updated SMT certificates
authorboehmes
Wed, 12 May 2010 23:54:06 +0200
changeset 36900 631e961a9e95
parent 36899 bcd6fce5bf06
child 36901 a20c5484dc9c
updated SMT certificates
src/HOL/Boogie/Examples/Boogie_Dijkstra.certs
src/HOL/Boogie/Examples/Boogie_Max.certs
src/HOL/Boogie/Examples/VCC_Max.certs
src/HOL/IsaMakefile
src/HOL/Multivariate_Analysis/Integration.certs
src/HOL/SMT_Examples/ROOT.ML
src/HOL/SMT_Examples/SMT_Examples.certs
src/HOL/SMT_Examples/SMT_Examples.thy
src/HOL/SMT_Examples/SMT_Tests.certs
src/HOL/SMT_Examples/SMT_Word_Examples.certs
--- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Wed May 12 23:54:04 2010 +0200
+++ b/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Wed May 12 23:54:06 2010 +0200
@@ -1,6543 +1,6890 @@
-d29d9bae6b4b919e45b23de87975f8734cce2039 6542 0
+2d5ecda945177c32dc13189db42e7a2391a39390 6889 0
 #2 := false
-decl up_6 :: (-> T4 T2 bool)
-decl ?x47!7 :: (-> T2 T2)
-decl ?x75!20 :: T2
-#2146 := ?x75!20
-#5823 := (?x47!7 ?x75!20)
-decl uf_23 :: T4
-#182 := uf_23
-#16800 := (up_6 uf_23 #5823)
-decl uf_2 :: (-> T1 T2)
-decl uf_1 :: (-> T2 T2 T1)
-decl uf_3 :: (-> T1 T2)
-decl uf_22 :: T2
-#174 := uf_22
-#4514 := (uf_1 uf_22 uf_22)
-#10482 := (uf_3 #4514)
-#15059 := (uf_1 #10482 ?x75!20)
-#15842 := (uf_3 #15059)
-#16792 := (uf_1 #5823 #15842)
-#19843 := (uf_2 #16792)
-decl uf_7 :: (-> T4 T2 T5 T4)
-decl uf_8 :: T5
-#33 := uf_8
-decl uf_15 :: T4
-#110 := uf_15
-#11444 := (uf_7 uf_15 #10482 uf_8)
-#27073 := (up_6 #11444 #19843)
-#27109 := (not #27073)
-#16801 := (not #16800)
-#27231 := (iff #16801 #27109)
-#27229 := (iff #16800 #27073)
-#27227 := (iff #27073 #16800)
-#27215 := (= #19843 #5823)
-#20888 := (= #5823 #19843)
-#11 := (:var 0 T2)
-#10 := (:var 1 T2)
-#12 := (uf_1 #10 #11)
-#3981 := (pattern #12)
-#16 := (uf_2 #12)
-#303 := (= #10 #16)
-#3988 := (forall (vars (?x4 T2) (?x5 T2)) (:pat #3981) #303)
-#307 := (forall (vars (?x4 T2) (?x5 T2)) #303)
-#3991 := (iff #307 #3988)
-#3989 := (iff #303 #303)
-#3990 := [refl]: #3989
-#3992 := [quant-intro #3990]: #3991
-#1642 := (~ #307 #307)
-#1676 := (~ #303 #303)
-#1677 := [refl]: #1676
-#1643 := [nnf-pos #1677]: #1642
-#17 := (= #16 #10)
-#18 := (forall (vars (?x4 T2) (?x5 T2)) #17)
-#308 := (iff #18 #307)
-#305 := (iff #17 #303)
-#306 := [rewrite]: #305
-#309 := [quant-intro #306]: #308
-#302 := [asserted]: #18
-#312 := [mp #302 #309]: #307
-#1678 := [mp~ #312 #1643]: #307
-#3993 := [mp #1678 #3992]: #3988
-#8415 := (not #3988)
-#20865 := (or #8415 #20888)
-#20879 := [quant-inst]: #20865
-#27214 := [unit-resolution #20879 #3993]: #20888
-#27216 := [symm #27214]: #27215
-#13523 := (= #11444 uf_23)
-#183 := (uf_7 uf_15 uf_22 uf_8)
-#7113 := (= #183 uf_23)
-#184 := (= uf_23 #183)
-#2150 := (uf_1 #11 ?x75!20)
-#4271 := (pattern #2150)
-decl uf_24 :: (-> T2 int)
-#191 := (uf_24 #11)
-#4211 := (pattern #191)
-#201 := (up_6 uf_23 #11)
-#4237 := (pattern #201)
-#52 := 0::int
-decl uf_10 :: (-> T1 int)
-#2151 := (uf_10 #2150)
-#2147 := (uf_24 ?x75!20)
-#1038 := -1::int
-#2148 := (* -1::int #2147)
-#2745 := (+ #2148 #2151)
-#2746 := (+ #191 #2745)
-#2749 := (= #2746 0::int)
-#3311 := (not #2749)
-#2149 := (+ #191 #2148)
-#2154 := (>= #2149 0::int)
-#208 := (not #201)
-#3312 := (or #208 #2154 #3311)
-#4272 := (forall (vars (?x76 T2)) (:pat #4237 #4211 #4271) #3312)
-#4277 := (not #4272)
-#87 := (uf_1 #11 #10)
-#4066 := (pattern #87)
-#211 := (uf_24 #10)
-#1318 := (* -1::int #211)
-#1319 := (+ #191 #1318)
-#88 := (uf_10 #87)
-#1344 := (+ #88 #1319)
-#1342 := (>= #1344 0::int)
-#1053 := (* -1::int #88)
-decl uf_9 :: int
-#53 := uf_9
-#1054 := (+ uf_9 #1053)
-#1055 := (<= #1054 0::int)
-#3303 := (or #208 #1055 #1342)
-#4263 := (forall (vars (?x71 T2) (?x72 T2)) (:pat #4066) #3303)
-#4268 := (not #4263)
-decl uf_11 :: T2
-#64 := uf_11
-#2721 := (= uf_11 ?x75!20)
-#2158 := (+ uf_9 #2148)
+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 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)
+#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)
+#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)
-#4280 := (or #2159 #2721 #4268 #4277)
-#4283 := (not #4280)
-decl ?x71!19 :: T2
-#2117 := ?x71!19
-decl ?x72!18 :: T2
-#2116 := ?x72!18
-#2122 := (uf_1 ?x72!18 ?x71!19)
-#2123 := (uf_10 #2122)
-#2126 := (* -1::int #2123)
-#2120 := (uf_24 ?x72!18)
-#2707 := (* -1::int #2120)
-#2708 := (+ #2707 #2126)
-#2118 := (uf_24 ?x71!19)
-#2709 := (+ #2118 #2708)
-#2710 := (<= #2709 0::int)
-#2130 := (up_6 uf_23 ?x72!18)
-#3266 := (not #2130)
-#2127 := (+ uf_9 #2126)
-#2128 := (<= #2127 0::int)
-#3281 := (or #2128 #3266 #2710)
-#3286 := (not #3281)
-#4286 := (or #3286 #4283)
+#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)
+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)
-#4254 := (pattern #191 #211)
-#1317 := (>= #1319 0::int)
-#209 := (up_6 uf_23 #10)
-#3243 := (not #209)
-#3258 := (or #201 #3243 #1317)
-#4255 := (forall (vars (?x67 T2) (?x68 T2)) (:pat #4254) #3258)
-#4260 := (not #4255)
-#4292 := (or #4260 #4289)
+#4292 := (or #4289 #3330)
 #4295 := (not #4292)
-decl ?x68!16 :: T2
-#2091 := ?x68!16
-#2095 := (uf_24 ?x68!16)
-#2681 := (* -1::int #2095)
-decl ?x67!17 :: T2
-#2092 := ?x67!17
-#2093 := (uf_24 ?x67!17)
-#2682 := (+ #2093 #2681)
-#2683 := (<= #2682 0::int)
-#2099 := (up_6 uf_23 ?x68!16)
-#2098 := (up_6 uf_23 ?x67!17)
-#3220 := (not #2098)
-#3235 := (or #3220 #2099 #2683)
-#3240 := (not #3235)
-#4298 := (or #3240 #4295)
+#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)
-#1308 := (>= #191 0::int)
-#4246 := (forall (vars (?x65 T2)) (:pat #4211) #1308)
-#4251 := (not #4246)
-#4304 := (or #4251 #4301)
+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)
-decl ?x65!15 :: T2
-#2076 := ?x65!15
-#2077 := (uf_24 ?x65!15)
-#2078 := (>= #2077 0::int)
-#2079 := (not #2078)
-#4310 := (or #2079 #4307)
+#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)
-#204 := (uf_24 uf_11)
-#205 := (= #204 0::int)
-#1305 := (not #205)
-#4316 := (or #1305 #4313)
-#4319 := (not #4316)
-#4322 := (or #1305 #4319)
-#4325 := (not #4322)
-decl uf_4 :: (-> T3 T2 int)
-decl uf_14 :: T3
-#104 := uf_14
-#107 := (uf_4 uf_14 #11)
-#4090 := (pattern #107)
-#645 := (= #107 #191)
-#662 := (or #208 #645)
-#4238 := (forall (vars (?x63 T2)) (:pat #4237 #4090 #4211) #662)
-#4243 := (not #4238)
-#4328 := (or #4243 #4325)
-#4331 := (not #4328)
-decl ?x63!14 :: T2
-#2052 := ?x63!14
-#2054 := (uf_4 uf_14 ?x63!14)
-#2053 := (uf_24 ?x63!14)
-#2658 := (= #2053 #2054)
-#2056 := (up_6 uf_23 ?x63!14)
-#2057 := (not #2056)
-#2661 := (or #2057 #2658)
-#2664 := (not #2661)
-#4334 := (or #2664 #4331)
-#4337 := (not #4334)
-#1293 := (* -1::int #191)
-#1294 := (+ #107 #1293)
-#1292 := (>= #1294 0::int)
-#4229 := (forall (vars (?x61 T2)) (:pat #4090 #4211) #1292)
+#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)
-#4340 := (or #4234 #4337)
-#4343 := (not #4340)
-decl ?x61!13 :: T2
-#2034 := ?x61!13
-#2037 := (uf_4 uf_14 ?x61!13)
-#2648 := (* -1::int #2037)
-#2035 := (uf_24 ?x61!13)
-#2649 := (+ #2035 #2648)
-#2650 := (<= #2649 0::int)
-#2655 := (not #2650)
-#4346 := (or #2655 #4343)
-#4349 := (not #4346)
-#185 := (uf_1 uf_22 #11)
-#4212 := (pattern #185)
-#186 := (uf_10 #185)
-#1431 := (+ #186 #1293)
-#177 := (uf_4 uf_14 uf_22)
-#1432 := (+ #177 #1431)
-#1433 := (= #1432 0::int)
-#1262 := (* -1::int #186)
-#1268 := (* -1::int #177)
-#1269 := (+ #1268 #1262)
-#1270 := (+ #107 #1269)
-#1271 := (<= #1270 0::int)
-#1263 := (+ uf_9 #1262)
-#1264 := (<= #1263 0::int)
-#3212 := (or #1264 #1271 #1433)
-#4221 := (forall (vars (?x59 T2)) (:pat #4212 #4090 #4211) #3212)
+#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)
-#3192 := (or #1264 #1271)
-#3193 := (not #3192)
-#3196 := (or #645 #3193)
-#4213 := (forall (vars (?x60 T2)) (:pat #4090 #4211 #4212) #3196)
-#4218 := (not #4213)
-decl ?x48!12 :: T2
-#2011 := ?x48!12
-#2017 := (up_6 uf_15 ?x48!12)
-#2012 := (uf_4 uf_14 ?x48!12)
-#2013 := (* -1::int #2012)
-#2014 := (+ uf_9 #2013)
-#2015 := (<= #2014 0::int)
-#1458 := (+ uf_9 #1268)
-#1459 := (<= #1458 0::int)
-#111 := (up_6 uf_15 #11)
-#4132 := (pattern #111)
-#1446 := (+ #107 #1268)
-#1445 := (>= #1446 0::int)
-#1449 := (or #111 #1445)
-#4203 := (forall (vars (?x58 T2)) (:pat #4132 #4090) #1449)
-#4208 := (not #4203)
-#825 := (not #184)
-#175 := (up_6 uf_15 uf_22)
-#4352 := (or #175 #825 #4208 #1459 #2015 #2017 #4218 #4226 #4349)
-#4355 := (not #4352)
-decl ?x53!11 :: T2
-#1945 := ?x53!11
-decl ?x54!10 :: T2
-#1944 := ?x54!10
-#1950 := (uf_1 ?x54!10 ?x53!11)
-#1951 := (uf_10 #1950)
-#1958 := (* -1::int #1951)
-decl uf_19 :: T3
-#141 := uf_19
-#1948 := (uf_4 uf_19 ?x54!10)
-#1954 := (* -1::int #1948)
-#2605 := (+ #1954 #1958)
-#1946 := (uf_4 uf_19 ?x53!11)
-#2606 := (+ #1946 #2605)
-#2607 := (<= #2606 0::int)
-#1959 := (+ uf_9 #1958)
-#1960 := (<= #1959 0::int)
-#1955 := (+ uf_9 #1954)
-#1956 := (<= #1955 0::int)
-#3156 := (or #1956 #1960 #2607)
-#3161 := (not #3156)
-#149 := (uf_4 uf_19 #10)
-#1175 := (* -1::int #149)
-#146 := (uf_4 uf_19 #11)
-#1176 := (+ #146 #1175)
-#1182 := (+ #88 #1176)
-#1205 := (>= #1182 0::int)
-#1162 := (* -1::int #146)
-#1163 := (+ uf_9 #1162)
-#1164 := (<= #1163 0::int)
-#3124 := (or #1055 #1164 #1205)
-#4165 := (forall (vars (?x53 T2) (?x54 T2)) (:pat #4066) #3124)
-#4170 := (not #4165)
-#161 := (uf_4 uf_19 uf_11)
-#162 := (= #161 0::int)
-#4173 := (or #162 #4170)
-#4176 := (not #4173)
-#4179 := (or #4176 #3161)
-#4182 := (not #4179)
-#4141 := (pattern #146)
-decl ?x50!9 :: (-> T2 T2)
-#1921 := (?x50!9 #11)
-#1924 := (uf_1 #1921 #11)
-#1925 := (uf_10 #1924)
-#2575 := (* -1::int #1925)
-#1922 := (uf_4 uf_19 #1921)
-#2558 := (* -1::int #1922)
-#2576 := (+ #2558 #2575)
-#2577 := (+ #146 #2576)
-#2578 := (= #2577 0::int)
-#3094 := (not #2578)
-#2559 := (+ #146 #2558)
-#2560 := (<= #2559 0::int)
-#3095 := (or #2560 #3094)
-#3096 := (not #3095)
-#65 := (= #11 uf_11)
-#3102 := (or #65 #1164 #3096)
-#4157 := (forall (vars (?x49 T2)) (:pat #4141) #3102)
-#4162 := (not #4157)
-#4185 := (or #4162 #4182)
-#4188 := (not #4185)
-decl ?x49!8 :: T2
-#1881 := ?x49!8
-#1885 := (uf_1 #11 ?x49!8)
-#4142 := (pattern #1885)
-#1886 := (uf_10 #1885)
-#1882 := (uf_4 uf_19 ?x49!8)
-#1883 := (* -1::int #1882)
-#2528 := (+ #1883 #1886)
-#2529 := (+ #146 #2528)
-#2532 := (= #2529 0::int)
-#3058 := (not #2532)
-#1884 := (+ #146 #1883)
-#1889 := (>= #1884 0::int)
-#3059 := (or #1889 #3058)
-#4143 := (forall (vars (?x50 T2)) (:pat #4141 #4142) #3059)
-#4148 := (not #4143)
-#2504 := (= uf_11 ?x49!8)
-#1893 := (+ uf_9 #1883)
-#1894 := (<= #1893 0::int)
-#4151 := (or #1894 #2504 #4148)
-#4154 := (not #4151)
-#4191 := (or #4154 #4188)
-#4194 := (not #4191)
-#1117 := (* -1::int #107)
-#1118 := (+ uf_9 #1117)
-#1119 := (<= #1118 0::int)
-#3044 := (or #111 #1119)
-#4133 := (forall (vars (?x48 T2)) (:pat #4132 #4090) #3044)
-#4138 := (not #4133)
-#495 := (= uf_14 uf_19)
-#586 := (not #495)
-decl uf_16 :: T4
-#136 := uf_16
-#492 := (= uf_15 uf_16)
-#604 := (not #492)
-decl uf_21 :: T3
-#144 := uf_21
-decl uf_20 :: T3
-#143 := uf_20
-#145 := (= uf_20 uf_21)
-#577 := (not #145)
-decl uf_18 :: T2
-#139 := uf_18
-decl uf_17 :: T2
-#138 := uf_17
-#140 := (= uf_17 uf_18)
-#595 := (not #140)
-#4197 := (or #595 #577 #604 #586 #4138 #4194)
-#4200 := (not #4197)
-#4358 := (or #4200 #4355)
-#4361 := (not #4358)
-#1845 := (?x47!7 #11)
-#1846 := (uf_4 uf_14 #1845)
-#2463 := (* -1::int #1846)
-#2478 := (+ #107 #2463)
-#2479 := (<= #2478 0::int)
-#1850 := (uf_1 #1845 #11)
-#1851 := (uf_10 #1850)
-#2464 := (* -1::int #1851)
-#2465 := (+ #2463 #2464)
-#2466 := (+ #107 #2465)
-#2467 := (= #2466 0::int)
-#3028 := (not #2467)
-#1854 := (up_6 uf_15 #1845)
-#3027 := (not #1854)
-#3029 := (or #3027 #3028 #2479)
-#3030 := (not #3029)
-#3036 := (or #65 #1119 #3030)
-#4124 := (forall (vars (?x46 T2)) (:pat #4090) #3036)
-#4129 := (not #4124)
-decl uf_12 :: (-> T2 int)
-#66 := (uf_12 #11)
-#4042 := (pattern #66)
-decl ?x38!6 :: (-> T2 T2)
-#1818 := (?x38!6 #11)
-#1822 := (uf_12 #1818)
-#2422 := (* -1::int #1822)
-#1819 := (uf_1 #1818 #11)
-#1820 := (uf_10 #1819)
-#2439 := (* -1::int #1820)
-#2440 := (+ #2439 #2422)
-#2441 := (+ #66 #2440)
-#2442 := (= #2441 0::int)
-#3000 := (not #2442)
-#2423 := (+ #66 #2422)
-#2424 := (<= #2423 0::int)
-decl up_13 :: (-> T2 bool)
-#1828 := (up_13 #1818)
-#2999 := (not #1828)
-#3001 := (or #2999 #2424 #3000)
-#3002 := (not #3001)
-#1079 := (* -1::int #66)
-#1080 := (+ uf_9 #1079)
-#1081 := (<= #1080 0::int)
-#3008 := (or #65 #1081 #3002)
-#4116 := (forall (vars (?x37 T2)) (:pat #4042) #3008)
-#4121 := (not #4116)
-#113 := (up_6 uf_15 #10)
-#4107 := (pattern #111 #113)
-#115 := (uf_4 uf_14 #10)
-#1131 := (* -1::int #115)
-#1132 := (+ #107 #1131)
-#1135 := (>= #1132 0::int)
-#2965 := (not #113)
-#2980 := (or #111 #2965 #1135)
-#4108 := (forall (vars (?x42 T2) (?x43 T2)) (:pat #4107) #2980)
-#4113 := (not #4108)
-#1133 := (+ #88 #1132)
-#1513 := (>= #1133 0::int)
-#112 := (not #111)
-#2957 := (or #112 #1055 #1513)
-#4099 := (forall (vars (?x44 T2) (?x45 T2)) (:pat #4066) #2957)
-#4104 := (not #4099)
-#1536 := (>= #107 0::int)
-#4091 := (forall (vars (?x41 T2)) (:pat #4090) #1536)
-#4096 := (not #4091)
-#105 := (uf_4 uf_14 uf_11)
-#106 := (= #105 0::int)
-#1547 := (not #106)
-#4364 := (or #1547 #4096 #4104 #4113 #4121 #4129 #4361)
-#4367 := (not #4364)
-decl ?x37!5 :: T2
-#1774 := ?x37!5
-#1775 := (uf_1 #11 ?x37!5)
-#4075 := (pattern #1775)
-#74 := (up_13 #11)
-#4035 := (pattern #74)
-#1777 := (uf_12 ?x37!5)
-#1778 := (* -1::int #1777)
-#1776 := (uf_10 #1775)
-#2390 := (+ #1776 #1778)
-#2391 := (+ #66 #2390)
-#2394 := (= #2391 0::int)
-#2918 := (not #2394)
-#1782 := (+ #66 #1778)
-#1783 := (>= #1782 0::int)
-#75 := (not #74)
-#2919 := (or #75 #1783 #2918)
-#4076 := (forall (vars (?x38 T2)) (:pat #4035 #4042 #4075) #2919)
-#4081 := (not #4076)
-#2366 := (= uf_11 ?x37!5)
-#1787 := (+ uf_9 #1778)
-#1788 := (<= #1787 0::int)
-#4084 := (or #1788 #2366 #4081)
-#4087 := (not #4084)
-#4370 := (or #4087 #4367)
-#4373 := (not #4370)
-#83 := (uf_12 #10)
-#1041 := (* -1::int #83)
-#1068 := (+ #1041 #88)
-#1069 := (+ #66 #1068)
-#1066 := (>= #1069 0::int)
-#2910 := (or #75 #1055 #1066)
-#4067 := (forall (vars (?x33 T2) (?x34 T2)) (:pat #4066) #2910)
-#4072 := (not #4067)
-#4376 := (or #4072 #4373)
-#4379 := (not #4376)
-decl ?x34!3 :: T2
-#1744 := ?x34!3
-#1751 := (uf_12 ?x34!3)
-decl ?x33!4 :: T2
-#1745 := ?x33!4
-#1748 := (uf_12 ?x33!4)
-#1749 := (* -1::int #1748)
-#2353 := (+ #1749 #1751)
-#1746 := (uf_1 ?x34!3 ?x33!4)
-#1747 := (uf_10 #1746)
-#2354 := (+ #1747 #2353)
-#2357 := (>= #2354 0::int)
-#1758 := (up_13 ?x34!3)
-#2873 := (not #1758)
-#1754 := (* -1::int #1747)
-#1755 := (+ uf_9 #1754)
-#1756 := (<= #1755 0::int)
-#2888 := (or #1756 #2873 #2357)
-#8152 := [hypothesis]: #1758
-#4036 := (forall (vars (?x26 T2)) (:pat #4035) #75)
-#76 := (forall (vars (?x26 T2)) #75)
-#4039 := (iff #76 #4036)
-#4037 := (iff #75 #75)
-#4038 := [refl]: #4037
-#4040 := [quant-intro #4038]: #4039
-#1658 := (~ #76 #76)
-#1695 := (~ #75 #75)
-#1696 := [refl]: #1695
-#1659 := [nnf-pos #1696]: #1658
+#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)
-#70 := (not #65)
-#1605 := (or #70 #67)
-#1608 := (forall (vars (?x24 T2)) #1605)
-#1611 := (not #1608)
-#1539 := (forall (vars (?x41 T2)) #1536)
-#1542 := (not #1539)
-#114 := (and #112 #113)
-#440 := (not #114)
-#1527 := (or #440 #1135)
-#1530 := (forall (vars (?x42 T2) (?x43 T2)) #1527)
-#1533 := (not #1530)
-#1056 := (not #1055)
-#1505 := (and #111 #1056)
-#1510 := (not #1505)
-#1516 := (or #1510 #1513)
-#1519 := (forall (vars (?x44 T2) (?x45 T2)) #1516)
-#1522 := (not #1519)
-#1452 := (forall (vars (?x58 T2)) #1449)
-#1455 := (not #1452)
-#1272 := (not #1271)
-#1265 := (not #1264)
-#1275 := (and #1265 #1272)
-#1428 := (not #1275)
-#1436 := (or #1428 #1433)
-#1439 := (forall (vars (?x59 T2)) #1436)
-#1442 := (not #1439)
-#1366 := (= #1344 0::int)
-#1369 := (not #1317)
-#1378 := (and #201 #1369 #1366)
-#1383 := (exists (vars (?x76 T2)) #1378)
-#1355 := (+ uf_9 #1293)
-#1356 := (<= #1355 0::int)
-#1357 := (not #1356)
-#1360 := (and #70 #1357)
-#1363 := (not #1360)
-#1386 := (or #1363 #1383)
-#1389 := (forall (vars (?x75 T2)) #1386)
-#1334 := (and #201 #1056)
-#1339 := (not #1334)
-#1346 := (or #1339 #1342)
-#1349 := (forall (vars (?x71 T2) (?x72 T2)) #1346)
-#1352 := (not #1349)
-#1392 := (or #1352 #1389)
-#1395 := (and #1349 #1392)
-#210 := (and #208 #209)
-#673 := (not #210)
-#1322 := (or #673 #1317)
-#1325 := (forall (vars (?x67 T2) (?x68 T2)) #1322)
-#1328 := (not #1325)
-#1398 := (or #1328 #1395)
-#1401 := (and #1325 #1398)
-#1311 := (forall (vars (?x65 T2)) #1308)
-#1314 := (not #1311)
-#1404 := (or #1314 #1401)
-#1407 := (and #1311 #1404)
-#1410 := (or #1305 #1407)
-#1413 := (and #205 #1410)
-#667 := (forall (vars (?x63 T2)) #662)
-#783 := (not #667)
-#1416 := (or #783 #1413)
-#1419 := (and #667 #1416)
-#1297 := (forall (vars (?x61 T2)) #1292)
+#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)
+#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)
-#1422 := (or #1300 #1419)
-#1425 := (and #1297 #1422)
-#1281 := (or #645 #1275)
-#1286 := (forall (vars (?x60 T2)) #1281)
-#1289 := (not #1286)
-#1120 := (not #1119)
-#1236 := (and #112 #1120)
-#1239 := (exists (vars (?x48 T2)) #1236)
-#1470 := (not #1239)
-#1494 := (or #175 #825 #1470 #1289 #1425 #1442 #1455 #1459)
-#1165 := (not #1164)
-#1199 := (and #1056 #1165)
-#1202 := (not #1199)
-#1208 := (or #1202 #1205)
-#1211 := (forall (vars (?x53 T2) (?x54 T2)) #1208)
-#1214 := (not #1211)
-#1222 := (or #162 #1214)
-#1227 := (and #1211 #1222)
-#1180 := (= #1182 0::int)
-#1174 := (>= #1176 0::int)
-#1177 := (not #1174)
-#1184 := (and #1177 #1180)
-#1187 := (exists (vars (?x50 T2)) #1184)
-#1168 := (and #70 #1165)
-#1171 := (not #1168)
-#1190 := (or #1171 #1187)
-#1193 := (forall (vars (?x49 T2)) #1190)
-#1196 := (not #1193)
-#1230 := (or #1196 #1227)
-#1233 := (and #1193 #1230)
-#1257 := (or #595 #577 #604 #586 #1233 #1239)
-#1499 := (and #1257 #1494)
-#1136 := (not #1135)
-#1129 := (= #1133 0::int)
-#1145 := (and #111 #1129 #1136)
-#1150 := (exists (vars (?x47 T2)) #1145)
-#1123 := (and #70 #1120)
-#1126 := (not #1123)
-#1153 := (or #1126 #1150)
-#1156 := (forall (vars (?x46 T2)) #1153)
-#1159 := (not #1156)
-#1091 := (= #1069 0::int)
-#1042 := (+ #66 #1041)
-#1040 := (>= #1042 0::int)
-#1094 := (not #1040)
-#1103 := (and #74 #1094 #1091)
-#1108 := (exists (vars (?x38 T2)) #1103)
-#1082 := (not #1081)
-#1085 := (and #70 #1082)
-#1088 := (not #1085)
-#1111 := (or #1088 #1108)
-#1114 := (forall (vars (?x37 T2)) #1111)
-#1550 := (not #1114)
-#1571 := (or #1547 #1550 #1159 #1499 #1522 #1533 #1542)
-#1576 := (and #1114 #1571)
-#1059 := (and #74 #1056)
-#1062 := (not #1059)
-#1070 := (or #1062 #1066)
-#1073 := (forall (vars (?x33 T2) (?x34 T2)) #1070)
-#1076 := (not #1073)
-#1579 := (or #1076 #1576)
-#1582 := (and #1073 #1579)
-#81 := (up_13 #10)
-#82 := (and #75 #81)
-#416 := (not #82)
-#1044 := (or #416 #1040)
-#1047 := (forall (vars (?x29 T2) (?x30 T2)) #1044)
-#1050 := (not #1047)
-#1585 := (or #1050 #1582)
-#1588 := (and #1047 #1585)
-#1031 := (>= #66 0::int)
-#1032 := (forall (vars (?x27 T2)) #1031)
-#1035 := (not #1032)
-#1591 := (or #1035 #1588)
-#1594 := (and #1032 #1591)
-#77 := (uf_12 uf_11)
-#78 := (= #77 0::int)
-#1026 := (not #78)
-#1597 := (or #1026 #1594)
-#1600 := (and #78 #1597)
-#399 := (= uf_9 #66)
-#405 := (or #65 #399)
-#410 := (forall (vars (?x25 T2)) #405)
-#999 := (not #410)
-#990 := (not #76)
-#1623 := (or #990 #999 #1600 #1611)
-#1628 := (not #1623)
-#1 := true
-#216 := (+ #191 #88)
-#223 := (= #211 #216)
-#224 := (and #201 #223)
-#222 := (< #191 #211)
-#225 := (and #222 #224)
-#226 := (exists (vars (?x76 T2)) #225)
-#220 := (< #191 uf_9)
-#221 := (and #70 #220)
-#227 := (implies #221 #226)
-#228 := (forall (vars (?x75 T2)) #227)
-#229 := (and #228 true)
-#217 := (<= #211 #216)
-#89 := (< #88 uf_9)
-#215 := (and #201 #89)
-#218 := (implies #215 #217)
-#219 := (forall (vars (?x71 T2) (?x72 T2)) #218)
-#230 := (implies #219 #229)
-#231 := (and #219 #230)
-#212 := (<= #211 #191)
-#213 := (implies #210 #212)
