 := (or #9080 #9078)
-#9314 := (not #9309)
-#9315 := (= #2182 #2180)
-#9316 := (or #9315 #9314)
-#9352 := (or #4331 #9316)
-#9455 := (iff #9352 #9351)
-#9350 := (or #9317 #9324)
-#9354 := (or #4331 #9350)
-#9454 := (iff #9354 #9351)
-#9449 := [rewrite]: #9454
-#9355 := (iff #9352 #9354)
-#9345 := (iff #9316 #9350)
-#9348 := (iff #9314 #9324)
-#9346 := (iff #9309 #9328)
-#9164 := (iff #9078 #9161)
-#9109 := (+ #2182 #9059)
-#9111 := (+ #1359 #9109)
-#9158 := (<= #9111 0::int)
-#9162 := (iff #9158 #9161)
-#9163 := [rewrite]: #9162
-#9159 := (iff #9078 #9158)
-#9112 := (= #9077 #9111)
-#9157 := [rewrite]: #9112
-#9154 := [monotonicity #9157]: #9159
-#9189 := [trans #9154 #9163]: #9164
-#9347 := [monotonicity #9189]: #9346
-#9349 := [monotonicity #9347]: #9348
-#9318 := (iff #9315 #9317)
-#9327 := [rewrite]: #9318
-#9323 := [monotonicity #9327 #9349]: #9345
-#9453 := [monotonicity #9323]: #9355
-#9456 := [trans #9453 #9449]: #9455
-#9353 := [quant-inst]: #9352
-#9452 := [mp #9353 #9456]: #9351
-#9543 := [unit-resolution #9452 #9542 #9539]: #9324
-#9459 := (or #9328 #9458)
-#9464 := [def-axiom]: #9459
-#9544 := [unit-resolution #9464 #9543]: #9458
-#9465 := (not #9161)
-#9489 := (or #9328 #9465)
-#9490 := [def-axiom]: #9489
-#9545 := [unit-resolution #9490 #9543]: #9465
-#8755 := (or #9080 #9161 #9223)
-#4009 := (or #4465 #4334)
-#3982 := [def-axiom]: #4009
-#9546 := [unit-resolution #3982 #9541]: #4334
-#9188 := (or #4339 #9080 #9161 #9223)
-#9074 := (+ #9073 #2181)
-#9075 := (+ #141 #9074)
-#9076 := (= #9075 0::int)
-#9108 := (or #9080 #9078 #9076)
-#9226 := (or #4339 #9108)
-#9258 := (iff #9226 #9188)
-#9228 := (or #4339 #8755)
-#9232 := (iff #9228 #9188)
-#9257 := [rewrite]: #9232
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-#8857 := (iff #9108 #8755)
-#9224 := (iff #9076 #9223)
-#9195 := (= #9075 #9197)
-#9198 := [rewrite]: #9195
-#8754 := [monotonicity #9198]: #9224
-#8858 := [monotonicity #9189 #8754]: #8857
-#9231 := [monotonicity #8858]: #9230
-#9261 := [trans #9231 #9257]: #9258
-#9227 := [quant-inst]: #9226
-#9312 := [mp #9227 #9261]: #9188
-#9547 := [unit-resolution #9312 #9546]: #8755
-#9548 := [unit-resolution #9547 #9545 #9544]: #9223
-#9549 := (not #9223)
-#9550 := (or #9549 #9308)
-#9551 := [th-lemma]: #9550
-#9552 := [unit-resolution #9551 #9548]: #9308
-#9457 := (>= #2798 0::int)
-#9553 := (or #9457 #2799)
-#9554 := [th-lemma]: #9553
-#9555 := [unit-resolution #9554 #9533]: #9457
-#9556 := [th-lemma #9555 #9545 #9552]: false
-#9557 := [lemma #9556]: #2799
-#3983 := (or #4465 #4459)
-#3984 := [def-axiom]: #3983
-#11132 := [unit-resolution #3984 #9541]: #4459
-#4013 := (or #4462 #2804 #4456)
-#4014 := [def-axiom]: #4013
-#11133 := [unit-resolution #4014 #11132]: #4459
-#11134 := [unit-resolution #11133 #9557]: #4456
-#4026 := (or #4453 #4342)
-#4027 := [def-axiom]: #4026
-#11135 := [unit-resolution #4027 #11134]: #4342
-#7252 := (or #4347 #4939)
-#7208 := [quant-inst]: #7252
-#15735 := [unit-resolution #7208 #11135]: #4939
-#23980 := (not #4939)
-#23981 := (or #5027 #8050 #23980)
-#23976 := [th-lemma]: #23981
-#23982 := [unit-resolution #23976 #6999 #15735]: #5027
-#9413 := (not #5027)
-#23984 := (or #170 #9413 #23983)
-#23985 := [th-lemma]: #23984
-#23988 := [unit-resolution #23985 #23982]: #23986
-#23989 := [unit-resolution #23988 #23979]: #170
-#4028 := (or #4453 #4447)
-#4029 := [def-axiom]: #4028
-#13683 := [unit-resolution #4029 #11134]: #4447
-#9621 := (* -1::int #2202)
-#9622 := (+ #2201 #9621)
-#10140 := (>= #9622 0::int)
-#11140 := (not #10140)
-#9623 := (<= #9622 0::int)
-#9833 := (or #4347 #9623)
-#9612 := (* -1::int #2201)
-#9613 := (+ #2202 #9612)
-#9614 := (>= #9613 0::int)
-#9790 := (or #4347 #9614)
-#9835 := (iff #9790 #9833)
-#9836 := (iff #9833 #9833)
-#9837 := [rewrite]: #9836
-#9626 := (iff #9614 #9623)
-#9615 := (+ #9612 #2202)
-#9618 := (>= #9615 0::int)
-#9624 := (iff #9618 #9623)
-#9625 := [rewrite]: #9624
-#9619 := (iff #9614 #9618)
-#9616 := (= #9613 #9615)
-#9617 := [rewrite]: #9616
-#9620 := [monotonicity #9617]: #9619
-#9627 := [trans #9620 #9625]: #9626
-#9842 := [monotonicity #9627]: #9835
-#9838 := [trans #9842 #9837]: #9835
-#9834 := [quant-inst]: #9790
-#9849 := [mp #9834 #9838]: #9833
-#11136 := [unit-resolution #9849 #11135]: #9623
-#4087 := (not #2807)
-#11137 := [hypothesis]: #2818
-#4088 := (or #2813 #4087)
-#4093 := [def-axiom]: #4088
-#11138 := [unit-resolution #4093 #11137]: #4087
-#11139 := (not #9623)
-#11141 := (or #2807 #11139 #11140)
-#11142 := [th-lemma]: #11141
-#11143 := [unit-resolution #11142 #11138 #11136]: #11140
-#9797 := (f5 #9605 ?v0!14)
-#9798 := (f4 #9797)
-#9850 := (* -1::int #9798)
-#9668 := (f5 f19 ?v0!14)
-#9669 := (f4 #9668)
-#10545 := (+ #9669 #9850)
-#10726 := (>= #10545 0::int)
-#10491 := (= #9669 #9798)
-#11146 := (= #9798 #9669)
-#11144 := (= #9797 #9668)
-#11145 := [monotonicity #10826]: #11144
-#11147 := [monotonicity #11145]: #11146
-#11148 := [symm #11147]: #10491
-#11149 := (not #10491)
-#11150 := (or #11149 #10726)
-#11151 := [th-lemma]: #11150
-#11152 := [unit-resolution #11151 #11148]: #10726
-#10318 := (>= #9798 0::int)
-#10440 := (<= #9798 0::int)
-#10442 := (not #10440)
-#10274 := (= ?v0!14 #9605)
-#10305 := (not #10274)
-#10634 := (or #10305 #2807)
-#10168 := (= #141 #2202)
-#10166 := (= #2202 #141)
-#10813 := (= ?v0!14 f19)
-#9839 := [hypothesis]: #10274
-#9822 := [trans #9839 #10826]: #10813
-#10167 := [monotonicity #9822]: #10166
-#10169 := [symm #10167]: #10168
-#10163 := (= #2201 #141)
-#4730 := (f22 f19)
-#10182 := (= #4730 #141)
-#4731 := (= #141 #4730)
-#4722 := (* -1::int #4719)
-#4726 := (+ f3 #4722)
-#4727 := (<= #4726 0::int)
-#4743 := (or #4727 #4738)
-#4767 := (or #4743 #4766)
-#4768 := [def-axiom]: #4767
-#10125 := [unit-resolution #4768 #10413]: #4743
-#4746 := (not #4743)
-#4749 := (or #4731 #4746)
-#8613 := (or #4331 #4731 #4746)
-#4723 := (+ #1359 #4722)
-#4724 := (+ #141 #4723)
-#4725 := (<= #4724 0::int)
-#4728 := (or #4727 #4725)
-#4729 := (not #4728)
-#4732 := (or #4731 #4729)
-#8614 := (or #4331 #4732)
-#8647 := (iff #8614 #8613)
-#8612 := (or #4331 #4749)
-#8640 := (iff #8612 #8613)
-#8646 := [rewrite]: #8640
-#8644 := (iff #8614 #8612)
-#4750 := (iff #4732 #4749)
-#4747 := (iff #4729 #4746)
-#4744 := (iff #4728 #4743)
-#4741 := (iff #4725 #4738)
-#4735 := (<= #4722 0::int)
-#4739 := (iff #4735 #4738)
-#4740 := [rewrite]: #4739
-#4736 := (iff #4725 #4735)
-#4733 := (= #4724 #4722)
-#4734 := [rewrite]: #4733
-#4737 := [monotonicity #4734]: #4736
-#4742 := [trans #4737 #4740]: #4741
-#4745 := [monotonicity #4742]: #4744
-#4748 := [monotonicity #4745]: #4747
-#4751 := [monotonicity #4748]: #4750
-#8645 := [monotonicity #4751]: #8644
-#8653 := [trans #8645 #8646]: #8647
-#8643 := [quant-inst]: #8614
-#8654 := [mp #8643 #8653]: #8613
-#10126 := [unit-resolution #8654 #9542]: #4749
-#10137 := [unit-resolution #10126 #10125]: #4731
-#10164 := [symm #10137]: #10182
-#10138 := (= #2201 #4730)
-#10161 := [monotonicity #9822]: #10138
-#10170 := [trans #10161 #10164]: #10163
-#10543 := [trans #10170 #10169]: #2807
-#10781 := [hypothesis]: #4087
-#10628 := [unit-resolution #10781 #10543]: false
-#10694 := [lemma #10628]: #10634
-#11153 := [unit-resolution #10694 #11138]: #10305
-#10444 := (or #10274 #10442)
-#10316 := (or #7253 #10274 #10442)
-#10416 := (= #9605 ?v0!14)
-#10443 := (or #10416 #10442)
-#10363 := (or #7253 #10443)
-#10551 := (iff #10363 #10316)
-#10315 := (or #7253 #10444)
-#10436 := (iff #10315 #10316)
-#10544 := [rewrite]: #10436
-#10299 := (iff #10363 #10315)
-#10445 := (iff #10443 #10444)
-#10422 := (iff #10416 #10274)
-#10423 := [rewrite]: #10422
-#10446 := [monotonicity #10423]: #10445
-#10435 := [monotonicity #10446]: #10299
-#10554 := [trans #10435 #10544]: #10551
-#10298 := [quant-inst]: #10363
-#10555 := [mp #10298 #10554]: #10316
-#11154 := [unit-resolution #10555 #4147]: #10444
-#11155 := [unit-resolution #11154 #11153]: #10442
-#11156 := (or #10318 #10440)
-#11157 := [th-lemma]: #11156
-#11158 := [unit-resolution #11157 #11155]: #10318
-#10323 := (f24 #9797)
-#10727 := (f9 f10 #10323)
-#10728 := (* -1::int #10727)
-#10773 := (+ #2202 #10728)
-#10783 := (<= #10773 0::int)
-#10782 := (= #2202 #10727)
-#10799 := (= #10727 #2202)
-#10792 := (= #10323 ?v0!14)
-#10324 := (= ?v0!14 #10323)
-#10306 := (or #7210 #10324)
-#10272 := [quant-inst]: #10306
-#10789 := [unit-resolution #10272 #4566]: #10324
-#10793 := [symm #10789]: #10792
-#10800 := [monotonicity #10793]: #10799
-#10798 := [symm #10800]: #10782
-#10801 := (not #10782)
-#10802 := (or #10801 #10783)
-#10803 := [th-lemma]: #10802
-#10809 := [unit-resolution #10803 #10798]: #10783
-#9717 := (f9 f10 #9605)
-#10729 := (+ #9717 #10728)
-#10730 := (>= #10729 0::int)
-#10725 := (f11 f12 #10323)
-#10731 := (= f1 #10725)
-#9639 := (f11 f12 ?v0!14)
-#9881 := (= #9639 #10725)
-#10811 := (= #10725 #9639)
-#10812 := [monotonicity #10793]: #10811
-#9887 := [symm #10812]: #9881
-#9640 := (= f1 #9639)
-#10275 := (ite #10274 #3747 #9640)
-#10309 := (f11 #10278 ?v0!14)
-#10310 := (= f1 #10309)
-#10312 := (iff #10275 #10310)
-#10114 := (or #8843 #10312)
-#10311 := (iff #10310 #10275)
-#10109 := (or #8843 #10311)
-#10127 := (iff #10109 #10114)
-#10103 := (iff #10114 #10114)
-#10104 := [rewrite]: #10103
-#10313 := (iff #10311 #10312)
-#10314 := [rewrite]: #10313
-#10145 := [monotonicity #10314]: #10127
-#10105 := [trans #10145 #10104]: #10127
-#10144 := [quant-inst]: #10109
-#10106 := [mp #10144 #10105]: #10114
-#11159 := [unit-resolution #10106 #4554]: #10312
-#11175 := (= #2198 #10309)
-#11171 := (= #10309 #2198)
-#11169 := (= #10278 f20)
-#11167 := (= #147 f20)
-#11168 := [symm #11161]: #11167
-#11170 := [trans #11166 #11168]: #11169
-#11172 := [monotonicity #11170]: #11171
-#11176 := [symm #11172]: #11175
-#4091 := (or #2813 #2199)
-#4092 := [def-axiom]: #4091
-#11160 := [unit-resolution #4092 #11137]: #2199
-#11177 := [trans #11160 #11176]: #10310
-#10136 := (not #10310)
-#10130 := (not #10312)
-#10162 := (or #10130 #10275 #10136)
-#10174 := [def-axiom]: #10162
-#11178 := [unit-resolution #10174 #11177 #11159]: #10275
-#10107 := (not #10275)
-#10120 := (or #10107 #10274 #9640)
-#10121 := [def-axiom]: #10120
-#11179 := [unit-resolution #10121 #11153 #11178]: #9640
-#11182 := [trans #11179 #9887]: #10731
-#9720 := (f11 f12 #9605)
-#9703 := (= f1 #9720)
-#10871 := (not #9703)
-#10872 := (iff #671 #10871)
-#10869 := (iff #668 #9703)
-#10867 := (iff #9703 #668)
-#10865 := (= #9720 #138)
-#10866 := [monotonicity #10826]: #10865
-#10868 := [monotonicity #10866]: #10867
-#10870 := [symm #10868]: #10869
-#10873 := [monotonicity #10870]: #10872
-#4017 := (or #4465 #671)
-#4012 := [def-axiom]: #4017
-#10641 := [unit-resolution #4012 #9541]: #671
-#10874 := [mp #10641 #10873]: #10871
-#10732 := (not #10731)
-#10706 := (or #9703 #10730 #10732)
-#3925 := (or #4477 #4221)
-#3980 := [def-axiom]: #3925
-#10875 := [unit-resolution #3980 #6995]: #4221
-#10688 := (or #4226 #9703 #10730 #10732)
-#10733 := (or #9703 #10732 #10730)
-#10689 := (or #4226 #10733)
-#10779 := (iff #10689 #10688)
-#10690 := (or #4226 #10706)
-#10692 := (iff #10690 #10688)
-#10693 := [rewrite]: #10692
-#10685 := (iff #10689 #10690)
-#10686 := (iff #10733 #10706)
-#10687 := [rewrite]: #10686
-#10691 := [monotonicity #10687]: #10685
-#10780 := [trans #10691 #10693]: #10779
-#10705 := [quant-inst]: #10689
-#10778 := [mp #10705 #10780]: #10688
-#9934 := [unit-resolution #10778 #10875]: #10706
-#11183 := [unit-resolution #9934 #10874 #11182]: #10730
-#9710 := (* -1::int #9717)
-#10090 := (+ #141 #9710)
-#10100 := (>= #10090 0::int)
-#10116 := (= #141 #9717)
-#10827 := (= #9717 #141)
-#10828 := [monotonicity #10826]: #10827
-#10829 := [symm #10828]: #10116
-#10830 := (not #10116)
-#10831 := (or #10830 #10100)
-#10832 := [th-lemma]: #10831
-#10833 := [unit-resolution #10832 #10829]: #10100
-#9725 := (+ #9612 #9669)
-#9726 := (+ #141 #9725)
-#10023 := (<= #9726 0::int)
-#9729 := (= #9726 0::int)
-#9670 := (* -1::int #9669)
-#9674 := (+ f3 #9670)
-#9675 := (<= #9674 0::int)
-#9980 := (not #9675)
-#9686 := (+ #9621 #9669)
-#9687 := (+ #141 #9686)
-#9688 := (>= #9687 0::int)
-#9693 := (or #9675 #9688)
-#9696 := (not #9693)
-#9886 := (or #4331 #2807 #9696)
-#9671 := (+ #1359 #9670)
-#9672 := (+ #2202 #9671)
-#9673 := (<= #9672 0::int)
-#9676 := (or #9675 #9673)
-#9677 := (not #9676)
-#9678 := (or #2203 #9677)
-#9936 := (or #4331 #9678)
-#9973 := (iff #9936 #9886)
-#9699 := (or #2807 #9696)
-#9938 := (or #4331 #9699)
-#9975 := (iff #9938 #9886)
-#9978 := [rewrite]: #9975
-#9939 := (iff #9936 #9938)
-#9700 := (iff #9678 #9699)
-#9697 := (iff #9677 #9696)
-#9694 := (iff #9676 #9693)
-#9691 := (iff #9673 #9688)
-#9679 := (+ #2202 #9670)
-#9680 := (+ #1359 #9679)
-#9683 := (<= #9680 0::int)
-#9689 := (iff #9683 #9688)
-#9690 := [rewrite]: #9689
-#9684 := (iff #9673 #9683)
-#9681 := (= #9672 #9680)
-#9682 := [rewrite]: #9681
-#9685 := [monotonicity #9682]: #9684
-#9692 := [trans #9685 #9690]: #9691
-#9695 := [monotonicity #9692]: #9694
-#9698 := [monotonicity #9695]: #9697
-#9701 := [monotonicity #2809 #9698]: #9700
-#9974 := [monotonicity #9701]: #9939
-#9977 := [trans #9974 #9978]: #9973
-#9937 := [quant-inst]: #9936
-#9979 := [mp #9937 #9977]: #9886
-#11184 := [unit-resolution #9979 #9542 #11138]: #9696
-#9981 := (or #9693 #9980)
-#9982 := [def-axiom]: #9981
-#11185 := [unit-resolution #9982 #11184]: #9980
-#9976 := (not #9688)
-#9965 := (or #9693 #9976)
-#9967 := [def-axiom]: #9965
-#11186 := [unit-resolution #9967 #11184]: #9976
-#9732 := (or #9675 #9688 #9729)
-#9970 := (or #4339 #9675 #9688 #9729)
-#9721 := (+ #9669 #9612)
-#9722 := (+ #141 #9721)
-#9723 := (= #9722 0::int)
-#9724 := (or #9675 #9673 #9723)
-#9971 := (or #4339 #9724)
-#10021 := (iff #9971 #9970)
-#10018 := (or #4339 #9732)
-#9964 := (iff #10018 #9970)
-#10020 := [rewrite]: #9964
-#10019 := (iff #9971 #10018)
-#9733 := (iff #9724 #9732)
-#9730 := (iff #9723 #9729)
-#9727 := (= #9722 #9726)
-#9728 := [rewrite]: #9727
-#9731 := [monotonicity #9728]: #9730
-#9734 := [monotonicity #9692 #9731]: #9733
-#9966 := [monotonicity #9734]: #10019
-#10022 := [trans #9966 #10020]: #10021
-#9972 := [quant-inst]: #9971
-#10017 := [mp #9972 #10022]: #9970
-#11187 := [unit-resolution #10017 #9546]: #9732
-#11188 := [unit-resolution #11187 #11186 #11185]: #9729
-#11189 := (not #9729)
-#11190 := (or #11189 #10023)
-#11191 := [th-lemma]: #11190
-#11192 := [unit-resolution #11191 #11188]: #10023
-#11193 := [th-lemma #11192 #10833 #11183 #10809 #11158 #11152 #11143]: false
-#11194 := [lemma #11193]: #2813
-#4024 := (or #4450 #2818 #4444)
-#4025 := [def-axiom]: #4024
-#13684 := [unit-resolution #4025 #11194 #13683]: #4444
-#4037 := (or #4441 #4435)
-#4038 := [def-axiom]: #4037
-#23990 := [unit-resolution #4038 #13684]: #4435
-#4047 := (or #4438 #1396 #4432)
-#4033 := [def-axiom]: #4047
-#23991 := [unit-resolution #4033 #23990]: #4435
-#23992 := [unit-resolution #23991 #23989]: #4432
-#4056 := (or #4429 #4423)
-#4040 := [def-axiom]: #4056
-#23987 := [unit-resolution #4040 #23992]: #4423
-#23993 := (or #4426 #4420)
-#7708 := (f9 f10 ?v0!15)
-#11503 := (>= #7708 0::int)
-#12960 := (or #4209 #11503)
-#12962 := [quant-inst]: #12960
-#13895 := [unit-resolution #12962 #7124]: #11503
-#7789 := (* -1::int #7708)
-#7790 := (+ #2223 #7789)
-#13166 := (>= #7790 0::int)
-#7711 := (= #2223 #7708)
-#7886 := [hypothesis]: #2225
-#13707 := (or #7711 #2224)
-#7805 := (f5 f19 ?v0!15)
-#7806 := (f4 #7805)
-#5059 := (* -1::int #2223)
-#7831 := (+ #5059 #7806)
-#7832 := (+ #141 #7831)
-#12906 := (<= #7832 0::int)
-#7835 := (= #7832 0::int)
-#7810 := (* -1::int #7806)
-#7814 := (+ f3 #7810)
-#7815 := (<= #7814 0::int)
-#12912 := (not #7815)
-#7824 := (+ #7789 #7806)
-#7825 := (+ #141 #7824)
-#7826 := (>= #7825 0::int)
-#7857 := (or #7815 #7826)
-#7860 := (not #7857)
-#13222 := (not #7711)
-#13341 := [hypothesis]: #13222
-#7863 := (or #7711 #7860)
-#12889 := (or #4331 #7711 #7860)
-#7811 := (+ #1359 #7810)
-#7812 := (+ #7708 #7811)
-#7813 := (<= #7812 0::int)
-#7854 := (or #7815 #7813)
-#7855 := (not #7854)
-#7709 := (= #7708 #2223)
-#7856 := (or #7709 #7855)
-#12908 := (or #4331 #7856)
-#12916 := (iff #12908 #12889)
-#12909 := (or #4331 #7863)
-#12913 := (iff #12909 #12889)
-#12915 := [rewrite]: #12913
-#12910 := (iff #12908 #12909)
-#7864 := (iff #7856 #7863)
-#7861 := (iff #7855 #7860)
-#7858 := (iff #7854 #7857)
-#7829 := (iff #7813 #7826)
-#7817 := (+ #7708 #7810)
-#7818 := (+ #1359 #7817)
-#7821 := (<= #7818 0::int)
-#7827 := (iff #7821 #7826)
-#7828 := [rewrite]: #7827
-#7822 := (iff #7813 #7821)
-#7819 := (= #7812 #7818)
-#7820 := [rewrite]: #7819
-#7823 := [monotonicity #7820]: #7822
-#7830 := [trans #7823 #7828]: #7829
-#7859 := [monotonicity #7830]: #7858
-#7862 := [monotonicity #7859]: #7861
-#7712 := (iff #7709 #7711)
-#7713 := [rewrite]: #7712
-#7865 := [monotonicity #7713 #7862]: #7864
-#12911 := [monotonicity #7865]: #12910
-#12917 := [trans #12911 #12915]: #12916
-#12903 := [quant-inst]: #12908
-#12918 := [mp #12903 #12917]: #12889
-#13464 := [unit-resolution #12918 #9542]: #7863
-#13465 := [unit-resolution #13464 #13341]: #7860
-#12919 := (or #7857 #12912)
-#12914 := [def-axiom]: #12919
-#13515 := [unit-resolution #12914 #13465]: #12912
-#12920 := (not #7826)
-#12921 := (or #7857 #12920)
-#12922 := [def-axiom]: #12921
-#13516 := [unit-resolution #12922 #13465]: #12920
-#7838 := (or #7815 #7826 #7835)
-#12871 := (or #4339 #7815 #7826 #7835)
-#7807 := (+ #7806 #5059)
-#7808 := (+ #141 #7807)
-#7809 := (= #7808 0::int)
-#7816 := (or #7815 #7813 #7809)
-#12872 := (or #4339 #7816)
-#12890 := (iff #12872 #12871)
-#12873 := (or #4339 #7838)
-#12878 := (iff #12873 #12871)
-#12879 := [rewrite]: #12878
-#12874 := (iff #12872 #12873)
-#7839 := (iff #7816 #7838)
-#7836 := (iff #7809 #7835)
-#7833 := (= #7808 #7832)
-#7834 := [rewrite]: #7833
-#7837 := [monotonicity #7834]: #7836
-#7840 := [monotonicity #7830 #7837]: #7839
-#12875 := [monotonicity #7840]: #12874
-#12904 := [trans #12875 #12879]: #12890
-#12868 := [quant-inst]: #12872
-#12905 := [mp #12868 #12904]: #12871
-#13645 := [unit-resolution #12905 #9546]: #7838
-#13668 := [unit-resolution #13645 #13516 #13515]: #7835
-#13669 := (not #7835)
-#13670 := (or #13669 #12906)
-#13671 := [th-lemma]: #13670
-#13672 := [unit-resolution #13671 #13668]: #12906
-#13167 := (f5 #9605 ?v0!15)
-#13148 := (f4 #13167)
-#13168 := (* -1::int #13148)
-#13239 := (+ #7806 #13168)
-#13257 := (>= #13239 0::int)
-#13238 := (= #7806 #13148)
-#13675 := (= #13148 #7806)
-#13673 := (= #13167 #7805)
-#13674 := [monotonicity #10826]: #13673
-#13676 := [monotonicity #13674]: #13675
-#13677 := [symm #13676]: #13238
-#13678 := (not #13238)
-#13679 := (or #13678 #13257)
-#13680 := [th-lemma]: #13679
-#13681 := [unit-resolution #13680 #13677]: #13257
-#13633 := (>= #13148 0::int)
-#13232 := (<= #13148 0::int)
-#13338 := (not #13232)
-#12653 := (= ?v0!15 #9605)
-#12964 := (not #12653)
-#7733 := (f11 f12 ?v0!15)
-#7734 := (= f1 #7733)
-#12825 := (ite #12653 #3747 #7734)
-#12963 := (not #12825)
-#12826 := (f11 #10278 ?v0!15)
-#11335 := (= f1 #12826)
-#12891 := (iff #11335 #12825)
-#12902 := (or #8843 #12891)
-#12897 := [quant-inst]: #12902
-#13682 := [unit-resolution #12897 #4554]: #12891
-#12586 := (not #11335)
-#5062 := (f11 f20 ?v0!15)
-#5063 := (= f1 #5062)
-#5064 := (not #5063)
-#13694 := (iff #5064 #12586)
-#13692 := (iff #5063 #11335)
-#13690 := (iff #11335 #5063)
-#13688 := (= #12826 #5062)
-#13689 := [monotonicity #11170]: #13688
-#13691 := [monotonicity #13689]: #13690
-#13693 := [symm #13691]: #13692
-#13695 := [monotonicity #13693]: #13694
-#7717 := (or #5064 #7711)
-#4034 := (or #4441 #4351)
-#4036 := [def-axiom]: #4034
-#13685 := [unit-resolution #4036 #13684]: #4351
-#12848 := (or #4356 #5064 #7711)
-#7710 := (or #7709 #5064)
-#12843 := (or #4356 #7710)
-#12877 := (iff #12843 #12848)
-#12849 := (or #4356 #7717)
-#12852 := (iff #12849 #12848)
-#12853 := [rewrite]: #12852
-#12850 := (iff #12843 #12849)
-#7720 := (iff #7710 #7717)
-#7714 := (or #7711 #5064)
-#7718 := (iff #7714 #7717)
-#7719 := [rewrite]: #7718
-#7715 := (iff #7710 #7714)
-#7716 := [monotonicity #7713]: #7715
-#7721 := [trans #7716 #7719]: #7720
-#12851 := [monotonicity #7721]: #12850
-#12882 := [trans #12851 #12853]: #12877
-#12844 := [quant-inst]: #12843
-#12883 := [mp #12844 #12882]: #12848
-#13686 := [unit-resolution #12883 #13685]: #7717
-#13687 := [unit-resolution #13686 #13341]: #5064
-#13696 := [mp #13687 #13695]: #12586
-#13147 := (not #12891)
-#13129 := (or #13147 #11335 #12963)
-#11390 := [def-axiom]: #13129
-#13697 := [unit-resolution #11390 #13696 #13682]: #12963
-#13698 := (or #12825 #12964)
-#13123 := (or #12825 #12964 #8984)
-#13124 := [def-axiom]: #13123
-#13699 := [unit-resolution #13124 #11162]: #13698
-#13700 := [unit-resolution #13699 #13697]: #12964
-#13351 := (or #12653 #13338)
-#13639 := (or #7253 #12653 #13338)
-#13231 := (= #9605 ?v0!15)
-#13353 := (or #13231 #13338)
-#13640 := (or #7253 #13353)
-#13120 := (iff #13640 #13639)
-#13659 := (or #7253 #13351)
-#12370 := (iff #13659 #13639)
-#13119 := [rewrite]: #12370
-#13660 := (iff #13640 #13659)
-#13357 := (iff #13353 #13351)
-#13358 := (iff #13231 #12653)
-#13359 := [rewrite]: #13358
-#13360 := [monotonicity #13359]: #13357
-#13661 := [monotonicity #13360]: #13660
-#13162 := [trans #13661 #13119]: #13120
-#13658 := [quant-inst]: #13640
-#13163 := [mp #13658 #13162]: #13639
-#13701 := [unit-resolution #13163 #4147]: #13351
-#13702 := [unit-resolution #13701 #13700]: #13338
-#13703 := (or #13633 #13232)
-#13704 := [th-lemma]: #13703
-#13705 := [unit-resolution #13704 #13702]: #13633
-#13706 := [th-lemma #7886 #13705 #13681 #13672 #13339]: false
-#13708 := [lemma #13706]: #13707
-#13896 := [unit-resolution #13708 #7886]: #7711
-#13205 := (or #13222 #13166)
-#13635 := (not #13166)
-#13118 := [hypothesis]: #13635
-#13221 := [hypothesis]: #7711
-#12972 := [th-lemma]: #13205
-#13220 := [unit-resolution #12972 #13221 #13118]: false
-#12966 := [lemma #13220]: #13205
-#13897 := [unit-resolution #12966 #13896]: #13166
-#13898 := [th-lemma #7886 #13897 #13895]: false
-#13899 := [lemma #13898]: #2224
-#4053 := (or #4426 #2225 #4420)
-#4054 := [def-axiom]: #4053
-#23994 := [unit-resolution #4054 #13899]: #23993
-#23995 := [unit-resolution #23994 #23987]: #4420
-#4048 := (or #4417 #4411)
-#4050 := [def-axiom]: #4048
-#23884 := [unit-resolution #4050 #23995]: #4411
-#23887 := (or #4414 #4408)
-#15926 := (= #2239 #4730)
-#6430 := (= ?v0!17 f19)
-#15697 := (= ?v0!17 #9605)
-#6420 := (f11 f12 ?v0!17)
-#6421 := (= f1 #6420)
-#15698 := (ite #15697 #3747 #6421)
-#15699 := (f11 #10278 ?v0!17)
-#15700 := (= f1 #15699)
-#15702 := (iff #15698 #15700)
-#13144 := (or #8843 #15702)
-#15701 := (iff #15700 #15698)
-#9825 := (or #8843 #15701)
-#11083 := (iff #9825 #13144)
-#12347 := (iff #13144 #13144)
-#9826 := [rewrite]: #12347
-#15703 := (iff #15701 #15702)
-#15704 := [rewrite]: #15703
-#9803 := [monotonicity #15704]: #11083
-#12901 := [trans #9803 #9826]: #11083
-#13051 := [quant-inst]: #9825
-#9828 := [mp #13051 #12901]: #13144
-#14086 := [unit-resolution #9828 #4554]: #15702
-#14157 := (= #2244 #15699)
-#14119 := (= #15699 #2244)
-#14057 := [monotonicity #11170]: #14119
-#14161 := [symm #14057]: #14157
-#6736 := [hypothesis]: #3409
-#4095 := (or #3404 #2245)
-#3936 := [def-axiom]: #4095
-#6739 := [unit-resolution #3936 #6736]: #2245
-#14088 := [trans #6739 #14161]: #15700
-#12459 := (not #15700)
-#12466 := (not #15702)
-#11355 := (or #12466 #15698 #12459)
-#13796 := [def-axiom]: #11355
-#14160 := [unit-resolution #13796 #14088 #14086]: #15698
-#12406 := (not #6421)
-#6386 := (f9 f10 ?v0!17)
-#16046 := (+ #6386 #9710)
-#16079 := (<= #16046 0::int)
-#16254 := (not #16079)
-#4771 := (* -1::int #4730)
-#6374 := (+ #2239 #4771)
-#12447 := (<= #6374 0::int)
-#16248 := (not #12447)
-#6617 := (f9 f10 ?v1!16)
-#6634 := (* -1::int #6617)
-#6450 := (+ #141 #6634)
-#6451 := (<= #6450 0::int)
-#6474 := (f11 f12 ?v1!16)
-#6475 := (= f1 #6474)
-#12936 := (not #6475)
-#13966 := (= ?v1!16 #9605)
-#13969 := (ite #13966 #3747 #6475)
-#12822 := (not #13969)
-#13970 := (f11 #10278 ?v1!16)
-#13971 := (= f1 #13970)
-#13965 := (iff #13969 #13971)
-#12863 := (or #8843 #13965)
-#13972 := (iff #13971 #13969)
-#12870 := (or #8843 #13972)
-#12761 := (iff #12870 #12863)
-#12818 := (iff #12863 #12863)
-#12946 := [rewrite]: #12818
-#13973 := (iff #13972 #13965)
-#13974 := [rewrite]: #13973
-#12817 := [monotonicity #13974]: #12761
-#12820 := [trans #12817 #12946]: #12761
-#12979 := [quant-inst]: #12870
-#12824 := [mp #12979 #12820]: #12863
-#13975 := [unit-resolution #12824 #4554]: #13965
-#12978 := (not #13971)
-#13996 := (iff #2248 #12978)
-#13992 := (iff #2247 #13971)
-#13964 := (iff #13971 #2247)
-#13986 := (= #13970 #2246)
-#14054 := [monotonicity #11170]: #13986
-#13984 := [monotonicity #14054]: #13964
-#13995 := [symm #13984]: #13992
-#13989 := [monotonicity #13995]: #13996
-#3937 := (or #3404 #2248)
-#3938 := [def-axiom]: #3937
-#6738 := [unit-resolution #3938 #6736]: #2248
-#13963 := [mp #6738 #13989]: #12978
-#12952 := (not #13965)
-#12741 := (or #12952 #12822 #13971)
-#13007 := [def-axiom]: #12741
-#13998 := [unit-resolution #13007 #13963 #13975]: #12822
-#12929 := (not #13966)
-#13999 := (or #13969 #12929)
-#12949 := (or #13969 #12929 #8984)
-#12951 := [def-axiom]: #12949
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-#14000 := [unit-resolution #13994 #13998]: #12929
-#12937 := (or #13969 #13966 #12936)
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-#6505 := (or #6451 #6475)
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-#4004 := [def-axiom]: #4018
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-#13933 := (or #4321 #6451 #6475)
-#6471 := (+ #6617 #1359)
-#6472 := (>= #6471 0::int)
-#6473 := (or #6475 #6472)
-#13917 := (or #4321 #6473)
-#13923 := (iff #13917 #13933)
-#13918 := (or #4321 #6505)
-#13922 := (iff #13918 #13933)
-#13929 := [rewrite]: #13922
-#13920 := (iff #13917 #13918)
-#6508 := (iff #6473 #6505)
-#6502 := (or #6475 #6451)
-#6506 := (iff #6502 #6505)
-#6507 := [rewrite]: #6506
-#6503 := (iff #6473 #6502)
-#6500 := (iff #6472 #6451)
-#6445 := (+ #1359 #6617)
-#6447 := (>= #6445 0::int)
-#6452 := (iff #6447 #6451)
-#6499 := [rewrite]: #6452
-#6448 := (iff #6472 #6447)
-#6446 := (= #6471 #6445)
-#6444 := [rewrite]: #6446
-#6449 := [monotonicity #6444]: #6448
-#6501 := [trans #6449 #6499]: #6500
-#6504 := [monotonicity #6501]: #6503
-#6509 := [trans #6504 #6507]: #6508
-#13921 := [monotonicity #6509]: #13920
-#13936 := [trans #13921 #13929]: #13923
-#13930 := [quant-inst]: #13917
-#13947 := [mp #13930 #13936]: #13933
-#13997 := [unit-resolution #13947 #12045]: #6505
-#14056 := [unit-resolution #13997 #14055]: #6451
-#4080 := (not #2837)
-#4081 := (or #3404 #4080)
-#4082 := [def-axiom]: #4081
-#6737 := [unit-resolution #4082 #6736]: #4080
-#16144 := (not #6451)
-#16270 := (or #16248 #2837 #13966 #16144)
-#15791 := (f5 #9605 ?v1!16)
-#15792 := (f4 #15791)
-#15793 := (* -1::int #15792)
-#6650 := (f5 f19 ?v1!16)
-#6651 := (f4 #6650)
-#15942 := (+ #6651 #15793)
-#16238 := (>= #15942 0::int)
-#15927 := (= #6651 #15792)
-#16241 := (= #15792 #6651)
-#16239 := (= #15791 #6650)
-#16240 := [monotonicity #10826]: #16239
-#16212 := [monotonicity #16240]: #16241
-#16242 := [symm #16212]: #15927
-#16237 := (not #15927)
-#16243 := (or #16237 #16238)
-#16244 := [th-lemma]: #16243
-#16245 := [unit-resolution #16244 #16242]: #16238
-#16130 := [hypothesis]: #4080
-#4992 := (+ #141 #4771)
-#4993 := (>= #4992 0::int)
-#7312 := (or #4347 #4993)
-#7364 := [quant-inst]: #7312
-#15949 := [unit-resolution #7364 #11135]: #4993
-#15989 := [hypothesis]: #12447
-#6676 := (+ #2835 #6651)
-#6677 := (+ #141 #6676)
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-#6680 := (= #6677 0::int)
-#6669 := (+ #6634 #6651)
-#6670 := (+ #141 #6669)
-#6671 := (>= #6670 0::int)
-#6655 := (* -1::int #6651)
-#6659 := (+ f3 #6655)
-#6660 := (<= #6659 0::int)
-#6706 := (or #6660 #6671)
-#6709 := (not #6706)
-#6703 := (= #2241 #6617)
-#16257 := (not #6703)
-#6635 := (+ #2241 #6634)
-#12715 := (>= #6635 0::int)
-#16143 := (not #12715)
-#16129 := [hypothesis]: #6451
-#9516 := (not #4993)
-#16249 := (or #16143 #16248 #9516 #2837 #16144)
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-#16251 := [unit-resolution #16250 #15989 #16129 #16130 #15949]: #16143
-#16258 := (or #16257 #12715)
-#16259 := [th-lemma]: #16258
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-#6712 := (or #6703 #6709)
-#12401 := (or #4331 #6703 #6709)
-#6656 := (+ #1359 #6655)
-#6657 := (+ #6617 #6656)
-#6658 := (<= #6657 0::int)
-#6699 := (or #6660 #6658)
-#6700 := (not #6699)
-#6701 := (= #6617 #2241)
-#6702 := (or #6701 #6700)
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-#6710 := (iff #6700 #6709)
-#6707 := (iff #6699 #6706)
-#6674 := (iff #6658 #6671)
-#6662 := (+ #6617 #6655)
-#6663 := (+ #1359 #6662)
-#6666 := (<= #6663 0::int)
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-#6673 := [rewrite]: #6672
-#6667 := (iff #6658 #6666)
-#6664 := (= #6657 #6663)
-#6665 := [rewrite]: #6664
-#6668 := [monotonicity #6665]: #6667
-#6675 := [trans #6668 #6673]: #6674
-#6708 := [monotonicity #6675]: #6707
-#6711 := [monotonicity #6708]: #6710
-#6704 := (iff #6701 #6703)
-#6705 := [rewrite]: #6704
-#6714 := [monotonicity #6705 #6711]: #6713
-#12847 := [monotonicity #6714]: #12685
-#12749 := [trans #12847 #12743]: #12745
-#12753 := [quant-inst]: #12465
-#12695 := [mp #12753 #12749]: #12401
-#16261 := [unit-resolution #12695 #9542]: #6712
-#16262 := [unit-resolution #16261 #16260]: #6709
-#15783 := (or #6706 #6680)
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-#12400 := (not #6671)
-#12433 := (or #6706 #12400)
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-#6683 := (or #6660 #6671 #6680)
-#12392 := (or #4339 #6660 #6671 #6680)
-#6652 := (+ #6651 #2835)
-#6653 := (+ #141 #6652)
-#6654 := (= #6653 0::int)
-#6661 := (or #6660 #6658 #6654)
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-#6681 := (iff #6654 #6680)
-#6678 := (= #6653 #6677)
-#6679 := [rewrite]: #6678
-#6682 := [monotonicity #6679]: #6681
-#6685 := [monotonicity #6675 #6682]: #6684
-#12396 := [monotonicity #6685]: #12402
-#12679 := [trans #12396 #12420]: #12677
-#12395 := [quant-inst]: #13894
-#12425 := [mp #12395 #12679]: #12392
-#15673 := [unit-resolution #12425 #9546]: #6683
-#15782 := [unit-resolution #15673 #15672 #15668 #15582]: false
-#15790 := [lemma #15782]: #15783
-#16263 := [unit-resolution #15790 #16262]: #6680
-#16264 := (or #15531 #12467)
-#16265 := [th-lemma]: #16264
-#16266 := [unit-resolution #16265 #16263]: #12467
-#15925 := (<= #15792 0::int)
-#15928 := (not #15925)
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-#11437 := (or #7253 #13966 #15928)
-#15924 := (= #9605 ?v1!16)
-#15929 := (or #15924 #15928)
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-#12441 := (iff #11530 #11437)
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-#15930 := (iff #15924 #13966)
-#15931 := [rewrite]: #15930
-#15934 := [monotonicity #15931]: #15933
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-#12442 := [trans #12439 #12446]: #12441
-#12423 := [quant-inst]: #11530
-#15908 := [mp #12423 #12442]: #11437
-#16268 := [unit-resolution #15908 #4147 #16267]: #15928
-#16269 := [th-lemma #16268 #16266 #15989 #15949 #16130 #16245]: false
-#16271 := [lemma #16269]: #16270
-#14053 := [unit-resolution #16271 #6737 #14000 #14056]: #16248
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-#15737 := (not #4731)
-#15738 := (or #15737 #5026)
-#15739 := [th-lemma]: #15738
-#15740 := [unit-resolution #15739 #10137]: #5026
-#5558 := (* -1::int #6386)
-#5658 := (+ #2239 #5558)
-#5682 := (<= #5658 0::int)
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-#5651 := (+ #6386 #2240)
-#5652 := (>= #5651 0::int)
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-#5683 := (iff #5655 #5682)
-#5684 := [rewrite]: #5683
-#5656 := (iff #5652 #5655)
-#5648 := (= #5651 #5653)
-#5654 := [rewrite]: #5648
-#5657 := [monotonicity #5654]: #5656
-#5686 := [trans #5657 #5684]: #5685
-#12899 := [monotonicity #5686]: #13136
-#12382 := [trans #12899 #13135]: #13136
-#12470 := [quant-inst]: #13134
-#12305 := [mp #12470 #12382]: #12387
-#16169 := [unit-resolution #12305 #11135]: #5682
-#14087 := (not #10100)
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-#14083 := (not #5682)
-#14123 := (or #16254 #14083 #12447 #9517 #14087)
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-#14125 := [unit-resolution #14124 #16169 #10833 #15740 #14053]: #16254
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-#16041 := (+ #5558 #9717)
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-#16078 := [rewrite]: #16080
-#16044 := (iff #16039 #16043)
-#16036 := (= #16038 #16041)
-#16042 := [rewrite]: #16036
-#16045 := [monotonicity #16042]: #16044
-#16082 := [trans #16045 #16078]: #16081
-#16111 := [monotonicity #16082]: #16110
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-#15913 := [monotonicity #16115]: #15907
-#15917 := [trans #15913 #15915]: #15916
-#15911 := [quant-inst]: #15910
-#15922 := [mp #15911 #15917]: #15909
-#15946 := [unit-resolution #15922 #10875 #10874 #16247 #16246]: false
-#15948 := [lemma #15946]: #15947
-#14090 := [unit-resolution #15948 #14125]: #12406
-#11628 := (not #15698)
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-#14092 := [trans #14091 #10826]: #6430
-#14117 := [monotonicity #14092]: #15926
-#15923 := (not #15926)
-#14058 := (or #15923 #12447)
-#14059 := [th-lemma]: #14058
-#14049 := [unit-resolution #14059 #14053]: #15923
-#14093 := [unit-resolution #14049 #14117]: false
-#14089 := [lemma #14093]: #3404
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-#19776 := [hypothesis]: #3455
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-#7083 := (f5 f19 ?v0!19)
-#7084 := (f4 #7083)
-#7088 := (* -1::int #7084)
-#19640 := (+ #2271 #7088)
-#19655 := (>= #19640 0::int)
-#19638 := (= #2271 #7084)
-#19801 := (= #2270 #7083)
-#6123 := (= ?v1!18 f19)
-#17992 := (= ?v1!18 #9605)
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-#6114 := (= f1 #6113)
-#17993 := (ite #17992 #3747 #6114)
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-#19305 := [quant-inst]: #19304
-#19311 := [mp #19305 #19310]: #19303
-#19775 := [unit-resolution #19311 #4554]: #17997
-#19784 := (= #2278 #17994)
-#19779 := (= #17994 #2278)
-#19780 := [monotonicity #11170]: #19779
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-#4079 := [def-axiom]: #4085
-#19778 := [unit-resolution #4079 #19776]: #2279
-#19788 := [trans #19778 #19787]: #17995
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-#19322 := (not #17997)
-#19324 := (or #19322 #17993 #19323)
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-#7193 := (+ #6079 #7067)
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-#7195 := (>= #7194 0::int)
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-#6175 := (* -1::int #6079)
-#6176 := (+ #2268 #6175)
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+#8820 := [monotonicity #4922]: #8819
+#8826 := [trans #8820 #8827]: #8828
+#8816 := [quant-inst]: #8811
+#8832 := [mp #8816 #8826]: #8815
+#10429 := [unit-resolution #8832 #9177]: #4920
+#10430 := [unit-resolution #10429 #10428]: #4912
+#14727 := [mp #10430 #14722]: #204
+#4046 := (or #4484 #4478)
+#4047 := [def-axiom]: #4046
+#14697 := [unit-resolution #4047 #11608]: #4478
+#4056 := (or #4481 #1463 #4475)
+#4042 := [def-axiom]: #4056
+#14729 := [unit-resolution #4042 #14697 #14727]: #4475
+#4065 := (or #4472 #4466)
+#4049 := [def-axiom]: #4065
+#14730 := [unit-resolution #4049 #14729]: #4466
+#4062 := (or #4469 #2249 #4463)
+#4063 := [def-axiom]: #4062
+#14731 := [unit-resolution #4063 #14730]: #4466
+#14715 := [unit-resolution #14731 #11127]: #4463
+#4057 := (or #4460 #4454)
+#4059 := [def-axiom]: #4057
+#30774 := [unit-resolution #4059 #14715]: #4454
+#4079 := (or #4457 #3418 #4451)
+#4066 := [def-axiom]: #4079
+#30775 := [unit-resolution #4066 #30774]: #4454
+#30776 := [unit-resolution #30775 #20314]: #4451
+#3973 := (or #4448 #4442)
+#3981 := [def-axiom]: #3973
+#30777 := [unit-resolution #3981 #30776]: #4442
+#30778 := (or #4445 #4439)
+#7080 := (f3 f22 ?v0!19)
+#7081 := (f9 #7080)
+#7029 := (f13 f14 ?v0!19)
+#7064 := (* -1::int #7029)
+#7099 := (+ #7064 #7081)
+#7100 := (+ #174 #7099)
+#7101 := (>= #7100 0::int)
+#7155 := (not #7101)
+#7085 := (* -1::int #7081)
+#16605 := (+ #2295 #7085)
+#16602 := (>= #16605 0::int)
+#16604 := (= #2295 #7081)
+#16770 := (= #2294 #7080)
+#7266 := (f5 #2294)
+#17040 := (f3 #9390 #7266)
+#21668 := (= #17040 #7080)
+#21666 := (= #7266 ?v0!19)
+#7267 := (= ?v0!19 #7266)
+#14776 := (or #6745 #7267)
+#14796 := [quant-inst]: #14776
+#16702 := [unit-resolution #14796 #4158]: #7267
+#16703 := [symm #16702]: #21666
+#16769 := [monotonicity #10000 #16703]: #21668
+#16767 := (= #2294 #17040)
+#16646 := (= ?v1!18 #9390)
+#6110 := (f6 f15 ?v1!18)
+#6111 := (= f1 #6110)
+#16647 := (ite #16646 #3805 #6111)
+#16648 := (f6 #9617 ?v1!18)
+#16649 := (= f1 #16648)
+#16651 := (iff #16647 #16649)
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+#14721 := (iff #14732 #14706)
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+#14735 := [rewrite]: #14734
+#16652 := (iff #16650 #16651)
+#16653 := [rewrite]: #16652
+#14733 := [monotonicity #16653]: #14721
+#14736 := [trans #14733 #14735]: #14721
+#14705 := [quant-inst]: #14732
+#14737 := [mp #14705 #14736]: #14706
+#16695 := [unit-resolution #14737 #4171]: #16651
+#16711 := (= #2302 #16648)
+#16699 := (= #16648 #2302)
+#16694 := [monotonicity #10052]: #16699
+#16712 := [symm #16694]: #16711
+#16696 := [hypothesis]: #3464
+#4094 := (or #3459 #2303)
+#4088 := [def-axiom]: #4094
+#16698 := [unit-resolution #4088 #16696]: #2303
+#16708 := [trans #16698 #16712]: #16649
+#14765 := (not #16649)
+#14750 := (not #16651)
+#14766 := (or #14750 #16647 #14765)
+#14764 := [def-axiom]: #14766
+#16713 := [unit-resolution #14764 #16708 #16695]: #16647
+#7177 := (not #6111)
+#6076 := (f13 f14 ?v1!18)
+#7190 := (+ #6076 #7064)
+#7191 := (+ #2295 #7190)
+#7192 := (>= #7191 0::int)
+#16745 := (not #7192)
+#6172 := (* -1::int #6076)
+#6173 := (+ #2292 #6172)
+#15701 := (>= #6173 0::int)
+#6081 := (= #2292 #6076)
+#14671 := (or #4399 #3444 #6081)
+#6077 := (= #6076 #2292)
+#6080 := (or #6077 #3444)
+#14672 := (or #4399 #6080)
+#14690 := (iff #14672 #14671)
+#6087 := (or #3444 #6081)
+#14686 := (or #4399 #6087)
+#14689 := (iff #14686 #14671)
+#14684 := [rewrite]: #14689
+#14687 := (iff #14672 #14686)
+#6090 := (iff #6080 #6087)
+#6084 := (or #6081 #3444)
+#6088 := (iff #6084 #6087)
+#6089 := [rewrite]: #6088
 #6085 := (iff #6080 #6084)
-#6086 := [rewrite]: #6085
-#6089 := [monotonicity #6086]: #6088
-#6094 := [trans #6089 #6092]: #6093
-#19297 := [monotonicity #6094]: #19296
-#19301 := [trans #19297 #19299]: #19300
-#19294 := [quant-inst]: #19291
-#19302 := [mp #19294 #19301]: #19290
-#19783 := [unit-resolution #19302 #13685 #19778]: #6084
-#19790 := (not #6084)
-#19791 := (or #19790 #19502)
-#19792 := [th-lemma]: #19791
-#19793 := [unit-resolution #19792 #19783]: #19502
-#4086 := (not #2864)
-#3915 := (or #3450 #4086)
-#3917 := [def-axiom]: #3915
-#19782 := [unit-resolution #3917 #19776]: #4086
-#19682 := (not #19502)
-#19677 := (or #19681 #2864 #19682)
-#19691 := [hypothesis]: #19502
-#7068 := (+ #2266 #7067)
-#7069 := (<= #7068 0::int)
-#19439 := (or #4347 #7069)
-#7059 := (+ #7032 #2267)
-#7060 := (>= #7059 0::int)
-#19440 := (or #4347 #7060)
-#19442 := (iff #19440 #19439)
-#19444 := (iff #19439 #19439)
-#19445 := [rewrite]: #19444
-#7072 := (iff #7060 #7069)
-#7061 := (+ #2267 #7032)
-#7064 := (>= #7061 0::int)
-#7070 := (iff #7064 #7069)
-#7071 := [rewrite]: #7070
-#7065 := (iff #7060 #7064)
-#7062 := (= #7059 #7061)
-#7063 := [rewrite]: #7062
-#7066 := [monotonicity #7063]: #7065
-#7073 := [trans #7066 #7071]: #7072
-#19443 := [monotonicity #7073]: #19442
-#19446 := [trans #19443 #19445]: #19442
-#19441 := [quant-inst]: #19440
-#19447 := [mp #19441 #19446]: #19439
-#19692 := [unit-resolution #19447 #11135]: #7069
-#19678 := [hypothesis]: #7195
-#19679 := [hypothesis]: #4086
-#19680 := [th-lemma #19679 #19678 #19692 #19691]: false
-#19683 := [lemma #19680]: #19677
-#19794 := [unit-resolution #19683 #19782 #19793]: #19681
-#19795 := (or #7180 #7195)
-#19480 := (or #4217 #2276 #7180 #7195)
-#7196 := (or #7180 #2276 #7195)
-#19481 := (or #4217 #7196)
-#19488 := (iff #19481 #19480)
-#7197 := (or #2276 #7180 #7195)
-#19483 := (or #4217 #7197)
-#19486 := (iff #19483 #19480)
-#19487 := [rewrite]: #19486
-#19484 := (iff #19481 #19483)
-#7198 := (iff #7196 #7197)
-#7199 := [rewrite]: #7198
-#19485 := [monotonicity #7199]: #19484
-#19489 := [trans #19485 #19487]: #19488
-#19482 := [quant-inst]: #19481
-#19490 := [mp #19482 #19489]: #19480
-#19796 := [unit-resolution #19490 #7050 #19777]: #19795
-#19797 := [unit-resolution #19796 #19794]: #7180
-#19312 := (not #17993)
-#19316 := (or #19312 #17992 #6114)
-#19317 := [def-axiom]: #19316
-#19798 := [unit-resolution #19317 #19797 #19789]: #17992
-#19800 := [trans #19798 #10826]: #6123
-#19802 := [monotonicity #19800]: #19801
-#19803 := [monotonicity #19802]: #19638
-#19804 := (not #19638)
-#19799 := (or #19804 #19655)
-#19805 := [th-lemma]: #19799
-#19806 := [unit-resolution #19805 #19803]: #19655
-#7092 := (+ f3 #7088)
-#7093 := (<= #7092 0::int)
-#7102 := (+ #7067 #7084)
-#7103 := (+ #141 #7102)
-#7104 := (>= #7103 0::int)
-#19475 := (not #7104)
-#7249 := (f23 #2270)
-#7273 := (f9 f10 #7249)
-#7292 := (* -1::int #7273)
-#19590 := (+ #6079 #7292)
-#19594 := (>= #19590 0::int)
-#19589 := (= #6079 #7273)
-#19811 := (= #7273 #6079)
-#19808 := (= #7249 ?v1!18)
-#7250 := (= ?v1!18 #7249)
-#19506 := (or #9574 #7250)
-#19507 := [quant-inst]: #19506
-#19807 := [unit-resolution #19507 #4560]: #7250
-#19809 := [symm #19807]: #19808
-#19812 := [monotonicity #19809]: #19811
-#19813 := [symm #19812]: #19589
-#19814 := (not #19589)
-#19815 := (or #19814 #19594)
-#19810 := [th-lemma]: #19815
-#19816 := [unit-resolution #19810 #19813]: #19594
-#7293 := (+ #141 #7292)
-#7294 := (<= #7293 0::int)
-#7283 := (f11 f12 #7249)
-#7284 := (= f1 #7283)
-#19602 := (not #7284)
-#19824 := (iff #7180 #19602)
-#19822 := (iff #6114 #7284)
-#19819 := (iff #7284 #6114)
-#19817 := (= #7283 #6113)
-#19818 := [monotonicity #19809]: #19817
-#19820 := [monotonicity #19818]: #19819
-#19823 := [symm #19820]: #19822
-#19825 := [monotonicity #19823]: #19824
-#19826 := [mp #19797 #19825]: #19602
-#7299 := (or #7284 #7294)
-#19521 := (or #4321 #7284 #7294)
-#7281 := (+ #7273 #1359)
-#7282 := (>= #7281 0::int)
-#7285 := (or #7284 #7282)
-#19522 := (or #4321 #7285)
-#19529 := (iff #19522 #19521)
-#19524 := (or #4321 #7299)
-#19527 := (iff #19524 #19521)
-#19528 := [rewrite]: #19527
-#19525 := (iff #19522 #19524)
-#7300 := (iff #7285 #7299)
-#7297 := (iff #7282 #7294)
-#7286 := (+ #1359 #7273)
-#7289 := (>= #7286 0::int)
-#7295 := (iff #7289 #7294)
-#7296 := [rewrite]: #7295
-#7290 := (iff #7282 #7289)
-#7287 := (= #7281 #7286)
-#7288 := [rewrite]: #7287
-#7291 := [monotonicity #7288]: #7290
-#7298 := [trans #7291 #7296]: #7297
-#7301 := [monotonicity #7298]: #7300
-#19526 := [monotonicity #7301]: #19525
-#19530 := [trans #19526 #19528]: #19529
-#19523 := [quant-inst]: #19522
-#19531 := [mp #19523 #19530]: #19521
-#19821 := [unit-resolution #19531 #12045]: #7299
-#19827 := [unit-resolution #19821 #19826]: #7294
-#19831 := (not #7294)
-#19830 := (not #19594)
-#19829 := (not #19655)
-#19828 := (not #7069)
-#19833 := (or #19475 #19828 #19829 #2864 #19682 #19830 #19831)
-#19834 := [th-lemma]: #19833
-#19835 := [unit-resolution #19834 #19692 #19782 #19793 #19827 #19816 #19806]: #19475
-#7109 := (+ #2267 #7084)
-#7110 := (+ #141 #7109)
-#7113 := (= #7110 0::int)
-#19839 := (not #7113)
-#19460 := (>= #7110 0::int)
-#19836 := (not #19460)
-#19837 := (or #19836 #19829 #2864 #19682 #19830 #19831)
-#19832 := [th-lemma]: #19837
-#19838 := [unit-resolution #19832 #19782 #19793 #19827 #19816 #19806]: #19836
-#19840 := (or #19839 #19460)
-#19841 := [th-lemma]: #19840
-#19842 := [unit-resolution #19841 #19838]: #19839
-#7116 := (or #7093 #7104 #7113)
-#19448 := (or #4339 #7093 #7104 #7113)
-#7085 := (+ #7084 #2267)
-#7086 := (+ #141 #7085)
-#7087 := (= #7086 0::int)
-#7089 := (+ #1359 #7088)
-#7090 := (+ #7032 #7089)
-#7091 := (<= #7090 0::int)
-#7094 := (or #7093 #7091 #7087)
-#19449 := (or #4339 #7094)
-#19456 := (iff #19449 #19448)
-#19451 := (or #4339 #7116)
-#19454 := (iff #19451 #19448)
-#19455 := [rewrite]: #19454
-#19452 := (iff #19449 #19451)
-#7117 := (iff #7094 #7116)
-#7114 := (iff #7087 #7113)
-#7111 := (= #7086 #7110)
-#7112 := [rewrite]: #7111
-#7115 := [monotonicity #7112]: #7114
-#7107 := (iff #7091 #7104)
-#7095 := (+ #7032 #7088)
-#7096 := (+ #1359 #7095)
-#7099 := (<= #7096 0::int)
-#7105 := (iff #7099 #7104)
-#7106 := [rewrite]: #7105
-#7100 := (iff #7091 #7099)
-#7097 := (= #7090 #7096)
-#7098 := [rewrite]: #7097
-#7101 := [monotonicity #7098]: #7100
-#7108 := [trans #7101 #7106]: #7107
-#7118 := [monotonicity #7108 #7115]: #7117
-#19453 := [monotonicity #7118]: #19452
-#19457 := [trans #19453 #19455]: #19456
-#19450 := [quant-inst]: #19449
-#19458 := [mp #19450 #19457]: #19448
-#19844 := [unit-resolution #19458 #9546]: #7116
-#19845 := [unit-resolution #19844 #19842 #19835]: #7093
-#19846 := [th-lemma #19845 #19806 #19777]: false
-#19847 := [lemma #19846]: #3450
-#3953 := (or #4402 #3455 #4396)
-#3968 := [def-axiom]: #3953
-#27040 := [unit-resolution #3968 #19847]: #27039
-#27041 := [unit-resolution #27040 #27038]: #4396
-#4072 := (or #4393 #2309)
-#4074 := [def-axiom]: #4072
-#27042 := [unit-resolution #4074 #27041]: #2309
-#5795 := (+ #2296 #5794)
-#14667 := (>= #5795 0::int)
-#5764 := (= #2296 #5759)
-#3959 := (or #4393 #4385)
-#3960 := [def-axiom]: #3959
-#27043 := [unit-resolution #3960 #27041]: #4385
-#22264 := (or #5764 #4390)
-#14232 := (f11 f20 #9605)
-#14233 := (= f1 #14232)
-#15750 := (= #3738 #14232)
-#15748 := (= #14232 #3738)
-#15749 := [monotonicity #11161 #10826]: #15748
-#15751 := [symm #15749]: #15750
-#15752 := [trans #11162 #15751]: #14233
-#13804 := (f22 #9605)
-#13848 := (* -1::int #13804)
-#12393 := (+ #2296 #13848)
-#14441 := (<= #12393 0::int)
-#22244 := (not #14441)
-#14152 := (f5 #9605 ?v0!20)
-#14357 := (f4 #14152)
-#21545 := (<= #14357 0::int)
-#21515 := (not #21545)
-#21371 := (= ?v0!20 #9605)
-#21359 := (not #21371)
-#5998 := (f11 f12 ?v0!20)
-#5999 := (= f1 #5998)
-#21372 := (ite #21371 #3747 #5999)
-#21358 := (not #21372)
-#21373 := (f11 #10278 ?v0!20)
-#21374 := (= f1 #21373)
-#21376 := (iff #21372 #21374)
-#21348 := (or #8843 #21376)
-#21375 := (iff #21374 #21372)
-#21349 := (or #8843 #21375)
-#21345 := (iff #21349 #21348)
-#21352 := (iff #21348 #21348)
-#21353 := [rewrite]: #21352
-#21377 := (iff #21375 #21376)
-#21378 := [rewrite]: #21377
-#21351 := [monotonicity #21378]: #21345
-#21354 := [trans #21351 #21353]: #21345
-#21350 := [quant-inst]: #21349
-#21355 := [mp #21350 #21354]: #21348
-#22187 := [unit-resolution #21355 #4554]: #21376
-#21367 := (not #21374)
-#5153 := (f11 f20 ?v0!20)
-#5154 := (= f1 #5153)
-#5155 := (not #5154)
-#22213 := (iff #5155 #21367)
-#22166 := (iff #5154 #21374)
-#22164 := (iff #21374 #5154)
-#22162 := (= #21373 #5153)
-#22163 := [monotonicity #11170]: #22162
-#22165 := [monotonicity #22163]: #22164
-#22167 := [symm #22165]: #22166
-#22214 := [monotonicity #22167]: #22213
-#22188 := (not #5764)
-#22160 := [hypothesis]: #22188
-#5770 := (or #5155 #5764)
-#16321 := (or #4356 #5155 #5764)
-#5760 := (= #5759 #2296)
-#5763 := (or #5760 #5155)
-#16323 := (or #4356 #5763)
-#12632 := (iff #16323 #16321)
-#16440 := (or #4356 #5770)
-#12536 := (iff #16440 #16321)
-#12262 := [rewrite]: #12536
-#16429 := (iff #16323 #16440)
-#5773 := (iff #5763 #5770)
-#5767 := (or #5764 #5155)
-#5771 := (iff #5767 #5770)
-#5772 := [rewrite]: #5771
-#5768 := (iff #5763 #5767)
+#6082 := (iff #6077 #6081)
+#6083 := [rewrite]: #6082
+#6086 := [monotonicity #6083]: #6085
+#6091 := [trans #6086 #6089]: #6090
+#14688 := [monotonicity #6091]: #14687
+#14691 := [trans #14688 #14684]: #14690
+#14685 := [quant-inst]: #14672
+#14692 := [mp #14685 #14691]: #14671
+#16714 := [unit-resolution #14692 #11609 #16698]: #6081
+#16715 := (not #6081)
+#16740 := (or #16715 #15701)
+#16741 := [th-lemma]: #16740
+#16743 := [unit-resolution #16741 #16714]: #15701
+#4095 := (not #2888)
+#3924 := (or #3459 #4095)
+#3926 := [def-axiom]: #3924
+#16744 := [unit-resolution #3926 #16696]: #4095
+#7065 := (+ #2290 #7064)
+#7066 := (<= #7065 0::int)
+#13062 := (or #4390 #7066)
+#7056 := (+ #7029 #2291)
+#7057 := (>= #7056 0::int)
+#13057 := (or #4390 #7057)
+#13063 := (iff #13057 #13062)
+#13089 := (iff #13062 #13062)
+#13090 := [rewrite]: #13089
+#7069 := (iff #7057 #7066)
+#7058 := (+ #2291 #7029)
+#7061 := (>= #7058 0::int)
+#7067 := (iff #7061 #7066)
+#7068 := [rewrite]: #7067
+#7062 := (iff #7057 #7061)
+#7059 := (= #7056 #7058)
+#7060 := [rewrite]: #7059
+#7063 := [monotonicity #7060]: #7062
+#7070 := [trans #7063 #7068]: #7069
+#13088 := [monotonicity #7070]: #13063
+#13091 := [trans #13088 #13090]: #13063
+#13058 := [quant-inst]: #13057
+#13869 := [mp #13058 #13091]: #13062
+#16739 := [unit-resolution #13869 #9875]: #7066
+#7600 := (not #7066)
+#16746 := (not #15701)
+#16742 := (or #16745 #16746 #7600 #2888)
+#16747 := [th-lemma]: #16742
+#16748 := [unit-resolution #16747 #16739 #16744 #16743]: #16745
+#16752 := (or #7177 #7192)
+#4087 := (or #3459 #2301)
+#4093 := [def-axiom]: #4087
+#16749 := [unit-resolution #4093 #16696]: #2301
+#14754 := (or #4260 #2300 #7177 #7192)
+#7193 := (or #7177 #2300 #7192)
+#14752 := (or #4260 #7193)
+#14758 := (iff #14752 #14754)
+#7194 := (or #2300 #7177 #7192)
+#14756 := (or #4260 #7194)
+#14759 := (iff #14756 #14754)
+#14760 := [rewrite]: #14759
+#14757 := (iff #14752 #14756)
+#7195 := (iff #7193 #7194)
+#7196 := [rewrite]: #7195
+#14753 := [monotonicity #7196]: #14757
+#14761 := [trans #14753 #14760]: #14758
+#14755 := [quant-inst]: #14752
+#14762 := [mp #14755 #14761]: #14754
+#16753 := [unit-resolution #14762 #6949 #16749]: #16752
+#16766 := [unit-resolution #16753 #16748]: #7177
+#14742 := (not #16647)
+#14745 := (or #14742 #16646 #6111)
+#14741 := [def-axiom]: #14745
+#16761 := [unit-resolution #14741 #16766 #16713]: #16646
+#16768 := [monotonicity #16761 #16702]: #16767
+#16771 := [trans #16768 #16769]: #16770
+#16785 := [monotonicity #16771]: #16604
+#16786 := (not #16604)
+#16787 := (or #16786 #16602)
+#16788 := [th-lemma]: #16787
+#16789 := [unit-resolution #16788 #16785]: #16602
+#16620 := (+ #2292 #4768)
+#16629 := (>= #16620 0::int)
+#16625 := (= #2292 #4727)
+#6120 := (= ?v1!18 f22)
+#16790 := [trans #16761 #10000]: #6120
+#16791 := [monotonicity #16790]: #16625
+#16792 := (not #16625)
+#16775 := (or #16792 #16629)
+#16776 := [th-lemma]: #16775
+#16777 := [unit-resolution #16776 #16791]: #16629
+#9296 := (<= #4989 0::int)
+#9379 := (f24 #9390)
+#9381 := (= #9379 #9900)
+#11618 := (iff #9381 #4728)
+#11616 := (iff #9381 #10073)
+#11614 := (= #9379 #4727)
+#11612 := (= #4727 #9379)
+#11613 := [monotonicity #9998]: #11612
+#11615 := [symm #11613]: #11614
+#11617 := [monotonicity #11615 #10015]: #11616
+#11619 := [trans #11617 #10077]: #11618
+#9374 := (f6 f23 #9390)
+#9377 := (= f1 #9374)
+#11604 := (= #3804 #9374)
+#11602 := (= #9374 #3804)
+#11603 := [monotonicity #9890 #10000]: #11602
+#11605 := [symm #11603]: #11604
+#11606 := [trans #9891 #11605]: #9377
+#9378 := (not #9377)
+#9454 := (or #9378 #9381)
+#9608 := (or #4399 #9378 #9381)
+#9380 := (= #9900 #9379)
+#9376 := (or #9380 #9378)
+#9609 := (or #4399 #9376)
+#9568 := (iff #9609 #9608)
+#9611 := (or #4399 #9454)
+#9564 := (iff #9611 #9608)
+#9567 := [rewrite]: #9564
+#9612 := (iff #9609 #9611)
+#9573 := (iff #9376 #9454)
+#9428 := (or #9381 #9378)
+#9569 := (iff #9428 #9454)
+#9570 := [rewrite]: #9569
+#9429 := (iff #9376 #9428)
+#9382 := (iff #9380 #9381)
+#9427 := [rewrite]: #9382
+#9453 := [monotonicity #9427]: #9429
+#9607 := [trans #9453 #9570]: #9573
+#9563 := [monotonicity #9607]: #9612
+#9295 := [trans #9563 #9567]: #9568
+#9610 := [quant-inst]: #9609
+#9511 := [mp #9610 #9295]: #9608
+#11610 := [unit-resolution #9511 #11609]: #9454
+#11611 := [unit-resolution #11610 #11606]: #9381
+#11620 := [mp #11611 #11619]: #4728
+#11621 := (or #10080 #9296)
+#11622 := [th-lemma]: #11621
+#11623 := [unit-resolution #11622 #11620]: #9296
+#11627 := (not #9296)
+#16778 := (not #16629)
+#16707 := (not #16602)
+#16779 := (or #7155 #7600 #16707 #2888 #16778 #11627)
+#16757 := [th-lemma]: #16779
+#16758 := [unit-resolution #16757 #16744 #16739 #11623 #16777 #16789]: #7155
+#7089 := (+ f8 #7085)
+#7090 := (<= #7089 0::int)
+#7152 := (not #7090)
+#16709 := (or #7152 #16707 #2300)
+#16701 := [hypothesis]: #2301
+#16697 := [hypothesis]: #16602
+#16704 := [hypothesis]: #7090
+#16706 := [th-lemma #16704 #16697 #16701]: false
+#16710 := [lemma #16706]: #16709
+#16756 := [unit-resolution #16710 #16789 #16749]: #7152
+#7106 := (+ #2291 #7081)
+#7107 := (+ #174 #7106)
+#7110 := (= #7107 0::int)
+#7528 := (not #7110)
+#7128 := (>= #7107 0::int)
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+#38692 := (= f1 #38691)
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+#39864 := (f5 #17311)
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+#46058 := (= #38691 #46220)
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+#46212 := (= #44419 #9390)
+#46213 := (ite #46212 #3805 #42562)
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+#42541 := [unit-resolution #42540 #41880]: #38695
+#42542 := (not #38695)
+#42537 := (or #42542 #43479)
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+#17663 := (>= #17661 0::int)
+#17660 := (= #5808 #17200)
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+#11140 := (+ #174 #10792)
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+#11502 := (= #174 #9379)
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+#20696 := (not #17663)
+#20695 := (not #11133)
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+#17234 := (+ #10792 #17233)
+#17235 := (+ #2320 #17234)
+#17236 := (= #17235 0::int)
+#17247 := (>= #17235 0::int)
+#20701 := (or #17247 #20695 #20696 #20697)
+#20702 := [th-lemma]: #20701
+#20703 := [unit-resolution #20702 #20693 #20688 #20682]: #17247
+#17246 := (<= #17235 0::int)
+#17662 := (<= #17661 0::int)
+#20704 := (or #20679 #17662)
+#20705 := [th-lemma]: #20704
+#20706 := [unit-resolution #20705 #20678]: #17662
+#11141 := (<= #11140 0::int)
+#20707 := (or #20685 #11141)
+#20708 := [th-lemma]: #20707
+#20709 := [unit-resolution #20708 #20684]: #11141
+#17180 := (>= #5834 0::int)
+#20710 := (or #20690 #17180)
+#20711 := [th-lemma]: #20710
+#20712 := [unit-resolution #20711 #20689]: #17180
+#20715 := (not #17180)
+#20714 := (not #17662)
+#20713 := (not #11141)
+#20716 := (or #17246 #20713 #20714 #20715)
+#20717 := [th-lemma]: #20716
+#20718 := [unit-resolution #20717 #20712 #20709 #20706]: #17246
+#20720 := (not #17247)
+#20719 := (not #17246)
+#20721 := (or #17236 #20719 #20720)
+#20722 := [th-lemma]: #20721
+#20723 := [unit-resolution #20722 #20718 #20703]: #17236
+#17258 := (not #17236)
+#20725 := (or #17224 #17258)
+#20724 := [hypothesis]: #4428
+#17264 := (or #4433 #9378 #17224 #17258)
+#17205 := (+ #2321 #17200)
+#17206 := (+ #9379 #17205)
+#17204 := (= #17206 0::int)
+#17207 := (not #17204)
+#17208 := (+ #9379 #2321)
+#17209 := (>= #17208 0::int)
+#17214 := (or #9378 #17209 #17207)
+#17265 := (or #4433 #17214)
+#17272 := (iff #17265 #17264)
+#17261 := (or #9378 #17224 #17258)
+#17267 := (or #4433 #17261)
+#17270 := (iff #17267 #17264)
+#17271 := [rewrite]: #17270
+#17268 := (iff #17265 #17267)
+#17262 := (iff #17214 #17261)
+#17259 := (iff #17207 #17258)
+#17256 := (iff #17204 #17236)
+#17221 := (+ #9379 #17200)
+#17228 := (+ #2321 #17221)
+#17231 := (= #17228 0::int)
+#17254 := (iff #17231 #17236)
+#17255 := [rewrite]: #17254
+#17220 := (iff #17204 #17231)
+#17229 := (= #17206 #17228)
+#17230 := [rewrite]: #17229
+#17232 := [monotonicity #17230]: #17220
+#17257 := [trans #17232 #17255]: #17256
+#17260 := [monotonicity #17257]: #17259
+#17226 := (iff #17209 #17224)
+#17215 := (+ #2321 #9379)
+#17217 := (>= #17215 0::int)
+#17222 := (iff #17217 #17224)
+#17225 := [rewrite]: #17222
+#17218 := (iff #17209 #17217)
+#17213 := (= #17208 #17215)
+#17216 := [rewrite]: #17213
+#17223 := [monotonicity #17216]: #17218
+#17227 := [trans #17223 #17225]: #17226
+#17263 := [monotonicity #17227 #17260]: #17262
+#17269 := [monotonicity #17263]: #17268
+#17273 := [trans #17269 #17271]: #17272
+#17266 := [quant-inst]: #17265
+#17274 := [mp #17266 #17273]: #17264
+#20726 := [unit-resolution #17274 #20724 #11606]: #20725
+#20727 := [unit-resolution #20726 #20723 #20700]: false
+#20729 := [lemma #20727]: #20728
+#12665 := [unit-resolution #20729 #41882]: #10315
+#12075 := [unit-resolution #12665 #12082]: #17237
+#12307 := [trans #12075 #10000]: #12111
+#21107 := [monotonicity #12307]: #10317
+#14839 := [symm #21107]: #12275
+#21382 := (= #2320 #174)
+#12109 := (= #2320 #9900)
+#10470 := (= #2320 #9379)
+#21480 := (= #2320 #4727)
+#5738 := (+ #2320 #4768)
+#5739 := (>= #5738 0::int)
+#17016 := (>= #17015 0::int)
+#5150 := (f6 f23 ?v0!20)
+#5151 := (= f1 #5150)
+#5152 := (not #5151)
+#5767 := (or #5152 #5761)
+#15800 := (or #4399 #5152 #5761)
+#5760 := (or #5757 #5152)
+#16501 := (or #4399 #5760)
+#17178 := (iff #16501 #15800)
+#14945 := (or #4399 #5767)
+#17195 := (iff #14945 #15800)
+#17175 := [rewrite]: #17195
+#17007 := (iff #16501 #14945)
+#5770 := (iff #5760 #5767)
+#5764 := (or #5761 #5152)
+#5768 := (iff #5764 #5767)
+#5769 := [rewrite]: #5768
 #5765 := (iff #5760 #5764)
-#5766 := [rewrite]: #5765
-#5769 := [monotonicity #5766]: #5768
-#5774 := [trans #5769 #5772]: #5773
-#11409 := [monotonicity #5774]: #16429
-#12602 := [trans #11409 #12262]: #12632
-#16437 := [quant-inst]: #16323
-#12626 := [mp #16437 #12602]: #16321
-#22161 := [unit-resolution #12626 #13685]: #5770
-#22159 := [unit-resolution #22161 #22160]: #5155
-#22215 := [mp #22159 #22214]: #21367
-#21366 := (not #21376)
-#21370 := (or #21366 #21358 #21374)
-#21388 := [def-axiom]: #21370
-#22216 := [unit-resolution #21388 #22215 #22187]: #21358
-#22217 := (or #21372 #21359)
-#21363 := (or #21372 #21359 #8984)
-#21364 := [def-axiom]: #21363
-#22212 := [unit-resolution #21364 #11162]: #22217
-#22218 := [unit-resolution #22212 #22216]: #21359
-#21531 := (or #21371 #21515)
-#21514 := (or #7253 #21371 #21515)
-#21507 := (= #9605 ?v0!20)
-#21530 := (or #21507 #21515)
-#21534 := (or #7253 #21530)
-#21550 := (iff #21534 #21514)
-#21536 := (or #7253 #21531)
-#21548 := (iff #21536 #21514)
-#21549 := [rewrite]: #21548
-#21537 := (iff #21534 #21536)
-#21532 := (iff #21530 #21531)
-#21516 := (iff #21507 #21371)
-#21519 := [rewrite]: #21516
-#21533 := [monotonicity #21519]: #21532
-#21538 := [monotonicity #21533]: #21537
-#21551 := [trans #21538 #21549]: #21550
-#21535 := [quant-inst]: #21534
-#21552 := [mp #21535 #21551]: #21514
-#22219 := [unit-resolution #21552 #4147]: #21531
-#22220 := [unit-resolution #22219 #22218]: #21515
-#14465 := (* -1::int #14357)
-#5810 := (f5 f19 ?v0!20)
-#5811 := (f4 #5810)
-#19182 := (+ #5811 #14465)
-#19183 := (>= #19182 0::int)
-#19180 := (= #5811 #14357)
-#22225 := (= #14357 #5811)
-#22221 := (= #14152 #5810)
-#22222 := [monotonicity #10826]: #22221
-#22226 := [monotonicity #22222]: #22225
-#22236 := [symm #22226]: #19180
-#22237 := (not #19180)
-#22238 := (or #22237 #19183)
-#22239 := [th-lemma]: #22238
-#22240 := [unit-resolution #22239 #22236]: #19183
-#13868 := (+ #4730 #13848)
-#13435 := (>= #13868 0::int)
-#13837 := (= #4730 #13804)
-#15741 := (= #13804 #4730)
-#15742 := [monotonicity #10826]: #15741
-#15743 := [symm #15742]: #13837
-#15744 := (not #13837)
-#22241 := (or #15744 #13435)
-#22242 := [th-lemma]: #22241
-#22224 := [unit-resolution #22242 #15743]: #13435
-#5836 := (+ #2297 #5811)
-#5837 := (+ #141 #5836)
-#12534 := (<= #5837 0::int)
-#5840 := (= #5837 0::int)
-#5815 := (* -1::int #5811)
-#5819 := (+ f3 #5815)
-#5820 := (<= #5819 0::int)
-#16515 := (not #5820)
-#5829 := (+ #5794 #5811)
-#5830 := (+ #141 #5829)
-#5831 := (>= #5830 0::int)
-#5862 := (or #5820 #5831)
-#5865 := (not #5862)
-#5868 := (or #5764 #5865)
-#16483 := (or #4331 #5764 #5865)
-#5816 := (+ #1359 #5815)
-#5817 := (+ #5759 #5816)
-#5818 := (<= #5817 0::int)
-#5859 := (or #5820 #5818)
-#5860 := (not #5859)
-#5861 := (or #5760 #5860)
-#16511 := (or #4331 #5861)
-#16585 := (iff #16511 #16483)
-#12532 := (or #4331 #5868)
-#16479 := (iff #12532 #16483)
-#16584 := [rewrite]: #16479
-#12520 := (iff #16511 #12532)
-#5869 := (iff #5861 #5868)
-#5866 := (iff #5860 #5865)
-#5863 := (iff #5859 #5862)
-#5834 := (iff #5818 #5831)
-#5822 := (+ #5759 #5815)
-#5823 := (+ #1359 #5822)
-#5826 := (<= #5823 0::int)
-#5832 := (iff #5826 #5831)
-#5833 := [rewrite]: #5832
-#5827 := (iff #5818 #5826)
-#5824 := (= #5817 #5823)
-#5825 := [rewrite]: #5824
-#5828 := [monotonicity #5825]: #5827
-#5835 := [trans #5828 #5833]: #5834
-#5864 := [monotonicity #5835]: #5863
-#5867 := [monotonicity #5864]: #5866
-#5870 := [monotonicity #5766 #5867]: #5869
-#16478 := [monotonicity #5870]: #12520
-#16609 := [trans #16478 #16584]: #16585
-#16477 := [quant-inst]: #16511
-#16581 := [mp #16477 #16609]: #16483
-#22227 := [unit-resolution #16581 #9542]: #5868
-#22228 := [unit-resolution #22227 #22160]: #5865
-#16610 := (or #5862 #16515)
-#16583 := [def-axiom]: #16610
-#22229 := [unit-resolution #16583 #22228]: #16515
-#16611 := (not #5831)
-#16612 := (or #5862 #16611)
-#16613 := [def-axiom]: #16612
-#22230 := [unit-resolution #16613 #22228]: #16611
-#5843 := (or #5820 #5831 #5840)
-#11396 := (or #4339 #5820 #5831 #5840)
-#5812 := (+ #5811 #2297)
-#5813 := (+ #141 #5812)
-#5814 := (= #5813 0::int)
-#5821 := (or #5820 #5818 #5814)
-#15370 := (or #4339 #5821)
-#12429 := (iff #15370 #11396)
-#12541 := (or #4339 #5843)
-#12538 := (iff #12541 #11396)
-#12533 := [rewrite]: #12538
-#15256 := (iff #15370 #12541)
-#5844 := (iff #5821 #5843)
-#5841 := (iff #5814 #5840)
-#5838 := (= #5813 #5837)
-#5839 := [rewrite]: #5838
-#5842 := [monotonicity #5839]: #5841
-#5845 := [monotonicity #5835 #5842]: #5844
-#12450 := [monotonicity #5845]: #15256
-#16484 := [trans #12450 #12533]: #12429
-#16435 := [quant-inst]: #15370
-#16485 := [mp #16435 #16484]: #11396
-#22223 := [unit-resolution #16485 #9546]: #5843
-#22231 := [unit-resolution #22223 #22230 #22229]: #5840
-#22232 := (not #5840)
-#22233 := (or #22232 #12534)
-#22234 := [th-lemma]: #22233
-#22235 := [unit-resolution #22234 #22231]: #12534
-#22247 := (not #19183)
-#22246 := (not #13435)
-#22245 := (not #12534)
-#22248 := (or #22244 #22245 #9516 #22246 #21545 #22247)
-#22243 := [th-lemma]: #22248
-#22249 := [unit-resolution #22243 #22235 #22224 #15949 #22240 #22220]: #22244
-#14466 := (+ #13848 #14465)
-#14421 := (+ #2296 #14466)
-#14360 := (= #14421 0::int)
-#18610 := (<= #14421 0::int)
-#19176 := (<= #19182 0::int)
-#22250 := (or #22237 #19176)
-#22251 := [th-lemma]: #22250
-#22252 := [unit-resolution #22251 #22236]: #19176
-#13869 := (<= #13868 0::int)
-#15745 := (or #15744 #13869)
-#15746 := [th-lemma]: #15745
-#15747 := [unit-resolution #15746 #15743]: #13869
-#16486 := (>= #5837 0::int)
-#22253 := (or #22232 #16486)
-#22267 := [th-lemma]: #22253
-#22268 := [unit-resolution #22267 #22231]: #16486
-#22271 := (not #19176)
-#22270 := (not #13869)
-#22269 := (not #16486)
-#22272 := (or #18610 #22269 #9517 #22270 #22271)
-#22273 := [th-lemma]: #22272
-#22274 := [unit-resolution #22273 #22268 #15747 #15740 #22252]: #18610
-#18602 := (>= #14421 0::int)
-#22275 := (or #18602 #22245 #9516 #22246 #22247)
-#22255 := [th-lemma]: #22275
-#22256 := [unit-resolution #22255 #22235 #22224 #15949 #22240]: #18602
-#22258 := (not #18602)
-#22257 := (not #18610)
-#22259 := (or #14360 #22257 #22258)
-#22254 := [th-lemma]: #22259
-#22260 := [unit-resolution #22254 #22256 #22274]: #14360
-#14539 := (not #14360)
-#14234 := (not #14233)
-#14534 := (or #14234 #14539 #14441)
-#22261 := [hypothesis]: #4385
-#15611 := (or #4390 #14234 #14539 #14441)
-#14356 := (+ #2297 #14357)
-#14395 := (+ #13804 #14356)
-#14394 := (= #14395 0::int)
-#14358 := (not #14394)
-#14464 := (+ #13804 #2297)
-#14439 := (>= #14464 0::int)
-#14440 := (or #14234 #14439 #14358)
-#12480 := (or #4390 #14440)
-#17563 := (iff #12480 #15611)
-#17425 := (or #4390 #14534)
-#17458 := (iff #17425 #15611)
-#17521 := [rewrite]: #17458
-#17406 := (iff #12480 #17425)
-#14502 := (iff #14440 #14534)
-#14567 := (or #14234 #14441 #14539)
-#14569 := (iff #14567 #14534)
-#14571 := [rewrite]: #14569
-#14540 := (iff #14440 #14567)
-#14572 := (iff #14358 #14539)
-#14426 := (iff #14394 #14360)
-#14363 := (+ #13804 #14357)
-#14393 := (+ #2297 #14363)
-#14425 := (= #14393 0::int)
-#14533 := (iff #14425 #14360)
-#14538 := [rewrite]: #14533
-#14467 := (iff #14394 #14425)
-#14390 := (= #14395 #14393)
-#14424 := [rewrite]: #14390
-#14387 := [monotonicity #14424]: #14467
-#14541 := [trans #14387 #14538]: #14426
-#14566 := [monotonicity #14541]: #14572
-#14392 := (iff #14439 #14441)
-#14288 := (+ #2297 #13804)
-#14396 := (>= #14288 0::int)
-#14391 := (iff #14396 #14441)
-#14355 := [rewrite]: #14391
-#14389 := (iff #14439 #14396)
-#14388 := (= #14464 #14288)
-#14353 := [rewrite]: #14388
-#14359 := [monotonicity #14353]: #14389
-#14436 := [trans #14359 #14355]: #14392
-#14568 := [monotonicity #14436 #14566]: #14540
-#14575 := [trans #14568 #14571]: #14502
-#17497 := [monotonicity #14575]: #17406
-#18193 := [trans #17497 #17521]: #17563
-#17271 := [quant-inst]: #12480
-#18181 := [mp #17271 #18193]: #15611
-#22262 := [unit-resolution #18181 #22261]: #14534
-#22263 := [unit-resolution #22262 #22260 #22249 #15752]: false
-#22278 := [lemma #22263]: #22264
-#27044 := [unit-resolution #22278 #27043]: #5764
-#27045 := (or #22188 #14667)
-#27046 := [th-lemma]: #27045
-#27047 := [unit-resolution #27046 #27044]: #14667
-#27048 := [hypothesis]: #6045
-#27049 := [th-lemma #27048 #27047 #27042]: false
-#27051 := [lemma #27049]: #27050
-#30676 := (or #6045 #6050)
-#4075 := (or #4393 #2878)
-#4073 := [def-axiom]: #4075
-#30675 := [unit-resolution #4073 #27041]: #2878
-#6740 := (or #4242 #2875 #6045 #6050)
-#6042 := (or #6041 #6038 #6031)
-#6043 := (not #6042)
-#6046 := (or #2310 #6045 #6043)
-#6742 := (or #4242 #6046)
-#10921 := (iff #6742 #6740)
-#6053 := (or #2875 #6045 #6050)
-#7885 := (or #4242 #6053)
-#10820 := (iff #7885 #6740)
-#10925 := [rewrite]: #10820
-#7888 := (iff #6742 #7885)
-#6054 := (iff #6046 #6053)
-#6051 := (iff #6043 #6050)
-#6048 := (iff #6042 #6047)
-#6049 := [rewrite]: #6048
-#6052 := [monotonicity #6049]: #6051
-#6055 := [monotonicity #2877 #6052]: #6054
-#10815 := [monotonicity #6055]: #7888
-#13454 := [trans #10815 #10925]: #10921
-#11022 := [quant-inst]: #6742
-#6589 := [mp #11022 #13454]: #6740
-#30677 := [unit-resolution #6589 #8211 #30675]: #30676
-#30678 := [unit-resolution #30677 #27051]: #6050
-#15614 := (or #6047 #6040)
-#17383 := [def-axiom]: #15614
-#30679 := [unit-resolution #17383 #30678]: #6040
-#30689 := [trans #30679 #30688]: #24663
-#24664 := (not #24663)
-#30510 := (or #30487 #30484 #24664)
-#30511 := [def-axiom]: #30510
-#30691 := [unit-resolution #30511 #30689]: #30690
-#30692 := [unit-resolution #30691 #30674 #30665]: false
-#30693 := [lemma #30692]: #30487
-#24550 := (or #24485 #30482 #30502)
-#24534 := [def-axiom]: #24550
-#24565 := [unit-resolution #24534 #30693]: #24569
-#24554 := [unit-resolution #24565 #24564]: #30482
-#24585 := [trans #24554 #24598]: #16616
-#18640 := (not #16616)
-#17931 := (f22 #6027)
-#11054 := (* -1::int #17931)
-#19418 := (+ #6034 #11054)
-#19546 := (+ #2296 #19418)
-#19767 := (>= #19546 0::int)
-#10933 := (+ #6028 #11054)
-#11085 := (>= #10933 0::int)
-#15145 := (or #4347 #11085)
-#15116 := [quant-inst]: #15145
-#31365 := [unit-resolution #15116 #11135]: #11085
-#15329 := (>= #6036 0::int)
-#14748 := (or #6047 #6037)
-#18244 := [def-axiom]: #14748
-#31366 := [unit-resolution #18244 #30678]: #6037
-#31367 := (or #6038 #15329)
-#31368 := [th-lemma]: #31367
-#31369 := [unit-resolution #31368 #31366]: #15329
-#31372 := (not #11085)
-#31371 := (not #15329)
-#31370 := (not #14667)
-#31373 := (or #19767 #31370 #31371 #31372)
-#31374 := [th-lemma]: #31373
-#31375 := [unit-resolution #31374 #31369 #31365 #27047]: #19767
-#19407 := (<= #19546 0::int)
-#31376 := [hypothesis]: #16616
-#31385 := (or #18640 #19407)
-#19432 := (+ f3 #6034)
-#19379 := (<= #19432 0::int)
-#31378 := (not #19379)
-#19384 := (>= #6028 0::int)
-#19385 := (or #4209 #19384)
-#19389 := [quant-inst]: #19385
-#31377 := [unit-resolution #19389 #7124]: #19384
-#31379 := (not #19384)
-#31380 := (or #31378 #31371 #2308 #31370 #31379)
-#31381 := [th-lemma]: #31380
-#31382 := [unit-resolution #31381 #27047 #31369 #31377 #27042]: #31378
-#15574 := (or #18640 #19379 #19407)
-#4076 := (or #4393 #4376)
-#3958 := [def-axiom]: #4076
-#31383 := [unit-resolution #3958 #27041]: #4376
-#16357 := (or #4381 #18640 #19379 #19407)
-#19370 := (+ #17931 #2297)
-#19394 := (+ #6033 #19370)
-#19374 := (>= #19394 0::int)
-#19408 := (or #18640 #19379 #19374)
-#19716 := (or #4381 #19408)
-#17518 := (iff #19716 #16357)
-#17219 := (or #4381 #15574)
-#16858 := (iff #17219 #16357)
-#17505 := [rewrite]: #16858
-#16891 := (iff #19716 #17219)
-#12448 := (iff #19408 #15574)
-#13959 := (iff #19374 #19407)
-#19434 := (+ #6033 #17931)
-#19383 := (+ #2297 #19434)
-#19433 := (>= #19383 0::int)
-#15734 := (iff #19433 #19407)
-#16396 := [rewrite]: #15734
-#19402 := (iff #19374 #19433)
-#19414 := (= #19394 #19383)
-#19387 := [rewrite]: #19414
-#19410 := [monotonicity #19387]: #19402
-#16307 := [trans #19410 #16396]: #13959
-#15718 := [monotonicity #16307]: #12448
-#16859 := [monotonicity #15718]: #16891
-#16874 := [trans #16859 #17505]: #17518
-#19533 := [quant-inst]: #19716
-#11410 := [mp #19533 #16874]: #16357
-#31384 := [unit-resolution #11410 #31383]: #15574
-#31386 := [unit-resolution #31384 #31382]: #31385
-#31387 := [unit-resolution #31386 #31376]: #19407
-#16399 := (= #19546 0::int)
-#19631 := (not #16399)
-#18788 := (+ #2296 #11054)
-#19057 := (<= #18788 0::int)
-#31389 := (not #19057)
-#13430 := (not #6031)
-#14811 := (or #6047 #13430)
-#15075 := [def-axiom]: #14811
-#31388 := [unit-resolution #15075 #30678]: #13430
-#31390 := (or #31389 #31370 #6031 #31372)
-#31391 := [th-lemma]: #31390
-#31392 := [unit-resolution #31391 #31388 #31365 #27047]: #31389
-#16287 := (or #19631 #18640 #19057)
-#19786 := (or #4390 #19631 #18640 #19057)
-#17668 := (+ #2297 #6033)
-#14507 := (+ #17931 #17668)
-#19668 := (= #14507 0::int)
-#18631 := (not #19668)
-#16825 := (>= #19370 0::int)
-#19579 := (or #18640 #16825 #18631)
-#19843 := (or #4390 #19579)
-#19770 := (iff #19843 #19786)
-#19865 := (or #4390 #16287)
-#19630 := (iff #19865 #19786)
-#19637 := [rewrite]: #19630
-#19633 := (iff #19843 #19865)
-#19654 := (iff #19579 #16287)
-#19056 := (or #18640 #19057 #19631)
-#19596 := (iff #19056 #16287)
-#19258 := [rewrite]: #19596
-#19634 := (iff #19579 #19056)
-#16213 := (iff #18631 #19631)
-#19632 := (iff #19668 #16399)
-#19376 := (= #19383 0::int)
-#17504 := (iff #19376 #16399)
-#18789 := [rewrite]: #17504
-#18823 := (iff #19668 #19376)
-#19535 := (= #14507 #19383)
-#18601 := [rewrite]: #19535
-#19024 := [monotonicity #18601]: #18823
-#19578 := [trans #19024 #18789]: #19632
-#19694 := [monotonicity #19578]: #16213
-#19670 := (iff #16825 #19057)
-#19666 := (+ #2297 #17931)
-#19760 := (>= #19666 0::int)
-#19747 := (iff #19760 #19057)
-#18824 := [rewrite]: #19747
-#19671 := (iff #16825 #19760)
-#19735 := (= #19370 #19666)
-#18598 := [rewrite]: #19735
-#19597 := [monotonicity #18598]: #19671
-#19598 := [trans #19597 #18824]: #19670
-#19766 := [monotonicity #19598 #19694]: #19634
-#19848 := [trans #19766 #19258]: #19654
-#19595 := [monotonicity #19848]: #19633
-#19768 := [trans #19595 #19637]: #19770
-#19769 := [quant-inst]: #19843
-#19377 := [mp #19769 #19768]: #19786
-#31393 := [unit-resolution #19377 #27043]: #16287
-#31394 := [unit-resolution #31393 #31376 #31392]: #19631
-#31396 := (not #19767)
-#31395 := (not #19407)
-#31397 := (or #16399 #31395 #31396)
-#31398 := [th-lemma]: #31397
-#31399 := [unit-resolution #31398 #31394 #31387 #31375]: false
-#31400 := [lemma #31399]: #18640
-[unit-resolution #31400 #24585]: false
+#5766 := [monotonicity #5763]: #5765
+#5771 := [trans #5766 #5769]: #5770
+#17162 := [monotonicity #5771]: #17007
+#17012 := [trans #17162 #17175]: #17178
+#14900 := [quant-inst]: #16501
+#17174 := [mp #14900 #17012]: #15800
+#12112 := [unit-resolution #17174 #11609]: #5767
+#12680 := [unit-resolution #12112 #21983]: #5152
+#12681 := (or #5151 #17016)
+#3979 := (or #4448 #4411)
+#3980 := [def-axiom]: #3979
+#36791 := [unit-resolution #3980 #30776]: #4411
+#16635 := (or #4416 #5151 #9378 #17016)
+#17073 := (or #5151 #9378 #17016)
+#16641 := (or #4416 #17073)
+#14699 := (iff #16641 #16635)
+#16688 := [rewrite]: #14699
+#16637 := [quant-inst]: #16641
+#16640 := [mp #16637 #16688]: #16635
+#12340 := [unit-resolution #16640 #36791 #11606]: #12681
+#10310 := [unit-resolution #12340 #12680]: #17016
+#23497 := (not #17016)
+#12283 := (or #5739 #23497)
+#10471 := (or #5739 #11593 #23497 #20713)
+#19706 := [th-lemma]: #10471
+#10322 := [unit-resolution #19706 #20709 #11587]: #12283
+#12288 := [unit-resolution #10322 #10310]: #5739
+#5899 := (<= #5738 0::int)
+#12137 := [unit-resolution #20692 #12082]: #17179
+#12281 := [unit-resolution #20711 #12082]: #17180
+#25013 := (or #17246 #20715)
+#24998 := (= #5807 #17199)
+#24999 := [symm #20675]: #24998
+#25000 := [monotonicity #24999]: #17660
+#25001 := [unit-resolution #20705 #25000]: #17662
+#25014 := [unit-resolution #20717 #20709 #25001]: #25013
+#21108 := [unit-resolution #25014 #12281]: #17246
+#17006 := (or #17247 #20697)
+#25035 := [unit-resolution #20681 #25000]: #17663
+#10294 := [unit-resolution #20702 #20688 #25035]: #17006
+#10291 := [unit-resolution #10294 #12137]: #17247
+#19780 := [unit-resolution #20722 #10291 #21108]: #17236
+#12106 := [unit-resolution #17274 #41882 #11606]: #20725
+#20766 := [unit-resolution #12106 #19780]: #17224
+#10530 := (or #20694 #20644 #20697)
+#12087 := [unit-resolution #20699 #20688 #25035]: #10530
+#12084 := [unit-resolution #12087 #20766 #12137]: #20644
+#12076 := (or #5899 #11627 #20715 #20714 #20645)
+#12113 := [th-lemma]: #12076
+#12083 := [unit-resolution #12113 #12281 #25001 #12084 #11623]: #5899
+#12286 := (not #5739)
+#12081 := (not #5899)
+#12110 := (or #21480 #12081 #12286)
+#10918 := [th-lemma]: #12110
+#10327 := [unit-resolution #10918 #12083 #12288]: #21480
+#10404 := [trans #10327 #11613]: #10470
+#16576 := [trans #10404 #11611]: #12109
+#19770 := [trans #16576 #10015]: #21382
+#12135 := [trans #19770 #14839]: #5761
+[unit-resolution #21983 #12135]: false
 unsat

--- a/src/HOL/Boogie/Examples/Boogie_Max.certs	Tue Dec 07 15:01:42 2010 +0100
+++ b/src/HOL/Boogie/Examples/Boogie_Max.certs	Tue Dec 07 15:44:38 2010 +0100
@@ -1,4 +1,4 @@
-dea36391893064c022de7bc923e15ef446cb4303 2224 0
[phone]ab21ec3906ce34cbb3ab2562fd15b389 2224 0
 #2 := false
 #8 := 0::int
 decl f5 :: (-> int int)

--- a/src/HOL/Boogie/Examples/VCC_Max.certs	Tue Dec 07 15:01:42 2010 +0100
+++ b/src/HOL/Boogie/Examples/VCC_Max.certs	Tue Dec 07 15:44:38 2010 +0100
@@ -1,4 +1,4 @@
-9e8f6c5e5fd53eee967069dced75f48858a605e7 7862 0
+842fcac6393e6d26f846dd8d9d59c48584951c7d 7862 0
 #2 := false
 decl f111 :: (-> S4 S5 int)
 decl f67 :: (-> S5 int S3 S5)

--- a/src/HOL/Multivariate_Analysis/Integration.certs	Tue Dec 07 15:01:42 2010 +0100
+++ b/src/HOL/Multivariate_Analysis/Integration.certs	Tue Dec 07 15:44:38 2010 +0100
@@ -1,243 +1,243 @@
-2e15025784d0676586e79b418a67bcb9811380a1 238 0
+9e44dd3ac188e9daa13e7206098bcc6edcecb255 238 0
 #2 := false
-#48 := 0::real
-decl f19 :: (-> S3 S10 real)
-decl f20 :: S10
-#43 := f20
+#66 := 0::real
+decl f26 :: (-> S3 S19 real)
+decl f27 :: S19
+#61 := f27
 decl f4 :: S3
 #8 := f4
-#58 := (f19 f4 f20)
-#109 := -1::real
-#153 := (* -1::real #58)
+#76 := (f26 f4 f27)
+#132 := -1::real
+#177 := (* -1::real #76)
 decl f5 :: (-> S4 S5 real)
 decl f8 :: S5
 #13 := f8
-decl f22 :: S4
-#54 := f22
-#55 := (f5 f22 f8)
-#154 := (+ #55 #153)
-#137 := (* -1::real #55)
-#144 := (+ #137 #58)
-#188 := (<= #154 0::real)
-#195 := (ite #188 #144 #154)
-#451 := (* -1::real #195)
-#452 := (+ #144 #451)
+decl f29 :: S4
+#72 := f29
+#73 := (f5 f29 f8)
+#178 := (+ #73 #177)
+#161 := (* -1::real #73)
+#168 := (+ #161 #76)
+#212 := (<= #178 0::real)
+#219 := (ite #212 #168 #178)
+#451 := (* -1::real #219)
+#452 := (+ #168 #451)
 #453 := (<= #452 0::real)
-#435 := (= #144 #195)
-decl f21 :: S4
-#45 := f21
-#46 := (f5 f21 f8)
+#435 := (= #168 #219)
+decl f28 :: S4
+#63 := f28
+#64 := (f5 f28 f8)
 decl f9 :: S3
 #17 := f9
-#44 := (f19 f9 f20)
-#120 := (* -1::real #44)
-#121 := (+ #120 #46)
-#110 := (* -1::real #46)
-#111 := (+ #44 #110)
-#216 := (>= #111 0::real)
-#223 := (ite #216 #111 #121)
-#447 := (* -1::real #223)
-#450 := (+ #121 #447)
+#62 := (f26 f9 f27)
+#144 := (* -1::real #62)
+#145 := (+ #144 #64)
+#134 := (* -1::real #64)
+#135 := (+ #62 #134)
+#240 := (>= #135 0::real)
+#247 := (ite #240 #135 #145)
+#447 := (* -1::real #247)
+#450 := (+ #145 #447)
 #454 := (<= #450 0::real)
-#442 := (= #121 #223)
-#217 := (not #216)
-#455 := [hypothesis]: #216
-#184 := (+ #44 #153)
-#185 := (<= #184 0::real)
-#206 := -3::real
-#234 := (* -3::real #223)
-#235 := (+ #137 #234)
-#236 := (+ #46 #235)
-#237 := (<= #236 0::real)
-#238 := (not #237)
-#207 := (* -3::real #195)
-#208 := (+ #137 #207)
-#209 := (+ #46 #208)
-#210 := (<= #209 0::real)
-#211 := (not #210)
-#249 := (and #185 #211 #238)
-#65 := (<= #44 #58)
-#56 := (- #46 #55)
-#52 := 3::real
-#59 := (- #58 #55)
-#61 := (- #59)
-#60 := (< #59 0::real)
-#62 := (ite #60 #61 #59)
-#63 := (* #62 3::real)
-#64 := (< #63 #56)
-#66 := (and #64 #65)
-#47 := (- #44 #46)
-#50 := (- #47)
-#49 := (< #47 0::real)
-#51 := (ite #49 #50 #47)
-#53 := (* #51 3::real)
-#57 := (< #53 #56)
-#67 := (and #57 #66)
-#254 := (iff #67 #249)
-#138 := (+ #46 #137)
-#147 := (< #144 0::real)
-#159 := (ite #147 #154 #144)
-#165 := (* 3::real #159)
-#170 := (< #165 #138)
-#176 := (and #65 #170)
-#114 := (< #111 0::real)
-#126 := (ite #114 #121 #111)
-#132 := (* 3::real #126)
-#141 := (< #132 #138)
-#181 := (and #141 #176)
-#252 := (iff #181 #249)
-#243 := (and #185 #211)
-#246 := (and #238 #243)
-#250 := (iff #246 #249)
-#251 := [rewrite]: #250
-#247 := (iff #181 #246)
-#244 := (iff #176 #243)
-#214 := (iff #170 #211)
-#200 := (* 3::real #195)
-#203 := (< #200 #138)
-#212 := (iff #203 #211)
-#213 := [rewrite]: #212
-#204 := (iff #170 #203)
-#201 := (= #165 #200)
-#198 := (= #159 #195)
-#189 := (not #188)
-#192 := (ite #189 #154 #144)
-#196 := (= #192 #195)
-#197 := [rewrite]: #196
-#193 := (= #159 #192)
-#190 := (iff #147 #189)
+#442 := (= #145 #247)
+#241 := (not #240)
+#455 := [hypothesis]: #240
+#208 := (+ #62 #177)
+#209 := (<= #208 0::real)
+#230 := -3::real
+#258 := (* -3::real #247)
+#259 := (+ #161 #258)
+#260 := (+ #64 #259)
+#261 := (<= #260 0::real)
+#262 := (not #261)
+#231 := (* -3::real #219)
+#232 := (+ #161 #231)
+#233 := (+ #64 #232)
+#234 := (<= #233 0::real)
+#235 := (not #234)
+#273 := (and #209 #235 #262)
+#83 := (<= #62 #76)
+#74 := (- #64 #73)
+#70 := 3::real
+#77 := (- #76 #73)
+#79 := (- #77)
+#78 := (< #77 0::real)
+#80 := (ite #78 #79 #77)
+#81 := (* #80 3::real)
+#82 := (< #81 #74)
+#84 := (and #82 #83)
+#65 := (- #62 #64)
+#68 := (- #65)
+#67 := (< #65 0::real)
+#69 := (ite #67 #68 #65)
+#71 := (* #69 3::real)
+#75 := (< #71 #74)
+#85 := (and #75 #84)
+#278 := (iff #85 #273)
+#162 := (+ #64 #161)
+#171 := (< #168 0::real)
+#183 := (ite #171 #178 #168)
+#189 := (* 3::real #183)
+#194 := (< #189 #162)
+#200 := (and #83 #194)
+#138 := (< #135 0::real)
+#150 := (ite #138 #145 #135)
+#156 := (* 3::real #150)
+#165 := (< #156 #162)
+#205 := (and #165 #200)
+#276 := (iff #205 #273)
+#267 := (and #209 #235)
+#270 := (and #262 #267)
+#274 := (iff #270 #273)
+#275 := [rewrite]: #274
+#271 := (iff #205 #270)
+#268 := (iff #200 #267)
+#238 := (iff #194 #235)
+#224 := (* 3::real #219)
+#227 := (< #224 #162)
+#236 := (iff #227 #235)
+#237 := [rewrite]: #236
+#228 := (iff #194 #227)
+#225 := (= #189 #224)
+#222 := (= #183 #219)
+#213 := (not #212)
+#216 := (ite #213 #178 #168)
+#220 := (= #216 #219)
+#221 := [rewrite]: #220
+#217 := (= #183 #216)
+#214 := (iff #171 #213)
+#215 := [rewrite]: #214
+#218 := [monotonicity #215]: #217
+#223 := [trans #218 #221]: #222
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#239 := [trans #229 #237]: #238
+#210 := (iff #83 #209)
+#211 := [rewrite]: #210
+#269 := [monotonicity #211 #239]: #268
+#265 := (iff #165 #262)
+#252 := (* 3::real #247)
+#255 := (< #252 #162)
+#263 := (iff #255 #262)
+#264 := [rewrite]: #263
+#256 := (iff #165 #255)
+#253 := (= #156 #252)
+#250 := (= #150 #247)
+#244 := (ite #241 #145 #135)
+#248 := (= #244 #247)
+#249 := [rewrite]: #248
+#245 := (= #150 #244)
+#242 := (iff #138 #241)
+#243 := [rewrite]: #242
+#246 := [monotonicity #243]: #245
+#251 := [trans #246 #249]: #250
+#254 := [monotonicity #251]: #253
+#257 := [monotonicity #254]: #256
+#266 := [trans #257 #264]: #265
+#272 := [monotonicity #266 #269]: #271
+#277 := [trans #272 #275]: #276
+#206 := (iff #85 #205)
+#203 := (iff #84 #200)
+#197 := (and #194 #83)
+#201 := (iff #197 #200)
+#202 := [rewrite]: #201
+#198 := (iff #84 #197)
+#195 := (iff #82 #194)
+#163 := (= #74 #162)
+#164 := [rewrite]: #163
+#192 := (= #81 #189)
+#186 := (* #183 3::real)
+#190 := (= #186 #189)
 #191 := [rewrite]: #190
-#194 := [monotonicity #191]: #193
-#199 := [trans #194 #197]: #198
-#202 := [monotonicity #199]: #201
-#205 := [monotonicity #202]: #204
-#215 := [trans #205 #213]: #214
-#186 := (iff #65 #185)
-#187 := [rewrite]: #186
-#245 := [monotonicity #187 #215]: #244
-#241 := (iff #141 #238)
-#228 := (* 3::real #223)
-#231 := (< #228 #138)
-#239 := (iff #231 #238)
-#240 := [rewrite]: #239
-#232 := (iff #141 #231)
-#229 := (= #132 #228)
-#226 := (= #126 #223)
-#220 := (ite #217 #121 #111)
-#224 := (= #220 #223)
-#225 := [rewrite]: #224
-#221 := (= #126 #220)
-#218 := (iff #114 #217)
-#219 := [rewrite]: #218
-#222 := [monotonicity #219]: #221
-#227 := [trans #222 #225]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#242 := [trans #233 #240]: #241
-#248 := [monotonicity #242 #245]: #247
-#253 := [trans #248 #251]: #252
-#182 := (iff #67 #181)
-#179 := (iff #66 #176)
-#173 := (and #170 #65)
-#177 := (iff #173 #176)
-#178 := [rewrite]: #177
-#174 := (iff #66 #173)
-#171 := (iff #64 #170)
-#139 := (= #56 #138)
-#140 := [rewrite]: #139
-#168 := (= #63 #165)
-#162 := (* #159 3::real)
-#166 := (= #162 #165)
-#167 := [rewrite]: #166
-#163 := (= #63 #162)
-#160 := (= #62 #159)
-#145 := (= #59 #144)
-#146 := [rewrite]: #145
-#157 := (= #61 #154)
-#150 := (- #144)
-#155 := (= #150 #154)
-#156 := [rewrite]: #155
-#151 := (= #61 #150)
-#152 := [monotonicity #146]: #151
-#158 := [trans #152 #156]: #157
-#148 := (iff #60 #147)
-#149 := [monotonicity #146]: #148
-#161 := [monotonicity #149 #158 #146]: #160
-#164 := [monotonicity #161]: #163
-#169 := [trans #164 #167]: #168
-#172 := [monotonicity #169 #140]: #171
-#175 := [monotonicity #172]: #174
-#180 := [trans #175 #178]: #179
-#142 := (iff #57 #141)
-#135 := (= #53 #132)
-#129 := (* #126 3::real)
-#133 := (= #129 #132)
-#134 := [rewrite]: #133
-#130 := (= #53 #129)
-#127 := (= #51 #126)
-#112 := (= #47 #111)
-#113 := [rewrite]: #112
-#124 := (= #50 #121)
-#117 := (- #111)
-#122 := (= #117 #121)
-#123 := [rewrite]: #122
-#118 := (= #50 #117)
-#119 := [monotonicity #113]: #118
-#125 := [trans #119 #123]: #124
-#115 := (iff #49 #114)
-#116 := [monotonicity #113]: #115
-#128 := [monotonicity #116 #125 #113]: #127
-#131 := [monotonicity #128]: #130
-#136 := [trans #131 #134]: #135
-#143 := [monotonicity #136 #140]: #142
-#183 := [monotonicity #143 #180]: #182
-#255 := [trans #183 #253]: #254
-#108 := [asserted]: #67
-#256 := [mp #108 #255]: #249
-#257 := [and-elim #256]: #185
-#259 := [and-elim #256]: #238
-#448 := (+ #111 #447)
+#187 := (= #81 #186)
+#184 := (= #80 #183)
+#169 := (= #77 #168)
+#170 := [rewrite]: #169
+#181 := (= #79 #178)
+#174 := (- #168)
+#179 := (= #174 #178)
+#180 := [rewrite]: #179
+#175 := (= #79 #174)
+#176 := [monotonicity #170]: #175
+#182 := [trans #176 #180]: #181
+#172 := (iff #78 #171)
+#173 := [monotonicity #170]: #172
+#185 := [monotonicity #173 #182 #170]: #184
+#188 := [monotonicity #185]: #187
+#193 := [trans #188 #191]: #192
+#196 := [monotonicity #193 #164]: #195
+#199 := [monotonicity #196]: #198
+#204 := [trans #199 #202]: #203
+#166 := (iff #75 #165)
+#159 := (= #71 #156)
+#153 := (* #150 3::real)
+#157 := (= #153 #156)
+#158 := [rewrite]: #157
+#154 := (= #71 #153)
+#151 := (= #69 #150)
+#136 := (= #65 #135)
+#137 := [rewrite]: #136
+#148 := (= #68 #145)
+#141 := (- #135)
+#146 := (= #141 #145)
+#147 := [rewrite]: #146
+#142 := (= #68 #141)
+#143 := [monotonicity #137]: #142
+#149 := [trans #143 #147]: #148
+#139 := (iff #67 #138)
+#140 := [monotonicity #137]: #139
+#152 := [monotonicity #140 #149 #137]: #151
+#155 := [monotonicity #152]: #154
+#160 := [trans #155 #158]: #159
+#167 := [monotonicity #160 #164]: #166
+#207 := [monotonicity #167 #204]: #206
+#279 := [trans #207 #277]: #278
+#131 := [asserted]: #85
+#280 := [mp #131 #279]: #273
+#281 := [and-elim #280]: #209
+#283 := [and-elim #280]: #262
+#448 := (+ #135 #447)
 #449 := (<= #448 0::real)
-#441 := (= #111 #223)
-#443 := (or #217 #441)
+#441 := (= #135 #247)
+#443 := (or #241 #441)
 #444 := [def-axiom]: #443
 #467 := [unit-resolution #444 #455]: #441
 #468 := (not #441)
 #469 := (or #468 #449)
 #470 := [th-lemma]: #469
 #471 := [unit-resolution #470 #467]: #449
-#463 := (or #189 #217)
-#456 := [hypothesis]: #188
-#258 := [and-elim #256]: #211
-#437 := (or #189 #435)
+#463 := (or #213 #241)
+#456 := [hypothesis]: #212
+#282 := [and-elim #280]: #235
+#437 := (or #213 #435)
 #438 := [def-axiom]: #437
 #457 := [unit-resolution #438 #456]: #435
 #458 := (not #435)
 #459 := (or #458 #453)
 #460 := [th-lemma]: #459
 #461 := [unit-resolution #460 #457]: #453
-#462 := [th-lemma #257 #461 #258 #456 #455]: false
+#462 := [th-lemma #281 #461 #282 #456 #455]: false
 #464 := [lemma #462]: #463
-#472 := [unit-resolution #464 #455]: #189
-#473 := [th-lemma #472 #471 #259 #257 #455]: false
-#474 := [lemma #473]: #217
-#445 := (or #216 #442)
+#472 := [unit-resolution #464 #455]: #213
+#473 := [th-lemma #472 #471 #283 #281 #455]: false
+#474 := [lemma #473]: #241
+#445 := (or #240 #442)
 #446 := [def-axiom]: #445
 #475 := [unit-resolution #446 #474]: #442
 #476 := (not #442)
 #477 := (or #476 #454)
 #478 := [th-lemma]: #477
 #479 := [unit-resolution #478 #475]: #454
-#481 := (not #185)
+#481 := (not #209)
 #480 := (not #454)
-#482 := (or #188 #480 #237 #481 #216)
+#482 := (or #212 #480 #261 #481 #240)
 #483 := [th-lemma]: #482
-#484 := [unit-resolution #483 #257 #474 #259 #479]: #188
+#484 := [unit-resolution #483 #281 #474 #283 #479]: #212
 #485 := [unit-resolution #438 #484]: #435
 #486 := [unit-resolution #460 #485]: #453
-[th-lemma #479 #259 #257 #474 #258 #486]: false
+[th-lemma #479 #283 #281 #474 #282 #486]: false
 unsat
-4c0d1f43a6268b5d3a850361d3ff86d073eaf489 333 0
[phone]f9b173abcf2f39dbb596598ca 333 0
 #2 := false
 #11 := 0::real
 decl ?v2!1 :: real
@@ -571,65 +571,65 @@
 #408 := [lemma #407]: #230
 [th-lemma #406 #301 #408 #396 #303]: false
 unsat
-40822b724c71d6702c01ad1e865c13dca0ab3c21 57 0
+40cbce81b3fe1243dfc608ed96b948eede22a796 57 0
 #2 := false
-decl f13 :: (-> S4 S4 S5)
-#44 := (:var 0 S4)
-#43 := (:var 1 S4)
-#45 := (f13 #43 #44)
-#252 := (pattern #45)
-#39 := 0::real
+#35 := 0::real
 decl f12 :: (-> S5 real)
-#46 := (f12 #45)
-#133 := (>= #46 0::real)
-#253 := (forall (vars (?v0 S4) (?v1 S4)) (:pat #252) #133)
-#135 := (forall (vars (?v0 S4) (?v1 S4)) #133)
-#256 := (iff #135 #253)
-#254 := (iff #133 #133)
-#255 := [refl]: #254
-#257 := [quant-intro #255]: #256
-#150 := (~ #135 #135)
-#139 := (~ #133 #133)
-#130 := [refl]: #139
-#151 := [nnf-pos #130]: #150
-#47 := (<= 0::real #46)
-#48 := (forall (vars (?v0 S4) (?v1 S4)) #47)
-#136 := (iff #48 #135)
-#132 := (iff #47 #133)
-#134 := [rewrite]: #132
-#137 := [quant-intro #134]: #136
-#129 := [asserted]: #48
-#138 := [mp #129 #137]: #135
-#152 := [mp~ #138 #151]: #135
-#258 := [mp #152 #257]: #253
+decl f13 :: (-> S4 S4 S5)
 decl f14 :: (-> S3 S4)
 decl f4 :: S3
 #8 := f4
-#36 := (f14 f4)
+#43 := (f14 f4)
 decl f10 :: S3
 #24 := f10
-#35 := (f14 f10)
-#37 := (f13 #35 #36)
-#38 := (f12 #37)
-#259 := (>= #38 0::real)
-#261 := (not #259)
-#41 := (= #38 0::real)
-#42 := (not #41)
-#128 := [asserted]: #42
-#267 := (or #41 #261)
-#40 := (<= #38 0::real)
-#127 := [asserted]: #40
-#260 := (not #40)
-#265 := (or #41 #260 #261)
-#266 := [th-lemma]: #265
-#268 := [unit-resolution #266 #127]: #267
-#269 := [unit-resolution #268 #128]: #261
-#262 := (not #253)
-#263 := (or #262 #259)
-#264 := [quant-inst]: #263
-[unit-resolution #264 #269 #258]: false
+#42 := (f14 f10)
+#44 := (f13 #42 #43)
+#45 := (f12 #44)
+#269 := (>= #45 0::real)
+#271 := (not #269)
+#47 := (= #45 0::real)
+#48 := (not #47)
+#129 := [asserted]: #48
+#277 := (or #47 #271)
+#46 := (<= #45 0::real)
+#128 := [asserted]: #46
+#270 := (not #46)
+#275 := (or #47 #270 #271)
+#276 := [th-lemma]: #275
+#278 := [unit-resolution #276 #128]: #277
+#279 := [unit-resolution #278 #129]: #271
+#37 := (:var 0 S4)
+#36 := (:var 1 S4)
+#38 := (f13 #36 #37)
+#262 := (pattern #38)
+#39 := (f12 #38)
+#131 := (>= #39 0::real)
+#263 := (forall (vars (?v0 S4) (?v1 S4)) (:pat #262) #131)
+#133 := (forall (vars (?v0 S4) (?v1 S4)) #131)
+#266 := (iff #133 #263)
+#264 := (iff #131 #131)
+#265 := [refl]: #264
+#267 := [quant-intro #265]: #266
+#160 := (~ #133 #133)
+#149 := (~ #131 #131)
+#147 := [refl]: #149
+#161 := [nnf-pos #147]: #160
+#40 := (<= 0::real #39)
+#41 := (forall (vars (?v0 S4) (?v1 S4)) #40)
+#134 := (iff #41 #133)
+#130 := (iff #40 #131)
+#132 := [rewrite]: #130
+#135 := [quant-intro #132]: #134
+#127 := [asserted]: #41
+#136 := [mp #127 #135]: #133
+#162 := [mp~ #136 #161]: #133
+#268 := [mp #162 #267]: #263
+#272 := (not #263)
+#273 := (or #272 #269)
+#274 := [quant-inst]: #273
+[unit-resolution #274 #268 #279]: false
 unsat
-ae79dfdacb760a3554ce388b846d335064f674de 318 0
+ebd0a667a6c59e734a99dabd03ef5b542d87ab7f 318 0
 #2 := false
 #25 := 0::real
 decl f8 :: (-> S4 S2 real)
@@ -948,7 +948,7 @@
 #622 := [th-lemma]: #621
 [unit-resolution #622 #619 #604]: false
 unsat
-4c36877468848170cffdf0ddcda5eb522e99ab42 295 0
+e25cfa9aafb64ca680e53fe155a9e8b195b43ff5 295 0
 #2 := false
 #25 := 0::real
 decl f8 :: (-> S4 S2 real)
@@ -1244,7 +1244,7 @@
 #694 := [th-lemma]: #693
 [unit-resolution #694 #691 #677]: false
 unsat
-f2fb6a78bd5ef0d3bd81c73f0edb01f05b9ead4b 204 0
+955c468c14be1f08edb50f3d04b7ac25ec92868a 204 0
 #2 := false
 #46 := 0::real
 decl f5 :: (-> S3 S2 real)
@@ -1449,7 +1449,7 @@
 #533 := [unit-resolution #532 #153]: #473
 [th-lemma #533 #529 #514]: false
 unsat
-c57edc9b53558e5e0a7337a056a91568e455bc48 870 0
+96e3af5dc395ffc923358a51ec8eb32fa3076419 870 0
 #2 := false
 #11 := 0::real
 decl f5 :: real

--- a/src/HOL/SMT_Examples/SMT_Examples.certs	Tue Dec 07 15:01:42 2010 +0100
+++ b/src/HOL/SMT_Examples/SMT_Examples.certs	Tue Dec 07 15:44:38 2010 +0100
@@ -1,4 +1,4 @@
-24d44e2684a632b0246b194cc850faec2cea7de6 33 0
+fc240ca706e2afb45ac99ed81ac8b1c880202f6e 33 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -32,7 +32,7 @@
 #29 := [asserted]: #12
 [mp #29 #49]: false
 unsat
-1b7b7e7109fa2efdf94c204be8d611210920badb 8 0
+27f3d7664eb694b08bf7c88f0f09b921356d5fea 8 0
 #2 := false
 #1 := true
 #8 := (not true)
@@ -41,7 +41,7 @@
 #25 := [asserted]: #8
 [mp #25 #27]: false
 unsat
-10a83d48b539d27c174c61f5874470265d21b40f 37 0
+368ad424ca75638589e4c70a835edc00c6230db7 37 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -79,7 +79,7 @@
 #29 := [asserted]: #12
 [mp #29 #53]: false
 unsat
-060c210941c0fd9eca58c8250fc66d664e976010 66 0
+02044173beff1ab91acfe25dc46973c9c3661be9 66 0
 #2 := false
 decl f4 :: S1
 #10 := f4
@@ -146,9 +146,9 @@
 #71 := [and-elim #69]: #40
 [mp #71 #85]: false
 unsat
-b0eed80076353895afe2bbf37d588b79cf593079 1 0
-unsat
-d37af75fba79a43c8aa95dbef345ea660c999f99 94 0
+b73beebe843d6f6b6668b07899f763420b9a2a4e 1 0
+unsat
+88e70178e39332a364ba37d967c5530977fa5629 94 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -243,7 +243,7 @@
 #39 := [asserted]: #22
 [mp #39 #108]: false
 unsat
-b3ee7b71753d028d8ffbc5d42df5f0f79660f6e7 72 0
+1c5e9504bb6b90952679bac27416520abf816b19 72 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -316,7 +316,7 @@
 #36 := [asserted]: #19
 [mp #36 #88]: false
 unsat
-b6f4097a3d567e9383135805312389841b9ed5f3 234 0
+d2b17144ad45d64438c0595be2d8ec622dfb97ce 234 0
 #2 := false
 decl f6 :: S1
 #14 := f6
@@ -551,60 +551,60 @@
 #96 := [mp #69 #95]: #91
 [mp #96 #299]: false
 unsat
-75e07bc80c3184013212c0a5c60b827b399474ad 52 0
-#2 := false
-decl f4 :: (-> S2 S2 S2)
-#16 := (:var 1 S2)
-#17 := (:var 0 S2)
-#19 := (f4 #17 #16)
-#535 := (pattern #19)
-#18 := (f4 #16 #17)
-#534 := (pattern #18)
-#20 := (= #18 #19)
-#536 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #534 #535) #20)
-#21 := (forall (vars (?v0 S2) (?v1 S2)) #20)
-#539 := (iff #21 #536)
-#537 := (iff #20 #20)
+7b4b543d0e43b7340967d161cba2cdc17d6ac7aa 52 0
+#2 := false
+decl f3 :: (-> S2 S2 S2)
+decl f4 :: S2
+#14 := f4
+decl f5 :: S2
+#16 := f5
+#18 := (f3 f5 f4)
+#17 := (f3 f4 f5)
+#19 := (= #17 #18)
+#49 := (not #19)
+#15 := (= f4 f4)
+#20 := (and #15 #19)
+#21 := (not #20)
+#50 := (iff #21 #49)
+#47 := (iff #20 #19)
+#1 := true
+#42 := (and true #19)
+#45 := (iff #42 #19)
+#46 := [rewrite]: #45
+#43 := (iff #20 #42)
+#40 := (iff #15 true)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#48 := [trans #44 #46]: #47
+#51 := [monotonicity #48]: #50
+#39 := [asserted]: #21
+#54 := [mp #39 #51]: #49
+#8 := (:var 1 S2)
+#9 := (:var 0 S2)
+#11 := (f3 #9 #8)
+#535 := (pattern #11)
+#10 := (f3 #8 #9)
+#534 := (pattern #10)
+#12 := (= #10 #11)
+#536 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #534 #535) #12)
+#13 := (forall (vars (?v0 S2) (?v1 S2)) #12)
+#539 := (iff #13 #536)
+#537 := (iff #12 #12)
 #538 := [refl]: #537
 #540 := [quant-intro #538]: #539
-#62 := (~ #21 #21)
-#60 := (~ #20 #20)
+#62 := (~ #13 #13)
+#60 := (~ #12 #12)
 #61 := [refl]: #60
 #63 := [nnf-pos #61]: #62
-#51 := [asserted]: #21
-#56 := [mp~ #51 #63]: #21
-#541 := [mp #56 #540]: #536
-decl f3 :: S2
-#8 := f3
-decl f5 :: S2
-#10 := f5
-#12 := (f4 f5 f3)
-#11 := (f4 f3 f5)
-#13 := (= #11 #12)
-#48 := (not #13)
-#9 := (= f3 f3)
-#14 := (and #9 #13)
-#15 := (not #14)
-#49 := (iff #15 #48)
-#46 := (iff #14 #13)
-#1 := true
-#41 := (and true #13)
-#44 := (iff #41 #13)
-#45 := [rewrite]: #44
-#42 := (iff #14 #41)
-#39 := (iff #9 true)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#50 := [monotonicity #47]: #49
-#38 := [asserted]: #15
-#53 := [mp #38 #50]: #48
+#38 := [asserted]: #13
+#55 := [mp~ #38 #63]: #13
+#541 := [mp #55 #540]: #536
 #117 := (not #536)
-#204 := (or #117 #13)
+#204 := (or #117 #19)
 #118 := [quant-inst]: #204
-[unit-resolution #118 #53 #541]: false
-unsat
-836f826330ec23da3f93f44a06ef6c00563d7781 2578 0
+[unit-resolution #118 #541 #54]: false
+unsat
+7e2e7bb07882f96841bd79a84298a534331a1bfd 2578 0
 #2 := false
 decl f35 :: S1
 #112 := f35
@@ -3183,7 +3183,7 @@
 #3638 := [unit-resolution #705 #3637 #3636 #3635]: #683
 [unit-resolution #1968 #3638 #3634]: false
 unsat
-49266526e51dee0fe0083e5120f86525e2ef1056 95 0
+0e0405e00e1db857b4d13553d793f29fac01967a 95 0
 #2 := false
 decl f3 :: (-> int S1)
 decl ?v0!0 :: int
@@ -3279,7 +3279,7 @@
 #102 := [and-elim #101]: #76
 [unit-resolution #102 #115]: false
 unsat
-107e72fe657296bfbc7688086b83c6164eff0b08 146 0
+9c268042fff487e7b26b60e0665b29c4f9035fd9 146 0
 #2 := false
 decl f3 :: (-> S1 S2 S1)
 #9 := (:var 0 S2)
@@ -3426,7 +3426,7 @@
 #261 := [quant-inst]: #256
 [unit-resolution #261 #584 #284]: false
 unsat
-2bb8a8ad07066951b9c2ff8c6c6ea8a4b3a62bfc 146 2
+84b4090aec162b66cf0450b7d84090e9d75558ae 146 2
 #2 := false
 decl f3 :: (-> S1 S2 S1)
 #9 := (:var 0 S2)
@@ -3575,7 +3575,7 @@
 unsat
 WARNING: failed to find a pattern for quantifier (quantifier id: k!13)
 
-3415c51851ea95b52ee39d82ddb23d7a42cd9b2f 91 0
+ac5d145f65d7c243f233206c12f40ac62829b79d 91 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl f4 :: S2
@@ -3667,7 +3667,7 @@
 #162 := [quant-inst]: #248
 [unit-resolution #162 #582 #79]: false
 unsat
-44eecf236b490147dbc51a13ab3759021603fcea 17 0
+8ec3689427316325ec1985fe59ea5618ec7318a2 17 0
 #2 := false
 #8 := 3::int
 #9 := (= 3::int 3::int)
@@ -3685,7 +3685,7 @@
 #27 := [asserted]: #10
 [mp #27 #36]: false
 unsat
-f79c070f64eae6123a31ed43ab22ff256427a856 17 0
+df5b3a48c37e6835717fda0b39e49a97c98242e3 17 0
 #2 := false
 #8 := 3::real
 #9 := (= 3::real 3::real)
@@ -3703,7 +3703,7 @@
 #27 := [asserted]: #10
 [mp #27 #36]: false
 unsat
-4ebfd0cdcde15d352023497277a471fa091558e8 26 0
+9a83587f08e45fa0c86a86787b5852f3dae7a31a 26 0
 #2 := false
 #11 := 4::int
 #9 := 1::int
@@ -3730,7 +3730,7 @@
 #30 := [asserted]: #13
 [mp #30 #45]: false
 unsat
-c45eaaff3b4218ae166b1ee5b57daee45f751625 41 0
+22bf9099fbafaf6441822d212def68271e5543c2 41 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -3772,7 +3772,7 @@
 #33 := [asserted]: #16
 [mp #33 #57]: false
 unsat
-c12d97c9fd2930565ac865f67ef562b3c45fbf6a 35 0
+34b2179303cd4545725b4372e0c313389934e272 35 0
 #2 := false
 #9 := 3::int
 #10 := 8::int
@@ -3808,7 +3808,7 @@
 #31 := [asserted]: #14
 [mp #31 #56]: false
 unsat
-7cb5a788981ee8a217912588519fd956ced665e2 209 0
+5162151cc0aa13db7036579b135b5e4956a6d3ad 209 0
 #2 := false
 #11 := 0::real
 decl f4 :: real
@@ -4018,50 +4018,61 @@
 #231 := [unit-resolution #159 #230]: #150
 [th-lemma #125 #220 #227 #231]: false
 unsat
-1e234cc93c775a7f92c9808afe1122152dd4b38c 42 0
+8cadccb54aba63c5a507abf7579c610476d2ae45 53 0
 #2 := false
 decl f3 :: (-> S1 S2)
+decl f2 :: S1
+#5 := f2
 decl f1 :: S1
 #4 := f1
-#13 := (f3 f1)
-decl f2 :: S1
-#5 := f2
+#1 := true
+#13 := (ite true f1 f2)
+#14 := (f3 #13)
 #9 := 3::int
 #8 := 2::int
 #10 := (< 2::int 3::int)
 #11 := (ite #10 f1 f2)
 #12 := (f3 #11)
-#14 := (= #12 #13)
-#15 := (not #14)
-#57 := (iff #15 false)
-#1 := true
-#52 := (not true)
-#55 := (iff #52 false)
+#15 := (= #12 #14)
+#16 := (not #15)
+#66 := (iff #16 false)
+#36 := (f3 f1)
+#39 := (= #12 #36)
+#42 := (not #39)
+#64 := (iff #42 false)
+#59 := (not true)
+#62 := (iff #59 false)
+#63 := [rewrite]: #62
+#60 := (iff #42 #59)
+#57 := (iff #39 true)
+#52 := (= #36 #36)
+#55 := (iff #52 true)
 #56 := [rewrite]: #55
-#53 := (iff #15 #52)
-#50 := (iff #14 true)
-#45 := (= #13 #13)
-#48 := (iff #45 true)
-#49 := [rewrite]: #48
-#46 := (iff #14 #45)
-#42 := (= #11 f1)
-#37 := (ite true f1 f2)
-#40 := (= #37 f1)
-#41 := [rewrite]: #40
-#38 := (= #11 #37)
-#35 := (iff #10 true)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#43 := [trans #39 #41]: #42
-#44 := [monotonicity #43]: #14
-#47 := [monotonicity #44]: #46
-#51 := [trans #47 #49]: #50
+#53 := (iff #39 #52)
+#49 := (= #11 f1)
+#34 := (= #13 f1)
+#35 := [rewrite]: #34
+#47 := (= #11 #13)
+#45 := (iff #10 true)
+#46 := [rewrite]: #45
+#48 := [monotonicity #46]: #47
+#50 := [trans #48 #35]: #49
+#51 := [monotonicity #50]: #39
 #54 := [monotonicity #51]: #53
 #58 := [trans #54 #56]: #57
-#32 := [asserted]: #15
-[mp #32 #58]: false
-unsat
-b18c0c1cf966295783ca6ddab09d2dabebd74ff7 54 0
+#61 := [monotonicity #58]: #60
+#65 := [trans #61 #63]: #64
+#43 := (iff #16 #42)
+#40 := (iff #15 #39)
+#37 := (= #14 #36)
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#44 := [monotonicity #41]: #43
+#67 := [trans #44 #65]: #66
+#33 := [asserted]: #16
+[mp #33 #67]: false
+unsat
+9ee8bccddf2109c959aa713167ad64d38274a3ce 54 0
 #2 := false
 #13 := 1::int
 decl f3 :: int
@@ -4116,7 +4127,7 @@
 #33 := [asserted]: #16
 [mp #33 #72]: false
 unsat
-3db1a0441939b3cc14e2a4efb4f74cab6c664bd5 63 0
+306069d37156d9128c5200f6ece7cc1c2c32a1ca 63 0
 #2 := false
 #15 := 0::int
 decl f4 :: int
@@ -4180,7 +4191,7 @@
 #81 := [mp #57 #80]: #68
 [mp #81 #93]: false
 unsat
-08fc4e7efc68a91cbed93f860a54fb029c71bcbb 35 0
+503d52dce584b309a1acdc08d36958c3ac5ae3ae 35 0
 #2 := false
 #10 := 5::int
 #8 := 2::int
@@ -4216,7 +4227,7 @@
 #30 := [asserted]: #13
 [mp #30 #54]: false
 unsat
-3adb493c0d9d387d1aebf7bcb353d3c00a0851a0 45 0
+c99d2f0ab7bdeadc342741456e2e67ddfe8c6df7 45 0
 #2 := false
 #15 := 4::real
 decl f4 :: real
@@ -4262,7 +4273,7 @@
 #65 := [mp #41 #64]: #56
 [th-lemma #65 #52 #43]: false
 unsat
-5ee51bc5647785432ba0c87ce1c0376c614df467 59 0
+7be2e8e88cc2e8ec69e024f23a41c838fc271cf8 59 0
 #2 := false
 #20 := (not false)
 decl f4 :: int
@@ -4322,51 +4333,105 @@
 #39 := [asserted]: #22
 [mp #39 #76]: false
 unsat
-28a095b5ca08adc7ff0222dfacd76cf43a8ba449 43 0
-#2 := false
+f13245dba328ba82a1856f65d75c48730a2be16a 97 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f2 :: S1
+#5 := f2
+#9 := 3::int
 decl f3 :: int
 #8 := f3
-#9 := 3::int
-#11 := (<= 3::int f3)
+#46 := (>= f3 3::int)
+#51 := (ite #46 f2 f1)
+#73 := (= f1 #51)
+#58 := (ite #46 f1 f2)
+#69 := (= f1 #58)
+#115 := (iff #69 #73)
+#113 := (iff #73 #69)
+#61 := (= #51 #58)
+#12 := (<= 3::int f3)
+#13 := (ite #12 f1 f2)
 #10 := (< f3 3::int)
-#12 := (iff #10 #11)
-#13 := (not #12)
-#14 := (not #13)
-#61 := (iff #14 false)
-#59 := (iff #12 false)
-#50 := (>= f3 3::int)
-#48 := (not #50)
-#54 := (iff #48 #50)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #12 #54)
-#52 := (iff #11 #50)
+#11 := (ite #10 f1 f2)
+#14 := (distinct #11 #13)
+#15 := (not #14)
+#64 := (iff #15 #61)
+#33 := (= #11 #13)
+#62 := (iff #33 #61)
+#59 := (= #13 #58)
+#56 := (iff #12 #46)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#54 := (= #11 #51)
+#44 := (not #46)
+#48 := (ite #44 f1 f2)
+#52 := (= #48 #51)
 #53 := [rewrite]: #52
-#49 := (iff #10 #48)
-#51 := [rewrite]: #49
-#56 := [monotonicity #51 #53]: #55
-#60 := [trans #56 #58]: #59
-#46 := (iff #14 #12)
-#40 := (iff #11 #10)
-#44 := (iff #40 #12)
-#45 := [rewrite]: #44
-#42 := (iff #14 #40)
-#32 := (not #10)
-#33 := (iff #11 #32)
-#36 := (not #33)
-#39 := (iff #36 #40)
-#41 := [rewrite]: #39
-#37 := (iff #14 #36)
-#34 := (iff #13 #33)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#43 := [trans #38 #41]: #42
-#47 := [trans #43 #45]: #46
-#62 := [trans #47 #60]: #61
-#31 := [asserted]: #14
-[mp #31 #62]: false
-unsat
-d13adc55a1937ef83f29c016ef8623fe1fda09eb 86 0
+#49 := (= #11 #48)
+#45 := (iff #10 #44)
+#47 := [rewrite]: #45
+#50 := [monotonicity #47]: #49
+#55 := [trans #50 #53]: #54
+#63 := [monotonicity #55 #60]: #62
+#42 := (iff #15 #33)
+#34 := (not #33)
+#37 := (not #34)
+#40 := (iff #37 #33)
+#41 := [rewrite]: #40
+#38 := (iff #15 #37)
+#35 := (iff #14 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#43 := [trans #39 #41]: #42
+#65 := [trans #43 #63]: #64
+#32 := [asserted]: #15
+#66 := [mp #32 #65]: #61
+#114 := [monotonicity #66]: #113
+#116 := [symm #114]: #115
+#109 := (not #73)
+#6 := (= f1 f2)
+#67 := (= f2 #58)
+#105 := (iff #67 #6)
+#103 := (iff #6 #67)
+#98 := (= #58 f2)
+#101 := (iff #98 #67)
+#102 := [commutativity]: #101
+#99 := (iff #6 #98)
+#96 := [hypothesis]: #73
+#97 := [trans #96 #66]: #69
+#100 := [monotonicity #97]: #99
+#104 := [trans #100 #102]: #103
+#106 := [symm #104]: #105
+#72 := (= f2 #51)
+#84 := (iff #72 #67)
+#85 := [monotonicity #66]: #84
+#80 := (not #67)
+#81 := [hypothesis]: #80
+#78 := (or #46 #67)
+#79 := [def-axiom]: #78
+#82 := [unit-resolution #79 #81]: #46
+#74 := (or #44 #72)
+#75 := [def-axiom]: #74
+#83 := [unit-resolution #75 #82]: #72
+#86 := [mp #83 #85]: #67
+#87 := [unit-resolution #81 #86]: false
+#88 := [lemma #87]: #67
+#107 := [mp #88 #106]: #6
+#7 := (not #6)
+#31 := [asserted]: #7
+#108 := [unit-resolution #31 #107]: false
+#110 := [lemma #108]: #109
+#70 := (or #46 #73)
+#71 := [def-axiom]: #70
+#111 := [unit-resolution #71 #110]: #46
+#76 := (or #44 #69)
+#77 := [def-axiom]: #76
+#112 := [unit-resolution #77 #111]: #69
+#117 := [mp #112 #116]: #73
+[unit-resolution #110 #117]: false
+unsat
+20ba41076072795cda240a8a9748e86d10779a3c 86 0
 #2 := false
 decl f3 :: int
 #9 := f3
@@ -4453,7 +4518,7 @@
 #104 := [unit-resolution #82 #103 #96 #87]: #65
 [unit-resolution #104 #117]: false
 unsat
-372a6ad969cb318322945cf566c5d0dc9eaab120 551 0
+c7dd77e223fba57a1414f2ac31bcf364581c0489 551 0
 #2 := false
 #174 := 0::int
 decl f4 :: int
@@ -5005,7 +5070,7 @@
 #617 := [unit-resolution #411 #614]: #421
 [unit-resolution #601 #617 #593 #616]: false
 unsat
-79f1383c7c06e3e99fb5b45b946ee8edd0a67644 2109 0
+7933e79d3cd73c97f525ad1b5130b2e50570acf4 2109 0
 #2 := false
 #10 := 0::int
 decl f3 :: int
@@ -7115,7 +7180,7 @@
 #2119 := [unit-resolution #2118 #2109 #2056 #2114 #2113 #2112 #2096 #2108]: #945
 [unit-resolution #1969 #2119 #2109 #2096 #2042 #2105 #2108]: false
 unsat
-e5059b0c3e879c6b6b3ce8026895b93ab92e0728 52 0
+fa5f0f4797c0756b87438a177b9cadbd589f29ce 52 0
 #2 := false
 #12 := 1::real
 decl f3 :: real
@@ -7168,7 +7233,7 @@
 #34 := [asserted]: #17
 [mp #34 #70]: false
 unsat
-58d0d0a0a699999905091a630166f1e00b881d19 348 0
+cb2e9115ca66826b4d3a05cbfae773d42313c9e8 348 0
 #2 := false
 #11 := 0::int
 decl f5 :: int
@@ -7517,7 +7582,7 @@
 #638 := [unit-resolution #642 #647]: #643
 [unit-resolution #638 #640 #637]: false
 unsat
-4fc7df80f9cc116a2a88bcb88017dc9b0c75f7fc 354 0
+e1ee840c294e23269abf2c4622852c1bd3fa4be1 354 0
 #2 := false
 #11 := 0::int
 decl f5 :: int
@@ -7872,7 +7937,7 @@
 #626 := [unit-resolution #621 #634]: #753
 [unit-resolution #626 #619 #508]: false
 unsat
-391853aefaeecebad29422aff20420b5c8400b71 101 0
+69cd5fda1074c29ecf66dafd109105cee62629d2 101 0
 #2 := false
 #9 := 0::real
 decl f3 :: real
@@ -7974,7 +8039,7 @@
 #120 := [th-lemma]: #119
 [unit-resolution #120 #116 #109 #43]: false
 unsat
-fee0ab8e0ed90b0d56c8dc3103c9526d6f1496af 943 0
+c062eef3c5708d2de57fa6436f78f78380109cb0 943 0
 #2 := false
 #49 := 1::int
 decl f4 :: (-> int int int)
@@ -8918,7 +8983,7 @@
 #1294 := [unit-resolution #1107 #1293 #1239]: #405
 [unit-resolution #1252 #1294 #1292]: false
 unsat
-a36cefa1a79f7b6b132d839263e2dbea9c7e87fc 24 0
+68c699417de116421e825411767435a3c1384b16 24 0
 #2 := false
 #8 := (exists (vars (?v0 int)) false)
 #9 := (not #8)
@@ -8943,7 +9008,7 @@
 #27 := [asserted]: #10
 [mp #27 #43]: false
 unsat
-54fcba387e363cf8083d4867a9793bbccb7a0314 24 0
+6b6a516b5bfeaa4eefcd34f4237f7e12561eee89 24 0
 #2 := false
 #8 := (exists (vars (?v0 real)) false)
 #9 := (not #8)
@@ -8968,13 +9033,13 @@
 #27 := [asserted]: #10
 [mp #27 #43]: false
 unsat
-fb9fab32fe487ed4f4e3d6fe3002d02a0faf856f 1 0
-unsat
-04a6b607d97a19c61cf9fb86541a5de438beb133 1 0
-unsat
-12094d1935a50c8a07214f044f89a779adda7144 1 0
-unsat
-5e524c2f74a70173d25f03f6292e4c1715c27295 67 0
+d6869997502ff0714d93cc35b1ef3122ecda7c88 1 0
+unsat
+95e052f4c9a5732c8ce45aff11ae1af02647de9a 1 0
+unsat
+cfb36ea62266ff4713577d89f992ba4e95f3a037 1 0
+unsat
+7b7950d9e8b1bb67ce337ab127fa685513156901 67 0
 #2 := false
 #9 := 0::int
 #12 := 1::int
@@ -9042,7 +9107,7 @@
 #143 := [trans #141 #80]: #142
 [mp #143 #145]: false
 unsat
-8d9412b39d1e4ff552ff059a2a38b571d1cc91d5 82 0
+a4d28a94dd63cac9469a1696c52b30c687cdf5cb 82 0
 #2 := false
 #9 := (:var 0 int)
 #11 := 0::int
@@ -9125,7 +9190,7 @@
 #35 := [asserted]: #18
 [mp #35 #101]: false
 unsat
-27ab42ad2d8b0d1fd722c36b1b4da113e0100061 78 0
+56bbb4b2f5d821b38f91a3e4872b388583d60377 78 0
 #2 := false
 #9 := (:var 0 int)
 #11 := 2::int
@@ -9204,7 +9269,7 @@
 #36 := [asserted]: #19
 [mp #36 #97]: false
 unsat
-df217f217128f3754a777d8b086332e1f6ca39ed 61 0
+5cabe3217d155dc3acf1647715348ec2dcd4dc81 61 0
 #2 := false
 #13 := (:var 0 int)
 #8 := 2::int
@@ -9266,7 +9331,7 @@
 #35 := [asserted]: #18
 [mp #35 #80]: false
 unsat
-ae3d6219d877e775dfed10c63209e257accf66b7 111 0
+625e23e52edb34e94a66506c3c57ff44e4d017bd 111 0
 #2 := false
 #8 := 2::int
 decl ?v0!1 :: int
@@ -9378,7 +9443,7 @@
 #189 := [th-lemma]: #188
 [unit-resolution #189 #132 #130 #131]: false
 unsat
-13bee6926c3836fd51ee6bc754d5c22e812fc512 89 0
+8f413540fb5f60c0499d83ef3fc732b58abc7a96 89 0
 #2 := false
 #8 := 0::int
 decl ?v0!0 :: int
@@ -9468,7 +9533,7 @@
 #172 := [unit-resolution #157 #95]: #171
 [unit-resolution #172 #170 #167]: false
 unsat
-d8021ae1b4589558d9fd489bf446659dddb6bd92 83 2
+d07c63ee97a8f60d315d90b4b130fd8ac42deedf 83 2
 #2 := false
 #9 := 0::int
 #8 := (:var 0 int)
@@ -9554,7 +9619,7 @@
 unsat
 WARNING: failed to find a pattern for quantifier (quantifier id: k!9)
 
-d2e44415b02dc3e73faa264730b98a3e42a2c4b7 180 2
+9a9269049a0a959c1316104f39491be47908d35f 180 2
 #2 := false
 #16 := 3::int
 #37 := -1::int
@@ -9737,7 +9802,7 @@
 unsat
 WARNING: failed to find a pattern for quantifier (quantifier id: k!9)
 
-4b7d931172988b3d273106901290917cf166502b 68 0
+1ff2984f63665b8540e3fb3ed449f8b35bc4338c 68 0
 #2 := false
 #16 := 1::int
 #13 := (:var 1 int)
@@ -9806,7 +9871,7 @@
 #37 := [asserted]: #20
 [mp #37 #88]: false
 unsat
-3bad73f4a46430e1cd795e36a5d12f24c1d02fca 107 0
+7bf4f68751887bb031fd0b55bde3dba937693da8 107 0
 #2 := false
 #8 := 0::int
 decl ?v1!1 :: int
@@ -9914,7 +9979,7 @@
 #128 := [and-elim #106]: #93
 [th-lemma #128 #129 #130]: false
 unsat
-87d0780ec63c3625f21f826c074cd13be4d62e3f 117 0
+55a31d7583f4f045069bbb513171666d429d1c4b 117 0
 #2 := false
 #8 := 0::int
 decl ?v1!1 :: int
@@ -10032,7 +10097,7 @@
 #193 := [unit-resolution #192 #115]: #103
 [unit-resolution #193 #135]: false
 unsat
-8cf44aadad8c0d87f2f57333fcb342b5ab385732 148 0
+170f84855d9005d40ffde97bc6917d636084a3e6 148 0
 #2 := false
 #149 := (not false)
 #11 := 0::int
@@ -10181,7 +10246,7 @@
 #163 := [mp #131 #162]: #158
 [mp #163 #186]: false
 unsat
-505b296c347b1d80912f4657132db5ad5ac9be4f 67 0
+3d8bba4839380d81383d236278dcf751a8b91e19 67 0
 #2 := false
 #8 := (:var 0 int)
 #9 := (pattern #8)
@@ -10249,9 +10314,9 @@
 #35 := [asserted]: #18
 [mp #35 #85]: false
 unsat
-69b5f9a8c6931a47249060824265e608f534018d 1 0
-unsat
-153386649b53dd5f988fd1bc7b72bcd290f53da9 75 0
+60a76dc7c0f44320c5deeebd42c0e5f535f6bea5 1 0
+unsat
+d9291d10b9f36cd8fdb0de4c1eae205071171c6a 75 0
 #2 := false
 #10 := 1::int
 decl f5 :: int
@@ -10327,7 +10392,7 @@
 #37 := [asserted]: #20
 [mp #37 #91]: false
 unsat
-68a3071b380f0f7c03304499d1f2835f0bf361c3 62 0
+dfe38da181b88ba6b4b62323e9d3a77ba60f80ef 62 0
 #2 := false
 decl f4 :: real
 #10 := f4
@@ -10390,7 +10455,7 @@
 #37 := [asserted]: #20
 [mp #37 #79]: false
 unsat
-b6399504e06b7554863175061a53aa7486cc9086 141 0
+c3458fb64511798cff4b5e9982d22853bfb81cf0 141 0
 #2 := false
 decl f6 :: int
 #13 := f6
@@ -10532,7 +10597,7 @@
 #50 := [asserted]: #33
 [mp #50 #155]: false
 unsat
-161d4df3b39a91bf1bc07402c22e85ffba8398b2 252 0
+043a836287de542d8a809f5adc4d78a4d49e5f62 252 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -10785,7 +10850,7 @@
 #544 := [unit-resolution #537 #456]: #562
 [th-lemma #460 #544 #542 #551]: false
 unsat
-2eacc8bb83fecb0fe81d96fc93fc64a7d11a9e4d 227 0
+ce1ab0c618fcab19a8a2dc122408577fac0c71ab 227 0
 #2 := false
 #27 := 3::int
 decl f4 :: (-> S2 int)
@@ -11013,7 +11078,7 @@
 #607 := [unit-resolution #602 #605]: #632
 [th-lemma #161 #607 #160]: false
 unsat
-61d261a95e60947f23f698475332084ad9cfd094 367 0
+bf1e0ad2495acc888e0de7cd990a24e2435f945e 367 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -11381,7 +11446,7 @@
 #461 := [th-lemma]: #460
 [unit-resolution #461 #469 #457]: false
 unsat
-ddf1adc32377020a68931e791f8d3bc93a479493 299 0
+fe37ed862726b19938d1bae1268f8dba5e58a394 299 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -11681,7 +11746,7 @@
 #603 := [unit-resolution #617 #615]: #685
 [th-lemma #625 #190 #603 #630]: false
 unsat
-044639db28fa915f30475668c634e5237efaa068 458 0
+2addf67c013d33ae3428e2558f560bbddeccb7e2 458 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -12140,7 +12205,7 @@
 #355 := [unit-resolution #374 #372]: #373
 [unit-resolution #355 #328]: false
 unsat
-35a0968e29848376b1a21560a270f15f6d19aed4 161 0
+419554e7e67067e10dc5e408bab61ba3d2f52467 161 0
 #2 := false
 #13 := 0::int
 decl f5 :: int
@@ -12302,7 +12367,7 @@
 #366 := [unit-resolution #644 #660]: #652
 [th-lemma #661 #366 #266]: false
 unsat
-30478456884b028b09fee79763641a90a5f3dc95 604 0
+700cb6e25916af8647e57cef66cccee0c6fccb9b 604 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -12907,379 +12972,379 @@
 #1005 := [unit-resolution #599 #859]: #455
 [unit-resolution #1005 #1004 #994]: false
 unsat
-b7294e8991937b94c2eeb87ee3638d9d5f007d01 61 0
-#2 := false
-decl f7 :: S3
-#12 := f7
-decl f5 :: S3
-#8 := f5
-#14 := (= f5 f7)
-decl f3 :: (-> S2 S3)
-decl f4 :: (-> S3 S4 S2)
-decl f6 :: S4
-#9 := f6
-#10 := (f4 f5 f6)
-#11 := (f3 #10)
-#13 := (= #11 f7)
-#49 := (not #13)
-#50 := (or #49 #14)
-#53 := (not #50)
-#15 := (implies #13 #14)
-#16 := (not #15)
-#54 := (iff #16 #53)
-#51 := (iff #15 #50)
-#52 := [rewrite]: #51
-#55 := [monotonicity #52]: #54
-#48 := [asserted]: #16
-#58 := [mp #48 #55]: #53
-#56 := [not-or-elim #58]: #13
-#157 := (= f5 #11)
-#18 := (:var 0 S4)
-#17 := (:var 1 S3)
-#19 := (f4 #17 #18)
-#575 := (pattern #19)
-#20 := (f3 #19)
-#61 := (= #17 #20)
-#576 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #575) #61)
-#64 := (forall (vars (?v0 S3) (?v1 S4)) #61)
-#579 := (iff #64 #576)
-#577 := (iff #61 #61)
-#578 := [refl]: #577
-#580 := [quant-intro #578]: #579
-#99 := (~ #64 #64)
-#97 := (~ #61 #61)
-#98 := [refl]: #97
-#100 := [nnf-pos #98]: #99
-#21 := (= #20 #17)
+368d810de4ec653cd293bf439b046eb86d97318f 61 0
+#2 := false
+decl f8 :: S3
+#27 := f8
+decl f6 :: S3
+#23 := f6
+#29 := (= f6 f8)
+decl f4 :: (-> S2 S3)
+decl f3 :: (-> S3 S4 S2)
+decl f7 :: S4
+#24 := f7
+#25 := (f3 f6 f7)
+#26 := (f4 #25)
+#28 := (= #26 f8)
+#72 := (not #28)
+#74 := (or #72 #29)
+#77 := (not #74)
+#30 := (implies #28 #29)
+#31 := (not #30)
+#78 := (iff #31 #77)
+#75 := (iff #30 #74)
+#76 := [rewrite]: #75
+#79 := [monotonicity #76]: #78
+#71 := [asserted]: #31
+#82 := [mp #71 #79]: #77
+#80 := [not-or-elim #82]: #28
+#159 := (= f6 #26)
+#15 := (:var 0 S4)
+#14 := (:var 1 S3)
+#16 := (f3 #14 #15)
+#583 := (pattern #16)
+#20 := (f4 #16)
+#64 := (= #14 #20)
+#590 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #583) #64)
+#68 := (forall (vars (?v0 S3) (?v1 S4)) #64)
+#593 := (iff #68 #590)
+#591 := (iff #64 #64)
+#592 := [refl]: #591
+#594 := [quant-intro #592]: #593
+#89 := (~ #68 #68)
+#103 := (~ #64 #64)
+#104 := [refl]: #103
+#90 := [nnf-pos #104]: #89
+#21 := (= #20 #14)
 #22 := (forall (vars (?v0 S3) (?v1 S4)) #21)
-#65 := (iff #22 #64)
-#62 := (iff #21 #61)
-#63 := [rewrite]: #62
-#66 := [quant-intro #63]: #65
-#60 := [asserted]: #22
-#69 := [mp #60 #66]: #64
-#89 := [mp~ #69 #100]: #64
-#581 := [mp #89 #580]: #576
-#245 := (not #576)
-#159 := (or #245 #157)
-#246 := [quant-inst]: #159
-#247 := [unit-resolution #246 #581]: #157
-#251 := [trans #247 #56]: #14
-#57 := (not #14)
-#59 := [not-or-elim #58]: #57
-[unit-resolution #59 #251]: false
-unsat
-0eb592b66cd32b0b3c146dc31bf114d3abca5113 116 0
-#2 := false
-decl f10 :: (-> S5 S3)
-decl f7 :: S5
-#13 := f7
-#18 := (f10 f7)
-decl f9 :: (-> S2 S3)
-decl f3 :: S2
-#8 := f3
-#17 := (f9 f3)
-#19 := (= #17 #18)
-decl f8 :: (-> S4 S3 S5)
-decl f5 :: S3
-#9 := f5
-decl f6 :: S4
-#10 := f6
-#14 := (f8 f6 f5)
-#219 := (f10 #14)
-#275 := (= #219 #18)
-#273 := (= #18 #219)
-#15 := (= f7 #14)
-decl f4 :: (-> S3 S4 S2)
-#11 := (f4 f5 f6)
-#12 := (= f3 #11)
-#16 := (and #12 #15)
-#69 := (not #16)
-#70 := (or #69 #19)
-#73 := (not #70)
-#20 := (implies #16 #19)
-#21 := (not #20)
-#74 := (iff #21 #73)
-#71 := (iff #20 #70)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#68 := [asserted]: #21
-#78 := [mp #68 #75]: #73
-#76 := [not-or-elim #78]: #16
-#79 := [and-elim #76]: #15
-#274 := [monotonicity #79]: #273
+#69 := (iff #22 #68)
+#66 := (iff #21 #64)
+#67 := [rewrite]: #66
+#70 := [quant-intro #67]: #69
+#63 := [asserted]: #22
+#73 := [mp #63 #70]: #68
+#105 := [mp~ #73 #90]: #68
+#595 := [mp #105 #594]: #590
+#230 := (not #590)
+#567 := (or #230 #159)
+#569 := [quant-inst]: #567
+#249 := [unit-resolution #569 #595]: #159
+#251 := [trans #249 #80]: #29
+#81 := (not #29)
+#83 := [not-or-elim #82]: #81
+[unit-resolution #83 #251]: false
+unsat
+640737c0605c299e543c64374ff230f778c733c6 116 0
+#2 := false
+decl f5 :: (-> S2 S4)
+decl f12 :: S2
+#43 := f12
+#48 := (f5 f12)
+decl f7 :: (-> S5 S4)
+decl f9 :: S5
+#38 := f9
+#47 := (f7 f9)
+#49 := (= #47 #48)
+decl f3 :: (-> S3 S4 S2)
+decl f10 :: S4
+#39 := f10
+decl f11 :: S3
+#40 := f11
+#44 := (f3 f11 f10)
+#218 := (f5 #44)
+#275 := (= #218 #48)
+#273 := (= #48 #218)
+#45 := (= f12 #44)
+decl f6 :: (-> S4 S3 S5)
+#41 := (f6 f10 f11)
+#42 := (= f9 #41)
+#46 := (and #42 #45)
+#116 := (not #46)
+#118 := (or #116 #49)
+#121 := (not #118)
+#50 := (implies #46 #49)
+#51 := (not #50)
+#122 := (iff #51 #121)
+#119 := (iff #50 #118)
+#120 := [rewrite]: #119
+#123 := [monotonicity #120]: #122
+#115 := [asserted]: #51
+#126 := [mp #115 #123]: #121
+#124 := [not-or-elim #126]: #46
+#127 := [and-elim #124]: #45
+#274 := [monotonicity #127]: #273
 #613 := [symm #274]: #275
-#616 := (= #17 #219)
-#306 := (= f5 #219)
-#23 := (:var 0 S3)
-#22 := (:var 1 S4)
-#24 := (f8 #22 #23)
-#636 := (pattern #24)
-#34 := (f10 #24)
-#98 := (= #23 #34)
-#650 := (forall (vars (?v0 S4) (?v1 S3)) (:pat #636) #98)
-#102 := (forall (vars (?v0 S4) (?v1 S3)) #98)
-#653 := (iff #102 #650)
-#651 := (iff #98 #98)
-#652 := [refl]: #651
-#654 := [quant-intro #652]: #653
-#141 := (~ #102 #102)
-#133 := (~ #98 #98)
-#134 := [refl]: #133
-#142 := [nnf-pos #134]: #141
-#35 := (= #34 #23)
-#36 := (forall (vars (?v0 S4) (?v1 S3)) #35)
-#103 := (iff #36 #102)
-#100 := (iff #35 #98)
-#101 := [rewrite]: #100
-#104 := [quant-intro #101]: #103
-#97 := [asserted]: #36
-#107 := [mp #97 #104]: #102
-#132 := [mp~ #107 #142]: #102
-#655 := [mp #132 #654]: #650
-#238 := (not #650)
-#311 := (or #238 #306)
-#308 := [quant-inst]: #311
-#625 := [unit-resolution #308 #655]: #306
-#614 := (= #17 f5)
-#309 := (f9 #11)
-#611 := (= #309 f5)
-#310 := (= f5 #309)
-#29 := (:var 0 S4)
-#28 := (:var 1 S3)
-#30 := (f4 #28 #29)
-#643 := (pattern #30)
-#31 := (f9 #30)
-#90 := (= #28 #31)
-#644 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #643) #90)
-#94 := (forall (vars (?v0 S3) (?v1 S4)) #90)
-#647 := (iff #94 #644)
-#645 := (iff #90 #90)
-#646 := [refl]: #645
-#648 := [quant-intro #646]: #647
-#139 := (~ #94 #94)
-#138 := (~ #90 #90)
-#135 := [refl]: #138
-#140 := [nnf-pos #135]: #139
-#32 := (= #31 #28)
-#33 := (forall (vars (?v0 S3) (?v1 S4)) #32)
-#95 := (iff #33 #94)
-#92 := (iff #32 #90)
-#93 := [rewrite]: #92
-#96 := [quant-intro #93]: #95
-#89 := [asserted]: #33
-#99 := [mp #89 #96]: #94
-#136 := [mp~ #99 #140]: #94
-#649 := [mp #136 #648]: #644
-#628 := (not #644)
-#630 := (or #628 #310)
-#285 := [quant-inst]: #630
-#283 := [unit-resolution #285 #649]: #310
+#616 := (= #47 #218)
+#308 := (= f10 #218)
+#21 := (:var 0 S4)
+#20 := (:var 1 S3)
+#22 := (f3 #20 #21)
+#652 := (pattern #22)
+#23 := (f5 #22)
+#84 := (= #21 #23)
+#653 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #652) #84)
+#88 := (forall (vars (?v0 S3) (?v1 S4)) #84)
+#656 := (iff #88 #653)
+#654 := (iff #84 #84)
+#655 := [refl]: #654
+#657 := [quant-intro #655]: #656
+#135 := (~ #88 #88)
+#157 := (~ #84 #84)
+#158 := [refl]: #157
+#136 := [nnf-pos #158]: #135
+#24 := (= #23 #21)
+#25 := (forall (vars (?v0 S3) (?v1 S4)) #24)
+#89 := (iff #25 #88)
+#86 := (iff #24 #84)
+#87 := [rewrite]: #86
+#90 := [quant-intro #87]: #89
+#83 := [asserted]: #25
+#93 := [mp #83 #90]: #88
+#159 := [mp~ #93 #136]: #88
+#658 := [mp #159 #657]: #653
+#417 := (not #653)
+#624 := (or #417 #308)
+#296 := [quant-inst]: #624
+#634 := [unit-resolution #296 #658]: #308
+#614 := (= #47 f10)
+#307 := (f7 #41)
+#611 := (= #307 f10)
+#297 := (= f10 #307)
+#27 := (:var 0 S3)
+#26 := (:var 1 S4)
+#28 := (f6 #26 #27)
+#659 := (pattern #28)
+#35 := (f7 #28)
+#108 := (= #26 #35)
+#672 := (forall (vars (?v0 S4) (?v1 S3)) (:pat #659) #108)
+#112 := (forall (vars (?v0 S4) (?v1 S3)) #108)
+#675 := (iff #112 #672)
+#673 := (iff #108 #108)
+#674 := [refl]: #673
+#676 := [quant-intro #674]: #675
+#141 := (~ #112 #112)
+#166 := (~ #108 #108)
+#167 := [refl]: #166
+#142 := [nnf-pos #167]: #141
+#36 := (= #35 #26)
+#37 := (forall (vars (?v0 S4) (?v1 S3)) #36)
+#113 := (iff #37 #112)
+#110 := (iff #36 #108)
+#111 := [rewrite]: #110
+#114 := [quant-intro #111]: #113
+#107 := [asserted]: #37
+#117 := [mp #107 #114]: #112
+#168 := [mp~ #117 #142]: #112
+#677 := [mp #168 #676]: #672
+#288 := (not #672)
+#626 := (or #288 #297)
+#284 := [quant-inst]: #626
+#283 := [unit-resolution #284 #677]: #297
 #272 := [symm #283]: #611
-#627 := (= #17 #309)
-#77 := [and-elim #76]: #12
-#268 := [monotonicity #77]: #627
+#627 := (= #47 #307)
+#125 := [and-elim #124]: #42
+#268 := [monotonicity #125]: #627
 #615 := [trans #268 #272]: #614
-#617 := [trans #615 #625]: #616
-#612 := [trans #617 #613]: #19
-#80 := (not #19)
-#81 := [not-or-elim #78]: #80
-[unit-resolution #81 #612]: false
-unsat
-919519ba12504066a1609e5f376b9f35de340ebd 192 0
-#2 := false
-decl f6 :: (-> S3 S2 S4)
-decl f3 :: S2
-#8 := f3
-decl f8 :: S3
-#16 := f8
-#22 := (f6 f8 f3)
-decl f7 :: (-> S3 S2 S4 S3)
+#617 := [trans #615 #634]: #616
+#612 := [trans #617 #613]: #49
+#128 := (not #49)
+#129 := [not-or-elim #126]: #128
+[unit-resolution #129 #612]: false
+unsat
+78432c0558d849a6a565c450d2bc6b66780548c7 192 0
+#2 := false
+decl f3 :: (-> S2 S3 S4)
+decl f5 :: S3
+#26 := f5
+decl f8 :: S2
+#34 := f8
+#40 := (f3 f8 f5)
+decl f4 :: (-> S2 S3 S4 S2)
 decl f10 :: S4
-#19 := f10
-decl f5 :: S2
-#12 := f5
+#37 := f10
+decl f7 :: S3
+#30 := f7
 decl f9 :: S4
-#17 := f9
-decl f4 :: S2
-#9 := f4
-#18 := (f7 f8 f4 f9)
-#20 := (f7 #18 f5 f10)
-#21 := (f6 #20 f3)
-#23 := (= #21 #22)
-#173 := (f6 #18 f4)
-#570 := (f7 f8 f4 #173)
-#538 := (f6 #570 f3)
-#539 := (= #538 #22)
-#542 := (= #22 #538)
-#533 := (= #173 #538)
-#10 := (= f3 f4)
-#374 := (ite #10 #533 #542)
-#37 := (:var 0 S2)
-#35 := (:var 1 S4)
-#34 := (:var 2 S2)
-#33 := (:var 3 S3)
-#36 := (f7 #33 #34 #35)
-#38 := (f6 #36 #37)
-#599 := (pattern #38)
-#40 := (f6 #33 #37)
-#100 := (= #38 #40)
-#99 := (= #35 #38)
-#82 := (= #34 #37)
-#107 := (ite #82 #99 #100)
-#600 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) (:pat #599) #107)
-#95 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) #107)
-#603 := (iff #95 #600)
-#601 := (iff #107 #107)
-#602 := [refl]: #601
-#604 := [quant-intro #602]: #603
-#86 := (ite #82 #35 #40)
-#89 := (= #38 #86)
-#92 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) #89)
-#113 := (iff #92 #95)
-#108 := (iff #89 #107)
-#98 := [rewrite]: #108
-#114 := [quant-intro #98]: #113
-#105 := (~ #92 #92)
-#104 := (~ #89 #89)
-#101 := [refl]: #104
-#106 := [nnf-pos #101]: #105
-#39 := (= #37 #34)
-#41 := (ite #39 #35 #40)
-#42 := (= #38 #41)
-#43 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) #42)
-#93 := (iff #43 #92)
-#90 := (iff #42 #89)
-#87 := (= #41 #86)
-#84 := (iff #39 #82)
-#85 := [rewrite]: #84
-#88 := [monotonicity #85]: #87
-#91 := [monotonicity #88]: #90
-#94 := [quant-intro #91]: #93
-#81 := [asserted]: #43
-#97 := [mp #81 #94]: #92
-#102 := [mp~ #97 #106]: #92
-#115 := [mp #102 #114]: #95
-#605 := [mp #115 #604]: #600
-#251 := (not #600)
-#530 := (or #251 #374)
-#534 := (= f4 f3)
-#540 := (ite #534 #533 #539)
-#531 := (or #251 #540)
-#532 := (iff #531 #530)
-#415 := (iff #530 #530)
-#416 := [rewrite]: #415
-#527 := (iff #540 #374)
-#371 := (iff #539 #542)
-#373 := [rewrite]: #371
-#541 := (iff #534 #10)
-#535 := [rewrite]: #541
-#528 := [monotonicity #535 #373]: #527
-#414 := [monotonicity #528]: #532
-#375 := [trans #414 #416]: #532
-#529 := [quant-inst]: #531
-#523 := [mp #529 #375]: #530
-#526 := [unit-resolution #523 #605]: #374
-#425 := (not #374)
-#513 := (or #425 #542)
-#11 := (not #10)
-#13 := (= f3 f5)
-#14 := (not #13)
-#15 := (and #11 #14)
-#61 := (not #15)
-#62 := (or #61 #23)
-#65 := (not #62)
-#24 := (implies #15 #23)
-#25 := (not #24)
-#66 := (iff #25 #65)
-#63 := (iff #24 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#60 := [asserted]: #25
-#70 := [mp #60 #67]: #65
-#68 := [not-or-elim #70]: #15
-#69 := [and-elim #68]: #11
-#524 := (or #425 #10 #542)
-#409 := [def-axiom]: #524
-#515 := [unit-resolution #409 #69]: #513
-#507 := [unit-resolution #515 #526]: #542
-#509 := [symm #507]: #539
-#510 := (= #21 #538)
-#264 := (f6 #18 f3)
-#519 := (= #264 #538)
-#518 := (= #538 #264)
-#525 := (= #570 #18)
-#431 := (= #173 f9)
-#260 := (= f9 #173)
-#28 := (:var 0 S4)
-#27 := (:var 1 S2)
-#26 := (:var 2 S3)
-#29 := (f7 #26 #27 #28)
-#591 := (pattern #29)
-#30 := (f6 #29 #27)
-#75 := (= #28 #30)
-#593 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) (:pat #591) #75)
-#78 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #75)
-#592 := (iff #78 #593)
-#595 := (iff #593 #593)
-#596 := [rewrite]: #595
-#594 := [rewrite]: #592
-#597 := [trans #594 #596]: #592
-#111 := (~ #78 #78)
-#109 := (~ #75 #75)
+#35 := f9
+decl f6 :: S3
+#27 := f6
+#36 := (f4 f8 f6 f9)
+#38 := (f4 #36 f7 f10)
+#39 := (f3 #38 f5)
+#41 := (= #39 #40)
+#239 := (f3 #36 f6)
+#230 := (f4 f8 f6 #239)
+#568 := (f3 #230 f5)
+#571 := (= #568 #40)
+#576 := (= #40 #568)
+#572 := (= #239 #568)
+#28 := (= f5 f6)
+#577 := (ite #28 #572 #576)
+#12 := (:var 0 S3)
+#10 := (:var 1 S4)
+#9 := (:var 2 S3)
+#8 := (:var 3 S2)
+#11 := (f4 #8 #9 #10)
+#13 := (f3 #11 #12)
+#591 := (pattern #13)
+#15 := (f3 #8 #12)
+#116 := (= #13 #15)
+#115 := (= #10 #13)
+#61 := (= #9 #12)
+#101 := (ite #61 #115 #116)
+#592 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #591) #101)
+#108 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #101)
+#595 := (iff #108 #592)
+#593 := (iff #101 #101)
+#594 := [refl]: #593
+#596 := [quant-intro #594]: #595
+#64 := (ite #61 #10 #15)
+#67 := (= #13 #64)
+#70 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #67)
+#105 := (iff #70 #108)
+#102 := (iff #67 #101)
+#107 := [rewrite]: #102
+#106 := [quant-intro #107]: #105
+#111 := (~ #70 #70)
+#109 := (~ #67 #67)
 #110 := [refl]: #109
 #112 := [nnf-pos #110]: #111
-#31 := (= #30 #28)
-#32 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #31)
-#79 := (iff #32 #78)
-#76 := (iff #31 #75)
+#14 := (= #12 #9)
+#16 := (ite #14 #10 #15)
+#17 := (= #13 #16)
+#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17)
+#71 := (iff #18 #70)
+#68 := (iff #17 #67)
+#65 := (= #16 #64)
+#62 := (iff #14 #61)
+#63 := [rewrite]: #62
+#66 := [monotonicity #63]: #65
+#69 := [monotonicity #66]: #68
+#72 := [quant-intro #69]: #71
+#60 := [asserted]: #18
+#75 := [mp #60 #72]: #70
+#98 := [mp~ #75 #112]: #70
+#103 := [mp #98 #106]: #108
+#597 := [mp #103 #596]: #592
+#266 := (not #592)
+#564 := (or #266 #577)
+#567 := (= f6 f5)
+#573 := (ite #567 #572 #571)
+#565 := (or #266 #573)
+#287 := (iff #565 #564)
+#289 := (iff #564 #564)
+#275 := [rewrite]: #289
+#575 := (iff #573 #577)
+#214 := (iff #571 #576)
+#215 := [rewrite]: #214
+#209 := (iff #567 #28)
+#574 := [rewrite]: #209
+#578 := [monotonicity #574 #215]: #575
+#288 := [monotonicity #578]: #287
+#290 := [trans #288 #275]: #287
+#271 := [quant-inst]: #565
+#181 := [mp #271 #290]: #564
+#526 := [unit-resolution #181 #597]: #577
+#560 := (not #577)
+#513 := (or #560 #576)
+#29 := (not #28)
+#31 := (= f5 f7)
+#32 := (not #31)
+#33 := (and #29 #32)
+#82 := (not #33)
+#84 := (or #82 #41)
+#87 := (not #84)
+#42 := (implies #33 #41)
+#43 := (not #42)
+#88 := (iff #43 #87)
+#85 := (iff #42 #84)
+#86 := [rewrite]: #85
+#89 := [monotonicity #86]: #88
+#81 := [asserted]: #43
+#92 := [mp #81 #89]: #87
+#90 := [not-or-elim #92]: #33
+#91 := [and-elim #90]: #29
+#284 := (or #560 #28 #576)
+#558 := [def-axiom]: #284
+#515 := [unit-resolution #558 #91]: #513
+#507 := [unit-resolution #515 #526]: #576
+#509 := [symm #507]: #571
+#510 := (= #39 #568)
+#173 := (f3 #36 f5)
+#519 := (= #173 #568)
+#518 := (= #568 #173)
+#525 := (= #230 #36)
+#431 := (= #239 f9)
+#582 := (= f9 #239)
+#21 := (:var 0 S4)
+#20 := (:var 1 S3)
+#19 := (:var 2 S2)
+#22 := (f4 #19 #20 #21)
+#598 := (pattern #22)
+#23 := (f3 #22 #20)
+#74 := (= #21 #23)
+#600 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #598) #74)
+#78 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #74)
+#599 := (iff #78 #600)
+#602 := (iff #600 #600)
+#603 := [rewrite]: #602
+#601 := [rewrite]: #599
+#604 := [trans #601 #603]: #599
+#99 := (~ #78 #78)
+#96 := (~ #74 #74)
+#113 := [refl]: #96
+#100 := [nnf-pos #113]: #99
+#24 := (= #23 #21)
+#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #24)
+#79 := (iff #25 #78)
+#76 := (iff #24 #74)
 #77 := [rewrite]: #76
 #80 := [quant-intro #77]: #79
-#74 := [asserted]: #32
-#83 := [mp #74 #80]: #78
-#103 := [mp~ #83 #112]: #78
-#598 := [mp #103 #597]: #593
-#175 := (not #593)
-#262 := (or #175 #260)
-#253 := [quant-inst]: #262
-#430 := [unit-resolution #253 #598]: #260
+#73 := [asserted]: #25
+#83 := [mp #73 #80]: #78
+#114 := [mp~ #83 #100]: #78
+#605 := [mp #114 #604]: #600
+#227 := (not #600)
+#228 := (or #227 #582)
+#229 := [quant-inst]: #228
+#430 := [unit-resolution #229 #605]: #582
 #432 := [symm #430]: #431
 #522 := [monotonicity #432]: #525
 #514 := [monotonicity #522]: #518
 #508 := [symm #514]: #519
-#265 := (= #21 #264)
-#263 := (= f10 #21)
-#240 := (ite #13 #263 #265)
-#252 := (or #251 #240)
-#267 := (= f5 f3)
-#246 := (ite #267 #263 #265)
-#586 := (or #251 #246)
-#588 := (iff #586 #252)
-#584 := (iff #252 #252)
-#590 := [rewrite]: #584
-#372 := (iff #246 #240)
-#583 := (iff #267 #13)
-#585 := [rewrite]: #583
-#579 := [monotonicity #585]: #372
-#589 := [monotonicity #579]: #588
-#580 := [trans #589 #590]: #588
-#587 := [quant-inst]: #586
-#238 := [mp #587 #580]: #252
-#504 := [unit-resolution #238 #605]: #240
-#243 := (not #240)
-#506 := (or #243 #265)
-#71 := [and-elim #68]: #14
-#582 := (or #243 #13 #265)
-#223 := [def-axiom]: #582
-#516 := [unit-resolution #223 #71]: #506
-#517 := [unit-resolution #516 #504]: #265
+#260 := (= #39 #173)
+#174 := (= f10 #39)
+#264 := (ite #31 #174 #260)
+#263 := (or #266 #264)
+#261 := (= f7 f5)
+#175 := (ite #261 #174 #260)
+#267 := (or #266 #175)
+#583 := (iff #267 #263)
+#240 := (iff #263 #263)
+#372 := [rewrite]: #240
+#265 := (iff #175 #264)
+#262 := (iff #261 #31)
+#253 := [rewrite]: #262
+#193 := [monotonicity #253]: #265
+#585 := [monotonicity #193]: #583
+#579 := [trans #585 #372]: #583
+#246 := [quant-inst]: #267
+#251 := [mp #246 #579]: #263
+#504 := [unit-resolution #251 #597]: #264
+#252 := (not #264)
+#506 := (or #252 #260)
+#93 := [and-elim #90]: #32
+#588 := (or #252 #31 #260)
+#589 := [def-axiom]: #588
+#516 := [unit-resolution #589 #93]: #506
+#517 := [unit-resolution #516 #504]: #260
 #511 := [trans #517 #508]: #510
-#505 := [trans #511 #509]: #23
-#72 := (not #23)
-#73 := [not-or-elim #70]: #72
-[unit-resolution #73 #505]: false
-unsat
-0e78b14dde5af897ffb16aaeab92efe89c61b5d1 80 0
+#505 := [trans #511 #509]: #41
+#94 := (not #41)
+#95 := [not-or-elim #92]: #94
+[unit-resolution #95 #505]: false
+unsat
+234820d946e273acfa4a19ddd440fa7b662b0b4a 80 0
 #2 := false
 decl f6 :: (-> S2 S3 S1)
 decl f5 :: S3
@@ -13360,234 +13425,252 @@
 #75 := [not-or-elim #69]: #74
 [mp #75 #96]: false
 unsat
-df98f2515329e244654c3b6826b0db995088c21e 128 0
+cfa5239afba9e02efaba4f8540ed9ac0fc0e8c77 146 0
 #2 := false
 decl f3 :: (-> S2 S2)
-#15 := (:var 0 S2)
-#16 := (f3 #15)
-#577 := (pattern #16)
-#55 := (= #15 #16)
-#578 := (forall (vars (?v0 S2)) (:pat #577) #55)
-#59 := (forall (vars (?v0 S2)) #55)
-#581 := (iff #59 #578)
-#579 := (iff #55 #55)
-#580 := [refl]: #579
-#582 := [quant-intro #580]: #581
-#88 := (~ #59 #59)
-#86 := (~ #55 #55)
-#87 := [refl]: #86
-#89 := [nnf-pos #87]: #88
-#17 := (= #16 #15)
-#18 := (forall (vars (?v0 S2)) #17)
-#60 := (iff #18 #59)
-#57 := (iff #17 #55)
-#58 := [rewrite]: #57
-#61 := [quant-intro #58]: #60
-#54 := [asserted]: #18
-#64 := [mp #54 #61]: #59
-#80 := [mp~ #64 #89]: #59
-#583 := [mp #80 #582]: #578
-decl f4 :: S2
-#8 := f4
-#9 := (f3 f4)
-#42 := (= f4 #9)
-#90 := (not #42)
-decl f5 :: (-> S1 S1)
+decl f5 :: (-> int S2)
+decl f6 :: (-> int int)
+decl f7 :: int
+#18 := f7
+#19 := (f6 f7)
+#20 := (f6 #19)
+#21 := (f5 #20)
+#22 := (f3 #21)
+#67 := (= #21 #22)
+#106 := (not #67)
+decl f4 :: (-> S1 S1)
 decl f1 :: S1
 #4 := f1
-#11 := (f5 f1)
-#45 := (= f1 #11)
-#19 := (:var 0 S1)
-#20 := (f5 #19)
-#584 := (pattern #20)
-#67 := (= f1 #19)
-#63 := (= f1 #20)
-#70 := (iff #63 #67)
-#585 := (forall (vars (?v0 S1)) (:pat #584) #70)
-#73 := (forall (vars (?v0 S1)) #70)
-#588 := (iff #73 #585)
-#586 := (iff #70 #70)
-#587 := [refl]: #586
-#589 := [quant-intro #587]: #588
-#82 := (~ #73 #73)
-#81 := (~ #70 #70)
-#79 := [refl]: #81
-#83 := [nnf-pos #79]: #82
-#22 := (= #19 f1)
-#21 := (= #20 f1)
-#23 := (iff #21 #22)
-#24 := (forall (vars (?v0 S1)) #23)
-#74 := (iff #24 #73)
-#71 := (iff #23 #70)
-#68 := (iff #22 #67)
-#69 := [rewrite]: #68
-#65 := (iff #21 #63)
-#66 := [rewrite]: #65
-#72 := [monotonicity #66 #69]: #71
-#75 := [quant-intro #72]: #74
-#62 := [asserted]: #24
-#78 := [mp #62 #75]: #73
-#76 := [mp~ #78 #83]: #73
-#590 := [mp #76 #589]: #585
-#91 := (not #45)
-#572 := [hypothesis]: #91
-#249 := (not #585)
-#253 := (or #249 #45)
-#159 := (= f1 f1)
-#246 := (iff #45 #159)
-#232 := (or #249 #246)
-#571 := (iff #232 #253)
-#358 := (iff #253 #253)
-#565 := [rewrite]: #358
-#179 := (iff #246 #45)
+#73 := (f4 f1)
+#79 := (= f1 #73)
+#107 := (not #79)
+#586 := [hypothesis]: #107
+#12 := (:var 0 S1)
+#13 := (f4 #12)
+#598 := (pattern #13)
+#57 := (= f1 #12)
+#53 := (= f1 #13)
+#60 := (iff #53 #57)
+#599 := (forall (vars (?v0 S1)) (:pat #598) #60)
+#63 := (forall (vars (?v0 S1)) #60)
+#602 := (iff #63 #599)
+#600 := (iff #60 #60)
+#601 := [refl]: #600
+#603 := [quant-intro #601]: #602
+#94 := (~ #63 #63)
+#90 := (~ #60 #60)
+#104 := [refl]: #90
+#95 := [nnf-pos #104]: #94
+#15 := (= #12 f1)
+#14 := (= #13 f1)
+#16 := (iff #14 #15)
+#17 := (forall (vars (?v0 S1)) #16)
+#64 := (iff #17 #63)
+#61 := (iff #16 #60)
+#58 := (iff #15 #57)
+#59 := [rewrite]: #58
+#55 := (iff #14 #53)
+#56 := [rewrite]: #55
+#62 := [monotonicity #56 #59]: #61
+#65 := [quant-intro #62]: #64
+#52 := [asserted]: #17
+#68 := [mp #52 #65]: #63
+#105 := [mp~ #68 #95]: #63
+#604 := [mp #105 #603]: #599
+#263 := (not #599)
+#267 := (or #263 #79)
+#173 := (= f1 f1)
+#260 := (iff #79 #173)
+#246 := (or #263 #260)
+#585 := (iff #246 #267)
+#372 := (iff #267 #267)
+#579 := [rewrite]: #372
+#193 := (iff #260 #79)
 #1 := true
-#161 := (iff #45 true)
-#250 := (iff #161 #45)
-#251 := [rewrite]: #250
-#248 := (iff #246 #161)
-#160 := (iff #159 true)
-#247 := [rewrite]: #160
-#239 := [monotonicity #247]: #248
-#252 := [trans #239 #251]: #179
-#226 := [monotonicity #252]: #571
-#237 := [trans #226 #565]: #571
-#569 := [quant-inst]: #232
-#238 := [mp #569 #237]: #253
-#573 := [unit-resolution #238 #572 #590]: false
-#574 := [lemma #573]: #45
-#84 := (or #90 #91)
-#48 := (and #42 #45)
-#51 := (not #48)
-#99 := (iff #51 #84)
-#85 := (not #84)
-#94 := (not #85)
-#97 := (iff #94 #84)
-#98 := [rewrite]: #97
-#95 := (iff #51 #94)
-#92 := (iff #48 #85)
-#93 := [rewrite]: #92
-#96 := [monotonicity #93]: #95
-#100 := [trans #96 #98]: #99
-#12 := (= #11 f1)
-#10 := (= #9 f4)
-#13 := (and #10 #12)
-#14 := (not #13)
-#52 := (iff #14 #51)
-#49 := (iff #13 #48)
-#46 := (iff #12 #45)
-#47 := [rewrite]: #46
-#43 := (iff #10 #42)
-#44 := [rewrite]: #43
-#50 := [monotonicity #44 #47]: #49
-#53 := [monotonicity #50]: #52
-#41 := [asserted]: #14
-#56 := [mp #41 #53]: #51
-#101 := [mp #56 #100]: #84
-#575 := [unit-resolution #101 #574]: #90
-#576 := (not #578)
-#566 := (or #576 #42)
-#224 := [quant-inst]: #566
-[unit-resolution #224 #575 #583]: false
-unsat
-be52fda02d5daa6359d2f1d2bccf2f909cea5a49 469 0
+#175 := (iff #79 true)
+#264 := (iff #175 #79)
+#265 := [rewrite]: #264
+#262 := (iff #260 #175)
+#174 := (iff #173 true)
+#261 := [rewrite]: #174
+#253 := [monotonicity #261]: #262
+#266 := [trans #253 #265]: #193
+#240 := [monotonicity #266]: #585
+#251 := [trans #240 #579]: #585
+#583 := [quant-inst]: #246
+#252 := [mp #583 #251]: #267
+#587 := [unit-resolution #252 #604 #586]: false
+#588 := [lemma #587]: #79
+#96 := (or #106 #107)
+#84 := (and #67 #79)
+#87 := (not #84)
+#113 := (iff #87 #96)
+#97 := (not #96)
+#108 := (not #97)
+#111 := (iff #108 #96)
+#112 := [rewrite]: #111
+#109 := (iff #87 #108)
+#98 := (iff #84 #97)
+#99 := [rewrite]: #98
+#110 := [monotonicity #99]: #109
+#114 := [trans #110 #112]: #113
+decl f2 :: S1
+#5 := f2
+#24 := (ite true f1 f2)
+#25 := (f4 #24)
+#26 := (= #25 f1)
+#23 := (= #22 #21)
+#27 := (and #23 #26)
+#28 := (not #27)
+#88 := (iff #28 #87)
+#85 := (iff #27 #84)
+#82 := (iff #26 #79)
+#76 := (= #73 f1)
+#80 := (iff #76 #79)
+#81 := [rewrite]: #80
+#77 := (iff #26 #76)
+#74 := (= #25 #73)
+#71 := (= #24 f1)
+#72 := [rewrite]: #71
+#75 := [monotonicity #72]: #74
+#78 := [monotonicity #75]: #77
+#83 := [trans #78 #81]: #82
+#69 := (iff #23 #67)
+#70 := [rewrite]: #69
+#86 := [monotonicity #70 #83]: #85
+#89 := [monotonicity #86]: #88
+#66 := [asserted]: #28
+#92 := [mp #66 #89]: #87
+#115 := [mp #92 #114]: #96
+#589 := [unit-resolution #115 #588]: #106
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#591 := (pattern #9)
+#46 := (= #8 #9)
+#592 := (forall (vars (?v0 S2)) (:pat #591) #46)
+#49 := (forall (vars (?v0 S2)) #46)
+#595 := (iff #49 #592)
+#593 := (iff #46 #46)
+#594 := [refl]: #593
+#596 := [quant-intro #594]: #595
+#102 := (~ #49 #49)
+#100 := (~ #46 #46)
+#101 := [refl]: #100
+#103 := [nnf-pos #101]: #102
+#10 := (= #9 #8)
+#11 := (forall (vars (?v0 S2)) #10)
+#50 := (iff #11 #49)
+#47 := (iff #10 #46)
+#48 := [rewrite]: #47
+#51 := [quant-intro #48]: #50
+#45 := [asserted]: #11
+#54 := [mp #45 #51]: #49
+#93 := [mp~ #54 #103]: #49
+#597 := [mp #93 #596]: #592
+#590 := (not #592)
+#580 := (or #590 #67)
+#238 := [quant-inst]: #580
+[unit-resolution #238 #597 #589]: false
+unsat
+cb1a1c56598b7b2b9fb4f67d2d62604895ce83a9 464 0
 #2 := false
 decl f8 :: (-> S2 S4 S4)
 decl f9 :: S4
-#34 := f9
+#28 := f9
 decl f5 :: (-> int S2)
-#38 := 2::int
-#39 := (f5 2::int)
-#40 := (f8 #39 f9)
+#52 := 2::int
+#53 := (f5 2::int)
+#54 := (f8 #53 f9)
 #12 := 1::int
-#33 := (f5 1::int)
-#41 := (f8 #33 #40)
+#48 := (f5 1::int)
+#55 := (f8 #48 #54)
 decl f7 :: (-> S3 S4 S4)
-#35 := (f8 #33 f9)
-#20 := 0::int
-#32 := (f5 0::int)
-#36 := (f8 #32 #35)
+#49 := (f8 #48 f9)
+#35 := 0::int
+#47 := (f5 0::int)
+#50 := (f8 #47 #49)
 decl f4 :: S3
 #8 := f4
-#37 := (f7 f4 #36)
-#42 := (= #37 #41)
-#519 := (f7 f4 #35)
+#51 := (f7 f4 #50)
+#56 := (= #51 #55)
+#271 := (f7 f4 #49)
 decl f3 :: (-> S3 S2 S2)
-#521 := (f3 f4 #32)
-#522 := (f8 #521 #519)
-#812 := (= #522 #41)
-#810 := (= #41 #522)
-#773 := (= #40 #519)
-#598 := (f7 f4 f9)
-#599 := (f3 f4 #33)
-#584 := (f8 #599 #598)
-#771 := (= #584 #519)
-#585 := (= #519 #584)
-#50 := (:var 0 S4)
-#48 := (:var 2 S3)
-#54 := (f7 #48 #50)
-#49 := (:var 1 S2)
-#53 := (f3 #48 #49)
-#55 := (f8 #53 #54)
-#722 := (pattern #55)
-#51 := (f8 #49 #50)
-#52 := (f7 #48 #51)
-#721 := (pattern #52)
-#56 := (= #52 #55)
-#723 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) (:pat #721 #722) #56)
-#57 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #56)
-#726 := (iff #57 #723)
-#724 := (iff #56 #56)
-#725 := [refl]: #724
-#727 := [quant-intro #725]: #726
-#196 := (~ #57 #57)
-#195 := (~ #56 #56)
-#214 := [refl]: #195
-#197 := [nnf-pos #214]: #196
-#181 := [asserted]: #57
-#215 := [mp~ #181 #197]: #57
-#728 := [mp #215 #727]: #723
-#525 := (not #723)
-#589 := (or #525 #585)
+#356 := (f3 f4 #47)
+#272 := (f8 #356 #271)
+#796 := (= #272 #55)
+#794 := (= #55 #272)
+#757 := (= #54 #271)
+#526 := (f7 f4 f9)
+#527 := (f3 f4 #48)
+#620 := (f8 #527 #526)
+#755 := (= #620 #271)
+#617 := (= #271 #620)
+#19 := (:var 0 S4)
+#17 := (:var 2 S3)
+#23 := (f7 #17 #19)
+#18 := (:var 1 S2)
+#22 := (f3 #17 #18)
+#24 := (f8 #22 #23)
+#695 := (pattern #24)
+#20 := (f8 #18 #19)
+#21 := (f7 #17 #20)
+#694 := (pattern #21)
+#25 := (= #21 #24)
+#696 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) (:pat #694 #695) #25)
+#26 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #25)
+#699 := (iff #26 #696)
+#697 := (iff #25 #25)
+#698 := [refl]: #697
+#700 := [quant-intro #698]: #699
+#186 := (~ #26 #26)
+#183 := (~ #25 #25)
+#204 := [refl]: #183
+#187 := [nnf-pos #204]: #186
+#87 := [asserted]: #26
+#205 := [mp~ #87 #187]: #26
+#701 := [mp #205 #700]: #696
+#360 := (not #696)
+#610 := (or #360 #617)
+#602 := [quant-inst]: #610
+#279 := [unit-resolution #602 #701]: #617
+#756 := [symm #279]: #755
+#753 := (= #54 #620)
+#584 := (= f9 #526)
+#27 := (:var 0 S3)
+#29 := (f7 #27 f9)
+#702 := (pattern #29)
+#90 := (= f9 #29)
+#703 := (forall (vars (?v0 S3)) (:pat #702) #90)
+#93 := (forall (vars (?v0 S3)) #90)
+#706 := (iff #93 #703)
+#704 := (iff #90 #90)
+#705 := [refl]: #704
+#707 := [quant-intro #705]: #706
+#188 := (~ #93 #93)
+#206 := (~ #90 #90)
+#207 := [refl]: #206
+#189 := [nnf-pos #207]: #188
+#30 := (= #29 f9)
+#31 := (forall (vars (?v0 S3)) #30)
+#94 := (iff #31 #93)
+#91 := (iff #30 #90)
+#92 := [rewrite]: #91
+#95 := [quant-intro #92]: #94
+#88 := [asserted]: #31
+#98 := [mp #88 #95]: #93
+#208 := [mp~ #98 #189]: #93
+#708 := [mp #208 #707]: #703
+#588 := (not #703)
+#589 := (or #588 #584)
 #586 := [quant-inst]: #589
-#731 := [unit-resolution #586 #728]: #585
-#772 := [symm #731]: #771
-#769 := (= #40 #584)
-#397 := (= f9 #598)
-#44 := (:var 0 S3)
-#45 := (f7 #44 f9)
-#714 := (pattern #45)
-#175 := (= f9 #45)
-#715 := (forall (vars (?v0 S3)) (:pat #714) #175)
-#178 := (forall (vars (?v0 S3)) #175)
-#718 := (iff #178 #715)
-#716 := (iff #175 #175)
-#717 := [refl]: #716
-#719 := [quant-intro #717]: #718
-#192 := (~ #178 #178)
-#212 := (~ #175 #175)
-#213 := [refl]: #212
-#193 := [nnf-pos #213]: #192
-#46 := (= #45 f9)
-#47 := (forall (vars (?v0 S3)) #46)
-#179 := (iff #47 #178)
-#176 := (iff #46 #175)
-#177 := [rewrite]: #176
-#180 := [quant-intro #177]: #179
-#174 := [asserted]: #47
-#183 := [mp #174 #180]: #178
-#194 := [mp~ #183 #193]: #178
-#720 := [mp #194 #719]: #715
-#388 := (not #715)
-#380 := (or #388 #397)
-#389 := [quant-inst]: #380
-#732 := [unit-resolution #389 #720]: #397
-#767 := (= #39 #599)
+#280 := [unit-resolution #586 #708]: #584
+#751 := (= #53 #527)
 decl f6 :: (-> S2 int)
-#305 := (f6 #33)
-#617 := (+ 1::int #305)
-#621 := (f5 #617)
-#763 := (= #621 #599)
-#601 := (= #599 #621)
+#673 := (f6 #48)
+#601 := (+ 1::int #673)
+#611 := (f5 #601)
+#747 := (= #611 #527)
+#614 := (= #527 #611)
 #9 := (:var 0 S2)
 #11 := (f6 #9)
 #687 := (pattern #11)
@@ -13622,344 +13705,339 @@
 #89 := [mp #74 #86]: #84
 #185 := [mp~ #89 #203]: #84
 #693 := [mp #185 #692]: #688
-#608 := (not #688)
-#613 := (or #608 #601)
-#609 := [quant-inst]: #613
-#735 := [unit-resolution #609 #693]: #601
-#764 := [symm #735]: #763
-#765 := (= #39 #621)
-#507 := (f6 #621)
-#313 := (f5 #507)
-#292 := (= #313 #621)
-#17 := (f5 #11)
-#88 := (= #9 #17)
-#694 := (forall (vars (?v0 S2)) (:pat #687) #88)
-#92 := (forall (vars (?v0 S2)) #88)
-#695 := (iff #92 #694)
-#697 := (iff #694 #694)
-#698 := [rewrite]: #697
-#696 := [rewrite]: #695
-#699 := [trans #696 #698]: #695
-#186 := (~ #92 #92)
-#182 := (~ #88 #88)
-#204 := [refl]: #182
-#187 := [nnf-pos #204]: #186
-#18 := (= #17 #9)
-#19 := (forall (vars (?v0 S2)) #18)
-#93 := (iff #19 #92)
-#90 := (iff #18 #88)
-#91 := [rewrite]: #90
-#94 := [quant-intro #91]: #93
-#87 := [asserted]: #19
-#97 := [mp #87 #94]: #92
-#205 := [mp~ #97 #187]: #92
-#700 := [mp #205 #699]: #694
-#354 := (not #694)
-#300 := (or #354 #292)
-#288 := (= #621 #313)
-#301 := (or #354 #288)
-#299 := (iff #301 #300)
-#287 := (iff #300 #300)
-#290 := [rewrite]: #287
-#293 := (iff #288 #292)
-#298 := [rewrite]: #293
-#304 := [monotonicity #298]: #299
-#291 := [trans #304 #290]: #299
-#303 := [quant-inst]: #301
-#294 := [mp #303 #291]: #300
-#736 := [unit-resolution #294 #700]: #292
-#761 := (= #39 #313)
-#759 := (= 2::int #507)
-#757 := (= #507 2::int)
-#579 := -1::int
-#517 := (* -1::int #507)
-#518 := (+ #305 #517)
-#480 := (<= #518 -1::int)
-#528 := (= #518 -1::int)
-#484 := (>= #305 -1::int)
-#570 := (>= #305 1::int)
-#672 := (= #305 1::int)
-#21 := (:var 0 int)
-#23 := (f5 #21)
-#701 := (pattern #23)
-#114 := (>= #21 0::int)
-#115 := (not #114)
-#24 := (f6 #23)
-#96 := (= #21 #24)
-#121 := (or #96 #115)
-#702 := (forall (vars (?v0 int)) (:pat #701) #121)
-#126 := (forall (vars (?v0 int)) #121)
-#705 := (iff #126 #702)
-#703 := (iff #121 #121)
-#704 := [refl]: #703
-#706 := [quant-intro #704]: #705
-#188 := (~ #126 #126)
-#206 := (~ #121 #121)
-#207 := [refl]: #206
-#189 := [nnf-pos #207]: #188
-#25 := (= #24 #21)
-#22 := (<= 0::int #21)
-#26 := (implies #22 #25)
-#27 := (forall (vars (?v0 int)) #26)
-#129 := (iff #27 #126)
-#103 := (not #22)
-#104 := (or #103 #96)
-#109 := (forall (vars (?v0 int)) #104)
-#127 := (iff #109 #126)
-#124 := (iff #104 #121)
-#118 := (or #115 #96)
-#122 := (iff #118 #121)
-#123 := [rewrite]: #122
-#119 := (iff #104 #118)
-#116 := (iff #103 #115)
-#112 := (iff #22 #114)
-#113 := [rewrite]: #112
-#117 := [monotonicity #113]: #116
-#120 := [monotonicity #117]: #119
-#125 := [trans #120 #123]: #124
-#128 := [quant-intro #125]: #127
-#110 := (iff #27 #109)
-#107 := (iff #26 #104)
-#100 := (implies #22 #96)
-#105 := (iff #100 #104)
-#106 := [rewrite]: #105
-#101 := (iff #26 #100)
-#98 := (iff #25 #96)
-#99 := [rewrite]: #98
-#102 := [monotonicity #99]: #101
-#108 := [trans #102 #106]: #107
-#111 := [quant-intro #108]: #110
-#130 := [trans #111 #128]: #129
-#95 := [asserted]: #27
-#131 := [mp #95 #130]: #126
-#208 := [mp~ #131 #189]: #126
-#707 := [mp #208 #706]: #702
-#685 := (not #702)
-#379 := (or #685 #672)
-#662 := (>= 1::int 0::int)
-#668 := (not #662)
-#669 := (= 1::int #305)
-#671 := (or #669 #668)
-#653 := (or #685 #671)
-#654 := (iff #653 #379)
-#368 := (iff #379 #379)
-#369 := [rewrite]: #368
-#656 := (iff #671 #672)
-#383 := (or #672 false)
-#278 := (iff #383 #672)
-#655 := [rewrite]: #278
-#384 := (iff #671 #383)
-#367 := (iff #668 false)
+#612 := (not #688)
+#605 := (or #612 #614)
+#606 := [quant-inst]: #605
+#283 := [unit-resolution #606 #693]: #614
+#748 := [symm #283]: #747
+#749 := (= #53 #611)
+#531 := (f6 #611)
+#330 := (f5 #531)
+#332 := (= #330 #611)
+#32 := (f5 #11)
+#97 := (= #9 #32)
+#709 := (forall (vars (?v0 S2)) (:pat #687) #97)
+#101 := (forall (vars (?v0 S2)) #97)
+#710 := (iff #101 #709)
+#712 := (iff #709 #709)
+#713 := [rewrite]: #712
+#711 := [rewrite]: #710
+#714 := [trans #711 #713]: #710
+#190 := (~ #101 #101)
+#209 := (~ #97 #97)
+#210 := [refl]: #209
+#191 := [nnf-pos #210]: #190
+#33 := (= #32 #9)
+#34 := (forall (vars (?v0 S2)) #33)
+#102 := (iff #34 #101)
+#99 := (iff #33 #97)
+#100 := [rewrite]: #99
+#103 := [quant-intro #100]: #102
+#96 := [asserted]: #34
+#106 := [mp #96 #103]: #101
+#211 := [mp~ #106 #191]: #101
+#715 := [mp #211 #714]: #709
+#373 := (not #709)
+#314 := (or #373 #332)
+#331 := (= #611 #330)
+#316 := (or #373 #331)
+#315 := (iff #316 #314)
+#306 := (iff #314 #314)
+#308 := [rewrite]: #306
+#321 := (iff #331 #332)
+#333 := [rewrite]: #321
+#318 := [monotonicity #333]: #315
+#309 := [trans #318 #308]: #315
+#317 := [quant-inst]: #316
+#312 := [mp #317 #309]: #314
+#284 := [unit-resolution #312 #715]: #332
+#745 := (= #53 #330)
+#743 := (= 2::int #531)
+#741 := (= #531 2::int)
+#573 := -1::int
+#538 := (* -1::int #673)
+#506 := (+ #531 #538)
+#486 := (<= #506 1::int)
+#532 := (= #506 1::int)
+#472 := (>= #673 -1::int)
+#597 := (>= #673 1::int)
+#383 := (= #673 1::int)
+#36 := (:var 0 int)
+#38 := (f5 #36)
+#716 := (pattern #38)
+#123 := (>= #36 0::int)
+#124 := (not #123)
+#39 := (f6 #38)
+#105 := (= #36 #39)
+#130 := (or #105 #124)
+#717 := (forall (vars (?v0 int)) (:pat #716) #130)
+#135 := (forall (vars (?v0 int)) #130)
+#720 := (iff #135 #717)
+#718 := (iff #130 #130)
+#719 := [refl]: #718
+#721 := [quant-intro #719]: #720
+#192 := (~ #135 #135)
+#212 := (~ #130 #130)
+#213 := [refl]: #212
+#193 := [nnf-pos #213]: #192
+#40 := (= #39 #36)
+#37 := (<= 0::int #36)
+#41 := (implies #37 #40)
+#42 := (forall (vars (?v0 int)) #41)
+#138 := (iff #42 #135)
+#112 := (not #37)
+#113 := (or #112 #105)
+#118 := (forall (vars (?v0 int)) #113)
+#136 := (iff #118 #135)
+#133 := (iff #113 #130)
+#127 := (or #124 #105)
+#131 := (iff #127 #130)
+#132 := [rewrite]: #131
+#128 := (iff #113 #127)
+#125 := (iff #112 #124)
+#121 := (iff #37 #123)
+#122 := [rewrite]: #121
+#126 := [monotonicity #122]: #125
+#129 := [monotonicity #126]: #128
+#134 := [trans #129 #132]: #133
+#137 := [quant-intro #134]: #136
+#119 := (iff #42 #118)
+#116 := (iff #41 #113)
+#109 := (implies #37 #105)
+#114 := (iff #109 #113)
+#115 := [rewrite]: #114
+#110 := (iff #41 #109)
+#107 := (iff #40 #105)
+#108 := [rewrite]: #107
+#111 := [monotonicity #108]: #110
+#117 := [trans #111 #115]: #116
+#120 := [quant-intro #117]: #119
+#139 := [trans #120 #137]: #138
+#104 := [asserted]: #42
+#140 := [mp #104 #139]: #135
+#214 := [mp~ #140 #193]: #135
+#722 := [mp #214 #721]: #717
+#319 := (not #717)
+#370 := (or #319 #383)
+#672 := (>= 1::int 0::int)
+#670 := (not #672)
+#659 := (= 1::int #673)
+#660 := (or #659 #670)
+#371 := (or #319 #660)
+#650 := (iff #371 #370)
+#647 := (iff #370 #370)
+#651 := [rewrite]: #647
+#368 := (iff #660 #383)
+#379 := (or #383 false)
+#654 := (iff #379 #383)
+#658 := [rewrite]: #654
+#653 := (iff #660 #379)
+#656 := (iff #670 false)
 #1 := true
-#363 := (not true)
-#680 := (iff #363 false)
-#336 := [rewrite]: #680
-#659 := (iff #668 #363)
-#670 := (iff #662 true)
-#673 := [rewrite]: #670
-#660 := [monotonicity #673]: #659
-#382 := [trans #660 #336]: #367
-#310 := (iff #669 #672)
-#311 := [rewrite]: #310
-#385 := [monotonicity #311 #382]: #384
-#378 := [trans #385 #655]: #656
-#658 := [monotonicity #378]: #654
-#370 := [trans #658 #369]: #654
-#657 := [quant-inst]: #653
-#371 := [mp #657 #370]: #379
-#737 := [unit-resolution #371 #707]: #672
-#738 := (not #672)
-#739 := (or #738 #570)
-#740 := [th-lemma]: #739
-#741 := [unit-resolution #740 #737]: #570
-#742 := (not #570)
-#743 := (or #742 #484)
-#744 := [th-lemma]: #743
-#745 := [unit-resolution #744 #741]: #484
-#491 := (not #484)
-#486 := (or #685 #491 #528)
-#503 := (>= #617 0::int)
-#505 := (not #503)
-#514 := (= #617 #507)
-#516 := (or #514 #505)
-#502 := (or #685 #516)
-#477 := (iff #502 #486)
-#497 := (or #491 #528)
-#464 := (or #685 #497)
-#474 := (iff #464 #486)
-#475 := [rewrite]: #474
-#471 := (iff #502 #464)
-#500 := (iff #516 #497)
-#494 := (or #528 #491)
-#498 := (iff #494 #497)
-#499 := [rewrite]: #498
-#495 := (iff #516 #494)
-#492 := (iff #505 #491)
-#485 := (iff #503 #484)
-#490 := [rewrite]: #485
-#493 := [monotonicity #490]: #492
-#508 := (iff #514 #528)
-#529 := [rewrite]: #508
-#496 := [monotonicity #529 #493]: #495
-#501 := [trans #496 #499]: #500
-#473 := [monotonicity #501]: #471
-#478 := [trans #473 #475]: #477
-#463 := [quant-inst]: #502
-#479 := [mp #463 #478]: #486
-#746 := [unit-resolution #479 #707 #745]: #528
-#747 := (not #528)
-#748 := (or #747 #480)
-#749 := [th-lemma]: #748
-#750 := [unit-resolution #749 #746]: #480
-#481 := (>= #518 -1::int)
-#751 := (or #747 #481)
-#752 := [th-lemma]: #751
-#753 := [unit-resolution #752 #746]: #481
-#590 := (<= #305 1::int)
-#754 := (or #738 #590)
-#755 := [th-lemma]: #754
-#756 := [unit-resolution #755 #737]: #590
-#758 := [th-lemma #741 #756 #753 #750]: #757
-#760 := [symm #758]: #759
-#762 := [monotonicity #760]: #761
-#766 := [trans #762 #736]: #765
-#768 := [trans #766 #764]: #767
-#770 := [monotonicity #768 #732]: #769
-#774 := [trans #770 #772]: #773
-#807 := (= #33 #521)
-#272 := (f6 #32)
-#523 := (+ 1::int #272)
-#524 := (f5 #523)
-#803 := (= #524 #521)
-#620 := (= #521 #524)
-#610 := (or #608 #620)
-#602 := [quant-inst]: #610
-#775 := [unit-resolution #602 #693]: #620
-#804 := [symm #775]: #803
-#805 := (= #33 #524)
-#576 := (f6 #524)
-#337 := (f5 #576)
-#351 := (= #337 #524)
-#344 := (or #354 #351)
-#350 := (= #524 #337)
-#355 := (or #354 #350)
-#340 := (iff #355 #344)
-#320 := (iff #344 #344)
-#322 := [rewrite]: #320
-#352 := (iff #350 #351)
-#353 := [rewrite]: #352
-#341 := [monotonicity #353]: #340
-#327 := [trans #341 #322]: #340
-#338 := [quant-inst]: #355
-#328 := [mp #338 #327]: #344
-#776 := [unit-resolution #328 #700]: #351
-#801 := (= #33 #337)
-#799 := (= 1::int #576)
-#797 := (= #576 1::int)
-#580 := (* -1::int #576)
-#581 := (+ #272 #580)
-#541 := (<= #581 -1::int)
-#582 := (= #581 -1::int)
-#561 := (>= #272 -1::int)
-#588 := (>= #272 0::int)
-#361 := (= #272 0::int)
-#675 := (or #685 #361)
-#271 := (>= 0::int 0::int)
-#356 := (not #271)
-#357 := (= 0::int #272)
-#358 := (or #357 #356)
-#334 := (or #685 #358)
-#676 := (iff #334 #675)
-#677 := (iff #675 #675)
-#319 := [rewrite]: #677
-#684 := (iff #358 #361)
-#347 := (or #361 false)
-#682 := (iff #347 #361)
+#347 := (not true)
+#682 := (iff #347 false)
 #683 := [rewrite]: #682
-#348 := (iff #358 #347)
-#467 := (iff #356 false)
-#342 := (iff #356 #363)
-#362 := (iff #271 true)
-#359 := [rewrite]: #362
-#678 := [monotonicity #359]: #342
-#674 := [trans #678 #336]: #467
-#349 := (iff #357 #361)
-#360 := [rewrite]: #349
-#681 := [monotonicity #360 #674]: #348
+#278 := (iff #670 #347)
+#384 := (iff #672 true)
+#385 := [rewrite]: #384
+#655 := [monotonicity #385]: #278
+#378 := [trans #655 #683]: #656
+#367 := (iff #659 #383)
+#382 := [rewrite]: #367
+#657 := [monotonicity #382 #378]: #653
+#369 := [trans #657 #658]: #368
+#364 := [monotonicity #369]: #650
+#648 := [trans #364 #651]: #650
+#649 := [quant-inst]: #371
+#652 := [mp #649 #648]: #370
+#285 := [unit-resolution #652 #722]: #383
+#281 := (not #383)
+#286 := (or #281 #597)
+#273 := [th-lemma]: #286
+#275 := [unit-resolution #273 #285]: #597
+#276 := (not #597)
+#274 := (or #276 #472)
+#277 := [th-lemma]: #274
+#729 := [unit-resolution #277 #275]: #472
+#507 := (not #472)
+#491 := (or #319 #507 #532)
+#530 := (>= #601 0::int)
+#476 := (not #530)
+#512 := (= #601 #531)
+#536 := (or #512 #476)
+#492 := (or #319 #536)
+#499 := (iff #492 #491)
+#508 := (or #507 #532)
+#494 := (or #319 #508)
+#497 := (iff #494 #491)
+#498 := [rewrite]: #497
+#495 := (iff #492 #494)
+#485 := (iff #536 #508)
+#517 := (or #532 #507)
+#529 := (iff #517 #508)
+#484 := [rewrite]: #529
+#518 := (iff #536 #517)
+#514 := (iff #476 #507)
+#503 := (iff #530 #472)
+#505 := [rewrite]: #503
+#516 := [monotonicity #505]: #514
+#537 := (iff #512 #532)
+#513 := [rewrite]: #537
+#528 := [monotonicity #513 #516]: #518
+#490 := [trans #528 #484]: #485
+#496 := [monotonicity #490]: #495
+#500 := [trans #496 #498]: #499
+#493 := [quant-inst]: #492
+#501 := [mp #493 #500]: #491
+#730 := [unit-resolution #501 #722 #729]: #532
+#731 := (not #532)
+#732 := (or #731 #486)
+#733 := [th-lemma]: #732
+#734 := [unit-resolution #733 #730]: #486
+#502 := (>= #506 1::int)
+#735 := (or #731 #502)
+#736 := [th-lemma]: #735
+#737 := [unit-resolution #736 #730]: #502
+#596 := (<= #673 1::int)
+#738 := (or #281 #596)
+#739 := [th-lemma]: #738
+#740 := [unit-resolution #739 #285]: #596
+#742 := [th-lemma #275 #740 #737 #734]: #741
+#744 := [symm #742]: #743
+#746 := [monotonicity #744]: #745
+#750 := [trans #746 #284]: #749
+#752 := [trans #750 #748]: #751
+#754 := [monotonicity #752 #280]: #753
+#758 := [trans #754 #756]: #757
+#791 := (= #48 #356)
+#359 := (f6 #47)
+#621 := (+ 1::int #359)
+#608 := (f5 #621)
+#787 := (= #608 #356)
+#599 := (= #356 #608)
+#613 := (or #612 #599)
+#609 := [quant-inst]: #613
+#759 := [unit-resolution #609 #693]: #599
+#788 := [symm #759]: #787
+#789 := (= #48 #608)
+#590 := (f6 #608)
+#389 := (f5 #590)
+#381 := (= #389 #608)
+#374 := (or #373 #381)
+#390 := (= #608 #389)
+#365 := (or #373 #390)
+#376 := (iff #365 #374)
+#377 := (iff #374 #374)
+#343 := [rewrite]: #377
+#391 := (iff #390 #381)
+#372 := [rewrite]: #391
+#366 := [monotonicity #372]: #376
+#345 := [trans #366 #343]: #376
+#375 := [quant-inst]: #365
+#346 := [mp #375 #345]: #374
+#760 := [unit-resolution #346 #715]: #381
+#785 := (= #48 #389)
+#783 := (= 1::int #590)
+#781 := (= #590 1::int)
+#574 := (* -1::int #590)
+#575 := (+ #359 #574)
+#557 := (<= #575 -1::int)
+#576 := (= #575 -1::int)
+#579 := (>= #359 -1::int)
+#592 := (>= #359 0::int)
+#336 := (= #359 0::int)
+#661 := (or #319 #336)
+#358 := (>= 0::int 0::int)
+#349 := (not #358)
+#363 := (= 0::int #359)
+#342 := (or #363 #349)
+#323 := (or #319 #342)
+#325 := (iff #323 #661)
+#663 := (iff #661 #661)
+#664 := [rewrite]: #663
+#335 := (iff #342 #336)
+#685 := (or #336 false)
+#339 := (iff #685 #336)
+#676 := [rewrite]: #339
+#675 := (iff #342 #685)
+#684 := (iff #349 false)
+#348 := (iff #349 #347)
+#467 := (iff #358 true)
+#674 := [rewrite]: #467
+#681 := [monotonicity #674]: #348
 #679 := [trans #681 #683]: #684
-#335 := [monotonicity #679]: #676
-#661 := [trans #335 #319]: #676
-#339 := [quant-inst]: #334
-#323 := [mp #339 #661]: #675
