updated SMT certificates

--- 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)
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+#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)
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+#200 := (implies #172 #199)
+#201 := (and #172 #200)
+#202 := (implies #170 #201)
+#203 := (and #170 #202)
+#160 := (= #155 #68)
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+#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)
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+#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)
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+#139 := (= #138 f1)
+#140 := (not #139)
+#213 := (implies #140 #212)
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+#96 := (and #74 #87)
+#97 := (exists (vars (?v0 S2)) #96)
+#214 := (implies #97 #213)
+#215 := (implies true #214)
+#126 := (and #125 true)
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+#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)
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+#100 := (= f13 f12)
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+#98 := (not #97)
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+#136 := (implies true #135)
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+#88 := (and #29 #87)
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+#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)
+#894 := (iff #889 #893)
+#895 := [rewrite]: #894
+#890 := (iff #209 #889)
+#887 := (iff #208 #884)
+#880 := (implies #710 #877)
+#885 := (iff #880 #884)
+#886 := [rewrite]: #885
+#881 := (iff #208 #880)
+#878 := (iff #207 #877)
+#875 := (iff #206 #872)
+#868 := (implies #164 #865)
+#873 := (iff #868 #872)
+#874 := [rewrite]: #873
+#869 := (iff #206 #868)
+#866 := (iff #205 #865)
+#863 := (iff #204 #860)
+#856 := (implies #725 #853)
+#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)
-#840 := (implies #178 #835)
-#845 := (iff #840 #844)
-#846 := [rewrite]: #845
-#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)
-#799 := (iff #240 #796)
-#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)
-#774 := [rewrite]: #773
-#769 := (iff #236 #768)
-#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)
-#744 := (implies #677 #741)
-#749 := (iff #744 #748)
-#750 := [rewrite]: #749
-#745 := (iff #232 #744)
-#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
-#726 := (iff #229 #725)
-#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)
-#503 := [monotonicity #500]: #502
-#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)
-#486 := [rewrite]: #485
-#481 := (iff #131 #480)
-#478 := (iff #130 #477)
-#475 := (iff #129 #474)
-#472 := (iff #128 #471)
-#469 := (iff #127 #468)
-#451 := (= #120 #450)
-#452 := [rewrite]: #451
-#470 := [monotonicity #452]: #469
-#473 := [monotonicity #470]: #472
-#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)
-#4126 := [refl]: #4125
-#4128 := [quant-intro #4126]: #4127
-#4131 := [monotonicity #4128]: #4130
-#4122 := (iff #3426 #4121)
-#4119 := (iff #3013 #4116)
-#4117 := (iff #3008 #3008)
-#4118 := [refl]: #4117
-#4120 := [quant-intro #4118]: #4119
-#4123 := [monotonicity #4120]: #4122
-#4114 := (iff #3425 #4113)
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 #2160 := (not #2159)
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+#3491 := [trans #3487 #3489]: #3490
+#3494 := [quant-intro #3491]: #3493
+#3478 := (iff #1445 #3477)
+#3475 := (iff #1442 #3472)
+#3458 := (or #719 #1141)
+#3469 := (or #3458 #1438)
+#3473 := (iff #3469 #3472)
+#3474 := [rewrite]: #3473
+#3470 := (iff #1442 #3469)
+#3467 := (iff #1435 #3458)
+#3459 := (not #3458)
+#3462 := (not #3459)
+#3465 := (iff #3462 #3458)
+#3466 := [rewrite]: #3465
+#3463 := (iff #1435 #3462)
+#3460 := (iff #1430 #3459)
+#3461 := [rewrite]: #3460
+#3464 := [monotonicity #3461]: #3463
+#3468 := [trans #3464 #3466]: #3467
+#3471 := [monotonicity #3468]: #3470
+#3476 := [trans #3471 #3474]: #3475
+#3479 := [quant-intro #3476]: #3478
+#3497 := [monotonicity #3479 #3494]: #3496
+#3505 := [trans #3497 #3503]: #3504
+#3456 := (iff #2872 #3455)
+#3453 := (iff #2869 #3450)
+#3436 := (or #2276 #3435)
+#3447 := (or #3436 #2864)
+#3451 := (iff #3447 #3450)
+#3452 := [rewrite]: #3451
+#3448 := (iff #2869 #3447)
+#3445 := (iff #2851 #3436)
+#3437 := (not #3436)
+#3440 := (not #3437)
+#3443 := (iff #3440 #3436)
+#3444 := [rewrite]: #3443
+#3441 := (iff #2851 #3440)
+#3438 := (iff #2848 #3437)
+#3439 := [rewrite]: #3438
+#3442 := [monotonicity #3439]: #3441
+#3446 := [trans #3442 #3444]: #3445
+#3449 := [monotonicity #3446]: #3448
+#3454 := [trans #3449 #3452]: #3453
+#3457 := [monotonicity #3454]: #3456
+#3508 := [monotonicity #3457 #3505]: #3507
+#3433 := (iff #1421 #3432)
+#3430 := (iff #1416 #3427)
+#3413 := (or #713 #3412)
+#3424 := (or #3413 #1408)
+#3428 := (iff #3424 #3427)
+#3429 := [rewrite]: #3428
+#3425 := (iff #1416 #3424)
+#3422 := (iff #742 #3413)
+#3414 := (not #3413)
+#3417 := (not #3414)
+#3420 := (iff #3417 #3413)
+#3421 := [rewrite]: #3420
+#3418 := (iff #742 #3417)
+#3415 := (iff #736 #3414)
+#3416 := [rewrite]: #3415
+#3419 := [monotonicity #3416]: #3418
+#3423 := [trans #3419 #3421]: #3422
+#3426 := [monotonicity #3423]: #3425
+#3431 := [trans #3426 #3429]: #3430
+#3434 := [quant-intro #3431]: #3433
+#3511 := [monotonicity #3434 #3508]: #3510
+#3519 := [trans #3511 #3517]: #3518
+#3410 := (iff #2845 #3409)
+#3407 := (iff #2842 #3404)
+#3390 := (or #3389 #2247)
+#3401 := (or #3390 #2837)
+#3405 := (iff #3401 #3404)
+#3406 := [rewrite]: #3405
+#3402 := (iff #2842 #3401)
+#3399 := (iff #2826 #3390)
+#3391 := (not #3390)
+#3394 := (not #3391)
+#3397 := (iff #3394 #3390)
+#3398 := [rewrite]: #3397
+#3395 := (iff #2826 #3394)
+#3392 := (iff #2823 #3391)
+#3393 := [rewrite]: #3392
+#3396 := [monotonicity #3393]: #3395
+#3400 := [trans #3396 #3398]: #3399
+#3403 := [monotonicity #3400]: #3402
+#3408 := [trans #3403 #3406]: #3407
+#3411 := [monotonicity #3408]: #3410
+#3522 := [monotonicity #3411 #3519]: #3521
+#3525 := [monotonicity #3522]: #3524
+#3532 := [trans #3525 #3530]: #3531
+#3535 := [monotonicity #3532]: #3534
+#3538 := [monotonicity #3535]: #3537
+#3545 := [trans #3538 #3543]: #3544
+#3548 := [monotonicity #3545]: #3547
+#3551 := [monotonicity #3548]: #3550
+#3558 := [trans #3551 #3556]: #3557
+#3561 := [monotonicity #3558]: #3560
+#3564 := [monotonicity #3561]: #3563
+#3571 := [trans #3564 #3569]: #3570
+#3574 := [monotonicity #3571]: #3573
+#3387 := (iff #1535 #3386)
+#3384 := (iff #1532 #3381)
+#3378 := (or #3361 #1529)
+#3382 := (iff #3378 #3381)
+#3383 := [rewrite]: #3382
+#3379 := (iff #1532 #3378)
+#3376 := (iff #1524 #3361)
+#3371 := (not #3362)
+#3374 := (iff #3371 #3361)
+#3375 := [rewrite]: #3374
+#3372 := (iff #1524 #3371)
+#3363 := (iff #1366 #3362)
+#3364 := [rewrite]: #3363
+#3373 := [monotonicity #3364]: #3372
+#3377 := [trans #3373 #3375]: #3376
+#3380 := [monotonicity #3377]: #3379
+#3385 := [trans #3380 #3383]: #3384
+#3388 := [quant-intro #3385]: #3387
+#3369 := (iff #1377 #3368)
+#3366 := (iff #1372 #3365)
+#3367 := [monotonicity #3364]: #3366
+#3370 := [quant-intro #3367]: #3369
+#3577 := [monotonicity #3370 #3388 #3574]: #3576
+#3586 := [trans #3577 #3584]: #3585
+#3359 := (iff #2784 #3356)
+#3350 := (and #103 #108 #535 #538 #3224 #3347)
+#3357 := (iff #3350 #3356)
+#3358 := [rewrite]: #3357
+#3351 := (iff #2784 #3350)
+#3348 := (iff #2778 #3347)
+#3345 := (iff #2775 #3342)
+#3336 := (and #3276 #3333)
+#3343 := (iff #3336 #3342)
+#3344 := [rewrite]: #3343
+#3337 := (iff #2775 #3336)
+#3334 := (iff #2770 #3333)
+#3331 := (iff #2764 #3330)
+#3328 := (iff #2761 #3325)
+#3311 := (or #2100 #2104)
+#3322 := (or #3311 #2756)
+#3326 := (iff #3322 #3325)
+#3327 := [rewrite]: #3326
+#3323 := (iff #2761 #3322)
+#3320 := (iff #2744 #3311)
+#3312 := (not #3311)
+#3315 := (not #3312)
+#3318 := (iff #3315 #3311)
+#3319 := [rewrite]: #3318
+#3316 := (iff #2744 #3315)
+#3313 := (iff #2741 #3312)
+#3314 := [rewrite]: #3313
+#3317 := [monotonicity #3314]: #3316
+#3321 := [trans #3317 #3319]: #3320
+#3324 := [monotonicity #3321]: #3323
+#3329 := [trans #3324 #3327]: #3328
+#3332 := [monotonicity #3329]: #3331
+#3309 := (iff #2124 #3306)
+#3301 := (and #2114 #3298)
+#3307 := (iff #3301 #3306)
+#3308 := [rewrite]: #3307
+#3302 := (iff #2124 #3301)
+#3299 := (iff #1297 #3298)
+#3296 := (iff #1294 #3293)
+#3279 := (or #1141 #1250)
+#3290 := (or #3279 #1291)
+#3294 := (iff #3290 #3293)
+#3295 := [rewrite]: #3294
+#3291 := (iff #1294 #3290)
+#3288 := (iff #1288 #3279)
+#3280 := (not #3279)
+#3283 := (not #3280)
+#3286 := (iff #3283 #3279)
+#3287 := [rewrite]: #3286
+#3284 := (iff #1288 #3283)
+#3281 := (iff #1285 #3280)
+#3282 := [rewrite]: #3281
+#3285 := [monotonicity #3282]: #3284
+#3289 := [trans #3285 #3287]: #3288
+#3292 := [monotonicity #3289]: #3291
+#3297 := [trans #3292 #3295]: #3296
+#3300 := [quant-intro #3297]: #3299
+#3303 := [monotonicity #3300]: #3302
+#3310 := [trans #3303 #3308]: #3309
+#3335 := [monotonicity #3310 #3332]: #3334
+#3277 := (iff #2738 #3276)
+#3274 := (iff #2735 #3271)
+#3252 := (or #24 #1250)
+#3268 := (or #3252 #3265)
+#3272 := (iff #3268 #3271)
+#3273 := [rewrite]: #3272
+#3269 := (iff #2735 #3268)
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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
-#3088 := (iff #1171 #3087)
-#3085 := (iff #1168 #3084)
-#3086 := [rewrite]: #3085
-#3089 := [monotonicity #3086]: #3088
-#3093 := [trans #3089 #3091]: #3092
-#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)
-#3079 := (iff #3073 #3078)
-#3080 := [rewrite]: #3079
-#3074 := (iff #2547 #3073)
-#3071 := (iff #2541 #3070)
-#3068 := (iff #2538 #3059)
-#3060 := (not #3059)
-#3063 := (not #3060)
-#3066 := (iff #3063 #3059)
-#3067 := [rewrite]: #3066
-#3064 := (iff #2538 #3063)
-#3061 := (iff #2535 #3060)
-#3062 := [rewrite]: #3061
-#3065 := [monotonicity #3062]: #3064
-#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)
-#3051 := (iff #3048 #3044)
-#3052 := [rewrite]: #3051
-#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)
-#3016 := (or #65 #1119)
-#3033 := (or #3016 #3030)
-#3037 := (iff #3033 #3036)
-#3038 := [rewrite]: #3037
-#3034 := (iff #2490 #3033)
-#3031 := (iff #2487 #3030)
-#3032 := [rewrite]: #3031
-#3025 := (iff #1126 #3016)
-#3017 := (not #3016)
-#3020 := (not #3017)
-#3023 := (iff #3020 #3016)
-#3024 := [rewrite]: #3023
-#3021 := (iff #1126 #3020)
-#3018 := (iff #1123 #3017)
-#3019 := [rewrite]: #3018
-#3022 := [monotonicity #3019]: #3021
-#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)
-#3009 := (iff #3005 #3008)
-#3010 := [rewrite]: #3009
-#3006 := (iff #2450 #3005)
-#3003 := (iff #2447 #3002)
-#3004 := [rewrite]: #3003
-#2997 := (iff #1088 #2988)
-#2989 := (not #2988)
-#2992 := (not #2989)
-#2995 := (iff #2992 #2988)
-#2996 := [rewrite]: #2995
-#2993 := (iff #1088 #2992)
-#2990 := (iff #1085 #2989)
-#2991 := [rewrite]: #2990
-#2994 := [monotonicity #2991]: #2993
-#2998 := [trans #2994 #2996]: #2997
-#3007 := [monotonicity #2998 #3004]: #3006
-#3012 := [trans #3007 #3010]: #3011
-#3015 := [quant-intro #3012]: #3014
-#2986 := (iff #1530 #2985)
-#2983 := (iff #1527 #2980)
-#2966 := (or #111 #2965)
-#2977 := (or #2966 #1135)
-#2981 := (iff #2977 #2980)
-#2982 := [rewrite]: #2981
-#2978 := (iff #1527 #2977)
-#2975 := (iff #440 #2966)
-#2967 := (not #2966)
-#2970 := (not #2967)
-#2973 := (iff #2970 #2966)
-#2974 := [rewrite]: #2973
-#2971 := (iff #440 #2970)
-#2968 := (iff #114 #2967)
-#2969 := [rewrite]: #2968
-#2972 := [monotonicity #2969]: #2971
-#2976 := [trans #2972 #2974]: #2975
-#2979 := [monotonicity #2976]: #2978
-#2984 := [trans #2979 #2982]: #2983
-#2987 := [quant-intro #2984]: #2986
-#2963 := (iff #1519 #2962)
-#2960 := (iff #1516 #2957)
-#2943 := (or #112 #1055)
-#2954 := (or #2943 #1513)
-#2958 := (iff #2954 #2957)
-#2959 := [rewrite]: #2958
-#2955 := (iff #1516 #2954)
-#2952 := (iff #1510 #2943)
-#2944 := (not #2943)
-#2947 := (not #2944)
-#2950 := (iff #2947 #2943)
-#2951 := [rewrite]: #2950
-#2948 := (iff #1510 #2947)
-#2945 := (iff #1505 #2944)
-#2946 := [rewrite]: #2945
-#2949 := [monotonicity #2946]: #2948
-#2953 := [trans #2949 #2951]: #2952
-#2956 := [monotonicity #2953]: #2955
-#2961 := [trans #2956 #2959]: #2960
-#2964 := [quant-intro #2961]: #2963
-#3423 := [monotonicity #2964 #2987 #3015 #3043 #3420]: #3422
-#3434 := [trans #3423 #3432]: #3433
-#2941 := (iff #2409 #2938)
-#2933 := (and #1789 #2369 #2930)
-#2939 := (iff #2933 #2938)
-#2940 := [rewrite]: #2939
-#2934 := (iff #2409 #2933)
-#2931 := (iff #2403 #2930)
-#2928 := (iff #2400 #2919)
-#2920 := (not #2919)
-#2923 := (not #2920)
-#2926 := (iff #2923 #2919)
-#2927 := [rewrite]: #2926
-#2924 := (iff #2400 #2923)
-#2921 := (iff #2397 #2920)
-#2922 := [rewrite]: #2921
-#2925 := [monotonicity #2922]: #2924
-#2929 := [trans #2925 #2927]: #2928
-#2932 := [quant-intro #2929]: #2931
-#2935 := [monotonicity #2932]: #2934
-#2942 := [trans #2935 #2940]: #2941
-#3437 := [monotonicity #2942 #3434]: #3436
-#2916 := (iff #1073 #2915)
-#2913 := (iff #1070 #2910)
-#2896 := (or #75 #1055)
-#2907 := (or #2896 #1066)
-#2911 := (iff #2907 #2910)
-#2912 := [rewrite]: #2911
-#2908 := (iff #1070 #2907)
-#2905 := (iff #1062 #2896)
-#2897 := (not #2896)
-#2900 := (not #2897)
-#2903 := (iff #2900 #2896)
-#2904 := [rewrite]: #2903
-#2901 := (iff #1062 #2900)
-#2898 := (iff #1059 #2897)
-#2899 := [rewrite]: #2898
-#2902 := [monotonicity #2899]: #2901
-#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
-#2894 := (iff #2363 #2893)
-#2891 := (iff #2360 #2888)
-#2874 := (or #1756 #2873)
-#2885 := (or #2874 #2357)
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-#2890 := [rewrite]: #2889
-#2886 := (iff #2360 #2885)
-#2883 := (iff #2350 #2874)
-#2875 := (not #2874)
-#2878 := (not #2875)
-#2881 := (iff #2878 #2874)
-#2882 := [rewrite]: #2881
-#2879 := (iff #2350 #2878)
-#2876 := (iff #2347 #2875)
+#3094 := [monotonicity #3091]: #3093
+#3098 := [trans #3094 #3096]: #3097
+#3101 := [quant-intro #3098]: #3100
+#3104 := [monotonicity #3101]: #3103
+#3111 := [trans #3104 #3109]: #3110
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+#3082 := (iff #1156 #3079)
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+#3076 := (or #1136 #3065)
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+#3069 := (not #3066)
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+#3075 := [trans #3071 #3073]: #3074
+#3078 := [monotonicity #3075]: #3077
+#3083 := [trans #3078 #3081]: #3082
+#3086 := [quant-intro #3083]: #3085
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+#3063 := (iff #2512 #3062)
+#3060 := (iff #2509 #3057)
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+#3054 := (or #2500 #3043)
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+#3047 := (not #3044)
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+#3051 := [rewrite]: #3050
+#3048 := (iff #2506 #3047)
+#3045 := (iff #2503 #3044)
+#3046 := [rewrite]: #3045
+#3049 := [monotonicity #3046]: #3048
+#3053 := [trans #3049 #3051]: #3052
+#3056 := [monotonicity #3053]: #3055
+#3061 := [trans #3056 #3059]: #3060
+#3064 := [monotonicity #3061]: #3063
+#3620 := [monotonicity #3064 #3617]: #3619
+#3040 := (iff #1128 #3039)
+#3037 := (iff #1123 #3034)
+#3020 := (or #368 #3019)
+#3031 := (or #3020 #1116)
+#3035 := (iff #3031 #3034)
+#3036 := [rewrite]: #3035
+#3032 := (iff #1123 #3031)
+#3029 := (iff #389 #3020)
+#3021 := (not #3020)
+#3024 := (not #3021)
+#3027 := (iff #3024 #3020)
+#3028 := [rewrite]: #3027
+#3025 := (iff #389 #3024)
+#3022 := (iff #383 #3021)
+#3023 := [rewrite]: #3022
+#3026 := [monotonicity #3023]: #3025
+#3030 := [trans #3026 #3028]: #3029
+#3033 := [monotonicity #3030]: #3032
+#3038 := [trans #3033 #3036]: #3037
+#3041 := [quant-intro #3038]: #3040
+#3623 := [monotonicity #3041 #3620]: #3622
+#3631 := [trans #3623 #3629]: #3630
+#3017 := (iff #2493 #3016)
+#3014 := (iff #2490 #3011)
+#2113 := (or #2112 #1868)
+#3008 := (or #2113 #2485)
+#3012 := (iff #3008 #3011)
+#3013 := [rewrite]: #3012
+#3009 := (iff #2490 #3008)
+#3006 := (iff #2474 #2113)
+#1828 := (not #2113)
+#1976 := (not #1828)
+#2468 := (iff #1976 #2113)
+#3005 := [rewrite]: #2468
+#2208 := (iff #2474 #1976)
+#1829 := (iff #2471 #1828)
+#1975 := [rewrite]: #1829
+#2209 := [monotonicity #1975]: #2208
+#3007 := [trans #2209 #3005]: #3006
+#3010 := [monotonicity #3007]: #3009
+#3015 := [trans #3010 #3013]: #3014
+#3018 := [monotonicity #3015]: #3017
+#3634 := [monotonicity #3018 #3631]: #3633
+#3637 := [monotonicity #3634]: #3636
+#3644 := [trans #3637 #3642]: #3643
+#3647 := [monotonicity #3644]: #3646
+#3650 := [monotonicity #3647]: #3649
+#3657 := [trans #3650 #3655]: #3656
+#3660 := [monotonicity #3657]: #3659
+#2301 := (+ #2300 #2298)
+#2302 := (= #2301 0::int)
+#2305 := (and #713 #2304 #2302)
+#2322 := (not #2305)
+#2325 := (forall (vars (?v1 S2)) #2322)
+#2310 := (= ?v0!20 f6)
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+#2312 := (and #2311 #2309)
+#2313 := (not #2312)
+#2319 := (not #2313)
+#2329 := (and #2319 #2325)
+#2334 := (and #1445 #2329)
+#2267 := (* -1::int #2266)
+#2269 := (+ #2268 #2267)
+#2272 := (+ #2271 #2269)
+#2273 := (>= #2272 0::int)
+#2280 := (and #2279 #2277)
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+#2342 := (and #1421 #2338)
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+#2242 := (+ #2241 #2240)
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+#2249 := (and #2248 #2245)
+#2250 := (not #2249)
+#2251 := (or #2250 #2243)
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+#2203 := (= #2202 #2201)
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+#2370 := (or #2205 #2366)
+#2374 := (and #1388 #2370)
+#2181 := (* -1::int #2180)
+#2183 := (+ #2182 #2181)
+#2184 := (>= #2183 0::int)
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+#2378 := (or #2185 #2374)
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+#2091 := (* -1::int #2090)
+#2093 := (+ #2092 #2091)
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+#2097 := (>= #2096 0::int)
+#2106 := (and #2105 #2101)
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+#2128 := (or #2109 #2124)
+#2067 := (+ #2066 #1248)
+#2070 := (+ #2069 #2067)
+#2071 := (= #2070 0::int)
+#2072 := (>= #2067 0::int)
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+#2132 := (and #2082 #2128)
+#2031 := (+ #2030 #2028)
+#2032 := (= #2031 0::int)
+#2035 := (and #2034 #2032)
+#2051 := (not #2035)
+#2054 := (forall (vars (?v1 S2)) #2051)
+#2040 := (= ?v0!8 f6)
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+#2022 := (not #629)
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+#2402 := (or #2146 #2398)
+#1990 := (+ #1989 #1203)
+#1991 := (>= #1990 0::int)
+#1992 := (not #1991)
+#1995 := (+ #1994 #1990)
+#1996 := (= #1995 0::int)
+#1999 := (and #1998 #1996 #1992)
+#2004 := (or #1212 #1999)
+#2007 := (forall (vars (?v0 S2)) #2004)
+#1963 := (+ #1165 #1962)
+#1965 := (+ #1964 #1963)
+#1966 := (= #1965 0::int)
+#1967 := (+ #1964 #1165)
+#1968 := (>= #1967 0::int)
+#1969 := (not #1968)
+#1972 := (and #1971 #1969 #1966)
+#1977 := (or #1174 #1972)
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+#1955 := (not #1653)
+#2427 := (and #1955 #1980 #2007 #2402 #1620 #1636 #1645)
+#1921 := (+ #1920 #1918)
+#1922 := (+ #25 #1921)
+#1923 := (= #1922 0::int)
+#1927 := (and #368 #1926 #1923)
+#1943 := (not #1927)
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+#1932 := (= ?v0!5 f6)
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+#1934 := (and #1933 #1931)
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+#2431 := (or #1950 #2427)
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+#1895 := (and #1894 #1892)
+#1896 := (not #1895)
+#1899 := (+ #1898 #1888)
+#1901 := (+ #1900 #1899)
+#1902 := (>= #1901 0::int)
+#1903 := (or #1902 #1896)
+#1904 := (not #1903)
+#2439 := (or #1904 #2435)
+#2443 := (and #1128 #2439)
+#1861 := (* -1::int #1860)
+#1863 := (+ #1862 #1861)
+#1864 := (>= #1863 0::int)
+#1870 := (and #1869 #1866)
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+#1872 := (or #1871 #1864)
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+#2970 := (and #67 #2602 #2642 #2967 #1620 #1636 #1645)
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+#2975 := [rewrite]: #2974
+#2971 := (iff #2427 #2970)
+#2968 := (iff #2402 #2967)
+#2965 := (iff #2398 #2962)
+#2959 := (and #148 #671 #2164 #1377 #2956 #1535 #1553 #1561)
+#2963 := (iff #2959 #2962)
+#2964 := [rewrite]: #2963
+#2960 := (iff #2398 #2959)
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+#2954 := (iff #2374 #2953)
+#2951 := (iff #2370 #2950)
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+#2933 := (iff #2346 #2932)
+#2930 := (iff #2342 #2929)
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+#2884 := (and #2309 #2878)
+#2915 := (and #2884 #2912)
+#2918 := (and #1445 #2915)
+#2922 := (iff #2918 #2921)
+#2923 := [rewrite]: #2922
+#2919 := (iff #2334 #2918)
+#2916 := (iff #2329 #2915)
+#2913 := (iff #2325 #2912)
+#2910 := (iff #2322 #2909)
+#2907 := (iff #2305 #2906)
+#2904 := (iff #2302 #2903)
+#2901 := (= #2301 #2900)
+#2902 := [rewrite]: #2901
+#2905 := [monotonicity #2902]: #2904
+#2908 := [monotonicity #2905]: #2907
+#2911 := [monotonicity #2908]: #2910
+#2914 := [quant-intro #2911]: #2913
+#2897 := (iff #2319 #2884)
+#2889 := (not #2884)
+#2892 := (not #2889)
+#2895 := (iff #2892 #2884)
+#2896 := [rewrite]: #2895
+#2893 := (iff #2319 #2892)
+#2890 := (iff #2313 #2889)
+#2887 := (iff #2312 #2884)
+#2881 := (and #2878 #2309)
+#2885 := (iff #2881 #2884)
+#2886 := [rewrite]: #2885
+#2882 := (iff #2312 #2881)
+#2879 := (iff #2311 #2878)
+#2876 := (iff #2310 #2875)
 #2877 := [rewrite]: #2876
 #2880 := [monotonicity #2877]: #2879
-#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)
-#36 := (ite #24 #34 #35)
-#37 := (iff #32 #36)
-#4002 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) (:pat #4001) #37)
-#38 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) #37)
-#4005 := (iff #38 #4002)
-#4003 := (iff #37 #37)
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-#6453 := (iff #6444 #6452)
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-#6451 := [rewrite]: #6450
-#6454 := [monotonicity #6451]: #6453
-#6461 := [trans #6454 #6459]: #6460
-#6494 := [monotonicity #6461]: #6493
-#6497 := [monotonicity #6494]: #6496
-#6490 := (iff #6487 #6489)
-#6491 := [rewrite]: #6490
-#6500 := [monotonicity #6491 #6497]: #6499
-#13051 := [monotonicity #6500]: #13050
-#13054 := [trans #13051 #13047]: #13053
-#13048 := [quant-inst]: #13036
-#13055 := [mp #13048 #13054]: #13035
-#13387 := [unit-resolution #13055 #10373]: #6498
-#13388 := [unit-resolution #13387 #13409]: #6495
-#13385 := (or #6492 #6466)
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-#13435 := [hypothesis]: #13434
-#13057 := (not #6446)
-#13439 := [hypothesis]: #6495
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-#13078 := [def-axiom]: #13077
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-#13079 := (not #6457)
-#13080 := (or #6492 #13079)
-#13081 := [def-axiom]: #13080
-#13366 := [unit-resolution #13081 #13439]: #13079
-#6469 := (or #6446 #6457 #6466)
-#13012 := (or #4226 #6446 #6457 #6466)
-#6438 := (+ #6437 #2681)
-#6439 := (+ #177 #6438)
-#6440 := (= #6439 0::int)
-#6447 := (or #6446 #6444 #6440)
-#13013 := (or #4226 #6447)
-#13031 := (iff #13013 #13012)
-#13015 := (or #4226 #6469)
-#13029 := (iff #13015 #13012)
-#13030 := [rewrite]: #13029
-#13027 := (iff #13013 #13015)
-#6470 := (iff #6447 #6469)
-#6467 := (iff #6440 #6466)
-#6464 := (= #6439 #6463)
-#6465 := [rewrite]: #6464
-#6468 := [monotonicity #6465]: #6467
-#6471 := [monotonicity #6461 #6468]: #6470
-#13028 := [monotonicity #6471]: #13027
-#13026 := [trans #13028 #13030]: #13031
-#13014 := [quant-inst]: #13013
-#13032 := [mp #13014 #13026]: #13012
-#13367 := [unit-resolution #13032 #10825]: #6469
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-#13386 := [lemma #13368]: #13385
-#13488 := [unit-resolution #13386 #13388]: #6466
-#13588 := (or #13434 #13033)
-#13589 := [th-lemma]: #13588
-#13590 := [unit-resolution #13589 #13488]: #13033
-#12924 := (uf_1 #10482 ?x68!16)
-#12925 := (uf_10 #12924)
-#13060 := (* -1::int #12925)
-#13437 := (+ #6437 #13060)
-#13441 := (>= #13437 0::int)
-#13436 := (= #6437 #12925)
-#13445 := (= #12925 #6437)
-#13443 := (= #12924 #6436)
-#13444 := [monotonicity #13347]: #13443
-#13446 := [monotonicity #13444]: #13445
-#13447 := [symm #13446]: #13436
-#13448 := (not #13436)
-#13449 := (or #13448 #13441)
-#13450 := [th-lemma]: #13449
-#13451 := [unit-resolution #13450 #13447]: #13441
-#13410 := (<= #12925 0::int)
-#13411 := (not #13410)
-#12833 := (not #12761)
-#12834 := (or #12767 #12833)
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-#56 := (uf_10 #12)
-#371 := (<= #56 0::int)
-#372 := (not #371)
-#55 := (= #10 #11)
-#375 := (or #55 #372)
-#4029 := (forall (vars (?x22 T2) (?x23 T2)) (:pat #3981) #375)
-#378 := (forall (vars (?x22 T2) (?x23 T2)) #375)
-#4032 := (iff #378 #4029)
-#4030 := (iff #375 #375)
-#4031 := [refl]: #4030
-#4033 := [quant-intro #4031]: #4032
-#1656 := (~ #378 #378)
-#1655 := (~ #375 #375)
-#1693 := [refl]: #1655
-#1657 := [nnf-pos #1693]: #1656
-#61 := (< 0::int #56)
-#60 := (not #55)
-#62 := (implies #60 #61)
-#63 := (forall (vars (?x22 T2) (?x23 T2)) #62)
-#381 := (iff #63 #378)
-#365 := (or #55 #61)
-#368 := (forall (vars (?x22 T2) (?x23 T2)) #365)
-#379 := (iff #368 #378)
-#376 := (iff #365 #375)
-#373 := (iff #61 #372)
-#374 := [rewrite]: #373
-#377 := [monotonicity #374]: #376
-#380 := [quant-intro #377]: #379
-#369 := (iff #63 #368)
-#366 := (iff #62 #365)
-#367 := [rewrite]: #366
-#370 := [quant-intro #367]: #369
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-#364 := [asserted]: #63
-#383 := [mp #364 #382]: #378
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-#13419 := (or #7051 #12761 #13411)
-#13412 := (= #10482 ?x68!16)
-#13413 := (or #13412 #13411)
-#13420 := (or #7051 #13413)
-#13427 := (iff #13420 #13419)
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-#13426 := [rewrite]: #13425
-#13423 := (iff #13420 #13422)
-#13417 := (iff #13413 #13416)
-#13414 := (iff #13412 #12761)
-#13415 := [rewrite]: #13414
-#13418 := [monotonicity #13415]: #13417
-#13424 := [monotonicity #13418]: #13423
-#13428 := [trans #13424 #13426]: #13427
-#13421 := [quant-inst]: #13420
-#13429 := [mp #13421 #13428]: #13419
-#13592 := [unit-resolution #13429 #4034 #13591]: #13411
-#13463 := (not #13033)
-#13465 := (or #13463 #2683 #13464 #12761)
-#13442 := [hypothesis]: #13288
-#13452 := [hypothesis]: #12833
-#13453 := [unit-resolution #13429 #4034 #13452]: #13411
-#13454 := [hypothesis]: #13033
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-#13594 := [unit-resolution #13587 #13593]: #10290
-#13595 := [unit-resolution #12958 #13594 #13537]: #12929
-#13596 := [trans #13595 #13347]: #6206
-#13597 := [monotonicity #13596]: #13334
-#13598 := [unit-resolution #13438 #13597]: #13335
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-#13851 := [lemma #13863]: #3235
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-#8410 := (= uf_22 #8409)
-#8416 := (or #8415 #8410)
-#8417 := [quant-inst]: #8416
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-#10477 := [monotonicity #8694]: #8563
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-#7477 := (uf_10 #7476)
-#6712 := (* -1::int #2054)
-#7563 := (+ #6712 #7477)
-#7564 := (+ #177 #7563)
-#7637 := (>= #7564 0::int)
-#7832 := (not #7637)
-#7478 := (* -1::int #7477)
-#7480 := (+ uf_9 #7478)
-#7481 := (<= #7480 0::int)
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-#7381 := (= #7479 #7380)
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-#7370 := [monotonicity #7498]: #7369
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-#7700 := [quant-inst]: #7694
-#7483 := [mp #7700 #7303]: #7698
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-#7872 := [def-axiom]: #7871
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-#8188 := (= uf_22 ?x63!14)
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-#7408 := (+ #177 #6712)
-#8885 := (>= #7408 0::int)
-#8884 := (= #177 #2054)
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-#8985 := (or #8984 #8885)
-#8981 := [th-lemma]: #8985
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-#4026 := (iff #358 #4023)
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-#359 := (iff #350 #358)
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-#363 := [mp #332 #362]: #358
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-#8403 := (or #7068 #8399)
-#8405 := (iff #8403 #8402)
-#8406 := [rewrite]: #8405
-#8404 := [quant-inst]: #8403
-#8407 := [mp #8404 #8406]: #8402
-#8986 := [unit-resolution #8407 #4028]: #8399
-#8987 := [unit-resolution #8986 #8946]: #8398
-#9015 := (not #8398)
-#9016 := (or #9015 #8408)
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-#8130 := (ite #8129 #3681 #7164)
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-#8191 := (ite #8188 true #7164)
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-#8195 := [rewrite]: #8194
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-#8189 := (iff #8129 #8188)
-#8190 := [rewrite]: #8189
-#8192 := [monotonicity #8190 #3673]: #8186
-#8205 := [trans #8192 #8195]: #8196
-#8208 := [monotonicity #8205]: #8207
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-#8247 := [mp #8210 #8246]: #8209
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-#8291 := (or #8287 #8290 #8193)
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-#10073 := (>= #10072 0::int)
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-#8401 := (= ?x63!14 #8400)
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-#10095 := (+ #2054 #10071)
-#10102 := (<= #10095 0::int)
-#10094 := (= #2054 #10070)
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-#8536 := (* -1::int #8525)
-#8803 := (+ #177 #8536)
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-#7729 := [unit-resolution #3877 #7728]: #4322
-#4709 := (= #105 #204)
-#7748 := (iff #4709 #205)
-#7747 := [commutativity]: #1303
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-#7749 := [trans #7746 #7747]: #7748
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-#7741 := [th-lemma]: #7730
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-#7743 := [unit-resolution #3876 #7728]: #4238
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-#7160 := (not #4721)
-#7162 := (or #4709 #7160 #7161 #825 #4243 #4218)
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-#6983 := (<= #4668 0::int)
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-#4606 := (= uf_11 uf_22)
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-#4650 := (up_6 uf_15 uf_11)
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-#7328 := (up_6 #183 uf_11)
-#7338 := (iff #7328 #7333)
-#3737 := (or #6538 #7338)
-#7327 := (ite #4606 #3681 #4650)
-#7329 := (iff #7328 #7327)
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-#6821 := (iff #3737 #3737)
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-#7339 := (iff #7329 #7338)
-#7336 := (iff #7327 #7333)
-#7330 := (ite #4606 true #4650)
-#7334 := (iff #7330 #7333)
-#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
-#6824 := [mp #6819 #6823]: #3737
-#7083 := [unit-resolution #6824 #4007]: #7338
-#6842 := (not #7328)
-#4795 := (up_6 uf_23 uf_11)
-#4796 := (not #4795)
-#7169 := (iff #4796 #6842)
-#7167 := (iff #4795 #7328)
-#7115 := (iff #7328 #4795)
-#7114 := [symm #7112]: #7113
-#7116 := [monotonicity #7114]: #7115
-#7168 := [symm #7116]: #7167
-#7170 := [monotonicity #7168]: #7169
-#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)
-#6728 := (or #4243 #4798)
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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
-#6829 := (or #7333 #6828)
-#6827 := [def-axiom]: #6829
-#7173 := [unit-resolution #6827 #7172]: #6828
-#6986 := (or #4606 #6984)
-#6989 := (or #7051 #4606 #6984)
-#4604 := (= uf_22 uf_11)
-#6985 := (or #4604 #6984)
-#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
-#7174 := [unit-resolution #6980 #4034]: #6986
-#7175 := [unit-resolution #7174 #7173]: #6984
-#4672 := (* -1::int #4668)
-#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)
-#4714 := (not #4711)
-#4717 := (or #4709 #4714)
-#6326 := (or #4218 #4709 #4714)
-#4707 := (or #4677 #4675)
-#4708 := (not #4707)
-#4710 := (or #4709 #4708)
-#6355 := (or #4218 #4710)
-#6360 := (iff #6355 #6326)
-#6357 := (or #4218 #4717)
-#6354 := (iff #6357 #6326)
-#6359 := [rewrite]: #6354
-#6352 := (iff #6355 #6357)
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-#4715 := (iff #4708 #4714)
-#4712 := (iff #4707 #4711)
-#4713 := [rewrite]: #4712
-#4716 := [monotonicity #4713]: #4715
-#4719 := [monotonicity #4716]: #4718
-#6358 := [monotonicity #4719]: #6352
-#6361 := [trans #6358 #6359]: #6360
-#6356 := [quant-inst]: #6355
-#6362 := [mp #6356 #6361]: #6326
-#7155 := [unit-resolution #6362 #6754]: #4717
-#7156 := [unit-resolution #7155 #7109]: #4714
-#6531 := (or #4711 #6530)
-#6532 := [def-axiom]: #6531
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-#7158 := [hypothesis]: #4645
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-#7745 := [mp #7744 #7749]: #205
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-#3881 := [def-axiom]: #3879
-#7761 := [unit-resolution #3881 #7750]: #4310
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-#3887 := [def-axiom]: #3893
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-#7917 := (or #7878 #2078 #7916)
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-#7876 := [hypothesis]: #7870
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-#7792 := [hypothesis]: #7878
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-#7359 := (or #6838 #7356)
-#7362 := (or #4218 #6838 #7356)
-#7207 := (+ #1268 #7206)
-#7208 := (+ #6830 #7207)
-#7209 := (<= #7208 0::int)
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-#7305 := (not #7304)
-#6831 := (= #6830 #2077)
-#7306 := (or #6831 #7305)
-#7363 := (or #4218 #7306)
-#7343 := (iff #7363 #7362)
-#7365 := (or #4218 #7359)
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-#7354 := (iff #7304 #7351)
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-#7353 := [rewrite]: #7352
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-#7253 := [rewrite]: #7252
-#7268 := (iff #7209 #7267)
-#7265 := (= #7208 #7264)
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-#7269 := [monotonicity #7266]: #7268
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-#7350 := [monotonicity #7254]: #7308
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-#7358 := [monotonicity #7355]: #7357
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-#7361 := [monotonicity #6843 #7358]: #7360
-#7367 := [monotonicity #7361]: #7366
-#7341 := [trans #7367 #7342]: #7343
-#7364 := [quant-inst]: #7363
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-#8361 := [unit-resolution #7344 #6754]: #7359
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-#7200 := (= #7205 0::int)
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-#7274 := (iff #7200 #7273)
-#7257 := (= #7205 #7256)
-#7258 := [rewrite]: #7257
-#7309 := [monotonicity #7258]: #7274
-#7312 := [monotonicity #7254 #7309]: #7311
-#7317 := [trans #7312 #7315]: #7316
-#7323 := [monotonicity #7317]: #7322
-#7301 := [trans #7323 #7325]: #7326
-#7320 := [quant-inst]: #7319
-#7302 := [mp #7320 #7301]: #7318
-#8365 := [unit-resolution #7302 #6758]: #7313
-#7624 := [unit-resolution #8365 #7795 #7789]: #7273
-#8367 := (not #7273)
-#8368 := (or #8367 #7300)
-#8369 := [th-lemma]: #8368
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-#7701 := (>= #7203 0::int)
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-#7613 := (not #7612)
-#7514 := (= uf_22 ?x65!15)
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-#7416 := (up_6 uf_15 ?x65!15)
-#7539 := (or #7416 #7514)
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-#7522 := (iff #7495 #7539)
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-#7508 := (= ?x65!15 uf_22)
-#7509 := (ite #7508 #3681 #7416)
-#7510 := (iff #7495 #7509)
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-#7496 := [monotonicity #7521]: #7538
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-#6955 := [mp #6949 #6954]: #6854
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-#7377 := [def-axiom]: #7376
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-#7667 := [quant-inst]: #7665
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-#7573 := [th-lemma]: #7572
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-#19141 := (>= #19137 0::int)
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-#15400 := (= ?x72!18 #10482)
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-#6888 := (>= #6887 0::int)
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-#6890 := (= #6887 #6889)
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-#5879 := (= #2120 #5874)
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-#15422 := [monotonicity #15419]: #15421
-#17069 := [monotonicity #15422]: #17071
-#17076 := [trans #17069 #17033]: #17071
-#17070 := [quant-inst]: #17041
-#17077 := [mp #17070 #17076]: #17068
-#19567 := [unit-resolution #17077 #4007]: #15420
-#19566 := (iff #2130 #15410)
-#19561 := (iff #15410 #2130)
-#19568 := [monotonicity #13524]: #19561
-#19576 := [symm #19568]: #19566
-#19577 := [mp #19549 #19576]: #15410
-#17132 := (not #15410)
-#17134 := (not #15420)
-#17137 := (or #17134 #17132 #15415)
-#17138 := [def-axiom]: #17137
-#19571 := [unit-resolution #17138 #19577 #19567]: #15415
-#17112 := (not #15415)
-#17133 := (or #17112 #5903 #15400)
-#17128 := [def-axiom]: #17133
-#19546 := [unit-resolution #17128 #19571 #19562]: #15400
-#18949 := [trans #19546 #13347]: #5904
-#19152 := [monotonicity #18949]: #19003
-#19266 := [monotonicity #19152]: #19136
-#19321 := (not #19136)
-#18783 := (or #19321 #19141)
-#19327 := [th-lemma]: #18783
-#19424 := [unit-resolution #19327 #19266]: #19141
-#7076 := (uf_2 #2122)
-#7082 := (uf_4 uf_14 #7076)
-#7096 := (* -1::int #7082)
-#7097 := (+ #177 #7096)
-#7098 := (<= #7097 0::int)
-#19129 := (= #177 #7082)
-#19009 := (= #7082 #177)
-#19025 := (= #7076 uf_22)
-#19026 := (= #7076 #10482)
-#19488 := (= #7076 ?x72!18)
-#7077 := (= ?x72!18 #7076)
-#18938 := (or #8415 #7077)
-#18939 := [quant-inst]: #18938
-#19425 := [unit-resolution #18939 #3993]: #7077
-#19489 := [symm #19425]: #19488
-#19027 := [trans #19489 #19546]: #19026
-#19116 := [trans #19027 #13347]: #19025
-#19117 := [monotonicity #19116]: #19009
-#19124 := [symm #19117]: #19129
-#19125 := (not #19129)
-#19118 := (or #19125 #7098)
-#19126 := [th-lemma]: #19118
-#19494 := [unit-resolution #19126 #19124]: #7098
-#18959 := (+ #5874 #7096)
-#18942 := (>= #18959 0::int)
-#18958 := (= #5874 #7082)
-#19503 := [monotonicity #19425]: #18958
-#19714 := (not #18958)
-#19715 := (or #19714 #18942)
-#19716 := [th-lemma]: #19715
-#19717 := [unit-resolution #19716 #19503]: #18942
-#19840 := (not #19141)
-#19719 := (not #18942)
-#19718 := (not #7098)
-#19720 := (or #18852 #19579 #2710 #19718 #19719 #19578 #19840)
-#19721 := [th-lemma]: #19720
-#19722 := [unit-resolution #19721 #19541 #19557 #19548 #19717 #19494 #19424]: #18852
-#6920 := (+ uf_9 #6916)
-#6921 := (<= #6920 0::int)
-#18850 := (not #6921)
-#19841 := (or #18850 #19840 #2128)
-#19836 := [hypothesis]: #2129
-#19837 := [hypothesis]: #6921
-#19838 := [hypothesis]: #19141
-#19839 := [th-lemma #19838 #19837 #19836]: false
-#19842 := [lemma #19839]: #19841
-#19748 := [unit-resolution #19842 #19424 #19575]: #18850
-#6937 := (+ #2119 #6912)
-#6938 := (+ #177 #6937)
-#6941 := (= #6938 0::int)
-#19752 := (not #6941)
-#18700 := (>= #6938 0::int)
-#19749 := (not #18700)
-#19750 := (or #19749 #2710 #19718 #19719 #19578 #19840)
-#19746 := [th-lemma]: #19750
-#19747 := [unit-resolution #19746 #19557 #19548 #19717 #19494 #19424]: #19749
-#19753 := (or #19752 #18700)
-#19754 := [th-lemma]: #19753
-#19751 := [unit-resolution #19754 #19747]: #19752
-#6944 := (or #6921 #6932 #6941)
-#18751 := (or #4226 #6921 #6932 #6941)
-#6913 := (+ #6912 #2119)
-#6914 := (+ #177 #6913)
-#6915 := (= #6914 0::int)
-#6917 := (+ #1268 #6916)
-#6918 := (+ #6865 #6917)
-#6919 := (<= #6918 0::int)
-#6922 := (or #6921 #6919 #6915)
-#18752 := (or #4226 #6922)
-#18697 := (iff #18752 #18751)
-#18811 := (or #4226 #6944)
-#18691 := (iff #18811 #18751)
-#18696 := [rewrite]: #18691
-#18695 := (iff #18752 #18811)
-#6945 := (iff #6922 #6944)
-#6942 := (iff #6915 #6941)
-#6939 := (= #6914 #6938)
-#6940 := [rewrite]: #6939
-#6943 := [monotonicity #6940]: #6942
-#6935 := (iff #6919 #6932)
-#6923 := (+ #6865 #6916)
-#6924 := (+ #1268 #6923)
-#6927 := (<= #6924 0::int)
-#6933 := (iff #6927 #6932)
-#6934 := [rewrite]: #6933
-#6928 := (iff #6919 #6927)
-#6925 := (= #6918 #6924)
-#6926 := [rewrite]: #6925
-#6929 := [monotonicity #6926]: #6928
-#6936 := [trans #6929 #6934]: #6935
-#6946 := [monotonicity #6936 #6943]: #6945
-#18690 := [monotonicity #6946]: #18695
-#18694 := [trans #18690 #18696]: #18697
-#18816 := [quant-inst]: #18752
-#18698 := [mp #18816 #18694]: #18751
-#19755 := [unit-resolution #18698 #10825]: #6944
-#19756 := [unit-resolution #19755 #19751 #19748 #19722]: false
-#19782 := [lemma #19756]: #3281
-#3808 := (or #4289 #3286 #4283)
-#3809 := [def-axiom]: #3808
-#27204 := [unit-resolution #3809 #19782]: #27203
-#27205 := [unit-resolution #27204 #27202]: #4283
-#3913 := (or #4280 #2160)
-#3911 := [def-axiom]: #3913
-#27206 := [unit-resolution #3911 #27205]: #2160
-#5592 := (+ #2147 #5591)
-#18461 := (>= #5592 0::int)
-#5566 := (= #2147 #5561)
-#3757 := (or #4280 #4272)
-#3905 := [def-axiom]: #3757
-#27207 := [unit-resolution #3905 #27205]: #4272
-#18570 := (or #5566 #4277)
-#15060 := (uf_10 #15059)
-#15086 := (* -1::int #15060)
-#11725 := (uf_24 #10482)
-#11723 := (* -1::int #11725)
-#15087 := (+ #11723 #15086)
-#15088 := (+ #2147 #15087)
-#15741 := (>= #15088 0::int)
-#5607 := (uf_1 uf_22 ?x75!20)
-#5608 := (uf_10 #5607)
-#15832 := (+ #5608 #15086)
-#15834 := (>= #15832 0::int)
-#15831 := (= #5608 #15060)
-#18427 := (= #15060 #5608)
-#18425 := (= #15059 #5607)
-#18426 := [monotonicity #13347]: #18425
-#18428 := [monotonicity #18426]: #18427
-#18429 := [symm #18428]: #15831
-#18424 := (not #15831)
-#18430 := (or #18424 #15834)
-#18431 := [th-lemma]: #18430
-#18432 := [unit-resolution #18431 #18429]: #15834
-#11677 := (+ #4526 #11723)
-#8662 := (>= #11677 0::int)
-#8604 := (= #4526 #11725)
-#18433 := (= #11725 #4526)
-#18434 := [monotonicity #13347]: #18433
-#18441 := [symm #18434]: #8604
-#18442 := (not #8604)
-#18440 := (or #18442 #8662)
-#18443 := [th-lemma]: #18440
-#18444 := [unit-resolution #18443 #18441]: #8662
-#5633 := (+ #2148 #5608)
-#5634 := (+ #177 #5633)
-#15560 := (<= #5634 0::int)
-#5637 := (= #5634 0::int)
-#5612 := (* -1::int #5608)
-#5616 := (+ uf_9 #5612)
-#5617 := (<= #5616 0::int)
-#15577 := (not #5617)
-#5626 := (+ #5591 #5608)
-#5627 := (+ #177 #5626)
-#5628 := (>= #5627 0::int)
-#5659 := (or #5617 #5628)
-#5662 := (not #5659)
-#18518 := (not #5566)
-#18445 := [hypothesis]: #18518
-#5665 := (or #5566 #5662)
-#15564 := (or #4218 #5566 #5662)
-#5613 := (+ #1268 #5612)
-#5614 := (+ #5561 #5613)
-#5615 := (<= #5614 0::int)
-#5656 := (or #5617 #5615)
-#5657 := (not #5656)
-#5562 := (= #5561 #2147)
-#5658 := (or #5562 #5657)
-#15565 := (or #4218 #5658)
-#15574 := (iff #15565 #15564)
-#15567 := (or #4218 #5665)
-#15570 := (iff #15567 #15564)
-#15571 := [rewrite]: #15570
-#15568 := (iff #15565 #15567)
-#5666 := (iff #5658 #5665)
-#5663 := (iff #5657 #5662)
-#5660 := (iff #5656 #5659)
-#5631 := (iff #5615 #5628)
-#5619 := (+ #5561 #5612)
-#5620 := (+ #1268 #5619)
-#5623 := (<= #5620 0::int)
-#5629 := (iff #5623 #5628)
-#5630 := [rewrite]: #5629
-#5624 := (iff #5615 #5623)
-#5621 := (= #5614 #5620)
-#5622 := [rewrite]: #5621
-#5625 := [monotonicity #5622]: #5624
-#5632 := [trans #5625 #5630]: #5631
-#5661 := [monotonicity #5632]: #5660
-#5664 := [monotonicity #5661]: #5663
-#5567 := (iff #5562 #5566)
-#5568 := [rewrite]: #5567
-#5667 := [monotonicity #5568 #5664]: #5666
-#15569 := [monotonicity #5667]: #15568
-#15575 := [trans #15569 #15571]: #15574
-#15566 := [quant-inst]: #15565
-#15576 := [mp #15566 #15575]: #15564
-#18449 := [unit-resolution #15576 #10373]: #5665
-#18450 := [unit-resolution #18449 #18445]: #5662
-#15578 := (or #5659 #15577)
-#15608 := [def-axiom]: #15578
-#18453 := [unit-resolution #15608 #18450]: #15577
-#15724 := (not #5628)
-#15725 := (or #5659 #15724)
-#15726 := [def-axiom]: #15725
-#18454 := [unit-resolution #15726 #18450]: #15724
-#5640 := (or #5617 #5628 #5637)
-#15352 := (or #4226 #5617 #5628 #5637)
-#5609 := (+ #5608 #2148)
-#5610 := (+ #177 #5609)
-#5611 := (= #5610 0::int)
-#5618 := (or #5617 #5615 #5611)
-#15353 := (or #4226 #5618)
-#15526 := (iff #15353 #15352)
-#15377 := (or #4226 #5640)
-#15505 := (iff #15377 #15352)
-#15506 := [rewrite]: #15505
-#15408 := (iff #15353 #15377)
-#5641 := (iff #5618 #5640)
-#5638 := (iff #5611 #5637)
-#5635 := (= #5610 #5634)
-#5636 := [rewrite]: #5635
-#5639 := [monotonicity #5636]: #5638
-#5642 := [monotonicity #5632 #5639]: #5641
-#15409 := [monotonicity #5642]: #15408
-#15549 := [trans #15409 #15506]: #15526
-#15376 := [quant-inst]: #15353
-#15550 := [mp #15376 #15549]: #15352
-#18490 := [unit-resolution #15550 #10825]: #5640
-#18491 := [unit-resolution #18490 #18454 #18453]: #5637
-#18492 := (not #5637)
-#18493 := (or #18492 #15560)
-#18494 := [th-lemma]: #18493
-#18495 := [unit-resolution #18494 #18491]: #15560
-#18499 := (not #15834)
-#18498 := (not #4769)
-#18497 := (not #8662)
-#18496 := (not #15560)
-#18500 := (or #15741 #18496 #18497 #18498 #18499)
-#18501 := [th-lemma]: #18500
-#18502 := [unit-resolution #18501 #18495 #18444 #10836 #18432]: #15741
-#15740 := (<= #15088 0::int)
-#15833 := (<= #15832 0::int)
-#18503 := (or #18424 #15833)
-#18504 := [th-lemma]: #18503
-#18505 := [unit-resolution #18504 #18429]: #15833
-#9287 := (<= #4768 0::int)
-#4527 := (= #177 #4526)
-#4776 := (up_6 uf_23 uf_22)
-#3683 := (up_6 #183 uf_22)
-#10821 := (iff #3683 #4776)
-#10819 := (iff #4776 #3683)
-#10820 := [monotonicity #10380]: #10819
-#10822 := [symm #10820]: #10821
-#46 := (:var 0 T5)
-#45 := (:var 2 T4)
-#47 := (uf_7 #45 #10 #46)
-#4016 := (pattern #47)
-#321 := (= uf_8 #46)
-#48 := (up_6 #47 #10)
-#325 := (iff #48 #321)
-#4017 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) (:pat #4016) #325)
-#328 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) #325)
-#4020 := (iff #328 #4017)
-#4018 := (iff #325 #325)
-#4019 := [refl]: #4018
-#4021 := [quant-intro #4019]: #4020
-#1650 := (~ #328 #328)
-#1688 := (~ #325 #325)
-#1689 := [refl]: #1688
-#1651 := [nnf-pos #1689]: #1650
-#49 := (= #46 uf_8)
-#50 := (iff #48 #49)
-#51 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) #50)
-#329 := (iff #51 #328)
-#326 := (iff #50 #325)
-#323 := (iff #49 #321)
-#324 := [rewrite]: #323
-#327 := [monotonicity #324]: #326
-#330 := [quant-intro #327]: #329
-#320 := [asserted]: #51
-#333 := [mp #320 #330]: #328
-#1690 := [mp~ #333 #1651]: #328
-#4022 := [mp #1690 #4021]: #4017
-#8841 := (not #4017)
-#8843 := (or #8841 #3683)
-#3682 := (iff #3683 #3681)
-#8837 := (or #8841 #3682)
-#8844 := (iff #8837 #8843)
-#8846 := (iff #8843 #8843)
-#8847 := [rewrite]: #8846
-#3668 := (iff #3682 #3683)
-#3674 := (iff #3683 true)
-#3676 := (iff #3674 #3683)
-#3677 := [rewrite]: #3676
-#3675 := (iff #3682 #3674)
-#3667 := [monotonicity #3673]: #3675
-#3678 := [trans #3667 #3677]: #3668
-#8845 := [monotonicity #3678]: #8844
-#8842 := [trans #8845 #8847]: #8844
-#8838 := [quant-inst]: #8837
-#9410 := [mp #8838 #8842]: #8843
-#10818 := [unit-resolution #9410 #4022]: #3683
-#10823 := [mp #10818 #10822]: #4776
-#4777 := (not #4776)
-#4781 := (or #4527 #4777)
-#10191 := (or #4243 #4527 #4777)
-#4780 := (or #4777 #4527)
-#10192 := (or #4243 #4780)
-#10250 := (iff #10192 #10191)
-#10193 := (or #4243 #4781)
-#10248 := (iff #10193 #10191)
-#10249 := [rewrite]: #10248
-#10194 := (iff #10192 #10193)
-#4782 := (iff #4780 #4781)
-#4783 := [rewrite]: #4782
-#10247 := [monotonicity #4783]: #10194
-#10252 := [trans #10247 #10249]: #10250
-#10190 := [quant-inst]: #10192
-#10253 := [mp #10190 #10252]: #10191
-#10832 := [unit-resolution #10253 #10831]: #4781
-#10833 := [unit-resolution #10832 #10823]: #4527
-#9343 := (not #4527)
-#9344 := (or #9343 #9287)
-#9345 := [th-lemma]: #9344
-#10834 := [unit-resolution #9345 #10833]: #9287
-#11672 := (<= #11677 0::int)
-#18506 := (or #18442 #11672)
-#18507 := [th-lemma]: #18506
-#18508 := [unit-resolution #18507 #18441]: #11672
-#15561 := (>= #5634 0::int)
-#18482 := (or #18492 #15561)
-#18483 := [th-lemma]: #18482
-#18481 := [unit-resolution #18483 #18491]: #15561
-#18487 := (not #15833)
-#18486 := (not #9287)
-#18485 := (not #11672)
-#18484 := (not #15561)
-#18488 := (or #15740 #18484 #18485 #18486 #18487)
-#18489 := [th-lemma]: #18488
-#17776 := [unit-resolution #18489 #18481 #18508 #10834 #18505]: #15740
-#15089 := (= #15088 0::int)
-#15094 := (not #15089)
-#14996 := (+ #2147 #11723)
-#15074 := (<= #14996 0::int)
-#18551 := (not #15074)
-#17160 := (uf_3 #5828)
-#17947 := (uf_1 #10482 #17160)
-#17948 := (uf_10 #17947)
-#17950 := (* -1::int #17948)
-#18119 := (+ #5608 #17950)
-#18161 := (>= #18119 0::int)
-#18116 := (= #5608 #17948)
-#17971 := (= #17948 #5608)
-#17965 := (= #17947 #5607)
-#17826 := (= #17160 ?x75!20)
-#17161 := (= ?x75!20 #17160)
-#17164 := (or #7756 #17161)
-#17165 := [quant-inst]: #17164
-#17777 := [unit-resolution #17165 #3987]: #17161
-#17827 := [symm #17777]: #17826
-#17970 := [monotonicity #13347 #17827]: #17965
-#17974 := [monotonicity #17970]: #17971
-#17975 := [symm #17974]: #18116
-#17976 := (not #18116)
-#17979 := (or #17976 #18161)
-#18037 := [th-lemma]: #17979
-#18038 := [unit-resolution #18037 #17975]: #18161
-#18048 := (<= #17948 0::int)
-#18049 := (not #18048)
-#18467 := (= #10482 #17160)
-#17898 := (not #18467)
-#18462 := (up_6 uf_15 #17160)
-#18473 := (or #18462 #18467)
-#17926 := (not #18473)
-#18465 := (up_6 #11444 #17160)
-#18478 := (iff #18465 #18473)
-#17873 := (or #6538 #18478)
-#18463 := (= #17160 #10482)
-#18464 := (ite #18463 #3681 #18462)
-#18466 := (iff #18465 #18464)
-#17874 := (or #6538 #18466)
-#17876 := (iff #17874 #17873)
-#17892 := (iff #17873 #17873)
-#17893 := [rewrite]: #17892
-#18479 := (iff #18466 #18478)
-#18476 := (iff #18464 #18473)
-#18470 := (ite #18467 true #18462)
-#18474 := (iff #18470 #18473)
-#18475 := [rewrite]: #18474
-#18471 := (iff #18464 #18470)
-#18468 := (iff #18463 #18467)
-#18469 := [rewrite]: #18468
-#18472 := [monotonicity #18469 #3673]: #18471
-#18477 := [trans #18472 #18475]: #18476
-#18480 := [monotonicity #18477]: #18479
-#17891 := [monotonicity #18480]: #17876
-#17894 := [trans #17891 #17893]: #17876
-#17875 := [quant-inst]: #17874
-#17895 := [mp #17875 #17894]: #17873
-#18337 := [unit-resolution #17895 #4007]: #18478
-#17931 := (not #18465)
-#4948 := (up_6 uf_23 ?x75!20)
-#4949 := (not #4948)
-#18452 := (iff #4949 #17931)
-#18352 := (iff #4948 #18465)
-#18341 := (iff #18465 #4948)
-#18342 := [monotonicity #13524 #17827]: #18341
-#18451 := [symm #18342]: #18352
-#18455 := [monotonicity #18451]: #18452
-#5569 := (or #4949 #5566)
-#14917 := (or #4243 #4949 #5566)
-#5565 := (or #4949 #5562)
-#14918 := (or #4243 #5565)
-#15338 := (iff #14918 #14917)
-#15153 := (or #4243 #5569)
-#15201 := (iff #15153 #14917)
-#15202 := [rewrite]: #15201
-#15162 := (iff #14918 #15153)
-#5570 := (iff #5565 #5569)
-#5571 := [monotonicity #5568]: #5570
-#15163 := [monotonicity #5571]: #15162
-#15339 := [trans #15163 #15202]: #15338
-#15152 := [quant-inst]: #14918
-#15340 := [mp #15152 #15339]: #14917
-#18516 := [unit-resolution #15340 #10831]: #5569
-#18338 := [unit-resolution #18516 #18445]: #4949
-#18456 := [mp #18338 #18455]: #17931
-#17929 := (not #18478)
-#17930 := (or #17929 #18465 #17926)
-#17925 := [def-axiom]: #17930
-#18457 := [unit-resolution #17925 #18456 #18337]: #17926
-#17899 := (or #18473 #17898)
-#17900 := [def-axiom]: #17899
-#18460 := [unit-resolution #17900 #18457]: #17898
-#18064 := (or #18049 #18467)
-#18066 := (or #7051 #18049 #18467)
-#18063 := (or #18467 #18049)
-#18067 := (or #7051 #18063)
-#18081 := (iff #18067 #18066)
-#18073 := (or #7051 #18064)
-#18075 := (iff #18073 #18066)
-#18076 := [rewrite]: #18075
-#18071 := (iff #18067 #18073)
-#18062 := (iff #18063 #18064)
-#18065 := [rewrite]: #18062
-#18074 := [monotonicity #18065]: #18071
-#18082 := [trans #18074 #18076]: #18081
-#18072 := [quant-inst]: #18067
-#18080 := [mp #18072 #18082]: #18066
-#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
-#17020 := [monotonicity #17017]: #17019
-#17025 := [trans #17020 #17023]: #17024
-#17028 := [monotonicity #17025]: #17027
-#17014 := (iff #17002 #17011)
-#17004 := (+ #2148 #16798)
-#17007 := (>= #17004 0::int)
-#17012 := (iff #17007 #17011)
-#17013 := [rewrite]: #17012
-#17008 := (iff #17002 #17007)
-#17005 := (= #16962 #17004)
-#17006 := [rewrite]: #17005
-#17009 := [monotonicity #17006]: #17008
-#17015 := [trans #17009 #17013]: #17014
-#17031 := [monotonicity #17015 #17028]: #17030
-#20025 := [monotonicity #17031]: #20138
-#20123 := [trans #20025 #19874]: #19850
-#19878 := [quant-inst]: #19880
-#19916 := [mp #19878 #20123]: #19879
-#23081 := [unit-resolution #19916 #27207]: #17029
-[unit-resolution #23081 #23182 #18055 #27235]: false
+#2137 := (not #1319)
+#2138 := (~ #2137 #2136)
+#2133 := (not #1316)
+#2134 := (~ #2133 #2132)
+#2129 := (not #1313)
+#2130 := (~ #2129 #2128)
+#2125 := (not #1308)
+#2126 := (~ #2125 #2124)
+#2121 := (not #1300)
+#2122 := (~ #2121 #1297)
+#2119 := (~ #1297 #1297)
+#2117 := (~ #1294 #1294)
+#2118 := [refl]: #2117
+#2120 := [nnf-pos #2118]: #2119
+#2123 := [nnf-neg #2120]: #2122
+#2115 := (~ #2114 #2114)
+#2116 := [refl]: #2115
+#2127 := [nnf-neg #2116 #2123]: #2126
+#2110 := (~ #1300 #2109)
+#2111 := [sk]: #2110
+#2131 := [nnf-neg #2111 #2127]: #2130
+#2085 := (not #1282)
+#2086 := (~ #2085 #2082)
+#2083 := (~ #1279 #2082)
+#2080 := (~ #1276 #2079)
+#2075 := (~ #1273 #2074)
+#2076 := [sk]: #2075
+#2063 := (~ #1257 #1257)
+#2064 := [refl]: #2063
+#2081 := [monotonicity #2064 #2076]: #2080
+#2084 := [nnf-pos #2081]: #2083
+#2087 := [nnf-neg #2084]: #2086
+#2135 := [nnf-neg #2087 #2131]: #2134
+#2061 := (~ #1282 #2058)
+#2036 := (exists (vars (?v1 S2)) #2035)
+#2044 := (or #2043 #2036)
+#2045 := (not #2044)
+#2059 := (~ #2045 #2058)
+#2055 := (not #2036)
+#2056 := (~ #2055 #2054)
+#2052 := (~ #2051 #2051)
+#2053 := [refl]: #2052
+#2057 := [nnf-neg #2053]: #2056
+#2049 := (~ #2048 #2048)
+#2050 := [refl]: #2049
+#2060 := [nnf-neg #2050 #2057]: #2059
+#2046 := (~ #1282 #2045)
+#2047 := [sk]: #2046
+#2062 := [trans #2047 #2060]: #2061
+#2139 := [nnf-neg #2062 #2135]: #2138
+#2023 := (~ #2022 #2022)
+#2024 := [refl]: #2023
+#2020 := (~ #2019 #2019)
+#2021 := [refl]: #2020
+#2017 := (~ #2016 #2016)
+#2018 := [refl]: #2017
+#2014 := (~ #2013 #2013)
+#2015 := [refl]: #2014
+#2149 := [nnf-neg #2015 #2018 #2021 #2024 #2139 #2145]: #2148
+#2405 := [nnf-neg #2149 #2401]: #2404
+#2010 := (not #1245)
+#2011 := (~ #2010 #2007)
+#2008 := (~ #1242 #2007)
+#2005 := (~ #1239 #2004)
+#2000 := (~ #1236 #1999)
+#2001 := [sk]: #2000
+#1986 := (~ #1212 #1212)
+#1987 := [refl]: #1986
+#2006 := [monotonicity #1987 #2001]: #2005
+#2009 := [nnf-pos #2006]: #2008
+#2012 := [nnf-neg #2009]: #2011
+#1983 := (not #1656)
+#1984 := (~ #1983 #1980)
+#1981 := (~ #1200 #1980)
+#1978 := (~ #1197 #1977)
+#1973 := (~ #1194 #1972)
+#1974 := [sk]: #1973
+#1958 := (~ #1174 #1174)
+#1959 := [refl]: #1958
+#1979 := [monotonicity #1959 #1974]: #1978
+#1982 := [nnf-pos #1979]: #1981
+#1985 := [nnf-neg #1982]: #1984
+#1956 := (~ #1955 #1955)
+#1957 := [refl]: #1956
+#2430 := [nnf-neg #1957 #1985 #2012 #2405 #2412 #2419 #2426]: #2429
+#1953 := (~ #1656 #1950)
+#1928 := (exists (vars (?v1 S2)) #1927)
+#1936 := (or #1935 #1928)
+#1937 := (not #1936)
+#1951 := (~ #1937 #1950)
+#1947 := (not #1928)
+#1948 := (~ #1947 #1946)
+#1944 := (~ #1943 #1943)
+#1945 := [refl]: #1944
+#1949 := [nnf-neg #1945]: #1948
+#1941 := (~ #1940 #1940)
+#1942 := [refl]: #1941
+#1952 := [nnf-neg #1942 #1949]: #1951
+#1938 := (~ #1656 #1937)
+#1939 := [sk]: #1938
+#1954 := [trans #1939 #1952]: #1953
+#2434 := [nnf-neg #1954 #2430]: #2433
+#1913 := (not #1162)
+#1914 := (~ #1913 #1159)
+#1911 := (~ #1159 #1159)
+#1909 := (~ #1156 #1156)
+#1910 := [refl]: #1909
+#1912 := [nnf-pos #1910]: #1911
+#1915 := [nnf-neg #1912]: #1914
+#2438 := [nnf-neg #1915 #2434]: #2437
+#1905 := (~ #1162 #1904)
+#1906 := [sk]: #1905
+#2442 := [nnf-neg #1906 #2438]: #2441
+#1882 := (not #1131)
+#1883 := (~ #1882 #1128)
+#1880 := (~ #1128 #1128)
+#1878 := (~ #1123 #1123)
+#1879 := [refl]: #1878
+#1881 := [nnf-pos #1879]: #1880
+#1884 := [nnf-neg #1881]: #1883
+#2446 := [nnf-neg #1884 #2442]: #2445
+#1874 := (~ #1131 #1873)
+#1875 := [sk]: #1874
+#2450 := [nnf-neg #1875 #2446]: #2449
+#1855 := (not #1111)
+#1856 := (~ #1855 #1108)
+#1853 := (~ #1108 #1108)
+#1851 := (~ #1107 #1107)
+#1852 := [refl]: #1851
+#1854 := [nnf-pos #1852]: #1853
+#1857 := [nnf-neg #1854]: #1856
+#2454 := [nnf-neg #1857 #2450]: #2453
+#1847 := (~ #1111 #1846)
+#1848 := [sk]: #1847
+#2458 := [nnf-neg #1848 #2454]: #2457
+#1815 := (~ #1814 #1814)
+#1842 := [refl]: #1815
+#2462 := [nnf-neg #1842 #2458]: #2461
+#1840 := (~ #1102 #1102)
+#1841 := [refl]: #1840
+#2465 := [nnf-neg #1841 #2462]: #2464
+#1743 := [not-or-elim #1739]: #1742
+#2466 := [mp~ #1743 #2465]: #2463
+#2467 := [mp #2466 #3004]: #3002
+#3661 := [mp #2467 #3660]: #3658
+#4534 := [mp #3661 #4533]: #4531
+#6983 := [unit-resolution #4534 #4636]: #4528
+#3907 := (or #4525 #4519)
+#3908 := [def-axiom]: #3907
+#6984 := [unit-resolution #3908 #6983]: #4519
+#290 := (<= f3 0::int)
+#291 := (not #290)
+#10 := (< 0::int f3)
+#292 := (iff #10 #291)
+#293 := [rewrite]: #292
+#287 := [asserted]: #10
+#294 := [mp #287 #293]: #291
+#4697 := (* -1::int #1844)
+#4698 := (+ f3 #4697)
+#4699 := (<= #4698 0::int)
+#4625 := (= f3 #1844)
+#4628 := (= f6 ?v0!0)
+#4703 := (not #4628)
+#4695 := (= #1844 0::int)
+#4845 := (not #4695)
+#4844 := [hypothesis]: #1846
+#4846 := (or #4845 #1845)
+#4847 := [th-lemma]: #4846
+#4848 := [unit-resolution #4847 #4844]: #4845
+#4770 := (or #4588 #4703 #4695)
+#4626 := (= ?v0!0 f6)
+#4701 := (not #4626)
+#4702 := (or #4701 #4695)
+#4753 := (or #4588 #4702)
+#4759 := (iff #4753 #4770)
+#4720 := (or #4703 #4695)
+#4755 := (or #4588 #4720)
+#4752 := (iff #4755 #4770)
+#4758 := [rewrite]: #4752
+#4756 := (iff #4753 #4755)
+#4721 := (iff #4702 #4720)
+#4704 := (iff #4701 #4703)
+#4629 := (iff #4626 #4628)
+#4647 := [rewrite]: #4629
+#4705 := [monotonicity #4647]: #4704
+#4769 := [monotonicity #4705]: #4721
+#4757 := [monotonicity #4769]: #4756
+#4760 := [trans #4757 #4758]: #4759
+#4754 := [quant-inst]: #4753
+#4761 := [mp #4754 #4760]: #4770
+#4849 := [unit-resolution #4761 #4540 #4848]: #4703
+#4651 := (or #4625 #4628)
+#4149 := (forall (vars (?v0 S2)) (:pat #4148) #360)
+#4152 := (iff #365 #4149)
+#4150 := (iff #360 #360)
+#4151 := [refl]: #4150
+#4153 := [quant-intro #4151]: #4152
+#1810 := (~ #365 #365)
+#1834 := (~ #360 #360)
+#1835 := [refl]: #1834
+#1811 := [nnf-pos #1835]: #1810
+#1740 := [not-or-elim #1739]: #365
+#1836 := [mp~ #1740 #1811]: #365
+#4154 := [mp #1836 #4153]: #4149
+#4655 := (not #4149)
+#4656 := (or #4655 #4625 #4628)
+#4627 := (or #4626 #4625)
+#4708 := (or #4655 #4627)
+#4715 := (iff #4708 #4656)
+#4710 := (or #4655 #4651)
+#4713 := (iff #4710 #4656)
+#4714 := [rewrite]: #4713
+#4711 := (iff #4708 #4710)
+#4653 := (iff #4627 #4651)
+#4648 := (or #4628 #4625)
+#4646 := (iff #4648 #4651)
+#4652 := [rewrite]: #4646
+#4649 := (iff #4627 #4648)
+#4650 := [monotonicity #4647]: #4649
+#4654 := [trans #4650 #4652]: #4653
+#4712 := [monotonicity #4654]: #4711
+#4716 := [trans #4712 #4714]: #4715
+#4709 := [quant-inst]: #4708
+#4696 := [mp #4709 #4716]: #4656
+#4853 := [unit-resolution #4696 #4154]: #4651
+#4854 := [unit-resolution #4853 #4849]: #4625
+#4901 := (not #4625)
+#4902 := (or #4901 #4699)
+#4903 := [th-lemma]: #4902
+#4904 := [unit-resolution #4903 #4854]: #4699
+#4762 := (<= #1844 0::int)
+#4905 := (or #4762 #1845)
+#4900 := [th-lemma]: #4905
+#4906 := [unit-resolution #4900 #4844]: #4762
+#4907 := [th-lemma #4906 #4904 #294]: false
+#4908 := [lemma #4907]: #1845
+#3902 := (or #4522 #1846 #4516)
+#3903 := [def-axiom]: #3902
+#6955 := [unit-resolution #3903 #4908 #6984]: #4516
+#3926 := (or #4513 #4507)
+#3927 := [def-axiom]: #3926
+#6985 := [unit-resolution #3927 #6955]: #4507
+#5112 := [hypothesis]: #1866
+#4156 := (forall (vars (?v0 S2)) (:pat #4155) #371)
+#4159 := (iff #374 #4156)
+#4157 := (iff #371 #371)
+#4158 := [refl]: #4157
+#4160 := [quant-intro #4158]: #4159
+#1812 := (~ #374 #374)
+#1837 := (~ #371 #371)
+#1838 := [refl]: #1837
+#1813 := [nnf-pos #1838]: #1812
+#1741 := [not-or-elim #1739]: #374
+#1839 := [mp~ #1741 #1813]: #374
+#4161 := [mp #1839 #4160]: #4156
+#3899 := (not #4156)
+#4942 := (or #3899 #2112)
+#4943 := [quant-inst]: #4942
+#5113 := [unit-resolution #4943 #4161 #5112]: false
+#5125 := [lemma #5113]: #2112
+#3719 := (or #3011 #1866)
+#3806 := [def-axiom]: #3719
+#6986 := [unit-resolution #3806 #5125]: #3011
+#3920 := (or #4510 #3016 #4504)
+#3922 := [def-axiom]: #3920
+#6981 := [unit-resolution #3922 #6986 #6985]: #4504
+#3947 := (or #4501 #4495)
+#3948 := [def-axiom]: #3947
+#6987 := [unit-resolution #3948 #6981]: #4495
+#6988 := (or #4498 #4492)
+#4583 := [hypothesis]: #1894
+#3900 := (or #3899 #3042)
+#3898 := [quant-inst]: #3900
+#4584 := [unit-resolution #3898 #4161 #4583]: false
+#4592 := [lemma #4584]: #3042
+#3809 := (or #3057 #1894)
+#3813 := [def-axiom]: #3809
+#6954 := [unit-resolution #3813 #4592]: #3057
+#3943 := (or #4498 #3062 #4492)
+#3944 := [def-axiom]: #3943
+#6989 := [unit-resolution #3944 #6954]: #6988
+#6990 := [unit-resolution #6989 #6987]: #4492
+#3957 := (or #4489 #4483)
+#3978 := [def-axiom]: #3957
+#6991 := [unit-resolution #3978 #6990]: #4483
+#5069 := (= f3 #1919)
+#5212 := (not #5069)
+#5185 := [hypothesis]: #4200
+#4123 := (or #4197 #1931)
+#3797 := [def-axiom]: #4123
+#5190 := [unit-resolution #3797 #5185]: #1931
+#5213 := (or #5212 #1930)
+#5178 := [th-lemma]: #5213
+#5214 := [unit-resolution #5178 #5190]: #5212
+#3798 := (or #4197 #2518)
+#4130 := [def-axiom]: #3798
+#5215 := [unit-resolution #4130 #5185]: #2518
+#5107 := (or #4655 #2515 #5069)
+#5070 := (or #1932 #5069)
+#5094 := (or #4655 #5070)
+#4988 := (iff #5094 #5107)
+#5096 := (or #2515 #5069)
+#5103 := (or #4655 #5096)
+#5110 := (iff #5103 #5107)
+#4987 := [rewrite]: #5110
+#5104 := (iff #5094 #5103)
+#5105 := (iff #5070 #5096)
+#5106 := [monotonicity #2517]: #5105
+#5109 := [monotonicity #5106]: #5104
+#4989 := [trans #5109 #4987]: #4988
+#5108 := [quant-inst]: #5094
+#5008 := [mp #5108 #4989]: #5107
+#5216 := [unit-resolution #5008 #4154 #5215 #5214]: false
+#5211 := [lemma #5216]: #4197
+#3965 := (or #4486 #4200 #4480)
+#3966 := [def-axiom]: #3965
+#6995 := [unit-resolution #3966 #5211 #6991]: #4480
+#3987 := (or #4477 #4471)
+#3955 := [def-axiom]: #3987
+#9540 := [unit-resolution #3955 #6995]: #4471
+#6497 := [hypothesis]: #4313
+#4098 := (or #4310 #538)
+#4099 := [def-axiom]: #4098
+#6498 := [unit-resolution #4099 #6497]: #538
+#4100 := (or #4310 #4304)
+#4097 := [def-axiom]: #4100
+#6538 := [unit-resolution #4097 #6497]: #4304
+#3996 := (or #4477 #67)
+#3997 := [def-axiom]: #3996
+#6994 := [unit-resolution #3997 #6995]: #67
+#6569 := (= #124 #66)
+#6495 := [symm #6498]: #105
+#6570 := [monotonicity #6495]: #6569
+#6364 := [trans #6570 #6994]: #125
+#4110 := (or #4286 #2114)
+#3773 := [def-axiom]: #4110
+#6366 := [unit-resolution #3773 #6364]: #4286
+#3814 := (or #4310 #4246)
+#4096 := [def-axiom]: #3814
+#6387 := [unit-resolution #4096 #6497]: #4246
+#8856 := (or #3325 #4251 #629)
+#8080 := (f9 f10 ?v1!10)
+#8078 := (* -1::int #8080)
+#8081 := (+ f3 #8078)
+#8135 := (<= #8081 0::int)
+#9265 := (not #8135)
+#8756 := [hypothesis]: #3330
+#4113 := (or #3325 #2101)
+#4114 := [def-axiom]: #4113
+#8751 := [unit-resolution #4114 #8756]: #2101
+#8701 := (+ #2092 #8078)
+#8703 := (>= #8701 0::int)
+#8700 := (= #2092 #8080)
+#8757 := (= #8080 #2092)
+#8129 := [hypothesis]: #538
+#8758 := [monotonicity #8129]: #8757
+#8759 := [symm #8758]: #8700
+#8760 := (not #8700)
+#8761 := (or #8760 #8703)
+#8744 := [th-lemma]: #8761
+#8745 := [unit-resolution #8744 #8759]: #8703
+#9266 := (not #8703)
+#9310 := (or #9265 #9266 #2100)
+#9256 := [hypothesis]: #2101
+#9262 := [hypothesis]: #8703
+#9263 := [hypothesis]: #8135
+#9264 := [th-lemma #9263 #9262 #9256]: false
+#9311 := [lemma #9264]: #9310
+#8740 := [unit-resolution #9311 #8745 #8751]: #9265
+#8136 := (f11 f12 ?v1!10)
+#6426 := (= f1 #8136)
+#8482 := (not #6426)
+#6573 := (f9 f10 ?v0!11)
+#6574 := (* -1::int #6573)
+#8484 := (+ #6574 #8080)
+#8479 := (+ #2095 #8484)
+#8487 := (>= #8479 0::int)
+#8775 := (not #8487)
+#8680 := (+ #2090 #6574)
+#8698 := (<= #8680 0::int)
+#8679 := (= #2090 #6573)
+#8746 := (= #6573 #2090)
+#8747 := [monotonicity #8129]: #8746
+#8743 := [symm #8747]: #8679
+#8748 := (not #8679)
+#8749 := (or #8748 #8698)
+#8750 := [th-lemma]: #8749
+#8752 := [unit-resolution #8750 #8743]: #8698
+#4111 := (not #2756)
+#4117 := (or #3325 #4111)
+#3755 := [def-axiom]: #4117
+#8753 := [unit-resolution #3755 #8756]: #4111
+#8776 := (not #8698)
+#8779 := (or #8775 #8776 #2756 #9266)
+#8780 := [th-lemma]: #8779
+#8781 := [unit-resolution #8780 #8753 #8752 #8745]: #8775
+#8782 := (or #8482 #8487)
+#4115 := (or #3325 #2105)
+#4116 := [def-axiom]: #4115
+#8774 := [unit-resolution #4116 #8756]: #2105
+#3999 := (or #4477 #4212)
+#3979 := [def-axiom]: #3999
+#7050 := [unit-resolution #3979 #6995]: #4212
+#8513 := (or #4217 #2104 #8482 #8487)
+#8454 := (+ #8080 #6574)
+#8455 := (+ #2095 #8454)
+#8481 := (>= #8455 0::int)
+#8483 := (or #8482 #2104 #8481)
+#8514 := (or #4217 #8483)
+#8520 := (iff #8514 #8513)
+#8498 := (or #2104 #8482 #8487)
+#8510 := (or #4217 #8498)
+#8518 := (iff #8510 #8513)
+#8519 := [rewrite]: #8518
+#8516 := (iff #8514 #8510)
+#8511 := (iff #8483 #8498)
+#8496 := (or #8482 #2104 #8487)
+#8499 := (iff #8496 #8498)
+#8500 := [rewrite]: #8499
+#8497 := (iff #8483 #8496)
+#8488 := (iff #8481 #8487)
+#8485 := (= #8455 #8479)
+#8486 := [rewrite]: #8485
+#8489 := [monotonicity #8486]: #8488
+#8495 := [monotonicity #8489]: #8497
+#8512 := [trans #8495 #8500]: #8511
+#8517 := [monotonicity #8512]: #8516
+#8544 := [trans #8517 #8519]: #8520
+#8515 := [quant-inst]: #8514
+#8545 := [mp #8515 #8544]: #8513
+#8783 := [unit-resolution #8545 #7050 #8774]: #8782
+#8778 := [unit-resolution #8783 #8781]: #8482
+#6427 := (or #6426 #8135)
+#7034 := [hypothesis]: #4246
+#6917 := (or #4251 #6426 #8135)
+#6918 := (or #4251 #6427)
+#7082 := (iff #6918 #6917)
+#7258 := [rewrite]: #7082
+#6919 := [quant-inst]: #6918
+#7256 := [mp #6919 #7258]: #6917
+#8784 := [unit-resolution #7256 #7034]: #6427
+#8785 := [unit-resolution #8784 #8778 #8740]: false
+#8859 := [lemma #8785]: #8856
+#6404 := [unit-resolution #8859 #6387 #6498]: #3325
+#4122 := (or #4295 #4289 #3330)
+#4108 := [def-axiom]: #4122
+#6405 := [unit-resolution #4108 #6404 #6366]: #4295
+#3832 := (or #4298 #4292)
+#3833 := [def-axiom]: #3832
+#6412 := [unit-resolution #3833 #6405]: #4298
+#4102 := (or #4307 #4267 #4301)
+#4106 := [def-axiom]: #4102
+#6363 := [unit-resolution #4106 #6412 #6538]: #4267
+#4134 := (or #4264 #2039)
+#4124 := [def-axiom]: #4134
+#6406 := [unit-resolution #4124 #6363]: #2039
+#8285 := (or #4264 #629 #2038)
+#5344 := (?v1!7 ?v0!8)
+#5850 := (f9 f16 #5344)
+#5807 := (* -1::int #5850)
+#6152 := (+ #2026 #5807)
+#6153 := (<= #6152 0::int)
+#8215 := (not #6153)
+#5345 := (f9 f10 #5344)
+#6786 := (+ #5345 #5807)
+#6788 := (>= #6786 0::int)
+#6784 := (= #5345 #5850)
+#8131 := (= #5850 #5345)
+#8130 := [symm #8129]: #105
+#8132 := [monotonicity #8130]: #8131
+#8147 := [symm #8132]: #6784
+#8148 := (not #6784)
+#8173 := (or #8148 #6788)
+#8174 := [th-lemma]: #8173
+#8175 := [unit-resolution #8174 #8147]: #6788
+#5346 := (* -1::int #5345)
+#5282 := (f9 f10 ?v0!8)
+#5347 := (+ #5282 #5346)
+#5373 := (<= #5347 0::int)
+#5405 := (not #5373)
+#5379 := (f11 f12 #5344)
+#5380 := (= f1 #5379)
+#5381 := (not #5380)
+#5374 := (f5 #5344 ?v0!8)
+#5375 := (f4 #5374)
+#5376 := (* -1::int #5375)
+#5371 := (+ #5346 #5376)
+#5372 := (+ #5282 #5371)
+#5377 := (= #5372 0::int)
+#5378 := (not #5377)
+#5435 := (or #5373 #5378 #5381)
+#5438 := (not #5435)
+#5283 := (* -1::int #5282)
+#5284 := (+ f3 #5283)
+#5310 := (<= #5284 0::int)
+#5809 := (not #5310)
+#5691 := [hypothesis]: #2039
+#5625 := (+ #2026 #5283)
+#5690 := (>= #5625 0::int)
+#5681 := (= #2026 #5282)
+#8176 := (= #5282 #2026)
+#8177 := [monotonicity #8129]: #8176
+#8172 := [symm #8177]: #5681
+#8178 := (not #5681)
+#8179 := (or #8178 #5690)
+#8180 := [th-lemma]: #8179
+#8181 := [unit-resolution #8180 #8172]: #5690
+#5847 := (not #5690)
+#5848 := (or #5809 #5847 #2038)
+#5715 := [hypothesis]: #5310
+#5716 := [hypothesis]: #5690
+#5808 := [th-lemma #5716 #5715 #5691]: false
+#5849 := [lemma #5808]: #5848
+#8182 := [unit-resolution #5849 #8181 #5691]: #5809
+#8212 := (or #5310 #5438)
+#8209 := [hypothesis]: #4267
+#3784 := (or #4264 #2656)
+#3789 := [def-axiom]: #3784
+#8210 := [unit-resolution #3789 #8209]: #2656
+#3986 := (or #4477 #4237)
+#3981 := [def-axiom]: #3986
+#8211 := [unit-resolution #3981 #6995]: #4237
+#5443 := (or #4242 #2653 #5310 #5438)
+#5409 := (or #5381 #5378 #5373)
+#5410 := (not #5409)
+#5434 := (or #2040 #5310 #5410)
+#5491 := (or #4242 #5434)
+#5501 := (iff #5491 #5443)
+#5440 := (or #2653 #5310 #5438)
+#5493 := (or #4242 #5440)
+#5497 := (iff #5493 #5443)
+#5500 := [rewrite]: #5497
+#5498 := (iff #5491 #5493)
+#5441 := (iff #5434 #5440)
+#5433 := (iff #5410 #5438)
+#5436 := (iff #5409 #5435)
+#5437 := [rewrite]: #5436
+#5439 := [monotonicity #5437]: #5433
+#5442 := [monotonicity #2655 #5439]: #5441
+#5499 := [monotonicity #5442]: #5498
+#5402 := [trans #5499 #5500]: #5501
+#5492 := [quant-inst]: #5491
+#5403 := [mp #5492 #5402]: #5443
+#8213 := [unit-resolution #5403 #8211 #8210]: #8212
+#8208 := [unit-resolution #8213 #8182]: #5438
+#5400 := (or #5435 #5405)
+#5406 := [def-axiom]: #5400
+#8214 := [unit-resolution #5406 #8208]: #5405
+#8216 := (not #6788)
+#8217 := (or #8215 #5847 #5373 #8216)
+#8218 := [th-lemma]: #8217
+#8223 := [unit-resolution #8218 #8181 #8214 #8175]: #8215
+#5875 := (+ #5376 #5807)
+#5879 := (+ #2026 #5875)
+#5880 := (= #5879 0::int)
+#6187 := (>= #5879 0::int)
+#5404 := (>= #5372 0::int)
+#5407 := (or #5435 #5377)
+#5408 := [def-axiom]: #5407
+#8224 := [unit-resolution #5408 #8208]: #5377
+#8227 := (or #5378 #5404)
+#8228 := [th-lemma]: #8227
+#8246 := [unit-resolution #8228 #8224]: #5404
+#7153 := (not #5404)
+#8247 := (or #6187 #5847 #7153 #8216)
+#8248 := [th-lemma]: #8247
+#8249 := [unit-resolution #8248 #8181 #8246 #8175]: #6187
+#6211 := (<= #5879 0::int)
+#6785 := (<= #6786 0::int)
+#8250 := (or #8148 #6785)
+#8245 := [th-lemma]: #8250
+#8251 := [unit-resolution #8245 #8147]: #6785
+#5401 := (<= #5372 0::int)
+#8252 := (or #5378 #5401)
+#8253 := [th-lemma]: #8252
+#8254 := [unit-resolution #8253 #8224]: #5401
+#5689 := (<= #5625 0::int)
+#8255 := (or #8178 #5689)
+#8264 := [th-lemma]: #8255
+#8265 := [unit-resolution #8264 #8172]: #5689
+#8268 := (not #6785)
+#8267 := (not #5401)
+#8266 := (not #5689)
+#8263 := (or #6211 #8266 #8267 #8268)
+#8269 := [th-lemma]: #8263
+#8270 := [unit-resolution #8269 #8265 #8254 #8251]: #6211
+#8272 := (not #6187)
+#8271 := (not #6211)
+#8273 := (or #5880 #8271 #8272)
+#8286 := [th-lemma]: #8273
+#8287 := [unit-resolution #8286 #8270 #8249]: #5880
+#6115 := (not #5880)
+#6146 := (or #6115 #6153)
+#4125 := (or #4264 #4256)
+#3785 := [def-axiom]: #4125
+#8288 := [unit-resolution #3785 #8209]: #4256
+#6327 := (or #4261 #6115 #6153)
+#5717 := (+ #2027 #5375)
+#5851 := (+ #5850 #5717)
+#5846 := (= #5851 0::int)
+#5783 := (not #5846)
+#5784 := (+ #5850 #2027)
+#5802 := (>= #5784 0::int)
+#5803 := (or #5802 #5783)
+#6328 := (or #4261 #5803)
+#6189 := (iff #6328 #6327)
+#6308 := (or #4261 #6146)
+#6311 := (iff #6308 #6327)
+#6312 := [rewrite]: #6311
+#6309 := (iff #6328 #6308)
+#6149 := (iff #5803 #6146)
+#6105 := (or #6153 #6115)
+#6147 := (iff #6105 #6146)
+#6148 := [rewrite]: #6147
+#6116 := (iff #5803 #6105)
+#6118 := (iff #5783 #6115)
+#5929 := (iff #5846 #5880)
+#6158 := (+ #5375 #5850)
+#6159 := (+ #2027 #6158)
+#5877 := (= #6159 0::int)
+#5881 := (iff #5877 #5880)
+#5928 := [rewrite]: #5881
+#5878 := (iff #5846 #5877)
+#5876 := (= #5851 #6159)
+#5871 := [rewrite]: #5876
+#5874 := [monotonicity #5871]: #5878
+#6117 := [trans #5874 #5928]: #5929
+#6119 := [monotonicity #6117]: #6118
+#6156 := (iff #5802 #6153)
+#5785 := (+ #2027 #5850)
+#5804 := (>= #5785 0::int)
+#6154 := (iff #5804 #6153)
+#6155 := [rewrite]: #6154
+#5805 := (iff #5802 #5804)
+#5782 := (= #5784 #5785)
+#5801 := [rewrite]: #5782
+#5806 := [monotonicity #5801]: #5805
+#6157 := [trans #5806 #6155]: #6156
+#6120 := [monotonicity #6157 #6119]: #6116
+#6326 := [trans #6120 #6148]: #6149
+#6310 := [monotonicity #6326]: #6309
+#6190 := [trans #6310 #6312]: #6189
+#6323 := [quant-inst]: #6328
+#6210 := [mp #6323 #6190]: #6327
+#8289 := [unit-resolution #6210 #8288]: #6146
+#8290 := [unit-resolution #8289 #8287 #8223]: false
+#8291 := [lemma #8290]: #8285
+#6402 := [unit-resolution #8291 #6406 #6363 #6498]: false
+#6403 := [lemma #6402]: #4310
+#3992 := (or #4474 #4313 #4468)
+#3993 := [def-axiom]: #3992
+#9541 := [unit-resolution #3993 #6403 #9540]: #4468
+#4015 := (or #4465 #148)
+#4016 := [def-axiom]: #4015
+#11161 := [unit-resolution #4016 #9541]: #148
+#13559 := [trans #11161 #13557]: #13558
+#24553 := [monotonicity #13559 #30680]: #24573
+#24598 := [symm #24553]: #24597
+#30482 := (= f1 #30481)
+#24659 := (f11 f12 #19988)
+#24663 := (= f1 #24659)
+#30484 := (= #9605 #19988)
+#30487 := (ite #30484 #3747 #24663)
+#30490 := (iff #30482 #30487)
+#248 := (:var 1 S1)
+#247 := (:var 2 S2)
+#246 := (:var 3 S5)
+#249 := (f21 #246 #247 #248)
+#250 := (f11 #249 #12)
+#4548 := (pattern #250)
+#254 := (f11 #246 #12)
+#1766 := (= f1 #254)
+#1763 := (= f1 #248)
+#252 := (= #12 #247)
+#1769 := (ite #252 #1763 #1766)
+#1759 := (= f1 #250)
+#1772 := (iff #1759 #1769)
+#4549 := (forall (vars (?v0 S5) (?v1 S2) (?v2 S1) (?v3 S2)) (:pat #4548) #1772)
+#1775 := (forall (vars (?v0 S5) (?v1 S2) (?v2 S1) (?v3 S2)) #1772)
+#4552 := (iff #1775 #4549)
+#4550 := (iff #1772 #1772)
+#4551 := [refl]: #4550
+#4553 := [quant-intro #4551]: #4552
+#1820 := (~ #1775 #1775)
+#1907 := (~ #1772 #1772)
+#1908 := [refl]: #1907
+#1821 := [nnf-pos #1908]: #1820
+#255 := (= #254 f1)
+#253 := (= #248 f1)
+#256 := (ite #252 #253 #255)
+#251 := (= #250 f1)
+#257 := (iff #251 #256)
+#258 := (forall (vars (?v0 S5) (?v1 S2) (?v2 S1) (?v3 S2)) #257)
+#1776 := (iff #258 #1775)
+#1773 := (iff #257 #1772)
+#1770 := (iff #256 #1769)
+#1767 := (iff #255 #1766)
+#1768 := [rewrite]: #1767
+#1764 := (iff #253 #1763)
+#1765 := [rewrite]: #1764
+#1771 := [monotonicity #1765 #1768]: #1770
+#1761 := (iff #251 #1759)
+#1762 := [rewrite]: #1761
+#1774 := [monotonicity #1762 #1771]: #1773
+#1777 := [quant-intro #1774]: #1776
+#1758 := [asserted]: #258
+#1780 := [mp #1758 #1777]: #1775
+#2077 := [mp~ #1780 #1821]: #1775
+#4554 := [mp #2077 #4553]: #4549
+#8843 := (not #4549)
+#24530 := (or #8843 #30490)
+#30477 := (= #19988 #9605)
+#30478 := (ite #30477 #3747 #24663)
+#30483 := (iff #30482 #30478)
+#24540 := (or #8843 #30483)
+#24451 := (iff #24540 #24530)
+#24524 := (iff #24530 #24530)
+#24546 := [rewrite]: #24524
+#30491 := (iff #30483 #30490)
+#30488 := (iff #30478 #30487)
+#30485 := (iff #30477 #30484)
+#30486 := [rewrite]: #30485
+#30489 := [monotonicity #30486]: #30488
+#30492 := [monotonicity #30489]: #30491
+#24497 := [monotonicity #30492]: #24451
+#24549 := [trans #24497 #24546]: #24451
+#24501 := [quant-inst]: #24540
+#24537 := [mp #24501 #24549]: #24530
+#24564 := [unit-resolution #24537 #4554]: #30490
+#24485 := (not #30490)
+#24569 := (or #24485 #30482)
+#30502 := (not #30487)
+#30665 := [hypothesis]: #30502
+#30503 := (not #30484)
+#30666 := (or #30487 #30503)
+#8984 := (not #3747)
+#30508 := (or #30487 #30503 #8984)
+#30509 := [def-axiom]: #30508
+#30673 := [unit-resolution #30509 #11162]: #30666
+#30674 := [unit-resolution #30673 #30665]: #30503
+#30690 := (or #30487 #30484)
+#6039 := (f11 f12 #6027)
+#30687 := (= #6039 #24659)
+#30683 := (= #24659 #6039)
+#30681 := (= #19988 #6027)
+#30682 := [symm #30680]: #30681
+#30684 := [monotonicity #30682]: #30683
+#30688 := [symm #30684]: #30687
+#6040 := (= f1 #6039)
+#6041 := (not #6040)
+#6033 := (f4 #6032)
+#6034 := (* -1::int #6033)
+#6028 := (f9 f10 #6027)
+#6029 := (* -1::int #6028)
+#6035 := (+ #6029 #6034)
+#5759 := (f9 f10 ?v0!20)
+#6036 := (+ #5759 #6035)
+#6037 := (= #6036 0::int)
+#6038 := (not #6037)
+#6030 := (+ #5759 #6029)
+#6031 := (<= #6030 0::int)
+#6047 := (or #6031 #6038 #6041)
+#6050 := (not #6047)
+#5794 := (* -1::int #5759)
+#6044 := (+ f3 #5794)
+#6045 := (<= #6044 0::int)
+#27050 := (not #6045)
+#5034 := (>= #169 0::int)
+#4872 := (* -1::int #169)
+#4937 := (+ #66 #4872)
+#8861 := (<= #4937 0::int)
+#4915 := (= #66 #169)
+#4873 := (f5 f19 f6)
+#4874 := (f4 #4873)
+#4878 := (* -1::int #4874)
+#4882 := (+ f3 #4878)
+#4883 := (<= #4882 0::int)
+#4879 := (+ #1359 #4878)
+#4880 := (+ #66 #4879)
+#4881 := (<= #4880 0::int)
+#4917 := (or #4881 #4883)
+#4719 := (f4 #4718)
+#9807 := (+ #4719 #4878)
+#9787 := (<= #9807 0::int)
+#10503 := (f5 #9605 f6)
+#10504 := (f4 #10503)
+#18022 := (>= #10504 0::int)
+#10553 := (= #10504 0::int)
+#18544 := (not #10553)
+#18543 := (not #18022)
+#18541 := [hypothesis]: #18543
+#18545 := (or #18544 #18022)
+#18546 := [th-lemma]: #18545
+#18551 := [unit-resolution #18546 #18541]: #18544
+#10558 := (= f6 #9605)
+#10583 := (<= #10504 0::int)
+#18552 := (or #18022 #10583)
+#18550 := [th-lemma]: #18552
+#18553 := [unit-resolution #18550 #18541]: #10583
+#10585 := (not #10583)
+#10587 := (or #10558 #10585)
+#15 := (f4 #14)
+#326 := (<= #15 0::int)
+#327 := (not #326)
+#13 := (= #11 #12)
+#330 := (or #13 #327)
+#4142 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4135) #330)
+#333 := (forall (vars (?v0 S2) (?v1 S2)) #330)
+#4145 := (iff #333 #4142)
+#4143 := (iff #330 #330)
+#4144 := [refl]: #4143
+#4146 := [quant-intro #4144]: #4145
+#1808 := (~ #333 #333)
+#1807 := (~ #330 #330)
+#1805 := [refl]: #1807
+#1809 := [nnf-pos #1805]: #1808
+#20 := (< 0::int #15)
+#19 := (not #13)
+#21 := (implies #19 #20)
+#22 := (forall (vars (?v0 S2) (?v1 S2)) #21)
+#336 := (iff #22 #333)
+#320 := (or #13 #20)
+#323 := (forall (vars (?v0 S2) (?v1 S2)) #320)
+#334 := (iff #323 #333)
+#331 := (iff #320 #330)
+#328 := (iff #20 #327)
+#329 := [rewrite]: #328
+#332 := [monotonicity #329]: #331
+#335 := [quant-intro #332]: #334
+#324 := (iff #22 #323)
+#321 := (iff #21 #320)
+#322 := [rewrite]: #321
+#325 := [quant-intro #322]: #324
+#337 := [trans #325 #335]: #336
+#319 := [asserted]: #22
+#338 := [mp #319 #337]: #333
+#1802 := [mp~ #338 #1809]: #333
+#4147 := [mp #1802 #4146]: #4142
+#7253 := (not #4142)
+#18023 := (or #7253 #10558 #10585)
+#10552 := (= #9605 f6)
+#10586 := (or #10552 #10585)
+#18024 := (or #7253 #10586)
+#18000 := (iff #18024 #18023)
+#18026 := (or #7253 #10587)
+#18001 := (iff #18026 #18023)
+#18002 := [rewrite]: #18001
+#18027 := (iff #18024 #18026)
+#10588 := (iff #10586 #10587)
+#10559 := (iff #10552 #10558)
+#10560 := [rewrite]: #10559
+#10589 := [monotonicity #10560]: #10588
+#18028 := [monotonicity #10589]: #18027
+#18003 := [trans #18028 #18002]: #18000
+#18025 := [quant-inst]: #18024