-#214 := (forall (vars (?x67 T2) (?x68 T2)) #213)
-#232 := (implies #214 #231)
-#233 := (and #214 #232)
-#206 := (<= 0::int #191)
-#207 := (forall (vars (?x65 T2)) #206)
-#234 := (implies #207 #233)
-#235 := (and #207 #234)
-#236 := (implies #205 #235)
-#237 := (and #205 #236)
-#196 := (= #191 #107)
-#202 := (implies #201 #196)
-#203 := (forall (vars (?x63 T2)) #202)
-#238 := (implies #203 #237)
-#239 := (and #203 #238)
-#199 := (<= #191 #107)
-#200 := (forall (vars (?x61 T2)) #199)
-#240 := (implies #200 #239)
-#241 := (and #200 #240)
-#188 := (+ #177 #186)
-#189 := (< #188 #107)
-#187 := (< #186 uf_9)
-#190 := (and #187 #189)
-#195 := (not #190)
-#197 := (implies #195 #196)
-#198 := (forall (vars (?x60 T2)) #197)
-#242 := (implies #198 #241)
-#192 := (= #191 #188)
-#193 := (implies #190 #192)
-#194 := (forall (vars (?x59 T2)) #193)
-#243 := (implies #194 #242)
-#244 := (implies #184 #243)
-#179 := (<= #177 #107)
-#180 := (implies #112 #179)
-#181 := (forall (vars (?x58 T2)) #180)
-#245 := (implies #181 #244)
-#178 := (< #177 uf_9)
-#246 := (implies #178 #245)
-#176 := (not #175)
-#247 := (implies #176 #246)
-#124 := (< #107 uf_9)
-#133 := (and #112 #124)
-#134 := (exists (vars (?x48 T2)) #133)
-#248 := (implies #134 #247)
-#249 := (implies true #248)
-#163 := (and #162 true)
-#151 := (+ #146 #88)
-#158 := (<= #149 #151)
-#147 := (< #146 uf_9)
-#157 := (and #147 #89)
-#159 := (implies #157 #158)
-#160 := (forall (vars (?x53 T2) (?x54 T2)) #159)
-#164 := (implies #160 #163)
-#165 := (and #160 #164)
-#152 := (= #149 #151)
-#150 := (< #146 #149)
-#153 := (and #150 #152)
-#154 := (exists (vars (?x50 T2)) #153)
-#148 := (and #70 #147)
-#155 := (implies #148 #154)
-#156 := (forall (vars (?x49 T2)) #155)
-#166 := (implies #156 #165)
-#167 := (and #156 #166)
-#168 := (implies #145 #167)
-#142 := (= uf_19 uf_14)
-#169 := (implies #142 #168)
-#170 := (implies #140 #169)
-#137 := (= uf_16 uf_15)
-#171 := (implies #137 #170)
-#135 := (not #134)
-#172 := (implies #135 #171)
-#173 := (implies true #172)
-#250 := (and #173 #249)
-#120 := (+ #107 #88)
-#127 := (= #115 #120)
-#128 := (and #111 #127)
-#126 := (< #107 #115)
-#129 := (and #126 #128)
-#130 := (exists (vars (?x47 T2)) #129)
-#125 := (and #70 #124)
-#131 := (implies #125 #130)
-#132 := (forall (vars (?x46 T2)) #131)
-#251 := (implies #132 #250)
-#121 := (<= #115 #120)
-#119 := (and #111 #89)
-#122 := (implies #119 #121)
-#123 := (forall (vars (?x44 T2) (?x45 T2)) #122)
-#252 := (implies #123 #251)
-#116 := (<= #115 #107)
-#117 := (implies #114 #116)
-#118 := (forall (vars (?x42 T2) (?x43 T2)) #117)
-#253 := (implies #118 #252)
-#108 := (<= 0::int #107)
-#109 := (forall (vars (?x41 T2)) #108)
-#254 := (implies #109 #253)
-#255 := (implies #106 #254)
-#256 := (implies true #255)
-#91 := (+ #66 #88)
-#98 := (= #83 #91)
-#99 := (and #74 #98)
-#97 := (< #66 #83)
-#100 := (and #97 #99)
-#101 := (exists (vars (?x38 T2)) #100)
-#95 := (< #66 uf_9)
-#96 := (and #70 #95)
-#102 := (implies #96 #101)
-#103 := (forall (vars (?x37 T2)) #102)
-#257 := (implies #103 #256)
-#258 := (and #103 #257)
-#92 := (<= #83 #91)
-#90 := (and #74 #89)
-#93 := (implies #90 #92)
-#94 := (forall (vars (?x33 T2) (?x34 T2)) #93)
-#259 := (implies #94 #258)
-#260 := (and #94 #259)
-#84 := (<= #83 #66)
+#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)
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+#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 (?x29 T2) (?x30 T2)) #85)
-#261 := (implies #86 #260)
-#262 := (and #86 #261)
-#79 := (<= 0::int #66)
-#80 := (forall (vars (?x27 T2)) #79)
-#263 := (implies #80 #262)
-#264 := (and #80 #263)
-#265 := (implies #78 #264)
-#266 := (and #78 #265)
-#267 := (implies #76 #266)
-#71 := (= #66 uf_9)
-#72 := (implies #70 #71)
-#73 := (forall (vars (?x25 T2)) #72)
-#268 := (implies #73 #267)
-#68 := (implies #65 #67)
-#69 := (forall (vars (?x24 T2)) #68)
-#269 := (implies #69 #268)
-#270 := (implies true #269)
-#271 := (not #270)
-#1631 := (iff #271 #1628)
-#683 := (+ #88 #191)
-#701 := (= #211 #683)
-#704 := (and #201 #701)
-#707 := (and #222 #704)
-#710 := (exists (vars (?x76 T2)) #707)
-#716 := (not #221)
-#717 := (or #716 #710)
-#722 := (forall (vars (?x75 T2)) #717)
-#686 := (<= #211 #683)
-#680 := (and #89 #201)
-#692 := (not #680)
-#693 := (or #692 #686)
-#698 := (forall (vars (?x71 T2) (?x72 T2)) #693)
-#735 := (not #698)
-#736 := (or #735 #722)
-#741 := (and #698 #736)
-#674 := (or #673 #212)
-#677 := (forall (vars (?x67 T2) (?x68 T2)) #674)
-#747 := (not #677)
-#748 := (or #747 #741)
-#753 := (and #677 #748)
-#759 := (not #207)
-#760 := (or #759 #753)
-#765 := (and #207 #760)
-#670 := (= 0::int #204)
-#771 := (not #670)
-#772 := (or #771 #765)
-#777 := (and #670 #772)
-#784 := (or #783 #777)
-#789 := (and #667 #784)
-#795 := (not #200)
-#796 := (or #795 #789)
-#801 := (and #200 #796)
-#651 := (or #190 #645)
-#656 := (forall (vars (?x60 T2)) #651)
-#807 := (not #656)
-#808 := (or #807 #801)
-#631 := (= #188 #191)
-#637 := (or #195 #631)
-#642 := (forall (vars (?x59 T2)) #637)
-#816 := (not #642)
-#817 := (or #816 #808)
-#826 := (or #825 #817)
-#625 := (or #111 #179)
-#628 := (forall (vars (?x58 T2)) #625)
-#834 := (not #628)
-#835 := (or #834 #826)
-#843 := (not #178)
-#844 := (or #843 #835)
-#852 := (or #175 #844)
-#860 := (or #135 #852)
-#540 := (= 0::int #161)
-#498 := (+ #88 #146)
-#525 := (<= #149 #498)
-#522 := (and #89 #147)
-#531 := (not #522)
-#532 := (or #531 #525)
-#537 := (forall (vars (?x53 T2) (?x54 T2)) #532)
-#553 := (not #537)
-#554 := (or #553 #540)
-#559 := (and #537 #554)
-#501 := (= #149 #498)
-#504 := (and #150 #501)
-#507 := (exists (vars (?x50 T2)) #504)
-#513 := (not #148)
-#514 := (or #513 #507)
-#519 := (forall (vars (?x49 T2)) #514)
-#565 := (not #519)
-#566 := (or #565 #559)
-#571 := (and #519 #566)
-#578 := (or #577 #571)
-#587 := (or #586 #578)
-#596 := (or #595 #587)
-#605 := (or #604 #596)
-#613 := (or #134 #605)
-#872 := (and #613 #860)
-#450 := (+ #88 #107)
-#468 := (= #115 #450)
-#471 := (and #111 #468)
-#474 := (and #126 #471)
-#477 := (exists (vars (?x47 T2)) #474)
-#483 := (not #125)
-#484 := (or #483 #477)
-#489 := (forall (vars (?x46 T2)) #484)
-#878 := (not #489)
-#879 := (or #878 #872)
-#453 := (<= #115 #450)
-#447 := (and #89 #111)
-#459 := (not #447)
-#460 := (or #459 #453)
-#465 := (forall (vars (?x44 T2) (?x45 T2)) #460)
-#887 := (not #465)
-#888 := (or #887 #879)
-#441 := (or #440 #116)
-#444 := (forall (vars (?x42 T2) (?x43 T2)) #441)
-#896 := (not #444)
-#897 := (or #896 #888)
-#905 := (not #109)
-#906 := (or #905 #897)
-#437 := (= 0::int #105)
-#914 := (not #437)
-#915 := (or #914 #906)
-#430 := (not #96)
-#431 := (or #430 #101)
-#434 := (forall (vars (?x37 T2)) #431)
-#930 := (not #434)
-#931 := (or #930 #915)
-#936 := (and #434 #931)
-#423 := (not #90)
-#424 := (or #423 #92)
-#427 := (forall (vars (?x33 T2) (?x34 T2)) #424)
-#942 := (not #427)
-#943 := (or #942 #936)
-#948 := (and #427 #943)
-#417 := (or #416 #84)
-#420 := (forall (vars (?x29 T2) (?x30 T2)) #417)
-#954 := (not #420)
+#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)
+#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)
-#960 := (and #420 #955)
-#966 := (not #80)
-#967 := (or #966 #960)
-#972 := (and #80 #967)
-#413 := (= 0::int #77)
-#978 := (not #413)
-#979 := (or #978 #972)
-#984 := (and #413 #979)
-#991 := (or #990 #984)
-#1000 := (or #999 #991)
-#385 := (= 0::int #66)
-#391 := (or #70 #385)
-#396 := (forall (vars (?x24 T2)) #391)
-#1008 := (not #396)
-#1009 := (or #1008 #1000)
-#1021 := (not #1009)
-#1629 := (iff #1021 #1628)
-#1626 := (iff #1009 #1623)
-#1614 := (or #990 #1600)
-#1617 := (or #999 #1614)
-#1620 := (or #1611 #1617)
-#1624 := (iff #1620 #1623)
-#1625 := [rewrite]: #1624
-#1621 := (iff #1009 #1620)
-#1618 := (iff #1000 #1617)
-#1615 := (iff #991 #1614)
-#1601 := (iff #984 #1600)
-#1598 := (iff #979 #1597)
-#1595 := (iff #972 #1594)
-#1592 := (iff #967 #1591)
-#1589 := (iff #960 #1588)
-#1586 := (iff #955 #1585)
-#1583 := (iff #948 #1582)
-#1580 := (iff #943 #1579)
-#1577 := (iff #936 #1576)
-#1574 := (iff #931 #1571)
-#1553 := (or #1159 #1499)
-#1556 := (or #1522 #1553)
-#1559 := (or #1533 #1556)
-#1562 := (or #1542 #1559)
-#1565 := (or #1547 #1562)
-#1568 := (or #1550 #1565)
-#1572 := (iff #1568 #1571)
-#1573 := [rewrite]: #1572
-#1569 := (iff #931 #1568)
-#1566 := (iff #915 #1565)
-#1563 := (iff #906 #1562)
-#1560 := (iff #897 #1559)
-#1557 := (iff #888 #1556)
-#1554 := (iff #879 #1553)
-#1500 := (iff #872 #1499)
-#1497 := (iff #860 #1494)
-#1473 := (or #1289 #1425)
-#1476 := (or #1442 #1473)
-#1479 := (or #825 #1476)
-#1482 := (or #1455 #1479)
-#1485 := (or #1459 #1482)
-#1488 := (or #175 #1485)
-#1491 := (or #1470 #1488)
-#1495 := (iff #1491 #1494)
-#1496 := [rewrite]: #1495
-#1492 := (iff #860 #1491)
-#1489 := (iff #852 #1488)
-#1486 := (iff #844 #1485)
-#1483 := (iff #835 #1482)
-#1480 := (iff #826 #1479)
-#1477 := (iff #817 #1476)
-#1474 := (iff #808 #1473)
-#1426 := (iff #801 #1425)
-#1423 := (iff #796 #1422)
-#1420 := (iff #789 #1419)
-#1417 := (iff #784 #1416)
-#1414 := (iff #777 #1413)
-#1411 := (iff #772 #1410)
-#1408 := (iff #765 #1407)
-#1405 := (iff #760 #1404)
-#1402 := (iff #753 #1401)
-#1399 := (iff #748 #1398)
-#1396 := (iff #741 #1395)
-#1393 := (iff #736 #1392)
-#1390 := (iff #722 #1389)
-#1387 := (iff #717 #1386)
-#1384 := (iff #710 #1383)
-#1381 := (iff #707 #1378)
-#1372 := (and #201 #1366)
-#1375 := (and #1369 #1372)
-#1379 := (iff #1375 #1378)
-#1380 := [rewrite]: #1379
-#1376 := (iff #707 #1375)
-#1373 := (iff #704 #1372)
-#1367 := (iff #701 #1366)
-#1368 := [rewrite]: #1367
-#1374 := [monotonicity #1368]: #1373
-#1370 := (iff #222 #1369)
-#1371 := [rewrite]: #1370
-#1377 := [monotonicity #1371 #1374]: #1376
-#1382 := [trans #1377 #1380]: #1381
-#1385 := [quant-intro #1382]: #1384
-#1364 := (iff #716 #1363)
-#1361 := (iff #221 #1360)
-#1358 := (iff #220 #1357)
-#1359 := [rewrite]: #1358
-#1362 := [monotonicity #1359]: #1361
-#1365 := [monotonicity #1362]: #1364
-#1388 := [monotonicity #1365 #1385]: #1387
-#1391 := [quant-intro #1388]: #1390
-#1353 := (iff #735 #1352)
-#1350 := (iff #698 #1349)
-#1347 := (iff #693 #1346)
-#1343 := (iff #686 #1342)
-#1345 := [rewrite]: #1343
-#1340 := (iff #692 #1339)
-#1337 := (iff #680 #1334)
-#1331 := (and #1056 #201)
-#1335 := (iff #1331 #1334)
-#1336 := [rewrite]: #1335
-#1332 := (iff #680 #1331)
-#1057 := (iff #89 #1056)
-#1058 := [rewrite]: #1057
-#1333 := [monotonicity #1058]: #1332
-#1338 := [trans #1333 #1336]: #1337
-#1341 := [monotonicity #1338]: #1340
-#1348 := [monotonicity #1341 #1345]: #1347
-#1351 := [quant-intro #1348]: #1350
-#1354 := [monotonicity #1351]: #1353
-#1394 := [monotonicity #1354 #1391]: #1393
-#1397 := [monotonicity #1351 #1394]: #1396
-#1329 := (iff #747 #1328)
-#1326 := (iff #677 #1325)
-#1323 := (iff #674 #1322)
-#1320 := (iff #212 #1317)
-#1321 := [rewrite]: #1320
-#1324 := [monotonicity #1321]: #1323
-#1327 := [quant-intro #1324]: #1326
-#1330 := [monotonicity #1327]: #1329
-#1400 := [monotonicity #1330 #1397]: #1399
-#1403 := [monotonicity #1327 #1400]: #1402
-#1315 := (iff #759 #1314)
-#1312 := (iff #207 #1311)
-#1309 := (iff #206 #1308)
+#482 := (<= #78 #479)
+#474 := (and #50 #447)
+#488 := (not #474)
+#489 := (or #488 #482)
+#494 := (forall (vars (?v0 S2) (?v1 S2)) #489)
+#963 := (not #494)
+#964 := (or #963 #955)
+#463 := (or #79 #462)
+#468 := (forall (vars (?v0 S2) (?v1 S2)) #463)
+#972 := (not #468)
+#973 := (or #972 #964)
+#981 := (not #70)
+#982 := (or #981 #973)
+#444 := (= 0::int #66)
+#990 := (not #444)
+#991 := (or #990 #982)
+#421 := (and #59 #368)
+#426 := (and #58 #421)
+#429 := (exists (vars (?v1 S2)) #426)
+#435 := (not #57)
+#436 := (or #435 #429)
+#441 := (forall (vars (?v0 S2)) #436)
+#1006 := (not #441)
+#1007 := (or #1006 #991)
+#1012 := (and #441 #1007)
+#401 := (and #50 #368)
+#409 := (not #401)
+#410 := (or #53 #409)
+#415 := (forall (vars (?v0 S2) (?v1 S2)) #410)
+#1018 := (not #415)
+#1019 := (or #1018 #1012)
+#1024 := (and #415 #1019)
+#390 := (or #45 #389)
+#395 := (forall (vars (?v0 S2) (?v1 S2)) #390)
+#1030 := (not #395)
+#1031 := (or #1030 #1024)
+#1036 := (and #395 #1031)
+#1042 := (not #40)
+#1043 := (or #1042 #1036)
+#1048 := (and #40 #1043)
+#377 := (= 0::int #37)
+#1054 := (not #377)
+#1055 := (or #1054 #1048)
+#1060 := (and #377 #1055)
+#1067 := (or #1066 #1060)
+#1076 := (or #1075 #1067)
+#340 := (= 0::int #25)
+#346 := (or #29 #340)
+#351 := (forall (vars (?v0 S2)) #346)
+#1084 := (not #351)
+#1085 := (or #1084 #1076)
+#1097 := (not #1085)
+#1735 := (iff #1097 #1734)
+#1732 := (iff #1085 #1729)
+#1720 := (or #1066 #1706)
+#1723 := (or #1075 #1720)
+#1726 := (or #1717 #1723)
+#1730 := (iff #1726 #1729)
+#1731 := [rewrite]: #1730
+#1727 := (iff #1085 #1726)
+#1724 := (iff #1076 #1723)
+#1721 := (iff #1067 #1720)
+#1707 := (iff #1060 #1706)
+#1704 := (iff #1055 #1703)
+#1701 := (iff #1048 #1700)
+#1698 := (iff #1043 #1697)
+#1695 := (iff #1036 #1694)
+#1692 := (iff #1031 #1691)
+#1689 := (iff #1024 #1688)
+#1686 := (iff #1019 #1685)
+#1683 := (iff #1012 #1682)
+#1680 := (iff #1007 #1677)
+#1659 := (or #1245 #1600)
+#1662 := (or #1623 #1659)
+#1665 := (or #1639 #1662)
+#1668 := (or #1648 #1665)
+#1671 := (or #1653 #1668)
+#1674 := (or #1656 #1671)
+#1678 := (iff #1674 #1677)
+#1679 := [rewrite]: #1678
+#1675 := (iff #1007 #1674)
+#1672 := (iff #991 #1671)
+#1669 := (iff #982 #1668)
+#1666 := (iff #973 #1665)
+#1663 := (iff #964 #1662)
+#1660 := (iff #955 #1659)
+#1601 := (iff #948 #1600)
+#1598 := (iff #936 #1595)
+#1574 := (or #1380 #1521)
+#1577 := (or #1538 #1574)
+#1580 := (or #901 #1577)
+#1583 := (or #1556 #1580)
+#1586 := (or #1560 #1583)
+#1589 := (or #668 #1586)
+#1592 := (or #1571 #1589)
+#1596 := (iff #1592 #1595)
+#1597 := [rewrite]: #1596
+#1593 := (iff #936 #1592)
+#1590 := (iff #928 #1589)
+#1587 := (iff #920 #1586)
+#1584 := (iff #911 #1583)
+#1581 := (iff #902 #1580)
+#1578 := (iff #893 #1577)
+#1575 := (iff #884 #1574)
+#1522 := (iff #877 #1521)
+#1519 := (iff #872 #1518)
+#1516 := (iff #865 #1515)
+#1513 := (iff #860 #1512)
+#1510 := (iff #853 #1509)
+#1507 := (iff #848 #1506)
+#1504 := (iff #841 #1503)
+#1501 := (iff #836 #1500)
+#1498 := (iff #829 #1497)
+#1495 := (iff #824 #1494)
+#1492 := (iff #817 #1491)
+#1489 := (iff #812 #1488)
+#1486 := (iff #798 #1485)
+#1483 := (iff #793 #1482)
+#1480 := (iff #786 #1479)
+#1477 := (iff #783 #1474)
+#1468 := (and #713 #1462)
+#1471 := (and #1465 #1468)
+#1475 := (iff #1471 #1474)
+#1476 := [rewrite]: #1475
+#1472 := (iff #783 #1471)
+#1469 := (iff #780 #1468)
+#1463 := (iff #777 #1462)
+#1464 := [rewrite]: #1463
+#1470 := [monotonicity #1464]: #1469
+#1466 := (iff #188 #1465)
+#1467 := [rewrite]: #1466
+#1473 := [monotonicity #1467 #1470]: #1472
+#1478 := [trans #1473 #1476]: #1477
+#1481 := [quant-intro #1478]: #1480
+#1460 := (iff #792 #1459)
+#1457 := (iff #187 #1456)
+#1454 := (iff #186 #1453)
+#1455 := [rewrite]: #1454
+#1458 := [monotonicity #1455]: #1457
+#1461 := [monotonicity #1458]: #1460
+#1484 := [monotonicity #1461 #1481]: #1483
+#1487 := [quant-intro #1484]: #1486
+#1449 := (iff #811 #1448)
+#1446 := (iff #774 #1445)
+#1443 := (iff #769 #1442)
+#1439 := (iff #762 #1438)
+#1441 := [rewrite]: #1439
+#1436 := (iff #768 #1435)
+#1433 := (iff #754 #1430)
+#1427 := (and #1142 #713)
+#1431 := (iff #1427 #1430)
+#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
-#1313 := [quant-intro #1310]: #1312
-#1316 := [monotonicity #1313]: #1315
-#1406 := [monotonicity #1316 #1403]: #1405
-#1409 := [monotonicity #1313 #1406]: #1408
-#1306 := (iff #771 #1305)
-#1303 := (iff #670 #205)
+#1306 := (iff #597 #1305)
+#1303 := (iff #583 #125)
 #1304 := [rewrite]: #1303
-#1307 := [monotonicity #1304]: #1306
-#1412 := [monotonicity #1307 #1409]: #1411
-#1415 := [monotonicity #1304 #1412]: #1414
-#1418 := [monotonicity #1415]: #1417
-#1421 := [monotonicity #1418]: #1420
-#1301 := (iff #795 #1300)
-#1298 := (iff #200 #1297)
-#1295 := (iff #199 #1292)
-#1296 := [rewrite]: #1295
+#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
-#1424 := [monotonicity #1302 #1421]: #1423
-#1427 := [monotonicity #1299 #1424]: #1426
-#1290 := (iff #807 #1289)
-#1287 := (iff #656 #1286)
-#1284 := (iff #651 #1281)
-#1278 := (or #1275 #645)
-#1282 := (iff #1278 #1281)
-#1283 := [rewrite]: #1282
-#1279 := (iff #651 #1278)
-#1276 := (iff #190 #1275)
-#1273 := (iff #189 #1272)
-#1274 := [rewrite]: #1273
-#1266 := (iff #187 #1265)
-#1267 := [rewrite]: #1266
-#1277 := [monotonicity #1267 #1274]: #1276
-#1280 := [monotonicity #1277]: #1279
-#1285 := [trans #1280 #1283]: #1284
-#1288 := [quant-intro #1285]: #1287
-#1291 := [monotonicity #1288]: #1290
-#1475 := [monotonicity #1291 #1427]: #1474
-#1443 := (iff #816 #1442)
-#1440 := (iff #642 #1439)
-#1437 := (iff #637 #1436)
-#1434 := (iff #631 #1433)
-#1435 := [rewrite]: #1434
-#1429 := (iff #195 #1428)
-#1430 := [monotonicity #1277]: #1429
-#1438 := [monotonicity #1430 #1435]: #1437
-#1441 := [quant-intro #1438]: #1440
-#1444 := [monotonicity #1441]: #1443
-#1478 := [monotonicity #1444 #1475]: #1477
-#1481 := [monotonicity #1478]: #1480
-#1456 := (iff #834 #1455)
-#1453 := (iff #628 #1452)
-#1450 := (iff #625 #1449)
-#1447 := (iff #179 #1445)
-#1448 := [rewrite]: #1447
-#1451 := [monotonicity #1448]: #1450
-#1454 := [quant-intro #1451]: #1453
-#1457 := [monotonicity #1454]: #1456
-#1484 := [monotonicity #1457 #1481]: #1483
-#1468 := (iff #843 #1459)
-#1460 := (not #1459)
-#1463 := (not #1460)
-#1466 := (iff #1463 #1459)
-#1467 := [rewrite]: #1466
-#1464 := (iff #843 #1463)
-#1461 := (iff #178 #1460)
-#1462 := [rewrite]: #1461
-#1465 := [monotonicity #1462]: #1464
-#1469 := [trans #1465 #1467]: #1468
-#1487 := [monotonicity #1469 #1484]: #1486
-#1490 := [monotonicity #1487]: #1489
-#1471 := (iff #135 #1470)
-#1240 := (iff #134 #1239)
-#1237 := (iff #133 #1236)
-#1121 := (iff #124 #1120)
-#1122 := [rewrite]: #1121
-#1238 := [monotonicity #1122]: #1237
-#1241 := [quant-intro #1238]: #1240
-#1472 := [monotonicity #1241]: #1471
-#1493 := [monotonicity #1472 #1490]: #1492
-#1498 := [trans #1493 #1496]: #1497
-#1260 := (iff #613 #1257)
-#1242 := (or #577 #1233)
-#1245 := (or #586 #1242)
-#1248 := (or #595 #1245)
-#1251 := (or #604 #1248)
-#1254 := (or #1239 #1251)
-#1258 := (iff #1254 #1257)
-#1259 := [rewrite]: #1258
-#1255 := (iff #613 #1254)
-#1252 := (iff #605 #1251)
-#1249 := (iff #596 #1248)
-#1246 := (iff #587 #1245)
-#1243 := (iff #578 #1242)
-#1234 := (iff #571 #1233)
-#1231 := (iff #566 #1230)
-#1228 := (iff #559 #1227)
-#1225 := (iff #554 #1222)
-#1219 := (or #1214 #162)
-#1223 := (iff #1219 #1222)
+#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
-#1220 := (iff #554 #1219)
-#1217 := (iff #540 #162)
-#1218 := [rewrite]: #1217
-#1215 := (iff #553 #1214)
-#1212 := (iff #537 #1211)
-#1209 := (iff #532 #1208)
-#1206 := (iff #525 #1205)
-#1207 := [rewrite]: #1206
-#1203 := (iff #531 #1202)
-#1200 := (iff #522 #1199)
-#1166 := (iff #147 #1165)
-#1167 := [rewrite]: #1166
-#1201 := [monotonicity #1058 #1167]: #1200
-#1204 := [monotonicity #1201]: #1203
-#1210 := [monotonicity #1204 #1207]: #1209
-#1213 := [quant-intro #1210]: #1212
-#1216 := [monotonicity #1213]: #1215
-#1221 := [monotonicity #1216 #1218]: #1220
-#1226 := [trans #1221 #1224]: #1225
-#1229 := [monotonicity #1213 #1226]: #1228
-#1197 := (iff #565 #1196)
-#1194 := (iff #519 #1193)
-#1191 := (iff #514 #1190)
-#1188 := (iff #507 #1187)
-#1185 := (iff #504 #1184)
-#1181 := (iff #501 #1180)
-#1183 := [rewrite]: #1181
-#1178 := (iff #150 #1177)
-#1179 := [rewrite]: #1178
-#1186 := [monotonicity #1179 #1183]: #1185
-#1189 := [quant-intro #1186]: #1188
-#1172 := (iff #513 #1171)
-#1169 := (iff #148 #1168)
-#1170 := [monotonicity #1167]: #1169
-#1173 := [monotonicity #1170]: #1172
-#1192 := [monotonicity #1173 #1189]: #1191
-#1195 := [quant-intro #1192]: #1194
-#1198 := [monotonicity #1195]: #1197
-#1232 := [monotonicity #1198 #1229]: #1231
-#1235 := [monotonicity #1195 #1232]: #1234
-#1244 := [monotonicity #1235]: #1243
+#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
-#1250 := [monotonicity #1247]: #1249