-#777 := [unit-resolution #323 #707]: #361
-#778 := (not #361)
-#779 := (or #778 #588)
-#780 := [th-lemma]: #779
-#781 := [unit-resolution #780 #777]: #588
-#782 := (not #588)
-#783 := (or #782 #561)
-#784 := [th-lemma]: #783
-#785 := [unit-resolution #784 #781]: #561
-#565 := (not #561)
-#557 := (or #685 #565 #582)
-#574 := (>= #523 0::int)
-#575 := (not #574)
-#577 := (= #523 #576)
-#578 := (or #577 #575)
-#558 := (or #685 #578)
-#428 := (iff #558 #557)
-#555 := (or #565 #582)
-#554 := (or #685 #555)
-#534 := (iff #554 #557)
-#535 := [rewrite]: #534
-#560 := (iff #558 #554)
-#553 := (iff #578 #555)
-#568 := (or #582 #565)
-#551 := (iff #568 #555)
-#552 := [rewrite]: #551
-#563 := (iff #578 #568)
-#566 := (iff #575 #565)
-#562 := (iff #574 #561)
-#564 := [rewrite]: #562
-#567 := [monotonicity #564]: #566
-#572 := (iff #577 #582)
-#583 := [rewrite]: #572
-#569 := [monotonicity #583 #567]: #563
-#556 := [trans #569 #552]: #553
-#533 := [monotonicity #556]: #560
-#539 := [trans #533 #535]: #428
-#559 := [quant-inst]: #558
-#540 := [mp #559 #539]: #557
-#786 := [unit-resolution #540 #707 #785]: #582
-#787 := (not #582)
-#788 := (or #787 #541)
-#789 := [th-lemma]: #788
-#790 := [unit-resolution #789 #786]: #541
-#546 := (>= #581 -1::int)
-#791 := (or #787 #546)
-#792 := [th-lemma]: #791
-#793 := [unit-resolution #792 #786]: #546
-#587 := (<= #272 0::int)
-#794 := (or #778 #587)
-#795 := [th-lemma]: #794
-#796 := [unit-resolution #795 #777]: #587
-#798 := [th-lemma #781 #796 #793 #790]: #797
-#800 := [symm #798]: #799
-#802 := [monotonicity #800]: #801
-#806 := [trans #802 #776]: #805
-#808 := [trans #806 #804]: #807
-#811 := [monotonicity #808 #774]: #810
-#813 := [symm #811]: #812
-#515 := (= #37 #522)
-#526 := (or #525 #515)
-#527 := [quant-inst]: #526
-#809 := [unit-resolution #527 #728]: #515
-#814 := [trans #809 #813]: #42
-#43 := (not #42)
-#173 := [asserted]: #43
-[unit-resolution #173 #814]: false
-unsat
-ee30427d464b4fb3f94aa1806f026182963de849 38 0
+#678 := (iff #363 #336)
+#680 := [rewrite]: #678
+#334 := [monotonicity #680 #679]: #675
+#677 := [trans #334 #676]: #335
+#326 := [monotonicity #677]: #325
+#665 := [trans #326 #664]: #325
+#324 := [quant-inst]: #323
+#666 := [mp #324 #665]: #661
+#761 := [unit-resolution #666 #722]: #336
+#762 := (not #336)
+#763 := (or #762 #592)
+#764 := [th-lemma]: #763
+#765 := [unit-resolution #764 #761]: #592
+#766 := (not #592)
+#767 := (or #766 #579)
+#768 := [th-lemma]: #767
+#769 := [unit-resolution #768 #765]: #579
+#582 := (not #579)
+#565 := (or #319 #576 #582)
+#585 := (>= #621 0::int)
+#587 := (not #585)
+#570 := (= #621 #590)
+#571 := (or #570 #587)
+#566 := (or #319 #571)
+#552 := (iff #566 #565)
+#561 := (or #576 #582)
+#568 := (or #319 #561)
+#555 := (iff #568 #565)
+#551 := [rewrite]: #555
+#563 := (iff #566 #568)
+#562 := (iff #571 #561)
+#572 := (iff #587 #582)
+#580 := (iff #585 #579)
+#581 := [rewrite]: #580
+#583 := [monotonicity #581]: #572
+#577 := (iff #570 #576)
+#578 := [rewrite]: #577
+#564 := [monotonicity #578 #583]: #562
+#569 := [monotonicity #564]: #563
+#553 := [trans #569 #551]: #552
+#567 := [quant-inst]: #566
+#556 := [mp #567 #553]: #565
+#770 := [unit-resolution #556 #722 #769]: #576
+#771 := (not #576)
+#772 := (or #771 #557)
+#773 := [th-lemma]: #772
+#774 := [unit-resolution #773 #770]: #557
+#558 := (>= #575 -1::int)
+#775 := (or #771 #558)
+#776 := [th-lemma]: #775
+#777 := [unit-resolution #776 #770]: #558
+#591 := (<= #359 0::int)
+#778 := (or #762 #591)
+#779 := [th-lemma]: #778
+#780 := [unit-resolution #779 #761]: #591
+#782 := [th-lemma #765 #780 #777 #774]: #781
+#784 := [symm #782]: #783
+#786 := [monotonicity #784]: #785
+#790 := [trans #786 #760]: #789
+#792 := [trans #790 #788]: #791
+#795 := [monotonicity #792 #758]: #794
+#797 := [symm #795]: #796
+#357 := (= #51 #272)
+#361 := (or #360 #357)
+#362 := [quant-inst]: #361
+#793 := [unit-resolution #362 #701]: #357
+#798 := [trans #793 #797]: #56
+#57 := (not #56)
+#182 := [asserted]: #57
+[unit-resolution #182 #798]: false
+unsat
+fd95e530253726c02553f27818cb8e2eea2a4b33 38 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -13998,7 +14076,7 @@
 #31 := [asserted]: #14
 [mp #31 #54]: false
 unsat
-bb6927e05e73f0d1fe00658a23b5a23277a4c6fa 366 0
+e00bc51b49b06334d071f1e1c40b572f23bfbc3c 366 0
 #2 := false
 decl f3 :: (-> int S2)
 #41 := 6::int
@@ -14365,7 +14443,7 @@
 #187 := [asserted]: #44
 [unit-resolution #187 #404]: false
 unsat
-760a08d06b818c4b3a173eacf882e5d9145febb7 1271 0
+65953f98dc6fbf172ad6f11cfa297280d624458a 1271 0
 #2 := false
 decl f6 :: (-> int int int)
 #12 := 2::int
@@ -15637,657 +15715,588 @@
 #615 := [unit-resolution #638 #1762]: #367
 [unit-resolution #615 #1764]: false
 unsat
-1739856e83271d60ba99b4dd0f8fab6bba11b19a 76 0
+4d0565847e51fa1e70e0f66f5c05a0d01bccb4d7 76 0
 #2 := false
 decl f3 :: (-> int S1)
-#12 := (:var 0 int)
-#13 := (f3 #12)
-#1016 := (pattern #13)
+#129 := 1::int
+#130 := (f3 1::int)
 decl f1 :: S1
 #4 := f1
-#157 := (= f1 #13)
-#1017 := (forall (vars (?v0 int)) (:pat #1016) #157)
-#181 := (forall (vars (?v0 int)) #157)
-#1020 := (iff #181 #1017)
-#1018 := (iff #157 #157)
+#457 := (= f1 #130)
+#461 := (not #457)
+#131 := (= #130 f1)
+#132 := (not #131)
+#462 := (iff #132 #461)
+#459 := (iff #131 #457)
+#460 := [rewrite]: #459
+#463 := [monotonicity #460]: #462
+#456 := [asserted]: #132
+#466 := [mp #456 #463]: #461
+#8 := (:var 0 int)
+#9 := (f3 #8)
+#1016 := (pattern #9)
+#150 := (= f1 #9)
+#1017 := (forall (vars (?v0 int)) (:pat #1016) #150)
+#173 := (forall (vars (?v0 int)) #150)
+#1020 := (iff #173 #1017)
+#1018 := (iff #150 #150)
 #1019 := [refl]: #1018
 #1021 := [quant-intro #1019]: #1020
-#494 := (~ #181 #181)
-#492 := (~ #157 #157)
+#494 := (~ #173 #173)
+#492 := (~ #150 #150)
 #493 := [refl]: #492
 #495 := [nnf-pos #493]: #494
 decl f4 :: (-> S2 S1)
 decl f5 :: (-> int S2 S2)
 decl f6 :: S2
-#15 := f6
-#16 := (f5 #12 f6)
-#17 := (f4 #16)
-#18 := (= #17 f1)
-#19 := (not #18)
-#20 := (or #18 #19)
+#11 := f6
+#12 := (f5 #8 f6)
+#13 := (f4 #12)
 #14 := (= #13 f1)
-#21 := (and #14 #20)
-#22 := (forall (vars (?v0 int)) #21)
-#182 := (iff #22 #181)
-#179 := (iff #21 #157)
+#15 := (not #14)
+#16 := (or #14 #15)
+#10 := (= #9 f1)
+#17 := (and #10 #16)
+#18 := (forall (vars (?v0 int)) #17)
+#174 := (iff #18 #173)
+#171 := (iff #17 #150)
 #1 := true
-#174 := (and #157 true)
-#177 := (iff #174 #157)
-#178 := [rewrite]: #177
-#175 := (iff #21 #174)
-#172 := (iff #20 true)
-#161 := (= f1 #17)
-#164 := (not #161)
-#167 := (or #161 #164)
-#170 := (iff #167 true)
-#171 := [rewrite]: #170
-#168 := (iff #20 #167)
-#165 := (iff #19 #164)
-#162 := (iff #18 #161)
+#166 := (and #150 true)
+#169 := (iff #166 #150)
+#170 := [rewrite]: #169
+#167 := (iff #17 #166)
+#164 := (iff #16 true)
+#153 := (= f1 #13)
+#156 := (not #153)
+#159 := (or #153 #156)
+#162 := (iff #159 true)
 #163 := [rewrite]: #162
-#166 := [monotonicity #163]: #165
-#169 := [monotonicity #163 #166]: #168
-#173 := [trans #169 #171]: #172
-#159 := (iff #14 #157)
-#160 := [rewrite]: #159
-#176 := [monotonicity #160 #173]: #175
-#180 := [trans #176 #178]: #179
-#183 := [quant-intro #180]: #182
-#156 := [asserted]: #22
-#186 := [mp #156 #183]: #181
-#468 := [mp~ #186 #495]: #181
-#1022 := [mp #468 #1021]: #1017
-#8 := 1::int
-#9 := (f3 1::int)
-#150 := (= f1 #9)
-#153 := (not #150)
-#10 := (= #9 f1)
-#11 := (not #10)
-#154 := (iff #11 #153)
+#160 := (iff #16 #159)
+#157 := (iff #15 #156)
+#154 := (iff #14 #153)
+#155 := [rewrite]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #155 #158]: #160
+#165 := [trans #161 #163]: #164
 #151 := (iff #10 #150)
 #152 := [rewrite]: #151
-#155 := [monotonicity #152]: #154
-#149 := [asserted]: #11
-#158 := [mp #149 #155]: #153
+#168 := [monotonicity #152 #165]: #167
+#172 := [trans #168 #170]: #171
+#175 := [quant-intro #172]: #174
+#149 := [asserted]: #18
+#178 := [mp #149 #175]: #173
+#467 := [mp~ #178 #495]: #173
+#1022 := [mp #467 #1021]: #1017
 #603 := (not #1017)
-#688 := (or #603 #150)
+#688 := (or #603 #457)
 #689 := [quant-inst]: #688
-[unit-resolution #689 #158 #1022]: false
-unsat
-e1c7435780cfee6dd8c9bac28159418631b73635 478 0
-#2 := false
-decl f7 :: (-> S4 S2)
-decl f8 :: (-> S1 S4)
+[unit-resolution #689 #1022 #466]: false
+unsat
+2ca63958e3f098d25e6ec678f9170833411e17cf 507 0
+#2 := false
+decl f19 :: (-> S8 S3)
+decl f22 :: (-> S1 S8)
 decl f1 :: S1
 #4 := f1
-#28 := (f8 f1)
-#29 := (f7 #28)
-decl f5 :: (-> S3 S2)
-decl f6 :: (-> int S3)
-#25 := 3::int
-#26 := (f6 3::int)
-#27 := (f5 #26)
-#30 := (= #27 #29)
-decl f12 :: (-> S6 S2)
-decl f13 :: (-> S1 S6 S6)
-decl f14 :: S6
-#42 := f14
-#857 := (f13 f1 f14)
-#496 := (f12 #857)
-#602 := (= #496 #29)
-#859 := (= #29 #496)
-#39 := (:var 0 S1)
-#43 := (f13 #39 f14)
-#902 := (pattern #43)
-#40 := (f8 #39)
-#901 := (pattern #40)
-#44 := (f12 #43)
-#41 := (f7 #40)
-#45 := (= #41 #44)
-#903 := (forall (vars (?v0 S1)) (:pat #901 #902) #45)
-#46 := (forall (vars (?v0 S1)) #45)
-#906 := (iff #46 #903)
-#904 := (iff #45 #45)
-#905 := [refl]: #904
-#907 := [quant-intro #905]: #906
-#346 := (~ #46 #46)
-#345 := (~ #45 #45)
-#389 := [refl]: #345
-#347 := [nnf-pos #389]: #346
-#225 := [asserted]: #46
-#390 := [mp~ #225 #347]: #46
-#908 := [mp #390 #907]: #903
-#553 := (not #903)
-#568 := (or #553 #859)
-#569 := [quant-inst]: #568
-#625 := [unit-resolution #569 #908]: #859
-#603 := [symm #625]: #602
-#590 := (= #27 #496)
-decl f18 :: (-> S6 S2)
-#814 := (f18 #857)
-#600 := (= #814 #496)
-#815 := (= #496 #814)
-#62 := (:var 0 S6)
-#64 := (f18 #62)
-#918 := (pattern #64)
-#63 := (f12 #62)
-#917 := (pattern #63)
-#65 := (= #63 #64)
-#919 := (forall (vars (?v0 S6)) (:pat #917 #918) #65)
-#66 := (forall (vars (?v0 S6)) #65)
-#922 := (iff #66 #919)
-#920 := (iff #65 #65)
-#921 := [refl]: #920
-#923 := [quant-intro #921]: #922
-#358 := (~ #66 #66)
-#357 := (~ #65 #65)
-#354 := [refl]: #357
-#359 := [nnf-pos #354]: #358
-#238 := [asserted]: #66
-#355 := [mp~ #238 #359]: #66
-#924 := [mp #355 #923]: #919
-#564 := (not #919)
-#816 := (or #564 #815)
-#823 := [quant-inst]: #816
-#617 := [unit-resolution #823 #924]: #815
-#601 := [symm #617]: #600
-#588 := (= #27 #814)
-decl f3 :: (-> int S2)
-decl f4 :: (-> S2 int)
-#108 := (f18 f14)
-#821 := (f4 #108)
-#85 := 1::int
-#252 := (f3 1::int)
-#255 := (f4 #252)
-#655 := (+ #255 #821)
-#811 := (f3 #655)
-#697 := (= #811 #814)
-#94 := (:var 1 S1)
-#95 := (f13 #94 #62)
-#960 := (pattern #95)
-#117 := (f4 #64)
-#321 := (+ #117 #255)
-#325 := (f3 #321)
-#116 := (f18 #95)
-#328 := (= #116 #325)
-#961 := (forall (vars (?v0 S1) (?v1 S6)) (:pat #960) #328)
-#331 := (forall (vars (?v0 S1) (?v1 S6)) #328)
-#964 := (iff #331 #961)
-#962 := (iff #328 #328)
-#963 := [refl]: #962
-#965 := [quant-intro #963]: #964
-#374 := (~ #331 #331)
-#373 := (~ #328 #328)
-#370 := [refl]: #373
-#375 := [nnf-pos #370]: #374
-#13 := 0::int
-#86 := (+ 0::int 1::int)
-#87 := (f3 #86)
-#88 := (f4 #87)
-#118 := (+ #117 #88)
-#119 := (f3 #118)
-#120 := (= #116 #119)
-#121 := (forall (vars (?v0 S1) (?v1 S6)) #120)
-#332 := (iff #121 #331)
-#329 := (iff #120 #328)
-#326 := (= #119 #325)
-#323 := (= #118 #321)
-#256 := (= #88 #255)
-#253 := (= #87 #252)
-#249 := (= #86 1::int)
-#251 := [rewrite]: #249
-#254 := [monotonicity #251]: #253
-#257 := [monotonicity #254]: #256
-#324 := [monotonicity #257]: #323
-#327 := [monotonicity #324]: #326
-#330 := [monotonicity #327]: #329
-#333 := [quant-intro #330]: #332
-#320 := [asserted]: #121
-#336 := [mp #320 #333]: #331
-#371 := [mp~ #336 #375]: #331
-#966 := [mp #371 #965]: #961
-#802 := (not #961)
-#805 := (or #802 #697)
-#822 := (+ #821 #255)
-#652 := (f3 #822)
-#654 := (= #814 #652)
-#690 := (or #802 #654)
-#707 := (iff #690 #805)
-#701 := (iff #805 #805)
-#709 := [rewrite]: #701
-#706 := (iff #654 #697)
-#813 := (= #814 #811)
-#656 := (iff #813 #697)
-#804 := [rewrite]: #656
-#695 := (iff #654 #813)
-#812 := (= #652 #811)
-#808 := (= #822 #655)
-#809 := [rewrite]: #808
-#810 := [monotonicity #809]: #812
-#696 := [monotonicity #810]: #695
-#801 := [trans #696 #804]: #706
-#708 := [monotonicity #801]: #707
-#710 := [trans #708 #709]: #707
-#705 := [quant-inst]: #690
-#711 := [mp #705 #710]: #805
-#624 := [unit-resolution #711 #966]: #697
-#586 := (= #27 #811)
-#598 := (= #252 #811)
-#622 := (= #811 #252)
-#619 := (= #655 1::int)
-#807 := (<= #821 0::int)
-#803 := (= #821 0::int)
-#69 := (f3 0::int)
-#543 := (f4 #69)
-#548 := (= #543 0::int)
-#14 := (:var 0 int)
-#16 := (f3 #14)
-#880 := (pattern #16)
-#164 := (>= #14 0::int)
-#165 := (not #164)
-#17 := (f4 #16)
-#146 := (= #14 #17)
-#171 := (or #146 #165)
-#881 := (forall (vars (?v0 int)) (:pat #880) #171)
-#176 := (forall (vars (?v0 int)) #171)
-#884 := (iff #176 #881)
-#882 := (iff #171 #171)
-#883 := [refl]: #882
-#885 := [quant-intro #883]: #884
-#338 := (~ #176 #176)
-#334 := (~ #171 #171)
-#382 := [refl]: #334
-#339 := [nnf-pos #382]: #338
-#18 := (= #17 #14)
-#15 := (<= 0::int #14)
-#19 := (implies #15 #18)
-#20 := (forall (vars (?v0 int)) #19)
-#179 := (iff #20 #176)
-#153 := (not #15)
-#154 := (or #153 #146)
-#159 := (forall (vars (?v0 int)) #154)
-#177 := (iff #159 #176)
-#174 := (iff #154 #171)
-#168 := (or #165 #146)
-#172 := (iff #168 #171)
-#173 := [rewrite]: #172
-#169 := (iff #154 #168)
-#166 := (iff #153 #165)
-#162 := (iff #15 #164)
-#163 := [rewrite]: #162
-#167 := [monotonicity #163]: #166
+#355 := (f22 f1)
+#358 := (f19 #355)
+decl f17 :: (-> S7 S3)
+decl f21 :: (-> int S7)
+#115 := 3::int
+#116 := (f21 3::int)
+#117 := (f17 #116)
+#361 := (= #117 #358)
+decl f16 :: (-> S4 S3)
+decl f8 :: (-> S1 S4 S4)
+decl f10 :: S4
+#37 := f10
+#897 := (f8 f1 f10)
+#899 := (f16 #897)
+#640 := (= #899 #358)
+#566 := (= #358 #899)
+#93 := (:var 0 S1)
+#96 := (f8 #93 f10)
+#972 := (pattern #96)
+#94 := (f22 #93)
+#971 := (pattern #94)
+#97 := (f16 #96)
+#95 := (f19 #94)
+#98 := (= #95 #97)
+#973 := (forall (vars (?v0 S1)) (:pat #971 #972) #98)
+#99 := (forall (vars (?v0 S1)) #98)
+#976 := (iff #99 #973)
+#974 := (iff #98 #98)
+#975 := [refl]: #974
+#977 := [quant-intro #975]: #976
+#399 := (~ #99 #99)
+#398 := (~ #98 #98)
+#395 := [refl]: #398
+#400 := [nnf-pos #395]: #399
+#265 := [asserted]: #99
+#396 := [mp~ #265 #400]: #99
+#978 := [mp #396 #977]: #973
+#901 := (not #973)
+#902 := (or #901 #566)
+#903 := [quant-inst]: #902
+#644 := [unit-resolution #903 #978]: #566
+#617 := [symm #644]: #640
+#612 := (= #117 #899)
+decl f7 :: (-> S4 S3)
+#856 := (f7 #897)
+#685 := (= #856 #899)
+#24 := (:var 0 S4)
+#73 := (f16 #24)
+#956 := (pattern #73)
+#27 := (f7 #24)
+#955 := (pattern #27)
+#245 := (= #27 #73)
+#957 := (forall (vars (?v0 S4)) (:pat #955 #956) #245)
+#249 := (forall (vars (?v0 S4)) #245)
+#960 := (iff #249 #957)
+#958 := (iff #245 #245)
+#959 := [refl]: #958
+#961 := [quant-intro #959]: #960
+#387 := (~ #249 #249)
+#428 := (~ #245 #245)
+#429 := [refl]: #428
+#388 := [nnf-pos #429]: #387
+#74 := (= #73 #27)
+#75 := (forall (vars (?v0 S4)) #74)
+#250 := (iff #75 #249)
+#247 := (iff #74 #245)
+#248 := [rewrite]: #247
+#251 := [quant-intro #248]: #250
+#244 := [asserted]: #75
+#254 := [mp #244 #251]: #249
+#430 := [mp~ #254 #388]: #249
+#962 := [mp #430 #961]: #957
+#581 := (not #957)
+#841 := (or #581 #685)
+#842 := [quant-inst]: #841
+#643 := [unit-resolution #842 #962]: #685
+#626 := (= #117 #856)
+decl f5 :: (-> int S3)
+decl f6 :: (-> S3 int)
+#38 := (f7 f10)
+#687 := (f6 #38)
+#15 := 1::int
+#142 := (f5 1::int)
+#145 := (f6 #142)
+#843 := (+ #145 #687)
+#729 := (f5 #843)
+#835 := (= #729 #856)
+#23 := (:var 1 S1)
+#25 := (f8 #23 #24)
+#912 := (pattern #25)
+#28 := (f6 #27)
+#161 := (+ #28 #145)
+#165 := (f5 #161)
+#26 := (f7 #25)
+#168 := (= #26 #165)
+#913 := (forall (vars (?v0 S1) (?v1 S4)) (:pat #912) #168)
+#171 := (forall (vars (?v0 S1) (?v1 S4)) #168)
+#916 := (iff #171 #913)
+#914 := (iff #168 #168)
+#915 := [refl]: #914
+#917 := [quant-intro #915]: #916
+#371 := (~ #171 #171)
+#367 := (~ #168 #168)
+#415 := [refl]: #367
+#372 := [nnf-pos #415]: #371
+#14 := 0::int
+#16 := (+ 0::int 1::int)
+#17 := (f5 #16)
+#18 := (f6 #17)
+#29 := (+ #28 #18)
+#30 := (f5 #29)
+#31 := (= #26 #30)
+#32 := (forall (vars (?v0 S1) (?v1 S4)) #31)
+#172 := (iff #32 #171)
+#169 := (iff #31 #168)
+#166 := (= #30 #165)
+#163 := (= #29 #161)
+#146 := (= #18 #145)
+#143 := (= #17 #142)
+#140 := (= #16 1::int)
+#141 := [rewrite]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#164 := [monotonicity #147]: #163
+#167 := [monotonicity #164]: #166
 #170 := [monotonicity #167]: #169
-#175 := [trans #170 #173]: #174
-#178 := [quant-intro #175]: #177
-#160 := (iff #20 #159)
-#157 := (iff #19 #154)
-#150 := (implies #15 #146)
-#155 := (iff #150 #154)
-#156 := [rewrite]: #155
-#151 := (iff #19 #150)
-#148 := (iff #18 #146)
-#149 := [rewrite]: #148
-#152 := [monotonicity #149]: #151
-#158 := [trans #152 #156]: #157
-#161 := [quant-intro #158]: #160
-#180 := [trans #161 #178]: #179
-#145 := [asserted]: #20
-#181 := [mp #145 #180]: #176
-#383 := [mp~ #181 #339]: #176
-#886 := [mp #383 #885]: #881
-#861 := (not #881)
-#520 := (or #861 #548)
-#458 := (>= 0::int 0::int)
-#542 := (not #458)
-#544 := (= 0::int #543)
-#535 := (or #544 #542)
-#525 := (or #861 #535)
-#521 := (iff #525 #520)
-#505 := (iff #520 #520)
-#847 := [rewrite]: #505
-#865 := (iff #535 #548)
-#534 := (or #548 false)
-#869 := (iff #534 #548)
-#870 := [rewrite]: #869
-#867 := (iff #535 #534)
-#860 := (iff #542 false)
+#173 := [quant-intro #170]: #172
+#160 := [asserted]: #32
+#176 := [mp #160 #173]: #171
+#416 := [mp~ #176 #372]: #171
+#918 := [mp #416 #917]: #913
+#741 := (not #913)
+#734 := (or #741 #835)
+#688 := (+ #687 #145)
+#844 := (f5 #688)
+#845 := (= #856 #844)
+#742 := (or #741 #845)
+#744 := (iff #742 #734)
+#746 := (iff #734 #734)
+#839 := [rewrite]: #746
+#738 := (iff #845 #835)
+#837 := (= #856 #729)
+#838 := (iff #837 #835)
+#723 := [rewrite]: #838
+#739 := (iff #845 #837)
+#730 := (= #844 #729)
+#846 := (= #688 #843)
+#728 := [rewrite]: #846
+#689 := [monotonicity #728]: #730
+#834 := [monotonicity #689]: #739
+#740 := [trans #834 #723]: #738
+#745 := [monotonicity #740]: #744
+#836 := [trans #745 #839]: #744
+#743 := [quant-inst]: #742
+#840 := [mp #743 #836]: #734
+#641 := [unit-resolution #840 #918]: #835
+#625 := (= #117 #729)
+#639 := (= #142 #729)
+#630 := (= #729 #142)
+#654 := (= #843 1::int)
+#820 := (<= #687 0::int)
+#818 := (= #687 0::int)
+#35 := (f5 0::int)
+#898 := (f6 #35)
+#895 := (= #898 0::int)
+#86 := (:var 0 int)
+#106 := (f5 #86)
+#987 := (pattern #106)
+#293 := (>= #86 0::int)
+#294 := (not #293)
+#107 := (f6 #106)
+#275 := (= #86 #107)
+#300 := (or #275 #294)
+#988 := (forall (vars (?v0 int)) (:pat #987) #300)
+#305 := (forall (vars (?v0 int)) #300)
+#991 := (iff #305 #988)
+#989 := (iff #300 #300)
+#990 := [refl]: #989
+#992 := [quant-intro #990]: #991
+#403 := (~ #305 #305)
+#392 := (~ #300 #300)
+#433 := [refl]: #392
+#404 := [nnf-pos #433]: #403
+#108 := (= #107 #86)
+#105 := (<= 0::int #86)
+#109 := (implies #105 #108)
+#110 := (forall (vars (?v0 int)) #109)
+#308 := (iff #110 #305)
+#282 := (not #105)
+#283 := (or #282 #275)
+#288 := (forall (vars (?v0 int)) #283)
+#306 := (iff #288 #305)
+#303 := (iff #283 #300)
+#297 := (or #294 #275)
+#301 := (iff #297 #300)
+#302 := [rewrite]: #301
+#298 := (iff #283 #297)
+#295 := (iff #282 #294)
+#291 := (iff #105 #293)
+#292 := [rewrite]: #291
+#296 := [monotonicity #292]: #295
+#299 := [monotonicity #296]: #298
+#304 := [trans #299 #302]: #303
+#307 := [quant-intro #304]: #306
+#289 := (iff #110 #288)
+#286 := (iff #109 #283)
+#279 := (implies #105 #275)
+#284 := (iff #279 #283)
+#285 := [rewrite]: #284
+#280 := (iff #109 #279)
+#277 := (iff #108 #275)
+#278 := [rewrite]: #277
+#281 := [monotonicity #278]: #280
+#287 := [trans #281 #285]: #286
+#290 := [quant-intro #287]: #289
+#309 := [trans #290 #307]: #308
+#274 := [asserted]: #110
+#310 := [mp #274 #309]: #305
+#434 := [mp~ #310 #404]: #305
+#993 := [mp #434 #992]: #988
+#888 := (not #988)
+#890 := (or #888 #895)
+#567 := (>= 0::int 0::int)
+#900 := (not #567)
+#904 := (= 0::int #898)
+#894 := (or #904 #900)
+#529 := (or #888 #894)
+#891 := (iff #529 #890)
+#892 := (iff #890 #890)
+#878 := [rewrite]: #892
+#887 := (iff #894 #895)
+#883 := (or #895 false)
+#886 := (iff #883 #895)
+#881 := [rewrite]: #886
+#884 := (iff #894 #883)
+#545 := (iff #900 false)
 #1 := true
-#528 := (not true)
-#522 := (iff #528 false)
-#653 := [rewrite]: #522
-#864 := (iff #542 #528)
-#545 := (iff #458 true)
-#549 := [rewrite]: #545
-#866 := [monotonicity #549]: #864
-#533 := [trans #866 #653]: #860
-#546 := (iff #544 #548)
-#547 := [rewrite]: #546
-#868 := [monotonicity #547 #533]: #867
-#871 := [trans #868 #870]: #865
-#863 := [monotonicity #871]: #521
-#509 := [trans #863 #847]: #521
-#862 := [quant-inst]: #525
-#510 := [mp #862 #509]: #520
-#664 := [unit-resolution #510 #886]: #548
-#626 := (= #821 #543)
-#109 := (= #108 #69)
-#302 := (= #69 #108)
-#304 := (iff #109 #302)
-#305 := [rewrite]: #304
-#301 := [asserted]: #109
-#308 := [mp #301 #305]: #302
-#638 := [symm #308]: #109
-#629 := [monotonicity #638]: #626
-#631 := [trans #629 #664]: #803
-#632 := (not #803)
-#628 := (or #632 #807)
-#633 := [th-lemma]: #628
-#623 := [unit-resolution #633 #631]: #807
-#794 := (>= #821 0::int)
-#613 := (or #632 #794)
-#615 := [th-lemma]: #613
-#616 := [unit-resolution #615 #631]: #794
-#726 := (<= #255 1::int)
-#747 := (= #255 1::int)
-#744 := (or #861 #747)
-#756 := (>= 1::int 0::int)
-#757 := (not #756)
-#768 := (= 1::int #255)
-#758 := (or #768 #757)
-#745 := (or #861 #758)
-#746 := (iff #745 #744)
-#720 := (iff #744 #744)
-#721 := [rewrite]: #720
-#742 := (iff #758 #747)
-#755 := (or #747 false)
-#738 := (iff #755 #747)
-#739 := [rewrite]: #738
-#741 := (iff #758 #755)
-#754 := (iff #757 false)
-#752 := (iff #757 #528)
-#750 := (iff #756 true)
-#751 := [rewrite]: #750
-#753 := [monotonicity #751]: #752
-#749 := [trans #753 #653]: #754
-#769 := (iff #768 #747)
-#748 := [rewrite]: #769
-#737 := [monotonicity #748 #749]: #741
-#743 := [trans #737 #739]: #742
-#719 := [monotonicity #743]: #746
-#614 := [trans #719 #721]: #746
-#740 := [quant-inst]: #745
-#725 := [mp #740 #614]: #744
-#645 := [unit-resolution #725 #886]: #747
-#646 := (not #747)
-#488 := (or #646 #726)
-#647 := [th-lemma]: #488
-#643 := [unit-resolution #647 #645]: #726
-#727 := (>= #255 1::int)
-#648 := (or #646 #727)
-#627 := [th-lemma]: #648
-#630 := [unit-resolution #627 #645]: #727
-#620 := [th-lemma #630 #643 #616 #623]: #619
-#608 := [monotonicity #620]: #622
-#599 := [symm #608]: #598
-#607 := (= #27 #252)
-decl f17 :: (-> S5 S2)
-decl f11 :: S5
-#34 := f11
-#106 := (f17 f11)
-#843 := (f4 #106)
-#557 := (+ #255 #843)
-#550 := (f3 #557)
-#596 := (= #550 #252)
-#610 := (= #252 #550)
-#637 := (= 1::int #557)
-#634 := (= #557 1::int)
-#713 := (<= #843 0::int)
-#712 := (= #843 0::int)
-#666 := (= #843 #543)
-#107 := (= #106 #69)
-#297 := (= #69 #106)
-#299 := (iff #107 #297)
-#300 := [rewrite]: #299
-#296 := [asserted]: #107
-#303 := [mp #296 #300]: #297
-#665 := [symm #303]: #107
-#667 := [monotonicity #665]: #666
-#668 := [trans #667 #664]: #712
-#651 := (not #712)
-#669 := (or #651 #713)
-#639 := [th-lemma]: #669
-#640 := [unit-resolution #639 #668]: #713
-#806 := (>= #843 0::int)
-#641 := (or #651 #806)
-#642 := [th-lemma]: #641
-#644 := [unit-resolution #642 #668]: #806
-#636 := [th-lemma #630 #643 #644 #640]: #634
-#635 := [symm #636]: #637
-#611 := [monotonicity #635]: #610
-#597 := [symm #611]: #596
-#606 := (= #27 #550)
-decl f10 :: (-> int S5 S5)
-#854 := (f10 3::int f11)
-#570 := (f17 #854)
-#834 := (= #570 #550)
-#828 := (= #550 #570)
-#57 := (:var 0 S5)
-#77 := (:var 1 int)
-#78 := (f10 #77 #57)
-#953 := (pattern #78)
-#59 := (f17 #57)
-#111 := (f4 #59)
-#307 := (+ #111 #255)
-#311 := (f3 #307)
-#110 := (f17 #78)
-#314 := (= #110 #311)
-#954 := (forall (vars (?v0 int) (?v1 S5)) (:pat #953) #314)
-#317 := (forall (vars (?v0 int) (?v1 S5)) #314)
-#957 := (iff #317 #954)
-#955 := (iff #314 #314)
-#956 := [refl]: #955
-#958 := [quant-intro #956]: #957
-#368 := (~ #317 #317)
-#401 := (~ #314 #314)
-#402 := [refl]: #401
-#369 := [nnf-pos #402]: #368
-#112 := (+ #111 #88)
-#113 := (f3 #112)
-#114 := (= #110 #113)
-#115 := (forall (vars (?v0 int) (?v1 S5)) #114)
-#318 := (iff #115 #317)
-#315 := (iff #114 #314)
-#312 := (= #113 #311)
-#309 := (= #112 #307)
-#310 := [monotonicity #257]: #309
-#313 := [monotonicity #310]: #312
-#316 := [monotonicity #313]: #315
-#319 := [quant-intro #316]: #318
-#306 := [asserted]: #115
-#322 := [mp #306 #319]: #317
-#372 := [mp~ #322 #369]: #317
-#959 := [mp #372 #958]: #954
-#831 := (not #954)
-#826 := (or #831 #828)
-#840 := (+ #843 #255)
-#555 := (f3 #840)
-#556 := (= #570 #555)
-#832 := (or #831 #556)
-#674 := (iff #832 #826)
-#817 := (iff #826 #826)
-#818 := [rewrite]: #817
-#825 := (iff #556 #828)
-#829 := (iff #834 #828)
-#824 := [rewrite]: #829
-#838 := (iff #556 #834)
-#833 := (= #555 #550)
-#835 := (= #840 #557)
-#836 := [rewrite]: #835
-#837 := [monotonicity #836]: #833
-#827 := [monotonicity #837]: #838
-#830 := [trans #827 #824]: #825
-#675 := [monotonicity #830]: #674
-#819 := [trans #675 #818]: #674
-#673 := [quant-inst]: #832
-#820 := [mp #673 #819]: #826
-#659 := [unit-resolution #820 #959]: #828
-#594 := [symm #659]: #834
-#604 := (= #27 #570)
-decl f9 :: (-> S5 S2)
-#491 := (f9 #854)
-#842 := (= #491 #570)
-#910 := (pattern #59)
-#58 := (f9 #57)
-#909 := (pattern #58)
-#60 := (= #58 #59)
-#911 := (forall (vars (?v0 S5)) (:pat #909 #910) #60)
-#61 := (forall (vars (?v0 S5)) #60)
-#914 := (iff #61 #911)
-#912 := (iff #60 #60)
-#913 := [refl]: #912
-#915 := [quant-intro #913]: #914
-#348 := (~ #61 #61)
-#391 := (~ #60 #60)
-#392 := [refl]: #391
-#349 := [nnf-pos #392]: #348
-#237 := [asserted]: #61
-#356 := [mp~ #237 #349]: #61
-#916 := [mp #356 #915]: #911
-#571 := (not #911)
-#844 := (or #571 #842)
-#554 := [quant-inst]: #844
-#657 := [unit-resolution #554 #916]: #842
-#855 := (= #27 #491)
-#35 := (f10 #14 f11)
-#894 := (pattern #35)
-#32 := (f6 #14)
-#893 := (pattern #32)
-#36 := (f9 #35)
-#33 := (f5 #32)
-#37 := (= #33 #36)
-#895 := (forall (vars (?v0 int)) (:pat #893 #894) #37)
-#38 := (forall (vars (?v0 int)) #37)
-#898 := (iff #38 #895)
-#896 := (iff #37 #37)
-#897 := [refl]: #896
-#899 := [quant-intro #897]: #898
-#342 := (~ #38 #38)
-#387 := (~ #37 #37)
-#388 := [refl]: #387
-#343 := [nnf-pos #388]: #342
-#224 := [asserted]: #38
-#344 := [mp~ #224 #343]: #38
-#900 := [mp #344 #899]: #895
-#497 := (not #895)
-#858 := (or #497 #855)
-#856 := [quant-inst]: #858
-#618 := [unit-resolution #856 #900]: #855
-#605 := [trans #618 #657]: #604
-#595 := [trans #605 #594]: #606
-#584 := [trans #595 #597]: #607
-#587 := [trans #584 #599]: #586
-#589 := [trans #587 #624]: #588
-#591 := [trans #589 #601]: #590
-#592 := [trans #591 #603]: #30
-#31 := (not #30)
-#223 := [asserted]: #31
-[unit-resolution #223 #592]: false
-unsat
-030f06ff279b2b609c311e25ffea5c845380fd2c 97 0
-#2 := false
-decl f1 :: S1
-#4 := f1
+#538 := (not true)
+#543 := (iff #538 false)
+#544 := [rewrite]: #543
+#880 := (iff #900 #538)
+#554 := (iff #567 true)
+#896 := [rewrite]: #554
+#542 := [monotonicity #896]: #880
+#882 := [trans #542 #544]: #545
+#553 := (iff #904 #895)
+#558 := [rewrite]: #553
+#885 := [monotonicity #558 #882]: #884
+#524 := [trans #885 #881]: #887
+#889 := [monotonicity #524]: #891
+#879 := [trans #889 #878]: #891
+#530 := [quant-inst]: #529
+#586 := [mp #530 #879]: #890
+#684 := [unit-resolution #586 #993]: #895
+#656 := (= #687 #898)
+#39 := (= #38 #35)
+#177 := (= #35 #38)
+#178 := (iff #39 #177)
+#179 := [rewrite]: #178
+#175 := [asserted]: #39
+#182 := [mp #175 #179]: #177
+#666 := [symm #182]: #39
+#646 := [monotonicity #666]: #656
+#648 := [trans #646 #684]: #818
+#649 := (not #818)
+#652 := (or #649 #820)
+#653 := [th-lemma]: #652
+#657 := [unit-resolution #653 #648]: #820
+#830 := (>= #687 0::int)
+#650 := (or #649 #830)
+#658 := [th-lemma]: #650
+#651 := [unit-resolution #658 #648]: #830
+#763 := (<= #145 1::int)
+#786 := (= #145 1::int)
+#753 := (or #888 #786)
+#795 := (>= 1::int 0::int)
+#796 := (not #795)
+#783 := (= 1::int #145)
+#784 := (or #783 #796)
+#754 := (or #888 #784)
+#758 := (iff #754 #753)
+#760 := (iff #753 #753)
+#765 := [rewrite]: #760
+#779 := (iff #784 #786)
+#775 := (or #786 false)
+#778 := (iff #775 #786)
+#773 := [rewrite]: #778
+#776 := (iff #784 #775)
+#771 := (iff #796 false)
+#774 := (iff #796 #538)
+#782 := (iff #795 true)
+#788 := [rewrite]: #782
+#770 := [monotonicity #788]: #774
+#772 := [trans #770 #544]: #771
+#785 := (iff #783 #786)
+#787 := [rewrite]: #785
+#777 := [monotonicity #787 #772]: #776
+#752 := [trans #777 #773]: #779
+#759 := [monotonicity #752]: #758
+#761 := [trans #759 #765]: #758
+#647 := [quant-inst]: #754
+#762 := [mp #647 #761]: #753
+#660 := [unit-resolution #762 #993]: #786
+#663 := (not #786)
+#667 := (or #663 #763)
+#669 := [th-lemma]: #667
+#670 := [unit-resolution #669 #660]: #763
+#766 := (>= #145 1::int)
+#668 := (or #663 #766)
+#671 := [th-lemma]: #668
+#659 := [unit-resolution #671 #660]: #766
+#655 := [th-lemma #659 #670 #651 #657]: #654
+#631 := [monotonicity #655]: #630
+#628 := [symm #631]: #639
+#623 := (= #117 #142)
+decl f3 :: (-> S2 S3)
+decl f9 :: S2
+#33 := f9
+#34 := (f3 f9)
+#867 := (f6 #34)
+#862 := (+ #145 #867)
+#863 := (f5 #862)
+#637 := (= #863 #142)
+#632 := (= #142 #863)
+#665 := (= 1::int #862)
+#662 := (= #862 1::int)
+#829 := (<= #867 0::int)
+#827 := (= #867 0::int)
+#673 := (= #867 #898)
+#36 := (= #34 #35)
+#174 := [asserted]: #36
+#674 := [monotonicity #174]: #673
+#675 := [trans #674 #684]: #827
+#677 := (not #827)
+#678 := (or #677 #829)
+#679 := [th-lemma]: #678
+#521 := [unit-resolution #679 #675]: #829
+#821 := (>= #867 0::int)
+#680 := (or #677 #821)
+#676 := [th-lemma]: #680
+#681 := [unit-resolution #676 #675]: #821
+#664 := [th-lemma #659 #670 #681 #521]: #662
+#661 := [symm #664]: #665
+#633 := [monotonicity #661]: #632
+#638 := [symm #633]: #637
+#621 := (= #117 #863)
+decl f4 :: (-> int S2 S2)
+#576 := (f4 3::int f9)
+#598 := (f3 #576)
+#865 := (= #598 #863)
+#9 := (:var 0 S2)
+#8 := (:var 1 int)
+#10 := (f4 #8 #9)
+#905 := (pattern #10)
+#12 := (f3 #9)
+#13 := (f6 #12)
+#148 := (+ #13 #145)
+#151 := (f5 #148)
+#11 := (f3 #10)
+#154 := (= #11 #151)
+#906 := (forall (vars (?v0 int) (?v1 S2)) (:pat #905) #154)
+#157 := (forall (vars (?v0 int) (?v1 S2)) #154)
+#909 := (iff #157 #906)
+#907 := (iff #154 #154)
+#908 := [refl]: #907
+#910 := [quant-intro #908]: #909
+#413 := (~ #157 #157)
+#411 := (~ #154 #154)
+#412 := [refl]: #411
+#414 := [nnf-pos #412]: #413
+#19 := (+ #13 #18)
+#20 := (f5 #19)
+#21 := (= #11 #20)
+#22 := (forall (vars (?v0 int) (?v1 S2)) #21)
+#158 := (iff #22 #157)
+#155 := (iff #21 #154)
+#152 := (= #20 #151)
+#149 := (= #19 #148)
+#150 := [monotonicity #147]: #149
+#153 := [monotonicity #150]: #152
+#156 := [monotonicity #153]: #155
+#159 := [quant-intro #156]: #158
+#139 := [asserted]: #22
+#162 := [mp #139 #159]: #157
+#370 := [mp~ #162 #414]: #157
+#911 := [mp #370 #910]: #906
+#708 := (not #906)
+#850 := (or #708 #865)
+#871 := (+ #867 #145)
+#860 := (f5 #871)
+#861 := (= #598 #860)
+#851 := (or #708 #861)
+#853 := (iff #851 #850)
+#848 := (iff #850 #850)
+#854 := [rewrite]: #848
+#706 := (iff #861 #865)
+#864 := (= #860 #863)
+#857 := (= #871 #862)
+#858 := [rewrite]: #857
+#859 := [monotonicity #858]: #864
+#707 := [monotonicity #859]: #706
+#847 := [monotonicity #707]: #853
+#855 := [trans #847 #854]: #853
+#852 := [quant-inst]: #851
+#849 := [mp #852 #855]: #850
+#698 := [unit-resolution #849 #911]: #865
+#619 := (= #117 #598)
+decl f15 :: (-> S2 S3)
+#580 := (f15 #576)
+#876 := (= #580 #598)
+#70 := (f15 #9)
+#948 := (pattern #70)
+#947 := (pattern #12)
+#237 := (= #12 #70)
+#949 := (forall (vars (?v0 S2)) (:pat #947 #948) #237)
+#241 := (forall (vars (?v0 S2)) #237)
+#952 := (iff #241 #949)
+#950 := (iff #237 #237)
+#951 := [refl]: #950
+#953 := [quant-intro #951]: #952
+#385 := (~ #241 #241)
+#425 := (~ #237 #237)
+#426 := [refl]: #425
+#386 := [nnf-pos #426]: #385
+#71 := (= #70 #12)
+#72 := (forall (vars (?v0 S2)) #71)
+#242 := (iff #72 #241)
+#239 := (iff #71 #237)
+#240 := [rewrite]: #239
+#243 := [quant-intro #240]: #242
+#236 := [asserted]: #72
+#246 := [mp #236 #243]: #241
+#427 := [mp~ #246 #386]: #241
+#954 := [mp #427 #953]: #949
+#577 := (not #949)
+#587 := (or #577 #876)
+#872 := (= #598 #580)
+#588 := (or #577 #872)
+#590 := (iff #588 #587)
+#869 := (iff #587 #587)
+#583 := [rewrite]: #869
+#873 := (iff #872 #876)
+#877 := [rewrite]: #873
+#868 := [monotonicity #877]: #590
+#866 := [trans #868 #583]: #590
+#589 := [quant-inst]: #588
+#870 := [mp #589 #866]: #587
+#697 := [unit-resolution #870 #954]: #876
+#561 := (= #117 #580)
+#89 := (f4 #86 f9)
+#964 := (pattern #89)
+#87 := (f21 #86)
+#963 := (pattern #87)
+#90 := (f15 #89)
+#88 := (f17 #87)
+#91 := (= #88 #90)
+#965 := (forall (vars (?v0 int)) (:pat #963 #964) #91)
+#92 := (forall (vars (?v0 int)) #91)
+#968 := (iff #92 #965)
+#966 := (iff #91 #91)
+#967 := [refl]: #966
+#969 := [quant-intro #967]: #968
+#389 := (~ #92 #92)
+#431 := (~ #91 #91)
+#432 := [refl]: #431
+#390 := [nnf-pos #432]: #389
+#264 := [asserted]: #92
+#397 := [mp~ #264 #390]: #92
+#970 := [mp #397 #969]: #965
+#555 := (not #965)
+#686 := (or #555 #561)
+#893 := [quant-inst]: #686
+#642 := [unit-resolution #893 #970]: #561
+#620 := [trans #642 #697]: #619
+#622 := [trans #620 #698]: #621
+#624 := [trans #622 #638]: #623
+#618 := [trans #624 #628]: #625
+#611 := [trans #618 #641]: #626
+#613 := [trans #611 #643]: #612
+#615 := [trans #613 #617]: #361
+#364 := (not #361)
 decl f2 :: S1
 #5 := f2
-#9 := 3::int
-decl f3 :: int
-#8 := f3
-#46 := (>= f3 3::int)
-#51 := (ite #46 f2 f1)
-#73 := (= f1 #51)
-#58 := (ite #46 f1 f2)
-#69 := (= f1 #58)
-#115 := (iff #69 #73)
-#113 := (iff #73 #69)
-#61 := (= #51 #58)
-#12 := (<= 3::int f3)
-#13 := (ite #12 f1 f2)
-#10 := (< f3 3::int)
-#11 := (ite #10 f1 f2)
-#14 := (distinct #11 #13)
-#15 := (not #14)
-#64 := (iff #15 #61)
-#33 := (= #11 #13)
-#62 := (iff #33 #61)
-#59 := (= #13 #58)
-#56 := (iff #12 #46)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#54 := (= #11 #51)
-#44 := (not #46)
-#48 := (ite #44 f1 f2)
-#52 := (= #48 #51)
-#53 := [rewrite]: #52
-#49 := (= #11 #48)
-#45 := (iff #10 #44)
-#47 := [rewrite]: #45
-#50 := [monotonicity #47]: #49
-#55 := [trans #50 #53]: #54
-#63 := [monotonicity #55 #60]: #62
-#42 := (iff #15 #33)
-#34 := (not #33)
-#37 := (not #34)
-#40 := (iff #37 #33)
-#41 := [rewrite]: #40
-#38 := (iff #15 #37)
-#35 := (iff #14 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#43 := [trans #39 #41]: #42
-#65 := [trans #43 #63]: #64
-#32 := [asserted]: #15
-#66 := [mp #32 #65]: #61
-#114 := [monotonicity #66]: #113
-#116 := [symm #114]: #115
-#109 := (not #73)
-#6 := (= f1 f2)
-#67 := (= f2 #58)
-#105 := (iff #67 #6)
-#103 := (iff #6 #67)
-#98 := (= #58 f2)
-#101 := (iff #98 #67)
-#102 := [commutativity]: #101
-#99 := (iff #6 #98)
-#96 := [hypothesis]: #73
-#97 := [trans #96 #66]: #69
-#100 := [monotonicity #97]: #99
-#104 := [trans #100 #102]: #103
-#106 := [symm #104]: #105
-#72 := (= f2 #51)
-#84 := (iff #72 #67)
-#85 := [monotonicity #66]: #84
-#80 := (not #67)
-#81 := [hypothesis]: #80
-#78 := (or #46 #67)
-#79 := [def-axiom]: #78
-#82 := [unit-resolution #79 #81]: #46
-#74 := (or #44 #72)
-#75 := [def-axiom]: #74
-#83 := [unit-resolution #75 #82]: #72
-#86 := [mp #83 #85]: #67
-#87 := [unit-resolution #81 #86]: false
-#88 := [lemma #87]: #67
-#107 := [mp #88 #106]: #6
-#7 := (not #6)
-#31 := [asserted]: #7
-#108 := [unit-resolution #31 #107]: false
-#110 := [lemma #108]: #109
-#70 := (or #46 #73)
-#71 := [def-axiom]: #70
-#111 := [unit-resolution #71 #110]: #46
-#76 := (or #44 #69)
-#77 := [def-axiom]: #76
-#112 := [unit-resolution #77 #111]: #69
-#117 := [mp #112 #116]: #73
-[unit-resolution #110 #117]: false
-unsat
+#118 := (ite true f1 f2)
+#119 := (f22 #118)
+#120 := (f19 #119)
+#121 := (= #117 #120)
+#122 := (not #121)
+#365 := (iff #122 #364)
+#362 := (iff #121 #361)
+#359 := (= #120 #358)
+#356 := (= #119 #355)
+#353 := (= #118 f1)
+#354 := [rewrite]: #353
+#357 := [monotonicity #354]: #356
+#360 := [monotonicity #357]: #359
+#363 := [monotonicity #360]: #362
+#366 := [monotonicity #363]: #365
+#352 := [asserted]: #122
+#369 := [mp #352 #366]: #364
+[unit-resolution #369 #615]: false
+unsat

--- a/src/HOL/SMT_Examples/SMT_Tests.certs	Tue Dec 07 15:01:42 2010 +0100
+++ b/src/HOL/SMT_Examples/SMT_Tests.certs	Tue Dec 07 15:44:38 2010 +0100
@@ -1,4 +1,4 @@
-1b7b7e7109fa2efdf94c204be8d611210920badb 8 0
+27f3d7664eb694b08bf7c88f0f09b921356d5fea 8 0
 #2 := false
 #1 := true
 #8 := (not true)
@@ -7,7 +7,97 @@
 #25 := [asserted]: #8
 [mp #25 #27]: false
 unsat
-24d44e2684a632b0246b194cc850faec2cea7de6 33 0
+7bb4486255a1690e20bf9760b1235d3e037d98e9 16 0
+#2 := false
+#8 := (not false)
+#9 := (not #8)
+#34 := (iff #9 false)
+#1 := true
+#29 := (not true)
+#32 := (iff #29 false)
+#33 := [rewrite]: #32
+#30 := (iff #9 #29)
+#27 := (iff #8 true)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#35 := [trans #31 #33]: #34
+#26 := [asserted]: #9
+[mp #26 #35]: false
+unsat
+072b5b67a4edb88cdfcfa44b3f443bed4c4c0ef4 21 0
+#2 := false
+#1 := true
+#8 := (not true)
+#9 := (not #8)
+#10 := (not #9)
+#39 := (iff #10 false)
+#28 := (iff #8 false)
+#29 := [rewrite]: #28
+#37 := (iff #10 #8)
+#35 := (iff #9 true)
+#30 := (not false)
+#33 := (iff #30 true)
+#34 := [rewrite]: #33
+#31 := (iff #9 #30)
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#38 := [monotonicity #36]: #37
+#40 := [trans #38 #29]: #39
+#27 := [asserted]: #10
+[mp #27 #40]: false
+unsat
+4c707ebe2e6f66c7bbcde6020a7ec4f65dcccb79 16 0
+#2 := false
+#1 := true
+#8 := (and true true)
+#9 := (not #8)
+#34 := (iff #9 false)
+#29 := (not true)
+#32 := (iff #29 false)
+#33 := [rewrite]: #32
+#30 := (iff #9 #29)
+#27 := (iff #8 true)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#35 := [trans #31 #33]: #34
+#26 := [asserted]: #9
+[mp #26 #35]: false
+unsat
+ef6c58f81472b258f0f2137921a2a94eab384ff7 16 0
+#2 := false
+#1 := true
+#8 := (or true false)
+#9 := (not #8)
+#34 := (iff #9 false)
+#29 := (not true)
+#32 := (iff #29 false)
+#33 := [rewrite]: #32
+#30 := (iff #9 #29)
+#27 := (iff #8 true)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#35 := [trans #31 #33]: #34
+#26 := [asserted]: #9
+[mp #26 #35]: false
+unsat
+209b382eef0e852d5577153b1de372bdd198f7e1 16 0
+#2 := false
+#1 := true
+#8 := (implies false true)
+#9 := (not #8)
+#34 := (iff #9 false)
+#29 := (not true)
+#32 := (iff #29 false)
+#33 := [rewrite]: #32
+#30 := (iff #9 #29)
+#27 := (iff #8 true)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#35 := [trans #31 #33]: #34
+#26 := [asserted]: #9
+[mp #26 #35]: false
+unsat
+fc240ca706e2afb45ac99ed81ac8b1c880202f6e 33 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -41,24 +131,7 @@
 #29 := [asserted]: #12
 [mp #29 #49]: false
 unsat
-e13aa83df86f7aa731de8803590214f1f328e559 16 0
-#2 := false
-#8 := (not false)
-#9 := (not #8)
-#34 := (iff #9 false)
-#1 := true
-#29 := (not true)
-#32 := (iff #29 false)
-#33 := [rewrite]: #32
-#30 := (iff #9 #29)
-#27 := (iff #8 true)
-#28 := [rewrite]: #27
-#31 := [monotonicity #28]: #30
-#35 := [trans #31 #33]: #34
-#26 := [asserted]: #9
-[mp #26 #35]: false
-unsat
-f420673acb14abe98ee018177f96f582264715f6 41 0
+e385314f79c5a5b8dbbdfaaf9a6c8d6828128c4a 41 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -100,29 +173,7 @@
 #30 := [asserted]: #13
 [mp #30 #57]: false
 unsat
-1ca9ca5e02de1f4179a12b1248e2289c51261af2 21 0
-#2 := false
-#1 := true
-#8 := (not true)
-#9 := (not #8)
-#10 := (not #9)
-#39 := (iff #10 false)
-#28 := (iff #8 false)
-#29 := [rewrite]: #28
-#37 := (iff #10 #8)
-#35 := (iff #9 true)
-#30 := (not false)
-#33 := (iff #30 true)
-#34 := [rewrite]: #33
-#31 := (iff #9 #30)
-#32 := [monotonicity #29]: #31
-#36 := [trans #32 #34]: #35
-#38 := [monotonicity #36]: #37
-#40 := [trans #38 #29]: #39
-#27 := [asserted]: #10
-[mp #27 #40]: false
-unsat
-cdbc0ed6463ef1f60801c650813ddb76e5fc1674 65 0
+ec944116b678571769e708d1cc09c6b68699f503 65 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -188,24 +239,7 @@
 #33 := [asserted]: #16
 [mp #33 #81]: false
 unsat
-717a63b9f4d0d299b9c3ce33521d4ac56124d7b8 16 0
-#2 := false
-#1 := true
-#8 := (and true true)
-#9 := (not #8)
-#34 := (iff #9 false)
-#29 := (not true)
-#32 := (iff #29 false)
-#33 := [rewrite]: #32
-#30 := (iff #9 #29)
-#27 := (iff #8 true)
-#28 := [rewrite]: #27
-#31 := [monotonicity #28]: #30
-#35 := [trans #31 #33]: #34
-#26 := [asserted]: #9
-[mp #26 #35]: false
-unsat
-c378fcdabec52ebd4390861a6f8953415c34a0b9 29 0
+c76deee2b63c9556d2aea2bdd3c683287afa20e3 29 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -235,24 +269,7 @@
 #28 := [asserted]: #11
 [mp #28 #45]: false
 unsat
-383085ca96bed3199fce8a7516860e635411bc13 16 0
-#2 := false
-#1 := true
-#8 := (or true false)
-#9 := (not #8)
-#34 := (iff #9 false)
-#29 := (not true)
-#32 := (iff #29 false)
-#33 := [rewrite]: #32
-#30 := (iff #9 #29)
-#27 := (iff #8 true)
-#28 := [rewrite]: #27
-#31 := [monotonicity #28]: #30
-#35 := [trans #31 #33]: #34
-#26 := [asserted]: #9
-[mp #26 #35]: false
-unsat
-b8d5743ec1146548a209ace4cd6155117ecb0983 41 0
+be450040b15ee19fc486621652f216dade137c79 41 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -294,24 +311,7 @@
 #30 := [asserted]: #13
 [mp #30 #57]: false
 unsat
-bfcbf10bac83ae3af48158f2275ff2d80613bb1c 16 0
-#2 := false
-#1 := true
-#8 := (implies false true)
-#9 := (not #8)
-#34 := (iff #9 false)
-#29 := (not true)
-#32 := (iff #29 false)
-#33 := [rewrite]: #32
-#30 := (iff #9 #29)
-#27 := (iff #8 true)
-#28 := [rewrite]: #27
-#31 := [monotonicity #28]: #30
-#35 := [trans #31 #33]: #34
-#26 := [asserted]: #9
-[mp #26 #35]: false
-unsat
-1318ba8c39667bffead89e0e37453cef395b803a 47 0
[phone]b42807eb585206954a1cc3f02581d6 47 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -359,157 +359,7 @@
 #32 := [asserted]: #15
 [mp #32 #62]: false
 unsat
-3613b4af790179e90308b88e5d17e375488860dc 149 0
-#2 := false
-decl f5 :: S1
-#12 := f5
-decl f1 :: S1
-#4 := f1
-#44 := (= f1 f5)
-decl f4 :: S1
-#10 := f4
-#41 := (= f1 f4)
-decl f3 :: S1
-#8 := f3
-#38 := (= f1 f3)
-#47 := (ite #38 #41 #44)
-#53 := (not #38)
-#54 := (or #53 #41)
-#64 := (or #38 #44)
-#91 := (not #64)
-#90 := (not #54)
-#92 := (or #90 #91)
-#143 := [hypothesis]: #90
-#128 := (or #92 #54)
-#129 := [def-axiom]: #128
-#144 := [unit-resolution #129 #143]: #92
-#78 := (not #47)
-#116 := (or #54 #38)
-#117 := [def-axiom]: #116
-#145 := [unit-resolution #117 #143]: #38
-#110 := (not #41)
-#118 := (or #54 #110)
-#119 := [def-axiom]: #118
-#146 := [unit-resolution #119 #143]: #110
-#106 := (or #78 #53 #41)
-#107 := [def-axiom]: #106
-#147 := [unit-resolution #107 #146 #145]: #78
-#93 := (not #92)
-#137 := (or #47 #93)
-#100 := (iff #47 #92)
-#69 := (and #54 #64)
-#79 := (iff #69 #78)
-#103 := (iff #79 #100)
-#95 := (iff #92 #47)
-#101 := (iff #95 #100)
-#102 := [rewrite]: #101
-#98 := (iff #79 #95)
-#87 := (iff #93 #78)
-#96 := (iff #87 #95)
-#97 := [rewrite]: #96
-#84 := (iff #79 #87)
-#88 := (iff #69 #93)
-#89 := [rewrite]: #88
-#94 := [monotonicity #89]: #84
-#99 := [trans #94 #97]: #98
-#104 := [trans #99 #102]: #103
-#13 := (= f5 f1)
-#9 := (= f3 f1)
-#16 := (not #9)
-#17 := (implies #16 #13)
-#11 := (= f4 f1)
-#15 := (implies #9 #11)
-#18 := (and #15 #17)
-#14 := (ite #9 #11 #13)
-#19 := (iff #14 #18)
-#20 := (not #19)
-#82 := (iff #20 #79)
-#72 := (iff #47 #69)
-#75 := (not #72)
-#80 := (iff #75 #79)
-#81 := [rewrite]: #80
-#76 := (iff #20 #75)
-#73 := (iff #19 #72)
-#70 := (iff #18 #69)
-#67 := (iff #17 #64)
-#61 := (implies #53 #44)
-#65 := (iff #61 #64)
-#66 := [rewrite]: #65
-#62 := (iff #17 #61)
-#45 := (iff #13 #44)
-#46 := [rewrite]: #45
-#59 := (iff #16 #53)
-#39 := (iff #9 #38)
-#40 := [rewrite]: #39
-#60 := [monotonicity #40]: #59
-#63 := [monotonicity #60 #46]: #62
-#68 := [trans #63 #66]: #67
-#57 := (iff #15 #54)
-#50 := (implies #38 #41)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #15 #50)
-#42 := (iff #11 #41)
-#43 := [rewrite]: #42
-#52 := [monotonicity #40 #43]: #51
-#58 := [trans #52 #56]: #57
-#71 := [monotonicity #58 #68]: #70
-#48 := (iff #14 #47)
-#49 := [monotonicity #40 #43 #46]: #48
-#74 := [monotonicity #49 #71]: #73
-#77 := [monotonicity #74]: #76
-#83 := [trans #77 #81]: #82
-#37 := [asserted]: #20
-#86 := [mp #37 #83]: #79
-#105 := [mp #86 #104]: #100
-#134 := (not #100)
-#135 := (or #47 #93 #134)
-#136 := [def-axiom]: #135
-#138 := [unit-resolution #136 #105]: #137
-#148 := [unit-resolution #138 #147 #144]: false
-#149 := [lemma #148]: #54
-#150 := [hypothesis]: #78
-#156 := (or #38 #47)
-#151 := [unit-resolution #138 #150]: #93
-#130 := (or #92 #64)
-#131 := [def-axiom]: #130
-#152 := [unit-resolution #131 #151]: #64
-#153 := [hypothesis]: #53
-#113 := (not #44)
-#114 := (or #47 #38 #113)
-#115 := [def-axiom]: #114
-#154 := [unit-resolution #115 #153 #150]: #113
-#126 := (or #91 #38 #44)
-#127 := [def-axiom]: #126
-#155 := [unit-resolution #127 #154 #153 #152]: false
-#157 := [lemma #155]: #156
-#158 := [unit-resolution #157 #150]: #38
-#111 := (or #47 #53 #110)
-#112 := [def-axiom]: #111
-#159 := [unit-resolution #112 #158 #150]: #110
-#120 := (or #90 #53 #41)
-#121 := [def-axiom]: #120
-#160 := [unit-resolution #121 #159 #158 #149]: false
-#161 := [lemma #160]: #47
-#141 := (or #78 #92)
-#139 := (or #78 #92 #134)
-#140 := [def-axiom]: #139
-#142 := [unit-resolution #140 #105]: #141
-#162 := [unit-resolution #142 #161]: #92
-#132 := (or #93 #90 #91)
-#133 := [def-axiom]: #132
-#163 := [unit-resolution #133 #162 #149]: #91
-#122 := (or #64 #53)
-#123 := [def-axiom]: #122
-#164 := [unit-resolution #123 #163]: #53
-#124 := (or #64 #113)
-#125 := [def-axiom]: #124
-#165 := [unit-resolution #125 #163]: #113
-#108 := (or #78 #38 #44)
-#109 := [def-axiom]: #108
-[unit-resolution #109 #165 #164 #161]: false
-unsat
-f66e70c965ea5e45c5d8d8afc12c5c9d8f438bbf 47 0
+1fcb3e8fb3886b4e41baf22a375337d02cacf5b0 47 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -557,74 +407,7 @@
 #32 := [asserted]: #15
 [mp #32 #62]: false
 unsat
-6a02b3f460d6b73a1c8bb9bc10adaf8bab0c8e8d 66 0
-#2 := false
-decl f3 :: S1
-#8 := f3
-decl f1 :: S1
-#4 := f1
-#33 := (= f1 f3)
-#51 := (not #33)
-#87 := [hypothesis]: #33
-decl f4 :: S1
-#10 := f4
-#36 := (= f1 f4)
-#42 := (not #36)
-#43 := (or #33 #42)
-#69 := (or #43 #51)
-#70 := [def-axiom]: #69
-#88 := [unit-resolution #70 #87]: #43
-#67 := (not #43)
-#89 := (or #51 #67)
-#52 := (or #51 #36)
-#57 := (ite #33 #43 #52)
-#60 := (not #57)
-#11 := (= f4 f1)
-#9 := (= f3 f1)
-#13 := (implies #9 #11)
-#12 := (implies #11 #9)
-#14 := (ite #9 #12 #13)
-#15 := (not #14)
-#61 := (iff #15 #60)
-#58 := (iff #14 #57)
-#55 := (iff #13 #52)
-#48 := (implies #33 #36)
-#53 := (iff #48 #52)
-#54 := [rewrite]: #53
-#49 := (iff #13 #48)
-#37 := (iff #11 #36)
-#38 := [rewrite]: #37
-#34 := (iff #9 #33)
-#35 := [rewrite]: #34
-#50 := [monotonicity #35 #38]: #49
-#56 := [trans #50 #54]: #55
-#46 := (iff #12 #43)
-#39 := (implies #36 #33)
-#44 := (iff #39 #43)
-#45 := [rewrite]: #44
-#40 := (iff #12 #39)
-#41 := [monotonicity #38 #35]: #40
-#47 := [trans #41 #45]: #46
-#59 := [monotonicity #35 #47 #56]: #58
-#62 := [monotonicity #59]: #61
-#32 := [asserted]: #15
-#65 := [mp #32 #62]: #60
-#83 := (or #57 #51 #67)
-#84 := [def-axiom]: #83
-#90 := [unit-resolution #84 #65]: #89
-#91 := [unit-resolution #90 #88 #87]: false
-#92 := [lemma #91]: #51
-#63 := (or #52 #33)
-#73 := [def-axiom]: #63
-#93 := [unit-resolution #73 #92]: #52
-#76 := (not #52)
-#94 := (or #33 #76)
-#85 := (or #57 #33 #76)
-#86 := [def-axiom]: #85
-#95 := [unit-resolution #86 #65]: #94
-[unit-resolution #95 #93 #92]: false
-unsat
-6ad20e70359f46e3ce1c064a3b8026cad7cd2ff8 55 0
+b178802033a170fc6ecb904aa96ba25da6ec1165 55 0
 #2 := false
 decl f3 :: S1
 #8 := f3
@@ -680,75 +463,7 @@
 #71 := [and-elim #70]: #33
 [mp #71 #77]: false
 unsat
-6b05ab468934ffcc0e31bde41bfd81d0a9deefeb 67 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f6 :: S1
-#15 := f6
-#16 := (= f6 f1)
-decl f5 :: S1
-#13 := f5
-#14 := (= f5 f1)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#18 := (ite #11 #14 #16)
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#19 := (ite #9 #14 #18)
-#12 := (or #9 #11)
-#17 := (ite #12 #14 #16)
-#20 := (iff #17 #19)
-#21 := (not #20)
-#79 := (iff #21 false)
-#1 := true
-#74 := (not true)
-#77 := (iff #74 false)
-#78 := [rewrite]: #77
-#75 := (iff #21 #74)
-#72 := (iff #20 true)
-#51 := (= f1 f6)
-#48 := (= f1 f5)
-#42 := (= f1 f4)
-#39 := (= f1 f3)
-#45 := (or #39 #42)
-#54 := (ite #45 #48 #51)
-#67 := (iff #54 #54)
-#70 := (iff #67 true)
-#71 := [rewrite]: #70
-#68 := (iff #20 #67)
-#65 := (iff #19 #54)
-#57 := (ite #42 #48 #51)
-#60 := (ite #39 #48 #57)
-#63 := (iff #60 #54)
-#64 := [rewrite]: #63
-#61 := (iff #19 #60)
-#58 := (iff #18 #57)
-#52 := (iff #16 #51)
-#53 := [rewrite]: #52
-#49 := (iff #14 #48)
-#50 := [rewrite]: #49
-#43 := (iff #11 #42)
-#44 := [rewrite]: #43
-#59 := [monotonicity #44 #50 #53]: #58
-#40 := (iff #9 #39)
-#41 := [rewrite]: #40
-#62 := [monotonicity #41 #50 #59]: #61
-#66 := [trans #62 #64]: #65
-#55 := (iff #17 #54)
-#46 := (iff #12 #45)
-#47 := [monotonicity #41 #44]: #46
-#56 := [monotonicity #47 #50 #53]: #55
-#69 := [monotonicity #56 #66]: #68
-#73 := [trans #69 #71]: #72
-#76 := [monotonicity #73]: #75
-#80 := [trans #76 #78]: #79
-#38 := [asserted]: #21
-[mp #38 #80]: false
-unsat
-2b253648b79acb0e52fb9e262cb32419808d9871 55 0
+59cf6501e494fe14a36d21c4ab5189ac053d2eca 55 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -804,75 +519,7 @@
 #33 := [asserted]: #16
 [mp #33 #70]: false
 unsat
-641947287e52d98b055b0c416150e15eb1a766da 67 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f6 :: S1
-#15 := f6
-#16 := (= f6 f1)
-decl f5 :: S1
-#13 := f5
-#14 := (= f5 f1)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#18 := (ite #11 #14 #16)
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#19 := (ite #9 #18 #16)
-#12 := (and #9 #11)
-#17 := (ite #12 #14 #16)
-#20 := (iff #17 #19)
-#21 := (not #20)
-#79 := (iff #21 false)
-#1 := true
-#74 := (not true)
-#77 := (iff #74 false)
-#78 := [rewrite]: #77
-#75 := (iff #21 #74)
-#72 := (iff #20 true)
-#51 := (= f1 f6)
-#48 := (= f1 f5)
-#42 := (= f1 f4)
-#39 := (= f1 f3)
-#45 := (and #39 #42)
-#54 := (ite #45 #48 #51)
-#67 := (iff #54 #54)
-#70 := (iff #67 true)
-#71 := [rewrite]: #70
-#68 := (iff #20 #67)
-#65 := (iff #19 #54)
-#57 := (ite #42 #48 #51)
-#60 := (ite #39 #57 #51)
-#63 := (iff #60 #54)
-#64 := [rewrite]: #63
-#61 := (iff #19 #60)
-#52 := (iff #16 #51)
-#53 := [rewrite]: #52
-#58 := (iff #18 #57)
-#49 := (iff #14 #48)
-#50 := [rewrite]: #49
-#43 := (iff #11 #42)
-#44 := [rewrite]: #43
-#59 := [monotonicity #44 #50 #53]: #58
-#40 := (iff #9 #39)
-#41 := [rewrite]: #40
-#62 := [monotonicity #41 #59 #53]: #61
-#66 := [trans #62 #64]: #65
-#55 := (iff #17 #54)
-#46 := (iff #12 #45)
-#47 := [monotonicity #41 #44]: #46
-#56 := [monotonicity #47 #50 #53]: #55
-#69 := [monotonicity #56 #66]: #68
-#73 := [trans #69 #71]: #72
-#76 := [monotonicity #73]: #75
-#80 := [trans #76 #78]: #79
-#38 := [asserted]: #21
-[mp #38 #80]: false
-unsat
-9b964feeca237f6b2088e905866f89fe7614b790 55 0
+6220da01bb600f0ca7f9e59911510ed14e1df0e7 55 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -928,194 +575,7 @@
 #33 := [asserted]: #16
 [mp #33 #70]: false
 unsat
-d314e49b3b13f8d1c45bdec28f1a923eafa9dd30 186 0
-#2 := false
-decl f5 :: S1
-#12 := f5
-decl f1 :: S1
-#4 := f1
-#47 := (= f1 f5)
-decl f3 :: S1
-#8 := f3
-#41 := (= f1 f3)
-#59 := (not #41)
-#76 := (or #59 #47)
-#119 := (not #76)
-decl f4 :: S1
-#10 := f4
-#44 := (= f1 f4)
-#68 := (or #59 #44)
-decl f6 :: S1
-#14 := f6
-#50 := (= f1 f6)
-#84 := (or #59 #50)
-#89 := (ite #68 #76 #84)
-#130 := (not #89)
-#53 := (ite #44 #47 #50)
-#60 := (or #59 #53)
-#112 := (not #44)
-#165 := [hypothesis]: #112
-#172 := (or #60 #44)
-#98 := (not #60)
-#163 := [hypothesis]: #98
-#148 := (or #60 #41)
-#149 := [def-axiom]: #148
-#164 := [unit-resolution #149 #163]: #41
-#124 := (not #50)
-#139 := (not #53)
-#150 := (or #60 #139)
-#151 := [def-axiom]: #150
-#166 := [unit-resolution #151 #163]: #139
-#146 := (or #53 #44 #124)
-#147 := [def-axiom]: #146
-#167 := [unit-resolution #147 #166 #165]: #124
-#157 := (or #89 #60)
-#99 := (iff #89 #98)
-#15 := (= f6 f1)
-#9 := (= f3 f1)
-#20 := (implies #9 #15)
-#13 := (= f5 f1)
-#19 := (implies #9 #13)
-#11 := (= f4 f1)
-#18 := (implies #9 #11)
-#21 := (ite #18 #19 #20)
-#16 := (ite #11 #13 #15)
-#17 := (implies #9 #16)
-#22 := (iff #17 #21)
-#23 := (not #22)
-#102 := (iff #23 #99)
-#92 := (iff #60 #89)
-#95 := (not #92)
-#100 := (iff #95 #99)
-#101 := [rewrite]: #100
-#96 := (iff #23 #95)
-#93 := (iff #22 #92)
-#90 := (iff #21 #89)
-#87 := (iff #20 #84)
-#81 := (implies #41 #50)
-#85 := (iff #81 #84)
-#86 := [rewrite]: #85
-#82 := (iff #20 #81)
-#51 := (iff #15 #50)
-#52 := [rewrite]: #51
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#83 := [monotonicity #43 #52]: #82
-#88 := [trans #83 #86]: #87
-#79 := (iff #19 #76)
-#73 := (implies #41 #47)
-#77 := (iff #73 #76)
-#78 := [rewrite]: #77
-#74 := (iff #19 #73)
-#48 := (iff #13 #47)
-#49 := [rewrite]: #48
-#75 := [monotonicity #43 #49]: #74
-#80 := [trans #75 #78]: #79
-#71 := (iff #18 #68)
-#65 := (implies #41 #44)
-#69 := (iff #65 #68)
-#70 := [rewrite]: #69
-#66 := (iff #18 #65)
-#45 := (iff #11 #44)
-#46 := [rewrite]: #45
-#67 := [monotonicity #43 #46]: #66
-#72 := [trans #67 #70]: #71
-#91 := [monotonicity #72 #80 #88]: #90
-#63 := (iff #17 #60)
-#56 := (implies #41 #53)
-#61 := (iff #56 #60)
-#62 := [rewrite]: #61
-#57 := (iff #17 #56)
-#54 := (iff #16 #53)
-#55 := [monotonicity #46 #49 #52]: #54
-#58 := [monotonicity #43 #55]: #57
-#64 := [trans #58 #62]: #63
-#94 := [monotonicity #64 #91]: #93
-#97 := [monotonicity #94]: #96
-#103 := [trans #97 #101]: #102
-#40 := [asserted]: #23
-#106 := [mp #40 #103]: #99
-#154 := (not #99)
-#155 := (or #89 #60 #154)
-#156 := [def-axiom]: #155
-#158 := [unit-resolution #156 #106]: #157
-#168 := [unit-resolution #158 #163]: #89
-#109 := (not #68)
-#107 := (or #109 #59 #44)
-#104 := [def-axiom]: #107
-#169 := [unit-resolution #104 #164 #165]: #109
-#133 := (or #130 #68 #84)
-#134 := [def-axiom]: #133
-#170 := [unit-resolution #134 #169 #168]: #84
-#127 := (not #84)
-#128 := (or #127 #59 #50)
-#129 := [def-axiom]: #128
-#171 := [unit-resolution #129 #170 #167 #164]: false
-#173 := [lemma #171]: #172
-#176 := [unit-resolution #173 #165]: #60
-#161 := (or #130 #98)
-#159 := (or #130 #98 #154)
-#160 := [def-axiom]: #159
-#162 := [unit-resolution #160 #106]: #161
-#182 := [unit-resolution #162 #176]: #130
-#180 := (or #84 #44)
-#174 := [hypothesis]: #127
-#125 := (or #84 #124)
-#126 := [def-axiom]: #125
-#175 := [unit-resolution #126 #174]: #124
-#122 := (or #84 #41)
-#123 := [def-axiom]: #122
-#177 := [unit-resolution #123 #174]: #41
-#152 := (or #98 #59 #53)
-#153 := [def-axiom]: #152
-#178 := [unit-resolution #153 #177 #176]: #53
-#142 := (or #139 #44 #50)
-#143 := [def-axiom]: #142
-#179 := [unit-resolution #143 #178 #175 #165]: false
-#181 := [lemma #179]: #180
-#183 := [unit-resolution #181 #165]: #84
-#137 := (or #89 #68 #127)
-#138 := [def-axiom]: #137
-#184 := [unit-resolution #138 #183 #182]: #68
-#135 := (or #89 #109 #119)
-#136 := [def-axiom]: #135
-#185 := [unit-resolution #136 #184 #182]: #119
-#186 := [unit-resolution #104 #184 #165]: #59
-#114 := (or #76 #41)
-#115 := [def-axiom]: #114
-#187 := [unit-resolution #115 #186 #185]: false
-#188 := [lemma #187]: #44
-#113 := (or #68 #112)
-#108 := [def-axiom]: #113
-#191 := [unit-resolution #108 #188]: #68
-#189 := [hypothesis]: #59
-#190 := [unit-resolution #149 #189]: #60
-#192 := [unit-resolution #115 #189]: #76
-#193 := [unit-resolution #136 #192 #191]: #89
-#194 := [unit-resolution #162 #193 #190]: false
-#195 := [lemma #194]: #41
-#116 := (not #47)
-#144 := (or #53 #112 #116)
-#145 := [def-axiom]: #144
-#196 := [unit-resolution #145 #166 #188]: #116
-#131 := (or #130 #109 #76)
-#132 := [def-axiom]: #131
-#197 := [unit-resolution #132 #168 #191]: #76
-#120 := (or #119 #59 #47)
-#121 := [def-axiom]: #120
-#198 := [unit-resolution #121 #197 #196 #195]: false
-#199 := [lemma #198]: #60
-#200 := [unit-resolution #162 #199]: #130
-#201 := [unit-resolution #136 #200 #191]: #119
-#202 := [unit-resolution #153 #199 #195]: #53
-#140 := (or #139 #112 #47)
-#141 := [def-axiom]: #140
-#203 := [unit-resolution #141 #202 #188]: #47
-#117 := (or #76 #116)
-#118 := [def-axiom]: #117
-[unit-resolution #118 #203 #201]: false
-unsat
-9edb7fb964a6bff17daa4ba37de7c9c60f75b958 49 0
+722d76167f69901e5e517b9ce7dbced7df05219a 49 0
 #2 := false
 decl f3 :: S1
 #8 := f3
@@ -1165,41 +625,7 @@
 #63 := [and-elim #61]: #34
 [mp #63 #69]: false
 unsat
-a7388049ad99f131accb8444cd89b6a9c1fac45f 33 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#10 := (not #9)
-#11 := (ite #9 #9 #10)
-#12 := (not #11)
-#48 := (iff #12 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (iff #11 true)
-#30 := (= f1 f3)
-#33 := (not #30)
-#36 := (ite #30 #30 #33)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (iff #10 #33)
-#31 := (iff #9 #30)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#38 := [monotonicity #32 #32 #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#29 := [asserted]: #12
-[mp #29 #49]: false
-unsat
-60c47bbe18daad2442ee45433370ee0806f6bb96 54 0
+009c8e0b629d50a9319d944965a95df2ef001769 54 0
 #2 := false
 decl f3 :: S1
 #8 := f3
@@ -1254,41 +680,7 @@
 #68 := [and-elim #66]: #34
 [mp #68 #74]: false
 unsat
-39f56c1d543d6413fc0dc639b2b6f15664655196 33 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#10 := (not #9)
-#11 := (ite #10 #10 #9)
-#12 := (not #11)
-#48 := (iff #12 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (iff #11 true)
-#30 := (= f1 f3)
-#33 := (not #30)
-#36 := (ite #33 #33 #30)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#31 := (iff #9 #30)
-#32 := [rewrite]: #31
-#34 := (iff #10 #33)
-#35 := [monotonicity #32]: #34
-#38 := [monotonicity #35 #35 #32]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#29 := [asserted]: #12
-[mp #29 #49]: false
-unsat
-4262551db767bfb5375132641dc2c0e90be1daa4 60 0
+5e8d3e4e571a6be75302ab3922f28b8a389d8db0 60 0
 #2 := false
 decl f4 :: S1
 #10 := f4
@@ -1349,26 +741,7 @@
 #70 := [mp #35 #67]: #64
 [mp #70 #68]: false
 unsat
-6a7b76cfae07a340fb39c8963a01cd95eedd8bf9 18 0
-#2 := false
-decl f3 :: S2
-#8 := f3
-#9 := (= f3 f3)
-#10 := (not #9)
-#35 := (iff #10 false)
-#1 := true
-#30 := (not true)
-#33 := (iff #30 false)
-#34 := [rewrite]: #33
-#31 := (iff #10 #30)
-#28 := (iff #9 true)
-#29 := [rewrite]: #28
-#32 := [monotonicity #29]: #31
-#36 := [trans #32 #34]: #35
-#27 := [asserted]: #10
-[mp #27 #36]: false
-unsat
-09afbbf0eb362cf37facfae99f9d6f31556e820b 79 0
+a3787341d3326ac09e6f21f682cc6e58f515bbff 79 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -1448,37 +821,7 @@
 #36 := [asserted]: #19
 [mp #36 #93]: false
 unsat
-902a92cdc108cc8b99cf8896d6549c8ca538e3d0 29 0
-#2 := false
-decl f3 :: S2
-#8 := f3
-decl f4 :: S2
-#9 := f4
-#11 := (= f4 f3)
-#10 := (= f3 f4)
-#12 := (implies #10 #11)
-#13 := (not #12)
-#45 := (iff #13 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #13 #40)
-#38 := (iff #12 true)
-#33 := (implies #10 #10)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #12 #33)
-#31 := (iff #11 #10)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#30 := [asserted]: #13
-[mp #30 #46]: false
-unsat
-be971aad38d2b7ade1dc5cd9703570a52b3c13d8 94 0
+270a0cae20cbd732ed90f673daa3c9b353a23b96 94 0
 #2 := false
 decl f5 :: S1
 #13 := f5
@@ -1573,42 +916,7 @@
 #96 := [not-or-elim #89]: #70
 [mp #96 #112]: false
 unsat
-adac1ab250a9687a951445e1ab79aef512dbc4ce 34 0
-#2 := false
-decl f5 :: S2
-#11 := f5
-decl f3 :: S2
-#8 := f3
-#14 := (= f3 f5)
-decl f4 :: S2
-#9 := f4
-#12 := (= f4 f5)
-#58 := (iff #12 #14)
-#56 := (iff #14 #12)
-#10 := (= f3 f4)
-#13 := (and #10 #12)
-#34 := (not #13)
-#35 := (or #34 #14)
-#38 := (not #35)
-#15 := (implies #13 #14)
-#16 := (not #15)
-#39 := (iff #16 #38)
-#36 := (iff #15 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#33 := [asserted]: #16
-#43 := [mp #33 #40]: #38
-#41 := [not-or-elim #43]: #13
-#42 := [and-elim #41]: #10
-#57 := [monotonicity #42]: #56
-#59 := [symm #57]: #58
-#44 := [and-elim #41]: #12
-#54 := [mp #44 #59]: #14
-#45 := (not #14)
-#46 := [not-or-elim #43]: #45
-[unit-resolution #46 #54]: false
-unsat
-e22b0ec4c7a382fdc38d1cae4e9ead0e7119241c 114 0
+51b392e35cc2e80b3fc739019a4888f77b93369c 114 0
 #2 := false
 decl f5 :: S1
 #13 := f5
@@ -1723,35 +1031,7 @@
 #136 := [unit-resolution #109 #135]: #87
 [unit-resolution #93 #136 #134]: false
 unsat
-fecb07c630f2b4838d9143ebd9c448ef1d8c0d9f 27 0
-#2 := false
-decl f5 :: (-> S2 S2)
-decl f4 :: S2
-#9 := f4
-#12 := (f5 f4)
-decl f3 :: S2
-#8 := f3
-#11 := (f5 f3)
-#13 := (= #11 #12)
-#10 := (= f3 f4)
-#33 := (not #10)
-#34 := (or #33 #13)
-#37 := (not #34)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#38 := (iff #15 #37)
-#35 := (iff #14 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#32 := [asserted]: #15
-#42 := [mp #32 #39]: #37
-#40 := [not-or-elim #42]: #10
-#51 := [monotonicity #40]: #13
-#41 := (not #13)
-#43 := [not-or-elim #42]: #41
-[unit-resolution #43 #51]: false
-unsat
-bd0235065d3ae8e8f7120ef8c728cacf6335092d 121 0
+c42384063a08c7420f8333e32fa97fd6b34bd630 121 0
 #2 := false
 decl f5 :: S1
 #13 := f5
@@ -1873,39 +1153,7 @@
 #99 := [not-or-elim #92]: #98
 [mp #99 #138]: false
 unsat
-d0fff77820573b42e578c359c531050dc8cc1cb7 31 0
-#2 := false
-decl f5 :: (-> S2 S2 S3)
-decl f3 :: S2
-#8 := f3
-decl f4 :: S2
-#9 := f4
-#12 := (f5 f4 f3)
-#11 := (f5 f3 f4)
-#13 := (= #11 #12)
-#53 := (= #12 #11)
-#10 := (= f3 f4)
-#33 := (not #10)
-#34 := (or #33 #13)
-#37 := (not #34)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#38 := (iff #15 #37)
-#35 := (iff #14 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#32 := [asserted]: #15
-#42 := [mp #32 #39]: #37
-#40 := [not-or-elim #42]: #10
-#51 := (= f4 f3)
-#52 := [symm #40]: #51
-#54 := [monotonicity #52 #40]: #53
-#49 := [symm #54]: #13
-#41 := (not #13)
-#43 := [not-or-elim #42]: #41
-[unit-resolution #43 #49]: false
-unsat
-b0ca15f9e66f88090a8bcf746cc11c5e9df6c55c 110 0
+cec0cddb259f90d6deedc5613c8283444ad481b7 110 0
 #2 := false
 decl f4 :: S1
 #10 := f4
@@ -2016,71 +1264,7 @@
 #84 := [and-elim #83]: #44
 [mp #84 #129]: false
 unsat
-18f8f90b1403ab11e524a667a0fd98ca5bbf61ca 63 0
-#2 := false
-decl f3 :: (-> S2 S2)
-decl f4 :: S2
-#8 := f4
-#9 := (f3 f4)
-#46 := (= f4 #9)
-#10 := (f3 #9)
-#12 := (f3 #10)
-#78 := (= #12 #9)
-#76 := (= #9 #12)
-#37 := (= f4 #10)
-#13 := (f3 #12)
-#14 := (f3 #13)
-#40 := (= f4 #14)
-#43 := (and #37 #40)
-#52 := (not #43)
-#53 := (or #52 #46)
-#58 := (not #53)
-#17 := (= #9 f4)
-#15 := (= #14 f4)
-#11 := (= #10 f4)
-#16 := (and #11 #15)
-#18 := (implies #16 #17)
-#19 := (not #18)
-#59 := (iff #19 #58)
-#56 := (iff #18 #53)
-#49 := (implies #43 #46)
-#54 := (iff #49 #53)
-#55 := [rewrite]: #54
-#50 := (iff #18 #49)
-#47 := (iff #17 #46)
-#48 := [rewrite]: #47
-#44 := (iff #16 #43)
-#41 := (iff #15 #40)
-#42 := [rewrite]: #41
-#38 := (iff #11 #37)
-#39 := [rewrite]: #38
-#45 := [monotonicity #39 #42]: #44
-#51 := [monotonicity #45 #48]: #50
-#57 := [trans #51 #55]: #56
-#60 := [monotonicity #57]: #59
-#36 := [asserted]: #19
-#63 := [mp #36 #60]: #58
-#61 := [not-or-elim #63]: #43
-#62 := [and-elim #61]: #37
-#77 := [monotonicity #62]: #76
-#79 := [symm #77]: #78
-#81 := (= f4 #12)
-#67 := (= #14 #12)
-#70 := (= #12 #14)
-#72 := (= #10 #13)
-#74 := (= #13 #10)
-#75 := [monotonicity #79]: #74
-#73 := [symm #75]: #72
-#71 := [monotonicity #73]: #70
-#80 := [symm #71]: #67
-#64 := [and-elim #61]: #40
-#82 := [trans #64 #80]: #81
-#83 := [trans #82 #79]: #46
-#65 := (not #46)
-#66 := [not-or-elim #63]: #65
-[unit-resolution #66 #83]: false
-unsat
-a46bdf5ddd9c6bc8726e86b886e63d5fce2aa764 127 0
+d4c96b4039c5892a80f4e3e2fde2c5a1b9d87ba4 127 0
 #2 := false
 decl f5 :: S1
 #13 := f5
@@ -2208,203 +1392,7 @@
 #149 := [unit-resolution #131 #147]: #97
 [unit-resolution #108 #149 #148]: false
 unsat
-937f73f84ea1ebaa68a1a0ee6c81cfd2f4fda91b 195 0
-#2 := false
-decl f6 :: S2
-#13 := f6
-decl f4 :: S2
-#10 := f4
-#15 := (= f4 f6)
-decl f5 :: S2
-#11 := f5
-decl f3 :: S1
-#8 := f3
-decl f1 :: S1
-#4 := f1
-#40 := (= f1 f3)
-#43 := (ite #40 f4 f5)
-#49 := (= f6 #43)
-#200 := (iff #49 #15)
-#198 := (iff #15 #49)
-#46 := (= #43 f6)
-#50 := (iff #46 #49)
-#197 := [commutativity]: #50
-#195 := (iff #15 #46)
-#110 := (= f4 #43)
-#111 := (= f5 #43)
-#57 := (not #40)
-#180 := [hypothesis]: #57
-#114 := (or #40 #111)
-#115 := [def-axiom]: #114
-#184 := [unit-resolution #115 #180]: #111
-#185 := (= f6 f5)
-#18 := (= f5 f6)
-#174 := (iff #110 #15)
-#172 := (iff #15 #110)
-#68 := (or #18 #40)
-#95 := (not #68)
-#58 := (or #15 #57)
-#94 := (not #58)
-#96 := (or #94 #95)
-#123 := (not #18)
-#147 := [hypothesis]: #123
-#157 := (or #96 #18)
-#97 := (not #96)
-#145 := [hypothesis]: #97
-#132 := (or #96 #68)
-#133 := [def-axiom]: #132
-#148 := [unit-resolution #133 #145]: #68
-#128 := (or #95 #18 #40)
-#129 := [def-axiom]: #128
-#149 := [unit-resolution #129 #148 #147]: #40
-#112 := (or #57 #110)
-#113 := [def-axiom]: #112
-#150 := [unit-resolution #113 #149]: #110
-#153 := (= f6 f4)
-#130 := (or #96 #58)
-#131 := [def-axiom]: #130
-#151 := [unit-resolution #131 #145]: #58
-#121 := (or #94 #15 #57)
-#122 := [def-axiom]: #121
-#152 := [unit-resolution #122 #149 #151]: #15
-#154 := [symm #152]: #153
-#155 := [trans #154 #150]: #49
-#82 := (not #49)
-#143 := (or #82 #96)
-#104 := (iff #49 #96)
-#73 := (and #58 #68)
-#83 := (iff #73 #82)
-#107 := (iff #83 #104)
-#99 := (iff #96 #49)
-#105 := (iff #99 #104)
-#106 := [rewrite]: #105
-#102 := (iff #83 #99)
-#91 := (iff #97 #82)
-#100 := (iff #91 #99)
-#101 := [rewrite]: #100
-#88 := (iff #83 #91)
-#92 := (iff #73 #97)
-#93 := [rewrite]: #92
-#98 := [monotonicity #93]: #88
-#103 := [trans #98 #101]: #102
-#108 := [trans #103 #106]: #107
-#9 := (= f3 f1)
-#17 := (not #9)
-#19 := (implies #17 #18)
-#16 := (implies #9 #15)
-#20 := (and #16 #19)
-#12 := (ite #9 f4 f5)
-#14 := (= #12 f6)
-#21 := (iff #14 #20)
-#22 := (not #21)
-#86 := (iff #22 #83)
-#76 := (iff #49 #73)
-#79 := (not #76)
-#84 := (iff #79 #83)
-#85 := [rewrite]: #84
-#80 := (iff #22 #79)
-#77 := (iff #21 #76)
-#74 := (iff #20 #73)
-#71 := (iff #19 #68)
-#65 := (implies #57 #18)
-#69 := (iff #65 #68)
-#70 := [rewrite]: #69
-#66 := (iff #19 #65)
-#63 := (iff #17 #57)
-#41 := (iff #9 #40)
-#42 := [rewrite]: #41
-#64 := [monotonicity #42]: #63
-#67 := [monotonicity #64]: #66
-#72 := [trans #67 #70]: #71
-#61 := (iff #16 #58)
-#54 := (implies #40 #15)
-#59 := (iff #54 #58)
-#60 := [rewrite]: #59
-#55 := (iff #16 #54)
-#56 := [monotonicity #42]: #55
-#62 := [trans #56 #60]: #61
-#75 := [monotonicity #62 #72]: #74
-#52 := (iff #14 #49)
-#51 := [rewrite]: #50
-#47 := (iff #14 #46)
-#44 := (= #12 #43)
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#53 := [trans #48 #51]: #52
-#78 := [monotonicity #53 #75]: #77
-#81 := [monotonicity #78]: #80
-#87 := [trans #81 #85]: #86
-#39 := [asserted]: #22
-#90 := [mp #39 #87]: #83
-#109 := [mp #90 #108]: #104
-#136 := (not #104)
-#141 := (or #82 #96 #136)
-#142 := [def-axiom]: #141
-#144 := [unit-resolution #142 #109]: #143
-#146 := [unit-resolution #144 #145]: #82
-#156 := [unit-resolution #146 #155]: false
-#158 := [lemma #156]: #157
-#159 := [unit-resolution #158 #147]: #96
-#139 := (or #49 #97)
-#137 := (or #49 #97 #136)
-#138 := [def-axiom]: #137
-#140 := [unit-resolution #138 #109]: #139
-#160 := [unit-resolution #140 #159]: #49
-#173 := [monotonicity #160]: #172
-#175 := [symm #173]: #174
-#163 := (not #111)
-#164 := (iff #123 #163)
-#161 := (iff #18 #111)
-#162 := [monotonicity #160]: #161
-#165 := [monotonicity #162]: #164
-#166 := [mp #147 #165]: #163
-#167 := [unit-resolution #115 #166]: #40
-#171 := [unit-resolution #113 #167]: #110
-#176 := [mp #171 #175]: #15
-#116 := (not #15)
-#126 := (or #68 #57)
-#127 := [def-axiom]: #126
-#168 := [unit-resolution #127 #167]: #68
-#134 := (or #97 #94 #95)
-#135 := [def-axiom]: #134
-#169 := [unit-resolution #135 #168 #159]: #94
-#117 := (or #58 #116)
-#118 := [def-axiom]: #117
-#170 := [unit-resolution #118 #169]: #116
-#177 := [unit-resolution #170 #176]: false
-#178 := [lemma #177]: #18
-#186 := [symm #178]: #185
-#187 := [trans #186 #184]: #49
-#124 := (or #68 #123)
-#125 := [def-axiom]: #124
-#179 := [unit-resolution #125 #178]: #68
-#119 := (or #58 #40)
-#120 := [def-axiom]: #119
-#181 := [unit-resolution #120 #180]: #58
-#182 := [unit-resolution #135 #181 #179]: #97
-#183 := [unit-resolution #144 #182]: #82
-#188 := [unit-resolution #183 #187]: false
-#189 := [lemma #188]: #40
-#194 := [unit-resolution #113 #189]: #110
-#196 := [monotonicity #194]: #195
-#199 := [trans #196 #197]: #198
-#201 := [symm #199]: #200
-#202 := (iff #82 #116)
-#203 := [monotonicity #201]: #202
-#190 := [hypothesis]: #82
-#204 := [mp #190 #203]: #116
-#191 := [unit-resolution #140 #190]: #97
-#192 := [unit-resolution #131 #191]: #58
-#193 := [unit-resolution #122 #192 #189]: #15
-#205 := [unit-resolution #193 #204]: false
-#206 := [lemma #205]: #49
-#210 := [mp #206 #201]: #15
-#207 := [unit-resolution #144 #206]: #96
-#208 := [unit-resolution #135 #207 #179]: #94
-#209 := [unit-resolution #118 #208]: #116
-[unit-resolution #209 #210]: false
-unsat
-622e9d57e1cdc32316cdcbb8529fc67f719c97a9 66 0
+58d42da4d2fc3bf1d0deaebbdc2b39920dc4ca47 66 0
 #2 := false
 decl f3 :: S1
 #8 := f3
@@ -2471,7 +1459,7 @@
 #74 := [not-or-elim #84]: #33
 [unit-resolution #69 #74]: false
 unsat
-2e293f73ef5ad101901501ab2dcfcefd193999bd 156 0
+4d70ce282766c8e62a597d6306537b6d05756176 156 0
 #2 := false
 decl f5 :: S1
 #13 := f5
@@ -2628,7 +1616,7 @@
 #114 := [def-axiom]: #113
 [unit-resolution #114 #172 #170]: false
 unsat
-ab1dfd2f679d7dbdde93be399a76ec5036d3899f 114 0
+1cb1add1e3b1dfeb1d711784a7c208f84678a0d9 114 0
 #2 := false
 decl f5 :: S1
 #13 := f5
@@ -2743,7 +1731,7 @@
 #101 := [mp #36 #100]: #94
 [mp #101 #130]: false
 unsat
-2bb827008c60da1ea2c111246c9460521c7fdcf1 198 0
+23293b41d6a5ad2616587e474beecdda1f9568ef 198 0
 #2 := false
 decl f5 :: S1
 #14 := f5
@@ -2942,7 +1930,7 @@
 #141 := [not-or-elim #136]: #93
 [mp #141 #215]: false
 unsat
-6ab97d6ee969f9713508f655f280864782914283 134 0
+53cd213efadac08155ca536222059e95193eb915 134 0
 #2 := false
 decl f5 :: S1
 #14 := f5
@@ -3077,44 +2065,7 @@
 #121 := [not-or-elim #116]: #81
 [mp #121 #151]: false
 unsat
-9cc560481317ca8682cca4f4dca87fc7141c9928 36 0
-#2 := false
-decl f5 :: S2
-#10 := f5
-decl f3 :: S2
-#8 := f3
-#12 := (= f3 f5)
-#13 := (not #12)
-decl f4 :: S2
-#9 := f4
-#11 := (distinct f3 f4 f5)
-#33 := (not #11)
-#34 := (or #33 #13)
-#37 := (not #34)
-#14 := (implies #11 #13)
-#15 := (not #14)
-#38 := (iff #15 #37)
-#35 := (iff #14 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#32 := [asserted]: #15
-#42 := [mp #32 #39]: #37
-#41 := [not-or-elim #42]: #12
-#52 := (= f4 f5)
-#53 := (not #52)
-#50 := (= f3 f4)
-#51 := (not #50)
-#48 := (and #51 #13 #53)
-#40 := [not-or-elim #42]: #11
-#58 := (or #33 #48)
-#59 := [def-axiom]: #58
-#62 := [unit-resolution #59 #40]: #48
-#49 := (not #48)
-#45 := (or #49 #13)
-#43 := [def-axiom]: #45
-[unit-resolution #43 #62 #41]: false
-unsat
-d6c8bfd9e0a388a9f9feea361765c0999d6f6245 162 0
+6702062f648f00a98bab630b1b620cd3add21bfa 162 0
 #2 := false
 decl f5 :: S1
 #12 := f5
@@ -3277,85 +2228,7 @@
 #178 := [unit-resolution #128 #177]: #70
 [unit-resolution #136 #178 #176 #168]: false
 unsat
-4a0a614367c2678ce3a689bf35cf13d010d59c1c 77 0
-#2 := false
-decl f4 :: S2
-#9 := f4
-decl f3 :: S2
-#8 := f3
-#81 := (= f3 f4)
-decl f6 :: S2
-#12 := f6
-#36 := (= f4 f6)
-#100 := (iff #36 #81)
-#98 := (iff #81 #36)
-#13 := (= f6 f4)
-#37 := (iff #13 #36)
-#97 := [commutativity]: #37
-#95 := (iff #81 #13)
-#14 := (= f3 f6)
-#42 := (not #36)
-#15 := (not #14)
-decl f5 :: S2
-#10 := f5
-#11 := (distinct f3 f4 f5)
-#51 := (not #11)
-#60 := (or #51 #15 #42)
-#63 := (not #60)
-#16 := (implies #13 #15)
-#17 := (implies #11 #16)
-#18 := (not #17)
-#66 := (iff #18 #63)
-#43 := (or #15 #42)
-#52 := (or #51 #43)
-#57 := (not #52)
-#64 := (iff #57 #63)
-#61 := (iff #52 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#58 := (iff #18 #57)
-#55 := (iff #17 #52)
-#48 := (implies #11 #43)
-#53 := (iff #48 #52)
-#54 := [rewrite]: #53
-#49 := (iff #17 #48)
-#46 := (iff #16 #43)
-#39 := (implies #36 #15)
-#44 := (iff #39 #43)
-#45 := [rewrite]: #44
-#40 := (iff #16 #39)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#47 := [trans #41 #45]: #46
-#50 := [monotonicity #47]: #49
-#56 := [trans #50 #54]: #55
-#59 := [monotonicity #56]: #58
-#67 := [trans #59 #65]: #66
-#35 := [asserted]: #18
-#68 := [mp #35 #67]: #63
-#70 := [not-or-elim #68]: #14
-#96 := [monotonicity #70]: #95
-#99 := [trans #96 #97]: #98
-#101 := [symm #99]: #100
-#71 := [not-or-elim #68]: #36
-#102 := [mp #71 #101]: #81
-#82 := (not #81)
-#79 := (= f4 f5)
-#80 := (not #79)
-#83 := (= f3 f5)
-#84 := (not #83)
-#77 := (and #82 #84 #80)
-#69 := [not-or-elim #68]: #11
-#89 := (or #51 #77)
-#90 := [def-axiom]: #89
-#93 := [unit-resolution #90 #69]: #77
-#78 := (not #77)
-#75 := (or #78 #82)
-#76 := [def-axiom]: #75
-#94 := [unit-resolution #76 #93]: #82
-[unit-resolution #94 #102]: false
-unsat
-0758d598d78862cf824e4f1011456a0914ccf6a2 54 0
+d96349c9740061e8c73eeede21ae8428e07d488a 54 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -3410,36 +2283,7 @@
 #31 := [asserted]: #14
 [mp #31 #69]: false
 unsat
-1c0d1ac708791c5472b4c7d4618f1f27059a330a 28 0
-#2 := false
-decl f4 :: S2
-#9 := f4
-decl f3 :: S2
-#8 := f3
-#10 := (distinct f3 f4 f3 f4)
-#11 := (not #10)
-#12 := (not #11)
-#44 := (iff #12 false)
-#1 := true
-#39 := (not true)
-#42 := (iff #39 false)
-#43 := [rewrite]: #42
-#40 := (iff #12 #39)
-#37 := (iff #11 true)
-#32 := (not false)
-#35 := (iff #32 true)
-#36 := [rewrite]: #35
-#33 := (iff #11 #32)
-#30 := (iff #10 false)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31]: #33
-#38 := [trans #34 #36]: #37
-#41 := [monotonicity #38]: #40
-#45 := [trans #41 #43]: #44
-#29 := [asserted]: #12
-[mp #29 #45]: false
-unsat
-d823881369082411f62355b0e1a48f25c2d70d32 144 0
+b66aba4abb1abadacc2b7883456eaf2c7aa12977 144 0
 #2 := false
 decl f5 :: S1
 #12 := f5
@@ -3584,38 +2428,7 @@
 #126 := [not-or-elim #121]: #102
 [mp #126 #161]: false
 unsat
-2b10f8f450bda227c77b2302c26fe079a9366159 30 0
-#2 := false
-decl f4 :: S2
-#9 := f4
-decl f3 :: S2
-#8 := f3
-#10 := (= f3 f4)
-#11 := (not #10)
-#12 := (not #11)
-#13 := (implies #10 #12)
-#14 := (not #13)
-#46 := (iff #14 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #14 #41)
-#39 := (iff #13 true)
-#34 := (implies #10 #10)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #13 #34)
-#32 := (iff #12 #10)
-#33 := [rewrite]: #32
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#31 := [asserted]: #14
-[mp #31 #47]: false
-unsat
-8bc104940e4bdef62a563b12c192439ecd08c6c2 121 0
+1a277449532cd73fa9304d67c89484ad0b48cccb 121 0
 #2 := false
 decl f5 :: S1
 #13 := f5
@@ -3737,48 +2550,7 @@
 #115 := [not-or-elim #109]: #90
 [mp #115 #138]: false
 unsat
-c9f554ce0537c03818658e81b19fe84ceb0185a6 40 0
-#2 := false
-decl f5 :: S2
-#11 := f5
-decl f4 :: S2
-#9 := f4
-decl f3 :: S2
-#8 := f3
-#14 := (distinct f3 f4 f5)
-#15 := (not #14)
-#12 := (= f3 f5)
-#10 := (= f3 f4)
-#13 := (and #10 #12)
-#35 := (not #13)
-#36 := (or #35 #15)
-#39 := (not #36)
-#16 := (implies #13 #15)
-#17 := (not #16)
-#40 := (iff #17 #39)
-#37 := (iff #16 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#34 := [asserted]: #17
-#44 := [mp #34 #41]: #39
-#46 := [not-or-elim #44]: #14
-#58 := (= f4 f5)
-#59 := (not #58)
-#57 := (not #12)
-#56 := (not #10)
-#54 := (and #56 #57 #59)
-#55 := (not #54)
-#42 := [not-or-elim #44]: #13
-#43 := [and-elim #42]: #10
-#52 := (or #55 #56)
-#53 := [def-axiom]: #52
-#66 := [unit-resolution #53 #43]: #55
-#62 := (or #15 #54)
-#63 := [def-axiom]: #62
-#67 := [unit-resolution #63 #66]: #15
-[unit-resolution #67 #46]: false
-unsat
-43b0ec204044e8a9ddd46de106038d6a70829412 123 0
+f33edc3b0a48d09d8e2c7769a8f6835a6c065ee4 123 0
 #2 := false
 decl f4 :: S1
 #10 := f4
@@ -3902,41 +2674,7 @@
 #92 := [not-or-elim #91]: #72
 [mp #92 #141]: false
 unsat
-b4be7a04408986e429b4f7b85392a0d8faa4a56b 33 0
-#2 := false
-decl f3 :: S2
-#8 := f3
-decl f5 :: S2
-#10 := f5
-decl f4 :: S2
-#9 := f4
-decl f6 :: S2
-#11 := f6
-#13 := (distinct f6 f4 f5 f3)
-#12 := (distinct f3 f4 f5 f6)
-#14 := (implies #12 #13)
-#15 := (not #14)
-#47 := (iff #15 false)
-#1 := true
-#42 := (not true)
-#45 := (iff #42 false)
-#46 := [rewrite]: #45
-#43 := (iff #15 #42)
-#40 := (iff #14 true)
-#35 := (implies #12 #12)
-#38 := (iff #35 true)
-#39 := [rewrite]: #38
-#36 := (iff #14 #35)
-#33 := (iff #13 #12)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#32 := [asserted]: #15
-[mp #32 #48]: false
-unsat
-65d147f6ee969d919cd3b4f850a39f6a343f10f2 60 0
+383ece7b02c55c30a001c04e97c12d3f4c655a3e 60 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -3997,99 +2735,7 @@
 #34 := [asserted]: #17
 [mp #34 #75]: false
 unsat
-58054335ac968ebfdfe24a066ff933b0b06bebaf 91 0
-#2 := false
-decl f5 :: S2
-#10 := f5
-decl f4 :: S2
-#9 := f4
-decl f3 :: S2
-#8 := f3
-#13 := (distinct f3 f4 f5)
-#67 := (= f4 f5)
-#68 := (not #67)
-#63 := (= f3 f5)
-#64 := (not #63)
-#61 := (= f3 f4)
-#62 := (not #61)
-#93 := (and #62 #64 #68)
-decl f6 :: S2
-#11 := f6
-#71 := (= f5 f6)
-#72 := (not #71)
-#69 := (= f4 f6)
-#70 := (not #69)
-#65 := (= f3 f6)
-#66 := (not #65)
-#73 := (and #62 #64 #66 #68 #70 #72)
-#12 := (distinct f3 f4 f5 f6)
-#14 := (distinct f4 f5 f6)
-#15 := (and #13 #14)
-#35 := (not #12)
-#36 := (or #35 #15)
-#39 := (not #36)
-#16 := (implies #12 #15)
-#17 := (not #16)
-#40 := (iff #17 #39)
-#37 := (iff #16 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#34 := [asserted]: #17
-#44 := [mp #34 #41]: #39
-#42 := [not-or-elim #44]: #12
-#89 := (or #35 #73)
-#90 := [def-axiom]: #89
-#121 := [unit-resolution #90 #42]: #73
-#74 := (not #73)
-#75 := (or #74 #62)
-#76 := [def-axiom]: #75
-#122 := [unit-resolution #76 #121]: #62
-#81 := (or #74 #68)
-#82 := [def-axiom]: #81
-#123 := [unit-resolution #82 #121]: #68
-#77 := (or #74 #64)
-#78 := [def-axiom]: #77
-#124 := [unit-resolution #78 #121]: #64
-#101 := (or #93 #61 #63 #67)
-#102 := [def-axiom]: #101
-#125 := [unit-resolution #102 #124 #123 #122]: #93
-#94 := (not #93)
-#105 := (or #13 #94)
-#106 := [def-axiom]: #105
-#126 := [unit-resolution #106 #125]: #13
-#107 := (and #68 #70 #72)
-#85 := (or #74 #72)
-#86 := [def-axiom]: #85
-#127 := [unit-resolution #86 #121]: #72
-#83 := (or #74 #70)
-#84 := [def-axiom]: #83
-#128 := [unit-resolution #84 #121]: #70
-#115 := (or #107 #67 #69 #71)
-#116 := [def-axiom]: #115
-#129 := [unit-resolution #116 #128 #127 #123]: #107
-#108 := (not #107)
-#119 := (or #14 #108)
-#120 := [def-axiom]: #119
-#130 := [unit-resolution #120 #129]: #14
-#54 := (not #14)
-#53 := (not #13)
-#55 := (or #53 #54)
-#43 := (not #15)
-#58 := (iff #43 #55)
-#56 := (not #55)
-#49 := (not #56)
-#46 := (iff #49 #55)
-#57 := [rewrite]: #46
-#50 := (iff #43 #49)
-#51 := (iff #15 #56)
-#52 := [rewrite]: #51
-#48 := [monotonicity #52]: #50
-#59 := [trans #48 #57]: #58
-#45 := [not-or-elim #44]: #43
-#60 := [mp #45 #59]: #55
-[unit-resolution #60 #130 #126]: false
-unsat
-baf592f0a849ff17a84a15f9f01a6198981eb2cc 121 0
+b54db28c4e304df3dceea479292f30730c6d77ec 121 0
 #2 := false
 decl f5 :: S1
 #12 := f5
@@ -4211,33 +2857,7 @@
 #115 := [not-or-elim #109]: #90
 [mp #115 #138]: false
 unsat
-99555255ecbea462034ff141a5c25be38b45dd0f 25 0
-#2 := false
-#8 := (:var 0 S2)
-#9 := (= #8 #8)
-#10 := (forall (vars (?v0 S2)) #9)
-#11 := (not #10)
-#43 := (iff #11 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #11 #38)
-#36 := (iff #10 true)
-#31 := (forall (vars (?v0 S2)) true)
-#34 := (iff #31 true)
-#35 := [elim-unused]: #34
-#32 := (iff #10 #31)
-#29 := (iff #9 true)
-#30 := [rewrite]: #29
-#33 := [quant-intro #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#28 := [asserted]: #11
-[mp #28 #44]: false
-unsat
-882516ca3718492c49c1d6f4497b372b324593e7 84 0
+0330c761fb6e776ffa0aab83519bf2b97491b66a 84 0
 #2 := false
 decl f4 :: S1
 #10 := f4
@@ -4322,42 +2942,7 @@
 #96 := [unit-resolution #85 #93]: #83
 [unit-resolution #96 #101 #100]: false
 unsat
-38463bf62ec87c56bbacd6ee7e49d6b7b9e553c8 34 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: (-> S2 S1)
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#10 := (= #9 f1)
-#11 := (forall (vars (?v0 S2)) #10)
-#12 := (iff #11 #11)
-#13 := (not #12)
-#49 := (iff #13 false)
-#1 := true
-#44 := (not true)
-#47 := (iff #44 false)
-#48 := [rewrite]: #47
-#45 := (iff #13 #44)
-#42 := (iff #12 true)
-#31 := (= f1 #9)
-#34 := (forall (vars (?v0 S2)) #31)
-#37 := (iff #34 #34)
-#40 := (iff #37 true)
-#41 := [rewrite]: #40
-#38 := (iff #12 #37)
-#35 := (iff #11 #34)
-#32 := (iff #10 #31)
-#33 := [rewrite]: #32
-#36 := [quant-intro #33]: #35
-#39 := [monotonicity #36 #36]: #38
-#43 := [trans #39 #41]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#30 := [asserted]: #13
-[mp #30 #50]: false
-unsat
-c1b8de1fea5b45b3a67eb085640285bc1cfbb463 47 0
+cea538aeac5963aee31cb297e368816826235a9a 47 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -4405,7 +2990,1606 @@
 #32 := [asserted]: #15
 [mp #32 #62]: false
 unsat
-1709b6be330c8fe39899c2448147237ac354e6ac 95 0
[phone]e54deac48988da87a88c36ac7832 41 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#10 := (not #9)
+#11 := (iff #9 #10)
+#12 := (not #11)
+#13 := (not #12)
+#56 := (iff #13 false)
+#1 := true
+#51 := (not true)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #13 #51)
+#49 := (iff #12 true)
+#44 := (not false)
+#47 := (iff #44 true)
+#48 := [rewrite]: #47
+#45 := (iff #12 #44)
+#42 := (iff #11 false)
+#31 := (= f1 f3)
+#34 := (not #31)
+#37 := (iff #31 #34)
+#40 := (iff #37 false)
+#41 := [rewrite]: #40
+#38 := (iff #11 #37)
+#35 := (iff #10 #34)
+#32 := (iff #9 #31)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#39 := [monotonicity #33 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#30 := [asserted]: #13
+[mp #30 #57]: false
+unsat
+31716c0711575d307ea26c9bb489b7e38b19b7ed 60 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#14 := (not #9)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#13 := (not #11)
+#15 := (implies #13 #14)
+#12 := (implies #9 #11)
+#16 := (iff #12 #15)
+#17 := (not #16)
+#74 := (iff #17 false)
+#1 := true
+#69 := (not true)
+#72 := (iff #69 false)
+#73 := [rewrite]: #72
+#70 := (iff #17 #69)
+#67 := (iff #16 true)
+#38 := (= f1 f4)
+#35 := (= f1 f3)
+#44 := (not #35)
+#45 := (or #44 #38)
+#62 := (iff #45 #45)
+#65 := (iff #62 true)
+#66 := [rewrite]: #65
+#63 := (iff #16 #62)
+#60 := (iff #15 #45)
+#50 := (not #38)
+#55 := (implies #50 #44)
+#58 := (iff #55 #45)
+#59 := [rewrite]: #58
+#56 := (iff #15 #55)
+#53 := (iff #14 #44)
+#36 := (iff #9 #35)
+#37 := [rewrite]: #36
+#54 := [monotonicity #37]: #53
+#51 := (iff #13 #50)
+#39 := (iff #11 #38)
+#40 := [rewrite]: #39
+#52 := [monotonicity #40]: #51
+#57 := [monotonicity #52 #54]: #56
+#61 := [trans #57 #59]: #60
+#48 := (iff #12 #45)
+#41 := (implies #35 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #12 #41)
+#43 := [monotonicity #37 #40]: #42
+#49 := [trans #43 #47]: #48
+#64 := [monotonicity #49 #61]: #63
+#68 := [trans #64 #66]: #67
+#71 := [monotonicity #68]: #70
+#75 := [trans #71 #73]: #74
+#34 := [asserted]: #17
+[mp #34 #75]: false
+unsat
+ca6e3dd276584a8dfaaba79f5d93af33246ccdcc 72 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#10 := (iff #9 #9)
+#11 := (iff #9 #10)
+#12 := (iff #9 #11)
+#13 := (iff #9 #12)
+#14 := (iff #9 #13)
+#15 := (iff #9 #14)
+#16 := (iff #9 #15)
+#17 := (iff #9 #16)
+#18 := (iff #9 #17)
+#19 := (not #18)
+#87 := (iff #19 false)
+#1 := true
+#82 := (not true)
+#85 := (iff #82 false)
+#86 := [rewrite]: #85
+#83 := (iff #19 #82)
+#80 := (iff #18 true)
+#37 := (= f1 f3)
+#40 := (iff #37 #37)
+#43 := (iff #40 true)
+#44 := [rewrite]: #43
+#78 := (iff #18 #40)
+#76 := (iff #17 #37)
+#47 := (iff #37 true)
+#50 := (iff #47 #37)
+#51 := [rewrite]: #50
+#74 := (iff #17 #47)
+#72 := (iff #16 true)
+#70 := (iff #16 #40)
+#68 := (iff #15 #37)
+#66 := (iff #15 #47)
+#64 := (iff #14 true)
+#62 := (iff #14 #40)
+#60 := (iff #13 #37)
+#58 := (iff #13 #47)
+#56 := (iff #12 true)
+#54 := (iff #12 #40)
+#52 := (iff #11 #37)
+#48 := (iff #11 #47)
+#45 := (iff #10 true)
+#41 := (iff #10 #40)
+#38 := (iff #9 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39 #39]: #41
+#46 := [trans #42 #44]: #45
+#49 := [monotonicity #39 #46]: #48
+#53 := [trans #49 #51]: #52
+#55 := [monotonicity #39 #53]: #54
+#57 := [trans #55 #44]: #56
+#59 := [monotonicity #39 #57]: #58
+#61 := [trans #59 #51]: #60
+#63 := [monotonicity #39 #61]: #62
+#65 := [trans #63 #44]: #64
+#67 := [monotonicity #39 #65]: #66
+#69 := [trans #67 #51]: #68
+#71 := [monotonicity #39 #69]: #70
+#73 := [trans #71 #44]: #72
+#75 := [monotonicity #39 #73]: #74
+#77 := [trans #75 #51]: #76
+#79 := [monotonicity #39 #77]: #78
+#81 := [trans #79 #44]: #80
+#84 := [monotonicity #81]: #83
+#88 := [trans #84 #86]: #87
+#36 := [asserted]: #19
+[mp #36 #88]: false
+unsat
+8a86d4ce1fa1c422a93b13299451309ab9cab1ee 149 0
+#2 := false
+decl f5 :: S1
+#12 := f5
+decl f1 :: S1
+#4 := f1
+#44 := (= f1 f5)
+decl f4 :: S1
+#10 := f4
+#41 := (= f1 f4)
+decl f3 :: S1
+#8 := f3
+#38 := (= f1 f3)
+#47 := (ite #38 #41 #44)
+#53 := (not #38)
+#54 := (or #53 #41)
+#64 := (or #38 #44)
+#91 := (not #64)
+#90 := (not #54)
+#92 := (or #90 #91)
+#143 := [hypothesis]: #90
+#128 := (or #92 #54)
+#129 := [def-axiom]: #128
+#144 := [unit-resolution #129 #143]: #92
+#78 := (not #47)
+#116 := (or #54 #38)
+#117 := [def-axiom]: #116
+#145 := [unit-resolution #117 #143]: #38
+#110 := (not #41)
+#118 := (or #54 #110)
+#119 := [def-axiom]: #118
+#146 := [unit-resolution #119 #143]: #110
+#106 := (or #78 #53 #41)
+#107 := [def-axiom]: #106
+#147 := [unit-resolution #107 #146 #145]: #78
+#93 := (not #92)
+#137 := (or #47 #93)
+#100 := (iff #47 #92)
+#69 := (and #54 #64)
+#79 := (iff #69 #78)
+#103 := (iff #79 #100)
+#95 := (iff #92 #47)
+#101 := (iff #95 #100)
+#102 := [rewrite]: #101
+#98 := (iff #79 #95)
+#87 := (iff #93 #78)
+#96 := (iff #87 #95)
+#97 := [rewrite]: #96
+#84 := (iff #79 #87)
+#88 := (iff #69 #93)
+#89 := [rewrite]: #88
+#94 := [monotonicity #89]: #84
+#99 := [trans #94 #97]: #98
+#104 := [trans #99 #102]: #103
+#13 := (= f5 f1)
+#9 := (= f3 f1)
+#16 := (not #9)
+#17 := (implies #16 #13)
+#11 := (= f4 f1)
+#15 := (implies #9 #11)
+#18 := (and #15 #17)
+#14 := (ite #9 #11 #13)
+#19 := (iff #14 #18)
+#20 := (not #19)
+#82 := (iff #20 #79)
+#72 := (iff #47 #69)
+#75 := (not #72)
+#80 := (iff #75 #79)
+#81 := [rewrite]: #80
+#76 := (iff #20 #75)
+#73 := (iff #19 #72)
+#70 := (iff #18 #69)
+#67 := (iff #17 #64)
+#61 := (implies #53 #44)
+#65 := (iff #61 #64)
+#66 := [rewrite]: #65
+#62 := (iff #17 #61)
+#45 := (iff #13 #44)
+#46 := [rewrite]: #45
+#59 := (iff #16 #53)
+#39 := (iff #9 #38)
+#40 := [rewrite]: #39
+#60 := [monotonicity #40]: #59
+#63 := [monotonicity #60 #46]: #62
+#68 := [trans #63 #66]: #67
+#57 := (iff #15 #54)
+#50 := (implies #38 #41)
+#55 := (iff #50 #54)
+#56 := [rewrite]: #55
+#51 := (iff #15 #50)
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#52 := [monotonicity #40 #43]: #51
+#58 := [trans #52 #56]: #57
+#71 := [monotonicity #58 #68]: #70
+#48 := (iff #14 #47)
+#49 := [monotonicity #40 #43 #46]: #48
+#74 := [monotonicity #49 #71]: #73
+#77 := [monotonicity #74]: #76
+#83 := [trans #77 #81]: #82
+#37 := [asserted]: #20
+#86 := [mp #37 #83]: #79
+#105 := [mp #86 #104]: #100
+#134 := (not #100)
+#135 := (or #47 #93 #134)
+#136 := [def-axiom]: #135
+#138 := [unit-resolution #136 #105]: #137
+#148 := [unit-resolution #138 #147 #144]: false
+#149 := [lemma #148]: #54
+#150 := [hypothesis]: #78
+#156 := (or #38 #47)
+#151 := [unit-resolution #138 #150]: #93
+#130 := (or #92 #64)
+#131 := [def-axiom]: #130
+#152 := [unit-resolution #131 #151]: #64
+#153 := [hypothesis]: #53
+#113 := (not #44)
+#114 := (or #47 #38 #113)
+#115 := [def-axiom]: #114
+#154 := [unit-resolution #115 #153 #150]: #113
+#126 := (or #91 #38 #44)
+#127 := [def-axiom]: #126
+#155 := [unit-resolution #127 #154 #153 #152]: false
+#157 := [lemma #155]: #156
+#158 := [unit-resolution #157 #150]: #38
+#111 := (or #47 #53 #110)
+#112 := [def-axiom]: #111
+#159 := [unit-resolution #112 #158 #150]: #110
+#120 := (or #90 #53 #41)
+#121 := [def-axiom]: #120
+#160 := [unit-resolution #121 #159 #158 #149]: false
+#161 := [lemma #160]: #47
+#141 := (or #78 #92)
+#139 := (or #78 #92 #134)
+#140 := [def-axiom]: #139
+#142 := [unit-resolution #140 #105]: #141
+#162 := [unit-resolution #142 #161]: #92
+#132 := (or #93 #90 #91)
+#133 := [def-axiom]: #132
+#163 := [unit-resolution #133 #162 #149]: #91
+#122 := (or #64 #53)
+#123 := [def-axiom]: #122
+#164 := [unit-resolution #123 #163]: #53
+#124 := (or #64 #113)
+#125 := [def-axiom]: #124
+#165 := [unit-resolution #125 #163]: #113
+#108 := (or #78 #38 #44)
+#109 := [def-axiom]: #108
+[unit-resolution #109 #165 #164 #161]: false
+unsat
+9c8ddb9dedc1ae5880605a597b91051309bfb2e5 66 0
+#2 := false
+decl f3 :: S1
+#8 := f3
+decl f1 :: S1
+#4 := f1
+#33 := (= f1 f3)
+#51 := (not #33)
+#87 := [hypothesis]: #33
+decl f4 :: S1
+#10 := f4
+#36 := (= f1 f4)
+#42 := (not #36)
+#43 := (or #33 #42)
+#69 := (or #43 #51)
+#70 := [def-axiom]: #69
+#88 := [unit-resolution #70 #87]: #43
+#67 := (not #43)
+#89 := (or #51 #67)
+#52 := (or #51 #36)
+#57 := (ite #33 #43 #52)
+#60 := (not #57)
+#11 := (= f4 f1)
+#9 := (= f3 f1)
+#13 := (implies #9 #11)
+#12 := (implies #11 #9)
+#14 := (ite #9 #12 #13)
+#15 := (not #14)
+#61 := (iff #15 #60)
+#58 := (iff #14 #57)
+#55 := (iff #13 #52)
+#48 := (implies #33 #36)
+#53 := (iff #48 #52)
+#54 := [rewrite]: #53
+#49 := (iff #13 #48)
+#37 := (iff #11 #36)
+#38 := [rewrite]: #37
+#34 := (iff #9 #33)
+#35 := [rewrite]: #34
+#50 := [monotonicity #35 #38]: #49
+#56 := [trans #50 #54]: #55
+#46 := (iff #12 #43)
+#39 := (implies #36 #33)
+#44 := (iff #39 #43)
+#45 := [rewrite]: #44
+#40 := (iff #12 #39)
+#41 := [monotonicity #38 #35]: #40
+#47 := [trans #41 #45]: #46
+#59 := [monotonicity #35 #47 #56]: #58
+#62 := [monotonicity #59]: #61
+#32 := [asserted]: #15
+#65 := [mp #32 #62]: #60
+#83 := (or #57 #51 #67)
+#84 := [def-axiom]: #83
+#90 := [unit-resolution #84 #65]: #89
+#91 := [unit-resolution #90 #88 #87]: false
+#92 := [lemma #91]: #51
+#63 := (or #52 #33)
+#73 := [def-axiom]: #63
+#93 := [unit-resolution #73 #92]: #52
+#76 := (not #52)
+#94 := (or #33 #76)
+#85 := (or #57 #33 #76)
+#86 := [def-axiom]: #85
+#95 := [unit-resolution #86 #65]: #94
+[unit-resolution #95 #93 #92]: false
+unsat
+57ef5c510d48fa340950eb624d67dcdea6c19cee 67 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f6 :: S1
+#15 := f6
+#16 := (= f6 f1)
+decl f5 :: S1
+#13 := f5
+#14 := (= f5 f1)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#18 := (ite #11 #14 #16)
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#19 := (ite #9 #14 #18)
+#12 := (or #9 #11)
+#17 := (ite #12 #14 #16)
+#20 := (iff #17 #19)
+#21 := (not #20)
+#79 := (iff #21 false)
+#1 := true
+#74 := (not true)
+#77 := (iff #74 false)
+#78 := [rewrite]: #77
+#75 := (iff #21 #74)
+#72 := (iff #20 true)
+#51 := (= f1 f6)
+#48 := (= f1 f5)
+#42 := (= f1 f4)
+#39 := (= f1 f3)
+#45 := (or #39 #42)
+#54 := (ite #45 #48 #51)
+#67 := (iff #54 #54)
+#70 := (iff #67 true)
+#71 := [rewrite]: #70
+#68 := (iff #20 #67)
+#65 := (iff #19 #54)
+#57 := (ite #42 #48 #51)
+#60 := (ite #39 #48 #57)
+#63 := (iff #60 #54)
+#64 := [rewrite]: #63
+#61 := (iff #19 #60)
+#58 := (iff #18 #57)
+#52 := (iff #16 #51)
+#53 := [rewrite]: #52
+#49 := (iff #14 #48)
+#50 := [rewrite]: #49
+#43 := (iff #11 #42)
+#44 := [rewrite]: #43
+#59 := [monotonicity #44 #50 #53]: #58
+#40 := (iff #9 #39)
+#41 := [rewrite]: #40
+#62 := [monotonicity #41 #50 #59]: #61
+#66 := [trans #62 #64]: #65
+#55 := (iff #17 #54)
+#46 := (iff #12 #45)
+#47 := [monotonicity #41 #44]: #46
+#56 := [monotonicity #47 #50 #53]: #55
+#69 := [monotonicity #56 #66]: #68
+#73 := [trans #69 #71]: #72
+#76 := [monotonicity #73]: #75
+#80 := [trans #76 #78]: #79
+#38 := [asserted]: #21
+[mp #38 #80]: false
+unsat
+a2a38d19c0ee3408b8ff43bb0b259ae677eaad50 67 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f6 :: S1
+#15 := f6
+#16 := (= f6 f1)
+decl f5 :: S1
+#13 := f5
+#14 := (= f5 f1)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#18 := (ite #11 #14 #16)
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#19 := (ite #9 #18 #16)
+#12 := (and #9 #11)
+#17 := (ite #12 #14 #16)
+#20 := (iff #17 #19)
+#21 := (not #20)
+#79 := (iff #21 false)
+#1 := true
+#74 := (not true)
+#77 := (iff #74 false)
+#78 := [rewrite]: #77
+#75 := (iff #21 #74)
+#72 := (iff #20 true)
+#51 := (= f1 f6)
+#48 := (= f1 f5)
+#42 := (= f1 f4)
+#39 := (= f1 f3)
+#45 := (and #39 #42)
+#54 := (ite #45 #48 #51)
+#67 := (iff #54 #54)
+#70 := (iff #67 true)
+#71 := [rewrite]: #70
+#68 := (iff #20 #67)
+#65 := (iff #19 #54)
+#57 := (ite #42 #48 #51)
+#60 := (ite #39 #57 #51)
+#63 := (iff #60 #54)
+#64 := [rewrite]: #63
+#61 := (iff #19 #60)
+#52 := (iff #16 #51)
+#53 := [rewrite]: #52
+#58 := (iff #18 #57)
+#49 := (iff #14 #48)
+#50 := [rewrite]: #49
+#43 := (iff #11 #42)
+#44 := [rewrite]: #43
+#59 := [monotonicity #44 #50 #53]: #58
+#40 := (iff #9 #39)
+#41 := [rewrite]: #40
+#62 := [monotonicity #41 #59 #53]: #61
+#66 := [trans #62 #64]: #65
+#55 := (iff #17 #54)
+#46 := (iff #12 #45)
+#47 := [monotonicity #41 #44]: #46
+#56 := [monotonicity #47 #50 #53]: #55
+#69 := [monotonicity #56 #66]: #68
+#73 := [trans #69 #71]: #72
+#76 := [monotonicity #73]: #75
+#80 := [trans #76 #78]: #79
+#38 := [asserted]: #21
+[mp #38 #80]: false
+unsat
+fc255defa96f0ef5d520766aa2632cf0aad3a5bc 186 0
+#2 := false
+decl f5 :: S1
+#12 := f5
+decl f1 :: S1
+#4 := f1
+#47 := (= f1 f5)
+decl f3 :: S1
+#8 := f3
+#41 := (= f1 f3)
+#59 := (not #41)
+#76 := (or #59 #47)
+#119 := (not #76)
+decl f4 :: S1
+#10 := f4
+#44 := (= f1 f4)
+#68 := (or #59 #44)
+decl f6 :: S1
+#14 := f6
+#50 := (= f1 f6)
+#84 := (or #59 #50)
+#89 := (ite #68 #76 #84)
+#130 := (not #89)
+#53 := (ite #44 #47 #50)
+#60 := (or #59 #53)
+#112 := (not #44)
+#165 := [hypothesis]: #112
+#172 := (or #60 #44)
+#98 := (not #60)
+#163 := [hypothesis]: #98
+#148 := (or #60 #41)
+#149 := [def-axiom]: #148
+#164 := [unit-resolution #149 #163]: #41
+#124 := (not #50)
+#139 := (not #53)
+#150 := (or #60 #139)
+#151 := [def-axiom]: #150
+#166 := [unit-resolution #151 #163]: #139
+#146 := (or #53 #44 #124)
+#147 := [def-axiom]: #146
+#167 := [unit-resolution #147 #166 #165]: #124
+#157 := (or #89 #60)
+#99 := (iff #89 #98)
+#15 := (= f6 f1)
+#9 := (= f3 f1)
+#20 := (implies #9 #15)
+#13 := (= f5 f1)
+#19 := (implies #9 #13)
+#11 := (= f4 f1)
+#18 := (implies #9 #11)
+#21 := (ite #18 #19 #20)
+#16 := (ite #11 #13 #15)
+#17 := (implies #9 #16)
+#22 := (iff #17 #21)
+#23 := (not #22)
+#102 := (iff #23 #99)
+#92 := (iff #60 #89)
+#95 := (not #92)
+#100 := (iff #95 #99)
+#101 := [rewrite]: #100
+#96 := (iff #23 #95)
+#93 := (iff #22 #92)
+#90 := (iff #21 #89)
+#87 := (iff #20 #84)
+#81 := (implies #41 #50)
+#85 := (iff #81 #84)
+#86 := [rewrite]: #85
+#82 := (iff #20 #81)
+#51 := (iff #15 #50)
+#52 := [rewrite]: #51
+#42 := (iff #9 #41)
+#43 := [rewrite]: #42
+#83 := [monotonicity #43 #52]: #82
+#88 := [trans #83 #86]: #87
+#79 := (iff #19 #76)
+#73 := (implies #41 #47)
+#77 := (iff #73 #76)
+#78 := [rewrite]: #77
+#74 := (iff #19 #73)
+#48 := (iff #13 #47)
+#49 := [rewrite]: #48
+#75 := [monotonicity #43 #49]: #74
+#80 := [trans #75 #78]: #79
+#71 := (iff #18 #68)
+#65 := (implies #41 #44)
+#69 := (iff #65 #68)
+#70 := [rewrite]: #69
+#66 := (iff #18 #65)
+#45 := (iff #11 #44)
+#46 := [rewrite]: #45
+#67 := [monotonicity #43 #46]: #66
+#72 := [trans #67 #70]: #71
+#91 := [monotonicity #72 #80 #88]: #90
+#63 := (iff #17 #60)
+#56 := (implies #41 #53)
+#61 := (iff #56 #60)
+#62 := [rewrite]: #61
+#57 := (iff #17 #56)
+#54 := (iff #16 #53)
+#55 := [monotonicity #46 #49 #52]: #54
+#58 := [monotonicity #43 #55]: #57
+#64 := [trans #58 #62]: #63
+#94 := [monotonicity #64 #91]: #93
+#97 := [monotonicity #94]: #96
+#103 := [trans #97 #101]: #102
+#40 := [asserted]: #23
+#106 := [mp #40 #103]: #99
+#154 := (not #99)
+#155 := (or #89 #60 #154)
+#156 := [def-axiom]: #155
+#158 := [unit-resolution #156 #106]: #157
+#168 := [unit-resolution #158 #163]: #89
+#109 := (not #68)
+#107 := (or #109 #59 #44)
+#104 := [def-axiom]: #107
+#169 := [unit-resolution #104 #164 #165]: #109
+#133 := (or #130 #68 #84)
+#134 := [def-axiom]: #133
+#170 := [unit-resolution #134 #169 #168]: #84
+#127 := (not #84)
+#128 := (or #127 #59 #50)
+#129 := [def-axiom]: #128
+#171 := [unit-resolution #129 #170 #167 #164]: false
+#173 := [lemma #171]: #172
+#176 := [unit-resolution #173 #165]: #60
+#161 := (or #130 #98)
+#159 := (or #130 #98 #154)
+#160 := [def-axiom]: #159
+#162 := [unit-resolution #160 #106]: #161
+#182 := [unit-resolution #162 #176]: #130
+#180 := (or #84 #44)
+#174 := [hypothesis]: #127
+#125 := (or #84 #124)
+#126 := [def-axiom]: #125
+#175 := [unit-resolution #126 #174]: #124
+#122 := (or #84 #41)
+#123 := [def-axiom]: #122
+#177 := [unit-resolution #123 #174]: #41
+#152 := (or #98 #59 #53)
+#153 := [def-axiom]: #152
+#178 := [unit-resolution #153 #177 #176]: #53
+#142 := (or #139 #44 #50)
+#143 := [def-axiom]: #142
+#179 := [unit-resolution #143 #178 #175 #165]: false
+#181 := [lemma #179]: #180
+#183 := [unit-resolution #181 #165]: #84
+#137 := (or #89 #68 #127)
+#138 := [def-axiom]: #137
+#184 := [unit-resolution #138 #183 #182]: #68
+#135 := (or #89 #109 #119)
+#136 := [def-axiom]: #135
+#185 := [unit-resolution #136 #184 #182]: #119
+#186 := [unit-resolution #104 #184 #165]: #59
+#114 := (or #76 #41)
+#115 := [def-axiom]: #114
+#187 := [unit-resolution #115 #186 #185]: false
+#188 := [lemma #187]: #44
+#113 := (or #68 #112)
+#108 := [def-axiom]: #113
+#191 := [unit-resolution #108 #188]: #68
+#189 := [hypothesis]: #59
+#190 := [unit-resolution #149 #189]: #60
+#192 := [unit-resolution #115 #189]: #76
+#193 := [unit-resolution #136 #192 #191]: #89
+#194 := [unit-resolution #162 #193 #190]: false
+#195 := [lemma #194]: #41
+#116 := (not #47)
+#144 := (or #53 #112 #116)
+#145 := [def-axiom]: #144
+#196 := [unit-resolution #145 #166 #188]: #116
+#131 := (or #130 #109 #76)
+#132 := [def-axiom]: #131
+#197 := [unit-resolution #132 #168 #191]: #76
+#120 := (or #119 #59 #47)
+#121 := [def-axiom]: #120
+#198 := [unit-resolution #121 #197 #196 #195]: false
+#199 := [lemma #198]: #60
+#200 := [unit-resolution #162 #199]: #130
+#201 := [unit-resolution #136 #200 #191]: #119
+#202 := [unit-resolution #153 #199 #195]: #53
+#140 := (or #139 #112 #47)
+#141 := [def-axiom]: #140
+#203 := [unit-resolution #141 #202 #188]: #47
+#117 := (or #76 #116)
+#118 := [def-axiom]: #117
+[unit-resolution #118 #203 #201]: false
+unsat
+0da1431887410ee6080863b748e51ed21e6c9dce 33 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#10 := (not #9)
+#11 := (ite #9 #9 #10)
+#12 := (not #11)
+#48 := (iff #12 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (iff #11 true)
+#30 := (= f1 f3)
+#33 := (not #30)
+#36 := (ite #30 #30 #33)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #11 #36)
+#34 := (iff #10 #33)
+#31 := (iff #9 #30)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#38 := [monotonicity #32 #32 #35]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#29 := [asserted]: #12
+[mp #29 #49]: false
+unsat
+80619a5b516a6a3937b11283c4d725afb9ce0774 33 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#10 := (not #9)
+#11 := (ite #10 #10 #9)
+#12 := (not #11)
+#48 := (iff #12 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (iff #11 true)
+#30 := (= f1 f3)
+#33 := (not #30)
+#36 := (ite #33 #33 #30)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #11 #36)
+#31 := (iff #9 #30)
+#32 := [rewrite]: #31
+#34 := (iff #10 #33)
+#35 := [monotonicity #32]: #34
+#38 := [monotonicity #35 #35 #32]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#29 := [asserted]: #12
+[mp #29 #49]: false
+unsat
+cbbce30b0560c731da14df6a781bb825b2bf5fd2 18 0
+#2 := false
+decl f3 :: S2
+#8 := f3
+#9 := (= f3 f3)
+#10 := (not #9)
+#35 := (iff #10 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #10 #30)
+#28 := (iff #9 true)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#27 := [asserted]: #10
+[mp #27 #36]: false
+unsat
+33496c6e5af74b71dae5b3c85192a376e90617d4 29 0
+#2 := false
+decl f3 :: S2
+#8 := f3
+decl f4 :: S2
+#9 := f4
+#11 := (= f4 f3)
+#10 := (= f3 f4)
+#12 := (implies #10 #11)
+#13 := (not #12)
+#45 := (iff #13 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #13 #40)
+#38 := (iff #12 true)
+#33 := (implies #10 #10)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #12 #33)
+#31 := (iff #11 #10)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#30 := [asserted]: #13
+[mp #30 #46]: false
+unsat
+d6876a0d24521bcd5c58ccb82f1d0b861030006c 34 0
+#2 := false
+decl f5 :: S2
+#11 := f5
+decl f3 :: S2
+#8 := f3
+#14 := (= f3 f5)
+decl f4 :: S2
+#9 := f4
+#12 := (= f4 f5)
+#58 := (iff #12 #14)
+#56 := (iff #14 #12)
+#10 := (= f3 f4)
+#13 := (and #10 #12)
+#34 := (not #13)
+#35 := (or #34 #14)
+#38 := (not #35)
+#15 := (implies #13 #14)
+#16 := (not #15)
+#39 := (iff #16 #38)
+#36 := (iff #15 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#33 := [asserted]: #16
+#43 := [mp #33 #40]: #38
+#41 := [not-or-elim #43]: #13
+#42 := [and-elim #41]: #10
+#57 := [monotonicity #42]: #56
+#59 := [symm #57]: #58
+#44 := [and-elim #41]: #12
+#54 := [mp #44 #59]: #14
+#45 := (not #14)
+#46 := [not-or-elim #43]: #45
+[unit-resolution #46 #54]: false
+unsat
+22095339787946156a1734d793c0c53e8ff5889b 27 0
+#2 := false
+decl f5 :: (-> S2 S2)
+decl f4 :: S2
+#9 := f4
+#12 := (f5 f4)
+decl f3 :: S2
+#8 := f3
+#11 := (f5 f3)
+#13 := (= #11 #12)
+#10 := (= f3 f4)
+#33 := (not #10)
+#34 := (or #33 #13)
+#37 := (not #34)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#38 := (iff #15 #37)
+#35 := (iff #14 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#32 := [asserted]: #15
+#42 := [mp #32 #39]: #37
+#40 := [not-or-elim #42]: #10
+#51 := [monotonicity #40]: #13
+#41 := (not #13)
+#43 := [not-or-elim #42]: #41
+[unit-resolution #43 #51]: false
+unsat
+08411a598c9c5c89a5ae533c3b99f5be607e2c7b 31 0
+#2 := false
+decl f5 :: (-> S2 S2 S3)
+decl f3 :: S2
+#8 := f3
+decl f4 :: S2
+#9 := f4
+#12 := (f5 f4 f3)
+#11 := (f5 f3 f4)
+#13 := (= #11 #12)
+#53 := (= #12 #11)
+#10 := (= f3 f4)
+#33 := (not #10)
+#34 := (or #33 #13)
+#37 := (not #34)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#38 := (iff #15 #37)
+#35 := (iff #14 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#32 := [asserted]: #15
+#42 := [mp #32 #39]: #37
+#40 := [not-or-elim #42]: #10
+#51 := (= f4 f3)
+#52 := [symm #40]: #51
+#54 := [monotonicity #52 #40]: #53
+#49 := [symm #54]: #13
+#41 := (not #13)
+#43 := [not-or-elim #42]: #41
+[unit-resolution #43 #49]: false
+unsat
+d8d5377f895c077efa991d5a06439e5dd483fb3c 63 0
+#2 := false
+decl f3 :: (-> S2 S2)
+decl f4 :: S2
+#8 := f4
+#9 := (f3 f4)
+#46 := (= f4 #9)
+#10 := (f3 #9)
+#12 := (f3 #10)
+#78 := (= #12 #9)
+#76 := (= #9 #12)
+#37 := (= f4 #10)
+#13 := (f3 #12)
+#14 := (f3 #13)
+#40 := (= f4 #14)
+#43 := (and #37 #40)
+#52 := (not #43)
+#53 := (or #52 #46)
+#58 := (not #53)
+#17 := (= #9 f4)
+#15 := (= #14 f4)
+#11 := (= #10 f4)
+#16 := (and #11 #15)
+#18 := (implies #16 #17)
+#19 := (not #18)
+#59 := (iff #19 #58)
+#56 := (iff #18 #53)
+#49 := (implies #43 #46)
+#54 := (iff #49 #53)
+#55 := [rewrite]: #54
+#50 := (iff #18 #49)
+#47 := (iff #17 #46)
+#48 := [rewrite]: #47
+#44 := (iff #16 #43)
+#41 := (iff #15 #40)
+#42 := [rewrite]: #41
+#38 := (iff #11 #37)
+#39 := [rewrite]: #38
+#45 := [monotonicity #39 #42]: #44
+#51 := [monotonicity #45 #48]: #50
+#57 := [trans #51 #55]: #56
+#60 := [monotonicity #57]: #59
+#36 := [asserted]: #19
+#63 := [mp #36 #60]: #58
+#61 := [not-or-elim #63]: #43
+#62 := [and-elim #61]: #37
+#77 := [monotonicity #62]: #76
+#79 := [symm #77]: #78
+#81 := (= f4 #12)
+#67 := (= #14 #12)
+#70 := (= #12 #14)
+#72 := (= #10 #13)
+#74 := (= #13 #10)
+#75 := [monotonicity #79]: #74
+#73 := [symm #75]: #72
+#71 := [monotonicity #73]: #70
+#80 := [symm #71]: #67
+#64 := [and-elim #61]: #40
+#82 := [trans #64 #80]: #81
+#83 := [trans #82 #79]: #46
+#65 := (not #46)
+#66 := [not-or-elim #63]: #65
+[unit-resolution #66 #83]: false
+unsat
+ea85eebbc2b6c3fd1539238e6bc69fc1689b7b7d 195 0
+#2 := false
+decl f6 :: S2
+#13 := f6
+decl f4 :: S2
+#10 := f4
+#15 := (= f4 f6)
+decl f5 :: S2
+#11 := f5
+decl f3 :: S1
+#8 := f3
+decl f1 :: S1
+#4 := f1
+#40 := (= f1 f3)
+#43 := (ite #40 f4 f5)
+#49 := (= f6 #43)
+#200 := (iff #49 #15)
+#198 := (iff #15 #49)
+#46 := (= #43 f6)
+#50 := (iff #46 #49)
+#197 := [commutativity]: #50
+#195 := (iff #15 #46)
+#110 := (= f4 #43)
+#111 := (= f5 #43)
+#57 := (not #40)
+#180 := [hypothesis]: #57
+#114 := (or #40 #111)
+#115 := [def-axiom]: #114
+#184 := [unit-resolution #115 #180]: #111
+#185 := (= f6 f5)
+#18 := (= f5 f6)
+#174 := (iff #110 #15)
+#172 := (iff #15 #110)
+#68 := (or #18 #40)
+#95 := (not #68)
+#58 := (or #15 #57)
+#94 := (not #58)
+#96 := (or #94 #95)
+#123 := (not #18)
+#147 := [hypothesis]: #123
+#157 := (or #96 #18)
+#97 := (not #96)
+#145 := [hypothesis]: #97
+#132 := (or #96 #68)
+#133 := [def-axiom]: #132
+#148 := [unit-resolution #133 #145]: #68
+#128 := (or #95 #18 #40)
+#129 := [def-axiom]: #128
+#149 := [unit-resolution #129 #148 #147]: #40
+#112 := (or #57 #110)
+#113 := [def-axiom]: #112
+#150 := [unit-resolution #113 #149]: #110
+#153 := (= f6 f4)
+#130 := (or #96 #58)
+#131 := [def-axiom]: #130
+#151 := [unit-resolution #131 #145]: #58
+#121 := (or #94 #15 #57)
+#122 := [def-axiom]: #121
+#152 := [unit-resolution #122 #149 #151]: #15
+#154 := [symm #152]: #153
+#155 := [trans #154 #150]: #49
+#82 := (not #49)
+#143 := (or #82 #96)
+#104 := (iff #49 #96)
+#73 := (and #58 #68)
+#83 := (iff #73 #82)
+#107 := (iff #83 #104)
+#99 := (iff #96 #49)
+#105 := (iff #99 #104)
+#106 := [rewrite]: #105
+#102 := (iff #83 #99)
+#91 := (iff #97 #82)
+#100 := (iff #91 #99)
+#101 := [rewrite]: #100
+#88 := (iff #83 #91)
+#92 := (iff #73 #97)
+#93 := [rewrite]: #92
+#98 := [monotonicity #93]: #88
+#103 := [trans #98 #101]: #102
+#108 := [trans #103 #106]: #107
+#9 := (= f3 f1)
+#17 := (not #9)
+#19 := (implies #17 #18)
+#16 := (implies #9 #15)
+#20 := (and #16 #19)
+#12 := (ite #9 f4 f5)
+#14 := (= #12 f6)
+#21 := (iff #14 #20)
+#22 := (not #21)
+#86 := (iff #22 #83)
+#76 := (iff #49 #73)
+#79 := (not #76)
+#84 := (iff #79 #83)
+#85 := [rewrite]: #84
+#80 := (iff #22 #79)
+#77 := (iff #21 #76)
+#74 := (iff #20 #73)
+#71 := (iff #19 #68)
+#65 := (implies #57 #18)
+#69 := (iff #65 #68)
+#70 := [rewrite]: #69
+#66 := (iff #19 #65)
+#63 := (iff #17 #57)
+#41 := (iff #9 #40)
+#42 := [rewrite]: #41
+#64 := [monotonicity #42]: #63
+#67 := [monotonicity #64]: #66
+#72 := [trans #67 #70]: #71
+#61 := (iff #16 #58)
+#54 := (implies #40 #15)
+#59 := (iff #54 #58)
+#60 := [rewrite]: #59
+#55 := (iff #16 #54)
+#56 := [monotonicity #42]: #55
+#62 := [trans #56 #60]: #61
+#75 := [monotonicity #62 #72]: #74
+#52 := (iff #14 #49)
+#51 := [rewrite]: #50
+#47 := (iff #14 #46)
+#44 := (= #12 #43)
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#53 := [trans #48 #51]: #52
+#78 := [monotonicity #53 #75]: #77
+#81 := [monotonicity #78]: #80
+#87 := [trans #81 #85]: #86
+#39 := [asserted]: #22
+#90 := [mp #39 #87]: #83
+#109 := [mp #90 #108]: #104
+#136 := (not #104)
+#141 := (or #82 #96 #136)
+#142 := [def-axiom]: #141
+#144 := [unit-resolution #142 #109]: #143
+#146 := [unit-resolution #144 #145]: #82
+#156 := [unit-resolution #146 #155]: false
+#158 := [lemma #156]: #157
+#159 := [unit-resolution #158 #147]: #96
+#139 := (or #49 #97)
+#137 := (or #49 #97 #136)
+#138 := [def-axiom]: #137
+#140 := [unit-resolution #138 #109]: #139
+#160 := [unit-resolution #140 #159]: #49
+#173 := [monotonicity #160]: #172
+#175 := [symm #173]: #174
+#163 := (not #111)
+#164 := (iff #123 #163)
+#161 := (iff #18 #111)
+#162 := [monotonicity #160]: #161
+#165 := [monotonicity #162]: #164
+#166 := [mp #147 #165]: #163
+#167 := [unit-resolution #115 #166]: #40
+#171 := [unit-resolution #113 #167]: #110
+#176 := [mp #171 #175]: #15
+#116 := (not #15)
+#126 := (or #68 #57)
+#127 := [def-axiom]: #126
+#168 := [unit-resolution #127 #167]: #68
+#134 := (or #97 #94 #95)
+#135 := [def-axiom]: #134
+#169 := [unit-resolution #135 #168 #159]: #94
+#117 := (or #58 #116)
+#118 := [def-axiom]: #117
+#170 := [unit-resolution #118 #169]: #116
+#177 := [unit-resolution #170 #176]: false
+#178 := [lemma #177]: #18
+#186 := [symm #178]: #185
+#187 := [trans #186 #184]: #49
+#124 := (or #68 #123)
+#125 := [def-axiom]: #124
+#179 := [unit-resolution #125 #178]: #68
+#119 := (or #58 #40)
+#120 := [def-axiom]: #119
+#181 := [unit-resolution #120 #180]: #58
+#182 := [unit-resolution #135 #181 #179]: #97
+#183 := [unit-resolution #144 #182]: #82
+#188 := [unit-resolution #183 #187]: false
+#189 := [lemma #188]: #40
+#194 := [unit-resolution #113 #189]: #110
+#196 := [monotonicity #194]: #195
+#199 := [trans #196 #197]: #198
+#201 := [symm #199]: #200
+#202 := (iff #82 #116)
+#203 := [monotonicity #201]: #202
+#190 := [hypothesis]: #82
+#204 := [mp #190 #203]: #116
+#191 := [unit-resolution #140 #190]: #97
+#192 := [unit-resolution #131 #191]: #58
+#193 := [unit-resolution #122 #192 #189]: #15
+#205 := [unit-resolution #193 #204]: false
+#206 := [lemma #205]: #49
+#210 := [mp #206 #201]: #15
+#207 := [unit-resolution #144 #206]: #96
+#208 := [unit-resolution #135 #207 #179]: #94
+#209 := [unit-resolution #118 #208]: #116
+[unit-resolution #209 #210]: false
+unsat
+ed21364e0880708fc99ba7b47600769d1d18aae3 36 0
+#2 := false
+decl f5 :: S2
+#10 := f5
+decl f3 :: S2
+#8 := f3
+#12 := (= f3 f5)
+#13 := (not #12)
+decl f4 :: S2
+#9 := f4
+#11 := (distinct f3 f4 f5)
+#33 := (not #11)
+#34 := (or #33 #13)
+#37 := (not #34)
+#14 := (implies #11 #13)
+#15 := (not #14)
+#38 := (iff #15 #37)
+#35 := (iff #14 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#32 := [asserted]: #15
+#42 := [mp #32 #39]: #37
+#41 := [not-or-elim #42]: #12
+#52 := (= f4 f5)
+#53 := (not #52)
+#50 := (= f3 f4)
+#51 := (not #50)
+#48 := (and #51 #13 #53)
+#40 := [not-or-elim #42]: #11
+#58 := (or #33 #48)
+#59 := [def-axiom]: #58
+#62 := [unit-resolution #59 #40]: #48
+#49 := (not #48)
+#45 := (or #49 #13)
+#43 := [def-axiom]: #45
+[unit-resolution #43 #62 #41]: false
+unsat
+ee48d855894dea92be3659c134766a85dc778a6c 77 0
+#2 := false
+decl f4 :: S2
+#9 := f4
+decl f3 :: S2
+#8 := f3
+#81 := (= f3 f4)
+decl f6 :: S2
+#12 := f6
+#36 := (= f4 f6)
+#100 := (iff #36 #81)
+#98 := (iff #81 #36)
+#13 := (= f6 f4)
+#37 := (iff #13 #36)
+#97 := [commutativity]: #37
+#95 := (iff #81 #13)
+#14 := (= f3 f6)
+#42 := (not #36)
+#15 := (not #14)
+decl f5 :: S2
+#10 := f5
+#11 := (distinct f3 f4 f5)
+#51 := (not #11)
+#60 := (or #51 #15 #42)
+#63 := (not #60)
+#16 := (implies #13 #15)
+#17 := (implies #11 #16)
+#18 := (not #17)
+#66 := (iff #18 #63)
+#43 := (or #15 #42)
+#52 := (or #51 #43)
+#57 := (not #52)
+#64 := (iff #57 #63)
+#61 := (iff #52 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#58 := (iff #18 #57)
+#55 := (iff #17 #52)
+#48 := (implies #11 #43)
+#53 := (iff #48 #52)
+#54 := [rewrite]: #53
+#49 := (iff #17 #48)
+#46 := (iff #16 #43)
+#39 := (implies #36 #15)
+#44 := (iff #39 #43)
+#45 := [rewrite]: #44
+#40 := (iff #16 #39)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#47 := [trans #41 #45]: #46
+#50 := [monotonicity #47]: #49
+#56 := [trans #50 #54]: #55
+#59 := [monotonicity #56]: #58
+#67 := [trans #59 #65]: #66
+#35 := [asserted]: #18
+#68 := [mp #35 #67]: #63
+#70 := [not-or-elim #68]: #14
+#96 := [monotonicity #70]: #95
+#99 := [trans #96 #97]: #98
+#101 := [symm #99]: #100
+#71 := [not-or-elim #68]: #36
+#102 := [mp #71 #101]: #81
+#82 := (not #81)
+#79 := (= f4 f5)
+#80 := (not #79)
+#83 := (= f3 f5)
+#84 := (not #83)
+#77 := (and #82 #84 #80)
+#69 := [not-or-elim #68]: #11
+#89 := (or #51 #77)
+#90 := [def-axiom]: #89
+#93 := [unit-resolution #90 #69]: #77
+#78 := (not #77)
+#75 := (or #78 #82)
+#76 := [def-axiom]: #75
+#94 := [unit-resolution #76 #93]: #82
+[unit-resolution #94 #102]: false
+unsat
+b7c26a6ed487c4e2a79d6033b039adbf38b310b7 28 0
+#2 := false
+decl f4 :: S2
+#9 := f4
+decl f3 :: S2
+#8 := f3
+#10 := (distinct f3 f4 f3 f4)
+#11 := (not #10)
+#12 := (not #11)
+#44 := (iff #12 false)
+#1 := true
+#39 := (not true)
+#42 := (iff #39 false)
+#43 := [rewrite]: #42
+#40 := (iff #12 #39)
+#37 := (iff #11 true)
+#32 := (not false)
+#35 := (iff #32 true)
+#36 := [rewrite]: #35
+#33 := (iff #11 #32)
+#30 := (iff #10 false)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31]: #33
+#38 := [trans #34 #36]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#29 := [asserted]: #12
+[mp #29 #45]: false
+unsat
+2ebe1a50382625b7919ba2af83bb26a74825ba20 38 0
+#2 := false
+decl f4 :: S2
+#9 := f4
+decl f3 :: S2
+#8 := f3
+#11 := (distinct f3 f4)
+#12 := (not #11)
+#10 := (= f3 f4)
+#13 := (implies #10 #12)
+#14 := (not #13)
+#54 := (iff #14 false)
+#1 := true
+#49 := (not true)
+#52 := (iff #49 false)
+#53 := [rewrite]: #52
+#50 := (iff #14 #49)
+#47 := (iff #13 true)
+#42 := (implies #10 #10)
+#45 := (iff #42 true)
+#46 := [rewrite]: #45
+#43 := (iff #13 #42)
+#40 := (iff #12 #10)
+#32 := (not #10)
+#35 := (not #32)
+#38 := (iff #35 #10)
+#39 := [rewrite]: #38
+#36 := (iff #12 #35)
+#33 := (iff #11 #32)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#41 := [trans #37 #39]: #40
+#44 := [monotonicity #41]: #43
+#48 := [trans #44 #46]: #47
+#51 := [monotonicity #48]: #50
+#55 := [trans #51 #53]: #54
+#31 := [asserted]: #14
+[mp #31 #55]: false
+unsat
+d23458b1c7e8e0285ade7e9f908f405813c22a0a 40 0
+#2 := false
+decl f5 :: S2
+#11 := f5
+decl f4 :: S2
+#9 := f4
+decl f3 :: S2
+#8 := f3
+#14 := (distinct f3 f4 f5)
+#15 := (not #14)
+#12 := (= f3 f5)
+#10 := (= f3 f4)
+#13 := (and #10 #12)
+#35 := (not #13)
+#36 := (or #35 #15)
+#39 := (not #36)
+#16 := (implies #13 #15)
+#17 := (not #16)
+#40 := (iff #17 #39)
+#37 := (iff #16 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#34 := [asserted]: #17
+#44 := [mp #34 #41]: #39
+#46 := [not-or-elim #44]: #14
+#58 := (= f4 f5)
+#59 := (not #58)
+#57 := (not #12)
+#56 := (not #10)
+#54 := (and #56 #57 #59)
+#55 := (not #54)
+#42 := [not-or-elim #44]: #13
+#43 := [and-elim #42]: #10
+#52 := (or #55 #56)
+#53 := [def-axiom]: #52
+#66 := [unit-resolution #53 #43]: #55
+#62 := (or #15 #54)
+#63 := [def-axiom]: #62
+#67 := [unit-resolution #63 #66]: #15
+[unit-resolution #67 #46]: false
+unsat
+17322e6836f62009c064780949b8d484180ad04f 33 0
+#2 := false
+decl f3 :: S2
+#8 := f3
+decl f5 :: S2
+#10 := f5
+decl f4 :: S2
+#9 := f4
+decl f6 :: S2
+#11 := f6
+#13 := (distinct f6 f4 f5 f3)
+#12 := (distinct f3 f4 f5 f6)
+#14 := (implies #12 #13)
+#15 := (not #14)
+#47 := (iff #15 false)
+#1 := true
+#42 := (not true)
+#45 := (iff #42 false)
+#46 := [rewrite]: #45
+#43 := (iff #15 #42)
+#40 := (iff #14 true)
+#35 := (implies #12 #12)
+#38 := (iff #35 true)
+#39 := [rewrite]: #38
+#36 := (iff #14 #35)
+#33 := (iff #13 #12)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#41 := [trans #37 #39]: #40
+#44 := [monotonicity #41]: #43
+#48 := [trans #44 #46]: #47
+#32 := [asserted]: #15
+[mp #32 #48]: false
+unsat
+8651539edbeda7889276cfc7220314932747463c 91 0
+#2 := false
+decl f5 :: S2
+#10 := f5
+decl f4 :: S2
+#9 := f4
+decl f3 :: S2
+#8 := f3
+#13 := (distinct f3 f4 f5)
+#67 := (= f4 f5)
+#68 := (not #67)
+#63 := (= f3 f5)
+#64 := (not #63)
+#61 := (= f3 f4)
+#62 := (not #61)
+#93 := (and #62 #64 #68)
+decl f6 :: S2
+#11 := f6
+#71 := (= f5 f6)
+#72 := (not #71)
+#69 := (= f4 f6)
+#70 := (not #69)
+#65 := (= f3 f6)
+#66 := (not #65)
+#73 := (and #62 #64 #66 #68 #70 #72)
+#12 := (distinct f3 f4 f5 f6)
+#14 := (distinct f4 f5 f6)
+#15 := (and #13 #14)
+#35 := (not #12)
+#36 := (or #35 #15)
+#39 := (not #36)
+#16 := (implies #12 #15)
+#17 := (not #16)
+#40 := (iff #17 #39)
+#37 := (iff #16 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#34 := [asserted]: #17
+#44 := [mp #34 #41]: #39
+#42 := [not-or-elim #44]: #12
+#89 := (or #35 #73)
+#90 := [def-axiom]: #89
+#121 := [unit-resolution #90 #42]: #73
+#74 := (not #73)
+#75 := (or #74 #62)
+#76 := [def-axiom]: #75
+#122 := [unit-resolution #76 #121]: #62
+#81 := (or #74 #68)
+#82 := [def-axiom]: #81
+#123 := [unit-resolution #82 #121]: #68
+#77 := (or #74 #64)
+#78 := [def-axiom]: #77
+#124 := [unit-resolution #78 #121]: #64
+#101 := (or #93 #61 #63 #67)
+#102 := [def-axiom]: #101
+#125 := [unit-resolution #102 #124 #123 #122]: #93
+#94 := (not #93)
+#105 := (or #13 #94)
+#106 := [def-axiom]: #105
+#126 := [unit-resolution #106 #125]: #13
+#107 := (and #68 #70 #72)
+#85 := (or #74 #72)
+#86 := [def-axiom]: #85
+#127 := [unit-resolution #86 #121]: #72
+#83 := (or #74 #70)
+#84 := [def-axiom]: #83
+#128 := [unit-resolution #84 #121]: #70
+#115 := (or #107 #67 #69 #71)
+#116 := [def-axiom]: #115
+#129 := [unit-resolution #116 #128 #127 #123]: #107
+#108 := (not #107)
+#119 := (or #14 #108)
+#120 := [def-axiom]: #119
+#130 := [unit-resolution #120 #129]: #14
+#54 := (not #14)
+#53 := (not #13)
+#55 := (or #53 #54)
+#43 := (not #15)
+#58 := (iff #43 #55)
+#56 := (not #55)
+#49 := (not #56)
+#46 := (iff #49 #55)
+#57 := [rewrite]: #46
+#50 := (iff #43 #49)
+#51 := (iff #15 #56)
+#52 := [rewrite]: #51
+#48 := [monotonicity #52]: #50
+#59 := [trans #48 #57]: #58
+#45 := [not-or-elim #44]: #43
+#60 := [mp #45 #59]: #55
+[unit-resolution #60 #130 #126]: false
+unsat
+85339c45b965486197d18350eeac3a19766f36f6 25 0
+#2 := false
+#8 := (:var 0 S2)
+#9 := (= #8 #8)
+#10 := (forall (vars (?v0 S2)) #9)
+#11 := (not #10)
+#43 := (iff #11 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #11 #38)
+#36 := (iff #10 true)
+#31 := (forall (vars (?v0 S2)) true)
+#34 := (iff #31 true)
+#35 := [elim-unused]: #34
+#32 := (iff #10 #31)
+#29 := (iff #9 true)
+#30 := [rewrite]: #29
+#33 := [quant-intro #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#28 := [asserted]: #11
+[mp #28 #44]: false
+unsat
+702c9039a9922073e04bc391e23f155949d7c13c 34 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S2 S1)
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#10 := (= #9 f1)
+#11 := (forall (vars (?v0 S2)) #10)
+#12 := (iff #11 #11)
+#13 := (not #12)
+#49 := (iff #13 false)
+#1 := true
+#44 := (not true)
+#47 := (iff #44 false)
+#48 := [rewrite]: #47
+#45 := (iff #13 #44)
+#42 := (iff #12 true)
+#31 := (= f1 #9)
+#34 := (forall (vars (?v0 S2)) #31)
+#37 := (iff #34 #34)
+#40 := (iff #37 true)
+#41 := [rewrite]: #40
+#38 := (iff #12 #37)
+#35 := (iff #11 #34)
+#32 := (iff #10 #31)
+#33 := [rewrite]: #32
+#36 := [quant-intro #33]: #35
+#39 := [monotonicity #36 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#30 := [asserted]: #13
+[mp #30 #50]: false
+unsat
+2ebc70598429c0929dd8a31ee63ac374586b6fd2 95 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl ?v0!0 :: S2
@@ -4501,49 +4685,7 @@
 #102 := [and-elim #101]: #76
 [unit-resolution #102 #115]: false
 unsat
-f7433bc79c74698b7150f9252f1663dfbc7714ae 41 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#10 := (not #9)
-#11 := (iff #9 #10)
-#12 := (not #11)
-#13 := (not #12)
-#56 := (iff #13 false)
-#1 := true
-#51 := (not true)
-#54 := (iff #51 false)
-#55 := [rewrite]: #54
-#52 := (iff #13 #51)
-#49 := (iff #12 true)
-#44 := (not false)
-#47 := (iff #44 true)
-#48 := [rewrite]: #47
-#45 := (iff #12 #44)
-#42 := (iff #11 false)
-#31 := (= f1 f3)
-#34 := (not #31)
-#37 := (iff #31 #34)
-#40 := (iff #37 false)
-#41 := [rewrite]: #40
-#38 := (iff #11 #37)
-#35 := (iff #10 #34)
-#32 := (iff #9 #31)
-#33 := [rewrite]: #32
-#36 := [monotonicity #33]: #35
-#39 := [monotonicity #33 #36]: #38
-#43 := [trans #39 #41]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#30 := [asserted]: #13
-[mp #30 #57]: false
-unsat
-9e92d358b4d87bdfb0816755e800e46f3d76b51e 300 0
+ea94722d6f51e37912f9513e9341d861dfbe1bd5 300 0
 #2 := false
 decl f4 :: (-> S2 S1)
 decl ?v0!1 :: S2
@@ -4844,68 +4986,7 @@
 #609 := [quant-inst]: #615
 [unit-resolution #609 #257 #603]: false
 unsat
-4f091688bc1fe0b9d20810549460b1f682c6b9ee 60 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#14 := (not #9)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#13 := (not #11)
-#15 := (implies #13 #14)
-#12 := (implies #9 #11)
-#16 := (iff #12 #15)
-#17 := (not #16)
-#74 := (iff #17 false)
-#1 := true
-#69 := (not true)
-#72 := (iff #69 false)
-#73 := [rewrite]: #72
-#70 := (iff #17 #69)
-#67 := (iff #16 true)
-#38 := (= f1 f4)
-#35 := (= f1 f3)
-#44 := (not #35)
-#45 := (or #44 #38)
-#62 := (iff #45 #45)
-#65 := (iff #62 true)
-#66 := [rewrite]: #65
-#63 := (iff #16 #62)
-#60 := (iff #15 #45)
-#50 := (not #38)
-#55 := (implies #50 #44)
-#58 := (iff #55 #45)
-#59 := [rewrite]: #58
-#56 := (iff #15 #55)
-#53 := (iff #14 #44)
-#36 := (iff #9 #35)
-#37 := [rewrite]: #36
-#54 := [monotonicity #37]: #53
-#51 := (iff #13 #50)
-#39 := (iff #11 #38)
-#40 := [rewrite]: #39
-#52 := [monotonicity #40]: #51
-#57 := [monotonicity #52 #54]: #56
-#61 := [trans #57 #59]: #60
-#48 := (iff #12 #45)
-#41 := (implies #35 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #12 #41)
-#43 := [monotonicity #37 #40]: #42
-#49 := [trans #43 #47]: #48
-#64 := [monotonicity #49 #61]: #63
-#68 := [trans #64 #66]: #67
-#71 := [monotonicity #68]: #70
-#75 := [trans #71 #73]: #74
-#34 := [asserted]: #17
-[mp #34 #75]: false
-unsat
-27355f82e9f880139491584519c5f457388ba8e4 201 0
+ad0ac9e0dd9730392bd01ba30823921723fd005a 201 0
 #2 := false
 decl f3 :: (-> S2 S1)
 #8 := (:var 0 S2)
@@ -5107,80 +5188,7 @@
 #211 := [quant-inst]: #320
 [unit-resolution #211 #595 #319]: false
 unsat
-45c3801b7a47fb920cbab9584d402164b65dd356 72 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#10 := (iff #9 #9)
-#11 := (iff #9 #10)
-#12 := (iff #9 #11)
-#13 := (iff #9 #12)
-#14 := (iff #9 #13)
-#15 := (iff #9 #14)
-#16 := (iff #9 #15)
-#17 := (iff #9 #16)
-#18 := (iff #9 #17)
-#19 := (not #18)
-#87 := (iff #19 false)
-#1 := true
-#82 := (not true)
-#85 := (iff #82 false)
-#86 := [rewrite]: #85
-#83 := (iff #19 #82)
-#80 := (iff #18 true)
-#37 := (= f1 f3)
-#40 := (iff #37 #37)
-#43 := (iff #40 true)
-#44 := [rewrite]: #43
-#78 := (iff #18 #40)
-#76 := (iff #17 #37)
-#47 := (iff #37 true)
-#50 := (iff #47 #37)
-#51 := [rewrite]: #50
-#74 := (iff #17 #47)
-#72 := (iff #16 true)
-#70 := (iff #16 #40)
-#68 := (iff #15 #37)
-#66 := (iff #15 #47)
-#64 := (iff #14 true)
-#62 := (iff #14 #40)
-#60 := (iff #13 #37)
-#58 := (iff #13 #47)
-#56 := (iff #12 true)
-#54 := (iff #12 #40)
-#52 := (iff #11 #37)
-#48 := (iff #11 #47)
-#45 := (iff #10 true)
-#41 := (iff #10 #40)
-#38 := (iff #9 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39 #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #39 #46]: #48
-#53 := [trans #49 #51]: #52
-#55 := [monotonicity #39 #53]: #54
-#57 := [trans #55 #44]: #56
-#59 := [monotonicity #39 #57]: #58
-#61 := [trans #59 #51]: #60
-#63 := [monotonicity #39 #61]: #62
-#65 := [trans #63 #44]: #64
-#67 := [monotonicity #39 #65]: #66
-#69 := [trans #67 #51]: #68
-#71 := [monotonicity #39 #69]: #70
-#73 := [trans #71 #44]: #72
-#75 := [monotonicity #39 #73]: #74
-#77 := [trans #75 #51]: #76
-#79 := [monotonicity #39 #77]: #78
-#81 := [trans #79 #44]: #80
-#84 := [monotonicity #81]: #83
-#88 := [trans #84 #86]: #87
-#36 := [asserted]: #19
-[mp #36 #88]: false
-unsat
-392dbae729e3baf705095d1fa80eee1de09292e0 244 0
+6ead1db7621b79533f3ce759ae68e1566483a7f3 244 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl ?v0!0 :: S2
@@ -5425,33 +5433,7 @@
 #616 := [mp #343 #237]: #621
 [unit-resolution #616 #629 #330]: false
 unsat
-17f9e5be62669f8acfb50769a06b9e675836393a 25 0
-#2 := false
-#8 := (:var 0 S2)
-#9 := (= #8 #8)
-#10 := (exists (vars (?v0 S2)) #9)
-#11 := (not #10)
-#43 := (iff #11 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #11 #38)
-#36 := (iff #10 true)
-#31 := (exists (vars (?v0 S2)) true)
-#34 := (iff #31 true)
-#35 := [elim-unused]: #34
-#32 := (iff #10 #31)
-#29 := (iff #9 true)
-#30 := [rewrite]: #29
-#33 := [quant-intro #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#28 := [asserted]: #11
-[mp #28 #44]: false
-unsat
-f1a2d09c5ae97f135cf03b06910805f4101ff509 49 0
+52800e938db8875d1625eb073b4e9f8fae322c7d 49 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -5501,42 +5483,7 @@
 #35 := [asserted]: #18
 [mp #35 #65]: false
 unsat
-cc5c33d65644020014560f00b4d749ba7046207d 34 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: (-> S2 S1)
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#10 := (= #9 f1)
-#11 := (exists (vars (?v0 S2)) #10)
-#12 := (iff #11 #11)
-#13 := (not #12)
-#49 := (iff #13 false)
-#1 := true
-#44 := (not true)
-#47 := (iff #44 false)
-#48 := [rewrite]: #47
-#45 := (iff #13 #44)
-#42 := (iff #12 true)
-#31 := (= f1 #9)
-#34 := (exists (vars (?v0 S2)) #31)
-#37 := (iff #34 #34)
-#40 := (iff #37 true)
-#41 := [rewrite]: #40
-#38 := (iff #12 #37)
-#35 := (iff #11 #34)
-#32 := (iff #10 #31)
-#33 := [rewrite]: #32
-#36 := [quant-intro #33]: #35
-#39 := [monotonicity #36 #36]: #38
-#43 := [trans #39 #41]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#30 := [asserted]: #13
-[mp #30 #50]: false
-unsat
-c0659ef2eb86b9abb113a352ce049de7f5cf2d4d 136 0
+68d4267233ffd53b13ce9ee4f5a11ca8ee26f30e 136 0
 #2 := false
 decl f3 :: (-> S2 S2 S1)
 decl f4 :: S2
@@ -5673,7 +5620,509 @@
 #593 := [quant-inst]: #592
 [unit-resolution #593 #610 #258]: false
 unsat
-c32773e30c401fac91663753c8932e4d15be0cde 258 0
+b6cfd4e11ead10d4f3ccc7c07ed7ce72f8b50779 124 0
+#2 := false
+decl f3 :: (-> S2 S1)
+decl f4 :: (-> S2 S2)
+decl f5 :: S2
+#16 := f5
+#20 := (f4 f5)
+#21 := (f4 #20)
+#154 := (f3 #21)
+decl f1 :: S1
+#4 := f1
+#241 := (= f1 #154)
+#152 := (f3 #20)
+#239 := (= f1 #152)
+#17 := (f3 f5)
+#62 := (= f1 #17)
+#8 := (:var 0 S2)
+#11 := (f4 #8)
+#12 := (f3 #11)
+#47 := (= f1 #12)
+#9 := (f3 #8)
+#44 := (= f1 #9)
+#53 := (not #44)
+#54 := (or #53 #47)
+#59 := (forall (vars (?v0 S2)) #54)
+#65 := (and #59 #62)
+#22 := (f4 #21)
+#23 := (f3 #22)
+#68 := (= f1 #23)
+#74 := (not #65)
+#75 := (or #74 #68)
+#80 := (not #75)
+#24 := (= #23 f1)
+#18 := (= #17 f1)
+#13 := (= #12 f1)
+#10 := (= #9 f1)
+#14 := (implies #10 #13)
+#15 := (forall (vars (?v0 S2)) #14)
+#19 := (and #15 #18)
+#25 := (implies #19 #24)
+#26 := (not #25)
+#81 := (iff #26 #80)
+#78 := (iff #25 #75)
+#71 := (implies #65 #68)
+#76 := (iff #71 #75)
+#77 := [rewrite]: #76
+#72 := (iff #25 #71)
+#69 := (iff #24 #68)
+#70 := [rewrite]: #69
+#66 := (iff #19 #65)
+#63 := (iff #18 #62)
+#64 := [rewrite]: #63
+#60 := (iff #15 #59)
+#57 := (iff #14 #54)
+#50 := (implies #44 #47)
+#55 := (iff #50 #54)
+#56 := [rewrite]: #55
+#51 := (iff #14 #50)
+#48 := (iff #13 #47)
+#49 := [rewrite]: #48
+#45 := (iff #10 #44)
+#46 := [rewrite]: #45
+#52 := [monotonicity #46 #49]: #51
+#58 := [trans #52 #56]: #57
+#61 := [quant-intro #58]: #60
+#67 := [monotonicity #61 #64]: #66
+#73 := [monotonicity #67 #70]: #72
+#79 := [trans #73 #77]: #78
+#82 := [monotonicity #79]: #81
+#43 := [asserted]: #26
+#85 := [mp #43 #82]: #80
+#83 := [not-or-elim #85]: #65
+#86 := [and-elim #83]: #62
+#570 := (pattern #11)
+#571 := (forall (vars (?v0 S2)) (:pat #570) #54)
+#574 := (iff #59 #571)
+#572 := (iff #54 #54)
+#573 := [refl]: #572
+#575 := [quant-intro #573]: #574
+#100 := (~ #59 #59)
+#98 := (~ #54 #54)
+#99 := [refl]: #98
+#101 := [nnf-pos #99]: #100
+#84 := [and-elim #83]: #59
+#91 := [mp~ #84 #101]: #59
+#576 := [mp #91 #575]: #571
+#153 := (not #62)
+#232 := (not #571)
+#243 := (or #232 #153 #239)
+#240 := (or #153 #239)
+#244 := (or #232 #240)
+#245 := (iff #244 #243)
+#242 := [rewrite]: #245
+#172 := [quant-inst]: #244
+#246 := [mp #172 #242]: #243
+#208 := [unit-resolution #246 #576 #86]: #239
+#225 := (not #239)
+#351 := (or #232 #225 #241)
+#562 := (or #225 #241)
+#558 := (or #232 #562)
+#231 := (iff #558 #351)
+#565 := [rewrite]: #231
+#230 := [quant-inst]: #558
+#566 := [mp #230 #565]: #351
+#209 := [unit-resolution #566 #576 #208]: #241
+#87 := (not #68)
+#88 := [not-or-elim #85]: #87
+#564 := (not #241)
+#569 := (or #232 #68 #564)
+#219 := (or #564 #68)
+#559 := (or #232 #219)
+#545 := (iff #559 #569)
+#567 := (or #68 #564)
+#222 := (or #232 #567)
+#561 := (iff #222 #569)
+#202 := [rewrite]: #561
+#560 := (iff #559 #222)
+#568 := (iff #219 #567)
+#563 := [rewrite]: #568
+#218 := [monotonicity #563]: #560
+#206 := [trans #218 #202]: #545
+#217 := [quant-inst]: #559
+#207 := [mp #217 #206]: #569
+[unit-resolution #207 #576 #88 #209]: false
+unsat
+166b39ee349d51ba92ecccc1da9d7f64b81aa13f 64 0
+#2 := false
+decl f3 :: (-> S2 S2 S3)
+decl f4 :: S2
+#14 := f4
+decl f5 :: S2
+#16 := f5
+#18 := (f3 f5 f4)
+#17 := (f3 f4 f5)
+#19 := (= #17 #18)
+#62 := (not #19)
+#8 := (:var 1 S2)
+#9 := (:var 0 S2)
+#11 := (f3 #9 #8)
+#10 := (f3 #8 #9)
+#12 := (= #10 #11)
+#13 := (forall (vars (?v0 S2) (?v1 S2)) #12)
+#52 := (not #13)
+#53 := (or #52 #19)
+#58 := (not #53)
+#15 := (= f4 f4)
+#20 := (and #15 #19)
+#21 := (implies #13 #20)
+#22 := (not #21)
+#59 := (iff #22 #58)
+#56 := (iff #21 #53)
+#49 := (implies #13 #19)
+#54 := (iff #49 #53)
+#55 := [rewrite]: #54
+#50 := (iff #21 #49)
+#47 := (iff #20 #19)
+#1 := true
+#42 := (and true #19)
+#45 := (iff #42 #19)
+#46 := [rewrite]: #45
+#43 := (iff #20 #42)
+#40 := (iff #15 true)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#48 := [trans #44 #46]: #47
+#51 := [monotonicity #48]: #50
+#57 := [trans #51 #55]: #56
+#60 := [monotonicity #57]: #59
+#39 := [asserted]: #22
+#63 := [mp #39 #60]: #58
+#64 := [not-or-elim #63]: #62
+#547 := (pattern #11)
+#546 := (pattern #10)
+#548 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #546 #547) #12)
+#551 := (iff #13 #548)
+#549 := (iff #12 #12)
+#550 := [refl]: #549
+#552 := [quant-intro #550]: #551
+#74 := (~ #13 #13)
+#72 := (~ #12 #12)
+#73 := [refl]: #72
+#75 := [nnf-pos #73]: #74
+#61 := [not-or-elim #63]: #13
+#67 := [mp~ #61 #75]: #13
+#553 := [mp #67 #552]: #548
+#129 := (not #548)
+#216 := (or #129 #19)
+#130 := [quant-inst]: #216
+[unit-resolution #130 #553 #64]: false
+unsat
+e07f073dde11c886712e3b9a9b79eb5298bca014 250 0
+#2 := false
+decl f3 :: (-> S2 S1)
+decl f7 :: S2
+#22 := f7
+#25 := (f3 f7)
+decl f1 :: S1
+#4 := f1
+#94 := (= f1 #25)
+#283 := (not #94)
+decl f4 :: (-> S2 S1)
+#8 := (:var 0 S2)
+#11 := (f4 #8)
+#702 := (pattern #11)
+#9 := (f3 #8)
+#701 := (pattern #9)
+#57 := (= f1 #11)
+#54 := (= f1 #9)
+#63 := (not #54)
+#64 := (or #63 #57)
+#703 := (forall (vars (?v0 S2)) (:pat #701 #702) #64)
+#69 := (forall (vars (?v0 S2)) #64)
+#706 := (iff #69 #703)
+#704 := (iff #64 #64)
+#705 := [refl]: #704
+#707 := [quant-intro #705]: #706
+#187 := (~ #69 #69)
+#201 := (~ #64 #64)
+#202 := [refl]: #201
+#188 := [nnf-pos #202]: #187
+decl f6 :: (-> S2 S1)
+#23 := (f6 f7)
+#91 := (= f1 #23)
+#78 := (not #57)
+#86 := (and #63 #78)
+#103 := (not #86)
+#136 := (or #103 #91 #94)
+#139 := (forall (vars (?v0 S2)) #136)
+decl f5 :: S2
+#15 := f5
+#16 := (f4 f5)
+#72 := (= f1 #16)
+#75 := (not #72)
+#148 := (and #69 #75 #139)
+#153 := (not #148)
+#32 := (f4 f7)
+#118 := (= f1 #32)
+#159 := (or #91 #118 #153)
+#164 := (not #159)
+#33 := (= #32 f1)
+#24 := (= #23 f1)
+#34 := (or #24 #33)
+#26 := (= #25 f1)
+#27 := (or #24 #26)
+#10 := (= #9 f1)
+#20 := (not #10)
+#12 := (= #11 f1)
+#19 := (not #12)
+#21 := (and #19 #20)
+#28 := (implies #21 #27)
+#29 := (forall (vars (?v0 S2)) #28)
+#17 := (= #16 f1)
+#18 := (not #17)
+#30 := (and #18 #29)
+#13 := (implies #10 #12)
+#14 := (forall (vars (?v0 S2)) #13)
+#31 := (and #14 #30)
+#35 := (implies #31 #34)
+#36 := (not #35)
+#167 := (iff #36 #164)
+#121 := (or #91 #118)
+#97 := (or #91 #94)
+#104 := (or #103 #97)
+#109 := (forall (vars (?v0 S2)) #104)
+#112 := (and #75 #109)
+#115 := (and #69 #112)
+#127 := (not #115)
+#128 := (or #127 #121)
+#133 := (not #128)
+#165 := (iff #133 #164)
+#162 := (iff #128 #159)
+#156 := (or #153 #121)
+#160 := (iff #156 #159)
+#161 := [rewrite]: #160
+#157 := (iff #128 #156)
+#154 := (iff #127 #153)
+#151 := (iff #115 #148)
+#142 := (and #75 #139)
+#145 := (and #69 #142)
+#149 := (iff #145 #148)
+#150 := [rewrite]: #149
+#146 := (iff #115 #145)
+#143 := (iff #112 #142)
+#140 := (iff #109 #139)
+#137 := (iff #104 #136)
+#138 := [rewrite]: #137
+#141 := [quant-intro #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#152 := [trans #147 #150]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#163 := [trans #158 #161]: #162
+#166 := [monotonicity #163]: #165
+#134 := (iff #36 #133)
+#131 := (iff #35 #128)
+#124 := (implies #115 #121)
+#129 := (iff #124 #128)
+#130 := [rewrite]: #129
+#125 := (iff #35 #124)
+#122 := (iff #34 #121)
+#119 := (iff #33 #118)
+#120 := [rewrite]: #119
+#92 := (iff #24 #91)
+#93 := [rewrite]: #92
+#123 := [monotonicity #93 #120]: #122
+#116 := (iff #31 #115)
+#113 := (iff #30 #112)
+#110 := (iff #29 #109)
+#107 := (iff #28 #104)
+#100 := (implies #86 #97)
+#105 := (iff #100 #104)
+#106 := [rewrite]: #105
+#101 := (iff #28 #100)
+#98 := (iff #27 #97)
+#95 := (iff #26 #94)
+#96 := [rewrite]: #95
+#99 := [monotonicity #93 #96]: #98
+#89 := (iff #21 #86)
+#83 := (and #78 #63)
+#87 := (iff #83 #86)
+#88 := [rewrite]: #87
+#84 := (iff #21 #83)
+#81 := (iff #20 #63)
+#55 := (iff #10 #54)
+#56 := [rewrite]: #55
+#82 := [monotonicity #56]: #81
+#79 := (iff #19 #78)
+#58 := (iff #12 #57)
+#59 := [rewrite]: #58
+#80 := [monotonicity #59]: #79
+#85 := [monotonicity #80 #82]: #84
+#90 := [trans #85 #88]: #89
+#102 := [monotonicity #90 #99]: #101
+#108 := [trans #102 #106]: #107
+#111 := [quant-intro #108]: #110
+#76 := (iff #18 #75)
+#73 := (iff #17 #72)
+#74 := [rewrite]: #73
+#77 := [monotonicity #74]: #76
+#114 := [monotonicity #77 #111]: #113
+#70 := (iff #14 #69)
+#67 := (iff #13 #64)
+#60 := (implies #54 #57)
+#65 := (iff #60 #64)
+#66 := [rewrite]: #65
+#61 := (iff #13 #60)
+#62 := [monotonicity #56 #59]: #61
+#68 := [trans #62 #66]: #67
+#71 := [quant-intro #68]: #70
+#117 := [monotonicity #71 #114]: #116
+#126 := [monotonicity #117 #123]: #125
+#132 := [trans #126 #130]: #131
+#135 := [monotonicity #132]: #134
+#168 := [trans #135 #166]: #167
+#53 := [asserted]: #36
+#169 := [mp #53 #168]: #164
+#174 := [not-or-elim #169]: #148
+#175 := [and-elim #174]: #69
+#185 := [mp~ #175 #188]: #69
+#708 := [mp #185 #707]: #703
+#172 := (not #118)
+#173 := [not-or-elim #169]: #172
+#285 := (not #703)
+#372 := (or #285 #283 #118)
+#370 := (or #283 #118)
+#363 := (or #285 #370)
+#375 := (iff #363 #372)
+#303 := [rewrite]: #375
+#374 := [quant-inst]: #363
+#376 := [mp #374 #303]: #372
+#398 := [unit-resolution #376 #173 #708]: #283
+#217 := (or #54 #57 #94)
+#709 := (forall (vars (?v0 S2)) (:pat #701 #702) #217)
+#222 := (forall (vars (?v0 S2)) #217)
+#712 := (iff #222 #709)
+#710 := (iff #217 #217)
+#711 := [refl]: #710
+#713 := [quant-intro #711]: #712
+#192 := (or #103 #94)
+#197 := (forall (vars (?v0 S2)) #192)
+#223 := (iff #197 #222)
+#220 := (iff #192 #217)
+#203 := (or #54 #57)
+#214 := (or #203 #94)
+#218 := (iff #214 #217)
+#219 := [rewrite]: #218
+#215 := (iff #192 #214)
+#212 := (iff #103 #203)
+#204 := (not #203)
+#207 := (not #204)
+#210 := (iff #207 #203)
+#211 := [rewrite]: #210
+#208 := (iff #103 #207)
+#205 := (iff #86 #204)
+#206 := [rewrite]: #205
+#209 := [monotonicity #206]: #208
+#213 := [trans #209 #211]: #212
+#216 := [monotonicity #213]: #215
+#221 := [trans #216 #219]: #220
+#224 := [quant-intro #221]: #223
+#184 := (~ #197 #197)
+#186 := (~ #192 #192)
+#183 := [refl]: #186
+#180 := [nnf-pos #183]: #184
+#198 := (iff #139 #197)
+#195 := (iff #136 #192)
+#189 := (or #103 false #94)
+#193 := (iff #189 #192)
+#194 := [rewrite]: #193
+#190 := (iff #136 #189)
+#181 := (iff #91 false)
+#170 := (not #91)
+#171 := [not-or-elim #169]: #170
+#182 := [iff-false #171]: #181
+#191 := [monotonicity #182]: #190
+#196 := [trans #191 #194]: #195
+#199 := [quant-intro #196]: #198
+#177 := [and-elim #174]: #139
+#200 := [mp #177 #199]: #197
+#178 := [mp~ #200 #180]: #197
+#225 := [mp #178 #224]: #222
+#714 := [mp #225 #713]: #709
+#356 := (not #709)
+#693 := (or #356 #94 #118)
+#284 := (or #94 #118 #94)
+#695 := (or #356 #284)
+#697 := (iff #695 #693)
+#371 := (or #94 #118)
+#482 := (or #356 #371)
+#362 := (iff #482 #693)
+#696 := [rewrite]: #362
+#689 := (iff #695 #482)
+#373 := (iff #284 #371)
+#377 := [rewrite]: #373
+#361 := [monotonicity #377]: #689
+#698 := [trans #361 #696]: #697
+#350 := [quant-inst]: #695
+#699 := [mp #350 #698]: #693
+[unit-resolution #699 #173 #714 #398]: false
+unsat
+822b667791af0a48c0a74f521e617843a190d051 25 0
+#2 := false
+#8 := (:var 0 S2)
+#9 := (= #8 #8)
+#10 := (exists (vars (?v0 S2)) #9)
+#11 := (not #10)
+#43 := (iff #11 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #11 #38)
+#36 := (iff #10 true)
+#31 := (exists (vars (?v0 S2)) true)
+#34 := (iff #31 true)
+#35 := [elim-unused]: #34
+#32 := (iff #10 #31)
+#29 := (iff #9 true)
+#30 := [rewrite]: #29
+#33 := [quant-intro #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#28 := [asserted]: #11
+[mp #28 #44]: false
+unsat
+58d8ca2fb7821109746146ba7d99cd1daf6d6654 34 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S2 S1)
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#10 := (= #9 f1)
+#11 := (exists (vars (?v0 S2)) #10)
+#12 := (iff #11 #11)
+#13 := (not #12)
+#49 := (iff #13 false)
+#1 := true
+#44 := (not true)
+#47 := (iff #44 false)
+#48 := [rewrite]: #47
+#45 := (iff #13 #44)
+#42 := (iff #12 true)
+#31 := (= f1 #9)
+#34 := (exists (vars (?v0 S2)) #31)
+#37 := (iff #34 #34)
+#40 := (iff #37 true)
+#41 := [rewrite]: #40
+#38 := (iff #12 #37)
+#35 := (iff #11 #34)
+#32 := (iff #10 #31)
+#33 := [rewrite]: #32
+#36 := [quant-intro #33]: #35
+#39 := [monotonicity #36 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#30 := [asserted]: #13
+[mp #30 #50]: false
+unsat
+21a512539aace318c438fde0ff904d0bc94ee0fa 258 0
 #2 := false
 decl f4 :: (-> S2 S1)
 decl ?v0!2 :: S2
@@ -5932,132 +6381,7 @@
 #579 := [quant-inst]: #578
 [unit-resolution #579 #432 #573]: false
 unsat
-c94ebedde81defab6c020062b6dae6aec5aa6893 124 0
-#2 := false
-decl f3 :: (-> S2 S1)
-decl f4 :: (-> S2 S2)
-decl f5 :: S2
-#16 := f5
-#20 := (f4 f5)
-#21 := (f4 #20)
-#154 := (f3 #21)
-decl f1 :: S1
-#4 := f1
-#241 := (= f1 #154)
-#152 := (f3 #20)
-#239 := (= f1 #152)
-#17 := (f3 f5)
-#62 := (= f1 #17)
-#8 := (:var 0 S2)
-#11 := (f4 #8)
-#12 := (f3 #11)
-#47 := (= f1 #12)
-#9 := (f3 #8)
-#44 := (= f1 #9)
-#53 := (not #44)
-#54 := (or #53 #47)
-#59 := (forall (vars (?v0 S2)) #54)
-#65 := (and #59 #62)
-#22 := (f4 #21)
-#23 := (f3 #22)
-#68 := (= f1 #23)
-#74 := (not #65)
-#75 := (or #74 #68)
-#80 := (not #75)
-#24 := (= #23 f1)
-#18 := (= #17 f1)
-#13 := (= #12 f1)
-#10 := (= #9 f1)
-#14 := (implies #10 #13)
-#15 := (forall (vars (?v0 S2)) #14)
-#19 := (and #15 #18)
-#25 := (implies #19 #24)
-#26 := (not #25)
-#81 := (iff #26 #80)
-#78 := (iff #25 #75)
-#71 := (implies #65 #68)
-#76 := (iff #71 #75)
-#77 := [rewrite]: #76
-#72 := (iff #25 #71)
-#69 := (iff #24 #68)
-#70 := [rewrite]: #69
-#66 := (iff #19 #65)
-#63 := (iff #18 #62)
-#64 := [rewrite]: #63
-#60 := (iff #15 #59)
-#57 := (iff #14 #54)
-#50 := (implies #44 #47)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #14 #50)
-#48 := (iff #13 #47)
-#49 := [rewrite]: #48
-#45 := (iff #10 #44)
-#46 := [rewrite]: #45
-#52 := [monotonicity #46 #49]: #51
-#58 := [trans #52 #56]: #57
-#61 := [quant-intro #58]: #60
-#67 := [monotonicity #61 #64]: #66
-#73 := [monotonicity #67 #70]: #72
-#79 := [trans #73 #77]: #78
-#82 := [monotonicity #79]: #81
-#43 := [asserted]: #26
-#85 := [mp #43 #82]: #80
-#83 := [not-or-elim #85]: #65
-#86 := [and-elim #83]: #62
-#570 := (pattern #11)
-#571 := (forall (vars (?v0 S2)) (:pat #570) #54)
-#574 := (iff #59 #571)
-#572 := (iff #54 #54)
-#573 := [refl]: #572
-#575 := [quant-intro #573]: #574
-#100 := (~ #59 #59)
-#98 := (~ #54 #54)
-#99 := [refl]: #98
-#101 := [nnf-pos #99]: #100
-#84 := [and-elim #83]: #59
-#91 := [mp~ #84 #101]: #59
-#576 := [mp #91 #575]: #571
-#153 := (not #62)
-#232 := (not #571)
-#243 := (or #232 #153 #239)
-#240 := (or #153 #239)
-#244 := (or #232 #240)
-#245 := (iff #244 #243)
-#242 := [rewrite]: #245
-#172 := [quant-inst]: #244
-#246 := [mp #172 #242]: #243
-#208 := [unit-resolution #246 #576 #86]: #239
-#225 := (not #239)
-#351 := (or #232 #225 #241)
-#562 := (or #225 #241)
-#558 := (or #232 #562)
-#231 := (iff #558 #351)
-#565 := [rewrite]: #231
-#230 := [quant-inst]: #558
-#566 := [mp #230 #565]: #351
-#209 := [unit-resolution #566 #576 #208]: #241
-#87 := (not #68)
-#88 := [not-or-elim #85]: #87
-#564 := (not #241)
-#569 := (or #232 #68 #564)
-#219 := (or #564 #68)
-#559 := (or #232 #219)
-#545 := (iff #559 #569)
-#567 := (or #68 #564)
-#222 := (or #232 #567)
-#561 := (iff #222 #569)
-#202 := [rewrite]: #561
-#560 := (iff #559 #222)
-#568 := (iff #219 #567)
-#563 := [rewrite]: #568
-#218 := [monotonicity #563]: #560
-#206 := [trans #218 #202]: #545
-#217 := [quant-inst]: #559
-#207 := [mp #217 #206]: #569
-[unit-resolution #207 #576 #88 #209]: false
-unsat
-29a00825da3cfb6f45d89e9d7c24512d752b68eb 222 0
+df57559635c5ccc05715d1d9c382b9c2913c20a6 222 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl ?v0!0 :: S2
@@ -6280,72 +6604,7 @@
 #610 := [quant-inst]: #609
 [unit-resolution #610 #339 #320]: false
 unsat
-d6381b0e6162629304a9edd3be9ca3c00c481087 64 0
-#2 := false
-decl f3 :: (-> S2 S2 S3)
-decl f4 :: S2
-#14 := f4
-decl f5 :: S2
-#16 := f5
-#18 := (f3 f5 f4)
-#17 := (f3 f4 f5)
-#19 := (= #17 #18)
-#62 := (not #19)
-#8 := (:var 1 S2)
-#9 := (:var 0 S2)
-#11 := (f3 #9 #8)
-#10 := (f3 #8 #9)
-#12 := (= #10 #11)
-#13 := (forall (vars (?v0 S2) (?v1 S2)) #12)
-#52 := (not #13)
-#53 := (or #52 #19)
-#58 := (not #53)
-#15 := (= f4 f4)
-#20 := (and #15 #19)
-#21 := (implies #13 #20)
-#22 := (not #21)
-#59 := (iff #22 #58)
-#56 := (iff #21 #53)
-#49 := (implies #13 #19)
-#54 := (iff #49 #53)
-#55 := [rewrite]: #54
-#50 := (iff #21 #49)
-#47 := (iff #20 #19)
-#1 := true
-#42 := (and true #19)
-#45 := (iff #42 #19)
-#46 := [rewrite]: #45
-#43 := (iff #20 #42)
-#40 := (iff #15 true)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#51 := [monotonicity #48]: #50
-#57 := [trans #51 #55]: #56
-#60 := [monotonicity #57]: #59
-#39 := [asserted]: #22
-#63 := [mp #39 #60]: #58
-#64 := [not-or-elim #63]: #62
-#547 := (pattern #11)
-#546 := (pattern #10)
-#548 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #546 #547) #12)
-#551 := (iff #13 #548)
-#549 := (iff #12 #12)
-#550 := [refl]: #549
-#552 := [quant-intro #550]: #551
-#74 := (~ #13 #13)
-#72 := (~ #12 #12)
-#73 := [refl]: #72
-#75 := [nnf-pos #73]: #74
-#61 := [not-or-elim #63]: #13
-#67 := [mp~ #61 #75]: #13
-#553 := [mp #67 #552]: #548
-#129 := (not #548)
-#216 := (or #129 #19)
-#130 := [quant-inst]: #216
-[unit-resolution #130 #553 #64]: false
-unsat
-a59143663975583139cdacfbcd52f21f568835d6 49 0
+71aa2c50555bb8151642ab271b54a39dd7a7bb46 49 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -6395,258 +6654,7 @@
 #35 := [asserted]: #18
 [mp #35 #65]: false
 unsat
-7f4c24ba00666fac3b960c74d81cc061e8e4c71c 250 0
-#2 := false
-decl f3 :: (-> S2 S1)
-decl f7 :: S2
-#22 := f7
-#25 := (f3 f7)
-decl f1 :: S1
-#4 := f1
-#94 := (= f1 #25)
-#283 := (not #94)
-decl f4 :: (-> S2 S1)
-#8 := (:var 0 S2)
-#11 := (f4 #8)
-#702 := (pattern #11)
-#9 := (f3 #8)
-#701 := (pattern #9)
-#57 := (= f1 #11)
-#54 := (= f1 #9)
-#63 := (not #54)
-#64 := (or #63 #57)
-#703 := (forall (vars (?v0 S2)) (:pat #701 #702) #64)
-#69 := (forall (vars (?v0 S2)) #64)
-#706 := (iff #69 #703)
-#704 := (iff #64 #64)
-#705 := [refl]: #704
-#707 := [quant-intro #705]: #706
-#187 := (~ #69 #69)
-#201 := (~ #64 #64)
-#202 := [refl]: #201
-#188 := [nnf-pos #202]: #187
-decl f6 :: (-> S2 S1)
-#23 := (f6 f7)
-#91 := (= f1 #23)
-#78 := (not #57)
-#86 := (and #63 #78)
-#103 := (not #86)
-#136 := (or #103 #91 #94)
-#139 := (forall (vars (?v0 S2)) #136)
-decl f5 :: S2
-#15 := f5
-#16 := (f4 f5)
-#72 := (= f1 #16)
-#75 := (not #72)
-#148 := (and #69 #75 #139)
-#153 := (not #148)
-#32 := (f4 f7)
-#118 := (= f1 #32)
-#159 := (or #91 #118 #153)
-#164 := (not #159)
-#33 := (= #32 f1)
-#24 := (= #23 f1)
-#34 := (or #24 #33)
-#26 := (= #25 f1)
-#27 := (or #24 #26)
-#10 := (= #9 f1)
-#20 := (not #10)
-#12 := (= #11 f1)
-#19 := (not #12)
-#21 := (and #19 #20)
-#28 := (implies #21 #27)
-#29 := (forall (vars (?v0 S2)) #28)
-#17 := (= #16 f1)
-#18 := (not #17)
-#30 := (and #18 #29)
-#13 := (implies #10 #12)
-#14 := (forall (vars (?v0 S2)) #13)
-#31 := (and #14 #30)
-#35 := (implies #31 #34)
-#36 := (not #35)
-#167 := (iff #36 #164)
-#121 := (or #91 #118)
-#97 := (or #91 #94)
-#104 := (or #103 #97)
-#109 := (forall (vars (?v0 S2)) #104)
-#112 := (and #75 #109)
-#115 := (and #69 #112)
-#127 := (not #115)
-#128 := (or #127 #121)
-#133 := (not #128)
-#165 := (iff #133 #164)
-#162 := (iff #128 #159)
-#156 := (or #153 #121)
-#160 := (iff #156 #159)
-#161 := [rewrite]: #160
-#157 := (iff #128 #156)
-#154 := (iff #127 #153)
-#151 := (iff #115 #148)
-#142 := (and #75 #139)
-#145 := (and #69 #142)
-#149 := (iff #145 #148)
-#150 := [rewrite]: #149
-#146 := (iff #115 #145)
-#143 := (iff #112 #142)
-#140 := (iff #109 #139)
-#137 := (iff #104 #136)
-#138 := [rewrite]: #137
-#141 := [quant-intro #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#152 := [trans #147 #150]: #151
-#155 := [monotonicity #152]: #154
-#158 := [monotonicity #155]: #157
-#163 := [trans #158 #161]: #162
-#166 := [monotonicity #163]: #165
-#134 := (iff #36 #133)
-#131 := (iff #35 #128)
-#124 := (implies #115 #121)
-#129 := (iff #124 #128)
-#130 := [rewrite]: #129
-#125 := (iff #35 #124)
-#122 := (iff #34 #121)
-#119 := (iff #33 #118)
-#120 := [rewrite]: #119
-#92 := (iff #24 #91)
-#93 := [rewrite]: #92
-#123 := [monotonicity #93 #120]: #122
-#116 := (iff #31 #115)
-#113 := (iff #30 #112)
-#110 := (iff #29 #109)
-#107 := (iff #28 #104)
-#100 := (implies #86 #97)
-#105 := (iff #100 #104)
-#106 := [rewrite]: #105
-#101 := (iff #28 #100)
-#98 := (iff #27 #97)
-#95 := (iff #26 #94)
-#96 := [rewrite]: #95
-#99 := [monotonicity #93 #96]: #98
-#89 := (iff #21 #86)
-#83 := (and #78 #63)
-#87 := (iff #83 #86)
-#88 := [rewrite]: #87
-#84 := (iff #21 #83)
-#81 := (iff #20 #63)
-#55 := (iff #10 #54)
-#56 := [rewrite]: #55
-#82 := [monotonicity #56]: #81
-#79 := (iff #19 #78)
-#58 := (iff #12 #57)
-#59 := [rewrite]: #58
-#80 := [monotonicity #59]: #79
-#85 := [monotonicity #80 #82]: #84
-#90 := [trans #85 #88]: #89
-#102 := [monotonicity #90 #99]: #101
-#108 := [trans #102 #106]: #107
-#111 := [quant-intro #108]: #110
-#76 := (iff #18 #75)
-#73 := (iff #17 #72)
-#74 := [rewrite]: #73
-#77 := [monotonicity #74]: #76
-#114 := [monotonicity #77 #111]: #113
-#70 := (iff #14 #69)
-#67 := (iff #13 #64)
-#60 := (implies #54 #57)
-#65 := (iff #60 #64)
-#66 := [rewrite]: #65
-#61 := (iff #13 #60)
-#62 := [monotonicity #56 #59]: #61
-#68 := [trans #62 #66]: #67
-#71 := [quant-intro #68]: #70
-#117 := [monotonicity #71 #114]: #116
-#126 := [monotonicity #117 #123]: #125
-#132 := [trans #126 #130]: #131
-#135 := [monotonicity #132]: #134
-#168 := [trans #135 #166]: #167
-#53 := [asserted]: #36
-#169 := [mp #53 #168]: #164
-#174 := [not-or-elim #169]: #148
-#175 := [and-elim #174]: #69
-#185 := [mp~ #175 #188]: #69
-#708 := [mp #185 #707]: #703
-#172 := (not #118)
-#173 := [not-or-elim #169]: #172
-#285 := (not #703)
-#372 := (or #285 #283 #118)
-#370 := (or #283 #118)
-#363 := (or #285 #370)
-#375 := (iff #363 #372)
-#303 := [rewrite]: #375
-#374 := [quant-inst]: #363
-#376 := [mp #374 #303]: #372
-#398 := [unit-resolution #376 #173 #708]: #283
-#217 := (or #54 #57 #94)
-#709 := (forall (vars (?v0 S2)) (:pat #701 #702) #217)
-#222 := (forall (vars (?v0 S2)) #217)
-#712 := (iff #222 #709)
-#710 := (iff #217 #217)
-#711 := [refl]: #710
-#713 := [quant-intro #711]: #712
-#192 := (or #103 #94)
-#197 := (forall (vars (?v0 S2)) #192)
-#223 := (iff #197 #222)
-#220 := (iff #192 #217)
-#203 := (or #54 #57)
-#214 := (or #203 #94)
-#218 := (iff #214 #217)
-#219 := [rewrite]: #218
-#215 := (iff #192 #214)
-#212 := (iff #103 #203)
-#204 := (not #203)
-#207 := (not #204)
-#210 := (iff #207 #203)
-#211 := [rewrite]: #210
-#208 := (iff #103 #207)
-#205 := (iff #86 #204)
-#206 := [rewrite]: #205
-#209 := [monotonicity #206]: #208
-#213 := [trans #209 #211]: #212
-#216 := [monotonicity #213]: #215
-#221 := [trans #216 #219]: #220
-#224 := [quant-intro #221]: #223
-#184 := (~ #197 #197)
-#186 := (~ #192 #192)
-#183 := [refl]: #186
-#180 := [nnf-pos #183]: #184
-#198 := (iff #139 #197)
-#195 := (iff #136 #192)
-#189 := (or #103 false #94)
-#193 := (iff #189 #192)
-#194 := [rewrite]: #193
-#190 := (iff #136 #189)
-#181 := (iff #91 false)
-#170 := (not #91)
-#171 := [not-or-elim #169]: #170
-#182 := [iff-false #171]: #181
-#191 := [monotonicity #182]: #190
-#196 := [trans #191 #194]: #195
-#199 := [quant-intro #196]: #198
-#177 := [and-elim #174]: #139
-#200 := [mp #177 #199]: #197
-#178 := [mp~ #200 #180]: #197
-#225 := [mp #178 #224]: #222
-#714 := [mp #225 #713]: #709
-#356 := (not #709)
-#693 := (or #356 #94 #118)
-#284 := (or #94 #118 #94)
-#695 := (or #356 #284)
-#697 := (iff #695 #693)
-#371 := (or #94 #118)
-#482 := (or #356 #371)
-#362 := (iff #482 #693)
-#696 := [rewrite]: #362
-#689 := (iff #695 #482)
-#373 := (iff #284 #371)
-#377 := [rewrite]: #373
-#361 := [monotonicity #377]: #689
-#698 := [trans #361 #696]: #697
-#350 := [quant-inst]: #695
-#699 := [mp #350 #698]: #693
-[unit-resolution #699 #173 #714 #398]: false
-unsat
-55ab12f407bdf7fa84c1317fb83d267ee6dbe0b9 122 0
+c8380a6ec9b0206f310f0bc62a94f27e6fe8ae4c 122 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl ?v0!1 :: S2
@@ -6769,21 +6777,21 @@
 #287 := [quant-inst]: #200
 [unit-resolution #287 #620 #138]: false
 unsat
-615edcc1b5967710c13cc8530677bd4b60ed143e 1 2
+59fe9aa84437dd4a1950728c65a346cceb463e1e 1 2
 unsat
 WARNING: failed to find a pattern for quantifier (quantifier id: k!9)
 
-cd545152cc212d0c395f2d5b056f6b9ac9c802b6 1 0
-unsat
-f064b99fb73e74622b958a2068a0d0b4edd902b2 1 0
-unsat
-2d8e7a5bcefce0c794a69f82f7029712f925b8a0 1 0
-unsat
-2c03da3c2314f743fe9232bb9b9c3ba10bf6d5ef 1 0
-unsat
-e41045b4d3521f41a792e556bf2332e60d77ec7a 1 0
-unsat
-1a85b2998fdcf0e23a359440a42ba41df7200751 105 0
+437ee69a165aa47e1be41cc6f68bc71591f84b01 1 0
+unsat
+92fc9eb5cd618bd57856016cf2cac1ccd5d7ca03 1 0
+unsat
+8cb3b7fcc6eabb32254f7a9ccadb140de44776cc 1 0
+unsat
+db36ffa1f078e036bd0e43127da017927731d0fd 1 0
+unsat
+59e05b7375ccb96e242672b444c1f4a1d1b4143b 1 0
+unsat
+64b8fbabaa816ff2a3417119ecd8bda16ede2dc2 105 0
 #2 := false
 decl f3 :: (-> S1 S1)
 decl ?v0!1 :: S1
@@ -6889,7 +6897,7 @@
 #261 := [quant-inst]: #188
 [unit-resolution #261 #590 #259]: false
 unsat
-598fbc0a61e9e499866f4757d97c531ce37db1ae 230 0
+946ebb583ce5af16db726beb09ceecc293b794dd 230 0
 #2 := false
 decl f3 :: (-> S1 S1)
 decl ?v0!0 :: S1
@@ -7120,7 +7128,7 @@
 #309 := [quant-inst]: #308
 [unit-resolution #309 #590 #312]: false
 unsat
-cac0a2176ec80fb1c96e1c40b7d14da0fa6af78c 156 0
+f53b1d3aa99bd604ef2c4a7d0872966141b2f13e 156 0
 #2 := false
 decl f3 :: (-> S1 S2 S1)
 #9 := (:var 0 S2)
@@ -7277,7 +7285,7 @@
 #269 := [quant-inst]: #264
 [unit-resolution #269 #592 #292]: false
 unsat
-49ea124a0c85794588287d88e4a10f91ec534ee7 74 0
+ada6aac46a243252175bbef4890ea4e272bf296b 74 0
 #2 := false
 decl f3 :: (-> S2 S3 S4)
 #9 := (:var 0 S3)
@@ -7352,7 +7360,7 @@
 #548 := [mp #55 #547]: #543
 [unit-resolution #548 #537]: false
 unsat
-f922619aea5365bdf4744142fd24ae3f3d91080e 108 0
+805e1aa19dfc9d11e14fad057b8523ea811f7aae 108 0
 #2 := false
 decl f3 :: (-> S1 S1)
 #11 := (:var 0 S1)
@@ -7461,7 +7469,7 @@
 #179 := [quant-inst]: #265
 [unit-resolution #179 #96 #599]: false
 unsat
-ccfa103f9dc86cc5a39d3a0bd17ea6e15ed83789 183 2
+2ed1bdbbcf222ab042db8b377c2b5a532cfbf28a 183 2
 #2 := false
 decl f3 :: (-> S1 S2 S1)
 #9 := (:var 0 S2)
@@ -7647,15 +7655,23 @@
 unsat
 WARNING: failed to find a pattern for quantifier (quantifier id: k!12)
 
-04a10002b6cfbd9320b025e8add4b15624e7ca83 1 0
-unsat
-56c3c1aac521682b0935ad2f17220b3ea8838cd3 1 2
+9cb5773d40d323d9ae7232afa82167b32b074678 1 0
+unsat
+6ad5fae2fb672b745c4eb5325c0501a9c2b3fc57 1 2
 unsat
 WARNING: failed to find a pattern for quantifier (quantifier id: k!12)
 
-5211d0658c8aa96a06f5b015ae31d3fe55c3cab1 1 0
-unsat
-c20f820d839321d9bf17ab605375903e475f33e6 107 0
+29deb2b2e519c8e3b6f1b74e2d6930a83fc91212 1 0
+unsat
+3fc5aae5fb0df8767a8c9eadb150b3a5c73e18de 1 0
+unsat
+7b610087941e1fe4f88d45f46fad928aa9af0f09 1 0
+unsat
+20b5ef2f1702df64169ec83a69017044745c06e3 1 0
+unsat
+faf257f2b78d6c6530134a452629187d275e10df 1 0
+unsat
+8e5c225400452884ef757ae1c905df29e2ecb6e5 107 0
 #2 := false
 decl f3 :: (-> S2 S1)
 #8 := (:var 0 S2)
@@ -7763,9 +7779,7 @@
 #279 := [quant-inst]: #193
 [unit-resolution #279 #102 #618]: false
 unsat
-677e024c66187dc21b71678cb1488477fcd87167 1 0
-unsat
-872e0bf32f19bb056d35b742419e7bfe9bc7d3b4 75 0
+c49815d35da5debf93ccb24e6deb44cf3bdb9f3a 75 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -7841,9 +7855,7 @@
 #41 := [asserted]: #24
 [mp #41 #91]: false
 unsat
-ac8a74b907f6dc5eac6d550dfb9933eb000058e1 1 0
-unsat
-90c127d5cedd68c871816f3946c02cfc6b8af4a9 207 0
+89a398b08c2ef3da10491e4f9b93114b632b7b4b 207 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl ?v1!0 :: (-> S2 S2)
@@ -8051,9 +8063,7 @@
 #622 := [mp #616 #257]: #277
 [unit-resolution #622 #645 #591 #596]: false
 unsat
-5a145de81e4f4eeae6397f2aeade9a713df0b402 1 0
-unsat
-8bc50e9ee1d32eca0b2ec9f707ee916f7233c543 250 0
+ea2c6c9fa630b6248b3b6d51413430e946215eb4 250 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl ?v1!1 :: (-> S2 S2)
@@ -8304,9 +8314,7 @@
 #616 := [mp #628 #615]: #622
 [unit-resolution #616 #128 #676 #607 #606]: false
 unsat
-294a32d87135d8d12940225c21b358de5bcb1008 1 0
-unsat
-f2c8c9d3021edc718ea5a2b825764e713b11fd77 238 0
+78cdfb5ab60f55b88bbf60cd2daa3bad360efc21 238 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl ?v1!1 :: (-> S2 S2)
@@ -8545,7 +8553,7 @@
 #338 := [mp #643 #632]: #276
 [unit-resolution #338 #664 #617 #616]: false
 unsat
-f085880cbe2b6e218620939fd09c5950c149f5a2 93 0
+2c5b2347001f4b18141d163d5bfc1c682924b4df 93 0
 #2 := false
 decl f5 :: (-> S2 S1)
 decl f6 :: S2
@@ -8639,7 +8647,7 @@
 #248 := [mp #246 #175]: #244
 [unit-resolution #248 #578 #83 #85]: false
 unsat
-9ef609620af3ecd94cdef1f843003b8483978fbb 113 0
+6192bca695b73a86b969253f2dd03bcbf04d87fc 113 0
 #2 := false
 decl f3 :: (-> S2 S3 S1)
 decl f4 :: S3
@@ -8753,7 +8761,7 @@
 #365 := [mp #188 #235]: #259
 [unit-resolution #365 #591 #76 #77]: false
 unsat
-b1e70439cf48151ac262711545999d4078fe3f18 43 0
+1b1437e3e73cf4662f9fcb53a06bc87f039babdb 43 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -8797,7 +8805,7 @@
 #32 := [asserted]: #15
 [mp #32 #58]: false
 unsat
-5c6baa5560c27cbea391f380f1d2efa0c31ad451 27 0
+a2b1ae1f1b9350c774e71e885f07b6c1e3d70110 27 0
 #2 := false
 #1 := true
 #9 := (or false true)
@@ -8825,7 +8833,7 @@
 #28 := [asserted]: #11
 [mp #28 #46]: false
 unsat
-ca24bad9d30cd7adb4d8824254fb1d868566dba8 31 0
+62ec3236da9815c004bd70d8e8667074e466dd55 31 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -8857,7 +8865,7 @@
 #29 := [asserted]: #12
 [mp #29 #46]: false
 unsat
-4c370ded875fbae45221845a75b0cee6f100c565 33 0
+b17864b1c8eb2860baa03dfe4eecc5b904037f2e 33 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -8891,43 +8899,46 @@
 #30 := [asserted]: #13
 [mp #30 #47]: false
 unsat
-1796e5eebe3961668a10c629c8446aea6b05d0ff 35 0
+56440e444950f65beb2b3f75b6cf6ee27719cae3 38 0
 #2 := false
 decl f1 :: S1
 #4 := f1
 decl f3 :: (-> S2 S1)
-decl f4 :: S2
-#8 := f4
-#9 := (f3 f4)
+#8 := (:var 0 S2)
+#9 := (f3 #8)
 #10 := (= #9 f1)
-#11 := (not #10)
-#12 := (ite #10 #10 #11)
-#13 := (not #12)
-#49 := (iff #13 false)
-#1 := true
-#44 := (not true)
-#47 := (iff #44 false)
-#48 := [rewrite]: #47
-#45 := (iff #13 #44)
-#42 := (iff #12 true)
-#31 := (= f1 #9)
-#34 := (not #31)
-#37 := (ite #31 #31 #34)
-#40 := (iff #37 true)
-#41 := [rewrite]: #40
-#38 := (iff #12 #37)
-#35 := (iff #11 #34)
-#32 := (iff #10 #31)
-#33 := [rewrite]: #32
-#36 := [monotonicity #33]: #35
-#39 := [monotonicity #33 #33 #36]: #38
-#43 := [trans #39 #41]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#30 := [asserted]: #13
-[mp #30 #50]: false
-unsat
-6cbede560f4445a6195546ba14a38ce4cef82756 38 0
+#11 := (forall (vars (?v0 S2)) #10)
+#12 := (not #11)
+#13 := (ite #11 #11 #12)
+#14 := (not #13)
+#53 := (iff #14 false)
+#1 := true
+#48 := (not true)
+#51 := (iff #48 false)
+#52 := [rewrite]: #51
+#49 := (iff #14 #48)
+#46 := (iff #13 true)
+#32 := (= f1 #9)