+#18004 := [mp #18025 #18003]: #18023
+#18554 := [unit-resolution #18004 #4147]: #10587
+#18555 := [unit-resolution #18554 #18553]: #10558
+#10561 := (not #10558)
+#10567 := (or #10553 #10561)
+#16 := (= #15 0::int)
+#310 := (or #19 #16)
+#4136 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4135) #310)
+#313 := (forall (vars (?v0 S2) (?v1 S2)) #310)
+#4139 := (iff #313 #4136)
+#4137 := (iff #310 #310)
+#4138 := [refl]: #4137
+#4140 := [quant-intro #4138]: #4139
+#1832 := (~ #313 #313)
+#1830 := (~ #310 #310)
+#1831 := [refl]: #1830
+#1833 := [nnf-pos #1831]: #1832
+#17 := (implies #13 #16)
+#18 := (forall (vars (?v0 S2) (?v1 S2)) #17)
+#316 := (iff #18 #313)
+#289 := (= 0::int #15)
+#300 := (or #19 #289)
+#305 := (forall (vars (?v0 S2) (?v1 S2)) #300)
+#314 := (iff #305 #313)
+#311 := (iff #300 #310)
+#308 := (iff #289 #16)
+#309 := [rewrite]: #308
+#312 := [monotonicity #309]: #311
+#315 := [quant-intro #312]: #314
+#306 := (iff #18 #305)
+#303 := (iff #17 #300)
+#297 := (implies #13 #289)
+#301 := (iff #297 #300)
+#302 := [rewrite]: #301
+#298 := (iff #17 #297)
+#295 := (iff #16 #289)
+#296 := [rewrite]: #295
+#299 := [monotonicity #296]: #298
+#304 := [trans #299 #302]: #303
+#307 := [quant-intro #304]: #306
+#317 := [trans #307 #315]: #316
+#288 := [asserted]: #18
+#318 := [mp #288 #317]: #313
+#1806 := [mp~ #318 #1833]: #313
+#4141 := [mp #1806 #4140]: #4136
+#7236 := (not #4136)
+#18009 := (or #7236 #10553 #10561)
+#10556 := (not #10552)
+#10557 := (or #10556 #10553)
+#18010 := (or #7236 #10557)
+#18019 := (iff #18010 #18009)
+#18014 := (or #7236 #10567)
+#18017 := (iff #18014 #18009)
+#18018 := [rewrite]: #18017
+#18015 := (iff #18010 #18014)
+#10570 := (iff #10557 #10567)
+#10564 := (or #10561 #10553)
+#10568 := (iff #10564 #10567)
+#10569 := [rewrite]: #10568
+#10565 := (iff #10557 #10564)
+#10562 := (iff #10556 #10561)
+#10563 := [monotonicity #10560]: #10562
+#10566 := [monotonicity #10563]: #10565
+#10571 := [trans #10566 #10569]: #10570
+#18016 := [monotonicity #10571]: #18015
+#18020 := [trans #18016 #18018]: #18019
+#18013 := [quant-inst]: #18010
+#18021 := [mp #18013 #18020]: #18009
+#18557 := [unit-resolution #18021 #4141]: #10567
+#18558 := [unit-resolution #18557 #18555 #18551]: false
+#18556 := [lemma #18558]: #18022
+#9716 := (<= #4719 0::int)
+#9610 := (= #4719 0::int)
+#9657 := (or #7236 #9610)
+#4948 := (= f19 f19)
+#9611 := (not #4948)
+#9628 := (or #9611 #9610)
+#9663 := (or #7236 #9628)
+#9665 := (iff #9663 #9657)
+#9667 := (iff #9657 #9657)
+#9713 := [rewrite]: #9667
+#9661 := (iff #9628 #9610)
+#9635 := (or false #9610)
+#9659 := (iff #9635 #9610)
+#9660 := [rewrite]: #9659
+#9636 := (iff #9628 #9635)
+#9633 := (iff #9611 false)
+#9631 := (iff #9611 #9474)
+#4954 := (iff #4948 true)
+#4955 := [rewrite]: #4954
+#9632 := [monotonicity #4955]: #9631
+#9634 := [trans #9632 #9478]: #9633
+#9658 := [monotonicity #9634]: #9636
+#9662 := [trans #9658 #9660]: #9661
+#9666 := [monotonicity #9662]: #9665
+#9714 := [trans #9666 #9713]: #9665
+#9664 := [quant-inst]: #9663
+#9715 := [mp #9664 #9714]: #9657
+#21178 := [unit-resolution #9715 #4141]: #9610
+#21179 := (not #9610)
+#21176 := (or #21179 #9716)
+#21189 := [th-lemma]: #21176
+#21190 := [unit-resolution #21189 #21178]: #9716
+#10505 := (* -1::int #10504)
+#10602 := (+ #4874 #10505)
+#9802 := (>= #10602 0::int)
+#9801 := (= #4874 #10504)
+#21192 := (= #10504 #4874)
+#21191 := (= #10503 #4873)
+#21181 := [monotonicity #10826]: #21191
+#21193 := [monotonicity #21181]: #21192
+#21187 := [symm #21193]: #9801
+#21188 := (not #9801)
+#21180 := (or #21188 #9802)
+#21194 := [th-lemma]: #21180
+#21195 := [unit-resolution #21194 #21187]: #9802
+#21197 := (not #9716)
+#21196 := (not #9802)
+#21214 := (or #9787 #18543 #21196 #21197)
+#21217 := [th-lemma]: #21214
+#21218 := [unit-resolution #21217 #21195 #21190 #18556]: #9787
+#21202 := (not #9787)
+#21205 := (or #4881 #21202)
+#4851 := (+ #66 #1359)
+#9804 := (<= #4851 0::int)
+#3888 := (<= #66 0::int)
+#6997 := (or #1653 #3888)
+#6998 := [th-lemma]: #6997
+#6999 := [unit-resolution #6998 #6994]: #3888
+#4850 := (>= #141 0::int)
+#3998 := (or #4477 #4204)
+#3994 := [def-axiom]: #3998
+#7124 := [unit-resolution #3994 #6995]: #4204
+#8670 := (or #4209 #4850)
+#8671 := [quant-inst]: #8670
+#13339 := [unit-resolution #8671 #7124]: #4850
+#8050 := (not #3888)
+#21216 := (not #4850)
+#21219 := (or #9804 #21216 #8050)
+#21220 := [th-lemma]: #21219
+#21222 := [unit-resolution #21220 #13339 #6999]: #9804
+#21210 := (not #9804)
+#21199 := (or #4881 #21210 #21202)
+#4738 := (>= #4719 0::int)
+#9568 := (f23 #4873)
+#10325 := (f5 #9568 #9568)
+#10326 := (f4 #10325)
+#10327 := (* -1::int #10326)
+#10391 := (+ #4719 #10327)
+#10393 := (>= #10391 0::int)
+#10390 := (= #4719 #10326)
+#10399 := (= #4718 #10325)
+#10397 := (= #10325 #4718)
+#10395 := (= #9568 f19)
+#9569 := (= f19 #9568)
+#9575 := (or #9574 #9569)
+#9576 := [quant-inst]: #9575
+#10394 := [unit-resolution #9576 #4560]: #9569
+#10396 := [symm #10394]: #10395
+#10398 := [monotonicity #10396 #10396]: #10397
+#10400 := [symm #10398]: #10399
+#10401 := [monotonicity #10400]: #10390
+#10402 := (not #10390)
+#10403 := (or #10402 #10393)
+#10404 := [th-lemma]: #10403
+#10405 := [unit-resolution #10404 #10401]: #10393
+#10336 := (>= #10326 0::int)
+#10364 := (= #10326 0::int)
+#10380 := (or #7236 #10364)
+#9942 := (= #9568 #9568)
+#10365 := (not #9942)
+#10368 := (or #10365 #10364)
+#10381 := (or #7236 #10368)
+#10383 := (iff #10381 #10380)
+#10385 := (iff #10380 #10380)
+#10386 := [rewrite]: #10385
+#10378 := (iff #10368 #10364)
+#10373 := (or false #10364)
+#10376 := (iff #10373 #10364)
+#10377 := [rewrite]: #10376
+#10374 := (iff #10368 #10373)
+#10371 := (iff #10365 false)
+#10369 := (iff #10365 #9474)
+#9947 := (iff #9942 true)
+#9948 := [rewrite]: #9947
+#10370 := [monotonicity #9948]: #10369
+#10372 := [trans #10370 #9478]: #10371
+#10375 := [monotonicity #10372]: #10374
+#10379 := [trans #10375 #10377]: #10378
+#10384 := [monotonicity #10379]: #10383
+#10387 := [trans #10384 #10386]: #10383
+#10382 := [quant-inst]: #10381
+#10388 := [mp #10382 #10387]: #10380
+#10406 := [unit-resolution #10388 #4141]: #10364
+#10407 := (not #10364)
+#10408 := (or #10407 #10336)
+#10409 := [th-lemma]: #10408
+#10410 := [unit-resolution #10409 #10406]: #10336
+#4766 := (not #4738)
+#10411 := [hypothesis]: #4766
+#10412 := [th-lemma #10411 #10410 #10405]: false
+#10413 := [lemma #10412]: #4738
+#21203 := (or #4881 #21210 #4766 #21202)
+#21204 := [th-lemma]: #21203
+#21215 := [unit-resolution #21204 #10413]: #21199
+#21201 := [unit-resolution #21215 #21222]: #21205
+#21206 := [unit-resolution #21201 #21218]: #4881
+#8866 := (not #4881)
+#8867 := (or #4917 #8866)
+#8865 := [def-axiom]: #8867
+#21207 := [unit-resolution #8865 #21206]: #4917
+#4920 := (not #4917)
+#4923 := (or #4915 #4920)
+#4008 := (or #4465 #4326)
+#4003 := [def-axiom]: #4008
+#9542 := [unit-resolution #4003 #9541]: #4326
+#6425 := (or #4331 #4915 #4920)
+#4913 := (or #4883 #4881)
+#4914 := (not #4913)
+#4916 := (or #4915 #4914)
+#6496 := (or #4331 #4916)
+#8699 := (iff #6496 #6425)
+#6879 := (or #4331 #4923)
+#8405 := (iff #6879 #6425)
+#8677 := [rewrite]: #8405
+#7530 := (iff #6496 #6879)
+#4924 := (iff #4916 #4923)
+#4921 := (iff #4914 #4920)
+#4918 := (iff #4913 #4917)
+#4919 := [rewrite]: #4918
+#4922 := [monotonicity #4919]: #4921
+#4925 := [monotonicity #4922]: #4924
+#8404 := [monotonicity #4925]: #7530
+#8702 := [trans #8404 #8677]: #8699
+#6875 := [quant-inst]: #6496
+#8860 := [mp #6875 #8702]: #6425
+#21208 := [unit-resolution #8860 #9542]: #4923
+#21234 := [unit-resolution #21208 #21207]: #4915
+#21235 := (not #4915)
+#21237 := (or #21235 #8861)
+#21232 := [th-lemma]: #21237
+#21238 := [unit-resolution #21232 #21234]: #8861
+#23936 := (not #8861)
+#23977 := (or #5034 #23936)
+#3897 := (>= #66 0::int)
+#23933 := (or #1653 #3897)
+#23928 := [th-lemma]: #23933
+#23934 := [unit-resolution #23928 #6994]: #3897
+#23935 := (not #3897)
+#23937 := (or #5034 #23935 #23936)
+#23938 := [th-lemma]: #23937
+#23978 := [unit-resolution #23938 #23934]: #23977
+#23979 := [unit-resolution #23978 #21238]: #5034
+#23983 := (not #5034)
+#23986 := (or #170 #23983)
+#5027 := (<= #169 0::int)
+#4939 := (>= #4937 0::int)
+#9072 := (f5 f19 ?v0!13)
+#9073 := (f4 #9072)
+#9196 := (+ #2181 #9073)
+#9197 := (+ #141 #9196)
+#9308 := (>= #9197 0::int)
+#9223 := (= #9197 0::int)
+#9059 := (* -1::int #9073)
+#9079 := (+ f3 #9059)
+#9080 := (<= #9079 0::int)
+#9458 := (not #9080)
+#9160 := (+ #2797 #9073)
+#9156 := (+ #141 #9160)
+#9161 := (>= #9156 0::int)
+#9328 := (or #9080 #9161)
+#9324 := (not #9328)
+#9317 := (= #2180 #2182)
+#9534 := (not #9317)
+#9533 := [hypothesis]: #2804
+#9537 := (or #9534 #2799)
+#9538 := [th-lemma]: #9537
+#9539 := [unit-resolution #9538 #9533]: #9534
+#9351 := (or #4331 #9317 #9324)
+#9071 := (+ #1359 #9059)
+#9077 := (+ #2182 #9071)
+#9078 := (<= #9077 0::int)
+#9309 := (or #9080 #9078)
+#9314 := (not #9309)
+#9315 := (= #2182 #2180)
+#9316 := (or #9315 #9314)
+#9352 := (or #4331 #9316)
+#9455 := (iff #9352 #9351)
+#9350 := (or #9317 #9324)
+#9354 := (or #4331 #9350)
+#9454 := (iff #9354 #9351)
+#9449 := [rewrite]: #9454
+#9355 := (iff #9352 #9354)
+#9345 := (iff #9316 #9350)
+#9348 := (iff #9314 #9324)
+#9346 := (iff #9309 #9328)
+#9164 := (iff #9078 #9161)
+#9109 := (+ #2182 #9059)
+#9111 := (+ #1359 #9109)
+#9158 := (<= #9111 0::int)
+#9162 := (iff #9158 #9161)
+#9163 := [rewrite]: #9162
+#9159 := (iff #9078 #9158)
+#9112 := (= #9077 #9111)
+#9157 := [rewrite]: #9112
+#9154 := [monotonicity #9157]: #9159
+#9189 := [trans #9154 #9163]: #9164
+#9347 := [monotonicity #9189]: #9346
+#9349 := [monotonicity #9347]: #9348
+#9318 := (iff #9315 #9317)
+#9327 := [rewrite]: #9318
+#9323 := [monotonicity #9327 #9349]: #9345
+#9453 := [monotonicity #9323]: #9355
+#9456 := [trans #9453 #9449]: #9455
+#9353 := [quant-inst]: #9352
+#9452 := [mp #9353 #9456]: #9351
+#9543 := [unit-resolution #9452 #9542 #9539]: #9324
+#9459 := (or #9328 #9458)
+#9464 := [def-axiom]: #9459
+#9544 := [unit-resolution #9464 #9543]: #9458
+#9465 := (not #9161)
+#9489 := (or #9328 #9465)
+#9490 := [def-axiom]: #9489
+#9545 := [unit-resolution #9490 #9543]: #9465
+#8755 := (or #9080 #9161 #9223)
+#4009 := (or #4465 #4334)
+#3982 := [def-axiom]: #4009
+#9546 := [unit-resolution #3982 #9541]: #4334
+#9188 := (or #4339 #9080 #9161 #9223)
+#9074 := (+ #9073 #2181)
+#9075 := (+ #141 #9074)
+#9076 := (= #9075 0::int)
+#9108 := (or #9080 #9078 #9076)
+#9226 := (or #4339 #9108)
+#9258 := (iff #9226 #9188)
+#9228 := (or #4339 #8755)
+#9232 := (iff #9228 #9188)
+#9257 := [rewrite]: #9232
+#9230 := (iff #9226 #9228)
+#8857 := (iff #9108 #8755)
+#9224 := (iff #9076 #9223)
+#9195 := (= #9075 #9197)
+#9198 := [rewrite]: #9195
+#8754 := [monotonicity #9198]: #9224
+#8858 := [monotonicity #9189 #8754]: #8857
+#9231 := [monotonicity #8858]: #9230
+#9261 := [trans #9231 #9257]: #9258
+#9227 := [quant-inst]: #9226
+#9312 := [mp #9227 #9261]: #9188
+#9547 := [unit-resolution #9312 #9546]: #8755
+#9548 := [unit-resolution #9547 #9545 #9544]: #9223
+#9549 := (not #9223)
+#9550 := (or #9549 #9308)
+#9551 := [th-lemma]: #9550
+#9552 := [unit-resolution #9551 #9548]: #9308
+#9457 := (>= #2798 0::int)
+#9553 := (or #9457 #2799)
+#9554 := [th-lemma]: #9553
+#9555 := [unit-resolution #9554 #9533]: #9457
+#9556 := [th-lemma #9555 #9545 #9552]: false
+#9557 := [lemma #9556]: #2799
+#3983 := (or #4465 #4459)
+#3984 := [def-axiom]: #3983
+#11132 := [unit-resolution #3984 #9541]: #4459
+#4013 := (or #4462 #2804 #4456)
+#4014 := [def-axiom]: #4013
+#11133 := [unit-resolution #4014 #11132]: #4459
+#11134 := [unit-resolution #11133 #9557]: #4456
+#4026 := (or #4453 #4342)
+#4027 := [def-axiom]: #4026
+#11135 := [unit-resolution #4027 #11134]: #4342
+#7252 := (or #4347 #4939)
+#7208 := [quant-inst]: #7252
+#15735 := [unit-resolution #7208 #11135]: #4939
+#23980 := (not #4939)
+#23981 := (or #5027 #8050 #23980)
+#23976 := [th-lemma]: #23981
+#23982 := [unit-resolution #23976 #6999 #15735]: #5027
+#9413 := (not #5027)
+#23984 := (or #170 #9413 #23983)
+#23985 := [th-lemma]: #23984
+#23988 := [unit-resolution #23985 #23982]: #23986
+#23989 := [unit-resolution #23988 #23979]: #170
+#4028 := (or #4453 #4447)
+#4029 := [def-axiom]: #4028
+#13683 := [unit-resolution #4029 #11134]: #4447
+#9621 := (* -1::int #2202)
+#9622 := (+ #2201 #9621)
+#10140 := (>= #9622 0::int)
+#11140 := (not #10140)
+#9623 := (<= #9622 0::int)
+#9833 := (or #4347 #9623)
+#9612 := (* -1::int #2201)
+#9613 := (+ #2202 #9612)
+#9614 := (>= #9613 0::int)
+#9790 := (or #4347 #9614)
+#9835 := (iff #9790 #9833)
+#9836 := (iff #9833 #9833)
+#9837 := [rewrite]: #9836
+#9626 := (iff #9614 #9623)
+#9615 := (+ #9612 #2202)
+#9618 := (>= #9615 0::int)
+#9624 := (iff #9618 #9623)
+#9625 := [rewrite]: #9624
+#9619 := (iff #9614 #9618)
+#9616 := (= #9613 #9615)
+#9617 := [rewrite]: #9616
+#9620 := [monotonicity #9617]: #9619
+#9627 := [trans #9620 #9625]: #9626
+#9842 := [monotonicity #9627]: #9835
+#9838 := [trans #9842 #9837]: #9835
+#9834 := [quant-inst]: #9790
+#9849 := [mp #9834 #9838]: #9833
+#11136 := [unit-resolution #9849 #11135]: #9623
+#4087 := (not #2807)
+#11137 := [hypothesis]: #2818
+#4088 := (or #2813 #4087)
+#4093 := [def-axiom]: #4088
+#11138 := [unit-resolution #4093 #11137]: #4087
+#11139 := (not #9623)
+#11141 := (or #2807 #11139 #11140)
+#11142 := [th-lemma]: #11141
+#11143 := [unit-resolution #11142 #11138 #11136]: #11140
+#9797 := (f5 #9605 ?v0!14)
+#9798 := (f4 #9797)
+#9850 := (* -1::int #9798)
+#9668 := (f5 f19 ?v0!14)
+#9669 := (f4 #9668)
+#10545 := (+ #9669 #9850)
+#10726 := (>= #10545 0::int)
+#10491 := (= #9669 #9798)
+#11146 := (= #9798 #9669)
+#11144 := (= #9797 #9668)
+#11145 := [monotonicity #10826]: #11144
+#11147 := [monotonicity #11145]: #11146
+#11148 := [symm #11147]: #10491
+#11149 := (not #10491)
+#11150 := (or #11149 #10726)
+#11151 := [th-lemma]: #11150
+#11152 := [unit-resolution #11151 #11148]: #10726
+#10318 := (>= #9798 0::int)
+#10440 := (<= #9798 0::int)
+#10442 := (not #10440)
+#10274 := (= ?v0!14 #9605)
+#10305 := (not #10274)
+#10634 := (or #10305 #2807)
+#10168 := (= #141 #2202)
+#10166 := (= #2202 #141)
+#10813 := (= ?v0!14 f19)
+#9839 := [hypothesis]: #10274
+#9822 := [trans #9839 #10826]: #10813
+#10167 := [monotonicity #9822]: #10166
+#10169 := [symm #10167]: #10168
+#10163 := (= #2201 #141)
+#4730 := (f22 f19)
+#10182 := (= #4730 #141)
+#4731 := (= #141 #4730)
+#4722 := (* -1::int #4719)
+#4726 := (+ f3 #4722)
+#4727 := (<= #4726 0::int)
+#4743 := (or #4727 #4738)
+#4767 := (or #4743 #4766)
+#4768 := [def-axiom]: #4767
+#10125 := [unit-resolution #4768 #10413]: #4743
+#4746 := (not #4743)
+#4749 := (or #4731 #4746)
+#8613 := (or #4331 #4731 #4746)
+#4723 := (+ #1359 #4722)
+#4724 := (+ #141 #4723)
+#4725 := (<= #4724 0::int)
+#4728 := (or #4727 #4725)
+#4729 := (not #4728)
+#4732 := (or #4731 #4729)
+#8614 := (or #4331 #4732)
+#8647 := (iff #8614 #8613)
+#8612 := (or #4331 #4749)
+#8640 := (iff #8612 #8613)
+#8646 := [rewrite]: #8640
+#8644 := (iff #8614 #8612)
+#4750 := (iff #4732 #4749)
+#4747 := (iff #4729 #4746)
+#4744 := (iff #4728 #4743)
+#4741 := (iff #4725 #4738)
+#4735 := (<= #4722 0::int)
+#4739 := (iff #4735 #4738)
+#4740 := [rewrite]: #4739
+#4736 := (iff #4725 #4735)
+#4733 := (= #4724 #4722)
+#4734 := [rewrite]: #4733
+#4737 := [monotonicity #4734]: #4736
+#4742 := [trans #4737 #4740]: #4741
+#4745 := [monotonicity #4742]: #4744
+#4748 := [monotonicity #4745]: #4747
+#4751 := [monotonicity #4748]: #4750
+#8645 := [monotonicity #4751]: #8644
+#8653 := [trans #8645 #8646]: #8647
+#8643 := [quant-inst]: #8614
+#8654 := [mp #8643 #8653]: #8613
+#10126 := [unit-resolution #8654 #9542]: #4749
+#10137 := [unit-resolution #10126 #10125]: #4731
+#10164 := [symm #10137]: #10182
+#10138 := (= #2201 #4730)
+#10161 := [monotonicity #9822]: #10138
+#10170 := [trans #10161 #10164]: #10163
+#10543 := [trans #10170 #10169]: #2807
+#10781 := [hypothesis]: #4087
+#10628 := [unit-resolution #10781 #10543]: false
+#10694 := [lemma #10628]: #10634
+#11153 := [unit-resolution #10694 #11138]: #10305
+#10444 := (or #10274 #10442)
+#10316 := (or #7253 #10274 #10442)
+#10416 := (= #9605 ?v0!14)
+#10443 := (or #10416 #10442)
+#10363 := (or #7253 #10443)
+#10551 := (iff #10363 #10316)
+#10315 := (or #7253 #10444)
+#10436 := (iff #10315 #10316)
+#10544 := [rewrite]: #10436
+#10299 := (iff #10363 #10315)
+#10445 := (iff #10443 #10444)
+#10422 := (iff #10416 #10274)
+#10423 := [rewrite]: #10422
+#10446 := [monotonicity #10423]: #10445
+#10435 := [monotonicity #10446]: #10299
+#10554 := [trans #10435 #10544]: #10551
+#10298 := [quant-inst]: #10363
+#10555 := [mp #10298 #10554]: #10316
+#11154 := [unit-resolution #10555 #4147]: #10444
+#11155 := [unit-resolution #11154 #11153]: #10442
+#11156 := (or #10318 #10440)
+#11157 := [th-lemma]: #11156
+#11158 := [unit-resolution #11157 #11155]: #10318
+#10323 := (f24 #9797)
+#10727 := (f9 f10 #10323)
+#10728 := (* -1::int #10727)
+#10773 := (+ #2202 #10728)
+#10783 := (<= #10773 0::int)
+#10782 := (= #2202 #10727)
+#10799 := (= #10727 #2202)
+#10792 := (= #10323 ?v0!14)
+#10324 := (= ?v0!14 #10323)
+#10306 := (or #7210 #10324)
+#10272 := [quant-inst]: #10306
+#10789 := [unit-resolution #10272 #4566]: #10324
+#10793 := [symm #10789]: #10792
+#10800 := [monotonicity #10793]: #10799
+#10798 := [symm #10800]: #10782
+#10801 := (not #10782)
+#10802 := (or #10801 #10783)
+#10803 := [th-lemma]: #10802
+#10809 := [unit-resolution #10803 #10798]: #10783
+#9717 := (f9 f10 #9605)
+#10729 := (+ #9717 #10728)
+#10730 := (>= #10729 0::int)
+#10725 := (f11 f12 #10323)
+#10731 := (= f1 #10725)
+#9639 := (f11 f12 ?v0!14)
+#9881 := (= #9639 #10725)
+#10811 := (= #10725 #9639)
+#10812 := [monotonicity #10793]: #10811
+#9887 := [symm #10812]: #9881
+#9640 := (= f1 #9639)
+#10275 := (ite #10274 #3747 #9640)
+#10309 := (f11 #10278 ?v0!14)
+#10310 := (= f1 #10309)
+#10312 := (iff #10275 #10310)
+#10114 := (or #8843 #10312)
+#10311 := (iff #10310 #10275)
+#10109 := (or #8843 #10311)
+#10127 := (iff #10109 #10114)
+#10103 := (iff #10114 #10114)
+#10104 := [rewrite]: #10103
+#10313 := (iff #10311 #10312)
+#10314 := [rewrite]: #10313
+#10145 := [monotonicity #10314]: #10127
+#10105 := [trans #10145 #10104]: #10127
+#10144 := [quant-inst]: #10109
+#10106 := [mp #10144 #10105]: #10114
+#11159 := [unit-resolution #10106 #4554]: #10312
+#11175 := (= #2198 #10309)
+#11171 := (= #10309 #2198)
+#11169 := (= #10278 f20)
+#11167 := (= #147 f20)
+#11168 := [symm #11161]: #11167
+#11170 := [trans #11166 #11168]: #11169
+#11172 := [monotonicity #11170]: #11171
+#11176 := [symm #11172]: #11175
+#4091 := (or #2813 #2199)
+#4092 := [def-axiom]: #4091
+#11160 := [unit-resolution #4092 #11137]: #2199
+#11177 := [trans #11160 #11176]: #10310
+#10136 := (not #10310)
+#10130 := (not #10312)
+#10162 := (or #10130 #10275 #10136)
+#10174 := [def-axiom]: #10162
+#11178 := [unit-resolution #10174 #11177 #11159]: #10275
+#10107 := (not #10275)
+#10120 := (or #10107 #10274 #9640)
+#10121 := [def-axiom]: #10120
+#11179 := [unit-resolution #10121 #11153 #11178]: #9640
+#11182 := [trans #11179 #9887]: #10731
+#9720 := (f11 f12 #9605)
+#9703 := (= f1 #9720)
+#10871 := (not #9703)
+#10872 := (iff #671 #10871)
+#10869 := (iff #668 #9703)
+#10867 := (iff #9703 #668)
+#10865 := (= #9720 #138)
+#10866 := [monotonicity #10826]: #10865
+#10868 := [monotonicity #10866]: #10867
+#10870 := [symm #10868]: #10869
+#10873 := [monotonicity #10870]: #10872
+#4017 := (or #4465 #671)
+#4012 := [def-axiom]: #4017
+#10641 := [unit-resolution #4012 #9541]: #671
+#10874 := [mp #10641 #10873]: #10871
+#10732 := (not #10731)
+#10706 := (or #9703 #10730 #10732)
+#3925 := (or #4477 #4221)
+#3980 := [def-axiom]: #3925
+#10875 := [unit-resolution #3980 #6995]: #4221
+#10688 := (or #4226 #9703 #10730 #10732)
+#10733 := (or #9703 #10732 #10730)
+#10689 := (or #4226 #10733)
+#10779 := (iff #10689 #10688)
+#10690 := (or #4226 #10706)
+#10692 := (iff #10690 #10688)
+#10693 := [rewrite]: #10692
+#10685 := (iff #10689 #10690)
+#10686 := (iff #10733 #10706)
+#10687 := [rewrite]: #10686
+#10691 := [monotonicity #10687]: #10685
+#10780 := [trans #10691 #10693]: #10779
+#10705 := [quant-inst]: #10689
+#10778 := [mp #10705 #10780]: #10688
+#9934 := [unit-resolution #10778 #10875]: #10706
+#11183 := [unit-resolution #9934 #10874 #11182]: #10730
+#9710 := (* -1::int #9717)
+#10090 := (+ #141 #9710)
+#10100 := (>= #10090 0::int)
+#10116 := (= #141 #9717)
+#10827 := (= #9717 #141)
+#10828 := [monotonicity #10826]: #10827
+#10829 := [symm #10828]: #10116
+#10830 := (not #10116)
+#10831 := (or #10830 #10100)
+#10832 := [th-lemma]: #10831
+#10833 := [unit-resolution #10832 #10829]: #10100
+#9725 := (+ #9612 #9669)
+#9726 := (+ #141 #9725)
+#10023 := (<= #9726 0::int)
+#9729 := (= #9726 0::int)
+#9670 := (* -1::int #9669)
+#9674 := (+ f3 #9670)
+#9675 := (<= #9674 0::int)
+#9980 := (not #9675)
+#9686 := (+ #9621 #9669)
+#9687 := (+ #141 #9686)
+#9688 := (>= #9687 0::int)
+#9693 := (or #9675 #9688)
+#9696 := (not #9693)
+#9886 := (or #4331 #2807 #9696)
+#9671 := (+ #1359 #9670)
+#9672 := (+ #2202 #9671)
+#9673 := (<= #9672 0::int)
+#9676 := (or #9675 #9673)
+#9677 := (not #9676)
+#9678 := (or #2203 #9677)
+#9936 := (or #4331 #9678)
+#9973 := (iff #9936 #9886)
+#9699 := (or #2807 #9696)
+#9938 := (or #4331 #9699)
+#9975 := (iff #9938 #9886)
+#9978 := [rewrite]: #9975
+#9939 := (iff #9936 #9938)
+#9700 := (iff #9678 #9699)
+#9697 := (iff #9677 #9696)
+#9694 := (iff #9676 #9693)
+#9691 := (iff #9673 #9688)
+#9679 := (+ #2202 #9670)
+#9680 := (+ #1359 #9679)
+#9683 := (<= #9680 0::int)
+#9689 := (iff #9683 #9688)
+#9690 := [rewrite]: #9689
+#9684 := (iff #9673 #9683)
+#9681 := (= #9672 #9680)
+#9682 := [rewrite]: #9681
+#9685 := [monotonicity #9682]: #9684
+#9692 := [trans #9685 #9690]: #9691
+#9695 := [monotonicity #9692]: #9694
+#9698 := [monotonicity #9695]: #9697
+#9701 := [monotonicity #2809 #9698]: #9700
+#9974 := [monotonicity #9701]: #9939
+#9977 := [trans #9974 #9978]: #9973
+#9937 := [quant-inst]: #9936
+#9979 := [mp #9937 #9977]: #9886
+#11184 := [unit-resolution #9979 #9542 #11138]: #9696
+#9981 := (or #9693 #9980)
+#9982 := [def-axiom]: #9981
+#11185 := [unit-resolution #9982 #11184]: #9980
+#9976 := (not #9688)
+#9965 := (or #9693 #9976)
+#9967 := [def-axiom]: #9965
+#11186 := [unit-resolution #9967 #11184]: #9976
+#9732 := (or #9675 #9688 #9729)
+#9970 := (or #4339 #9675 #9688 #9729)
+#9721 := (+ #9669 #9612)
+#9722 := (+ #141 #9721)
+#9723 := (= #9722 0::int)
+#9724 := (or #9675 #9673 #9723)
+#9971 := (or #4339 #9724)
+#10021 := (iff #9971 #9970)
+#10018 := (or #4339 #9732)
+#9964 := (iff #10018 #9970)
+#10020 := [rewrite]: #9964
+#10019 := (iff #9971 #10018)
+#9733 := (iff #9724 #9732)
+#9730 := (iff #9723 #9729)
+#9727 := (= #9722 #9726)
+#9728 := [rewrite]: #9727
+#9731 := [monotonicity #9728]: #9730
+#9734 := [monotonicity #9692 #9731]: #9733
+#9966 := [monotonicity #9734]: #10019
+#10022 := [trans #9966 #10020]: #10021
+#9972 := [quant-inst]: #9971
+#10017 := [mp #9972 #10022]: #9970
+#11187 := [unit-resolution #10017 #9546]: #9732
+#11188 := [unit-resolution #11187 #11186 #11185]: #9729
+#11189 := (not #9729)
+#11190 := (or #11189 #10023)
+#11191 := [th-lemma]: #11190
+#11192 := [unit-resolution #11191 #11188]: #10023
+#11193 := [th-lemma #11192 #10833 #11183 #10809 #11158 #11152 #11143]: false
+#11194 := [lemma #11193]: #2813
+#4024 := (or #4450 #2818 #4444)
+#4025 := [def-axiom]: #4024
+#13684 := [unit-resolution #4025 #11194 #13683]: #4444
+#4037 := (or #4441 #4435)
+#4038 := [def-axiom]: #4037
+#23990 := [unit-resolution #4038 #13684]: #4435
+#4047 := (or #4438 #1396 #4432)
+#4033 := [def-axiom]: #4047
+#23991 := [unit-resolution #4033 #23990]: #4435
+#23992 := [unit-resolution #23991 #23989]: #4432
+#4056 := (or #4429 #4423)
+#4040 := [def-axiom]: #4056
+#23987 := [unit-resolution #4040 #23992]: #4423
+#23993 := (or #4426 #4420)
+#7708 := (f9 f10 ?v0!15)
+#11503 := (>= #7708 0::int)
+#12960 := (or #4209 #11503)
+#12962 := [quant-inst]: #12960
+#13895 := [unit-resolution #12962 #7124]: #11503
+#7789 := (* -1::int #7708)
+#7790 := (+ #2223 #7789)
+#13166 := (>= #7790 0::int)
+#7711 := (= #2223 #7708)
+#7886 := [hypothesis]: #2225
+#13707 := (or #7711 #2224)
+#7805 := (f5 f19 ?v0!15)
+#7806 := (f4 #7805)
+#5059 := (* -1::int #2223)
+#7831 := (+ #5059 #7806)
+#7832 := (+ #141 #7831)
+#12906 := (<= #7832 0::int)
+#7835 := (= #7832 0::int)
+#7810 := (* -1::int #7806)
+#7814 := (+ f3 #7810)
+#7815 := (<= #7814 0::int)
+#12912 := (not #7815)
+#7824 := (+ #7789 #7806)
+#7825 := (+ #141 #7824)
+#7826 := (>= #7825 0::int)
+#7857 := (or #7815 #7826)
+#7860 := (not #7857)
+#13222 := (not #7711)
+#13341 := [hypothesis]: #13222
+#7863 := (or #7711 #7860)
+#12889 := (or #4331 #7711 #7860)
+#7811 := (+ #1359 #7810)
+#7812 := (+ #7708 #7811)
+#7813 := (<= #7812 0::int)
+#7854 := (or #7815 #7813)
+#7855 := (not #7854)
+#7709 := (= #7708 #2223)
+#7856 := (or #7709 #7855)
+#12908 := (or #4331 #7856)
+#12916 := (iff #12908 #12889)
+#12909 := (or #4331 #7863)
+#12913 := (iff #12909 #12889)
+#12915 := [rewrite]: #12913
+#12910 := (iff #12908 #12909)
+#7864 := (iff #7856 #7863)
+#7861 := (iff #7855 #7860)
+#7858 := (iff #7854 #7857)
+#7829 := (iff #7813 #7826)
+#7817 := (+ #7708 #7810)
+#7818 := (+ #1359 #7817)
+#7821 := (<= #7818 0::int)
+#7827 := (iff #7821 #7826)
+#7828 := [rewrite]: #7827
+#7822 := (iff #7813 #7821)
+#7819 := (= #7812 #7818)
+#7820 := [rewrite]: #7819
+#7823 := [monotonicity #7820]: #7822
+#7830 := [trans #7823 #7828]: #7829
+#7859 := [monotonicity #7830]: #7858
+#7862 := [monotonicity #7859]: #7861
+#7712 := (iff #7709 #7711)
+#7713 := [rewrite]: #7712
+#7865 := [monotonicity #7713 #7862]: #7864
+#12911 := [monotonicity #7865]: #12910
+#12917 := [trans #12911 #12915]: #12916
+#12903 := [quant-inst]: #12908
+#12918 := [mp #12903 #12917]: #12889
+#13464 := [unit-resolution #12918 #9542]: #7863
+#13465 := [unit-resolution #13464 #13341]: #7860
+#12919 := (or #7857 #12912)
+#12914 := [def-axiom]: #12919
+#13515 := [unit-resolution #12914 #13465]: #12912
+#12920 := (not #7826)
+#12921 := (or #7857 #12920)
+#12922 := [def-axiom]: #12921
+#13516 := [unit-resolution #12922 #13465]: #12920
+#7838 := (or #7815 #7826 #7835)
+#12871 := (or #4339 #7815 #7826 #7835)
+#7807 := (+ #7806 #5059)
+#7808 := (+ #141 #7807)
+#7809 := (= #7808 0::int)
+#7816 := (or #7815 #7813 #7809)
+#12872 := (or #4339 #7816)
+#12890 := (iff #12872 #12871)
+#12873 := (or #4339 #7838)
+#12878 := (iff #12873 #12871)
+#12879 := [rewrite]: #12878
+#12874 := (iff #12872 #12873)
+#7839 := (iff #7816 #7838)
+#7836 := (iff #7809 #7835)
+#7833 := (= #7808 #7832)
+#7834 := [rewrite]: #7833
+#7837 := [monotonicity #7834]: #7836
+#7840 := [monotonicity #7830 #7837]: #7839
+#12875 := [monotonicity #7840]: #12874
+#12904 := [trans #12875 #12879]: #12890
+#12868 := [quant-inst]: #12872
+#12905 := [mp #12868 #12904]: #12871
+#13645 := [unit-resolution #12905 #9546]: #7838
+#13668 := [unit-resolution #13645 #13516 #13515]: #7835
+#13669 := (not #7835)
+#13670 := (or #13669 #12906)
+#13671 := [th-lemma]: #13670
+#13672 := [unit-resolution #13671 #13668]: #12906
+#13167 := (f5 #9605 ?v0!15)
+#13148 := (f4 #13167)
+#13168 := (* -1::int #13148)
+#13239 := (+ #7806 #13168)
+#13257 := (>= #13239 0::int)
+#13238 := (= #7806 #13148)
+#13675 := (= #13148 #7806)
+#13673 := (= #13167 #7805)
+#13674 := [monotonicity #10826]: #13673
+#13676 := [monotonicity #13674]: #13675
+#13677 := [symm #13676]: #13238
+#13678 := (not #13238)
+#13679 := (or #13678 #13257)
+#13680 := [th-lemma]: #13679
+#13681 := [unit-resolution #13680 #13677]: #13257
+#13633 := (>= #13148 0::int)
+#13232 := (<= #13148 0::int)
+#13338 := (not #13232)
+#12653 := (= ?v0!15 #9605)
+#12964 := (not #12653)
+#7733 := (f11 f12 ?v0!15)
+#7734 := (= f1 #7733)
+#12825 := (ite #12653 #3747 #7734)
+#12963 := (not #12825)
+#12826 := (f11 #10278 ?v0!15)
+#11335 := (= f1 #12826)
+#12891 := (iff #11335 #12825)
+#12902 := (or #8843 #12891)
+#12897 := [quant-inst]: #12902
+#13682 := [unit-resolution #12897 #4554]: #12891
+#12586 := (not #11335)
+#5062 := (f11 f20 ?v0!15)
+#5063 := (= f1 #5062)
+#5064 := (not #5063)
+#13694 := (iff #5064 #12586)
+#13692 := (iff #5063 #11335)
+#13690 := (iff #11335 #5063)
+#13688 := (= #12826 #5062)
+#13689 := [monotonicity #11170]: #13688
+#13691 := [monotonicity #13689]: #13690
+#13693 := [symm #13691]: #13692
+#13695 := [monotonicity #13693]: #13694
+#7717 := (or #5064 #7711)
+#4034 := (or #4441 #4351)
+#4036 := [def-axiom]: #4034
+#13685 := [unit-resolution #4036 #13684]: #4351
+#12848 := (or #4356 #5064 #7711)
+#7710 := (or #7709 #5064)
+#12843 := (or #4356 #7710)
+#12877 := (iff #12843 #12848)
+#12849 := (or #4356 #7717)
+#12852 := (iff #12849 #12848)
+#12853 := [rewrite]: #12852
+#12850 := (iff #12843 #12849)
+#7720 := (iff #7710 #7717)
+#7714 := (or #7711 #5064)
+#7718 := (iff #7714 #7717)
+#7719 := [rewrite]: #7718
+#7715 := (iff #7710 #7714)
+#7716 := [monotonicity #7713]: #7715
+#7721 := [trans #7716 #7719]: #7720
+#12851 := [monotonicity #7721]: #12850
+#12882 := [trans #12851 #12853]: #12877
+#12844 := [quant-inst]: #12843
+#12883 := [mp #12844 #12882]: #12848
+#13686 := [unit-resolution #12883 #13685]: #7717
+#13687 := [unit-resolution #13686 #13341]: #5064
+#13696 := [mp #13687 #13695]: #12586
+#13147 := (not #12891)
+#13129 := (or #13147 #11335 #12963)
+#11390 := [def-axiom]: #13129
+#13697 := [unit-resolution #11390 #13696 #13682]: #12963
+#13698 := (or #12825 #12964)
+#13123 := (or #12825 #12964 #8984)
+#13124 := [def-axiom]: #13123
+#13699 := [unit-resolution #13124 #11162]: #13698
+#13700 := [unit-resolution #13699 #13697]: #12964
+#13351 := (or #12653 #13338)
+#13639 := (or #7253 #12653 #13338)
+#13231 := (= #9605 ?v0!15)
+#13353 := (or #13231 #13338)
+#13640 := (or #7253 #13353)
+#13120 := (iff #13640 #13639)
+#13659 := (or #7253 #13351)
+#12370 := (iff #13659 #13639)
+#13119 := [rewrite]: #12370
+#13660 := (iff #13640 #13659)
+#13357 := (iff #13353 #13351)
+#13358 := (iff #13231 #12653)
+#13359 := [rewrite]: #13358
+#13360 := [monotonicity #13359]: #13357
+#13661 := [monotonicity #13360]: #13660
+#13162 := [trans #13661 #13119]: #13120
+#13658 := [quant-inst]: #13640
+#13163 := [mp #13658 #13162]: #13639
+#13701 := [unit-resolution #13163 #4147]: #13351
+#13702 := [unit-resolution #13701 #13700]: #13338
+#13703 := (or #13633 #13232)
+#13704 := [th-lemma]: #13703
+#13705 := [unit-resolution #13704 #13702]: #13633
+#13706 := [th-lemma #7886 #13705 #13681 #13672 #13339]: false
+#13708 := [lemma #13706]: #13707
+#13896 := [unit-resolution #13708 #7886]: #7711
+#13205 := (or #13222 #13166)
+#13635 := (not #13166)
+#13118 := [hypothesis]: #13635
+#13221 := [hypothesis]: #7711
+#12972 := [th-lemma]: #13205
+#13220 := [unit-resolution #12972 #13221 #13118]: false
+#12966 := [lemma #13220]: #13205
+#13897 := [unit-resolution #12966 #13896]: #13166
+#13898 := [th-lemma #7886 #13897 #13895]: false
+#13899 := [lemma #13898]: #2224
+#4053 := (or #4426 #2225 #4420)
+#4054 := [def-axiom]: #4053
+#23994 := [unit-resolution #4054 #13899]: #23993
+#23995 := [unit-resolution #23994 #23987]: #4420
+#4048 := (or #4417 #4411)
+#4050 := [def-axiom]: #4048
+#23884 := [unit-resolution #4050 #23995]: #4411
+#23887 := (or #4414 #4408)
+#15926 := (= #2239 #4730)
+#6430 := (= ?v0!17 f19)
+#15697 := (= ?v0!17 #9605)
+#6420 := (f11 f12 ?v0!17)
+#6421 := (= f1 #6420)
+#15698 := (ite #15697 #3747 #6421)
+#15699 := (f11 #10278 ?v0!17)
+#15700 := (= f1 #15699)
+#15702 := (iff #15698 #15700)
+#13144 := (or #8843 #15702)
+#15701 := (iff #15700 #15698)
+#9825 := (or #8843 #15701)
+#11083 := (iff #9825 #13144)
+#12347 := (iff #13144 #13144)
+#9826 := [rewrite]: #12347
+#15703 := (iff #15701 #15702)
+#15704 := [rewrite]: #15703
+#9803 := [monotonicity #15704]: #11083
+#12901 := [trans #9803 #9826]: #11083
+#13051 := [quant-inst]: #9825
+#9828 := [mp #13051 #12901]: #13144
+#14086 := [unit-resolution #9828 #4554]: #15702
+#14157 := (= #2244 #15699)
+#14119 := (= #15699 #2244)
+#14057 := [monotonicity #11170]: #14119
+#14161 := [symm #14057]: #14157
+#6736 := [hypothesis]: #3409
+#4095 := (or #3404 #2245)
+#3936 := [def-axiom]: #4095
+#6739 := [unit-resolution #3936 #6736]: #2245
+#14088 := [trans #6739 #14161]: #15700
+#12459 := (not #15700)
+#12466 := (not #15702)
+#11355 := (or #12466 #15698 #12459)
+#13796 := [def-axiom]: #11355
+#14160 := [unit-resolution #13796 #14088 #14086]: #15698
+#12406 := (not #6421)
+#6386 := (f9 f10 ?v0!17)
+#16046 := (+ #6386 #9710)
+#16079 := (<= #16046 0::int)
+#16254 := (not #16079)
+#4771 := (* -1::int #4730)
+#6374 := (+ #2239 #4771)
+#12447 := (<= #6374 0::int)
+#16248 := (not #12447)
+#6617 := (f9 f10 ?v1!16)
+#6634 := (* -1::int #6617)
+#6450 := (+ #141 #6634)
+#6451 := (<= #6450 0::int)
+#6474 := (f11 f12 ?v1!16)
+#6475 := (= f1 #6474)
+#12936 := (not #6475)
+#13966 := (= ?v1!16 #9605)
+#13969 := (ite #13966 #3747 #6475)
+#12822 := (not #13969)
+#13970 := (f11 #10278 ?v1!16)
+#13971 := (= f1 #13970)
+#13965 := (iff #13969 #13971)
+#12863 := (or #8843 #13965)
+#13972 := (iff #13971 #13969)
+#12870 := (or #8843 #13972)
+#12761 := (iff #12870 #12863)
+#12818 := (iff #12863 #12863)
+#12946 := [rewrite]: #12818
+#13973 := (iff #13972 #13965)
+#13974 := [rewrite]: #13973
+#12817 := [monotonicity #13974]: #12761
+#12820 := [trans #12817 #12946]: #12761
+#12979 := [quant-inst]: #12870
+#12824 := [mp #12979 #12820]: #12863
+#13975 := [unit-resolution #12824 #4554]: #13965
+#12978 := (not #13971)
+#13996 := (iff #2248 #12978)
+#13992 := (iff #2247 #13971)
+#13964 := (iff #13971 #2247)
+#13986 := (= #13970 #2246)
+#14054 := [monotonicity #11170]: #13986
+#13984 := [monotonicity #14054]: #13964
+#13995 := [symm #13984]: #13992
+#13989 := [monotonicity #13995]: #13996
+#3937 := (or #3404 #2248)
+#3938 := [def-axiom]: #3937
+#6738 := [unit-resolution #3938 #6736]: #2248
+#13963 := [mp #6738 #13989]: #12978
+#12952 := (not #13965)
+#12741 := (or #12952 #12822 #13971)
+#13007 := [def-axiom]: #12741
+#13998 := [unit-resolution #13007 #13963 #13975]: #12822
+#12929 := (not #13966)
+#13999 := (or #13969 #12929)
+#12949 := (or #13969 #12929 #8984)
+#12951 := [def-axiom]: #12949
+#13994 := [unit-resolution #12951 #11162]: #13999
+#14000 := [unit-resolution #13994 #13998]: #12929
+#12937 := (or #13969 #13966 #12936)
+#12938 := [def-axiom]: #12937
+#14055 := [unit-resolution #12938 #14000 #13998]: #12936
+#6505 := (or #6451 #6475)
+#4018 := (or #4465 #4316)
+#4004 := [def-axiom]: #4018
+#12045 := [unit-resolution #4004 #9541]: #4316
+#13933 := (or #4321 #6451 #6475)
+#6471 := (+ #6617 #1359)
+#6472 := (>= #6471 0::int)
+#6473 := (or #6475 #6472)
+#13917 := (or #4321 #6473)
+#13923 := (iff #13917 #13933)
+#13918 := (or #4321 #6505)
+#13922 := (iff #13918 #13933)
+#13929 := [rewrite]: #13922
+#13920 := (iff #13917 #13918)
+#6508 := (iff #6473 #6505)
+#6502 := (or #6475 #6451)
+#6506 := (iff #6502 #6505)
+#6507 := [rewrite]: #6506
+#6503 := (iff #6473 #6502)
+#6500 := (iff #6472 #6451)
+#6445 := (+ #1359 #6617)
+#6447 := (>= #6445 0::int)
+#6452 := (iff #6447 #6451)
+#6499 := [rewrite]: #6452
+#6448 := (iff #6472 #6447)
+#6446 := (= #6471 #6445)
+#6444 := [rewrite]: #6446
+#6449 := [monotonicity #6444]: #6448
+#6501 := [trans #6449 #6499]: #6500
+#6504 := [monotonicity #6501]: #6503
+#6509 := [trans #6504 #6507]: #6508
+#13921 := [monotonicity #6509]: #13920
+#13936 := [trans #13921 #13929]: #13923
+#13930 := [quant-inst]: #13917
+#13947 := [mp #13930 #13936]: #13933
+#13997 := [unit-resolution #13947 #12045]: #6505
+#14056 := [unit-resolution #13997 #14055]: #6451
+#4080 := (not #2837)
+#4081 := (or #3404 #4080)
+#4082 := [def-axiom]: #4081
+#6737 := [unit-resolution #4082 #6736]: #4080
+#16144 := (not #6451)
+#16270 := (or #16248 #2837 #13966 #16144)
+#15791 := (f5 #9605 ?v1!16)
+#15792 := (f4 #15791)
+#15793 := (* -1::int #15792)
+#6650 := (f5 f19 ?v1!16)
+#6651 := (f4 #6650)
+#15942 := (+ #6651 #15793)
+#16238 := (>= #15942 0::int)
+#15927 := (= #6651 #15792)
+#16241 := (= #15792 #6651)
+#16239 := (= #15791 #6650)
+#16240 := [monotonicity #10826]: #16239
+#16212 := [monotonicity #16240]: #16241
+#16242 := [symm #16212]: #15927
+#16237 := (not #15927)
+#16243 := (or #16237 #16238)
+#16244 := [th-lemma]: #16243
+#16245 := [unit-resolution #16244 #16242]: #16238
+#16130 := [hypothesis]: #4080
+#4992 := (+ #141 #4771)
+#4993 := (>= #4992 0::int)
+#7312 := (or #4347 #4993)
+#7364 := [quant-inst]: #7312
+#15949 := [unit-resolution #7364 #11135]: #4993
+#15989 := [hypothesis]: #12447
+#6676 := (+ #2835 #6651)
+#6677 := (+ #141 #6676)
+#12467 := (<= #6677 0::int)
+#6680 := (= #6677 0::int)
+#6669 := (+ #6634 #6651)
+#6670 := (+ #141 #6669)
+#6671 := (>= #6670 0::int)
+#6655 := (* -1::int #6651)
+#6659 := (+ f3 #6655)
+#6660 := (<= #6659 0::int)
+#6706 := (or #6660 #6671)
+#6709 := (not #6706)
+#6703 := (= #2241 #6617)
+#16257 := (not #6703)
+#6635 := (+ #2241 #6634)
+#12715 := (>= #6635 0::int)
+#16143 := (not #12715)
+#16129 := [hypothesis]: #6451
+#9516 := (not #4993)
+#16249 := (or #16143 #16248 #9516 #2837 #16144)
+#16250 := [th-lemma]: #16249
+#16251 := [unit-resolution #16250 #15989 #16129 #16130 #15949]: #16143
+#16258 := (or #16257 #12715)
+#16259 := [th-lemma]: #16258
+#16260 := [unit-resolution #16259 #16251]: #16257
+#6712 := (or #6703 #6709)
+#12401 := (or #4331 #6703 #6709)
+#6656 := (+ #1359 #6655)
+#6657 := (+ #6617 #6656)
+#6658 := (<= #6657 0::int)
+#6699 := (or #6660 #6658)
+#6700 := (not #6699)
+#6701 := (= #6617 #2241)
+#6702 := (or #6701 #6700)
+#12465 := (or #4331 #6702)
+#12745 := (iff #12465 #12401)
+#12754 := (or #4331 #6712)
+#12720 := (iff #12754 #12401)
+#12743 := [rewrite]: #12720
+#12685 := (iff #12465 #12754)
+#6713 := (iff #6702 #6712)
+#6710 := (iff #6700 #6709)
+#6707 := (iff #6699 #6706)
+#6674 := (iff #6658 #6671)
+#6662 := (+ #6617 #6655)
+#6663 := (+ #1359 #6662)
+#6666 := (<= #6663 0::int)
+#6672 := (iff #6666 #6671)
+#6673 := [rewrite]: #6672
+#6667 := (iff #6658 #6666)
+#6664 := (= #6657 #6663)
+#6665 := [rewrite]: #6664
+#6668 := [monotonicity #6665]: #6667
+#6675 := [trans #6668 #6673]: #6674
+#6708 := [monotonicity #6675]: #6707
+#6711 := [monotonicity #6708]: #6710
+#6704 := (iff #6701 #6703)
+#6705 := [rewrite]: #6704
+#6714 := [monotonicity #6705 #6711]: #6713
+#12847 := [monotonicity #6714]: #12685
+#12749 := [trans #12847 #12743]: #12745
+#12753 := [quant-inst]: #12465
+#12695 := [mp #12753 #12749]: #12401
+#16261 := [unit-resolution #12695 #9542]: #6712
+#16262 := [unit-resolution #16261 #16260]: #6709
+#15783 := (or #6706 #6680)
+#15531 := (not #6680)
+#15582 := [hypothesis]: #15531
+#12750 := (not #6660)
+#15667 := [hypothesis]: #6709
+#12398 := (or #6706 #12750)
+#12399 := [def-axiom]: #12398
+#15668 := [unit-resolution #12399 #15667]: #12750
+#12400 := (not #6671)
+#12433 := (or #6706 #12400)
+#12940 := [def-axiom]: #12433
+#15672 := [unit-resolution #12940 #15667]: #12400
+#6683 := (or #6660 #6671 #6680)
+#12392 := (or #4339 #6660 #6671 #6680)
+#6652 := (+ #6651 #2835)
+#6653 := (+ #141 #6652)
+#6654 := (= #6653 0::int)
+#6661 := (or #6660 #6658 #6654)
+#13894 := (or #4339 #6661)
+#12677 := (iff #13894 #12392)
+#12391 := (or #4339 #6683)
+#12419 := (iff #12391 #12392)
+#12420 := [rewrite]: #12419
+#12402 := (iff #13894 #12391)
+#6684 := (iff #6661 #6683)
+#6681 := (iff #6654 #6680)
+#6678 := (= #6653 #6677)
+#6679 := [rewrite]: #6678
+#6682 := [monotonicity #6679]: #6681
+#6685 := [monotonicity #6675 #6682]: #6684
+#12396 := [monotonicity #6685]: #12402
+#12679 := [trans #12396 #12420]: #12677
+#12395 := [quant-inst]: #13894
+#12425 := [mp #12395 #12679]: #12392
+#15673 := [unit-resolution #12425 #9546]: #6683
+#15782 := [unit-resolution #15673 #15672 #15668 #15582]: false
+#15790 := [lemma #15782]: #15783
+#16263 := [unit-resolution #15790 #16262]: #6680
+#16264 := (or #15531 #12467)
+#16265 := [th-lemma]: #16264
+#16266 := [unit-resolution #16265 #16263]: #12467
+#15925 := (<= #15792 0::int)
+#15928 := (not #15925)
+#16267 := [hypothesis]: #12929
+#11437 := (or #7253 #13966 #15928)
+#15924 := (= #9605 ?v1!16)
+#15929 := (or #15924 #15928)
+#11530 := (or #7253 #15929)
+#12441 := (iff #11530 #11437)
+#15932 := (or #13966 #15928)
+#12424 := (or #7253 #15932)
+#12422 := (iff #12424 #11437)
+#12446 := [rewrite]: #12422
+#12431 := (iff #11530 #12424)
+#15933 := (iff #15929 #15932)
+#15930 := (iff #15924 #13966)
+#15931 := [rewrite]: #15930
+#15934 := [monotonicity #15931]: #15933
+#12439 := [monotonicity #15934]: #12431
+#12442 := [trans #12439 #12446]: #12441
+#12423 := [quant-inst]: #11530
+#15908 := [mp #12423 #12442]: #11437
+#16268 := [unit-resolution #15908 #4147 #16267]: #15928
+#16269 := [th-lemma #16268 #16266 #15989 #15949 #16130 #16245]: false
+#16271 := [lemma #16269]: #16270
+#14053 := [unit-resolution #16271 #6737 #14000 #14056]: #16248
+#5026 := (<= #4992 0::int)
+#15737 := (not #4731)
+#15738 := (or #15737 #5026)
+#15739 := [th-lemma]: #15738
+#15740 := [unit-resolution #15739 #10137]: #5026
+#5558 := (* -1::int #6386)
+#5658 := (+ #2239 #5558)
+#5682 := (<= #5658 0::int)
+#12387 := (or #4347 #5682)
+#5651 := (+ #6386 #2240)
+#5652 := (>= #5651 0::int)
+#13134 := (or #4347 #5652)
+#13136 := (iff #13134 #12387)
+#12359 := (iff #12387 #12387)
+#13135 := [rewrite]: #12359
+#5685 := (iff #5652 #5682)
+#5653 := (+ #2240 #6386)
+#5655 := (>= #5653 0::int)
+#5683 := (iff #5655 #5682)
+#5684 := [rewrite]: #5683
+#5656 := (iff #5652 #5655)
+#5648 := (= #5651 #5653)
+#5654 := [rewrite]: #5648
+#5657 := [monotonicity #5654]: #5656
+#5686 := [trans #5657 #5684]: #5685
+#12899 := [monotonicity #5686]: #13136
+#12382 := [trans #12899 #13135]: #13136
+#12470 := [quant-inst]: #13134
+#12305 := [mp #12470 #12382]: #12387
+#16169 := [unit-resolution #12305 #11135]: #5682
+#14087 := (not #10100)
+#9517 := (not #5026)
+#14083 := (not #5682)
+#14123 := (or #16254 #14083 #12447 #9517 #14087)
+#14124 := [th-lemma]: #14123
+#14125 := [unit-resolution #14124 #16169 #10833 #15740 #14053]: #16254
+#15947 := (or #12406 #16079)
+#16246 := [hypothesis]: #16254
+#16247 := [hypothesis]: #6421
+#15909 := (or #4226 #12406 #9703 #16079)
+#16038 := (+ #9717 #5558)
+#16039 := (>= #16038 0::int)
+#16040 := (or #9703 #12406 #16039)
+#15910 := (or #4226 #16040)
+#15916 := (iff #15910 #15909)
+#16112 := (or #12406 #9703 #16079)
+#15912 := (or #4226 #16112)
+#15914 := (iff #15912 #15909)
+#15915 := [rewrite]: #15914
+#15907 := (iff #15910 #15912)
+#16109 := (iff #16040 #16112)
+#16083 := (or #9703 #12406 #16079)
+#16113 := (iff #16083 #16112)
+#16114 := [rewrite]: #16113
+#16110 := (iff #16040 #16083)
+#16081 := (iff #16039 #16079)
+#16041 := (+ #5558 #9717)
+#16043 := (>= #16041 0::int)
+#16080 := (iff #16043 #16079)
+#16078 := [rewrite]: #16080
+#16044 := (iff #16039 #16043)
+#16036 := (= #16038 #16041)
+#16042 := [rewrite]: #16036
+#16045 := [monotonicity #16042]: #16044
+#16082 := [trans #16045 #16078]: #16081
+#16111 := [monotonicity #16082]: #16110
+#16115 := [trans #16111 #16114]: #16109
+#15913 := [monotonicity #16115]: #15907
+#15917 := [trans #15913 #15915]: #15916
+#15911 := [quant-inst]: #15910
+#15922 := [mp #15911 #15917]: #15909
+#15946 := [unit-resolution #15922 #10875 #10874 #16247 #16246]: false
+#15948 := [lemma #15946]: #15947
+#14090 := [unit-resolution #15948 #14125]: #12406
+#11628 := (not #15698)
+#12394 := (or #11628 #15697 #6421)
+#12385 := [def-axiom]: #12394
+#14091 := [unit-resolution #12385 #14090 #14160]: #15697
+#14092 := [trans #14091 #10826]: #6430
+#14117 := [monotonicity #14092]: #15926
+#15923 := (not #15926)
+#14058 := (or #15923 #12447)
+#14059 := [th-lemma]: #14058
+#14049 := [unit-resolution #14059 #14053]: #15923
+#14093 := [unit-resolution #14049 #14117]: false
+#14089 := [lemma #14093]: #3404
+#4070 := (or #4414 #3409 #4408)
+#4057 := [def-axiom]: #4070
+#23888 := [unit-resolution #4057 #14089]: #23887
+#23892 := [unit-resolution #23888 #23884]: #4408
+#3964 := (or #4405 #4399)
+#3972 := [def-axiom]: #3964
+#27038 := [unit-resolution #3972 #23892]: #4399
+#27039 := (or #4402 #4396)
+#19776 := [hypothesis]: #3455
+#4078 := (or #3450 #2277)
+#4084 := [def-axiom]: #4078
+#19777 := [unit-resolution #4084 #19776]: #2277
+#7083 := (f5 f19 ?v0!19)
+#7084 := (f4 #7083)
+#7088 := (* -1::int #7084)
+#19640 := (+ #2271 #7088)
+#19655 := (>= #19640 0::int)
+#19638 := (= #2271 #7084)
+#19801 := (= #2270 #7083)
+#6123 := (= ?v1!18 f19)
+#17992 := (= ?v1!18 #9605)
+#6113 := (f11 f12 ?v1!18)
+#6114 := (= f1 #6113)
+#17993 := (ite #17992 #3747 #6114)
+#17994 := (f11 #10278 ?v1!18)
+#17995 := (= f1 #17994)
+#17997 := (iff #17993 #17995)
+#19303 := (or #8843 #17997)
+#17996 := (iff #17995 #17993)
+#19304 := (or #8843 #17996)
+#19306 := (iff #19304 #19303)
+#19308 := (iff #19303 #19303)
+#19309 := [rewrite]: #19308
+#17998 := (iff #17996 #17997)
+#17999 := [rewrite]: #17998
+#19307 := [monotonicity #17999]: #19306
+#19310 := [trans #19307 #19309]: #19306
+#19305 := [quant-inst]: #19304
+#19311 := [mp #19305 #19310]: #19303
+#19775 := [unit-resolution #19311 #4554]: #17997
+#19784 := (= #2278 #17994)
+#19779 := (= #17994 #2278)
+#19780 := [monotonicity #11170]: #19779
+#19787 := [symm #19780]: #19784
+#4085 := (or #3450 #2279)
+#4079 := [def-axiom]: #4085
+#19778 := [unit-resolution #4079 #19776]: #2279
+#19788 := [trans #19778 #19787]: #17995
+#19323 := (not #17995)
+#19322 := (not #17997)
+#19324 := (or #19322 #17993 #19323)
+#19325 := [def-axiom]: #19324
+#19789 := [unit-resolution #19325 #19788 #19775]: #17993
+#7180 := (not #6114)
+#7032 := (f9 f10 ?v0!19)
+#7067 := (* -1::int #7032)
+#6079 := (f9 f10 ?v1!18)
+#7193 := (+ #6079 #7067)
+#7194 := (+ #2271 #7193)
+#7195 := (>= #7194 0::int)
+#19681 := (not #7195)
+#6175 := (* -1::int #6079)
+#6176 := (+ #2268 #6175)
+#19502 := (>= #6176 0::int)
+#6084 := (= #2268 #6079)
+#19290 := (or #4356 #3435 #6084)
+#6080 := (= #6079 #2268)
+#6083 := (or #6080 #3435)
+#19291 := (or #4356 #6083)
+#19300 := (iff #19291 #19290)
+#6090 := (or #3435 #6084)
+#19295 := (or #4356 #6090)
+#19298 := (iff #19295 #19290)
+#19299 := [rewrite]: #19298
+#19296 := (iff #19291 #19295)
+#6093 := (iff #6083 #6090)
+#6087 := (or #6084 #3435)
+#6091 := (iff #6087 #6090)
+#6092 := [rewrite]: #6091
+#6088 := (iff #6083 #6087)
+#6085 := (iff #6080 #6084)
+#6086 := [rewrite]: #6085
+#6089 := [monotonicity #6086]: #6088
+#6094 := [trans #6089 #6092]: #6093
+#19297 := [monotonicity #6094]: #19296
+#19301 := [trans #19297 #19299]: #19300
+#19294 := [quant-inst]: #19291
+#19302 := [mp #19294 #19301]: #19290
+#19783 := [unit-resolution #19302 #13685 #19778]: #6084
+#19790 := (not #6084)
+#19791 := (or #19790 #19502)
+#19792 := [th-lemma]: #19791
+#19793 := [unit-resolution #19792 #19783]: #19502
+#4086 := (not #2864)
+#3915 := (or #3450 #4086)
+#3917 := [def-axiom]: #3915
+#19782 := [unit-resolution #3917 #19776]: #4086
+#19682 := (not #19502)
+#19677 := (or #19681 #2864 #19682)
+#19691 := [hypothesis]: #19502
+#7068 := (+ #2266 #7067)
+#7069 := (<= #7068 0::int)
+#19439 := (or #4347 #7069)
+#7059 := (+ #7032 #2267)
+#7060 := (>= #7059 0::int)
+#19440 := (or #4347 #7060)
+#19442 := (iff #19440 #19439)
+#19444 := (iff #19439 #19439)
+#19445 := [rewrite]: #19444
+#7072 := (iff #7060 #7069)
+#7061 := (+ #2267 #7032)
+#7064 := (>= #7061 0::int)
+#7070 := (iff #7064 #7069)
+#7071 := [rewrite]: #7070
+#7065 := (iff #7060 #7064)
+#7062 := (= #7059 #7061)
+#7063 := [rewrite]: #7062
+#7066 := [monotonicity #7063]: #7065
+#7073 := [trans #7066 #7071]: #7072
+#19443 := [monotonicity #7073]: #19442
+#19446 := [trans #19443 #19445]: #19442
+#19441 := [quant-inst]: #19440
+#19447 := [mp #19441 #19446]: #19439
+#19692 := [unit-resolution #19447 #11135]: #7069
+#19678 := [hypothesis]: #7195
+#19679 := [hypothesis]: #4086
+#19680 := [th-lemma #19679 #19678 #19692 #19691]: false
+#19683 := [lemma #19680]: #19677
+#19794 := [unit-resolution #19683 #19782 #19793]: #19681
+#19795 := (or #7180 #7195)
+#19480 := (or #4217 #2276 #7180 #7195)
+#7196 := (or #7180 #2276 #7195)
+#19481 := (or #4217 #7196)
+#19488 := (iff #19481 #19480)
+#7197 := (or #2276 #7180 #7195)
+#19483 := (or #4217 #7197)
+#19486 := (iff #19483 #19480)
+#19487 := [rewrite]: #19486
+#19484 := (iff #19481 #19483)
+#7198 := (iff #7196 #7197)
+#7199 := [rewrite]: #7198
+#19485 := [monotonicity #7199]: #19484
+#19489 := [trans #19485 #19487]: #19488
+#19482 := [quant-inst]: #19481
+#19490 := [mp #19482 #19489]: #19480
+#19796 := [unit-resolution #19490 #7050 #19777]: #19795
+#19797 := [unit-resolution #19796 #19794]: #7180
+#19312 := (not #17993)
+#19316 := (or #19312 #17992 #6114)
+#19317 := [def-axiom]: #19316
+#19798 := [unit-resolution #19317 #19797 #19789]: #17992
+#19800 := [trans #19798 #10826]: #6123
+#19802 := [monotonicity #19800]: #19801
+#19803 := [monotonicity #19802]: #19638
+#19804 := (not #19638)
+#19799 := (or #19804 #19655)
+#19805 := [th-lemma]: #19799
+#19806 := [unit-resolution #19805 #19803]: #19655
+#7092 := (+ f3 #7088)
+#7093 := (<= #7092 0::int)
+#7102 := (+ #7067 #7084)
+#7103 := (+ #141 #7102)
+#7104 := (>= #7103 0::int)
+#19475 := (not #7104)
+#7249 := (f23 #2270)
+#7273 := (f9 f10 #7249)
+#7292 := (* -1::int #7273)
+#19590 := (+ #6079 #7292)
+#19594 := (>= #19590 0::int)
+#19589 := (= #6079 #7273)
+#19811 := (= #7273 #6079)
+#19808 := (= #7249 ?v1!18)
+#7250 := (= ?v1!18 #7249)
+#19506 := (or #9574 #7250)
+#19507 := [quant-inst]: #19506
+#19807 := [unit-resolution #19507 #4560]: #7250
+#19809 := [symm #19807]: #19808
+#19812 := [monotonicity #19809]: #19811
+#19813 := [symm #19812]: #19589
+#19814 := (not #19589)
+#19815 := (or #19814 #19594)
+#19810 := [th-lemma]: #19815
+#19816 := [unit-resolution #19810 #19813]: #19594
+#7293 := (+ #141 #7292)
+#7294 := (<= #7293 0::int)
+#7283 := (f11 f12 #7249)
+#7284 := (= f1 #7283)
+#19602 := (not #7284)
+#19824 := (iff #7180 #19602)
+#19822 := (iff #6114 #7284)
+#19819 := (iff #7284 #6114)
+#19817 := (= #7283 #6113)
+#19818 := [monotonicity #19809]: #19817
+#19820 := [monotonicity #19818]: #19819
+#19823 := [symm #19820]: #19822
+#19825 := [monotonicity #19823]: #19824
+#19826 := [mp #19797 #19825]: #19602
+#7299 := (or #7284 #7294)
+#19521 := (or #4321 #7284 #7294)
+#7281 := (+ #7273 #1359)
+#7282 := (>= #7281 0::int)
+#7285 := (or #7284 #7282)
+#19522 := (or #4321 #7285)
+#19529 := (iff #19522 #19521)
+#19524 := (or #4321 #7299)
+#19527 := (iff #19524 #19521)
+#19528 := [rewrite]: #19527
+#19525 := (iff #19522 #19524)
+#7300 := (iff #7285 #7299)
+#7297 := (iff #7282 #7294)
+#7286 := (+ #1359 #7273)
+#7289 := (>= #7286 0::int)
+#7295 := (iff #7289 #7294)
+#7296 := [rewrite]: #7295
+#7290 := (iff #7282 #7289)
+#7287 := (= #7281 #7286)
+#7288 := [rewrite]: #7287
+#7291 := [monotonicity #7288]: #7290
+#7298 := [trans #7291 #7296]: #7297
+#7301 := [monotonicity #7298]: #7300
+#19526 := [monotonicity #7301]: #19525
+#19530 := [trans #19526 #19528]: #19529
+#19523 := [quant-inst]: #19522
+#19531 := [mp #19523 #19530]: #19521
+#19821 := [unit-resolution #19531 #12045]: #7299
+#19827 := [unit-resolution #19821 #19826]: #7294
+#19831 := (not #7294)
+#19830 := (not #19594)
+#19829 := (not #19655)
+#19828 := (not #7069)
+#19833 := (or #19475 #19828 #19829 #2864 #19682 #19830 #19831)
+#19834 := [th-lemma]: #19833
+#19835 := [unit-resolution #19834 #19692 #19782 #19793 #19827 #19816 #19806]: #19475
+#7109 := (+ #2267 #7084)
+#7110 := (+ #141 #7109)
+#7113 := (= #7110 0::int)
+#19839 := (not #7113)
+#19460 := (>= #7110 0::int)
+#19836 := (not #19460)
+#19837 := (or #19836 #19829 #2864 #19682 #19830 #19831)
+#19832 := [th-lemma]: #19837
+#19838 := [unit-resolution #19832 #19782 #19793 #19827 #19816 #19806]: #19836
+#19840 := (or #19839 #19460)
+#19841 := [th-lemma]: #19840
+#19842 := [unit-resolution #19841 #19838]: #19839
+#7116 := (or #7093 #7104 #7113)
+#19448 := (or #4339 #7093 #7104 #7113)
+#7085 := (+ #7084 #2267)
+#7086 := (+ #141 #7085)
+#7087 := (= #7086 0::int)
+#7089 := (+ #1359 #7088)
+#7090 := (+ #7032 #7089)
+#7091 := (<= #7090 0::int)
+#7094 := (or #7093 #7091 #7087)
+#19449 := (or #4339 #7094)
+#19456 := (iff #19449 #19448)
+#19451 := (or #4339 #7116)
+#19454 := (iff #19451 #19448)
+#19455 := [rewrite]: #19454
+#19452 := (iff #19449 #19451)
+#7117 := (iff #7094 #7116)
+#7114 := (iff #7087 #7113)
+#7111 := (= #7086 #7110)
+#7112 := [rewrite]: #7111
+#7115 := [monotonicity #7112]: #7114
+#7107 := (iff #7091 #7104)
+#7095 := (+ #7032 #7088)
+#7096 := (+ #1359 #7095)
+#7099 := (<= #7096 0::int)
+#7105 := (iff #7099 #7104)
+#7106 := [rewrite]: #7105
+#7100 := (iff #7091 #7099)
+#7097 := (= #7090 #7096)
+#7098 := [rewrite]: #7097
+#7101 := [monotonicity #7098]: #7100
+#7108 := [trans #7101 #7106]: #7107
+#7118 := [monotonicity #7108 #7115]: #7117
+#19453 := [monotonicity #7118]: #19452
+#19457 := [trans #19453 #19455]: #19456
+#19450 := [quant-inst]: #19449
+#19458 := [mp #19450 #19457]: #19448
+#19844 := [unit-resolution #19458 #9546]: #7116
+#19845 := [unit-resolution #19844 #19842 #19835]: #7093
+#19846 := [th-lemma #19845 #19806 #19777]: false
+#19847 := [lemma #19846]: #3450
+#3953 := (or #4402 #3455 #4396)
+#3968 := [def-axiom]: #3953
+#27040 := [unit-resolution #3968 #19847]: #27039
+#27041 := [unit-resolution #27040 #27038]: #4396
+#4072 := (or #4393 #2309)
+#4074 := [def-axiom]: #4072
+#27042 := [unit-resolution #4074 #27041]: #2309
+#5795 := (+ #2296 #5794)
+#14667 := (>= #5795 0::int)
+#5764 := (= #2296 #5759)
+#3959 := (or #4393 #4385)
+#3960 := [def-axiom]: #3959
+#27043 := [unit-resolution #3960 #27041]: #4385
+#22264 := (or #5764 #4390)
+#14232 := (f11 f20 #9605)
+#14233 := (= f1 #14232)
+#15750 := (= #3738 #14232)
+#15748 := (= #14232 #3738)
+#15749 := [monotonicity #11161 #10826]: #15748
+#15751 := [symm #15749]: #15750
+#15752 := [trans #11162 #15751]: #14233
+#13804 := (f22 #9605)
+#13848 := (* -1::int #13804)
+#12393 := (+ #2296 #13848)
+#14441 := (<= #12393 0::int)
+#22244 := (not #14441)
+#14152 := (f5 #9605 ?v0!20)
+#14357 := (f4 #14152)
+#21545 := (<= #14357 0::int)
+#21515 := (not #21545)
+#21371 := (= ?v0!20 #9605)
+#21359 := (not #21371)
+#5998 := (f11 f12 ?v0!20)
+#5999 := (= f1 #5998)
+#21372 := (ite #21371 #3747 #5999)
+#21358 := (not #21372)
+#21373 := (f11 #10278 ?v0!20)
+#21374 := (= f1 #21373)
+#21376 := (iff #21372 #21374)
+#21348 := (or #8843 #21376)
+#21375 := (iff #21374 #21372)
+#21349 := (or #8843 #21375)
+#21345 := (iff #21349 #21348)
+#21352 := (iff #21348 #21348)
+#21353 := [rewrite]: #21352
+#21377 := (iff #21375 #21376)
+#21378 := [rewrite]: #21377
+#21351 := [monotonicity #21378]: #21345
+#21354 := [trans #21351 #21353]: #21345
+#21350 := [quant-inst]: #21349
+#21355 := [mp #21350 #21354]: #21348
+#22187 := [unit-resolution #21355 #4554]: #21376
+#21367 := (not #21374)
+#5153 := (f11 f20 ?v0!20)
+#5154 := (= f1 #5153)
+#5155 := (not #5154)
+#22213 := (iff #5155 #21367)
+#22166 := (iff #5154 #21374)
+#22164 := (iff #21374 #5154)
+#22162 := (= #21373 #5153)
+#22163 := [monotonicity #11170]: #22162
+#22165 := [monotonicity #22163]: #22164
+#22167 := [symm #22165]: #22166
+#22214 := [monotonicity #22167]: #22213
+#22188 := (not #5764)
+#22160 := [hypothesis]: #22188
+#5770 := (or #5155 #5764)
+#16321 := (or #4356 #5155 #5764)
+#5760 := (= #5759 #2296)
+#5763 := (or #5760 #5155)
+#16323 := (or #4356 #5763)
+#12632 := (iff #16323 #16321)
+#16440 := (or #4356 #5770)
+#12536 := (iff #16440 #16321)
+#12262 := [rewrite]: #12536
+#16429 := (iff #16323 #16440)
+#5773 := (iff #5763 #5770)
+#5767 := (or #5764 #5155)
+#5771 := (iff #5767 #5770)
+#5772 := [rewrite]: #5771
+#5768 := (iff #5763 #5767)
+#5765 := (iff #5760 #5764)
+#5766 := [rewrite]: #5765
+#5769 := [monotonicity #5766]: #5768
+#5774 := [trans #5769 #5772]: #5773
+#11409 := [monotonicity #5774]: #16429
+#12602 := [trans #11409 #12262]: #12632
+#16437 := [quant-inst]: #16323
+#12626 := [mp #16437 #12602]: #16321
+#22161 := [unit-resolution #12626 #13685]: #5770
+#22159 := [unit-resolution #22161 #22160]: #5155
+#22215 := [mp #22159 #22214]: #21367
+#21366 := (not #21376)
+#21370 := (or #21366 #21358 #21374)
+#21388 := [def-axiom]: #21370
+#22216 := [unit-resolution #21388 #22215 #22187]: #21358
+#22217 := (or #21372 #21359)
+#21363 := (or #21372 #21359 #8984)
+#21364 := [def-axiom]: #21363
+#22212 := [unit-resolution #21364 #11162]: #22217
+#22218 := [unit-resolution #22212 #22216]: #21359
+#21531 := (or #21371 #21515)
+#21514 := (or #7253 #21371 #21515)
+#21507 := (= #9605 ?v0!20)
+#21530 := (or #21507 #21515)
+#21534 := (or #7253 #21530)
+#21550 := (iff #21534 #21514)
+#21536 := (or #7253 #21531)
+#21548 := (iff #21536 #21514)
+#21549 := [rewrite]: #21548
+#21537 := (iff #21534 #21536)
+#21532 := (iff #21530 #21531)
+#21516 := (iff #21507 #21371)
+#21519 := [rewrite]: #21516
+#21533 := [monotonicity #21519]: #21532
+#21538 := [monotonicity #21533]: #21537
+#21551 := [trans #21538 #21549]: #21550
+#21535 := [quant-inst]: #21534
+#21552 := [mp #21535 #21551]: #21514
+#22219 := [unit-resolution #21552 #4147]: #21531
+#22220 := [unit-resolution #22219 #22218]: #21515
+#14465 := (* -1::int #14357)
+#5810 := (f5 f19 ?v0!20)
+#5811 := (f4 #5810)
+#19182 := (+ #5811 #14465)
+#19183 := (>= #19182 0::int)
+#19180 := (= #5811 #14357)
+#22225 := (= #14357 #5811)
+#22221 := (= #14152 #5810)
+#22222 := [monotonicity #10826]: #22221
+#22226 := [monotonicity #22222]: #22225
+#22236 := [symm #22226]: #19180
+#22237 := (not #19180)
+#22238 := (or #22237 #19183)
+#22239 := [th-lemma]: #22238
+#22240 := [unit-resolution #22239 #22236]: #19183
+#13868 := (+ #4730 #13848)
+#13435 := (>= #13868 0::int)
+#13837 := (= #4730 #13804)
+#15741 := (= #13804 #4730)
+#15742 := [monotonicity #10826]: #15741
+#15743 := [symm #15742]: #13837
+#15744 := (not #13837)
+#22241 := (or #15744 #13435)
+#22242 := [th-lemma]: #22241
+#22224 := [unit-resolution #22242 #15743]: #13435
+#5836 := (+ #2297 #5811)
+#5837 := (+ #141 #5836)
+#12534 := (<= #5837 0::int)
+#5840 := (= #5837 0::int)
+#5815 := (* -1::int #5811)
+#5819 := (+ f3 #5815)
+#5820 := (<= #5819 0::int)
+#16515 := (not #5820)
+#5829 := (+ #5794 #5811)
+#5830 := (+ #141 #5829)
+#5831 := (>= #5830 0::int)
+#5862 := (or #5820 #5831)
+#5865 := (not #5862)
+#5868 := (or #5764 #5865)
+#16483 := (or #4331 #5764 #5865)
+#5816 := (+ #1359 #5815)
+#5817 := (+ #5759 #5816)
+#5818 := (<= #5817 0::int)
+#5859 := (or #5820 #5818)
+#5860 := (not #5859)
+#5861 := (or #5760 #5860)
+#16511 := (or #4331 #5861)
+#16585 := (iff #16511 #16483)
+#12532 := (or #4331 #5868)
+#16479 := (iff #12532 #16483)
+#16584 := [rewrite]: #16479
+#12520 := (iff #16511 #12532)
+#5869 := (iff #5861 #5868)
+#5866 := (iff #5860 #5865)
+#5863 := (iff #5859 #5862)
+#5834 := (iff #5818 #5831)
+#5822 := (+ #5759 #5815)
+#5823 := (+ #1359 #5822)
+#5826 := (<= #5823 0::int)
+#5832 := (iff #5826 #5831)
+#5833 := [rewrite]: #5832
+#5827 := (iff #5818 #5826)
+#5824 := (= #5817 #5823)
+#5825 := [rewrite]: #5824
+#5828 := [monotonicity #5825]: #5827
+#5835 := [trans #5828 #5833]: #5834
+#5864 := [monotonicity #5835]: #5863
+#5867 := [monotonicity #5864]: #5866
+#5870 := [monotonicity #5766 #5867]: #5869
+#16478 := [monotonicity #5870]: #12520
+#16609 := [trans #16478 #16584]: #16585
+#16477 := [quant-inst]: #16511
+#16581 := [mp #16477 #16609]: #16483
+#22227 := [unit-resolution #16581 #9542]: #5868
+#22228 := [unit-resolution #22227 #22160]: #5865
+#16610 := (or #5862 #16515)
+#16583 := [def-axiom]: #16610
+#22229 := [unit-resolution #16583 #22228]: #16515
+#16611 := (not #5831)
+#16612 := (or #5862 #16611)
+#16613 := [def-axiom]: #16612
+#22230 := [unit-resolution #16613 #22228]: #16611
+#5843 := (or #5820 #5831 #5840)
+#11396 := (or #4339 #5820 #5831 #5840)
+#5812 := (+ #5811 #2297)
+#5813 := (+ #141 #5812)
+#5814 := (= #5813 0::int)
+#5821 := (or #5820 #5818 #5814)
+#15370 := (or #4339 #5821)
+#12429 := (iff #15370 #11396)
+#12541 := (or #4339 #5843)
+#12538 := (iff #12541 #11396)
+#12533 := [rewrite]: #12538
+#15256 := (iff #15370 #12541)
+#5844 := (iff #5821 #5843)
+#5841 := (iff #5814 #5840)
+#5838 := (= #5813 #5837)
+#5839 := [rewrite]: #5838
+#5842 := [monotonicity #5839]: #5841
+#5845 := [monotonicity #5835 #5842]: #5844
+#12450 := [monotonicity #5845]: #15256
+#16484 := [trans #12450 #12533]: #12429
+#16435 := [quant-inst]: #15370
+#16485 := [mp #16435 #16484]: #11396
+#22223 := [unit-resolution #16485 #9546]: #5843
+#22231 := [unit-resolution #22223 #22230 #22229]: #5840
+#22232 := (not #5840)
+#22233 := (or #22232 #12534)
+#22234 := [th-lemma]: #22233
+#22235 := [unit-resolution #22234 #22231]: #12534
+#22247 := (not #19183)
+#22246 := (not #13435)
+#22245 := (not #12534)
+#22248 := (or #22244 #22245 #9516 #22246 #21545 #22247)
+#22243 := [th-lemma]: #22248
+#22249 := [unit-resolution #22243 #22235 #22224 #15949 #22240 #22220]: #22244
+#14466 := (+ #13848 #14465)
+#14421 := (+ #2296 #14466)
+#14360 := (= #14421 0::int)
+#18610 := (<= #14421 0::int)
+#19176 := (<= #19182 0::int)
+#22250 := (or #22237 #19176)
+#22251 := [th-lemma]: #22250
+#22252 := [unit-resolution #22251 #22236]: #19176
+#13869 := (<= #13868 0::int)
+#15745 := (or #15744 #13869)
+#15746 := [th-lemma]: #15745
+#15747 := [unit-resolution #15746 #15743]: #13869
+#16486 := (>= #5837 0::int)
+#22253 := (or #22232 #16486)
+#22267 := [th-lemma]: #22253
+#22268 := [unit-resolution #22267 #22231]: #16486
+#22271 := (not #19176)
+#22270 := (not #13869)
+#22269 := (not #16486)
+#22272 := (or #18610 #22269 #9517 #22270 #22271)
+#22273 := [th-lemma]: #22272
+#22274 := [unit-resolution #22273 #22268 #15747 #15740 #22252]: #18610
+#18602 := (>= #14421 0::int)
+#22275 := (or #18602 #22245 #9516 #22246 #22247)
+#22255 := [th-lemma]: #22275
+#22256 := [unit-resolution #22255 #22235 #22224 #15949 #22240]: #18602
+#22258 := (not #18602)
+#22257 := (not #18610)
+#22259 := (or #14360 #22257 #22258)
+#22254 := [th-lemma]: #22259
+#22260 := [unit-resolution #22254 #22256 #22274]: #14360
+#14539 := (not #14360)
+#14234 := (not #14233)
+#14534 := (or #14234 #14539 #14441)
+#22261 := [hypothesis]: #4385
+#15611 := (or #4390 #14234 #14539 #14441)
+#14356 := (+ #2297 #14357)
+#14395 := (+ #13804 #14356)
+#14394 := (= #14395 0::int)
+#14358 := (not #14394)
+#14464 := (+ #13804 #2297)
+#14439 := (>= #14464 0::int)
+#14440 := (or #14234 #14439 #14358)
+#12480 := (or #4390 #14440)
+#17563 := (iff #12480 #15611)
+#17425 := (or #4390 #14534)
+#17458 := (iff #17425 #15611)
+#17521 := [rewrite]: #17458
+#17406 := (iff #12480 #17425)
+#14502 := (iff #14440 #14534)
+#14567 := (or #14234 #14441 #14539)
+#14569 := (iff #14567 #14534)
+#14571 := [rewrite]: #14569
+#14540 := (iff #14440 #14567)
+#14572 := (iff #14358 #14539)
+#14426 := (iff #14394 #14360)
+#14363 := (+ #13804 #14357)
+#14393 := (+ #2297 #14363)
+#14425 := (= #14393 0::int)
+#14533 := (iff #14425 #14360)
+#14538 := [rewrite]: #14533
+#14467 := (iff #14394 #14425)
+#14390 := (= #14395 #14393)
+#14424 := [rewrite]: #14390
+#14387 := [monotonicity #14424]: #14467
+#14541 := [trans #14387 #14538]: #14426
+#14566 := [monotonicity #14541]: #14572
+#14392 := (iff #14439 #14441)
+#14288 := (+ #2297 #13804)
+#14396 := (>= #14288 0::int)
+#14391 := (iff #14396 #14441)
+#14355 := [rewrite]: #14391
+#14389 := (iff #14439 #14396)
+#14388 := (= #14464 #14288)
+#14353 := [rewrite]: #14388
+#14359 := [monotonicity #14353]: #14389
+#14436 := [trans #14359 #14355]: #14392
+#14568 := [monotonicity #14436 #14566]: #14540
+#14575 := [trans #14568 #14571]: #14502
+#17497 := [monotonicity #14575]: #17406
+#18193 := [trans #17497 #17521]: #17563
+#17271 := [quant-inst]: #12480
+#18181 := [mp #17271 #18193]: #15611
+#22262 := [unit-resolution #18181 #22261]: #14534
+#22263 := [unit-resolution #22262 #22260 #22249 #15752]: false
+#22278 := [lemma #22263]: #22264
+#27044 := [unit-resolution #22278 #27043]: #5764
+#27045 := (or #22188 #14667)
+#27046 := [th-lemma]: #27045
+#27047 := [unit-resolution #27046 #27044]: #14667
+#27048 := [hypothesis]: #6045
+#27049 := [th-lemma #27048 #27047 #27042]: false
+#27051 := [lemma #27049]: #27050
+#30676 := (or #6045 #6050)
+#4075 := (or #4393 #2878)
+#4073 := [def-axiom]: #4075
+#30675 := [unit-resolution #4073 #27041]: #2878
+#6740 := (or #4242 #2875 #6045 #6050)
+#6042 := (or #6041 #6038 #6031)
+#6043 := (not #6042)
+#6046 := (or #2310 #6045 #6043)
+#6742 := (or #4242 #6046)
+#10921 := (iff #6742 #6740)
+#6053 := (or #2875 #6045 #6050)
+#7885 := (or #4242 #6053)
+#10820 := (iff #7885 #6740)
+#10925 := [rewrite]: #10820
+#7888 := (iff #6742 #7885)
+#6054 := (iff #6046 #6053)
+#6051 := (iff #6043 #6050)
+#6048 := (iff #6042 #6047)
+#6049 := [rewrite]: #6048
+#6052 := [monotonicity #6049]: #6051
+#6055 := [monotonicity #2877 #6052]: #6054
+#10815 := [monotonicity #6055]: #7888
+#13454 := [trans #10815 #10925]: #10921
+#11022 := [quant-inst]: #6742
+#6589 := [mp #11022 #13454]: #6740
+#30677 := [unit-resolution #6589 #8211 #30675]: #30676
+#30678 := [unit-resolution #30677 #27051]: #6050
+#15614 := (or #6047 #6040)
+#17383 := [def-axiom]: #15614
+#30679 := [unit-resolution #17383 #30678]: #6040
+#30689 := [trans #30679 #30688]: #24663
+#24664 := (not #24663)
+#30510 := (or #30487 #30484 #24664)
+#30511 := [def-axiom]: #30510
+#30691 := [unit-resolution #30511 #30689]: #30690
+#30692 := [unit-resolution #30691 #30674 #30665]: false
+#30693 := [lemma #30692]: #30487
+#24550 := (or #24485 #30482 #30502)
+#24534 := [def-axiom]: #24550
+#24565 := [unit-resolution #24534 #30693]: #24569
+#24554 := [unit-resolution #24565 #24564]: #30482
+#24585 := [trans #24554 #24598]: #16616
+#18640 := (not #16616)
+#17931 := (f22 #6027)
+#11054 := (* -1::int #17931)
+#19418 := (+ #6034 #11054)
+#19546 := (+ #2296 #19418)
+#19767 := (>= #19546 0::int)
+#10933 := (+ #6028 #11054)
+#11085 := (>= #10933 0::int)
+#15145 := (or #4347 #11085)
+#15116 := [quant-inst]: #15145
+#31365 := [unit-resolution #15116 #11135]: #11085
+#15329 := (>= #6036 0::int)
+#14748 := (or #6047 #6037)
+#18244 := [def-axiom]: #14748
+#31366 := [unit-resolution #18244 #30678]: #6037
+#31367 := (or #6038 #15329)
+#31368 := [th-lemma]: #31367
+#31369 := [unit-resolution #31368 #31366]: #15329
+#31372 := (not #11085)
+#31371 := (not #15329)
+#31370 := (not #14667)
+#31373 := (or #19767 #31370 #31371 #31372)
+#31374 := [th-lemma]: #31373
+#31375 := [unit-resolution #31374 #31369 #31365 #27047]: #19767
+#19407 := (<= #19546 0::int)
+#31376 := [hypothesis]: #16616
+#31385 := (or #18640 #19407)
+#19432 := (+ f3 #6034)
+#19379 := (<= #19432 0::int)
+#31378 := (not #19379)
+#19384 := (>= #6028 0::int)
+#19385 := (or #4209 #19384)
+#19389 := [quant-inst]: #19385
+#31377 := [unit-resolution #19389 #7124]: #19384
+#31379 := (not #19384)
+#31380 := (or #31378 #31371 #2308 #31370 #31379)
+#31381 := [th-lemma]: #31380
+#31382 := [unit-resolution #31381 #27047 #31369 #31377 #27042]: #31378
+#15574 := (or #18640 #19379 #19407)
+#4076 := (or #4393 #4376)
+#3958 := [def-axiom]: #4076
+#31383 := [unit-resolution #3958 #27041]: #4376
+#16357 := (or #4381 #18640 #19379 #19407)
+#19370 := (+ #17931 #2297)
+#19394 := (+ #6033 #19370)
+#19374 := (>= #19394 0::int)
+#19408 := (or #18640 #19379 #19374)
+#19716 := (or #4381 #19408)
+#17518 := (iff #19716 #16357)
+#17219 := (or #4381 #15574)
+#16858 := (iff #17219 #16357)
+#17505 := [rewrite]: #16858
+#16891 := (iff #19716 #17219)
+#12448 := (iff #19408 #15574)
+#13959 := (iff #19374 #19407)
+#19434 := (+ #6033 #17931)
+#19383 := (+ #2297 #19434)
+#19433 := (>= #19383 0::int)
+#15734 := (iff #19433 #19407)
+#16396 := [rewrite]: #15734
+#19402 := (iff #19374 #19433)
+#19414 := (= #19394 #19383)
+#19387 := [rewrite]: #19414
+#19410 := [monotonicity #19387]: #19402
+#16307 := [trans #19410 #16396]: #13959
+#15718 := [monotonicity #16307]: #12448
+#16859 := [monotonicity #15718]: #16891
+#16874 := [trans #16859 #17505]: #17518
+#19533 := [quant-inst]: #19716
+#11410 := [mp #19533 #16874]: #16357
+#31384 := [unit-resolution #11410 #31383]: #15574
+#31386 := [unit-resolution #31384 #31382]: #31385
+#31387 := [unit-resolution #31386 #31376]: #19407
+#16399 := (= #19546 0::int)
+#19631 := (not #16399)
+#18788 := (+ #2296 #11054)
+#19057 := (<= #18788 0::int)
+#31389 := (not #19057)
+#13430 := (not #6031)
+#14811 := (or #6047 #13430)
+#15075 := [def-axiom]: #14811
+#31388 := [unit-resolution #15075 #30678]: #13430
+#31390 := (or #31389 #31370 #6031 #31372)
+#31391 := [th-lemma]: #31390
+#31392 := [unit-resolution #31391 #31388 #31365 #27047]: #31389
+#16287 := (or #19631 #18640 #19057)
+#19786 := (or #4390 #19631 #18640 #19057)
+#17668 := (+ #2297 #6033)
+#14507 := (+ #17931 #17668)
+#19668 := (= #14507 0::int)
+#18631 := (not #19668)
+#16825 := (>= #19370 0::int)
+#19579 := (or #18640 #16825 #18631)
+#19843 := (or #4390 #19579)
+#19770 := (iff #19843 #19786)
+#19865 := (or #4390 #16287)
+#19630 := (iff #19865 #19786)
+#19637 := [rewrite]: #19630
+#19633 := (iff #19843 #19865)
+#19654 := (iff #19579 #16287)
+#19056 := (or #18640 #19057 #19631)
+#19596 := (iff #19056 #16287)
+#19258 := [rewrite]: #19596
+#19634 := (iff #19579 #19056)
+#16213 := (iff #18631 #19631)
+#19632 := (iff #19668 #16399)
+#19376 := (= #19383 0::int)
+#17504 := (iff #19376 #16399)
+#18789 := [rewrite]: #17504
+#18823 := (iff #19668 #19376)
+#19535 := (= #14507 #19383)
+#18601 := [rewrite]: #19535
+#19024 := [monotonicity #18601]: #18823
+#19578 := [trans #19024 #18789]: #19632
+#19694 := [monotonicity #19578]: #16213
+#19670 := (iff #16825 #19057)
+#19666 := (+ #2297 #17931)
+#19760 := (>= #19666 0::int)
+#19747 := (iff #19760 #19057)
+#18824 := [rewrite]: #19747
+#19671 := (iff #16825 #19760)
+#19735 := (= #19370 #19666)
+#18598 := [rewrite]: #19735
+#19597 := [monotonicity #18598]: #19671
+#19598 := [trans #19597 #18824]: #19670
+#19766 := [monotonicity #19598 #19694]: #19634
+#19848 := [trans #19766 #19258]: #19654
+#19595 := [monotonicity #19848]: #19633
+#19768 := [trans #19595 #19637]: #19770
+#19769 := [quant-inst]: #19843
+#19377 := [mp #19769 #19768]: #19786
+#31393 := [unit-resolution #19377 #27043]: #16287
+#31394 := [unit-resolution #31393 #31376 #31392]: #19631
+#31396 := (not #19767)
+#31395 := (not #19407)
+#31397 := (or #16399 #31395 #31396)
+#31398 := [th-lemma]: #31397
+#31399 := [unit-resolution #31398 #31394 #31387 #31375]: false
+#31400 := [lemma #31399]: #18640
+[unit-resolution #31400 #24585]: false
 unsat

--- a/src/HOL/Boogie/Examples/Boogie_Max.certs	Wed May 12 23:54:04 2010 +0200
+++ b/src/HOL/Boogie/Examples/Boogie_Max.certs	Wed May 12 23:54:06 2010 +0200
@@ -1,2225 +1,2225 @@
-eafecd70b5ba5010589b5ae443c033b4aa8eb332 2224 0
+fa119d1e7e3988808a55c43e2ba918fefc69c8fd 2224 0
 #2 := false
-#4 := 0::int
-decl uf_3 :: (-> int int)
-#8 := (uf_3 0::int)
-#647 := -1::int
-#2054 := (* -1::int #8)
-decl uf_2 :: int
-#7 := uf_2
-#2050 := (+ uf_2 #2054)
-#2051 := (>= #2050 0::int)
-#9 := (= uf_2 #8)
-decl uf_1 :: int
-#5 := uf_1
-#965 := (<= uf_1 0::int)
-decl uf_6 :: int
-#32 := uf_6
-#922 := (* -1::int uf_6)
-#16 := (:var 0 int)
-#20 := (uf_3 #16)
-#923 := (+ #20 #922)
-#924 := (<= #923 0::int)
-decl uf_5 :: int
-#27 := uf_5
-#717 := (* -1::int uf_5)
-#912 := (+ #16 #717)
-#911 := (>= #912 0::int)
-#913 := (not #911)
-#636 := (>= #16 0::int)
-#916 := (and #636 #913)
-#919 := (not #916)
-#927 := (or #919 #924)
-#930 := (forall (vars (?x3 int)) #927)
-#933 := (not #930)
-#64 := (uf_3 uf_5)
-#815 := (* -1::int #64)
-#816 := (+ uf_6 #815)
-#814 := (>= #816 0::int)
-#813 := (not #814)
-decl uf_11 :: int
-#69 := uf_11
-#749 := (>= uf_11 0::int)
-#11 := 1::int
-#666 := (>= uf_5 1::int)
-#804 := (and #666 #749)
-#807 := (not #804)
-decl uf_13 :: int
-#75 := uf_13
-#761 := (* -1::int uf_13)
-#798 := (+ uf_5 #761)
-#797 := (= #798 -1::int)
-#801 := (not #797)
-decl uf_12 :: int
-#71 := uf_12
-#772 := (* -1::int uf_12)
-#773 := (+ #20 #772)
-#774 := (<= #773 0::int)
-#762 := (+ #16 #761)
-#760 := (>= #762 0::int)
-#763 := (not #760)
-#766 := (and #636 #763)
-#769 := (not #766)
-#777 := (or #769 #774)
-#780 := (forall (vars (?x7 int)) #777)
-#783 := (not #780)
-#86 := (uf_3 uf_11)
-#302 := (= uf_12 #86)
-#789 := (or #302 #783)
-#794 := (and #780 #789)
-#78 := 2::int
-#752 := (>= uf_13 2::int)
-#754 := (and #749 #752)
-#757 := (not #754)
-decl uf_4 :: int
-#25 := uf_4
-#663 := (>= uf_4 0::int)
-#668 := (and #663 #666)
-#671 := (not #668)
-#421 := (= uf_6 uf_12)
-#427 := (not #421)
-#418 := (= uf_4 uf_11)
-#436 := (not #418)
-#877 := (or #436 #427 #671 #757 #794 #801 #807 #813)
-#810 := (not #666)
-decl uf_10 :: int
-#66 := uf_10
-#283 := (= uf_10 uf_12)
-#361 := (not #283)
-#280 := (= uf_5 uf_11)
-#370 := (not #280)
-#275 := (= #64 uf_10)
-#388 := (not #275)
-#853 := (or #388 #370 #361 #810 #671 #757 #794 #801 #807 #814)
-#882 := (and #853 #877)
-#718 := (+ uf_1 #717)
-#719 := (<= #718 0::int)
-#903 := (or #671 #719 #882)
-#722 := (not #719)
-decl uf_8 :: int
-#41 := uf_8
-#700 := (* -1::int uf_8)
-#701 := (+ #20 #700)
-#702 := (<= #701 0::int)
-#674 := (* -1::int #16)
-#675 := (+ uf_1 #674)
-#676 := (<= #675 0::int)
-#677 := (not #676)
-#680 := (and #636 #677)
-#683 := (not #680)
-#705 := (or #683 #702)
-#708 := (forall (vars (?x6 int)) #705)
-#47 := (= #20 uf_8)
-#689 := (or #47 #683)
-#694 := (exists (vars (?x4 int)) #689)
-#697 := (not #694)
-#711 := (or #697 #708)
-#714 := (and #694 #711)
-decl uf_9 :: int
-#43 := uf_9
-#180 := (= uf_5 uf_9)
-#218 := (not #180)
-#177 := (= uf_6 uf_8)
-#227 := (not #177)
-decl uf_7 :: int
-#39 := uf_7
-#174 := (= uf_4 uf_7)
-#236 := (not #174)
-#743 := (or #236 #227 #218 #671 #714 #722)
-#908 := (and #743 #903)
-#36 := (uf_3 uf_4)
-#171 := (= uf_6 #36)
-#523 := (not #171)
-#556 := (not #9)
-#951 := (or #556 #523 #671 #908 #933)
-#956 := (and #9 #951)
-#650 := (* -1::int #20)
-#651 := (+ uf_2 #650)
-#649 := (>= #651 0::int)
-#639 := (>= #16 1::int)
-#637 := (not #639)
-#641 := (and #636 #637)
-#644 := (not #641)
-#653 := (or #644 #649)
-#656 := (forall (vars (?x1 int)) #653)
-#659 := (not #656)
-#959 := (or #659 #956)
-#962 := (and #656 #959)
-#985 := (or #556 #962 #965)
-#990 := (not #985)
+#8 := 0::int
+decl f5 :: (-> int int)
+decl ?v0!3 :: int
+#1153 := ?v0!3
+#1154 := (f5 ?v0!3)
+#652 := -1::int
+#1356 := (* -1::int #1154)
+decl f7 :: int
+#31 := f7
+#68 := (f5 f7)
+#2646 := (+ #68 #1356)
+#2648 := (>= #2646 0::int)
+#2645 := (= #68 #1154)
+#2494 := (= f7 ?v0!3)
+#1334 := (* -1::int ?v0!3)
+#2380 := (+ f7 #1334)
+#2496 := (>= #2380 0::int)
+decl f15 :: int
+#79 := f15
+#1335 := (+ f15 #1334)
+#1336 := (<= #1335 0::int)
+#1341 := (not #1336)
+decl f14 :: int
+#75 := f14
+#1357 := (+ f14 #1356)
+#1358 := (>= #1357 0::int)
+#1160 := (>= ?v0!3 0::int)
+#1609 := (not #1160)
+#1624 := (or #1609 #1336 #1358)
+#1629 := (not #1624)
+#20 := (:var 0 int)
+#24 := (f5 #20)
+#2199 := (pattern #24)
+#777 := (* -1::int f14)
+#778 := (+ #24 #777)
+#779 := (<= #778 0::int)
+#766 := (* -1::int f15)
+#767 := (+ #20 #766)
+#765 := (>= #767 0::int)
+#641 := (>= #20 0::int)
+#1440 := (not #641)
+#1591 := (or #1440 #765 #779)
+#2216 := (forall (vars (?v0 int)) (:pat #2199) #1591)
+#2221 := (not #2216)
+decl f13 :: int
+#73 := f13
+#90 := (f5 f13)
+#307 := (= f14 #90)
+#2224 := (or #307 #2221)
+#2227 := (not #2224)
+#2230 := (or #2227 #1629)
+#2233 := (not #2230)
+#820 := (* -1::int #68)
+decl f8 :: int
+#36 := f8
+#821 := (+ f8 #820)
+#819 := (>= #821 0::int)
+#818 := (not #819)
+#803 := (+ f7 #766)
+#802 := (= #803 -1::int)
+#806 := (not #802)
+#82 := 2::int
+#757 := (>= f15 2::int)
+#1639 := (not #757)
+#754 := (>= f13 0::int)
+#1638 := (not #754)
+#15 := 1::int
+#671 := (>= f7 1::int)
+#815 := (not #671)
+decl f6 :: int
+#29 := f6
+#668 := (>= f6 0::int)
+#1569 := (not #668)
+#426 := (= f8 f14)
+#432 := (not #426)
+#423 := (= f6 f13)
+#441 := (not #423)
+#2242 := (or #441 #432 #1569 #815 #1638 #1639 #806 #818 #2233)
+#2245 := (not #2242)
+decl f12 :: int
+#70 := f12
+#288 := (= f12 f14)
+#366 := (not #288)
+#285 := (= f7 f13)
+#375 := (not #285)
+#280 := (= #68 f12)
+#393 := (not #280)
+#2236 := (or #393 #375 #366 #1569 #815 #1638 #1639 #806 #819 #2233)
+#2239 := (not #2236)
+#2248 := (or #2239 #2245)
+#2251 := (not #2248)
+#722 := (* -1::int f7)
+decl f3 :: int
+#9 := f3
+#723 := (+ f3 #722)
+#724 := (<= #723 0::int)
+#2254 := (or #1569 #815 #724 #2251)
+#2257 := (not #2254)
+decl ?v0!1 :: int
+#1086 := ?v0!1
+#1094 := (f5 ?v0!1)
+decl f10 :: int
+#45 := f10
+#1267 := (= f10 #1094)
+#1091 := (>= ?v0!1 0::int)
+#1510 := (not #1091)
+#1087 := (* -1::int ?v0!1)
+#1088 := (+ f3 #1087)
+#1089 := (<= #1088 0::int)
+#1525 := (or #1089 #1510 #1267)
+#1556 := (not #1525)
+decl ?v0!2 :: int
+#1104 := ?v0!2
+#1105 := (f5 ?v0!2)
+#1291 := (* -1::int #1105)
+#1292 := (+ f10 #1291)
+#1293 := (>= #1292 0::int)
+#1112 := (>= ?v0!2 0::int)
+#1530 := (not #1112)
+#1108 := (* -1::int ?v0!2)
+#1109 := (+ f3 #1108)
+#1110 := (<= #1109 0::int)
+#1687 := (or #1110 #1530 #1293 #1556)
+#1690 := (not #1687)
+#679 := (* -1::int #20)
+#680 := (+ f3 #679)
+#681 := (<= #680 0::int)
+#51 := (= #24 f10)
+#1499 := (or #51 #1440 #681)
+#1504 := (not #1499)
+#2260 := (forall (vars (?v0 int)) (:pat #2199) #1504)
+#2265 := (or #2260 #1690)
+#2268 := (not #2265)
+#727 := (not #724)
+decl f11 :: int
+#47 := f11
+#185 := (= f7 f11)
+#223 := (not #185)
+#182 := (= f8 f10)
+#232 := (not #182)
+decl f9 :: int
+#43 := f9
+#179 := (= f6 f9)
+#241 := (not #179)
+#2271 := (or #241 #232 #223 #1569 #815 #727 #2268)
+#927 := (* -1::int f8)
+#928 := (+ #24 #927)
+#929 := (<= #928 0::int)
+#917 := (+ #20 #722)
+#916 := (>= #917 0::int)
+#1477 := (or #1440 #916 #929)
+#2208 := (forall (vars (?v0 int)) (:pat #2199) #1477)
+#2274 := (not #2271)
+#2277 := (or #2257 #2274)
+#2280 := (not #2277)
+#2213 := (not #2208)
+#655 := (* -1::int #24)
+decl f4 :: int
+#11 := f4
+#656 := (+ f4 #655)
+#654 := (>= #656 0::int)
+#644 := (>= #20 1::int)
+#1455 := (or #1440 #644 #654)
+#2200 := (forall (vars (?v0 int)) (:pat #2199) #1455)
+#2205 := (not #2200)
+#40 := (f5 f6)
+#176 := (= f8 #40)
+#528 := (not #176)
+#2283 := (or #528 #1569 #815 #2205 #2213 #2280)
+#2286 := (not #2283)
+decl ?v0!0 :: int
+#1046 := ?v0!0
+#1049 := (>= ?v0!0 0::int)
+#1167 := (not #1049)
+#1047 := (f5 ?v0!0)
+#1044 := (* -1::int #1047)
+#1045 := (+ f4 #1044)
+#1007 := (>= #1045 0::int)
+#1005 := (>= ?v0!0 1::int)
+#1432 := (or #1005 #1007 #1167)
+#2072 := (= f4 #1047)
+#12 := (f5 0::int)
+#2053 := (= #12 #1047)
+#1941 := (= #1047 #12)
+#2071 := (= ?v0!0 0::int)
+#1048 := (not #1005)
+#1437 := (not #1432)
+#2073 := [hypothesis]: #1437
+#1785 := (or #1432 #1048)
+#1870 := [def-axiom]: #1785
+#2046 := [unit-resolution #1870 #2073]: #1048
+#1863 := (or #1432 #1049)
+#1874 := [def-axiom]: #1863
+#2047 := [unit-resolution #1874 #2073]: #1049
+#2048 := [th-lemma #2047 #2046]: #2071
+#2052 := [monotonicity #2048]: #1941
+#2054 := [symm #2052]: #2053
+#13 := (= f4 #12)
+#970 := (<= f3 0::int)
+#918 := (not #916)
+#921 := (and #641 #918)
+#924 := (not #921)
+#932 := (or #924 #929)
+#935 := (forall (vars (?v0 int)) #932)
+#938 := (not #935)
+#809 := (and #671 #754)
+#812 := (not #809)
+#768 := (not #765)
+#771 := (and #641 #768)
+#774 := (not #771)
+#782 := (or #774 #779)
+#785 := (forall (vars (?v0 int)) #782)
+#788 := (not #785)
+#794 := (or #307 #788)
+#799 := (and #785 #794)
+#759 := (and #754 #757)
+#762 := (not #759)
+#673 := (and #668 #671)
+#676 := (not #673)
+#882 := (or #441 #432 #676 #762 #799 #806 #812 #818)
+#858 := (or #393 #375 #366 #815 #676 #762 #799 #806 #812 #819)
+#887 := (and #858 #882)
+#908 := (or #676 #724 #887)
+#705 := (* -1::int f10)
+#706 := (+ #24 #705)
+#707 := (<= #706 0::int)
+#682 := (not #681)
+#685 := (and #641 #682)
+#688 := (not #685)
+#710 := (or #688 #707)
+#713 := (forall (vars (?v0 int)) #710)
+#694 := (or #51 #688)
+#699 := (exists (vars (?v0 int)) #694)
+#702 := (not #699)
+#716 := (or #702 #713)
+#719 := (and #699 #716)
+#748 := (or #241 #232 #223 #676 #719 #727)