-#1253 := [monotonicity #1250]: #1252
-#1256 := [monotonicity #1241 #1253]: #1255
-#1261 := [trans #1256 #1259]: #1260
-#1501 := [monotonicity #1261 #1498]: #1500
-#1160 := (iff #878 #1159)
-#1157 := (iff #489 #1156)
-#1154 := (iff #484 #1153)
-#1151 := (iff #477 #1150)
-#1148 := (iff #474 #1145)
-#1139 := (and #111 #1129)
-#1142 := (and #1136 #1139)
-#1146 := (iff #1142 #1145)
-#1147 := [rewrite]: #1146
-#1143 := (iff #474 #1142)
-#1140 := (iff #471 #1139)
-#1130 := (iff #468 #1129)
-#1134 := [rewrite]: #1130
-#1141 := [monotonicity #1134]: #1140
-#1137 := (iff #126 #1136)
-#1138 := [rewrite]: #1137
-#1144 := [monotonicity #1138 #1141]: #1143
-#1149 := [trans #1144 #1147]: #1148
-#1152 := [quant-intro #1149]: #1151
-#1127 := (iff #483 #1126)
-#1124 := (iff #125 #1123)
-#1125 := [monotonicity #1122]: #1124
-#1128 := [monotonicity #1125]: #1127
-#1155 := [monotonicity #1128 #1152]: #1154
-#1158 := [quant-intro #1155]: #1157
-#1161 := [monotonicity #1158]: #1160
-#1555 := [monotonicity #1161 #1501]: #1554
-#1523 := (iff #887 #1522)
-#1520 := (iff #465 #1519)
-#1517 := (iff #460 #1516)
-#1514 := (iff #453 #1513)
-#1515 := [rewrite]: #1514
-#1511 := (iff #459 #1510)
-#1508 := (iff #447 #1505)
-#1502 := (and #1056 #111)
-#1506 := (iff #1502 #1505)
-#1507 := [rewrite]: #1506
-#1503 := (iff #447 #1502)
-#1504 := [monotonicity #1058]: #1503
-#1509 := [trans #1504 #1507]: #1508
-#1512 := [monotonicity #1509]: #1511
-#1518 := [monotonicity #1512 #1515]: #1517
-#1521 := [quant-intro #1518]: #1520
-#1524 := [monotonicity #1521]: #1523
-#1558 := [monotonicity #1524 #1555]: #1557
-#1534 := (iff #896 #1533)
-#1531 := (iff #444 #1530)
-#1528 := (iff #441 #1527)
-#1525 := (iff #116 #1135)
-#1526 := [rewrite]: #1525
-#1529 := [monotonicity #1526]: #1528
-#1532 := [quant-intro #1529]: #1531
-#1535 := [monotonicity #1532]: #1534
-#1561 := [monotonicity #1535 #1558]: #1560
-#1543 := (iff #905 #1542)
-#1540 := (iff #109 #1539)
-#1537 := (iff #108 #1536)
-#1538 := [rewrite]: #1537
-#1541 := [quant-intro #1538]: #1540
-#1544 := [monotonicity #1541]: #1543
-#1564 := [monotonicity #1544 #1561]: #1563
-#1548 := (iff #914 #1547)
-#1545 := (iff #437 #106)
-#1546 := [rewrite]: #1545
-#1549 := [monotonicity #1546]: #1548
-#1567 := [monotonicity #1549 #1564]: #1566
-#1551 := (iff #930 #1550)
-#1115 := (iff #434 #1114)
-#1112 := (iff #431 #1111)
-#1109 := (iff #101 #1108)
-#1106 := (iff #100 #1103)
-#1097 := (and #74 #1091)
-#1100 := (and #1094 #1097)
-#1104 := (iff #1100 #1103)
-#1105 := [rewrite]: #1104
-#1101 := (iff #100 #1100)
-#1098 := (iff #99 #1097)
-#1092 := (iff #98 #1091)
-#1093 := [rewrite]: #1092
-#1099 := [monotonicity #1093]: #1098
-#1095 := (iff #97 #1094)
-#1096 := [rewrite]: #1095
-#1102 := [monotonicity #1096 #1099]: #1101
-#1107 := [trans #1102 #1105]: #1106
-#1110 := [quant-intro #1107]: #1109
-#1089 := (iff #430 #1088)
-#1086 := (iff #96 #1085)
-#1083 := (iff #95 #1082)
-#1084 := [rewrite]: #1083
-#1087 := [monotonicity #1084]: #1086
-#1090 := [monotonicity #1087]: #1089
-#1113 := [monotonicity #1090 #1110]: #1112
-#1116 := [quant-intro #1113]: #1115
-#1552 := [monotonicity #1116]: #1551
-#1570 := [monotonicity #1552 #1567]: #1569
-#1575 := [trans #1570 #1573]: #1574
-#1578 := [monotonicity #1116 #1575]: #1577
-#1077 := (iff #942 #1076)
-#1074 := (iff #427 #1073)
-#1071 := (iff #424 #1070)
-#1065 := (iff #92 #1066)
-#1067 := [rewrite]: #1065
-#1063 := (iff #423 #1062)
-#1060 := (iff #90 #1059)
-#1061 := [monotonicity #1058]: #1060
-#1064 := [monotonicity #1061]: #1063
-#1072 := [monotonicity #1064 #1067]: #1071
-#1075 := [quant-intro #1072]: #1074
-#1078 := [monotonicity #1075]: #1077
-#1581 := [monotonicity #1078 #1578]: #1580
-#1584 := [monotonicity #1075 #1581]: #1583
-#1051 := (iff #954 #1050)
-#1048 := (iff #420 #1047)
-#1045 := (iff #417 #1044)
-#1039 := (iff #84 #1040)
-#1043 := [rewrite]: #1039
-#1046 := [monotonicity #1043]: #1045
-#1049 := [quant-intro #1046]: #1048
-#1052 := [monotonicity #1049]: #1051
-#1587 := [monotonicity #1052 #1584]: #1586
-#1590 := [monotonicity #1049 #1587]: #1589
-#1036 := (iff #966 #1035)
-#1033 := (iff #80 #1032)
-#1029 := (iff #79 #1031)
-#1030 := [rewrite]: #1029
-#1034 := [quant-intro #1030]: #1033
-#1037 := [monotonicity #1034]: #1036
-#1593 := [monotonicity #1037 #1590]: #1592
-#1596 := [monotonicity #1034 #1593]: #1595
-#1027 := (iff #978 #1026)
-#1024 := (iff #413 #78)
-#1025 := [rewrite]: #1024
-#1028 := [monotonicity #1025]: #1027
-#1599 := [monotonicity #1028 #1596]: #1598
-#1602 := [monotonicity #1025 #1599]: #1601
-#1616 := [monotonicity #1602]: #1615
-#1619 := [monotonicity #1616]: #1618
-#1612 := (iff #1008 #1611)
-#1609 := (iff #396 #1608)
-#1606 := (iff #391 #1605)
-#1603 := (iff #385 #67)
-#1604 := [rewrite]: #1603
-#1607 := [monotonicity #1604]: #1606
-#1610 := [quant-intro #1607]: #1609
+#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
-#1622 := [monotonicity #1613 #1619]: #1621
-#1627 := [trans #1622 #1625]: #1626
+#1619 := [monotonicity #1613 #1616]: #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
-#1022 := (iff #271 #1021)
-#1019 := (iff #270 #1009)
-#1014 := (implies true #1009)
-#1017 := (iff #1014 #1009)
-#1018 := [rewrite]: #1017
-#1015 := (iff #270 #1014)
-#1012 := (iff #269 #1009)
-#1005 := (implies #396 #1000)
-#1010 := (iff #1005 #1009)
-#1011 := [rewrite]: #1010
-#1006 := (iff #269 #1005)
-#1003 := (iff #268 #1000)
-#996 := (implies #410 #991)
-#1001 := (iff #996 #1000)
-#1002 := [rewrite]: #1001
-#997 := (iff #268 #996)
-#994 := (iff #267 #991)
-#987 := (implies #76 #984)
+#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)
+#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 #267 #987)
-#985 := (iff #266 #984)
-#982 := (iff #265 #979)
-#975 := (implies #413 #972)
-#980 := (iff #975 #979)
-#981 := [rewrite]: #980
-#976 := (iff #265 #975)
-#973 := (iff #264 #972)
-#970 := (iff #263 #967)
-#963 := (implies #80 #960)
-#968 := (iff #963 #967)
-#969 := [rewrite]: #968
-#964 := (iff #263 #963)
-#961 := (iff #262 #960)
-#958 := (iff #261 #955)
-#951 := (implies #420 #948)
+#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 #261 #951)
-#949 := (iff #260 #948)
-#946 := (iff #259 #943)
-#939 := (implies #427 #936)
-#944 := (iff #939 #943)
+#952 := (iff #217 #951)
+#949 := (iff #216 #948)
+#946 := (iff #215 #936)
+#941 := (implies true #936)
+#944 := (iff #941 #936)
 #945 := [rewrite]: #944
-#940 := (iff #259 #939)
-#937 := (iff #258 #936)
-#934 := (iff #257 #931)
-#927 := (implies #434 #915)
-#932 := (iff #927 #931)
-#933 := [rewrite]: #932
-#928 := (iff #257 #927)
-#925 := (iff #256 #915)
-#920 := (implies true #915)
-#923 := (iff #920 #915)
-#924 := [rewrite]: #923
-#921 := (iff #256 #920)
-#918 := (iff #255 #915)
-#911 := (implies #437 #906)
-#916 := (iff #911 #915)
-#917 := [rewrite]: #916
-#912 := (iff #255 #911)
-#909 := (iff #254 #906)
-#902 := (implies #109 #897)
-#907 := (iff #902 #906)
-#908 := [rewrite]: #907
-#903 := (iff #254 #902)
-#900 := (iff #253 #897)
-#893 := (implies #444 #888)
-#898 := (iff #893 #897)
-#899 := [rewrite]: #898
-#894 := (iff #253 #893)
-#891 := (iff #252 #888)
-#884 := (implies #465 #879)
-#889 := (iff #884 #888)
-#890 := [rewrite]: #889
-#885 := (iff #252 #884)
-#882 := (iff #251 #879)
-#875 := (implies #489 #872)
-#880 := (iff #875 #879)
-#881 := [rewrite]: #880
-#876 := (iff #251 #875)
-#873 := (iff #250 #872)
-#870 := (iff #249 #860)
-#865 := (implies true #860)
-#868 := (iff #865 #860)
-#869 := [rewrite]: #868
-#866 := (iff #249 #865)
-#863 := (iff #248 #860)
-#857 := (implies #134 #852)
-#861 := (iff #857 #860)
+#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)
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+#885 := (iff #880 #884)
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+#878 := (iff #207 #877)
+#875 := (iff #206 #872)
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+#866 := (iff #205 #865)
+#863 := (iff #204 #860)
+#856 := (implies #725 #853)
+#861 := (iff #856 #860)
 #862 := [rewrite]: #861
-#858 := (iff #248 #857)
-#855 := (iff #247 #852)
-#849 := (implies #176 #844)
-#853 := (iff #849 #852)
-#854 := [rewrite]: #853
-#850 := (iff #247 #849)
-#847 := (iff #246 #844)
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-#845 := (iff #840 #844)
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-#841 := (iff #246 #840)
-#838 := (iff #245 #835)
-#831 := (implies #628 #826)
-#836 := (iff #831 #835)
-#837 := [rewrite]: #836
-#832 := (iff #245 #831)
-#829 := (iff #244 #826)
-#822 := (implies #184 #817)
-#827 := (iff #822 #826)
-#828 := [rewrite]: #827
-#823 := (iff #244 #822)
-#820 := (iff #243 #817)
-#813 := (implies #642 #808)
-#818 := (iff #813 #817)
-#819 := [rewrite]: #818
-#814 := (iff #243 #813)
-#811 := (iff #242 #808)
-#804 := (implies #656 #801)
-#809 := (iff #804 #808)
-#810 := [rewrite]: #809
-#805 := (iff #242 #804)
-#802 := (iff #241 #801)
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-#792 := (implies #200 #789)
-#797 := (iff #792 #796)
-#798 := [rewrite]: #797
-#793 := (iff #240 #792)
-#790 := (iff #239 #789)
-#787 := (iff #238 #784)
-#780 := (implies #667 #777)
-#785 := (iff #780 #784)
-#786 := [rewrite]: #785
-#781 := (iff #238 #780)
-#778 := (iff #237 #777)
-#775 := (iff #236 #772)
-#768 := (implies #670 #765)
-#773 := (iff #768 #772)
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-#766 := (iff #235 #765)
-#763 := (iff #234 #760)
-#756 := (implies #207 #753)
-#761 := (iff #756 #760)
-#762 := [rewrite]: #761
-#757 := (iff #234 #756)
-#754 := (iff #233 #753)
-#751 := (iff #232 #748)
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-#749 := (iff #744 #748)
-#750 := [rewrite]: #749
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-#742 := (iff #231 #741)
-#739 := (iff #230 #736)
-#732 := (implies #698 #722)
-#737 := (iff #732 #736)
-#738 := [rewrite]: #737
-#733 := (iff #230 #732)
-#730 := (iff #229 #722)
-#725 := (and #722 true)
-#728 := (iff #725 #722)
-#729 := [rewrite]: #728
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-#723 := (iff #228 #722)
-#720 := (iff #227 #717)
-#713 := (implies #221 #710)
-#718 := (iff #713 #717)
-#719 := [rewrite]: #718
-#714 := (iff #227 #713)
-#711 := (iff #226 #710)
-#708 := (iff #225 #707)
-#705 := (iff #224 #704)
-#702 := (iff #223 #701)
-#684 := (= #216 #683)
-#685 := [rewrite]: #684
-#703 := [monotonicity #685]: #702
-#706 := [monotonicity #703]: #705
-#709 := [monotonicity #706]: #708
-#712 := [quant-intro #709]: #711
-#715 := [monotonicity #712]: #714
-#721 := [trans #715 #719]: #720
-#724 := [quant-intro #721]: #723
-#727 := [monotonicity #724]: #726
-#731 := [trans #727 #729]: #730
-#699 := (iff #219 #698)
-#696 := (iff #218 #693)
-#689 := (implies #680 #686)
-#694 := (iff #689 #693)
-#695 := [rewrite]: #694
-#690 := (iff #218 #689)
-#687 := (iff #217 #686)
-#688 := [monotonicity #685]: #687
-#681 := (iff #215 #680)
-#682 := [rewrite]: #681
-#691 := [monotonicity #682 #688]: #690
-#697 := [trans #691 #695]: #696
-#700 := [quant-intro #697]: #699
-#734 := [monotonicity #700 #731]: #733
-#740 := [trans #734 #738]: #739
-#743 := [monotonicity #700 #740]: #742
-#678 := (iff #214 #677)
-#675 := (iff #213 #674)
-#676 := [rewrite]: #675
-#679 := [quant-intro #676]: #678
-#746 := [monotonicity #679 #743]: #745
-#752 := [trans #746 #750]: #751
-#755 := [monotonicity #679 #752]: #754
-#758 := [monotonicity #755]: #757
-#764 := [trans #758 #762]: #763
-#767 := [monotonicity #764]: #766
-#671 := (iff #205 #670)
-#672 := [rewrite]: #671
-#770 := [monotonicity #672 #767]: #769
-#776 := [trans #770 #774]: #775
-#779 := [monotonicity #672 #776]: #778
-#668 := (iff #203 #667)
-#665 := (iff #202 #662)
-#659 := (implies #201 #645)
-#663 := (iff #659 #662)
-#664 := [rewrite]: #663
-#660 := (iff #202 #659)
-#646 := (iff #196 #645)
-#647 := [rewrite]: #646
-#661 := [monotonicity #647]: #660
-#666 := [trans #661 #664]: #665
-#669 := [quant-intro #666]: #668
-#782 := [monotonicity #669 #779]: #781
-#788 := [trans #782 #786]: #787
-#791 := [monotonicity #669 #788]: #790
-#794 := [monotonicity #791]: #793
-#800 := [trans #794 #798]: #799
+#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)
+#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
-#657 := (iff #198 #656)
-#654 := (iff #197 #651)
-#648 := (implies #195 #645)
-#652 := (iff #648 #651)
-#653 := [rewrite]: #652
-#649 := (iff #197 #648)
-#650 := [monotonicity #647]: #649
-#655 := [trans #650 #653]: #654
-#658 := [quant-intro #655]: #657
-#806 := [monotonicity #658 #803]: #805
-#812 := [trans #806 #810]: #811
-#643 := (iff #194 #642)
-#640 := (iff #193 #637)
-#634 := (implies #190 #631)
-#638 := (iff #634 #637)
-#639 := [rewrite]: #638
-#635 := (iff #193 #634)
-#632 := (iff #192 #631)
-#633 := [rewrite]: #632
-#636 := [monotonicity #633]: #635
-#641 := [trans #636 #639]: #640
-#644 := [quant-intro #641]: #643
-#815 := [monotonicity #644 #812]: #814
-#821 := [trans #815 #819]: #820
-#824 := [monotonicity #821]: #823
-#830 := [trans #824 #828]: #829
-#629 := (iff #181 #628)
-#626 := (iff #180 #625)
-#627 := [rewrite]: #626
-#630 := [quant-intro #627]: #629
-#833 := [monotonicity #630 #830]: #832
-#839 := [trans #833 #837]: #838
-#842 := [monotonicity #839]: #841
-#848 := [trans #842 #846]: #847
-#851 := [monotonicity #848]: #850
-#856 := [trans #851 #854]: #855
-#859 := [monotonicity #856]: #858
-#864 := [trans #859 #862]: #863
-#867 := [monotonicity #864]: #866
-#871 := [trans #867 #869]: #870
-#623 := (iff #173 #613)
-#618 := (implies true #613)
-#621 := (iff #618 #613)
-#622 := [rewrite]: #621
-#619 := (iff #173 #618)
-#616 := (iff #172 #613)
-#610 := (implies #135 #605)
-#614 := (iff #610 #613)
-#615 := [rewrite]: #614
-#611 := (iff #172 #610)
-#608 := (iff #171 #605)
-#601 := (implies #492 #596)
-#606 := (iff #601 #605)
-#607 := [rewrite]: #606
-#602 := (iff #171 #601)
-#599 := (iff #170 #596)
-#592 := (implies #140 #587)
-#597 := (iff #592 #596)
-#598 := [rewrite]: #597
-#593 := (iff #170 #592)
-#590 := (iff #169 #587)
-#583 := (implies #495 #578)
-#588 := (iff #583 #587)
-#589 := [rewrite]: #588
-#584 := (iff #169 #583)
-#581 := (iff #168 #578)
-#574 := (implies #145 #571)
-#579 := (iff #574 #578)
-#580 := [rewrite]: #579
-#575 := (iff #168 #574)
-#572 := (iff #167 #571)
-#569 := (iff #166 #566)
-#562 := (implies #519 #559)
-#567 := (iff #562 #566)
-#568 := [rewrite]: #567
-#563 := (iff #166 #562)
-#560 := (iff #165 #559)
-#557 := (iff #164 #554)
-#550 := (implies #537 #540)
-#555 := (iff #550 #554)
-#556 := [rewrite]: #555
-#551 := (iff #164 #550)
-#548 := (iff #163 #540)
-#543 := (and #540 true)
-#546 := (iff #543 #540)
-#547 := [rewrite]: #546
-#544 := (iff #163 #543)
-#541 := (iff #162 #540)
-#542 := [rewrite]: #541
-#545 := [monotonicity #542]: #544
-#549 := [trans #545 #547]: #548
-#538 := (iff #160 #537)
-#535 := (iff #159 #532)
-#528 := (implies #522 #525)
-#533 := (iff #528 #532)
-#534 := [rewrite]: #533
-#529 := (iff #159 #528)
-#526 := (iff #158 #525)
-#499 := (= #151 #498)
-#500 := [rewrite]: #499
-#527 := [monotonicity #500]: #526
-#523 := (iff #157 #522)
-#524 := [rewrite]: #523
-#530 := [monotonicity #524 #527]: #529
-#536 := [trans #530 #534]: #535
-#539 := [quant-intro #536]: #538
-#552 := [monotonicity #539 #549]: #551
-#558 := [trans #552 #556]: #557
-#561 := [monotonicity #539 #558]: #560
-#520 := (iff #156 #519)
-#517 := (iff #155 #514)
-#510 := (implies #148 #507)
-#515 := (iff #510 #514)
-#516 := [rewrite]: #515
-#511 := (iff #155 #510)
-#508 := (iff #154 #507)
-#505 := (iff #153 #504)
-#502 := (iff #152 #501)
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-#506 := [monotonicity #503]: #505
-#509 := [quant-intro #506]: #508
-#512 := [monotonicity #509]: #511
-#518 := [trans #512 #516]: #517
-#521 := [quant-intro #518]: #520
-#564 := [monotonicity #521 #561]: #563
-#570 := [trans #564 #568]: #569
-#573 := [monotonicity #521 #570]: #572
-#576 := [monotonicity #573]: #575
-#582 := [trans #576 #580]: #581
-#496 := (iff #142 #495)
-#497 := [rewrite]: #496
-#585 := [monotonicity #497 #582]: #584
-#591 := [trans #585 #589]: #590
-#594 := [monotonicity #591]: #593
-#600 := [trans #594 #598]: #599
-#493 := (iff #137 #492)
-#494 := [rewrite]: #493
-#603 := [monotonicity #494 #600]: #602
-#609 := [trans #603 #607]: #608
-#612 := [monotonicity #609]: #611
-#617 := [trans #612 #615]: #616
-#620 := [monotonicity #617]: #619
-#624 := [trans #620 #622]: #623
-#874 := [monotonicity #624 #871]: #873
-#490 := (iff #132 #489)
-#487 := (iff #131 #484)
-#480 := (implies #125 #477)
-#485 := (iff #480 #484)
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-#475 := (iff #129 #474)
-#472 := (iff #128 #471)
-#469 := (iff #127 #468)
-#451 := (= #120 #450)
-#452 := [rewrite]: #451
-#470 := [monotonicity #452]: #469
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-#476 := [monotonicity #473]: #475
-#479 := [quant-intro #476]: #478
-#482 := [monotonicity #479]: #481
-#488 := [trans #482 #486]: #487
-#491 := [quant-intro #488]: #490
-#877 := [monotonicity #491 #874]: #876
-#883 := [trans #877 #881]: #882
-#466 := (iff #123 #465)
-#463 := (iff #122 #460)
-#456 := (implies #447 #453)
-#461 := (iff #456 #460)
-#462 := [rewrite]: #461
-#457 := (iff #122 #456)
-#454 := (iff #121 #453)
-#455 := [monotonicity #452]: #454
-#448 := (iff #119 #447)
+#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
+#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
-#458 := [monotonicity #449 #455]: #457
-#464 := [trans #458 #462]: #463
-#467 := [quant-intro #464]: #466
-#886 := [monotonicity #467 #883]: #885
-#892 := [trans #886 #890]: #891
-#445 := (iff #118 #444)
-#442 := (iff #117 #441)
-#443 := [rewrite]: #442
-#446 := [quant-intro #443]: #445
-#895 := [monotonicity #446 #892]: #894
-#901 := [trans #895 #899]: #900
-#904 := [monotonicity #901]: #903
-#910 := [trans #904 #908]: #909
-#438 := (iff #106 #437)
-#439 := [rewrite]: #438
-#913 := [monotonicity #439 #910]: #912
-#919 := [trans #913 #917]: #918
-#922 := [monotonicity #919]: #921
-#926 := [trans #922 #924]: #925
-#435 := (iff #103 #434)
-#432 := (iff #102 #431)
-#433 := [rewrite]: #432
-#436 := [quant-intro #433]: #435
-#929 := [monotonicity #436 #926]: #928
-#935 := [trans #929 #933]: #934
-#938 := [monotonicity #436 #935]: #937
-#428 := (iff #94 #427)
-#425 := (iff #93 #424)
-#426 := [rewrite]: #425
-#429 := [quant-intro #426]: #428
-#941 := [monotonicity #429 #938]: #940
-#947 := [trans #941 #945]: #946
-#950 := [monotonicity #429 #947]: #949
-#421 := (iff #86 #420)
-#418 := (iff #85 #417)
-#419 := [rewrite]: #418
-#422 := [quant-intro #419]: #421
-#953 := [monotonicity #422 #950]: #952
+#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
+#511 := [monotonicity #508]: #510
+#517 := [trans #511 #515]: #516
+#520 := [quant-intro #517]: #519
+#953 := [monotonicity #520 #950]: #952
 #959 := [trans #953 #957]: #958
-#962 := [monotonicity #422 #959]: #961
-#965 := [monotonicity #962]: #964
-#971 := [trans #965 #969]: #970
-#974 := [monotonicity #971]: #973
-#414 := (iff #78 #413)
-#415 := [rewrite]: #414
-#977 := [monotonicity #415 #974]: #976
-#983 := [trans #977 #981]: #982
-#986 := [monotonicity #415 #983]: #985
-#989 := [monotonicity #986]: #988
+#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
-#411 := (iff #73 #410)
-#408 := (iff #72 #405)
-#402 := (implies #70 #399)
-#406 := (iff #402 #405)
-#407 := [rewrite]: #406
-#403 := (iff #72 #402)
-#400 := (iff #71 #399)
-#401 := [rewrite]: #400
-#404 := [monotonicity #401]: #403
-#409 := [trans #404 #407]: #408
-#412 := [quant-intro #409]: #411
-#998 := [monotonicity #412 #995]: #997
-#1004 := [trans #998 #1002]: #1003
-#397 := (iff #69 #396)
-#394 := (iff #68 #391)
-#388 := (implies #65 #385)
-#392 := (iff #388 #391)
-#393 := [rewrite]: #392
-#389 := (iff #68 #388)
-#386 := (iff #67 #385)
-#387 := [rewrite]: #386
-#390 := [monotonicity #387]: #389
-#395 := [trans #390 #393]: #394
-#398 := [quant-intro #395]: #397
-#1007 := [monotonicity #398 #1004]: #1006
-#1013 := [trans #1007 #1011]: #1012
-#1016 := [monotonicity #1013]: #1015
-#1020 := [trans #1016 #1018]: #1019