+#35 := (forall (vars (?v0 S2)) #32)
+#38 := (not #35)
+#41 := (ite #35 #35 #38)
+#44 := (iff #41 true)
+#45 := [rewrite]: #44
+#42 := (iff #13 #41)
+#39 := (iff #12 #38)
+#36 := (iff #11 #35)
+#33 := (iff #10 #32)
+#34 := [rewrite]: #33
+#37 := [quant-intro #34]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #37 #37 #40]: #42
+#47 := [trans #43 #45]: #46
+#50 := [monotonicity #47]: #49
+#54 := [trans #50 #52]: #53
+#31 := [asserted]: #14
+[mp #31 #54]: false
+unsat
+a41a0eb742f5edc1d4fc78737a3beb25e5949f9b 38 0
 #2 := false
 decl f3 :: (-> S2 S2)
 decl f4 :: S2
@@ -8966,19 +8977,25 @@
 #114 := [quant-inst]: #200
 [unit-resolution #114 #51 #50]: false
 unsat
-3951eb981ad2121ce0b01ef0fb8385398766b219 30 0
+8398a3c394529f4aff2a970e201a7384f8dae583 36 0
 #2 := false
 decl f4 :: (-> S3 S4)
-decl f6 :: S3
-#17 := f6
-#18 := (f4 f6)
+decl f6 :: (-> int S3)
+decl f7 :: (-> int int)
+decl f8 :: (-> int int)
+decl f9 :: int
+#17 := f9
+#18 := (f8 f9)
+#19 := (f7 #18)
+#20 := (f6 #19)
+#21 := (f4 #20)
 decl f3 :: (-> S2 S4)
 decl f5 :: S2
 #15 := f5
 #16 := (f3 f5)
-#19 := (= #16 #18)
-#20 := (not #19)
-#38 := [asserted]: #20
+#22 := (= #16 #21)
+#23 := (not #22)
+#41 := [asserted]: #23
 #10 := (:var 0 S3)
 #11 := (f4 #10)
 #8 := (:var 1 S2)
@@ -8986,18 +9003,18 @@
 #12 := (pattern #9 #11)
 #13 := (= #9 #11)
 #14 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #12) #13)
-#48 := (~ #14 #14)
-#46 := (~ #13 #13)
-#47 := [refl]: #46
-#49 := [nnf-pos #47]: #48
-#37 := [asserted]: #14
-#41 := [mp~ #37 #49]: #14
-#103 := (not #14)
-#190 := (or #103 #19)
-#104 := [quant-inst]: #190
-[unit-resolution #104 #41 #38]: false
-unsat
-cfb7ec1e9520aafa7d5b29cfb983793ee2d6f2b3 16 0
+#51 := (~ #14 #14)
+#49 := (~ #13 #13)
+#50 := [refl]: #49
+#52 := [nnf-pos #50]: #51
+#40 := [asserted]: #14
+#44 := [mp~ #40 #52]: #14
+#106 := (not #14)
+#193 := (or #106 #22)
+#107 := [quant-inst]: #193
+[unit-resolution #107 #44 #41]: false
+unsat
+79f97c590d9af969a754f5256e7d357de52be600 16 0
 #2 := false
 #1 := true
 #8 := (implies true true)
@@ -9014,7 +9031,7 @@
 #26 := [asserted]: #9
 [mp #26 #35]: false
 unsat
-7cbcb79eb27355ecf4f8c83e03297c7b412bce52 16 0
+d1fecf522b59adab5c433a96a5164ba5408f6ac5 16 0
 #2 := false
 #8 := (implies false false)
 #9 := (not #8)
@@ -9031,7 +9048,7 @@
 #26 := [asserted]: #9
 [mp #26 #35]: false
 unsat
-abfb47efa43a4820aa829461952d8e31f18076ce 31 0
[phone]b22a7ec2bd890e9c1875924f44c3f2c4 31 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -9063,7 +9080,7 @@
 #29 := [asserted]: #12
 [mp #29 #46]: false
 unsat
-68233e17fde29c54af280784ff125abdb937332e 48 0
+d532f01e027b1a8aa32199495950f5f9b40d623f 48 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -9112,7 +9129,7 @@
 #31 := [asserted]: #14
 [mp #31 #63]: false
 unsat
-f363d14bd402cc293d16ba4871e3b8a53de5f8dc 53 0
+d78a4a05ec612c065c2cdeb90d9ac948ac67fbd6 53 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -9166,7 +9183,7 @@
 #31 := [asserted]: #14
 [mp #31 #68]: false
 unsat
-9f187e77426ab643b39435558d6d1a14dc433609 56 0
+5fe02cf14c01c60bef581779284a507f5deafab2 56 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -9223,7 +9240,7 @@
 #32 := [asserted]: #15
 [mp #32 #71]: false
 unsat
-510a0fc3c1359f943c6e00e7c3aafbf7737756e9 89 0
+41a26b140bc7e62ad32c007895819b6c94d338d1 89 0
 #2 := false
 decl f4 :: S1
 #10 := f4
@@ -9313,7 +9330,7 @@
 #86 := [not-or-elim #83]: #48
 [mp #86 #107]: false
 unsat
-356f92e13256c637921f76eda9e7cbbac3ef8f53 57 0
+2060c88fdb9e91cc8830dab4c104fcec3d9c483e 57 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl f4 :: S2
@@ -9371,11 +9388,7 @@
 #59 := [not-or-elim #57]: #58
 [mp #59 #74]: false
 unsat
-ff9d25294dc1a17176296b8b02c6fb61dd5a7105 3 0
-#2 := false
-[asserted]: false
-unsat
-f77cd44869b8452f0b9cdbc4acee77106cfc0c39 50 0
+0b5e09d1f83c9fa3f7822dab4e00442c0d34bdf4 50 0
 #2 := false
 decl f5 :: S2
 #11 := f5
@@ -9426,26 +9439,7 @@
 #62 := [not-or-elim #58]: #61
 [unit-resolution #62 #70]: false
 unsat
-ae97c364e76e6bda750550b3359e25f9363fc00f 18 0
-#2 := false
-#9 := 1::int
-#8 := 0::int
-#10 := (< 0::int 1::int)
-#11 := (not #10)
-#38 := (iff #11 false)
-#1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #11 #33)
-#31 := (iff #10 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#28 := [asserted]: #11
-[mp #28 #39]: false
-unsat
-6168df6e70405fbcc2600c1e033ec5aaad4d620c 27 0
+8b34fcaac30e107fde78c7fc430ec24797ca1227 27 0
 #2 := false
 decl f5 :: (-> S2 S3)
 decl f4 :: S2
@@ -9473,26 +9467,7 @@
 #43 := [not-or-elim #42]: #41
 [unit-resolution #43 #51]: false
 unsat
-93d89a3ed53f09b21acbcbce4122ad8ab50daca2 18 0
-#2 := false
-#9 := 1::int
-#8 := 0::int
-#10 := (<= 0::int 1::int)
-#11 := (not #10)
-#38 := (iff #11 false)
-#1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #11 #33)
-#31 := (iff #10 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#28 := [asserted]: #11
-[mp #28 #39]: false
-unsat
-5a8fd4dc177700b7e623e63e345f854da9c68ee0 73 0
+3acd054d80d36988fb0cff8383b9779b6dccf405 73 0
 #2 := false
 decl f3 :: (-> S1 S1)
 decl f4 :: S1
@@ -9566,26 +9541,7 @@
 #146 := [quant-inst]: #232
 [unit-resolution #146 #566 #74]: false
 unsat
-80b6a701eb48d11531bbc36b28f9be8ab306b56a 18 0
-#2 := false
-#9 := 2345678901::int
-#8 := 123456789::int
-#10 := (< 123456789::int 2345678901::int)
-#11 := (not #10)
-#38 := (iff #11 false)
-#1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #11 #33)
-#31 := (iff #10 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#28 := [asserted]: #11
-[mp #28 #39]: false
-unsat
-f13cda4935d2ad2244c0ae2a16ca60c9a8153f04 106 0
+95a5e24071204d451411ae621b394e9cf0810bf9 106 0
 #2 := false
 decl f3 :: (-> S2 S2 S1)
 decl ?v0!0 :: S2
@@ -9692,7 +9648,7 @@
 #239 := [mp #568 #238]: #254
 [unit-resolution #239 #583 #88]: false
 unsat
-060c210941c0fd9eca58c8250fc66d664e976010 66 0
+02044173beff1ab91acfe25dc46973c9c3661be9 66 0
 #2 := false
 decl f4 :: S1
 #10 := f4
@@ -9759,7 +9715,7 @@
 #71 := [and-elim #69]: #40
 [mp #71 #85]: false
 unsat
-51b1554c8079ae450aaa843f46db3a132a62d2a4 59 0
+0ebc552891db88bb58b39563a0b6f0c99cebf0a5 59 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -9819,7 +9775,68 @@
 #37 := [asserted]: #20
 [mp #37 #72]: false
 unsat
-84b3ad1ba10175f629ea45974dd1f7204028ffdc 30 0
+e90032f2c4f8aae53cc1fa2261924f5d9f8673ab 3 0
+#2 := false
+[asserted]: false
+unsat
+d3443d2cadde3810f0bd25ca63309ea8510f3631 18 0
+#2 := false
+#9 := 1::int
+#8 := 0::int
+#10 := (< 0::int 1::int)
+#11 := (not #10)
+#38 := (iff #11 false)
+#1 := true
+#33 := (not true)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (iff #10 true)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#28 := [asserted]: #11
+[mp #28 #39]: false
+unsat
+41970dcaece09dcdc842d869407e18809563233c 18 0
+#2 := false
+#9 := 1::int
+#8 := 0::int
+#10 := (<= 0::int 1::int)
+#11 := (not #10)
+#38 := (iff #11 false)
+#1 := true
+#33 := (not true)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (iff #10 true)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#28 := [asserted]: #11
+[mp #28 #39]: false
+unsat
+b6a5f38ff1839cef4ec9d4aad3c4ad7c0f5e6c78 18 0
+#2 := false
+#9 := 2345678901::int
+#8 := 123456789::int
+#10 := (< 123456789::int 2345678901::int)
+#11 := (not #10)
+#38 := (iff #11 false)
+#1 := true
+#33 := (not true)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (iff #10 true)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#28 := [asserted]: #11
+[mp #28 #39]: false
+unsat
+1514a39baa96bbdf92629268a5adf55bd15bd402 30 0
 #2 := false
 decl f3 :: (-> int S2)
 #25 := 1::int
@@ -9850,7 +9867,7 @@
 #132 := [asserted]: #30
 [mp #132 #149]: false
 unsat
-fc798ca35949786a7df6c3211b951fe889ed5aca 33 0
+147a4fe7bc4098262bd621c9e154063784d9d7de 33 0
 #2 := false
 #27 := 1::int
 decl f4 :: (-> S2 int)
@@ -9884,68 +9901,7 @@
 #132 := [asserted]: #30
 [mp #132 #152]: false
 unsat
-1a658a61136d181e832caa6664fb39c44f4496ee 60 0
-#2 := false
-decl f3 :: (-> int S2)
-decl f4 :: (-> S2 int)
-decl f5 :: S2
-#25 := f5
-#26 := (f4 f5)
-#135 := (f3 #26)
-#141 := (= f5 #135)
-#146 := (not #141)
-#13 := 0::int
-#27 := (+ #26 0::int)
-#28 := (f3 #27)
-#29 := (= #28 f5)
-#30 := (not #29)
-#147 := (iff #30 #146)
-#144 := (iff #29 #141)
-#138 := (= #135 f5)
-#142 := (iff #138 #141)
-#143 := [rewrite]: #142
-#139 := (iff #29 #138)
-#136 := (= #28 #135)
-#133 := (= #27 #26)
-#134 := [rewrite]: #133
-#137 := [monotonicity #134]: #136
-#140 := [monotonicity #137]: #139
-#145 := [trans #140 #143]: #144
-#148 := [monotonicity #145]: #147
-#132 := [asserted]: #30
-#151 := [mp #132 #148]: #146
-#8 := (:var 0 S2)
-#9 := (f4 #8)
-#639 := (pattern #9)
-#10 := (f3 #9)
-#48 := (= #8 #10)
-#640 := (forall (vars (?v0 S2)) (:pat #639) #48)
-#51 := (forall (vars (?v0 S2)) #48)
-#641 := (iff #51 #640)
-#643 := (iff #640 #640)
-#644 := [rewrite]: #643
-#642 := [rewrite]: #641
-#645 := [trans #642 #644]: #641
-#163 := (~ #51 #51)
-#161 := (~ #48 #48)
-#162 := [refl]: #161
-#164 := [nnf-pos #162]: #163
-#11 := (= #10 #8)
-#12 := (forall (vars (?v0 S2)) #11)
-#52 := (iff #12 #51)
-#49 := (iff #11 #48)
-#50 := [rewrite]: #49
-#53 := [quant-intro #50]: #52
-#47 := [asserted]: #12
-#56 := [mp #47 #53]: #51
-#152 := [mp~ #56 #164]: #51
-#646 := [mp #152 #645]: #640
-#224 := (not #640)
-#310 := (or #224 #141)
-#311 := [quant-inst]: #310
-[unit-resolution #311 #646 #151]: false
-unsat
-ed39783643eee7923ab14b3fef066b0bb836f7e4 428 0
+bf67611eba21f4423b0b8a8a66c23a3782c99542 428 0
 #2 := false
 decl f4 :: (-> S2 int)
 decl f6 :: S2
@@ -10374,149 +10330,7 @@
 #393 := [unit-resolution #403 #411 #414]: #443
 [unit-resolution #393 #424]: false
 unsat
-99ce906c39baeb082cce24e7e191930744f68770 60 0
-#2 := false
-decl f3 :: (-> int S2)
-decl f4 :: (-> S2 int)
-decl f5 :: S2
-#25 := f5
-#26 := (f4 f5)
-#135 := (f3 #26)
-#141 := (= f5 #135)
-#146 := (not #141)
-#13 := 0::int
-#27 := (+ 0::int #26)
-#28 := (f3 #27)
-#29 := (= #28 f5)
-#30 := (not #29)
-#147 := (iff #30 #146)
-#144 := (iff #29 #141)
-#138 := (= #135 f5)
-#142 := (iff #138 #141)
-#143 := [rewrite]: #142
-#139 := (iff #29 #138)
-#136 := (= #28 #135)
-#133 := (= #27 #26)
-#134 := [rewrite]: #133
-#137 := [monotonicity #134]: #136
-#140 := [monotonicity #137]: #139
-#145 := [trans #140 #143]: #144
-#148 := [monotonicity #145]: #147
-#132 := [asserted]: #30
-#151 := [mp #132 #148]: #146
-#8 := (:var 0 S2)
-#9 := (f4 #8)
-#639 := (pattern #9)
-#10 := (f3 #9)
-#48 := (= #8 #10)
-#640 := (forall (vars (?v0 S2)) (:pat #639) #48)
-#51 := (forall (vars (?v0 S2)) #48)
-#641 := (iff #51 #640)
-#643 := (iff #640 #640)
-#644 := [rewrite]: #643
-#642 := [rewrite]: #641
-#645 := [trans #642 #644]: #641
-#163 := (~ #51 #51)
-#161 := (~ #48 #48)
-#162 := [refl]: #161
-#164 := [nnf-pos #162]: #163
-#11 := (= #10 #8)
-#12 := (forall (vars (?v0 S2)) #11)
-#52 := (iff #12 #51)
-#49 := (iff #11 #48)
-#50 := [rewrite]: #49
-#53 := [quant-intro #50]: #52
-#47 := [asserted]: #12
-#56 := [mp #47 #53]: #51
-#152 := [mp~ #56 #164]: #51
-#646 := [mp #152 #645]: #640
-#224 := (not #640)
-#310 := (or #224 #141)
-#311 := [quant-inst]: #310
-[unit-resolution #311 #646 #151]: false
-unsat
-fd4ffa575704f079b1ec52c184c82cdd44b22127 37 0
-#2 := false
-decl f3 :: (-> int S2)
-decl f4 :: (-> S2 int)
-decl f5 :: S2
-#25 := f5
-#26 := (f4 f5)
-decl f6 :: S2
-#27 := f6
-#28 := (f4 f6)
-#31 := (+ #28 #26)
-#32 := (f3 #31)
-#29 := (+ #26 #28)
-#30 := (f3 #29)
-#33 := (= #30 #32)
-#34 := (not #33)
-#153 := (iff #34 false)
-#1 := true
-#148 := (not true)
-#151 := (iff #148 false)
-#152 := [rewrite]: #151
-#149 := (iff #34 #148)
-#146 := (iff #33 true)
-#141 := (= #30 #30)
-#144 := (iff #141 true)
-#145 := [rewrite]: #144
-#142 := (iff #33 #141)
-#139 := (= #32 #30)
-#137 := (= #31 #29)
-#138 := [rewrite]: #137
-#140 := [monotonicity #138]: #139
-#143 := [monotonicity #140]: #142
-#147 := [trans #143 #145]: #146
-#150 := [monotonicity #147]: #149
-#154 := [trans #150 #152]: #153
-#136 := [asserted]: #34
-[mp #136 #154]: false
-unsat
-503b4a1dda22c52727c27668172fc65c05cdd044 42 0
-#2 := false
-decl f3 :: (-> int S2)
-decl f4 :: (-> S2 int)
-decl f7 :: S2
-#29 := f7
-#30 := (f4 f7)
-decl f6 :: S2
-#27 := f6
-#28 := (f4 f6)
-decl f5 :: S2
-#25 := f5
-#26 := (f4 f5)
-#34 := (+ #26 #28)
-#35 := (+ #34 #30)
-#36 := (f3 #35)
-#31 := (+ #28 #30)
-#32 := (+ #26 #31)
-#33 := (f3 #32)
-#37 := (= #33 #36)
-#38 := (not #37)
-#157 := (iff #38 false)
-#1 := true
-#152 := (not true)
-#155 := (iff #152 false)
-#156 := [rewrite]: #155
-#153 := (iff #38 #152)
-#150 := (iff #37 true)
-#145 := (= #33 #33)
-#148 := (iff #145 true)
-#149 := [rewrite]: #148
-#146 := (iff #37 #145)
-#143 := (= #36 #33)
-#141 := (= #35 #32)
-#142 := [rewrite]: #141
-#144 := [monotonicity #142]: #143
-#147 := [monotonicity #144]: #146
-#151 := [trans #147 #149]: #150
-#154 := [monotonicity #151]: #153
-#158 := [trans #154 #156]: #157
-#140 := [asserted]: #38
-[mp #140 #158]: false
-unsat
-7c830a2352021a9371ebd4587ef2e48d76d26c2e 364 0
+4c8d5628c68150e84ccb6583cec50db077ccb3b3 364 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -10881,7 +10695,210 @@
 #500 := [unit-resolution #469 #535]: #379
 [th-lemma #500 #534 #195]: false
 unsat
-1632348bdee81a166d57559522a36ec81b67e22e 438 0
+1e2a0a538ec8201638e51a4f39645f0b59e038f7 60 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#135 := (f3 #26)
+#141 := (= f5 #135)
+#146 := (not #141)
+#13 := 0::int
+#27 := (+ #26 0::int)
+#28 := (f3 #27)
+#29 := (= #28 f5)
+#30 := (not #29)
+#147 := (iff #30 #146)
+#144 := (iff #29 #141)
+#138 := (= #135 f5)
+#142 := (iff #138 #141)
+#143 := [rewrite]: #142
+#139 := (iff #29 #138)
+#136 := (= #28 #135)
+#133 := (= #27 #26)
+#134 := [rewrite]: #133
+#137 := [monotonicity #134]: #136
+#140 := [monotonicity #137]: #139
+#145 := [trans #140 #143]: #144
+#148 := [monotonicity #145]: #147
+#132 := [asserted]: #30
+#151 := [mp #132 #148]: #146
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#639 := (pattern #9)
+#10 := (f3 #9)
+#48 := (= #8 #10)
+#640 := (forall (vars (?v0 S2)) (:pat #639) #48)
+#51 := (forall (vars (?v0 S2)) #48)
+#641 := (iff #51 #640)
+#643 := (iff #640 #640)
+#644 := [rewrite]: #643
+#642 := [rewrite]: #641
+#645 := [trans #642 #644]: #641
+#163 := (~ #51 #51)
+#161 := (~ #48 #48)
+#162 := [refl]: #161
+#164 := [nnf-pos #162]: #163
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#52 := (iff #12 #51)
+#49 := (iff #11 #48)
+#50 := [rewrite]: #49
+#53 := [quant-intro #50]: #52
+#47 := [asserted]: #12
+#56 := [mp #47 #53]: #51
+#152 := [mp~ #56 #164]: #51
+#646 := [mp #152 #645]: #640
+#224 := (not #640)
+#310 := (or #224 #141)
+#311 := [quant-inst]: #310
+[unit-resolution #311 #646 #151]: false
+unsat
+1d6123bb9bcf8029248a020d8a52fdbd8072a999 60 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#135 := (f3 #26)
+#141 := (= f5 #135)
+#146 := (not #141)
+#13 := 0::int
+#27 := (+ 0::int #26)
+#28 := (f3 #27)
+#29 := (= #28 f5)
+#30 := (not #29)
+#147 := (iff #30 #146)
+#144 := (iff #29 #141)
+#138 := (= #135 f5)
+#142 := (iff #138 #141)
+#143 := [rewrite]: #142
+#139 := (iff #29 #138)
+#136 := (= #28 #135)
+#133 := (= #27 #26)
+#134 := [rewrite]: #133
+#137 := [monotonicity #134]: #136
+#140 := [monotonicity #137]: #139
+#145 := [trans #140 #143]: #144
+#148 := [monotonicity #145]: #147
+#132 := [asserted]: #30
+#151 := [mp #132 #148]: #146
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#639 := (pattern #9)
+#10 := (f3 #9)
+#48 := (= #8 #10)
+#640 := (forall (vars (?v0 S2)) (:pat #639) #48)
+#51 := (forall (vars (?v0 S2)) #48)
+#641 := (iff #51 #640)
+#643 := (iff #640 #640)
+#644 := [rewrite]: #643
+#642 := [rewrite]: #641
+#645 := [trans #642 #644]: #641
+#163 := (~ #51 #51)
+#161 := (~ #48 #48)
+#162 := [refl]: #161
+#164 := [nnf-pos #162]: #163
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#52 := (iff #12 #51)
+#49 := (iff #11 #48)
+#50 := [rewrite]: #49
+#53 := [quant-intro #50]: #52
+#47 := [asserted]: #12
+#56 := [mp #47 #53]: #51
+#152 := [mp~ #56 #164]: #51
+#646 := [mp #152 #645]: #640
+#224 := (not #640)
+#310 := (or #224 #141)
+#311 := [quant-inst]: #310
+[unit-resolution #311 #646 #151]: false
+unsat
+4329fac3878894e3df9dcc32442240c37b226f2e 37 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#31 := (+ #28 #26)
+#32 := (f3 #31)
+#29 := (+ #26 #28)
+#30 := (f3 #29)
+#33 := (= #30 #32)
+#34 := (not #33)
+#153 := (iff #34 false)
+#1 := true
+#148 := (not true)
+#151 := (iff #148 false)
+#152 := [rewrite]: #151
+#149 := (iff #34 #148)
+#146 := (iff #33 true)
+#141 := (= #30 #30)
+#144 := (iff #141 true)
+#145 := [rewrite]: #144
+#142 := (iff #33 #141)
+#139 := (= #32 #30)
+#137 := (= #31 #29)
+#138 := [rewrite]: #137
+#140 := [monotonicity #138]: #139
+#143 := [monotonicity #140]: #142
+#147 := [trans #143 #145]: #146
+#150 := [monotonicity #147]: #149
+#154 := [trans #150 #152]: #153
+#136 := [asserted]: #34
+[mp #136 #154]: false
+unsat
+5f86768264615b9165a9ee7706f67675f6593986 42 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f7 :: S2
+#29 := f7
+#30 := (f4 f7)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#34 := (+ #26 #28)
+#35 := (+ #34 #30)
+#36 := (f3 #35)
+#31 := (+ #28 #30)
+#32 := (+ #26 #31)
+#33 := (f3 #32)
+#37 := (= #33 #36)
+#38 := (not #37)
+#157 := (iff #38 false)
+#1 := true
+#152 := (not true)
+#155 := (iff #152 false)
+#156 := [rewrite]: #155
+#153 := (iff #38 #152)
+#150 := (iff #37 true)
+#145 := (= #33 #33)
+#148 := (iff #145 true)
+#149 := [rewrite]: #148
+#146 := (iff #37 #145)
+#143 := (= #36 #33)
+#141 := (= #35 #32)
+#142 := [rewrite]: #141
+#144 := [monotonicity #142]: #143
+#147 := [monotonicity #144]: #146
+#151 := [trans #147 #149]: #150
+#154 := [monotonicity #151]: #153
+#158 := [trans #154 #156]: #157
+#140 := [asserted]: #38
+[mp #140 #158]: false
+unsat
+f9b0ec53c27cf20d4d1f0aa5227e8e11e3bff80c 438 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -11320,7 +11337,7 @@
 #404 := [unit-resolution #379 #434]: #485
 [unit-resolution #404 #396]: false
 unsat
-5608753e6b659a303b2db701801c7222764e7e28 60 0
+0204e5ed51c33050b21f9b2a7360428d499dfd6d 60 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -11381,7 +11398,7 @@
 #311 := [quant-inst]: #310
 [unit-resolution #311 #646 #151]: false
 unsat
-c6004ce59328c5780acd8bd7e43d352cf78599e0 179 0
+14d57ed4170767e9a1108099047b1f91ac873d3c 179 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -11561,7 +11578,7 @@
 #175 := [and-elim #174]: #154
 [unit-resolution #175 #587]: false
 unsat
-fcfdc4289ad5f9140cb116c6f4c4919f2b4f4923 321 0
+c2dbd53482350455482e0a15536ebc6c5ee22fe3 321 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -11883,7 +11900,7 @@
 #181 := [and-elim #183]: #157
 [unit-resolution #181 #478]: false
 unsat
-68d29112e746194ea996aa3a623d8373cc08ac2a 329 0
+ed11ae136e39f0baf3f78dfc4db398e6681d8aa0 329 0
 #2 := false
 decl f6 :: S2
 #27 := f6
@@ -12213,41 +12230,7 @@
 #500 := [trans #499 #542]: #188
 [unit-resolution #198 #500]: false
 unsat
-af3fc323e3a9c9867187efb63d27fdabc458b972 33 0
-#2 := false
-decl f3 :: (-> int S2)
-#13 := 0::int
-#29 := (f3 0::int)
-decl f4 :: (-> S2 int)
-decl f5 :: S2
-#25 := f5
-#26 := (f4 f5)
-#27 := (* #26 0::int)
-#28 := (f3 #27)
-#30 := (= #28 #29)
-#31 := (not #30)
-#149 := (iff #31 false)
-#1 := true
-#144 := (not true)
-#147 := (iff #144 false)
-#148 := [rewrite]: #147
-#145 := (iff #31 #144)
-#142 := (iff #30 true)
-#137 := (= #29 #29)
-#140 := (iff #137 true)
-#141 := [rewrite]: #140
-#138 := (iff #30 #137)
-#134 := (= #27 0::int)
-#135 := [rewrite]: #134
-#136 := [monotonicity #135]: #30
-#139 := [monotonicity #136]: #138
-#143 := [trans #139 #141]: #142
-#146 := [monotonicity #143]: #145
-#150 := [trans #146 #148]: #149
-#133 := [asserted]: #31
-[mp #133 #150]: false
-unsat
-afc7043a4955320d1d41ce87a7eed9f5e9408f88 517 0
+d402a60a4806e5b5b7858e1fcc316591e359b607 517 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -12765,7 +12748,41 @@
 #282 := [unit-resolution #419 #286]: #319
 [unit-resolution #424 #282 #300]: false
 unsat
-e2cc58543dd5ad16fc6af5d366bfe8cd7b5b7c23 33 0
+34c85c064e755096449620c2ae5cc7d890259fdc 33 0
+#2 := false
+decl f3 :: (-> int S2)
+#13 := 0::int
+#29 := (f3 0::int)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#27 := (* #26 0::int)
+#28 := (f3 #27)
+#30 := (= #28 #29)
+#31 := (not #30)
+#149 := (iff #31 false)
+#1 := true
+#144 := (not true)
+#147 := (iff #144 false)
+#148 := [rewrite]: #147
+#145 := (iff #31 #144)
+#142 := (iff #30 true)
+#137 := (= #29 #29)
+#140 := (iff #137 true)
+#141 := [rewrite]: #140
+#138 := (iff #30 #137)
+#134 := (= #27 0::int)
+#135 := [rewrite]: #134
+#136 := [monotonicity #135]: #30
+#139 := [monotonicity #136]: #138
+#143 := [trans #139 #141]: #142
+#146 := [monotonicity #143]: #145
+#150 := [trans #146 #148]: #149
+#133 := [asserted]: #31
+[mp #133 #150]: false
+unsat
+a40b50f2914e672fde91a7bd5e887fd6262edb39 33 0
 #2 := false
 decl f3 :: (-> int S2)
 #13 := 0::int
@@ -12799,7 +12816,7 @@
 #133 := [asserted]: #31
 [mp #133 #150]: false
 unsat
-bdaf29198446643e2cae690c3f0cac29f38941fc 60 0
+fb5c697bef2be42b36d4d5a8368554db7eedb7ba 60 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -12860,7 +12877,7 @@
 #311 := [quant-inst]: #310
 [unit-resolution #311 #646 #152]: false
 unsat
-2bc16a4276212362a5a76abffcf9b2b6da841754 60 0
+ac48b2e311d2bbcc584e0dad187f583adfca9fa1 60 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -12921,7 +12938,7 @@
 #311 := [quant-inst]: #310
 [unit-resolution #311 #646 #152]: false
 unsat
-2b450a9ee4af266a70157af65786bf2e05023359 35 0
+d7b156e64cfcfb13cc7a33d352c2cfb841189d84 35 0
 #2 := false
 decl f3 :: (-> int S2)
 #25 := 3::int
@@ -12957,7 +12974,7 @@
 #135 := [asserted]: #33
 [mp #135 #153]: false
 unsat
-f58726aba38b36bcc4264b070f4c61db1533ea41 250 0
+cdb6b8d2217614159e4f438c94539fc72e7be9d7 250 0
 #2 := false
 decl f5 :: (-> int S2)
 #11 := 0::int
@@ -13208,282 +13225,7 @@
 #269 := [asserted]: #57
 [unit-resolution #269 #746]: false
 unsat
-f9ec262ae3b89f82ea2dac0232937218e79cd135 274 0
-#2 := false
-decl f5 :: (-> int S2)
-#11 := 0::int
-#55 := (f5 0::int)
-decl f4 :: (-> int int int)
-#53 := (f4 0::int 0::int)
-#54 := (f5 #53)
-#56 := (= #54 #55)
-#831 := (= #53 0::int)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#850 := (pattern #29)
-#81 := -1::int
-#85 := (* -1::int #9)
-#82 := (* -1::int #8)
-#140 := (mod #82 #85)
-#361 := (+ #29 #140)
-#362 := (= #361 0::int)
-#30 := (mod #8 #9)
-#358 := (* -1::int #30)
-#359 := (+ #29 #358)
-#360 := (= #359 0::int)
-#107 := (<= #9 0::int)
-#103 := (<= #8 0::int)
-#300 := (or #103 #107)
-#301 := (not #300)
-#114 := (>= #8 0::int)
-#283 := (or #107 #114)
-#284 := (not #283)
-#307 := (or #284 #301)
-#363 := (ite #307 #360 #362)
-#357 := (= #29 0::int)
-#12 := (= #8 0::int)
-#364 := (ite #12 #357 #363)
-#356 := (= #8 #29)
-#13 := (= #9 0::int)
-#365 := (ite #13 #356 #364)
-#851 := (forall (vars (?v0 int) (?v1 int)) (:pat #850) #365)
-#368 := (forall (vars (?v0 int) (?v1 int)) #365)
-#854 := (iff #368 #851)
-#852 := (iff #365 #365)
-#853 := [refl]: #852
-#855 := [quant-intro #853]: #854
-#146 := (* -1::int #140)
-#325 := (ite #307 #30 #146)
-#328 := (ite #12 0::int #325)
-#331 := (ite #13 #8 #328)
-#334 := (= #29 #331)
-#337 := (forall (vars (?v0 int) (?v1 int)) #334)
-#369 := (iff #337 #368)
-#366 := (iff #334 #365)
-#367 := [rewrite]: #366
-#370 := [quant-intro #367]: #369
-#115 := (not #114)
-#108 := (not #107)
-#118 := (and #108 #115)
-#104 := (not #103)
-#111 := (and #104 #108)
-#121 := (or #111 #118)
-#166 := (ite #121 #30 #146)
-#169 := (ite #12 0::int #166)
-#172 := (ite #13 #8 #169)
-#175 := (= #29 #172)
-#178 := (forall (vars (?v0 int) (?v1 int)) #175)
-#338 := (iff #178 #337)
-#335 := (iff #175 #334)
-#332 := (= #172 #331)
-#329 := (= #169 #328)
-#326 := (= #166 #325)
-#310 := (iff #121 #307)
-#304 := (or #301 #284)
-#308 := (iff #304 #307)
-#309 := [rewrite]: #308
-#305 := (iff #121 #304)
-#302 := (iff #118 #284)
-#303 := [rewrite]: #302
-#281 := (iff #111 #301)
-#282 := [rewrite]: #281
-#306 := [monotonicity #282 #303]: #305
-#311 := [trans #306 #309]: #310
-#327 := [monotonicity #311]: #326
-#330 := [monotonicity #327]: #329
-#333 := [monotonicity #330]: #332
-#336 := [monotonicity #333]: #335
-#339 := [quant-intro #336]: #338
-#273 := (~ #178 #178)
-#270 := (~ #175 #175)
-#289 := [refl]: #270
-#274 := [nnf-pos #289]: #273
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#181 := (iff #37 #178)
-#75 := (and #16 #18)
-#78 := (or #17 #75)
-#151 := (ite #78 #30 #146)
-#154 := (ite #12 0::int #151)
-#157 := (ite #13 #8 #154)
-#160 := (= #29 #157)
-#163 := (forall (vars (?v0 int) (?v1 int)) #160)
-#179 := (iff #163 #178)
-#176 := (iff #160 #175)
-#173 := (= #157 #172)
-#170 := (= #154 #169)
-#167 := (= #151 #166)
-#122 := (iff #78 #121)
-#119 := (iff #75 #118)
-#116 := (iff #18 #115)
-#117 := [rewrite]: #116
-#109 := (iff #16 #108)
-#110 := [rewrite]: #109
-#120 := [monotonicity #110 #117]: #119
-#112 := (iff #17 #111)
-#105 := (iff #15 #104)
-#106 := [rewrite]: #105
-#113 := [monotonicity #106 #110]: #112
-#123 := [monotonicity #113 #120]: #122
-#168 := [monotonicity #123]: #167
-#171 := [monotonicity #168]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [quant-intro #177]: #179
-#164 := (iff #37 #163)
-#161 := (iff #36 #160)
-#158 := (= #35 #157)
-#155 := (= #34 #154)
-#152 := (= #33 #151)
-#149 := (= #32 #146)
-#143 := (- #140)
-#147 := (= #143 #146)
-#148 := [rewrite]: #147
-#144 := (= #32 #143)
-#141 := (= #31 #140)
-#86 := (= #23 #85)
-#87 := [rewrite]: #86
-#83 := (= #22 #82)
-#84 := [rewrite]: #83
-#142 := [monotonicity #84 #87]: #141
-#145 := [monotonicity #142]: #144
-#150 := [trans #145 #148]: #149
-#79 := (iff #20 #78)
-#76 := (iff #19 #75)
-#77 := [rewrite]: #76
-#80 := [monotonicity #77]: #79
-#153 := [monotonicity #80 #150]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#182 := [trans #165 #180]: #181
-#139 := [asserted]: #37
-#183 := [mp #139 #182]: #178
-#290 := [mp~ #183 #274]: #178
-#340 := [mp #290 #339]: #337
-#371 := [mp #340 #370]: #368
-#856 := [mp #371 #855]: #851
-#646 := (not #851)
-#788 := (or #646 #831)
-#429 := (* -1::int 0::int)
-#514 := (mod #429 #429)
-#515 := (+ #53 #514)
-#516 := (= #515 0::int)
-#507 := (mod 0::int 0::int)
-#518 := (* -1::int #507)
-#519 := (+ #53 #518)
-#447 := (= #519 0::int)
-#520 := (<= 0::int 0::int)
-#517 := (or #520 #520)
-#521 := (not #517)
-#500 := (>= 0::int 0::int)
-#835 := (or #520 #500)
-#837 := (not #835)
-#494 := (or #837 #521)
-#624 := (ite #494 #447 #516)
-#505 := (= 0::int 0::int)
-#506 := (ite #505 #831 #624)
-#838 := (= 0::int #53)
-#839 := (ite #505 #838 #506)
-#789 := (or #646 #839)
-#791 := (iff #789 #788)
-#786 := (iff #788 #788)
-#792 := [rewrite]: #786
-#644 := (iff #839 #831)
-#1 := true
-#796 := (ite true #831 #831)
-#797 := (iff #796 #831)
-#803 := [rewrite]: #797
-#801 := (iff #839 #796)
-#800 := (iff #506 #831)
-#536 := (+ #53 #507)
-#811 := (= #536 0::int)
-#808 := (ite true #831 #811)
-#798 := (iff #808 #831)
-#799 := [rewrite]: #798
-#805 := (iff #506 #808)
-#522 := (iff #624 #811)
-#526 := (ite false #447 #811)
-#806 := (iff #526 #811)
-#807 := [rewrite]: #806
-#527 := (iff #624 #526)
-#815 := (iff #516 #811)
-#810 := (= #515 #536)
-#813 := (= #514 #507)
-#435 := (= #429 0::int)
-#812 := [rewrite]: #435
-#535 := [monotonicity #812 #812]: #813
-#814 := [monotonicity #535]: #810
-#525 := [monotonicity #814]: #815
-#541 := (iff #494 false)
-#830 := (or false false)
-#539 := (iff #830 false)
-#540 := [rewrite]: #539
-#816 := (iff #494 #830)
-#829 := (iff #521 false)
-#484 := (not true)
-#822 := (iff #484 false)
-#823 := [rewrite]: #822
-#468 := (iff #521 #484)
-#826 := (iff #517 true)
-#493 := (or true true)
-#818 := (iff #493 true)
-#481 := [rewrite]: #818
-#825 := (iff #517 #493)
-#832 := (iff #520 true)
-#492 := [rewrite]: #832
-#463 := [monotonicity #492 #492]: #825
-#828 := [trans #463 #481]: #826
-#469 := [monotonicity #828]: #468
-#827 := [trans #469 #823]: #829
-#824 := (iff #837 false)
-#820 := (iff #837 #484)
-#482 := (iff #835 true)
-#834 := (iff #835 #493)
-#497 := (iff #500 true)
-#833 := [rewrite]: #497
-#477 := [monotonicity #492 #833]: #834
-#483 := [trans #477 #481]: #482
-#821 := [monotonicity #483]: #820
-#819 := [trans #821 #823]: #824
-#817 := [monotonicity #819 #827]: #816
-#542 := [trans #817 #540]: #541
-#528 := [monotonicity #542 #525]: #527
-#804 := [trans #528 #807]: #522
-#840 := (iff #505 true)
-#841 := [rewrite]: #840
-#809 := [monotonicity #841 #804]: #805
-#795 := [trans #809 #799]: #800
-#836 := (iff #838 #831)
-#842 := [rewrite]: #836
-#802 := [monotonicity #841 #842 #795]: #801
-#645 := [trans #802 #803]: #644
-#785 := [monotonicity #645]: #791
-#793 := [trans #785 #792]: #791
-#790 := [quant-inst]: #789
-#787 := [mp #790 #793]: #788
-#741 := [unit-resolution #787 #856]: #831
-#742 := [monotonicity #741]: #56
-#57 := (not #56)
-#269 := [asserted]: #57
-[unit-resolution #269 #742]: false
-unsat
-2445ca30fa757c71a9c6aa886c0159c1fde53406 265 0
+2a8cb19ff1234c4bba5f61e321308695169685e1 265 0
 #2 := false
 decl f5 :: (-> int S2)
 #11 := 0::int
@@ -13749,7 +13491,7 @@
 #271 := [asserted]: #59
 [unit-resolution #271 #738]: false
 unsat
-7a16e7d1cff95b977a46175f34e2f58dc17b201b 287 0
+8e30b3cd58b8801e5ddb5a68ef7720db1f121bd9 287 0
 #2 := false
 decl f5 :: (-> int S2)
 #11 := 0::int
@@ -14037,329 +13779,7 @@
 #270 := [asserted]: #58
 [unit-resolution #270 #691]: false
 unsat
-3fde1aa3674893464f069812a19859471255da8e 321 0
-#2 := false
-decl f5 :: (-> int S2)
-decl f4 :: (-> int int int)
-#11 := 0::int
-decl f6 :: (-> S2 int)
-decl f7 :: S2
-#53 := f7
-#54 := (f6 f7)
-#55 := (f4 #54 0::int)
-#56 := (f5 #55)
-#271 := (= f7 #56)
-#795 := (f5 #54)
-#772 := (= #795 #56)
-#771 := (= #56 #795)
-#768 := (= #55 #54)
-#848 := (= #54 #55)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#858 := (pattern #29)
-#82 := -1::int
-#86 := (* -1::int #9)
-#83 := (* -1::int #8)
-#141 := (mod #83 #86)
-#369 := (+ #29 #141)
-#370 := (= #369 0::int)
-#30 := (mod #8 #9)
-#366 := (* -1::int #30)
-#367 := (+ #29 #366)
-#368 := (= #367 0::int)
-#108 := (<= #9 0::int)
-#104 := (<= #8 0::int)
-#308 := (or #104 #108)
-#309 := (not #308)
-#115 := (>= #8 0::int)
-#291 := (or #108 #115)
-#292 := (not #291)
-#315 := (or #292 #309)
-#371 := (ite #315 #368 #370)
-#365 := (= #29 0::int)
-#12 := (= #8 0::int)
-#372 := (ite #12 #365 #371)
-#364 := (= #8 #29)
-#13 := (= #9 0::int)
-#373 := (ite #13 #364 #372)
-#859 := (forall (vars (?v0 int) (?v1 int)) (:pat #858) #373)
-#376 := (forall (vars (?v0 int) (?v1 int)) #373)
-#862 := (iff #376 #859)
-#860 := (iff #373 #373)
-#861 := [refl]: #860
-#863 := [quant-intro #861]: #862
-#147 := (* -1::int #141)
-#333 := (ite #315 #30 #147)
-#336 := (ite #12 0::int #333)
-#339 := (ite #13 #8 #336)
-#342 := (= #29 #339)
-#345 := (forall (vars (?v0 int) (?v1 int)) #342)
-#377 := (iff #345 #376)
-#374 := (iff #342 #373)
-#375 := [rewrite]: #374
-#378 := [quant-intro #375]: #377
-#116 := (not #115)
-#109 := (not #108)
-#119 := (and #109 #116)
-#105 := (not #104)
-#112 := (and #105 #109)
-#122 := (or #112 #119)
-#167 := (ite #122 #30 #147)
-#170 := (ite #12 0::int #167)
-#173 := (ite #13 #8 #170)
-#176 := (= #29 #173)
-#179 := (forall (vars (?v0 int) (?v1 int)) #176)
-#346 := (iff #179 #345)
-#343 := (iff #176 #342)
-#340 := (= #173 #339)
-#337 := (= #170 #336)
-#334 := (= #167 #333)
-#318 := (iff #122 #315)
-#312 := (or #309 #292)
-#316 := (iff #312 #315)
-#317 := [rewrite]: #316
-#313 := (iff #122 #312)
-#310 := (iff #119 #292)
-#311 := [rewrite]: #310
-#289 := (iff #112 #309)
-#290 := [rewrite]: #289
-#314 := [monotonicity #290 #311]: #313
-#319 := [trans #314 #317]: #318
-#335 := [monotonicity #319]: #334
-#338 := [monotonicity #335]: #337
-#341 := [monotonicity #338]: #340
-#344 := [monotonicity #341]: #343
-#347 := [quant-intro #344]: #346
-#281 := (~ #179 #179)
-#277 := (~ #176 #176)
-#297 := [refl]: #277
-#282 := [nnf-pos #297]: #281
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#182 := (iff #37 #179)
-#76 := (and #16 #18)
-#79 := (or #17 #76)
-#152 := (ite #79 #30 #147)
-#155 := (ite #12 0::int #152)
-#158 := (ite #13 #8 #155)
-#161 := (= #29 #158)
-#164 := (forall (vars (?v0 int) (?v1 int)) #161)
-#180 := (iff #164 #179)
-#177 := (iff #161 #176)
-#174 := (= #158 #173)
-#171 := (= #155 #170)
-#168 := (= #152 #167)
-#123 := (iff #79 #122)
-#120 := (iff #76 #119)
-#117 := (iff #18 #116)
-#118 := [rewrite]: #117
-#110 := (iff #16 #109)
-#111 := [rewrite]: #110
-#121 := [monotonicity #111 #118]: #120
-#113 := (iff #17 #112)
-#106 := (iff #15 #105)
-#107 := [rewrite]: #106
-#114 := [monotonicity #107 #111]: #113
-#124 := [monotonicity #114 #121]: #123
-#169 := [monotonicity #124]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [quant-intro #178]: #180
-#165 := (iff #37 #164)
-#162 := (iff #36 #161)
-#159 := (= #35 #158)
-#156 := (= #34 #155)
-#153 := (= #33 #152)
-#150 := (= #32 #147)
-#144 := (- #141)
-#148 := (= #144 #147)
-#149 := [rewrite]: #148
-#145 := (= #32 #144)
-#142 := (= #31 #141)
-#87 := (= #23 #86)
-#88 := [rewrite]: #87
-#84 := (= #22 #83)
-#85 := [rewrite]: #84
-#143 := [monotonicity #85 #88]: #142
-#146 := [monotonicity #143]: #145
-#151 := [trans #146 #149]: #150
-#80 := (iff #20 #79)
-#77 := (iff #19 #76)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#154 := [monotonicity #81 #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#183 := [trans #166 #181]: #182
-#140 := [asserted]: #37
-#184 := [mp #140 #183]: #179
-#298 := [mp~ #184 #282]: #179
-#348 := [mp #298 #347]: #345
-#379 := [mp #348 #378]: #376
-#864 := [mp #379 #863]: #859
-#653 := (not #859)
-#654 := (or #653 #848)
-#437 := (* -1::int 0::int)
-#522 := (* -1::int #54)
-#523 := (mod #522 #437)
-#524 := (+ #55 #523)
-#515 := (= #524 0::int)
-#526 := (mod #54 0::int)
-#527 := (* -1::int #526)
-#455 := (+ #55 #527)
-#528 := (= #455 0::int)
-#525 := (<= 0::int 0::int)
-#529 := (<= #54 0::int)
-#508 := (or #529 #525)
-#843 := (not #508)
-#845 := (>= #54 0::int)
-#502 := (or #525 #845)
-#632 := (not #502)
-#839 := (or #632 #843)
-#513 := (ite #839 #528 #515)
-#514 := (= #55 0::int)
-#846 := (= #54 0::int)
-#847 := (ite #846 #514 #513)
-#849 := (= 0::int 0::int)
-#844 := (ite #849 #848 #847)
-#796 := (or #653 #844)
-#798 := (iff #796 #654)
-#793 := (iff #654 #654)
-#794 := [rewrite]: #793
-#811 := (iff #844 #848)
-#544 := (mod #522 0::int)
-#819 := (+ #55 #544)
-#534 := (= #819 0::int)
-#806 := (ite #846 #514 #534)
-#1 := true
-#803 := (ite true #848 #806)
-#810 := (iff #803 #848)
-#805 := [rewrite]: #810
-#804 := (iff #844 #803)
-#807 := (iff #847 #806)
-#813 := (iff #513 #534)
-#814 := (ite false #528 #534)
-#812 := (iff #814 #534)
-#816 := [rewrite]: #812
-#815 := (iff #513 #814)
-#535 := (iff #515 #534)
-#823 := (= #524 #819)
-#818 := (= #523 #544)
-#821 := (= #437 0::int)
-#543 := [rewrite]: #821
-#822 := [monotonicity #543]: #818
-#533 := [monotonicity #822]: #823
-#536 := [monotonicity #533]: #535
-#443 := (iff #839 false)
-#825 := (or false false)
-#549 := (iff #825 false)
-#550 := [rewrite]: #549
-#547 := (iff #839 #825)
-#838 := (iff #843 false)
-#491 := (not true)
-#829 := (iff #491 false)
-#830 := [rewrite]: #829
-#837 := (iff #843 #491)
-#476 := (iff #508 true)
-#827 := (or #529 true)
-#834 := (iff #827 true)
-#836 := [rewrite]: #834
-#833 := (iff #508 #827)
-#500 := (iff #525 true)
-#505 := [rewrite]: #500
-#471 := [monotonicity #505]: #833
-#477 := [trans #471 #836]: #476
-#835 := [monotonicity #477]: #837
-#824 := [trans #835 #830]: #838
-#831 := (iff #632 false)
-#492 := (iff #632 #491)
-#489 := (iff #502 true)
-#841 := (or true #845)
-#485 := (iff #841 true)
-#826 := [rewrite]: #485
-#501 := (iff #502 #841)
-#842 := [monotonicity #505]: #501
-#490 := [trans #842 #826]: #489
-#828 := [monotonicity #490]: #492
-#832 := [trans #828 #830]: #831
-#548 := [monotonicity #832 #824]: #547
-#820 := [trans #548 #550]: #443
-#530 := [monotonicity #820 #536]: #815
-#817 := [trans #530 #816]: #813
-#808 := [monotonicity #817]: #807
-#850 := (iff #849 true)
-#840 := [rewrite]: #850
-#809 := [monotonicity #840 #808]: #804
-#652 := [trans #809 #805]: #811
-#799 := [monotonicity #652]: #798
-#800 := [trans #799 #794]: #798
-#797 := [quant-inst]: #796
-#801 := [mp #797 #800]: #654
-#779 := [unit-resolution #801 #864]: #848
-#769 := [symm #779]: #768
-#765 := [monotonicity #769]: #771
-#756 := [symm #765]: #772
-#802 := (= f7 #795)
-#38 := (:var 0 S2)
-#39 := (f6 #38)
-#865 := (pattern #39)
-#40 := (f5 #39)
-#186 := (= #38 #40)
-#866 := (forall (vars (?v0 S2)) (:pat #865) #186)
-#189 := (forall (vars (?v0 S2)) #186)
-#867 := (iff #189 #866)
-#869 := (iff #866 #866)
-#870 := [rewrite]: #869
-#868 := [rewrite]: #867
-#871 := [trans #868 #870]: #867
-#283 := (~ #189 #189)
-#299 := (~ #186 #186)
-#300 := [refl]: #299
-#284 := [nnf-pos #300]: #283
-#41 := (= #40 #38)
-#42 := (forall (vars (?v0 S2)) #41)
-#190 := (iff #42 #189)
-#187 := (iff #41 #186)
-#188 := [rewrite]: #187
-#191 := [quant-intro #188]: #190
-#185 := [asserted]: #42
-#194 := [mp #185 #191]: #189
-#301 := [mp~ #194 #284]: #189
-#872 := [mp #301 #871]: #866
-#634 := (not #866)
-#787 := (or #634 #802)
-#788 := [quant-inst]: #787
-#770 := [unit-resolution #788 #872]: #802
-#757 := [trans #770 #756]: #271
-#274 := (not #271)
-#57 := (= #56 f7)
-#58 := (not #57)
-#275 := (iff #58 #274)
-#272 := (iff #57 #271)
-#273 := [rewrite]: #272
-#276 := [monotonicity #273]: #275
-#270 := [asserted]: #58
-#279 := [mp #270 #276]: #274
-[unit-resolution #279 #757]: false
-unsat
-c6bc1ae49d3543060aab7bd42065cc7be0e98df3 287 0
+546d45a2e6332d005e3b7662d6401bed72e20524 287 0
 #2 := false
 decl f5 :: (-> int S2)
 #53 := 1::int
@@ -14647,312 +14067,7 @@
 #270 := [asserted]: #58
 [unit-resolution #270 #692]: false
 unsat
-1ce1abcb126a1a568a3f8f5f2b0d8898293280b4 304 0
-#2 := false
-decl f5 :: (-> int S2)
-#11 := 0::int
-#56 := (f5 0::int)
-decl f4 :: (-> int int int)
-#53 := 1::int
-#54 := (f4 0::int 1::int)
-#55 := (f5 #54)
-#57 := (= #55 #56)
-#838 := (= #54 0::int)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#850 := (pattern #29)
-#82 := -1::int
-#86 := (* -1::int #9)
-#83 := (* -1::int #8)
-#141 := (mod #83 #86)
-#362 := (+ #29 #141)
-#363 := (= #362 0::int)
-#30 := (mod #8 #9)
-#359 := (* -1::int #30)
-#360 := (+ #29 #359)
-#361 := (= #360 0::int)
-#108 := (<= #9 0::int)
-#104 := (<= #8 0::int)
-#301 := (or #104 #108)
-#302 := (not #301)
-#115 := (>= #8 0::int)
-#284 := (or #108 #115)
-#285 := (not #284)
-#308 := (or #285 #302)
-#364 := (ite #308 #361 #363)
-#358 := (= #29 0::int)
-#12 := (= #8 0::int)
-#365 := (ite #12 #358 #364)
-#357 := (= #8 #29)
-#13 := (= #9 0::int)
-#366 := (ite #13 #357 #365)
-#851 := (forall (vars (?v0 int) (?v1 int)) (:pat #850) #366)
-#369 := (forall (vars (?v0 int) (?v1 int)) #366)
-#854 := (iff #369 #851)
-#852 := (iff #366 #366)
-#853 := [refl]: #852
-#855 := [quant-intro #853]: #854
-#147 := (* -1::int #141)
-#326 := (ite #308 #30 #147)
-#329 := (ite #12 0::int #326)
-#332 := (ite #13 #8 #329)
-#335 := (= #29 #332)
-#338 := (forall (vars (?v0 int) (?v1 int)) #335)
-#370 := (iff #338 #369)
-#367 := (iff #335 #366)
-#368 := [rewrite]: #367
-#371 := [quant-intro #368]: #370
-#116 := (not #115)
-#109 := (not #108)
-#119 := (and #109 #116)
-#105 := (not #104)
-#112 := (and #105 #109)
-#122 := (or #112 #119)
-#167 := (ite #122 #30 #147)
-#170 := (ite #12 0::int #167)
-#173 := (ite #13 #8 #170)
-#176 := (= #29 #173)
-#179 := (forall (vars (?v0 int) (?v1 int)) #176)
-#339 := (iff #179 #338)
-#336 := (iff #176 #335)
-#333 := (= #173 #332)
-#330 := (= #170 #329)
-#327 := (= #167 #326)
-#311 := (iff #122 #308)
-#305 := (or #302 #285)
-#309 := (iff #305 #308)
-#310 := [rewrite]: #309
-#306 := (iff #122 #305)
-#303 := (iff #119 #285)
-#304 := [rewrite]: #303
-#282 := (iff #112 #302)
-#283 := [rewrite]: #282
-#307 := [monotonicity #283 #304]: #306
-#312 := [trans #307 #310]: #311
-#328 := [monotonicity #312]: #327
-#331 := [monotonicity #328]: #330
-#334 := [monotonicity #331]: #333
-#337 := [monotonicity #334]: #336
-#340 := [quant-intro #337]: #339
-#274 := (~ #179 #179)
-#271 := (~ #176 #176)
-#290 := [refl]: #271
-#275 := [nnf-pos #290]: #274
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#182 := (iff #37 #179)
-#76 := (and #16 #18)
-#79 := (or #17 #76)
-#152 := (ite #79 #30 #147)
-#155 := (ite #12 0::int #152)
-#158 := (ite #13 #8 #155)
-#161 := (= #29 #158)
-#164 := (forall (vars (?v0 int) (?v1 int)) #161)
-#180 := (iff #164 #179)
-#177 := (iff #161 #176)
-#174 := (= #158 #173)
-#171 := (= #155 #170)
-#168 := (= #152 #167)
-#123 := (iff #79 #122)
-#120 := (iff #76 #119)
-#117 := (iff #18 #116)
-#118 := [rewrite]: #117
-#110 := (iff #16 #109)
-#111 := [rewrite]: #110
-#121 := [monotonicity #111 #118]: #120
-#113 := (iff #17 #112)
-#106 := (iff #15 #105)
-#107 := [rewrite]: #106
-#114 := [monotonicity #107 #111]: #113
-#124 := [monotonicity #114 #121]: #123
-#169 := [monotonicity #124]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [quant-intro #178]: #180
-#165 := (iff #37 #164)
-#162 := (iff #36 #161)
-#159 := (= #35 #158)
-#156 := (= #34 #155)
-#153 := (= #33 #152)
-#150 := (= #32 #147)
-#144 := (- #141)
-#148 := (= #144 #147)
-#149 := [rewrite]: #148
-#145 := (= #32 #144)
-#142 := (= #31 #141)
-#87 := (= #23 #86)
-#88 := [rewrite]: #87
-#84 := (= #22 #83)
-#85 := [rewrite]: #84
-#143 := [monotonicity #85 #88]: #142
-#146 := [monotonicity #143]: #145
-#151 := [trans #146 #149]: #150
-#80 := (iff #20 #79)
-#77 := (iff #19 #76)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#154 := [monotonicity #81 #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#183 := [trans #166 #181]: #182
-#140 := [asserted]: #37
-#184 := [mp #140 #183]: #179
-#291 := [mp~ #184 #275]: #179
-#341 := [mp #291 #340]: #338
-#372 := [mp #341 #371]: #369
-#856 := [mp #372 #855]: #851
-#676 := (not #851)
-#678 := (or #676 #838)
-#430 := (* -1::int 1::int)
-#514 := (* -1::int 0::int)
-#515 := (mod #514 #430)
-#516 := (+ #54 #515)
-#507 := (= #516 0::int)
-#518 := (mod 0::int 1::int)
-#519 := (* -1::int #518)
-#520 := (+ #54 #519)
-#517 := (= #520 0::int)
-#521 := (<= 1::int 0::int)
-#500 := (<= 0::int 0::int)
-#835 := (or #500 #521)
-#837 := (not #835)
-#494 := (>= 0::int 0::int)
-#624 := (or #521 #494)
-#831 := (not #624)
-#505 := (or #831 #837)
-#506 := (ite #505 #517 #507)
-#839 := (= 0::int 0::int)
-#840 := (ite #839 #838 #506)
-#841 := (= 0::int #54)
-#836 := (= 1::int 0::int)
-#842 := (ite #836 #841 #840)
-#679 := (or #676 #842)
-#680 := (iff #679 #678)
-#682 := (iff #678 #678)
-#683 := [rewrite]: #682
-#776 := (iff #842 #838)
-#625 := (ite false #838 #838)
-#780 := (iff #625 #838)
-#782 := [rewrite]: #780
-#772 := (iff #842 #625)
-#775 := (iff #840 #838)
-#1 := true
-#784 := (ite true #838 #838)
-#668 := (iff #784 #838)
-#627 := [rewrite]: #668
-#666 := (iff #840 #784)
-#783 := (iff #506 #838)
-#626 := (iff #506 #625)
-#794 := (iff #507 #838)
-#793 := (= #516 #54)
-#809 := (+ #54 0::int)
-#800 := (= #809 #54)
-#795 := [rewrite]: #800
-#786 := (= #516 #809)
-#791 := (= #515 0::int)
-#645 := (mod 0::int -1::int)
-#789 := (= #645 0::int)
-#790 := [rewrite]: #789
-#646 := (= #515 #645)
-#803 := (= #430 -1::int)
-#644 := [rewrite]: #803
-#522 := (= #514 0::int)
-#804 := [rewrite]: #522
-#788 := [monotonicity #804 #644]: #646
-#785 := [trans #788 #790]: #791
-#792 := [monotonicity #785]: #786
-#787 := [trans #792 #795]: #793
-#623 := [monotonicity #787]: #794
-#802 := (iff #517 #838)
-#796 := (= #520 #54)
-#798 := (= #520 #809)
-#808 := (= #519 0::int)
-#806 := (= #519 #514)
-#527 := (= #518 0::int)
-#528 := [rewrite]: #527
-#807 := [monotonicity #528]: #806
-#805 := [trans #807 #804]: #808
-#799 := [monotonicity #805]: #798
-#801 := [trans #799 #795]: #796
-#797 := [monotonicity #801]: #802
-#525 := (iff #505 false)
-#536 := (or false false)
-#811 := (iff #536 false)
-#815 := [rewrite]: #811
-#810 := (iff #505 #536)
-#813 := (iff #837 false)
-#819 := (not true)
-#826 := (iff #819 false)
-#828 := [rewrite]: #826
-#436 := (iff #837 #819)
-#541 := (iff #835 true)
-#830 := (or true false)
-#539 := (iff #830 true)
-#540 := [rewrite]: #539
-#816 := (iff #835 #830)
-#477 := (iff #521 false)
-#818 := [rewrite]: #477
-#829 := (iff #500 true)
-#827 := [rewrite]: #829
-#817 := [monotonicity #827 #818]: #816
-#542 := [trans #817 #540]: #541
-#812 := [monotonicity #542]: #436
-#535 := [trans #812 #828]: #813
-#468 := (iff #831 false)
-#825 := (iff #831 #819)
-#823 := (iff #624 true)
-#483 := (or false true)
-#821 := (iff #483 true)
-#822 := [rewrite]: #821
-#484 := (iff #624 #483)
-#481 := (iff #494 true)
-#482 := [rewrite]: #481
-#820 := [monotonicity #818 #482]: #484
-#824 := [trans #820 #822]: #823
-#463 := [monotonicity #824]: #825
-#469 := [trans #463 #828]: #468
-#814 := [monotonicity #469 #535]: #810
-#526 := [trans #814 #815]: #525
-#779 := [monotonicity #526 #797 #623]: #626
-#781 := [trans #779 #782]: #783
-#493 := (iff #839 true)
-#834 := [rewrite]: #493
-#667 := [monotonicity #834 #781]: #666
-#677 := [trans #667 #627]: #775
-#497 := (iff #841 #838)
-#833 := [rewrite]: #497
-#832 := (iff #836 false)
-#492 := [rewrite]: #832
-#773 := [monotonicity #492 #833 #677]: #772
-#661 := [trans #773 #782]: #776
-#681 := [monotonicity #661]: #680
-#684 := [trans #681 #683]: #680
-#672 := [quant-inst]: #679
-#777 := [mp #672 #684]: #678
-#712 := [unit-resolution #777 #856]: #838
-#708 := [monotonicity #712]: #57
-#58 := (not #57)
-#270 := [asserted]: #58
-[unit-resolution #270 #708]: false
-unsat
-8182954e616c62f0cc886f21c7ebfe80a132d572 298 0
+6c7b15b5e87a0e1b48c9df8d22a64ee18b1a6aca 298 0
 #2 := false
 decl f5 :: (-> int S2)
 #53 := 3::int
@@ -15251,310 +14366,7 @@
 #271 := [asserted]: #59
 [unit-resolution #271 #706]: false
 unsat
-a73336d8974d339785d03ee7b06059fa66e36b1e 302 0
-#2 := false
-decl f5 :: (-> int S2)
-#11 := 0::int
-#56 := (f5 0::int)
-decl f4 :: (-> int int int)
-#53 := 1::int
-#54 := (f4 1::int 1::int)
-#55 := (f5 #54)
-#57 := (= #55 #56)
-#505 := (= #54 0::int)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#850 := (pattern #29)
-#82 := -1::int
-#86 := (* -1::int #9)
-#83 := (* -1::int #8)
-#141 := (mod #83 #86)
-#362 := (+ #29 #141)
-#363 := (= #362 0::int)
-#30 := (mod #8 #9)
-#359 := (* -1::int #30)
-#360 := (+ #29 #359)
-#361 := (= #360 0::int)
-#108 := (<= #9 0::int)
-#104 := (<= #8 0::int)
-#301 := (or #104 #108)
-#302 := (not #301)
-#115 := (>= #8 0::int)
-#284 := (or #108 #115)
-#285 := (not #284)
-#308 := (or #285 #302)
-#364 := (ite #308 #361 #363)
-#358 := (= #29 0::int)
-#12 := (= #8 0::int)
-#365 := (ite #12 #358 #364)
-#357 := (= #8 #29)
-#13 := (= #9 0::int)
-#366 := (ite #13 #357 #365)
-#851 := (forall (vars (?v0 int) (?v1 int)) (:pat #850) #366)
-#369 := (forall (vars (?v0 int) (?v1 int)) #366)
-#854 := (iff #369 #851)
-#852 := (iff #366 #366)
-#853 := [refl]: #852
-#855 := [quant-intro #853]: #854
-#147 := (* -1::int #141)
-#326 := (ite #308 #30 #147)
-#329 := (ite #12 0::int #326)
-#332 := (ite #13 #8 #329)
-#335 := (= #29 #332)
-#338 := (forall (vars (?v0 int) (?v1 int)) #335)
-#370 := (iff #338 #369)
-#367 := (iff #335 #366)
-#368 := [rewrite]: #367
-#371 := [quant-intro #368]: #370
-#116 := (not #115)
-#109 := (not #108)
-#119 := (and #109 #116)
-#105 := (not #104)
-#112 := (and #105 #109)
-#122 := (or #112 #119)
-#167 := (ite #122 #30 #147)
-#170 := (ite #12 0::int #167)
-#173 := (ite #13 #8 #170)
-#176 := (= #29 #173)
-#179 := (forall (vars (?v0 int) (?v1 int)) #176)
-#339 := (iff #179 #338)
-#336 := (iff #176 #335)
-#333 := (= #173 #332)
-#330 := (= #170 #329)
-#327 := (= #167 #326)
-#311 := (iff #122 #308)
-#305 := (or #302 #285)
-#309 := (iff #305 #308)
-#310 := [rewrite]: #309
-#306 := (iff #122 #305)
-#303 := (iff #119 #285)
-#304 := [rewrite]: #303
-#282 := (iff #112 #302)
-#283 := [rewrite]: #282
-#307 := [monotonicity #283 #304]: #306
-#312 := [trans #307 #310]: #311
-#328 := [monotonicity #312]: #327
-#331 := [monotonicity #328]: #330
-#334 := [monotonicity #331]: #333
-#337 := [monotonicity #334]: #336
-#340 := [quant-intro #337]: #339
-#274 := (~ #179 #179)
-#271 := (~ #176 #176)
-#290 := [refl]: #271
-#275 := [nnf-pos #290]: #274
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#182 := (iff #37 #179)
-#76 := (and #16 #18)
-#79 := (or #17 #76)
-#152 := (ite #79 #30 #147)
-#155 := (ite #12 0::int #152)
-#158 := (ite #13 #8 #155)
-#161 := (= #29 #158)
-#164 := (forall (vars (?v0 int) (?v1 int)) #161)
-#180 := (iff #164 #179)
-#177 := (iff #161 #176)
-#174 := (= #158 #173)
-#171 := (= #155 #170)
-#168 := (= #152 #167)
-#123 := (iff #79 #122)
-#120 := (iff #76 #119)
-#117 := (iff #18 #116)
-#118 := [rewrite]: #117
-#110 := (iff #16 #109)
-#111 := [rewrite]: #110
-#121 := [monotonicity #111 #118]: #120
-#113 := (iff #17 #112)
-#106 := (iff #15 #105)
-#107 := [rewrite]: #106
-#114 := [monotonicity #107 #111]: #113
-#124 := [monotonicity #114 #121]: #123
-#169 := [monotonicity #124]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [quant-intro #178]: #180
-#165 := (iff #37 #164)
-#162 := (iff #36 #161)
-#159 := (= #35 #158)
-#156 := (= #34 #155)
-#153 := (= #33 #152)
-#150 := (= #32 #147)
-#144 := (- #141)
-#148 := (= #144 #147)
-#149 := [rewrite]: #148
-#145 := (= #32 #144)
-#142 := (= #31 #141)
-#87 := (= #23 #86)
-#88 := [rewrite]: #87
-#84 := (= #22 #83)
-#85 := [rewrite]: #84
-#143 := [monotonicity #85 #88]: #142
-#146 := [monotonicity #143]: #145
-#151 := [trans #146 #149]: #150
-#80 := (iff #20 #79)
-#77 := (iff #19 #76)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#154 := [monotonicity #81 #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#183 := [trans #166 #181]: #182
-#140 := [asserted]: #37
-#184 := [mp #140 #183]: #179
-#291 := [mp~ #184 #275]: #179
-#341 := [mp #291 #340]: #338
-#372 := [mp #341 #371]: #369
-#856 := [mp #372 #855]: #851
-#776 := (not #851)
-#661 := (or #776 #505)
-#430 := (* -1::int 1::int)
-#514 := (mod #430 #430)
-#515 := (+ #54 #514)
-#516 := (= #515 0::int)
-#507 := (mod 1::int 1::int)
-#518 := (* -1::int #507)
-#519 := (+ #54 #518)
-#520 := (= #519 0::int)
-#517 := (<= 1::int 0::int)
-#521 := (or #517 #517)
-#500 := (not #521)
-#835 := (>= 1::int 0::int)
-#837 := (or #517 #835)
-#494 := (not #837)
-#624 := (or #494 #500)
-#831 := (ite #624 #520 #516)
-#506 := (= 1::int 0::int)
-#838 := (ite #506 #505 #831)
-#839 := (= 1::int #54)
-#840 := (ite #506 #839 #838)
-#676 := (or #776 #840)
-#679 := (iff #676 #661)
-#680 := (iff #661 #661)
-#681 := [rewrite]: #680
-#772 := (iff #840 #505)
-#832 := (= #54 1::int)
-#667 := (ite false #832 #505)
-#775 := (iff #667 #505)
-#677 := [rewrite]: #775
-#668 := (iff #840 #667)
-#784 := (iff #838 #505)
-#779 := (ite false #505 #505)
-#783 := (iff #779 #505)
-#781 := [rewrite]: #783
-#780 := (iff #838 #779)
-#625 := (iff #831 #505)
-#1 := true
-#792 := (ite true #505 #505)
-#794 := (iff #792 #505)
-#623 := [rewrite]: #794
-#793 := (iff #831 #792)
-#785 := (iff #516 #505)
-#790 := (= #515 #54)
-#807 := (+ #54 0::int)
-#808 := (= #807 #54)
-#805 := [rewrite]: #808
-#788 := (= #515 #807)
-#645 := (= #514 0::int)
-#801 := (mod -1::int -1::int)
-#803 := (= #801 0::int)
-#644 := [rewrite]: #803
-#802 := (= #514 #801)
-#795 := (= #430 -1::int)
-#796 := [rewrite]: #795
-#797 := [monotonicity #796 #796]: #802
-#646 := [trans #797 #644]: #645
-#789 := [monotonicity #646]: #788
-#791 := [trans #789 #805]: #790
-#786 := [monotonicity #791]: #785
-#799 := (iff #520 #505)
-#809 := (= #519 #54)
-#522 := (= #519 #807)
-#528 := (= #518 0::int)
-#811 := (* -1::int 0::int)
-#526 := (= #811 0::int)
-#527 := [rewrite]: #526
-#815 := (= #518 #811)
-#810 := (= #507 0::int)
-#814 := [rewrite]: #810
-#525 := [monotonicity #814]: #815
-#806 := [trans #525 #527]: #528
-#804 := [monotonicity #806]: #522
-#798 := [trans #804 #805]: #809
-#800 := [monotonicity #798]: #799
-#535 := (iff #624 true)
-#477 := (or false true)
-#482 := (iff #477 true)
-#483 := [rewrite]: #482
-#812 := (iff #624 #477)
-#542 := (iff #500 true)
-#816 := (not false)
-#540 := (iff #816 true)
-#541 := [rewrite]: #540
-#817 := (iff #500 #816)
-#827 := (iff #521 false)
-#826 := (or false false)
-#469 := (iff #826 false)
-#829 := [rewrite]: #469
-#828 := (iff #521 #826)
-#497 := (iff #517 false)
-#833 := [rewrite]: #497
-#468 := [monotonicity #833 #833]: #828
-#830 := [trans #468 #829]: #827
-#539 := [monotonicity #830]: #817
-#436 := [trans #539 #541]: #542
-#825 := (iff #494 false)
-#821 := (not true)
-#824 := (iff #821 false)
-#819 := [rewrite]: #824
-#822 := (iff #494 #821)
-#484 := (iff #837 true)
-#818 := (iff #837 #477)
-#493 := (iff #835 true)
-#834 := [rewrite]: #493
-#481 := [monotonicity #833 #834]: #818
-#820 := [trans #481 #483]: #484
-#823 := [monotonicity #820]: #822
-#463 := [trans #823 #819]: #825
-#813 := [monotonicity #463 #436]: #812
-#536 := [trans #813 #483]: #535
-#787 := [monotonicity #536 #800 #786]: #793
-#626 := [trans #787 #623]: #625
-#841 := (iff #506 false)
-#836 := [rewrite]: #841
-#782 := [monotonicity #836 #626]: #780
-#666 := [trans #782 #781]: #784
-#842 := (iff #839 #832)
-#492 := [rewrite]: #842
-#627 := [monotonicity #836 #492 #666]: #668
-#773 := [trans #627 #677]: #772
-#672 := [monotonicity #773]: #679
-#682 := [trans #672 #681]: #679
-#678 := [quant-inst]: #676
-#683 := [mp #678 #682]: #661
-#703 := [unit-resolution #683 #856]: #505
-#699 := [monotonicity #703]: #57
-#58 := (not #57)
-#270 := [asserted]: #58
-[unit-resolution #270 #699]: false
-unsat
-aa365ca33021a3af06f636ef2547aa25906c3855 360 0
+9c15b3a4815405ea457af5f076f302f3f9facce0 360 0
 #2 := false
 decl f5 :: (-> int S2)
 decl f3 :: (-> int int int)
@@ -15915,321 +14727,7 @@
 #557 := [trans #620 #572]: #272
 [unit-resolution #280 #557]: false
 unsat
-79a0fde07c4517bfcd8cf389acc12b7fcaddd64c 313 0
-#2 := false
-decl f5 :: (-> int S2)
-#11 := 0::int
-#57 := (f5 0::int)
-decl f4 :: (-> int int int)
-#54 := 1::int
-#53 := 3::int
-#55 := (f4 3::int 1::int)
-#56 := (f5 #55)
-#58 := (= #56 #57)
-#839 := (= #55 0::int)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#851 := (pattern #29)
-#83 := -1::int
-#87 := (* -1::int #9)
-#84 := (* -1::int #8)
-#142 := (mod #84 #87)
-#363 := (+ #29 #142)
-#364 := (= #363 0::int)
-#30 := (mod #8 #9)
-#360 := (* -1::int #30)
-#361 := (+ #29 #360)
-#362 := (= #361 0::int)
-#109 := (<= #9 0::int)
-#105 := (<= #8 0::int)
-#302 := (or #105 #109)
-#303 := (not #302)
-#116 := (>= #8 0::int)
-#285 := (or #109 #116)
-#286 := (not #285)
-#309 := (or #286 #303)
-#365 := (ite #309 #362 #364)
-#359 := (= #29 0::int)
-#12 := (= #8 0::int)
-#366 := (ite #12 #359 #365)
-#358 := (= #8 #29)
-#13 := (= #9 0::int)
-#367 := (ite #13 #358 #366)
-#852 := (forall (vars (?v0 int) (?v1 int)) (:pat #851) #367)
-#370 := (forall (vars (?v0 int) (?v1 int)) #367)
-#855 := (iff #370 #852)
-#853 := (iff #367 #367)
-#854 := [refl]: #853
-#856 := [quant-intro #854]: #855
-#148 := (* -1::int #142)
-#327 := (ite #309 #30 #148)
-#330 := (ite #12 0::int #327)
-#333 := (ite #13 #8 #330)
-#336 := (= #29 #333)
-#339 := (forall (vars (?v0 int) (?v1 int)) #336)
-#371 := (iff #339 #370)
-#368 := (iff #336 #367)
-#369 := [rewrite]: #368
-#372 := [quant-intro #369]: #371
-#117 := (not #116)
-#110 := (not #109)
-#120 := (and #110 #117)
-#106 := (not #105)
-#113 := (and #106 #110)
-#123 := (or #113 #120)
-#168 := (ite #123 #30 #148)
-#171 := (ite #12 0::int #168)
-#174 := (ite #13 #8 #171)
-#177 := (= #29 #174)
-#180 := (forall (vars (?v0 int) (?v1 int)) #177)
-#340 := (iff #180 #339)
-#337 := (iff #177 #336)
-#334 := (= #174 #333)
-#331 := (= #171 #330)
-#328 := (= #168 #327)
-#312 := (iff #123 #309)
-#306 := (or #303 #286)
-#310 := (iff #306 #309)
-#311 := [rewrite]: #310
-#307 := (iff #123 #306)
-#304 := (iff #120 #286)
-#305 := [rewrite]: #304
-#283 := (iff #113 #303)
-#284 := [rewrite]: #283
-#308 := [monotonicity #284 #305]: #307
-#313 := [trans #308 #311]: #312
-#329 := [monotonicity #313]: #328
-#332 := [monotonicity #329]: #331
-#335 := [monotonicity #332]: #334
-#338 := [monotonicity #335]: #337
-#341 := [quant-intro #338]: #340
-#275 := (~ #180 #180)
-#272 := (~ #177 #177)
-#291 := [refl]: #272
-#276 := [nnf-pos #291]: #275
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#183 := (iff #37 #180)
-#77 := (and #16 #18)
-#80 := (or #17 #77)
-#153 := (ite #80 #30 #148)
-#156 := (ite #12 0::int #153)
-#159 := (ite #13 #8 #156)
-#162 := (= #29 #159)
-#165 := (forall (vars (?v0 int) (?v1 int)) #162)
-#181 := (iff #165 #180)
-#178 := (iff #162 #177)
-#175 := (= #159 #174)
-#172 := (= #156 #171)
-#169 := (= #153 #168)
-#124 := (iff #80 #123)
-#121 := (iff #77 #120)
-#118 := (iff #18 #117)
-#119 := [rewrite]: #118
-#111 := (iff #16 #110)
-#112 := [rewrite]: #111
-#122 := [monotonicity #112 #119]: #121
-#114 := (iff #17 #113)
-#107 := (iff #15 #106)
-#108 := [rewrite]: #107
-#115 := [monotonicity #108 #112]: #114
-#125 := [monotonicity #115 #122]: #124
-#170 := [monotonicity #125]: #169
-#173 := [monotonicity #170]: #172
-#176 := [monotonicity #173]: #175
-#179 := [monotonicity #176]: #178
-#182 := [quant-intro #179]: #181
-#166 := (iff #37 #165)
-#163 := (iff #36 #162)
-#160 := (= #35 #159)
-#157 := (= #34 #156)
-#154 := (= #33 #153)
-#151 := (= #32 #148)
-#145 := (- #142)
-#149 := (= #145 #148)
-#150 := [rewrite]: #149
-#146 := (= #32 #145)
-#143 := (= #31 #142)
-#88 := (= #23 #87)
-#89 := [rewrite]: #88
-#85 := (= #22 #84)
-#86 := [rewrite]: #85
-#144 := [monotonicity #86 #89]: #143
-#147 := [monotonicity #144]: #146
-#152 := [trans #147 #150]: #151
-#81 := (iff #20 #80)
-#78 := (iff #19 #77)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#155 := [monotonicity #82 #152]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [quant-intro #164]: #166
-#184 := [trans #167 #182]: #183
-#141 := [asserted]: #37
-#185 := [mp #141 #184]: #180
-#292 := [mp~ #185 #276]: #180
-#342 := [mp #292 #341]: #339
-#373 := [mp #342 #372]: #370
-#857 := [mp #373 #856]: #852
-#685 := (not #852)
-#778 := (or #685 #839)
-#431 := (* -1::int 1::int)
-#515 := (* -1::int 3::int)
-#516 := (mod #515 #431)
-#517 := (+ #55 #516)
-#508 := (= #517 0::int)
-#519 := (mod 3::int 1::int)
-#520 := (* -1::int #519)
-#521 := (+ #55 #520)
-#518 := (= #521 0::int)
-#522 := (<= 1::int 0::int)
-#501 := (<= 3::int 0::int)
-#836 := (or #501 #522)
-#838 := (not #836)
-#495 := (>= 3::int 0::int)
-#625 := (or #522 #495)
-#832 := (not #625)
-#506 := (or #832 #838)
-#507 := (ite #506 #518 #508)
-#840 := (= 3::int 0::int)
-#841 := (ite #840 #839 #507)
-#842 := (= 3::int #55)
-#837 := (= 1::int 0::int)
-#843 := (ite #837 #842 #841)
-#775 := (or #685 #843)
-#766 := (iff #775 #778)
-#760 := (iff #778 #778)
-#757 := [rewrite]: #760
-#683 := (iff #843 #839)
-#834 := (= #55 3::int)
-#679 := (ite false #834 #839)
-#681 := (iff #679 #839)
-#682 := [rewrite]: #681
-#680 := (iff #843 #679)
-#662 := (iff #841 #839)
-#776 := (ite false #839 #839)
-#774 := (iff #776 #839)
-#777 := [rewrite]: #774
-#678 := (iff #841 #776)
-#669 := (iff #507 #839)
-#1 := true
-#784 := (ite true #839 #839)
-#667 := (iff #784 #839)
-#668 := [rewrite]: #667
-#782 := (iff #507 #784)
-#781 := (iff #508 #839)
-#627 := (= #517 #55)
-#800 := (+ #55 0::int)
-#797 := (= #800 #55)
-#802 := [rewrite]: #797
-#624 := (= #517 #800)
-#788 := (= #516 0::int)
-#646 := -3::int
-#792 := (mod -3::int -1::int)
-#793 := (= #792 0::int)
-#794 := [rewrite]: #793
-#786 := (= #516 #792)
-#790 := (= #431 -1::int)
-#791 := [rewrite]: #790
-#647 := (= #515 -3::int)
-#789 := [rewrite]: #647
-#787 := [monotonicity #789 #791]: #786
-#795 := [trans #787 #794]: #788
-#626 := [monotonicity #795]: #624
-#780 := [trans #626 #802]: #627
-#783 := [monotonicity #780]: #781
-#804 := (iff #518 #839)
-#803 := (= #521 #55)
-#801 := (= #521 #800)
-#810 := (= #520 0::int)
-#808 := (* -1::int 0::int)
-#809 := (= #808 0::int)
-#806 := [rewrite]: #809
-#523 := (= #520 #808)
-#529 := (= #519 0::int)
-#807 := [rewrite]: #529
-#805 := [monotonicity #807]: #523
-#799 := [trans #805 #806]: #810
-#796 := [monotonicity #799]: #801
-#798 := [trans #796 #802]: #803
-#645 := [monotonicity #798]: #804
-#527 := (iff #506 true)
-#485 := (or false true)
-#823 := (iff #485 true)
-#824 := [rewrite]: #823
-#816 := (iff #506 #485)
-#815 := (iff #838 true)
-#813 := (not false)
-#537 := (iff #813 true)
-#811 := [rewrite]: #537
-#814 := (iff #838 #813)
-#543 := (iff #836 false)
-#817 := (or false false)
-#541 := (iff #817 false)
-#542 := [rewrite]: #541
-#818 := (iff #836 #817)
-#819 := (iff #522 false)
-#482 := [rewrite]: #819
-#828 := (iff #501 false)
-#831 := [rewrite]: #828
-#540 := [monotonicity #831 #482]: #818
-#437 := [trans #540 #542]: #543
-#536 := [monotonicity #437]: #814
-#812 := [trans #536 #811]: #815
-#470 := (iff #832 false)
-#826 := (not true)
-#829 := (iff #826 false)
-#469 := [rewrite]: #829
-#464 := (iff #832 #826)
-#825 := (iff #625 true)
-#821 := (iff #625 #485)
-#483 := (iff #495 true)
-#484 := [rewrite]: #483
-#822 := [monotonicity #482 #484]: #821
-#820 := [trans #822 #824]: #825
-#827 := [monotonicity #820]: #464
-#830 := [trans #827 #469]: #470
-#526 := [monotonicity #830 #812]: #816
-#528 := [trans #526 #824]: #527
-#785 := [monotonicity #528 #645 #783]: #782
-#628 := [trans #785 #668]: #669
-#835 := (iff #840 false)
-#478 := [rewrite]: #835
-#773 := [monotonicity #478 #628]: #678
-#677 := [trans #773 #777]: #662
-#498 := (iff #842 #834)
-#494 := [rewrite]: #498
-#833 := (iff #837 false)
-#493 := [rewrite]: #833
-#673 := [monotonicity #493 #494 #677]: #680
-#684 := [trans #673 #682]: #683
-#768 := [monotonicity #684]: #766
-#759 := [trans #768 #757]: #766
-#779 := [quant-inst]: #775
-#769 := [mp #779 #759]: #778
-#701 := [unit-resolution #769 #857]: #839
-#702 := [monotonicity #701]: #58
-#59 := (not #58)
-#271 := [asserted]: #59
-[unit-resolution #271 #702]: false
-unsat
-b6098bbff5fba6e8ac8e634e284360adde41d954 288 0
+1f03e32b436211763665c8081f05641b8f2b3f4b 288 0
 #2 := false
 decl f5 :: (-> int S2)
 #11 := 0::int
@@ -16518,7 +15016,7 @@
 #270 := [asserted]: #58
 [unit-resolution #270 #692]: false
 unsat
-86ae6406add6790c99d1c1c3b3a6bf3c60c7e019 302 0
+4d63e0251302af868da9188b73e2874657b72cb0 302 0
 #2 := false
 decl f5 :: (-> int S2)
 #11 := 0::int
@@ -16821,455 +15319,7 @@
 #271 := [asserted]: #59
 [unit-resolution #271 #702]: false
 unsat
-0aa64721f85c4c9c0df00c84259b25141ea1f07e 447 0
-#2 := false
-#11 := 0::int
-decl f6 :: (-> S2 int)
-decl f7 :: S2
-#53 := f7
-#54 := (f6 f7)
-#496 := (>= #54 0::int)
-decl f5 :: (-> int S2)
-#762 := (f5 #54)
-#708 := (f6 #762)
-#704 := (= #708 0::int)
-#655 := (not #704)
-#841 := (= #54 0::int)
-#674 := (not #841)
-#656 := (iff #674 #655)
-#653 := (iff #841 #704)
-#651 := (iff #704 #841)
-#649 := (= #708 #54)
-#643 := (= #762 f7)
-#763 := (= f7 #762)
-#38 := (:var 0 S2)
-#39 := (f6 #38)
-#859 := (pattern #39)
-#40 := (f5 #39)
-#188 := (= #38 #40)
-#860 := (forall (vars (?v0 S2)) (:pat #859) #188)
-#191 := (forall (vars (?v0 S2)) #188)
-#861 := (iff #191 #860)
-#863 := (iff #860 #860)
-#864 := [rewrite]: #863
-#862 := [rewrite]: #861
-#865 := [trans #862 #864]: #861
-#278 := (~ #191 #191)
-#294 := (~ #188 #188)
-#295 := [refl]: #294
-#279 := [nnf-pos #295]: #278
-#41 := (= #40 #38)
-#42 := (forall (vars (?v0 S2)) #41)
-#192 := (iff #42 #191)
-#189 := (iff #41 #188)
-#190 := [rewrite]: #189
-#193 := [quant-intro #190]: #192
-#187 := [asserted]: #42
-#196 := [mp #187 #193]: #191
-#296 := [mp~ #196 #279]: #191
-#866 := [mp #296 #865]: #860
-#759 := (not #860)
-#766 := (or #759 #763)
-#750 := [quant-inst]: #766
-#688 := [unit-resolution #750 #866]: #763
-#644 := [symm #688]: #643
-#650 := [monotonicity #644]: #649
-#652 := [monotonicity #650]: #651
-#654 := [symm #652]: #653
-#657 := [monotonicity #654]: #656
-#486 := (not #496)
-#673 := [hypothesis]: #486
-#677 := (or #674 #496)
-#687 := [th-lemma]: #677
-#667 := [unit-resolution #687 #673]: #674
-#658 := [mp #667 #657]: #655
-#689 := (or #496 #704)
-#9 := (:var 0 int)
-#44 := (f5 #9)
-#867 := (pattern #44)
-#211 := (>= #9 0::int)
-#45 := (f6 #44)
-#50 := (= #45 0::int)
-#261 := (or #50 #211)
-#874 := (forall (vars (?v0 int)) (:pat #867) #261)
-#266 := (forall (vars (?v0 int)) #261)
-#877 := (iff #266 #874)
-#875 := (iff #261 #261)
-#876 := [refl]: #875
-#878 := [quant-intro #876]: #877
-#282 := (~ #266 #266)
-#300 := (~ #261 #261)
-#301 := [refl]: #300
-#283 := [nnf-pos #301]: #282
-#49 := (< #9 0::int)
-#51 := (implies #49 #50)
-#52 := (forall (vars (?v0 int)) #51)
-#269 := (iff #52 #266)
-#232 := (= 0::int #45)
-#238 := (not #49)
-#239 := (or #238 #232)
-#244 := (forall (vars (?v0 int)) #239)
-#267 := (iff #244 #266)
-#264 := (iff #239 #261)
-#258 := (or #211 #50)
-#262 := (iff #258 #261)
-#263 := [rewrite]: #262
-#259 := (iff #239 #258)
-#256 := (iff #232 #50)
-#257 := [rewrite]: #256
-#254 := (iff #238 #211)
-#214 := (not #211)
-#249 := (not #214)
-#252 := (iff #249 #211)
-#253 := [rewrite]: #252
-#250 := (iff #238 #249)
-#247 := (iff #49 #214)
-#248 := [rewrite]: #247
-#251 := [monotonicity #248]: #250
-#255 := [trans #251 #253]: #254
-#260 := [monotonicity #255 #257]: #259
-#265 := [trans #260 #263]: #264
-#268 := [quant-intro #265]: #267
-#245 := (iff #52 #244)
-#242 := (iff #51 #239)
-#235 := (implies #49 #232)
-#240 := (iff #235 #239)
-#241 := [rewrite]: #240
-#236 := (iff #51 #235)
-#233 := (iff #50 #232)
-#234 := [rewrite]: #233
-#237 := [monotonicity #234]: #236
-#243 := [trans #237 #241]: #242
-#246 := [quant-intro #243]: #245
-#270 := [trans #246 #268]: #269
-#231 := [asserted]: #52
-#271 := [mp #231 #270]: #266
-#302 := [mp~ #271 #283]: #266
-#879 := [mp #302 #878]: #874
-#729 := (not #874)
-#671 := (or #729 #496 #704)
-#709 := (or #704 #496)
-#695 := (or #729 #709)
-#662 := (iff #695 #671)
-#691 := (or #729 #689)
-#672 := (iff #691 #671)
-#631 := [rewrite]: #672
-#697 := (iff #695 #691)
-#635 := (iff #709 #689)
-#690 := [rewrite]: #635
-#665 := [monotonicity #690]: #697
-#664 := [trans #665 #631]: #662
-#696 := [quant-inst]: #695
-#666 := [mp #696 #664]: #671
-#675 := [unit-resolution #666 #879]: #689
-#676 := [unit-resolution #675 #673]: #704
-#659 := [unit-resolution #676 #658]: false
-#660 := [lemma #659]: #496
-#502 := (<= #54 0::int)
-#830 := (not #502)
-#625 := (or #486 #830 #841)
-#684 := (not #625)
-decl f4 :: (-> int int int)
-#55 := 1::int
-#56 := (f4 #54 1::int)
-#840 := (= #56 0::int)
-#760 := (not #840)
-#58 := (f5 0::int)
-#57 := (f5 #56)
-#59 := (= #57 #58)
-#645 := [hypothesis]: #840
-#661 := [monotonicity #645]: #59
-#60 := (not #59)
-#272 := [asserted]: #60
-#622 := [unit-resolution #272 #661]: false
-#623 := [lemma #622]: #760
-#632 := (or #684 #840)
-#84 := -1::int
-#516 := (* -1::int #54)
-#809 := (mod #516 -1::int)
-#810 := (+ #56 #809)
-#800 := (= #810 0::int)
-#781 := (ite #625 #840 #800)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#852 := (pattern #29)
-#88 := (* -1::int #9)
-#85 := (* -1::int #8)
-#143 := (mod #85 #88)
-#364 := (+ #29 #143)
-#365 := (= #364 0::int)
-#30 := (mod #8 #9)
-#361 := (* -1::int #30)
-#362 := (+ #29 #361)
-#363 := (= #362 0::int)
-#110 := (<= #9 0::int)
-#106 := (<= #8 0::int)
-#303 := (or #106 #110)
-#304 := (not #303)
-#117 := (>= #8 0::int)
-#286 := (or #110 #117)
-#287 := (not #286)
-#310 := (or #287 #304)
-#366 := (ite #310 #363 #365)
-#360 := (= #29 0::int)
-#12 := (= #8 0::int)
-#367 := (ite #12 #360 #366)
-#359 := (= #8 #29)
-#13 := (= #9 0::int)
-#368 := (ite #13 #359 #367)
-#853 := (forall (vars (?v0 int) (?v1 int)) (:pat #852) #368)
-#371 := (forall (vars (?v0 int) (?v1 int)) #368)
-#856 := (iff #371 #853)
-#854 := (iff #368 #368)
-#855 := [refl]: #854
-#857 := [quant-intro #855]: #856
-#149 := (* -1::int #143)
-#328 := (ite #310 #30 #149)
-#331 := (ite #12 0::int #328)
-#334 := (ite #13 #8 #331)
-#337 := (= #29 #334)
-#340 := (forall (vars (?v0 int) (?v1 int)) #337)
-#372 := (iff #340 #371)
-#369 := (iff #337 #368)
-#370 := [rewrite]: #369
-#373 := [quant-intro #370]: #372
-#118 := (not #117)
-#111 := (not #110)
-#121 := (and #111 #118)
-#107 := (not #106)
-#114 := (and #107 #111)
-#124 := (or #114 #121)
-#169 := (ite #124 #30 #149)
-#172 := (ite #12 0::int #169)
-#175 := (ite #13 #8 #172)
-#178 := (= #29 #175)
-#181 := (forall (vars (?v0 int) (?v1 int)) #178)
-#341 := (iff #181 #340)
-#338 := (iff #178 #337)
-#335 := (= #175 #334)
-#332 := (= #172 #331)
-#329 := (= #169 #328)
-#313 := (iff #124 #310)
-#307 := (or #304 #287)
-#311 := (iff #307 #310)
-#312 := [rewrite]: #311
-#308 := (iff #124 #307)
-#305 := (iff #121 #287)
-#306 := [rewrite]: #305
-#284 := (iff #114 #304)
-#285 := [rewrite]: #284
-#309 := [monotonicity #285 #306]: #308
-#314 := [trans #309 #312]: #313
-#330 := [monotonicity #314]: #329
-#333 := [monotonicity #330]: #332
-#336 := [monotonicity #333]: #335
-#339 := [monotonicity #336]: #338
-#342 := [quant-intro #339]: #341
-#276 := (~ #181 #181)
-#273 := (~ #178 #178)
-#292 := [refl]: #273
-#277 := [nnf-pos #292]: #276
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#184 := (iff #37 #181)
-#78 := (and #16 #18)
-#81 := (or #17 #78)
-#154 := (ite #81 #30 #149)
-#157 := (ite #12 0::int #154)
-#160 := (ite #13 #8 #157)
-#163 := (= #29 #160)
-#166 := (forall (vars (?v0 int) (?v1 int)) #163)
-#182 := (iff #166 #181)
-#179 := (iff #163 #178)
-#176 := (= #160 #175)
-#173 := (= #157 #172)
-#170 := (= #154 #169)
-#125 := (iff #81 #124)
-#122 := (iff #78 #121)
-#119 := (iff #18 #118)
-#120 := [rewrite]: #119
-#112 := (iff #16 #111)
-#113 := [rewrite]: #112
-#123 := [monotonicity #113 #120]: #122
-#115 := (iff #17 #114)
-#108 := (iff #15 #107)
-#109 := [rewrite]: #108
-#116 := [monotonicity #109 #113]: #115
-#126 := [monotonicity #116 #123]: #125
-#171 := [monotonicity #126]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [quant-intro #180]: #182
-#167 := (iff #37 #166)
-#164 := (iff #36 #163)
-#161 := (= #35 #160)
-#158 := (= #34 #157)
-#155 := (= #33 #154)
-#152 := (= #32 #149)
-#146 := (- #143)
-#150 := (= #146 #149)
-#151 := [rewrite]: #150
-#147 := (= #32 #146)
-#144 := (= #31 #143)
-#89 := (= #23 #88)
-#90 := [rewrite]: #89
-#86 := (= #22 #85)
-#87 := [rewrite]: #86
-#145 := [monotonicity #87 #90]: #144
-#148 := [monotonicity #145]: #147
-#153 := [trans #148 #151]: #152
-#82 := (iff #20 #81)
-#79 := (iff #19 #78)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#156 := [monotonicity #83 #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [monotonicity #162]: #164
-#168 := [quant-intro #165]: #167
-#185 := [trans #168 #183]: #184
-#142 := [asserted]: #37
-#186 := [mp #142 #185]: #181
-#293 := [mp~ #186 #277]: #181
-#343 := [mp #293 #342]: #340
-#374 := [mp #343 #373]: #371
-#858 := [mp #374 #857]: #853
-#786 := (not #853)
-#668 := (or #786 #781)
-#432 := (* -1::int 1::int)
-#517 := (mod #516 #432)
-#518 := (+ #56 #517)
-#509 := (= #518 0::int)
-#520 := (mod #54 1::int)
-#521 := (* -1::int #520)
-#522 := (+ #56 #521)
-#519 := (= #522 0::int)
-#523 := (<= 1::int 0::int)
-#837 := (or #502 #523)
-#839 := (not #837)
-#626 := (or #523 #496)
-#833 := (not #626)
-#507 := (or #833 #839)
-#508 := (ite #507 #519 #509)
-#842 := (ite #841 #840 #508)
-#843 := (= #54 #56)
-#838 := (= 1::int 0::int)
-#844 := (ite #838 #843 #842)
-#669 := (or #786 #844)
-#629 := (iff #669 #668)
-#679 := (iff #668 #668)
-#774 := [rewrite]: #679
-#785 := (iff #844 #781)
-#831 := (or #486 #830)
-#646 := (or #831 #841)
-#647 := (ite #646 #840 #800)
-#782 := (iff #647 #781)
-#627 := (iff #646 #625)
-#628 := [rewrite]: #627
-#784 := [monotonicity #628]: #782
-#789 := (iff #844 #647)
-#793 := (ite false #843 #647)
-#794 := (iff #793 #647)
-#795 := [rewrite]: #794
-#787 := (iff #844 #793)
-#791 := (iff #842 #647)
-#797 := (ite #831 #840 #800)
-#804 := (ite #841 #840 #797)
-#648 := (iff #804 #647)
-#790 := [rewrite]: #648
-#799 := (iff #842 #804)
-#798 := (iff #508 #797)
-#801 := (iff #509 #800)
-#807 := (= #518 #810)
-#524 := (= #517 #809)
-#530 := (= #432 -1::int)
-#808 := [rewrite]: #530
-#806 := [monotonicity #808]: #524
-#811 := [monotonicity #806]: #807
-#802 := [monotonicity #811]: #801
-#528 := (iff #519 #840)
-#817 := (= #522 #56)
-#537 := (+ #56 0::int)
-#816 := (= #537 #56)
-#813 := [rewrite]: #816
-#538 := (= #522 #537)
-#814 := (= #521 0::int)
-#541 := (* -1::int 0::int)
-#544 := (= #541 0::int)
-#438 := [rewrite]: #544
-#542 := (= #521 #541)
-#818 := (= #520 0::int)
-#819 := [rewrite]: #818
-#543 := [monotonicity #819]: #542
-#815 := [trans #543 #438]: #814
-#812 := [monotonicity #815]: #538
-#527 := [trans #812 #813]: #817
-#529 := [monotonicity #527]: #528
-#829 := (iff #507 #831)
-#470 := (iff #839 #830)
-#465 := (iff #837 #502)
-#824 := (or #502 false)
-#821 := (iff #824 #502)
-#827 := [rewrite]: #821
-#825 := (iff #837 #824)
-#499 := (iff #523 false)
-#835 := [rewrite]: #499
-#826 := [monotonicity #835]: #825
-#828 := [trans #826 #827]: #465
-#471 := [monotonicity #828]: #470
-#822 := (iff #833 #486)
-#484 := (iff #626 #496)
-#495 := (or false #496)
-#820 := (iff #495 #496)
-#483 := [rewrite]: #820
-#836 := (iff #626 #495)
-#479 := [monotonicity #835]: #836
-#485 := [trans #479 #483]: #484
-#823 := [monotonicity #485]: #822
-#832 := [monotonicity #823 #471]: #829
-#803 := [monotonicity #832 #529 #802]: #798
-#805 := [monotonicity #803]: #799
-#792 := [trans #805 #790]: #791
-#834 := (iff #838 false)
-#494 := [rewrite]: #834
-#788 := [monotonicity #494 #792]: #787
-#796 := [trans #788 #795]: #789
-#783 := [trans #796 #784]: #785
-#777 := [monotonicity #783]: #629
-#775 := [trans #777 #774]: #629
-#670 := [quant-inst]: #669
-#778 := [mp #670 #775]: #668
-#630 := [unit-resolution #778 #858]: #781
-#780 := (not #781)
-#767 := (or #780 #684 #840)
-#769 := [def-axiom]: #767
-#633 := [unit-resolution #769 #630]: #632
-#634 := [unit-resolution #633 #623]: #684
-#680 := (or #625 #502)
-#681 := [def-axiom]: #680
-#636 := [unit-resolution #681 #634]: #502
-#682 := (or #625 #674)
-#683 := [def-axiom]: #682
-#637 := [unit-resolution #683 #634]: #674
-#638 := (or #841 #830 #486)
-#639 := [th-lemma]: #638
-[unit-resolution #639 #637 #636 #660]: false
-unsat
-a2a1b7b5735fca4ed872e71176348b8f63dcb65b 292 0
+fda2f2aa154f09feaa92a3ba2529a82a6fa08bed 292 0
 #2 := false
 decl f5 :: (-> int S2)
 #56 := 1::int
@@ -17562,313 +15612,7 @@
 #271 := [asserted]: #59
 [unit-resolution #271 #701]: false
 unsat
-5c15f7e076aa5690517f22531eb4e4a8a733ed8e 305 0
-#2 := false
-decl f5 :: (-> int S2)
-#11 := 0::int
-#56 := (f5 0::int)
-decl f4 :: (-> int int int)
-#53 := 3::int
-#54 := (f4 0::int 3::int)
-#55 := (f5 #54)
-#57 := (= #55 #56)
-#507 := (= #54 0::int)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#851 := (pattern #29)
-#82 := -1::int
-#86 := (* -1::int #9)
-#83 := (* -1::int #8)
-#141 := (mod #83 #86)
-#362 := (+ #29 #141)
-#363 := (= #362 0::int)
-#30 := (mod #8 #9)
-#359 := (* -1::int #30)
-#360 := (+ #29 #359)
-#361 := (= #360 0::int)
-#108 := (<= #9 0::int)
-#104 := (<= #8 0::int)
-#301 := (or #104 #108)
-#302 := (not #301)
-#115 := (>= #8 0::int)
-#284 := (or #108 #115)
-#285 := (not #284)
-#308 := (or #285 #302)
-#364 := (ite #308 #361 #363)
-#358 := (= #29 0::int)
-#12 := (= #8 0::int)
-#365 := (ite #12 #358 #364)
-#357 := (= #8 #29)
-#13 := (= #9 0::int)
-#366 := (ite #13 #357 #365)
-#852 := (forall (vars (?v0 int) (?v1 int)) (:pat #851) #366)
-#369 := (forall (vars (?v0 int) (?v1 int)) #366)
-#855 := (iff #369 #852)
-#853 := (iff #366 #366)
-#854 := [refl]: #853
-#856 := [quant-intro #854]: #855
-#147 := (* -1::int #141)
-#326 := (ite #308 #30 #147)
-#329 := (ite #12 0::int #326)
-#332 := (ite #13 #8 #329)
-#335 := (= #29 #332)
-#338 := (forall (vars (?v0 int) (?v1 int)) #335)
-#370 := (iff #338 #369)
-#367 := (iff #335 #366)
-#368 := [rewrite]: #367
-#371 := [quant-intro #368]: #370
-#116 := (not #115)
-#109 := (not #108)
-#119 := (and #109 #116)
-#105 := (not #104)
-#112 := (and #105 #109)
-#122 := (or #112 #119)
-#167 := (ite #122 #30 #147)
-#170 := (ite #12 0::int #167)
-#173 := (ite #13 #8 #170)
-#176 := (= #29 #173)
-#179 := (forall (vars (?v0 int) (?v1 int)) #176)
-#339 := (iff #179 #338)
-#336 := (iff #176 #335)
-#333 := (= #173 #332)
-#330 := (= #170 #329)
-#327 := (= #167 #326)
-#311 := (iff #122 #308)
-#305 := (or #302 #285)
-#309 := (iff #305 #308)
-#310 := [rewrite]: #309
-#306 := (iff #122 #305)
-#303 := (iff #119 #285)
-#304 := [rewrite]: #303
-#282 := (iff #112 #302)
-#283 := [rewrite]: #282
-#307 := [monotonicity #283 #304]: #306
-#312 := [trans #307 #310]: #311
-#328 := [monotonicity #312]: #327
-#331 := [monotonicity #328]: #330
-#334 := [monotonicity #331]: #333
-#337 := [monotonicity #334]: #336
-#340 := [quant-intro #337]: #339
-#274 := (~ #179 #179)
-#271 := (~ #176 #176)
-#290 := [refl]: #271
-#275 := [nnf-pos #290]: #274
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#182 := (iff #37 #179)
-#76 := (and #16 #18)
-#79 := (or #17 #76)
-#152 := (ite #79 #30 #147)
-#155 := (ite #12 0::int #152)
-#158 := (ite #13 #8 #155)
-#161 := (= #29 #158)
-#164 := (forall (vars (?v0 int) (?v1 int)) #161)
-#180 := (iff #164 #179)
-#177 := (iff #161 #176)
-#174 := (= #158 #173)
-#171 := (= #155 #170)
-#168 := (= #152 #167)
-#123 := (iff #79 #122)
-#120 := (iff #76 #119)
-#117 := (iff #18 #116)
-#118 := [rewrite]: #117
-#110 := (iff #16 #109)
-#111 := [rewrite]: #110
-#121 := [monotonicity #111 #118]: #120
-#113 := (iff #17 #112)
-#106 := (iff #15 #105)
-#107 := [rewrite]: #106
-#114 := [monotonicity #107 #111]: #113
-#124 := [monotonicity #114 #121]: #123
-#169 := [monotonicity #124]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [quant-intro #178]: #180
-#165 := (iff #37 #164)
-#162 := (iff #36 #161)
-#159 := (= #35 #158)
-#156 := (= #34 #155)
-#153 := (= #33 #152)
-#150 := (= #32 #147)
-#144 := (- #141)
-#148 := (= #144 #147)
-#149 := [rewrite]: #148
-#145 := (= #32 #144)
-#142 := (= #31 #141)
-#87 := (= #23 #86)
-#88 := [rewrite]: #87
-#84 := (= #22 #83)
-#85 := [rewrite]: #84
-#143 := [monotonicity #85 #88]: #142
-#146 := [monotonicity #143]: #145
-#151 := [trans #146 #149]: #150
-#80 := (iff #20 #79)
-#77 := (iff #19 #76)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#154 := [monotonicity #81 #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#183 := [trans #166 #181]: #182
-#140 := [asserted]: #37
-#184 := [mp #140 #183]: #179
-#291 := [mp~ #184 #275]: #179
-#341 := [mp #291 #340]: #338
-#372 := [mp #341 #371]: #369
-#857 := [mp #372 #856]: #852
-#677 := (not #852)
-#679 := (or #677 #507)
-#430 := (* -1::int 3::int)
-#515 := (* -1::int 0::int)
-#516 := (mod #515 #430)
-#517 := (+ #54 #516)
-#508 := (= #517 0::int)
-#519 := (mod 0::int 3::int)
-#520 := (* -1::int #519)
-#448 := (+ #54 #520)
-#521 := (= #448 0::int)
-#518 := (<= 3::int 0::int)
-#522 := (<= 0::int 0::int)
-#501 := (or #522 #518)
-#836 := (not #501)
-#838 := (>= 0::int 0::int)
-#495 := (or #518 #838)
-#625 := (not #495)
-#832 := (or #625 #836)
-#506 := (ite #832 #521 #508)
-#839 := (= 0::int 0::int)
-#840 := (ite #839 #507 #506)
-#841 := (= 0::int #54)
-#842 := (= 3::int 0::int)
-#837 := (ite #842 #841 #840)
-#680 := (or #677 #837)
-#681 := (iff #680 #679)
-#683 := (iff #679 #679)
-#684 := [rewrite]: #683
-#777 := (iff #837 #507)
-#626 := (ite false #507 #507)
-#781 := (iff #626 #507)
-#783 := [rewrite]: #781
-#773 := (iff #837 #626)
-#776 := (iff #840 #507)
-#1 := true
-#785 := (ite true #507 #507)
-#669 := (iff #785 #507)
-#628 := [rewrite]: #669
-#667 := (iff #840 #785)
-#784 := (iff #506 #507)
-#627 := (iff #506 #626)
-#795 := (iff #508 #507)
-#794 := (= #517 #54)
-#806 := (+ #54 0::int)
-#800 := (= #806 #54)
-#801 := [rewrite]: #800
-#787 := (= #517 #806)
-#792 := (= #516 0::int)
-#798 := -3::int
-#646 := (mod 0::int -3::int)
-#790 := (= #646 0::int)
-#791 := [rewrite]: #790
-#647 := (= #516 #646)
-#804 := (= #430 -3::int)
-#645 := [rewrite]: #804
-#808 := (= #515 0::int)
-#523 := [rewrite]: #808
-#789 := [monotonicity #523 #645]: #647
-#786 := [trans #789 #791]: #792
-#793 := [monotonicity #786]: #787
-#788 := [trans #793 #801]: #794
-#624 := [monotonicity #788]: #795
-#802 := (iff #521 #507)
-#796 := (= #448 #54)
-#810 := (= #448 #806)
-#805 := (= #520 0::int)
-#529 := (= #520 #515)
-#527 := (= #519 0::int)
-#528 := [rewrite]: #527
-#807 := [monotonicity #528]: #529
-#809 := [trans #807 #523]: #805
-#799 := [monotonicity #809]: #810
-#797 := [trans #799 #801]: #796
-#803 := [monotonicity #797]: #802
-#816 := (iff #832 false)
-#536 := (or false false)
-#815 := (iff #536 false)
-#812 := [rewrite]: #815
-#537 := (iff #832 #536)
-#813 := (iff #836 false)
-#825 := (not true)
-#464 := (iff #825 false)
-#827 := [rewrite]: #464
-#543 := (iff #836 #825)
-#541 := (iff #501 true)
-#828 := (or true false)
-#818 := (iff #828 true)
-#540 := [rewrite]: #818
-#831 := (iff #501 #828)
-#835 := (iff #518 false)
-#478 := [rewrite]: #835
-#470 := (iff #522 true)
-#830 := [rewrite]: #470
-#817 := [monotonicity #830 #478]: #831
-#542 := [trans #817 #540]: #541
-#436 := [monotonicity #542]: #543
-#814 := [trans #436 #827]: #813
-#829 := (iff #625 false)
-#820 := (iff #625 #825)
-#823 := (iff #495 true)
-#483 := (or false true)
-#821 := (iff #483 true)
-#822 := [rewrite]: #821
-#484 := (iff #495 #483)
-#819 := (iff #838 true)
-#482 := [rewrite]: #819
-#485 := [monotonicity #478 #482]: #484
-#824 := [trans #485 #822]: #823
-#826 := [monotonicity #824]: #820
-#469 := [trans #826 #827]: #829
-#811 := [monotonicity #469 #814]: #537
-#526 := [trans #811 #812]: #816
-#780 := [monotonicity #526 #803 #624]: #627
-#782 := [trans #780 #783]: #784
-#834 := (iff #839 true)
-#494 := [rewrite]: #834
-#668 := [monotonicity #494 #782]: #667
-#678 := [trans #668 #628]: #776
-#493 := (iff #841 #507)
-#498 := [rewrite]: #493
-#843 := (iff #842 false)
-#833 := [rewrite]: #843
-#774 := [monotonicity #833 #498 #678]: #773
-#662 := [trans #774 #783]: #777
-#682 := [monotonicity #662]: #681
-#685 := [trans #682 #684]: #681
-#673 := [quant-inst]: #680
-#778 := [mp #673 #685]: #679
-#713 := [unit-resolution #778 #857]: #507
-#709 := [monotonicity #713]: #57
-#58 := (not #57)
-#270 := [asserted]: #58
-[unit-resolution #270 #709]: false
-unsat
-8c2d3e4568510c293138be5f353975b23e5bdc6e 538 0
+d1702c7b0ebf2a07e3a41fab065abb768e63fc00 538 0
 #2 := false
 #11 := 0::int
 decl f6 :: (-> S2 int)
@@ -18407,336 +16151,7 @@
 #593 := [trans #591 #608]: #781
 [unit-resolution #661 #593]: false
 unsat
-6dd67c9a5af172ae1a01724c38372069dc3347ac 328 0
-#2 := false
-decl f5 :: (-> int S2)
-#53 := 1::int
-#57 := (f5 1::int)
-decl f4 :: (-> int int int)
-#54 := 3::int
-#55 := (f4 1::int 3::int)
-#56 := (f5 #55)
-#58 := (= #56 #57)
-#834 := (= #55 1::int)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#851 := (pattern #29)
-#11 := 0::int
-#83 := -1::int
-#87 := (* -1::int #9)
-#84 := (* -1::int #8)
-#142 := (mod #84 #87)
-#363 := (+ #29 #142)
-#364 := (= #363 0::int)
-#30 := (mod #8 #9)
-#360 := (* -1::int #30)
-#361 := (+ #29 #360)
-#362 := (= #361 0::int)
-#109 := (<= #9 0::int)
-#105 := (<= #8 0::int)
-#302 := (or #105 #109)
-#303 := (not #302)
-#116 := (>= #8 0::int)
-#285 := (or #109 #116)
-#286 := (not #285)
-#309 := (or #286 #303)
-#365 := (ite #309 #362 #364)
-#359 := (= #29 0::int)
-#12 := (= #8 0::int)
-#366 := (ite #12 #359 #365)
-#358 := (= #8 #29)
-#13 := (= #9 0::int)
-#367 := (ite #13 #358 #366)
-#852 := (forall (vars (?v0 int) (?v1 int)) (:pat #851) #367)
-#370 := (forall (vars (?v0 int) (?v1 int)) #367)
-#855 := (iff #370 #852)
-#853 := (iff #367 #367)
-#854 := [refl]: #853
-#856 := [quant-intro #854]: #855
-#148 := (* -1::int #142)
-#327 := (ite #309 #30 #148)
-#330 := (ite #12 0::int #327)
-#333 := (ite #13 #8 #330)
-#336 := (= #29 #333)
-#339 := (forall (vars (?v0 int) (?v1 int)) #336)
-#371 := (iff #339 #370)
-#368 := (iff #336 #367)
-#369 := [rewrite]: #368
-#372 := [quant-intro #369]: #371
-#117 := (not #116)
-#110 := (not #109)
-#120 := (and #110 #117)
-#106 := (not #105)
-#113 := (and #106 #110)
-#123 := (or #113 #120)
-#168 := (ite #123 #30 #148)
-#171 := (ite #12 0::int #168)
-#174 := (ite #13 #8 #171)
-#177 := (= #29 #174)
-#180 := (forall (vars (?v0 int) (?v1 int)) #177)
-#340 := (iff #180 #339)
-#337 := (iff #177 #336)
-#334 := (= #174 #333)
-#331 := (= #171 #330)
-#328 := (= #168 #327)
-#312 := (iff #123 #309)
-#306 := (or #303 #286)
-#310 := (iff #306 #309)
-#311 := [rewrite]: #310
-#307 := (iff #123 #306)
-#304 := (iff #120 #286)
-#305 := [rewrite]: #304
-#283 := (iff #113 #303)
-#284 := [rewrite]: #283
-#308 := [monotonicity #284 #305]: #307
-#313 := [trans #308 #311]: #312
-#329 := [monotonicity #313]: #328
-#332 := [monotonicity #329]: #331
-#335 := [monotonicity #332]: #334
-#338 := [monotonicity #335]: #337
-#341 := [quant-intro #338]: #340
-#275 := (~ #180 #180)
-#272 := (~ #177 #177)
-#291 := [refl]: #272
-#276 := [nnf-pos #291]: #275
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#183 := (iff #37 #180)
-#77 := (and #16 #18)
-#80 := (or #17 #77)
-#153 := (ite #80 #30 #148)
-#156 := (ite #12 0::int #153)
-#159 := (ite #13 #8 #156)
-#162 := (= #29 #159)
-#165 := (forall (vars (?v0 int) (?v1 int)) #162)
-#181 := (iff #165 #180)
-#178 := (iff #162 #177)
-#175 := (= #159 #174)
-#172 := (= #156 #171)
-#169 := (= #153 #168)
-#124 := (iff #80 #123)
-#121 := (iff #77 #120)
-#118 := (iff #18 #117)
-#119 := [rewrite]: #118
-#111 := (iff #16 #110)
-#112 := [rewrite]: #111
-#122 := [monotonicity #112 #119]: #121
-#114 := (iff #17 #113)
-#107 := (iff #15 #106)
-#108 := [rewrite]: #107
-#115 := [monotonicity #108 #112]: #114
-#125 := [monotonicity #115 #122]: #124
-#170 := [monotonicity #125]: #169
-#173 := [monotonicity #170]: #172
-#176 := [monotonicity #173]: #175
-#179 := [monotonicity #176]: #178
-#182 := [quant-intro #179]: #181
-#166 := (iff #37 #165)
-#163 := (iff #36 #162)
-#160 := (= #35 #159)
-#157 := (= #34 #156)
-#154 := (= #33 #153)
-#151 := (= #32 #148)
-#145 := (- #142)
-#149 := (= #145 #148)
-#150 := [rewrite]: #149
-#146 := (= #32 #145)
-#143 := (= #31 #142)
-#88 := (= #23 #87)
-#89 := [rewrite]: #88
-#85 := (= #22 #84)
-#86 := [rewrite]: #85
-#144 := [monotonicity #86 #89]: #143
-#147 := [monotonicity #144]: #146
-#152 := [trans #147 #150]: #151
-#81 := (iff #20 #80)
-#78 := (iff #19 #77)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#155 := [monotonicity #82 #152]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [quant-intro #164]: #166
-#184 := [trans #167 #182]: #183
-#141 := [asserted]: #37
-#185 := [mp #141 #184]: #180
-#292 := [mp~ #185 #276]: #180
-#342 := [mp #292 #341]: #339
-#373 := [mp #342 #372]: #370
-#857 := [mp #373 #856]: #852
-#762 := (not #852)
-#763 := (or #762 #834)
-#431 := (* -1::int 3::int)
-#515 := (* -1::int 1::int)
-#516 := (mod #515 #431)
-#517 := (+ #55 #516)
-#508 := (= #517 0::int)
-#519 := (mod 1::int 3::int)
-#520 := (* -1::int #519)
-#521 := (+ #55 #520)
-#518 := (= #521 0::int)
-#522 := (<= 3::int 0::int)
-#501 := (<= 1::int 0::int)
-#836 := (or #501 #522)
-#838 := (not #836)
-#495 := (>= 1::int 0::int)
-#625 := (or #522 #495)
-#832 := (not #625)
-#506 := (or #832 #838)
-#507 := (ite #506 #518 #508)
-#839 := (= #55 0::int)
-#840 := (= 1::int 0::int)
-#841 := (ite #840 #839 #507)
-#842 := (= 1::int #55)
-#837 := (= 3::int 0::int)
-#843 := (ite #837 #842 #841)
-#764 := (or #762 #843)
-#765 := (iff #764 #763)
-#750 := (iff #763 #763)
-#752 := [rewrite]: #750
-#772 := (iff #843 #834)
-#759 := (ite false #834 #834)
-#771 := (iff #759 #834)
-#767 := [rewrite]: #771
-#769 := (iff #843 #759)
-#760 := (iff #841 #834)
-#778 := (ite false #839 #834)
-#766 := (iff #778 #834)
-#768 := [rewrite]: #766
-#775 := (iff #841 #778)
-#684 := (iff #507 #834)
-#773 := -2::int
-#774 := (= #55 -2::int)
-#1 := true
-#680 := (ite true #834 #774)
-#682 := (iff #680 #834)
-#683 := [rewrite]: #682
-#673 := (iff #507 #680)
-#677 := (iff #508 #774)
-#795 := 2::int
-#782 := (+ 2::int #55)
-#628 := (= #782 0::int)
-#777 := (iff #628 #774)
-#662 := [rewrite]: #777
-#776 := (iff #508 #628)
-#668 := (= #517 #782)
-#781 := (+ #55 2::int)
-#785 := (= #781 #782)
-#667 := [rewrite]: #785
-#783 := (= #517 #781)
-#627 := (= #516 2::int)
-#792 := -3::int
-#793 := (mod -1::int -3::int)
-#624 := (= #793 2::int)
-#626 := [rewrite]: #624
-#794 := (= #516 #793)
-#786 := (= #431 -3::int)
-#787 := [rewrite]: #786
-#805 := (= #515 -1::int)
-#809 := [rewrite]: #805
-#788 := [monotonicity #809 #787]: #794
-#780 := [trans #788 #626]: #627
-#784 := [monotonicity #780]: #783
-#669 := [trans #784 #667]: #668
-#678 := [monotonicity #669]: #776
-#679 := [trans #678 #662]: #677
-#790 := (iff #518 #834)
-#796 := (+ -1::int #55)
-#804 := (= #796 0::int)
-#647 := (iff #804 #834)
-#789 := [rewrite]: #647
-#645 := (iff #518 #804)
-#803 := (= #521 #796)
-#799 := (+ #55 -1::int)
-#797 := (= #799 #796)
-#802 := [rewrite]: #797
-#800 := (= #521 #799)
-#806 := (= #520 -1::int)
-#808 := (= #520 #515)
-#529 := (= #519 1::int)
-#807 := [rewrite]: #529
-#523 := [monotonicity #807]: #808
-#810 := [trans #523 #809]: #806
-#801 := [monotonicity #810]: #800
-#798 := [trans #801 #802]: #803
-#646 := [monotonicity #798]: #645
-#791 := [trans #646 #789]: #790
-#527 := (iff #506 true)
-#485 := (or false true)
-#823 := (iff #485 true)
-#824 := [rewrite]: #823
-#816 := (iff #506 #485)
-#815 := (iff #838 true)
-#813 := (not false)
-#537 := (iff #813 true)
-#811 := [rewrite]: #537
-#814 := (iff #838 #813)
-#543 := (iff #836 false)
-#817 := (or false false)
-#541 := (iff #817 false)
-#542 := [rewrite]: #541
-#818 := (iff #836 #817)
-#819 := (iff #522 false)
-#482 := [rewrite]: #819
-#828 := (iff #501 false)
-#831 := [rewrite]: #828
-#540 := [monotonicity #831 #482]: #818
-#437 := [trans #540 #542]: #543
-#536 := [monotonicity #437]: #814
-#812 := [trans #536 #811]: #815
-#470 := (iff #832 false)
-#826 := (not true)
-#829 := (iff #826 false)
-#469 := [rewrite]: #829
-#464 := (iff #832 #826)
-#825 := (iff #625 true)
-#821 := (iff #625 #485)
-#483 := (iff #495 true)
-#484 := [rewrite]: #483
-#822 := [monotonicity #482 #484]: #821
-#820 := [trans #822 #824]: #825
-#827 := [monotonicity #820]: #464
-#830 := [trans #827 #469]: #470
-#526 := [monotonicity #830 #812]: #816
-#528 := [trans #526 #824]: #527
-#681 := [monotonicity #528 #791 #679]: #673
-#685 := [trans #681 #683]: #684
-#835 := (iff #840 false)
-#478 := [rewrite]: #835
-#779 := [monotonicity #478 #685]: #775
-#757 := [trans #779 #768]: #760
-#498 := (iff #842 #834)
-#494 := [rewrite]: #498
-#833 := (iff #837 false)
-#493 := [rewrite]: #833
-#770 := [monotonicity #493 #494 #757]: #769
-#761 := [trans #770 #767]: #772
-#749 := [monotonicity #761]: #765
-#753 := [trans #749 #752]: #765
-#758 := [quant-inst]: #764
-#754 := [mp #758 #753]: #763
-#703 := [unit-resolution #754 #857]: #834
-#708 := [monotonicity #703]: #58
-#59 := (not #58)
-#271 := [asserted]: #59
-[unit-resolution #271 #708]: false
-unsat
-d632f2ce3ea3569341b3f434b727f0c2aca7fff1 605 0
+bc7853f506d3f9cfeab494af8b75e50704c64354 605 0
 #2 := false
 decl f5 :: (-> int S2)
 #11 := 0::int
@@ -19342,7 +16757,2609 @@
 #603 := [unit-resolution #535 #671]: #61
 [unit-resolution #603 #596]: false
 unsat
-35e52a261c60456fe5328f3a2bc282a72801535d 303 0
+1b875f066bd0c93410ace2c47e4bd980f3a5d4a2 274 0
+#2 := false
+decl f5 :: (-> int S2)
+#11 := 0::int
+#55 := (f5 0::int)
+decl f4 :: (-> int int int)
+#53 := (f4 0::int 0::int)
+#54 := (f5 #53)
+#56 := (= #54 #55)
+#831 := (= #53 0::int)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#850 := (pattern #29)
+#81 := -1::int
+#85 := (* -1::int #9)
+#82 := (* -1::int #8)
+#140 := (mod #82 #85)
+#361 := (+ #29 #140)
+#362 := (= #361 0::int)
+#30 := (mod #8 #9)
+#358 := (* -1::int #30)
+#359 := (+ #29 #358)
+#360 := (= #359 0::int)
+#107 := (<= #9 0::int)
+#103 := (<= #8 0::int)
+#300 := (or #103 #107)
+#301 := (not #300)
+#114 := (>= #8 0::int)
+#283 := (or #107 #114)
+#284 := (not #283)
+#307 := (or #284 #301)
+#363 := (ite #307 #360 #362)
+#357 := (= #29 0::int)
+#12 := (= #8 0::int)
+#364 := (ite #12 #357 #363)
+#356 := (= #8 #29)
+#13 := (= #9 0::int)
+#365 := (ite #13 #356 #364)
+#851 := (forall (vars (?v0 int) (?v1 int)) (:pat #850) #365)
+#368 := (forall (vars (?v0 int) (?v1 int)) #365)
+#854 := (iff #368 #851)
+#852 := (iff #365 #365)
+#853 := [refl]: #852
+#855 := [quant-intro #853]: #854
+#146 := (* -1::int #140)
+#325 := (ite #307 #30 #146)
+#328 := (ite #12 0::int #325)
+#331 := (ite #13 #8 #328)
+#334 := (= #29 #331)
+#337 := (forall (vars (?v0 int) (?v1 int)) #334)
+#369 := (iff #337 #368)
+#366 := (iff #334 #365)
+#367 := [rewrite]: #366
+#370 := [quant-intro #367]: #369
+#115 := (not #114)
+#108 := (not #107)
+#118 := (and #108 #115)
+#104 := (not #103)
+#111 := (and #104 #108)
+#121 := (or #111 #118)
+#166 := (ite #121 #30 #146)
+#169 := (ite #12 0::int #166)
+#172 := (ite #13 #8 #169)
+#175 := (= #29 #172)
+#178 := (forall (vars (?v0 int) (?v1 int)) #175)
+#338 := (iff #178 #337)
+#335 := (iff #175 #334)
+#332 := (= #172 #331)
+#329 := (= #169 #328)
+#326 := (= #166 #325)
+#310 := (iff #121 #307)
+#304 := (or #301 #284)
+#308 := (iff #304 #307)
+#309 := [rewrite]: #308
+#305 := (iff #121 #304)
+#302 := (iff #118 #284)
+#303 := [rewrite]: #302
+#281 := (iff #111 #301)
+#282 := [rewrite]: #281
+#306 := [monotonicity #282 #303]: #305
+#311 := [trans #306 #309]: #310
+#327 := [monotonicity #311]: #326
+#330 := [monotonicity #327]: #329
+#333 := [monotonicity #330]: #332
+#336 := [monotonicity #333]: #335
+#339 := [quant-intro #336]: #338
+#273 := (~ #178 #178)
+#270 := (~ #175 #175)
+#289 := [refl]: #270
+#274 := [nnf-pos #289]: #273
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#181 := (iff #37 #178)
+#75 := (and #16 #18)
+#78 := (or #17 #75)
+#151 := (ite #78 #30 #146)
+#154 := (ite #12 0::int #151)
+#157 := (ite #13 #8 #154)
+#160 := (= #29 #157)
+#163 := (forall (vars (?v0 int) (?v1 int)) #160)
+#179 := (iff #163 #178)
+#176 := (iff #160 #175)
+#173 := (= #157 #172)
+#170 := (= #154 #169)
+#167 := (= #151 #166)
+#122 := (iff #78 #121)
+#119 := (iff #75 #118)
+#116 := (iff #18 #115)
+#117 := [rewrite]: #116
+#109 := (iff #16 #108)
+#110 := [rewrite]: #109
+#120 := [monotonicity #110 #117]: #119
+#112 := (iff #17 #111)
+#105 := (iff #15 #104)
+#106 := [rewrite]: #105
+#113 := [monotonicity #106 #110]: #112
+#123 := [monotonicity #113 #120]: #122
+#168 := [monotonicity #123]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#180 := [quant-intro #177]: #179
+#164 := (iff #37 #163)
+#161 := (iff #36 #160)
+#158 := (= #35 #157)
+#155 := (= #34 #154)
+#152 := (= #33 #151)
+#149 := (= #32 #146)
+#143 := (- #140)
+#147 := (= #143 #146)
+#148 := [rewrite]: #147
+#144 := (= #32 #143)
+#141 := (= #31 #140)
+#86 := (= #23 #85)
+#87 := [rewrite]: #86
+#83 := (= #22 #82)
+#84 := [rewrite]: #83
+#142 := [monotonicity #84 #87]: #141
+#145 := [monotonicity #142]: #144
+#150 := [trans #145 #148]: #149
+#79 := (iff #20 #78)
+#76 := (iff #19 #75)
+#77 := [rewrite]: #76
+#80 := [monotonicity #77]: #79
+#153 := [monotonicity #80 #150]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [quant-intro #162]: #164
+#182 := [trans #165 #180]: #181
+#139 := [asserted]: #37
+#183 := [mp #139 #182]: #178
+#290 := [mp~ #183 #274]: #178
+#340 := [mp #290 #339]: #337
+#371 := [mp #340 #370]: #368
+#856 := [mp #371 #855]: #851
+#646 := (not #851)
+#788 := (or #646 #831)
+#429 := (* -1::int 0::int)
+#514 := (mod #429 #429)
+#515 := (+ #53 #514)
+#516 := (= #515 0::int)
+#507 := (mod 0::int 0::int)
+#518 := (* -1::int #507)
+#519 := (+ #53 #518)
+#447 := (= #519 0::int)
+#520 := (<= 0::int 0::int)
+#517 := (or #520 #520)
+#521 := (not #517)
+#500 := (>= 0::int 0::int)
+#835 := (or #520 #500)
+#837 := (not #835)
+#494 := (or #837 #521)
+#624 := (ite #494 #447 #516)
+#505 := (= 0::int 0::int)
+#506 := (ite #505 #831 #624)
+#838 := (= 0::int #53)
+#839 := (ite #505 #838 #506)
+#789 := (or #646 #839)
+#791 := (iff #789 #788)
+#786 := (iff #788 #788)
+#792 := [rewrite]: #786
+#644 := (iff #839 #831)
+#1 := true
+#796 := (ite true #831 #831)
+#797 := (iff #796 #831)
+#803 := [rewrite]: #797
+#801 := (iff #839 #796)
+#800 := (iff #506 #831)
+#536 := (+ #53 #507)
+#811 := (= #536 0::int)
+#808 := (ite true #831 #811)
+#798 := (iff #808 #831)
+#799 := [rewrite]: #798
+#805 := (iff #506 #808)
+#522 := (iff #624 #811)
+#526 := (ite false #447 #811)
+#806 := (iff #526 #811)
+#807 := [rewrite]: #806
+#527 := (iff #624 #526)
+#815 := (iff #516 #811)
+#810 := (= #515 #536)
+#813 := (= #514 #507)
+#435 := (= #429 0::int)
+#812 := [rewrite]: #435
+#535 := [monotonicity #812 #812]: #813
+#814 := [monotonicity #535]: #810
+#525 := [monotonicity #814]: #815
+#541 := (iff #494 false)
+#830 := (or false false)
+#539 := (iff #830 false)
+#540 := [rewrite]: #539
+#816 := (iff #494 #830)
+#829 := (iff #521 false)
+#484 := (not true)
+#822 := (iff #484 false)
+#823 := [rewrite]: #822
+#468 := (iff #521 #484)
+#826 := (iff #517 true)
+#493 := (or true true)
+#818 := (iff #493 true)
+#481 := [rewrite]: #818
+#825 := (iff #517 #493)
+#832 := (iff #520 true)
+#492 := [rewrite]: #832
+#463 := [monotonicity #492 #492]: #825
+#828 := [trans #463 #481]: #826
+#469 := [monotonicity #828]: #468
+#827 := [trans #469 #823]: #829
+#824 := (iff #837 false)
+#820 := (iff #837 #484)
+#482 := (iff #835 true)
+#834 := (iff #835 #493)
+#497 := (iff #500 true)
+#833 := [rewrite]: #497
+#477 := [monotonicity #492 #833]: #834
+#483 := [trans #477 #481]: #482
+#821 := [monotonicity #483]: #820
+#819 := [trans #821 #823]: #824
+#817 := [monotonicity #819 #827]: #816
+#542 := [trans #817 #540]: #541
+#528 := [monotonicity #542 #525]: #527
+#804 := [trans #528 #807]: #522
+#840 := (iff #505 true)
+#841 := [rewrite]: #840
+#809 := [monotonicity #841 #804]: #805
+#795 := [trans #809 #799]: #800
+#836 := (iff #838 #831)
+#842 := [rewrite]: #836
+#802 := [monotonicity #841 #842 #795]: #801
+#645 := [trans #802 #803]: #644
+#785 := [monotonicity #645]: #791
+#793 := [trans #785 #792]: #791
+#790 := [quant-inst]: #789
+#787 := [mp #790 #793]: #788
+#741 := [unit-resolution #787 #856]: #831
+#742 := [monotonicity #741]: #56
+#57 := (not #56)
+#269 := [asserted]: #57
+[unit-resolution #269 #742]: false
+unsat
+88b5be8b8bac537ecdf2731a7740e95362692528 321 0
+#2 := false
+decl f5 :: (-> int S2)
+decl f4 :: (-> int int int)
+#11 := 0::int
+decl f6 :: (-> S2 int)
+decl f7 :: S2
+#53 := f7
+#54 := (f6 f7)
+#55 := (f4 #54 0::int)
+#56 := (f5 #55)
+#271 := (= f7 #56)
+#795 := (f5 #54)
+#772 := (= #795 #56)
+#771 := (= #56 #795)
+#768 := (= #55 #54)
+#848 := (= #54 #55)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#858 := (pattern #29)
+#82 := -1::int
+#86 := (* -1::int #9)
+#83 := (* -1::int #8)
+#141 := (mod #83 #86)
+#369 := (+ #29 #141)
+#370 := (= #369 0::int)
+#30 := (mod #8 #9)
+#366 := (* -1::int #30)
+#367 := (+ #29 #366)
+#368 := (= #367 0::int)
+#108 := (<= #9 0::int)
+#104 := (<= #8 0::int)
+#308 := (or #104 #108)
+#309 := (not #308)
+#115 := (>= #8 0::int)
+#291 := (or #108 #115)
+#292 := (not #291)
+#315 := (or #292 #309)
+#371 := (ite #315 #368 #370)
+#365 := (= #29 0::int)
+#12 := (= #8 0::int)
+#372 := (ite #12 #365 #371)
+#364 := (= #8 #29)
+#13 := (= #9 0::int)
+#373 := (ite #13 #364 #372)
+#859 := (forall (vars (?v0 int) (?v1 int)) (:pat #858) #373)
+#376 := (forall (vars (?v0 int) (?v1 int)) #373)
+#862 := (iff #376 #859)
+#860 := (iff #373 #373)
+#861 := [refl]: #860
+#863 := [quant-intro #861]: #862
+#147 := (* -1::int #141)
+#333 := (ite #315 #30 #147)
+#336 := (ite #12 0::int #333)
+#339 := (ite #13 #8 #336)
+#342 := (= #29 #339)
+#345 := (forall (vars (?v0 int) (?v1 int)) #342)
+#377 := (iff #345 #376)
+#374 := (iff #342 #373)
+#375 := [rewrite]: #374
+#378 := [quant-intro #375]: #377
+#116 := (not #115)
+#109 := (not #108)
+#119 := (and #109 #116)
+#105 := (not #104)
+#112 := (and #105 #109)
+#122 := (or #112 #119)
+#167 := (ite #122 #30 #147)
+#170 := (ite #12 0::int #167)
+#173 := (ite #13 #8 #170)
+#176 := (= #29 #173)
+#179 := (forall (vars (?v0 int) (?v1 int)) #176)
+#346 := (iff #179 #345)
+#343 := (iff #176 #342)
+#340 := (= #173 #339)
+#337 := (= #170 #336)
+#334 := (= #167 #333)
+#318 := (iff #122 #315)
+#312 := (or #309 #292)
+#316 := (iff #312 #315)
+#317 := [rewrite]: #316
+#313 := (iff #122 #312)
+#310 := (iff #119 #292)
+#311 := [rewrite]: #310
+#289 := (iff #112 #309)
+#290 := [rewrite]: #289
+#314 := [monotonicity #290 #311]: #313
+#319 := [trans #314 #317]: #318
+#335 := [monotonicity #319]: #334
+#338 := [monotonicity #335]: #337
+#341 := [monotonicity #338]: #340
+#344 := [monotonicity #341]: #343
+#347 := [quant-intro #344]: #346
+#281 := (~ #179 #179)
+#277 := (~ #176 #176)
+#297 := [refl]: #277
+#282 := [nnf-pos #297]: #281
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#182 := (iff #37 #179)
+#76 := (and #16 #18)
+#79 := (or #17 #76)
+#152 := (ite #79 #30 #147)
+#155 := (ite #12 0::int #152)
+#158 := (ite #13 #8 #155)
+#161 := (= #29 #158)
+#164 := (forall (vars (?v0 int) (?v1 int)) #161)
+#180 := (iff #164 #179)
+#177 := (iff #161 #176)
+#174 := (= #158 #173)
+#171 := (= #155 #170)
+#168 := (= #152 #167)
+#123 := (iff #79 #122)
+#120 := (iff #76 #119)
+#117 := (iff #18 #116)
+#118 := [rewrite]: #117
+#110 := (iff #16 #109)
+#111 := [rewrite]: #110
+#121 := [monotonicity #111 #118]: #120
+#113 := (iff #17 #112)
+#106 := (iff #15 #105)
+#107 := [rewrite]: #106
+#114 := [monotonicity #107 #111]: #113
+#124 := [monotonicity #114 #121]: #123
+#169 := [monotonicity #124]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [quant-intro #178]: #180
+#165 := (iff #37 #164)
+#162 := (iff #36 #161)
+#159 := (= #35 #158)
+#156 := (= #34 #155)
+#153 := (= #33 #152)
+#150 := (= #32 #147)
+#144 := (- #141)
+#148 := (= #144 #147)
+#149 := [rewrite]: #148
+#145 := (= #32 #144)
+#142 := (= #31 #141)
+#87 := (= #23 #86)
+#88 := [rewrite]: #87
+#84 := (= #22 #83)
+#85 := [rewrite]: #84
+#143 := [monotonicity #85 #88]: #142
+#146 := [monotonicity #143]: #145
+#151 := [trans #146 #149]: #150
+#80 := (iff #20 #79)
+#77 := (iff #19 #76)
+#78 := [rewrite]: #77
+#81 := [monotonicity #78]: #80
+#154 := [monotonicity #81 #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [quant-intro #163]: #165
+#183 := [trans #166 #181]: #182
+#140 := [asserted]: #37
+#184 := [mp #140 #183]: #179
+#298 := [mp~ #184 #282]: #179
+#348 := [mp #298 #347]: #345
+#379 := [mp #348 #378]: #376
+#864 := [mp #379 #863]: #859
+#653 := (not #859)
+#654 := (or #653 #848)
+#437 := (* -1::int 0::int)
+#522 := (* -1::int #54)
+#523 := (mod #522 #437)
+#524 := (+ #55 #523)
+#515 := (= #524 0::int)
+#526 := (mod #54 0::int)
+#527 := (* -1::int #526)
+#455 := (+ #55 #527)
+#528 := (= #455 0::int)
+#525 := (<= 0::int 0::int)
+#529 := (<= #54 0::int)
+#508 := (or #529 #525)
+#843 := (not #508)
+#845 := (>= #54 0::int)
+#502 := (or #525 #845)
+#632 := (not #502)
+#839 := (or #632 #843)
+#513 := (ite #839 #528 #515)
+#514 := (= #55 0::int)
+#846 := (= #54 0::int)
+#847 := (ite #846 #514 #513)
+#849 := (= 0::int 0::int)
+#844 := (ite #849 #848 #847)
+#796 := (or #653 #844)
+#798 := (iff #796 #654)
+#793 := (iff #654 #654)
+#794 := [rewrite]: #793
+#811 := (iff #844 #848)
+#544 := (mod #522 0::int)
+#819 := (+ #55 #544)
+#534 := (= #819 0::int)
+#806 := (ite #846 #514 #534)
+#1 := true
+#803 := (ite true #848 #806)
+#810 := (iff #803 #848)
+#805 := [rewrite]: #810
+#804 := (iff #844 #803)
+#807 := (iff #847 #806)
+#813 := (iff #513 #534)
+#814 := (ite false #528 #534)
+#812 := (iff #814 #534)
+#816 := [rewrite]: #812
+#815 := (iff #513 #814)
+#535 := (iff #515 #534)
+#823 := (= #524 #819)
+#818 := (= #523 #544)
+#821 := (= #437 0::int)
+#543 := [rewrite]: #821
+#822 := [monotonicity #543]: #818
+#533 := [monotonicity #822]: #823
+#536 := [monotonicity #533]: #535
+#443 := (iff #839 false)
+#825 := (or false false)
+#549 := (iff #825 false)
+#550 := [rewrite]: #549
+#547 := (iff #839 #825)
+#838 := (iff #843 false)
+#491 := (not true)
+#829 := (iff #491 false)
+#830 := [rewrite]: #829
+#837 := (iff #843 #491)
+#476 := (iff #508 true)
+#827 := (or #529 true)
+#834 := (iff #827 true)
+#836 := [rewrite]: #834
+#833 := (iff #508 #827)
+#500 := (iff #525 true)
+#505 := [rewrite]: #500
+#471 := [monotonicity #505]: #833
+#477 := [trans #471 #836]: #476
+#835 := [monotonicity #477]: #837
+#824 := [trans #835 #830]: #838
+#831 := (iff #632 false)
+#492 := (iff #632 #491)
+#489 := (iff #502 true)
+#841 := (or true #845)
+#485 := (iff #841 true)
+#826 := [rewrite]: #485
+#501 := (iff #502 #841)
+#842 := [monotonicity #505]: #501
+#490 := [trans #842 #826]: #489
+#828 := [monotonicity #490]: #492
+#832 := [trans #828 #830]: #831
+#548 := [monotonicity #832 #824]: #547
+#820 := [trans #548 #550]: #443
+#530 := [monotonicity #820 #536]: #815
+#817 := [trans #530 #816]: #813
+#808 := [monotonicity #817]: #807
+#850 := (iff #849 true)
+#840 := [rewrite]: #850
+#809 := [monotonicity #840 #808]: #804
+#652 := [trans #809 #805]: #811
+#799 := [monotonicity #652]: #798
+#800 := [trans #799 #794]: #798
+#797 := [quant-inst]: #796
+#801 := [mp #797 #800]: #654
+#779 := [unit-resolution #801 #864]: #848
+#769 := [symm #779]: #768
+#765 := [monotonicity #769]: #771
+#756 := [symm #765]: #772
+#802 := (= f7 #795)
+#38 := (:var 0 S2)
+#39 := (f6 #38)
+#865 := (pattern #39)
+#40 := (f5 #39)
+#186 := (= #38 #40)
+#866 := (forall (vars (?v0 S2)) (:pat #865) #186)
+#189 := (forall (vars (?v0 S2)) #186)
+#867 := (iff #189 #866)
+#869 := (iff #866 #866)
+#870 := [rewrite]: #869
+#868 := [rewrite]: #867
+#871 := [trans #868 #870]: #867
+#283 := (~ #189 #189)
+#299 := (~ #186 #186)
+#300 := [refl]: #299
+#284 := [nnf-pos #300]: #283
+#41 := (= #40 #38)
+#42 := (forall (vars (?v0 S2)) #41)
+#190 := (iff #42 #189)
+#187 := (iff #41 #186)
+#188 := [rewrite]: #187
+#191 := [quant-intro #188]: #190
+#185 := [asserted]: #42
+#194 := [mp #185 #191]: #189
+#301 := [mp~ #194 #284]: #189
+#872 := [mp #301 #871]: #866
+#634 := (not #866)
+#787 := (or #634 #802)
+#788 := [quant-inst]: #787
+#770 := [unit-resolution #788 #872]: #802
+#757 := [trans #770 #756]: #271
+#274 := (not #271)
+#57 := (= #56 f7)
+#58 := (not #57)
+#275 := (iff #58 #274)
+#272 := (iff #57 #271)
+#273 := [rewrite]: #272
+#276 := [monotonicity #273]: #275
+#270 := [asserted]: #58
+#279 := [mp #270 #276]: #274
+[unit-resolution #279 #757]: false
+unsat
+9da934b492dff6e7ee2b833a8505acdd8a3a684e 304 0
+#2 := false
+decl f5 :: (-> int S2)
+#11 := 0::int
+#56 := (f5 0::int)
+decl f4 :: (-> int int int)
+#53 := 1::int
+#54 := (f4 0::int 1::int)
+#55 := (f5 #54)
+#57 := (= #55 #56)
+#838 := (= #54 0::int)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#850 := (pattern #29)
+#82 := -1::int
+#86 := (* -1::int #9)
+#83 := (* -1::int #8)
+#141 := (mod #83 #86)
+#362 := (+ #29 #141)
+#363 := (= #362 0::int)
+#30 := (mod #8 #9)
+#359 := (* -1::int #30)
+#360 := (+ #29 #359)
+#361 := (= #360 0::int)
+#108 := (<= #9 0::int)
+#104 := (<= #8 0::int)
+#301 := (or #104 #108)
+#302 := (not #301)
+#115 := (>= #8 0::int)
+#284 := (or #108 #115)
+#285 := (not #284)
+#308 := (or #285 #302)
+#364 := (ite #308 #361 #363)
+#358 := (= #29 0::int)
+#12 := (= #8 0::int)
+#365 := (ite #12 #358 #364)
+#357 := (= #8 #29)
+#13 := (= #9 0::int)
+#366 := (ite #13 #357 #365)
+#851 := (forall (vars (?v0 int) (?v1 int)) (:pat #850) #366)
+#369 := (forall (vars (?v0 int) (?v1 int)) #366)
+#854 := (iff #369 #851)
+#852 := (iff #366 #366)
+#853 := [refl]: #852
+#855 := [quant-intro #853]: #854
+#147 := (* -1::int #141)
+#326 := (ite #308 #30 #147)
+#329 := (ite #12 0::int #326)
+#332 := (ite #13 #8 #329)
+#335 := (= #29 #332)
+#338 := (forall (vars (?v0 int) (?v1 int)) #335)
+#370 := (iff #338 #369)
+#367 := (iff #335 #366)
+#368 := [rewrite]: #367
+#371 := [quant-intro #368]: #370
+#116 := (not #115)
+#109 := (not #108)
+#119 := (and #109 #116)
+#105 := (not #104)
+#112 := (and #105 #109)
+#122 := (or #112 #119)
+#167 := (ite #122 #30 #147)
+#170 := (ite #12 0::int #167)
+#173 := (ite #13 #8 #170)
+#176 := (= #29 #173)
+#179 := (forall (vars (?v0 int) (?v1 int)) #176)
+#339 := (iff #179 #338)
+#336 := (iff #176 #335)
+#333 := (= #173 #332)
+#330 := (= #170 #329)
+#327 := (= #167 #326)
+#311 := (iff #122 #308)
+#305 := (or #302 #285)
+#309 := (iff #305 #308)
+#310 := [rewrite]: #309
+#306 := (iff #122 #305)
+#303 := (iff #119 #285)
+#304 := [rewrite]: #303
+#282 := (iff #112 #302)
+#283 := [rewrite]: #282
+#307 := [monotonicity #283 #304]: #306
+#312 := [trans #307 #310]: #311
+#328 := [monotonicity #312]: #327
+#331 := [monotonicity #328]: #330
+#334 := [monotonicity #331]: #333
+#337 := [monotonicity #334]: #336
+#340 := [quant-intro #337]: #339
+#274 := (~ #179 #179)
+#271 := (~ #176 #176)
+#290 := [refl]: #271
+#275 := [nnf-pos #290]: #274
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#182 := (iff #37 #179)
+#76 := (and #16 #18)
+#79 := (or #17 #76)
+#152 := (ite #79 #30 #147)
+#155 := (ite #12 0::int #152)
+#158 := (ite #13 #8 #155)
+#161 := (= #29 #158)
+#164 := (forall (vars (?v0 int) (?v1 int)) #161)
+#180 := (iff #164 #179)
+#177 := (iff #161 #176)
+#174 := (= #158 #173)
+#171 := (= #155 #170)
+#168 := (= #152 #167)
+#123 := (iff #79 #122)
+#120 := (iff #76 #119)
+#117 := (iff #18 #116)
+#118 := [rewrite]: #117
+#110 := (iff #16 #109)
+#111 := [rewrite]: #110
+#121 := [monotonicity #111 #118]: #120
+#113 := (iff #17 #112)
+#106 := (iff #15 #105)
+#107 := [rewrite]: #106
+#114 := [monotonicity #107 #111]: #113
+#124 := [monotonicity #114 #121]: #123
+#169 := [monotonicity #124]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [quant-intro #178]: #180
+#165 := (iff #37 #164)
+#162 := (iff #36 #161)
+#159 := (= #35 #158)
+#156 := (= #34 #155)
+#153 := (= #33 #152)
+#150 := (= #32 #147)
+#144 := (- #141)
+#148 := (= #144 #147)
+#149 := [rewrite]: #148
+#145 := (= #32 #144)
+#142 := (= #31 #141)
+#87 := (= #23 #86)
+#88 := [rewrite]: #87
+#84 := (= #22 #83)
+#85 := [rewrite]: #84
+#143 := [monotonicity #85 #88]: #142
+#146 := [monotonicity #143]: #145
+#151 := [trans #146 #149]: #150
+#80 := (iff #20 #79)
+#77 := (iff #19 #76)
+#78 := [rewrite]: #77
+#81 := [monotonicity #78]: #80
+#154 := [monotonicity #81 #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [quant-intro #163]: #165
+#183 := [trans #166 #181]: #182
+#140 := [asserted]: #37
+#184 := [mp #140 #183]: #179
+#291 := [mp~ #184 #275]: #179
+#341 := [mp #291 #340]: #338
+#372 := [mp #341 #371]: #369
+#856 := [mp #372 #855]: #851
+#676 := (not #851)
+#678 := (or #676 #838)
+#430 := (* -1::int 1::int)
+#514 := (* -1::int 0::int)
+#515 := (mod #514 #430)
+#516 := (+ #54 #515)
+#507 := (= #516 0::int)
+#518 := (mod 0::int 1::int)
+#519 := (* -1::int #518)
+#520 := (+ #54 #519)
+#517 := (= #520 0::int)
+#521 := (<= 1::int 0::int)
+#500 := (<= 0::int 0::int)
+#835 := (or #500 #521)
+#837 := (not #835)
+#494 := (>= 0::int 0::int)
+#624 := (or #521 #494)
+#831 := (not #624)
+#505 := (or #831 #837)
+#506 := (ite #505 #517 #507)
+#839 := (= 0::int 0::int)
+#840 := (ite #839 #838 #506)
+#841 := (= 0::int #54)
+#836 := (= 1::int 0::int)
+#842 := (ite #836 #841 #840)
+#679 := (or #676 #842)
+#680 := (iff #679 #678)
+#682 := (iff #678 #678)
+#683 := [rewrite]: #682
+#776 := (iff #842 #838)
+#625 := (ite false #838 #838)
+#780 := (iff #625 #838)
+#782 := [rewrite]: #780
+#772 := (iff #842 #625)
+#775 := (iff #840 #838)
+#1 := true
+#784 := (ite true #838 #838)
+#668 := (iff #784 #838)
+#627 := [rewrite]: #668
+#666 := (iff #840 #784)
+#783 := (iff #506 #838)
+#626 := (iff #506 #625)
+#794 := (iff #507 #838)
+#793 := (= #516 #54)
+#809 := (+ #54 0::int)
+#800 := (= #809 #54)
+#795 := [rewrite]: #800
+#786 := (= #516 #809)
+#791 := (= #515 0::int)
+#645 := (mod 0::int -1::int)
+#789 := (= #645 0::int)
+#790 := [rewrite]: #789
+#646 := (= #515 #645)
+#803 := (= #430 -1::int)
+#644 := [rewrite]: #803
+#522 := (= #514 0::int)
+#804 := [rewrite]: #522
+#788 := [monotonicity #804 #644]: #646
+#785 := [trans #788 #790]: #791
+#792 := [monotonicity #785]: #786
+#787 := [trans #792 #795]: #793
+#623 := [monotonicity #787]: #794
+#802 := (iff #517 #838)
+#796 := (= #520 #54)
+#798 := (= #520 #809)
+#808 := (= #519 0::int)
+#806 := (= #519 #514)
+#527 := (= #518 0::int)
+#528 := [rewrite]: #527
+#807 := [monotonicity #528]: #806
+#805 := [trans #807 #804]: #808
+#799 := [monotonicity #805]: #798
+#801 := [trans #799 #795]: #796
+#797 := [monotonicity #801]: #802
+#525 := (iff #505 false)
+#536 := (or false false)
+#811 := (iff #536 false)
+#815 := [rewrite]: #811
+#810 := (iff #505 #536)
+#813 := (iff #837 false)
+#819 := (not true)
+#826 := (iff #819 false)
+#828 := [rewrite]: #826
+#436 := (iff #837 #819)
+#541 := (iff #835 true)
+#830 := (or true false)
+#539 := (iff #830 true)
+#540 := [rewrite]: #539
+#816 := (iff #835 #830)
+#477 := (iff #521 false)
+#818 := [rewrite]: #477
+#829 := (iff #500 true)
+#827 := [rewrite]: #829
+#817 := [monotonicity #827 #818]: #816
+#542 := [trans #817 #540]: #541
+#812 := [monotonicity #542]: #436
+#535 := [trans #812 #828]: #813
+#468 := (iff #831 false)
+#825 := (iff #831 #819)
+#823 := (iff #624 true)
+#483 := (or false true)
+#821 := (iff #483 true)
+#822 := [rewrite]: #821
+#484 := (iff #624 #483)
+#481 := (iff #494 true)
+#482 := [rewrite]: #481
+#820 := [monotonicity #818 #482]: #484
+#824 := [trans #820 #822]: #823
+#463 := [monotonicity #824]: #825
+#469 := [trans #463 #828]: #468
+#814 := [monotonicity #469 #535]: #810
+#526 := [trans #814 #815]: #525
+#779 := [monotonicity #526 #797 #623]: #626
+#781 := [trans #779 #782]: #783
+#493 := (iff #839 true)
+#834 := [rewrite]: #493
+#667 := [monotonicity #834 #781]: #666
+#677 := [trans #667 #627]: #775
+#497 := (iff #841 #838)
+#833 := [rewrite]: #497
+#832 := (iff #836 false)
+#492 := [rewrite]: #832
+#773 := [monotonicity #492 #833 #677]: #772
+#661 := [trans #773 #782]: #776
+#681 := [monotonicity #661]: #680
+#684 := [trans #681 #683]: #680
+#672 := [quant-inst]: #679
+#777 := [mp #672 #684]: #678
+#712 := [unit-resolution #777 #856]: #838
+#708 := [monotonicity #712]: #57
+#58 := (not #57)
+#270 := [asserted]: #58
+[unit-resolution #270 #708]: false
+unsat
+761b398da392cd56cdfbcef786fc856a445054e3 302 0
+#2 := false
+decl f5 :: (-> int S2)
+#11 := 0::int
+#56 := (f5 0::int)
+decl f4 :: (-> int int int)
+#53 := 1::int
+#54 := (f4 1::int 1::int)
+#55 := (f5 #54)
+#57 := (= #55 #56)
+#505 := (= #54 0::int)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#850 := (pattern #29)
+#82 := -1::int
+#86 := (* -1::int #9)
+#83 := (* -1::int #8)
+#141 := (mod #83 #86)
+#362 := (+ #29 #141)
+#363 := (= #362 0::int)
+#30 := (mod #8 #9)
+#359 := (* -1::int #30)
+#360 := (+ #29 #359)
+#361 := (= #360 0::int)
+#108 := (<= #9 0::int)
+#104 := (<= #8 0::int)
+#301 := (or #104 #108)
+#302 := (not #301)
+#115 := (>= #8 0::int)
+#284 := (or #108 #115)
+#285 := (not #284)
+#308 := (or #285 #302)
+#364 := (ite #308 #361 #363)
+#358 := (= #29 0::int)
+#12 := (= #8 0::int)
+#365 := (ite #12 #358 #364)
+#357 := (= #8 #29)
+#13 := (= #9 0::int)
+#366 := (ite #13 #357 #365)
+#851 := (forall (vars (?v0 int) (?v1 int)) (:pat #850) #366)
+#369 := (forall (vars (?v0 int) (?v1 int)) #366)
+#854 := (iff #369 #851)
+#852 := (iff #366 #366)
+#853 := [refl]: #852
+#855 := [quant-intro #853]: #854
+#147 := (* -1::int #141)
+#326 := (ite #308 #30 #147)
+#329 := (ite #12 0::int #326)
+#332 := (ite #13 #8 #329)
+#335 := (= #29 #332)
+#338 := (forall (vars (?v0 int) (?v1 int)) #335)
+#370 := (iff #338 #369)
+#367 := (iff #335 #366)
+#368 := [rewrite]: #367
+#371 := [quant-intro #368]: #370
+#116 := (not #115)
+#109 := (not #108)
+#119 := (and #109 #116)
+#105 := (not #104)
+#112 := (and #105 #109)
+#122 := (or #112 #119)
+#167 := (ite #122 #30 #147)
+#170 := (ite #12 0::int #167)
+#173 := (ite #13 #8 #170)
+#176 := (= #29 #173)
+#179 := (forall (vars (?v0 int) (?v1 int)) #176)
+#339 := (iff #179 #338)
+#336 := (iff #176 #335)
+#333 := (= #173 #332)
+#330 := (= #170 #329)
+#327 := (= #167 #326)
+#311 := (iff #122 #308)
+#305 := (or #302 #285)
+#309 := (iff #305 #308)
+#310 := [rewrite]: #309
+#306 := (iff #122 #305)
+#303 := (iff #119 #285)
+#304 := [rewrite]: #303
+#282 := (iff #112 #302)
+#283 := [rewrite]: #282
+#307 := [monotonicity #283 #304]: #306
+#312 := [trans #307 #310]: #311
+#328 := [monotonicity #312]: #327
+#331 := [monotonicity #328]: #330
+#334 := [monotonicity #331]: #333
+#337 := [monotonicity #334]: #336
+#340 := [quant-intro #337]: #339
+#274 := (~ #179 #179)
+#271 := (~ #176 #176)
+#290 := [refl]: #271
+#275 := [nnf-pos #290]: #274
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#182 := (iff #37 #179)
+#76 := (and #16 #18)
+#79 := (or #17 #76)
+#152 := (ite #79 #30 #147)
+#155 := (ite #12 0::int #152)
+#158 := (ite #13 #8 #155)
+#161 := (= #29 #158)
+#164 := (forall (vars (?v0 int) (?v1 int)) #161)
+#180 := (iff #164 #179)
+#177 := (iff #161 #176)
+#174 := (= #158 #173)
+#171 := (= #155 #170)
+#168 := (= #152 #167)
+#123 := (iff #79 #122)
+#120 := (iff #76 #119)
+#117 := (iff #18 #116)
+#118 := [rewrite]: #117
+#110 := (iff #16 #109)
+#111 := [rewrite]: #110
+#121 := [monotonicity #111 #118]: #120
+#113 := (iff #17 #112)
+#106 := (iff #15 #105)
+#107 := [rewrite]: #106
+#114 := [monotonicity #107 #111]: #113
+#124 := [monotonicity #114 #121]: #123
+#169 := [monotonicity #124]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [quant-intro #178]: #180
+#165 := (iff #37 #164)
+#162 := (iff #36 #161)
+#159 := (= #35 #158)
+#156 := (= #34 #155)
+#153 := (= #33 #152)
+#150 := (= #32 #147)
+#144 := (- #141)
+#148 := (= #144 #147)
+#149 := [rewrite]: #148
+#145 := (= #32 #144)
+#142 := (= #31 #141)
+#87 := (= #23 #86)
+#88 := [rewrite]: #87
+#84 := (= #22 #83)
+#85 := [rewrite]: #84
+#143 := [monotonicity #85 #88]: #142
+#146 := [monotonicity #143]: #145
+#151 := [trans #146 #149]: #150
+#80 := (iff #20 #79)
+#77 := (iff #19 #76)
+#78 := [rewrite]: #77
+#81 := [monotonicity #78]: #80
+#154 := [monotonicity #81 #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [quant-intro #163]: #165
+#183 := [trans #166 #181]: #182
+#140 := [asserted]: #37
+#184 := [mp #140 #183]: #179
+#291 := [mp~ #184 #275]: #179
+#341 := [mp #291 #340]: #338
+#372 := [mp #341 #371]: #369
+#856 := [mp #372 #855]: #851
+#776 := (not #851)
+#661 := (or #776 #505)
+#430 := (* -1::int 1::int)
+#514 := (mod #430 #430)
+#515 := (+ #54 #514)
+#516 := (= #515 0::int)
+#507 := (mod 1::int 1::int)
+#518 := (* -1::int #507)
+#519 := (+ #54 #518)
+#520 := (= #519 0::int)
+#517 := (<= 1::int 0::int)
+#521 := (or #517 #517)
+#500 := (not #521)
+#835 := (>= 1::int 0::int)
+#837 := (or #517 #835)
+#494 := (not #837)
+#624 := (or #494 #500)
+#831 := (ite #624 #520 #516)
+#506 := (= 1::int 0::int)
+#838 := (ite #506 #505 #831)
+#839 := (= 1::int #54)
+#840 := (ite #506 #839 #838)
+#676 := (or #776 #840)
+#679 := (iff #676 #661)
+#680 := (iff #661 #661)
+#681 := [rewrite]: #680
+#772 := (iff #840 #505)
+#832 := (= #54 1::int)
+#667 := (ite false #832 #505)
+#775 := (iff #667 #505)
+#677 := [rewrite]: #775
+#668 := (iff #840 #667)
+#784 := (iff #838 #505)
+#779 := (ite false #505 #505)
+#783 := (iff #779 #505)
+#781 := [rewrite]: #783
+#780 := (iff #838 #779)
+#625 := (iff #831 #505)
+#1 := true
+#792 := (ite true #505 #505)
+#794 := (iff #792 #505)
+#623 := [rewrite]: #794
+#793 := (iff #831 #792)
+#785 := (iff #516 #505)
+#790 := (= #515 #54)
+#807 := (+ #54 0::int)
+#808 := (= #807 #54)
+#805 := [rewrite]: #808
+#788 := (= #515 #807)
+#645 := (= #514 0::int)
+#801 := (mod -1::int -1::int)
+#803 := (= #801 0::int)
+#644 := [rewrite]: #803
+#802 := (= #514 #801)
+#795 := (= #430 -1::int)
+#796 := [rewrite]: #795
+#797 := [monotonicity #796 #796]: #802
+#646 := [trans #797 #644]: #645
+#789 := [monotonicity #646]: #788
+#791 := [trans #789 #805]: #790
+#786 := [monotonicity #791]: #785
+#799 := (iff #520 #505)
+#809 := (= #519 #54)
+#522 := (= #519 #807)
+#528 := (= #518 0::int)
+#811 := (* -1::int 0::int)
+#526 := (= #811 0::int)
+#527 := [rewrite]: #526
+#815 := (= #518 #811)
+#810 := (= #507 0::int)
+#814 := [rewrite]: #810
+#525 := [monotonicity #814]: #815
+#806 := [trans #525 #527]: #528
+#804 := [monotonicity #806]: #522
+#798 := [trans #804 #805]: #809
+#800 := [monotonicity #798]: #799
+#535 := (iff #624 true)
+#477 := (or false true)
+#482 := (iff #477 true)
+#483 := [rewrite]: #482
+#812 := (iff #624 #477)
+#542 := (iff #500 true)
+#816 := (not false)
+#540 := (iff #816 true)
+#541 := [rewrite]: #540
+#817 := (iff #500 #816)
+#827 := (iff #521 false)
+#826 := (or false false)
+#469 := (iff #826 false)
+#829 := [rewrite]: #469
+#828 := (iff #521 #826)
+#497 := (iff #517 false)
+#833 := [rewrite]: #497
+#468 := [monotonicity #833 #833]: #828
+#830 := [trans #468 #829]: #827
+#539 := [monotonicity #830]: #817
+#436 := [trans #539 #541]: #542
+#825 := (iff #494 false)
+#821 := (not true)
+#824 := (iff #821 false)
+#819 := [rewrite]: #824
+#822 := (iff #494 #821)
+#484 := (iff #837 true)
+#818 := (iff #837 #477)
+#493 := (iff #835 true)
+#834 := [rewrite]: #493
+#481 := [monotonicity #833 #834]: #818
+#820 := [trans #481 #483]: #484
+#823 := [monotonicity #820]: #822
+#463 := [trans #823 #819]: #825
+#813 := [monotonicity #463 #436]: #812
+#536 := [trans #813 #483]: #535
+#787 := [monotonicity #536 #800 #786]: #793
+#626 := [trans #787 #623]: #625
+#841 := (iff #506 false)
+#836 := [rewrite]: #841
+#782 := [monotonicity #836 #626]: #780
+#666 := [trans #782 #781]: #784
+#842 := (iff #839 #832)
+#492 := [rewrite]: #842
+#627 := [monotonicity #836 #492 #666]: #668
+#773 := [trans #627 #677]: #772
+#672 := [monotonicity #773]: #679
+#682 := [trans #672 #681]: #679
+#678 := [quant-inst]: #676
+#683 := [mp #678 #682]: #661
+#703 := [unit-resolution #683 #856]: #505
+#699 := [monotonicity #703]: #57
+#58 := (not #57)
+#270 := [asserted]: #58
+[unit-resolution #270 #699]: false
+unsat
+553b87757f4e354afaed957c5556c64eea40e1e0 313 0
+#2 := false
+decl f5 :: (-> int S2)
+#11 := 0::int
+#57 := (f5 0::int)
+decl f4 :: (-> int int int)
+#54 := 1::int
+#53 := 3::int
+#55 := (f4 3::int 1::int)
+#56 := (f5 #55)
+#58 := (= #56 #57)
+#839 := (= #55 0::int)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#851 := (pattern #29)
+#83 := -1::int
+#87 := (* -1::int #9)
+#84 := (* -1::int #8)
+#142 := (mod #84 #87)
+#363 := (+ #29 #142)
+#364 := (= #363 0::int)
+#30 := (mod #8 #9)
+#360 := (* -1::int #30)
+#361 := (+ #29 #360)
+#362 := (= #361 0::int)
+#109 := (<= #9 0::int)
+#105 := (<= #8 0::int)
+#302 := (or #105 #109)
+#303 := (not #302)
+#116 := (>= #8 0::int)
+#285 := (or #109 #116)
+#286 := (not #285)
+#309 := (or #286 #303)
+#365 := (ite #309 #362 #364)
+#359 := (= #29 0::int)
+#12 := (= #8 0::int)
+#366 := (ite #12 #359 #365)
+#358 := (= #8 #29)
+#13 := (= #9 0::int)
+#367 := (ite #13 #358 #366)
+#852 := (forall (vars (?v0 int) (?v1 int)) (:pat #851) #367)
+#370 := (forall (vars (?v0 int) (?v1 int)) #367)
+#855 := (iff #370 #852)
+#853 := (iff #367 #367)
+#854 := [refl]: #853
+#856 := [quant-intro #854]: #855
+#148 := (* -1::int #142)
+#327 := (ite #309 #30 #148)
+#330 := (ite #12 0::int #327)
+#333 := (ite #13 #8 #330)
+#336 := (= #29 #333)
+#339 := (forall (vars (?v0 int) (?v1 int)) #336)
+#371 := (iff #339 #370)
+#368 := (iff #336 #367)
+#369 := [rewrite]: #368
+#372 := [quant-intro #369]: #371
+#117 := (not #116)
+#110 := (not #109)
+#120 := (and #110 #117)
+#106 := (not #105)
+#113 := (and #106 #110)
+#123 := (or #113 #120)
+#168 := (ite #123 #30 #148)
+#171 := (ite #12 0::int #168)
+#174 := (ite #13 #8 #171)
+#177 := (= #29 #174)
+#180 := (forall (vars (?v0 int) (?v1 int)) #177)
+#340 := (iff #180 #339)
+#337 := (iff #177 #336)
+#334 := (= #174 #333)
+#331 := (= #171 #330)
+#328 := (= #168 #327)
+#312 := (iff #123 #309)
+#306 := (or #303 #286)
+#310 := (iff #306 #309)
+#311 := [rewrite]: #310
+#307 := (iff #123 #306)
+#304 := (iff #120 #286)
+#305 := [rewrite]: #304
+#283 := (iff #113 #303)
+#284 := [rewrite]: #283
+#308 := [monotonicity #284 #305]: #307
+#313 := [trans #308 #311]: #312
+#329 := [monotonicity #313]: #328
+#332 := [monotonicity #329]: #331
+#335 := [monotonicity #332]: #334
+#338 := [monotonicity #335]: #337
+#341 := [quant-intro #338]: #340
+#275 := (~ #180 #180)
+#272 := (~ #177 #177)
+#291 := [refl]: #272
+#276 := [nnf-pos #291]: #275
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#183 := (iff #37 #180)
+#77 := (and #16 #18)
+#80 := (or #17 #77)
+#153 := (ite #80 #30 #148)
+#156 := (ite #12 0::int #153)
+#159 := (ite #13 #8 #156)
+#162 := (= #29 #159)
+#165 := (forall (vars (?v0 int) (?v1 int)) #162)
+#181 := (iff #165 #180)
+#178 := (iff #162 #177)
+#175 := (= #159 #174)
+#172 := (= #156 #171)
+#169 := (= #153 #168)
+#124 := (iff #80 #123)
+#121 := (iff #77 #120)
+#118 := (iff #18 #117)
+#119 := [rewrite]: #118
+#111 := (iff #16 #110)
+#112 := [rewrite]: #111
+#122 := [monotonicity #112 #119]: #121
+#114 := (iff #17 #113)
+#107 := (iff #15 #106)
+#108 := [rewrite]: #107
+#115 := [monotonicity #108 #112]: #114
+#125 := [monotonicity #115 #122]: #124
+#170 := [monotonicity #125]: #169
+#173 := [monotonicity #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [monotonicity #176]: #178
+#182 := [quant-intro #179]: #181
+#166 := (iff #37 #165)
+#163 := (iff #36 #162)
+#160 := (= #35 #159)
+#157 := (= #34 #156)
+#154 := (= #33 #153)
+#151 := (= #32 #148)
+#145 := (- #142)
+#149 := (= #145 #148)
+#150 := [rewrite]: #149
+#146 := (= #32 #145)
+#143 := (= #31 #142)
+#88 := (= #23 #87)
+#89 := [rewrite]: #88
+#85 := (= #22 #84)
+#86 := [rewrite]: #85
+#144 := [monotonicity #86 #89]: #143
+#147 := [monotonicity #144]: #146
+#152 := [trans #147 #150]: #151
+#81 := (iff #20 #80)
+#78 := (iff #19 #77)
+#79 := [rewrite]: #78
+#82 := [monotonicity #79]: #81
+#155 := [monotonicity #82 #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [quant-intro #164]: #166
+#184 := [trans #167 #182]: #183
+#141 := [asserted]: #37
+#185 := [mp #141 #184]: #180
+#292 := [mp~ #185 #276]: #180
+#342 := [mp #292 #341]: #339
+#373 := [mp #342 #372]: #370
+#857 := [mp #373 #856]: #852
+#685 := (not #852)
+#778 := (or #685 #839)
+#431 := (* -1::int 1::int)
+#515 := (* -1::int 3::int)
+#516 := (mod #515 #431)
+#517 := (+ #55 #516)
+#508 := (= #517 0::int)
+#519 := (mod 3::int 1::int)
+#520 := (* -1::int #519)
+#521 := (+ #55 #520)
+#518 := (= #521 0::int)
+#522 := (<= 1::int 0::int)
+#501 := (<= 3::int 0::int)
+#836 := (or #501 #522)
+#838 := (not #836)
+#495 := (>= 3::int 0::int)
+#625 := (or #522 #495)
+#832 := (not #625)
+#506 := (or #832 #838)
+#507 := (ite #506 #518 #508)
+#840 := (= 3::int 0::int)
+#841 := (ite #840 #839 #507)
+#842 := (= 3::int #55)
+#837 := (= 1::int 0::int)
+#843 := (ite #837 #842 #841)
+#775 := (or #685 #843)
+#766 := (iff #775 #778)
+#760 := (iff #778 #778)
+#757 := [rewrite]: #760
+#683 := (iff #843 #839)
+#834 := (= #55 3::int)
+#679 := (ite false #834 #839)
+#681 := (iff #679 #839)
+#682 := [rewrite]: #681
+#680 := (iff #843 #679)
+#662 := (iff #841 #839)
+#776 := (ite false #839 #839)
+#774 := (iff #776 #839)
+#777 := [rewrite]: #774
+#678 := (iff #841 #776)
+#669 := (iff #507 #839)
+#1 := true
+#784 := (ite true #839 #839)
+#667 := (iff #784 #839)
+#668 := [rewrite]: #667
+#782 := (iff #507 #784)
+#781 := (iff #508 #839)
+#627 := (= #517 #55)
+#800 := (+ #55 0::int)
+#797 := (= #800 #55)
+#802 := [rewrite]: #797
+#624 := (= #517 #800)
+#788 := (= #516 0::int)
+#646 := -3::int
+#792 := (mod -3::int -1::int)
+#793 := (= #792 0::int)
+#794 := [rewrite]: #793
+#786 := (= #516 #792)
+#790 := (= #431 -1::int)
+#791 := [rewrite]: #790
+#647 := (= #515 -3::int)
+#789 := [rewrite]: #647
+#787 := [monotonicity #789 #791]: #786
+#795 := [trans #787 #794]: #788
+#626 := [monotonicity #795]: #624
+#780 := [trans #626 #802]: #627
+#783 := [monotonicity #780]: #781
+#804 := (iff #518 #839)
+#803 := (= #521 #55)
+#801 := (= #521 #800)
+#810 := (= #520 0::int)
+#808 := (* -1::int 0::int)
+#809 := (= #808 0::int)
+#806 := [rewrite]: #809
+#523 := (= #520 #808)
+#529 := (= #519 0::int)
+#807 := [rewrite]: #529
+#805 := [monotonicity #807]: #523
+#799 := [trans #805 #806]: #810
+#796 := [monotonicity #799]: #801
+#798 := [trans #796 #802]: #803
+#645 := [monotonicity #798]: #804
+#527 := (iff #506 true)
+#485 := (or false true)
+#823 := (iff #485 true)
+#824 := [rewrite]: #823
+#816 := (iff #506 #485)
+#815 := (iff #838 true)
+#813 := (not false)
+#537 := (iff #813 true)
+#811 := [rewrite]: #537
+#814 := (iff #838 #813)
+#543 := (iff #836 false)
+#817 := (or false false)
+#541 := (iff #817 false)
+#542 := [rewrite]: #541
+#818 := (iff #836 #817)
+#819 := (iff #522 false)
+#482 := [rewrite]: #819
+#828 := (iff #501 false)
+#831 := [rewrite]: #828
+#540 := [monotonicity #831 #482]: #818
+#437 := [trans #540 #542]: #543
+#536 := [monotonicity #437]: #814
+#812 := [trans #536 #811]: #815
+#470 := (iff #832 false)
+#826 := (not true)
+#829 := (iff #826 false)
+#469 := [rewrite]: #829
+#464 := (iff #832 #826)
+#825 := (iff #625 true)
+#821 := (iff #625 #485)
+#483 := (iff #495 true)
+#484 := [rewrite]: #483
+#822 := [monotonicity #482 #484]: #821
+#820 := [trans #822 #824]: #825
+#827 := [monotonicity #820]: #464
+#830 := [trans #827 #469]: #470
+#526 := [monotonicity #830 #812]: #816
+#528 := [trans #526 #824]: #527
+#785 := [monotonicity #528 #645 #783]: #782
+#628 := [trans #785 #668]: #669
+#835 := (iff #840 false)
+#478 := [rewrite]: #835
+#773 := [monotonicity #478 #628]: #678
+#677 := [trans #773 #777]: #662
+#498 := (iff #842 #834)
+#494 := [rewrite]: #498
+#833 := (iff #837 false)
+#493 := [rewrite]: #833
+#673 := [monotonicity #493 #494 #677]: #680
+#684 := [trans #673 #682]: #683
+#768 := [monotonicity #684]: #766
+#759 := [trans #768 #757]: #766
+#779 := [quant-inst]: #775
+#769 := [mp #779 #759]: #778
+#701 := [unit-resolution #769 #857]: #839
+#702 := [monotonicity #701]: #58
+#59 := (not #58)
+#271 := [asserted]: #59
+[unit-resolution #271 #702]: false
+unsat
+7aa61137cf722d7e5bbbc51b49c9308e1f861019 447 0
+#2 := false
+#11 := 0::int
+decl f6 :: (-> S2 int)
+decl f7 :: S2
+#53 := f7
+#54 := (f6 f7)
+#496 := (>= #54 0::int)
+decl f5 :: (-> int S2)
+#762 := (f5 #54)
+#708 := (f6 #762)
+#704 := (= #708 0::int)
+#655 := (not #704)
+#841 := (= #54 0::int)
+#674 := (not #841)
+#656 := (iff #674 #655)
+#653 := (iff #841 #704)
+#651 := (iff #704 #841)
+#649 := (= #708 #54)
+#643 := (= #762 f7)
+#763 := (= f7 #762)
+#38 := (:var 0 S2)
+#39 := (f6 #38)
+#859 := (pattern #39)
+#40 := (f5 #39)
+#188 := (= #38 #40)
+#860 := (forall (vars (?v0 S2)) (:pat #859) #188)
+#191 := (forall (vars (?v0 S2)) #188)
+#861 := (iff #191 #860)
+#863 := (iff #860 #860)
+#864 := [rewrite]: #863
+#862 := [rewrite]: #861
+#865 := [trans #862 #864]: #861
+#278 := (~ #191 #191)
+#294 := (~ #188 #188)
+#295 := [refl]: #294
+#279 := [nnf-pos #295]: #278
+#41 := (= #40 #38)
+#42 := (forall (vars (?v0 S2)) #41)
+#192 := (iff #42 #191)
+#189 := (iff #41 #188)
+#190 := [rewrite]: #189
+#193 := [quant-intro #190]: #192
+#187 := [asserted]: #42
+#196 := [mp #187 #193]: #191
+#296 := [mp~ #196 #279]: #191
+#866 := [mp #296 #865]: #860
+#759 := (not #860)
+#766 := (or #759 #763)
+#750 := [quant-inst]: #766
+#688 := [unit-resolution #750 #866]: #763
+#644 := [symm #688]: #643
+#650 := [monotonicity #644]: #649
+#652 := [monotonicity #650]: #651
+#654 := [symm #652]: #653
+#657 := [monotonicity #654]: #656
+#486 := (not #496)
+#673 := [hypothesis]: #486
+#677 := (or #674 #496)
+#687 := [th-lemma]: #677
+#667 := [unit-resolution #687 #673]: #674
+#658 := [mp #667 #657]: #655
+#689 := (or #496 #704)
+#9 := (:var 0 int)
+#44 := (f5 #9)
+#867 := (pattern #44)
+#211 := (>= #9 0::int)
+#45 := (f6 #44)
+#50 := (= #45 0::int)
+#261 := (or #50 #211)
+#874 := (forall (vars (?v0 int)) (:pat #867) #261)
+#266 := (forall (vars (?v0 int)) #261)
+#877 := (iff #266 #874)
+#875 := (iff #261 #261)
+#876 := [refl]: #875
+#878 := [quant-intro #876]: #877
+#282 := (~ #266 #266)
+#300 := (~ #261 #261)
+#301 := [refl]: #300
+#283 := [nnf-pos #301]: #282
+#49 := (< #9 0::int)
+#51 := (implies #49 #50)
+#52 := (forall (vars (?v0 int)) #51)
+#269 := (iff #52 #266)
+#232 := (= 0::int #45)
+#238 := (not #49)
+#239 := (or #238 #232)
+#244 := (forall (vars (?v0 int)) #239)
+#267 := (iff #244 #266)
+#264 := (iff #239 #261)
+#258 := (or #211 #50)
+#262 := (iff #258 #261)
+#263 := [rewrite]: #262
+#259 := (iff #239 #258)
+#256 := (iff #232 #50)
+#257 := [rewrite]: #256
+#254 := (iff #238 #211)
+#214 := (not #211)
+#249 := (not #214)
+#252 := (iff #249 #211)
+#253 := [rewrite]: #252
+#250 := (iff #238 #249)
+#247 := (iff #49 #214)
+#248 := [rewrite]: #247
+#251 := [monotonicity #248]: #250
+#255 := [trans #251 #253]: #254
+#260 := [monotonicity #255 #257]: #259
+#265 := [trans #260 #263]: #264
+#268 := [quant-intro #265]: #267
+#245 := (iff #52 #244)
+#242 := (iff #51 #239)
+#235 := (implies #49 #232)
+#240 := (iff #235 #239)
+#241 := [rewrite]: #240
+#236 := (iff #51 #235)
+#233 := (iff #50 #232)
+#234 := [rewrite]: #233
+#237 := [monotonicity #234]: #236
+#243 := [trans #237 #241]: #242
+#246 := [quant-intro #243]: #245
+#270 := [trans #246 #268]: #269
+#231 := [asserted]: #52
+#271 := [mp #231 #270]: #266
+#302 := [mp~ #271 #283]: #266
+#879 := [mp #302 #878]: #874
+#729 := (not #874)
+#671 := (or #729 #496 #704)
+#709 := (or #704 #496)
+#695 := (or #729 #709)
+#662 := (iff #695 #671)
+#691 := (or #729 #689)
+#672 := (iff #691 #671)
+#631 := [rewrite]: #672
+#697 := (iff #695 #691)
+#635 := (iff #709 #689)
+#690 := [rewrite]: #635
+#665 := [monotonicity #690]: #697
+#664 := [trans #665 #631]: #662
+#696 := [quant-inst]: #695
+#666 := [mp #696 #664]: #671
+#675 := [unit-resolution #666 #879]: #689
+#676 := [unit-resolution #675 #673]: #704
+#659 := [unit-resolution #676 #658]: false
+#660 := [lemma #659]: #496
+#502 := (<= #54 0::int)
+#830 := (not #502)
+#625 := (or #486 #830 #841)
+#684 := (not #625)
+decl f4 :: (-> int int int)
+#55 := 1::int
+#56 := (f4 #54 1::int)
+#840 := (= #56 0::int)
+#760 := (not #840)
+#58 := (f5 0::int)
+#57 := (f5 #56)
+#59 := (= #57 #58)
+#645 := [hypothesis]: #840
+#661 := [monotonicity #645]: #59
+#60 := (not #59)
+#272 := [asserted]: #60
+#622 := [unit-resolution #272 #661]: false
+#623 := [lemma #622]: #760
+#632 := (or #684 #840)
+#84 := -1::int
+#516 := (* -1::int #54)
+#809 := (mod #516 -1::int)
+#810 := (+ #56 #809)
+#800 := (= #810 0::int)
+#781 := (ite #625 #840 #800)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#852 := (pattern #29)
+#88 := (* -1::int #9)
+#85 := (* -1::int #8)
+#143 := (mod #85 #88)
+#364 := (+ #29 #143)
+#365 := (= #364 0::int)
+#30 := (mod #8 #9)
+#361 := (* -1::int #30)
+#362 := (+ #29 #361)
+#363 := (= #362 0::int)
+#110 := (<= #9 0::int)
+#106 := (<= #8 0::int)
+#303 := (or #106 #110)
+#304 := (not #303)
+#117 := (>= #8 0::int)
+#286 := (or #110 #117)
+#287 := (not #286)
+#310 := (or #287 #304)
+#366 := (ite #310 #363 #365)
+#360 := (= #29 0::int)
+#12 := (= #8 0::int)
+#367 := (ite #12 #360 #366)
+#359 := (= #8 #29)
+#13 := (= #9 0::int)
+#368 := (ite #13 #359 #367)
+#853 := (forall (vars (?v0 int) (?v1 int)) (:pat #852) #368)
+#371 := (forall (vars (?v0 int) (?v1 int)) #368)
+#856 := (iff #371 #853)
+#854 := (iff #368 #368)
+#855 := [refl]: #854
+#857 := [quant-intro #855]: #856
+#149 := (* -1::int #143)
+#328 := (ite #310 #30 #149)
+#331 := (ite #12 0::int #328)
+#334 := (ite #13 #8 #331)
+#337 := (= #29 #334)
+#340 := (forall (vars (?v0 int) (?v1 int)) #337)
+#372 := (iff #340 #371)
+#369 := (iff #337 #368)
+#370 := [rewrite]: #369
+#373 := [quant-intro #370]: #372
+#118 := (not #117)
+#111 := (not #110)
+#121 := (and #111 #118)
+#107 := (not #106)
+#114 := (and #107 #111)
+#124 := (or #114 #121)
+#169 := (ite #124 #30 #149)
+#172 := (ite #12 0::int #169)
+#175 := (ite #13 #8 #172)
+#178 := (= #29 #175)
+#181 := (forall (vars (?v0 int) (?v1 int)) #178)
+#341 := (iff #181 #340)
+#338 := (iff #178 #337)
+#335 := (= #175 #334)
+#332 := (= #172 #331)
+#329 := (= #169 #328)
+#313 := (iff #124 #310)
+#307 := (or #304 #287)
+#311 := (iff #307 #310)
+#312 := [rewrite]: #311
+#308 := (iff #124 #307)
+#305 := (iff #121 #287)
+#306 := [rewrite]: #305
+#284 := (iff #114 #304)
+#285 := [rewrite]: #284
+#309 := [monotonicity #285 #306]: #308
+#314 := [trans #309 #312]: #313
+#330 := [monotonicity #314]: #329
+#333 := [monotonicity #330]: #332
+#336 := [monotonicity #333]: #335
+#339 := [monotonicity #336]: #338
+#342 := [quant-intro #339]: #341
+#276 := (~ #181 #181)
+#273 := (~ #178 #178)
+#292 := [refl]: #273
+#277 := [nnf-pos #292]: #276
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#184 := (iff #37 #181)
+#78 := (and #16 #18)
+#81 := (or #17 #78)
+#154 := (ite #81 #30 #149)
+#157 := (ite #12 0::int #154)
+#160 := (ite #13 #8 #157)
+#163 := (= #29 #160)
+#166 := (forall (vars (?v0 int) (?v1 int)) #163)
+#182 := (iff #166 #181)
+#179 := (iff #163 #178)
+#176 := (= #160 #175)
+#173 := (= #157 #172)
+#170 := (= #154 #169)
+#125 := (iff #81 #124)
+#122 := (iff #78 #121)
+#119 := (iff #18 #118)
+#120 := [rewrite]: #119
+#112 := (iff #16 #111)
+#113 := [rewrite]: #112
+#123 := [monotonicity #113 #120]: #122
+#115 := (iff #17 #114)
+#108 := (iff #15 #107)
+#109 := [rewrite]: #108
+#116 := [monotonicity #109 #113]: #115
+#126 := [monotonicity #116 #123]: #125
+#171 := [monotonicity #126]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#180 := [monotonicity #177]: #179
+#183 := [quant-intro #180]: #182
+#167 := (iff #37 #166)
+#164 := (iff #36 #163)
+#161 := (= #35 #160)
+#158 := (= #34 #157)
+#155 := (= #33 #154)
+#152 := (= #32 #149)
+#146 := (- #143)
+#150 := (= #146 #149)
+#151 := [rewrite]: #150
+#147 := (= #32 #146)
+#144 := (= #31 #143)
+#89 := (= #23 #88)
+#90 := [rewrite]: #89
+#86 := (= #22 #85)
+#87 := [rewrite]: #86
+#145 := [monotonicity #87 #90]: #144
+#148 := [monotonicity #145]: #147
+#153 := [trans #148 #151]: #152
+#82 := (iff #20 #81)
+#79 := (iff #19 #78)
+#80 := [rewrite]: #79
+#83 := [monotonicity #80]: #82
+#156 := [monotonicity #83 #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [monotonicity #162]: #164
+#168 := [quant-intro #165]: #167
+#185 := [trans #168 #183]: #184
+#142 := [asserted]: #37
+#186 := [mp #142 #185]: #181
+#293 := [mp~ #186 #277]: #181
+#343 := [mp #293 #342]: #340
+#374 := [mp #343 #373]: #371
+#858 := [mp #374 #857]: #853
+#786 := (not #853)
+#668 := (or #786 #781)
+#432 := (* -1::int 1::int)
+#517 := (mod #516 #432)
+#518 := (+ #56 #517)
+#509 := (= #518 0::int)
+#520 := (mod #54 1::int)
+#521 := (* -1::int #520)
+#522 := (+ #56 #521)
+#519 := (= #522 0::int)
+#523 := (<= 1::int 0::int)
+#837 := (or #502 #523)
+#839 := (not #837)
+#626 := (or #523 #496)
+#833 := (not #626)
+#507 := (or #833 #839)
+#508 := (ite #507 #519 #509)
+#842 := (ite #841 #840 #508)
+#843 := (= #54 #56)
+#838 := (= 1::int 0::int)
+#844 := (ite #838 #843 #842)
+#669 := (or #786 #844)
+#629 := (iff #669 #668)
+#679 := (iff #668 #668)
+#774 := [rewrite]: #679
+#785 := (iff #844 #781)
+#831 := (or #486 #830)
+#646 := (or #831 #841)
+#647 := (ite #646 #840 #800)
+#782 := (iff #647 #781)
+#627 := (iff #646 #625)
+#628 := [rewrite]: #627
+#784 := [monotonicity #628]: #782
+#789 := (iff #844 #647)
+#793 := (ite false #843 #647)
+#794 := (iff #793 #647)
+#795 := [rewrite]: #794
+#787 := (iff #844 #793)
+#791 := (iff #842 #647)
+#797 := (ite #831 #840 #800)
+#804 := (ite #841 #840 #797)
+#648 := (iff #804 #647)
+#790 := [rewrite]: #648
+#799 := (iff #842 #804)
+#798 := (iff #508 #797)
+#801 := (iff #509 #800)
+#807 := (= #518 #810)
+#524 := (= #517 #809)
+#530 := (= #432 -1::int)
+#808 := [rewrite]: #530
+#806 := [monotonicity #808]: #524
+#811 := [monotonicity #806]: #807
+#802 := [monotonicity #811]: #801
+#528 := (iff #519 #840)
+#817 := (= #522 #56)
+#537 := (+ #56 0::int)
+#816 := (= #537 #56)
+#813 := [rewrite]: #816
+#538 := (= #522 #537)
+#814 := (= #521 0::int)
+#541 := (* -1::int 0::int)
+#544 := (= #541 0::int)
+#438 := [rewrite]: #544
+#542 := (= #521 #541)
+#818 := (= #520 0::int)
+#819 := [rewrite]: #818
+#543 := [monotonicity #819]: #542
+#815 := [trans #543 #438]: #814
+#812 := [monotonicity #815]: #538
+#527 := [trans #812 #813]: #817
+#529 := [monotonicity #527]: #528
+#829 := (iff #507 #831)
+#470 := (iff #839 #830)
+#465 := (iff #837 #502)
+#824 := (or #502 false)
+#821 := (iff #824 #502)
+#827 := [rewrite]: #821
+#825 := (iff #837 #824)
+#499 := (iff #523 false)
+#835 := [rewrite]: #499
+#826 := [monotonicity #835]: #825
+#828 := [trans #826 #827]: #465
+#471 := [monotonicity #828]: #470
+#822 := (iff #833 #486)
+#484 := (iff #626 #496)
+#495 := (or false #496)
+#820 := (iff #495 #496)
+#483 := [rewrite]: #820
+#836 := (iff #626 #495)
+#479 := [monotonicity #835]: #836
+#485 := [trans #479 #483]: #484
+#823 := [monotonicity #485]: #822
+#832 := [monotonicity #823 #471]: #829
+#803 := [monotonicity #832 #529 #802]: #798
+#805 := [monotonicity #803]: #799
+#792 := [trans #805 #790]: #791
+#834 := (iff #838 false)
+#494 := [rewrite]: #834
+#788 := [monotonicity #494 #792]: #787
+#796 := [trans #788 #795]: #789
+#783 := [trans #796 #784]: #785
+#777 := [monotonicity #783]: #629
+#775 := [trans #777 #774]: #629
+#670 := [quant-inst]: #669
+#778 := [mp #670 #775]: #668
+#630 := [unit-resolution #778 #858]: #781
+#780 := (not #781)
+#767 := (or #780 #684 #840)
+#769 := [def-axiom]: #767
+#633 := [unit-resolution #769 #630]: #632
+#634 := [unit-resolution #633 #623]: #684
+#680 := (or #625 #502)
+#681 := [def-axiom]: #680
+#636 := [unit-resolution #681 #634]: #502
+#682 := (or #625 #674)
+#683 := [def-axiom]: #682
+#637 := [unit-resolution #683 #634]: #674
+#638 := (or #841 #830 #486)
+#639 := [th-lemma]: #638
+[unit-resolution #639 #637 #636 #660]: false
+unsat
+605887aef2db6fc1de967f017eea6f7e2cb901f4 305 0
+#2 := false
+decl f5 :: (-> int S2)
+#11 := 0::int
+#56 := (f5 0::int)
+decl f4 :: (-> int int int)
+#53 := 3::int
+#54 := (f4 0::int 3::int)
+#55 := (f5 #54)
+#57 := (= #55 #56)
+#507 := (= #54 0::int)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#851 := (pattern #29)
+#82 := -1::int
+#86 := (* -1::int #9)
+#83 := (* -1::int #8)
+#141 := (mod #83 #86)
+#362 := (+ #29 #141)
+#363 := (= #362 0::int)
+#30 := (mod #8 #9)
+#359 := (* -1::int #30)
+#360 := (+ #29 #359)
+#361 := (= #360 0::int)
+#108 := (<= #9 0::int)
+#104 := (<= #8 0::int)
+#301 := (or #104 #108)
+#302 := (not #301)
+#115 := (>= #8 0::int)
+#284 := (or #108 #115)
+#285 := (not #284)
+#308 := (or #285 #302)
+#364 := (ite #308 #361 #363)
+#358 := (= #29 0::int)
+#12 := (= #8 0::int)
+#365 := (ite #12 #358 #364)
+#357 := (= #8 #29)
+#13 := (= #9 0::int)
+#366 := (ite #13 #357 #365)
+#852 := (forall (vars (?v0 int) (?v1 int)) (:pat #851) #366)
+#369 := (forall (vars (?v0 int) (?v1 int)) #366)
+#855 := (iff #369 #852)
+#853 := (iff #366 #366)
+#854 := [refl]: #853
+#856 := [quant-intro #854]: #855
+#147 := (* -1::int #141)
+#326 := (ite #308 #30 #147)
+#329 := (ite #12 0::int #326)
+#332 := (ite #13 #8 #329)
+#335 := (= #29 #332)
+#338 := (forall (vars (?v0 int) (?v1 int)) #335)
+#370 := (iff #338 #369)
+#367 := (iff #335 #366)
+#368 := [rewrite]: #367
+#371 := [quant-intro #368]: #370
+#116 := (not #115)
+#109 := (not #108)
+#119 := (and #109 #116)
+#105 := (not #104)
+#112 := (and #105 #109)
+#122 := (or #112 #119)
+#167 := (ite #122 #30 #147)
+#170 := (ite #12 0::int #167)
+#173 := (ite #13 #8 #170)
+#176 := (= #29 #173)
+#179 := (forall (vars (?v0 int) (?v1 int)) #176)
+#339 := (iff #179 #338)
+#336 := (iff #176 #335)
+#333 := (= #173 #332)
+#330 := (= #170 #329)
+#327 := (= #167 #326)
+#311 := (iff #122 #308)
+#305 := (or #302 #285)
+#309 := (iff #305 #308)
+#310 := [rewrite]: #309
+#306 := (iff #122 #305)
+#303 := (iff #119 #285)
+#304 := [rewrite]: #303
+#282 := (iff #112 #302)
+#283 := [rewrite]: #282
+#307 := [monotonicity #283 #304]: #306
+#312 := [trans #307 #310]: #311
+#328 := [monotonicity #312]: #327
+#331 := [monotonicity #328]: #330
+#334 := [monotonicity #331]: #333
+#337 := [monotonicity #334]: #336
+#340 := [quant-intro #337]: #339
+#274 := (~ #179 #179)
+#271 := (~ #176 #176)
+#290 := [refl]: #271
+#275 := [nnf-pos #290]: #274
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#182 := (iff #37 #179)
+#76 := (and #16 #18)
+#79 := (or #17 #76)
+#152 := (ite #79 #30 #147)
+#155 := (ite #12 0::int #152)
+#158 := (ite #13 #8 #155)
+#161 := (= #29 #158)
+#164 := (forall (vars (?v0 int) (?v1 int)) #161)
+#180 := (iff #164 #179)
+#177 := (iff #161 #176)
+#174 := (= #158 #173)
+#171 := (= #155 #170)
+#168 := (= #152 #167)
+#123 := (iff #79 #122)
+#120 := (iff #76 #119)
+#117 := (iff #18 #116)
+#118 := [rewrite]: #117
+#110 := (iff #16 #109)
+#111 := [rewrite]: #110
+#121 := [monotonicity #111 #118]: #120
+#113 := (iff #17 #112)
+#106 := (iff #15 #105)
+#107 := [rewrite]: #106
+#114 := [monotonicity #107 #111]: #113
+#124 := [monotonicity #114 #121]: #123
+#169 := [monotonicity #124]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [quant-intro #178]: #180
+#165 := (iff #37 #164)
+#162 := (iff #36 #161)
+#159 := (= #35 #158)
+#156 := (= #34 #155)
+#153 := (= #33 #152)
+#150 := (= #32 #147)
+#144 := (- #141)
+#148 := (= #144 #147)
+#149 := [rewrite]: #148
+#145 := (= #32 #144)
+#142 := (= #31 #141)
+#87 := (= #23 #86)
+#88 := [rewrite]: #87
+#84 := (= #22 #83)
+#85 := [rewrite]: #84
+#143 := [monotonicity #85 #88]: #142
+#146 := [monotonicity #143]: #145
+#151 := [trans #146 #149]: #150
+#80 := (iff #20 #79)
+#77 := (iff #19 #76)
+#78 := [rewrite]: #77
+#81 := [monotonicity #78]: #80
+#154 := [monotonicity #81 #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [quant-intro #163]: #165
+#183 := [trans #166 #181]: #182
+#140 := [asserted]: #37
+#184 := [mp #140 #183]: #179
+#291 := [mp~ #184 #275]: #179
+#341 := [mp #291 #340]: #338
+#372 := [mp #341 #371]: #369
+#857 := [mp #372 #856]: #852
+#677 := (not #852)
+#679 := (or #677 #507)
+#430 := (* -1::int 3::int)
+#515 := (* -1::int 0::int)
+#516 := (mod #515 #430)
+#517 := (+ #54 #516)
+#508 := (= #517 0::int)
+#519 := (mod 0::int 3::int)
+#520 := (* -1::int #519)
+#448 := (+ #54 #520)
+#521 := (= #448 0::int)
+#518 := (<= 3::int 0::int)
+#522 := (<= 0::int 0::int)
+#501 := (or #522 #518)
+#836 := (not #501)
+#838 := (>= 0::int 0::int)
+#495 := (or #518 #838)
+#625 := (not #495)
+#832 := (or #625 #836)
+#506 := (ite #832 #521 #508)
+#839 := (= 0::int 0::int)
+#840 := (ite #839 #507 #506)
+#841 := (= 0::int #54)
+#842 := (= 3::int 0::int)
+#837 := (ite #842 #841 #840)
+#680 := (or #677 #837)
+#681 := (iff #680 #679)
+#683 := (iff #679 #679)
+#684 := [rewrite]: #683
+#777 := (iff #837 #507)
+#626 := (ite false #507 #507)
+#781 := (iff #626 #507)
+#783 := [rewrite]: #781
+#773 := (iff #837 #626)
+#776 := (iff #840 #507)
+#1 := true
+#785 := (ite true #507 #507)
+#669 := (iff #785 #507)
+#628 := [rewrite]: #669
+#667 := (iff #840 #785)
+#784 := (iff #506 #507)
+#627 := (iff #506 #626)
+#795 := (iff #508 #507)
+#794 := (= #517 #54)
+#806 := (+ #54 0::int)
+#800 := (= #806 #54)
+#801 := [rewrite]: #800
+#787 := (= #517 #806)
+#792 := (= #516 0::int)
+#798 := -3::int
+#646 := (mod 0::int -3::int)
+#790 := (= #646 0::int)
+#791 := [rewrite]: #790
+#647 := (= #516 #646)
+#804 := (= #430 -3::int)
+#645 := [rewrite]: #804
+#808 := (= #515 0::int)
+#523 := [rewrite]: #808
+#789 := [monotonicity #523 #645]: #647
+#786 := [trans #789 #791]: #792
+#793 := [monotonicity #786]: #787
+#788 := [trans #793 #801]: #794
+#624 := [monotonicity #788]: #795
+#802 := (iff #521 #507)
+#796 := (= #448 #54)
+#810 := (= #448 #806)
+#805 := (= #520 0::int)
+#529 := (= #520 #515)
+#527 := (= #519 0::int)
+#528 := [rewrite]: #527
+#807 := [monotonicity #528]: #529
+#809 := [trans #807 #523]: #805
+#799 := [monotonicity #809]: #810
+#797 := [trans #799 #801]: #796
+#803 := [monotonicity #797]: #802
+#816 := (iff #832 false)
+#536 := (or false false)
+#815 := (iff #536 false)
+#812 := [rewrite]: #815
+#537 := (iff #832 #536)
+#813 := (iff #836 false)
+#825 := (not true)
+#464 := (iff #825 false)
+#827 := [rewrite]: #464
+#543 := (iff #836 #825)
+#541 := (iff #501 true)
+#828 := (or true false)
+#818 := (iff #828 true)
+#540 := [rewrite]: #818
+#831 := (iff #501 #828)
+#835 := (iff #518 false)
+#478 := [rewrite]: #835
+#470 := (iff #522 true)
+#830 := [rewrite]: #470
+#817 := [monotonicity #830 #478]: #831
+#542 := [trans #817 #540]: #541
+#436 := [monotonicity #542]: #543
+#814 := [trans #436 #827]: #813
+#829 := (iff #625 false)
+#820 := (iff #625 #825)
+#823 := (iff #495 true)
+#483 := (or false true)
+#821 := (iff #483 true)
+#822 := [rewrite]: #821
+#484 := (iff #495 #483)
+#819 := (iff #838 true)
+#482 := [rewrite]: #819
+#485 := [monotonicity #478 #482]: #484
+#824 := [trans #485 #822]: #823
+#826 := [monotonicity #824]: #820
+#469 := [trans #826 #827]: #829
+#811 := [monotonicity #469 #814]: #537
+#526 := [trans #811 #812]: #816
+#780 := [monotonicity #526 #803 #624]: #627
+#782 := [trans #780 #783]: #784
+#834 := (iff #839 true)
+#494 := [rewrite]: #834
+#668 := [monotonicity #494 #782]: #667
+#678 := [trans #668 #628]: #776
+#493 := (iff #841 #507)
+#498 := [rewrite]: #493
+#843 := (iff #842 false)
+#833 := [rewrite]: #843
+#774 := [monotonicity #833 #498 #678]: #773
+#662 := [trans #774 #783]: #777
+#682 := [monotonicity #662]: #681
+#685 := [trans #682 #684]: #681
+#673 := [quant-inst]: #680
+#778 := [mp #673 #685]: #679
+#713 := [unit-resolution #778 #857]: #507
+#709 := [monotonicity #713]: #57
+#58 := (not #57)
+#270 := [asserted]: #58
+[unit-resolution #270 #709]: false
+unsat
+ad99c35859dd12a060d5c8007e61deedab6979cb 328 0
+#2 := false
+decl f5 :: (-> int S2)
+#53 := 1::int
+#57 := (f5 1::int)
+decl f4 :: (-> int int int)
+#54 := 3::int
+#55 := (f4 1::int 3::int)
+#56 := (f5 #55)
+#58 := (= #56 #57)
+#834 := (= #55 1::int)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#851 := (pattern #29)
+#11 := 0::int
+#83 := -1::int
+#87 := (* -1::int #9)
+#84 := (* -1::int #8)
+#142 := (mod #84 #87)
+#363 := (+ #29 #142)
+#364 := (= #363 0::int)
+#30 := (mod #8 #9)
+#360 := (* -1::int #30)
+#361 := (+ #29 #360)
+#362 := (= #361 0::int)
+#109 := (<= #9 0::int)
+#105 := (<= #8 0::int)
+#302 := (or #105 #109)
+#303 := (not #302)
+#116 := (>= #8 0::int)
+#285 := (or #109 #116)
+#286 := (not #285)
+#309 := (or #286 #303)
+#365 := (ite #309 #362 #364)
+#359 := (= #29 0::int)
+#12 := (= #8 0::int)
+#366 := (ite #12 #359 #365)
+#358 := (= #8 #29)
+#13 := (= #9 0::int)
+#367 := (ite #13 #358 #366)
+#852 := (forall (vars (?v0 int) (?v1 int)) (:pat #851) #367)
+#370 := (forall (vars (?v0 int) (?v1 int)) #367)
+#855 := (iff #370 #852)
+#853 := (iff #367 #367)
+#854 := [refl]: #853
+#856 := [quant-intro #854]: #855
+#148 := (* -1::int #142)
+#327 := (ite #309 #30 #148)
+#330 := (ite #12 0::int #327)
+#333 := (ite #13 #8 #330)
+#336 := (= #29 #333)
+#339 := (forall (vars (?v0 int) (?v1 int)) #336)
+#371 := (iff #339 #370)
+#368 := (iff #336 #367)
+#369 := [rewrite]: #368
+#372 := [quant-intro #369]: #371
+#117 := (not #116)
+#110 := (not #109)
+#120 := (and #110 #117)
+#106 := (not #105)
+#113 := (and #106 #110)
+#123 := (or #113 #120)
+#168 := (ite #123 #30 #148)
+#171 := (ite #12 0::int #168)
+#174 := (ite #13 #8 #171)
+#177 := (= #29 #174)
+#180 := (forall (vars (?v0 int) (?v1 int)) #177)
+#340 := (iff #180 #339)
+#337 := (iff #177 #336)
+#334 := (= #174 #333)
+#331 := (= #171 #330)
+#328 := (= #168 #327)
+#312 := (iff #123 #309)
+#306 := (or #303 #286)
+#310 := (iff #306 #309)
+#311 := [rewrite]: #310
+#307 := (iff #123 #306)
+#304 := (iff #120 #286)
+#305 := [rewrite]: #304
+#283 := (iff #113 #303)
+#284 := [rewrite]: #283
+#308 := [monotonicity #284 #305]: #307
+#313 := [trans #308 #311]: #312
+#329 := [monotonicity #313]: #328
+#332 := [monotonicity #329]: #331
+#335 := [monotonicity #332]: #334
+#338 := [monotonicity #335]: #337
+#341 := [quant-intro #338]: #340
+#275 := (~ #180 #180)
+#272 := (~ #177 #177)
+#291 := [refl]: #272
+#276 := [nnf-pos #291]: #275
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#183 := (iff #37 #180)
+#77 := (and #16 #18)
+#80 := (or #17 #77)
+#153 := (ite #80 #30 #148)
+#156 := (ite #12 0::int #153)
+#159 := (ite #13 #8 #156)
+#162 := (= #29 #159)
+#165 := (forall (vars (?v0 int) (?v1 int)) #162)
+#181 := (iff #165 #180)
+#178 := (iff #162 #177)
+#175 := (= #159 #174)
+#172 := (= #156 #171)
+#169 := (= #153 #168)
+#124 := (iff #80 #123)
+#121 := (iff #77 #120)
+#118 := (iff #18 #117)
+#119 := [rewrite]: #118
+#111 := (iff #16 #110)
+#112 := [rewrite]: #111
+#122 := [monotonicity #112 #119]: #121
+#114 := (iff #17 #113)
+#107 := (iff #15 #106)
+#108 := [rewrite]: #107
+#115 := [monotonicity #108 #112]: #114
+#125 := [monotonicity #115 #122]: #124
+#170 := [monotonicity #125]: #169
+#173 := [monotonicity #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [monotonicity #176]: #178
+#182 := [quant-intro #179]: #181
+#166 := (iff #37 #165)
+#163 := (iff #36 #162)
+#160 := (= #35 #159)
+#157 := (= #34 #156)
+#154 := (= #33 #153)
+#151 := (= #32 #148)
+#145 := (- #142)
+#149 := (= #145 #148)
+#150 := [rewrite]: #149
+#146 := (= #32 #145)
+#143 := (= #31 #142)
+#88 := (= #23 #87)
+#89 := [rewrite]: #88
+#85 := (= #22 #84)
+#86 := [rewrite]: #85
+#144 := [monotonicity #86 #89]: #143
+#147 := [monotonicity #144]: #146
+#152 := [trans #147 #150]: #151
+#81 := (iff #20 #80)
+#78 := (iff #19 #77)
+#79 := [rewrite]: #78
+#82 := [monotonicity #79]: #81
+#155 := [monotonicity #82 #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [quant-intro #164]: #166
+#184 := [trans #167 #182]: #183
+#141 := [asserted]: #37
+#185 := [mp #141 #184]: #180
+#292 := [mp~ #185 #276]: #180
+#342 := [mp #292 #341]: #339
+#373 := [mp #342 #372]: #370
+#857 := [mp #373 #856]: #852
+#762 := (not #852)
+#763 := (or #762 #834)
+#431 := (* -1::int 3::int)
+#515 := (* -1::int 1::int)
+#516 := (mod #515 #431)
+#517 := (+ #55 #516)
+#508 := (= #517 0::int)
+#519 := (mod 1::int 3::int)
+#520 := (* -1::int #519)
+#521 := (+ #55 #520)
+#518 := (= #521 0::int)
+#522 := (<= 3::int 0::int)
+#501 := (<= 1::int 0::int)
+#836 := (or #501 #522)
+#838 := (not #836)
+#495 := (>= 1::int 0::int)
+#625 := (or #522 #495)
+#832 := (not #625)
+#506 := (or #832 #838)
+#507 := (ite #506 #518 #508)
+#839 := (= #55 0::int)
+#840 := (= 1::int 0::int)
+#841 := (ite #840 #839 #507)
+#842 := (= 1::int #55)
+#837 := (= 3::int 0::int)
+#843 := (ite #837 #842 #841)
+#764 := (or #762 #843)
+#765 := (iff #764 #763)
+#750 := (iff #763 #763)
+#752 := [rewrite]: #750
+#772 := (iff #843 #834)
+#759 := (ite false #834 #834)
+#771 := (iff #759 #834)
+#767 := [rewrite]: #771
+#769 := (iff #843 #759)
+#760 := (iff #841 #834)
+#778 := (ite false #839 #834)
+#766 := (iff #778 #834)
+#768 := [rewrite]: #766
+#775 := (iff #841 #778)
+#684 := (iff #507 #834)
+#773 := -2::int
+#774 := (= #55 -2::int)
+#1 := true
+#680 := (ite true #834 #774)
+#682 := (iff #680 #834)
+#683 := [rewrite]: #682
+#673 := (iff #507 #680)
+#677 := (iff #508 #774)
+#795 := 2::int
+#782 := (+ 2::int #55)
+#628 := (= #782 0::int)
+#777 := (iff #628 #774)
+#662 := [rewrite]: #777
+#776 := (iff #508 #628)
+#668 := (= #517 #782)
+#781 := (+ #55 2::int)
+#785 := (= #781 #782)
+#667 := [rewrite]: #785
+#783 := (= #517 #781)
+#627 := (= #516 2::int)
+#792 := -3::int
+#793 := (mod -1::int -3::int)
+#624 := (= #793 2::int)
+#626 := [rewrite]: #624
+#794 := (= #516 #793)
+#786 := (= #431 -3::int)
+#787 := [rewrite]: #786
+#805 := (= #515 -1::int)
+#809 := [rewrite]: #805
+#788 := [monotonicity #809 #787]: #794
+#780 := [trans #788 #626]: #627
+#784 := [monotonicity #780]: #783
+#669 := [trans #784 #667]: #668
+#678 := [monotonicity #669]: #776
+#679 := [trans #678 #662]: #677
+#790 := (iff #518 #834)
+#796 := (+ -1::int #55)
+#804 := (= #796 0::int)
+#647 := (iff #804 #834)
+#789 := [rewrite]: #647
+#645 := (iff #518 #804)
+#803 := (= #521 #796)
+#799 := (+ #55 -1::int)
+#797 := (= #799 #796)
+#802 := [rewrite]: #797
+#800 := (= #521 #799)
+#806 := (= #520 -1::int)
+#808 := (= #520 #515)
+#529 := (= #519 1::int)
+#807 := [rewrite]: #529
+#523 := [monotonicity #807]: #808
+#810 := [trans #523 #809]: #806
+#801 := [monotonicity #810]: #800
+#798 := [trans #801 #802]: #803
+#646 := [monotonicity #798]: #645
+#791 := [trans #646 #789]: #790
+#527 := (iff #506 true)
+#485 := (or false true)
+#823 := (iff #485 true)
+#824 := [rewrite]: #823
+#816 := (iff #506 #485)
+#815 := (iff #838 true)
+#813 := (not false)
+#537 := (iff #813 true)
+#811 := [rewrite]: #537
+#814 := (iff #838 #813)
+#543 := (iff #836 false)
+#817 := (or false false)
+#541 := (iff #817 false)
+#542 := [rewrite]: #541
+#818 := (iff #836 #817)
+#819 := (iff #522 false)
+#482 := [rewrite]: #819
+#828 := (iff #501 false)
+#831 := [rewrite]: #828
+#540 := [monotonicity #831 #482]: #818
+#437 := [trans #540 #542]: #543
+#536 := [monotonicity #437]: #814
+#812 := [trans #536 #811]: #815
+#470 := (iff #832 false)
+#826 := (not true)
+#829 := (iff #826 false)
+#469 := [rewrite]: #829
+#464 := (iff #832 #826)
+#825 := (iff #625 true)
+#821 := (iff #625 #485)
+#483 := (iff #495 true)
+#484 := [rewrite]: #483
+#822 := [monotonicity #482 #484]: #821
+#820 := [trans #822 #824]: #825
+#827 := [monotonicity #820]: #464
+#830 := [trans #827 #469]: #470
+#526 := [monotonicity #830 #812]: #816
+#528 := [trans #526 #824]: #527
+#681 := [monotonicity #528 #791 #679]: #673
+#685 := [trans #681 #683]: #684
+#835 := (iff #840 false)
+#478 := [rewrite]: #835
+#779 := [monotonicity #478 #685]: #775
+#757 := [trans #779 #768]: #760
+#498 := (iff #842 #834)
+#494 := [rewrite]: #498
+#833 := (iff #837 false)
+#493 := [rewrite]: #833
+#770 := [monotonicity #493 #494 #757]: #769
+#761 := [trans #770 #767]: #772
+#749 := [monotonicity #761]: #765
+#753 := [trans #749 #752]: #765
+#758 := [quant-inst]: #764