+#913 := (and #748 #908)
+#561 := (not #13)
+#956 := (or #561 #528 #676 #913 #938)
+#961 := (and #13 #956)
+#642 := (not #644)
+#646 := (and #641 #642)
+#649 := (not #646)
+#658 := (or #649 #654)
+#661 := (forall (vars (?v0 int)) #658)
+#664 := (not #661)
+#964 := (or #664 #961)
+#967 := (and #661 #964)
+#990 := (or #561 #967 #970)
+#995 := (not #990)
 #1 := true
-#87 := (= #86 uf_12)
-#88 := (and #87 true)
-#83 := (<= #20 uf_12)
-#81 := (< #16 uf_13)
-#17 := (<= 0::int #16)
-#82 := (and #17 #81)
-#84 := (implies #82 #83)
-#85 := (forall (vars (?x7 int)) #84)
-#89 := (implies #85 #88)
-#90 := (and #85 #89)
-#79 := (<= 2::int uf_13)
-#73 := (<= 0::int uf_11)
-#80 := (and #73 #79)
-#91 := (implies #80 #90)
-#76 := (+ uf_5 1::int)
-#77 := (= uf_13 #76)
-#92 := (implies #77 #91)
-#28 := (<= 1::int uf_5)
-#74 := (and #73 #28)
-#93 := (implies #74 #92)
-#94 := (implies true #93)
-#104 := (= uf_12 uf_6)
-#105 := (implies #104 #94)
-#103 := (= uf_11 uf_4)
-#106 := (implies #103 #105)
-#26 := (<= 0::int uf_4)
-#29 := (and #26 #28)
-#107 := (implies #29 #106)
-#102 := (<= #64 uf_6)
-#108 := (implies #102 #107)
-#109 := (implies #29 #108)
-#110 := (implies true #109)
-#72 := (= uf_12 uf_10)
-#95 := (implies #72 #94)
-#70 := (= uf_11 uf_5)
-#96 := (implies #70 #95)
-#68 := (and #28 #28)
-#97 := (implies #68 #96)
-#67 := (= uf_10 #64)
-#98 := (implies #67 #97)
-#65 := (< uf_6 #64)
-#99 := (implies #65 #98)
-#100 := (implies #29 #99)
-#101 := (implies true #100)
-#111 := (and #101 #110)
-#112 := (implies #29 #111)
-#63 := (< uf_5 uf_1)
-#113 := (implies #63 #112)
-#114 := (implies #29 #113)
-#115 := (implies true #114)
-#50 := (<= #20 uf_8)
-#45 := (< #16 uf_1)
-#46 := (and #17 #45)
-#51 := (implies #46 #50)
-#52 := (forall (vars (?x6 int)) #51)
-#53 := (and #52 true)
-#48 := (implies #46 #47)
-#49 := (exists (vars (?x4 int)) #48)
-#54 := (implies #49 #53)
-#55 := (and #49 #54)
-#44 := (= uf_9 uf_5)
-#56 := (implies #44 #55)
-#42 := (= uf_8 uf_6)
-#57 := (implies #42 #56)
-#40 := (= uf_7 uf_4)
-#58 := (implies #40 #57)
-#59 := (implies #29 #58)
-#38 := (<= uf_1 uf_5)
-#60 := (implies #38 #59)
-#61 := (implies #29 #60)
-#62 := (implies true #61)
-#116 := (and #62 #115)
-#117 := (implies #29 #116)
-#37 := (= #36 uf_6)
-#118 := (implies #37 #117)
-#33 := (<= #20 uf_6)
-#30 := (< #16 uf_5)
-#31 := (and #17 #30)
-#34 := (implies #31 #33)
-#35 := (forall (vars (?x3 int)) #34)
-#119 := (implies #35 #118)
-#120 := (implies #29 #119)
-#121 := (implies true #120)
-#24 := (= #8 uf_2)
-#122 := (implies #24 #121)
-#123 := (and #24 #122)
-#21 := (<= #20 uf_2)
-#18 := (< #16 1::int)
-#19 := (and #17 #18)
-#22 := (implies #19 #21)
-#23 := (forall (vars (?x1 int)) #22)
-#124 := (implies #23 #123)
-#125 := (and #23 #124)
-#12 := (<= 1::int 1::int)
-#13 := (and #12 #12)
-#10 := (<= 0::int 0::int)
-#14 := (and #10 #13)
-#15 := (and #10 #14)
-#126 := (implies #15 #125)
-#127 := (implies #9 #126)
-#6 := (< 0::int uf_1)
-#128 := (implies #6 #127)
-#129 := (implies true #128)
-#130 := (not #129)
-#993 := (iff #130 #990)
-#295 := (not #82)
-#296 := (or #295 #83)
-#299 := (forall (vars (?x7 int)) #296)
-#315 := (not #299)
-#316 := (or #315 #302)
-#321 := (and #299 #316)
-#327 := (not #80)
-#328 := (or #327 #321)
-#289 := (+ 1::int uf_5)
-#292 := (= uf_13 #289)
-#336 := (not #292)
-#337 := (or #336 #328)
-#286 := (and #28 #73)
-#345 := (not #286)
-#346 := (or #345 #337)
-#428 := (or #346 #427)
-#437 := (or #436 #428)
-#245 := (not #29)
-#445 := (or #245 #437)
-#453 := (not #102)
-#454 := (or #453 #445)
-#462 := (or #245 #454)
-#362 := (or #361 #346)
-#371 := (or #370 #362)
-#379 := (not #28)
-#380 := (or #379 #371)
-#389 := (or #388 #380)
-#397 := (not #65)
-#398 := (or #397 #389)
-#406 := (or #245 #398)
-#474 := (and #406 #462)
-#480 := (or #245 #474)
-#488 := (not #63)
-#489 := (or #488 #480)
-#497 := (or #245 #489)
-#183 := (not #46)
-#190 := (or #183 #50)
-#193 := (forall (vars (?x6 int)) #190)
-#184 := (or #183 #47)
-#187 := (exists (vars (?x4 int)) #184)
-#206 := (not #187)
-#207 := (or #206 #193)
-#212 := (and #187 #207)
-#219 := (or #218 #212)
-#228 := (or #227 #219)
-#237 := (or #236 #228)
-#246 := (or #245 #237)
-#254 := (not #38)
-#255 := (or #254 #246)
-#263 := (or #245 #255)
-#509 := (and #263 #497)
-#515 := (or #245 #509)
-#524 := (or #523 #515)
-#164 := (not #31)
-#165 := (or #164 #33)
-#168 := (forall (vars (?x3 int)) #165)
-#532 := (not #168)
-#533 := (or #532 #524)
-#541 := (or #245 #533)
-#557 := (or #556 #541)
-#562 := (and #9 #557)
-#155 := (not #19)
-#156 := (or #155 #21)
-#159 := (forall (vars (?x1 int)) #156)
-#568 := (not #159)
-#569 := (or #568 #562)
-#574 := (and #159 #569)
-#149 := (and #10 #12)
-#152 := (and #10 #149)
-#580 := (not #152)
-#581 := (or #580 #574)
-#589 := (or #556 #581)
-#597 := (not #6)
-#598 := (or #597 #589)
-#610 := (not #598)
-#991 := (iff #610 #990)
-#988 := (iff #598 #985)
-#976 := (or false #962)
-#979 := (or #556 #976)
-#982 := (or #965 #979)
-#986 := (iff #982 #985)
-#987 := [rewrite]: #986
-#983 := (iff #598 #982)
-#980 := (iff #589 #979)
-#977 := (iff #581 #976)
-#963 := (iff #574 #962)
-#960 := (iff #569 #959)
-#957 := (iff #562 #956)
-#954 := (iff #557 #951)
-#936 := (or #671 #908)
-#939 := (or #523 #936)
-#942 := (or #933 #939)
-#945 := (or #671 #942)
-#948 := (or #556 #945)
-#952 := (iff #948 #951)
-#953 := [rewrite]: #952
-#949 := (iff #557 #948)
-#946 := (iff #541 #945)
-#943 := (iff #533 #942)
-#940 := (iff #524 #939)
-#937 := (iff #515 #936)
-#909 := (iff #509 #908)
-#906 := (iff #497 #903)
-#894 := (or #671 #882)
-#897 := (or #719 #894)
-#900 := (or #671 #897)
-#904 := (iff #900 #903)
-#905 := [rewrite]: #904
-#901 := (iff #497 #900)
-#898 := (iff #489 #897)
-#895 := (iff #480 #894)
-#883 := (iff #474 #882)
-#880 := (iff #462 #877)
-#826 := (or #757 #794)
-#829 := (or #801 #826)
-#832 := (or #807 #829)
-#862 := (or #832 #427)
-#865 := (or #436 #862)
-#868 := (or #671 #865)
-#871 := (or #813 #868)
-#874 := (or #671 #871)
-#878 := (iff #874 #877)
-#879 := [rewrite]: #878
-#875 := (iff #462 #874)
-#872 := (iff #454 #871)
-#869 := (iff #445 #868)
-#866 := (iff #437 #865)
-#863 := (iff #428 #862)
-#833 := (iff #346 #832)
-#830 := (iff #337 #829)
-#827 := (iff #328 #826)
-#795 := (iff #321 #794)
-#792 := (iff #316 #789)
-#786 := (or #783 #302)
-#790 := (iff #786 #789)
-#791 := [rewrite]: #790
-#787 := (iff #316 #786)
-#784 := (iff #315 #783)
-#781 := (iff #299 #780)
-#778 := (iff #296 #777)
-#775 := (iff #83 #774)
-#776 := [rewrite]: #775
-#770 := (iff #295 #769)
-#767 := (iff #82 #766)
-#764 := (iff #81 #763)
-#765 := [rewrite]: #764
-#634 := (iff #17 #636)
-#635 := [rewrite]: #634
-#768 := [monotonicity #635 #765]: #767
-#771 := [monotonicity #768]: #770
-#779 := [monotonicity #771 #776]: #778
-#782 := [quant-intro #779]: #781
-#785 := [monotonicity #782]: #784
-#788 := [monotonicity #785]: #787
-#793 := [trans #788 #791]: #792
-#796 := [monotonicity #782 #793]: #795
-#758 := (iff #327 #757)
-#755 := (iff #80 #754)
-#751 := (iff #79 #752)
-#753 := [rewrite]: #751
-#748 := (iff #73 #749)
-#750 := [rewrite]: #748
-#756 := [monotonicity #750 #753]: #755
-#759 := [monotonicity #756]: #758
-#828 := [monotonicity #759 #796]: #827
-#802 := (iff #336 #801)
-#799 := (iff #292 #797)
-#800 := [rewrite]: #799
-#803 := [monotonicity #800]: #802
-#831 := [monotonicity #803 #828]: #830
-#808 := (iff #345 #807)
-#805 := (iff #286 #804)
-#665 := (iff #28 #666)
-#667 := [rewrite]: #665
-#806 := [monotonicity #667 #750]: #805
-#809 := [monotonicity #806]: #808
-#834 := [monotonicity #809 #831]: #833
-#864 := [monotonicity #834]: #863
-#867 := [monotonicity #864]: #866
-#672 := (iff #245 #671)
-#669 := (iff #29 #668)
-#662 := (iff #26 #663)
-#664 := [rewrite]: #662
-#670 := [monotonicity #664 #667]: #669
-#673 := [monotonicity #670]: #672
-#870 := [monotonicity #673 #867]: #869
-#860 := (iff #453 #813)
-#858 := (iff #102 #814)
-#859 := [rewrite]: #858
-#861 := [monotonicity #859]: #860
-#873 := [monotonicity #861 #870]: #872
-#876 := [monotonicity #673 #873]: #875
-#881 := [trans #876 #879]: #880
-#856 := (iff #406 #853)
-#835 := (or #361 #832)
-#838 := (or #370 #835)
-#841 := (or #810 #838)
-#844 := (or #388 #841)
-#847 := (or #814 #844)
-#850 := (or #671 #847)
-#854 := (iff #850 #853)
-#855 := [rewrite]: #854
-#851 := (iff #406 #850)
-#848 := (iff #398 #847)
-#845 := (iff #389 #844)
-#842 := (iff #380 #841)
-#839 := (iff #371 #838)
-#836 := (iff #362 #835)
-#837 := [monotonicity #834]: #836
-#840 := [monotonicity #837]: #839
-#811 := (iff #379 #810)
-#812 := [monotonicity #667]: #811
-#843 := [monotonicity #812 #840]: #842
-#846 := [monotonicity #843]: #845
-#824 := (iff #397 #814)
-#819 := (not #813)
-#822 := (iff #819 #814)
+#91 := (= #90 f14)
+#92 := (and #91 true)
+#87 := (<= #24 f14)
+#85 := (< #20 f15)
+#21 := (<= 0::int #20)
+#86 := (and #21 #85)
+#88 := (implies #86 #87)
+#89 := (forall (vars (?v0 int)) #88)
+#93 := (implies #89 #92)
+#94 := (and #89 #93)
+#83 := (<= 2::int f15)
+#77 := (<= 0::int f13)
+#84 := (and #77 #83)
+#95 := (implies #84 #94)
+#80 := (+ f7 1::int)
+#81 := (= f15 #80)
+#96 := (implies #81 #95)
+#32 := (<= 1::int f7)
+#78 := (and #77 #32)
+#97 := (implies #78 #96)
+#98 := (implies true #97)
+#108 := (= f14 f8)
+#109 := (implies #108 #98)
+#107 := (= f13 f6)
+#110 := (implies #107 #109)
+#30 := (<= 0::int f6)
+#33 := (and #30 #32)
+#111 := (implies #33 #110)
+#106 := (<= #68 f8)
+#112 := (implies #106 #111)
+#113 := (implies #33 #112)
+#114 := (implies true #113)
+#76 := (= f14 f12)
+#99 := (implies #76 #98)
+#74 := (= f13 f7)
+#100 := (implies #74 #99)
+#72 := (and #32 #32)
+#101 := (implies #72 #100)
+#71 := (= f12 #68)
+#102 := (implies #71 #101)
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+#18 := (and #14 #17)
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+#988 := (iff #603 #987)
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+#948 := (iff #538 #947)
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+#942 := (iff #520 #941)
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+#902 := (or #724 #899)
+#905 := (or #676 #902)
+#909 := (iff #905 #908)
+#910 := [rewrite]: #909
+#906 := (iff #502 #905)
+#903 := (iff #494 #902)
+#900 := (iff #485 #899)
+#888 := (iff #479 #887)
+#885 := (iff #467 #882)
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+#873 := (or #676 #870)
+#876 := (or #818 #873)
+#879 := (or #676 #876)
+#883 := (iff #879 #882)
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+#874 := (iff #450 #873)
+#871 := (iff #442 #870)
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+#786 := (iff #304 #785)
+#783 := (iff #301 #782)
+#780 := (iff #87 #779)
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+#769 := (iff #85 #768)
+#770 := [rewrite]: #769
+#639 := (iff #21 #641)
+#640 := [rewrite]: #639
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+#776 := [monotonicity #773]: #775
+#784 := [monotonicity #776 #781]: #783
+#787 := [quant-intro #784]: #786
+#790 := [monotonicity #787]: #789
+#793 := [monotonicity #790]: #792
+#798 := [trans #793 #796]: #797
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+#763 := (iff #332 #762)
+#760 := (iff #84 #759)
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+#758 := [rewrite]: #756
+#753 := (iff #77 #754)
+#755 := [rewrite]: #753
+#761 := [monotonicity #755 #758]: #760
+#764 := [monotonicity #761]: #763
+#833 := [monotonicity #764 #801]: #832
+#807 := (iff #341 #806)
+#804 := (iff #297 #802)
+#805 := [rewrite]: #804
+#808 := [monotonicity #805]: #807
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+#813 := (iff #350 #812)
+#810 := (iff #291 #809)
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+#674 := (iff #33 #673)
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+#678 := [monotonicity #675]: #677
+#875 := [monotonicity #678 #872]: #874
+#865 := (iff #458 #818)
+#863 := (iff #106 #819)
+#864 := [rewrite]: #863
+#866 := [monotonicity #864]: #865
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+#881 := [monotonicity #678 #878]: #880
+#886 := [trans #881 #884]: #885
+#861 := (iff #411 #858)
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+#843 := (or #375 #840)
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+#816 := (iff #384 #815)
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+#848 := [monotonicity #817 #845]: #847
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+#829 := (iff #402 #819)
+#824 := (not #818)
+#827 := (iff #824 #819)
+#828 := [rewrite]: #827
+#825 := (iff #402 #824)
+#822 := (iff #69 #818)
 #823 := [rewrite]: #822
-#820 := (iff #397 #819)
-#817 := (iff #65 #813)
-#818 := [rewrite]: #817
-#821 := [monotonicity #818]: #820
-#825 := [trans #821 #823]: #824
-#849 := [monotonicity #825 #846]: #848
-#852 := [monotonicity #673 #849]: #851
-#857 := [trans #852 #855]: #856
-#884 := [monotonicity #857 #881]: #883
-#896 := [monotonicity #673 #884]: #895
-#892 := (iff #488 #719)
-#887 := (not #722)
-#890 := (iff #887 #719)
+#826 := [monotonicity #823]: #825
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+#854 := [monotonicity #830 #851]: #853
+#857 := [monotonicity #678 #854]: #856
+#862 := [trans #857 #860]: #861
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+#901 := [monotonicity #678 #889]: #900
+#897 := (iff #493 #724)
+#892 := (not #727)
+#895 := (iff #892 #724)
+#896 := [rewrite]: #895
+#893 := (iff #493 #892)
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 #891 := [rewrite]: #890
-#888 := (iff #488 #887)
-#885 := (iff #63 #722)
-#886 := [rewrite]: #885
-#889 := [monotonicity #886]: #888
-#893 := [trans #889 #891]: #892
-#899 := [monotonicity #893 #896]: #898
-#902 := [monotonicity #673 #899]: #901
-#907 := [trans #902 #905]: #906
-#746 := (iff #263 #743)
-#725 := (or #218 #714)
-#728 := (or #227 #725)
-#731 := (or #236 #728)
-#734 := (or #671 #731)
-#737 := (or #722 #734)
-#740 := (or #671 #737)
-#744 := (iff #740 #743)
-#745 := [rewrite]: #744
-#741 := (iff #263 #740)
-#738 := (iff #255 #737)
-#735 := (iff #246 #734)
-#732 := (iff #237 #731)
-#729 := (iff #228 #728)
-#726 := (iff #219 #725)
-#715 := (iff #212 #714)
-#712 := (iff #207 #711)
-#709 := (iff #193 #708)
-#706 := (iff #190 #705)
-#703 := (iff #50 #702)
-#704 := [rewrite]: #703
-#684 := (iff #183 #683)
-#681 := (iff #46 #680)
-#678 := (iff #45 #677)
-#679 := [rewrite]: #678
-#682 := [monotonicity #635 #679]: #681
-#685 := [monotonicity #682]: #684
-#707 := [monotonicity #685 #704]: #706
-#710 := [quant-intro #707]: #709
-#698 := (iff #206 #697)
-#695 := (iff #187 #694)
-#692 := (iff #184 #689)
-#686 := (or #683 #47)
-#690 := (iff #686 #689)
-#691 := [rewrite]: #690
-#687 := (iff #184 #686)
-#688 := [monotonicity #685]: #687
-#693 := [trans #688 #691]: #692
-#696 := [quant-intro #693]: #695
-#699 := [monotonicity #696]: #698
-#713 := [monotonicity #699 #710]: #712
-#716 := [monotonicity #696 #713]: #715
-#727 := [monotonicity #716]: #726
-#730 := [monotonicity #727]: #729
-#733 := [monotonicity #730]: #732
-#736 := [monotonicity #673 #733]: #735
-#723 := (iff #254 #722)
-#720 := (iff #38 #719)
-#721 := [rewrite]: #720
-#724 := [monotonicity #721]: #723
-#739 := [monotonicity #724 #736]: #738
-#742 := [monotonicity #673 #739]: #741
-#747 := [trans #742 #745]: #746
-#910 := [monotonicity #747 #907]: #909
-#938 := [monotonicity #673 #910]: #937
-#941 := [monotonicity #938]: #940
-#934 := (iff #532 #933)
-#931 := (iff #168 #930)
-#928 := (iff #165 #927)
-#925 := (iff #33 #924)
-#926 := [rewrite]: #925
-#920 := (iff #164 #919)
-#917 := (iff #31 #916)
-#914 := (iff #30 #913)
-#915 := [rewrite]: #914
-#918 := [monotonicity #635 #915]: #917
-#921 := [monotonicity #918]: #920
-#929 := [monotonicity #921 #926]: #928
-#932 := [quant-intro #929]: #931
-#935 := [monotonicity #932]: #934
-#944 := [monotonicity #935 #941]: #943
-#947 := [monotonicity #673 #944]: #946
-#950 := [monotonicity #947]: #949
-#955 := [trans #950 #953]: #954
-#958 := [monotonicity #955]: #957
-#660 := (iff #568 #659)
-#657 := (iff #159 #656)
-#654 := (iff #156 #653)
-#648 := (iff #21 #649)
-#652 := [rewrite]: #648
-#645 := (iff #155 #644)
-#642 := (iff #19 #641)
-#638 := (iff #18 #637)
-#640 := [rewrite]: #638
-#643 := [monotonicity #635 #640]: #642
-#646 := [monotonicity #643]: #645
-#655 := [monotonicity #646 #652]: #654
-#658 := [quant-intro #655]: #657
-#661 := [monotonicity #658]: #660
-#961 := [monotonicity #661 #958]: #960
-#964 := [monotonicity #658 #961]: #963
-#632 := (iff #580 false)
-#627 := (not true)
-#630 := (iff #627 false)
-#631 := [rewrite]: #630
-#628 := (iff #580 #627)
-#625 := (iff #152 true)
-#617 := (and true true)
-#620 := (and true #617)
-#623 := (iff #620 true)
-#624 := [rewrite]: #623
-#621 := (iff #152 #620)
-#618 := (iff #149 #617)
-#615 := (iff #12 true)
-#616 := [rewrite]: #615
-#613 := (iff #10 true)
-#614 := [rewrite]: #613
-#619 := [monotonicity #614 #616]: #618
-#622 := [monotonicity #614 #619]: #621
-#626 := [trans #622 #624]: #625
-#629 := [monotonicity #626]: #628
-#633 := [trans #629 #631]: #632
-#978 := [monotonicity #633 #964]: #977
-#981 := [monotonicity #978]: #980
-#974 := (iff #597 #965)
-#966 := (not #965)
-#969 := (not #966)
-#972 := (iff #969 #965)
+#894 := [monotonicity #891]: #893
+#898 := [trans #894 #896]: #897
+#904 := [monotonicity #898 #901]: #903
+#907 := [monotonicity #678 #904]: #906
+#912 := [trans #907 #910]: #911
+#751 := (iff #268 #748)
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+#733 := (or #232 #730)
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+#739 := (or #676 #736)
+#742 := (or #727 #739)
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+#749 := (iff #745 #748)
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+#746 := (iff #268 #745)
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+#740 := (iff #251 #739)
+#737 := (iff #242 #736)
+#734 := (iff #233 #733)
+#731 := (iff #224 #730)
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+#717 := (iff #212 #716)
+#714 := (iff #198 #713)
+#711 := (iff #195 #710)
+#708 := (iff #54 #707)
+#709 := [rewrite]: #708
+#689 := (iff #188 #688)
+#686 := (iff #50 #685)
+#683 := (iff #49 #682)
+#684 := [rewrite]: #683
+#687 := [monotonicity #640 #684]: #686
+#690 := [monotonicity #687]: #689
+#712 := [monotonicity #690 #709]: #711
+#715 := [quant-intro #712]: #714
+#703 := (iff #211 #702)
+#700 := (iff #192 #699)
+#697 := (iff #189 #694)
+#691 := (or #688 #51)
+#695 := (iff #691 #694)
+#696 := [rewrite]: #695
+#692 := (iff #189 #691)
+#693 := [monotonicity #690]: #692
+#698 := [trans #693 #696]: #697
+#701 := [quant-intro #698]: #700
+#704 := [monotonicity #701]: #703
+#718 := [monotonicity #704 #715]: #717
+#721 := [monotonicity #701 #718]: #720
+#732 := [monotonicity #721]: #731
+#735 := [monotonicity #732]: #734
+#738 := [monotonicity #735]: #737
+#741 := [monotonicity #678 #738]: #740
+#728 := (iff #259 #727)
+#725 := (iff #42 #724)
+#726 := [rewrite]: #725
+#729 := [monotonicity #726]: #728
+#744 := [monotonicity #729 #741]: #743
+#747 := [monotonicity #678 #744]: #746
+#752 := [trans #747 #750]: #751
+#915 := [monotonicity #752 #912]: #914
+#943 := [monotonicity #678 #915]: #942
+#946 := [monotonicity #943]: #945
+#939 := (iff #537 #938)
+#936 := (iff #173 #935)
+#933 := (iff #170 #932)
+#930 := (iff #37 #929)
+#931 := [rewrite]: #930
+#925 := (iff #169 #924)
+#922 := (iff #35 #921)
+#919 := (iff #34 #918)
+#920 := [rewrite]: #919
+#923 := [monotonicity #640 #920]: #922
+#926 := [monotonicity #923]: #925
+#934 := [monotonicity #926 #931]: #933
+#937 := [quant-intro #934]: #936
+#940 := [monotonicity #937]: #939
+#949 := [monotonicity #940 #946]: #948
+#952 := [monotonicity #678 #949]: #951
+#955 := [monotonicity #952]: #954
+#960 := [trans #955 #958]: #959
+#963 := [monotonicity #960]: #962
+#665 := (iff #573 #664)
+#662 := (iff #164 #661)
+#659 := (iff #161 #658)
+#653 := (iff #25 #654)
+#657 := [rewrite]: #653
+#650 := (iff #160 #649)
+#647 := (iff #23 #646)
+#643 := (iff #22 #642)
+#645 := [rewrite]: #643
+#648 := [monotonicity #640 #645]: #647
+#651 := [monotonicity #648]: #650
+#660 := [monotonicity #651 #657]: #659
+#663 := [quant-intro #660]: #662
+#666 := [monotonicity #663]: #665
+#966 := [monotonicity #666 #963]: #965
+#969 := [monotonicity #663 #966]: #968
+#637 := (iff #585 false)
+#632 := (not true)
+#635 := (iff #632 false)
+#636 := [rewrite]: #635
+#633 := (iff #585 #632)
+#630 := (iff #157 true)
+#622 := (and true true)
+#625 := (and true #622)
+#628 := (iff #625 true)
+#629 := [rewrite]: #628
+#626 := (iff #157 #625)
+#623 := (iff #154 #622)
+#620 := (iff #16 true)
+#621 := [rewrite]: #620
+#618 := (iff #14 true)
+#619 := [rewrite]: #618
+#624 := [monotonicity #619 #621]: #623
+#627 := [monotonicity #619 #624]: #626
+#631 := [trans #627 #629]: #630
+#634 := [monotonicity #631]: #633
+#638 := [trans #634 #636]: #637
+#983 := [monotonicity #638 #969]: #982
+#986 := [monotonicity #983]: #985
+#979 := (iff #602 #970)
+#971 := (not #970)
+#974 := (not #971)
+#977 := (iff #974 #970)
+#978 := [rewrite]: #977
+#975 := (iff #602 #974)
+#972 := (iff #10 #971)
 #973 := [rewrite]: #972
-#970 := (iff #597 #969)
-#967 := (iff #6 #966)
-#968 := [rewrite]: #967
-#971 := [monotonicity #968]: #970
-#975 := [trans #971 #973]: #974
-#984 := [monotonicity #975 #981]: #983
-#989 := [trans #984 #987]: #988
-#992 := [monotonicity #989]: #991
-#611 := (iff #130 #610)
-#608 := (iff #129 #598)
-#603 := (implies true #598)
-#606 := (iff #603 #598)
-#607 := [rewrite]: #606
-#604 := (iff #129 #603)
-#601 := (iff #128 #598)
-#594 := (implies #6 #589)
-#599 := (iff #594 #598)
-#600 := [rewrite]: #599
-#595 := (iff #128 #594)
-#592 := (iff #127 #589)
-#586 := (implies #9 #581)
-#590 := (iff #586 #589)
-#591 := [rewrite]: #590
-#587 := (iff #127 #586)
-#584 := (iff #126 #581)
-#577 := (implies #152 #574)
-#582 := (iff #577 #581)
-#583 := [rewrite]: #582
-#578 := (iff #126 #577)
-#575 := (iff #125 #574)
-#572 := (iff #124 #569)
-#565 := (implies #159 #562)
-#570 := (iff #565 #569)
-#571 := [rewrite]: #570
-#566 := (iff #124 #565)
-#563 := (iff #123 #562)
-#560 := (iff #122 #557)
-#553 := (implies #9 #541)
-#558 := (iff #553 #557)
-#559 := [rewrite]: #558
-#554 := (iff #122 #553)
-#551 := (iff #121 #541)
-#546 := (implies true #541)
-#549 := (iff #546 #541)
-#550 := [rewrite]: #549
-#547 := (iff #121 #546)
-#544 := (iff #120 #541)
-#538 := (implies #29 #533)
-#542 := (iff #538 #541)
-#543 := [rewrite]: #542
-#539 := (iff #120 #538)
-#536 := (iff #119 #533)
-#529 := (implies #168 #524)
-#534 := (iff #529 #533)
-#535 := [rewrite]: #534
-#530 := (iff #119 #529)
-#527 := (iff #118 #524)
-#520 := (implies #171 #515)
-#525 := (iff #520 #524)
-#526 := [rewrite]: #525
-#521 := (iff #118 #520)
-#518 := (iff #117 #515)
-#512 := (implies #29 #509)
-#516 := (iff #512 #515)
-#517 := [rewrite]: #516
-#513 := (iff #117 #512)
-#510 := (iff #116 #509)
-#507 := (iff #115 #497)
-#502 := (implies true #497)
-#505 := (iff #502 #497)
-#506 := [rewrite]: #505
-#503 := (iff #115 #502)
-#500 := (iff #114 #497)
-#494 := (implies #29 #489)
-#498 := (iff #494 #497)
-#499 := [rewrite]: #498
-#495 := (iff #114 #494)
-#492 := (iff #113 #489)
-#485 := (implies #63 #480)
-#490 := (iff #485 #489)
-#491 := [rewrite]: #490
-#486 := (iff #113 #485)
-#483 := (iff #112 #480)
-#477 := (implies #29 #474)
-#481 := (iff #477 #480)
-#482 := [rewrite]: #481
-#478 := (iff #112 #477)
-#475 := (iff #111 #474)
-#472 := (iff #110 #462)
-#467 := (implies true #462)
-#470 := (iff #467 #462)
-#471 := [rewrite]: #470
-#468 := (iff #110 #467)
-#465 := (iff #109 #462)
-#459 := (implies #29 #454)
-#463 := (iff #459 #462)
-#464 := [rewrite]: #463
-#460 := (iff #109 #459)
-#457 := (iff #108 #454)
-#450 := (implies #102 #445)
-#455 := (iff #450 #454)
-#456 := [rewrite]: #455
-#451 := (iff #108 #450)
-#448 := (iff #107 #445)
-#442 := (implies #29 #437)
-#446 := (iff #442 #445)
-#447 := [rewrite]: #446
-#443 := (iff #107 #442)
-#440 := (iff #106 #437)
-#433 := (implies #418 #428)
-#438 := (iff #433 #437)
-#439 := [rewrite]: #438
-#434 := (iff #106 #433)
-#431 := (iff #105 #428)
-#424 := (implies #421 #346)
-#429 := (iff #424 #428)
-#430 := [rewrite]: #429
-#425 := (iff #105 #424)
-#356 := (iff #94 #346)
-#351 := (implies true #346)
-#354 := (iff #351 #346)
-#355 := [rewrite]: #354
-#352 := (iff #94 #351)
-#349 := (iff #93 #346)
-#342 := (implies #286 #337)
-#347 := (iff #342 #346)
-#348 := [rewrite]: #347
-#343 := (iff #93 #342)
-#340 := (iff #92 #337)
-#333 := (implies #292 #328)
-#338 := (iff #333 #337)
-#339 := [rewrite]: #338
-#334 := (iff #92 #333)
-#331 := (iff #91 #328)
-#324 := (implies #80 #321)
-#329 := (iff #324 #328)
-#330 := [rewrite]: #329
-#325 := (iff #91 #324)
-#322 := (iff #90 #321)
-#319 := (iff #89 #316)
-#312 := (implies #299 #302)
-#317 := (iff #312 #316)
-#318 := [rewrite]: #317
-#313 := (iff #89 #312)
-#310 := (iff #88 #302)
-#305 := (and #302 true)
-#308 := (iff #305 #302)
+#976 := [monotonicity #973]: #975
+#980 := [trans #976 #978]: #979
+#989 := [monotonicity #980 #986]: #988
+#994 := [trans #989 #992]: #993
+#997 := [monotonicity #994]: #996
+#616 := (iff #134 #615)
+#613 := (iff #133 #603)
+#608 := (implies true #603)
+#611 := (iff #608 #603)
+#612 := [rewrite]: #611
+#609 := (iff #133 #608)
+#606 := (iff #132 #603)
+#599 := (implies #10 #594)
+#604 := (iff #599 #603)
+#605 := [rewrite]: #604
+#600 := (iff #132 #599)
+#597 := (iff #131 #594)
+#591 := (implies #13 #586)
+#595 := (iff #591 #594)
+#596 := [rewrite]: #595
+#592 := (iff #131 #591)
+#589 := (iff #130 #586)
+#582 := (implies #157 #579)
+#587 := (iff #582 #586)
+#588 := [rewrite]: #587
+#583 := (iff #130 #582)
+#580 := (iff #129 #579)
+#577 := (iff #128 #574)
+#570 := (implies #164 #567)
+#575 := (iff #570 #574)
+#576 := [rewrite]: #575
+#571 := (iff #128 #570)
+#568 := (iff #127 #567)
+#565 := (iff #126 #562)
+#558 := (implies #13 #546)
+#563 := (iff #558 #562)
+#564 := [rewrite]: #563
+#559 := (iff #126 #558)
+#556 := (iff #125 #546)
+#551 := (implies true #546)
+#554 := (iff #551 #546)
+#555 := [rewrite]: #554
+#552 := (iff #125 #551)
+#549 := (iff #124 #546)
+#543 := (implies #33 #538)
+#547 := (iff #543 #546)
+#548 := [rewrite]: #547
+#544 := (iff #124 #543)
+#541 := (iff #123 #538)
+#534 := (implies #173 #529)
+#539 := (iff #534 #538)
+#540 := [rewrite]: #539
+#535 := (iff #123 #534)
+#532 := (iff #122 #529)
+#525 := (implies #176 #520)
+#530 := (iff #525 #529)
+#531 := [rewrite]: #530
+#526 := (iff #122 #525)
+#523 := (iff #121 #520)
+#517 := (implies #33 #514)
+#521 := (iff #517 #520)
+#522 := [rewrite]: #521
+#518 := (iff #121 #517)
+#515 := (iff #120 #514)
+#512 := (iff #119 #502)
+#507 := (implies true #502)
+#510 := (iff #507 #502)
+#511 := [rewrite]: #510
+#508 := (iff #119 #507)
+#505 := (iff #118 #502)
+#499 := (implies #33 #494)
+#503 := (iff #499 #502)
+#504 := [rewrite]: #503
+#500 := (iff #118 #499)
+#497 := (iff #117 #494)
+#490 := (implies #67 #485)
+#495 := (iff #490 #494)
+#496 := [rewrite]: #495
+#491 := (iff #117 #490)
+#488 := (iff #116 #485)
+#482 := (implies #33 #479)
+#486 := (iff #482 #485)
+#487 := [rewrite]: #486
+#483 := (iff #116 #482)
+#480 := (iff #115 #479)
+#477 := (iff #114 #467)
+#472 := (implies true #467)
+#475 := (iff #472 #467)
+#476 := [rewrite]: #475
+#473 := (iff #114 #472)
+#470 := (iff #113 #467)
+#464 := (implies #33 #459)
+#468 := (iff #464 #467)
+#469 := [rewrite]: #468
+#465 := (iff #113 #464)
+#462 := (iff #112 #459)
+#455 := (implies #106 #450)
+#460 := (iff #455 #459)
+#461 := [rewrite]: #460
+#456 := (iff #112 #455)
+#453 := (iff #111 #450)
+#447 := (implies #33 #442)
+#451 := (iff #447 #450)
+#452 := [rewrite]: #451
+#448 := (iff #111 #447)
+#445 := (iff #110 #442)
+#438 := (implies #423 #433)
+#443 := (iff #438 #442)
+#444 := [rewrite]: #443
+#439 := (iff #110 #438)
+#436 := (iff #109 #433)
+#429 := (implies #426 #351)
+#434 := (iff #429 #433)
+#435 := [rewrite]: #434
+#430 := (iff #109 #429)
+#361 := (iff #98 #351)
+#356 := (implies true #351)
+#359 := (iff #356 #351)
+#360 := [rewrite]: #359
+#357 := (iff #98 #356)
+#354 := (iff #97 #351)
+#347 := (implies #291 #342)
+#352 := (iff #347 #351)
+#353 := [rewrite]: #352
+#348 := (iff #97 #347)
+#345 := (iff #96 #342)
+#338 := (implies #297 #333)
+#343 := (iff #338 #342)
+#344 := [rewrite]: #343
+#339 := (iff #96 #338)
+#336 := (iff #95 #333)
+#329 := (implies #84 #326)
+#334 := (iff #329 #333)
+#335 := [rewrite]: #334
+#330 := (iff #95 #329)
+#327 := (iff #94 #326)
+#324 := (iff #93 #321)
+#317 := (implies #304 #307)
+#322 := (iff #317 #321)
+#323 := [rewrite]: #322
+#318 := (iff #93 #317)
+#315 := (iff #92 #307)
+#310 := (and #307 true)
+#313 := (iff #310 #307)
+#314 := [rewrite]: #313
+#311 := (iff #92 #310)
+#308 := (iff #91 #307)
 #309 := [rewrite]: #308
-#306 := (iff #88 #305)
-#303 := (iff #87 #302)
-#304 := [rewrite]: #303
-#307 := [monotonicity #304]: #306
-#311 := [trans #307 #309]: #310
-#300 := (iff #85 #299)
-#297 := (iff #84 #296)
-#298 := [rewrite]: #297
-#301 := [quant-intro #298]: #300
-#314 := [monotonicity #301 #311]: #313
-#320 := [trans #314 #318]: #319
-#323 := [monotonicity #301 #320]: #322
-#326 := [monotonicity #323]: #325
-#332 := [trans #326 #330]: #331
-#293 := (iff #77 #292)
-#290 := (= #76 #289)
-#291 := [rewrite]: #290
-#294 := [monotonicity #291]: #293
-#335 := [monotonicity #294 #332]: #334
-#341 := [trans #335 #339]: #340
-#287 := (iff #74 #286)
-#288 := [rewrite]: #287
-#344 := [monotonicity #288 #341]: #343
-#350 := [trans #344 #348]: #349
-#353 := [monotonicity #350]: #352
-#357 := [trans #353 #355]: #356
-#422 := (iff #104 #421)
-#423 := [rewrite]: #422
-#426 := [monotonicity #423 #357]: #425
-#432 := [trans #426 #430]: #431
-#419 := (iff #103 #418)
+#312 := [monotonicity #309]: #311
+#316 := [trans #312 #314]: #315
+#305 := (iff #89 #304)
+#302 := (iff #88 #301)
+#303 := [rewrite]: #302
+#306 := [quant-intro #303]: #305
+#319 := [monotonicity #306 #316]: #318
+#325 := [trans #319 #323]: #324
+#328 := [monotonicity #306 #325]: #327
+#331 := [monotonicity #328]: #330
+#337 := [trans #331 #335]: #336
+#298 := (iff #81 #297)
+#295 := (= #80 #294)
+#296 := [rewrite]: #295
+#299 := [monotonicity #296]: #298
+#340 := [monotonicity #299 #337]: #339
+#346 := [trans #340 #344]: #345
+#292 := (iff #78 #291)
+#293 := [rewrite]: #292
+#349 := [monotonicity #293 #346]: #348
+#355 := [trans #349 #353]: #354
+#358 := [monotonicity #355]: #357
+#362 := [trans #358 #360]: #361
+#427 := (iff #108 #426)
+#428 := [rewrite]: #427
+#431 := [monotonicity #428 #362]: #430
+#437 := [trans #431 #435]: #436
+#424 := (iff #107 #423)
+#425 := [rewrite]: #424
+#440 := [monotonicity #425 #437]: #439
+#446 := [trans #440 #444]: #445
+#449 := [monotonicity #446]: #448
+#454 := [trans #449 #452]: #453
+#457 := [monotonicity #454]: #456
+#463 := [trans #457 #461]: #462
+#466 := [monotonicity #463]: #465
+#471 := [trans #466 #469]: #470
+#474 := [monotonicity #471]: #473
+#478 := [trans #474 #476]: #477
+#421 := (iff #105 #411)
+#416 := (implies true #411)
+#419 := (iff #416 #411)
 #420 := [rewrite]: #419
-#435 := [monotonicity #420 #432]: #434
-#441 := [trans #435 #439]: #440
-#444 := [monotonicity #441]: #443
-#449 := [trans #444 #447]: #448
-#452 := [monotonicity #449]: #451
-#458 := [trans #452 #456]: #457
-#461 := [monotonicity #458]: #460
-#466 := [trans #461 #464]: #465
-#469 := [monotonicity #466]: #468
-#473 := [trans #469 #471]: #472
-#416 := (iff #101 #406)
-#411 := (implies true #406)
-#414 := (iff #411 #406)
-#415 := [rewrite]: #414
-#412 := (iff #101 #411)
-#409 := (iff #100 #406)
-#403 := (implies #29 #398)
-#407 := (iff #403 #406)
-#408 := [rewrite]: #407
-#404 := (iff #100 #403)
-#401 := (iff #99 #398)
-#394 := (implies #65 #389)
-#399 := (iff #394 #398)
-#400 := [rewrite]: #399
-#395 := (iff #99 #394)
-#392 := (iff #98 #389)
-#385 := (implies #275 #380)
-#390 := (iff #385 #389)
-#391 := [rewrite]: #390
-#386 := (iff #98 #385)
-#383 := (iff #97 #380)
-#376 := (implies #28 #371)
-#381 := (iff #376 #380)
-#382 := [rewrite]: #381
-#377 := (iff #97 #376)
-#374 := (iff #96 #371)
-#367 := (implies #280 #362)
-#372 := (iff #367 #371)
-#373 := [rewrite]: #372
-#368 := (iff #96 #367)
-#365 := (iff #95 #362)
-#358 := (implies #283 #346)
-#363 := (iff #358 #362)
-#364 := [rewrite]: #363
-#359 := (iff #95 #358)
-#284 := (iff #72 #283)
-#285 := [rewrite]: #284
-#360 := [monotonicity #285 #357]: #359
-#366 := [trans #360 #364]: #365
-#281 := (iff #70 #280)
+#417 := (iff #105 #416)
+#414 := (iff #104 #411)
+#408 := (implies #33 #403)
+#412 := (iff #408 #411)
+#413 := [rewrite]: #412
+#409 := (iff #104 #408)
+#406 := (iff #103 #403)
+#399 := (implies #69 #394)
+#404 := (iff #399 #403)
+#405 := [rewrite]: #404
+#400 := (iff #103 #399)
+#397 := (iff #102 #394)
+#390 := (implies #280 #385)
+#395 := (iff #390 #394)
+#396 := [rewrite]: #395
+#391 := (iff #102 #390)
+#388 := (iff #101 #385)
+#381 := (implies #32 #376)
+#386 := (iff #381 #385)
+#387 := [rewrite]: #386
+#382 := (iff #101 #381)
+#379 := (iff #100 #376)
+#372 := (implies #285 #367)
+#377 := (iff #372 #376)
+#378 := [rewrite]: #377
+#373 := (iff #100 #372)
+#370 := (iff #99 #367)
+#363 := (implies #288 #351)
+#368 := (iff #363 #367)
+#369 := [rewrite]: #368
+#364 := (iff #99 #363)
+#289 := (iff #76 #288)
+#290 := [rewrite]: #289
+#365 := [monotonicity #290 #362]: #364
+#371 := [trans #365 #369]: #370
+#286 := (iff #74 #285)
+#287 := [rewrite]: #286
+#374 := [monotonicity #287 #371]: #373
+#380 := [trans #374 #378]: #379
+#283 := (iff #72 #32)
+#284 := [rewrite]: #283
+#383 := [monotonicity #284 #380]: #382
+#389 := [trans #383 #387]: #388
+#281 := (iff #71 #280)
 #282 := [rewrite]: #281
-#369 := [monotonicity #282 #366]: #368
-#375 := [trans #369 #373]: #374
-#278 := (iff #68 #28)
-#279 := [rewrite]: #278
-#378 := [monotonicity #279 #375]: #377
-#384 := [trans #378 #382]: #383
-#276 := (iff #67 #275)
+#392 := [monotonicity #282 #389]: #391
+#398 := [trans #392 #396]: #397
+#401 := [monotonicity #398]: #400
+#407 := [trans #401 #405]: #406
+#410 := [monotonicity #407]: #409
+#415 := [trans #410 #413]: #414
+#418 := [monotonicity #415]: #417
+#422 := [trans #418 #420]: #421
+#481 := [monotonicity #422 #478]: #480
+#484 := [monotonicity #481]: #483
+#489 := [trans #484 #487]: #488
+#492 := [monotonicity #489]: #491
+#498 := [trans #492 #496]: #497
+#501 := [monotonicity #498]: #500
+#506 := [trans #501 #504]: #505
+#509 := [monotonicity #506]: #508
+#513 := [trans #509 #511]: #512
+#278 := (iff #66 #268)
+#273 := (implies true #268)
+#276 := (iff #273 #268)
 #277 := [rewrite]: #276
-#387 := [monotonicity #277 #384]: #386
-#393 := [trans #387 #391]: #392
-#396 := [monotonicity #393]: #395
-#402 := [trans #396 #400]: #401
-#405 := [monotonicity #402]: #404
-#410 := [trans #405 #408]: #409
-#413 := [monotonicity #410]: #412
-#417 := [trans #413 #415]: #416
-#476 := [monotonicity #417 #473]: #475
-#479 := [monotonicity #476]: #478
-#484 := [trans #479 #482]: #483
-#487 := [monotonicity #484]: #486
-#493 := [trans #487 #491]: #492
-#496 := [monotonicity #493]: #495
-#501 := [trans #496 #499]: #500
-#504 := [monotonicity #501]: #503
-#508 := [trans #504 #506]: #507
-#273 := (iff #62 #263)
-#268 := (implies true #263)
-#271 := (iff #268 #263)
-#272 := [rewrite]: #271
-#269 := (iff #62 #268)
-#266 := (iff #61 #263)
-#260 := (implies #29 #255)
-#264 := (iff #260 #263)
-#265 := [rewrite]: #264
-#261 := (iff #61 #260)
-#258 := (iff #60 #255)
-#251 := (implies #38 #246)
-#256 := (iff #251 #255)
-#257 := [rewrite]: #256
-#252 := (iff #60 #251)
-#249 := (iff #59 #246)
-#242 := (implies #29 #237)
-#247 := (iff #242 #246)
-#248 := [rewrite]: #247
-#243 := (iff #59 #242)
-#240 := (iff #58 #237)
-#233 := (implies #174 #228)
-#238 := (iff #233 #237)
-#239 := [rewrite]: #238
-#234 := (iff #58 #233)
-#231 := (iff #57 #228)
-#224 := (implies #177 #219)
-#229 := (iff #224 #228)
-#230 := [rewrite]: #229
-#225 := (iff #57 #224)
-#222 := (iff #56 #219)
-#215 := (implies #180 #212)
-#220 := (iff #215 #219)
-#221 := [rewrite]: #220
-#216 := (iff #56 #215)
-#213 := (iff #55 #212)
-#210 := (iff #54 #207)
-#203 := (implies #187 #193)
-#208 := (iff #203 #207)
-#209 := [rewrite]: #208
-#204 := (iff #54 #203)
-#201 := (iff #53 #193)
-#196 := (and #193 true)
-#199 := (iff #196 #193)
-#200 := [rewrite]: #199
-#197 := (iff #53 #196)
-#194 := (iff #52 #193)
-#191 := (iff #51 #190)
-#192 := [rewrite]: #191
-#195 := [quant-intro #192]: #194
-#198 := [monotonicity #195]: #197
-#202 := [trans #198 #200]: #201
-#188 := (iff #49 #187)
-#185 := (iff #48 #184)
-#186 := [rewrite]: #185
-#189 := [quant-intro #186]: #188
-#205 := [monotonicity #189 #202]: #204
-#211 := [trans #205 #209]: #210
-#214 := [monotonicity #189 #211]: #213
-#181 := (iff #44 #180)
-#182 := [rewrite]: #181
-#217 := [monotonicity #182 #214]: #216
-#223 := [trans #217 #221]: #222
-#178 := (iff #42 #177)
-#179 := [rewrite]: #178
-#226 := [monotonicity #179 #223]: #225
-#232 := [trans #226 #230]: #231
-#175 := (iff #40 #174)
-#176 := [rewrite]: #175
-#235 := [monotonicity #176 #232]: #234
-#241 := [trans #235 #239]: #240
-#244 := [monotonicity #241]: #243
-#250 := [trans #244 #248]: #249
-#253 := [monotonicity #250]: #252
-#259 := [trans #253 #257]: #258
-#262 := [monotonicity #259]: #261
-#267 := [trans #262 #265]: #266
-#270 := [monotonicity #267]: #269
-#274 := [trans #270 #272]: #273
-#511 := [monotonicity #274 #508]: #510
-#514 := [monotonicity #511]: #513
-#519 := [trans #514 #517]: #518
-#172 := (iff #37 #171)
-#173 := [rewrite]: #172
-#522 := [monotonicity #173 #519]: #521
-#528 := [trans #522 #526]: #527
-#169 := (iff #35 #168)
-#166 := (iff #34 #165)
-#167 := [rewrite]: #166
-#170 := [quant-intro #167]: #169
-#531 := [monotonicity #170 #528]: #530
-#537 := [trans #531 #535]: #536
-#540 := [monotonicity #537]: #539
-#545 := [trans #540 #543]: #544
-#548 := [monotonicity #545]: #547
-#552 := [trans #548 #550]: #551
-#162 := (iff #24 #9)
+#274 := (iff #66 #273)
+#271 := (iff #65 #268)
+#265 := (implies #33 #260)
+#269 := (iff #265 #268)
+#270 := [rewrite]: #269
+#266 := (iff #65 #265)
+#263 := (iff #64 #260)
+#256 := (implies #42 #251)
+#261 := (iff #256 #260)
+#262 := [rewrite]: #261
+#257 := (iff #64 #256)
+#254 := (iff #63 #251)
+#247 := (implies #33 #242)
+#252 := (iff #247 #251)
+#253 := [rewrite]: #252
+#248 := (iff #63 #247)
+#245 := (iff #62 #242)
+#238 := (implies #179 #233)
+#243 := (iff #238 #242)
+#244 := [rewrite]: #243
+#239 := (iff #62 #238)
+#236 := (iff #61 #233)
+#229 := (implies #182 #224)
+#234 := (iff #229 #233)
+#235 := [rewrite]: #234
+#230 := (iff #61 #229)
+#227 := (iff #60 #224)
+#220 := (implies #185 #217)
+#225 := (iff #220 #224)
+#226 := [rewrite]: #225
+#221 := (iff #60 #220)
+#218 := (iff #59 #217)
+#215 := (iff #58 #212)
+#208 := (implies #192 #198)
+#213 := (iff #208 #212)
+#214 := [rewrite]: #213
+#209 := (iff #58 #208)
+#206 := (iff #57 #198)
+#201 := (and #198 true)
+#204 := (iff #201 #198)
+#205 := [rewrite]: #204
+#202 := (iff #57 #201)
+#199 := (iff #56 #198)
+#196 := (iff #55 #195)
+#197 := [rewrite]: #196
+#200 := [quant-intro #197]: #199
+#203 := [monotonicity #200]: #202
+#207 := [trans #203 #205]: #206
+#193 := (iff #53 #192)
+#190 := (iff #52 #189)
+#191 := [rewrite]: #190
+#194 := [quant-intro #191]: #193
+#210 := [monotonicity #194 #207]: #209
+#216 := [trans #210 #214]: #215
+#219 := [monotonicity #194 #216]: #218
+#186 := (iff #48 #185)
+#187 := [rewrite]: #186
+#222 := [monotonicity #187 #219]: #221
+#228 := [trans #222 #226]: #227
+#183 := (iff #46 #182)
+#184 := [rewrite]: #183
+#231 := [monotonicity #184 #228]: #230
+#237 := [trans #231 #235]: #236
+#180 := (iff #44 #179)
+#181 := [rewrite]: #180
+#240 := [monotonicity #181 #237]: #239
+#246 := [trans #240 #244]: #245
+#249 := [monotonicity #246]: #248
+#255 := [trans #249 #253]: #254
+#258 := [monotonicity #255]: #257
+#264 := [trans #258 #262]: #263
+#267 := [monotonicity #264]: #266
+#272 := [trans #267 #270]: #271
+#275 := [monotonicity #272]: #274
+#279 := [trans #275 #277]: #278
+#516 := [monotonicity #279 #513]: #515
+#519 := [monotonicity #516]: #518
+#524 := [trans #519 #522]: #523
+#177 := (iff #41 #176)
+#178 := [rewrite]: #177
+#527 := [monotonicity #178 #524]: #526
+#533 := [trans #527 #531]: #532
+#174 := (iff #39 #173)
+#171 := (iff #38 #170)
+#172 := [rewrite]: #171
+#175 := [quant-intro #172]: #174
+#536 := [monotonicity #175 #533]: #535
+#542 := [trans #536 #540]: #541
+#545 := [monotonicity #542]: #544
+#550 := [trans #545 #548]: #549
+#553 := [monotonicity #550]: #552
+#557 := [trans #553 #555]: #556
+#167 := (iff #28 #13)
+#168 := [rewrite]: #167
+#560 := [monotonicity #168 #557]: #559
+#566 := [trans #560 #564]: #565
+#569 := [monotonicity #168 #566]: #568
+#165 := (iff #27 #164)
+#162 := (iff #26 #161)
 #163 := [rewrite]: #162
-#555 := [monotonicity #163 #552]: #554
-#561 := [trans #555 #559]: #560
-#564 := [monotonicity #163 #561]: #563
-#160 := (iff #23 #159)
-#157 := (iff #22 #156)
-#158 := [rewrite]: #157
-#161 := [quant-intro #158]: #160
-#567 := [monotonicity #161 #564]: #566
-#573 := [trans #567 #571]: #572
-#576 := [monotonicity #161 #573]: #575
-#153 := (iff #15 #152)
-#150 := (iff #14 #149)
-#147 := (iff #13 #12)
-#148 := [rewrite]: #147
-#151 := [monotonicity #148]: #150
-#154 := [monotonicity #151]: #153
-#579 := [monotonicity #154 #576]: #578
-#585 := [trans #579 #583]: #584
-#588 := [monotonicity #585]: #587
-#593 := [trans #588 #591]: #592
-#596 := [monotonicity #593]: #595
-#602 := [trans #596 #600]: #601
-#605 := [monotonicity #602]: #604
-#609 := [trans #605 #607]: #608
-#612 := [monotonicity #609]: #611
-#994 := [trans #612 #992]: #993
-#146 := [asserted]: #130
-#995 := [mp #146 #994]: #990
-#996 := [not-or-elim #995]: #9
-#2042 := (or #556 #2051)
-#2066 := [th-lemma]: #2042
-#2043 := [unit-resolution #2066 #996]: #2051
-decl ?x1!0 :: int
-#1039 := ?x1!0
-#1040 := (uf_3 ?x1!0)
-#1037 := (* -1::int #1040)
-#1038 := (+ uf_2 #1037)
-#1041 := (>= #1038 0::int)
-#1780 := (not #1041)
-#1044 := (>= ?x1!0 0::int)
-#1094 := (not #1044)
-#1042 := (>= ?x1!0 1::int)
-#1427 := (or #1041 #1042 #1094)
-#1432 := (not #1427)
-decl ?x4!1 :: int
-#1081 := ?x4!1
-#1089 := (uf_3 ?x4!1)
-#1262 := (= uf_8 #1089)
-#1086 := (>= ?x4!1 0::int)
-#1505 := (not #1086)
-#1082 := (* -1::int ?x4!1)
-#1083 := (+ uf_1 #1082)
-#1084 := (<= #1083 0::int)
-#1520 := (or #1084 #1505 #1262)
-#1551 := (not #1520)
-decl ?x6!2 :: int
-#1099 := ?x6!2
-#1100 := (uf_3 ?x6!2)
-#1286 := (* -1::int #1100)
-#1287 := (+ uf_8 #1286)
-#1288 := (>= #1287 0::int)
-#1107 := (>= ?x6!2 0::int)
-#1525 := (not #1107)
-#1103 := (* -1::int ?x6!2)
-#1104 := (+ uf_1 #1103)
-#1105 := (<= #1104 0::int)
-#1682 := (or #1105 #1525 #1288 #1551)
-#1685 := (not #1682)
-#2194 := (pattern #20)
-#1435 := (not #636)
-#1494 := (or #47 #1435 #676)
-#1499 := (not #1494)
-#2255 := (forall (vars (?x4 int)) (:pat #2194) #1499)
-#2260 := (or #2255 #1685)
-#2263 := (not #2260)
-#1564 := (not #663)
-#2266 := (or #236 #227 #218 #1564 #810 #722 #2263)
-#2269 := (not #2266)
-decl ?x7!3 :: int
-#1148 := ?x7!3
-#1149 := (uf_3 ?x7!3)
-#1351 := (* -1::int #1149)
-#1352 := (+ uf_12 #1351)
-#1353 := (>= #1352 0::int)
-#1329 := (* -1::int ?x7!3)
-#1330 := (+ uf_13 #1329)
-#1331 := (<= #1330 0::int)
-#1155 := (>= ?x7!3 0::int)
-#1604 := (not #1155)
-#1619 := (or #1604 #1331 #1353)
-#1624 := (not #1619)
-#1586 := (or #1435 #760 #774)
-#2211 := (forall (vars (?x7 int)) (:pat #2194) #1586)
-#2216 := (not #2211)
-#2219 := (or #302 #2216)
-#2222 := (not #2219)
-#2225 := (or #2222 #1624)
-#2228 := (not #2225)
-#1634 := (not #752)
-#1633 := (not #749)
-#2237 := (or #436 #427 #1564 #810 #1633 #1634 #801 #813 #2228)
-#2240 := (not #2237)
-#2231 := (or #388 #370 #361 #1564 #810 #1633 #1634 #801 #814 #2228)
-#2234 := (not #2231)
-#2243 := (or #2234 #2240)
-#2246 := (not #2243)
-#2249 := (or #1564 #810 #719 #2246)
-#2252 := (not #2249)
-#2272 := (or #2252 #2269)
-#2275 := (not #2272)
-#1472 := (or #1435 #911 #924)
-#2203 := (forall (vars (?x3 int)) (:pat #2194) #1472)
-#2208 := (not #2203)
-#1450 := (or #1435 #639 #649)
-#2195 := (forall (vars (?x1 int)) (:pat #2194) #1450)
-#2200 := (not #2195)
-#2278 := (or #523 #1564 #810 #2200 #2208 #2275)
-#1336 := (not #1331)
-#2281 := (not #2278)
-#2525 := [hypothesis]: #2281
-#2115 := (or #2278 #171)
-#2099 := [def-axiom]: #2115
-#2526 := [unit-resolution #2099 #2525]: #171
-#2093 := (or #2278 #2272)
-#2095 := [def-axiom]: #2093
-#2527 := [unit-resolution #2095 #2525]: #2272
-#2106 := (or #2278 #2203)
-#2092 := [def-axiom]: #2106
-#2528 := [unit-resolution #2092 #2525]: #2203
-#2347 := (or #2266 #523 #2208)
-#1786 := (uf_3 uf_7)
-#2291 := (= uf_8 #1786)
-#2341 := (= #36 #1786)
-#2339 := (= #1786 #36)
-#2324 := [hypothesis]: #2269
-#2032 := (or #2266 #174)
-#2033 := [def-axiom]: #2032
-#2335 := [unit-resolution #2033 #2324]: #174
-#2336 := [symm #2335]: #40
-#2340 := [monotonicity #2336]: #2339
-#2342 := [symm #2340]: #2341
-#2343 := (= uf_8 #36)
-#2337 := [hypothesis]: #171
-#2034 := (or #2266 #177)
-#2035 := [def-axiom]: #2034
-#2326 := [unit-resolution #2035 #2324]: #177
-#2338 := [symm #2326]: #42
-#2344 := [trans #2338 #2337]: #2343
-#2345 := [trans #2344 #2342]: #2291
-#2319 := (not #2291)
-#1785 := (>= uf_7 0::int)
-#1783 := (not #1785)
-#1795 := (* -1::int uf_7)
-#1782 := (+ uf_1 #1795)
-#1784 := (<= #1782 0::int)
-#2297 := (or #1784 #1783 #2291)
-#2302 := (not #2297)
-#2119 := (or #2266 #2260)
-#2120 := [def-axiom]: #2119
-#2325 := [unit-resolution #2120 #2324]: #2260
-#1953 := (+ uf_6 #700)
-#1954 := (<= #1953 0::int)
-#2327 := (or #227 #1954)
-#2328 := [th-lemma]: #2327
-#2329 := [unit-resolution #2328 #2326]: #1954
-#1831 := [hypothesis]: #2203
-#2107 := (or #2266 #719)
-#2109 := [def-axiom]: #2107
-#2330 := [unit-resolution #2109 #2324]: #719
-#1862 := (not #1954)
-#1841 := (or #1682 #722 #2208 #1862)
-#1864 := [hypothesis]: #719
-#1943 := (+ uf_5 #1103)
-#1944 := (<= #1943 0::int)
-#1922 := (+ uf_6 #1286)
-#1923 := (>= #1922 0::int)
-#1861 := (not #1923)
-#1855 := [hypothesis]: #1954
-#2018 := (not #1288)
-#1847 := [hypothesis]: #1685
-#2019 := (or #1682 #2018)
-#1978 := [def-axiom]: #2019
-#1849 := [unit-resolution #1978 #1847]: #2018
-#1863 := (or #1861 #1288 #1862)
-#1846 := [hypothesis]: #2018
-#1859 := [hypothesis]: #1923
-#1860 := [th-lemma #1859 #1846 #1855]: false
-#1853 := [lemma #1860]: #1863
-#1850 := [unit-resolution #1853 #1849 #1855]: #1861
-#1836 := (or #1923 #1944)
-#2135 := (or #1682 #1107)
-#2017 := [def-axiom]: #2135
-#1829 := [unit-resolution #2017 #1847]: #1107
-#1912 := (or #2208 #1525 #1923 #1944)
-#1955 := (+ #1100 #922)
-#1945 := (<= #1955 0::int)
-#1935 := (+ ?x6!2 #717)
-#1937 := (>= #1935 0::int)
-#1938 := (or #1525 #1937 #1945)
-#1913 := (or #2208 #1938)
-#1904 := (iff #1913 #1912)
-#1906 := (or #1525 #1923 #1944)
-#1907 := (or #2208 #1906)
-#1901 := (iff #1907 #1912)
-#1902 := [rewrite]: #1901
-#1915 := (iff #1913 #1907)
-#1910 := (iff #1938 #1906)
-#1928 := (or #1525 #1944 #1923)
-#1908 := (iff #1928 #1906)
-#1909 := [rewrite]: #1908
-#1917 := (iff #1938 #1928)
-#1926 := (iff #1945 #1923)
-#1934 := (+ #922 #1100)
-#1919 := (<= #1934 0::int)
-#1924 := (iff #1919 #1923)
-#1925 := [rewrite]: #1924
-#1920 := (iff #1945 #1919)
-#1916 := (= #1955 #1934)
-#1918 := [rewrite]: #1916
-#1921 := [monotonicity #1918]: #1920
-#1927 := [trans #1921 #1925]: #1926
-#1933 := (iff #1937 #1944)
-#1941 := (+ #717 ?x6!2)
-#1939 := (>= #1941 0::int)
-#1930 := (iff #1939 #1944)
-#1932 := [rewrite]: #1930
-#1947 := (iff #1937 #1939)
-#1942 := (= #1935 #1941)
-#1946 := [rewrite]: #1942
-#1940 := [monotonicity #1946]: #1947
-#1931 := [trans #1940 #1932]: #1933
-#1929 := [monotonicity #1931 #1927]: #1917
-#1911 := [trans #1929 #1909]: #1910
-#1900 := [monotonicity #1911]: #1915
-#1903 := [trans #1900 #1902]: #1904
-#1914 := [quant-inst]: #1913
-#1905 := [mp #1914 #1903]: #1912
-#1837 := [unit-resolution #1905 #1831 #1829]: #1836
-#1838 := [unit-resolution #1837 #1850]: #1944
-#1106 := (not #1105)
-#2134 := (or #1682 #1106)
-#2132 := [def-axiom]: #2134
-#1839 := [unit-resolution #2132 #1847]: #1106
-#1840 := [th-lemma #1839 #1838 #1864]: false
-#1830 := [lemma #1840]: #1841
-#2331 := [unit-resolution #1830 #2330 #1831 #2329]: #1682
-#2023 := (or #2263 #2255 #1685)
-#2031 := [def-axiom]: #2023
-#2332 := [unit-resolution #2031 #2331 #2325]: #2255
-#2127 := (not #2255)
-#2305 := (or #2127 #2302)
-#2288 := (= #1786 uf_8)
-#2289 := (or #2288 #1783 #1784)
-#2290 := (not #2289)
-#2306 := (or #2127 #2290)
-#2308 := (iff #2306 #2305)
-#2310 := (iff #2305 #2305)
-#2311 := [rewrite]: #2310
-#2303 := (iff #2290 #2302)
-#2300 := (iff #2289 #2297)
-#2294 := (or #2291 #1783 #1784)
-#2298 := (iff #2294 #2297)
-#2299 := [rewrite]: #2298
-#2295 := (iff #2289 #2294)
-#2292 := (iff #2288 #2291)
-#2293 := [rewrite]: #2292
-#2296 := [monotonicity #2293]: #2295
-#2301 := [trans #2296 #2299]: #2300
-#2304 := [monotonicity #2301]: #2303
-#2309 := [monotonicity #2304]: #2308
-#2312 := [trans #2309 #2311]: #2308
-#2307 := [quant-inst]: #2306
-#2313 := [mp #2307 #2312]: #2305
-#2333 := [unit-resolution #2313 #2332]: #2302
-#2320 := (or #2297 #2319)
-#2321 := [def-axiom]: #2320
-#2334 := [unit-resolution #2321 #2333]: #2319
-#2346 := [unit-resolution #2334 #2345]: false
-#2348 := [lemma #2346]: #2347
-#2529 := [unit-resolution #2348 #2526 #2528]: #2266
-#2114 := (or #2275 #2252 #2269)
-#2108 := [def-axiom]: #2114
-#2548 := [unit-resolution #2108 #2529 #2527]: #2252
-#2142 := (or #2249 #2243)
-#2136 := [def-axiom]: #2142
-#2614 := [unit-resolution #2136 #2548]: #2243
-#2355 := (or #302 #2246 #523)
-#2349 := (= #64 #86)
-#1950 := (= #86 #64)
-#2314 := [hypothesis]: #2243
-#1164 := (not #302)
-#1791 := [hypothesis]: #1164
-#1803 := (or #2237 #302 #523)
-#1808 := (= #36 #86)
-#1790 := (= #86 #36)
-#1788 := [hypothesis]: #2240
-#1886 := (or #2237 #418)
-#1887 := [def-axiom]: #1886
-#1789 := [unit-resolution #1887 #1788]: #418
-#1792 := [symm #1789]: #103
-#1812 := [monotonicity #1792]: #1790
-#1810 := [symm #1812]: #1808
-#1813 := (= uf_12 #36)
-#2161 := (or #2237 #421)
-#2165 := [def-axiom]: #2161
-#1793 := [unit-resolution #2165 #1788]: #421
-#1794 := [symm #1793]: #104
-#1796 := [trans #1794 #2337]: #1813
-#1799 := [trans #1796 #1810]: #302
-#1800 := [unit-resolution #1791 #1799]: false
-#1804 := [lemma #1800]: #1803
-#2315 := [unit-resolution #1804 #1791 #2337]: #2237
-#2148 := (or #2246 #2234 #2240)
-#2154 := [def-axiom]: #2148
-#2316 := [unit-resolution #2154 #2315 #2314]: #2234
-#1833 := (or #2231 #280)
-#1834 := [def-axiom]: #1833
-#2322 := [unit-resolution #1834 #2316]: #280
-#2323 := [symm #2322]: #70
-#1805 := [monotonicity #2323]: #1950
-#2350 := [symm #1805]: #2349
-#2351 := (= uf_12 #64)
-#2169 := (or #2231 #275)
-#1832 := [def-axiom]: #2169
-#2318 := [unit-resolution #1832 #2316]: #275
-#1806 := [symm #2318]: #67
-#1835 := (or #2231 #283)
-#2171 := [def-axiom]: #1835
-#2317 := [unit-resolution #2171 #2316]: #283
-#1798 := [symm #2317]: #72
-#2352 := [trans #1798 #1806]: #2351
-#2353 := [trans #2352 #2350]: #302
-#2354 := [unit-resolution #1791 #2353]: false
-#2356 := [lemma #2354]: #2355
-#2615 := [unit-resolution #2356 #2614 #2526]: #302
-#1851 := (or #2219 #1164)
-#2186 := [def-axiom]: #1851
-#2616 := [unit-resolution #2186 #2615]: #2219
-#2612 := (or #2237 #2208 #2222)
-#2583 := [hypothesis]: #2219
-#2160 := (or #2237 #2225)
-#2149 := [def-axiom]: #2160
-#2584 := [unit-resolution #2149 #1788]: #2225
-#2185 := (or #2228 #2222 #1624)
-#1828 := [def-axiom]: #2185
-#2585 := [unit-resolution #1828 #2584 #2583]: #1624
-#2189 := (or #1619 #1336)
-#2190 := [def-axiom]: #2189
-#2586 := [unit-resolution #2190 #2585]: #1336
-#2415 := (+ uf_5 #1329)
-#2560 := (>= #2415 0::int)
-#2601 := (not #2560)
-#2549 := (= uf_5 ?x7!3)
-#2580 := (not #2549)
-#2559 := (= #64 #1149)
-#2564 := (not #2559)
-#2563 := (+ #64 #1351)
-#2565 := (>= #2563 0::int)
-#2569 := (not #2565)
-#2159 := (or #2237 #814)
-#2156 := [def-axiom]: #2159
-#2587 := [unit-resolution #2156 #1788]: #814
-#2191 := (not #1353)
-#2192 := (or #1619 #2191)
-#2187 := [def-axiom]: #2192
-#2588 := [unit-resolution #2187 #2585]: #2191
-#1787 := (+ uf_6 #772)
-#2163 := (<= #1787 0::int)
-#2589 := (or #427 #2163)
-#2590 := [th-lemma]: #2589
-#2591 := [unit-resolution #2590 #1793]: #2163
-#2539 := (not #2163)
-#2570 := (or #2569 #2539 #1353 #813)
-#2566 := [hypothesis]: #814
-#2531 := [hypothesis]: #2191
-#2533 := [hypothesis]: #2163
-#2567 := [hypothesis]: #2565
-#2568 := [th-lemma #2567 #2533 #2531 #2566]: false
-#2571 := [lemma #2568]: #2570
-#2592 := [unit-resolution #2571 #2591 #2588 #2587]: #2569
-#2572 := (or #2564 #2565)
-#2573 := [th-lemma]: #2572
-#2593 := [unit-resolution #2573 #2592]: #2564
-#2581 := (or #2580 #2559)
-#2577 := [hypothesis]: #2549
-#2578 := [monotonicity #2577]: #2559
-#2576 := [hypothesis]: #2564
-#2579 := [unit-resolution #2576 #2578]: false
-#2582 := [lemma #2579]: #2581
-#2594 := [unit-resolution #2582 #2593]: #2580
-#2604 := (or #2549 #2601)
-#2416 := (<= #2415 0::int)
-#2427 := (+ uf_6 #1351)
-#2428 := (>= #2427 0::int)
-#2545 := (not #2428)
-#2546 := (or #2545 #2539 #1353)
-#2543 := [hypothesis]: #2428
-#2544 := [th-lemma #2533 #2531 #2543]: false
-#2547 := [lemma #2544]: #2546
-#2595 := [unit-resolution #2547 #2591 #2588]: #2545
-#2597 := (or #2416 #2428)
-#1856 := (or #1619 #1155)
-#1857 := [def-axiom]: #1856
-#2596 := [unit-resolution #1857 #2585]: #1155
-#2436 := (or #2208 #1604 #2416 #2428)
-#2404 := (+ #1149 #922)
-#2405 := (<= #2404 0::int)
-#2406 := (+ ?x7!3 #717)
-#2407 := (>= #2406 0::int)
-#2408 := (or #1604 #2407 #2405)
-#2437 := (or #2208 #2408)
-#2444 := (iff #2437 #2436)
-#2433 := (or #1604 #2416 #2428)
-#2439 := (or #2208 #2433)
-#2442 := (iff #2439 #2436)
-#2443 := [rewrite]: #2442
-#2440 := (iff #2437 #2439)
-#2434 := (iff #2408 #2433)
-#2431 := (iff #2405 #2428)
-#2421 := (+ #922 #1149)
-#2424 := (<= #2421 0::int)
-#2429 := (iff #2424 #2428)
-#2430 := [rewrite]: #2429
-#2425 := (iff #2405 #2424)
-#2422 := (= #2404 #2421)
-#2423 := [rewrite]: #2422
-#2426 := [monotonicity #2423]: #2425
-#2432 := [trans #2426 #2430]: #2431
-#2419 := (iff #2407 #2416)
-#2409 := (+ #717 ?x7!3)
-#2412 := (>= #2409 0::int)
-#2417 := (iff #2412 #2416)
-#2418 := [rewrite]: #2417
-#2413 := (iff #2407 #2412)
-#2410 := (= #2406 #2409)
-#2411 := [rewrite]: #2410
-#2414 := [monotonicity #2411]: #2413
-#2420 := [trans #2414 #2418]: #2419
-#2435 := [monotonicity #2420 #2432]: #2434
-#2441 := [monotonicity #2435]: #2440
-#2445 := [trans #2441 #2443]: #2444
-#2438 := [quant-inst]: #2437
-#2446 := [mp #2438 #2445]: #2436
-#2598 := [unit-resolution #2446 #1831 #2596]: #2597
-#2599 := [unit-resolution #2598 #2595]: #2416
-#2600 := (not #2416)
-#2602 := (or #2549 #2600 #2601)
-#2603 := [th-lemma]: #2602
-#2605 := [unit-resolution #2603 #2599]: #2604
-#2606 := [unit-resolution #2605 #2594]: #2601
-#1872 := (>= #798 -1::int)
-#1873 := (or #2237 #797)
-#2155 := [def-axiom]: #1873
-#2607 := [unit-resolution #2155 #1788]: #797
-#2608 := (or #801 #1872)
-#2609 := [th-lemma]: #2608
-#2610 := [unit-resolution #2609 #2607]: #1872
-#2611 := [th-lemma #2610 #2606 #2586]: false
-#2613 := [lemma #2611]: #2612
-#2617 := [unit-resolution #2613 #2528 #2616]: #2237
-#2618 := [unit-resolution #2154 #2617 #2614]: #2234
-#2178 := (or #2231 #2225)
-#2181 := [def-axiom]: #2178
-#2619 := [unit-resolution #2181 #2618]: #2225
-#2620 := [unit-resolution #1828 #2619 #2616]: #1624
-#2621 := [unit-resolution #2190 #2620]: #1336
-#2397 := (+ #64 #772)
-#2398 := (<= #2397 0::int)
-#2396 := (= #64 uf_12)
-#2622 := [unit-resolution #2171 #2618]: #283
-#2623 := [unit-resolution #1832 #2618]: #275
-#2624 := [trans #2623 #2622]: #2396
-#2625 := (not #2396)
-#2626 := (or #2625 #2398)
-#2627 := [th-lemma]: #2626
-#2628 := [unit-resolution #2627 #2624]: #2398
-#1820 := (or #2231 #813)
-#2180 := [def-axiom]: #1820
-#2629 := [unit-resolution #2180 #2618]: #813
-#2630 := [unit-resolution #2187 #2620]: #2191
-#2631 := (not #2398)
-#2632 := (or #2545 #1353 #2631 #814)
-#2633 := [th-lemma]: #2632
-#2634 := [unit-resolution #2633 #2630 #2629 #2628]: #2545
-#2635 := [unit-resolution #1857 #2620]: #1155
-#2636 := [unit-resolution #2446 #2528 #2635]: #2597
-#2637 := [unit-resolution #2636 #2634]: #2416
-#2638 := (or #2569 #1353 #2631)
-#2639 := [th-lemma]: #2638
-#2640 := [unit-resolution #2639 #2630 #2628]: #2569
-#2641 := [unit-resolution #2573 #2640]: #2564
-#2642 := [unit-resolution #2582 #2641]: #2580
-#2643 := [unit-resolution #2603 #2642 #2637]: #2601
-#2179 := (or #2231 #797)
-#1819 := [def-axiom]: #2179
-#2644 := [unit-resolution #1819 #2618]: #797
-#2645 := [unit-resolution #2609 #2644]: #1872
-#2646 := [th-lemma #2645 #2643 #2621]: false
-#2647 := [lemma #2646]: #2278
-#2284 := (or #1432 #2281)
-#1502 := (forall (vars (?x4 int)) #1499)
-#1688 := (or #1502 #1685)
-#1691 := (not #1688)
-#1694 := (or #236 #227 #218 #1564 #810 #722 #1691)
-#1697 := (not #1694)
-#1591 := (forall (vars (?x7 int)) #1586)
-#1597 := (not #1591)
-#1598 := (or #302 #1597)
-#1599 := (not #1598)
-#1627 := (or #1599 #1624)
-#1635 := (not #1627)
-#1645 := (or #436 #427 #1564 #810 #1633 #1634 #801 #813 #1635)
-#1646 := (not #1645)
-#1636 := (or #388 #370 #361 #1564 #810 #1633 #1634 #801 #814 #1635)
-#1637 := (not #1636)
-#1651 := (or #1637 #1646)
-#1657 := (not #1651)
-#1658 := (or #1564 #810 #719 #1657)
-#1659 := (not #1658)
-#1703 := (or #1659 #1697)
-#1708 := (not #1703)
-#1477 := (forall (vars (?x3 int)) #1472)
-#1671 := (not #1477)
-#1455 := (forall (vars (?x1 int)) #1450)
-#1670 := (not #1455)
-#1711 := (or #523 #1564 #810 #1670 #1671 #1708)
-#1714 := (not #1711)
-#1717 := (or #1432 #1714)
-#2285 := (iff #1717 #2284)
-#2282 := (iff #1714 #2281)
-#2279 := (iff #1711 #2278)
-#2276 := (iff #1708 #2275)
-#2273 := (iff #1703 #2272)
-#2270 := (iff #1697 #2269)
-#2267 := (iff #1694 #2266)
-#2264 := (iff #1691 #2263)
-#2261 := (iff #1688 #2260)
-#2258 := (iff #1502 #2255)
-#2256 := (iff #1499 #1499)
-#2257 := [refl]: #2256
-#2259 := [quant-intro #2257]: #2258
-#2262 := [monotonicity #2259]: #2261
-#2265 := [monotonicity #2262]: #2264
-#2268 := [monotonicity #2265]: #2267
-#2271 := [monotonicity #2268]: #2270
-#2253 := (iff #1659 #2252)
-#2250 := (iff #1658 #2249)
-#2247 := (iff #1657 #2246)
-#2244 := (iff #1651 #2243)
-#2241 := (iff #1646 #2240)
-#2238 := (iff #1645 #2237)
-#2229 := (iff #1635 #2228)
-#2226 := (iff #1627 #2225)
-#2223 := (iff #1599 #2222)
-#2220 := (iff #1598 #2219)
-#2217 := (iff #1597 #2216)
-#2214 := (iff #1591 #2211)
-#2212 := (iff #1586 #1586)
-#2213 := [refl]: #2212
-#2215 := [quant-intro #2213]: #2214
-#2218 := [monotonicity #2215]: #2217
-#2221 := [monotonicity #2218]: #2220
-#2224 := [monotonicity #2221]: #2223
-#2227 := [monotonicity #2224]: #2226
-#2230 := [monotonicity #2227]: #2229
-#2239 := [monotonicity #2230]: #2238
-#2242 := [monotonicity #2239]: #2241
-#2235 := (iff #1637 #2234)
-#2232 := (iff #1636 #2231)
-#2233 := [monotonicity #2230]: #2232
-#2236 := [monotonicity #2233]: #2235
-#2245 := [monotonicity #2236 #2242]: #2244
-#2248 := [monotonicity #2245]: #2247
-#2251 := [monotonicity #2248]: #2250
-#2254 := [monotonicity #2251]: #2253
-#2274 := [monotonicity #2254 #2271]: #2273
-#2277 := [monotonicity #2274]: #2276
-#2209 := (iff #1671 #2208)
-#2206 := (iff #1477 #2203)
-#2204 := (iff #1472 #1472)
-#2205 := [refl]: #2204
-#2207 := [quant-intro #2205]: #2206
-#2210 := [monotonicity #2207]: #2209
-#2201 := (iff #1670 #2200)
-#2198 := (iff #1455 #2195)
-#2196 := (iff #1450 #1450)
-#2197 := [refl]: #2196
-#2199 := [quant-intro #2197]: #2198
-#2202 := [monotonicity #2199]: #2201
-#2280 := [monotonicity #2202 #2210 #2277]: #2279
-#2283 := [monotonicity #2280]: #2282
-#2286 := [monotonicity #2283]: #2285
-#1339 := (and #1155 #1336)
-#1342 := (not #1339)
-#1358 := (or #1342 #1353)
-#1361 := (not #1358)
-#1174 := (and #1164 #780)
-#1367 := (or #1174 #1361)
-#1391 := (and #418 #421 #663 #666 #749 #752 #797 #814 #1367)
-#1379 := (and #275 #280 #283 #663 #666 #749 #752 #797 #813 #1367)
-#1396 := (or #1379 #1391)
-#1402 := (and #663 #666 #722 #1396)
-#1274 := (and #1106 #1107)
-#1277 := (not #1274)
-#1293 := (or #1277 #1288)
-#1296 := (not #1293)
-#1085 := (not #1084)
-#1265 := (and #1085 #1086)
-#1268 := (not #1265)
-#1271 := (or #1262 #1268)
-#1299 := (and #1271 #1296)
-#1075 := (not #689)
-#1078 := (forall (vars (?x4 int)) #1075)
-#1302 := (or #1078 #1299)
-#1308 := (and #174 #177 #180 #663 #666 #719 #1302)
-#1407 := (or #1308 #1402)
-#1413 := (and #171 #656 #663 #666 #930 #1407)
-#1043 := (not #1042)
-#1235 := (and #1043 #1044)
-#1238 := (not #1235)
-#1244 := (or #1041 #1238)
-#1249 := (not #1244)
-#1418 := (or #1249 #1413)
-#1720 := (iff #1418 #1717)
-#1540 := (or #1105 #1525 #1288)
-#1552 := (or #1551 #1540)
-#1553 := (not #1552)
-#1558 := (or #1502 #1553)
-#1565 := (not #1558)
-#1566 := (or #236 #227 #218 #1564 #810 #722 #1565)
-#1567 := (not #1566)
-#1664 := (or #1567 #1659)
-#1672 := (not #1664)
-#1673 := (or #523 #1564 #810 #1670 #1671 #1672)
-#1674 := (not #1673)
-#1679 := (or #1432 #1674)
-#1718 := (iff #1679 #1717)
-#1715 := (iff #1674 #1714)
-#1712 := (iff #1673 #1711)
-#1709 := (iff #1672 #1708)
-#1706 := (iff #1664 #1703)
-#1700 := (or #1697 #1659)
-#1704 := (iff #1700 #1703)
-#1705 := [rewrite]: #1704
-#1701 := (iff #1664 #1700)
-#1698 := (iff #1567 #1697)
-#1695 := (iff #1566 #1694)
-#1692 := (iff #1565 #1691)
-#1689 := (iff #1558 #1688)
-#1686 := (iff #1553 #1685)
-#1683 := (iff #1552 #1682)
-#1684 := [rewrite]: #1683
-#1687 := [monotonicity #1684]: #1686
-#1690 := [monotonicity #1687]: #1689
-#1693 := [monotonicity #1690]: #1692
-#1696 := [monotonicity #1693]: #1695
-#1699 := [monotonicity #1696]: #1698
-#1702 := [monotonicity #1699]: #1701
-#1707 := [trans #1702 #1705]: #1706
-#1710 := [monotonicity #1707]: #1709
-#1713 := [monotonicity #1710]: #1712
-#1716 := [monotonicity #1713]: #1715
-#1719 := [monotonicity #1716]: #1718
-#1680 := (iff #1418 #1679)
-#1677 := (iff #1413 #1674)
-#1667 := (and #171 #1455 #663 #666 #1477 #1664)
-#1675 := (iff #1667 #1674)
-#1676 := [rewrite]: #1675
-#1668 := (iff #1413 #1667)
-#1665 := (iff #1407 #1664)
-#1662 := (iff #1402 #1659)
-#1654 := (and #663 #666 #722 #1651)
-#1660 := (iff #1654 #1659)
-#1661 := [rewrite]: #1660
-#1655 := (iff #1402 #1654)
-#1652 := (iff #1396 #1651)
-#1649 := (iff #1391 #1646)
-#1642 := (and #418 #421 #663 #666 #749 #752 #797 #814 #1627)
-#1647 := (iff #1642 #1646)
-#1648 := [rewrite]: #1647
-#1643 := (iff #1391 #1642)
-#1628 := (iff #1367 #1627)
-#1625 := (iff #1361 #1624)
-#1622 := (iff #1358 #1619)
-#1605 := (or #1604 #1331)
-#1616 := (or #1605 #1353)
-#1620 := (iff #1616 #1619)
-#1621 := [rewrite]: #1620
-#1617 := (iff #1358 #1616)
-#1614 := (iff #1342 #1605)
-#1606 := (not #1605)
-#1609 := (not #1606)
-#1612 := (iff #1609 #1605)
+#166 := [quant-intro #163]: #165
+#572 := [monotonicity #166 #569]: #571
+#578 := [trans #572 #576]: #577
+#581 := [monotonicity #166 #578]: #580
+#158 := (iff #19 #157)
+#155 := (iff #18 #154)
+#152 := (iff #17 #16)
+#153 := [rewrite]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#584 := [monotonicity #159 #581]: #583
+#590 := [trans #584 #588]: #589
+#593 := [monotonicity #590]: #592
+#598 := [trans #593 #596]: #597
+#601 := [monotonicity #598]: #600
+#607 := [trans #601 #605]: #606
+#610 := [monotonicity #607]: #609
+#614 := [trans #610 #612]: #613
+#617 := [monotonicity #614]: #616
+#999 := [trans #617 #997]: #998
+#151 := [asserted]: #134
+#1000 := [mp #151 #999]: #995
+#1001 := [not-or-elim #1000]: #13
+#2045 := [trans #1001 #2054]: #2072
+#1786 := (not #1007)
+#1871 := (or #1432 #1786)
+#1872 := [def-axiom]: #1871
+#2051 := [unit-resolution #1872 #2073]: #1786
+#2050 := (not #2072)
+#2019 := (or #2050 #1007)
+#2026 := [th-lemma]: #2019
+#1985 := [unit-resolution #2026 #2051 #2045]: false
+#2016 := [lemma #1985]: #1432
+#2289 := (or #1437 #2286)
+#1507 := (forall (vars (?v0 int)) #1504)
+#1693 := (or #1507 #1690)
+#1696 := (not #1693)
+#1699 := (or #241 #232 #223 #1569 #815 #727 #1696)
+#1702 := (not #1699)
+#1596 := (forall (vars (?v0 int)) #1591)
+#1602 := (not #1596)
+#1603 := (or #307 #1602)
+#1604 := (not #1603)
+#1632 := (or #1604 #1629)
+#1640 := (not #1632)
+#1650 := (or #441 #432 #1569 #815 #1638 #1639 #806 #818 #1640)
+#1651 := (not #1650)
+#1641 := (or #393 #375 #366 #1569 #815 #1638 #1639 #806 #819 #1640)
+#1642 := (not #1641)
+#1656 := (or #1642 #1651)
+#1662 := (not #1656)
+#1663 := (or #1569 #815 #724 #1662)
+#1664 := (not #1663)
+#1708 := (or #1664 #1702)
+#1713 := (not #1708)
+#1482 := (forall (vars (?v0 int)) #1477)
+#1676 := (not #1482)
+#1460 := (forall (vars (?v0 int)) #1455)
+#1675 := (not #1460)
+#1716 := (or #528 #1569 #815 #1675 #1676 #1713)
+#1719 := (not #1716)
+#1722 := (or #1437 #1719)
+#2290 := (iff #1722 #2289)
+#2287 := (iff #1719 #2286)
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+#2278 := (iff #1708 #2277)
+#2275 := (iff #1702 #2274)
+#2272 := (iff #1699 #2271)
+#2269 := (iff #1696 #2268)
+#2266 := (iff #1693 #2265)
+#2263 := (iff #1507 #2260)
+#2261 := (iff #1504 #1504)
+#2262 := [refl]: #2261
+#2264 := [quant-intro #2262]: #2263
+#2267 := [monotonicity #2264]: #2266
+#2270 := [monotonicity #2267]: #2269
+#2273 := [monotonicity #2270]: #2272
+#2276 := [monotonicity #2273]: #2275
+#2258 := (iff #1664 #2257)
+#2255 := (iff #1663 #2254)
+#2252 := (iff #1662 #2251)
+#2249 := (iff #1656 #2248)
+#2246 := (iff #1651 #2245)
+#2243 := (iff #1650 #2242)
+#2234 := (iff #1640 #2233)
+#2231 := (iff #1632 #2230)
+#2228 := (iff #1604 #2227)
+#2225 := (iff #1603 #2224)
+#2222 := (iff #1602 #2221)
+#2219 := (iff #1596 #2216)
+#2217 := (iff #1591 #1591)
+#2218 := [refl]: #2217
+#2220 := [quant-intro #2218]: #2219
+#2223 := [monotonicity #2220]: #2222
+#2226 := [monotonicity #2223]: #2225
+#2229 := [monotonicity #2226]: #2228
+#2232 := [monotonicity #2229]: #2231
+#2235 := [monotonicity #2232]: #2234
+#2244 := [monotonicity #2235]: #2243
+#2247 := [monotonicity #2244]: #2246
+#2240 := (iff #1642 #2239)
+#2237 := (iff #1641 #2236)
+#2238 := [monotonicity #2235]: #2237
+#2241 := [monotonicity #2238]: #2240
+#2250 := [monotonicity #2241 #2247]: #2249
+#2253 := [monotonicity #2250]: #2252
+#2256 := [monotonicity #2253]: #2255
+#2259 := [monotonicity #2256]: #2258
+#2279 := [monotonicity #2259 #2276]: #2278
+#2282 := [monotonicity #2279]: #2281
+#2214 := (iff #1676 #2213)
+#2211 := (iff #1482 #2208)
+#2209 := (iff #1477 #1477)
+#2210 := [refl]: #2209
+#2212 := [quant-intro #2210]: #2211
+#2215 := [monotonicity #2212]: #2214
+#2206 := (iff #1675 #2205)
+#2203 := (iff #1460 #2200)
+#2201 := (iff #1455 #1455)
+#2202 := [refl]: #2201
+#2204 := [quant-intro #2202]: #2203
+#2207 := [monotonicity #2204]: #2206
+#2285 := [monotonicity #2207 #2215 #2282]: #2284
+#2288 := [monotonicity #2285]: #2287
+#2291 := [monotonicity #2288]: #2290
+#1344 := (and #1160 #1341)
+#1347 := (not #1344)
+#1363 := (or #1347 #1358)
+#1366 := (not #1363)
+#1169 := (not #307)
+#1179 := (and #1169 #785)
+#1372 := (or #1179 #1366)
+#1396 := (and #423 #426 #668 #671 #754 #757 #802 #819 #1372)
+#1384 := (and #280 #285 #288 #668 #671 #754 #757 #802 #818 #1372)
+#1401 := (or #1384 #1396)
+#1407 := (and #668 #671 #727 #1401)
+#1111 := (not #1110)
+#1279 := (and #1111 #1112)
+#1282 := (not #1279)
+#1298 := (or #1282 #1293)
+#1301 := (not #1298)
+#1090 := (not #1089)
+#1270 := (and #1090 #1091)
+#1273 := (not #1270)
+#1276 := (or #1267 #1273)
+#1304 := (and #1276 #1301)
+#1080 := (not #694)
+#1083 := (forall (vars (?v0 int)) #1080)
+#1307 := (or #1083 #1304)
+#1313 := (and #179 #182 #185 #668 #671 #724 #1307)
+#1412 := (or #1313 #1407)
+#1418 := (and #176 #661 #668 #671 #935 #1412)
+#1240 := (and #1048 #1049)
+#1243 := (not #1240)
+#1249 := (or #1007 #1243)
+#1254 := (not #1249)
+#1423 := (or #1254 #1418)
+#1725 := (iff #1423 #1722)
+#1545 := (or #1110 #1530 #1293)
+#1557 := (or #1556 #1545)
+#1558 := (not #1557)
+#1563 := (or #1507 #1558)
+#1570 := (not #1563)
+#1571 := (or #241 #232 #223 #1569 #815 #727 #1570)
+#1572 := (not #1571)
+#1669 := (or #1572 #1664)
+#1677 := (not #1669)
+#1678 := (or #528 #1569 #815 #1675 #1676 #1677)
+#1679 := (not #1678)
+#1684 := (or #1437 #1679)
+#1723 := (iff #1684 #1722)
+#1720 := (iff #1679 #1719)
+#1717 := (iff #1678 #1716)
+#1714 := (iff #1677 #1713)
+#1711 := (iff #1669 #1708)
+#1705 := (or #1702 #1664)
+#1709 := (iff #1705 #1708)
+#1710 := [rewrite]: #1709
+#1706 := (iff #1669 #1705)
+#1703 := (iff #1572 #1702)
+#1700 := (iff #1571 #1699)
+#1697 := (iff #1570 #1696)
+#1694 := (iff #1563 #1693)
+#1691 := (iff #1558 #1690)
+#1688 := (iff #1557 #1687)
+#1689 := [rewrite]: #1688
+#1692 := [monotonicity #1689]: #1691
+#1695 := [monotonicity #1692]: #1694
+#1698 := [monotonicity #1695]: #1697
+#1701 := [monotonicity #1698]: #1700
+#1704 := [monotonicity #1701]: #1703
+#1707 := [monotonicity #1704]: #1706
+#1712 := [trans #1707 #1710]: #1711
+#1715 := [monotonicity #1712]: #1714
+#1718 := [monotonicity #1715]: #1717
+#1721 := [monotonicity #1718]: #1720
+#1724 := [monotonicity #1721]: #1723
+#1685 := (iff #1423 #1684)
+#1682 := (iff #1418 #1679)
+#1672 := (and #176 #1460 #668 #671 #1482 #1669)
+#1680 := (iff #1672 #1679)
+#1681 := [rewrite]: #1680
+#1673 := (iff #1418 #1672)
+#1670 := (iff #1412 #1669)
+#1667 := (iff #1407 #1664)
+#1659 := (and #668 #671 #727 #1656)
+#1665 := (iff #1659 #1664)
+#1666 := [rewrite]: #1665
+#1660 := (iff #1407 #1659)
+#1657 := (iff #1401 #1656)
+#1654 := (iff #1396 #1651)
+#1647 := (and #423 #426 #668 #671 #754 #757 #802 #819 #1632)
+#1652 := (iff #1647 #1651)
+#1653 := [rewrite]: #1652
+#1648 := (iff #1396 #1647)
+#1633 := (iff #1372 #1632)
+#1630 := (iff #1366 #1629)
+#1627 := (iff #1363 #1624)
+#1610 := (or #1609 #1336)
+#1621 := (or #1610 #1358)
+#1625 := (iff #1621 #1624)
+#1626 := [rewrite]: #1625
+#1622 := (iff #1363 #1621)
+#1619 := (iff #1347 #1610)
+#1611 := (not #1610)
+#1614 := (not #1611)
+#1617 := (iff #1614 #1610)
+#1618 := [rewrite]: #1617
+#1615 := (iff #1347 #1614)
+#1612 := (iff #1344 #1611)
 #1613 := [rewrite]: #1612
-#1610 := (iff #1342 #1609)
-#1607 := (iff #1339 #1606)
-#1608 := [rewrite]: #1607
-#1611 := [monotonicity #1608]: #1610
-#1615 := [trans #1611 #1613]: #1614
-#1618 := [monotonicity #1615]: #1617
-#1623 := [trans #1618 #1621]: #1622
-#1626 := [monotonicity #1623]: #1625
-#1602 := (iff #1174 #1599)
-#1594 := (and #1164 #1591)
-#1600 := (iff #1594 #1599)
-#1601 := [rewrite]: #1600
-#1595 := (iff #1174 #1594)
-#1592 := (iff #780 #1591)
-#1589 := (iff #777 #1586)
-#1572 := (or #1435 #760)
-#1583 := (or #1572 #774)
-#1587 := (iff #1583 #1586)
-#1588 := [rewrite]: #1587
-#1584 := (iff #777 #1583)
-#1581 := (iff #769 #1572)
-#1573 := (not #1572)
-#1576 := (not #1573)
-#1579 := (iff #1576 #1572)
+#1616 := [monotonicity #1613]: #1615
+#1620 := [trans #1616 #1618]: #1619
+#1623 := [monotonicity #1620]: #1622
+#1628 := [trans #1623 #1626]: #1627
+#1631 := [monotonicity #1628]: #1630
+#1607 := (iff #1179 #1604)
+#1599 := (and #1169 #1596)
+#1605 := (iff #1599 #1604)
+#1606 := [rewrite]: #1605
+#1600 := (iff #1179 #1599)
+#1597 := (iff #785 #1596)
+#1594 := (iff #782 #1591)
+#1577 := (or #1440 #765)
+#1588 := (or #1577 #779)
+#1592 := (iff #1588 #1591)
+#1593 := [rewrite]: #1592
+#1589 := (iff #782 #1588)
+#1586 := (iff #774 #1577)
+#1578 := (not #1577)
+#1581 := (not #1578)
+#1584 := (iff #1581 #1577)
+#1585 := [rewrite]: #1584
+#1582 := (iff #774 #1581)
+#1579 := (iff #771 #1578)
 #1580 := [rewrite]: #1579
-#1577 := (iff #769 #1576)
-#1574 := (iff #766 #1573)
-#1575 := [rewrite]: #1574
-#1578 := [monotonicity #1575]: #1577
-#1582 := [trans #1578 #1580]: #1581
-#1585 := [monotonicity #1582]: #1584
-#1590 := [trans #1585 #1588]: #1589
-#1593 := [quant-intro #1590]: #1592
-#1596 := [monotonicity #1593]: #1595
-#1603 := [trans #1596 #1601]: #1602
-#1629 := [monotonicity #1603 #1626]: #1628
-#1644 := [monotonicity #1629]: #1643
-#1650 := [trans #1644 #1648]: #1649
-#1640 := (iff #1379 #1637)
-#1630 := (and #275 #280 #283 #663 #666 #749 #752 #797 #813 #1627)
-#1638 := (iff #1630 #1637)
-#1639 := [rewrite]: #1638
-#1631 := (iff #1379 #1630)
-#1632 := [monotonicity #1629]: #1631
-#1641 := [trans #1632 #1639]: #1640
-#1653 := [monotonicity #1641 #1650]: #1652
-#1656 := [monotonicity #1653]: #1655
-#1663 := [trans #1656 #1661]: #1662
-#1570 := (iff #1308 #1567)
-#1561 := (and #174 #177 #180 #663 #666 #719 #1558)
-#1568 := (iff #1561 #1567)
-#1569 := [rewrite]: #1568
-#1562 := (iff #1308 #1561)
-#1559 := (iff #1302 #1558)
-#1556 := (iff #1299 #1553)
-#1545 := (not #1540)
-#1548 := (and #1520 #1545)
-#1554 := (iff #1548 #1553)
-#1555 := [rewrite]: #1554
-#1549 := (iff #1299 #1548)
-#1546 := (iff #1296 #1545)
-#1543 := (iff #1293 #1540)
-#1526 := (or #1105 #1525)
-#1537 := (or #1526 #1288)
-#1541 := (iff #1537 #1540)
-#1542 := [rewrite]: #1541
-#1538 := (iff #1293 #1537)
-#1535 := (iff #1277 #1526)
-#1527 := (not #1526)
-#1530 := (not #1527)
-#1533 := (iff #1530 #1526)
+#1583 := [monotonicity #1580]: #1582
+#1587 := [trans #1583 #1585]: #1586
+#1590 := [monotonicity #1587]: #1589
+#1595 := [trans #1590 #1593]: #1594
+#1598 := [quant-intro #1595]: #1597
+#1601 := [monotonicity #1598]: #1600
+#1608 := [trans #1601 #1606]: #1607
+#1634 := [monotonicity #1608 #1631]: #1633
+#1649 := [monotonicity #1634]: #1648
+#1655 := [trans #1649 #1653]: #1654
+#1645 := (iff #1384 #1642)
+#1635 := (and #280 #285 #288 #668 #671 #754 #757 #802 #818 #1632)
+#1643 := (iff #1635 #1642)
+#1644 := [rewrite]: #1643
+#1636 := (iff #1384 #1635)
+#1637 := [monotonicity #1634]: #1636
+#1646 := [trans #1637 #1644]: #1645
+#1658 := [monotonicity #1646 #1655]: #1657
+#1661 := [monotonicity #1658]: #1660
+#1668 := [trans #1661 #1666]: #1667
+#1575 := (iff #1313 #1572)
+#1566 := (and #179 #182 #185 #668 #671 #724 #1563)
+#1573 := (iff #1566 #1572)
+#1574 := [rewrite]: #1573
+#1567 := (iff #1313 #1566)
+#1564 := (iff #1307 #1563)
+#1561 := (iff #1304 #1558)
+#1550 := (not #1545)
+#1553 := (and #1525 #1550)
+#1559 := (iff #1553 #1558)
+#1560 := [rewrite]: #1559
+#1554 := (iff #1304 #1553)
+#1551 := (iff #1301 #1550)
+#1548 := (iff #1298 #1545)
+#1531 := (or #1110 #1530)
+#1542 := (or #1531 #1293)
+#1546 := (iff #1542 #1545)
+#1547 := [rewrite]: #1546
+#1543 := (iff #1298 #1542)
+#1540 := (iff #1282 #1531)
+#1532 := (not #1531)
+#1535 := (not #1532)
+#1538 := (iff #1535 #1531)
+#1539 := [rewrite]: #1538
+#1536 := (iff #1282 #1535)
+#1533 := (iff #1279 #1532)
 #1534 := [rewrite]: #1533
-#1531 := (iff #1277 #1530)
-#1528 := (iff #1274 #1527)
-#1529 := [rewrite]: #1528
-#1532 := [monotonicity #1529]: #1531
-#1536 := [trans #1532 #1534]: #1535
-#1539 := [monotonicity #1536]: #1538
-#1544 := [trans #1539 #1542]: #1543
-#1547 := [monotonicity #1544]: #1546
-#1523 := (iff #1271 #1520)
-#1506 := (or #1084 #1505)
-#1517 := (or #1262 #1506)
-#1521 := (iff #1517 #1520)
-#1522 := [rewrite]: #1521
-#1518 := (iff #1271 #1517)
-#1515 := (iff #1268 #1506)
-#1507 := (not #1506)
-#1510 := (not #1507)
-#1513 := (iff #1510 #1506)
+#1537 := [monotonicity #1534]: #1536
+#1541 := [trans #1537 #1539]: #1540
+#1544 := [monotonicity #1541]: #1543
+#1549 := [trans #1544 #1547]: #1548
+#1552 := [monotonicity #1549]: #1551
+#1528 := (iff #1276 #1525)
+#1511 := (or #1089 #1510)
+#1522 := (or #1267 #1511)
+#1526 := (iff #1522 #1525)
+#1527 := [rewrite]: #1526
+#1523 := (iff #1276 #1522)
+#1520 := (iff #1273 #1511)
+#1512 := (not #1511)
+#1515 := (not #1512)
+#1518 := (iff #1515 #1511)
+#1519 := [rewrite]: #1518
+#1516 := (iff #1273 #1515)
+#1513 := (iff #1270 #1512)
 #1514 := [rewrite]: #1513
-#1511 := (iff #1268 #1510)
-#1508 := (iff #1265 #1507)
-#1509 := [rewrite]: #1508
-#1512 := [monotonicity #1509]: #1511
-#1516 := [trans #1512 #1514]: #1515
-#1519 := [monotonicity #1516]: #1518
-#1524 := [trans #1519 #1522]: #1523
-#1550 := [monotonicity #1524 #1547]: #1549
-#1557 := [trans #1550 #1555]: #1556
-#1503 := (iff #1078 #1502)
-#1500 := (iff #1075 #1499)
-#1497 := (iff #689 #1494)
-#1480 := (or #1435 #676)
-#1491 := (or #47 #1480)
-#1495 := (iff #1491 #1494)
-#1496 := [rewrite]: #1495
-#1492 := (iff #689 #1491)
-#1489 := (iff #683 #1480)
-#1481 := (not #1480)
-#1484 := (not #1481)
-#1487 := (iff #1484 #1480)
+#1517 := [monotonicity #1514]: #1516
+#1521 := [trans #1517 #1519]: #1520
+#1524 := [monotonicity #1521]: #1523
+#1529 := [trans #1524 #1527]: #1528
+#1555 := [monotonicity #1529 #1552]: #1554
+#1562 := [trans #1555 #1560]: #1561
+#1508 := (iff #1083 #1507)
+#1505 := (iff #1080 #1504)
+#1502 := (iff #694 #1499)
+#1485 := (or #1440 #681)
+#1496 := (or #51 #1485)
+#1500 := (iff #1496 #1499)
+#1501 := [rewrite]: #1500
+#1497 := (iff #694 #1496)
+#1494 := (iff #688 #1485)
+#1486 := (not #1485)
+#1489 := (not #1486)
+#1492 := (iff #1489 #1485)
+#1493 := [rewrite]: #1492
+#1490 := (iff #688 #1489)
+#1487 := (iff #685 #1486)
 #1488 := [rewrite]: #1487
-#1485 := (iff #683 #1484)
-#1482 := (iff #680 #1481)
-#1483 := [rewrite]: #1482
-#1486 := [monotonicity #1483]: #1485
-#1490 := [trans #1486 #1488]: #1489
-#1493 := [monotonicity #1490]: #1492
-#1498 := [trans #1493 #1496]: #1497
-#1501 := [monotonicity #1498]: #1500
-#1504 := [quant-intro #1501]: #1503
-#1560 := [monotonicity #1504 #1557]: #1559
-#1563 := [monotonicity #1560]: #1562
-#1571 := [trans #1563 #1569]: #1570
-#1666 := [monotonicity #1571 #1663]: #1665
-#1478 := (iff #930 #1477)
-#1475 := (iff #927 #1472)
-#1458 := (or #1435 #911)
-#1469 := (or #1458 #924)
-#1473 := (iff #1469 #1472)
-#1474 := [rewrite]: #1473
-#1470 := (iff #927 #1469)
-#1467 := (iff #919 #1458)
-#1459 := (not #1458)
-#1462 := (not #1459)
-#1465 := (iff #1462 #1458)
+#1491 := [monotonicity #1488]: #1490
+#1495 := [trans #1491 #1493]: #1494
+#1498 := [monotonicity #1495]: #1497
+#1503 := [trans #1498 #1501]: #1502
+#1506 := [monotonicity #1503]: #1505
+#1509 := [quant-intro #1506]: #1508
+#1565 := [monotonicity #1509 #1562]: #1564
+#1568 := [monotonicity #1565]: #1567
+#1576 := [trans #1568 #1574]: #1575
+#1671 := [monotonicity #1576 #1668]: #1670
+#1483 := (iff #935 #1482)
+#1480 := (iff #932 #1477)
+#1463 := (or #1440 #916)
+#1474 := (or #1463 #929)
+#1478 := (iff #1474 #1477)
+#1479 := [rewrite]: #1478
+#1475 := (iff #932 #1474)
+#1472 := (iff #924 #1463)
+#1464 := (not #1463)
+#1467 := (not #1464)
+#1470 := (iff #1467 #1463)
+#1471 := [rewrite]: #1470
+#1468 := (iff #924 #1467)
+#1465 := (iff #921 #1464)
 #1466 := [rewrite]: #1465
-#1463 := (iff #919 #1462)
-#1460 := (iff #916 #1459)
-#1461 := [rewrite]: #1460
-#1464 := [monotonicity #1461]: #1463
-#1468 := [trans #1464 #1466]: #1467
-#1471 := [monotonicity #1468]: #1470
-#1476 := [trans #1471 #1474]: #1475
-#1479 := [quant-intro #1476]: #1478
-#1456 := (iff #656 #1455)
-#1453 := (iff #653 #1450)
-#1436 := (or #1435 #639)
-#1447 := (or #1436 #649)
-#1451 := (iff #1447 #1450)
-#1452 := [rewrite]: #1451
-#1448 := (iff #653 #1447)
-#1445 := (iff #644 #1436)
-#1437 := (not #1436)
-#1440 := (not #1437)
-#1443 := (iff #1440 #1436)
+#1469 := [monotonicity #1466]: #1468
+#1473 := [trans #1469 #1471]: #1472
+#1476 := [monotonicity #1473]: #1475
+#1481 := [trans #1476 #1479]: #1480
+#1484 := [quant-intro #1481]: #1483
+#1461 := (iff #661 #1460)
+#1458 := (iff #658 #1455)
+#1441 := (or #1440 #644)
+#1452 := (or #1441 #654)
+#1456 := (iff #1452 #1455)
+#1457 := [rewrite]: #1456
+#1453 := (iff #658 #1452)
+#1450 := (iff #649 #1441)
+#1442 := (not #1441)
+#1445 := (not #1442)
+#1448 := (iff #1445 #1441)
+#1449 := [rewrite]: #1448
+#1446 := (iff #649 #1445)
+#1443 := (iff #646 #1442)
 #1444 := [rewrite]: #1443
-#1441 := (iff #644 #1440)
-#1438 := (iff #641 #1437)
-#1439 := [rewrite]: #1438
-#1442 := [monotonicity #1439]: #1441
-#1446 := [trans #1442 #1444]: #1445
-#1449 := [monotonicity #1446]: #1448
-#1454 := [trans #1449 #1452]: #1453
-#1457 := [quant-intro #1454]: #1456
-#1669 := [monotonicity #1457 #1479 #1666]: #1668
-#1678 := [trans #1669 #1676]: #1677