-#1023 := [monotonicity #1020]: #1022
-#1632 := [trans #1023 #1630]: #1631
-#384 := [asserted]: #271
-#1633 := [mp #384 #1632]: #1628
-#1634 := [not-or-elim #1633]: #76
-#1697 := [mp~ #1634 #1659]: #76
-#4041 := [mp #1697 #4040]: #4036
-#5203 := (not #4036)
-#5204 := (or #5203 #2873)
-#5205 := [quant-inst]: #5204
-#8153 := [unit-resolution #5205 #4041 #8152]: false
-#8156 := [lemma #8153]: #2873
-#3630 := (or #2888 #1758)
-#3965 := [def-axiom]: #3630
-#10020 := [unit-resolution #3965 #8156]: #2888
-#2893 := (not #2888)
-#4382 := (or #2893 #4379)
-#4385 := (not #4382)
-#4057 := (pattern #74 #81)
-#2319 := (not #81)
-#2865 := (or #74 #2319 #1040)
-#4058 := (forall (vars (?x29 T2) (?x30 T2)) (:pat #4057) #2865)
-#4063 := (not #4058)
-#4388 := (or #4063 #4385)
-#4391 := (not #4388)
-decl ?x30!1 :: T2
-#1719 := ?x30!1
-#1723 := (uf_12 ?x30!1)
-#2334 := (* -1::int #1723)
-decl ?x29!2 :: T2
-#1720 := ?x29!2
-#1721 := (uf_12 ?x29!2)
-#2335 := (+ #1721 #2334)
-#2336 := (<= #2335 0::int)
-#1727 := (up_13 ?x30!1)
-#1726 := (up_13 ?x29!2)
-#1766 := (not #1726)
-#1968 := (or #1766 #1727 #2336)
-#8727 := [hypothesis]: #1726
-#5149 := (or #5203 #1766)
-#5178 := [quant-inst]: #5149
-#8728 := [unit-resolution #5178 #4041 #8727]: false
-#8729 := [lemma #8728]: #1766
-#3559 := (or #1968 #1726)
-#3644 := [def-axiom]: #3559
-#10021 := [unit-resolution #3644 #8729]: #1968
-#2108 := (not #1968)
-#4394 := (or #2108 #4391)
-#4397 := (not #4394)
-#4049 := (forall (vars (?x27 T2)) (:pat #4042) #1031)
-#4054 := (not #4049)
-#4400 := (or #4054 #4397)
-#4403 := (not #4400)
-decl ?x27!0 :: T2
-#1704 := ?x27!0
-#1705 := (uf_12 ?x27!0)
-#1706 := (>= #1705 0::int)
-#1707 := (not #1706)
-#4406 := (or #1707 #4403)
-#4409 := (not #4406)
-#4412 := (or #1026 #4409)
-#4415 := (not #4412)
-#4422 := (forall (vars (?x24 T2)) (:pat #4042) #1605)
-#4425 := (iff #1608 #4422)
-#4423 := (iff #1605 #1605)
-#4424 := [refl]: #4423
-#4426 := [quant-intro #4424]: #4425
-#1933 := (~ #1608 #1608)
-#2022 := (~ #1605 #1605)
-#2023 := [refl]: #2022
-#1934 := [nnf-pos #2023]: #1933
-#1638 := [not-or-elim #1633]: #1608
-#1765 := [mp~ #1638 #1934]: #1608
-#4427 := [mp #1765 #4426]: #4422
-#4964 := [hypothesis]: #1026
-#3570 := (not #4422)
-#4986 := (or #3570 #78)
-#4909 := (= uf_11 uf_11)
-#4907 := (not #4909)
-#4899 := (or #4907 #78)
-#4987 := (or #3570 #4899)
-#4989 := (iff #4987 #4986)
-#4980 := (iff #4986 #4986)
-#5014 := [rewrite]: #4980
-#4981 := (iff #4899 #78)
-#4970 := (or false #78)
-#4974 := (iff #4970 #78)
-#4975 := [rewrite]: #4974
-#4973 := (iff #4899 #4970)
-#4923 := (iff #4907 false)
-#8612 := (not true)
-#8647 := (iff #8612 false)
-#8648 := [rewrite]: #8647
-#4921 := (iff #4907 #8612)
-#4919 := (iff #4909 true)
-#4920 := [rewrite]: #4919
-#4922 := [monotonicity #4920]: #4921
-#4972 := [trans #4922 #8648]: #4923
-#4963 := [monotonicity #4972]: #4973
-#4982 := [trans #4963 #4975]: #4981
-#4990 := [monotonicity #4982]: #4989
-#5015 := [trans #4990 #5014]: #4989
-#4988 := [quant-inst]: #4987
-#5016 := [mp #4988 #5015]: #4986
-#4971 := [unit-resolution #5016 #4964 #4427]: false
-#5020 := [lemma #4971]: #78
-#4418 := (or #1026 #4415)
-#3323 := (forall (vars (?x76 T2)) #3312)
-#3330 := (not #3323)
-#3308 := (forall (vars (?x71 T2) (?x72 T2)) #3303)
-#3329 := (not #3308)
-#3331 := (or #2159 #2721 #3329 #3330)
-#3332 := (not #3331)
-#3337 := (or #3286 #3332)
-#3344 := (not #3337)
-#3263 := (forall (vars (?x67 T2) (?x68 T2)) #3258)
-#3343 := (not #3263)
-#3345 := (or #3343 #3344)
-#3346 := (not #3345)
-#3351 := (or #3240 #3346)
-#3357 := (not #3351)
-#3358 := (or #1314 #3357)
-#3359 := (not #3358)
-#3364 := (or #2079 #3359)
-#3370 := (not #3364)
-#3371 := (or #1305 #3370)
-#3372 := (not #3371)
-#3377 := (or #1305 #3372)
-#3383 := (not #3377)
-#3384 := (or #783 #3383)
-#3385 := (not #3384)
-#3390 := (or #2664 #3385)
-#3396 := (not #3390)
-#3397 := (or #1300 #3396)
-#3398 := (not #3397)
-#3403 := (or #2655 #3398)
-#3411 := (not #3403)
-#3217 := (forall (vars (?x59 T2)) #3212)
-#3410 := (not #3217)
-#3199 := (forall (vars (?x60 T2)) #3196)
-#3409 := (not #3199)
-#3412 := (or #175 #825 #1455 #1459 #2015 #2017 #3409 #3410 #3411)
-#3413 := (not #3412)
-#3129 := (forall (vars (?x53 T2) (?x54 T2)) #3124)
-#3135 := (not #3129)
-#3136 := (or #162 #3135)
-#3137 := (not #3136)
-#3164 := (or #3137 #3161)
-#3171 := (not #3164)
-#3107 := (forall (vars (?x49 T2)) #3102)
-#3170 := (not #3107)
-#3172 := (or #3170 #3171)
-#3173 := (not #3172)
-#3070 := (forall (vars (?x50 T2)) #3059)
-#3076 := (not #3070)
-#3077 := (or #1894 #2504 #3076)
-#3078 := (not #3077)
-#3178 := (or #3078 #3173)
-#3185 := (not #3178)
-#3055 := (forall (vars (?x48 T2)) #3044)
-#3184 := (not #3055)
-#3186 := (or #595 #577 #604 #586 #3184 #3185)
-#3187 := (not #3186)
-#3418 := (or #3187 #3413)
-#3428 := (not #3418)
-#3041 := (forall (vars (?x46 T2)) #3036)
-#3427 := (not #3041)
-#3013 := (forall (vars (?x37 T2)) #3008)
-#3426 := (not #3013)
-#2985 := (forall (vars (?x42 T2) (?x43 T2)) #2980)
-#3425 := (not #2985)
-#2962 := (forall (vars (?x44 T2) (?x45 T2)) #2957)
-#3424 := (not #2962)
-#3429 := (or #1547 #1542 #3424 #3425 #3426 #3427 #3428)
-#3430 := (not #3429)
-#2930 := (forall (vars (?x38 T2)) #2919)
-#2936 := (not #2930)
-#2937 := (or #1788 #2366 #2936)
-#2938 := (not #2937)
-#3435 := (or #2938 #3430)
-#3442 := (not #3435)
-#2915 := (forall (vars (?x33 T2) (?x34 T2)) #2910)
-#3441 := (not #2915)
-#3443 := (or #3441 #3442)
-#3444 := (not #3443)
-#3449 := (or #2893 #3444)
-#3456 := (not #3449)
-#2870 := (forall (vars (?x29 T2) (?x30 T2)) #2865)
-#3455 := (not #2870)
-#3457 := (or #3455 #3456)
-#3458 := (not #3457)
-#3463 := (or #2108 #3458)
-#3469 := (not #3463)
-#3470 := (or #1035 #3469)
-#3471 := (not #3470)
-#3476 := (or #1707 #3471)
-#3482 := (not #3476)
-#3483 := (or #1026 #3482)
-#3484 := (not #3483)
-#3489 := (or #1026 #3484)
-#4419 := (iff #3489 #4418)
-#4416 := (iff #3484 #4415)
-#4413 := (iff #3483 #4412)
-#4410 := (iff #3482 #4409)
-#4407 := (iff #3476 #4406)
-#4404 := (iff #3471 #4403)
-#4401 := (iff #3470 #4400)
-#4398 := (iff #3469 #4397)
-#4395 := (iff #3463 #4394)
-#4392 := (iff #3458 #4391)
-#4389 := (iff #3457 #4388)
-#4386 := (iff #3456 #4385)
-#4383 := (iff #3449 #4382)
-#4380 := (iff #3444 #4379)
-#4377 := (iff #3443 #4376)
-#4374 := (iff #3442 #4373)
-#4371 := (iff #3435 #4370)
-#4368 := (iff #3430 #4367)
-#4365 := (iff #3429 #4364)
-#4362 := (iff #3428 #4361)
-#4359 := (iff #3418 #4358)
-#4356 := (iff #3413 #4355)
-#4353 := (iff #3412 #4352)
-#4350 := (iff #3411 #4349)
-#4347 := (iff #3403 #4346)
-#4344 := (iff #3398 #4343)
-#4341 := (iff #3397 #4340)
-#4338 := (iff #3396 #4337)
-#4335 := (iff #3390 #4334)
-#4332 := (iff #3385 #4331)
-#4329 := (iff #3384 #4328)
-#4326 := (iff #3383 #4325)
-#4323 := (iff #3377 #4322)
-#4320 := (iff #3372 #4319)
-#4317 := (iff #3371 #4316)
-#4314 := (iff #3370 #4313)
-#4311 := (iff #3364 #4310)
-#4308 := (iff #3359 #4307)
-#4305 := (iff #3358 #4304)
-#4302 := (iff #3357 #4301)
-#4299 := (iff #3351 #4298)
-#4296 := (iff #3346 #4295)
-#4293 := (iff #3345 #4292)
-#4290 := (iff #3344 #4289)
-#4287 := (iff #3337 #4286)
-#4284 := (iff #3332 #4283)
-#4281 := (iff #3331 #4280)
-#4278 := (iff #3330 #4277)
-#4275 := (iff #3323 #4272)
-#4273 := (iff #3312 #3312)
-#4274 := [refl]: #4273
-#4276 := [quant-intro #4274]: #4275
-#4279 := [monotonicity #4276]: #4278
-#4269 := (iff #3329 #4268)
-#4266 := (iff #3308 #4263)
-#4264 := (iff #3303 #3303)
-#4265 := [refl]: #4264
-#4267 := [quant-intro #4265]: #4266
-#4270 := [monotonicity #4267]: #4269
-#4282 := [monotonicity #4270 #4279]: #4281
+#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
+#1035 := [trans #1029 #1033]: #1034
+#1038 := [monotonicity #397 #1035]: #1037
+#1041 := [monotonicity #1038]: #1040
+#1047 := [trans #1041 #1045]: #1046
+#1050 := [monotonicity #1047]: #1049
+#378 := (iff #38 #377)
+#379 := [rewrite]: #378
+#1053 := [monotonicity #379 #1050]: #1052
+#1059 := [trans #1053 #1057]: #1058
+#1062 := [monotonicity #379 #1059]: #1061
+#375 := (iff #36 #374)
+#376 := [quant-intro #373]: #375
+#1065 := [monotonicity #376 #1062]: #1064
+#1071 := [trans #1065 #1069]: #1070
+#366 := (iff #32 #365)
+#363 := (iff #31 #360)
+#357 := (implies #29 #354)
+#361 := (iff #357 #360)
+#362 := [rewrite]: #361
+#358 := (iff #31 #357)
+#355 := (iff #30 #354)
+#356 := [rewrite]: #355
+#359 := [monotonicity #356]: #358
+#364 := [trans #359 #362]: #363
+#367 := [quant-intro #364]: #366
+#1074 := [monotonicity #367 #1071]: #1073
+#1080 := [trans #1074 #1078]: #1079
+#352 := (iff #28 #351)
+#349 := (iff #27 #346)
+#343 := (implies #24 #340)
+#347 := (iff #343 #346)
+#348 := [rewrite]: #347
+#344 := (iff #27 #343)
+#341 := (iff #26 #340)
+#342 := [rewrite]: #341
+#345 := [monotonicity #342]: #344
+#350 := [trans #345 #348]: #349
+#353 := [quant-intro #350]: #352
+#1083 := [monotonicity #353 #1080]: #1082
+#1089 := [trans #1083 #1087]: #1088
+#1092 := [monotonicity #1089]: #1091
+#1096 := [trans #1092 #1094]: #1095
+#1099 := [monotonicity #1096]: #1098
+#1738 := [trans #1099 #1736]: #1737
+#339 := [asserted]: #237
+#1739 := [mp #339 #1738]: #1734
+#1744 := [not-or-elim #1739]: #1714
+#2002 := [mp~ #1744 #2168]: #1714
+#4540 := [mp #2002 #4539]: #4535
+#4634 := [hypothesis]: #1102
+#4588 := (not #4535)
+#4586 := (or #4588 #38)
+#3871 := (= f6 f6)
+#3836 := (not #3871)
+#3837 := (or #3836 #38)
+#4589 := (or #4588 #3837)
+#4591 := (iff #4589 #4586)
+#4630 := (iff #4586 #4586)
+#4631 := [rewrite]: #4630
+#4587 := (iff #3837 #38)
+#3800 := (or false #38)
+#4577 := (iff #3800 #38)
+#4585 := [rewrite]: #4577
+#3801 := (iff #3837 #3800)
+#3796 := (iff #3836 false)
+#9474 := (not true)
+#9477 := (iff #9474 false)
+#9478 := [rewrite]: #9477
+#3795 := (iff #3836 #9474)
+#3840 := (iff #3871 true)
+#3821 := [rewrite]: #3840
+#3835 := [monotonicity #3821]: #3795
+#3787 := [trans #3835 #9478]: #3796
+#3793 := [monotonicity #3787]: #3801
+#4578 := [trans #3793 #4585]: #4587
+#3911 := [monotonicity #4578]: #4591
+#4632 := [trans #3911 #4631]: #4591
+#4590 := [quant-inst]: #4589
+#4633 := [mp #4590 #4632]: #4586
+#4635 := [unit-resolution #4633 #4634 #4540]: false
+#4636 := [lemma #4635]: #38
+#4531 := (or #1102 #4528)
+#3492 := (forall (vars (?v1 S2)) #3481)
+#3499 := (not #3492)
+#3477 := (forall (vars (?v0 S2) (?v1 S2)) #3472)
+#3498 := (not #3477)
+#3500 := (or #2308 #2875 #3498 #3499)
+#3501 := (not #3500)
+#3506 := (or #3455 #3501)
+#3513 := (not #3506)
+#3432 := (forall (vars (?v0 S2) (?v1 S2)) #3427)
+#3512 := (not #3432)
+#3514 := (or #3512 #3513)
+#3515 := (not #3514)
+#3520 := (or #3409 #3515)
+#3526 := (not #3520)
+#3527 := (or #1405 #3526)
+#3528 := (not #3527)
+#3533 := (or #2225 #3528)
+#3539 := (not #3533)
+#3540 := (or #1396 #3539)
+#3541 := (not #3540)
+#3546 := (or #1396 #3541)
+#3552 := (not #3546)
+#3553 := (or #859 #3552)
+#3554 := (not #3553)
+#3559 := (or #2818 #3554)
+#3565 := (not #3559)
+#3566 := (or #1391 #3565)
+#3567 := (not #3566)
+#3572 := (or #2804 #3567)
+#3580 := (not #3572)
+#3386 := (forall (vars (?v0 S2)) #3381)
+#3579 := (not #3386)
+#3368 := (forall (vars (?v0 S2)) #3365)
+#3578 := (not #3368)
+#3581 := (or #901 #668 #1556 #1560 #2159 #2162 #3578 #3579 #3580)
+#3582 := (not #3581)
+#3298 := (forall (vars (?v0 S2) (?v1 S2)) #3293)
+#3304 := (not #3298)
+#3305 := (or #125 #3304)
+#3306 := (not #3305)
+#3333 := (or #3306 #3330)
+#3340 := (not #3333)
+#3276 := (forall (vars (?v0 S2)) #3271)
+#3339 := (not #3276)
+#3341 := (or #3339 #3340)
+#3342 := (not #3341)
+#3239 := (forall (vars (?v1 S2)) #3228)
+#3245 := (not #3239)
+#3246 := (or #2038 #2653 #3245)
+#3247 := (not #3246)
+#3347 := (or #3247 #3342)
+#3354 := (not #3347)
+#3224 := (forall (vars (?v0 S2)) #3213)
+#3353 := (not #3224)
+#3355 := (or #638 #620 #647 #629 #3353 #3354)
+#3356 := (not #3355)
+#3587 := (or #3356 #3582)
+#3597 := (not #3587)
+#3210 := (forall (vars (?v0 S2)) #3205)
+#3596 := (not #3210)
+#3182 := (forall (vars (?v0 S2)) #3177)
+#3595 := (not #3182)
+#3154 := (forall (vars (?v0 S2) (?v1 S2)) #3149)
+#3594 := (not #3154)
+#3131 := (forall (vars (?v0 S2) (?v1 S2)) #3126)
+#3593 := (not #3131)
+#3598 := (or #1653 #1648 #3593 #3594 #3595 #3596 #3597)
+#3599 := (not #3598)
+#3099 := (forall (vars (?v1 S2)) #3088)
+#3105 := (not #3099)
+#3106 := (or #1930 #2515 #3105)
+#3107 := (not #3106)
+#3604 := (or #3107 #3599)
+#3611 := (not #3604)
+#3084 := (forall (vars (?v0 S2) (?v1 S2)) #3079)
+#3610 := (not #3084)
+#3612 := (or #3610 #3611)
+#3613 := (not #3612)
+#3618 := (or #3062 #3613)
+#3625 := (not #3618)
+#3039 := (forall (vars (?v0 S2) (?v1 S2)) #3034)
+#3624 := (not #3039)
+#3626 := (or #3624 #3625)
+#3627 := (not #3626)
+#3632 := (or #3016 #3627)
+#3638 := (not #3632)
+#3639 := (or #1111 #3638)
+#3640 := (not #3639)
+#3645 := (or #1846 #3640)
+#3651 := (not #3645)
+#3652 := (or #1102 #3651)
+#3653 := (not #3652)
+#3658 := (or #1102 #3653)
+#4532 := (iff #3658 #4531)
+#4529 := (iff #3653 #4528)
+#4526 := (iff #3652 #4525)
+#4523 := (iff #3651 #4522)
+#4520 := (iff #3645 #4519)
+#4517 := (iff #3640 #4516)
+#4514 := (iff #3639 #4513)
+#4511 := (iff #3638 #4510)
+#4508 := (iff #3632 #4507)
+#4505 := (iff #3627 #4504)
+#4502 := (iff #3626 #4501)
+#4499 := (iff #3625 #4498)
+#4496 := (iff #3618 #4495)
+#4493 := (iff #3613 #4492)
+#4490 := (iff #3612 #4489)
+#4487 := (iff #3611 #4486)
+#4484 := (iff #3604 #4483)
+#4481 := (iff #3599 #4480)
+#4478 := (iff #3598 #4477)
+#4475 := (iff #3597 #4474)
+#4472 := (iff #3587 #4471)
+#4469 := (iff #3582 #4468)
+#4466 := (iff #3581 #4465)
+#4463 := (iff #3580 #4462)
+#4460 := (iff #3572 #4459)
+#4457 := (iff #3567 #4456)
+#4454 := (iff #3566 #4453)
+#4451 := (iff #3565 #4450)
+#4448 := (iff #3559 #4447)
+#4445 := (iff #3554 #4444)
+#4442 := (iff #3553 #4441)
+#4439 := (iff #3552 #4438)
+#4436 := (iff #3546 #4435)
+#4433 := (iff #3541 #4432)
+#4430 := (iff #3540 #4429)
+#4427 := (iff #3539 #4426)
+#4424 := (iff #3533 #4423)
+#4421 := (iff #3528 #4420)
+#4418 := (iff #3527 #4417)
+#4415 := (iff #3526 #4414)
+#4412 := (iff #3520 #4411)
+#4409 := (iff #3515 #4408)
+#4406 := (iff #3514 #4405)
+#4403 := (iff #3513 #4402)
+#4400 := (iff #3506 #4399)
+#4397 := (iff #3501 #4396)
+#4394 := (iff #3500 #4393)
+#4391 := (iff #3499 #4390)
+#4388 := (iff #3492 #4385)
+#4386 := (iff #3481 #3481)
+#4387 := [refl]: #4386
+#4389 := [quant-intro #4387]: #4388
+#4392 := [monotonicity #4389]: #4391
+#4382 := (iff #3498 #4381)
+#4379 := (iff #3477 #4376)
+#4377 := (iff #3472 #3472)
+#4378 := [refl]: #4377
+#4380 := [quant-intro #4378]: #4379
+#4383 := [monotonicity #4380]: #4382
+#4395 := [monotonicity #4383 #4392]: #4394
+#4398 := [monotonicity #4395]: #4397
+#4401 := [monotonicity #4398]: #4400
+#4404 := [monotonicity #4401]: #4403
+#4374 := (iff #3512 #4373)
+#4371 := (iff #3432 #4368)
+#4369 := (iff #3427 #3427)
+#4370 := [refl]: #4369
+#4372 := [quant-intro #4370]: #4371
+#4375 := [monotonicity #4372]: #4374
+#4407 := [monotonicity #4375 #4404]: #4406
+#4410 := [monotonicity #4407]: #4409
+#4413 := [monotonicity #4410]: #4412
+#4416 := [monotonicity #4413]: #4415
+#4365 := (iff #1405 #4364)
+#4362 := (iff #1402 #4359)
+#4360 := (iff #1399 #1399)
+#4361 := [refl]: #4360
+#4363 := [quant-intro #4361]: #4362
+#4366 := [monotonicity #4363]: #4365
+#4419 := [monotonicity #4366 #4416]: #4418
+#4422 := [monotonicity #4419]: #4421
+#4425 := [monotonicity #4422]: #4424
+#4428 := [monotonicity #4425]: #4427
+#4431 := [monotonicity #4428]: #4430
+#4434 := [monotonicity #4431]: #4433
+#4437 := [monotonicity #4434]: #4436
+#4440 := [monotonicity #4437]: #4439
+#4357 := (iff #859 #4356)
+#4354 := (iff #725 #4351)
+#4352 := (iff #720 #720)
+#4353 := [refl]: #4352
+#4355 := [quant-intro #4353]: #4354
+#4358 := [monotonicity #4355]: #4357
+#4443 := [monotonicity #4358 #4440]: #4442
+#4446 := [monotonicity #4443]: #4445
+#4449 := [monotonicity #4446]: #4448
+#4452 := [monotonicity #4449]: #4451
+#4348 := (iff #1391 #4347)
+#4345 := (iff #1388 #4342)
+#4343 := (iff #1383 #1383)
+#4344 := [refl]: #4343
+#4346 := [quant-intro #4344]: #4345
+#4349 := [monotonicity #4346]: #4348
+#4455 := [monotonicity #4349 #4452]: #4454
+#4458 := [monotonicity #4455]: #4457
+#4461 := [monotonicity #4458]: #4460
+#4464 := [monotonicity #4461]: #4463
+#4340 := (iff #3579 #4339)
+#4337 := (iff #3386 #4334)
+#4335 := (iff #3381 #3381)
+#4336 := [refl]: #4335
+#4338 := [quant-intro #4336]: #4337
+#4341 := [monotonicity #4338]: #4340
+#4332 := (iff #3578 #4331)
+#4329 := (iff #3368 #4326)
+#4327 := (iff #3365 #3365)
+#4328 := [refl]: #4327
+#4330 := [quant-intro #4328]: #4329
+#4333 := [monotonicity #4330]: #4332
+#4322 := (iff #1556 #4321)
+#4319 := (iff #1553 #4316)
+#4317 := (iff #1548 #1548)
+#4318 := [refl]: #4317
+#4320 := [quant-intro #4318]: #4319
+#4323 := [monotonicity #4320]: #4322
+#4467 := [monotonicity #4323 #4333 #4341 #4464]: #4466
+#4470 := [monotonicity #4467]: #4469
+#4314 := (iff #3356 #4313)
+#4311 := (iff #3355 #4310)
+#4308 := (iff #3354 #4307)
+#4305 := (iff #3347 #4304)
+#4302 := (iff #3342 #4301)
+#4299 := (iff #3341 #4298)
+#4296 := (iff #3340 #4295)
+#4293 := (iff #3333 #4292)
+#4290 := (iff #3306 #4289)
+#4287 := (iff #3305 #4286)
+#4284 := (iff #3304 #4283)
+#4281 := (iff #3298 #4278)
+#4279 := (iff #3293 #3293)
+#4280 := [refl]: #4279
+#4282 := [quant-intro #4280]: #4281
 #4285 := [monotonicity #4282]: #4284
 #4288 := [monotonicity #4285]: #4287
 #4291 := [monotonicity #4288]: #4290
-#4261 := (iff #3343 #4260)
-#4258 := (iff #3263 #4255)
-#4256 := (iff #3258 #3258)
-#4257 := [refl]: #4256
-#4259 := [quant-intro #4257]: #4258
-#4262 := [monotonicity #4259]: #4261
-#4294 := [monotonicity #4262 #4291]: #4293
+#4294 := [monotonicity #4291]: #4293
 #4297 := [monotonicity #4294]: #4296
-#4300 := [monotonicity #4297]: #4299
+#4276 := (iff #3339 #4275)
+#4273 := (iff #3276 #4270)
+#4271 := (iff #3271 #3271)
+#4272 := [refl]: #4271
+#4274 := [quant-intro #4272]: #4273
+#4277 := [monotonicity #4274]: #4276
+#4300 := [monotonicity #4277 #4297]: #4299
 #4303 := [monotonicity #4300]: #4302
-#4252 := (iff #1314 #4251)
-#4249 := (iff #1311 #4246)
-#4247 := (iff #1308 #1308)
+#4268 := (iff #3247 #4267)
+#4265 := (iff #3246 #4264)
+#4262 := (iff #3245 #4261)
+#4259 := (iff #3239 #4256)
+#4257 := (iff #3228 #3228)
+#4258 := [refl]: #4257
+#4260 := [quant-intro #4258]: #4259
+#4263 := [monotonicity #4260]: #4262
+#4266 := [monotonicity #4263]: #4265
+#4269 := [monotonicity #4266]: #4268
+#4306 := [monotonicity #4269 #4303]: #4305
+#4309 := [monotonicity #4306]: #4308
+#4252 := (iff #3353 #4251)
+#4249 := (iff #3224 #4246)
+#4247 := (iff #3213 #3213)
 #4248 := [refl]: #4247
 #4250 := [quant-intro #4248]: #4249
 #4253 := [monotonicity #4250]: #4252
-#4306 := [monotonicity #4253 #4303]: #4305
-#4309 := [monotonicity #4306]: #4308
-#4312 := [monotonicity #4309]: #4311
+#4312 := [monotonicity #4253 #4309]: #4311
 #4315 := [monotonicity #4312]: #4314
-#4318 := [monotonicity #4315]: #4317
-#4321 := [monotonicity #4318]: #4320
-#4324 := [monotonicity #4321]: #4323
-#4327 := [monotonicity #4324]: #4326
-#4244 := (iff #783 #4243)
-#4241 := (iff #667 #4238)
-#4239 := (iff #662 #662)
-#4240 := [refl]: #4239
-#4242 := [quant-intro #4240]: #4241
-#4245 := [monotonicity #4242]: #4244
-#4330 := [monotonicity #4245 #4327]: #4329
-#4333 := [monotonicity #4330]: #4332
-#4336 := [monotonicity #4333]: #4335
-#4339 := [monotonicity #4336]: #4338
-#4235 := (iff #1300 #4234)
-#4232 := (iff #1297 #4229)
-#4230 := (iff #1292 #1292)
+#4473 := [monotonicity #4315 #4470]: #4472
+#4476 := [monotonicity #4473]: #4475
+#4243 := (iff #3596 #4242)
+#4240 := (iff #3210 #4237)
+#4238 := (iff #3205 #3205)
+#4239 := [refl]: #4238
+#4241 := [quant-intro #4239]: #4240
+#4244 := [monotonicity #4241]: #4243
+#4235 := (iff #3595 #4234)
+#4232 := (iff #3182 #4229)
+#4230 := (iff #3177 #3177)
 #4231 := [refl]: #4230
 #4233 := [quant-intro #4231]: #4232
 #4236 := [monotonicity #4233]: #4235
-#4342 := [monotonicity #4236 #4339]: #4341
-#4345 := [monotonicity #4342]: #4344
-#4348 := [monotonicity #4345]: #4347
-#4351 := [monotonicity #4348]: #4350
-#4227 := (iff #3410 #4226)