+#754 := [mp #758 #753]: #763
+#703 := [unit-resolution #754 #857]: #834
+#708 := [monotonicity #703]: #58
+#59 := (not #58)
+#271 := [asserted]: #59
+[unit-resolution #271 #708]: false
+unsat
+38f50cef581a3bd6e214a067d77920bd5e0a7c47 303 0
 #2 := false
 decl f5 :: (-> int S2)
 #11 := 0::int
@@ -19646,7 +19663,1213 @@
 #270 := [asserted]: #58
 [unit-resolution #270 #700]: false
 unsat
-dfe2acff8e1fa8b5c4e4ba1cf8fef0ce4556ee21 848 0
+e9653bbdabe90411c23d58da2e6d56517bf2c0fa 533 0
+#2 := false
+#55 := 3::int
+decl f6 :: (-> S2 int)
+decl f7 :: S2
+#53 := f7
+#54 := (f6 f7)
+#533 := (mod #54 3::int)
+#664 := (>= #533 3::int)
+#665 := (not #664)
+#1 := true
+#75 := [true-axiom]: true
+#674 := (or false #665)
+#635 := [th-lemma]: #674
+#636 := [unit-resolution #635 #75]: #665
+#11 := 0::int
+decl f5 :: (-> int S2)
+decl f4 :: (-> int int int)
+#56 := (f4 #54 3::int)
+#57 := (f5 #56)
+#58 := (f6 #57)
+#84 := -1::int
+#779 := (* -1::int #58)
+#763 := (+ #56 #779)
+#766 := (>= #763 0::int)
+#773 := (= #56 #58)
+#780 := (>= #56 0::int)
+#784 := (= #58 0::int)
+#649 := (not #784)
+#746 := (<= #58 0::int)
+#643 := (not #746)
+#276 := (>= #58 3::int)
+#59 := (< #58 3::int)
+#60 := (not #59)
+#284 := (iff #60 #276)
+#275 := (not #276)
+#279 := (not #275)
+#282 := (iff #279 #276)
+#283 := [rewrite]: #282
+#280 := (iff #60 #279)
+#277 := (iff #59 #275)
+#278 := [rewrite]: #277
+#281 := [monotonicity #278]: #280
+#285 := [trans #281 #283]: #284
+#272 := [asserted]: #60
+#286 := [mp #272 #285]: #276
+#645 := (or #643 #275)
+#646 := [th-lemma]: #645
+#647 := [unit-resolution #646 #286]: #643
+#650 := (or #649 #746)
+#651 := [th-lemma]: #650
+#652 := [unit-resolution #651 #647]: #649
+#9 := (:var 0 int)
+#44 := (f5 #9)
+#880 := (pattern #44)
+#211 := (>= #9 0::int)
+#45 := (f6 #44)
+#50 := (= #45 0::int)
+#261 := (or #50 #211)
+#887 := (forall (vars (?v0 int)) (:pat #880) #261)
+#266 := (forall (vars (?v0 int)) #261)
+#890 := (iff #266 #887)
+#888 := (iff #261 #261)
+#889 := [refl]: #888
+#891 := [quant-intro #889]: #890
+#294 := (~ #266 #266)
+#312 := (~ #261 #261)
+#313 := [refl]: #312
+#295 := [nnf-pos #313]: #294
+#49 := (< #9 0::int)
+#51 := (implies #49 #50)
+#52 := (forall (vars (?v0 int)) #51)
+#269 := (iff #52 #266)
+#232 := (= 0::int #45)
+#238 := (not #49)
+#239 := (or #238 #232)
+#244 := (forall (vars (?v0 int)) #239)
+#267 := (iff #244 #266)
+#264 := (iff #239 #261)
+#258 := (or #211 #50)
+#262 := (iff #258 #261)
+#263 := [rewrite]: #262
+#259 := (iff #239 #258)
+#256 := (iff #232 #50)
+#257 := [rewrite]: #256
+#254 := (iff #238 #211)
+#214 := (not #211)
+#249 := (not #214)
+#252 := (iff #249 #211)
+#253 := [rewrite]: #252
+#250 := (iff #238 #249)
+#247 := (iff #49 #214)
+#248 := [rewrite]: #247
+#251 := [monotonicity #248]: #250
+#255 := [trans #251 #253]: #254
+#260 := [monotonicity #255 #257]: #259
+#265 := [trans #260 #263]: #264
+#268 := [quant-intro #265]: #267
+#245 := (iff #52 #244)
+#242 := (iff #51 #239)
+#235 := (implies #49 #232)
+#240 := (iff #235 #239)
+#241 := [rewrite]: #240
+#236 := (iff #51 #235)
+#233 := (iff #50 #232)
+#234 := [rewrite]: #233
+#237 := [monotonicity #234]: #236
+#243 := [trans #237 #241]: #242
+#246 := [quant-intro #243]: #245
+#270 := [trans #246 #268]: #269
+#231 := [asserted]: #52
+#271 := [mp #231 #270]: #266
+#314 := [mp~ #271 #295]: #266
+#892 := [mp #314 #891]: #887
+#765 := (not #887)
+#770 := (or #765 #780 #784)
+#785 := (or #784 #780)
+#756 := (or #765 #785)
+#742 := (iff #756 #770)
+#767 := (or #780 #784)
+#759 := (or #765 #767)
+#758 := (iff #759 #770)
+#762 := [rewrite]: #758
+#760 := (iff #756 #759)
+#768 := (iff #785 #767)
+#769 := [rewrite]: #768
+#761 := [monotonicity #769]: #760
+#743 := [trans #761 #762]: #742
+#757 := [quant-inst]: #756
+#745 := [mp #757 #743]: #770
+#653 := [unit-resolution #745 #892 #652]: #780
+#782 := (not #780)
+#783 := (or #773 #782)
+#195 := (= #9 #45)
+#220 := (or #195 #214)
+#881 := (forall (vars (?v0 int)) (:pat #880) #220)
+#225 := (forall (vars (?v0 int)) #220)
+#884 := (iff #225 #881)
+#882 := (iff #220 #220)
+#883 := [refl]: #882
+#885 := [quant-intro #883]: #884
+#292 := (~ #225 #225)
+#309 := (~ #220 #220)
+#310 := [refl]: #309
+#293 := [nnf-pos #310]: #292
+#46 := (= #45 #9)
+#43 := (<= 0::int #9)
+#47 := (implies #43 #46)
+#48 := (forall (vars (?v0 int)) #47)
+#228 := (iff #48 #225)
+#202 := (not #43)
+#203 := (or #202 #195)
+#208 := (forall (vars (?v0 int)) #203)
+#226 := (iff #208 #225)
+#223 := (iff #203 #220)
+#217 := (or #214 #195)
+#221 := (iff #217 #220)
+#222 := [rewrite]: #221
+#218 := (iff #203 #217)
+#215 := (iff #202 #214)
+#212 := (iff #43 #211)
+#213 := [rewrite]: #212
+#216 := [monotonicity #213]: #215
+#219 := [monotonicity #216]: #218
+#224 := [trans #219 #222]: #223
+#227 := [quant-intro #224]: #226
+#209 := (iff #48 #208)
+#206 := (iff #47 #203)
+#199 := (implies #43 #195)
+#204 := (iff #199 #203)
+#205 := [rewrite]: #204
+#200 := (iff #47 #199)
+#197 := (iff #46 #195)
+#198 := [rewrite]: #197
+#201 := [monotonicity #198]: #200
+#207 := [trans #201 #205]: #206
+#210 := [quant-intro #207]: #209
+#229 := [trans #210 #227]: #228
+#194 := [asserted]: #48
+#230 := [mp #194 #229]: #225
+#311 := [mp~ #230 #293]: #225
+#886 := [mp #311 #885]: #881
+#781 := (not #881)
+#786 := (or #781 #773 #782)
+#775 := (or #781 #783)
+#777 := (iff #775 #786)
+#778 := [rewrite]: #777
+#776 := [quant-inst]: #775
+#772 := [mp #776 #778]: #786
+#654 := [unit-resolution #772 #886]: #783
+#637 := [unit-resolution #654 #653]: #773
+#655 := (not #773)
+#625 := (or #655 #766)
+#626 := [th-lemma]: #625
+#627 := [unit-resolution #626 #637]: #766
+#534 := (* -1::int #533)
+#462 := (+ #56 #534)
+#802 := (<= #462 0::int)
+#535 := (= #462 0::int)
+#556 := -3::int
+#529 := (* -1::int #54)
+#827 := (mod #529 -3::int)
+#551 := (+ #56 #827)
+#826 := (= #551 0::int)
+#852 := (>= #54 0::int)
+#498 := (not #852)
+#536 := (<= #54 0::int)
+#841 := (not #536)
+#845 := (or #841 #498)
+#541 := (ite #845 #535 #826)
+#521 := (= #56 0::int)
+#853 := (= #54 0::int)
+#821 := (ite #853 #521 #541)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#865 := (pattern #29)
+#88 := (* -1::int #9)
+#85 := (* -1::int #8)
+#143 := (mod #85 #88)
+#376 := (+ #29 #143)
+#377 := (= #376 0::int)
+#30 := (mod #8 #9)
+#373 := (* -1::int #30)
+#374 := (+ #29 #373)
+#375 := (= #374 0::int)
+#110 := (<= #9 0::int)
+#106 := (<= #8 0::int)
+#315 := (or #106 #110)
+#316 := (not #315)
+#117 := (>= #8 0::int)
+#298 := (or #110 #117)
+#299 := (not #298)
+#322 := (or #299 #316)
+#378 := (ite #322 #375 #377)
+#372 := (= #29 0::int)
+#12 := (= #8 0::int)
+#379 := (ite #12 #372 #378)
+#371 := (= #8 #29)
+#13 := (= #9 0::int)
+#380 := (ite #13 #371 #379)
+#866 := (forall (vars (?v0 int) (?v1 int)) (:pat #865) #380)
+#383 := (forall (vars (?v0 int) (?v1 int)) #380)
+#869 := (iff #383 #866)
+#867 := (iff #380 #380)
+#868 := [refl]: #867
+#870 := [quant-intro #868]: #869
+#149 := (* -1::int #143)
+#340 := (ite #322 #30 #149)
+#343 := (ite #12 0::int #340)
+#346 := (ite #13 #8 #343)
+#349 := (= #29 #346)
+#352 := (forall (vars (?v0 int) (?v1 int)) #349)
+#384 := (iff #352 #383)
+#381 := (iff #349 #380)
+#382 := [rewrite]: #381
+#385 := [quant-intro #382]: #384
+#118 := (not #117)
+#111 := (not #110)
+#121 := (and #111 #118)
+#107 := (not #106)
+#114 := (and #107 #111)
+#124 := (or #114 #121)
+#169 := (ite #124 #30 #149)
+#172 := (ite #12 0::int #169)
+#175 := (ite #13 #8 #172)
+#178 := (= #29 #175)
+#181 := (forall (vars (?v0 int) (?v1 int)) #178)
+#353 := (iff #181 #352)
+#350 := (iff #178 #349)
+#347 := (= #175 #346)
+#344 := (= #172 #343)
+#341 := (= #169 #340)
+#325 := (iff #124 #322)
+#319 := (or #316 #299)
+#323 := (iff #319 #322)
+#324 := [rewrite]: #323
+#320 := (iff #124 #319)
+#317 := (iff #121 #299)
+#318 := [rewrite]: #317
+#296 := (iff #114 #316)
+#297 := [rewrite]: #296
+#321 := [monotonicity #297 #318]: #320
+#326 := [trans #321 #324]: #325
+#342 := [monotonicity #326]: #341
+#345 := [monotonicity #342]: #344
+#348 := [monotonicity #345]: #347
+#351 := [monotonicity #348]: #350
+#354 := [quant-intro #351]: #353
+#288 := (~ #181 #181)
+#273 := (~ #178 #178)
+#304 := [refl]: #273
+#289 := [nnf-pos #304]: #288
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#184 := (iff #37 #181)
+#78 := (and #16 #18)
+#81 := (or #17 #78)
+#154 := (ite #81 #30 #149)
+#157 := (ite #12 0::int #154)
+#160 := (ite #13 #8 #157)
+#163 := (= #29 #160)
+#166 := (forall (vars (?v0 int) (?v1 int)) #163)
+#182 := (iff #166 #181)
+#179 := (iff #163 #178)
+#176 := (= #160 #175)
+#173 := (= #157 #172)
+#170 := (= #154 #169)
+#125 := (iff #81 #124)
+#122 := (iff #78 #121)
+#119 := (iff #18 #118)
+#120 := [rewrite]: #119
+#112 := (iff #16 #111)
+#113 := [rewrite]: #112
+#123 := [monotonicity #113 #120]: #122
+#115 := (iff #17 #114)
+#108 := (iff #15 #107)
+#109 := [rewrite]: #108
+#116 := [monotonicity #109 #113]: #115
+#126 := [monotonicity #116 #123]: #125
+#171 := [monotonicity #126]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#180 := [monotonicity #177]: #179
+#183 := [quant-intro #180]: #182
+#167 := (iff #37 #166)
+#164 := (iff #36 #163)
+#161 := (= #35 #160)
+#158 := (= #34 #157)
+#155 := (= #33 #154)
+#152 := (= #32 #149)
+#146 := (- #143)
+#150 := (= #146 #149)
+#151 := [rewrite]: #150
+#147 := (= #32 #146)
+#144 := (= #31 #143)
+#89 := (= #23 #88)
+#90 := [rewrite]: #89
+#86 := (= #22 #85)
+#87 := [rewrite]: #86
+#145 := [monotonicity #87 #90]: #144
+#148 := [monotonicity #145]: #147
+#153 := [trans #148 #151]: #152
+#82 := (iff #20 #81)
+#79 := (iff #19 #78)
+#80 := [rewrite]: #79
+#83 := [monotonicity #80]: #82
+#156 := [monotonicity #83 #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [monotonicity #162]: #164
+#168 := [quant-intro #165]: #167
+#185 := [trans #168 #183]: #184
+#142 := [asserted]: #37
+#186 := [mp #142 #185]: #181
+#305 := [mp~ #186 #289]: #181
+#355 := [mp #305 #354]: #352
+#386 := [mp #355 #385]: #383
+#871 := [mp #386 #870]: #866
+#810 := (not #866)
+#811 := (or #810 #821)
+#444 := (* -1::int 3::int)
+#530 := (mod #529 #444)
+#531 := (+ #56 #530)
+#522 := (= #531 0::int)
+#532 := (<= 3::int 0::int)
+#515 := (or #536 #532)
+#850 := (not #515)
+#509 := (or #532 #852)
+#639 := (not #509)
+#846 := (or #639 #850)
+#520 := (ite #846 #535 #522)
+#854 := (ite #853 #521 #520)
+#855 := (= #54 #56)
+#856 := (= 3::int 0::int)
+#851 := (ite #856 #855 #854)
+#816 := (or #810 #851)
+#812 := (iff #816 #811)
+#659 := (iff #811 #811)
+#660 := [rewrite]: #659
+#814 := (iff #851 #821)
+#819 := (ite false #855 #821)
+#824 := (iff #819 #821)
+#813 := [rewrite]: #824
+#823 := (iff #851 #819)
+#822 := (iff #854 #821)
+#542 := (iff #520 #541)
+#830 := (iff #522 #826)
+#825 := (= #531 #551)
+#828 := (= #530 #827)
+#557 := (= #444 -3::int)
+#450 := [rewrite]: #557
+#550 := [monotonicity #450]: #828
+#829 := [monotonicity #550]: #825
+#540 := [monotonicity #829]: #830
+#554 := (iff #846 #845)
+#484 := (or #498 #841)
+#831 := (iff #484 #845)
+#832 := [rewrite]: #831
+#844 := (iff #846 #484)
+#843 := (iff #850 #841)
+#840 := (iff #515 #536)
+#836 := (or #536 false)
+#839 := (iff #836 #536)
+#834 := [rewrite]: #839
+#837 := (iff #515 #836)
+#507 := (iff #532 false)
+#512 := [rewrite]: #507
+#838 := [monotonicity #512]: #837
+#478 := [trans #838 #834]: #840
+#483 := [monotonicity #478]: #843
+#499 := (iff #639 #498)
+#496 := (iff #509 #852)
+#848 := (or false #852)
+#492 := (iff #848 #852)
+#833 := [rewrite]: #492
+#508 := (iff #509 #848)
+#849 := [monotonicity #512]: #508
+#497 := [trans #849 #833]: #496
+#835 := [monotonicity #497]: #499
+#842 := [monotonicity #835 #483]: #844
+#555 := [trans #842 #832]: #554
+#543 := [monotonicity #555 #540]: #542
+#537 := [monotonicity #543]: #822
+#857 := (iff #856 false)
+#847 := [rewrite]: #857
+#820 := [monotonicity #847 #537]: #823
+#815 := [trans #820 #813]: #814
+#818 := [monotonicity #815]: #812
+#661 := [trans #818 #660]: #812
+#817 := [quant-inst]: #816
+#803 := [mp #817 #661]: #811
+#628 := [unit-resolution #803 #871]: #821
+#692 := (not #853)
+#691 := (not #521)
+#633 := (iff #649 #691)
+#632 := (iff #784 #521)
+#630 := (iff #521 #784)
+#631 := [monotonicity #637]: #630
+#475 := [symm #631]: #632
+#629 := [monotonicity #475]: #633
+#634 := [mp #652 #629]: #691
+#790 := (not #821)
+#787 := (or #790 #692 #521)
+#788 := [def-axiom]: #787
+#613 := [unit-resolution #788 #634 #628]: #692
+#791 := (or #790 #853 #541)
+#676 := [def-axiom]: #791
+#616 := [unit-resolution #676 #613 #628]: #541
+#696 := (f5 #54)
+#748 := (f6 #696)
+#749 := (= #748 0::int)
+#614 := (not #749)
+#619 := (iff #692 #614)
+#617 := (iff #853 #749)
+#612 := (iff #749 #853)
+#621 := (= #748 #54)
+#622 := (= #696 f7)
+#697 := (= f7 #696)
+#38 := (:var 0 S2)
+#39 := (f6 #38)
+#872 := (pattern #39)
+#40 := (f5 #39)
+#188 := (= #38 #40)
+#873 := (forall (vars (?v0 S2)) (:pat #872) #188)
+#191 := (forall (vars (?v0 S2)) #188)
+#874 := (iff #191 #873)
+#876 := (iff #873 #873)
+#877 := [rewrite]: #876
+#875 := [rewrite]: #874
+#878 := [trans #875 #877]: #874
+#290 := (~ #191 #191)
+#306 := (~ #188 #188)
+#307 := [refl]: #306
+#291 := [nnf-pos #307]: #290
+#41 := (= #40 #38)
+#42 := (forall (vars (?v0 S2)) #41)
+#192 := (iff #42 #191)
+#189 := (iff #41 #188)
+#190 := [rewrite]: #189
+#193 := [quant-intro #190]: #192
+#187 := [asserted]: #42
+#196 := [mp #187 #193]: #191
+#308 := [mp~ #196 #291]: #191
+#879 := [mp #308 #878]: #873
+#792 := (not #873)
+#789 := (or #792 #697)
+#793 := [quant-inst]: #789
+#620 := [unit-resolution #793 #879]: #697
+#623 := [symm #620]: #622
+#624 := [monotonicity #623]: #621
+#615 := [monotonicity #624]: #612
+#618 := [symm #615]: #617
+#609 := [monotonicity #618]: #619
+#599 := [mp #613 #609]: #614
+#750 := (or #749 #852)
+#753 := (or #765 #749 #852)
+#754 := (or #765 #750)
+#755 := (iff #754 #753)
+#733 := [rewrite]: #755
+#744 := [quant-inst]: #754
+#734 := [mp #744 #733]: #753
+#601 := [unit-resolution #734 #892]: #750
+#602 := [unit-resolution #601 #599]: #852
+#605 := (or #853 #841 #498)
+#606 := [th-lemma]: #605
+#610 := [unit-resolution #606 #613]: #845
+#603 := [unit-resolution #610 #602]: #841
+#804 := (or #845 #536)
+#805 := [def-axiom]: #804
+#611 := [unit-resolution #805 #603]: #845
+#801 := (not #845)
+#641 := (not #541)
+#794 := (or #641 #801 #535)
+#795 := [def-axiom]: #794
+#604 := [unit-resolution #795 #611 #616]: #535
+#796 := (not #535)
+#607 := (or #796 #802)
+#608 := [th-lemma]: #607
+#594 := [unit-resolution #608 #604]: #802
+[th-lemma #594 #286 #627 #636]: false
+unsat
+9a3fc48607c2a546441c817d6b983f5f594a50cf 671 0
+#2 := false
+decl f6 :: (-> S2 int)
+decl f5 :: (-> int S2)
+decl f4 :: (-> int int int)
+#55 := 3::int
+decl f7 :: S2
+#53 := f7
+#54 := (f6 f7)
+#56 := (f4 #54 3::int)
+#57 := (f5 #56)
+#805 := (f6 #57)
+#806 := (= #56 #805)
+#476 := (not #806)
+#514 := (= #54 #56)
+#692 := (not #514)
+#473 := (iff #692 #476)
+#483 := (iff #514 #806)
+#490 := (iff #806 #514)
+#679 := (= #56 #54)
+#486 := (iff #679 #514)
+#489 := [commutativity]: #486
+#481 := (iff #806 #679)
+#494 := (= #805 #54)
+#58 := (= #57 f7)
+#274 := (= f7 #57)
+#286 := (>= #54 3::int)
+#11 := 0::int
+#870 := (= #56 0::int)
+#549 := (iff #870 #514)
+#547 := (iff #514 #870)
+#702 := (= 0::int #56)
+#545 := (iff #702 #870)
+#546 := [commutativity]: #545
+#541 := (iff #514 #702)
+#530 := (= #54 0::int)
+#285 := (not #286)
+#632 := [hypothesis]: #285
+#538 := (or #530 #286)
+#708 := 1::int
+#769 := (div #54 3::int)
+#628 := -2::int
+#618 := (* -2::int #769)
+#661 := (mod #54 3::int)
+#85 := -1::int
+#868 := (* -1::int #661)
+#619 := (+ #868 #618)
+#617 := (+ #54 #619)
+#620 := (>= #617 1::int)
+#627 := (not #620)
+#802 := (>= #56 0::int)
+#729 := (>= #661 0::int)
+#1 := true
+#76 := [true-axiom]: true
+#630 := (or false #729)
+#616 := [th-lemma]: #630
+#602 := [unit-resolution #616 #76]: #729
+#542 := (+ #56 #868)
+#817 := (>= #542 0::int)
+#543 := (= #542 0::int)
+#572 := -3::int
+#537 := (* -1::int #54)
+#851 := (mod #537 -3::int)
+#562 := (+ #56 #851)
+#565 := (= #562 0::int)
+#876 := (<= #54 0::int)
+#577 := (not #876)
+#873 := (>= #54 0::int)
+#863 := (not #873)
+#472 := (or #863 #577)
+#559 := (ite #472 #543 #565)
+#713 := (not #530)
+#604 := [hypothesis]: #713
+#606 := (or #530 #559)
+#842 := (ite #530 #870 #559)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#887 := (pattern #29)
+#89 := (* -1::int #9)
+#86 := (* -1::int #8)
+#144 := (mod #86 #89)
+#398 := (+ #29 #144)
+#399 := (= #398 0::int)
+#30 := (mod #8 #9)
+#395 := (* -1::int #30)
+#396 := (+ #29 #395)
+#397 := (= #396 0::int)
+#111 := (<= #9 0::int)
+#107 := (<= #8 0::int)
+#337 := (or #107 #111)
+#338 := (not #337)
+#118 := (>= #8 0::int)
+#320 := (or #111 #118)
+#321 := (not #320)
+#344 := (or #321 #338)
+#400 := (ite #344 #397 #399)
+#394 := (= #29 0::int)
+#12 := (= #8 0::int)
+#401 := (ite #12 #394 #400)
+#393 := (= #8 #29)
+#13 := (= #9 0::int)
+#402 := (ite #13 #393 #401)
+#888 := (forall (vars (?v0 int) (?v1 int)) (:pat #887) #402)
+#405 := (forall (vars (?v0 int) (?v1 int)) #402)
+#891 := (iff #405 #888)
+#889 := (iff #402 #402)
+#890 := [refl]: #889
+#892 := [quant-intro #890]: #891
+#150 := (* -1::int #144)
+#362 := (ite #344 #30 #150)
+#365 := (ite #12 0::int #362)
+#368 := (ite #13 #8 #365)
+#371 := (= #29 #368)
+#374 := (forall (vars (?v0 int) (?v1 int)) #371)
+#406 := (iff #374 #405)
+#403 := (iff #371 #402)
+#404 := [rewrite]: #403
+#407 := [quant-intro #404]: #406
+#119 := (not #118)
+#112 := (not #111)
+#122 := (and #112 #119)
+#108 := (not #107)
+#115 := (and #108 #112)
+#125 := (or #115 #122)
+#170 := (ite #125 #30 #150)
+#173 := (ite #12 0::int #170)
+#176 := (ite #13 #8 #173)
+#179 := (= #29 #176)
+#182 := (forall (vars (?v0 int) (?v1 int)) #179)
+#375 := (iff #182 #374)
+#372 := (iff #179 #371)
+#369 := (= #176 #368)
+#366 := (= #173 #365)
+#363 := (= #170 #362)
+#347 := (iff #125 #344)
+#341 := (or #338 #321)
+#345 := (iff #341 #344)
+#346 := [rewrite]: #345
+#342 := (iff #125 #341)
+#339 := (iff #122 #321)
+#340 := [rewrite]: #339
+#318 := (iff #115 #338)
+#319 := [rewrite]: #318
+#343 := [monotonicity #319 #340]: #342
+#348 := [trans #343 #346]: #347
+#364 := [monotonicity #348]: #363
+#367 := [monotonicity #364]: #366
+#370 := [monotonicity #367]: #369
+#373 := [monotonicity #370]: #372
+#376 := [quant-intro #373]: #375
+#310 := (~ #182 #182)
+#307 := (~ #179 #179)
+#326 := [refl]: #307
+#311 := [nnf-pos #326]: #310
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#185 := (iff #37 #182)
+#79 := (and #16 #18)
+#82 := (or #17 #79)
+#155 := (ite #82 #30 #150)
+#158 := (ite #12 0::int #155)
+#161 := (ite #13 #8 #158)
+#164 := (= #29 #161)
+#167 := (forall (vars (?v0 int) (?v1 int)) #164)
+#183 := (iff #167 #182)
+#180 := (iff #164 #179)
+#177 := (= #161 #176)
+#174 := (= #158 #173)
+#171 := (= #155 #170)
+#126 := (iff #82 #125)
+#123 := (iff #79 #122)
+#120 := (iff #18 #119)
+#121 := [rewrite]: #120
+#113 := (iff #16 #112)
+#114 := [rewrite]: #113
+#124 := [monotonicity #114 #121]: #123
+#116 := (iff #17 #115)
+#109 := (iff #15 #108)
+#110 := [rewrite]: #109
+#117 := [monotonicity #110 #114]: #116
+#127 := [monotonicity #117 #124]: #126
+#172 := [monotonicity #127]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [monotonicity #178]: #180
+#184 := [quant-intro #181]: #183
+#168 := (iff #37 #167)
+#165 := (iff #36 #164)
+#162 := (= #35 #161)
+#159 := (= #34 #158)
+#156 := (= #33 #155)
+#153 := (= #32 #150)
+#147 := (- #144)
+#151 := (= #147 #150)
+#152 := [rewrite]: #151
+#148 := (= #32 #147)
+#145 := (= #31 #144)
+#90 := (= #23 #89)
+#91 := [rewrite]: #90
+#87 := (= #22 #86)
+#88 := [rewrite]: #87
+#146 := [monotonicity #88 #91]: #145
+#149 := [monotonicity #146]: #148
+#154 := [trans #149 #152]: #153
+#83 := (iff #20 #82)
+#80 := (iff #19 #79)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#157 := [monotonicity #84 #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [monotonicity #163]: #165
+#169 := [quant-intro #166]: #168
+#186 := [trans #169 #184]: #185
+#143 := [asserted]: #37
+#187 := [mp #143 #186]: #182
+#327 := [mp~ #187 #311]: #182
+#377 := [mp #327 #376]: #374
+#408 := [mp #377 #407]: #405
+#893 := [mp #408 #892]: #888
+#840 := (not #888)
+#681 := (or #840 #842)
+#558 := (* -1::int 3::int)
+#872 := (mod #537 #558)
+#874 := (+ #56 #872)
+#531 := (= #874 0::int)
+#875 := (<= 3::int 0::int)
+#877 := (or #876 #875)
+#878 := (not #877)
+#879 := (or #875 #873)
+#869 := (not #879)
+#529 := (or #869 #878)
+#534 := (ite #529 #543 #531)
+#871 := (ite #530 #870 #534)
+#855 := (= 3::int 0::int)
+#518 := (ite #855 #514 #871)
+#682 := (or #840 #518)
+#825 := (iff #682 #681)
+#827 := (iff #681 #681)
+#828 := [rewrite]: #827
+#839 := (iff #518 #842)
+#836 := (ite false #514 #842)
+#833 := (iff #836 #842)
+#838 := [rewrite]: #833
+#837 := (iff #518 #836)
+#846 := (iff #871 #842)
+#841 := (iff #534 #559)
+#843 := (iff #531 #565)
+#563 := (= #874 #562)
+#848 := (= #872 #851)
+#573 := (= #558 -3::int)
+#847 := [rewrite]: #573
+#852 := [monotonicity #847]: #848
+#564 := [monotonicity #852]: #563
+#844 := [monotonicity #564]: #843
+#849 := (iff #529 #472)
+#578 := (iff #878 #577)
+#854 := (iff #877 #876)
+#506 := (or #876 false)
+#867 := (iff #506 #876)
+#853 := [rewrite]: #867
+#866 := (iff #877 #506)
+#521 := (iff #875 false)
+#857 := [rewrite]: #521
+#864 := [monotonicity #857]: #866
+#576 := [trans #864 #853]: #854
+#579 := [monotonicity #576]: #578
+#865 := (iff #869 #863)
+#862 := (iff #879 #873)
+#858 := (or false #873)
+#861 := (iff #858 #873)
+#856 := [rewrite]: #861
+#859 := (iff #879 #858)
+#860 := [monotonicity #857]: #859
+#500 := [trans #860 #856]: #862
+#505 := [monotonicity #500]: #865
+#850 := [monotonicity #505 #579]: #849
+#845 := [monotonicity #850 #844]: #841
+#835 := [monotonicity #845]: #846
+#519 := (iff #855 false)
+#520 := [rewrite]: #519
+#832 := [monotonicity #520 #835]: #837
+#834 := [trans #832 #838]: #839
+#826 := [monotonicity #834]: #825
+#822 := [trans #826 #828]: #825
+#683 := [quant-inst]: #682
+#823 := [mp #683 #822]: #681
+#605 := [unit-resolution #823 #893]: #842
+#698 := (not #842)
+#709 := (or #698 #530 #559)
+#717 := [def-axiom]: #709
+#607 := [unit-resolution #717 #605]: #606
+#608 := [unit-resolution #607 #604]: #559
+#811 := (f5 #54)
+#779 := (f6 #811)
+#781 := (= #779 0::int)
+#592 := (not #781)
+#594 := (iff #713 #592)
+#603 := (iff #530 #781)
+#613 := (iff #781 #530)
+#611 := (= #779 #54)
+#609 := (= #811 f7)
+#815 := (= f7 #811)
+#38 := (:var 0 S2)
+#39 := (f6 #38)
+#894 := (pattern #39)
+#40 := (f5 #39)
+#189 := (= #38 #40)
+#895 := (forall (vars (?v0 S2)) (:pat #894) #189)
+#192 := (forall (vars (?v0 S2)) #189)
+#896 := (iff #192 #895)
+#898 := (iff #895 #895)
+#899 := [rewrite]: #898
+#897 := [rewrite]: #896
+#900 := [trans #897 #899]: #896
+#312 := (~ #192 #192)
+#328 := (~ #189 #189)
+#329 := [refl]: #328
+#313 := [nnf-pos #329]: #312
+#41 := (= #40 #38)
+#42 := (forall (vars (?v0 S2)) #41)
+#193 := (iff #42 #192)
+#190 := (iff #41 #189)
+#191 := [rewrite]: #190
+#194 := [quant-intro #191]: #193
+#188 := [asserted]: #42
+#197 := [mp #188 #194]: #192
+#330 := [mp~ #197 #313]: #192
+#901 := [mp #330 #900]: #895
+#796 := (not #895)
+#793 := (or #796 #815)
+#795 := [quant-inst]: #793
+#685 := [unit-resolution #795 #901]: #815
+#610 := [symm #685]: #609
+#612 := [monotonicity #610]: #611
+#614 := [monotonicity #612]: #613
+#615 := [symm #614]: #603
+#595 := [monotonicity #615]: #594
+#596 := [mp #604 #595]: #592
+#768 := (or #781 #873)
+#44 := (f5 #9)
+#902 := (pattern #44)
+#212 := (>= #9 0::int)
+#45 := (f6 #44)
+#50 := (= #45 0::int)
+#262 := (or #50 #212)
+#909 := (forall (vars (?v0 int)) (:pat #902) #262)
+#267 := (forall (vars (?v0 int)) #262)
+#912 := (iff #267 #909)
+#910 := (iff #262 #262)
+#911 := [refl]: #910
+#913 := [quant-intro #911]: #912
+#316 := (~ #267 #267)
+#334 := (~ #262 #262)
+#335 := [refl]: #334
+#317 := [nnf-pos #335]: #316
+#49 := (< #9 0::int)
+#51 := (implies #49 #50)
+#52 := (forall (vars (?v0 int)) #51)
+#270 := (iff #52 #267)
+#233 := (= 0::int #45)
+#239 := (not #49)
+#240 := (or #239 #233)
+#245 := (forall (vars (?v0 int)) #240)
+#268 := (iff #245 #267)
+#265 := (iff #240 #262)
+#259 := (or #212 #50)
+#263 := (iff #259 #262)
+#264 := [rewrite]: #263
+#260 := (iff #240 #259)
+#257 := (iff #233 #50)
+#258 := [rewrite]: #257
+#255 := (iff #239 #212)
+#215 := (not #212)
+#250 := (not #215)
+#253 := (iff #250 #212)
+#254 := [rewrite]: #253
+#251 := (iff #239 #250)
+#248 := (iff #49 #215)
+#249 := [rewrite]: #248
+#252 := [monotonicity #249]: #251
+#256 := [trans #252 #254]: #255
+#261 := [monotonicity #256 #258]: #260
+#266 := [trans #261 #264]: #265
+#269 := [quant-intro #266]: #268
+#246 := (iff #52 #245)
+#243 := (iff #51 #240)
+#236 := (implies #49 #233)
+#241 := (iff #236 #240)
+#242 := [rewrite]: #241
+#237 := (iff #51 #236)
+#234 := (iff #50 #233)
+#235 := [rewrite]: #234
+#238 := [monotonicity #235]: #237
+#244 := [trans #238 #242]: #243
+#247 := [quant-intro #244]: #246
+#271 := [trans #247 #269]: #270
+#232 := [asserted]: #52
+#272 := [mp #232 #271]: #267
+#336 := [mp~ #272 #317]: #267
+#914 := [mp #336 #913]: #909
+#782 := (not #909)
+#771 := (or #782 #781 #873)
+#772 := (or #782 #768)
+#774 := (iff #772 #771)
+#775 := [rewrite]: #774
+#773 := [quant-inst]: #772
+#776 := [mp #773 #775]: #771
+#597 := [unit-resolution #776 #914]: #768
+#598 := [unit-resolution #597 #596]: #873
+#599 := (or #530 #577 #863)
+#600 := [th-lemma]: #599
+#593 := [unit-resolution #600 #598 #604]: #577
+#824 := (or #472 #876)
+#831 := [def-axiom]: #824
+#601 := [unit-resolution #831 #593]: #472
+#660 := (not #472)
+#818 := (not #559)
+#821 := (or #818 #660 #543)
+#703 := [def-axiom]: #821
+#586 := [unit-resolution #703 #601 #608]: #543
+#664 := (not #543)
+#587 := (or #664 #817)
+#588 := [th-lemma]: #587
+#590 := [unit-resolution #588 #586]: #817
+#591 := (not #729)
+#589 := (not #817)
+#580 := (or #802 #589 #591)
+#581 := [th-lemma]: #580
+#582 := [unit-resolution #581 #590 #602]: #802
+#816 := (<= #542 0::int)
+#574 := (or #664 #816)
+#583 := [th-lemma]: #574
+#584 := [unit-resolution #583 #586]: #816
+#804 := (not #802)
+#649 := (not #816)
+#626 := (or #627 #286 #649 #804)
+#625 := [hypothesis]: #802
+#747 := (* -3::int #769)
+#750 := (+ #868 #747)
+#751 := (+ #54 #750)
+#727 := (<= #751 0::int)
+#746 := (= #751 0::int)
+#657 := (or false #746)
+#695 := [th-lemma]: #657
+#680 := [unit-resolution #695 #76]: #746
+#658 := (not #746)
+#665 := (or #658 #727)
+#667 := [th-lemma]: #665
+#668 := [unit-resolution #667 #680]: #727
+#677 := [hypothesis]: #816
+#633 := [hypothesis]: #620
+#624 := [th-lemma #632 #633 #677 #668 #625]: false
+#629 := [lemma #624]: #626
+#575 := [unit-resolution #629 #584 #632 #582]: #627
+#666 := (>= #751 0::int)
+#640 := (or #658 #666)
+#636 := [th-lemma]: #640
+#641 := [unit-resolution #636 #680]: #666
+#711 := (* -1::int #56)
+#712 := (+ #54 #711)
+#722 := (<= #712 0::int)
+#560 := (not #722)
+#555 := (not #274)
+#557 := (or #555 #286)
+#299 := (iff #274 #286)
+#59 := (< #54 3::int)
+#60 := (not #59)
+#61 := (iff #58 #60)
+#304 := (iff #61 #299)
+#280 := (iff #60 #274)
+#302 := (iff #280 #299)
+#296 := (iff #286 #274)
+#300 := (iff #296 #299)
+#301 := [rewrite]: #300
+#297 := (iff #280 #296)
+#294 := (iff #60 #286)
+#289 := (not #285)
+#292 := (iff #289 #286)
+#293 := [rewrite]: #292
+#290 := (iff #60 #289)
+#287 := (iff #59 #285)
+#288 := [rewrite]: #287
+#291 := [monotonicity #288]: #290
+#295 := [trans #291 #293]: #294
+#298 := [monotonicity #295]: #297
+#303 := [trans #298 #301]: #302
+#283 := (iff #61 #280)
+#277 := (iff #274 #60)
+#281 := (iff #277 #280)
+#282 := [rewrite]: #281
+#278 := (iff #61 #277)
+#275 := (iff #58 #274)
+#276 := [rewrite]: #275
+#279 := [monotonicity #276]: #278
+#284 := [trans #279 #282]: #283
+#305 := [trans #284 #303]: #304
+#273 := [asserted]: #61
+#306 := [mp #273 #305]: #299
+#466 := (not #299)
+#556 := (or #555 #286 #466)
+#484 := [def-axiom]: #556
+#554 := [unit-resolution #484 #306]: #557
+#585 := [unit-resolution #554 #632]: #555
+#693 := (or #692 #274)
+#688 := (= #811 #57)
+#686 := (= #57 #811)
+#678 := [hypothesis]: #514
+#684 := [symm #678]: #679
+#687 := [monotonicity #684]: #686
+#689 := [symm #687]: #688
+#690 := [trans #685 #689]: #274
+#723 := [hypothesis]: #555
+#691 := [unit-resolution #723 #690]: false
+#694 := [lemma #691]: #693
+#566 := [unit-resolution #694 #585]: #692
+#707 := (>= #712 0::int)
+#669 := (* -1::int #769)
+#671 := (+ #868 #669)
+#637 := (+ #54 #671)
+#639 := (>= #637 0::int)
+#621 := (or #639 #876)
+#645 := (not #639)
+#634 := [hypothesis]: #645
+#706 := (>= #661 3::int)
+#730 := (not #706)
+#675 := (or false #730)
+#676 := [th-lemma]: #675
+#659 := [unit-resolution #676 #76]: #730
+#696 := [hypothesis]: #577
+#631 := [th-lemma #696 #659 #641 #634]: false
+#623 := [lemma #631]: #621
+#567 := [unit-resolution #623 #593]: #639
+#643 := (or #645 #649 #707)
+#642 := (not #707)
+#644 := [hypothesis]: #642
+#635 := [hypothesis]: #639
+#638 := [th-lemma #677 #635 #668 #644]: false
+#646 := [lemma #638]: #643
+#568 := [unit-resolution #646 #567 #584]: #707
+#569 := (or #514 #560 #642)
+#570 := [th-lemma]: #569
+#561 := [unit-resolution #570 #568 #566]: #560
+#571 := [th-lemma #590 #561 #641 #575]: false
+#540 := [lemma #571]: #538
+#697 := [unit-resolution #540 #632]: #530
+#532 := [monotonicity #697]: #541
+#548 := [trans #532 #546]: #547
+#539 := [symm #548]: #549
+#699 := (or #713 #870)
+#715 := (or #698 #713 #870)
+#716 := [def-axiom]: #715
+#701 := [unit-resolution #716 #605]: #699
+#728 := [unit-resolution #701 #697]: #870
+#550 := [mp #728 #539]: #514
+#533 := [unit-resolution #566 #550]: false
+#535 := [lemma #533]: #286
+#553 := (or #274 #285)
+#551 := (or #274 #285 #466)
+#552 := [def-axiom]: #551
+#544 := [unit-resolution #552 #306]: #553
+#496 := [unit-resolution #544 #535]: #274
+#498 := [symm #496]: #58
+#499 := [monotonicity #498]: #494
+#485 := [monotonicity #499]: #481
+#491 := [trans #485 #489]: #490
+#492 := [symm #491]: #483
+#474 := [monotonicity #492]: #473
+#524 := (or #577 #285)
+#525 := [th-lemma]: #524
+#526 := [unit-resolution #525 #535]: #577
+#527 := (or #713 #876)
+#516 := [th-lemma]: #527
+#528 := [unit-resolution #516 #526]: #713
+#509 := [unit-resolution #607 #528]: #559
+#511 := [unit-resolution #831 #526]: #472
+#512 := [unit-resolution #703 #511 #509]: #543
+#502 := [unit-resolution #583 #512]: #816
+#508 := (or #560 #285 #706 #649)
+#482 := [th-lemma]: #508
+#487 := [unit-resolution #482 #502 #535 #659]: #560
+#488 := (or #692 #722)
+#493 := [th-lemma]: #488
+#495 := [unit-resolution #493 #487]: #692
+#477 := [mp #495 #474]: #476
+#510 := [unit-resolution #588 #512]: #817
+#513 := (or #802 #591 #589)
+#501 := [th-lemma]: #513
+#503 := [unit-resolution #501 #510 #602]: #802
+#803 := (or #804 #806)
+#196 := (= #9 #45)
+#221 := (or #196 #215)
+#903 := (forall (vars (?v0 int)) (:pat #902) #221)
+#226 := (forall (vars (?v0 int)) #221)
+#906 := (iff #226 #903)
+#904 := (iff #221 #221)
+#905 := [refl]: #904
+#907 := [quant-intro #905]: #906
+#314 := (~ #226 #226)
+#331 := (~ #221 #221)
+#332 := [refl]: #331
+#315 := [nnf-pos #332]: #314
+#46 := (= #45 #9)
+#43 := (<= 0::int #9)
+#47 := (implies #43 #46)
+#48 := (forall (vars (?v0 int)) #47)
+#229 := (iff #48 #226)
+#203 := (not #43)
+#204 := (or #203 #196)
+#209 := (forall (vars (?v0 int)) #204)
+#227 := (iff #209 #226)
+#224 := (iff #204 #221)
+#218 := (or #215 #196)
+#222 := (iff #218 #221)
+#223 := [rewrite]: #222
+#219 := (iff #204 #218)
+#216 := (iff #203 #215)
+#213 := (iff #43 #212)
+#214 := [rewrite]: #213
+#217 := [monotonicity #214]: #216
+#220 := [monotonicity #217]: #219
+#225 := [trans #220 #223]: #224
+#228 := [quant-intro #225]: #227
+#210 := (iff #48 #209)
+#207 := (iff #47 #204)
+#200 := (implies #43 #196)
+#205 := (iff #200 #204)
+#206 := [rewrite]: #205
+#201 := (iff #47 #200)
+#198 := (iff #46 #196)
+#199 := [rewrite]: #198
+#202 := [monotonicity #199]: #201
+#208 := [trans #202 #206]: #207
+#211 := [quant-intro #208]: #210
+#230 := [trans #211 #228]: #229
+#195 := [asserted]: #48
+#231 := [mp #195 #230]: #226
+#333 := [mp~ #231 #315]: #226
+#908 := [mp #333 #907]: #903
+#798 := (not #903)
+#799 := (or #798 #804 #806)
+#807 := (or #806 #804)
+#800 := (or #798 #807)
+#790 := (iff #800 #799)
+#801 := (or #798 #803)
+#788 := (iff #801 #799)
+#789 := [rewrite]: #788
+#785 := (iff #800 #801)
+#808 := (iff #807 #803)
+#797 := [rewrite]: #808
+#786 := [monotonicity #797]: #785
+#791 := [trans #786 #789]: #790
+#794 := [quant-inst]: #800
+#787 := [mp #794 #791]: #799
+#504 := [unit-resolution #787 #908]: #803
+#507 := [unit-resolution #504 #503]: #806
+[unit-resolution #507 #477]: false
+unsat
+006c5a23106f99ba6bb43c9c4ac1994ef786bd5d 848 0
 #2 := false
 decl f5 :: (-> int S2)
 decl f6 :: (-> S2 int)
@@ -20495,541 +21718,7 @@
 #1103 := [trans #935 #1102]: #300
 [unit-resolution #308 #1103]: false
 unsat
-ca0580f7bff73a2d860730ec786524526e0ba0ea 533 0
-#2 := false
-#55 := 3::int
-decl f6 :: (-> S2 int)
-decl f7 :: S2
-#53 := f7
-#54 := (f6 f7)
-#533 := (mod #54 3::int)
-#664 := (>= #533 3::int)
-#665 := (not #664)
-#1 := true
-#75 := [true-axiom]: true
-#674 := (or false #665)
-#635 := [th-lemma]: #674
-#636 := [unit-resolution #635 #75]: #665
-#11 := 0::int
-decl f5 :: (-> int S2)
-decl f4 :: (-> int int int)
-#56 := (f4 #54 3::int)
-#57 := (f5 #56)
-#58 := (f6 #57)
-#84 := -1::int
-#779 := (* -1::int #58)
-#763 := (+ #56 #779)
-#766 := (>= #763 0::int)
-#773 := (= #56 #58)
-#780 := (>= #56 0::int)
-#784 := (= #58 0::int)
-#649 := (not #784)
-#746 := (<= #58 0::int)
-#643 := (not #746)
-#276 := (>= #58 3::int)
-#59 := (< #58 3::int)
-#60 := (not #59)
-#284 := (iff #60 #276)
-#275 := (not #276)
-#279 := (not #275)
-#282 := (iff #279 #276)
-#283 := [rewrite]: #282
-#280 := (iff #60 #279)
-#277 := (iff #59 #275)
-#278 := [rewrite]: #277
-#281 := [monotonicity #278]: #280
-#285 := [trans #281 #283]: #284
-#272 := [asserted]: #60
-#286 := [mp #272 #285]: #276
-#645 := (or #643 #275)
-#646 := [th-lemma]: #645
-#647 := [unit-resolution #646 #286]: #643
-#650 := (or #649 #746)
-#651 := [th-lemma]: #650
-#652 := [unit-resolution #651 #647]: #649
-#9 := (:var 0 int)
-#44 := (f5 #9)
-#880 := (pattern #44)
-#211 := (>= #9 0::int)
-#45 := (f6 #44)
-#50 := (= #45 0::int)
-#261 := (or #50 #211)
-#887 := (forall (vars (?v0 int)) (:pat #880) #261)
-#266 := (forall (vars (?v0 int)) #261)
-#890 := (iff #266 #887)
-#888 := (iff #261 #261)
-#889 := [refl]: #888
-#891 := [quant-intro #889]: #890
-#294 := (~ #266 #266)
-#312 := (~ #261 #261)
-#313 := [refl]: #312
-#295 := [nnf-pos #313]: #294
-#49 := (< #9 0::int)
-#51 := (implies #49 #50)
-#52 := (forall (vars (?v0 int)) #51)
-#269 := (iff #52 #266)
-#232 := (= 0::int #45)
-#238 := (not #49)
-#239 := (or #238 #232)
-#244 := (forall (vars (?v0 int)) #239)
-#267 := (iff #244 #266)
-#264 := (iff #239 #261)
-#258 := (or #211 #50)
-#262 := (iff #258 #261)
-#263 := [rewrite]: #262
-#259 := (iff #239 #258)
-#256 := (iff #232 #50)
-#257 := [rewrite]: #256
-#254 := (iff #238 #211)
-#214 := (not #211)
-#249 := (not #214)
-#252 := (iff #249 #211)
-#253 := [rewrite]: #252
-#250 := (iff #238 #249)
-#247 := (iff #49 #214)
-#248 := [rewrite]: #247
-#251 := [monotonicity #248]: #250
-#255 := [trans #251 #253]: #254
-#260 := [monotonicity #255 #257]: #259
-#265 := [trans #260 #263]: #264
-#268 := [quant-intro #265]: #267
-#245 := (iff #52 #244)
-#242 := (iff #51 #239)
-#235 := (implies #49 #232)
-#240 := (iff #235 #239)
-#241 := [rewrite]: #240
-#236 := (iff #51 #235)
-#233 := (iff #50 #232)
-#234 := [rewrite]: #233
-#237 := [monotonicity #234]: #236
-#243 := [trans #237 #241]: #242
-#246 := [quant-intro #243]: #245
-#270 := [trans #246 #268]: #269
-#231 := [asserted]: #52
-#271 := [mp #231 #270]: #266
-#314 := [mp~ #271 #295]: #266
-#892 := [mp #314 #891]: #887
-#765 := (not #887)
-#770 := (or #765 #780 #784)
-#785 := (or #784 #780)
-#756 := (or #765 #785)
-#742 := (iff #756 #770)
-#767 := (or #780 #784)
-#759 := (or #765 #767)
-#758 := (iff #759 #770)
-#762 := [rewrite]: #758
-#760 := (iff #756 #759)
-#768 := (iff #785 #767)
-#769 := [rewrite]: #768
-#761 := [monotonicity #769]: #760
-#743 := [trans #761 #762]: #742
-#757 := [quant-inst]: #756
-#745 := [mp #757 #743]: #770
-#653 := [unit-resolution #745 #892 #652]: #780
-#782 := (not #780)
-#783 := (or #773 #782)
-#195 := (= #9 #45)
-#220 := (or #195 #214)
-#881 := (forall (vars (?v0 int)) (:pat #880) #220)
-#225 := (forall (vars (?v0 int)) #220)
-#884 := (iff #225 #881)
-#882 := (iff #220 #220)
-#883 := [refl]: #882
-#885 := [quant-intro #883]: #884
-#292 := (~ #225 #225)
-#309 := (~ #220 #220)
-#310 := [refl]: #309
-#293 := [nnf-pos #310]: #292
-#46 := (= #45 #9)
-#43 := (<= 0::int #9)
-#47 := (implies #43 #46)
-#48 := (forall (vars (?v0 int)) #47)
-#228 := (iff #48 #225)
-#202 := (not #43)
-#203 := (or #202 #195)
-#208 := (forall (vars (?v0 int)) #203)
-#226 := (iff #208 #225)
-#223 := (iff #203 #220)
-#217 := (or #214 #195)
-#221 := (iff #217 #220)
-#222 := [rewrite]: #221
-#218 := (iff #203 #217)
-#215 := (iff #202 #214)
-#212 := (iff #43 #211)
-#213 := [rewrite]: #212
-#216 := [monotonicity #213]: #215
-#219 := [monotonicity #216]: #218
-#224 := [trans #219 #222]: #223
-#227 := [quant-intro #224]: #226
-#209 := (iff #48 #208)
-#206 := (iff #47 #203)
-#199 := (implies #43 #195)
-#204 := (iff #199 #203)
-#205 := [rewrite]: #204
-#200 := (iff #47 #199)
-#197 := (iff #46 #195)
-#198 := [rewrite]: #197
-#201 := [monotonicity #198]: #200
-#207 := [trans #201 #205]: #206
-#210 := [quant-intro #207]: #209
-#229 := [trans #210 #227]: #228
-#194 := [asserted]: #48
-#230 := [mp #194 #229]: #225
-#311 := [mp~ #230 #293]: #225
-#886 := [mp #311 #885]: #881
-#781 := (not #881)
-#786 := (or #781 #773 #782)
-#775 := (or #781 #783)
-#777 := (iff #775 #786)
-#778 := [rewrite]: #777
-#776 := [quant-inst]: #775
-#772 := [mp #776 #778]: #786
-#654 := [unit-resolution #772 #886]: #783
-#637 := [unit-resolution #654 #653]: #773
-#655 := (not #773)
-#625 := (or #655 #766)
-#626 := [th-lemma]: #625
-#627 := [unit-resolution #626 #637]: #766
-#534 := (* -1::int #533)
-#462 := (+ #56 #534)
-#802 := (<= #462 0::int)
-#535 := (= #462 0::int)
-#556 := -3::int
-#529 := (* -1::int #54)
-#827 := (mod #529 -3::int)
-#551 := (+ #56 #827)
-#826 := (= #551 0::int)
-#852 := (>= #54 0::int)
-#498 := (not #852)
-#536 := (<= #54 0::int)
-#841 := (not #536)
-#845 := (or #841 #498)
-#541 := (ite #845 #535 #826)
-#521 := (= #56 0::int)
-#853 := (= #54 0::int)
-#821 := (ite #853 #521 #541)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#865 := (pattern #29)
-#88 := (* -1::int #9)
-#85 := (* -1::int #8)
-#143 := (mod #85 #88)
-#376 := (+ #29 #143)
-#377 := (= #376 0::int)
-#30 := (mod #8 #9)
-#373 := (* -1::int #30)
-#374 := (+ #29 #373)
-#375 := (= #374 0::int)
-#110 := (<= #9 0::int)
-#106 := (<= #8 0::int)
-#315 := (or #106 #110)
-#316 := (not #315)
-#117 := (>= #8 0::int)
-#298 := (or #110 #117)
-#299 := (not #298)
-#322 := (or #299 #316)
-#378 := (ite #322 #375 #377)
-#372 := (= #29 0::int)
-#12 := (= #8 0::int)
-#379 := (ite #12 #372 #378)
-#371 := (= #8 #29)
-#13 := (= #9 0::int)
-#380 := (ite #13 #371 #379)
-#866 := (forall (vars (?v0 int) (?v1 int)) (:pat #865) #380)
-#383 := (forall (vars (?v0 int) (?v1 int)) #380)
-#869 := (iff #383 #866)
-#867 := (iff #380 #380)
-#868 := [refl]: #867
-#870 := [quant-intro #868]: #869
-#149 := (* -1::int #143)
-#340 := (ite #322 #30 #149)
-#343 := (ite #12 0::int #340)
-#346 := (ite #13 #8 #343)
-#349 := (= #29 #346)
-#352 := (forall (vars (?v0 int) (?v1 int)) #349)
-#384 := (iff #352 #383)
-#381 := (iff #349 #380)
-#382 := [rewrite]: #381
-#385 := [quant-intro #382]: #384
-#118 := (not #117)
-#111 := (not #110)
-#121 := (and #111 #118)
-#107 := (not #106)
-#114 := (and #107 #111)
-#124 := (or #114 #121)
-#169 := (ite #124 #30 #149)
-#172 := (ite #12 0::int #169)
-#175 := (ite #13 #8 #172)
-#178 := (= #29 #175)
-#181 := (forall (vars (?v0 int) (?v1 int)) #178)
-#353 := (iff #181 #352)
-#350 := (iff #178 #349)
-#347 := (= #175 #346)
-#344 := (= #172 #343)
-#341 := (= #169 #340)
-#325 := (iff #124 #322)
-#319 := (or #316 #299)
-#323 := (iff #319 #322)
-#324 := [rewrite]: #323
-#320 := (iff #124 #319)
-#317 := (iff #121 #299)
-#318 := [rewrite]: #317
-#296 := (iff #114 #316)
-#297 := [rewrite]: #296
-#321 := [monotonicity #297 #318]: #320
-#326 := [trans #321 #324]: #325
-#342 := [monotonicity #326]: #341
-#345 := [monotonicity #342]: #344
-#348 := [monotonicity #345]: #347
-#351 := [monotonicity #348]: #350
-#354 := [quant-intro #351]: #353
-#288 := (~ #181 #181)
-#273 := (~ #178 #178)
-#304 := [refl]: #273
-#289 := [nnf-pos #304]: #288
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#184 := (iff #37 #181)
-#78 := (and #16 #18)
-#81 := (or #17 #78)
-#154 := (ite #81 #30 #149)
-#157 := (ite #12 0::int #154)
-#160 := (ite #13 #8 #157)
-#163 := (= #29 #160)
-#166 := (forall (vars (?v0 int) (?v1 int)) #163)
-#182 := (iff #166 #181)
-#179 := (iff #163 #178)
-#176 := (= #160 #175)
-#173 := (= #157 #172)
-#170 := (= #154 #169)
-#125 := (iff #81 #124)
-#122 := (iff #78 #121)
-#119 := (iff #18 #118)
-#120 := [rewrite]: #119
-#112 := (iff #16 #111)
-#113 := [rewrite]: #112
-#123 := [monotonicity #113 #120]: #122
-#115 := (iff #17 #114)
-#108 := (iff #15 #107)
-#109 := [rewrite]: #108
-#116 := [monotonicity #109 #113]: #115
-#126 := [monotonicity #116 #123]: #125
-#171 := [monotonicity #126]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [quant-intro #180]: #182
-#167 := (iff #37 #166)
-#164 := (iff #36 #163)
-#161 := (= #35 #160)
-#158 := (= #34 #157)
-#155 := (= #33 #154)
-#152 := (= #32 #149)
-#146 := (- #143)
-#150 := (= #146 #149)
-#151 := [rewrite]: #150
-#147 := (= #32 #146)
-#144 := (= #31 #143)
-#89 := (= #23 #88)
-#90 := [rewrite]: #89
-#86 := (= #22 #85)
-#87 := [rewrite]: #86
-#145 := [monotonicity #87 #90]: #144
-#148 := [monotonicity #145]: #147
-#153 := [trans #148 #151]: #152
-#82 := (iff #20 #81)
-#79 := (iff #19 #78)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#156 := [monotonicity #83 #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [monotonicity #162]: #164
-#168 := [quant-intro #165]: #167
-#185 := [trans #168 #183]: #184
-#142 := [asserted]: #37
-#186 := [mp #142 #185]: #181
-#305 := [mp~ #186 #289]: #181
-#355 := [mp #305 #354]: #352
-#386 := [mp #355 #385]: #383
-#871 := [mp #386 #870]: #866
-#810 := (not #866)
-#811 := (or #810 #821)
-#444 := (* -1::int 3::int)
-#530 := (mod #529 #444)
-#531 := (+ #56 #530)
-#522 := (= #531 0::int)
-#532 := (<= 3::int 0::int)
-#515 := (or #536 #532)
-#850 := (not #515)
-#509 := (or #532 #852)
-#639 := (not #509)
-#846 := (or #639 #850)
-#520 := (ite #846 #535 #522)
-#854 := (ite #853 #521 #520)
-#855 := (= #54 #56)
-#856 := (= 3::int 0::int)
-#851 := (ite #856 #855 #854)
-#816 := (or #810 #851)
-#812 := (iff #816 #811)
-#659 := (iff #811 #811)
-#660 := [rewrite]: #659
-#814 := (iff #851 #821)
-#819 := (ite false #855 #821)
-#824 := (iff #819 #821)
-#813 := [rewrite]: #824
-#823 := (iff #851 #819)
-#822 := (iff #854 #821)
-#542 := (iff #520 #541)
-#830 := (iff #522 #826)
-#825 := (= #531 #551)
-#828 := (= #530 #827)
-#557 := (= #444 -3::int)
-#450 := [rewrite]: #557
-#550 := [monotonicity #450]: #828
-#829 := [monotonicity #550]: #825
-#540 := [monotonicity #829]: #830
-#554 := (iff #846 #845)
-#484 := (or #498 #841)
-#831 := (iff #484 #845)
-#832 := [rewrite]: #831
-#844 := (iff #846 #484)
-#843 := (iff #850 #841)
-#840 := (iff #515 #536)
-#836 := (or #536 false)
-#839 := (iff #836 #536)
-#834 := [rewrite]: #839
-#837 := (iff #515 #836)
-#507 := (iff #532 false)
-#512 := [rewrite]: #507
-#838 := [monotonicity #512]: #837
-#478 := [trans #838 #834]: #840
-#483 := [monotonicity #478]: #843
-#499 := (iff #639 #498)
-#496 := (iff #509 #852)
-#848 := (or false #852)
-#492 := (iff #848 #852)
-#833 := [rewrite]: #492
-#508 := (iff #509 #848)
-#849 := [monotonicity #512]: #508
-#497 := [trans #849 #833]: #496
-#835 := [monotonicity #497]: #499
-#842 := [monotonicity #835 #483]: #844
-#555 := [trans #842 #832]: #554
-#543 := [monotonicity #555 #540]: #542
-#537 := [monotonicity #543]: #822
-#857 := (iff #856 false)
-#847 := [rewrite]: #857
-#820 := [monotonicity #847 #537]: #823
-#815 := [trans #820 #813]: #814
-#818 := [monotonicity #815]: #812
-#661 := [trans #818 #660]: #812
-#817 := [quant-inst]: #816
-#803 := [mp #817 #661]: #811
-#628 := [unit-resolution #803 #871]: #821
-#692 := (not #853)
-#691 := (not #521)
-#633 := (iff #649 #691)
-#632 := (iff #784 #521)
-#630 := (iff #521 #784)
-#631 := [monotonicity #637]: #630
-#475 := [symm #631]: #632
-#629 := [monotonicity #475]: #633
-#634 := [mp #652 #629]: #691
-#790 := (not #821)
-#787 := (or #790 #692 #521)
-#788 := [def-axiom]: #787
-#613 := [unit-resolution #788 #634 #628]: #692
-#791 := (or #790 #853 #541)
-#676 := [def-axiom]: #791
-#616 := [unit-resolution #676 #613 #628]: #541
-#696 := (f5 #54)
-#748 := (f6 #696)
-#749 := (= #748 0::int)
-#614 := (not #749)
-#619 := (iff #692 #614)
-#617 := (iff #853 #749)
-#612 := (iff #749 #853)
-#621 := (= #748 #54)
-#622 := (= #696 f7)
-#697 := (= f7 #696)
-#38 := (:var 0 S2)
-#39 := (f6 #38)
-#872 := (pattern #39)
-#40 := (f5 #39)
-#188 := (= #38 #40)
-#873 := (forall (vars (?v0 S2)) (:pat #872) #188)
-#191 := (forall (vars (?v0 S2)) #188)
-#874 := (iff #191 #873)
-#876 := (iff #873 #873)
-#877 := [rewrite]: #876
-#875 := [rewrite]: #874
-#878 := [trans #875 #877]: #874
-#290 := (~ #191 #191)
-#306 := (~ #188 #188)
-#307 := [refl]: #306
-#291 := [nnf-pos #307]: #290
-#41 := (= #40 #38)
-#42 := (forall (vars (?v0 S2)) #41)
-#192 := (iff #42 #191)
-#189 := (iff #41 #188)
-#190 := [rewrite]: #189
-#193 := [quant-intro #190]: #192
-#187 := [asserted]: #42
-#196 := [mp #187 #193]: #191
-#308 := [mp~ #196 #291]: #191
-#879 := [mp #308 #878]: #873
-#792 := (not #873)
-#789 := (or #792 #697)
-#793 := [quant-inst]: #789
-#620 := [unit-resolution #793 #879]: #697
-#623 := [symm #620]: #622
-#624 := [monotonicity #623]: #621
-#615 := [monotonicity #624]: #612
-#618 := [symm #615]: #617
-#609 := [monotonicity #618]: #619
-#599 := [mp #613 #609]: #614
-#750 := (or #749 #852)
-#753 := (or #765 #749 #852)
-#754 := (or #765 #750)
-#755 := (iff #754 #753)
-#733 := [rewrite]: #755
-#744 := [quant-inst]: #754
-#734 := [mp #744 #733]: #753
-#601 := [unit-resolution #734 #892]: #750
-#602 := [unit-resolution #601 #599]: #852
-#605 := (or #853 #841 #498)
-#606 := [th-lemma]: #605
-#610 := [unit-resolution #606 #613]: #845
-#603 := [unit-resolution #610 #602]: #841
-#804 := (or #845 #536)
-#805 := [def-axiom]: #804
-#611 := [unit-resolution #805 #603]: #845
-#801 := (not #845)
-#641 := (not #541)
-#794 := (or #641 #801 #535)
-#795 := [def-axiom]: #794
-#604 := [unit-resolution #795 #611 #616]: #535
-#796 := (not #535)
-#607 := (or #796 #802)
-#608 := [th-lemma]: #607
-#594 := [unit-resolution #608 #604]: #802
-[th-lemma #594 #286 #627 #636]: false
-unsat
-a9c34a43767d7d2678eb5dde12b17fe190a6efe1 961 0
+54734d9a543064fae65bd375e731a971fc14cf75 961 0
 #2 := false
 decl f5 :: (-> int S2)
 decl f6 :: (-> S2 int)
@@ -21991,679 +22680,7 @@
 #1225 := [trans #1224 #1218]: #301
 [unit-resolution #309 #1225]: false
 unsat
-5967f5c1592ecf001d4f064122298df3a0ca76b7 671 0
-#2 := false
-decl f6 :: (-> S2 int)
-decl f5 :: (-> int S2)
-decl f4 :: (-> int int int)
-#55 := 3::int
-decl f7 :: S2
-#53 := f7
-#54 := (f6 f7)
-#56 := (f4 #54 3::int)
-#57 := (f5 #56)
-#805 := (f6 #57)
-#806 := (= #56 #805)
-#476 := (not #806)
-#514 := (= #54 #56)
-#692 := (not #514)
-#473 := (iff #692 #476)
-#483 := (iff #514 #806)
-#490 := (iff #806 #514)
-#679 := (= #56 #54)
-#486 := (iff #679 #514)
-#489 := [commutativity]: #486
-#481 := (iff #806 #679)
-#494 := (= #805 #54)
-#58 := (= #57 f7)
-#274 := (= f7 #57)
-#286 := (>= #54 3::int)
-#11 := 0::int
-#870 := (= #56 0::int)
-#549 := (iff #870 #514)
-#547 := (iff #514 #870)
-#702 := (= 0::int #56)
-#545 := (iff #702 #870)
-#546 := [commutativity]: #545
-#541 := (iff #514 #702)
-#530 := (= #54 0::int)
-#285 := (not #286)
-#632 := [hypothesis]: #285
-#538 := (or #530 #286)
-#708 := 1::int
-#769 := (div #54 3::int)
-#628 := -2::int
-#618 := (* -2::int #769)
-#661 := (mod #54 3::int)
-#85 := -1::int
-#868 := (* -1::int #661)
-#619 := (+ #868 #618)
-#617 := (+ #54 #619)
-#620 := (>= #617 1::int)
-#627 := (not #620)
-#802 := (>= #56 0::int)
-#729 := (>= #661 0::int)
-#1 := true
-#76 := [true-axiom]: true
-#630 := (or false #729)
-#616 := [th-lemma]: #630
-#602 := [unit-resolution #616 #76]: #729
-#542 := (+ #56 #868)
-#817 := (>= #542 0::int)
-#543 := (= #542 0::int)
-#572 := -3::int
-#537 := (* -1::int #54)
-#851 := (mod #537 -3::int)
-#562 := (+ #56 #851)
-#565 := (= #562 0::int)
-#876 := (<= #54 0::int)
-#577 := (not #876)
-#873 := (>= #54 0::int)
-#863 := (not #873)
-#472 := (or #863 #577)
-#559 := (ite #472 #543 #565)
-#713 := (not #530)
-#604 := [hypothesis]: #713
-#606 := (or #530 #559)
-#842 := (ite #530 #870 #559)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#887 := (pattern #29)
-#89 := (* -1::int #9)
-#86 := (* -1::int #8)
-#144 := (mod #86 #89)
-#398 := (+ #29 #144)
-#399 := (= #398 0::int)
-#30 := (mod #8 #9)
-#395 := (* -1::int #30)
-#396 := (+ #29 #395)
-#397 := (= #396 0::int)
-#111 := (<= #9 0::int)
-#107 := (<= #8 0::int)
-#337 := (or #107 #111)
-#338 := (not #337)
-#118 := (>= #8 0::int)
-#320 := (or #111 #118)
-#321 := (not #320)
-#344 := (or #321 #338)
-#400 := (ite #344 #397 #399)
-#394 := (= #29 0::int)
-#12 := (= #8 0::int)
-#401 := (ite #12 #394 #400)
-#393 := (= #8 #29)
-#13 := (= #9 0::int)
-#402 := (ite #13 #393 #401)
-#888 := (forall (vars (?v0 int) (?v1 int)) (:pat #887) #402)
-#405 := (forall (vars (?v0 int) (?v1 int)) #402)
-#891 := (iff #405 #888)
-#889 := (iff #402 #402)
-#890 := [refl]: #889
-#892 := [quant-intro #890]: #891
-#150 := (* -1::int #144)
-#362 := (ite #344 #30 #150)
-#365 := (ite #12 0::int #362)
-#368 := (ite #13 #8 #365)
-#371 := (= #29 #368)
-#374 := (forall (vars (?v0 int) (?v1 int)) #371)
-#406 := (iff #374 #405)
-#403 := (iff #371 #402)
-#404 := [rewrite]: #403
-#407 := [quant-intro #404]: #406
-#119 := (not #118)
-#112 := (not #111)
-#122 := (and #112 #119)
-#108 := (not #107)
-#115 := (and #108 #112)
-#125 := (or #115 #122)
-#170 := (ite #125 #30 #150)
-#173 := (ite #12 0::int #170)
-#176 := (ite #13 #8 #173)
-#179 := (= #29 #176)
-#182 := (forall (vars (?v0 int) (?v1 int)) #179)
-#375 := (iff #182 #374)
-#372 := (iff #179 #371)
-#369 := (= #176 #368)
-#366 := (= #173 #365)
-#363 := (= #170 #362)
-#347 := (iff #125 #344)
-#341 := (or #338 #321)
-#345 := (iff #341 #344)
-#346 := [rewrite]: #345
-#342 := (iff #125 #341)
-#339 := (iff #122 #321)
-#340 := [rewrite]: #339
-#318 := (iff #115 #338)
-#319 := [rewrite]: #318
-#343 := [monotonicity #319 #340]: #342
-#348 := [trans #343 #346]: #347
-#364 := [monotonicity #348]: #363
-#367 := [monotonicity #364]: #366
-#370 := [monotonicity #367]: #369
-#373 := [monotonicity #370]: #372
-#376 := [quant-intro #373]: #375
-#310 := (~ #182 #182)
-#307 := (~ #179 #179)
-#326 := [refl]: #307
-#311 := [nnf-pos #326]: #310
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#185 := (iff #37 #182)
-#79 := (and #16 #18)
-#82 := (or #17 #79)
-#155 := (ite #82 #30 #150)
-#158 := (ite #12 0::int #155)
-#161 := (ite #13 #8 #158)
-#164 := (= #29 #161)
-#167 := (forall (vars (?v0 int) (?v1 int)) #164)
-#183 := (iff #167 #182)
-#180 := (iff #164 #179)
-#177 := (= #161 #176)
-#174 := (= #158 #173)
-#171 := (= #155 #170)
-#126 := (iff #82 #125)
-#123 := (iff #79 #122)
-#120 := (iff #18 #119)
-#121 := [rewrite]: #120
-#113 := (iff #16 #112)
-#114 := [rewrite]: #113
-#124 := [monotonicity #114 #121]: #123
-#116 := (iff #17 #115)
-#109 := (iff #15 #108)
-#110 := [rewrite]: #109
-#117 := [monotonicity #110 #114]: #116
-#127 := [monotonicity #117 #124]: #126
-#172 := [monotonicity #127]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [monotonicity #178]: #180
-#184 := [quant-intro #181]: #183
-#168 := (iff #37 #167)
-#165 := (iff #36 #164)
-#162 := (= #35 #161)
-#159 := (= #34 #158)
-#156 := (= #33 #155)
-#153 := (= #32 #150)
-#147 := (- #144)
-#151 := (= #147 #150)
-#152 := [rewrite]: #151
-#148 := (= #32 #147)
-#145 := (= #31 #144)
-#90 := (= #23 #89)
-#91 := [rewrite]: #90
-#87 := (= #22 #86)
-#88 := [rewrite]: #87
-#146 := [monotonicity #88 #91]: #145
-#149 := [monotonicity #146]: #148
-#154 := [trans #149 #152]: #153
-#83 := (iff #20 #82)
-#80 := (iff #19 #79)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#157 := [monotonicity #84 #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [monotonicity #163]: #165
-#169 := [quant-intro #166]: #168
-#186 := [trans #169 #184]: #185
-#143 := [asserted]: #37
-#187 := [mp #143 #186]: #182
-#327 := [mp~ #187 #311]: #182
-#377 := [mp #327 #376]: #374
-#408 := [mp #377 #407]: #405
-#893 := [mp #408 #892]: #888
-#840 := (not #888)
-#681 := (or #840 #842)
-#558 := (* -1::int 3::int)
-#872 := (mod #537 #558)
-#874 := (+ #56 #872)
-#531 := (= #874 0::int)
-#875 := (<= 3::int 0::int)
-#877 := (or #876 #875)
-#878 := (not #877)
-#879 := (or #875 #873)
-#869 := (not #879)
-#529 := (or #869 #878)
-#534 := (ite #529 #543 #531)
-#871 := (ite #530 #870 #534)
-#855 := (= 3::int 0::int)
-#518 := (ite #855 #514 #871)
-#682 := (or #840 #518)
-#825 := (iff #682 #681)
-#827 := (iff #681 #681)
-#828 := [rewrite]: #827
-#839 := (iff #518 #842)
-#836 := (ite false #514 #842)
-#833 := (iff #836 #842)
-#838 := [rewrite]: #833
-#837 := (iff #518 #836)
-#846 := (iff #871 #842)
-#841 := (iff #534 #559)
-#843 := (iff #531 #565)
-#563 := (= #874 #562)
-#848 := (= #872 #851)
-#573 := (= #558 -3::int)
-#847 := [rewrite]: #573
-#852 := [monotonicity #847]: #848
-#564 := [monotonicity #852]: #563
-#844 := [monotonicity #564]: #843
-#849 := (iff #529 #472)
-#578 := (iff #878 #577)
-#854 := (iff #877 #876)
-#506 := (or #876 false)
-#867 := (iff #506 #876)
-#853 := [rewrite]: #867
-#866 := (iff #877 #506)
-#521 := (iff #875 false)
-#857 := [rewrite]: #521
-#864 := [monotonicity #857]: #866
-#576 := [trans #864 #853]: #854
-#579 := [monotonicity #576]: #578
-#865 := (iff #869 #863)
-#862 := (iff #879 #873)
-#858 := (or false #873)
-#861 := (iff #858 #873)
-#856 := [rewrite]: #861
-#859 := (iff #879 #858)
-#860 := [monotonicity #857]: #859
-#500 := [trans #860 #856]: #862
-#505 := [monotonicity #500]: #865
-#850 := [monotonicity #505 #579]: #849
-#845 := [monotonicity #850 #844]: #841
-#835 := [monotonicity #845]: #846
-#519 := (iff #855 false)
-#520 := [rewrite]: #519
-#832 := [monotonicity #520 #835]: #837
-#834 := [trans #832 #838]: #839
-#826 := [monotonicity #834]: #825
-#822 := [trans #826 #828]: #825
-#683 := [quant-inst]: #682
-#823 := [mp #683 #822]: #681
-#605 := [unit-resolution #823 #893]: #842
-#698 := (not #842)
-#709 := (or #698 #530 #559)
-#717 := [def-axiom]: #709
-#607 := [unit-resolution #717 #605]: #606
-#608 := [unit-resolution #607 #604]: #559
-#811 := (f5 #54)
-#779 := (f6 #811)
-#781 := (= #779 0::int)
-#592 := (not #781)
-#594 := (iff #713 #592)
-#603 := (iff #530 #781)
-#613 := (iff #781 #530)
-#611 := (= #779 #54)
-#609 := (= #811 f7)
-#815 := (= f7 #811)
-#38 := (:var 0 S2)
-#39 := (f6 #38)
-#894 := (pattern #39)
-#40 := (f5 #39)
-#189 := (= #38 #40)
-#895 := (forall (vars (?v0 S2)) (:pat #894) #189)
-#192 := (forall (vars (?v0 S2)) #189)
-#896 := (iff #192 #895)
-#898 := (iff #895 #895)
-#899 := [rewrite]: #898
-#897 := [rewrite]: #896
-#900 := [trans #897 #899]: #896
-#312 := (~ #192 #192)
-#328 := (~ #189 #189)
-#329 := [refl]: #328
-#313 := [nnf-pos #329]: #312
-#41 := (= #40 #38)
-#42 := (forall (vars (?v0 S2)) #41)
-#193 := (iff #42 #192)
-#190 := (iff #41 #189)
-#191 := [rewrite]: #190
-#194 := [quant-intro #191]: #193
-#188 := [asserted]: #42
-#197 := [mp #188 #194]: #192
-#330 := [mp~ #197 #313]: #192
-#901 := [mp #330 #900]: #895
-#796 := (not #895)
-#793 := (or #796 #815)
-#795 := [quant-inst]: #793
-#685 := [unit-resolution #795 #901]: #815
-#610 := [symm #685]: #609
-#612 := [monotonicity #610]: #611
-#614 := [monotonicity #612]: #613
-#615 := [symm #614]: #603
-#595 := [monotonicity #615]: #594
-#596 := [mp #604 #595]: #592
-#768 := (or #781 #873)
-#44 := (f5 #9)
-#902 := (pattern #44)
-#212 := (>= #9 0::int)
-#45 := (f6 #44)
-#50 := (= #45 0::int)
-#262 := (or #50 #212)
-#909 := (forall (vars (?v0 int)) (:pat #902) #262)
-#267 := (forall (vars (?v0 int)) #262)
-#912 := (iff #267 #909)
-#910 := (iff #262 #262)
-#911 := [refl]: #910
-#913 := [quant-intro #911]: #912
-#316 := (~ #267 #267)
-#334 := (~ #262 #262)
-#335 := [refl]: #334
-#317 := [nnf-pos #335]: #316
-#49 := (< #9 0::int)
-#51 := (implies #49 #50)
-#52 := (forall (vars (?v0 int)) #51)
-#270 := (iff #52 #267)
-#233 := (= 0::int #45)
-#239 := (not #49)
-#240 := (or #239 #233)
-#245 := (forall (vars (?v0 int)) #240)
-#268 := (iff #245 #267)
-#265 := (iff #240 #262)
-#259 := (or #212 #50)
-#263 := (iff #259 #262)
-#264 := [rewrite]: #263
-#260 := (iff #240 #259)
-#257 := (iff #233 #50)
-#258 := [rewrite]: #257
-#255 := (iff #239 #212)
-#215 := (not #212)
-#250 := (not #215)
-#253 := (iff #250 #212)
-#254 := [rewrite]: #253
-#251 := (iff #239 #250)
-#248 := (iff #49 #215)
-#249 := [rewrite]: #248
-#252 := [monotonicity #249]: #251
-#256 := [trans #252 #254]: #255
-#261 := [monotonicity #256 #258]: #260
-#266 := [trans #261 #264]: #265
-#269 := [quant-intro #266]: #268
-#246 := (iff #52 #245)
-#243 := (iff #51 #240)
-#236 := (implies #49 #233)
-#241 := (iff #236 #240)
-#242 := [rewrite]: #241
-#237 := (iff #51 #236)
-#234 := (iff #50 #233)
-#235 := [rewrite]: #234
-#238 := [monotonicity #235]: #237
-#244 := [trans #238 #242]: #243
-#247 := [quant-intro #244]: #246
-#271 := [trans #247 #269]: #270
-#232 := [asserted]: #52
-#272 := [mp #232 #271]: #267
-#336 := [mp~ #272 #317]: #267
-#914 := [mp #336 #913]: #909
-#782 := (not #909)
-#771 := (or #782 #781 #873)
-#772 := (or #782 #768)
-#774 := (iff #772 #771)
-#775 := [rewrite]: #774
-#773 := [quant-inst]: #772
-#776 := [mp #773 #775]: #771
-#597 := [unit-resolution #776 #914]: #768
-#598 := [unit-resolution #597 #596]: #873
-#599 := (or #530 #577 #863)
-#600 := [th-lemma]: #599
-#593 := [unit-resolution #600 #598 #604]: #577
-#824 := (or #472 #876)
-#831 := [def-axiom]: #824
-#601 := [unit-resolution #831 #593]: #472
-#660 := (not #472)
-#818 := (not #559)
-#821 := (or #818 #660 #543)
-#703 := [def-axiom]: #821
-#586 := [unit-resolution #703 #601 #608]: #543
-#664 := (not #543)
-#587 := (or #664 #817)
-#588 := [th-lemma]: #587
-#590 := [unit-resolution #588 #586]: #817
-#591 := (not #729)
-#589 := (not #817)
-#580 := (or #802 #589 #591)
-#581 := [th-lemma]: #580
-#582 := [unit-resolution #581 #590 #602]: #802
-#816 := (<= #542 0::int)
-#574 := (or #664 #816)
-#583 := [th-lemma]: #574
-#584 := [unit-resolution #583 #586]: #816
-#804 := (not #802)
-#649 := (not #816)
-#626 := (or #627 #286 #649 #804)
-#625 := [hypothesis]: #802
-#747 := (* -3::int #769)
-#750 := (+ #868 #747)
-#751 := (+ #54 #750)
-#727 := (<= #751 0::int)
-#746 := (= #751 0::int)
-#657 := (or false #746)
-#695 := [th-lemma]: #657
-#680 := [unit-resolution #695 #76]: #746
-#658 := (not #746)
-#665 := (or #658 #727)
-#667 := [th-lemma]: #665
-#668 := [unit-resolution #667 #680]: #727
-#677 := [hypothesis]: #816
-#633 := [hypothesis]: #620
-#624 := [th-lemma #632 #633 #677 #668 #625]: false
-#629 := [lemma #624]: #626
-#575 := [unit-resolution #629 #584 #632 #582]: #627
-#666 := (>= #751 0::int)
-#640 := (or #658 #666)
-#636 := [th-lemma]: #640
-#641 := [unit-resolution #636 #680]: #666
-#711 := (* -1::int #56)
-#712 := (+ #54 #711)
-#722 := (<= #712 0::int)
-#560 := (not #722)
-#555 := (not #274)
-#557 := (or #555 #286)
-#299 := (iff #274 #286)
-#59 := (< #54 3::int)
-#60 := (not #59)
-#61 := (iff #58 #60)
-#304 := (iff #61 #299)
-#280 := (iff #60 #274)
-#302 := (iff #280 #299)
-#296 := (iff #286 #274)
-#300 := (iff #296 #299)
-#301 := [rewrite]: #300
-#297 := (iff #280 #296)
-#294 := (iff #60 #286)
-#289 := (not #285)
-#292 := (iff #289 #286)
-#293 := [rewrite]: #292
-#290 := (iff #60 #289)
-#287 := (iff #59 #285)
-#288 := [rewrite]: #287
-#291 := [monotonicity #288]: #290
-#295 := [trans #291 #293]: #294
-#298 := [monotonicity #295]: #297
-#303 := [trans #298 #301]: #302
-#283 := (iff #61 #280)
-#277 := (iff #274 #60)
-#281 := (iff #277 #280)
-#282 := [rewrite]: #281
-#278 := (iff #61 #277)
-#275 := (iff #58 #274)
-#276 := [rewrite]: #275
-#279 := [monotonicity #276]: #278
-#284 := [trans #279 #282]: #283
-#305 := [trans #284 #303]: #304
-#273 := [asserted]: #61
-#306 := [mp #273 #305]: #299
-#466 := (not #299)
-#556 := (or #555 #286 #466)
-#484 := [def-axiom]: #556
-#554 := [unit-resolution #484 #306]: #557
-#585 := [unit-resolution #554 #632]: #555
-#693 := (or #692 #274)
-#688 := (= #811 #57)
-#686 := (= #57 #811)
-#678 := [hypothesis]: #514
-#684 := [symm #678]: #679
-#687 := [monotonicity #684]: #686
-#689 := [symm #687]: #688
-#690 := [trans #685 #689]: #274
-#723 := [hypothesis]: #555
-#691 := [unit-resolution #723 #690]: false
-#694 := [lemma #691]: #693
-#566 := [unit-resolution #694 #585]: #692
-#707 := (>= #712 0::int)
-#669 := (* -1::int #769)
-#671 := (+ #868 #669)
-#637 := (+ #54 #671)
-#639 := (>= #637 0::int)
-#621 := (or #639 #876)
-#645 := (not #639)
-#634 := [hypothesis]: #645
-#706 := (>= #661 3::int)
-#730 := (not #706)
-#675 := (or false #730)
-#676 := [th-lemma]: #675
-#659 := [unit-resolution #676 #76]: #730
-#696 := [hypothesis]: #577
-#631 := [th-lemma #696 #659 #641 #634]: false
-#623 := [lemma #631]: #621
-#567 := [unit-resolution #623 #593]: #639
-#643 := (or #645 #649 #707)
-#642 := (not #707)
-#644 := [hypothesis]: #642
-#635 := [hypothesis]: #639
-#638 := [th-lemma #677 #635 #668 #644]: false
-#646 := [lemma #638]: #643
-#568 := [unit-resolution #646 #567 #584]: #707
-#569 := (or #514 #560 #642)
-#570 := [th-lemma]: #569
-#561 := [unit-resolution #570 #568 #566]: #560
-#571 := [th-lemma #590 #561 #641 #575]: false
-#540 := [lemma #571]: #538
-#697 := [unit-resolution #540 #632]: #530
-#532 := [monotonicity #697]: #541
-#548 := [trans #532 #546]: #547
-#539 := [symm #548]: #549
-#699 := (or #713 #870)
-#715 := (or #698 #713 #870)
-#716 := [def-axiom]: #715
-#701 := [unit-resolution #716 #605]: #699
-#728 := [unit-resolution #701 #697]: #870
-#550 := [mp #728 #539]: #514
-#533 := [unit-resolution #566 #550]: false
-#535 := [lemma #533]: #286
-#553 := (or #274 #285)
-#551 := (or #274 #285 #466)
-#552 := [def-axiom]: #551
-#544 := [unit-resolution #552 #306]: #553
-#496 := [unit-resolution #544 #535]: #274
-#498 := [symm #496]: #58
-#499 := [monotonicity #498]: #494
-#485 := [monotonicity #499]: #481
-#491 := [trans #485 #489]: #490
-#492 := [symm #491]: #483
-#474 := [monotonicity #492]: #473
-#524 := (or #577 #285)
-#525 := [th-lemma]: #524
-#526 := [unit-resolution #525 #535]: #577
-#527 := (or #713 #876)
-#516 := [th-lemma]: #527
-#528 := [unit-resolution #516 #526]: #713
-#509 := [unit-resolution #607 #528]: #559
-#511 := [unit-resolution #831 #526]: #472
-#512 := [unit-resolution #703 #511 #509]: #543
-#502 := [unit-resolution #583 #512]: #816
-#508 := (or #560 #285 #706 #649)
-#482 := [th-lemma]: #508
-#487 := [unit-resolution #482 #502 #535 #659]: #560
-#488 := (or #692 #722)
-#493 := [th-lemma]: #488
-#495 := [unit-resolution #493 #487]: #692
-#477 := [mp #495 #474]: #476
-#510 := [unit-resolution #588 #512]: #817
-#513 := (or #802 #591 #589)
-#501 := [th-lemma]: #513
-#503 := [unit-resolution #501 #510 #602]: #802
-#803 := (or #804 #806)
-#196 := (= #9 #45)
-#221 := (or #196 #215)
-#903 := (forall (vars (?v0 int)) (:pat #902) #221)
-#226 := (forall (vars (?v0 int)) #221)
-#906 := (iff #226 #903)
-#904 := (iff #221 #221)
-#905 := [refl]: #904
-#907 := [quant-intro #905]: #906
-#314 := (~ #226 #226)
-#331 := (~ #221 #221)
-#332 := [refl]: #331
-#315 := [nnf-pos #332]: #314
-#46 := (= #45 #9)
-#43 := (<= 0::int #9)
-#47 := (implies #43 #46)
-#48 := (forall (vars (?v0 int)) #47)
-#229 := (iff #48 #226)
-#203 := (not #43)
-#204 := (or #203 #196)
-#209 := (forall (vars (?v0 int)) #204)
-#227 := (iff #209 #226)
-#224 := (iff #204 #221)
-#218 := (or #215 #196)
-#222 := (iff #218 #221)
-#223 := [rewrite]: #222
-#219 := (iff #204 #218)
-#216 := (iff #203 #215)
-#213 := (iff #43 #212)
-#214 := [rewrite]: #213
-#217 := [monotonicity #214]: #216
-#220 := [monotonicity #217]: #219
-#225 := [trans #220 #223]: #224
-#228 := [quant-intro #225]: #227
-#210 := (iff #48 #209)
-#207 := (iff #47 #204)
-#200 := (implies #43 #196)
-#205 := (iff #200 #204)
-#206 := [rewrite]: #205
-#201 := (iff #47 #200)
-#198 := (iff #46 #196)
-#199 := [rewrite]: #198
-#202 := [monotonicity #199]: #201
-#208 := [trans #202 #206]: #207
-#211 := [quant-intro #208]: #210
-#230 := [trans #211 #228]: #229
-#195 := [asserted]: #48
-#231 := [mp #195 #230]: #226
-#333 := [mp~ #231 #315]: #226
-#908 := [mp #333 #907]: #903
-#798 := (not #903)
-#799 := (or #798 #804 #806)
-#807 := (or #806 #804)
-#800 := (or #798 #807)
-#790 := (iff #800 #799)
-#801 := (or #798 #803)
-#788 := (iff #801 #799)
-#789 := [rewrite]: #788
-#785 := (iff #800 #801)
-#808 := (iff #807 #803)
-#797 := [rewrite]: #808
-#786 := [monotonicity #797]: #785
-#791 := [trans #786 #789]: #790
-#794 := [quant-inst]: #800
-#787 := [mp #794 #791]: #799
-#504 := [unit-resolution #787 #908]: #803
-#507 := [unit-resolution #504 #503]: #806
-[unit-resolution #507 #477]: false
-unsat
-b7e0eef92ca8fea2ccc91684e833dc3dce9b2d04 60 0
+4074dbc15aab16237aedd305561f8f85160e4534 60 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -22724,7 +22741,7 @@
 #630 := [unit-resolution #632 #631]: #266
 [th-lemma #159 #629 #630]: false
 unsat
-5617bc6b938b986893bfcfa7ce1760c2311e1366 60 0
+9442a35efa1592899520592c7d46119b2144010b 60 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -22785,68 +22802,7 @@
 #630 := [th-lemma]: #632
 [unit-resolution #630 #271 #159]: false
 unsat
-050c8f359b390869bd7cdf1db28b2773829a0360 60 0
-#2 := false
-#13 := 0::int
-decl f4 :: (-> S2 int)
-decl f5 :: S2
-#25 := f5
-#26 := (f4 f5)
-decl f6 :: S2
-#27 := f6
-#28 := (f4 f6)
-#137 := -1::int
-#138 := (* -1::int #28)
-#139 := (+ #26 #138)
-#140 := (<= #139 0::int)
-#143 := (ite #140 #28 #26)
-#149 := (* -1::int #143)
-#150 := (+ #26 #149)
-#151 := (<= #150 0::int)
-#156 := (not #151)
-#29 := (<= #26 #28)
-#30 := (ite #29 #28 #26)
-#31 := (<= #26 #30)
-#32 := (not #31)
-#157 := (iff #32 #156)
-#154 := (iff #31 #151)
-#146 := (<= #26 #143)
-#152 := (iff #146 #151)
-#153 := [rewrite]: #152
-#147 := (iff #31 #146)
-#144 := (= #30 #143)
-#141 := (iff #29 #140)
-#142 := [rewrite]: #141
-#145 := [monotonicity #142]: #144
-#148 := [monotonicity #145]: #147
-#155 := [trans #148 #153]: #154
-#158 := [monotonicity #155]: #157
-#134 := [asserted]: #32
-#159 := [mp #134 #158]: #156
-#317 := (= #26 #143)
-#232 := (not #140)
-#625 := [hypothesis]: #140
-#637 := (+ #28 #149)
-#280 := (<= #637 0::int)
-#231 := (= #28 #143)
-#318 := (or #232 #231)
-#319 := [def-axiom]: #318
-#626 := [unit-resolution #319 #625]: #231
-#627 := (not #231)
-#622 := (or #627 #280)
-#628 := [th-lemma]: #622
-#266 := [unit-resolution #628 #626]: #280
-#629 := [th-lemma #266 #159 #625]: false
-#631 := [lemma #629]: #232
-#310 := (or #140 #317)
-#321 := [def-axiom]: #310
-#271 := [unit-resolution #321 #631]: #317
-#272 := (not #317)
-#632 := (or #272 #151)
-#630 := [th-lemma]: #632
-[unit-resolution #630 #271 #159]: false
-unsat
-04cc411b96731925afb67c561af17d4cb6d68cf0 253 0
+eb08c6d90226991816b4f3abfe6264a0f1fa3905 253 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -23100,68 +23056,7 @@
 #473 := [lemma #472]: #233
 [unit-resolution #631 #473 #487]: false
 unsat
-80aafa9ce13a262b7746b90465ebd387a9798fb0 60 0
-#2 := false
-#13 := 0::int
-decl f4 :: (-> S2 int)
-decl f6 :: S2
-#27 := f6
-#28 := (f4 f6)
-decl f5 :: S2
-#25 := f5
-#26 := (f4 f5)
-#137 := -1::int
-#140 := (* -1::int #28)
-#141 := (+ #26 #140)
-#139 := (>= #141 0::int)
-#143 := (ite #139 #26 #28)
-#149 := (* -1::int #143)
-#637 := (+ #28 #149)
-#628 := (<= #637 0::int)
-#317 := (= #28 #143)
-#232 := (not #139)
-#231 := (= #26 #143)
-#624 := (not #231)
-#150 := (+ #26 #149)
-#151 := (<= #150 0::int)
-#156 := (not #151)
-#29 := (<= #28 #26)
-#30 := (ite #29 #26 #28)
-#31 := (<= #26 #30)
-#32 := (not #31)
-#157 := (iff #32 #156)
-#154 := (iff #31 #151)
-#146 := (<= #26 #143)
-#152 := (iff #146 #151)
-#153 := [rewrite]: #152
-#147 := (iff #31 #146)
-#144 := (= #30 #143)
-#138 := (iff #29 #139)
-#142 := [rewrite]: #138
-#145 := [monotonicity #142]: #144
-#148 := [monotonicity #145]: #147
-#155 := [trans #148 #153]: #154
-#158 := [monotonicity #155]: #157
-#134 := [asserted]: #32
-#159 := [mp #134 #158]: #156
-#280 := [hypothesis]: #231
-#625 := (or #624 #151)
-#626 := [th-lemma]: #625
-#627 := [unit-resolution #626 #280 #159]: false
-#622 := [lemma #627]: #624
-#318 := (or #232 #231)
-#319 := [def-axiom]: #318
-#629 := [unit-resolution #319 #622]: #232
-#310 := (or #139 #317)
-#321 := [def-axiom]: #310
-#631 := [unit-resolution #321 #629]: #317
-#271 := (not #317)
-#272 := (or #271 #628)
-#632 := [th-lemma]: #272
-#630 := [unit-resolution #632 #631]: #628
-[th-lemma #159 #629 #630]: false
-unsat
-afcf8a254d165c5e9d701ed584fa3d55dcc74a09 103 0
+10d1d752d0a0c4e3c0dc122dff179efd1e39b4f9 103 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -23265,7 +23160,404 @@
 #642 := [unit-resolution #636 #635]: #638
 [th-lemma #642 #193 #194]: false
 unsat
-b9568adc9ac22f504348a42395408d6d8271d777 437 0
+c6f1492295e45b3c74df0329c8861d7ab1ee2b99 117 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#13 := 0::int
+#141 := -1::int
+#142 := (* -1::int #28)
+#143 := (+ #26 #142)
+#154 := (>= #143 0::int)
+#156 := (ite #154 #28 #26)
+#159 := (f3 #156)
+#144 := (<= #143 0::int)
+#147 := (ite #144 #26 #28)
+#150 := (f3 #147)
+#162 := (= #150 #159)
+#649 := (f3 #26)
+#558 := (= #649 #159)
+#556 := (= #159 #649)
+#564 := (= #156 #26)
+#259 := (= #26 #156)
+#436 := (f3 #28)
+#577 := (= #436 #159)
+#586 := (= #159 #436)
+#479 := (= #156 #28)
+#331 := (= #28 #156)
+#489 := (not #259)
+#584 := [hypothesis]: #489
+#312 := (or #154 #259)
+#647 := [def-axiom]: #312
+#588 := [unit-resolution #647 #584]: #154
+#332 := (not #154)
+#329 := (or #332 #331)
+#333 := [def-axiom]: #329
+#490 := [unit-resolution #333 #588]: #331
+#480 := [symm #490]: #479
+#590 := [monotonicity #480]: #586
+#579 := [symm #590]: #577
+#491 := (= #150 #436)
+#492 := (= #147 #28)
+#326 := (= #28 #147)
+#241 := (not #144)
+#496 := (or #241 #259)
+#473 := (= #26 #28)
+#585 := [hypothesis]: #144
+#488 := [th-lemma #588 #585]: #473
+#494 := [trans #488 #490]: #259
+#495 := [unit-resolution #584 #494]: false
+#589 := [lemma #495]: #496
+#439 := [unit-resolution #589 #584]: #241
+#319 := (or #144 #326)
+#330 := [def-axiom]: #319
+#587 := [unit-resolution #330 #439]: #326
+#493 := [symm #587]: #492
+#484 := [monotonicity #493]: #491
+#571 := [trans #484 #579]: #162
+#165 := (not #162)
+#32 := (<= #28 #26)
+#33 := (ite #32 #28 #26)
+#34 := (f3 #33)
+#29 := (<= #26 #28)
+#30 := (ite #29 #26 #28)
+#31 := (f3 #30)
+#35 := (= #31 #34)
+#36 := (not #35)
+#166 := (iff #36 #165)
+#163 := (iff #35 #162)
+#160 := (= #34 #159)
+#157 := (= #33 #156)
+#153 := (iff #32 #154)
+#155 := [rewrite]: #153
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#151 := (= #31 #150)
+#148 := (= #30 #147)
+#145 := (iff #29 #144)
+#146 := [rewrite]: #145
+#149 := [monotonicity #146]: #148
+#152 := [monotonicity #149]: #151
+#164 := [monotonicity #152 #161]: #163
+#167 := [monotonicity #164]: #166
+#138 := [asserted]: #36
+#168 := [mp #138 #167]: #165
+#568 := [unit-resolution #168 #571]: false
+#570 := [lemma #568]: #259
+#565 := [symm #570]: #564
+#557 := [monotonicity #565]: #556
+#555 := [symm #557]: #558
+#553 := (= #150 #649)
+#562 := (= #147 #26)
+#240 := (= #26 #147)
+#435 := [hypothesis]: #241
+#437 := (or #154 #144)
+#596 := [th-lemma]: #437
+#478 := [unit-resolution #596 #435]: #154
+#580 := [unit-resolution #333 #478]: #331
+#581 := [symm #580]: #479
+#572 := [monotonicity #581]: #586
+#573 := [symm #572]: #577
+#582 := [unit-resolution #330 #435]: #326
+#578 := [symm #582]: #492
+#583 := [monotonicity #578]: #491
+#574 := [trans #583 #573]: #162
+#575 := [unit-resolution #168 #574]: false
+#569 := [lemma #575]: #144
+#327 := (or #241 #240)
+#328 := [def-axiom]: #327
+#566 := [unit-resolution #328 #569]: #240
+#567 := [symm #566]: #562
+#554 := [monotonicity #567]: #553
+#559 := [trans #554 #555]: #162
+[unit-resolution #168 #559]: false
+unsat
+38c6093f0f392dc5915b448aa2995bf2f0bfe107 156 0
+#2 := false
+decl f3 :: (-> int S2)
+#13 := 0::int
+#30 := (f3 0::int)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#27 := (<= #26 0::int)
+#28 := (ite #27 #26 0::int)
+#29 := (f3 #28)
+#31 := (= #29 #30)
+#294 := (= #28 0::int)
+#299 := (f3 #26)
+#576 := (f4 #299)
+#577 := (= #576 0::int)
+#442 := (= #26 0::int)
+#567 := (not #294)
+#573 := [hypothesis]: #567
+#287 := (or #27 #294)
+#298 := [def-axiom]: #287
+#404 := [unit-resolution #298 #573]: #27
+#581 := (>= #26 0::int)
+#408 := (not #577)
+#556 := (iff #567 #408)
+#448 := (iff #294 #577)
+#565 := (= #28 #576)
+#564 := (= #26 #576)
+#561 := (= #576 #26)
+#568 := (= #299 f5)
+#227 := (= f5 #299)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#624 := (pattern #9)
+#10 := (f3 #9)
+#50 := (= #8 #10)
+#625 := (forall (vars (?v0 S2)) (:pat #624) #50)
+#53 := (forall (vars (?v0 S2)) #50)
+#626 := (iff #53 #625)
+#628 := (iff #625 #625)
+#629 := [rewrite]: #628
+#627 := [rewrite]: #626
+#630 := [trans #627 #629]: #626
+#148 := (~ #53 #53)
+#146 := (~ #50 #50)
+#147 := [refl]: #146
+#149 := [nnf-pos #147]: #148
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#54 := (iff #12 #53)
+#51 := (iff #11 #50)
+#52 := [rewrite]: #51
+#55 := [quant-intro #52]: #54
+#49 := [asserted]: #12
+#58 := [mp #49 #55]: #53
+#137 := [mp~ #58 #149]: #53
+#631 := [mp #137 #630]: #625
+#301 := (not #625)
+#280 := (or #301 #227)
+#616 := [quant-inst]: #280
+#574 := [unit-resolution #616 #631]: #227
+#575 := [symm #574]: #568
+#563 := [monotonicity #575]: #561
+#562 := [symm #563]: #564
+#407 := (= #28 #26)
+#208 := (= #26 #28)
+#209 := (not #27)
+#295 := (or #209 #208)
+#296 := [def-axiom]: #295
+#406 := [unit-resolution #296 #404]: #208
+#560 := [symm #406]: #407
+#447 := [trans #560 #562]: #565
+#449 := [monotonicity #447]: #448
+#458 := [monotonicity #449]: #556
+#553 := [mp #573 #458]: #408
+#582 := (or #577 #581)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#632 := (pattern #16)
+#75 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#123 := (or #22 #75)
+#639 := (forall (vars (?v0 int)) (:pat #632) #123)
+#128 := (forall (vars (?v0 int)) #123)
+#642 := (iff #128 #639)
+#640 := (iff #123 #123)
+#641 := [refl]: #640
+#643 := [quant-intro #641]: #642
+#140 := (~ #128 #128)
+#152 := (~ #123 #123)
+#153 := [refl]: #152
+#141 := [nnf-pos #153]: #140
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#131 := (iff #24 #128)
+#94 := (= 0::int #17)
+#100 := (not #21)
+#101 := (or #100 #94)
+#106 := (forall (vars (?v0 int)) #101)
+#129 := (iff #106 #128)
+#126 := (iff #101 #123)
+#120 := (or #75 #22)
+#124 := (iff #120 #123)
+#125 := [rewrite]: #124
+#121 := (iff #101 #120)
+#118 := (iff #94 #22)
+#119 := [rewrite]: #118
+#116 := (iff #100 #75)
+#76 := (not #75)
+#111 := (not #76)
+#114 := (iff #111 #75)
+#115 := [rewrite]: #114
+#112 := (iff #100 #111)
+#109 := (iff #21 #76)
+#110 := [rewrite]: #109
+#113 := [monotonicity #110]: #112
+#117 := [trans #113 #115]: #116
+#122 := [monotonicity #117 #119]: #121
+#127 := [trans #122 #125]: #126
+#130 := [quant-intro #127]: #129
+#107 := (iff #24 #106)
+#104 := (iff #23 #101)
+#97 := (implies #21 #94)
+#102 := (iff #97 #101)
+#103 := [rewrite]: #102
+#98 := (iff #23 #97)
+#95 := (iff #22 #94)
+#96 := [rewrite]: #95
+#99 := [monotonicity #96]: #98
+#105 := [trans #99 #103]: #104
+#108 := [quant-intro #105]: #107
+#132 := [trans #108 #130]: #131
+#93 := [asserted]: #24
+#133 := [mp #93 #132]: #128
+#154 := [mp~ #133 #141]: #128
+#644 := [mp #154 #643]: #639
+#614 := (not #639)
+#584 := (or #614 #577 #581)
+#425 := (or #614 #582)
+#427 := (iff #425 #584)
+#569 := [rewrite]: #427
+#426 := [quant-inst]: #425
+#570 := [mp #426 #569]: #584
+#554 := [unit-resolution #570 #644]: #582
+#557 := [unit-resolution #554 #553]: #581
+#457 := [th-lemma #557 #404]: #442
+#459 := [trans #563 #457]: #577
+#460 := [unit-resolution #553 #459]: false
+#453 := [lemma #460]: #294
+#583 := [monotonicity #453]: #31
+#32 := (not #31)
+#134 := [asserted]: #32
+[unit-resolution #134 #583]: false
+unsat
+4caa7a6de95275e585bcbfa107fdfb54d2012d31 60 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#137 := -1::int
+#138 := (* -1::int #28)
+#139 := (+ #26 #138)
+#140 := (<= #139 0::int)
+#143 := (ite #140 #28 #26)
+#149 := (* -1::int #143)
+#150 := (+ #26 #149)
+#151 := (<= #150 0::int)
+#156 := (not #151)
+#29 := (<= #26 #28)
+#30 := (ite #29 #28 #26)
+#31 := (<= #26 #30)
+#32 := (not #31)
+#157 := (iff #32 #156)
+#154 := (iff #31 #151)
+#146 := (<= #26 #143)
+#152 := (iff #146 #151)
+#153 := [rewrite]: #152
+#147 := (iff #31 #146)
+#144 := (= #30 #143)
+#141 := (iff #29 #140)
+#142 := [rewrite]: #141
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#155 := [trans #148 #153]: #154
+#158 := [monotonicity #155]: #157
+#134 := [asserted]: #32
+#159 := [mp #134 #158]: #156
+#317 := (= #26 #143)
+#232 := (not #140)
+#625 := [hypothesis]: #140
+#637 := (+ #28 #149)
+#280 := (<= #637 0::int)
+#231 := (= #28 #143)
+#318 := (or #232 #231)
+#319 := [def-axiom]: #318
+#626 := [unit-resolution #319 #625]: #231
+#627 := (not #231)
+#622 := (or #627 #280)
+#628 := [th-lemma]: #622
+#266 := [unit-resolution #628 #626]: #280
+#629 := [th-lemma #266 #159 #625]: false
+#631 := [lemma #629]: #232
+#310 := (or #140 #317)
+#321 := [def-axiom]: #310
+#271 := [unit-resolution #321 #631]: #317
+#272 := (not #317)
+#632 := (or #272 #151)
+#630 := [th-lemma]: #632
+[unit-resolution #630 #271 #159]: false
+unsat
+fbd182f7c2ad46bc5fee5b8d11bd416e7c294329 60 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#137 := -1::int
+#140 := (* -1::int #28)
+#141 := (+ #26 #140)
+#139 := (>= #141 0::int)
+#143 := (ite #139 #26 #28)
+#149 := (* -1::int #143)
+#637 := (+ #28 #149)
+#628 := (<= #637 0::int)
+#317 := (= #28 #143)
+#232 := (not #139)
+#231 := (= #26 #143)
+#624 := (not #231)
+#150 := (+ #26 #149)
+#151 := (<= #150 0::int)
+#156 := (not #151)
+#29 := (<= #28 #26)
+#30 := (ite #29 #26 #28)
+#31 := (<= #26 #30)
+#32 := (not #31)
+#157 := (iff #32 #156)
+#154 := (iff #31 #151)
+#146 := (<= #26 #143)
+#152 := (iff #146 #151)
+#153 := [rewrite]: #152
+#147 := (iff #31 #146)
+#144 := (= #30 #143)
+#138 := (iff #29 #139)
+#142 := [rewrite]: #138
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#155 := [trans #148 #153]: #154
+#158 := [monotonicity #155]: #157
+#134 := [asserted]: #32
+#159 := [mp #134 #158]: #156
+#280 := [hypothesis]: #231
+#625 := (or #624 #151)
+#626 := [th-lemma]: #625
+#627 := [unit-resolution #626 #280 #159]: false
+#622 := [lemma #627]: #624
+#318 := (or #232 #231)
+#319 := [def-axiom]: #318
+#629 := [unit-resolution #319 #622]: #232
+#310 := (or #139 #317)
+#321 := [def-axiom]: #310
+#631 := [unit-resolution #321 #629]: #317
+#271 := (not #317)
+#272 := (or #271 #628)
+#632 := [th-lemma]: #272
+#630 := [unit-resolution #632 #631]: #628
+[th-lemma #159 #629 #630]: false
+unsat
+61951a09fb52ca2089f14d4ffbd54536b2b1af8e 437 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -23703,125 +23995,7 @@
 #462 := [unit-resolution #492 #479]: #669
 [th-lemma #462 #528 #194 #475 #461]: false
 unsat
-caea920980c91680caa298496d6beb2d2bf61295 117 0
-#2 := false
-decl f3 :: (-> int S2)
-decl f4 :: (-> S2 int)
-decl f5 :: S2
-#25 := f5
-#26 := (f4 f5)
-decl f6 :: S2
-#27 := f6
-#28 := (f4 f6)
-#13 := 0::int
-#141 := -1::int
-#142 := (* -1::int #28)
-#143 := (+ #26 #142)
-#154 := (>= #143 0::int)
-#156 := (ite #154 #28 #26)
-#159 := (f3 #156)
-#144 := (<= #143 0::int)
-#147 := (ite #144 #26 #28)
-#150 := (f3 #147)
-#162 := (= #150 #159)
-#649 := (f3 #26)
-#558 := (= #649 #159)
-#556 := (= #159 #649)
-#564 := (= #156 #26)
-#259 := (= #26 #156)
-#436 := (f3 #28)
-#577 := (= #436 #159)
-#586 := (= #159 #436)
-#479 := (= #156 #28)
-#331 := (= #28 #156)
-#489 := (not #259)
-#584 := [hypothesis]: #489
-#312 := (or #154 #259)
-#647 := [def-axiom]: #312
-#588 := [unit-resolution #647 #584]: #154
-#332 := (not #154)
-#329 := (or #332 #331)
-#333 := [def-axiom]: #329
-#490 := [unit-resolution #333 #588]: #331
-#480 := [symm #490]: #479
-#590 := [monotonicity #480]: #586
-#579 := [symm #590]: #577
-#491 := (= #150 #436)
-#492 := (= #147 #28)
-#326 := (= #28 #147)
-#241 := (not #144)
-#496 := (or #241 #259)
-#473 := (= #26 #28)
-#585 := [hypothesis]: #144
-#488 := [th-lemma #588 #585]: #473
-#494 := [trans #488 #490]: #259
-#495 := [unit-resolution #584 #494]: false
-#589 := [lemma #495]: #496
-#439 := [unit-resolution #589 #584]: #241
-#319 := (or #144 #326)
-#330 := [def-axiom]: #319
-#587 := [unit-resolution #330 #439]: #326
-#493 := [symm #587]: #492
-#484 := [monotonicity #493]: #491
-#571 := [trans #484 #579]: #162
-#165 := (not #162)
-#32 := (<= #28 #26)
-#33 := (ite #32 #28 #26)
-#34 := (f3 #33)
-#29 := (<= #26 #28)
-#30 := (ite #29 #26 #28)
-#31 := (f3 #30)
-#35 := (= #31 #34)
-#36 := (not #35)
-#166 := (iff #36 #165)
-#163 := (iff #35 #162)
-#160 := (= #34 #159)
-#157 := (= #33 #156)
-#153 := (iff #32 #154)
-#155 := [rewrite]: #153
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#151 := (= #31 #150)
-#148 := (= #30 #147)
-#145 := (iff #29 #144)
-#146 := [rewrite]: #145
-#149 := [monotonicity #146]: #148
-#152 := [monotonicity #149]: #151
-#164 := [monotonicity #152 #161]: #163
-#167 := [monotonicity #164]: #166
-#138 := [asserted]: #36
-#168 := [mp #138 #167]: #165
-#568 := [unit-resolution #168 #571]: false
-#570 := [lemma #568]: #259
-#565 := [symm #570]: #564
-#557 := [monotonicity #565]: #556
-#555 := [symm #557]: #558
-#553 := (= #150 #649)
-#562 := (= #147 #26)
-#240 := (= #26 #147)
-#435 := [hypothesis]: #241
-#437 := (or #154 #144)
-#596 := [th-lemma]: #437
-#478 := [unit-resolution #596 #435]: #154
-#580 := [unit-resolution #333 #478]: #331
-#581 := [symm #580]: #479
-#572 := [monotonicity #581]: #586
-#573 := [symm #572]: #577
-#582 := [unit-resolution #330 #435]: #326
-#578 := [symm #582]: #492
-#583 := [monotonicity #578]: #491
-#574 := [trans #583 #573]: #162
-#575 := [unit-resolution #168 #574]: false
-#569 := [lemma #575]: #144
-#327 := (or #241 #240)
-#328 := [def-axiom]: #327
-#566 := [unit-resolution #328 #569]: #240
-#567 := [symm #566]: #562
-#554 := [monotonicity #567]: #553
-#559 := [trans #554 #555]: #162
-[unit-resolution #168 #559]: false
-unsat
-d7b83db7c0c4e066fdea2d94e35ab3cc620d56df 103 0
+66c028c24c4c559b994678db25313aa09de4710c 103 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -23925,164 +24099,7 @@
 #642 := [unit-resolution #636 #635]: #639
 [th-lemma #642 #195 #194]: false
 unsat
-140237685072a702cc83b447cdc8b15858b3f321 156 0
-#2 := false
-decl f3 :: (-> int S2)
-#13 := 0::int
-#30 := (f3 0::int)
-decl f4 :: (-> S2 int)
-decl f5 :: S2
-#25 := f5
-#26 := (f4 f5)
-#27 := (<= #26 0::int)
-#28 := (ite #27 #26 0::int)
-#29 := (f3 #28)
-#31 := (= #29 #30)
-#294 := (= #28 0::int)
-#299 := (f3 #26)
-#576 := (f4 #299)
-#577 := (= #576 0::int)
-#442 := (= #26 0::int)
-#567 := (not #294)
-#573 := [hypothesis]: #567
-#287 := (or #27 #294)
-#298 := [def-axiom]: #287
-#404 := [unit-resolution #298 #573]: #27
-#581 := (>= #26 0::int)
-#408 := (not #577)
-#556 := (iff #567 #408)
-#448 := (iff #294 #577)
-#565 := (= #28 #576)
-#564 := (= #26 #576)
-#561 := (= #576 #26)
-#568 := (= #299 f5)
-#227 := (= f5 #299)
-#8 := (:var 0 S2)
-#9 := (f4 #8)
-#624 := (pattern #9)
-#10 := (f3 #9)
-#50 := (= #8 #10)
-#625 := (forall (vars (?v0 S2)) (:pat #624) #50)
-#53 := (forall (vars (?v0 S2)) #50)
-#626 := (iff #53 #625)
-#628 := (iff #625 #625)
-#629 := [rewrite]: #628
-#627 := [rewrite]: #626
-#630 := [trans #627 #629]: #626
-#148 := (~ #53 #53)
-#146 := (~ #50 #50)
-#147 := [refl]: #146
-#149 := [nnf-pos #147]: #148
-#11 := (= #10 #8)
-#12 := (forall (vars (?v0 S2)) #11)
-#54 := (iff #12 #53)
-#51 := (iff #11 #50)
-#52 := [rewrite]: #51
-#55 := [quant-intro #52]: #54
-#49 := [asserted]: #12
-#58 := [mp #49 #55]: #53
-#137 := [mp~ #58 #149]: #53
-#631 := [mp #137 #630]: #625
-#301 := (not #625)
-#280 := (or #301 #227)
-#616 := [quant-inst]: #280
-#574 := [unit-resolution #616 #631]: #227
-#575 := [symm #574]: #568
-#563 := [monotonicity #575]: #561
-#562 := [symm #563]: #564
-#407 := (= #28 #26)
-#208 := (= #26 #28)
-#209 := (not #27)
-#295 := (or #209 #208)
-#296 := [def-axiom]: #295
-#406 := [unit-resolution #296 #404]: #208
-#560 := [symm #406]: #407
-#447 := [trans #560 #562]: #565
-#449 := [monotonicity #447]: #448
-#458 := [monotonicity #449]: #556
-#553 := [mp #573 #458]: #408
-#582 := (or #577 #581)
-#14 := (:var 0 int)
-#16 := (f3 #14)
-#632 := (pattern #16)
-#75 := (>= #14 0::int)
-#17 := (f4 #16)
-#22 := (= #17 0::int)
-#123 := (or #22 #75)
-#639 := (forall (vars (?v0 int)) (:pat #632) #123)
-#128 := (forall (vars (?v0 int)) #123)
-#642 := (iff #128 #639)
-#640 := (iff #123 #123)
-#641 := [refl]: #640
-#643 := [quant-intro #641]: #642
-#140 := (~ #128 #128)
-#152 := (~ #123 #123)
-#153 := [refl]: #152
-#141 := [nnf-pos #153]: #140
-#21 := (< #14 0::int)
-#23 := (implies #21 #22)
-#24 := (forall (vars (?v0 int)) #23)
-#131 := (iff #24 #128)
-#94 := (= 0::int #17)
-#100 := (not #21)
-#101 := (or #100 #94)
-#106 := (forall (vars (?v0 int)) #101)
-#129 := (iff #106 #128)
-#126 := (iff #101 #123)
-#120 := (or #75 #22)
-#124 := (iff #120 #123)
-#125 := [rewrite]: #124
-#121 := (iff #101 #120)
-#118 := (iff #94 #22)
-#119 := [rewrite]: #118
-#116 := (iff #100 #75)
-#76 := (not #75)
-#111 := (not #76)
-#114 := (iff #111 #75)
-#115 := [rewrite]: #114
-#112 := (iff #100 #111)
-#109 := (iff #21 #76)
-#110 := [rewrite]: #109
-#113 := [monotonicity #110]: #112
-#117 := [trans #113 #115]: #116
-#122 := [monotonicity #117 #119]: #121
-#127 := [trans #122 #125]: #126
-#130 := [quant-intro #127]: #129
-#107 := (iff #24 #106)
-#104 := (iff #23 #101)
-#97 := (implies #21 #94)
-#102 := (iff #97 #101)
-#103 := [rewrite]: #102
-#98 := (iff #23 #97)
-#95 := (iff #22 #94)
-#96 := [rewrite]: #95
-#99 := [monotonicity #96]: #98
-#105 := [trans #99 #103]: #104
-#108 := [quant-intro #105]: #107
-#132 := [trans #108 #130]: #131
-#93 := [asserted]: #24
-#133 := [mp #93 #132]: #128
-#154 := [mp~ #133 #141]: #128
-#644 := [mp #154 #643]: #639
-#614 := (not #639)
-#584 := (or #614 #577 #581)
-#425 := (or #614 #582)
-#427 := (iff #425 #584)
-#569 := [rewrite]: #427
-#426 := [quant-inst]: #425
-#570 := [mp #426 #569]: #584
-#554 := [unit-resolution #570 #644]: #582
-#557 := [unit-resolution #554 #553]: #581
-#457 := [th-lemma #557 #404]: #442
-#459 := [trans #563 #457]: #577
-#460 := [unit-resolution #553 #459]: false
-#453 := [lemma #460]: #294
-#583 := [monotonicity #453]: #31
-#32 := (not #31)
-#134 := [asserted]: #32
-[unit-resolution #134 #583]: false
-unsat
-7941a5e6f861d5ba779c3ff6672cac31550af836 119 0
+c7ef08ae30d09ac3bf3a67f4c70b9f016d5c193d 119 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -24202,7 +24219,7 @@
 #540 := [trans #557 #539]: #162
 [unit-resolution #168 #540]: false
 unsat
-fbf28453c2565ae4248c42863556e4f8088a62a2 164 0
+de0569dfa609484291fd81eb9f8f2d06ac7df87e 164 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -24367,7 +24384,7 @@
 #142 := [mp #133 #139]: #137
 [unit-resolution #142 #586]: false
 unsat
-c457a6610bcddee5fbeec4bb3572ce6f1d88807f 139 0
+c8eeb350cb516605831698143f1f1d1d3e6b51b8 139 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -24507,7 +24524,7 @@
 #260 := [th-lemma]: #618
 [unit-resolution #260 #139 #617]: false
 unsat
-f025d25f9f9c8e38fac474962b7f2dfba4e1a07a 75 0
+a677190c79920172b4c094aa328e083224d68a2e 75 0
 #2 := false
 decl f3 :: (-> int S2)
 #28 := 1::int
@@ -24583,7 +24600,7 @@
 #153 := [and-elim #151]: #32
 [unit-resolution #153 #339]: false
 unsat
-c8f2ead1c220dd8ed211af0515b88614b1941079 20 0
+d5039e16983283e82085df5e73a771ee0e6bf12f 20 0
 #2 := false
 decl f4 :: (-> S2 int)
 decl f5 :: S2
@@ -24604,7 +24621,7 @@
 #130 := [asserted]: #28
 [mp #130 #141]: false
 unsat
-747cc264821ac8db5ad7ac37788ade0f4e407c6a 319 0
+cad8e547443c8bd397b95f47a3959f36a56a30e7 319 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -24924,51 +24941,7 @@
 #507 := [unit-resolution #506 #504]: #623
 [th-lemma #507 #516 #163 #162]: false
 unsat
-ee051bde3c817c0890ce724f834fd4253b261c0e 17 0
-#2 := false
-#8 := 0::int
-#9 := (= 0::int 0::int)
-#10 := (not #9)
-#35 := (iff #10 false)
-#1 := true
-#30 := (not true)
-#33 := (iff #30 false)
-#34 := [rewrite]: #33
-#31 := (iff #10 #30)
-#28 := (iff #9 true)
-#29 := [rewrite]: #28
-#32 := [monotonicity #29]: #31
-#36 := [trans #32 #34]: #35
-#27 := [asserted]: #10
-[mp #27 #36]: false
-unsat
-28a8e8694abd02c43e1fd53f8a8f970f52a27053 25 0
-#2 := false
-#8 := 0::int
-#9 := (- 0::int)
-#10 := (= 0::int #9)
-#11 := (not #10)
-#43 := (iff #11 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #11 #38)
-#36 := (iff #10 true)
-#31 := (= 0::int 0::int)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #10 #31)
-#29 := (= #9 0::int)
-#30 := [rewrite]: #29
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#28 := [asserted]: #11
-[mp #28 #44]: false
-unsat
-0df3e9ed226dfff3cefc71e4bc79cb937d7b5379 325 0
+6a1f854efc2b68dbbc1c6ad0b95ab4d173e0f832 325 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -25294,60 +25267,7 @@
 #515 := [th-lemma]: #519
 [unit-resolution #515 #510 #517]: false
 unsat
-7e2eed6546d767248580207671baf3c1fef46bda 17 0
-#2 := false
-#8 := 1::int
-#9 := (= 1::int 1::int)
-#10 := (not #9)
-#35 := (iff #10 false)
-#1 := true
-#30 := (not true)
-#33 := (iff #30 false)
-#34 := [rewrite]: #33
-#31 := (iff #10 #30)
-#28 := (iff #9 true)
-#29 := [rewrite]: #28
-#32 := [monotonicity #29]: #31
-#36 := [trans #32 #34]: #35
-#27 := [asserted]: #10
-[mp #27 #36]: false
-unsat
-83be50b0dfcaa8788a3a347c206dfe65b71396c0 34 0
-#2 := false
-#8 := 1::int
-#9 := (- 1::int)
-#10 := (= #9 1::int)
-#11 := (not #10)
-#12 := (not #11)
-#52 := (iff #12 false)
-#1 := true
-#47 := (not true)
-#50 := (iff #47 false)
-#51 := [rewrite]: #50
-#48 := (iff #12 #47)
-#45 := (iff #11 true)
-#40 := (not false)
-#43 := (iff #40 true)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 false)
-#30 := -1::int
-#33 := (= -1::int 1::int)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#31 := (= #9 -1::int)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#29 := [asserted]: #12
-[mp #29 #53]: false
-unsat
-87afea5c9ab9449c41123c8fdd4e20f06a72b155 38 0
+2ec72668db3b36f3b8a69c427d7a238fd684db71 38 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -25386,79 +25306,7 @@
 #228 := [unit-resolution #313 #154]: #144
 [unit-resolution #228 #155]: false
 unsat
-6b06bc907860e099747eaf937729c46239164204 40 0
-#2 := false
-#12 := 567::int
-#10 := 345::int
-#8 := 123::int
-#9 := (- 123::int)
-#11 := (+ #9 345::int)
-#13 := (< #11 567::int)
-#14 := (not #13)
-#58 := (iff #14 false)
-#38 := 222::int
-#43 := (< 222::int 567::int)
-#46 := (not #43)
-#56 := (iff #46 false)
-#1 := true
-#51 := (not true)
-#54 := (iff #51 false)
-#55 := [rewrite]: #54
-#52 := (iff #46 #51)
-#49 := (iff #43 true)
-#50 := [rewrite]: #49
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#47 := (iff #14 #46)
-#44 := (iff #13 #43)
-#41 := (= #11 222::int)
-#32 := -123::int
-#35 := (+ -123::int 345::int)
-#39 := (= #35 222::int)
-#40 := [rewrite]: #39
-#36 := (= #11 #35)
-#33 := (= #9 -123::int)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#42 := [trans #37 #40]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#59 := [trans #48 #57]: #58
-#31 := [asserted]: #14
-[mp #31 #59]: false
-unsat
-b28c9714ddda449b19d3e58f8860da63f62b1deb 30 0
-#2 := false
-#10 := 2345678901::int
-#8 := 123456789::int
-#9 := (- 123456789::int)
-#11 := (< #9 2345678901::int)
-#12 := (not #11)
-#48 := (iff #12 false)
-#30 := -123456789::int
-#33 := (< -123456789::int 2345678901::int)
-#36 := (not #33)
-#46 := (iff #36 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #36 #41)
-#39 := (iff #33 true)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#37 := (iff #12 #36)
-#34 := (iff #11 #33)
-#31 := (= #9 -123456789::int)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#38 := [monotonicity #35]: #37
-#49 := [trans #38 #47]: #48
-#29 := [asserted]: #12
-[mp #29 #49]: false
-unsat
-c7398895db207a7bb660baa83c993733723b339a 70 0
+d330a1f8ebf2d0fec7be03f5037c32f58639f99c 70 0
 #2 := false
 #149 := -1::int
 decl f4 :: (-> S2 int)
@@ -25529,34 +25377,7 @@
 #333 := [unit-resolution #247 #172]: #332
 [unit-resolution #333 #352 #253]: false
 unsat
-fbc565374e3b4fadcdcd336b454d25bde6467984 26 0
-#2 := false
-decl f3 :: int
-#8 := f3
-#9 := 0::int
-#10 := (+ f3 0::int)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-1c6447ae3efd555f314253453337411963c9b538 11 0
[phone]e188d4717956cbaeb240c5f4e2cba2 11 0
 #2 := false
 decl f4 :: (-> S2 int)
 decl f5 :: S2
@@ -25568,34 +25389,7 @@
 #129 := [asserted]: #27
 [mp #129 #133]: false
 unsat
-1e80490820921041707f27ae0a0d7240e7d720ab 26 0
-#2 := false
-decl f3 :: int
-#9 := f3
-#8 := 0::int
-#10 := (+ 0::int f3)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-efe17b9041c87fa89222f21112652ecefaf9bedd 54 0
+52c2ac6921be6bd2c71f4ab8f4c44a928bcb997b 54 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -25650,37 +25444,7 @@
 #171 := [and-elim #170]: #144
 [th-lemma #171 #172 #173]: false
 unsat
-71f4e35d43eaaeb0679a8b9fedb7bbbab02c4bce 29 0
-#2 := false
-decl f3 :: int
-#8 := f3
-decl f4 :: int
-#9 := f4
-#11 := (+ f4 f3)
-#10 := (+ f3 f4)
-#12 := (= #10 #11)
-#13 := (not #12)
-#45 := (iff #13 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #13 #40)
-#38 := (iff #12 true)
-#33 := (= #10 #10)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #12 #33)
-#31 := (= #11 #10)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#30 := [asserted]: #13
-[mp #30 #46]: false
-unsat
-c6c3e4476b55ace179a4bf0db3bd85166dd656f0 55 0
+5eae2a4fbd0e54456548290c77334af0468cece5 55 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -25736,41 +25500,7 @@
 #172 := [and-elim #171]: #144
 [th-lemma #172 #173 #174]: false
 unsat
-29b7b3cf808acec0133f90b0ff01d3741beb5a05 33 0
-#2 := false
-decl f5 :: int
-#10 := f5
-decl f4 :: int
-#9 := f4
-decl f3 :: int
-#8 := f3
-#13 := (+ f3 f4)
-#14 := (+ #13 f5)
-#11 := (+ f4 f5)
-#12 := (+ f3 #11)
-#15 := (= #12 #14)
-#16 := (not #15)
-#48 := (iff #16 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #16 #43)
-#41 := (iff #15 true)
-#36 := (= #12 #12)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #15 #36)
-#34 := (= #14 #12)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#33 := [asserted]: #16
-[mp #33 #49]: false
-unsat
-8b0fe59ad928398852287cdf2c2184de1f57bfbd 55 0
+0c36d79220934231280882d1d54867396cd0031a 55 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -25826,80 +25556,7 @@
 #173 := [and-elim #171]: #152
 [th-lemma #173 #172 #174]: false
 unsat
-4237cbb86bd8822b359c36bc821360aed38710bb 45 0
-#2 := false
-decl f4 :: int
-#9 := f4
-#13 := (- f4)
-decl f3 :: int
-#8 := f3
-#14 := (= f3 #13)
-#11 := 0::int
-#10 := (+ f3 f4)
-#12 := (= #10 0::int)
-#15 := (iff #12 #14)
-#16 := (not #15)
-#62 := (iff #16 false)
-#47 := (not #12)
-#34 := -1::int
-#35 := (* -1::int f4)
-#38 := (= f3 #35)
-#48 := (iff #38 #47)
-#60 := (iff #48 false)
-#55 := (iff #12 #47)
-#58 := (iff #55 false)
-#59 := [rewrite]: #58
-#56 := (iff #48 #55)
-#53 := (iff #38 #12)
-#54 := [rewrite]: #53
-#57 := [monotonicity #54]: #56
-#61 := [trans #57 #59]: #60
-#51 := (iff #16 #48)
-#41 := (iff #12 #38)
-#44 := (not #41)
-#49 := (iff #44 #48)
-#50 := [rewrite]: #49
-#45 := (iff #16 #44)
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
-#36 := (= #13 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#52 := [trans #46 #50]: #51
-#63 := [trans #52 #61]: #62
-#33 := [asserted]: #16
-[mp #33 #63]: false
-unsat
-113be911296a33250bbcd43128973cc59f93526e 26 0
-#2 := false
-#8 := 1::int
-#9 := (- 1::int)
-#10 := (= #9 #9)
-#11 := (not #10)
-#44 := (iff #11 false)
-#1 := true
-#39 := (not true)
-#42 := (iff #39 false)
-#43 := [rewrite]: #42
-#40 := (iff #11 #39)
-#37 := (iff #10 true)
-#29 := -1::int
-#32 := (= -1::int -1::int)
-#35 := (iff #32 true)
-#36 := [rewrite]: #35
-#33 := (iff #10 #32)
-#30 := (= #9 -1::int)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31 #31]: #33
-#38 := [trans #34 #36]: #37
-#41 := [monotonicity #38]: #40
-#45 := [trans #41 #43]: #44
-#28 := [asserted]: #11
-[mp #28 #45]: false
-unsat
-f6ff37f2a66568ce60ecd5249eff25718c85c238 61 0
+c93058caf36a057964e1bab33e7f686758590a7e 61 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -25961,34 +25618,7 @@
 #179 := [and-elim #177]: #149
 [th-lemma #179 #178 #180]: false
 unsat
-cec95d65322be695abf9c2181f05ec8f90e8a935 26 0
-#2 := false
-#8 := 3::int
-#9 := (- 3::int)
-#10 := (= #9 #9)
-#11 := (not #10)
-#44 := (iff #11 false)
-#1 := true
-#39 := (not true)
-#42 := (iff #39 false)
-#43 := [rewrite]: #42
-#40 := (iff #11 #39)
-#37 := (iff #10 true)
-#29 := -3::int
-#32 := (= -3::int -3::int)
-#35 := (iff #32 true)
-#36 := [rewrite]: #35
-#33 := (iff #10 #32)
-#30 := (= #9 -3::int)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31 #31]: #33
-#38 := [trans #34 #36]: #37
-#41 := [monotonicity #38]: #40
-#45 := [trans #41 #43]: #44
-#28 := [asserted]: #11
-[mp #28 #45]: false
-unsat
-dab3885ba8215d926ee3c6f413de786f19602704 53 0
+26a905c581a2781c4b9313a01ce57c14a146f3a4 53 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -26042,7 +25672,394 @@
 #171 := [and-elim #169]: #149
 [th-lemma #171 #170 #172]: false
 unsat
-9d1587620b1ac03e716760e9b77670cdcbc0d869 58 0
+e6bd262de3d717c48ae59eb4ff8475e32e795575 17 0
+#2 := false
+#8 := 0::int
+#9 := (= 0::int 0::int)
+#10 := (not #9)
+#35 := (iff #10 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #10 #30)
+#28 := (iff #9 true)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#27 := [asserted]: #10
+[mp #27 #36]: false
+unsat
+ea4874d7a9ef1bea29138e12697c45ed117f01c7 25 0
+#2 := false
+#8 := 0::int
+#9 := (- 0::int)
+#10 := (= 0::int #9)
+#11 := (not #10)
+#43 := (iff #11 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #11 #38)
+#36 := (iff #10 true)
+#31 := (= 0::int 0::int)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #10 #31)
+#29 := (= #9 0::int)
+#30 := [rewrite]: #29
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#28 := [asserted]: #11
+[mp #28 #44]: false
+unsat
+5d406d304b7c2e1977b6b205d2a8acd758e7e9d6 17 0
+#2 := false
+#8 := 1::int
+#9 := (= 1::int 1::int)
+#10 := (not #9)
+#35 := (iff #10 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #10 #30)
+#28 := (iff #9 true)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#27 := [asserted]: #10
+[mp #27 #36]: false
+unsat
+09e199f0d90bbb2bf232c73122105189c833791b 34 0
+#2 := false
+#8 := 1::int
+#9 := (- 1::int)
+#10 := (= #9 1::int)
+#11 := (not #10)
+#12 := (not #11)
+#52 := (iff #12 false)
+#1 := true
+#47 := (not true)
+#50 := (iff #47 false)
+#51 := [rewrite]: #50
+#48 := (iff #12 #47)
+#45 := (iff #11 true)
+#40 := (not false)
+#43 := (iff #40 true)
+#44 := [rewrite]: #43
+#41 := (iff #11 #40)
+#38 := (iff #10 false)
+#30 := -1::int
+#33 := (= -1::int 1::int)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #10 #33)
+#31 := (= #9 -1::int)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#49 := [monotonicity #46]: #48
+#53 := [trans #49 #51]: #52
+#29 := [asserted]: #12
+[mp #29 #53]: false
+unsat
+e2a67322774c86302ba3178437319069d13a3a75 40 0
+#2 := false
+#12 := 567::int
+#10 := 345::int
+#8 := 123::int
+#9 := (- 123::int)
+#11 := (+ #9 345::int)
+#13 := (< #11 567::int)
+#14 := (not #13)
+#58 := (iff #14 false)
+#38 := 222::int
+#43 := (< 222::int 567::int)
+#46 := (not #43)
+#56 := (iff #46 false)
+#1 := true
+#51 := (not true)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #46 #51)
+#49 := (iff #43 true)
+#50 := [rewrite]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#47 := (iff #14 #46)
+#44 := (iff #13 #43)
+#41 := (= #11 222::int)
+#32 := -123::int
+#35 := (+ -123::int 345::int)
+#39 := (= #35 222::int)
+#40 := [rewrite]: #39
+#36 := (= #11 #35)
+#33 := (= #9 -123::int)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#42 := [trans #37 #40]: #41
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#59 := [trans #48 #57]: #58
+#31 := [asserted]: #14
+[mp #31 #59]: false
+unsat
+50e1f8fb4287fc584888510f6d6ab76b2777719b 30 0
+#2 := false
+#10 := 2345678901::int
+#8 := 123456789::int
+#9 := (- 123456789::int)
+#11 := (< #9 2345678901::int)
+#12 := (not #11)
+#48 := (iff #12 false)
+#30 := -123456789::int
+#33 := (< -123456789::int 2345678901::int)
+#36 := (not #33)
+#46 := (iff #36 false)
+#1 := true
+#41 := (not true)
+#44 := (iff #41 false)
+#45 := [rewrite]: #44
+#42 := (iff #36 #41)
+#39 := (iff #33 true)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#37 := (iff #12 #36)
+#34 := (iff #11 #33)
+#31 := (= #9 -123456789::int)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#38 := [monotonicity #35]: #37
+#49 := [trans #38 #47]: #48
+#29 := [asserted]: #12
+[mp #29 #49]: false
+unsat
+c5504a64a0a0a3c5426e45f1a782c6e6d431e66d 26 0
+#2 := false
+decl f3 :: int
+#8 := f3
+#9 := 0::int
+#10 := (+ f3 0::int)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+e592e6b2534442c3dff94b68f94c1aee18f9632b 26 0
+#2 := false
+decl f3 :: int
+#9 := f3
+#8 := 0::int
+#10 := (+ 0::int f3)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+8226bbe61388476a973d63d7687a92354da01bef 29 0
+#2 := false
+decl f3 :: int
+#8 := f3
+decl f4 :: int
+#9 := f4
+#11 := (+ f4 f3)
+#10 := (+ f3 f4)
+#12 := (= #10 #11)
+#13 := (not #12)
+#45 := (iff #13 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #13 #40)
+#38 := (iff #12 true)
+#33 := (= #10 #10)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #12 #33)
+#31 := (= #11 #10)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#30 := [asserted]: #13
+[mp #30 #46]: false
+unsat
+a3cc8378c3590a2ccf8ae1cba8093d50ae445cde 33 0
+#2 := false
+decl f5 :: int
+#10 := f5
+decl f4 :: int
+#9 := f4
+decl f3 :: int
+#8 := f3
+#13 := (+ f3 f4)
+#14 := (+ #13 f5)
+#11 := (+ f4 f5)
+#12 := (+ f3 #11)
+#15 := (= #12 #14)
+#16 := (not #15)
+#48 := (iff #16 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #16 #43)
+#41 := (iff #15 true)
+#36 := (= #12 #12)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #15 #36)
+#34 := (= #14 #12)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#33 := [asserted]: #16
+[mp #33 #49]: false
+unsat
+08075bd55ad9ddab0e3fbca70cb9ca5d72303dbd 45 0
+#2 := false
+decl f4 :: int
+#9 := f4
+#13 := (- f4)
+decl f3 :: int
+#8 := f3
+#14 := (= f3 #13)
+#11 := 0::int
+#10 := (+ f3 f4)
+#12 := (= #10 0::int)
+#15 := (iff #12 #14)
+#16 := (not #15)
+#62 := (iff #16 false)
+#47 := (not #12)
+#34 := -1::int
+#35 := (* -1::int f4)
+#38 := (= f3 #35)
+#48 := (iff #38 #47)
+#60 := (iff #48 false)
+#55 := (iff #12 #47)
+#58 := (iff #55 false)
+#59 := [rewrite]: #58
+#56 := (iff #48 #55)
+#53 := (iff #38 #12)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#51 := (iff #16 #48)
+#41 := (iff #12 #38)
+#44 := (not #41)
+#49 := (iff #44 #48)
+#50 := [rewrite]: #49
+#45 := (iff #16 #44)
+#42 := (iff #15 #41)
+#39 := (iff #14 #38)
+#36 := (= #13 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#46 := [monotonicity #43]: #45
+#52 := [trans #46 #50]: #51
+#63 := [trans #52 #61]: #62
+#33 := [asserted]: #16
+[mp #33 #63]: false
+unsat
+ba430c8a44bab7eb1828eca75ad021d7dd513926 26 0
+#2 := false
+#8 := 1::int
+#9 := (- 1::int)
+#10 := (= #9 #9)
+#11 := (not #10)
+#44 := (iff #11 false)
+#1 := true
+#39 := (not true)
+#42 := (iff #39 false)
+#43 := [rewrite]: #42
+#40 := (iff #11 #39)
+#37 := (iff #10 true)
+#29 := -1::int
+#32 := (= -1::int -1::int)
+#35 := (iff #32 true)
+#36 := [rewrite]: #35
+#33 := (iff #10 #32)
+#30 := (= #9 -1::int)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31 #31]: #33
+#38 := [trans #34 #36]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#28 := [asserted]: #11
+[mp #28 #45]: false
+unsat
+50356c04df69dfa829f918064c98c6a7f2ec540f 26 0
+#2 := false
+#8 := 3::int
+#9 := (- 3::int)
+#10 := (= #9 #9)
+#11 := (not #10)
+#44 := (iff #11 false)
+#1 := true
+#39 := (not true)
+#42 := (iff #39 false)
+#43 := [rewrite]: #42
+#40 := (iff #11 #39)
+#37 := (iff #10 true)
+#29 := -3::int
+#32 := (= -3::int -3::int)
+#35 := (iff #32 true)
+#36 := [rewrite]: #35
+#33 := (iff #10 #32)
+#30 := (= #9 -3::int)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31 #31]: #33
+#38 := [trans #34 #36]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#28 := [asserted]: #11
+[mp #28 #45]: false
+unsat
+2876964f2e9f9de6f1b8bdf26bcd62db4061e963 58 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -26101,7 +26118,7 @@
 #31 := [asserted]: #14
 [mp #31 #77]: false
 unsat
-2fe4017173baaf767c6629bd6852a7b438932e50 61 0
+c404564f91090d797ca0c4d6ac4d2725a94a3008 61 0
 #2 := false
 #8 := 0::int
 decl f3 :: int
@@ -26163,34 +26180,7 @@
 #31 := [asserted]: #14
 [mp #31 #79]: false
 unsat
-6f7f580886df4b14f8fb404c5d3a00f03fbd8ee6 26 0
-#2 := false
-decl f3 :: int
-#8 := f3
-#9 := 0::int
-#10 := (- f3 0::int)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-fdb98420125ded457439e02e837bc03d7148c23c 61 0
+cf893c1bd9e3559197de2c51c1e19f108f84c273 61 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -26252,7 +26242,34 @@
 #31 := [asserted]: #14
 [mp #31 #79]: false
 unsat
-445783642ee7433013df57b7e4cef00ffeb157e0 32 0
+2147bf456f0bde5886de21d8e7658b53b0b9b24a 26 0
+#2 := false
+decl f3 :: int
+#8 := f3
+#9 := 0::int
+#10 := (- f3 0::int)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+b1b317f6f3f9d1cf66ad920159ac5de2168fd773 32 0
 #2 := false
 decl f3 :: int
 #9 := f3
@@ -26285,7 +26302,7 @@
 #30 := [asserted]: #13
 [mp #30 #50]: false
 unsat
-ed57db9b5bc45b814efcbe55950db276a0ae6227 64 0
+aaec5802e18a03261b352fc88937049c0c5144ac 64 0
 #2 := false
 #12 := 0::int
 decl f4 :: int
@@ -26350,61 +26367,7 @@
 #32 := [asserted]: #15
 [mp #32 #81]: false
 unsat
-5fea704d847c1f572f04828761c6aeed07320331 26 0
-#2 := false
-#9 := 0::int
-decl f3 :: int
-#8 := f3
-#10 := (* f3 0::int)
-#11 := (= #10 0::int)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= 0::int 0::int)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-afeb47d1fabcd35b9434330dd3b684867663bcd6 26 0
-#2 := false
-#8 := 0::int
-decl f3 :: int
-#9 := f3
-#10 := (* 0::int f3)
-#11 := (= #10 0::int)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= 0::int 0::int)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-5f6eb6ae429716b4776e5fd2a14d9da3158d991d 44 0
+b5265c805ba121ad3da02d19dff3261548664016 44 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -26449,34 +26412,7 @@
 #31 := [asserted]: #14
 [mp #31 #61]: false
 unsat
-1eeb11e60a6bbbe94fa15811311d2d40ac3f4033 26 0
-#2 := false
-decl f3 :: int
-#8 := f3
-#9 := 1::int
-#10 := (* f3 1::int)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-fd6e7c25e63ac8e70326ced7855970dd3a736cfa 42 0
+fbeba7843ef1b6fb5537e98ff3aede1e719f841d 42 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -26519,34 +26455,7 @@
 #31 := [asserted]: #14
 [mp #31 #59]: false
 unsat
-08503fa6172915df238b523388ddb33a24fd4cb7 26 0
-#2 := false
-decl f3 :: int
-#9 := f3
-#8 := 1::int
-#10 := (* 1::int f3)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-250ddfb8ca251f84a346d955cf6715564ce90b7a 48 0
+0d460b99cc2f72a399f4da24ddcac20a14d04f78 48 0
 #2 := false
 decl f5 :: int
 #11 := f5
@@ -26595,7 +26504,115 @@
 #33 := [asserted]: #16
 [mp #33 #64]: false
 unsat
-2c2b089e4b5c6cb37aa179a9f71ce56ba7d47fd2 40 0
+489455ffdf128288e7746942fe5732cf048ebcdc 26 0
+#2 := false
+#9 := 0::int
+decl f3 :: int
+#8 := f3
+#10 := (* f3 0::int)
+#11 := (= #10 0::int)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= 0::int 0::int)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+9c08216a16bf789716e84d06ce553cc7f028e758 26 0
+#2 := false
+#8 := 0::int
+decl f3 :: int
+#9 := f3
+#10 := (* 0::int f3)
+#11 := (= #10 0::int)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= 0::int 0::int)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+53822dd60fa6e81f5b61e653eca34c1634d4be2a 26 0
+#2 := false
+decl f3 :: int
+#8 := f3
+#9 := 1::int
+#10 := (* f3 1::int)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+338165f614ec3b9e8256ea27fe765fbe3e9fa28c 26 0
+#2 := false
+decl f3 :: int
+#9 := f3
+#8 := 1::int
+#10 := (* 1::int f3)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+cbed9de51f3cb9976f8bc26465342d1ea6fdbc04 40 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -26636,7 +26653,7 @@
 #31 := [asserted]: #14
 [mp #31 #58]: false
 unsat
-df5f08c8b5312cfbfbb1f5bf1a74e868b8d5f32a 35 0
+940f94613c41ab129022169048ef750c49362b77 35 0
 #2 := false
 decl f3 :: int
 #10 := f3
@@ -26672,7 +26689,36 @@
 #31 := [asserted]: #14
 [mp #31 #53]: false
 unsat
-56201244c1c31fc8628969c3f353db10a7f712f1 244 0
+c493b175a6fed3d53b76ecb86bc9380f02650437 28 0
+#2 := false
+#8 := 3::int
+decl f3 :: int
+#9 := f3
+#11 := (* f3 3::int)
+#10 := (* 3::int f3)
+#12 := (= #10 #11)
+#13 := (not #12)
+#45 := (iff #13 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #13 #40)
+#38 := (iff #12 true)
+#33 := (= #10 #10)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #12 #33)
+#31 := (= #11 #10)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#30 := [asserted]: #13
+[mp #30 #46]: false
+unsat
+ce5e35dc168826b1bfeaec92e1e5e2a69f4e8dce 244 0
 #2 := false
 #11 := 0::int
 decl f3 :: (-> int int int)
@@ -26917,305 +26963,7 @@
 #683 := [mp #696 #682]: #695
 [unit-resolution #683 #742 #167]: false
 unsat
-738d46bed422c47f454cfba0aef7d0d41195018e 28 0
-#2 := false
-#8 := 3::int
-decl f3 :: int
-#9 := f3
-#11 := (* f3 3::int)
-#10 := (* 3::int f3)
-#12 := (= #10 #11)
-#13 := (not #12)
-#45 := (iff #13 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #13 #40)
-#38 := (iff #12 true)
-#33 := (= #10 #10)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #12 #33)
-#31 := (= #11 #10)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#30 := [asserted]: #13
-[mp #30 #46]: false
-unsat
-b55995757cc7c0e54ef05dc5c7ed8997164e973f 268 0
-#2 := false
-#11 := 0::int
-decl f4 :: (-> int int int)
-#38 := (f4 0::int 0::int)
-#39 := (= #38 0::int)
-#40 := (not #39)
-#167 := [asserted]: #40
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#743 := (pattern #29)
-#64 := -1::int
-#68 := (* -1::int #9)
-#65 := (* -1::int #8)
-#123 := (mod #65 #68)
-#254 := (+ #29 #123)
-#255 := (= #254 0::int)
-#30 := (mod #8 #9)
-#251 := (* -1::int #30)
-#252 := (+ #29 #251)
-#253 := (= #252 0::int)
-#90 := (<= #9 0::int)
-#86 := (<= #8 0::int)
-#193 := (or #86 #90)
-#194 := (not #193)
-#97 := (>= #8 0::int)
-#185 := (or #90 #97)
-#186 := (not #185)
-#200 := (or #186 #194)
-#256 := (ite #200 #253 #255)
-#250 := (= #29 0::int)
-#12 := (= #8 0::int)
-#257 := (ite #12 #250 #256)
-#249 := (= #8 #29)
-#13 := (= #9 0::int)
-#258 := (ite #13 #249 #257)
-#744 := (forall (vars (?v0 int) (?v1 int)) (:pat #743) #258)
-#261 := (forall (vars (?v0 int) (?v1 int)) #258)
-#747 := (iff #261 #744)
-#745 := (iff #258 #258)
-#746 := [refl]: #745
-#748 := [quant-intro #746]: #747
-#129 := (* -1::int #123)
-#218 := (ite #200 #30 #129)
-#221 := (ite #12 0::int #218)
-#224 := (ite #13 #8 #221)
-#227 := (= #29 #224)
-#230 := (forall (vars (?v0 int) (?v1 int)) #227)
-#262 := (iff #230 #261)
-#259 := (iff #227 #258)
-#260 := [rewrite]: #259
-#263 := [quant-intro #260]: #262
-#98 := (not #97)
-#91 := (not #90)
-#101 := (and #91 #98)
-#87 := (not #86)
-#94 := (and #87 #91)
-#104 := (or #94 #101)
-#149 := (ite #104 #30 #129)
-#152 := (ite #12 0::int #149)
-#155 := (ite #13 #8 #152)
-#158 := (= #29 #155)
-#161 := (forall (vars (?v0 int) (?v1 int)) #158)
-#231 := (iff #161 #230)
-#228 := (iff #158 #227)
-#225 := (= #155 #224)
-#222 := (= #152 #221)
-#219 := (= #149 #218)
-#203 := (iff #104 #200)
-#197 := (or #194 #186)
-#201 := (iff #197 #200)
-#202 := [rewrite]: #201
-#198 := (iff #104 #197)
-#195 := (iff #101 #186)
-#196 := [rewrite]: #195
-#183 := (iff #94 #194)
-#184 := [rewrite]: #183
-#199 := [monotonicity #184 #196]: #198
-#204 := [trans #199 #202]: #203
-#220 := [monotonicity #204]: #219
-#223 := [monotonicity #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [quant-intro #229]: #231
-#181 := (~ #161 #161)
-#178 := (~ #158 #158)
-#191 := [refl]: #178
-#182 := [nnf-pos #191]: #181
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#164 := (iff #37 #161)
-#58 := (and #16 #18)
-#61 := (or #17 #58)
-#134 := (ite #61 #30 #129)
-#137 := (ite #12 0::int #134)
-#140 := (ite #13 #8 #137)
-#143 := (= #29 #140)
-#146 := (forall (vars (?v0 int) (?v1 int)) #143)
-#162 := (iff #146 #161)
-#159 := (iff #143 #158)
-#156 := (= #140 #155)
-#153 := (= #137 #152)
-#150 := (= #134 #149)
-#105 := (iff #61 #104)
-#102 := (iff #58 #101)
-#99 := (iff #18 #98)
-#100 := [rewrite]: #99
-#92 := (iff #16 #91)
-#93 := [rewrite]: #92
-#103 := [monotonicity #93 #100]: #102
-#95 := (iff #17 #94)
-#88 := (iff #15 #87)
-#89 := [rewrite]: #88
-#96 := [monotonicity #89 #93]: #95
-#106 := [monotonicity #96 #103]: #105
-#151 := [monotonicity #106]: #150
-#154 := [monotonicity #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [quant-intro #160]: #162
-#147 := (iff #37 #146)
-#144 := (iff #36 #143)
-#141 := (= #35 #140)
-#138 := (= #34 #137)
-#135 := (= #33 #134)
-#132 := (= #32 #129)
-#126 := (- #123)
-#130 := (= #126 #129)
-#131 := [rewrite]: #130
-#127 := (= #32 #126)
-#124 := (= #31 #123)
-#69 := (= #23 #68)
-#70 := [rewrite]: #69
-#66 := (= #22 #65)
-#67 := [rewrite]: #66
-#125 := [monotonicity #67 #70]: #124
-#128 := [monotonicity #125]: #127
-#133 := [trans #128 #131]: #132
-#62 := (iff #20 #61)
-#59 := (iff #19 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#136 := [monotonicity #63 #133]: #135
-#139 := [monotonicity #136]: #138
-#142 := [monotonicity #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [quant-intro #145]: #147
-#165 := [trans #148 #163]: #164
-#122 := [asserted]: #37
-#166 := [mp #122 #165]: #161
-#192 := [mp~ #166 #182]: #161
-#233 := [mp #192 #232]: #230
-#264 := [mp #233 #263]: #261
-#749 := [mp #264 #748]: #744
-#690 := (not #744)
-#696 := (or #690 #39)
-#322 := (* -1::int 0::int)
-#407 := (mod #322 #322)
-#408 := (+ #38 #407)
-#409 := (= #408 0::int)
-#400 := (mod 0::int 0::int)
-#411 := (* -1::int #400)
-#412 := (+ #38 #411)
-#340 := (= #412 0::int)
-#413 := (<= 0::int 0::int)
-#410 := (or #413 #413)
-#414 := (not #410)
-#393 := (>= 0::int 0::int)
-#728 := (or #413 #393)
-#730 := (not #728)
-#387 := (or #730 #414)
-#517 := (ite #387 #340 #409)
-#724 := (= 0::int 0::int)
-#398 := (ite #724 #39 #517)
-#168 := (= 0::int #38)
-#399 := (ite #724 #168 #398)
-#537 := (or #690 #399)
-#539 := (iff #537 #696)
-#682 := (iff #696 #696)
-#683 := [rewrite]: #682
-#694 := (iff #399 #39)
-#1 := true
-#691 := (ite true #39 #39)
-#688 := (iff #691 #39)
-#689 := [rewrite]: #688
-#692 := (iff #399 #691)
-#698 := (iff #398 #39)
-#328 := (+ #38 #400)
-#428 := (= #328 0::int)
-#699 := (ite true #39 #428)
-#697 := (iff #699 #39)
-#701 := [rewrite]: #697
-#700 := (iff #398 #699)
-#420 := (iff #517 #428)
-#707 := (ite false #340 #428)
-#418 := (iff #707 #428)
-#419 := [rewrite]: #418
-#704 := (iff #517 #707)
-#429 := (iff #409 #428)
-#705 := (= #408 #328)
-#434 := (= #407 #400)
-#432 := (= #322 0::int)
-#433 := [rewrite]: #432
-#435 := [monotonicity #433 #433]: #434
-#706 := [monotonicity #435]: #705
-#703 := [monotonicity #706]: #429
-#709 := (iff #387 false)
-#361 := (or false false)
-#720 := (iff #361 false)
-#723 := [rewrite]: #720
-#362 := (iff #387 #361)
-#719 := (iff #414 false)
-#711 := (not true)
-#376 := (iff #711 false)
-#377 := [rewrite]: #376
-#718 := (iff #414 #711)
-#717 := (iff #410 true)
-#725 := (or true true)
-#726 := (iff #725 true)
-#386 := [rewrite]: #726
-#715 := (iff #410 #725)
-#733 := (iff #413 true)
-#734 := [rewrite]: #733
-#716 := [monotonicity #734 #734]: #715
-#712 := [trans #716 #386]: #717
-#356 := [monotonicity #712]: #718
-#721 := [trans #356 #377]: #719
-#713 := (iff #730 false)
-#374 := (iff #730 #711)
-#727 := (iff #728 true)
-#385 := (iff #728 #725)
-#729 := (iff #393 true)
-#735 := [rewrite]: #729
-#390 := [monotonicity #734 #735]: #385
-#370 := [trans #390 #386]: #727
-#375 := [monotonicity #370]: #374
-#714 := [trans #375 #377]: #713
-#722 := [monotonicity #714 #721]: #362
-#710 := [trans #722 #723]: #709
-#708 := [monotonicity #710 #703]: #704
-#421 := [trans #708 #419]: #420
-#731 := (iff #724 true)
-#732 := [rewrite]: #731
-#415 := [monotonicity #732 #421]: #700
-#702 := [trans #415 #701]: #698
-#174 := (iff #168 #39)
-#175 := [rewrite]: #174
-#693 := [monotonicity #732 #175 #702]: #692
-#695 := [trans #693 #689]: #694
-#681 := [monotonicity #695]: #539
-#684 := [trans #681 #683]: #539
-#538 := [quant-inst]: #537
-#678 := [mp #538 #684]: #696
-[unit-resolution #678 #749 #167]: false
-unsat
-fa3f22f8699f818222604ac64aca7fd59a22aa11 257 0
+642bc9b337aeacbe5fb93c93a30fa2c7adff6654 257 0
 #2 := false
 #11 := 0::int
 decl f3 :: (-> int int int)
@@ -27473,284 +27221,7 @@
 #673 := [mp #687 #520]: #680
 [unit-resolution #673 #743 #168]: false
 unsat
-706350a91145c463c7f48c3bf9879c01a9686cec 276 0
-#2 := false
-decl f4 :: (-> int int int)
-#11 := 0::int
-decl f5 :: int
-#38 := f5
-#39 := (f4 f5 0::int)
-#169 := (= f5 #39)
-#172 := (not #169)
-#40 := (= #39 f5)
-#41 := (not #40)
-#173 := (iff #41 #172)
-#170 := (iff #40 #169)
-#171 := [rewrite]: #170
-#174 := [monotonicity #171]: #173
-#168 := [asserted]: #41
-#177 := [mp #168 #174]: #172
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#741 := (pattern #29)
-#65 := -1::int
-#69 := (* -1::int #9)
-#66 := (* -1::int #8)
-#124 := (mod #66 #69)
-#252 := (+ #29 #124)
-#253 := (= #252 0::int)
-#30 := (mod #8 #9)
-#249 := (* -1::int #30)
-#250 := (+ #29 #249)
-#251 := (= #250 0::int)
-#91 := (<= #9 0::int)
-#87 := (<= #8 0::int)
-#191 := (or #87 #91)
-#192 := (not #191)
-#98 := (>= #8 0::int)
-#183 := (or #91 #98)
-#184 := (not #183)
-#198 := (or #184 #192)
-#254 := (ite #198 #251 #253)
-#248 := (= #29 0::int)
-#12 := (= #8 0::int)
-#255 := (ite #12 #248 #254)
-#247 := (= #8 #29)
-#13 := (= #9 0::int)
-#256 := (ite #13 #247 #255)
-#742 := (forall (vars (?v0 int) (?v1 int)) (:pat #741) #256)
-#259 := (forall (vars (?v0 int) (?v1 int)) #256)
-#745 := (iff #259 #742)
-#743 := (iff #256 #256)
-#744 := [refl]: #743
-#746 := [quant-intro #744]: #745
-#130 := (* -1::int #124)
-#216 := (ite #198 #30 #130)
-#219 := (ite #12 0::int #216)
-#222 := (ite #13 #8 #219)
-#225 := (= #29 #222)
-#228 := (forall (vars (?v0 int) (?v1 int)) #225)
-#260 := (iff #228 #259)
-#257 := (iff #225 #256)
-#258 := [rewrite]: #257
-#261 := [quant-intro #258]: #260
-#99 := (not #98)
-#92 := (not #91)
-#102 := (and #92 #99)
-#88 := (not #87)
-#95 := (and #88 #92)
-#105 := (or #95 #102)
-#150 := (ite #105 #30 #130)
-#153 := (ite #12 0::int #150)
-#156 := (ite #13 #8 #153)
-#159 := (= #29 #156)
-#162 := (forall (vars (?v0 int) (?v1 int)) #159)
-#229 := (iff #162 #228)
-#226 := (iff #159 #225)
-#223 := (= #156 #222)
-#220 := (= #153 #219)
-#217 := (= #150 #216)
-#201 := (iff #105 #198)
-#195 := (or #192 #184)
-#199 := (iff #195 #198)
-#200 := [rewrite]: #199
-#196 := (iff #105 #195)
-#193 := (iff #102 #184)
-#194 := [rewrite]: #193
-#181 := (iff #95 #192)
-#182 := [rewrite]: #181
-#197 := [monotonicity #182 #194]: #196
-#202 := [trans #197 #200]: #201
-#218 := [monotonicity #202]: #217
-#221 := [monotonicity #218]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [quant-intro #227]: #229
-#179 := (~ #162 #162)
-#175 := (~ #159 #159)
-#189 := [refl]: #175
-#180 := [nnf-pos #189]: #179
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#165 := (iff #37 #162)
-#59 := (and #16 #18)
-#62 := (or #17 #59)
-#135 := (ite #62 #30 #130)
-#138 := (ite #12 0::int #135)
-#141 := (ite #13 #8 #138)
-#144 := (= #29 #141)
-#147 := (forall (vars (?v0 int) (?v1 int)) #144)
-#163 := (iff #147 #162)
-#160 := (iff #144 #159)
-#157 := (= #141 #156)
-#154 := (= #138 #153)
-#151 := (= #135 #150)
-#106 := (iff #62 #105)
-#103 := (iff #59 #102)
-#100 := (iff #18 #99)
-#101 := [rewrite]: #100
-#93 := (iff #16 #92)
-#94 := [rewrite]: #93
-#104 := [monotonicity #94 #101]: #103
-#96 := (iff #17 #95)
-#89 := (iff #15 #88)
-#90 := [rewrite]: #89
-#97 := [monotonicity #90 #94]: #96
-#107 := [monotonicity #97 #104]: #106
-#152 := [monotonicity #107]: #151
-#155 := [monotonicity #152]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [quant-intro #161]: #163
-#148 := (iff #37 #147)
-#145 := (iff #36 #144)
-#142 := (= #35 #141)
-#139 := (= #34 #138)
-#136 := (= #33 #135)
-#133 := (= #32 #130)
-#127 := (- #124)
-#131 := (= #127 #130)
-#132 := [rewrite]: #131
-#128 := (= #32 #127)
-#125 := (= #31 #124)
-#70 := (= #23 #69)
-#71 := [rewrite]: #70
-#67 := (= #22 #66)
-#68 := [rewrite]: #67
-#126 := [monotonicity #68 #71]: #125
-#129 := [monotonicity #126]: #128
-#134 := [trans #129 #132]: #133
-#63 := (iff #20 #62)
-#60 := (iff #19 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#137 := [monotonicity #64 #134]: #136
-#140 := [monotonicity #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [quant-intro #146]: #148
-#166 := [trans #149 #164]: #165
-#123 := [asserted]: #37
-#167 := [mp #123 #166]: #162
-#190 := [mp~ #167 #180]: #162
-#231 := [mp #190 #230]: #228
-#262 := [mp #231 #261]: #259
-#747 := [mp #262 #746]: #742
-#535 := (not #742)
-#536 := (or #535 #169)
-#320 := (* -1::int 0::int)
-#405 := (* -1::int f5)
-#406 := (mod #405 #320)
-#407 := (+ #39 #406)
-#398 := (= #407 0::int)
-#409 := (mod f5 0::int)
-#410 := (* -1::int #409)
-#338 := (+ #39 #410)
-#411 := (= #338 0::int)
-#408 := (<= 0::int 0::int)
-#412 := (<= f5 0::int)
-#391 := (or #412 #408)
-#726 := (not #391)
-#728 := (>= f5 0::int)
-#385 := (or #408 #728)
-#515 := (not #385)
-#722 := (or #515 #726)
-#396 := (ite #722 #411 #398)
-#397 := (= #39 0::int)
-#729 := (= f5 0::int)
-#730 := (ite #729 #397 #396)
-#731 := (= 0::int 0::int)
-#732 := (ite #731 #169 #730)
-#537 := (or #535 #732)
-#680 := (iff #537 #536)
-#682 := (iff #536 #536)
-#676 := [rewrite]: #682
-#688 := (iff #732 #169)
-#426 := (mod #405 0::int)
-#705 := (+ #39 #426)
-#416 := (= #705 0::int)
-#700 := (ite #729 #397 #416)
-#1 := true
-#691 := (ite true #169 #700)
-#692 := (iff #691 #169)
-#693 := [rewrite]: #692
-#686 := (iff #732 #691)
-#689 := (iff #730 #700)
-#699 := (iff #396 #416)
-#419 := (ite false #411 #416)
-#413 := (iff #419 #416)
-#695 := [rewrite]: #413
-#697 := (iff #396 #419)
-#417 := (iff #398 #416)
-#702 := (= #407 #705)
-#427 := (= #406 #426)
-#703 := (= #320 0::int)
-#704 := [rewrite]: #703
-#701 := [monotonicity #704]: #427
-#706 := [monotonicity #701]: #702
-#418 := [monotonicity #706]: #417
-#433 := (iff #722 false)
-#707 := (or false false)
-#431 := (iff #707 false)
-#432 := [rewrite]: #431
-#708 := (iff #722 #707)
-#718 := (iff #726 false)
-#373 := (not true)
-#711 := (iff #373 false)
-#712 := [rewrite]: #711
-#360 := (iff #726 #373)
-#719 := (iff #391 true)
-#715 := (or #412 true)
-#354 := (iff #715 true)
-#717 := [rewrite]: #354
-#710 := (iff #391 #715)
-#723 := (iff #408 true)
-#383 := [rewrite]: #723
-#716 := [monotonicity #383]: #710
-#359 := [trans #716 #717]: #719
-#720 := [monotonicity #359]: #360
-#721 := [trans #720 #712]: #718
-#713 := (iff #515 false)
-#374 := (iff #515 #373)
-#709 := (iff #385 true)
-#388 := (or true #728)
-#725 := (iff #388 true)
-#368 := [rewrite]: #725
-#724 := (iff #385 #388)
-#384 := [monotonicity #383]: #724
-#372 := [trans #384 #368]: #709
-#375 := [monotonicity #372]: #374
-#714 := [trans #375 #712]: #713
-#430 := [monotonicity #714 #721]: #708
-#326 := [trans #430 #432]: #433
-#698 := [monotonicity #326 #418]: #697
-#696 := [trans #698 #695]: #699
-#690 := [monotonicity #696]: #689
-#727 := (iff #731 true)
-#733 := [rewrite]: #727
-#687 := [monotonicity #733 #690]: #686
-#694 := [trans #687 #693]: #688
-#681 := [monotonicity #694]: #680
-#677 := [trans #681 #676]: #680
-#679 := [quant-inst]: #537
-#683 := [mp #679 #677]: #536
-[unit-resolution #683 #747 #177]: false
-unsat
-f347a4adcb7fcad632a20b1470ae003828031f6b 281 0
+ec51dd5da50a95bcf426f485ae7bcbbb2780776d 281 0
 #2 := false
 #11 := 0::int
 decl f3 :: (-> int int int)
@@ -28032,7 +27503,7 @@
 #667 := [mp #573 #670]: #572
 [unit-resolution #667 #742 #168]: false
 unsat
-9f3a2d1e5184a5f18507c2cbcaba7052c2f44041 281 0
+a9f81f93ee2054f520eef980ca383c9b53df9071 281 0
 #2 := false
 #38 := 1::int
 decl f3 :: (-> int int int)
@@ -28314,306 +27785,7 @@
 #667 := [mp #573 #670]: #572
 [unit-resolution #667 #742 #168]: false
 unsat
-6a680acca8e4fb44be34c90aae6eeffc77e0f409 298 0
-#2 := false
-#11 := 0::int
-decl f4 :: (-> int int int)
-#38 := 1::int
-#39 := (f4 0::int 1::int)
-#40 := (= #39 0::int)
-#41 := (not #40)
-#168 := [asserted]: #41
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#743 := (pattern #29)
-#65 := -1::int
-#69 := (* -1::int #9)
-#66 := (* -1::int #8)
-#124 := (mod #66 #69)
-#255 := (+ #29 #124)
-#256 := (= #255 0::int)
-#30 := (mod #8 #9)
-#252 := (* -1::int #30)
-#253 := (+ #29 #252)
-#254 := (= #253 0::int)
-#91 := (<= #9 0::int)
-#87 := (<= #8 0::int)
-#194 := (or #87 #91)
-#195 := (not #194)
-#98 := (>= #8 0::int)
-#186 := (or #91 #98)
-#187 := (not #186)
-#201 := (or #187 #195)
-#257 := (ite #201 #254 #256)
-#251 := (= #29 0::int)
-#12 := (= #8 0::int)
-#258 := (ite #12 #251 #257)
-#250 := (= #8 #29)
-#13 := (= #9 0::int)
-#259 := (ite #13 #250 #258)
-#744 := (forall (vars (?v0 int) (?v1 int)) (:pat #743) #259)
-#262 := (forall (vars (?v0 int) (?v1 int)) #259)
-#747 := (iff #262 #744)
-#745 := (iff #259 #259)
-#746 := [refl]: #745
-#748 := [quant-intro #746]: #747
-#130 := (* -1::int #124)
-#219 := (ite #201 #30 #130)
-#222 := (ite #12 0::int #219)
-#225 := (ite #13 #8 #222)
-#228 := (= #29 #225)
-#231 := (forall (vars (?v0 int) (?v1 int)) #228)
-#263 := (iff #231 #262)
-#260 := (iff #228 #259)
-#261 := [rewrite]: #260
-#264 := [quant-intro #261]: #263
-#99 := (not #98)
-#92 := (not #91)
-#102 := (and #92 #99)
-#88 := (not #87)
-#95 := (and #88 #92)
-#105 := (or #95 #102)
-#150 := (ite #105 #30 #130)
-#153 := (ite #12 0::int #150)
-#156 := (ite #13 #8 #153)
-#159 := (= #29 #156)
-#162 := (forall (vars (?v0 int) (?v1 int)) #159)
-#232 := (iff #162 #231)
-#229 := (iff #159 #228)
-#226 := (= #156 #225)
-#223 := (= #153 #222)
-#220 := (= #150 #219)
-#204 := (iff #105 #201)
-#198 := (or #195 #187)
-#202 := (iff #198 #201)
-#203 := [rewrite]: #202
-#199 := (iff #105 #198)
-#196 := (iff #102 #187)
-#197 := [rewrite]: #196
-#184 := (iff #95 #195)
-#185 := [rewrite]: #184
-#200 := [monotonicity #185 #197]: #199
-#205 := [trans #200 #203]: #204
-#221 := [monotonicity #205]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [quant-intro #230]: #232
-#182 := (~ #162 #162)
-#179 := (~ #159 #159)
-#192 := [refl]: #179
-#183 := [nnf-pos #192]: #182
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#165 := (iff #37 #162)
-#59 := (and #16 #18)
-#62 := (or #17 #59)
-#135 := (ite #62 #30 #130)
-#138 := (ite #12 0::int #135)
-#141 := (ite #13 #8 #138)
-#144 := (= #29 #141)
-#147 := (forall (vars (?v0 int) (?v1 int)) #144)
-#163 := (iff #147 #162)
-#160 := (iff #144 #159)
-#157 := (= #141 #156)
-#154 := (= #138 #153)
-#151 := (= #135 #150)
-#106 := (iff #62 #105)
-#103 := (iff #59 #102)
-#100 := (iff #18 #99)
-#101 := [rewrite]: #100
-#93 := (iff #16 #92)
-#94 := [rewrite]: #93
-#104 := [monotonicity #94 #101]: #103
-#96 := (iff #17 #95)
-#89 := (iff #15 #88)
-#90 := [rewrite]: #89
-#97 := [monotonicity #90 #94]: #96
-#107 := [monotonicity #97 #104]: #106
-#152 := [monotonicity #107]: #151
-#155 := [monotonicity #152]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [quant-intro #161]: #163
-#148 := (iff #37 #147)
-#145 := (iff #36 #144)
-#142 := (= #35 #141)
-#139 := (= #34 #138)
-#136 := (= #33 #135)
-#133 := (= #32 #130)
-#127 := (- #124)
-#131 := (= #127 #130)
-#132 := [rewrite]: #131
-#128 := (= #32 #127)
-#125 := (= #31 #124)
-#70 := (= #23 #69)
-#71 := [rewrite]: #70
-#67 := (= #22 #66)
-#68 := [rewrite]: #67
-#126 := [monotonicity #68 #71]: #125
-#129 := [monotonicity #126]: #128
-#134 := [trans #129 #132]: #133
-#63 := (iff #20 #62)
-#60 := (iff #19 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#137 := [monotonicity #64 #134]: #136
-#140 := [monotonicity #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [quant-intro #146]: #148
-#166 := [trans #149 #164]: #165
-#123 := [asserted]: #37
-#167 := [mp #123 #166]: #162
-#193 := [mp~ #167 #183]: #162
-#234 := [mp #193 #233]: #231
-#265 := [mp #234 #264]: #262
-#749 := [mp #265 #748]: #744
-#665 := (not #744)
-#666 := (or #665 #40)
-#323 := (* -1::int 1::int)
-#407 := (* -1::int 0::int)
-#408 := (mod #407 #323)
-#409 := (+ #39 #408)
-#400 := (= #409 0::int)
-#411 := (mod 0::int 1::int)
-#412 := (* -1::int #411)
-#413 := (+ #39 #412)
-#410 := (= #413 0::int)
-#414 := (<= 1::int 0::int)
-#393 := (<= 0::int 0::int)
-#728 := (or #393 #414)
-#730 := (not #728)
-#387 := (>= 0::int 0::int)
-#517 := (or #414 #387)
-#724 := (not #517)
-#398 := (or #724 #730)
-#399 := (ite #398 #410 #400)
-#731 := (= 0::int 0::int)
-#732 := (ite #731 #40 #399)
-#169 := (= 0::int #39)
-#733 := (= 1::int 0::int)
-#734 := (ite #733 #169 #732)
-#669 := (or #665 #734)
-#569 := (iff #669 #666)
-#572 := (iff #666 #666)
-#565 := [rewrite]: #572
-#668 := (iff #734 #40)
-#686 := (ite false #40 #40)
-#516 := (iff #686 #40)
-#518 := [rewrite]: #516
-#561 := (iff #734 #686)
-#559 := (iff #732 #40)
-#1 := true
-#673 := (ite true #40 #40)
-#674 := (iff #673 #40)
-#677 := [rewrite]: #674
-#675 := (iff #732 #673)
-#519 := (iff #399 #40)
-#680 := (iff #399 #686)
-#679 := (iff #400 #40)
-#684 := (= #409 #39)
-#415 := (+ #39 0::int)
-#698 := (= #415 #39)
-#702 := [rewrite]: #698
-#682 := (= #409 #415)
-#539 := (= #408 0::int)
-#695 := (mod 0::int -1::int)
-#537 := (= #695 0::int)
-#538 := [rewrite]: #537
-#690 := (= #408 #695)
-#689 := (= #323 -1::int)
-#694 := [rewrite]: #689
-#420 := (= #407 0::int)
-#421 := [rewrite]: #420
-#696 := [monotonicity #421 #694]: #690
-#681 := [trans #696 #538]: #539
-#683 := [monotonicity #681]: #682
-#678 := [trans #683 #702]: #684
-#685 := [monotonicity #678]: #679
-#693 := (iff #410 #40)
-#691 := (= #413 #39)
-#697 := (= #413 #415)
-#699 := (= #412 0::int)
-#418 := (= #412 #407)
-#704 := (= #411 0::int)
-#708 := [rewrite]: #704
-#419 := [monotonicity #708]: #418
-#700 := [trans #419 #421]: #699
-#701 := [monotonicity #700]: #697
-#692 := [trans #701 #702]: #691
-#688 := [monotonicity #692]: #693
-#703 := (iff #398 false)
-#329 := (or false false)
-#428 := (iff #329 false)
-#429 := [rewrite]: #428
-#705 := (iff #398 #329)
-#434 := (iff #730 false)
-#714 := (not true)
-#717 := (iff #714 false)
-#712 := [rewrite]: #717
-#432 := (iff #730 #714)
-#709 := (iff #728 true)
-#361 := (or true false)
-#720 := (iff #361 true)
-#723 := [rewrite]: #720
-#362 := (iff #728 #361)
-#390 := (iff #414 false)
-#726 := [rewrite]: #390
-#719 := (iff #393 true)
-#721 := [rewrite]: #719
-#722 := [monotonicity #721 #726]: #362
-#710 := [trans #722 #723]: #709
-#433 := [monotonicity #710]: #432
-#435 := [trans #433 #712]: #434
-#718 := (iff #724 false)
-#715 := (iff #724 #714)
-#377 := (iff #517 true)
-#370 := (or false true)
-#375 := (iff #370 true)
-#376 := [rewrite]: #375
-#711 := (iff #517 #370)
-#386 := (iff #387 true)
-#727 := [rewrite]: #386
-#374 := [monotonicity #726 #727]: #711
-#713 := [trans #374 #376]: #377
-#716 := [monotonicity #713]: #715
-#356 := [trans #716 #712]: #718
-#706 := [monotonicity #356 #435]: #705
-#707 := [trans #706 #429]: #703
-#687 := [monotonicity #707 #688 #685]: #680
-#672 := [trans #687 #518]: #519
-#725 := (iff #731 true)
-#385 := [rewrite]: #725
-#676 := [monotonicity #385 #672]: #675
-#560 := [trans #676 #677]: #559
-#175 := (iff #169 #40)
-#176 := [rewrite]: #175
-#729 := (iff #733 false)
-#735 := [rewrite]: #729
-#520 := [monotonicity #735 #176 #560]: #561
-#570 := [trans #520 #518]: #668
-#571 := [monotonicity #570]: #569
-#573 := [trans #571 #565]: #569
-#554 := [quant-inst]: #669
-#574 := [mp #554 #573]: #666
-[unit-resolution #574 #749 #168]: false
-unsat
-724afb6ea0d36c4f4d7be70cf80c093f76cab778 292 0
+b5deb231aa878a20847070827dcf77ff81350a3b 292 0
 #2 := false
 #38 := 3::int
 decl f3 :: (-> int int int)
@@ -28906,304 +28078,7 @@
 #660 := [mp #653 #664]: #659
 [unit-resolution #660 #743 #169]: false
 unsat
-3d7d433cca19abbbfd4e4b784dad4abf4567789e 296 0
-#2 := false
-#11 := 0::int
-decl f4 :: (-> int int int)
-#38 := 1::int
-#39 := (f4 1::int 1::int)
-#40 := (= #39 0::int)
-#41 := (not #40)
-#168 := [asserted]: #41
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#743 := (pattern #29)
-#65 := -1::int
-#69 := (* -1::int #9)
-#66 := (* -1::int #8)
-#124 := (mod #66 #69)
-#255 := (+ #29 #124)
-#256 := (= #255 0::int)
-#30 := (mod #8 #9)
-#252 := (* -1::int #30)
-#253 := (+ #29 #252)
-#254 := (= #253 0::int)
-#91 := (<= #9 0::int)
-#87 := (<= #8 0::int)
-#194 := (or #87 #91)
-#195 := (not #194)
-#98 := (>= #8 0::int)
-#186 := (or #91 #98)
-#187 := (not #186)
-#201 := (or #187 #195)
-#257 := (ite #201 #254 #256)
-#251 := (= #29 0::int)
-#12 := (= #8 0::int)
-#258 := (ite #12 #251 #257)
-#250 := (= #8 #29)
-#13 := (= #9 0::int)
-#259 := (ite #13 #250 #258)
-#744 := (forall (vars (?v0 int) (?v1 int)) (:pat #743) #259)
-#262 := (forall (vars (?v0 int) (?v1 int)) #259)
-#747 := (iff #262 #744)
-#745 := (iff #259 #259)
-#746 := [refl]: #745
-#748 := [quant-intro #746]: #747
-#130 := (* -1::int #124)
-#219 := (ite #201 #30 #130)
-#222 := (ite #12 0::int #219)
-#225 := (ite #13 #8 #222)
-#228 := (= #29 #225)
-#231 := (forall (vars (?v0 int) (?v1 int)) #228)
-#263 := (iff #231 #262)
-#260 := (iff #228 #259)
-#261 := [rewrite]: #260
-#264 := [quant-intro #261]: #263
-#99 := (not #98)
-#92 := (not #91)
-#102 := (and #92 #99)
-#88 := (not #87)
-#95 := (and #88 #92)
-#105 := (or #95 #102)
-#150 := (ite #105 #30 #130)
-#153 := (ite #12 0::int #150)
-#156 := (ite #13 #8 #153)
-#159 := (= #29 #156)
-#162 := (forall (vars (?v0 int) (?v1 int)) #159)
-#232 := (iff #162 #231)
-#229 := (iff #159 #228)
-#226 := (= #156 #225)
-#223 := (= #153 #222)
-#220 := (= #150 #219)
-#204 := (iff #105 #201)
-#198 := (or #195 #187)
-#202 := (iff #198 #201)
-#203 := [rewrite]: #202
-#199 := (iff #105 #198)
-#196 := (iff #102 #187)
-#197 := [rewrite]: #196
-#184 := (iff #95 #195)
-#185 := [rewrite]: #184
-#200 := [monotonicity #185 #197]: #199
-#205 := [trans #200 #203]: #204
-#221 := [monotonicity #205]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [quant-intro #230]: #232
-#182 := (~ #162 #162)
-#179 := (~ #159 #159)
-#192 := [refl]: #179
-#183 := [nnf-pos #192]: #182
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#165 := (iff #37 #162)
-#59 := (and #16 #18)
-#62 := (or #17 #59)
-#135 := (ite #62 #30 #130)
-#138 := (ite #12 0::int #135)
-#141 := (ite #13 #8 #138)
-#144 := (= #29 #141)
-#147 := (forall (vars (?v0 int) (?v1 int)) #144)
-#163 := (iff #147 #162)
-#160 := (iff #144 #159)
-#157 := (= #141 #156)
-#154 := (= #138 #153)
-#151 := (= #135 #150)
-#106 := (iff #62 #105)
-#103 := (iff #59 #102)
-#100 := (iff #18 #99)
-#101 := [rewrite]: #100
-#93 := (iff #16 #92)
-#94 := [rewrite]: #93
-#104 := [monotonicity #94 #101]: #103
-#96 := (iff #17 #95)
-#89 := (iff #15 #88)
-#90 := [rewrite]: #89
-#97 := [monotonicity #90 #94]: #96
-#107 := [monotonicity #97 #104]: #106
-#152 := [monotonicity #107]: #151
-#155 := [monotonicity #152]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [quant-intro #161]: #163
-#148 := (iff #37 #147)
-#145 := (iff #36 #144)
-#142 := (= #35 #141)
-#139 := (= #34 #138)
-#136 := (= #33 #135)
-#133 := (= #32 #130)
-#127 := (- #124)
-#131 := (= #127 #130)
-#132 := [rewrite]: #131
-#128 := (= #32 #127)
-#125 := (= #31 #124)
-#70 := (= #23 #69)
-#71 := [rewrite]: #70
-#67 := (= #22 #66)
-#68 := [rewrite]: #67
-#126 := [monotonicity #68 #71]: #125
-#129 := [monotonicity #126]: #128
-#134 := [trans #129 #132]: #133
-#63 := (iff #20 #62)
-#60 := (iff #19 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#137 := [monotonicity #64 #134]: #136
-#140 := [monotonicity #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [quant-intro #146]: #148
-#166 := [trans #149 #164]: #165
-#123 := [asserted]: #37
-#167 := [mp #123 #166]: #162
-#193 := [mp~ #167 #183]: #162
-#234 := [mp #193 #233]: #231
-#265 := [mp #234 #264]: #262
-#749 := [mp #265 #748]: #744
-#666 := (not #744)
-#669 := (or #666 #40)
-#323 := (* -1::int 1::int)
-#407 := (mod #323 #323)
-#408 := (+ #39 #407)
-#409 := (= #408 0::int)
-#400 := (mod 1::int 1::int)
-#411 := (* -1::int #400)
-#412 := (+ #39 #411)
-#413 := (= #412 0::int)
-#410 := (<= 1::int 0::int)
-#414 := (or #410 #410)
-#393 := (not #414)
-#728 := (>= 1::int 0::int)
-#730 := (or #410 #728)
-#387 := (not #730)
-#517 := (or #387 #393)
-#724 := (ite #517 #413 #409)
-#398 := (= 1::int 0::int)
-#399 := (ite #398 #40 #724)
-#731 := (= 1::int #39)
-#732 := (ite #398 #731 #399)
-#554 := (or #666 #732)
-#571 := (iff #554 #669)
-#565 := (iff #669 #669)
-#573 := [rewrite]: #565
-#570 := (iff #732 #40)
-#735 := (= #39 1::int)
-#559 := (ite false #735 #40)
-#520 := (iff #559 #40)
-#668 := [rewrite]: #520
-#560 := (iff #732 #559)
-#674 := (iff #399 #40)
-#519 := (ite false #40 #40)
-#675 := (iff #519 #40)
-#676 := [rewrite]: #675
-#672 := (iff #399 #519)
-#516 := (iff #724 #40)
-#1 := true
-#679 := (ite true #40 #40)
-#680 := (iff #679 #40)
-#687 := [rewrite]: #680
-#685 := (iff #724 #679)
-#684 := (iff #409 #40)
-#682 := (= #408 #39)
-#699 := (+ #39 0::int)
-#697 := (= #699 #39)
-#701 := [rewrite]: #697
-#539 := (= #408 #699)
-#537 := (= #407 0::int)
-#689 := (mod -1::int -1::int)
-#690 := (= #689 0::int)
-#696 := [rewrite]: #690
-#694 := (= #407 #689)
-#693 := (= #323 -1::int)
-#688 := [rewrite]: #693
-#695 := [monotonicity #688 #688]: #694
-#538 := [trans #695 #696]: #537
-#681 := [monotonicity #538]: #539
-#683 := [trans #681 #701]: #682
-#678 := [monotonicity #683]: #684
-#691 := (iff #413 #40)
-#698 := (= #412 #39)
-#700 := (= #412 #699)
-#420 := (= #411 0::int)
-#707 := (* -1::int 0::int)
-#418 := (= #707 0::int)
-#419 := [rewrite]: #418
-#704 := (= #411 #707)
-#429 := (= #400 0::int)
-#703 := [rewrite]: #429
-#708 := [monotonicity #703]: #704
-#421 := [trans #708 #419]: #420
-#415 := [monotonicity #421]: #700
-#702 := [trans #415 #701]: #698
-#692 := [monotonicity #702]: #691
-#706 := (iff #517 true)
-#727 := (or false true)
-#374 := (iff #727 true)
-#375 := [rewrite]: #374
-#329 := (iff #517 #727)
-#434 := (iff #393 true)
-#723 := (not false)
-#432 := (iff #723 true)
-#433 := [rewrite]: #432
-#709 := (iff #393 #723)
-#722 := (iff #414 false)
-#356 := (or false false)
-#361 := (iff #356 false)
-#362 := [rewrite]: #361
-#719 := (iff #414 #356)
-#385 := (iff #410 false)
-#390 := [rewrite]: #385
-#721 := [monotonicity #390 #390]: #719
-#720 := [trans #721 #362]: #722
-#710 := [monotonicity #720]: #709
-#435 := [trans #710 #433]: #434
-#712 := (iff #387 false)
-#713 := (not true)
-#716 := (iff #713 false)
-#717 := [rewrite]: #716
-#714 := (iff #387 #713)
-#376 := (iff #730 true)
-#370 := (iff #730 #727)
-#726 := (iff #728 true)
-#386 := [rewrite]: #726
-#711 := [monotonicity #390 #386]: #370
-#377 := [trans #711 #375]: #376
-#715 := [monotonicity #377]: #714
-#718 := [trans #715 #717]: #712
-#705 := [monotonicity #718 #435]: #329
-#428 := [trans #705 #375]: #706
-#686 := [monotonicity #428 #692 #678]: #685
-#518 := [trans #686 #687]: #516
-#733 := (iff #398 false)
-#734 := [rewrite]: #733
-#673 := [monotonicity #734 #518]: #672
-#677 := [trans #673 #676]: #674
-#729 := (iff #731 #735)
-#725 := [rewrite]: #729
-#561 := [monotonicity #734 #725 #677]: #560
-#665 := [trans #561 #668]: #570
-#572 := [monotonicity #665]: #571
-#574 := [trans #572 #573]: #571
-#569 := [quant-inst]: #554
-#575 := [mp #569 #574]: #669
-[unit-resolution #575 #749 #168]: false
-unsat
-92529b3476781962ca1626bb5307f530f9b5594f 335 0
+dbf21567f422d5b46c86f1fcfa917f07efeefde3 335 0
 #2 := false
 decl f3 :: (-> int int int)
 #39 := 1::int
@@ -29539,315 +28414,7 @@
 #500 := [mp #530 #497]: #170
 [unit-resolution #178 #500]: false
 unsat
-7eb8a7aa41cf540c32626b3af4825722acd864ac 307 0
-#2 := false
-#11 := 0::int
-decl f4 :: (-> int int int)
-#39 := 1::int
-#38 := 3::int
-#40 := (f4 3::int 1::int)
-#41 := (= #40 0::int)
-#42 := (not #41)
-#169 := [asserted]: #42
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#744 := (pattern #29)
-#66 := -1::int
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#125 := (mod #67 #70)
-#256 := (+ #29 #125)
-#257 := (= #256 0::int)
-#30 := (mod #8 #9)
-#253 := (* -1::int #30)
-#254 := (+ #29 #253)
-#255 := (= #254 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#195 := (or #88 #92)
-#196 := (not #195)
-#99 := (>= #8 0::int)
-#187 := (or #92 #99)
-#188 := (not #187)
-#202 := (or #188 #196)
-#258 := (ite #202 #255 #257)
-#252 := (= #29 0::int)
-#12 := (= #8 0::int)
-#259 := (ite #12 #252 #258)
-#251 := (= #8 #29)
-#13 := (= #9 0::int)
-#260 := (ite #13 #251 #259)
-#745 := (forall (vars (?v0 int) (?v1 int)) (:pat #744) #260)
-#263 := (forall (vars (?v0 int) (?v1 int)) #260)
-#748 := (iff #263 #745)
-#746 := (iff #260 #260)
-#747 := [refl]: #746
-#749 := [quant-intro #747]: #748
-#131 := (* -1::int #125)
-#220 := (ite #202 #30 #131)
-#223 := (ite #12 0::int #220)
-#226 := (ite #13 #8 #223)
-#229 := (= #29 #226)
-#232 := (forall (vars (?v0 int) (?v1 int)) #229)
-#264 := (iff #232 #263)
-#261 := (iff #229 #260)
-#262 := [rewrite]: #261
-#265 := [quant-intro #262]: #264
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#151 := (ite #106 #30 #131)
-#154 := (ite #12 0::int #151)
-#157 := (ite #13 #8 #154)
-#160 := (= #29 #157)
-#163 := (forall (vars (?v0 int) (?v1 int)) #160)
-#233 := (iff #163 #232)
-#230 := (iff #160 #229)
-#227 := (= #157 #226)
-#224 := (= #154 #223)
-#221 := (= #151 #220)
-#205 := (iff #106 #202)
-#199 := (or #196 #188)
-#203 := (iff #199 #202)
-#204 := [rewrite]: #203
-#200 := (iff #106 #199)
-#197 := (iff #103 #188)
-#198 := [rewrite]: #197
-#185 := (iff #96 #196)
-#186 := [rewrite]: #185
-#201 := [monotonicity #186 #198]: #200
-#206 := [trans #201 #204]: #205
-#222 := [monotonicity #206]: #221
-#225 := [monotonicity #222]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [quant-intro #231]: #233
-#183 := (~ #163 #163)
-#180 := (~ #160 #160)
-#193 := [refl]: #180
-#184 := [nnf-pos #193]: #183
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#166 := (iff #37 #163)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#136 := (ite #63 #30 #131)
-#139 := (ite #12 0::int #136)
-#142 := (ite #13 #8 #139)
-#145 := (= #29 #142)
-#148 := (forall (vars (?v0 int) (?v1 int)) #145)
-#164 := (iff #148 #163)
-#161 := (iff #145 #160)
-#158 := (= #142 #157)
-#155 := (= #139 #154)
-#152 := (= #136 #151)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#153 := [monotonicity #108]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#149 := (iff #37 #148)
-#146 := (iff #36 #145)
-#143 := (= #35 #142)
-#140 := (= #34 #139)
-#137 := (= #33 #136)
-#134 := (= #32 #131)
-#128 := (- #125)
-#132 := (= #128 #131)
-#133 := [rewrite]: #132
-#129 := (= #32 #128)
-#126 := (= #31 #125)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#127 := [monotonicity #69 #72]: #126
-#130 := [monotonicity #127]: #129
-#135 := [trans #130 #133]: #134
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#138 := [monotonicity #65 #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [quant-intro #147]: #149
-#167 := [trans #150 #165]: #166
-#124 := [asserted]: #37
-#168 := [mp #124 #167]: #163
-#194 := [mp~ #168 #184]: #163
-#235 := [mp #194 #234]: #232
-#266 := [mp #235 #265]: #263
-#750 := [mp #266 #749]: #745
-#577 := (not #745)
-#578 := (or #577 #41)
-#324 := (* -1::int 1::int)
-#408 := (* -1::int 3::int)
-#409 := (mod #408 #324)
-#410 := (+ #40 #409)
-#401 := (= #410 0::int)
-#412 := (mod 3::int 1::int)
-#413 := (* -1::int #412)
-#414 := (+ #40 #413)
-#411 := (= #414 0::int)
-#415 := (<= 1::int 0::int)
-#394 := (<= 3::int 0::int)
-#729 := (or #394 #415)
-#731 := (not #729)
-#388 := (>= 3::int 0::int)
-#518 := (or #415 #388)
-#725 := (not #518)
-#399 := (or #725 #731)
-#400 := (ite #399 #411 #401)
-#732 := (= 3::int 0::int)
-#733 := (ite #732 #41 #400)
-#734 := (= 3::int #40)
-#735 := (= 1::int 0::int)
-#730 := (ite #735 #734 #733)
-#671 := (or #577 #730)
-#672 := (iff #671 #578)
-#661 := (iff #578 #578)
-#653 := [rewrite]: #661
-#575 := (iff #730 #41)
-#391 := (= #40 3::int)
-#570 := (ite false #391 #41)
-#566 := (iff #570 #41)
-#574 := [rewrite]: #566
-#572 := (iff #730 #570)
-#670 := (iff #733 #41)
-#521 := (ite false #41 #41)
-#666 := (iff #521 #41)
-#667 := [rewrite]: #666
-#669 := (iff #733 #521)
-#561 := (iff #400 #41)
-#1 := true
-#676 := (ite true #41 #41)
-#678 := (iff #676 #41)
-#560 := [rewrite]: #678
-#677 := (iff #400 #676)
-#673 := (iff #401 #41)
-#519 := (= #410 #40)
-#692 := (+ #40 0::int)
-#689 := (= #692 #40)
-#690 := [rewrite]: #689
-#688 := (= #410 #692)
-#687 := (= #409 0::int)
-#538 := -3::int
-#684 := (mod -3::int -1::int)
-#680 := (= #684 0::int)
-#686 := [rewrite]: #680
-#685 := (= #409 #684)
-#682 := (= #324 -1::int)
-#683 := [rewrite]: #682
-#539 := (= #408 -3::int)
-#540 := [rewrite]: #539
-#679 := [monotonicity #540 #683]: #685
-#681 := [trans #679 #686]: #687
-#517 := [monotonicity #681]: #688
-#520 := [trans #517 #690]: #519
-#674 := [monotonicity #520]: #673
-#691 := (iff #411 #41)
-#695 := (= #414 #40)
-#693 := (= #414 #692)
-#699 := (= #413 0::int)
-#700 := (* -1::int 0::int)
-#698 := (= #700 0::int)
-#702 := [rewrite]: #698
-#701 := (= #413 #700)
-#421 := (= #412 0::int)
-#422 := [rewrite]: #421
-#416 := [monotonicity #422]: #701
-#703 := [trans #416 #702]: #699
-#694 := [monotonicity #703]: #693
-#696 := [trans #694 #690]: #695
-#697 := [monotonicity #696]: #691
-#419 := (iff #399 true)
-#377 := (or false true)
-#715 := (iff #377 true)
-#716 := [rewrite]: #715
-#705 := (iff #399 #377)
-#704 := (iff #731 true)
-#330 := (not false)
-#429 := (iff #330 true)
-#430 := [rewrite]: #429
-#706 := (iff #731 #330)
-#435 := (iff #729 false)
-#724 := (or false false)
-#433 := (iff #724 false)
-#434 := [rewrite]: #433
-#710 := (iff #729 #724)
-#371 := (iff #415 false)
-#712 := [rewrite]: #371
-#723 := (iff #394 false)
-#721 := [rewrite]: #723
-#711 := [monotonicity #721 #712]: #710
-#436 := [trans #711 #434]: #435
-#707 := [monotonicity #436]: #706
-#708 := [trans #707 #430]: #704
-#362 := (iff #725 false)
-#713 := (not true)
-#720 := (iff #713 false)
-#722 := [rewrite]: #720
-#719 := (iff #725 #713)
-#717 := (iff #518 true)
-#378 := (iff #518 #377)
-#375 := (iff #388 true)
-#376 := [rewrite]: #375
-#714 := [monotonicity #712 #376]: #378
-#718 := [trans #714 #716]: #717
-#357 := [monotonicity #718]: #719
-#363 := [trans #357 #722]: #362
-#709 := [monotonicity #363 #708]: #705
-#420 := [trans #709 #716]: #419
-#675 := [monotonicity #420 #697 #674]: #677
-#562 := [trans #675 #560]: #561
-#387 := (iff #732 false)
-#728 := [rewrite]: #387
-#571 := [monotonicity #728 #562]: #669
-#555 := [trans #571 #667]: #670
-#386 := (iff #734 #391)
-#727 := [rewrite]: #386
-#736 := (iff #735 false)
-#726 := [rewrite]: #736
-#573 := [monotonicity #726 #727 #555]: #572
-#576 := [trans #573 #574]: #575
-#659 := [monotonicity #576]: #672
-#650 := [trans #659 #653]: #672
-#668 := [quant-inst]: #671
-#652 := [mp #668 #650]: #578
-[unit-resolution #652 #750 #169]: false
-unsat
-bcd6aa81c95602060c016443dc50a08e0f15fea6 306 0
+bb20ebe7c25411e4b91bb24e9a9cf291e53220f5 306 0
 #2 := false
 #11 := 0::int
 decl f3 :: (-> int int int)
@@ -30154,7 +28721,7 @@
 #682 := [mp #588 #685]: #587
 [unit-resolution #682 #757 #193]: false
 unsat
-c5e0a78cd4281adc96eca6cb66f3bfdd83b7f982 315 0
+079dbdead0d272beb5183f7176cc988b0984a691 315 0
 #2 := false
 #66 := -1::int
 decl f3 :: (-> int int int)
@@ -30470,316 +29037,7 @@
 #678 := [mp #675 #677]: #686
 [unit-resolution #678 #757 #193]: false
 unsat
-5fd03e95521b145801ae320c34d2eabe8b033de9 308 0
-#2 := false
-#11 := 0::int
-decl f5 :: int
-#38 := f5
-#732 := (= f5 0::int)
-#573 := (not #732)
-#394 := (<= f5 0::int)
-#720 := (not #394)
-#388 := (>= f5 0::int)
-#377 := (not #388)
-#688 := (or #377 #720 #732)
-#575 := (not #688)
-#66 := -1::int
-#408 := (* -1::int f5)
-#700 := (mod #408 -1::int)
-decl f4 :: (-> int int int)
-#39 := 1::int
-#40 := (f4 f5 1::int)
-#698 := (+ #40 #700)
-#703 := (= #698 0::int)
-#41 := (= #40 0::int)
-#520 := (ite #688 #41 #703)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#744 := (pattern #29)
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#125 := (mod #67 #70)
-#256 := (+ #29 #125)
-#257 := (= #256 0::int)
-#30 := (mod #8 #9)
-#253 := (* -1::int #30)
-#254 := (+ #29 #253)
-#255 := (= #254 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#195 := (or #88 #92)
-#196 := (not #195)
-#99 := (>= #8 0::int)
-#187 := (or #92 #99)
-#188 := (not #187)
-#202 := (or #188 #196)
-#258 := (ite #202 #255 #257)
-#252 := (= #29 0::int)
-#12 := (= #8 0::int)
-#259 := (ite #12 #252 #258)
-#251 := (= #8 #29)
-#13 := (= #9 0::int)
-#260 := (ite #13 #251 #259)
-#745 := (forall (vars (?v0 int) (?v1 int)) (:pat #744) #260)
-#263 := (forall (vars (?v0 int) (?v1 int)) #260)
-#748 := (iff #263 #745)
-#746 := (iff #260 #260)
-#747 := [refl]: #746
-#749 := [quant-intro #747]: #748
-#131 := (* -1::int #125)
-#220 := (ite #202 #30 #131)
-#223 := (ite #12 0::int #220)
-#226 := (ite #13 #8 #223)
-#229 := (= #29 #226)
-#232 := (forall (vars (?v0 int) (?v1 int)) #229)
-#264 := (iff #232 #263)
-#261 := (iff #229 #260)
-#262 := [rewrite]: #261
-#265 := [quant-intro #262]: #264
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#151 := (ite #106 #30 #131)
-#154 := (ite #12 0::int #151)
-#157 := (ite #13 #8 #154)
-#160 := (= #29 #157)
-#163 := (forall (vars (?v0 int) (?v1 int)) #160)
-#233 := (iff #163 #232)
-#230 := (iff #160 #229)
-#227 := (= #157 #226)
-#224 := (= #154 #223)
-#221 := (= #151 #220)
-#205 := (iff #106 #202)
-#199 := (or #196 #188)
-#203 := (iff #199 #202)
-#204 := [rewrite]: #203
-#200 := (iff #106 #199)
-#197 := (iff #103 #188)
-#198 := [rewrite]: #197
-#185 := (iff #96 #196)
-#186 := [rewrite]: #185
-#201 := [monotonicity #186 #198]: #200
-#206 := [trans #201 #204]: #205
-#222 := [monotonicity #206]: #221
-#225 := [monotonicity #222]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [quant-intro #231]: #233
-#183 := (~ #163 #163)
-#180 := (~ #160 #160)
-#193 := [refl]: #180
-#184 := [nnf-pos #193]: #183
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#166 := (iff #37 #163)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#136 := (ite #63 #30 #131)
-#139 := (ite #12 0::int #136)
-#142 := (ite #13 #8 #139)
-#145 := (= #29 #142)
-#148 := (forall (vars (?v0 int) (?v1 int)) #145)
-#164 := (iff #148 #163)
-#161 := (iff #145 #160)
-#158 := (= #142 #157)
-#155 := (= #139 #154)
-#152 := (= #136 #151)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#153 := [monotonicity #108]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#149 := (iff #37 #148)
-#146 := (iff #36 #145)
-#143 := (= #35 #142)
-#140 := (= #34 #139)
-#137 := (= #33 #136)
-#134 := (= #32 #131)
-#128 := (- #125)
-#132 := (= #128 #131)
-#133 := [rewrite]: #132
-#129 := (= #32 #128)
-#126 := (= #31 #125)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#127 := [monotonicity #69 #72]: #126
-#130 := [monotonicity #127]: #129
-#135 := [trans #130 #133]: #134
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#138 := [monotonicity #65 #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [quant-intro #147]: #149
-#167 := [trans #150 #165]: #166
-#124 := [asserted]: #37
-#168 := [mp #124 #167]: #163
-#194 := [mp~ #168 #184]: #163
-#235 := [mp #194 #234]: #232
-#266 := [mp #235 #265]: #263
-#750 := [mp #266 #749]: #745
-#675 := (not #745)
-#678 := (or #675 #520)
-#324 := (* -1::int 1::int)
-#409 := (mod #408 #324)
-#410 := (+ #40 #409)
-#401 := (= #410 0::int)
-#412 := (mod f5 1::int)
-#413 := (* -1::int #412)
-#414 := (+ #40 #413)
-#411 := (= #414 0::int)
-#415 := (<= 1::int 0::int)
-#729 := (or #394 #415)
-#731 := (not #729)
-#518 := (or #415 #388)
-#725 := (not #518)
-#399 := (or #725 #731)
-#400 := (ite #399 #411 #401)
-#733 := (ite #732 #41 #400)
-#734 := (= f5 #40)
-#735 := (= 1::int 0::int)
-#730 := (ite #735 #734 #733)
-#560 := (or #675 #730)
-#562 := (iff #560 #678)
-#669 := (iff #678 #678)
-#571 := [rewrite]: #669
-#676 := (iff #730 #520)
-#363 := (or #377 #720)
-#697 := (or #363 #732)
-#538 := (ite #697 #41 #703)
-#673 := (iff #538 #520)
-#517 := (iff #697 #688)
-#519 := [rewrite]: #517
-#674 := [monotonicity #519]: #673
-#687 := (iff #730 #538)
-#684 := (ite false #734 #538)
-#680 := (iff #684 #538)
-#686 := [rewrite]: #680
-#685 := (iff #730 #684)
-#682 := (iff #733 #538)
-#694 := (ite #363 #41 #703)
-#695 := (ite #732 #41 #694)
-#539 := (iff #695 #538)
-#540 := [rewrite]: #539
-#696 := (iff #733 #695)
-#689 := (iff #400 #694)
-#692 := (iff #401 #703)
-#702 := (= #410 #698)
-#701 := (= #409 #700)
-#421 := (= #324 -1::int)
-#422 := [rewrite]: #421
-#416 := [monotonicity #422]: #701
-#699 := [monotonicity #416]: #702
-#693 := [monotonicity #699]: #692
-#419 := (iff #411 #41)
-#705 := (= #414 #40)
-#707 := (+ #40 0::int)
-#704 := (= #707 #40)
-#708 := [rewrite]: #704
-#429 := (= #414 #707)
-#330 := (= #413 0::int)
-#711 := (* -1::int 0::int)
-#435 := (= #711 0::int)
-#436 := [rewrite]: #435
-#433 := (= #413 #711)
-#724 := (= #412 0::int)
-#710 := [rewrite]: #724
-#434 := [monotonicity #710]: #433
-#706 := [trans #434 #436]: #330
-#430 := [monotonicity #706]: #429
-#709 := [trans #430 #708]: #705
-#420 := [monotonicity #709]: #419
-#723 := (iff #399 #363)
-#722 := (iff #731 #720)
-#719 := (iff #729 #394)
-#715 := (or #394 false)
-#718 := (iff #715 #394)
-#713 := [rewrite]: #718
-#716 := (iff #729 #715)
-#386 := (iff #415 false)
-#391 := [rewrite]: #386
-#717 := [monotonicity #391]: #716
-#357 := [trans #717 #713]: #719
-#362 := [monotonicity #357]: #722
-#378 := (iff #725 #377)
-#375 := (iff #518 #388)
-#727 := (or false #388)
-#371 := (iff #727 #388)
-#712 := [rewrite]: #371
-#387 := (iff #518 #727)
-#728 := [monotonicity #391]: #387
-#376 := [trans #728 #712]: #375
-#714 := [monotonicity #376]: #378
-#721 := [monotonicity #714 #362]: #723
-#690 := [monotonicity #721 #420 #693]: #689
-#691 := [monotonicity #690]: #696
-#683 := [trans #691 #540]: #682
-#736 := (iff #735 false)
-#726 := [rewrite]: #736
-#679 := [monotonicity #726 #683]: #685
-#681 := [trans #679 #686]: #687
-#677 := [trans #681 #674]: #676
-#521 := [monotonicity #677]: #562
-#666 := [trans #521 #571]: #562
-#561 := [quant-inst]: #560
-#667 := [mp #561 #666]: #678
-#660 := [unit-resolution #667 #750]: #520
-#668 := (not #520)
-#665 := (or #668 #575)
-#42 := (not #41)
-#169 := [asserted]: #42
-#672 := (or #668 #575 #41)
-#659 := [def-axiom]: #672
-#654 := [unit-resolution #659 #169]: #665
-#655 := [unit-resolution #654 #660]: #575
-#566 := (or #688 #573)
-#574 := [def-axiom]: #566
-#656 := [unit-resolution #574 #655]: #573
-#670 := (or #688 #388)
-#555 := [def-axiom]: #670
-#657 := [unit-resolution #555 #655]: #388
-#570 := (or #688 #394)
-#572 := [def-axiom]: #570
-#651 := [unit-resolution #572 #655]: #394
-#658 := (or #732 #720 #377)
-#642 := [th-lemma]: #658
-[unit-resolution #642 #651 #657 #656]: false
-unsat
-313d9507d6b102d4601325c684027a26955dd8c8 311 0
+029017481d4674b27ca8cd5eb791fee9a4afaca5 311 0
 #2 := false
 #177 := -3::int
 decl f3 :: (-> int int int)
@@ -31091,325 +29349,7 @@
 #661 := [mp #659 #672]: #660
 [unit-resolution #661 #750 #188]: false
 unsat
-3d32e1abf69ce0e5041899ca9973bae87dfc28de 317 0
-#2 := false
-#11 := 0::int
-decl f4 :: (-> int int int)
-#66 := -1::int
-#172 := (f4 0::int -1::int)
-#175 := (= #172 0::int)
-#188 := (not #175)
-#38 := 1::int
-#39 := (- 1::int)
-#40 := (f4 0::int #39)
-#41 := (= #40 0::int)
-#42 := (not #41)
-#191 := (iff #42 #188)
-#178 := (= 0::int #172)
-#183 := (not #178)
-#189 := (iff #183 #188)
-#186 := (iff #178 #175)
-#187 := [rewrite]: #186
-#190 := [monotonicity #187]: #189
-#184 := (iff #42 #183)
-#181 := (iff #41 #178)
-#179 := (iff #175 #178)
-#180 := [rewrite]: #179
-#176 := (iff #41 #175)
-#173 := (= #40 #172)
-#170 := (= #39 -1::int)
-#171 := [rewrite]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#182 := [trans #177 #180]: #181
-#185 := [monotonicity #182]: #184
-#192 := [trans #185 #190]: #191
-#169 := [asserted]: #42
-#193 := [mp #169 #192]: #188
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#758 := (pattern #29)
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#125 := (mod #67 #70)
-#270 := (+ #29 #125)
-#271 := (= #270 0::int)
-#30 := (mod #8 #9)
-#267 := (* -1::int #30)
-#268 := (+ #29 #267)
-#269 := (= #268 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#209 := (or #88 #92)
-#210 := (not #209)
-#99 := (>= #8 0::int)
-#201 := (or #92 #99)
-#202 := (not #201)