-#1433 := (iff #1249 #1432)
-#1430 := (iff #1244 #1427)
-#1095 := (or #1042 #1094)
-#1424 := (or #1041 #1095)
-#1428 := (iff #1424 #1427)
-#1429 := [rewrite]: #1428
-#1425 := (iff #1244 #1424)
-#1422 := (iff #1238 #1095)
-#1162 := (not #1095)
-#1052 := (not #1162)
-#1234 := (iff #1052 #1095)
-#1421 := [rewrite]: #1234
-#1115 := (iff #1238 #1052)
-#1163 := (iff #1235 #1162)
-#1051 := [rewrite]: #1163
-#1116 := [monotonicity #1051]: #1115
-#1423 := [trans #1116 #1421]: #1422
-#1426 := [monotonicity #1423]: #1425
-#1431 := [trans #1426 #1429]: #1430
-#1434 := [monotonicity #1431]: #1433
-#1681 := [monotonicity #1434 #1678]: #1680
-#1721 := [trans #1681 #1719]: #1720
-#1185 := (not #807)
-#1182 := (not #801)
-#1150 := (+ #1149 #772)
-#1151 := (<= #1150 0::int)
-#1152 := (+ ?x7!3 #761)
-#1153 := (>= #1152 0::int)
-#1154 := (not #1153)
-#1156 := (and #1155 #1154)
-#1157 := (not #1156)
-#1158 := (or #1157 #1151)
+#1447 := [monotonicity #1444]: #1446
+#1451 := [trans #1447 #1449]: #1450
+#1454 := [monotonicity #1451]: #1453
+#1459 := [trans #1454 #1457]: #1458
+#1462 := [quant-intro #1459]: #1461
+#1674 := [monotonicity #1462 #1484 #1671]: #1673
+#1683 := [trans #1674 #1681]: #1682
+#1438 := (iff #1254 #1437)
+#1435 := (iff #1249 #1432)
+#1168 := (or #1005 #1167)
+#1429 := (or #1007 #1168)
+#1433 := (iff #1429 #1432)
+#1434 := [rewrite]: #1433
+#1430 := (iff #1249 #1429)
+#1427 := (iff #1243 #1168)
+#1099 := (not #1168)
+#1057 := (not #1099)
+#1239 := (iff #1057 #1168)
+#1426 := [rewrite]: #1239
+#1120 := (iff #1243 #1057)
+#1100 := (iff #1240 #1099)
+#1056 := [rewrite]: #1100
+#1121 := [monotonicity #1056]: #1120
+#1428 := [trans #1121 #1426]: #1427
+#1431 := [monotonicity #1428]: #1430
+#1436 := [trans #1431 #1434]: #1435
+#1439 := [monotonicity #1436]: #1438
+#1686 := [monotonicity #1439 #1683]: #1685
+#1726 := [trans #1686 #1724]: #1725
+#1190 := (not #812)
+#1187 := (not #806)
+#1155 := (+ #1154 #777)
+#1156 := (<= #1155 0::int)
+#1157 := (+ ?v0!3 #766)
+#1158 := (>= #1157 0::int)
 #1159 := (not #1158)
-#1178 := (or #1159 #1174)
-#1145 := (not #757)
-#1063 := (not #671)
-#1197 := (not #427)
-#1194 := (not #436)
-#1202 := (and #1194 #1197 #1063 #1145 #1178 #1182 #1185 #819)
-#1142 := (not #810)
-#1139 := (not #361)
-#1136 := (not #370)
-#1133 := (not #388)
-#1190 := (and #1133 #1136 #1139 #1142 #1063 #1145 #1178 #1182 #1185 #813)
-#1206 := (or #1190 #1202)
-#1210 := (and #1063 #722 #1206)
-#1101 := (+ #1100 #700)
-#1102 := (<= #1101 0::int)
-#1108 := (and #1107 #1106)
-#1109 := (not #1108)
-#1110 := (or #1109 #1102)
-#1111 := (not #1110)
-#1087 := (and #1086 #1085)
-#1088 := (not #1087)
-#1090 := (= #1089 uf_8)
-#1091 := (or #1090 #1088)
-#1117 := (and #1091 #1111)
-#1121 := (or #1078 #1117)
-#1072 := (not #218)
-#1069 := (not #227)
-#1066 := (not #236)
-#1127 := (and #1066 #1069 #1072 #1063 #1121 #887)
-#1214 := (or #1127 #1210)
-#1053 := (not #523)
-#1225 := (and #1053 #656 #1063 #1214 #930)
-#1045 := (and #1044 #1043)
-#1046 := (not #1045)
-#1047 := (or #1046 #1041)
-#1048 := (not #1047)
-#1229 := (or #1048 #1225)
-#1419 := (iff #1229 #1418)
-#1416 := (iff #1225 #1413)
-#1410 := (and #171 #656 #668 #1407 #930)
-#1414 := (iff #1410 #1413)
-#1415 := [rewrite]: #1414
-#1411 := (iff #1225 #1410)
-#1408 := (iff #1214 #1407)
-#1405 := (iff #1210 #1402)
-#1399 := (and #668 #722 #1396)
-#1403 := (iff #1399 #1402)
-#1404 := [rewrite]: #1403
-#1400 := (iff #1210 #1399)
-#1397 := (iff #1206 #1396)
-#1394 := (iff #1202 #1391)
-#1388 := (and #418 #421 #668 #754 #1367 #797 #804 #814)
-#1392 := (iff #1388 #1391)
-#1393 := [rewrite]: #1392
-#1389 := (iff #1202 #1388)
-#1374 := (iff #1185 #804)
-#1375 := [rewrite]: #1374
-#1372 := (iff #1182 #797)
-#1373 := [rewrite]: #1372
-#1370 := (iff #1178 #1367)
-#1364 := (or #1361 #1174)
-#1368 := (iff #1364 #1367)
-#1369 := [rewrite]: #1368
-#1365 := (iff #1178 #1364)
-#1362 := (iff #1159 #1361)
-#1359 := (iff #1158 #1358)
-#1356 := (iff #1151 #1353)
-#1345 := (+ #772 #1149)
-#1348 := (<= #1345 0::int)
-#1354 := (iff #1348 #1353)
-#1355 := [rewrite]: #1354
-#1349 := (iff #1151 #1348)
-#1346 := (= #1150 #1345)
-#1347 := [rewrite]: #1346
-#1350 := [monotonicity #1347]: #1349
-#1357 := [trans #1350 #1355]: #1356
-#1343 := (iff #1157 #1342)
-#1340 := (iff #1156 #1339)
-#1337 := (iff #1154 #1336)
-#1334 := (iff #1153 #1331)
-#1323 := (+ #761 ?x7!3)
-#1326 := (>= #1323 0::int)
-#1332 := (iff #1326 #1331)
-#1333 := [rewrite]: #1332
-#1327 := (iff #1153 #1326)
-#1324 := (= #1152 #1323)
+#1161 := (and #1160 #1159)
+#1162 := (not #1161)
+#1163 := (or #1162 #1156)
+#1164 := (not #1163)
+#1183 := (or #1164 #1179)
+#1150 := (not #762)
+#1068 := (not #676)
+#1202 := (not #432)
+#1199 := (not #441)
+#1207 := (and #1199 #1202 #1068 #1150 #1183 #1187 #1190 #824)
+#1147 := (not #815)
+#1144 := (not #366)
+#1141 := (not #375)
+#1138 := (not #393)
+#1195 := (and #1138 #1141 #1144 #1147 #1068 #1150 #1183 #1187 #1190 #818)
+#1211 := (or #1195 #1207)
+#1215 := (and #1068 #727 #1211)
+#1106 := (+ #1105 #705)
+#1107 := (<= #1106 0::int)
+#1113 := (and #1112 #1111)
+#1114 := (not #1113)
+#1115 := (or #1114 #1107)
+#1116 := (not #1115)
+#1092 := (and #1091 #1090)
+#1093 := (not #1092)
+#1095 := (= #1094 f10)
+#1096 := (or #1095 #1093)
+#1122 := (and #1096 #1116)
+#1126 := (or #1083 #1122)
+#1077 := (not #223)
+#1074 := (not #232)
+#1071 := (not #241)
+#1132 := (and #1071 #1074 #1077 #1068 #1126 #892)
+#1219 := (or #1132 #1215)
+#1058 := (not #528)
+#1230 := (and #1058 #661 #1068 #1219 #935)
+#1050 := (and #1049 #1048)
+#1051 := (not #1050)
+#1052 := (or #1051 #1007)
+#1053 := (not #1052)
+#1234 := (or #1053 #1230)
+#1424 := (iff #1234 #1423)
+#1421 := (iff #1230 #1418)
+#1415 := (and #176 #661 #673 #1412 #935)
+#1419 := (iff #1415 #1418)
+#1420 := [rewrite]: #1419
+#1416 := (iff #1230 #1415)
+#1413 := (iff #1219 #1412)
+#1410 := (iff #1215 #1407)
+#1404 := (and #673 #727 #1401)
+#1408 := (iff #1404 #1407)
+#1409 := [rewrite]: #1408
+#1405 := (iff #1215 #1404)
+#1402 := (iff #1211 #1401)
+#1399 := (iff #1207 #1396)
+#1393 := (and #423 #426 #673 #759 #1372 #802 #809 #819)
+#1397 := (iff #1393 #1396)
+#1398 := [rewrite]: #1397
+#1394 := (iff #1207 #1393)
+#1379 := (iff #1190 #809)
+#1380 := [rewrite]: #1379
+#1377 := (iff #1187 #802)
+#1378 := [rewrite]: #1377
+#1375 := (iff #1183 #1372)
+#1369 := (or #1366 #1179)
+#1373 := (iff #1369 #1372)
+#1374 := [rewrite]: #1373
+#1370 := (iff #1183 #1369)
+#1367 := (iff #1164 #1366)
+#1364 := (iff #1163 #1363)
+#1361 := (iff #1156 #1358)
+#1350 := (+ #777 #1154)
+#1353 := (<= #1350 0::int)
+#1359 := (iff #1353 #1358)
+#1360 := [rewrite]: #1359
+#1354 := (iff #1156 #1353)
+#1351 := (= #1155 #1350)
+#1352 := [rewrite]: #1351
+#1355 := [monotonicity #1352]: #1354
+#1362 := [trans #1355 #1360]: #1361
+#1348 := (iff #1162 #1347)
+#1345 := (iff #1161 #1344)
+#1342 := (iff #1159 #1341)
+#1339 := (iff #1158 #1336)
+#1328 := (+ #766 ?v0!3)
+#1331 := (>= #1328 0::int)
+#1337 := (iff #1331 #1336)
+#1338 := [rewrite]: #1337
+#1332 := (iff #1158 #1331)
+#1329 := (= #1157 #1328)
+#1330 := [rewrite]: #1329
+#1333 := [monotonicity #1330]: #1332
+#1340 := [trans #1333 #1338]: #1339
+#1343 := [monotonicity #1340]: #1342
+#1346 := [monotonicity #1343]: #1345
+#1349 := [monotonicity #1346]: #1348
+#1365 := [monotonicity #1349 #1362]: #1364
+#1368 := [monotonicity #1365]: #1367
+#1371 := [monotonicity #1368]: #1370
+#1376 := [trans #1371 #1374]: #1375
+#1326 := (iff #1150 #759)
+#1327 := [rewrite]: #1326
+#1259 := (iff #1068 #673)
+#1260 := [rewrite]: #1259
+#1391 := (iff #1202 #426)
+#1392 := [rewrite]: #1391
+#1389 := (iff #1199 #423)
+#1390 := [rewrite]: #1389
+#1395 := [monotonicity #1390 #1392 #1260 #1327 #1376 #1378 #1380 #828]: #1394
+#1400 := [trans #1395 #1398]: #1399
+#1387 := (iff #1195 #1384)
+#1381 := (and #280 #285 #288 #671 #673 #759 #1372 #802 #809 #818)
+#1385 := (iff #1381 #1384)
+#1386 := [rewrite]: #1385
+#1382 := (iff #1195 #1381)
+#1324 := (iff #1147 #671)
 #1325 := [rewrite]: #1324
-#1328 := [monotonicity #1325]: #1327
-#1335 := [trans #1328 #1333]: #1334
-#1338 := [monotonicity #1335]: #1337
-#1341 := [monotonicity #1338]: #1340
-#1344 := [monotonicity #1341]: #1343
-#1360 := [monotonicity #1344 #1357]: #1359
-#1363 := [monotonicity #1360]: #1362
-#1366 := [monotonicity #1363]: #1365
-#1371 := [trans #1366 #1369]: #1370
-#1321 := (iff #1145 #754)
-#1322 := [rewrite]: #1321
-#1254 := (iff #1063 #668)
-#1255 := [rewrite]: #1254
-#1386 := (iff #1197 #421)
-#1387 := [rewrite]: #1386
-#1384 := (iff #1194 #418)
-#1385 := [rewrite]: #1384
-#1390 := [monotonicity #1385 #1387 #1255 #1322 #1371 #1373 #1375 #823]: #1389
-#1395 := [trans #1390 #1393]: #1394
-#1382 := (iff #1190 #1379)
-#1376 := (and #275 #280 #283 #666 #668 #754 #1367 #797 #804 #813)
-#1380 := (iff #1376 #1379)
-#1381 := [rewrite]: #1380
-#1377 := (iff #1190 #1376)
-#1319 := (iff #1142 #666)
-#1320 := [rewrite]: #1319
-#1317 := (iff #1139 #283)
-#1318 := [rewrite]: #1317
-#1315 := (iff #1136 #280)
-#1316 := [rewrite]: #1315
-#1313 := (iff #1133 #275)
-#1314 := [rewrite]: #1313
-#1378 := [monotonicity #1314 #1316 #1318 #1320 #1255 #1322 #1371 #1373 #1375]: #1377
-#1383 := [trans #1378 #1381]: #1382
-#1398 := [monotonicity #1383 #1395]: #1397
-#1401 := [monotonicity #1255 #1398]: #1400
-#1406 := [trans #1401 #1404]: #1405
-#1311 := (iff #1127 #1308)
-#1305 := (and #174 #177 #180 #668 #1302 #719)
-#1309 := (iff #1305 #1308)
-#1310 := [rewrite]: #1309
-#1306 := (iff #1127 #1305)
-#1303 := (iff #1121 #1302)
-#1300 := (iff #1117 #1299)
-#1297 := (iff #1111 #1296)
-#1294 := (iff #1110 #1293)
-#1291 := (iff #1102 #1288)
-#1280 := (+ #700 #1100)
-#1283 := (<= #1280 0::int)
-#1289 := (iff #1283 #1288)
-#1290 := [rewrite]: #1289
-#1284 := (iff #1102 #1283)
-#1281 := (= #1101 #1280)
-#1282 := [rewrite]: #1281
-#1285 := [monotonicity #1282]: #1284
-#1292 := [trans #1285 #1290]: #1291
-#1278 := (iff #1109 #1277)
-#1275 := (iff #1108 #1274)
-#1276 := [rewrite]: #1275
-#1279 := [monotonicity #1276]: #1278
-#1295 := [monotonicity #1279 #1292]: #1294
-#1298 := [monotonicity #1295]: #1297
-#1272 := (iff #1091 #1271)
-#1269 := (iff #1088 #1268)
-#1266 := (iff #1087 #1265)
-#1267 := [rewrite]: #1266
-#1270 := [monotonicity #1267]: #1269
-#1263 := (iff #1090 #1262)
+#1322 := (iff #1144 #288)
+#1323 := [rewrite]: #1322
+#1320 := (iff #1141 #285)
+#1321 := [rewrite]: #1320
+#1318 := (iff #1138 #280)
+#1319 := [rewrite]: #1318
+#1383 := [monotonicity #1319 #1321 #1323 #1325 #1260 #1327 #1376 #1378 #1380]: #1382
+#1388 := [trans #1383 #1386]: #1387
+#1403 := [monotonicity #1388 #1400]: #1402
+#1406 := [monotonicity #1260 #1403]: #1405
+#1411 := [trans #1406 #1409]: #1410
+#1316 := (iff #1132 #1313)
+#1310 := (and #179 #182 #185 #673 #1307 #724)
+#1314 := (iff #1310 #1313)
+#1315 := [rewrite]: #1314
+#1311 := (iff #1132 #1310)
+#1308 := (iff #1126 #1307)
+#1305 := (iff #1122 #1304)
+#1302 := (iff #1116 #1301)
+#1299 := (iff #1115 #1298)
+#1296 := (iff #1107 #1293)
+#1285 := (+ #705 #1105)
+#1288 := (<= #1285 0::int)
+#1294 := (iff #1288 #1293)
+#1295 := [rewrite]: #1294
+#1289 := (iff #1107 #1288)
+#1286 := (= #1106 #1285)
+#1287 := [rewrite]: #1286
+#1290 := [monotonicity #1287]: #1289
+#1297 := [trans #1290 #1295]: #1296
+#1283 := (iff #1114 #1282)
+#1280 := (iff #1113 #1279)
+#1281 := [rewrite]: #1280
+#1284 := [monotonicity #1281]: #1283
+#1300 := [monotonicity #1284 #1297]: #1299
+#1303 := [monotonicity #1300]: #1302
+#1277 := (iff #1096 #1276)
+#1274 := (iff #1093 #1273)
+#1271 := (iff #1092 #1270)
+#1272 := [rewrite]: #1271
+#1275 := [monotonicity #1272]: #1274
+#1268 := (iff #1095 #1267)
+#1269 := [rewrite]: #1268
+#1278 := [monotonicity #1269 #1275]: #1277
+#1306 := [monotonicity #1278 #1303]: #1305
+#1309 := [monotonicity #1306]: #1308
+#1265 := (iff #1077 #185)
+#1266 := [rewrite]: #1265
+#1263 := (iff #1074 #182)
 #1264 := [rewrite]: #1263
-#1273 := [monotonicity #1264 #1270]: #1272
-#1301 := [monotonicity #1273 #1298]: #1300
-#1304 := [monotonicity #1301]: #1303
-#1260 := (iff #1072 #180)
-#1261 := [rewrite]: #1260
-#1258 := (iff #1069 #177)
-#1259 := [rewrite]: #1258
-#1256 := (iff #1066 #174)
-#1257 := [rewrite]: #1256
-#1307 := [monotonicity #1257 #1259 #1261 #1255 #1304 #891]: #1306
-#1312 := [trans #1307 #1310]: #1311
-#1409 := [monotonicity #1312 #1406]: #1408
-#1252 := (iff #1053 #171)
-#1253 := [rewrite]: #1252
-#1412 := [monotonicity #1253 #1255 #1409]: #1411
-#1417 := [trans #1412 #1415]: #1416
-#1250 := (iff #1048 #1249)
-#1247 := (iff #1047 #1244)
-#1241 := (or #1238 #1041)
-#1245 := (iff #1241 #1244)
-#1246 := [rewrite]: #1245
-#1242 := (iff #1047 #1241)
-#1239 := (iff #1046 #1238)
-#1236 := (iff #1045 #1235)
-#1237 := [rewrite]: #1236
-#1240 := [monotonicity #1237]: #1239
-#1243 := [monotonicity #1240]: #1242
-#1248 := [trans #1243 #1246]: #1247
-#1251 := [monotonicity #1248]: #1250
-#1420 := [monotonicity #1251 #1417]: #1419
-#1025 := (or #523 #659 #671 #908 #933)
-#1030 := (and #656 #1025)
-#1033 := (not #1030)
-#1230 := (~ #1033 #1229)
-#1226 := (not #1025)
-#1227 := (~ #1226 #1225)
-#1222 := (not #933)
-#1223 := (~ #1222 #930)
-#1220 := (~ #930 #930)
-#1218 := (~ #927 #927)
-#1219 := [refl]: #1218
-#1221 := [nnf-pos #1219]: #1220
-#1224 := [nnf-neg #1221]: #1223
-#1215 := (not #908)
-#1216 := (~ #1215 #1214)
-#1211 := (not #903)
-#1212 := (~ #1211 #1210)
-#1207 := (not #882)
-#1208 := (~ #1207 #1206)
-#1203 := (not #877)
-#1204 := (~ #1203 #1202)
-#1200 := (~ #819 #819)
-#1201 := [refl]: #1200
-#1186 := (~ #1185 #1185)
-#1187 := [refl]: #1186
-#1183 := (~ #1182 #1182)
-#1184 := [refl]: #1183
-#1179 := (not #794)
-#1180 := (~ #1179 #1178)
-#1175 := (not #789)
-#1176 := (~ #1175 #1174)
-#1171 := (not #783)
-#1172 := (~ #1171 #780)
-#1169 := (~ #780 #780)
-#1167 := (~ #777 #777)
-#1168 := [refl]: #1167
-#1170 := [nnf-pos #1168]: #1169
-#1173 := [nnf-neg #1170]: #1172
-#1165 := (~ #1164 #1164)
-#1166 := [refl]: #1165
-#1177 := [nnf-neg #1166 #1173]: #1176
-#1160 := (~ #783 #1159)
-#1161 := [sk]: #1160
-#1181 := [nnf-neg #1161 #1177]: #1180
-#1146 := (~ #1145 #1145)
-#1147 := [refl]: #1146
-#1064 := (~ #1063 #1063)
-#1065 := [refl]: #1064
-#1198 := (~ #1197 #1197)
-#1199 := [refl]: #1198
-#1195 := (~ #1194 #1194)
-#1196 := [refl]: #1195
-#1205 := [nnf-neg #1196 #1199 #1065 #1147 #1181 #1184 #1187 #1201]: #1204
-#1191 := (not #853)
-#1192 := (~ #1191 #1190)
-#1188 := (~ #813 #813)
+#1261 := (iff #1071 #179)
+#1262 := [rewrite]: #1261
+#1312 := [monotonicity #1262 #1264 #1266 #1260 #1309 #896]: #1311
+#1317 := [trans #1312 #1315]: #1316
+#1414 := [monotonicity #1317 #1411]: #1413
+#1257 := (iff #1058 #176)
+#1258 := [rewrite]: #1257
+#1417 := [monotonicity #1258 #1260 #1414]: #1416
+#1422 := [trans #1417 #1420]: #1421
+#1255 := (iff #1053 #1254)
+#1252 := (iff #1052 #1249)
+#1246 := (or #1243 #1007)
+#1250 := (iff #1246 #1249)
+#1251 := [rewrite]: #1250
+#1247 := (iff #1052 #1246)
+#1244 := (iff #1051 #1243)
+#1241 := (iff #1050 #1240)
+#1242 := [rewrite]: #1241
+#1245 := [monotonicity #1242]: #1244
+#1248 := [monotonicity #1245]: #1247
+#1253 := [trans #1248 #1251]: #1252
+#1256 := [monotonicity #1253]: #1255
+#1425 := [monotonicity #1256 #1422]: #1424
+#1032 := (or #528 #664 #676 #913 #938)
+#1037 := (and #661 #1032)
+#1040 := (not #1037)
+#1235 := (~ #1040 #1234)
+#1231 := (not #1032)
+#1232 := (~ #1231 #1230)
+#1227 := (not #938)
+#1228 := (~ #1227 #935)
+#1225 := (~ #935 #935)
+#1223 := (~ #932 #932)
+#1224 := [refl]: #1223
+#1226 := [nnf-pos #1224]: #1225
+#1229 := [nnf-neg #1226]: #1228
+#1220 := (not #913)
+#1221 := (~ #1220 #1219)
+#1216 := (not #908)
+#1217 := (~ #1216 #1215)
+#1212 := (not #887)
+#1213 := (~ #1212 #1211)
+#1208 := (not #882)
+#1209 := (~ #1208 #1207)
+#1205 := (~ #824 #824)
+#1206 := [refl]: #1205
+#1191 := (~ #1190 #1190)
+#1192 := [refl]: #1191
+#1188 := (~ #1187 #1187)
 #1189 := [refl]: #1188
-#1143 := (~ #1142 #1142)
-#1144 := [refl]: #1143
-#1140 := (~ #1139 #1139)
-#1141 := [refl]: #1140
-#1137 := (~ #1136 #1136)
-#1138 := [refl]: #1137
-#1134 := (~ #1133 #1133)
-#1135 := [refl]: #1134
-#1193 := [nnf-neg #1135 #1138 #1141 #1144 #1065 #1147 #1181 #1184 #1187 #1189]: #1192
-#1209 := [nnf-neg #1193 #1205]: #1208
-#1131 := (~ #722 #722)
-#1132 := [refl]: #1131
-#1213 := [nnf-neg #1065 #1132 #1209]: #1212
-#1128 := (not #743)
-#1129 := (~ #1128 #1127)
-#1125 := (~ #887 #887)
-#1126 := [refl]: #1125
-#1122 := (not #714)
-#1123 := (~ #1122 #1121)
-#1118 := (not #711)
-#1119 := (~ #1118 #1117)
-#1112 := (not #708)
-#1113 := (~ #1112 #1111)
-#1114 := [sk]: #1113
-#1096 := (not #697)
-#1097 := (~ #1096 #1091)
-#1092 := (~ #694 #1091)
-#1093 := [sk]: #1092
-#1098 := [nnf-neg #1093]: #1097
-#1120 := [nnf-neg #1098 #1114]: #1119
-#1079 := (~ #697 #1078)
-#1076 := (~ #1075 #1075)
-#1077 := [refl]: #1076
-#1080 := [nnf-neg #1077]: #1079
-#1124 := [nnf-neg #1080 #1120]: #1123
-#1073 := (~ #1072 #1072)
-#1074 := [refl]: #1073
-#1070 := (~ #1069 #1069)
-#1071 := [refl]: #1070
-#1067 := (~ #1066 #1066)
-#1068 := [refl]: #1067
-#1130 := [nnf-neg #1068 #1071 #1074 #1065 #1124 #1126]: #1129
-#1217 := [nnf-neg #1130 #1213]: #1216
-#1060 := (not #659)
-#1061 := (~ #1060 #656)
-#1058 := (~ #656 #656)
-#1056 := (~ #653 #653)
-#1057 := [refl]: #1056
-#1059 := [nnf-pos #1057]: #1058
-#1062 := [nnf-neg #1059]: #1061
-#1054 := (~ #1053 #1053)
-#1055 := [refl]: #1054
-#1228 := [nnf-neg #1055 #1062 #1065 #1217 #1224]: #1227
-#1049 := (~ #659 #1048)
-#1050 := [sk]: #1049
-#1231 := [nnf-neg #1050 #1228]: #1230
-#997 := (not #962)
-#1034 := (iff #997 #1033)
-#1031 := (iff #962 #1030)
-#1028 := (iff #959 #1025)
-#1010 := (or #523 #671 #908 #933)
-#1022 := (or #659 #1010)
-#1026 := (iff #1022 #1025)
-#1027 := [rewrite]: #1026
-#1023 := (iff #959 #1022)
-#1020 := (iff #956 #1010)
-#1015 := (and true #1010)
-#1018 := (iff #1015 #1010)
+#1184 := (not #799)
+#1185 := (~ #1184 #1183)
+#1180 := (not #794)
+#1181 := (~ #1180 #1179)
+#1176 := (not #788)
+#1177 := (~ #1176 #785)
+#1174 := (~ #785 #785)
+#1172 := (~ #782 #782)
+#1173 := [refl]: #1172
+#1175 := [nnf-pos #1173]: #1174
+#1178 := [nnf-neg #1175]: #1177
+#1170 := (~ #1169 #1169)
+#1171 := [refl]: #1170
+#1182 := [nnf-neg #1171 #1178]: #1181
+#1165 := (~ #788 #1164)
+#1166 := [sk]: #1165
+#1186 := [nnf-neg #1166 #1182]: #1185
+#1151 := (~ #1150 #1150)
+#1152 := [refl]: #1151
+#1069 := (~ #1068 #1068)
+#1070 := [refl]: #1069
+#1203 := (~ #1202 #1202)
+#1204 := [refl]: #1203
+#1200 := (~ #1199 #1199)
+#1201 := [refl]: #1200
+#1210 := [nnf-neg #1201 #1204 #1070 #1152 #1186 #1189 #1192 #1206]: #1209
+#1196 := (not #858)
+#1197 := (~ #1196 #1195)
+#1193 := (~ #818 #818)
+#1194 := [refl]: #1193
+#1148 := (~ #1147 #1147)
+#1149 := [refl]: #1148
+#1145 := (~ #1144 #1144)
+#1146 := [refl]: #1145
+#1142 := (~ #1141 #1141)
+#1143 := [refl]: #1142
+#1139 := (~ #1138 #1138)
+#1140 := [refl]: #1139
+#1198 := [nnf-neg #1140 #1143 #1146 #1149 #1070 #1152 #1186 #1189 #1192 #1194]: #1197
+#1214 := [nnf-neg #1198 #1210]: #1213
+#1136 := (~ #727 #727)
+#1137 := [refl]: #1136
+#1218 := [nnf-neg #1070 #1137 #1214]: #1217
+#1133 := (not #748)
+#1134 := (~ #1133 #1132)
+#1130 := (~ #892 #892)
+#1131 := [refl]: #1130
+#1127 := (not #719)
+#1128 := (~ #1127 #1126)
+#1123 := (not #716)
+#1124 := (~ #1123 #1122)
+#1117 := (not #713)
+#1118 := (~ #1117 #1116)
+#1119 := [sk]: #1118
+#1101 := (not #702)
+#1102 := (~ #1101 #1096)
+#1097 := (~ #699 #1096)
+#1098 := [sk]: #1097
+#1103 := [nnf-neg #1098]: #1102
+#1125 := [nnf-neg #1103 #1119]: #1124
+#1084 := (~ #702 #1083)
+#1081 := (~ #1080 #1080)
+#1082 := [refl]: #1081
+#1085 := [nnf-neg #1082]: #1084
+#1129 := [nnf-neg #1085 #1125]: #1128
+#1078 := (~ #1077 #1077)
+#1079 := [refl]: #1078
+#1075 := (~ #1074 #1074)
+#1076 := [refl]: #1075
+#1072 := (~ #1071 #1071)
+#1073 := [refl]: #1072
+#1135 := [nnf-neg #1073 #1076 #1079 #1070 #1129 #1131]: #1134
+#1222 := [nnf-neg #1135 #1218]: #1221
+#1065 := (not #664)
+#1066 := (~ #1065 #661)
+#1063 := (~ #661 #661)
+#1061 := (~ #658 #658)
+#1062 := [refl]: #1061
+#1064 := [nnf-pos #1062]: #1063
+#1067 := [nnf-neg #1064]: #1066
+#1059 := (~ #1058 #1058)
+#1060 := [refl]: #1059
+#1233 := [nnf-neg #1060 #1067 #1070 #1222 #1229]: #1232
+#1054 := (~ #664 #1053)
+#1055 := [sk]: #1054
+#1236 := [nnf-neg #1055 #1233]: #1235
+#1002 := (not #967)
+#1041 := (iff #1002 #1040)
+#1038 := (iff #967 #1037)
+#1035 := (iff #964 #1032)
+#1017 := (or #528 #676 #913 #938)
+#1029 := (or #664 #1017)
+#1033 := (iff #1029 #1032)
+#1034 := [rewrite]: #1033
+#1030 := (iff #964 #1029)
+#1027 := (iff #961 #1017)
+#1022 := (and true #1017)
+#1025 := (iff #1022 #1017)
+#1026 := [rewrite]: #1025
+#1023 := (iff #961 #1022)
+#1020 := (iff #956 #1017)
+#1014 := (or false #528 #676 #913 #938)
+#1018 := (iff #1014 #1017)
 #1019 := [rewrite]: #1018
-#1016 := (iff #956 #1015)
-#1013 := (iff #951 #1010)
-#1007 := (or false #523 #671 #908 #933)
-#1011 := (iff #1007 #1010)
-#1012 := [rewrite]: #1011
-#1008 := (iff #951 #1007)
-#1005 := (iff #556 false)
-#1003 := (iff #556 #627)
-#1002 := (iff #9 true)
-#1000 := [iff-true #996]: #1002
-#1004 := [monotonicity #1000]: #1003
-#1006 := [trans #1004 #631]: #1005
-#1009 := [monotonicity #1006]: #1008
-#1014 := [trans #1009 #1012]: #1013
-#1017 := [monotonicity #1000 #1014]: #1016
-#1021 := [trans #1017 #1019]: #1020
-#1024 := [monotonicity #1021]: #1023
-#1029 := [trans #1024 #1027]: #1028
-#1032 := [monotonicity #1029]: #1031
-#1035 := [monotonicity #1032]: #1034
-#998 := [not-or-elim #995]: #997
-#1036 := [mp #998 #1035]: #1033
-#1232 := [mp~ #1036 #1231]: #1229
-#1233 := [mp #1232 #1420]: #1418
-#1722 := [mp #1233 #1721]: #1717
-#2287 := [mp #1722 #2286]: #2284
-#1936 := [unit-resolution #2287 #2647]: #1432
-#1865 := (or #1427 #1780)
-#1781 := [def-axiom]: #1865
-#2047 := [unit-resolution #1781 #1936]: #1780
-#2062 := (+ #8 #1037)
-#2041 := (>= #2062 0::int)
-#2067 := (= #8 #1040)
-#2045 := (= #1040 #8)
-#2040 := (= ?x1!0 0::int)
-#1866 := (or #1427 #1043)
-#1867 := [def-axiom]: #1866
-#2048 := [unit-resolution #1867 #1936]: #1043
-#1858 := (or #1427 #1044)
-#1869 := [def-axiom]: #1858
-#2049 := [unit-resolution #1869 #1936]: #1044
-#2046 := [th-lemma #2049 #2048]: #2040
-#2014 := [monotonicity #2046]: #2045
-#2021 := [symm #2014]: #2067
-#1980 := (not #2067)
-#2011 := (or #1980 #2041)
-#2013 := [th-lemma]: #2011
-#2015 := [unit-resolution #2013 #2021]: #2041
-[th-lemma #2015 #2047 #2043]: false
+#1015 := (iff #956 #1014)
+#1012 := (iff #561 false)
+#1010 := (iff #561 #632)
+#1008 := (iff #13 true)
+#1009 := [iff-true #1001]: #1008
+#1011 := [monotonicity #1009]: #1010
+#1013 := [trans #1011 #636]: #1012
+#1016 := [monotonicity #1013]: #1015
+#1021 := [trans #1016 #1019]: #1020
+#1024 := [monotonicity #1009 #1021]: #1023
+#1028 := [trans #1024 #1026]: #1027
+#1031 := [monotonicity #1028]: #1030
+#1036 := [trans #1031 #1034]: #1035
+#1039 := [monotonicity #1036]: #1038
+#1042 := [monotonicity #1039]: #1041
+#1003 := [not-or-elim #1000]: #1002
+#1043 := [mp #1003 #1042]: #1040
+#1237 := [mp~ #1043 #1236]: #1234
+#1238 := [mp #1237 #1425]: #1423
+#1727 := [mp #1238 #1726]: #1722
+#2292 := [mp #1727 #2291]: #2289
+#2556 := [unit-resolution #2292 #2016]: #2286
+#2111 := (or #2283 #2208)
+#2097 := [def-axiom]: #2111
+#2557 := [unit-resolution #2097 #2556]: #2208
+#2120 := (or #2283 #176)
+#2104 := [def-axiom]: #2120
+#2620 := [unit-resolution #2104 #2556]: #176
+#2352 := (or #2271 #528 #2213)
+#1791 := (f5 f9)
+#2296 := (= f10 #1791)
+#2346 := (= #40 #1791)
+#2344 := (= #1791 #40)
+#2329 := [hypothesis]: #2274
+#2037 := (or #2271 #179)
+#2038 := [def-axiom]: #2037
+#2340 := [unit-resolution #2038 #2329]: #179
+#2341 := [symm #2340]: #44
+#2345 := [monotonicity #2341]: #2344
+#2347 := [symm #2345]: #2346
+#2348 := (= f10 #40)
+#2342 := [hypothesis]: #176
+#2039 := (or #2271 #182)
+#2040 := [def-axiom]: #2039
+#2331 := [unit-resolution #2040 #2329]: #182
+#2343 := [symm #2331]: #46
+#2349 := [trans #2343 #2342]: #2348
+#2350 := [trans #2349 #2347]: #2296
+#2324 := (not #2296)
+#1790 := (>= f9 0::int)
+#1788 := (not #1790)
+#1800 := (* -1::int f9)
+#1787 := (+ f3 #1800)
+#1789 := (<= #1787 0::int)
+#2302 := (or #1789 #1788 #2296)
+#2307 := (not #2302)
+#2124 := (or #2271 #2265)
+#2125 := [def-axiom]: #2124
+#2330 := [unit-resolution #2125 #2329]: #2265
+#1958 := (+ f8 #705)
+#1959 := (<= #1958 0::int)
+#2332 := (or #232 #1959)
+#2333 := [th-lemma]: #2332
+#2334 := [unit-resolution #2333 #2331]: #1959
+#1836 := [hypothesis]: #2208
+#2112 := (or #2271 #724)
+#2114 := [def-axiom]: #2112
+#2335 := [unit-resolution #2114 #2329]: #724
+#1867 := (not #1959)
+#1846 := (or #1687 #727 #2213 #1867)
+#1869 := [hypothesis]: #724
+#1948 := (+ f7 #1108)
+#1949 := (<= #1948 0::int)
+#1927 := (+ f8 #1291)
+#1928 := (>= #1927 0::int)
+#1866 := (not #1928)
+#1860 := [hypothesis]: #1959
+#2023 := (not #1293)
+#1852 := [hypothesis]: #1690
+#2024 := (or #1687 #2023)
+#1983 := [def-axiom]: #2024
+#1854 := [unit-resolution #1983 #1852]: #2023
+#1868 := (or #1866 #1293 #1867)
+#1851 := [hypothesis]: #2023
+#1864 := [hypothesis]: #1928
+#1865 := [th-lemma #1864 #1851 #1860]: false
+#1858 := [lemma #1865]: #1868
+#1855 := [unit-resolution #1858 #1854 #1860]: #1866
+#1841 := (or #1928 #1949)
+#2140 := (or #1687 #1112)
+#2022 := [def-axiom]: #2140
+#1834 := [unit-resolution #2022 #1852]: #1112
+#1917 := (or #2213 #1530 #1928 #1949)
+#1960 := (+ #1105 #927)
+#1950 := (<= #1960 0::int)
+#1940 := (+ ?v0!2 #722)
+#1942 := (>= #1940 0::int)
+#1943 := (or #1530 #1942 #1950)
+#1918 := (or #2213 #1943)
+#1909 := (iff #1918 #1917)
+#1911 := (or #1530 #1928 #1949)
+#1912 := (or #2213 #1911)
+#1906 := (iff #1912 #1917)
+#1907 := [rewrite]: #1906
+#1920 := (iff #1918 #1912)
+#1915 := (iff #1943 #1911)
+#1933 := (or #1530 #1949 #1928)
+#1913 := (iff #1933 #1911)
+#1914 := [rewrite]: #1913
+#1922 := (iff #1943 #1933)
+#1931 := (iff #1950 #1928)
+#1939 := (+ #927 #1105)
+#1924 := (<= #1939 0::int)
+#1929 := (iff #1924 #1928)
+#1930 := [rewrite]: #1929
+#1925 := (iff #1950 #1924)
+#1921 := (= #1960 #1939)
+#1923 := [rewrite]: #1921
+#1926 := [monotonicity #1923]: #1925
+#1932 := [trans #1926 #1930]: #1931
+#1938 := (iff #1942 #1949)
+#1946 := (+ #722 ?v0!2)
+#1944 := (>= #1946 0::int)
+#1935 := (iff #1944 #1949)
+#1937 := [rewrite]: #1935
+#1952 := (iff #1942 #1944)
+#1947 := (= #1940 #1946)
+#1951 := [rewrite]: #1947
+#1945 := [monotonicity #1951]: #1952
+#1936 := [trans #1945 #1937]: #1938
+#1934 := [monotonicity #1936 #1932]: #1922
+#1916 := [trans #1934 #1914]: #1915
+#1905 := [monotonicity #1916]: #1920
+#1908 := [trans #1905 #1907]: #1909
+#1919 := [quant-inst]: #1918
+#1910 := [mp #1919 #1908]: #1917
+#1842 := [unit-resolution #1910 #1836 #1834]: #1841
+#1843 := [unit-resolution #1842 #1855]: #1949
+#2139 := (or #1687 #1111)
+#2137 := [def-axiom]: #2139
+#1844 := [unit-resolution #2137 #1852]: #1111
+#1845 := [th-lemma #1844 #1843 #1869]: false
+#1835 := [lemma #1845]: #1846
+#2336 := [unit-resolution #1835 #2335 #1836 #2334]: #1687
+#2028 := (or #2268 #2260 #1690)
+#2036 := [def-axiom]: #2028
+#2337 := [unit-resolution #2036 #2336 #2330]: #2260
+#2132 := (not #2260)
+#2310 := (or #2132 #2307)
+#2293 := (= #1791 f10)
+#2294 := (or #2293 #1788 #1789)
+#2295 := (not #2294)
+#2311 := (or #2132 #2295)
+#2313 := (iff #2311 #2310)
+#2315 := (iff #2310 #2310)
+#2316 := [rewrite]: #2315
+#2308 := (iff #2295 #2307)
+#2305 := (iff #2294 #2302)
+#2299 := (or #2296 #1788 #1789)
+#2303 := (iff #2299 #2302)
+#2304 := [rewrite]: #2303
+#2300 := (iff #2294 #2299)
+#2297 := (iff #2293 #2296)
+#2298 := [rewrite]: #2297
+#2301 := [monotonicity #2298]: #2300
+#2306 := [trans #2301 #2304]: #2305
+#2309 := [monotonicity #2306]: #2308
+#2314 := [monotonicity #2309]: #2313
+#2317 := [trans #2314 #2316]: #2313
+#2312 := [quant-inst]: #2311
+#2318 := [mp #2312 #2317]: #2310
+#2338 := [unit-resolution #2318 #2337]: #2307
+#2325 := (or #2302 #2324)
+#2326 := [def-axiom]: #2325
+#2339 := [unit-resolution #2326 #2338]: #2324
+#2351 := [unit-resolution #2339 #2350]: false
+#2353 := [lemma #2351]: #2352
+#2621 := [unit-resolution #2353 #2620 #2557]: #2271
+#2098 := (or #2283 #2277)
+#2100 := [def-axiom]: #2098
+#2622 := [unit-resolution #2100 #2556]: #2277
+#2119 := (or #2280 #2257 #2274)
+#2113 := [def-axiom]: #2119
+#2623 := [unit-resolution #2113 #2622 #2621]: #2257
+#2147 := (or #2254 #2248)
+#2141 := [def-axiom]: #2147
+#2624 := [unit-resolution #2141 #2623]: #2248
+#1793 := [hypothesis]: #2239
+#2183 := (or #2236 #2230)
+#2186 := [def-axiom]: #2183
+#2528 := [unit-resolution #2186 #1793]: #2230
+#2319 := (or #2236 #307)
+#1818 := (= #68 #90)
+#1795 := (= #90 #68)
+#1838 := (or #2236 #285)
+#1839 := [def-axiom]: #1838
+#1798 := [unit-resolution #1839 #1793]: #285
+#1799 := [symm #1798]: #74
+#1817 := [monotonicity #1799]: #1795
+#1801 := [symm #1817]: #1818
+#1804 := (= f14 #68)
+#2174 := (or #2236 #280)
+#1837 := [def-axiom]: #2174
+#1797 := [unit-resolution #1837 #1793]: #280
+#1815 := [symm #1797]: #71
+#1840 := (or #2236 #288)
+#2176 := [def-axiom]: #1840
+#1794 := [unit-resolution #2176 #1793]: #288
+#1813 := [symm #1794]: #76
+#1805 := [trans #1813 #1815]: #1804
+#1808 := [trans #1805 #1801]: #307
+#1796 := [hypothesis]: #1169
+#1809 := [unit-resolution #1796 #1808]: false
+#2320 := [lemma #1809]: #2319
+#2529 := [unit-resolution #2320 #1793]: #307
+#1856 := (or #2224 #1169)
+#2191 := [def-axiom]: #1856
+#2530 := [unit-resolution #2191 #2529]: #2224
+#2190 := (or #2233 #2227 #1629)
+#1833 := [def-axiom]: #2190
+#2531 := [unit-resolution #1833 #2530 #2528]: #1629
+#2194 := (or #1624 #1341)
+#2195 := [def-axiom]: #2194
+#2532 := [unit-resolution #2195 #2531]: #1341
+#1877 := (>= #803 -1::int)
+#2184 := (or #2236 #802)
+#1824 := [def-axiom]: #2184
+#2533 := [unit-resolution #1824 #1793]: #802
+#2534 := (or #806 #1877)
+#2535 := [th-lemma]: #2534
+#2536 := [unit-resolution #2535 #2533]: #1877
+#2562 := (not #2496)
+#2525 := (not #2494)
+#2495 := (= #90 #1154)
+#2499 := (not #2495)
+#2502 := (+ #90 #1356)
+#2504 := (>= #2502 0::int)
+#2509 := (not #2504)
+#2196 := (not #1358)
+#2197 := (or #1624 #2196)
+#2192 := [def-axiom]: #2197
+#2537 := [unit-resolution #2192 #2531]: #2196
+#2451 := (* -1::int #90)
+#2490 := (+ f14 #2451)
+#2492 := (>= #2490 0::int)
+#2538 := (or #1169 #2492)
+#2539 := [th-lemma]: #2538
+#2540 := [unit-resolution #2539 #2529]: #2492
+#2510 := (not #2492)
+#2511 := (or #2509 #2510 #1358)
+#2505 := [hypothesis]: #2504
+#2506 := [hypothesis]: #2196
+#2507 := [hypothesis]: #2492
+#2508 := [th-lemma #2507 #2506 #2505]: false
+#2512 := [lemma #2508]: #2511
+#2541 := [unit-resolution #2512 #2540 #2537]: #2509
+#2500 := (or #2499 #2504)
+#2501 := [th-lemma]: #2500
+#2542 := [unit-resolution #2501 #2541]: #2499
+#2526 := (or #2525 #2495 #375)
+#2521 := (= #1154 #90)
+#2519 := (= ?v0!3 f13)
+#2515 := [hypothesis]: #285
+#2517 := (= ?v0!3 f7)
+#2516 := [hypothesis]: #2494
+#2518 := [symm #2516]: #2517
+#2520 := [trans #2518 #2515]: #2519
+#2522 := [monotonicity #2520]: #2521
+#2523 := [symm #2522]: #2495
+#2514 := [hypothesis]: #2499
+#2524 := [unit-resolution #2514 #2523]: false
+#2527 := [lemma #2524]: #2526
+#2543 := [unit-resolution #2527 #2542 #1798]: #2525
+#2565 := (or #2494 #2562)
+#2381 := (<= #2380 0::int)
+#2392 := (+ f8 #1356)
+#2393 := (>= #2392 0::int)
+#2550 := (not #2393)
+#1825 := (or #2236 #818)
+#2185 := [def-axiom]: #1825
+#2544 := [unit-resolution #2185 #1793]: #818
+#2366 := (+ #68 #777)
+#2367 := (<= #2366 0::int)
+#2365 := (= #68 f14)
+#2545 := [trans #1797 #1794]: #2365
+#2546 := (not #2365)
+#2547 := (or #2546 #2367)
+#2548 := [th-lemma]: #2547
+#2549 := [unit-resolution #2548 #2545]: #2367
+#2551 := (not #2367)
+#2552 := (or #2550 #1358 #2551 #819)
+#2553 := [th-lemma]: #2552
+#2554 := [unit-resolution #2553 #2537 #2549 #2544]: #2550
+#2558 := (or #2381 #2393)
+#1861 := (or #1624 #1160)
+#1862 := [def-axiom]: #1861
+#2555 := [unit-resolution #1862 #2531]: #1160
+#2401 := (or #2213 #1609 #2381 #2393)
+#2369 := (+ #1154 #927)
+#2370 := (<= #2369 0::int)
+#2371 := (+ ?v0!3 #722)
+#2372 := (>= #2371 0::int)
+#2373 := (or #1609 #2372 #2370)
+#2402 := (or #2213 #2373)
+#2409 := (iff #2402 #2401)
+#2398 := (or #1609 #2381 #2393)
+#2404 := (or #2213 #2398)
+#2407 := (iff #2404 #2401)
+#2408 := [rewrite]: #2407
+#2405 := (iff #2402 #2404)
+#2399 := (iff #2373 #2398)
+#2396 := (iff #2370 #2393)
+#2386 := (+ #927 #1154)
+#2389 := (<= #2386 0::int)
+#2394 := (iff #2389 #2393)
+#2395 := [rewrite]: #2394
+#2390 := (iff #2370 #2389)
+#2387 := (= #2369 #2386)
+#2388 := [rewrite]: #2387
+#2391 := [monotonicity #2388]: #2390
+#2397 := [trans #2391 #2395]: #2396
+#2384 := (iff #2372 #2381)
+#2374 := (+ #722 ?v0!3)
+#2377 := (>= #2374 0::int)
+#2382 := (iff #2377 #2381)
+#2383 := [rewrite]: #2382
+#2378 := (iff #2372 #2377)
+#2375 := (= #2371 #2374)
+#2376 := [rewrite]: #2375
+#2379 := [monotonicity #2376]: #2378
+#2385 := [trans #2379 #2383]: #2384
+#2400 := [monotonicity #2385 #2397]: #2399
+#2406 := [monotonicity #2400]: #2405
+#2410 := [trans #2406 #2408]: #2409
+#2403 := [quant-inst]: #2402
+#2411 := [mp #2403 #2410]: #2401
+#2559 := [unit-resolution #2411 #2557 #2555]: #2558
+#2560 := [unit-resolution #2559 #2554]: #2381
+#2561 := (not #2381)
+#2563 := (or #2494 #2561 #2562)
+#2564 := [th-lemma]: #2563
+#2566 := [unit-resolution #2564 #2560]: #2565
+#2567 := [unit-resolution #2566 #2543]: #2562
+#2568 := [th-lemma #2567 #2536 #2532]: false
+#2569 := [lemma #2568]: #2236
+#2153 := (or #2251 #2239 #2245)
+#2159 := [def-axiom]: #2153
+#2625 := [unit-resolution #2159 #2569 #2624]: #2245
+#2165 := (or #2242 #2230)
+#2154 := [def-axiom]: #2165
+#2626 := [unit-resolution #2154 #2625]: #2230
+#2421 := (= #40 #90)
+#2631 := (= #90 #40)
+#1891 := (or #2242 #423)
+#1892 := [def-axiom]: #1891
+#2627 := [unit-resolution #1892 #2625]: #423
+#2628 := [symm #2627]: #107
+#2632 := [monotonicity #2628]: #2631
+#2633 := [symm #2632]: #2421
+#2634 := (= f14 #40)
+#2166 := (or #2242 #426)
+#2170 := [def-axiom]: #2166
+#2629 := [unit-resolution #2170 #2625]: #426
+#2630 := [symm #2629]: #108
+#2635 := [trans #2630 #2620]: #2634
+#2636 := [trans #2635 #2633]: #307
+#2637 := [unit-resolution #2191 #2636]: #2224
+#2638 := [unit-resolution #1833 #2637 #2626]: #1629
+#2639 := [unit-resolution #2195 #2638]: #1341
+#1878 := (or #2242 #802)
+#2160 := [def-axiom]: #1878
+#2640 := [unit-resolution #2160 #2625]: #802
+#2641 := [unit-resolution #2535 #2640]: #1877
+#2642 := [hypothesis]: #2562
+#2643 := [th-lemma #2642 #2641 #2639]: false
+#2644 := [lemma #2643]: #2496
+#2649 := [unit-resolution #2192 #2638]: #2196
+#1792 := (+ f8 #777)
+#2168 := (<= #1792 0::int)
+#2650 := (or #432 #2168)
+#2651 := [th-lemma]: #2650
+#2652 := [unit-resolution #2651 #2629]: #2168
+#2653 := (not #2168)
+#2654 := (or #2550 #1358 #2653)
+#2655 := [th-lemma]: #2654
+#2656 := [unit-resolution #2655 #2652 #2649]: #2550
+#2657 := [unit-resolution #1862 #2638]: #1160
+#2658 := [unit-resolution #2411 #2557 #2657 #2656]: #2381
+#2659 := [unit-resolution #2564 #2658]: #2565
+#2660 := [unit-resolution #2659 #2644]: #2494
+#2661 := [monotonicity #2660]: #2645
+#2662 := (not #2645)
+#2663 := (or #2662 #2648)
+#2664 := [th-lemma]: #2663
+#2665 := [unit-resolution #2664 #2661]: #2648
+#2164 := (or #2242 #819)
+#2161 := [def-axiom]: #2164
+#2666 := [unit-resolution #2161 #2625]: #819
+[th-lemma #2666 #2649 #2652 #2665]: false
 unsat

--- a/src/HOL/Boogie/Examples/VCC_Max.certs	Wed May 12 23:54:04 2010 +0200
+++ b/src/HOL/Boogie/Examples/VCC_Max.certs	Wed May 12 23:54:06 2010 +0200
@@ -1,7791 +1,7863 @@
-ecd63e557c7e66d192e7c9b7445f98b44f79ca34 7790 0
+95b4b08061ee75475bbfdf75c59af3c86af542dc 7862 0
 #2 := false
-decl uf_110 :: (-> T4 T5 int)
-decl uf_66 :: (-> T5 int T3 T5)
-decl uf_7 :: T3
-#10 := uf_7
-decl ?x785!14 :: int
-#18296 := ?x785!14
-decl uf_43 :: (-> T3 int T5)
-decl uf_288 :: int
-#2978 := uf_288
-#2979 := (uf_43 uf_7 uf_288)
-#18301 := (uf_66 #2979 ?x785!14 uf_7)
-decl uf_287 :: T4
-#2976 := uf_287
-#18302 := (uf_110 uf_287 #18301)
-decl uf_298 :: int
-#3069 := uf_298
-#3181 := (uf_66 #2979 uf_298 uf_7)
-#3190 := (uf_110 uf_287 #3181)
-#30497 := (= #3190 #18302)
-#30502 := (not #30497)
-#121 := 0::int
-#4044 := -1::int
-#18623 := (* -1::int #18302)
-#30501 := (+ #3190 #18623)
-#30503 := (>= #30501 0::int)
-#30513 := (not #30503)
-decl uf_304 :: int
-#3197 := uf_304
-#13279 := (* -1::int uf_304)
-#30155 := (+ #3190 #13279)
-#30108 := (<= #30155 0::int)
-#30154 := (= #3190 uf_304)
-decl uf_303 :: int
-#3192 := uf_303
-#12313 := (= uf_303 uf_304)
-#18624 := (+ uf_304 #18623)
-#18625 := (>= #18624 0::int)
-#18610 := (* -1::int ?x785!14)
-decl uf_306 :: int
-#3207 := uf_306
-#18611 := (+ uf_306 #18610)
-#18612 := (<= #18611 0::int)
-#18298 := (>= ?x785!14 0::int)
-#22078 := (not #18298)
-#7473 := 4294967295::int
-#18297 := (<= ?x785!14 4294967295::int)
-#22077 := (not #18297)
-#22093 := (or #22077 #22078 #18612 #18625)
-#22098 := (not #22093)
-#161 := (:var 0 int)
-#3053 := (uf_66 #2979 #161 uf_7)
-#23000 := (pattern #3053)
-#14916 := (<= #161 4294967295::int)
-#19295 := (not #14916)
-#3054 := (uf_110 uf_287 #3053)
-#13280 := (+ #3054 #13279)
-#13281 := (<= #13280 0::int)
-#13260 := (* -1::int uf_306)
-#13268 := (+ #161 #13260)
-#13267 := (>= #13268 0::int)
-#4043 := (>= #161 0::int)
-#4965 := (not #4043)
-#22059 := (or #4965 #13267 #13281 #19295)
-#23017 := (forall (vars (?x785 int)) (:pat #23000) #22059)
-#23022 := (not #23017)
-decl uf_305 :: int
-#3199 := uf_305
-#13301 := (* -1::int uf_305)
-decl uf_286 :: int
-#2973 := uf_286
-#13302 := (+ uf_286 #13301)
-#13303 := (<= #13302 0::int)
-#3219 := (uf_66 #2979 uf_305 uf_7)
-#3220 := (uf_110 uf_287 #3219)
-#12352 := (= uf_304 #3220)
-#22044 := (not #12352)
-#22045 := (or #22044 #13303)
-#22046 := (not #22045)
-#23025 := (or #22046 #23022)
-#23028 := (not #23025)
-#23031 := (or #23028 #22098)
-#23034 := (not #23031)
-#13261 := (+ uf_286 #13260)
-#13259 := (>= #13261 0::int)
-#13264 := (not #13259)
-#23037 := (or #13264 #23034)
-#23040 := (not #23037)
-#23043 := (or #13264 #23040)
-#23046 := (not #23043)
-#15608 := 4294967294::int
-#15609 := (<= uf_298 4294967294::int)
-#18279 := (not #15609)
-#13328 := (+ uf_298 #13260)
-#13327 := (= #13328 -1::int)
-#13331 := (not #13327)
-#892 := 2::int
-#13251 := (>= uf_306 2::int)
-#22121 := (not #13251)
-#13243 := (>= uf_298 -1::int)
-#18276 := (not #13243)
-#13234 := (>= uf_305 0::int)
-#22120 := (not #13234)
-decl up_291 :: (-> T4 T1 T1 int T3 bool)
-decl uf_4 :: T3
-#7 := uf_4
-decl uf_273 :: T1
-#2946 := uf_273
-decl uf_269 :: T1
-#2942 := uf_269
-#3209 := (up_291 uf_287 uf_269 uf_273 uf_306 uf_4)
-#12401 := (not #3209)
-#23049 := (or #12401 #22120 #18276 #22121 #13331 #18279 #23046)
-#23052 := (not #23049)
-#23055 := (or #18276 #18279 #23052)
-#23058 := (not #23055)
-#4 := 1::int
-#13225 := (>= uf_298 1::int)
-#13365 := (not #13225)
-#12316 := (= uf_298 uf_305)
-#12440 := (not #12316)
-#12449 := (not #12313)
-#12308 := (= #3190 uf_303)
-#12485 := (not #12308)
-decl uf_68 :: (-> T4 T5 T2)
-#3187 := (uf_68 uf_287 #3181)
-decl uf_9 :: T2
-#19 := uf_9
-#12302 := (= uf_9 #3187)
-#18247 := (not #12302)
-decl uf_48 :: (-> T5 T3 T2)
-#3182 := (uf_48 #3181 uf_7)
-#12293 := (= uf_9 #3182)
-#18238 := (not #12293)
-decl uf_275 :: T1
-#2948 := uf_275
-decl uf_270 :: T1
-#2943 := uf_270
-#3195 := (up_291 uf_287 uf_270 uf_275 uf_298 uf_4)
-#12467 := (not #3195)
-decl uf_277 :: T1
-#2950 := uf_277
-decl uf_271 :: T1
-#2944 := uf_271
-#3194 := (up_291 uf_287 uf_271 uf_277 uf_303 uf_7)
-#12476 := (not #3194)
-#23061 := (or #12476 #12467 #18238 #18247 #12485 #12449 #12440 #13365 #22120 #23058)
-#23064 := (not #23061)
-#13418 := (* -1::int #3190)
-decl uf_296 :: int
-#3061 := uf_296
-#13419 := (+ uf_296 #13418)
-#13417 := (>= #13419 0::int)
-#13416 := (not #13417)
-decl uf_297 :: int
-#3065 := uf_297
-#13222 := (>= uf_297 0::int)
-#22161 := (not #13222)
-#12551 := (= uf_297 uf_305)
-#12557 := (not #12551)
-#12548 := (= uf_296 uf_304)
-#12566 := (not #12548)
-#23091 := (or #12566 #12557 #22161 #13365 #22120 #13416 #23058)
-#23094 := (not #23091)
-#23067 := (or #18238 #18247 #23064)
-#23070 := (not #23067)
-decl uf_24 :: (-> T4 T5 T2)
-#3184 := (uf_24 uf_287 #3181)
-#12296 := (= uf_9 #3184)
-#18241 := (not #12296)
-#23073 := (or #18238 #18241 #23070)
-#23076 := (not #23073)
-#23079 := (or #18238 #18241 #23076)
-#23082 := (not #23079)
-#23085 := (or #22161 #13365 #13417 #23082)
-#23088 := (not #23085)
-#23097 := (or #23088 #23094)
-#23100 := (not #23097)
-#23103 := (or #18238 #18247 #22161 #13365 #23100)
-#23106 := (not #23103)
-decl uf_25 :: (-> T4 T5 T5)
-decl uf_135 :: (-> T14 T5)
-decl uf_58 :: (-> T13 T5 T14)
-decl uf_59 :: (-> T4 T13)
-#3150 := (uf_59 uf_287)
-#27629 := (uf_58 #3150 #3181)
-#29089 := (uf_135 #27629)
-#29092 := (uf_25 uf_287 #29089)
-decl uf_26 :: T5
-#77 := uf_26
-#29093 := (= uf_26 #29092)
-decl uf_210 :: (-> T4 T5 T2)
-#29090 := (uf_210 uf_287 #29089)
-#29091 := (= uf_9 #29090)
-#29149 := (or #29091 #29093)
-#29152 := (not #29149)
-decl uf_136 :: (-> T14 T2)
-#29102 := (uf_136 #27629)
-#29103 := (= uf_9 #29102)
-#29104 := (not #29103)
-decl uf_27 :: (-> T4 T5 T2)
-#29099 := (uf_27 uf_287 #29089)
-#29100 := (= uf_9 #29099)
-#29101 := (not #29100)
-#29143 := (or #29101 #29104)
-#29146 := (not #29143)
-decl uf_12 :: (-> T3 T8)
-decl uf_13 :: (-> T5 T3)
-#27885 := (uf_13 #3181)
-#29107 := (uf_12 #27885)
-decl uf_14 :: T8
-#28 := uf_14
-#29125 := (= uf_14 #29107)
-#29140 := (not #29125)
-#29096 := (uf_13 #29089)
-#29097 := (uf_12 #29096)
-#29098 := (= uf_14 #29097)
-#29158 := (or #29098 #29140 #29146 #29152)
-#29163 := (not #29158)
-#29114 := (uf_25 uf_287 #3181)
-#29115 := (= uf_26 #29114)
-#29112 := (uf_210 uf_287 #3181)
-#29113 := (= uf_9 #29112)
-#29128 := (or #29113 #29115)
-#29131 := (not #29128)
-#29134 := (or #29125 #29131)
-#29137 := (not #29134)
-#29166 := (or #29137 #29163)
-#29169 := (not #29166)
-#29172 := (or #18241 #29169)
-#29175 := (not #29172)
-#29178 := (iff #12302 #29175)
-#29750 := (not #29178)
-#29945 := [hypothesis]: #29750
-#23 := (:var 0 T5)
-#47 := (:var 1 T4)
-#2381 := (uf_68 #47 #23)
-#2382 := (pattern #2381)
-#282 := (uf_59 #47)
-#2384 := (uf_58 #282 #23)
-#2388 := (uf_135 #2384)
-#2399 := (uf_210 #47 #2388)
-#10480 := (= uf_9 #2399)
-#2397 := (uf_25 #47 #2388)
-#10477 := (= uf_26 #2397)
-#10483 := (or #10477 #10480)
-#21752 := (not #10483)
-#2393 := (uf_13 #2388)
-#2394 := (uf_12 #2393)
-#10471 := (= uf_14 #2394)
-#2389 := (uf_27 #47 #2388)
-#10462 := (= uf_9 #2389)
-#10465 := (not #10462)
-#2385 := (uf_136 #2384)
-#10456 := (= uf_9 #2385)
-#10459 := (not #10456)
-#10468 := (or #10459 #10465)
-#21751 := (not #10468)
-#26 := (uf_13 #23)
-#27 := (uf_12 #26)
-#29 := (= #27 uf_14)
-#52 := (not #29)
-#21753 := (or #52 #21751 #10471 #21752)
-#21754 := (not #21753)
-#2405 := (uf_210 #47 #23)
-#10495 := (= uf_9 #2405)
-#142 := (uf_25 #47 #23)
-#3617 := (= uf_26 #142)
-#10498 := (or #3617 #10495)
-#21746 := (not #10498)
-#21747 := (or #29 #21746)
-#21748 := (not #21747)
-#21757 := (or #21748 #21754)
-#21763 := (not #21757)
-#146 := (uf_24 #47 #23)
-#3623 := (= uf_9 #146)
-#11068 := (not #3623)
-#21764 := (or #11068 #21763)
-#21765 := (not #21764)
-#10452 := (= uf_9 #2381)
-#21770 := (iff #10452 #21765)
-#21773 := (forall (vars (?x632 T4) (?x633 T5)) (:pat #2382) #21770)
-#10474 := (not #10471)
-#10516 := (and #29 #10468 #10474 #10483)
-#10501 := (and #52 #10498)
-#10522 := (or #10501 #10516)
-#10527 := (and #3623 #10522)
-#10530 := (iff #10452 #10527)
-#10533 := (forall (vars (?x632 T4) (?x633 T5)) (:pat #2382) #10530)
-#21774 := (iff #10533 #21773)
-#21771 := (iff #10530 #21770)
-#21768 := (iff #10527 #21765)
-#21760 := (and #3623 #21757)
-#21766 := (iff #21760 #21765)
-#21767 := [rewrite]: #21766
-#21761 := (iff #10527 #21760)
-#21758 := (iff #10522 #21757)
-#21755 := (iff #10516 #21754)
-#21756 := [rewrite]: #21755
-#21749 := (iff #10501 #21748)
-#21750 := [rewrite]: #21749
-#21759 := [monotonicity #21750 #21756]: #21758
-#21762 := [monotonicity #21759]: #21761
-#21769 := [trans #21762 #21767]: #21768
-#21772 := [monotonicity #21769]: #21771
-#21775 := [quant-intro #21772]: #21774
-#17696 := (~ #10533 #10533)
-#17694 := (~ #10530 #10530)
-#17695 := [refl]: #17694
-#17697 := [nnf-pos #17695]: #17696
-#2406 := (= #2405 uf_9)
-#143 := (= #142 uf_26)
-#2407 := (or #143 #2406)
-#2408 := (and #52 #2407)
-#2400 := (= #2399 uf_9)
-#2398 := (= #2397 uf_26)
-#2401 := (or #2398 #2400)
-#2395 := (= #2394 uf_14)
-#2396 := (not #2395)
-#2402 := (and #2396 #2401)
-#2390 := (= #2389 uf_9)
-#2391 := (not #2390)
-#2386 := (= #2385 uf_9)
-#2387 := (not #2386)
-#2392 := (or #2387 #2391)
-#2403 := (and #2392 #2402)
-#2404 := (and #29 #2403)
-#2409 := (or #2404 #2408)
-#147 := (= #146 uf_9)
-#2410 := (and #147 #2409)
-#2383 := (= #2381 uf_9)
-#2411 := (iff #2383 #2410)
-#2412 := (forall (vars (?x632 T4) (?x633 T5)) (:pat #2382) #2411)
-#10536 := (iff #2412 #10533)
-#10486 := (and #10474 #10483)
-#10489 := (and #10468 #10486)
-#10492 := (and #29 #10489)
-#10504 := (or #10492 #10501)
-#10507 := (and #3623 #10504)
-#10510 := (iff #10452 #10507)
-#10513 := (forall (vars (?x632 T4) (?x633 T5)) (:pat #2382) #10510)
-#10534 := (iff #10513 #10533)
-#10531 := (iff #10510 #10530)
-#10528 := (iff #10507 #10527)
-#10525 := (iff #10504 #10522)
-#10519 := (or #10516 #10501)
-#10523 := (iff #10519 #10522)
-#10524 := [rewrite]: #10523
-#10520 := (iff #10504 #10519)
-#10517 := (iff #10492 #10516)
-#10518 := [rewrite]: #10517
-#10521 := [monotonicity #10518]: #10520
-#10526 := [trans #10521 #10524]: #10525
-#10529 := [monotonicity #10526]: #10528
-#10532 := [monotonicity #10529]: #10531
-#10535 := [quant-intro #10532]: #10534
-#10514 := (iff #2412 #10513)
-#10511 := (iff #2411 #10510)
-#10508 := (iff #2410 #10507)
-#10505 := (iff #2409 #10504)
-#10502 := (iff #2408 #10501)
-#10499 := (iff #2407 #10498)
-#10496 := (iff #2406 #10495)
-#10497 := [rewrite]: #10496
-#3618 := (iff #143 #3617)
-#3619 := [rewrite]: #3618
-#10500 := [monotonicity #3619 #10497]: #10499
-#10503 := [monotonicity #10500]: #10502
-#10493 := (iff #2404 #10492)
-#10490 := (iff #2403 #10489)
-#10487 := (iff #2402 #10486)
-#10484 := (iff #2401 #10483)
-#10481 := (iff #2400 #10480)
-#10482 := [rewrite]: #10481
-#10478 := (iff #2398 #10477)
-#10479 := [rewrite]: #10478
-#10485 := [monotonicity #10479 #10482]: #10484
-#10475 := (iff #2396 #10474)
-#10472 := (iff #2395 #10471)
-#10473 := [rewrite]: #10472
-#10476 := [monotonicity #10473]: #10475
-#10488 := [monotonicity #10476 #10485]: #10487
-#10469 := (iff #2392 #10468)
-#10466 := (iff #2391 #10465)
-#10463 := (iff #2390 #10462)
-#10464 := [rewrite]: #10463
-#10467 := [monotonicity #10464]: #10466
-#10460 := (iff #2387 #10459)
-#10457 := (iff #2386 #10456)
-#10458 := [rewrite]: #10457
-#10461 := [monotonicity #10458]: #10460
-#10470 := [monotonicity #10461 #10467]: #10469
-#10491 := [monotonicity #10470 #10488]: #10490
-#10494 := [monotonicity #10491]: #10493
-#10506 := [monotonicity #10494 #10503]: #10505
-#3624 := (iff #147 #3623)
-#3625 := [rewrite]: #3624
-#10509 := [monotonicity #3625 #10506]: #10508
-#10454 := (iff #2383 #10452)
-#10455 := [rewrite]: #10454
-#10512 := [monotonicity #10455 #10509]: #10511
-#10515 := [quant-intro #10512]: #10514
-#10537 := [trans #10515 #10535]: #10536
-#10451 := [asserted]: #2412
-#10538 := [mp #10451 #10537]: #10533
-#17698 := [mp~ #10538 #17697]: #10533
-#21776 := [mp #17698 #21775]: #21773
-#27259 := (not #21773)
-#29859 := (or #27259 #29178)
-#29094 := (or #29093 #29091)
-#29095 := (not #29094)
-#29105 := (or #29104 #29101)
-#29106 := (not #29105)
-#29108 := (= #29107 uf_14)
-#29109 := (not #29108)
-#29110 := (or #29109 #29106 #29098 #29095)
-#29111 := (not #29110)
-#29116 := (or #29115 #29113)
-#29117 := (not #29116)
-#29118 := (or #29108 #29117)
-#29119 := (not #29118)
-#29120 := (or #29119 #29111)
-#29121 := (not #29120)
-#29122 := (or #18241 #29121)
-#29123 := (not #29122)
-#29124 := (iff #12302 #29123)
-#29860 := (or #27259 #29124)
-#29862 := (iff #29860 #29859)
-#29690 := (iff #29859 #29859)
-#29691 := [rewrite]: #29690
-#29179 := (iff #29124 #29178)
-#29176 := (iff #29123 #29175)
-#29173 := (iff #29122 #29172)
-#29170 := (iff #29121 #29169)
-#29167 := (iff #29120 #29166)
-#29164 := (iff #29111 #29163)
-#29161 := (iff #29110 #29158)
-#29155 := (or #29140 #29146 #29098 #29152)
-#29159 := (iff #29155 #29158)
-#29160 := [rewrite]: #29159
-#29156 := (iff #29110 #29155)
-#29153 := (iff #29095 #29152)
-#29150 := (iff #29094 #29149)
-#29151 := [rewrite]: #29150
-#29154 := [monotonicity #29151]: #29153
-#29147 := (iff #29106 #29146)
-#29144 := (iff #29105 #29143)
-#29145 := [rewrite]: #29144
-#29148 := [monotonicity #29145]: #29147
-#29141 := (iff #29109 #29140)
-#29126 := (iff #29108 #29125)
-#29127 := [rewrite]: #29126
-#29142 := [monotonicity #29127]: #29141
-#29157 := [monotonicity #29142 #29148 #29154]: #29156
-#29162 := [trans #29157 #29160]: #29161
-#29165 := [monotonicity #29162]: #29164
-#29138 := (iff #29119 #29137)
-#29135 := (iff #29118 #29134)
-#29132 := (iff #29117 #29131)
-#29129 := (iff #29116 #29128)
-#29130 := [rewrite]: #29129
-#29133 := [monotonicity #29130]: #29132
-#29136 := [monotonicity #29127 #29133]: #29135
-#29139 := [monotonicity #29136]: #29138
-#29168 := [monotonicity #29139 #29165]: #29167
-#29171 := [monotonicity #29168]: #29170
-#29174 := [monotonicity #29171]: #29173
-#29177 := [monotonicity #29174]: #29176
-#29180 := [monotonicity #29177]: #29179
-#29689 := [monotonicity #29180]: #29862
-#29674 := [trans #29689 #29691]: #29862
-#29861 := [quant-inst]: #29860
-#29675 := [mp #29861 #29674]: #29859
-#29979 := [unit-resolution #29675 #21776 #29945]: false
-#29980 := [lemma #29979]: #29178
-#30580 := (or #29750 #12302)
-#29847 := [hypothesis]: #29158
-decl uf_116 :: (-> T5 int)
-#2980 := (uf_116 #2979)
-decl uf_124 :: (-> T3 int T3)
-#2977 := (uf_124 uf_7 uf_286)
-#2981 := (uf_43 #2977 #2980)
-#2984 := (uf_25 uf_287 #2981)
-#29898 := (= #2984 #29092)
-#29899 := (= #29092 #2984)
-#30393 := (= #29089 #2981)
-decl uf_143 :: (-> T3 int)
-#24645 := (uf_143 #2977)
-decl uf_144 :: (-> T3 T3)
-#24643 := (uf_144 #2977)
-#26925 := (uf_124 #24643 #24645)
-#26926 := (uf_43 #26925 #2980)
-#28291 := (= #26926 #2981)
-#28289 := (= #26925 #2977)
-#28287 := (= #24645 uf_286)
-#24646 := (= uf_286 #24645)
-#326 := (:var 1 T3)
-#1358 := (uf_124 #326 #161)
-#1592 := (pattern #1358)
-#1602 := (uf_143 #1358)
-#8266 := (= #161 #1602)
-#8269 := (forall (vars (?x386 T3) (?x387 int)) (:pat #1592) #8266)
-#17072 := (~ #8269 #8269)
-#17070 := (~ #8266 #8266)
-#17071 := [refl]: #17070
-#17073 := [nnf-pos #17071]: #17072
-#1603 := (= #1602 #161)
-#1604 := (forall (vars (?x386 T3) (?x387 int)) (:pat #1592) #1603)
-#8270 := (iff #1604 #8269)
-#8267 := (iff #1603 #8266)
-#8268 := [rewrite]: #8267
-#8271 := [quant-intro #8268]: #8270
-#8265 := [asserted]: #1604
-#8274 := [mp #8265 #8271]: #8269
-#17074 := [mp~ #8274 #17073]: #8269
-#24652 := (not #8269)
-#24653 := (or #24652 #24646)
-#24654 := [quant-inst]: #24653
-#28210 := [unit-resolution #24654 #17074]: #24646
-#28288 := [symm #28210]: #28287
-#28189 := (= #24643 uf_7)
-#24644 := (= uf_7 #24643)
-#1605 := (uf_144 #1358)
-#8273 := (= #326 #1605)
-#8277 := (forall (vars (?x388 T3) (?x389 int)) (:pat #1592) #8273)
-#17077 := (~ #8277 #8277)
-#17075 := (~ #8273 #8273)
-#17076 := [refl]: #17075
-#17078 := [nnf-pos #17076]: #17077
-#1606 := (= #1605 #326)
-#1607 := (forall (vars (?x388 T3) (?x389 int)) (:pat #1592) #1606)
-#8278 := (iff #1607 #8277)
-#8275 := (iff #1606 #8273)
-#8276 := [rewrite]: #8275
-#8279 := [quant-intro #8276]: #8278
-#8272 := [asserted]: #1607
-#8282 := [mp #8272 #8279]: #8277
-#17079 := [mp~ #8282 #17078]: #8277
-#24647 := (not #8277)
-#24648 := (or #24647 #24644)
-#24649 := [quant-inst]: #24648
-#28188 := [unit-resolution #24649 #17079]: #24644
-#28190 := [symm #28188]: #28189
-#28290 := [monotonicity #28190 #28288]: #28289
-#28292 := [monotonicity #28290]: #28291
-#30391 := (= #29089 #26926)
-decl uf_125 :: (-> T5 T5 int)
-decl uf_28 :: (-> int T5)
-decl uf_29 :: (-> T5 int)
-#3013 := (uf_29 #2979)
-#24470 := (uf_28 #3013)
-#26903 := (uf_13 #24470)
-#28922 := (uf_66 #24470 uf_298 #26903)
-#28923 := (uf_125 #28922 #24470)
-#28947 := (uf_66 #26926 #28923 #24643)
-#28951 := (uf_58 #3150 #28947)
-#28954 := (uf_135 #28951)
-#30390 := (= #28954 #26926)
-#28955 := (= #26926 #28954)
-decl up_67 :: (-> T14 bool)
-#28957 := (up_67 #28951)
-#28958 := (not #28957)
-#28956 := (not #28955)
-#28952 := (uf_136 #28951)
-#28953 := (= uf_9 #28952)
-#28948 := (uf_24 uf_287 #28947)
-#28949 := (= uf_9 #28948)
-#28950 := (not #28949)
-#28979 := (or #28950 #28953 #28956 #28958)
-#28982 := (not #28979)
-#28972 := (* -1::int #28923)
-#28973 := (+ #24645 #28972)
-#28974 := (<= #28973 0::int)
-#30321 := (not #28974)
-#29082 := (+ uf_298 #28972)
-#29084 := (>= #29082 0::int)
-#28924 := (= uf_298 #28923)
-#15 := (:var 1 T5)
-#1390 := (uf_13 #15)
-#1391 := (uf_66 #15 #161 #1390)
-#1392 := (pattern #1391)
-#1393 := (uf_125 #1391 #15)
-#7665 := (= #161 #1393)
-#7669 := (forall (vars (?x319 T5) (?x320 int)) (:pat #1392) #7665)
-#16789 := (~ #7669 #7669)
-#16787 := (~ #7665 #7665)
-#16788 := [refl]: #16787
-#16790 := [nnf-pos #16788]: #16789
-#1394 := (= #1393 #161)
-#1395 := (forall (vars (?x319 T5) (?x320 int)) (:pat #1392) #1394)
-#7670 := (iff #1395 #7669)
-#7667 := (iff #1394 #7665)
-#7668 := [rewrite]: #7667
-#7671 := [quant-intro #7668]: #7670
-#7664 := [asserted]: #1395
-#7674 := [mp #7664 #7671]: #7669
-#16791 := [mp~ #7674 #16790]: #7669
-#26910 := (not #7669)
-#28927 := (or #26910 #28924)
-#28928 := [quant-inst]: #28927
-#29280 := [unit-resolution #28928 #16791]: #28924
-#29281 := (not #28924)
-#30320 := (or #29281 #29084)
-#30315 := [th-lemma]: #30320
-#30316 := [unit-resolution #30315 #29280]: #29084
-#13246 := (* -1::int uf_298)
-#13509 := (+ uf_286 #13246)
-#13510 := (<= #13509 0::int)
-#13511 := (not #13510)
-#23109 := (or #18238 #18247 #23106)
-#23112 := (not #23109)
-#23115 := (or #18238 #18241 #23112)
-#23118 := (not #23115)
-#23121 := (or #18238 #18241 #23118)
-#23124 := (not #23121)
-#23127 := (or #22161 #13365 #13510 #23124)
-#23130 := (not #23127)
-decl ?x776!15 :: int
-#18420 := ?x776!15
-#18425 := (uf_66 #2979 ?x776!15 uf_7)
-#18426 := (uf_110 uf_287 #18425)
-#18771 := (* -1::int #18426)
-decl uf_302 :: int
-#3096 := uf_302
-#18772 := (+ uf_302 #18771)
-#18773 := (>= #18772 0::int)
-#18758 := (* -1::int ?x776!15)
-#18759 := (+ uf_286 #18758)
-#18760 := (<= #18759 0::int)
-#18422 := (>= ?x776!15 0::int)
-#22255 := (not #18422)
-#18421 := (<= ?x776!15 4294967295::int)
-#22254 := (not #18421)
-#22270 := (or #22254 #22255 #18760 #18773)
-#22275 := (not #22270)
-#13151 := (* -1::int uf_286)
-#13539 := (+ #161 #13151)
-#13538 := (>= #13539 0::int)
-#3103 := (= #3054 uf_302)
-#22228 := (not #3103)
-#22229 := (or #22228 #4965 #13538 #19295)
-#23141 := (forall (vars (?x778 int)) (:pat #23000) #22229)
-#23146 := (not #23141)
-#13550 := (* -1::int uf_302)
-#13551 := (+ #3054 #13550)
-#13552 := (<= #13551 0::int)
-#22220 := (or #4965 #13538 #13552 #19295)
-#23133 := (forall (vars (?x776 int)) (:pat #23000) #22220)
-#23138 := (not #23133)
-#23149 := (or #23138 #23146)
-#23152 := (not #23149)
-#23155 := (or #23152 #22275)
-#23158 := (not #23155)
-#12017 := (= uf_296 uf_302)
-#12052 := (not #12017)
-decl uf_301 :: int
-#3094 := uf_301
-#12014 := (= uf_297 uf_301)
-#12061 := (not #12014)
-decl uf_300 :: int
-#3092 := uf_300
-#12011 := (= uf_298 uf_300)
-#12070 := (not #12011)
-decl uf_299 :: int
-#3090 := uf_299
-#12008 := (= uf_296 uf_299)
-#12079 := (not #12008)
-#23161 := (or #12079 #12070 #12061 #12052 #22161 #13365 #13511 #23158)
-#23164 := (not #23161)
-#23167 := (or #23130 #23164)
-#23170 := (not #23167)
-#13715 := (* -1::int uf_296)
-#13716 := (+ #3054 #13715)
-#13717 := (<= #13716 0::int)
-#13704 := (+ #161 #13246)
-#13703 := (>= #13704 0::int)
-#22036 := (or #4965 #13703 #13717 #19295)
-#23009 := (forall (vars (?x775 int)) (:pat #23000) #22036)
-#23014 := (not #23009)
-#1331 := 255::int
-#15594 := (<= uf_296 255::int)
-#22305 := (not #15594)
-#15577 := (<= uf_297 4294967295::int)
-#22304 := (not #15577)
-#15560 := (<= uf_298 4294967295::int)
-#22303 := (not #15560)
-#13765 := (>= uf_296 0::int)
-#22301 := (not #13765)
-#13743 := (>= uf_298 0::int)
-#22300 := (not #13743)
-#13737 := (>= #13509 0::int)
-#13740 := (not #13737)
-#13686 := (* -1::int uf_297)
-#13687 := (+ uf_286 #13686)
-#13688 := (<= #13687 0::int)
-#13217 := (<= uf_286 0::int)
-decl uf_178 :: (-> T4 T4 T2)
-#3162 := (uf_178 uf_287 uf_287)
-#12254 := (= uf_9 #3162)
-#13683 := (not #12254)
-decl uf_202 :: (-> T1 T4 T2)
-decl uf_272 :: T1
-#2945 := uf_272
-#3087 := (uf_202 uf_272 uf_287)
-#11997 := (= uf_9 #3087)
-#14996 := (not #11997)
-#3082 := (uf_66 #2979 uf_297 uf_7)
-#3083 := (uf_110 uf_287 #3082)
-#11989 := (= uf_296 #3083)
-#22299 := (not #11989)
-decl up_292 :: (-> T4 T1 T1 T5 T3 bool)
-decl uf_6 :: (-> T3 T3)
-#11 := (uf_6 uf_7)
-decl uf_280 :: T1
-#2953 := uf_280
-#3175 := (up_292 uf_287 uf_272 uf_280 #2979 #11)
-#22298 := (not #3175)
-#3174 := (up_291 uf_287 uf_272 uf_280 #3013 #11)
-#22297 := (not #3174)
-decl uf_279 :: T1
-#2952 := uf_279
-#3173 := (up_291 uf_287 uf_272 uf_279 uf_286 uf_4)
-#12742 := (not #3173)
-#3172 := (up_291 uf_287 uf_272 uf_277 uf_296 uf_7)
-#12751 := (not #3172)
-#3171 := (up_291 uf_287 uf_272 uf_275 uf_297 uf_4)
-#12760 := (not #3171)
-#3170 := (up_291 uf_287 uf_272 uf_273 uf_298 uf_4)
-#12769 := (not #3170)
-#3031 := (uf_66 #2979 0::int uf_7)
-#3041 := (uf_110 uf_287 #3031)
-decl uf_295 :: int
-#3040 := uf_295
-#3042 := (= uf_295 #3041)
-#12976 := (not #3042)
-#23173 := (or #12976 #12769 #12760 #12751 #12742 #22297 #22298 #22299 #14996 #13683 #13217 #22161 #13365 #13688 #13740 #22300 #22301 #22303 #22304 #22305 #23014 #23170)
-#23176 := (not #23173)
-#23179 := (or #12976 #13217 #23176)
-#23182 := (not #23179)
-#13197 := (* -1::int #3054)
-#13198 := (+ uf_295 #13197)
-#13196 := (>= #13198 0::int)
-#13184 := (>= #161 1::int)
-#22025 := (or #4965 #13184 #13196 #19295)
-#23001 := (forall (vars (?x773 int)) (:pat #23000) #22025)
-#23006 := (not #23001)
-#23185 := (or #23006 #23182)
-#23188 := (not #23185)
-decl ?x773!13 :: int
-#18159 := ?x773!13
-#18169 := (>= ?x773!13 1::int)
-#18164 := (uf_66 #2979 ?x773!13 uf_7)
-#18165 := (uf_110 uf_287 #18164)
-#18166 := (* -1::int #18165)
-#18167 := (+ uf_295 #18166)
-#18168 := (>= #18167 0::int)
-#18161 := (>= ?x773!13 0::int)
-#21999 := (not #18161)
-#18160 := (<= ?x773!13 4294967295::int)
-#21998 := (not #18160)
-#22014 := (or #21998 #21999 #18168 #18169)
-#22019 := (not #22014)
-#23191 := (or #22019 #23188)
-#23194 := (not #23191)
-#13178 := (>= uf_286 1::int)
-#13181 := (not #13178)
-#23197 := (or #13181 #23194)
-#23200 := (not #23197)
-#23203 := (or #13181 #23200)
-#23206 := (not #23203)
-#3037 := (uf_68 uf_287 #3031)
-#11937 := (= uf_9 #3037)
-#18136 := (not #11937)
-#3032 := (uf_48 #3031 uf_7)
-#11928 := (= uf_9 #3032)
-#18127 := (not #11928)
-decl uf_274 :: T1
-#2947 := uf_274
-#3045 := (up_291 uf_287 uf_274 uf_273 1::int uf_4)
-#12949 := (not #3045)
-decl uf_276 :: T1
-#2949 := uf_276
-#3044 := (up_291 uf_287 uf_276 uf_275 0::int uf_4)
-#12958 := (not #3044)
-decl uf_278 :: T1
-#2951 := uf_278
-#3043 := (up_291 uf_287 uf_278 uf_277 uf_295 uf_7)
-#12967 := (not #3043)
-#23209 := (or #12976 #12967 #12958 #12949 #18127 #18136 #23206)
-#23212 := (not #23209)
-#23215 := (or #18127 #18136 #23212)
-#23218 := (not #23215)
-#3034 := (uf_24 uf_287 #3031)
-#11931 := (= uf_9 #3034)
-#18130 := (not #11931)
-#23221 := (or #18127 #18130 #23218)
-#23224 := (not #23221)
-#23227 := (or #18127 #18130 #23224)
+decl f111 :: (-> S4 S5 int)
+decl f67 :: (-> S5 int S3 S5)
+decl f9 :: S3
+#16 := f9
+decl ?v0!14 :: int
+#18498 := ?v0!14
+decl f44 :: (-> S3 int S5)
+decl f288 :: int
+#3006 := f288
+#3007 := (f44 f9 f288)
+#18503 := (f67 #3007 ?v0!14 f9)
+decl f287 :: S4
+#3004 := f287
+#18504 := (f111 f287 #18503)
+decl f299 :: int
+#3104 := f299
+#3222 := (f67 #3007 f299 f9)
+#3231 := (f111 f287 #3222)
+#30499 := (= #3231 #18504)
+#30505 := (not #30499)
+#127 := 0::int
+#4119 := -1::int
+#18825 := (* -1::int #18504)
+#30500 := (+ #3231 #18825)
+#30502 := (>= #30500 0::int)
+#30512 := (not #30502)
+decl f305 :: int
+#3240 := f305
+#13479 := (* -1::int f305)
+#30081 := (+ #3231 #13479)
+#30011 := (<= #30081 0::int)
+#30077 := (= #3231 f305)
+decl f304 :: int
+#3233 := f304
+#12510 := (= f304 f305)
+#18826 := (+ f305 #18825)
+#18827 := (>= #18826 0::int)
+#18812 := (* -1::int ?v0!14)
+decl f307 :: int
+#3250 := f307
+#18813 := (+ f307 #18812)
+#18814 := (<= #18813 0::int)
+#18500 := (>= ?v0!14 0::int)
+#22280 := (not #18500)
+#7548 := 4294967295::int
+#18499 := (<= ?v0!14 4294967295::int)
+#22279 := (not #18499)
+#22295 := (or #22279 #22280 #18814 #18827)
+#22300 := (not #22295)
+#168 := (:var 0 int)
+#3088 := (f67 #3007 #168 f9)
+#23202 := (pattern #3088)
+#15118 := (<= #168 4294967295::int)
+#19497 := (not #15118)
+#3089 := (f111 f287 #3088)
+#13480 := (+ #3089 #13479)
+#13481 := (<= #13480 0::int)
+#13460 := (* -1::int f307)
+#13468 := (+ #168 #13460)
+#13467 := (>= #13468 0::int)
+#4118 := (>= #168 0::int)
+#5040 := (not #4118)
+#22261 := (or #5040 #13467 #13481 #19497)
+#23219 := (forall (vars (?v0 int)) (:pat #23202) #22261)
+#23224 := (not #23219)
+decl f306 :: int
+#3242 := f306
+#13501 := (* -1::int f306)
+decl f286 :: int
+#3001 := f286
+#13502 := (+ f286 #13501)
+#13503 := (<= #13502 0::int)
+#3263 := (f67 #3007 f306 f9)
+#3264 := (f111 f287 #3263)
+#12552 := (= f305 #3264)
+#22246 := (not #12552)
+#22247 := (or #22246 #13503)
+#22248 := (not #22247)
+#23227 := (or #22248 #23224)
 #23230 := (not #23227)
-decl uf_200 :: (-> T4 T5 T5 T16 T2)
-decl uf_282 :: T16
-#2957 := uf_282
-#3029 := (uf_200 uf_287 #2981 #2981 uf_282)
-#11925 := (= uf_9 #3029)
-#13009 := (not #11925)
-#23233 := (or #13009 #23230)
+#23233 := (or #23230 #22300)
 #23236 := (not #23233)
-#24545 := (uf_116 #2981)
-#25933 := (uf_43 #2977 #24545)
-#26480 := (uf_200 uf_287 #25933 #25933 uf_282)
-#26725 := (= #26480 #3029)
-#26728 := (= #3029 #26480)
-#25940 := (= #2981 #25933)
-#2986 := (uf_48 #2981 #2977)
-#11869 := (= uf_9 #2986)
-decl uf_23 :: (-> T3 T2)
-#2993 := (uf_23 #2977)
-#11881 := (= uf_9 #2993)
-#2990 := (uf_12 #2977)
-#11875 := (= uf_14 #2990)
-#11878 := (not #11875)
-#2988 := (uf_24 uf_287 #2981)
-#11872 := (= uf_9 #2988)
-#11866 := (= uf_26 #2984)
-#2982 := (uf_27 uf_287 #2981)
-#11862 := (= uf_9 #2982)
-#13937 := (and #11862 #11866 #11869 #11872 #11878 #11881)
-decl uf_283 :: int
-#2961 := uf_283
-#13993 := (* -1::int uf_283)
-decl uf_78 :: int
-#429 := uf_78
-#13994 := (+ uf_78 #13993)
-#13992 := (>= #13994 0::int)
-#13990 := (>= uf_283 0::int)
-#13997 := (and #13990 #13992)
-#14000 := (not #13997)
-decl uf_284 :: int
-#2965 := uf_284
-#13979 := (* -1::int uf_284)
-decl uf_76 :: int
-#409 := uf_76
-#13980 := (+ uf_76 #13979)
-#13978 := (>= #13980 0::int)
-#13976 := (>= uf_284 0::int)
-#13983 := (and #13976 #13978)
-#13986 := (not #13983)
-decl uf_285 :: int
-#2969 := uf_285
-#13965 := (* -1::int uf_285)
-#13966 := (+ uf_76 #13965)
-#13964 := (>= #13966 0::int)
-#13962 := (>= uf_285 0::int)
-#13969 := (and #13962 #13964)
-#13972 := (not #13969)
-#1042 := 1099511627776::int
-#13950 := (>= uf_286 1099511627776::int)
+#13461 := (+ f286 #13460)
+#13459 := (>= #13461 0::int)
+#13464 := (not #13459)
+#23239 := (or #13464 #23236)
+#23242 := (not #23239)
+#23245 := (or #13464 #23242)
+#23248 := (not #23245)
+#15808 := 4294967294::int
+#15809 := (<= f299 4294967294::int)
+#18481 := (not #15809)
+#13528 := (+ f299 #13460)
+#13527 := (= #13528 -1::int)
+#13531 := (not #13527)
+#901 := 2::int
+#13451 := (>= f307 2::int)
+#22323 := (not #13451)
+#13443 := (>= f299 -1::int)
+#18478 := (not #13443)
+#13434 := (>= f306 0::int)
+#22322 := (not #13434)
+decl f291 :: (-> S4 S2 S2 int S3 S1)
+decl f6 :: S3
+#12 := f6
+decl f274 :: S2
+#2977 := f274
+decl f270 :: S2
+#2973 := f270
+#3252 := (f291 f287 f270 f274 f307 f6)
+decl f1 :: S1
+#4 := f1
+#12531 := (= f1 #3252)
+#12601 := (not #12531)
+#23251 := (or #12601 #22322 #18478 #22323 #13531 #18481 #23248)
+#23254 := (not #23251)
+#23257 := (or #18478 #18481 #23254)
+#23260 := (not #23257)
+#8 := 1::int
+#13425 := (>= f299 1::int)
+#13565 := (not #13425)
+#12513 := (= f299 f306)
+#12640 := (not #12513)
+#12649 := (not #12510)
+decl f276 :: S2
+#2979 := f276
+decl f271 :: S2
+#2974 := f271
+#3237 := (f291 f287 f271 f276 f299 f6)
+#12505 := (= f1 #3237)
+#12667 := (not #12505)
+decl f278 :: S2
+#2981 := f278
+decl f272 :: S2
+#2975 := f272
+#3235 := (f291 f287 f272 f278 f304 f9)
+#12502 := (= f1 #3235)
+#12676 := (not #12502)
+#12499 := (= #3231 f304)
+#12685 := (not #12499)
+decl f69 :: (-> S4 S5 S1)
+#3228 := (f69 f287 #3222)
+#12493 := (= f1 #3228)
+#18449 := (not #12493)
+decl f49 :: (-> S5 S3 S1)
+#3223 := (f49 #3222 f9)
+#12484 := (= f1 #3223)
+#18440 := (not #12484)
+#23263 := (or #18440 #18449 #12685 #12676 #12667 #12649 #12640 #13565 #22322 #23260)
+#23266 := (not #23263)
+decl f26 :: (-> S4 S5 S5)
+decl f136 :: (-> S14 S5)
+decl f59 :: (-> S13 S5 S14)
+decl f60 :: (-> S4 S13)
+#3185 := (f60 f287)
+#27673 := (f59 #3185 #3222)
+#29196 := (f136 #27673)
+#29199 := (f26 f287 #29196)
+decl f27 :: S5
+#82 := f27
+#29200 := (= f27 #29199)
+decl f211 :: (-> S4 S5 S1)
+#29197 := (f211 f287 #29196)
+#29198 := (= f1 #29197)
+#29256 := (or #29198 #29200)
+#29259 := (not #29256)
+decl f137 :: (-> S14 S1)
+#29209 := (f137 #27673)
+#29210 := (= f1 #29209)
+#29211 := (not #29210)
+decl f28 :: (-> S4 S5 S1)
+#29206 := (f28 f287 #29196)
+#29207 := (= f1 #29206)
+#29208 := (not #29207)
+#29250 := (or #29208 #29211)
+#29253 := (not #29250)
+decl f13 :: (-> S3 S8)
+decl f14 :: (-> S5 S3)
+#27769 := (f14 #3222)
+#29214 := (f13 #27769)
+decl f15 :: S8
+#33 := f15
+#29232 := (= f15 #29214)
+#29247 := (not #29232)
+#29203 := (f14 #29196)
+#29204 := (f13 #29203)
+#29205 := (= f15 #29204)
+#29265 := (or #29205 #29247 #29253 #29259)
+#29270 := (not #29265)
+#29221 := (f26 f287 #3222)
+#29222 := (= f27 #29221)
+#29219 := (f211 f287 #3222)
+#29220 := (= f1 #29219)
+#29235 := (or #29220 #29222)
+#29238 := (not #29235)
+#29241 := (or #29232 #29238)
+#29244 := (not #29241)
+#29273 := (or #29244 #29270)
+#29276 := (not #29273)
+decl f25 :: (-> S4 S5 S1)
+#3225 := (f25 f287 #3222)
+#12487 := (= f1 #3225)
+#18443 := (not #12487)
+#29279 := (or #18443 #29276)
+#29282 := (not #29279)
+#29285 := (iff #12493 #29282)
+#29865 := (not #29285)
+#29981 := [hypothesis]: #29865
+#28 := (:var 0 S5)
+#52 := (:var 1 S4)
+#2404 := (f69 #52 #28)
+#2405 := (pattern #2404)
+#290 := (f60 #52)
+#2407 := (f59 #290 #28)
+#2411 := (f136 #2407)
+#2422 := (f211 #52 #2411)
+#10612 := (= f1 #2422)
+#2420 := (f26 #52 #2411)
+#10609 := (= f27 #2420)
+#10615 := (or #10609 #10612)
+#21954 := (not #10615)
+#2416 := (f14 #2411)
+#2417 := (f13 #2416)
+#10603 := (= f15 #2417)
+#2412 := (f28 #52 #2411)
+#10594 := (= f1 #2412)
+#10597 := (not #10594)
+#2408 := (f137 #2407)
+#10588 := (= f1 #2408)
+#10591 := (not #10588)
+#10600 := (or #10591 #10597)
+#21953 := (not #10600)
+#31 := (f14 #28)
+#32 := (f13 #31)
+#34 := (= #32 f15)
+#57 := (not #34)
+#21955 := (or #57 #21953 #10603 #21954)
+#21956 := (not #21955)
+#2428 := (f211 #52 #28)
+#10627 := (= f1 #2428)
+#148 := (f26 #52 #28)
+#3677 := (= f27 #148)
+#10630 := (or #3677 #10627)
+#21948 := (not #10630)
+#21949 := (or #34 #21948)
+#21950 := (not #21949)
+#21959 := (or #21950 #21956)
+#21965 := (not #21959)
+#152 := (f25 #52 #28)
+#3683 := (= f1 #152)
+#11206 := (not #3683)
+#21966 := (or #11206 #21965)
+#21967 := (not #21966)
+#10584 := (= f1 #2404)
+#21972 := (iff #10584 #21967)
+#21975 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2405) #21972)
+#10606 := (not #10603)
+#10648 := (and #34 #10600 #10606 #10615)
+#10633 := (and #57 #10630)
+#10654 := (or #10633 #10648)
+#10659 := (and #3683 #10654)
+#10662 := (iff #10584 #10659)
+#10665 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2405) #10662)
+#21976 := (iff #10665 #21975)
+#21973 := (iff #10662 #21972)
+#21970 := (iff #10659 #21967)
+#21962 := (and #3683 #21959)
+#21968 := (iff #21962 #21967)
+#21969 := [rewrite]: #21968
+#21963 := (iff #10659 #21962)
+#21960 := (iff #10654 #21959)
+#21957 := (iff #10648 #21956)
+#21958 := [rewrite]: #21957
+#21951 := (iff #10633 #21950)
+#21952 := [rewrite]: #21951
+#21961 := [monotonicity #21952 #21958]: #21960
+#21964 := [monotonicity #21961]: #21963
+#21971 := [trans #21964 #21969]: #21970
+#21974 := [monotonicity #21971]: #21973
+#21977 := [quant-intro #21974]: #21976
+#17898 := (~ #10665 #10665)
+#17896 := (~ #10662 #10662)
+#17897 := [refl]: #17896
+#17899 := [nnf-pos #17897]: #17898
+#2429 := (= #2428 f1)
+#149 := (= #148 f27)
+#2430 := (or #149 #2429)
+#2431 := (and #57 #2430)
+#2423 := (= #2422 f1)
+#2421 := (= #2420 f27)
+#2424 := (or #2421 #2423)
+#2418 := (= #2417 f15)
+#2419 := (not #2418)
+#2425 := (and #2419 #2424)
+#2413 := (= #2412 f1)
+#2414 := (not #2413)
+#2409 := (= #2408 f1)
+#2410 := (not #2409)
+#2415 := (or #2410 #2414)
+#2426 := (and #2415 #2425)
+#2427 := (and #34 #2426)
+#2432 := (or #2427 #2431)
+#153 := (= #152 f1)
+#2433 := (and #153 #2432)
+#2406 := (= #2404 f1)
+#2434 := (iff #2406 #2433)
+#2435 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2405) #2434)
+#10668 := (iff #2435 #10665)
+#10618 := (and #10606 #10615)
+#10621 := (and #10600 #10618)
+#10624 := (and #34 #10621)
+#10636 := (or #10624 #10633)
+#10639 := (and #3683 #10636)
+#10642 := (iff #10584 #10639)
+#10645 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2405) #10642)
+#10666 := (iff #10645 #10665)
+#10663 := (iff #10642 #10662)
+#10660 := (iff #10639 #10659)
+#10657 := (iff #10636 #10654)
+#10651 := (or #10648 #10633)
+#10655 := (iff #10651 #10654)
+#10656 := [rewrite]: #10655
+#10652 := (iff #10636 #10651)
+#10649 := (iff #10624 #10648)
+#10650 := [rewrite]: #10649
+#10653 := [monotonicity #10650]: #10652
+#10658 := [trans #10653 #10656]: #10657
+#10661 := [monotonicity #10658]: #10660
+#10664 := [monotonicity #10661]: #10663
+#10667 := [quant-intro #10664]: #10666
+#10646 := (iff #2435 #10645)
+#10643 := (iff #2434 #10642)
+#10640 := (iff #2433 #10639)
+#10637 := (iff #2432 #10636)
+#10634 := (iff #2431 #10633)
+#10631 := (iff #2430 #10630)
+#10628 := (iff #2429 #10627)
+#10629 := [rewrite]: #10628
+#3678 := (iff #149 #3677)
+#3679 := [rewrite]: #3678
+#10632 := [monotonicity #3679 #10629]: #10631
+#10635 := [monotonicity #10632]: #10634
+#10625 := (iff #2427 #10624)
+#10622 := (iff #2426 #10621)
+#10619 := (iff #2425 #10618)
+#10616 := (iff #2424 #10615)
+#10613 := (iff #2423 #10612)
+#10614 := [rewrite]: #10613
+#10610 := (iff #2421 #10609)
+#10611 := [rewrite]: #10610
+#10617 := [monotonicity #10611 #10614]: #10616
+#10607 := (iff #2419 #10606)
+#10604 := (iff #2418 #10603)
+#10605 := [rewrite]: #10604
+#10608 := [monotonicity #10605]: #10607
+#10620 := [monotonicity #10608 #10617]: #10619
+#10601 := (iff #2415 #10600)
+#10598 := (iff #2414 #10597)
+#10595 := (iff #2413 #10594)
+#10596 := [rewrite]: #10595
+#10599 := [monotonicity #10596]: #10598
+#10592 := (iff #2410 #10591)
+#10589 := (iff #2409 #10588)
+#10590 := [rewrite]: #10589
+#10593 := [monotonicity #10590]: #10592
+#10602 := [monotonicity #10593 #10599]: #10601
+#10623 := [monotonicity #10602 #10620]: #10622
+#10626 := [monotonicity #10623]: #10625
+#10638 := [monotonicity #10626 #10635]: #10637
+#3684 := (iff #153 #3683)
+#3685 := [rewrite]: #3684
+#10641 := [monotonicity #3685 #10638]: #10640
+#10586 := (iff #2406 #10584)
+#10587 := [rewrite]: #10586
+#10644 := [monotonicity #10587 #10641]: #10643
+#10647 := [quant-intro #10644]: #10646
+#10669 := [trans #10647 #10667]: #10668
+#10583 := [asserted]: #2435
+#10670 := [mp #10583 #10669]: #10665
+#17900 := [mp~ #10670 #17899]: #10665
+#21978 := [mp #17900 #21977]: #21975
+#27322 := (not #21975)
+#29781 := (or #27322 #29285)
+#29201 := (or #29200 #29198)
+#29202 := (not #29201)
+#29212 := (or #29211 #29208)
+#29213 := (not #29212)
+#29215 := (= #29214 f15)
+#29216 := (not #29215)
+#29217 := (or #29216 #29213 #29205 #29202)
+#29218 := (not #29217)
+#29223 := (or #29222 #29220)
+#29224 := (not #29223)
+#29225 := (or #29215 #29224)
+#29226 := (not #29225)
+#29227 := (or #29226 #29218)
+#29228 := (not #29227)
+#29229 := (or #18443 #29228)
+#29230 := (not #29229)
+#29231 := (iff #12493 #29230)
+#29782 := (or #27322 #29231)
+#29902 := (iff #29782 #29781)
+#29917 := (iff #29781 #29781)
+#29933 := [rewrite]: #29917
+#29286 := (iff #29231 #29285)
+#29283 := (iff #29230 #29282)
+#29280 := (iff #29229 #29279)
+#29277 := (iff #29228 #29276)
+#29274 := (iff #29227 #29273)
+#29271 := (iff #29218 #29270)
+#29268 := (iff #29217 #29265)
+#29262 := (or #29247 #29253 #29205 #29259)
+#29266 := (iff #29262 #29265)
+#29267 := [rewrite]: #29266
+#29263 := (iff #29217 #29262)
+#29260 := (iff #29202 #29259)
+#29257 := (iff #29201 #29256)
+#29258 := [rewrite]: #29257
+#29261 := [monotonicity #29258]: #29260
+#29254 := (iff #29213 #29253)
+#29251 := (iff #29212 #29250)
+#29252 := [rewrite]: #29251
+#29255 := [monotonicity #29252]: #29254
+#29248 := (iff #29216 #29247)
+#29233 := (iff #29215 #29232)
+#29234 := [rewrite]: #29233
+#29249 := [monotonicity #29234]: #29248
+#29264 := [monotonicity #29249 #29255 #29261]: #29263
+#29269 := [trans #29264 #29267]: #29268
+#29272 := [monotonicity #29269]: #29271
+#29245 := (iff #29226 #29244)
+#29242 := (iff #29225 #29241)
+#29239 := (iff #29224 #29238)
+#29236 := (iff #29223 #29235)
+#29237 := [rewrite]: #29236
+#29240 := [monotonicity #29237]: #29239
+#29243 := [monotonicity #29234 #29240]: #29242
+#29246 := [monotonicity #29243]: #29245
+#29275 := [monotonicity #29246 #29272]: #29274
+#29278 := [monotonicity #29275]: #29277
+#29281 := [monotonicity #29278]: #29280
+#29284 := [monotonicity #29281]: #29283
+#29287 := [monotonicity #29284]: #29286
+#29906 := [monotonicity #29287]: #29902
+#29798 := [trans #29906 #29933]: #29902
+#29896 := [quant-inst]: #29782
+#29799 := [mp #29896 #29798]: #29781
+#29774 := [unit-resolution #29799 #21978 #29981]: false
+#29946 := [lemma #29774]: #29285
+#30008 := (or #29865 #12493)
+#29909 := [hypothesis]: #29265
+decl f117 :: (-> S5 int)
+#3008 := (f117 #3007)
+decl f125 :: (-> S3 int S3)
+#3005 := (f125 f9 f286)
+#3009 := (f44 #3005 #3008)
+#3012 := (f26 f287 #3009)
+#29965 := (= #3012 #29199)
+#29974 := (= #29199 #3012)
+#30151 := (= #29196 #3009)
+decl f144 :: (-> S3 int)
+#24837 := (f144 #3005)
+decl f145 :: (-> S3 S3)
+#24835 := (f145 #3005)
+#26983 := (f125 #24835 #24837)
+#26984 := (f44 #26983 #3008)
+#28336 := (= #26984 #3009)
+#28334 := (= #26983 #3005)
+#28332 := (= #24837 f286)
+#24838 := (= f286 #24837)
+#335 := (:var 1 S3)
+#1367 := (f125 #335 #168)
+#1604 := (pattern #1367)
+#1615 := (f144 #1367)
+#8360 := (= #168 #1615)
+#8363 := (forall (vars (?v0 S3) (?v1 int)) (:pat #1604) #8360)
+#17274 := (~ #8363 #8363)
+#17272 := (~ #8360 #8360)
+#17273 := [refl]: #17272
+#17275 := [nnf-pos #17273]: #17274
+#1616 := (= #1615 #168)
+#1617 := (forall (vars (?v0 S3) (?v1 int)) (:pat #1604) #1616)
+#8364 := (iff #1617 #8363)
+#8361 := (iff #1616 #8360)
+#8362 := [rewrite]: #8361
+#8365 := [quant-intro #8362]: #8364
+#8359 := [asserted]: #1617
+#8368 := [mp #8359 #8365]: #8363
+#17276 := [mp~ #8368 #17275]: #8363
+#24844 := (not #8363)
+#24845 := (or #24844 #24838)
+#24846 := [quant-inst]: #24845
+#28245 := [unit-resolution #24846 #17276]: #24838
+#28333 := [symm #28245]: #28332
+#28224 := (= #24835 f9)
+#24836 := (= f9 #24835)
+#1618 := (f145 #1367)
+#8367 := (= #335 #1618)
+#8371 := (forall (vars (?v0 S3) (?v1 int)) (:pat #1604) #8367)
+#17279 := (~ #8371 #8371)
+#17277 := (~ #8367 #8367)
+#17278 := [refl]: #17277
+#17280 := [nnf-pos #17278]: #17279
+#1619 := (= #1618 #335)
+#1620 := (forall (vars (?v0 S3) (?v1 int)) (:pat #1604) #1619)
+#8372 := (iff #1620 #8371)
+#8369 := (iff #1619 #8367)
+#8370 := [rewrite]: #8369
+#8373 := [quant-intro #8370]: #8372
+#8366 := [asserted]: #1620
+#8376 := [mp #8366 #8373]: #8371
+#17281 := [mp~ #8376 #17280]: #8371
+#24839 := (not #8371)
+#24840 := (or #24839 #24836)
+#24841 := [quant-inst]: #24840
+#28223 := [unit-resolution #24841 #17281]: #24836
+#28225 := [symm #28223]: #28224
+#28335 := [monotonicity #28225 #28333]: #28334
+#28337 := [monotonicity #28335]: #28336
+#30149 := (= #29196 #26984)
+decl f126 :: (-> S5 S5 int)
+decl f29 :: (-> int S5)
+decl f30 :: (-> S5 int)
+#3041 := (f30 #3007)
+#24672 := (f29 #3041)
+#26961 := (f14 #24672)
+#28957 := (f67 #24672 f299 #26961)
+#28958 := (f126 #28957 #24672)
+#28982 := (f67 #26984 #28958 #24835)
+#28986 := (f59 #3185 #28982)
+#28992 := (f136 #28986)
+#30147 := (= #28992 #26984)
+#28993 := (= #26984 #28992)
+#28994 := (not #28993)
+#28990 := (f137 #28986)
+#28991 := (= f1 #28990)
+decl f68 :: (-> S14 S1)
+#28987 := (f68 #28986)
+#28988 := (= f1 #28987)
+#28989 := (not #28988)
+#28983 := (f25 f287 #28982)
+#28984 := (= f1 #28983)
+#28985 := (not #28984)
+#29015 := (or #28985 #28989 #28991 #28994)
+#29018 := (not #29015)
+#29008 := (* -1::int #28958)
+#29009 := (+ #24837 #29008)
+#29010 := (<= #29009 0::int)
+#30108 := (not #29010)
+#29118 := (+ f299 #29008)
+#29120 := (>= #29118 0::int)
+#28959 := (= f299 #28958)
+#21 := (:var 1 S5)
+#1399 := (f14 #21)
+#1400 := (f67 #21 #168 #1399)
+#1401 := (pattern #1400)
+#1402 := (f126 #1400 #21)
+#7740 := (= #168 #1402)
+#7744 := (forall (vars (?v0 S5) (?v1 int)) (:pat #1401) #7740)
+#16989 := (~ #7744 #7744)
+#16987 := (~ #7740 #7740)
+#16988 := [refl]: #16987
+#16990 := [nnf-pos #16988]: #16989
+#1403 := (= #1402 #168)
+#1404 := (forall (vars (?v0 S5) (?v1 int)) (:pat #1401) #1403)
+#7745 := (iff #1404 #7744)
+#7742 := (iff #1403 #7740)
+#7743 := [rewrite]: #7742
+#7746 := [quant-intro #7743]: #7745
+#7739 := [asserted]: #1404
+#7749 := [mp #7739 #7746]: #7744
+#16991 := [mp~ #7749 #16990]: #7744
+#26968 := (not #7744)
+#28962 := (or #26968 #28959)
+#28963 := [quant-inst]: #28962
+#29598 := [unit-resolution #28963 #16991]: #28959
+#29599 := (not #28959)
+#30105 := (or #29599 #29120)
+#30106 := [th-lemma]: #30105
+#30107 := [unit-resolution #30106 #29598]: #29120
+#13446 := (* -1::int f299)
+#13709 := (+ f286 #13446)
+#13710 := (<= #13709 0::int)
+#13711 := (not #13710)
+#13618 := (* -1::int #3231)
+decl f297 :: int
+#3096 := f297
+#13619 := (+ f297 #13618)
+#13617 := (>= #13619 0::int)
+#13616 := (not #13617)
+decl f298 :: int
+#3100 := f298
+#13422 := (>= f298 0::int)
+#22363 := (not #13422)
+#12751 := (= f298 f306)
+#12757 := (not #12751)
+#12748 := (= f297 f305)
+#12766 := (not #12748)
+#23293 := (or #12766 #12757 #22363 #13565 #22322 #13616 #23260)
+#23296 := (not #23293)
+#23269 := (or #18440 #18449 #23266)
+#23272 := (not #23269)
+#23275 := (or #18440 #18443 #23272)
+#23278 := (not #23275)
+#23281 := (or #18440 #18443 #23278)
+#23284 := (not #23281)
+#23287 := (or #22363 #13565 #13617 #23284)
+#23290 := (not #23287)
+#23299 := (or #23290 #23296)
+#23302 := (not #23299)
+#23305 := (or #18440 #18449 #22363 #13565 #23302)
+#23308 := (not #23305)
+#23311 := (or #18440 #18449 #23308)
+#23314 := (not #23311)
+#23317 := (or #18440 #18443 #23314)
+#23320 := (not #23317)
+#23323 := (or #18440 #18443 #23320)
+#23326 := (not #23323)
+#23329 := (or #22363 #13565 #13710 #23326)
+#23332 := (not #23329)
+decl ?v0!15 :: int
+#18622 := ?v0!15
+#18627 := (f67 #3007 ?v0!15 f9)
+#18628 := (f111 f287 #18627)
+#18973 := (* -1::int #18628)
+decl f303 :: int
+#3131 := f303
+#18974 := (+ f303 #18973)
+#18975 := (>= #18974 0::int)
+#18960 := (* -1::int ?v0!15)
+#18961 := (+ f286 #18960)
+#18962 := (<= #18961 0::int)
+#18624 := (>= ?v0!15 0::int)
+#22457 := (not #18624)
+#18623 := (<= ?v0!15 4294967295::int)
+#22456 := (not #18623)
+#22472 := (or #22456 #22457 #18962 #18975)
+#22477 := (not #22472)
+#13351 := (* -1::int f286)