-#4224 := (iff #3217 #4221)
-#4222 := (iff #3212 #3212)
+#4227 := (iff #3594 #4226)
+#4224 := (iff #3154 #4221)
+#4222 := (iff #3149 #3149)
 #4223 := [refl]: #4222
 #4225 := [quant-intro #4223]: #4224
 #4228 := [monotonicity #4225]: #4227
-#4219 := (iff #3409 #4218)
-#4216 := (iff #3199 #4213)
-#4214 := (iff #3196 #3196)
-#4215 := [refl]: #4214
-#4217 := [quant-intro #4215]: #4216
-#4220 := [monotonicity #4217]: #4219
-#4209 := (iff #1455 #4208)
-#4206 := (iff #1452 #4203)
-#4204 := (iff #1449 #1449)
-#4205 := [refl]: #4204
-#4207 := [quant-intro #4205]: #4206
-#4210 := [monotonicity #4207]: #4209
-#4354 := [monotonicity #4210 #4220 #4228 #4351]: #4353
-#4357 := [monotonicity #4354]: #4356
-#4201 := (iff #3187 #4200)
-#4198 := (iff #3186 #4197)
-#4195 := (iff #3185 #4194)
-#4192 := (iff #3178 #4191)
-#4189 := (iff #3173 #4188)
-#4186 := (iff #3172 #4185)
-#4183 := (iff #3171 #4182)
-#4180 := (iff #3164 #4179)
-#4177 := (iff #3137 #4176)
-#4174 := (iff #3136 #4173)
-#4171 := (iff #3135 #4170)
-#4168 := (iff #3129 #4165)
-#4166 := (iff #3124 #3124)
-#4167 := [refl]: #4166
-#4169 := [quant-intro #4167]: #4168
-#4172 := [monotonicity #4169]: #4171
-#4175 := [monotonicity #4172]: #4174
-#4178 := [monotonicity #4175]: #4177
-#4181 := [monotonicity #4178]: #4180
-#4184 := [monotonicity #4181]: #4183
-#4163 := (iff #3170 #4162)
-#4160 := (iff #3107 #4157)
-#4158 := (iff #3102 #3102)
-#4159 := [refl]: #4158
-#4161 := [quant-intro #4159]: #4160
-#4164 := [monotonicity #4161]: #4163
-#4187 := [monotonicity #4164 #4184]: #4186
-#4190 := [monotonicity #4187]: #4189
-#4155 := (iff #3078 #4154)
-#4152 := (iff #3077 #4151)
-#4149 := (iff #3076 #4148)
-#4146 := (iff #3070 #4143)
-#4144 := (iff #3059 #3059)
-#4145 := [refl]: #4144
-#4147 := [quant-intro #4145]: #4146
-#4150 := [monotonicity #4147]: #4149
-#4153 := [monotonicity #4150]: #4152
-#4156 := [monotonicity #4153]: #4155
-#4193 := [monotonicity #4156 #4190]: #4192
+#4218 := (iff #3593 #4217)
+#4215 := (iff #3131 #4212)
+#4213 := (iff #3126 #3126)
+#4214 := [refl]: #4213
+#4216 := [quant-intro #4214]: #4215
+#4219 := [monotonicity #4216]: #4218
+#4210 := (iff #1648 #4209)
+#4207 := (iff #1645 #4204)
+#4205 := (iff #1642 #1642)
+#4206 := [refl]: #4205
+#4208 := [quant-intro #4206]: #4207
+#4211 := [monotonicity #4208]: #4210
+#4479 := [monotonicity #4211 #4219 #4228 #4236 #4244 #4476]: #4478
+#4482 := [monotonicity #4479]: #4481
+#4201 := (iff #3107 #4200)
+#4198 := (iff #3106 #4197)
+#4195 := (iff #3105 #4194)
+#4192 := (iff #3099 #4189)
+#4190 := (iff #3088 #3088)
+#4191 := [refl]: #4190
+#4193 := [quant-intro #4191]: #4192
 #4196 := [monotonicity #4193]: #4195
-#4139 := (iff #3184 #4138)
-#4136 := (iff #3055 #4133)
-#4134 := (iff #3044 #3044)
-#4135 := [refl]: #4134
-#4137 := [quant-intro #4135]: #4136
-#4140 := [monotonicity #4137]: #4139
-#4199 := [monotonicity #4140 #4196]: #4198
+#4199 := [monotonicity #4196]: #4198
 #4202 := [monotonicity #4199]: #4201
-#4360 := [monotonicity #4202 #4357]: #4359
-#4363 := [monotonicity #4360]: #4362
-#4130 := (iff #3427 #4129)
-#4127 := (iff #3041 #4124)
-#4125 := (iff #3036 #3036)
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+#3483 := (iff #2906 #3482)
+#3484 := [rewrite]: #3483
+#3487 := [monotonicity #3484]: #3486
+#3491 := [trans #3487 #3489]: #3490
+#3494 := [quant-intro #3491]: #3493
+#3478 := (iff #1445 #3477)
+#3475 := (iff #1442 #3472)
+#3458 := (or #719 #1141)
+#3469 := (or #3458 #1438)
+#3473 := (iff #3469 #3472)
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+#3470 := (iff #1442 #3469)
+#3467 := (iff #1435 #3458)
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+#3461 := [rewrite]: #3460
+#3464 := [monotonicity #3461]: #3463
+#3468 := [trans #3464 #3466]: #3467
+#3471 := [monotonicity #3468]: #3470
+#3476 := [trans #3471 #3474]: #3475
+#3479 := [quant-intro #3476]: #3478
+#3497 := [monotonicity #3479 #3494]: #3496
+#3505 := [trans #3497 #3503]: #3504
+#3456 := (iff #2872 #3455)
+#3453 := (iff #2869 #3450)
+#3436 := (or #2276 #3435)
+#3447 := (or #3436 #2864)
+#3451 := (iff #3447 #3450)
+#3452 := [rewrite]: #3451
+#3448 := (iff #2869 #3447)
+#3445 := (iff #2851 #3436)
+#3437 := (not #3436)
+#3440 := (not #3437)
+#3443 := (iff #3440 #3436)
+#3444 := [rewrite]: #3443
+#3441 := (iff #2851 #3440)
+#3438 := (iff #2848 #3437)
+#3439 := [rewrite]: #3438
+#3442 := [monotonicity #3439]: #3441
+#3446 := [trans #3442 #3444]: #3445
+#3449 := [monotonicity #3446]: #3448
+#3454 := [trans #3449 #3452]: #3453
+#3457 := [monotonicity #3454]: #3456
+#3508 := [monotonicity #3457 #3505]: #3507
+#3433 := (iff #1421 #3432)
+#3430 := (iff #1416 #3427)
+#3413 := (or #713 #3412)
+#3424 := (or #3413 #1408)
+#3428 := (iff #3424 #3427)
+#3429 := [rewrite]: #3428
+#3425 := (iff #1416 #3424)
+#3422 := (iff #742 #3413)
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+#3417 := (not #3414)
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+#3421 := [rewrite]: #3420
+#3418 := (iff #742 #3417)
+#3415 := (iff #736 #3414)
+#3416 := [rewrite]: #3415
+#3419 := [monotonicity #3416]: #3418
+#3423 := [trans #3419 #3421]: #3422
+#3426 := [monotonicity #3423]: #3425
+#3431 := [trans #3426 #3429]: #3430
+#3434 := [quant-intro #3431]: #3433
+#3511 := [monotonicity #3434 #3508]: #3510
+#3519 := [trans #3511 #3517]: #3518
+#3410 := (iff #2845 #3409)
+#3407 := (iff #2842 #3404)
+#3390 := (or #3389 #2247)
+#3401 := (or #3390 #2837)
+#3405 := (iff #3401 #3404)
+#3406 := [rewrite]: #3405
+#3402 := (iff #2842 #3401)
+#3399 := (iff #2826 #3390)
+#3391 := (not #3390)
+#3394 := (not #3391)
+#3397 := (iff #3394 #3390)
+#3398 := [rewrite]: #3397
+#3395 := (iff #2826 #3394)
+#3392 := (iff #2823 #3391)
+#3393 := [rewrite]: #3392
+#3396 := [monotonicity #3393]: #3395
+#3400 := [trans #3396 #3398]: #3399
+#3403 := [monotonicity #3400]: #3402
+#3408 := [trans #3403 #3406]: #3407
+#3411 := [monotonicity #3408]: #3410
+#3522 := [monotonicity #3411 #3519]: #3521
+#3525 := [monotonicity #3522]: #3524
+#3532 := [trans #3525 #3530]: #3531
+#3535 := [monotonicity #3532]: #3534
+#3538 := [monotonicity #3535]: #3537
+#3545 := [trans #3538 #3543]: #3544
+#3548 := [monotonicity #3545]: #3547
+#3551 := [monotonicity #3548]: #3550
+#3558 := [trans #3551 #3556]: #3557
+#3561 := [monotonicity #3558]: #3560
+#3564 := [monotonicity #3561]: #3563
+#3571 := [trans #3564 #3569]: #3570
+#3574 := [monotonicity #3571]: #3573
+#3387 := (iff #1535 #3386)
+#3384 := (iff #1532 #3381)
+#3378 := (or #3361 #1529)
+#3382 := (iff #3378 #3381)
+#3383 := [rewrite]: #3382
+#3379 := (iff #1532 #3378)
+#3376 := (iff #1524 #3361)
+#3371 := (not #3362)
+#3374 := (iff #3371 #3361)
+#3375 := [rewrite]: #3374
+#3372 := (iff #1524 #3371)
+#3363 := (iff #1366 #3362)
+#3364 := [rewrite]: #3363
+#3373 := [monotonicity #3364]: #3372
+#3377 := [trans #3373 #3375]: #3376
+#3380 := [monotonicity #3377]: #3379
+#3385 := [trans #3380 #3383]: #3384
+#3388 := [quant-intro #3385]: #3387
+#3369 := (iff #1377 #3368)
+#3366 := (iff #1372 #3365)
+#3367 := [monotonicity #3364]: #3366
+#3370 := [quant-intro #3367]: #3369
+#3577 := [monotonicity #3370 #3388 #3574]: #3576
+#3586 := [trans #3577 #3584]: #3585
+#3359 := (iff #2784 #3356)
+#3350 := (and #103 #108 #535 #538 #3224 #3347)
+#3357 := (iff #3350 #3356)
+#3358 := [rewrite]: #3357
+#3351 := (iff #2784 #3350)
+#3348 := (iff #2778 #3347)
+#3345 := (iff #2775 #3342)
+#3336 := (and #3276 #3333)
+#3343 := (iff #3336 #3342)
+#3344 := [rewrite]: #3343
+#3337 := (iff #2775 #3336)
+#3334 := (iff #2770 #3333)
+#3331 := (iff #2764 #3330)
+#3328 := (iff #2761 #3325)
+#3311 := (or #2100 #2104)
+#3322 := (or #3311 #2756)
+#3326 := (iff #3322 #3325)
+#3327 := [rewrite]: #3326
+#3323 := (iff #2761 #3322)
+#3320 := (iff #2744 #3311)
+#3312 := (not #3311)
+#3315 := (not #3312)
+#3318 := (iff #3315 #3311)
+#3319 := [rewrite]: #3318
+#3316 := (iff #2744 #3315)
+#3313 := (iff #2741 #3312)
+#3314 := [rewrite]: #3313
+#3317 := [monotonicity #3314]: #3316
+#3321 := [trans #3317 #3319]: #3320
+#3324 := [monotonicity #3321]: #3323
+#3329 := [trans #3324 #3327]: #3328
+#3332 := [monotonicity #3329]: #3331
+#3309 := (iff #2124 #3306)
+#3301 := (and #2114 #3298)
+#3307 := (iff #3301 #3306)
+#3308 := [rewrite]: #3307
+#3302 := (iff #2124 #3301)
+#3299 := (iff #1297 #3298)
+#3296 := (iff #1294 #3293)
+#3279 := (or #1141 #1250)
+#3290 := (or #3279 #1291)
+#3294 := (iff #3290 #3293)
+#3295 := [rewrite]: #3294
+#3291 := (iff #1294 #3290)
+#3288 := (iff #1288 #3279)
+#3280 := (not #3279)
+#3283 := (not #3280)
+#3286 := (iff #3283 #3279)
+#3287 := [rewrite]: #3286
+#3284 := (iff #1288 #3283)
+#3281 := (iff #1285 #3280)
+#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)
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+#3267 := [rewrite]: #3266
+#3261 := (iff #1257 #3252)
+#3253 := (not #3252)
+#3256 := (not #3253)
+#3259 := (iff #3256 #3252)
 #3260 := [rewrite]: #3259
-#3256 := (iff #1322 #3255)
-#3253 := (iff #673 #3244)
-#3245 := (not #3244)
-#3248 := (not #3245)
-#3251 := (iff #3248 #3244)
-#3252 := [rewrite]: #3251
-#3249 := (iff #673 #3248)
-#3246 := (iff #210 #3245)
-#3247 := [rewrite]: #3246
-#3250 := [monotonicity #3247]: #3249
-#3254 := [trans #3250 #3252]: #3253
-#3257 := [monotonicity #3254]: #3256
-#3262 := [trans #3257 #3260]: #3261
-#3265 := [quant-intro #3262]: #3264
-#3342 := [monotonicity #3265 #3339]: #3341
-#3350 := [trans #3342 #3348]: #3349
-#3241 := (iff #2691 #3240)
-#3238 := (iff #2688 #3235)
-#3221 := (or #3220 #2099)
-#3232 := (or #3221 #2683)
-#3236 := (iff #3232 #3235)
-#3237 := [rewrite]: #3236
-#3233 := (iff #2688 #3232)
-#3230 := (iff #2672 #3221)
-#3222 := (not #3221)
-#3225 := (not #3222)
-#3228 := (iff #3225 #3221)
-#3229 := [rewrite]: #3228
-#3226 := (iff #2672 #3225)
-#3223 := (iff #2669 #3222)
-#3224 := [rewrite]: #3223
-#3227 := [monotonicity #3224]: #3226
-#3231 := [trans #3227 #3229]: #3230
+#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
-#3239 := [trans #3234 #3237]: #3238
-#3242 := [monotonicity #3239]: #3241
-#3353 := [monotonicity #3242 #3350]: #3352
-#3356 := [monotonicity #3353]: #3355
-#3363 := [trans #3356 #3361]: #3362
-#3366 := [monotonicity #3363]: #3365
-#3369 := [monotonicity #3366]: #3368
-#3376 := [trans #3369 #3374]: #3375
-#3379 := [monotonicity #3376]: #3378
-#3382 := [monotonicity #3379]: #3381
-#3389 := [trans #3382 #3387]: #3388
-#3392 := [monotonicity #3389]: #3391
-#3395 := [monotonicity #3392]: #3394
-#3402 := [trans #3395 #3400]: #3401
-#3405 := [monotonicity #3402]: #3404
-#3218 := (iff #1439 #3217)
-#3215 := (iff #1436 #3212)
-#3209 := (or #3192 #1433)
-#3213 := (iff #3209 #3212)
-#3214 := [rewrite]: #3213
-#3210 := (iff #1436 #3209)
-#3207 := (iff #1428 #3192)
-#3202 := (not #3193)
-#3205 := (iff #3202 #3192)
-#3206 := [rewrite]: #3205
-#3203 := (iff #1428 #3202)
-#3194 := (iff #1275 #3193)
-#3195 := [rewrite]: #3194
-#3204 := [monotonicity #3195]: #3203
-#3208 := [trans #3204 #3206]: #3207
-#3211 := [monotonicity #3208]: #3210
-#3216 := [trans #3211 #3214]: #3215
-#3219 := [quant-intro #3216]: #3218
-#3200 := (iff #1286 #3199)
-#3197 := (iff #1281 #3196)
-#3198 := [monotonicity #3195]: #3197
-#3201 := [quant-intro #3198]: #3200
-#3408 := [monotonicity #3201 #3219 #3405]: #3407
-#3417 := [trans #3408 #3415]: #3416
-#3190 := (iff #2635 #3187)
-#3181 := (and #140 #145 #492 #495 #3055 #3178)
-#3188 := (iff #3181 #3187)
-#3189 := [rewrite]: #3188
-#3182 := (iff #2635 #3181)
-#3179 := (iff #2629 #3178)
-#3176 := (iff #2626 #3173)
-#3167 := (and #3107 #3164)
-#3174 := (iff #3167 #3173)
-#3175 := [rewrite]: #3174
-#3168 := (iff #2626 #3167)
-#3165 := (iff #2621 #3164)
-#3162 := (iff #2615 #3161)
-#3159 := (iff #2612 #3156)
-#3142 := (or #1956 #1960)
-#3153 := (or #3142 #2607)
-#3157 := (iff #3153 #3156)
-#3158 := [rewrite]: #3157
-#3154 := (iff #2612 #3153)
-#3151 := (iff #2595 #3142)
-#3143 := (not #3142)
-#3146 := (not #3143)
-#3149 := (iff #3146 #3142)
-#3150 := [rewrite]: #3149
-#3147 := (iff #2595 #3146)
-#3144 := (iff #2592 #3143)
-#3145 := [rewrite]: #3144
+#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)
+#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)
+#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)
+#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
-#3152 := [trans #3148 #3150]: #3151
-#3155 := [monotonicity #3152]: #3154
-#3160 := [trans #3155 #3158]: #3159
-#3163 := [monotonicity #3160]: #3162
-#3140 := (iff #1980 #3137)
-#3132 := (and #1970 #3129)
-#3138 := (iff #3132 #3137)
-#3139 := [rewrite]: #3138
-#3133 := (iff #1980 #3132)
-#3130 := (iff #1211 #3129)
-#3127 := (iff #1208 #3124)
-#3110 := (or #1055 #1164)
-#3121 := (or #3110 #1205)
-#3125 := (iff #3121 #3124)
-#3126 := [rewrite]: #3125
-#3122 := (iff #1208 #3121)
-#3119 := (iff #1202 #3110)
-#3111 := (not #3110)
-#3114 := (not #3111)
-#3117 := (iff #3114 #3110)
-#3118 := [rewrite]: #3117
-#3115 := (iff #1202 #3114)
-#3112 := (iff #1199 #3111)
-#3113 := [rewrite]: #3112
-#3116 := [monotonicity #3113]: #3115
-#3120 := [trans #3116 #3118]: #3119
-#3123 := [monotonicity #3120]: #3122
-#3128 := [trans #3123 #3126]: #3127
-#3131 := [quant-intro #3128]: #3130
-#3134 := [monotonicity #3131]: #3133
-#3141 := [trans #3134 #3139]: #3140
-#3166 := [monotonicity #3141 #3163]: #3165
-#3108 := (iff #2589 #3107)
-#3105 := (iff #2586 #3102)
-#3083 := (or #65 #1164)
-#3099 := (or #3083 #3096)
-#3103 := (iff #3099 #3102)
-#3104 := [rewrite]: #3103
-#3100 := (iff #2586 #3099)
-#3097 := (iff #2583 #3096)
-#3098 := [rewrite]: #3097
-#3092 := (iff #1171 #3083)
-#3084 := (not #3083)
-#3087 := (not #3084)
-#3090 := (iff #3087 #3083)
+#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
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-#3085 := (iff #1168 #3084)
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-#3089 := [monotonicity #3086]: #3088
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-#3101 := [monotonicity #3093 #3098]: #3100
-#3106 := [trans #3101 #3104]: #3105
-#3109 := [quant-intro #3106]: #3108
-#3169 := [monotonicity #3109 #3166]: #3168
-#3177 := [trans #3169 #3175]: #3176
-#3081 := (iff #2547 #3078)
-#3073 := (and #1895 #2507 #3070)
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-#3069 := [trans #3065 #3067]: #3068
-#3072 := [quant-intro #3069]: #3071
-#3075 := [monotonicity #3072]: #3074
-#3082 := [trans #3075 #3080]: #3081
-#3180 := [monotonicity #3082 #3177]: #3179
-#3056 := (iff #1999 #3055)
-#3053 := (iff #1996 #3044)
-#3045 := (not #3044)
-#3048 := (not #3045)
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-#3049 := (iff #1996 #3048)
-#3046 := (iff #1236 #3045)
-#3047 := [rewrite]: #3046
-#3050 := [monotonicity #3047]: #3049
-#3054 := [trans #3050 #3052]: #3053
-#3057 := [quant-intro #3054]: #3056
-#3183 := [monotonicity #3057 #3180]: #3182
-#3191 := [trans #3183 #3189]: #3190
-#3420 := [monotonicity #3191 #3417]: #3419
-#3042 := (iff #2493 #3041)
-#3039 := (iff #2490 #3036)
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-#3019 := [rewrite]: #3018
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-#3026 := [trans #3022 #3024]: #3025
-#3035 := [monotonicity #3026 #3032]: #3034
-#3040 := [trans #3035 #3038]: #3039
-#3043 := [quant-intro #3040]: #3042
-#3014 := (iff #2453 #3013)
-#3011 := (iff #2450 #3008)
-#2988 := (or #65 #1081)
-#3005 := (or #2988 #3002)
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-#2994 := [monotonicity #2991]: #2993
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-#3007 := [monotonicity #2998 #3004]: #3006
-#3012 := [trans #3007 #3010]: #3011
-#3015 := [quant-intro #3012]: #3014
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-#2977 := (or #2966 #1135)
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-#2971 := (iff #440 #2970)
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-#2979 := [monotonicity #2976]: #2978
-#2984 := [trans #2979 #2982]: #2983
-#2987 := [quant-intro #2984]: #2986
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-#2956 := [monotonicity #2953]: #2955
-#2961 := [trans #2956 #2959]: #2960
-#2964 := [quant-intro #2961]: #2963
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-#3434 := [trans #3423 #3432]: #3433
-#2941 := (iff #2409 #2938)
-#2933 := (and #1789 #2369 #2930)
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-#2932 := [quant-intro #2929]: #2931
-#2935 := [monotonicity #2932]: #2934
-#2942 := [trans #2935 #2940]: #2941
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-#2906 := [trans #2902 #2904]: #2905
-#2909 := [monotonicity #2906]: #2908
-#2914 := [trans #2909 #2912]: #2913
-#2917 := [quant-intro #2914]: #2916
-#3440 := [monotonicity #2917 #3437]: #3439
-#3448 := [trans #3440 #3446]: #3447
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+#3094 := [monotonicity #3091]: #3093
+#3098 := [trans #3094 #3096]: #3097
+#3101 := [quant-intro #3098]: #3100
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+#3086 := [quant-intro #3083]: #3085
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+#3046 := [rewrite]: #3045
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+#3053 := [trans #3049 #3051]: #3052
+#3056 := [monotonicity #3053]: #3055
+#3061 := [trans #3056 #3059]: #3060
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+#3020 := (or #368 #3019)
+#3031 := (or #3020 #1116)
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+#3027 := (iff #3024 #3020)
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+#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
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+#3631 := [trans #3623 #3629]: #3630
+#3017 := (iff #2493 #3016)
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+#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)
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+#2305 := (and #713 #2304 #2302)
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+#2040 := (= ?v0!8 f6)
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+#1992 := (not #1991)
+#1995 := (+ #1994 #1990)
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+#1963 := (+ #1165 #1962)
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+#1967 := (+ #1964 #1165)
+#1968 := (>= #1967 0::int)
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+#1921 := (+ #1920 #1918)
+#1922 := (+ #25 #1921)
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+#1904 := (not #1903)
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+#2971 := (iff #2427 #2970)
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+#2923 := [rewrite]: #2922
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+#2913 := (iff #2325 #2912)
+#2910 := (iff #2322 #2909)
+#2907 := (iff #2305 #2906)
+#2904 := (iff #2302 #2903)
+#2901 := (= #2301 #2900)
+#2902 := [rewrite]: #2901
+#2905 := [monotonicity #2902]: #2904
+#2908 := [monotonicity #2905]: #2907
+#2911 := [monotonicity #2908]: #2910
+#2914 := [quant-intro #2911]: #2913
+#2897 := (iff #2319 #2884)
+#2889 := (not #2884)
+#2892 := (not #2889)
+#2895 := (iff #2892 #2884)
+#2896 := [rewrite]: #2895
+#2893 := (iff #2319 #2892)
+#2890 := (iff #2313 #2889)
+#2887 := (iff #2312 #2884)
+#2881 := (and #2878 #2309)
+#2885 := (iff #2881 #2884)
+#2886 := [rewrite]: #2885
+#2882 := (iff #2312 #2881)
+#2879 := (iff #2311 #2878)
+#2876 := (iff #2310 #2875)
 #2877 := [rewrite]: #2876
 #2880 := [monotonicity #2877]: #2879
-#2884 := [trans #2880 #2882]: #2883
-#2887 := [monotonicity #2884]: #2886
-#2892 := [trans #2887 #2890]: #2891
-#2895 := [monotonicity #2892]: #2894
-#3451 := [monotonicity #2895 #3448]: #3450
-#2871 := (iff #1047 #2870)
-#2868 := (iff #1044 #2865)
-#2851 := (or #74 #2319)
-#2862 := (or #2851 #1040)
-#2866 := (iff #2862 #2865)
-#2867 := [rewrite]: #2866
-#2863 := (iff #1044 #2862)
-#2860 := (iff #416 #2851)
-#2852 := (not #2851)
-#2855 := (not #2852)
-#2858 := (iff #2855 #2851)
-#2859 := [rewrite]: #2858
-#2856 := (iff #416 #2855)
-#2853 := (iff #82 #2852)
-#2854 := [rewrite]: #2853
-#2857 := [monotonicity #2854]: #2856
-#2861 := [trans #2857 #2859]: #2860
-#2864 := [monotonicity #2861]: #2863
-#2869 := [trans #2864 #2867]: #2868
-#2872 := [quant-intro #2869]: #2871