-#216 := (or #202 #210)
-#272 := (ite #216 #269 #271)
-#266 := (= #29 0::int)
-#12 := (= #8 0::int)
-#273 := (ite #12 #266 #272)
-#265 := (= #8 #29)
-#13 := (= #9 0::int)
-#274 := (ite #13 #265 #273)
-#759 := (forall (vars (?v0 int) (?v1 int)) (:pat #758) #274)
-#277 := (forall (vars (?v0 int) (?v1 int)) #274)
-#762 := (iff #277 #759)
-#760 := (iff #274 #274)
-#761 := [refl]: #760
-#763 := [quant-intro #761]: #762
-#131 := (* -1::int #125)
-#234 := (ite #216 #30 #131)
-#237 := (ite #12 0::int #234)
-#240 := (ite #13 #8 #237)
-#243 := (= #29 #240)
-#246 := (forall (vars (?v0 int) (?v1 int)) #243)
-#278 := (iff #246 #277)
-#275 := (iff #243 #274)
-#276 := [rewrite]: #275
-#279 := [quant-intro #276]: #278
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#151 := (ite #106 #30 #131)
-#154 := (ite #12 0::int #151)
-#157 := (ite #13 #8 #154)
-#160 := (= #29 #157)
-#163 := (forall (vars (?v0 int) (?v1 int)) #160)
-#247 := (iff #163 #246)
-#244 := (iff #160 #243)
-#241 := (= #157 #240)
-#238 := (= #154 #237)
-#235 := (= #151 #234)
-#219 := (iff #106 #216)
-#213 := (or #210 #202)
-#217 := (iff #213 #216)
-#218 := [rewrite]: #217
-#214 := (iff #106 #213)
-#211 := (iff #103 #202)
-#212 := [rewrite]: #211
-#199 := (iff #96 #210)
-#200 := [rewrite]: #199
-#215 := [monotonicity #200 #212]: #214
-#220 := [trans #215 #218]: #219
-#236 := [monotonicity #220]: #235
-#239 := [monotonicity #236]: #238
-#242 := [monotonicity #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [quant-intro #245]: #247
-#197 := (~ #163 #163)
-#194 := (~ #160 #160)
-#207 := [refl]: #194
-#198 := [nnf-pos #207]: #197
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#166 := (iff #37 #163)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#136 := (ite #63 #30 #131)
-#139 := (ite #12 0::int #136)
-#142 := (ite #13 #8 #139)
-#145 := (= #29 #142)
-#148 := (forall (vars (?v0 int) (?v1 int)) #145)
-#164 := (iff #148 #163)
-#161 := (iff #145 #160)
-#158 := (= #142 #157)
-#155 := (= #139 #154)
-#152 := (= #136 #151)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#153 := [monotonicity #108]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#149 := (iff #37 #148)
-#146 := (iff #36 #145)
-#143 := (= #35 #142)
-#140 := (= #34 #139)
-#137 := (= #33 #136)
-#134 := (= #32 #131)
-#128 := (- #125)
-#132 := (= #128 #131)
-#133 := [rewrite]: #132
-#129 := (= #32 #128)
-#126 := (= #31 #125)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#127 := [monotonicity #69 #72]: #126
-#130 := [monotonicity #127]: #129
-#135 := [trans #130 #133]: #134
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#138 := [monotonicity #65 #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [quant-intro #147]: #149
-#167 := [trans #150 #165]: #166
-#124 := [asserted]: #37
-#168 := [mp #124 #167]: #163
-#208 := [mp~ #168 #198]: #163
-#249 := [mp #208 #248]: #246
-#280 := [mp #249 #279]: #277
-#764 := [mp #280 #763]: #759
-#535 := (not #759)
-#683 := (or #535 #175)
-#338 := (* -1::int -1::int)
-#422 := (* -1::int 0::int)
-#423 := (mod #422 #338)
-#424 := (+ #172 #423)
-#415 := (= #424 0::int)
-#426 := (mod 0::int -1::int)
-#427 := (* -1::int #426)
-#428 := (+ #172 #427)
-#425 := (= #428 0::int)
-#429 := (<= -1::int 0::int)
-#408 := (<= 0::int 0::int)
-#743 := (or #408 #429)
-#745 := (not #743)
-#402 := (>= 0::int 0::int)
-#532 := (or #429 #402)
-#739 := (not #532)
-#413 := (or #739 #745)
-#414 := (ite #413 #425 #415)
-#746 := (= 0::int 0::int)
-#747 := (ite #746 #175 #414)
-#748 := (= -1::int 0::int)
-#749 := (ite #748 #178 #747)
-#585 := (or #535 #749)
-#681 := (iff #585 #683)
-#569 := (iff #683 #683)
-#584 := [rewrite]: #569
-#575 := (iff #749 #175)
-#693 := (ite false #175 #175)
-#701 := (iff #693 #175)
-#695 := [rewrite]: #701
-#692 := (iff #749 #693)
-#691 := (iff #747 #175)
-#1 := true
-#533 := (ite true #175 #175)
-#688 := (iff #533 #175)
-#690 := [rewrite]: #688
-#534 := (iff #747 #533)
-#702 := (iff #414 #175)
-#694 := (iff #414 #693)
-#698 := (iff #415 #175)
-#696 := (= #424 #172)
-#436 := (+ #172 0::int)
-#430 := (= #436 #172)
-#712 := [rewrite]: #430
-#553 := (= #424 #436)
-#711 := (= #423 0::int)
-#703 := (mod 0::int 1::int)
-#710 := (= #703 0::int)
-#705 := [rewrite]: #710
-#704 := (= #423 #703)
-#707 := (= #338 1::int)
-#708 := [rewrite]: #707
-#723 := (= #422 0::int)
-#433 := [rewrite]: #723
-#709 := [monotonicity #433 #708]: #704
-#552 := [trans #709 #705]: #711
-#554 := [monotonicity #552]: #553
-#697 := [trans #554 #712]: #696
-#699 := [monotonicity #697]: #698
-#717 := (iff #425 #175)
-#716 := (= #428 #172)
-#714 := (= #428 #436)
-#434 := (= #427 0::int)
-#722 := (= #427 #422)
-#444 := (= #426 0::int)
-#718 := [rewrite]: #444
-#719 := [monotonicity #718]: #722
-#435 := [trans #719 #433]: #434
-#715 := [monotonicity #435]: #714
-#713 := [trans #715 #712]: #716
-#706 := [monotonicity #713]: #717
-#721 := (iff #413 false)
-#448 := (or false false)
-#344 := (iff #448 false)
-#720 := [rewrite]: #344
-#449 := (iff #413 #448)
-#725 := (iff #745 false)
-#729 := (not true)
-#732 := (iff #729 false)
-#727 := [rewrite]: #732
-#738 := (iff #745 #729)
-#737 := (iff #743 true)
-#385 := (or true true)
-#390 := (iff #385 true)
-#391 := [rewrite]: #390
-#376 := (iff #743 #385)
-#405 := (iff #429 true)
-#741 := [rewrite]: #405
-#734 := (iff #408 true)
-#736 := [rewrite]: #734
-#377 := [monotonicity #736 #741]: #376
-#735 := [trans #377 #391]: #737
-#724 := [monotonicity #735]: #738
-#447 := [trans #724 #727]: #725
-#733 := (iff #739 false)
-#730 := (iff #739 #729)
-#392 := (iff #532 true)
-#726 := (iff #532 #385)
-#401 := (iff #402 true)
-#742 := [rewrite]: #401
-#389 := [monotonicity #741 #742]: #726
-#728 := [trans #389 #391]: #392
-#731 := [monotonicity #728]: #730
-#371 := [trans #731 #727]: #733
-#450 := [monotonicity #371 #447]: #449
-#443 := [trans #450 #720]: #721
-#700 := [monotonicity #443 #706 #699]: #694
-#531 := [trans #700 #695]: #702
-#740 := (iff #746 true)
-#400 := [rewrite]: #740
-#687 := [monotonicity #400 #531]: #534
-#689 := [trans #687 #690]: #691
-#744 := (iff #748 false)
-#750 := [rewrite]: #744
-#574 := [monotonicity #750 #187 #689]: #692
-#576 := [trans #574 #695]: #575
-#684 := [monotonicity #576]: #681
-#586 := [trans #684 #584]: #681
-#680 := [quant-inst]: #585
-#587 := [mp #680 #586]: #683
-[unit-resolution #587 #764 #193]: false
-unsat
-554be993a1782ec7f024b52e37aa60a3dc009c1f 362 0
+5348d5efd3f228f3b43acb1bc81e227275753058 362 0
 #2 := false
 #11 := 0::int
 #39 := 1::int
@@ -31772,7 +29712,6498 @@
 #563 := [th-lemma]: #562
 [unit-resolution #563 #561 #633]: false
 unsat
-658c83eb9ce09a5dbf189137f768372756f07aa7 327 0
+df344cc5200504ac56b3a56c141e9cfd738ef1e0 282 0
+#2 := false
+#11 := 0::int
+decl f3 :: (-> int int int)
+#38 := 3::int
+#39 := (f3 0::int 3::int)
+#40 := (= #39 0::int)
+#41 := (not #40)
+#168 := [asserted]: #41
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#737 := (pattern #10)
+#65 := -1::int
+#69 := (* -1::int #9)
+#66 := (* -1::int #8)
+#72 := (div #66 #69)
+#239 := (* -1::int #72)
+#240 := (+ #10 #239)
+#241 := (= #240 0::int)
+#21 := (div #8 #9)
+#236 := (* -1::int #21)
+#237 := (+ #10 #236)
+#238 := (= #237 0::int)
+#91 := (<= #9 0::int)
+#87 := (<= #8 0::int)
+#194 := (or #87 #91)
+#195 := (not #194)
+#98 := (>= #8 0::int)
+#186 := (or #91 #98)
+#187 := (not #186)
+#201 := (or #187 #195)
+#242 := (ite #201 #238 #241)
+#235 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#243 := (ite #14 #235 #242)
+#738 := (forall (vars (?v0 int) (?v1 int)) (:pat #737) #243)
+#246 := (forall (vars (?v0 int) (?v1 int)) #243)
+#741 := (iff #246 #738)
+#739 := (iff #243 #243)
+#740 := [refl]: #739
+#742 := [quant-intro #740]: #741
+#206 := (ite #201 #21 #72)
+#209 := (ite #14 0::int #206)
+#212 := (= #10 #209)
+#215 := (forall (vars (?v0 int) (?v1 int)) #212)
+#247 := (iff #215 #246)
+#244 := (iff #212 #243)
+#245 := [rewrite]: #244
+#248 := [quant-intro #245]: #247
+#99 := (not #98)
+#92 := (not #91)
+#102 := (and #92 #99)
+#88 := (not #87)
+#95 := (and #88 #92)
+#105 := (or #95 #102)
+#108 := (ite #105 #21 #72)
+#111 := (ite #14 0::int #108)
+#114 := (= #10 #111)
+#117 := (forall (vars (?v0 int) (?v1 int)) #114)
+#216 := (iff #117 #215)
+#213 := (iff #114 #212)
+#210 := (= #111 #209)
+#207 := (= #108 #206)
+#204 := (iff #105 #201)
+#198 := (or #195 #187)
+#202 := (iff #198 #201)
+#203 := [rewrite]: #202
+#199 := (iff #105 #198)
+#196 := (iff #102 #187)
+#197 := [rewrite]: #196
+#184 := (iff #95 #195)
+#185 := [rewrite]: #184
+#200 := [monotonicity #185 #197]: #199
+#205 := [trans #200 #203]: #204
+#208 := [monotonicity #205]: #207
+#211 := [monotonicity #208]: #210
+#214 := [monotonicity #211]: #213
+#217 := [quant-intro #214]: #216
+#190 := (~ #117 #117)
+#188 := (~ #114 #114)
+#189 := [refl]: #188
+#191 := [nnf-pos #189]: #190
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#120 := (iff #28 #117)
+#59 := (and #16 #18)
+#62 := (or #17 #59)
+#75 := (ite #62 #21 #72)
+#78 := (ite #14 0::int #75)
+#81 := (= #10 #78)
+#84 := (forall (vars (?v0 int) (?v1 int)) #81)
+#118 := (iff #84 #117)
+#115 := (iff #81 #114)
+#112 := (= #78 #111)
+#109 := (= #75 #108)
+#106 := (iff #62 #105)
+#103 := (iff #59 #102)
+#100 := (iff #18 #99)
+#101 := [rewrite]: #100
+#93 := (iff #16 #92)
+#94 := [rewrite]: #93
+#104 := [monotonicity #94 #101]: #103
+#96 := (iff #17 #95)
+#89 := (iff #15 #88)
+#90 := [rewrite]: #89
+#97 := [monotonicity #90 #94]: #96
+#107 := [monotonicity #97 #104]: #106
+#110 := [monotonicity #107]: #109
+#113 := [monotonicity #110]: #112
+#116 := [monotonicity #113]: #115
+#119 := [quant-intro #116]: #118
+#85 := (iff #28 #84)
+#82 := (iff #27 #81)
+#79 := (= #26 #78)
+#76 := (= #25 #75)
+#73 := (= #24 #72)
+#70 := (= #23 #69)
+#71 := [rewrite]: #70
+#67 := (= #22 #66)
+#68 := [rewrite]: #67
+#74 := [monotonicity #68 #71]: #73
+#63 := (iff #20 #62)
+#60 := (iff #19 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#77 := [monotonicity #64 #74]: #76
+#80 := [monotonicity #77]: #79
+#83 := [monotonicity #80]: #82
+#86 := [quant-intro #83]: #85
+#121 := [trans #86 #119]: #120
+#58 := [asserted]: #28
+#122 := [mp #58 #121]: #117
+#181 := [mp~ #122 #191]: #117
+#218 := [mp #181 #217]: #215
+#249 := [mp #218 #248]: #246
+#743 := [mp #249 #742]: #738
+#572 := (not #738)
+#573 := (or #572 #40)
+#323 := (* -1::int 3::int)
+#408 := (* -1::int 0::int)
+#409 := (div #408 #323)
+#410 := (* -1::int #409)
+#401 := (+ #39 #410)
+#412 := (= #401 0::int)
+#413 := (div 0::int 3::int)
+#341 := (* -1::int #413)
+#414 := (+ #39 #341)
+#411 := (= #414 0::int)
+#415 := (<= 3::int 0::int)
+#394 := (<= 0::int 0::int)
+#729 := (or #394 #415)
+#731 := (not #729)
+#388 := (>= 0::int 0::int)
+#518 := (or #415 #388)
+#725 := (not #518)
+#399 := (or #725 #731)
+#400 := (ite #399 #411 #412)
+#732 := (= 3::int 0::int)
+#733 := (= 0::int 0::int)
+#734 := (or #733 #732)
+#735 := (ite #734 #40 #400)
+#566 := (or #572 #735)
+#575 := (iff #566 #573)
+#577 := (iff #573 #573)
+#578 := [rewrite]: #577
+#555 := (iff #735 #40)
+#1 := true
+#669 := (ite true #40 #40)
+#667 := (iff #669 #40)
+#670 := [rewrite]: #667
+#571 := (iff #735 #669)
+#562 := (iff #400 #40)
+#677 := (ite false #40 #40)
+#560 := (iff #677 #40)
+#561 := [rewrite]: #560
+#675 := (iff #400 #677)
+#674 := (iff #412 #40)
+#520 := (= #401 #39)
+#703 := (+ #39 0::int)
+#694 := (= #703 #39)
+#689 := [rewrite]: #694
+#517 := (= #401 #703)
+#681 := (= #410 0::int)
+#416 := (= #408 0::int)
+#698 := [rewrite]: #416
+#686 := (= #410 #408)
+#679 := (= #409 0::int)
+#697 := -3::int
+#540 := (div 0::int -3::int)
+#684 := (= #540 0::int)
+#685 := [rewrite]: #684
+#682 := (= #409 #540)
+#538 := (= #323 -3::int)
+#539 := [rewrite]: #538
+#683 := [monotonicity #698 #539]: #682
+#680 := [trans #683 #685]: #679
+#687 := [monotonicity #680]: #686
+#688 := [trans #687 #698]: #681
+#519 := [monotonicity #688]: #517
+#673 := [trans #519 #689]: #520
+#676 := [monotonicity #673]: #674
+#696 := (iff #411 #40)
+#690 := (= #414 #39)
+#692 := (= #414 #703)
+#702 := (= #341 0::int)
+#700 := (= #341 #408)
+#421 := (= #413 0::int)
+#422 := [rewrite]: #421
+#701 := [monotonicity #422]: #700
+#699 := [trans #701 #698]: #702
+#693 := [monotonicity #699]: #692
+#695 := [trans #693 #689]: #690
+#691 := [monotonicity #695]: #696
+#419 := (iff #399 false)
+#430 := (or false false)
+#705 := (iff #430 false)
+#709 := [rewrite]: #705
+#704 := (iff #399 #430)
+#707 := (iff #731 false)
+#720 := (not true)
+#363 := (iff #720 false)
+#723 := [rewrite]: #363
+#329 := (iff #731 #720)
+#435 := (iff #729 true)
+#391 := (or true false)
+#728 := (iff #391 true)
+#371 := [rewrite]: #728
+#433 := (iff #729 #391)
+#376 := (iff #415 false)
+#377 := [rewrite]: #376
+#710 := (iff #394 true)
+#711 := [rewrite]: #710
+#434 := [monotonicity #711 #377]: #433
+#436 := [trans #434 #371]: #435
+#706 := [monotonicity #436]: #329
+#429 := [trans #706 #723]: #707
+#721 := (iff #725 false)
+#722 := (iff #725 #720)
+#719 := (iff #518 true)
+#715 := (or false true)
+#718 := (iff #715 true)
+#713 := [rewrite]: #718
+#716 := (iff #518 #715)
+#378 := (iff #388 true)
+#714 := [rewrite]: #378
+#717 := [monotonicity #377 #714]: #716
+#357 := [trans #717 #713]: #719
+#362 := [monotonicity #357]: #722
+#724 := [trans #362 #723]: #721
+#708 := [monotonicity #724 #429]: #704
+#420 := [trans #708 #709]: #419
+#678 := [monotonicity #420 #691 #676]: #675
+#521 := [trans #678 #561]: #562
+#712 := (iff #734 true)
+#727 := (iff #734 #391)
+#726 := (iff #732 false)
+#386 := [rewrite]: #726
+#730 := (iff #733 true)
+#736 := [rewrite]: #730
+#387 := [monotonicity #736 #386]: #727
+#375 := [trans #387 #371]: #712
+#666 := [monotonicity #375 #521]: #571
+#570 := [trans #666 #670]: #555
+#576 := [monotonicity #570]: #575
+#671 := [trans #576 #578]: #575
+#574 := [quant-inst]: #566
+#668 := [mp #574 #671]: #573
+[unit-resolution #668 #743 #168]: false
+unsat
+c6f86df3aa5bfccad83534807c7cfc3218b91544 307 0
+#2 := false
+#11 := 0::int
+decl f3 :: (-> int int int)
+#170 := -3::int
+#173 := (f3 0::int -3::int)
+#176 := (= #173 0::int)
+#189 := (not #176)
+#38 := 3::int
+#39 := (- 3::int)
+#40 := (f3 0::int #39)
+#41 := (= #40 0::int)
+#42 := (not #41)
+#192 := (iff #42 #189)
+#179 := (= 0::int #173)
+#184 := (not #179)
+#190 := (iff #184 #189)
+#187 := (iff #179 #176)
+#188 := [rewrite]: #187
+#191 := [monotonicity #188]: #190
+#185 := (iff #42 #184)
+#182 := (iff #41 #179)
+#180 := (iff #176 #179)
+#181 := [rewrite]: #180
+#177 := (iff #41 #176)
+#174 := (= #40 #173)
+#171 := (= #39 -3::int)
+#172 := [rewrite]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#183 := [trans #178 #181]: #182
+#186 := [monotonicity #183]: #185
+#193 := [trans #186 #191]: #192
+#169 := [asserted]: #42
+#194 := [mp #169 #193]: #189
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#753 := (pattern #10)
+#66 := -1::int
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#73 := (div #67 #70)
+#255 := (* -1::int #73)
+#256 := (+ #10 #255)
+#257 := (= #256 0::int)
+#21 := (div #8 #9)
+#252 := (* -1::int #21)
+#253 := (+ #10 #252)
+#254 := (= #253 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#210 := (or #88 #92)
+#211 := (not #210)
+#99 := (>= #8 0::int)
+#202 := (or #92 #99)
+#203 := (not #202)
+#217 := (or #203 #211)
+#258 := (ite #217 #254 #257)
+#251 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#259 := (ite #14 #251 #258)
+#754 := (forall (vars (?v0 int) (?v1 int)) (:pat #753) #259)
+#262 := (forall (vars (?v0 int) (?v1 int)) #259)
+#757 := (iff #262 #754)
+#755 := (iff #259 #259)
+#756 := [refl]: #755
+#758 := [quant-intro #756]: #757
+#222 := (ite #217 #21 #73)
+#225 := (ite #14 0::int #222)
+#228 := (= #10 #225)
+#231 := (forall (vars (?v0 int) (?v1 int)) #228)
+#263 := (iff #231 #262)
+#260 := (iff #228 #259)
+#261 := [rewrite]: #260
+#264 := [quant-intro #261]: #263
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#109 := (ite #106 #21 #73)
+#112 := (ite #14 0::int #109)
+#115 := (= #10 #112)
+#118 := (forall (vars (?v0 int) (?v1 int)) #115)
+#232 := (iff #118 #231)
+#229 := (iff #115 #228)
+#226 := (= #112 #225)
+#223 := (= #109 #222)
+#220 := (iff #106 #217)
+#214 := (or #211 #203)
+#218 := (iff #214 #217)
+#219 := [rewrite]: #218
+#215 := (iff #106 #214)
+#212 := (iff #103 #203)
+#213 := [rewrite]: #212
+#200 := (iff #96 #211)
+#201 := [rewrite]: #200
+#216 := [monotonicity #201 #213]: #215
+#221 := [trans #216 #219]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [quant-intro #230]: #232
+#206 := (~ #118 #118)
+#204 := (~ #115 #115)
+#205 := [refl]: #204
+#207 := [nnf-pos #205]: #206
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#121 := (iff #28 #118)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#76 := (ite #63 #21 #73)
+#79 := (ite #14 0::int #76)
+#82 := (= #10 #79)
+#85 := (forall (vars (?v0 int) (?v1 int)) #82)
+#119 := (iff #85 #118)
+#116 := (iff #82 #115)
+#113 := (= #79 #112)
+#110 := (= #76 #109)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#111 := [monotonicity #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [quant-intro #117]: #119
+#86 := (iff #28 #85)
+#83 := (iff #27 #82)
+#80 := (= #26 #79)
+#77 := (= #25 #76)
+#74 := (= #24 #73)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#75 := [monotonicity #69 #72]: #74
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#78 := [monotonicity #65 #75]: #77
+#81 := [monotonicity #78]: #80
+#84 := [monotonicity #81]: #83
+#87 := [quant-intro #84]: #86
+#122 := [trans #87 #120]: #121
+#59 := [asserted]: #28
+#123 := [mp #59 #122]: #118
+#197 := [mp~ #123 #207]: #118
+#234 := [mp #197 #233]: #231
+#265 := [mp #234 #264]: #262
+#759 := [mp #265 #758]: #754
+#586 := (not #754)
+#588 := (or #586 #176)
+#339 := (* -1::int -3::int)
+#424 := (* -1::int 0::int)
+#425 := (div #424 #339)
+#426 := (* -1::int #425)
+#417 := (+ #173 #426)
+#428 := (= #417 0::int)
+#429 := (div 0::int -3::int)
+#357 := (* -1::int #429)
+#430 := (+ #173 #357)
+#427 := (= #430 0::int)
+#431 := (<= -3::int 0::int)
+#410 := (<= 0::int 0::int)
+#745 := (or #410 #431)
+#747 := (not #745)
+#404 := (>= 0::int 0::int)
+#534 := (or #431 #404)
+#741 := (not #534)
+#415 := (or #741 #747)
+#416 := (ite #415 #427 #428)
+#748 := (= -3::int 0::int)
+#749 := (= 0::int 0::int)
+#750 := (or #749 #748)
+#751 := (ite #750 #176 #416)
+#589 := (or #586 #751)
+#590 := (iff #589 #588)
+#592 := (iff #588 #588)
+#593 := [rewrite]: #592
+#686 := (iff #751 #176)
+#1 := true
+#537 := (ite true #176 #176)
+#682 := (iff #537 #176)
+#683 := [rewrite]: #682
+#685 := (iff #751 #537)
+#577 := (iff #416 #176)
+#692 := (ite false #176 #176)
+#694 := (iff #692 #176)
+#576 := [rewrite]: #694
+#693 := (iff #416 #692)
+#689 := (iff #428 #176)
+#535 := (= #417 #173)
+#719 := (+ #173 0::int)
+#710 := (= #719 #173)
+#705 := [rewrite]: #710
+#704 := (= #417 #719)
+#703 := (= #426 0::int)
+#432 := (= #424 0::int)
+#714 := [rewrite]: #432
+#696 := (= #426 #424)
+#701 := (= #425 0::int)
+#555 := (div 0::int 3::int)
+#699 := (= #555 0::int)
+#700 := [rewrite]: #699
+#556 := (= #425 #555)
+#713 := (= #339 3::int)
+#554 := [rewrite]: #713
+#698 := [monotonicity #714 #554]: #556
+#695 := [trans #698 #700]: #701
+#702 := [monotonicity #695]: #696
+#697 := [trans #702 #714]: #703
+#533 := [monotonicity #697]: #704
+#536 := [trans #533 #705]: #535
+#690 := [monotonicity #536]: #689
+#712 := (iff #427 #176)
+#706 := (= #430 #173)
+#708 := (= #430 #719)
+#718 := (= #357 0::int)
+#716 := (= #357 #424)
+#437 := (= #429 0::int)
+#438 := [rewrite]: #437
+#717 := [monotonicity #438]: #716
+#715 := [trans #717 #714]: #718
+#709 := [monotonicity #715]: #708
+#711 := [trans #709 #705]: #706
+#707 := [monotonicity #711]: #712
+#435 := (iff #415 false)
+#446 := (or false false)
+#721 := (iff #446 false)
+#725 := [rewrite]: #721
+#720 := (iff #415 #446)
+#723 := (iff #747 false)
+#736 := (not true)
+#379 := (iff #736 false)
+#739 := [rewrite]: #379
+#345 := (iff #747 #736)
+#451 := (iff #745 true)
+#731 := (or true true)
+#734 := (iff #731 true)
+#729 := [rewrite]: #734
+#449 := (iff #745 #731)
+#392 := (iff #431 true)
+#393 := [rewrite]: #392
+#726 := (iff #410 true)
+#727 := [rewrite]: #726
+#450 := [monotonicity #727 #393]: #449
+#452 := [trans #450 #729]: #451
+#722 := [monotonicity #452]: #345
+#445 := [trans #722 #739]: #723
+#737 := (iff #741 false)
+#738 := (iff #741 #736)
+#735 := (iff #534 true)
+#732 := (iff #534 #731)
+#394 := (iff #404 true)
+#730 := [rewrite]: #394
+#733 := [monotonicity #393 #730]: #732
+#373 := [trans #733 #729]: #735
+#378 := [monotonicity #373]: #738
+#740 := [trans #378 #739]: #737
+#724 := [monotonicity #740 #445]: #720
+#436 := [trans #724 #725]: #435
+#691 := [monotonicity #436 #707 #690]: #693
+#578 := [trans #691 #576]: #577
+#728 := (iff #750 true)
+#407 := (or true false)
+#744 := (iff #407 true)
+#387 := [rewrite]: #744
+#743 := (iff #750 #407)
+#742 := (iff #748 false)
+#402 := [rewrite]: #742
+#746 := (iff #749 true)
+#752 := [rewrite]: #746
+#403 := [monotonicity #752 #402]: #743
+#391 := [trans #403 #387]: #728
+#587 := [monotonicity #391 #578]: #685
+#571 := [trans #587 #683]: #686
+#591 := [monotonicity #571]: #590
+#594 := [trans #591 #593]: #590
+#582 := [quant-inst]: #589
+#687 := [mp #582 #594]: #588
+[unit-resolution #687 #759 #194]: false
+unsat
+0c2d2678afa32d5b44f328eda5903613f1a031fa 296 0
+#2 := false
+#11 := 0::int
+decl f3 :: (-> int int int)
+#39 := 3::int
+#38 := 1::int
+#40 := (f3 1::int 3::int)
+#41 := (= #40 0::int)
+#42 := (not #41)
+#169 := [asserted]: #42
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#737 := (pattern #10)
+#66 := -1::int
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#73 := (div #67 #70)
+#240 := (* -1::int #73)
+#241 := (+ #10 #240)
+#242 := (= #241 0::int)
+#21 := (div #8 #9)
+#237 := (* -1::int #21)
+#238 := (+ #10 #237)
+#239 := (= #238 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#195 := (or #88 #92)
+#196 := (not #195)
+#99 := (>= #8 0::int)
+#187 := (or #92 #99)
+#188 := (not #187)
+#202 := (or #188 #196)
+#243 := (ite #202 #239 #242)
+#236 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#244 := (ite #14 #236 #243)
+#738 := (forall (vars (?v0 int) (?v1 int)) (:pat #737) #244)
+#247 := (forall (vars (?v0 int) (?v1 int)) #244)
+#741 := (iff #247 #738)
+#739 := (iff #244 #244)
+#740 := [refl]: #739
+#742 := [quant-intro #740]: #741
+#207 := (ite #202 #21 #73)
+#210 := (ite #14 0::int #207)
+#213 := (= #10 #210)
+#216 := (forall (vars (?v0 int) (?v1 int)) #213)
+#248 := (iff #216 #247)
+#245 := (iff #213 #244)
+#246 := [rewrite]: #245
+#249 := [quant-intro #246]: #248
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#109 := (ite #106 #21 #73)
+#112 := (ite #14 0::int #109)
+#115 := (= #10 #112)
+#118 := (forall (vars (?v0 int) (?v1 int)) #115)
+#217 := (iff #118 #216)
+#214 := (iff #115 #213)
+#211 := (= #112 #210)
+#208 := (= #109 #207)
+#205 := (iff #106 #202)
+#199 := (or #196 #188)
+#203 := (iff #199 #202)
+#204 := [rewrite]: #203
+#200 := (iff #106 #199)
+#197 := (iff #103 #188)
+#198 := [rewrite]: #197
+#185 := (iff #96 #196)
+#186 := [rewrite]: #185
+#201 := [monotonicity #186 #198]: #200
+#206 := [trans #201 #204]: #205
+#209 := [monotonicity #206]: #208
+#212 := [monotonicity #209]: #211
+#215 := [monotonicity #212]: #214
+#218 := [quant-intro #215]: #217
+#191 := (~ #118 #118)
+#189 := (~ #115 #115)
+#190 := [refl]: #189
+#192 := [nnf-pos #190]: #191
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#121 := (iff #28 #118)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#76 := (ite #63 #21 #73)
+#79 := (ite #14 0::int #76)
+#82 := (= #10 #79)
+#85 := (forall (vars (?v0 int) (?v1 int)) #82)
+#119 := (iff #85 #118)
+#116 := (iff #82 #115)
+#113 := (= #79 #112)
+#110 := (= #76 #109)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#111 := [monotonicity #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [quant-intro #117]: #119
+#86 := (iff #28 #85)
+#83 := (iff #27 #82)
+#80 := (= #26 #79)
+#77 := (= #25 #76)
+#74 := (= #24 #73)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#75 := [monotonicity #69 #72]: #74
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#78 := [monotonicity #65 #75]: #77
+#81 := [monotonicity #78]: #80
+#84 := [monotonicity #81]: #83
+#87 := [quant-intro #84]: #86
+#122 := [trans #87 #120]: #121
+#59 := [asserted]: #28
+#123 := [mp #59 #122]: #118
+#182 := [mp~ #123 #192]: #118
+#219 := [mp #182 #218]: #216
+#250 := [mp #219 #249]: #247
+#743 := [mp #250 #742]: #738
+#650 := (not #738)
+#652 := (or #650 #41)
+#324 := (* -1::int 3::int)
+#408 := (* -1::int 1::int)
+#409 := (div #408 #324)
+#410 := (* -1::int #409)
+#401 := (+ #40 #410)
+#412 := (= #401 0::int)
+#413 := (div 1::int 3::int)
+#414 := (* -1::int #413)
+#411 := (+ #40 #414)
+#415 := (= #411 0::int)
+#394 := (<= 3::int 0::int)
+#729 := (<= 1::int 0::int)
+#731 := (or #729 #394)
+#388 := (not #731)
+#518 := (>= 1::int 0::int)
+#725 := (or #394 #518)
+#399 := (not #725)
+#400 := (or #399 #388)
+#732 := (ite #400 #415 #412)
+#733 := (= 3::int 0::int)
+#734 := (= 1::int 0::int)
+#735 := (or #734 #733)
+#730 := (ite #735 #41 #732)
+#662 := (or #650 #730)
+#664 := (iff #662 #652)
+#665 := (iff #652 #652)
+#654 := [rewrite]: #665
+#661 := (iff #730 #41)
+#578 := (ite false #41 #41)
+#672 := (iff #578 #41)
+#659 := [rewrite]: #672
+#671 := (iff #730 #578)
+#576 := (iff #732 #41)
+#666 := (= #40 1::int)
+#1 := true
+#572 := (ite true #41 #666)
+#574 := (iff #572 #41)
+#575 := [rewrite]: #574
+#573 := (iff #732 #572)
+#555 := (iff #412 #666)
+#675 := (+ -1::int #40)
+#521 := (= #675 0::int)
+#667 := (iff #521 #666)
+#670 := [rewrite]: #667
+#669 := (iff #412 #521)
+#561 := (= #401 #675)
+#674 := (+ #40 -1::int)
+#678 := (= #674 #675)
+#560 := [rewrite]: #678
+#676 := (= #401 #674)
+#520 := (= #410 -1::int)
+#539 := (= #408 -1::int)
+#540 := [rewrite]: #539
+#517 := (= #410 #408)
+#681 := (= #409 1::int)
+#682 := -3::int
+#685 := (div -1::int -3::int)
+#686 := (= #685 1::int)
+#687 := [rewrite]: #686
+#679 := (= #409 #685)
+#683 := (= #324 -3::int)
+#684 := [rewrite]: #683
+#680 := [monotonicity #540 #684]: #679
+#688 := [trans #680 #687]: #681
+#519 := [monotonicity #688]: #517
+#673 := [trans #519 #540]: #520
+#677 := [monotonicity #673]: #676
+#562 := [trans #677 #560]: #561
+#571 := [monotonicity #562]: #669
+#570 := [trans #571 #670]: #555
+#697 := (iff #415 #41)
+#696 := (= #411 #40)
+#693 := (+ #40 0::int)
+#690 := (= #693 #40)
+#695 := [rewrite]: #690
+#694 := (= #411 #693)
+#703 := (= #414 0::int)
+#701 := (* -1::int 0::int)
+#702 := (= #701 0::int)
+#699 := [rewrite]: #702
+#416 := (= #414 #701)
+#422 := (= #413 0::int)
+#700 := [rewrite]: #422
+#698 := [monotonicity #700]: #416
+#692 := [trans #698 #699]: #703
+#689 := [monotonicity #692]: #694
+#691 := [trans #689 #695]: #696
+#538 := [monotonicity #691]: #697
+#420 := (iff #400 true)
+#716 := (or false true)
+#713 := (iff #716 true)
+#719 := [rewrite]: #713
+#709 := (iff #400 #716)
+#708 := (iff #388 true)
+#706 := (not false)
+#430 := (iff #706 true)
+#704 := [rewrite]: #430
+#707 := (iff #388 #706)
+#436 := (iff #731 false)
+#727 := (or false false)
+#371 := (iff #727 false)
+#712 := [rewrite]: #371
+#434 := (iff #731 #727)
+#377 := (iff #394 false)
+#378 := [rewrite]: #377
+#711 := (iff #729 false)
+#433 := [rewrite]: #711
+#435 := [monotonicity #433 #378]: #434
+#330 := [trans #435 #712]: #436
+#429 := [monotonicity #330]: #707
+#705 := [trans #429 #704]: #708
+#724 := (iff #399 false)
+#722 := (not true)
+#723 := (iff #722 false)
+#721 := [rewrite]: #723
+#362 := (iff #399 #722)
+#357 := (iff #725 true)
+#717 := (iff #725 #716)
+#714 := (iff #518 true)
+#715 := [rewrite]: #714
+#718 := [monotonicity #378 #715]: #717
+#720 := [trans #718 #719]: #357
+#363 := [monotonicity #720]: #362
+#710 := [trans #363 #721]: #724
+#419 := [monotonicity #710 #705]: #709
+#421 := [trans #419 #719]: #420
+#566 := [monotonicity #421 #538 #570]: #573
+#577 := [trans #566 #575]: #576
+#375 := (iff #735 false)
+#387 := (iff #735 #727)
+#386 := (iff #733 false)
+#391 := [rewrite]: #386
+#736 := (iff #734 false)
+#726 := [rewrite]: #736
+#728 := [monotonicity #726 #391]: #387
+#376 := [trans #728 #712]: #375
+#668 := [monotonicity #376 #577]: #671
+#653 := [trans #668 #659]: #661
+#660 := [monotonicity #653]: #664
+#655 := [trans #660 #654]: #664
+#663 := [quant-inst]: #662
+#656 := [mp #663 #655]: #652
+[unit-resolution #656 #743 #169]: false
+unsat
+ce92c78a9ed7dc1c93cc4b086df53bc0f2e9e93d 286 0
+#2 := false
+#40 := 1::int
+decl f3 :: (-> int int int)
+#38 := 3::int
+#39 := (f3 3::int 3::int)
+#41 := (= #39 1::int)
+#42 := (not #41)
+#169 := [asserted]: #42
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#727 := (pattern #10)
+#11 := 0::int
+#66 := -1::int
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#73 := (div #67 #70)
+#230 := (* -1::int #73)
+#231 := (+ #10 #230)
+#232 := (= #231 0::int)
+#21 := (div #8 #9)
+#227 := (* -1::int #21)
+#228 := (+ #10 #227)
+#229 := (= #228 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#185 := (or #88 #92)
+#186 := (not #185)
+#99 := (>= #8 0::int)
+#177 := (or #92 #99)
+#178 := (not #177)
+#192 := (or #178 #186)
+#233 := (ite #192 #229 #232)
+#226 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#234 := (ite #14 #226 #233)
+#728 := (forall (vars (?v0 int) (?v1 int)) (:pat #727) #234)
+#237 := (forall (vars (?v0 int) (?v1 int)) #234)
+#731 := (iff #237 #728)
+#729 := (iff #234 #234)
+#730 := [refl]: #729
+#732 := [quant-intro #730]: #731
+#197 := (ite #192 #21 #73)
+#200 := (ite #14 0::int #197)
+#203 := (= #10 #200)
+#206 := (forall (vars (?v0 int) (?v1 int)) #203)
+#238 := (iff #206 #237)
+#235 := (iff #203 #234)
+#236 := [rewrite]: #235
+#239 := [quant-intro #236]: #238
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#109 := (ite #106 #21 #73)
+#112 := (ite #14 0::int #109)
+#115 := (= #10 #112)
+#118 := (forall (vars (?v0 int) (?v1 int)) #115)
+#207 := (iff #118 #206)
+#204 := (iff #115 #203)
+#201 := (= #112 #200)
+#198 := (= #109 #197)
+#195 := (iff #106 #192)
+#189 := (or #186 #178)
+#193 := (iff #189 #192)
+#194 := [rewrite]: #193
+#190 := (iff #106 #189)
+#187 := (iff #103 #178)
+#188 := [rewrite]: #187
+#175 := (iff #96 #186)
+#176 := [rewrite]: #175
+#191 := [monotonicity #176 #188]: #190
+#196 := [trans #191 #194]: #195
+#199 := [monotonicity #196]: #198
+#202 := [monotonicity #199]: #201
+#205 := [monotonicity #202]: #204
+#208 := [quant-intro #205]: #207
+#181 := (~ #118 #118)
+#179 := (~ #115 #115)
+#180 := [refl]: #179
+#182 := [nnf-pos #180]: #181
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#121 := (iff #28 #118)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#76 := (ite #63 #21 #73)
+#79 := (ite #14 0::int #76)
+#82 := (= #10 #79)
+#85 := (forall (vars (?v0 int) (?v1 int)) #82)
+#119 := (iff #85 #118)
+#116 := (iff #82 #115)
+#113 := (= #79 #112)
+#110 := (= #76 #109)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#111 := [monotonicity #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [quant-intro #117]: #119
+#86 := (iff #28 #85)
+#83 := (iff #27 #82)
+#80 := (= #26 #79)
+#77 := (= #25 #76)
+#74 := (= #24 #73)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#75 := [monotonicity #69 #72]: #74
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#78 := [monotonicity #65 #75]: #77
+#81 := [monotonicity #78]: #80
+#84 := [monotonicity #81]: #83
+#87 := [quant-intro #84]: #86
+#122 := [trans #87 #120]: #121
+#59 := [asserted]: #28
+#123 := [mp #59 #122]: #118
+#172 := [mp~ #123 #182]: #118
+#209 := [mp #172 #208]: #206
+#240 := [mp #209 #239]: #237
+#733 := [mp #240 #732]: #728
+#565 := (not #728)
+#566 := (or #565 #41)
+#314 := (* -1::int 3::int)
+#398 := (div #314 #314)
+#399 := (* -1::int #398)
+#400 := (+ #39 #399)
+#391 := (= #400 0::int)
+#402 := (div 3::int 3::int)
+#403 := (* -1::int #402)
+#404 := (+ #39 #403)
+#401 := (= #404 0::int)
+#405 := (<= 3::int 0::int)
+#384 := (or #405 #405)
+#719 := (not #384)
+#721 := (>= 3::int 0::int)
+#378 := (or #405 #721)
+#508 := (not #378)
+#715 := (or #508 #719)
+#389 := (ite #715 #401 #391)
+#390 := (= #39 0::int)
+#722 := (= 3::int 0::int)
+#723 := (or #722 #722)
+#724 := (ite #723 #390 #389)
+#567 := (or #565 #724)
+#661 := (iff #567 #566)
+#662 := (iff #566 #566)
+#649 := [rewrite]: #662
+#556 := (iff #724 #41)
+#660 := (ite false #390 #41)
+#562 := (iff #660 #41)
+#563 := [rewrite]: #562
+#545 := (iff #724 #660)
+#656 := (iff #389 #41)
+#1 := true
+#551 := (ite true #41 #41)
+#659 := (iff #551 #41)
+#561 := [rewrite]: #659
+#552 := (iff #389 #551)
+#668 := (iff #391 #41)
+#689 := (+ -1::int #39)
+#679 := (= #689 0::int)
+#686 := (iff #679 #41)
+#681 := [rewrite]: #686
+#667 := (iff #391 #679)
+#664 := (= #400 #689)
+#406 := (+ #39 -1::int)
+#693 := (= #406 #689)
+#682 := [rewrite]: #693
+#510 := (= #400 #406)
+#507 := (= #399 -1::int)
+#699 := (* -1::int 1::int)
+#411 := (= #699 -1::int)
+#412 := [rewrite]: #411
+#671 := (= #399 #699)
+#676 := (= #398 1::int)
+#529 := -3::int
+#673 := (div -3::int -3::int)
+#669 := (= #673 1::int)
+#670 := [rewrite]: #669
+#674 := (= #398 #673)
+#530 := (= #314 -3::int)
+#672 := [rewrite]: #530
+#675 := [monotonicity #672 #672]: #674
+#677 := [trans #675 #670]: #676
+#678 := [monotonicity #677]: #671
+#509 := [trans #678 #412]: #507
+#663 := [monotonicity #509]: #510
+#666 := [trans #663 #682]: #664
+#665 := [monotonicity #666]: #667
+#550 := [trans #665 #681]: #668
+#687 := (iff #401 #41)
+#680 := (iff #401 #679)
+#683 := (= #404 #689)
+#688 := (= #404 #406)
+#690 := (= #403 -1::int)
+#409 := (= #403 #699)
+#698 := (= #402 1::int)
+#695 := [rewrite]: #698
+#410 := [monotonicity #695]: #409
+#691 := [trans #410 #412]: #690
+#692 := [monotonicity #691]: #688
+#684 := [trans #692 #682]: #683
+#685 := [monotonicity #684]: #680
+#528 := [trans #685 #681]: #687
+#420 := (iff #715 true)
+#367 := (or false true)
+#705 := (iff #367 true)
+#706 := [rewrite]: #705
+#697 := (iff #715 #367)
+#320 := (iff #719 true)
+#701 := (not false)
+#425 := (iff #701 true)
+#426 := [rewrite]: #425
+#423 := (iff #719 #701)
+#714 := (iff #384 false)
+#726 := (or false false)
+#381 := (iff #726 false)
+#717 := [rewrite]: #381
+#713 := (iff #384 #726)
+#361 := (iff #405 false)
+#702 := [rewrite]: #361
+#711 := [monotonicity #702 #702]: #713
+#700 := [trans #711 #717]: #714
+#424 := [monotonicity #700]: #423
+#696 := [trans #424 #426]: #320
+#352 := (iff #508 false)
+#703 := (not true)
+#710 := (iff #703 false)
+#712 := [rewrite]: #710
+#709 := (iff #508 #703)
+#707 := (iff #378 true)
+#368 := (iff #378 #367)
+#365 := (iff #721 true)
+#366 := [rewrite]: #365
+#704 := [monotonicity #702 #366]: #368
+#708 := [trans #704 #706]: #707
+#347 := [monotonicity #708]: #709
+#353 := [trans #347 #712]: #352
+#419 := [monotonicity #353 #696]: #697
+#694 := [trans #419 #706]: #420
+#511 := [monotonicity #694 #528 #550]: #552
+#657 := [trans #511 #561]: #656
+#377 := (iff #723 false)
+#716 := (iff #723 #726)
+#725 := (iff #722 false)
+#720 := [rewrite]: #725
+#376 := [monotonicity #720 #720]: #716
+#718 := [trans #376 #717]: #377
+#560 := [monotonicity #718 #657]: #545
+#564 := [trans #560 #563]: #556
+#658 := [monotonicity #564]: #661
+#651 := [trans #658 #649]: #661
+#568 := [quant-inst]: #567
+#643 := [mp #568 #651]: #566
+[unit-resolution #643 #733 #169]: false
+unsat
+917a2b605f2d9a403ab95f50b9380edeb8c8755e 310 0
+#2 := false
+#41 := 1::int
+decl f3 :: (-> int int int)
+#39 := 3::int
+#38 := 5::int
+#40 := (f3 5::int 3::int)
+#42 := (= #40 1::int)
+#43 := (not #42)
+#170 := [asserted]: #43
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#728 := (pattern #10)
+#11 := 0::int
+#67 := -1::int
+#71 := (* -1::int #9)
+#68 := (* -1::int #8)
+#74 := (div #68 #71)
+#231 := (* -1::int #74)
+#232 := (+ #10 #231)
+#233 := (= #232 0::int)
+#21 := (div #8 #9)
+#228 := (* -1::int #21)
+#229 := (+ #10 #228)
+#230 := (= #229 0::int)
+#93 := (<= #9 0::int)
+#89 := (<= #8 0::int)
+#186 := (or #89 #93)
+#187 := (not #186)
+#100 := (>= #8 0::int)
+#178 := (or #93 #100)
+#179 := (not #178)
+#193 := (or #179 #187)
+#234 := (ite #193 #230 #233)
+#227 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#235 := (ite #14 #227 #234)
+#729 := (forall (vars (?v0 int) (?v1 int)) (:pat #728) #235)
+#238 := (forall (vars (?v0 int) (?v1 int)) #235)
+#732 := (iff #238 #729)
+#730 := (iff #235 #235)
+#731 := [refl]: #730
+#733 := [quant-intro #731]: #732
+#198 := (ite #193 #21 #74)
+#201 := (ite #14 0::int #198)
+#204 := (= #10 #201)
+#207 := (forall (vars (?v0 int) (?v1 int)) #204)
+#239 := (iff #207 #238)
+#236 := (iff #204 #235)
+#237 := [rewrite]: #236
+#240 := [quant-intro #237]: #239
+#101 := (not #100)
+#94 := (not #93)
+#104 := (and #94 #101)
+#90 := (not #89)
+#97 := (and #90 #94)
+#107 := (or #97 #104)
+#110 := (ite #107 #21 #74)
+#113 := (ite #14 0::int #110)
+#116 := (= #10 #113)
+#119 := (forall (vars (?v0 int) (?v1 int)) #116)
+#208 := (iff #119 #207)
+#205 := (iff #116 #204)
+#202 := (= #113 #201)
+#199 := (= #110 #198)
+#196 := (iff #107 #193)
+#190 := (or #187 #179)
+#194 := (iff #190 #193)
+#195 := [rewrite]: #194
+#191 := (iff #107 #190)
+#188 := (iff #104 #179)
+#189 := [rewrite]: #188
+#176 := (iff #97 #187)
+#177 := [rewrite]: #176
+#192 := [monotonicity #177 #189]: #191
+#197 := [trans #192 #195]: #196
+#200 := [monotonicity #197]: #199
+#203 := [monotonicity #200]: #202
+#206 := [monotonicity #203]: #205
+#209 := [quant-intro #206]: #208
+#182 := (~ #119 #119)
+#180 := (~ #116 #116)
+#181 := [refl]: #180
+#183 := [nnf-pos #181]: #182
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#122 := (iff #28 #119)
+#61 := (and #16 #18)
+#64 := (or #17 #61)
+#77 := (ite #64 #21 #74)
+#80 := (ite #14 0::int #77)
+#83 := (= #10 #80)
+#86 := (forall (vars (?v0 int) (?v1 int)) #83)
+#120 := (iff #86 #119)
+#117 := (iff #83 #116)
+#114 := (= #80 #113)
+#111 := (= #77 #110)
+#108 := (iff #64 #107)
+#105 := (iff #61 #104)
+#102 := (iff #18 #101)
+#103 := [rewrite]: #102
+#95 := (iff #16 #94)
+#96 := [rewrite]: #95
+#106 := [monotonicity #96 #103]: #105
+#98 := (iff #17 #97)
+#91 := (iff #15 #90)
+#92 := [rewrite]: #91
+#99 := [monotonicity #92 #96]: #98
+#109 := [monotonicity #99 #106]: #108
+#112 := [monotonicity #109]: #111
+#115 := [monotonicity #112]: #114
+#118 := [monotonicity #115]: #117
+#121 := [quant-intro #118]: #120
+#87 := (iff #28 #86)
+#84 := (iff #27 #83)
+#81 := (= #26 #80)
+#78 := (= #25 #77)
+#75 := (= #24 #74)
+#72 := (= #23 #71)
+#73 := [rewrite]: #72
+#69 := (= #22 #68)
+#70 := [rewrite]: #69
+#76 := [monotonicity #70 #73]: #75
+#65 := (iff #20 #64)
+#62 := (iff #19 #61)
+#63 := [rewrite]: #62
+#66 := [monotonicity #63]: #65
+#79 := [monotonicity #66 #76]: #78
+#82 := [monotonicity #79]: #81
+#85 := [monotonicity #82]: #84
+#88 := [quant-intro #85]: #87
+#123 := [trans #88 #121]: #122
+#60 := [asserted]: #28
+#124 := [mp #60 #123]: #119
+#173 := [mp~ #124 #183]: #119
+#210 := [mp #173 #209]: #207
+#241 := [mp #210 #240]: #238
+#734 := [mp #241 #733]: #729
+#633 := (not #729)
+#634 := (or #633 #42)
+#315 := (* -1::int 3::int)
+#399 := (* -1::int 5::int)
+#400 := (div #399 #315)
+#401 := (* -1::int #400)
+#392 := (+ #40 #401)
+#403 := (= #392 0::int)
+#404 := (div 5::int 3::int)
+#405 := (* -1::int #404)
+#402 := (+ #40 #405)
+#406 := (= #402 0::int)
+#385 := (<= 3::int 0::int)
+#720 := (<= 5::int 0::int)
+#722 := (or #720 #385)
+#379 := (not #722)
+#509 := (>= 5::int 0::int)
+#716 := (or #385 #509)
+#390 := (not #716)
+#391 := (or #390 #379)
+#723 := (ite #391 #406 #403)
+#724 := (= #40 0::int)
+#725 := (= 3::int 0::int)
+#726 := (= 5::int 0::int)
+#721 := (or #726 #725)
+#727 := (ite #721 #724 #723)
+#636 := (or #633 #727)
+#638 := (iff #636 #634)
+#635 := (iff #634 #634)
+#640 := [rewrite]: #635
+#642 := (iff #727 #42)
+#656 := (ite false #724 #42)
+#647 := (iff #656 #42)
+#648 := [rewrite]: #647
+#645 := (iff #727 #656)
+#655 := (iff #723 #42)
+#665 := 2::int
+#662 := (= #40 2::int)
+#1 := true
+#644 := (ite true #42 #662)
+#653 := (iff #644 #42)
+#654 := [rewrite]: #653
+#641 := (iff #723 #644)
+#650 := (iff #403 #662)
+#512 := -2::int
+#563 := (+ -2::int #40)
+#567 := (= #563 0::int)
+#659 := (iff #567 #662)
+#663 := [rewrite]: #659
+#568 := (iff #403 #567)
+#565 := (= #392 #563)
+#661 := (+ #40 -2::int)
+#564 := (= #661 #563)
+#557 := [rewrite]: #564
+#546 := (= #392 #661)
+#657 := (= #401 -2::int)
+#551 := (* -1::int 2::int)
+#660 := (= #551 -2::int)
+#562 := [rewrite]: #660
+#552 := (= #401 #551)
+#666 := (= #400 2::int)
+#672 := -3::int
+#671 := -5::int
+#510 := (div -5::int -3::int)
+#667 := (= #510 2::int)
+#668 := [rewrite]: #667
+#511 := (= #400 #510)
+#679 := (= #315 -3::int)
+#508 := [rewrite]: #679
+#677 := (= #399 -5::int)
+#678 := [rewrite]: #677
+#664 := [monotonicity #678 #508]: #511
+#669 := [trans #664 #668]: #666
+#553 := [monotonicity #669]: #552
+#658 := [trans #553 #562]: #657
+#561 := [monotonicity #658]: #546
+#566 := [trans #561 #557]: #565
+#569 := [monotonicity #566]: #568
+#652 := [trans #569 #663]: #650
+#676 := (iff #406 #42)
+#686 := (+ -1::int #40)
+#530 := (= #686 0::int)
+#674 := (iff #530 #42)
+#675 := [rewrite]: #674
+#531 := (iff #406 #530)
+#688 := (= #402 #686)
+#685 := (+ #40 -1::int)
+#687 := (= #685 #686)
+#682 := [rewrite]: #687
+#680 := (= #402 #685)
+#683 := (= #405 -1::int)
+#407 := (* -1::int 1::int)
+#690 := (= #407 -1::int)
+#694 := [rewrite]: #690
+#689 := (= #405 #407)
+#691 := (= #404 1::int)
+#692 := [rewrite]: #691
+#693 := [monotonicity #692]: #689
+#684 := [trans #693 #694]: #683
+#681 := [monotonicity #684]: #680
+#529 := [trans #681 #682]: #688
+#673 := [monotonicity #529]: #531
+#670 := [trans #673 #675]: #676
+#412 := (iff #391 true)
+#708 := (or false true)
+#710 := (iff #708 true)
+#348 := [rewrite]: #710
+#410 := (iff #391 #708)
+#696 := (iff #379 true)
+#698 := (not false)
+#695 := (iff #698 true)
+#699 := [rewrite]: #695
+#420 := (iff #379 #698)
+#321 := (iff #722 false)
+#378 := (or false false)
+#703 := (iff #378 false)
+#366 := [rewrite]: #703
+#426 := (iff #722 #378)
+#369 := (iff #385 false)
+#705 := [rewrite]: #369
+#424 := (iff #720 false)
+#425 := [rewrite]: #424
+#427 := [monotonicity #425 #705]: #426
+#697 := [trans #427 #366]: #321
+#421 := [monotonicity #697]: #420
+#700 := [trans #421 #699]: #696
+#701 := (iff #390 false)
+#353 := (not true)
+#712 := (iff #353 false)
+#715 := [rewrite]: #712
+#354 := (iff #390 #353)
+#711 := (iff #716 true)
+#709 := (iff #716 #708)
+#706 := (iff #509 true)
+#707 := [rewrite]: #706
+#704 := [monotonicity #705 #707]: #709
+#713 := [trans #704 #348]: #711
+#714 := [monotonicity #713]: #354
+#702 := [trans #714 #715]: #701
+#411 := [monotonicity #702 #700]: #410
+#413 := [trans #411 #348]: #412
+#643 := [monotonicity #413 #670 #652]: #641
+#651 := [trans #643 #654]: #655
+#367 := (iff #721 false)
+#719 := (iff #721 #378)
+#382 := (iff #725 false)
+#718 := [rewrite]: #382
+#717 := (iff #726 false)
+#377 := [rewrite]: #717
+#362 := [monotonicity #377 #718]: #719
+#368 := [trans #362 #366]: #367
+#646 := [monotonicity #368 #651]: #645
+#649 := [trans #646 #648]: #642
+#639 := [monotonicity #649]: #638
+#626 := [trans #639 #640]: #638
+#637 := [quant-inst]: #636
+#627 := [mp #637 #626]: #634
+[unit-resolution #627 #734 #170]: false
+unsat
+58821dfa96819bd628fd32a642914f3ce4ecfe98 324 0
+#2 := false
+#68 := -1::int
+decl f3 :: (-> int int int)
+#172 := -3::int
+#38 := 1::int
+#175 := (f3 1::int -3::int)
+#180 := (= #175 -1::int)
+#193 := (not #180)
+#42 := (- 1::int)
+#39 := 3::int
+#40 := (- 3::int)
+#41 := (f3 1::int #40)
+#43 := (= #41 #42)
+#44 := (not #43)
+#196 := (iff #44 #193)
+#183 := (= -1::int #175)
+#188 := (not #183)
+#194 := (iff #188 #193)
+#191 := (iff #183 #180)
+#192 := [rewrite]: #191
+#195 := [monotonicity #192]: #194
+#189 := (iff #44 #188)
+#186 := (iff #43 #183)
+#184 := (iff #180 #183)
+#185 := [rewrite]: #184
+#181 := (iff #43 #180)
+#178 := (= #42 -1::int)
+#179 := [rewrite]: #178
+#176 := (= #41 #175)
+#173 := (= #40 -3::int)
+#174 := [rewrite]: #173
+#177 := [monotonicity #174]: #176
+#182 := [monotonicity #177 #179]: #181
+#187 := [trans #182 #185]: #186
+#190 := [monotonicity #187]: #189
+#197 := [trans #190 #195]: #196
+#171 := [asserted]: #44
+#198 := [mp #171 #197]: #193
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#756 := (pattern #10)
+#11 := 0::int
+#72 := (* -1::int #9)
+#69 := (* -1::int #8)
+#75 := (div #69 #72)
+#259 := (* -1::int #75)
+#260 := (+ #10 #259)
+#261 := (= #260 0::int)
+#21 := (div #8 #9)
+#256 := (* -1::int #21)
+#257 := (+ #10 #256)
+#258 := (= #257 0::int)
+#94 := (<= #9 0::int)
+#90 := (<= #8 0::int)
+#214 := (or #90 #94)
+#215 := (not #214)
+#101 := (>= #8 0::int)
+#206 := (or #94 #101)
+#207 := (not #206)
+#221 := (or #207 #215)
+#262 := (ite #221 #258 #261)
+#255 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#263 := (ite #14 #255 #262)
+#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
+#266 := (forall (vars (?v0 int) (?v1 int)) #263)
+#760 := (iff #266 #757)
+#758 := (iff #263 #263)
+#759 := [refl]: #758
+#761 := [quant-intro #759]: #760
+#226 := (ite #221 #21 #75)
+#229 := (ite #14 0::int #226)
+#232 := (= #10 #229)
+#235 := (forall (vars (?v0 int) (?v1 int)) #232)
+#267 := (iff #235 #266)
+#264 := (iff #232 #263)
+#265 := [rewrite]: #264
+#268 := [quant-intro #265]: #267
+#102 := (not #101)
+#95 := (not #94)
+#105 := (and #95 #102)
+#91 := (not #90)
+#98 := (and #91 #95)
+#108 := (or #98 #105)
+#111 := (ite #108 #21 #75)
+#114 := (ite #14 0::int #111)
+#117 := (= #10 #114)
+#120 := (forall (vars (?v0 int) (?v1 int)) #117)
+#236 := (iff #120 #235)
+#233 := (iff #117 #232)
+#230 := (= #114 #229)
+#227 := (= #111 #226)
+#224 := (iff #108 #221)
+#218 := (or #215 #207)
+#222 := (iff #218 #221)
+#223 := [rewrite]: #222
+#219 := (iff #108 #218)
+#216 := (iff #105 #207)
+#217 := [rewrite]: #216
+#204 := (iff #98 #215)
+#205 := [rewrite]: #204
+#220 := [monotonicity #205 #217]: #219
+#225 := [trans #220 #223]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [quant-intro #234]: #236
+#210 := (~ #120 #120)
+#208 := (~ #117 #117)
+#209 := [refl]: #208
+#211 := [nnf-pos #209]: #210
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#123 := (iff #28 #120)
+#62 := (and #16 #18)
+#65 := (or #17 #62)
+#78 := (ite #65 #21 #75)
+#81 := (ite #14 0::int #78)
+#84 := (= #10 #81)
+#87 := (forall (vars (?v0 int) (?v1 int)) #84)
+#121 := (iff #87 #120)
+#118 := (iff #84 #117)
+#115 := (= #81 #114)
+#112 := (= #78 #111)
+#109 := (iff #65 #108)
+#106 := (iff #62 #105)
+#103 := (iff #18 #102)
+#104 := [rewrite]: #103
+#96 := (iff #16 #95)
+#97 := [rewrite]: #96
+#107 := [monotonicity #97 #104]: #106
+#99 := (iff #17 #98)
+#92 := (iff #15 #91)
+#93 := [rewrite]: #92
+#100 := [monotonicity #93 #97]: #99
+#110 := [monotonicity #100 #107]: #109
+#113 := [monotonicity #110]: #112
+#116 := [monotonicity #113]: #115
+#119 := [monotonicity #116]: #118
+#122 := [quant-intro #119]: #121
+#88 := (iff #28 #87)
+#85 := (iff #27 #84)
+#82 := (= #26 #81)
+#79 := (= #25 #78)
+#76 := (= #24 #75)
+#73 := (= #23 #72)
+#74 := [rewrite]: #73
+#70 := (= #22 #69)
+#71 := [rewrite]: #70
+#77 := [monotonicity #71 #74]: #76
+#66 := (iff #20 #65)
+#63 := (iff #19 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#80 := [monotonicity #67 #77]: #79
+#83 := [monotonicity #80]: #82
+#86 := [monotonicity #83]: #85
+#89 := [quant-intro #86]: #88
+#124 := [trans #89 #122]: #123
+#61 := [asserted]: #28
+#125 := [mp #61 #124]: #120
+#201 := [mp~ #125 #211]: #120
+#238 := [mp #201 #237]: #235
+#269 := [mp #238 #268]: #266
+#762 := [mp #269 #761]: #757
+#672 := (not #757)
+#669 := (or #672 #180)
+#343 := (* -1::int -3::int)
+#427 := (* -1::int 1::int)
+#428 := (div #427 #343)
+#429 := (* -1::int #428)
+#420 := (+ #175 #429)
+#431 := (= #420 0::int)
+#432 := (div 1::int -3::int)
+#433 := (* -1::int #432)
+#430 := (+ #175 #433)
+#434 := (= #430 0::int)
+#413 := (<= -3::int 0::int)
+#748 := (<= 1::int 0::int)
+#750 := (or #748 #413)
+#407 := (not #750)
+#537 := (>= 1::int 0::int)
+#744 := (or #413 #537)
+#418 := (not #744)
+#419 := (or #418 #407)
+#751 := (ite #419 #434 #431)
+#752 := (= #175 0::int)
+#753 := (= -3::int 0::int)
+#754 := (= 1::int 0::int)
+#749 := (or #754 #753)
+#755 := (ite #749 #752 #751)
+#671 := (or #672 #755)
+#682 := (iff #671 #669)
+#679 := (iff #669 #669)
+#684 := [rewrite]: #679
+#678 := (iff #755 #180)
+#585 := (ite false #752 #180)
+#595 := (iff #585 #180)
+#596 := [rewrite]: #595
+#687 := (iff #755 #585)
+#597 := (iff #751 #180)
+#593 := (iff #751 #585)
+#591 := (iff #431 #180)
+#580 := (+ 1::int #175)
+#685 := (= #580 0::int)
+#574 := (iff #685 #180)
+#589 := [rewrite]: #574
+#686 := (iff #431 #685)
+#688 := (= #420 #580)
+#694 := (+ #175 1::int)
+#581 := (= #694 #580)
+#540 := [rewrite]: #581
+#697 := (= #420 #694)
+#695 := (= #429 1::int)
+#536 := (* -1::int -1::int)
+#692 := (= #536 1::int)
+#693 := [rewrite]: #692
+#538 := (= #429 #536)
+#700 := (= #428 -1::int)
+#704 := (div -1::int 3::int)
+#705 := (= #704 -1::int)
+#706 := [rewrite]: #705
+#698 := (= #428 #704)
+#702 := (= #343 3::int)
+#703 := [rewrite]: #702
+#559 := (= #427 -1::int)
+#701 := [rewrite]: #559
+#699 := [monotonicity #701 #703]: #698
+#707 := [trans #699 #706]: #700
+#539 := [monotonicity #707]: #538
+#696 := [trans #539 #693]: #695
+#579 := [monotonicity #696]: #697
+#590 := [trans #579 #540]: #688
+#689 := [monotonicity #590]: #686
+#592 := [trans #689 #589]: #591
+#557 := (iff #434 #752)
+#710 := (= #430 #175)
+#713 := (+ #175 0::int)
+#714 := (= #713 #175)
+#715 := [rewrite]: #714
+#708 := (= #430 #713)
+#711 := (= #433 0::int)
+#435 := (* -1::int 0::int)
+#718 := (= #435 0::int)
+#722 := [rewrite]: #718
+#717 := (= #433 #435)
+#719 := (= #432 0::int)
+#720 := [rewrite]: #719
+#721 := [monotonicity #720]: #717
+#712 := [trans #721 #722]: #711
+#709 := [monotonicity #712]: #708
+#716 := [trans #709 #715]: #710
+#558 := [monotonicity #716]: #557
+#440 := (iff #419 false)
+#406 := (or false false)
+#731 := (iff #406 false)
+#394 := [rewrite]: #731
+#438 := (iff #419 #406)
+#724 := (iff #407 false)
+#1 := true
+#381 := (not true)
+#740 := (iff #381 false)
+#743 := [rewrite]: #740
+#723 := (iff #407 #381)
+#448 := (iff #750 true)
+#454 := (or false true)
+#725 := (iff #454 true)
+#726 := [rewrite]: #725
+#455 := (iff #750 #454)
+#397 := (iff #413 true)
+#733 := [rewrite]: #397
+#452 := (iff #748 false)
+#453 := [rewrite]: #452
+#349 := [monotonicity #453 #733]: #455
+#449 := [trans #349 #726]: #448
+#727 := [monotonicity #449]: #723
+#728 := [trans #727 #743]: #724
+#729 := (iff #418 false)
+#382 := (iff #418 #381)
+#739 := (iff #744 true)
+#736 := (or true true)
+#738 := (iff #736 true)
+#376 := [rewrite]: #738
+#737 := (iff #744 #736)
+#734 := (iff #537 true)
+#735 := [rewrite]: #734
+#732 := [monotonicity #733 #735]: #737
+#741 := [trans #732 #376]: #739
+#742 := [monotonicity #741]: #382
+#730 := [trans #742 #743]: #729
+#439 := [monotonicity #730 #728]: #438
+#441 := [trans #439 #394]: #440
+#594 := [monotonicity #441 #558 #592]: #593
+#690 := [trans #594 #596]: #597
+#395 := (iff #749 false)
+#747 := (iff #749 #406)
+#410 := (iff #753 false)
+#746 := [rewrite]: #410
+#745 := (iff #754 false)
+#405 := [rewrite]: #745
+#390 := [monotonicity #405 #746]: #747
+#396 := [trans #390 #394]: #395
+#691 := [monotonicity #396 #690]: #687
+#680 := [trans #691 #596]: #678
+#683 := [monotonicity #680]: #682
+#673 := [trans #683 #684]: #682
+#681 := [quant-inst]: #671
+#674 := [mp #681 #673]: #669
+[unit-resolution #674 #762 #198]: false
+unsat
+e324d2dcbb42d1c1608b214b224b3ba3708fb0ec 323 0
+#2 := false
+#68 := -1::int
+decl f3 :: (-> int int int)
+#172 := -3::int
+#38 := 3::int
+#175 := (f3 3::int -3::int)
+#180 := (= #175 -1::int)
+#193 := (not #180)
+#41 := 1::int
+#42 := (- 1::int)
+#39 := (- 3::int)
+#40 := (f3 3::int #39)
+#43 := (= #40 #42)
+#44 := (not #43)
+#196 := (iff #44 #193)
+#183 := (= -1::int #175)
+#188 := (not #183)
+#194 := (iff #188 #193)
+#191 := (iff #183 #180)
+#192 := [rewrite]: #191
+#195 := [monotonicity #192]: #194
+#189 := (iff #44 #188)
+#186 := (iff #43 #183)
+#184 := (iff #180 #183)
+#185 := [rewrite]: #184
+#181 := (iff #43 #180)
+#178 := (= #42 -1::int)
+#179 := [rewrite]: #178
+#176 := (= #40 #175)
+#173 := (= #39 -3::int)
+#174 := [rewrite]: #173
+#177 := [monotonicity #174]: #176
+#182 := [monotonicity #177 #179]: #181
+#187 := [trans #182 #185]: #186
+#190 := [monotonicity #187]: #189
+#197 := [trans #190 #195]: #196
+#171 := [asserted]: #44
+#198 := [mp #171 #197]: #193
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#756 := (pattern #10)
+#11 := 0::int
+#72 := (* -1::int #9)
+#69 := (* -1::int #8)
+#75 := (div #69 #72)
+#259 := (* -1::int #75)
+#260 := (+ #10 #259)
+#261 := (= #260 0::int)
+#21 := (div #8 #9)
+#256 := (* -1::int #21)
+#257 := (+ #10 #256)
+#258 := (= #257 0::int)
+#94 := (<= #9 0::int)
+#90 := (<= #8 0::int)
+#214 := (or #90 #94)
+#215 := (not #214)
+#101 := (>= #8 0::int)
+#206 := (or #94 #101)
+#207 := (not #206)
+#221 := (or #207 #215)
+#262 := (ite #221 #258 #261)
+#255 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#263 := (ite #14 #255 #262)
+#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
+#266 := (forall (vars (?v0 int) (?v1 int)) #263)
+#760 := (iff #266 #757)
+#758 := (iff #263 #263)
+#759 := [refl]: #758
+#761 := [quant-intro #759]: #760
+#226 := (ite #221 #21 #75)
+#229 := (ite #14 0::int #226)
+#232 := (= #10 #229)
+#235 := (forall (vars (?v0 int) (?v1 int)) #232)
+#267 := (iff #235 #266)
+#264 := (iff #232 #263)
+#265 := [rewrite]: #264
+#268 := [quant-intro #265]: #267
+#102 := (not #101)
+#95 := (not #94)
+#105 := (and #95 #102)
+#91 := (not #90)
+#98 := (and #91 #95)
+#108 := (or #98 #105)
+#111 := (ite #108 #21 #75)
+#114 := (ite #14 0::int #111)
+#117 := (= #10 #114)
+#120 := (forall (vars (?v0 int) (?v1 int)) #117)
+#236 := (iff #120 #235)
+#233 := (iff #117 #232)
+#230 := (= #114 #229)
+#227 := (= #111 #226)
+#224 := (iff #108 #221)
+#218 := (or #215 #207)
+#222 := (iff #218 #221)
+#223 := [rewrite]: #222
+#219 := (iff #108 #218)
+#216 := (iff #105 #207)
+#217 := [rewrite]: #216
+#204 := (iff #98 #215)
+#205 := [rewrite]: #204
+#220 := [monotonicity #205 #217]: #219
+#225 := [trans #220 #223]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [quant-intro #234]: #236
+#210 := (~ #120 #120)
+#208 := (~ #117 #117)
+#209 := [refl]: #208
+#211 := [nnf-pos #209]: #210
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#123 := (iff #28 #120)
+#62 := (and #16 #18)
+#65 := (or #17 #62)
+#78 := (ite #65 #21 #75)
+#81 := (ite #14 0::int #78)
+#84 := (= #10 #81)
+#87 := (forall (vars (?v0 int) (?v1 int)) #84)
+#121 := (iff #87 #120)
+#118 := (iff #84 #117)
+#115 := (= #81 #114)
+#112 := (= #78 #111)
+#109 := (iff #65 #108)
+#106 := (iff #62 #105)
+#103 := (iff #18 #102)
+#104 := [rewrite]: #103
+#96 := (iff #16 #95)
+#97 := [rewrite]: #96
+#107 := [monotonicity #97 #104]: #106
+#99 := (iff #17 #98)
+#92 := (iff #15 #91)
+#93 := [rewrite]: #92
+#100 := [monotonicity #93 #97]: #99
+#110 := [monotonicity #100 #107]: #109
+#113 := [monotonicity #110]: #112
+#116 := [monotonicity #113]: #115
+#119 := [monotonicity #116]: #118
+#122 := [quant-intro #119]: #121
+#88 := (iff #28 #87)
+#85 := (iff #27 #84)
+#82 := (= #26 #81)
+#79 := (= #25 #78)
+#76 := (= #24 #75)
+#73 := (= #23 #72)
+#74 := [rewrite]: #73
+#70 := (= #22 #69)
+#71 := [rewrite]: #70
+#77 := [monotonicity #71 #74]: #76
+#66 := (iff #20 #65)
+#63 := (iff #19 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#80 := [monotonicity #67 #77]: #79
+#83 := [monotonicity #80]: #82
+#86 := [monotonicity #83]: #85
+#89 := [quant-intro #86]: #88
+#124 := [trans #89 #122]: #123
+#61 := [asserted]: #28
+#125 := [mp #61 #124]: #120
+#201 := [mp~ #125 #211]: #120
+#238 := [mp #201 #237]: #235
+#269 := [mp #238 #268]: #266
+#762 := [mp #269 #761]: #757
+#680 := (not #757)
+#672 := (or #680 #180)
+#343 := (* -1::int -3::int)
+#427 := (* -1::int 3::int)
+#428 := (div #427 #343)
+#429 := (* -1::int #428)
+#420 := (+ #175 #429)
+#431 := (= #420 0::int)
+#432 := (div 3::int -3::int)
+#433 := (* -1::int #432)
+#430 := (+ #175 #433)
+#434 := (= #430 0::int)
+#413 := (<= -3::int 0::int)
+#748 := (<= 3::int 0::int)
+#750 := (or #748 #413)
+#407 := (not #750)
+#537 := (>= 3::int 0::int)
+#744 := (or #413 #537)
+#418 := (not #744)
+#419 := (or #418 #407)
+#751 := (ite #419 #434 #431)
+#752 := (= #175 0::int)
+#753 := (= -3::int 0::int)
+#754 := (= 3::int 0::int)
+#749 := (or #754 #753)
+#755 := (ite #749 #752 #751)
+#669 := (or #680 #755)
+#681 := (iff #669 #672)
+#683 := (iff #672 #672)
+#679 := [rewrite]: #683
+#691 := (iff #755 #180)
+#595 := (ite false #752 #180)
+#690 := (iff #595 #180)
+#687 := [rewrite]: #690
+#596 := (iff #755 #595)
+#593 := (iff #751 #180)
+#574 := (ite false #180 #180)
+#592 := (iff #574 #180)
+#585 := [rewrite]: #592
+#589 := (iff #751 #574)
+#686 := (iff #431 #180)
+#714 := (+ 1::int #175)
+#558 := (= #714 0::int)
+#702 := (iff #558 #180)
+#703 := [rewrite]: #702
+#590 := (iff #431 #558)
+#540 := (= #420 #714)
+#713 := (+ #175 1::int)
+#715 := (= #713 #714)
+#710 := [rewrite]: #715
+#580 := (= #420 #713)
+#697 := (= #429 1::int)
+#435 := (* -1::int -1::int)
+#718 := (= #435 1::int)
+#722 := [rewrite]: #718
+#696 := (= #429 #435)
+#693 := (= #428 -1::int)
+#707 := (div -3::int 3::int)
+#539 := (= #707 -1::int)
+#692 := [rewrite]: #539
+#536 := (= #428 #707)
+#706 := (= #343 3::int)
+#700 := [rewrite]: #706
+#699 := (= #427 -3::int)
+#705 := [rewrite]: #699
+#538 := [monotonicity #705 #700]: #536
+#695 := [trans #538 #692]: #693
+#694 := [monotonicity #695]: #696
+#579 := [trans #694 #722]: #697
+#581 := [monotonicity #579]: #580
+#688 := [trans #581 #710]: #540
+#685 := [monotonicity #688]: #590
+#689 := [trans #685 #703]: #686
+#704 := (iff #434 #180)
+#559 := (iff #434 #558)
+#716 := (= #430 #714)
+#708 := (= #430 #713)
+#711 := (= #433 1::int)
+#717 := (= #433 #435)
+#719 := (= #432 -1::int)
+#720 := [rewrite]: #719
+#721 := [monotonicity #720]: #717
+#712 := [trans #721 #722]: #711
+#709 := [monotonicity #712]: #708
+#557 := [trans #709 #710]: #716
+#701 := [monotonicity #557]: #559
+#698 := [trans #701 #703]: #704
+#440 := (iff #419 false)
+#406 := (or false false)
+#731 := (iff #406 false)
+#394 := [rewrite]: #731
+#438 := (iff #419 #406)
+#724 := (iff #407 false)
+#1 := true
+#381 := (not true)
+#740 := (iff #381 false)
+#743 := [rewrite]: #740
+#723 := (iff #407 #381)
+#448 := (iff #750 true)
+#454 := (or false true)
+#725 := (iff #454 true)
+#726 := [rewrite]: #725
+#455 := (iff #750 #454)
+#397 := (iff #413 true)
+#733 := [rewrite]: #397
+#452 := (iff #748 false)
+#453 := [rewrite]: #452
+#349 := [monotonicity #453 #733]: #455
+#449 := [trans #349 #726]: #448
+#727 := [monotonicity #449]: #723
+#728 := [trans #727 #743]: #724
+#729 := (iff #418 false)
+#382 := (iff #418 #381)
+#739 := (iff #744 true)
+#736 := (or true true)
+#738 := (iff #736 true)
+#376 := [rewrite]: #738
+#737 := (iff #744 #736)
+#734 := (iff #537 true)
+#735 := [rewrite]: #734
+#732 := [monotonicity #733 #735]: #737
+#741 := [trans #732 #376]: #739
+#742 := [monotonicity #741]: #382
+#730 := [trans #742 #743]: #729
+#439 := [monotonicity #730 #728]: #438
+#441 := [trans #439 #394]: #440
+#591 := [monotonicity #441 #698 #689]: #589
+#594 := [trans #591 #585]: #593
+#395 := (iff #749 false)
+#747 := (iff #749 #406)
+#410 := (iff #753 false)
+#746 := [rewrite]: #410
+#745 := (iff #754 false)
+#405 := [rewrite]: #745
+#390 := [monotonicity #405 #746]: #747
+#396 := [trans #390 #394]: #395
+#597 := [monotonicity #396 #594]: #596
+#678 := [trans #597 #687]: #691
+#682 := [monotonicity #678]: #681
+#684 := [trans #682 #679]: #681
+#671 := [quant-inst]: #669
+#673 := [mp #671 #684]: #672
+[unit-resolution #673 #762 #198]: false
+unsat
+434ef00c2361be87b5251cd35b03968cfe5c5ccc 326 0
+#2 := false
+#179 := -2::int
+decl f3 :: (-> int int int)
+#173 := -3::int
+#38 := 5::int
+#176 := (f3 5::int -3::int)
+#182 := (= #176 -2::int)
+#185 := (not #182)
+#42 := 2::int
+#43 := (- 2::int)
+#39 := 3::int
+#40 := (- 3::int)
+#41 := (f3 5::int #40)
+#44 := (= #41 #43)
+#45 := (not #44)
+#186 := (iff #45 #185)
+#183 := (iff #44 #182)
+#180 := (= #43 -2::int)
+#181 := [rewrite]: #180
+#177 := (= #41 #176)
+#174 := (= #40 -3::int)
+#175 := [rewrite]: #174
+#178 := [monotonicity #175]: #177
+#184 := [monotonicity #178 #181]: #183
+#187 := [monotonicity #184]: #186
+#172 := [asserted]: #45
+#190 := [mp #172 #187]: #185
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#747 := (pattern #10)
+#11 := 0::int
+#69 := -1::int
+#73 := (* -1::int #9)
+#70 := (* -1::int #8)
+#76 := (div #70 #73)
+#249 := (* -1::int #76)
+#250 := (+ #10 #249)
+#251 := (= #250 0::int)
+#21 := (div #8 #9)
+#246 := (* -1::int #21)
+#247 := (+ #10 #246)
+#248 := (= #247 0::int)
+#95 := (<= #9 0::int)
+#91 := (<= #8 0::int)
+#204 := (or #91 #95)
+#205 := (not #204)
+#102 := (>= #8 0::int)
+#196 := (or #95 #102)
+#197 := (not #196)
+#211 := (or #197 #205)
+#252 := (ite #211 #248 #251)
+#245 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#253 := (ite #14 #245 #252)
+#748 := (forall (vars (?v0 int) (?v1 int)) (:pat #747) #253)
+#256 := (forall (vars (?v0 int) (?v1 int)) #253)
+#751 := (iff #256 #748)
+#749 := (iff #253 #253)
+#750 := [refl]: #749
+#752 := [quant-intro #750]: #751
+#216 := (ite #211 #21 #76)
+#219 := (ite #14 0::int #216)
+#222 := (= #10 #219)
+#225 := (forall (vars (?v0 int) (?v1 int)) #222)
+#257 := (iff #225 #256)
+#254 := (iff #222 #253)
+#255 := [rewrite]: #254
+#258 := [quant-intro #255]: #257
+#103 := (not #102)
+#96 := (not #95)
+#106 := (and #96 #103)
+#92 := (not #91)
+#99 := (and #92 #96)
+#109 := (or #99 #106)
+#112 := (ite #109 #21 #76)
+#115 := (ite #14 0::int #112)
+#118 := (= #10 #115)
+#121 := (forall (vars (?v0 int) (?v1 int)) #118)
+#226 := (iff #121 #225)
+#223 := (iff #118 #222)
+#220 := (= #115 #219)
+#217 := (= #112 #216)
+#214 := (iff #109 #211)
+#208 := (or #205 #197)
+#212 := (iff #208 #211)
+#213 := [rewrite]: #212
+#209 := (iff #109 #208)
+#206 := (iff #106 #197)
+#207 := [rewrite]: #206
+#194 := (iff #99 #205)
+#195 := [rewrite]: #194
+#210 := [monotonicity #195 #207]: #209
+#215 := [trans #210 #213]: #214
+#218 := [monotonicity #215]: #217
+#221 := [monotonicity #218]: #220
+#224 := [monotonicity #221]: #223
+#227 := [quant-intro #224]: #226
+#200 := (~ #121 #121)
+#198 := (~ #118 #118)
+#199 := [refl]: #198
+#201 := [nnf-pos #199]: #200
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#124 := (iff #28 #121)
+#63 := (and #16 #18)
+#66 := (or #17 #63)
+#79 := (ite #66 #21 #76)
+#82 := (ite #14 0::int #79)
+#85 := (= #10 #82)
+#88 := (forall (vars (?v0 int) (?v1 int)) #85)
+#122 := (iff #88 #121)
+#119 := (iff #85 #118)
+#116 := (= #82 #115)
+#113 := (= #79 #112)
+#110 := (iff #66 #109)
+#107 := (iff #63 #106)
+#104 := (iff #18 #103)
+#105 := [rewrite]: #104
+#97 := (iff #16 #96)
+#98 := [rewrite]: #97
+#108 := [monotonicity #98 #105]: #107
+#100 := (iff #17 #99)
+#93 := (iff #15 #92)
+#94 := [rewrite]: #93
+#101 := [monotonicity #94 #98]: #100
+#111 := [monotonicity #101 #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [monotonicity #117]: #119
+#123 := [quant-intro #120]: #122
+#89 := (iff #28 #88)
+#86 := (iff #27 #85)
+#83 := (= #26 #82)
+#80 := (= #25 #79)
+#77 := (= #24 #76)
+#74 := (= #23 #73)
+#75 := [rewrite]: #74
+#71 := (= #22 #70)
+#72 := [rewrite]: #71
+#78 := [monotonicity #72 #75]: #77
+#67 := (iff #20 #66)
+#64 := (iff #19 #63)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#81 := [monotonicity #68 #78]: #80
+#84 := [monotonicity #81]: #83
+#87 := [monotonicity #84]: #86
+#90 := [quant-intro #87]: #89
+#125 := [trans #90 #123]: #124
+#62 := [asserted]: #28
+#126 := [mp #62 #125]: #121
+#191 := [mp~ #126 #201]: #121
+#228 := [mp #191 #227]: #225
+#259 := [mp #228 #258]: #256
+#753 := [mp #259 #752]: #748
+#667 := (not #748)
+#661 := (or #667 #182)
+#333 := (* -1::int -3::int)
+#418 := (* -1::int 5::int)
+#419 := (div #418 #333)
+#420 := (* -1::int #419)
+#411 := (+ #176 #420)
+#422 := (= #411 0::int)
+#423 := (div 5::int -3::int)
+#351 := (* -1::int #423)
+#424 := (+ #176 #351)
+#421 := (= #424 0::int)
+#425 := (<= -3::int 0::int)
+#404 := (<= 5::int 0::int)
+#739 := (or #404 #425)
+#741 := (not #739)
+#398 := (>= 5::int 0::int)
+#528 := (or #425 #398)
+#735 := (not #528)
+#409 := (or #735 #741)
+#410 := (ite #409 #421 #422)
+#742 := (= #176 0::int)
+#743 := (= -3::int 0::int)
+#744 := (= 5::int 0::int)
+#745 := (or #744 #743)
+#740 := (ite #745 #742 #410)
+#668 := (or #667 #740)
+#653 := (iff #668 #661)
+#656 := (iff #661 #661)
+#657 := [rewrite]: #656
+#665 := (iff #740 #182)
+#673 := (ite false #742 #182)
+#675 := (iff #673 #182)
+#664 := [rewrite]: #675
+#674 := (iff #740 #673)
+#662 := (iff #410 #182)
+#693 := (= #176 -1::int)
+#682 := (ite false #693 #182)
+#663 := (iff #682 #182)
+#660 := [rewrite]: #663
+#669 := (iff #410 #682)
+#681 := (iff #422 #182)
+#565 := (+ 2::int #176)
+#584 := (= #565 0::int)
+#587 := (iff #584 #182)
+#588 := [rewrite]: #587
+#585 := (iff #422 #584)
+#583 := (= #411 #565)
+#676 := (+ #176 2::int)
+#580 := (= #676 #565)
+#582 := [rewrite]: #580
+#677 := (= #411 #676)
+#679 := (= #420 2::int)
+#688 := (* -1::int -2::int)
+#572 := (= #688 2::int)
+#531 := [rewrite]: #572
+#570 := (= #420 #688)
+#687 := (= #419 -2::int)
+#696 := -5::int
+#529 := (div -5::int 3::int)
+#684 := (= #529 -2::int)
+#686 := [rewrite]: #684
+#530 := (= #419 #529)
+#698 := (= #333 3::int)
+#527 := [rewrite]: #698
+#697 := (= #418 -5::int)
+#691 := [rewrite]: #697
+#683 := [monotonicity #691 #527]: #530
+#685 := [trans #683 #686]: #687
+#571 := [monotonicity #685]: #570
+#581 := [trans #571 #531]: #679
+#680 := [monotonicity #581]: #677
+#576 := [trans #680 #582]: #583
+#586 := [monotonicity #576]: #585
+#678 := [trans #586 #588]: #681
+#689 := (iff #421 #693)
+#712 := 1::int
+#705 := (+ 1::int #176)
+#549 := (= #705 0::int)
+#694 := (iff #549 #693)
+#695 := [rewrite]: #694
+#550 := (iff #421 #549)
+#707 := (= #424 #705)
+#704 := (+ #176 1::int)
+#706 := (= #704 #705)
+#701 := [rewrite]: #706
+#699 := (= #424 #704)
+#702 := (= #351 1::int)
+#711 := (* -1::int -1::int)
+#709 := (= #711 1::int)
+#713 := [rewrite]: #709
+#426 := (= #351 #711)
+#432 := (= #423 -1::int)
+#710 := [rewrite]: #432
+#708 := [monotonicity #710]: #426
+#703 := [trans #708 #713]: #702
+#700 := [monotonicity #703]: #699
+#548 := [trans #700 #701]: #707
+#692 := [monotonicity #548]: #550
+#690 := [trans #692 #695]: #689
+#430 := (iff #409 false)
+#737 := (or false false)
+#381 := (iff #737 false)
+#722 := [rewrite]: #381
+#719 := (iff #409 #737)
+#718 := (iff #741 false)
+#1 := true
+#732 := (not true)
+#733 := (iff #732 false)
+#731 := [rewrite]: #733
+#440 := (iff #741 #732)
+#717 := (iff #739 true)
+#444 := (or false true)
+#339 := (iff #444 true)
+#716 := [rewrite]: #339
+#445 := (iff #739 #444)
+#387 := (iff #425 true)
+#388 := [rewrite]: #387
+#721 := (iff #404 false)
+#443 := [rewrite]: #721
+#446 := [monotonicity #443 #388]: #445
+#439 := [trans #446 #716]: #717
+#714 := [monotonicity #439]: #440
+#715 := [trans #714 #731]: #718
+#734 := (iff #735 false)
+#372 := (iff #735 #732)
+#367 := (iff #528 true)
+#726 := (or true true)
+#723 := (iff #726 true)
+#729 := [rewrite]: #723
+#727 := (iff #528 #726)
+#724 := (iff #398 true)
+#725 := [rewrite]: #724
+#728 := [monotonicity #388 #725]: #727
+#730 := [trans #728 #729]: #367
+#373 := [monotonicity #730]: #372
+#720 := [trans #373 #731]: #734
+#429 := [monotonicity #720 #715]: #719
+#431 := [trans #429 #722]: #430
+#671 := [monotonicity #431 #690 #678]: #669
+#672 := [trans #671 #660]: #662
+#385 := (iff #745 false)
+#397 := (iff #745 #737)
+#396 := (iff #743 false)
+#401 := [rewrite]: #396
+#746 := (iff #744 false)
+#736 := [rewrite]: #746
+#738 := [monotonicity #736 #401]: #397
+#386 := [trans #738 #722]: #385
+#670 := [monotonicity #386 #672]: #674
+#666 := [trans #670 #664]: #665
+#655 := [monotonicity #666]: #653
+#658 := [trans #655 #657]: #653
+#652 := [quant-inst]: #668
+#654 := [mp #652 #658]: #661
+[unit-resolution #654 #753 #190]: false
+unsat
+ff8f86eb28f84123aac176b636d7798cfd6a8662 321 0
+#2 := false
+#67 := -1::int
+decl f3 :: (-> int int int)
+#40 := 3::int
+#173 := (f3 -1::int 3::int)
+#176 := (= #173 -1::int)
+#189 := (not #176)
+#38 := 1::int
+#39 := (- 1::int)
+#41 := (f3 #39 3::int)
+#42 := (= #41 #39)
+#43 := (not #42)
+#192 := (iff #43 #189)
+#179 := (= -1::int #173)
+#184 := (not #179)
+#190 := (iff #184 #189)
+#187 := (iff #179 #176)
+#188 := [rewrite]: #187
+#191 := [monotonicity #188]: #190
+#185 := (iff #43 #184)
+#182 := (iff #42 #179)
+#180 := (iff #176 #179)
+#181 := [rewrite]: #180
+#177 := (iff #42 #176)
+#171 := (= #39 -1::int)
+#172 := [rewrite]: #171
+#174 := (= #41 #173)
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175 #172]: #177
+#183 := [trans #178 #181]: #182
+#186 := [monotonicity #183]: #185
+#193 := [trans #186 #191]: #192
+#170 := [asserted]: #43
+#194 := [mp #170 #193]: #189
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#752 := (pattern #10)
+#11 := 0::int
+#71 := (* -1::int #9)
+#68 := (* -1::int #8)
+#74 := (div #68 #71)
+#255 := (* -1::int #74)
+#256 := (+ #10 #255)
+#257 := (= #256 0::int)
+#21 := (div #8 #9)
+#252 := (* -1::int #21)
+#253 := (+ #10 #252)
+#254 := (= #253 0::int)
+#93 := (<= #9 0::int)
+#89 := (<= #8 0::int)
+#210 := (or #89 #93)
+#211 := (not #210)
+#100 := (>= #8 0::int)
+#202 := (or #93 #100)
+#203 := (not #202)
+#217 := (or #203 #211)
+#258 := (ite #217 #254 #257)
+#251 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#259 := (ite #14 #251 #258)
+#753 := (forall (vars (?v0 int) (?v1 int)) (:pat #752) #259)
+#262 := (forall (vars (?v0 int) (?v1 int)) #259)
+#756 := (iff #262 #753)
+#754 := (iff #259 #259)
+#755 := [refl]: #754
+#757 := [quant-intro #755]: #756
+#222 := (ite #217 #21 #74)
+#225 := (ite #14 0::int #222)
+#228 := (= #10 #225)
+#231 := (forall (vars (?v0 int) (?v1 int)) #228)
+#263 := (iff #231 #262)
+#260 := (iff #228 #259)
+#261 := [rewrite]: #260
+#264 := [quant-intro #261]: #263
+#101 := (not #100)
+#94 := (not #93)
+#104 := (and #94 #101)
+#90 := (not #89)
+#97 := (and #90 #94)
+#107 := (or #97 #104)
+#110 := (ite #107 #21 #74)
+#113 := (ite #14 0::int #110)
+#116 := (= #10 #113)
+#119 := (forall (vars (?v0 int) (?v1 int)) #116)
+#232 := (iff #119 #231)
+#229 := (iff #116 #228)
+#226 := (= #113 #225)
+#223 := (= #110 #222)
+#220 := (iff #107 #217)
+#214 := (or #211 #203)
+#218 := (iff #214 #217)
+#219 := [rewrite]: #218
+#215 := (iff #107 #214)
+#212 := (iff #104 #203)
+#213 := [rewrite]: #212
+#200 := (iff #97 #211)
+#201 := [rewrite]: #200
+#216 := [monotonicity #201 #213]: #215
+#221 := [trans #216 #219]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [quant-intro #230]: #232
+#206 := (~ #119 #119)
+#204 := (~ #116 #116)
+#205 := [refl]: #204
+#207 := [nnf-pos #205]: #206
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#122 := (iff #28 #119)
+#61 := (and #16 #18)
+#64 := (or #17 #61)
+#77 := (ite #64 #21 #74)
+#80 := (ite #14 0::int #77)
+#83 := (= #10 #80)
+#86 := (forall (vars (?v0 int) (?v1 int)) #83)
+#120 := (iff #86 #119)
+#117 := (iff #83 #116)
+#114 := (= #80 #113)
+#111 := (= #77 #110)
+#108 := (iff #64 #107)
+#105 := (iff #61 #104)
+#102 := (iff #18 #101)
+#103 := [rewrite]: #102
+#95 := (iff #16 #94)
+#96 := [rewrite]: #95
+#106 := [monotonicity #96 #103]: #105
+#98 := (iff #17 #97)
+#91 := (iff #15 #90)
+#92 := [rewrite]: #91
+#99 := [monotonicity #92 #96]: #98
+#109 := [monotonicity #99 #106]: #108
+#112 := [monotonicity #109]: #111
+#115 := [monotonicity #112]: #114
+#118 := [monotonicity #115]: #117
+#121 := [quant-intro #118]: #120
+#87 := (iff #28 #86)
+#84 := (iff #27 #83)
+#81 := (= #26 #80)
+#78 := (= #25 #77)
+#75 := (= #24 #74)
+#72 := (= #23 #71)
+#73 := [rewrite]: #72
+#69 := (= #22 #68)
+#70 := [rewrite]: #69
+#76 := [monotonicity #70 #73]: #75
+#65 := (iff #20 #64)
+#62 := (iff #19 #61)
+#63 := [rewrite]: #62
+#66 := [monotonicity #63]: #65
+#79 := [monotonicity #66 #76]: #78
+#82 := [monotonicity #79]: #81
+#85 := [monotonicity #82]: #84
+#88 := [quant-intro #85]: #87
+#123 := [trans #88 #121]: #122
+#60 := [asserted]: #28
+#124 := [mp #60 #123]: #119
+#197 := [mp~ #124 #207]: #119
+#234 := [mp #197 #233]: #231
+#265 := [mp #234 #264]: #262
+#758 := [mp #265 #757]: #753
+#665 := (not #753)
+#667 := (or #665 #176)
+#339 := (* -1::int 3::int)
+#423 := (* -1::int -1::int)
+#424 := (div #423 #339)
+#425 := (* -1::int #424)
+#416 := (+ #173 #425)
+#427 := (= #416 0::int)
+#428 := (div -1::int 3::int)
+#429 := (* -1::int #428)
+#426 := (+ #173 #429)
+#430 := (= #426 0::int)
+#409 := (<= 3::int 0::int)
+#744 := (<= -1::int 0::int)
+#746 := (or #744 #409)
+#403 := (not #746)
+#533 := (>= -1::int 0::int)
+#740 := (or #409 #533)
+#414 := (not #740)
+#415 := (or #414 #403)
+#747 := (ite #415 #430 #427)
+#748 := (= #173 0::int)
+#749 := (= 3::int 0::int)
+#750 := (= -1::int 0::int)
+#745 := (or #750 #749)
+#751 := (ite #745 #748 #747)
+#677 := (or #665 #751)
+#679 := (iff #677 #667)
+#680 := (iff #667 #667)
+#669 := [rewrite]: #680
+#676 := (iff #751 #176)
+#593 := (ite false #748 #176)
+#687 := (iff #593 #176)
+#674 := [rewrite]: #687
+#686 := (iff #751 #593)
+#591 := (iff #747 #176)
+#1 := true
+#587 := (ite true #176 #748)
+#589 := (iff #587 #176)
+#590 := [rewrite]: #589
+#588 := (iff #747 #587)
+#570 := (iff #427 #748)
+#682 := (= #416 #173)
+#577 := (+ #173 0::int)
+#586 := (= #577 #173)
+#681 := [rewrite]: #586
+#536 := (= #416 #577)
+#575 := (= #425 0::int)
+#689 := (* -1::int 0::int)
+#690 := (= #689 0::int)
+#693 := [rewrite]: #690
+#691 := (= #425 #689)
+#535 := (= #424 0::int)
+#694 := -3::int
+#702 := (div 1::int -3::int)
+#532 := (= #702 0::int)
+#534 := [rewrite]: #532
+#696 := (= #424 #702)
+#695 := (= #339 -3::int)
+#701 := [rewrite]: #695
+#717 := (= #423 1::int)
+#714 := [rewrite]: #717
+#703 := [monotonicity #714 #701]: #696
+#688 := [trans #703 #534]: #535
+#692 := [monotonicity #688]: #691
+#576 := [trans #692 #693]: #575
+#684 := [monotonicity #576]: #536
+#685 := [trans #684 #681]: #682
+#585 := [monotonicity #685]: #570
+#699 := (iff #430 #176)
+#705 := (+ 1::int #173)
+#553 := (= #705 0::int)
+#697 := (iff #553 #176)
+#698 := [rewrite]: #697
+#554 := (iff #430 #553)
+#706 := (= #426 #705)
+#708 := (+ #173 1::int)
+#710 := (= #708 #705)
+#711 := [rewrite]: #710
+#709 := (= #426 #708)
+#718 := (= #429 1::int)
+#431 := (= #429 #423)
+#715 := (= #428 -1::int)
+#716 := [rewrite]: #715
+#713 := [monotonicity #716]: #431
+#707 := [trans #713 #714]: #718
+#704 := [monotonicity #707]: #709
+#712 := [trans #704 #711]: #706
+#555 := [monotonicity #712]: #554
+#700 := [trans #555 #698]: #699
+#436 := (iff #415 true)
+#726 := (or true false)
+#450 := (iff #726 true)
+#451 := [rewrite]: #450
+#434 := (iff #415 #726)
+#720 := (iff #403 false)
+#722 := (not true)
+#719 := (iff #722 false)
+#723 := [rewrite]: #719
+#444 := (iff #403 #722)
+#345 := (iff #746 true)
+#448 := (iff #746 #726)
+#393 := (iff #409 false)
+#729 := [rewrite]: #393
+#739 := (iff #744 true)
+#725 := [rewrite]: #739
+#449 := [monotonicity #725 #729]: #448
+#721 := [trans #449 #451]: #345
+#445 := [monotonicity #721]: #444
+#724 := [trans #445 #723]: #720
+#738 := (iff #414 true)
+#372 := (not false)
+#377 := (iff #372 true)
+#378 := [rewrite]: #377
+#735 := (iff #414 #372)
+#728 := (iff #740 false)
+#402 := (or false false)
+#727 := (iff #402 false)
+#390 := [rewrite]: #727
+#732 := (iff #740 #402)
+#730 := (iff #533 false)
+#731 := [rewrite]: #730
+#733 := [monotonicity #729 #731]: #732
+#734 := [trans #733 #390]: #728
+#737 := [monotonicity #734]: #735
+#736 := [trans #737 #378]: #738
+#435 := [monotonicity #736 #724]: #434
+#437 := [trans #435 #451]: #436
+#581 := [monotonicity #437 #700 #585]: #588
+#592 := [trans #581 #590]: #591
+#391 := (iff #745 false)
+#743 := (iff #745 #402)
+#406 := (iff #749 false)
+#742 := [rewrite]: #406
+#741 := (iff #750 false)
+#401 := [rewrite]: #741
+#386 := [monotonicity #401 #742]: #743
+#392 := [trans #386 #390]: #391
+#683 := [monotonicity #392 #592]: #686
+#668 := [trans #683 #674]: #676
+#675 := [monotonicity #668]: #679
+#670 := [trans #675 #669]: #679
+#678 := [quant-inst]: #677
+#671 := [mp #678 #670]: #667
+[unit-resolution #671 #758 #194]: false
+unsat
+3a21c45c123733996bd5da9d4a171d44f436dea5 323 0
+#2 := false
+#68 := -1::int
+decl f3 :: (-> int int int)
+#38 := 3::int
+#172 := -3::int
+#175 := (f3 -3::int 3::int)
+#180 := (= #175 -1::int)
+#193 := (not #180)
+#41 := 1::int
+#42 := (- 1::int)
+#39 := (- 3::int)
+#40 := (f3 #39 3::int)
+#43 := (= #40 #42)
+#44 := (not #43)
+#196 := (iff #44 #193)
+#183 := (= -1::int #175)
+#188 := (not #183)
+#194 := (iff #188 #193)
+#191 := (iff #183 #180)
+#192 := [rewrite]: #191
+#195 := [monotonicity #192]: #194
+#189 := (iff #44 #188)
+#186 := (iff #43 #183)
+#184 := (iff #180 #183)
+#185 := [rewrite]: #184
+#181 := (iff #43 #180)
+#178 := (= #42 -1::int)
+#179 := [rewrite]: #178
+#176 := (= #40 #175)
+#173 := (= #39 -3::int)
+#174 := [rewrite]: #173
+#177 := [monotonicity #174]: #176
+#182 := [monotonicity #177 #179]: #181
+#187 := [trans #182 #185]: #186
+#190 := [monotonicity #187]: #189
+#197 := [trans #190 #195]: #196
+#171 := [asserted]: #44
+#198 := [mp #171 #197]: #193
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#756 := (pattern #10)
+#11 := 0::int
+#72 := (* -1::int #9)
+#69 := (* -1::int #8)
+#75 := (div #69 #72)
+#259 := (* -1::int #75)
+#260 := (+ #10 #259)
+#261 := (= #260 0::int)
+#21 := (div #8 #9)
+#256 := (* -1::int #21)
+#257 := (+ #10 #256)
+#258 := (= #257 0::int)
+#94 := (<= #9 0::int)
+#90 := (<= #8 0::int)
+#214 := (or #90 #94)
+#215 := (not #214)
+#101 := (>= #8 0::int)
+#206 := (or #94 #101)
+#207 := (not #206)
+#221 := (or #207 #215)
+#262 := (ite #221 #258 #261)
+#255 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#263 := (ite #14 #255 #262)
+#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
+#266 := (forall (vars (?v0 int) (?v1 int)) #263)
+#760 := (iff #266 #757)
+#758 := (iff #263 #263)
+#759 := [refl]: #758
+#761 := [quant-intro #759]: #760
+#226 := (ite #221 #21 #75)
+#229 := (ite #14 0::int #226)
+#232 := (= #10 #229)
+#235 := (forall (vars (?v0 int) (?v1 int)) #232)
+#267 := (iff #235 #266)
+#264 := (iff #232 #263)
+#265 := [rewrite]: #264
+#268 := [quant-intro #265]: #267
+#102 := (not #101)
+#95 := (not #94)
+#105 := (and #95 #102)
+#91 := (not #90)
+#98 := (and #91 #95)
+#108 := (or #98 #105)
+#111 := (ite #108 #21 #75)
+#114 := (ite #14 0::int #111)
+#117 := (= #10 #114)
+#120 := (forall (vars (?v0 int) (?v1 int)) #117)
+#236 := (iff #120 #235)
+#233 := (iff #117 #232)
+#230 := (= #114 #229)
+#227 := (= #111 #226)
+#224 := (iff #108 #221)
+#218 := (or #215 #207)
+#222 := (iff #218 #221)
+#223 := [rewrite]: #222
+#219 := (iff #108 #218)
+#216 := (iff #105 #207)
+#217 := [rewrite]: #216
+#204 := (iff #98 #215)
+#205 := [rewrite]: #204
+#220 := [monotonicity #205 #217]: #219
+#225 := [trans #220 #223]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [quant-intro #234]: #236
+#210 := (~ #120 #120)
+#208 := (~ #117 #117)
+#209 := [refl]: #208
+#211 := [nnf-pos #209]: #210
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#123 := (iff #28 #120)
+#62 := (and #16 #18)
+#65 := (or #17 #62)
+#78 := (ite #65 #21 #75)
+#81 := (ite #14 0::int #78)
+#84 := (= #10 #81)
+#87 := (forall (vars (?v0 int) (?v1 int)) #84)
+#121 := (iff #87 #120)
+#118 := (iff #84 #117)
+#115 := (= #81 #114)
+#112 := (= #78 #111)
+#109 := (iff #65 #108)
+#106 := (iff #62 #105)
+#103 := (iff #18 #102)
+#104 := [rewrite]: #103
+#96 := (iff #16 #95)
+#97 := [rewrite]: #96
+#107 := [monotonicity #97 #104]: #106
+#99 := (iff #17 #98)
+#92 := (iff #15 #91)
+#93 := [rewrite]: #92
+#100 := [monotonicity #93 #97]: #99
+#110 := [monotonicity #100 #107]: #109
+#113 := [monotonicity #110]: #112
+#116 := [monotonicity #113]: #115
+#119 := [monotonicity #116]: #118
+#122 := [quant-intro #119]: #121
+#88 := (iff #28 #87)
+#85 := (iff #27 #84)
+#82 := (= #26 #81)
+#79 := (= #25 #78)
+#76 := (= #24 #75)
+#73 := (= #23 #72)
+#74 := [rewrite]: #73
+#70 := (= #22 #69)
+#71 := [rewrite]: #70
+#77 := [monotonicity #71 #74]: #76
+#66 := (iff #20 #65)
+#63 := (iff #19 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#80 := [monotonicity #67 #77]: #79
+#83 := [monotonicity #80]: #82
+#86 := [monotonicity #83]: #85
+#89 := [quant-intro #86]: #88
+#124 := [trans #89 #122]: #123
+#61 := [asserted]: #28
+#125 := [mp #61 #124]: #120
+#201 := [mp~ #125 #211]: #120
+#238 := [mp #201 #237]: #235
+#269 := [mp #238 #268]: #266
+#762 := [mp #269 #761]: #757
+#680 := (not #757)
+#672 := (or #680 #180)
+#343 := (* -1::int 3::int)
+#427 := (* -1::int -3::int)
+#428 := (div #427 #343)
+#429 := (* -1::int #428)
+#420 := (+ #175 #429)
+#431 := (= #420 0::int)
+#432 := (div -3::int 3::int)
+#433 := (* -1::int #432)
+#430 := (+ #175 #433)
+#434 := (= #430 0::int)
+#413 := (<= 3::int 0::int)
+#748 := (<= -3::int 0::int)
+#750 := (or #748 #413)
+#407 := (not #750)
+#537 := (>= -3::int 0::int)
+#744 := (or #413 #537)
+#418 := (not #744)
+#419 := (or #418 #407)
+#751 := (ite #419 #434 #431)
+#752 := (= #175 0::int)
+#753 := (= 3::int 0::int)
+#754 := (= -3::int 0::int)
+#749 := (or #754 #753)
+#755 := (ite #749 #752 #751)
+#669 := (or #680 #755)
+#681 := (iff #669 #672)
+#683 := (iff #672 #672)
+#679 := [rewrite]: #683
+#691 := (iff #755 #180)
+#595 := (ite false #752 #180)
+#690 := (iff #595 #180)
+#687 := [rewrite]: #690
+#596 := (iff #755 #595)
+#593 := (iff #751 #180)
+#1 := true
+#574 := (ite true #180 #180)
+#592 := (iff #574 #180)
+#585 := [rewrite]: #592
+#589 := (iff #751 #574)
+#686 := (iff #431 #180)
+#714 := (+ 1::int #175)
+#558 := (= #714 0::int)
+#702 := (iff #558 #180)
+#703 := [rewrite]: #702
+#590 := (iff #431 #558)
+#540 := (= #420 #714)
+#713 := (+ #175 1::int)
+#715 := (= #713 #714)
+#710 := [rewrite]: #715
+#580 := (= #420 #713)
+#697 := (= #429 1::int)
+#435 := (* -1::int -1::int)
+#718 := (= #435 1::int)
+#722 := [rewrite]: #718
+#696 := (= #429 #435)
+#693 := (= #428 -1::int)
+#707 := (div 3::int -3::int)
+#539 := (= #707 -1::int)
+#692 := [rewrite]: #539
+#536 := (= #428 #707)
+#706 := (= #343 -3::int)
+#700 := [rewrite]: #706
+#699 := (= #427 3::int)
+#705 := [rewrite]: #699
+#538 := [monotonicity #705 #700]: #536
+#695 := [trans #538 #692]: #693
+#694 := [monotonicity #695]: #696
+#579 := [trans #694 #722]: #697
+#581 := [monotonicity #579]: #580
+#688 := [trans #581 #710]: #540
+#685 := [monotonicity #688]: #590
+#689 := [trans #685 #703]: #686
+#704 := (iff #434 #180)
+#559 := (iff #434 #558)
+#716 := (= #430 #714)
+#708 := (= #430 #713)
+#711 := (= #433 1::int)
+#717 := (= #433 #435)
+#719 := (= #432 -1::int)
+#720 := [rewrite]: #719
+#721 := [monotonicity #720]: #717
+#712 := [trans #721 #722]: #711
+#709 := [monotonicity #712]: #708
+#557 := [trans #709 #710]: #716
+#701 := [monotonicity #557]: #559
+#698 := [trans #701 #703]: #704
+#440 := (iff #419 true)
+#730 := (or true false)
+#454 := (iff #730 true)
+#455 := [rewrite]: #454
+#438 := (iff #419 #730)
+#724 := (iff #407 false)
+#726 := (not true)
+#723 := (iff #726 false)
+#727 := [rewrite]: #723
+#448 := (iff #407 #726)
+#349 := (iff #750 true)
+#452 := (iff #750 #730)
+#397 := (iff #413 false)
+#733 := [rewrite]: #397
+#743 := (iff #748 true)
+#729 := [rewrite]: #743
+#453 := [monotonicity #729 #733]: #452
+#725 := [trans #453 #455]: #349
+#449 := [monotonicity #725]: #448
+#728 := [trans #449 #727]: #724
+#742 := (iff #418 true)
+#376 := (not false)
+#381 := (iff #376 true)
+#382 := [rewrite]: #381
+#739 := (iff #418 #376)
+#732 := (iff #744 false)
+#406 := (or false false)
+#731 := (iff #406 false)
+#394 := [rewrite]: #731
+#736 := (iff #744 #406)
+#734 := (iff #537 false)
+#735 := [rewrite]: #734
+#737 := [monotonicity #733 #735]: #736
+#738 := [trans #737 #394]: #732
+#741 := [monotonicity #738]: #739
+#740 := [trans #741 #382]: #742
+#439 := [monotonicity #740 #728]: #438
+#441 := [trans #439 #455]: #440
+#591 := [monotonicity #441 #698 #689]: #589
+#594 := [trans #591 #585]: #593
+#395 := (iff #749 false)
+#747 := (iff #749 #406)
+#410 := (iff #753 false)
+#746 := [rewrite]: #410
+#745 := (iff #754 false)
+#405 := [rewrite]: #745
+#390 := [monotonicity #405 #746]: #747
+#396 := [trans #390 #394]: #395
+#597 := [monotonicity #396 #594]: #596
+#678 := [trans #597 #687]: #691
+#682 := [monotonicity #678]: #681
+#684 := [trans #682 #679]: #681
+#671 := [quant-inst]: #669
+#673 := [mp #671 #684]: #672
+[unit-resolution #673 #762 #198]: false
+unsat
+448a7cea8211330ab0cab0aedbfc681ca04868f7 326 0
+#2 := false
+#179 := -2::int
+decl f3 :: (-> int int int)
+#40 := 3::int
+#173 := -5::int
+#176 := (f3 -5::int 3::int)
+#182 := (= #176 -2::int)
+#185 := (not #182)
+#42 := 2::int
+#43 := (- 2::int)
+#38 := 5::int
+#39 := (- 5::int)
+#41 := (f3 #39 3::int)
+#44 := (= #41 #43)
+#45 := (not #44)
+#186 := (iff #45 #185)
+#183 := (iff #44 #182)
+#180 := (= #43 -2::int)
+#181 := [rewrite]: #180
+#177 := (= #41 #176)
+#174 := (= #39 -5::int)
+#175 := [rewrite]: #174
+#178 := [monotonicity #175]: #177
+#184 := [monotonicity #178 #181]: #183
+#187 := [monotonicity #184]: #186
+#172 := [asserted]: #45
+#190 := [mp #172 #187]: #185
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#747 := (pattern #10)
+#11 := 0::int
+#69 := -1::int
+#73 := (* -1::int #9)
+#70 := (* -1::int #8)
+#76 := (div #70 #73)
+#249 := (* -1::int #76)
+#250 := (+ #10 #249)
+#251 := (= #250 0::int)
+#21 := (div #8 #9)
+#246 := (* -1::int #21)
+#247 := (+ #10 #246)
+#248 := (= #247 0::int)
+#95 := (<= #9 0::int)
+#91 := (<= #8 0::int)
+#204 := (or #91 #95)
+#205 := (not #204)
+#102 := (>= #8 0::int)
+#196 := (or #95 #102)
+#197 := (not #196)
+#211 := (or #197 #205)
+#252 := (ite #211 #248 #251)
+#245 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#253 := (ite #14 #245 #252)
+#748 := (forall (vars (?v0 int) (?v1 int)) (:pat #747) #253)
+#256 := (forall (vars (?v0 int) (?v1 int)) #253)
+#751 := (iff #256 #748)
+#749 := (iff #253 #253)
+#750 := [refl]: #749
+#752 := [quant-intro #750]: #751
+#216 := (ite #211 #21 #76)
+#219 := (ite #14 0::int #216)
+#222 := (= #10 #219)
+#225 := (forall (vars (?v0 int) (?v1 int)) #222)
+#257 := (iff #225 #256)
+#254 := (iff #222 #253)
+#255 := [rewrite]: #254
+#258 := [quant-intro #255]: #257
+#103 := (not #102)
+#96 := (not #95)
+#106 := (and #96 #103)
+#92 := (not #91)
+#99 := (and #92 #96)
+#109 := (or #99 #106)
+#112 := (ite #109 #21 #76)
+#115 := (ite #14 0::int #112)
+#118 := (= #10 #115)
+#121 := (forall (vars (?v0 int) (?v1 int)) #118)
+#226 := (iff #121 #225)
+#223 := (iff #118 #222)
+#220 := (= #115 #219)
+#217 := (= #112 #216)
+#214 := (iff #109 #211)
+#208 := (or #205 #197)
+#212 := (iff #208 #211)
+#213 := [rewrite]: #212
+#209 := (iff #109 #208)
+#206 := (iff #106 #197)
+#207 := [rewrite]: #206
+#194 := (iff #99 #205)
+#195 := [rewrite]: #194
+#210 := [monotonicity #195 #207]: #209
+#215 := [trans #210 #213]: #214
+#218 := [monotonicity #215]: #217
+#221 := [monotonicity #218]: #220
+#224 := [monotonicity #221]: #223
+#227 := [quant-intro #224]: #226
+#200 := (~ #121 #121)
+#198 := (~ #118 #118)
+#199 := [refl]: #198
+#201 := [nnf-pos #199]: #200
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#124 := (iff #28 #121)
+#63 := (and #16 #18)
+#66 := (or #17 #63)
+#79 := (ite #66 #21 #76)
+#82 := (ite #14 0::int #79)
+#85 := (= #10 #82)
+#88 := (forall (vars (?v0 int) (?v1 int)) #85)
+#122 := (iff #88 #121)
+#119 := (iff #85 #118)
+#116 := (= #82 #115)
+#113 := (= #79 #112)
+#110 := (iff #66 #109)
+#107 := (iff #63 #106)
+#104 := (iff #18 #103)
+#105 := [rewrite]: #104
+#97 := (iff #16 #96)
+#98 := [rewrite]: #97
+#108 := [monotonicity #98 #105]: #107
+#100 := (iff #17 #99)
+#93 := (iff #15 #92)
+#94 := [rewrite]: #93
+#101 := [monotonicity #94 #98]: #100
+#111 := [monotonicity #101 #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [monotonicity #117]: #119
+#123 := [quant-intro #120]: #122
+#89 := (iff #28 #88)
+#86 := (iff #27 #85)
+#83 := (= #26 #82)
+#80 := (= #25 #79)
+#77 := (= #24 #76)
+#74 := (= #23 #73)
+#75 := [rewrite]: #74
+#71 := (= #22 #70)
+#72 := [rewrite]: #71
+#78 := [monotonicity #72 #75]: #77
+#67 := (iff #20 #66)
+#64 := (iff #19 #63)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#81 := [monotonicity #68 #78]: #80
+#84 := [monotonicity #81]: #83
+#87 := [monotonicity #84]: #86
+#90 := [quant-intro #87]: #89
+#125 := [trans #90 #123]: #124
+#62 := [asserted]: #28
+#126 := [mp #62 #125]: #121
+#191 := [mp~ #126 #201]: #121
+#228 := [mp #191 #227]: #225
+#259 := [mp #228 #258]: #256
+#753 := [mp #259 #752]: #748
+#667 := (not #748)
+#661 := (or #667 #182)
+#333 := (* -1::int 3::int)
+#418 := (* -1::int -5::int)
+#419 := (div #418 #333)
+#420 := (* -1::int #419)
+#411 := (+ #176 #420)
+#422 := (= #411 0::int)
+#423 := (div -5::int 3::int)
+#351 := (* -1::int #423)
+#424 := (+ #176 #351)
+#421 := (= #424 0::int)
+#425 := (<= 3::int 0::int)
+#404 := (<= -5::int 0::int)
+#739 := (or #404 #425)
+#741 := (not #739)
+#398 := (>= -5::int 0::int)
+#528 := (or #425 #398)
+#735 := (not #528)
+#409 := (or #735 #741)
+#410 := (ite #409 #421 #422)
+#742 := (= #176 0::int)
+#743 := (= 3::int 0::int)
+#744 := (= -5::int 0::int)
+#745 := (or #744 #743)
+#740 := (ite #745 #742 #410)
+#668 := (or #667 #740)
+#653 := (iff #668 #661)
+#656 := (iff #661 #661)
+#657 := [rewrite]: #656
+#665 := (iff #740 #182)
+#673 := (ite false #742 #182)
+#675 := (iff #673 #182)
+#664 := [rewrite]: #675
+#674 := (iff #740 #673)
+#662 := (iff #410 #182)
+#586 := (= #176 -1::int)
+#1 := true
+#682 := (ite true #182 #586)
+#663 := (iff #682 #182)
+#660 := [rewrite]: #663
+#669 := (iff #410 #682)
+#681 := (iff #422 #586)
+#570 := 1::int
+#680 := (+ 1::int #176)
+#576 := (= #680 0::int)
+#587 := (iff #576 #586)
+#588 := [rewrite]: #587
+#584 := (iff #422 #576)
+#582 := (= #411 #680)
+#581 := (+ #176 1::int)
+#565 := (= #581 #680)
+#580 := [rewrite]: #565
+#676 := (= #411 #581)
+#531 := (= #420 1::int)
+#687 := (* -1::int -1::int)
+#571 := (= #687 1::int)
+#572 := [rewrite]: #571
+#685 := (= #420 #687)
+#684 := (= #419 -1::int)
+#696 := -3::int
+#698 := (div 5::int -3::int)
+#530 := (= #698 -1::int)
+#683 := [rewrite]: #530
+#527 := (= #419 #698)
+#697 := (= #333 -3::int)
+#691 := [rewrite]: #697
+#689 := (= #418 5::int)
+#690 := [rewrite]: #689
+#529 := [monotonicity #690 #691]: #527
+#686 := [trans #529 #683]: #684
+#688 := [monotonicity #686]: #685
+#679 := [trans #688 #572]: #531
+#677 := [monotonicity #679]: #676
+#583 := [trans #677 #580]: #582
+#585 := [monotonicity #583]: #584
+#678 := [trans #585 #588]: #681
+#694 := (iff #421 #182)
+#700 := (+ 2::int #176)
+#548 := (= #700 0::int)
+#692 := (iff #548 #182)
+#693 := [rewrite]: #692
+#549 := (iff #421 #548)
+#701 := (= #424 #700)
+#703 := (+ #176 2::int)
+#705 := (= #703 #700)
+#706 := [rewrite]: #705
+#704 := (= #424 #703)
+#713 := (= #351 2::int)
+#711 := (* -1::int -2::int)
+#712 := (= #711 2::int)
+#709 := [rewrite]: #712
+#426 := (= #351 #711)
+#432 := (= #423 -2::int)
+#710 := [rewrite]: #432
+#708 := [monotonicity #710]: #426
+#702 := [trans #708 #709]: #713
+#699 := [monotonicity #702]: #704
+#707 := [trans #699 #706]: #701
+#550 := [monotonicity #707]: #549
+#695 := [trans #550 #693]: #694
+#430 := (iff #409 true)
+#720 := (or true false)
+#444 := (iff #720 true)
+#445 := [rewrite]: #444
+#719 := (iff #409 #720)
+#718 := (iff #741 false)
+#716 := (not true)
+#440 := (iff #716 false)
+#714 := [rewrite]: #440
+#717 := (iff #741 #716)
+#446 := (iff #739 true)
+#721 := (iff #739 #720)
+#387 := (iff #425 false)
+#388 := [rewrite]: #387
+#731 := (iff #404 true)
+#734 := [rewrite]: #731
+#443 := [monotonicity #734 #388]: #721
+#339 := [trans #443 #445]: #446
+#439 := [monotonicity #339]: #717
+#715 := [trans #439 #714]: #718
+#373 := (iff #735 true)
+#729 := (not false)
+#732 := (iff #729 true)
+#372 := [rewrite]: #732
+#367 := (iff #735 #729)
+#728 := (iff #528 false)
+#737 := (or false false)
+#381 := (iff #737 false)
+#722 := [rewrite]: #381
+#726 := (iff #528 #737)
+#724 := (iff #398 false)
+#725 := [rewrite]: #724
+#727 := [monotonicity #388 #725]: #726
+#723 := [trans #727 #722]: #728
+#730 := [monotonicity #723]: #367
+#733 := [trans #730 #372]: #373
+#429 := [monotonicity #733 #715]: #719
+#431 := [trans #429 #445]: #430
+#671 := [monotonicity #431 #695 #678]: #669
+#672 := [trans #671 #660]: #662
+#385 := (iff #745 false)
+#397 := (iff #745 #737)
+#396 := (iff #743 false)
+#401 := [rewrite]: #396
+#746 := (iff #744 false)
+#736 := [rewrite]: #746
+#738 := [monotonicity #736 #401]: #397
+#386 := [trans #738 #722]: #385
+#670 := [monotonicity #386 #672]: #674
+#666 := [trans #670 #664]: #665
+#655 := [monotonicity #666]: #653
+#658 := [trans #655 #657]: #653
+#652 := [quant-inst]: #668
+#654 := [mp #652 #658]: #661
+[unit-resolution #654 #753 #190]: false
+unsat
+38bcba887b30db840b90aa84ecd9357ae616af65 327 0
+#2 := false
+#11 := 0::int
+decl f3 :: (-> int int int)
+#174 := -3::int
+#68 := -1::int
+#177 := (f3 -1::int -3::int)
+#180 := (= #177 0::int)
+#193 := (not #180)
+#40 := 3::int
+#41 := (- 3::int)
+#38 := 1::int
+#39 := (- 1::int)
+#42 := (f3 #39 #41)
+#43 := (= #42 0::int)
+#44 := (not #43)
+#196 := (iff #44 #193)
+#183 := (= 0::int #177)
+#188 := (not #183)
+#194 := (iff #188 #193)
+#191 := (iff #183 #180)
+#192 := [rewrite]: #191
+#195 := [monotonicity #192]: #194
+#189 := (iff #44 #188)
+#186 := (iff #43 #183)
+#184 := (iff #180 #183)
+#185 := [rewrite]: #184
+#181 := (iff #43 #180)
+#178 := (= #42 #177)
+#175 := (= #41 -3::int)
+#176 := [rewrite]: #175
+#172 := (= #39 -1::int)
+#173 := [rewrite]: #172
+#179 := [monotonicity #173 #176]: #178
+#182 := [monotonicity #179]: #181
+#187 := [trans #182 #185]: #186
+#190 := [monotonicity #187]: #189
+#197 := [trans #190 #195]: #196
+#171 := [asserted]: #44
+#198 := [mp #171 #197]: #193
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#756 := (pattern #10)
+#72 := (* -1::int #9)
+#69 := (* -1::int #8)
+#75 := (div #69 #72)
+#259 := (* -1::int #75)
+#260 := (+ #10 #259)
+#261 := (= #260 0::int)
+#21 := (div #8 #9)
+#256 := (* -1::int #21)
+#257 := (+ #10 #256)
+#258 := (= #257 0::int)
+#94 := (<= #9 0::int)
+#90 := (<= #8 0::int)
+#214 := (or #90 #94)
+#215 := (not #214)
+#101 := (>= #8 0::int)
+#206 := (or #94 #101)
+#207 := (not #206)
+#221 := (or #207 #215)
+#262 := (ite #221 #258 #261)
+#255 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#263 := (ite #14 #255 #262)
+#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
+#266 := (forall (vars (?v0 int) (?v1 int)) #263)
+#760 := (iff #266 #757)
+#758 := (iff #263 #263)
+#759 := [refl]: #758
+#761 := [quant-intro #759]: #760
+#226 := (ite #221 #21 #75)
+#229 := (ite #14 0::int #226)
+#232 := (= #10 #229)
+#235 := (forall (vars (?v0 int) (?v1 int)) #232)
+#267 := (iff #235 #266)
+#264 := (iff #232 #263)
+#265 := [rewrite]: #264
+#268 := [quant-intro #265]: #267
+#102 := (not #101)
+#95 := (not #94)
+#105 := (and #95 #102)
+#91 := (not #90)
+#98 := (and #91 #95)
+#108 := (or #98 #105)
+#111 := (ite #108 #21 #75)
+#114 := (ite #14 0::int #111)
+#117 := (= #10 #114)
+#120 := (forall (vars (?v0 int) (?v1 int)) #117)
+#236 := (iff #120 #235)
+#233 := (iff #117 #232)
+#230 := (= #114 #229)
+#227 := (= #111 #226)
+#224 := (iff #108 #221)
+#218 := (or #215 #207)
+#222 := (iff #218 #221)
+#223 := [rewrite]: #222
+#219 := (iff #108 #218)
+#216 := (iff #105 #207)
+#217 := [rewrite]: #216
+#204 := (iff #98 #215)
+#205 := [rewrite]: #204
+#220 := [monotonicity #205 #217]: #219
+#225 := [trans #220 #223]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [quant-intro #234]: #236
+#210 := (~ #120 #120)
+#208 := (~ #117 #117)
+#209 := [refl]: #208
+#211 := [nnf-pos #209]: #210
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#123 := (iff #28 #120)
+#62 := (and #16 #18)
+#65 := (or #17 #62)
+#78 := (ite #65 #21 #75)
+#81 := (ite #14 0::int #78)
+#84 := (= #10 #81)
+#87 := (forall (vars (?v0 int) (?v1 int)) #84)
+#121 := (iff #87 #120)
+#118 := (iff #84 #117)
+#115 := (= #81 #114)
+#112 := (= #78 #111)
+#109 := (iff #65 #108)
+#106 := (iff #62 #105)
+#103 := (iff #18 #102)
+#104 := [rewrite]: #103
+#96 := (iff #16 #95)
+#97 := [rewrite]: #96
+#107 := [monotonicity #97 #104]: #106
+#99 := (iff #17 #98)
+#92 := (iff #15 #91)
+#93 := [rewrite]: #92
+#100 := [monotonicity #93 #97]: #99
+#110 := [monotonicity #100 #107]: #109
+#113 := [monotonicity #110]: #112
+#116 := [monotonicity #113]: #115
+#119 := [monotonicity #116]: #118
+#122 := [quant-intro #119]: #121
+#88 := (iff #28 #87)
+#85 := (iff #27 #84)
+#82 := (= #26 #81)
+#79 := (= #25 #78)
+#76 := (= #24 #75)
+#73 := (= #23 #72)
+#74 := [rewrite]: #73
+#70 := (= #22 #69)
+#71 := [rewrite]: #70
+#77 := [monotonicity #71 #74]: #76
+#66 := (iff #20 #65)
+#63 := (iff #19 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#80 := [monotonicity #67 #77]: #79
+#83 := [monotonicity #80]: #82
+#86 := [monotonicity #83]: #85
+#89 := [quant-intro #86]: #88
+#124 := [trans #89 #122]: #123
+#61 := [asserted]: #28
+#125 := [mp #61 #124]: #120
+#201 := [mp~ #125 #211]: #120
+#238 := [mp #201 #237]: #235
+#269 := [mp #238 #268]: #266
+#762 := [mp #269 #761]: #757
+#681 := (not #757)
+#682 := (or #681 #180)
+#343 := (* -1::int -3::int)
+#427 := (* -1::int -1::int)
+#428 := (div #427 #343)
+#429 := (* -1::int #428)
+#420 := (+ #177 #429)
+#431 := (= #420 0::int)
+#432 := (div -1::int -3::int)
+#433 := (* -1::int #432)
+#430 := (+ #177 #433)
+#434 := (= #430 0::int)
+#413 := (<= -3::int 0::int)
+#748 := (<= -1::int 0::int)
+#750 := (or #748 #413)
+#407 := (not #750)
+#537 := (>= -1::int 0::int)
+#744 := (or #413 #537)
+#418 := (not #744)
+#419 := (or #418 #407)
+#751 := (ite #419 #434 #431)
+#752 := (= -3::int 0::int)
+#753 := (= -1::int 0::int)
+#754 := (or #753 #752)
+#749 := (ite #754 #180 #751)
+#683 := (or #681 #749)
+#684 := (iff #683 #682)
+#674 := (iff #682 #682)
+#675 := [rewrite]: #674
+#669 := (iff #749 #180)
+#687 := (ite false #180 #180)
+#680 := (iff #687 #180)
+#672 := [rewrite]: #680
+#691 := (iff #749 #687)
+#597 := (iff #751 #180)
+#701 := (= #177 1::int)
+#585 := (ite false #701 #180)
+#595 := (iff #585 #180)
+#596 := [rewrite]: #595
+#593 := (iff #751 #585)
+#591 := (iff #431 #180)
+#574 := (= #420 #177)
+#688 := (+ #177 0::int)
+#686 := (= #688 #177)
+#689 := [rewrite]: #686
+#590 := (= #420 #688)
+#581 := (= #429 0::int)
+#696 := (* -1::int 0::int)
+#579 := (= #696 0::int)
+#580 := [rewrite]: #579
+#694 := (= #429 #696)
+#693 := (= #428 0::int)
+#707 := (div 1::int 3::int)
+#539 := (= #707 0::int)
+#692 := [rewrite]: #539
+#536 := (= #428 #707)
+#706 := (= #343 3::int)
+#700 := [rewrite]: #706
+#699 := (= #427 1::int)
+#705 := [rewrite]: #699
+#538 := [monotonicity #705 #700]: #536
+#695 := [trans #538 #692]: #693
+#697 := [monotonicity #695]: #694
+#540 := [trans #697 #580]: #581
+#685 := [monotonicity #540]: #590
+#589 := [trans #685 #689]: #574
+#592 := [monotonicity #589]: #591
+#704 := (iff #434 #701)
+#709 := (+ -1::int #177)
+#557 := (= #709 0::int)
+#702 := (iff #557 #701)
+#703 := [rewrite]: #702
+#558 := (iff #434 #557)
+#710 := (= #430 #709)
+#712 := (+ #177 -1::int)
+#714 := (= #712 #709)
+#715 := [rewrite]: #714
+#713 := (= #430 #712)
+#722 := (= #433 -1::int)
+#720 := (* -1::int 1::int)
+#721 := (= #720 -1::int)
+#718 := [rewrite]: #721
+#435 := (= #433 #720)
+#441 := (= #432 1::int)
+#719 := [rewrite]: #441
+#717 := [monotonicity #719]: #435
+#711 := [trans #717 #718]: #722
+#708 := [monotonicity #711]: #713
+#716 := [trans #708 #715]: #710
+#559 := [monotonicity #716]: #558
+#698 := [trans #559 #703]: #704
+#439 := (iff #419 false)
+#746 := (or false false)
+#390 := (iff #746 false)
+#731 := [rewrite]: #390
+#728 := (iff #419 #746)
+#727 := (iff #407 false)
+#1 := true
+#741 := (not true)
+#742 := (iff #741 false)
+#740 := [rewrite]: #742
+#449 := (iff #407 #741)
+#726 := (iff #750 true)
+#453 := (or true true)
+#349 := (iff #453 true)
+#725 := [rewrite]: #349
+#454 := (iff #750 #453)
+#396 := (iff #413 true)
+#397 := [rewrite]: #396
+#730 := (iff #748 true)
+#452 := [rewrite]: #730
+#455 := [monotonicity #452 #397]: #454
+#448 := [trans #455 #725]: #726
+#723 := [monotonicity #448]: #449
+#724 := [trans #723 #740]: #727
+#743 := (iff #418 false)
+#381 := (iff #418 #741)
+#376 := (iff #744 true)
+#735 := (or true false)
+#732 := (iff #735 true)
+#738 := [rewrite]: #732
+#736 := (iff #744 #735)
+#733 := (iff #537 false)
+#734 := [rewrite]: #733
+#737 := [monotonicity #397 #734]: #736
+#739 := [trans #737 #738]: #376
+#382 := [monotonicity #739]: #381
+#729 := [trans #382 #740]: #743
+#438 := [monotonicity #729 #724]: #728
+#440 := [trans #438 #731]: #439
+#594 := [monotonicity #440 #698 #592]: #593
+#690 := [trans #594 #596]: #597
+#394 := (iff #754 false)
+#406 := (iff #754 #746)
+#405 := (iff #752 false)
+#410 := [rewrite]: #405
+#755 := (iff #753 false)
+#745 := [rewrite]: #755
+#747 := [monotonicity #745 #410]: #406
+#395 := [trans #747 #731]: #394
+#678 := [monotonicity #395 #690]: #691
+#671 := [trans #678 #672]: #669
+#673 := [monotonicity #671]: #684
+#676 := [trans #673 #675]: #684
+#679 := [quant-inst]: #683
+#670 := [mp #679 #676]: #682
+[unit-resolution #670 #762 #198]: false
+unsat
+8565b2cb5539e8fc61188a819aa671e0d424985f 311 0
+#2 := false
+#41 := 1::int
+decl f3 :: (-> int int int)
+#171 := -3::int
+#174 := (f3 -3::int -3::int)
+#177 := (= #174 1::int)
+#190 := (not #177)
+#38 := 3::int
+#39 := (- 3::int)
+#40 := (f3 #39 #39)
+#42 := (= #40 1::int)
+#43 := (not #42)
+#193 := (iff #43 #190)
+#180 := (= 1::int #174)
+#185 := (not #180)
+#191 := (iff #185 #190)
+#188 := (iff #180 #177)
+#189 := [rewrite]: #188
+#192 := [monotonicity #189]: #191
+#186 := (iff #43 #185)
+#183 := (iff #42 #180)
+#181 := (iff #177 #180)
+#182 := [rewrite]: #181
+#178 := (iff #42 #177)
+#175 := (= #40 #174)
+#172 := (= #39 -3::int)
+#173 := [rewrite]: #172
+#176 := [monotonicity #173 #173]: #175
+#179 := [monotonicity #176]: #178
+#184 := [trans #179 #182]: #183
+#187 := [monotonicity #184]: #186
+#194 := [trans #187 #192]: #193
+#170 := [asserted]: #43
+#195 := [mp #170 #194]: #190
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#753 := (pattern #10)
+#11 := 0::int
+#67 := -1::int
+#71 := (* -1::int #9)
+#68 := (* -1::int #8)
+#74 := (div #68 #71)
+#256 := (* -1::int #74)
+#257 := (+ #10 #256)
+#258 := (= #257 0::int)
+#21 := (div #8 #9)
+#253 := (* -1::int #21)
+#254 := (+ #10 #253)
+#255 := (= #254 0::int)
+#93 := (<= #9 0::int)
+#89 := (<= #8 0::int)
+#211 := (or #89 #93)
+#212 := (not #211)
+#100 := (>= #8 0::int)
+#203 := (or #93 #100)
+#204 := (not #203)
+#218 := (or #204 #212)
+#259 := (ite #218 #255 #258)
+#252 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#260 := (ite #14 #252 #259)
+#754 := (forall (vars (?v0 int) (?v1 int)) (:pat #753) #260)
+#263 := (forall (vars (?v0 int) (?v1 int)) #260)
+#757 := (iff #263 #754)
+#755 := (iff #260 #260)
+#756 := [refl]: #755
+#758 := [quant-intro #756]: #757
+#223 := (ite #218 #21 #74)
+#226 := (ite #14 0::int #223)
+#229 := (= #10 #226)
+#232 := (forall (vars (?v0 int) (?v1 int)) #229)
+#264 := (iff #232 #263)
+#261 := (iff #229 #260)
+#262 := [rewrite]: #261
+#265 := [quant-intro #262]: #264
+#101 := (not #100)
+#94 := (not #93)
+#104 := (and #94 #101)
+#90 := (not #89)
+#97 := (and #90 #94)
+#107 := (or #97 #104)
+#110 := (ite #107 #21 #74)
+#113 := (ite #14 0::int #110)
+#116 := (= #10 #113)
+#119 := (forall (vars (?v0 int) (?v1 int)) #116)
+#233 := (iff #119 #232)
+#230 := (iff #116 #229)
+#227 := (= #113 #226)
+#224 := (= #110 #223)
+#221 := (iff #107 #218)
+#215 := (or #212 #204)
+#219 := (iff #215 #218)
+#220 := [rewrite]: #219
+#216 := (iff #107 #215)
+#213 := (iff #104 #204)
+#214 := [rewrite]: #213
+#201 := (iff #97 #212)
+#202 := [rewrite]: #201
+#217 := [monotonicity #202 #214]: #216
+#222 := [trans #217 #220]: #221
+#225 := [monotonicity #222]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [quant-intro #231]: #233
+#207 := (~ #119 #119)
+#205 := (~ #116 #116)
+#206 := [refl]: #205
+#208 := [nnf-pos #206]: #207
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#122 := (iff #28 #119)
+#61 := (and #16 #18)
+#64 := (or #17 #61)
+#77 := (ite #64 #21 #74)
+#80 := (ite #14 0::int #77)
+#83 := (= #10 #80)
+#86 := (forall (vars (?v0 int) (?v1 int)) #83)
+#120 := (iff #86 #119)
+#117 := (iff #83 #116)
+#114 := (= #80 #113)
+#111 := (= #77 #110)
+#108 := (iff #64 #107)
+#105 := (iff #61 #104)
+#102 := (iff #18 #101)
+#103 := [rewrite]: #102
+#95 := (iff #16 #94)
+#96 := [rewrite]: #95
+#106 := [monotonicity #96 #103]: #105
+#98 := (iff #17 #97)
+#91 := (iff #15 #90)
+#92 := [rewrite]: #91
+#99 := [monotonicity #92 #96]: #98
+#109 := [monotonicity #99 #106]: #108
+#112 := [monotonicity #109]: #111
+#115 := [monotonicity #112]: #114
+#118 := [monotonicity #115]: #117
+#121 := [quant-intro #118]: #120
+#87 := (iff #28 #86)
+#84 := (iff #27 #83)
+#81 := (= #26 #80)
+#78 := (= #25 #77)
+#75 := (= #24 #74)
+#72 := (= #23 #71)
+#73 := [rewrite]: #72
+#69 := (= #22 #68)
+#70 := [rewrite]: #69
+#76 := [monotonicity #70 #73]: #75
+#65 := (iff #20 #64)
+#62 := (iff #19 #61)
+#63 := [rewrite]: #62
+#66 := [monotonicity #63]: #65
+#79 := [monotonicity #66 #76]: #78
+#82 := [monotonicity #79]: #81
+#85 := [monotonicity #82]: #84
+#88 := [quant-intro #85]: #87
+#123 := [trans #88 #121]: #122
+#60 := [asserted]: #28
+#124 := [mp #60 #123]: #119
+#198 := [mp~ #124 #208]: #119
+#235 := [mp #198 #234]: #232
+#266 := [mp #235 #265]: #263
+#759 := [mp #266 #758]: #754
+#590 := (not #754)
+#591 := (or #590 #177)
+#340 := (* -1::int -3::int)
+#424 := (div #340 #340)
+#425 := (* -1::int #424)
+#426 := (+ #174 #425)
+#417 := (= #426 0::int)
+#428 := (div -3::int -3::int)
+#429 := (* -1::int #428)
+#430 := (+ #174 #429)
+#427 := (= #430 0::int)
+#431 := (<= -3::int 0::int)
+#410 := (or #431 #431)
+#745 := (not #410)
+#747 := (>= -3::int 0::int)
+#404 := (or #431 #747)
+#534 := (not #404)
+#741 := (or #534 #745)
+#415 := (ite #741 #427 #417)
+#416 := (= #174 0::int)
+#748 := (= -3::int 0::int)
+#749 := (or #748 #748)
+#750 := (ite #749 #416 #415)
+#592 := (or #590 #750)
+#594 := (iff #592 #591)
+#684 := (iff #591 #591)
+#688 := [rewrite]: #684
+#589 := (iff #750 #177)
+#683 := (ite false #416 #177)
+#586 := (iff #683 #177)
+#588 := [rewrite]: #586
+#686 := (iff #750 #683)
+#587 := (iff #415 #177)
+#576 := (ite false #177 #177)
+#537 := (iff #576 #177)
+#685 := [rewrite]: #537
+#577 := (iff #415 #576)
+#691 := (iff #417 #177)
+#715 := (+ -1::int #174)
+#705 := (= #715 0::int)
+#712 := (iff #705 #177)
+#707 := [rewrite]: #712
+#692 := (iff #417 #705)
+#689 := (= #426 #715)
+#432 := (+ #174 -1::int)
+#719 := (= #432 #715)
+#708 := [rewrite]: #719
+#535 := (= #426 #432)
+#704 := (= #425 -1::int)
+#725 := (* -1::int 1::int)
+#437 := (= #725 -1::int)
+#438 := [rewrite]: #437
+#703 := (= #425 #725)
+#696 := (= #424 1::int)
+#698 := (div 3::int 3::int)
+#701 := (= #698 1::int)
+#695 := [rewrite]: #701
+#699 := (= #424 #698)
+#555 := (= #340 3::int)
+#556 := [rewrite]: #555
+#700 := [monotonicity #556 #556]: #699
+#702 := [trans #700 #695]: #696
+#697 := [monotonicity #702]: #703
+#533 := [trans #697 #438]: #704
+#536 := [monotonicity #533]: #535
+#690 := [trans #536 #708]: #689
+#693 := [monotonicity #690]: #692
+#694 := [trans #693 #707]: #691
+#713 := (iff #427 #177)
+#706 := (iff #427 #705)
+#709 := (= #430 #715)
+#714 := (= #430 #432)
+#716 := (= #429 -1::int)
+#435 := (= #429 #725)
+#724 := (= #428 1::int)
+#721 := [rewrite]: #724
+#436 := [monotonicity #721]: #435
+#717 := [trans #436 #438]: #716
+#718 := [monotonicity #717]: #714
+#710 := [trans #718 #708]: #709
+#711 := [monotonicity #710]: #706
+#554 := [trans #711 #707]: #713
+#446 := (iff #741 false)
+#752 := (or false false)
+#407 := (iff #752 false)
+#743 := [rewrite]: #407
+#723 := (iff #741 #752)
+#346 := (iff #745 false)
+#1 := true
+#729 := (not true)
+#736 := (iff #729 false)
+#738 := [rewrite]: #736
+#451 := (iff #745 #729)
+#449 := (iff #410 true)
+#739 := (or true true)
+#726 := (iff #739 true)
+#727 := [rewrite]: #726
+#737 := (iff #410 #739)
+#387 := (iff #431 true)
+#728 := [rewrite]: #387
+#740 := [monotonicity #728 #728]: #737
+#450 := [trans #740 #727]: #449
+#452 := [monotonicity #450]: #451
+#722 := [trans #452 #738]: #346
+#378 := (iff #534 false)
+#735 := (iff #534 #729)
+#733 := (iff #404 true)
+#393 := (or true false)
+#731 := (iff #393 true)
+#732 := [rewrite]: #731
+#394 := (iff #404 #393)
+#391 := (iff #747 false)
+#392 := [rewrite]: #391
+#730 := [monotonicity #728 #392]: #394
+#734 := [trans #730 #732]: #733
+#373 := [monotonicity #734]: #735
+#379 := [trans #373 #738]: #378
+#445 := [monotonicity #379 #722]: #723
+#720 := [trans #445 #743]: #446
+#578 := [monotonicity #720 #554 #694]: #577
+#682 := [trans #578 #685]: #587
+#403 := (iff #749 false)
+#742 := (iff #749 #752)
+#751 := (iff #748 false)
+#746 := [rewrite]: #751
+#402 := [monotonicity #746 #746]: #742
+#744 := [trans #402 #743]: #403
+#571 := [monotonicity #744 #682]: #686
+#582 := [trans #571 #588]: #589
+#687 := [monotonicity #582]: #594
+#675 := [trans #687 #688]: #594
+#593 := [quant-inst]: #592
+#677 := [mp #593 #675]: #591
+[unit-resolution #677 #759 #195]: false
+unsat
+56b7b9e5e53e359f9d0cf68cac2ca010ed6b2ba0 338 0
+#2 := false
+#43 := 1::int
+decl f3 :: (-> int int int)
+#176 := -3::int
+#173 := -5::int
+#179 := (f3 -5::int -3::int)
+#182 := (= #179 1::int)
+#195 := (not #182)
+#40 := 3::int
+#41 := (- 3::int)
+#38 := 5::int
+#39 := (- 5::int)
+#42 := (f3 #39 #41)
+#44 := (= #42 1::int)
+#45 := (not #44)
+#198 := (iff #45 #195)
+#185 := (= 1::int #179)
+#190 := (not #185)
+#196 := (iff #190 #195)
+#193 := (iff #185 #182)
+#194 := [rewrite]: #193
+#197 := [monotonicity #194]: #196
+#191 := (iff #45 #190)
+#188 := (iff #44 #185)
+#186 := (iff #182 #185)
+#187 := [rewrite]: #186
+#183 := (iff #44 #182)
+#180 := (= #42 #179)
+#177 := (= #41 -3::int)
+#178 := [rewrite]: #177
+#174 := (= #39 -5::int)
+#175 := [rewrite]: #174
+#181 := [monotonicity #175 #178]: #180
+#184 := [monotonicity #181]: #183
+#189 := [trans #184 #187]: #188
+#192 := [monotonicity #189]: #191
+#199 := [trans #192 #197]: #198
+#172 := [asserted]: #45
+#200 := [mp #172 #199]: #195
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#758 := (pattern #10)
+#11 := 0::int
+#69 := -1::int
+#73 := (* -1::int #9)
+#70 := (* -1::int #8)
+#76 := (div #70 #73)
+#261 := (* -1::int #76)
+#262 := (+ #10 #261)
+#263 := (= #262 0::int)
+#21 := (div #8 #9)
+#258 := (* -1::int #21)
+#259 := (+ #10 #258)
+#260 := (= #259 0::int)
+#95 := (<= #9 0::int)
+#91 := (<= #8 0::int)
+#216 := (or #91 #95)
+#217 := (not #216)
+#102 := (>= #8 0::int)
+#208 := (or #95 #102)
+#209 := (not #208)
+#223 := (or #209 #217)
+#264 := (ite #223 #260 #263)
+#257 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#265 := (ite #14 #257 #264)
+#759 := (forall (vars (?v0 int) (?v1 int)) (:pat #758) #265)
+#268 := (forall (vars (?v0 int) (?v1 int)) #265)
+#762 := (iff #268 #759)
+#760 := (iff #265 #265)
+#761 := [refl]: #760
+#763 := [quant-intro #761]: #762
+#228 := (ite #223 #21 #76)
+#231 := (ite #14 0::int #228)
+#234 := (= #10 #231)
+#237 := (forall (vars (?v0 int) (?v1 int)) #234)
+#269 := (iff #237 #268)
+#266 := (iff #234 #265)
+#267 := [rewrite]: #266
+#270 := [quant-intro #267]: #269
+#103 := (not #102)
+#96 := (not #95)
+#106 := (and #96 #103)
+#92 := (not #91)
+#99 := (and #92 #96)
+#109 := (or #99 #106)
+#112 := (ite #109 #21 #76)
+#115 := (ite #14 0::int #112)
+#118 := (= #10 #115)
+#121 := (forall (vars (?v0 int) (?v1 int)) #118)
+#238 := (iff #121 #237)
+#235 := (iff #118 #234)
+#232 := (= #115 #231)
+#229 := (= #112 #228)
+#226 := (iff #109 #223)
+#220 := (or #217 #209)
+#224 := (iff #220 #223)
+#225 := [rewrite]: #224
+#221 := (iff #109 #220)
+#218 := (iff #106 #209)
+#219 := [rewrite]: #218
+#206 := (iff #99 #217)
+#207 := [rewrite]: #206
+#222 := [monotonicity #207 #219]: #221
+#227 := [trans #222 #225]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [monotonicity #233]: #235
+#239 := [quant-intro #236]: #238
+#212 := (~ #121 #121)
+#210 := (~ #118 #118)
+#211 := [refl]: #210
+#213 := [nnf-pos #211]: #212
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#124 := (iff #28 #121)
+#63 := (and #16 #18)
+#66 := (or #17 #63)
+#79 := (ite #66 #21 #76)
+#82 := (ite #14 0::int #79)
+#85 := (= #10 #82)
+#88 := (forall (vars (?v0 int) (?v1 int)) #85)
+#122 := (iff #88 #121)
+#119 := (iff #85 #118)
+#116 := (= #82 #115)
+#113 := (= #79 #112)
+#110 := (iff #66 #109)
+#107 := (iff #63 #106)
+#104 := (iff #18 #103)
+#105 := [rewrite]: #104
+#97 := (iff #16 #96)
+#98 := [rewrite]: #97
+#108 := [monotonicity #98 #105]: #107
+#100 := (iff #17 #99)
+#93 := (iff #15 #92)
+#94 := [rewrite]: #93
+#101 := [monotonicity #94 #98]: #100
+#111 := [monotonicity #101 #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [monotonicity #117]: #119
+#123 := [quant-intro #120]: #122
+#89 := (iff #28 #88)
+#86 := (iff #27 #85)
+#83 := (= #26 #82)
+#80 := (= #25 #79)
+#77 := (= #24 #76)
+#74 := (= #23 #73)
+#75 := [rewrite]: #74
+#71 := (= #22 #70)
+#72 := [rewrite]: #71
+#78 := [monotonicity #72 #75]: #77
+#67 := (iff #20 #66)
+#64 := (iff #19 #63)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#81 := [monotonicity #68 #78]: #80
+#84 := [monotonicity #81]: #83
+#87 := [monotonicity #84]: #86
+#90 := [quant-intro #87]: #89
+#125 := [trans #90 #123]: #124
+#62 := [asserted]: #28
+#126 := [mp #62 #125]: #121
+#203 := [mp~ #126 #213]: #121
+#240 := [mp #203 #239]: #237
+#271 := [mp #240 #270]: #268
+#764 := [mp #271 #763]: #759
+#672 := (not #759)
+#679 := (or #672 #182)
+#345 := (* -1::int -3::int)
+#429 := (* -1::int -5::int)
+#430 := (div #429 #345)
+#431 := (* -1::int #430)
+#422 := (+ #179 #431)
+#433 := (= #422 0::int)
+#434 := (div -5::int -3::int)
+#435 := (* -1::int #434)
+#432 := (+ #179 #435)
+#436 := (= #432 0::int)
+#415 := (<= -3::int 0::int)
+#750 := (<= -5::int 0::int)
+#752 := (or #750 #415)
+#409 := (not #752)
+#539 := (>= -5::int 0::int)
+#746 := (or #415 #539)
+#420 := (not #746)
+#421 := (or #420 #409)
+#753 := (ite #421 #436 #433)
+#754 := (= #179 0::int)
+#755 := (= -3::int 0::int)
+#756 := (= -5::int 0::int)
+#751 := (or #756 #755)
+#757 := (ite #751 #754 #753)
+#663 := (or #672 #757)
+#666 := (iff #663 #679)
+#668 := (iff #679 #679)
+#669 := [rewrite]: #668
+#677 := (iff #757 #182)
+#685 := (ite false #754 #182)
+#675 := (iff #685 #182)
+#676 := [rewrite]: #675
+#681 := (iff #757 #685)
+#683 := (iff #753 #182)
+#721 := 2::int
+#706 := (= #179 2::int)
+#680 := (ite false #706 #182)
+#671 := (iff #680 #182)
+#673 := [rewrite]: #671
+#682 := (iff #753 #680)
+#689 := (iff #433 #182)
+#591 := (+ -1::int #179)
+#596 := (= #591 0::int)
+#599 := (iff #596 #182)
+#692 := [rewrite]: #599
+#597 := (iff #433 #596)
+#587 := (= #422 #591)
+#688 := (+ #179 -1::int)
+#593 := (= #688 #591)
+#594 := [rewrite]: #593
+#691 := (= #422 #688)
+#592 := (= #431 -1::int)
+#581 := (* -1::int 1::int)
+#542 := (= #581 -1::int)
+#690 := [rewrite]: #542
+#582 := (= #431 #581)
+#696 := (= #430 1::int)
+#541 := (div 5::int 3::int)
+#697 := (= #541 1::int)
+#698 := [rewrite]: #697
+#694 := (= #430 #541)
+#538 := (= #345 3::int)
+#540 := [rewrite]: #538
+#702 := (= #429 5::int)
+#709 := [rewrite]: #702
+#695 := [monotonicity #709 #540]: #694
+#699 := [trans #695 #698]: #696
+#583 := [monotonicity #699]: #582
+#687 := [trans #583 #690]: #592
+#576 := [monotonicity #687]: #691
+#595 := [trans #576 #594]: #587
+#598 := [monotonicity #595]: #597
+#693 := [trans #598 #692]: #689
+#707 := (iff #436 #706)
+#724 := -2::int
+#712 := (+ -2::int #179)
+#703 := (= #712 0::int)
+#700 := (iff #703 #706)
+#701 := [rewrite]: #700
+#704 := (iff #436 #703)
+#560 := (= #432 #712)
+#711 := (+ #179 -2::int)
+#718 := (= #711 #712)
+#559 := [rewrite]: #718
+#716 := (= #432 #711)
+#715 := (= #435 -2::int)
+#719 := (* -1::int 2::int)
+#713 := (= #719 -2::int)
+#714 := [rewrite]: #713
+#723 := (= #435 #719)
+#722 := (= #434 2::int)
+#437 := [rewrite]: #722
+#720 := [monotonicity #437]: #723
+#710 := [trans #720 #714]: #715
+#717 := [monotonicity #710]: #716
+#561 := [trans #717 #559]: #560
+#705 := [monotonicity #561]: #704
+#708 := [trans #705 #701]: #707
+#442 := (iff #421 false)
+#408 := (or false false)
+#733 := (iff #408 false)
+#396 := [rewrite]: #733
+#440 := (iff #421 #408)
+#726 := (iff #409 false)
+#1 := true
+#383 := (not true)
+#742 := (iff #383 false)
+#745 := [rewrite]: #742
+#725 := (iff #409 #383)
+#450 := (iff #752 true)
+#456 := (or true true)
+#727 := (iff #456 true)
+#728 := [rewrite]: #727
+#457 := (iff #752 #456)
+#399 := (iff #415 true)
+#735 := [rewrite]: #399
+#454 := (iff #750 true)
+#455 := [rewrite]: #454
+#351 := [monotonicity #455 #735]: #457
+#451 := [trans #351 #728]: #450
+#729 := [monotonicity #451]: #725
+#730 := [trans #729 #745]: #726
+#731 := (iff #420 false)
+#384 := (iff #420 #383)
+#741 := (iff #746 true)
+#738 := (or true false)
+#740 := (iff #738 true)
+#378 := [rewrite]: #740
+#739 := (iff #746 #738)
+#736 := (iff #539 false)
+#737 := [rewrite]: #736
+#734 := [monotonicity #735 #737]: #739
+#743 := [trans #734 #378]: #741
+#744 := [monotonicity #743]: #384
+#732 := [trans #744 #745]: #731
+#441 := [monotonicity #732 #730]: #440
+#443 := [trans #441 #396]: #442
+#674 := [monotonicity #443 #708 #693]: #682
+#684 := [trans #674 #673]: #683
+#397 := (iff #751 false)
+#749 := (iff #751 #408)
+#412 := (iff #755 false)
+#748 := [rewrite]: #412
+#747 := (iff #756 false)
+#407 := [rewrite]: #747
+#392 := [monotonicity #407 #748]: #749
+#398 := [trans #392 #396]: #397
+#686 := [monotonicity #398 #684]: #681
+#678 := [trans #686 #676]: #677
+#667 := [monotonicity #678]: #666
+#665 := [trans #667 #669]: #666
+#664 := [quant-inst]: #663
+#670 := [mp #664 #665]: #679
+[unit-resolution #670 #764 #200]: false
+unsat
+f9042a4e5a7156fa6250d95ed2fad8e2089a5515 268 0
+#2 := false
+#11 := 0::int
+decl f4 :: (-> int int int)
+#38 := (f4 0::int 0::int)
+#39 := (= #38 0::int)
+#40 := (not #39)
+#167 := [asserted]: #40
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#743 := (pattern #29)
+#64 := -1::int
+#68 := (* -1::int #9)
+#65 := (* -1::int #8)
+#123 := (mod #65 #68)
+#254 := (+ #29 #123)
+#255 := (= #254 0::int)
+#30 := (mod #8 #9)
+#251 := (* -1::int #30)
+#252 := (+ #29 #251)
+#253 := (= #252 0::int)
+#90 := (<= #9 0::int)
+#86 := (<= #8 0::int)
+#193 := (or #86 #90)
+#194 := (not #193)
+#97 := (>= #8 0::int)
+#185 := (or #90 #97)
+#186 := (not #185)
+#200 := (or #186 #194)
+#256 := (ite #200 #253 #255)
+#250 := (= #29 0::int)
+#12 := (= #8 0::int)
+#257 := (ite #12 #250 #256)
+#249 := (= #8 #29)
+#13 := (= #9 0::int)
+#258 := (ite #13 #249 #257)
+#744 := (forall (vars (?v0 int) (?v1 int)) (:pat #743) #258)
+#261 := (forall (vars (?v0 int) (?v1 int)) #258)
+#747 := (iff #261 #744)
+#745 := (iff #258 #258)
+#746 := [refl]: #745
+#748 := [quant-intro #746]: #747
+#129 := (* -1::int #123)
+#218 := (ite #200 #30 #129)
+#221 := (ite #12 0::int #218)
+#224 := (ite #13 #8 #221)
+#227 := (= #29 #224)
+#230 := (forall (vars (?v0 int) (?v1 int)) #227)
+#262 := (iff #230 #261)
+#259 := (iff #227 #258)
+#260 := [rewrite]: #259
+#263 := [quant-intro #260]: #262
+#98 := (not #97)
+#91 := (not #90)
+#101 := (and #91 #98)
+#87 := (not #86)
+#94 := (and #87 #91)
+#104 := (or #94 #101)
+#149 := (ite #104 #30 #129)
+#152 := (ite #12 0::int #149)
+#155 := (ite #13 #8 #152)
+#158 := (= #29 #155)
+#161 := (forall (vars (?v0 int) (?v1 int)) #158)
+#231 := (iff #161 #230)
+#228 := (iff #158 #227)
+#225 := (= #155 #224)
+#222 := (= #152 #221)
+#219 := (= #149 #218)
+#203 := (iff #104 #200)
+#197 := (or #194 #186)
+#201 := (iff #197 #200)
+#202 := [rewrite]: #201
+#198 := (iff #104 #197)
+#195 := (iff #101 #186)
+#196 := [rewrite]: #195
+#183 := (iff #94 #194)
+#184 := [rewrite]: #183
+#199 := [monotonicity #184 #196]: #198
+#204 := [trans #199 #202]: #203
+#220 := [monotonicity #204]: #219
+#223 := [monotonicity #220]: #222
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [quant-intro #229]: #231
+#181 := (~ #161 #161)
+#178 := (~ #158 #158)
+#191 := [refl]: #178
+#182 := [nnf-pos #191]: #181
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#164 := (iff #37 #161)
+#58 := (and #16 #18)
+#61 := (or #17 #58)
+#134 := (ite #61 #30 #129)
+#137 := (ite #12 0::int #134)
+#140 := (ite #13 #8 #137)
+#143 := (= #29 #140)
+#146 := (forall (vars (?v0 int) (?v1 int)) #143)
+#162 := (iff #146 #161)
+#159 := (iff #143 #158)
+#156 := (= #140 #155)
+#153 := (= #137 #152)
+#150 := (= #134 #149)
+#105 := (iff #61 #104)
+#102 := (iff #58 #101)
+#99 := (iff #18 #98)
+#100 := [rewrite]: #99
+#92 := (iff #16 #91)
+#93 := [rewrite]: #92
+#103 := [monotonicity #93 #100]: #102
+#95 := (iff #17 #94)
+#88 := (iff #15 #87)
+#89 := [rewrite]: #88
+#96 := [monotonicity #89 #93]: #95
+#106 := [monotonicity #96 #103]: #105
+#151 := [monotonicity #106]: #150
+#154 := [monotonicity #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [quant-intro #160]: #162
+#147 := (iff #37 #146)
+#144 := (iff #36 #143)
+#141 := (= #35 #140)
+#138 := (= #34 #137)
+#135 := (= #33 #134)
+#132 := (= #32 #129)
+#126 := (- #123)
+#130 := (= #126 #129)
+#131 := [rewrite]: #130
+#127 := (= #32 #126)
+#124 := (= #31 #123)
+#69 := (= #23 #68)
+#70 := [rewrite]: #69
+#66 := (= #22 #65)
+#67 := [rewrite]: #66
+#125 := [monotonicity #67 #70]: #124
+#128 := [monotonicity #125]: #127
+#133 := [trans #128 #131]: #132
+#62 := (iff #20 #61)
+#59 := (iff #19 #58)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#136 := [monotonicity #63 #133]: #135
+#139 := [monotonicity #136]: #138
+#142 := [monotonicity #139]: #141
+#145 := [monotonicity #142]: #144
+#148 := [quant-intro #145]: #147
+#165 := [trans #148 #163]: #164
+#122 := [asserted]: #37
+#166 := [mp #122 #165]: #161
+#192 := [mp~ #166 #182]: #161
+#233 := [mp #192 #232]: #230
+#264 := [mp #233 #263]: #261
+#749 := [mp #264 #748]: #744
+#690 := (not #744)
+#696 := (or #690 #39)
+#322 := (* -1::int 0::int)
+#407 := (mod #322 #322)
+#408 := (+ #38 #407)
+#409 := (= #408 0::int)
+#400 := (mod 0::int 0::int)
+#411 := (* -1::int #400)
+#412 := (+ #38 #411)
+#340 := (= #412 0::int)
+#413 := (<= 0::int 0::int)
+#410 := (or #413 #413)
+#414 := (not #410)
+#393 := (>= 0::int 0::int)
+#728 := (or #413 #393)
+#730 := (not #728)
+#387 := (or #730 #414)
+#517 := (ite #387 #340 #409)
+#724 := (= 0::int 0::int)
+#398 := (ite #724 #39 #517)
+#168 := (= 0::int #38)
+#399 := (ite #724 #168 #398)
+#537 := (or #690 #399)
+#539 := (iff #537 #696)
+#682 := (iff #696 #696)
+#683 := [rewrite]: #682
+#694 := (iff #399 #39)
+#1 := true
+#691 := (ite true #39 #39)
+#688 := (iff #691 #39)
+#689 := [rewrite]: #688
+#692 := (iff #399 #691)
+#698 := (iff #398 #39)
+#328 := (+ #38 #400)
+#428 := (= #328 0::int)
+#699 := (ite true #39 #428)
+#697 := (iff #699 #39)
+#701 := [rewrite]: #697
+#700 := (iff #398 #699)
+#420 := (iff #517 #428)
+#707 := (ite false #340 #428)
+#418 := (iff #707 #428)
+#419 := [rewrite]: #418
+#704 := (iff #517 #707)
+#429 := (iff #409 #428)
+#705 := (= #408 #328)
+#434 := (= #407 #400)
+#432 := (= #322 0::int)
+#433 := [rewrite]: #432
+#435 := [monotonicity #433 #433]: #434
+#706 := [monotonicity #435]: #705
+#703 := [monotonicity #706]: #429
+#709 := (iff #387 false)
+#361 := (or false false)
+#720 := (iff #361 false)
+#723 := [rewrite]: #720
+#362 := (iff #387 #361)
+#719 := (iff #414 false)
+#711 := (not true)
+#376 := (iff #711 false)
+#377 := [rewrite]: #376
+#718 := (iff #414 #711)
+#717 := (iff #410 true)
+#725 := (or true true)
+#726 := (iff #725 true)
+#386 := [rewrite]: #726
+#715 := (iff #410 #725)
+#733 := (iff #413 true)
+#734 := [rewrite]: #733
+#716 := [monotonicity #734 #734]: #715
+#712 := [trans #716 #386]: #717
+#356 := [monotonicity #712]: #718
+#721 := [trans #356 #377]: #719
+#713 := (iff #730 false)
+#374 := (iff #730 #711)
+#727 := (iff #728 true)
+#385 := (iff #728 #725)
+#729 := (iff #393 true)
+#735 := [rewrite]: #729
+#390 := [monotonicity #734 #735]: #385
+#370 := [trans #390 #386]: #727
+#375 := [monotonicity #370]: #374
+#714 := [trans #375 #377]: #713
+#722 := [monotonicity #714 #721]: #362
+#710 := [trans #722 #723]: #709
+#708 := [monotonicity #710 #703]: #704
+#421 := [trans #708 #419]: #420
+#731 := (iff #724 true)
+#732 := [rewrite]: #731
+#415 := [monotonicity #732 #421]: #700
+#702 := [trans #415 #701]: #698
+#174 := (iff #168 #39)
+#175 := [rewrite]: #174
+#693 := [monotonicity #732 #175 #702]: #692
+#695 := [trans #693 #689]: #694
+#681 := [monotonicity #695]: #539
+#684 := [trans #681 #683]: #539
+#538 := [quant-inst]: #537
+#678 := [mp #538 #684]: #696
+[unit-resolution #678 #749 #167]: false
+unsat
+1425ff33c7a46da240218085e6495adda51b3a40 276 0
+#2 := false
+decl f4 :: (-> int int int)
+#11 := 0::int
+decl f5 :: int
+#38 := f5
+#39 := (f4 f5 0::int)
+#169 := (= f5 #39)
+#172 := (not #169)
+#40 := (= #39 f5)
+#41 := (not #40)
+#173 := (iff #41 #172)
+#170 := (iff #40 #169)
+#171 := [rewrite]: #170
+#174 := [monotonicity #171]: #173
+#168 := [asserted]: #41
+#177 := [mp #168 #174]: #172
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#741 := (pattern #29)
+#65 := -1::int
+#69 := (* -1::int #9)
+#66 := (* -1::int #8)
+#124 := (mod #66 #69)
+#252 := (+ #29 #124)
+#253 := (= #252 0::int)
+#30 := (mod #8 #9)
+#249 := (* -1::int #30)
+#250 := (+ #29 #249)
+#251 := (= #250 0::int)
+#91 := (<= #9 0::int)
+#87 := (<= #8 0::int)
+#191 := (or #87 #91)
+#192 := (not #191)
+#98 := (>= #8 0::int)
+#183 := (or #91 #98)
+#184 := (not #183)
+#198 := (or #184 #192)
+#254 := (ite #198 #251 #253)
+#248 := (= #29 0::int)
+#12 := (= #8 0::int)
+#255 := (ite #12 #248 #254)
+#247 := (= #8 #29)
+#13 := (= #9 0::int)
+#256 := (ite #13 #247 #255)
+#742 := (forall (vars (?v0 int) (?v1 int)) (:pat #741) #256)
+#259 := (forall (vars (?v0 int) (?v1 int)) #256)
+#745 := (iff #259 #742)
+#743 := (iff #256 #256)
+#744 := [refl]: #743
+#746 := [quant-intro #744]: #745
+#130 := (* -1::int #124)
+#216 := (ite #198 #30 #130)
+#219 := (ite #12 0::int #216)
+#222 := (ite #13 #8 #219)
+#225 := (= #29 #222)
+#228 := (forall (vars (?v0 int) (?v1 int)) #225)
+#260 := (iff #228 #259)
+#257 := (iff #225 #256)
+#258 := [rewrite]: #257
+#261 := [quant-intro #258]: #260
+#99 := (not #98)
+#92 := (not #91)
+#102 := (and #92 #99)
+#88 := (not #87)
+#95 := (and #88 #92)
+#105 := (or #95 #102)
+#150 := (ite #105 #30 #130)
+#153 := (ite #12 0::int #150)
+#156 := (ite #13 #8 #153)
+#159 := (= #29 #156)
+#162 := (forall (vars (?v0 int) (?v1 int)) #159)
+#229 := (iff #162 #228)
+#226 := (iff #159 #225)
+#223 := (= #156 #222)
+#220 := (= #153 #219)
+#217 := (= #150 #216)
+#201 := (iff #105 #198)
+#195 := (or #192 #184)
+#199 := (iff #195 #198)
+#200 := [rewrite]: #199
+#196 := (iff #105 #195)
+#193 := (iff #102 #184)
+#194 := [rewrite]: #193
+#181 := (iff #95 #192)
+#182 := [rewrite]: #181
+#197 := [monotonicity #182 #194]: #196
+#202 := [trans #197 #200]: #201
+#218 := [monotonicity #202]: #217
+#221 := [monotonicity #218]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [quant-intro #227]: #229
+#179 := (~ #162 #162)
+#175 := (~ #159 #159)
+#189 := [refl]: #175
+#180 := [nnf-pos #189]: #179
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#165 := (iff #37 #162)
+#59 := (and #16 #18)
+#62 := (or #17 #59)
+#135 := (ite #62 #30 #130)
+#138 := (ite #12 0::int #135)
+#141 := (ite #13 #8 #138)
+#144 := (= #29 #141)
+#147 := (forall (vars (?v0 int) (?v1 int)) #144)
+#163 := (iff #147 #162)
+#160 := (iff #144 #159)
+#157 := (= #141 #156)
+#154 := (= #138 #153)
+#151 := (= #135 #150)
+#106 := (iff #62 #105)
+#103 := (iff #59 #102)
+#100 := (iff #18 #99)
+#101 := [rewrite]: #100
+#93 := (iff #16 #92)
+#94 := [rewrite]: #93
+#104 := [monotonicity #94 #101]: #103
+#96 := (iff #17 #95)
+#89 := (iff #15 #88)
+#90 := [rewrite]: #89
+#97 := [monotonicity #90 #94]: #96
+#107 := [monotonicity #97 #104]: #106
+#152 := [monotonicity #107]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [quant-intro #161]: #163
+#148 := (iff #37 #147)
+#145 := (iff #36 #144)
+#142 := (= #35 #141)
+#139 := (= #34 #138)
+#136 := (= #33 #135)
+#133 := (= #32 #130)
+#127 := (- #124)
+#131 := (= #127 #130)
+#132 := [rewrite]: #131
+#128 := (= #32 #127)
+#125 := (= #31 #124)
+#70 := (= #23 #69)
+#71 := [rewrite]: #70
+#67 := (= #22 #66)
+#68 := [rewrite]: #67
+#126 := [monotonicity #68 #71]: #125
+#129 := [monotonicity #126]: #128
+#134 := [trans #129 #132]: #133
+#63 := (iff #20 #62)
+#60 := (iff #19 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#137 := [monotonicity #64 #134]: #136
+#140 := [monotonicity #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [quant-intro #146]: #148
+#166 := [trans #149 #164]: #165
+#123 := [asserted]: #37
+#167 := [mp #123 #166]: #162
+#190 := [mp~ #167 #180]: #162
+#231 := [mp #190 #230]: #228
+#262 := [mp #231 #261]: #259
+#747 := [mp #262 #746]: #742
+#535 := (not #742)
+#536 := (or #535 #169)
+#320 := (* -1::int 0::int)
+#405 := (* -1::int f5)
+#406 := (mod #405 #320)
+#407 := (+ #39 #406)
+#398 := (= #407 0::int)
+#409 := (mod f5 0::int)
+#410 := (* -1::int #409)
+#338 := (+ #39 #410)
+#411 := (= #338 0::int)
+#408 := (<= 0::int 0::int)
+#412 := (<= f5 0::int)
+#391 := (or #412 #408)
+#726 := (not #391)
+#728 := (>= f5 0::int)
+#385 := (or #408 #728)
+#515 := (not #385)
+#722 := (or #515 #726)
+#396 := (ite #722 #411 #398)
+#397 := (= #39 0::int)
+#729 := (= f5 0::int)
+#730 := (ite #729 #397 #396)
+#731 := (= 0::int 0::int)
+#732 := (ite #731 #169 #730)
+#537 := (or #535 #732)
+#680 := (iff #537 #536)
+#682 := (iff #536 #536)
+#676 := [rewrite]: #682
+#688 := (iff #732 #169)
+#426 := (mod #405 0::int)
+#705 := (+ #39 #426)
+#416 := (= #705 0::int)
+#700 := (ite #729 #397 #416)
+#1 := true
+#691 := (ite true #169 #700)
+#692 := (iff #691 #169)
+#693 := [rewrite]: #692
+#686 := (iff #732 #691)
+#689 := (iff #730 #700)
+#699 := (iff #396 #416)
+#419 := (ite false #411 #416)
+#413 := (iff #419 #416)
+#695 := [rewrite]: #413
+#697 := (iff #396 #419)
+#417 := (iff #398 #416)
+#702 := (= #407 #705)
+#427 := (= #406 #426)
+#703 := (= #320 0::int)
+#704 := [rewrite]: #703
+#701 := [monotonicity #704]: #427
+#706 := [monotonicity #701]: #702
+#418 := [monotonicity #706]: #417
+#433 := (iff #722 false)
+#707 := (or false false)
+#431 := (iff #707 false)
+#432 := [rewrite]: #431
+#708 := (iff #722 #707)
+#718 := (iff #726 false)
+#373 := (not true)
+#711 := (iff #373 false)
+#712 := [rewrite]: #711
+#360 := (iff #726 #373)
+#719 := (iff #391 true)
+#715 := (or #412 true)
+#354 := (iff #715 true)
+#717 := [rewrite]: #354
+#710 := (iff #391 #715)
+#723 := (iff #408 true)
+#383 := [rewrite]: #723
+#716 := [monotonicity #383]: #710
+#359 := [trans #716 #717]: #719
+#720 := [monotonicity #359]: #360
+#721 := [trans #720 #712]: #718
+#713 := (iff #515 false)
+#374 := (iff #515 #373)
+#709 := (iff #385 true)
+#388 := (or true #728)
+#725 := (iff #388 true)
+#368 := [rewrite]: #725
+#724 := (iff #385 #388)
+#384 := [monotonicity #383]: #724
+#372 := [trans #384 #368]: #709
+#375 := [monotonicity #372]: #374
+#714 := [trans #375 #712]: #713
+#430 := [monotonicity #714 #721]: #708
+#326 := [trans #430 #432]: #433
+#698 := [monotonicity #326 #418]: #697
+#696 := [trans #698 #695]: #699
+#690 := [monotonicity #696]: #689
+#727 := (iff #731 true)
+#733 := [rewrite]: #727
+#687 := [monotonicity #733 #690]: #686
+#694 := [trans #687 #693]: #688
+#681 := [monotonicity #694]: #680
+#677 := [trans #681 #676]: #680
+#679 := [quant-inst]: #537
+#683 := [mp #679 #677]: #536
+[unit-resolution #683 #747 #177]: false
+unsat
+439aba36c56d2b32a9918b0d37f2b36fe9fce631 298 0
+#2 := false
+#11 := 0::int
+decl f4 :: (-> int int int)
+#38 := 1::int
+#39 := (f4 0::int 1::int)
+#40 := (= #39 0::int)
+#41 := (not #40)
+#168 := [asserted]: #41
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#743 := (pattern #29)
+#65 := -1::int
+#69 := (* -1::int #9)
+#66 := (* -1::int #8)
+#124 := (mod #66 #69)
+#255 := (+ #29 #124)
+#256 := (= #255 0::int)
+#30 := (mod #8 #9)
+#252 := (* -1::int #30)
+#253 := (+ #29 #252)
+#254 := (= #253 0::int)
+#91 := (<= #9 0::int)
+#87 := (<= #8 0::int)
+#194 := (or #87 #91)
+#195 := (not #194)
+#98 := (>= #8 0::int)
+#186 := (or #91 #98)
+#187 := (not #186)
+#201 := (or #187 #195)
+#257 := (ite #201 #254 #256)
+#251 := (= #29 0::int)
+#12 := (= #8 0::int)
+#258 := (ite #12 #251 #257)
+#250 := (= #8 #29)
+#13 := (= #9 0::int)
+#259 := (ite #13 #250 #258)
+#744 := (forall (vars (?v0 int) (?v1 int)) (:pat #743) #259)
+#262 := (forall (vars (?v0 int) (?v1 int)) #259)
+#747 := (iff #262 #744)
+#745 := (iff #259 #259)
+#746 := [refl]: #745
+#748 := [quant-intro #746]: #747
+#130 := (* -1::int #124)
+#219 := (ite #201 #30 #130)
+#222 := (ite #12 0::int #219)
+#225 := (ite #13 #8 #222)
+#228 := (= #29 #225)
+#231 := (forall (vars (?v0 int) (?v1 int)) #228)
+#263 := (iff #231 #262)
+#260 := (iff #228 #259)
+#261 := [rewrite]: #260
+#264 := [quant-intro #261]: #263
+#99 := (not #98)
+#92 := (not #91)
+#102 := (and #92 #99)
+#88 := (not #87)
+#95 := (and #88 #92)
+#105 := (or #95 #102)
+#150 := (ite #105 #30 #130)
+#153 := (ite #12 0::int #150)
+#156 := (ite #13 #8 #153)
+#159 := (= #29 #156)
+#162 := (forall (vars (?v0 int) (?v1 int)) #159)
+#232 := (iff #162 #231)
+#229 := (iff #159 #228)
+#226 := (= #156 #225)
+#223 := (= #153 #222)
+#220 := (= #150 #219)
+#204 := (iff #105 #201)
+#198 := (or #195 #187)
+#202 := (iff #198 #201)
+#203 := [rewrite]: #202
+#199 := (iff #105 #198)
+#196 := (iff #102 #187)
+#197 := [rewrite]: #196
+#184 := (iff #95 #195)
+#185 := [rewrite]: #184
+#200 := [monotonicity #185 #197]: #199
+#205 := [trans #200 #203]: #204
+#221 := [monotonicity #205]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [quant-intro #230]: #232
+#182 := (~ #162 #162)
+#179 := (~ #159 #159)
+#192 := [refl]: #179
+#183 := [nnf-pos #192]: #182
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#165 := (iff #37 #162)
+#59 := (and #16 #18)
+#62 := (or #17 #59)
+#135 := (ite #62 #30 #130)
+#138 := (ite #12 0::int #135)
+#141 := (ite #13 #8 #138)
+#144 := (= #29 #141)
+#147 := (forall (vars (?v0 int) (?v1 int)) #144)
+#163 := (iff #147 #162)
+#160 := (iff #144 #159)
+#157 := (= #141 #156)
+#154 := (= #138 #153)
+#151 := (= #135 #150)
+#106 := (iff #62 #105)
+#103 := (iff #59 #102)
+#100 := (iff #18 #99)
+#101 := [rewrite]: #100
+#93 := (iff #16 #92)
+#94 := [rewrite]: #93
+#104 := [monotonicity #94 #101]: #103
+#96 := (iff #17 #95)
+#89 := (iff #15 #88)
+#90 := [rewrite]: #89
+#97 := [monotonicity #90 #94]: #96
+#107 := [monotonicity #97 #104]: #106
+#152 := [monotonicity #107]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [quant-intro #161]: #163
+#148 := (iff #37 #147)
+#145 := (iff #36 #144)
+#142 := (= #35 #141)
+#139 := (= #34 #138)
+#136 := (= #33 #135)
+#133 := (= #32 #130)
+#127 := (- #124)
+#131 := (= #127 #130)
+#132 := [rewrite]: #131
+#128 := (= #32 #127)
+#125 := (= #31 #124)
+#70 := (= #23 #69)
+#71 := [rewrite]: #70
+#67 := (= #22 #66)
+#68 := [rewrite]: #67
+#126 := [monotonicity #68 #71]: #125
+#129 := [monotonicity #126]: #128
+#134 := [trans #129 #132]: #133
+#63 := (iff #20 #62)
+#60 := (iff #19 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#137 := [monotonicity #64 #134]: #136
+#140 := [monotonicity #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [quant-intro #146]: #148
+#166 := [trans #149 #164]: #165
+#123 := [asserted]: #37
+#167 := [mp #123 #166]: #162
+#193 := [mp~ #167 #183]: #162
+#234 := [mp #193 #233]: #231
+#265 := [mp #234 #264]: #262
+#749 := [mp #265 #748]: #744
+#665 := (not #744)
+#666 := (or #665 #40)
+#323 := (* -1::int 1::int)
+#407 := (* -1::int 0::int)
+#408 := (mod #407 #323)
+#409 := (+ #39 #408)
+#400 := (= #409 0::int)
+#411 := (mod 0::int 1::int)
+#412 := (* -1::int #411)
+#413 := (+ #39 #412)
+#410 := (= #413 0::int)
+#414 := (<= 1::int 0::int)
+#393 := (<= 0::int 0::int)
+#728 := (or #393 #414)
+#730 := (not #728)
+#387 := (>= 0::int 0::int)
+#517 := (or #414 #387)
+#724 := (not #517)
+#398 := (or #724 #730)
+#399 := (ite #398 #410 #400)
+#731 := (= 0::int 0::int)
+#732 := (ite #731 #40 #399)
+#169 := (= 0::int #39)
+#733 := (= 1::int 0::int)
+#734 := (ite #733 #169 #732)
+#669 := (or #665 #734)
+#569 := (iff #669 #666)
+#572 := (iff #666 #666)
+#565 := [rewrite]: #572
+#668 := (iff #734 #40)
+#686 := (ite false #40 #40)
+#516 := (iff #686 #40)
+#518 := [rewrite]: #516
+#561 := (iff #734 #686)
+#559 := (iff #732 #40)
+#1 := true
+#673 := (ite true #40 #40)
+#674 := (iff #673 #40)
+#677 := [rewrite]: #674
+#675 := (iff #732 #673)
+#519 := (iff #399 #40)
+#680 := (iff #399 #686)
+#679 := (iff #400 #40)
+#684 := (= #409 #39)
+#415 := (+ #39 0::int)
+#698 := (= #415 #39)
+#702 := [rewrite]: #698
+#682 := (= #409 #415)
+#539 := (= #408 0::int)
+#695 := (mod 0::int -1::int)
+#537 := (= #695 0::int)
+#538 := [rewrite]: #537
+#690 := (= #408 #695)
+#689 := (= #323 -1::int)
+#694 := [rewrite]: #689
+#420 := (= #407 0::int)
+#421 := [rewrite]: #420
+#696 := [monotonicity #421 #694]: #690
+#681 := [trans #696 #538]: #539
+#683 := [monotonicity #681]: #682
+#678 := [trans #683 #702]: #684
+#685 := [monotonicity #678]: #679
+#693 := (iff #410 #40)
+#691 := (= #413 #39)
+#697 := (= #413 #415)
+#699 := (= #412 0::int)
+#418 := (= #412 #407)
+#704 := (= #411 0::int)
+#708 := [rewrite]: #704
+#419 := [monotonicity #708]: #418
+#700 := [trans #419 #421]: #699
+#701 := [monotonicity #700]: #697
+#692 := [trans #701 #702]: #691
+#688 := [monotonicity #692]: #693
+#703 := (iff #398 false)
+#329 := (or false false)
+#428 := (iff #329 false)
+#429 := [rewrite]: #428
+#705 := (iff #398 #329)
+#434 := (iff #730 false)
+#714 := (not true)
+#717 := (iff #714 false)
+#712 := [rewrite]: #717
+#432 := (iff #730 #714)
+#709 := (iff #728 true)
+#361 := (or true false)
+#720 := (iff #361 true)
+#723 := [rewrite]: #720
+#362 := (iff #728 #361)
+#390 := (iff #414 false)
+#726 := [rewrite]: #390
+#719 := (iff #393 true)
+#721 := [rewrite]: #719
+#722 := [monotonicity #721 #726]: #362
+#710 := [trans #722 #723]: #709
+#433 := [monotonicity #710]: #432
+#435 := [trans #433 #712]: #434
+#718 := (iff #724 false)
+#715 := (iff #724 #714)
+#377 := (iff #517 true)
+#370 := (or false true)
+#375 := (iff #370 true)
+#376 := [rewrite]: #375
+#711 := (iff #517 #370)
+#386 := (iff #387 true)
+#727 := [rewrite]: #386
+#374 := [monotonicity #726 #727]: #711
+#713 := [trans #374 #376]: #377
+#716 := [monotonicity #713]: #715
+#356 := [trans #716 #712]: #718
+#706 := [monotonicity #356 #435]: #705
+#707 := [trans #706 #429]: #703
+#687 := [monotonicity #707 #688 #685]: #680
+#672 := [trans #687 #518]: #519
+#725 := (iff #731 true)
+#385 := [rewrite]: #725
+#676 := [monotonicity #385 #672]: #675
+#560 := [trans #676 #677]: #559
+#175 := (iff #169 #40)
+#176 := [rewrite]: #175
+#729 := (iff #733 false)
+#735 := [rewrite]: #729
+#520 := [monotonicity #735 #176 #560]: #561
+#570 := [trans #520 #518]: #668
+#571 := [monotonicity #570]: #569
+#573 := [trans #571 #565]: #569
+#554 := [quant-inst]: #669
+#574 := [mp #554 #573]: #666
+[unit-resolution #574 #749 #168]: false
+unsat
+c891403625882fb790a1e99b91722f5d4b79f8ba 296 0
+#2 := false
+#11 := 0::int
+decl f4 :: (-> int int int)
+#38 := 1::int
+#39 := (f4 1::int 1::int)
+#40 := (= #39 0::int)
+#41 := (not #40)
+#168 := [asserted]: #41
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#743 := (pattern #29)
+#65 := -1::int
+#69 := (* -1::int #9)
+#66 := (* -1::int #8)
+#124 := (mod #66 #69)
+#255 := (+ #29 #124)
+#256 := (= #255 0::int)
+#30 := (mod #8 #9)
+#252 := (* -1::int #30)
+#253 := (+ #29 #252)
+#254 := (= #253 0::int)
+#91 := (<= #9 0::int)
+#87 := (<= #8 0::int)
+#194 := (or #87 #91)
+#195 := (not #194)
+#98 := (>= #8 0::int)
+#186 := (or #91 #98)
+#187 := (not #186)
+#201 := (or #187 #195)
+#257 := (ite #201 #254 #256)
+#251 := (= #29 0::int)
+#12 := (= #8 0::int)
+#258 := (ite #12 #251 #257)
+#250 := (= #8 #29)
+#13 := (= #9 0::int)
+#259 := (ite #13 #250 #258)
+#744 := (forall (vars (?v0 int) (?v1 int)) (:pat #743) #259)
+#262 := (forall (vars (?v0 int) (?v1 int)) #259)
+#747 := (iff #262 #744)
+#745 := (iff #259 #259)
+#746 := [refl]: #745
+#748 := [quant-intro #746]: #747
+#130 := (* -1::int #124)
+#219 := (ite #201 #30 #130)
+#222 := (ite #12 0::int #219)
+#225 := (ite #13 #8 #222)
+#228 := (= #29 #225)
+#231 := (forall (vars (?v0 int) (?v1 int)) #228)
+#263 := (iff #231 #262)
+#260 := (iff #228 #259)
+#261 := [rewrite]: #260
+#264 := [quant-intro #261]: #263
+#99 := (not #98)
+#92 := (not #91)
+#102 := (and #92 #99)
+#88 := (not #87)
+#95 := (and #88 #92)
+#105 := (or #95 #102)
+#150 := (ite #105 #30 #130)
+#153 := (ite #12 0::int #150)
+#156 := (ite #13 #8 #153)
+#159 := (= #29 #156)
+#162 := (forall (vars (?v0 int) (?v1 int)) #159)
+#232 := (iff #162 #231)
+#229 := (iff #159 #228)
+#226 := (= #156 #225)
+#223 := (= #153 #222)
+#220 := (= #150 #219)
+#204 := (iff #105 #201)
+#198 := (or #195 #187)
+#202 := (iff #198 #201)
+#203 := [rewrite]: #202
+#199 := (iff #105 #198)
+#196 := (iff #102 #187)
+#197 := [rewrite]: #196
+#184 := (iff #95 #195)
+#185 := [rewrite]: #184
+#200 := [monotonicity #185 #197]: #199
+#205 := [trans #200 #203]: #204
+#221 := [monotonicity #205]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [quant-intro #230]: #232
+#182 := (~ #162 #162)
+#179 := (~ #159 #159)
+#192 := [refl]: #179
+#183 := [nnf-pos #192]: #182
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#165 := (iff #37 #162)
+#59 := (and #16 #18)
+#62 := (or #17 #59)
+#135 := (ite #62 #30 #130)
+#138 := (ite #12 0::int #135)
+#141 := (ite #13 #8 #138)
+#144 := (= #29 #141)
+#147 := (forall (vars (?v0 int) (?v1 int)) #144)
+#163 := (iff #147 #162)
+#160 := (iff #144 #159)
+#157 := (= #141 #156)
+#154 := (= #138 #153)
+#151 := (= #135 #150)
+#106 := (iff #62 #105)
+#103 := (iff #59 #102)
+#100 := (iff #18 #99)
+#101 := [rewrite]: #100
+#93 := (iff #16 #92)
+#94 := [rewrite]: #93
+#104 := [monotonicity #94 #101]: #103
+#96 := (iff #17 #95)
+#89 := (iff #15 #88)
+#90 := [rewrite]: #89
+#97 := [monotonicity #90 #94]: #96
+#107 := [monotonicity #97 #104]: #106
+#152 := [monotonicity #107]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [quant-intro #161]: #163
+#148 := (iff #37 #147)
+#145 := (iff #36 #144)
+#142 := (= #35 #141)
+#139 := (= #34 #138)
+#136 := (= #33 #135)
+#133 := (= #32 #130)
+#127 := (- #124)
+#131 := (= #127 #130)
+#132 := [rewrite]: #131
+#128 := (= #32 #127)
+#125 := (= #31 #124)
+#70 := (= #23 #69)
+#71 := [rewrite]: #70
+#67 := (= #22 #66)
+#68 := [rewrite]: #67
+#126 := [monotonicity #68 #71]: #125
+#129 := [monotonicity #126]: #128
+#134 := [trans #129 #132]: #133
+#63 := (iff #20 #62)
+#60 := (iff #19 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#137 := [monotonicity #64 #134]: #136
+#140 := [monotonicity #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [quant-intro #146]: #148
+#166 := [trans #149 #164]: #165
+#123 := [asserted]: #37
+#167 := [mp #123 #166]: #162
+#193 := [mp~ #167 #183]: #162
+#234 := [mp #193 #233]: #231
+#265 := [mp #234 #264]: #262
+#749 := [mp #265 #748]: #744
+#666 := (not #744)
+#669 := (or #666 #40)
+#323 := (* -1::int 1::int)
+#407 := (mod #323 #323)
+#408 := (+ #39 #407)
+#409 := (= #408 0::int)
+#400 := (mod 1::int 1::int)
+#411 := (* -1::int #400)
+#412 := (+ #39 #411)
+#413 := (= #412 0::int)
+#410 := (<= 1::int 0::int)
+#414 := (or #410 #410)
+#393 := (not #414)
+#728 := (>= 1::int 0::int)
+#730 := (or #410 #728)
+#387 := (not #730)
+#517 := (or #387 #393)
+#724 := (ite #517 #413 #409)
+#398 := (= 1::int 0::int)
+#399 := (ite #398 #40 #724)
+#731 := (= 1::int #39)
+#732 := (ite #398 #731 #399)
+#554 := (or #666 #732)
+#571 := (iff #554 #669)
+#565 := (iff #669 #669)
+#573 := [rewrite]: #565
+#570 := (iff #732 #40)
+#735 := (= #39 1::int)
+#559 := (ite false #735 #40)
+#520 := (iff #559 #40)
+#668 := [rewrite]: #520
+#560 := (iff #732 #559)
+#674 := (iff #399 #40)
+#519 := (ite false #40 #40)
+#675 := (iff #519 #40)
+#676 := [rewrite]: #675
+#672 := (iff #399 #519)
+#516 := (iff #724 #40)
+#1 := true
+#679 := (ite true #40 #40)
+#680 := (iff #679 #40)
+#687 := [rewrite]: #680
+#685 := (iff #724 #679)
+#684 := (iff #409 #40)
+#682 := (= #408 #39)
+#699 := (+ #39 0::int)
+#697 := (= #699 #39)
+#701 := [rewrite]: #697
+#539 := (= #408 #699)
+#537 := (= #407 0::int)
+#689 := (mod -1::int -1::int)
+#690 := (= #689 0::int)
+#696 := [rewrite]: #690
+#694 := (= #407 #689)
+#693 := (= #323 -1::int)
+#688 := [rewrite]: #693
+#695 := [monotonicity #688 #688]: #694
+#538 := [trans #695 #696]: #537
+#681 := [monotonicity #538]: #539
+#683 := [trans #681 #701]: #682
+#678 := [monotonicity #683]: #684
+#691 := (iff #413 #40)
+#698 := (= #412 #39)
+#700 := (= #412 #699)
+#420 := (= #411 0::int)
+#707 := (* -1::int 0::int)
+#418 := (= #707 0::int)
+#419 := [rewrite]: #418
+#704 := (= #411 #707)
+#429 := (= #400 0::int)
+#703 := [rewrite]: #429
+#708 := [monotonicity #703]: #704
+#421 := [trans #708 #419]: #420
+#415 := [monotonicity #421]: #700
+#702 := [trans #415 #701]: #698
+#692 := [monotonicity #702]: #691
+#706 := (iff #517 true)
+#727 := (or false true)
+#374 := (iff #727 true)
+#375 := [rewrite]: #374
+#329 := (iff #517 #727)
+#434 := (iff #393 true)
+#723 := (not false)
+#432 := (iff #723 true)
+#433 := [rewrite]: #432
+#709 := (iff #393 #723)
+#722 := (iff #414 false)
+#356 := (or false false)
+#361 := (iff #356 false)
+#362 := [rewrite]: #361
+#719 := (iff #414 #356)
+#385 := (iff #410 false)
+#390 := [rewrite]: #385
+#721 := [monotonicity #390 #390]: #719
+#720 := [trans #721 #362]: #722
+#710 := [monotonicity #720]: #709
+#435 := [trans #710 #433]: #434
+#712 := (iff #387 false)
+#713 := (not true)
+#716 := (iff #713 false)
+#717 := [rewrite]: #716
+#714 := (iff #387 #713)
+#376 := (iff #730 true)
+#370 := (iff #730 #727)
+#726 := (iff #728 true)
+#386 := [rewrite]: #726
+#711 := [monotonicity #390 #386]: #370
+#377 := [trans #711 #375]: #376
+#715 := [monotonicity #377]: #714
+#718 := [trans #715 #717]: #712
+#705 := [monotonicity #718 #435]: #329
+#428 := [trans #705 #375]: #706
+#686 := [monotonicity #428 #692 #678]: #685
+#518 := [trans #686 #687]: #516
+#733 := (iff #398 false)
+#734 := [rewrite]: #733
+#673 := [monotonicity #734 #518]: #672
+#677 := [trans #673 #676]: #674
+#729 := (iff #731 #735)
+#725 := [rewrite]: #729
+#561 := [monotonicity #734 #725 #677]: #560
+#665 := [trans #561 #668]: #570
+#572 := [monotonicity #665]: #571
+#574 := [trans #572 #573]: #571
+#569 := [quant-inst]: #554
+#575 := [mp #569 #574]: #669
+[unit-resolution #575 #749 #168]: false
+unsat
+b54941920ecdb84fbb15def6125be1996b2f8cfb 307 0
+#2 := false
+#11 := 0::int
+decl f4 :: (-> int int int)
+#39 := 1::int
+#38 := 3::int
+#40 := (f4 3::int 1::int)
+#41 := (= #40 0::int)
+#42 := (not #41)
+#169 := [asserted]: #42
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#744 := (pattern #29)
+#66 := -1::int
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#125 := (mod #67 #70)
+#256 := (+ #29 #125)
+#257 := (= #256 0::int)
+#30 := (mod #8 #9)
+#253 := (* -1::int #30)
+#254 := (+ #29 #253)
+#255 := (= #254 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#195 := (or #88 #92)
+#196 := (not #195)
+#99 := (>= #8 0::int)
+#187 := (or #92 #99)
+#188 := (not #187)
+#202 := (or #188 #196)
+#258 := (ite #202 #255 #257)
+#252 := (= #29 0::int)
+#12 := (= #8 0::int)
+#259 := (ite #12 #252 #258)
+#251 := (= #8 #29)
+#13 := (= #9 0::int)
+#260 := (ite #13 #251 #259)
+#745 := (forall (vars (?v0 int) (?v1 int)) (:pat #744) #260)
+#263 := (forall (vars (?v0 int) (?v1 int)) #260)
+#748 := (iff #263 #745)
+#746 := (iff #260 #260)
+#747 := [refl]: #746
+#749 := [quant-intro #747]: #748
+#131 := (* -1::int #125)
+#220 := (ite #202 #30 #131)
+#223 := (ite #12 0::int #220)
+#226 := (ite #13 #8 #223)
+#229 := (= #29 #226)
+#232 := (forall (vars (?v0 int) (?v1 int)) #229)
+#264 := (iff #232 #263)
+#261 := (iff #229 #260)
+#262 := [rewrite]: #261
+#265 := [quant-intro #262]: #264
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#151 := (ite #106 #30 #131)
+#154 := (ite #12 0::int #151)
+#157 := (ite #13 #8 #154)
+#160 := (= #29 #157)
+#163 := (forall (vars (?v0 int) (?v1 int)) #160)
+#233 := (iff #163 #232)
+#230 := (iff #160 #229)
+#227 := (= #157 #226)
+#224 := (= #154 #223)
+#221 := (= #151 #220)
+#205 := (iff #106 #202)
+#199 := (or #196 #188)
+#203 := (iff #199 #202)
+#204 := [rewrite]: #203
+#200 := (iff #106 #199)
+#197 := (iff #103 #188)
+#198 := [rewrite]: #197
+#185 := (iff #96 #196)
+#186 := [rewrite]: #185
+#201 := [monotonicity #186 #198]: #200
+#206 := [trans #201 #204]: #205
+#222 := [monotonicity #206]: #221
+#225 := [monotonicity #222]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [quant-intro #231]: #233
+#183 := (~ #163 #163)
+#180 := (~ #160 #160)
+#193 := [refl]: #180
+#184 := [nnf-pos #193]: #183
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#166 := (iff #37 #163)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#136 := (ite #63 #30 #131)
+#139 := (ite #12 0::int #136)
+#142 := (ite #13 #8 #139)
+#145 := (= #29 #142)
+#148 := (forall (vars (?v0 int) (?v1 int)) #145)
+#164 := (iff #148 #163)
+#161 := (iff #145 #160)
+#158 := (= #142 #157)
+#155 := (= #139 #154)
+#152 := (= #136 #151)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#153 := [monotonicity #108]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [quant-intro #162]: #164
+#149 := (iff #37 #148)
+#146 := (iff #36 #145)
+#143 := (= #35 #142)
+#140 := (= #34 #139)
+#137 := (= #33 #136)
+#134 := (= #32 #131)
+#128 := (- #125)
+#132 := (= #128 #131)
+#133 := [rewrite]: #132
+#129 := (= #32 #128)
+#126 := (= #31 #125)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#127 := [monotonicity #69 #72]: #126
+#130 := [monotonicity #127]: #129
+#135 := [trans #130 #133]: #134
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#138 := [monotonicity #65 #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [quant-intro #147]: #149
+#167 := [trans #150 #165]: #166
+#124 := [asserted]: #37
+#168 := [mp #124 #167]: #163
+#194 := [mp~ #168 #184]: #163
+#235 := [mp #194 #234]: #232
+#266 := [mp #235 #265]: #263
+#750 := [mp #266 #749]: #745
+#577 := (not #745)
+#578 := (or #577 #41)
+#324 := (* -1::int 1::int)
+#408 := (* -1::int 3::int)
+#409 := (mod #408 #324)
+#410 := (+ #40 #409)
+#401 := (= #410 0::int)
+#412 := (mod 3::int 1::int)
+#413 := (* -1::int #412)
+#414 := (+ #40 #413)
+#411 := (= #414 0::int)
+#415 := (<= 1::int 0::int)
+#394 := (<= 3::int 0::int)
+#729 := (or #394 #415)
+#731 := (not #729)
+#388 := (>= 3::int 0::int)
+#518 := (or #415 #388)
+#725 := (not #518)
+#399 := (or #725 #731)
+#400 := (ite #399 #411 #401)
+#732 := (= 3::int 0::int)
+#733 := (ite #732 #41 #400)
+#734 := (= 3::int #40)
+#735 := (= 1::int 0::int)
+#730 := (ite #735 #734 #733)
+#671 := (or #577 #730)
+#672 := (iff #671 #578)
+#661 := (iff #578 #578)
+#653 := [rewrite]: #661
+#575 := (iff #730 #41)
+#391 := (= #40 3::int)
+#570 := (ite false #391 #41)
+#566 := (iff #570 #41)
+#574 := [rewrite]: #566
+#572 := (iff #730 #570)
+#670 := (iff #733 #41)
+#521 := (ite false #41 #41)
+#666 := (iff #521 #41)
+#667 := [rewrite]: #666
+#669 := (iff #733 #521)
+#561 := (iff #400 #41)
+#1 := true
+#676 := (ite true #41 #41)
+#678 := (iff #676 #41)
+#560 := [rewrite]: #678
+#677 := (iff #400 #676)
+#673 := (iff #401 #41)
+#519 := (= #410 #40)
+#692 := (+ #40 0::int)
+#689 := (= #692 #40)
+#690 := [rewrite]: #689
+#688 := (= #410 #692)
+#687 := (= #409 0::int)
+#538 := -3::int
+#684 := (mod -3::int -1::int)
+#680 := (= #684 0::int)
+#686 := [rewrite]: #680
+#685 := (= #409 #684)
+#682 := (= #324 -1::int)
+#683 := [rewrite]: #682
+#539 := (= #408 -3::int)
+#540 := [rewrite]: #539
+#679 := [monotonicity #540 #683]: #685
+#681 := [trans #679 #686]: #687
+#517 := [monotonicity #681]: #688
+#520 := [trans #517 #690]: #519
+#674 := [monotonicity #520]: #673
+#691 := (iff #411 #41)
+#695 := (= #414 #40)
+#693 := (= #414 #692)
+#699 := (= #413 0::int)
+#700 := (* -1::int 0::int)
+#698 := (= #700 0::int)
+#702 := [rewrite]: #698
+#701 := (= #413 #700)
+#421 := (= #412 0::int)
+#422 := [rewrite]: #421
+#416 := [monotonicity #422]: #701
+#703 := [trans #416 #702]: #699
+#694 := [monotonicity #703]: #693
+#696 := [trans #694 #690]: #695
+#697 := [monotonicity #696]: #691
+#419 := (iff #399 true)
+#377 := (or false true)
+#715 := (iff #377 true)
+#716 := [rewrite]: #715
+#705 := (iff #399 #377)
+#704 := (iff #731 true)
+#330 := (not false)
+#429 := (iff #330 true)
+#430 := [rewrite]: #429
+#706 := (iff #731 #330)
+#435 := (iff #729 false)
+#724 := (or false false)
+#433 := (iff #724 false)
+#434 := [rewrite]: #433
+#710 := (iff #729 #724)
+#371 := (iff #415 false)
+#712 := [rewrite]: #371
+#723 := (iff #394 false)
+#721 := [rewrite]: #723
+#711 := [monotonicity #721 #712]: #710
+#436 := [trans #711 #434]: #435
+#707 := [monotonicity #436]: #706
+#708 := [trans #707 #430]: #704
+#362 := (iff #725 false)
+#713 := (not true)
+#720 := (iff #713 false)
+#722 := [rewrite]: #720
+#719 := (iff #725 #713)
+#717 := (iff #518 true)
+#378 := (iff #518 #377)
+#375 := (iff #388 true)
+#376 := [rewrite]: #375
+#714 := [monotonicity #712 #376]: #378
+#718 := [trans #714 #716]: #717
+#357 := [monotonicity #718]: #719
+#363 := [trans #357 #722]: #362
+#709 := [monotonicity #363 #708]: #705
+#420 := [trans #709 #716]: #419
+#675 := [monotonicity #420 #697 #674]: #677
+#562 := [trans #675 #560]: #561
+#387 := (iff #732 false)
+#728 := [rewrite]: #387
+#571 := [monotonicity #728 #562]: #669
+#555 := [trans #571 #667]: #670
+#386 := (iff #734 #391)
+#727 := [rewrite]: #386
+#736 := (iff #735 false)
+#726 := [rewrite]: #736
+#573 := [monotonicity #726 #727 #555]: #572
+#576 := [trans #573 #574]: #575
+#659 := [monotonicity #576]: #672
+#650 := [trans #659 #653]: #672
+#668 := [quant-inst]: #671
+#652 := [mp #668 #650]: #578
+[unit-resolution #652 #750 #169]: false
+unsat
+cf6bd9f3cadb0728e891414f5be1e70fbba3fb1a 308 0
+#2 := false
+#11 := 0::int
+decl f5 :: int
+#38 := f5
+#732 := (= f5 0::int)
+#573 := (not #732)
+#394 := (<= f5 0::int)
+#720 := (not #394)
+#388 := (>= f5 0::int)
+#377 := (not #388)
+#688 := (or #377 #720 #732)
+#575 := (not #688)
+#66 := -1::int
+#408 := (* -1::int f5)
+#700 := (mod #408 -1::int)
+decl f4 :: (-> int int int)
+#39 := 1::int
+#40 := (f4 f5 1::int)
+#698 := (+ #40 #700)
+#703 := (= #698 0::int)
+#41 := (= #40 0::int)
+#520 := (ite #688 #41 #703)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#744 := (pattern #29)
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#125 := (mod #67 #70)
+#256 := (+ #29 #125)
+#257 := (= #256 0::int)
+#30 := (mod #8 #9)
+#253 := (* -1::int #30)
+#254 := (+ #29 #253)
+#255 := (= #254 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#195 := (or #88 #92)
+#196 := (not #195)
+#99 := (>= #8 0::int)
+#187 := (or #92 #99)
+#188 := (not #187)
+#202 := (or #188 #196)
+#258 := (ite #202 #255 #257)
+#252 := (= #29 0::int)
+#12 := (= #8 0::int)
+#259 := (ite #12 #252 #258)
+#251 := (= #8 #29)
+#13 := (= #9 0::int)
+#260 := (ite #13 #251 #259)
+#745 := (forall (vars (?v0 int) (?v1 int)) (:pat #744) #260)
+#263 := (forall (vars (?v0 int) (?v1 int)) #260)
+#748 := (iff #263 #745)
+#746 := (iff #260 #260)
+#747 := [refl]: #746
+#749 := [quant-intro #747]: #748
+#131 := (* -1::int #125)
+#220 := (ite #202 #30 #131)
+#223 := (ite #12 0::int #220)
+#226 := (ite #13 #8 #223)
+#229 := (= #29 #226)
+#232 := (forall (vars (?v0 int) (?v1 int)) #229)
+#264 := (iff #232 #263)
+#261 := (iff #229 #260)
+#262 := [rewrite]: #261
+#265 := [quant-intro #262]: #264
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#151 := (ite #106 #30 #131)
+#154 := (ite #12 0::int #151)
+#157 := (ite #13 #8 #154)
+#160 := (= #29 #157)
+#163 := (forall (vars (?v0 int) (?v1 int)) #160)
+#233 := (iff #163 #232)
+#230 := (iff #160 #229)
+#227 := (= #157 #226)
+#224 := (= #154 #223)
+#221 := (= #151 #220)
+#205 := (iff #106 #202)
+#199 := (or #196 #188)
+#203 := (iff #199 #202)
+#204 := [rewrite]: #203
+#200 := (iff #106 #199)
+#197 := (iff #103 #188)
+#198 := [rewrite]: #197
+#185 := (iff #96 #196)
+#186 := [rewrite]: #185
+#201 := [monotonicity #186 #198]: #200
+#206 := [trans #201 #204]: #205
+#222 := [monotonicity #206]: #221
+#225 := [monotonicity #222]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [quant-intro #231]: #233
+#183 := (~ #163 #163)
+#180 := (~ #160 #160)
+#193 := [refl]: #180
+#184 := [nnf-pos #193]: #183
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#166 := (iff #37 #163)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#136 := (ite #63 #30 #131)
+#139 := (ite #12 0::int #136)
+#142 := (ite #13 #8 #139)
+#145 := (= #29 #142)
+#148 := (forall (vars (?v0 int) (?v1 int)) #145)
+#164 := (iff #148 #163)
+#161 := (iff #145 #160)
+#158 := (= #142 #157)
+#155 := (= #139 #154)
+#152 := (= #136 #151)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#153 := [monotonicity #108]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [quant-intro #162]: #164
+#149 := (iff #37 #148)
+#146 := (iff #36 #145)
+#143 := (= #35 #142)