+#13739 := (+ #168 #13351)
+#13738 := (>= #13739 0::int)
+#3138 := (= #3089 f303)
+#22430 := (not #3138)
+#22431 := (or #22430 #5040 #13738 #19497)
+#23343 := (forall (vars (?v0 int)) (:pat #23202) #22431)
+#23348 := (not #23343)
+#13750 := (* -1::int f303)
+#13751 := (+ #3089 #13750)
+#13752 := (<= #13751 0::int)
+#22422 := (or #5040 #13738 #13752 #19497)
+#23335 := (forall (vars (?v0 int)) (:pat #23202) #22422)
+#23340 := (not #23335)
+#23351 := (or #23340 #23348)
+#23354 := (not #23351)
+#23357 := (or #23354 #22477)
+#23360 := (not #23357)
+#12187 := (= f297 f303)
+#12222 := (not #12187)
+decl f302 :: int
+#3129 := f302
+#12184 := (= f298 f302)
+#12231 := (not #12184)
+decl f301 :: int
+#3127 := f301
+#12181 := (= f299 f301)
+#12240 := (not #12181)
+decl f300 :: int
+#3125 := f300
+#12178 := (= f297 f300)
+#12249 := (not #12178)
+#23363 := (or #12249 #12240 #12231 #12222 #22363 #13565 #13711 #23360)
+#23366 := (not #23363)
+#23369 := (or #23332 #23366)
+#23372 := (not #23369)
+#13915 := (* -1::int f297)
+#13916 := (+ #3089 #13915)
+#13917 := (<= #13916 0::int)
+#13904 := (+ #168 #13446)
+#13903 := (>= #13904 0::int)
+#22238 := (or #5040 #13903 #13917 #19497)
+#23211 := (forall (vars (?v0 int)) (:pat #23202) #22238)
+#23216 := (not #23211)
+#1340 := 255::int
+#15794 := (<= f297 255::int)
+#22507 := (not #15794)
+#15777 := (<= f298 4294967295::int)
+#22506 := (not #15777)
+#15760 := (<= f299 4294967295::int)
+#22505 := (not #15760)
+#13965 := (>= f297 0::int)
+#22503 := (not #13965)
+#13943 := (>= f299 0::int)
+#22502 := (not #13943)
+#13937 := (>= #13709 0::int)
 #13940 := (not #13937)
-decl uf_289 :: (-> T19 int)
-#3007 := (:var 0 T19)
-#3008 := (uf_289 #3007)
-#3009 := (pattern #3008)
-decl uf_290 :: int
-#3010 := uf_290
-#13927 := (* -1::int uf_290)
-#13928 := (+ #3008 #13927)
-#13926 := (>= #13928 0::int)
-#13925 := (not #13926)
-#13931 := (forall (vars (?x771 T19)) (:pat #3009) #13925)
+#13886 := (* -1::int f298)
+#13887 := (+ f286 #13886)
+#13888 := (<= #13887 0::int)
+#13417 := (<= f286 0::int)
+decl f292 :: (-> S4 S2 S2 S5 S3 S1)
+decl f8 :: (-> S3 S3)
+#17 := (f8 f9)
+decl f281 :: S2
+#2984 := f281
+decl f273 :: S2
+#2976 := f273
+#3215 := (f292 f287 f273 f281 #3007 #17)
+#12467 := (= f1 #3215)
+#22501 := (not #12467)
+#3213 := (f291 f287 f273 f281 #3041 #17)
+#12464 := (= f1 #3213)
+#22500 := (not #12464)
+decl f280 :: S2
+#2983 := f280
+#3211 := (f291 f287 f273 f280 f286 f6)
+#12461 := (= f1 #3211)
+#12942 := (not #12461)
+#3209 := (f291 f287 f273 f278 f297 f9)
+#12458 := (= f1 #3209)
+#12951 := (not #12458)
+#3207 := (f291 f287 f273 f276 f298 f6)
+#12455 := (= f1 #3207)
+#12960 := (not #12455)
+#3205 := (f291 f287 f273 f274 f299 f6)
+#12452 := (= f1 #3205)
+#12969 := (not #12452)
+decl f179 :: (-> S4 S4 S1)
+#3197 := (f179 f287 f287)
+#12424 := (= f1 #3197)
+#13883 := (not #12424)
+decl f203 :: (-> S2 S4 S1)
+#3122 := (f203 f273 f287)
+#12167 := (= f1 #3122)
+#15198 := (not #12167)
+#3117 := (f67 #3007 f298 f9)
+#3118 := (f111 f287 #3117)
+#12159 := (= f297 #3118)
+#22499 := (not #12159)
+#3063 := (f67 #3007 0::int f9)
+#3073 := (f111 f287 #3063)
+decl f296 :: int
+#3072 := f296
+#3074 := (= f296 #3073)
+#13176 := (not #3074)
+#23375 := (or #13176 #22499 #15198 #13883 #12969 #12960 #12951 #12942 #22500 #22501 #13417 #22363 #13565 #13888 #13940 #22502 #22503 #22505 #22506 #22507 #23216 #23372)
+#23378 := (not #23375)
+#23381 := (or #13176 #13417 #23378)
+#23384 := (not #23381)
+#13397 := (* -1::int #3089)
+#13398 := (+ f296 #13397)
+#13396 := (>= #13398 0::int)
+#13384 := (>= #168 1::int)
+#22227 := (or #5040 #13384 #13396 #19497)
+#23203 := (forall (vars (?v0 int)) (:pat #23202) #22227)
+#23208 := (not #23203)
+#23387 := (or #23208 #23384)
+#23390 := (not #23387)
+decl ?v0!13 :: int
+#18361 := ?v0!13
+#18371 := (>= ?v0!13 1::int)
+#18366 := (f67 #3007 ?v0!13 f9)
+#18367 := (f111 f287 #18366)
+#18368 := (* -1::int #18367)
+#18369 := (+ f296 #18368)
+#18370 := (>= #18369 0::int)
+#18363 := (>= ?v0!13 0::int)
+#22201 := (not #18363)
+#18362 := (<= ?v0!13 4294967295::int)
+#22200 := (not #18362)
+#22216 := (or #22200 #22201 #18370 #18371)
+#22221 := (not #22216)
+#23393 := (or #22221 #23390)
+#23396 := (not #23393)
+#13378 := (>= f286 1::int)
+#13381 := (not #13378)
+#23399 := (or #13381 #23396)
+#23402 := (not #23399)
+#23405 := (or #13381 #23402)
+#23408 := (not #23405)
+decl f275 :: S2
+#2978 := f275
+#3079 := (f291 f287 f275 f274 1::int f6)
+#12110 := (= f1 #3079)
+#13149 := (not #12110)
+decl f277 :: S2
+#2980 := f277
+#3077 := (f291 f287 f277 f276 0::int f6)
+#12107 := (= f1 #3077)
+#13158 := (not #12107)
+decl f279 :: S2
+#2982 := f279
+#3075 := (f291 f287 f279 f278 f296 f9)
+#12104 := (= f1 #3075)
+#13167 := (not #12104)
+#3069 := (f69 f287 #3063)
+#12098 := (= f1 #3069)
+#18338 := (not #12098)
+#3064 := (f49 #3063 f9)
+#12089 := (= f1 #3064)
+#18329 := (not #12089)
+#23411 := (or #13176 #18329 #18338 #13167 #13158 #13149 #23408)
+#23414 := (not #23411)
+#23417 := (or #18329 #18338 #23414)
+#23420 := (not #23417)
+#3066 := (f25 f287 #3063)
+#12092 := (= f1 #3066)
+#18332 := (not #12092)
+#23423 := (or #18329 #18332 #23420)
+#23426 := (not #23423)
+#23429 := (or #18329 #18332 #23426)
+#23432 := (not #23429)
+decl f201 :: (-> S4 S5 S5 S16 S1)
+decl f295 :: S16
+#3060 := f295
+#3061 := (f201 f287 #3009 #3009 f295)
+#12086 := (= f1 #3061)
+#13209 := (not #12086)
+#23435 := (or #13209 #23432)
+#23438 := (not #23435)
+#24719 := (f117 #3009)
+#26021 := (f44 #3005 #24719)
+#26555 := (f201 f287 #26021 #26021 f295)
+#26805 := (= #26555 #3061)
+#26808 := (= #3061 #26555)
+#26028 := (= #3009 #26021)
+#3014 := (f49 #3009 #3005)
+#12018 := (= f1 #3014)
+decl f24 :: (-> S3 S1)
+#3021 := (f24 #3005)
+#12030 := (= f1 #3021)
+#3018 := (f13 #3005)
+#12024 := (= f15 #3018)
+#12027 := (not #12024)
+#3016 := (f25 f287 #3009)
+#12021 := (= f1 #3016)
+#12015 := (= f27 #3012)
+#3010 := (f28 f287 #3009)
+#12011 := (= f1 #3010)
+#14137 := (and #12011 #12015 #12018 #12021 #12027 #12030)
+decl f283 :: int
+#2989 := f283
+#14193 := (* -1::int f283)
+decl f79 :: int
+#438 := f79
+#14194 := (+ f79 #14193)
+#14192 := (>= #14194 0::int)
+#14190 := (>= f283 0::int)
+#14197 := (and #14190 #14192)
+#14200 := (not #14197)
+decl f284 :: int
+#2993 := f284
+#14179 := (* -1::int f284)
+decl f77 :: int
+#418 := f77
+#14180 := (+ f77 #14179)
+#14178 := (>= #14180 0::int)
+#14176 := (>= f284 0::int)
+#14183 := (and #14176 #14178)
+#14186 := (not #14183)
+decl f285 :: int
+#2997 := f285
+#14165 := (* -1::int f285)
+#14166 := (+ f77 #14165)
+#14164 := (>= #14166 0::int)
+#14162 := (>= f285 0::int)
+#14169 := (and #14162 #14164)
+#14172 := (not #14169)
+#1051 := 1099511627776::int
+#14150 := (>= f286 1099511627776::int)
+#14140 := (not #14137)
+decl f289 :: (-> S19 int)
+#3035 := (:var 0 S19)
+#3036 := (f289 #3035)
+#3037 := (pattern #3036)
+decl f290 :: int
+#3038 := f290
+#14127 := (* -1::int f290)
+#14128 := (+ #3036 #14127)
+#14126 := (>= #14128 0::int)
+#14125 := (not #14126)
+#14131 := (forall (vars (?v0 S19)) (:pat #3037) #14125)
+#14134 := (not #14131)
+#13418 := (not #13417)
+#13981 := (and #3074 #13418)
+#13986 := (not #13981)
+#13969 := (+ f79 #13915)
+#13968 := (>= #13969 0::int)
+#13972 := (and #13965 #13968)
+#13975 := (not #13972)
+#13956 := (+ f77 #13886)
+#13955 := (>= #13956 0::int)
+#13959 := (and #13422 #13955)
+#13962 := (not #13959)
+#13447 := (+ f77 #13446)
+#13946 := (>= #13447 0::int)
+#13949 := (and #13943 #13946)
+#13952 := (not #13949)
+#4430 := (* -1::int f77)
+#4431 := (+ #168 #4430)
+#4432 := (<= #4431 0::int)
+#4439 := (and #4118 #4432)
+#5654 := (not #4439)
+#13926 := (or #5654 #13903 #13917)
+#13931 := (forall (vars (?v0 int)) #13926)
 #13934 := (not #13931)
-#13218 := (not #13217)
-#13781 := (and #3042 #13218)
-#13786 := (not #13781)
-#13769 := (+ uf_78 #13715)
-#13768 := (>= #13769 0::int)
-#13772 := (and #13765 #13768)
-#13775 := (not #13772)
-#13756 := (+ uf_76 #13686)
-#13755 := (>= #13756 0::int)
-#13759 := (and #13222 #13755)
-#13762 := (not #13759)
-#13247 := (+ uf_76 #13246)
-#13746 := (>= #13247 0::int)
-#13749 := (and #13743 #13746)
-#13752 := (not #13749)
-#4355 := (* -1::int uf_76)
-#4356 := (+ #161 #4355)
-#4357 := (<= #4356 0::int)
-#4364 := (and #4043 #4357)
-#5579 := (not #4364)
-#13726 := (or #5579 #13703 #13717)
-#13731 := (forall (vars (?x775 int)) #13726)
-#13734 := (not #13731)
-#13689 := (not #13688)
-#13695 := (and #11989 #13689)
-#13700 := (not #13695)
-#13540 := (not #13538)
-#13578 := (and #3103 #4043 #4357 #13540)
-#13583 := (exists (vars (?x778 int)) #13578)
-#13561 := (or #5579 #13538 #13552)
-#13566 := (forall (vars (?x776 int)) #13561)
-#13586 := (not #13566)
-#13592 := (or #13586 #13583)
-#13597 := (and #13566 #13592)
-#13227 := (and #13222 #13225)
-#13230 := (not #13227)
-decl up_216 :: bool
-#2482 := up_216
-#12113 := (not up_216)
-#13624 := (or #12113 #12079 #12070 #12061 #12052 #13230 #13597)
-#13629 := (and up_216 #13624)
-#13654 := (or #13230 #13511 #13629)
-#13245 := (>= #13247 1::int)
-#13334 := (and #13243 #13245)
-#13337 := (not #13334)
-#13304 := (not #13303)
-#13310 := (and #12352 #13304)
-#13290 := (or #5579 #13267 #13281)
-#13295 := (forall (vars (?x785 int)) #13290)
-#13298 := (not #13295)
-#13315 := (or #13298 #13310)
-#13318 := (and #13295 #13315)
-#13321 := (or #13264 #13318)
-#13324 := (and #13259 #13321)
-#13253 := (and #13234 #13251)
-#13256 := (not #13253)
-#13352 := (or #12401 #13256 #13324 #13331 #13337)
-#13360 := (and #13243 #13245 #13352)
-#13236 := (and #13225 #13234)
-#13239 := (not #13236)
-#13471 := (or #12566 #12557 #13230 #13239 #13360 #13416)
-#12305 := (and #12293 #12302)
-#12494 := (not #12305)
-#13392 := (or #12476 #12467 #12494 #12485 #12449 #12440 #13365 #13239 #13360)
-#13400 := (and #12293 #12302 #13392)
-#12299 := (and #12293 #12296)
-#12506 := (not #12299)
-#13405 := (or #12506 #13400)
-#13411 := (and #12293 #12296 #13405)
-#13441 := (or #13230 #13411 #13417)
-#13476 := (and #13441 #13471)
-#13485 := (or #12494 #13230 #13476)
-#13493 := (and #12293 #12302 #13485)
-#13498 := (or #12506 #13493)
-#13504 := (and #12293 #12296 #13498)
-#13533 := (or #13230 #13504 #13510)
-#13659 := (and #13533 #13654)
-decl uf_55 :: (-> T4 T2)
-#3004 := (uf_55 uf_287)
-#11905 := (= uf_9 #3004)
-#12003 := (and #11905 #11997)
-#12141 := (not #12003)
-#3176 := (and #3174 #3175)
-#12733 := (not #3176)
-#13852 := (or #12769 #12760 #12751 #12742 #12733 #12141 #13683 #13230 #13659 #13700 #13734 #13740 #13752 #13762 #13775 #13786)
-#13860 := (and #3042 #13218 #13852)
-#13206 := (or #5579 #13184 #13196)
-#13211 := (forall (vars (?x773 int)) #13206)
-#13214 := (not #13211)
-#13865 := (or #13214 #13860)
-#13868 := (and #13211 #13865)
-#13871 := (or #13181 #13868)
-#13874 := (and #13178 #13871)
-#11940 := (and #11928 #11937)
-#12985 := (not #11940)
-#13895 := (or #12976 #12967 #12958 #12949 #12985 #13874)
-#13903 := (and #11928 #11937 #13895)
-#11934 := (and #11928 #11931)
-#12997 := (not #11934)
-#13908 := (or #12997 #13903)
-#13914 := (and #11928 #11931 #13908)
-#13919 := (or #13009 #13914)
-#13922 := (and #11925 #13919)
-#13152 := (+ uf_76 #13151)
-#13150 := (>= #13152 0::int)
-#13148 := (>= uf_286 0::int)
-#13155 := (and #13148 #13150)
-#13158 := (not #13155)
-decl uf_294 :: (-> int T5 T2)
-decl uf_293 :: int
-#3018 := uf_293
-#3021 := (uf_294 uf_293 #23)
-#3022 := (pattern #3021)
-#11911 := (= uf_9 #3021)
-#11917 := (not #11911)
-#11922 := (forall (vars (?x772 T5)) (:pat #3022) #11917)
-#13030 := (not #11922)
-decl uf_281 :: T1
-#2954 := uf_281
-#3002 := (uf_202 uf_281 uf_287)
-#11902 := (= uf_9 #3002)
-#11908 := (and #11902 #11905)
-#13075 := (not #11908)
-decl uf_203 :: (-> T4 T2)
-#3000 := (uf_203 uf_287)
-#11899 := (= uf_9 #3000)
-#13084 := (not #11899)
-decl uf_173 :: (-> T4 int)
-#3019 := (uf_173 uf_287)
-#3020 := (= uf_293 #3019)
-#13039 := (not #3020)
-#3017 := (up_291 uf_287 uf_281 uf_279 uf_286 uf_4)
-#13048 := (not #3017)
-#3015 := (up_292 uf_287 uf_281 uf_280 #2979 #11)
-#3014 := (up_291 uf_287 uf_281 uf_280 #3013 #11)
-#3016 := (and #3014 #3015)
-#13057 := (not #3016)
-#14045 := (or #13057 #13048 #13039 #13084 #13075 #13030 #13158 #13217 #13922 #13934 #13940 #13950 #13972 #13986 #14000)
-#14050 := (not #14045)
+#13889 := (not #13888)
+#13895 := (and #12159 #13889)
+#13900 := (not #13895)
+#13740 := (not #13738)
+#13778 := (and #3138 #4118 #4432 #13740)
+#13783 := (exists (vars (?v0 int)) #13778)
+#13761 := (or #5654 #13738 #13752)
+#13766 := (forall (vars (?v0 int)) #13761)
+#13786 := (not #13766)
+#13792 := (or #13786 #13783)
+#13797 := (and #13766 #13792)
+#13427 := (and #13422 #13425)
+#13430 := (not #13427)
+decl f217 :: S1
+#2506 := f217
+#10869 := (= f1 f217)
+#12283 := (not #10869)
+#13824 := (or #12283 #12249 #12240 #12231 #12222 #13430 #13797)
+#13829 := (and #10869 #13824)
+#13854 := (or #13430 #13711 #13829)
+#13445 := (>= #13447 1::int)
+#13534 := (and #13443 #13445)
+#13537 := (not #13534)
+#13504 := (not #13503)
+#13510 := (and #12552 #13504)
+#13490 := (or #5654 #13467 #13481)
+#13495 := (forall (vars (?v0 int)) #13490)
+#13498 := (not #13495)
+#13515 := (or #13498 #13510)
+#13518 := (and #13495 #13515)
+#13521 := (or #13464 #13518)
+#13524 := (and #13459 #13521)
+#13453 := (and #13434 #13451)
+#13456 := (not #13453)
+#13552 := (or #12601 #13456 #13524 #13531 #13537)
+#13560 := (and #13443 #13445 #13552)
+#13436 := (and #13425 #13434)
+#13439 := (not #13436)
+#13671 := (or #12766 #12757 #13430 #13439 #13560 #13616)
+#12496 := (and #12484 #12493)
+#12694 := (not #12496)
+#13592 := (or #12694 #12685 #12676 #12667 #12649 #12640 #13565 #13439 #13560)
+#13600 := (and #12484 #12493 #13592)
+#12490 := (and #12484 #12487)
+#12706 := (not #12490)
+#13605 := (or #12706 #13600)
+#13611 := (and #12484 #12487 #13605)
+#13641 := (or #13430 #13611 #13617)
+#13676 := (and #13641 #13671)
+#13685 := (or #12694 #13430 #13676)
+#13693 := (and #12484 #12493 #13685)
+#13698 := (or #12706 #13693)
+#13704 := (and #12484 #12487 #13698)
+#13733 := (or #13430 #13704 #13710)
+#13859 := (and #13733 #13854)
+#12470 := (and #12464 #12467)
+#12933 := (not #12470)
+decl f56 :: (-> S4 S1)
+#3032 := (f56 f287)
+#12054 := (= f1 #3032)
+#12173 := (and #12054 #12167)
+#12311 := (not #12173)
+#14052 := (or #12311 #13883 #12969 #12960 #12951 #12942 #12933 #13430 #13859 #13900 #13934 #13940 #13952 #13962 #13975 #13986)
+#14060 := (and #3074 #13418 #14052)
+#13406 := (or #5654 #13384 #13396)
+#13411 := (forall (vars (?v0 int)) #13406)
+#13414 := (not #13411)
+#14065 := (or #13414 #14060)
+#14068 := (and #13411 #14065)
+#14071 := (or #13381 #14068)
+#14074 := (and #13378 #14071)
+#12101 := (and #12089 #12098)
+#13185 := (not #12101)
+#14095 := (or #13176 #13185 #13167 #13158 #13149 #14074)
+#14103 := (and #12089 #12098 #14095)
+#12095 := (and #12089 #12092)
+#13197 := (not #12095)
+#14108 := (or #13197 #14103)
+#14114 := (and #12089 #12092 #14108)
+#14119 := (or #13209 #14114)
+#14122 := (and #12086 #14119)
+#13352 := (+ f77 #13351)
+#13350 := (>= #13352 0::int)
+#13348 := (>= f286 0::int)
+#13355 := (and #13348 #13350)
+#13358 := (not #13355)
+decl f294 :: (-> int S5 S1)
+decl f293 :: int
+#3049 := f293
+#3052 := (f294 f293 #28)
+#3053 := (pattern #3052)
+#12072 := (= f1 #3052)
+#12078 := (not #12072)
+#12083 := (forall (vars (?v0 S5)) (:pat #3053) #12078)
+#13230 := (not #12083)
+decl f282 :: S2
+#2985 := f282
+#3047 := (f291 f287 f282 f280 f286 f6)
+#12069 := (= f1 #3047)
+#13248 := (not #12069)
+#3044 := (f292 f287 f282 f281 #3007 #17)
+#12063 := (= f1 #3044)
+#3042 := (f291 f287 f282 f281 #3041 #17)
+#12060 := (= f1 #3042)
+#12066 := (and #12060 #12063)
+#13257 := (not #12066)
+#3030 := (f203 f282 f287)
+#12051 := (= f1 #3030)
+#12057 := (and #12051 #12054)
+#13275 := (not #12057)
+decl f204 :: (-> S4 S1)
+#3028 := (f204 f287)
+#12048 := (= f1 #3028)
+#13284 := (not #12048)
+decl f174 :: (-> S4 int)
+#3050 := (f174 f287)
+#3051 := (= f293 #3050)
+#13239 := (not #3051)
+#14245 := (or #13239 #13284 #13275 #13257 #13248 #13230 #13358 #13417 #14122 #14134 #14140 #14150 #14172 #14186 #14200)
+#14250 := (not #14245)
 #1 := true
-#3098 := (< #161 uf_286)
-#3104 := (and #3098 #3103)
-#411 := (<= #161 uf_76)
-#3105 := (and #411 #3104)
-#285 := (<= 0::int #161)
-#3106 := (and #285 #3105)
-#3107 := (exists (vars (?x778 int)) #3106)
-#3108 := (and #3107 true)
-#3099 := (<= #3054 uf_302)
-#3100 := (implies #3098 #3099)
-#412 := (and #285 #411)
-#3101 := (implies #412 #3100)
-#3102 := (forall (vars (?x776 int)) #3101)
-#3109 := (implies #3102 #3108)
-#3110 := (and #3102 #3109)
-#3097 := (= uf_302 uf_296)
-#3111 := (implies #3097 #3110)
-#3095 := (= uf_301 uf_297)
-#3112 := (implies #3095 #3111)
-#3093 := (= uf_300 uf_298)
-#3113 := (implies #3093 #3112)
-#3091 := (= uf_299 uf_296)
-#3114 := (implies #3091 #3113)
-#3066 := (<= 0::int uf_297)
-#3073 := (<= 1::int uf_298)
-#3074 := (and #3073 #3066)
-#3115 := (implies #3074 #3114)
-#3116 := (implies #3074 #3115)
-#3117 := (implies #3074 #3116)
-#3118 := (implies up_216 #3117)
-#3119 := (and up_216 #3118)
-#3120 := (implies #3074 #3119)
-#3121 := (implies #3074 #3120)
-#3269 := (implies #3074 #3121)
-#3270 := (implies #3074 #3269)
-#3268 := (<= uf_286 uf_298)
-#3271 := (implies #3268 #3270)
-#3272 := (implies #3074 #3271)
-#3221 := (= #3220 uf_304)
-#3218 := (< uf_305 uf_286)
-#3222 := (and #3218 #3221)
-#3223 := (and #3222 true)
-#3214 := (<= #3054 uf_304)
-#3213 := (< #161 uf_306)
-#3215 := (implies #3213 #3214)
-#3216 := (implies #412 #3215)
-#3217 := (forall (vars (?x785 int)) #3216)
-#3224 := (implies #3217 #3223)
-#3225 := (and #3217 #3224)
-#3212 := (<= uf_306 uf_286)
-#3226 := (implies #3212 #3225)
-#3227 := (and #3212 #3226)
-#3201 := (<= 0::int uf_305)
-#3210 := (<= 2::int uf_306)
-#3211 := (and #3210 #3201)
-#3228 := (implies #3211 #3227)
-#3229 := (implies #3209 #3228)
-#3203 := (+ uf_298 1::int)
-#3208 := (= uf_306 #3203)
-#3230 := (implies #3208 #3229)
-#3205 := (<= #3203 uf_76)
-#3204 := (<= 0::int #3203)
-#3206 := (and #3204 #3205)
-#3231 := (implies #3206 #3230)
-#3232 := (and #3206 #3231)
-#3202 := (and #3073 #3201)
-#3233 := (implies #3202 #3232)
-#3250 := (= uf_305 uf_297)
-#3251 := (implies #3250 #3233)
-#3249 := (= uf_304 uf_296)
-#3252 := (implies #3249 #3251)
-#3253 := (implies #3074 #3252)
-#3254 := (implies #3074 #3253)
-#3255 := (implies #3074 #3254)
-#3248 := (<= #3190 uf_296)
-#3256 := (implies #3248 #3255)
-#3257 := (implies #3074 #3256)
-#3200 := (= uf_305 uf_298)
-#3234 := (implies #3200 #3233)
-#3198 := (= uf_304 uf_303)
-#3235 := (implies #3198 #3234)
-#3196 := (and #3073 #3073)
-#3236 := (implies #3196 #3235)
-#3237 := (implies #3195 #3236)
-#3238 := (implies #3194 #3237)
-#3193 := (= uf_303 #3190)
-#3239 := (implies #3193 #3238)
-#3188 := (= #3187 uf_9)
-#3183 := (= #3182 uf_9)
-#3189 := (and #3183 #3188)
-#3240 := (implies #3189 #3239)
-#3241 := (and #3189 #3240)
-#3185 := (= #3184 uf_9)
-#3186 := (and #3183 #3185)
-#3242 := (implies #3186 #3241)
-#3243 := (and #3186 #3242)
-#3244 := (implies #3074 #3243)
-#3245 := (implies #3074 #3244)
-#3191 := (< uf_296 #3190)
-#3246 := (implies #3191 #3245)
-#3247 := (implies #3074 #3246)
-#3258 := (and #3247 #3257)
-#3259 := (implies #3074 #3258)
-#3260 := (implies #3189 #3259)
-#3261 := (and #3189 #3260)
-#3262 := (implies #3186 #3261)
-#3263 := (and #3186 #3262)
-#3264 := (implies #3074 #3263)
-#3265 := (implies #3074 #3264)
-#3180 := (< uf_298 uf_286)
-#3266 := (implies #3180 #3265)
-#3267 := (implies #3074 #3266)
-#3273 := (and #3267 #3272)
-#3274 := (implies #3074 #3273)
-decl uf_41 :: (-> T4 T12)
-#3127 := (uf_41 uf_287)
-#3178 := (= #3127 #3127)
-#3177 := (= #3150 #3150)
-#3179 := (and #3177 #3178)
-#3275 := (implies #3179 #3274)
-#3276 := (implies #3176 #3275)
-#3277 := (implies #3173 #3276)
-#3278 := (implies #3172 #3277)
-#3279 := (implies #3171 #3278)
-#3280 := (implies #3170 #3279)
-#3005 := (= #3004 uf_9)
-#3088 := (= #3087 uf_9)
-#3089 := (and #3088 #3005)
-#3281 := (implies #3089 #3280)
-#3163 := (= #3162 uf_9)
-decl uf_172 :: (-> T4 T5 int)
-#3158 := (uf_172 uf_287 #23)
-#3159 := (pattern #3158)
-#3160 := (<= #3158 #3158)
-#3161 := (forall (vars (?x783 T5)) (:pat #3159) #3160)
-#3164 := (and #3161 #3163)
-#3157 := (<= #3019 #3019)
-#3165 := (and #3157 #3164)
-#3282 := (implies #3165 #3281)
-#3151 := (uf_58 #3150 #23)
-#3152 := (pattern #3151)
-#3140 := (uf_68 uf_287 #23)
-#3141 := (= #3140 uf_9)
-#3153 := (= #3151 #3151)
-#3154 := (and #3153 #3141)
-#3155 := (implies #3141 #3154)
-#3156 := (forall (vars (?x782 T5)) (:pat #3152) #3155)
-#3166 := (and #3156 #3165)
-decl uf_40 :: (-> T12 T5 T11)
-#3128 := (uf_40 #3127 #23)
-#3129 := (pattern #3128)
-#3146 := (= #3128 #3128)
-#3147 := (and #3146 #3141)
-#3148 := (implies #3141 #3147)
-#3149 := (forall (vars (?x781 T5)) (:pat #3129) #3148)
-#3167 := (and #3149 #3166)
-decl uf_19 :: (-> T9 T5 int)
-decl uf_20 :: (-> T4 T9)
-#3137 := (uf_20 uf_287)
-#3138 := (uf_19 #3137 #23)
-#3139 := (pattern #3138)
-#3142 := (= #3138 #3138)
-#3143 := (and #3142 #3141)
-#3144 := (implies #3141 #3143)
-#3145 := (forall (vars (?x780 T5)) (:pat #3139) #3144)
-#3168 := (and #3145 #3167)
-decl uf_261 :: T8
-#2837 := uf_261
-#3130 := (uf_25 uf_287 #23)
-#3131 := (uf_13 #3130)
-#3132 := (uf_12 #3131)
-#3133 := (= #3132 uf_261)
-#3134 := (not #3133)
-#3135 := (implies #3134 #3134)
-#3136 := (forall (vars (?x779 T5)) (:pat #3129) #3135)
-#3169 := (and #3136 #3168)
-#3283 := (implies #3169 #3282)
-#3284 := (implies #3074 #3283)
-#3285 := (implies #3074 #3284)
-#3286 := (implies #3074 #3285)
-#3122 := (implies #3089 #3121)
-#3123 := (implies #3074 #3122)
-#3124 := (implies #3074 #3123)
-#3086 := (not true)
-#3125 := (implies #3086 #3124)
-#3126 := (implies #3074 #3125)
-#3287 := (and #3126 #3286)
-#3288 := (implies #3074 #3287)
-#3084 := (= #3083 uf_296)
-#3081 := (< uf_297 uf_286)
+#3133 := (< #168 f286)
+#3139 := (and #3133 #3138)
+#420 := (<= #168 f77)
+#3140 := (and #420 #3139)
+#293 := (<= 0::int #168)
+#3141 := (and #293 #3140)
+#3142 := (exists (vars (?v0 int)) #3141)
+#3143 := (and #3142 true)
+#3134 := (<= #3089 f303)
+#3135 := (implies #3133 #3134)
+#421 := (and #293 #420)
+#3136 := (implies #421 #3135)
+#3137 := (forall (vars (?v0 int)) #3136)
+#3144 := (implies #3137 #3143)
+#3145 := (and #3137 #3144)
+#3132 := (= f303 f297)
+#3146 := (implies #3132 #3145)
+#3130 := (= f302 f298)
+#3147 := (implies #3130 #3146)
+#3128 := (= f301 f299)
+#3148 := (implies #3128 #3147)
+#3126 := (= f300 f297)
+#3149 := (implies #3126 #3148)
+#3101 := (<= 0::int f298)
+#3108 := (<= 1::int f299)
+#3109 := (and #3108 #3101)
+#3150 := (implies #3109 #3149)
+#3151 := (implies #3109 #3150)
+#3152 := (implies #3109 #3151)
+#2507 := (= f217 f1)
+#3153 := (implies #2507 #3152)
+#3154 := (and #2507 #3153)
+#3155 := (implies #3109 #3154)
+#3156 := (implies #3109 #3155)
+#3313 := (implies #3109 #3156)
+#3314 := (implies #3109 #3313)
+#3312 := (<= f286 f299)
+#3315 := (implies #3312 #3314)
+#3316 := (implies #3109 #3315)
+#3265 := (= #3264 f305)
+#3262 := (< f306 f286)
+#3266 := (and #3262 #3265)
+#3267 := (and #3266 true)
+#3258 := (<= #3089 f305)
+#3257 := (< #168 f307)
+#3259 := (implies #3257 #3258)
+#3260 := (implies #421 #3259)
+#3261 := (forall (vars (?v0 int)) #3260)
+#3268 := (implies #3261 #3267)
+#3269 := (and #3261 #3268)
+#3256 := (<= f307 f286)
+#3270 := (implies #3256 #3269)
+#3271 := (and #3256 #3270)
+#3244 := (<= 0::int f306)
+#3254 := (<= 2::int f307)
+#3255 := (and #3254 #3244)
+#3272 := (implies #3255 #3271)
+#3253 := (= #3252 f1)
+#3273 := (implies #3253 #3272)
+#3246 := (+ f299 1::int)
+#3251 := (= f307 #3246)
+#3274 := (implies #3251 #3273)
+#3248 := (<= #3246 f77)
+#3247 := (<= 0::int #3246)
+#3249 := (and #3247 #3248)
+#3275 := (implies #3249 #3274)
+#3276 := (and #3249 #3275)
+#3245 := (and #3108 #3244)
+#3277 := (implies #3245 #3276)
+#3294 := (= f306 f298)
+#3295 := (implies #3294 #3277)
+#3293 := (= f305 f297)
+#3296 := (implies #3293 #3295)
+#3297 := (implies #3109 #3296)
+#3298 := (implies #3109 #3297)
+#3299 := (implies #3109 #3298)
+#3292 := (<= #3231 f297)
+#3300 := (implies #3292 #3299)
+#3301 := (implies #3109 #3300)
+#3243 := (= f306 f299)
+#3278 := (implies #3243 #3277)
+#3241 := (= f305 f304)
+#3279 := (implies #3241 #3278)
+#3239 := (and #3108 #3108)
+#3280 := (implies #3239 #3279)
+#3238 := (= #3237 f1)
+#3281 := (implies #3238 #3280)
+#3236 := (= #3235 f1)
+#3282 := (implies #3236 #3281)
+#3234 := (= f304 #3231)
+#3283 := (implies #3234 #3282)
+#3229 := (= #3228 f1)
+#3224 := (= #3223 f1)
+#3230 := (and #3224 #3229)
+#3284 := (implies #3230 #3283)
+#3285 := (and #3230 #3284)
+#3226 := (= #3225 f1)
+#3227 := (and #3224 #3226)
+#3286 := (implies #3227 #3285)
+#3287 := (and #3227 #3286)
+#3288 := (implies #3109 #3287)
+#3289 := (implies #3109 #3288)
+#3232 := (< f297 #3231)
+#3290 := (implies #3232 #3289)
+#3291 := (implies #3109 #3290)
+#3302 := (and #3291 #3301)
+#3303 := (implies #3109 #3302)
+#3304 := (implies #3230 #3303)
+#3305 := (and #3230 #3304)
+#3306 := (implies #3227 #3305)
+#3307 := (and #3227 #3306)
+#3308 := (implies #3109 #3307)
+#3309 := (implies #3109 #3308)
+#3221 := (< f299 f286)
+#3310 := (implies #3221 #3309)
+#3311 := (implies #3109 #3310)
+#3317 := (and #3311 #3316)
+#3318 := (implies #3109 #3317)
+decl f42 :: (-> S4 S12)
+#3162 := (f42 f287)
+#3219 := (= #3162 #3162)
+#3218 := (= #3185 #3185)
+#3220 := (and #3218 #3219)
+#3319 := (implies #3220 #3318)
+#3216 := (= #3215 f1)
+#3214 := (= #3213 f1)
+#3217 := (and #3214 #3216)
+#3320 := (implies #3217 #3319)
+#3212 := (= #3211 f1)
+#3321 := (implies #3212 #3320)
+#3210 := (= #3209 f1)
+#3322 := (implies #3210 #3321)
+#3208 := (= #3207 f1)
+#3323 := (implies #3208 #3322)
+#3206 := (= #3205 f1)
+#3324 := (implies #3206 #3323)
+#3033 := (= #3032 f1)
+#3123 := (= #3122 f1)
+#3124 := (and #3123 #3033)
+#3325 := (implies #3124 #3324)
+#3198 := (= #3197 f1)
+decl f173 :: (-> S4 S5 int)
+#3193 := (f173 f287 #28)
+#3194 := (pattern #3193)
+#3195 := (<= #3193 #3193)
+#3196 := (forall (vars (?v0 S5)) (:pat #3194) #3195)
+#3199 := (and #3196 #3198)
+#3192 := (<= #3050 #3050)
+#3200 := (and #3192 #3199)
+#3326 := (implies #3200 #3325)
+#3186 := (f59 #3185 #28)
+#3187 := (pattern #3186)
+#3175 := (f69 f287 #28)
+#3176 := (= #3175 f1)
+#3188 := (= #3186 #3186)
+#3189 := (and #3188 #3176)
+#3190 := (implies #3176 #3189)
+#3191 := (forall (vars (?v0 S5)) (:pat #3187) #3190)
+#3201 := (and #3191 #3200)
+decl f41 :: (-> S12 S5 S11)
+#3163 := (f41 #3162 #28)
+#3164 := (pattern #3163)
+#3181 := (= #3163 #3163)
+#3182 := (and #3181 #3176)
+#3183 := (implies #3176 #3182)
+#3184 := (forall (vars (?v0 S5)) (:pat #3164) #3183)
+#3202 := (and #3184 #3201)
+decl f20 :: (-> S9 S5 int)
+decl f21 :: (-> S4 S9)
+#3172 := (f21 f287)
+#3173 := (f20 #3172 #28)
+#3174 := (pattern #3173)
+#3177 := (= #3173 #3173)
+#3178 := (and #3177 #3176)
+#3179 := (implies #3176 #3178)
+#3180 := (forall (vars (?v0 S5)) (:pat #3174) #3179)
+#3203 := (and #3180 #3202)
+decl f262 :: S8
+#2868 := f262
+#3165 := (f26 f287 #28)
+#3166 := (f14 #3165)
+#3167 := (f13 #3166)
+#3168 := (= #3167 f262)
+#3169 := (not #3168)
+#3170 := (implies #3169 #3169)
+#3171 := (forall (vars (?v0 S5)) (:pat #3164) #3170)
+#3204 := (and #3171 #3203)
+#3327 := (implies #3204 #3326)
+#3328 := (implies #3109 #3327)
+#3329 := (implies #3109 #3328)
+#3330 := (implies #3109 #3329)
+#3157 := (implies #3124 #3156)
+#3158 := (implies #3109 #3157)
+#3159 := (implies #3109 #3158)
+#3121 := (not true)
+#3160 := (implies #3121 #3159)
+#3161 := (implies #3109 #3160)
+#3331 := (and #3161 #3330)
+#3332 := (implies #3109 #3331)
+#3119 := (= #3118 f297)
+#3116 := (< f298 f286)
+#3120 := (and #3116 #3119)
+#3333 := (implies #3120 #3332)
+#3112 := (<= #3089 f297)
+#3111 := (< #168 f299)
+#3113 := (implies #3111 #3112)
+#3114 := (implies #421 #3113)
+#3115 := (forall (vars (?v0 int)) #3114)
+#3334 := (implies #3115 #3333)
+#3110 := (<= f299 f286)
+#3335 := (implies #3110 #3334)
+#3336 := (implies #3109 #3335)
+#3106 := (<= f299 f77)
+#3105 := (<= 0::int f299)
+#3107 := (and #3105 #3106)
+#3337 := (implies #3107 #3336)
+#3102 := (<= f298 f77)
+#3103 := (and #3101 #3102)
+#3338 := (implies #3103 #3337)
+#3098 := (<= f297 f79)
+#3097 := (<= 0::int f297)
+#3099 := (and #3097 #3098)
+#3339 := (implies #3099 #3338)
+#3094 := (= #3073 f296)
+#3003 := (< 0::int f286)
+#3095 := (and #3003 #3094)
+#3340 := (implies #3095 #3339)
+#3341 := (and #3095 #3340)
+#3090 := (<= #3089 f296)
+#3087 := (< #168 1::int)
+#3091 := (implies #3087 #3090)
+#3092 := (implies #421 #3091)
+#3093 := (forall (vars (?v0 int)) #3092)
+#3342 := (implies #3093 #3341)
+#3343 := (and #3093 #3342)
+#3086 := (<= 1::int f286)
+#3344 := (implies #3086 #3343)
+#3345 := (and #3086 #3344)
+#3082 := (<= 0::int 0::int)
+#3083 := (and #3082 #3082)
+#3081 := (<= 1::int 1::int)
+#3084 := (and #3081 #3083)
 #3085 := (and #3081 #3084)
-#3289 := (implies #3085 #3288)
-#3077 := (<= #3054 uf_296)
-#3076 := (< #161 uf_298)
-#3078 := (implies #3076 #3077)
-#3079 := (implies #412 #3078)
-#3080 := (forall (vars (?x775 int)) #3079)
-#3290 := (implies #3080 #3289)
-#3075 := (<= uf_298 uf_286)
-#3291 := (implies #3075 #3290)
-#3292 := (implies #3074 #3291)
-#3071 := (<= uf_298 uf_76)
-#3070 := (<= 0::int uf_298)
-#3072 := (and #3070 #3071)
-#3293 := (implies #3072 #3292)
-#3067 := (<= uf_297 uf_76)
-#3068 := (and #3066 #3067)
-#3294 := (implies #3068 #3293)
-#3063 := (<= uf_296 uf_78)
-#3062 := (<= 0::int uf_296)
-#3064 := (and #3062 #3063)
-#3295 := (implies #3064 #3294)
-#3059 := (= #3041 uf_295)
-#2975 := (< 0::int uf_286)
-#3060 := (and #2975 #3059)
-#3296 := (implies #3060 #3295)
-#3297 := (and #3060 #3296)
-#3055 := (<= #3054 uf_295)
-#3052 := (< #161 1::int)
-#3056 := (implies #3052 #3055)
-#3057 := (implies #412 #3056)
-#3058 := (forall (vars (?x773 int)) #3057)
-#3298 := (implies #3058 #3297)
-#3299 := (and #3058 #3298)
-#3051 := (<= 1::int uf_286)
-#3300 := (implies #3051 #3299)
-#3301 := (and #3051 #3300)
-#3047 := (<= 0::int 0::int)
-#3048 := (and #3047 #3047)
-#3046 := (<= 1::int 1::int)
-#3049 := (and #3046 #3048)
-#3050 := (and #3046 #3049)
-#3302 := (implies #3050 #3301)
-#3303 := (implies #3045 #3302)
-#3304 := (implies #3044 #3303)
-#3305 := (implies #3043 #3304)
-#3306 := (implies #3042 #3305)
-#3038 := (= #3037 uf_9)
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-#3012 := (forall (vars (?x771 T19)) (:pat #3009) #3011)
-#3318 := (implies #3012 #3317)
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-#3006 := (and #3003 #3005)
-#3319 := (implies #3006 #3318)
-#3001 := (= #3000 uf_9)
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-#2991 := (= #2990 uf_14)
-#2992 := (not #2991)
-#2995 := (and #2992 #2994)
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-#2996 := (and #2989 #2995)
-#2987 := (= #2986 uf_9)
-#2997 := (and #2987 #2996)
-#2985 := (= #2984 uf_26)
-#2998 := (and #2985 #2997)
-#2983 := (= #2982 uf_9)
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-#3321 := (implies #2999 #3320)
-#3322 := (implies #2975 #3321)
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-#3323 := (implies #2974 #3322)
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-#2970 := (<= 0::int uf_285)
-#2972 := (and #2970 #2971)
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-#2967 := (<= uf_284 uf_76)
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-#2963 := (<= uf_283 uf_78)
-#2962 := (<= 0::int uf_283)
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-#12062 := (or #12061 #12053)
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-#12752 := (or #12751 #12743)
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-#12905 := (or #12904 #12896)
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-#11963 := (forall (vars (?x773 int)) #11958)
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-#13138 := (not #2964)
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+#13581 := (iff #12668 #13580)
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+#13575 := (iff #12650 #13574)
+#13572 := (iff #12641 #13571)
+#13573 := [monotonicity #13570]: #13572
+#13576 := [monotonicity #13573]: #13575
+#13566 := (iff #12658 #13565)
+#13567 := [monotonicity #13426]: #13566
+#13579 := [monotonicity #13567 #13576]: #13578
+#13582 := [monotonicity #13579]: #13581
+#13585 := [monotonicity #13582]: #13584
+#13588 := [monotonicity #13585]: #13587
+#13591 := [monotonicity #13588]: #13590
+#13596 := [trans #13591 #13594]: #13595
+#13599 := [monotonicity #13596]: #13598
+#13604 := [trans #13599 #13602]: #13603
+#13607 := [monotonicity #13604]: #13606
+#13610 := [monotonicity #13607]: #13609
+#13615 := [trans #13610 #13613]: #13614
+#13631 := [monotonicity #13432 #13615]: #13630
+#13634 := [monotonicity #13432 #13631]: #13633
+#13627 := (iff #12734 #13617)
+#13622 := (not #13616)
+#13625 := (iff #13622 #13617)
+#13626 := [rewrite]: #13625
+#13623 := (iff #12734 #13622)
+#13620 := (iff #3232 #13616)
+#13621 := [rewrite]: #13620
+#13624 := [monotonicity #13621]: #13623
+#13628 := [trans #13624 #13626]: #13627
+#13637 := [monotonicity #13628 #13634]: #13636
+#13640 := [monotonicity #13432 #13637]: #13639
+#13645 := [trans #13640 #13643]: #13644
+#13678 := [monotonicity #13645 #13675]: #13677
+#13681 := [monotonicity #13432 #13678]: #13680
+#13684 := [monotonicity #13681]: #13683
+#13689 := [trans #13684 #13687]: #13688
+#13692 := [monotonicity #13689]: #13691
+#13697 := [trans #13692 #13695]: #13696
+#13700 := [monotonicity #13697]: #13699
+#13703 := [monotonicity #13700]: #13702
+#13708 := [trans #13703 #13706]: #13707
+#13723 := [monotonicity #13432 #13708]: #13722
+#13726 := [monotonicity #13432 #13723]: #13725
+#13719 := (iff #12865 #13710)
+#13714 := (not #13711)
+#13717 := (iff #13714 #13710)
+#13718 := [rewrite]: #13717
+#13715 := (iff #12865 #13714)
+#13712 := (iff #3221 #13711)
+#13713 := [rewrite]: #13712
+#13716 := [monotonicity #13713]: #13715
+#13720 := [trans #13716 #13718]: #13719
+#13729 := [monotonicity #13720 #13726]: #13728
+#13732 := [monotonicity #13432 #13729]: #13731
+#13737 := [trans #13732 #13735]: #13736
+#13861 := [monotonicity #13737 #13858]: #13860
+#13991 := [monotonicity #13432 #13861]: #13990
+#13994 := [monotonicity #13991]: #13993
+#13997 := [monotonicity #13994]: #13996
+#14000 := [monotonicity #13997]: #13999
+#14003 := [monotonicity #14000]: #14002
+#14006 := [monotonicity #14003]: #14005
+#14009 := [monotonicity #14006]: #14008
+#13884 := (iff #12986 #13883)
+#13881 := (iff #12430 #12424)
+#13873 := (and true #12424)
+#13876 := (and true #13873)
+#13879 := (iff #13876 #12424)
+#13880 := [rewrite]: #13879
+#13877 := (iff #12430 #13876)
+#13874 := (iff #12427 #13873)
+#13869 := (iff #3196 true)
+#13864 := (forall (vars (?v0 S5)) (:pat #3194) true)
+#13867 := (iff #13864 true)
+#13868 := [elim-unused]: #13867
+#13865 := (iff #3196 #13864)
+#13862 := (iff #3195 true)
+#13863 := [rewrite]: #13862
+#13866 := [quant-intro #13863]: #13865
+#13870 := [trans #13866 #13868]: #13869
+#13875 := [monotonicity #13870]: #13874
+#13871 := (iff #3192 true)
+#13872 := [rewrite]: #13871
+#13878 := [monotonicity #13872 #13875]: #13877
+#13882 := [trans #13878 #13880]: #13881
+#13885 := [monotonicity #13882]: #13884
+#14012 := [monotonicity #13885 #14009]: #14011
+#14015 := [monotonicity #13885 #14012]: #14014
+#14018 := [monotonicity #13432 #14015]: #14017
+#14021 := [monotonicity #13432 #14018]: #14020
+#14024 := [monotonicity #13432 #14021]: #14023
+#14027 := [monotonicity #13432 #14024]: #14026
+#13901 := (iff #13042 #13900)
+#13898 := (iff #12162 #13895)
+#13892 := (and #13889 #12159)
 #13896 := (iff #13892 #13895)
 #13897 := [rewrite]: #13896
-#13893 := (iff #12986 #13892)
-#13890 := (iff #12977 #13889)
-#13887 := (iff #12968 #13886)
-#13884 := (iff #12959 #13883)
-#13881 := (iff #12950 #13880)
-#13878 := (iff #12941 #13877)
-#13875 := (iff #12934 #13874)
-#13872 := (iff #12929 #13871)
-#13869 := (iff #12922 #13868)
-#13866 := (iff #12917 #13865)
-#13863 := (iff #12910 #13860)
-#13778 := (and #13218 #3042)
-#13857 := (and #13778 #13852)
-#13861 := (iff #13857 #13860)
-#13862 := [rewrite]: #13861
-#13858 := (iff #12910 #13857)
-#13855 := (iff #12905 #13852)
-#13789 := (or #13230 #13659)
-#13792 := (or #12733 #13789)
-#13795 := (or #12742 #13792)
-#13798 := (or #12751 #13795)
-#13801 := (or #12760 #13798)
-#13804 := (or #12769 #13801)
-#13807 := (or #12141 #13804)
-#13810 := (or #13683 #13807)
-#13813 := (or #13683 #13810)
-#13816 := (or #13230 #13813)
-#13819 := (or #13230 #13816)
-#13822 := (or #13230 #13819)
-#13825 := (or #13230 #13822)
-#13828 := (or #13700 #13825)
-#13831 := (or #13734 #13828)
-#13834 := (or #13740 #13831)
-#13837 := (or #13230 #13834)
-#13840 := (or #13752 #13837)
-#13843 := (or #13762 #13840)
-#13846 := (or #13775 #13843)
-#13849 := (or #13786 #13846)
-#13853 := (iff #13849 #13852)
-#13854 := [rewrite]: #13853
-#13850 := (iff #12905 #13849)
-#13847 := (iff #12896 #13846)
-#13844 := (iff #12887 #13843)
-#13841 := (iff #12878 #13840)
-#13838 := (iff #12869 #13837)
-#13835 := (iff #12861 #13834)
-#13832 := (iff #12852 #13831)
-#13829 := (iff #12843 #13828)
-#13826 := (iff #12834 #13825)
-#13823 := (iff #12819 #13822)
-#13820 := (iff #12811 #13819)
-#13817 := (iff #12803 #13816)
-#13814 := (iff #12795 #13813)
-#13811 := (iff #12787 #13810)
-#13808 := (iff #12778 #13807)
-#13805 := (iff #12770 #13804)
-#13802 := (iff #12761 #13801)
-#13799 := (iff #12752 #13798)
-#13796 := (iff #12743 #13795)
-#13793 := (iff #12734 #13792)
-#13790 := (iff #12718 #13789)
-#13660 := (iff #12712 #13659)
-#13657 := (iff #12707 #13654)
-#13636 := (or #13230 #13629)
-#13639 := (or #13230 #13636)
-#13642 := (or #13230 #13639)
-#13645 := (or #13230 #13642)
-#13648 := (or #13511 #13645)
-#13651 := (or #13230 #13648)
-#13655 := (iff #13651 #13654)
-#13656 := [rewrite]: #13655
-#13652 := (iff #12707 #13651)
-#13649 := (iff #12699 #13648)
-#13646 := (iff #12690 #13645)
-#13643 := (iff #12682 #13642)
-#13640 := (iff #12133 #13639)
-#13637 := (iff #12125 #13636)
-#13630 := (iff #12119 #13629)
-#13627 := (iff #12114 #13624)
-#13600 := (or #12052 #13597)
-#13603 := (or #12061 #13600)
-#13606 := (or #12070 #13603)
-#13609 := (or #12079 #13606)
-#13612 := (or #13230 #13609)
-#13615 := (or #13230 #13612)
-#13618 := (or #13230 #13615)
-#13621 := (or #12113 #13618)
-#13625 := (iff #13621 #13624)
-#13626 := [rewrite]: #13625
-#13622 := (iff #12114 #13621)
-#13619 := (iff #12105 #13618)
-#13616 := (iff #12097 #13615)
-#13613 := (iff #12089 #13612)
-#13610 := (iff #12080 #13609)
-#13607 := (iff #12071 #13606)
-#13604 := (iff #12062 #13603)
-#13601 := (iff #12053 #13600)
-#13598 := (iff #12046 #13597)
-#13595 := (iff #12041 #13592)
-#13589 := (or #13583 #13586)
-#13593 := (iff #13589 #13592)
-#13594 := [rewrite]: #13593
-#13590 := (iff #12041 #13589)
-#13587 := (iff #12040 #13586)
-#13567 := (iff #12032 #13566)
-#13564 := (iff #12027 #13561)
-#13555 := (or #13538 #13552)
-#13558 := (or #5579 #13555)
-#13562 := (iff #13558 #13561)
-#13563 := [rewrite]: #13562
-#13559 := (iff #12027 #13558)
-#13556 := (iff #12021 #13555)
-#13553 := (iff #3099 #13552)
-#13554 := [rewrite]: #13553
-#13548 := (iff #12020 #13538)
-#13543 := (not #13540)
-#13546 := (iff #13543 #13538)
-#13547 := [rewrite]: #13546
-#13544 := (iff #12020 #13543)
-#13541 := (iff #3098 #13540)
-#13542 := [rewrite]: #13541
-#13545 := [monotonicity #13542]: #13544
-#13549 := [trans #13545 #13547]: #13548
-#13557 := [monotonicity #13549 #13554]: #13556
-#5580 := (iff #5570 #5579)
-#4365 := (iff #412 #4364)
-#4358 := (iff #411 #4357)
-#4359 := [rewrite]: #4358
-#4041 := (iff #285 #4043)
-#4042 := [rewrite]: #4041
-#4366 := [monotonicity #4042 #4359]: #4365
-#5581 := [monotonicity #4366]: #5580
-#13560 := [monotonicity #5581 #13557]: #13559
-#13565 := [trans #13560 #13563]: #13564
-#13568 := [quant-intro #13565]: #13567
-#13588 := [monotonicity #13568]: #13587
-#13584 := (iff #3107 #13583)
-#13581 := (iff #3106 #13578)
-#13569 := (and #13540 #3103)
-#13572 := (and #4357 #13569)
-#13575 := (and #4043 #13572)
-#13579 := (iff #13575 #13578)
-#13580 := [rewrite]: #13579
-#13576 := (iff #3106 #13575)
-#13573 := (iff #3105 #13572)
-#13570 := (iff #3104 #13569)
-#13571 := [monotonicity #13542]: #13570
-#13574 := [monotonicity #4359 #13571]: #13573
-#13577 := [monotonicity #4042 #13574]: #13576
-#13582 := [trans #13577 #13580]: #13581
-#13585 := [quant-intro #13582]: #13584
-#13591 := [monotonicity #13585 #13588]: #13590
-#13596 := [trans #13591 #13594]: #13595
-#13599 := [monotonicity #13568 #13596]: #13598
-#13602 := [monotonicity #13599]: #13601
-#13605 := [monotonicity #13602]: #13604
-#13608 := [monotonicity #13605]: #13607
-#13611 := [monotonicity #13608]: #13610
-#13231 := (iff #12088 #13230)
-#13228 := (iff #11971 #13227)
-#13224 := (iff #3073 #13225)
-#13226 := [rewrite]: #13224
-#13221 := (iff #3066 #13222)
-#13223 := [rewrite]: #13221
-#13229 := [monotonicity #13223 #13226]: #13228
-#13232 := [monotonicity #13229]: #13231
-#13614 := [monotonicity #13232 #13611]: #13613
-#13617 := [monotonicity #13232 #13614]: #13616
-#13620 := [monotonicity #13232 #13617]: #13619
-#13623 := [monotonicity #13620]: #13622
-#13628 := [trans #13623 #13626]: #13627
-#13631 := [monotonicity #13628]: #13630
-#13638 := [monotonicity #13232 #13631]: #13637
-#13641 := [monotonicity #13232 #13638]: #13640
-#13644 := [monotonicity #13232 #13641]: #13643
-#13647 := [monotonicity #13232 #13644]: #13646
-#13634 := (iff #12698 #13511)
-#13632 := (iff #3268 #13510)
-#13633 := [rewrite]: #13632
-#13635 := [monotonicity #13633]: #13634
-#13650 := [monotonicity #13635 #13647]: #13649
-#13653 := [monotonicity #13232 #13650]: #13652
-#13658 := [trans #13653 #13656]: #13657
-#13536 := (iff #12674 #13533)
-#13521 := (or #13230 #13504)
-#13524 := (or #13230 #13521)
-#13527 := (or #13510 #13524)
-#13530 := (or #13230 #13527)
-#13534 := (iff #13530 #13533)
-#13535 := [rewrite]: #13534
-#13531 := (iff #12674 #13530)
-#13528 := (iff #12666 #13527)
-#13525 := (iff #12657 #13524)
-#13522 := (iff #12649 #13521)
-#13507 := (iff #12643 #13504)
-#13501 := (and #12299 #13498)
-#13505 := (iff #13501 #13504)
-#13506 := [rewrite]: #13505
-#13502 := (iff #12643 #13501)
-#13499 := (iff #12638 #13498)
-#13496 := (iff #12632 #13493)
-#13490 := (and #12305 #13485)
-#13494 := (iff #13490 #13493)
-#13495 := [rewrite]: #13494
-#13491 := (iff #12632 #13490)
-#13488 := (iff #12627 #13485)
-#13479 := (or #13230 #13476)
-#13482 := (or #12494 #13479)
-#13486 := (iff #13482 #13485)
-#13487 := [rewrite]: #13486
-#13483 := (iff #12627 #13482)
-#13480 := (iff #12619 #13479)
-#13477 := (iff #12613 #13476)
-#13474 := (iff #12608 #13471)
-#13368 := (or #13239 #13360)
-#13450 := (or #13368 #12557)
-#13453 := (or #12566 #13450)
-#13456 := (or #13230 #13453)
-#13459 := (or #13230 #13456)
-#13462 := (or #13230 #13459)
-#13465 := (or #13416 #13462)
-#13468 := (or #13230 #13465)
-#13472 := (iff #13468 #13471)
-#13473 := [rewrite]: #13472
-#13469 := (iff #12608 #13468)
-#13466 := (iff #12600 #13465)
-#13463 := (iff #12591 #13462)
-#13460 := (iff #12583 #13459)
-#13457 := (iff #12575 #13456)
-#13454 := (iff #12567 #13453)
-#13451 := (iff #12558 #13450)
-#13369 := (iff #12432 #13368)
-#13363 := (iff #12425 #13360)
-#13357 := (and #13334 #13352)
-#13361 := (iff #13357 #13360)
-#13362 := [rewrite]: #13361
-#13358 := (iff #12425 #13357)
-#13355 := (iff #12420 #13352)
-#13340 := (or #13256 #13324)
-#13343 := (or #12401 #13340)
-#13346 := (or #13331 #13343)
-#13349 := (or #13337 #13346)
-#13353 := (iff #13349 #13352)
-#13354 := [rewrite]: #13353
-#13350 := (iff #12420 #13349)
-#13347 := (iff #12411 #13346)
-#13344 := (iff #12402 #13343)
-#13341 := (iff #12393 #13340)
-#13325 := (iff #12386 #13324)
-#13322 := (iff #12381 #13321)
-#13319 := (iff #12374 #13318)
-#13316 := (iff #12369 #13315)
-#13313 := (iff #12355 #13310)
-#13307 := (and #13304 #12352)
-#13311 := (iff #13307 #13310)
-#13312 := [rewrite]: #13311
-#13308 := (iff #12355 #13307)
-#13305 := (iff #3218 #13304)
-#13306 := [rewrite]: #13305
-#13309 := [monotonicity #13306]: #13308
-#13314 := [trans #13309 #13312]: #13313
-#13299 := (iff #12368 #13298)
-#13296 := (iff #12349 #13295)
-#13293 := (iff #12344 #13290)
-#13284 := (or #13267 #13281)
-#13287 := (or #5579 #13284)
-#13291 := (iff #13287 #13290)
-#13292 := [rewrite]: #13291
-#13288 := (iff #12344 #13287)
-#13285 := (iff #12338 #13284)
-#13282 := (iff #3214 #13281)
-#13283 := [rewrite]: #13282
-#13277 := (iff #12337 #13267)
-#13269 := (not #13267)
-#13272 := (not #13269)
-#13275 := (iff #13272 #13267)
-#13276 := [rewrite]: #13275
-#13273 := (iff #12337 #13272)
-#13270 := (iff #3213 #13269)
-#13271 := [rewrite]: #13270
-#13274 := [monotonicity #13271]: #13273
-#13278 := [trans #13274 #13276]: #13277
-#13286 := [monotonicity #13278 #13283]: #13285
-#13289 := [monotonicity #5581 #13286]: #13288
-#13294 := [trans #13289 #13292]: #13293
-#13297 := [quant-intro #13294]: #13296
-#13300 := [monotonicity #13297]: #13299
-#13317 := [monotonicity #13300 #13314]: #13316
-#13320 := [monotonicity #13297 #13317]: #13319
-#13265 := (iff #12380 #13264)
-#13262 := (iff #3212 #13259)
-#13263 := [rewrite]: #13262
-#13266 := [monotonicity #13263]: #13265
-#13323 := [monotonicity #13266 #13320]: #13322
-#13326 := [monotonicity #13263 #13323]: #13325
-#13257 := (iff #12392 #13256)
-#13254 := (iff #12334 #13253)
-#13250 := (iff #3210 #13251)
-#13252 := [rewrite]: #13250
-#13233 := (iff #3201 #13234)
-#13235 := [rewrite]: #13233
-#13255 := [monotonicity #13235 #13252]: #13254
-#13258 := [monotonicity #13255]: #13257
-#13342 := [monotonicity #13258 #13326]: #13341
-#13345 := [monotonicity #13342]: #13344
-#13332 := (iff #12410 #13331)
-#13329 := (iff #12331 #13327)
-#13330 := [rewrite]: #13329
-#13333 := [monotonicity #13330]: #13332
-#13348 := [monotonicity #13333 #13345]: #13347
-#13338 := (iff #12419 #13337)
-#13335 := (iff #12328 #13334)
-#13248 := (iff #12325 #13245)
-#13249 := [rewrite]: #13248
-#13242 := (iff #12322 #13243)
-#13244 := [rewrite]: #13242
-#13336 := [monotonicity #13244 #13249]: #13335
-#13339 := [monotonicity #13336]: #13338
-#13351 := [monotonicity #13339 #13348]: #13350
-#13356 := [trans #13351 #13354]: #13355
-#13359 := [monotonicity #13336 #13356]: #13358
-#13364 := [trans #13359 #13362]: #13363
-#13240 := (iff #12431 #13239)
-#13237 := (iff #3202 #13236)
-#13238 := [monotonicity #13226 #13235]: #13237
-#13241 := [monotonicity #13238]: #13240
-#13370 := [monotonicity #13241 #13364]: #13369
-#13452 := [monotonicity #13370]: #13451
-#13455 := [monotonicity #13452]: #13454
-#13458 := [monotonicity #13232 #13455]: #13457
-#13461 := [monotonicity #13232 #13458]: #13460
-#13464 := [monotonicity #13232 #13461]: #13463
-#13448 := (iff #12599 #13416)
-#13446 := (iff #3248 #13417)
-#13447 := [rewrite]: #13446
-#13449 := [monotonicity #13447]: #13448
-#13467 := [monotonicity #13449 #13464]: #13466
-#13470 := [monotonicity #13232 #13467]: #13469
-#13475 := [trans #13470 #13473]: #13474
-#13444 := (iff #12543 #13441)
-#13429 := (or #13230 #13411)
-#13432 := (or #13230 #13429)
-#13435 := (or #13417 #13432)
-#13438 := (or #13230 #13435)
-#13442 := (iff #13438 #13441)
-#13443 := [rewrite]: #13442
-#13439 := (iff #12543 #13438)
-#13436 := (iff #12535 #13435)
-#13433 := (iff #12526 #13432)
-#13430 := (iff #12518 #13429)
-#13414 := (iff #12512 #13411)
-#13408 := (and #12299 #13405)
-#13412 := (iff #13408 #13411)
-#13413 := [rewrite]: #13412
-#13409 := (iff #12512 #13408)
-#13406 := (iff #12507 #13405)
-#13403 := (iff #12500 #13400)
-#13397 := (and #12305 #13392)
-#13401 := (iff #13397 #13400)
-#13402 := [rewrite]: #13401
-#13398 := (iff #12500 #13397)
-#13395 := (iff #12495 #13392)
-#13371 := (or #12440 #13368)
-#13374 := (or #12449 #13371)
-#13377 := (or #13365 #13374)
-#13380 := (or #12467 #13377)
-#13383 := (or #12476 #13380)
-#13386 := (or #12485 #13383)
-#13389 := (or #12494 #13386)
-#13393 := (iff #13389 #13392)
-#13394 := [rewrite]: #13393
-#13390 := (iff #12495 #13389)
-#13387 := (iff #12486 #13386)
-#13384 := (iff #12477 #13383)
-#13381 := (iff #12468 #13380)
-#13378 := (iff #12459 #13377)
-#13375 := (iff #12450 #13374)
-#13372 := (iff #12441 #13371)
-#13373 := [monotonicity #13370]: #13372
-#13376 := [monotonicity #13373]: #13375
-#13366 := (iff #12458 #13365)
-#13367 := [monotonicity #13226]: #13366
-#13379 := [monotonicity #13367 #13376]: #13378
-#13382 := [monotonicity #13379]: #13381
-#13385 := [monotonicity #13382]: #13384
-#13388 := [monotonicity #13385]: #13387
-#13391 := [monotonicity #13388]: #13390
-#13396 := [trans #13391 #13394]: #13395
-#13399 := [monotonicity #13396]: #13398
-#13404 := [trans #13399 #13402]: #13403
-#13407 := [monotonicity #13404]: #13406
-#13410 := [monotonicity #13407]: #13409
-#13415 := [trans #13410 #13413]: #13414
-#13431 := [monotonicity #13232 #13415]: #13430
-#13434 := [monotonicity #13232 #13431]: #13433
-#13427 := (iff #12534 #13417)
-#13422 := (not #13416)
-#13425 := (iff #13422 #13417)
-#13426 := [rewrite]: #13425
-#13423 := (iff #12534 #13422)
-#13420 := (iff #3191 #13416)
-#13421 := [rewrite]: #13420
-#13424 := [monotonicity #13421]: #13423
-#13428 := [trans #13424 #13426]: #13427
-#13437 := [monotonicity #13428 #13434]: #13436
-#13440 := [monotonicity #13232 #13437]: #13439
-#13445 := [trans #13440 #13443]: #13444
-#13478 := [monotonicity #13445 #13475]: #13477
-#13481 := [monotonicity #13232 #13478]: #13480
-#13484 := [monotonicity #13481]: #13483
-#13489 := [trans #13484 #13487]: #13488
-#13492 := [monotonicity #13489]: #13491
-#13497 := [trans #13492 #13495]: #13496
-#13500 := [monotonicity #13497]: #13499
-#13503 := [monotonicity #13500]: #13502
-#13508 := [trans #13503 #13506]: #13507
-#13523 := [monotonicity #13232 #13508]: #13522
-#13526 := [monotonicity #13232 #13523]: #13525
-#13519 := (iff #12665 #13510)
-#13514 := (not #13511)
-#13517 := (iff #13514 #13510)
-#13518 := [rewrite]: #13517
-#13515 := (iff #12665 #13514)
-#13512 := (iff #3180 #13511)
-#13513 := [rewrite]: #13512
-#13516 := [monotonicity #13513]: #13515
-#13520 := [trans #13516 #13518]: #13519
-#13529 := [monotonicity #13520 #13526]: #13528
-#13532 := [monotonicity #13232 #13529]: #13531
-#13537 := [trans #13532 #13535]: #13536
-#13661 := [monotonicity #13537 #13658]: #13660
-#13791 := [monotonicity #13232 #13661]: #13790
-#13794 := [monotonicity #13791]: #13793
-#13797 := [monotonicity #13794]: #13796
-#13800 := [monotonicity #13797]: #13799
-#13803 := [monotonicity #13800]: #13802
-#13806 := [monotonicity #13803]: #13805
-#13809 := [monotonicity #13806]: #13808
-#13684 := (iff #12786 #13683)
-#13681 := (iff #12260 #12254)
-#13673 := (and true #12254)
-#13676 := (and true #13673)
-#13679 := (iff #13676 #12254)
-#13680 := [rewrite]: #13679
-#13677 := (iff #12260 #13676)
-#13674 := (iff #12257 #13673)
-#13669 := (iff #3161 true)
-#13664 := (forall (vars (?x783 T5)) (:pat #3159) true)
-#13667 := (iff #13664 true)
-#13668 := [elim-unused]: #13667
-#13665 := (iff #3161 #13664)
-#13662 := (iff #3160 true)
-#13663 := [rewrite]: #13662
-#13666 := [quant-intro #13663]: #13665
-#13670 := [trans #13666 #13668]: #13669
-#13675 := [monotonicity #13670]: #13674
-#13671 := (iff #3157 true)
-#13672 := [rewrite]: #13671
-#13678 := [monotonicity #13672 #13675]: #13677
-#13682 := [trans #13678 #13680]: #13681
-#13685 := [monotonicity #13682]: #13684
-#13812 := [monotonicity #13685 #13809]: #13811
-#13815 := [monotonicity #13685 #13812]: #13814
-#13818 := [monotonicity #13232 #13815]: #13817
-#13821 := [monotonicity #13232 #13818]: #13820
-#13824 := [monotonicity #13232 #13821]: #13823
-#13827 := [monotonicity #13232 #13824]: #13826
-#13701 := (iff #12842 #13700)
-#13698 := (iff #11992 #13695)
-#13692 := (and #13689 #11989)
-#13696 := (iff #13692 #13695)
-#13697 := [rewrite]: #13696
-#13693 := (iff #11992 #13692)
-#13690 := (iff #3081 #13689)
-#13691 := [rewrite]: #13690
-#13694 := [monotonicity #13691]: #13693
-#13699 := [trans #13694 #13697]: #13698
-#13702 := [monotonicity #13699]: #13701
-#13830 := [monotonicity #13702 #13827]: #13829
-#13735 := (iff #12851 #13734)
-#13732 := (iff #11986 #13731)
-#13729 := (iff #11981 #13726)
-#13720 := (or #13703 #13717)
-#13723 := (or #5579 #13720)
-#13727 := (iff #13723 #13726)
-#13728 := [rewrite]: #13727
-#13724 := (iff #11981 #13723)
-#13721 := (iff #11975 #13720)
-#13718 := (iff #3077 #13717)
-#13719 := [rewrite]: #13718
-#13713 := (iff #11974 #13703)
-#13705 := (not #13703)
-#13708 := (not #13705)
-#13711 := (iff #13708 #13703)
-#13712 := [rewrite]: #13711
-#13709 := (iff #11974 #13708)
-#13706 := (iff #3076 #13705)
-#13707 := [rewrite]: #13706
-#13710 := [monotonicity #13707]: #13709
-#13714 := [trans #13710 #13712]: #13713
-#13722 := [monotonicity #13714 #13719]: #13721
-#13725 := [monotonicity #5581 #13722]: #13724
-#13730 := [trans #13725 #13728]: #13729
-#13733 := [quant-intro #13730]: #13732
-#13736 := [monotonicity #13733]: #13735
-#13833 := [monotonicity #13736 #13830]: #13832
-#13741 := (iff #12860 #13740)
-#13738 := (iff #3075 #13737)
-#13739 := [rewrite]: #13738
-#13742 := [monotonicity #13739]: #13741
-#13836 := [monotonicity #13742 #13833]: #13835
-#13839 := [monotonicity #13232 #13836]: #13838
-#13753 := (iff #12877 #13752)
-#13750 := (iff #3072 #13749)
-#13747 := (iff #3071 #13746)
-#13748 := [rewrite]: #13747
-#13744 := (iff #3070 #13743)
-#13745 := [rewrite]: #13744
-#13751 := [monotonicity #13745 #13748]: #13750
-#13754 := [monotonicity #13751]: #13753
-#13842 := [monotonicity #13754 #13839]: #13841
-#13763 := (iff #12886 #13762)
-#13760 := (iff #3068 #13759)
-#13757 := (iff #3067 #13755)
-#13758 := [rewrite]: #13757
-#13761 := [monotonicity #13223 #13758]: #13760
-#13764 := [monotonicity #13761]: #13763
-#13845 := [monotonicity #13764 #13842]: #13844
-#13776 := (iff #12895 #13775)
-#13773 := (iff #3064 #13772)
-#13770 := (iff #3063 #13768)
-#13771 := [rewrite]: #13770
-#13766 := (iff #3062 #13765)
-#13767 := [rewrite]: #13766
-#13774 := [monotonicity #13767 #13771]: #13773
-#13777 := [monotonicity #13774]: #13776
-#13848 := [monotonicity #13777 #13845]: #13847
-#13787 := (iff #12904 #13786)
-#13784 := (iff #11968 #13781)
-#13782 := (iff #13778 #13781)
-#13783 := [rewrite]: #13782
-#13779 := (iff #11968 #13778)
-#13219 := (iff #2975 #13218)
-#13220 := [rewrite]: #13219
-#13780 := [monotonicity #13220]: #13779
-#13785 := [trans #13780 #13783]: #13784
-#13788 := [monotonicity #13785]: #13787
-#13851 := [monotonicity #13788 #13848]: #13850
-#13856 := [trans #13851 #13854]: #13855
-#13859 := [monotonicity #13780 #13856]: #13858
-#13864 := [trans #13859 #13862]: #13863
-#13215 := (iff #12916 #13214)
-#13212 := (iff #11963 #13211)
-#13209 := (iff #11958 #13206)
-#13200 := (or #13184 #13196)
-#13203 := (or #5579 #13200)
-#13207 := (iff #13203 #13206)
-#13208 := [rewrite]: #13207
-#13204 := (iff #11958 #13203)
-#13201 := (iff #11952 #13200)
-#13195 := (iff #3055 #13196)
-#13199 := [rewrite]: #13195
-#13193 := (iff #11951 #13184)
-#13185 := (not #13184)
-#13188 := (not #13185)
-#13191 := (iff #13188 #13184)
-#13192 := [rewrite]: #13191
-#13189 := (iff #11951 #13188)
-#13186 := (iff #3052 #13185)
-#13187 := [rewrite]: #13186
-#13190 := [monotonicity #13187]: #13189
-#13194 := [trans #13190 #13192]: #13193
-#13202 := [monotonicity #13194 #13199]: #13201
-#13205 := [monotonicity #5581 #13202]: #13204
-#13210 := [trans #13205 #13208]: #13209
-#13213 := [quant-intro #13210]: #13212
-#13216 := [monotonicity #13213]: #13215
-#13867 := [monotonicity #13216 #13864]: #13866
-#13870 := [monotonicity #13213 #13867]: #13869
-#13182 := (iff #12928 #13181)
-#13179 := (iff #3051 #13178)
-#13180 := [rewrite]: #13179
-#13183 := [monotonicity #13180]: #13182
-#13873 := [monotonicity #13183 #13870]: #13872
-#13876 := [monotonicity #13180 #13873]: #13875
-#13176 := (iff #12940 false)
-#11995 := (iff #3086 false)
-#11996 := [rewrite]: #11995
-#13174 := (iff #12940 #3086)
-#13172 := (iff #11948 true)
-#12286 := (and true true)
-#13167 := (and true #12286)
-#13170 := (iff #13167 true)
-#13171 := [rewrite]: #13170
-#13168 := (iff #11948 #13167)
-#13165 := (iff #11945 #12286)
-#13163 := (iff #3047 true)
-#13164 := [rewrite]: #13163
-#13161 := (iff #3046 true)
-#13162 := [rewrite]: #13161
-#13166 := [monotonicity #13162 #13164]: #13165
-#13169 := [monotonicity #13162 #13166]: #13168
-#13173 := [trans #13169 #13171]: #13172
-#13175 := [monotonicity #13173]: #13174
-#13177 := [trans #13175 #11996]: #13176
-#13879 := [monotonicity #13177 #13876]: #13878
-#13882 := [monotonicity #13879]: #13881
-#13885 := [monotonicity #13882]: #13884
-#13888 := [monotonicity #13885]: #13887
-#13891 := [monotonicity #13888]: #13890
+#13893 := (iff #12162 #13892)
+#13890 := (iff #3116 #13889)
+#13891 := [rewrite]: #13890
 #13894 := [monotonicity #13891]: #13893
 #13899 := [trans #13894 #13897]: #13898
 #13902 := [monotonicity #13899]: #13901
-#13907 := [trans #13902 #13905]: #13906
+#14030 := [monotonicity #13902 #14027]: #14029
+#13935 := (iff #13051 #13934)
+#13932 := (iff #12156 #13931)
+#13929 := (iff #12151 #13926)
+#13920 := (or #13903 #13917)
+#13923 := (or #5654 #13920)
+#13927 := (iff #13923 #13926)
+#13928 := [rewrite]: #13927
+#13924 := (iff #12151 #13923)
+#13921 := (iff #12145 #13920)
+#13918 := (iff #3112 #13917)
+#13919 := [rewrite]: #13918
+#13913 := (iff #12144 #13903)
+#13905 := (not #13903)
+#13908 := (not #13905)
+#13911 := (iff #13908 #13903)
+#13912 := [rewrite]: #13911
+#13909 := (iff #12144 #13908)
+#13906 := (iff #3111 #13905)
+#13907 := [rewrite]: #13906
 #13910 := [monotonicity #13907]: #13909
-#13913 := [monotonicity #13910]: #13912
-#13918 := [trans #13913 #13916]: #13917
-#13921 := [monotonicity #13918]: #13920
-#13924 := [monotonicity #13921]: #13923
-#13159 := (iff #13021 #13158)
-#13156 := (iff #3028 #13155)
-#13153 := (iff #3027 #13150)
-#13154 := [rewrite]: #13153
-#13147 := (iff #3026 #13148)
-#13149 := [rewrite]: #13147
-#13157 := [monotonicity #13149 #13154]: #13156
-#13160 := [monotonicity #13157]: #13159
-#14005 := [monotonicity #13160 #13924]: #14004
-#14008 := [monotonicity #14005]: #14007
-#14011 := [monotonicity #14008]: #14010
-#14014 := [monotonicity #14011]: #14013
-#14017 := [monotonicity #14014]: #14016
-#13935 := (iff #13066 #13934)
-#13932 := (iff #3012 #13931)
-#13929 := (iff #3011 #13925)
-#13930 := [rewrite]: #13929
+#13914 := [trans #13910 #13912]: #13913
+#13922 := [monotonicity #13914 #13919]: #13921
+#13925 := [monotonicity #5656 #13922]: #13924
+#13930 := [trans #13925 #13928]: #13929
 #13933 := [quant-intro #13930]: #13932
 #13936 := [monotonicity #13933]: #13935
-#14020 := [monotonicity #13936 #14017]: #14019
-#14023 := [monotonicity #14020]: #14022
-#14026 := [monotonicity #14023]: #14025
-#13941 := (iff #13093 #13940)
-#13938 := (iff #11896 #13937)
+#14033 := [monotonicity #13936 #14030]: #14032
+#13941 := (iff #13060 #13940)
+#13938 := (iff #3110 #13937)
 #13939 := [rewrite]: #13938
 #13942 := [monotonicity #13939]: #13941
-#14029 := [monotonicity #13942 #14026]: #14028
-#13948 := (iff #13102 #13217)
-#13943 := (not #13218)
-#13946 := (iff #13943 #13217)
-#13947 := [rewrite]: #13946
-#13944 := (iff #13102 #13943)
-#13945 := [monotonicity #13220]: #13944
-#13949 := [trans #13945 #13947]: #13948
-#14032 := [monotonicity #13949 #14029]: #14031
-#13959 := (iff #13111 #13950)
-#13951 := (not #13950)
-#13954 := (not #13951)
-#13957 := (iff #13954 #13950)
+#14036 := [monotonicity #13942 #14033]: #14035
+#14039 := [monotonicity #13432 #14036]: #14038
+#13953 := (iff #13077 #13952)
+#13950 := (iff #3107 #13949)
+#13947 := (iff #3106 #13946)
+#13948 := [rewrite]: #13947
+#13944 := (iff #3105 #13943)
+#13945 := [rewrite]: #13944
+#13951 := [monotonicity #13945 #13948]: #13950
+#13954 := [monotonicity #13951]: #13953
+#14042 := [monotonicity #13954 #14039]: #14041
+#13963 := (iff #13086 #13962)
+#13960 := (iff #3103 #13959)
+#13957 := (iff #3102 #13955)
 #13958 := [rewrite]: #13957
-#13955 := (iff #13111 #13954)
-#13952 := (iff #2974 #13951)
-#13953 := [rewrite]: #13952
-#13956 := [monotonicity #13953]: #13955
-#13960 := [trans #13956 #13958]: #13959
-#14035 := [monotonicity #13960 #14032]: #14034
-#13973 := (iff #13120 #13972)
-#13970 := (iff #2972 #13969)
-#13967 := (iff #2971 #13964)
-#13968 := [rewrite]: #13967
-#13961 := (iff #2970 #13962)
-#13963 := [rewrite]: #13961
-#13971 := [monotonicity #13963 #13968]: #13970
-#13974 := [monotonicity #13971]: #13973
-#14038 := [monotonicity #13974 #14035]: #14037
-#13987 := (iff #13129 #13986)
-#13984 := (iff #2968 #13983)
-#13981 := (iff #2967 #13978)
-#13982 := [rewrite]: #13981
-#13975 := (iff #2966 #13976)
-#13977 := [rewrite]: #13975
-#13985 := [monotonicity #13977 #13982]: #13984
+#13961 := [monotonicity #13423 #13958]: #13960
+#13964 := [monotonicity #13961]: #13963
+#14045 := [monotonicity #13964 #14042]: #14044
+#13976 := (iff #13095 #13975)
+#13973 := (iff #3099 #13972)
+#13970 := (iff #3098 #13968)
+#13971 := [rewrite]: #13970
+#13966 := (iff #3097 #13965)
+#13967 := [rewrite]: #13966
+#13974 := [monotonicity #13967 #13971]: #13973
+#13977 := [monotonicity #13974]: #13976
+#14048 := [monotonicity #13977 #14045]: #14047
+#13987 := (iff #13104 #13986)
+#13984 := (iff #12138 #13981)
+#13982 := (iff #13978 #13981)
+#13983 := [rewrite]: #13982
+#13979 := (iff #12138 #13978)
+#13419 := (iff #3003 #13418)
+#13420 := [rewrite]: #13419
+#13980 := [monotonicity #13420]: #13979
+#13985 := [trans #13980 #13983]: #13984
 #13988 := [monotonicity #13985]: #13987
-#14041 := [monotonicity #13988 #14038]: #14040
-#14001 := (iff #13138 #14000)
-#13998 := (iff #2964 #13997)
-#13995 := (iff #2963 #13992)
-#13996 := [rewrite]: #13995
-#13989 := (iff #2962 #13990)
-#13991 := [rewrite]: #13989
-#13999 := [monotonicity #13991 #13996]: #13998
-#14002 := [monotonicity #13999]: #14001
-#14044 := [monotonicity #14002 #14041]: #14043
-#14049 := [trans #14044 #14047]: #14048
-#14052 := [monotonicity #14049]: #14051
-#13145 := (iff #3327 #13144)
-#13142 := (iff #3326 #13139)
-#13135 := (implies #2964 #13130)
-#13140 := (iff #13135 #13139)
-#13141 := [rewrite]: #13140
-#13136 := (iff #3326 #13135)
-#13133 := (iff #3325 #13130)
-#13126 := (implies #2968 #13121)
-#13131 := (iff #13126 #13130)
-#13132 := [rewrite]: #13131
-#13127 := (iff #3325 #13126)
-#13124 := (iff #3324 #13121)
-#13117 := (implies #2972 #13112)
-#13122 := (iff #13117 #13121)
-#13123 := [rewrite]: #13122
-#13118 := (iff #3324 #13117)
-#13115 := (iff #3323 #13112)
-#13108 := (implies #2974 #13103)
-#13113 := (iff #13108 #13112)
-#13114 := [rewrite]: #13113
-#13109 := (iff #3323 #13108)
-#13106 := (iff #3322 #13103)
-#13099 := (implies #2975 #13094)
-#13104 := (iff #13099 #13103)
-#13105 := [rewrite]: #13104
-#13100 := (iff #3322 #13099)
-#13097 := (iff #3321 #13094)
-#13090 := (implies #11896 #13085)
-#13095 := (iff #13090 #13094)
-#13096 := [rewrite]: #13095
-#13091 := (iff #3321 #13090)
-#13088 := (iff #3320 #13085)
-#13081 := (implies #11899 #13076)
-#13086 := (iff #13081 #13085)
-#13087 := [rewrite]: #13086
-#13082 := (iff #3320 #13081)
-#13079 := (iff #3319 #13076)
-#13072 := (implies #11908 #13067)
-#13077 := (iff #13072 #13076)
-#13078 := [rewrite]: #13077
-#13073 := (iff #3319 #13072)
-#13070 := (iff #3318 #13067)
-#13063 := (implies #3012 #13058)
-#13068 := (iff #13063 #13067)
-#13069 := [rewrite]: #13068
-#13064 := (iff #3318 #13063)
-#13061 := (iff #3317 #13058)
-#13054 := (implies #3016 #13049)
-#13059 := (iff #13054 #13058)
-#13060 := [rewrite]: #13059
-#13055 := (iff #3317 #13054)
-#13052 := (iff #3316 #13049)
-#13045 := (implies #3017 #13040)
-#13050 := (iff #13045 #13049)
-#13051 := [rewrite]: #13050
-#13046 := (iff #3316 #13045)
-#13043 := (iff #3315 #13040)
-#13036 := (implies #3020 #13031)
-#13041 := (iff #13036 #13040)
-#13042 := [rewrite]: #13041
-#13037 := (iff #3315 #13036)
-#13034 := (iff #3314 #13031)
-#13027 := (implies #11922 #13022)
-#13032 := (iff #13027 #13031)
-#13033 := [rewrite]: #13032
-#13028 := (iff #3314 #13027)
-#13025 := (iff #3313 #13022)
-#13018 := (implies #3028 #13015)
-#13023 := (iff #13018 #13022)
-#13024 := [rewrite]: #13023
-#13019 := (iff #3313 #13018)
-#13016 := (iff #3312 #13015)
-#13013 := (iff #3311 #13010)
-#13006 := (implies #11925 #13003)
-#13011 := (iff #13006 #13010)
-#13012 := [rewrite]: #13011
-#13007 := (iff #3311 #13006)
-#13004 := (iff #3310 #13003)
-#13001 := (iff #3309 #12998)
-#12994 := (implies #11934 #12991)
-#12999 := (iff #12994 #12998)
-#13000 := [rewrite]: #12999
-#12995 := (iff #3309 #12994)
-#12992 := (iff #3308 #12991)
-#12989 := (iff #3307 #12986)
-#12982 := (implies #11940 #12977)
-#12987 := (iff #12982 #12986)
-#12988 := [rewrite]: #12987
-#12983 := (iff #3307 #12982)
-#12980 := (iff #3306 #12977)
-#12973 := (implies #3042 #12968)
-#12978 := (iff #12973 #12977)
-#12979 := [rewrite]: #12978
-#12974 := (iff #3306 #12973)
-#12971 := (iff #3305 #12968)
-#12964 := (implies #3043 #12959)
-#12969 := (iff #12964 #12968)
-#12970 := [rewrite]: #12969
-#12965 := (iff #3305 #12964)
-#12962 := (iff #3304 #12959)
-#12955 := (implies #3044 #12950)
-#12960 := (iff #12955 #12959)
-#12961 := [rewrite]: #12960
-#12956 := (iff #3304 #12955)
-#12953 := (iff #3303 #12950)
-#12946 := (implies #3045 #12941)
-#12951 := (iff #12946 #12950)
-#12952 := [rewrite]: #12951
-#12947 := (iff #3303 #12946)
-#12944 := (iff #3302 #12941)
-#12937 := (implies #11948 #12934)
-#12942 := (iff #12937 #12941)
-#12943 := [rewrite]: #12942
-#12938 := (iff #3302 #12937)
-#12935 := (iff #3301 #12934)
-#12932 := (iff #3300 #12929)
-#12925 := (implies #3051 #12922)
-#12930 := (iff #12925 #12929)
-#12931 := [rewrite]: #12930
-#12926 := (iff #3300 #12925)
-#12923 := (iff #3299 #12922)
-#12920 := (iff #3298 #12917)
-#12913 := (implies #11963 #12910)
-#12918 := (iff #12913 #12917)
-#12919 := [rewrite]: #12918
-#12914 := (iff #3298 #12913)
-#12911 := (iff #3297 #12910)
-#12908 := (iff #3296 #12905)
-#12901 := (implies #11968 #12896)
-#12906 := (iff #12901 #12905)
-#12907 := [rewrite]: #12906
-#12902 := (iff #3296 #12901)
-#12899 := (iff #3295 #12896)
-#12892 := (implies #3064 #12887)
-#12897 := (iff #12892 #12896)
-#12898 := [rewrite]: #12897
-#12893 := (iff #3295 #12892)
-#12890 := (iff #3294 #12887)
-#12883 := (implies #3068 #12878)
-#12888 := (iff #12883 #12887)
-#12889 := [rewrite]: #12888
-#12884 := (iff #3294 #12883)
-#12881 := (iff #3293 #12878)
-#12874 := (implies #3072 #12869)
-#12879 := (iff #12874 #12878)
-#12880 := [rewrite]: #12879
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-#12857 := (implies #3075 #12852)
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-#12858 := (iff #3291 #12857)
-#12855 := (iff #3290 #12852)
-#12848 := (implies #11986 #12843)
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-#12839 := (implies #11992 #12834)
-#12844 := (iff #12839 #12843)
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-#12840 := (iff #3289 #12839)
-#12837 := (iff #3288 #12834)
-#12831 := (implies #11971 #12819)
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-#12829 := (iff #3287 #12819)
-#12824 := (and true #12819)
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-#12828 := [rewrite]: #12827
-#12825 := (iff #3287 #12824)
-#12822 := (iff #3286 #12819)
-#12816 := (implies #11971 #12811)
+#14051 := [monotonicity #13988 #14048]: #14050
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+#14064 := [trans #14059 #14062]: #14063
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+#13412 := (iff #12133 #13411)
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+#13400 := (or #13384 #13396)
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+#13405 := [monotonicity #5656 #13402]: #13404
+#13410 := [trans #13405 #13408]: #13409
+#13413 := [quant-intro #13410]: #13412
+#13416 := [monotonicity #13413]: #13415
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+#14070 := [monotonicity #13413 #14067]: #14069
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+#13380 := [rewrite]: #13379
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+#13376 := (iff #13140 false)
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+#13369 := [monotonicity #13362 #13366]: #13368
+#13373 := [trans #13369 #13371]: #13372
+#13375 := [monotonicity #13373]: #13374
+#13377 := [trans #13375 #12166]: #13376
+#14079 := [monotonicity #13377 #14076]: #14078
+#14082 := [monotonicity #14079]: #14081
+#14085 := [monotonicity #14082]: #14084
+#14088 := [monotonicity #14085]: #14087
+#14091 := [monotonicity #14088]: #14090
+#14094 := [monotonicity #14091]: #14093
+#14099 := [trans #14094 #14097]: #14098
+#14102 := [monotonicity #14099]: #14101
+#14107 := [trans #14102 #14105]: #14106
+#14110 := [monotonicity #14107]: #14109
+#14113 := [monotonicity #14110]: #14112
+#14118 := [trans #14113 #14116]: #14117
+#14121 := [monotonicity #14118]: #14120
+#14124 := [monotonicity #14121]: #14123
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+#13356 := (iff #3059 #13355)
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+#13354 := [rewrite]: #13353
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+#13349 := [rewrite]: #13347
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+#13360 := [monotonicity #13357]: #13359
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+#14208 := [monotonicity #14205]: #14207
+#14211 := [monotonicity #14208]: #14210
+#14214 := [monotonicity #14211]: #14213
+#14217 := [monotonicity #14214]: #14216
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+#14130 := [rewrite]: #14129
+#14133 := [quant-intro #14130]: #14132
+#14136 := [monotonicity #14133]: #14135
+#14220 := [monotonicity #14136 #14217]: #14219
+#14223 := [monotonicity #14220]: #14222
+#14226 := [monotonicity #14223]: #14225
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+#14142 := [monotonicity #14139]: #14141
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+#14143 := (not #13418)
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+#14147 := [rewrite]: #14146
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+#14145 := [monotonicity #13420]: #14144
+#14149 := [trans #14145 #14147]: #14148
+#14232 := [monotonicity #14149 #14229]: #14231
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+#14151 := (not #14150)
+#14154 := (not #14151)
+#14157 := (iff #14154 #14150)
+#14158 := [rewrite]: #14157
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+#14153 := [rewrite]: #14152
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+#14160 := [trans #14156 #14158]: #14159
+#14235 := [monotonicity #14160 #14232]: #14234
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+#14163 := [rewrite]: #14161
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+#14174 := [monotonicity #14171]: #14173
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+#14177 := [rewrite]: #14175
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+#14188 := [monotonicity #14185]: #14187
+#14241 := [monotonicity #14188 #14238]: #14240
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+#14196 := [rewrite]: #14195
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+#14191 := [rewrite]: #14189
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+#14202 := [monotonicity #14199]: #14201
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+#14249 := [trans #14244 #14247]: #14248
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+#13024 := (and true #13019)
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+#12244 := (iff #3148 #12241)
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+#12243 := [rewrite]: #12242
+#12238 := (iff #3148 #12237)
+#12235 := (iff #3147 #12232)
+#12228 := (implies #12184 #12223)
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+#12226 := (iff #3146 #12223)
+#12219 := (implies #12187 #12216)
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+#12208 := (iff #3144 #12207)
+#12205 := (iff #3143 #3142)
+#12206 := [rewrite]: #12205
+#12203 := (iff #3137 #12202)
+#12200 := (iff #3136 #12197)
+#12194 := (implies #421 #12191)
+#12198 := (iff #12194 #12197)
+#12199 := [rewrite]: #12198
+#12195 := (iff #3136 #12194)
+#12192 := (iff #3135 #12191)
+#12193 := [rewrite]: #12192
+#12196 := [monotonicity #12193]: #12195
+#12201 := [trans #12196 #12199]: #12200
+#12204 := [quant-intro #12201]: #12203
+#12209 := [monotonicity #12204 #12206]: #12208
+#12215 := [trans #12209 #12213]: #12214
+#12218 := [monotonicity #12204 #12215]: #12217
+#12188 := (iff #3132 #12187)
+#12189 := [rewrite]: #12188
+#12221 := [monotonicity #12189 #12218]: #12220
+#12227 := [trans #12221 #12225]: #12226
+#12185 := (iff #3130 #12184)
+#12186 := [rewrite]: #12185
+#12230 := [monotonicity #12186 #12227]: #12229
+#12236 := [trans #12230 #12234]: #12235
+#12182 := (iff #3128 #12181)
+#12183 := [rewrite]: #12182
+#12239 := [monotonicity #12183 #12236]: #12238
+#12245 := [trans #12239 #12243]: #12244
+#12179 := (iff #3126 #12178)
+#12180 := [rewrite]: #12179
+#12248 := [monotonicity #12180 #12245]: #12247
+#12254 := [trans #12248 #12252]: #12253
+#12142 := (iff #3109 #12141)
+#12143 := [rewrite]: #12142
+#12257 := [monotonicity #12143 #12254]: #12256
+#12263 := [trans #12257 #12261]: #12262
+#12266 := [monotonicity #12143 #12263]: #12265
+#12271 := [trans #12266 #12269]: #12270
+#12274 := [monotonicity #12143 #12271]: #12273
+#12279 := [trans #12274 #12277]: #12278
+#10871 := (iff #2507 #10869)
+#10872 := [rewrite]: #10871
+#12282 := [monotonicity #10872 #12279]: #12281
+#12288 := [trans #12282 #12286]: #12287
+#12291 := [monotonicity #10872 #12288]: #12290
+#12294 := [monotonicity #12143 #12291]: #12293
+#12299 := [trans #12294 #12297]: #12298
+#12302 := [monotonicity #12143 #12299]: #12301
+#12307 := [trans #12302 #12305]: #12306
+#12881 := [monotonicity #12143 #12307]: #12880
+#12886 := [trans #12881 #12884]: #12885
+#12889 := [monotonicity #12143 #12886]: #12888
+#12894 := [trans #12889 #12892]: #12893
+#12897 := [monotonicity #12894]: #12896
+#12903 := [trans #12897 #12901]: #12902
+#12906 := [monotonicity #12143 #12903]: #12905
+#12911 := [trans #12906 #12909]: #12910
+#12877 := (iff #3311 #12874)
+#12871 := (implies #12141 #12866)
+#12875 := (iff #12871 #12874)
+#12876 := [rewrite]: #12875
+#12872 := (iff #3311 #12871)
+#12869 := (iff #3310 #12866)
+#12862 := (implies #3221 #12857)
+#12867 := (iff #12862 #12866)
+#12868 := [rewrite]: #12867
+#12863 := (iff #3310 #12862)
+#12860 := (iff #3309 #12857)
+#12854 := (implies #12141 #12849)
+#12858 := (iff #12854 #12857)
+#12859 := [rewrite]: #12858
+#12855 := (iff #3309 #12854)
+#12852 := (iff #3308 #12849)
+#12846 := (implies #12141 #12843)
+#12850 := (iff #12846 #12849)
+#12851 := [rewrite]: #12850
+#12847 := (iff #3308 #12846)
+#12844 := (iff #3307 #12843)
+#12841 := (iff #3306 #12838)
+#12835 := (implies #12490 #12832)
+#12839 := (iff #12835 #12838)
+#12840 := [rewrite]: #12839
+#12836 := (iff #3306 #12835)
+#12833 := (iff #3305 #12832)
+#12830 := (iff #3304 #12827)
+#12824 := (implies #12496 #12819)
+#12828 := (iff #12824 #12827)
+#12829 := [rewrite]: #12828
+#12825 := (iff #3304 #12824)
+#12822 := (iff #3303 #12819)
+#12816 := (implies #12141 #12813)
 #12820 := (iff #12816 #12819)
 #12821 := [rewrite]: #12820
-#12817 := (iff #3286 #12816)
-#12814 := (iff #3285 #12811)
-#12808 := (implies #11971 #12803)
-#12812 := (iff #12808 #12811)
-#12813 := [rewrite]: #12812
-#12809 := (iff #3285 #12808)
-#12806 := (iff #3284 #12803)
-#12800 := (implies #11971 #12795)
-#12804 := (iff #12800 #12803)
-#12805 := [rewrite]: #12804
-#12801 := (iff #3284 #12800)
-#12798 := (iff #3283 #12795)
-#12792 := (implies #12260 #12787)
-#12796 := (iff #12792 #12795)
-#12797 := [rewrite]: #12796
-#12793 := (iff #3283 #12792)
-#12790 := (iff #3282 #12787)
-#12783 := (implies #12260 #12778)
-#12788 := (iff #12783 #12787)
-#12789 := [rewrite]: #12788
-#12784 := (iff #3282 #12783)
-#12781 := (iff #3281 #12778)
-#12775 := (implies #12003 #12770)
-#12779 := (iff #12775 #12778)
-#12780 := [rewrite]: #12779
-#12776 := (iff #3281 #12775)
-#12773 := (iff #3280 #12770)
-#12766 := (implies #3170 #12761)
-#12771 := (iff #12766 #12770)
-#12772 := [rewrite]: #12771
-#12767 := (iff #3280 #12766)
-#12764 := (iff #3279 #12761)
-#12757 := (implies #3171 #12752)
-#12762 := (iff #12757 #12761)
-#12763 := [rewrite]: #12762
-#12758 := (iff #3279 #12757)
-#12755 := (iff #3278 #12752)
-#12748 := (implies #3172 #12743)
-#12753 := (iff #12748 #12752)
-#12754 := [rewrite]: #12753
-#12749 := (iff #3278 #12748)
-#12746 := (iff #3277 #12743)
-#12739 := (implies #3173 #12734)
-#12744 := (iff #12739 #12743)
+#12817 := (iff #3303 #12816)
+#12814 := (iff #3302 #12813)
+#12811 := (iff #3301 #12808)
+#12805 := (implies #12141 #12800)
+#12809 := (iff #12805 #12808)
+#12810 := [rewrite]: #12809
+#12806 := (iff #3301 #12805)
+#12803 := (iff #3300 #12800)
+#12796 := (implies #3292 #12791)
+#12801 := (iff #12796 #12800)
+#12802 := [rewrite]: #12801
+#12797 := (iff #3300 #12796)
+#12794 := (iff #3299 #12791)
+#12788 := (implies #12141 #12783)
+#12792 := (iff #12788 #12791)
+#12793 := [rewrite]: #12792
+#12789 := (iff #3299 #12788)
+#12786 := (iff #3298 #12783)
+#12780 := (implies #12141 #12775)
+#12784 := (iff #12780 #12783)
+#12785 := [rewrite]: #12784
+#12781 := (iff #3298 #12780)
+#12778 := (iff #3297 #12775)
+#12772 := (implies #12141 #12767)
+#12776 := (iff #12772 #12775)
+#12777 := [rewrite]: #12776
+#12773 := (iff #3297 #12772)
+#12770 := (iff #3296 #12767)
+#12763 := (implies #12748 #12758)
+#12768 := (iff #12763 #12767)
+#12769 := [rewrite]: #12768
+#12764 := (iff #3296 #12763)
+#12761 := (iff #3295 #12758)
+#12754 := (implies #12751 #12632)
+#12759 := (iff #12754 #12758)
+#12760 := [rewrite]: #12759
+#12755 := (iff #3295 #12754)
+#12635 := (iff #3277 #12632)
+#12628 := (implies #3245 #12625)
+#12633 := (iff #12628 #12632)
+#12634 := [rewrite]: #12633
+#12629 := (iff #3277 #12628)
+#12626 := (iff #3276 #12625)
+#12623 := (iff #3275 #12620)
+#12616 := (implies #12525 #12611)
+#12621 := (iff #12616 #12620)
+#12622 := [rewrite]: #12621
+#12617 := (iff #3275 #12616)
+#12614 := (iff #3274 #12611)
+#12607 := (implies #12528 #12602)
+#12612 := (iff #12607 #12611)
+#12613 := [rewrite]: #12612
+#12608 := (iff #3274 #12607)
+#12605 := (iff #3273 #12602)
+#12598 := (implies #12531 #12593)
+#12603 := (iff #12598 #12602)
+#12604 := [rewrite]: #12603
+#12599 := (iff #3273 #12598)
+#12596 := (iff #3272 #12593)
+#12589 := (implies #12534 #12586)
+#12594 := (iff #12589 #12593)
+#12595 := [rewrite]: #12594
+#12590 := (iff #3272 #12589)
+#12587 := (iff #3271 #12586)
+#12584 := (iff #3270 #12581)
+#12577 := (implies #3256 #12574)
+#12582 := (iff #12577 #12581)
+#12583 := [rewrite]: #12582
+#12578 := (iff #3270 #12577)
+#12575 := (iff #3269 #12574)
+#12572 := (iff #3268 #12569)
+#12565 := (implies #12549 #12555)
+#12570 := (iff #12565 #12569)
+#12571 := [rewrite]: #12570
+#12566 := (iff #3268 #12565)
+#12563 := (iff #3267 #12555)
+#12558 := (and #12555 true)
+#12561 := (iff #12558 #12555)
+#12562 := [rewrite]: #12561
+#12559 := (iff #3267 #12558)
+#12556 := (iff #3266 #12555)
+#12553 := (iff #3265 #12552)
+#12554 := [rewrite]: #12553
+#12557 := [monotonicity #12554]: #12556
+#12560 := [monotonicity #12557]: #12559
+#12564 := [trans #12560 #12562]: #12563
+#12550 := (iff #3261 #12549)
+#12547 := (iff #3260 #12544)
+#12541 := (implies #421 #12538)
+#12545 := (iff #12541 #12544)
+#12546 := [rewrite]: #12545
+#12542 := (iff #3260 #12541)
+#12539 := (iff #3259 #12538)
+#12540 := [rewrite]: #12539
+#12543 := [monotonicity #12540]: #12542
+#12548 := [trans #12543 #12546]: #12547
+#12551 := [quant-intro #12548]: #12550
+#12567 := [monotonicity #12551 #12564]: #12566
+#12573 := [trans #12567 #12571]: #12572
+#12576 := [monotonicity #12551 #12573]: #12575
+#12579 := [monotonicity #12576]: #12578
+#12585 := [trans #12579 #12583]: #12584
+#12588 := [monotonicity #12585]: #12587
+#12535 := (iff #3255 #12534)
+#12536 := [rewrite]: #12535
+#12591 := [monotonicity #12536 #12588]: #12590