-#3454 := [monotonicity #2872 #3451]: #3453
-#3462 := [trans #3454 #3460]: #3461
-#1832 := (iff #2344 #2108)
-#1711 := (iff #2341 #1968)
-#2062 := (or #1766 #1727)
-#1736 := (or #2062 #2336)
-#1969 := (iff #1736 #1968)
-#1710 := [rewrite]: #1969
-#2043 := (iff #2341 #1736)
-#2083 := (iff #2325 #2062)
-#1666 := (not #2062)
-#2137 := (not #1666)
-#1859 := (iff #2137 #2062)
-#2082 := [rewrite]: #1859
-#2138 := (iff #2325 #2137)
-#1667 := (iff #2322 #1666)
-#2063 := [rewrite]: #1667
-#1858 := [monotonicity #2063]: #2138
-#1735 := [trans #1858 #2082]: #2083
-#2044 := [monotonicity #1735]: #2043
-#2107 := [trans #2044 #1710]: #1711
-#1833 := [monotonicity #2107]: #1832
-#3465 := [monotonicity #1833 #3462]: #3464
-#3468 := [monotonicity #3465]: #3467
-#3475 := [trans #3468 #3473]: #3474
-#3478 := [monotonicity #3475]: #3477
-#3481 := [monotonicity #3478]: #3480
-#3488 := [trans #3481 #3486]: #3487
-#3491 := [monotonicity #3488]: #3490
-#2152 := (+ #2151 #2149)
-#2153 := (= #2152 0::int)
-#2156 := (and #201 #2155 #2153)
-#2173 := (not #2156)
-#2176 := (forall (vars (?x76 T2)) #2173)
-#2161 := (= ?x75!20 uf_11)
-#2162 := (not #2161)
-#2163 := (and #2162 #2160)
-#2164 := (not #2163)
-#2170 := (not #2164)
-#2180 := (and #2170 #2176)
-#2185 := (and #1349 #2180)
-#2119 := (* -1::int #2118)
-#2121 := (+ #2120 #2119)
-#2124 := (+ #2123 #2121)
-#2125 := (>= #2124 0::int)
-#2131 := (and #2130 #2129)
-#2132 := (not #2131)
-#2133 := (or #2132 #2125)
-#2134 := (not #2133)
-#2189 := (or #2134 #2185)
-#2193 := (and #1325 #2189)
-#2094 := (* -1::int #2093)
-#2096 := (+ #2095 #2094)
-#2097 := (>= #2096 0::int)
-#2101 := (and #2100 #2098)
-#2102 := (not #2101)
-#2103 := (or #2102 #2097)
-#2104 := (not #2103)
-#2197 := (or #2104 #2193)
-#2201 := (and #1311 #2197)
-#2205 := (or #2079 #2201)
-#2073 := (not #1305)
-#2209 := (and #2073 #2205)
-#2213 := (or #1305 #2209)
-#2217 := (and #667 #2213)
-#2055 := (= #2054 #2053)
-#2058 := (or #2057 #2055)
-#2059 := (not #2058)
-#2221 := (or #2059 #2217)
-#2225 := (and #1297 #2221)
-#2036 := (* -1::int #2035)
-#2038 := (+ #2037 #2036)
-#2039 := (>= #2038 0::int)
-#2040 := (not #2039)
-#2229 := (or #2040 #2225)
-#2019 := (and #2018 #2016)
-#2008 := (not #825)
-#2249 := (and #176 #2008 #2019 #1286 #2229 #1439 #1452 #1460)
-#1947 := (* -1::int #1946)
-#1949 := (+ #1948 #1947)
-#1952 := (+ #1951 #1949)
-#1953 := (>= #1952 0::int)
-#1962 := (and #1961 #1957)
-#1963 := (not #1962)
-#1964 := (or #1963 #1953)
-#1965 := (not #1964)
-#1984 := (or #1965 #1980)
-#1923 := (+ #1922 #1162)
-#1926 := (+ #1925 #1923)
-#1927 := (= #1926 0::int)
-#1928 := (>= #1923 0::int)
-#1929 := (not #1928)
-#1930 := (and #1929 #1927)
-#1935 := (or #1171 #1930)
-#1938 := (forall (vars (?x49 T2)) #1935)
-#1988 := (and #1938 #1984)
-#1887 := (+ #1886 #1884)
-#1888 := (= #1887 0::int)
-#1891 := (and #1890 #1888)
-#1907 := (not #1891)
-#1910 := (forall (vars (?x50 T2)) #1907)
-#1896 := (= ?x49!8 uf_11)
-#1897 := (not #1896)
-#1898 := (and #1897 #1895)
-#1899 := (not #1898)
-#1904 := (not #1899)
-#1914 := (and #1904 #1910)
-#1992 := (or #1914 #1988)
-#1878 := (not #586)
-#1875 := (not #604)
-#1872 := (not #577)
-#1869 := (not #595)
-#2002 := (and #1869 #1872 #1875 #1878 #1992 #1999)
-#2253 := (or #2002 #2249)
-#1847 := (+ #1846 #1117)
-#1848 := (>= #1847 0::int)
-#1849 := (not #1848)
-#1852 := (+ #1851 #1847)
-#1853 := (= #1852 0::int)
-#1855 := (and #1854 #1853 #1849)
-#1860 := (or #1126 #1855)
-#1863 := (forall (vars (?x46 T2)) #1860)
-#1821 := (+ #1079 #1820)
-#1823 := (+ #1822 #1821)
-#1824 := (= #1823 0::int)
-#1825 := (+ #1822 #1079)
-#1826 := (>= #1825 0::int)
-#1827 := (not #1826)
-#1829 := (and #1828 #1827 #1824)
-#1834 := (or #1088 #1829)
-#1837 := (forall (vars (?x37 T2)) #1834)
-#1813 := (not #1547)
-#2278 := (and #1813 #1837 #1863 #2253 #1519 #1530 #1539)
-#1779 := (+ #1778 #1776)
-#1780 := (+ #66 #1779)
-#1781 := (= #1780 0::int)
-#1785 := (and #74 #1784 #1781)
-#1801 := (not #1785)
-#1804 := (forall (vars (?x38 T2)) #1801)
-#1790 := (= ?x37!5 uf_11)
-#1791 := (not #1790)
-#1792 := (and #1791 #1789)
-#1793 := (not #1792)
-#1798 := (not #1793)
-#1808 := (and #1798 #1804)
-#2282 := (or #1808 #2278)
-#2286 := (and #1073 #2282)
-#1750 := (+ #1749 #1747)
-#1752 := (+ #1751 #1750)
-#1753 := (>= #1752 0::int)
-#1759 := (and #1758 #1757)
-#1760 := (not #1759)
-#1761 := (or #1760 #1753)
-#1762 := (not #1761)
-#2290 := (or #1762 #2286)
-#2294 := (and #1047 #2290)
-#1722 := (* -1::int #1721)
-#1724 := (+ #1723 #1722)
-#1725 := (>= #1724 0::int)
-#1729 := (and #1728 #1726)
-#1730 := (not #1729)
-#1731 := (or #1730 #1725)
-#1732 := (not #1731)
-#2298 := (or #1732 #2294)
-#2302 := (and #1032 #2298)
-#2306 := (or #1707 #2302)
-#1662 := (not #1026)
-#2310 := (and #1662 #2306)
-#2314 := (or #1026 #2310)
-#2849 := (iff #2314 #2848)
-#2846 := (iff #2310 #2845)
-#2843 := (iff #2306 #2842)
-#2840 := (iff #2302 #2839)
-#2837 := (iff #2298 #2836)
-#2834 := (iff #2294 #2833)
-#2831 := (iff #2290 #2830)
-#2828 := (iff #2286 #2827)
-#2825 := (iff #2282 #2824)
-#2822 := (iff #2278 #2819)
-#2816 := (and #106 #2453 #2493 #2813 #1519 #1530 #1539)
-#2820 := (iff #2816 #2819)
-#2821 := [rewrite]: #2820
-#2817 := (iff #2278 #2816)
-#2814 := (iff #2253 #2813)
-#2811 := (iff #2249 #2808)
-#2805 := (and #176 #184 #2019 #1286 #2802 #1439 #1452 #1460)
-#2809 := (iff #2805 #2808)
-#2810 := [rewrite]: #2809
-#2806 := (iff #2249 #2805)
-#2803 := (iff #2229 #2802)
-#2800 := (iff #2225 #2799)
-#2797 := (iff #2221 #2796)
-#2794 := (iff #2217 #2793)
-#2791 := (iff #2213 #2790)
-#2788 := (iff #2209 #2787)
-#2785 := (iff #2205 #2784)
-#2782 := (iff #2201 #2781)
-#2779 := (iff #2197 #2778)
-#2776 := (iff #2193 #2775)
-#2773 := (iff #2189 #2772)
-#2770 := (iff #2185 #2767)
-#2730 := (and #2160 #2724)
-#2761 := (and #2730 #2758)
-#2764 := (and #1349 #2761)
-#2768 := (iff #2764 #2767)
-#2769 := [rewrite]: #2768
-#2765 := (iff #2185 #2764)
-#2762 := (iff #2180 #2761)
-#2759 := (iff #2176 #2758)
-#2756 := (iff #2173 #2755)
-#2753 := (iff #2156 #2752)
-#2750 := (iff #2153 #2749)
-#2747 := (= #2152 #2746)
-#2748 := [rewrite]: #2747
-#2751 := [monotonicity #2748]: #2750
-#2754 := [monotonicity #2751]: #2753
-#2757 := [monotonicity #2754]: #2756
-#2760 := [quant-intro #2757]: #2759
-#2743 := (iff #2170 #2730)
-#2735 := (not #2730)
-#2738 := (not #2735)
-#2741 := (iff #2738 #2730)
-#2742 := [rewrite]: #2741
-#2739 := (iff #2170 #2738)
-#2736 := (iff #2164 #2735)
-#2733 := (iff #2163 #2730)
-#2727 := (and #2724 #2160)
-#2731 := (iff #2727 #2730)
-#2732 := [rewrite]: #2731
-#2728 := (iff #2163 #2727)
-#2725 := (iff #2162 #2724)
-#2722 := (iff #2161 #2721)
-#2723 := [rewrite]: #2722
-#2726 := [monotonicity #2723]: #2725
-#2729 := [monotonicity #2726]: #2728
-#2734 := [trans #2729 #2732]: #2733
-#2737 := [monotonicity #2734]: #2736
-#2740 := [monotonicity #2737]: #2739
-#2744 := [trans #2740 #2742]: #2743
-#2763 := [monotonicity #2744 #2760]: #2762
+#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)
+#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)
+#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
+#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
-#2771 := [trans #2766 #2769]: #2770
-#2719 := (iff #2134 #2718)
-#2716 := (iff #2133 #2715)
-#2713 := (iff #2125 #2710)
-#2700 := (+ #2120 #2123)
-#2701 := (+ #2119 #2700)
+#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)
-#2711 := (iff #2704 #2710)
-#2712 := [rewrite]: #2711
-#2705 := (iff #2125 #2704)
-#2702 := (= #2124 #2701)
+#2710 := (iff #2704 #2709)
+#2711 := [rewrite]: #2710
+#2705 := (iff #2072 #2704)
+#2702 := (= #2067 #2701)
 #2703 := [rewrite]: #2702
 #2706 := [monotonicity #2703]: #2705
-#2714 := [trans #2706 #2712]: #2713
-#2698 := (iff #2132 #2697)
-#2695 := (iff #2131 #2694)
-#2696 := [rewrite]: #2695
-#2699 := [monotonicity #2696]: #2698
-#2717 := [monotonicity #2699 #2714]: #2716
-#2720 := [monotonicity #2717]: #2719
-#2774 := [monotonicity #2720 #2771]: #2773
-#2777 := [monotonicity #2774]: #2776
-#2692 := (iff #2104 #2691)
-#2689 := (iff #2103 #2688)
-#2686 := (iff #2097 #2683)
-#2675 := (+ #2094 #2095)
-#2678 := (>= #2675 0::int)
-#2684 := (iff #2678 #2683)
-#2685 := [rewrite]: #2684
-#2679 := (iff #2097 #2678)
-#2676 := (= #2096 #2675)
-#2677 := [rewrite]: #2676
-#2680 := [monotonicity #2677]: #2679
-#2687 := [trans #2680 #2685]: #2686
-#2673 := (iff #2102 #2672)
-#2670 := (iff #2101 #2669)
-#2671 := [rewrite]: #2670
-#2674 := [monotonicity #2671]: #2673
-#2690 := [monotonicity #2674 #2687]: #2689
-#2693 := [monotonicity #2690]: #2692
-#2780 := [monotonicity #2693 #2777]: #2779
-#2783 := [monotonicity #2780]: #2782
-#2786 := [monotonicity #2783]: #2785
-#2667 := (iff #2073 #205)
-#2668 := [rewrite]: #2667
-#2789 := [monotonicity #2668 #2786]: #2788
-#2792 := [monotonicity #2789]: #2791
-#2795 := [monotonicity #2792]: #2794
-#2665 := (iff #2059 #2664)
-#2662 := (iff #2058 #2661)
-#2659 := (iff #2055 #2658)
-#2660 := [rewrite]: #2659
-#2663 := [monotonicity #2660]: #2662
-#2666 := [monotonicity #2663]: #2665
-#2798 := [monotonicity #2666 #2795]: #2797
-#2801 := [monotonicity #2798]: #2800
-#2656 := (iff #2040 #2655)
-#2653 := (iff #2039 #2650)
-#2642 := (+ #2036 #2037)
-#2645 := (>= #2642 0::int)
-#2651 := (iff #2645 #2650)
+#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)
+#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)
+#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
-#2646 := (iff #2039 #2645)
-#2643 := (= #2038 #2642)
-#2644 := [rewrite]: #2643
-#2647 := [monotonicity #2644]: #2646
-#2654 := [trans #2647 #2652]: #2653
-#2657 := [monotonicity #2654]: #2656
-#2804 := [monotonicity #2657 #2801]: #2803
-#2640 := (iff #2008 #184)
-#2641 := [rewrite]: #2640
-#2807 := [monotonicity #2641 #2804]: #2806
-#2812 := [trans #2807 #2810]: #2811
-#2638 := (iff #2002 #2635)
-#2632 := (and #140 #145 #492 #495 #2629 #1999)
-#2636 := (iff #2632 #2635)
-#2637 := [rewrite]: #2636
-#2633 := (iff #2002 #2632)
-#2630 := (iff #1992 #2629)
-#2627 := (iff #1988 #2626)
-#2624 := (iff #1984 #2621)
-#2618 := (or #2615 #1980)
-#2622 := (iff #2618 #2621)
+#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
-#2619 := (iff #1984 #2618)
-#2616 := (iff #1965 #2615)
-#2613 := (iff #1964 #2612)
-#2610 := (iff #1953 #2607)
-#2598 := (+ #1948 #1951)
-#2599 := (+ #1947 #2598)
-#2602 := (>= #2599 0::int)
-#2608 := (iff #2602 #2607)
-#2609 := [rewrite]: #2608
-#2603 := (iff #1953 #2602)
-#2600 := (= #1952 #2599)
-#2601 := [rewrite]: #2600
-#2604 := [monotonicity #2601]: #2603
-#2611 := [trans #2604 #2609]: #2610
-#2596 := (iff #1963 #2595)
-#2593 := (iff #1962 #2592)
-#2594 := [rewrite]: #2593
-#2597 := [monotonicity #2594]: #2596
-#2614 := [monotonicity #2597 #2611]: #2613
-#2617 := [monotonicity #2614]: #2616
-#2620 := [monotonicity #2617]: #2619
-#2625 := [trans #2620 #2623]: #2624
-#2590 := (iff #1938 #2589)
-#2587 := (iff #1935 #2586)
-#2584 := (iff #1930 #2583)
-#2581 := (iff #1927 #2578)
-#2568 := (+ #1922 #1925)
-#2569 := (+ #1162 #2568)
-#2572 := (= #2569 0::int)
-#2579 := (iff #2572 #2578)
-#2580 := [rewrite]: #2579
-#2573 := (iff #1927 #2572)
-#2570 := (= #1926 #2569)
-#2571 := [rewrite]: #2570
-#2574 := [monotonicity #2571]: #2573
-#2582 := [trans #2574 #2580]: #2581
-#2566 := (iff #1929 #2565)
-#2563 := (iff #1928 #2560)
-#2552 := (+ #1162 #1922)
-#2555 := (>= #2552 0::int)
-#2561 := (iff #2555 #2560)
-#2562 := [rewrite]: #2561
-#2556 := (iff #1928 #2555)
-#2553 := (= #1923 #2552)
-#2554 := [rewrite]: #2553
-#2557 := [monotonicity #2554]: #2556
-#2564 := [trans #2557 #2562]: #2563
-#2567 := [monotonicity #2564]: #2566
-#2585 := [monotonicity #2567 #2582]: #2584
-#2588 := [monotonicity #2585]: #2587
-#2591 := [quant-intro #2588]: #2590
-#2628 := [monotonicity #2591 #2625]: #2627
-#2550 := (iff #1914 #2547)
-#2513 := (and #1895 #2507)
-#2544 := (and #2513 #2541)
-#2548 := (iff #2544 #2547)
-#2549 := [rewrite]: #2548
-#2545 := (iff #1914 #2544)
-#2542 := (iff #1910 #2541)
-#2539 := (iff #1907 #2538)
-#2536 := (iff #1891 #2535)
-#2533 := (iff #1888 #2532)
-#2530 := (= #1887 #2529)
-#2531 := [rewrite]: #2530
-#2534 := [monotonicity #2531]: #2533
-#2537 := [monotonicity #2534]: #2536
-#2540 := [monotonicity #2537]: #2539
-#2543 := [quant-intro #2540]: #2542
-#2526 := (iff #1904 #2513)
-#2518 := (not #2513)
-#2521 := (not #2518)
-#2524 := (iff #2521 #2513)
-#2525 := [rewrite]: #2524
-#2522 := (iff #1904 #2521)
-#2519 := (iff #1899 #2518)
-#2516 := (iff #1898 #2513)
-#2510 := (and #2507 #1895)
-#2514 := (iff #2510 #2513)
-#2515 := [rewrite]: #2514
-#2511 := (iff #1898 #2510)
-#2508 := (iff #1897 #2507)
-#2505 := (iff #1896 #2504)
-#2506 := [rewrite]: #2505
-#2509 := [monotonicity #2506]: #2508
-#2512 := [monotonicity #2509]: #2511
-#2517 := [trans #2512 #2515]: #2516
+#2626 := [monotonicity #2623]: #2625
+#2632 := [trans #2626 #2630]: #2631
+#2635 := [monotonicity #2632]: #2634
+#2619 := (iff #1996 #2616)
+#2605 := (+ #1989 #1994)
+#2606 := (+ #1203 #2605)
+#2609 := (= #2606 0::int)
+#2617 := (iff #2609 #2616)
+#2618 := [rewrite]: #2617
+#2610 := (iff #1996 #2609)
+#2607 := (= #1995 #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)
+#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)
+#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
-#2527 := [trans #2523 #2525]: #2526
-#2546 := [monotonicity #2527 #2543]: #2545
-#2551 := [trans #2546 #2549]: #2550
-#2631 := [monotonicity #2551 #2628]: #2630
-#2502 := (iff #1878 #495)
-#2503 := [rewrite]: #2502
-#2500 := (iff #1875 #492)
-#2501 := [rewrite]: #2500
-#2498 := (iff #1872 #145)
+#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
-#2496 := (iff #1869 #140)
-#2497 := [rewrite]: #2496
-#2634 := [monotonicity #2497 #2499 #2501 #2503 #2631]: #2633
-#2639 := [trans #2634 #2637]: #2638
-#2815 := [monotonicity #2639 #2812]: #2814
-#2494 := (iff #1863 #2493)
-#2491 := (iff #1860 #2490)
-#2488 := (iff #1855 #2487)
-#2485 := (iff #1849 #2484)
-#2482 := (iff #1848 #2479)
-#2472 := (+ #1117 #1846)
-#2475 := (>= #2472 0::int)
-#2480 := (iff #2475 #2479)
-#2481 := [rewrite]: #2480
-#2476 := (iff #1848 #2475)
-#2473 := (= #1847 #2472)
-#2474 := [rewrite]: #2473
-#2477 := [monotonicity #2474]: #2476
-#2483 := [trans #2477 #2481]: #2482
-#2486 := [monotonicity #2483]: #2485
-#2470 := (iff #1853 #2467)
-#2456 := (+ #1846 #1851)
-#2457 := (+ #1117 #2456)
-#2460 := (= #2457 0::int)
-#2468 := (iff #2460 #2467)
-#2469 := [rewrite]: #2468
-#2461 := (iff #1853 #2460)
-#2458 := (= #1852 #2457)
-#2459 := [rewrite]: #2458
-#2462 := [monotonicity #2459]: #2461
-#2471 := [trans #2462 #2469]: #2470
-#2489 := [monotonicity #2471 #2486]: #2488
-#2492 := [monotonicity #2489]: #2491
-#2495 := [quant-intro #2492]: #2494
-#2454 := (iff #1837 #2453)
-#2451 := (iff #1834 #2450)
-#2448 := (iff #1829 #2447)
-#2445 := (iff #1824 #2442)
-#2432 := (+ #1820 #1822)
-#2433 := (+ #1079 #2432)
-#2436 := (= #2433 0::int)
-#2443 := (iff #2436 #2442)
-#2444 := [rewrite]: #2443
-#2437 := (iff #1824 #2436)
-#2434 := (= #1823 #2433)
-#2435 := [rewrite]: #2434
-#2438 := [monotonicity #2435]: #2437
-#2446 := [trans #2438 #2444]: #2445
-#2430 := (iff #1827 #2429)
-#2427 := (iff #1826 #2424)
-#2416 := (+ #1079 #1822)
-#2419 := (>= #2416 0::int)
-#2425 := (iff #2419 #2424)
-#2426 := [rewrite]: #2425
-#2420 := (iff #1826 #2419)
-#2417 := (= #1825 #2416)
-#2418 := [rewrite]: #2417
-#2421 := [monotonicity #2418]: #2420
-#2428 := [trans #2421 #2426]: #2427
-#2431 := [monotonicity #2428]: #2430
-#2449 := [monotonicity #2431 #2446]: #2448
-#2452 := [monotonicity #2449]: #2451
-#2455 := [quant-intro #2452]: #2454
-#2414 := (iff #1813 #106)
-#2415 := [rewrite]: #2414
-#2818 := [monotonicity #2415 #2455 #2495 #2815]: #2817
-#2823 := [trans #2818 #2821]: #2822
-#2412 := (iff #1808 #2409)
-#2375 := (and #1789 #2369)
-#2406 := (and #2375 #2403)
-#2410 := (iff #2406 #2409)
-#2411 := [rewrite]: #2410
-#2407 := (iff #1808 #2406)
-#2404 := (iff #1804 #2403)
-#2401 := (iff #1801 #2400)
-#2398 := (iff #1785 #2397)
-#2395 := (iff #1781 #2394)
-#2392 := (= #1780 #2391)
-#2393 := [rewrite]: #2392
-#2396 := [monotonicity #2393]: #2395
-#2399 := [monotonicity #2396]: #2398
-#2402 := [monotonicity #2399]: #2401
-#2405 := [quant-intro #2402]: #2404
-#2388 := (iff #1798 #2375)
-#2380 := (not #2375)
-#2383 := (not #2380)
-#2386 := (iff #2383 #2375)
-#2387 := [rewrite]: #2386
-#2384 := (iff #1798 #2383)
-#2381 := (iff #1793 #2380)
-#2378 := (iff #1792 #2375)
-#2372 := (and #2369 #1789)
-#2376 := (iff #2372 #2375)
-#2377 := [rewrite]: #2376
-#2373 := (iff #1792 #2372)
-#2370 := (iff #1791 #2369)
-#2367 := (iff #1790 #2366)
-#2368 := [rewrite]: #2367
-#2371 := [monotonicity #2368]: #2370
-#2374 := [monotonicity #2371]: #2373
-#2379 := [trans #2374 #2377]: #2378
-#2382 := [monotonicity #2379]: #2381
-#2385 := [monotonicity #2382]: #2384
-#2389 := [trans #2385 #2387]: #2388
-#2408 := [monotonicity #2389 #2405]: #2407
-#2413 := [trans #2408 #2411]: #2412
-#2826 := [monotonicity #2413 #2823]: #2825
-#2829 := [monotonicity #2826]: #2828
-#2364 := (iff #1762 #2363)
-#2361 := (iff #1761 #2360)
-#2358 := (iff #1753 #2357)
-#2355 := (= #1752 #2354)
-#2356 := [rewrite]: #2355
-#2359 := [monotonicity #2356]: #2358
-#2351 := (iff #1760 #2350)
-#2348 := (iff #1759 #2347)
-#2349 := [rewrite]: #2348
-#2352 := [monotonicity #2349]: #2351
-#2362 := [monotonicity #2352 #2359]: #2361
-#2365 := [monotonicity #2362]: #2364
-#2832 := [monotonicity #2365 #2829]: #2831
-#2835 := [monotonicity #2832]: #2834
-#2345 := (iff #1732 #2344)
-#2342 := (iff #1731 #2341)
-#2339 := (iff #1725 #2336)
-#2328 := (+ #1722 #1723)
-#2331 := (>= #2328 0::int)
-#2337 := (iff #2331 #2336)
-#2338 := [rewrite]: #2337
-#2332 := (iff #1725 #2331)
-#2329 := (= #1724 #2328)
-#2330 := [rewrite]: #2329
-#2333 := [monotonicity #2330]: #2332
-#2340 := [trans #2333 #2338]: #2339
-#2326 := (iff #1730 #2325)
-#2323 := (iff #1729 #2322)
-#2324 := [rewrite]: #2323
-#2327 := [monotonicity #2324]: #2326
-#2343 := [monotonicity #2327 #2340]: #2342
-#2346 := [monotonicity #2343]: #2345
-#2838 := [monotonicity #2346 #2835]: #2837
-#2841 := [monotonicity #2838]: #2840
-#2844 := [monotonicity #2841]: #2843
-#2320 := (iff #1662 #78)
-#2321 := [rewrite]: #2320
-#2847 := [monotonicity #2321 #2844]: #2846
-#2850 := [monotonicity #2847]: #2849
-#1636 := (not #1600)
-#2315 := (~ #1636 #2314)
-#2311 := (not #1597)
-#2312 := (~ #2311 #2310)
-#2307 := (not #1594)
-#2308 := (~ #2307 #2306)
-#2303 := (not #1591)
-#2304 := (~ #2303 #2302)
-#2299 := (not #1588)
-#2300 := (~ #2299 #2298)
-#2295 := (not #1585)
-#2296 := (~ #2295 #2294)
-#2291 := (not #1582)
-#2292 := (~ #2291 #2290)
-#2287 := (not #1579)
-#2288 := (~ #2287 #2286)
-#2283 := (not #1576)
-#2284 := (~ #2283 #2282)
-#2279 := (not #1571)
-#2280 := (~ #2279 #2278)
-#2275 := (not #1542)
-#2276 := (~ #2275 #1539)
-#2273 := (~ #1539 #1539)
-#2271 := (~ #1536 #1536)
-#2272 := [refl]: #2271
-#2274 := [nnf-pos #2272]: #2273
-#2277 := [nnf-neg #2274]: #2276
-#2268 := (not #1533)
-#2269 := (~ #2268 #1530)
-#2266 := (~ #1530 #1530)
-#2264 := (~ #1527 #1527)
-#2265 := [refl]: #2264
-#2267 := [nnf-pos #2265]: #2266
-#2270 := [nnf-neg #2267]: #2269
-#2261 := (not #1522)
-#2262 := (~ #2261 #1519)
-#2259 := (~ #1519 #1519)
-#2257 := (~ #1516 #1516)
+#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)
+#2461 := (~ #2460 #2459)
+#2456 := (not #1700)
+#2457 := (~ #2456 #2455)
+#2452 := (not #1697)
+#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)
+#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)
+#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)
+#2407 := [refl]: #2406
+#2409 := [nnf-pos #2407]: #2408
+#2412 := [nnf-neg #2409]: #2411
+#2403 := (not #1600)
+#2404 := (~ #2403 #2402)
+#2399 := (not #1595)
+#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)
+#2380 := (~ #2379 #2378)
+#2375 := (not #1518)
+#2376 := (~ #2375 #2374)
+#2371 := (not #1515)
+#2372 := (~ #2371 #2370)
+#2367 := (not #1512)
+#2368 := (~ #2367 #2366)
+#2363 := (not #1509)
+#2364 := (~ #2363 #2362)
+#2359 := (not #1506)
+#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
-#2254 := (not #1499)
-#2255 := (~ #2254 #2253)