+#140 := (= #34 #139)
+#137 := (= #33 #136)
+#134 := (= #32 #131)
+#128 := (- #125)
+#132 := (= #128 #131)
+#133 := [rewrite]: #132
+#129 := (= #32 #128)
+#126 := (= #31 #125)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#127 := [monotonicity #69 #72]: #126
+#130 := [monotonicity #127]: #129
+#135 := [trans #130 #133]: #134
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#138 := [monotonicity #65 #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [quant-intro #147]: #149
+#167 := [trans #150 #165]: #166
+#124 := [asserted]: #37
+#168 := [mp #124 #167]: #163
+#194 := [mp~ #168 #184]: #163
+#235 := [mp #194 #234]: #232
+#266 := [mp #235 #265]: #263
+#750 := [mp #266 #749]: #745
+#675 := (not #745)
+#678 := (or #675 #520)
+#324 := (* -1::int 1::int)
+#409 := (mod #408 #324)
+#410 := (+ #40 #409)
+#401 := (= #410 0::int)
+#412 := (mod f5 1::int)
+#413 := (* -1::int #412)
+#414 := (+ #40 #413)
+#411 := (= #414 0::int)
+#415 := (<= 1::int 0::int)
+#729 := (or #394 #415)
+#731 := (not #729)
+#518 := (or #415 #388)
+#725 := (not #518)
+#399 := (or #725 #731)
+#400 := (ite #399 #411 #401)
+#733 := (ite #732 #41 #400)
+#734 := (= f5 #40)
+#735 := (= 1::int 0::int)
+#730 := (ite #735 #734 #733)
+#560 := (or #675 #730)
+#562 := (iff #560 #678)
+#669 := (iff #678 #678)
+#571 := [rewrite]: #669
+#676 := (iff #730 #520)
+#363 := (or #377 #720)
+#697 := (or #363 #732)
+#538 := (ite #697 #41 #703)
+#673 := (iff #538 #520)
+#517 := (iff #697 #688)
+#519 := [rewrite]: #517
+#674 := [monotonicity #519]: #673
+#687 := (iff #730 #538)
+#684 := (ite false #734 #538)
+#680 := (iff #684 #538)
+#686 := [rewrite]: #680
+#685 := (iff #730 #684)
+#682 := (iff #733 #538)
+#694 := (ite #363 #41 #703)
+#695 := (ite #732 #41 #694)
+#539 := (iff #695 #538)
+#540 := [rewrite]: #539
+#696 := (iff #733 #695)
+#689 := (iff #400 #694)
+#692 := (iff #401 #703)
+#702 := (= #410 #698)
+#701 := (= #409 #700)
+#421 := (= #324 -1::int)
+#422 := [rewrite]: #421
+#416 := [monotonicity #422]: #701
+#699 := [monotonicity #416]: #702
+#693 := [monotonicity #699]: #692
+#419 := (iff #411 #41)
+#705 := (= #414 #40)
+#707 := (+ #40 0::int)
+#704 := (= #707 #40)
+#708 := [rewrite]: #704
+#429 := (= #414 #707)
+#330 := (= #413 0::int)
+#711 := (* -1::int 0::int)
+#435 := (= #711 0::int)
+#436 := [rewrite]: #435
+#433 := (= #413 #711)
+#724 := (= #412 0::int)
+#710 := [rewrite]: #724
+#434 := [monotonicity #710]: #433
+#706 := [trans #434 #436]: #330
+#430 := [monotonicity #706]: #429
+#709 := [trans #430 #708]: #705
+#420 := [monotonicity #709]: #419
+#723 := (iff #399 #363)
+#722 := (iff #731 #720)
+#719 := (iff #729 #394)
+#715 := (or #394 false)
+#718 := (iff #715 #394)
+#713 := [rewrite]: #718
+#716 := (iff #729 #715)
+#386 := (iff #415 false)
+#391 := [rewrite]: #386
+#717 := [monotonicity #391]: #716
+#357 := [trans #717 #713]: #719
+#362 := [monotonicity #357]: #722
+#378 := (iff #725 #377)
+#375 := (iff #518 #388)
+#727 := (or false #388)
+#371 := (iff #727 #388)
+#712 := [rewrite]: #371
+#387 := (iff #518 #727)
+#728 := [monotonicity #391]: #387
+#376 := [trans #728 #712]: #375
+#714 := [monotonicity #376]: #378
+#721 := [monotonicity #714 #362]: #723
+#690 := [monotonicity #721 #420 #693]: #689
+#691 := [monotonicity #690]: #696
+#683 := [trans #691 #540]: #682
+#736 := (iff #735 false)
+#726 := [rewrite]: #736
+#679 := [monotonicity #726 #683]: #685
+#681 := [trans #679 #686]: #687
+#677 := [trans #681 #674]: #676
+#521 := [monotonicity #677]: #562
+#666 := [trans #521 #571]: #562
+#561 := [quant-inst]: #560
+#667 := [mp #561 #666]: #678
+#660 := [unit-resolution #667 #750]: #520
+#668 := (not #520)
+#665 := (or #668 #575)
+#42 := (not #41)
+#169 := [asserted]: #42
+#672 := (or #668 #575 #41)
+#659 := [def-axiom]: #672
+#654 := [unit-resolution #659 #169]: #665
+#655 := [unit-resolution #654 #660]: #575
+#566 := (or #688 #573)
+#574 := [def-axiom]: #566
+#656 := [unit-resolution #574 #655]: #573
+#670 := (or #688 #388)
+#555 := [def-axiom]: #670
+#657 := [unit-resolution #555 #655]: #388
+#570 := (or #688 #394)
+#572 := [def-axiom]: #570
+#651 := [unit-resolution #572 #655]: #394
+#658 := (or #732 #720 #377)
+#642 := [th-lemma]: #658
+[unit-resolution #642 #651 #657 #656]: false
+unsat
+9a7376cdac1572c47af1a76b7884975b78ef1203 317 0
+#2 := false
+#11 := 0::int
+decl f4 :: (-> int int int)
+#66 := -1::int
+#172 := (f4 0::int -1::int)
+#175 := (= #172 0::int)
+#188 := (not #175)
+#38 := 1::int
+#39 := (- 1::int)
+#40 := (f4 0::int #39)
+#41 := (= #40 0::int)
+#42 := (not #41)
+#191 := (iff #42 #188)
+#178 := (= 0::int #172)
+#183 := (not #178)
+#189 := (iff #183 #188)
+#186 := (iff #178 #175)
+#187 := [rewrite]: #186
+#190 := [monotonicity #187]: #189
+#184 := (iff #42 #183)
+#181 := (iff #41 #178)
+#179 := (iff #175 #178)
+#180 := [rewrite]: #179
+#176 := (iff #41 #175)
+#173 := (= #40 #172)
+#170 := (= #39 -1::int)
+#171 := [rewrite]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#182 := [trans #177 #180]: #181
+#185 := [monotonicity #182]: #184
+#192 := [trans #185 #190]: #191
+#169 := [asserted]: #42
+#193 := [mp #169 #192]: #188
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#758 := (pattern #29)
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#125 := (mod #67 #70)
+#270 := (+ #29 #125)
+#271 := (= #270 0::int)
+#30 := (mod #8 #9)
+#267 := (* -1::int #30)
+#268 := (+ #29 #267)
+#269 := (= #268 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#209 := (or #88 #92)
+#210 := (not #209)
+#99 := (>= #8 0::int)
+#201 := (or #92 #99)
+#202 := (not #201)
+#216 := (or #202 #210)
+#272 := (ite #216 #269 #271)
+#266 := (= #29 0::int)
+#12 := (= #8 0::int)
+#273 := (ite #12 #266 #272)
+#265 := (= #8 #29)
+#13 := (= #9 0::int)
+#274 := (ite #13 #265 #273)
+#759 := (forall (vars (?v0 int) (?v1 int)) (:pat #758) #274)
+#277 := (forall (vars (?v0 int) (?v1 int)) #274)
+#762 := (iff #277 #759)
+#760 := (iff #274 #274)
+#761 := [refl]: #760
+#763 := [quant-intro #761]: #762
+#131 := (* -1::int #125)
+#234 := (ite #216 #30 #131)
+#237 := (ite #12 0::int #234)
+#240 := (ite #13 #8 #237)
+#243 := (= #29 #240)
+#246 := (forall (vars (?v0 int) (?v1 int)) #243)
+#278 := (iff #246 #277)
+#275 := (iff #243 #274)
+#276 := [rewrite]: #275
+#279 := [quant-intro #276]: #278
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#151 := (ite #106 #30 #131)
+#154 := (ite #12 0::int #151)
+#157 := (ite #13 #8 #154)
+#160 := (= #29 #157)
+#163 := (forall (vars (?v0 int) (?v1 int)) #160)
+#247 := (iff #163 #246)
+#244 := (iff #160 #243)
+#241 := (= #157 #240)
+#238 := (= #154 #237)
+#235 := (= #151 #234)
+#219 := (iff #106 #216)
+#213 := (or #210 #202)
+#217 := (iff #213 #216)
+#218 := [rewrite]: #217
+#214 := (iff #106 #213)
+#211 := (iff #103 #202)
+#212 := [rewrite]: #211
+#199 := (iff #96 #210)
+#200 := [rewrite]: #199
+#215 := [monotonicity #200 #212]: #214
+#220 := [trans #215 #218]: #219
+#236 := [monotonicity #220]: #235
+#239 := [monotonicity #236]: #238
+#242 := [monotonicity #239]: #241
+#245 := [monotonicity #242]: #244
+#248 := [quant-intro #245]: #247
+#197 := (~ #163 #163)
+#194 := (~ #160 #160)
+#207 := [refl]: #194
+#198 := [nnf-pos #207]: #197
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#166 := (iff #37 #163)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#136 := (ite #63 #30 #131)
+#139 := (ite #12 0::int #136)
+#142 := (ite #13 #8 #139)
+#145 := (= #29 #142)
+#148 := (forall (vars (?v0 int) (?v1 int)) #145)
+#164 := (iff #148 #163)
+#161 := (iff #145 #160)
+#158 := (= #142 #157)
+#155 := (= #139 #154)
+#152 := (= #136 #151)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#153 := [monotonicity #108]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [quant-intro #162]: #164
+#149 := (iff #37 #148)
+#146 := (iff #36 #145)
+#143 := (= #35 #142)
+#140 := (= #34 #139)
+#137 := (= #33 #136)
+#134 := (= #32 #131)
+#128 := (- #125)
+#132 := (= #128 #131)
+#133 := [rewrite]: #132
+#129 := (= #32 #128)
+#126 := (= #31 #125)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#127 := [monotonicity #69 #72]: #126
+#130 := [monotonicity #127]: #129
+#135 := [trans #130 #133]: #134
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#138 := [monotonicity #65 #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [quant-intro #147]: #149
+#167 := [trans #150 #165]: #166
+#124 := [asserted]: #37
+#168 := [mp #124 #167]: #163
+#208 := [mp~ #168 #198]: #163
+#249 := [mp #208 #248]: #246
+#280 := [mp #249 #279]: #277
+#764 := [mp #280 #763]: #759
+#535 := (not #759)
+#683 := (or #535 #175)
+#338 := (* -1::int -1::int)
+#422 := (* -1::int 0::int)
+#423 := (mod #422 #338)
+#424 := (+ #172 #423)
+#415 := (= #424 0::int)
+#426 := (mod 0::int -1::int)
+#427 := (* -1::int #426)
+#428 := (+ #172 #427)
+#425 := (= #428 0::int)
+#429 := (<= -1::int 0::int)
+#408 := (<= 0::int 0::int)
+#743 := (or #408 #429)
+#745 := (not #743)
+#402 := (>= 0::int 0::int)
+#532 := (or #429 #402)
+#739 := (not #532)
+#413 := (or #739 #745)
+#414 := (ite #413 #425 #415)
+#746 := (= 0::int 0::int)
+#747 := (ite #746 #175 #414)
+#748 := (= -1::int 0::int)
+#749 := (ite #748 #178 #747)
+#585 := (or #535 #749)
+#681 := (iff #585 #683)
+#569 := (iff #683 #683)
+#584 := [rewrite]: #569
+#575 := (iff #749 #175)
+#693 := (ite false #175 #175)
+#701 := (iff #693 #175)
+#695 := [rewrite]: #701
+#692 := (iff #749 #693)
+#691 := (iff #747 #175)
+#1 := true
+#533 := (ite true #175 #175)
+#688 := (iff #533 #175)
+#690 := [rewrite]: #688
+#534 := (iff #747 #533)
+#702 := (iff #414 #175)
+#694 := (iff #414 #693)
+#698 := (iff #415 #175)
+#696 := (= #424 #172)
+#436 := (+ #172 0::int)
+#430 := (= #436 #172)
+#712 := [rewrite]: #430
+#553 := (= #424 #436)
+#711 := (= #423 0::int)
+#703 := (mod 0::int 1::int)
+#710 := (= #703 0::int)
+#705 := [rewrite]: #710
+#704 := (= #423 #703)
+#707 := (= #338 1::int)
+#708 := [rewrite]: #707
+#723 := (= #422 0::int)
+#433 := [rewrite]: #723
+#709 := [monotonicity #433 #708]: #704
+#552 := [trans #709 #705]: #711
+#554 := [monotonicity #552]: #553
+#697 := [trans #554 #712]: #696
+#699 := [monotonicity #697]: #698
+#717 := (iff #425 #175)
+#716 := (= #428 #172)
+#714 := (= #428 #436)
+#434 := (= #427 0::int)
+#722 := (= #427 #422)
+#444 := (= #426 0::int)
+#718 := [rewrite]: #444
+#719 := [monotonicity #718]: #722
+#435 := [trans #719 #433]: #434
+#715 := [monotonicity #435]: #714
+#713 := [trans #715 #712]: #716
+#706 := [monotonicity #713]: #717
+#721 := (iff #413 false)
+#448 := (or false false)
+#344 := (iff #448 false)
+#720 := [rewrite]: #344
+#449 := (iff #413 #448)
+#725 := (iff #745 false)
+#729 := (not true)
+#732 := (iff #729 false)
+#727 := [rewrite]: #732
+#738 := (iff #745 #729)
+#737 := (iff #743 true)
+#385 := (or true true)
+#390 := (iff #385 true)
+#391 := [rewrite]: #390
+#376 := (iff #743 #385)
+#405 := (iff #429 true)
+#741 := [rewrite]: #405
+#734 := (iff #408 true)
+#736 := [rewrite]: #734
+#377 := [monotonicity #736 #741]: #376
+#735 := [trans #377 #391]: #737
+#724 := [monotonicity #735]: #738
+#447 := [trans #724 #727]: #725
+#733 := (iff #739 false)
+#730 := (iff #739 #729)
+#392 := (iff #532 true)
+#726 := (iff #532 #385)
+#401 := (iff #402 true)
+#742 := [rewrite]: #401
+#389 := [monotonicity #741 #742]: #726
+#728 := [trans #389 #391]: #392
+#731 := [monotonicity #728]: #730
+#371 := [trans #731 #727]: #733
+#450 := [monotonicity #371 #447]: #449
+#443 := [trans #450 #720]: #721
+#700 := [monotonicity #443 #706 #699]: #694
+#531 := [trans #700 #695]: #702
+#740 := (iff #746 true)
+#400 := [rewrite]: #740
+#687 := [monotonicity #400 #531]: #534
+#689 := [trans #687 #690]: #691
+#744 := (iff #748 false)
+#750 := [rewrite]: #744
+#574 := [monotonicity #750 #187 #689]: #692
+#576 := [trans #574 #695]: #575
+#684 := [monotonicity #576]: #681
+#586 := [trans #684 #584]: #681
+#680 := [quant-inst]: #585
+#587 := [mp #680 #586]: #683
+[unit-resolution #587 #764 #193]: false
+unsat
+5d55ad01457614eb8108c03c5b2b58faed77191c 327 0
 #2 := false
 #11 := 0::int
 decl f4 :: (-> int int int)
@@ -32100,290 +36531,7 @@
 #673 := [mp #590 #686]: #588
 [unit-resolution #673 #764 #193]: false
 unsat
-637a9fb4751b1db772b995626b3d6e97b52eb701 282 0
-#2 := false
-#11 := 0::int
-decl f3 :: (-> int int int)
-#38 := 3::int
-#39 := (f3 0::int 3::int)
-#40 := (= #39 0::int)
-#41 := (not #40)
-#168 := [asserted]: #41
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#737 := (pattern #10)
-#65 := -1::int
-#69 := (* -1::int #9)
-#66 := (* -1::int #8)
-#72 := (div #66 #69)
-#239 := (* -1::int #72)
-#240 := (+ #10 #239)
-#241 := (= #240 0::int)
-#21 := (div #8 #9)
-#236 := (* -1::int #21)
-#237 := (+ #10 #236)
-#238 := (= #237 0::int)
-#91 := (<= #9 0::int)
-#87 := (<= #8 0::int)
-#194 := (or #87 #91)
-#195 := (not #194)
-#98 := (>= #8 0::int)
-#186 := (or #91 #98)
-#187 := (not #186)
-#201 := (or #187 #195)
-#242 := (ite #201 #238 #241)
-#235 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#243 := (ite #14 #235 #242)
-#738 := (forall (vars (?v0 int) (?v1 int)) (:pat #737) #243)
-#246 := (forall (vars (?v0 int) (?v1 int)) #243)
-#741 := (iff #246 #738)
-#739 := (iff #243 #243)
-#740 := [refl]: #739
-#742 := [quant-intro #740]: #741
-#206 := (ite #201 #21 #72)
-#209 := (ite #14 0::int #206)
-#212 := (= #10 #209)
-#215 := (forall (vars (?v0 int) (?v1 int)) #212)
-#247 := (iff #215 #246)
-#244 := (iff #212 #243)
-#245 := [rewrite]: #244
-#248 := [quant-intro #245]: #247
-#99 := (not #98)
-#92 := (not #91)
-#102 := (and #92 #99)
-#88 := (not #87)
-#95 := (and #88 #92)
-#105 := (or #95 #102)
-#108 := (ite #105 #21 #72)
-#111 := (ite #14 0::int #108)
-#114 := (= #10 #111)
-#117 := (forall (vars (?v0 int) (?v1 int)) #114)
-#216 := (iff #117 #215)
-#213 := (iff #114 #212)
-#210 := (= #111 #209)
-#207 := (= #108 #206)
-#204 := (iff #105 #201)
-#198 := (or #195 #187)
-#202 := (iff #198 #201)
-#203 := [rewrite]: #202
-#199 := (iff #105 #198)
-#196 := (iff #102 #187)
-#197 := [rewrite]: #196
-#184 := (iff #95 #195)
-#185 := [rewrite]: #184
-#200 := [monotonicity #185 #197]: #199
-#205 := [trans #200 #203]: #204
-#208 := [monotonicity #205]: #207
-#211 := [monotonicity #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [quant-intro #214]: #216
-#190 := (~ #117 #117)
-#188 := (~ #114 #114)
-#189 := [refl]: #188
-#191 := [nnf-pos #189]: #190
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#120 := (iff #28 #117)
-#59 := (and #16 #18)
-#62 := (or #17 #59)
-#75 := (ite #62 #21 #72)
-#78 := (ite #14 0::int #75)
-#81 := (= #10 #78)
-#84 := (forall (vars (?v0 int) (?v1 int)) #81)
-#118 := (iff #84 #117)
-#115 := (iff #81 #114)
-#112 := (= #78 #111)
-#109 := (= #75 #108)
-#106 := (iff #62 #105)
-#103 := (iff #59 #102)
-#100 := (iff #18 #99)
-#101 := [rewrite]: #100
-#93 := (iff #16 #92)
-#94 := [rewrite]: #93
-#104 := [monotonicity #94 #101]: #103
-#96 := (iff #17 #95)
-#89 := (iff #15 #88)
-#90 := [rewrite]: #89
-#97 := [monotonicity #90 #94]: #96
-#107 := [monotonicity #97 #104]: #106
-#110 := [monotonicity #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [quant-intro #116]: #118
-#85 := (iff #28 #84)
-#82 := (iff #27 #81)
-#79 := (= #26 #78)
-#76 := (= #25 #75)
-#73 := (= #24 #72)
-#70 := (= #23 #69)
-#71 := [rewrite]: #70
-#67 := (= #22 #66)
-#68 := [rewrite]: #67
-#74 := [monotonicity #68 #71]: #73
-#63 := (iff #20 #62)
-#60 := (iff #19 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#77 := [monotonicity #64 #74]: #76
-#80 := [monotonicity #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [quant-intro #83]: #85
-#121 := [trans #86 #119]: #120
-#58 := [asserted]: #28
-#122 := [mp #58 #121]: #117
-#181 := [mp~ #122 #191]: #117
-#218 := [mp #181 #217]: #215
-#249 := [mp #218 #248]: #246
-#743 := [mp #249 #742]: #738
-#572 := (not #738)
-#573 := (or #572 #40)
-#323 := (* -1::int 3::int)
-#408 := (* -1::int 0::int)
-#409 := (div #408 #323)
-#410 := (* -1::int #409)
-#401 := (+ #39 #410)
-#412 := (= #401 0::int)
-#413 := (div 0::int 3::int)
-#341 := (* -1::int #413)
-#414 := (+ #39 #341)
-#411 := (= #414 0::int)
-#415 := (<= 3::int 0::int)
-#394 := (<= 0::int 0::int)
-#729 := (or #394 #415)
-#731 := (not #729)
-#388 := (>= 0::int 0::int)
-#518 := (or #415 #388)
-#725 := (not #518)
-#399 := (or #725 #731)
-#400 := (ite #399 #411 #412)
-#732 := (= 3::int 0::int)
-#733 := (= 0::int 0::int)
-#734 := (or #733 #732)
-#735 := (ite #734 #40 #400)
-#566 := (or #572 #735)
-#575 := (iff #566 #573)
-#577 := (iff #573 #573)
-#578 := [rewrite]: #577
-#555 := (iff #735 #40)
-#1 := true
-#669 := (ite true #40 #40)
-#667 := (iff #669 #40)
-#670 := [rewrite]: #667
-#571 := (iff #735 #669)
-#562 := (iff #400 #40)
-#677 := (ite false #40 #40)
-#560 := (iff #677 #40)
-#561 := [rewrite]: #560
-#675 := (iff #400 #677)
-#674 := (iff #412 #40)
-#520 := (= #401 #39)
-#703 := (+ #39 0::int)
-#694 := (= #703 #39)
-#689 := [rewrite]: #694
-#517 := (= #401 #703)
-#681 := (= #410 0::int)
-#416 := (= #408 0::int)
-#698 := [rewrite]: #416
-#686 := (= #410 #408)
-#679 := (= #409 0::int)
-#697 := -3::int
-#540 := (div 0::int -3::int)
-#684 := (= #540 0::int)
-#685 := [rewrite]: #684
-#682 := (= #409 #540)
-#538 := (= #323 -3::int)
-#539 := [rewrite]: #538
-#683 := [monotonicity #698 #539]: #682
-#680 := [trans #683 #685]: #679
-#687 := [monotonicity #680]: #686
-#688 := [trans #687 #698]: #681
-#519 := [monotonicity #688]: #517
-#673 := [trans #519 #689]: #520
-#676 := [monotonicity #673]: #674
-#696 := (iff #411 #40)
-#690 := (= #414 #39)
-#692 := (= #414 #703)
-#702 := (= #341 0::int)
-#700 := (= #341 #408)
-#421 := (= #413 0::int)
-#422 := [rewrite]: #421
-#701 := [monotonicity #422]: #700
-#699 := [trans #701 #698]: #702
-#693 := [monotonicity #699]: #692
-#695 := [trans #693 #689]: #690
-#691 := [monotonicity #695]: #696
-#419 := (iff #399 false)
-#430 := (or false false)
-#705 := (iff #430 false)
-#709 := [rewrite]: #705
-#704 := (iff #399 #430)
-#707 := (iff #731 false)
-#720 := (not true)
-#363 := (iff #720 false)
-#723 := [rewrite]: #363
-#329 := (iff #731 #720)
-#435 := (iff #729 true)
-#391 := (or true false)
-#728 := (iff #391 true)
-#371 := [rewrite]: #728
-#433 := (iff #729 #391)
-#376 := (iff #415 false)
-#377 := [rewrite]: #376
-#710 := (iff #394 true)
-#711 := [rewrite]: #710
-#434 := [monotonicity #711 #377]: #433
-#436 := [trans #434 #371]: #435
-#706 := [monotonicity #436]: #329
-#429 := [trans #706 #723]: #707
-#721 := (iff #725 false)
-#722 := (iff #725 #720)
-#719 := (iff #518 true)
-#715 := (or false true)
-#718 := (iff #715 true)
-#713 := [rewrite]: #718
-#716 := (iff #518 #715)
-#378 := (iff #388 true)
-#714 := [rewrite]: #378
-#717 := [monotonicity #377 #714]: #716
-#357 := [trans #717 #713]: #719
-#362 := [monotonicity #357]: #722
-#724 := [trans #362 #723]: #721
-#708 := [monotonicity #724 #429]: #704
-#420 := [trans #708 #709]: #419
-#678 := [monotonicity #420 #691 #676]: #675
-#521 := [trans #678 #561]: #562
-#712 := (iff #734 true)
-#727 := (iff #734 #391)
-#726 := (iff #732 false)
-#386 := [rewrite]: #726
-#730 := (iff #733 true)
-#736 := [rewrite]: #730
-#387 := [monotonicity #736 #386]: #727
-#375 := [trans #387 #371]: #712
-#666 := [monotonicity #375 #521]: #571
-#570 := [trans #666 #670]: #555
-#576 := [monotonicity #570]: #575
-#671 := [trans #576 #578]: #575
-#574 := [quant-inst]: #566
-#668 := [mp #574 #671]: #573
-[unit-resolution #668 #743 #168]: false
-unsat
-7760bfb909b598c1c9e59b0475683ef8155b0972 329 0
+8dfd3a95fba21b02a3c9c40827dc123538d3ae1a 329 0
 #2 := false
 #11 := 0::int
 decl f4 :: (-> int int int)
@@ -32713,315 +36861,7 @@
 #676 := [mp #592 #674]: #590
 [unit-resolution #676 #765 #194]: false
 unsat
-3720824b257034758f7a600c278307a5f80b6e02 307 0
-#2 := false
-#11 := 0::int
-decl f3 :: (-> int int int)
-#170 := -3::int
-#173 := (f3 0::int -3::int)
-#176 := (= #173 0::int)
-#189 := (not #176)
-#38 := 3::int
-#39 := (- 3::int)
-#40 := (f3 0::int #39)
-#41 := (= #40 0::int)
-#42 := (not #41)
-#192 := (iff #42 #189)
-#179 := (= 0::int #173)
-#184 := (not #179)
-#190 := (iff #184 #189)
-#187 := (iff #179 #176)
-#188 := [rewrite]: #187
-#191 := [monotonicity #188]: #190
-#185 := (iff #42 #184)
-#182 := (iff #41 #179)
-#180 := (iff #176 #179)
-#181 := [rewrite]: #180
-#177 := (iff #41 #176)
-#174 := (= #40 #173)
-#171 := (= #39 -3::int)
-#172 := [rewrite]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#183 := [trans #178 #181]: #182
-#186 := [monotonicity #183]: #185
-#193 := [trans #186 #191]: #192
-#169 := [asserted]: #42
-#194 := [mp #169 #193]: #189
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#753 := (pattern #10)
-#66 := -1::int
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#73 := (div #67 #70)
-#255 := (* -1::int #73)
-#256 := (+ #10 #255)
-#257 := (= #256 0::int)
-#21 := (div #8 #9)
-#252 := (* -1::int #21)
-#253 := (+ #10 #252)
-#254 := (= #253 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#210 := (or #88 #92)
-#211 := (not #210)
-#99 := (>= #8 0::int)
-#202 := (or #92 #99)
-#203 := (not #202)
-#217 := (or #203 #211)
-#258 := (ite #217 #254 #257)
-#251 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#259 := (ite #14 #251 #258)
-#754 := (forall (vars (?v0 int) (?v1 int)) (:pat #753) #259)
-#262 := (forall (vars (?v0 int) (?v1 int)) #259)
-#757 := (iff #262 #754)
-#755 := (iff #259 #259)
-#756 := [refl]: #755
-#758 := [quant-intro #756]: #757
-#222 := (ite #217 #21 #73)
-#225 := (ite #14 0::int #222)
-#228 := (= #10 #225)
-#231 := (forall (vars (?v0 int) (?v1 int)) #228)
-#263 := (iff #231 #262)
-#260 := (iff #228 #259)
-#261 := [rewrite]: #260
-#264 := [quant-intro #261]: #263
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#109 := (ite #106 #21 #73)
-#112 := (ite #14 0::int #109)
-#115 := (= #10 #112)
-#118 := (forall (vars (?v0 int) (?v1 int)) #115)
-#232 := (iff #118 #231)
-#229 := (iff #115 #228)
-#226 := (= #112 #225)
-#223 := (= #109 #222)
-#220 := (iff #106 #217)
-#214 := (or #211 #203)
-#218 := (iff #214 #217)
-#219 := [rewrite]: #218
-#215 := (iff #106 #214)
-#212 := (iff #103 #203)
-#213 := [rewrite]: #212
-#200 := (iff #96 #211)
-#201 := [rewrite]: #200
-#216 := [monotonicity #201 #213]: #215
-#221 := [trans #216 #219]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [quant-intro #230]: #232
-#206 := (~ #118 #118)
-#204 := (~ #115 #115)
-#205 := [refl]: #204
-#207 := [nnf-pos #205]: #206
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#121 := (iff #28 #118)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#76 := (ite #63 #21 #73)
-#79 := (ite #14 0::int #76)
-#82 := (= #10 #79)
-#85 := (forall (vars (?v0 int) (?v1 int)) #82)
-#119 := (iff #85 #118)
-#116 := (iff #82 #115)
-#113 := (= #79 #112)
-#110 := (= #76 #109)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#111 := [monotonicity #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [quant-intro #117]: #119
-#86 := (iff #28 #85)
-#83 := (iff #27 #82)
-#80 := (= #26 #79)
-#77 := (= #25 #76)
-#74 := (= #24 #73)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#75 := [monotonicity #69 #72]: #74
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#78 := [monotonicity #65 #75]: #77
-#81 := [monotonicity #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [quant-intro #84]: #86
-#122 := [trans #87 #120]: #121
-#59 := [asserted]: #28
-#123 := [mp #59 #122]: #118
-#197 := [mp~ #123 #207]: #118
-#234 := [mp #197 #233]: #231
-#265 := [mp #234 #264]: #262
-#759 := [mp #265 #758]: #754
-#586 := (not #754)
-#588 := (or #586 #176)
-#339 := (* -1::int -3::int)
-#424 := (* -1::int 0::int)
-#425 := (div #424 #339)
-#426 := (* -1::int #425)
-#417 := (+ #173 #426)
-#428 := (= #417 0::int)
-#429 := (div 0::int -3::int)
-#357 := (* -1::int #429)
-#430 := (+ #173 #357)
-#427 := (= #430 0::int)
-#431 := (<= -3::int 0::int)
-#410 := (<= 0::int 0::int)
-#745 := (or #410 #431)
-#747 := (not #745)
-#404 := (>= 0::int 0::int)
-#534 := (or #431 #404)
-#741 := (not #534)
-#415 := (or #741 #747)
-#416 := (ite #415 #427 #428)
-#748 := (= -3::int 0::int)
-#749 := (= 0::int 0::int)
-#750 := (or #749 #748)
-#751 := (ite #750 #176 #416)
-#589 := (or #586 #751)
-#590 := (iff #589 #588)
-#592 := (iff #588 #588)
-#593 := [rewrite]: #592
-#686 := (iff #751 #176)
-#1 := true
-#537 := (ite true #176 #176)
-#682 := (iff #537 #176)
-#683 := [rewrite]: #682
-#685 := (iff #751 #537)
-#577 := (iff #416 #176)
-#692 := (ite false #176 #176)
-#694 := (iff #692 #176)
-#576 := [rewrite]: #694
-#693 := (iff #416 #692)
-#689 := (iff #428 #176)
-#535 := (= #417 #173)
-#719 := (+ #173 0::int)
-#710 := (= #719 #173)
-#705 := [rewrite]: #710
-#704 := (= #417 #719)
-#703 := (= #426 0::int)
-#432 := (= #424 0::int)
-#714 := [rewrite]: #432
-#696 := (= #426 #424)
-#701 := (= #425 0::int)
-#555 := (div 0::int 3::int)
-#699 := (= #555 0::int)
-#700 := [rewrite]: #699
-#556 := (= #425 #555)
-#713 := (= #339 3::int)
-#554 := [rewrite]: #713
-#698 := [monotonicity #714 #554]: #556
-#695 := [trans #698 #700]: #701
-#702 := [monotonicity #695]: #696
-#697 := [trans #702 #714]: #703
-#533 := [monotonicity #697]: #704
-#536 := [trans #533 #705]: #535
-#690 := [monotonicity #536]: #689
-#712 := (iff #427 #176)
-#706 := (= #430 #173)
-#708 := (= #430 #719)
-#718 := (= #357 0::int)
-#716 := (= #357 #424)
-#437 := (= #429 0::int)
-#438 := [rewrite]: #437
-#717 := [monotonicity #438]: #716
-#715 := [trans #717 #714]: #718
-#709 := [monotonicity #715]: #708
-#711 := [trans #709 #705]: #706
-#707 := [monotonicity #711]: #712
-#435 := (iff #415 false)
-#446 := (or false false)
-#721 := (iff #446 false)
-#725 := [rewrite]: #721
-#720 := (iff #415 #446)
-#723 := (iff #747 false)
-#736 := (not true)
-#379 := (iff #736 false)
-#739 := [rewrite]: #379
-#345 := (iff #747 #736)
-#451 := (iff #745 true)
-#731 := (or true true)
-#734 := (iff #731 true)
-#729 := [rewrite]: #734
-#449 := (iff #745 #731)
-#392 := (iff #431 true)
-#393 := [rewrite]: #392
-#726 := (iff #410 true)
-#727 := [rewrite]: #726
-#450 := [monotonicity #727 #393]: #449
-#452 := [trans #450 #729]: #451
-#722 := [monotonicity #452]: #345
-#445 := [trans #722 #739]: #723
-#737 := (iff #741 false)
-#738 := (iff #741 #736)
-#735 := (iff #534 true)
-#732 := (iff #534 #731)
-#394 := (iff #404 true)
-#730 := [rewrite]: #394
-#733 := [monotonicity #393 #730]: #732
-#373 := [trans #733 #729]: #735
-#378 := [monotonicity #373]: #738
-#740 := [trans #378 #739]: #737
-#724 := [monotonicity #740 #445]: #720
-#436 := [trans #724 #725]: #435
-#691 := [monotonicity #436 #707 #690]: #693
-#578 := [trans #691 #576]: #577
-#728 := (iff #750 true)
-#407 := (or true false)
-#744 := (iff #407 true)
-#387 := [rewrite]: #744
-#743 := (iff #750 #407)
-#742 := (iff #748 false)
-#402 := [rewrite]: #742
-#746 := (iff #749 true)
-#752 := [rewrite]: #746
-#403 := [monotonicity #752 #402]: #743
-#391 := [trans #403 #387]: #728
-#587 := [monotonicity #391 #578]: #685
-#571 := [trans #587 #683]: #686
-#591 := [monotonicity #571]: #590
-#594 := [trans #591 #593]: #590
-#582 := [quant-inst]: #589
-#687 := [mp #582 #594]: #588
-[unit-resolution #687 #759 #194]: false
-unsat
-8c2ddb2baafdfdaa50382790d0f6610f91f76e27 306 0
+c03265f4c0df1ce6bab828a9bdd5d936d131126e 306 0
 #2 := false
 #11 := 0::int
 decl f4 :: (-> int int int)
@@ -33328,591 +37168,7 @@
 #693 := [mp #535 #690]: #532
 [unit-resolution #693 #765 #194]: false
 unsat
-f3e8e6f2d42536caa9e4ddd3735d660dddce72ee 296 0
-#2 := false
-#11 := 0::int
-decl f3 :: (-> int int int)
-#39 := 3::int
-#38 := 1::int
-#40 := (f3 1::int 3::int)
-#41 := (= #40 0::int)
-#42 := (not #41)
-#169 := [asserted]: #42
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#737 := (pattern #10)
-#66 := -1::int
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#73 := (div #67 #70)
-#240 := (* -1::int #73)
-#241 := (+ #10 #240)
-#242 := (= #241 0::int)
-#21 := (div #8 #9)
-#237 := (* -1::int #21)
-#238 := (+ #10 #237)
-#239 := (= #238 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#195 := (or #88 #92)
-#196 := (not #195)
-#99 := (>= #8 0::int)
-#187 := (or #92 #99)
-#188 := (not #187)
-#202 := (or #188 #196)
-#243 := (ite #202 #239 #242)
-#236 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#244 := (ite #14 #236 #243)
-#738 := (forall (vars (?v0 int) (?v1 int)) (:pat #737) #244)
-#247 := (forall (vars (?v0 int) (?v1 int)) #244)
-#741 := (iff #247 #738)
-#739 := (iff #244 #244)
-#740 := [refl]: #739
-#742 := [quant-intro #740]: #741
-#207 := (ite #202 #21 #73)
-#210 := (ite #14 0::int #207)
-#213 := (= #10 #210)
-#216 := (forall (vars (?v0 int) (?v1 int)) #213)
-#248 := (iff #216 #247)
-#245 := (iff #213 #244)
-#246 := [rewrite]: #245
-#249 := [quant-intro #246]: #248
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#109 := (ite #106 #21 #73)
-#112 := (ite #14 0::int #109)
-#115 := (= #10 #112)
-#118 := (forall (vars (?v0 int) (?v1 int)) #115)
-#217 := (iff #118 #216)
-#214 := (iff #115 #213)
-#211 := (= #112 #210)
-#208 := (= #109 #207)
-#205 := (iff #106 #202)
-#199 := (or #196 #188)
-#203 := (iff #199 #202)
-#204 := [rewrite]: #203
-#200 := (iff #106 #199)
-#197 := (iff #103 #188)
-#198 := [rewrite]: #197
-#185 := (iff #96 #196)
-#186 := [rewrite]: #185
-#201 := [monotonicity #186 #198]: #200
-#206 := [trans #201 #204]: #205
-#209 := [monotonicity #206]: #208
-#212 := [monotonicity #209]: #211
-#215 := [monotonicity #212]: #214
-#218 := [quant-intro #215]: #217
-#191 := (~ #118 #118)
-#189 := (~ #115 #115)
-#190 := [refl]: #189
-#192 := [nnf-pos #190]: #191
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#121 := (iff #28 #118)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#76 := (ite #63 #21 #73)
-#79 := (ite #14 0::int #76)
-#82 := (= #10 #79)
-#85 := (forall (vars (?v0 int) (?v1 int)) #82)
-#119 := (iff #85 #118)
-#116 := (iff #82 #115)
-#113 := (= #79 #112)
-#110 := (= #76 #109)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#111 := [monotonicity #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [quant-intro #117]: #119
-#86 := (iff #28 #85)
-#83 := (iff #27 #82)
-#80 := (= #26 #79)
-#77 := (= #25 #76)
-#74 := (= #24 #73)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#75 := [monotonicity #69 #72]: #74
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#78 := [monotonicity #65 #75]: #77
-#81 := [monotonicity #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [quant-intro #84]: #86
-#122 := [trans #87 #120]: #121
-#59 := [asserted]: #28
-#123 := [mp #59 #122]: #118
-#182 := [mp~ #123 #192]: #118
-#219 := [mp #182 #218]: #216
-#250 := [mp #219 #249]: #247
-#743 := [mp #250 #742]: #738
-#650 := (not #738)
-#652 := (or #650 #41)
-#324 := (* -1::int 3::int)
-#408 := (* -1::int 1::int)
-#409 := (div #408 #324)
-#410 := (* -1::int #409)
-#401 := (+ #40 #410)
-#412 := (= #401 0::int)
-#413 := (div 1::int 3::int)
-#414 := (* -1::int #413)
-#411 := (+ #40 #414)
-#415 := (= #411 0::int)
-#394 := (<= 3::int 0::int)
-#729 := (<= 1::int 0::int)
-#731 := (or #729 #394)
-#388 := (not #731)
-#518 := (>= 1::int 0::int)
-#725 := (or #394 #518)
-#399 := (not #725)
-#400 := (or #399 #388)
-#732 := (ite #400 #415 #412)
-#733 := (= 3::int 0::int)
-#734 := (= 1::int 0::int)
-#735 := (or #734 #733)
-#730 := (ite #735 #41 #732)
-#662 := (or #650 #730)
-#664 := (iff #662 #652)
-#665 := (iff #652 #652)
-#654 := [rewrite]: #665
-#661 := (iff #730 #41)
-#578 := (ite false #41 #41)
-#672 := (iff #578 #41)
-#659 := [rewrite]: #672
-#671 := (iff #730 #578)
-#576 := (iff #732 #41)
-#666 := (= #40 1::int)
-#1 := true
-#572 := (ite true #41 #666)
-#574 := (iff #572 #41)
-#575 := [rewrite]: #574
-#573 := (iff #732 #572)
-#555 := (iff #412 #666)
-#675 := (+ -1::int #40)
-#521 := (= #675 0::int)
-#667 := (iff #521 #666)
-#670 := [rewrite]: #667
-#669 := (iff #412 #521)
-#561 := (= #401 #675)
-#674 := (+ #40 -1::int)
-#678 := (= #674 #675)
-#560 := [rewrite]: #678
-#676 := (= #401 #674)
-#520 := (= #410 -1::int)
-#539 := (= #408 -1::int)
-#540 := [rewrite]: #539
-#517 := (= #410 #408)
-#681 := (= #409 1::int)
-#682 := -3::int
-#685 := (div -1::int -3::int)
-#686 := (= #685 1::int)
-#687 := [rewrite]: #686
-#679 := (= #409 #685)
-#683 := (= #324 -3::int)
-#684 := [rewrite]: #683
-#680 := [monotonicity #540 #684]: #679
-#688 := [trans #680 #687]: #681
-#519 := [monotonicity #688]: #517
-#673 := [trans #519 #540]: #520
-#677 := [monotonicity #673]: #676
-#562 := [trans #677 #560]: #561
-#571 := [monotonicity #562]: #669
-#570 := [trans #571 #670]: #555
-#697 := (iff #415 #41)
-#696 := (= #411 #40)
-#693 := (+ #40 0::int)
-#690 := (= #693 #40)
-#695 := [rewrite]: #690
-#694 := (= #411 #693)
-#703 := (= #414 0::int)
-#701 := (* -1::int 0::int)
-#702 := (= #701 0::int)
-#699 := [rewrite]: #702
-#416 := (= #414 #701)
-#422 := (= #413 0::int)
-#700 := [rewrite]: #422
-#698 := [monotonicity #700]: #416
-#692 := [trans #698 #699]: #703
-#689 := [monotonicity #692]: #694
-#691 := [trans #689 #695]: #696
-#538 := [monotonicity #691]: #697
-#420 := (iff #400 true)
-#716 := (or false true)
-#713 := (iff #716 true)
-#719 := [rewrite]: #713
-#709 := (iff #400 #716)
-#708 := (iff #388 true)
-#706 := (not false)
-#430 := (iff #706 true)
-#704 := [rewrite]: #430
-#707 := (iff #388 #706)
-#436 := (iff #731 false)
-#727 := (or false false)
-#371 := (iff #727 false)
-#712 := [rewrite]: #371
-#434 := (iff #731 #727)
-#377 := (iff #394 false)
-#378 := [rewrite]: #377
-#711 := (iff #729 false)
-#433 := [rewrite]: #711
-#435 := [monotonicity #433 #378]: #434
-#330 := [trans #435 #712]: #436
-#429 := [monotonicity #330]: #707
-#705 := [trans #429 #704]: #708
-#724 := (iff #399 false)
-#722 := (not true)
-#723 := (iff #722 false)
-#721 := [rewrite]: #723
-#362 := (iff #399 #722)
-#357 := (iff #725 true)
-#717 := (iff #725 #716)
-#714 := (iff #518 true)
-#715 := [rewrite]: #714
-#718 := [monotonicity #378 #715]: #717
-#720 := [trans #718 #719]: #357
-#363 := [monotonicity #720]: #362
-#710 := [trans #363 #721]: #724
-#419 := [monotonicity #710 #705]: #709
-#421 := [trans #419 #719]: #420
-#566 := [monotonicity #421 #538 #570]: #573
-#577 := [trans #566 #575]: #576
-#375 := (iff #735 false)
-#387 := (iff #735 #727)
-#386 := (iff #733 false)
-#391 := [rewrite]: #386
-#736 := (iff #734 false)
-#726 := [rewrite]: #736
-#728 := [monotonicity #726 #391]: #387
-#376 := [trans #728 #712]: #375
-#668 := [monotonicity #376 #577]: #671
-#653 := [trans #668 #659]: #661
-#660 := [monotonicity #653]: #664
-#655 := [trans #660 #654]: #664
-#663 := [quant-inst]: #662
-#656 := [mp #663 #655]: #652
-[unit-resolution #656 #743 #169]: false
-unsat
-93736e6f4586e3d8675e6c2a74bb3371d5238b60 286 0
-#2 := false
-#40 := 1::int
-decl f3 :: (-> int int int)
-#38 := 3::int
-#39 := (f3 3::int 3::int)
-#41 := (= #39 1::int)
-#42 := (not #41)
-#169 := [asserted]: #42
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#727 := (pattern #10)
-#11 := 0::int
-#66 := -1::int
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#73 := (div #67 #70)
-#230 := (* -1::int #73)
-#231 := (+ #10 #230)
-#232 := (= #231 0::int)
-#21 := (div #8 #9)
-#227 := (* -1::int #21)
-#228 := (+ #10 #227)
-#229 := (= #228 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#185 := (or #88 #92)
-#186 := (not #185)
-#99 := (>= #8 0::int)
-#177 := (or #92 #99)
-#178 := (not #177)
-#192 := (or #178 #186)
-#233 := (ite #192 #229 #232)
-#226 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#234 := (ite #14 #226 #233)
-#728 := (forall (vars (?v0 int) (?v1 int)) (:pat #727) #234)
-#237 := (forall (vars (?v0 int) (?v1 int)) #234)
-#731 := (iff #237 #728)
-#729 := (iff #234 #234)
-#730 := [refl]: #729
-#732 := [quant-intro #730]: #731
-#197 := (ite #192 #21 #73)
-#200 := (ite #14 0::int #197)
-#203 := (= #10 #200)
-#206 := (forall (vars (?v0 int) (?v1 int)) #203)
-#238 := (iff #206 #237)
-#235 := (iff #203 #234)
-#236 := [rewrite]: #235
-#239 := [quant-intro #236]: #238
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#109 := (ite #106 #21 #73)
-#112 := (ite #14 0::int #109)
-#115 := (= #10 #112)
-#118 := (forall (vars (?v0 int) (?v1 int)) #115)
-#207 := (iff #118 #206)
-#204 := (iff #115 #203)
-#201 := (= #112 #200)
-#198 := (= #109 #197)
-#195 := (iff #106 #192)
-#189 := (or #186 #178)
-#193 := (iff #189 #192)
-#194 := [rewrite]: #193
-#190 := (iff #106 #189)
-#187 := (iff #103 #178)
-#188 := [rewrite]: #187
-#175 := (iff #96 #186)
-#176 := [rewrite]: #175
-#191 := [monotonicity #176 #188]: #190
-#196 := [trans #191 #194]: #195
-#199 := [monotonicity #196]: #198
-#202 := [monotonicity #199]: #201
-#205 := [monotonicity #202]: #204
-#208 := [quant-intro #205]: #207
-#181 := (~ #118 #118)
-#179 := (~ #115 #115)
-#180 := [refl]: #179
-#182 := [nnf-pos #180]: #181
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#121 := (iff #28 #118)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#76 := (ite #63 #21 #73)
-#79 := (ite #14 0::int #76)
-#82 := (= #10 #79)
-#85 := (forall (vars (?v0 int) (?v1 int)) #82)
-#119 := (iff #85 #118)
-#116 := (iff #82 #115)
-#113 := (= #79 #112)
-#110 := (= #76 #109)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#111 := [monotonicity #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [quant-intro #117]: #119
-#86 := (iff #28 #85)
-#83 := (iff #27 #82)
-#80 := (= #26 #79)
-#77 := (= #25 #76)
-#74 := (= #24 #73)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#75 := [monotonicity #69 #72]: #74
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#78 := [monotonicity #65 #75]: #77
-#81 := [monotonicity #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [quant-intro #84]: #86
-#122 := [trans #87 #120]: #121
-#59 := [asserted]: #28
-#123 := [mp #59 #122]: #118
-#172 := [mp~ #123 #182]: #118
-#209 := [mp #172 #208]: #206
-#240 := [mp #209 #239]: #237
-#733 := [mp #240 #732]: #728
-#565 := (not #728)
-#566 := (or #565 #41)
-#314 := (* -1::int 3::int)
-#398 := (div #314 #314)
-#399 := (* -1::int #398)
-#400 := (+ #39 #399)
-#391 := (= #400 0::int)
-#402 := (div 3::int 3::int)
-#403 := (* -1::int #402)
-#404 := (+ #39 #403)
-#401 := (= #404 0::int)
-#405 := (<= 3::int 0::int)
-#384 := (or #405 #405)
-#719 := (not #384)
-#721 := (>= 3::int 0::int)
-#378 := (or #405 #721)
-#508 := (not #378)
-#715 := (or #508 #719)
-#389 := (ite #715 #401 #391)
-#390 := (= #39 0::int)
-#722 := (= 3::int 0::int)
-#723 := (or #722 #722)
-#724 := (ite #723 #390 #389)
-#567 := (or #565 #724)
-#661 := (iff #567 #566)
-#662 := (iff #566 #566)
-#649 := [rewrite]: #662
-#556 := (iff #724 #41)
-#660 := (ite false #390 #41)
-#562 := (iff #660 #41)
-#563 := [rewrite]: #562
-#545 := (iff #724 #660)
-#656 := (iff #389 #41)
-#1 := true
-#551 := (ite true #41 #41)
-#659 := (iff #551 #41)
-#561 := [rewrite]: #659
-#552 := (iff #389 #551)
-#668 := (iff #391 #41)
-#689 := (+ -1::int #39)
-#679 := (= #689 0::int)
-#686 := (iff #679 #41)
-#681 := [rewrite]: #686
-#667 := (iff #391 #679)
-#664 := (= #400 #689)
-#406 := (+ #39 -1::int)
-#693 := (= #406 #689)
-#682 := [rewrite]: #693
-#510 := (= #400 #406)
-#507 := (= #399 -1::int)
-#699 := (* -1::int 1::int)
-#411 := (= #699 -1::int)
-#412 := [rewrite]: #411
-#671 := (= #399 #699)
-#676 := (= #398 1::int)
-#529 := -3::int
-#673 := (div -3::int -3::int)
-#669 := (= #673 1::int)
-#670 := [rewrite]: #669
-#674 := (= #398 #673)
-#530 := (= #314 -3::int)
-#672 := [rewrite]: #530
-#675 := [monotonicity #672 #672]: #674
-#677 := [trans #675 #670]: #676
-#678 := [monotonicity #677]: #671
-#509 := [trans #678 #412]: #507
-#663 := [monotonicity #509]: #510
-#666 := [trans #663 #682]: #664
-#665 := [monotonicity #666]: #667
-#550 := [trans #665 #681]: #668
-#687 := (iff #401 #41)
-#680 := (iff #401 #679)
-#683 := (= #404 #689)
-#688 := (= #404 #406)
-#690 := (= #403 -1::int)
-#409 := (= #403 #699)
-#698 := (= #402 1::int)
-#695 := [rewrite]: #698
-#410 := [monotonicity #695]: #409
-#691 := [trans #410 #412]: #690
-#692 := [monotonicity #691]: #688
-#684 := [trans #692 #682]: #683
-#685 := [monotonicity #684]: #680
-#528 := [trans #685 #681]: #687
-#420 := (iff #715 true)
-#367 := (or false true)
-#705 := (iff #367 true)
-#706 := [rewrite]: #705
-#697 := (iff #715 #367)
-#320 := (iff #719 true)
-#701 := (not false)
-#425 := (iff #701 true)
-#426 := [rewrite]: #425
-#423 := (iff #719 #701)
-#714 := (iff #384 false)
-#726 := (or false false)
-#381 := (iff #726 false)
-#717 := [rewrite]: #381
-#713 := (iff #384 #726)
-#361 := (iff #405 false)
-#702 := [rewrite]: #361
-#711 := [monotonicity #702 #702]: #713
-#700 := [trans #711 #717]: #714
-#424 := [monotonicity #700]: #423
-#696 := [trans #424 #426]: #320
-#352 := (iff #508 false)
-#703 := (not true)
-#710 := (iff #703 false)
-#712 := [rewrite]: #710
-#709 := (iff #508 #703)
-#707 := (iff #378 true)
-#368 := (iff #378 #367)
-#365 := (iff #721 true)
-#366 := [rewrite]: #365
-#704 := [monotonicity #702 #366]: #368
-#708 := [trans #704 #706]: #707
-#347 := [monotonicity #708]: #709
-#353 := [trans #347 #712]: #352
-#419 := [monotonicity #353 #696]: #697
-#694 := [trans #419 #706]: #420
-#511 := [monotonicity #694 #528 #550]: #552
-#657 := [trans #511 #561]: #656
-#377 := (iff #723 false)
-#716 := (iff #723 #726)
-#725 := (iff #722 false)
-#720 := [rewrite]: #725
-#376 := [monotonicity #720 #720]: #716
-#718 := [trans #376 #717]: #377
-#560 := [monotonicity #718 #657]: #545
-#564 := [trans #560 #563]: #556
-#658 := [monotonicity #564]: #661
-#651 := [trans #658 #649]: #661
-#568 := [quant-inst]: #567
-#643 := [mp #568 #651]: #566
-[unit-resolution #643 #733 #169]: false
-unsat
-3b0f74b1f071a3ff5876e6e320a42af764cd8901 299 0
+bb78ad15779fa5cac8bd8d5cece6ed79702f7563 299 0
 #2 := false
 #11 := 0::int
 decl f4 :: (-> int int int)
@@ -34212,318 +37468,7 @@
 #575 := [mp #555 #574]: #667
 [unit-resolution #575 #750 #168]: false
 unsat
-47a39d6a04f9615c07eaa600e336bda0f6475ecd 310 0
-#2 := false
-#41 := 1::int
-decl f3 :: (-> int int int)
-#39 := 3::int
-#38 := 5::int
-#40 := (f3 5::int 3::int)
-#42 := (= #40 1::int)
-#43 := (not #42)
-#170 := [asserted]: #43
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#728 := (pattern #10)
-#11 := 0::int
-#67 := -1::int
-#71 := (* -1::int #9)
-#68 := (* -1::int #8)
-#74 := (div #68 #71)
-#231 := (* -1::int #74)
-#232 := (+ #10 #231)
-#233 := (= #232 0::int)
-#21 := (div #8 #9)
-#228 := (* -1::int #21)
-#229 := (+ #10 #228)
-#230 := (= #229 0::int)
-#93 := (<= #9 0::int)
-#89 := (<= #8 0::int)
-#186 := (or #89 #93)
-#187 := (not #186)
-#100 := (>= #8 0::int)
-#178 := (or #93 #100)
-#179 := (not #178)
-#193 := (or #179 #187)
-#234 := (ite #193 #230 #233)
-#227 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#235 := (ite #14 #227 #234)
-#729 := (forall (vars (?v0 int) (?v1 int)) (:pat #728) #235)
-#238 := (forall (vars (?v0 int) (?v1 int)) #235)
-#732 := (iff #238 #729)
-#730 := (iff #235 #235)
-#731 := [refl]: #730
-#733 := [quant-intro #731]: #732
-#198 := (ite #193 #21 #74)
-#201 := (ite #14 0::int #198)
-#204 := (= #10 #201)
-#207 := (forall (vars (?v0 int) (?v1 int)) #204)
-#239 := (iff #207 #238)
-#236 := (iff #204 #235)
-#237 := [rewrite]: #236
-#240 := [quant-intro #237]: #239
-#101 := (not #100)
-#94 := (not #93)
-#104 := (and #94 #101)
-#90 := (not #89)
-#97 := (and #90 #94)
-#107 := (or #97 #104)
-#110 := (ite #107 #21 #74)
-#113 := (ite #14 0::int #110)
-#116 := (= #10 #113)
-#119 := (forall (vars (?v0 int) (?v1 int)) #116)
-#208 := (iff #119 #207)
-#205 := (iff #116 #204)
-#202 := (= #113 #201)
-#199 := (= #110 #198)
-#196 := (iff #107 #193)
-#190 := (or #187 #179)
-#194 := (iff #190 #193)
-#195 := [rewrite]: #194
-#191 := (iff #107 #190)
-#188 := (iff #104 #179)
-#189 := [rewrite]: #188
-#176 := (iff #97 #187)
-#177 := [rewrite]: #176
-#192 := [monotonicity #177 #189]: #191
-#197 := [trans #192 #195]: #196
-#200 := [monotonicity #197]: #199
-#203 := [monotonicity #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [quant-intro #206]: #208
-#182 := (~ #119 #119)
-#180 := (~ #116 #116)
-#181 := [refl]: #180
-#183 := [nnf-pos #181]: #182
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#122 := (iff #28 #119)
-#61 := (and #16 #18)
-#64 := (or #17 #61)
-#77 := (ite #64 #21 #74)
-#80 := (ite #14 0::int #77)
-#83 := (= #10 #80)
-#86 := (forall (vars (?v0 int) (?v1 int)) #83)
-#120 := (iff #86 #119)
-#117 := (iff #83 #116)
-#114 := (= #80 #113)
-#111 := (= #77 #110)
-#108 := (iff #64 #107)
-#105 := (iff #61 #104)
-#102 := (iff #18 #101)
-#103 := [rewrite]: #102
-#95 := (iff #16 #94)
-#96 := [rewrite]: #95
-#106 := [monotonicity #96 #103]: #105
-#98 := (iff #17 #97)
-#91 := (iff #15 #90)
-#92 := [rewrite]: #91
-#99 := [monotonicity #92 #96]: #98
-#109 := [monotonicity #99 #106]: #108
-#112 := [monotonicity #109]: #111
-#115 := [monotonicity #112]: #114
-#118 := [monotonicity #115]: #117
-#121 := [quant-intro #118]: #120
-#87 := (iff #28 #86)
-#84 := (iff #27 #83)
-#81 := (= #26 #80)
-#78 := (= #25 #77)
-#75 := (= #24 #74)
-#72 := (= #23 #71)
-#73 := [rewrite]: #72
-#69 := (= #22 #68)
-#70 := [rewrite]: #69
-#76 := [monotonicity #70 #73]: #75
-#65 := (iff #20 #64)
-#62 := (iff #19 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#79 := [monotonicity #66 #76]: #78
-#82 := [monotonicity #79]: #81
-#85 := [monotonicity #82]: #84
-#88 := [quant-intro #85]: #87
-#123 := [trans #88 #121]: #122
-#60 := [asserted]: #28
-#124 := [mp #60 #123]: #119
-#173 := [mp~ #124 #183]: #119
-#210 := [mp #173 #209]: #207
-#241 := [mp #210 #240]: #238
-#734 := [mp #241 #733]: #729
-#633 := (not #729)
-#634 := (or #633 #42)
-#315 := (* -1::int 3::int)
-#399 := (* -1::int 5::int)
-#400 := (div #399 #315)
-#401 := (* -1::int #400)
-#392 := (+ #40 #401)
-#403 := (= #392 0::int)
-#404 := (div 5::int 3::int)
-#405 := (* -1::int #404)
-#402 := (+ #40 #405)
-#406 := (= #402 0::int)
-#385 := (<= 3::int 0::int)
-#720 := (<= 5::int 0::int)
-#722 := (or #720 #385)
-#379 := (not #722)
-#509 := (>= 5::int 0::int)
-#716 := (or #385 #509)
-#390 := (not #716)
-#391 := (or #390 #379)
-#723 := (ite #391 #406 #403)
-#724 := (= #40 0::int)
-#725 := (= 3::int 0::int)
-#726 := (= 5::int 0::int)
-#721 := (or #726 #725)
-#727 := (ite #721 #724 #723)
-#636 := (or #633 #727)
-#638 := (iff #636 #634)
-#635 := (iff #634 #634)
-#640 := [rewrite]: #635
-#642 := (iff #727 #42)
-#656 := (ite false #724 #42)
-#647 := (iff #656 #42)
-#648 := [rewrite]: #647
-#645 := (iff #727 #656)
-#655 := (iff #723 #42)
-#665 := 2::int
-#662 := (= #40 2::int)
-#1 := true
-#644 := (ite true #42 #662)
-#653 := (iff #644 #42)
-#654 := [rewrite]: #653
-#641 := (iff #723 #644)
-#650 := (iff #403 #662)
-#512 := -2::int
-#563 := (+ -2::int #40)
-#567 := (= #563 0::int)
-#659 := (iff #567 #662)
-#663 := [rewrite]: #659
-#568 := (iff #403 #567)
-#565 := (= #392 #563)
-#661 := (+ #40 -2::int)
-#564 := (= #661 #563)
-#557 := [rewrite]: #564
-#546 := (= #392 #661)
-#657 := (= #401 -2::int)
-#551 := (* -1::int 2::int)
-#660 := (= #551 -2::int)
-#562 := [rewrite]: #660
-#552 := (= #401 #551)
-#666 := (= #400 2::int)
-#672 := -3::int
-#671 := -5::int
-#510 := (div -5::int -3::int)
-#667 := (= #510 2::int)
-#668 := [rewrite]: #667
-#511 := (= #400 #510)
-#679 := (= #315 -3::int)
-#508 := [rewrite]: #679
-#677 := (= #399 -5::int)
-#678 := [rewrite]: #677
-#664 := [monotonicity #678 #508]: #511
-#669 := [trans #664 #668]: #666
-#553 := [monotonicity #669]: #552
-#658 := [trans #553 #562]: #657
-#561 := [monotonicity #658]: #546
-#566 := [trans #561 #557]: #565
-#569 := [monotonicity #566]: #568
-#652 := [trans #569 #663]: #650
-#676 := (iff #406 #42)
-#686 := (+ -1::int #40)
-#530 := (= #686 0::int)
-#674 := (iff #530 #42)
-#675 := [rewrite]: #674
-#531 := (iff #406 #530)
-#688 := (= #402 #686)
-#685 := (+ #40 -1::int)
-#687 := (= #685 #686)
-#682 := [rewrite]: #687
-#680 := (= #402 #685)
-#683 := (= #405 -1::int)
-#407 := (* -1::int 1::int)
-#690 := (= #407 -1::int)
-#694 := [rewrite]: #690
-#689 := (= #405 #407)
-#691 := (= #404 1::int)
-#692 := [rewrite]: #691
-#693 := [monotonicity #692]: #689
-#684 := [trans #693 #694]: #683
-#681 := [monotonicity #684]: #680
-#529 := [trans #681 #682]: #688
-#673 := [monotonicity #529]: #531
-#670 := [trans #673 #675]: #676
-#412 := (iff #391 true)
-#708 := (or false true)
-#710 := (iff #708 true)
-#348 := [rewrite]: #710
-#410 := (iff #391 #708)
-#696 := (iff #379 true)
-#698 := (not false)
-#695 := (iff #698 true)
-#699 := [rewrite]: #695
-#420 := (iff #379 #698)
-#321 := (iff #722 false)
-#378 := (or false false)
-#703 := (iff #378 false)
-#366 := [rewrite]: #703
-#426 := (iff #722 #378)
-#369 := (iff #385 false)
-#705 := [rewrite]: #369
-#424 := (iff #720 false)
-#425 := [rewrite]: #424
-#427 := [monotonicity #425 #705]: #426
-#697 := [trans #427 #366]: #321
-#421 := [monotonicity #697]: #420
-#700 := [trans #421 #699]: #696
-#701 := (iff #390 false)
-#353 := (not true)
-#712 := (iff #353 false)
-#715 := [rewrite]: #712
-#354 := (iff #390 #353)
-#711 := (iff #716 true)
-#709 := (iff #716 #708)
-#706 := (iff #509 true)
-#707 := [rewrite]: #706
-#704 := [monotonicity #705 #707]: #709
-#713 := [trans #704 #348]: #711
-#714 := [monotonicity #713]: #354
-#702 := [trans #714 #715]: #701
-#411 := [monotonicity #702 #700]: #410
-#413 := [trans #411 #348]: #412
-#643 := [monotonicity #413 #670 #652]: #641
-#651 := [trans #643 #654]: #655
-#367 := (iff #721 false)
-#719 := (iff #721 #378)
-#382 := (iff #725 false)
-#718 := [rewrite]: #382
-#717 := (iff #726 false)
-#377 := [rewrite]: #717
-#362 := [monotonicity #377 #718]: #719
-#368 := [trans #362 #366]: #367
-#646 := [monotonicity #368 #651]: #645
-#649 := [trans #646 #648]: #642
-#639 := [monotonicity #649]: #638
-#626 := [trans #639 #640]: #638
-#637 := [quant-inst]: #636
-#627 := [mp #637 #626]: #634
-[unit-resolution #627 #734 #170]: false
-unsat
-297aa7cb47f4ebcdd849638dea24e69f28ead5a8 318 0
+d1d3ed08ad0798f8a72c82292b749840ff9d745d 318 0
 #2 := false
 #11 := 0::int
 decl f4 :: (-> int int int)
@@ -34842,332 +37787,7 @@
 #588 := [mp #587 #586]: #537
 [unit-resolution #588 #766 #194]: false
 unsat
-5b0e88fc80a274fa3e863e03464470bfb173c5f7 324 0
-#2 := false
-#68 := -1::int
-decl f3 :: (-> int int int)
-#172 := -3::int
-#38 := 1::int
-#175 := (f3 1::int -3::int)
-#180 := (= #175 -1::int)
-#193 := (not #180)
-#42 := (- 1::int)
-#39 := 3::int
-#40 := (- 3::int)
-#41 := (f3 1::int #40)
-#43 := (= #41 #42)
-#44 := (not #43)
-#196 := (iff #44 #193)
-#183 := (= -1::int #175)
-#188 := (not #183)
-#194 := (iff #188 #193)
-#191 := (iff #183 #180)
-#192 := [rewrite]: #191
-#195 := [monotonicity #192]: #194
-#189 := (iff #44 #188)
-#186 := (iff #43 #183)
-#184 := (iff #180 #183)
-#185 := [rewrite]: #184
-#181 := (iff #43 #180)
-#178 := (= #42 -1::int)
-#179 := [rewrite]: #178
-#176 := (= #41 #175)
-#173 := (= #40 -3::int)
-#174 := [rewrite]: #173
-#177 := [monotonicity #174]: #176
-#182 := [monotonicity #177 #179]: #181
-#187 := [trans #182 #185]: #186
-#190 := [monotonicity #187]: #189
-#197 := [trans #190 #195]: #196
-#171 := [asserted]: #44
-#198 := [mp #171 #197]: #193
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#756 := (pattern #10)
-#11 := 0::int
-#72 := (* -1::int #9)
-#69 := (* -1::int #8)
-#75 := (div #69 #72)
-#259 := (* -1::int #75)
-#260 := (+ #10 #259)
-#261 := (= #260 0::int)
-#21 := (div #8 #9)
-#256 := (* -1::int #21)
-#257 := (+ #10 #256)
-#258 := (= #257 0::int)
-#94 := (<= #9 0::int)
-#90 := (<= #8 0::int)
-#214 := (or #90 #94)
-#215 := (not #214)
-#101 := (>= #8 0::int)
-#206 := (or #94 #101)
-#207 := (not #206)
-#221 := (or #207 #215)
-#262 := (ite #221 #258 #261)
-#255 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#263 := (ite #14 #255 #262)
-#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
-#266 := (forall (vars (?v0 int) (?v1 int)) #263)
-#760 := (iff #266 #757)
-#758 := (iff #263 #263)
-#759 := [refl]: #758
-#761 := [quant-intro #759]: #760
-#226 := (ite #221 #21 #75)
-#229 := (ite #14 0::int #226)
-#232 := (= #10 #229)
-#235 := (forall (vars (?v0 int) (?v1 int)) #232)
-#267 := (iff #235 #266)
-#264 := (iff #232 #263)
-#265 := [rewrite]: #264
-#268 := [quant-intro #265]: #267
-#102 := (not #101)
-#95 := (not #94)
-#105 := (and #95 #102)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#111 := (ite #108 #21 #75)
-#114 := (ite #14 0::int #111)
-#117 := (= #10 #114)
-#120 := (forall (vars (?v0 int) (?v1 int)) #117)
-#236 := (iff #120 #235)
-#233 := (iff #117 #232)
-#230 := (= #114 #229)
-#227 := (= #111 #226)
-#224 := (iff #108 #221)
-#218 := (or #215 #207)
-#222 := (iff #218 #221)
-#223 := [rewrite]: #222
-#219 := (iff #108 #218)
-#216 := (iff #105 #207)
-#217 := [rewrite]: #216
-#204 := (iff #98 #215)
-#205 := [rewrite]: #204
-#220 := [monotonicity #205 #217]: #219
-#225 := [trans #220 #223]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [quant-intro #234]: #236
-#210 := (~ #120 #120)
-#208 := (~ #117 #117)
-#209 := [refl]: #208
-#211 := [nnf-pos #209]: #210
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#123 := (iff #28 #120)
-#62 := (and #16 #18)
-#65 := (or #17 #62)
-#78 := (ite #65 #21 #75)
-#81 := (ite #14 0::int #78)
-#84 := (= #10 #81)
-#87 := (forall (vars (?v0 int) (?v1 int)) #84)
-#121 := (iff #87 #120)
-#118 := (iff #84 #117)
-#115 := (= #81 #114)
-#112 := (= #78 #111)
-#109 := (iff #65 #108)
-#106 := (iff #62 #105)
-#103 := (iff #18 #102)
-#104 := [rewrite]: #103
-#96 := (iff #16 #95)
-#97 := [rewrite]: #96
-#107 := [monotonicity #97 #104]: #106
-#99 := (iff #17 #98)
-#92 := (iff #15 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [monotonicity #116]: #118
-#122 := [quant-intro #119]: #121
-#88 := (iff #28 #87)
-#85 := (iff #27 #84)
-#82 := (= #26 #81)
-#79 := (= #25 #78)
-#76 := (= #24 #75)
-#73 := (= #23 #72)
-#74 := [rewrite]: #73
-#70 := (= #22 #69)
-#71 := [rewrite]: #70
-#77 := [monotonicity #71 #74]: #76
-#66 := (iff #20 #65)
-#63 := (iff #19 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#80 := [monotonicity #67 #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [monotonicity #83]: #85
-#89 := [quant-intro #86]: #88
-#124 := [trans #89 #122]: #123
-#61 := [asserted]: #28
-#125 := [mp #61 #124]: #120
-#201 := [mp~ #125 #211]: #120
-#238 := [mp #201 #237]: #235
-#269 := [mp #238 #268]: #266
-#762 := [mp #269 #761]: #757
-#672 := (not #757)
-#669 := (or #672 #180)
-#343 := (* -1::int -3::int)
-#427 := (* -1::int 1::int)
-#428 := (div #427 #343)
-#429 := (* -1::int #428)
-#420 := (+ #175 #429)
-#431 := (= #420 0::int)
-#432 := (div 1::int -3::int)
-#433 := (* -1::int #432)
-#430 := (+ #175 #433)
-#434 := (= #430 0::int)
-#413 := (<= -3::int 0::int)
-#748 := (<= 1::int 0::int)
-#750 := (or #748 #413)
-#407 := (not #750)
-#537 := (>= 1::int 0::int)
-#744 := (or #413 #537)
-#418 := (not #744)
-#419 := (or #418 #407)
-#751 := (ite #419 #434 #431)
-#752 := (= #175 0::int)
-#753 := (= -3::int 0::int)
-#754 := (= 1::int 0::int)
-#749 := (or #754 #753)
-#755 := (ite #749 #752 #751)
-#671 := (or #672 #755)
-#682 := (iff #671 #669)
-#679 := (iff #669 #669)
-#684 := [rewrite]: #679
-#678 := (iff #755 #180)
-#585 := (ite false #752 #180)
-#595 := (iff #585 #180)
-#596 := [rewrite]: #595
-#687 := (iff #755 #585)
-#597 := (iff #751 #180)
-#593 := (iff #751 #585)
-#591 := (iff #431 #180)
-#580 := (+ 1::int #175)
-#685 := (= #580 0::int)
-#574 := (iff #685 #180)
-#589 := [rewrite]: #574
-#686 := (iff #431 #685)
-#688 := (= #420 #580)
-#694 := (+ #175 1::int)
-#581 := (= #694 #580)
-#540 := [rewrite]: #581
-#697 := (= #420 #694)
-#695 := (= #429 1::int)
-#536 := (* -1::int -1::int)
-#692 := (= #536 1::int)
-#693 := [rewrite]: #692
-#538 := (= #429 #536)
-#700 := (= #428 -1::int)
-#704 := (div -1::int 3::int)
-#705 := (= #704 -1::int)
-#706 := [rewrite]: #705
-#698 := (= #428 #704)
-#702 := (= #343 3::int)
-#703 := [rewrite]: #702
-#559 := (= #427 -1::int)
-#701 := [rewrite]: #559
-#699 := [monotonicity #701 #703]: #698
-#707 := [trans #699 #706]: #700
-#539 := [monotonicity #707]: #538
-#696 := [trans #539 #693]: #695
-#579 := [monotonicity #696]: #697
-#590 := [trans #579 #540]: #688
-#689 := [monotonicity #590]: #686
-#592 := [trans #689 #589]: #591
-#557 := (iff #434 #752)
-#710 := (= #430 #175)
-#713 := (+ #175 0::int)
-#714 := (= #713 #175)
-#715 := [rewrite]: #714
-#708 := (= #430 #713)
-#711 := (= #433 0::int)
-#435 := (* -1::int 0::int)
-#718 := (= #435 0::int)
-#722 := [rewrite]: #718
-#717 := (= #433 #435)
-#719 := (= #432 0::int)
-#720 := [rewrite]: #719
-#721 := [monotonicity #720]: #717
-#712 := [trans #721 #722]: #711
-#709 := [monotonicity #712]: #708
-#716 := [trans #709 #715]: #710
-#558 := [monotonicity #716]: #557
-#440 := (iff #419 false)
-#406 := (or false false)
-#731 := (iff #406 false)
-#394 := [rewrite]: #731
-#438 := (iff #419 #406)
-#724 := (iff #407 false)
-#1 := true
-#381 := (not true)
-#740 := (iff #381 false)
-#743 := [rewrite]: #740
-#723 := (iff #407 #381)
-#448 := (iff #750 true)
-#454 := (or false true)
-#725 := (iff #454 true)
-#726 := [rewrite]: #725
-#455 := (iff #750 #454)
-#397 := (iff #413 true)
-#733 := [rewrite]: #397
-#452 := (iff #748 false)
-#453 := [rewrite]: #452
-#349 := [monotonicity #453 #733]: #455
-#449 := [trans #349 #726]: #448
-#727 := [monotonicity #449]: #723
-#728 := [trans #727 #743]: #724
-#729 := (iff #418 false)
-#382 := (iff #418 #381)
-#739 := (iff #744 true)
-#736 := (or true true)
-#738 := (iff #736 true)
-#376 := [rewrite]: #738
-#737 := (iff #744 #736)
-#734 := (iff #537 true)
-#735 := [rewrite]: #734
-#732 := [monotonicity #733 #735]: #737
-#741 := [trans #732 #376]: #739
-#742 := [monotonicity #741]: #382
-#730 := [trans #742 #743]: #729
-#439 := [monotonicity #730 #728]: #438
-#441 := [trans #439 #394]: #440
-#594 := [monotonicity #441 #558 #592]: #593
-#690 := [trans #594 #596]: #597
-#395 := (iff #749 false)
-#747 := (iff #749 #406)
-#410 := (iff #753 false)
-#746 := [rewrite]: #410
-#745 := (iff #754 false)
-#405 := [rewrite]: #745
-#390 := [monotonicity #405 #746]: #747
-#396 := [trans #390 #394]: #395
-#691 := [monotonicity #396 #690]: #687
-#680 := [trans #691 #596]: #678
-#683 := [monotonicity #680]: #682
-#673 := [trans #683 #684]: #682
-#681 := [quant-inst]: #671
-#674 := [mp #681 #673]: #669
-[unit-resolution #674 #762 #198]: false
-unsat
-c6240466c20be0ec4a8775881ce8a00f5857e767 322 0
+25cc4c546e6d40b419a9367ee8726016c3237aaf 322 0
 #2 := false
 #38 := 1::int
 decl f4 :: (-> int int int)
@@ -35490,658 +38110,7 @@
 #642 := [mp #654 #658]: #660
 [unit-resolution #642 #750 #169]: false
 unsat
-6267f0b993e2728f85ea31149fbe98cf106912d9 323 0
-#2 := false
-#68 := -1::int
-decl f3 :: (-> int int int)
-#172 := -3::int
-#38 := 3::int
-#175 := (f3 3::int -3::int)
-#180 := (= #175 -1::int)
-#193 := (not #180)
-#41 := 1::int
-#42 := (- 1::int)
-#39 := (- 3::int)
-#40 := (f3 3::int #39)
-#43 := (= #40 #42)
-#44 := (not #43)
-#196 := (iff #44 #193)
-#183 := (= -1::int #175)
-#188 := (not #183)
-#194 := (iff #188 #193)
-#191 := (iff #183 #180)
-#192 := [rewrite]: #191
-#195 := [monotonicity #192]: #194
-#189 := (iff #44 #188)
-#186 := (iff #43 #183)
-#184 := (iff #180 #183)
-#185 := [rewrite]: #184
-#181 := (iff #43 #180)
-#178 := (= #42 -1::int)
-#179 := [rewrite]: #178
-#176 := (= #40 #175)
-#173 := (= #39 -3::int)
-#174 := [rewrite]: #173
-#177 := [monotonicity #174]: #176
-#182 := [monotonicity #177 #179]: #181
-#187 := [trans #182 #185]: #186
-#190 := [monotonicity #187]: #189
-#197 := [trans #190 #195]: #196
-#171 := [asserted]: #44
-#198 := [mp #171 #197]: #193
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#756 := (pattern #10)
-#11 := 0::int
-#72 := (* -1::int #9)
-#69 := (* -1::int #8)
-#75 := (div #69 #72)
-#259 := (* -1::int #75)
-#260 := (+ #10 #259)
-#261 := (= #260 0::int)
-#21 := (div #8 #9)
-#256 := (* -1::int #21)
-#257 := (+ #10 #256)
-#258 := (= #257 0::int)
-#94 := (<= #9 0::int)
-#90 := (<= #8 0::int)
-#214 := (or #90 #94)
-#215 := (not #214)
-#101 := (>= #8 0::int)
-#206 := (or #94 #101)
-#207 := (not #206)
-#221 := (or #207 #215)
-#262 := (ite #221 #258 #261)
-#255 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#263 := (ite #14 #255 #262)
-#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
-#266 := (forall (vars (?v0 int) (?v1 int)) #263)
-#760 := (iff #266 #757)
-#758 := (iff #263 #263)
-#759 := [refl]: #758
-#761 := [quant-intro #759]: #760
-#226 := (ite #221 #21 #75)
-#229 := (ite #14 0::int #226)
-#232 := (= #10 #229)
-#235 := (forall (vars (?v0 int) (?v1 int)) #232)
-#267 := (iff #235 #266)
-#264 := (iff #232 #263)
-#265 := [rewrite]: #264
-#268 := [quant-intro #265]: #267
-#102 := (not #101)
-#95 := (not #94)
-#105 := (and #95 #102)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#111 := (ite #108 #21 #75)
-#114 := (ite #14 0::int #111)
-#117 := (= #10 #114)
-#120 := (forall (vars (?v0 int) (?v1 int)) #117)
-#236 := (iff #120 #235)
-#233 := (iff #117 #232)
-#230 := (= #114 #229)
-#227 := (= #111 #226)
-#224 := (iff #108 #221)
-#218 := (or #215 #207)
-#222 := (iff #218 #221)
-#223 := [rewrite]: #222
-#219 := (iff #108 #218)
-#216 := (iff #105 #207)
-#217 := [rewrite]: #216
-#204 := (iff #98 #215)
-#205 := [rewrite]: #204
-#220 := [monotonicity #205 #217]: #219
-#225 := [trans #220 #223]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [quant-intro #234]: #236
-#210 := (~ #120 #120)
-#208 := (~ #117 #117)
-#209 := [refl]: #208
-#211 := [nnf-pos #209]: #210
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#123 := (iff #28 #120)
-#62 := (and #16 #18)
-#65 := (or #17 #62)
-#78 := (ite #65 #21 #75)
-#81 := (ite #14 0::int #78)
-#84 := (= #10 #81)
-#87 := (forall (vars (?v0 int) (?v1 int)) #84)
-#121 := (iff #87 #120)
-#118 := (iff #84 #117)
-#115 := (= #81 #114)
-#112 := (= #78 #111)
-#109 := (iff #65 #108)
-#106 := (iff #62 #105)
-#103 := (iff #18 #102)
-#104 := [rewrite]: #103
-#96 := (iff #16 #95)
-#97 := [rewrite]: #96
-#107 := [monotonicity #97 #104]: #106
-#99 := (iff #17 #98)
-#92 := (iff #15 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [monotonicity #116]: #118
-#122 := [quant-intro #119]: #121
-#88 := (iff #28 #87)
-#85 := (iff #27 #84)
-#82 := (= #26 #81)
-#79 := (= #25 #78)
-#76 := (= #24 #75)
-#73 := (= #23 #72)
-#74 := [rewrite]: #73
-#70 := (= #22 #69)
-#71 := [rewrite]: #70
-#77 := [monotonicity #71 #74]: #76
-#66 := (iff #20 #65)
-#63 := (iff #19 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#80 := [monotonicity #67 #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [monotonicity #83]: #85
-#89 := [quant-intro #86]: #88
-#124 := [trans #89 #122]: #123
-#61 := [asserted]: #28
-#125 := [mp #61 #124]: #120
-#201 := [mp~ #125 #211]: #120
-#238 := [mp #201 #237]: #235
-#269 := [mp #238 #268]: #266
-#762 := [mp #269 #761]: #757
-#680 := (not #757)
-#672 := (or #680 #180)
-#343 := (* -1::int -3::int)
-#427 := (* -1::int 3::int)
-#428 := (div #427 #343)
-#429 := (* -1::int #428)
-#420 := (+ #175 #429)
-#431 := (= #420 0::int)
-#432 := (div 3::int -3::int)
-#433 := (* -1::int #432)
-#430 := (+ #175 #433)
-#434 := (= #430 0::int)
-#413 := (<= -3::int 0::int)
-#748 := (<= 3::int 0::int)
-#750 := (or #748 #413)
-#407 := (not #750)
-#537 := (>= 3::int 0::int)
-#744 := (or #413 #537)
-#418 := (not #744)
-#419 := (or #418 #407)
-#751 := (ite #419 #434 #431)
-#752 := (= #175 0::int)
-#753 := (= -3::int 0::int)
-#754 := (= 3::int 0::int)
-#749 := (or #754 #753)
-#755 := (ite #749 #752 #751)
-#669 := (or #680 #755)
-#681 := (iff #669 #672)
-#683 := (iff #672 #672)
-#679 := [rewrite]: #683
-#691 := (iff #755 #180)
-#595 := (ite false #752 #180)
-#690 := (iff #595 #180)
-#687 := [rewrite]: #690
-#596 := (iff #755 #595)
-#593 := (iff #751 #180)
-#574 := (ite false #180 #180)
-#592 := (iff #574 #180)
-#585 := [rewrite]: #592
-#589 := (iff #751 #574)
-#686 := (iff #431 #180)
-#714 := (+ 1::int #175)
-#558 := (= #714 0::int)
-#702 := (iff #558 #180)
-#703 := [rewrite]: #702
-#590 := (iff #431 #558)
-#540 := (= #420 #714)
-#713 := (+ #175 1::int)
-#715 := (= #713 #714)
-#710 := [rewrite]: #715
-#580 := (= #420 #713)
-#697 := (= #429 1::int)
-#435 := (* -1::int -1::int)
-#718 := (= #435 1::int)
-#722 := [rewrite]: #718
-#696 := (= #429 #435)
-#693 := (= #428 -1::int)
-#707 := (div -3::int 3::int)
-#539 := (= #707 -1::int)
-#692 := [rewrite]: #539
-#536 := (= #428 #707)
-#706 := (= #343 3::int)
-#700 := [rewrite]: #706
-#699 := (= #427 -3::int)
-#705 := [rewrite]: #699
-#538 := [monotonicity #705 #700]: #536
-#695 := [trans #538 #692]: #693
-#694 := [monotonicity #695]: #696
-#579 := [trans #694 #722]: #697
-#581 := [monotonicity #579]: #580
-#688 := [trans #581 #710]: #540
-#685 := [monotonicity #688]: #590
-#689 := [trans #685 #703]: #686
-#704 := (iff #434 #180)
-#559 := (iff #434 #558)
-#716 := (= #430 #714)
-#708 := (= #430 #713)
-#711 := (= #433 1::int)
-#717 := (= #433 #435)
-#719 := (= #432 -1::int)
-#720 := [rewrite]: #719
-#721 := [monotonicity #720]: #717
-#712 := [trans #721 #722]: #711
-#709 := [monotonicity #712]: #708
-#557 := [trans #709 #710]: #716
-#701 := [monotonicity #557]: #559
-#698 := [trans #701 #703]: #704
-#440 := (iff #419 false)
-#406 := (or false false)
-#731 := (iff #406 false)
-#394 := [rewrite]: #731
-#438 := (iff #419 #406)
-#724 := (iff #407 false)
-#1 := true
-#381 := (not true)
-#740 := (iff #381 false)
-#743 := [rewrite]: #740
-#723 := (iff #407 #381)
-#448 := (iff #750 true)
-#454 := (or false true)
-#725 := (iff #454 true)
-#726 := [rewrite]: #725
-#455 := (iff #750 #454)
-#397 := (iff #413 true)
-#733 := [rewrite]: #397
-#452 := (iff #748 false)
-#453 := [rewrite]: #452
-#349 := [monotonicity #453 #733]: #455
-#449 := [trans #349 #726]: #448
-#727 := [monotonicity #449]: #723
-#728 := [trans #727 #743]: #724
-#729 := (iff #418 false)
-#382 := (iff #418 #381)
-#739 := (iff #744 true)
-#736 := (or true true)
-#738 := (iff #736 true)
-#376 := [rewrite]: #738
-#737 := (iff #744 #736)
-#734 := (iff #537 true)
-#735 := [rewrite]: #734
-#732 := [monotonicity #733 #735]: #737
-#741 := [trans #732 #376]: #739
-#742 := [monotonicity #741]: #382
-#730 := [trans #742 #743]: #729
-#439 := [monotonicity #730 #728]: #438
-#441 := [trans #439 #394]: #440
-#591 := [monotonicity #441 #698 #689]: #589
-#594 := [trans #591 #585]: #593
-#395 := (iff #749 false)
-#747 := (iff #749 #406)
-#410 := (iff #753 false)
-#746 := [rewrite]: #410
-#745 := (iff #754 false)
-#405 := [rewrite]: #745
-#390 := [monotonicity #405 #746]: #747
-#396 := [trans #390 #394]: #395
-#597 := [monotonicity #396 #594]: #596
-#678 := [trans #597 #687]: #691
-#682 := [monotonicity #678]: #681
-#684 := [trans #682 #679]: #681
-#671 := [quant-inst]: #669
-#673 := [mp #671 #684]: #672
-[unit-resolution #673 #762 #198]: false
-unsat
-ab3ee722b1a4b13d571e9569335a5a4521f8479c 326 0
-#2 := false
-#179 := -2::int
-decl f3 :: (-> int int int)
-#173 := -3::int
-#38 := 5::int
-#176 := (f3 5::int -3::int)
-#182 := (= #176 -2::int)
-#185 := (not #182)
-#42 := 2::int
-#43 := (- 2::int)
-#39 := 3::int
-#40 := (- 3::int)
-#41 := (f3 5::int #40)
-#44 := (= #41 #43)
-#45 := (not #44)
-#186 := (iff #45 #185)
-#183 := (iff #44 #182)
-#180 := (= #43 -2::int)
-#181 := [rewrite]: #180
-#177 := (= #41 #176)
-#174 := (= #40 -3::int)
-#175 := [rewrite]: #174
-#178 := [monotonicity #175]: #177
-#184 := [monotonicity #178 #181]: #183
-#187 := [monotonicity #184]: #186
-#172 := [asserted]: #45
-#190 := [mp #172 #187]: #185
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#747 := (pattern #10)
-#11 := 0::int
-#69 := -1::int
-#73 := (* -1::int #9)
-#70 := (* -1::int #8)
-#76 := (div #70 #73)
-#249 := (* -1::int #76)
-#250 := (+ #10 #249)
-#251 := (= #250 0::int)
-#21 := (div #8 #9)
-#246 := (* -1::int #21)
-#247 := (+ #10 #246)
-#248 := (= #247 0::int)
-#95 := (<= #9 0::int)
-#91 := (<= #8 0::int)
-#204 := (or #91 #95)
-#205 := (not #204)
-#102 := (>= #8 0::int)
-#196 := (or #95 #102)
-#197 := (not #196)
-#211 := (or #197 #205)
-#252 := (ite #211 #248 #251)
-#245 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#253 := (ite #14 #245 #252)
-#748 := (forall (vars (?v0 int) (?v1 int)) (:pat #747) #253)
-#256 := (forall (vars (?v0 int) (?v1 int)) #253)
-#751 := (iff #256 #748)
-#749 := (iff #253 #253)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#216 := (ite #211 #21 #76)
-#219 := (ite #14 0::int #216)
-#222 := (= #10 #219)
-#225 := (forall (vars (?v0 int) (?v1 int)) #222)
-#257 := (iff #225 #256)
-#254 := (iff #222 #253)
-#255 := [rewrite]: #254
-#258 := [quant-intro #255]: #257
-#103 := (not #102)
-#96 := (not #95)
-#106 := (and #96 #103)
-#92 := (not #91)
-#99 := (and #92 #96)
-#109 := (or #99 #106)
-#112 := (ite #109 #21 #76)
-#115 := (ite #14 0::int #112)
-#118 := (= #10 #115)
-#121 := (forall (vars (?v0 int) (?v1 int)) #118)
-#226 := (iff #121 #225)
-#223 := (iff #118 #222)
-#220 := (= #115 #219)
-#217 := (= #112 #216)
-#214 := (iff #109 #211)
-#208 := (or #205 #197)
-#212 := (iff #208 #211)
-#213 := [rewrite]: #212
-#209 := (iff #109 #208)
-#206 := (iff #106 #197)
-#207 := [rewrite]: #206
-#194 := (iff #99 #205)
-#195 := [rewrite]: #194
-#210 := [monotonicity #195 #207]: #209
-#215 := [trans #210 #213]: #214
-#218 := [monotonicity #215]: #217
-#221 := [monotonicity #218]: #220
-#224 := [monotonicity #221]: #223
-#227 := [quant-intro #224]: #226
-#200 := (~ #121 #121)
-#198 := (~ #118 #118)
-#199 := [refl]: #198
-#201 := [nnf-pos #199]: #200
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#124 := (iff #28 #121)
-#63 := (and #16 #18)
-#66 := (or #17 #63)
-#79 := (ite #66 #21 #76)
-#82 := (ite #14 0::int #79)
-#85 := (= #10 #82)
-#88 := (forall (vars (?v0 int) (?v1 int)) #85)
-#122 := (iff #88 #121)
-#119 := (iff #85 #118)
-#116 := (= #82 #115)
-#113 := (= #79 #112)
-#110 := (iff #66 #109)
-#107 := (iff #63 #106)
-#104 := (iff #18 #103)
-#105 := [rewrite]: #104
-#97 := (iff #16 #96)
-#98 := [rewrite]: #97
-#108 := [monotonicity #98 #105]: #107
-#100 := (iff #17 #99)
-#93 := (iff #15 #92)
-#94 := [rewrite]: #93
-#101 := [monotonicity #94 #98]: #100
-#111 := [monotonicity #101 #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [monotonicity #117]: #119
-#123 := [quant-intro #120]: #122
-#89 := (iff #28 #88)
-#86 := (iff #27 #85)
-#83 := (= #26 #82)
-#80 := (= #25 #79)
-#77 := (= #24 #76)
-#74 := (= #23 #73)
-#75 := [rewrite]: #74
-#71 := (= #22 #70)
-#72 := [rewrite]: #71
-#78 := [monotonicity #72 #75]: #77
-#67 := (iff #20 #66)
-#64 := (iff #19 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#81 := [monotonicity #68 #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [monotonicity #84]: #86
-#90 := [quant-intro #87]: #89
-#125 := [trans #90 #123]: #124
-#62 := [asserted]: #28
-#126 := [mp #62 #125]: #121
-#191 := [mp~ #126 #201]: #121
-#228 := [mp #191 #227]: #225
-#259 := [mp #228 #258]: #256
-#753 := [mp #259 #752]: #748
-#667 := (not #748)
-#661 := (or #667 #182)
-#333 := (* -1::int -3::int)
-#418 := (* -1::int 5::int)
-#419 := (div #418 #333)
-#420 := (* -1::int #419)
-#411 := (+ #176 #420)
-#422 := (= #411 0::int)
-#423 := (div 5::int -3::int)
-#351 := (* -1::int #423)
-#424 := (+ #176 #351)
-#421 := (= #424 0::int)
-#425 := (<= -3::int 0::int)
-#404 := (<= 5::int 0::int)
-#739 := (or #404 #425)
-#741 := (not #739)
-#398 := (>= 5::int 0::int)
-#528 := (or #425 #398)
-#735 := (not #528)
-#409 := (or #735 #741)
-#410 := (ite #409 #421 #422)
-#742 := (= #176 0::int)
-#743 := (= -3::int 0::int)
-#744 := (= 5::int 0::int)
-#745 := (or #744 #743)
-#740 := (ite #745 #742 #410)
-#668 := (or #667 #740)
-#653 := (iff #668 #661)
-#656 := (iff #661 #661)
-#657 := [rewrite]: #656
-#665 := (iff #740 #182)
-#673 := (ite false #742 #182)
-#675 := (iff #673 #182)
-#664 := [rewrite]: #675
-#674 := (iff #740 #673)
-#662 := (iff #410 #182)
-#693 := (= #176 -1::int)
-#682 := (ite false #693 #182)
-#663 := (iff #682 #182)
-#660 := [rewrite]: #663
-#669 := (iff #410 #682)
-#681 := (iff #422 #182)
-#565 := (+ 2::int #176)
-#584 := (= #565 0::int)
-#587 := (iff #584 #182)
-#588 := [rewrite]: #587
-#585 := (iff #422 #584)
-#583 := (= #411 #565)
-#676 := (+ #176 2::int)
-#580 := (= #676 #565)
-#582 := [rewrite]: #580
-#677 := (= #411 #676)
-#679 := (= #420 2::int)
-#688 := (* -1::int -2::int)
-#572 := (= #688 2::int)
-#531 := [rewrite]: #572
-#570 := (= #420 #688)
-#687 := (= #419 -2::int)
-#696 := -5::int
-#529 := (div -5::int 3::int)
-#684 := (= #529 -2::int)
-#686 := [rewrite]: #684
-#530 := (= #419 #529)
-#698 := (= #333 3::int)
-#527 := [rewrite]: #698
-#697 := (= #418 -5::int)
-#691 := [rewrite]: #697
-#683 := [monotonicity #691 #527]: #530
-#685 := [trans #683 #686]: #687
-#571 := [monotonicity #685]: #570
-#581 := [trans #571 #531]: #679
-#680 := [monotonicity #581]: #677
-#576 := [trans #680 #582]: #583
-#586 := [monotonicity #576]: #585
-#678 := [trans #586 #588]: #681
-#689 := (iff #421 #693)
-#712 := 1::int
-#705 := (+ 1::int #176)
-#549 := (= #705 0::int)
-#694 := (iff #549 #693)
-#695 := [rewrite]: #694
-#550 := (iff #421 #549)
-#707 := (= #424 #705)
-#704 := (+ #176 1::int)
-#706 := (= #704 #705)
-#701 := [rewrite]: #706
-#699 := (= #424 #704)
-#702 := (= #351 1::int)
-#711 := (* -1::int -1::int)
-#709 := (= #711 1::int)
-#713 := [rewrite]: #709
-#426 := (= #351 #711)
-#432 := (= #423 -1::int)
-#710 := [rewrite]: #432
-#708 := [monotonicity #710]: #426
-#703 := [trans #708 #713]: #702
-#700 := [monotonicity #703]: #699
-#548 := [trans #700 #701]: #707
-#692 := [monotonicity #548]: #550
-#690 := [trans #692 #695]: #689
-#430 := (iff #409 false)
-#737 := (or false false)
-#381 := (iff #737 false)
-#722 := [rewrite]: #381
-#719 := (iff #409 #737)
-#718 := (iff #741 false)
-#1 := true
-#732 := (not true)
-#733 := (iff #732 false)
-#731 := [rewrite]: #733
-#440 := (iff #741 #732)
-#717 := (iff #739 true)
-#444 := (or false true)
-#339 := (iff #444 true)
-#716 := [rewrite]: #339
-#445 := (iff #739 #444)
-#387 := (iff #425 true)
-#388 := [rewrite]: #387
-#721 := (iff #404 false)
-#443 := [rewrite]: #721
-#446 := [monotonicity #443 #388]: #445
-#439 := [trans #446 #716]: #717
-#714 := [monotonicity #439]: #440
-#715 := [trans #714 #731]: #718
-#734 := (iff #735 false)
-#372 := (iff #735 #732)
-#367 := (iff #528 true)
-#726 := (or true true)
-#723 := (iff #726 true)
-#729 := [rewrite]: #723
-#727 := (iff #528 #726)
-#724 := (iff #398 true)
-#725 := [rewrite]: #724
-#728 := [monotonicity #388 #725]: #727
-#730 := [trans #728 #729]: #367
-#373 := [monotonicity #730]: #372
-#720 := [trans #373 #731]: #734
-#429 := [monotonicity #720 #715]: #719
-#431 := [trans #429 #722]: #430
-#671 := [monotonicity #431 #690 #678]: #669
-#672 := [trans #671 #660]: #662
-#385 := (iff #745 false)
-#397 := (iff #745 #737)
-#396 := (iff #743 false)
-#401 := [rewrite]: #396
-#746 := (iff #744 false)
-#736 := [rewrite]: #746
-#738 := [monotonicity #736 #401]: #397
-#386 := [trans #738 #722]: #385
-#670 := [monotonicity #386 #672]: #674
-#666 := [trans #670 #664]: #665
-#655 := [monotonicity #666]: #653
-#658 := [trans #655 #657]: #653
-#652 := [quant-inst]: #668
-#654 := [mp #652 #658]: #661
-[unit-resolution #654 #753 #190]: false
-unsat
-289a94002efb27d5f9eb28105782f378a655ffff 297 0
+6cc6bcae732930b666a4886edd2cc45bd9e12201 297 0
 #2 := false
 #11 := 0::int
 decl f4 :: (-> int int int)
@@ -36439,329 +38408,7 @@
 #576 := [mp #570 #575]: #670
 [unit-resolution #576 #750 #168]: false
 unsat
-df3c3180cbba903cfcccf082cba5dc63ba7e5462 321 0
-#2 := false
-#67 := -1::int
-decl f3 :: (-> int int int)
-#40 := 3::int
-#173 := (f3 -1::int 3::int)
-#176 := (= #173 -1::int)
-#189 := (not #176)
-#38 := 1::int
-#39 := (- 1::int)
-#41 := (f3 #39 3::int)
-#42 := (= #41 #39)
-#43 := (not #42)
-#192 := (iff #43 #189)
-#179 := (= -1::int #173)
-#184 := (not #179)
-#190 := (iff #184 #189)
-#187 := (iff #179 #176)
-#188 := [rewrite]: #187
-#191 := [monotonicity #188]: #190
-#185 := (iff #43 #184)
-#182 := (iff #42 #179)
-#180 := (iff #176 #179)
-#181 := [rewrite]: #180
-#177 := (iff #42 #176)
-#171 := (= #39 -1::int)
-#172 := [rewrite]: #171
-#174 := (= #41 #173)
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175 #172]: #177
-#183 := [trans #178 #181]: #182
-#186 := [monotonicity #183]: #185
-#193 := [trans #186 #191]: #192
-#170 := [asserted]: #43
-#194 := [mp #170 #193]: #189
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#752 := (pattern #10)
-#11 := 0::int
-#71 := (* -1::int #9)
-#68 := (* -1::int #8)
-#74 := (div #68 #71)
-#255 := (* -1::int #74)
-#256 := (+ #10 #255)
-#257 := (= #256 0::int)
-#21 := (div #8 #9)
-#252 := (* -1::int #21)
-#253 := (+ #10 #252)
-#254 := (= #253 0::int)
-#93 := (<= #9 0::int)
-#89 := (<= #8 0::int)
-#210 := (or #89 #93)
-#211 := (not #210)
-#100 := (>= #8 0::int)
-#202 := (or #93 #100)
-#203 := (not #202)
-#217 := (or #203 #211)
-#258 := (ite #217 #254 #257)
-#251 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#259 := (ite #14 #251 #258)
-#753 := (forall (vars (?v0 int) (?v1 int)) (:pat #752) #259)
-#262 := (forall (vars (?v0 int) (?v1 int)) #259)
-#756 := (iff #262 #753)
-#754 := (iff #259 #259)
-#755 := [refl]: #754
-#757 := [quant-intro #755]: #756
-#222 := (ite #217 #21 #74)
-#225 := (ite #14 0::int #222)
-#228 := (= #10 #225)
-#231 := (forall (vars (?v0 int) (?v1 int)) #228)
-#263 := (iff #231 #262)
-#260 := (iff #228 #259)
-#261 := [rewrite]: #260
-#264 := [quant-intro #261]: #263
-#101 := (not #100)
-#94 := (not #93)
-#104 := (and #94 #101)
-#90 := (not #89)
-#97 := (and #90 #94)
-#107 := (or #97 #104)
-#110 := (ite #107 #21 #74)
-#113 := (ite #14 0::int #110)
-#116 := (= #10 #113)
-#119 := (forall (vars (?v0 int) (?v1 int)) #116)
-#232 := (iff #119 #231)
-#229 := (iff #116 #228)
-#226 := (= #113 #225)
-#223 := (= #110 #222)
-#220 := (iff #107 #217)
-#214 := (or #211 #203)
-#218 := (iff #214 #217)
-#219 := [rewrite]: #218
-#215 := (iff #107 #214)
-#212 := (iff #104 #203)
-#213 := [rewrite]: #212
-#200 := (iff #97 #211)
-#201 := [rewrite]: #200
-#216 := [monotonicity #201 #213]: #215
-#221 := [trans #216 #219]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [quant-intro #230]: #232
-#206 := (~ #119 #119)
-#204 := (~ #116 #116)
-#205 := [refl]: #204
-#207 := [nnf-pos #205]: #206
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#122 := (iff #28 #119)
-#61 := (and #16 #18)
-#64 := (or #17 #61)
-#77 := (ite #64 #21 #74)
-#80 := (ite #14 0::int #77)
-#83 := (= #10 #80)
-#86 := (forall (vars (?v0 int) (?v1 int)) #83)
-#120 := (iff #86 #119)
-#117 := (iff #83 #116)
-#114 := (= #80 #113)
-#111 := (= #77 #110)
-#108 := (iff #64 #107)
-#105 := (iff #61 #104)
-#102 := (iff #18 #101)
-#103 := [rewrite]: #102
-#95 := (iff #16 #94)
-#96 := [rewrite]: #95
-#106 := [monotonicity #96 #103]: #105
-#98 := (iff #17 #97)
-#91 := (iff #15 #90)
-#92 := [rewrite]: #91
-#99 := [monotonicity #92 #96]: #98
-#109 := [monotonicity #99 #106]: #108
-#112 := [monotonicity #109]: #111
-#115 := [monotonicity #112]: #114
-#118 := [monotonicity #115]: #117
-#121 := [quant-intro #118]: #120
-#87 := (iff #28 #86)
-#84 := (iff #27 #83)
-#81 := (= #26 #80)
-#78 := (= #25 #77)
-#75 := (= #24 #74)
-#72 := (= #23 #71)
-#73 := [rewrite]: #72
-#69 := (= #22 #68)
-#70 := [rewrite]: #69
-#76 := [monotonicity #70 #73]: #75
-#65 := (iff #20 #64)
-#62 := (iff #19 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#79 := [monotonicity #66 #76]: #78
-#82 := [monotonicity #79]: #81
-#85 := [monotonicity #82]: #84
-#88 := [quant-intro #85]: #87
-#123 := [trans #88 #121]: #122
-#60 := [asserted]: #28
-#124 := [mp #60 #123]: #119
-#197 := [mp~ #124 #207]: #119
-#234 := [mp #197 #233]: #231
-#265 := [mp #234 #264]: #262
-#758 := [mp #265 #757]: #753
-#665 := (not #753)
-#667 := (or #665 #176)
-#339 := (* -1::int 3::int)
-#423 := (* -1::int -1::int)
-#424 := (div #423 #339)
-#425 := (* -1::int #424)
-#416 := (+ #173 #425)
-#427 := (= #416 0::int)
-#428 := (div -1::int 3::int)
-#429 := (* -1::int #428)
-#426 := (+ #173 #429)
-#430 := (= #426 0::int)
-#409 := (<= 3::int 0::int)
-#744 := (<= -1::int 0::int)
-#746 := (or #744 #409)
-#403 := (not #746)
-#533 := (>= -1::int 0::int)
-#740 := (or #409 #533)
-#414 := (not #740)
-#415 := (or #414 #403)
-#747 := (ite #415 #430 #427)
-#748 := (= #173 0::int)
-#749 := (= 3::int 0::int)
-#750 := (= -1::int 0::int)
-#745 := (or #750 #749)
-#751 := (ite #745 #748 #747)
-#677 := (or #665 #751)
-#679 := (iff #677 #667)
-#680 := (iff #667 #667)
-#669 := [rewrite]: #680
-#676 := (iff #751 #176)
-#593 := (ite false #748 #176)
-#687 := (iff #593 #176)
-#674 := [rewrite]: #687
-#686 := (iff #751 #593)
-#591 := (iff #747 #176)
-#1 := true
-#587 := (ite true #176 #748)
-#589 := (iff #587 #176)
-#590 := [rewrite]: #589
-#588 := (iff #747 #587)
-#570 := (iff #427 #748)
-#682 := (= #416 #173)
-#577 := (+ #173 0::int)
-#586 := (= #577 #173)
-#681 := [rewrite]: #586
-#536 := (= #416 #577)
-#575 := (= #425 0::int)
-#689 := (* -1::int 0::int)
-#690 := (= #689 0::int)
-#693 := [rewrite]: #690
-#691 := (= #425 #689)
-#535 := (= #424 0::int)
-#694 := -3::int
-#702 := (div 1::int -3::int)
-#532 := (= #702 0::int)
-#534 := [rewrite]: #532
-#696 := (= #424 #702)
-#695 := (= #339 -3::int)
-#701 := [rewrite]: #695
-#717 := (= #423 1::int)
-#714 := [rewrite]: #717
-#703 := [monotonicity #714 #701]: #696
-#688 := [trans #703 #534]: #535
-#692 := [monotonicity #688]: #691
-#576 := [trans #692 #693]: #575
-#684 := [monotonicity #576]: #536
-#685 := [trans #684 #681]: #682
-#585 := [monotonicity #685]: #570
-#699 := (iff #430 #176)
-#705 := (+ 1::int #173)
-#553 := (= #705 0::int)
-#697 := (iff #553 #176)
-#698 := [rewrite]: #697
-#554 := (iff #430 #553)
-#706 := (= #426 #705)
-#708 := (+ #173 1::int)
-#710 := (= #708 #705)
-#711 := [rewrite]: #710
-#709 := (= #426 #708)
-#718 := (= #429 1::int)
-#431 := (= #429 #423)
-#715 := (= #428 -1::int)
-#716 := [rewrite]: #715
-#713 := [monotonicity #716]: #431
-#707 := [trans #713 #714]: #718
-#704 := [monotonicity #707]: #709
-#712 := [trans #704 #711]: #706
-#555 := [monotonicity #712]: #554
-#700 := [trans #555 #698]: #699
-#436 := (iff #415 true)
-#726 := (or true false)
-#450 := (iff #726 true)
-#451 := [rewrite]: #450
-#434 := (iff #415 #726)
-#720 := (iff #403 false)
-#722 := (not true)
-#719 := (iff #722 false)
-#723 := [rewrite]: #719
-#444 := (iff #403 #722)
-#345 := (iff #746 true)
-#448 := (iff #746 #726)
-#393 := (iff #409 false)
-#729 := [rewrite]: #393
-#739 := (iff #744 true)
-#725 := [rewrite]: #739
-#449 := [monotonicity #725 #729]: #448
-#721 := [trans #449 #451]: #345
-#445 := [monotonicity #721]: #444
-#724 := [trans #445 #723]: #720
-#738 := (iff #414 true)
-#372 := (not false)
-#377 := (iff #372 true)
-#378 := [rewrite]: #377
-#735 := (iff #414 #372)
-#728 := (iff #740 false)
-#402 := (or false false)
-#727 := (iff #402 false)
-#390 := [rewrite]: #727
-#732 := (iff #740 #402)
-#730 := (iff #533 false)
-#731 := [rewrite]: #730
-#733 := [monotonicity #729 #731]: #732
-#734 := [trans #733 #390]: #728
-#737 := [monotonicity #734]: #735
-#736 := [trans #737 #378]: #738
-#435 := [monotonicity #736 #724]: #434
-#437 := [trans #435 #451]: #436
-#581 := [monotonicity #437 #700 #585]: #588
-#592 := [trans #581 #590]: #591
-#391 := (iff #745 false)
-#743 := (iff #745 #402)
-#406 := (iff #749 false)
-#742 := [rewrite]: #406
-#741 := (iff #750 false)
-#401 := [rewrite]: #741
-#386 := [monotonicity #401 #742]: #743
-#392 := [trans #386 #390]: #391
-#683 := [monotonicity #392 #592]: #686
-#668 := [trans #683 #674]: #676
-#675 := [monotonicity #668]: #679
-#670 := [trans #675 #669]: #679
-#678 := [quant-inst]: #677
-#671 := [mp #678 #670]: #667
-[unit-resolution #671 #758 #194]: false
-unsat
-033c174f82b5a84d7fb4bb3712b35d17f518a720 328 0
+47a460702ba45566a8d5b00684a6805c8d1bccde 328 0
 #2 := false
 #41 := 2::int
 decl f4 :: (-> int int int)
@@ -37090,331 +38737,7 @@
 #641 := [mp #635 #636]: #650
 [unit-resolution #641 #742 #170]: false
 unsat
-d42aa6984a7dce484750bcd7fd3519e7754fc33c 323 0
-#2 := false
-#68 := -1::int
-decl f3 :: (-> int int int)
-#38 := 3::int
-#172 := -3::int
-#175 := (f3 -3::int 3::int)
-#180 := (= #175 -1::int)
-#193 := (not #180)
-#41 := 1::int
-#42 := (- 1::int)
-#39 := (- 3::int)
-#40 := (f3 #39 3::int)
-#43 := (= #40 #42)
-#44 := (not #43)
-#196 := (iff #44 #193)
-#183 := (= -1::int #175)
-#188 := (not #183)
-#194 := (iff #188 #193)
-#191 := (iff #183 #180)
-#192 := [rewrite]: #191
-#195 := [monotonicity #192]: #194
-#189 := (iff #44 #188)
-#186 := (iff #43 #183)
-#184 := (iff #180 #183)
-#185 := [rewrite]: #184
-#181 := (iff #43 #180)
-#178 := (= #42 -1::int)
-#179 := [rewrite]: #178
-#176 := (= #40 #175)
-#173 := (= #39 -3::int)
-#174 := [rewrite]: #173
-#177 := [monotonicity #174]: #176
-#182 := [monotonicity #177 #179]: #181
-#187 := [trans #182 #185]: #186
-#190 := [monotonicity #187]: #189
-#197 := [trans #190 #195]: #196
-#171 := [asserted]: #44
-#198 := [mp #171 #197]: #193
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#756 := (pattern #10)
-#11 := 0::int
-#72 := (* -1::int #9)
-#69 := (* -1::int #8)
-#75 := (div #69 #72)
-#259 := (* -1::int #75)
-#260 := (+ #10 #259)
-#261 := (= #260 0::int)
-#21 := (div #8 #9)
-#256 := (* -1::int #21)
-#257 := (+ #10 #256)
-#258 := (= #257 0::int)
-#94 := (<= #9 0::int)
-#90 := (<= #8 0::int)
-#214 := (or #90 #94)
-#215 := (not #214)
-#101 := (>= #8 0::int)
-#206 := (or #94 #101)
-#207 := (not #206)
-#221 := (or #207 #215)
-#262 := (ite #221 #258 #261)
-#255 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#263 := (ite #14 #255 #262)
-#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
-#266 := (forall (vars (?v0 int) (?v1 int)) #263)
-#760 := (iff #266 #757)
-#758 := (iff #263 #263)
-#759 := [refl]: #758
-#761 := [quant-intro #759]: #760
-#226 := (ite #221 #21 #75)
-#229 := (ite #14 0::int #226)
-#232 := (= #10 #229)
-#235 := (forall (vars (?v0 int) (?v1 int)) #232)
-#267 := (iff #235 #266)
-#264 := (iff #232 #263)
-#265 := [rewrite]: #264
-#268 := [quant-intro #265]: #267
-#102 := (not #101)
-#95 := (not #94)
-#105 := (and #95 #102)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#111 := (ite #108 #21 #75)
-#114 := (ite #14 0::int #111)
-#117 := (= #10 #114)
-#120 := (forall (vars (?v0 int) (?v1 int)) #117)
-#236 := (iff #120 #235)
-#233 := (iff #117 #232)
-#230 := (= #114 #229)
-#227 := (= #111 #226)
-#224 := (iff #108 #221)
-#218 := (or #215 #207)
-#222 := (iff #218 #221)
-#223 := [rewrite]: #222
-#219 := (iff #108 #218)
-#216 := (iff #105 #207)
-#217 := [rewrite]: #216
-#204 := (iff #98 #215)
-#205 := [rewrite]: #204
-#220 := [monotonicity #205 #217]: #219
-#225 := [trans #220 #223]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [quant-intro #234]: #236
-#210 := (~ #120 #120)
-#208 := (~ #117 #117)
-#209 := [refl]: #208
-#211 := [nnf-pos #209]: #210
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#123 := (iff #28 #120)
-#62 := (and #16 #18)
-#65 := (or #17 #62)
-#78 := (ite #65 #21 #75)
-#81 := (ite #14 0::int #78)
-#84 := (= #10 #81)
-#87 := (forall (vars (?v0 int) (?v1 int)) #84)
-#121 := (iff #87 #120)
-#118 := (iff #84 #117)
-#115 := (= #81 #114)
-#112 := (= #78 #111)
-#109 := (iff #65 #108)
-#106 := (iff #62 #105)
-#103 := (iff #18 #102)
-#104 := [rewrite]: #103
-#96 := (iff #16 #95)
-#97 := [rewrite]: #96
-#107 := [monotonicity #97 #104]: #106
-#99 := (iff #17 #98)
-#92 := (iff #15 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [monotonicity #116]: #118
-#122 := [quant-intro #119]: #121
-#88 := (iff #28 #87)
-#85 := (iff #27 #84)
-#82 := (= #26 #81)
-#79 := (= #25 #78)
-#76 := (= #24 #75)
-#73 := (= #23 #72)
-#74 := [rewrite]: #73
-#70 := (= #22 #69)
-#71 := [rewrite]: #70
-#77 := [monotonicity #71 #74]: #76
-#66 := (iff #20 #65)
-#63 := (iff #19 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#80 := [monotonicity #67 #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [monotonicity #83]: #85
-#89 := [quant-intro #86]: #88
-#124 := [trans #89 #122]: #123
-#61 := [asserted]: #28
-#125 := [mp #61 #124]: #120
-#201 := [mp~ #125 #211]: #120
-#238 := [mp #201 #237]: #235
-#269 := [mp #238 #268]: #266
-#762 := [mp #269 #761]: #757
-#680 := (not #757)
-#672 := (or #680 #180)
-#343 := (* -1::int 3::int)
-#427 := (* -1::int -3::int)
-#428 := (div #427 #343)
-#429 := (* -1::int #428)
-#420 := (+ #175 #429)
-#431 := (= #420 0::int)
-#432 := (div -3::int 3::int)
-#433 := (* -1::int #432)
-#430 := (+ #175 #433)
-#434 := (= #430 0::int)
-#413 := (<= 3::int 0::int)
-#748 := (<= -3::int 0::int)
-#750 := (or #748 #413)
-#407 := (not #750)
-#537 := (>= -3::int 0::int)
-#744 := (or #413 #537)
-#418 := (not #744)
-#419 := (or #418 #407)
-#751 := (ite #419 #434 #431)
-#752 := (= #175 0::int)
-#753 := (= 3::int 0::int)
-#754 := (= -3::int 0::int)
-#749 := (or #754 #753)
-#755 := (ite #749 #752 #751)
-#669 := (or #680 #755)
-#681 := (iff #669 #672)
-#683 := (iff #672 #672)
-#679 := [rewrite]: #683
-#691 := (iff #755 #180)
-#595 := (ite false #752 #180)
-#690 := (iff #595 #180)
-#687 := [rewrite]: #690
-#596 := (iff #755 #595)
-#593 := (iff #751 #180)
-#1 := true
-#574 := (ite true #180 #180)
-#592 := (iff #574 #180)
-#585 := [rewrite]: #592
-#589 := (iff #751 #574)
-#686 := (iff #431 #180)
-#714 := (+ 1::int #175)
-#558 := (= #714 0::int)
-#702 := (iff #558 #180)
-#703 := [rewrite]: #702
-#590 := (iff #431 #558)
-#540 := (= #420 #714)
-#713 := (+ #175 1::int)
-#715 := (= #713 #714)
-#710 := [rewrite]: #715
-#580 := (= #420 #713)
-#697 := (= #429 1::int)
-#435 := (* -1::int -1::int)
-#718 := (= #435 1::int)
-#722 := [rewrite]: #718
-#696 := (= #429 #435)
-#693 := (= #428 -1::int)
-#707 := (div 3::int -3::int)
-#539 := (= #707 -1::int)
-#692 := [rewrite]: #539
-#536 := (= #428 #707)
-#706 := (= #343 -3::int)
-#700 := [rewrite]: #706
-#699 := (= #427 3::int)
-#705 := [rewrite]: #699
-#538 := [monotonicity #705 #700]: #536
-#695 := [trans #538 #692]: #693
-#694 := [monotonicity #695]: #696
-#579 := [trans #694 #722]: #697
-#581 := [monotonicity #579]: #580
-#688 := [trans #581 #710]: #540
-#685 := [monotonicity #688]: #590
-#689 := [trans #685 #703]: #686
-#704 := (iff #434 #180)
-#559 := (iff #434 #558)
-#716 := (= #430 #714)
-#708 := (= #430 #713)
-#711 := (= #433 1::int)
-#717 := (= #433 #435)
-#719 := (= #432 -1::int)
-#720 := [rewrite]: #719
-#721 := [monotonicity #720]: #717
-#712 := [trans #721 #722]: #711
-#709 := [monotonicity #712]: #708
-#557 := [trans #709 #710]: #716
-#701 := [monotonicity #557]: #559
-#698 := [trans #701 #703]: #704
-#440 := (iff #419 true)
-#730 := (or true false)
-#454 := (iff #730 true)
-#455 := [rewrite]: #454
-#438 := (iff #419 #730)
-#724 := (iff #407 false)
-#726 := (not true)
-#723 := (iff #726 false)
-#727 := [rewrite]: #723
-#448 := (iff #407 #726)
-#349 := (iff #750 true)
-#452 := (iff #750 #730)
-#397 := (iff #413 false)
-#733 := [rewrite]: #397
-#743 := (iff #748 true)
-#729 := [rewrite]: #743
-#453 := [monotonicity #729 #733]: #452
-#725 := [trans #453 #455]: #349
-#449 := [monotonicity #725]: #448
-#728 := [trans #449 #727]: #724
-#742 := (iff #418 true)
-#376 := (not false)
-#381 := (iff #376 true)
-#382 := [rewrite]: #381
-#739 := (iff #418 #376)
-#732 := (iff #744 false)
-#406 := (or false false)
-#731 := (iff #406 false)
-#394 := [rewrite]: #731
-#736 := (iff #744 #406)
-#734 := (iff #537 false)
-#735 := [rewrite]: #734
-#737 := [monotonicity #733 #735]: #736
-#738 := [trans #737 #394]: #732
-#741 := [monotonicity #738]: #739
-#740 := [trans #741 #382]: #742
-#439 := [monotonicity #740 #728]: #438
-#441 := [trans #439 #455]: #440
-#591 := [monotonicity #441 #698 #689]: #589
-#594 := [trans #591 #585]: #593
-#395 := (iff #749 false)
-#747 := (iff #749 #406)
-#410 := (iff #753 false)
-#746 := [rewrite]: #410
-#745 := (iff #754 false)
-#405 := [rewrite]: #745
-#390 := [monotonicity #405 #746]: #747
-#396 := [trans #390 #394]: #395
-#597 := [monotonicity #396 #594]: #596
-#678 := [trans #597 #687]: #691
-#682 := [monotonicity #678]: #681
-#684 := [trans #682 #679]: #681
-#671 := [quant-inst]: #669
-#673 := [mp #671 #684]: #672
-[unit-resolution #673 #762 #198]: false
-unsat
-9a87ecccd917767a2618c6aa64ea49313201d461 335 0
+de0ec7a435e7304171835bddd953950ecd5768ae 335 0
 #2 := false
 #179 := -2::int
 decl f4 :: (-> int int int)
@@ -37750,334 +39073,7 @@
 #666 := [mp #673 #665]: #671
 [unit-resolution #666 #759 #190]: false
 unsat
-ad2a6875c2ba06fc01a6747490a7bde0bd97929e 326 0
-#2 := false
-#179 := -2::int
-decl f3 :: (-> int int int)
-#40 := 3::int
-#173 := -5::int
-#176 := (f3 -5::int 3::int)
-#182 := (= #176 -2::int)
-#185 := (not #182)
-#42 := 2::int
-#43 := (- 2::int)
-#38 := 5::int
-#39 := (- 5::int)
-#41 := (f3 #39 3::int)
-#44 := (= #41 #43)
-#45 := (not #44)
-#186 := (iff #45 #185)
-#183 := (iff #44 #182)
-#180 := (= #43 -2::int)
-#181 := [rewrite]: #180
-#177 := (= #41 #176)
-#174 := (= #39 -5::int)
-#175 := [rewrite]: #174
-#178 := [monotonicity #175]: #177
-#184 := [monotonicity #178 #181]: #183
-#187 := [monotonicity #184]: #186
-#172 := [asserted]: #45
-#190 := [mp #172 #187]: #185
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#747 := (pattern #10)
-#11 := 0::int
-#69 := -1::int
-#73 := (* -1::int #9)
-#70 := (* -1::int #8)
-#76 := (div #70 #73)
-#249 := (* -1::int #76)
-#250 := (+ #10 #249)
-#251 := (= #250 0::int)
-#21 := (div #8 #9)
-#246 := (* -1::int #21)
-#247 := (+ #10 #246)
-#248 := (= #247 0::int)
-#95 := (<= #9 0::int)
-#91 := (<= #8 0::int)
-#204 := (or #91 #95)
-#205 := (not #204)
-#102 := (>= #8 0::int)
-#196 := (or #95 #102)
-#197 := (not #196)
-#211 := (or #197 #205)
-#252 := (ite #211 #248 #251)
-#245 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#253 := (ite #14 #245 #252)
-#748 := (forall (vars (?v0 int) (?v1 int)) (:pat #747) #253)
-#256 := (forall (vars (?v0 int) (?v1 int)) #253)
-#751 := (iff #256 #748)
-#749 := (iff #253 #253)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#216 := (ite #211 #21 #76)
-#219 := (ite #14 0::int #216)
-#222 := (= #10 #219)
-#225 := (forall (vars (?v0 int) (?v1 int)) #222)
-#257 := (iff #225 #256)
-#254 := (iff #222 #253)
-#255 := [rewrite]: #254
-#258 := [quant-intro #255]: #257
-#103 := (not #102)
-#96 := (not #95)
-#106 := (and #96 #103)
-#92 := (not #91)
-#99 := (and #92 #96)
-#109 := (or #99 #106)
-#112 := (ite #109 #21 #76)
-#115 := (ite #14 0::int #112)
-#118 := (= #10 #115)
-#121 := (forall (vars (?v0 int) (?v1 int)) #118)
-#226 := (iff #121 #225)
-#223 := (iff #118 #222)
-#220 := (= #115 #219)
-#217 := (= #112 #216)
-#214 := (iff #109 #211)
-#208 := (or #205 #197)
-#212 := (iff #208 #211)
-#213 := [rewrite]: #212
-#209 := (iff #109 #208)
-#206 := (iff #106 #197)
-#207 := [rewrite]: #206
-#194 := (iff #99 #205)
-#195 := [rewrite]: #194
-#210 := [monotonicity #195 #207]: #209
-#215 := [trans #210 #213]: #214
-#218 := [monotonicity #215]: #217
-#221 := [monotonicity #218]: #220
-#224 := [monotonicity #221]: #223
-#227 := [quant-intro #224]: #226
-#200 := (~ #121 #121)
-#198 := (~ #118 #118)
-#199 := [refl]: #198
-#201 := [nnf-pos #199]: #200
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#124 := (iff #28 #121)
-#63 := (and #16 #18)
-#66 := (or #17 #63)
-#79 := (ite #66 #21 #76)
-#82 := (ite #14 0::int #79)
-#85 := (= #10 #82)
-#88 := (forall (vars (?v0 int) (?v1 int)) #85)
-#122 := (iff #88 #121)
-#119 := (iff #85 #118)
-#116 := (= #82 #115)
-#113 := (= #79 #112)
-#110 := (iff #66 #109)
-#107 := (iff #63 #106)
-#104 := (iff #18 #103)
-#105 := [rewrite]: #104
-#97 := (iff #16 #96)
-#98 := [rewrite]: #97
-#108 := [monotonicity #98 #105]: #107
-#100 := (iff #17 #99)
-#93 := (iff #15 #92)
-#94 := [rewrite]: #93
-#101 := [monotonicity #94 #98]: #100
-#111 := [monotonicity #101 #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [monotonicity #117]: #119
-#123 := [quant-intro #120]: #122
-#89 := (iff #28 #88)
-#86 := (iff #27 #85)
-#83 := (= #26 #82)
-#80 := (= #25 #79)
-#77 := (= #24 #76)
-#74 := (= #23 #73)
-#75 := [rewrite]: #74
-#71 := (= #22 #70)
-#72 := [rewrite]: #71
-#78 := [monotonicity #72 #75]: #77
-#67 := (iff #20 #66)
-#64 := (iff #19 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#81 := [monotonicity #68 #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [monotonicity #84]: #86
-#90 := [quant-intro #87]: #89
-#125 := [trans #90 #123]: #124
-#62 := [asserted]: #28
-#126 := [mp #62 #125]: #121
-#191 := [mp~ #126 #201]: #121
-#228 := [mp #191 #227]: #225
-#259 := [mp #228 #258]: #256
-#753 := [mp #259 #752]: #748
-#667 := (not #748)
-#661 := (or #667 #182)
-#333 := (* -1::int 3::int)
-#418 := (* -1::int -5::int)
-#419 := (div #418 #333)
-#420 := (* -1::int #419)
-#411 := (+ #176 #420)
-#422 := (= #411 0::int)
-#423 := (div -5::int 3::int)
-#351 := (* -1::int #423)
-#424 := (+ #176 #351)
-#421 := (= #424 0::int)
-#425 := (<= 3::int 0::int)
-#404 := (<= -5::int 0::int)
-#739 := (or #404 #425)
-#741 := (not #739)
-#398 := (>= -5::int 0::int)
-#528 := (or #425 #398)
-#735 := (not #528)
-#409 := (or #735 #741)
-#410 := (ite #409 #421 #422)
-#742 := (= #176 0::int)
-#743 := (= 3::int 0::int)
-#744 := (= -5::int 0::int)
-#745 := (or #744 #743)
-#740 := (ite #745 #742 #410)
-#668 := (or #667 #740)
-#653 := (iff #668 #661)
-#656 := (iff #661 #661)
-#657 := [rewrite]: #656
-#665 := (iff #740 #182)
-#673 := (ite false #742 #182)
-#675 := (iff #673 #182)
-#664 := [rewrite]: #675
-#674 := (iff #740 #673)
-#662 := (iff #410 #182)
-#586 := (= #176 -1::int)
-#1 := true
-#682 := (ite true #182 #586)
-#663 := (iff #682 #182)
-#660 := [rewrite]: #663
-#669 := (iff #410 #682)
-#681 := (iff #422 #586)
-#570 := 1::int
-#680 := (+ 1::int #176)
-#576 := (= #680 0::int)
-#587 := (iff #576 #586)
-#588 := [rewrite]: #587
-#584 := (iff #422 #576)
-#582 := (= #411 #680)
-#581 := (+ #176 1::int)
-#565 := (= #581 #680)
-#580 := [rewrite]: #565
-#676 := (= #411 #581)
-#531 := (= #420 1::int)
-#687 := (* -1::int -1::int)
-#571 := (= #687 1::int)
-#572 := [rewrite]: #571
-#685 := (= #420 #687)
-#684 := (= #419 -1::int)
-#696 := -3::int
-#698 := (div 5::int -3::int)
-#530 := (= #698 -1::int)
-#683 := [rewrite]: #530
-#527 := (= #419 #698)
-#697 := (= #333 -3::int)
-#691 := [rewrite]: #697
-#689 := (= #418 5::int)
-#690 := [rewrite]: #689
-#529 := [monotonicity #690 #691]: #527
-#686 := [trans #529 #683]: #684
-#688 := [monotonicity #686]: #685
-#679 := [trans #688 #572]: #531
-#677 := [monotonicity #679]: #676
-#583 := [trans #677 #580]: #582
-#585 := [monotonicity #583]: #584
-#678 := [trans #585 #588]: #681
-#694 := (iff #421 #182)
-#700 := (+ 2::int #176)
-#548 := (= #700 0::int)
-#692 := (iff #548 #182)
-#693 := [rewrite]: #692
-#549 := (iff #421 #548)
-#701 := (= #424 #700)
-#703 := (+ #176 2::int)
-#705 := (= #703 #700)
-#706 := [rewrite]: #705
-#704 := (= #424 #703)
-#713 := (= #351 2::int)
-#711 := (* -1::int -2::int)
-#712 := (= #711 2::int)
-#709 := [rewrite]: #712
-#426 := (= #351 #711)
-#432 := (= #423 -2::int)
-#710 := [rewrite]: #432
-#708 := [monotonicity #710]: #426
-#702 := [trans #708 #709]: #713
-#699 := [monotonicity #702]: #704
-#707 := [trans #699 #706]: #701
-#550 := [monotonicity #707]: #549
-#695 := [trans #550 #693]: #694
-#430 := (iff #409 true)
-#720 := (or true false)
-#444 := (iff #720 true)
-#445 := [rewrite]: #444
-#719 := (iff #409 #720)
-#718 := (iff #741 false)
-#716 := (not true)
-#440 := (iff #716 false)
-#714 := [rewrite]: #440
-#717 := (iff #741 #716)
-#446 := (iff #739 true)
-#721 := (iff #739 #720)
-#387 := (iff #425 false)
-#388 := [rewrite]: #387
-#731 := (iff #404 true)
-#734 := [rewrite]: #731
-#443 := [monotonicity #734 #388]: #721
-#339 := [trans #443 #445]: #446
-#439 := [monotonicity #339]: #717
-#715 := [trans #439 #714]: #718
-#373 := (iff #735 true)
-#729 := (not false)
-#732 := (iff #729 true)
-#372 := [rewrite]: #732
-#367 := (iff #735 #729)
-#728 := (iff #528 false)
-#737 := (or false false)
-#381 := (iff #737 false)
-#722 := [rewrite]: #381
-#726 := (iff #528 #737)
-#724 := (iff #398 false)
-#725 := [rewrite]: #724
-#727 := [monotonicity #388 #725]: #726
-#723 := [trans #727 #722]: #728
-#730 := [monotonicity #723]: #367
-#733 := [trans #730 #372]: #373
-#429 := [monotonicity #733 #715]: #719
-#431 := [trans #429 #445]: #430
-#671 := [monotonicity #431 #695 #678]: #669
-#672 := [trans #671 #660]: #662
-#385 := (iff #745 false)
-#397 := (iff #745 #737)
-#396 := (iff #743 false)
-#401 := [rewrite]: #396
-#746 := (iff #744 false)
-#736 := [rewrite]: #746
-#738 := [monotonicity #736 #401]: #397
-#386 := [trans #738 #722]: #385
-#670 := [monotonicity #386 #672]: #674
-#666 := [trans #670 #664]: #665
-#655 := [monotonicity #666]: #653
-#658 := [trans #655 #657]: #653
-#652 := [quant-inst]: #668
-#654 := [mp #652 #658]: #661
-[unit-resolution #654 #753 #190]: false
-unsat
-b80549d22ecf7f5cd139430555c8f40a8bf6eaf1 328 0
+b86a23760e56f2e748a59bf6f0d2def230b36628 328 0
 #2 := false
 #11 := 0::int
 decl f4 :: (-> int int int)
@@ -38406,335 +39402,7 @@
 #688 := [mp #591 #684]: #582
 [unit-resolution #688 #766 #194]: false
 unsat
-f5bac51774cbba53d38c1b1a54df34cd76c05e60 327 0
-#2 := false
-#11 := 0::int
-decl f3 :: (-> int int int)
-#174 := -3::int
-#68 := -1::int
-#177 := (f3 -1::int -3::int)
-#180 := (= #177 0::int)
-#193 := (not #180)
-#40 := 3::int
-#41 := (- 3::int)
-#38 := 1::int
-#39 := (- 1::int)
-#42 := (f3 #39 #41)
-#43 := (= #42 0::int)
-#44 := (not #43)
-#196 := (iff #44 #193)
-#183 := (= 0::int #177)
-#188 := (not #183)
-#194 := (iff #188 #193)
-#191 := (iff #183 #180)
-#192 := [rewrite]: #191
-#195 := [monotonicity #192]: #194
-#189 := (iff #44 #188)
-#186 := (iff #43 #183)
-#184 := (iff #180 #183)
-#185 := [rewrite]: #184
-#181 := (iff #43 #180)
-#178 := (= #42 #177)
-#175 := (= #41 -3::int)
-#176 := [rewrite]: #175
-#172 := (= #39 -1::int)
-#173 := [rewrite]: #172
-#179 := [monotonicity #173 #176]: #178
-#182 := [monotonicity #179]: #181
-#187 := [trans #182 #185]: #186
-#190 := [monotonicity #187]: #189
-#197 := [trans #190 #195]: #196
-#171 := [asserted]: #44
-#198 := [mp #171 #197]: #193
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#756 := (pattern #10)
-#72 := (* -1::int #9)
-#69 := (* -1::int #8)
-#75 := (div #69 #72)
-#259 := (* -1::int #75)
-#260 := (+ #10 #259)
-#261 := (= #260 0::int)
-#21 := (div #8 #9)
-#256 := (* -1::int #21)
-#257 := (+ #10 #256)
-#258 := (= #257 0::int)
-#94 := (<= #9 0::int)
-#90 := (<= #8 0::int)
-#214 := (or #90 #94)
-#215 := (not #214)
-#101 := (>= #8 0::int)
-#206 := (or #94 #101)
-#207 := (not #206)
-#221 := (or #207 #215)
-#262 := (ite #221 #258 #261)
-#255 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#263 := (ite #14 #255 #262)
-#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
-#266 := (forall (vars (?v0 int) (?v1 int)) #263)
-#760 := (iff #266 #757)
-#758 := (iff #263 #263)
-#759 := [refl]: #758
-#761 := [quant-intro #759]: #760
-#226 := (ite #221 #21 #75)
-#229 := (ite #14 0::int #226)
-#232 := (= #10 #229)
-#235 := (forall (vars (?v0 int) (?v1 int)) #232)
-#267 := (iff #235 #266)
-#264 := (iff #232 #263)
-#265 := [rewrite]: #264
-#268 := [quant-intro #265]: #267
-#102 := (not #101)
-#95 := (not #94)
-#105 := (and #95 #102)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#111 := (ite #108 #21 #75)
-#114 := (ite #14 0::int #111)
-#117 := (= #10 #114)
-#120 := (forall (vars (?v0 int) (?v1 int)) #117)
-#236 := (iff #120 #235)
-#233 := (iff #117 #232)
-#230 := (= #114 #229)
-#227 := (= #111 #226)
-#224 := (iff #108 #221)
-#218 := (or #215 #207)
-#222 := (iff #218 #221)
-#223 := [rewrite]: #222
-#219 := (iff #108 #218)
-#216 := (iff #105 #207)
-#217 := [rewrite]: #216
-#204 := (iff #98 #215)
-#205 := [rewrite]: #204
-#220 := [monotonicity #205 #217]: #219
-#225 := [trans #220 #223]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [quant-intro #234]: #236
-#210 := (~ #120 #120)
-#208 := (~ #117 #117)
-#209 := [refl]: #208
-#211 := [nnf-pos #209]: #210
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#123 := (iff #28 #120)
-#62 := (and #16 #18)
-#65 := (or #17 #62)
-#78 := (ite #65 #21 #75)
-#81 := (ite #14 0::int #78)
-#84 := (= #10 #81)
-#87 := (forall (vars (?v0 int) (?v1 int)) #84)
-#121 := (iff #87 #120)
-#118 := (iff #84 #117)
-#115 := (= #81 #114)
-#112 := (= #78 #111)
-#109 := (iff #65 #108)
-#106 := (iff #62 #105)
-#103 := (iff #18 #102)
-#104 := [rewrite]: #103
-#96 := (iff #16 #95)
-#97 := [rewrite]: #96
-#107 := [monotonicity #97 #104]: #106
-#99 := (iff #17 #98)
-#92 := (iff #15 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [monotonicity #116]: #118
-#122 := [quant-intro #119]: #121
-#88 := (iff #28 #87)
-#85 := (iff #27 #84)
-#82 := (= #26 #81)
-#79 := (= #25 #78)
-#76 := (= #24 #75)
-#73 := (= #23 #72)
-#74 := [rewrite]: #73
-#70 := (= #22 #69)
-#71 := [rewrite]: #70
-#77 := [monotonicity #71 #74]: #76
-#66 := (iff #20 #65)
-#63 := (iff #19 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#80 := [monotonicity #67 #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [monotonicity #83]: #85
-#89 := [quant-intro #86]: #88
-#124 := [trans #89 #122]: #123
-#61 := [asserted]: #28
-#125 := [mp #61 #124]: #120
-#201 := [mp~ #125 #211]: #120
-#238 := [mp #201 #237]: #235
-#269 := [mp #238 #268]: #266
-#762 := [mp #269 #761]: #757
-#681 := (not #757)
-#682 := (or #681 #180)
-#343 := (* -1::int -3::int)
-#427 := (* -1::int -1::int)
-#428 := (div #427 #343)
-#429 := (* -1::int #428)
-#420 := (+ #177 #429)
-#431 := (= #420 0::int)
-#432 := (div -1::int -3::int)
-#433 := (* -1::int #432)
-#430 := (+ #177 #433)
-#434 := (= #430 0::int)
-#413 := (<= -3::int 0::int)
-#748 := (<= -1::int 0::int)
-#750 := (or #748 #413)
-#407 := (not #750)
-#537 := (>= -1::int 0::int)
-#744 := (or #413 #537)
-#418 := (not #744)
-#419 := (or #418 #407)
-#751 := (ite #419 #434 #431)
-#752 := (= -3::int 0::int)
-#753 := (= -1::int 0::int)
-#754 := (or #753 #752)
-#749 := (ite #754 #180 #751)
-#683 := (or #681 #749)
-#684 := (iff #683 #682)
-#674 := (iff #682 #682)
-#675 := [rewrite]: #674
-#669 := (iff #749 #180)
-#687 := (ite false #180 #180)
-#680 := (iff #687 #180)
-#672 := [rewrite]: #680
-#691 := (iff #749 #687)
-#597 := (iff #751 #180)
-#701 := (= #177 1::int)
-#585 := (ite false #701 #180)
-#595 := (iff #585 #180)
-#596 := [rewrite]: #595
-#593 := (iff #751 #585)
-#591 := (iff #431 #180)
-#574 := (= #420 #177)
-#688 := (+ #177 0::int)
-#686 := (= #688 #177)
-#689 := [rewrite]: #686
-#590 := (= #420 #688)
-#581 := (= #429 0::int)
-#696 := (* -1::int 0::int)
-#579 := (= #696 0::int)
-#580 := [rewrite]: #579
-#694 := (= #429 #696)
-#693 := (= #428 0::int)
-#707 := (div 1::int 3::int)
-#539 := (= #707 0::int)
-#692 := [rewrite]: #539
-#536 := (= #428 #707)
-#706 := (= #343 3::int)
-#700 := [rewrite]: #706
-#699 := (= #427 1::int)
-#705 := [rewrite]: #699
-#538 := [monotonicity #705 #700]: #536
-#695 := [trans #538 #692]: #693
-#697 := [monotonicity #695]: #694
-#540 := [trans #697 #580]: #581
-#685 := [monotonicity #540]: #590
-#589 := [trans #685 #689]: #574
-#592 := [monotonicity #589]: #591
-#704 := (iff #434 #701)
-#709 := (+ -1::int #177)
-#557 := (= #709 0::int)
-#702 := (iff #557 #701)
-#703 := [rewrite]: #702
-#558 := (iff #434 #557)
-#710 := (= #430 #709)
-#712 := (+ #177 -1::int)
-#714 := (= #712 #709)
-#715 := [rewrite]: #714
-#713 := (= #430 #712)
-#722 := (= #433 -1::int)
-#720 := (* -1::int 1::int)
-#721 := (= #720 -1::int)
-#718 := [rewrite]: #721
-#435 := (= #433 #720)
-#441 := (= #432 1::int)
-#719 := [rewrite]: #441
-#717 := [monotonicity #719]: #435
-#711 := [trans #717 #718]: #722
-#708 := [monotonicity #711]: #713
-#716 := [trans #708 #715]: #710
-#559 := [monotonicity #716]: #558
-#698 := [trans #559 #703]: #704
-#439 := (iff #419 false)
-#746 := (or false false)
-#390 := (iff #746 false)
-#731 := [rewrite]: #390
-#728 := (iff #419 #746)
-#727 := (iff #407 false)
-#1 := true
-#741 := (not true)
-#742 := (iff #741 false)
-#740 := [rewrite]: #742
-#449 := (iff #407 #741)
-#726 := (iff #750 true)
-#453 := (or true true)
-#349 := (iff #453 true)
-#725 := [rewrite]: #349
-#454 := (iff #750 #453)
-#396 := (iff #413 true)
-#397 := [rewrite]: #396
-#730 := (iff #748 true)
-#452 := [rewrite]: #730
-#455 := [monotonicity #452 #397]: #454
-#448 := [trans #455 #725]: #726
-#723 := [monotonicity #448]: #449
-#724 := [trans #723 #740]: #727
-#743 := (iff #418 false)
-#381 := (iff #418 #741)
-#376 := (iff #744 true)
-#735 := (or true false)
-#732 := (iff #735 true)
-#738 := [rewrite]: #732
-#736 := (iff #744 #735)
-#733 := (iff #537 false)
-#734 := [rewrite]: #733
-#737 := [monotonicity #397 #734]: #736
-#739 := [trans #737 #738]: #376
-#382 := [monotonicity #739]: #381
-#729 := [trans #382 #740]: #743
-#438 := [monotonicity #729 #724]: #728
-#440 := [trans #438 #731]: #439
-#594 := [monotonicity #440 #698 #592]: #593
-#690 := [trans #594 #596]: #597
-#394 := (iff #754 false)
-#406 := (iff #754 #746)
-#405 := (iff #752 false)
-#410 := [rewrite]: #405
-#755 := (iff #753 false)
-#745 := [rewrite]: #755
-#747 := [monotonicity #745 #410]: #406
-#395 := [trans #747 #731]: #394
-#678 := [monotonicity #395 #690]: #691
-#671 := [trans #678 #672]: #669
-#673 := [monotonicity #671]: #684
-#676 := [trans #673 #675]: #684
-#679 := [quant-inst]: #683
-#670 := [mp #679 #676]: #682
-[unit-resolution #670 #762 #198]: false
-unsat
-0b4939d8f1f4bc7cd881c6a957ccad857d8a1074 356 0
+f6e2227a0efe09b841529747f2e15c52767424fc 356 0
 #2 := false
 #69 := -1::int
 decl f4 :: (-> int int int)
@@ -39091,319 +39759,7 @@
 #669 := [mp #663 #664]: #678
 [unit-resolution #669 #770 #199]: false
 unsat
-970747fa305dc2e610f7c82f817720c0ccc3a165 311 0
-#2 := false
-#41 := 1::int
-decl f3 :: (-> int int int)
-#171 := -3::int
-#174 := (f3 -3::int -3::int)
-#177 := (= #174 1::int)
-#190 := (not #177)
-#38 := 3::int
-#39 := (- 3::int)
-#40 := (f3 #39 #39)
-#42 := (= #40 1::int)
-#43 := (not #42)
-#193 := (iff #43 #190)
-#180 := (= 1::int #174)
-#185 := (not #180)
-#191 := (iff #185 #190)
-#188 := (iff #180 #177)
-#189 := [rewrite]: #188
-#192 := [monotonicity #189]: #191
-#186 := (iff #43 #185)
-#183 := (iff #42 #180)
-#181 := (iff #177 #180)
-#182 := [rewrite]: #181
-#178 := (iff #42 #177)
-#175 := (= #40 #174)
-#172 := (= #39 -3::int)
-#173 := [rewrite]: #172
-#176 := [monotonicity #173 #173]: #175
-#179 := [monotonicity #176]: #178
-#184 := [trans #179 #182]: #183
-#187 := [monotonicity #184]: #186
-#194 := [trans #187 #192]: #193
-#170 := [asserted]: #43
-#195 := [mp #170 #194]: #190
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#753 := (pattern #10)
-#11 := 0::int
-#67 := -1::int
-#71 := (* -1::int #9)
-#68 := (* -1::int #8)
-#74 := (div #68 #71)
-#256 := (* -1::int #74)
-#257 := (+ #10 #256)
-#258 := (= #257 0::int)
-#21 := (div #8 #9)
-#253 := (* -1::int #21)
-#254 := (+ #10 #253)
-#255 := (= #254 0::int)
-#93 := (<= #9 0::int)
-#89 := (<= #8 0::int)
-#211 := (or #89 #93)
-#212 := (not #211)
-#100 := (>= #8 0::int)
-#203 := (or #93 #100)
-#204 := (not #203)
-#218 := (or #204 #212)
-#259 := (ite #218 #255 #258)
-#252 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#260 := (ite #14 #252 #259)
-#754 := (forall (vars (?v0 int) (?v1 int)) (:pat #753) #260)
-#263 := (forall (vars (?v0 int) (?v1 int)) #260)
-#757 := (iff #263 #754)
-#755 := (iff #260 #260)
-#756 := [refl]: #755
-#758 := [quant-intro #756]: #757
-#223 := (ite #218 #21 #74)
-#226 := (ite #14 0::int #223)
-#229 := (= #10 #226)
-#232 := (forall (vars (?v0 int) (?v1 int)) #229)
-#264 := (iff #232 #263)
-#261 := (iff #229 #260)
-#262 := [rewrite]: #261
-#265 := [quant-intro #262]: #264
-#101 := (not #100)
-#94 := (not #93)
-#104 := (and #94 #101)
-#90 := (not #89)
-#97 := (and #90 #94)
-#107 := (or #97 #104)
-#110 := (ite #107 #21 #74)
-#113 := (ite #14 0::int #110)
-#116 := (= #10 #113)
-#119 := (forall (vars (?v0 int) (?v1 int)) #116)
-#233 := (iff #119 #232)
-#230 := (iff #116 #229)
-#227 := (= #113 #226)
-#224 := (= #110 #223)
-#221 := (iff #107 #218)
-#215 := (or #212 #204)
-#219 := (iff #215 #218)
-#220 := [rewrite]: #219
-#216 := (iff #107 #215)
-#213 := (iff #104 #204)
-#214 := [rewrite]: #213
-#201 := (iff #97 #212)
-#202 := [rewrite]: #201
-#217 := [monotonicity #202 #214]: #216
-#222 := [trans #217 #220]: #221
-#225 := [monotonicity #222]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [quant-intro #231]: #233
-#207 := (~ #119 #119)
-#205 := (~ #116 #116)
-#206 := [refl]: #205
-#208 := [nnf-pos #206]: #207
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#122 := (iff #28 #119)
-#61 := (and #16 #18)
-#64 := (or #17 #61)
-#77 := (ite #64 #21 #74)
-#80 := (ite #14 0::int #77)
-#83 := (= #10 #80)
-#86 := (forall (vars (?v0 int) (?v1 int)) #83)
-#120 := (iff #86 #119)
-#117 := (iff #83 #116)
-#114 := (= #80 #113)
-#111 := (= #77 #110)
-#108 := (iff #64 #107)
-#105 := (iff #61 #104)
-#102 := (iff #18 #101)
-#103 := [rewrite]: #102
-#95 := (iff #16 #94)
-#96 := [rewrite]: #95
-#106 := [monotonicity #96 #103]: #105
-#98 := (iff #17 #97)
-#91 := (iff #15 #90)
-#92 := [rewrite]: #91
-#99 := [monotonicity #92 #96]: #98
-#109 := [monotonicity #99 #106]: #108
-#112 := [monotonicity #109]: #111
-#115 := [monotonicity #112]: #114
-#118 := [monotonicity #115]: #117
-#121 := [quant-intro #118]: #120
-#87 := (iff #28 #86)
-#84 := (iff #27 #83)
-#81 := (= #26 #80)
-#78 := (= #25 #77)
-#75 := (= #24 #74)
-#72 := (= #23 #71)
-#73 := [rewrite]: #72
-#69 := (= #22 #68)
-#70 := [rewrite]: #69
-#76 := [monotonicity #70 #73]: #75
-#65 := (iff #20 #64)
-#62 := (iff #19 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#79 := [monotonicity #66 #76]: #78
-#82 := [monotonicity #79]: #81
-#85 := [monotonicity #82]: #84
-#88 := [quant-intro #85]: #87
-#123 := [trans #88 #121]: #122
-#60 := [asserted]: #28
-#124 := [mp #60 #123]: #119
-#198 := [mp~ #124 #208]: #119
-#235 := [mp #198 #234]: #232
-#266 := [mp #235 #265]: #263
-#759 := [mp #266 #758]: #754
-#590 := (not #754)
-#591 := (or #590 #177)
-#340 := (* -1::int -3::int)
-#424 := (div #340 #340)
-#425 := (* -1::int #424)
-#426 := (+ #174 #425)
-#417 := (= #426 0::int)
-#428 := (div -3::int -3::int)
-#429 := (* -1::int #428)
-#430 := (+ #174 #429)
-#427 := (= #430 0::int)
-#431 := (<= -3::int 0::int)
-#410 := (or #431 #431)
-#745 := (not #410)
-#747 := (>= -3::int 0::int)
-#404 := (or #431 #747)
-#534 := (not #404)
-#741 := (or #534 #745)
-#415 := (ite #741 #427 #417)
-#416 := (= #174 0::int)
-#748 := (= -3::int 0::int)
-#749 := (or #748 #748)
-#750 := (ite #749 #416 #415)
-#592 := (or #590 #750)
-#594 := (iff #592 #591)
-#684 := (iff #591 #591)
-#688 := [rewrite]: #684
-#589 := (iff #750 #177)
-#683 := (ite false #416 #177)
-#586 := (iff #683 #177)
-#588 := [rewrite]: #586
-#686 := (iff #750 #683)
-#587 := (iff #415 #177)
-#576 := (ite false #177 #177)
-#537 := (iff #576 #177)
-#685 := [rewrite]: #537
-#577 := (iff #415 #576)
-#691 := (iff #417 #177)
-#715 := (+ -1::int #174)
-#705 := (= #715 0::int)
-#712 := (iff #705 #177)
-#707 := [rewrite]: #712
-#692 := (iff #417 #705)
-#689 := (= #426 #715)
-#432 := (+ #174 -1::int)
-#719 := (= #432 #715)
-#708 := [rewrite]: #719
-#535 := (= #426 #432)
-#704 := (= #425 -1::int)
-#725 := (* -1::int 1::int)
-#437 := (= #725 -1::int)
-#438 := [rewrite]: #437
-#703 := (= #425 #725)
-#696 := (= #424 1::int)
-#698 := (div 3::int 3::int)
-#701 := (= #698 1::int)
-#695 := [rewrite]: #701
-#699 := (= #424 #698)
-#555 := (= #340 3::int)
-#556 := [rewrite]: #555
-#700 := [monotonicity #556 #556]: #699
-#702 := [trans #700 #695]: #696
-#697 := [monotonicity #702]: #703
-#533 := [trans #697 #438]: #704
-#536 := [monotonicity #533]: #535
-#690 := [trans #536 #708]: #689
-#693 := [monotonicity #690]: #692
-#694 := [trans #693 #707]: #691
-#713 := (iff #427 #177)
-#706 := (iff #427 #705)
-#709 := (= #430 #715)
-#714 := (= #430 #432)
-#716 := (= #429 -1::int)
-#435 := (= #429 #725)
-#724 := (= #428 1::int)
-#721 := [rewrite]: #724
-#436 := [monotonicity #721]: #435
-#717 := [trans #436 #438]: #716
-#718 := [monotonicity #717]: #714
-#710 := [trans #718 #708]: #709
-#711 := [monotonicity #710]: #706
-#554 := [trans #711 #707]: #713
-#446 := (iff #741 false)
-#752 := (or false false)
-#407 := (iff #752 false)
-#743 := [rewrite]: #407
-#723 := (iff #741 #752)
-#346 := (iff #745 false)
-#1 := true
-#729 := (not true)
-#736 := (iff #729 false)
-#738 := [rewrite]: #736
-#451 := (iff #745 #729)
-#449 := (iff #410 true)
-#739 := (or true true)
-#726 := (iff #739 true)
-#727 := [rewrite]: #726
-#737 := (iff #410 #739)
-#387 := (iff #431 true)
-#728 := [rewrite]: #387
-#740 := [monotonicity #728 #728]: #737
-#450 := [trans #740 #727]: #449
-#452 := [monotonicity #450]: #451
-#722 := [trans #452 #738]: #346
-#378 := (iff #534 false)
-#735 := (iff #534 #729)
-#733 := (iff #404 true)
-#393 := (or true false)
-#731 := (iff #393 true)
-#732 := [rewrite]: #731
-#394 := (iff #404 #393)
-#391 := (iff #747 false)
-#392 := [rewrite]: #391
-#730 := [monotonicity #728 #392]: #394
-#734 := [trans #730 #732]: #733
-#373 := [monotonicity #734]: #735
-#379 := [trans #373 #738]: #378
-#445 := [monotonicity #379 #722]: #723
-#720 := [trans #445 #743]: #446
-#578 := [monotonicity #720 #554 #694]: #577
-#682 := [trans #578 #685]: #587
-#403 := (iff #749 false)
-#742 := (iff #749 #752)
-#751 := (iff #748 false)
-#746 := [rewrite]: #751
-#402 := [monotonicity #746 #746]: #742
-#744 := [trans #402 #743]: #403
-#571 := [monotonicity #744 #682]: #686
-#582 := [trans #571 #588]: #589
-#687 := [monotonicity #582]: #594
-#675 := [trans #687 #688]: #594
-#593 := [quant-inst]: #592
-#677 := [mp #593 #675]: #591
-[unit-resolution #677 #759 #195]: false
-unsat
-fdc90ed3bd1ececd431bc0c6098387ca00c73cfc 350 0
+420d6230497abd2cabbe6482e60faddb2e7baf3c 350 0
 #2 := false
 #42 := 2::int
 decl f4 :: (-> int int int)
@@ -39754,346 +40110,7 @@
 #664 := [mp #674 #663]: #673
 [unit-resolution #664 #766 #195]: false
 unsat
-b3920b336e88838381046f8db8a66873eedc037f 338 0
-#2 := false
-#43 := 1::int
-decl f3 :: (-> int int int)
-#176 := -3::int
-#173 := -5::int
-#179 := (f3 -5::int -3::int)
-#182 := (= #179 1::int)
-#195 := (not #182)
-#40 := 3::int
-#41 := (- 3::int)
-#38 := 5::int
-#39 := (- 5::int)
-#42 := (f3 #39 #41)
-#44 := (= #42 1::int)
-#45 := (not #44)
-#198 := (iff #45 #195)
-#185 := (= 1::int #179)
-#190 := (not #185)
-#196 := (iff #190 #195)
-#193 := (iff #185 #182)
-#194 := [rewrite]: #193
-#197 := [monotonicity #194]: #196
-#191 := (iff #45 #190)
-#188 := (iff #44 #185)
-#186 := (iff #182 #185)
-#187 := [rewrite]: #186
-#183 := (iff #44 #182)
-#180 := (= #42 #179)
-#177 := (= #41 -3::int)
-#178 := [rewrite]: #177
-#174 := (= #39 -5::int)
-#175 := [rewrite]: #174
-#181 := [monotonicity #175 #178]: #180
-#184 := [monotonicity #181]: #183
-#189 := [trans #184 #187]: #188
-#192 := [monotonicity #189]: #191
-#199 := [trans #192 #197]: #198
-#172 := [asserted]: #45
-#200 := [mp #172 #199]: #195
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#758 := (pattern #10)
-#11 := 0::int
-#69 := -1::int
-#73 := (* -1::int #9)
-#70 := (* -1::int #8)
-#76 := (div #70 #73)
-#261 := (* -1::int #76)
-#262 := (+ #10 #261)
-#263 := (= #262 0::int)
-#21 := (div #8 #9)
-#258 := (* -1::int #21)
-#259 := (+ #10 #258)
-#260 := (= #259 0::int)
-#95 := (<= #9 0::int)
-#91 := (<= #8 0::int)
-#216 := (or #91 #95)
-#217 := (not #216)
-#102 := (>= #8 0::int)
-#208 := (or #95 #102)
-#209 := (not #208)
-#223 := (or #209 #217)
-#264 := (ite #223 #260 #263)
-#257 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#265 := (ite #14 #257 #264)
-#759 := (forall (vars (?v0 int) (?v1 int)) (:pat #758) #265)
-#268 := (forall (vars (?v0 int) (?v1 int)) #265)
-#762 := (iff #268 #759)
-#760 := (iff #265 #265)
-#761 := [refl]: #760
-#763 := [quant-intro #761]: #762
-#228 := (ite #223 #21 #76)
-#231 := (ite #14 0::int #228)
-#234 := (= #10 #231)
-#237 := (forall (vars (?v0 int) (?v1 int)) #234)
-#269 := (iff #237 #268)
-#266 := (iff #234 #265)
-#267 := [rewrite]: #266
-#270 := [quant-intro #267]: #269
-#103 := (not #102)
-#96 := (not #95)
-#106 := (and #96 #103)
-#92 := (not #91)
-#99 := (and #92 #96)
-#109 := (or #99 #106)
-#112 := (ite #109 #21 #76)
-#115 := (ite #14 0::int #112)
-#118 := (= #10 #115)
-#121 := (forall (vars (?v0 int) (?v1 int)) #118)
-#238 := (iff #121 #237)
-#235 := (iff #118 #234)
-#232 := (= #115 #231)
-#229 := (= #112 #228)
-#226 := (iff #109 #223)
-#220 := (or #217 #209)
-#224 := (iff #220 #223)
-#225 := [rewrite]: #224
-#221 := (iff #109 #220)
-#218 := (iff #106 #209)
-#219 := [rewrite]: #218
-#206 := (iff #99 #217)
-#207 := [rewrite]: #206
-#222 := [monotonicity #207 #219]: #221
-#227 := [trans #222 #225]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [monotonicity #233]: #235
-#239 := [quant-intro #236]: #238
-#212 := (~ #121 #121)
-#210 := (~ #118 #118)
-#211 := [refl]: #210
-#213 := [nnf-pos #211]: #212
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#124 := (iff #28 #121)
-#63 := (and #16 #18)
-#66 := (or #17 #63)
-#79 := (ite #66 #21 #76)
-#82 := (ite #14 0::int #79)
-#85 := (= #10 #82)
-#88 := (forall (vars (?v0 int) (?v1 int)) #85)
-#122 := (iff #88 #121)
-#119 := (iff #85 #118)
-#116 := (= #82 #115)
-#113 := (= #79 #112)
-#110 := (iff #66 #109)
-#107 := (iff #63 #106)
-#104 := (iff #18 #103)
-#105 := [rewrite]: #104
-#97 := (iff #16 #96)
-#98 := [rewrite]: #97
-#108 := [monotonicity #98 #105]: #107
-#100 := (iff #17 #99)
-#93 := (iff #15 #92)
-#94 := [rewrite]: #93
-#101 := [monotonicity #94 #98]: #100
-#111 := [monotonicity #101 #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [monotonicity #117]: #119
-#123 := [quant-intro #120]: #122
-#89 := (iff #28 #88)
-#86 := (iff #27 #85)
-#83 := (= #26 #82)
-#80 := (= #25 #79)
-#77 := (= #24 #76)
-#74 := (= #23 #73)
-#75 := [rewrite]: #74
-#71 := (= #22 #70)
-#72 := [rewrite]: #71
-#78 := [monotonicity #72 #75]: #77
-#67 := (iff #20 #66)
-#64 := (iff #19 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#81 := [monotonicity #68 #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [monotonicity #84]: #86
-#90 := [quant-intro #87]: #89
-#125 := [trans #90 #123]: #124
-#62 := [asserted]: #28
-#126 := [mp #62 #125]: #121
-#203 := [mp~ #126 #213]: #121
-#240 := [mp #203 #239]: #237
-#271 := [mp #240 #270]: #268
-#764 := [mp #271 #763]: #759
-#672 := (not #759)
-#679 := (or #672 #182)
-#345 := (* -1::int -3::int)
-#429 := (* -1::int -5::int)
-#430 := (div #429 #345)
-#431 := (* -1::int #430)
-#422 := (+ #179 #431)
-#433 := (= #422 0::int)
-#434 := (div -5::int -3::int)
-#435 := (* -1::int #434)
-#432 := (+ #179 #435)
-#436 := (= #432 0::int)
-#415 := (<= -3::int 0::int)
-#750 := (<= -5::int 0::int)
-#752 := (or #750 #415)
-#409 := (not #752)
-#539 := (>= -5::int 0::int)
-#746 := (or #415 #539)
-#420 := (not #746)
-#421 := (or #420 #409)
-#753 := (ite #421 #436 #433)
-#754 := (= #179 0::int)
-#755 := (= -3::int 0::int)
-#756 := (= -5::int 0::int)
-#751 := (or #756 #755)
-#757 := (ite #751 #754 #753)
-#663 := (or #672 #757)
-#666 := (iff #663 #679)
-#668 := (iff #679 #679)
-#669 := [rewrite]: #668
-#677 := (iff #757 #182)
-#685 := (ite false #754 #182)
-#675 := (iff #685 #182)
-#676 := [rewrite]: #675
-#681 := (iff #757 #685)
-#683 := (iff #753 #182)
-#721 := 2::int
-#706 := (= #179 2::int)
-#680 := (ite false #706 #182)
-#671 := (iff #680 #182)
-#673 := [rewrite]: #671
-#682 := (iff #753 #680)
-#689 := (iff #433 #182)
-#591 := (+ -1::int #179)
-#596 := (= #591 0::int)
-#599 := (iff #596 #182)
-#692 := [rewrite]: #599
-#597 := (iff #433 #596)
-#587 := (= #422 #591)
-#688 := (+ #179 -1::int)
-#593 := (= #688 #591)
-#594 := [rewrite]: #593
-#691 := (= #422 #688)
-#592 := (= #431 -1::int)
-#581 := (* -1::int 1::int)
-#542 := (= #581 -1::int)
-#690 := [rewrite]: #542
-#582 := (= #431 #581)
-#696 := (= #430 1::int)
-#541 := (div 5::int 3::int)
-#697 := (= #541 1::int)
-#698 := [rewrite]: #697
-#694 := (= #430 #541)
-#538 := (= #345 3::int)
-#540 := [rewrite]: #538
-#702 := (= #429 5::int)
-#709 := [rewrite]: #702
-#695 := [monotonicity #709 #540]: #694
-#699 := [trans #695 #698]: #696
-#583 := [monotonicity #699]: #582
-#687 := [trans #583 #690]: #592
-#576 := [monotonicity #687]: #691
-#595 := [trans #576 #594]: #587
-#598 := [monotonicity #595]: #597
-#693 := [trans #598 #692]: #689
-#707 := (iff #436 #706)
-#724 := -2::int
-#712 := (+ -2::int #179)
-#703 := (= #712 0::int)
-#700 := (iff #703 #706)
-#701 := [rewrite]: #700
-#704 := (iff #436 #703)
-#560 := (= #432 #712)
-#711 := (+ #179 -2::int)
-#718 := (= #711 #712)
-#559 := [rewrite]: #718
-#716 := (= #432 #711)
-#715 := (= #435 -2::int)
-#719 := (* -1::int 2::int)
-#713 := (= #719 -2::int)
-#714 := [rewrite]: #713
-#723 := (= #435 #719)
-#722 := (= #434 2::int)
-#437 := [rewrite]: #722
-#720 := [monotonicity #437]: #723
-#710 := [trans #720 #714]: #715
-#717 := [monotonicity #710]: #716
-#561 := [trans #717 #559]: #560
-#705 := [monotonicity #561]: #704
-#708 := [trans #705 #701]: #707
-#442 := (iff #421 false)
-#408 := (or false false)
-#733 := (iff #408 false)
-#396 := [rewrite]: #733
-#440 := (iff #421 #408)
-#726 := (iff #409 false)
-#1 := true
-#383 := (not true)
-#742 := (iff #383 false)
-#745 := [rewrite]: #742
-#725 := (iff #409 #383)
-#450 := (iff #752 true)
-#456 := (or true true)
-#727 := (iff #456 true)
-#728 := [rewrite]: #727
-#457 := (iff #752 #456)
-#399 := (iff #415 true)
-#735 := [rewrite]: #399
-#454 := (iff #750 true)
-#455 := [rewrite]: #454
-#351 := [monotonicity #455 #735]: #457
-#451 := [trans #351 #728]: #450
-#729 := [monotonicity #451]: #725
-#730 := [trans #729 #745]: #726
-#731 := (iff #420 false)
-#384 := (iff #420 #383)
-#741 := (iff #746 true)
-#738 := (or true false)
-#740 := (iff #738 true)
-#378 := [rewrite]: #740
-#739 := (iff #746 #738)
-#736 := (iff #539 false)
-#737 := [rewrite]: #736
-#734 := [monotonicity #735 #737]: #739
-#743 := [trans #734 #378]: #741
-#744 := [monotonicity #743]: #384
-#732 := [trans #744 #745]: #731
-#441 := [monotonicity #732 #730]: #440
-#443 := [trans #441 #396]: #442
-#674 := [monotonicity #443 #708 #693]: #682
-#684 := [trans #674 #673]: #683
-#397 := (iff #751 false)
-#749 := (iff #751 #408)
-#412 := (iff #755 false)
-#748 := [rewrite]: #412
-#747 := (iff #756 false)
-#407 := [rewrite]: #747
-#392 := [monotonicity #407 #748]: #749
-#398 := [trans #392 #396]: #397
-#686 := [monotonicity #398 #684]: #681
-#678 := [trans #686 #676]: #677
-#667 := [monotonicity #678]: #666
-#665 := [trans #667 #669]: #666
-#664 := [quant-inst]: #663
-#670 := [mp #664 #665]: #679
-[unit-resolution #670 #764 #200]: false
-unsat
-751a59e3560a9cccfdefaac76c413ce978cf57af 331 0
+0d0e0c6107609a6b3997438469b4d07f2362e110 331 0
 #2 := false
 #11 := 0::int
 decl f4 :: (-> int int int)
@@ -40425,7 +40442,2054 @@
 #669 := [mp #594 #677]: #592
 [unit-resolution #669 #766 #194]: false
 unsat
-1e04803c850b7955989debde9ec201f52ca7253f 592 0
+31a3171017870e6c702f8fe602587339166a696d 353 0
+#2 := false
+#42 := 1::int
+decl f4 :: (-> int int int)
+#40 := 3::int
+#172 := -5::int
+#175 := (f4 -5::int 3::int)
+#178 := (= #175 1::int)
+#191 := (not #178)
+#38 := 5::int
+#39 := (- 5::int)
+#41 := (f4 #39 3::int)
+#43 := (= #41 1::int)
+#44 := (not #43)
+#194 := (iff #44 #191)
+#181 := (= 1::int #175)
+#186 := (not #181)
+#192 := (iff #186 #191)
+#189 := (iff #181 #178)
+#190 := [rewrite]: #189
+#193 := [monotonicity #190]: #192
+#187 := (iff #44 #186)
+#184 := (iff #43 #181)
+#182 := (iff #178 #181)
+#183 := [rewrite]: #182
+#179 := (iff #43 #178)
+#176 := (= #41 #175)
+#173 := (= #39 -5::int)
+#174 := [rewrite]: #173
+#177 := [monotonicity #174]: #176
+#180 := [monotonicity #177]: #179
+#185 := [trans #180 #183]: #184
+#188 := [monotonicity #185]: #187
+#195 := [trans #188 #193]: #194
+#171 := [asserted]: #44
+#196 := [mp #171 #195]: #191
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#761 := (pattern #29)
+#11 := 0::int
+#68 := -1::int
+#72 := (* -1::int #9)
+#69 := (* -1::int #8)
+#127 := (mod #69 #72)
+#273 := (+ #29 #127)
+#274 := (= #273 0::int)
+#30 := (mod #8 #9)
+#270 := (* -1::int #30)
+#271 := (+ #29 #270)
+#272 := (= #271 0::int)
+#94 := (<= #9 0::int)
+#90 := (<= #8 0::int)
+#212 := (or #90 #94)
+#213 := (not #212)
+#101 := (>= #8 0::int)
+#204 := (or #94 #101)
+#205 := (not #204)
+#219 := (or #205 #213)
+#275 := (ite #219 #272 #274)
+#269 := (= #29 0::int)
+#12 := (= #8 0::int)
+#276 := (ite #12 #269 #275)
+#268 := (= #8 #29)
+#13 := (= #9 0::int)
+#277 := (ite #13 #268 #276)
+#762 := (forall (vars (?v0 int) (?v1 int)) (:pat #761) #277)
+#280 := (forall (vars (?v0 int) (?v1 int)) #277)
+#765 := (iff #280 #762)
+#763 := (iff #277 #277)
+#764 := [refl]: #763
+#766 := [quant-intro #764]: #765
+#133 := (* -1::int #127)
+#237 := (ite #219 #30 #133)
+#240 := (ite #12 0::int #237)
+#243 := (ite #13 #8 #240)
+#246 := (= #29 #243)
+#249 := (forall (vars (?v0 int) (?v1 int)) #246)
+#281 := (iff #249 #280)
+#278 := (iff #246 #277)
+#279 := [rewrite]: #278
+#282 := [quant-intro #279]: #281
+#102 := (not #101)
+#95 := (not #94)
+#105 := (and #95 #102)
+#91 := (not #90)
+#98 := (and #91 #95)
+#108 := (or #98 #105)
+#153 := (ite #108 #30 #133)
+#156 := (ite #12 0::int #153)
+#159 := (ite #13 #8 #156)
+#162 := (= #29 #159)
+#165 := (forall (vars (?v0 int) (?v1 int)) #162)
+#250 := (iff #165 #249)
+#247 := (iff #162 #246)
+#244 := (= #159 #243)
+#241 := (= #156 #240)
+#238 := (= #153 #237)
+#222 := (iff #108 #219)
+#216 := (or #213 #205)
+#220 := (iff #216 #219)
+#221 := [rewrite]: #220
+#217 := (iff #108 #216)
+#214 := (iff #105 #205)
+#215 := [rewrite]: #214
+#202 := (iff #98 #213)
+#203 := [rewrite]: #202
+#218 := [monotonicity #203 #215]: #217
+#223 := [trans #218 #221]: #222
+#239 := [monotonicity #223]: #238
+#242 := [monotonicity #239]: #241
+#245 := [monotonicity #242]: #244
+#248 := [monotonicity #245]: #247
+#251 := [quant-intro #248]: #250
+#200 := (~ #165 #165)
+#197 := (~ #162 #162)
+#210 := [refl]: #197
+#201 := [nnf-pos #210]: #200
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#168 := (iff #37 #165)
+#62 := (and #16 #18)
+#65 := (or #17 #62)
+#138 := (ite #65 #30 #133)
+#141 := (ite #12 0::int #138)
+#144 := (ite #13 #8 #141)
+#147 := (= #29 #144)
+#150 := (forall (vars (?v0 int) (?v1 int)) #147)
+#166 := (iff #150 #165)
+#163 := (iff #147 #162)
+#160 := (= #144 #159)
+#157 := (= #141 #156)
+#154 := (= #138 #153)
+#109 := (iff #65 #108)
+#106 := (iff #62 #105)
+#103 := (iff #18 #102)
+#104 := [rewrite]: #103
+#96 := (iff #16 #95)
+#97 := [rewrite]: #96
+#107 := [monotonicity #97 #104]: #106
+#99 := (iff #17 #98)
+#92 := (iff #15 #91)
+#93 := [rewrite]: #92
+#100 := [monotonicity #93 #97]: #99
+#110 := [monotonicity #100 #107]: #109
+#155 := [monotonicity #110]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [quant-intro #164]: #166
+#151 := (iff #37 #150)
+#148 := (iff #36 #147)
+#145 := (= #35 #144)
+#142 := (= #34 #141)
+#139 := (= #33 #138)
+#136 := (= #32 #133)
+#130 := (- #127)
+#134 := (= #130 #133)
+#135 := [rewrite]: #134
+#131 := (= #32 #130)
+#128 := (= #31 #127)
+#73 := (= #23 #72)
+#74 := [rewrite]: #73
+#70 := (= #22 #69)
+#71 := [rewrite]: #70
+#129 := [monotonicity #71 #74]: #128
+#132 := [monotonicity #129]: #131
+#137 := [trans #132 #135]: #136
+#66 := (iff #20 #65)
+#63 := (iff #19 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#140 := [monotonicity #67 #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [monotonicity #146]: #148
+#152 := [quant-intro #149]: #151
+#169 := [trans #152 #167]: #168
+#126 := [asserted]: #37
+#170 := [mp #126 #169]: #165
+#211 := [mp~ #170 #201]: #165
+#252 := [mp #211 #251]: #249
+#283 := [mp #252 #282]: #280
+#767 := [mp #283 #766]: #762
+#668 := (not #762)
+#675 := (or #668 #178)
+#341 := (* -1::int 3::int)
+#425 := (* -1::int -5::int)
+#426 := (mod #425 #341)
+#427 := (+ #175 #426)
+#418 := (= #427 0::int)
+#429 := (mod -5::int 3::int)
+#430 := (* -1::int #429)
+#431 := (+ #175 #430)
+#428 := (= #431 0::int)
+#432 := (<= 3::int 0::int)
+#411 := (<= -5::int 0::int)
+#746 := (or #411 #432)
+#748 := (not #746)
+#405 := (>= -5::int 0::int)
+#535 := (or #432 #405)
+#742 := (not #535)
+#416 := (or #742 #748)
+#417 := (ite #416 #428 #418)
+#749 := (= #175 0::int)
+#750 := (= -5::int 0::int)
+#751 := (ite #750 #749 #417)
+#752 := (= -5::int #175)
+#747 := (= 3::int 0::int)
+#753 := (ite #747 #752 #751)
+#659 := (or #668 #753)
+#662 := (iff #659 #675)
+#664 := (iff #675 #675)
+#665 := [rewrite]: #664
+#673 := (iff #753 #178)
+#744 := (= #175 -5::int)
+#681 := (ite false #744 #178)
+#671 := (iff #681 #178)
+#672 := [rewrite]: #671
+#677 := (iff #753 #681)
+#679 := (iff #751 #178)
+#676 := (ite false #749 #178)
+#667 := (iff #676 #178)
+#669 := [rewrite]: #667
+#678 := (iff #751 #676)
+#685 := (iff #417 #178)
+#572 := -2::int
+#587 := (= #175 -2::int)
+#1 := true
+#592 := (ite true #178 #587)
+#595 := (iff #592 #178)
+#688 := [rewrite]: #595
+#593 := (iff #417 #592)
+#583 := (iff #418 #587)
+#537 := 2::int
+#578 := (+ 2::int #175)
+#683 := (= #578 0::int)
+#589 := (iff #683 #587)
+#590 := [rewrite]: #589
+#684 := (iff #418 #683)
+#686 := (= #427 #578)
+#692 := (+ #175 2::int)
+#579 := (= #692 #578)
+#538 := [rewrite]: #579
+#695 := (= #427 #692)
+#693 := (= #426 2::int)
+#703 := -3::int
+#705 := (mod 5::int -3::int)
+#690 := (= #705 2::int)
+#691 := [rewrite]: #690
+#534 := (= #426 #705)
+#704 := (= #341 -3::int)
+#698 := [rewrite]: #704
+#696 := (= #425 5::int)
+#697 := [rewrite]: #696
+#536 := [monotonicity #697 #698]: #534
+#694 := [trans #536 #691]: #693
+#577 := [monotonicity #694]: #695
+#588 := [trans #577 #538]: #686
+#687 := [monotonicity #588]: #684
+#591 := [trans #687 #590]: #583
+#701 := (iff #428 #178)
+#707 := (+ -1::int #175)
+#555 := (= #707 0::int)
+#699 := (iff #555 #178)
+#700 := [rewrite]: #699
+#556 := (iff #428 #555)
+#708 := (= #431 #707)
+#710 := (+ #175 -1::int)
+#712 := (= #710 #707)
+#713 := [rewrite]: #712
+#711 := (= #431 #710)
+#720 := (= #430 -1::int)
+#718 := (* -1::int 1::int)
+#719 := (= #718 -1::int)
+#716 := [rewrite]: #719
+#433 := (= #430 #718)
+#439 := (= #429 1::int)
+#717 := [rewrite]: #439
+#715 := [monotonicity #717]: #433
+#709 := [trans #715 #716]: #720
+#706 := [monotonicity #709]: #711
+#714 := [trans #706 #713]: #708
+#557 := [monotonicity #714]: #556
+#702 := [trans #557 #700]: #701
+#437 := (iff #416 true)
+#727 := (or true false)
+#451 := (iff #727 true)
+#452 := [rewrite]: #451
+#726 := (iff #416 #727)
+#725 := (iff #748 false)
+#723 := (not true)
+#447 := (iff #723 false)
+#721 := [rewrite]: #447
+#724 := (iff #748 #723)
+#453 := (iff #746 true)
+#728 := (iff #746 #727)
+#729 := (iff #432 false)
+#392 := [rewrite]: #729
+#738 := (iff #411 true)
+#741 := [rewrite]: #738
+#450 := [monotonicity #741 #392]: #728
+#347 := [trans #450 #452]: #453
+#446 := [monotonicity #347]: #724
+#722 := [trans #446 #721]: #725
+#380 := (iff #742 true)
+#736 := (not false)
+#739 := (iff #736 true)
+#379 := [rewrite]: #739
+#374 := (iff #742 #736)
+#735 := (iff #535 false)
+#395 := (or false false)
+#733 := (iff #395 false)
+#734 := [rewrite]: #733
+#731 := (iff #535 #395)
+#393 := (iff #405 false)
+#394 := [rewrite]: #393
+#732 := [monotonicity #392 #394]: #731
+#730 := [trans #732 #734]: #735
+#737 := [monotonicity #730]: #374
+#740 := [trans #737 #379]: #380
+#436 := [monotonicity #740 #722]: #726
+#438 := [trans #436 #452]: #437
+#594 := [monotonicity #438 #702 #591]: #593
+#689 := [trans #594 #688]: #685
+#745 := (iff #750 false)
+#388 := [rewrite]: #745
+#670 := [monotonicity #388 #689]: #678
+#680 := [trans #670 #669]: #679
+#408 := (iff #752 #744)
+#404 := [rewrite]: #408
+#743 := (iff #747 false)
+#403 := [rewrite]: #743
+#682 := [monotonicity #403 #404 #680]: #677
+#674 := [trans #682 #672]: #673
+#663 := [monotonicity #674]: #662
+#661 := [trans #663 #665]: #662
+#660 := [quant-inst]: #659
+#666 := [mp #660 #661]: #675
+[unit-resolution #666 #767 #196]: false
+unsat
+f0cf0b269f03cceb1871f475a82678245ba862aa 350 0
+#2 := false
+#68 := -1::int
+decl f4 :: (-> int int int)
+#174 := -3::int
+#177 := (f4 -1::int -3::int)
+#180 := (= #177 -1::int)
+#193 := (not #180)
+#38 := 1::int
+#39 := (- 1::int)
+#40 := 3::int
+#41 := (- 3::int)
+#42 := (f4 #39 #41)
+#43 := (= #42 #39)
+#44 := (not #43)
+#196 := (iff #44 #193)
+#183 := (= -1::int #177)
+#188 := (not #183)
+#194 := (iff #188 #193)
+#191 := (iff #183 #180)
+#192 := [rewrite]: #191
+#195 := [monotonicity #192]: #194
+#189 := (iff #44 #188)
+#186 := (iff #43 #183)
+#184 := (iff #180 #183)
+#185 := [rewrite]: #184
+#181 := (iff #43 #180)
+#172 := (= #39 -1::int)
+#173 := [rewrite]: #172
+#178 := (= #42 #177)
+#175 := (= #41 -3::int)
+#176 := [rewrite]: #175
+#179 := [monotonicity #173 #176]: #178
+#182 := [monotonicity #179 #173]: #181
+#187 := [trans #182 #185]: #186
+#190 := [monotonicity #187]: #189
+#197 := [trans #190 #195]: #196
+#171 := [asserted]: #44
+#198 := [mp #171 #197]: #193
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#763 := (pattern #29)
+#11 := 0::int
+#72 := (* -1::int #9)
+#69 := (* -1::int #8)
+#127 := (mod #69 #72)
+#275 := (+ #29 #127)
+#276 := (= #275 0::int)
+#30 := (mod #8 #9)
+#272 := (* -1::int #30)
+#273 := (+ #29 #272)
+#274 := (= #273 0::int)
+#94 := (<= #9 0::int)
+#90 := (<= #8 0::int)
+#214 := (or #90 #94)
+#215 := (not #214)
+#101 := (>= #8 0::int)
+#206 := (or #94 #101)
+#207 := (not #206)
+#221 := (or #207 #215)
+#277 := (ite #221 #274 #276)
+#271 := (= #29 0::int)
+#12 := (= #8 0::int)
+#278 := (ite #12 #271 #277)
+#270 := (= #8 #29)
+#13 := (= #9 0::int)
+#279 := (ite #13 #270 #278)
+#764 := (forall (vars (?v0 int) (?v1 int)) (:pat #763) #279)
+#282 := (forall (vars (?v0 int) (?v1 int)) #279)
+#767 := (iff #282 #764)
+#765 := (iff #279 #279)
+#766 := [refl]: #765
+#768 := [quant-intro #766]: #767
+#133 := (* -1::int #127)
+#239 := (ite #221 #30 #133)
+#242 := (ite #12 0::int #239)
+#245 := (ite #13 #8 #242)
+#248 := (= #29 #245)
+#251 := (forall (vars (?v0 int) (?v1 int)) #248)
+#283 := (iff #251 #282)
+#280 := (iff #248 #279)
+#281 := [rewrite]: #280
+#284 := [quant-intro #281]: #283
+#102 := (not #101)
+#95 := (not #94)
+#105 := (and #95 #102)
+#91 := (not #90)
+#98 := (and #91 #95)
+#108 := (or #98 #105)
+#153 := (ite #108 #30 #133)
+#156 := (ite #12 0::int #153)
+#159 := (ite #13 #8 #156)
+#162 := (= #29 #159)
+#165 := (forall (vars (?v0 int) (?v1 int)) #162)
+#252 := (iff #165 #251)
+#249 := (iff #162 #248)
+#246 := (= #159 #245)
+#243 := (= #156 #242)
+#240 := (= #153 #239)
+#224 := (iff #108 #221)
+#218 := (or #215 #207)
+#222 := (iff #218 #221)
+#223 := [rewrite]: #222
+#219 := (iff #108 #218)
+#216 := (iff #105 #207)
+#217 := [rewrite]: #216
+#204 := (iff #98 #215)
+#205 := [rewrite]: #204
+#220 := [monotonicity #205 #217]: #219
+#225 := [trans #220 #223]: #224
+#241 := [monotonicity #225]: #240
+#244 := [monotonicity #241]: #243
+#247 := [monotonicity #244]: #246
+#250 := [monotonicity #247]: #249
+#253 := [quant-intro #250]: #252
+#202 := (~ #165 #165)
+#199 := (~ #162 #162)
+#212 := [refl]: #199
+#203 := [nnf-pos #212]: #202
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#168 := (iff #37 #165)
+#62 := (and #16 #18)
+#65 := (or #17 #62)
+#138 := (ite #65 #30 #133)
+#141 := (ite #12 0::int #138)
+#144 := (ite #13 #8 #141)
+#147 := (= #29 #144)
+#150 := (forall (vars (?v0 int) (?v1 int)) #147)
+#166 := (iff #150 #165)
+#163 := (iff #147 #162)
+#160 := (= #144 #159)
+#157 := (= #141 #156)
+#154 := (= #138 #153)
+#109 := (iff #65 #108)
+#106 := (iff #62 #105)
+#103 := (iff #18 #102)
+#104 := [rewrite]: #103
+#96 := (iff #16 #95)
+#97 := [rewrite]: #96
+#107 := [monotonicity #97 #104]: #106
+#99 := (iff #17 #98)
+#92 := (iff #15 #91)
+#93 := [rewrite]: #92
+#100 := [monotonicity #93 #97]: #99
+#110 := [monotonicity #100 #107]: #109
+#155 := [monotonicity #110]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [quant-intro #164]: #166
+#151 := (iff #37 #150)
+#148 := (iff #36 #147)
+#145 := (= #35 #144)
+#142 := (= #34 #141)
+#139 := (= #33 #138)
+#136 := (= #32 #133)
+#130 := (- #127)
+#134 := (= #130 #133)
+#135 := [rewrite]: #134
+#131 := (= #32 #130)
+#128 := (= #31 #127)
+#73 := (= #23 #72)
+#74 := [rewrite]: #73
+#70 := (= #22 #69)
+#71 := [rewrite]: #70
+#129 := [monotonicity #71 #74]: #128
+#132 := [monotonicity #129]: #131
+#137 := [trans #132 #135]: #136
+#66 := (iff #20 #65)
+#63 := (iff #19 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#140 := [monotonicity #67 #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [monotonicity #146]: #148
+#152 := [quant-intro #149]: #151
+#169 := [trans #152 #167]: #168
+#126 := [asserted]: #37
+#170 := [mp #126 #169]: #165
+#213 := [mp~ #170 #203]: #165
+#254 := [mp #213 #253]: #251
+#285 := [mp #254 #284]: #282
+#769 := [mp #285 #768]: #764
+#684 := (not #764)
+#673 := (or #684 #180)
+#343 := (* -1::int -3::int)
+#427 := (* -1::int -1::int)
+#428 := (mod #427 #343)
+#429 := (+ #177 #428)
+#420 := (= #429 0::int)
+#431 := (mod -1::int -3::int)
+#432 := (* -1::int #431)
+#433 := (+ #177 #432)
+#430 := (= #433 0::int)
+#434 := (<= -3::int 0::int)
+#413 := (<= -1::int 0::int)
+#748 := (or #413 #434)
+#750 := (not #748)
+#407 := (>= -1::int 0::int)
+#537 := (or #434 #407)
+#744 := (not #537)
+#418 := (or #744 #750)
+#419 := (ite #418 #430 #420)
+#751 := (= #177 0::int)
+#752 := (= -1::int 0::int)
+#753 := (ite #752 #751 #419)
+#754 := (= -3::int 0::int)
+#749 := (ite #754 #183 #753)
+#674 := (or #684 #749)
+#676 := (iff #674 #673)
+#677 := (iff #673 #673)
+#661 := [rewrite]: #677
+#683 := (iff #749 #180)
+#672 := (ite false #180 #180)
+#681 := (iff #672 #180)
+#682 := [rewrite]: #681
+#669 := (iff #749 #672)
+#678 := (iff #753 #180)
+#596 := (ite false #751 #180)
+#687 := (iff #596 #180)
+#691 := [rewrite]: #687
+#597 := (iff #753 #596)
+#594 := (iff #419 #180)
+#728 := 2::int
+#558 := (= #177 2::int)
+#589 := (ite false #558 #180)
+#585 := (iff #589 #180)
+#593 := [rewrite]: #585
+#591 := (iff #419 #589)
+#689 := (iff #420 #180)
+#694 := (+ 1::int #177)
+#540 := (= #694 0::int)
+#685 := (iff #540 #180)
+#686 := [rewrite]: #685
+#688 := (iff #420 #540)
+#580 := (= #429 #694)
+#693 := (+ #177 1::int)
+#697 := (= #693 #694)
+#579 := [rewrite]: #697
+#695 := (= #429 #693)
+#539 := (= #428 1::int)
+#706 := (mod 1::int 3::int)
+#536 := (= #706 1::int)
+#538 := [rewrite]: #536
+#700 := (= #428 #706)
+#699 := (= #343 3::int)
+#705 := [rewrite]: #699
+#704 := (= #427 1::int)
+#698 := [rewrite]: #704
+#707 := [monotonicity #698 #705]: #700
+#692 := [trans #707 #538]: #539
+#696 := [monotonicity #692]: #695
+#581 := [trans #696 #579]: #580
+#590 := [monotonicity #581]: #688
+#574 := [trans #590 #686]: #689
+#702 := (iff #430 #558)
+#720 := -2::int
+#713 := (+ -2::int #177)
+#710 := (= #713 0::int)
+#559 := (iff #710 #558)
+#701 := [rewrite]: #559
+#716 := (iff #430 #710)
+#714 := (= #433 #713)
+#722 := (+ #177 -2::int)
+#708 := (= #722 #713)
+#709 := [rewrite]: #708
+#711 := (= #433 #722)
+#721 := (= #432 -2::int)
+#440 := (* -1::int 2::int)
+#435 := (= #440 -2::int)
+#717 := [rewrite]: #435
+#441 := (= #432 #440)
+#438 := (= #431 2::int)
+#439 := [rewrite]: #438
+#719 := [monotonicity #439]: #441
+#718 := [trans #719 #717]: #721
+#712 := [monotonicity #718]: #711
+#715 := [trans #712 #709]: #714
+#557 := [monotonicity #715]: #716
+#703 := [trans #557 #701]: #702
+#727 := (iff #418 false)
+#725 := (or false false)
+#449 := (iff #725 false)
+#723 := [rewrite]: #449
+#726 := (iff #418 #725)
+#455 := (iff #750 false)
+#1 := true
+#735 := (not true)
+#732 := (iff #735 false)
+#738 := [rewrite]: #732
+#453 := (iff #750 #735)
+#730 := (iff #748 true)
+#382 := (or true true)
+#743 := (iff #382 true)
+#729 := [rewrite]: #743
+#742 := (iff #748 #382)
+#746 := (iff #434 true)
+#406 := [rewrite]: #746
+#741 := (iff #413 true)
+#381 := [rewrite]: #741
+#740 := [monotonicity #381 #406]: #742
+#452 := [trans #740 #729]: #730
+#454 := [monotonicity #452]: #453
+#349 := [trans #454 #738]: #455
+#376 := (iff #744 false)
+#736 := (iff #744 #735)
+#733 := (iff #537 true)
+#731 := (or true false)
+#396 := (iff #731 true)
+#397 := [rewrite]: #396
+#394 := (iff #537 #731)
+#747 := (iff #407 false)
+#390 := [rewrite]: #747
+#395 := [monotonicity #406 #390]: #394
+#734 := [trans #395 #397]: #733
+#737 := [monotonicity #734]: #736
+#739 := [trans #737 #738]: #376
+#448 := [monotonicity #739 #349]: #726
+#724 := [trans #448 #723]: #727
+#592 := [monotonicity #724 #703 #574]: #591
+#595 := [trans #592 #593]: #594
+#405 := (iff #752 false)
+#410 := [rewrite]: #405
+#690 := [monotonicity #410 #595]: #597
+#680 := [trans #690 #691]: #678
+#755 := (iff #754 false)
+#745 := [rewrite]: #755
+#671 := [monotonicity #745 #192 #680]: #669
+#679 := [trans #671 #682]: #683
+#670 := [monotonicity #679]: #676
+#662 := [trans #670 #661]: #676
+#675 := [quant-inst]: #674
+#664 := [mp #675 #662]: #673
+[unit-resolution #664 #769 #198]: false
+unsat
+1bceda17feead712acb5cdc4842332c75363e332 319 0
+#2 := false
+#11 := 0::int
+decl f4 :: (-> int int int)
+#170 := -3::int
+#173 := (f4 -3::int -3::int)
+#176 := (= #173 0::int)
+#189 := (not #176)
+#38 := 3::int
+#39 := (- 3::int)
+#40 := (f4 #39 #39)
+#41 := (= #40 0::int)
+#42 := (not #41)
+#192 := (iff #42 #189)
+#179 := (= 0::int #173)
+#184 := (not #179)
+#190 := (iff #184 #189)
+#187 := (iff #179 #176)
+#188 := [rewrite]: #187
+#191 := [monotonicity #188]: #190
+#185 := (iff #42 #184)
+#182 := (iff #41 #179)
+#180 := (iff #176 #179)
+#181 := [rewrite]: #180
+#177 := (iff #41 #176)
+#174 := (= #40 #173)
+#171 := (= #39 -3::int)
+#172 := [rewrite]: #171
+#175 := [monotonicity #172 #172]: #174
+#178 := [monotonicity #175]: #177
+#183 := [trans #178 #181]: #182
+#186 := [monotonicity #183]: #185
+#193 := [trans #186 #191]: #192
+#169 := [asserted]: #42
+#194 := [mp #169 #193]: #189
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#760 := (pattern #29)
+#66 := -1::int
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#125 := (mod #67 #70)
+#271 := (+ #29 #125)
+#272 := (= #271 0::int)
+#30 := (mod #8 #9)
+#268 := (* -1::int #30)
+#269 := (+ #29 #268)
+#270 := (= #269 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#210 := (or #88 #92)
+#211 := (not #210)
+#99 := (>= #8 0::int)
+#202 := (or #92 #99)
+#203 := (not #202)
+#217 := (or #203 #211)
+#273 := (ite #217 #270 #272)
+#267 := (= #29 0::int)
+#12 := (= #8 0::int)
+#274 := (ite #12 #267 #273)
+#266 := (= #8 #29)
+#13 := (= #9 0::int)
+#275 := (ite #13 #266 #274)
+#761 := (forall (vars (?v0 int) (?v1 int)) (:pat #760) #275)
+#278 := (forall (vars (?v0 int) (?v1 int)) #275)
+#764 := (iff #278 #761)
+#762 := (iff #275 #275)
+#763 := [refl]: #762
+#765 := [quant-intro #763]: #764
+#131 := (* -1::int #125)
+#235 := (ite #217 #30 #131)
+#238 := (ite #12 0::int #235)
+#241 := (ite #13 #8 #238)
+#244 := (= #29 #241)
+#247 := (forall (vars (?v0 int) (?v1 int)) #244)
+#279 := (iff #247 #278)
+#276 := (iff #244 #275)
+#277 := [rewrite]: #276
+#280 := [quant-intro #277]: #279
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#151 := (ite #106 #30 #131)
+#154 := (ite #12 0::int #151)
+#157 := (ite #13 #8 #154)
+#160 := (= #29 #157)
+#163 := (forall (vars (?v0 int) (?v1 int)) #160)
+#248 := (iff #163 #247)
+#245 := (iff #160 #244)
+#242 := (= #157 #241)
+#239 := (= #154 #238)
+#236 := (= #151 #235)
+#220 := (iff #106 #217)
+#214 := (or #211 #203)
+#218 := (iff #214 #217)
+#219 := [rewrite]: #218
+#215 := (iff #106 #214)
+#212 := (iff #103 #203)
+#213 := [rewrite]: #212
+#200 := (iff #96 #211)
+#201 := [rewrite]: #200
+#216 := [monotonicity #201 #213]: #215
+#221 := [trans #216 #219]: #220
+#237 := [monotonicity #221]: #236
+#240 := [monotonicity #237]: #239
+#243 := [monotonicity #240]: #242
+#246 := [monotonicity #243]: #245
+#249 := [quant-intro #246]: #248
+#198 := (~ #163 #163)
+#195 := (~ #160 #160)
+#208 := [refl]: #195
+#199 := [nnf-pos #208]: #198
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#166 := (iff #37 #163)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#136 := (ite #63 #30 #131)
+#139 := (ite #12 0::int #136)
+#142 := (ite #13 #8 #139)
+#145 := (= #29 #142)
+#148 := (forall (vars (?v0 int) (?v1 int)) #145)
+#164 := (iff #148 #163)
+#161 := (iff #145 #160)
+#158 := (= #142 #157)
+#155 := (= #139 #154)
+#152 := (= #136 #151)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#153 := [monotonicity #108]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [quant-intro #162]: #164
+#149 := (iff #37 #148)
+#146 := (iff #36 #145)
+#143 := (= #35 #142)
+#140 := (= #34 #139)
+#137 := (= #33 #136)
+#134 := (= #32 #131)
+#128 := (- #125)
+#132 := (= #128 #131)
+#133 := [rewrite]: #132
+#129 := (= #32 #128)
+#126 := (= #31 #125)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#127 := [monotonicity #69 #72]: #126
+#130 := [monotonicity #127]: #129
+#135 := [trans #130 #133]: #134
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#138 := [monotonicity #65 #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [quant-intro #147]: #149
+#167 := [trans #150 #165]: #166
+#124 := [asserted]: #37
+#168 := [mp #124 #167]: #163
+#209 := [mp~ #168 #199]: #163
+#250 := [mp #209 #249]: #247
+#281 := [mp #250 #280]: #278
+#766 := [mp #281 #765]: #761
+#537 := (not #761)
+#685 := (or #537 #176)
+#339 := (* -1::int -3::int)
+#424 := (mod #339 #339)
+#425 := (+ #173 #424)
+#426 := (= #425 0::int)
+#417 := (mod -3::int -3::int)
+#428 := (* -1::int #417)
+#429 := (+ #173 #428)
+#357 := (= #429 0::int)
+#430 := (<= -3::int 0::int)
+#427 := (or #430 #430)
+#431 := (not #427)
+#410 := (>= -3::int 0::int)
+#745 := (or #430 #410)
+#747 := (not #745)
+#404 := (or #747 #431)
+#534 := (ite #404 #357 #426)
+#741 := (= -3::int 0::int)
+#415 := (ite #741 #176 #534)
+#416 := (= -3::int #173)
+#748 := (ite #741 #416 #415)
+#587 := (or #537 #748)
+#683 := (iff #587 #685)
+#571 := (iff #685 #685)
+#586 := [rewrite]: #571
+#577 := (iff #748 #176)
+#746 := (= #173 -3::int)
+#692 := (ite false #746 #176)
+#694 := (iff #692 #176)
+#576 := [rewrite]: #694
+#693 := (iff #748 #692)
+#689 := (iff #415 #176)
+#695 := (ite false #176 #176)
+#703 := (iff #695 #176)
+#697 := [rewrite]: #703
+#535 := (iff #415 #695)
+#704 := (iff #534 #176)
+#696 := (iff #534 #695)
+#700 := (iff #426 #176)
+#698 := (= #425 #173)
+#438 := (+ #173 0::int)
+#432 := (= #438 #173)
+#714 := [rewrite]: #432
+#555 := (= #425 #438)
+#713 := (= #424 0::int)
+#705 := (mod 3::int 3::int)
+#712 := (= #705 0::int)
+#707 := [rewrite]: #712
+#706 := (= #424 #705)
+#709 := (= #339 3::int)
+#710 := [rewrite]: #709
+#711 := [monotonicity #710 #710]: #706
+#554 := [trans #711 #707]: #713
+#556 := [monotonicity #554]: #555
+#699 := [trans #556 #714]: #698
+#701 := [monotonicity #699]: #700
+#719 := (iff #357 #176)
+#718 := (= #429 #173)
+#716 := (= #429 #438)
+#436 := (= #428 0::int)
+#720 := (* -1::int 0::int)
+#725 := (= #720 0::int)
+#435 := [rewrite]: #725
+#724 := (= #428 #720)
+#445 := (= #417 0::int)
+#446 := [rewrite]: #445
+#721 := [monotonicity #446]: #724
+#437 := [trans #721 #435]: #436
+#717 := [monotonicity #437]: #716
+#715 := [trans #717 #714]: #718
+#708 := [monotonicity #715]: #719
+#722 := (iff #404 false)
+#449 := (or false false)
+#452 := (iff #449 false)
+#345 := [rewrite]: #452
+#450 := (iff #404 #449)
+#726 := (iff #431 false)
+#1 := true
+#394 := (not true)
+#732 := (iff #394 false)
+#733 := [rewrite]: #732
+#737 := (iff #431 #394)
+#379 := (iff #427 true)
+#735 := (or true true)
+#738 := (iff #735 true)
+#378 := [rewrite]: #738
+#373 := (iff #427 #735)
+#742 := (iff #430 true)
+#402 := [rewrite]: #742
+#736 := [monotonicity #402 #402]: #373
+#739 := [trans #736 #378]: #379
+#740 := [monotonicity #739]: #737
+#727 := [trans #740 #733]: #726
+#734 := (iff #747 false)
+#730 := (iff #747 #394)
+#392 := (iff #745 true)
+#403 := (or true false)
+#728 := (iff #403 true)
+#391 := [rewrite]: #728
+#744 := (iff #745 #403)
+#407 := (iff #410 false)
+#743 := [rewrite]: #407
+#387 := [monotonicity #402 #743]: #744
+#393 := [trans #387 #391]: #392
+#731 := [monotonicity #393]: #730
+#729 := [trans #731 #733]: #734
+#451 := [monotonicity #729 #727]: #450
+#723 := [trans #451 #345]: #722
+#702 := [monotonicity #723 #708 #701]: #696
+#533 := [trans #702 #697]: #704
+#749 := (iff #741 false)
+#750 := [rewrite]: #749
+#536 := [monotonicity #750 #533]: #535
+#690 := [trans #536 #697]: #689
+#751 := (iff #416 #746)
+#752 := [rewrite]: #751
+#691 := [monotonicity #750 #752 #690]: #693
+#578 := [trans #691 #576]: #577
+#686 := [monotonicity #578]: #683
+#588 := [trans #686 #586]: #683
+#682 := [quant-inst]: #587
+#589 := [mp #682 #588]: #685
+[unit-resolution #589 #766 #194]: false
+unsat
+a780ce648e23f3eae00ee43963c42659a1a7c923 347 0
+#2 := false
+#183 := -2::int
+decl f4 :: (-> int int int)
+#177 := -3::int
+#174 := -5::int
+#180 := (f4 -5::int -3::int)
+#186 := (= #180 -2::int)
+#189 := (not #186)
+#43 := 2::int
+#44 := (- 2::int)
+#40 := 3::int
+#41 := (- 3::int)
+#38 := 5::int
+#39 := (- 5::int)
+#42 := (f4 #39 #41)
+#45 := (= #42 #44)
+#46 := (not #45)
+#190 := (iff #46 #189)
+#187 := (iff #45 #186)
+#184 := (= #44 -2::int)
+#185 := [rewrite]: #184
+#181 := (= #42 #180)
+#178 := (= #41 -3::int)
+#179 := [rewrite]: #178
+#175 := (= #39 -5::int)
+#176 := [rewrite]: #175
+#182 := [monotonicity #176 #179]: #181
+#188 := [monotonicity #182 #185]: #187
+#191 := [monotonicity #188]: #190
+#173 := [asserted]: #46
+#194 := [mp #173 #191]: #189
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#758 := (pattern #29)
+#11 := 0::int
+#70 := -1::int
+#74 := (* -1::int #9)
+#71 := (* -1::int #8)
+#129 := (mod #71 #74)
+#269 := (+ #29 #129)
+#270 := (= #269 0::int)
+#30 := (mod #8 #9)
+#266 := (* -1::int #30)
+#267 := (+ #29 #266)
+#268 := (= #267 0::int)
+#96 := (<= #9 0::int)
+#92 := (<= #8 0::int)
+#208 := (or #92 #96)
+#209 := (not #208)
+#103 := (>= #8 0::int)
+#200 := (or #96 #103)
+#201 := (not #200)
+#215 := (or #201 #209)
+#271 := (ite #215 #268 #270)
+#265 := (= #29 0::int)
+#12 := (= #8 0::int)
+#272 := (ite #12 #265 #271)
+#264 := (= #8 #29)
+#13 := (= #9 0::int)
+#273 := (ite #13 #264 #272)
+#759 := (forall (vars (?v0 int) (?v1 int)) (:pat #758) #273)
+#276 := (forall (vars (?v0 int) (?v1 int)) #273)
+#762 := (iff #276 #759)
+#760 := (iff #273 #273)
+#761 := [refl]: #760
+#763 := [quant-intro #761]: #762
+#135 := (* -1::int #129)
+#233 := (ite #215 #30 #135)
+#236 := (ite #12 0::int #233)
+#239 := (ite #13 #8 #236)
+#242 := (= #29 #239)
+#245 := (forall (vars (?v0 int) (?v1 int)) #242)
+#277 := (iff #245 #276)
+#274 := (iff #242 #273)
+#275 := [rewrite]: #274
+#278 := [quant-intro #275]: #277
+#104 := (not #103)
+#97 := (not #96)
+#107 := (and #97 #104)
+#93 := (not #92)
+#100 := (and #93 #97)
+#110 := (or #100 #107)
+#155 := (ite #110 #30 #135)
+#158 := (ite #12 0::int #155)
+#161 := (ite #13 #8 #158)
+#164 := (= #29 #161)
+#167 := (forall (vars (?v0 int) (?v1 int)) #164)
+#246 := (iff #167 #245)
+#243 := (iff #164 #242)
+#240 := (= #161 #239)
+#237 := (= #158 #236)
+#234 := (= #155 #233)
+#218 := (iff #110 #215)
+#212 := (or #209 #201)
+#216 := (iff #212 #215)
+#217 := [rewrite]: #216
+#213 := (iff #110 #212)
+#210 := (iff #107 #201)
+#211 := [rewrite]: #210
+#198 := (iff #100 #209)
+#199 := [rewrite]: #198
+#214 := [monotonicity #199 #211]: #213
+#219 := [trans #214 #217]: #218
+#235 := [monotonicity #219]: #234
+#238 := [monotonicity #235]: #237
+#241 := [monotonicity #238]: #240
+#244 := [monotonicity #241]: #243
+#247 := [quant-intro #244]: #246
+#196 := (~ #167 #167)
+#192 := (~ #164 #164)
+#206 := [refl]: #192
+#197 := [nnf-pos #206]: #196
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#170 := (iff #37 #167)
+#64 := (and #16 #18)
+#67 := (or #17 #64)
+#140 := (ite #67 #30 #135)
+#143 := (ite #12 0::int #140)
+#146 := (ite #13 #8 #143)
+#149 := (= #29 #146)
+#152 := (forall (vars (?v0 int) (?v1 int)) #149)
+#168 := (iff #152 #167)
+#165 := (iff #149 #164)
+#162 := (= #146 #161)
+#159 := (= #143 #158)
+#156 := (= #140 #155)
+#111 := (iff #67 #110)
+#108 := (iff #64 #107)
+#105 := (iff #18 #104)
+#106 := [rewrite]: #105
+#98 := (iff #16 #97)
+#99 := [rewrite]: #98
+#109 := [monotonicity #99 #106]: #108
+#101 := (iff #17 #100)
+#94 := (iff #15 #93)
+#95 := [rewrite]: #94
+#102 := [monotonicity #95 #99]: #101
+#112 := [monotonicity #102 #109]: #111
+#157 := [monotonicity #112]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [monotonicity #163]: #165
+#169 := [quant-intro #166]: #168
+#153 := (iff #37 #152)
+#150 := (iff #36 #149)
+#147 := (= #35 #146)
+#144 := (= #34 #143)
+#141 := (= #33 #140)
+#138 := (= #32 #135)
+#132 := (- #129)
+#136 := (= #132 #135)
+#137 := [rewrite]: #136
+#133 := (= #32 #132)
+#130 := (= #31 #129)
+#75 := (= #23 #74)
+#76 := [rewrite]: #75
+#72 := (= #22 #71)
+#73 := [rewrite]: #72
+#131 := [monotonicity #73 #76]: #130
+#134 := [monotonicity #131]: #133
+#139 := [trans #134 #137]: #138
+#68 := (iff #20 #67)
+#65 := (iff #19 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#142 := [monotonicity #69 #139]: #141
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#151 := [monotonicity #148]: #150
+#154 := [quant-intro #151]: #153
+#171 := [trans #154 #169]: #170
+#128 := [asserted]: #37
+#172 := [mp #128 #171]: #167
+#207 := [mp~ #172 #197]: #167
+#248 := [mp #207 #247]: #245
+#279 := [mp #248 #278]: #276
+#764 := [mp #279 #763]: #759
+#669 := (not #759)
+#670 := (or #669 #186)
+#337 := (* -1::int -3::int)
+#422 := (* -1::int -5::int)
+#423 := (mod #422 #337)
+#424 := (+ #180 #423)
+#415 := (= #424 0::int)
+#426 := (mod -5::int -3::int)
+#427 := (* -1::int #426)
+#355 := (+ #180 #427)
+#428 := (= #355 0::int)
+#425 := (<= -3::int 0::int)
+#429 := (<= -5::int 0::int)
+#408 := (or #429 #425)
+#743 := (not #408)
+#745 := (>= -5::int 0::int)
+#402 := (or #425 #745)
+#532 := (not #402)
+#739 := (or #532 #743)
+#413 := (ite #739 #428 #415)
+#414 := (= #180 0::int)
+#746 := (= -5::int 0::int)
+#747 := (ite #746 #414 #413)
+#748 := (= -5::int #180)
+#749 := (= -3::int 0::int)
+#744 := (ite #749 #748 #747)
+#671 := (or #669 #744)
+#672 := (iff #671 #670)
+#657 := (iff #670 #670)
+#659 := [rewrite]: #657
+#679 := (iff #744 #186)
+#405 := (= #180 -5::int)