+#12597 := [trans #12591 #12595]: #12596
+#12532 := (iff #3253 #12531)
+#12533 := [rewrite]: #12532
+#12600 := [monotonicity #12533 #12597]: #12599
+#12606 := [trans #12600 #12604]: #12605
+#12529 := (iff #3251 #12528)
+#12517 := (= #3246 #12516)
+#12518 := [rewrite]: #12517
+#12530 := [monotonicity #12518]: #12529
+#12609 := [monotonicity #12530 #12606]: #12608
+#12615 := [trans #12609 #12613]: #12614
+#12526 := (iff #3249 #12525)
+#12523 := (iff #3248 #12522)
+#12524 := [monotonicity #12518]: #12523
+#12520 := (iff #3247 #12519)
+#12521 := [monotonicity #12518]: #12520
+#12527 := [monotonicity #12521 #12524]: #12526
+#12618 := [monotonicity #12527 #12615]: #12617
+#12624 := [trans #12618 #12622]: #12623
+#12627 := [monotonicity #12527 #12624]: #12626
+#12630 := [monotonicity #12627]: #12629
+#12636 := [trans #12630 #12634]: #12635
+#12752 := (iff #3294 #12751)
+#12753 := [rewrite]: #12752
+#12756 := [monotonicity #12753 #12636]: #12755
+#12762 := [trans #12756 #12760]: #12761
+#12749 := (iff #3293 #12748)
+#12750 := [rewrite]: #12749
+#12765 := [monotonicity #12750 #12762]: #12764
+#12771 := [trans #12765 #12769]: #12770
+#12774 := [monotonicity #12143 #12771]: #12773
+#12779 := [trans #12774 #12777]: #12778
+#12782 := [monotonicity #12143 #12779]: #12781
+#12787 := [trans #12782 #12785]: #12786
+#12790 := [monotonicity #12143 #12787]: #12789
+#12795 := [trans #12790 #12793]: #12794
+#12798 := [monotonicity #12795]: #12797
+#12804 := [trans #12798 #12802]: #12803
+#12807 := [monotonicity #12143 #12804]: #12806
+#12812 := [trans #12807 #12810]: #12811
+#12746 := (iff #3291 #12743)
+#12740 := (implies #12141 #12735)
+#12744 := (iff #12740 #12743)
 #12745 := [rewrite]: #12744
-#12740 := (iff #3277 #12739)
-#12737 := (iff #3276 #12734)
-#12730 := (implies #3176 #12718)
-#12735 := (iff #12730 #12734)
-#12736 := [rewrite]: #12735
-#12731 := (iff #3276 #12730)
-#12728 := (iff #3275 #12718)
-#12723 := (implies true #12718)
-#12726 := (iff #12723 #12718)
-#12727 := [rewrite]: #12726
-#12724 := (iff #3275 #12723)
-#12721 := (iff #3274 #12718)
-#12715 := (implies #11971 #12712)
+#12741 := (iff #3291 #12740)
+#12738 := (iff #3290 #12735)
+#12731 := (implies #3232 #12726)
+#12736 := (iff #12731 #12735)
+#12737 := [rewrite]: #12736
+#12732 := (iff #3290 #12731)
+#12729 := (iff #3289 #12726)
+#12723 := (implies #12141 #12718)
+#12727 := (iff #12723 #12726)
+#12728 := [rewrite]: #12727
+#12724 := (iff #3289 #12723)
+#12721 := (iff #3288 #12718)
+#12715 := (implies #12141 #12712)
 #12719 := (iff #12715 #12718)
 #12720 := [rewrite]: #12719
-#12716 := (iff #3274 #12715)
-#12713 := (iff #3273 #12712)
-#12710 := (iff #3272 #12707)
-#12704 := (implies #11971 #12699)
-#12708 := (iff #12704 #12707)
+#12716 := (iff #3288 #12715)
+#12713 := (iff #3287 #12712)
+#12710 := (iff #3286 #12707)
+#12703 := (implies #12490 #12700)
+#12708 := (iff #12703 #12707)
 #12709 := [rewrite]: #12708
-#12705 := (iff #3272 #12704)
-#12702 := (iff #3271 #12699)
-#12695 := (implies #3268 #12690)
-#12700 := (iff #12695 #12699)
-#12701 := [rewrite]: #12700
-#12696 := (iff #3271 #12695)
-#12693 := (iff #3270 #12690)
-#12687 := (implies #11971 #12682)
-#12691 := (iff #12687 #12690)
-#12692 := [rewrite]: #12691
-#12688 := (iff #3270 #12687)
-#12685 := (iff #3269 #12682)
-#12679 := (implies #11971 #12133)
-#12683 := (iff #12679 #12682)
-#12684 := [rewrite]: #12683
-#12680 := (iff #3269 #12679)
-#12136 := (iff #3121 #12133)
-#12130 := (implies #11971 #12125)
-#12134 := (iff #12130 #12133)
-#12135 := [rewrite]: #12134
-#12131 := (iff #3121 #12130)
-#12128 := (iff #3120 #12125)
-#12122 := (implies #11971 #12119)
-#12126 := (iff #12122 #12125)
-#12127 := [rewrite]: #12126
-#12123 := (iff #3120 #12122)
-#12120 := (iff #3119 #12119)
-#12117 := (iff #3118 #12114)
-#12110 := (implies up_216 #12105)
-#12115 := (iff #12110 #12114)
-#12116 := [rewrite]: #12115
-#12111 := (iff #3118 #12110)
-#12108 := (iff #3117 #12105)
-#12102 := (implies #11971 #12097)
-#12106 := (iff #12102 #12105)
-#12107 := [rewrite]: #12106
-#12103 := (iff #3117 #12102)
-#12100 := (iff #3116 #12097)
-#12094 := (implies #11971 #12089)
-#12098 := (iff #12094 #12097)
-#12099 := [rewrite]: #12098
-#12095 := (iff #3116 #12094)
-#12092 := (iff #3115 #12089)
-#12085 := (implies #11971 #12080)
-#12090 := (iff #12085 #12089)
-#12091 := [rewrite]: #12090
-#12086 := (iff #3115 #12085)
-#12083 := (iff #3114 #12080)
-#12076 := (implies #12008 #12071)
-#12081 := (iff #12076 #12080)
-#12082 := [rewrite]: #12081
-#12077 := (iff #3114 #12076)
-#12074 := (iff #3113 #12071)
-#12067 := (implies #12011 #12062)
-#12072 := (iff #12067 #12071)
-#12073 := [rewrite]: #12072
-#12068 := (iff #3113 #12067)
-#12065 := (iff #3112 #12062)
-#12058 := (implies #12014 #12053)
-#12063 := (iff #12058 #12062)
-#12064 := [rewrite]: #12063
-#12059 := (iff #3112 #12058)
-#12056 := (iff #3111 #12053)
-#12049 := (implies #12017 #12046)
-#12054 := (iff #12049 #12053)
-#12055 := [rewrite]: #12054
-#12050 := (iff #3111 #12049)
-#12047 := (iff #3110 #12046)
-#12044 := (iff #3109 #12041)
-#12037 := (implies #12032 #3107)
-#12042 := (iff #12037 #12041)
-#12043 := [rewrite]: #12042
-#12038 := (iff #3109 #12037)
-#12035 := (iff #3108 #3107)
-#12036 := [rewrite]: #12035
-#12033 := (iff #3102 #12032)
-#12030 := (iff #3101 #12027)
-#12024 := (implies #412 #12021)
-#12028 := (iff #12024 #12027)
-#12029 := [rewrite]: #12028
-#12025 := (iff #3101 #12024)
-#12022 := (iff #3100 #12021)
-#12023 := [rewrite]: #12022
-#12026 := [monotonicity #12023]: #12025
-#12031 := [trans #12026 #12029]: #12030
-#12034 := [quant-intro #12031]: #12033
-#12039 := [monotonicity #12034 #12036]: #12038
-#12045 := [trans #12039 #12043]: #12044
-#12048 := [monotonicity #12034 #12045]: #12047
-#12018 := (iff #3097 #12017)
-#12019 := [rewrite]: #12018
-#12051 := [monotonicity #12019 #12048]: #12050
-#12057 := [trans #12051 #12055]: #12056
-#12015 := (iff #3095 #12014)
-#12016 := [rewrite]: #12015
-#12060 := [monotonicity #12016 #12057]: #12059
-#12066 := [trans #12060 #12064]: #12065
-#12012 := (iff #3093 #12011)
-#12013 := [rewrite]: #12012
-#12069 := [monotonicity #12013 #12066]: #12068
-#12075 := [trans #12069 #12073]: #12074
-#12009 := (iff #3091 #12008)
-#12010 := [rewrite]: #12009
-#12078 := [monotonicity #12010 #12075]: #12077
-#12084 := [trans #12078 #12082]: #12083
-#11972 := (iff #3074 #11971)
-#11973 := [rewrite]: #11972
-#12087 := [monotonicity #11973 #12084]: #12086
-#12093 := [trans #12087 #12091]: #12092
-#12096 := [monotonicity #11973 #12093]: #12095
-#12101 := [trans #12096 #12099]: #12100
-#12104 := [monotonicity #11973 #12101]: #12103
-#12109 := [trans #12104 #12107]: #12108
-#12112 := [monotonicity #12109]: #12111
-#12118 := [trans #12112 #12116]: #12117
-#12121 := [monotonicity #12118]: #12120
-#12124 := [monotonicity #11973 #12121]: #12123
-#12129 := [trans #12124 #12127]: #12128
-#12132 := [monotonicity #11973 #12129]: #12131
-#12137 := [trans #12132 #12135]: #12136
-#12681 := [monotonicity #11973 #12137]: #12680
-#12686 := [trans #12681 #12684]: #12685
-#12689 := [monotonicity #11973 #12686]: #12688
-#12694 := [trans #12689 #12692]: #12693
-#12697 := [monotonicity #12694]: #12696
-#12703 := [trans #12697 #12701]: #12702
-#12706 := [monotonicity #11973 #12703]: #12705
-#12711 := [trans #12706 #12709]: #12710
-#12677 := (iff #3267 #12674)
-#12671 := (implies #11971 #12666)
-#12675 := (iff #12671 #12674)
-#12676 := [rewrite]: #12675
-#12672 := (iff #3267 #12671)
-#12669 := (iff #3266 #12666)
-#12662 := (implies #3180 #12657)
-#12667 := (iff #12662 #12666)
-#12668 := [rewrite]: #12667
-#12663 := (iff #3266 #12662)
-#12660 := (iff #3265 #12657)
-#12654 := (implies #11971 #12649)
-#12658 := (iff #12654 #12657)
-#12659 := [rewrite]: #12658
-#12655 := (iff #3265 #12654)
-#12652 := (iff #3264 #12649)
-#12646 := (implies #11971 #12643)
-#12650 := (iff #12646 #12649)
-#12651 := [rewrite]: #12650
-#12647 := (iff #3264 #12646)
-#12644 := (iff #3263 #12643)
-#12641 := (iff #3262 #12638)
-#12635 := (implies #12299 #12632)
-#12639 := (iff #12635 #12638)
-#12640 := [rewrite]: #12639
-#12636 := (iff #3262 #12635)
-#12633 := (iff #3261 #12632)
-#12630 := (iff #3260 #12627)
-#12624 := (implies #12305 #12619)
-#12628 := (iff #12624 #12627)
-#12629 := [rewrite]: #12628
-#12625 := (iff #3260 #12624)
-#12622 := (iff #3259 #12619)
-#12616 := (implies #11971 #12613)
-#12620 := (iff #12616 #12619)
-#12621 := [rewrite]: #12620
-#12617 := (iff #3259 #12616)
-#12614 := (iff #3258 #12613)
-#12611 := (iff #3257 #12608)
-#12605 := (implies #11971 #12600)
-#12609 := (iff #12605 #12608)
-#12610 := [rewrite]: #12609
-#12606 := (iff #3257 #12605)
-#12603 := (iff #3256 #12600)
-#12596 := (implies #3248 #12591)
-#12601 := (iff #12596 #12600)
-#12602 := [rewrite]: #12601
-#12597 := (iff #3256 #12596)
-#12594 := (iff #3255 #12591)
-#12588 := (implies #11971 #12583)
-#12592 := (iff #12588 #12591)
-#12593 := [rewrite]: #12592
-#12589 := (iff #3255 #12588)
-#12586 := (iff #3254 #12583)
-#12580 := (implies #11971 #12575)
-#12584 := (iff #12580 #12583)
-#12585 := [rewrite]: #12584
-#12581 := (iff #3254 #12580)
-#12578 := (iff #3253 #12575)
-#12572 := (implies #11971 #12567)
-#12576 := (iff #12572 #12575)
-#12577 := [rewrite]: #12576
-#12573 := (iff #3253 #12572)
-#12570 := (iff #3252 #12567)
-#12563 := (implies #12548 #12558)
-#12568 := (iff #12563 #12567)
-#12569 := [rewrite]: #12568
-#12564 := (iff #3252 #12563)
-#12561 := (iff #3251 #12558)
-#12554 := (implies #12551 #12432)
-#12559 := (iff #12554 #12558)
-#12560 := [rewrite]: #12559
-#12555 := (iff #3251 #12554)
-#12435 := (iff #3233 #12432)
-#12428 := (implies #3202 #12425)
-#12433 := (iff #12428 #12432)
-#12434 := [rewrite]: #12433
-#12429 := (iff #3233 #12428)
-#12426 := (iff #3232 #12425)
-#12423 := (iff #3231 #12420)
-#12416 := (implies #12328 #12411)
-#12421 := (iff #12416 #12420)
-#12422 := [rewrite]: #12421
-#12417 := (iff #3231 #12416)
-#12414 := (iff #3230 #12411)
-#12407 := (implies #12331 #12402)
-#12412 := (iff #12407 #12411)
-#12413 := [rewrite]: #12412
-#12408 := (iff #3230 #12407)
-#12405 := (iff #3229 #12402)
-#12398 := (implies #3209 #12393)
-#12403 := (iff #12398 #12402)
-#12404 := [rewrite]: #12403
-#12399 := (iff #3229 #12398)
-#12396 := (iff #3228 #12393)
-#12389 := (implies #12334 #12386)
-#12394 := (iff #12389 #12393)
-#12395 := [rewrite]: #12394
-#12390 := (iff #3228 #12389)
-#12387 := (iff #3227 #12386)
-#12384 := (iff #3226 #12381)
-#12377 := (implies #3212 #12374)
-#12382 := (iff #12377 #12381)
-#12383 := [rewrite]: #12382
-#12378 := (iff #3226 #12377)
-#12375 := (iff #3225 #12374)
-#12372 := (iff #3224 #12369)
-#12365 := (implies #12349 #12355)
-#12370 := (iff #12365 #12369)
-#12371 := [rewrite]: #12370
-#12366 := (iff #3224 #12365)
-#12363 := (iff #3223 #12355)
-#12358 := (and #12355 true)
-#12361 := (iff #12358 #12355)
-#12362 := [rewrite]: #12361
-#12359 := (iff #3223 #12358)
-#12356 := (iff #3222 #12355)
-#12353 := (iff #3221 #12352)
-#12354 := [rewrite]: #12353
-#12357 := [monotonicity #12354]: #12356
-#12360 := [monotonicity #12357]: #12359
-#12364 := [trans #12360 #12362]: #12363
-#12350 := (iff #3217 #12349)
-#12347 := (iff #3216 #12344)
-#12341 := (implies #412 #12338)
-#12345 := (iff #12341 #12344)
-#12346 := [rewrite]: #12345
-#12342 := (iff #3216 #12341)
-#12339 := (iff #3215 #12338)
-#12340 := [rewrite]: #12339
-#12343 := [monotonicity #12340]: #12342
-#12348 := [trans #12343 #12346]: #12347
-#12351 := [quant-intro #12348]: #12350
-#12367 := [monotonicity #12351 #12364]: #12366
-#12373 := [trans #12367 #12371]: #12372
-#12376 := [monotonicity #12351 #12373]: #12375
-#12379 := [monotonicity #12376]: #12378
-#12385 := [trans #12379 #12383]: #12384
-#12388 := [monotonicity #12385]: #12387
-#12335 := (iff #3211 #12334)
-#12336 := [rewrite]: #12335
-#12391 := [monotonicity #12336 #12388]: #12390
-#12397 := [trans #12391 #12395]: #12396
-#12400 := [monotonicity #12397]: #12399
-#12406 := [trans #12400 #12404]: #12405
-#12332 := (iff #3208 #12331)
-#12320 := (= #3203 #12319)
-#12321 := [rewrite]: #12320
-#12333 := [monotonicity #12321]: #12332
-#12409 := [monotonicity #12333 #12406]: #12408
-#12415 := [trans #12409 #12413]: #12414
-#12329 := (iff #3206 #12328)
-#12326 := (iff #3205 #12325)
-#12327 := [monotonicity #12321]: #12326
-#12323 := (iff #3204 #12322)
-#12324 := [monotonicity #12321]: #12323
-#12330 := [monotonicity #12324 #12327]: #12329
-#12418 := [monotonicity #12330 #12415]: #12417
-#12424 := [trans #12418 #12422]: #12423
-#12427 := [monotonicity #12330 #12424]: #12426
-#12430 := [monotonicity #12427]: #12429
-#12436 := [trans #12430 #12434]: #12435
-#12552 := (iff #3250 #12551)
-#12553 := [rewrite]: #12552
-#12556 := [monotonicity #12553 #12436]: #12555
-#12562 := [trans #12556 #12560]: #12561
-#12549 := (iff #3249 #12548)
-#12550 := [rewrite]: #12549
-#12565 := [monotonicity #12550 #12562]: #12564
-#12571 := [trans #12565 #12569]: #12570
-#12574 := [monotonicity #11973 #12571]: #12573
-#12579 := [trans #12574 #12577]: #12578
-#12582 := [monotonicity #11973 #12579]: #12581
-#12587 := [trans #12582 #12585]: #12586
-#12590 := [monotonicity #11973 #12587]: #12589
-#12595 := [trans #12590 #12593]: #12594
-#12598 := [monotonicity #12595]: #12597
-#12604 := [trans #12598 #12602]: #12603
-#12607 := [monotonicity #11973 #12604]: #12606
-#12612 := [trans #12607 #12610]: #12611
-#12546 := (iff #3247 #12543)
-#12540 := (implies #11971 #12535)
-#12544 := (iff #12540 #12543)
-#12545 := [rewrite]: #12544
-#12541 := (iff #3247 #12540)
-#12538 := (iff #3246 #12535)
-#12531 := (implies #3191 #12526)
-#12536 := (iff #12531 #12535)
-#12537 := [rewrite]: #12536
-#12532 := (iff #3246 #12531)
-#12529 := (iff #3245 #12526)
-#12523 := (implies #11971 #12518)
-#12527 := (iff #12523 #12526)
-#12528 := [rewrite]: #12527
-#12524 := (iff #3245 #12523)
-#12521 := (iff #3244 #12518)
-#12515 := (implies #11971 #12512)
-#12519 := (iff #12515 #12518)
-#12520 := [rewrite]: #12519
-#12516 := (iff #3244 #12515)
-#12513 := (iff #3243 #12512)
-#12510 := (iff #3242 #12507)
-#12503 := (implies #12299 #12500)
-#12508 := (iff #12503 #12507)
+#12704 := (iff #3286 #12703)
+#12701 := (iff #3285 #12700)
+#12698 := (iff #3284 #12695)
+#12691 := (implies #12496 #12686)
+#12696 := (iff #12691 #12695)
+#12697 := [rewrite]: #12696
+#12692 := (iff #3284 #12691)
+#12689 := (iff #3283 #12686)
+#12682 := (implies #12499 #12677)
+#12687 := (iff #12682 #12686)
+#12688 := [rewrite]: #12687
+#12683 := (iff #3283 #12682)
+#12680 := (iff #3282 #12677)
+#12673 := (implies #12502 #12668)
+#12678 := (iff #12673 #12677)
+#12679 := [rewrite]: #12678
+#12674 := (iff #3282 #12673)
+#12671 := (iff #3281 #12668)
+#12664 := (implies #12505 #12659)
+#12669 := (iff #12664 #12668)
+#12670 := [rewrite]: #12669
+#12665 := (iff #3281 #12664)
+#12662 := (iff #3280 #12659)
+#12655 := (implies #3108 #12650)
+#12660 := (iff #12655 #12659)
+#12661 := [rewrite]: #12660
+#12656 := (iff #3280 #12655)
+#12653 := (iff #3279 #12650)
+#12646 := (implies #12510 #12641)
+#12651 := (iff #12646 #12650)
+#12652 := [rewrite]: #12651
+#12647 := (iff #3279 #12646)
+#12644 := (iff #3278 #12641)
+#12637 := (implies #12513 #12632)
+#12642 := (iff #12637 #12641)
+#12643 := [rewrite]: #12642
+#12638 := (iff #3278 #12637)
+#12514 := (iff #3243 #12513)
+#12515 := [rewrite]: #12514
+#12639 := [monotonicity #12515 #12636]: #12638
+#12645 := [trans #12639 #12643]: #12644
+#12511 := (iff #3241 #12510)
+#12512 := [rewrite]: #12511
+#12648 := [monotonicity #12512 #12645]: #12647
+#12654 := [trans #12648 #12652]: #12653
+#12508 := (iff #3239 #3108)
 #12509 := [rewrite]: #12508
-#12504 := (iff #3242 #12503)
-#12501 := (iff #3241 #12500)
-#12498 := (iff #3240 #12495)
-#12491 := (implies #12305 #12486)
-#12496 := (iff #12491 #12495)
-#12497 := [rewrite]: #12496
-#12492 := (iff #3240 #12491)
-#12489 := (iff #3239 #12486)
-#12482 := (implies #12308 #12477)
-#12487 := (iff #12482 #12486)
-#12488 := [rewrite]: #12487
-#12483 := (iff #3239 #12482)
-#12480 := (iff #3238 #12477)
-#12473 := (implies #3194 #12468)
-#12478 := (iff #12473 #12477)
-#12479 := [rewrite]: #12478
-#12474 := (iff #3238 #12473)
-#12471 := (iff #3237 #12468)
-#12464 := (implies #3195 #12459)
-#12469 := (iff #12464 #12468)
-#12470 := [rewrite]: #12469
-#12465 := (iff #3237 #12464)
-#12462 := (iff #3236 #12459)
-#12455 := (implies #3073 #12450)
-#12460 := (iff #12455 #12459)
-#12461 := [rewrite]: #12460
-#12456 := (iff #3236 #12455)
-#12453 := (iff #3235 #12450)
-#12446 := (implies #12313 #12441)
-#12451 := (iff #12446 #12450)
-#12452 := [rewrite]: #12451
-#12447 := (iff #3235 #12446)
-#12444 := (iff #3234 #12441)
-#12437 := (implies #12316 #12432)
-#12442 := (iff #12437 #12441)
-#12443 := [rewrite]: #12442
-#12438 := (iff #3234 #12437)
-#12317 := (iff #3200 #12316)
-#12318 := [rewrite]: #12317
-#12439 := [monotonicity #12318 #12436]: #12438
-#12445 := [trans #12439 #12443]: #12444
-#12314 := (iff #3198 #12313)
-#12315 := [rewrite]: #12314
-#12448 := [monotonicity #12315 #12445]: #12447
-#12454 := [trans #12448 #12452]: #12453
-#12311 := (iff #3196 #3073)
-#12312 := [rewrite]: #12311
-#12457 := [monotonicity #12312 #12454]: #12456
-#12463 := [trans #12457 #12461]: #12462
-#12466 := [monotonicity #12463]: #12465
-#12472 := [trans #12466 #12470]: #12471
-#12475 := [monotonicity #12472]: #12474
-#12481 := [trans #12475 #12479]: #12480
-#12309 := (iff #3193 #12308)
-#12310 := [rewrite]: #12309
-#12484 := [monotonicity #12310 #12481]: #12483
-#12490 := [trans #12484 #12488]: #12489
-#12306 := (iff #3189 #12305)
-#12303 := (iff #3188 #12302)
-#12304 := [rewrite]: #12303
-#12294 := (iff #3183 #12293)
-#12295 := [rewrite]: #12294
-#12307 := [monotonicity #12295 #12304]: #12306
-#12493 := [monotonicity #12307 #12490]: #12492
-#12499 := [trans #12493 #12497]: #12498
-#12502 := [monotonicity #12307 #12499]: #12501
-#12300 := (iff #3186 #12299)
-#12297 := (iff #3185 #12296)
-#12298 := [rewrite]: #12297
-#12301 := [monotonicity #12295 #12298]: #12300
-#12505 := [monotonicity #12301 #12502]: #12504
-#12511 := [trans #12505 #12509]: #12510
-#12514 := [monotonicity #12301 #12511]: #12513
-#12517 := [monotonicity #11973 #12514]: #12516
-#12522 := [trans #12517 #12520]: #12521
-#12525 := [monotonicity #11973 #12522]: #12524
-#12530 := [trans #12525 #12528]: #12529
-#12533 := [monotonicity #12530]: #12532
-#12539 := [trans #12533 #12537]: #12538
-#12542 := [monotonicity #11973 #12539]: #12541
-#12547 := [trans #12542 #12545]: #12546
-#12615 := [monotonicity #12547 #12612]: #12614
-#12618 := [monotonicity #11973 #12615]: #12617
-#12623 := [trans #12618 #12621]: #12622
-#12626 := [monotonicity #12307 #12623]: #12625
-#12631 := [trans #12626 #12629]: #12630
-#12634 := [monotonicity #12307 #12631]: #12633
-#12637 := [monotonicity #12301 #12634]: #12636
-#12642 := [trans #12637 #12640]: #12641
-#12645 := [monotonicity #12301 #12642]: #12644
-#12648 := [monotonicity #11973 #12645]: #12647
-#12653 := [trans #12648 #12651]: #12652
-#12656 := [monotonicity #11973 #12653]: #12655
-#12661 := [trans #12656 #12659]: #12660
-#12664 := [monotonicity #12661]: #12663
-#12670 := [trans #12664 #12668]: #12669
-#12673 := [monotonicity #11973 #12670]: #12672
-#12678 := [trans #12673 #12676]: #12677
-#12714 := [monotonicity #12678 #12711]: #12713
-#12717 := [monotonicity #11973 #12714]: #12716
+#12657 := [monotonicity #12509 #12654]: #12656
+#12663 := [trans #12657 #12661]: #12662
+#12506 := (iff #3238 #12505)
+#12507 := [rewrite]: #12506
+#12666 := [monotonicity #12507 #12663]: #12665
+#12672 := [trans #12666 #12670]: #12671
+#12503 := (iff #3236 #12502)
+#12504 := [rewrite]: #12503
+#12675 := [monotonicity #12504 #12672]: #12674
+#12681 := [trans #12675 #12679]: #12680
+#12500 := (iff #3234 #12499)
+#12501 := [rewrite]: #12500
+#12684 := [monotonicity #12501 #12681]: #12683
+#12690 := [trans #12684 #12688]: #12689
+#12497 := (iff #3230 #12496)
+#12494 := (iff #3229 #12493)
+#12495 := [rewrite]: #12494
+#12485 := (iff #3224 #12484)
+#12486 := [rewrite]: #12485
+#12498 := [monotonicity #12486 #12495]: #12497
+#12693 := [monotonicity #12498 #12690]: #12692
+#12699 := [trans #12693 #12697]: #12698
+#12702 := [monotonicity #12498 #12699]: #12701
+#12491 := (iff #3227 #12490)
+#12488 := (iff #3226 #12487)
+#12489 := [rewrite]: #12488
+#12492 := [monotonicity #12486 #12489]: #12491
+#12705 := [monotonicity #12492 #12702]: #12704
+#12711 := [trans #12705 #12709]: #12710
+#12714 := [monotonicity #12492 #12711]: #12713
+#12717 := [monotonicity #12143 #12714]: #12716
 #12722 := [trans #12717 #12720]: #12721
-#12291 := (iff #3179 true)
-#12289 := (iff #12286 true)
-#12290 := [rewrite]: #12289
-#12287 := (iff #3179 #12286)
-#12284 := (iff #3178 true)
-#12285 := [rewrite]: #12284
-#12282 := (iff #3177 true)
-#12283 := [rewrite]: #12282
-#12288 := [monotonicity #12283 #12285]: #12287
-#12292 := [trans #12288 #12290]: #12291
-#12725 := [monotonicity #12292 #12722]: #12724
-#12729 := [trans #12725 #12727]: #12728
-#12732 := [monotonicity #12729]: #12731
-#12738 := [trans #12732 #12736]: #12737
-#12741 := [monotonicity #12738]: #12740
-#12747 := [trans #12741 #12745]: #12746
-#12750 := [monotonicity #12747]: #12749
-#12756 := [trans #12750 #12754]: #12755
-#12759 := [monotonicity #12756]: #12758
-#12765 := [trans #12759 #12763]: #12764
-#12768 := [monotonicity #12765]: #12767
-#12774 := [trans #12768 #12772]: #12773
-#12006 := (iff #3089 #12003)
-#12000 := (and #11997 #11905)
-#12004 := (iff #12000 #12003)
-#12005 := [rewrite]: #12004
-#12001 := (iff #3089 #12000)
-#11906 := (iff #3005 #11905)
-#11907 := [rewrite]: #11906
-#11998 := (iff #3088 #11997)
-#11999 := [rewrite]: #11998
-#12002 := [monotonicity #11999 #11907]: #12001
-#12007 := [trans #12002 #12005]: #12006
-#12777 := [monotonicity #12007 #12774]: #12776
-#12782 := [trans #12777 #12780]: #12781
-#12261 := (iff #3165 #12260)
-#12258 := (iff #3164 #12257)
-#12255 := (iff #3163 #12254)
-#12256 := [rewrite]: #12255
-#12259 := [monotonicity #12256]: #12258
-#12262 := [monotonicity #12259]: #12261
-#12785 := [monotonicity #12262 #12782]: #12784
-#12791 := [trans #12785 #12789]: #12790
-#12280 := (iff #3169 #12260)
-#12263 := (and true #12260)
-#12266 := (iff #12263 #12260)
-#12267 := [rewrite]: #12266
-#12278 := (iff #3169 #12263)
-#12276 := (iff #3168 #12260)
-#12274 := (iff #3168 #12263)
-#12272 := (iff #3167 #12260)
-#12270 := (iff #3167 #12263)
-#12268 := (iff #3166 #12260)
-#12264 := (iff #3166 #12263)
-#12252 := (iff #3156 true)
-#12247 := (forall (vars (?x782 T5)) (:pat #3152) true)
-#12250 := (iff #12247 true)
-#12251 := [elim-unused]: #12250
-#12248 := (iff #3156 #12247)
-#12245 := (iff #3155 true)
-#12197 := (= uf_9 #3140)
-#12209 := (implies #12197 #12197)
-#12212 := (iff #12209 true)
-#12213 := [rewrite]: #12212
-#12243 := (iff #3155 #12209)
-#12241 := (iff #3154 #12197)
-#12202 := (and true #12197)
-#12205 := (iff #12202 #12197)
-#12206 := [rewrite]: #12205
-#12239 := (iff #3154 #12202)
-#12198 := (iff #3141 #12197)
-#12199 := [rewrite]: #12198
-#12237 := (iff #3153 true)
-#12238 := [rewrite]: #12237
-#12240 := [monotonicity #12238 #12199]: #12239
-#12242 := [trans #12240 #12206]: #12241
-#12244 := [monotonicity #12199 #12242]: #12243
-#12246 := [trans #12244 #12213]: #12245
-#12249 := [quant-intro #12246]: #12248
-#12253 := [trans #12249 #12251]: #12252
-#12265 := [monotonicity #12253 #12262]: #12264
-#12269 := [trans #12265 #12267]: #12268
-#12235 := (iff #3149 true)
-#12190 := (forall (vars (?x779 T5)) (:pat #3129) true)
-#12193 := (iff #12190 true)
-#12194 := [elim-unused]: #12193
-#12233 := (iff #3149 #12190)
-#12231 := (iff #3148 true)
-#12229 := (iff #3148 #12209)
-#12227 := (iff #3147 #12197)
-#12225 := (iff #3147 #12202)
-#12223 := (iff #3146 true)
-#12224 := [rewrite]: #12223
-#12226 := [monotonicity #12224 #12199]: #12225
-#12228 := [trans #12226 #12206]: #12227
-#12230 := [monotonicity #12199 #12228]: #12229
-#12232 := [trans #12230 #12213]: #12231
-#12234 := [quant-intro #12232]: #12233
-#12236 := [trans #12234 #12194]: #12235
-#12271 := [monotonicity #12236 #12269]: #12270
-#12273 := [trans #12271 #12267]: #12272
-#12221 := (iff #3145 true)
-#12216 := (forall (vars (?x780 T5)) (:pat #3139) true)
-#12219 := (iff #12216 true)
-#12220 := [elim-unused]: #12219
-#12217 := (iff #3145 #12216)
-#12214 := (iff #3144 true)
-#12210 := (iff #3144 #12209)
-#12207 := (iff #3143 #12197)
-#12203 := (iff #3143 #12202)
-#12200 := (iff #3142 true)
-#12201 := [rewrite]: #12200
-#12204 := [monotonicity #12201 #12199]: #12203
-#12208 := [trans #12204 #12206]: #12207
-#12211 := [monotonicity #12199 #12208]: #12210
-#12215 := [trans #12211 #12213]: #12214
-#12218 := [quant-intro #12215]: #12217
-#12222 := [trans #12218 #12220]: #12221
-#12275 := [monotonicity #12222 #12273]: #12274
-#12277 := [trans #12275 #12267]: #12276
-#12195 := (iff #3136 true)
-#12191 := (iff #3136 #12190)
-#12188 := (iff #3135 true)
-#12177 := (= uf_261 #3132)
-#12180 := (not #12177)
-#12183 := (implies #12180 #12180)
-#12186 := (iff #12183 true)
-#12187 := [rewrite]: #12186
-#12184 := (iff #3135 #12183)
-#12181 := (iff #3134 #12180)
-#12178 := (iff #3133 #12177)
-#12179 := [rewrite]: #12178
-#12182 := [monotonicity #12179]: #12181
-#12185 := [monotonicity #12182 #12182]: #12184
-#12189 := [trans #12185 #12187]: #12188
-#12192 := [quant-intro #12189]: #12191
-#12196 := [trans #12192 #12194]: #12195
-#12279 := [monotonicity #12196 #12277]: #12278
-#12281 := [trans #12279 #12267]: #12280
-#12794 := [monotonicity #12281 #12791]: #12793
-#12799 := [trans #12794 #12797]: #12798
-#12802 := [monotonicity #11973 #12799]: #12801
-#12807 := [trans #12802 #12805]: #12806
-#12810 := [monotonicity #11973 #12807]: #12809
-#12815 := [trans #12810 #12813]: #12814
-#12818 := [monotonicity #11973 #12815]: #12817
+#12725 := [monotonicity #12143 #12722]: #12724
+#12730 := [trans #12725 #12728]: #12729
+#12733 := [monotonicity #12730]: #12732
+#12739 := [trans #12733 #12737]: #12738
+#12742 := [monotonicity #12143 #12739]: #12741
+#12747 := [trans #12742 #12745]: #12746
+#12815 := [monotonicity #12747 #12812]: #12814
+#12818 := [monotonicity #12143 #12815]: #12817
 #12823 := [trans #12818 #12821]: #12822
-#12175 := (iff #3126 true)
-#12170 := (implies #11971 true)
-#12173 := (iff #12170 true)
-#12174 := [rewrite]: #12173
-#12171 := (iff #3126 #12170)
-#12168 := (iff #3125 true)
-#12142 := (or #12141 #12133)
-#12150 := (or #12088 #12142)
-#12158 := (or #12088 #12150)
-#12163 := (implies false #12158)
-#12166 := (iff #12163 true)
-#12167 := [rewrite]: #12166
-#12164 := (iff #3125 #12163)
-#12161 := (iff #3124 #12158)
-#12155 := (implies #11971 #12150)
-#12159 := (iff #12155 #12158)
-#12160 := [rewrite]: #12159
-#12156 := (iff #3124 #12155)
-#12153 := (iff #3123 #12150)
-#12147 := (implies #11971 #12142)
-#12151 := (iff #12147 #12150)
-#12152 := [rewrite]: #12151
-#12148 := (iff #3123 #12147)
-#12145 := (iff #3122 #12142)
-#12138 := (implies #12003 #12133)
-#12143 := (iff #12138 #12142)
-#12144 := [rewrite]: #12143
-#12139 := (iff #3122 #12138)
-#12140 := [monotonicity #12007 #12137]: #12139
-#12146 := [trans #12140 #12144]: #12145
-#12149 := [monotonicity #11973 #12146]: #12148
-#12154 := [trans #12149 #12152]: #12153
-#12157 := [monotonicity #11973 #12154]: #12156
-#12162 := [trans #12157 #12160]: #12161
-#12165 := [monotonicity #11996 #12162]: #12164
-#12169 := [trans #12165 #12167]: #12168
-#12172 := [monotonicity #11973 #12169]: #12171
-#12176 := [trans #12172 #12174]: #12175
-#12826 := [monotonicity #12176 #12823]: #12825
-#12830 := [trans #12826 #12828]: #12829
-#12833 := [monotonicity #11973 #12830]: #12832
-#12838 := [trans #12833 #12836]: #12837
-#11993 := (iff #3085 #11992)
-#11990 := (iff #3084 #11989)
-#11991 := [rewrite]: #11990
-#11994 := [monotonicity #11991]: #11993
-#12841 := [monotonicity #11994 #12838]: #12840
-#12847 := [trans #12841 #12845]: #12846
-#11987 := (iff #3080 #11986)
-#11984 := (iff #3079 #11981)
-#11978 := (implies #412 #11975)
-#11982 := (iff #11978 #11981)
-#11983 := [rewrite]: #11982
-#11979 := (iff #3079 #11978)
-#11976 := (iff #3078 #11975)
-#11977 := [rewrite]: #11976
-#11980 := [monotonicity #11977]: #11979
-#11985 := [trans #11980 #11983]: #11984
-#11988 := [quant-intro #11985]: #11987
-#12850 := [monotonicity #11988 #12847]: #12849
-#12856 := [trans #12850 #12854]: #12855
-#12859 := [monotonicity #12856]: #12858
-#12865 := [trans #12859 #12863]: #12864
-#12868 := [monotonicity #11973 #12865]: #12867
-#12873 := [trans #12868 #12871]: #12872
-#12876 := [monotonicity #12873]: #12875
-#12882 := [trans #12876 #12880]: #12881
-#12885 := [monotonicity #12882]: #12884
-#12891 := [trans #12885 #12889]: #12890
-#12894 := [monotonicity #12891]: #12893
-#12900 := [trans #12894 #12898]: #12899
-#11969 := (iff #3060 #11968)
-#11966 := (iff #3059 #3042)
-#11967 := [rewrite]: #11966
-#11970 := [monotonicity #11967]: #11969
-#12903 := [monotonicity #11970 #12900]: #12902
-#12909 := [trans #12903 #12907]: #12908
-#12912 := [monotonicity #11970 #12909]: #12911
-#11964 := (iff #3058 #11963)
-#11961 := (iff #3057 #11958)
-#11955 := (implies #412 #11952)
-#11959 := (iff #11955 #11958)
-#11960 := [rewrite]: #11959
-#11956 := (iff #3057 #11955)
-#11953 := (iff #3056 #11952)
-#11954 := [rewrite]: #11953
-#11957 := [monotonicity #11954]: #11956
-#11962 := [trans #11957 #11960]: #11961
-#11965 := [quant-intro #11962]: #11964
-#12915 := [monotonicity #11965 #12912]: #12914
-#12921 := [trans #12915 #12919]: #12920
-#12924 := [monotonicity #11965 #12921]: #12923
-#12927 := [monotonicity #12924]: #12926
-#12933 := [trans #12927 #12931]: #12932
-#12936 := [monotonicity #12933]: #12935
-#11949 := (iff #3050 #11948)
-#11946 := (iff #3049 #11945)
-#11943 := (iff #3048 #3047)
-#11944 := [rewrite]: #11943
-#11947 := [monotonicity #11944]: #11946
-#11950 := [monotonicity #11947]: #11949
-#12939 := [monotonicity #11950 #12936]: #12938
-#12945 := [trans #12939 #12943]: #12944
-#12948 := [monotonicity #12945]: #12947
-#12954 := [trans #12948 #12952]: #12953
-#12957 := [monotonicity #12954]: #12956
-#12963 := [trans #12957 #12961]: #12962
-#12966 := [monotonicity #12963]: #12965
-#12972 := [trans #12966 #12970]: #12971
-#12975 := [monotonicity #12972]: #12974
-#12981 := [trans #12975 #12979]: #12980
-#11941 := (iff #3039 #11940)
-#11938 := (iff #3038 #11937)
-#11939 := [rewrite]: #11938
-#11929 := (iff #3033 #11928)
-#11930 := [rewrite]: #11929
-#11942 := [monotonicity #11930 #11939]: #11941
-#12984 := [monotonicity #11942 #12981]: #12983
-#12990 := [trans #12984 #12988]: #12989
-#12993 := [monotonicity #11942 #12990]: #12992
-#11935 := (iff #3036 #11934)
-#11932 := (iff #3035 #11931)
-#11933 := [rewrite]: #11932
-#11936 := [monotonicity #11930 #11933]: #11935
-#12996 := [monotonicity #11936 #12993]: #12995
-#13002 := [trans #12996 #13000]: #13001
-#13005 := [monotonicity #11936 #13002]: #13004
-#11926 := (iff #3030 #11925)
-#11927 := [rewrite]: #11926
-#13008 := [monotonicity #11927 #13005]: #13007
-#13014 := [trans #13008 #13012]: #13013
-#13017 := [monotonicity #11927 #13014]: #13016
-#13020 := [monotonicity #13017]: #13019
-#13026 := [trans #13020 #13024]: #13025
-#11923 := (iff #3025 #11922)
-#11920 := (iff #3024 #11917)
-#11914 := (iff #11911 false)
-#11918 := (iff #11914 #11917)
-#11919 := [rewrite]: #11918
-#11915 := (iff #3024 #11914)
-#11912 := (iff #3023 #11911)
-#11913 := [rewrite]: #11912
-#11916 := [monotonicity #11913]: #11915
-#11921 := [trans #11916 #11919]: #11920
-#11924 := [quant-intro #11921]: #11923
-#13029 := [monotonicity #11924 #13026]: #13028
-#13035 := [trans #13029 #13033]: #13034
-#13038 := [monotonicity #13035]: #13037
-#13044 := [trans #13038 #13042]: #13043
-#13047 := [monotonicity #13044]: #13046
-#13053 := [trans #13047 #13051]: #13052
-#13056 := [monotonicity #13053]: #13055
-#13062 := [trans #13056 #13060]: #13061
-#13065 := [monotonicity #13062]: #13064
-#13071 := [trans #13065 #13069]: #13070
-#11909 := (iff #3006 #11908)
-#11903 := (iff #3003 #11902)
-#11904 := [rewrite]: #11903
-#11910 := [monotonicity #11904 #11907]: #11909
-#13074 := [monotonicity #11910 #13071]: #13073
-#13080 := [trans #13074 #13078]: #13079
-#11900 := (iff #3001 #11899)
-#11901 := [rewrite]: #11900
-#13083 := [monotonicity #11901 #13080]: #13082
-#13089 := [trans #13083 #13087]: #13088
-#11897 := (iff #2999 #11896)
-#11894 := (iff #2998 #11893)
-#11891 := (iff #2997 #11890)
-#11888 := (iff #2996 #11887)
-#11885 := (iff #2995 #11884)
-#11882 := (iff #2994 #11881)
-#11883 := [rewrite]: #11882
-#11879 := (iff #2992 #11878)
-#11876 := (iff #2991 #11875)
-#11877 := [rewrite]: #11876
-#11880 := [monotonicity #11877]: #11879
-#11886 := [monotonicity #11880 #11883]: #11885
-#11873 := (iff #2989 #11872)
-#11874 := [rewrite]: #11873
-#11889 := [monotonicity #11874 #11886]: #11888
-#11870 := (iff #2987 #11869)
-#11871 := [rewrite]: #11870
-#11892 := [monotonicity #11871 #11889]: #11891
-#11867 := (iff #2985 #11866)
-#11868 := [rewrite]: #11867
-#11895 := [monotonicity #11868 #11892]: #11894
-#11864 := (iff #2983 #11862)
-#11865 := [rewrite]: #11864
-#11898 := [monotonicity #11865 #11895]: #11897
-#13092 := [monotonicity #11898 #13089]: #13091
-#13098 := [trans #13092 #13096]: #13097
-#13101 := [monotonicity #13098]: #13100
-#13107 := [trans #13101 #13105]: #13106
-#13110 := [monotonicity #13107]: #13109
-#13116 := [trans #13110 #13114]: #13115
-#13119 := [monotonicity #13116]: #13118
-#13125 := [trans #13119 #13123]: #13124
-#13128 := [monotonicity #13125]: #13127
-#13134 := [trans #13128 #13132]: #13133
-#13137 := [monotonicity #13134]: #13136
-#13143 := [trans #13137 #13141]: #13142
-#13146 := [monotonicity #13143]: #13145
-#14054 := [trans #13146 #14052]: #14053
-#11861 := [asserted]: #3327
-#14055 := [mp #11861 #14054]: #14050
-#14073 := [not-or-elim #14055]: #13937
-#14076 := [and-elim #14073]: #11869
-#233 := (:var 0 T3)
-#2666 := (uf_48 #15 #233)
-#2667 := (pattern #2666)
-#11140 := (= uf_9 #2666)
-#11147 := (not #11140)
-#1259 := (uf_116 #15)
-#2669 := (uf_43 #233 #1259)
-#2670 := (= #15 #2669)
-#11148 := (or #2670 #11147)
-#11153 := (forall (vars (?x710 T5) (?x711 T3)) (:pat #2667) #11148)
-#17964 := (~ #11153 #11153)
-#17962 := (~ #11148 #11148)
-#17963 := [refl]: #17962
-#17965 := [nnf-pos #17963]: #17964
-#2668 := (= #2666 uf_9)
-#2671 := (implies #2668 #2670)
-#2672 := (forall (vars (?x710 T5) (?x711 T3)) (:pat #2667) #2671)
-#11154 := (iff #2672 #11153)
-#11151 := (iff #2671 #11148)
-#11144 := (implies #11140 #2670)
-#11149 := (iff #11144 #11148)
-#11150 := [rewrite]: #11149
-#11145 := (iff #2671 #11144)
-#11142 := (iff #2668 #11140)
-#11143 := [rewrite]: #11142
-#11146 := [monotonicity #11143]: #11145
-#11152 := [trans #11146 #11150]: #11151
-#11155 := [quant-intro #11152]: #11154
-#11139 := [asserted]: #2672
-#11158 := [mp #11139 #11155]: #11153
-#17966 := [mp~ #11158 #17965]: #11153
-#25932 := (not #11869)
-#25945 := (not #11153)
-#25946 := (or #25945 #25932 #25940)
-#25941 := (or #25940 #25932)
-#25947 := (or #25945 #25941)
-#25954 := (iff #25947 #25946)
-#25942 := (or #25932 #25940)
-#25949 := (or #25945 #25942)
-#25952 := (iff #25949 #25946)
-#25953 := [rewrite]: #25952
-#25950 := (iff #25947 #25949)
-#25943 := (iff #25941 #25942)
-#25944 := [rewrite]: #25943
-#25951 := [monotonicity #25944]: #25950
-#25955 := [trans #25951 #25953]: #25954
-#25948 := [quant-inst]: #25947
-#25956 := [mp #25948 #25955]: #25946
-#28304 := [unit-resolution #25956 #17966 #14076]: #25940
-#26515 := [monotonicity #28304 #28304]: #26728
-#26577 := [symm #26515]: #26725
-#26481 := (= uf_9 #26480)
-decl uf_196 :: (-> T4 T5 T5 T2)
-#26478 := (uf_196 uf_287 #25933 #25933)
-#26479 := (= uf_9 #26478)
-#26483 := (iff #26479 #26481)
-#2245 := (:var 0 T16)
-#21 := (:var 2 T5)
-#13 := (:var 3 T4)
-#2256 := (uf_200 #13 #21 #15 #2245)
-#2257 := (pattern #2256)
-#2259 := (uf_196 #13 #21 #15)
-#10103 := (= uf_9 #2259)
-#10099 := (= uf_9 #2256)
-#10106 := (iff #10099 #10103)
-#10109 := (forall (vars (?x586 T4) (?x587 T5) (?x588 T5) (?x589 T16)) (:pat #2257) #10106)
-#17606 := (~ #10109 #10109)
-#17604 := (~ #10106 #10106)
-#17605 := [refl]: #17604
-#17607 := [nnf-pos #17605]: #17606
-#2260 := (= #2259 uf_9)
-#2258 := (= #2256 uf_9)
-#2261 := (iff #2258 #2260)
-#2262 := (forall (vars (?x586 T4) (?x587 T5) (?x588 T5) (?x589 T16)) (:pat #2257) #2261)
-#10110 := (iff #2262 #10109)
-#10107 := (iff #2261 #10106)
-#10104 := (iff #2260 #10103)
-#10105 := [rewrite]: #10104
-#10101 := (iff #2258 #10099)
-#10102 := [rewrite]: #10101
-#10108 := [monotonicity #10102 #10105]: #10107
-#10111 := [quant-intro #10108]: #10110
-#10098 := [asserted]: #2262
-#10114 := [mp #10098 #10111]: #10109
-#17608 := [mp~ #10114 #17607]: #10109
-#26501 := (not #10109)
-#26502 := (or #26501 #26483)
-#26482 := (iff #26481 #26479)
-#26499 := (or #26501 #26482)
-#26504 := (iff #26499 #26502)
-#26506 := (iff #26502 #26502)
-#26486 := [rewrite]: #26506
-#26484 := (iff #26482 #26483)
-#26485 := [rewrite]: #26484
-#26505 := [monotonicity #26485]: #26504
-#26488 := [trans #26505 #26486]: #26504
-#26503 := [quant-inst]: #26499
-#26489 := [mp #26503 #26488]: #26502
-#26699 := [unit-resolution #26489 #17608]: #26483
-#26490 := (not #26483)
-#26518 := (or #26490 #26481)
-#26344 := (uf_13 #25933)
-#26590 := (uf_12 #26344)
-#26593 := (= uf_14 #26590)
-#26712 := (not #26593)
-#26713 := (iff #11878 #26712)
-#26710 := (iff #11875 #26593)
-#26729 := (iff #26593 #11875)
-#26705 := (= #26590 #2990)
-#26703 := (= #26344 #2977)
-#24763 := (uf_13 #2981)
-#28352 := (= #24763 #2977)
-#24766 := (= #2977 #24763)
-#2697 := (uf_43 #326 #161)
-#22937 := (pattern #2697)
-#2701 := (uf_13 #2697)
-#11218 := (= #326 #2701)
-#22944 := (forall (vars (?x720 T3) (?x721 int)) (:pat #22937) #11218)
-#11222 := (forall (vars (?x720 T3) (?x721 int)) #11218)
-#22947 := (iff #11222 #22944)
-#22945 := (iff #11218 #11218)
-#22946 := [refl]: #22945
-#22948 := [quant-intro #22946]: #22947
-#17989 := (~ #11222 #11222)
-#17987 := (~ #11218 #11218)
-#17988 := [refl]: #17987
-#17990 := [nnf-pos #17988]: #17989
-#2702 := (= #2701 #326)
-#2703 := (forall (vars (?x720 T3) (?x721 int)) #2702)
-#11223 := (iff #2703 #11222)
-#11220 := (iff #2702 #11218)
-#11221 := [rewrite]: #11220
-#11224 := [quant-intro #11221]: #11223
-#11217 := [asserted]: #2703
-#11227 := [mp #11217 #11224]: #11222
-#17991 := [mp~ #11227 #17990]: #11222
-#22949 := [mp #17991 #22948]: #22944
-#24710 := (not #22944)
-#24771 := (or #24710 #24766)
-#24772 := [quant-inst]: #24771
-#28286 := [unit-resolution #24772 #22949]: #24766
-#28353 := [symm #28286]: #28352
-#26696 := (= #26344 #24763)
-#28305 := (= #25933 #2981)
-#28306 := [symm #28304]: #28305
-#26702 := [monotonicity #28306]: #26696
-#26704 := [trans #26702 #28353]: #26703
-#26706 := [monotonicity #26704]: #26705
-#26708 := [monotonicity #26706]: #26729
-#26711 := [symm #26708]: #26710
-#26727 := [monotonicity #26711]: #26713
-#14078 := [and-elim #14073]: #11878
-#26737 := [mp #14078 #26727]: #26712
-#26582 := (uf_24 uf_287 #25933)
-#26583 := (= uf_9 #26582)
-#26744 := (= #2988 #26582)
-#26738 := (= #26582 #2988)
-#26719 := [monotonicity #28306]: #26738
-#26747 := [symm #26719]: #26744
-#14077 := [and-elim #14073]: #11872
-#26746 := [trans #14077 #26747]: #26583
-#26585 := (uf_48 #25933 #26344)
-#26586 := (= uf_9 #26585)
-#26751 := (= #2986 #26585)
-#26748 := (= #26585 #2986)
-#26749 := [monotonicity #28306 #26704]: #26748
-#26752 := [symm #26749]: #26751
-#26758 := [trans #14076 #26752]: #26586
-#26587 := (not #26586)
-#26584 := (not #26583)
-#26819 := (or #26584 #26587 #26593)
-#26356 := (uf_25 uf_287 #25933)
-#26588 := (= uf_26 #26356)
-#26784 := (= #2984 #26356)
-#26780 := (= #26356 #2984)
-#26781 := [monotonicity #28306]: #26780
-#26785 := [symm #26781]: #26784
-#14075 := [and-elim #14073]: #11866
-#26779 := [trans #14075 #26785]: #26588
-#26500 := (not #26479)
-#26786 := [hypothesis]: #26500
-#26382 := (uf_27 uf_287 #25933)
-#26383 := (= uf_9 #26382)
-#26789 := (= #2982 #26382)
-#26759 := (= #26382 #2982)
-#26787 := [monotonicity #28306]: #26759
-#26810 := [symm #26787]: #26789
-#14074 := [and-elim #14073]: #11862
-#26811 := [trans #14074 #26810]: #26383
-#26345 := (uf_23 #26344)
-#26352 := (= uf_9 #26345)
-#26835 := (= #2993 #26345)
-#26812 := (= #26345 #2993)
-#26813 := [monotonicity #26704]: #26812
-#26800 := [symm #26813]: #26835
-#14079 := [and-elim #14073]: #11881
-#26836 := [trans #14079 #26800]: #26352
-#14062 := [not-or-elim #14055]: #11908
-#14064 := [and-elim #14062]: #11905
-#2217 := (uf_196 #47 #23 #23)
-#2218 := (pattern #2217)
-#9984 := (= uf_9 #2217)
-#227 := (uf_55 #47)
-#3899 := (= uf_9 #227)
-#19163 := (not #3899)
-#144 := (uf_48 #23 #26)
-#3620 := (= uf_9 #144)
-#19038 := (not #3620)
-#19037 := (not #3617)
-#135 := (uf_27 #47 #23)
-#3602 := (= uf_9 #135)
-#10693 := (not #3602)
-#71 := (uf_23 #26)
-#3455 := (= uf_9 #71)
-#10748 := (not #3455)
-#21596 := (or #29 #10748 #10693 #19037 #19038 #11068 #19163 #9984)
-#21601 := (forall (vars (?x572 T4) (?x573 T5)) (:pat #2218) #21596)
-#9999 := (and #52 #3455 #3602 #3617 #3620 #3623 #3899)
-#10002 := (not #9999)
-#10008 := (or #9984 #10002)
-#10013 := (forall (vars (?x572 T4) (?x573 T5)) (:pat #2218) #10008)
-#21602 := (iff #10013 #21601)
-#21599 := (iff #10008 #21596)
-#21582 := (or #29 #10748 #10693 #19037 #19038 #11068 #19163)
-#21593 := (or #9984 #21582)
-#21597 := (iff #21593 #21596)
-#21598 := [rewrite]: #21597
-#21594 := (iff #10008 #21593)
-#21591 := (iff #10002 #21582)
-#21583 := (not #21582)
-#21586 := (not #21583)
-#21589 := (iff #21586 #21582)
-#21590 := [rewrite]: #21589
-#21587 := (iff #10002 #21586)
-#21584 := (iff #9999 #21583)
-#21585 := [rewrite]: #21584
-#21588 := [monotonicity #21585]: #21587
-#21592 := [trans #21588 #21590]: #21591
-#21595 := [monotonicity #21592]: #21594
-#21600 := [trans #21595 #21598]: #21599
-#21603 := [quant-intro #21600]: #21602
-#17574 := (~ #10013 #10013)
-#17572 := (~ #10008 #10008)
-#17573 := [refl]: #17572
-#17575 := [nnf-pos #17573]: #17574
-#2225 := (= #2217 uf_9)
-#72 := (= #71 uf_9)
-#2219 := (and #52 #72)
-#2220 := (and #147 #2219)
-#145 := (= #144 uf_9)
-#2221 := (and #145 #2220)
-#2222 := (and #143 #2221)
-#136 := (= #135 uf_9)
-#2223 := (and #136 #2222)
-#229 := (= #227 uf_9)
-#2224 := (and #229 #2223)
-#2226 := (implies #2224 #2225)
-#2227 := (forall (vars (?x572 T4) (?x573 T5)) (:pat #2218) #2226)
-#10016 := (iff #2227 #10013)
-#9965 := (and #52 #3455)
-#9969 := (and #3623 #9965)
-#9972 := (and #3620 #9969)
-#9975 := (and #3617 #9972)
-#9978 := (and #3602 #9975)
-#9981 := (and #3899 #9978)
-#9990 := (not #9981)
-#9991 := (or #9990 #9984)
-#9996 := (forall (vars (?x572 T4) (?x573 T5)) (:pat #2218) #9991)
-#10014 := (iff #9996 #10013)
-#10011 := (iff #9991 #10008)
-#10005 := (or #10002 #9984)
-#10009 := (iff #10005 #10008)
-#10010 := [rewrite]: #10009
-#10006 := (iff #9991 #10005)
-#10003 := (iff #9990 #10002)
-#10000 := (iff #9981 #9999)
-#10001 := [rewrite]: #10000
-#10004 := [monotonicity #10001]: #10003
-#10007 := [monotonicity #10004]: #10006
-#10012 := [trans #10007 #10010]: #10011
-#10015 := [quant-intro #10012]: #10014
-#9997 := (iff #2227 #9996)
-#9994 := (iff #2226 #9991)
-#9987 := (implies #9981 #9984)
-#9992 := (iff #9987 #9991)
-#9993 := [rewrite]: #9992
-#9988 := (iff #2226 #9987)
-#9985 := (iff #2225 #9984)
-#9986 := [rewrite]: #9985
-#9982 := (iff #2224 #9981)
-#9979 := (iff #2223 #9978)
-#9976 := (iff #2222 #9975)
-#9973 := (iff #2221 #9972)
-#9970 := (iff #2220 #9969)
-#9967 := (iff #2219 #9965)
-#3456 := (iff #72 #3455)
-#3457 := [rewrite]: #3456
-#9968 := [monotonicity #3457]: #9967
-#9971 := [monotonicity #3625 #9968]: #9970
-#3621 := (iff #145 #3620)
-#3622 := [rewrite]: #3621
-#9974 := [monotonicity #3622 #9971]: #9973
-#9977 := [monotonicity #3619 #9974]: #9976
-#3604 := (iff #136 #3602)
-#3605 := [rewrite]: #3604
-#9980 := [monotonicity #3605 #9977]: #9979
-#3901 := (iff #229 #3899)
-#3902 := [rewrite]: #3901
-#9983 := [monotonicity #3902 #9980]: #9982
-#9989 := [monotonicity #9983 #9986]: #9988
-#9995 := [trans #9989 #9993]: #9994
-#9998 := [quant-intro #9995]: #9997
-#10017 := [trans #9998 #10015]: #10016
-#9964 := [asserted]: #2227
-#10018 := [mp #9964 #10017]: #10013
-#17576 := [mp~ #10018 #17575]: #10013
-#21604 := [mp #17576 #21603]: #21601
-#26589 := (not #26588)
-#26409 := (not #26383)
-#26353 := (not #26352)
-#24483 := (not #11905)
-#26517 := (not #21601)
-#26520 := (or #26517 #24483 #26353 #26409 #26479 #26584 #26587 #26589 #26593)
-#26591 := (= #26590 uf_14)
-#26592 := (or #26591 #26353 #26409 #26589 #26587 #26584 #24483 #26479)
-#26521 := (or #26517 #26592)
-#26572 := (iff #26521 #26520)
-#26599 := (or #24483 #26353 #26409 #26479 #26584 #26587 #26589 #26593)
-#26523 := (or #26517 #26599)
-#26570 := (iff #26523 #26520)
-#26571 := [rewrite]: #26570
-#26574 := (iff #26521 #26523)
-#26602 := (iff #26592 #26599)
-#26596 := (or #26593 #26353 #26409 #26589 #26587 #26584 #24483 #26479)
-#26600 := (iff #26596 #26599)
-#26601 := [rewrite]: #26600
-#26597 := (iff #26592 #26596)
-#26594 := (iff #26591 #26593)
-#26595 := [rewrite]: #26594
-#26598 := [monotonicity #26595]: #26597
-#26603 := [trans #26598 #26601]: #26602
-#26569 := [monotonicity #26603]: #26574
-#26568 := [trans #26569 #26571]: #26572
-#26522 := [quant-inst]: #26521
-#26573 := [mp #26522 #26568]: #26520
-#26837 := [unit-resolution #26573 #21604 #14064 #26836 #26811 #26786 #26779]: #26819
-#26838 := [unit-resolution #26837 #26758 #26746 #26737]: false
-#26899 := [lemma #26838]: #26479
-#26492 := (or #26490 #26500 #26481)
-#26493 := [def-axiom]: #26492
-#26513 := [unit-resolution #26493 #26899]: #26518
-#26519 := [unit-resolution #26513 #26699]: #26481
-#26578 := [trans #26519 #26577]: #11925
-#26514 := [hypothesis]: #13009
-#26580 := [unit-resolution #26514 #26578]: false
-#26581 := [lemma #26580]: #11925
-#23239 := (or #13009 #23236)
-#22240 := (forall (vars (?x778 int)) #22229)
-#22247 := (not #22240)
-#22225 := (forall (vars (?x776 int)) #22220)
-#22246 := (not #22225)
-#22248 := (or #22246 #22247)
-#22249 := (not #22248)
-#22278 := (or #22249 #22275)
-#22284 := (not #22278)
-#22285 := (or #12079 #12070 #12061 #12052 #22161 #13365 #13511 #22284)
-#22286 := (not #22285)
-#22064 := (forall (vars (?x785 int)) #22059)
-#22070 := (not #22064)
-#22071 := (or #22046 #22070)
-#22072 := (not #22071)
-#22101 := (or #22072 #22098)
-#22107 := (not #22101)
-#22108 := (or #13264 #22107)
-#22109 := (not #22108)
-#22114 := (or #13264 #22109)
-#22122 := (not #22114)
-#22123 := (or #12401 #22120 #18276 #22121 #13331 #18279 #22122)
-#22124 := (not #22123)
-#22129 := (or #18276 #18279 #22124)
-#22135 := (not #22129)
-#22172 := (or #12566 #12557 #22161 #13365 #22120 #13416 #22135)
-#22173 := (not #22172)
-#22136 := (or #12476 #12467 #18238 #18247 #12485 #12449 #12440 #13365 #22120 #22135)
-#22137 := (not #22136)
-#22142 := (or #18238 #18247 #22137)
-#22148 := (not #22142)
-#22149 := (or #18238 #18241 #22148)
-#22150 := (not #22149)
-#22155 := (or #18238 #18241 #22150)
-#22162 := (not #22155)
-#22163 := (or #22161 #13365 #13417 #22162)
-#22164 := (not #22163)
-#22178 := (or #22164 #22173)
-#22184 := (not #22178)
-#22185 := (or #18238 #18247 #22161 #13365 #22184)
-#22186 := (not #22185)
-#22191 := (or #18238 #18247 #22186)
-#22197 := (not #22191)
-#22198 := (or #18238 #18241 #22197)
-#22199 := (not #22198)
-#22204 := (or #18238 #18241 #22199)
-#22210 := (not #22204)
-#22211 := (or #22161 #13365 #13510 #22210)
-#22212 := (not #22211)
-#22291 := (or #22212 #22286)
-#22306 := (not #22291)
-#22041 := (forall (vars (?x775 int)) #22036)
-#22302 := (not #22041)
-#22307 := (or #12976 #12769 #12760 #12751 #12742 #22297 #22298 #22299 #14996 #13683 #13217 #22161 #13365 #13688 #13740 #22300 #22301 #22303 #22304 #22305 #22302 #22306)
-#22308 := (not #22307)
-#22313 := (or #12976 #13217 #22308)
-#22320 := (not #22313)
-#22030 := (forall (vars (?x773 int)) #22025)
-#22319 := (not #22030)
-#22321 := (or #22319 #22320)
-#22322 := (not #22321)
-#22327 := (or #22019 #22322)
-#22333 := (not #22327)
-#22334 := (or #13181 #22333)
-#22335 := (not #22334)
-#22340 := (or #13181 #22335)
-#22346 := (not #22340)
-#22347 := (or #12976 #12967 #12958 #12949 #18127 #18136 #22346)
-#22348 := (not #22347)
-#22353 := (or #18127 #18136 #22348)
-#22359 := (not #22353)
-#22360 := (or #18127 #18130 #22359)
-#22361 := (not #22360)
-#22366 := (or #18127 #18130 #22361)
-#22372 := (not #22366)
-#22373 := (or #13009 #22372)
-#22374 := (not #22373)
-#22379 := (or #13009 #22374)
-#23240 := (iff #22379 #23239)
-#23237 := (iff #22374 #23236)
-#23234 := (iff #22373 #23233)
-#23231 := (iff #22372 #23230)
-#23228 := (iff #22366 #23227)
-#23225 := (iff #22361 #23224)
-#23222 := (iff #22360 #23221)
-#23219 := (iff #22359 #23218)
-#23216 := (iff #22353 #23215)
-#23213 := (iff #22348 #23212)
-#23210 := (iff #22347 #23209)
-#23207 := (iff #22346 #23206)
-#23204 := (iff #22340 #23203)
-#23201 := (iff #22335 #23200)
-#23198 := (iff #22334 #23197)
-#23195 := (iff #22333 #23194)
-#23192 := (iff #22327 #23191)
-#23189 := (iff #22322 #23188)
-#23186 := (iff #22321 #23185)
-#23183 := (iff #22320 #23182)
-#23180 := (iff #22313 #23179)
-#23177 := (iff #22308 #23176)
-#23174 := (iff #22307 #23173)
-#23171 := (iff #22306 #23170)
-#23168 := (iff #22291 #23167)
-#23165 := (iff #22286 #23164)
-#23162 := (iff #22285 #23161)
-#23159 := (iff #22284 #23158)
-#23156 := (iff #22278 #23155)
-#23153 := (iff #22249 #23152)
-#23150 := (iff #22248 #23149)
-#23147 := (iff #22247 #23146)
-#23144 := (iff #22240 #23141)
-#23142 := (iff #22229 #22229)
-#23143 := [refl]: #23142
-#23145 := [quant-intro #23143]: #23144
-#23148 := [monotonicity #23145]: #23147
-#23139 := (iff #22246 #23138)
-#23136 := (iff #22225 #23133)
-#23134 := (iff #22220 #22220)
-#23135 := [refl]: #23134
-#23137 := [quant-intro #23135]: #23136
-#23140 := [monotonicity #23137]: #23139
-#23151 := [monotonicity #23140 #23148]: #23150
-#23154 := [monotonicity #23151]: #23153
-#23157 := [monotonicity #23154]: #23156
-#23160 := [monotonicity #23157]: #23159
-#23163 := [monotonicity #23160]: #23162
-#23166 := [monotonicity #23163]: #23165
-#23131 := (iff #22212 #23130)
-#23128 := (iff #22211 #23127)
-#23125 := (iff #22210 #23124)
-#23122 := (iff #22204 #23121)
-#23119 := (iff #22199 #23118)
-#23116 := (iff #22198 #23115)
-#23113 := (iff #22197 #23112)
-#23110 := (iff #22191 #23109)
-#23107 := (iff #22186 #23106)
-#23104 := (iff #22185 #23103)
-#23101 := (iff #22184 #23100)
-#23098 := (iff #22178 #23097)
-#23095 := (iff #22173 #23094)
-#23092 := (iff #22172 #23091)
-#23059 := (iff #22135 #23058)
-#23056 := (iff #22129 #23055)
-#23053 := (iff #22124 #23052)
-#23050 := (iff #22123 #23049)
-#23047 := (iff #22122 #23046)
-#23044 := (iff #22114 #23043)
-#23041 := (iff #22109 #23040)
-#23038 := (iff #22108 #23037)
-#23035 := (iff #22107 #23034)
-#23032 := (iff #22101 #23031)
-#23029 := (iff #22072 #23028)
-#23026 := (iff #22071 #23025)
-#23023 := (iff #22070 #23022)
-#23020 := (iff #22064 #23017)
-#23018 := (iff #22059 #22059)
-#23019 := [refl]: #23018
-#23021 := [quant-intro #23019]: #23020
-#23024 := [monotonicity #23021]: #23023
-#23027 := [monotonicity #23024]: #23026
-#23030 := [monotonicity #23027]: #23029
-#23033 := [monotonicity #23030]: #23032
-#23036 := [monotonicity #23033]: #23035
-#23039 := [monotonicity #23036]: #23038
-#23042 := [monotonicity #23039]: #23041
-#23045 := [monotonicity #23042]: #23044
-#23048 := [monotonicity #23045]: #23047
-#23051 := [monotonicity #23048]: #23050
-#23054 := [monotonicity #23051]: #23053
-#23057 := [monotonicity #23054]: #23056
-#23060 := [monotonicity #23057]: #23059
-#23093 := [monotonicity #23060]: #23092
-#23096 := [monotonicity #23093]: #23095
-#23089 := (iff #22164 #23088)
-#23086 := (iff #22163 #23085)
-#23083 := (iff #22162 #23082)
-#23080 := (iff #22155 #23079)
-#23077 := (iff #22150 #23076)
-#23074 := (iff #22149 #23073)
-#23071 := (iff #22148 #23070)
-#23068 := (iff #22142 #23067)
-#23065 := (iff #22137 #23064)
-#23062 := (iff #22136 #23061)
-#23063 := [monotonicity #23060]: #23062
-#23066 := [monotonicity #23063]: #23065
-#23069 := [monotonicity #23066]: #23068
-#23072 := [monotonicity #23069]: #23071
-#23075 := [monotonicity #23072]: #23074
-#23078 := [monotonicity #23075]: #23077
-#23081 := [monotonicity #23078]: #23080
-#23084 := [monotonicity #23081]: #23083
-#23087 := [monotonicity #23084]: #23086
-#23090 := [monotonicity #23087]: #23089
-#23099 := [monotonicity #23090 #23096]: #23098
-#23102 := [monotonicity #23099]: #23101
-#23105 := [monotonicity #23102]: #23104
-#23108 := [monotonicity #23105]: #23107
-#23111 := [monotonicity #23108]: #23110
-#23114 := [monotonicity #23111]: #23113
-#23117 := [monotonicity #23114]: #23116
-#23120 := [monotonicity #23117]: #23119
-#23123 := [monotonicity #23120]: #23122
-#23126 := [monotonicity #23123]: #23125
-#23129 := [monotonicity #23126]: #23128
-#23132 := [monotonicity #23129]: #23131
-#23169 := [monotonicity #23132 #23166]: #23168
-#23172 := [monotonicity #23169]: #23171
-#23015 := (iff #22302 #23014)
-#23012 := (iff #22041 #23009)
-#23010 := (iff #22036 #22036)
-#23011 := [refl]: #23010
-#23013 := [quant-intro #23011]: #23012
-#23016 := [monotonicity #23013]: #23015
-#23175 := [monotonicity #23016 #23172]: #23174
-#23178 := [monotonicity #23175]: #23177
-#23181 := [monotonicity #23178]: #23180
-#23184 := [monotonicity #23181]: #23183
-#23007 := (iff #22319 #23006)
-#23004 := (iff #22030 #23001)
-#23002 := (iff #22025 #22025)
-#23003 := [refl]: #23002
-#23005 := [quant-intro #23003]: #23004
-#23008 := [monotonicity #23005]: #23007
-#23187 := [monotonicity #23008 #23184]: #23186
-#23190 := [monotonicity #23187]: #23189
-#23193 := [monotonicity #23190]: #23192
-#23196 := [monotonicity #23193]: #23195
-#23199 := [monotonicity #23196]: #23198
-#23202 := [monotonicity #23199]: #23201
-#23205 := [monotonicity #23202]: #23204
-#23208 := [monotonicity #23205]: #23207
-#23211 := [monotonicity #23208]: #23210
-#23214 := [monotonicity #23211]: #23213
-#23217 := [monotonicity #23214]: #23216
-#23220 := [monotonicity #23217]: #23219
-#23223 := [monotonicity #23220]: #23222
+#12826 := [monotonicity #12498 #12823]: #12825
+#12831 := [trans #12826 #12829]: #12830
+#12834 := [monotonicity #12498 #12831]: #12833
+#12837 := [monotonicity #12492 #12834]: #12836
+#12842 := [trans #12837 #12840]: #12841
+#12845 := [monotonicity #12492 #12842]: #12844
+#12848 := [monotonicity #12143 #12845]: #12847
+#12853 := [trans #12848 #12851]: #12852
+#12856 := [monotonicity #12143 #12853]: #12855
+#12861 := [trans #12856 #12859]: #12860
+#12864 := [monotonicity #12861]: #12863
+#12870 := [trans #12864 #12868]: #12869
+#12873 := [monotonicity #12143 #12870]: #12872
+#12878 := [trans #12873 #12876]: #12877
+#12914 := [monotonicity #12878 #12911]: #12913
+#12917 := [monotonicity #12143 #12914]: #12916
+#12922 := [trans #12917 #12920]: #12921
+#12482 := (iff #3220 true)
+#12480 := (iff #12477 true)
+#12481 := [rewrite]: #12480
+#12478 := (iff #3220 #12477)
+#12475 := (iff #3219 true)
+#12476 := [rewrite]: #12475
+#12473 := (iff #3218 true)
+#12474 := [rewrite]: #12473
+#12479 := [monotonicity #12474 #12476]: #12478
+#12483 := [trans #12479 #12481]: #12482
+#12925 := [monotonicity #12483 #12922]: #12924
+#12929 := [trans #12925 #12927]: #12928
+#12471 := (iff #3217 #12470)
+#12468 := (iff #3216 #12467)
+#12469 := [rewrite]: #12468
+#12465 := (iff #3214 #12464)
+#12466 := [rewrite]: #12465
+#12472 := [monotonicity #12466 #12469]: #12471
+#12932 := [monotonicity #12472 #12929]: #12931
+#12938 := [trans #12932 #12936]: #12937
+#12462 := (iff #3212 #12461)
+#12463 := [rewrite]: #12462
+#12941 := [monotonicity #12463 #12938]: #12940
+#12947 := [trans #12941 #12945]: #12946
+#12459 := (iff #3210 #12458)
+#12460 := [rewrite]: #12459
+#12950 := [monotonicity #12460 #12947]: #12949
+#12956 := [trans #12950 #12954]: #12955
+#12456 := (iff #3208 #12455)
+#12457 := [rewrite]: #12456
+#12959 := [monotonicity #12457 #12956]: #12958
+#12965 := [trans #12959 #12963]: #12964
+#12453 := (iff #3206 #12452)
+#12454 := [rewrite]: #12453
+#12968 := [monotonicity #12454 #12965]: #12967
+#12974 := [trans #12968 #12972]: #12973
+#12176 := (iff #3124 #12173)
+#12170 := (and #12167 #12054)
+#12174 := (iff #12170 #12173)
+#12175 := [rewrite]: #12174
+#12171 := (iff #3124 #12170)
+#12055 := (iff #3033 #12054)
+#12056 := [rewrite]: #12055
+#12168 := (iff #3123 #12167)
+#12169 := [rewrite]: #12168
+#12172 := [monotonicity #12169 #12056]: #12171
+#12177 := [trans #12172 #12175]: #12176
+#12977 := [monotonicity #12177 #12974]: #12976
+#12982 := [trans #12977 #12980]: #12981
+#12431 := (iff #3200 #12430)
+#12428 := (iff #3199 #12427)
+#12425 := (iff #3198 #12424)
+#12426 := [rewrite]: #12425
+#12429 := [monotonicity #12426]: #12428
+#12432 := [monotonicity #12429]: #12431
+#12985 := [monotonicity #12432 #12982]: #12984
+#12991 := [trans #12985 #12989]: #12990
+#12450 := (iff #3204 #12430)
+#12433 := (and true #12430)
+#12436 := (iff #12433 #12430)
+#12437 := [rewrite]: #12436
+#12448 := (iff #3204 #12433)
+#12446 := (iff #3203 #12430)
+#12444 := (iff #3203 #12433)
+#12442 := (iff #3202 #12430)
+#12440 := (iff #3202 #12433)
+#12438 := (iff #3201 #12430)
+#12434 := (iff #3201 #12433)
+#12422 := (iff #3191 true)
+#12417 := (forall (vars (?v0 S5)) (:pat #3187) true)
+#12420 := (iff #12417 true)
+#12421 := [elim-unused]: #12420
+#12418 := (iff #3191 #12417)
+#12415 := (iff #3190 true)
+#12367 := (= f1 #3175)
+#12379 := (implies #12367 #12367)
+#12382 := (iff #12379 true)
+#12383 := [rewrite]: #12382
+#12413 := (iff #3190 #12379)
+#12411 := (iff #3189 #12367)
+#12372 := (and true #12367)
+#12375 := (iff #12372 #12367)
+#12376 := [rewrite]: #12375
+#12409 := (iff #3189 #12372)
+#12368 := (iff #3176 #12367)
+#12369 := [rewrite]: #12368
+#12407 := (iff #3188 true)
+#12408 := [rewrite]: #12407
+#12410 := [monotonicity #12408 #12369]: #12409
+#12412 := [trans #12410 #12376]: #12411
+#12414 := [monotonicity #12369 #12412]: #12413
+#12416 := [trans #12414 #12383]: #12415
+#12419 := [quant-intro #12416]: #12418
+#12423 := [trans #12419 #12421]: #12422
+#12435 := [monotonicity #12423 #12432]: #12434
+#12439 := [trans #12435 #12437]: #12438
+#12405 := (iff #3184 true)
+#12360 := (forall (vars (?v0 S5)) (:pat #3164) true)
+#12363 := (iff #12360 true)
+#12364 := [elim-unused]: #12363
+#12403 := (iff #3184 #12360)
+#12401 := (iff #3183 true)
+#12399 := (iff #3183 #12379)
+#12397 := (iff #3182 #12367)
+#12395 := (iff #3182 #12372)
+#12393 := (iff #3181 true)
+#12394 := [rewrite]: #12393
+#12396 := [monotonicity #12394 #12369]: #12395
+#12398 := [trans #12396 #12376]: #12397
+#12400 := [monotonicity #12369 #12398]: #12399
+#12402 := [trans #12400 #12383]: #12401
+#12404 := [quant-intro #12402]: #12403
+#12406 := [trans #12404 #12364]: #12405
+#12441 := [monotonicity #12406 #12439]: #12440
+#12443 := [trans #12441 #12437]: #12442
+#12391 := (iff #3180 true)
+#12386 := (forall (vars (?v0 S5)) (:pat #3174) true)
+#12389 := (iff #12386 true)
+#12390 := [elim-unused]: #12389
+#12387 := (iff #3180 #12386)
+#12384 := (iff #3179 true)
+#12380 := (iff #3179 #12379)
+#12377 := (iff #3178 #12367)
+#12373 := (iff #3178 #12372)
+#12370 := (iff #3177 true)
+#12371 := [rewrite]: #12370
+#12374 := [monotonicity #12371 #12369]: #12373
+#12378 := [trans #12374 #12376]: #12377
+#12381 := [monotonicity #12369 #12378]: #12380
+#12385 := [trans #12381 #12383]: #12384
+#12388 := [quant-intro #12385]: #12387
+#12392 := [trans #12388 #12390]: #12391
+#12445 := [monotonicity #12392 #12443]: #12444
+#12447 := [trans #12445 #12437]: #12446
+#12365 := (iff #3171 true)
+#12361 := (iff #3171 #12360)
+#12358 := (iff #3170 true)
+#12347 := (= f262 #3167)
+#12350 := (not #12347)
+#12353 := (implies #12350 #12350)
+#12356 := (iff #12353 true)
+#12357 := [rewrite]: #12356
+#12354 := (iff #3170 #12353)
+#12351 := (iff #3169 #12350)
+#12348 := (iff #3168 #12347)
+#12349 := [rewrite]: #12348
+#12352 := [monotonicity #12349]: #12351
+#12355 := [monotonicity #12352 #12352]: #12354
+#12359 := [trans #12355 #12357]: #12358
+#12362 := [quant-intro #12359]: #12361
+#12366 := [trans #12362 #12364]: #12365
+#12449 := [monotonicity #12366 #12447]: #12448
+#12451 := [trans #12449 #12437]: #12450
+#12994 := [monotonicity #12451 #12991]: #12993
+#12999 := [trans #12994 #12997]: #12998
+#13002 := [monotonicity #12143 #12999]: #13001
+#13007 := [trans #13002 #13005]: #13006
+#13010 := [monotonicity #12143 #13007]: #13009
+#13015 := [trans #13010 #13013]: #13014
+#13018 := [monotonicity #12143 #13015]: #13017
+#13023 := [trans #13018 #13021]: #13022
+#12345 := (iff #3161 true)
+#12340 := (implies #12141 true)
+#12343 := (iff #12340 true)
+#12344 := [rewrite]: #12343
+#12341 := (iff #3161 #12340)
+#12338 := (iff #3160 true)
+#12312 := (or #12311 #12303)
+#12320 := (or #12258 #12312)
+#12328 := (or #12258 #12320)
+#12333 := (implies false #12328)
+#12336 := (iff #12333 true)
+#12337 := [rewrite]: #12336
+#12334 := (iff #3160 #12333)
+#12331 := (iff #3159 #12328)
+#12325 := (implies #12141 #12320)
+#12329 := (iff #12325 #12328)
+#12330 := [rewrite]: #12329
+#12326 := (iff #3159 #12325)
+#12323 := (iff #3158 #12320)
+#12317 := (implies #12141 #12312)
+#12321 := (iff #12317 #12320)
+#12322 := [rewrite]: #12321
+#12318 := (iff #3158 #12317)
+#12315 := (iff #3157 #12312)
+#12308 := (implies #12173 #12303)
+#12313 := (iff #12308 #12312)
+#12314 := [rewrite]: #12313
+#12309 := (iff #3157 #12308)
+#12310 := [monotonicity #12177 #12307]: #12309
+#12316 := [trans #12310 #12314]: #12315
+#12319 := [monotonicity #12143 #12316]: #12318
+#12324 := [trans #12319 #12322]: #12323
+#12327 := [monotonicity #12143 #12324]: #12326
+#12332 := [trans #12327 #12330]: #12331
+#12335 := [monotonicity #12166 #12332]: #12334
+#12339 := [trans #12335 #12337]: #12338
+#12342 := [monotonicity #12143 #12339]: #12341
+#12346 := [trans #12342 #12344]: #12345
+#13026 := [monotonicity #12346 #13023]: #13025
+#13030 := [trans #13026 #13028]: #13029
+#13033 := [monotonicity #12143 #13030]: #13032
+#13038 := [trans #13033 #13036]: #13037
+#12163 := (iff #3120 #12162)
+#12160 := (iff #3119 #12159)
+#12161 := [rewrite]: #12160
+#12164 := [monotonicity #12161]: #12163
+#13041 := [monotonicity #12164 #13038]: #13040
+#13047 := [trans #13041 #13045]: #13046
+#12157 := (iff #3115 #12156)
+#12154 := (iff #3114 #12151)
+#12148 := (implies #421 #12145)
+#12152 := (iff #12148 #12151)
+#12153 := [rewrite]: #12152
+#12149 := (iff #3114 #12148)
+#12146 := (iff #3113 #12145)
+#12147 := [rewrite]: #12146
+#12150 := [monotonicity #12147]: #12149
+#12155 := [trans #12150 #12153]: #12154
+#12158 := [quant-intro #12155]: #12157
+#13050 := [monotonicity #12158 #13047]: #13049
+#13056 := [trans #13050 #13054]: #13055
+#13059 := [monotonicity #13056]: #13058
+#13065 := [trans #13059 #13063]: #13064
+#13068 := [monotonicity #12143 #13065]: #13067
+#13073 := [trans #13068 #13071]: #13072
+#13076 := [monotonicity #13073]: #13075
+#13082 := [trans #13076 #13080]: #13081
+#13085 := [monotonicity #13082]: #13084
+#13091 := [trans #13085 #13089]: #13090
+#13094 := [monotonicity #13091]: #13093
+#13100 := [trans #13094 #13098]: #13099
+#12139 := (iff #3095 #12138)
+#12136 := (iff #3094 #3074)
+#12137 := [rewrite]: #12136
+#12140 := [monotonicity #12137]: #12139
+#13103 := [monotonicity #12140 #13100]: #13102
+#13109 := [trans #13103 #13107]: #13108
+#13112 := [monotonicity #12140 #13109]: #13111
+#12134 := (iff #3093 #12133)
+#12131 := (iff #3092 #12128)
+#12125 := (implies #421 #12122)
+#12129 := (iff #12125 #12128)
+#12130 := [rewrite]: #12129
+#12126 := (iff #3092 #12125)
+#12123 := (iff #3091 #12122)
+#12124 := [rewrite]: #12123
+#12127 := [monotonicity #12124]: #12126
+#12132 := [trans #12127 #12130]: #12131
+#12135 := [quant-intro #12132]: #12134
+#13115 := [monotonicity #12135 #13112]: #13114
+#13121 := [trans #13115 #13119]: #13120
+#13124 := [monotonicity #12135 #13121]: #13123
+#13127 := [monotonicity #13124]: #13126
+#13133 := [trans #13127 #13131]: #13132
+#13136 := [monotonicity #13133]: #13135
+#12119 := (iff #3085 #12118)
+#12116 := (iff #3084 #12115)
+#12113 := (iff #3083 #3082)
+#12114 := [rewrite]: #12113
+#12117 := [monotonicity #12114]: #12116
+#12120 := [monotonicity #12117]: #12119
+#13139 := [monotonicity #12120 #13136]: #13138
+#13145 := [trans #13139 #13143]: #13144
+#12111 := (iff #3080 #12110)
+#12112 := [rewrite]: #12111
+#13148 := [monotonicity #12112 #13145]: #13147
+#13154 := [trans #13148 #13152]: #13153
+#12108 := (iff #3078 #12107)
+#12109 := [rewrite]: #12108
+#13157 := [monotonicity #12109 #13154]: #13156
+#13163 := [trans #13157 #13161]: #13162
+#12105 := (iff #3076 #12104)
+#12106 := [rewrite]: #12105
+#13166 := [monotonicity #12106 #13163]: #13165
+#13172 := [trans #13166 #13170]: #13171
+#13175 := [monotonicity #13172]: #13174
+#13181 := [trans #13175 #13179]: #13180
+#12102 := (iff #3071 #12101)
+#12099 := (iff #3070 #12098)
+#12100 := [rewrite]: #12099
+#12090 := (iff #3065 #12089)
+#12091 := [rewrite]: #12090
+#12103 := [monotonicity #12091 #12100]: #12102
+#13184 := [monotonicity #12103 #13181]: #13183
+#13190 := [trans #13184 #13188]: #13189
+#13193 := [monotonicity #12103 #13190]: #13192
+#12096 := (iff #3068 #12095)
+#12093 := (iff #3067 #12092)
+#12094 := [rewrite]: #12093
+#12097 := [monotonicity #12091 #12094]: #12096
+#13196 := [monotonicity #12097 #13193]: #13195
+#13202 := [trans #13196 #13200]: #13201
+#13205 := [monotonicity #12097 #13202]: #13204
+#12087 := (iff #3062 #12086)
+#12088 := [rewrite]: #12087
+#13208 := [monotonicity #12088 #13205]: #13207
+#13214 := [trans #13208 #13212]: #13213
+#13217 := [monotonicity #12088 #13214]: #13216
+#13220 := [monotonicity #13217]: #13219
+#13226 := [trans #13220 #13224]: #13225
+#12084 := (iff #3056 #12083)
+#12081 := (iff #3055 #12078)
+#12075 := (iff #12072 false)
+#12079 := (iff #12075 #12078)
+#12080 := [rewrite]: #12079
+#12076 := (iff #3055 #12075)
+#12073 := (iff #3054 #12072)
+#12074 := [rewrite]: #12073
+#12077 := [monotonicity #12074]: #12076
+#12082 := [trans #12077 #12080]: #12081
+#12085 := [quant-intro #12082]: #12084
+#13229 := [monotonicity #12085 #13226]: #13228
+#13235 := [trans #13229 #13233]: #13234
+#13238 := [monotonicity #13235]: #13237
+#13244 := [trans #13238 #13242]: #13243
+#12070 := (iff #3048 #12069)
+#12071 := [rewrite]: #12070
+#13247 := [monotonicity #12071 #13244]: #13246
+#13253 := [trans #13247 #13251]: #13252
+#12067 := (iff #3046 #12066)
+#12064 := (iff #3045 #12063)
+#12065 := [rewrite]: #12064
+#12061 := (iff #3043 #12060)
+#12062 := [rewrite]: #12061
+#12068 := [monotonicity #12062 #12065]: #12067
+#13256 := [monotonicity #12068 #13253]: #13255
+#13262 := [trans #13256 #13260]: #13261
+#13265 := [monotonicity #13262]: #13264
+#13271 := [trans #13265 #13269]: #13270
+#12058 := (iff #3034 #12057)
+#12052 := (iff #3031 #12051)
+#12053 := [rewrite]: #12052
+#12059 := [monotonicity #12053 #12056]: #12058
+#13274 := [monotonicity #12059 #13271]: #13273
+#13280 := [trans #13274 #13278]: #13279
+#12049 := (iff #3029 #12048)
+#12050 := [rewrite]: #12049
+#13283 := [monotonicity #12050 #13280]: #13282
+#13289 := [trans #13283 #13287]: #13288
+#12046 := (iff #3027 #12045)
+#12043 := (iff #3026 #12042)
+#12040 := (iff #3025 #12039)
+#12037 := (iff #3024 #12036)
+#12034 := (iff #3023 #12033)
+#12031 := (iff #3022 #12030)
+#12032 := [rewrite]: #12031
+#12028 := (iff #3020 #12027)
+#12025 := (iff #3019 #12024)
+#12026 := [rewrite]: #12025
+#12029 := [monotonicity #12026]: #12028
+#12035 := [monotonicity #12029 #12032]: #12034
+#12022 := (iff #3017 #12021)
+#12023 := [rewrite]: #12022
+#12038 := [monotonicity #12023 #12035]: #12037
+#12019 := (iff #3015 #12018)
+#12020 := [rewrite]: #12019
+#12041 := [monotonicity #12020 #12038]: #12040
+#12016 := (iff #3013 #12015)
+#12017 := [rewrite]: #12016
+#12044 := [monotonicity #12017 #12041]: #12043
+#12013 := (iff #3011 #12011)
+#12014 := [rewrite]: #12013
+#12047 := [monotonicity #12014 #12044]: #12046
+#13292 := [monotonicity #12047 #13289]: #13291
+#13298 := [trans #13292 #13296]: #13297
+#13301 := [monotonicity #13298]: #13300
+#13307 := [trans #13301 #13305]: #13306
+#13310 := [monotonicity #13307]: #13309
+#13316 := [trans #13310 #13314]: #13315
+#13319 := [monotonicity #13316]: #13318
+#13325 := [trans #13319 #13323]: #13324
+#13328 := [monotonicity #13325]: #13327
+#13334 := [trans #13328 #13332]: #13333
+#13337 := [monotonicity #13334]: #13336
+#13343 := [trans #13337 #13341]: #13342
+#13346 := [monotonicity #13343]: #13345
+#14254 := [trans #13346 #14252]: #14253
+#12010 := [asserted]: #3371
+#14255 := [mp #12010 #14254]: #14250
+#14273 := [not-or-elim #14255]: #14137
+#14276 := [and-elim #14273]: #12018
+#241 := (:var 0 S3)
+#2694 := (f49 #21 #241)
+#2695 := (pattern #2694)
+#11278 := (= f1 #2694)
+#11285 := (not #11278)
+#1268 := (f117 #21)
+#2697 := (f44 #241 #1268)
+#2698 := (= #21 #2697)
+#11286 := (or #2698 #11285)
+#11291 := (forall (vars (?v0 S5) (?v1 S3)) (:pat #2695) #11286)
+#18166 := (~ #11291 #11291)
+#18164 := (~ #11286 #11286)
+#18165 := [refl]: #18164
+#18167 := [nnf-pos #18165]: #18166
+#2696 := (= #2694 f1)
+#2699 := (implies #2696 #2698)
+#2700 := (forall (vars (?v0 S5) (?v1 S3)) (:pat #2695) #2699)
+#11292 := (iff #2700 #11291)
+#11289 := (iff #2699 #11286)
+#11282 := (implies #11278 #2698)
+#11287 := (iff #11282 #11286)
+#11288 := [rewrite]: #11287
+#11283 := (iff #2699 #11282)
+#11280 := (iff #2696 #11278)
+#11281 := [rewrite]: #11280
+#11284 := [monotonicity #11281]: #11283
+#11290 := [trans #11284 #11288]: #11289
+#11293 := [quant-intro #11290]: #11292
+#11277 := [asserted]: #2700
+#11296 := [mp #11277 #11293]: #11291
+#18168 := [mp~ #11296 #18167]: #11291
+#26020 := (not #12018)
+#26033 := (not #11291)
+#26034 := (or #26033 #26020 #26028)
+#26029 := (or #26028 #26020)
+#26035 := (or #26033 #26029)
+#26042 := (iff #26035 #26034)
+#26030 := (or #26020 #26028)
+#26037 := (or #26033 #26030)
+#26040 := (iff #26037 #26034)
+#26041 := [rewrite]: #26040
+#26038 := (iff #26035 #26037)
+#26031 := (iff #26029 #26030)
+#26032 := [rewrite]: #26031
+#26039 := [monotonicity #26032]: #26038
+#26043 := [trans #26039 #26041]: #26042
+#26036 := [quant-inst]: #26035
+#26044 := [mp #26036 #26043]: #26034
+#28349 := [unit-resolution #26044 #18168 #14276]: #26028
+#26591 := [monotonicity #28349 #28349]: #26808
+#26645 := [symm #26591]: #26805
+#26556 := (= f1 #26555)
+decl f197 :: (-> S4 S5 S5 S1)
+#26553 := (f197 f287 #26021 #26021)
+#26554 := (= f1 #26553)
+#26558 := (iff #26554 #26556)
+#2265 := (:var 0 S16)
+#26 := (:var 2 S5)
+#19 := (:var 3 S4)
+#2277 := (f201 #19 #26 #21 #2265)
+#2278 := (pattern #2277)
+#2280 := (f197 #19 #26 #21)
+#10234 := (= f1 #2280)
+#10230 := (= f1 #2277)
+#10237 := (iff #10230 #10234)
+#10240 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S5) (?v3 S16)) (:pat #2278) #10237)
+#17808 := (~ #10240 #10240)
+#17806 := (~ #10237 #10237)
+#17807 := [refl]: #17806
+#17809 := [nnf-pos #17807]: #17808
+#2281 := (= #2280 f1)
+#2279 := (= #2277 f1)
+#2282 := (iff #2279 #2281)
+#2283 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S5) (?v3 S16)) (:pat #2278) #2282)
+#10241 := (iff #2283 #10240)
+#10238 := (iff #2282 #10237)
+#10235 := (iff #2281 #10234)
+#10236 := [rewrite]: #10235
+#10232 := (iff #2279 #10230)
+#10233 := [rewrite]: #10232
+#10239 := [monotonicity #10233 #10236]: #10238
+#10242 := [quant-intro #10239]: #10241
+#10229 := [asserted]: #2283
+#10245 := [mp #10229 #10242]: #10240
+#17810 := [mp~ #10245 #17809]: #10240
+#26576 := (not #10240)
+#26577 := (or #26576 #26558)
+#26557 := (iff #26556 #26554)
+#26574 := (or #26576 #26557)
+#26579 := (iff #26574 #26577)
+#26581 := (iff #26577 #26577)
+#26561 := [rewrite]: #26581
+#26559 := (iff #26557 #26558)
+#26560 := [rewrite]: #26559
+#26580 := [monotonicity #26560]: #26579
+#26563 := [trans #26580 #26561]: #26579
+#26578 := [quant-inst]: #26574
+#26564 := [mp #26578 #26563]: #26577
+#26790 := [unit-resolution #26564 #17810]: #26558
+#26565 := (not #26558)
+#26594 := (or #26565 #26556)
+#26425 := (f14 #26021)
+#26667 := (f13 #26425)
+#26670 := (= f15 #26667)
+#26781 := (not #26670)
+#26782 := (iff #12027 #26781)
+#26779 := (iff #12024 #26670)
+#26741 := (iff #26670 #12024)
+#26745 := (= #26667 #3018)
+#26743 := (= #26425 #3005)
+#24956 := (f14 #3009)
+#28397 := (= #24956 #3005)
+#24959 := (= #3005 #24956)
+#2726 := (f44 #335 #168)
+#23139 := (pattern #2726)
+#2730 := (f14 #2726)
+#11362 := (= #335 #2730)
+#23146 := (forall (vars (?v0 S3) (?v1 int)) (:pat #23139) #11362)
+#11366 := (forall (vars (?v0 S3) (?v1 int)) #11362)
+#23149 := (iff #11366 #23146)
+#23147 := (iff #11362 #11362)
+#23148 := [refl]: #23147
+#23150 := [quant-intro #23148]: #23149
+#18191 := (~ #11366 #11366)
+#18189 := (~ #11362 #11362)
+#18190 := [refl]: #18189
+#18192 := [nnf-pos #18190]: #18191
+#2731 := (= #2730 #335)
+#2732 := (forall (vars (?v0 S3) (?v1 int)) #2731)
+#11367 := (iff #2732 #11366)
+#11364 := (iff #2731 #11362)
+#11365 := [rewrite]: #11364
+#11368 := [quant-intro #11365]: #11367
+#11361 := [asserted]: #2732
+#11371 := [mp #11361 #11368]: #11366
+#18193 := [mp~ #11371 #18192]: #11366
+#23151 := [mp #18193 #23150]: #23146
+#24903 := (not #23146)
+#24964 := (or #24903 #24959)
+#24965 := [quant-inst]: #24964
+#28331 := [unit-resolution #24965 #23151]: #24959
+#28398 := [symm #28331]: #28397
+#26742 := (= #26425 #24956)
+#28350 := (= #26021 #3009)
+#28351 := [symm #28349]: #28350
+#26719 := [monotonicity #28351]: #26742
+#26744 := [trans #26719 #28398]: #26743
+#26746 := [monotonicity #26744]: #26745
+#26773 := [monotonicity #26746]: #26741
+#26780 := [symm #26773]: #26779
+#26783 := [monotonicity #26780]: #26782
+#14278 := [and-elim #14273]: #12027
+#26799 := [mp #14278 #26783]: #26781
+#26659 := (f25 f287 #26021)
+#26660 := (= f1 #26659)
+#26812 := (= #3016 #26659)
+#26807 := (= #26659 #3016)
+#26804 := [monotonicity #28351]: #26807
+#26815 := [symm #26804]: #26812
+#14277 := [and-elim #14273]: #12021
+#26801 := [trans #14277 #26815]: #26660
+#26662 := (f49 #26021 #26425)
+#26663 := (= f1 #26662)
+#26819 := (= #3014 #26662)
+#26816 := (= #26662 #3014)
+#26817 := [monotonicity #28351 #26744]: #26816
+#26820 := [symm #26817]: #26819
+#26826 := [trans #14276 #26820]: #26663
+#26664 := (not #26663)
+#26661 := (not #26660)
+#26898 := (or #26661 #26664 #26670)
+#26437 := (f26 f287 #26021)
+#26665 := (= f27 #26437)
+#26846 := (= #3012 #26437)
+#26840 := (= #26437 #3012)
+#26841 := [monotonicity #28351]: #26840
+#26847 := [symm #26841]: #26846
+#14275 := [and-elim #14273]: #12015
+#26848 := [trans #14275 #26847]: #26665
+#26575 := (not #26554)
+#26868 := [hypothesis]: #26575
+#26465 := (f28 f287 #26021)
+#26466 := (= f1 #26465)
+#26871 := (= #3010 #26465)
+#26869 := (= #26465 #3010)
+#26859 := [monotonicity #28351]: #26869
+#26893 := [symm #26859]: #26871
+#14274 := [and-elim #14273]: #12011
+#26854 := [trans #14274 #26893]: #26466
+#26426 := (f24 #26425)
+#26433 := (= f1 #26426)
+#26896 := (= #3021 #26426)
+#26877 := (= #26426 #3021)
+#26895 := [monotonicity #26744]: #26877
+#26856 := [symm #26895]: #26896
+#14279 := [and-elim #14273]: #12030
+#26897 := [trans #14279 #26856]: #26433
+#14258 := [not-or-elim #14255]: #12057
+#14260 := [and-elim #14258]: #12054
+#2236 := (f197 #52 #28 #28)
+#2237 := (pattern #2236)
+#10106 := (= f1 #2236)
+#235 := (f56 #52)
+#3971 := (= f1 #235)
+#19365 := (not #3971)
+#150 := (f49 #28 #31)
+#3680 := (= f1 #150)
+#19239 := (not #3680)
+#19238 := (not #3677)
+#141 := (f28 #52 #28)
+#3662 := (= f1 #141)
+#10819 := (not #3662)
+#76 := (f24 #31)
+#3511 := (= f1 #76)
+#10878 := (not #3511)
+#21798 := (or #34 #10878 #10819 #19238 #19239 #11206 #19365 #10106)
+#21803 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2237) #21798)
+#10121 := (and #57 #3511 #3662 #3677 #3680 #3683 #3971)
+#10124 := (not #10121)
+#10130 := (or #10106 #10124)
+#10135 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2237) #10130)
+#21804 := (iff #10135 #21803)
+#21801 := (iff #10130 #21798)
+#21784 := (or #34 #10878 #10819 #19238 #19239 #11206 #19365)
+#21795 := (or #10106 #21784)
+#21799 := (iff #21795 #21798)
+#21800 := [rewrite]: #21799
+#21796 := (iff #10130 #21795)
+#21793 := (iff #10124 #21784)
+#21785 := (not #21784)
+#21788 := (not #21785)
+#21791 := (iff #21788 #21784)
+#21792 := [rewrite]: #21791
+#21789 := (iff #10124 #21788)
+#21786 := (iff #10121 #21785)
+#21787 := [rewrite]: #21786
+#21790 := [monotonicity #21787]: #21789
+#21794 := [trans #21790 #21792]: #21793
+#21797 := [monotonicity #21794]: #21796
+#21802 := [trans #21797 #21800]: #21801
+#21805 := [quant-intro #21802]: #21804
+#17776 := (~ #10135 #10135)
+#17774 := (~ #10130 #10130)
+#17775 := [refl]: #17774
+#17777 := [nnf-pos #17775]: #17776
+#2244 := (= #2236 f1)
+#77 := (= #76 f1)
+#2238 := (and #57 #77)
+#2239 := (and #153 #2238)
+#151 := (= #150 f1)
+#2240 := (and #151 #2239)
+#2241 := (and #149 #2240)
+#142 := (= #141 f1)
+#2242 := (and #142 #2241)
+#237 := (= #235 f1)
+#2243 := (and #237 #2242)
+#2245 := (implies #2243 #2244)
+#2246 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2237) #2245)
+#10138 := (iff #2246 #10135)
+#10087 := (and #57 #3511)
+#10091 := (and #3683 #10087)
+#10094 := (and #3680 #10091)
+#10097 := (and #3677 #10094)
+#10100 := (and #3662 #10097)
+#10103 := (and #3971 #10100)
+#10112 := (not #10103)
+#10113 := (or #10112 #10106)
+#10118 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2237) #10113)
+#10136 := (iff #10118 #10135)
+#10133 := (iff #10113 #10130)
+#10127 := (or #10124 #10106)
+#10131 := (iff #10127 #10130)
+#10132 := [rewrite]: #10131
+#10128 := (iff #10113 #10127)
+#10125 := (iff #10112 #10124)
+#10122 := (iff #10103 #10121)
+#10123 := [rewrite]: #10122
+#10126 := [monotonicity #10123]: #10125
+#10129 := [monotonicity #10126]: #10128
+#10134 := [trans #10129 #10132]: #10133
+#10137 := [quant-intro #10134]: #10136
+#10119 := (iff #2246 #10118)
+#10116 := (iff #2245 #10113)
+#10109 := (implies #10103 #10106)
+#10114 := (iff #10109 #10113)
+#10115 := [rewrite]: #10114
+#10110 := (iff #2245 #10109)
+#10107 := (iff #2244 #10106)
+#10108 := [rewrite]: #10107
+#10104 := (iff #2243 #10103)
+#10101 := (iff #2242 #10100)
+#10098 := (iff #2241 #10097)
+#10095 := (iff #2240 #10094)
+#10092 := (iff #2239 #10091)
+#10089 := (iff #2238 #10087)
+#3512 := (iff #77 #3511)
+#3513 := [rewrite]: #3512
+#10090 := [monotonicity #3513]: #10089
+#10093 := [monotonicity #3685 #10090]: #10092
+#3681 := (iff #151 #3680)
+#3682 := [rewrite]: #3681
+#10096 := [monotonicity #3682 #10093]: #10095
+#10099 := [monotonicity #3679 #10096]: #10098
+#3664 := (iff #142 #3662)
+#3665 := [rewrite]: #3664
+#10102 := [monotonicity #3665 #10099]: #10101
+#3973 := (iff #237 #3971)
+#3974 := [rewrite]: #3973
+#10105 := [monotonicity #3974 #10102]: #10104
+#10111 := [monotonicity #10105 #10108]: #10110
+#10117 := [trans #10111 #10115]: #10116
+#10120 := [quant-intro #10117]: #10119
+#10139 := [trans #10120 #10137]: #10138
+#10086 := [asserted]: #2246
+#10140 := [mp #10086 #10139]: #10135
+#17778 := [mp~ #10140 #17777]: #10135
+#21806 := [mp #17778 #21805]: #21803
+#26666 := (not #26665)
+#26488 := (not #26466)
+#26434 := (not #26433)
+#24685 := (not #12054)
+#26593 := (not #21803)
+#26596 := (or #26593 #24685 #26434 #26488 #26554 #26661 #26664 #26666 #26670)
+#26668 := (= #26667 f15)
+#26669 := (or #26668 #26434 #26488 #26666 #26664 #26661 #24685 #26554)
+#26597 := (or #26593 #26669)
+#26648 := (iff #26597 #26596)
+#26676 := (or #24685 #26434 #26488 #26554 #26661 #26664 #26666 #26670)
+#26599 := (or #26593 #26676)
+#26642 := (iff #26599 #26596)
+#26647 := [rewrite]: #26642
+#26651 := (iff #26597 #26599)
+#26679 := (iff #26669 #26676)
+#26673 := (or #26670 #26434 #26488 #26666 #26664 #26661 #24685 #26554)
+#26677 := (iff #26673 #26676)
+#26678 := [rewrite]: #26677
+#26674 := (iff #26669 #26673)