-#2250 := (not #1494)
-#2251 := (~ #2250 #2249)
-#2247 := (~ #1460 #1460)
-#2248 := [refl]: #2247
-#2244 := (not #1455)
-#2245 := (~ #2244 #1452)
-#2242 := (~ #1452 #1452)
-#2240 := (~ #1449 #1449)
-#2241 := [refl]: #2240
-#2243 := [nnf-pos #2241]: #2242
-#2246 := [nnf-neg #2243]: #2245
-#2237 := (not #1442)
-#2238 := (~ #2237 #1439)
-#2235 := (~ #1439 #1439)
-#2233 := (~ #1436 #1436)
-#2234 := [refl]: #2233
-#2236 := [nnf-pos #2234]: #2235
-#2239 := [nnf-neg #2236]: #2238
-#2230 := (not #1425)
-#2231 := (~ #2230 #2229)
-#2226 := (not #1422)
-#2227 := (~ #2226 #2225)
-#2222 := (not #1419)
-#2223 := (~ #2222 #2221)
-#2218 := (not #1416)
-#2219 := (~ #2218 #2217)
-#2214 := (not #1413)
-#2215 := (~ #2214 #2213)
-#2210 := (not #1410)
-#2211 := (~ #2210 #2209)
-#2206 := (not #1407)
-#2207 := (~ #2206 #2205)
-#2202 := (not #1404)
-#2203 := (~ #2202 #2201)
-#2198 := (not #1401)
-#2199 := (~ #2198 #2197)
-#2194 := (not #1398)
-#2195 := (~ #2194 #2193)
-#2190 := (not #1395)
-#2191 := (~ #2190 #2189)
-#2186 := (not #1392)
-#2187 := (~ #2186 #2185)
-#2167 := (not #1389)
-#2183 := (~ #2167 #2180)
-#2157 := (exists (vars (?x76 T2)) #2156)
-#2165 := (or #2164 #2157)
-#2166 := (not #2165)
-#2181 := (~ #2166 #2180)
-#2177 := (not #2157)
-#2178 := (~ #2177 #2176)
-#2174 := (~ #2173 #2173)
-#2175 := [refl]: #2174
-#2179 := [nnf-neg #2175]: #2178
-#2171 := (~ #2170 #2170)
-#2172 := [refl]: #2171
-#2182 := [nnf-neg #2172 #2179]: #2181
-#2168 := (~ #2167 #2166)
-#2169 := [sk]: #2168
-#2184 := [trans #2169 #2182]: #2183
-#2143 := (not #1352)
-#2144 := (~ #2143 #1349)
-#2141 := (~ #1349 #1349)
-#2139 := (~ #1346 #1346)
-#2140 := [refl]: #2139
-#2142 := [nnf-pos #2140]: #2141
+#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)
+#2142 := [refl]: #2141
 #2145 := [nnf-neg #2142]: #2144
-#2188 := [nnf-neg #2145 #2184]: #2187
-#2135 := (~ #1352 #2134)
-#2136 := [sk]: #2135
-#2192 := [nnf-neg #2136 #2188]: #2191
-#2113 := (not #1328)
-#2114 := (~ #2113 #1325)
-#2111 := (~ #1325 #1325)
-#2109 := (~ #1322 #1322)
-#2110 := [refl]: #2109
-#2112 := [nnf-pos #2110]: #2111
-#2115 := [nnf-neg #2112]: #2114
-#2196 := [nnf-neg #2115 #2192]: #2195
-#2105 := (~ #1328 #2104)
-#2106 := [sk]: #2105
-#2200 := [nnf-neg #2106 #2196]: #2199
-#2088 := (not #1314)
-#2089 := (~ #2088 #1311)
-#2086 := (~ #1311 #1311)
-#2084 := (~ #1308 #1308)
-#2085 := [refl]: #2084
-#2087 := [nnf-pos #2085]: #2086
-#2090 := [nnf-neg #2087]: #2089
-#2204 := [nnf-neg #2090 #2200]: #2203
-#2080 := (~ #1314 #2079)
-#2081 := [sk]: #2080
-#2208 := [nnf-neg #2081 #2204]: #2207
-#2074 := (~ #2073 #2073)
-#2075 := [refl]: #2074
-#2212 := [nnf-neg #2075 #2208]: #2211
-#2071 := (~ #1305 #1305)
-#2072 := [refl]: #2071
-#2216 := [nnf-neg #2072 #2212]: #2215
-#2068 := (not #783)
-#2069 := (~ #2068 #667)
-#2066 := (~ #667 #667)
-#2064 := (~ #662 #662)
-#2065 := [refl]: #2064
-#2067 := [nnf-pos #2065]: #2066
-#2070 := [nnf-neg #2067]: #2069
-#2220 := [nnf-neg #2070 #2216]: #2219
-#2060 := (~ #783 #2059)
-#2061 := [sk]: #2060
-#2224 := [nnf-neg #2061 #2220]: #2223
-#2049 := (not #1300)
-#2050 := (~ #2049 #1297)
-#2047 := (~ #1297 #1297)
-#2045 := (~ #1292 #1292)
-#2046 := [refl]: #2045
-#2048 := [nnf-pos #2046]: #2047
-#2051 := [nnf-neg #2048]: #2050
-#2228 := [nnf-neg #2051 #2224]: #2227
-#2041 := (~ #1300 #2040)
-#2042 := [sk]: #2041
-#2232 := [nnf-neg #2042 #2228]: #2231
-#2031 := (not #1289)
-#2032 := (~ #2031 #1286)
-#2029 := (~ #1286 #1286)
-#2027 := (~ #1281 #1281)
-#2028 := [refl]: #2027
-#2030 := [nnf-pos #2028]: #2029
-#2033 := [nnf-neg #2030]: #2032
-#2024 := (not #1470)
-#2025 := (~ #2024 #2019)
-#2020 := (~ #1239 #2019)
-#2021 := [sk]: #2020
-#2026 := [nnf-neg #2021]: #2025
-#2009 := (~ #2008 #2008)
-#2010 := [refl]: #2009
-#2006 := (~ #176 #176)
-#2007 := [refl]: #2006
-#2252 := [nnf-neg #2007 #2010 #2026 #2033 #2232 #2239 #2246 #2248]: #2251
-#2003 := (not #1257)
-#2004 := (~ #2003 #2002)
-#2000 := (~ #1470 #1999)
-#1997 := (~ #1996 #1996)
-#1998 := [refl]: #1997
-#2001 := [nnf-neg #1998]: #2000
-#1993 := (not #1233)
-#1994 := (~ #1993 #1992)
-#1989 := (not #1230)
-#1990 := (~ #1989 #1988)
-#1985 := (not #1227)
-#1986 := (~ #1985 #1984)
-#1981 := (not #1222)
-#1982 := (~ #1981 #1980)
-#1977 := (not #1214)
-#1978 := (~ #1977 #1211)
-#1975 := (~ #1211 #1211)
-#1973 := (~ #1208 #1208)
-#1974 := [refl]: #1973
-#1976 := [nnf-pos #1974]: #1975
-#1979 := [nnf-neg #1976]: #1978
-#1971 := (~ #1970 #1970)
-#1972 := [refl]: #1971
-#1983 := [nnf-neg #1972 #1979]: #1982
-#1966 := (~ #1214 #1965)
-#1967 := [sk]: #1966
-#1987 := [nnf-neg #1967 #1983]: #1986
-#1941 := (not #1196)
-#1942 := (~ #1941 #1938)
-#1939 := (~ #1193 #1938)
-#1936 := (~ #1190 #1935)
-#1931 := (~ #1187 #1930)
-#1932 := [sk]: #1931
-#1919 := (~ #1171 #1171)
-#1920 := [refl]: #1919
-#1937 := [monotonicity #1920 #1932]: #1936
-#1940 := [nnf-pos #1937]: #1939
-#1943 := [nnf-neg #1940]: #1942
-#1991 := [nnf-neg #1943 #1987]: #1990
-#1917 := (~ #1196 #1914)
-#1892 := (exists (vars (?x50 T2)) #1891)
-#1900 := (or #1899 #1892)
-#1901 := (not #1900)
-#1915 := (~ #1901 #1914)
-#1911 := (not #1892)
-#1912 := (~ #1911 #1910)
-#1908 := (~ #1907 #1907)
-#1909 := [refl]: #1908
-#1913 := [nnf-neg #1909]: #1912
-#1905 := (~ #1904 #1904)
-#1906 := [refl]: #1905
-#1916 := [nnf-neg #1906 #1913]: #1915
-#1902 := (~ #1196 #1901)
-#1903 := [sk]: #1902
-#1918 := [trans #1903 #1916]: #1917
-#1995 := [nnf-neg #1918 #1991]: #1994
-#1879 := (~ #1878 #1878)
-#1880 := [refl]: #1879
-#1876 := (~ #1875 #1875)
-#1877 := [refl]: #1876
-#1873 := (~ #1872 #1872)
-#1874 := [refl]: #1873
-#1870 := (~ #1869 #1869)
-#1871 := [refl]: #1870
-#2005 := [nnf-neg #1871 #1874 #1877 #1880 #1995 #2001]: #2004
-#2256 := [nnf-neg #2005 #2252]: #2255
-#1866 := (not #1159)
-#1867 := (~ #1866 #1863)
-#1864 := (~ #1156 #1863)
-#1861 := (~ #1153 #1860)
-#1856 := (~ #1150 #1855)
-#1857 := [sk]: #1856
-#1843 := (~ #1126 #1126)
-#1844 := [refl]: #1843
-#1862 := [monotonicity #1844 #1857]: #1861
-#1865 := [nnf-pos #1862]: #1864
-#1868 := [nnf-neg #1865]: #1867
-#1840 := (not #1550)
-#1841 := (~ #1840 #1837)
-#1838 := (~ #1114 #1837)
-#1835 := (~ #1111 #1834)
-#1830 := (~ #1108 #1829)
-#1831 := [sk]: #1830
-#1816 := (~ #1088 #1088)
-#1817 := [refl]: #1816
-#1836 := [monotonicity #1817 #1831]: #1835
-#1839 := [nnf-pos #1836]: #1838
-#1842 := [nnf-neg #1839]: #1841
-#1814 := (~ #1813 #1813)
-#1815 := [refl]: #1814
-#2281 := [nnf-neg #1815 #1842 #1868 #2256 #2263 #2270 #2277]: #2280
-#1811 := (~ #1550 #1808)
-#1786 := (exists (vars (?x38 T2)) #1785)
-#1794 := (or #1793 #1786)
-#1795 := (not #1794)
-#1809 := (~ #1795 #1808)
-#1805 := (not #1786)
-#1806 := (~ #1805 #1804)
-#1802 := (~ #1801 #1801)
-#1803 := [refl]: #1802
-#1807 := [nnf-neg #1803]: #1806
-#1799 := (~ #1798 #1798)
-#1800 := [refl]: #1799
-#1810 := [nnf-neg #1800 #1807]: #1809
-#1796 := (~ #1550 #1795)
-#1797 := [sk]: #1796
-#1812 := [trans #1797 #1810]: #1811
-#2285 := [nnf-neg #1812 #2281]: #2284
-#1771 := (not #1076)
-#1772 := (~ #1771 #1073)
-#1769 := (~ #1073 #1073)
-#1767 := (~ #1070 #1070)
-#1768 := [refl]: #1767
-#1770 := [nnf-pos #1768]: #1769
-#1773 := [nnf-neg #1770]: #1772
-#2289 := [nnf-neg #1773 #2285]: #2288
-#1763 := (~ #1076 #1762)
-#1764 := [sk]: #1763
-#2293 := [nnf-neg #1764 #2289]: #2292
-#1741 := (not #1050)
-#1742 := (~ #1741 #1047)
-#1739 := (~ #1047 #1047)
-#1737 := (~ #1044 #1044)
-#1738 := [refl]: #1737
-#1740 := [nnf-pos #1738]: #1739
-#1743 := [nnf-neg #1740]: #1742
-#2297 := [nnf-neg #1743 #2293]: #2296
-#1733 := (~ #1050 #1732)
-#1734 := [sk]: #1733
-#2301 := [nnf-neg #1734 #2297]: #2300
-#1716 := (not #1035)
-#1717 := (~ #1716 #1032)
-#1714 := (~ #1032 #1032)
-#1712 := (~ #1031 #1031)
-#1713 := [refl]: #1712
-#1715 := [nnf-pos #1713]: #1714
-#1718 := [nnf-neg #1715]: #1717
-#2305 := [nnf-neg #1718 #2301]: #2304
-#1708 := (~ #1035 #1707)
-#1709 := [sk]: #1708
-#2309 := [nnf-neg #1709 #2305]: #2308
-#1663 := (~ #1662 #1662)
-#1703 := [refl]: #1663
-#2313 := [nnf-neg #1703 #2309]: #2312
-#1701 := (~ #1026 #1026)
-#1702 := [refl]: #1701
-#2316 := [nnf-neg #1702 #2313]: #2315
-#1637 := [not-or-elim #1633]: #1636
-#2317 := [mp~ #1637 #2316]: #2314
-#2318 := [mp #2317 #2850]: #2848
-#3492 := [mp #2318 #3491]: #3489
-#4421 := [mp #3492 #4420]: #4418
-#10019 := [unit-resolution #4421 #5020]: #4415
-#3747 := (or #4412 #4406)
-#3590 := [def-axiom]: #3747
-#10022 := [unit-resolution #3590 #10019]: #4406
-#10023 := (or #4409 #4403)
-#3664 := (* -1::int #1705)
-#3631 := (+ uf_9 #3664)
-#3633 := (<= #3631 0::int)
-#3738 := (= uf_9 #1705)
-#3712 := (= uf_11 ?x27!0)
-#3561 := (not #3712)
-#3560 := (= #1705 0::int)
-#4453 := (not #3560)
-#4452 := [hypothesis]: #1707
-#4504 := (or #4453 #1706)
-#4505 := [th-lemma]: #4504
-#4506 := [unit-resolution #4505 #4452]: #4453
-#3571 := (or #3570 #3560 #3561)
-#3727 := (= ?x27!0 uf_11)
-#3562 := (not #3727)
-#3563 := (or #3562 #3560)
-#3572 := (or #3570 #3563)
-#4443 := (iff #3572 #3571)
-#3585 := (or #3560 #3561)
-#4444 := (or #3570 #3585)
-#4447 := (iff #4444 #3571)
-#4448 := [rewrite]: #4447
-#4445 := (iff #3572 #4444)
-#3583 := (iff #3563 #3585)
-#4429 := (or #3561 #3560)
-#3569 := (iff #4429 #3585)
-#3566 := [rewrite]: #3569
-#3584 := (iff #3563 #4429)
-#3564 := (iff #3562 #3561)
-#3710 := (iff #3727 #3712)
-#3713 := [rewrite]: #3710
-#4428 := [monotonicity #3713]: #3564
-#3576 := [monotonicity #4428]: #3584
-#3567 := [trans #3576 #3566]: #3583
-#4446 := [monotonicity #3567]: #4445
-#4449 := [trans #4446 #4448]: #4443
-#3568 := [quant-inst]: #3572
-#4450 := [mp #3568 #4449]: #3571
-#4507 := [unit-resolution #4450 #4427 #4506]: #3561
-#3695 := (or #3712 #3738)
-#4043 := (forall (vars (?x25 T2)) (:pat #4042) #405)
-#4046 := (iff #410 #4043)
-#4044 := (iff #405 #405)
-#4045 := [refl]: #4044
-#4047 := [quant-intro #4045]: #4046
-#1660 := (~ #410 #410)
-#1698 := (~ #405 #405)
-#1699 := [refl]: #1698
-#1661 := [nnf-pos #1699]: #1660
-#1635 := [not-or-elim #1633]: #410
-#1700 := [mp~ #1635 #1661]: #410
-#4048 := [mp #1700 #4047]: #4043
-#3698 := (not #4043)
-#3699 := (or #3698 #3712 #3738)
-#3730 := (or #3727 #3738)
-#3700 := (or #3698 #3730)
-#3662 := (iff #3700 #3699)
-#3702 := (or #3698 #3695)
-#3653 := (iff #3702 #3699)
-#3660 := [rewrite]: #3653
-#3659 := (iff #3700 #3702)
-#3697 := (iff #3730 #3695)
-#3711 := [monotonicity #3713]: #3697
-#3661 := [monotonicity #3711]: #3659
-#3663 := [trans #3661 #3660]: #3662
-#3701 := [quant-inst]: #3700
-#3654 := [mp #3701 #3663]: #3699
-#4508 := [unit-resolution #3654 #4048]: #3695
-#4509 := [unit-resolution #4508 #4507]: #3738
-#4510 := (not #3738)
-#4511 := (or #4510 #3633)
-#4512 := [th-lemma]: #4511
-#4492 := [unit-resolution #4512 #4509]: #3633
-#4451 := (<= #1705 0::int)
-#4493 := (or #4451 #1706)
-#4494 := [th-lemma]: #4493
-#4495 := [unit-resolution #4494 #4452]: #4451
-#335 := (<= uf_9 0::int)
-#336 := (not #335)
-#54 := (< 0::int uf_9)
-#337 := (iff #54 #336)
-#338 := [rewrite]: #337
-#331 := [asserted]: #54
-#339 := [mp #331 #338]: #336
-#4496 := [th-lemma #339 #4495 #4492]: false
-#4491 := [lemma #4496]: #1706
-#3742 := (or #4409 #1707 #4403)
-#3743 := [def-axiom]: #3742
-#10024 := [unit-resolution #3743 #4491]: #10023
-#10025 := [unit-resolution #10024 #10022]: #4403
-#3766 := (or #4400 #4394)
-#3767 := [def-axiom]: #3766
-#10018 := [unit-resolution #3767 #10025]: #4394
-#3761 := (or #4397 #2108 #4391)
-#3762 := [def-axiom]: #3761
-#10026 := [unit-resolution #3762 #10018]: #4394
-#10027 := [unit-resolution #10026 #10021]: #4391
-#3787 := (or #4388 #4382)
-#3788 := [def-axiom]: #3787
-#10028 := [unit-resolution #3788 #10027]: #4382
-#3783 := (or #4385 #2893 #4379)
-#3784 := [def-axiom]: #3783
-#10029 := [unit-resolution #3784 #10028 #10020]: #4379
-#3771 := (or #4376 #4370)
-#3772 := [def-axiom]: #3771
-#10030 := [unit-resolution #3772 #10029]: #4370
-#10032 := (or #4373 #4367)
-#4499 := [hypothesis]: #4087
-#3969 := (or #4084 #2369)
-#3970 := [def-axiom]: #3969
-#4636 := [unit-resolution #3970 #4499]: #2369
-#4584 := (= uf_9 #1777)
-#4727 := (not #4584)
-#3636 := (or #4084 #1789)
-#3968 := [def-axiom]: #3636
-#4637 := [unit-resolution #3968 #4499]: #1789
-#4737 := (or #4727 #1788)
-#4738 := [th-lemma]: #4737
-#4739 := [unit-resolution #4738 #4637]: #4727
-#4758 := (or #4584 #2366)
-#4728 := [hypothesis]: #4727
-#4729 := [hypothesis]: #2369
-#4641 := (or #3698 #2366 #4584)
-#4585 := (or #1790 #4584)
-#4642 := (or #3698 #4585)
-#4628 := (iff #4642 #4641)
-#4638 := (or #2366 #4584)
-#4644 := (or #3698 #4638)
-#4626 := (iff #4644 #4641)
-#4627 := [rewrite]: #4626
-#4624 := (iff #4642 #4644)
-#4639 := (iff #4585 #4638)
-#4640 := [monotonicity #2368]: #4639
-#4625 := [monotonicity #4640]: #4624
-#4623 := [trans #4625 #4627]: #4628
-#4643 := [quant-inst]: #4642
-#4629 := [mp #4643 #4623]: #4641
-#4730 := [unit-resolution #4629 #4048 #4729 #4728]: false
-#4760 := [lemma #4730]: #4758
-#4740 := [unit-resolution #4760 #4739 #4636]: false
-#4741 := [lemma #4740]: #4084
-#3805 := (or #4373 #4087 #4367)
-#3815 := [def-axiom]: #3805
-#10033 := [unit-resolution #3815 #4741]: #10032
-#10034 := [unit-resolution #10033 #10030]: #4367
-#3800 := (or #4364 #4358)
-#3759 := [def-axiom]: #3800
-#10246 := [unit-resolution #3759 #10034]: #4358
-#3593 := (not #2607)
-#3836 := (or #4364 #106)
-#3832 := [def-axiom]: #3836
-#10035 := [unit-resolution #3832 #10034]: #106
-#8124 := (= #161 #105)
-#4885 := [hypothesis]: #4200
-#3652 := (or #4197 #495)
-#3934 := [def-axiom]: #3652
-#4886 := [unit-resolution #3934 #4885]: #495
-#8139 := [symm #4886]: #142
-#7937 := [monotonicity #8139]: #8124
-#4736 := [trans #7937 #10035]: #162
-#3612 := (or #4173 #1970)
-#3613 := [def-axiom]: #3612
-#7107 := [unit-resolution #3613 #4736]: #4173
-#3939 := (or #4197 #4191)
-#3928 := [def-axiom]: #3939
-#8726 := [unit-resolution #3928 #4885]: #4191
-#10469 := (or #4151 #586)
-#8744 := (?x47!7 ?x49!8)
-#8817 := (uf_4 uf_19 #8744)
-#8836 := (* -1::int #8817)
-#8739 := (uf_4 uf_14 #8744)
-#9868 := (+ #8739 #8836)
-#9874 := (>= #9868 0::int)
-#9867 := (= #8739 #8817)
-#10418 := (= #8817 #8739)
-#6250 := [hypothesis]: #495
-#10417 := [symm #6250]: #142
-#10419 := [monotonicity #10417]: #10418
-#10420 := [symm #10419]: #9867
-#10421 := (not #9867)
-#10416 := (or #10421 #9874)
-#10422 := [th-lemma]: #10416
-#10423 := [unit-resolution #10422 #10420]: #9874
-#8745 := (* -1::int #8739)
-#8586 := (uf_4 uf_14 ?x49!8)
-#8746 := (+ #8586 #8745)
-#8747 := (<= #8746 0::int)
-#8789 := (not #8747)
-#8770 := (up_6 uf_15 #8744)
-#8771 := (not #8770)
-#8748 := (uf_1 #8744 ?x49!8)
-#8749 := (uf_10 #8748)
-#8765 := (* -1::int #8749)
-#8766 := (+ #8745 #8765)
-#8767 := (+ #8586 #8766)
-#8768 := (= #8767 0::int)
-#8769 := (not #8768)
-#8754 := (or #8747 #8769 #8771)
-#8757 := (not #8754)
-#8721 := (* -1::int #8586)
-#8734 := (+ uf_9 #8721)
-#8722 := (<= #8734 0::int)
-#8939 := (not #8722)
-#10424 := [hypothesis]: #4154
-#3622 := (or #4151 #1895)
-#3627 := [def-axiom]: #3622
-#10425 := [unit-resolution #3627 #10424]: #1895
-#8935 := (+ #1882 #8721)
-#8932 := (>= #8935 0::int)
-#8934 := (= #1882 #8586)
-#10426 := (= #8586 #1882)
-#10427 := [monotonicity #6250]: #10426
-#10428 := [symm #10427]: #8934
-#10429 := (not #8934)
-#10430 := (or #10429 #8932)
-#10431 := [th-lemma]: #10430
-#10432 := [unit-resolution #10431 #10428]: #8932
-#8931 := (not #8932)
-#8940 := (or #8939 #8931 #1894)
-#8936 := [hypothesis]: #1895
-#8933 := [hypothesis]: #8722
-#8937 := [hypothesis]: #8932
-#8938 := [th-lemma #8937 #8933 #8936]: false
-#8738 := [lemma #8938]: #8940
-#10433 := [unit-resolution #8738 #10432 #10425]: #8939
-#10443 := (or #8722 #8757)
-#3963 := (or #4151 #2507)
-#3623 := [def-axiom]: #3963
-#10434 := [unit-resolution #3623 #10424]: #2507
-#3825 := (or #4364 #4124)
-#3793 := [def-axiom]: #3825
-#10442 := [unit-resolution #3793 #10034]: #4124
-#8762 := (or #4129 #2504 #8722 #8757)
-#8772 := (or #8771 #8769 #8747)
-#8773 := (not #8772)
-#8753 := (or #1896 #8722 #8773)
-#8775 := (or #4129 #8753)
-#8781 := (iff #8775 #8762)
-#8759 := (or #2504 #8722 #8757)
-#8777 := (or #4129 #8759)
-#8774 := (iff #8777 #8762)
-#8780 := [rewrite]: #8774
-#8778 := (iff #8775 #8777)
-#8760 := (iff #8753 #8759)
-#8752 := (iff #8773 #8757)
-#8755 := (iff #8772 #8754)
-#8756 := [rewrite]: #8755
-#8758 := [monotonicity #8756]: #8752
-#8761 := [monotonicity #2506 #8758]: #8760
-#8779 := [monotonicity #8761]: #8778
-#8782 := [trans #8779 #8780]: #8781
-#8776 := [quant-inst]: #8775
-#8783 := [mp #8776 #8782]: #8762
-#10444 := [unit-resolution #8783 #10442 #10434]: #10443
-#10445 := [unit-resolution #10444 #10433]: #8757
-#8787 := (or #8754 #8789)
-#8790 := [def-axiom]: #8787
-#10446 := [unit-resolution #8790 #10445]: #8789
-#8831 := (+ #1882 #8836)
-#8848 := (<= #8831 0::int)
-#8893 := (+ #8765 #8836)
-#8894 := (+ #1882 #8893)
-#8912 := (= #8894 0::int)
-#9084 := (<= #8894 0::int)
-#9871 := (<= #9868 0::int)
-#10447 := (or #10421 #9871)
-#10448 := [th-lemma]: #10447
-#10449 := [unit-resolution #10448 #10420]: #9871
-#8784 := (<= #8767 0::int)
-#8791 := (or #8754 #8768)
-#8792 := [def-axiom]: #8791
-#10450 := [unit-resolution #8792 #10445]: #8768
-#10451 := (or #8769 #8784)
-#10452 := [th-lemma]: #10451
-#10453 := [unit-resolution #10452 #10450]: #8784
-#8930 := (<= #8935 0::int)
-#10454 := (or #10429 #8930)
-#10455 := [th-lemma]: #10454
-#10456 := [unit-resolution #10455 #10428]: #8930
-#10096 := (not #9871)
-#10098 := (not #8784)
-#10097 := (not #8930)
-#10099 := (or #9084 #10097 #10098 #10096)
-#10059 := [hypothesis]: #9871
-#10060 := [hypothesis]: #8784
-#10062 := [hypothesis]: #8930
-#10063 := (not #9084)
-#10064 := [hypothesis]: #10063
-#10065 := [th-lemma #10064 #10062 #10060 #10059]: false
-#10100 := [lemma #10065]: #10099
-#10457 := [unit-resolution #10100 #10456 #10453 #10449]: #9084
-#9068 := (>= #8894 0::int)
-#8788 := (>= #8767 0::int)
-#10458 := (or #8769 #8788)
-#10459 := [th-lemma]: #10458
-#10460 := [unit-resolution #10459 #10450]: #8788
-#10439 := (not #9874)
-#10007 := (not #8788)
-#10440 := (or #9068 #8931 #10007 #10439)
-#10435 := [hypothesis]: #9874
-#9938 := [hypothesis]: #8788
-#10436 := (not #9068)
-#10437 := [hypothesis]: #10436
-#10438 := [th-lemma #10437 #8937 #9938 #10435]: false
-#10441 := [lemma #10438]: #10440
-#10461 := [unit-resolution #10441 #10432 #10460 #10423]: #9068
-#10462 := (or #8912 #10063 #10436)
-#10463 := [th-lemma]: #10462
-#10464 := [unit-resolution #10463 #10461 #10457]: #8912
-#8911 := (not #8912)
-#8918 := (or #8848 #8911)
-#3964 := (or #4151 #4143)
-#3607 := [def-axiom]: #3964
-#10465 := [unit-resolution #3607 #10424]: #4143
-#9022 := (or #4148 #8848 #8911)
-#8815 := (+ #1883 #8749)
-#8818 := (+ #8817 #8815)
-#8819 := (= #8818 0::int)
-#8820 := (not #8819)
-#8821 := (+ #8817 #1883)
-#8825 := (>= #8821 0::int)
-#8826 := (or #8825 #8820)
-#9031 := (or #4148 #8826)
-#9081 := (iff #9031 #9022)
-#9078 := (or #4148 #8918)
-#9024 := (iff #9078 #9022)
-#9080 := [rewrite]: #9024
-#9079 := (iff #9031 #9078)
-#8919 := (iff #8826 #8918)
-#8916 := (iff #8820 #8911)
-#8915 := (iff #8819 #8912)
-#8886 := (+ #8749 #8817)
-#8887 := (+ #1883 #8886)
-#8890 := (= #8887 0::int)
-#8913 := (iff #8890 #8912)
-#8914 := [rewrite]: #8913
-#8891 := (iff #8819 #8890)
-#8888 := (= #8818 #8887)
-#8889 := [rewrite]: #8888
-#8892 := [monotonicity #8889]: #8891
-#8910 := [trans #8892 #8914]: #8915
-#8917 := [monotonicity #8910]: #8916
-#8857 := (iff #8825 #8848)
-#8827 := (+ #1883 #8817)
-#8833 := (>= #8827 0::int)
-#8849 := (iff #8833 #8848)
-#8856 := [rewrite]: #8849
-#8834 := (iff #8825 #8833)
-#8829 := (= #8821 #8827)
-#8832 := [rewrite]: #8829
-#8835 := [monotonicity #8832]: #8834
-#8858 := [trans #8835 #8856]: #8857
-#8920 := [monotonicity #8858 #8917]: #8919
-#9023 := [monotonicity #8920]: #9079
-#9082 := [trans #9023 #9080]: #9081
-#9032 := [quant-inst]: #9031
-#9083 := [mp #9032 #9082]: #9022
-#10466 := [unit-resolution #9083 #10465]: #8918
-#10467 := [unit-resolution #10466 #10464]: #8848
-#10468 := [th-lemma #10432 #10467 #10446 #10423]: false
-#10470 := [lemma #10468]: #10469
-#8740 := [unit-resolution #10470 #4886]: #4151
-#3941 := (or #4194 #4154 #4188)