+#666 := (ite false #405 #186)
+#678 := (iff #666 #186)
+#674 := [rewrite]: #678
+#676 := (iff #744 #666)
+#667 := (iff #747 #186)
+#685 := (ite false #414 #186)
+#673 := (iff #685 #186)
+#675 := [rewrite]: #673
+#682 := (iff #747 #685)
+#591 := (iff #413 #186)
+#435 := 1::int
+#696 := (= #180 1::int)
+#587 := (ite false #696 #186)
+#589 := (iff #587 #186)
+#590 := [rewrite]: #589
+#580 := (iff #413 #587)
+#584 := (iff #415 #186)
+#574 := (+ 2::int #180)
+#585 := (= #574 0::int)
+#684 := (iff #585 #186)
+#569 := [rewrite]: #684
+#680 := (iff #415 #585)
+#535 := (= #424 #574)
+#691 := (+ #180 2::int)
+#575 := (= #691 #574)
+#576 := [rewrite]: #575
+#689 := (= #424 #691)
+#688 := (= #423 2::int)
+#702 := (mod 5::int 3::int)
+#534 := (= #702 2::int)
+#687 := [rewrite]: #534
+#531 := (= #423 #702)
+#701 := (= #337 3::int)
+#695 := [rewrite]: #701
+#694 := (= #422 5::int)
+#700 := [rewrite]: #694
+#533 := [monotonicity #700 #695]: #531
+#690 := [trans #533 #687]: #688
+#692 := [monotonicity #690]: #689
+#683 := [trans #692 #576]: #535
+#681 := [monotonicity #683]: #680
+#586 := [trans #681 #569]: #584
+#699 := (iff #428 #696)
+#704 := (+ -1::int #180)
+#552 := (= #704 0::int)
+#697 := (iff #552 #696)
+#698 := [rewrite]: #697
+#553 := (iff #428 #552)
+#705 := (= #355 #704)
+#707 := (+ #180 -1::int)
+#709 := (= #707 #704)
+#710 := [rewrite]: #709
+#708 := (= #355 #707)
+#717 := (= #427 -1::int)
+#715 := (* -1::int 1::int)
+#716 := (= #715 -1::int)
+#713 := [rewrite]: #716
+#430 := (= #427 #715)
+#436 := (= #426 1::int)
+#714 := [rewrite]: #436
+#712 := [monotonicity #714]: #430
+#706 := [trans #712 #713]: #717
+#703 := [monotonicity #706]: #708
+#711 := [trans #703 #710]: #705
+#554 := [monotonicity #711]: #553
+#693 := [trans #554 #698]: #699
+#433 := (iff #739 false)
+#444 := (or false false)
+#719 := (iff #444 false)
+#723 := [rewrite]: #719
+#718 := (iff #739 #444)
+#721 := (iff #743 false)
+#1 := true
+#727 := (not true)
+#734 := (iff #727 false)
+#736 := [rewrite]: #734
+#343 := (iff #743 #727)
+#449 := (iff #408 true)
+#738 := (or true true)
+#447 := (iff #738 true)
+#448 := [rewrite]: #447
+#724 := (iff #408 #738)
+#385 := (iff #425 true)
+#726 := [rewrite]: #385
+#737 := (iff #429 true)
+#735 := [rewrite]: #737
+#725 := [monotonicity #735 #726]: #724
+#450 := [trans #725 #448]: #449
+#720 := [monotonicity #450]: #343
+#443 := [trans #720 #736]: #721
+#376 := (iff #532 false)
+#733 := (iff #532 #727)
+#731 := (iff #402 true)
+#391 := (or true false)
+#729 := (iff #391 true)
+#730 := [rewrite]: #729
+#392 := (iff #402 #391)
+#389 := (iff #745 false)
+#390 := [rewrite]: #389
+#728 := [monotonicity #726 #390]: #392
+#732 := [trans #728 #730]: #731
+#371 := [monotonicity #732]: #733
+#377 := [trans #371 #736]: #376
+#722 := [monotonicity #377 #443]: #718
+#434 := [trans #722 #723]: #433
+#588 := [monotonicity #434 #693 #586]: #580
+#592 := [trans #588 #590]: #591
+#401 := (iff #746 false)
+#742 := [rewrite]: #401
+#686 := [monotonicity #742 #592]: #682
+#664 := [trans #686 #675]: #667
+#400 := (iff #748 #405)
+#741 := [rewrite]: #400
+#750 := (iff #749 false)
+#740 := [rewrite]: #750
+#677 := [monotonicity #740 #741 #664]: #676
+#668 := [trans #677 #674]: #679
+#656 := [monotonicity #668]: #672
+#660 := [trans #656 #659]: #672
+#665 := [quant-inst]: #671
+#661 := [mp #665 #660]: #670
+[unit-resolution #661 #764 #194]: false
+unsat
+2f7ad29232f8d50954ed0686842bef03cb647ce4 327 0
+#2 := false
+#11 := 0::int
+decl f5 :: int
+#38 := f5
+#418 := (<= f5 0::int)
+#734 := (>= f5 0::int)
+#380 := (not #734)
+#723 := (not #418)
+#727 := (or #723 #380)
+#690 := (not #727)
+#39 := 3::int
+#415 := (mod f5 3::int)
+#66 := -1::int
+#416 := (* -1::int #415)
+decl f4 :: (-> int int int)
+#40 := (f4 f5 3::int)
+#344 := (+ #40 #416)
+#417 := (= #344 0::int)
+#563 := (not #417)
+#520 := (<= #344 0::int)
+#623 := (not #520)
+#631 := (>= #415 3::int)
+#632 := (not #631)
+#1 := true
+#57 := [true-axiom]: true
+#619 := (or false #632)
+#620 := [th-lemma]: #619
+#621 := [unit-resolution #620 #57]: #632
+#622 := [hypothesis]: #520
+#173 := (>= #40 3::int)
+#41 := (< #40 3::int)
+#42 := (not #41)
+#181 := (iff #42 #173)
+#172 := (not #173)
+#176 := (not #172)
+#179 := (iff #176 #173)
+#180 := [rewrite]: #179
+#177 := (iff #42 #176)
+#174 := (iff #41 #172)
+#175 := [rewrite]: #174
+#178 := [monotonicity #175]: #177
+#182 := [trans #178 #180]: #181
+#169 := [asserted]: #42
+#183 := [mp #169 #182]: #173
+#617 := [th-lemma #183 #622 #621]: false
+#609 := [lemma #617]: #623
+#626 := (or #563 #520)
+#637 := [th-lemma]: #626
+#615 := [unit-resolution #637 #609]: #563
+#614 := (or #690 #417)
+#438 := -3::int
+#411 := (* -1::int f5)
+#709 := (mod #411 -3::int)
+#433 := (+ #40 #709)
+#708 := (= #433 0::int)
+#423 := (ite #727 #417 #708)
+#403 := (= #40 0::int)
+#735 := (= f5 0::int)
+#703 := (ite #735 #403 #423)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#747 := (pattern #29)
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#125 := (mod #67 #70)
+#258 := (+ #29 #125)
+#259 := (= #258 0::int)
+#30 := (mod #8 #9)
+#255 := (* -1::int #30)
+#256 := (+ #29 #255)
+#257 := (= #256 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#197 := (or #88 #92)
+#198 := (not #197)
+#99 := (>= #8 0::int)
+#189 := (or #92 #99)
+#190 := (not #189)
+#204 := (or #190 #198)
+#260 := (ite #204 #257 #259)
+#254 := (= #29 0::int)
+#12 := (= #8 0::int)
+#261 := (ite #12 #254 #260)
+#253 := (= #8 #29)
+#13 := (= #9 0::int)
+#262 := (ite #13 #253 #261)
+#748 := (forall (vars (?v0 int) (?v1 int)) (:pat #747) #262)
+#265 := (forall (vars (?v0 int) (?v1 int)) #262)
+#751 := (iff #265 #748)
+#749 := (iff #262 #262)
+#750 := [refl]: #749
+#752 := [quant-intro #750]: #751
+#131 := (* -1::int #125)
+#222 := (ite #204 #30 #131)
+#225 := (ite #12 0::int #222)
+#228 := (ite #13 #8 #225)
+#231 := (= #29 #228)
+#234 := (forall (vars (?v0 int) (?v1 int)) #231)
+#266 := (iff #234 #265)
+#263 := (iff #231 #262)
+#264 := [rewrite]: #263
+#267 := [quant-intro #264]: #266
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#151 := (ite #106 #30 #131)
+#154 := (ite #12 0::int #151)
+#157 := (ite #13 #8 #154)
+#160 := (= #29 #157)
+#163 := (forall (vars (?v0 int) (?v1 int)) #160)
+#235 := (iff #163 #234)
+#232 := (iff #160 #231)
+#229 := (= #157 #228)
+#226 := (= #154 #225)
+#223 := (= #151 #222)
+#207 := (iff #106 #204)
+#201 := (or #198 #190)
+#205 := (iff #201 #204)
+#206 := [rewrite]: #205
+#202 := (iff #106 #201)
+#199 := (iff #103 #190)
+#200 := [rewrite]: #199
+#187 := (iff #96 #198)
+#188 := [rewrite]: #187
+#203 := [monotonicity #188 #200]: #202
+#208 := [trans #203 #206]: #207
+#224 := [monotonicity #208]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [quant-intro #233]: #235
+#185 := (~ #163 #163)
+#170 := (~ #160 #160)
+#195 := [refl]: #170
+#186 := [nnf-pos #195]: #185
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#166 := (iff #37 #163)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#136 := (ite #63 #30 #131)
+#139 := (ite #12 0::int #136)
+#142 := (ite #13 #8 #139)
+#145 := (= #29 #142)
+#148 := (forall (vars (?v0 int) (?v1 int)) #145)
+#164 := (iff #148 #163)
+#161 := (iff #145 #160)
+#158 := (= #142 #157)
+#155 := (= #139 #154)
+#152 := (= #136 #151)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#153 := [monotonicity #108]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [quant-intro #162]: #164
+#149 := (iff #37 #148)
+#146 := (iff #36 #145)
+#143 := (= #35 #142)
+#140 := (= #34 #139)
+#137 := (= #33 #136)
+#134 := (= #32 #131)
+#128 := (- #125)
+#132 := (= #128 #131)
+#133 := [rewrite]: #132
+#129 := (= #32 #128)
+#126 := (= #31 #125)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#127 := [monotonicity #69 #72]: #126
+#130 := [monotonicity #127]: #129
+#135 := [trans #130 #133]: #134
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#138 := [monotonicity #65 #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [quant-intro #147]: #149
+#167 := [trans #150 #165]: #166
+#124 := [asserted]: #37
+#168 := [mp #124 #167]: #163
+#196 := [mp~ #168 #186]: #163
+#237 := [mp #196 #236]: #234
+#268 := [mp #237 #267]: #265
+#753 := [mp #268 #752]: #748
+#692 := (not #748)
+#693 := (or #692 #703)
+#326 := (* -1::int 3::int)
+#412 := (mod #411 #326)
+#413 := (+ #40 #412)
+#404 := (= #413 0::int)
+#414 := (<= 3::int 0::int)
+#397 := (or #418 #414)
+#732 := (not #397)
+#391 := (or #414 #734)
+#521 := (not #391)
+#728 := (or #521 #732)
+#402 := (ite #728 #417 #404)
+#736 := (ite #735 #403 #402)
+#737 := (= f5 #40)
+#738 := (= 3::int 0::int)
+#733 := (ite #738 #737 #736)
+#698 := (or #692 #733)
+#694 := (iff #698 #693)
+#541 := (iff #693 #693)
+#542 := [rewrite]: #541
+#696 := (iff #733 #703)
+#701 := (ite false #737 #703)
+#706 := (iff #701 #703)
+#695 := [rewrite]: #706
+#705 := (iff #733 #701)
+#704 := (iff #736 #703)
+#424 := (iff #402 #423)
+#712 := (iff #404 #708)
+#707 := (= #413 #433)
+#710 := (= #412 #709)
+#439 := (= #326 -3::int)
+#332 := [rewrite]: #439
+#432 := [monotonicity #332]: #710
+#711 := [monotonicity #432]: #707
+#422 := [monotonicity #711]: #712
+#436 := (iff #728 #727)
+#366 := (or #380 #723)
+#713 := (iff #366 #727)
+#714 := [rewrite]: #713
+#726 := (iff #728 #366)
+#725 := (iff #732 #723)
+#722 := (iff #397 #418)
+#718 := (or #418 false)
+#721 := (iff #718 #418)
+#716 := [rewrite]: #721
+#719 := (iff #397 #718)
+#389 := (iff #414 false)
+#394 := [rewrite]: #389
+#720 := [monotonicity #394]: #719
+#360 := [trans #720 #716]: #722
+#365 := [monotonicity #360]: #725
+#381 := (iff #521 #380)
+#378 := (iff #391 #734)
+#730 := (or false #734)
+#374 := (iff #730 #734)
+#715 := [rewrite]: #374
+#390 := (iff #391 #730)
+#731 := [monotonicity #394]: #390
+#379 := [trans #731 #715]: #378
+#717 := [monotonicity #379]: #381
+#724 := [monotonicity #717 #365]: #726
+#437 := [trans #724 #714]: #436
+#425 := [monotonicity #437 #422]: #424
+#419 := [monotonicity #425]: #704
+#739 := (iff #738 false)
+#729 := [rewrite]: #739
+#702 := [monotonicity #729 #419]: #705
+#697 := [trans #702 #695]: #696
+#700 := [monotonicity #697]: #694
+#543 := [trans #700 #542]: #694
+#699 := [quant-inst]: #698
+#685 := [mp #699 #543]: #693
+#616 := [unit-resolution #685 #753]: #703
+#670 := (not #735)
+#669 := (not #703)
+#611 := (or #669 #670)
+#576 := (not #403)
+#686 := (<= #40 0::int)
+#618 := (not #686)
+#648 := (or #618 #172)
+#649 := [th-lemma]: #648
+#605 := [unit-resolution #649 #183]: #618
+#606 := (or #576 #686)
+#607 := [th-lemma]: #606
+#610 := [unit-resolution #607 #605]: #576
+#673 := (or #669 #670 #403)
+#558 := [def-axiom]: #673
+#612 := [unit-resolution #558 #610]: #611
+#613 := [unit-resolution #612 #616]: #670
+#573 := (or #669 #735 #423)
+#575 := [def-axiom]: #573
+#608 := [unit-resolution #575 #613 #616]: #423
+#677 := (not #423)
+#679 := (or #677 #690 #417)
+#680 := [def-axiom]: #679
+#587 := [unit-resolution #680 #608]: #614
+#588 := [unit-resolution #587 #615]: #690
+#688 := (or #727 #418)
+#682 := [def-axiom]: #688
+#589 := [unit-resolution #682 #588]: #418
+#683 := (or #727 #734)
+#689 := [def-axiom]: #683
+#482 := [unit-resolution #689 #588]: #734
+#593 := (or #735 #723 #380)
+#594 := [th-lemma]: #593
+#595 := [unit-resolution #594 #613]: #727
+[unit-resolution #595 #482 #589]: false
+unsat
+216003a1ebd8e56d3100995884d1e31eca49b8d0 345 0
+#2 := false
+#39 := 3::int
+decl f4 :: (-> int int int)
+decl f5 :: int
+#38 := f5
+#40 := (f4 f5 3::int)
+#441 := (mod #40 3::int)
+#657 := (>= #441 3::int)
+#658 := (not #657)
+#1 := true
+#59 := [true-axiom]: true
+#647 := (or false #658)
+#642 := [th-lemma]: #647
+#648 := [unit-resolution #642 #59]: #658
+#11 := 0::int
+#68 := -1::int
+#436 := (* -1::int #40)
+#600 := (+ f5 #436)
+#601 := (<= #600 0::int)
+#172 := (= f5 #40)
+#188 := (>= f5 3::int)
+#187 := (not #188)
+#178 := (not #172)
+#194 := (or #178 #187)
+#199 := (not #194)
+#42 := (< f5 3::int)
+#41 := (= #40 f5)
+#43 := (implies #41 #42)
+#44 := (not #43)
+#202 := (iff #44 #199)
+#179 := (or #42 #178)
+#184 := (not #179)
+#200 := (iff #184 #199)
+#197 := (iff #179 #194)
+#191 := (or #187 #178)
+#195 := (iff #191 #194)
+#196 := [rewrite]: #195
+#192 := (iff #179 #191)
+#189 := (iff #42 #187)
+#190 := [rewrite]: #189
+#193 := [monotonicity #190]: #192
+#198 := [trans #193 #196]: #197
+#201 := [monotonicity #198]: #200
+#185 := (iff #44 #184)
+#182 := (iff #43 #179)
+#175 := (implies #172 #42)
+#180 := (iff #175 #179)
+#181 := [rewrite]: #180
+#176 := (iff #43 #175)
+#173 := (iff #41 #172)
+#174 := [rewrite]: #173
+#177 := [monotonicity #174]: #176
+#183 := [trans #177 #181]: #182
+#186 := [monotonicity #183]: #185
+#203 := [trans #186 #201]: #202
+#171 := [asserted]: #44
+#204 := [mp #171 #203]: #199
+#205 := [not-or-elim #204]: #172
+#634 := (or #178 #601)
+#630 := [th-lemma]: #634
+#631 := [unit-resolution #630 #205]: #601
+#206 := [not-or-elim #204]: #188
+#438 := (f4 #40 3::int)
+#602 := (* -1::int #438)
+#603 := (+ #40 #602)
+#604 := (<= #603 0::int)
+#763 := (= #40 #438)
+#635 := (= #438 #40)
+#632 := [symm #205]: #41
+#636 := [monotonicity #632]: #635
+#637 := [symm #636]: #763
+#638 := (not #763)
+#633 := (or #638 #604)
+#639 := [th-lemma]: #633
+#612 := [unit-resolution #639 #637]: #604
+#369 := (* -1::int #441)
+#442 := (+ #438 #369)
+#707 := (<= #442 0::int)
+#439 := (= #442 0::int)
+#738 := -3::int
+#462 := (mod #436 -3::int)
+#357 := (+ #438 #462)
+#457 := (= #357 0::int)
+#422 := (<= #40 0::int)
+#750 := (not #422)
+#416 := (>= #40 0::int)
+#406 := (not #416)
+#751 := (or #406 #750)
+#736 := (ite #751 #439 #457)
+#760 := (= #438 0::int)
+#761 := (= #40 0::int)
+#447 := (ite #761 #760 #736)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#772 := (pattern #29)
+#72 := (* -1::int #9)
+#69 := (* -1::int #8)
+#127 := (mod #69 #72)
+#283 := (+ #29 #127)
+#284 := (= #283 0::int)
+#30 := (mod #8 #9)
+#280 := (* -1::int #30)
+#281 := (+ #29 #280)
+#282 := (= #281 0::int)
+#94 := (<= #9 0::int)
+#90 := (<= #8 0::int)
+#224 := (or #90 #94)
+#225 := (not #224)
+#101 := (>= #8 0::int)
+#216 := (or #94 #101)
+#217 := (not #216)
+#229 := (or #217 #225)
+#285 := (ite #229 #282 #284)
+#279 := (= #29 0::int)
+#12 := (= #8 0::int)
+#286 := (ite #12 #279 #285)
+#278 := (= #8 #29)
+#13 := (= #9 0::int)
+#287 := (ite #13 #278 #286)
+#773 := (forall (vars (?v0 int) (?v1 int)) (:pat #772) #287)
+#290 := (forall (vars (?v0 int) (?v1 int)) #287)
+#776 := (iff #290 #773)
+#774 := (iff #287 #287)
+#775 := [refl]: #774
+#777 := [quant-intro #775]: #776
+#133 := (* -1::int #127)
+#247 := (ite #229 #30 #133)
+#250 := (ite #12 0::int #247)
+#253 := (ite #13 #8 #250)
+#256 := (= #29 #253)
+#259 := (forall (vars (?v0 int) (?v1 int)) #256)
+#291 := (iff #259 #290)
+#288 := (iff #256 #287)
+#289 := [rewrite]: #288
+#292 := [quant-intro #289]: #291
+#102 := (not #101)
+#95 := (not #94)
+#105 := (and #95 #102)
+#91 := (not #90)
+#98 := (and #91 #95)
+#108 := (or #98 #105)
+#153 := (ite #108 #30 #133)
+#156 := (ite #12 0::int #153)
+#159 := (ite #13 #8 #156)
+#162 := (= #29 #159)
+#165 := (forall (vars (?v0 int) (?v1 int)) #162)
+#260 := (iff #165 #259)
+#257 := (iff #162 #256)
+#254 := (= #159 #253)
+#251 := (= #156 #250)
+#248 := (= #153 #247)
+#232 := (iff #108 #229)
+#226 := (or #225 #217)
+#230 := (iff #226 #229)
+#231 := [rewrite]: #230
+#227 := (iff #108 #226)
+#214 := (iff #105 #217)
+#215 := [rewrite]: #214
+#212 := (iff #98 #225)
+#213 := [rewrite]: #212
+#228 := [monotonicity #213 #215]: #227
+#233 := [trans #228 #231]: #232
+#249 := [monotonicity #233]: #248
+#252 := [monotonicity #249]: #251
+#255 := [monotonicity #252]: #254
+#258 := [monotonicity #255]: #257
+#261 := [quant-intro #258]: #260
+#210 := (~ #165 #165)
+#207 := (~ #162 #162)
+#222 := [refl]: #207
+#211 := [nnf-pos #222]: #210
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#168 := (iff #37 #165)
+#62 := (and #16 #18)
+#65 := (or #17 #62)
+#138 := (ite #65 #30 #133)
+#141 := (ite #12 0::int #138)
+#144 := (ite #13 #8 #141)
+#147 := (= #29 #144)
+#150 := (forall (vars (?v0 int) (?v1 int)) #147)
+#166 := (iff #150 #165)
+#163 := (iff #147 #162)
+#160 := (= #144 #159)
+#157 := (= #141 #156)
+#154 := (= #138 #153)
+#109 := (iff #65 #108)
+#106 := (iff #62 #105)
+#103 := (iff #18 #102)
+#104 := [rewrite]: #103
+#96 := (iff #16 #95)
+#97 := [rewrite]: #96
+#107 := [monotonicity #97 #104]: #106
+#99 := (iff #17 #98)
+#92 := (iff #15 #91)
+#93 := [rewrite]: #92
+#100 := [monotonicity #93 #97]: #99
+#110 := [monotonicity #100 #107]: #109
+#155 := [monotonicity #110]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [quant-intro #164]: #166
+#151 := (iff #37 #150)
+#148 := (iff #36 #147)
+#145 := (= #35 #144)
+#142 := (= #34 #141)
+#139 := (= #33 #138)
+#136 := (= #32 #133)
+#130 := (- #127)
+#134 := (= #130 #133)
+#135 := [rewrite]: #134
+#131 := (= #32 #130)
+#128 := (= #31 #127)
+#73 := (= #23 #72)
+#74 := [rewrite]: #73
+#70 := (= #22 #69)
+#71 := [rewrite]: #70
+#129 := [monotonicity #71 #74]: #128
+#132 := [monotonicity #129]: #131
+#137 := [trans #132 #135]: #136
+#66 := (iff #20 #65)
+#63 := (iff #19 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#140 := [monotonicity #67 #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [monotonicity #146]: #148
+#152 := [quant-intro #149]: #151
+#169 := [trans #152 #167]: #168
+#126 := [asserted]: #37
+#170 := [mp #126 #169]: #165
+#223 := [mp~ #170 #211]: #165
+#262 := [mp #223 #261]: #259
+#293 := [mp #262 #292]: #290
+#778 := [mp #293 #777]: #773
+#731 := (not #773)
+#720 := (or #731 #447)
+#351 := (* -1::int 3::int)
+#437 := (mod #436 #351)
+#429 := (+ #438 #437)
+#440 := (= #429 0::int)
+#443 := (<= 3::int 0::int)
+#757 := (or #422 #443)
+#759 := (not #757)
+#546 := (or #443 #416)
+#753 := (not #546)
+#427 := (or #753 #759)
+#428 := (ite #427 #439 #440)
+#762 := (ite #761 #760 #428)
+#758 := (= 3::int 0::int)
+#764 := (ite #758 #763 #762)
+#721 := (or #731 #764)
+#717 := (iff #721 #720)
+#723 := (iff #720 #720)
+#724 := [rewrite]: #723
+#730 := (iff #764 #447)
+#450 := (ite false #763 #447)
+#444 := (iff #450 #447)
+#726 := [rewrite]: #444
+#728 := (iff #764 #450)
+#448 := (iff #762 #447)
+#733 := (iff #428 #736)
+#458 := (iff #440 #457)
+#734 := (= #429 #357)
+#463 := (= #437 #462)
+#739 := (= #351 -3::int)
+#461 := [rewrite]: #739
+#464 := [monotonicity #461]: #463
+#735 := [monotonicity #464]: #734
+#732 := [monotonicity #735]: #458
+#749 := (iff #427 #751)
+#390 := (iff #759 #750)
+#385 := (iff #757 #422)
+#744 := (or #422 false)
+#741 := (iff #744 #422)
+#747 := [rewrite]: #741
+#745 := (iff #757 #744)
+#419 := (iff #443 false)
+#755 := [rewrite]: #419
+#746 := [monotonicity #755]: #745
+#748 := [trans #746 #747]: #385
+#391 := [monotonicity #748]: #390
+#742 := (iff #753 #406)
+#404 := (iff #546 #416)
+#415 := (or false #416)
+#740 := (iff #415 #416)
+#403 := [rewrite]: #740
+#756 := (iff #546 #415)
+#399 := [monotonicity #755]: #756
+#405 := [trans #399 #403]: #404
+#743 := [monotonicity #405]: #742
+#752 := [monotonicity #743 #391]: #749
+#737 := [monotonicity #752 #732]: #733
+#449 := [monotonicity #737]: #448
+#754 := (iff #758 false)
+#414 := [rewrite]: #754
+#729 := [monotonicity #414 #449]: #728
+#727 := [trans #729 #726]: #730
+#718 := [monotonicity #727]: #717
+#719 := [trans #718 #724]: #717
+#722 := [quant-inst]: #721
+#725 := [mp #722 #719]: #720
+#613 := [unit-resolution #725 #778]: #447
+#589 := (not #761)
+#614 := (not #601)
+#507 := (or #750 #187 #614)
+#618 := [th-lemma]: #507
+#619 := [unit-resolution #618 #206 #631]: #750
+#620 := (or #589 #422)
+#625 := [th-lemma]: #620
+#621 := [unit-resolution #625 #619]: #589
+#588 := (not #447)
+#697 := (or #588 #761 #736)
+#599 := [def-axiom]: #697
+#622 := [unit-resolution #599 #621 #613]: #736
+#568 := (or #751 #422)
+#710 := [def-axiom]: #568
+#623 := [unit-resolution #710 #619]: #751
+#711 := (not #751)
+#709 := (not #736)
+#716 := (or #709 #711 #439)
+#545 := [def-axiom]: #716
+#626 := [unit-resolution #545 #623 #622]: #439
+#701 := (not #439)
+#627 := (or #701 #707)
+#628 := [th-lemma]: #627
+#624 := [unit-resolution #628 #626]: #707
+[th-lemma #624 #612 #206 #631 #648]: false
+unsat
+5fd09db561a34542fa7100a699cfcf794f5f6fde 592 0
 #2 := false
 #11 := 0::int
 decl f3 :: (-> int int int)
@@ -41018,361 +43082,7 @@
 #362 := [unit-resolution #397 #361]: #600
 [th-lemma #362 #415 #382 #378]: false
 unsat
-0014d0664084b0406eb7d7fe8514292d539673ea 353 0
-#2 := false
-#42 := 1::int
-decl f4 :: (-> int int int)
-#40 := 3::int
-#172 := -5::int
-#175 := (f4 -5::int 3::int)
-#178 := (= #175 1::int)
-#191 := (not #178)
-#38 := 5::int
-#39 := (- 5::int)
-#41 := (f4 #39 3::int)
-#43 := (= #41 1::int)
-#44 := (not #43)
-#194 := (iff #44 #191)
-#181 := (= 1::int #175)
-#186 := (not #181)
-#192 := (iff #186 #191)
-#189 := (iff #181 #178)
-#190 := [rewrite]: #189
-#193 := [monotonicity #190]: #192
-#187 := (iff #44 #186)
-#184 := (iff #43 #181)
-#182 := (iff #178 #181)
-#183 := [rewrite]: #182
-#179 := (iff #43 #178)
-#176 := (= #41 #175)
-#173 := (= #39 -5::int)
-#174 := [rewrite]: #173
-#177 := [monotonicity #174]: #176
-#180 := [monotonicity #177]: #179
-#185 := [trans #180 #183]: #184
-#188 := [monotonicity #185]: #187
-#195 := [trans #188 #193]: #194
-#171 := [asserted]: #44
-#196 := [mp #171 #195]: #191
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#761 := (pattern #29)
-#11 := 0::int
-#68 := -1::int
-#72 := (* -1::int #9)
-#69 := (* -1::int #8)
-#127 := (mod #69 #72)
-#273 := (+ #29 #127)
-#274 := (= #273 0::int)
-#30 := (mod #8 #9)
-#270 := (* -1::int #30)
-#271 := (+ #29 #270)
-#272 := (= #271 0::int)
-#94 := (<= #9 0::int)
-#90 := (<= #8 0::int)
-#212 := (or #90 #94)
-#213 := (not #212)
-#101 := (>= #8 0::int)
-#204 := (or #94 #101)
-#205 := (not #204)
-#219 := (or #205 #213)
-#275 := (ite #219 #272 #274)
-#269 := (= #29 0::int)
-#12 := (= #8 0::int)
-#276 := (ite #12 #269 #275)
-#268 := (= #8 #29)
-#13 := (= #9 0::int)
-#277 := (ite #13 #268 #276)
-#762 := (forall (vars (?v0 int) (?v1 int)) (:pat #761) #277)
-#280 := (forall (vars (?v0 int) (?v1 int)) #277)
-#765 := (iff #280 #762)
-#763 := (iff #277 #277)
-#764 := [refl]: #763
-#766 := [quant-intro #764]: #765
-#133 := (* -1::int #127)
-#237 := (ite #219 #30 #133)
-#240 := (ite #12 0::int #237)
-#243 := (ite #13 #8 #240)
-#246 := (= #29 #243)
-#249 := (forall (vars (?v0 int) (?v1 int)) #246)
-#281 := (iff #249 #280)
-#278 := (iff #246 #277)
-#279 := [rewrite]: #278
-#282 := [quant-intro #279]: #281
-#102 := (not #101)
-#95 := (not #94)
-#105 := (and #95 #102)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#153 := (ite #108 #30 #133)
-#156 := (ite #12 0::int #153)
-#159 := (ite #13 #8 #156)
-#162 := (= #29 #159)
-#165 := (forall (vars (?v0 int) (?v1 int)) #162)
-#250 := (iff #165 #249)
-#247 := (iff #162 #246)
-#244 := (= #159 #243)
-#241 := (= #156 #240)
-#238 := (= #153 #237)
-#222 := (iff #108 #219)
-#216 := (or #213 #205)
-#220 := (iff #216 #219)
-#221 := [rewrite]: #220
-#217 := (iff #108 #216)
-#214 := (iff #105 #205)
-#215 := [rewrite]: #214
-#202 := (iff #98 #213)
-#203 := [rewrite]: #202
-#218 := [monotonicity #203 #215]: #217
-#223 := [trans #218 #221]: #222
-#239 := [monotonicity #223]: #238
-#242 := [monotonicity #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [monotonicity #245]: #247
-#251 := [quant-intro #248]: #250
-#200 := (~ #165 #165)
-#197 := (~ #162 #162)
-#210 := [refl]: #197
-#201 := [nnf-pos #210]: #200
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#168 := (iff #37 #165)
-#62 := (and #16 #18)
-#65 := (or #17 #62)
-#138 := (ite #65 #30 #133)
-#141 := (ite #12 0::int #138)
-#144 := (ite #13 #8 #141)
-#147 := (= #29 #144)
-#150 := (forall (vars (?v0 int) (?v1 int)) #147)
-#166 := (iff #150 #165)
-#163 := (iff #147 #162)
-#160 := (= #144 #159)
-#157 := (= #141 #156)
-#154 := (= #138 #153)
-#109 := (iff #65 #108)
-#106 := (iff #62 #105)
-#103 := (iff #18 #102)
-#104 := [rewrite]: #103
-#96 := (iff #16 #95)
-#97 := [rewrite]: #96
-#107 := [monotonicity #97 #104]: #106
-#99 := (iff #17 #98)
-#92 := (iff #15 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#155 := [monotonicity #110]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [quant-intro #164]: #166
-#151 := (iff #37 #150)
-#148 := (iff #36 #147)
-#145 := (= #35 #144)
-#142 := (= #34 #141)
-#139 := (= #33 #138)
-#136 := (= #32 #133)
-#130 := (- #127)
-#134 := (= #130 #133)
-#135 := [rewrite]: #134
-#131 := (= #32 #130)
-#128 := (= #31 #127)
-#73 := (= #23 #72)
-#74 := [rewrite]: #73
-#70 := (= #22 #69)
-#71 := [rewrite]: #70
-#129 := [monotonicity #71 #74]: #128
-#132 := [monotonicity #129]: #131
-#137 := [trans #132 #135]: #136
-#66 := (iff #20 #65)
-#63 := (iff #19 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#140 := [monotonicity #67 #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [quant-intro #149]: #151
-#169 := [trans #152 #167]: #168
-#126 := [asserted]: #37
-#170 := [mp #126 #169]: #165
-#211 := [mp~ #170 #201]: #165
-#252 := [mp #211 #251]: #249
-#283 := [mp #252 #282]: #280
-#767 := [mp #283 #766]: #762
-#668 := (not #762)
-#675 := (or #668 #178)
-#341 := (* -1::int 3::int)
-#425 := (* -1::int -5::int)
-#426 := (mod #425 #341)
-#427 := (+ #175 #426)
-#418 := (= #427 0::int)
-#429 := (mod -5::int 3::int)
-#430 := (* -1::int #429)
-#431 := (+ #175 #430)
-#428 := (= #431 0::int)
-#432 := (<= 3::int 0::int)
-#411 := (<= -5::int 0::int)
-#746 := (or #411 #432)
-#748 := (not #746)
-#405 := (>= -5::int 0::int)
-#535 := (or #432 #405)
-#742 := (not #535)
-#416 := (or #742 #748)
-#417 := (ite #416 #428 #418)
-#749 := (= #175 0::int)
-#750 := (= -5::int 0::int)
-#751 := (ite #750 #749 #417)
-#752 := (= -5::int #175)
-#747 := (= 3::int 0::int)
-#753 := (ite #747 #752 #751)
-#659 := (or #668 #753)
-#662 := (iff #659 #675)
-#664 := (iff #675 #675)
-#665 := [rewrite]: #664
-#673 := (iff #753 #178)
-#744 := (= #175 -5::int)
-#681 := (ite false #744 #178)
-#671 := (iff #681 #178)
-#672 := [rewrite]: #671
-#677 := (iff #753 #681)
-#679 := (iff #751 #178)
-#676 := (ite false #749 #178)
-#667 := (iff #676 #178)
-#669 := [rewrite]: #667
-#678 := (iff #751 #676)
-#685 := (iff #417 #178)
-#572 := -2::int
-#587 := (= #175 -2::int)
-#1 := true
-#592 := (ite true #178 #587)
-#595 := (iff #592 #178)
-#688 := [rewrite]: #595
-#593 := (iff #417 #592)
-#583 := (iff #418 #587)
-#537 := 2::int
-#578 := (+ 2::int #175)
-#683 := (= #578 0::int)
-#589 := (iff #683 #587)
-#590 := [rewrite]: #589
-#684 := (iff #418 #683)
-#686 := (= #427 #578)
-#692 := (+ #175 2::int)
-#579 := (= #692 #578)
-#538 := [rewrite]: #579
-#695 := (= #427 #692)
-#693 := (= #426 2::int)
-#703 := -3::int
-#705 := (mod 5::int -3::int)
-#690 := (= #705 2::int)
-#691 := [rewrite]: #690
-#534 := (= #426 #705)
-#704 := (= #341 -3::int)
-#698 := [rewrite]: #704
-#696 := (= #425 5::int)
-#697 := [rewrite]: #696
-#536 := [monotonicity #697 #698]: #534
-#694 := [trans #536 #691]: #693
-#577 := [monotonicity #694]: #695
-#588 := [trans #577 #538]: #686
-#687 := [monotonicity #588]: #684
-#591 := [trans #687 #590]: #583
-#701 := (iff #428 #178)
-#707 := (+ -1::int #175)
-#555 := (= #707 0::int)
-#699 := (iff #555 #178)
-#700 := [rewrite]: #699
-#556 := (iff #428 #555)
-#708 := (= #431 #707)
-#710 := (+ #175 -1::int)
-#712 := (= #710 #707)
-#713 := [rewrite]: #712
-#711 := (= #431 #710)
-#720 := (= #430 -1::int)
-#718 := (* -1::int 1::int)
-#719 := (= #718 -1::int)
-#716 := [rewrite]: #719
-#433 := (= #430 #718)
-#439 := (= #429 1::int)
-#717 := [rewrite]: #439
-#715 := [monotonicity #717]: #433
-#709 := [trans #715 #716]: #720
-#706 := [monotonicity #709]: #711
-#714 := [trans #706 #713]: #708
-#557 := [monotonicity #714]: #556
-#702 := [trans #557 #700]: #701
-#437 := (iff #416 true)
-#727 := (or true false)
-#451 := (iff #727 true)
-#452 := [rewrite]: #451
-#726 := (iff #416 #727)
-#725 := (iff #748 false)
-#723 := (not true)
-#447 := (iff #723 false)
-#721 := [rewrite]: #447
-#724 := (iff #748 #723)
-#453 := (iff #746 true)
-#728 := (iff #746 #727)
-#729 := (iff #432 false)
-#392 := [rewrite]: #729
-#738 := (iff #411 true)
-#741 := [rewrite]: #738
-#450 := [monotonicity #741 #392]: #728
-#347 := [trans #450 #452]: #453
-#446 := [monotonicity #347]: #724
-#722 := [trans #446 #721]: #725
-#380 := (iff #742 true)
-#736 := (not false)
-#739 := (iff #736 true)
-#379 := [rewrite]: #739
-#374 := (iff #742 #736)
-#735 := (iff #535 false)
-#395 := (or false false)
-#733 := (iff #395 false)
-#734 := [rewrite]: #733
-#731 := (iff #535 #395)
-#393 := (iff #405 false)
-#394 := [rewrite]: #393
-#732 := [monotonicity #392 #394]: #731
-#730 := [trans #732 #734]: #735
-#737 := [monotonicity #730]: #374
-#740 := [trans #737 #379]: #380
-#436 := [monotonicity #740 #722]: #726
-#438 := [trans #436 #452]: #437
-#594 := [monotonicity #438 #702 #591]: #593
-#689 := [trans #594 #688]: #685
-#745 := (iff #750 false)
-#388 := [rewrite]: #745
-#670 := [monotonicity #388 #689]: #678
-#680 := [trans #670 #669]: #679
-#408 := (iff #752 #744)
-#404 := [rewrite]: #408
-#743 := (iff #747 false)
-#403 := [rewrite]: #743
-#682 := [monotonicity #403 #404 #680]: #677
-#674 := [trans #682 #672]: #673
-#663 := [monotonicity #674]: #662
-#661 := [trans #663 #665]: #662
-#660 := [quant-inst]: #659
-#666 := [mp #660 #661]: #675
-[unit-resolution #666 #767 #196]: false
-unsat
-b73a0de984e1278677e252eddd5f49245a89ef43 549 0
[phone]ecd73982feaa9bcaa8149f88727923 549 0
 #2 := false
 #11 := 0::int
 decl f3 :: (-> int int int)
@@ -41922,678 +43632,7 @@
 #478 := [unit-resolution #470 #507]: #751
 [th-lemma #478 #476 #486 #472]: false
 unsat
-69b248ec4c8c22d71fd11309dbdf636ac009612d 350 0
-#2 := false
-#68 := -1::int
-decl f4 :: (-> int int int)
-#174 := -3::int
-#177 := (f4 -1::int -3::int)
-#180 := (= #177 -1::int)
-#193 := (not #180)
-#38 := 1::int
-#39 := (- 1::int)
-#40 := 3::int
-#41 := (- 3::int)
-#42 := (f4 #39 #41)
-#43 := (= #42 #39)
-#44 := (not #43)
-#196 := (iff #44 #193)
-#183 := (= -1::int #177)
-#188 := (not #183)
-#194 := (iff #188 #193)
-#191 := (iff #183 #180)
-#192 := [rewrite]: #191
-#195 := [monotonicity #192]: #194
-#189 := (iff #44 #188)
-#186 := (iff #43 #183)
-#184 := (iff #180 #183)
-#185 := [rewrite]: #184
-#181 := (iff #43 #180)
-#172 := (= #39 -1::int)
-#173 := [rewrite]: #172
-#178 := (= #42 #177)
-#175 := (= #41 -3::int)
-#176 := [rewrite]: #175
-#179 := [monotonicity #173 #176]: #178
-#182 := [monotonicity #179 #173]: #181
-#187 := [trans #182 #185]: #186
-#190 := [monotonicity #187]: #189
-#197 := [trans #190 #195]: #196
-#171 := [asserted]: #44
-#198 := [mp #171 #197]: #193
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#763 := (pattern #29)
-#11 := 0::int
-#72 := (* -1::int #9)
-#69 := (* -1::int #8)
-#127 := (mod #69 #72)
-#275 := (+ #29 #127)
-#276 := (= #275 0::int)
-#30 := (mod #8 #9)
-#272 := (* -1::int #30)
-#273 := (+ #29 #272)
-#274 := (= #273 0::int)
-#94 := (<= #9 0::int)
-#90 := (<= #8 0::int)
-#214 := (or #90 #94)
-#215 := (not #214)
-#101 := (>= #8 0::int)
-#206 := (or #94 #101)
-#207 := (not #206)
-#221 := (or #207 #215)
-#277 := (ite #221 #274 #276)
-#271 := (= #29 0::int)
-#12 := (= #8 0::int)
-#278 := (ite #12 #271 #277)
-#270 := (= #8 #29)
-#13 := (= #9 0::int)
-#279 := (ite #13 #270 #278)
-#764 := (forall (vars (?v0 int) (?v1 int)) (:pat #763) #279)
-#282 := (forall (vars (?v0 int) (?v1 int)) #279)
-#767 := (iff #282 #764)
-#765 := (iff #279 #279)
-#766 := [refl]: #765
-#768 := [quant-intro #766]: #767
-#133 := (* -1::int #127)
-#239 := (ite #221 #30 #133)
-#242 := (ite #12 0::int #239)
-#245 := (ite #13 #8 #242)
-#248 := (= #29 #245)
-#251 := (forall (vars (?v0 int) (?v1 int)) #248)
-#283 := (iff #251 #282)
-#280 := (iff #248 #279)
-#281 := [rewrite]: #280
-#284 := [quant-intro #281]: #283
-#102 := (not #101)
-#95 := (not #94)
-#105 := (and #95 #102)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#153 := (ite #108 #30 #133)
-#156 := (ite #12 0::int #153)
-#159 := (ite #13 #8 #156)
-#162 := (= #29 #159)
-#165 := (forall (vars (?v0 int) (?v1 int)) #162)
-#252 := (iff #165 #251)
-#249 := (iff #162 #248)
-#246 := (= #159 #245)
-#243 := (= #156 #242)
-#240 := (= #153 #239)
-#224 := (iff #108 #221)
-#218 := (or #215 #207)
-#222 := (iff #218 #221)
-#223 := [rewrite]: #222
-#219 := (iff #108 #218)
-#216 := (iff #105 #207)
-#217 := [rewrite]: #216
-#204 := (iff #98 #215)
-#205 := [rewrite]: #204
-#220 := [monotonicity #205 #217]: #219
-#225 := [trans #220 #223]: #224
-#241 := [monotonicity #225]: #240
-#244 := [monotonicity #241]: #243
-#247 := [monotonicity #244]: #246
-#250 := [monotonicity #247]: #249
-#253 := [quant-intro #250]: #252
-#202 := (~ #165 #165)
-#199 := (~ #162 #162)
-#212 := [refl]: #199
-#203 := [nnf-pos #212]: #202
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#168 := (iff #37 #165)
-#62 := (and #16 #18)
-#65 := (or #17 #62)
-#138 := (ite #65 #30 #133)
-#141 := (ite #12 0::int #138)
-#144 := (ite #13 #8 #141)
-#147 := (= #29 #144)
-#150 := (forall (vars (?v0 int) (?v1 int)) #147)
-#166 := (iff #150 #165)
-#163 := (iff #147 #162)
-#160 := (= #144 #159)
-#157 := (= #141 #156)
-#154 := (= #138 #153)
-#109 := (iff #65 #108)
-#106 := (iff #62 #105)
-#103 := (iff #18 #102)
-#104 := [rewrite]: #103
-#96 := (iff #16 #95)
-#97 := [rewrite]: #96
-#107 := [monotonicity #97 #104]: #106
-#99 := (iff #17 #98)
-#92 := (iff #15 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#155 := [monotonicity #110]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [quant-intro #164]: #166
-#151 := (iff #37 #150)
-#148 := (iff #36 #147)
-#145 := (= #35 #144)
-#142 := (= #34 #141)
-#139 := (= #33 #138)
-#136 := (= #32 #133)
-#130 := (- #127)
-#134 := (= #130 #133)
-#135 := [rewrite]: #134
-#131 := (= #32 #130)
-#128 := (= #31 #127)
-#73 := (= #23 #72)
-#74 := [rewrite]: #73
-#70 := (= #22 #69)
-#71 := [rewrite]: #70
-#129 := [monotonicity #71 #74]: #128
-#132 := [monotonicity #129]: #131
-#137 := [trans #132 #135]: #136
-#66 := (iff #20 #65)
-#63 := (iff #19 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#140 := [monotonicity #67 #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [quant-intro #149]: #151
-#169 := [trans #152 #167]: #168
-#126 := [asserted]: #37
-#170 := [mp #126 #169]: #165
-#213 := [mp~ #170 #203]: #165
-#254 := [mp #213 #253]: #251
-#285 := [mp #254 #284]: #282
-#769 := [mp #285 #768]: #764
-#684 := (not #764)
-#673 := (or #684 #180)
-#343 := (* -1::int -3::int)
-#427 := (* -1::int -1::int)
-#428 := (mod #427 #343)
-#429 := (+ #177 #428)
-#420 := (= #429 0::int)
-#431 := (mod -1::int -3::int)
-#432 := (* -1::int #431)
-#433 := (+ #177 #432)
-#430 := (= #433 0::int)
-#434 := (<= -3::int 0::int)
-#413 := (<= -1::int 0::int)
-#748 := (or #413 #434)
-#750 := (not #748)
-#407 := (>= -1::int 0::int)
-#537 := (or #434 #407)
-#744 := (not #537)
-#418 := (or #744 #750)
-#419 := (ite #418 #430 #420)
-#751 := (= #177 0::int)
-#752 := (= -1::int 0::int)
-#753 := (ite #752 #751 #419)
-#754 := (= -3::int 0::int)
-#749 := (ite #754 #183 #753)
-#674 := (or #684 #749)
-#676 := (iff #674 #673)
-#677 := (iff #673 #673)
-#661 := [rewrite]: #677
-#683 := (iff #749 #180)
-#672 := (ite false #180 #180)
-#681 := (iff #672 #180)
-#682 := [rewrite]: #681
-#669 := (iff #749 #672)
-#678 := (iff #753 #180)
-#596 := (ite false #751 #180)
-#687 := (iff #596 #180)
-#691 := [rewrite]: #687
-#597 := (iff #753 #596)
-#594 := (iff #419 #180)
-#728 := 2::int
-#558 := (= #177 2::int)
-#589 := (ite false #558 #180)
-#585 := (iff #589 #180)
-#593 := [rewrite]: #585
-#591 := (iff #419 #589)
-#689 := (iff #420 #180)
-#694 := (+ 1::int #177)
-#540 := (= #694 0::int)
-#685 := (iff #540 #180)
-#686 := [rewrite]: #685
-#688 := (iff #420 #540)
-#580 := (= #429 #694)
-#693 := (+ #177 1::int)
-#697 := (= #693 #694)
-#579 := [rewrite]: #697
-#695 := (= #429 #693)
-#539 := (= #428 1::int)
-#706 := (mod 1::int 3::int)
-#536 := (= #706 1::int)
-#538 := [rewrite]: #536
-#700 := (= #428 #706)
-#699 := (= #343 3::int)
-#705 := [rewrite]: #699
-#704 := (= #427 1::int)
-#698 := [rewrite]: #704
-#707 := [monotonicity #698 #705]: #700
-#692 := [trans #707 #538]: #539
-#696 := [monotonicity #692]: #695
-#581 := [trans #696 #579]: #580
-#590 := [monotonicity #581]: #688
-#574 := [trans #590 #686]: #689
-#702 := (iff #430 #558)
-#720 := -2::int
-#713 := (+ -2::int #177)
-#710 := (= #713 0::int)
-#559 := (iff #710 #558)
-#701 := [rewrite]: #559
-#716 := (iff #430 #710)
-#714 := (= #433 #713)
-#722 := (+ #177 -2::int)
-#708 := (= #722 #713)
-#709 := [rewrite]: #708
-#711 := (= #433 #722)
-#721 := (= #432 -2::int)
-#440 := (* -1::int 2::int)
-#435 := (= #440 -2::int)
-#717 := [rewrite]: #435
-#441 := (= #432 #440)
-#438 := (= #431 2::int)
-#439 := [rewrite]: #438
-#719 := [monotonicity #439]: #441
-#718 := [trans #719 #717]: #721
-#712 := [monotonicity #718]: #711
-#715 := [trans #712 #709]: #714
-#557 := [monotonicity #715]: #716
-#703 := [trans #557 #701]: #702
-#727 := (iff #418 false)
-#725 := (or false false)
-#449 := (iff #725 false)
-#723 := [rewrite]: #449
-#726 := (iff #418 #725)
-#455 := (iff #750 false)
-#1 := true
-#735 := (not true)
-#732 := (iff #735 false)
-#738 := [rewrite]: #732
-#453 := (iff #750 #735)
-#730 := (iff #748 true)
-#382 := (or true true)
-#743 := (iff #382 true)
-#729 := [rewrite]: #743
-#742 := (iff #748 #382)
-#746 := (iff #434 true)
-#406 := [rewrite]: #746
-#741 := (iff #413 true)
-#381 := [rewrite]: #741
-#740 := [monotonicity #381 #406]: #742
-#452 := [trans #740 #729]: #730
-#454 := [monotonicity #452]: #453
-#349 := [trans #454 #738]: #455
-#376 := (iff #744 false)
-#736 := (iff #744 #735)
-#733 := (iff #537 true)
-#731 := (or true false)
-#396 := (iff #731 true)
-#397 := [rewrite]: #396
-#394 := (iff #537 #731)
-#747 := (iff #407 false)
-#390 := [rewrite]: #747
-#395 := [monotonicity #406 #390]: #394
-#734 := [trans #395 #397]: #733
-#737 := [monotonicity #734]: #736
-#739 := [trans #737 #738]: #376
-#448 := [monotonicity #739 #349]: #726
-#724 := [trans #448 #723]: #727
-#592 := [monotonicity #724 #703 #574]: #591
-#595 := [trans #592 #593]: #594
-#405 := (iff #752 false)
-#410 := [rewrite]: #405
-#690 := [monotonicity #410 #595]: #597
-#680 := [trans #690 #691]: #678
-#755 := (iff #754 false)
-#745 := [rewrite]: #755
-#671 := [monotonicity #745 #192 #680]: #669
-#679 := [trans #671 #682]: #683
-#670 := [monotonicity #679]: #676
-#662 := [trans #670 #661]: #676
-#675 := [quant-inst]: #674
-#664 := [mp #675 #662]: #673
-[unit-resolution #664 #769 #198]: false
-unsat
-206d37ba92a2e6c0100ce1d13f8823dad1d40cd1 319 0
-#2 := false
-#11 := 0::int
-decl f4 :: (-> int int int)
-#170 := -3::int
-#173 := (f4 -3::int -3::int)
-#176 := (= #173 0::int)
-#189 := (not #176)
-#38 := 3::int
-#39 := (- 3::int)
-#40 := (f4 #39 #39)
-#41 := (= #40 0::int)
-#42 := (not #41)
-#192 := (iff #42 #189)
-#179 := (= 0::int #173)
-#184 := (not #179)
-#190 := (iff #184 #189)
-#187 := (iff #179 #176)
-#188 := [rewrite]: #187
-#191 := [monotonicity #188]: #190
-#185 := (iff #42 #184)
-#182 := (iff #41 #179)
-#180 := (iff #176 #179)
-#181 := [rewrite]: #180
-#177 := (iff #41 #176)
-#174 := (= #40 #173)
-#171 := (= #39 -3::int)
-#172 := [rewrite]: #171
-#175 := [monotonicity #172 #172]: #174
-#178 := [monotonicity #175]: #177
-#183 := [trans #178 #181]: #182
-#186 := [monotonicity #183]: #185
-#193 := [trans #186 #191]: #192
-#169 := [asserted]: #42
-#194 := [mp #169 #193]: #189
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#760 := (pattern #29)
-#66 := -1::int
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#125 := (mod #67 #70)
-#271 := (+ #29 #125)
-#272 := (= #271 0::int)
-#30 := (mod #8 #9)
-#268 := (* -1::int #30)
-#269 := (+ #29 #268)
-#270 := (= #269 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#210 := (or #88 #92)
-#211 := (not #210)
-#99 := (>= #8 0::int)
-#202 := (or #92 #99)
-#203 := (not #202)
-#217 := (or #203 #211)
-#273 := (ite #217 #270 #272)
-#267 := (= #29 0::int)
-#12 := (= #8 0::int)
-#274 := (ite #12 #267 #273)
-#266 := (= #8 #29)
-#13 := (= #9 0::int)
-#275 := (ite #13 #266 #274)
-#761 := (forall (vars (?v0 int) (?v1 int)) (:pat #760) #275)
-#278 := (forall (vars (?v0 int) (?v1 int)) #275)
-#764 := (iff #278 #761)
-#762 := (iff #275 #275)
-#763 := [refl]: #762
-#765 := [quant-intro #763]: #764
-#131 := (* -1::int #125)
-#235 := (ite #217 #30 #131)
-#238 := (ite #12 0::int #235)
-#241 := (ite #13 #8 #238)
-#244 := (= #29 #241)
-#247 := (forall (vars (?v0 int) (?v1 int)) #244)
-#279 := (iff #247 #278)
-#276 := (iff #244 #275)
-#277 := [rewrite]: #276
-#280 := [quant-intro #277]: #279
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#151 := (ite #106 #30 #131)
-#154 := (ite #12 0::int #151)
-#157 := (ite #13 #8 #154)
-#160 := (= #29 #157)
-#163 := (forall (vars (?v0 int) (?v1 int)) #160)
-#248 := (iff #163 #247)
-#245 := (iff #160 #244)
-#242 := (= #157 #241)
-#239 := (= #154 #238)
-#236 := (= #151 #235)
-#220 := (iff #106 #217)
-#214 := (or #211 #203)
-#218 := (iff #214 #217)
-#219 := [rewrite]: #218
-#215 := (iff #106 #214)
-#212 := (iff #103 #203)
-#213 := [rewrite]: #212
-#200 := (iff #96 #211)
-#201 := [rewrite]: #200
-#216 := [monotonicity #201 #213]: #215
-#221 := [trans #216 #219]: #220
-#237 := [monotonicity #221]: #236
-#240 := [monotonicity #237]: #239
-#243 := [monotonicity #240]: #242
-#246 := [monotonicity #243]: #245
-#249 := [quant-intro #246]: #248
-#198 := (~ #163 #163)
-#195 := (~ #160 #160)
-#208 := [refl]: #195
-#199 := [nnf-pos #208]: #198
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#166 := (iff #37 #163)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#136 := (ite #63 #30 #131)
-#139 := (ite #12 0::int #136)
-#142 := (ite #13 #8 #139)
-#145 := (= #29 #142)
-#148 := (forall (vars (?v0 int) (?v1 int)) #145)
-#164 := (iff #148 #163)
-#161 := (iff #145 #160)
-#158 := (= #142 #157)
-#155 := (= #139 #154)
-#152 := (= #136 #151)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#153 := [monotonicity #108]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#149 := (iff #37 #148)
-#146 := (iff #36 #145)
-#143 := (= #35 #142)
-#140 := (= #34 #139)
-#137 := (= #33 #136)
-#134 := (= #32 #131)
-#128 := (- #125)
-#132 := (= #128 #131)
-#133 := [rewrite]: #132
-#129 := (= #32 #128)
-#126 := (= #31 #125)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#127 := [monotonicity #69 #72]: #126
-#130 := [monotonicity #127]: #129
-#135 := [trans #130 #133]: #134
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#138 := [monotonicity #65 #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [quant-intro #147]: #149
-#167 := [trans #150 #165]: #166
-#124 := [asserted]: #37
-#168 := [mp #124 #167]: #163
-#209 := [mp~ #168 #199]: #163
-#250 := [mp #209 #249]: #247
-#281 := [mp #250 #280]: #278
-#766 := [mp #281 #765]: #761
-#537 := (not #761)
-#685 := (or #537 #176)
-#339 := (* -1::int -3::int)
-#424 := (mod #339 #339)
-#425 := (+ #173 #424)
-#426 := (= #425 0::int)
-#417 := (mod -3::int -3::int)
-#428 := (* -1::int #417)
-#429 := (+ #173 #428)
-#357 := (= #429 0::int)
-#430 := (<= -3::int 0::int)
-#427 := (or #430 #430)
-#431 := (not #427)
-#410 := (>= -3::int 0::int)
-#745 := (or #430 #410)
-#747 := (not #745)
-#404 := (or #747 #431)
-#534 := (ite #404 #357 #426)
-#741 := (= -3::int 0::int)
-#415 := (ite #741 #176 #534)
-#416 := (= -3::int #173)
-#748 := (ite #741 #416 #415)
-#587 := (or #537 #748)
-#683 := (iff #587 #685)
-#571 := (iff #685 #685)
-#586 := [rewrite]: #571
-#577 := (iff #748 #176)
-#746 := (= #173 -3::int)
-#692 := (ite false #746 #176)
-#694 := (iff #692 #176)
-#576 := [rewrite]: #694
-#693 := (iff #748 #692)
-#689 := (iff #415 #176)
-#695 := (ite false #176 #176)
-#703 := (iff #695 #176)
-#697 := [rewrite]: #703
-#535 := (iff #415 #695)
-#704 := (iff #534 #176)
-#696 := (iff #534 #695)
-#700 := (iff #426 #176)
-#698 := (= #425 #173)
-#438 := (+ #173 0::int)
-#432 := (= #438 #173)
-#714 := [rewrite]: #432
-#555 := (= #425 #438)
-#713 := (= #424 0::int)
-#705 := (mod 3::int 3::int)
-#712 := (= #705 0::int)
-#707 := [rewrite]: #712
-#706 := (= #424 #705)
-#709 := (= #339 3::int)
-#710 := [rewrite]: #709
-#711 := [monotonicity #710 #710]: #706
-#554 := [trans #711 #707]: #713
-#556 := [monotonicity #554]: #555
-#699 := [trans #556 #714]: #698
-#701 := [monotonicity #699]: #700
-#719 := (iff #357 #176)
-#718 := (= #429 #173)
-#716 := (= #429 #438)
-#436 := (= #428 0::int)
-#720 := (* -1::int 0::int)
-#725 := (= #720 0::int)
-#435 := [rewrite]: #725
-#724 := (= #428 #720)
-#445 := (= #417 0::int)
-#446 := [rewrite]: #445
-#721 := [monotonicity #446]: #724
-#437 := [trans #721 #435]: #436
-#717 := [monotonicity #437]: #716
-#715 := [trans #717 #714]: #718
-#708 := [monotonicity #715]: #719
-#722 := (iff #404 false)
-#449 := (or false false)
-#452 := (iff #449 false)
-#345 := [rewrite]: #452
-#450 := (iff #404 #449)
-#726 := (iff #431 false)
-#1 := true
-#394 := (not true)
-#732 := (iff #394 false)
-#733 := [rewrite]: #732
-#737 := (iff #431 #394)
-#379 := (iff #427 true)
-#735 := (or true true)
-#738 := (iff #735 true)
-#378 := [rewrite]: #738
-#373 := (iff #427 #735)
-#742 := (iff #430 true)
-#402 := [rewrite]: #742
-#736 := [monotonicity #402 #402]: #373
-#739 := [trans #736 #378]: #379
-#740 := [monotonicity #739]: #737
-#727 := [trans #740 #733]: #726
-#734 := (iff #747 false)
-#730 := (iff #747 #394)
-#392 := (iff #745 true)
-#403 := (or true false)
-#728 := (iff #403 true)
-#391 := [rewrite]: #728
-#744 := (iff #745 #403)
-#407 := (iff #410 false)
-#743 := [rewrite]: #407
-#387 := [monotonicity #402 #743]: #744
-#393 := [trans #387 #391]: #392
-#731 := [monotonicity #393]: #730
-#729 := [trans #731 #733]: #734
-#451 := [monotonicity #729 #727]: #450
-#723 := [trans #451 #345]: #722
-#702 := [monotonicity #723 #708 #701]: #696
-#533 := [trans #702 #697]: #704
-#749 := (iff #741 false)
-#750 := [rewrite]: #749
-#536 := [monotonicity #750 #533]: #535
-#690 := [trans #536 #697]: #689
-#751 := (iff #416 #746)
-#752 := [rewrite]: #751
-#691 := [monotonicity #750 #752 #690]: #693
-#578 := [trans #691 #576]: #577
-#686 := [monotonicity #578]: #683
-#588 := [trans #686 #586]: #683
-#682 := [quant-inst]: #587
-#589 := [mp #682 #588]: #685
-[unit-resolution #589 #766 #194]: false
-unsat
-cc9432c40327db517dd79cbbd0d9d26dcbfe5cac 75 0
+014fdc8ec18682bd52b2f30aeba93d205e444540 75 0
 #2 := false
 #8 := 0::int
 decl f3 :: int
@@ -42669,7 +43708,7 @@
 #96 := [unit-resolution #95 #92]: #90
 [th-lemma #89 #70 #96]: false
 unsat
-48eb42104c7475e8c3a01fc47d1fb95a5b64e0b9 132 0
+5eafdb76bec2d657bfd5c526da93e42174e2c21d 132 0
 #2 := false
 #9 := 0::int
 decl f3 :: int
@@ -42802,7 +43841,7 @@
 #162 := [th-lemma]: #161
 [unit-resolution #162 #160 #143]: false
 unsat
-029c5fe4db8f26b45338d7437b6be2ddd1a19e85 103 0
+61b1e1b6ad21d34fcca5bf630a853ce6a0dfa947 103 0
 #2 := false
 #8 := 0::int
 decl f3 :: int
@@ -42906,355 +43945,7 @@
 #124 := [unit-resolution #123 #120]: #115
 [th-lemma #110 #124]: false
 unsat
-830c72401ff6ad8a8e8d6573aef1bb4cebf52b34 347 0
-#2 := false
-#183 := -2::int
-decl f4 :: (-> int int int)
-#177 := -3::int
-#174 := -5::int
-#180 := (f4 -5::int -3::int)
-#186 := (= #180 -2::int)
-#189 := (not #186)
-#43 := 2::int
-#44 := (- 2::int)
-#40 := 3::int
-#41 := (- 3::int)
-#38 := 5::int
-#39 := (- 5::int)
-#42 := (f4 #39 #41)
-#45 := (= #42 #44)
-#46 := (not #45)
-#190 := (iff #46 #189)
-#187 := (iff #45 #186)
-#184 := (= #44 -2::int)
-#185 := [rewrite]: #184
-#181 := (= #42 #180)
-#178 := (= #41 -3::int)
-#179 := [rewrite]: #178
-#175 := (= #39 -5::int)
-#176 := [rewrite]: #175
-#182 := [monotonicity #176 #179]: #181
-#188 := [monotonicity #182 #185]: #187
-#191 := [monotonicity #188]: #190
-#173 := [asserted]: #46
-#194 := [mp #173 #191]: #189
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#758 := (pattern #29)
-#11 := 0::int
-#70 := -1::int
-#74 := (* -1::int #9)
-#71 := (* -1::int #8)
-#129 := (mod #71 #74)
-#269 := (+ #29 #129)
-#270 := (= #269 0::int)
-#30 := (mod #8 #9)
-#266 := (* -1::int #30)
-#267 := (+ #29 #266)
-#268 := (= #267 0::int)
-#96 := (<= #9 0::int)
-#92 := (<= #8 0::int)
-#208 := (or #92 #96)
-#209 := (not #208)
-#103 := (>= #8 0::int)
-#200 := (or #96 #103)
-#201 := (not #200)
-#215 := (or #201 #209)
-#271 := (ite #215 #268 #270)
-#265 := (= #29 0::int)
-#12 := (= #8 0::int)
-#272 := (ite #12 #265 #271)
-#264 := (= #8 #29)
-#13 := (= #9 0::int)
-#273 := (ite #13 #264 #272)
-#759 := (forall (vars (?v0 int) (?v1 int)) (:pat #758) #273)
-#276 := (forall (vars (?v0 int) (?v1 int)) #273)
-#762 := (iff #276 #759)
-#760 := (iff #273 #273)
-#761 := [refl]: #760
-#763 := [quant-intro #761]: #762
-#135 := (* -1::int #129)
-#233 := (ite #215 #30 #135)
-#236 := (ite #12 0::int #233)
-#239 := (ite #13 #8 #236)
-#242 := (= #29 #239)
-#245 := (forall (vars (?v0 int) (?v1 int)) #242)
-#277 := (iff #245 #276)
-#274 := (iff #242 #273)
-#275 := [rewrite]: #274
-#278 := [quant-intro #275]: #277
-#104 := (not #103)
-#97 := (not #96)
-#107 := (and #97 #104)
-#93 := (not #92)
-#100 := (and #93 #97)
-#110 := (or #100 #107)
-#155 := (ite #110 #30 #135)
-#158 := (ite #12 0::int #155)
-#161 := (ite #13 #8 #158)
-#164 := (= #29 #161)
-#167 := (forall (vars (?v0 int) (?v1 int)) #164)
-#246 := (iff #167 #245)
-#243 := (iff #164 #242)
-#240 := (= #161 #239)
-#237 := (= #158 #236)
-#234 := (= #155 #233)
-#218 := (iff #110 #215)
-#212 := (or #209 #201)
-#216 := (iff #212 #215)
-#217 := [rewrite]: #216
-#213 := (iff #110 #212)
-#210 := (iff #107 #201)
-#211 := [rewrite]: #210
-#198 := (iff #100 #209)
-#199 := [rewrite]: #198
-#214 := [monotonicity #199 #211]: #213
-#219 := [trans #214 #217]: #218
-#235 := [monotonicity #219]: #234
-#238 := [monotonicity #235]: #237
-#241 := [monotonicity #238]: #240
-#244 := [monotonicity #241]: #243
-#247 := [quant-intro #244]: #246
-#196 := (~ #167 #167)
-#192 := (~ #164 #164)
-#206 := [refl]: #192
-#197 := [nnf-pos #206]: #196
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#170 := (iff #37 #167)
-#64 := (and #16 #18)
-#67 := (or #17 #64)
-#140 := (ite #67 #30 #135)
-#143 := (ite #12 0::int #140)
-#146 := (ite #13 #8 #143)
-#149 := (= #29 #146)
-#152 := (forall (vars (?v0 int) (?v1 int)) #149)
-#168 := (iff #152 #167)
-#165 := (iff #149 #164)
-#162 := (= #146 #161)
-#159 := (= #143 #158)
-#156 := (= #140 #155)
-#111 := (iff #67 #110)
-#108 := (iff #64 #107)
-#105 := (iff #18 #104)
-#106 := [rewrite]: #105
-#98 := (iff #16 #97)
-#99 := [rewrite]: #98
-#109 := [monotonicity #99 #106]: #108
-#101 := (iff #17 #100)
-#94 := (iff #15 #93)
-#95 := [rewrite]: #94
-#102 := [monotonicity #95 #99]: #101
-#112 := [monotonicity #102 #109]: #111
-#157 := [monotonicity #112]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [monotonicity #163]: #165
-#169 := [quant-intro #166]: #168
-#153 := (iff #37 #152)
-#150 := (iff #36 #149)
-#147 := (= #35 #146)
-#144 := (= #34 #143)
-#141 := (= #33 #140)
-#138 := (= #32 #135)
-#132 := (- #129)
-#136 := (= #132 #135)
-#137 := [rewrite]: #136
-#133 := (= #32 #132)
-#130 := (= #31 #129)
-#75 := (= #23 #74)
-#76 := [rewrite]: #75
-#72 := (= #22 #71)
-#73 := [rewrite]: #72
-#131 := [monotonicity #73 #76]: #130
-#134 := [monotonicity #131]: #133
-#139 := [trans #134 #137]: #138
-#68 := (iff #20 #67)
-#65 := (iff #19 #64)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#142 := [monotonicity #69 #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [monotonicity #145]: #147
-#151 := [monotonicity #148]: #150
-#154 := [quant-intro #151]: #153
-#171 := [trans #154 #169]: #170
-#128 := [asserted]: #37
-#172 := [mp #128 #171]: #167
-#207 := [mp~ #172 #197]: #167
-#248 := [mp #207 #247]: #245
-#279 := [mp #248 #278]: #276
-#764 := [mp #279 #763]: #759
-#669 := (not #759)
-#670 := (or #669 #186)
-#337 := (* -1::int -3::int)
-#422 := (* -1::int -5::int)
-#423 := (mod #422 #337)
-#424 := (+ #180 #423)
-#415 := (= #424 0::int)
-#426 := (mod -5::int -3::int)
-#427 := (* -1::int #426)
-#355 := (+ #180 #427)
-#428 := (= #355 0::int)
-#425 := (<= -3::int 0::int)
-#429 := (<= -5::int 0::int)
-#408 := (or #429 #425)
-#743 := (not #408)
-#745 := (>= -5::int 0::int)
-#402 := (or #425 #745)
-#532 := (not #402)
-#739 := (or #532 #743)
-#413 := (ite #739 #428 #415)
-#414 := (= #180 0::int)
-#746 := (= -5::int 0::int)
-#747 := (ite #746 #414 #413)
-#748 := (= -5::int #180)
-#749 := (= -3::int 0::int)
-#744 := (ite #749 #748 #747)
-#671 := (or #669 #744)
-#672 := (iff #671 #670)
-#657 := (iff #670 #670)
-#659 := [rewrite]: #657
-#679 := (iff #744 #186)
-#405 := (= #180 -5::int)
-#666 := (ite false #405 #186)
-#678 := (iff #666 #186)
-#674 := [rewrite]: #678
-#676 := (iff #744 #666)
-#667 := (iff #747 #186)
-#685 := (ite false #414 #186)
-#673 := (iff #685 #186)
-#675 := [rewrite]: #673
-#682 := (iff #747 #685)
-#591 := (iff #413 #186)
-#435 := 1::int
-#696 := (= #180 1::int)
-#587 := (ite false #696 #186)
-#589 := (iff #587 #186)
-#590 := [rewrite]: #589
-#580 := (iff #413 #587)
-#584 := (iff #415 #186)
-#574 := (+ 2::int #180)
-#585 := (= #574 0::int)
-#684 := (iff #585 #186)
-#569 := [rewrite]: #684
-#680 := (iff #415 #585)
-#535 := (= #424 #574)
-#691 := (+ #180 2::int)
-#575 := (= #691 #574)
-#576 := [rewrite]: #575
-#689 := (= #424 #691)
-#688 := (= #423 2::int)
-#702 := (mod 5::int 3::int)
-#534 := (= #702 2::int)
-#687 := [rewrite]: #534
-#531 := (= #423 #702)
-#701 := (= #337 3::int)
-#695 := [rewrite]: #701
-#694 := (= #422 5::int)
-#700 := [rewrite]: #694
-#533 := [monotonicity #700 #695]: #531
-#690 := [trans #533 #687]: #688
-#692 := [monotonicity #690]: #689
-#683 := [trans #692 #576]: #535
-#681 := [monotonicity #683]: #680
-#586 := [trans #681 #569]: #584
-#699 := (iff #428 #696)
-#704 := (+ -1::int #180)
-#552 := (= #704 0::int)
-#697 := (iff #552 #696)
-#698 := [rewrite]: #697
-#553 := (iff #428 #552)
-#705 := (= #355 #704)
-#707 := (+ #180 -1::int)
-#709 := (= #707 #704)
-#710 := [rewrite]: #709
-#708 := (= #355 #707)
-#717 := (= #427 -1::int)
-#715 := (* -1::int 1::int)
-#716 := (= #715 -1::int)
-#713 := [rewrite]: #716
-#430 := (= #427 #715)
-#436 := (= #426 1::int)
-#714 := [rewrite]: #436
-#712 := [monotonicity #714]: #430
-#706 := [trans #712 #713]: #717
-#703 := [monotonicity #706]: #708
-#711 := [trans #703 #710]: #705
-#554 := [monotonicity #711]: #553
-#693 := [trans #554 #698]: #699
-#433 := (iff #739 false)
-#444 := (or false false)
-#719 := (iff #444 false)
-#723 := [rewrite]: #719
-#718 := (iff #739 #444)
-#721 := (iff #743 false)
-#1 := true
-#727 := (not true)
-#734 := (iff #727 false)
-#736 := [rewrite]: #734
-#343 := (iff #743 #727)
-#449 := (iff #408 true)
-#738 := (or true true)
-#447 := (iff #738 true)
-#448 := [rewrite]: #447
-#724 := (iff #408 #738)
-#385 := (iff #425 true)
-#726 := [rewrite]: #385
-#737 := (iff #429 true)
-#735 := [rewrite]: #737
-#725 := [monotonicity #735 #726]: #724
-#450 := [trans #725 #448]: #449
-#720 := [monotonicity #450]: #343
-#443 := [trans #720 #736]: #721
-#376 := (iff #532 false)
-#733 := (iff #532 #727)
-#731 := (iff #402 true)
-#391 := (or true false)
-#729 := (iff #391 true)
-#730 := [rewrite]: #729
-#392 := (iff #402 #391)
-#389 := (iff #745 false)
-#390 := [rewrite]: #389
-#728 := [monotonicity #726 #390]: #392
-#732 := [trans #728 #730]: #731
-#371 := [monotonicity #732]: #733
-#377 := [trans #371 #736]: #376
-#722 := [monotonicity #377 #443]: #718
-#434 := [trans #722 #723]: #433
-#588 := [monotonicity #434 #693 #586]: #580
-#592 := [trans #588 #590]: #591
-#401 := (iff #746 false)
-#742 := [rewrite]: #401
-#686 := [monotonicity #742 #592]: #682
-#664 := [trans #686 #675]: #667
-#400 := (iff #748 #405)
-#741 := [rewrite]: #400
-#750 := (iff #749 false)
-#740 := [rewrite]: #750
-#677 := [monotonicity #740 #741 #664]: #676
-#668 := [trans #677 #674]: #679
-#656 := [monotonicity #668]: #672
-#660 := [trans #656 #659]: #672
-#665 := [quant-inst]: #671
-#661 := [mp #665 #660]: #670
-[unit-resolution #661 #764 #194]: false
-unsat
-52af3e6f56c34eae5bf2a6d6b943c47275276ffc 149 0
+e5403404de5fa4ae5826ab64854c4250909b0b94 149 0
 #2 := false
 #9 := 0::int
 decl f3 :: int
@@ -43404,7 +44095,7 @@
 #170 := [unit-resolution #169 #155]: #97
 [th-lemma #159 #170 #167]: false
 unsat
-a6116a7f03a76aa4ac7d1dcd46146a27d6d63ab1 114 0
+78a6e8e64c7e332e261c629452ee5bd9e724dcbc 114 0
 #2 := false
 #9 := 0::int
 decl f3 :: int
@@ -43519,7 +44210,7 @@
 #143 := [unit-resolution #142 #139]: #137
 [th-lemma #136 #134 #143]: false
 unsat
-e4b94493f8fddbc193be4dbfae372055ca4cbda1 57 0
+3c368d7ddb6c70684e83fe0ffbfe4b918abf488b 57 0
 #2 := false
 #36 := 0::int
 decl f4 :: int
@@ -43577,335 +44268,7 @@
 #77 := [th-lemma]: #76
 [unit-resolution #77 #74 #56]: false
 unsat
-0296c8b047bf7c4a566214ff7059485e4b909dfc 327 0
-#2 := false
-#11 := 0::int
-decl f5 :: int
-#38 := f5
-#418 := (<= f5 0::int)
-#734 := (>= f5 0::int)
-#380 := (not #734)
-#723 := (not #418)
-#727 := (or #723 #380)
-#690 := (not #727)
-#39 := 3::int
-#415 := (mod f5 3::int)
-#66 := -1::int
-#416 := (* -1::int #415)
-decl f4 :: (-> int int int)
-#40 := (f4 f5 3::int)
-#344 := (+ #40 #416)
-#417 := (= #344 0::int)
-#563 := (not #417)
-#520 := (<= #344 0::int)
-#623 := (not #520)
-#631 := (>= #415 3::int)
-#632 := (not #631)
-#1 := true
-#57 := [true-axiom]: true
-#619 := (or false #632)
-#620 := [th-lemma]: #619
-#621 := [unit-resolution #620 #57]: #632
-#622 := [hypothesis]: #520
-#173 := (>= #40 3::int)
-#41 := (< #40 3::int)
-#42 := (not #41)
-#181 := (iff #42 #173)
-#172 := (not #173)
-#176 := (not #172)
-#179 := (iff #176 #173)
-#180 := [rewrite]: #179
-#177 := (iff #42 #176)
-#174 := (iff #41 #172)
-#175 := [rewrite]: #174
-#178 := [monotonicity #175]: #177
-#182 := [trans #178 #180]: #181
-#169 := [asserted]: #42
-#183 := [mp #169 #182]: #173
-#617 := [th-lemma #183 #622 #621]: false
-#609 := [lemma #617]: #623
-#626 := (or #563 #520)
-#637 := [th-lemma]: #626
-#615 := [unit-resolution #637 #609]: #563
-#614 := (or #690 #417)
-#438 := -3::int
-#411 := (* -1::int f5)
-#709 := (mod #411 -3::int)
-#433 := (+ #40 #709)
-#708 := (= #433 0::int)
-#423 := (ite #727 #417 #708)
-#403 := (= #40 0::int)
-#735 := (= f5 0::int)
-#703 := (ite #735 #403 #423)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#747 := (pattern #29)
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#125 := (mod #67 #70)
-#258 := (+ #29 #125)
-#259 := (= #258 0::int)
-#30 := (mod #8 #9)
-#255 := (* -1::int #30)
-#256 := (+ #29 #255)
-#257 := (= #256 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#197 := (or #88 #92)
-#198 := (not #197)
-#99 := (>= #8 0::int)
-#189 := (or #92 #99)
-#190 := (not #189)
-#204 := (or #190 #198)
-#260 := (ite #204 #257 #259)
-#254 := (= #29 0::int)
-#12 := (= #8 0::int)
-#261 := (ite #12 #254 #260)
-#253 := (= #8 #29)
-#13 := (= #9 0::int)
-#262 := (ite #13 #253 #261)
-#748 := (forall (vars (?v0 int) (?v1 int)) (:pat #747) #262)
-#265 := (forall (vars (?v0 int) (?v1 int)) #262)
-#751 := (iff #265 #748)
-#749 := (iff #262 #262)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#131 := (* -1::int #125)
-#222 := (ite #204 #30 #131)
-#225 := (ite #12 0::int #222)
-#228 := (ite #13 #8 #225)
-#231 := (= #29 #228)
-#234 := (forall (vars (?v0 int) (?v1 int)) #231)
-#266 := (iff #234 #265)
-#263 := (iff #231 #262)
-#264 := [rewrite]: #263
-#267 := [quant-intro #264]: #266
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#151 := (ite #106 #30 #131)
-#154 := (ite #12 0::int #151)
-#157 := (ite #13 #8 #154)
-#160 := (= #29 #157)
-#163 := (forall (vars (?v0 int) (?v1 int)) #160)
-#235 := (iff #163 #234)
-#232 := (iff #160 #231)
-#229 := (= #157 #228)
-#226 := (= #154 #225)
-#223 := (= #151 #222)
-#207 := (iff #106 #204)
-#201 := (or #198 #190)
-#205 := (iff #201 #204)
-#206 := [rewrite]: #205
-#202 := (iff #106 #201)
-#199 := (iff #103 #190)
-#200 := [rewrite]: #199
-#187 := (iff #96 #198)
-#188 := [rewrite]: #187
-#203 := [monotonicity #188 #200]: #202
-#208 := [trans #203 #206]: #207
-#224 := [monotonicity #208]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [quant-intro #233]: #235
-#185 := (~ #163 #163)
-#170 := (~ #160 #160)
-#195 := [refl]: #170
-#186 := [nnf-pos #195]: #185
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#166 := (iff #37 #163)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#136 := (ite #63 #30 #131)
-#139 := (ite #12 0::int #136)
-#142 := (ite #13 #8 #139)
-#145 := (= #29 #142)
-#148 := (forall (vars (?v0 int) (?v1 int)) #145)
-#164 := (iff #148 #163)
-#161 := (iff #145 #160)
-#158 := (= #142 #157)
-#155 := (= #139 #154)
-#152 := (= #136 #151)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#153 := [monotonicity #108]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#149 := (iff #37 #148)
-#146 := (iff #36 #145)
-#143 := (= #35 #142)
-#140 := (= #34 #139)
-#137 := (= #33 #136)
-#134 := (= #32 #131)
-#128 := (- #125)
-#132 := (= #128 #131)
-#133 := [rewrite]: #132
-#129 := (= #32 #128)
-#126 := (= #31 #125)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#127 := [monotonicity #69 #72]: #126
-#130 := [monotonicity #127]: #129
-#135 := [trans #130 #133]: #134
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#138 := [monotonicity #65 #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [quant-intro #147]: #149
-#167 := [trans #150 #165]: #166
-#124 := [asserted]: #37
-#168 := [mp #124 #167]: #163
-#196 := [mp~ #168 #186]: #163
-#237 := [mp #196 #236]: #234
-#268 := [mp #237 #267]: #265
-#753 := [mp #268 #752]: #748
-#692 := (not #748)
-#693 := (or #692 #703)
-#326 := (* -1::int 3::int)
-#412 := (mod #411 #326)
-#413 := (+ #40 #412)
-#404 := (= #413 0::int)
-#414 := (<= 3::int 0::int)
-#397 := (or #418 #414)
-#732 := (not #397)
-#391 := (or #414 #734)
-#521 := (not #391)
-#728 := (or #521 #732)
-#402 := (ite #728 #417 #404)
-#736 := (ite #735 #403 #402)
-#737 := (= f5 #40)
-#738 := (= 3::int 0::int)
-#733 := (ite #738 #737 #736)
-#698 := (or #692 #733)
-#694 := (iff #698 #693)
-#541 := (iff #693 #693)
-#542 := [rewrite]: #541
-#696 := (iff #733 #703)
-#701 := (ite false #737 #703)
-#706 := (iff #701 #703)
-#695 := [rewrite]: #706
-#705 := (iff #733 #701)
-#704 := (iff #736 #703)
-#424 := (iff #402 #423)
-#712 := (iff #404 #708)
-#707 := (= #413 #433)
-#710 := (= #412 #709)
-#439 := (= #326 -3::int)
-#332 := [rewrite]: #439
-#432 := [monotonicity #332]: #710
-#711 := [monotonicity #432]: #707
-#422 := [monotonicity #711]: #712
-#436 := (iff #728 #727)
-#366 := (or #380 #723)
-#713 := (iff #366 #727)
-#714 := [rewrite]: #713
-#726 := (iff #728 #366)
-#725 := (iff #732 #723)
-#722 := (iff #397 #418)
-#718 := (or #418 false)
-#721 := (iff #718 #418)
-#716 := [rewrite]: #721
-#719 := (iff #397 #718)
-#389 := (iff #414 false)
-#394 := [rewrite]: #389
-#720 := [monotonicity #394]: #719
-#360 := [trans #720 #716]: #722
-#365 := [monotonicity #360]: #725
-#381 := (iff #521 #380)
-#378 := (iff #391 #734)
-#730 := (or false #734)
-#374 := (iff #730 #734)
-#715 := [rewrite]: #374
-#390 := (iff #391 #730)
-#731 := [monotonicity #394]: #390
-#379 := [trans #731 #715]: #378
-#717 := [monotonicity #379]: #381
-#724 := [monotonicity #717 #365]: #726
-#437 := [trans #724 #714]: #436
-#425 := [monotonicity #437 #422]: #424
-#419 := [monotonicity #425]: #704
-#739 := (iff #738 false)
-#729 := [rewrite]: #739
-#702 := [monotonicity #729 #419]: #705
-#697 := [trans #702 #695]: #696
-#700 := [monotonicity #697]: #694
-#543 := [trans #700 #542]: #694
-#699 := [quant-inst]: #698
-#685 := [mp #699 #543]: #693
-#616 := [unit-resolution #685 #753]: #703
-#670 := (not #735)
-#669 := (not #703)
-#611 := (or #669 #670)
-#576 := (not #403)
-#686 := (<= #40 0::int)
-#618 := (not #686)
-#648 := (or #618 #172)
-#649 := [th-lemma]: #648
-#605 := [unit-resolution #649 #183]: #618
-#606 := (or #576 #686)
-#607 := [th-lemma]: #606
-#610 := [unit-resolution #607 #605]: #576
-#673 := (or #669 #670 #403)
-#558 := [def-axiom]: #673
-#612 := [unit-resolution #558 #610]: #611
-#613 := [unit-resolution #612 #616]: #670
-#573 := (or #669 #735 #423)
-#575 := [def-axiom]: #573
-#608 := [unit-resolution #575 #613 #616]: #423
-#677 := (not #423)
-#679 := (or #677 #690 #417)
-#680 := [def-axiom]: #679
-#587 := [unit-resolution #680 #608]: #614
-#588 := [unit-resolution #587 #615]: #690
-#688 := (or #727 #418)
-#682 := [def-axiom]: #688
-#589 := [unit-resolution #682 #588]: #418
-#683 := (or #727 #734)
-#689 := [def-axiom]: #683
-#482 := [unit-resolution #689 #588]: #734
-#593 := (or #735 #723 #380)
-#594 := [th-lemma]: #593
-#595 := [unit-resolution #594 #613]: #727
-[unit-resolution #595 #482 #589]: false
-unsat
-91e3b65fe0735963e19e3d7ce9fe3c5222eb3f2d 57 0
+072cfd8219c35a3b429bb30277a49c3e7a1c16d3 57 0
 #2 := false
 #36 := 0::int
 decl f4 :: int
@@ -43963,7 +44326,7 @@
 #77 := [unit-resolution #76 #73]: #71
 [th-lemma #77 #56 #72]: false
 unsat
-e8ac648521d18274c15ba44956491a942644e11b 103 0
+f63820940f5c256ffad329cf88b74841a5d01c0b 103 0
 #2 := false
 #45 := 0::int
 decl f5 :: int
@@ -44067,7 +44430,7 @@
 #122 := [unit-resolution #121 #118]: #115
 [th-lemma #122 #92 #93]: false
 unsat
-ce75b686fb3c3081849ae555f6c4209952006101 86 0
+68f191b773df3b412b17e629ba69256053403e55 86 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -44154,7 +44517,7 @@
 #105 := [trans #104 #83]: #51
 [unit-resolution #57 #105]: false
 unsat
-5ed6ad8b6d8d132011755b1d04d869cf48c13481 68 0
+c4072005c8e1795531da8c1b5e11e377dcff53e0 68 0
 #2 := false
 #8 := 0::int
 decl f3 :: int
@@ -44223,353 +44586,7 @@
 #88 := [trans #87 #84]: #13
 [unit-resolution #71 #88]: false
 unsat
-f33aa883aeb7c21943e04cb493978fec1eef7863 345 0
-#2 := false
-#39 := 3::int
-decl f4 :: (-> int int int)
-decl f5 :: int
-#38 := f5
-#40 := (f4 f5 3::int)
-#441 := (mod #40 3::int)
-#657 := (>= #441 3::int)
-#658 := (not #657)
-#1 := true
-#59 := [true-axiom]: true
-#647 := (or false #658)
-#642 := [th-lemma]: #647
-#648 := [unit-resolution #642 #59]: #658
-#11 := 0::int
-#68 := -1::int
-#436 := (* -1::int #40)
-#600 := (+ f5 #436)
-#601 := (<= #600 0::int)
-#172 := (= f5 #40)
-#188 := (>= f5 3::int)
-#187 := (not #188)
-#178 := (not #172)
-#194 := (or #178 #187)
-#199 := (not #194)
-#42 := (< f5 3::int)
-#41 := (= #40 f5)
-#43 := (implies #41 #42)
-#44 := (not #43)
-#202 := (iff #44 #199)
-#179 := (or #42 #178)
-#184 := (not #179)
-#200 := (iff #184 #199)
-#197 := (iff #179 #194)
-#191 := (or #187 #178)
-#195 := (iff #191 #194)
-#196 := [rewrite]: #195
-#192 := (iff #179 #191)
-#189 := (iff #42 #187)
-#190 := [rewrite]: #189
-#193 := [monotonicity #190]: #192
-#198 := [trans #193 #196]: #197
-#201 := [monotonicity #198]: #200
-#185 := (iff #44 #184)
-#182 := (iff #43 #179)
-#175 := (implies #172 #42)
-#180 := (iff #175 #179)
-#181 := [rewrite]: #180
-#176 := (iff #43 #175)
-#173 := (iff #41 #172)
-#174 := [rewrite]: #173
-#177 := [monotonicity #174]: #176
-#183 := [trans #177 #181]: #182
-#186 := [monotonicity #183]: #185
-#203 := [trans #186 #201]: #202
-#171 := [asserted]: #44
-#204 := [mp #171 #203]: #199
-#205 := [not-or-elim #204]: #172
-#634 := (or #178 #601)
-#630 := [th-lemma]: #634
-#631 := [unit-resolution #630 #205]: #601
-#206 := [not-or-elim #204]: #188
-#438 := (f4 #40 3::int)
-#602 := (* -1::int #438)
-#603 := (+ #40 #602)
-#604 := (<= #603 0::int)
-#763 := (= #40 #438)
-#635 := (= #438 #40)
-#632 := [symm #205]: #41
-#636 := [monotonicity #632]: #635
-#637 := [symm #636]: #763
-#638 := (not #763)
-#633 := (or #638 #604)
-#639 := [th-lemma]: #633
-#612 := [unit-resolution #639 #637]: #604
-#369 := (* -1::int #441)
-#442 := (+ #438 #369)
-#707 := (<= #442 0::int)
-#439 := (= #442 0::int)
-#738 := -3::int
-#462 := (mod #436 -3::int)
-#357 := (+ #438 #462)
-#457 := (= #357 0::int)
-#422 := (<= #40 0::int)
-#750 := (not #422)
-#416 := (>= #40 0::int)
-#406 := (not #416)
-#751 := (or #406 #750)
-#736 := (ite #751 #439 #457)
-#760 := (= #438 0::int)
-#761 := (= #40 0::int)
-#447 := (ite #761 #760 #736)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#772 := (pattern #29)
-#72 := (* -1::int #9)
-#69 := (* -1::int #8)
-#127 := (mod #69 #72)
-#283 := (+ #29 #127)
-#284 := (= #283 0::int)
-#30 := (mod #8 #9)
-#280 := (* -1::int #30)
-#281 := (+ #29 #280)
-#282 := (= #281 0::int)
-#94 := (<= #9 0::int)
-#90 := (<= #8 0::int)
-#224 := (or #90 #94)
-#225 := (not #224)
-#101 := (>= #8 0::int)
-#216 := (or #94 #101)
-#217 := (not #216)
-#229 := (or #217 #225)
-#285 := (ite #229 #282 #284)
-#279 := (= #29 0::int)
-#12 := (= #8 0::int)
-#286 := (ite #12 #279 #285)
-#278 := (= #8 #29)
-#13 := (= #9 0::int)
-#287 := (ite #13 #278 #286)
-#773 := (forall (vars (?v0 int) (?v1 int)) (:pat #772) #287)
-#290 := (forall (vars (?v0 int) (?v1 int)) #287)
-#776 := (iff #290 #773)
-#774 := (iff #287 #287)
-#775 := [refl]: #774
-#777 := [quant-intro #775]: #776
-#133 := (* -1::int #127)
-#247 := (ite #229 #30 #133)
-#250 := (ite #12 0::int #247)
-#253 := (ite #13 #8 #250)
-#256 := (= #29 #253)
-#259 := (forall (vars (?v0 int) (?v1 int)) #256)
-#291 := (iff #259 #290)
-#288 := (iff #256 #287)
-#289 := [rewrite]: #288
-#292 := [quant-intro #289]: #291
-#102 := (not #101)
-#95 := (not #94)
-#105 := (and #95 #102)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#153 := (ite #108 #30 #133)
-#156 := (ite #12 0::int #153)
-#159 := (ite #13 #8 #156)
-#162 := (= #29 #159)
-#165 := (forall (vars (?v0 int) (?v1 int)) #162)
-#260 := (iff #165 #259)
-#257 := (iff #162 #256)
-#254 := (= #159 #253)
-#251 := (= #156 #250)
-#248 := (= #153 #247)
-#232 := (iff #108 #229)
-#226 := (or #225 #217)
-#230 := (iff #226 #229)
-#231 := [rewrite]: #230
-#227 := (iff #108 #226)
-#214 := (iff #105 #217)
-#215 := [rewrite]: #214
-#212 := (iff #98 #225)
-#213 := [rewrite]: #212
-#228 := [monotonicity #213 #215]: #227
-#233 := [trans #228 #231]: #232
-#249 := [monotonicity #233]: #248
-#252 := [monotonicity #249]: #251
-#255 := [monotonicity #252]: #254
-#258 := [monotonicity #255]: #257
-#261 := [quant-intro #258]: #260
-#210 := (~ #165 #165)
-#207 := (~ #162 #162)
-#222 := [refl]: #207
-#211 := [nnf-pos #222]: #210
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#168 := (iff #37 #165)
-#62 := (and #16 #18)
-#65 := (or #17 #62)
-#138 := (ite #65 #30 #133)
-#141 := (ite #12 0::int #138)
-#144 := (ite #13 #8 #141)
-#147 := (= #29 #144)
-#150 := (forall (vars (?v0 int) (?v1 int)) #147)
-#166 := (iff #150 #165)
-#163 := (iff #147 #162)
-#160 := (= #144 #159)
-#157 := (= #141 #156)
-#154 := (= #138 #153)
-#109 := (iff #65 #108)
-#106 := (iff #62 #105)
-#103 := (iff #18 #102)
-#104 := [rewrite]: #103
-#96 := (iff #16 #95)
-#97 := [rewrite]: #96
-#107 := [monotonicity #97 #104]: #106
-#99 := (iff #17 #98)
-#92 := (iff #15 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#155 := [monotonicity #110]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [quant-intro #164]: #166
-#151 := (iff #37 #150)
-#148 := (iff #36 #147)
-#145 := (= #35 #144)
-#142 := (= #34 #141)
-#139 := (= #33 #138)
-#136 := (= #32 #133)
-#130 := (- #127)
-#134 := (= #130 #133)
-#135 := [rewrite]: #134
-#131 := (= #32 #130)
-#128 := (= #31 #127)
-#73 := (= #23 #72)
-#74 := [rewrite]: #73
-#70 := (= #22 #69)
-#71 := [rewrite]: #70
-#129 := [monotonicity #71 #74]: #128
-#132 := [monotonicity #129]: #131
-#137 := [trans #132 #135]: #136
-#66 := (iff #20 #65)
-#63 := (iff #19 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#140 := [monotonicity #67 #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [quant-intro #149]: #151
-#169 := [trans #152 #167]: #168
-#126 := [asserted]: #37
-#170 := [mp #126 #169]: #165
-#223 := [mp~ #170 #211]: #165
-#262 := [mp #223 #261]: #259
-#293 := [mp #262 #292]: #290
-#778 := [mp #293 #777]: #773
-#731 := (not #773)
-#720 := (or #731 #447)
-#351 := (* -1::int 3::int)
-#437 := (mod #436 #351)
-#429 := (+ #438 #437)
-#440 := (= #429 0::int)
-#443 := (<= 3::int 0::int)
-#757 := (or #422 #443)
-#759 := (not #757)
-#546 := (or #443 #416)
-#753 := (not #546)
-#427 := (or #753 #759)
-#428 := (ite #427 #439 #440)
-#762 := (ite #761 #760 #428)
-#758 := (= 3::int 0::int)
-#764 := (ite #758 #763 #762)
-#721 := (or #731 #764)
-#717 := (iff #721 #720)
-#723 := (iff #720 #720)
-#724 := [rewrite]: #723
-#730 := (iff #764 #447)
-#450 := (ite false #763 #447)
-#444 := (iff #450 #447)
-#726 := [rewrite]: #444
-#728 := (iff #764 #450)
-#448 := (iff #762 #447)
-#733 := (iff #428 #736)
-#458 := (iff #440 #457)
-#734 := (= #429 #357)
-#463 := (= #437 #462)
-#739 := (= #351 -3::int)
-#461 := [rewrite]: #739
-#464 := [monotonicity #461]: #463
-#735 := [monotonicity #464]: #734
-#732 := [monotonicity #735]: #458
-#749 := (iff #427 #751)
-#390 := (iff #759 #750)
-#385 := (iff #757 #422)
-#744 := (or #422 false)
-#741 := (iff #744 #422)
-#747 := [rewrite]: #741
-#745 := (iff #757 #744)
-#419 := (iff #443 false)
-#755 := [rewrite]: #419
-#746 := [monotonicity #755]: #745
-#748 := [trans #746 #747]: #385
-#391 := [monotonicity #748]: #390
-#742 := (iff #753 #406)
-#404 := (iff #546 #416)
-#415 := (or false #416)
-#740 := (iff #415 #416)
-#403 := [rewrite]: #740
-#756 := (iff #546 #415)
-#399 := [monotonicity #755]: #756
-#405 := [trans #399 #403]: #404
-#743 := [monotonicity #405]: #742
-#752 := [monotonicity #743 #391]: #749
-#737 := [monotonicity #752 #732]: #733
-#449 := [monotonicity #737]: #448
-#754 := (iff #758 false)
-#414 := [rewrite]: #754
-#729 := [monotonicity #414 #449]: #728
-#727 := [trans #729 #726]: #730
-#718 := [monotonicity #727]: #717
-#719 := [trans #718 #724]: #717
-#722 := [quant-inst]: #721
-#725 := [mp #722 #719]: #720
-#613 := [unit-resolution #725 #778]: #447
-#589 := (not #761)
-#614 := (not #601)
-#507 := (or #750 #187 #614)
-#618 := [th-lemma]: #507
-#619 := [unit-resolution #618 #206 #631]: #750
-#620 := (or #589 #422)
-#625 := [th-lemma]: #620
-#621 := [unit-resolution #625 #619]: #589
-#588 := (not #447)
-#697 := (or #588 #761 #736)
-#599 := [def-axiom]: #697
-#622 := [unit-resolution #599 #621 #613]: #736
-#568 := (or #751 #422)
-#710 := [def-axiom]: #568
-#623 := [unit-resolution #710 #619]: #751
-#711 := (not #751)
-#709 := (not #736)
-#716 := (or #709 #711 #439)
-#545 := [def-axiom]: #716
-#626 := [unit-resolution #545 #623 #622]: #439
-#701 := (not #439)
-#627 := (or #701 #707)
-#628 := [th-lemma]: #627
-#624 := [unit-resolution #628 #626]: #707
-[th-lemma #624 #612 #206 #631 #648]: false
-unsat
-676aec4873ed7d4eeb51bdde607873c00764a075 124 0
+6ff6fa8a0f1c9c5f56bb5345e3f7dae237dbfbda 124 0
 #2 := false
 #13 := 0::int
 decl f4 :: int
@@ -44694,7 +44711,7 @@
 #145 := [unit-resolution #117 #144]: #106
 [th-lemma #131 #143 #141 #85 #145]: false
 unsat
-8c7ea6775a14dcc4e6e4353a2f19b1779116c872 57 0
+25ccec15a602a1c54ac65064428b0d7e8e49a157 57 0
 #2 := false
 #36 := 0::int
 decl f4 :: int
@@ -44752,7 +44769,7 @@
 #77 := [unit-resolution #76 #73]: #70
 [th-lemma #77 #56 #72]: false
 unsat
-d2ac6a0bd8f242b6fea1d95d6a700ca235f7739e 57 0
+826d0f295042ed751be7cd991724b70343966127 57 0
 #2 := false
 #35 := 0::int
 decl f4 :: int
@@ -44810,7 +44827,7 @@
 #77 := [th-lemma]: #76
 [unit-resolution #77 #74 #56]: false
 unsat
-8bc37b5efc45a2f7051f9fdaf148c2248f44ab13 103 0
+faa737b4932c0aa5150131d8b782d7d669ed0113 103 0
 #2 := false
 #45 := 0::int
 decl f3 :: int
@@ -44914,7 +44931,7 @@
 #122 := [unit-resolution #121 #118]: #116
 [th-lemma #122 #91 #93]: false
 unsat
-3bd554374bbb33d45f736a3866c11a3228de58fe 88 0
+b85a0b83921360b33aeac166308bca158d0b98fc 88 0
 #2 := false
 decl f4 :: int
 #9 := f4
@@ -45003,7 +45020,7 @@
 #109 := [trans #108 #83]: #51
 [unit-resolution #57 #109]: false
 unsat
-0a0200d3ff0127396d33719b1042db644955b4a6 66 0
+c1d9eb6aa500cf84264fa06f0164040270b4b113 66 0
 #2 := false
 decl f3 :: int
 #9 := f3
@@ -45070,7 +45087,7 @@
 #86 := [trans #83 #85]: #33
 [unit-resolution #69 #86]: false
 unsat
-8577a1a174a114007fec8ab3e02f9bb87a08d3a4 228 0
+37af311b9ecd8b8850526a981f094de0aaf7d3cd 228 0
 #2 := false
 #9 := 0::int
 decl f4 :: int
@@ -45299,7 +45316,7 @@
 #250 := [unit-resolution #196 #249]: #190
 [th-lemma #236 #250 #131 #234 #248 #238]: false
 unsat
-5113b523f1372e7b618c36a10fb907e6373d5abd 56 0
+3adfffc1ab7359b9b1007b29c2557c38e2960f02 56 0
 #2 := false
 #11 := 1::int
 decl f3 :: int
@@ -45356,7 +45373,7 @@
 #71 := [not-or-elim #69]: #70
 [unit-resolution #71 #85]: false
 unsat
-62b700db02f2de2fa17813b51c0e2aba7a4c9eab 18 0
+7928fa49e84e0e2eeb9e58ad600a296a4893ef27 18 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -45375,7 +45392,7 @@
 #27 := [asserted]: #10
 [mp #27 #38]: false
 unsat
-096109feda0c7355b238e40d53b92530b4dac963 51 0
+b97417937bf2455125b622159c8863efc4fa7507 51 0
 #2 := false
 decl f4 :: int
 #9 := f4
@@ -45427,7 +45444,7 @@
 #33 := [asserted]: #16
 [mp #33 #68]: false
 unsat
-b5e5bf38e2f1c07ae123d010d3ca139589460e87 56 0
+a42d51312b9fa7c69d967efe1269dff8f72c6658 56 0
 #2 := false
 decl f4 :: int
 #9 := f4
@@ -45484,7 +45501,7 @@
 #33 := [asserted]: #16
 [mp #33 #73]: false
 unsat
-fed98b15794bca1381978ee51c537989f6976c21 52 0
+0ec9f06df1cdb139b74a09cc966c9ce378f13851 52 0
 #2 := false
 #40 := 0::int
 decl f4 :: int
@@ -45537,7 +45554,7 @@
 #77 := [unit-resolution #76 #65]: #53
 [unit-resolution #77 #67]: false
 unsat
-87f174d87c949beb4788f98812dca55337bf0039 73 0
+ce16fe974de62cf3c0ef75529dc61d4efa890f06 73 0
 #2 := false
 #58 := 0::int
 decl f4 :: int
@@ -45611,7 +45628,7 @@
 #78 := [unit-resolution #82 #74]: #83
 [unit-resolution #78 #92 #89]: false
 unsat
-e9fb6be58fab173c96da99cb14354ad048f64a9a 15 0
+74933f512913afc01d9a78eb88557f932533c336 15 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -45627,7 +45644,7 @@
 #28 := [asserted]: #11
 [mp #28 #34]: false
 unsat
-2e519318d3bea148863de330ab0d886976088a08 75 0
+7661e8426489f0b35379268b8502d1300d87ab45 75 0
 #2 := false
 #53 := 0::int
 decl f4 :: int
@@ -45703,7 +45720,7 @@
 #89 := [not-or-elim #88]: #54
 [th-lemma #89 #91 #92]: false
 unsat
-d957e317464f75f14f0257c9a9e3944a4c7e56fa 80 0
+2255615b52ddeb127b4641b41f76c4291059c1c6 80 0
 #2 := false
 #53 := 0::int
 decl f4 :: int
@@ -45784,7 +45801,7 @@
 #94 := [not-or-elim #93]: #54
 [th-lemma #94 #96 #97]: false
 unsat
-1e6359b823e59d7a3bc20a06b7948d9799fc1ea2 80 0
+f72c5837f3527c531ec8ab57fa7038de783af727 80 0
 #2 := false
 #52 := 0::int
 decl f4 :: int
@@ -45865,7 +45882,7 @@
 #96 := [not-or-elim #93]: #95
 [th-lemma #96 #94 #97]: false
 unsat
-70f0bd2ca61ea7f7f79a865b60edecada1e579bc 85 0
+4d6de342eb4a79df07deb8d4a6715a405ee8705b 85 0
 #2 := false
 #52 := 0::int
 decl f4 :: int
@@ -45951,7 +45968,7 @@
 #101 := [not-or-elim #99]: #66
 [th-lemma #101 #100 #102]: false
 unsat
-d4b9d7236f58deec9d8b880ed595e162ac78698f 69 0
+01d41a6defe536be3c36f4fc18beb209fedeb2b9 69 0
 #2 := false
 #44 := 0::int
 decl f5 :: int
@@ -46021,7 +46038,7 @@
 #85 := [and-elim #83]: #53
 [th-lemma #85 #84 #86]: false
 unsat
-93f88e9d9942aeac0995634bc80288f6b3124d6e 17 0
+f28afc0a495606cd18c03d1ef7b735dbcdbac7da 17 0
 #2 := false
 #8 := 0::real
 #9 := (= 0::real 0::real)
@@ -46039,7 +46056,7 @@
 #27 := [asserted]: #10
 [mp #27 #36]: false
 unsat
-c76a2eba918417f6f2e01b2b723c524c06e861cf 25 0
+606c342b7c615ebb689898f0c941f7d1c48ec2f5 25 0
 #2 := false
 #8 := 0::real
 #9 := (- 0::real)
@@ -46065,7 +46082,7 @@
 #28 := [asserted]: #11
 [mp #28 #44]: false
 unsat
-124d21d085906b9b1a287c6fb023579c3d29d71e 17 0
+03174d2c94da8e32d99b511a2d2d8af637a1cc0a 17 0
 #2 := false
 #8 := 1::real
 #9 := (= 1::real 1::real)
@@ -46083,7 +46100,7 @@
 #27 := [asserted]: #10
 [mp #27 #36]: false
 unsat
-5560886df3c18f9a0c150a7d43e759132adbc67a 34 0
+e8a0e00cd5697b0530a493b0f960990c6172eb4b 34 0
 #2 := false
 #8 := 1::real
 #9 := (- 1::real)
@@ -46118,7 +46135,7 @@
 #29 := [asserted]: #12
 [mp #29 #53]: false
 unsat
-ea1032005c0c668000f0638ca6458e10715452d1 18 0
+ea5a319299c7c169ca8cf4134daecbf4e9f6b611 18 0
 #2 := false
 #9 := 1::real
 #8 := 0::real
@@ -46137,7 +46154,7 @@
 #28 := [asserted]: #11
 [mp #28 #39]: false
 unsat
-9bf86956cfc4183079f2d625e7fb67e79d8e3a6f 18 0
+0326ffc3ee68a4d3d9a0132853c1927704b6a984 18 0
 #2 := false
 #9 := 1::real
 #8 := 0::real
@@ -46156,34 +46173,7 @@
 #28 := [asserted]: #11
 [mp #28 #39]: false
 unsat
-462b078573a7260cabbe050e6e8a010e81307468 26 0
-#2 := false
-decl f3 :: real
-#8 := f3
-#9 := 0::real
-#10 := (+ f3 0::real)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-fbe5b7285614f32e77c7dc8b02bdfaab1ce33767 40 0
+7a08ee76cf424de3a3f28861d2070ada9d6084ad 40 0
 #2 := false
 #12 := 567::real
 #10 := 345::real
@@ -46224,34 +46214,7 @@
 #31 := [asserted]: #14
 [mp #31 #59]: false
 unsat
-440f4e3d826b24104b71d716ed035b8fcf2e496d 26 0
-#2 := false
-decl f3 :: real
-#9 := f3
-#8 := 0::real
-#10 := (+ 0::real f3)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-0f930aea7df79d93cedef0ce68be2ff1d1da57e3 18 0
+613428b13c7b70e2e27b5d78c2d2549aa7176b33 18 0
 #2 := false
 #9 := 2345678901::real
 #8 := 123456789::real
@@ -46270,37 +46233,7 @@
 #28 := [asserted]: #11
 [mp #28 #39]: false
 unsat
-20e0c3ffbf68f93c4311b4bf54c2ea3efe010e7a 29 0
-#2 := false
-decl f3 :: real
-#8 := f3
-decl f4 :: real
-#9 := f4
-#11 := (+ f4 f3)
-#10 := (+ f3 f4)
-#12 := (= #10 #11)
-#13 := (not #12)
-#45 := (iff #13 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #13 #40)
-#38 := (iff #12 true)
-#33 := (= #10 #10)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #12 #33)
-#31 := (= #11 #10)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#30 := [asserted]: #13
-[mp #30 #46]: false
-unsat
-39b152c2721f346c536c8037f243dbf8a4709b1b 30 0
+50fc66824d89eee5337412b045c3468014730d70 30 0
 #2 := false
 #10 := 2345678901::real
 #8 := 123456789::real
@@ -46331,7 +46264,91 @@
 #29 := [asserted]: #12
 [mp #29 #49]: false
 unsat
-2fbcb3e0a00b30b4d1cfcecd9304791b2a48d7f4 33 0
+f117454df9fb8a2aec2f275902e353b4d4a911e3 26 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := 0::real
+#10 := (+ f3 0::real)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+b2bb47b9838aa12a0cc91e044661711edc166d8b 26 0
+#2 := false
+decl f3 :: real
+#9 := f3
+#8 := 0::real
+#10 := (+ 0::real f3)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+bbb9ec4e976eca277d6ebc762c0b62131ff5bfe6 29 0
+#2 := false
+decl f3 :: real
+#8 := f3
+decl f4 :: real
+#9 := f4
+#11 := (+ f4 f3)
+#10 := (+ f3 f4)
+#12 := (= #10 #11)
+#13 := (not #12)
+#45 := (iff #13 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #13 #40)
+#38 := (iff #12 true)
+#33 := (= #10 #10)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #12 #33)
+#31 := (= #11 #10)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#30 := [asserted]: #13
+[mp #30 #46]: false
+unsat
+75603b63d988a71cae7da7ebaffb8d08a69e885c 33 0
 #2 := false
 decl f5 :: real
 #10 := f5
@@ -46365,7 +46382,7 @@
 #33 := [asserted]: #16
 [mp #33 #49]: false
 unsat
-2ec6b499b5be496e928bd834c349a1c431eea001 45 0
+60381fd2f88c5efc8d4130a5c6fc2252f6c46269 45 0
 #2 := false
 decl f4 :: real
 #9 := f4
@@ -46411,34 +46428,7 @@
 #33 := [asserted]: #16
 [mp #33 #63]: false
 unsat
-fc436284003e8c697b8dbb37e8945314d2bc0428 26 0
-#2 := false
-decl f3 :: real
-#8 := f3
-#9 := 0::real
-#10 := (- f3 0::real)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-d3d5a890beab517bd089563bbca4f1f153a58428 58 0
+f6d7acda843f47d927998cbca26c86310fc362be 58 0
 #2 := false
 decl f3 :: real
 #8 := f3
@@ -46497,40 +46487,7 @@
 #31 := [asserted]: #14
 [mp #31 #77]: false
 unsat
-e32be0c9d1b02319d3e7244ea2d0e549b6430915 32 0
-#2 := false
-decl f3 :: real
-#9 := f3
-#11 := (- f3)
-#8 := 0::real
-#10 := (- 0::real f3)
-#12 := (= #10 #11)
-#13 := (not #12)
-#49 := (iff #13 false)
-#1 := true
-#44 := (not true)
-#47 := (iff #44 false)
-#48 := [rewrite]: #47
-#45 := (iff #13 #44)
-#42 := (iff #12 true)
-#31 := -1::real
-#32 := (* -1::real f3)
-#37 := (= #32 #32)
-#40 := (iff #37 true)
-#41 := [rewrite]: #40
-#38 := (iff #12 #37)
-#35 := (= #11 #32)
-#36 := [rewrite]: #35
-#33 := (= #10 #32)
-#34 := [rewrite]: #33
-#39 := [monotonicity #34 #36]: #38
-#43 := [trans #39 #41]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#30 := [asserted]: #13
-[mp #30 #50]: false
-unsat
-eb2eb6c8c377b3314725038ad15c0d85d1554cd5 61 0
+8ee1fdcfda6d0ba1c8e9f0190394cdc304ae0ac2 61 0
 #2 := false
 #8 := 0::real
 decl f3 :: real
@@ -46592,7 +46549,129 @@
 #31 := [asserted]: #14
 [mp #31 #79]: false
 unsat
-83589b9e6143db146b7355cf95d479fdd7008de6 64 0
+896c3827a8365ede8326c68345ecd5d1745e2096 61 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#11 := (- f3)
+#9 := 0::real
+#12 := (< 0::real #11)
+#10 := (< f3 0::real)
+#13 := (implies #10 #12)
+#14 := (not #13)
+#78 := (iff #14 false)
+#32 := -1::real
+#33 := (* -1::real f3)
+#36 := (< 0::real #33)
+#42 := (not #10)
+#43 := (or #42 #36)
+#48 := (not #43)
+#76 := (iff #48 false)
+#1 := true
+#71 := (not true)
+#74 := (iff #71 false)
+#75 := [rewrite]: #74
+#72 := (iff #48 #71)
+#69 := (iff #43 true)
+#51 := (>= f3 0::real)
+#52 := (not #51)
+#64 := (or #51 #52)
+#67 := (iff #64 true)
+#68 := [rewrite]: #67
+#65 := (iff #43 #64)
+#62 := (iff #36 #52)
+#63 := [rewrite]: #62
+#60 := (iff #42 #51)
+#55 := (not #52)
+#58 := (iff #55 #51)
+#59 := [rewrite]: #58
+#56 := (iff #42 #55)
+#53 := (iff #10 #52)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#66 := [monotonicity #61 #63]: #65
+#70 := [trans #66 #68]: #69
+#73 := [monotonicity #70]: #72
+#77 := [trans #73 #75]: #76
+#49 := (iff #14 #48)
+#46 := (iff #13 #43)
+#39 := (implies #10 #36)
+#44 := (iff #39 #43)
+#45 := [rewrite]: #44
+#40 := (iff #13 #39)
+#37 := (iff #12 #36)
+#34 := (= #11 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#47 := [trans #41 #45]: #46
+#50 := [monotonicity #47]: #49
+#79 := [trans #50 #77]: #78
+#31 := [asserted]: #14
+[mp #31 #79]: false
+unsat
+621e22bec50c8078bb9185c48553875354b94486 26 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := 0::real
+#10 := (- f3 0::real)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+253e69096bc26c823c402767e9d98f949614052e 32 0
+#2 := false
+decl f3 :: real
+#9 := f3
+#11 := (- f3)
+#8 := 0::real
+#10 := (- 0::real f3)
+#12 := (= #10 #11)
+#13 := (not #12)
+#49 := (iff #13 false)
+#1 := true
+#44 := (not true)
+#47 := (iff #44 false)
+#48 := [rewrite]: #47
+#45 := (iff #13 #44)
+#42 := (iff #12 true)
+#31 := -1::real
+#32 := (* -1::real f3)
+#37 := (= #32 #32)
+#40 := (iff #37 true)
+#41 := [rewrite]: #40
+#38 := (iff #12 #37)
+#35 := (= #11 #32)
+#36 := [rewrite]: #35
+#33 := (= #10 #32)
+#34 := [rewrite]: #33
+#39 := [monotonicity #34 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#30 := [asserted]: #13
+[mp #30 #50]: false
+unsat
+cbdf060ae9e69eb58fc6c65ffc92cb2a9298736b 64 0
 #2 := false
 #12 := 0::real
 decl f4 :: real
@@ -46657,69 +46736,7 @@
 #32 := [asserted]: #15
 [mp #32 #81]: false
 unsat
-20175dd1cbc4733e0e0a6808b337d3ef714bc8ea 61 0
-#2 := false
-decl f3 :: real
-#8 := f3
-#11 := (- f3)
-#9 := 0::real
-#12 := (< 0::real #11)
-#10 := (< f3 0::real)
-#13 := (implies #10 #12)
-#14 := (not #13)
-#78 := (iff #14 false)
-#32 := -1::real
-#33 := (* -1::real f3)
-#36 := (< 0::real #33)
-#42 := (not #10)
-#43 := (or #42 #36)
-#48 := (not #43)
-#76 := (iff #48 false)
-#1 := true
-#71 := (not true)
-#74 := (iff #71 false)
-#75 := [rewrite]: #74
-#72 := (iff #48 #71)
-#69 := (iff #43 true)
-#51 := (>= f3 0::real)
-#52 := (not #51)
-#64 := (or #51 #52)
-#67 := (iff #64 true)
-#68 := [rewrite]: #67
-#65 := (iff #43 #64)
-#62 := (iff #36 #52)
-#63 := [rewrite]: #62
-#60 := (iff #42 #51)
-#55 := (not #52)
-#58 := (iff #55 #51)
-#59 := [rewrite]: #58
-#56 := (iff #42 #55)
-#53 := (iff #10 #52)
-#54 := [rewrite]: #53
-#57 := [monotonicity #54]: #56
-#61 := [trans #57 #59]: #60
-#66 := [monotonicity #61 #63]: #65
-#70 := [trans #66 #68]: #69
-#73 := [monotonicity #70]: #72
-#77 := [trans #73 #75]: #76
-#49 := (iff #14 #48)
-#46 := (iff #13 #43)
-#39 := (implies #10 #36)
-#44 := (iff #39 #43)
-#45 := [rewrite]: #44
-#40 := (iff #13 #39)
-#37 := (iff #12 #36)
-#34 := (= #11 #33)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#41 := [monotonicity #38]: #40
-#47 := [trans #41 #45]: #46
-#50 := [monotonicity #47]: #49
-#79 := [trans #50 #77]: #78
-#31 := [asserted]: #14
-[mp #31 #79]: false
-unsat
-0edbb7a2c42cbb0fdbf200f800919445d8fe0fcd 44 0
+b972394b300baf8aaa9486f331f2557a703161b7 44 0
 #2 := false
 decl f3 :: real
 #8 := f3
@@ -46764,7 +46781,7 @@
 #31 := [asserted]: #14
 [mp #31 #61]: false
 unsat
-07f4f6c399af663ebc560d31da386f4b6f8eceaa 42 0
+a6daeae6c5f9b10e9913708193bddaeeeab231d6 42 0
 #2 := false
 decl f3 :: real
 #8 := f3
@@ -46807,7 +46824,7 @@
 #31 := [asserted]: #14
 [mp #31 #59]: false
 unsat
-11d02f55135438b9126f773087ae5fbc1bfb4b1f 48 0
+c9bf648f3d046441ad2eb8ce5a83843d275d848f 48 0
 #2 := false
 decl f5 :: real
 #11 := f5
@@ -46856,7 +46873,7 @@
 #33 := [asserted]: #16
 [mp #33 #64]: false
 unsat
-43b7b87cca59f261804e2de323813ff74305eab9 30 0
+3a4050aa853f574f613f1bf43664c63ec57ba315 30 0
 #2 := false
 #8 := 1::real
 #9 := 2::real
@@ -46887,7 +46904,7 @@
 #29 := [asserted]: #12
 [mp #29 #49]: false
 unsat
-53cfe5e87c16fffbe2f16f255256cca3098e68ab 27 0
+c12a2ff1f9932fed353a346ae57b1ad07fe8af67 27 0
 #2 := false
 #9 := 3::real
 #8 := 1::real
@@ -46915,44 +46932,7 @@
 #29 := [asserted]: #12
 [mp #29 #46]: false
 unsat
-a0dc8948916e6295727989d5921bca6fbb1b7702 36 0
-#2 := false
-decl f3 :: real
-#9 := f3
-#8 := 3::real
-#10 := (/ f3 3::real)
-#11 := (* 3::real #10)
-#12 := (= #11 f3)
-#13 := (not #12)
-#53 := (iff #13 false)
-#1 := true
-#48 := (not true)
-#51 := (iff #48 false)
-#52 := [rewrite]: #51
-#49 := (iff #13 #48)
-#46 := (iff #12 true)
-#41 := (= f3 f3)
-#44 := (iff #41 true)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#31 := 1/3::real
-#32 := (* 1/3::real f3)
-#35 := (* 3::real #32)
-#38 := (= #35 f3)
-#39 := [rewrite]: #38
-#36 := (= #11 #35)
-#33 := (= #10 #32)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#40 := [trans #37 #39]: #12
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#50 := [monotonicity #47]: #49
-#54 := [trans #50 #52]: #53
-#30 := [asserted]: #13
-[mp #30 #54]: false
-unsat
-26808346607eaf4342e6db7ed90e590a0bd9c647 48 0
+6e841a011430a698a24c878ef0e827af9cbb5aaf 48 0
 #2 := false
 #9 := 3::real
 #8 := 1::real
@@ -47001,43 +46981,7 @@
 #32 := [asserted]: #15
 [mp #32 #67]: false
 unsat
-09202bff4da2c74e9a8dbe43ef21689e4bdfaae9 35 0
-#2 := false
-decl f3 :: real
-#8 := f3
-#9 := 3::real
-#10 := (* f3 3::real)
-#11 := (/ #10 3::real)
-#12 := (= #11 f3)
-#13 := (not #12)
-#52 := (iff #13 false)
-#1 := true
-#47 := (not true)
-#50 := (iff #47 false)
-#51 := [rewrite]: #50
-#48 := (iff #13 #47)
-#45 := (iff #12 true)
-#40 := (= f3 f3)
-#43 := (iff #40 true)
-#44 := [rewrite]: #43
-#41 := (iff #12 #40)
-#31 := (* 3::real f3)
-#34 := (/ #31 3::real)
-#37 := (= #34 f3)
-#38 := [rewrite]: #37
-#35 := (= #11 #34)
-#32 := (= #10 #31)
-#33 := [rewrite]: #32
-#36 := [monotonicity #33]: #35
-#39 := [trans #36 #38]: #12
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#30 := [asserted]: #13
-[mp #30 #53]: false
-unsat
-b76505782dfbae0f8341048039ea3f79ecdab350 36 0
+e33f03d506eac30dad600124f9023211fa4e619a 36 0
 #2 := false
 #10 := 3::real
 #8 := 1::real
@@ -47074,7 +47018,273 @@
 #30 := [asserted]: #13
 [mp #30 #55]: false
 unsat
-0c13c4469b276c16009a975c07b71cc3daa7abc5 62 0
+20564fbaa0151379e4ea7ab91c8c3824ec82b3c0 43 0
+#2 := false
+#10 := 3::real
+#8 := 1::real
+#13 := (/ 1::real 3::real)
+#11 := (- 3::real)
+#9 := (- 1::real)
+#12 := (/ #9 #11)
+#14 := (= #12 #13)
+#15 := (not #14)
+#61 := (iff #15 false)
+#1 := true
+#56 := (not true)
+#59 := (iff #56 false)
+#60 := [rewrite]: #59
+#57 := (iff #15 #56)
+#54 := (iff #14 true)
+#42 := 1/3::real
+#49 := (= 1/3::real 1/3::real)
+#52 := (iff #49 true)
+#53 := [rewrite]: #52
+#50 := (iff #14 #49)
+#47 := (= #13 1/3::real)
+#48 := [rewrite]: #47
+#45 := (= #12 1/3::real)
+#36 := -3::real
+#33 := -1::real
+#39 := (/ -1::real -3::real)
+#43 := (= #39 1/3::real)
+#44 := [rewrite]: #43
+#40 := (= #12 #39)
+#37 := (= #11 -3::real)
+#38 := [rewrite]: #37
+#34 := (= #9 -1::real)
+#35 := [rewrite]: #34
+#41 := [monotonicity #35 #38]: #40
+#46 := [trans #41 #44]: #45
+#51 := [monotonicity #46 #48]: #50
+#55 := [trans #51 #53]: #54
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#32 := [asserted]: #15
+[mp #32 #62]: false
+unsat
+f37f9f929a96e85a9393ef767c4e8c9fc5d590fe 26 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := 1::real
+#10 := (/ f3 1::real)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+ed3d8e9b94d240ecfe9b9b4629871111c78abf90 60 0
+#2 := false
+#8 := 0::real
+decl f3 :: real
+#9 := f3
+#65 := 2/3::real
+#66 := (* 2/3::real f3)
+#67 := (<= #66 0::real)
+#63 := (not #67)
+#52 := (<= f3 0::real)
+#69 := (or #52 #63)
+#72 := (not #69)
+#11 := 3::real
+#12 := (/ f3 3::real)
+#13 := (< #12 f3)
+#10 := (< 0::real f3)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#75 := (iff #15 #72)
+#33 := 1/3::real
+#34 := (* 1/3::real f3)
+#37 := (< #34 f3)
+#43 := (not #10)
+#44 := (or #43 #37)
+#49 := (not #44)
+#73 := (iff #49 #72)
+#70 := (iff #44 #69)
+#64 := (iff #37 #63)
+#68 := [rewrite]: #64
+#61 := (iff #43 #52)
+#53 := (not #52)
+#56 := (not #53)
+#59 := (iff #56 #52)
+#60 := [rewrite]: #59
+#57 := (iff #43 #56)
+#54 := (iff #10 #53)
+#55 := [rewrite]: #54
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#71 := [monotonicity #62 #68]: #70
+#74 := [monotonicity #71]: #73
+#50 := (iff #15 #49)
+#47 := (iff #14 #44)
+#40 := (implies #10 #37)
+#45 := (iff #40 #44)
+#46 := [rewrite]: #45
+#41 := (iff #14 #40)
+#38 := (iff #13 #37)
+#35 := (= #12 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#42 := [monotonicity #39]: #41
+#48 := [trans #42 #46]: #47
+#51 := [monotonicity #48]: #50
+#76 := [trans #51 #74]: #75
+#32 := [asserted]: #15
+#77 := [mp #32 #76]: #72
+#79 := [not-or-elim #77]: #67
+#78 := [not-or-elim #77]: #53
+[th-lemma #78 #79]: false
+unsat
+11d14951f36209bf8f30601465632250d45d551c 60 0
+#2 := false
+#9 := 0::real
+decl f3 :: real
+#8 := f3
+#67 := 2/3::real
+#68 := (* 2/3::real f3)
+#65 := (>= #68 0::real)
+#63 := (not #65)
+#54 := (>= f3 0::real)
+#69 := (or #54 #63)
+#72 := (not #69)
+#11 := 3::real
+#12 := (/ f3 3::real)
+#13 := (< f3 #12)
+#10 := (< f3 0::real)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#75 := (iff #15 #72)
+#33 := 1/3::real
+#34 := (* 1/3::real f3)
+#37 := (< f3 #34)
+#43 := (not #10)
+#44 := (or #43 #37)
+#49 := (not #44)
+#73 := (iff #49 #72)
+#70 := (iff #44 #69)
+#64 := (iff #37 #63)
+#66 := [rewrite]: #64
+#61 := (iff #43 #54)
+#52 := (not #54)
+#56 := (not #52)
+#59 := (iff #56 #54)
+#60 := [rewrite]: #59
+#57 := (iff #43 #56)
+#53 := (iff #10 #52)
+#55 := [rewrite]: #53
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#71 := [monotonicity #62 #66]: #70
+#74 := [monotonicity #71]: #73
+#50 := (iff #15 #49)
+#47 := (iff #14 #44)
+#40 := (implies #10 #37)
+#45 := (iff #40 #44)
+#46 := [rewrite]: #45
+#41 := (iff #14 #40)
+#38 := (iff #13 #37)
+#35 := (= #12 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#42 := [monotonicity #39]: #41
+#48 := [trans #42 #46]: #47
+#51 := [monotonicity #48]: #50
+#76 := [trans #51 #74]: #75
+#32 := [asserted]: #15
+#77 := [mp #32 #76]: #72
+#79 := [not-or-elim #77]: #65
+#78 := [not-or-elim #77]: #52
+[th-lemma #78 #79]: false
+unsat
+caeefe50d420a4e762d36be1e2d664719689719d 36 0
+#2 := false
+decl f3 :: real
+#9 := f3
+#8 := 3::real
+#10 := (/ f3 3::real)
+#11 := (* 3::real #10)
+#12 := (= #11 f3)
+#13 := (not #12)
+#53 := (iff #13 false)
+#1 := true
+#48 := (not true)
+#51 := (iff #48 false)
+#52 := [rewrite]: #51
+#49 := (iff #13 #48)
+#46 := (iff #12 true)
+#41 := (= f3 f3)
+#44 := (iff #41 true)
+#45 := [rewrite]: #44
+#42 := (iff #12 #41)
+#31 := 1/3::real
+#32 := (* 1/3::real f3)
+#35 := (* 3::real #32)
+#38 := (= #35 f3)
+#39 := [rewrite]: #38
+#36 := (= #11 #35)
+#33 := (= #10 #32)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#40 := [trans #37 #39]: #12
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#50 := [monotonicity #47]: #49
+#54 := [trans #50 #52]: #53
+#30 := [asserted]: #13
+[mp #30 #54]: false
+unsat
+086c8eb8aaeb53cde2df9b97bdcc22fa17e9a97a 35 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := 3::real
+#10 := (* f3 3::real)
+#11 := (/ #10 3::real)
+#12 := (= #11 f3)
+#13 := (not #12)
+#52 := (iff #13 false)
+#1 := true
+#47 := (not true)
+#50 := (iff #47 false)
+#51 := [rewrite]: #50
+#48 := (iff #13 #47)
+#45 := (iff #12 true)
+#40 := (= f3 f3)
+#43 := (iff #40 true)
+#44 := [rewrite]: #43
+#41 := (iff #12 #40)
+#31 := (* 3::real f3)
+#34 := (/ #31 3::real)
+#37 := (= #34 f3)
+#38 := [rewrite]: #37
+#35 := (= #11 #34)
+#32 := (= #10 #31)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#39 := [trans #36 #38]: #12
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#49 := [monotonicity #46]: #48
+#53 := [trans #49 #51]: #52
+#30 := [asserted]: #13
+[mp #30 #53]: false
+unsat
+49ec9aa80edfec547bf2761e7a0e2fe1b163cf3b 62 0
 #2 := false
 #8 := 0::real
 decl f3 :: real
@@ -47137,51 +47347,7 @@
 #80 := [not-or-elim #79]: #55
 [th-lemma #80 #81]: false
 unsat
-bc88a01de6db0490fffd7e188b191be86acfd954 43 0
-#2 := false
-#10 := 3::real
-#8 := 1::real
-#13 := (/ 1::real 3::real)
-#11 := (- 3::real)
-#9 := (- 1::real)
-#12 := (/ #9 #11)
-#14 := (= #12 #13)
-#15 := (not #14)
-#61 := (iff #15 false)
-#1 := true
-#56 := (not true)
-#59 := (iff #56 false)
-#60 := [rewrite]: #59
-#57 := (iff #15 #56)
-#54 := (iff #14 true)
-#42 := 1/3::real
-#49 := (= 1/3::real 1/3::real)
-#52 := (iff #49 true)
-#53 := [rewrite]: #52
-#50 := (iff #14 #49)
-#47 := (= #13 1/3::real)
-#48 := [rewrite]: #47
-#45 := (= #12 1/3::real)
-#36 := -3::real
-#33 := -1::real
-#39 := (/ -1::real -3::real)
-#43 := (= #39 1/3::real)
-#44 := [rewrite]: #43
-#40 := (= #12 #39)
-#37 := (= #11 -3::real)
-#38 := [rewrite]: #37
-#34 := (= #9 -1::real)
-#35 := [rewrite]: #34
-#41 := [monotonicity #35 #38]: #40
-#46 := [trans #41 #44]: #45
-#51 := [monotonicity #46 #48]: #50
-#55 := [trans #51 #53]: #54
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#32 := [asserted]: #15
-[mp #32 #62]: false
-unsat
-27ba361ee1bcc866b25f3de9b0470e4e247364ed 62 0
+84cb5ffc40241b444b7a289375c31377805f81fe 62 0
 #2 := false
 #9 := 0::real
 decl f3 :: real
@@ -47244,95 +47410,7 @@
 #80 := [not-or-elim #79]: #54
 [th-lemma #80 #81]: false
 unsat
-e1161936dfae097cefecc5afb0c61d7cd7a9394d 26 0
-#2 := false
-decl f3 :: real
-#8 := f3
-#9 := 1::real
-#10 := (/ f3 1::real)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-501254910821a4c83220ee640918ae11739106cb 60 0
-#2 := false
-#8 := 0::real
-decl f3 :: real
-#9 := f3
-#65 := 2/3::real
-#66 := (* 2/3::real f3)
-#67 := (<= #66 0::real)
-#63 := (not #67)
-#52 := (<= f3 0::real)
-#69 := (or #52 #63)
-#72 := (not #69)
-#11 := 3::real
-#12 := (/ f3 3::real)
-#13 := (< #12 f3)
-#10 := (< 0::real f3)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#75 := (iff #15 #72)
-#33 := 1/3::real
-#34 := (* 1/3::real f3)
-#37 := (< #34 f3)
-#43 := (not #10)
-#44 := (or #43 #37)
-#49 := (not #44)
-#73 := (iff #49 #72)
-#70 := (iff #44 #69)
-#64 := (iff #37 #63)
-#68 := [rewrite]: #64
-#61 := (iff #43 #52)
-#53 := (not #52)
-#56 := (not #53)
-#59 := (iff #56 #52)
-#60 := [rewrite]: #59
-#57 := (iff #43 #56)
-#54 := (iff #10 #53)
-#55 := [rewrite]: #54
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#71 := [monotonicity #62 #68]: #70
-#74 := [monotonicity #71]: #73
-#50 := (iff #15 #49)
-#47 := (iff #14 #44)
-#40 := (implies #10 #37)
-#45 := (iff #40 #44)
-#46 := [rewrite]: #45
-#41 := (iff #14 #40)
-#38 := (iff #13 #37)
-#35 := (= #12 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#42 := [monotonicity #39]: #41
-#48 := [trans #42 #46]: #47
-#51 := [monotonicity #48]: #50
-#76 := [trans #51 #74]: #75
-#32 := [asserted]: #15
-#77 := [mp #32 #76]: #72
-#79 := [not-or-elim #77]: #67
-#78 := [not-or-elim #77]: #53
-[th-lemma #78 #79]: false
-unsat
-86149959970b3ea28fbf17dcb380883b8a659842 75 0
+58384e364716b53d97a68f064b15e01fd5bd666a 75 0
 #2 := false
 #8 := 0::real
 decl f3 :: real
@@ -47408,68 +47486,7 @@
 #96 := [unit-resolution #95 #92]: #90
 [th-lemma #89 #70 #96]: false
 unsat
-3adfdc99c7629ab533bda7bf39a3bd8e76e15d1b 60 0
-#2 := false
-#9 := 0::real
-decl f3 :: real
-#8 := f3
-#67 := 2/3::real
-#68 := (* 2/3::real f3)
-#65 := (>= #68 0::real)
-#63 := (not #65)
-#54 := (>= f3 0::real)
-#69 := (or #54 #63)
-#72 := (not #69)
-#11 := 3::real
-#12 := (/ f3 3::real)
-#13 := (< f3 #12)
-#10 := (< f3 0::real)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#75 := (iff #15 #72)
-#33 := 1/3::real
-#34 := (* 1/3::real f3)
-#37 := (< f3 #34)
-#43 := (not #10)
-#44 := (or #43 #37)
-#49 := (not #44)
-#73 := (iff #49 #72)
-#70 := (iff #44 #69)
-#64 := (iff #37 #63)
-#66 := [rewrite]: #64
-#61 := (iff #43 #54)
-#52 := (not #54)
-#56 := (not #52)
-#59 := (iff #56 #54)
-#60 := [rewrite]: #59
-#57 := (iff #43 #56)
-#53 := (iff #10 #52)
-#55 := [rewrite]: #53
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#71 := [monotonicity #62 #66]: #70
-#74 := [monotonicity #71]: #73
-#50 := (iff #15 #49)
-#47 := (iff #14 #44)
-#40 := (implies #10 #37)
-#45 := (iff #40 #44)
-#46 := [rewrite]: #45
-#41 := (iff #14 #40)
-#38 := (iff #13 #37)
-#35 := (= #12 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#42 := [monotonicity #39]: #41
-#48 := [trans #42 #46]: #47
-#51 := [monotonicity #48]: #50
-#76 := [trans #51 #74]: #75
-#32 := [asserted]: #15
-#77 := [mp #32 #76]: #72
-#79 := [not-or-elim #77]: #65
-#78 := [not-or-elim #77]: #52
-[th-lemma #78 #79]: false
-unsat
-9239e81a3a819598711273c035c67b58cc850e19 132 0
+c2ead3e3a9ab782b88994fc5cb438d2bcb1433d1 132 0
 #2 := false
 #9 := 0::real
 decl f3 :: real
@@ -47602,7 +47619,7 @@
 #162 := [th-lemma]: #161
 [unit-resolution #162 #160 #143]: false
 unsat
-e3b48db6caf5e610a2e9a0bcae40a85fdd5e39bf 103 0
+40a9a91aa044a83b6a02e422a4541d4ed02beff0 103 0
 #2 := false
 #8 := 0::real
 decl f3 :: real
@@ -47706,65 +47723,7 @@
 #124 := [unit-resolution #123 #120]: #115
 [th-lemma #110 #124]: false
 unsat
-e9188136c9d6e220e6ee3a401a574bb3b56f838f 57 0
-#2 := false
-#36 := 0::real
-decl f4 :: real
-#9 := f4
-decl f3 :: real
-#8 := f3
-#33 := -1::real
-#34 := (* -1::real f4)
-#35 := (+ f3 #34)
-#37 := (<= #35 0::real)
-#40 := (ite #37 f3 f4)
-#48 := (* -1::real #40)
-#49 := (+ f3 #48)
-#47 := (>= #49 0::real)
-#53 := (not #47)
-#10 := (<= f3 f4)
-#11 := (ite #10 f3 f4)
-#12 := (<= #11 f3)
-#13 := (not #12)
-#54 := (iff #13 #53)
-#51 := (iff #12 #47)
-#43 := (<= #40 f3)
-#46 := (iff #43 #47)
-#50 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (= #11 #40)
-#38 := (iff #10 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#52 := [trans #45 #50]: #51
-#55 := [monotonicity #52]: #54
-#30 := [asserted]: #13
-#56 := [mp #30 #55]: #53
-#60 := (= f3 #40)
-#31 := (+ f4 #48)
-#65 := (>= #31 0::real)
-#61 := (= f4 #40)
-#62 := (not #37)
-#66 := [hypothesis]: #62
-#59 := (or #37 #61)
-#57 := [def-axiom]: #59
-#67 := [unit-resolution #57 #66]: #61
-#68 := (not #61)
-#69 := (or #68 #65)
-#70 := [th-lemma]: #69
-#71 := [unit-resolution #70 #67]: #65
-#72 := [th-lemma #56 #66 #71]: false
-#73 := [lemma #72]: #37
-#63 := (or #62 #60)
-#58 := [def-axiom]: #63
-#74 := [unit-resolution #58 #73]: #60
-#75 := (not #60)
-#76 := (or #75 #47)
-#77 := [th-lemma]: #76
-[unit-resolution #77 #74 #56]: false
-unsat
-00baaea05aa472fbe57df430837e148f4a44397f 149 0
+bfc0f0ec5cb8da2a67a07bba2556d02aecd62401 149 0
 #2 := false
 #9 := 0::real
 decl f3 :: real
@@ -47914,169 +47873,7 @@
 #170 := [unit-resolution #169 #155]: #97
 [th-lemma #159 #170 #167]: false
 unsat
-6166959cee3110b0d0634dd50d7cb2cfabb9eb5a 57 0
-#2 := false
-#36 := 0::real
-decl f4 :: real
-#9 := f4
-#33 := -1::real
-#34 := (* -1::real f4)
-decl f3 :: real
-#8 := f3
-#35 := (+ f3 #34)
-#37 := (<= #35 0::real)
-#40 := (ite #37 f3 f4)
-#61 := (= f4 #40)
-#65 := (not #61)
-#47 := (* -1::real #40)
-#48 := (+ f4 #47)
-#46 := (>= #48 0::real)
-#53 := (not #46)
-#10 := (<= f3 f4)
-#11 := (ite #10 f3 f4)
-#12 := (<= #11 f4)
-#13 := (not #12)
-#54 := (iff #13 #53)
-#51 := (iff #12 #46)
-#43 := (<= #40 f4)
-#49 := (iff #43 #46)
-#50 := [rewrite]: #49
-#44 := (iff #12 #43)
-#41 := (= #11 #40)
-#38 := (iff #10 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#52 := [trans #45 #50]: #51
-#55 := [monotonicity #52]: #54
-#30 := [asserted]: #13
-#56 := [mp #30 #55]: #53
-#64 := [hypothesis]: #61
-#66 := (or #65 #46)
-#67 := [th-lemma]: #66
-#68 := [unit-resolution #67 #64 #56]: false
-#69 := [lemma #68]: #65
-#59 := (or #37 #61)
-#57 := [def-axiom]: #59
-#72 := [unit-resolution #57 #69]: #37
-#31 := (+ f3 #47)
-#71 := (>= #31 0::real)
-#60 := (= f3 #40)
-#62 := (not #37)
-#63 := (or #62 #60)
-#58 := [def-axiom]: #63
-#73 := [unit-resolution #58 #72]: #60
-#74 := (not #60)
-#75 := (or #74 #71)
-#76 := [th-lemma]: #75
-#77 := [unit-resolution #76 #73]: #71
-[th-lemma #77 #56 #72]: false
-unsat
-92d942d88d8ad274a6c24a4a1642ec3e151829bd 103 0
-#2 := false
-#45 := 0::real
-decl f5 :: real
-#11 := f5
-decl f4 :: real
-#9 := f4
-#43 := -1::real
-#53 := (* -1::real f5)
-#63 := (+ f4 #53)
-#64 := (<= #63 0::real)
-#67 := (ite #64 f4 f5)
-#75 := (* -1::real #67)
-decl f3 :: real
-#8 := f3
-#76 := (+ f3 #75)
-#74 := (>= #76 0::real)
-#73 := (not #74)
-#54 := (+ f3 #53)
-#52 := (>= #54 0::real)
-#51 := (not #52)
-#47 := (* -1::real f4)
-#48 := (+ f3 #47)
-#46 := (>= #48 0::real)
-#44 := (not #46)
-#57 := (and #44 #51)
-#60 := (not #57)
-#81 := (or #60 #73)
-#84 := (not #81)
-#14 := (<= f4 f5)
-#15 := (ite #14 f4 f5)
-#16 := (< f3 #15)
-#12 := (< f3 f5)
-#10 := (< f3 f4)
-#13 := (and #10 #12)
-#17 := (implies #13 #16)
-#18 := (not #17)
-#87 := (iff #18 #84)
-#36 := (not #13)
-#37 := (or #36 #16)
-#40 := (not #37)
-#85 := (iff #40 #84)
-#82 := (iff #37 #81)
-#79 := (iff #16 #73)
-#70 := (< f3 #67)
-#77 := (iff #70 #73)
-#78 := [rewrite]: #77
-#71 := (iff #16 #70)
-#68 := (= #15 #67)
-#65 := (iff #14 #64)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#80 := [trans #72 #78]: #79
-#61 := (iff #36 #60)
-#58 := (iff #13 #57)
-#55 := (iff #12 #51)
-#56 := [rewrite]: #55
-#49 := (iff #10 #44)
-#50 := [rewrite]: #49
-#59 := [monotonicity #50 #56]: #58
-#62 := [monotonicity #59]: #61
-#83 := [monotonicity #62 #80]: #82
-#86 := [monotonicity #83]: #85
-#41 := (iff #18 #40)
-#38 := (iff #17 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#88 := [trans #42 #86]: #87
-#35 := [asserted]: #18
-#89 := [mp #35 #88]: #84
-#93 := [not-or-elim #89]: #74
-#90 := [not-or-elim #89]: #57
-#92 := [and-elim #90]: #51
-#98 := (+ f5 #75)
-#115 := (<= #98 0::real)
-#104 := (= f5 #67)
-#105 := (not #64)
-#103 := (= f4 #67)
-#110 := (not #103)
-#100 := (+ f4 #75)
-#97 := (<= #100 0::real)
-#107 := (not #97)
-#91 := [and-elim #90]: #44
-#96 := [hypothesis]: #97
-#94 := [th-lemma #96 #91 #93]: false
-#108 := [lemma #94]: #107
-#109 := [hypothesis]: #103
-#111 := (or #110 #97)
-#112 := [th-lemma]: #111
-#113 := [unit-resolution #112 #109 #108]: false
-#114 := [lemma #113]: #110
-#106 := (or #105 #103)
-#101 := [def-axiom]: #106
-#117 := [unit-resolution #101 #114]: #105
-#102 := (or #64 #104)
-#99 := [def-axiom]: #102
-#118 := [unit-resolution #99 #117]: #104
-#119 := (not #104)
-#120 := (or #119 #115)
-#121 := [th-lemma]: #120
-#122 := [unit-resolution #121 #118]: #115
-[th-lemma #122 #92 #93]: false
-unsat
-ebd0660c7140785afcd9de0809a5083ea0dcee04 114 0
+d7c757f846b61825ea5365419ef887a1260a9632 114 0
 #2 := false
 #9 := 0::real
 decl f3 :: real
@@ -48191,7 +47988,227 @@
 #143 := [unit-resolution #142 #139]: #137
 [th-lemma #136 #134 #143]: false
 unsat
-bc553cd04d1e096b5239cc4030cde6a6b1f35726 86 0
+5f87f6aa8068d5144865da469552932c1e3df9c0 57 0
+#2 := false
+#36 := 0::real
+decl f4 :: real
+#9 := f4
+decl f3 :: real
+#8 := f3
+#33 := -1::real
+#34 := (* -1::real f4)
+#35 := (+ f3 #34)
+#37 := (<= #35 0::real)
+#40 := (ite #37 f3 f4)
+#48 := (* -1::real #40)
+#49 := (+ f3 #48)
+#47 := (>= #49 0::real)
+#53 := (not #47)
+#10 := (<= f3 f4)
+#11 := (ite #10 f3 f4)
+#12 := (<= #11 f3)
+#13 := (not #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #47)
+#43 := (<= #40 f3)
+#46 := (iff #43 #47)
+#50 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#52 := [trans #45 #50]: #51
+#55 := [monotonicity #52]: #54
+#30 := [asserted]: #13
+#56 := [mp #30 #55]: #53
+#60 := (= f3 #40)
+#31 := (+ f4 #48)
+#65 := (>= #31 0::real)
+#61 := (= f4 #40)
+#62 := (not #37)
+#66 := [hypothesis]: #62
+#59 := (or #37 #61)
+#57 := [def-axiom]: #59
+#67 := [unit-resolution #57 #66]: #61
+#68 := (not #61)
+#69 := (or #68 #65)
+#70 := [th-lemma]: #69
+#71 := [unit-resolution #70 #67]: #65
+#72 := [th-lemma #56 #66 #71]: false
+#73 := [lemma #72]: #37
+#63 := (or #62 #60)
+#58 := [def-axiom]: #63
+#74 := [unit-resolution #58 #73]: #60
+#75 := (not #60)
+#76 := (or #75 #47)
+#77 := [th-lemma]: #76
+[unit-resolution #77 #74 #56]: false
+unsat
+dca68bd964a7f319e9f3edb4313ff04c05af843a 57 0
+#2 := false
+#36 := 0::real
+decl f4 :: real
+#9 := f4
+#33 := -1::real
+#34 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#35 := (+ f3 #34)
+#37 := (<= #35 0::real)
+#40 := (ite #37 f3 f4)
+#61 := (= f4 #40)
+#65 := (not #61)
+#47 := (* -1::real #40)
+#48 := (+ f4 #47)
+#46 := (>= #48 0::real)
+#53 := (not #46)
+#10 := (<= f3 f4)
+#11 := (ite #10 f3 f4)
+#12 := (<= #11 f4)
+#13 := (not #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #46)
+#43 := (<= #40 f4)
+#49 := (iff #43 #46)
+#50 := [rewrite]: #49
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#52 := [trans #45 #50]: #51
+#55 := [monotonicity #52]: #54
+#30 := [asserted]: #13
+#56 := [mp #30 #55]: #53
+#64 := [hypothesis]: #61
+#66 := (or #65 #46)
+#67 := [th-lemma]: #66
+#68 := [unit-resolution #67 #64 #56]: false
+#69 := [lemma #68]: #65
+#59 := (or #37 #61)
+#57 := [def-axiom]: #59
+#72 := [unit-resolution #57 #69]: #37
+#31 := (+ f3 #47)
+#71 := (>= #31 0::real)
+#60 := (= f3 #40)
+#62 := (not #37)
+#63 := (or #62 #60)
+#58 := [def-axiom]: #63
+#73 := [unit-resolution #58 #72]: #60
+#74 := (not #60)
+#75 := (or #74 #71)
+#76 := [th-lemma]: #75
+#77 := [unit-resolution #76 #73]: #71
+[th-lemma #77 #56 #72]: false
+unsat
+4b5b8ec41ae2a0300d769bcec62fc31388575980 103 0
+#2 := false
+#45 := 0::real
+decl f5 :: real
+#11 := f5
+decl f4 :: real
+#9 := f4
+#43 := -1::real
+#53 := (* -1::real f5)
+#63 := (+ f4 #53)
+#64 := (<= #63 0::real)
+#67 := (ite #64 f4 f5)
+#75 := (* -1::real #67)
+decl f3 :: real
+#8 := f3
+#76 := (+ f3 #75)
+#74 := (>= #76 0::real)
+#73 := (not #74)
+#54 := (+ f3 #53)
+#52 := (>= #54 0::real)
+#51 := (not #52)
+#47 := (* -1::real f4)
+#48 := (+ f3 #47)
+#46 := (>= #48 0::real)
+#44 := (not #46)
+#57 := (and #44 #51)
+#60 := (not #57)
+#81 := (or #60 #73)
+#84 := (not #81)
+#14 := (<= f4 f5)
+#15 := (ite #14 f4 f5)
+#16 := (< f3 #15)
+#12 := (< f3 f5)
+#10 := (< f3 f4)
+#13 := (and #10 #12)
+#17 := (implies #13 #16)
+#18 := (not #17)
+#87 := (iff #18 #84)
+#36 := (not #13)
+#37 := (or #36 #16)
+#40 := (not #37)
+#85 := (iff #40 #84)
+#82 := (iff #37 #81)
+#79 := (iff #16 #73)
+#70 := (< f3 #67)
+#77 := (iff #70 #73)
+#78 := [rewrite]: #77
+#71 := (iff #16 #70)
+#68 := (= #15 #67)
+#65 := (iff #14 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#72 := [monotonicity #69]: #71
+#80 := [trans #72 #78]: #79
+#61 := (iff #36 #60)
+#58 := (iff #13 #57)
+#55 := (iff #12 #51)
+#56 := [rewrite]: #55
+#49 := (iff #10 #44)
+#50 := [rewrite]: #49
+#59 := [monotonicity #50 #56]: #58
+#62 := [monotonicity #59]: #61
+#83 := [monotonicity #62 #80]: #82
+#86 := [monotonicity #83]: #85
+#41 := (iff #18 #40)
+#38 := (iff #17 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#88 := [trans #42 #86]: #87
+#35 := [asserted]: #18
+#89 := [mp #35 #88]: #84
+#93 := [not-or-elim #89]: #74
+#90 := [not-or-elim #89]: #57
+#92 := [and-elim #90]: #51
+#98 := (+ f5 #75)
+#115 := (<= #98 0::real)
+#104 := (= f5 #67)
+#105 := (not #64)
+#103 := (= f4 #67)
+#110 := (not #103)
+#100 := (+ f4 #75)
+#97 := (<= #100 0::real)
+#107 := (not #97)
+#91 := [and-elim #90]: #44
+#96 := [hypothesis]: #97
+#94 := [th-lemma #96 #91 #93]: false
+#108 := [lemma #94]: #107
+#109 := [hypothesis]: #103
+#111 := (or #110 #97)
+#112 := [th-lemma]: #111
+#113 := [unit-resolution #112 #109 #108]: false
+#114 := [lemma #113]: #110
+#106 := (or #105 #103)
+#101 := [def-axiom]: #106
+#117 := [unit-resolution #101 #114]: #105
+#102 := (or #64 #104)
+#99 := [def-axiom]: #102
+#118 := [unit-resolution #99 #117]: #104
+#119 := (not #104)
+#120 := (or #119 #115)
+#121 := [th-lemma]: #120
+#122 := [unit-resolution #121 #118]: #115
+[th-lemma #122 #92 #93]: false
+unsat
+d96d88ad7cc4c8dd063cc281ae5c634c4e609258 86 0
 #2 := false
 decl f3 :: real
 #8 := f3
@@ -48278,7 +48295,7 @@
 #105 := [trans #104 #83]: #51
 [unit-resolution #57 #105]: false
 unsat
-ace00ee2ae241d978310b9741895c318a66ed629 68 0
+f325a5af4fd9621db591f9f98ca0efcfdecb55e1 68 0
 #2 := false
 #8 := 0::real
 decl f3 :: real
@@ -48347,65 +48364,7 @@
 #88 := [trans #87 #84]: #13
 [unit-resolution #71 #88]: false
 unsat
-e81fb3c2654f8ea7635466cd1678fb1937f5d399 57 0
-#2 := false
-#36 := 0::real
-decl f4 :: real
-#9 := f4
-#33 := -1::real
-#34 := (* -1::real f4)
-decl f3 :: real
-#8 := f3
-#35 := (+ f3 #34)
-#37 := (<= #35 0::real)
-#40 := (ite #37 f4 f3)
-#61 := (= f3 #40)
-#65 := (not #61)
-#46 := (* -1::real #40)
-#47 := (+ f3 #46)
-#48 := (<= #47 0::real)
-#53 := (not #48)
-#10 := (<= f3 f4)
-#11 := (ite #10 f4 f3)
-#12 := (<= f3 #11)
-#13 := (not #12)
-#54 := (iff #13 #53)
-#51 := (iff #12 #48)
-#43 := (<= f3 #40)
-#49 := (iff #43 #48)
-#50 := [rewrite]: #49
-#44 := (iff #12 #43)
-#41 := (= #11 #40)
-#38 := (iff #10 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#52 := [trans #45 #50]: #51
-#55 := [monotonicity #52]: #54
-#30 := [asserted]: #13
-#56 := [mp #30 #55]: #53
-#64 := [hypothesis]: #61
-#66 := (or #65 #48)
-#67 := [th-lemma]: #66
-#68 := [unit-resolution #67 #64 #56]: false
-#69 := [lemma #68]: #65
-#59 := (or #37 #61)
-#57 := [def-axiom]: #59
-#72 := [unit-resolution #57 #69]: #37
-#31 := (+ f4 #46)
-#70 := (<= #31 0::real)
-#60 := (= f4 #40)
-#62 := (not #37)
-#63 := (or #62 #60)
-#58 := [def-axiom]: #63
-#73 := [unit-resolution #58 #72]: #60
-#74 := (not #60)
-#75 := (or #74 #70)
-#76 := [th-lemma]: #75
-#77 := [unit-resolution #76 #73]: #70
-[th-lemma #77 #56 #72]: false
-unsat
-3664abc26f14854ad536c42c42a627c251d7213d 124 0
+331ba690a563ad2f5de476217673bc813f21f417 124 0
 #2 := false
 #13 := 0::real
 decl f4 :: real
@@ -48530,7 +48489,65 @@
 #145 := [unit-resolution #117 #144]: #106
 [th-lemma #131 #143 #141 #85 #145]: false
 unsat
-927cad57bf38ad7e837486701c357c7d04ee43f1 57 0
+a89291139825b1c9ddead83f6a1061532a40f3b0 57 0
+#2 := false
+#36 := 0::real
+decl f4 :: real
+#9 := f4
+#33 := -1::real
+#34 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#35 := (+ f3 #34)
+#37 := (<= #35 0::real)
+#40 := (ite #37 f4 f3)
+#61 := (= f3 #40)
+#65 := (not #61)
+#46 := (* -1::real #40)
+#47 := (+ f3 #46)
+#48 := (<= #47 0::real)
+#53 := (not #48)
+#10 := (<= f3 f4)
+#11 := (ite #10 f4 f3)
+#12 := (<= f3 #11)
+#13 := (not #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #48)
+#43 := (<= f3 #40)
+#49 := (iff #43 #48)
+#50 := [rewrite]: #49
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#52 := [trans #45 #50]: #51
+#55 := [monotonicity #52]: #54
+#30 := [asserted]: #13
+#56 := [mp #30 #55]: #53
+#64 := [hypothesis]: #61
+#66 := (or #65 #48)
+#67 := [th-lemma]: #66
+#68 := [unit-resolution #67 #64 #56]: false
+#69 := [lemma #68]: #65
+#59 := (or #37 #61)
+#57 := [def-axiom]: #59
+#72 := [unit-resolution #57 #69]: #37
+#31 := (+ f4 #46)
+#70 := (<= #31 0::real)
+#60 := (= f4 #40)
+#62 := (not #37)
+#63 := (or #62 #60)
+#58 := [def-axiom]: #63
+#73 := [unit-resolution #58 #72]: #60
+#74 := (not #60)
+#75 := (or #74 #70)
+#76 := [th-lemma]: #75
+#77 := [unit-resolution #76 #73]: #70
+[th-lemma #77 #56 #72]: false
+unsat
+d46a1de74f200e03a475d97fb866d2d3152b1193 57 0
 #2 := false
 #35 := 0::real
 decl f4 :: real
@@ -48588,7 +48605,7 @@
 #77 := [th-lemma]: #76
 [unit-resolution #77 #74 #56]: false
 unsat
-d6fff20b692527fbc5f2c570f30f65c6b5299749 103 0
+fdfd1c65d13b95d1e90d21e6ff5483eb614329ae 103 0
 #2 := false
 #45 := 0::real
 decl f3 :: real
@@ -48692,7 +48709,7 @@
 #122 := [unit-resolution #121 #118]: #116
 [th-lemma #122 #91 #93]: false
 unsat
-71c351bb1819ddd2772bbf0065af1d459d5e627d 88 0
+b11e859727aa5426d09865504d29a27662ef9d6b 88 0
 #2 := false
 decl f4 :: real
 #9 := f4
@@ -48781,7 +48798,7 @@
 #109 := [trans #108 #83]: #51
 [unit-resolution #57 #109]: false
 unsat
-0871a2d7a1a8feb4c622a99d4a7c9677b08adbc1 66 0
+a7d7f90833ce73ff2e9504e5320d8ff064fc33be 66 0
 #2 := false
 decl f3 :: real
 #9 := f3
@@ -48848,7 +48865,7 @@
 #86 := [trans #83 #85]: #33
 [unit-resolution #69 #86]: false
 unsat
-f25887cff9f186252a40569f295759f63c1a99d5 228 0
+0acd3595e9fdd38349436bdd7df1dec30c6436d0 228 0
 #2 := false
 #9 := 0::real
 decl f4 :: real
@@ -49077,7 +49094,7 @@
 #250 := [unit-resolution #196 #249]: #190
 [th-lemma #236 #250 #131 #234 #248 #238]: false
 unsat
-dec7d4cc8bde2cdb0d27eb6949a1b3c0be77f81d 18 0
+465ed153c1f53ab2effd01c43a4eaf71a3a89162 18 0
 #2 := false
 decl f3 :: real
 #8 := f3
@@ -49096,7 +49113,7 @@
 #27 := [asserted]: #10
 [mp #27 #38]: false
 unsat
-a4cd1ac41bf4526fafd89a49dac8eaa0aa8148d4 50 0
+2451b746b800ba46ad2e48c92fe36818f39974ff 50 0
 #2 := false
 #44 := 0::real
 decl f4 :: real
@@ -49147,7 +49164,7 @@
 #68 := [not-or-elim #65]: #67
 [th-lemma #68 #66]: false
 unsat
-f04ec87433f814fae44c74b8e4463331c99ee4d7 55 0
+78a85713334031ff95970f2a3d8e75091888b05c 55 0
 #2 := false
 #43 := 0::real
 decl f4 :: real
@@ -49203,7 +49220,7 @@
 #72 := [not-or-elim #71]: #42
 [th-lemma #72 #73]: false
 unsat
-306ff8b8fc070291a5ab7a64ab57d274b4990969 52 0
+8c856f0ed2350b6e51c83cf5111bc988b9ce3e85 52 0
 #2 := false
 #40 := 0::real
 decl f4 :: real
@@ -49256,7 +49273,7 @@
 #77 := [unit-resolution #76 #65]: #53
 [unit-resolution #77 #67]: false
 unsat
-3e97f3eb9f24bfae7990e01bc01c5a21dda19218 15 0
+574a1518d9b4f07bb8d51e1361a34b1b4e25dd09 15 0
 #2 := false
 decl f3 :: real
 #8 := f3
@@ -49272,7 +49289,7 @@
 #28 := [asserted]: #11
 [mp #28 #34]: false
 unsat
-21d10b6d12abf591475883c4d7507c1168d34b59 75 0
+76cf4db9dbe97747ea948c92dee279b708e4416b 75 0
 #2 := false
 #53 := 0::real
 decl f4 :: real
@@ -49348,7 +49365,7 @@
 #89 := [not-or-elim #88]: #54
 [th-lemma #89 #91 #92]: false
 unsat
-a2e7adbf25ec843eff2ffcb678b0be5736d7d96c 80 0
+241a2ba16fba09b5958f7f79e9921ffa83d782f5 80 0
 #2 := false
 #53 := 0::real
 decl f4 :: real
@@ -49429,7 +49446,7 @@
 #94 := [not-or-elim #93]: #54
 [th-lemma #94 #96 #97]: false
 unsat
-1a6c859282e9f174eccf2c9ae56d2a4283272a9d 80 0
+78bc9f516accce754486725963970cacaef14dac 80 0
 #2 := false
 #52 := 0::real
 decl f4 :: real
@@ -49510,7 +49527,7 @@
 #96 := [not-or-elim #93]: #95
 [th-lemma #96 #94 #97]: false
 unsat
-a456c127f26b5322f4e875bd59145cba8570dfda 85 0
+d9bb51a24b46d850002e3a49640516d1328989a0 85 0
 #2 := false
 #52 := 0::real
 decl f4 :: real
@@ -49596,7 +49613,7 @@
 #101 := [not-or-elim #99]: #66
 [th-lemma #101 #100 #102]: false
 unsat
-8a69c429281dbce5e808c8ed794578e8f39d3940 69 0
+878699f96cfb401b8d22b6c58f87ea73d47ef168 69 0
 #2 := false
 #44 := 0::real
 decl f5 :: real
@@ -49666,2385 +49683,2508 @@
 #85 := [and-elim #83]: #53
 [th-lemma #85 #84 #86]: false
 unsat
-857d7ddf089457505996d95feeeae40661d0b2f9 43 0
-#2 := false
-decl f5 :: (-> S2 S2 S3)
-#15 := (:var 0 S2)
-#14 := (:var 1 S2)
-#16 := (f5 #14 #15)
-#561 := (pattern #16)
-decl f4 :: (-> S3 S2)
-#17 := (f4 #16)
-#47 := (= #14 #17)
-#562 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #561) #47)
-#50 := (forall (vars (?v0 S2) (?v1 S2)) #47)
-#565 := (iff #50 #562)
-#563 := (iff #47 #47)
-#564 := [refl]: #563
-#566 := [quant-intro #564]: #565
-#83 := (~ #50 #50)
-#81 := (~ #47 #47)
-#82 := [refl]: #81
-#84 := [nnf-pos #82]: #83
-#18 := (= #17 #14)
-#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
-#51 := (iff #19 #50)
-#48 := (iff #18 #47)
-#49 := [rewrite]: #48
-#52 := [quant-intro #49]: #51
-#46 := [asserted]: #19
-#55 := [mp #46 #52]: #50
-#73 := [mp~ #55 #84]: #50
-#567 := [mp #73 #566]: #562
-decl f6 :: S2
-#9 := f6
-decl f3 :: S2
-#8 := f3
-#10 := (f5 f3 f6)
-#11 := (f4 #10)
-#12 := (= f3 #11)
-#13 := (not #12)
-#45 := [asserted]: #13
-#144 := (not #562)
-#231 := (or #144 #12)
-#145 := [quant-inst]: #231
-[unit-resolution #145 #45 #567]: false
-unsat
-23637ccd7eefaf0528eb9dd850aad7beaa4e7354 43 0
-#2 := false
-decl f5 :: (-> S2 S2 S3)
-#15 := (:var 0 S2)
-#14 := (:var 1 S2)
-#16 := (f5 #14 #15)
-#561 := (pattern #16)
-decl f4 :: (-> S3 S2)
+aa5da88c9c446592ab9de8853ae0d68f6aea51d4 43 0
+#2 := false
+decl f4 :: (-> S2 S3)
+decl f3 :: (-> S3 S3 S2)
+decl f7 :: S3
+#24 := f7
+decl f6 :: S3
+#23 := f6
+#25 := (f3 f6 f7)
+#26 := (f4 #25)
+#27 := (= f6 #26)
+#28 := (not #27)
+#68 := [asserted]: #28
+#15 := (:var 0 S3)
+#14 := (:var 1 S3)
+#16 := (f3 #14 #15)
+#569 := (pattern #16)
 #20 := (f4 #16)
-#54 := (= #15 #20)
-#568 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #561) #54)
-#58 := (forall (vars (?v0 S2) (?v1 S2)) #54)
-#571 := (iff #58 #568)
-#569 := (iff #54 #54)
-#570 := [refl]: #569
-#572 := [quant-intro #570]: #571
-#75 := (~ #58 #58)
-#74 := (~ #54 #54)
-#72 := [refl]: #74
-#76 := [nnf-pos #72]: #75
-#21 := (= #20 #15)
-#22 := (forall (vars (?v0 S2) (?v1 S2)) #21)
-#59 := (iff #22 #58)
-#56 := (iff #21 #54)
-#57 := [rewrite]: #56
-#60 := [quant-intro #57]: #59
-#53 := [asserted]: #22
-#63 := [mp #53 #60]: #58
-#69 := [mp~ #63 #76]: #58
-#573 := [mp #69 #572]: #568
-decl f3 :: S2
-#8 := f3
-decl f6 :: S2
-#9 := f6
-#10 := (f5 f6 f3)
-#11 := (f4 #10)
-#12 := (= f3 #11)
-#13 := (not #12)
-#45 := [asserted]: #13
-#234 := (not #568)
-#235 := (or #234 #12)
-#163 := [quant-inst]: #235
-[unit-resolution #163 #45 #573]: false
-unsat
-9a00f879e91964e9d6bb28cc5e490183e3742924 85 0
-#2 := false
-decl f5 :: S2
-#9 := f5
-decl f4 :: S2
-#8 := f4
-#13 := (= f4 f5)
-decl f6 :: (-> S3 S2)
-decl f3 :: (-> S2 S2 S3)
-#11 := (f3 f5 f4)
-#349 := (f6 #11)
-#548 := (= #349 f5)
-#556 := (= f5 #349)
-#17 := (:var 0 S2)
-#16 := (:var 1 S2)
-#18 := (f3 #16 #17)
-#568 := (pattern #18)
-#19 := (f6 #18)
-#53 := (= #16 #19)
-#569 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #568) #53)
-#57 := (forall (vars (?v0 S2) (?v1 S2)) #53)
-#572 := (iff #57 #569)
-#570 := (iff #53 #53)
-#571 := [refl]: #570
-#573 := [quant-intro #571]: #572
-#90 := (~ #57 #57)
-#88 := (~ #53 #53)
-#89 := [refl]: #88
-#91 := [nnf-pos #89]: #90
-#20 := (= #19 #16)
-#21 := (forall (vars (?v0 S2) (?v1 S2)) #20)
-#58 := (iff #21 #57)
-#55 := (iff #20 #53)
+#61 := (= #14 #20)
+#576 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #569) #61)
+#65 := (forall (vars (?v0 S3) (?v1 S3)) #61)
+#579 := (iff #65 #576)
+#577 := (iff #61 #61)
+#578 := [refl]: #577
+#580 := [quant-intro #578]: #579
+#75 := (~ #65 #65)
+#87 := (~ #61 #61)
+#88 := [refl]: #87
+#76 := [nnf-pos #88]: #75
+#21 := (= #20 #14)
+#22 := (forall (vars (?v0 S3) (?v1 S3)) #21)
+#66 := (iff #22 #65)
+#63 := (iff #21 #61)
+#64 := [rewrite]: #63
+#67 := [quant-intro #64]: #66
+#60 := [asserted]: #22
+#70 := [mp #60 #67]: #65
+#89 := [mp~ #70 #76]: #65
+#581 := [mp #89 #580]: #576
+#237 := (not #576)
+#216 := (or #237 #27)
+#553 := [quant-inst]: #216
+[unit-resolution #553 #581 #68]: false
+unsat
+45a7b53be4820cb5214a3fa1bff6221bc9e3216a 43 0
+#2 := false
+decl f5 :: (-> S2 S3)
+decl f3 :: (-> S3 S3 S2)
+decl f6 :: S3
+#23 := f6
+decl f7 :: S3
+#24 := f7
+#25 := (f3 f7 f6)
+#26 := (f5 #25)
+#27 := (= f6 #26)
+#28 := (not #27)
+#68 := [asserted]: #28
+#15 := (:var 0 S3)
+#14 := (:var 1 S3)
+#16 := (f3 #14 #15)
+#569 := (pattern #16)
+#17 := (f5 #16)
+#53 := (= #15 #17)
+#570 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #569) #53)
+#57 := (forall (vars (?v0 S3) (?v1 S3)) #53)
+#573 := (iff #57 #570)
+#571 := (iff #53 #53)
+#572 := [refl]: #571
+#574 := [quant-intro #572]: #573
+#73 := (~ #57 #57)
+#69 := (~ #53 #53)
+#85 := [refl]: #69
+#74 := [nnf-pos #85]: #73
+#18 := (= #17 #15)
+#19 := (forall (vars (?v0 S3) (?v1 S3)) #18)
+#58 := (iff #19 #57)
+#55 := (iff #18 #53)
 #56 := [rewrite]: #55
 #59 := [quant-intro #56]: #58
-#52 := [asserted]: #21
+#52 := [asserted]: #19
 #62 := [mp #52 #59]: #57
-#80 := [mp~ #62 #91]: #57
-#574 := [mp #80 #573]: #569
-#560 := (not #569)
-#566 := (or #560 #556)
-#561 := [quant-inst]: #566
-#207 := [unit-resolution #561 #574]: #556
-#549 := [symm #207]: #548
-#544 := (= f4 #349)
-#10 := (f3 f4 f5)
-#243 := (f6 #10)
+#86 := [mp~ #62 #74]: #57
+#575 := [mp #86 #574]: #570
+#235 := (not #570)
+#163 := (or #235 #27)
+#236 := [quant-inst]: #163
+[unit-resolution #236 #575 #68]: false
+unsat
+b6bd8a29d464a3e859a0a8adcae6058075d54503 87 0
+#2 := false
+decl f7 :: S3
+#24 := f7
+decl f6 :: S3
+#23 := f6
+#28 := (= f6 f7)
+decl f5 :: (-> S2 S3)
+decl f3 :: (-> S3 S3 S2)
+#25 := (f3 f6 f7)
+#243 := (f5 #25)
+#186 := (= #243 f7)
+#240 := (= f7 #243)
+#15 := (:var 0 S3)
+#14 := (:var 1 S3)
+#16 := (f3 #14 #15)
+#576 := (pattern #16)
+#17 := (f5 #16)
+#55 := (= #15 #17)
+#577 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #576) #55)
+#59 := (forall (vars (?v0 S3) (?v1 S3)) #55)
+#580 := (iff #59 #577)
+#578 := (iff #55 #55)
+#579 := [refl]: #578
+#581 := [quant-intro #579]: #580
+#80 := (~ #59 #59)
+#76 := (~ #55 #55)
+#92 := [refl]: #76
+#81 := [nnf-pos #92]: #80
+#18 := (= #17 #15)
+#19 := (forall (vars (?v0 S3) (?v1 S3)) #18)
+#60 := (iff #19 #59)
+#57 := (iff #18 #55)
+#58 := [rewrite]: #57
+#61 := [quant-intro #58]: #60
+#54 := [asserted]: #19
+#64 := [mp #54 #61]: #59
+#93 := [mp~ #64 #81]: #59
+#582 := [mp #93 #581]: #577
+#560 := (not #577)
+#562 := (or #560 #240)
+#217 := [quant-inst]: #562
+#545 := [unit-resolution #217 #582]: #240
+#551 := [symm #545]: #186
+#553 := (= f6 #243)
+#26 := (f3 f7 f6)
+#349 := (f5 #26)
+#544 := (= #349 #243)
 #546 := (= #243 #349)
-#12 := (= #10 #11)
-#559 := (= #11 #10)
-#48 := (not #12)
-#567 := [hypothesis]: #48
-#238 := (or #13 #12)
-#49 := (iff #13 #48)
-#14 := (iff #12 #13)
-#15 := (not #14)
-#50 := (iff #15 #49)
-#51 := [rewrite]: #50
-#47 := [asserted]: #15
-#54 := [mp #47 #51]: #49
-#150 := (not #49)
-#237 := (or #13 #12 #150)
+#27 := (= #25 #26)
+#559 := (= #26 #25)
+#71 := (not #27)
+#567 := [hypothesis]: #71
+#238 := (or #28 #27)
+#73 := (iff #28 #71)
+#29 := (iff #27 #28)
+#30 := (not #29)
+#74 := (iff #30 #73)
+#75 := [rewrite]: #74
+#70 := [asserted]: #30
+#78 := [mp #70 #75]: #73
+#150 := (not #73)
+#237 := (or #28 #27 #150)
 #151 := [def-axiom]: #237
-#152 := [unit-resolution #151 #54]: #238
-#557 := [unit-resolution #152 #567]: #13
-#558 := (= f5 f4)
+#152 := [unit-resolution #151 #78]: #238
+#557 := [unit-resolution #152 #567]: #28
+#558 := (= f7 f6)
 #216 := [symm #557]: #558
 #200 := [monotonicity #216 #557]: #559
-#543 := [symm #200]: #12
+#543 := [symm #200]: #27
 #204 := [unit-resolution #567 #543]: false
-#205 := [lemma #204]: #12
+#205 := [lemma #204]: #27
 #547 := [monotonicity #205]: #546
-#240 := (= f4 #243)
-#562 := (or #560 #240)
-#217 := [quant-inst]: #562
-#545 := [unit-resolution #217 #574]: #240
-#550 := [trans #545 #547]: #544
-#186 := [trans #550 #549]: #13
-#239 := (not #13)
-#242 := (or #239 #48)
-#230 := (or #239 #48 #150)
+#550 := [symm #547]: #544
+#556 := (= f6 #349)
+#566 := (or #560 #556)
+#561 := [quant-inst]: #566
+#207 := [unit-resolution #561 #582]: #556
+#191 := [trans #207 #550]: #553
+#192 := [trans #191 #551]: #28
+#239 := (not #28)
+#242 := (or #239 #71)
+#230 := (or #239 #71 #150)
 #241 := [def-axiom]: #230
-#170 := [unit-resolution #241 #54]: #242
+#170 := [unit-resolution #241 #78]: #242
 #206 := [unit-resolution #170 #205]: #239
-[unit-resolution #206 #186]: false
-unsat
-8760f419b4705bba51bf2708287a0ef4a7175b9e 155 0
-#2 := false
-decl f7 :: S2
-#12 := f7
-decl f5 :: S2
-#9 := f5
-#16 := (= f5 f7)
-#100 := (not #16)
-decl f6 :: S2
-#11 := f6
-decl f4 :: S2
-#8 := f4
-#15 := (= f4 f6)
-#99 := (not #15)
-#90 := (or #99 #100)
-decl f3 :: (-> S2 S2 S3)
-#13 := (f3 f6 f7)
-#10 := (f3 f4 f5)
-#14 := (= #10 #13)
-#91 := (not #90)
-#240 := [hypothesis]: #91
-#175 := (or #90 #16)
+[unit-resolution #206 #192]: false
+unsat
+c0df0056215193fa946730fc70347a03d1a2a1e5 155 0
+#2 := false
+decl f9 :: S3
+#27 := f9
+decl f7 :: S3
+#24 := f7
+#31 := (= f7 f9)
+#102 := (not #31)
+decl f8 :: S3
+#26 := f8
+decl f6 :: S3
+#23 := f6
+#30 := (= f6 f8)
+#101 := (not #30)
+#88 := (or #101 #102)
+decl f3 :: (-> S3 S3 S2)
+#28 := (f3 f8 f9)
+#25 := (f3 f6 f7)
+#29 := (= #25 #28)
+#89 := (not #88)
+#240 := [hypothesis]: #89
+#175 := (or #88 #31)
 #262 := [def-axiom]: #175
-#228 := [unit-resolution #262 #240]: #16
-#174 := (or #90 #15)
+#228 := [unit-resolution #262 #240]: #31
+#174 := (or #88 #30)
 #261 := [def-axiom]: #174
-#229 := [unit-resolution #261 #240]: #15
-#230 := [monotonicity #229 #228]: #14
-#52 := (not #14)
-#247 := (or #52 #90)
-#111 := (iff #14 #90)
-#17 := (and #15 #16)
-#53 := (iff #17 #52)
-#114 := (iff #53 #111)
-#106 := (iff #90 #14)
+#229 := [unit-resolution #261 #240]: #30
+#230 := [monotonicity #229 #228]: #29
+#75 := (not #29)
+#247 := (or #75 #88)
+#111 := (iff #29 #88)
+#32 := (and #30 #31)
+#77 := (iff #32 #75)
+#114 := (iff #77 #111)
+#106 := (iff #88 #29)
 #112 := (iff #106 #111)
 #113 := [rewrite]: #112
-#109 := (iff #53 #106)
-#103 := (iff #91 #52)
+#109 := (iff #77 #106)
+#103 := (iff #89 #75)
 #107 := (iff #103 #106)
 #108 := [rewrite]: #107
-#104 := (iff #53 #103)
-#101 := (iff #17 #91)
-#102 := [rewrite]: #101
-#105 := [monotonicity #102]: #104
+#104 := (iff #77 #103)
+#90 := (iff #32 #89)
+#91 := [rewrite]: #90
+#105 := [monotonicity #91]: #104
 #110 := [trans #105 #108]: #109
 #115 := [trans #110 #113]: #114
-#18 := (iff #14 #17)
-#19 := (not #18)
-#54 := (iff #19 #53)
-#55 := [rewrite]: #54
-#51 := [asserted]: #19
-#58 := [mp #51 #55]: #53
-#116 := [mp #58 #115]: #111
+#33 := (iff #29 #32)
+#34 := (not #33)
+#78 := (iff #34 #77)
+#79 := [rewrite]: #78
+#74 := [asserted]: #34
+#82 := [mp #74 #79]: #77
+#116 := [mp #82 #115]: #111
 #254 := (not #111)
-#264 := (or #52 #90 #254)
+#264 := (or #75 #88 #254)
 #268 := [def-axiom]: #264
 #584 := [unit-resolution #268 #116]: #247
-#583 := [unit-resolution #584 #240]: #52
+#583 := [unit-resolution #584 #240]: #75
 #231 := [unit-resolution #583 #230]: false
-#569 := [lemma #231]: #90
-decl f8 :: (-> S3 S2)
-#588 := (f8 #13)
-#574 := (= #588 f6)
-#589 := (= f6 #588)
-#21 := (:var 0 S2)
-#20 := (:var 1 S2)
-#22 := (f3 #20 #21)
-#592 := (pattern #22)
-#23 := (f8 #22)
-#57 := (= #20 #23)
-#593 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #592) #57)
-#61 := (forall (vars (?v0 S2) (?v1 S2)) #57)
-#596 := (iff #61 #593)
-#594 := (iff #57 #57)
-#595 := [refl]: #594
-#597 := [quant-intro #595]: #596
-#94 := (~ #61 #61)
-#92 := (~ #57 #57)
-#93 := [refl]: #92
-#95 := [nnf-pos #93]: #94
-#24 := (= #23 #20)
-#25 := (forall (vars (?v0 S2) (?v1 S2)) #24)
-#62 := (iff #25 #61)
-#59 := (iff #24 #57)
-#60 := [rewrite]: #59
-#63 := [quant-intro #60]: #62
-#56 := [asserted]: #25
-#66 := [mp #56 #63]: #61
-#84 := [mp~ #66 #95]: #61
-#598 := [mp #84 #597]: #593
-#252 := (not #593)
+#569 := [lemma #231]: #88
+decl f5 :: (-> S2 S3)
+#588 := (f5 #28)
+#574 := (= #588 f9)
+#589 := (= f9 #588)
+#15 := (:var 0 S3)
+#14 := (:var 1 S3)
+#16 := (f3 #14 #15)
+#600 := (pattern #16)
+#17 := (f5 #16)
+#59 := (= #15 #17)
+#601 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #600) #59)
+#63 := (forall (vars (?v0 S3) (?v1 S3)) #59)
+#604 := (iff #63 #601)
+#602 := (iff #59 #59)
+#603 := [refl]: #602
+#605 := [quant-intro #603]: #604
+#84 := (~ #63 #63)
+#80 := (~ #59 #59)
+#96 := [refl]: #80
+#85 := [nnf-pos #96]: #84
+#18 := (= #17 #15)
+#19 := (forall (vars (?v0 S3) (?v1 S3)) #18)
+#64 := (iff #19 #63)
+#61 := (iff #18 #59)
+#62 := [rewrite]: #61
+#65 := [quant-intro #62]: #64
+#58 := [asserted]: #19
+#68 := [mp #58 #65]: #63
+#97 := [mp~ #68 #85]: #63
+#606 := [mp #97 #605]: #601
+#252 := (not #601)
 #244 := (or #252 #589)
 #582 := [quant-inst]: #244
-#570 := [unit-resolution #582 #598]: #589
+#570 := [unit-resolution #582 #606]: #589
 #210 := [symm #570]: #574
-#575 := (= f4 #588)
-#586 := (f8 #10)
+#575 := (= f7 #588)
+#586 := (f5 #25)
 #573 := (= #586 #588)
-#194 := (or #14 #91)
-#265 := (or #14 #91 #254)
+#194 := (or #29 #89)
+#265 := (or #29 #89 #254)
 #266 := [def-axiom]: #265
 #267 := [unit-resolution #266 #116]: #194
-#571 := [unit-resolution #267 #569]: #14
+#571 := [unit-resolution #267 #569]: #29
 #568 := [monotonicity #571]: #573
-#241 := (= f4 #586)
+#241 := (= f7 #586)
 #253 := (or #252 #241)
 #587 := [quant-inst]: #253
-#572 := [unit-resolution #587 #598]: #241
+#572 := [unit-resolution #587 #606]: #241
 #577 := [trans #572 #568]: #575
-#215 := [trans #577 #210]: #15
-decl f9 :: (-> S3 S2)
-#581 := (f9 #13)
-#565 := (= #581 f7)
-#239 := (= f7 #581)
-#26 := (f9 #22)
-#65 := (= #21 #26)
-#599 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #592) #65)
-#69 := (forall (vars (?v0 S2) (?v1 S2)) #65)
-#602 := (iff #69 #599)
-#600 := (iff #65 #65)
-#601 := [refl]: #600
-#603 := [quant-intro #601]: #602
-#86 := (~ #69 #69)
-#85 := (~ #65 #65)
-#83 := [refl]: #85
-#87 := [nnf-pos #83]: #86
-#27 := (= #26 #21)
-#28 := (forall (vars (?v0 S2) (?v1 S2)) #27)
-#70 := (iff #28 #69)
-#67 := (iff #27 #65)
-#68 := [rewrite]: #67
-#71 := [quant-intro #68]: #70
-#64 := [asserted]: #28
-#74 := [mp #64 #71]: #69
-#80 := [mp~ #74 #87]: #69
-#604 := [mp #80 #603]: #599
-#590 := (not #599)
+#215 := [trans #577 #210]: #31
+decl f4 :: (-> S2 S3)
+#581 := (f4 #28)
+#565 := (= #581 f8)
+#239 := (= f8 #581)
+#20 := (f4 #16)
+#67 := (= #14 #20)
+#607 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #600) #67)
+#71 := (forall (vars (?v0 S3) (?v1 S3)) #67)
+#610 := (iff #71 #607)
+#608 := (iff #67 #67)
+#609 := [refl]: #608
+#611 := [quant-intro #609]: #610
+#86 := (~ #71 #71)
+#98 := (~ #67 #67)
+#99 := [refl]: #98
+#87 := [nnf-pos #99]: #86
+#21 := (= #20 #14)
+#22 := (forall (vars (?v0 S3) (?v1 S3)) #21)
+#72 := (iff #22 #71)
+#69 := (iff #21 #67)
+#70 := [rewrite]: #69
+#73 := [quant-intro #70]: #72
+#66 := [asserted]: #22
+#76 := [mp #66 #73]: #71
+#100 := [mp~ #76 #87]: #71
+#612 := [mp #100 #611]: #607
+#590 := (not #607)
 #224 := (or #590 #239)
 #567 := [quant-inst]: #224
-#216 := [unit-resolution #567 #604]: #239
+#216 := [unit-resolution #567 #612]: #239
 #566 := [symm #216]: #565
-#272 := (= f5 #581)
-#373 := (f9 #10)
+#272 := (= f6 #581)
+#373 := (f4 #25)
 #576 := (= #373 #581)
 #579 := [monotonicity #571]: #576
-#580 := (= f5 #373)
+#580 := (= f6 #373)
 #585 := (or #590 #580)
 #591 := [quant-inst]: #585
-#578 := [unit-resolution #591 #604]: #580
+#578 := [unit-resolution #591 #612]: #580
 #288 := [trans #578 #579]: #272
-#289 := [trans #288 #566]: #16
-#176 := (or #91 #99 #100)
+#289 := [trans #288 #566]: #30
+#176 := (or #89 #101 #102)
 #263 := [def-axiom]: #176
 [unit-resolution #263 #289 #215 #569]: false
 unsat
-9b011b5f1ccfc0c5952d2a8ce428ee6a14bd5a78 91 0
-#2 := false
+97f7817764929810a38ae176da1c6898cd7e5357 91 0
+#2 := false
+decl f12 :: S3
+#42 := f12
 decl f9 :: S3
-#14 := f9
-decl f5 :: S3
-#8 := f5
-#21 := (= f5 f9)
-decl f3 :: (-> S2 S3)
-decl f4 :: (-> S3 S4 S2)
-decl f6 :: (-> S3 S5 S4)
-decl f11 :: S5
-#16 := f11
+#36 := f9
+#49 := (= f9 f12)
+decl f7 :: (-> S5 S3)
+decl f6 :: (-> S3 S2 S5)
+decl f3 :: (-> S3 S4 S2)
+decl f14 :: S4
+#44 := f14
+decl f13 :: S3
+#43 := f13
+#45 := (f3 f13 f14)
+#46 := (f6 f12 #45)
+#47 := (f7 #46)
+decl f11 :: S4
+#38 := f11
 decl f10 :: S3
-#15 := f10
-#17 := (f6 f10 f11)
-#18 := (f4 f9 #17)
-#19 := (f3 #18)
-decl f8 :: S5
-#10 := f8
-decl f7 :: S3
-#9 := f7
-#11 := (f6 f7 f8)
-#12 := (f4 f5 #11)
-#13 := (f3 #12)
-#20 := (= #13 #19)
-#22 := (iff #20 #21)
-#324 := (iff #21 #20)
-#603 := (= f9 #19)
-#30 := (:var 0 S4)
-#24 := (:var 1 S3)
-#31 := (f4 #24 #30)
-#635 := (pattern #31)
-#32 := (f3 #31)
-#82 := (= #24 #32)
-#636 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #635) #82)
-#86 := (forall (vars (?v0 S3) (?v1 S4)) #82)
-#639 := (iff #86 #636)
-#637 := (iff #82 #82)
-#638 := [refl]: #637
-#640 := [quant-intro #638]: #639
-#127 := (~ #86 #86)
-#126 := (~ #82 #82)
-#124 := [refl]: #126
-#128 := [nnf-pos #124]: #127
-#33 := (= #32 #24)
-#34 := (forall (vars (?v0 S3) (?v1 S4)) #33)
-#87 := (iff #34 #86)
-#84 := (iff #33 #82)
-#85 := [rewrite]: #84
-#88 := [quant-intro #85]: #87
-#81 := [asserted]: #34
-#91 := [mp #81 #88]: #86
-#121 := [mp~ #91 #128]: #86
-#641 := [mp #121 #640]: #636
-#276 := (not #636)
-#606 := (or #276 #603)
-#607 := [quant-inst]: #606
-#602 := [unit-resolution #607 #641]: #603
-#627 := (= f5 #13)
-#619 := (or #276 #627)
-#260 := [quant-inst]: #619
-#308 := [unit-resolution #260 #641]: #627
+#37 := f10
+#39 := (f3 f10 f11)
+#40 := (f6 f9 #39)
+#41 := (f7 #40)
+#48 := (= #41 #47)
+#50 := (iff #48 #49)
+#324 := (iff #49 #48)
+#610 := (= f12 #47)
+#8 := (:var 0 S2)
+#20 := (:var 1 S3)
+#26 := (f6 #20 #8)
+#651 := (pattern #26)
+#33 := (f7 #26)
+#108 := (= #20 #33)
+#664 := (forall (vars (?v0 S3) (?v1 S2)) (:pat #651) #108)
+#112 := (forall (vars (?v0 S3) (?v1 S2)) #108)
+#667 := (iff #112 #664)
+#665 := (iff #108 #108)
+#666 := [refl]: #665
+#668 := [quant-intro #666]: #667
+#133 := (~ #112 #112)
+#154 := (~ #108 #108)
+#155 := [refl]: #154
+#134 := [nnf-pos #155]: #133
+#34 := (= #33 #20)
+#35 := (forall (vars (?v0 S3) (?v1 S2)) #34)
+#113 := (iff #35 #112)
+#110 := (iff #34 #108)
+#111 := [rewrite]: #110
+#114 := [quant-intro #111]: #113
+#107 := [asserted]: #35
+#117 := [mp #107 #114]: #112
+#156 := [mp~ #117 #134]: #112
+#669 := [mp #156 #668]: #664
+#246 := (not #664)
+#615 := (or #246 #610)
+#601 := [quant-inst]: #615
+#602 := [unit-resolution #601 #669]: #610
+#267 := (= f9 #41)
+#611 := (or #246 #267)
+#613 := [quant-inst]: #611
+#308 := [unit-resolution #613 #669]: #267
 #325 := [monotonicity #308 #602]: #324
-#326 := [symm #325]: #22
-#299 := (not #21)
-#69 := (not #20)
-#312 := (iff #69 #299)
+#326 := [symm #325]: #50
+#299 := (not #49)
+#116 := (not #48)
+#312 := (iff #116 #299)
 #327 := [monotonicity #326]: #312
-#614 := [hypothesis]: #69
-#218 := [mp #614 #327]: #299
-#298 := (or #21 #20)
-#70 := (iff #21 #69)
-#23 := (not #22)
-#71 := (iff #23 #70)
-#72 := [rewrite]: #71
-#68 := [asserted]: #23
-#75 := [mp #68 #72]: #70
-#210 := (not #70)
-#297 := (or #21 #20 #210)
+#251 := [hypothesis]: #116
+#218 := [mp #251 #327]: #299
+#298 := (or #49 #48)
+#118 := (iff #49 #116)
+#51 := (not #50)
+#119 := (iff #51 #118)
+#120 := [rewrite]: #119
+#115 := [asserted]: #51
+#123 := [mp #115 #120]: #118
+#210 := (not #118)
+#297 := (or #49 #48 #210)
 #211 := [def-axiom]: #297
-#212 := [unit-resolution #211 #75]: #298
-#612 := [unit-resolution #212 #614]: #21
+#212 := [unit-resolution #211 #123]: #298
+#612 := [unit-resolution #212 #251]: #49
 #597 := [unit-resolution #612 #218]: false
-#598 := [lemma #597]: #20
-#321 := [mp #598 #326]: #21
-#302 := (or #299 #69)
-#290 := (or #299 #69 #210)
+#598 := [lemma #597]: #48
+#321 := [mp #598 #326]: #49
+#302 := (or #299 #116)
+#290 := (or #299 #116 #210)
 #301 := [def-axiom]: #290
-#230 := [unit-resolution #301 #75]: #302
+#230 := [unit-resolution #301 #123]: #302
 #320 := [unit-resolution #230 #598]: #299
 [unit-resolution #320 #321]: false
 unsat
-15e3058b649be6d5463c784c16fd64eaa28f5f73 50 0
-#2 := false
-decl f3 :: (-> S2 S3 S4 S3 S4)
-#15 := (:var 1 S3)
-#16 := (:var 0 S4)
-#14 := (:var 2 S2)
-#17 := (f3 #14 #15 #16 #15)
-#571 := (pattern #17)
-#54 := (= #16 #17)
-#572 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #571) #54)
-#58 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #54)
-#575 := (iff #58 #572)
-#573 := (iff #54 #54)
-#574 := [refl]: #573
-#576 := [quant-intro #574]: #575
-#87 := (~ #58 #58)
-#85 := (~ #54 #54)
-#86 := [refl]: #85
-#88 := [nnf-pos #86]: #87
-#18 := (= #17 #16)
-#19 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #18)
-#59 := (iff #19 #58)
-#56 := (iff #18 #54)
-#57 := [rewrite]: #56
-#60 := [quant-intro #57]: #59
-#53 := [asserted]: #19
-#63 := [mp #53 #60]: #58
-#79 := [mp~ #63 #88]: #58
-#577 := [mp #79 #576]: #572
-decl f5 :: S3
-#9 := f5
-decl f6 :: S4
-#10 := f6
-decl f4 :: S2
-#8 := f4
-#11 := (f3 f4 f5 f6 f5)
-#47 := (= f6 #11)
-#50 := (not #47)
-#12 := (= #11 f6)
-#13 := (not #12)
-#51 := (iff #13 #50)
-#48 := (iff #12 #47)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#46 := [asserted]: #13
-#55 := [mp #46 #52]: #50
-#154 := (not #572)
-#241 := (or #154 #47)
-#155 := [quant-inst]: #241
-[unit-resolution #155 #55 #577]: false
-unsat
-a158237dab9b8e1ca3aee50fa8555cfce1bec7cc 210 0
-#2 := false
-decl f11 :: S5
-#16 := f11
-decl f8 :: S5
-#10 := f8
-#22 := (= f8 f11)
-#158 := (not #22)
-decl f10 :: S4
-#15 := f10
-decl f7 :: S4
-#9 := f7
-#21 := (= f7 f10)
-#157 := (not #21)
-#139 := (or #157 #158)
-decl f3 :: (-> S2 S3)
-decl f4 :: (-> S4 S3 S2)
-decl f6 :: (-> S4 S5 S3)
-#17 := (f6 f10 f11)
-decl f9 :: S4
-#14 := f9
-#18 := (f4 f9 #17)
-#19 := (f3 #18)
-#11 := (f6 f7 f8)
-decl f5 :: S4
-#8 := f5
-#12 := (f4 f5 #11)
-#13 := (f3 #12)
-#20 := (= #13 #19)
-#626 := (= #17 #19)
-#32 := (:var 0 S3)
-#26 := (:var 1 S4)
-#33 := (f4 #26 #32)
-#657 := (pattern #33)
-#40 := (f3 #33)
-#100 := (= #32 #40)
-#670 := (forall (vars (?v0 S4) (?v1 S3)) (:pat #657) #100)
-#104 := (forall (vars (?v0 S4) (?v1 S3)) #100)
-#673 := (iff #104 #670)
-#671 := (iff #100 #100)
-#672 := [refl]: #671
-#674 := [quant-intro #672]: #673
-#133 := (~ #104 #104)
-#148 := (~ #100 #100)
-#149 := [refl]: #148
-#134 := [nnf-pos #149]: #133
-#41 := (= #40 #32)
-#42 := (forall (vars (?v0 S4) (?v1 S3)) #41)
-#105 := (iff #42 #104)
-#102 := (iff #41 #100)
-#103 := [rewrite]: #102
-#106 := [quant-intro #103]: #105
-#99 := [asserted]: #42
-#109 := [mp #99 #106]: #104
-#150 := [mp~ #109 #134]: #104
-#675 := [mp #150 #674]: #670
-#629 := (not #670)
-#273 := (or #629 #626)
-#274 := [quant-inst]: #273
-#334 := [unit-resolution #274 #675]: #626
-#621 := (= #13 #17)
-#343 := (= #11 #17)
-#140 := (not #139)
-#330 := [hypothesis]: #140
-#233 := (or #139 #22)
+c86533de316dc270239d607a777173f56a515c3f 210 0
+#2 := false
+decl f14 :: S4
+#44 := f14
+decl f11 :: S4
+#38 := f11
+#50 := (= f11 f14)
+#160 := (not #50)
+decl f13 :: S3
+#43 := f13
+decl f10 :: S3
+#37 := f10
+#49 := (= f10 f13)
+#159 := (not #49)
+#137 := (or #159 #160)
+decl f8 :: (-> S5 S2)
+decl f6 :: (-> S3 S2 S5)
+decl f3 :: (-> S3 S4 S2)
+#45 := (f3 f13 f14)
+decl f12 :: S3
+#42 := f12
+#46 := (f6 f12 #45)
+#47 := (f8 #46)
+#39 := (f3 f10 f11)
+decl f9 :: S3
+#36 := f9
+#40 := (f6 f9 #39)
+#41 := (f8 #40)
+#48 := (= #41 #47)
+#268 := (= #45 #47)
+#8 := (:var 0 S2)
+#20 := (:var 1 S3)
+#26 := (f6 #20 #8)
+#673 := (pattern #26)
+#27 := (f8 #26)
+#94 := (= #8 #27)
+#674 := (forall (vars (?v0 S3) (?v1 S2)) (:pat #673) #94)
+#98 := (forall (vars (?v0 S3) (?v1 S2)) #94)
+#677 := (iff #98 #674)
+#675 := (iff #94 #94)
+#676 := [refl]: #675
+#678 := [quant-intro #676]: #677
+#131 := (~ #98 #98)
+#150 := (~ #94 #94)
+#151 := [refl]: #150
+#132 := [nnf-pos #151]: #131
+#28 := (= #27 #8)
+#29 := (forall (vars (?v0 S3) (?v1 S2)) #28)
+#99 := (iff #29 #98)
+#96 := (iff #28 #94)
+#97 := [rewrite]: #96
+#100 := [quant-intro #97]: #99
+#93 := [asserted]: #29
+#103 := [mp #93 #100]: #98
+#152 := [mp~ #103 #132]: #98
+#679 := [mp #152 #678]: #674
+#633 := (not #674)
+#624 := (or #633 #268)
+#330 := [quant-inst]: #624
+#334 := [unit-resolution #330 #679]: #268
+#621 := (= #41 #45)
+#343 := (= #39 #45)
+#138 := (not #137)
+#623 := [hypothesis]: #138
+#233 := (or #137 #50)
 #320 := [def-axiom]: #233
-#349 := [unit-resolution #320 #330]: #22
-#232 := (or #139 #21)
+#349 := [unit-resolution #320 #623]: #50
+#232 := (or #137 #49)
 #319 := [def-axiom]: #232
-#240 := [unit-resolution #319 #330]: #21
+#240 := [unit-resolution #319 #623]: #49
 #617 := [monotonicity #240 #349]: #343
-#620 := (= #13 #11)
-#286 := (= #11 #13)
-#630 := (or #629 #286)
-#631 := [quant-inst]: #630
-#619 := [unit-resolution #631 #675]: #286
+#620 := (= #41 #39)
+#630 := (= #39 #41)
+#635 := (or #633 #630)
+#273 := [quant-inst]: #635
+#619 := [unit-resolution #273 #679]: #630
 #342 := [symm #619]: #620
 #618 := [trans #342 #617]: #621
-#622 := [trans #618 #334]: #20
-#71 := (not #20)
-#305 := (or #71 #139)
-#169 := (iff #20 #139)
-#23 := (and #21 #22)
-#72 := (iff #23 #71)
-#172 := (iff #72 #169)
-#164 := (iff #139 #20)
+#622 := [trans #618 #334]: #48
+#118 := (not #48)
+#305 := (or #118 #137)
+#169 := (iff #48 #137)
+#51 := (and #49 #50)
+#120 := (iff #51 #118)
+#172 := (iff #120 #169)
+#164 := (iff #137 #48)
 #170 := (iff #164 #169)
 #171 := [rewrite]: #170
-#167 := (iff #72 #164)
-#161 := (iff #140 #71)
+#167 := (iff #120 #164)
+#161 := (iff #138 #118)
 #165 := (iff #161 #164)
 #166 := [rewrite]: #165
-#162 := (iff #72 #161)
-#159 := (iff #23 #140)
-#160 := [rewrite]: #159
-#163 := [monotonicity #160]: #162
+#162 := (iff #120 #161)
+#139 := (iff #51 #138)
+#140 := [rewrite]: #139
+#163 := [monotonicity #140]: #162
 #168 := [trans #163 #166]: #167
 #173 := [trans #168 #171]: #172
-#24 := (iff #20 #23)
-#25 := (not #24)
-#73 := (iff #25 #72)
-#74 := [rewrite]: #73
-#70 := [asserted]: #25
-#77 := [mp #70 #74]: #72
-#174 := [mp #77 #173]: #169
+#52 := (iff #48 #51)
+#53 := (not #52)
+#121 := (iff #53 #120)
+#122 := [rewrite]: #121
+#117 := [asserted]: #53
+#125 := [mp #117 #122]: #120
+#174 := [mp #125 #173]: #169
 #312 := (not #169)
-#322 := (or #71 #139 #312)
+#322 := (or #118 #137 #312)
 #326 := [def-axiom]: #322
 #642 := [unit-resolution #326 #174]: #305
-#346 := [unit-resolution #642 #330]: #71
+#346 := [unit-resolution #642 #623]: #118
 #331 := [unit-resolution #346 #622]: false
-#332 := [lemma #331]: #139
-decl f12 :: (-> S3 S4)
-#646 := (f12 #17)
-#606 := (= #646 f10)
-#647 := (= f10 #646)
-#27 := (:var 0 S5)
-#28 := (f6 #26 #27)
-#650 := (pattern #28)
-#29 := (f12 #28)
-#76 := (= #26 #29)
-#651 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #650) #76)
-#80 := (forall (vars (?v0 S4) (?v1 S5)) #76)
-#654 := (iff #80 #651)
-#652 := (iff #76 #76)
-#653 := [refl]: #652
-#655 := [quant-intro #653]: #654
-#143 := (~ #80 #80)
-#141 := (~ #76 #76)
-#142 := [refl]: #141
-#144 := [nnf-pos #142]: #143
-#30 := (= #29 #26)
-#31 := (forall (vars (?v0 S4) (?v1 S5)) #30)
-#81 := (iff #31 #80)
-#78 := (iff #30 #76)
-#79 := [rewrite]: #78
-#82 := [quant-intro #79]: #81
-#75 := [asserted]: #31
-#85 := [mp #75 #82]: #80
-#127 := [mp~ #85 #144]: #80
-#656 := [mp #127 #655]: #651
-#310 := (not #651)
-#302 := (or #310 #647)
-#640 := [quant-inst]: #302
-#333 := [unit-resolution #640 #656]: #647
+#332 := [lemma #331]: #137
+decl f5 :: (-> S2 S4)
+#282 := (f5 #45)
+#606 := (= #282 f14)
+#625 := (= f14 #282)
+#21 := (:var 0 S4)
+#22 := (f3 #20 #21)
+#666 := (pattern #22)
+#23 := (f5 #22)
+#86 := (= #21 #23)
+#667 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #666) #86)
+#90 := (forall (vars (?v0 S3) (?v1 S4)) #86)
+#670 := (iff #90 #667)
+#668 := (iff #86 #86)
+#669 := [refl]: #668
+#671 := [quant-intro #669]: #670
+#129 := (~ #90 #90)
+#147 := (~ #86 #86)
+#148 := [refl]: #147
+#130 := [nnf-pos #148]: #129
+#24 := (= #23 #21)
+#25 := (forall (vars (?v0 S3) (?v1 S4)) #24)
+#91 := (iff #25 #90)
+#88 := (iff #24 #86)
+#89 := [rewrite]: #88
+#92 := [quant-intro #89]: #91
+#85 := [asserted]: #25
+#95 := [mp #85 #92]: #90
+#149 := [mp~ #95 #130]: #90
+#672 := [mp #149 #671]: #667
+#640 := (not #667)
+#628 := (or #640 #625)
+#629 := [quant-inst]: #628
+#333 := [unit-resolution #629 #672]: #625
 #607 := [symm #333]: #606
-#602 := (= f7 #646)
-#644 := (f12 #11)
-#616 := (= #644 #646)
-#613 := (= #19 #17)
+#602 := (= f11 #282)
+#648 := (f5 #39)
+#616 := (= #648 #282)
+#613 := (= #47 #45)
 #614 := [symm #334]: #613
-#327 := (= #11 #19)
-#252 := (or #20 #140)
-#323 := (or #20 #140 #312)
+#327 := (= #39 #47)
+#252 := (or #48 #138)
+#323 := (or #48 #138 #312)
 #324 := [def-axiom]: #323
 #325 := [unit-resolution #324 #174]: #252
-#335 := [unit-resolution #325 #332]: #20
+#335 := [unit-resolution #325 #332]: #48
 #611 := [trans #619 #335]: #327
 #615 := [trans #611 #614]: #343
 #605 := [monotonicity #615]: #616
-#299 := (= f7 #644)
-#311 := (or #310 #299)
-#645 := [quant-inst]: #311
-#612 := [unit-resolution #645 #656]: #299
+#643 := (= f11 #648)
+#298 := (or #640 #643)
+#641 := [quant-inst]: #298
+#612 := [unit-resolution #641 #672]: #643
 #603 := [trans #612 #605]: #602
-#608 := [trans #603 #607]: #21
-decl f14 :: (-> S3 S5)
-#639 := (f14 #17)
-#452 := (= #639 f11)
-#297 := (= f11 #639)
-#37 := (f14 #28)
-#92 := (= #27 #37)
-#664 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #650) #92)
-#96 := (forall (vars (?v0 S4) (?v1 S5)) #92)
-#667 := (iff #96 #664)
-#665 := (iff #92 #92)
-#666 := [refl]: #665
-#668 := [quant-intro #666]: #667
-#131 := (~ #96 #96)
-#145 := (~ #92 #92)
-#146 := [refl]: #145
-#132 := [nnf-pos #146]: #131
-#38 := (= #37 #27)
-#39 := (forall (vars (?v0 S4) (?v1 S5)) #38)
-#97 := (iff #39 #96)
-#94 := (iff #38 #92)
-#95 := [rewrite]: #94
-#98 := [quant-intro #95]: #97
-#91 := [asserted]: #39
-#101 := [mp #91 #98]: #96
-#147 := [mp~ #101 #132]: #96
-#669 := [mp #147 #668]: #664
-#648 := (not #664)
-#282 := (or #648 #297)
-#625 := [quant-inst]: #282
-#609 := [unit-resolution #625 #669]: #297
+#608 := [trans #603 #607]: #50
+decl f4 :: (-> S2 S3)
+#289 := (f4 #45)
+#452 := (= #289 f13)
+#627 := (= f13 #289)
+#30 := (f4 #22)
+#102 := (= #20 #30)
+#680 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #666) #102)
+#106 := (forall (vars (?v0 S3) (?v1 S4)) #102)
+#683 := (iff #106 #680)
+#681 := (iff #102 #102)
+#682 := [refl]: #681
+#684 := [quant-intro #682]: #683
+#133 := (~ #106 #106)
+#153 := (~ #102 #102)
+#154 := [refl]: #153
+#134 := [nnf-pos #154]: #133
+#31 := (= #30 #20)
+#32 := (forall (vars (?v0 S3) (?v1 S4)) #31)
+#107 := (iff #32 #106)
+#104 := (iff #31 #102)
+#105 := [rewrite]: #104
+#108 := [quant-intro #105]: #107
+#101 := [asserted]: #32
+#111 := [mp #101 #108]: #106
+#155 := [mp~ #111 #134]: #106
+#685 := [mp #155 #684]: #680
+#286 := (not #680)
+#626 := (or #286 #627)
+#632 := [quant-inst]: #626
+#609 := [unit-resolution #632 #685]: #627
 #453 := [symm #609]: #452
-#595 := (= f8 #639)
-#431 := (f14 #11)
-#610 := (= #431 #639)
+#595 := (= f10 #289)
+#297 := (f4 #39)
+#610 := (= #297 #289)
 #451 := [monotonicity #615]: #610
-#638 := (= f8 #431)
-#643 := (or #648 #638)
-#649 := [quant-inst]: #643
-#604 := [unit-resolution #649 #669]: #638
+#302 := (= f10 #297)
+#287 := (or #286 #302)
+#288 := [quant-inst]: #287
+#604 := [unit-resolution #288 #685]: #302
 #596 := [trans #604 #451]: #595
-#597 := [trans #596 #453]: #22
-#234 := (or #140 #157 #158)
+#597 := [trans #596 #453]: #49
+#234 := (or #138 #159 #160)
 #321 := [def-axiom]: #234
 [unit-resolution #321 #597 #608 #332]: false
 unsat
-9e71fbaeab4696b5dac5d3a07643d4cf5689f72a 85 0
-#2 := false
-decl f8 :: (-> S3 S2 S4)
-decl f4 :: S2
-#9 := f4
-decl f6 :: S3
-#12 := f6
-#15 := (f8 f6 f4)
-decl f5 :: (-> S3 S2 S4 S2 S4)
-decl f7 :: S4
-#13 := f7
-decl f3 :: S2
-#8 := f3
-#14 := (f5 f6 f3 f7 f4)
-#16 := (= #14 #15)
-#161 := (= f7 #14)
-#10 := (= f3 f4)
-#248 := (ite #10 #161 #16)
-#252 := (not #248)
-#59 := (not #16)
-#52 := (or #10 #16)
-#55 := (not #52)
-#11 := (not #10)
-#17 := (implies #11 #16)
-#18 := (not #17)
-#56 := (iff #18 #55)
-#53 := (iff #17 #52)
-#54 := [rewrite]: #53
-#57 := [monotonicity #54]: #56
-#51 := [asserted]: #18
-#60 := [mp #51 #57]: #55
-#61 := [not-or-elim #60]: #59
-#58 := [not-or-elim #60]: #11
-#254 := (or #252 #10 #16)
-#251 := [def-axiom]: #254
-#162 := [unit-resolution #251 #58 #61]: #252
-#28 := (:var 0 S2)
-#27 := (:var 1 S4)
-#26 := (:var 2 S2)
-#25 := (:var 3 S3)
-#29 := (f5 #25 #26 #27 #28)
-#586 := (pattern #29)
-#31 := (f8 #25 #28)
-#83 := (= #29 #31)
-#86 := (= #27 #29)
-#70 := (= #26 #28)
-#93 := (ite #70 #86 #83)
-#587 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) (:pat #586) #93)
-#100 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) #93)
-#590 := (iff #100 #587)
-#588 := (iff #93 #93)
-#589 := [refl]: #588
-#591 := [quant-intro #589]: #590
-#74 := (ite #70 #27 #31)
-#77 := (= #29 #74)
-#80 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) #77)
-#101 := (iff #80 #100)
-#94 := (iff #77 #93)
-#99 := [rewrite]: #94
-#102 := [quant-intro #99]: #101
-#91 := (~ #80 #80)
-#90 := (~ #77 #77)
-#87 := [refl]: #90
-#92 := [nnf-pos #87]: #91
-#30 := (= #28 #26)
-#32 := (ite #30 #27 #31)
-#33 := (= #29 #32)
-#34 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) #33)
-#81 := (iff #34 #80)
-#78 := (iff #33 #77)
-#75 := (= #32 #74)
-#72 := (iff #30 #70)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#79 := [monotonicity #76]: #78
-#82 := [quant-intro #79]: #81
-#69 := [asserted]: #34
-#85 := [mp #69 #82]: #80
-#88 := [mp~ #85 #92]: #80
-#103 := [mp #88 #102]: #100
-#592 := [mp #103 #591]: #587
-#163 := (not #587)
-#250 := (or #163 #248)
-#241 := [quant-inst]: #250
-[unit-resolution #241 #592 #162]: false
-unsat
-acd9894f281a06eeaf416c1e8c82c6d84e7d6ad1 144 0
-#2 := false
-decl f11 :: S3
-#16 := f11
-decl f8 :: S3
-#9 := f8
-#23 := (= f8 f11)
-decl f3 :: (-> S2 S3)
-decl f4 :: (-> S4 S2)
-decl f5 :: (-> S3 S2 S4)
-decl f7 :: (-> S3 S5 S2)
-decl f12 :: S5
-#17 := f12
-#18 := (f7 f11 f12)
+0b58e800f34f9f49d4b2e598494259996df6db9f 144 0
+#2 := false
+decl f13 :: S3
+#44 := f13
 decl f10 :: S3
-#15 := f10
-#19 := (f5 f10 #18)
-#20 := (f4 #19)
-#21 := (f3 #20)
-decl f9 :: S5
-#10 := f9
-#11 := (f7 f8 f9)
-decl f6 :: S3
-#8 := f6
-#12 := (f5 f6 #11)
-#13 := (f4 #12)
-#14 := (f3 #13)
-#22 := (= #14 #21)
-#24 := (iff #22 #23)
-#315 := (= #21 f11)
-#411 := (f3 #18)
-#312 := (= #411 f11)
-#618 := (= f11 #411)
-#27 := (:var 0 S5)
-#26 := (:var 1 S3)
-#28 := (f7 #26 #27)
-#630 := (pattern #28)
-#29 := (f3 #28)
-#76 := (= #26 #29)
-#631 := (forall (vars (?v0 S3) (?v1 S5)) (:pat #630) #76)
-#80 := (forall (vars (?v0 S3) (?v1 S5)) #76)
-#634 := (iff #80 #631)
-#632 := (iff #76 #76)
-#633 := [refl]: #632
-#635 := [quant-intro #633]: #634
-#143 := (~ #80 #80)
-#141 := (~ #76 #76)
-#142 := [refl]: #141
-#144 := [nnf-pos #142]: #143
-#30 := (= #29 #26)
-#31 := (forall (vars (?v0 S3) (?v1 S5)) #30)
-#81 := (iff #31 #80)
-#78 := (iff #30 #76)
-#79 := [rewrite]: #78
-#82 := [quant-intro #79]: #81
-#75 := [asserted]: #31
-#85 := [mp #75 #82]: #80
-#127 := [mp~ #85 #144]: #80
-#636 := [mp #127 #635]: #631
-#622 := (not #631)
-#628 := (or #622 #618)
-#623 := [quant-inst]: #628
-#323 := [unit-resolution #623 #636]: #618
+#37 := f10
+#51 := (= f10 f13)
+decl f4 :: (-> S2 S3)
+decl f8 :: (-> S5 S2)
+decl f6 :: (-> S3 S2 S5)
+decl f3 :: (-> S3 S4 S2)
+decl f14 :: S4
+#45 := f14
+#46 := (f3 f13 f14)
+decl f12 :: S3
+#43 := f12
+#47 := (f6 f12 #46)
+#48 := (f8 #47)
+#49 := (f4 #48)
+decl f11 :: S4
+#38 := f11
+#39 := (f3 f10 f11)
+decl f9 :: S3
+#36 := f9
+#40 := (f6 f9 #39)
+#41 := (f8 #40)
+#42 := (f4 #41)
+#50 := (= #42 #49)
+#52 := (iff #50 #51)
+#315 := (= #49 f13)
+#606 := (f4 #46)
+#312 := (= #606 f13)
+#612 := (= f13 #606)
+#21 := (:var 0 S4)
+#20 := (:var 1 S3)
+#22 := (f3 #20 #21)
+#646 := (pattern #22)
+#30 := (f4 #22)
+#102 := (= #20 #30)
+#660 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #646) #102)
+#106 := (forall (vars (?v0 S3) (?v1 S4)) #102)
+#663 := (iff #106 #660)
+#661 := (iff #102 #102)
+#662 := [refl]: #661
+#664 := [quant-intro #662]: #663
+#133 := (~ #106 #106)
+#153 := (~ #102 #102)
+#154 := [refl]: #153
+#134 := [nnf-pos #154]: #133
+#31 := (= #30 #20)
+#32 := (forall (vars (?v0 S3) (?v1 S4)) #31)
+#107 := (iff #32 #106)
+#104 := (iff #31 #102)
+#105 := [rewrite]: #104
+#108 := [quant-intro #105]: #107
+#101 := [asserted]: #32
+#111 := [mp #101 #108]: #106
+#155 := [mp~ #111 #134]: #106
+#665 := [mp #155 #664]: #660
+#609 := (not #660)
+#254 := (or #609 #612)
+#616 := [quant-inst]: #254
+#323 := [unit-resolution #616 #665]: #612
 #313 := [symm #323]: #312
-#602 := (= #21 #411)
-#601 := (= #20 #18)
-#607 := (= #18 #20)
-#32 := (:var 0 S2)
-#33 := (f5 #26 #32)
-#637 := (pattern #33)
-#40 := (f4 #33)
-#100 := (= #32 #40)
-#650 := (forall (vars (?v0 S3) (?v1 S2)) (:pat #637) #100)
-#104 := (forall (vars (?v0 S3) (?v1 S2)) #100)
-#653 := (iff #104 #650)
-#651 := (iff #100 #100)
-#652 := [refl]: #651
-#654 := [quant-intro #652]: #653
-#133 := (~ #104 #104)
-#148 := (~ #100 #100)
-#149 := [refl]: #148
-#134 := [nnf-pos #149]: #133
-#41 := (= #40 #32)
-#42 := (forall (vars (?v0 S3) (?v1 S2)) #41)
-#105 := (iff #42 #104)
-#102 := (iff #41 #100)
-#103 := [rewrite]: #102
-#106 := [quant-intro #103]: #105
-#99 := [asserted]: #42
-#109 := [mp #99 #106]: #104
-#150 := [mp~ #109 #134]: #104
-#655 := [mp #150 #654]: #650
-#267 := (not #650)
-#606 := (or #267 #607)
-#612 := [quant-inst]: #606
-#597 := [unit-resolution #612 #655]: #607
+#602 := (= #49 #606)
+#601 := (= #48 #46)
+#614 := (= #46 #48)
+#8 := (:var 0 S2)
+#26 := (f6 #20 #8)
+#653 := (pattern #26)
+#27 := (f8 #26)
+#94 := (= #8 #27)
+#654 := (forall (vars (?v0 S3) (?v1 S2)) (:pat #653) #94)
+#98 := (forall (vars (?v0 S3) (?v1 S2)) #94)
+#657 := (iff #98 #654)
+#655 := (iff #94 #94)
+#656 := [refl]: #655
+#658 := [quant-intro #656]: #657
+#131 := (~ #98 #98)
+#150 := (~ #94 #94)
+#151 := [refl]: #150
+#132 := [nnf-pos #151]: #131
+#28 := (= #27 #8)
+#29 := (forall (vars (?v0 S3) (?v1 S2)) #28)
+#99 := (iff #29 #98)
+#96 := (iff #28 #94)
+#97 := [rewrite]: #96
+#100 := [quant-intro #97]: #99
+#93 := [asserted]: #29
+#103 := [mp #93 #100]: #98
+#152 := [mp~ #103 #132]: #98
+#659 := [mp #152 #658]: #654
+#617 := (not #654)
+#329 := (or #617 #614)
+#220 := [quant-inst]: #329
+#597 := [unit-resolution #220 #659]: #614
+#598 := [symm #597]: #601
+#311 := [monotonicity #598]: #602