+#26671 := (iff #26668 #26670)
+#26672 := [rewrite]: #26671
+#26675 := [monotonicity #26672]: #26674
+#26680 := [trans #26675 #26678]: #26679
+#26641 := [monotonicity #26680]: #26651
+#26646 := [trans #26641 #26647]: #26648
+#26598 := [quant-inst]: #26597
+#26649 := [mp #26598 #26646]: #26596
+#26899 := [unit-resolution #26649 #21806 #14260 #26897 #26854 #26868 #26848]: #26898
+#26900 := [unit-resolution #26899 #26826 #26801 #26799]: false
+#26949 := [lemma #26900]: #26554
+#26567 := (or #26565 #26575 #26556)
+#26568 := [def-axiom]: #26567
+#26589 := [unit-resolution #26568 #26949]: #26594
+#26595 := [unit-resolution #26589 #26790]: #26556
+#26640 := [trans #26595 #26645]: #12086
+#26590 := [hypothesis]: #13209
+#26656 := [unit-resolution #26590 #26640]: false
+#26657 := [lemma #26656]: #12086
+#23441 := (or #13209 #23438)
+#22442 := (forall (vars (?v0 int)) #22431)
+#22449 := (not #22442)
+#22427 := (forall (vars (?v0 int)) #22422)
+#22448 := (not #22427)
+#22450 := (or #22448 #22449)
+#22451 := (not #22450)
+#22480 := (or #22451 #22477)
+#22486 := (not #22480)
+#22487 := (or #12249 #12240 #12231 #12222 #22363 #13565 #13711 #22486)
+#22488 := (not #22487)
+#22266 := (forall (vars (?v0 int)) #22261)
+#22272 := (not #22266)
+#22273 := (or #22248 #22272)
+#22274 := (not #22273)
+#22303 := (or #22274 #22300)
+#22309 := (not #22303)
+#22310 := (or #13464 #22309)
+#22311 := (not #22310)
+#22316 := (or #13464 #22311)
+#22324 := (not #22316)
+#22325 := (or #12601 #22322 #18478 #22323 #13531 #18481 #22324)
+#22326 := (not #22325)
+#22331 := (or #18478 #18481 #22326)
+#22337 := (not #22331)
+#22374 := (or #12766 #12757 #22363 #13565 #22322 #13616 #22337)
+#22375 := (not #22374)
+#22338 := (or #18440 #18449 #12685 #12676 #12667 #12649 #12640 #13565 #22322 #22337)
+#22339 := (not #22338)
+#22344 := (or #18440 #18449 #22339)
+#22350 := (not #22344)
+#22351 := (or #18440 #18443 #22350)
+#22352 := (not #22351)
+#22357 := (or #18440 #18443 #22352)
+#22364 := (not #22357)
+#22365 := (or #22363 #13565 #13617 #22364)
+#22366 := (not #22365)
+#22380 := (or #22366 #22375)
+#22386 := (not #22380)
+#22387 := (or #18440 #18449 #22363 #13565 #22386)
+#22388 := (not #22387)
+#22393 := (or #18440 #18449 #22388)
+#22399 := (not #22393)
+#22400 := (or #18440 #18443 #22399)
+#22401 := (not #22400)
+#22406 := (or #18440 #18443 #22401)
+#22412 := (not #22406)
+#22413 := (or #22363 #13565 #13710 #22412)
+#22414 := (not #22413)
+#22493 := (or #22414 #22488)
+#22508 := (not #22493)
+#22243 := (forall (vars (?v0 int)) #22238)
+#22504 := (not #22243)
+#22509 := (or #13176 #22499 #15198 #13883 #12969 #12960 #12951 #12942 #22500 #22501 #13417 #22363 #13565 #13888 #13940 #22502 #22503 #22505 #22506 #22507 #22504 #22508)
+#22510 := (not #22509)
+#22515 := (or #13176 #13417 #22510)
+#22522 := (not #22515)
+#22232 := (forall (vars (?v0 int)) #22227)
+#22521 := (not #22232)
+#22523 := (or #22521 #22522)
+#22524 := (not #22523)
+#22529 := (or #22221 #22524)
+#22535 := (not #22529)
+#22536 := (or #13381 #22535)
+#22537 := (not #22536)
+#22542 := (or #13381 #22537)
+#22548 := (not #22542)
+#22549 := (or #13176 #18329 #18338 #13167 #13158 #13149 #22548)
+#22550 := (not #22549)
+#22555 := (or #18329 #18338 #22550)
+#22561 := (not #22555)
+#22562 := (or #18329 #18332 #22561)
+#22563 := (not #22562)
+#22568 := (or #18329 #18332 #22563)
+#22574 := (not #22568)
+#22575 := (or #13209 #22574)
+#22576 := (not #22575)
+#22581 := (or #13209 #22576)
+#23442 := (iff #22581 #23441)
+#23439 := (iff #22576 #23438)
+#23436 := (iff #22575 #23435)
+#23433 := (iff #22574 #23432)
+#23430 := (iff #22568 #23429)
+#23427 := (iff #22563 #23426)
+#23424 := (iff #22562 #23423)
+#23421 := (iff #22561 #23420)
+#23418 := (iff #22555 #23417)
+#23415 := (iff #22550 #23414)
+#23412 := (iff #22549 #23411)
+#23409 := (iff #22548 #23408)
+#23406 := (iff #22542 #23405)
+#23403 := (iff #22537 #23402)
+#23400 := (iff #22536 #23399)
+#23397 := (iff #22535 #23396)
+#23394 := (iff #22529 #23393)
+#23391 := (iff #22524 #23390)
+#23388 := (iff #22523 #23387)
+#23385 := (iff #22522 #23384)
+#23382 := (iff #22515 #23381)
+#23379 := (iff #22510 #23378)
+#23376 := (iff #22509 #23375)
+#23373 := (iff #22508 #23372)
+#23370 := (iff #22493 #23369)
+#23367 := (iff #22488 #23366)
+#23364 := (iff #22487 #23363)
+#23361 := (iff #22486 #23360)
+#23358 := (iff #22480 #23357)
+#23355 := (iff #22451 #23354)
+#23352 := (iff #22450 #23351)
+#23349 := (iff #22449 #23348)
+#23346 := (iff #22442 #23343)
+#23344 := (iff #22431 #22431)
+#23345 := [refl]: #23344
+#23347 := [quant-intro #23345]: #23346
+#23350 := [monotonicity #23347]: #23349
+#23341 := (iff #22448 #23340)
+#23338 := (iff #22427 #23335)
+#23336 := (iff #22422 #22422)
+#23337 := [refl]: #23336
+#23339 := [quant-intro #23337]: #23338
+#23342 := [monotonicity #23339]: #23341
+#23353 := [monotonicity #23342 #23350]: #23352
+#23356 := [monotonicity #23353]: #23355
+#23359 := [monotonicity #23356]: #23358
+#23362 := [monotonicity #23359]: #23361
+#23365 := [monotonicity #23362]: #23364
+#23368 := [monotonicity #23365]: #23367
+#23333 := (iff #22414 #23332)
+#23330 := (iff #22413 #23329)
+#23327 := (iff #22412 #23326)
+#23324 := (iff #22406 #23323)
+#23321 := (iff #22401 #23320)
+#23318 := (iff #22400 #23317)
+#23315 := (iff #22399 #23314)
+#23312 := (iff #22393 #23311)
+#23309 := (iff #22388 #23308)
+#23306 := (iff #22387 #23305)
+#23303 := (iff #22386 #23302)
+#23300 := (iff #22380 #23299)
+#23297 := (iff #22375 #23296)
+#23294 := (iff #22374 #23293)
+#23261 := (iff #22337 #23260)
+#23258 := (iff #22331 #23257)
+#23255 := (iff #22326 #23254)
+#23252 := (iff #22325 #23251)
+#23249 := (iff #22324 #23248)
+#23246 := (iff #22316 #23245)
+#23243 := (iff #22311 #23242)
+#23240 := (iff #22310 #23239)
+#23237 := (iff #22309 #23236)
+#23234 := (iff #22303 #23233)
+#23231 := (iff #22274 #23230)
+#23228 := (iff #22273 #23227)
+#23225 := (iff #22272 #23224)
+#23222 := (iff #22266 #23219)
+#23220 := (iff #22261 #22261)
+#23221 := [refl]: #23220
+#23223 := [quant-intro #23221]: #23222
 #23226 := [monotonicity #23223]: #23225
 #23229 := [monotonicity #23226]: #23228
 #23232 := [monotonicity #23229]: #23231
 #23235 := [monotonicity #23232]: #23234
 #23238 := [monotonicity #23235]: #23237
 #23241 := [monotonicity #23238]: #23240
-#18778 := (and #18421 #18422)
-#18781 := (not #18778)
-#18784 := (or #18760 #18773 #18781)
-#18787 := (not #18784)
-#15730 := (and #3103 #4043 #13540 #14916)
-#18444 := (not #15730)
-#18447 := (forall (vars (?x778 int)) #18444)
-#14159 := (and #4043 #14916)
-#14158 := (not #14159)
-#15716 := (or #13538 #13552 #14158)
-#15721 := (forall (vars (?x776 int)) #15716)
-#18451 := (and #15721 #18447)
-#18793 := (or #18451 #18787)
-#18801 := (and #12008 #12011 #12014 #12017 #13222 #13225 #13510 #18793)
-#18630 := (and #18297 #18298)
-#18633 := (not #18630)
-#18636 := (or #18612 #18625 #18633)
-#18639 := (not #18636)
-#15617 := (or #13267 #13281 #14158)
-#15622 := (forall (vars (?x785 int)) #15617)
-#18313 := (not #13310)
-#18323 := (and #18313 #15622)
-#18645 := (or #18323 #18639)
-#18650 := (and #13259 #18645)
-#18653 := (or #13264 #18650)
-#18661 := (and #3209 #13234 #13243 #13251 #13327 #15609 #18653)
-#18666 := (or #18276 #18279 #18661)
-#18706 := (and #12548 #12551 #13222 #13225 #13234 #13417 #18666)
-#18672 := (and #3194 #3195 #12293 #12302 #12308 #12313 #12316 #13225 #13234 #18666)
-#18677 := (or #18238 #18247 #18672)
-#18683 := (and #12293 #12296 #18677)
-#18688 := (or #18238 #18241 #18683)
-#18694 := (and #13222 #13225 #13416 #18688)
-#18711 := (or #18694 #18706)
-#18717 := (and #12293 #12302 #13222 #13225 #18711)
-#18722 := (or #18238 #18247 #18717)
-#18728 := (and #12293 #12296 #18722)
-#18733 := (or #18238 #18241 #18728)
-#18739 := (and #13222 #13225 #13511 #18733)
-#18806 := (or #18739 #18801)
-#15543 := (or #13703 #13717 #14158)
-#15548 := (forall (vars (?x775 int)) #15543)
-#18812 := (and #3042 #3170 #3171 #3172 #3173 #3174 #3175 #11989 #11997 #12254 #13218 #13222 #13225 #13689 #13737 #13743 #13765 #15548 #15560 #15577 #15594 #18806)
-#18817 := (or #12976 #13217 #18812)
-#15529 := (or #13184 #13196 #14158)
-#15534 := (forall (vars (?x773 int)) #15529)
-#18820 := (and #15534 #18817)
-#18533 := (and #18160 #18161)
-#18536 := (not #18533)
-#18542 := (or #18168 #18169 #18536)
-#18547 := (not #18542)
-#18823 := (or #18547 #18820)
-#18826 := (and #13178 #18823)
-#18829 := (or #13181 #18826)
-#18835 := (and #3042 #3043 #3044 #3045 #11928 #11937 #18829)
-#18840 := (or #18127 #18136 #18835)
-#18846 := (and #11928 #11931 #18840)
-#18851 := (or #18127 #18130 #18846)
-#18854 := (and #11925 #18851)
-#18857 := (or #13009 #18854)
-#22380 := (iff #18857 #22379)
-#22377 := (iff #18854 #22374)
-#22369 := (and #11925 #22366)
-#22375 := (iff #22369 #22374)
-#22376 := [rewrite]: #22375
-#22370 := (iff #18854 #22369)
-#22367 := (iff #18851 #22366)
-#22364 := (iff #18846 #22361)
-#22356 := (and #11928 #11931 #22353)
-#22362 := (iff #22356 #22361)
-#22363 := [rewrite]: #22362
-#22357 := (iff #18846 #22356)
-#22354 := (iff #18840 #22353)
-#22351 := (iff #18835 #22348)
-#22343 := (and #3042 #3043 #3044 #3045 #11928 #11937 #22340)
-#22349 := (iff #22343 #22348)
-#22350 := [rewrite]: #22349
-#22344 := (iff #18835 #22343)
-#22341 := (iff #18829 #22340)
-#22338 := (iff #18826 #22335)
-#22330 := (and #13178 #22327)
-#22336 := (iff #22330 #22335)
-#22337 := [rewrite]: #22336
-#22331 := (iff #18826 #22330)
-#22328 := (iff #18823 #22327)
-#22325 := (iff #18820 #22322)
-#22316 := (and #22030 #22313)
-#22323 := (iff #22316 #22322)
-#22324 := [rewrite]: #22323
-#22317 := (iff #18820 #22316)
-#22314 := (iff #18817 #22313)
-#22311 := (iff #18812 #22308)
-#22294 := (and #3042 #3170 #3171 #3172 #3173 #3174 #3175 #11989 #11997 #12254 #13218 #13222 #13225 #13689 #13737 #13743 #13765 #22041 #15560 #15577 #15594 #22291)
-#22309 := (iff #22294 #22308)
-#22310 := [rewrite]: #22309
-#22295 := (iff #18812 #22294)
-#22292 := (iff #18806 #22291)
-#22289 := (iff #18801 #22286)
-#22281 := (and #12008 #12011 #12014 #12017 #13222 #13225 #13510 #22278)
-#22287 := (iff #22281 #22286)
-#22288 := [rewrite]: #22287
-#22282 := (iff #18801 #22281)
-#22279 := (iff #18793 #22278)
-#22276 := (iff #18787 #22275)
-#22273 := (iff #18784 #22270)
-#22256 := (or #22254 #22255)
-#22267 := (or #18760 #18773 #22256)
-#22271 := (iff #22267 #22270)
-#22272 := [rewrite]: #22271
-#22268 := (iff #18784 #22267)
-#22265 := (iff #18781 #22256)
-#22257 := (not #22256)
-#22260 := (not #22257)
-#22263 := (iff #22260 #22256)
-#22264 := [rewrite]: #22263
-#22261 := (iff #18781 #22260)
-#22258 := (iff #18778 #22257)
-#22259 := [rewrite]: #22258
-#22262 := [monotonicity #22259]: #22261
-#22266 := [trans #22262 #22264]: #22265
-#22269 := [monotonicity #22266]: #22268
-#22274 := [trans #22269 #22272]: #22273
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-#22252 := (iff #18451 #22249)
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-#22250 := (iff #22243 #22249)
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-#22242 := [quant-intro #22239]: #22241
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-#19933 := (or #4965 #19295)
-#22217 := (or #13538 #13552 #19933)
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-#19942 := (iff #14158 #19933)
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-#19937 := (not #19934)
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-#19936 := [rewrite]: #19935
-#19939 := [monotonicity #19936]: #19938
-#19943 := [trans #19939 #19941]: #19942
-#22219 := [monotonicity #19943]: #22218
-#22224 := [trans #22219 #22222]: #22223
-#22227 := [quant-intro #22224]: #22226
-#22245 := [monotonicity #22227 #22242]: #22244
-#22253 := [trans #22245 #22251]: #22252
-#22280 := [monotonicity #22253 #22277]: #22279
-#22283 := [monotonicity #22280]: #22282
-#22290 := [trans #22283 #22288]: #22289
-#22215 := (iff #18739 #22212)
-#22207 := (and #13222 #13225 #13511 #22204)
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-#22141 := [trans #22134 #22139]: #22140
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+#18980 := (and #18623 #18624)
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+#18986 := (or #18962 #18975 #18983)
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+#18913 := (or #18896 #18908)
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+#22245 := [quant-intro #22242]: #22244
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+#18967 := (+ #13750 #18628)
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+#18977 := [rewrite]: #18976
+#18971 := (iff #18630 #18970)
+#18968 := (= #18629 #18967)
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+#18979 := [trans #18972 #18977]: #18978
+#18965 := (iff #18632 #18962)
+#18954 := (+ #13351 ?v0!15)
+#18957 := (>= #18954 0::int)
+#18963 := (iff #18957 #18962)
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+#18958 := (iff #18632 #18957)
+#18955 := (= #18631 #18954)
+#18956 := [rewrite]: #18955
+#18959 := [monotonicity #18956]: #18958
+#18966 := [trans #18959 #18964]: #18965
+#18988 := [monotonicity #18966 #18979 #18985]: #18987
+#18991 := [monotonicity #18988]: #18990
+#18994 := [monotonicity #18991]: #18993
+#18999 := [trans #18994 #18997]: #18998
+#18766 := (iff #18410 #13427)
+#18767 := [rewrite]: #18766
+#18952 := (iff #18617 #12187)
+#18953 := [rewrite]: #18952
+#18950 := (iff #18614 #12184)
+#18951 := [rewrite]: #18950
+#18948 := (iff #18611 #12181)
+#18949 := [rewrite]: #18948
+#18946 := (iff #18608 #12178)
+#18947 := [rewrite]: #18946
+#19002 := [monotonicity #18947 #18949 #18951 #18953 #18767 #13718 #18999]: #19001
+#19007 := [trans #19002 #19005]: #19006
+#18944 := (iff #18604 #18941)
+#18938 := (and #13427 #13711 #18935)
+#18942 := (iff #18938 #18941)
+#18943 := [rewrite]: #18942
+#18939 := (iff #18604 #18938)
+#18936 := (iff #18600 #18935)
+#18933 := (iff #18596 #18930)
+#18927 := (and #12490 #18924)
+#18931 := (iff #18927 #18930)
+#18932 := [rewrite]: #18931
+#18928 := (iff #18596 #18927)
+#18925 := (iff #18592 #18924)
+#18922 := (iff #18588 #18919)
+#18916 := (and #12496 #13427 #18913)
+#18920 := (iff #18916 #18919)
+#18921 := [rewrite]: #18920
+#18917 := (iff #18588 #18916)
+#18914 := (iff #18584 #18913)
+#18911 := (iff #18580 #18908)
+#18905 := (and #12748 #12751 #13427 #13436 #13617 #18868)
+#18909 := (iff #18905 #18908)
+#18910 := [rewrite]: #18909
+#18906 := (iff #18580 #18905)
+#18869 := (iff #18548 #18868)
+#18866 := (iff #18544 #18863)
+#18860 := (and #12531 #13453 #13527 #18855 #15845)
+#18864 := (iff #18860 #18863)
+#18865 := [rewrite]: #18864
+#18861 := (iff #18544 #18860)
+#18858 := (iff #18541 #15845)
+#18859 := [rewrite]: #18858
+#18856 := (iff #18537 #18855)
+#18853 := (iff #18533 #18852)
+#18850 := (iff #18529 #18847)
+#18844 := (or #18841 #18525)
+#18848 := (iff #18844 #18847)
+#18849 := [rewrite]: #18848
+#18845 := (iff #18529 #18844)
+#18842 := (iff #18510 #18841)
+#18839 := (iff #18509 #18838)
+#18836 := (iff #18502 #18835)
+#18833 := (iff #18501 #18832)
+#18834 := [rewrite]: #18833
+#18837 := [monotonicity #18834]: #18836
+#18830 := (iff #18506 #18827)
+#18819 := (+ #13479 #18504)
+#18822 := (<= #18819 0::int)
+#18828 := (iff #18822 #18827)
+#18829 := [rewrite]: #18828
+#18823 := (iff #18506 #18822)
+#18820 := (= #18505 #18819)
+#18821 := [rewrite]: #18820
+#18824 := [monotonicity #18821]: #18823
+#18831 := [trans #18824 #18829]: #18830
+#18817 := (iff #18508 #18814)
+#18806 := (+ #13460 ?v0!14)
+#18809 := (>= #18806 0::int)
+#18815 := (iff #18809 #18814)
+#18816 := [rewrite]: #18815
+#18810 := (iff #18508 #18809)
+#18807 := (= #18507 #18806)
+#18808 := [rewrite]: #18807
+#18811 := [monotonicity #18808]: #18810
+#18818 := [trans #18811 #18816]: #18817
+#18840 := [monotonicity #18818 #18831 #18837]: #18839
+#18843 := [monotonicity #18840]: #18842
+#18846 := [monotonicity #18843]: #18845
+#18851 := [trans #18846 #18849]: #18850
+#18804 := (iff #18495 #13459)
+#18805 := [rewrite]: #18804
+#18854 := [monotonicity #18805 #18851]: #18853
+#18857 := [monotonicity #18854]: #18856
+#18802 := (iff #18490 #13527)
 #18803 := [rewrite]: #18802
-#18799 := (iff #18459 #18798)
-#18796 := (iff #18455 #18793)
-#18790 := (or #18787 #18451)
-#18794 := (iff #18790 #18793)
+#18800 := (iff #18487 #13453)
+#18801 := [rewrite]: #18800
+#18798 := (iff #18484 #12531)
+#18799 := [rewrite]: #18798
+#18862 := [monotonicity #18799 #18801 #18803 #18857 #18859]: #18861
+#18867 := [trans #18862 #18865]: #18866
+#18870 := [monotonicity #18867]: #18869
+#18796 := (iff #18475 #13436)
+#18797 := [rewrite]: #18796
+#18903 := (iff #18575 #12751)
+#18904 := [rewrite]: #18903
+#18901 := (iff #18572 #12748)
+#18902 := [rewrite]: #18901
+#18907 := [monotonicity #18902 #18904 #18767 #18797 #13626 #18870]: #18906
+#18912 := [trans #18907 #18910]: #18911
+#18899 := (iff #18568 #18896)
+#18893 := (and #13427 #13616 #18890)
+#18897 := (iff #18893 #18896)
+#18898 := [rewrite]: #18897
+#18894 := (iff #18568 #18893)
+#18891 := (iff #18564 #18890)
+#18888 := (iff #18560 #18885)
+#18882 := (and #12490 #18879)
+#18886 := (iff #18882 #18885)
+#18887 := [rewrite]: #18886
+#18883 := (iff #18560 #18882)
+#18880 := (iff #18556 #18879)
+#18877 := (iff #18552 #18874)
+#18871 := (and #12496 #12499 #12502 #12505 #12510 #12513 #13425 #13436 #18868)
+#18875 := (iff #18871 #18874)
+#18876 := [rewrite]: #18875
+#18872 := (iff #18552 #18871)
+#18794 := (iff #18472 #13425)
 #18795 := [rewrite]: #18794
-#18791 := (iff #18455 #18790)
-#18788 := (iff #18432 #18787)
-#18785 := (iff #18431 #18784)
-#18782 := (iff #18424 #18781)
-#18779 := (iff #18423 #18778)
-#18780 := [rewrite]: #18779
-#18783 := [monotonicity #18780]: #18782
-#18776 := (iff #18428 #18773)
-#18765 := (+ #13550 #18426)
-#18768 := (<= #18765 0::int)
-#18774 := (iff #18768 #18773)
+#18792 := (iff #18469 #12513)
+#18793 := [rewrite]: #18792
+#18790 := (iff #18466 #12510)
+#18791 := [rewrite]: #18790
+#18788 := (iff #18463 #12505)
+#18789 := [rewrite]: #18788
+#18786 := (iff #18460 #12502)
+#18787 := [rewrite]: #18786
+#18784 := (iff #18457 #12499)
+#18785 := [rewrite]: #18784
+#18782 := (iff #18452 #12496)
+#18783 := [rewrite]: #18782
+#18873 := [monotonicity #18783 #18785 #18787 #18789 #18791 #18793 #18795 #18797 #18870]: #18872
+#18878 := [trans #18873 #18876]: #18877
+#18881 := [monotonicity #18878]: #18880
+#18780 := (iff #18446 #12490)
+#18781 := [rewrite]: #18780
+#18884 := [monotonicity #18781 #18881]: #18883
+#18889 := [trans #18884 #18887]: #18888
+#18892 := [monotonicity #18889]: #18891
+#18895 := [monotonicity #18767 #18892]: #18894
+#18900 := [trans #18895 #18898]: #18899
+#18915 := [monotonicity #18900 #18912]: #18914
+#18918 := [monotonicity #18783 #18767 #18915]: #18917
+#18923 := [trans #18918 #18921]: #18922
+#18926 := [monotonicity #18923]: #18925
+#18929 := [monotonicity #18781 #18926]: #18928
+#18934 := [trans #18929 #18932]: #18933
+#18937 := [monotonicity #18934]: #18936
+#18940 := [monotonicity #18767 #18937]: #18939
+#18945 := [trans #18940 #18943]: #18944
+#19010 := [monotonicity #18945 #19007]: #19009
+#18778 := (iff #18435 #15799)
+#18779 := [rewrite]: #18778
+#18776 := (iff #18432 #15782)
+#18777 := [rewrite]: #18776
+#18774 := (iff #18429 #15765)
 #18775 := [rewrite]: #18774
-#18769 := (iff #18428 #18768)
-#18766 := (= #18427 #18765)
-#18767 := [rewrite]: #18766
-#18770 := [monotonicity #18767]: #18769
-#18777 := [trans #18770 #18775]: #18776
-#18763 := (iff #18430 #18760)
-#18752 := (+ #13151 ?x776!15)
-#18755 := (>= #18752 0::int)
-#18761 := (iff #18755 #18760)
-#18762 := [rewrite]: #18761
-#18756 := (iff #18430 #18755)
-#18753 := (= #18429 #18752)
-#18754 := [rewrite]: #18753
-#18757 := [monotonicity #18754]: #18756
-#18764 := [trans #18757 #18762]: #18763
-#18786 := [monotonicity #18764 #18777 #18783]: #18785
-#18789 := [monotonicity #18786]: #18788
-#18792 := [monotonicity #18789]: #18791
-#18797 := [trans #18792 #18795]: #18796
-#18564 := (iff #18208 #13227)
-#18565 := [rewrite]: #18564
-#18750 := (iff #18415 #12017)
-#18751 := [rewrite]: #18750
-#18748 := (iff #18412 #12014)
-#18749 := [rewrite]: #18748
-#18746 := (iff #18409 #12011)
-#18747 := [rewrite]: #18746
-#18744 := (iff #18406 #12008)
-#18745 := [rewrite]: #18744
-#18800 := [monotonicity #18745 #18747 #18749 #18751 #18565 #13518 #18797]: #18799
-#18805 := [trans #18800 #18803]: #18804
-#18742 := (iff #18402 #18739)
-#18736 := (and #13227 #13511 #18733)
-#18740 := (iff #18736 #18739)
-#18741 := [rewrite]: #18740
-#18737 := (iff #18402 #18736)
-#18734 := (iff #18398 #18733)
-#18731 := (iff #18394 #18728)
-#18725 := (and #12299 #18722)
-#18729 := (iff #18725 #18728)
+#18772 := (iff #18419 #13981)
+#18773 := [rewrite]: #18772
+#18770 := (iff #18416 #13937)
+#18771 := [rewrite]: #18770
+#18768 := (iff #18413 #13895)
+#18769 := [rewrite]: #18768
+#18764 := (iff #18407 #12470)
+#18765 := [rewrite]: #18764
+#18762 := (iff #18404 #12461)
+#18763 := [rewrite]: #18762
+#18760 := (iff #18401 #12458)
+#18761 := [rewrite]: #18760
+#18758 := (iff #18398 #12455)
+#18759 := [rewrite]: #18758
+#18756 := (iff #18395 #12452)
+#18757 := [rewrite]: #18756
+#18754 := (iff #18392 #12424)
+#18755 := [rewrite]: #18754
+#18752 := (iff #18389 #12167)
+#18753 := [rewrite]: #18752
+#19013 := [monotonicity #18753 #18755 #18757 #18759 #18761 #18763 #18765 #18767 #18769 #18771 #18773 #18775 #18777 #18779 #19010]: #19012
+#19018 := [trans #19013 #19016]: #19017
+#19021 := [monotonicity #14147 #19018]: #19020
+#19024 := [monotonicity #19021]: #19023
+#18750 := (iff #18373 #18749)
+#18747 := (iff #18372 #18744)
+#18741 := (or #18371 #18370 #18738)
+#18745 := (iff #18741 #18744)
+#18746 := [rewrite]: #18745
+#18742 := (iff #18372 #18741)
+#18739 := (iff #18365 #18738)
+#18736 := (iff #18364 #18735)
+#18737 := [rewrite]: #18736
+#18740 := [monotonicity #18737]: #18739
+#18743 := [monotonicity #18740]: #18742
+#18748 := [trans #18743 #18746]: #18747
+#18751 := [monotonicity #18748]: #18750
+#19027 := [monotonicity #18751 #19024]: #19026
+#18733 := (iff #18358 #13378)
+#18734 := [rewrite]: #18733
+#19030 := [monotonicity #18734 #19027]: #19029
+#19033 := [monotonicity #19030]: #19032
+#18731 := (iff #18353 #12110)
+#18732 := [rewrite]: #18731
+#18729 := (iff #18350 #12107)
 #18730 := [rewrite]: #18729
-#18726 := (iff #18394 #18725)
-#18723 := (iff #18390 #18722)
-#18720 := (iff #18386 #18717)
-#18714 := (and #12305 #13227 #18711)
-#18718 := (iff #18714 #18717)
-#18719 := [rewrite]: #18718
-#18715 := (iff #18386 #18714)
-#18712 := (iff #18382 #18711)
-#18709 := (iff #18378 #18706)
-#18703 := (and #12548 #12551 #13227 #13236 #13417 #18666)
-#18707 := (iff #18703 #18706)
-#18708 := [rewrite]: #18707
-#18704 := (iff #18378 #18703)
-#18667 := (iff #18346 #18666)
-#18664 := (iff #18342 #18661)
-#18658 := (and #3209 #13253 #13327 #18653 #15645)
-#18662 := (iff #18658 #18661)
-#18663 := [rewrite]: #18662
-#18659 := (iff #18342 #18658)
-#18656 := (iff #18339 #15645)
-#18657 := [rewrite]: #18656
-#18654 := (iff #18335 #18653)
-#18651 := (iff #18331 #18650)
-#18648 := (iff #18327 #18645)
-#18642 := (or #18639 #18323)
-#18646 := (iff #18642 #18645)
-#18647 := [rewrite]: #18646
-#18643 := (iff #18327 #18642)
-#18640 := (iff #18308 #18639)
-#18637 := (iff #18307 #18636)
-#18634 := (iff #18300 #18633)
-#18631 := (iff #18299 #18630)
-#18632 := [rewrite]: #18631
-#18635 := [monotonicity #18632]: #18634
-#18628 := (iff #18304 #18625)
-#18617 := (+ #13279 #18302)
-#18620 := (<= #18617 0::int)
-#18626 := (iff #18620 #18625)
-#18627 := [rewrite]: #18626
-#18621 := (iff #18304 #18620)
-#18618 := (= #18303 #18617)
-#18619 := [rewrite]: #18618
-#18622 := [monotonicity #18619]: #18621
-#18629 := [trans #18622 #18627]: #18628
-#18615 := (iff #18306 #18612)
-#18604 := (+ #13260 ?x785!14)
-#18607 := (>= #18604 0::int)
-#18613 := (iff #18607 #18612)
-#18614 := [rewrite]: #18613
-#18608 := (iff #18306 #18607)
-#18605 := (= #18305 #18604)
-#18606 := [rewrite]: #18605
-#18609 := [monotonicity #18606]: #18608
-#18616 := [trans #18609 #18614]: #18615
-#18638 := [monotonicity #18616 #18629 #18635]: #18637
-#18641 := [monotonicity #18638]: #18640
-#18644 := [monotonicity #18641]: #18643
-#18649 := [trans #18644 #18647]: #18648
-#18602 := (iff #18293 #13259)
-#18603 := [rewrite]: #18602
-#18652 := [monotonicity #18603 #18649]: #18651
-#18655 := [monotonicity #18652]: #18654
-#18600 := (iff #18288 #13327)
-#18601 := [rewrite]: #18600
-#18598 := (iff #18285 #13253)
-#18599 := [rewrite]: #18598
-#18596 := (iff #18282 #3209)
-#18597 := [rewrite]: #18596
-#18660 := [monotonicity #18597 #18599 #18601 #18655 #18657]: #18659
-#18665 := [trans #18660 #18663]: #18664
-#18668 := [monotonicity #18665]: #18667
-#18594 := (iff #18273 #13236)
-#18595 := [rewrite]: #18594
-#18701 := (iff #18373 #12551)
-#18702 := [rewrite]: #18701
-#18699 := (iff #18370 #12548)
-#18700 := [rewrite]: #18699
-#18705 := [monotonicity #18700 #18702 #18565 #18595 #13426 #18668]: #18704
-#18710 := [trans #18705 #18708]: #18709
-#18697 := (iff #18366 #18694)
-#18691 := (and #13227 #13416 #18688)
-#18695 := (iff #18691 #18694)
-#18696 := [rewrite]: #18695
-#18692 := (iff #18366 #18691)
-#18689 := (iff #18362 #18688)
-#18686 := (iff #18358 #18683)
-#18680 := (and #12299 #18677)
-#18684 := (iff #18680 #18683)
-#18685 := [rewrite]: #18684
-#18681 := (iff #18358 #18680)
-#18678 := (iff #18354 #18677)
-#18675 := (iff #18350 #18672)
-#18669 := (and #3194 #3195 #12305 #12308 #12313 #12316 #13225 #13236 #18666)
-#18673 := (iff #18669 #18672)
-#18674 := [rewrite]: #18673
-#18670 := (iff #18350 #18669)
-#18592 := (iff #18270 #13225)
-#18593 := [rewrite]: #18592
-#18590 := (iff #18267 #12316)
-#18591 := [rewrite]: #18590
-#18588 := (iff #18264 #12313)
-#18589 := [rewrite]: #18588
-#18586 := (iff #18261 #12308)
-#18587 := [rewrite]: #18586
-#18580 := (iff #18250 #12305)
-#18581 := [rewrite]: #18580
-#18584 := (iff #18258 #3195)
-#18585 := [rewrite]: #18584
-#18582 := (iff #18255 #3194)
-#18583 := [rewrite]: #18582
-#18671 := [monotonicity #18583 #18585 #18581 #18587 #18589 #18591 #18593 #18595 #18668]: #18670
-#18676 := [trans #18671 #18674]: #18675
-#18679 := [monotonicity #18676]: #18678
-#18578 := (iff #18244 #12299)
-#18579 := [rewrite]: #18578
-#18682 := [monotonicity #18579 #18679]: #18681
-#18687 := [trans #18682 #18685]: #18686
-#18690 := [monotonicity #18687]: #18689
-#18693 := [monotonicity #18565 #18690]: #18692
-#18698 := [trans #18693 #18696]: #18697
-#18713 := [monotonicity #18698 #18710]: #18712
-#18716 := [monotonicity #18581 #18565 #18713]: #18715
-#18721 := [trans #18716 #18719]: #18720
-#18724 := [monotonicity #18721]: #18723
-#18727 := [monotonicity #18579 #18724]: #18726
-#18732 := [trans #18727 #18730]: #18731
-#18735 := [monotonicity #18732]: #18734
-#18738 := [monotonicity #18565 #18735]: #18737
-#18743 := [trans #18738 #18741]: #18742
-#18808 := [monotonicity #18743 #18805]: #18807
-#18576 := (iff #18233 #15599)
-#18577 := [rewrite]: #18576
-#18574 := (iff #18230 #15582)
-#18575 := [rewrite]: #18574
-#18572 := (iff #18227 #15565)
-#18573 := [rewrite]: #18572
-#18570 := (iff #18217 #13781)
-#18571 := [rewrite]: #18570
-#18568 := (iff #18214 #13737)
-#18569 := [rewrite]: #18568
-#18566 := (iff #18211 #13695)
-#18567 := [rewrite]: #18566
-#18562 := (iff #18205 #12254)
-#18563 := [rewrite]: #18562
-#18560 := (iff #18202 #11997)
-#18561 := [rewrite]: #18560
-#18558 := (iff #18199 #3176)
-#18559 := [rewrite]: #18558
-#18556 := (iff #18196 #3173)
-#18557 := [rewrite]: #18556
-#18554 := (iff #18193 #3172)
-#18555 := [rewrite]: #18554
-#18552 := (iff #18190 #3171)
-#18553 := [rewrite]: #18552
-#18550 := (iff #18187 #3170)
-#18551 := [rewrite]: #18550
-#18811 := [monotonicity #18551 #18553 #18555 #18557 #18559 #18561 #18563 #18565 #18567 #18569 #18571 #18573 #18575 #18577 #18808]: #18810
-#18816 := [trans #18811 #18814]: #18815
-#18819 := [monotonicity #13947 #18816]: #18818
-#18822 := [monotonicity #18819]: #18821
-#18548 := (iff #18171 #18547)
-#18545 := (iff #18170 #18542)
-#18539 := (or #18169 #18168 #18536)
-#18543 := (iff #18539 #18542)
-#18544 := [rewrite]: #18543
-#18540 := (iff #18170 #18539)
-#18537 := (iff #18163 #18536)
-#18534 := (iff #18162 #18533)
-#18535 := [rewrite]: #18534
-#18538 := [monotonicity #18535]: #18537
-#18541 := [monotonicity #18538]: #18540
-#18546 := [trans #18541 #18544]: #18545
-#18549 := [monotonicity #18546]: #18548
-#18825 := [monotonicity #18549 #18822]: #18824
-#18531 := (iff #18156 #13178)
-#18532 := [rewrite]: #18531
-#18828 := [monotonicity #18532 #18825]: #18827
-#18831 := [monotonicity #18828]: #18830
-#18529 := (iff #18151 #11940)
-#18530 := [rewrite]: #18529
-#18527 := (iff #18148 #3045)
-#18528 := [rewrite]: #18527
-#18525 := (iff #18145 #3044)
-#18526 := [rewrite]: #18525
-#18523 := (iff #18142 #3043)
-#18524 := [rewrite]: #18523
-#18521 := (iff #18139 #3042)
-#18522 := [rewrite]: #18521
-#18834 := [monotonicity #18522 #18524 #18526 #18528 #18530 #18831]: #18833
-#18839 := [trans #18834 #18837]: #18838
-#18842 := [monotonicity #18839]: #18841
-#18519 := (iff #18133 #11934)
-#18520 := [rewrite]: #18519
-#18845 := [monotonicity #18520 #18842]: #18844
-#18850 := [trans #18845 #18848]: #18849
-#18853 := [monotonicity #18850]: #18852
-#18517 := (iff #18124 #11925)
-#18518 := [rewrite]: #18517
-#18856 := [monotonicity #18518 #18853]: #18855
-#18859 := [monotonicity #18856]: #18858
-#15735 := (exists (vars (?x778 int)) #15730)
-#15724 := (not #15721)
-#15738 := (or #15724 #15735)
-#15741 := (and #15721 #15738)
-#15744 := (or #12079 #12070 #12061 #12052 #13230 #13511 #15741)
-#15625 := (not #15622)
-#15631 := (or #13310 #15625)
-#15636 := (and #15622 #15631)
-#15639 := (or #13264 #15636)
-#15642 := (and #13259 #15639)
-#15654 := (or #12401 #13256 #13331 #15642 #15648)
-#15659 := (and #13243 #15609 #15654)
-#15685 := (or #12566 #12557 #13230 #13239 #13416 #15659)
-#15662 := (or #12476 #12467 #12494 #12485 #12449 #12440 #13365 #13239 #15659)
-#15665 := (and #12293 #12302 #15662)
-#15668 := (or #12506 #15665)
-#15671 := (and #12293 #12296 #15668)
-#15677 := (or #13230 #13417 #15671)
-#15690 := (and #15677 #15685)
-#15693 := (or #12494 #13230 #15690)
-#15696 := (and #12293 #12302 #15693)
-#15699 := (or #12506 #15696)
-#15702 := (and #12293 #12296 #15699)
-#15708 := (or #13230 #13510 #15702)
-#15747 := (and #15708 #15744)
-#15551 := (not #15548)
-#15753 := (or #12769 #12760 #12751 #12742 #12733 #14996 #13683 #13230 #13700 #13740 #13786 #15551 #15568 #15585 #15602 #15747)
-#15758 := (and #3042 #13218 #15753)
-#15537 := (not #15534)
-#15761 := (or #15537 #15758)
-#15764 := (and #15534 #15761)
-#15767 := (or #13181 #15764)
-#15770 := (and #13178 #15767)
-#15773 := (or #12976 #12967 #12958 #12949 #12985 #15770)
-#15776 := (and #11928 #11937 #15773)
-#15779 := (or #12997 #15776)
-#15782 := (and #11928 #11931 #15779)
-#15785 := (or #13009 #15782)
-#15788 := (and #11925 #15785)
-#15791 := (not #15788)
-#18512 := (~ #15791 #18511)
-#18508 := (not #15785)
-#18509 := (~ #18508 #18507)
-#18504 := (not #15782)
-#18505 := (~ #18504 #18503)
-#18500 := (not #15779)
-#18501 := (~ #18500 #18499)
-#18496 := (not #15776)
-#18497 := (~ #18496 #18495)
-#18492 := (not #15773)
-#18493 := (~ #18492 #18491)
-#18488 := (not #15770)
-#18489 := (~ #18488 #18487)
-#18484 := (not #15767)
-#18485 := (~ #18484 #18483)
-#18480 := (not #15764)
-#18481 := (~ #18480 #18479)
-#18476 := (not #15761)
-#18477 := (~ #18476 #18475)
-#18472 := (not #15758)
-#18473 := (~ #18472 #18471)
-#18468 := (not #15753)
-#18469 := (~ #18468 #18467)
-#18464 := (not #15747)
-#18465 := (~ #18464 #18463)
-#18460 := (not #15744)
-#18461 := (~ #18460 #18459)
-#18456 := (not #15741)
-#18457 := (~ #18456 #18455)
-#18452 := (not #15738)
-#18453 := (~ #18452 #18451)
-#18448 := (not #15735)
-#18449 := (~ #18448 #18447)
-#18445 := (~ #18444 #18444)
-#18446 := [refl]: #18445
-#18450 := [nnf-neg #18446]: #18449
-#18441 := (not #15724)
-#18442 := (~ #18441 #15721)
-#18439 := (~ #15721 #15721)
-#18437 := (~ #15716 #15716)
-#18438 := [refl]: #18437
-#18440 := [nnf-pos #18438]: #18439
-#18443 := [nnf-neg #18440]: #18442
-#18454 := [nnf-neg #18443 #18450]: #18453
-#18433 := (~ #15724 #18432)
-#18434 := [sk]: #18433
-#18458 := [nnf-neg #18434 #18454]: #18457
-#18418 := (~ #13514 #13514)
-#18419 := [refl]: #18418
-#18209 := (~ #18208 #18208)
-#18210 := [refl]: #18209
-#18416 := (~ #18415 #18415)
-#18417 := [refl]: #18416
-#18413 := (~ #18412 #18412)
-#18414 := [refl]: #18413
-#18410 := (~ #18409 #18409)
-#18411 := [refl]: #18410
-#18407 := (~ #18406 #18406)
-#18408 := [refl]: #18407
-#18462 := [nnf-neg #18408 #18411 #18414 #18417 #18210 #18419 #18458]: #18461
-#18403 := (not #15708)
-#18404 := (~ #18403 #18402)
-#18399 := (not #15702)
-#18400 := (~ #18399 #18398)
-#18395 := (not #15699)
-#18396 := (~ #18395 #18394)
-#18391 := (not #15696)
-#18392 := (~ #18391 #18390)
-#18387 := (not #15693)
-#18388 := (~ #18387 #18386)
-#18383 := (not #15690)
-#18384 := (~ #18383 #18382)
-#18379 := (not #15685)
-#18380 := (~ #18379 #18378)
-#18347 := (not #15659)
-#18348 := (~ #18347 #18346)
-#18343 := (not #15654)
-#18344 := (~ #18343 #18342)
-#18340 := (~ #18339 #18339)
-#18341 := [refl]: #18340
-#18336 := (not #15642)
-#18337 := (~ #18336 #18335)
-#18332 := (not #15639)
-#18333 := (~ #18332 #18331)
-#18328 := (not #15636)
-#18329 := (~ #18328 #18327)
-#18324 := (not #15631)
-#18325 := (~ #18324 #18323)
-#18320 := (not #15625)
-#18321 := (~ #18320 #15622)
-#18318 := (~ #15622 #15622)
-#18316 := (~ #15617 #15617)
-#18317 := [refl]: #18316
-#18319 := [nnf-pos #18317]: #18318
-#18322 := [nnf-neg #18319]: #18321
-#18314 := (~ #18313 #18313)
-#18315 := [refl]: #18314
-#18326 := [nnf-neg #18315 #18322]: #18325
-#18309 := (~ #15625 #18308)
-#18310 := [sk]: #18309
-#18330 := [nnf-neg #18310 #18326]: #18329
-#18294 := (~ #18293 #18293)
-#18295 := [refl]: #18294
-#18334 := [nnf-neg #18295 #18330]: #18333
-#18291 := (~ #13264 #13264)
-#18292 := [refl]: #18291
-#18338 := [nnf-neg #18292 #18334]: #18337
-#18289 := (~ #18288 #18288)
-#18290 := [refl]: #18289
-#18286 := (~ #18285 #18285)
-#18287 := [refl]: #18286
-#18283 := (~ #18282 #18282)
-#18284 := [refl]: #18283
-#18345 := [nnf-neg #18284 #18287 #18290 #18338 #18341]: #18344
-#18280 := (~ #18279 #18279)
-#18281 := [refl]: #18280
-#18277 := (~ #18276 #18276)
-#18278 := [refl]: #18277
-#18349 := [nnf-neg #18278 #18281 #18345]: #18348
-#18376 := (~ #13422 #13422)
-#18377 := [refl]: #18376
-#18274 := (~ #18273 #18273)
-#18275 := [refl]: #18274
-#18374 := (~ #18373 #18373)
-#18375 := [refl]: #18374
-#18371 := (~ #18370 #18370)
-#18372 := [refl]: #18371
-#18381 := [nnf-neg #18372 #18375 #18210 #18275 #18377 #18349]: #18380
-#18367 := (not #15677)
-#18368 := (~ #18367 #18366)
-#18363 := (not #15671)
-#18364 := (~ #18363 #18362)
-#18359 := (not #15668)
-#18360 := (~ #18359 #18358)
-#18355 := (not #15665)
-#18356 := (~ #18355 #18354)
-#18351 := (not #15662)
-#18352 := (~ #18351 #18350)
-#18271 := (~ #18270 #18270)
-#18272 := [refl]: #18271
-#18268 := (~ #18267 #18267)
-#18269 := [refl]: #18268
-#18265 := (~ #18264 #18264)
-#18266 := [refl]: #18265
-#18262 := (~ #18261 #18261)
-#18263 := [refl]: #18262
-#18251 := (~ #18250 #18250)
-#18252 := [refl]: #18251
-#18259 := (~ #18258 #18258)
-#18260 := [refl]: #18259
-#18256 := (~ #18255 #18255)
-#18257 := [refl]: #18256
-#18353 := [nnf-neg #18257 #18260 #18252 #18263 #18266 #18269 #18272 #18275 #18349]: #18352
-#18248 := (~ #18247 #18247)
-#18249 := [refl]: #18248
-#18239 := (~ #18238 #18238)
-#18240 := [refl]: #18239
-#18357 := [nnf-neg #18240 #18249 #18353]: #18356
-#18245 := (~ #18244 #18244)
-#18246 := [refl]: #18245
-#18361 := [nnf-neg #18246 #18357]: #18360
-#18242 := (~ #18241 #18241)
-#18243 := [refl]: #18242
-#18365 := [nnf-neg #18240 #18243 #18361]: #18364
-#18253 := (~ #13416 #13416)
-#18254 := [refl]: #18253
-#18369 := [nnf-neg #18210 #18254 #18365]: #18368
-#18385 := [nnf-neg #18369 #18381]: #18384
-#18389 := [nnf-neg #18252 #18210 #18385]: #18388
-#18393 := [nnf-neg #18240 #18249 #18389]: #18392
-#18397 := [nnf-neg #18246 #18393]: #18396
-#18401 := [nnf-neg #18240 #18243 #18397]: #18400
-#18236 := (~ #13511 #13511)
-#18237 := [refl]: #18236
-#18405 := [nnf-neg #18210 #18237 #18401]: #18404
-#18466 := [nnf-neg #18405 #18462]: #18465
-#18234 := (~ #18233 #18233)
-#18235 := [refl]: #18234
-#18231 := (~ #18230 #18230)
-#18232 := [refl]: #18231
-#18228 := (~ #18227 #18227)
-#18229 := [refl]: #18228
-#18224 := (not #15551)
-#18225 := (~ #18224 #15548)
-#18222 := (~ #15548 #15548)
-#18220 := (~ #15543 #15543)
-#18221 := [refl]: #18220
-#18223 := [nnf-pos #18221]: #18222
-#18226 := [nnf-neg #18223]: #18225
-#18218 := (~ #18217 #18217)
-#18219 := [refl]: #18218
-#18215 := (~ #18214 #18214)
-#18216 := [refl]: #18215
-#18212 := (~ #18211 #18211)
-#18213 := [refl]: #18212
-#18206 := (~ #18205 #18205)
-#18207 := [refl]: #18206
-#18203 := (~ #18202 #18202)
-#18204 := [refl]: #18203
-#18200 := (~ #18199 #18199)
-#18201 := [refl]: #18200
-#18197 := (~ #18196 #18196)
-#18198 := [refl]: #18197
-#18194 := (~ #18193 #18193)
-#18195 := [refl]: #18194
-#18191 := (~ #18190 #18190)
-#18192 := [refl]: #18191
-#18188 := (~ #18187 #18187)
-#18189 := [refl]: #18188
-#18470 := [nnf-neg #18189 #18192 #18195 #18198 #18201 #18204 #18207 #18210 #18213 #18216 #18219 #18226 #18229 #18232 #18235 #18466]: #18469
-#18185 := (~ #13943 #13943)
-#18186 := [refl]: #18185
-#18183 := (~ #12976 #12976)
-#18184 := [refl]: #18183
-#18474 := [nnf-neg #18184 #18186 #18470]: #18473
-#18180 := (not #15537)
-#18181 := (~ #18180 #15534)
-#18178 := (~ #15534 #15534)
-#18176 := (~ #15529 #15529)
-#18177 := [refl]: #18176
-#18179 := [nnf-pos #18177]: #18178
-#18182 := [nnf-neg #18179]: #18181
-#18478 := [nnf-neg #18182 #18474]: #18477
-#18172 := (~ #15537 #18171)
-#18173 := [sk]: #18172
-#18482 := [nnf-neg #18173 #18478]: #18481
-#18157 := (~ #18156 #18156)
-#18158 := [refl]: #18157
-#18486 := [nnf-neg #18158 #18482]: #18485
-#18154 := (~ #13181 #13181)
-#18155 := [refl]: #18154
-#18490 := [nnf-neg #18155 #18486]: #18489
-#18152 := (~ #18151 #18151)
-#18153 := [refl]: #18152
-#18149 := (~ #18148 #18148)
-#18150 := [refl]: #18149
-#18146 := (~ #18145 #18145)
-#18147 := [refl]: #18146
-#18143 := (~ #18142 #18142)
-#18144 := [refl]: #18143
-#18140 := (~ #18139 #18139)
-#18141 := [refl]: #18140
-#18494 := [nnf-neg #18141 #18144 #18147 #18150 #18153 #18490]: #18493
-#18137 := (~ #18136 #18136)
-#18138 := [refl]: #18137
-#18128 := (~ #18127 #18127)
-#18129 := [refl]: #18128
-#18498 := [nnf-neg #18129 #18138 #18494]: #18497
-#18134 := (~ #18133 #18133)
-#18135 := [refl]: #18134
-#18502 := [nnf-neg #18135 #18498]: #18501
-#18131 := (~ #18130 #18130)
-#18132 := [refl]: #18131
-#18506 := [nnf-neg #18129 #18132 #18502]: #18505
-#18125 := (~ #18124 #18124)
-#18126 := [refl]: #18125
-#18510 := [nnf-neg #18126 #18506]: #18509
-#18122 := (~ #13009 #13009)
-#18123 := [refl]: #18122
-#18513 := [nnf-neg #18123 #18510]: #18512
-#15021 := (or #12079 #12070 #12061 #12052 #13230 #13511 #13597)
-#15026 := (and #13533 #15021)
-#15032 := (or #12769 #12760 #12751 #12742 #12733 #14996 #13683 #13230 #13700 #13734 #13740 #13752 #13762 #13775 #13786 #15026)
-#15037 := (and #3042 #13218 #15032)
-#15040 := (or #13214 #15037)
-#15043 := (and #13211 #15040)
-#15046 := (or #13181 #15043)
-#15049 := (and #13178 #15046)
-#15052 := (or #12976 #12967 #12958 #12949 #12985 #15049)
-#15055 := (and #11928 #11937 #15052)
-#15058 := (or #12997 #15055)
-#15061 := (and #11928 #11931 #15058)
-#15064 := (or #13009 #15061)
-#15067 := (and #11925 #15064)
-#15070 := (not #15067)
-#15792 := (iff #15070 #15791)
-#15789 := (iff #15067 #15788)
-#15786 := (iff #15064 #15785)
-#15783 := (iff #15061 #15782)
-#15780 := (iff #15058 #15779)
-#15777 := (iff #15055 #15776)
-#15774 := (iff #15052 #15773)
-#15771 := (iff #15049 #15770)
-#15768 := (iff #15046 #15767)
-#15765 := (iff #15043 #15764)
-#15762 := (iff #15040 #15761)
-#15759 := (iff #15037 #15758)
-#15756 := (iff #15032 #15753)
-#15750 := (or #12769 #12760 #12751 #12742 #12733 #14996 #13683 #13230 #13700 #15551 #13740 #15568 #15585 #15602 #13786 #15747)
-#15754 := (iff #15750 #15753)
-#15755 := [rewrite]: #15754
-#15751 := (iff #15032 #15750)
-#15748 := (iff #15026 #15747)
-#15745 := (iff #15021 #15744)
-#15742 := (iff #13597 #15741)
-#15739 := (iff #13592 #15738)
-#15736 := (iff #13583 #15735)
-#15733 := (iff #13578 #15730)
-#15727 := (and #3103 #4043 #14916 #13540)
-#15731 := (iff #15727 #15730)
-#15732 := [rewrite]: #15731
-#15728 := (iff #13578 #15727)
-#14911 := (iff #4357 #14916)
-#14932 := -4294967295::int
-#14924 := (+ -4294967295::int #161)
-#14917 := (<= #14924 0::int)
-#14913 := (iff #14917 #14916)
-#14914 := [rewrite]: #14913
-#14918 := (iff #4357 #14917)
-#14919 := (= #4356 #14924)
-#14925 := (+ #161 -4294967295::int)
-#14921 := (= #14925 #14924)
-#14922 := [rewrite]: #14921
-#14926 := (= #4356 #14925)
-#14927 := (= #4355 -4294967295::int)
-#14933 := (* -1::int 4294967295::int)
-#14929 := (= #14933 -4294967295::int)
-#14930 := [rewrite]: #14929
-#14934 := (= #4355 #14933)
-#7478 := (= uf_76 4294967295::int)
-#947 := 65536::int
-#1322 := (* 65536::int 65536::int)
-#1327 := (- #1322 1::int)
-#1328 := (= uf_76 #1327)
-#7479 := (iff #1328 #7478)
-#7476 := (= #1327 4294967295::int)
-#1010 := 4294967296::int
-#7469 := (- 4294967296::int 1::int)
-#7474 := (= #7469 4294967295::int)
-#7475 := [rewrite]: #7474
-#7471 := (= #1327 #7469)
-#7440 := (= #1322 4294967296::int)
-#7441 := [rewrite]: #7440
-#7472 := [monotonicity #7441]: #7471
-#7477 := [trans #7472 #7475]: #7476
-#7480 := [monotonicity #7477]: #7479
-#7468 := [asserted]: #1328
-#7483 := [mp #7468 #7480]: #7478
-#14931 := [monotonicity #7483]: #14934
-#14928 := [trans #14931 #14930]: #14927
-#14923 := [monotonicity #14928]: #14926
-#14920 := [trans #14923 #14922]: #14919
-#14915 := [monotonicity #14920]: #14918
-#14912 := [trans #14915 #14914]: #14911
-#15729 := [monotonicity #14912]: #15728
-#15734 := [trans #15729 #15732]: #15733
-#15737 := [quant-intro #15734]: #15736
-#15725 := (iff #13586 #15724)
-#15722 := (iff #13566 #15721)
-#15719 := (iff #13561 #15716)
-#15713 := (or #14158 #13538 #13552)
-#15717 := (iff #15713 #15716)
-#15718 := [rewrite]: #15717
-#15714 := (iff #13561 #15713)
-#14155 := (iff #5579 #14158)
-#14160 := (iff #4364 #14159)
-#14157 := [monotonicity #14912]: #14160
-#14156 := [monotonicity #14157]: #14155
-#15715 := [monotonicity #14156]: #15714
-#15720 := [trans #15715 #15718]: #15719
-#15723 := [quant-intro #15720]: #15722
-#15726 := [monotonicity #15723]: #15725
-#15740 := [monotonicity #15726 #15737]: #15739
-#15743 := [monotonicity #15723 #15740]: #15742
-#15746 := [monotonicity #15743]: #15745
-#15711 := (iff #13533 #15708)
-#15705 := (or #13230 #15702 #13510)
-#15709 := (iff #15705 #15708)
-#15710 := [rewrite]: #15709
-#15706 := (iff #13533 #15705)
-#15703 := (iff #13504 #15702)
-#15700 := (iff #13498 #15699)
-#15697 := (iff #13493 #15696)
-#15694 := (iff #13485 #15693)
-#15691 := (iff #13476 #15690)
-#15688 := (iff #13471 #15685)
-#15682 := (or #12566 #12557 #13230 #13239 #15659 #13416)
-#15686 := (iff #15682 #15685)
-#15687 := [rewrite]: #15686
-#15683 := (iff #13471 #15682)
-#15660 := (iff #13360 #15659)
-#15657 := (iff #13352 #15654)
-#15651 := (or #12401 #13256 #15642 #13331 #15648)
-#15655 := (iff #15651 #15654)
-#15656 := [rewrite]: #15655
-#15652 := (iff #13352 #15651)
-#15649 := (iff #13337 #15648)
-#15646 := (iff #13334 #15645)
-#15612 := (iff #13245 #15609)
-#15554 := (+ 4294967295::int #13246)
-#15605 := (>= #15554 1::int)
-#15610 := (iff #15605 #15609)
-#15611 := [rewrite]: #15610
-#15606 := (iff #13245 #15605)
-#15555 := (= #13247 #15554)
-#15556 := [monotonicity #7483]: #15555
-#15607 := [monotonicity #15556]: #15606
-#15613 := [trans #15607 #15611]: #15612
-#15647 := [monotonicity #15613]: #15646
-#15650 := [monotonicity #15647]: #15649
-#15643 := (iff #13324 #15642)
-#15640 := (iff #13321 #15639)
-#15637 := (iff #13318 #15636)
-#15634 := (iff #13315 #15631)
-#15628 := (or #15625 #13310)
-#15632 := (iff #15628 #15631)
-#15633 := [rewrite]: #15632
-#15629 := (iff #13315 #15628)
-#15626 := (iff #13298 #15625)
-#15623 := (iff #13295 #15622)
-#15620 := (iff #13290 #15617)
-#15614 := (or #14158 #13267 #13281)
-#15618 := (iff #15614 #15617)
-#15619 := [rewrite]: #15618
-#15615 := (iff #13290 #15614)
-#15616 := [monotonicity #14156]: #15615
-#15621 := [trans #15616 #15619]: #15620
-#15624 := [quant-intro #15621]: #15623
-#15627 := [monotonicity #15624]: #15626
-#15630 := [monotonicity #15627]: #15629
-#15635 := [trans #15630 #15633]: #15634
-#15638 := [monotonicity #15624 #15635]: #15637
-#15641 := [monotonicity #15638]: #15640
-#15644 := [monotonicity #15641]: #15643
-#15653 := [monotonicity #15644 #15650]: #15652
-#15658 := [trans #15653 #15656]: #15657
-#15661 := [monotonicity #15613 #15658]: #15660
-#15684 := [monotonicity #15661]: #15683
-#15689 := [trans #15684 #15687]: #15688
-#15680 := (iff #13441 #15677)
-#15674 := (or #13230 #15671 #13417)
-#15678 := (iff #15674 #15677)
-#15679 := [rewrite]: #15678
-#15675 := (iff #13441 #15674)
-#15672 := (iff #13411 #15671)
-#15669 := (iff #13405 #15668)
-#15666 := (iff #13400 #15665)
-#15663 := (iff #13392 #15662)
-#15664 := [monotonicity #15661]: #15663
-#15667 := [monotonicity #15664]: #15666
-#15670 := [monotonicity #15667]: #15669
-#15673 := [monotonicity #15670]: #15672
-#15676 := [monotonicity #15673]: #15675
-#15681 := [trans #15676 #15679]: #15680
-#15692 := [monotonicity #15681 #15689]: #15691
-#15695 := [monotonicity #15692]: #15694
-#15698 := [monotonicity #15695]: #15697
-#15701 := [monotonicity #15698]: #15700
-#15704 := [monotonicity #15701]: #15703
-#15707 := [monotonicity #15704]: #15706
-#15712 := [trans #15707 #15710]: #15711
-#15749 := [monotonicity #15712 #15746]: #15748
-#15603 := (iff #13775 #15602)
-#15600 := (iff #13772 #15599)
-#15597 := (iff #13768 #15594)
-#15588 := (+ 255::int #13715)
-#15591 := (>= #15588 0::int)
-#15595 := (iff #15591 #15594)
-#15596 := [rewrite]: #15595
-#15592 := (iff #13768 #15591)
-#15589 := (= #13769 #15588)
-#1332 := (= uf_78 255::int)
-#7482 := [asserted]: #1332
-#15590 := [monotonicity #7482]: #15589
-#15593 := [monotonicity #15590]: #15592
-#15598 := [trans #15593 #15596]: #15597
-#15601 := [monotonicity #15598]: #15600
-#15604 := [monotonicity #15601]: #15603
-#15586 := (iff #13762 #15585)
-#15583 := (iff #13759 #15582)
-#15580 := (iff #13755 #15577)
-#15571 := (+ 4294967295::int #13686)
-#15574 := (>= #15571 0::int)
-#15578 := (iff #15574 #15577)
-#15579 := [rewrite]: #15578
-#15575 := (iff #13755 #15574)
-#15572 := (= #13756 #15571)
-#15573 := [monotonicity #7483]: #15572
-#15576 := [monotonicity #15573]: #15575
-#15581 := [trans #15576 #15579]: #15580
-#15584 := [monotonicity #15581]: #15583
-#15587 := [monotonicity #15584]: #15586
-#15569 := (iff #13752 #15568)
-#15566 := (iff #13749 #15565)
-#15563 := (iff #13746 #15560)
-#15557 := (>= #15554 0::int)
-#15561 := (iff #15557 #15560)
-#15562 := [rewrite]: #15561
-#15558 := (iff #13746 #15557)
-#15559 := [monotonicity #15556]: #15558
-#15564 := [trans #15559 #15562]: #15563
-#15567 := [monotonicity #15564]: #15566
-#15570 := [monotonicity #15567]: #15569
-#15552 := (iff #13734 #15551)
-#15549 := (iff #13731 #15548)
-#15546 := (iff #13726 #15543)
-#15540 := (or #14158 #13703 #13717)
-#15544 := (iff #15540 #15543)
-#15545 := [rewrite]: #15544
-#15541 := (iff #13726 #15540)
-#15542 := [monotonicity #14156]: #15541
-#15547 := [trans #15542 #15545]: #15546
-#15550 := [quant-intro #15547]: #15549
-#15553 := [monotonicity #15550]: #15552
-#15752 := [monotonicity #15553 #15570 #15587 #15604 #15749]: #15751
-#15757 := [trans #15752 #15755]: #15756
-#15760 := [monotonicity #15757]: #15759
-#15538 := (iff #13214 #15537)
-#15535 := (iff #13211 #15534)
-#15532 := (iff #13206 #15529)
-#15526 := (or #14158 #13184 #13196)
-#15530 := (iff #15526 #15529)
-#15531 := [rewrite]: #15530
-#15527 := (iff #13206 #15526)
-#15528 := [monotonicity #14156]: #15527
-#15533 := [trans #15528 #15531]: #15532
-#15536 := [quant-intro #15533]: #15535
-#15539 := [monotonicity #15536]: #15538
-#15763 := [monotonicity #15539 #15760]: #15762
-#15766 := [monotonicity #15536 #15763]: #15765
-#15769 := [monotonicity #15766]: #15768
-#15772 := [monotonicity #15769]: #15771
-#15775 := [monotonicity #15772]: #15774
-#15778 := [monotonicity #15775]: #15777
-#15781 := [monotonicity #15778]: #15780
+#18727 := (iff #18347 #12104)
+#18728 := [rewrite]: #18727
+#18725 := (iff #18344 #12101)
+#18726 := [rewrite]: #18725
+#18723 := (iff #18341 #3074)
+#18724 := [rewrite]: #18723
+#19036 := [monotonicity #18724 #18726 #18728 #18730 #18732 #19033]: #19035
+#19041 := [trans #19036 #19039]: #19040
+#19044 := [monotonicity #19041]: #19043
+#18721 := (iff #18335 #12095)
+#18722 := [rewrite]: #18721
+#19047 := [monotonicity #18722 #19044]: #19046
+#19052 := [trans #19047 #19050]: #19051
+#19055 := [monotonicity #19052]: #19054
+#18719 := (iff #18326 #12086)
+#18720 := [rewrite]: #18719
+#19058 := [monotonicity #18720 #19055]: #19057
+#19061 := [monotonicity #19058]: #19060
+#15935 := (exists (vars (?v0 int)) #15930)
+#15924 := (not #15921)
+#15938 := (or #15924 #15935)
+#15941 := (and #15921 #15938)
+#15944 := (or #12249 #12240 #12231 #12222 #13430 #13711 #15941)
+#15825 := (not #15822)
+#15831 := (or #13510 #15825)
+#15836 := (and #15822 #15831)
+#15839 := (or #13464 #15836)
+#15842 := (and #13459 #15839)
+#15854 := (or #12601 #13456 #13531 #15842 #15848)
+#15859 := (and #13443 #15809 #15854)
+#15885 := (or #12766 #12757 #13430 #13439 #13616 #15859)
+#15862 := (or #12694 #12685 #12676 #12667 #12649 #12640 #13565 #13439 #15859)
+#15865 := (and #12484 #12493 #15862)
+#15868 := (or #12706 #15865)
+#15871 := (and #12484 #12487 #15868)
+#15877 := (or #13430 #13617 #15871)
+#15890 := (and #15877 #15885)
+#15893 := (or #12694 #13430 #15890)
+#15896 := (and #12484 #12493 #15893)
+#15899 := (or #12706 #15896)
+#15902 := (and #12484 #12487 #15899)
+#15908 := (or #13430 #13710 #15902)
+#15947 := (and #15908 #15944)
+#15751 := (not #15748)
+#15953 := (or #15198 #13883 #12969 #12960 #12951 #12942 #12933 #13430 #13900 #13940 #13986 #15751 #15768 #15785 #15802 #15947)
+#15958 := (and #3074 #13418 #15953)
+#15737 := (not #15734)
+#15961 := (or #15737 #15958)
+#15964 := (and #15734 #15961)
+#15967 := (or #13381 #15964)
+#15970 := (and #13378 #15967)
+#15973 := (or #13176 #13185 #13167 #13158 #13149 #15970)
+#15976 := (and #12089 #12098 #15973)
+#15979 := (or #13197 #15976)
+#15982 := (and #12089 #12092 #15979)
+#15985 := (or #13209 #15982)
+#15988 := (and #12086 #15985)
+#15991 := (not #15988)
+#18714 := (~ #15991 #18713)
+#18710 := (not #15985)
+#18711 := (~ #18710 #18709)
+#18706 := (not #15982)
+#18707 := (~ #18706 #18705)
+#18702 := (not #15979)
+#18703 := (~ #18702 #18701)
+#18698 := (not #15976)
+#18699 := (~ #18698 #18697)
+#18694 := (not #15973)
+#18695 := (~ #18694 #18693)
+#18690 := (not #15970)
+#18691 := (~ #18690 #18689)
+#18686 := (not #15967)
+#18687 := (~ #18686 #18685)
+#18682 := (not #15964)
+#18683 := (~ #18682 #18681)
+#18678 := (not #15961)
+#18679 := (~ #18678 #18677)
+#18674 := (not #15958)
+#18675 := (~ #18674 #18673)
+#18670 := (not #15953)
+#18671 := (~ #18670 #18669)
+#18666 := (not #15947)
+#18667 := (~ #18666 #18665)
+#18662 := (not #15944)
+#18663 := (~ #18662 #18661)
+#18658 := (not #15941)
+#18659 := (~ #18658 #18657)
+#18654 := (not #15938)
+#18655 := (~ #18654 #18653)
+#18650 := (not #15935)
+#18651 := (~ #18650 #18649)
+#18647 := (~ #18646 #18646)
+#18648 := [refl]: #18647
+#18652 := [nnf-neg #18648]: #18651
+#18643 := (not #15924)
+#18644 := (~ #18643 #15921)
+#18641 := (~ #15921 #15921)
+#18639 := (~ #15916 #15916)
+#18640 := [refl]: #18639
+#18642 := [nnf-pos #18640]: #18641
+#18645 := [nnf-neg #18642]: #18644
+#18656 := [nnf-neg #18645 #18652]: #18655
+#18635 := (~ #15924 #18634)
+#18636 := [sk]: #18635
+#18660 := [nnf-neg #18636 #18656]: #18659
+#18620 := (~ #13714 #13714)
+#18621 := [refl]: #18620
+#18411 := (~ #18410 #18410)
+#18412 := [refl]: #18411
+#18618 := (~ #18617 #18617)
+#18619 := [refl]: #18618
+#18615 := (~ #18614 #18614)
+#18616 := [refl]: #18615
+#18612 := (~ #18611 #18611)
+#18613 := [refl]: #18612
+#18609 := (~ #18608 #18608)
+#18610 := [refl]: #18609
+#18664 := [nnf-neg #18610 #18613 #18616 #18619 #18412 #18621 #18660]: #18663
+#18605 := (not #15908)
+#18606 := (~ #18605 #18604)
+#18601 := (not #15902)
+#18602 := (~ #18601 #18600)
+#18597 := (not #15899)
+#18598 := (~ #18597 #18596)
+#18593 := (not #15896)
+#18594 := (~ #18593 #18592)
+#18589 := (not #15893)
+#18590 := (~ #18589 #18588)
+#18585 := (not #15890)
+#18586 := (~ #18585 #18584)
+#18581 := (not #15885)
+#18582 := (~ #18581 #18580)
+#18549 := (not #15859)
+#18550 := (~ #18549 #18548)
+#18545 := (not #15854)
+#18546 := (~ #18545 #18544)
+#18542 := (~ #18541 #18541)
+#18543 := [refl]: #18542
+#18538 := (not #15842)
+#18539 := (~ #18538 #18537)
+#18534 := (not #15839)
+#18535 := (~ #18534 #18533)
+#18530 := (not #15836)
+#18531 := (~ #18530 #18529)
+#18526 := (not #15831)
+#18527 := (~ #18526 #18525)
+#18522 := (not #15825)
+#18523 := (~ #18522 #15822)
+#18520 := (~ #15822 #15822)
+#18518 := (~ #15817 #15817)
+#18519 := [refl]: #18518
+#18521 := [nnf-pos #18519]: #18520
+#18524 := [nnf-neg #18521]: #18523
+#18516 := (~ #18515 #18515)
+#18517 := [refl]: #18516
+#18528 := [nnf-neg #18517 #18524]: #18527
+#18511 := (~ #15825 #18510)
+#18512 := [sk]: #18511
+#18532 := [nnf-neg #18512 #18528]: #18531
+#18496 := (~ #18495 #18495)
+#18497 := [refl]: #18496
+#18536 := [nnf-neg #18497 #18532]: #18535
+#18493 := (~ #13464 #13464)
+#18494 := [refl]: #18493
+#18540 := [nnf-neg #18494 #18536]: #18539
+#18491 := (~ #18490 #18490)
+#18492 := [refl]: #18491
+#18488 := (~ #18487 #18487)
+#18489 := [refl]: #18488
+#18485 := (~ #18484 #18484)
+#18486 := [refl]: #18485
+#18547 := [nnf-neg #18486 #18489 #18492 #18540 #18543]: #18546
+#18482 := (~ #18481 #18481)
+#18483 := [refl]: #18482
+#18479 := (~ #18478 #18478)
+#18480 := [refl]: #18479
+#18551 := [nnf-neg #18480 #18483 #18547]: #18550
+#18578 := (~ #13622 #13622)
+#18579 := [refl]: #18578
+#18476 := (~ #18475 #18475)
+#18477 := [refl]: #18476
+#18576 := (~ #18575 #18575)
+#18577 := [refl]: #18576
+#18573 := (~ #18572 #18572)
+#18574 := [refl]: #18573
+#18583 := [nnf-neg #18574 #18577 #18412 #18477 #18579 #18551]: #18582
+#18569 := (not #15877)
+#18570 := (~ #18569 #18568)
+#18565 := (not #15871)
+#18566 := (~ #18565 #18564)
+#18561 := (not #15868)
+#18562 := (~ #18561 #18560)
+#18557 := (not #15865)
+#18558 := (~ #18557 #18556)
+#18553 := (not #15862)
+#18554 := (~ #18553 #18552)
+#18473 := (~ #18472 #18472)
+#18474 := [refl]: #18473
+#18470 := (~ #18469 #18469)
+#18471 := [refl]: #18470
+#18467 := (~ #18466 #18466)
+#18468 := [refl]: #18467
+#18464 := (~ #18463 #18463)
+#18465 := [refl]: #18464
+#18461 := (~ #18460 #18460)
+#18462 := [refl]: #18461
+#18458 := (~ #18457 #18457)
+#18459 := [refl]: #18458
+#18453 := (~ #18452 #18452)
+#18454 := [refl]: #18453
+#18555 := [nnf-neg #18454 #18459 #18462 #18465 #18468 #18471 #18474 #18477 #18551]: #18554
+#18450 := (~ #18449 #18449)
+#18451 := [refl]: #18450
+#18441 := (~ #18440 #18440)
+#18442 := [refl]: #18441
+#18559 := [nnf-neg #18442 #18451 #18555]: #18558
+#18447 := (~ #18446 #18446)
+#18448 := [refl]: #18447
+#18563 := [nnf-neg #18448 #18559]: #18562
+#18444 := (~ #18443 #18443)
+#18445 := [refl]: #18444
+#18567 := [nnf-neg #18442 #18445 #18563]: #18566
+#18455 := (~ #13616 #13616)
+#18456 := [refl]: #18455
+#18571 := [nnf-neg #18412 #18456 #18567]: #18570
+#18587 := [nnf-neg #18571 #18583]: #18586
+#18591 := [nnf-neg #18454 #18412 #18587]: #18590
+#18595 := [nnf-neg #18442 #18451 #18591]: #18594
+#18599 := [nnf-neg #18448 #18595]: #18598
+#18603 := [nnf-neg #18442 #18445 #18599]: #18602
+#18438 := (~ #13711 #13711)
+#18439 := [refl]: #18438
+#18607 := [nnf-neg #18412 #18439 #18603]: #18606
+#18668 := [nnf-neg #18607 #18664]: #18667
+#18436 := (~ #18435 #18435)
+#18437 := [refl]: #18436
+#18433 := (~ #18432 #18432)
+#18434 := [refl]: #18433
+#18430 := (~ #18429 #18429)
+#18431 := [refl]: #18430
+#18426 := (not #15751)
+#18427 := (~ #18426 #15748)
+#18424 := (~ #15748 #15748)
+#18422 := (~ #15743 #15743)
+#18423 := [refl]: #18422
+#18425 := [nnf-pos #18423]: #18424
+#18428 := [nnf-neg #18425]: #18427
+#18420 := (~ #18419 #18419)
+#18421 := [refl]: #18420
+#18417 := (~ #18416 #18416)
+#18418 := [refl]: #18417
+#18414 := (~ #18413 #18413)
+#18415 := [refl]: #18414
+#18408 := (~ #18407 #18407)
+#18409 := [refl]: #18408
+#18405 := (~ #18404 #18404)
+#18406 := [refl]: #18405
+#18402 := (~ #18401 #18401)
+#18403 := [refl]: #18402
+#18399 := (~ #18398 #18398)
+#18400 := [refl]: #18399
+#18396 := (~ #18395 #18395)
+#18397 := [refl]: #18396
+#18393 := (~ #18392 #18392)
+#18394 := [refl]: #18393
+#18390 := (~ #18389 #18389)
+#18391 := [refl]: #18390
+#18672 := [nnf-neg #18391 #18394 #18397 #18400 #18403 #18406 #18409 #18412 #18415 #18418 #18421 #18428 #18431 #18434 #18437 #18668]: #18671
+#18387 := (~ #14143 #14143)
+#18388 := [refl]: #18387
+#18385 := (~ #13176 #13176)
+#18386 := [refl]: #18385
+#18676 := [nnf-neg #18386 #18388 #18672]: #18675
+#18382 := (not #15737)
+#18383 := (~ #18382 #15734)
+#18380 := (~ #15734 #15734)
+#18378 := (~ #15729 #15729)
+#18379 := [refl]: #18378
+#18381 := [nnf-pos #18379]: #18380
+#18384 := [nnf-neg #18381]: #18383
+#18680 := [nnf-neg #18384 #18676]: #18679
+#18374 := (~ #15737 #18373)
+#18375 := [sk]: #18374
+#18684 := [nnf-neg #18375 #18680]: #18683
+#18359 := (~ #18358 #18358)
+#18360 := [refl]: #18359
+#18688 := [nnf-neg #18360 #18684]: #18687
+#18356 := (~ #13381 #13381)
+#18357 := [refl]: #18356
+#18692 := [nnf-neg #18357 #18688]: #18691
+#18354 := (~ #18353 #18353)
+#18355 := [refl]: #18354
+#18351 := (~ #18350 #18350)
+#18352 := [refl]: #18351
+#18348 := (~ #18347 #18347)
+#18349 := [refl]: #18348
+#18345 := (~ #18344 #18344)
+#18346 := [refl]: #18345
+#18342 := (~ #18341 #18341)
+#18343 := [refl]: #18342
+#18696 := [nnf-neg #18343 #18346 #18349 #18352 #18355 #18692]: #18695
+#18339 := (~ #18338 #18338)
+#18340 := [refl]: #18339
+#18330 := (~ #18329 #18329)
+#18331 := [refl]: #18330
+#18700 := [nnf-neg #18331 #18340 #18696]: #18699
+#18336 := (~ #18335 #18335)
+#18337 := [refl]: #18336
+#18704 := [nnf-neg #18337 #18700]: #18703
+#18333 := (~ #18332 #18332)
+#18334 := [refl]: #18333
+#18708 := [nnf-neg #18331 #18334 #18704]: #18707
+#18327 := (~ #18326 #18326)
+#18328 := [refl]: #18327
+#18712 := [nnf-neg #18328 #18708]: #18711
+#18324 := (~ #13209 #13209)
+#18325 := [refl]: #18324
+#18715 := [nnf-neg #18325 #18712]: #18714
+#15223 := (or #12249 #12240 #12231 #12222 #13430 #13711 #13797)
+#15228 := (and #13733 #15223)
+#15234 := (or #15198 #13883 #12969 #12960 #12951 #12942 #12933 #13430 #13900 #13934 #13940 #13952 #13962 #13975 #13986 #15228)
+#15239 := (and #3074 #13418 #15234)
+#15242 := (or #13414 #15239)
+#15245 := (and #13411 #15242)
+#15248 := (or #13381 #15245)
+#15251 := (and #13378 #15248)
+#15254 := (or #13176 #13185 #13167 #13158 #13149 #15251)
+#15257 := (and #12089 #12098 #15254)
+#15260 := (or #13197 #15257)
+#15263 := (and #12089 #12092 #15260)
+#15266 := (or #13209 #15263)
+#15269 := (and #12086 #15266)
+#15272 := (not #15269)
+#15992 := (iff #15272 #15991)
+#15989 := (iff #15269 #15988)
+#15986 := (iff #15266 #15985)
+#15983 := (iff #15263 #15982)
+#15980 := (iff #15260 #15979)
+#15977 := (iff #15257 #15976)
+#15974 := (iff #15254 #15973)
+#15971 := (iff #15251 #15970)
+#15968 := (iff #15248 #15967)
+#15965 := (iff #15245 #15964)
+#15962 := (iff #15242 #15961)
+#15959 := (iff #15239 #15958)
+#15956 := (iff #15234 #15953)
+#15950 := (or #15198 #13883 #12969 #12960 #12951 #12942 #12933 #13430 #13900 #15751 #13940 #15768 #15785 #15802 #13986 #15947)
+#15954 := (iff #15950 #15953)
+#15955 := [rewrite]: #15954
+#15951 := (iff #15234 #15950)
+#15948 := (iff #15228 #15947)
+#15945 := (iff #15223 #15944)
+#15942 := (iff #13797 #15941)
+#15939 := (iff #13792 #15938)
+#15936 := (iff #13783 #15935)
+#15933 := (iff #13778 #15930)
+#15927 := (and #3138 #4118 #15118 #13740)
+#15931 := (iff #15927 #15930)
+#15932 := [rewrite]: #15931
+#15928 := (iff #13778 #15927)
+#15113 := (iff #4432 #15118)
+#15134 := -4294967295::int
+#15126 := (+ -4294967295::int #168)
+#15119 := (<= #15126 0::int)
+#15115 := (iff #15119 #15118)
+#15116 := [rewrite]: #15115
+#15120 := (iff #4432 #15119)
+#15121 := (= #4431 #15126)
+#15127 := (+ #168 -4294967295::int)
+#15123 := (= #15127 #15126)
+#15124 := [rewrite]: #15123
+#15128 := (= #4431 #15127)
+#15129 := (= #4430 -4294967295::int)
+#15135 := (* -1::int 4294967295::int)
+#15131 := (= #15135 -4294967295::int)
+#15132 := [rewrite]: #15131
+#15136 := (= #4430 #15135)
+#7553 := (= f77 4294967295::int)
+#956 := 65536::int
+#1331 := (* 65536::int 65536::int)
+#1336 := (- #1331 1::int)
+#1337 := (= f77 #1336)
+#7554 := (iff #1337 #7553)
+#7551 := (= #1336 4294967295::int)
+#1019 := 4294967296::int
+#7544 := (- 4294967296::int 1::int)
+#7549 := (= #7544 4294967295::int)
+#7550 := [rewrite]: #7549
+#7546 := (= #1336 #7544)
+#7515 := (= #1331 4294967296::int)
+#7516 := [rewrite]: #7515
+#7547 := [monotonicity #7516]: #7546
+#7552 := [trans #7547 #7550]: #7551
+#7555 := [monotonicity #7552]: #7554
+#7543 := [asserted]: #1337
+#7558 := [mp #7543 #7555]: #7553
+#15133 := [monotonicity #7558]: #15136
+#15130 := [trans #15133 #15132]: #15129
+#15125 := [monotonicity #15130]: #15128
+#15122 := [trans #15125 #15124]: #15121
+#15117 := [monotonicity #15122]: #15120
+#15114 := [trans #15117 #15116]: #15113
+#15929 := [monotonicity #15114]: #15928
+#15934 := [trans #15929 #15932]: #15933
+#15937 := [quant-intro #15934]: #15936
+#15925 := (iff #13786 #15924)
+#15922 := (iff #13766 #15921)
+#15919 := (iff #13761 #15916)
+#15913 := (or #14360 #13738 #13752)
+#15917 := (iff #15913 #15916)
+#15918 := [rewrite]: #15917
+#15914 := (iff #13761 #15913)
+#14357 := (iff #5654 #14360)
+#14362 := (iff #4439 #14361)
+#14359 := [monotonicity #15114]: #14362
+#14358 := [monotonicity #14359]: #14357
+#15915 := [monotonicity #14358]: #15914
+#15920 := [trans #15915 #15918]: #15919
+#15923 := [quant-intro #15920]: #15922
+#15926 := [monotonicity #15923]: #15925
+#15940 := [monotonicity #15926 #15937]: #15939
+#15943 := [monotonicity #15923 #15940]: #15942
+#15946 := [monotonicity #15943]: #15945
+#15911 := (iff #13733 #15908)
+#15905 := (or #13430 #15902 #13710)
+#15909 := (iff #15905 #15908)
+#15910 := [rewrite]: #15909
+#15906 := (iff #13733 #15905)
+#15903 := (iff #13704 #15902)
+#15900 := (iff #13698 #15899)
+#15897 := (iff #13693 #15896)
+#15894 := (iff #13685 #15893)
+#15891 := (iff #13676 #15890)
+#15888 := (iff #13671 #15885)
+#15882 := (or #12766 #12757 #13430 #13439 #15859 #13616)
+#15886 := (iff #15882 #15885)
+#15887 := [rewrite]: #15886
+#15883 := (iff #13671 #15882)
+#15860 := (iff #13560 #15859)
+#15857 := (iff #13552 #15854)
+#15851 := (or #12601 #13456 #15842 #13531 #15848)
+#15855 := (iff #15851 #15854)
+#15856 := [rewrite]: #15855
+#15852 := (iff #13552 #15851)
+#15849 := (iff #13537 #15848)
+#15846 := (iff #13534 #15845)
+#15812 := (iff #13445 #15809)
+#15754 := (+ 4294967295::int #13446)
+#15805 := (>= #15754 1::int)
+#15810 := (iff #15805 #15809)
+#15811 := [rewrite]: #15810
+#15806 := (iff #13445 #15805)
+#15755 := (= #13447 #15754)
+#15756 := [monotonicity #7558]: #15755
+#15807 := [monotonicity #15756]: #15806
+#15813 := [trans #15807 #15811]: #15812
+#15847 := [monotonicity #15813]: #15846
+#15850 := [monotonicity #15847]: #15849
+#15843 := (iff #13524 #15842)
+#15840 := (iff #13521 #15839)
+#15837 := (iff #13518 #15836)
+#15834 := (iff #13515 #15831)
+#15828 := (or #15825 #13510)
+#15832 := (iff #15828 #15831)
+#15833 := [rewrite]: #15832
+#15829 := (iff #13515 #15828)
+#15826 := (iff #13498 #15825)
+#15823 := (iff #13495 #15822)
+#15820 := (iff #13490 #15817)
+#15814 := (or #14360 #13467 #13481)
+#15818 := (iff #15814 #15817)
+#15819 := [rewrite]: #15818
+#15815 := (iff #13490 #15814)
+#15816 := [monotonicity #14358]: #15815
+#15821 := [trans #15816 #15819]: #15820
+#15824 := [quant-intro #15821]: #15823
+#15827 := [monotonicity #15824]: #15826
+#15830 := [monotonicity #15827]: #15829
+#15835 := [trans #15830 #15833]: #15834
+#15838 := [monotonicity #15824 #15835]: #15837
+#15841 := [monotonicity #15838]: #15840
+#15844 := [monotonicity #15841]: #15843
+#15853 := [monotonicity #15844 #15850]: #15852
+#15858 := [trans #15853 #15856]: #15857
+#15861 := [monotonicity #15813 #15858]: #15860
+#15884 := [monotonicity #15861]: #15883
+#15889 := [trans #15884 #15887]: #15888
+#15880 := (iff #13641 #15877)
+#15874 := (or #13430 #15871 #13617)
+#15878 := (iff #15874 #15877)
+#15879 := [rewrite]: #15878
+#15875 := (iff #13641 #15874)
+#15872 := (iff #13611 #15871)
+#15869 := (iff #13605 #15868)
+#15866 := (iff #13600 #15865)
+#15863 := (iff #13592 #15862)
+#15864 := [monotonicity #15861]: #15863
+#15867 := [monotonicity #15864]: #15866
+#15870 := [monotonicity #15867]: #15869
+#15873 := [monotonicity #15870]: #15872
+#15876 := [monotonicity #15873]: #15875
+#15881 := [trans #15876 #15879]: #15880
+#15892 := [monotonicity #15881 #15889]: #15891
+#15895 := [monotonicity #15892]: #15894
+#15898 := [monotonicity #15895]: #15897
+#15901 := [monotonicity #15898]: #15900
+#15904 := [monotonicity #15901]: #15903
+#15907 := [monotonicity #15904]: #15906
+#15912 := [trans #15907 #15910]: #15911
+#15949 := [monotonicity #15912 #15946]: #15948
+#15803 := (iff #13975 #15802)
+#15800 := (iff #13972 #15799)
+#15797 := (iff #13968 #15794)
+#15788 := (+ 255::int #13915)
+#15791 := (>= #15788 0::int)
+#15795 := (iff #15791 #15794)
+#15796 := [rewrite]: #15795
+#15792 := (iff #13968 #15791)
+#15789 := (= #13969 #15788)
+#1341 := (= f79 255::int)
+#7557 := [asserted]: #1341
+#15790 := [monotonicity #7557]: #15789
+#15793 := [monotonicity #15790]: #15792
+#15798 := [trans #15793 #15796]: #15797
+#15801 := [monotonicity #15798]: #15800
+#15804 := [monotonicity #15801]: #15803
+#15786 := (iff #13962 #15785)
+#15783 := (iff #13959 #15782)
+#15780 := (iff #13955 #15777)
+#15771 := (+ 4294967295::int #13886)
+#15774 := (>= #15771 0::int)
+#15778 := (iff #15774 #15777)
+#15779 := [rewrite]: #15778
+#15775 := (iff #13955 #15774)
+#15772 := (= #13956 #15771)
+#15773 := [monotonicity #7558]: #15772
+#15776 := [monotonicity #15773]: #15775
+#15781 := [trans #15776 #15779]: #15780
 #15784 := [monotonicity #15781]: #15783
 #15787 := [monotonicity #15784]: #15786
-#15790 := [monotonicity #15787]: #15789
-#15793 := [monotonicity #15790]: #15792
-#14070 := (not #13922)
-#15071 := (iff #14070 #15070)
-#15068 := (iff #13922 #15067)
-#15065 := (iff #13919 #15064)
-#15062 := (iff #13914 #15061)
-#15059 := (iff #13908 #15058)
-#15056 := (iff #13903 #15055)
-#15053 := (iff #13895 #15052)
-#15050 := (iff #13874 #15049)
-#15047 := (iff #13871 #15046)
-#15044 := (iff #13868 #15043)
-#15041 := (iff #13865 #15040)
-#15038 := (iff #13860 #15037)
-#15035 := (iff #13852 #15032)
-#15029 := (or #12769 #12760 #12751 #12742 #12733 #14996 #13683 #13230 #15026 #13700 #13734 #13740 #13752 #13762 #13775 #13786)
-#15033 := (iff #15029 #15032)
-#15034 := [rewrite]: #15033
-#15030 := (iff #13852 #15029)
-#15027 := (iff #13659 #15026)
-#15024 := (iff #13654 #15021)
-#15006 := (or #12079 #12070 #12061 #12052 #13230 #13597)
-#15018 := (or #13230 #13511 #15006)
-#15022 := (iff #15018 #15021)
-#15023 := [rewrite]: #15022
-#15019 := (iff #13654 #15018)
-#15016 := (iff #13629 #15006)
-#15011 := (and true #15006)
-#15014 := (iff #15011 #15006)
-#15015 := [rewrite]: #15014
-#15012 := (iff #13629 #15011)
-#15009 := (iff #13624 #15006)
-#15003 := (or false #12079 #12070 #12061 #12052 #13230 #13597)
-#15007 := (iff #15003 #15006)
-#15008 := [rewrite]: #15007
-#15004 := (iff #13624 #15003)
-#15001 := (iff #12113 false)
-#14999 := (iff #12113 #3086)
-#14737 := (iff up_216 true)
-#10742 := [asserted]: up_216
-#14738 := [iff-true #10742]: #14737
-#15000 := [monotonicity #14738]: #14999
-#15002 := [trans #15000 #11996]: #15001
-#15005 := [monotonicity #15002]: #15004
-#15010 := [trans #15005 #15008]: #15009
-#15013 := [monotonicity #14738 #15010]: #15012
-#15017 := [trans #15013 #15015]: #15016
-#15020 := [monotonicity #15017]: #15019
-#15025 := [trans #15020 #15023]: #15024
-#15028 := [monotonicity #15025]: #15027
-#14997 := (iff #12141 #14996)
-#14994 := (iff #12003 #11997)
-#14989 := (and true #11997)
-#14992 := (iff #14989 #11997)
-#14993 := [rewrite]: #14992
-#14990 := (iff #12003 #14989)
-#14979 := (iff #11905 true)
-#14980 := [iff-true #14064]: #14979
-#14991 := [monotonicity #14980]: #14990
-#14995 := [trans #14991 #14993]: #14994
-#14998 := [monotonicity #14995]: #14997
-#15031 := [monotonicity #14998 #15028]: #15030
-#15036 := [trans #15031 #15034]: #15035
-#15039 := [monotonicity #15036]: #15038
-#15042 := [monotonicity #15039]: #15041
-#15045 := [monotonicity #15042]: #15044
-#15048 := [monotonicity #15045]: #15047
-#15051 := [monotonicity #15048]: #15050
-#15054 := [monotonicity #15051]: #15053
-#15057 := [monotonicity #15054]: #15056
-#15060 := [monotonicity #15057]: #15059
-#15063 := [monotonicity #15060]: #15062
-#15066 := [monotonicity #15063]: #15065
-#15069 := [monotonicity #15066]: #15068
-#15072 := [monotonicity #15069]: #15071
-#14071 := [not-or-elim #14055]: #14070
-#15073 := [mp #14071 #15072]: #15070
-#15794 := [mp #15073 #15793]: #15791
-#18514 := [mp~ #15794 #18513]: #18511
-#18515 := [mp #18514 #18859]: #18857
-#22382 := [mp #18515 #22381]: #22379
-#23242 := [mp #22382 #23241]: #23239
-#28633 := [unit-resolution #23242 #26581]: #23236
-#24466 := (or #23233 #23227)
-#24467 := [def-axiom]: #24466
-#28634 := [unit-resolution #24467 #28633]: #23227
-decl uf_15 :: (-> T5 T6 T2)
-decl uf_16 :: (-> T4 T5 T6)
-#26537 := (uf_16 uf_287 #25933)
-#27013 := (uf_15 #26926 #26537)
-#27014 := (= uf_9 #27013)
-#26538 := (uf_15 #25933 #26537)
-#26539 := (= uf_9 #26538)
-#26735 := (or #13009 #26539)
-#26726 := [monotonicity #28306 #28306]: #26725
-#26743 := [symm #26726]: #26728
-#26700 := [hypothesis]: #11925
-#26730 := [trans #26700 #26743]: #26481
-decl uf_53 :: (-> T4 T5 T6)
-#26528 := (uf_53 uf_287 #25933)
-#26529 := (uf_15 #23 #26528)
-#26534 := (pattern #26529)
-decl up_197 :: (-> T3 bool)
-#26532 := (up_197 #26344)
-#26530 := (= uf_9 #26529)
-#26531 := (not #26530)
-decl uf_147 :: (-> T5 T6 T2)
-decl uf_192 :: (-> T7 T6)
-decl uf_11 :: (-> T4 T5 T7)
-#26524 := (uf_11 uf_287 #25933)
-#26525 := (uf_192 #26524)
-#26526 := (uf_147 #23 #26525)
-#26527 := (= uf_9 #26526)
-#26544 := (or #26527 #26531 #26532)
-#26547 := (forall (vars (?x577 T5)) (:pat #26534) #26544)
-#26550 := (not #26547)
-#26540 := (not #26539)
-#26553 := (or #26409 #26540 #26550)
-#26732 := [hypothesis]: #26540
-#26626 := (or #26553 #26539)
-#26630 := [def-axiom]: #26626
-#26733 := [unit-resolution #26630 #26732]: #26553
-#14 := (:var 2 T4)
-#2166 := (uf_196 #14 #15 #23)
-#2228 := (pattern #2166)
-#2229 := (uf_53 #13 #21)
-#2230 := (uf_15 #23 #2229)
-#2231 := (pattern #2230)
-#2158 := (uf_11 #13 #15)
-#2236 := (uf_192 #2158)
-#2237 := (uf_147 #23 #2236)
-#10026 := (= uf_9 #2237)
-#10020 := (= uf_9 #2230)
-#21605 := (not #10020)
-#1382 := (uf_13 #21)
-#2232 := (up_197 #1382)
-#21620 := (or #2232 #21605 #10026)
-#21625 := (forall (vars (?x577 T5)) (:pat #2231) #21620)
-#21631 := (not #21625)
-#2145 := (uf_16 #14 #23)
-#2146 := (uf_15 #15 #2145)
-#9726 := (= uf_9 #2146)
-#21440 := (not #9726)
-#180 := (uf_27 #14 #15)
-#3720 := (= uf_9 #180)
-#10363 := (not #3720)
-#21632 := (or #10363 #21440 #21631)
-#21633 := (not #21632)
-#9774 := (= uf_9 #2166)
-#10050 := (not #9774)
-#21638 := (or #10050 #21633)
-#21641 := (forall (vars (?x574 T4) (?x575 T5) (?x576 T5)) (:pat #2228) #21638)
-#2233 := (not #2232)
-#10023 := (and #2233 #10020)
-#10032 := (not #10023)
-#10033 := (or #10032 #10026)
-#10038 := (forall (vars (?x577 T5)) (:pat #2231) #10033)
-#10059 := (and #3720 #9726 #10038)
-#10062 := (or #10050 #10059)
-#10065 := (forall (vars (?x574 T4) (?x575 T5) (?x576 T5)) (:pat #2228) #10062)
-#21642 := (iff #10065 #21641)
-#21639 := (iff #10062 #21638)
-#21636 := (iff #10059 #21633)
-#21628 := (and #3720 #9726 #21625)
-#21634 := (iff #21628 #21633)
-#21635 := [rewrite]: #21634
-#21629 := (iff #10059 #21628)
-#21626 := (iff #10038 #21625)
-#21623 := (iff #10033 #21620)
-#21606 := (or #2232 #21605)
-#21617 := (or #21606 #10026)
-#21621 := (iff #21617 #21620)
-#21622 := [rewrite]: #21621
-#21618 := (iff #10033 #21617)
-#21615 := (iff #10032 #21606)
-#21607 := (not #21606)
-#21610 := (not #21607)
-#21613 := (iff #21610 #21606)
-#21614 := [rewrite]: #21613
-#21611 := (iff #10032 #21610)
-#21608 := (iff #10023 #21607)
-#21609 := [rewrite]: #21608
-#21612 := [monotonicity #21609]: #21611
-#21616 := [trans #21612 #21614]: #21615
-#21619 := [monotonicity #21616]: #21618
-#21624 := [trans #21619 #21622]: #21623
-#21627 := [quant-intro #21624]: #21626
-#21630 := [monotonicity #21627]: #21629
-#21637 := [trans #21630 #21635]: #21636
-#21640 := [monotonicity #21637]: #21639
-#21643 := [quant-intro #21640]: #21642
-#17591 := (~ #10065 #10065)
-#17589 := (~ #10062 #10062)
-#17587 := (~ #10059 #10059)
-#17585 := (~ #10038 #10038)
-#17583 := (~ #10033 #10033)
-#17584 := [refl]: #17583
-#17586 := [nnf-pos #17584]: #17585
-#17581 := (~ #9726 #9726)
-#17582 := [refl]: #17581
-#17579 := (~ #3720 #3720)
-#17580 := [refl]: #17579
-#17588 := [monotonicity #17580 #17582 #17586]: #17587
-#17577 := (~ #10050 #10050)
-#17578 := [refl]: #17577
-#17590 := [monotonicity #17578 #17588]: #17589
-#17592 := [nnf-pos #17590]: #17591
-#2238 := (= #2237 uf_9)
-#2234 := (= #2230 uf_9)
-#2235 := (and #2233 #2234)
-#2239 := (implies #2235 #2238)
-#2240 := (forall (vars (?x577 T5)) (:pat #2231) #2239)
-#184 := (= #180 uf_9)
-#2241 := (and #184 #2240)
-#2151 := (= #2146 uf_9)
-#2242 := (and #2151 #2241)
-#2167 := (= #2166 uf_9)
-#2243 := (implies #2167 #2242)
-#2244 := (forall (vars (?x574 T4) (?x575 T5) (?x576 T5)) (:pat #2228) #2243)
-#10068 := (iff #2244 #10065)
-#10041 := (and #3720 #10038)
-#10044 := (and #9726 #10041)
-#10051 := (or #10050 #10044)
-#10056 := (forall (vars (?x574 T4) (?x575 T5) (?x576 T5)) (:pat #2228) #10051)
-#10066 := (iff #10056 #10065)
-#10063 := (iff #10051 #10062)
-#10060 := (iff #10044 #10059)
-#10061 := [rewrite]: #10060
-#10064 := [monotonicity #10061]: #10063
-#10067 := [quant-intro #10064]: #10066
-#10057 := (iff #2244 #10056)
-#10054 := (iff #2243 #10051)
-#10047 := (implies #9774 #10044)
-#10052 := (iff #10047 #10051)
-#10053 := [rewrite]: #10052
-#10048 := (iff #2243 #10047)
-#10045 := (iff #2242 #10044)
-#10042 := (iff #2241 #10041)
-#10039 := (iff #2240 #10038)
-#10036 := (iff #2239 #10033)
-#10029 := (implies #10023 #10026)
-#10034 := (iff #10029 #10033)
-#10035 := [rewrite]: #10034
-#10030 := (iff #2239 #10029)
-#10027 := (iff #2238 #10026)
-#10028 := [rewrite]: #10027
-#10024 := (iff #2235 #10023)
-#10021 := (iff #2234 #10020)
-#10022 := [rewrite]: #10021
-#10025 := [monotonicity #10022]: #10024
-#10031 := [monotonicity #10025 #10028]: #10030
-#10037 := [trans #10031 #10035]: #10036
-#10040 := [quant-intro #10037]: #10039
-#3721 := (iff #184 #3720)
-#3722 := [rewrite]: #3721
-#10043 := [monotonicity #3722 #10040]: #10042
-#9727 := (iff #2151 #9726)
-#9728 := [rewrite]: #9727
-#10046 := [monotonicity #9728 #10043]: #10045
-#9775 := (iff #2167 #9774)
-#9776 := [rewrite]: #9775
-#10049 := [monotonicity #9776 #10046]: #10048
-#10055 := [trans #10049 #10053]: #10054
-#10058 := [quant-intro #10055]: #10057
-#10069 := [trans #10058 #10067]: #10068
-#10019 := [asserted]: #2244
-#10070 := [mp #10019 #10069]: #10065
-#17593 := [mp~ #10070 #17592]: #10065
-#21644 := [mp #17593 #21643]: #21641
-#26556 := (not #26553)
-#26648 := (not #21641)
-#26649 := (or #26648 #26500 #26556)
-#26533 := (or #26532 #26531 #26527)
-#26535 := (forall (vars (?x577 T5)) (:pat #26534) #26533)
-#26536 := (not #26535)
-#26541 := (or #26409 #26540 #26536)
-#26542 := (not #26541)
-#26543 := (or #26500 #26542)
-#26637 := (or #26648 #26543)
-#26621 := (iff #26637 #26649)
-#26559 := (or #26500 #26556)
-#26639 := (or #26648 #26559)
-#26677 := (iff #26639 #26649)
-#26625 := [rewrite]: #26677
-#26675 := (iff #26637 #26639)
-#26560 := (iff #26543 #26559)
-#26557 := (iff #26542 #26556)
-#26554 := (iff #26541 #26553)
-#26551 := (iff #26536 #26550)
-#26548 := (iff #26535 #26547)
-#26545 := (iff #26533 #26544)
-#26546 := [rewrite]: #26545
-#26549 := [quant-intro #26546]: #26548
-#26552 := [monotonicity #26549]: #26551
-#26555 := [monotonicity #26552]: #26554
-#26558 := [monotonicity #26555]: #26557
-#26561 := [monotonicity #26558]: #26560
-#26676 := [monotonicity #26561]: #26675
-#26627 := [trans #26676 #26625]: #26621
-#26638 := [quant-inst]: #26637
-#26623 := [mp #26638 #26627]: #26649
-#26731 := [unit-resolution #26623 #21644 #26733]: #26500
-#26497 := (not #26481)
-#26491 := (or #26490 #26479 #26497)
-#26487 := [def-axiom]: #26491
-#26734 := [unit-resolution #26487 #26731 #26730 #26699]: false
-#26736 := [lemma #26734]: #26735
-#28635 := [unit-resolution #26736 #26581]: #26539
-#26723 := (or #26540 #27014)
-#26701 := (= #26538 #27013)
-#26697 := (= #27013 #26538)
-#28317 := (= #26926 #25933)
-#28318 := [trans #28292 #28304]: #28317
-#26698 := [monotonicity #28318]: #26697
-#26721 := [symm #26698]: #26701
-#26709 := [hypothesis]: #26539
-#26722 := [trans #26709 #26721]: #27014
-#27015 := (not #27014)
-#26695 := [hypothesis]: #27015
-#26720 := [unit-resolution #26695 #26722]: false
-#26724 := [lemma #26720]: #26723
-#28636 := [unit-resolution #26724 #28635]: #27014
-#27050 := (or #11931 #27015)
-#27003 := (uf_43 #24643 #2980)
-#27004 := (uf_66 #27003 0::int #24643)
-#27008 := (uf_24 uf_287 #27004)
-#27009 := (= uf_9 #27008)
-#27010 := (not #27009)
-#26985 := (iff #18130 #27010)
-#26983 := (iff #11931 #27009)
-#26980 := (iff #27009 #11931)
-#27001 := (= #27008 #3034)
-#26999 := (= #27004 #3031)
-#28196 := (= #27003 #2979)
-#28194 := (= #2980 uf_288)
-#24762 := (= uf_288 #2980)
-#2698 := (uf_116 #2697)
-#11210 := (= #161 #2698)
-#22938 := (forall (vars (?x718 T3) (?x719 int)) (:pat #22937) #11210)
-#11214 := (forall (vars (?x718 T3) (?x719 int)) #11210)
-#22941 := (iff #11214 #22938)
-#22939 := (iff #11210 #11210)
-#22940 := [refl]: #22939
-#22942 := [quant-intro #22940]: #22941
-#17984 := (~ #11214 #11214)
-#17982 := (~ #11210 #11210)
-#17983 := [refl]: #17982
-#17985 := [nnf-pos #17983]: #17984
-#2699 := (= #2698 #161)
-#2700 := (forall (vars (?x718 T3) (?x719 int)) #2699)
-#11215 := (iff #2700 #11214)
-#11212 := (iff #2699 #11210)
-#11213 := [rewrite]: #11212
-#11216 := [quant-intro #11213]: #11215
-#11209 := [asserted]: #2700
-#11219 := [mp #11209 #11216]: #11214
-#17986 := [mp~ #11219 #17985]: #11214
-#22943 := [mp #17986 #22942]: #22938
-#24716 := (not #22938)
-#24767 := (or #24716 #24762)
-#24768 := [quant-inst]: #24767
-#28193 := [unit-resolution #24768 #22943]: #24762
-#28195 := [symm #28193]: #28194
-#28197 := [monotonicity #28190 #28195]: #28196
-#27000 := [monotonicity #28197 #28190]: #26999
-#27002 := [monotonicity #27000]: #27001
-#26982 := [monotonicity #27002]: #26980
-#26984 := [symm #26982]: #26983
-#26986 := [monotonicity #26984]: #26985
-#26998 := [hypothesis]: #18130
-#26981 := [mp #26998 #26986]: #27010
-#27005 := (uf_58 #3150 #27004)
-#27006 := (uf_136 #27005)
-#27007 := (= uf_9 #27006)
-#27020 := (or #27007 #27010)
-#27023 := (not #27020)
-decl uf_22 :: (-> T3 T2)
-#27016 := (uf_22 #24643)
-#27017 := (= uf_9 #27016)
-#2783 := (uf_22 uf_7)
-#28228 := (= #2783 #27016)
-#28225 := (= #27016 #2783)
-#28226 := [monotonicity #28190]: #28225
-#28229 := [symm #28226]: #28228
-#11386 := (= uf_9 #2783)
-#2784 := (= #2783 uf_9)
-#11388 := (iff #2784 #11386)
-#11389 := [rewrite]: #11388
-#11385 := [asserted]: #2784
-#11392 := [mp #11385 #11389]: #11386