-#3945 := [def-axiom]: #3941
-#8741 := [unit-resolution #3945 #8740 #8726]: #4188
-#3672 := (or #4185 #4179)
-#3565 := [def-axiom]: #3672
-#8742 := [unit-resolution #3565 #8741]: #4179
-#3947 := (or #4182 #4176 #3161)
-#3669 := [def-axiom]: #3947
-#8743 := [unit-resolution #3669 #8742 #7107]: #3161
-#3956 := (or #3156 #3593)
-#3958 := [def-axiom]: #3956
-#8786 := [unit-resolution #3958 #8743]: #3593
-#3763 := (or #4364 #4099)
-#3818 := [def-axiom]: #3763
-#10042 := [unit-resolution #3818 #10034]: #4099
-#3953 := (or #3156 #1957)
-#3954 := [def-axiom]: #3953
-#8793 := [unit-resolution #3954 #8743]: #1957
-#3949 := (or #3156 #1961)
-#3955 := [def-axiom]: #3949
-#8794 := [unit-resolution #3955 #8743]: #1961
-#4870 := (or #4197 #1956 #4104 #1960 #2607)
-#4889 := (uf_4 uf_14 ?x53!11)
-#4883 := (= #1946 #4889)
-#4887 := (= #4889 #1946)
-#4882 := [monotonicity #4886]: #4887
-#4888 := [symm #4882]: #4883
-#4890 := (* -1::int #4889)
-#6163 := (+ #1946 #4890)
-#6178 := (<= #6163 0::int)
-#6288 := (not #6178)
-#6191 := [hypothesis]: #3593
-#6244 := [hypothesis]: #1961
-#6247 := [hypothesis]: #4099
-#6249 := [hypothesis]: #1957
-#3938 := (or #4197 #4133)
-#3935 := [def-axiom]: #3938
-#4841 := [unit-resolution #3935 #4885]: #4133
-#6294 := (or #6288 #1956 #4138 #4104 #1960 #2607 #586)
-#5206 := (uf_4 uf_14 ?x54!10)
-#5207 := (* -1::int #5206)
-#5202 := (+ uf_9 #5207)
-#5208 := (<= #5202 0::int)
-#5209 := (up_6 uf_15 ?x54!10)
-#5647 := (not #5209)
-#5579 := (+ #4890 #5206)
-#5580 := (+ #1951 #5579)
-#5572 := (>= #5580 0::int)
-#6194 := (not #5572)
-#6196 := (+ #1948 #5207)
-#6208 := (>= #6196 0::int)
-#6195 := (= #1948 #5206)
-#6209 := (= #5206 #1948)
-#6207 := [monotonicity #6250]: #6209
-#6210 := [symm #6207]: #6195
-#6211 := (not #6195)
-#6212 := (or #6211 #6208)
-#6241 := [th-lemma]: #6212
-#6242 := [unit-resolution #6241 #6210]: #6208
-#6192 := [hypothesis]: #6178
-#6289 := (not #6208)
-#6290 := (or #6194 #6288 #2607 #6289)
-#6190 := [hypothesis]: #6208
-#6187 := [hypothesis]: #5572
-#6193 := [th-lemma #6187 #6192 #6191 #6190]: false
-#6291 := [lemma #6193]: #6290
-#6243 := [unit-resolution #6291 #6192 #6191 #6242]: #6194
-#6248 := (or #5647 #5572)
-#5669 := (or #4104 #1960 #5647 #5572)
-#5605 := (+ #5206 #4890)
-#5606 := (+ #1951 #5605)
-#5646 := (>= #5606 0::int)
-#5578 := (or #5647 #1960 #5646)
-#5674 := (or #4104 #5578)
-#5939 := (iff #5674 #5669)
-#5670 := (or #1960 #5647 #5572)
-#5676 := (or #4104 #5670)
-#5909 := (iff #5676 #5669)
-#5910 := [rewrite]: #5909
-#5677 := (iff #5674 #5676)
-#5673 := (iff #5578 #5670)
-#5598 := (or #5647 #1960 #5572)
-#5671 := (iff #5598 #5670)
-#5672 := [rewrite]: #5671
-#5601 := (iff #5578 #5598)
-#5599 := (iff #5646 #5572)
-#5581 := (= #5606 #5580)
-#5582 := [rewrite]: #5581
-#5600 := [monotonicity #5582]: #5599
-#5602 := [monotonicity #5600]: #5601
-#5668 := [trans #5602 #5672]: #5673
-#5678 := [monotonicity #5668]: #5677
-#5940 := [trans #5678 #5910]: #5939
-#5675 := [quant-inst]: #5674
-#5941 := [mp #5675 #5940]: #5669
-#6177 := [unit-resolution #5941 #6247 #6244]: #6248
-#6189 := [unit-resolution #6177 #6243]: #5647
-#5211 := (or #5208 #5209)
-#6168 := [hypothesis]: #4133
-#5237 := (or #4138 #5208 #5209)
-#5210 := (or #5209 #5208)
-#5238 := (or #4138 #5210)
-#5244 := (iff #5238 #5237)
-#5240 := (or #4138 #5211)
-#5242 := (iff #5240 #5237)
-#5243 := [rewrite]: #5242
-#5235 := (iff #5238 #5240)
-#5212 := (iff #5210 #5211)
-#5236 := [rewrite]: #5212
-#5241 := [monotonicity #5236]: #5235
-#5245 := [trans #5241 #5243]: #5244
-#5239 := [quant-inst]: #5238
-#5293 := [mp #5239 #5245]: #5237
-#6292 := [unit-resolution #5293 #6168]: #5211
-#6287 := [unit-resolution #6292 #6189]: #5208
-#6293 := [th-lemma #6242 #6287 #6249]: false
-#6295 := [lemma #6293]: #6294
-#4866 := [unit-resolution #6295 #4841 #6249 #6247 #6244 #6191 #4886]: #6288
-#4867 := (not #4883)
-#4868 := (or #4867 #6178)
-#4869 := [th-lemma]: #4868
-#4840 := [unit-resolution #4869 #4866 #4888]: false
-#4865 := [lemma #4840]: #4870
-#8795 := [unit-resolution #4865 #8794 #8793 #10042 #4885 #8786]: false
-#8798 := [lemma #8795]: #4197
-#3834 := (or #4361 #4200 #4355)
-#3835 := [def-axiom]: #3834
-#10367 := [unit-resolution #3835 #8798 #10246]: #4355
-#3856 := (or #4352 #184)
-#3842 := [def-axiom]: #3856
-#10380 := [unit-resolution #3842 #10367]: #184
-#10381 := [symm #10380]: #7113
-#13521 := (= #11444 #183)
-#13346 := (= #10482 uf_22)
-#10483 := (= uf_22 #10482)
-#13 := (uf_3 #12)
-#295 := (= #11 #13)
-#3982 := (forall (vars (?x2 T2) (?x3 T2)) (:pat #3981) #295)
-#299 := (forall (vars (?x2 T2) (?x3 T2)) #295)
-#3985 := (iff #299 #3982)
-#3983 := (iff #295 #295)
-#3984 := [refl]: #3983
-#3986 := [quant-intro #3984]: #3985
-#1641 := (~ #299 #299)
-#1673 := (~ #295 #295)
-#1674 := [refl]: #1673
-#1639 := [nnf-pos #1674]: #1641
-#14 := (= #13 #11)
-#15 := (forall (vars (?x2 T2) (?x3 T2)) #14)
-#300 := (iff #15 #299)
-#297 := (iff #14 #295)
-#298 := [rewrite]: #297
-#301 := [quant-intro #298]: #300
-#294 := [asserted]: #15
-#304 := [mp #294 #301]: #299
-#1675 := [mp~ #304 #1639]: #299
-#3987 := [mp #1675 #3986]: #3982
-#7756 := (not #3982)
-#10489 := (or #7756 #10483)
-#10490 := [quant-inst]: #10489
-#13345 := [unit-resolution #10490 #3987]: #10483
-#13347 := [symm #13345]: #13346
-#13522 := [monotonicity #13347]: #13521
-#13524 := [trans #13522 #10381]: #13523
-#27228 := [monotonicity #13524 #27216]: #27227
-#27230 := [symm #27228]: #27229
-#27232 := [monotonicity #27230]: #27231
-#27226 := [hypothesis]: #16801
-#27233 := [mp #27226 #27232]: #27109
-#27075 := (= #10482 #19843)
-#25893 := (up_6 uf_15 #19843)
-#27081 := (or #25893 #27075)
-#27086 := (iff #27073 #27081)
-#30 := (:var 1 T5)
-#20 := (:var 2 T2)
-#29 := (:var 3 T4)
-#31 := (uf_7 #29 #20 #30)
-#32 := (up_6 #31 #11)
-#4001 := (pattern #32)
-#35 := (up_6 #29 #11)
-#34 := (= #30 uf_8)
-#24 := (= #11 #20)
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-#6453 := (iff #6444 #6452)
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-#13055 := [mp #13048 #13054]: #13035
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-#6440 := (= #6439 0::int)
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-#13441 := (>= #13437 0::int)
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-#56 := (uf_10 #12)
-#371 := (<= #56 0::int)
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-#55 := (= #10 #11)
-#375 := (or #55 #372)
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-#7747 := [commutativity]: #1303
-#7740 := (iff #4709 #670)
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-#7749 := [trans #7746 #7747]: #7748
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-#7730 := (or #1547 #4721)
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-#7160 := (not #4721)
-#7162 := (or #4709 #7160 #7161 #825 #4243 #4218)
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-#7328 := (up_6 #183 uf_11)
-#7338 := (iff #7328 #7333)
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-#7327 := (ite #4606 #3681 #4650)
-#7329 := (iff #7328 #7327)
-#6818 := (or #6538 #7329)
-#6814 := (iff #6818 #3737)
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-#7336 := (iff #7327 #7333)
-#7330 := (ite #4606 true #4650)
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-#7335 := [rewrite]: #7334
-#7331 := (iff #7327 #7330)
-#7332 := [monotonicity #3673]: #7331
-#7337 := [trans #7332 #7335]: #7336
-#7340 := [monotonicity #7337]: #7339
-#6820 := [monotonicity #7340]: #6814
-#6823 := [trans #6820 #6822]: #6814
-#6819 := [quant-inst]: #6818
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-#4795 := (up_6 uf_23 uf_11)
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-#7169 := (iff #4796 #6842)
-#7167 := (iff #4795 #7328)
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-#7114 := [symm #7112]: #7113
-#7116 := [monotonicity #7114]: #7115
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-#7084 := (not #4709)
-#7109 := [hypothesis]: #7084
-#4798 := (or #4709 #4796)
-#7110 := [hypothesis]: #4238
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-#4797 := (or #4796 #4709)
-#6729 := (or #4243 #4797)
-#6720 := (iff #6729 #6714)
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-#6719 := [rewrite]: #6718
-#6731 := (iff #6729 #6728)
-#4799 := (iff #4797 #4798)
-#4800 := [rewrite]: #4799
-#6717 := [monotonicity #4800]: #6731
-#6721 := [trans #6717 #6719]: #6720
-#6730 := [quant-inst]: #6729
-#6716 := [mp #6730 #6721]: #6714
-#7111 := [unit-resolution #6716 #7110]: #4798
-#7106 := [unit-resolution #7111 #7109]: #4796
-#7171 := [mp #7106 #7170]: #6842
-#6840 := (not #7338)
-#6841 := (or #6840 #7328 #6837)
-#6836 := [def-axiom]: #6841
-#7172 := [unit-resolution #6836 #7171 #7083]: #6837
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-#6827 := [def-axiom]: #6829
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-#6986 := (or #4606 #6984)
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-#4604 := (= uf_22 uf_11)
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-#6990 := (or #7051 #6985)
-#6978 := (iff #6990 #6989)
-#6974 := (or #7051 #6986)
-#6977 := (iff #6974 #6989)
-#6972 := [rewrite]: #6977
-#6975 := (iff #6990 #6974)
-#6987 := (iff #6985 #6986)
-#4607 := (iff #4604 #4606)
-#4608 := [rewrite]: #4607
-#6988 := [monotonicity #4608]: #6987
-#6976 := [monotonicity #6988]: #6975
-#6979 := [trans #6976 #6972]: #6978
-#6973 := [quant-inst]: #6990
-#6980 := [mp #6973 #6979]: #6989
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-#7175 := [unit-resolution #7174 #7173]: #6984
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-#4673 := (+ #1268 #4672)
-#4674 := (+ #105 #4673)
-#4675 := (<= #4674 0::int)
-#6530 := (not #4675)
-#4676 := (+ uf_9 #4672)
-#4677 := (<= #4676 0::int)
-#4711 := (or #4675 #4677)
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-#4717 := (or #4709 #4714)
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-#6354 := (iff #6357 #6326)
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-#4715 := (iff #4708 #4714)
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-#4713 := [rewrite]: #4712
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-#6831 := (= #6830 #2077)
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-#7265 := (= #7208 #7264)
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-#7361 := [monotonicity #6843 #7358]: #7360
-#7367 := [monotonicity #7361]: #7366
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-#7257 := (= #7205 #7256)
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-#7323 := [monotonicity #7317]: #7322
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-#8365 := [unit-resolution #7302 #6758]: #7313
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-#8367 := (not #7273)
-#8368 := (or #8367 #7300)
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-#7522 := (iff #7495 #7539)
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-#19561 := (iff #15410 #2130)
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-#19577 := [mp #19549 #19576]: #15410
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-#17134 := (not #15420)
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-#19327 := [th-lemma]: #18783
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-#7076 := (uf_2 #2122)
-#7082 := (uf_4 uf_14 #7076)
-#7096 := (* -1::int #7082)
-#7097 := (+ #177 #7096)
-#7098 := (<= #7097 0::int)
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-#19009 := (= #7082 #177)
-#19025 := (= #7076 uf_22)
-#19026 := (= #7076 #10482)
-#19488 := (= #7076 ?x72!18)
-#7077 := (= ?x72!18 #7076)
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-#19750 := (or #19749 #2710 #19718 #19719 #19578 #19840)
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-#18698 := [mp #18816 #18694]: #18751
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-#18549 := [unit-resolution #18080 #4034]: #18064
-#18550 := [unit-resolution #18549 #18460]: #18049
-#18552 := (not #18161)
-#18553 := (or #18551 #18496 #18497 #18498 #18048 #18552)
-#18554 := [th-lemma]: #18553
-#18555 := [unit-resolution #18554 #18495 #18444 #10836 #18550 #18038]: #18551
-#18562 := (or #15074 #15094)
-#11728 := (up_6 uf_23 #10482)
-#18558 := (iff #3683 #11728)
-#18556 := (iff #11728 #3683)
-#18557 := [monotonicity #10380 #13347]: #18556
-#18559 := [symm #18557]: #18558
-#18560 := [mp #10818 #18559]: #11728
-#18561 := [hypothesis]: #4272
-#11732 := (not #11728)
-#15729 := (or #4277 #11732 #15074 #15094)
-#15061 := (+ #2148 #15060)
-#15062 := (+ #11725 #15061)
-#15063 := (= #15062 0::int)
-#15064 := (not #15063)
-#15065 := (+ #11725 #2148)
-#15066 := (>= #15065 0::int)
-#15067 := (or #11732 #15066 #15064)
-#15730 := (or #4277 #15067)
-#15737 := (iff #15730 #15729)
-#15097 := (or #11732 #15074 #15094)
-#15732 := (or #4277 #15097)
-#15735 := (iff #15732 #15729)
-#15736 := [rewrite]: #15735
-#15733 := (iff #15730 #15732)
-#15098 := (iff #15067 #15097)
-#15095 := (iff #15064 #15094)
-#15092 := (iff #15063 #15089)
-#15079 := (+ #11725 #15060)
-#15080 := (+ #2148 #15079)
-#15083 := (= #15080 0::int)
-#15090 := (iff #15083 #15089)
-#15091 := [rewrite]: #15090
-#15084 := (iff #15063 #15083)
-#15081 := (= #15062 #15080)
-#15082 := [rewrite]: #15081
-#15085 := [monotonicity #15082]: #15084
-#15093 := [trans #15085 #15091]: #15092
-#15096 := [monotonicity #15093]: #15095
-#15077 := (iff #15066 #15074)
-#15068 := (+ #2148 #11725)
-#15071 := (>= #15068 0::int)
-#15075 := (iff #15071 #15074)
-#15076 := [rewrite]: #15075
-#15072 := (iff #15066 #15071)
-#15069 := (= #15065 #15068)
-#15070 := [rewrite]: #15069
-#15073 := [monotonicity #15070]: #15072
-#15078 := [trans #15073 #15076]: #15077
-#15099 := [monotonicity #15078 #15096]: #15098
-#15734 := [monotonicity #15099]: #15733
-#15738 := [trans #15734 #15736]: #15737
-#15731 := [quant-inst]: #15730
-#15739 := [mp #15731 #15738]: #15729
-#18563 := [unit-resolution #15739 #18561 #18560]: #18562
-#18564 := [unit-resolution #18563 #18555]: #15094
-#18566 := (not #15741)
-#18565 := (not #15740)
-#18567 := (or #15089 #18565 #18566)
-#18568 := [th-lemma]: #18567
-#18569 := [unit-resolution #18568 #18564 #17776 #18502]: false
-#18571 := [lemma #18569]: #18570
-#27208 := [unit-resolution #18571 #27207]: #5566
-#18519 := (or #18518 #18461)
-#18520 := [th-lemma]: #18519
-#27209 := [unit-resolution #18520 #27208]: #18461
-#22580 := (not #18461)
-#22586 := (or #22585 #22580 #2159)
-#22581 := [hypothesis]: #2160
-#22582 := [hypothesis]: #18461
-#22583 := [hypothesis]: #5840
-#22584 := [th-lemma #22583 #22582 #22581]: false
-#22587 := [lemma #22584]: #22586
-#27210 := [unit-resolution #22587 #27209 #27206]: #22585
-#3914 := (or #4280 #2724)
-#3796 := [def-axiom]: #3914
-#27211 := [unit-resolution #3796 #27205]: #2724
-#16286 := (or #4129 #2721 #5840 #5845)
-#5837 := (or #5836 #5834 #5827)
-#5838 := (not #5837)
-#5841 := (or #2161 #5840 #5838)
-#16309 := (or #4129 #5841)
-#16464 := (iff #16309 #16286)
-#5848 := (or #2721 #5840 #5845)
-#16025 := (or #4129 #5848)
-#16414 := (iff #16025 #16286)
-#16302 := [rewrite]: #16414
-#16445 := (iff #16309 #16025)
-#5849 := (iff #5841 #5848)
-#5846 := (iff #5838 #5845)
-#5843 := (iff #5837 #5842)
-#5844 := [rewrite]: #5843
-#5847 := [monotonicity #5844]: #5846
-#5850 := [monotonicity #2723 #5847]: #5849
-#16461 := [monotonicity #5850]: #16445
-#16413 := [trans #16461 #16302]: #16464
-#16307 := [quant-inst]: #16309
-#16444 := [mp #16307 #16413]: #16286
-#27212 := [unit-resolution #16444 #10442 #27211 #27210]: #5845
-#16693 := (or #5842 #5835)
-#16554 := [def-axiom]: #16693
-#27213 := [unit-resolution #16554 #27212]: #5835
-#27221 := [mp #27213 #27220]: #25893
-#25894 := (not #25893)
-#27098 := (or #27081 #25894)
-#27099 := [def-axiom]: #27098
-#27222 := [unit-resolution #27099 #27221]: #27081
-#27103 := (not #27081)
-#27107 := (or #27106 #27073 #27103)
-#27108 := [def-axiom]: #27107
-#27224 := [unit-resolution #27108 #27222]: #27223
-#27225 := [unit-resolution #27224 #27196]: #27073
-#27234 := [unit-resolution #27225 #27233]: false
-#27235 := [lemma #27234]: #16800
-#16798 := (uf_24 #5823)
-#16817 := (* -1::int #16798)
-#17010 := (+ #2147 #16817)
-#17011 := (<= #17010 0::int)
-#22559 := (not #17011)
-#15902 := (not #5827)
-#16589 := (or #5842 #15902)
-#16412 := [def-axiom]: #16589
-#22552 := [unit-resolution #16412 #27212]: #15902
-#16818 := (+ #5824 #16817)
-#16819 := (>= #16818 0::int)
-#16900 := (or #4234 #16819)
-#15938 := [quant-inst]: #16900
-#22558 := [unit-resolution #15938 #10835]: #16819
-#22544 := (not #16819)
-#23021 := (or #22559 #5827 #22580 #22544)
-#22554 := [th-lemma]: #23021
-#18055 := [unit-resolution #22554 #27209 #22558 #22552]: #22559
-#16977 := (+ #5830 #16817)
-#16978 := (+ #2147 #16977)
-#17021 := (= #16978 0::int)
-#19944 := (>= #16978 0::int)
-#9360 := (>= #5832 0::int)
-#16497 := (or #5842 #5833)
-#16618 := [def-axiom]: #16497
-#16042 := [unit-resolution #16618 #27212]: #5833
-#21361 := (or #5834 #9360)
-#21365 := [th-lemma]: #21361
-#22952 := [unit-resolution #21365 #16042]: #9360
-#22974 := (not #9360)
-#23033 := (or #19944 #22974 #22580 #22544)
-#22976 := [th-lemma]: #23033
-#22955 := [unit-resolution #22976 #22952 #22558 #27209]: #19944
-#16979 := (<= #16978 0::int)
-#22549 := (<= #16818 0::int)
-#16799 := (= #5824 #16798)
-#16803 := (or #16799 #16801)
-#17738 := (or #4243 #16799 #16801)
-#16802 := (or #16801 #16799)
-#18032 := (or #4243 #16802)
-#15937 := (iff #18032 #17738)
-#18787 := (or #4243 #16803)
-#18974 := (iff #18787 #17738)
-#19070 := [rewrite]: #18974
-#19064 := (iff #18032 #18787)
-#16804 := (iff #16802 #16803)
-#16805 := [rewrite]: #16804
-#17444 := [monotonicity #16805]: #19064
-#19082 := [trans #17444 #19070]: #15937
-#19040 := [quant-inst]: #18032
-#17767 := [mp #19040 #19082]: #17738
-#18817 := [unit-resolution #17767 #10831]: #16803
-#23050 := [unit-resolution #18817 #27235]: #16799
-#23024 := (not #16799)
-#23019 := (or #23024 #22549)
-#23047 := [th-lemma]: #23019
-#23015 := [unit-resolution #23047 #23050]: #22549
-#5593 := (<= #5592 0::int)
-#20441 := (not #5593)
-#20442 := [hypothesis]: #20441
-#20353 := (or #4234 #5593)
-#5583 := (+ #5561 #2148)
-#5584 := (>= #5583 0::int)
-#20370 := (or #4234 #5584)
-#20377 := (iff #20370 #20353)
-#20384 := (iff #20353 #20353)
-#20387 := [rewrite]: #20384
-#5596 := (iff #5584 #5593)
-#5585 := (+ #2148 #5561)
-#5588 := (>= #5585 0::int)
-#5594 := (iff #5588 #5593)
-#5595 := [rewrite]: #5594
-#5589 := (iff #5584 #5588)
-#5586 := (= #5583 #5585)
-#5587 := [rewrite]: #5586
-#5590 := [monotonicity #5587]: #5589
-#5597 := [trans #5590 #5595]: #5596
-#20383 := [monotonicity #5597]: #20377
-#20388 := [trans #20383 #20387]: #20377
-#20376 := [quant-inst]: #20370
-#20438 := [mp #20376 #20388]: #20353
-#20437 := [unit-resolution #20438 #10835 #20442]: false
-#20443 := [lemma #20437]: #5593
-#15900 := (<= #5832 0::int)
-#23077 := (or #5834 #15900)
-#23040 := [th-lemma]: #23077
-#23022 := [unit-resolution #23040 #16042]: #15900
-#23053 := (not #22549)
-#22936 := (not #15900)
-#23179 := (or #16979 #22936 #20441 #23053)
-#23061 := [th-lemma]: #23179
-#23075 := [unit-resolution #23061 #23022 #20443 #23015]: #16979
-#23181 := (not #19944)
-#23180 := (not #16979)
-#23059 := (or #17021 #23180 #23181)
-#23057 := [th-lemma]: #23059
-#23182 := [unit-resolution #23057 #23075 #22955]: #17021
-#17026 := (not #17021)
-#17029 := (or #16801 #17011 #17026)
-#19879 := (or #4277 #16801 #17011 #17026)
-#16998 := (+ #2148 #5829)
-#16999 := (+ #16798 #16998)
-#17000 := (= #16999 0::int)
-#17001 := (not #17000)
-#16962 := (+ #16798 #2148)
-#17002 := (>= #16962 0::int)
-#17003 := (or #16801 #17002 #17001)
-#19880 := (or #4277 #17003)
-#19850 := (iff #19880 #19879)
-#19873 := (or #4277 #17029)
-#19915 := (iff #19873 #19879)
-#19874 := [rewrite]: #19915
-#20138 := (iff #19880 #19873)
-#17030 := (iff #17003 #17029)
-#17027 := (iff #17001 #17026)
-#17024 := (iff #17000 #17021)
-#16970 := (+ #5829 #16798)
-#16971 := (+ #2148 #16970)
-#17018 := (= #16971 0::int)
-#17022 := (iff #17018 #17021)
-#17023 := [rewrite]: #17022
-#17019 := (iff #17000 #17018)
-#17016 := (= #16999 #16971)
-#17017 := [rewrite]: #17016