+#593 := [trans #311 #313]: #315
+#587 := (= #42 f10)
+#605 := (f4 #39)
+#585 := (= #605 f10)
+#266 := (= f10 #605)
+#610 := (or #609 #266)
+#611 := [quant-inst]: #610
+#594 := [unit-resolution #611 #665]: #266
+#586 := [symm #594]: #585
+#592 := (= #42 #605)
+#591 := (= #41 #39)
+#615 := (= #39 #41)
+#603 := (or #617 #615)
+#604 := [quant-inst]: #603
+#307 := [unit-resolution #604 #659]: #615
+#595 := [symm #307]: #591
+#596 := [monotonicity #595]: #592
+#582 := [trans #596 #586]: #587
+#583 := [monotonicity #582 #593]: #52
+#301 := (not #51)
+#118 := (not #50)
+#588 := (iff #118 #301)
+#589 := [monotonicity #583]: #588
+#314 := [hypothesis]: #118
+#584 := [mp #314 #589]: #301
+#300 := (or #51 #50)
+#120 := (iff #51 #118)
+#53 := (not #52)
+#121 := (iff #53 #120)
+#122 := [rewrite]: #121
+#117 := [asserted]: #53
+#125 := [mp #117 #122]: #120
+#212 := (not #120)
+#299 := (or #51 #50 #212)
+#213 := [def-axiom]: #299
+#214 := [unit-resolution #213 #125]: #300
+#599 := [unit-resolution #214 #314]: #51
+#590 := [unit-resolution #599 #584]: false
+#431 := [lemma #590]: #50
+#433 := [mp #431 #583]: #51
+#304 := (or #301 #118)
+#292 := (or #301 #118 #212)
+#303 := [def-axiom]: #292
+#232 := [unit-resolution #303 #125]: #304
+#432 := [unit-resolution #232 #431]: #301
+[unit-resolution #432 #433]: false
+unsat
+0c5e9ed09e8f9d88d5857b15408bbd8d3596939d 144 0
+#2 := false
+decl f14 :: S4
+#45 := f14
+decl f11 :: S4
+#38 := f11
+#51 := (= f11 f14)
+decl f5 :: (-> S2 S4)
+decl f8 :: (-> S5 S2)
+decl f6 :: (-> S3 S2 S5)
+decl f3 :: (-> S3 S4 S2)
+decl f13 :: S3
+#44 := f13
+#46 := (f3 f13 f14)
+decl f12 :: S3
+#43 := f12
+#47 := (f6 f12 #46)
+#48 := (f8 #47)
+#49 := (f5 #48)
+decl f10 :: S3
+#37 := f10
+#39 := (f3 f10 f11)
+decl f9 :: S3
+#36 := f9
+#40 := (f6 f9 #39)
+#41 := (f8 #40)
+#42 := (f5 #41)
+#50 := (= #42 #49)
+#52 := (iff #50 #51)
+#315 := (= #49 f14)
+#607 := (f5 #46)
+#312 := (= #607 f14)
+#608 := (= f14 #607)
+#21 := (:var 0 S4)
+#20 := (:var 1 S3)
+#22 := (f3 #20 #21)
+#646 := (pattern #22)
+#23 := (f5 #22)
+#86 := (= #21 #23)
+#647 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #646) #86)
+#90 := (forall (vars (?v0 S3) (?v1 S4)) #86)
+#650 := (iff #90 #647)
+#648 := (iff #86 #86)
+#649 := [refl]: #648
+#651 := [quant-intro #649]: #650
+#129 := (~ #90 #90)
+#147 := (~ #86 #86)
+#148 := [refl]: #147
+#130 := [nnf-pos #148]: #129
+#24 := (= #23 #21)
+#25 := (forall (vars (?v0 S3) (?v1 S4)) #24)
+#91 := (iff #25 #90)
+#88 := (iff #24 #86)
+#89 := [rewrite]: #88
+#92 := [quant-intro #89]: #91
+#85 := [asserted]: #25
+#95 := [mp #85 #92]: #90
+#149 := [mp~ #95 #130]: #90
+#652 := [mp #149 #651]: #647
+#267 := (not #647)
+#248 := (or #267 #608)
+#613 := [quant-inst]: #248
+#323 := [unit-resolution #613 #652]: #608
+#313 := [symm #323]: #312
+#602 := (= #49 #607)
+#601 := (= #48 #46)
+#614 := (= #46 #48)
+#8 := (:var 0 S2)
+#26 := (f6 #20 #8)
+#653 := (pattern #26)
+#27 := (f8 #26)
+#94 := (= #8 #27)
+#654 := (forall (vars (?v0 S3) (?v1 S2)) (:pat #653) #94)
+#98 := (forall (vars (?v0 S3) (?v1 S2)) #94)
+#657 := (iff #98 #654)
+#655 := (iff #94 #94)
+#656 := [refl]: #655
+#658 := [quant-intro #656]: #657
+#131 := (~ #98 #98)
+#150 := (~ #94 #94)
+#151 := [refl]: #150
+#132 := [nnf-pos #151]: #131
+#28 := (= #27 #8)
+#29 := (forall (vars (?v0 S3) (?v1 S2)) #28)
+#99 := (iff #29 #98)
+#96 := (iff #28 #94)
+#97 := [rewrite]: #96
+#100 := [quant-intro #97]: #99
+#93 := [asserted]: #29
+#103 := [mp #93 #100]: #98
+#152 := [mp~ #103 #132]: #98
+#659 := [mp #152 #658]: #654
+#617 := (not #654)
+#329 := (or #617 #614)
+#220 := [quant-inst]: #329
+#597 := [unit-resolution #220 #659]: #614
 #598 := [symm #597]: #601
 #311 := [monotonicity #598]: #602
 #593 := [trans #311 #313]: #315
-#587 := (= #14 f8)
-#305 := (f3 #11)
-#585 := (= #305 f8)
-#302 := (= f8 #305)
-#624 := (or #622 #302)
-#279 := [quant-inst]: #624
-#594 := [unit-resolution #279 #636]: #302
+#587 := (= #42 f11)
+#620 := (f5 #39)
+#585 := (= #620 f11)
+#278 := (= f11 #620)
+#268 := (or #267 #278)
+#269 := [quant-inst]: #268
+#594 := [unit-resolution #269 #652]: #278
 #586 := [symm #594]: #585
-#592 := (= #14 #305)
-#591 := (= #13 #11)
-#620 := (= #11 #13)
-#268 := (or #267 #620)
-#269 := [quant-inst]: #268
-#307 := [unit-resolution #269 #655]: #620
+#592 := (= #42 #620)
+#591 := (= #41 #39)
+#615 := (= #39 #41)
+#603 := (or #617 #615)
+#604 := [quant-inst]: #603
+#307 := [unit-resolution #604 #659]: #615
 #595 := [symm #307]: #591
 #596 := [monotonicity #595]: #592
 #582 := [trans #596 #586]: #587
-#583 := [monotonicity #582 #593]: #24
-#301 := (not #23)
-#71 := (not #22)
-#588 := (iff #71 #301)
+#583 := [monotonicity #582 #593]: #52
+#301 := (not #51)
+#118 := (not #50)
+#588 := (iff #118 #301)
 #589 := [monotonicity #583]: #588
-#220 := [hypothesis]: #71
-#584 := [mp #220 #589]: #301
-#300 := (or #23 #22)
-#72 := (iff #23 #71)
-#25 := (not #24)
-#73 := (iff #25 #72)
-#74 := [rewrite]: #73
-#70 := [asserted]: #25
-#77 := [mp #70 #74]: #72
-#212 := (not #72)
-#299 := (or #23 #22 #212)
+#314 := [hypothesis]: #118
+#584 := [mp #314 #589]: #301
+#300 := (or #51 #50)
+#120 := (iff #51 #118)
+#53 := (not #52)
+#121 := (iff #53 #120)
+#122 := [rewrite]: #121
+#117 := [asserted]: #53
+#125 := [mp #117 #122]: #120
+#212 := (not #120)
+#299 := (or #51 #50 #212)
 #213 := [def-axiom]: #299
-#214 := [unit-resolution #213 #77]: #300
-#599 := [unit-resolution #214 #220]: #23
+#214 := [unit-resolution #213 #125]: #300
+#599 := [unit-resolution #214 #314]: #51
 #590 := [unit-resolution #599 #584]: false
-#431 := [lemma #590]: #22
-#433 := [mp #431 #583]: #23
-#304 := (or #301 #71)
-#292 := (or #301 #71 #212)
+#431 := [lemma #590]: #50
+#433 := [mp #431 #583]: #51
+#304 := (or #301 #118)
+#292 := (or #301 #118 #212)
 #303 := [def-axiom]: #292
-#232 := [unit-resolution #303 #77]: #304
+#232 := [unit-resolution #303 #125]: #304
 #432 := [unit-resolution #232 #431]: #301
 [unit-resolution #432 #433]: false
 unsat
-417188282427933be953d50eedb6f8d3636fdcb9 158 0
-#2 := false
-decl f5 :: (-> S3 S2 S4)
-decl f3 :: S2
-#8 := f3
-decl f6 :: (-> S3 S2 S4 S3)
-decl f9 :: S4
-#15 := f9
-decl f4 :: S2
-#9 := f4
+975246c497a12d8a8bc67b54b209408654a9cd54 103 0
+#2 := false
+decl f7 :: S3
+#24 := f7
+decl f6 :: S3
+#23 := f6
+#29 := (= f6 f7)
+decl f5 :: (-> S2 S3)
+decl f3 :: (-> S3 S3 S2)
+#25 := (f3 f6 f7)
+#27 := (f5 #25)
+decl f4 :: (-> S2 S3)
+#26 := (f4 #25)
+#28 := (= #26 #27)
+#30 := (iff #28 #29)
+#558 := (iff #29 #28)
+#245 := (= f7 #27)
+#15 := (:var 0 S3)
+#14 := (:var 1 S3)
+#16 := (f3 #14 #15)
+#577 := (pattern #16)
+#17 := (f5 #16)
+#56 := (= #15 #17)
+#578 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #577) #56)
+#60 := (forall (vars (?v0 S3) (?v1 S3)) #56)
+#581 := (iff #60 #578)
+#579 := (iff #56 #56)
+#580 := [refl]: #579
+#582 := [quant-intro #580]: #581
+#81 := (~ #60 #60)
+#77 := (~ #56 #56)
+#93 := [refl]: #77
+#82 := [nnf-pos #93]: #81
+#18 := (= #17 #15)
+#19 := (forall (vars (?v0 S3) (?v1 S3)) #18)
+#61 := (iff #19 #60)
+#58 := (iff #18 #56)
+#59 := [rewrite]: #58
+#62 := [quant-intro #59]: #61
+#55 := [asserted]: #19
+#65 := [mp #55 #62]: #60
+#94 := [mp~ #65 #82]: #60
+#583 := [mp #94 #582]: #578
+#557 := (not #578)
+#229 := (or #557 #245)
+#230 := [quant-inst]: #229
+#562 := [unit-resolution #230 #583]: #245
+#224 := (= f6 #26)
+#20 := (f4 #16)
+#64 := (= #14 #20)
+#584 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #577) #64)
+#68 := (forall (vars (?v0 S3) (?v1 S3)) #64)
+#587 := (iff #68 #584)
+#585 := (iff #64 #64)
+#586 := [refl]: #585
+#588 := [quant-intro #586]: #587
+#83 := (~ #68 #68)
+#95 := (~ #64 #64)
+#96 := [refl]: #95
+#84 := [nnf-pos #96]: #83
+#21 := (= #20 #14)
+#22 := (forall (vars (?v0 S3) (?v1 S3)) #21)
+#69 := (iff #22 #68)
+#66 := (iff #21 #64)
+#67 := [rewrite]: #66
+#70 := [quant-intro #67]: #69
+#63 := [asserted]: #22
+#73 := [mp #63 #70]: #68
+#97 := [mp~ #73 #84]: #68
+#589 := [mp #97 #588]: #584
+#565 := (not #584)
+#566 := (or #565 #224)
+#567 := [quant-inst]: #566
+#568 := [unit-resolution #567 #589]: #224
+#216 := [monotonicity #568 #562]: #558
+#221 := [symm #216]: #30
+#240 := (not #29)
+#72 := (not #28)
+#559 := (iff #72 #240)
+#217 := [monotonicity #221]: #559
+#350 := [hypothesis]: #72
+#560 := [mp #350 #217]: #240
+#239 := (or #29 #28)
+#74 := (iff #29 #72)
+#31 := (not #30)
+#75 := (iff #31 #74)
+#76 := [rewrite]: #75
+#71 := [asserted]: #31
+#79 := [mp #71 #76]: #74
+#151 := (not #74)
+#238 := (or #29 #28 #151)
+#152 := [def-axiom]: #238
+#153 := [unit-resolution #152 #79]: #239
+#564 := [unit-resolution #153 #350]: #29
+#201 := [unit-resolution #564 #560]: false
+#544 := [lemma #201]: #28
+#206 := [mp #544 #221]: #29
+#243 := (or #240 #72)
+#231 := (or #240 #72 #151)
+#242 := [def-axiom]: #231
+#171 := [unit-resolution #242 #79]: #243
+#205 := [unit-resolution #171 #544]: #240
+[unit-resolution #205 #206]: false
+unsat
+9916906c135726422395203168d350fab5a123e3 111 0
+#2 := false
+decl f5 :: (-> S2 S3)
+decl f9 :: S2
+#28 := f9
+#33 := (f5 f9)
+decl f4 :: (-> S2 S3)
+decl f6 :: S2
+#23 := f6
+#32 := (f4 f6)
+#34 := (= #32 #33)
+decl f3 :: (-> S3 S3 S2)
+decl f7 :: S3
+#24 := f7
+decl f8 :: S3
+#25 := f8
+#29 := (f3 f8 f7)
+#166 := (f5 #29)
+#220 := (= #166 #33)
+#230 := (= #33 #166)
+#30 := (= f9 #29)
+#26 := (f3 f7 f8)
+#27 := (= f6 #26)
+#31 := (and #27 #30)
+#77 := (not #31)
+#79 := (or #77 #34)
+#82 := (not #79)
+#35 := (implies #31 #34)
+#36 := (not #35)
+#83 := (iff #36 #82)
+#80 := (iff #35 #79)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#76 := [asserted]: #36
+#87 := [mp #76 #84]: #82
+#85 := [not-or-elim #87]: #31
+#88 := [and-elim #85]: #30
+#573 := [monotonicity #88]: #230
+#221 := [symm #573]: #220
+#561 := (= #32 #166)
+#576 := (= f7 #166)
+#15 := (:var 0 S3)
+#14 := (:var 1 S3)
+#16 := (f3 #14 #15)
+#590 := (pattern #16)
+#17 := (f5 #16)
+#61 := (= #15 #17)
+#591 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #590) #61)
+#65 := (forall (vars (?v0 S3) (?v1 S3)) #61)
+#594 := (iff #65 #591)
+#592 := (iff #61 #61)
+#593 := [refl]: #592
+#595 := [quant-intro #593]: #594
+#94 := (~ #65 #65)
+#91 := (~ #61 #61)
+#110 := [refl]: #91
+#95 := [nnf-pos #110]: #94
+#18 := (= #17 #15)
+#19 := (forall (vars (?v0 S3) (?v1 S3)) #18)
+#66 := (iff #19 #65)
+#63 := (iff #18 #61)
+#64 := [rewrite]: #63
+#67 := [quant-intro #64]: #66
+#60 := [asserted]: #19
+#70 := [mp #60 #67]: #65
+#111 := [mp~ #70 #95]: #65
+#596 := [mp #111 #595]: #591
+#231 := (not #591)
+#580 := (or #231 #576)
+#575 := [quant-inst]: #580
+#581 := [unit-resolution #575 #596]: #576
+#559 := (= #32 f7)
+#251 := (f4 #26)
+#218 := (= #251 f7)
+#258 := (= f7 #251)
+#20 := (f4 #16)
+#69 := (= #14 #20)
+#597 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #590) #69)
+#73 := (forall (vars (?v0 S3) (?v1 S3)) #69)
+#600 := (iff #73 #597)
+#598 := (iff #69 #69)
+#599 := [refl]: #598
+#601 := [quant-intro #599]: #600
+#96 := (~ #73 #73)
+#112 := (~ #69 #69)
+#113 := [refl]: #112
+#97 := [nnf-pos #113]: #96
+#21 := (= #20 #14)
+#22 := (forall (vars (?v0 S3) (?v1 S3)) #21)
+#74 := (iff #22 #73)
+#71 := (iff #21 #69)
+#72 := [rewrite]: #71
+#75 := [quant-intro #72]: #74
+#68 := [asserted]: #22
+#78 := [mp #68 #75]: #73
+#114 := [mp~ #78 #97]: #73
+#602 := [mp #114 #601]: #597
+#243 := (not #597)
+#577 := (or #243 #258)
+#578 := [quant-inst]: #577
+#579 := [unit-resolution #578 #602]: #258
+#219 := [symm #579]: #218
+#234 := (= #32 #251)
+#86 := [and-elim #85]: #27
+#572 := [monotonicity #86]: #234
+#560 := [trans #572 #219]: #559
+#562 := [trans #560 #581]: #561
+#563 := [trans #562 #221]: #34
+#89 := (not #34)
+#90 := [not-or-elim #87]: #89
+[unit-resolution #90 #563]: false
+unsat
+4ad65d8265392e06bcf6dda591dc8fed065e695e 113 0
+#2 := false
+decl f3 :: (-> S3 S3 S2)
+decl f4 :: (-> S2 S3)
+decl f6 :: S2
+#23 := f6
+#24 := (f4 f6)
+decl f5 :: (-> S2 S3)
+#25 := (f5 f6)
+#27 := (f3 #25 #24)
+#28 := (= f6 #27)
+#243 := (f3 #24 #25)
+#547 := (= #243 #27)
+#545 := (= #27 #243)
+#26 := (= #24 #25)
+#244 := (f5 #27)
+#558 := (= #244 #25)
+#557 := (= #27 f6)
+#71 := (not #26)
+#564 := [hypothesis]: #71
+#238 := (or #28 #26)
+#73 := (iff #28 #71)
+#29 := (iff #26 #28)
+#30 := (not #29)
+#74 := (iff #30 #73)
+#75 := [rewrite]: #74
+#70 := [asserted]: #30
+#78 := [mp #70 #75]: #73
+#150 := (not #73)
+#237 := (or #28 #26 #150)
+#151 := [def-axiom]: #237
+#152 := [unit-resolution #151 #78]: #238
+#565 := [unit-resolution #152 #564]: #28
+#215 := [symm #565]: #557
+#216 := [monotonicity #215]: #558
+#223 := (= #24 #244)
+#15 := (:var 0 S3)
+#14 := (:var 1 S3)
+#16 := (f3 #14 #15)
+#576 := (pattern #16)
+#17 := (f5 #16)
+#55 := (= #15 #17)
+#577 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #576) #55)
+#59 := (forall (vars (?v0 S3) (?v1 S3)) #55)
+#580 := (iff #59 #577)
+#578 := (iff #55 #55)
+#579 := [refl]: #578
+#581 := [quant-intro #579]: #580
+#80 := (~ #59 #59)
+#76 := (~ #55 #55)
+#92 := [refl]: #76
+#81 := [nnf-pos #92]: #80
+#18 := (= #17 #15)
+#19 := (forall (vars (?v0 S3) (?v1 S3)) #18)
+#60 := (iff #19 #59)
+#57 := (iff #18 #55)
+#58 := [rewrite]: #57
+#61 := [quant-intro #58]: #60
+#54 := [asserted]: #19
+#64 := [mp #54 #61]: #59
+#93 := [mp~ #64 #81]: #59
+#582 := [mp #93 #581]: #577
+#228 := (not #577)
+#229 := (or #228 #223)
+#563 := [quant-inst]: #229
+#220 := [unit-resolution #563 #582]: #223
+#559 := [trans #220 #216]: #26
+#200 := [unit-resolution #564 #559]: false
+#543 := [lemma #200]: #26
+#205 := (= #25 #24)
+#206 := [symm #543]: #205
+#546 := [monotonicity #206 #543]: #545
+#548 := [symm #546]: #547
+#240 := (= f6 #243)
+#8 := (:var 0 S2)
+#10 := (f5 #8)
+#569 := (pattern #10)
+#9 := (f4 #8)
+#568 := (pattern #9)
+#11 := (f3 #9 #10)
+#48 := (= #8 #11)
+#570 := (forall (vars (?v0 S2)) (:pat #568 #569) #48)
+#51 := (forall (vars (?v0 S2)) #48)
+#573 := (iff #51 #570)
+#571 := (iff #48 #48)
+#572 := [refl]: #571
+#574 := [quant-intro #572]: #573
+#90 := (~ #51 #51)
+#88 := (~ #48 #48)
+#89 := [refl]: #88
+#91 := [nnf-pos #89]: #90
+#12 := (= #11 #8)
+#13 := (forall (vars (?v0 S2)) #12)
+#52 := (iff #13 #51)
+#49 := (iff #12 #48)
+#50 := [rewrite]: #49
+#53 := [quant-intro #50]: #52
+#47 := [asserted]: #13
+#56 := [mp #47 #53]: #51
+#79 := [mp~ #56 #91]: #51
+#575 := [mp #79 #574]: #570
+#560 := (not #570)
+#562 := (or #560 #240)
+#217 := [quant-inst]: #562
+#207 := [unit-resolution #217 #575]: #240
+#549 := [trans #207 #548]: #28
+#239 := (not #28)
+#242 := (or #239 #71)
+#230 := (or #239 #71 #150)
+#241 := [def-axiom]: #230
+#170 := [unit-resolution #241 #78]: #242
+#204 := [unit-resolution #170 #543]: #239
+[unit-resolution #204 #549]: false
+unsat
+faf992e3d182b734a43cf8ac5a0e4d109b0e1f8a 91 0
+#2 := false
+decl f3 :: (-> S2 S3 S4 S3 S4)
+decl f6 :: S3
+#25 := f6
+decl f7 :: S4
+#26 := f7
+decl f5 :: S2
+#24 := f5
+#27 := (f3 f5 f6 f7 f6)
+#68 := (= f7 #27)
+#72 := (not #68)
+#28 := (= #27 f7)
+#29 := (not #28)
+#73 := (iff #29 #72)
+#70 := (iff #28 #68)
+#71 := [rewrite]: #70
+#74 := [monotonicity #71]: #73
+#67 := [asserted]: #29
+#77 := [mp #67 #74]: #72
+#11 := (:var 0 S3)
+#10 := (:var 1 S4)
+#9 := (:var 2 S3)
+#8 := (:var 3 S2)
+#12 := (f3 #8 #9 #10 #11)
+#571 := (pattern #12)
+decl f4 :: (-> S2 S3 S4)
+#14 := (f4 #8 #11)
+#92 := (= #12 #14)
+#91 := (= #10 #12)
+#47 := (= #9 #11)
+#81 := (ite #47 #91 #92)
+#572 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #571) #81)
+#84 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #81)
+#575 := (iff #84 #572)
+#573 := (iff #81 #81)
+#574 := [refl]: #573
+#576 := [quant-intro #574]: #575
+#50 := (ite #47 #10 #14)
+#53 := (= #12 #50)
+#56 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #53)
+#93 := (iff #56 #84)
+#82 := (iff #53 #81)
+#83 := [rewrite]: #82
+#94 := [quant-intro #83]: #93
+#87 := (~ #56 #56)
+#85 := (~ #53 #53)
+#86 := [refl]: #85
+#88 := [nnf-pos #86]: #87
+#13 := (= #11 #9)
+#15 := (ite #13 #10 #14)
+#16 := (= #12 #15)
+#17 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #16)
+#57 := (iff #17 #56)
+#54 := (iff #16 #53)
+#51 := (= #15 #50)
+#48 := (iff #13 #47)
+#49 := [rewrite]: #48
+#52 := [monotonicity #49]: #51
+#55 := [monotonicity #52]: #54
+#58 := [quant-intro #55]: #57
+#46 := [asserted]: #17
+#61 := [mp #46 #58]: #56
+#78 := [mp~ #61 #88]: #56
+#95 := [mp #78 #94]: #84
+#577 := [mp #95 #576]: #572
+#226 := (not #572)
+#563 := (or #226 #68)
+#153 := (f4 f5 f6)
+#240 := (= #27 #153)
+#154 := (= f6 f6)
+#241 := (ite #154 #68 #240)
+#565 := (or #226 #241)
+#352 := (iff #565 #563)
+#231 := (iff #563 #563)
+#232 := [rewrite]: #231
+#243 := (iff #241 #68)
+#1 := true
+#233 := (ite true #68 #240)
+#173 := (iff #233 #68)
+#246 := [rewrite]: #173
+#244 := (iff #241 #233)
+#155 := (iff #154 true)
+#242 := [rewrite]: #155
+#245 := [monotonicity #242]: #244
+#247 := [trans #245 #246]: #243
+#559 := [monotonicity #247]: #352
+#566 := [trans #559 #232]: #352
+#220 := [quant-inst]: #565
+#567 := [mp #220 #566]: #563
+[unit-resolution #567 #577 #77]: false
+unsat
+743832d8228f2fc19c0448343a606555668d4291 85 0
+#2 := false
+decl f4 :: (-> S2 S3 S4)
+decl f6 :: S3
+#25 := f6
+decl f7 :: S2
+#28 := f7
+#31 := (f4 f7 f6)
+decl f3 :: (-> S2 S3 S4 S3 S4)
 decl f8 :: S4
-#13 := f8
-decl f7 :: S3
-#12 := f7
-#14 := (f6 f7 f3 f8)
-#16 := (f6 #14 f4 f9)
-#17 := (f5 #16 f3)
-#56 := (= f8 #17)
-#173 := (f5 #14 f3)
-#264 := (= #17 #173)
-#577 := (iff #264 #56)
-#214 := (iff #56 #264)
-#567 := (= #173 #17)
-#574 := (iff #567 #264)
+#29 := f8
+decl f5 :: S3
+#24 := f5
+#30 := (f3 f7 f5 f8 f6)
+#32 := (= #30 #31)
+#161 := (= f8 #30)
+#26 := (= f5 f6)
+#248 := (ite #26 #161 #32)
+#252 := (not #248)
+#81 := (not #32)
+#73 := (or #26 #32)
+#77 := (not #73)
+#27 := (not #26)
+#33 := (implies #27 #32)
+#34 := (not #33)
+#78 := (iff #34 #77)
+#75 := (iff #33 #73)
+#76 := [rewrite]: #75
+#79 := [monotonicity #76]: #78
+#72 := [asserted]: #34
+#82 := [mp #72 #79]: #77
+#83 := [not-or-elim #82]: #81
+#80 := [not-or-elim #82]: #27
+#254 := (or #252 #26 #32)
+#251 := [def-axiom]: #254
+#162 := [unit-resolution #251 #80 #83]: #252
+#11 := (:var 0 S3)
+#10 := (:var 1 S4)
+#9 := (:var 2 S3)
+#8 := (:var 3 S2)
+#12 := (f3 #8 #9 #10 #11)
+#579 := (pattern #12)
+#14 := (f4 #8 #11)
+#102 := (= #12 #14)
+#101 := (= #10 #12)
+#52 := (= #9 #11)
+#89 := (ite #52 #101 #102)
+#580 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #579) #89)
+#94 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #89)
+#583 := (iff #94 #580)
+#581 := (iff #89 #89)
+#582 := [refl]: #581
+#584 := [quant-intro #582]: #583
+#55 := (ite #52 #10 #14)
+#58 := (= #12 #55)
+#61 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #58)
+#91 := (iff #61 #94)
+#90 := (iff #58 #89)
+#93 := [rewrite]: #90
+#92 := [quant-intro #93]: #91
+#97 := (~ #61 #61)
+#95 := (~ #58 #58)
+#96 := [refl]: #95
+#98 := [nnf-pos #96]: #97
+#13 := (= #11 #9)
+#15 := (ite #13 #10 #14)
+#16 := (= #12 #15)
+#17 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #16)
+#62 := (iff #17 #61)
+#59 := (iff #16 #58)
+#56 := (= #15 #55)
+#53 := (iff #13 #52)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#60 := [monotonicity #57]: #59
+#63 := [quant-intro #60]: #62
+#51 := [asserted]: #17
+#66 := [mp #51 #63]: #61
+#86 := [mp~ #66 #98]: #61
+#103 := [mp #86 #92]: #94
+#585 := [mp #103 #584]: #580
+#163 := (not #580)
+#250 := (or #163 #248)
+#241 := [quant-inst]: #250
+[unit-resolution #241 #585 #162]: false
+unsat
+30efae1315ee3c7e9d8be67219725930610bf286 158 0
+#2 := false
+decl f3 :: (-> S2 S3 S4)
+decl f5 :: S3
+#26 := f5
+decl f4 :: (-> S2 S3 S4 S2)
+decl f9 :: S4
+#33 := f9
+decl f6 :: S3
+#27 := f6
+decl f8 :: S4
+#31 := f8
+decl f7 :: S2
+#30 := f7
+#32 := (f4 f7 f5 f8)
+#34 := (f4 #32 f6 f9)
+#35 := (f3 #34 f5)
+#77 := (= f8 #35)
+#173 := (f3 #32 f5)
+#260 := (= #35 #173)
+#577 := (iff #260 #77)
+#214 := (iff #77 #260)
+#567 := (= #173 #35)
+#574 := (iff #567 #260)
 #576 := [commutativity]: #574
-#573 := (iff #56 #567)
-#260 := (= f8 #173)
-#23 := (:var 0 S4)
-#22 := (:var 1 S2)
-#21 := (:var 2 S3)
-#24 := (f6 #21 #22 #23)
-#591 := (pattern #24)
-#25 := (f5 #24 #22)
-#75 := (= #23 #25)
-#593 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) (:pat #591) #75)
-#78 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #75)
-#592 := (iff #78 #593)
-#595 := (iff #593 #593)
-#596 := [rewrite]: #595
-#594 := [rewrite]: #592
-#597 := [trans #594 #596]: #592
-#109 := (~ #78 #78)
-#107 := (~ #75 #75)
-#108 := [refl]: #107
-#110 := [nnf-pos #108]: #109
-#26 := (= #25 #23)
-#27 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #26)
-#79 := (iff #27 #78)
-#76 := (iff #26 #75)
-#77 := [rewrite]: #76
-#80 := [quant-intro #77]: #79
-#74 := [asserted]: #27
-#83 := [mp #74 #80]: #78
-#101 := [mp~ #83 #110]: #78
-#598 := [mp #101 #597]: #593
-#175 := (not #593)
-#262 := (or #175 #260)
-#253 := [quant-inst]: #262
-#572 := [unit-resolution #253 #598]: #260
+#573 := (iff #77 #567)
+#239 := (= f8 #173)
+#21 := (:var 0 S4)
+#20 := (:var 1 S3)
+#19 := (:var 2 S2)
+#22 := (f4 #19 #20 #21)
+#598 := (pattern #22)
+#23 := (f3 #22 #20)
+#69 := (= #21 #23)
+#600 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #598) #69)
+#73 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #69)
+#599 := (iff #73 #600)
+#602 := (iff #600 #600)
+#603 := [rewrite]: #602
+#601 := [rewrite]: #599
+#604 := [trans #601 #603]: #599
+#99 := (~ #73 #73)
+#96 := (~ #69 #69)
+#111 := [refl]: #96
+#100 := [nnf-pos #111]: #99
+#24 := (= #23 #21)
+#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #24)
+#74 := (iff #25 #73)
+#71 := (iff #24 #69)
+#72 := [rewrite]: #71
+#75 := [quant-intro #72]: #74
+#68 := [asserted]: #25
+#78 := [mp #68 #75]: #73
+#112 := [mp~ #78 #100]: #73
+#605 := [mp #112 #604]: #600
+#566 := (not #600)
+#227 := (or #566 #239)
+#228 := [quant-inst]: #227
+#572 := [unit-resolution #228 #605]: #239
 #209 := [monotonicity #572]: #573
 #215 := [trans #209 #576]: #214
 #575 := [symm #215]: #577
-#265 := (= f9 #17)
-#10 := (= f3 f4)
-#585 := (ite #10 #265 #264)
-#32 := (:var 0 S2)
-#30 := (:var 1 S4)
-#29 := (:var 2 S2)
-#28 := (:var 3 S3)
-#31 := (f6 #28 #29 #30)
-#33 := (f5 #31 #32)
-#599 := (pattern #33)
-#35 := (f5 #28 #32)
-#95 := (= #33 #35)
-#98 := (= #30 #33)
-#82 := (= #29 #32)
-#105 := (ite #82 #98 #95)
-#600 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) (:pat #599) #105)
-#112 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) #105)
-#603 := (iff #112 #600)
-#601 := (iff #105 #105)
-#602 := [refl]: #601
-#604 := [quant-intro #602]: #603
-#86 := (ite #82 #30 #35)
-#89 := (= #33 #86)
-#92 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) #89)
-#113 := (iff #92 #112)
-#106 := (iff #89 #105)
-#111 := [rewrite]: #106
-#114 := [quant-intro #111]: #113
-#103 := (~ #92 #92)
-#102 := (~ #89 #89)
-#99 := [refl]: #102
-#104 := [nnf-pos #99]: #103
-#34 := (= #32 #29)
-#36 := (ite #34 #30 #35)
-#37 := (= #33 #36)
-#38 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) #37)
-#93 := (iff #38 #92)
+#174 := (= f9 #35)
+#28 := (= f5 f6)
+#264 := (ite #28 #174 #260)
+#12 := (:var 0 S3)
+#10 := (:var 1 S4)
+#9 := (:var 2 S3)
+#8 := (:var 3 S2)
+#11 := (f4 #8 #9 #10)
+#13 := (f3 #11 #12)
+#591 := (pattern #13)
+#15 := (f3 #8 #12)
+#114 := (= #13 #15)
+#113 := (= #10 #13)
+#56 := (= #9 #12)
+#101 := (ite #56 #113 #114)
+#592 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #591) #101)
+#106 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #101)
+#595 := (iff #106 #592)
+#593 := (iff #101 #101)
+#594 := [refl]: #593
+#596 := [quant-intro #594]: #595
+#59 := (ite #56 #10 #15)
+#62 := (= #13 #59)
+#65 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #62)
+#103 := (iff #65 #106)
+#102 := (iff #62 #101)
+#105 := [rewrite]: #102
+#104 := [quant-intro #105]: #103
+#109 := (~ #65 #65)
+#107 := (~ #62 #62)
+#108 := [refl]: #107
+#110 := [nnf-pos #108]: #109
+#14 := (= #12 #9)
+#16 := (ite #14 #10 #15)
+#17 := (= #13 #16)
+#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17)
+#66 := (iff #18 #65)
+#63 := (iff #17 #62)
+#60 := (= #16 #59)
+#57 := (iff #14 #56)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#64 := [monotonicity #61]: #63
+#67 := [quant-intro #64]: #66
+#55 := [asserted]: #18
+#70 := [mp #55 #67]: #65
+#98 := [mp~ #70 #110]: #65
+#115 := [mp #98 #104]: #106
+#597 := [mp #115 #596]: #592
+#266 := (not #592)
+#263 := (or #266 #264)
+#261 := (= f6 f5)
+#175 := (ite #261 #174 #260)
+#267 := (or #266 #175)
+#583 := (iff #267 #263)
+#240 := (iff #263 #263)
+#372 := [rewrite]: #240
+#265 := (iff #175 #264)
+#262 := (iff #261 #28)
+#253 := [rewrite]: #262
+#193 := [monotonicity #253]: #265
+#585 := [monotonicity #193]: #583
+#579 := [trans #585 #372]: #583
+#246 := [quant-inst]: #267
+#251 := [mp #246 #579]: #263
+#229 := [unit-resolution #251 #597]: #264
+#252 := (not #264)
+#230 := (or #252 #260)
+#29 := (not #28)
+#84 := (or #28 #77)
+#89 := (not #84)
+#36 := (= #35 f8)
+#37 := (implies #29 #36)
+#38 := (not #37)
+#90 := (iff #38 #89)
+#87 := (iff #37 #84)
+#81 := (implies #29 #77)
+#85 := (iff #81 #84)
+#86 := [rewrite]: #85
+#82 := (iff #37 #81)
+#79 := (iff #36 #77)
+#80 := [rewrite]: #79
+#83 := [monotonicity #80]: #82
+#88 := [trans #83 #86]: #87
+#91 := [monotonicity #88]: #90
+#76 := [asserted]: #38
+#94 := [mp #76 #91]: #89
+#92 := [not-or-elim #94]: #29
+#588 := (or #252 #28 #260)
+#589 := [def-axiom]: #588
+#570 := [unit-resolution #589 #92]: #230
+#571 := [unit-resolution #570 #229]: #260
+#578 := [mp #571 #575]: #77
+#93 := (not #77)
+#95 := [not-or-elim #94]: #93
+[unit-resolution #95 #578]: false
+unsat
+7dba7b1d50601d740ade8916d8a8d7554995ac18 111 0
+#2 := false
+decl f3 :: (-> S2 S3 S4)
+decl f6 :: S3
+#27 := f6
+decl f4 :: (-> S2 S3 S4 S2)
+decl f9 :: S4
+#33 := f9
+decl f8 :: S4
+#31 := f8
+decl f5 :: S3
+#26 := f5
+decl f7 :: S2
+#30 := f7
+#32 := (f4 f7 f5 f8)
+#34 := (f4 #32 f6 f9)
+#35 := (f3 #34 f6)
+#77 := (= f9 #35)
+#93 := (not #77)
+#28 := (= f5 f6)
+#84 := (or #28 #77)
+#89 := (not #84)
+#36 := (= #35 f9)
+#29 := (not #28)
+#37 := (implies #29 #36)
+#38 := (not #37)
+#90 := (iff #38 #89)
+#87 := (iff #37 #84)
+#81 := (implies #29 #77)
+#85 := (iff #81 #84)
+#86 := [rewrite]: #85
+#82 := (iff #37 #81)
+#79 := (iff #36 #77)
+#80 := [rewrite]: #79
+#83 := [monotonicity #80]: #82
+#88 := [trans #83 #86]: #87
+#91 := [monotonicity #88]: #90
+#76 := [asserted]: #38
+#94 := [mp #76 #91]: #89
+#95 := [not-or-elim #94]: #93
+#12 := (:var 0 S3)
+#10 := (:var 1 S4)
+#9 := (:var 2 S3)
+#8 := (:var 3 S2)
+#11 := (f4 #8 #9 #10)
+#13 := (f3 #11 #12)
+#591 := (pattern #13)
+#15 := (f3 #8 #12)
+#114 := (= #13 #15)
+#113 := (= #10 #13)
+#56 := (= #9 #12)
+#101 := (ite #56 #113 #114)
+#592 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #591) #101)
+#106 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #101)
+#595 := (iff #106 #592)
+#593 := (iff #101 #101)
+#594 := [refl]: #593
+#596 := [quant-intro #594]: #595
+#59 := (ite #56 #10 #15)
+#62 := (= #13 #59)
+#65 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #62)
+#103 := (iff #65 #106)
+#102 := (iff #62 #101)
+#105 := [rewrite]: #102
+#104 := [quant-intro #105]: #103
+#109 := (~ #65 #65)
+#107 := (~ #62 #62)
+#108 := [refl]: #107
+#110 := [nnf-pos #108]: #109
+#14 := (= #12 #9)
+#16 := (ite #14 #10 #15)
+#17 := (= #13 #16)
+#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17)
+#66 := (iff #18 #65)
+#63 := (iff #17 #62)
+#60 := (= #16 #59)
+#57 := (iff #14 #56)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#64 := [monotonicity #61]: #63
+#67 := [quant-intro #64]: #66
+#55 := [asserted]: #18
+#70 := [mp #55 #67]: #65
+#98 := [mp~ #70 #110]: #65
+#115 := [mp #98 #104]: #106
+#597 := [mp #115 #596]: #592
+#246 := (not #592)
+#583 := (or #246 #77)
+#173 := (f3 #32 f6)
+#260 := (= #35 #173)
+#174 := (= f6 f6)
+#261 := (ite #174 #77 #260)
+#585 := (or #246 #261)
+#372 := (iff #585 #583)
+#251 := (iff #583 #583)
+#252 := [rewrite]: #251
+#263 := (iff #261 #77)
+#1 := true
+#253 := (ite true #77 #260)
+#193 := (iff #253 #77)
+#266 := [rewrite]: #193
+#264 := (iff #261 #253)
+#175 := (iff #174 true)
+#262 := [rewrite]: #175
+#265 := [monotonicity #262]: #264
+#267 := [trans #265 #266]: #263
+#579 := [monotonicity #267]: #372
+#586 := [trans #579 #252]: #372
+#240 := [quant-inst]: #585
+#587 := [mp #240 #586]: #583
+[unit-resolution #587 #597 #95]: false
+unsat
+3452f1abfd3f7170343f6a4081c1bff43b8b5fc7 123 0
+#2 := false
+decl f3 :: (-> S2 S3 S4)
+decl f5 :: S3
+#26 := f5
+decl f4 :: (-> S2 S3 S4 S2)
+decl f9 :: S4
+#32 := f9
+decl f6 :: S3
+#27 := f6
+decl f8 :: S4
+#30 := f8
+decl f7 :: S2
+#29 := f7
+#31 := (f4 f7 f5 f8)
+#33 := (f4 #31 f6 f9)
+#34 := (f3 #33 f5)
+#76 := (= f9 #34)
+#260 := (f3 #33 f6)
+#568 := (= #260 #34)
+#582 := (= #34 #260)
+#28 := (= f5 f6)
+#83 := (not #28)
+#84 := (or #83 #76)
+#89 := (not #84)
+#35 := (= #34 f9)
+#36 := (implies #28 #35)
+#37 := (not #36)
 #90 := (iff #37 #89)
-#87 := (= #36 #86)
-#84 := (iff #34 #82)
-#85 := [rewrite]: #84
-#88 := [monotonicity #85]: #87
+#87 := (iff #36 #84)
+#80 := (implies #28 #76)
+#85 := (iff #80 #84)
+#86 := [rewrite]: #85
+#81 := (iff #36 #80)
+#78 := (iff #35 #76)
+#79 := [rewrite]: #78
+#82 := [monotonicity #79]: #81
+#88 := [trans #82 #86]: #87
 #91 := [monotonicity #88]: #90
-#94 := [quant-intro #91]: #93
-#81 := [asserted]: #38
-#97 := [mp #81 #94]: #92
-#100 := [mp~ #97 #104]: #92
-#115 := [mp #100 #114]: #112
-#605 := [mp #115 #604]: #600
-#579 := (not #600)
-#251 := (or #579 #585)
-#263 := (= f4 f3)
-#267 := (ite #263 #265 #264)
-#252 := (or #579 #267)
+#75 := [asserted]: #37
+#94 := [mp #75 #91]: #89
+#92 := [not-or-elim #94]: #28
+#230 := [monotonicity #92]: #582
+#569 := [symm #230]: #568
+#261 := (= f9 #260)
+#12 := (:var 0 S3)
+#10 := (:var 1 S4)
+#9 := (:var 2 S3)
+#8 := (:var 3 S2)
+#11 := (f4 #8 #9 #10)
+#13 := (f3 #11 #12)
+#591 := (pattern #13)
+#15 := (f3 #8 #12)
+#114 := (= #13 #15)
+#113 := (= #10 #13)
+#55 := (= #9 #12)
+#101 := (ite #55 #113 #114)
+#592 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #591) #101)
+#106 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #101)
+#595 := (iff #106 #592)
+#593 := (iff #101 #101)
+#594 := [refl]: #593
+#596 := [quant-intro #594]: #595
+#58 := (ite #55 #10 #15)
+#61 := (= #13 #58)
+#64 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #61)
+#103 := (iff #64 #106)
+#102 := (iff #61 #101)
+#105 := [rewrite]: #102
+#104 := [quant-intro #105]: #103
+#109 := (~ #64 #64)
+#107 := (~ #61 #61)
+#108 := [refl]: #107
+#110 := [nnf-pos #108]: #109
+#14 := (= #12 #9)
+#16 := (ite #14 #10 #15)
+#17 := (= #13 #16)
+#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17)
+#65 := (iff #18 #64)
+#62 := (iff #17 #61)
+#59 := (= #16 #58)
+#56 := (iff #14 #55)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#63 := [monotonicity #60]: #62
+#66 := [quant-intro #63]: #65
+#54 := [asserted]: #18
+#69 := [mp #54 #66]: #64
+#98 := [mp~ #69 #110]: #64
+#115 := [mp #98 #104]: #106
+#597 := [mp #115 #596]: #592
+#579 := (not #592)
+#251 := (or #579 #261)
+#173 := (f3 #31 f6)
+#174 := (= #260 #173)
+#175 := (= f6 f6)
+#262 := (ite #175 #261 #174)
+#252 := (or #579 #262)
 #587 := (iff #252 #251)
 #589 := (iff #251 #251)
 #584 := [rewrite]: #589
-#240 := (iff #267 #585)
-#246 := (iff #263 #10)
-#583 := [rewrite]: #246
-#372 := [monotonicity #583]: #240
+#240 := (iff #262 #261)
+#265 := (= #173 #260)
+#1 := true
+#263 := (ite true #261 #265)
+#583 := (iff #263 #261)
+#585 := [rewrite]: #583
+#267 := (iff #262 #263)
+#193 := (iff #174 #265)
+#266 := [rewrite]: #193
+#253 := (iff #175 true)
+#264 := [rewrite]: #253
+#246 := [monotonicity #264 #266]: #267
+#372 := [trans #246 #585]: #240
 #588 := [monotonicity #372]: #587
 #590 := [trans #588 #584]: #587
 #586 := [quant-inst]: #252
 #580 := [mp #586 #590]: #251
-#568 := [unit-resolution #580 #605]: #585
-#238 := (not #585)
-#569 := (or #238 #264)
-#11 := (not #10)
-#62 := (or #10 #56)
-#67 := (not #62)
-#18 := (= #17 f8)
-#19 := (implies #11 #18)
-#20 := (not #19)
-#68 := (iff #20 #67)
-#65 := (iff #19 #62)
-#59 := (implies #11 #56)
-#63 := (iff #59 #62)
-#64 := [rewrite]: #63
-#60 := (iff #19 #59)
-#57 := (iff #18 #56)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#66 := [trans #61 #64]: #65
-#69 := [monotonicity #66]: #68
-#55 := [asserted]: #20
-#72 := [mp #55 #69]: #67
-#70 := [not-or-elim #72]: #11
-#239 := (or #238 #10 #264)
-#582 := [def-axiom]: #239
-#570 := [unit-resolution #582 #70]: #569
-#571 := [unit-resolution #570 #568]: #264
-#578 := [mp #571 #575]: #56
-#71 := (not #56)
-#73 := [not-or-elim #72]: #71
-[unit-resolution #73 #578]: false
-unsat
-866d440edf643384cbf5eede7548231cbd17d588 144 0
-#2 := false
-decl f12 :: S3
-#17 := f12
-decl f9 :: S3
-#10 := f9
-#23 := (= f9 f12)
-decl f3 :: (-> S2 S3)
-decl f4 :: (-> S4 S2)
-decl f5 :: (-> S5 S2 S4)
-decl f7 :: (-> S5 S3 S2)
-decl f11 :: S5
-#16 := f11
-#18 := (f7 f11 f12)
-decl f10 :: S5
-#15 := f10
-#19 := (f5 f10 #18)
-#20 := (f4 #19)
-#21 := (f3 #20)
-decl f8 :: S5
-#9 := f8
-#11 := (f7 f8 f9)
-decl f6 :: S5
-#8 := f6
-#12 := (f5 f6 #11)
-#13 := (f4 #12)
-#14 := (f3 #13)
-#22 := (= #14 #21)
-#24 := (iff #22 #23)
-#315 := (= #21 f12)
-#626 := (f3 #18)
-#312 := (= #626 f12)
-#627 := (= f12 #626)
-#27 := (:var 0 S3)
-#26 := (:var 1 S5)
-#28 := (f7 #26 #27)
-#630 := (pattern #28)
-#37 := (f3 #28)
-#92 := (= #27 #37)
-#644 := (forall (vars (?v0 S5) (?v1 S3)) (:pat #630) #92)
-#96 := (forall (vars (?v0 S5) (?v1 S3)) #92)
-#647 := (iff #96 #644)
-#645 := (iff #92 #92)
-#646 := [refl]: #645
-#648 := [quant-intro #646]: #647
-#131 := (~ #96 #96)
-#145 := (~ #92 #92)
-#146 := [refl]: #145
-#132 := [nnf-pos #146]: #131
-#38 := (= #37 #27)
-#39 := (forall (vars (?v0 S5) (?v1 S3)) #38)
-#97 := (iff #39 #96)
-#94 := (iff #38 #92)
-#95 := [rewrite]: #94
-#98 := [quant-intro #95]: #97
-#91 := [asserted]: #39
-#101 := [mp #91 #98]: #96
-#147 := [mp~ #101 #132]: #96
-#649 := [mp #147 #648]: #644
-#290 := (not #644)
-#277 := (or #290 #627)
-#282 := [quant-inst]: #277
-#323 := [unit-resolution #282 #649]: #627
-#313 := [symm #323]: #312
-#602 := (= #21 #626)
-#601 := (= #20 #18)
-#607 := (= #18 #20)
-#32 := (:var 0 S2)
-#33 := (f5 #26 #32)
-#637 := (pattern #33)
-#40 := (f4 #33)
-#100 := (= #32 #40)
-#650 := (forall (vars (?v0 S5) (?v1 S2)) (:pat #637) #100)
-#104 := (forall (vars (?v0 S5) (?v1 S2)) #100)
-#653 := (iff #104 #650)
-#651 := (iff #100 #100)
-#652 := [refl]: #651
-#654 := [quant-intro #652]: #653
-#133 := (~ #104 #104)
-#148 := (~ #100 #100)
-#149 := [refl]: #148
-#134 := [nnf-pos #149]: #133
-#41 := (= #40 #32)
-#42 := (forall (vars (?v0 S5) (?v1 S2)) #41)
-#105 := (iff #42 #104)
-#102 := (iff #41 #100)
-#103 := [rewrite]: #102
-#106 := [quant-intro #103]: #105
-#99 := [asserted]: #42
-#109 := [mp #99 #106]: #104
-#150 := [mp~ #109 #134]: #104
-#655 := [mp #150 #654]: #650
-#267 := (not #650)
-#606 := (or #267 #607)
-#612 := [quant-inst]: #606
-#597 := [unit-resolution #612 #655]: #607
-#598 := [symm #597]: #601
-#311 := [monotonicity #598]: #602
-#593 := [trans #311 #313]: #315
-#587 := (= #14 f9)
-#306 := (f3 #11)
-#585 := (= #306 f9)
-#285 := (= f9 #306)
-#291 := (or #290 #285)
-#625 := [quant-inst]: #291
-#594 := [unit-resolution #625 #649]: #285
-#586 := [symm #594]: #585
-#592 := (= #14 #306)
-#591 := (= #13 #11)
-#620 := (= #11 #13)
-#268 := (or #267 #620)
-#269 := [quant-inst]: #268
-#307 := [unit-resolution #269 #655]: #620
-#595 := [symm #307]: #591
-#596 := [monotonicity #595]: #592
-#582 := [trans #596 #586]: #587
-#583 := [monotonicity #582 #593]: #24
-#301 := (not #23)
-#71 := (not #22)
-#588 := (iff #71 #301)
-#589 := [monotonicity #583]: #588
-#220 := [hypothesis]: #71
-#584 := [mp #220 #589]: #301
-#300 := (or #23 #22)
-#72 := (iff #23 #71)
-#25 := (not #24)
-#73 := (iff #25 #72)
-#74 := [rewrite]: #73
-#70 := [asserted]: #25
-#77 := [mp #70 #74]: #72
-#212 := (not #72)
-#299 := (or #23 #22 #212)
-#213 := [def-axiom]: #299
-#214 := [unit-resolution #213 #77]: #300
-#599 := [unit-resolution #214 #220]: #23
-#590 := [unit-resolution #599 #584]: false
-#431 := [lemma #590]: #22
-#433 := [mp #431 #583]: #23
-#304 := (or #301 #71)
-#292 := (or #301 #71 #212)
-#303 := [def-axiom]: #292
-#232 := [unit-resolution #303 #77]: #304
-#432 := [unit-resolution #232 #431]: #301
-[unit-resolution #432 #433]: false
-unsat
-3e56e54d471720a3a5d996ce27f17fcb7694aeb0 72 0
-#2 := false
-decl f6 :: (-> S3 S2 S4 S3)
-#23 := (:var 0 S4)
-#22 := (:var 1 S2)
-#21 := (:var 2 S3)
-#24 := (f6 #21 #22 #23)
-#591 := (pattern #24)
-decl f5 :: (-> S3 S2 S4)
-#25 := (f5 #24 #22)
-#75 := (= #23 #25)
-#593 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) (:pat #591) #75)
-#78 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #75)
-#592 := (iff #78 #593)
-#595 := (iff #593 #593)
-#596 := [rewrite]: #595
-#594 := [rewrite]: #592
-#597 := [trans #594 #596]: #592
-#109 := (~ #78 #78)
-#107 := (~ #75 #75)
-#108 := [refl]: #107
-#110 := [nnf-pos #108]: #109
-#26 := (= #25 #23)
-#27 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #26)
-#79 := (iff #27 #78)
-#76 := (iff #26 #75)
-#77 := [rewrite]: #76
-#80 := [quant-intro #77]: #79
-#74 := [asserted]: #27
-#83 := [mp #74 #80]: #78
-#101 := [mp~ #83 #110]: #78
-#598 := [mp #101 #597]: #593
-decl f4 :: S2
-#9 := f4
+#239 := [unit-resolution #580 #597]: #261
+#570 := [trans #239 #569]: #76
+#93 := (not #76)
+#95 := [not-or-elim #94]: #93
+[unit-resolution #95 #570]: false
+unsat
+b43b3bb9777320dbf682eab44f21423505ac2f47 190 0
+#2 := false
+decl f3 :: (-> S2 S3 S4)
+decl f7 :: S3
+#28 := f7
+decl f8 :: S2
+#30 := f8
+#36 := (f3 f8 f7)
+decl f4 :: (-> S2 S3 S4 S2)
+decl f10 :: S4
+#33 := f10
+decl f6 :: S3
+#27 := f6
 decl f9 :: S4
-#15 := f9
-decl f8 :: S4
-#13 := f8
-decl f3 :: S2
-#8 := f3
-decl f7 :: S3
-#12 := f7
-#14 := (f6 f7 f3 f8)
-#16 := (f6 #14 f4 f9)
-#17 := (f5 #16 f4)
-#56 := (= f9 #17)
-#71 := (not #56)
-#10 := (= f3 f4)
-#62 := (or #10 #56)
-#67 := (not #62)
-#18 := (= #17 f9)
-#11 := (not #10)
-#19 := (implies #11 #18)
-#20 := (not #19)
-#68 := (iff #20 #67)
-#65 := (iff #19 #62)
-#59 := (implies #11 #56)
-#63 := (iff #59 #62)
-#64 := [rewrite]: #63
-#60 := (iff #19 #59)
-#57 := (iff #18 #56)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#66 := [trans #61 #64]: #65
-#69 := [monotonicity #66]: #68
-#55 := [asserted]: #20
-#72 := [mp #55 #69]: #67
-#73 := [not-or-elim #72]: #71
-#175 := (not #593)
-#264 := (or #175 #56)
-#265 := [quant-inst]: #264
-[unit-resolution #265 #73 #598]: false
-unsat
-2ecc5cb618eddd0d10a797b2211747ef8a2776e2 103 0
-#2 := false
-decl f6 :: S3
-#9 := f6
+#31 := f9
 decl f5 :: S3
-#8 := f5
-#14 := (= f5 f6)
-decl f7 :: (-> S2 S3)
-decl f4 :: (-> S3 S3 S2)
-#10 := (f4 f5 f6)
-#12 := (f7 #10)
-decl f3 :: (-> S2 S3)
-#11 := (f3 #10)
-#13 := (= #11 #12)
-#15 := (iff #13 #14)
-#558 := (iff #14 #13)
-#241 := (= f6 #12)
-#18 := (:var 0 S3)
-#17 := (:var 1 S3)
-#19 := (f4 #17 #18)
-#569 := (pattern #19)
-#23 := (f7 #19)
-#62 := (= #18 #23)
-#576 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #569) #62)
-#66 := (forall (vars (?v0 S3) (?v1 S3)) #62)
-#579 := (iff #66 #576)
-#577 := (iff #62 #62)
-#578 := [refl]: #577
-#580 := [quant-intro #578]: #579
-#83 := (~ #66 #66)
-#82 := (~ #62 #62)
-#80 := [refl]: #82
-#84 := [nnf-pos #80]: #83
-#24 := (= #23 #18)
-#25 := (forall (vars (?v0 S3) (?v1 S3)) #24)
-#67 := (iff #25 #66)
-#64 := (iff #24 #62)
-#65 := [rewrite]: #64
+#26 := f5
+#32 := (f4 f8 f5 f9)
+#34 := (f4 #32 f6 f10)
+#35 := (f3 #34 f7)
+#37 := (= #35 #36)
+#583 := (f3 #32 f5)
+#567 := (f4 f8 f5 #583)
+#203 := (f3 #567 f7)
+#208 := (= #203 #36)
+#559 := (= #36 #203)
+#569 := (= #203 #583)
+#168 := (= f5 f7)
+#282 := (ite #168 #569 #559)
+#12 := (:var 0 S3)
+#10 := (:var 1 S4)
+#9 := (:var 2 S3)
+#8 := (:var 3 S2)
+#11 := (f4 #8 #9 #10)
+#13 := (f3 #11 #12)
+#585 := (pattern #13)
+#15 := (f3 #8 #12)
+#108 := (= #13 #15)
+#107 := (= #10 #13)
+#57 := (= #9 #12)
+#95 := (ite #57 #107 #108)
+#586 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #585) #95)
+#100 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #95)
+#589 := (iff #100 #586)
+#587 := (iff #95 #95)
+#588 := [refl]: #587
+#590 := [quant-intro #588]: #589
+#60 := (ite #57 #10 #15)
+#63 := (= #13 #60)
+#66 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #63)
+#97 := (iff #66 #100)
+#96 := (iff #63 #95)
+#99 := [rewrite]: #96
+#98 := [quant-intro #99]: #97
+#103 := (~ #66 #66)
+#101 := (~ #63 #63)
+#102 := [refl]: #101
+#104 := [nnf-pos #102]: #103
+#14 := (= #12 #9)
+#16 := (ite #14 #10 #15)
+#17 := (= #13 #16)
+#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17)
+#67 := (iff #18 #66)
+#64 := (iff #17 #63)
+#61 := (= #16 #60)
+#58 := (iff #14 #57)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#65 := [monotonicity #62]: #64
 #68 := [quant-intro #65]: #67
-#61 := [asserted]: #25
-#71 := [mp #61 #68]: #66
-#77 := [mp~ #71 #84]: #66
-#581 := [mp #77 #580]: #576
-#350 := (not #576)
-#557 := (or #350 #241)
-#229 := [quant-inst]: #557
-#562 := [unit-resolution #229 #581]: #241
-#244 := (= f5 #11)
-#20 := (f3 #19)
-#54 := (= #17 #20)
-#570 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #569) #54)
-#58 := (forall (vars (?v0 S3) (?v1 S3)) #54)
-#573 := (iff #58 #570)
-#571 := (iff #54 #54)
-#572 := [refl]: #571
-#574 := [quant-intro #572]: #573
-#91 := (~ #58 #58)
-#89 := (~ #54 #54)
-#90 := [refl]: #89
-#92 := [nnf-pos #90]: #91
-#21 := (= #20 #17)
-#22 := (forall (vars (?v0 S3) (?v1 S3)) #21)
-#59 := (iff #22 #58)
-#56 := (iff #21 #54)
-#57 := [rewrite]: #56
-#60 := [quant-intro #57]: #59
-#53 := [asserted]: #22
-#63 := [mp #53 #60]: #58
-#81 := [mp~ #63 #92]: #58
-#575 := [mp #81 #574]: #570
-#224 := (not #570)
-#561 := (or #224 #244)
-#563 := [quant-inst]: #561
-#568 := [unit-resolution #563 #575]: #244
-#216 := [monotonicity #568 #562]: #558
-#221 := [symm #216]: #15
-#240 := (not #14)
-#49 := (not #13)
-#559 := (iff #49 #240)
-#217 := [monotonicity #221]: #559
-#230 := [hypothesis]: #49
-#560 := [mp #230 #217]: #240
-#239 := (or #14 #13)
-#50 := (iff #14 #49)
-#16 := (not #15)
-#51 := (iff #16 #50)
-#52 := [rewrite]: #51
-#48 := [asserted]: #16
-#55 := [mp #48 #52]: #50
-#151 := (not #50)
-#238 := (or #14 #13 #151)
-#152 := [def-axiom]: #238
-#153 := [unit-resolution #152 #55]: #239
-#564 := [unit-resolution #153 #230]: #14
-#201 := [unit-resolution #564 #560]: false
-#544 := [lemma #201]: #13
-#206 := [mp #544 #221]: #14
-#243 := (or #240 #49)
-#231 := (or #240 #49 #151)
-#242 := [def-axiom]: #231
-#171 := [unit-resolution #242 #55]: #243
-#205 := [unit-resolution #171 #544]: #240
-[unit-resolution #205 #206]: false
-unsat
-40581b0e6cc161d835ae1db56e86336b57a7ee1b 81 0
-#2 := false
-decl f5 :: (-> S3 S2 S4)
-decl f3 :: S2
-#8 := f3
-decl f6 :: (-> S3 S2 S4 S3)
-decl f9 :: S4
-#14 := f9
-decl f4 :: S2
-#9 := f4
-decl f8 :: S4
-#12 := f8
-decl f7 :: S3
-#11 := f7
-#13 := (f6 f7 f3 f8)
-#15 := (f6 #13 f4 f9)
-#16 := (f5 #15 f3)
-#55 := (= f9 #16)
-#261 := (f5 #15 f4)
-#228 := (= #261 #16)
-#566 := (= #16 #261)
-#10 := (= f3 f4)
-#61 := (not #10)
-#62 := (or #61 #55)
-#67 := (not #62)
-#17 := (= #16 f9)
-#18 := (implies #10 #17)
-#19 := (not #18)
-#68 := (iff #19 #67)
-#65 := (iff #18 #62)
-#58 := (implies #10 #55)
-#63 := (iff #58 #62)
-#64 := [rewrite]: #63
-#59 := (iff #18 #58)
-#56 := (iff #17 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#66 := [trans #60 #64]: #65
-#69 := [monotonicity #66]: #68
-#54 := [asserted]: #19
-#72 := [mp #54 #69]: #67
-#70 := [not-or-elim #72]: #10
-#227 := [monotonicity #70]: #566
-#229 := [symm #227]: #228
-#175 := (= f9 #261)
-#22 := (:var 0 S4)
-#21 := (:var 1 S2)
-#20 := (:var 2 S3)
-#23 := (f6 #20 #21 #22)
-#591 := (pattern #23)
-#24 := (f5 #23 #21)
-#75 := (= #22 #24)
-#593 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) (:pat #591) #75)
-#78 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #75)
-#592 := (iff #78 #593)
-#595 := (iff #593 #593)
-#596 := [rewrite]: #595
-#594 := [rewrite]: #592
-#597 := [trans #594 #596]: #592
-#109 := (~ #78 #78)
-#107 := (~ #75 #75)
-#108 := [refl]: #107
-#110 := [nnf-pos #108]: #109
-#25 := (= #24 #22)
-#26 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #25)
-#79 := (iff #26 #78)
-#76 := (iff #25 #75)
-#77 := [rewrite]: #76
-#80 := [quant-intro #77]: #79
-#74 := [asserted]: #26
-#83 := [mp #74 #80]: #78
-#101 := [mp~ #83 #110]: #78
-#598 := [mp #101 #597]: #593
-#262 := (not #593)
-#266 := (or #262 #175)
-#263 := [quant-inst]: #266
-#223 := [unit-resolution #263 #598]: #175
-#230 := [trans #223 #229]: #55
-#71 := (not #55)
-#73 := [not-or-elim #72]: #71
-[unit-resolution #73 #230]: false
-unsat
-7886f0fda259625a913921a1bd89d90840edec3d 111 0
-#2 := false
-decl f9 :: (-> S2 S3)
-decl f7 :: S2
-#13 := f7
-#18 := (f9 f7)
-decl f8 :: (-> S2 S3)
-decl f3 :: S2
-#8 := f3
-#17 := (f8 f3)
-#19 := (= #17 #18)
-decl f4 :: (-> S3 S3 S2)
-decl f5 :: S3
-#9 := f5
-decl f6 :: S3
-#10 := f6
-#14 := (f4 f6 f5)
-#258 := (f9 #14)
-#220 := (= #258 #18)
-#230 := (= #18 #258)
-#15 := (= f7 #14)
-#11 := (f4 f5 f6)
-#12 := (= f3 #11)
-#16 := (and #12 #15)
-#54 := (not #16)
-#55 := (or #54 #19)
-#58 := (not #55)
-#20 := (implies #16 #19)
-#21 := (not #20)
-#59 := (iff #21 #58)
-#56 := (iff #20 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#53 := [asserted]: #21
-#63 := [mp #53 #60]: #58
-#61 := [not-or-elim #63]: #16
-#64 := [and-elim #61]: #15
-#573 := [monotonicity #64]: #230
-#221 := [symm #573]: #220
-#561 := (= #17 #258)
-#237 := (= f5 #258)
-#23 := (:var 0 S3)
-#22 := (:var 1 S3)
-#24 := (f4 #22 #23)
-#582 := (pattern #24)
-#28 := (f9 #24)
-#75 := (= #23 #28)
-#589 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #582) #75)
-#79 := (forall (vars (?v0 S3) (?v1 S3)) #75)
-#592 := (iff #79 #589)
-#590 := (iff #75 #75)
-#591 := [refl]: #590
-#593 := [quant-intro #591]: #592
-#100 := (~ #79 #79)
-#99 := (~ #75 #75)
-#96 := [refl]: #99
-#101 := [nnf-pos #96]: #100
-#29 := (= #28 #23)
-#30 := (forall (vars (?v0 S3) (?v1 S3)) #29)
-#80 := (iff #30 #79)
-#77 := (iff #29 #75)
-#78 := [rewrite]: #77
-#81 := [quant-intro #78]: #80
-#74 := [asserted]: #30
-#84 := [mp #74 #81]: #79
-#97 := [mp~ #84 #101]: #79
-#594 := [mp #97 #593]: #589
-#184 := (not #589)
-#570 := (or #184 #237)
-#242 := [quant-inst]: #570
-#581 := [unit-resolution #242 #594]: #237
-#559 := (= #17 f5)
-#164 := (f8 #11)
-#218 := (= #164 f5)
-#251 := (= f5 #164)
-#25 := (f8 #24)
-#68 := (= #22 #25)
-#583 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #582) #68)
-#71 := (forall (vars (?v0 S3) (?v1 S3)) #68)
-#586 := (iff #71 #583)
-#584 := (iff #68 #68)
-#585 := [refl]: #584
-#587 := [quant-intro #585]: #586
-#108 := (~ #71 #71)
-#106 := (~ #68 #68)
-#107 := [refl]: #106
-#109 := [nnf-pos #107]: #108
-#26 := (= #25 #22)
-#27 := (forall (vars (?v0 S3) (?v1 S3)) #26)
-#72 := (iff #27 #71)
-#69 := (iff #26 #68)
-#70 := [rewrite]: #69
-#73 := [quant-intro #70]: #72
-#67 := [asserted]: #27
-#76 := [mp #67 #73]: #71
-#98 := [mp~ #76 #109]: #71
-#588 := [mp #98 #587]: #583
-#166 := (not #583)
-#253 := (or #166 #251)
-#244 := [quant-inst]: #253
-#575 := [unit-resolution #244 #588]: #251
-#219 := [symm #575]: #218
-#234 := (= #17 #164)
-#62 := [and-elim #61]: #12
-#572 := [monotonicity #62]: #234
-#560 := [trans #572 #219]: #559
-#562 := [trans #560 #581]: #561
-#563 := [trans #562 #221]: #19
-#65 := (not #19)
-#66 := [not-or-elim #63]: #65
-[unit-resolution #66 #563]: false
-unsat
-8cd68e8e260f2f18965c0617f7c8e0414cba4ea7 187 0
-#2 := false
-decl f6 :: (-> S3 S2 S4)
-decl f5 :: S2
-#10 := f5
-decl f8 :: S3
-#12 := f8
-#18 := (f6 f8 f5)
-decl f7 :: (-> S3 S2 S4 S3)
-decl f10 :: S4
-#15 := f10
-decl f4 :: S2
-#9 := f4
-decl f9 :: S4
-#13 := f9
-decl f3 :: S2
-#8 := f3
-#14 := (f7 f8 f3 f9)
-#16 := (f7 #14 f4 f10)
-#17 := (f6 #16 f5)
-#19 := (= #17 #18)
-#246 := (f6 #14 f3)
-#560 := (f7 f8 f3 #246)
-#536 := (f6 #560 f5)
-#365 := (= #536 #18)
-#521 := (= #18 #536)
-#367 := (= #246 #536)
-#168 := (= f3 f5)
-#525 := (ite #168 #367 #521)
-#33 := (:var 0 S2)
-#31 := (:var 1 S4)
-#30 := (:var 2 S2)
-#29 := (:var 3 S3)
-#32 := (f7 #29 #30 #31)
-#34 := (f6 #32 #33)
-#593 := (pattern #34)
-#36 := (f6 #29 #33)
-#89 := (= #34 #36)
-#92 := (= #31 #34)
-#76 := (= #30 #33)
-#99 := (ite #76 #92 #89)
-#594 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) (:pat #593) #99)
-#106 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) #99)
-#597 := (iff #106 #594)
-#595 := (iff #99 #99)
-#596 := [refl]: #595
-#598 := [quant-intro #596]: #597
-#80 := (ite #76 #31 #36)
-#83 := (= #34 #80)
-#86 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) #83)
-#107 := (iff #86 #106)
-#100 := (iff #83 #99)
-#105 := [rewrite]: #100
-#108 := [quant-intro #105]: #107
-#97 := (~ #86 #86)
-#96 := (~ #83 #83)
-#93 := [refl]: #96
-#98 := [nnf-pos #93]: #97
-#35 := (= #33 #30)
-#37 := (ite #35 #31 #36)
-#38 := (= #34 #37)
-#39 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) #38)
-#87 := (iff #39 #86)
-#84 := (iff #38 #83)
-#81 := (= #37 #80)
-#78 := (iff #35 #76)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#85 := [monotonicity #82]: #84
-#88 := [quant-intro #85]: #87
-#75 := [asserted]: #39
-#91 := [mp #75 #88]: #86
-#94 := [mp~ #91 #98]: #86
-#109 := [mp #94 #108]: #106
-#599 := [mp #109 #598]: #594
-#221 := (not #594)
-#408 := (or #221 #525)
-#368 := (ite #168 #367 #365)
-#409 := (or #221 #368)
-#369 := (iff #409 #408)
-#419 := (iff #408 #408)
-#514 := [rewrite]: #419
-#523 := (iff #368 #525)
-#522 := (iff #365 #521)
-#524 := [rewrite]: #522
-#526 := [monotonicity #524]: #523
-#517 := [monotonicity #526]: #369
-#515 := [trans #517 #514]: #369
-#410 := [quant-inst]: #409
-#518 := [mp #410 #515]: #408
-#498 := [unit-resolution #518 #599]: #525
-#403 := (not #525)
-#511 := (or #403 #521)
+#56 := [asserted]: #18
+#71 := [mp #56 #68]: #66
+#92 := [mp~ #71 #104]: #66
+#109 := [mp #92 #98]: #100
+#591 := [mp #109 #590]: #586
+#584 := (not #586)
+#284 := (or #584 #282)
+#209 := (= #583 #203)
+#571 := (ite #168 #209 #208)
+#175 := (or #584 #571)
+#555 := (iff #175 #284)
+#278 := (iff #284 #284)
+#552 := [rewrite]: #278
+#283 := (iff #571 #282)
+#265 := (iff #208 #559)
+#281 := [rewrite]: #265
+#572 := (iff #209 #569)
+#558 := [rewrite]: #572
+#269 := [monotonicity #558 #281]: #283
+#277 := [monotonicity #269]: #555
+#556 := [trans #277 #552]: #555
+#554 := [quant-inst]: #175
+#553 := [mp #554 #556]: #284
+#513 := [unit-resolution #553 #591]: #282
+#557 := (not #282)
+#504 := (or #557 #559)
 #255 := (not #168)
-#169 := (= f4 f5)
+#169 := (= f6 f7)
 #256 := (not #169)
-#167 := (= f3 f4)
+#167 := (= f5 f6)
 #254 := (not #167)
 #247 := (and #254 #255 #256)
-#11 := (distinct f3 f4 f5)
-#57 := (not #11)
-#58 := (or #57 #19)
-#61 := (not #58)
-#20 := (implies #11 #19)
-#21 := (not #20)
-#62 := (iff #21 #61)
-#59 := (iff #20 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#56 := [asserted]: #21
-#66 := [mp #56 #63]: #61
-#64 := [not-or-elim #66]: #11
-#234 := (or #57 #247)
+#29 := (distinct f5 f6 f7)
+#78 := (not #29)
+#80 := (or #78 #37)
+#83 := (not #80)
+#38 := (implies #29 #37)
+#39 := (not #38)
+#84 := (iff #39 #83)
+#81 := (iff #38 #80)
+#82 := [rewrite]: #81
+#85 := [monotonicity #82]: #84
+#77 := [asserted]: #39
+#88 := [mp #77 #85]: #83
+#86 := [not-or-elim #88]: #29
+#234 := (or #78 #247)
 #366 := [def-axiom]: #234
-#500 := [unit-resolution #366 #64]: #247
+#502 := [unit-resolution #366 #86]: #247
 #258 := (not #247)
 #260 := (or #258 #255)
 #257 := [def-axiom]: #260
-#510 := [unit-resolution #257 #500]: #255
-#421 := (or #403 #168 #521)
-#414 := [def-axiom]: #421
-#512 := [unit-resolution #414 #510]: #511
-#508 := [unit-resolution #512 #498]: #521
-#493 := [symm #508]: #365
-#494 := (= #17 #536)
-#574 := (f6 #14 f5)
-#490 := (= #574 #536)
-#499 := (= #536 #574)
-#509 := (= #560 #14)
-#520 := (= #246 f9)
-#580 := (= f9 #246)
-#24 := (:var 0 S4)
-#23 := (:var 1 S2)
-#22 := (:var 2 S3)
-#25 := (f7 #22 #23 #24)
-#585 := (pattern #25)
-#26 := (f6 #25 #23)
-#69 := (= #24 #26)
-#587 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) (:pat #585) #69)
-#72 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #69)
-#586 := (iff #72 #587)
-#589 := (iff #587 #587)
-#590 := [rewrite]: #589
-#588 := [rewrite]: #586
-#591 := [trans #588 #590]: #586
-#103 := (~ #72 #72)
-#101 := (~ #69 #69)
-#102 := [refl]: #101
-#104 := [nnf-pos #102]: #103
-#27 := (= #26 #24)
-#28 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #27)
-#73 := (iff #28 #72)
-#70 := (iff #27 #69)
-#71 := [rewrite]: #70
-#74 := [quant-intro #71]: #73
-#68 := [asserted]: #28
-#77 := [mp #68 #74]: #72
-#95 := [mp~ #77 #104]: #72
-#592 := [mp #95 #591]: #587
-#583 := (not #587)
-#578 := (or #583 #580)
-#584 := [quant-inst]: #578
-#516 := [unit-resolution #584 #592]: #580
-#507 := [symm #516]: #520
-#501 := [monotonicity #507]: #509
-#506 := [monotonicity #501]: #499
-#491 := [symm #506]: #490
-#232 := (= #17 #574)
-#233 := (= f10 #17)
-#576 := (ite #169 #233 #232)
-#222 := (or #221 #576)
-#223 := [quant-inst]: #222
-#513 := [unit-resolution #223 #599]: #576
-#224 := (not #576)
-#503 := (or #224 #232)
+#503 := [unit-resolution #257 #502]: #255
+#268 := (or #557 #168 #559)
+#270 := [def-axiom]: #268
+#505 := [unit-resolution #270 #503]: #504
+#499 := [unit-resolution #505 #513]: #559
+#483 := [symm #499]: #208
+#484 := (= #35 #203)
+#246 := (f3 #32 f7)
+#492 := (= #246 #203)
+#495 := (= #203 #246)
+#512 := (= #567 #32)
+#510 := (= #583 f9)
+#578 := (= f9 #583)
+#21 := (:var 0 S4)
+#20 := (:var 1 S3)
+#19 := (:var 2 S2)
+#22 := (f4 #19 #20 #21)
+#592 := (pattern #22)
+#23 := (f3 #22 #20)
+#70 := (= #21 #23)
+#594 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #592) #70)
+#74 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #70)
+#593 := (iff #74 #594)
+#596 := (iff #594 #594)
+#597 := [rewrite]: #596
+#595 := [rewrite]: #593
+#598 := [trans #595 #597]: #593
+#93 := (~ #74 #74)
+#90 := (~ #70 #70)
+#105 := [refl]: #90
+#94 := [nnf-pos #105]: #93
+#24 := (= #23 #21)
+#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #24)
+#75 := (iff #25 #74)
+#72 := (iff #24 #70)
+#73 := [rewrite]: #72
+#76 := [quant-intro #73]: #75
+#69 := [asserted]: #25
+#79 := [mp #69 #76]: #74
+#106 := [mp~ #79 #94]: #74
+#599 := [mp #106 #598]: #594
+#565 := (not #594)
+#566 := (or #565 #578)
+#561 := [quant-inst]: #566
+#500 := [unit-resolution #561 #599]: #578
+#511 := [symm #500]: #510
+#508 := [monotonicity #511]: #512
+#496 := [monotonicity #508]: #495
+#497 := [symm #496]: #492
+#580 := (= #35 #246)
+#581 := (= f10 #35)
+#582 := (ite #169 #581 #580)
+#574 := (or #584 #582)
+#232 := [quant-inst]: #574
+#506 := [unit-resolution #232 #591]: #582
+#237 := (not #582)
+#491 := (or #237 #580)
 #261 := (or #258 #256)
 #240 := [def-axiom]: #261
-#502 := [unit-resolution #240 #500]: #256
-#564 := (or #224 #169 #232)
-#565 := [def-axiom]: #564
-#504 := [unit-resolution #565 #502]: #503
-#505 := [unit-resolution #504 #513]: #232
-#495 := [trans #505 #491]: #494
-#496 := [trans #495 #493]: #19
-#65 := (not #19)
-#67 := [not-or-elim #66]: #65
-[unit-resolution #67 #496]: false
-unsat
-11ff498c93ee1972d946dfaaf38aec4ff91ae83c 117 0
-#2 := false
-decl f6 :: (-> S3 S3 S2)
-decl f3 :: (-> S2 S3)
-decl f4 :: S2
-#8 := f4
-#9 := (f3 f4)
-decl f5 :: (-> S2 S3)
-#10 := (f5 f4)
-#12 := (f6 #10 #9)
-#13 := (= f4 #12)
-#349 := (f6 #9 #10)
-#550 := (= #349 #12)
-#549 := (= #12 #349)
-#11 := (= #9 #10)
-#243 := (f3 #12)
-#543 := (= #243 #10)
-#240 := (= #10 #243)
-#17 := (:var 0 S3)
-#16 := (:var 1 S3)
-#18 := (f6 #16 #17)
-#568 := (pattern #18)
-#19 := (f3 #18)
-#53 := (= #16 #19)
-#569 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #568) #53)
-#57 := (forall (vars (?v0 S3) (?v1 S3)) #53)
-#572 := (iff #57 #569)
-#570 := (iff #53 #53)
-#571 := [refl]: #570
-#573 := [quant-intro #571]: #572
-#90 := (~ #57 #57)
-#88 := (~ #53 #53)
-#89 := [refl]: #88
-#91 := [nnf-pos #89]: #90
-#20 := (= #19 #16)
-#21 := (forall (vars (?v0 S3) (?v1 S3)) #20)
-#58 := (iff #21 #57)
-#55 := (iff #20 #53)
-#56 := [rewrite]: #55
-#59 := [quant-intro #56]: #58
-#52 := [asserted]: #21
-#62 := [mp #52 #59]: #57
-#80 := [mp~ #62 #91]: #57
-#574 := [mp #80 #573]: #569
-#560 := (not #569)
-#562 := (or #560 #240)
-#217 := [quant-inst]: #562
-#220 := [unit-resolution #217 #574]: #240
-#204 := [symm #220]: #543
-#559 := (= #9 #243)
-#558 := (= #243 #9)
-#557 := (= #12 f4)
-#48 := (not #11)
-#564 := [hypothesis]: #48
-#238 := (or #13 #11)
-#49 := (iff #13 #48)
-#14 := (iff #11 #13)
-#15 := (not #14)
-#50 := (iff #15 #49)
-#51 := [rewrite]: #50
-#47 := [asserted]: #15
-#54 := [mp #47 #51]: #49
-#150 := (not #49)
-#237 := (or #13 #11 #150)
-#151 := [def-axiom]: #237
-#152 := [unit-resolution #151 #54]: #238
-#565 := [unit-resolution #152 #564]: #13
-#215 := [symm #565]: #557
-#216 := [monotonicity #215]: #558
-#200 := [symm #216]: #559
-#205 := [trans #200 #204]: #11
-#206 := [unit-resolution #564 #205]: false
-#207 := [lemma #206]: #11
-#546 := (= #10 #9)
-#547 := [symm #207]: #546
-#544 := [monotonicity #547 #207]: #549
-#186 := [symm #544]: #550
-#556 := (= f4 #349)
-#25 := (:var 0 S2)
-#27 := (f5 #25)
-#582 := (pattern #27)
-#26 := (f3 #25)
-#581 := (pattern #26)
-#28 := (f6 #26 #27)
-#69 := (= #25 #28)
-#583 := (forall (vars (?v0 S2)) (:pat #581 #582) #69)
-#73 := (forall (vars (?v0 S2)) #69)
-#586 := (iff #73 #583)
-#584 := (iff #69 #69)
-#585 := [refl]: #584
-#587 := [quant-intro #585]: #586
-#84 := (~ #73 #73)
-#92 := (~ #69 #69)
-#93 := [refl]: #92
-#85 := [nnf-pos #93]: #84
-#29 := (= #28 #25)
-#30 := (forall (vars (?v0 S2)) #29)
-#74 := (iff #30 #73)
-#71 := (iff #29 #69)
-#72 := [rewrite]: #71
-#75 := [quant-intro #72]: #74
-#68 := [asserted]: #30
-#78 := [mp #68 #75]: #73
-#94 := [mp~ #78 #85]: #73
-#588 := [mp #94 #587]: #583
-#566 := (not #583)
-#561 := (or #566 #556)
-#567 := [quant-inst]: #561
-#548 := [unit-resolution #567 #588]: #556
-#551 := [trans #548 #186]: #13
-#239 := (not #13)
-#242 := (or #239 #48)
-#230 := (or #239 #48 #150)
-#241 := [def-axiom]: #230
-#170 := [unit-resolution #241 #54]: #242
-#545 := [unit-resolution #170 #207]: #239
-[unit-resolution #545 #551]: false
-unsat
-4cd366e11e92a3096da693a1c949e0a0235771e1 31 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: (-> S2 S1)
-decl f4 :: S2
-#8 := f4
-#9 := (f3 f4)
-#10 := (= #9 f1)
-#11 := (iff #10 #10)
-#12 := (not #11)
-#78 := (iff #12 false)
-#1 := true
-#73 := (not true)
-#76 := (iff #73 false)
-#77 := [rewrite]: #76
-#74 := (iff #12 #73)
-#71 := (iff #11 true)
-#63 := (= f1 #9)
-#66 := (iff #63 #63)
-#69 := (iff #66 true)
-#70 := [rewrite]: #69
-#67 := (iff #11 #66)
-#64 := (iff #10 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65 #65]: #67
-#72 := [trans #68 #70]: #71
-#75 := [monotonicity #72]: #74
-#79 := [trans #75 #77]: #78
-#62 := [asserted]: #12
-[mp #62 #79]: false
-unsat
-862ca11132e978d4725394191af361fe43022f5f 58 0
-#2 := false
-decl f3 :: (-> S2 S1)
-#13 := (:var 0 S2)
-#14 := (f3 #13)
-#661 := (pattern #14)
-decl f1 :: S1
-#4 := f1
-#77 := (= f1 #14)
-#81 := (not #77)
-#662 := (forall (vars (?v0 S2)) (:pat #661) #81)
-#84 := (forall (vars (?v0 S2)) #81)
-#665 := (iff #84 #662)
-#663 := (iff #81 #81)
-#664 := [refl]: #663
-#666 := [quant-intro #664]: #665
-#151 := (~ #84 #84)
-#149 := (~ #81 #81)
-#150 := [refl]: #149
-#152 := [nnf-pos #150]: #151
-#15 := (= #14 f1)
-#16 := (not #15)
-#17 := (forall (vars (?v0 S2)) #16)
-#85 := (iff #17 #84)
-#82 := (iff #16 #81)
-#79 := (iff #15 #77)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#86 := [quant-intro #83]: #85
-#76 := [asserted]: #17
-#89 := [mp #76 #86]: #84
-#139 := [mp~ #89 #152]: #84
-#667 := [mp #139 #666]: #662
-decl f4 :: S2
-#8 := f4
-#9 := (f3 f4)
-#63 := (= f1 #9)
-#10 := (= #9 f1)
-#11 := (not #10)
-#12 := (not #11)
-#74 := (iff #12 #63)
-#66 := (not #63)
-#69 := (not #66)
-#72 := (iff #69 #63)
-#73 := [rewrite]: #72
-#70 := (iff #12 #69)
-#67 := (iff #11 #66)
-#64 := (iff #10 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#71 := [monotonicity #68]: #70
-#75 := [trans #71 #73]: #74
-#62 := [asserted]: #12
-#78 := [mp #62 #75]: #63
-#246 := (not #662)
-#333 := (or #246 #66)
+#490 := [unit-resolution #240 #502]: #256
+#576 := (or #237 #169 #580)
+#217 := [def-axiom]: #576
+#493 := [unit-resolution #217 #490]: #491
+#494 := [unit-resolution #493 #506]: #580
+#486 := [trans #494 #497]: #484
+#487 := [trans #486 #483]: #37
+#87 := (not #37)
+#89 := [not-or-elim #88]: #87
+[unit-resolution #89 #487]: false
+unsat
+a177c36a01cc9198872fdc2abe4aa29197d4230c 31 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f9 :: (-> S8 S1)
+decl f10 :: S8
+#41 := f10
+#42 := (f9 f10)
+#43 := (= #42 f1)
+#44 := (iff #43 #43)
+#45 := (not #44)
+#137 := (iff #45 false)
+#1 := true
+#132 := (not true)
+#135 := (iff #132 false)
+#136 := [rewrite]: #135
+#133 := (iff #45 #132)
+#130 := (iff #44 true)
+#121 := (= f1 #42)
+#125 := (iff #121 #121)
+#128 := (iff #125 true)
+#129 := [rewrite]: #128
+#126 := (iff #44 #125)
+#123 := (iff #43 #121)
+#124 := [rewrite]: #123
+#127 := [monotonicity #124 #124]: #126
+#131 := [trans #127 #129]: #130
+#134 := [monotonicity #131]: #133
+#138 := [trans #134 #136]: #137
+#120 := [asserted]: #45
+[mp #120 #138]: false
+unsat
+51ea908d872636cb465fd061709753d665c54bd1 58 0
+#2 := false
+decl f8 :: (-> S7 S1)
+decl f9 :: S7
+#41 := f9
+#42 := (f8 f9)
+decl f1 :: S1
+#4 := f1
+#121 := (= f1 #42)
+#43 := (= #42 f1)
+#44 := (not #43)
+#45 := (not #44)
+#133 := (iff #45 #121)
+#125 := (not #121)
+#128 := (not #125)
+#131 := (iff #128 #121)
+#132 := [rewrite]: #131
+#129 := (iff #45 #128)
+#126 := (iff #44 #125)
+#123 := (iff #43 #121)
+#124 := [rewrite]: #123
+#127 := [monotonicity #124]: #126
+#130 := [monotonicity #127]: #129
+#134 := [trans #130 #132]: #133
+#120 := [asserted]: #45
+#137 := [mp #120 #134]: #121
+#36 := (:var 0 S7)
+#37 := (f8 #36)
+#682 := (pattern #37)
+#110 := (= f1 #37)
+#114 := (not #110)
+#683 := (forall (vars (?v0 S7)) (:pat #682) #114)
+#117 := (forall (vars (?v0 S7)) #114)
+#686 := (iff #117 #683)
+#684 := (iff #114 #114)
+#685 := [refl]: #684
+#687 := [quant-intro #685]: #686
+#143 := (~ #117 #117)
+#158 := (~ #114 #114)
+#159 := [refl]: #158
+#144 := [nnf-pos #159]: #143
+#38 := (= #37 f1)
+#39 := (not #38)
+#40 := (forall (vars (?v0 S7)) #39)
+#118 := (iff #40 #117)
+#115 := (iff #39 #114)
+#112 := (iff #38 #110)
+#113 := [rewrite]: #112
+#116 := [monotonicity #113]: #115
+#119 := [quant-intro #116]: #118
+#109 := [asserted]: #40
+#122 := [mp #109 #119]: #117
+#160 := [mp~ #122 #144]: #117
+#688 := [mp #160 #687]: #683
+#246 := (not #683)
+#333 := (or #246 #125)
 #247 := [quant-inst]: #333
-[unit-resolution #247 #78 #667]: false
-unsat
-889c897f95d38c70626926b88d4e65240961bf38 46 0
-#2 := false
-decl f3 :: (-> S2 S1)
-#17 := (:var 0 S2)
-#18 := (f3 #17)
-#660 := (pattern #18)
-decl f1 :: S1
-#4 := f1
-#80 := (= f1 #18)
-#661 := (forall (vars (?v0 S2)) (:pat #660) #80)
-#84 := (forall (vars (?v0 S2)) #80)
-#664 := (iff #84 #661)
-#662 := (iff #80 #80)
-#663 := [refl]: #662
-#665 := [quant-intro #663]: #664
-#133 := (~ #84 #84)
-#132 := (~ #80 #80)
-#130 := [refl]: #132
-#134 := [nnf-pos #130]: #133
-#19 := (= #18 f1)
-#20 := (forall (vars (?v0 S2)) #19)
-#85 := (iff #20 #84)
-#82 := (iff #19 #80)
-#83 := [rewrite]: #82
-#86 := [quant-intro #83]: #85
-#79 := [asserted]: #20
-#89 := [mp #79 #86]: #84
-#127 := [mp~ #89 #134]: #84
-#666 := [mp #127 #665]: #661
-decl f4 :: S2
-#8 := f4
-#9 := (f3 f4)
-#62 := (= f1 #9)
-#65 := (not #62)
-#10 := (= #9 f1)
-#11 := (not #10)
-#66 := (iff #11 #65)
-#63 := (iff #10 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#61 := [asserted]: #11
-#70 := [mp #61 #67]: #65
-#238 := (not #661)
-#325 := (or #238 #62)
+[unit-resolution #247 #688 #137]: false
+unsat
+2aeb6ab697dcc311206feaf1f10aeaf4e6a05b04 46 0
+#2 := false
+decl f7 :: (-> S6 S1)
+decl f9 :: S6
+#41 := f9
+#42 := (f7 f9)
+decl f1 :: S1
+#4 := f1
+#120 := (= f1 #42)
+#124 := (not #120)
+#43 := (= #42 f1)
+#44 := (not #43)
+#125 := (iff #44 #124)
+#122 := (iff #43 #120)
+#123 := [rewrite]: #122
+#126 := [monotonicity #123]: #125
+#119 := [asserted]: #44
+#129 := [mp #119 #126]: #124
+#32 := (:var 0 S6)
+#33 := (f7 #32)
+#667 := (pattern #33)
+#101 := (= f1 #33)
+#668 := (forall (vars (?v0 S6)) (:pat #667) #101)
+#105 := (forall (vars (?v0 S6)) #101)
+#671 := (iff #105 #668)
+#669 := (iff #101 #101)
+#670 := [refl]: #669
+#672 := [quant-intro #670]: #671
+#133 := (~ #105 #105)
+#147 := (~ #101 #101)
+#148 := [refl]: #147
+#134 := [nnf-pos #148]: #133
+#34 := (= #33 f1)
+#35 := (forall (vars (?v0 S6)) #34)
+#106 := (iff #35 #105)
+#103 := (iff #34 #101)
+#104 := [rewrite]: #103
+#107 := [quant-intro #104]: #106
+#100 := [asserted]: #35
+#110 := [mp #100 #107]: #105
+#149 := [mp~ #110 #134]: #105
+#673 := [mp #149 #672]: #668
+#238 := (not #668)
+#325 := (or #238 #120)
 #239 := [quant-inst]: #325
-[unit-resolution #239 #70 #666]: false
-unsat
-f03c0d076b09a28f063ddbca092a33b823afb804 119 0
-#2 := false
-decl f3 :: (-> S2 S2 S3 S1)
-decl f6 :: S3
-#10 := f6
-decl f5 :: S2
-#9 := f5
-decl f4 :: S2
-#8 := f4
-#11 := (f3 f4 f5 f6)
-decl f1 :: S1
-#4 := f1
-#70 := (= f1 #11)
-#88 := (not #70)
-#667 := [hypothesis]: #88
-decl f7 :: (-> S2 S3 S1)
-#15 := (f7 f5 f6)
-#76 := (= f1 #15)
-#13 := (f7 f4 f6)
-#73 := (= f1 #13)
-#79 := (or #73 #76)
-#357 := (or #79 #70)
-#89 := (iff #79 #88)
-#16 := (= #15 f1)
-#14 := (= #13 f1)
-#17 := (or #14 #16)
-#12 := (= #11 f1)
-#18 := (iff #12 #17)
-#19 := (not #18)
-#92 := (iff #19 #89)
-#82 := (iff #70 #79)
-#85 := (not #82)
-#90 := (iff #85 #89)
-#91 := [rewrite]: #90
-#86 := (iff #19 #85)
-#83 := (iff #18 #82)
-#80 := (iff #17 #79)
-#77 := (iff #16 #76)
-#78 := [rewrite]: #77
-#74 := (iff #14 #73)
-#75 := [rewrite]: #74
-#81 := [monotonicity #75 #78]: #80
-#71 := (iff #12 #70)
-#72 := [rewrite]: #71
-#84 := [monotonicity #72 #81]: #83
-#87 := [monotonicity #84]: #86
-#93 := [trans #87 #91]: #92
-#69 := [asserted]: #19
-#96 := [mp #69 #93]: #89
-#283 := (not #89)
-#356 := (or #79 #70 #283)
+[unit-resolution #239 #673 #129]: false
+unsat
+701d85974e90172ee7a006ed1c192079b5a1ed15 119 0
+#2 := false
+decl f5 :: (-> S4 S4 S5 S1)
+decl f11 :: S5
+#43 := f11
+decl f10 :: S4
+#42 := f10
+decl f9 :: S4
+#41 := f9
+#44 := (f5 f9 f10 f11)
+decl f1 :: S1
+#4 := f1
+#128 := (= f1 #44)
+#147 := (not #128)
+#667 := [hypothesis]: #147
+decl f6 :: (-> S4 S5 S1)
+#48 := (f6 f10 f11)
+#135 := (= f1 #48)
+#46 := (f6 f9 f11)
+#132 := (= f1 #46)
+#138 := (or #132 #135)
+#357 := (or #138 #128)
+#148 := (iff #138 #147)
+#49 := (= #48 f1)
+#47 := (= #46 f1)
+#50 := (or #47 #49)
+#45 := (= #44 f1)
+#51 := (iff #45 #50)
+#52 := (not #51)
+#151 := (iff #52 #148)
+#141 := (iff #128 #138)
+#144 := (not #141)
+#149 := (iff #144 #148)
+#150 := [rewrite]: #149
+#145 := (iff #52 #144)
+#142 := (iff #51 #141)
+#139 := (iff #50 #138)
+#136 := (iff #49 #135)
+#137 := [rewrite]: #136
+#133 := (iff #47 #132)
+#134 := [rewrite]: #133
+#140 := [monotonicity #134 #137]: #139
+#130 := (iff #45 #128)
+#131 := [rewrite]: #130
+#143 := [monotonicity #131 #140]: #142
+#146 := [monotonicity #143]: #145
+#152 := [trans #146 #150]: #151
+#127 := [asserted]: #52
+#155 := [mp #127 #152]: #148
+#283 := (not #148)
+#356 := (or #138 #128 #283)
 #353 := [def-axiom]: #356
-#336 := [unit-resolution #353 #96]: #357
-#341 := [unit-resolution #336 #667]: #79
-#343 := (not #79)
-#670 := (or #70 #343)
-#31 := (:var 0 S3)
-#30 := (:var 1 S2)
-#29 := (:var 2 S2)
-#32 := (f3 #29 #30 #31)
-#693 := (pattern #32)
-#36 := (f7 #30 #31)
-#121 := (= f1 #36)
-#34 := (f7 #29 #31)
-#118 := (= f1 #34)
-#124 := (or #118 #121)
-#114 := (= f1 #32)
-#127 := (iff #114 #124)
-#694 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #693) #127)
-#130 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #127)
-#697 := (iff #130 #694)
-#695 := (iff #127 #127)
-#696 := [refl]: #695
-#698 := [quant-intro #696]: #697
-#161 := (~ #130 #130)
-#171 := (~ #127 #127)
-#172 := [refl]: #171
-#162 := [nnf-pos #172]: #161
-#37 := (= #36 f1)
-#35 := (= #34 f1)
-#38 := (or #35 #37)
-#33 := (= #32 f1)
-#39 := (iff #33 #38)
-#40 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #39)
-#131 := (iff #40 #130)
-#128 := (iff #39 #127)
-#125 := (iff #38 #124)
-#122 := (iff #37 #121)
-#123 := [rewrite]: #122
-#119 := (iff #35 #118)
-#120 := [rewrite]: #119
-#126 := [monotonicity #120 #123]: #125
-#116 := (iff #33 #114)
-#117 := [rewrite]: #116
-#129 := [monotonicity #117 #126]: #128
-#132 := [quant-intro #129]: #131
-#113 := [asserted]: #40
-#135 := [mp #113 #132]: #130
-#173 := [mp~ #135 #162]: #130
-#699 := [mp #173 #698]: #694
-#342 := (not #694)
-#674 := (or #342 #82)
+#336 := [unit-resolution #353 #155]: #357
+#341 := [unit-resolution #336 #667]: #138
+#343 := (not #138)
+#670 := (or #128 #343)
+#22 := (:var 0 S5)
+#21 := (:var 1 S4)
+#20 := (:var 2 S4)
+#23 := (f5 #20 #21 #22)
+#686 := (pattern #23)
+#27 := (f6 #21 #22)
+#96 := (= f1 #27)
+#25 := (f6 #20 #22)
+#93 := (= f1 #25)
+#99 := (or #93 #96)
+#89 := (= f1 #23)
+#102 := (iff #89 #99)
+#687 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #686) #102)
+#105 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #102)
+#690 := (iff #105 #687)
+#688 := (iff #102 #102)
+#689 := [refl]: #688
+#691 := [quant-intro #689]: #690
+#157 := (~ #105 #105)
+#153 := (~ #102 #102)
+#171 := [refl]: #153
+#158 := [nnf-pos #171]: #157
+#28 := (= #27 f1)
+#26 := (= #25 f1)
+#29 := (or #26 #28)
+#24 := (= #23 f1)
+#30 := (iff #24 #29)
+#31 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #30)
+#106 := (iff #31 #105)
+#103 := (iff #30 #102)
+#100 := (iff #29 #99)
+#97 := (iff #28 #96)
+#98 := [rewrite]: #97
+#94 := (iff #26 #93)
+#95 := [rewrite]: #94
+#101 := [monotonicity #95 #98]: #100
+#91 := (iff #24 #89)
+#92 := [rewrite]: #91
+#104 := [monotonicity #92 #101]: #103
+#107 := [quant-intro #104]: #106
+#88 := [asserted]: #31
+#110 := [mp #88 #107]: #105
+#172 := [mp~ #110 #158]: #105
+#692 := [mp #172 #691]: #687
+#342 := (not #687)
+#674 := (or #342 #141)
 #675 := [quant-inst]: #674
-#329 := [unit-resolution #675 #699]: #82
-#676 := (or #85 #70 #343)
+#329 := [unit-resolution #675 #692]: #141
+#676 := (or #144 #128 #343)
 #677 := [def-axiom]: #676
 #313 := [unit-resolution #677 #329]: #670
 #654 := [unit-resolution #313 #341 #667]: false
-#317 := [lemma #654]: #70
-#330 := (or #343 #88)
-#671 := (or #343 #88 #283)
+#317 := [lemma #654]: #128
+#330 := (or #343 #147)
+#671 := (or #343 #147 #283)
 #673 := [def-axiom]: #671
-#460 := [unit-resolution #673 #96]: #330
+#460 := [unit-resolution #673 #155]: #330
 #318 := [unit-resolution #460 #317]: #343
-#319 := (or #88 #79)
-#672 := (or #85 #88 #79)
+#319 := (or #147 #138)
+#672 := (or #144 #147 #138)
 #678 := [def-axiom]: #672
 #320 := [unit-resolution #678 #329]: #319
 [unit-resolution #320 #318 #317]: false
 unsat
-a6efe1b3687d3cc17ba5ea65fa9b7033b64122bf 154 0
-#2 := false
-decl f7 :: (-> S2 S3 S1)
-decl f6 :: S3
-#10 := f6
-decl f5 :: S2
-#9 := f5
-#346 := (f7 f5 f6)
+37cc4af448f3867f70588d51f6c5e21ac95b5980 154 0
+#2 := false
+decl f6 :: (-> S4 S5 S1)
+decl f10 :: S5
+#42 := f10
+decl f8 :: S4
+#36 := f8
+#346 := (f6 f8 f10)
 decl f1 :: S1
 #4 := f1
 #343 := (= f1 #346)
-decl f4 :: S2
-#8 := f4
-#13 := (f7 f4 f6)
-#69 := (= f1 #13)
-#347 := (or #69 #343)
-decl f3 :: (-> S2 S2 S3 S1)
-#11 := (f3 f4 f5 f6)
-#66 := (= f1 #11)
-#78 := (not #66)
-#661 := [hypothesis]: #78
-#341 := (or #69 #66)
-#79 := (iff #69 #78)
-#14 := (= #13 f1)
-#12 := (= #11 f1)
-#15 := (iff #12 #14)
-#16 := (not #15)
-#82 := (iff #16 #79)
-#72 := (iff #66 #69)
-#75 := (not #72)
-#80 := (iff #75 #79)
-#81 := [rewrite]: #80
-#76 := (iff #16 #75)
-#73 := (iff #15 #72)
-#70 := (iff #14 #69)
-#71 := [rewrite]: #70
-#67 := (iff #12 #66)
-#68 := [rewrite]: #67
-#74 := [monotonicity #68 #71]: #73
-#77 := [monotonicity #74]: #76
-#83 := [trans #77 #81]: #82
-#65 := [asserted]: #16
-#86 := [mp #65 #83]: #79
-#253 := (not #79)
-#340 := (or #69 #66 #253)
+decl f9 :: S4
+#41 := f9
+#45 := (f6 f9 f10)
+#128 := (= f1 #45)
+#347 := (or #128 #343)
+decl f5 :: (-> S4 S4 S5 S1)
+#43 := (f5 f9 f8 f10)
+#124 := (= f1 #43)
+#137 := (not #124)
+#661 := [hypothesis]: #137
+#341 := (or #128 #124)
+#138 := (iff #128 #137)
+#46 := (= #45 f1)
+#44 := (= #43 f1)
+#47 := (iff #44 #46)
+#48 := (not #47)
+#141 := (iff #48 #138)
+#131 := (iff #124 #128)
+#134 := (not #131)
+#139 := (iff #134 #138)
+#140 := [rewrite]: #139
+#135 := (iff #48 #134)
+#132 := (iff #47 #131)
+#129 := (iff #46 #128)
+#130 := [rewrite]: #129
+#126 := (iff #44 #124)
+#127 := [rewrite]: #126
+#133 := [monotonicity #127 #130]: #132
+#136 := [monotonicity #133]: #135
+#142 := [trans #136 #140]: #141
+#123 := [asserted]: #48
+#145 := [mp #123 #142]: #138
+#253 := (not #138)
+#340 := (or #128 #124 #253)
 #254 := [def-axiom]: #340
-#255 := [unit-resolution #254 #86]: #341
-#663 := [unit-resolution #255 #661]: #69
+#255 := [unit-resolution #254 #145]: #341
+#663 := [unit-resolution #255 #661]: #128
 #667 := (not #347)
-#309 := (or #66 #667)
-#326 := (iff #66 #347)
-#17 := (:var 0 S3)
-#27 := (:var 1 S2)
-#26 := (:var 2 S2)
-#28 := (f3 #26 #27 #17)
-#683 := (pattern #28)
-#32 := (f7 #27 #17)
-#111 := (= f1 #32)
-#30 := (f7 #26 #17)
-#108 := (= f1 #30)
-#114 := (or #108 #111)
-#104 := (= f1 #28)
-#117 := (iff #104 #114)
-#684 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #683) #117)
-#120 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #117)
-#687 := (iff #120 #684)
-#685 := (iff #117 #117)
-#686 := [refl]: #685
-#688 := [quant-intro #686]: #687
-#151 := (~ #120 #120)
-#161 := (~ #117 #117)
-#162 := [refl]: #161
-#152 := [nnf-pos #162]: #151
-#33 := (= #32 f1)
-#31 := (= #30 f1)
-#34 := (or #31 #33)
-#29 := (= #28 f1)
-#35 := (iff #29 #34)
-#36 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #35)
-#121 := (iff #36 #120)
-#118 := (iff #35 #117)
-#115 := (iff #34 #114)
-#112 := (iff #33 #111)
-#113 := [rewrite]: #112
-#109 := (iff #31 #108)
-#110 := [rewrite]: #109
-#116 := [monotonicity #110 #113]: #115
-#106 := (iff #29 #104)
-#107 := [rewrite]: #106
-#119 := [monotonicity #107 #116]: #118
-#122 := [quant-intro #119]: #121
-#103 := [asserted]: #36
-#125 := [mp #103 #122]: #120
-#163 := [mp~ #125 #152]: #120
-#689 := [mp #163 #688]: #684
-#320 := (not #684)
+#309 := (or #124 #667)
+#326 := (iff #124 #347)
+#22 := (:var 0 S5)
+#21 := (:var 1 S4)
+#20 := (:var 2 S4)
+#23 := (f5 #20 #21 #22)
+#676 := (pattern #23)
+#27 := (f6 #21 #22)
+#92 := (= f1 #27)
+#25 := (f6 #20 #22)
+#89 := (= f1 #25)
+#95 := (or #89 #92)
+#85 := (= f1 #23)
+#98 := (iff #85 #95)
+#677 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #676) #98)
+#101 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #98)
+#680 := (iff #101 #677)
+#678 := (iff #98 #98)
+#679 := [refl]: #678
+#681 := [quant-intro #679]: #680
+#147 := (~ #101 #101)
+#143 := (~ #98 #98)
+#161 := [refl]: #143
+#148 := [nnf-pos #161]: #147
+#28 := (= #27 f1)
+#26 := (= #25 f1)
+#29 := (or #26 #28)
+#24 := (= #23 f1)
+#30 := (iff #24 #29)
+#31 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #30)
+#102 := (iff #31 #101)
+#99 := (iff #30 #98)
+#96 := (iff #29 #95)
+#93 := (iff #28 #92)
+#94 := [rewrite]: #93
+#90 := (iff #26 #89)
+#91 := [rewrite]: #90
+#97 := [monotonicity #91 #94]: #96
+#87 := (iff #24 #85)
+#88 := [rewrite]: #87
+#100 := [monotonicity #88 #97]: #99
+#103 := [quant-intro #100]: #102
+#84 := [asserted]: #31
+#106 := [mp #84 #103]: #101
+#162 := [mp~ #106 #148]: #101
+#682 := [mp #162 #681]: #677
+#320 := (not #677)
 #450 := (or #320 #326)
 #657 := [quant-inst]: #450
-#308 := [unit-resolution #657 #689]: #326
+#308 := [unit-resolution #657 #682]: #326
 #658 := (not #326)
-#318 := (or #658 #66 #667)
+#318 := (or #658 #124 #667)
 #323 := [def-axiom]: #318
 #310 := [unit-resolution #323 #308]: #309
 #646 := [unit-resolution #310 #661]: #667
-#342 := (not #69)
+#342 := (not #128)
 #331 := (or #347 #342)
 #332 := [def-axiom]: #331
 #647 := [unit-resolution #332 #646 #663]: false
-#648 := [lemma #647]: #66
-#649 := (or #78 #347)
-#659 := (or #658 #78 #347)
+#648 := [lemma #647]: #124
+#649 := (or #137 #347)
+#659 := (or #658 #137 #347)
 #319 := [def-axiom]: #659
 #650 := [unit-resolution #319 #308]: #649
 #652 := [unit-resolution #650 #648]: #347
-#345 := (or #342 #78)
-#333 := (or #342 #78 #253)
+#345 := (or #342 #137)
+#333 := (or #342 #137 #253)
 #344 := [def-axiom]: #333
-#273 := [unit-resolution #344 #86]: #345
+#273 := [unit-resolution #344 #145]: #345
 #654 := [unit-resolution #273 #648]: #342
-#662 := (or #667 #69 #343)
+#662 := (or #667 #128 #343)
 #668 := [def-axiom]: #662
 #294 := [unit-resolution #668 #654 #652]: #343
-#18 := (f7 f5 #17)
-#669 := (pattern #18)
-#85 := (= f1 #18)
-#89 := (not #85)
-#670 := (forall (vars (?v0 S3)) (:pat #669) #89)
-#92 := (forall (vars (?v0 S3)) #89)
-#673 := (iff #92 #670)
-#671 := (iff #89 #89)
-#672 := [refl]: #671
-#674 := [quant-intro #672]: #673
-#159 := (~ #92 #92)
-#157 := (~ #89 #89)
-#158 := [refl]: #157
-#160 := [nnf-pos #158]: #159
-#19 := (= #18 f1)
-#20 := (not #19)
-#21 := (forall (vars (?v0 S3)) #20)
-#93 := (iff #21 #92)
-#90 := (iff #20 #89)
-#87 := (iff #19 #85)
-#88 := [rewrite]: #87
-#91 := [monotonicity #88]: #90
-#94 := [quant-intro #91]: #93
-#84 := [asserted]: #21
-#97 := [mp #84 #94]: #92
-#147 := [mp~ #97 #160]: #92
-#675 := [mp #147 #674]: #670
+#37 := (f6 f8 #22)
+#690 := (pattern #37)
+#113 := (= f1 #37)
+#117 := (not #113)
+#691 := (forall (vars (?v0 S5)) (:pat #690) #117)
+#120 := (forall (vars (?v0 S5)) #117)
+#694 := (iff #120 #691)
+#692 := (iff #117 #117)
+#693 := [refl]: #692
+#695 := [quant-intro #693]: #694
+#151 := (~ #120 #120)
+#166 := (~ #117 #117)
+#167 := [refl]: #166
+#152 := [nnf-pos #167]: #151
+#38 := (= #37 f1)
+#39 := (not #38)
+#40 := (forall (vars (?v0 S5)) #39)
+#121 := (iff #40 #120)
+#118 := (iff #39 #117)
+#115 := (iff #38 #113)
+#116 := [rewrite]: #115
+#119 := [monotonicity #116]: #118
+#122 := [quant-intro #119]: #121
+#112 := [asserted]: #40
+#125 := [mp #112 #122]: #120
+#168 := [mp~ #125 #152]: #120
+#696 := [mp #168 #695]: #691
 #664 := (not #343)
-#645 := (not #670)
+#645 := (not #691)
 #651 := (or #645 #664)
 #289 := [quant-inst]: #651
-[unit-resolution #289 #675 #294]: false
-unsat
-d1421e190f987aeaec441d0daf9b02a2f258566f 128 0
-#2 := false
-decl f8 :: (-> S2 S3 S1)
-decl f6 :: S3
-#10 := f6
-decl f5 :: S2
-#9 := f5
-#238 := (f8 f5 f6)
+[unit-resolution #289 #696 #294]: false
+unsat
+2ef7b3971bee2b3eaed3ee37e3f6f6a8f02f6b25 128 0
+#2 := false
+decl f6 :: (-> S4 S5 S1)
+decl f10 :: S5
+#42 := f10
+decl f7 :: S4
+#32 := f7
+#238 := (f6 f7 f10)
 decl f1 :: S1
 #4 := f1
 #325 := (= f1 #238)
 #650 := (not #325)
-decl f4 :: S2
-#8 := f4
-#239 := (f8 f4 f6)
+decl f9 :: S4
+#41 := f9
+#239 := (f6 f9 f10)
 #326 := (= f1 #239)
 #318 := (or #325 #326)
 #303 := (not #318)
-decl f3 :: (-> S2 S2 S3 S1)
-#11 := (f3 f4 f5 f6)
-#63 := (= f1 #11)
-#258 := (iff #63 #318)
-#19 := (:var 0 S3)
-#24 := (:var 1 S2)
-#23 := (:var 2 S2)
-#25 := (f3 #23 #24 #19)
-#668 := (pattern #25)
-#29 := (f8 #24 #19)
-#96 := (= f1 #29)
-#27 := (f8 #23 #19)
-#93 := (= f1 #27)
-#99 := (or #93 #96)
-#89 := (= f1 #25)
-#102 := (iff #89 #99)
-#669 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #668) #102)
-#105 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #102)
-#672 := (iff #105 #669)
-#670 := (iff #102 #102)
-#671 := [refl]: #670
-#673 := [quant-intro #671]: #672
-#136 := (~ #105 #105)
-#146 := (~ #102 #102)
-#147 := [refl]: #146
-#137 := [nnf-pos #147]: #136
-#30 := (= #29 f1)
+decl f5 :: (-> S4 S4 S5 S1)
+#43 := (f5 f9 f7 f10)
+#121 := (= f1 #43)
+#258 := (iff #121 #318)
+#22 := (:var 0 S5)
+#21 := (:var 1 S4)
+#20 := (:var 2 S4)
+#23 := (f5 #20 #21 #22)
+#661 := (pattern #23)
+#27 := (f6 #21 #22)
+#89 := (= f1 #27)
+#25 := (f6 #20 #22)
+#86 := (= f1 #25)
+#92 := (or #86 #89)
+#82 := (= f1 #23)
+#95 := (iff #82 #92)
+#662 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #661) #95)
+#98 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #95)
+#665 := (iff #98 #662)
+#663 := (iff #95 #95)
+#664 := [refl]: #663
+#666 := [quant-intro #664]: #665
+#132 := (~ #98 #98)
+#128 := (~ #95 #95)
+#146 := [refl]: #128
+#133 := [nnf-pos #146]: #132
 #28 := (= #27 f1)
-#31 := (or #28 #30)
 #26 := (= #25 f1)
-#32 := (iff #26 #31)
-#33 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #32)
-#106 := (iff #33 #105)
-#103 := (iff #32 #102)
-#100 := (iff #31 #99)
-#97 := (iff #30 #96)
-#98 := [rewrite]: #97
-#94 := (iff #28 #93)
-#95 := [rewrite]: #94
-#101 := [monotonicity #95 #98]: #100
-#91 := (iff #26 #89)
-#92 := [rewrite]: #91
-#104 := [monotonicity #92 #101]: #103
-#107 := [quant-intro #104]: #106
-#88 := [asserted]: #33
-#110 := [mp #88 #107]: #105
-#148 := [mp~ #110 #137]: #105
-#674 := [mp #148 #673]: #669
-#332 := (not #669)
+#29 := (or #26 #28)
+#24 := (= #23 f1)
+#30 := (iff #24 #29)
+#31 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #30)
+#99 := (iff #31 #98)
+#96 := (iff #30 #95)
+#93 := (iff #29 #92)
+#90 := (iff #28 #89)
+#91 := [rewrite]: #90
+#87 := (iff #26 #86)
+#88 := [rewrite]: #87
+#94 := [monotonicity #88 #91]: #93
+#84 := (iff #24 #82)
+#85 := [rewrite]: #84
+#97 := [monotonicity #85 #94]: #96
+#100 := [quant-intro #97]: #99
+#81 := [asserted]: #31
+#103 := [mp #81 #100]: #98
+#147 := [mp~ #103 #133]: #98
+#667 := [mp #147 #666]: #662
+#332 := (not #662)
 #311 := (or #332 #258)
 #240 := (or #326 #325)
-#327 := (iff #63 #240)
+#327 := (iff #121 #240)
 #646 := (or #332 #327)
 #305 := (iff #646 #311)
 #642 := (iff #311 #311)
@@ -52057,155 +52197,155 @@
 #317 := [trans #435 #316]: #305
 #648 := [quant-inst]: #646
 #649 := [mp #648 #317]: #311
-#632 := [unit-resolution #649 #674]: #258
+#632 := [unit-resolution #649 #667]: #258
 #304 := (not #258)
 #633 := (or #304 #303)
-#66 := (not #63)
-#12 := (= #11 f1)
-#13 := (not #12)
-#67 := (iff #13 #66)
-#64 := (iff #12 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#62 := [asserted]: #13
-#71 := [mp #62 #68]: #66
-#645 := (or #304 #63 #303)
+#125 := (not #121)
+#44 := (= #43 f1)
+#45 := (not #44)
+#126 := (iff #45 #125)
+#123 := (iff #44 #121)
+#124 := [rewrite]: #123
+#127 := [monotonicity #124]: #126
+#120 := [asserted]: #45
+#130 := [mp #120 #127]: #125
+#645 := (or #304 #121 #303)
 #288 := [def-axiom]: #645
-#636 := [unit-resolution #288 #71]: #633
+#636 := [unit-resolution #288 #130]: #633
 #274 := [unit-resolution #636 #632]: #303
 #651 := (or #318 #650)
 #652 := [def-axiom]: #651
 #637 := [unit-resolution #652 #274]: #650
-#20 := (f8 f5 #19)
-#661 := (pattern #20)
-#81 := (= f1 #20)
-#662 := (forall (vars (?v0 S3)) (:pat #661) #81)
-#85 := (forall (vars (?v0 S3)) #81)
-#665 := (iff #85 #662)
-#663 := (iff #81 #81)
-#664 := [refl]: #663
-#666 := [quant-intro #664]: #665
-#134 := (~ #85 #85)
-#133 := (~ #81 #81)
-#131 := [refl]: #133
-#135 := [nnf-pos #131]: #134
-#21 := (= #20 f1)
-#22 := (forall (vars (?v0 S3)) #21)
-#86 := (iff #22 #85)
-#83 := (iff #21 #81)
-#84 := [rewrite]: #83
-#87 := [quant-intro #84]: #86
-#80 := [asserted]: #22
-#90 := [mp #80 #87]: #85
-#128 := [mp~ #90 #135]: #85
-#667 := [mp #128 #666]: #662
-#634 := (not #662)
+#33 := (f6 f7 #22)
+#668 := (pattern #33)
+#102 := (= f1 #33)
+#669 := (forall (vars (?v0 S5)) (:pat #668) #102)
+#106 := (forall (vars (?v0 S5)) #102)
+#672 := (iff #106 #669)
+#670 := (iff #102 #102)
+#671 := [refl]: #670
+#673 := [quant-intro #671]: #672
+#134 := (~ #106 #106)
+#148 := (~ #102 #102)
+#149 := [refl]: #148
+#135 := [nnf-pos #149]: #134
+#34 := (= #33 f1)
+#35 := (forall (vars (?v0 S5)) #34)
+#107 := (iff #35 #106)
+#104 := (iff #34 #102)
+#105 := [rewrite]: #104
+#108 := [quant-intro #105]: #107
+#101 := [asserted]: #35
+#111 := [mp #101 #108]: #106
+#150 := [mp~ #111 #135]: #106
+#674 := [mp #150 #673]: #669
+#634 := (not #669)
 #635 := (or #634 #325)
 #630 := [quant-inst]: #635
-[unit-resolution #630 #667 #637]: false
-unsat
-db52b16fae67253deaefead0db41a82bcf2ebe59 146 0
-#2 := false
-decl f3 :: (-> S2 S2 S3 S1)
-decl f6 :: S3
-#10 := f6
-decl f4 :: S2
-#8 := f4
-decl f5 :: S2
-#9 := f5
-#13 := (f3 f5 f4 f6)
-decl f1 :: S1
-#4 := f1
-#70 := (= f1 #13)
-#343 := (not #70)
-#11 := (f3 f4 f5 f6)
-#67 := (= f1 #11)
-#79 := (not #67)
-#640 := [hypothesis]: #79
-#342 := (or #70 #67)
-#80 := (iff #70 #79)
-#14 := (= #13 f1)
-#12 := (= #11 f1)
-#15 := (iff #12 #14)
-#16 := (not #15)
-#83 := (iff #16 #80)
-#73 := (iff #67 #70)
-#76 := (not #73)
-#81 := (iff #76 #80)
-#82 := [rewrite]: #81
-#77 := (iff #16 #76)
-#74 := (iff #15 #73)
-#71 := (iff #14 #70)
-#72 := [rewrite]: #71
-#68 := (iff #12 #67)
-#69 := [rewrite]: #68
-#75 := [monotonicity #69 #72]: #74
-#78 := [monotonicity #75]: #77
-#84 := [trans #78 #82]: #83
-#66 := [asserted]: #16
-#87 := [mp #66 #84]: #80
-#254 := (not #80)
-#341 := (or #70 #67 #254)
+[unit-resolution #630 #674 #637]: false
+unsat
+dda75ba28de1afcdfdffa751179c98d66bc439e1 146 0
+#2 := false
+decl f5 :: (-> S4 S4 S5 S1)
+decl f11 :: S5
+#43 := f11
+decl f9 :: S4
+#41 := f9
+decl f10 :: S4
+#42 := f10
+#46 := (f5 f10 f9 f11)
+decl f1 :: S1
+#4 := f1
+#129 := (= f1 #46)
+#343 := (not #129)
+#44 := (f5 f9 f10 f11)
+#125 := (= f1 #44)
+#138 := (not #125)
+#640 := [hypothesis]: #138
+#342 := (or #129 #125)
+#139 := (iff #129 #138)
+#47 := (= #46 f1)
+#45 := (= #44 f1)
+#48 := (iff #45 #47)
+#49 := (not #48)
+#142 := (iff #49 #139)
+#132 := (iff #125 #129)
+#135 := (not #132)
+#140 := (iff #135 #139)
+#141 := [rewrite]: #140
+#136 := (iff #49 #135)
+#133 := (iff #48 #132)
+#130 := (iff #47 #129)
+#131 := [rewrite]: #130
+#127 := (iff #45 #125)
+#128 := [rewrite]: #127
+#134 := [monotonicity #128 #131]: #133
+#137 := [monotonicity #134]: #136
+#143 := [trans #137 #141]: #142
+#124 := [asserted]: #49
+#146 := [mp #124 #143]: #139
+#254 := (not #139)
+#341 := (or #129 #125 #254)
 #255 := [def-axiom]: #341
-#256 := [unit-resolution #255 #87]: #342
-#362 := [unit-resolution #256 #640]: #70
-decl f9 :: (-> S2 S3 S1)
-#347 := (f9 f4 f6)
+#256 := [unit-resolution #255 #146]: #342
+#362 := [unit-resolution #256 #640]: #129
+decl f6 :: (-> S4 S5 S1)
+#347 := (f6 f9 f11)
 #344 := (= f1 #347)
-#348 := (f9 f5 f6)
+#348 := (f6 f10 f11)
 #327 := (= f1 #348)
 #662 := (or #327 #344)
 #659 := (not #662)
-#637 := (or #67 #659)
-#649 := (iff #67 #662)
-#28 := (:var 0 S3)
-#27 := (:var 1 S2)
-#26 := (:var 2 S2)
-#29 := (f3 #26 #27 #28)
-#684 := (pattern #29)
-#33 := (f9 #27 #28)
-#112 := (= f1 #33)
-#31 := (f9 #26 #28)
-#109 := (= f1 #31)
-#115 := (or #109 #112)
-#105 := (= f1 #29)
-#118 := (iff #105 #115)
-#685 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #684) #118)
-#121 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #118)
-#688 := (iff #121 #685)
-#686 := (iff #118 #118)
-#687 := [refl]: #686
-#689 := [quant-intro #687]: #688
-#152 := (~ #121 #121)
-#162 := (~ #118 #118)
-#163 := [refl]: #162
-#153 := [nnf-pos #163]: #152
-#34 := (= #33 f1)
-#32 := (= #31 f1)
-#35 := (or #32 #34)
-#30 := (= #29 f1)
-#36 := (iff #30 #35)
-#37 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #36)
-#122 := (iff #37 #121)
-#119 := (iff #36 #118)
-#116 := (iff #35 #115)
-#113 := (iff #34 #112)
-#114 := [rewrite]: #113
-#110 := (iff #32 #109)
-#111 := [rewrite]: #110
-#117 := [monotonicity #111 #114]: #116
-#107 := (iff #30 #105)
-#108 := [rewrite]: #107
-#120 := [monotonicity #108 #117]: #119
-#123 := [quant-intro #120]: #122
-#104 := [asserted]: #37
-#126 := [mp #104 #123]: #121
-#164 := [mp~ #126 #153]: #121
-#690 := [mp #164 #689]: #685
-#658 := (not #685)
+#637 := (or #125 #659)
+#649 := (iff #125 #662)
+#22 := (:var 0 S5)
+#21 := (:var 1 S4)
+#20 := (:var 2 S4)
+#23 := (f5 #20 #21 #22)
+#677 := (pattern #23)
+#27 := (f6 #21 #22)
+#93 := (= f1 #27)
+#25 := (f6 #20 #22)
+#90 := (= f1 #25)
+#96 := (or #90 #93)
+#86 := (= f1 #23)
+#99 := (iff #86 #96)
+#678 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #677) #99)
+#102 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #99)
+#681 := (iff #102 #678)
+#679 := (iff #99 #99)
+#680 := [refl]: #679
+#682 := [quant-intro #680]: #681
+#148 := (~ #102 #102)
+#144 := (~ #99 #99)
+#162 := [refl]: #144
+#149 := [nnf-pos #162]: #148
+#28 := (= #27 f1)
+#26 := (= #25 f1)
+#29 := (or #26 #28)
+#24 := (= #23 f1)
+#30 := (iff #24 #29)
+#31 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #30)
+#103 := (iff #31 #102)
+#100 := (iff #30 #99)
+#97 := (iff #29 #96)
+#94 := (iff #28 #93)
+#95 := [rewrite]: #94
+#91 := (iff #26 #90)
+#92 := [rewrite]: #91
+#98 := [monotonicity #92 #95]: #97
+#88 := (iff #24 #86)
+#89 := [rewrite]: #88
+#101 := [monotonicity #89 #98]: #100
+#104 := [quant-intro #101]: #103
+#85 := [asserted]: #31
+#107 := [mp #85 #104]: #102
+#163 := [mp~ #107 #149]: #102
+#683 := [mp #163 #682]: #678
+#658 := (not #678)
 #646 := (or #658 #649)
 #321 := (or #344 #327)
-#451 := (iff #67 #321)
+#451 := (iff #125 #321)
 #652 := (or #658 #451)
 #653 := (iff #652 #646)
 #295 := (iff #646 #646)
@@ -52218,230 +52358,310 @@
 #656 := [trans #655 #296]: #653
 #290 := [quant-inst]: #652
 #654 := [mp #290 #656]: #646
-#363 := [unit-resolution #654 #690]: #649
+#363 := [unit-resolution #654 #683]: #649
 #657 := (not #649)
-#643 := (or #657 #67 #659)
+#643 := (or #657 #125 #659)
 #644 := [def-axiom]: #643
 #641 := [unit-resolution #644 #363]: #637
 #638 := [unit-resolution #641 #640]: #659
 #352 := (or #343 #662)
-#664 := (iff #70 #662)
+#664 := (iff #129 #662)
 #332 := (or #658 #664)
 #333 := [quant-inst]: #332
-#642 := [unit-resolution #333 #690]: #664
+#642 := [unit-resolution #333 #683]: #664
 #660 := (not #664)
 #304 := (or #660 #343 #662)
 #645 := [def-axiom]: #304
 #353 := [unit-resolution #645 #642]: #352
 #354 := [unit-resolution #353 #638 #362]: false
-#355 := [lemma #354]: #67
-#346 := (or #343 #79)
-#334 := (or #343 #79 #254)
+#355 := [lemma #354]: #125
+#346 := (or #343 #138)
+#334 := (or #343 #138 #254)
 #345 := [def-axiom]: #334
-#274 := [unit-resolution #345 #87]: #346
+#274 := [unit-resolution #345 #146]: #346
 #633 := [unit-resolution #274 #355]: #343
-#634 := (or #79 #662)
-#366 := (or #657 #79 #662)
+#634 := (or #138 #662)
+#366 := (or #657 #138 #662)
 #367 := [def-axiom]: #366
 #349 := [unit-resolution #367 #363]: #634
 #631 := [unit-resolution #349 #355]: #662
-#635 := (or #70 #659)
-#320 := (or #660 #70 #659)
+#635 := (or #129 #659)
+#320 := (or #660 #129 #659)
 #661 := [def-axiom]: #320
 #632 := [unit-resolution #661 #642]: #635
 [unit-resolution #632 #631 #633]: false
 unsat
-8f02554bbb40e6658b09b0c2823ecea18b08c91d 121 0
-#2 := false
-decl f3 :: (-> S2 S2 S3 S1)
-decl f5 :: S3
-#9 := f5
-decl f4 :: S2
-#8 := f4
-#10 := (f3 f4 f4 f5)
-decl f1 :: S1
-#4 := f1
-#66 := (= f1 #10)
-#78 := (not #66)
-#644 := [hypothesis]: #78
-decl f6 :: (-> S2 S3 S1)
-#12 := (f6 f4 f5)
-#69 := (= f1 #12)
-#341 := (or #69 #66)
-#79 := (iff #69 #78)
-#13 := (= #12 f1)
-#11 := (= #10 f1)
-#14 := (iff #11 #13)
-#15 := (not #14)
-#82 := (iff #15 #79)
-#72 := (iff #66 #69)
-#75 := (not #72)
-#80 := (iff #75 #79)
-#81 := [rewrite]: #80
-#76 := (iff #15 #75)
-#73 := (iff #14 #72)
-#70 := (iff #13 #69)
-#71 := [rewrite]: #70
-#67 := (iff #11 #66)
-#68 := [rewrite]: #67
-#74 := [monotonicity #68 #71]: #73
-#77 := [monotonicity #74]: #76
-#83 := [trans #77 #81]: #82
-#65 := [asserted]: #15
-#86 := [mp #65 #83]: #79
-#253 := (not #79)
-#340 := (or #69 #66 #253)
+f7108cc5549f3f4398bc8fd8e4f63f851b074824 121 0
+#2 := false
+decl f5 :: (-> S4 S4 S5 S1)
+decl f10 :: S5
+#42 := f10
+decl f9 :: S4
+#41 := f9
+#43 := (f5 f9 f9 f10)
+decl f1 :: S1
+#4 := f1
+#124 := (= f1 #43)
+#137 := (not #124)
+#644 := [hypothesis]: #137
+decl f6 :: (-> S4 S5 S1)
+#45 := (f6 f9 f10)
+#128 := (= f1 #45)
+#341 := (or #128 #124)
+#138 := (iff #128 #137)
+#46 := (= #45 f1)
+#44 := (= #43 f1)
+#47 := (iff #44 #46)
+#48 := (not #47)
+#141 := (iff #48 #138)
+#131 := (iff #124 #128)
+#134 := (not #131)
+#139 := (iff #134 #138)
+#140 := [rewrite]: #139
+#135 := (iff #48 #134)
+#132 := (iff #47 #131)
+#129 := (iff #46 #128)
+#130 := [rewrite]: #129
+#126 := (iff #44 #124)
+#127 := [rewrite]: #126
+#133 := [monotonicity #127 #130]: #132
+#136 := [monotonicity #133]: #135
+#142 := [trans #136 #140]: #141
+#123 := [asserted]: #48
+#145 := [mp #123 #142]: #138
+#253 := (not #138)
+#340 := (or #128 #124 #253)
 #254 := [def-axiom]: #340
-#255 := [unit-resolution #254 #86]: #341
-#307 := [unit-resolution #255 #644]: #69
-#342 := (not #69)
-#309 := (or #66 #342)
-#27 := (:var 0 S3)
-#26 := (:var 1 S2)
-#25 := (:var 2 S2)
-#28 := (f3 #25 #26 #27)
-#683 := (pattern #28)
-#32 := (f6 #26 #27)
-#111 := (= f1 #32)
-#30 := (f6 #25 #27)
-#108 := (= f1 #30)
-#114 := (or #108 #111)
-#104 := (= f1 #28)
-#117 := (iff #104 #114)
-#684 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #683) #117)
-#120 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #117)
-#687 := (iff #120 #684)
-#685 := (iff #117 #117)
-#686 := [refl]: #685
-#688 := [quant-intro #686]: #687
-#151 := (~ #120 #120)
-#161 := (~ #117 #117)
-#162 := [refl]: #161
-#152 := [nnf-pos #162]: #151
-#33 := (= #32 f1)
-#31 := (= #30 f1)
-#34 := (or #31 #33)
-#29 := (= #28 f1)
-#35 := (iff #29 #34)
-#36 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #35)
-#121 := (iff #36 #120)
-#118 := (iff #35 #117)
-#115 := (iff #34 #114)
-#112 := (iff #33 #111)
-#113 := [rewrite]: #112
-#109 := (iff #31 #108)
-#110 := [rewrite]: #109
-#116 := [monotonicity #110 #113]: #115
-#106 := (iff #29 #104)
-#107 := [rewrite]: #106
-#119 := [monotonicity #107 #116]: #118
-#122 := [quant-intro #119]: #121
-#103 := [asserted]: #36
-#125 := [mp #103 #122]: #120
-#163 := [mp~ #125 #152]: #120
-#689 := [mp #163 #688]: #684
-#320 := (not #684)
-#450 := (or #320 #72)
-#346 := (or #69 #69)
-#343 := (iff #66 #346)
+#255 := [unit-resolution #254 #145]: #341
+#307 := [unit-resolution #255 #644]: #128
+#342 := (not #128)
+#309 := (or #124 #342)
+#22 := (:var 0 S5)
+#21 := (:var 1 S4)
+#20 := (:var 2 S4)
+#23 := (f5 #20 #21 #22)
+#676 := (pattern #23)
+#27 := (f6 #21 #22)
+#92 := (= f1 #27)
+#25 := (f6 #20 #22)
+#89 := (= f1 #25)
+#95 := (or #89 #92)
+#85 := (= f1 #23)
+#98 := (iff #85 #95)
+#677 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #676) #98)
+#101 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #98)
+#680 := (iff #101 #677)
+#678 := (iff #98 #98)
+#679 := [refl]: #678
+#681 := [quant-intro #679]: #680
+#147 := (~ #101 #101)
+#143 := (~ #98 #98)
+#161 := [refl]: #143
+#148 := [nnf-pos #161]: #147
+#28 := (= #27 f1)
+#26 := (= #25 f1)
+#29 := (or #26 #28)
+#24 := (= #23 f1)
+#30 := (iff #24 #29)
+#31 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #30)
+#102 := (iff #31 #101)
+#99 := (iff #30 #98)
+#96 := (iff #29 #95)
+#93 := (iff #28 #92)
+#94 := [rewrite]: #93
+#90 := (iff #26 #89)
+#91 := [rewrite]: #90
+#97 := [monotonicity #91 #94]: #96
+#87 := (iff #24 #85)
+#88 := [rewrite]: #87
+#100 := [monotonicity #88 #97]: #99
+#103 := [quant-intro #100]: #102
+#84 := [asserted]: #31
+#106 := [mp #84 #103]: #101
+#162 := [mp~ #106 #148]: #101
+#682 := [mp #162 #681]: #677
+#320 := (not #677)
+#450 := (or #320 #131)
+#346 := (or #128 #128)
+#343 := (iff #124 #346)
 #657 := (or #320 #343)
 #332 := (iff #657 #450)
 #665 := (iff #450 #450)
 #666 := [rewrite]: #665
-#661 := (iff #343 #72)
-#347 := (iff #346 #69)
+#661 := (iff #343 #131)
+#347 := (iff #346 #128)
 #326 := [rewrite]: #347
 #663 := [monotonicity #326]: #661
 #664 := [monotonicity #663]: #332
 #667 := [trans #664 #666]: #332
 #331 := [quant-inst]: #657
 #662 := [mp #331 #667]: #450
-#308 := [unit-resolution #662 #689]: #72
-#668 := (or #75 #66 #342)
+#308 := [unit-resolution #662 #682]: #131
+#668 := (or #134 #124 #342)
 #658 := [def-axiom]: #668
 #310 := [unit-resolution #658 #308]: #309
 #646 := [unit-resolution #310 #307 #644]: false
-#647 := [lemma #646]: #66
-#345 := (or #342 #78)
-#333 := (or #342 #78 #253)
+#647 := [lemma #646]: #124
+#345 := (or #342 #137)
+#333 := (or #342 #137 #253)
 #344 := [def-axiom]: #333
-#273 := [unit-resolution #344 #86]: #345
+#273 := [unit-resolution #344 #145]: #345
 #648 := [unit-resolution #273 #647]: #342
-#649 := (or #78 #69)
-#318 := (or #75 #78 #69)
+#649 := (or #137 #128)
+#318 := (or #134 #137 #128)
 #323 := [def-axiom]: #318
 #650 := [unit-resolution #323 #308]: #649
 [unit-resolution #650 #648 #647]: false
 unsat
-2736190123a7d967c1298876eb9c2dad86e52b59 258 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f8 :: S3
-#13 := f8
-decl f6 :: S2
-#9 := f6
-#624 := (f3 f6 f8)
+e52426a3e0052053afbe64c744298686dcef71b8 259 0
+#2 := false
+decl f5 :: (-> S4 S5 S1)
+decl f12 :: S5
+#47 := f12
+decl f10 :: S4
+#43 := f10
+#624 := (f5 f10 f12)
 decl f1 :: S1
 #4 := f1
 #337 := (= f1 #624)
-decl f7 :: S2
-#10 := f7
-#335 := (f3 f7 f8)
+decl f11 :: S4
+#44 := f11
+#335 := (f5 f11 f12)
 #332 := (= f1 #335)
 #622 := (or #332 #337)
-decl f4 :: (-> S2 S2 S2)
-#11 := (f4 f6 f7)
-#309 := (f3 #11 f8)
+decl f6 :: (-> S4 S4 S4)
+#45 := (f6 f10 f11)
+#309 := (f5 #45 f12)
 #441 := (= f1 #309)
 #616 := (iff #441 #622)
 #582 := (not #616)
-#580 := [hypothesis]: #582
-#34 := (:var 0 S3)
-#32 := (:var 1 S2)
-#31 := (:var 2 S2)
-#33 := (f4 #31 #32)
-#35 := (f3 #33 #34)
-#674 := (pattern #35)
-#39 := (f3 #32 #34)
-#118 := (= f1 #39)
-#37 := (f3 #31 #34)
-#115 := (= f1 #37)
-#121 := (or #115 #118)
-#111 := (= f1 #35)
-#124 := (iff #111 #121)
-#675 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #674) #124)
-#127 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #124)
-#678 := (iff #127 #675)
-#676 := (iff #124 #124)
-#677 := [refl]: #676
-#679 := [quant-intro #677]: #678
-#158 := (~ #127 #127)
-#168 := (~ #124 #124)
-#169 := [refl]: #168
-#159 := [nnf-pos #169]: #158
-#40 := (= #39 f1)
-#38 := (= #37 f1)
-#41 := (or #38 #40)
-#36 := (= #35 f1)
-#42 := (iff #36 #41)
-#43 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #42)
-#128 := (iff #43 #127)
-#125 := (iff #42 #124)
-#122 := (iff #41 #121)
-#119 := (iff #40 #118)
-#120 := [rewrite]: #119
-#116 := (iff #38 #115)
-#117 := [rewrite]: #116
-#123 := [monotonicity #117 #120]: #122
-#113 := (iff #36 #111)
-#114 := [rewrite]: #113
-#126 := [monotonicity #114 #123]: #125
-#129 := [quant-intro #126]: #128
-#110 := [asserted]: #43
-#132 := [mp #110 #129]: #127
-#170 := [mp~ #132 #159]: #127
-#680 := [mp #170 #679]: #675
-#648 := (not #675)
+#594 := (not #622)
+#606 := (not #337)
+decl f9 :: S4
+#42 := f9
+#637 := (f5 f9 f12)
+#638 := (= f1 #637)
+#484 := (or #337 #638)
+#609 := (not #484)
+#50 := (f6 f9 f10)
+#336 := (f5 #50 f12)
+#315 := (= f1 #336)
+#592 := (iff #315 #484)
+#584 := (not #592)
+#577 := [hypothesis]: #584
+#23 := (:var 0 S5)
+#21 := (:var 1 S4)
+#20 := (:var 2 S4)
+#22 := (f6 #20 #21)
+#24 := (f5 #22 #23)
+#667 := (pattern #24)
+#28 := (f5 #21 #23)
+#99 := (= f1 #28)
+#26 := (f5 #20 #23)
+#96 := (= f1 #26)
+#102 := (or #96 #99)
+#92 := (= f1 #24)
+#105 := (iff #92 #102)
+#668 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #667) #105)
+#108 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #105)
+#671 := (iff #108 #668)
+#669 := (iff #105 #105)
+#670 := [refl]: #669
+#672 := [quant-intro #670]: #671
+#154 := (~ #108 #108)
+#150 := (~ #105 #105)
+#168 := [refl]: #150
+#155 := [nnf-pos #168]: #154
+#29 := (= #28 f1)
+#27 := (= #26 f1)
+#30 := (or #27 #29)
+#25 := (= #24 f1)
+#31 := (iff #25 #30)
+#32 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #31)
+#109 := (iff #32 #108)
+#106 := (iff #31 #105)
+#103 := (iff #30 #102)
+#100 := (iff #29 #99)
+#101 := [rewrite]: #100
+#97 := (iff #27 #96)
+#98 := [rewrite]: #97
+#104 := [monotonicity #98 #101]: #103
+#94 := (iff #25 #92)
+#95 := [rewrite]: #94
+#107 := [monotonicity #95 #104]: #106
+#110 := [quant-intro #107]: #109
+#91 := [asserted]: #32
+#113 := [mp #91 #110]: #108
+#169 := [mp~ #113 #155]: #108
+#673 := [mp #169 #672]: #668
+#648 := (not #668)
+#590 := (or #648 #592)
+#601 := (or #638 #337)
+#483 := (iff #315 #601)
+#593 := (or #648 #483)
+#493 := (iff #593 #590)
+#496 := (iff #590 #590)
+#489 := [rewrite]: #496
+#494 := (iff #483 #592)
+#485 := (iff #601 #484)
+#444 := [rewrite]: #485
+#589 := [monotonicity #444]: #494
+#495 := [monotonicity #589]: #493
+#497 := [trans #495 #489]: #493
+#478 := [quant-inst]: #593
+#498 := [mp #478 #497]: #590
+#578 := [unit-resolution #498 #673 #577]: false
+#579 := [lemma #578]: #592
+#655 := (not #315)
+#652 := (or #315 #332)
+#649 := (not #652)
+#51 := (f6 #50 f11)
+#52 := (f5 #51 f12)
+#135 := (= f1 #52)
+#331 := (not #135)
+#46 := (f6 f9 #45)
+#48 := (f5 #46 f12)
+#131 := (= f1 #48)
+#144 := (not #131)
+#580 := [hypothesis]: #144
+#330 := (or #135 #131)
+#145 := (iff #135 #144)
+#53 := (= #52 f1)
+#49 := (= #48 f1)
+#54 := (iff #49 #53)
+#55 := (not #54)
+#148 := (iff #55 #145)
+#138 := (iff #131 #135)
+#141 := (not #138)
+#146 := (iff #141 #145)
+#147 := [rewrite]: #146
+#142 := (iff #55 #141)
+#139 := (iff #54 #138)
+#136 := (iff #53 #135)
+#137 := [rewrite]: #136
+#133 := (iff #49 #131)
+#134 := [rewrite]: #133
+#140 := [monotonicity #134 #137]: #139
+#143 := [monotonicity #140]: #142
+#149 := [trans #143 #147]: #148
+#130 := [asserted]: #55
+#152 := [mp #130 #149]: #145
+#242 := (not #145)
+#329 := (or #135 #131 #242)
+#243 := [def-axiom]: #329
+#244 := [unit-resolution #243 #152]: #330
+#574 := [unit-resolution #244 #580]: #135
+#565 := (or #331 #652)
+#654 := (iff #135 #652)
+#320 := (or #648 #654)
+#321 := [quant-inst]: #320
+#581 := [unit-resolution #321 #673]: #654
+#650 := (not #654)
+#292 := (or #650 #331 #652)
+#635 := [def-axiom]: #292
+#566 := [unit-resolution #635 #581]: #565
+#568 := [unit-resolution #566 #574]: #652
+#658 := (not #332)
 #598 := (or #648 #616)
 #621 := (or #337 #332)
 #625 := (iff #441 #621)
@@ -52457,94 +52677,16 @@
 #462 := [trans #614 #461]: #613
 #619 := [quant-inst]: #618
 #463 := [mp #619 #462]: #598
-#574 := [unit-resolution #463 #680 #580]: false
-#581 := [lemma #574]: #616
-#594 := (not #622)
-#658 := (not #332)
-decl f5 :: S2
-#8 := f5
-#16 := (f4 f5 f6)
-#336 := (f3 #16 f8)
-#315 := (= f1 #336)
-#652 := (or #315 #332)
-#649 := (not #652)
-#17 := (f4 #16 f7)
-#18 := (f3 #17 f8)
-#76 := (= f1 #18)
-#331 := (not #76)
-#12 := (f4 f5 #11)
-#14 := (f3 #12 f8)
-#73 := (= f1 #14)
-#637 := (f3 f5 f8)
-#638 := (= f1 #637)
-#484 := (or #337 #638)
-#592 := (iff #315 #484)
-#584 := (not #592)
-#577 := [hypothesis]: #584
-#590 := (or #648 #592)
-#601 := (or #638 #337)
-#483 := (iff #315 #601)
-#593 := (or #648 #483)
-#493 := (iff #593 #590)
-#496 := (iff #590 #590)
-#489 := [rewrite]: #496
-#494 := (iff #483 #592)
-#485 := (iff #601 #484)
-#444 := [rewrite]: #485
-#589 := [monotonicity #444]: #494
-#495 := [monotonicity #589]: #493
-#497 := [trans #495 #489]: #493
-#478 := [quant-inst]: #593
-#498 := [mp #478 #497]: #590
-#578 := [unit-resolution #498 #680 #577]: false
-#579 := [lemma #578]: #592
-#85 := (not #73)
-#565 := [hypothesis]: #85
-#330 := (or #76 #73)
-#86 := (iff #76 #85)
-#19 := (= #18 f1)
-#15 := (= #14 f1)
-#20 := (iff #15 #19)
-#21 := (not #20)
-#89 := (iff #21 #86)
-#79 := (iff #73 #76)
-#82 := (not #79)
-#87 := (iff #82 #86)
-#88 := [rewrite]: #87
-#83 := (iff #21 #82)
-#80 := (iff #20 #79)
-#77 := (iff #19 #76)
-#78 := [rewrite]: #77
-#74 := (iff #15 #73)
-#75 := [rewrite]: #74
-#81 := [monotonicity #75 #78]: #80
-#84 := [monotonicity #81]: #83
-#90 := [trans #84 #88]: #89
-#72 := [asserted]: #21
-#93 := [mp #72 #90]: #86
-#242 := (not #86)
-#329 := (or #76 #73 #242)
-#243 := [def-axiom]: #329
-#244 := [unit-resolution #243 #93]: #330
-#566 := [unit-resolution #244 #565]: #76
-#569 := (or #331 #652)
-#654 := (iff #76 #652)
-#320 := (or #648 #654)
-#321 := [quant-inst]: #320
-#568 := [unit-resolution #321 #680]: #654
-#650 := (not #654)
-#292 := (or #650 #331 #652)
-#635 := [def-axiom]: #292
-#570 := [unit-resolution #635 #568]: #569
-#571 := [unit-resolution #570 #566]: #652
+#569 := [unit-resolution #463 #673]: #616
+#559 := (or #582 #594)
 #357 := (not #441)
 #641 := (or #441 #638)
 #630 := (not #641)
-#572 := (or #73 #630)
-#278 := (iff #73 #641)
+#571 := (or #131 #630)
+#278 := (iff #131 #641)
 #283 := (or #648 #278)
 #639 := (or #638 #441)
-#640 := (iff #73 #639)
+#640 := (iff #131 #639)
 #284 := (or #648 #640)
 #644 := (iff #284 #283)
 #633 := (iff #283 #283)
@@ -52557,134 +52699,196 @@
 #340 := [trans #647 #634]: #644
 #646 := [quant-inst]: #284
 #356 := [mp #646 #340]: #283
-#567 := [unit-resolution #356 #680]: #278
+#570 := [unit-resolution #356 #673]: #278
 #627 := (not #278)
-#631 := (or #627 #73 #630)
+#631 := (or #627 #131 #630)
 #628 := [def-axiom]: #631
-#558 := [unit-resolution #628 #567]: #572
-#559 := [unit-resolution #558 #565]: #630
+#567 := [unit-resolution #628 #570]: #571
+#572 := [unit-resolution #567 #580]: #630
 #358 := (or #641 #357)
 #344 := [def-axiom]: #358
-#561 := [unit-resolution #344 #559]: #357
+#558 := [unit-resolution #344 #572]: #357
 #576 := (or #582 #441 #594)
 #573 := [def-axiom]: #576
-#562 := [unit-resolution #573 #561 #581]: #594
+#561 := [unit-resolution #573 #558]: #559
+#562 := [unit-resolution #561 #569]: #594
 #605 := (or #622 #658)
 #499 := [def-axiom]: #605
 #563 := [unit-resolution #499 #562]: #658
 #307 := (or #649 #315 #332)
 #312 := [def-axiom]: #307
-#560 := [unit-resolution #312 #563 #571]: #315
-#609 := (not #484)
+#560 := [unit-resolution #312 #563 #568]: #315
 #359 := (not #638)
 #250 := (or #641 #359)
 #629 := [def-axiom]: #250
-#564 := [unit-resolution #629 #559]: #359
-#606 := (not #337)
+#564 := [unit-resolution #629 #572]: #359
 #500 := (or #622 #606)
 #501 := [def-axiom]: #500
 #544 := [unit-resolution #501 #562]: #606
 #610 := (or #609 #337 #638)
 #604 := [def-axiom]: #610
 #545 := [unit-resolution #604 #544 #564]: #609
-#655 := (not #315)
 #442 := (or #584 #655 #484)
 #443 := [def-axiom]: #442
 #547 := [unit-resolution #443 #545 #560 #579]: false
-#548 := [lemma #547]: #73
-#334 := (or #331 #85)
-#322 := (or #331 #85 #242)
+#548 := [lemma #547]: #131
+#334 := (or #331 #144)
+#322 := (or #331 #144 #242)
 #333 := [def-axiom]: #322
-#262 := [unit-resolution #333 #93]: #334
+#262 := [unit-resolution #333 #152]: #334
 #549 := [unit-resolution #262 #548]: #331
-#550 := (or #76 #649)
-#308 := (or #650 #76 #649)
+#550 := (or #135 #649)
+#308 := (or #650 #135 #649)
 #651 := [def-axiom]: #308
-#551 := [unit-resolution #651 #568]: #550
+#551 := [unit-resolution #651 #581]: #550
 #552 := [unit-resolution #551 #549]: #649
+#656 := (or #652 #655)
+#657 := [def-axiom]: #656
+#553 := [unit-resolution #657 #552]: #655
+#611 := (or #584 #315 #609)
+#440 := [def-axiom]: #611
+#554 := [unit-resolution #440 #553 #579]: #609
+#607 := (or #484 #606)
+#608 := [def-axiom]: #607
+#555 := [unit-resolution #608 #554]: #606
 #653 := (or #652 #658)
 #659 := [def-axiom]: #653
-#553 := [unit-resolution #659 #552]: #658
-#656 := (or #652 #655)
-#657 := [def-axiom]: #656
-#554 := [unit-resolution #657 #552]: #655
-#611 := (or #584 #315 #609)
-#440 := [def-axiom]: #611
-#555 := [unit-resolution #440 #554 #579]: #609
-#607 := (or #484 #606)
-#608 := [def-axiom]: #607
-#556 := [unit-resolution #608 #555]: #606
+#556 := [unit-resolution #659 #552]: #658
 #591 := (or #594 #332 #337)
 #595 := [def-axiom]: #591
-#546 := [unit-resolution #595 #556 #553]: #594
-#557 := (or #85 #641)
-#632 := (or #627 #85 #641)
+#546 := [unit-resolution #595 #556 #555]: #594
+#557 := (or #144 #641)
+#632 := (or #627 #144 #641)
 #341 := [def-axiom]: #632
-#535 := [unit-resolution #341 #567]: #557
+#535 := [unit-resolution #341 #570]: #557
 #536 := [unit-resolution #535 #548]: #641
 #602 := (or #484 #359)
 #603 := [def-axiom]: #602
-#538 := [unit-resolution #603 #555]: #359
+#538 := [unit-resolution #603 #554]: #359
 #352 := (or #630 #441 #638)
 #353 := [def-axiom]: #352
 #539 := [unit-resolution #353 #538 #536]: #441
 #575 := (or #582 #357 #622)
 #585 := [def-axiom]: #575
-[unit-resolution #585 #539 #546 #581]: false
-unsat
-eaeae96294c9f1d454cc1537d34925d3b42674d8 153 0
-#2 := false
-decl f7 :: (-> S2 S3 S1)
-decl f6 :: S3
-#10 := f6
-decl f5 :: S2
-#9 := f5
-#15 := (f7 f5 f6)
-decl f1 :: S1
-#4 := f1
+#540 := [unit-resolution #585 #539 #546]: #582
+[unit-resolution #463 #673 #540]: false
+unsat
+93fbe735de801e20a39bb6562cd0c0740027f61d 153 0
+#2 := false
+decl f4 :: (-> S2 S3 S1)
+decl f11 :: S3
+#43 := f11
+decl f10 :: S2
+#42 := f10
+#48 := (f4 f10 f11)
+decl f1 :: S1
+#4 := f1
+#135 := (= f1 #48)
+#189 := (not #135)
+decl f9 :: S2
+#41 := f9
+#46 := (f4 f9 f11)
+#132 := (= f1 #46)
+#188 := (not #132)
+#190 := (or #188 #189)
+#191 := (not #190)
+#350 := [hypothesis]: #191
+decl f3 :: (-> S2 S2 S3 S1)
+#44 := (f3 f9 f10 f11)
+#128 := (= f1 #44)
+#147 := (not #128)
+#356 := (or #147 #190)
+#202 := (iff #128 #190)
+#138 := (and #132 #135)
+#148 := (iff #138 #147)
+#205 := (iff #148 #202)
+#197 := (iff #190 #128)
+#203 := (iff #197 #202)
+#204 := [rewrite]: #203
+#200 := (iff #148 #197)
+#194 := (iff #191 #147)
+#198 := (iff #194 #197)
+#199 := [rewrite]: #198
+#195 := (iff #148 #194)
+#192 := (iff #138 #191)
+#193 := [rewrite]: #192
+#196 := [monotonicity #193]: #195
+#201 := [trans #196 #199]: #200
+#206 := [trans #201 #204]: #205
+#49 := (= #48 f1)
+#47 := (= #46 f1)
+#50 := (and #47 #49)
+#45 := (= #44 f1)
+#51 := (iff #45 #50)
+#52 := (not #51)
+#151 := (iff #52 #148)
+#141 := (iff #128 #138)
+#144 := (not #141)
+#149 := (iff #144 #148)
+#150 := [rewrite]: #149
+#145 := (iff #52 #144)
+#142 := (iff #51 #141)
+#139 := (iff #50 #138)
+#136 := (iff #49 #135)
+#137 := [rewrite]: #136
+#133 := (iff #47 #132)
+#134 := [rewrite]: #133
+#140 := [monotonicity #134 #137]: #139
+#130 := (iff #45 #128)
+#131 := [rewrite]: #130
+#143 := [monotonicity #131 #140]: #142
+#146 := [monotonicity #143]: #145
+#152 := [trans #146 #150]: #151
+#127 := [asserted]: #52
+#155 := [mp #127 #152]: #148
+#207 := [mp #155 #206]: #202
+#363 := (not #202)
+#373 := (or #147 #190 #363)
+#377 := [def-axiom]: #373
+#691 := [unit-resolution #377 #207]: #356
+#480 := [unit-resolution #691 #350]: #147
+#349 := (or #128 #190)
+#693 := (iff #128 #191)
+#10 := (:var 0 S3)
+#9 := (:var 1 S2)
+#8 := (:var 2 S2)
+#11 := (f3 #8 #9 #10)
+#699 := (pattern #11)
+#15 := (f4 #9 #10)
 #76 := (= f1 #15)
-#178 := (not #76)
-decl f4 :: S2
-#8 := f4
-#13 := (f7 f4 f6)
+#180 := (not #76)
+#13 := (f4 #8 #10)
 #73 := (= f1 #13)
-#177 := (not #73)
-#165 := (or #177 #178)
-#166 := (not #165)
-#350 := [hypothesis]: #166
-decl f3 :: (-> S2 S2 S3 S1)
-#11 := (f3 f4 f5 f6)
+#179 := (not #73)
+#163 := (or #179 #180)
+#164 := (not #163)
 #70 := (= f1 #11)
-#88 := (not #70)
-#356 := (or #88 #165)
-#189 := (iff #70 #165)
+#181 := (iff #70 #164)
+#700 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #699) #181)
+#184 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #181)
+#703 := (iff #184 #700)
+#701 := (iff #181 #181)
+#702 := [refl]: #701
+#704 := [quant-intro #702]: #703
 #79 := (and #73 #76)
-#89 := (iff #79 #88)
-#192 := (iff #89 #189)
-#184 := (iff #165 #70)
-#190 := (iff #184 #189)
-#191 := [rewrite]: #190
-#187 := (iff #89 #184)
-#181 := (iff #166 #88)
-#185 := (iff #181 #184)
-#186 := [rewrite]: #185
-#182 := (iff #89 #181)
-#179 := (iff #79 #166)
-#180 := [rewrite]: #179
-#183 := [monotonicity #180]: #182
-#188 := [trans #183 #186]: #187
-#193 := [trans #188 #191]: #192
+#82 := (iff #70 #79)
+#85 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #82)
+#185 := (iff #85 #184)
+#182 := (iff #82 #181)
+#165 := (iff #79 #164)
+#166 := [rewrite]: #165
+#183 := [monotonicity #166]: #182
+#186 := [quant-intro #183]: #185
+#169 := (~ #85 #85)
+#167 := (~ #82 #82)
+#168 := [refl]: #167
+#170 := [nnf-pos #168]: #169
 #16 := (= #15 f1)
 #14 := (= #13 f1)
 #17 := (and #14 #16)
 #12 := (= #11 f1)
 #18 := (iff #12 #17)
-#19 := (not #18)
-#92 := (iff #19 #89)
-#82 := (iff #70 #79)
-#85 := (not #82)
-#90 := (iff #85 #89)
-#91 := [rewrite]: #90
+#19 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #18)
 #86 := (iff #19 #85)
 #83 := (iff #18 #82)
 #80 := (iff #17 #79)
@@ -52696,532 +52900,469 @@
 #71 := (iff #12 #70)
 #72 := [rewrite]: #71
 #84 := [monotonicity #72 #81]: #83
-#87 := [monotonicity #84]: #86
-#93 := [trans #87 #91]: #92
+#87 := [quant-intro #84]: #86
 #69 := [asserted]: #19
-#96 := [mp #69 #93]: #89
-#194 := [mp #96 #193]: #189
-#363 := (not #189)
-#373 := (or #88 #165 #363)
-#377 := [def-axiom]: #373
-#691 := [unit-resolution #377 #194]: #356
-#480 := [unit-resolution #691 #350]: #88
-#349 := (or #70 #165)
-#693 := (iff #70 #166)
-#43 := (:var 0 S3)
-#42 := (:var 1 S2)
-#41 := (:var 2 S2)
-#44 := (f3 #41 #42 #43)
-#720 := (pattern #44)
-#48 := (f7 #42 #43)
-#141 := (= f1 #48)
-#196 := (not #141)
-#46 := (f7 #41 #43)
-#138 := (= f1 #46)
-#195 := (not #138)
-#197 := (or #195 #196)
-#198 := (not #197)
-#134 := (= f1 #44)
-#201 := (iff #134 #198)
-#721 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #720) #201)
-#204 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #201)
-#724 := (iff #204 #721)
-#722 := (iff #201 #201)
-#723 := [refl]: #722
-#725 := [quant-intro #723]: #724
-#144 := (and #138 #141)
-#147 := (iff #134 #144)
-#150 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #147)
-#205 := (iff #150 #204)
-#202 := (iff #147 #201)
-#199 := (iff #144 #198)
-#200 := [rewrite]: #199
-#203 := [monotonicity #200]: #202
-#206 := [quant-intro #203]: #205
-#163 := (~ #150 #150)
-#174 := (~ #147 #147)
-#175 := [refl]: #174
-#164 := [nnf-pos #175]: #163
-#49 := (= #48 f1)
-#47 := (= #46 f1)
-#50 := (and #47 #49)
-#45 := (= #44 f1)
-#51 := (iff #45 #50)
-#52 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #51)
-#151 := (iff #52 #150)
-#148 := (iff #51 #147)
-#145 := (iff #50 #144)
-#142 := (iff #49 #141)
-#143 := [rewrite]: #142
-#139 := (iff #47 #138)
-#140 := [rewrite]: #139
-#146 := [monotonicity #140 #143]: #145
-#136 := (iff #45 #134)
-#137 := [rewrite]: #136
-#149 := [monotonicity #137 #146]: #148
-#152 := [quant-intro #149]: #151
-#133 := [asserted]: #52
-#155 := [mp #133 #152]: #150
-#176 := [mp~ #155 #164]: #150
-#207 := [mp #176 #206]: #204
-#726 := [mp #207 #725]: #721
-#687 := (not #721)
+#90 := [mp #69 #87]: #85
+#156 := [mp~ #90 #170]: #85
+#187 := [mp #156 #186]: #184
+#705 := [mp #187 #704]: #700
+#687 := (not #700)
 #361 := (or #687 #693)
 #362 := [quant-inst]: #361
-#689 := [unit-resolution #362 #726]: #693
+#689 := [unit-resolution #362 #705]: #693
 #694 := (not #693)
-#695 := (or #694 #70 #165)
+#695 := (or #694 #128 #190)
 #696 := [def-axiom]: #695
 #690 := [unit-resolution #696 #689]: #349
 #333 := [unit-resolution #690 #480 #350]: false
-#674 := [lemma #333]: #165
-#303 := (or #70 #166)
-#374 := (or #70 #166 #363)
+#674 := [lemma #333]: #190
+#303 := (or #128 #191)
+#374 := (or #128 #191 #363)
 #375 := [def-axiom]: #374
-#376 := [unit-resolution #375 #194]: #303
-#337 := [unit-resolution #376 #674]: #70
-#338 := (or #88 #166)
-#697 := (or #694 #88 #166)
+#376 := [unit-resolution #375 #207]: #303
+#337 := [unit-resolution #376 #674]: #128
+#338 := (or #147 #191)
+#697 := (or #694 #147 #191)
 #692 := [def-axiom]: #697
 #339 := [unit-resolution #692 #689]: #338
 [unit-resolution #339 #337 #674]: false
 unsat
-95f397b9920f2327707ec91629a09aa96ab88f3c 141 0
-#2 := false
-decl f7 :: (-> S2 S3 S1)
-decl f6 :: S3
-#10 := f6
-decl f5 :: S2
-#9 := f5
-#246 := (f7 f5 f6)
+851ff8bcadccbc9cf1f800982f40e3e72c411669 141 0
+#2 := false
+decl f4 :: (-> S2 S3 S1)
+decl f10 :: S3
+#42 := f10
+decl f8 :: S2
+#36 := f8
+#246 := (f4 f8 f10)
 decl f1 :: S1
 #4 := f1
 #333 := (= f1 #246)
 #247 := (not #333)
-decl f4 :: S2
-#8 := f4
-#334 := (f7 f4 f6)
+decl f9 :: S2
+#41 := f9
+#334 := (f4 f9 f10)
 #248 := (= f1 #334)
 #335 := (not #248)
 #326 := (or #335 #247)
 #337 := (not #326)
 decl f3 :: (-> S2 S2 S3 S1)
-#11 := (f3 f4 f5 f6)
+#43 := (f3 f9 f8 f10)
+#122 := (= f1 #43)
+#338 := (iff #122 #337)
+#10 := (:var 0 S3)
+#9 := (:var 1 S2)
+#8 := (:var 2 S2)
+#11 := (f3 #8 #9 #10)
+#662 := (pattern #11)
+#15 := (f4 #9 #10)
+#70 := (= f1 #15)
+#163 := (not #70)
+#13 := (f4 #8 #10)
+#67 := (= f1 #13)
+#162 := (not #67)
+#146 := (or #162 #163)
+#147 := (not #146)
 #64 := (= f1 #11)
-#338 := (iff #64 #337)
-#15 := (:var 0 S3)
-#37 := (:var 1 S2)
-#36 := (:var 2 S2)
-#38 := (f3 #36 #37 #15)
-#683 := (pattern #38)
-#42 := (f7 #37 #15)
-#124 := (= f1 #42)
-#161 := (not #124)
-#40 := (f7 #36 #15)
-#121 := (= f1 #40)
-#160 := (not #121)
-#148 := (or #160 #161)
-#149 := (not #148)
-#117 := (= f1 #38)
-#164 := (iff #117 #149)
-#684 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #683) #164)
+#164 := (iff #64 #147)
+#663 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #662) #164)
 #167 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #164)
-#687 := (iff #167 #684)
-#685 := (iff #164 #164)
-#686 := [refl]: #685
-#688 := [quant-intro #686]: #687
-#127 := (and #121 #124)
-#130 := (iff #117 #127)
-#133 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #130)
-#168 := (iff #133 #167)
-#165 := (iff #130 #164)
-#162 := (iff #127 #149)
-#163 := [rewrite]: #162
-#166 := [monotonicity #163]: #165
+#666 := (iff #167 #663)
+#664 := (iff #164 #164)
+#665 := [refl]: #664
+#667 := [quant-intro #665]: #666
+#73 := (and #67 #70)
+#76 := (iff #64 #73)
+#79 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #76)
+#168 := (iff #79 #167)
+#165 := (iff #76 #164)
+#148 := (iff #73 #147)
+#149 := [rewrite]: #148
+#166 := [monotonicity #149]: #165
 #169 := [quant-intro #166]: #168
-#146 := (~ #133 #133)
-#157 := (~ #130 #130)
-#158 := [refl]: #157
-#147 := [nnf-pos #158]: #146
-#43 := (= #42 f1)
-#41 := (= #40 f1)
-#44 := (and #41 #43)
-#39 := (= #38 f1)
-#45 := (iff #39 #44)
-#46 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #45)
-#134 := (iff #46 #133)
-#131 := (iff #45 #130)
-#128 := (iff #44 #127)
-#125 := (iff #43 #124)
-#126 := [rewrite]: #125
-#122 := (iff #41 #121)
-#123 := [rewrite]: #122
-#129 := [monotonicity #123 #126]: #128
-#119 := (iff #39 #117)
-#120 := [rewrite]: #119
-#132 := [monotonicity #120 #129]: #131
-#135 := [quant-intro #132]: #134
-#116 := [asserted]: #46
-#138 := [mp #116 #135]: #133
-#159 := [mp~ #138 #147]: #133
-#170 := [mp #159 #169]: #167
-#689 := [mp #170 #688]: #684
-#336 := (not #684)
+#152 := (~ #79 #79)
+#150 := (~ #76 #76)
+#151 := [refl]: #150
+#153 := [nnf-pos #151]: #152
+#16 := (= #15 f1)
+#14 := (= #13 f1)
+#17 := (and #14 #16)
+#12 := (= #11 f1)
+#18 := (iff #12 #17)
+#19 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #18)
+#80 := (iff #19 #79)
+#77 := (iff #18 #76)
+#74 := (iff #17 #73)
+#71 := (iff #16 #70)
+#72 := [rewrite]: #71
+#68 := (iff #14 #67)
+#69 := [rewrite]: #68
+#75 := [monotonicity #69 #72]: #74
+#65 := (iff #12 #64)
+#66 := [rewrite]: #65
+#78 := [monotonicity #66 #75]: #77
+#81 := [quant-intro #78]: #80
+#63 := [asserted]: #19
+#84 := [mp #63 #81]: #79
+#139 := [mp~ #84 #153]: #79
+#170 := [mp #139 #169]: #167
+#668 := [mp #170 #667]: #663
+#336 := (not #663)
 #340 := (or #336 #338)
 #319 := [quant-inst]: #340
-#266 := [unit-resolution #319 #689]: #338
+#266 := [unit-resolution #319 #668]: #338
 #325 := (not #338)
 #339 := (or #325 #337)
-#12 := (= #11 f1)
-#13 := (not #12)
-#14 := (not #13)
-#75 := (iff #14 #64)
-#67 := (not #64)
-#70 := (not #67)
-#73 := (iff #70 #64)
-#74 := [rewrite]: #73
-#71 := (iff #14 #70)
-#68 := (iff #13 #67)
-#65 := (iff #12 #64)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#76 := [trans #72 #74]: #75
-#63 := [asserted]: #14
-#79 := [mp #63 #76]: #64
-#659 := (or #325 #67 #337)
+#44 := (= #43 f1)
+#45 := (not #44)
+#46 := (not #45)
+#134 := (iff #46 #122)
+#126 := (not #122)
+#129 := (not #126)
+#132 := (iff #129 #122)
+#133 := [rewrite]: #132
+#130 := (iff #46 #129)
+#127 := (iff #45 #126)
+#124 := (iff #44 #122)
+#125 := [rewrite]: #124
+#128 := [monotonicity #125]: #127
+#131 := [monotonicity #128]: #130
+#135 := [trans #131 #133]: #134
+#121 := [asserted]: #46
+#138 := [mp #121 #135]: #122
+#659 := (or #325 #126 #337)
 #660 := [def-axiom]: #659
-#653 := [unit-resolution #660 #79]: #339
+#653 := [unit-resolution #660 #138]: #339
 #296 := [unit-resolution #653 #266]: #337
 #313 := (or #326 #333)
 #443 := [def-axiom]: #313
 #637 := [unit-resolution #443 #296]: #333
-#16 := (f7 f5 #15)
-#662 := (pattern #16)
-#78 := (= f1 #16)
-#82 := (not #78)
-#663 := (forall (vars (?v0 S3)) (:pat #662) #82)
-#85 := (forall (vars (?v0 S3)) #82)
-#666 := (iff #85 #663)
-#664 := (iff #82 #82)
-#665 := [refl]: #664
-#667 := [quant-intro #665]: #666
-#152 := (~ #85 #85)
-#150 := (~ #82 #82)
-#151 := [refl]: #150
-#153 := [nnf-pos #151]: #152
-#17 := (= #16 f1)
-#18 := (not #17)
-#19 := (forall (vars (?v0 S3)) #18)
-#86 := (iff #19 #85)
-#83 := (iff #18 #82)
-#80 := (iff #17 #78)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#87 := [quant-intro #84]: #86
-#77 := [asserted]: #19
-#90 := [mp #77 #87]: #85
-#140 := [mp~ #90 #153]: #85
-#668 := [mp #140 #667]: #663
-#316 := (not #663)
+#37 := (f4 f8 #10)
+#683 := (pattern #37)
+#111 := (= f1 #37)
+#115 := (not #111)
+#684 := (forall (vars (?v0 S3)) (:pat #683) #115)
+#118 := (forall (vars (?v0 S3)) #115)
+#687 := (iff #118 #684)
+#685 := (iff #115 #115)
+#686 := [refl]: #685
+#688 := [quant-intro #686]: #687
+#144 := (~ #118 #118)
+#159 := (~ #115 #115)
+#160 := [refl]: #159
+#145 := [nnf-pos #160]: #144
+#38 := (= #37 f1)
+#39 := (not #38)
+#40 := (forall (vars (?v0 S3)) #39)
+#119 := (iff #40 #118)
+#116 := (iff #39 #115)
+#113 := (iff #38 #111)
+#114 := [rewrite]: #113
+#117 := [monotonicity #114]: #116
+#120 := [quant-intro #117]: #119
+#110 := [asserted]: #40
+#123 := [mp #110 #120]: #118
+#161 := [mp~ #123 #145]: #118
+#689 := [mp #161 #688]: #684
+#316 := (not #684)
 #652 := (or #316 #247)
 #312 := [quant-inst]: #652
-[unit-resolution #312 #668 #637]: false
-unsat
-7a53c3d1a097c7a7e4616fc3acc808abc59f3a4b 165 0
-#2 := false
-decl f7 :: (-> S2 S3 S1)
-decl f6 :: S3
-#10 := f6
-decl f4 :: S2
-#8 := f4
-#13 := (f7 f4 f6)
-decl f1 :: S1
-#4 := f1
-#69 := (= f1 #13)
-#342 := (not #69)
+[unit-resolution #312 #689 #637]: false
+unsat
+c8dc40dd3b0437286b6310dc7c352273b85f6166 165 0
+#2 := false
+decl f4 :: (-> S2 S3 S1)
+decl f10 :: S3
+#42 := f10
+decl f9 :: S2
+#41 := f9
+#45 := (f4 f9 f10)
+decl f1 :: S1
+#4 := f1
+#128 := (= f1 #45)
+#342 := (not #128)
 decl f3 :: (-> S2 S2 S3 S1)
-decl f5 :: S2
-#9 := f5
-#11 := (f3 f4 f5 f6)
-#66 := (= f1 #11)
-#346 := (f7 f5 f6)
+decl f7 :: S2
+#32 := f7
+#43 := (f3 f9 f7 f10)
+#124 := (= f1 #43)
+#346 := (f4 f7 f10)
 #343 := (= f1 #346)
 #347 := (not #343)
 #320 := [hypothesis]: #347
-#22 := (:var 0 S3)
-#23 := (f7 f5 #22)
-#676 := (pattern #23)
-#96 := (= f1 #23)
-#677 := (forall (vars (?v0 S3)) (:pat #676) #96)
-#100 := (forall (vars (?v0 S3)) #96)
-#680 := (iff #100 #677)
-#678 := (iff #96 #96)
-#679 := [refl]: #678
-#681 := [quant-intro #679]: #680
-#149 := (~ #100 #100)
-#148 := (~ #96 #96)
-#146 := [refl]: #148
-#150 := [nnf-pos #146]: #149
-#24 := (= #23 f1)
-#25 := (forall (vars (?v0 S3)) #24)
-#101 := (iff #25 #100)
-#98 := (iff #24 #96)
-#99 := [rewrite]: #98
-#102 := [quant-intro #99]: #101
-#95 := [asserted]: #25
-#105 := [mp #95 #102]: #100
-#143 := [mp~ #105 #150]: #100
-#682 := [mp #143 #681]: #677
-#308 := (not #677)
+#10 := (:var 0 S3)
+#33 := (f4 f7 #10)
+#683 := (pattern #33)
+#105 := (= f1 #33)
+#684 := (forall (vars (?v0 S3)) (:pat #683) #105)
+#109 := (forall (vars (?v0 S3)) #105)
+#687 := (iff #109 #684)
+#685 := (iff #105 #105)
+#686 := [refl]: #685
+#688 := [quant-intro #686]: #687
+#149 := (~ #109 #109)
+#163 := (~ #105 #105)
+#164 := [refl]: #163
+#150 := [nnf-pos #164]: #149
+#34 := (= #33 f1)
+#35 := (forall (vars (?v0 S3)) #34)
+#110 := (iff #35 #109)
+#107 := (iff #34 #105)
+#108 := [rewrite]: #107
+#111 := [quant-intro #108]: #110
+#104 := [asserted]: #35
+#114 := [mp #104 #111]: #109
+#165 := [mp~ #114 #150]: #109
+#689 := [mp #165 #688]: #684
+#308 := (not #684)
 #309 := (or #308 #343)
 #310 := [quant-inst]: #309
-#450 := [unit-resolution #310 #682 #320]: false
+#450 := [unit-resolution #310 #689 #320]: false
 #646 := [lemma #450]: #343
-#78 := (not #66)
-#647 := [hypothesis]: #78
-#341 := (or #69 #66)
-#79 := (iff #69 #78)
+#137 := (not #124)
+#647 := [hypothesis]: #137
+#341 := (or #128 #124)
+#138 := (iff #128 #137)
+#46 := (= #45 f1)
+#44 := (= #43 f1)
+#47 := (iff #44 #46)
+#48 := (not #47)
+#141 := (iff #48 #138)
+#131 := (iff #124 #128)
+#134 := (not #131)
+#139 := (iff #134 #138)
+#140 := [rewrite]: #139
+#135 := (iff #48 #134)
+#132 := (iff #47 #131)
+#129 := (iff #46 #128)
+#130 := [rewrite]: #129
+#126 := (iff #44 #124)
+#127 := [rewrite]: #126
+#133 := [monotonicity #127 #130]: #132
+#136 := [monotonicity #133]: #135
+#142 := [trans #136 #140]: #141
+#123 := [asserted]: #48
+#145 := [mp #123 #142]: #138
+#253 := (not #138)
+#340 := (or #128 #124 #253)
+#254 := [def-axiom]: #340
+#255 := [unit-resolution #254 #145]: #341
+#648 := [unit-resolution #255 #647]: #128
+#326 := (or #342 #347)
+#650 := (or #124 #326)
+#661 := (not #326)
+#663 := (iff #124 #661)
+#9 := (:var 1 S2)
+#8 := (:var 2 S2)
+#11 := (f3 #8 #9 #10)
+#669 := (pattern #11)
+#15 := (f4 #9 #10)
+#72 := (= f1 #15)
+#170 := (not #72)
+#13 := (f4 #8 #10)
+#69 := (= f1 #13)
+#169 := (not #69)
+#153 := (or #169 #170)
+#154 := (not #153)
+#66 := (= f1 #11)
+#171 := (iff #66 #154)
+#670 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #669) #171)
+#174 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #171)
+#673 := (iff #174 #670)
+#671 := (iff #171 #171)
+#672 := [refl]: #671
+#674 := [quant-intro #672]: #673
+#75 := (and #69 #72)
+#78 := (iff #66 #75)
+#81 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #78)
+#175 := (iff #81 #174)
+#172 := (iff #78 #171)
+#155 := (iff #75 #154)
+#156 := [rewrite]: #155
+#173 := [monotonicity #156]: #172
+#176 := [quant-intro #173]: #175
+#159 := (~ #81 #81)
+#157 := (~ #78 #78)
+#158 := [refl]: #157
+#160 := [nnf-pos #158]: #159
+#16 := (= #15 f1)
 #14 := (= #13 f1)
+#17 := (and #14 #16)
 #12 := (= #11 f1)
-#15 := (iff #12 #14)
-#16 := (not #15)
-#82 := (iff #16 #79)
-#72 := (iff #66 #69)
-#75 := (not #72)
-#80 := (iff #75 #79)
-#81 := [rewrite]: #80
-#76 := (iff #16 #75)
-#73 := (iff #15 #72)
+#18 := (iff #12 #17)
+#19 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #18)
+#82 := (iff #19 #81)
+#79 := (iff #18 #78)
+#76 := (iff #17 #75)
+#73 := (iff #16 #72)
+#74 := [rewrite]: #73
 #70 := (iff #14 #69)
 #71 := [rewrite]: #70
+#77 := [monotonicity #71 #74]: #76
 #67 := (iff #12 #66)
 #68 := [rewrite]: #67
-#74 := [monotonicity #68 #71]: #73
-#77 := [monotonicity #74]: #76
-#83 := [trans #77 #81]: #82
-#65 := [asserted]: #16
-#86 := [mp #65 #83]: #79
-#253 := (not #79)
-#340 := (or #69 #66 #253)
-#254 := [def-axiom]: #340
-#255 := [unit-resolution #254 #86]: #341
-#648 := [unit-resolution #255 #647]: #69
-#326 := (or #342 #347)
-#650 := (or #66 #326)
-#661 := (not #326)
-#663 := (iff #66 #661)
-#39 := (:var 1 S2)
-#38 := (:var 2 S2)
-#40 := (f3 #38 #39 #22)
-#690 := (pattern #40)
-#44 := (f7 #39 #22)
-#131 := (= f1 #44)
-#168 := (not #131)
-#42 := (f7 #38 #22)
-#128 := (= f1 #42)
-#167 := (not #128)
-#155 := (or #167 #168)
-#156 := (not #155)
-#124 := (= f1 #40)
-#171 := (iff #124 #156)
-#691 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #690) #171)
-#174 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #171)
-#694 := (iff #174 #691)
-#692 := (iff #171 #171)
-#693 := [refl]: #692
-#695 := [quant-intro #693]: #694
-#134 := (and #128 #131)
-#137 := (iff #124 #134)
-#140 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #137)
-#175 := (iff #140 #174)
-#172 := (iff #137 #171)
-#169 := (iff #134 #156)
-#170 := [rewrite]: #169
-#173 := [monotonicity #170]: #172
-#176 := [quant-intro #173]: #175
-#153 := (~ #140 #140)
-#164 := (~ #137 #137)
-#165 := [refl]: #164
-#154 := [nnf-pos #165]: #153
-#45 := (= #44 f1)
-#43 := (= #42 f1)
-#46 := (and #43 #45)
-#41 := (= #40 f1)
-#47 := (iff #41 #46)
-#48 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #47)
-#141 := (iff #48 #140)
-#138 := (iff #47 #137)
-#135 := (iff #46 #134)
-#132 := (iff #45 #131)
-#133 := [rewrite]: #132
-#129 := (iff #43 #128)
-#130 := [rewrite]: #129
-#136 := [monotonicity #130 #133]: #135
-#126 := (iff #41 #124)
-#127 := [rewrite]: #126
-#139 := [monotonicity #127 #136]: #138
-#142 := [quant-intro #139]: #141
-#123 := [asserted]: #48
-#145 := [mp #123 #142]: #140
-#166 := [mp~ #145 #154]: #140
-#177 := [mp #166 #176]: #174
-#696 := [mp #177 #695]: #691
-#657 := (not #691)
+#80 := [monotonicity #68 #77]: #79
+#83 := [quant-intro #80]: #82
+#65 := [asserted]: #19
+#86 := [mp #65 #83]: #81
+#146 := [mp~ #86 #160]: #81
+#177 := [mp #146 #176]: #174
+#675 := [mp #177 #674]: #670
+#657 := (not #670)
 #331 := (or #657 #663)
 #332 := [quant-inst]: #331
-#649 := [unit-resolution #332 #696]: #663
+#649 := [unit-resolution #332 #675]: #663
 #658 := (not #663)
-#318 := (or #658 #66 #326)
+#318 := (or #658 #124 #326)
 #323 := [def-axiom]: #318
 #645 := [unit-resolution #323 #649]: #650
 #651 := [unit-resolution #645 #647]: #326
 #662 := (or #661 #342 #347)
 #668 := [def-axiom]: #662
 #289 := [unit-resolution #668 #651 #648 #646]: false
-#652 := [lemma #289]: #66
-#345 := (or #342 #78)
-#333 := (or #342 #78 #253)
+#652 := [lemma #289]: #124
+#345 := (or #342 #137)
+#333 := (or #342 #137 #253)
 #344 := [def-axiom]: #333
-#273 := [unit-resolution #344 #86]: #345
+#273 := [unit-resolution #344 #145]: #345
 #654 := [unit-resolution #273 #652]: #342
-#294 := (or #78 #661)
-#659 := (or #658 #78 #661)
+#294 := (or #137 #661)
+#659 := (or #658 #137 #661)
 #319 := [def-axiom]: #659
 #295 := [unit-resolution #319 #649]: #294
 #655 := [unit-resolution #295 #652]: #661
-#664 := (or #326 #69)
+#664 := (or #326 #128)
 #665 := [def-axiom]: #664
 [unit-resolution #665 #655 #654]: false
 unsat
-f3ecd39108ba2067a1db25179cee7d64804b1fdb 164 0
+b50917d64a119ad0a5e2434a769ab9e43239ffb8 164 0
 #2 := false
 decl f3 :: (-> S2 S2 S3 S1)
-decl f6 :: S3
-#10 := f6
-decl f4 :: S2
-#8 := f4
-decl f5 :: S2
-#9 := f5
-#13 := (f3 f5 f4 f6)
-decl f1 :: S1
-#4 := f1
-#70 := (= f1 #13)
-#343 := (not #70)
-#11 := (f3 f4 f5 f6)
-#67 := (= f1 #11)
-#79 := (not #67)
-#643 := [hypothesis]: #79
-#342 := (or #70 #67)
-#80 := (iff #70 #79)
-#14 := (= #13 f1)
-#12 := (= #11 f1)
-#15 := (iff #12 #14)
-#16 := (not #15)
-#83 := (iff #16 #80)
-#73 := (iff #67 #70)
-#76 := (not #73)
-#81 := (iff #76 #80)
-#82 := [rewrite]: #81
-#77 := (iff #16 #76)
-#74 := (iff #15 #73)
-#71 := (iff #14 #70)
-#72 := [rewrite]: #71
-#68 := (iff #12 #67)
-#69 := [rewrite]: #68
-#75 := [monotonicity #69 #72]: #74
-#78 := [monotonicity #75]: #77
-#84 := [trans #78 #82]: #83
-#66 := [asserted]: #16
-#87 := [mp #66 #84]: #80
-#254 := (not #80)
-#341 := (or #70 #67 #254)
+decl f11 :: S3
+#43 := f11
+decl f9 :: S2
+#41 := f9
+decl f10 :: S2
+#42 := f10
+#46 := (f3 f10 f9 f11)
+decl f1 :: S1
+#4 := f1
+#129 := (= f1 #46)
+#343 := (not #129)
+#44 := (f3 f9 f10 f11)
+#125 := (= f1 #44)
+#138 := (not #125)
+#643 := [hypothesis]: #138
+#342 := (or #129 #125)
+#139 := (iff #129 #138)
+#47 := (= #46 f1)
+#45 := (= #44 f1)
+#48 := (iff #45 #47)
+#49 := (not #48)
+#142 := (iff #49 #139)
+#132 := (iff #125 #129)
+#135 := (not #132)
+#140 := (iff #135 #139)
+#141 := [rewrite]: #140
+#136 := (iff #49 #135)
+#133 := (iff #48 #132)
+#130 := (iff #47 #129)
+#131 := [rewrite]: #130
+#127 := (iff #45 #125)
+#128 := [rewrite]: #127
+#134 := [monotonicity #128 #131]: #133
+#137 := [monotonicity #134]: #136
+#143 := [trans #137 #141]: #142
+#124 := [asserted]: #49
+#146 := [mp #124 #143]: #139
+#254 := (not #139)
+#341 := (or #129 #125 #254)
 #255 := [def-axiom]: #341
-#256 := [unit-resolution #255 #87]: #342
-#644 := [unit-resolution #256 #643]: #70
-decl f11 :: (-> S2 S3 S1)
-#327 := (f11 f5 f6)
+#256 := [unit-resolution #255 #146]: #342
+#644 := [unit-resolution #256 #643]: #129
+decl f4 :: (-> S2 S3 S1)
+#327 := (f4 f10 f11)
 #662 := (= f1 #327)
 #664 := (not #662)
-#347 := (f11 f4 f6)
+#347 := (f4 f9 f11)
 #344 := (= f1 #347)
 #348 := (not #344)
 #332 := (or #348 #664)
-#642 := (or #67 #332)
+#642 := (or #125 #332)
 #666 := (not #332)
-#657 := (iff #67 #666)
-#40 := (:var 0 S3)
-#39 := (:var 1 S2)
-#38 := (:var 2 S2)
-#41 := (f3 #38 #39 #40)
-#691 := (pattern #41)
-#45 := (f11 #39 #40)
-#132 := (= f1 #45)
-#169 := (not #132)
-#43 := (f11 #38 #40)
-#129 := (= f1 #43)
-#168 := (not #129)
-#156 := (or #168 #169)
-#157 := (not #156)
-#125 := (= f1 #41)
-#172 := (iff #125 #157)
-#692 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #691) #172)
+#657 := (iff #125 #666)
+#10 := (:var 0 S3)
+#9 := (:var 1 S2)
+#8 := (:var 2 S2)
+#11 := (f3 #8 #9 #10)
+#670 := (pattern #11)
+#15 := (f4 #9 #10)
+#73 := (= f1 #15)
+#171 := (not #73)
+#13 := (f4 #8 #10)
+#70 := (= f1 #13)
+#170 := (not #70)
+#154 := (or #170 #171)
+#155 := (not #154)
+#67 := (= f1 #11)
+#172 := (iff #67 #155)
+#671 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #670) #172)
 #175 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #172)
-#695 := (iff #175 #692)
-#693 := (iff #172 #172)
-#694 := [refl]: #693
-#696 := [quant-intro #694]: #695
-#135 := (and #129 #132)
-#138 := (iff #125 #135)
-#141 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #138)
-#176 := (iff #141 #175)
-#173 := (iff #138 #172)
-#170 := (iff #135 #157)
-#171 := [rewrite]: #170
-#174 := [monotonicity #171]: #173
+#674 := (iff #175 #671)
+#672 := (iff #172 #172)
+#673 := [refl]: #672
+#675 := [quant-intro #673]: #674
+#76 := (and #70 #73)
+#79 := (iff #67 #76)
+#82 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #79)
+#176 := (iff #82 #175)
+#173 := (iff #79 #172)
+#156 := (iff #76 #155)
+#157 := [rewrite]: #156
+#174 := [monotonicity #157]: #173
 #177 := [quant-intro #174]: #176
-#154 := (~ #141 #141)
-#165 := (~ #138 #138)
-#166 := [refl]: #165
-#155 := [nnf-pos #166]: #154
-#46 := (= #45 f1)
-#44 := (= #43 f1)
-#47 := (and #44 #46)
-#42 := (= #41 f1)
-#48 := (iff #42 #47)
-#49 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #48)
-#142 := (iff #49 #141)
-#139 := (iff #48 #138)
-#136 := (iff #47 #135)
-#133 := (iff #46 #132)
-#134 := [rewrite]: #133
-#130 := (iff #44 #129)
-#131 := [rewrite]: #130
-#137 := [monotonicity #131 #134]: #136
-#127 := (iff #42 #125)
-#128 := [rewrite]: #127
-#140 := [monotonicity #128 #137]: #139
-#143 := [quant-intro #140]: #142
-#124 := [asserted]: #49
-#146 := [mp #124 #143]: #141
-#167 := [mp~ #146 #155]: #141
-#178 := [mp #167 #177]: #175
-#697 := [mp #178 #696]: #692
-#319 := (not #692)
+#160 := (~ #82 #82)
+#158 := (~ #79 #79)
+#159 := [refl]: #158
+#161 := [nnf-pos #159]: #160
+#16 := (= #15 f1)
+#14 := (= #13 f1)
+#17 := (and #14 #16)
+#12 := (= #11 f1)
+#18 := (iff #12 #17)
+#19 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #18)
+#83 := (iff #19 #82)
+#80 := (iff #18 #79)
+#77 := (iff #17 #76)
+#74 := (iff #16 #73)
+#75 := [rewrite]: #74
+#71 := (iff #14 #70)
+#72 := [rewrite]: #71
+#78 := [monotonicity #72 #75]: #77
+#68 := (iff #12 #67)
+#69 := [rewrite]: #68
+#81 := [monotonicity #69 #78]: #80
+#84 := [quant-intro #81]: #83
+#66 := [asserted]: #19
+#87 := [mp #66 #84]: #82
+#147 := [mp~ #87 #161]: #82
+#178 := [mp #147 #177]: #175
+#676 := [mp #178 #675]: #671
+#319 := (not #671)
 #366 := (or #319 #657)
 #367 := [quant-inst]: #366
-#638 := [unit-resolution #367 #697]: #657
+#638 := [unit-resolution #367 #676]: #657
 #368 := (not #657)
-#369 := (or #368 #67 #332)
+#369 := (or #368 #125 #332)
 #262 := [def-axiom]: #369
 #352 := [unit-resolution #262 #638]: #642
 #353 := [unit-resolution #352 #643]: #332
 #355 := (or #343 #666)
-#663 := (iff #70 #666)
+#663 := (iff #129 #666)
 #324 := (or #319 #663)
 #321 := (or #664 #348)
 #451 := (not #321)
-#658 := (iff #70 #451)
+#658 := (iff #129 #451)
 #660 := (or #319 #658)
 #661 := (iff #660 #324)
 #645 := (iff #324 #324)
@@ -53236,144 +53377,144 @@
 #309 := [trans #304 #308]: #661
 #320 := [quant-inst]: #660
 #310 := [mp #320 #309]: #324
-#354 := [unit-resolution #310 #697]: #663
+#354 := [unit-resolution #310 #676]: #663
 #646 := (not #663)
 #653 := (or #646 #343 #666)
 #655 := [def-axiom]: #653
 #633 := [unit-resolution #655 #354]: #355
 #634 := [unit-resolution #633 #353 #644]: false
-#349 := [lemma #634]: #67
-#346 := (or #343 #79)
-#334 := (or #343 #79 #254)
+#349 := [lemma #634]: #125
+#346 := (or #343 #138)
+#334 := (or #343 #138 #254)
 #345 := [def-axiom]: #334
-#274 := [unit-resolution #345 #87]: #346
+#274 := [unit-resolution #345 #146]: #346
 #631 := [unit-resolution #274 #349]: #343
-#635 := (or #79 #666)
-#639 := (or #368 #79 #666)
+#635 := (or #138 #666)
+#639 := (or #368 #138 #666)
 #640 := [def-axiom]: #639
 #632 := [unit-resolution #640 #638]: #635
 #636 := [unit-resolution #632 #349]: #666
-#625 := (or #70 #332)
-#652 := (or #646 #70 #332)
+#625 := (or #129 #332)
+#652 := (or #646 #129 #332)
 #290 := [def-axiom]: #652
 #626 := [unit-resolution #290 #354]: #625
 [unit-resolution #626 #636 #631]: false
 unsat
-f5598d5da2ef327dfa5f6213aebc49b5a19fb777 142 0
+a97bbc70b718b9572f51094824e10f2faa0e0a0b 142 0
 #2 := false
 decl f3 :: (-> S2 S2 S3 S1)
-decl f5 :: S3
-#9 := f5
-decl f4 :: S2
-#8 := f4
-#10 := (f3 f4 f4 f5)
-decl f1 :: S1
-#4 := f1
-#66 := (= f1 #10)
-#78 := (not #66)
-#649 := [hypothesis]: #78
-decl f6 :: (-> S2 S3 S1)
-#12 := (f6 f4 f5)
-#69 := (= f1 #12)
-#341 := (or #69 #66)
-#79 := (iff #69 #78)
-#13 := (= #12 f1)
-#11 := (= #10 f1)
-#14 := (iff #11 #13)
-#15 := (not #14)
-#82 := (iff #15 #79)
-#72 := (iff #66 #69)
-#75 := (not #72)
-#80 := (iff #75 #79)
-#81 := [rewrite]: #80
-#76 := (iff #15 #75)
-#73 := (iff #14 #72)
-#70 := (iff #13 #69)
-#71 := [rewrite]: #70
-#67 := (iff #11 #66)
-#68 := [rewrite]: #67
-#74 := [monotonicity #68 #71]: #73
-#77 := [monotonicity #74]: #76
-#83 := [trans #77 #81]: #82
-#65 := [asserted]: #15
-#86 := [mp #65 #83]: #79
-#253 := (not #79)
-#340 := (or #69 #66 #253)
+decl f10 :: S3
+#42 := f10
+decl f9 :: S2
+#41 := f9
+#43 := (f3 f9 f9 f10)
+decl f1 :: S1
+#4 := f1
+#124 := (= f1 #43)
+#137 := (not #124)
+#649 := [hypothesis]: #137
+decl f4 :: (-> S2 S3 S1)
+#45 := (f4 f9 f10)
+#128 := (= f1 #45)
+#341 := (or #128 #124)
+#138 := (iff #128 #137)
+#46 := (= #45 f1)
+#44 := (= #43 f1)
+#47 := (iff #44 #46)
+#48 := (not #47)
+#141 := (iff #48 #138)
+#131 := (iff #124 #128)
+#134 := (not #131)
+#139 := (iff #134 #138)
+#140 := [rewrite]: #139
+#135 := (iff #48 #134)
+#132 := (iff #47 #131)
+#129 := (iff #46 #128)
+#130 := [rewrite]: #129
+#126 := (iff #44 #124)
+#127 := [rewrite]: #126
+#133 := [monotonicity #127 #130]: #132
+#136 := [monotonicity #133]: #135
+#142 := [trans #136 #140]: #141
+#123 := [asserted]: #48
+#145 := [mp #123 #142]: #138
+#253 := (not #138)
+#340 := (or #128 #124 #253)
 #254 := [def-axiom]: #340
-#255 := [unit-resolution #254 #86]: #341
-#650 := [unit-resolution #255 #649]: #69
-#342 := (not #69)
-#651 := (or #66 #342)
-#39 := (:var 0 S3)
-#38 := (:var 1 S2)
-#37 := (:var 2 S2)
-#40 := (f3 #37 #38 #39)
-#690 := (pattern #40)
-#44 := (f6 #38 #39)
-#131 := (= f1 #44)
-#168 := (not #131)
-#42 := (f6 #37 #39)
-#128 := (= f1 #42)
-#167 := (not #128)
-#155 := (or #167 #168)
-#156 := (not #155)
-#124 := (= f1 #40)
-#171 := (iff #124 #156)
-#691 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #690) #171)
+#255 := [unit-resolution #254 #145]: #341
+#650 := [unit-resolution #255 #649]: #128
+#342 := (not #128)
+#651 := (or #124 #342)
+#10 := (:var 0 S3)
+#9 := (:var 1 S2)
+#8 := (:var 2 S2)
+#11 := (f3 #8 #9 #10)
+#669 := (pattern #11)
+#15 := (f4 #9 #10)
+#72 := (= f1 #15)
+#170 := (not #72)
+#13 := (f4 #8 #10)
+#69 := (= f1 #13)
+#169 := (not #69)
+#153 := (or #169 #170)
+#154 := (not #153)
+#66 := (= f1 #11)
+#171 := (iff #66 #154)
+#670 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #669) #171)
 #174 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #171)
-#694 := (iff #174 #691)
-#692 := (iff #171 #171)
-#693 := [refl]: #692
-#695 := [quant-intro #693]: #694
-#134 := (and #128 #131)
-#137 := (iff #124 #134)
-#140 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #137)
-#175 := (iff #140 #174)
-#172 := (iff #137 #171)
-#169 := (iff #134 #156)
-#170 := [rewrite]: #169
-#173 := [monotonicity #170]: #172
+#673 := (iff #174 #670)
+#671 := (iff #171 #171)
+#672 := [refl]: #671
+#674 := [quant-intro #672]: #673
+#75 := (and #69 #72)
+#78 := (iff #66 #75)
+#81 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #78)
+#175 := (iff #81 #174)
+#172 := (iff #78 #171)
+#155 := (iff #75 #154)
+#156 := [rewrite]: #155
+#173 := [monotonicity #156]: #172
 #176 := [quant-intro #173]: #175
-#153 := (~ #140 #140)
-#164 := (~ #137 #137)
-#165 := [refl]: #164
-#154 := [nnf-pos #165]: #153
-#45 := (= #44 f1)
-#43 := (= #42 f1)
-#46 := (and #43 #45)
-#41 := (= #40 f1)
-#47 := (iff #41 #46)
-#48 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #47)
-#141 := (iff #48 #140)
-#138 := (iff #47 #137)
-#135 := (iff #46 #134)
-#132 := (iff #45 #131)
-#133 := [rewrite]: #132
-#129 := (iff #43 #128)
-#130 := [rewrite]: #129
-#136 := [monotonicity #130 #133]: #135
-#126 := (iff #41 #124)
-#127 := [rewrite]: #126
-#139 := [monotonicity #127 #136]: #138
-#142 := [quant-intro #139]: #141
-#123 := [asserted]: #48
-#145 := [mp #123 #142]: #140
-#166 := [mp~ #145 #154]: #140
-#177 := [mp #166 #176]: #174
-#696 := [mp #177 #695]: #691
-#667 := (not #691)
-#662 := (or #667 #72)
+#159 := (~ #81 #81)
+#157 := (~ #78 #78)
+#158 := [refl]: #157
+#160 := [nnf-pos #158]: #159
+#16 := (= #15 f1)
+#14 := (= #13 f1)
+#17 := (and #14 #16)
+#12 := (= #11 f1)
+#18 := (iff #12 #17)
+#19 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #18)
+#82 := (iff #19 #81)
+#79 := (iff #18 #78)
+#76 := (iff #17 #75)
+#73 := (iff #16 #72)
+#74 := [rewrite]: #73
+#70 := (iff #14 #69)
+#71 := [rewrite]: #70
+#77 := [monotonicity #71 #74]: #76
+#67 := (iff #12 #66)
+#68 := [rewrite]: #67
+#80 := [monotonicity #68 #77]: #79
+#83 := [quant-intro #80]: #82
+#65 := [asserted]: #19
+#86 := [mp #65 #83]: #81
+#146 := [mp~ #86 #160]: #81
+#177 := [mp #146 #176]: #174
+#675 := [mp #177 #674]: #670
+#667 := (not #670)
+#662 := (or #667 #131)
 #346 := (or #342 #342)
 #343 := (not #346)
-#347 := (iff #66 #343)
+#347 := (iff #124 #343)
 #668 := (or #667 #347)
 #318 := (iff #668 #662)
 #659 := (iff #662 #662)
 #319 := [rewrite]: #659
-#665 := (iff #347 #72)
-#332 := (iff #343 #69)
+#665 := (iff #347 #131)
+#332 := (iff #343 #128)
 #663 := (not #342)
-#657 := (iff #663 #69)
+#657 := (iff #663 #128)
 #331 := [rewrite]: #657
 #320 := (iff #343 #663)
 #326 := (iff #346 #342)
@@ -53385,144 +53526,120 @@
 #660 := [trans #323 #319]: #318
 #658 := [quant-inst]: #668
 #303 := [mp #658 #660]: #662
-#645 := [unit-resolution #303 #696]: #72
-#644 := (or #75 #66 #342)
+#645 := [unit-resolution #303 #675]: #131
+#644 := (or #134 #124 #342)
 #307 := [def-axiom]: #644
 #289 := [unit-resolution #307 #645]: #651
 #652 := [unit-resolution #289 #650 #649]: false
-#654 := [lemma #652]: #66
-#345 := (or #342 #78)
-#333 := (or #342 #78 #253)
+#654 := [lemma #652]: #124
+#345 := (or #342 #137)
+#333 := (or #342 #137 #253)
 #344 := [def-axiom]: #333
-#273 := [unit-resolution #344 #86]: #345
+#273 := [unit-resolution #344 #145]: #345
 #294 := [unit-resolution #273 #654]: #342
-#295 := (or #78 #69)
-#308 := (or #75 #78 #69)
+#295 := (or #137 #128)
+#308 := (or #134 #137 #128)
 #309 := [def-axiom]: #308
 #655 := [unit-resolution #309 #645]: #295
 [unit-resolution #655 #294 #654]: false
 unsat
-11da52e001c270ce301b6d7c5a73bedb29349752 279 0
+b602e066bd6c40c94511d9684e6145f5299f0593 280 0
 #2 := false
 decl f3 :: (-> S2 S3 S1)
-decl f8 :: S3
-#13 := f8
+decl f12 :: S3
+#47 := f12
 decl f4 :: (-> S2 S2 S2)
-decl f6 :: S2
-#9 := f6
-decl f5 :: S2
-#8 := f5
-#16 := (f4 f5 f6)
-#315 := (f3 #16 f8)
+decl f10 :: S2
+#43 := f10
+decl f9 :: S2
+#42 := f9
+#50 := (f4 f9 f10)
+#315 := (f3 #50 f12)
 decl f1 :: S1
 #4 := f1
 #652 := (= f1 #315)
-#250 := (f3 f6 f8)
+#250 := (f3 f10 f12)
 #629 := (= f1 #250)
 #626 := (not #629)
-#340 := (f3 f5 f8)
+#340 := (f3 f9 f12)
 #356 := (= f1 #340)
 #357 := (not #356)
 #615 := (or #357 #626)
 #616 := (not #615)
 #612 := (iff #616 #652)
 #583 := (not #612)
-#571 := [hypothesis]: #583
-#46 := (:var 0 S3)
-#44 := (:var 1 S2)
-#43 := (:var 2 S2)
-#45 := (f4 #43 #44)
-#47 := (f3 #45 #46)
-#681 := (pattern #47)
-#51 := (f3 #44 #46)
-#138 := (= f1 #51)
-#175 := (not #138)
-#49 := (f3 #43 #46)
-#135 := (= f1 #49)
-#174 := (not #135)
-#162 := (or #174 #175)
-#163 := (not #162)
-#131 := (= f1 #47)
-#178 := (iff #131 #163)
-#682 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #681) #178)
-#181 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #178)
-#685 := (iff #181 #682)
-#683 := (iff #178 #178)
-#684 := [refl]: #683
-#686 := [quant-intro #684]: #685
-#141 := (and #135 #138)
-#144 := (iff #131 #141)
-#147 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #144)
-#182 := (iff #147 #181)
-#179 := (iff #144 #178)
-#176 := (iff #141 #163)
-#177 := [rewrite]: #176
-#180 := [monotonicity #177]: #179
-#183 := [quant-intro #180]: #182
-#160 := (~ #147 #147)
-#171 := (~ #144 #144)
-#172 := [refl]: #171
-#161 := [nnf-pos #172]: #160
-#52 := (= #51 f1)
-#50 := (= #49 f1)
-#53 := (and #50 #52)
-#48 := (= #47 f1)
-#54 := (iff #48 #53)
-#55 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #54)
-#148 := (iff #55 #147)
-#145 := (iff #54 #144)
-#142 := (iff #53 #141)
-#139 := (iff #52 #138)
-#140 := [rewrite]: #139
-#136 := (iff #50 #135)
-#137 := [rewrite]: #136
-#143 := [monotonicity #137 #140]: #142
-#133 := (iff #48 #131)
-#134 := [rewrite]: #133
-#146 := [monotonicity #134 #143]: #145
-#149 := [quant-intro #146]: #148
-#130 := [asserted]: #55
-#152 := [mp #130 #149]: #147
-#173 := [mp~ #152 #161]: #147
-#184 := [mp #173 #183]: #181
-#687 := [mp #184 #686]: #682
-#307 := (not #682)
-#598 := (or #307 #612)
-#617 := (iff #652 #616)
-#614 := (or #307 #617)
-#619 := (iff #614 #598)
-#462 := (iff #598 #598)
-#463 := [rewrite]: #462
-#613 := (iff #617 #612)
-#618 := [rewrite]: #613
-#461 := [monotonicity #618]: #619
-#605 := [trans #461 #463]: #619
-#620 := [quant-inst]: #614
-#606 := [mp #620 #605]: #598
-#567 := [unit-resolution #606 #687 #571]: false
-#572 := [lemma #567]: #612
-#654 := (not #652)
-decl f7 :: S2
-#10 := f7
-#335 := (f3 f7 f8)
+decl f11 :: S2
+#44 := f11
+#335 := (f3 f11 f12)
 #332 := (= f1 #335)
 #336 := (not #332)
-#320 := (or #336 #654)
-#17 := (f4 #16 f7)
-#18 := (f3 #17 f8)
-#76 := (= f1 #18)
-#331 := (not #76)
-#11 := (f4 f6 f7)
-#12 := (f4 f5 #11)
-#14 := (f3 #12 f8)
-#73 := (= f1 #14)
-#647 := (f3 #11 f8)
-#633 := (= f1 #647)
 #485 := (or #336 #626)
 #494 := (not #485)
+#45 := (f4 f10 f11)
+#647 := (f3 #45 f12)
+#633 := (= f1 #647)
 #495 := (iff #494 #633)
 #588 := (not #495)
 #568 := [hypothesis]: #588
+#11 := (:var 0 S3)
+#9 := (:var 1 S2)
+#8 := (:var 2 S2)
+#10 := (f4 #8 #9)
+#12 := (f3 #10 #11)
+#660 := (pattern #12)
+#16 := (f3 #9 #11)
+#79 := (= f1 #16)
+#177 := (not #79)
+#14 := (f3 #8 #11)
+#76 := (= f1 #14)
+#176 := (not #76)
+#160 := (or #176 #177)
+#161 := (not #160)
+#73 := (= f1 #12)
+#178 := (iff #73 #161)
+#661 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #660) #178)
+#181 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #178)
+#664 := (iff #181 #661)
+#662 := (iff #178 #178)
+#663 := [refl]: #662
+#665 := [quant-intro #663]: #664
+#82 := (and #76 #79)
+#85 := (iff #73 #82)
+#88 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #85)
+#182 := (iff #88 #181)
+#179 := (iff #85 #178)
+#162 := (iff #82 #161)
+#163 := [rewrite]: #162
+#180 := [monotonicity #163]: #179
+#183 := [quant-intro #180]: #182
+#166 := (~ #88 #88)
+#164 := (~ #85 #85)
+#165 := [refl]: #164
+#167 := [nnf-pos #165]: #166
+#17 := (= #16 f1)
+#15 := (= #14 f1)
+#18 := (and #15 #17)
+#13 := (= #12 f1)
+#19 := (iff #13 #18)
+#20 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #19)
+#89 := (iff #20 #88)
+#86 := (iff #19 #85)
+#83 := (iff #18 #82)
+#80 := (iff #17 #79)
+#81 := [rewrite]: #80
+#77 := (iff #15 #76)
+#78 := [rewrite]: #77
+#84 := [monotonicity #78 #81]: #83
+#74 := (iff #13 #73)
+#75 := [rewrite]: #74
+#87 := [monotonicity #75 #84]: #86
+#90 := [quant-intro #87]: #89
+#72 := [asserted]: #20
+#93 := [mp #72 #90]: #88
+#153 := [mp~ #93 #167]: #88
+#184 := [mp #153 #183]: #181
+#666 := [mp #184 #665]: #661
+#307 := (not #661)
 #499 := (or #307 #495)
 #601 := (or #626 #336)
 #483 := (not #601)
@@ -53546,57 +53663,80 @@
 #584 := [trans #591 #582]: #594
 #501 := [quant-inst]: #500
 #576 := [mp #501 #584]: #499
-#569 := [unit-resolution #576 #687 #568]: false
+#569 := [unit-resolution #576 #666 #568]: false
 #570 := [lemma #569]: #495
 #634 := (not #633)
 #358 := (or #357 #634)
-#85 := (not #73)
-#558 := [hypothesis]: #85
-#561 := (or #73 #358)
 #344 := (not #358)
-#359 := (iff #73 #344)
+#46 := (f4 f9 #45)
+#48 := (f3 #46 f12)
+#131 := (= f1 #48)
+#144 := (not #131)
+#571 := [hypothesis]: #144
+#572 := (or #131 #358)
+#359 := (iff #131 #344)
 #630 := (or #307 #359)
 #352 := [quant-inst]: #630
-#559 := [unit-resolution #352 #687]: #359
+#567 := [unit-resolution #352 #666]: #359
 #342 := (not #359)
-#343 := (or #342 #73 #358)
+#343 := (or #342 #131 #358)
 #345 := [def-axiom]: #343
-#562 := [unit-resolution #345 #559]: #561
-#563 := [unit-resolution #562 #558]: #358
+#558 := [unit-resolution #345 #567]: #572
+#559 := [unit-resolution #558 #571]: #358
+#598 := (or #307 #612)
+#617 := (iff #652 #616)
+#614 := (or #307 #617)
+#619 := (iff #614 #598)
+#462 := (iff #598 #598)
+#463 := [rewrite]: #462
+#613 := (iff #617 #612)
+#618 := [rewrite]: #613
+#461 := [monotonicity #618]: #619
+#605 := [trans #461 #463]: #619
+#620 := [quant-inst]: #614
+#606 := [mp #620 #605]: #598
+#561 := [unit-resolution #606 #666]: #612
+#547 := (or #583 #616)
+#654 := (not #652)
+#320 := (or #336 #654)
 #656 := (not #320)
-#330 := (or #76 #73)
-#86 := (iff #76 #85)
-#19 := (= #18 f1)
-#15 := (= #14 f1)
-#20 := (iff #15 #19)
-#21 := (not #20)
-#89 := (iff #21 #86)
-#79 := (iff #73 #76)
-#82 := (not #79)
-#87 := (iff #82 #86)
-#88 := [rewrite]: #87
-#83 := (iff #21 #82)
-#80 := (iff #20 #79)
-#77 := (iff #19 #76)
-#78 := [rewrite]: #77
-#74 := (iff #15 #73)
-#75 := [rewrite]: #74
-#81 := [monotonicity #75 #78]: #80
-#84 := [monotonicity #81]: #83
-#90 := [trans #84 #88]: #89
-#72 := [asserted]: #21
-#93 := [mp #72 #90]: #86
-#242 := (not #86)
-#329 := (or #76 #73 #242)
+#51 := (f4 #50 f11)
+#52 := (f3 #51 f12)
+#135 := (= f1 #52)
+#330 := (or #135 #131)
+#145 := (iff #135 #144)
+#53 := (= #52 f1)
+#49 := (= #48 f1)
+#54 := (iff #49 #53)
+#55 := (not #54)
+#148 := (iff #55 #145)
+#138 := (iff #131 #135)
+#141 := (not #138)
+#146 := (iff #141 #145)
+#147 := [rewrite]: #146
+#142 := (iff #55 #141)
+#139 := (iff #54 #138)
+#136 := (iff #53 #135)
+#137 := [rewrite]: #136
+#133 := (iff #49 #131)
+#134 := [rewrite]: #133
+#140 := [monotonicity #134 #137]: #139
+#143 := [monotonicity #140]: #142
+#149 := [trans #143 #147]: #148
+#130 := [asserted]: #55
+#152 := [mp #130 #149]: #145
+#242 := (not #145)
+#329 := (or #135 #131 #242)
 #243 := [def-axiom]: #329
-#244 := [unit-resolution #243 #93]: #330
-#560 := [unit-resolution #244 #558]: #76
-#544 := (or #331 #656)
-#653 := (iff #76 #656)
+#244 := [unit-resolution #243 #152]: #330
+#562 := [unit-resolution #244 #571]: #135
+#331 := (not #135)
+#560 := (or #331 #656)
+#653 := (iff #135 #656)
 #312 := (or #307 #653)
 #309 := (or #654 #336)
 #441 := (not #309)
-#648 := (iff #76 #441)
+#648 := (iff #135 #441)
 #650 := (or #307 #648)
 #651 := (iff #650 #312)
 #635 := (iff #312 #312)
@@ -53611,27 +53751,28 @@
 #297 := [trans #292 #296]: #651
 #308 := [quant-inst]: #650
 #298 := [mp #308 #297]: #312
-#564 := [unit-resolution #298 #687]: #653
+#563 := [unit-resolution #298 #666]: #653
 #636 := (not #653)
 #643 := (or #636 #331 #656)
 #645 := [def-axiom]: #643
-#545 := [unit-resolution #645 #564]: #544
-#547 := [unit-resolution #545 #560]: #656
+#564 := [unit-resolution #645 #563]: #560
+#544 := [unit-resolution #564 #562]: #656
 #638 := (or #320 #652)
 #639 := [def-axiom]: #638
-#548 := [unit-resolution #639 #547]: #652
+#545 := [unit-resolution #639 #544]: #652
 #577 := (or #583 #616 #654)
 #578 := [def-axiom]: #577
-#549 := [unit-resolution #578 #548 #572]: #616
+#548 := [unit-resolution #578 #545]: #547
+#549 := [unit-resolution #548 #561]: #616
 #607 := (or #615 #356)
 #573 := [def-axiom]: #607
 #550 := [unit-resolution #573 #549]: #356
 #632 := (or #344 #357 #634)
 #341 := [def-axiom]: #632
-#551 := [unit-resolution #341 #550 #563]: #634
+#551 := [unit-resolution #341 #550 #559]: #634
 #299 := (or #320 #332)
 #637 := [def-axiom]: #299
-#552 := [unit-resolution #637 #547]: #332
+#552 := [unit-resolution #637 #544]: #332
 #575 := (or #615 #629)
 #585 := [def-axiom]: #575
 #553 := [unit-resolution #585 #549]: #629
@@ -53641,102 +53782,64 @@
 #442 := (or #588 #485 #633)
 #443 := [def-axiom]: #442
 #555 := [unit-resolution #443 #554 #551 #570]: false
-#556 := [lemma #555]: #73
-#334 := (or #331 #85)
-#322 := (or #331 #85 #242)
-#333 := [def-axiom]: #322
-#262 := [unit-resolution #333 #93]: #334
-#546 := [unit-resolution #262 #556]: #331
-#557 := (or #76 #320)
-#642 := (or #636 #76 #320)
-#278 := [def-axiom]: #642
-#535 := [unit-resolution #278 #564]: #557
-#536 := [unit-resolution #535 #546]: #320
-#538 := (or #85 #344)
-#623 := (or #342 #85 #344)
+#556 := [lemma #555]: #131
+#546 := (or #144 #344)
+#623 := (or #342 #144 #344)
 #624 := [def-axiom]: #623
-#539 := [unit-resolution #624 #559]: #538
-#540 := [unit-resolution #539 #556]: #344
+#557 := [unit-resolution #624 #567]: #546
+#535 := [unit-resolution #557 #556]: #344
 #631 := (or #358 #633)
 #628 := [def-axiom]: #631
-#541 := [unit-resolution #628 #540]: #633
+#536 := [unit-resolution #628 #535]: #633
 #611 := (or #588 #494 #634)
 #440 := [def-axiom]: #611
-#542 := [unit-resolution #440 #541 #570]: #494
+#538 := [unit-resolution #440 #536 #570]: #494
+#603 := (or #485 #629)
+#609 := [def-axiom]: #603
+#539 := [unit-resolution #609 #538]: #629
+#353 := (or #358 #356)
+#627 := [def-axiom]: #353
+#540 := [unit-resolution #627 #535]: #356
+#586 := (or #616 #357 #626)
+#587 := [def-axiom]: #586
+#541 := [unit-resolution #587 #540 #539]: #616
+#334 := (or #331 #144)
+#322 := (or #331 #144 #242)
+#333 := [def-axiom]: #322
+#262 := [unit-resolution #333 #152]: #334
+#542 := [unit-resolution #262 #556]: #331
+#537 := (or #135 #320)
+#642 := (or #636 #135 #320)
+#278 := [def-axiom]: #642
+#543 := [unit-resolution #278 #563]: #537
+#529 := [unit-resolution #543 #542]: #320
 #608 := (or #485 #332)
 #602 := [def-axiom]: #608
-#537 := [unit-resolution #602 #542]: #332
+#525 := [unit-resolution #602 #538]: #332
 #640 := (or #656 #336 #654)
 #641 := [def-axiom]: #640
-#543 := [unit-resolution #641 #537 #536]: #654
-#353 := (or #358 #356)
-#627 := [def-axiom]: #353
-#529 := [unit-resolution #627 #540]: #356
-#603 := (or #485 #629)
-#609 := [def-axiom]: #603
-#525 := [unit-resolution #609 #542]: #629
-#586 := (or #616 #357 #626)
-#587 := [def-axiom]: #586
-#526 := [unit-resolution #587 #525 #529]: #616
+#526 := [unit-resolution #641 #525 #529]: #654
 #579 := (or #583 #615 #652)
 #580 := [def-axiom]: #579
-[unit-resolution #580 #526 #543 #572]: false
-unsat
-b948f53222b56a42099bea7be09fe4963a5cfdb3 18 0
-#2 := false
-decl f3 :: S2
-#8 := f3
-#9 := (= f3 f3)
-#10 := (not #9)
-#68 := (iff #10 false)
-#1 := true
-#63 := (not true)
-#66 := (iff #63 false)
-#67 := [rewrite]: #66
-#64 := (iff #10 #63)
-#61 := (iff #9 true)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#69 := [trans #65 #67]: #68
-#60 := [asserted]: #10
-[mp #60 #69]: false
-unsat
-c4d2e4408924ee75f6b9b17e513fd22b6307bf65 38 0
-#2 := false
-decl f4 :: S2
-#9 := f4
-decl f3 :: S2
-#8 := f3
-#11 := (distinct f3 f4)
-#12 := (not #11)
-#10 := (= f3 f4)
-#13 := (implies #10 #12)
-#14 := (not #13)
-#54 := (iff #14 false)
-#1 := true
-#49 := (not true)
-#52 := (iff #49 false)
-#53 := [rewrite]: #52
-#50 := (iff #14 #49)
-#47 := (iff #13 true)
-#42 := (implies #10 #10)
-#45 := (iff #42 true)
-#46 := [rewrite]: #45
-#43 := (iff #13 #42)
-#40 := (iff #12 #10)
-#32 := (not #10)
-#35 := (not #32)
-#38 := (iff #35 #10)
-#39 := [rewrite]: #38
-#36 := (iff #12 #35)
-#33 := (iff #11 #32)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#51 := [monotonicity #48]: #50
-#55 := [trans #51 #53]: #54
-#31 := [asserted]: #14
-[mp #31 #55]: false
-unsat
+#527 := [unit-resolution #580 #526 #541]: #583
+[unit-resolution #606 #666 #527]: false
+unsat
+a4a6b2c4c93afdaae7ab96c5883c0d14185909a3 18 0
+#2 := false
+decl f9 :: S8
+#41 := f9
+#42 := (= f9 f9)
+#43 := (not #42)
+#127 := (iff #43 false)
+#1 := true
+#122 := (not true)
+#125 := (iff #122 false)
+#126 := [rewrite]: #125
+#123 := (iff #43 #122)
+#119 := (iff #42 true)
+#121 := [rewrite]: #119
+#124 := [monotonicity #121]: #123
+#128 := [trans #124 #126]: #127
+#118 := [asserted]: #43
+[mp #118 #128]: false
+unsat

--- a/src/HOL/SMT_Examples/SMT_Word_Examples.certs	Tue Dec 07 15:01:42 2010 +0100
+++ b/src/HOL/SMT_Examples/SMT_Word_Examples.certs	Tue Dec 07 15:44:38 2010 +0100
@@ -1,50 +1,50 @@
-e1bd9b09ecc046c90fa67ab56ab4bc91c2137e7c 1 0
+8feec88bda876aef49ce85ea346ff6a145eb2f84 1 0
 unsat
-b0b514fa1c40f2df103dbe4bab9d6ee5e8e38622 1 0
+48892a95f694eea9655c4ebcdf3d0673a2fda935 1 0
 unsat
-4a2f9858de3b5f966f7cfe668d50b9fdbdccc28f 1 0
+517aa41cf07ed4cc7725322f0d4f39f622c17c4b 1 0
 unsat
-b403fe5b6096d56ba2e1efb5889c116ad939fb9a 1 0
+2602a0bf08ddc272218686654070d5162cae3e47 1 0
 unsat
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