-#28230 := [trans #11392 #28229]: #27017
-#27018 := (not #27017)
-#27046 := (or #27018 #27023)
-#28231 := [hypothesis]: #27014
-#26961 := (<= #24645 0::int)
-#26988 := (not #26961)
-#14069 := [not-or-elim #14055]: #13218
-#26944 := (* -1::int #24645)
-#27053 := (+ uf_286 #26944)
-#27054 := (<= #27053 0::int)
-#28211 := (not #24646)
-#28212 := (or #28211 #27054)
-#28213 := [th-lemma]: #28212
-#28214 := [unit-resolution #28213 #28210]: #27054
-#28220 := (not #27054)
-#26989 := (or #26988 #13217 #28220)
-#26990 := [th-lemma]: #26989
-#26991 := [unit-resolution #26990 #28214 #14069]: #26988
-#237 := (uf_22 #233)
-#247 := (:var 1 int)
-#762 := (:var 4 int)
-#2069 := (uf_43 #233 #762)
-#2070 := (uf_66 #2069 #247 #233)
-#1373 := (:var 5 T4)
-#2086 := (uf_25 #1373 #2070)
-#1365 := (:var 3 T5)
-#2067 := (uf_16 #1373 #1365)
-#268 := (:var 2 int)
-#2065 := (uf_124 #233 #268)
-#2066 := (uf_43 #2065 #762)
-#2068 := (uf_15 #2066 #2067)
-#2087 := (pattern #2068 #2086 #237)
-#1545 := (uf_59 #1373)
-#2084 := (uf_58 #1545 #2070)
-#2085 := (pattern #2068 #2084 #237)
-#2090 := (uf_136 #2084)
-#9534 := (= uf_9 #2090)
-#2088 := (uf_24 #1373 #2070)
-#9531 := (= uf_9 #2088)
-#21350 := (not #9531)
-#21351 := (or #21350 #9534)
-#21352 := (not #21351)
-#9475 := (= uf_9 #2068)
-#21326 := (not #9475)
-#2073 := (uf_55 #1373)
-#9472 := (= uf_9 #2073)
-#21325 := (not #9472)
-#4047 := (* -1::int #268)
-#6111 := (+ #247 #4047)
-#6708 := (>= #6111 0::int)
-#4309 := (>= #247 0::int)
-#19263 := (not #4309)
-#3928 := (= uf_9 #237)
-#10246 := (not #3928)
-#21358 := (or #10246 #19263 #6708 #21325 #21326 #21352)
-#21363 := (forall (vars (?x526 T4) (?x527 int) (?x528 T5) (?x529 int) (?x530 int) (?x531 T3)) (:pat #2085 #2087) #21358)
-#9537 := (not #9534)
-#9540 := (and #9531 #9537)
-#7775 := (not #6708)
-#9513 := (and #3928 #4309 #7775 #9472 #9475)
-#9518 := (not #9513)
-#9554 := (or #9518 #9540)
-#9557 := (forall (vars (?x526 T4) (?x527 int) (?x528 T5) (?x529 int) (?x530 int) (?x531 T3)) (:pat #2085 #2087) #9554)
-#21364 := (iff #9557 #21363)
-#21361 := (iff #9554 #21358)
-#21327 := (or #10246 #19263 #6708 #21325 #21326)
-#21355 := (or #21327 #21352)
-#21359 := (iff #21355 #21358)
-#21360 := [rewrite]: #21359
-#21356 := (iff #9554 #21355)
-#21353 := (iff #9540 #21352)
-#21354 := [rewrite]: #21353
-#21336 := (iff #9518 #21327)
-#21328 := (not #21327)
-#21331 := (not #21328)
-#21334 := (iff #21331 #21327)
-#21335 := [rewrite]: #21334
-#21332 := (iff #9518 #21331)
-#21329 := (iff #9513 #21328)
-#21330 := [rewrite]: #21329
-#21333 := [monotonicity #21330]: #21332
-#21337 := [trans #21333 #21335]: #21336
-#21357 := [monotonicity #21337 #21354]: #21356
-#21362 := [trans #21357 #21360]: #21361
-#21365 := [quant-intro #21362]: #21364
-#17457 := (~ #9557 #9557)
-#17455 := (~ #9554 #9554)
-#17456 := [refl]: #17455
-#17458 := [nnf-pos #17456]: #17457
-#2091 := (= #2090 uf_9)
-#2092 := (not #2091)
-#2089 := (= #2088 uf_9)
-#2093 := (and #2089 #2092)
-#1434 := (< #247 #268)
-#397 := (<= 0::int #247)
-#1435 := (and #397 #1434)
-#2075 := (= #2068 uf_9)
-#2076 := (and #2075 #1435)
-#238 := (= #237 uf_9)
-#2077 := (and #238 #2076)
-#2074 := (= #2073 uf_9)
-#2078 := (and #2074 #2077)
-#2094 := (implies #2078 #2093)
-#2095 := (forall (vars (?x526 T4) (?x527 int) (?x528 T5) (?x529 int) (?x530 int) (?x531 T3)) (:pat #2085 #2087) #2094)
-#9560 := (iff #2095 #9557)
-#9481 := (and #1435 #9475)
-#9486 := (and #3928 #9481)
-#9489 := (and #9472 #9486)
-#9495 := (not #9489)
-#9546 := (or #9495 #9540)
-#9551 := (forall (vars (?x526 T4) (?x527 int) (?x528 T5) (?x529 int) (?x530 int) (?x531 T3)) (:pat #2085 #2087) #9546)
-#9558 := (iff #9551 #9557)
-#9555 := (iff #9546 #9554)
-#9519 := (iff #9495 #9518)
-#9516 := (iff #9489 #9513)
-#7778 := (and #4309 #7775)
-#9504 := (and #7778 #9475)
-#9507 := (and #3928 #9504)
-#9510 := (and #9472 #9507)
-#9514 := (iff #9510 #9513)
-#9515 := [rewrite]: #9514
-#9511 := (iff #9489 #9510)
-#9508 := (iff #9486 #9507)
-#9505 := (iff #9481 #9504)
-#7779 := (iff #1435 #7778)
-#7776 := (iff #1434 #7775)
-#7777 := [rewrite]: #7776
-#4308 := (iff #397 #4309)
-#4310 := [rewrite]: #4308
-#7780 := [monotonicity #4310 #7777]: #7779
-#9506 := [monotonicity #7780]: #9505
-#9509 := [monotonicity #9506]: #9508
-#9512 := [monotonicity #9509]: #9511
-#9517 := [trans #9512 #9515]: #9516
-#9520 := [monotonicity #9517]: #9519
-#9556 := [monotonicity #9520]: #9555
-#9559 := [quant-intro #9556]: #9558
-#9552 := (iff #2095 #9551)
-#9549 := (iff #2094 #9546)
-#9543 := (implies #9489 #9540)
-#9547 := (iff #9543 #9546)
-#9548 := [rewrite]: #9547
-#9544 := (iff #2094 #9543)
-#9541 := (iff #2093 #9540)
-#9538 := (iff #2092 #9537)
-#9535 := (iff #2091 #9534)
-#9536 := [rewrite]: #9535
-#9539 := [monotonicity #9536]: #9538
-#9532 := (iff #2089 #9531)
-#9533 := [rewrite]: #9532
-#9542 := [monotonicity #9533 #9539]: #9541
-#9490 := (iff #2078 #9489)
-#9487 := (iff #2077 #9486)
-#9484 := (iff #2076 #9481)
-#9478 := (and #9475 #1435)
-#9482 := (iff #9478 #9481)
-#9483 := [rewrite]: #9482
-#9479 := (iff #2076 #9478)
-#9476 := (iff #2075 #9475)
-#9477 := [rewrite]: #9476
-#9480 := [monotonicity #9477]: #9479
-#9485 := [trans #9480 #9483]: #9484
-#3929 := (iff #238 #3928)
-#3930 := [rewrite]: #3929
-#9488 := [monotonicity #3930 #9485]: #9487
-#9473 := (iff #2074 #9472)
-#9474 := [rewrite]: #9473
-#9491 := [monotonicity #9474 #9488]: #9490
-#9545 := [monotonicity #9491 #9542]: #9544
-#9550 := [trans #9545 #9548]: #9549
-#9553 := [quant-intro #9550]: #9552
-#9561 := [trans #9553 #9559]: #9560
-#9530 := [asserted]: #2095
-#9562 := [mp #9530 #9561]: #9557
-#17459 := [mp~ #9562 #17458]: #9557
-#21366 := [mp #17459 #21365]: #21363
-#27034 := (not #21363)
-#26894 := (or #27034 #24483 #26961 #27015 #27018 #27023)
-#27011 := (or #27010 #27007)
-#27012 := (not #27011)
-#26945 := (+ 0::int #26944)
-#26946 := (>= #26945 0::int)
-#26947 := (>= 0::int 0::int)
-#26948 := (not #26947)
-#27019 := (or #27018 #26948 #26946 #24483 #27015 #27012)
-#26895 := (or #27034 #27019)
-#26916 := (iff #26895 #26894)
-#27029 := (or #24483 #26961 #27015 #27018 #27023)
-#26912 := (or #27034 #27029)
-#26914 := (iff #26912 #26894)
-#26915 := [rewrite]: #26914
-#26913 := (iff #26895 #26912)
-#27032 := (iff #27019 #27029)
-#27026 := (or #27018 false #26961 #24483 #27015 #27023)
-#27030 := (iff #27026 #27029)
-#27031 := [rewrite]: #27030
-#27027 := (iff #27019 #27026)
-#27024 := (iff #27012 #27023)
-#27021 := (iff #27011 #27020)
+#15769 := (iff #13952 #15768)
+#15766 := (iff #13949 #15765)
+#15763 := (iff #13946 #15760)
+#15757 := (>= #15754 0::int)
+#15761 := (iff #15757 #15760)
+#15762 := [rewrite]: #15761
+#15758 := (iff #13946 #15757)
+#15759 := [monotonicity #15756]: #15758
+#15764 := [trans #15759 #15762]: #15763
+#15767 := [monotonicity #15764]: #15766
+#15770 := [monotonicity #15767]: #15769
+#15752 := (iff #13934 #15751)
+#15749 := (iff #13931 #15748)
+#15746 := (iff #13926 #15743)
+#15740 := (or #14360 #13903 #13917)
+#15744 := (iff #15740 #15743)
+#15745 := [rewrite]: #15744
+#15741 := (iff #13926 #15740)
+#15742 := [monotonicity #14358]: #15741
+#15747 := [trans #15742 #15745]: #15746
+#15750 := [quant-intro #15747]: #15749
+#15753 := [monotonicity #15750]: #15752
+#15952 := [monotonicity #15753 #15770 #15787 #15804 #15949]: #15951
+#15957 := [trans #15952 #15955]: #15956
+#15960 := [monotonicity #15957]: #15959
+#15738 := (iff #13414 #15737)
+#15735 := (iff #13411 #15734)
+#15732 := (iff #13406 #15729)
+#15726 := (or #14360 #13384 #13396)
+#15730 := (iff #15726 #15729)
+#15731 := [rewrite]: #15730
+#15727 := (iff #13406 #15726)
+#15728 := [monotonicity #14358]: #15727
+#15733 := [trans #15728 #15731]: #15732
+#15736 := [quant-intro #15733]: #15735
+#15739 := [monotonicity #15736]: #15738
+#15963 := [monotonicity #15739 #15960]: #15962
+#15966 := [monotonicity #15736 #15963]: #15965
+#15969 := [monotonicity #15966]: #15968
+#15972 := [monotonicity #15969]: #15971
+#15975 := [monotonicity #15972]: #15974
+#15978 := [monotonicity #15975]: #15977
+#15981 := [monotonicity #15978]: #15980
+#15984 := [monotonicity #15981]: #15983
+#15987 := [monotonicity #15984]: #15986
+#15990 := [monotonicity #15987]: #15989
+#15993 := [monotonicity #15990]: #15992
+#14270 := (not #14122)
+#15273 := (iff #14270 #15272)
+#15270 := (iff #14122 #15269)
+#15267 := (iff #14119 #15266)
+#15264 := (iff #14114 #15263)
+#15261 := (iff #14108 #15260)
+#15258 := (iff #14103 #15257)
+#15255 := (iff #14095 #15254)
+#15252 := (iff #14074 #15251)
+#15249 := (iff #14071 #15248)
+#15246 := (iff #14068 #15245)
+#15243 := (iff #14065 #15242)
+#15240 := (iff #14060 #15239)
+#15237 := (iff #14052 #15234)
+#15231 := (or #15198 #13883 #12969 #12960 #12951 #12942 #12933 #13430 #15228 #13900 #13934 #13940 #13952 #13962 #13975 #13986)
+#15235 := (iff #15231 #15234)
+#15236 := [rewrite]: #15235
+#15232 := (iff #14052 #15231)
+#15229 := (iff #13859 #15228)
+#15226 := (iff #13854 #15223)
+#15208 := (or #12249 #12240 #12231 #12222 #13430 #13797)
+#15220 := (or #13430 #13711 #15208)
+#15224 := (iff #15220 #15223)
+#15225 := [rewrite]: #15224
+#15221 := (iff #13854 #15220)
+#15218 := (iff #13829 #15208)
+#15213 := (and true #15208)
+#15216 := (iff #15213 #15208)
+#15217 := [rewrite]: #15216
+#15214 := (iff #13829 #15213)
+#15211 := (iff #13824 #15208)
+#15205 := (or false #12249 #12240 #12231 #12222 #13430 #13797)
+#15209 := (iff #15205 #15208)
+#15210 := [rewrite]: #15209
+#15206 := (iff #13824 #15205)
+#15203 := (iff #12283 false)
+#15201 := (iff #12283 #3121)
+#14939 := (iff #10869 true)
+#10868 := [asserted]: #2507
+#10875 := [mp #10868 #10872]: #10869
+#14940 := [iff-true #10875]: #14939
+#15202 := [monotonicity #14940]: #15201
+#15204 := [trans #15202 #12166]: #15203
+#15207 := [monotonicity #15204]: #15206
+#15212 := [trans #15207 #15210]: #15211
+#15215 := [monotonicity #14940 #15212]: #15214
+#15219 := [trans #15215 #15217]: #15218
+#15222 := [monotonicity #15219]: #15221
+#15227 := [trans #15222 #15225]: #15226
+#15230 := [monotonicity #15227]: #15229
+#15199 := (iff #12311 #15198)
+#15196 := (iff #12173 #12167)
+#15191 := (and true #12167)
+#15194 := (iff #15191 #12167)
+#15195 := [rewrite]: #15194
+#15192 := (iff #12173 #15191)
+#15175 := (iff #12054 true)
+#15176 := [iff-true #14260]: #15175
+#15193 := [monotonicity #15176]: #15192
+#15197 := [trans #15193 #15195]: #15196
+#15200 := [monotonicity #15197]: #15199
+#15233 := [monotonicity #15200 #15230]: #15232
+#15238 := [trans #15233 #15236]: #15237
+#15241 := [monotonicity #15238]: #15240
+#15244 := [monotonicity #15241]: #15243
+#15247 := [monotonicity #15244]: #15246
+#15250 := [monotonicity #15247]: #15249
+#15253 := [monotonicity #15250]: #15252
+#15256 := [monotonicity #15253]: #15255
+#15259 := [monotonicity #15256]: #15258
+#15262 := [monotonicity #15259]: #15261
+#15265 := [monotonicity #15262]: #15264
+#15268 := [monotonicity #15265]: #15267
+#15271 := [monotonicity #15268]: #15270
+#15274 := [monotonicity #15271]: #15273
+#14271 := [not-or-elim #14255]: #14270
+#15275 := [mp #14271 #15274]: #15272
+#15994 := [mp #15275 #15993]: #15991
+#18716 := [mp~ #15994 #18715]: #18713
+#18717 := [mp #18716 #19061]: #19059
+#22584 := [mp #18717 #22583]: #22581
+#23444 := [mp #22584 #23443]: #23441
+#28678 := [unit-resolution #23444 #26657]: #23438
+#24668 := (or #23435 #23429)
+#24669 := [def-axiom]: #24668
+#28679 := [unit-resolution #24669 #28678]: #23429
+decl f16 :: (-> S5 S6 S1)
+decl f17 :: (-> S4 S5 S6)
+#26614 := (f17 f287 #26021)
+#27072 := (f16 #26984 #26614)
+#27073 := (= f1 #27072)
+#26615 := (f16 #26021 #26614)
+#26616 := (= f1 #26615)
+#26802 := (or #13209 #26616)
+#26806 := [monotonicity #28351 #28351]: #26805
+#26796 := [symm #26806]: #26808
+#26772 := [hypothesis]: #12086
+#26797 := [trans #26772 #26796]: #26556
+decl f54 :: (-> S4 S5 S6)
+#26604 := (f54 f287 #26021)
+#26605 := (f16 #28 #26604)
+#26611 := (pattern #26605)
+decl f198 :: (-> S3 S1)
+#26608 := (f198 #26425)
+#26609 := (= f1 #26608)
+#26606 := (= f1 #26605)
+#26607 := (not #26606)
+decl f148 :: (-> S5 S6 S1)
+decl f193 :: (-> S7 S6)
+decl f12 :: (-> S4 S5 S7)
+#26600 := (f12 f287 #26021)
+#26601 := (f193 #26600)
+#26602 := (f148 #28 #26601)
+#26603 := (= f1 #26602)
+#26621 := (or #26603 #26607 #26609)
+#26624 := (forall (vars (?v3 S5)) (:pat #26611) #26621)
+#26627 := (not #26624)
+#26617 := (not #26616)
+#26630 := (or #26488 #26617 #26627)
+#26798 := [hypothesis]: #26617
+#26692 := (or #26630 #26616)
+#26698 := [def-axiom]: #26692
+#26811 := [unit-resolution #26698 #26798]: #26630
+#20 := (:var 2 S4)
+#2184 := (f197 #20 #21 #28)
+#2247 := (pattern #2184)
+#2248 := (f54 #19 #26)
+#2249 := (f16 #28 #2248)
+#2250 := (pattern #2249)
+#2176 := (f12 #19 #21)
+#2256 := (f193 #2176)
+#2257 := (f148 #28 #2256)
+#10154 := (= f1 #2257)
+#10148 := (= f1 #2249)
+#21807 := (not #10148)
+#1391 := (f14 #26)
+#2251 := (f198 #1391)
+#10142 := (= f1 #2251)
+#21822 := (or #10142 #21807 #10154)
+#21827 := (forall (vars (?v3 S5)) (:pat #2250) #21822)
+#21833 := (not #21827)
+#2163 := (f17 #20 #28)
+#2164 := (f16 #21 #2163)
+#9842 := (= f1 #2164)
+#21642 := (not #9842)
+#187 := (f28 #20 #21)
+#3789 := (= f1 #187)
+#10492 := (not #3789)
+#21834 := (or #10492 #21642 #21833)
+#21835 := (not #21834)
+#9890 := (= f1 #2184)
+#10178 := (not #9890)
+#21840 := (or #10178 #21835)
+#21843 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S5)) (:pat #2247) #21840)
+#10145 := (not #10142)
+#10151 := (and #10145 #10148)
+#10160 := (not #10151)
+#10161 := (or #10160 #10154)
+#10166 := (forall (vars (?v3 S5)) (:pat #2250) #10161)
+#10187 := (and #3789 #9842 #10166)
+#10190 := (or #10178 #10187)
+#10193 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S5)) (:pat #2247) #10190)
+#21844 := (iff #10193 #21843)
+#21841 := (iff #10190 #21840)
+#21838 := (iff #10187 #21835)
+#21830 := (and #3789 #9842 #21827)
+#21836 := (iff #21830 #21835)
+#21837 := [rewrite]: #21836
+#21831 := (iff #10187 #21830)
+#21828 := (iff #10166 #21827)
+#21825 := (iff #10161 #21822)
+#21808 := (or #10142 #21807)
+#21819 := (or #21808 #10154)
+#21823 := (iff #21819 #21822)
+#21824 := [rewrite]: #21823
+#21820 := (iff #10161 #21819)
+#21817 := (iff #10160 #21808)
+#21809 := (not #21808)
+#21812 := (not #21809)
+#21815 := (iff #21812 #21808)
+#21816 := [rewrite]: #21815
+#21813 := (iff #10160 #21812)
+#21810 := (iff #10151 #21809)
+#21811 := [rewrite]: #21810
+#21814 := [monotonicity #21811]: #21813
+#21818 := [trans #21814 #21816]: #21817
+#21821 := [monotonicity #21818]: #21820
+#21826 := [trans #21821 #21824]: #21825
+#21829 := [quant-intro #21826]: #21828
+#21832 := [monotonicity #21829]: #21831
+#21839 := [trans #21832 #21837]: #21838
+#21842 := [monotonicity #21839]: #21841
+#21845 := [quant-intro #21842]: #21844
+#17793 := (~ #10193 #10193)
+#17791 := (~ #10190 #10190)
+#17789 := (~ #10187 #10187)
+#17787 := (~ #10166 #10166)
+#17785 := (~ #10161 #10161)
+#17786 := [refl]: #17785
+#17788 := [nnf-pos #17786]: #17787
+#17783 := (~ #9842 #9842)
+#17784 := [refl]: #17783
+#17781 := (~ #3789 #3789)
+#17782 := [refl]: #17781
+#17790 := [monotonicity #17782 #17784 #17788]: #17789
+#17779 := (~ #10178 #10178)
+#17780 := [refl]: #17779
+#17792 := [monotonicity #17780 #17790]: #17791
+#17794 := [nnf-pos #17792]: #17793
+#2258 := (= #2257 f1)
+#2254 := (= #2249 f1)
+#2252 := (= #2251 f1)
+#2253 := (not #2252)
+#2255 := (and #2253 #2254)
+#2259 := (implies #2255 #2258)
+#2260 := (forall (vars (?v3 S5)) (:pat #2250) #2259)
+#191 := (= #187 f1)
+#2261 := (and #191 #2260)
+#2169 := (= #2164 f1)
+#2262 := (and #2169 #2261)
+#2185 := (= #2184 f1)
+#2263 := (implies #2185 #2262)
+#2264 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S5)) (:pat #2247) #2263)
+#10196 := (iff #2264 #10193)
+#10169 := (and #3789 #10166)
+#10172 := (and #9842 #10169)
+#10179 := (or #10178 #10172)
+#10184 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S5)) (:pat #2247) #10179)
+#10194 := (iff #10184 #10193)
+#10191 := (iff #10179 #10190)
+#10188 := (iff #10172 #10187)
+#10189 := [rewrite]: #10188
+#10192 := [monotonicity #10189]: #10191
+#10195 := [quant-intro #10192]: #10194
+#10185 := (iff #2264 #10184)
+#10182 := (iff #2263 #10179)
+#10175 := (implies #9890 #10172)
+#10180 := (iff #10175 #10179)
+#10181 := [rewrite]: #10180
+#10176 := (iff #2263 #10175)
+#10173 := (iff #2262 #10172)
+#10170 := (iff #2261 #10169)
+#10167 := (iff #2260 #10166)
+#10164 := (iff #2259 #10161)
+#10157 := (implies #10151 #10154)
+#10162 := (iff #10157 #10161)
+#10163 := [rewrite]: #10162
+#10158 := (iff #2259 #10157)
+#10155 := (iff #2258 #10154)
+#10156 := [rewrite]: #10155
+#10152 := (iff #2255 #10151)
+#10149 := (iff #2254 #10148)
+#10150 := [rewrite]: #10149
+#10146 := (iff #2253 #10145)
+#10143 := (iff #2252 #10142)
+#10144 := [rewrite]: #10143
+#10147 := [monotonicity #10144]: #10146
+#10153 := [monotonicity #10147 #10150]: #10152
+#10159 := [monotonicity #10153 #10156]: #10158
+#10165 := [trans #10159 #10163]: #10164
+#10168 := [quant-intro #10165]: #10167
+#3790 := (iff #191 #3789)
+#3791 := [rewrite]: #3790
+#10171 := [monotonicity #3791 #10168]: #10170
+#9843 := (iff #2169 #9842)
+#9844 := [rewrite]: #9843
+#10174 := [monotonicity #9844 #10171]: #10173
+#9891 := (iff #2185 #9890)
+#9892 := [rewrite]: #9891
+#10177 := [monotonicity #9892 #10174]: #10176
+#10183 := [trans #10177 #10181]: #10182
+#10186 := [quant-intro #10183]: #10185
+#10197 := [trans #10186 #10195]: #10196
+#10141 := [asserted]: #2264
+#10198 := [mp #10141 #10197]: #10193
+#17795 := [mp~ #10198 #17794]: #10193
+#21846 := [mp #17795 #21845]: #21843
+#26633 := (not #26630)
+#26707 := (not #21843)
+#26708 := (or #26707 #26575 #26633)
+#26610 := (or #26609 #26607 #26603)
+#26612 := (forall (vars (?v3 S5)) (:pat #26611) #26610)
+#26613 := (not #26612)
+#26618 := (or #26488 #26617 #26613)
+#26619 := (not #26618)
+#26620 := (or #26575 #26619)
+#26717 := (or #26707 #26620)
+#26697 := (iff #26717 #26708)
+#26636 := (or #26575 #26633)
+#26724 := (or #26707 #26636)
+#26714 := (iff #26724 #26708)
+#26691 := [rewrite]: #26714
+#26725 := (iff #26717 #26724)
+#26637 := (iff #26620 #26636)
+#26634 := (iff #26619 #26633)
+#26631 := (iff #26618 #26630)
+#26628 := (iff #26613 #26627)
+#26625 := (iff #26612 #26624)
+#26622 := (iff #26610 #26621)
+#26623 := [rewrite]: #26622
+#26626 := [quant-intro #26623]: #26625
+#26629 := [monotonicity #26626]: #26628
+#26632 := [monotonicity #26629]: #26631
+#26635 := [monotonicity #26632]: #26634
+#26638 := [monotonicity #26635]: #26637
+#26726 := [monotonicity #26638]: #26725
+#26699 := [trans #26726 #26691]: #26697
+#26723 := [quant-inst]: #26717
+#26701 := [mp #26723 #26699]: #26708
+#26813 := [unit-resolution #26701 #21846 #26811]: #26575
+#26572 := (not #26556)
+#26566 := (or #26565 #26554 #26572)
+#26562 := [def-axiom]: #26566
+#26814 := [unit-resolution #26562 #26813 #26797 #26790]: false
+#26803 := [lemma #26814]: #26802
+#28680 := [unit-resolution #26803 #26657]: #26616
+#26777 := (or #26617 #27073)
+#26786 := (= #26615 #27072)
+#26788 := (= #27072 #26615)
+#28362 := (= #26984 #26021)
+#28363 := [trans #28337 #28349]: #28362
+#26789 := [monotonicity #28363]: #26788
+#26774 := [symm #26789]: #26786
+#26787 := [hypothesis]: #26616
+#26775 := [trans #26787 #26774]: #27073
+#27074 := (not #27073)
+#26785 := [hypothesis]: #27074
+#26776 := [unit-resolution #26785 #26775]: false
+#26778 := [lemma #26776]: #26777
+#28681 := [unit-resolution #26778 #28680]: #27073
+#27109 := (or #12092 #27074)
+#27062 := (f44 #24835 #3008)
+#27063 := (f67 #27062 0::int #24835)
+#27067 := (f25 f287 #27063)
+#27068 := (= f1 #27067)
+#27069 := (not #27068)
+#27044 := (iff #18332 #27069)
+#27042 := (iff #12092 #27068)
+#27039 := (iff #27068 #12092)
+#27060 := (= #27067 #3066)
+#27058 := (= #27063 #3063)
+#28231 := (= #27062 #3007)
+#28229 := (= #3008 f288)
+#24955 := (= f288 #3008)
+#2727 := (f117 #2726)
+#11354 := (= #168 #2727)
+#23140 := (forall (vars (?v0 S3) (?v1 int)) (:pat #23139) #11354)
+#11358 := (forall (vars (?v0 S3) (?v1 int)) #11354)
+#23143 := (iff #11358 #23140)
+#23141 := (iff #11354 #11354)
+#23142 := [refl]: #23141
+#23144 := [quant-intro #23142]: #23143
+#18186 := (~ #11358 #11358)
+#18184 := (~ #11354 #11354)
+#18185 := [refl]: #18184
+#18187 := [nnf-pos #18185]: #18186
+#2728 := (= #2727 #168)
+#2729 := (forall (vars (?v0 S3) (?v1 int)) #2728)
+#11359 := (iff #2729 #11358)
+#11356 := (iff #2728 #11354)
+#11357 := [rewrite]: #11356
+#11360 := [quant-intro #11357]: #11359
+#11353 := [asserted]: #2729
+#11363 := [mp #11353 #11360]: #11358
+#18188 := [mp~ #11363 #18187]: #11358
+#23145 := [mp #18188 #23144]: #23140
+#24909 := (not #23140)
+#24960 := (or #24909 #24955)
+#24961 := [quant-inst]: #24960
+#28228 := [unit-resolution #24961 #23145]: #24955
+#28230 := [symm #28228]: #28229
+#28232 := [monotonicity #28225 #28230]: #28231
+#27059 := [monotonicity #28232 #28225]: #27058
+#27061 := [monotonicity #27059]: #27060
+#27041 := [monotonicity #27061]: #27039
+#27043 := [symm #27041]: #27042
+#27045 := [monotonicity #27043]: #27044
+#27057 := [hypothesis]: #18332
+#27040 := [mp #27057 #27045]: #27069
+#27064 := (f59 #3185 #27063)
+#27065 := (f137 #27064)
+#27066 := (= f1 #27065)
+#27079 := (or #27066 #27069)
+#27082 := (not #27079)
+decl f23 :: (-> S3 S1)
+#27075 := (f23 #24835)
+#27076 := (= f1 #27075)
+#2813 := (f23 f9)
+#28263 := (= #2813 #27075)
+#28260 := (= #27075 #2813)
+#28261 := [monotonicity #28225]: #28260
+#28264 := [symm #28261]: #28263
+#11533 := (= f1 #2813)
+#2814 := (= #2813 f1)
+#11535 := (iff #2814 #11533)
+#11536 := [rewrite]: #11535
+#11532 := [asserted]: #2814
+#11539 := [mp #11532 #11536]: #11533
+#28265 := [trans #11539 #28264]: #27076
+#27077 := (not #27076)
+#27105 := (or #27077 #27082)
+#28266 := [hypothesis]: #27073
+#27020 := (<= #24837 0::int)
+#27047 := (not #27020)
+#14269 := [not-or-elim #14255]: #13418
+#27003 := (* -1::int #24837)
+#27112 := (+ f286 #27003)
+#27113 := (<= #27112 0::int)
+#28246 := (not #24838)
+#28247 := (or #28246 #27113)
+#28248 := [th-lemma]: #28247
+#28249 := [unit-resolution #28248 #28245]: #27113
+#28255 := (not #27113)
+#27048 := (or #27047 #13417 #28255)
+#27049 := [th-lemma]: #27048
+#27050 := [unit-resolution #27049 #28249 #14269]: #27047
+#245 := (f23 #241)
+#255 := (:var 1 int)
+#771 := (:var 4 int)
+#2087 := (f44 #241 #771)
+#2088 := (f67 #2087 #255 #241)
+#1382 := (:var 5 S4)
+#2104 := (f26 #1382 #2088)
+#1374 := (:var 3 S5)
+#2085 := (f17 #1382 #1374)
+#276 := (:var 2 int)
+#2083 := (f125 #241 #276)
+#2084 := (f44 #2083 #771)
+#2086 := (f16 #2084 #2085)
+#2105 := (pattern #2086 #2104 #245)
+#1556 := (f60 #1382)
+#2102 := (f59 #1556 #2088)
+#2103 := (pattern #2086 #2102 #245)
+#2108 := (f137 #2102)
+#9650 := (= f1 #2108)
+#2106 := (f25 #1382 #2088)
+#9647 := (= f1 #2106)
+#21552 := (not #9647)
+#21553 := (or #21552 #9650)
+#21554 := (not #21553)
+#9591 := (= f1 #2086)
+#21528 := (not #9591)
+#2091 := (f56 #1382)
+#9588 := (= f1 #2091)
+#21527 := (not #9588)
+#4122 := (* -1::int #276)
+#6186 := (+ #255 #4122)
+#6783 := (>= #6186 0::int)
+#4384 := (>= #255 0::int)
+#19465 := (not #4384)
+#4000 := (= f1 #245)
+#10377 := (not #4000)
+#21560 := (or #10377 #19465 #6783 #21527 #21528 #21554)
+#21565 := (forall (vars (?v0 S4) (?v1 int) (?v2 S5) (?v3 int) (?v4 int) (?v5 S3)) (:pat #2103 #2105) #21560)
+#9653 := (not #9650)
+#9656 := (and #9647 #9653)
+#7850 := (not #6783)
+#9629 := (and #4000 #4384 #7850 #9588 #9591)
+#9634 := (not #9629)
+#9670 := (or #9634 #9656)
+#9673 := (forall (vars (?v0 S4) (?v1 int) (?v2 S5) (?v3 int) (?v4 int) (?v5 S3)) (:pat #2103 #2105) #9670)
+#21566 := (iff #9673 #21565)
+#21563 := (iff #9670 #21560)
+#21529 := (or #10377 #19465 #6783 #21527 #21528)
+#21557 := (or #21529 #21554)
+#21561 := (iff #21557 #21560)
+#21562 := [rewrite]: #21561
+#21558 := (iff #9670 #21557)
+#21555 := (iff #9656 #21554)
+#21556 := [rewrite]: #21555
+#21538 := (iff #9634 #21529)
+#21530 := (not #21529)
+#21533 := (not #21530)
+#21536 := (iff #21533 #21529)
+#21537 := [rewrite]: #21536
+#21534 := (iff #9634 #21533)
+#21531 := (iff #9629 #21530)
+#21532 := [rewrite]: #21531
+#21535 := [monotonicity #21532]: #21534
+#21539 := [trans #21535 #21537]: #21538
+#21559 := [monotonicity #21539 #21556]: #21558
+#21564 := [trans #21559 #21562]: #21563
+#21567 := [quant-intro #21564]: #21566
+#17659 := (~ #9673 #9673)
+#17657 := (~ #9670 #9670)
+#17658 := [refl]: #17657
+#17660 := [nnf-pos #17658]: #17659
+#2109 := (= #2108 f1)
+#2110 := (not #2109)
+#2107 := (= #2106 f1)
+#2111 := (and #2107 #2110)
+#1443 := (< #255 #276)
+#406 := (<= 0::int #255)
+#1444 := (and #406 #1443)
+#2093 := (= #2086 f1)
+#2094 := (and #2093 #1444)
+#246 := (= #245 f1)
+#2095 := (and #246 #2094)
+#2092 := (= #2091 f1)
+#2096 := (and #2092 #2095)
+#2112 := (implies #2096 #2111)
+#2113 := (forall (vars (?v0 S4) (?v1 int) (?v2 S5) (?v3 int) (?v4 int) (?v5 S3)) (:pat #2103 #2105) #2112)
+#9676 := (iff #2113 #9673)
+#9597 := (and #1444 #9591)
+#9602 := (and #4000 #9597)
+#9605 := (and #9588 #9602)
+#9611 := (not #9605)
+#9662 := (or #9611 #9656)
+#9667 := (forall (vars (?v0 S4) (?v1 int) (?v2 S5) (?v3 int) (?v4 int) (?v5 S3)) (:pat #2103 #2105) #9662)
+#9674 := (iff #9667 #9673)
+#9671 := (iff #9662 #9670)
+#9635 := (iff #9611 #9634)
+#9632 := (iff #9605 #9629)
+#7853 := (and #4384 #7850)
+#9620 := (and #7853 #9591)
+#9623 := (and #4000 #9620)
+#9626 := (and #9588 #9623)
+#9630 := (iff #9626 #9629)
+#9631 := [rewrite]: #9630
+#9627 := (iff #9605 #9626)
+#9624 := (iff #9602 #9623)
+#9621 := (iff #9597 #9620)
+#7854 := (iff #1444 #7853)
+#7851 := (iff #1443 #7850)
+#7852 := [rewrite]: #7851
+#4383 := (iff #406 #4384)
+#4385 := [rewrite]: #4383
+#7855 := [monotonicity #4385 #7852]: #7854
+#9622 := [monotonicity #7855]: #9621
+#9625 := [monotonicity #9622]: #9624
+#9628 := [monotonicity #9625]: #9627
+#9633 := [trans #9628 #9631]: #9632
+#9636 := [monotonicity #9633]: #9635
+#9672 := [monotonicity #9636]: #9671
+#9675 := [quant-intro #9672]: #9674
+#9668 := (iff #2113 #9667)
+#9665 := (iff #2112 #9662)
+#9659 := (implies #9605 #9656)
+#9663 := (iff #9659 #9662)
+#9664 := [rewrite]: #9663
+#9660 := (iff #2112 #9659)
+#9657 := (iff #2111 #9656)
+#9654 := (iff #2110 #9653)
+#9651 := (iff #2109 #9650)
+#9652 := [rewrite]: #9651
+#9655 := [monotonicity #9652]: #9654
+#9648 := (iff #2107 #9647)
+#9649 := [rewrite]: #9648
+#9658 := [monotonicity #9649 #9655]: #9657
+#9606 := (iff #2096 #9605)
+#9603 := (iff #2095 #9602)
+#9600 := (iff #2094 #9597)
+#9594 := (and #9591 #1444)
+#9598 := (iff #9594 #9597)
+#9599 := [rewrite]: #9598
+#9595 := (iff #2094 #9594)
+#9592 := (iff #2093 #9591)
+#9593 := [rewrite]: #9592
+#9596 := [monotonicity #9593]: #9595
+#9601 := [trans #9596 #9599]: #9600
+#4001 := (iff #246 #4000)
+#4002 := [rewrite]: #4001
+#9604 := [monotonicity #4002 #9601]: #9603
+#9589 := (iff #2092 #9588)
+#9590 := [rewrite]: #9589
+#9607 := [monotonicity #9590 #9604]: #9606
+#9661 := [monotonicity #9607 #9658]: #9660
+#9666 := [trans #9661 #9664]: #9665
+#9669 := [quant-intro #9666]: #9668
+#9677 := [trans #9669 #9675]: #9676
+#9646 := [asserted]: #2113
+#9678 := [mp #9646 #9677]: #9673
+#17661 := [mp~ #9678 #17660]: #9673
+#21568 := [mp #17661 #21567]: #21565
+#27093 := (not #21565)
+#26952 := (or #27093 #24685 #27020 #27074 #27077 #27082)
+#27070 := (or #27069 #27066)
+#27071 := (not #27070)
+#27004 := (+ 0::int #27003)
+#27005 := (>= #27004 0::int)
+#27006 := (>= 0::int 0::int)
+#27007 := (not #27006)
+#27078 := (or #27077 #27007 #27005 #24685 #27074 #27071)
+#26953 := (or #27093 #27078)
+#26974 := (iff #26953 #26952)
+#27088 := (or #24685 #27020 #27074 #27077 #27082)
+#26970 := (or #27093 #27088)
+#26972 := (iff #26970 #26952)
+#26973 := [rewrite]: #26972
+#26971 := (iff #26953 #26970)
+#27091 := (iff #27078 #27088)
+#27085 := (or #27077 false #27020 #24685 #27074 #27082)
+#27089 := (iff #27085 #27088)
+#27090 := [rewrite]: #27089
+#27086 := (iff #27078 #27085)
+#27083 := (iff #27071 #27082)
+#27080 := (iff #27070 #27079)
+#27081 := [rewrite]: #27080
+#27084 := [monotonicity #27081]: #27083
+#27023 := (iff #27005 #27020)
+#27017 := (>= #27003 0::int)
+#27021 := (iff #27017 #27020)
 #27022 := [rewrite]: #27021
-#27025 := [monotonicity #27022]: #27024
-#26964 := (iff #26946 #26961)
-#26958 := (>= #26944 0::int)
-#26962 := (iff #26958 #26961)
-#26963 := [rewrite]: #26962
-#26959 := (iff #26946 #26958)
-#26956 := (= #26945 #26944)
-#26957 := [rewrite]: #26956
-#26960 := [monotonicity #26957]: #26959
-#26965 := [trans #26960 #26963]: #26964
-#26954 := (iff #26948 false)
-#26952 := (iff #26948 #3086)
-#26950 := (iff #26947 true)
-#26951 := [rewrite]: #26950
-#26953 := [monotonicity #26951]: #26952
-#26955 := [trans #26953 #11996]: #26954
-#27028 := [monotonicity #26955 #26965 #27025]: #27027
-#27033 := [trans #27028 #27031]: #27032
-#26911 := [monotonicity #27033]: #26913
-#26917 := [trans #26911 #26915]: #26916
-#26896 := [quant-inst]: #26895
-#26918 := [mp #26896 #26917]: #26894
-#27047 := [unit-resolution #26918 #21366 #14064 #26991 #28231]: #27046
-#27048 := [unit-resolution #27047 #28230]: #27023
-#26994 := (or #27020 #27009)
-#26995 := [def-axiom]: #26994
-#27049 := [unit-resolution #26995 #27048 #26981]: false
-#27051 := [lemma #27049]: #27050
-#28637 := [unit-resolution #27051 #28636]: #11931
-#26777 := (or #23215 #18130 #23230)
-#26772 := [hypothesis]: #23227
-#26773 := [hypothesis]: #11931
-#26774 := [hypothesis]: #23218
-#24440 := (or #23215 #11928)
-#24441 := [def-axiom]: #24440
-#26769 := [unit-resolution #24441 #26774]: #11928
-#24452 := (or #23221 #23215)
-#24453 := [def-axiom]: #24452
-#26775 := [unit-resolution #24453 #26774]: #23221
-#24462 := (or #23230 #18127 #18130 #23224)
-#24463 := [def-axiom]: #24462
-#26776 := [unit-resolution #24463 #26775 #26769 #26773 #26772]: false
-#26778 := [lemma #26776]: #26777
-#28638 := [unit-resolution #26778 #28637 #28634]: #23215
-#28373 := (or #11937 #27015)
-#26756 := (uf_58 #3150 #3031)
-#27079 := (uf_135 #26756)
-#27082 := (uf_25 uf_287 #27079)
-#27083 := (= uf_26 #27082)
-#27080 := (uf_210 uf_287 #27079)
-#27081 := (= uf_9 #27080)
-#27189 := (or #27081 #27083)
-#27202 := (not #27189)
-#27071 := (uf_136 #26756)
-#27072 := (= uf_9 #27071)
-#27073 := (not #27072)
-#27069 := (uf_27 uf_287 #27079)
-#27070 := (= uf_9 #27069)
-#27065 := (not #27070)
-#27184 := (or #27065 #27073)
-#27186 := (not #27184)
-#26820 := (uf_13 #3031)
-#27094 := (uf_12 #26820)
-#27144 := (= uf_14 #27094)
-#27181 := (not #27144)
-#27066 := (uf_13 #27079)
-#27067 := (uf_12 #27066)
-#27068 := (= uf_14 #27067)
-#27227 := (or #27068 #27181 #27186 #27202)
-#27231 := (not #27227)
-#27100 := (uf_25 uf_287 #3031)
-#27101 := (= uf_26 #27100)
-#27093 := (uf_210 uf_287 #3031)
-#27099 := (= uf_9 #27093)
-#27146 := (or #27099 #27101)
-#27149 := (not #27146)
-#27192 := (or #27144 #27149)
-#27195 := (not #27192)
-#27239 := (or #27195 #27231)
-#27243 := (not #27239)
-#27240 := (or #18130 #27243)
-#27248 := (not #27240)
-#27255 := (iff #11937 #27248)
-#27260 := (or #27259 #27255)
-#27084 := (or #27083 #27081)
-#27085 := (not #27084)
-#27074 := (or #27073 #27065)
-#27075 := (not #27074)
-#27095 := (= #27094 uf_14)
-#27096 := (not #27095)
-#27097 := (or #27096 #27075 #27068 #27085)
-#27098 := (not #27097)
-#27102 := (or #27101 #27099)
-#27103 := (not #27102)
-#27151 := (or #27095 #27103)
-#27152 := (not #27151)
-#27153 := (or #27152 #27098)
-#27154 := (not #27153)
-#27155 := (or #18130 #27154)
-#27156 := (not #27155)
-#27143 := (iff #11937 #27156)
-#27261 := (or #27259 #27143)
-#27288 := (iff #27261 #27260)
-#27290 := (iff #27260 #27260)
-#27291 := [rewrite]: #27290
-#27256 := (iff #27143 #27255)
-#27249 := (iff #27156 #27248)
-#27246 := (iff #27155 #27240)
-#27244 := (iff #27154 #27243)
-#27241 := (iff #27153 #27239)
-#27232 := (iff #27098 #27231)
-#27229 := (iff #27097 #27227)
-#27224 := (or #27181 #27186 #27068 #27202)
-#27228 := (iff #27224 #27227)
-#27223 := [rewrite]: #27228
-#27225 := (iff #27097 #27224)
-#27203 := (iff #27085 #27202)
-#27190 := (iff #27084 #27189)
-#27201 := [rewrite]: #27190
-#27222 := [monotonicity #27201]: #27203
-#27187 := (iff #27075 #27186)
-#27185 := (iff #27074 #27184)
-#27180 := [rewrite]: #27185
-#27188 := [monotonicity #27180]: #27187
-#27182 := (iff #27096 #27181)
-#27142 := (iff #27095 #27144)
-#27145 := [rewrite]: #27142
-#27183 := [monotonicity #27145]: #27182
-#27226 := [monotonicity #27183 #27188 #27222]: #27225
-#27230 := [trans #27226 #27223]: #27229
-#27233 := [monotonicity #27230]: #27232
-#27196 := (iff #27152 #27195)
-#27193 := (iff #27151 #27192)
-#27150 := (iff #27103 #27149)
-#27147 := (iff #27102 #27146)
-#27148 := [rewrite]: #27147
-#27191 := [monotonicity #27148]: #27150
-#27194 := [monotonicity #27145 #27191]: #27193
-#27179 := [monotonicity #27194]: #27196
-#27242 := [monotonicity #27179 #27233]: #27241
+#27018 := (iff #27005 #27017)
+#27015 := (= #27004 #27003)
+#27016 := [rewrite]: #27015
+#27019 := [monotonicity #27016]: #27018
+#27024 := [trans #27019 #27022]: #27023
+#27013 := (iff #27007 false)
+#27011 := (iff #27007 #3121)
+#27009 := (iff #27006 true)
+#27010 := [rewrite]: #27009
+#27012 := [monotonicity #27010]: #27011
+#27014 := [trans #27012 #12166]: #27013
+#27087 := [monotonicity #27014 #27024 #27084]: #27086
+#27092 := [trans #27087 #27090]: #27091
+#26969 := [monotonicity #27092]: #26971
+#26975 := [trans #26969 #26973]: #26974
+#26954 := [quant-inst]: #26953
+#26976 := [mp #26954 #26975]: #26952
+#27106 := [unit-resolution #26976 #21568 #14260 #27050 #28266]: #27105
+#27107 := [unit-resolution #27106 #28265]: #27082
+#27053 := (or #27079 #27068)
+#27054 := [def-axiom]: #27053
+#27108 := [unit-resolution #27054 #27107 #27040]: false
+#27110 := [lemma #27108]: #27109
+#28682 := [unit-resolution #27110 #28681]: #12092
+#26839 := (or #23417 #18332 #23432)
+#26849 := [hypothesis]: #23429
+#26835 := [hypothesis]: #12092
+#26836 := [hypothesis]: #23420
+#24642 := (or #23417 #12089)
+#24643 := [def-axiom]: #24642
+#26834 := [unit-resolution #24643 #26836]: #12089
+#24654 := (or #23423 #23417)
+#24655 := [def-axiom]: #24654
+#26837 := [unit-resolution #24655 #26836]: #23423
+#24664 := (or #23432 #18329 #18332 #23426)
+#24665 := [def-axiom]: #24664
+#26838 := [unit-resolution #24665 #26837 #26834 #26835 #26849]: false
+#26855 := [lemma #26838]: #26839
+#28683 := [unit-resolution #26855 #28682 #28679]: #23417
+#28418 := (or #12098 #27074)
+#26824 := (f59 #3185 #3063)
+#27130 := (f136 #26824)
+#27133 := (f26 f287 #27130)
+#27134 := (= f27 #27133)
+#27131 := (f211 f287 #27130)
+#27132 := (= f1 #27131)
+#27271 := (or #27132 #27134)
+#27275 := (not #27271)
+#27143 := (f137 #26824)
+#27144 := (= f1 #27143)
+#27145 := (not #27144)
+#27124 := (f28 f287 #27130)
+#27125 := (= f1 #27124)
+#27126 := (not #27125)
+#27237 := (or #27126 #27145)
+#27250 := (not #27237)
+#26878 := (f14 #3063)
+#27142 := (f13 #26878)
+#27197 := (= f15 #27142)
+#27229 := (not #27197)
+#27122 := (f14 #27130)
+#27123 := (f13 #27122)
+#27121 := (= f15 #27123)
+#27280 := (or #27121 #27229 #27250 #27275)
+#27291 := (not #27280)
+#27201 := (f26 f287 #3063)
+#27202 := (= f27 #27201)
+#27152 := (f211 f287 #3063)
+#27200 := (= f1 #27152)
+#27240 := (or #27200 #27202)
+#27243 := (not #27240)
+#27228 := (or #27197 #27243)
+#27232 := (not #27228)
+#27293 := (or #27232 #27291)
+#27299 := (not #27293)
+#27304 := (or #18332 #27299)
+#27332 := (not #27304)
+#27335 := (iff #12098 #27332)
+#27323 := (or #27322 #27335)
+#27135 := (or #27134 #27132)
+#27136 := (not #27135)
+#27146 := (or #27145 #27126)
+#27147 := (not #27146)
+#27148 := (= #27142 f15)
+#27149 := (not #27148)
+#27150 := (or #27149 #27147 #27121 #27136)
+#27151 := (not #27150)
+#27203 := (or #27202 #27200)
+#27204 := (not #27203)
+#27205 := (or #27148 #27204)
+#27192 := (not #27205)
+#27193 := (or #27192 #27151)
+#27191 := (not #27193)
+#27194 := (or #18332 #27191)
+#27195 := (not #27194)
+#27196 := (iff #12098 #27195)
+#27324 := (or #27322 #27196)
+#27320 := (iff #27324 #27323)
+#27327 := (iff #27323 #27323)
+#27328 := [rewrite]: #27327
+#27336 := (iff #27196 #27335)
+#27333 := (iff #27195 #27332)
+#27305 := (iff #27194 #27304)
+#27300 := (iff #27191 #27299)
+#27294 := (iff #27193 #27293)
+#27289 := (iff #27151 #27291)
+#27288 := (iff #27150 #27280)
+#27272 := (or #27229 #27250 #27121 #27275)
+#27281 := (iff #27272 #27280)
+#27282 := [rewrite]: #27281
+#27278 := (iff #27150 #27272)
+#27276 := (iff #27136 #27275)
+#27273 := (iff #27135 #27271)
+#27274 := [rewrite]: #27273
+#27277 := [monotonicity #27274]: #27276
+#27251 := (iff #27147 #27250)
+#27238 := (iff #27146 #27237)
+#27239 := [rewrite]: #27238
+#27252 := [monotonicity #27239]: #27251
+#27235 := (iff #27149 #27229)
+#27198 := (iff #27148 #27197)
+#27199 := [rewrite]: #27198
+#27236 := [monotonicity #27199]: #27235
+#27279 := [monotonicity #27236 #27252 #27277]: #27278
+#27290 := [trans #27279 #27282]: #27288
+#27292 := [monotonicity #27290]: #27289
+#27233 := (iff #27192 #27232)
+#27230 := (iff #27205 #27228)
+#27244 := (iff #27204 #27243)
+#27241 := (iff #27203 #27240)
+#27242 := [rewrite]: #27241
 #27245 := [monotonicity #27242]: #27244
-#27247 := [monotonicity #27245]: #27246
-#27250 := [monotonicity #27247]: #27249
-#27257 := [monotonicity #27250]: #27256
-#27289 := [monotonicity #27257]: #27288
-#27292 := [trans #27289 #27291]: #27288
-#27287 := [quant-inst]: #27261
-#27277 := [mp #27287 #27292]: #27260
-#28168 := [unit-resolution #27277 #21776]: #27255
-#27430 := (not #27255)
-#28169 := (or #27430 #27240)
-#28163 := [hypothesis]: #18136
-#27433 := (or #27430 #11937 #27240)
-#27434 := [def-axiom]: #27433
-#26920 := [unit-resolution #27434 #28163]: #28169
-#26921 := [unit-resolution #26920 #28168]: #27240
-#26923 := (or #27248 #27243)
-#26922 := [unit-resolution #27051 #28231]: #11931
-#27431 := (or #27248 #18130 #27243)
-#27432 := [def-axiom]: #27431
-#26924 := [unit-resolution #27432 #26922]: #26923
-#27055 := [unit-resolution #26924 #26921]: #27243
-#27389 := (or #27239 #27227)
-#27387 := [def-axiom]: #27389
-#27157 := [unit-resolution #27387 #27055]: #27227
-#27545 := (not #27007)
-#27206 := (iff #27545 #27073)
-#27204 := (iff #27007 #27072)
-#27199 := (= #27006 #27071)
-#27160 := (= #27005 #26756)
-#27161 := [monotonicity #27000]: #27160
-#27200 := [monotonicity #27161]: #27199
-#27205 := [monotonicity #27200]: #27204
-#27475 := [monotonicity #27205]: #27206
-#27546 := (or #27020 #27545)
-#27547 := [def-axiom]: #27546
-#27159 := [unit-resolution #27547 #27048]: #27545
-#27476 := [mp #27159 #27475]: #27073
-#27310 := (or #27184 #27072)
-#27305 := [def-axiom]: #27310
-#27477 := [unit-resolution #27305 #27476]: #27184
-#25182 := (uf_12 uf_7)
-#28283 := (= #25182 #27094)
-#28279 := (= #27094 #25182)
-#28277 := (= #26820 uf_7)
-#24758 := (uf_13 #2979)
-#28275 := (= #24758 uf_7)
-#24759 := (= uf_7 #24758)
-#24764 := (or #24710 #24759)
-#24765 := [quant-inst]: #24764
-#27482 := [unit-resolution #24765 #22949]: #24759
-#28276 := [symm #27482]: #28275
-#28273 := (= #26820 #24758)
-#28256 := (= #3031 #2979)
-#26851 := (uf_116 #24470)
-#26867 := (uf_43 #24643 #26851)
-#28252 := (= #26867 #2979)
-#27548 := (= #26851 uf_288)
-#28244 := (= #26851 #2980)
-#28242 := (= #24470 #2979)
-#24471 := (= #2979 #24470)
-#93 := (uf_29 #23)
-#22848 := (pattern #93)
-#94 := (uf_28 #93)
-#3542 := (= #23 #94)
-#22849 := (forall (vars (?x14 T5)) (:pat #22848) #3542)
-#3545 := (forall (vars (?x14 T5)) #3542)
-#22850 := (iff #3545 #22849)
-#22852 := (iff #22849 #22849)
-#22853 := [rewrite]: #22852
-#22851 := [rewrite]: #22850
-#22854 := [trans #22851 #22853]: #22850
-#16026 := (~ #3545 #3545)
-#16016 := (~ #3542 #3542)
-#16017 := [refl]: #16016
-#16082 := [nnf-pos #16017]: #16026
-#95 := (= #94 #23)
-#96 := (forall (vars (?x14 T5)) #95)
-#3546 := (iff #96 #3545)
-#3543 := (iff #95 #3542)
-#3544 := [rewrite]: #3543
-#3547 := [quant-intro #3544]: #3546
-#3541 := [asserted]: #96
-#3550 := [mp #3541 #3547]: #3545
-#16083 := [mp~ #3550 #16082]: #3545
-#22855 := [mp #16083 #22854]: #22849
-#24474 := (not #22849)
-#24475 := (or #24474 #24471)
-#24476 := [quant-inst]: #24475
-#28241 := [unit-resolution #24476 #22855]: #24471
-#28243 := [symm #28241]: #28242
-#28245 := [monotonicity #28243]: #28244
-#27549 := [trans #28245 #28195]: #27548
-#28126 := [monotonicity #28190 #27549]: #28252
-#28266 := (= #3031 #26867)
-#26845 := (uf_66 #24470 0::int #24643)
-#26870 := (= #26845 #26867)
-#26873 := (not #26870)
-decl uf_138 :: (-> T5 T5 T2)
-#26846 := (uf_138 #26845 #24470)
-#26847 := (= uf_9 #26846)
-#26848 := (not #26847)
-#26879 := (or #26848 #26873)
-#26884 := (not #26879)
-#1576 := (uf_66 #21 #247 #233)
-#1577 := (pattern #1576)
-#1578 := (uf_138 #1576 #21)
-#8222 := (= uf_9 #1578)
-#20914 := (not #8222)
-decl uf_139 :: (-> T3 int)
-#1581 := (uf_139 #233)
-#1582 := (* #247 #1581)
-#1580 := (uf_116 #21)
-#1583 := (+ #1580 #1582)
-#1584 := (uf_43 #233 #1583)
-#1585 := (= #1576 #1584)
-#20913 := (not #1585)
-#20915 := (or #20913 #20914)
-#20916 := (not #20915)
-#20919 := (forall (vars (?x375 T5) (?x376 int) (?x377 T3)) (:pat #1577) #20916)
-#8228 := (and #1585 #8222)
-#8233 := (forall (vars (?x375 T5) (?x376 int) (?x377 T3)) (:pat #1577) #8228)
-#20920 := (iff #8233 #20919)
-#20917 := (iff #8228 #20916)
-#20918 := [rewrite]: #20917
-#20921 := [quant-intro #20918]: #20920
-#17047 := (~ #8233 #8233)
-#17045 := (~ #8228 #8228)
-#17046 := [refl]: #17045
-#17048 := [nnf-pos #17046]: #17047
-#1579 := (= #1578 uf_9)
-#1586 := (and #1579 #1585)
-#1587 := (forall (vars (?x375 T5) (?x376 int) (?x377 T3)) (:pat #1577) #1586)
-#8234 := (iff #1587 #8233)
-#8231 := (iff #1586 #8228)
-#8225 := (and #8222 #1585)
-#8229 := (iff #8225 #8228)
-#8230 := [rewrite]: #8229
-#8226 := (iff #1586 #8225)
-#8223 := (iff #1579 #8222)
-#8224 := [rewrite]: #8223
-#8227 := [monotonicity #8224]: #8226
-#8232 := [trans #8227 #8230]: #8231
-#8235 := [quant-intro #8232]: #8234
-#8221 := [asserted]: #1587
-#8238 := [mp #8221 #8235]: #8233
-#17049 := [mp~ #8238 #17048]: #8233
-#20922 := [mp #17049 #20921]: #20919
-#26887 := (not #20919)
-#26833 := (or #26887 #26884)
-#26849 := (uf_139 #24643)
-#26850 := (* 0::int #26849)
-#26852 := (+ #26851 #26850)
-#26853 := (uf_43 #24643 #26852)
-#26854 := (= #26845 #26853)
-#26855 := (not #26854)
-#26856 := (or #26855 #26848)
-#26857 := (not #26856)
-#26834 := (or #26887 #26857)
-#26919 := (iff #26834 #26833)
-#26993 := (iff #26833 #26833)
-#26996 := [rewrite]: #26993
-#26885 := (iff #26857 #26884)
-#26882 := (iff #26856 #26879)
-#26876 := (or #26873 #26848)
-#26880 := (iff #26876 #26879)
-#26881 := [rewrite]: #26880
-#26877 := (iff #26856 #26876)
-#26874 := (iff #26855 #26873)
-#26871 := (iff #26854 #26870)
-#26868 := (= #26853 #26867)
-#26865 := (= #26852 #26851)
-#26860 := (+ #26851 0::int)
-#26863 := (= #26860 #26851)
-#26864 := [rewrite]: #26863
-#26861 := (= #26852 #26860)
-#26858 := (= #26850 0::int)
-#26859 := [rewrite]: #26858
-#26862 := [monotonicity #26859]: #26861
-#26866 := [trans #26862 #26864]: #26865
-#26869 := [monotonicity #26866]: #26868
-#26872 := [monotonicity #26869]: #26871
-#26875 := [monotonicity #26872]: #26874
-#26878 := [monotonicity #26875]: #26877
-#26883 := [trans #26878 #26881]: #26882
-#26886 := [monotonicity #26883]: #26885
-#26992 := [monotonicity #26886]: #26919
-#26997 := [trans #26992 #26996]: #26919
-#26897 := [quant-inst]: #26834
-#26987 := [mp #26897 #26997]: #26833
-#27579 := [unit-resolution #26987 #20922]: #26884
-#27037 := (or #26879 #26870)
-#27038 := [def-axiom]: #27037
-#27634 := [unit-resolution #27038 #27579]: #26870
-#28085 := (= #3031 #26845)
-#28125 := [monotonicity #28241 #28188]: #28085
-#28267 := [trans #28125 #27634]: #28266
-#28257 := [trans #28267 #28126]: #28256
-#28274 := [monotonicity #28257]: #28273
-#28278 := [trans #28274 #28276]: #28277
-#28280 := [monotonicity #28278]: #28279
-#28284 := [symm #28280]: #28283
-#25183 := (= uf_14 #25182)
-#25190 := (iff #11386 #25183)
-#2308 := (pattern #237)
-#2836 := (uf_12 #233)
-#11559 := (= uf_14 #2836)
-#11563 := (iff #3928 #11559)
-#11566 := (forall (vars (?x761 T3)) (:pat #2308) #11563)
-#18084 := (~ #11566 #11566)
-#18082 := (~ #11563 #11563)
-#18083 := [refl]: #18082
-#18085 := [nnf-pos #18083]: #18084
-#2849 := (= #2836 uf_14)
-#2850 := (iff #238 #2849)
-#2851 := (forall (vars (?x761 T3)) (:pat #2308) #2850)
-#11567 := (iff #2851 #11566)
-#11564 := (iff #2850 #11563)
-#11561 := (iff #2849 #11559)
-#11562 := [rewrite]: #11561
-#11565 := [monotonicity #3930 #11562]: #11564
-#11568 := [quant-intro #11565]: #11567
-#11558 := [asserted]: #2851
-#11571 := [mp #11558 #11568]: #11566
-#18086 := [mp~ #11571 #18085]: #11566
-#24814 := (not #11566)
-#25193 := (or #24814 #25190)
-#25194 := [quant-inst]: #25193
-#27478 := [unit-resolution #25194 #18086]: #25190
-#25195 := (not #25190)
-#27479 := (or #25195 #25183)
-#25199 := (not #11386)
-#25200 := (or #25195 #25199 #25183)
-#25201 := [def-axiom]: #25200
-#27480 := [unit-resolution #25201 #11392]: #27479
-#27481 := [unit-resolution #27480 #27478]: #25183
-#28285 := [trans #27481 #28284]: #27144
-#27341 := (not #27068)
-#28362 := (iff #11878 #27341)
-#28360 := (iff #11875 #27068)
-#28358 := (iff #27068 #11875)
-#28356 := (= #27067 #2990)
-#28354 := (= #27066 #2977)
-#28350 := (= #27066 #24763)
-#28348 := (= #27079 #2981)
-#28346 := (= #27079 #26926)
-#26927 := (uf_66 #26926 0::int #24643)
-#26931 := (uf_58 #3150 #26927)
-#26934 := (uf_135 #26931)
-#28344 := (= #26934 #26926)
-#26935 := (= #26926 #26934)
-#26937 := (up_67 #26931)
-#26938 := (not #26937)
-#26936 := (not #26935)
-#26932 := (uf_136 #26931)
-#26933 := (= uf_9 #26932)
-#26928 := (uf_24 uf_287 #26927)
-#26929 := (= uf_9 #26928)
-#26930 := (not #26929)
-#26966 := (or #26930 #26933 #26936 #26938)
-#26969 := (not #26966)
-#26941 := (uf_24 uf_287 #26926)
-#26942 := (= uf_9 #26941)
-#28296 := (= #2988 #26941)
-#28293 := (= #26941 #2988)
-#28294 := [monotonicity #28292]: #28293
-#28297 := [symm #28294]: #28296
-#28298 := [trans #14077 #28297]: #26942
-#26943 := (not #26942)
-#28299 := (or #26943 #26969)
-#277 := (:var 3 int)
-#310 := (:var 2 T3)
-#1470 := (uf_124 #310 #247)
-#1471 := (uf_43 #1470 #277)
-#1467 := (uf_43 #310 #277)
-#1468 := (uf_66 #1467 #161 #310)
-#35 := (:var 4 T4)
-#1473 := (uf_59 #35)
-#1474 := (uf_58 #1473 #1468)
-#1475 := (pattern #1474 #1471)
-#1466 := (uf_41 #35)
-#1469 := (uf_40 #1466 #1468)
-#1472 := (pattern #1469 #1471)
-#1478 := (uf_66 #1471 #161 #310)
-#1486 := (uf_24 #35 #1478)
-#7933 := (= uf_9 #1486)
-#20690 := (not #7933)
-#1479 := (uf_58 #1473 #1478)
-#1482 := (uf_136 #1479)
-#7927 := (= uf_9 #1482)
-#1480 := (uf_135 #1479)
-#7924 := (= #1471 #1480)
-#20689 := (not #7924)
-#1485 := (up_67 #1479)
-#20688 := (not #1485)
-#20691 := (or #20688 #20689 #7927 #20690)
-#20692 := (not #20691)
-#1476 := (uf_24 #35 #1471)
-#7921 := (= uf_9 #1476)
-#7956 := (not #7921)
-#5236 := (* -1::int #247)
-#6116 := (+ #161 #5236)
-#6117 := (>= #6116 0::int)
-#20698 := (or #4965 #6117 #7956 #20692)
-#20703 := (forall (vars (?x346 T4) (?x347 int) (?x348 T3) (?x349 int) (?x350 int)) (:pat #1472 #1475) #20698)
-#7930 := (not #7927)
-#7965 := (and #1485 #7924 #7930 #7933)
-#7620 := (not #6117)
-#7623 := (and #4043 #7620)
-#7626 := (not #7623)
-#7974 := (or #7626 #7956 #7965)
-#7979 := (forall (vars (?x346 T4) (?x347 int) (?x348 T3) (?x349 int) (?x350 int)) (:pat #1472 #1475) #7974)
-#20704 := (iff #7979 #20703)
-#20701 := (iff #7974 #20698)
-#20573 := (or #4965 #6117)
-#20695 := (or #20573 #7956 #20692)
-#20699 := (iff #20695 #20698)
-#20700 := [rewrite]: #20699
-#20696 := (iff #7974 #20695)
-#20693 := (iff #7965 #20692)
-#20694 := [rewrite]: #20693
-#20582 := (iff #7626 #20573)
-#20574 := (not #20573)
-#20577 := (not #20574)
-#20580 := (iff #20577 #20573)
-#20581 := [rewrite]: #20580
-#20578 := (iff #7626 #20577)
-#20575 := (iff #7623 #20574)
-#20576 := [rewrite]: #20575
-#20579 := [monotonicity #20576]: #20578
-#20583 := [trans #20579 #20581]: #20582
-#20697 := [monotonicity #20583 #20694]: #20696
-#20702 := [trans #20697 #20700]: #20701
-#20705 := [quant-intro #20702]: #20704
-#16824 := (~ #7979 #7979)
-#16822 := (~ #7974 #7974)
-#16823 := [refl]: #16822
-#16825 := [nnf-pos #16823]: #16824
-#1487 := (= #1486 uf_9)
-#1488 := (and #1485 #1487)
-#1483 := (= #1482 uf_9)
-#1484 := (not #1483)
-#1489 := (and #1484 #1488)
-#1481 := (= #1480 #1471)
-#1490 := (and #1481 #1489)
-#1371 := (< #161 #247)
-#1372 := (and #285 #1371)
-#1491 := (implies #1372 #1490)
-#1477 := (= #1476 uf_9)
-#1492 := (implies #1477 #1491)
-#1493 := (forall (vars (?x346 T4) (?x347 int) (?x348 T3) (?x349 int) (?x350 int)) (:pat #1472 #1475) #1492)
-#7982 := (iff #1493 #7979)
-#7936 := (and #1485 #7933)
-#7939 := (and #7930 #7936)
-#7942 := (and #7924 #7939)
-#7590 := (not #1372)
-#7948 := (or #7590 #7942)
-#7957 := (or #7956 #7948)
-#7962 := (forall (vars (?x346 T4) (?x347 int) (?x348 T3) (?x349 int) (?x350 int)) (:pat #1472 #1475) #7957)
-#7980 := (iff #7962 #7979)
-#7977 := (iff #7957 #7974)
-#7968 := (or #7626 #7965)
-#7971 := (or #7956 #7968)
-#7975 := (iff #7971 #7974)
-#7976 := [rewrite]: #7975
-#7972 := (iff #7957 #7971)
-#7969 := (iff #7948 #7968)
-#7966 := (iff #7942 #7965)
-#7967 := [rewrite]: #7966
-#7627 := (iff #7590 #7626)
-#7624 := (iff #1372 #7623)
-#7621 := (iff #1371 #7620)
-#7622 := [rewrite]: #7621
-#7625 := [monotonicity #4042 #7622]: #7624
-#7628 := [monotonicity #7625]: #7627
-#7970 := [monotonicity #7628 #7967]: #7969
-#7973 := [monotonicity #7970]: #7972
-#7978 := [trans #7973 #7976]: #7977
-#7981 := [quant-intro #7978]: #7980
-#7963 := (iff #1493 #7962)
-#7960 := (iff #1492 #7957)
-#7953 := (implies #7921 #7948)
-#7958 := (iff #7953 #7957)
-#7959 := [rewrite]: #7958
-#7954 := (iff #1492 #7953)
-#7951 := (iff #1491 #7948)
-#7945 := (implies #1372 #7942)
-#7949 := (iff #7945 #7948)
-#7950 := [rewrite]: #7949
-#7946 := (iff #1491 #7945)
-#7943 := (iff #1490 #7942)
-#7940 := (iff #1489 #7939)
-#7937 := (iff #1488 #7936)
-#7934 := (iff #1487 #7933)
-#7935 := [rewrite]: #7934
-#7938 := [monotonicity #7935]: #7937
-#7931 := (iff #1484 #7930)
-#7928 := (iff #1483 #7927)
-#7929 := [rewrite]: #7928
-#7932 := [monotonicity #7929]: #7931
-#7941 := [monotonicity #7932 #7938]: #7940
-#7925 := (iff #1481 #7924)
-#7926 := [rewrite]: #7925
-#7944 := [monotonicity #7926 #7941]: #7943
-#7947 := [monotonicity #7944]: #7946
-#7952 := [trans #7947 #7950]: #7951
-#7922 := (iff #1477 #7921)
-#7923 := [rewrite]: #7922
-#7955 := [monotonicity #7923 #7952]: #7954
-#7961 := [trans #7955 #7959]: #7960
-#7964 := [quant-intro #7961]: #7963
-#7983 := [trans #7964 #7981]: #7982
-#7920 := [asserted]: #1493
-#7984 := [mp #7920 #7983]: #7979
-#16826 := [mp~ #7984 #16825]: #7979
-#20706 := [mp #16826 #20705]: #20703
-#27469 := (not #20703)
-#27470 := (or #27469 #26943 #26961 #26969)
-#26939 := (or #26938 #26936 #26933 #26930)
-#26940 := (not #26939)
-#26949 := (or #26948 #26946 #26943 #26940)
-#27471 := (or #27469 #26949)
-#27516 := (iff #27471 #27470)
-#26975 := (or #26943 #26961 #26969)
-#27517 := (or #27469 #26975)
-#27520 := (iff #27517 #27470)
-#27521 := [rewrite]: #27520
-#27518 := (iff #27471 #27517)
-#26978 := (iff #26949 #26975)
-#26972 := (or false #26961 #26943 #26969)
-#26976 := (iff #26972 #26975)
-#26977 := [rewrite]: #26976
-#26973 := (iff #26949 #26972)
-#26970 := (iff #26940 #26969)
-#26967 := (iff #26939 #26966)
-#26968 := [rewrite]: #26967
-#26971 := [monotonicity #26968]: #26970
-#26974 := [monotonicity #26955 #26965 #26971]: #26973
-#26979 := [trans #26974 #26977]: #26978
-#27519 := [monotonicity #26979]: #27518
-#27522 := [trans #27519 #27521]: #27516
-#27472 := [quant-inst]: #27471
-#27523 := [mp #27472 #27522]: #27470
-#28300 := [unit-resolution #27523 #20706 #26991]: #28299
-#28301 := [unit-resolution #28300 #28298]: #26969
-#27540 := (or #26966 #26935)
-#27541 := [def-axiom]: #27540
-#28302 := [unit-resolution #27541 #28301]: #26935
-#28345 := [symm #28302]: #28344
-#28342 := (= #27079 #26934)
-#28340 := (= #26756 #26931)
-#28338 := (= #26931 #26756)
-#28336 := (= #26927 #3031)
-#28326 := (= #26845 #3031)
-#28327 := [symm #28125]: #28326
-#28334 := (= #26927 #26845)
-#28324 := (= #26867 #26845)
-#28325 := [symm #27634]: #28324
-#28332 := (= #26927 #26867)
-#28250 := (= #2979 #26867)
-#28323 := [symm #28126]: #28250
-#28330 := (= #26927 #2979)
-#27108 := (uf_116 #25933)
-#27122 := (uf_43 #24643 #27108)
-#28321 := (= #27122 #2979)
-#28313 := (= #27108 uf_288)
-#28311 := (= #27108 #2980)
-#28309 := (= #24545 #2980)
-#24769 := (= #2980 #24545)
-#24774 := (or #24716 #24769)
-#24775 := [quant-inst]: #24774
-#28303 := [unit-resolution #24775 #22943]: #24769
-#28310 := [symm #28303]: #28309
-#28307 := (= #27108 #24545)
-#28308 := [monotonicity #28306]: #28307
-#28312 := [trans #28308 #28310]: #28311
-#28314 := [trans #28312 #28195]: #28313
-#28322 := [monotonicity #28190 #28314]: #28321
-#28328 := (= #26927 #27122)
-#27104 := (uf_66 #25933 0::int #24643)
-#27125 := (= #27104 #27122)
-#27128 := (not #27125)
-#27105 := (uf_138 #27104 #25933)
-#27106 := (= uf_9 #27105)
-#27107 := (not #27106)
-#27134 := (or #27107 #27128)
-#27139 := (not #27134)
-#28084 := (or #26887 #27139)
-#27109 := (+ #27108 #26850)
-#27110 := (uf_43 #24643 #27109)
-#27111 := (= #27104 #27110)
-#27112 := (not #27111)
-#27113 := (or #27112 #27107)
-#27114 := (not #27113)
-#28069 := (or #26887 #27114)
-#28068 := (iff #28069 #28084)
-#28088 := (iff #28084 #28084)
-#28073 := [rewrite]: #28088
-#27140 := (iff #27114 #27139)
-#27137 := (iff #27113 #27134)
-#27131 := (or #27128 #27107)
-#27135 := (iff #27131 #27134)
-#27136 := [rewrite]: #27135
-#27132 := (iff #27113 #27131)
-#27129 := (iff #27112 #27128)
-#27126 := (iff #27111 #27125)
-#27123 := (= #27110 #27122)
-#27120 := (= #27109 #27108)
-#27115 := (+ #27108 0::int)
-#27118 := (= #27115 #27108)
-#27119 := [rewrite]: #27118
-#27116 := (= #27109 #27115)
-#27117 := [monotonicity #26859]: #27116
-#27121 := [trans #27117 #27119]: #27120
-#27124 := [monotonicity #27121]: #27123
-#27127 := [monotonicity #27124]: #27126
-#27130 := [monotonicity #27127]: #27129
-#27133 := [monotonicity #27130]: #27132
-#27138 := [trans #27133 #27136]: #27137
-#27141 := [monotonicity #27138]: #27140
-#28067 := [monotonicity #27141]: #28068
-#28074 := [trans #28067 #28073]: #28068
-#28070 := [quant-inst]: #28069
-#28075 := [mp #28070 #28074]: #28084
-#28315 := [unit-resolution #28075 #20922]: #27139
-#28124 := (or #27134 #27125)
-#28149 := [def-axiom]: #28124
-#28316 := [unit-resolution #28149 #28315]: #27125
-#28319 := (= #26927 #27104)
-#28320 := [monotonicity #28318]: #28319
-#28329 := [trans #28320 #28316]: #28328
-#28331 := [trans #28329 #28322]: #28330
-#28333 := [trans #28331 #28323]: #28332
-#28335 := [trans #28333 #28325]: #28334
-#28337 := [trans #28335 #28327]: #28336
+#27231 := [monotonicity #27199 #27245]: #27230
+#27234 := [monotonicity #27231]: #27233
+#27298 := [monotonicity #27234 #27292]: #27294
+#27303 := [monotonicity #27298]: #27300
+#27331 := [monotonicity #27303]: #27305
+#27334 := [monotonicity #27331]: #27333
+#27321 := [monotonicity #27334]: #27336
+#27326 := [monotonicity #27321]: #27320
+#27329 := [trans #27326 #27328]: #27320
+#27325 := [quant-inst]: #27324
+#27330 := [mp #27325 #27329]: #27323
+#26980 := [unit-resolution #27330 #21978]: #27335
+#27510 := (not #27335)
+#26982 := (or #27510 #27304)
+#26981 := [hypothesis]: #18338
+#27511 := (or #27510 #12098 #27304)
+#27506 := [def-axiom]: #27511
+#27114 := [unit-resolution #27506 #26981]: #26982
+#27206 := [unit-resolution #27114 #26980]: #27304
+#27208 := (or #27332 #27299)
+#27207 := [unit-resolution #27110 #28266]: #12092
+#27508 := (or #27332 #18332 #27299)
+#27509 := [def-axiom]: #27508
+#27209 := [unit-resolution #27509 #27207]: #27208
+#27210 := [unit-resolution #27209 #27206]: #27299
+#27474 := (or #27293 #27280)
+#27477 := [def-axiom]: #27474
+#27248 := [unit-resolution #27477 #27210]: #27280
+#27613 := (not #27066)
+#27523 := (iff #27613 #27145)
+#27521 := (iff #27066 #27144)
+#27519 := (= #27065 #27143)
+#27254 := (= #27064 #26824)
+#27255 := [monotonicity #27059]: #27254
+#27520 := [monotonicity #27255]: #27519
+#27522 := [monotonicity #27520]: #27521
+#27524 := [monotonicity #27522]: #27523
+#27614 := (or #27079 #27613)
+#27615 := [def-axiom]: #27614
+#27253 := [unit-resolution #27615 #27107]: #27613
+#27525 := [mp #27253 #27524]: #27145
+#27389 := (or #27237 #27144)
+#27390 := [def-axiom]: #27389
+#27526 := [unit-resolution #27390 #27525]: #27237
+#25340 := (f13 f9)
+#28328 := (= #25340 #27142)
+#28324 := (= #27142 #25340)
+#28322 := (= #26878 f9)
+#24951 := (f14 #3007)
+#28320 := (= #24951 f9)
+#24952 := (= f9 #24951)
+#24957 := (or #24903 #24952)
+#24958 := [quant-inst]: #24957
+#28104 := [unit-resolution #24958 #23151]: #24952
+#28321 := [symm #28104]: #28320
+#28318 := (= #26878 #24951)
+#28316 := (= #3063 #3007)
+#26909 := (f117 #24672)
+#26925 := (f44 #24835 #26909)
+#28292 := (= #26925 #3007)
+#28171 := (= #26909 f288)
+#28284 := (= #26909 #3008)
+#28282 := (= #24672 #3007)
+#24673 := (= #3007 #24672)
+#98 := (f30 #28)
+#23050 := (pattern #98)
+#99 := (f29 #98)
+#3598 := (= #28 #99)
+#23051 := (forall (vars (?v0 S5)) (:pat #23050) #3598)
+#3601 := (forall (vars (?v0 S5)) #3598)
+#23052 := (iff #3601 #23051)
+#23054 := (iff #23051 #23051)
+#23055 := [rewrite]: #23054
+#23053 := [rewrite]: #23052
+#23056 := [trans #23053 #23055]: #23052
+#16226 := (~ #3601 #3601)
+#16216 := (~ #3598 #3598)
+#16217 := [refl]: #16216
+#16282 := [nnf-pos #16217]: #16226
+#100 := (= #99 #28)
+#101 := (forall (vars (?v0 S5)) #100)
+#3602 := (iff #101 #3601)
+#3599 := (iff #100 #3598)
+#3600 := [rewrite]: #3599
+#3603 := [quant-intro #3600]: #3602
+#3597 := [asserted]: #101
+#3606 := [mp #3597 #3603]: #3601
+#16283 := [mp~ #3606 #16282]: #3601
+#23057 := [mp #16283 #23056]: #23051
+#24676 := (not #23051)
+#24677 := (or #24676 #24673)
+#24678 := [quant-inst]: #24677
+#28281 := [unit-resolution #24678 #23057]: #24673
+#28283 := [symm #28281]: #28282
+#28285 := [monotonicity #28283]: #28284
+#28179 := [trans #28285 #28230]: #28171
+#28313 := [monotonicity #28225 #28179]: #28292
+#28314 := (= #3063 #26925)
+#26903 := (f67 #24672 0::int #24835)
+#26928 := (= #26903 #26925)
+#26931 := (not #26928)
+decl f139 :: (-> S5 S5 S1)
+#26904 := (f139 #26903 #24672)
+#26905 := (= f1 #26904)
+#26906 := (not #26905)
+#26937 := (or #26906 #26931)
+#26942 := (not #26937)
+#1588 := (f67 #26 #255 #241)
+#1589 := (pattern #1588)
+#1590 := (f139 #1588 #26)
+#8306 := (= f1 #1590)
+#21116 := (not #8306)
+decl f140 :: (-> S3 int)
+#1593 := (f140 #241)
+#1594 := (* #255 #1593)
+#1592 := (f117 #26)
+#1595 := (+ #1592 #1594)
+#1596 := (f44 #241 #1595)
+#1597 := (= #1588 #1596)
+#21115 := (not #1597)
+#21117 := (or #21115 #21116)
+#21118 := (not #21117)
+#21121 := (forall (vars (?v0 S5) (?v1 int) (?v2 S3)) (:pat #1589) #21118)
+#8312 := (and #1597 #8306)
+#8317 := (forall (vars (?v0 S5) (?v1 int) (?v2 S3)) (:pat #1589) #8312)
+#21122 := (iff #8317 #21121)
+#21119 := (iff #8312 #21118)
+#21120 := [rewrite]: #21119
+#21123 := [quant-intro #21120]: #21122
+#17249 := (~ #8317 #8317)
+#17247 := (~ #8312 #8312)
+#17248 := [refl]: #17247
+#17250 := [nnf-pos #17248]: #17249
+#1591 := (= #1590 f1)
+#1598 := (and #1591 #1597)
+#1599 := (forall (vars (?v0 S5) (?v1 int) (?v2 S3)) (:pat #1589) #1598)
+#8318 := (iff #1599 #8317)
+#8315 := (iff #1598 #8312)
+#8309 := (and #8306 #1597)
+#8313 := (iff #8309 #8312)
+#8314 := [rewrite]: #8313
+#8310 := (iff #1598 #8309)
+#8307 := (iff #1591 #8306)
+#8308 := [rewrite]: #8307
+#8311 := [monotonicity #8308]: #8310
+#8316 := [trans #8311 #8314]: #8315
+#8319 := [quant-intro #8316]: #8318
+#8305 := [asserted]: #1599
+#8322 := [mp #8305 #8319]: #8317
+#17251 := [mp~ #8322 #17250]: #8317
+#21124 := [mp #17251 #21123]: #21121
+#26945 := (not #21121)
+#26891 := (or #26945 #26942)
+#26907 := (f140 #24835)
+#26908 := (* 0::int #26907)
+#26910 := (+ #26909 #26908)
+#26911 := (f44 #24835 #26910)
+#26912 := (= #26903 #26911)
+#26913 := (not #26912)
+#26914 := (or #26913 #26906)
+#26915 := (not #26914)
+#26892 := (or #26945 #26915)
+#26977 := (iff #26892 #26891)
+#27052 := (iff #26891 #26891)
+#27055 := [rewrite]: #27052
+#26943 := (iff #26915 #26942)
+#26940 := (iff #26914 #26937)
+#26934 := (or #26931 #26906)
+#26938 := (iff #26934 #26937)
+#26939 := [rewrite]: #26938
+#26935 := (iff #26914 #26934)
+#26932 := (iff #26913 #26931)
+#26929 := (iff #26912 #26928)
+#26926 := (= #26911 #26925)
+#26923 := (= #26910 #26909)
+#26918 := (+ #26909 0::int)
+#26921 := (= #26918 #26909)
+#26922 := [rewrite]: #26921
+#26919 := (= #26910 #26918)
+#26916 := (= #26908 0::int)
+#26917 := [rewrite]: #26916
+#26920 := [monotonicity #26917]: #26919
+#26924 := [trans #26920 #26922]: #26923
+#26927 := [monotonicity #26924]: #26926
+#26930 := [monotonicity #26927]: #26929
+#26933 := [monotonicity #26930]: #26932
+#26936 := [monotonicity #26933]: #26935
+#26941 := [trans #26936 #26939]: #26940
+#26944 := [monotonicity #26941]: #26943
+#27051 := [monotonicity #26944]: #26977
+#27056 := [trans #27051 #27055]: #26977
+#26955 := [quant-inst]: #26892
+#27046 := [mp #26955 #27056]: #26891
+#28306 := [unit-resolution #27046 #21124]: #26942
+#27096 := (or #26937 #26928)
+#27097 := [def-axiom]: #27096
+#28307 := [unit-resolution #27097 #28306]: #26928
+#28296 := (= #3063 #26903)
+#28297 := [monotonicity #28281 #28223]: #28296
+#28315 := [trans #28297 #28307]: #28314
+#28317 := [trans #28315 #28313]: #28316
+#28319 := [monotonicity #28317]: #28318
+#28323 := [trans #28319 #28321]: #28322
+#28325 := [monotonicity #28323]: #28324
+#28329 := [symm #28325]: #28328
+#25341 := (= f15 #25340)
+#25348 := (iff #11533 #25341)
+#2329 := (pattern #245)
+#2867 := (f13 #241)
+#11712 := (= f15 #2867)
+#11716 := (iff #4000 #11712)
+#11719 := (forall (vars (?v0 S3)) (:pat #2329) #11716)
+#18286 := (~ #11719 #11719)
+#18284 := (~ #11716 #11716)
+#18285 := [refl]: #18284
+#18287 := [nnf-pos #18285]: #18286
+#2880 := (= #2867 f15)
+#2881 := (iff #246 #2880)
+#2882 := (forall (vars (?v0 S3)) (:pat #2329) #2881)
+#11720 := (iff #2882 #11719)
+#11717 := (iff #2881 #11716)
+#11714 := (iff #2880 #11712)
+#11715 := [rewrite]: #11714
+#11718 := [monotonicity #4002 #11715]: #11717
+#11721 := [quant-intro #11718]: #11720
+#11711 := [asserted]: #2882
+#11724 := [mp #11711 #11721]: #11719
+#18288 := [mp~ #11724 #18287]: #11719
+#25007 := (not #11719)
+#25351 := (or #25007 #25348)
+#25352 := [quant-inst]: #25351
+#27592 := [unit-resolution #25352 #18288]: #25348
+#25353 := (not #25348)
+#27593 := (or #25353 #25341)
+#25357 := (not #11533)
+#25358 := (or #25353 #25357 #25341)
+#25359 := [def-axiom]: #25358
+#27623 := [unit-resolution #25359 #11539]: #27593
+#27678 := [unit-resolution #27623 #27592]: #25341
+#28330 := [trans #27678 #28329]: #27197
+#27444 := (not #27121)
+#28407 := (iff #12027 #27444)
+#28405 := (iff #12024 #27121)
+#28403 := (iff #27121 #12024)
+#28401 := (= #27123 #3018)
+#28399 := (= #27122 #3005)
+#28395 := (= #27122 #24956)
+#28393 := (= #27130 #3009)
+#28391 := (= #27130 #26984)
+#26985 := (f67 #26984 0::int #24835)
+#26989 := (f59 #3185 #26985)
+#26995 := (f136 #26989)
+#28389 := (= #26995 #26984)
+#26996 := (= #26984 #26995)
+#26997 := (not #26996)
+#26993 := (f137 #26989)
+#26994 := (= f1 #26993)
+#26990 := (f68 #26989)
+#26991 := (= f1 #26990)
+#26992 := (not #26991)
+#26986 := (f25 f287 #26985)
+#26987 := (= f1 #26986)
+#26988 := (not #26987)
+#27025 := (or #26988 #26992 #26994 #26997)
+#27028 := (not #27025)
+#27000 := (f25 f287 #26984)
+#27001 := (= f1 #27000)
+#28341 := (= #3016 #27000)
+#28338 := (= #27000 #3016)
 #28339 := [monotonicity #28337]: #28338
-#28341 := [symm #28339]: #28340
-#28343 := [monotonicity #28341]: #28342
-#28347 := [trans #28343 #28345]: #28346
-#28349 := [trans #28347 #28292]: #28348
-#28351 := [monotonicity #28349]: #28350
-#28355 := [trans #28351 #28353]: #28354
-#28357 := [monotonicity #28355]: #28356
-#28359 := [monotonicity #28357]: #28358
-#28361 := [symm #28359]: #28360
-#28363 := [monotonicity #28361]: #28362
-#28364 := [mp #14078 #28363]: #27341
-#28368 := (= #2984 #27082)
-#28365 := (= #27082 #2984)
-#28366 := [monotonicity #28349]: #28365
-#28369 := [symm #28366]: #28368
-#28370 := [trans #14075 #28369]: #27083
-#27342 := (not #27083)
-#27343 := (or #27189 #27342)
-#27344 := [def-axiom]: #27343
-#28371 := [unit-resolution #27344 #28370]: #27189
-#27399 := (or #27231 #27068 #27181 #27186 #27202)
-#27400 := [def-axiom]: #27399
-#28372 := [unit-resolution #27400 #28371 #28364 #28285 #27477 #27157]: false
-#28374 := [lemma #28372]: #28373
-#28639 := [unit-resolution #28374 #28636]: #11937
-#28640 := (or #23218 #18136 #23212)
-#26821 := (= #24643 #26820)
-#26794 := (uf_48 #3031 #24643)
-#26795 := (= uf_9 #26794)
-#26823 := (iff #26795 #26821)
-#9041 := (= #233 #1390)
-#11161 := (iff #9041 #11140)
-#22931 := (forall (vars (?x712 T5) (?x713 T3)) (:pat #2667) #11161)
-#11166 := (forall (vars (?x712 T5) (?x713 T3)) #11161)
-#22934 := (iff #11166 #22931)
-#22932 := (iff #11161 #11161)
-#22933 := [refl]: #22932
-#22935 := [quant-intro #22933]: #22934
-#17969 := (~ #11166 #11166)
-#17967 := (~ #11161 #11161)
-#17968 := [refl]: #17967
-#17970 := [nnf-pos #17968]: #17969
-#1890 := (= #1390 #233)
-#2673 := (iff #2668 #1890)
-#2674 := (forall (vars (?x712 T5) (?x713 T3)) #2673)
-#11167 := (iff #2674 #11166)
-#11164 := (iff #2673 #11161)
-#11157 := (iff #11140 #9041)
-#11162 := (iff #11157 #11161)
-#11163 := [rewrite]: #11162
-#11159 := (iff #2673 #11157)
-#9042 := (iff #1890 #9041)
-#9043 := [rewrite]: #9042
-#11160 := [monotonicity #11143 #9043]: #11159
-#11165 := [trans #11160 #11163]: #11164
-#11168 := [quant-intro #11165]: #11167
-#11156 := [asserted]: #2674
-#11171 := [mp #11156 #11168]: #11166
-#17971 := [mp~ #11171 #17970]: #11166
-#22936 := [mp #17971 #22935]: #22931
-#25961 := (not #22931)
-#26770 := (or #25961 #26823)
-#26822 := (iff #26821 #26795)
-#26771 := (or #25961 #26822)
-#26809 := (iff #26771 #26770)
-#26816 := (iff #26770 #26770)
-#26817 := [rewrite]: #26816
-#26824 := (iff #26822 #26823)
-#26825 := [rewrite]: #26824
-#26815 := [monotonicity #26825]: #26809
-#26818 := [trans #26815 #26817]: #26809
-#26814 := [quant-inst]: #26771
-#26796 := [mp #26814 #26818]: #26770
-#26798 := [unit-resolution #26796 #22936]: #26823
-#26802 := (not #26795)
-#26827 := (iff #18127 #26802)
-#26893 := (iff #11928 #26795)
-#26842 := (iff #26795 #11928)
-#26840 := (= #26794 #3032)
-#26841 := [monotonicity #28190]: #26840
-#26898 := [monotonicity #26841]: #26842
-#26843 := [symm #26898]: #26893
-#26828 := [monotonicity #26843]: #26827
-#26839 := [hypothesis]: #18127
-#26826 := [mp #26839 #26828]: #26802
-#26829 := (= #24758 #26820)
-#26830 := [symm #28274]: #26829
-#26844 := (= #24643 #24758)
-#26831 := [trans #28190 #27482]: #26844
-#26832 := [trans #26831 #26830]: #26821
-#26797 := (not #26821)
-#26799 := (not #26823)
-#26760 := (or #26799 #26795 #26797)
-#26783 := [def-axiom]: #26760
-#26900 := [unit-resolution #26783 #26832 #26826 #26798]: false
-#26901 := [lemma #26900]: #11928
-#24446 := (or #23218 #18127 #18136 #23212)
-#24447 := [def-axiom]: #24446
-#28641 := [unit-resolution #24447 #26901]: #28640
-#28642 := [unit-resolution #28641 #28639 #28638]: #23212
-#24424 := (or #23209 #3042)
-#24425 := [def-axiom]: #24424
-#28643 := [unit-resolution #24425 #28642]: #3042
-#24436 := (or #23209 #23203)
-#24437 := [def-axiom]: #24436
-#29322 := [unit-resolution #24437 #28642]: #23203
-#28521 := [hypothesis]: #13181
-#28522 := [th-lemma #14069 #28521]: false
-#28523 := [lemma #28522]: #13178
-#24422 := (or #23206 #13181 #23200)
-#24423 := [def-axiom]: #24422
-#29323 := [unit-resolution #24423 #28523 #29322]: #23200
-#24414 := (or #23197 #23191)
-#24415 := [def-axiom]: #24414
-#29332 := [unit-resolution #24415 #29323]: #23191
-#27410 := (* -1::int #3041)
-#27411 := (+ uf_295 #27410)
-#27412 := (>= #27411 0::int)
-#28644 := (or #12976 #27412)
-#28645 := [th-lemma]: #28644
-#28646 := [unit-resolution #28645 #28643]: #27412
-#24092 := (not #18168)
-#28647 := [hypothesis]: #22019
-#24093 := (or #22014 #24092)
-#24094 := [def-axiom]: #24093
-#28648 := [unit-resolution #24094 #28647]: #24092
-#28607 := (+ #3041 #18166)
-#28609 := (>= #28607 0::int)
-#28606 := (= #3041 #18165)
-#28655 := (= #18165 #3041)
-#28653 := (= #18164 #3031)
-#28651 := (= ?x773!13 0::int)
-#24095 := (not #18169)
-#24096 := (or #22014 #24095)
-#24097 := [def-axiom]: #24096
-#28649 := [unit-resolution #24097 #28647]: #24095
-#24090 := (or #22014 #18161)
-#24091 := [def-axiom]: #24090
-#28650 := [unit-resolution #24091 #28647]: #18161
-#28652 := [th-lemma #28650 #28649]: #28651
-#28654 := [monotonicity #28652]: #28653
-#28656 := [monotonicity #28654]: #28655
-#28657 := [symm #28656]: #28606
-#28658 := (not #28606)
-#28659 := (or #28658 #28609)
-#28660 := [th-lemma]: #28659
-#28661 := [unit-resolution #28660 #28657]: #28609
-#28662 := [th-lemma #28661 #28648 #28646]: false
-#28663 := [lemma #28662]: #22014
-#24410 := (or #23194 #22019 #23188)
-#24411 := [def-axiom]: #24410
-#29333 := [unit-resolution #24411 #28663 #29332]: #23188
-#24402 := (or #23185 #23179)
-#24403 := [def-axiom]: #24402
-#29334 := [unit-resolution #24403 #29333]: #23179
-#29335 := (or #23182 #12976 #23176)
-#24398 := (or #23182 #12976 #13217 #23176)
-#24399 := [def-axiom]: #24398
-#29336 := [unit-resolution #24399 #14069]: #29335
-#29337 := [unit-resolution #29336 #29334 #28643]: #23176
-#24388 := (or #23173 #23167)
-#24389 := [def-axiom]: #24388
-#29338 := [unit-resolution #24389 #29337]: #23167
-#24386 := (or #23173 #23009)
-#24387 := [def-axiom]: #24386
-#29339 := [unit-resolution #24387 #29337]: #23009
-#24360 := (or #23173 #11989)
-#24361 := [def-axiom]: #24360
-#29340 := [unit-resolution #24361 #29337]: #11989
-#24382 := (or #23173 #15577)
-#24383 := [def-axiom]: #24382
-#29341 := [unit-resolution #24383 #29337]: #15577
-#24372 := (or #23173 #13689)
-#24373 := [def-axiom]: #24372
-#29342 := [unit-resolution #24373 #29337]: #13689
-#27402 := (uf_13 #26867)
-#27403 := (uf_66 #26867 uf_297 #27402)
-#27404 := (uf_125 #27403 #26867)
-#27485 := (>= #27404 0::int)
-#24368 := (or #23173 #13222)
-#24369 := [def-axiom]: #24368
-#29343 := [unit-resolution #24369 #29337]: #13222
-#27501 := (* -1::int #27404)
-#27574 := (+ uf_297 #27501)
-#27575 := (<= #27574 0::int)
-#27405 := (= uf_297 #27404)
-#28694 := (uf_66 #24470 uf_297 #26903)
-#28695 := (uf_125 #28694 #24470)
-#29365 := (= #28695 #27404)
-#29363 := (= #27404 #28695)
-#29344 := (= #26867 #24470)
-#29345 := [trans #28126 #28241]: #29344
-#29360 := (= #27403 #28694)
-#29358 := (= #3082 #28694)
-#29356 := (= #28694 #3082)
-#29348 := (= #26903 uf_7)
-#29346 := (= #26903 #24758)
-#29347 := [monotonicity #28243]: #29346
-#29349 := [trans #29347 #28276]: #29348
-#29357 := [monotonicity #28243 #29349]: #29356
-#29359 := [symm #29357]: #29358
-#29354 := (= #27403 #3082)
-#29352 := (= #27402 uf_7)
-#29350 := (= #27402 #24758)
-#29351 := [monotonicity #28126]: #29350
-#29353 := [trans #29351 #28276]: #29352
-#29355 := [monotonicity #28126 #29353]: #29354
-#29361 := [trans #29355 #29359]: #29360
-#29364 := [monotonicity #29361 #29345]: #29363
-#29366 := [symm #29364]: #29365
-#28696 := (= uf_297 #28695)
-#28699 := (or #26910 #28696)
-#28700 := [quant-inst]: #28699
-#29362 := [unit-resolution #28700 #16791]: #28696
-#29367 := [trans #29362 #29366]: #27405
-#27913 := (not #27405)
-#29368 := (or #27913 #27575)
-#29369 := [th-lemma]: #29368
-#29370 := [unit-resolution #29369 #29367]: #27575
-#29371 := (not #27575)
-#29372 := (or #27485 #22161 #29371)
-#29373 := [th-lemma]: #29372
-#29374 := [unit-resolution #29373 #29370 #29343]: #27485
-#27486 := (not #27485)
-#27938 := (or #23161 #27486 #13688 #22304 #22299 #23014)
-#27783 := (uf_66 #2979 #27404 uf_7)
-#27784 := (uf_110 uf_287 #27783)
-#27787 := (= uf_302 #27784)
-#27893 := (= #3083 #27784)
-#27906 := (= #27784 #3083)
-#27900 := (= #27783 #3082)
-#27898 := (= #27404 uf_297)
-#27408 := (or #26910 #27405)
-#27409 := [quant-inst]: #27408
-#27897 := [unit-resolution #27409 #16791]: #27405
-#27899 := [symm #27897]: #27898
-#27901 := [monotonicity #27899]: #27900
-#27907 := [monotonicity #27901]: #27906
-#27908 := [symm #27907]: #27893
-#27909 := (= uf_302 #3083)
-#27902 := [hypothesis]: #11989
-#27903 := [hypothesis]: #23164
-#24328 := (or #23161 #12017)
-#24329 := [def-axiom]: #24328
-#27904 := [unit-resolution #24329 #27903]: #12017
-#27905 := [symm #27904]: #3097
-#27910 := [trans #27905 #27902]: #27909
-#27911 := [trans #27910 #27908]: #27787
-#27768 := (<= #27404 4294967295::int)
-#27912 := [hypothesis]: #15577
-#27576 := (>= #27574 0::int)
-#27914 := (or #27913 #27576)
-#27915 := [th-lemma]: #27914
-#27916 := [unit-resolution #27915 #27897]: #27576
-#27917 := (not #27576)
-#27918 := (or #27768 #22304 #27917)
-#27919 := [th-lemma]: #27918
-#27920 := [unit-resolution #27919 #27916 #27912]: #27768
-#27810 := (+ uf_286 #27501)
-#27811 := (<= #27810 0::int)
-#27922 := (not #27811)
-#27921 := [hypothesis]: #13689
-#27923 := (or #27922 #13688 #27917)
-#27924 := [th-lemma]: #27923
-#27925 := [unit-resolution #27924 #27916 #27921]: #27922
-#27790 := (not #27787)
-#27769 := (not #27768)
-#27935 := (or #27769 #27790 #27811)
-#27926 := [hypothesis]: #27485
-#24336 := (or #23161 #23155)
-#24337 := [def-axiom]: #24336
-#27927 := [unit-resolution #24337 #27903]: #23155
-#27580 := (+ uf_296 #13550)
-#27583 := (<= #27580 0::int)
-#27928 := (or #12052 #27583)
-#27929 := [th-lemma]: #27928
-#27930 := [unit-resolution #27929 #27904]: #27583
-#27834 := [hypothesis]: #23009
-#24334 := (or #23161 #13510)
-#24335 := [def-axiom]: #24334
-#27931 := [unit-resolution #24335 #27903]: #13510
-#27825 := (not #27583)
-#27840 := (or #22270 #13511 #23014 #27825)
-#27828 := [hypothesis]: #13510
-#27651 := (+ uf_298 #18758)
-#27652 := (<= #27651 0::int)
-#27663 := (+ uf_296 #18771)
-#27664 := (>= #27663 0::int)
-#27824 := (not #27664)
-#27818 := [hypothesis]: #27583
-#24311 := (not #18773)
-#27829 := [hypothesis]: #22275
-#24312 := (or #22270 #24311)
-#24313 := [def-axiom]: #24312
-#27830 := [unit-resolution #24313 #27829]: #24311
-#27826 := (or #27824 #18773 #27825)
-#27819 := [hypothesis]: #24311
-#27822 := [hypothesis]: #27664
-#27823 := [th-lemma #27822 #27819 #27818]: false
-#27827 := [lemma #27823]: #27826
-#27831 := [unit-resolution #27827 #27830 #27818]: #27824
-#27835 := (or #27652 #27664)
-#24306 := (or #22270 #18422)
-#24307 := [def-axiom]: #24306
-#27832 := [unit-resolution #24307 #27829]: #18422
-#24304 := (or #22270 #18421)
-#24305 := [def-axiom]: #24304
-#27833 := [unit-resolution #24305 #27829]: #18421
-#27677 := (or #23014 #22254 #22255 #27652 #27664)
-#27640 := (+ #18426 #13715)
-#27641 := (<= #27640 0::int)
-#27642 := (+ ?x776!15 #13246)
-#27643 := (>= #27642 0::int)
-#27644 := (or #22255 #27643 #27641 #22254)
-#27678 := (or #23014 #27644)
-#27685 := (iff #27678 #27677)
-#27672 := (or #22254 #22255 #27652 #27664)
-#27680 := (or #23014 #27672)
-#27683 := (iff #27680 #27677)
-#27684 := [rewrite]: #27683
-#27681 := (iff #27678 #27680)
-#27675 := (iff #27644 #27672)
-#27669 := (or #22255 #27652 #27664 #22254)
-#27673 := (iff #27669 #27672)
-#27674 := [rewrite]: #27673
-#27670 := (iff #27644 #27669)
-#27667 := (iff #27641 #27664)
-#27657 := (+ #13715 #18426)
-#27660 := (<= #27657 0::int)
-#27665 := (iff #27660 #27664)
-#27666 := [rewrite]: #27665
-#27661 := (iff #27641 #27660)
-#27658 := (= #27640 #27657)
-#27659 := [rewrite]: #27658
-#27662 := [monotonicity #27659]: #27661
-#27668 := [trans #27662 #27666]: #27667
-#27655 := (iff #27643 #27652)
-#27645 := (+ #13246 ?x776!15)
-#27648 := (>= #27645 0::int)
-#27653 := (iff #27648 #27652)
-#27654 := [rewrite]: #27653
-#27649 := (iff #27643 #27648)
-#27646 := (= #27642 #27645)
-#27647 := [rewrite]: #27646
-#27650 := [monotonicity #27647]: #27649
-#27656 := [trans #27650 #27654]: #27655
-#27671 := [monotonicity #27656 #27668]: #27670
-#27676 := [trans #27671 #27674]: #27675
-#27682 := [monotonicity #27676]: #27681
-#27686 := [trans #27682 #27684]: #27685
-#27679 := [quant-inst]: #27678
-#27687 := [mp #27679 #27686]: #27677
-#27836 := [unit-resolution #27687 #27834 #27833 #27832]: #27835
-#27837 := [unit-resolution #27836 #27831]: #27652
-#24308 := (not #18760)
-#24309 := (or #22270 #24308)
-#24310 := [def-axiom]: #24309
-#27838 := [unit-resolution #24310 #27829]: #24308
-#27839 := [th-lemma #27838 #27837 #27828]: false
-#27841 := [lemma #27839]: #27840
-#27932 := [unit-resolution #27841 #27931 #27834 #27930]: #22270
-#24320 := (or #23158 #23152 #22275)
-#24321 := [def-axiom]: #24320
-#27933 := [unit-resolution #24321 #27932 #27927]: #23152
-#24300 := (or #23149 #23141)
-#24301 := [def-axiom]: #24300
-#27934 := [unit-resolution #24301 #27933]: #23141
-#27847 := (or #23146 #27486 #27769 #27790 #27811)
-#27774 := (+ #27404 #13151)
-#27775 := (>= #27774 0::int)
-#27782 := (= #27784 uf_302)
-#27785 := (not #27782)
-#27786 := (or #27785 #27486 #27775 #27769)
-#27848 := (or #23146 #27786)
-#27855 := (iff #27848 #27847)
-#27842 := (or #27486 #27769 #27790 #27811)
-#27850 := (or #23146 #27842)
-#27853 := (iff #27850 #27847)
-#27854 := [rewrite]: #27853
-#27851 := (iff #27848 #27850)
-#27845 := (iff #27786 #27842)
-#27791 := (or #27790 #27486 #27811 #27769)
-#27843 := (iff #27791 #27842)
-#27844 := [rewrite]: #27843
-#27792 := (iff #27786 #27791)
-#27821 := (iff #27775 #27811)
-#27805 := (+ #13151 #27404)
-#27802 := (>= #27805 0::int)
-#27812 := (iff #27802 #27811)
-#27820 := [rewrite]: #27812
-#27808 := (iff #27775 #27802)
-#27806 := (= #27774 #27805)
-#27807 := [rewrite]: #27806
-#27809 := [monotonicity #27807]: #27808
-#27723 := [trans #27809 #27820]: #27821
-#27803 := (iff #27785 #27790)
-#27788 := (iff #27782 #27787)
-#27789 := [rewrite]: #27788
-#27804 := [monotonicity #27789]: #27803
-#27815 := [monotonicity #27804 #27723]: #27792
-#27846 := [trans #27815 #27844]: #27845
-#27852 := [monotonicity #27846]: #27851
-#27856 := [trans #27852 #27854]: #27855
-#27849 := [quant-inst]: #27848
-#27857 := [mp #27849 #27856]: #27847
-#27936 := [unit-resolution #27857 #27934 #27926]: #27935
-#27937 := [unit-resolution #27936 #27925 #27920 #27911]: false
-#27939 := [lemma #27937]: #27938
-#29375 := [unit-resolution #27939 #29374 #29342 #29341 #29340 #29339]: #23161
-#24344 := (or #23170 #23130 #23164)
-#24345 := [def-axiom]: #24344
-#29376 := [unit-resolution #24345 #29375 #29338]: #23130
-#24292 := (or #23127 #13511)
+#28342 := [symm #28339]: #28341
+#28343 := [trans #14277 #28342]: #27001
+#27002 := (not #27001)
+#28344 := (or #27002 #27028)
+#285 := (:var 3 int)
+#319 := (:var 2 S3)
+#1479 := (f125 #319 #255)
+#1480 := (f44 #1479 #285)
+#1476 := (f44 #319 #285)
+#1477 := (f67 #1476 #168 #319)
+#40 := (:var 4 S4)
+#1482 := (f60 #40)
+#1483 := (f59 #1482 #1477)
+#1484 := (pattern #1483 #1480)
+#1475 := (f42 #40)
+#1478 := (f41 #1475 #1477)
+#1481 := (pattern #1478 #1480)
+#1487 := (f67 #1480 #168 #319)
+#1496 := (f25 #40 #1487)
+#8011 := (= f1 #1496)
+#20892 := (not #8011)
+#1488 := (f59 #1482 #1487)
+#1494 := (f68 #1488)
+#8008 := (= f1 #1494)
+#20891 := (not #8008)
+#1491 := (f137 #1488)
+#8002 := (= f1 #1491)
+#1489 := (f136 #1488)
+#7999 := (= #1480 #1489)
+#20890 := (not #7999)
+#20893 := (or #20890 #8002 #20891 #20892)
+#20894 := (not #20893)
+#1485 := (f25 #40 #1480)
+#7996 := (= f1 #1485)
+#8034 := (not #7996)
+#5311 := (* -1::int #255)
+#6191 := (+ #168 #5311)
+#6192 := (>= #6191 0::int)
+#20900 := (or #5040 #6192 #8034 #20894)
+#20905 := (forall (vars (?v0 S4) (?v1 int) (?v2 S3) (?v3 int) (?v4 int)) (:pat #1481 #1484) #20900)
+#8005 := (not #8002)
+#8043 := (and #7999 #8005 #8008 #8011)
+#7695 := (not #6192)
+#7698 := (and #4118 #7695)
+#7701 := (not #7698)
+#8052 := (or #7701 #8034 #8043)
+#8057 := (forall (vars (?v0 S4) (?v1 int) (?v2 S3) (?v3 int) (?v4 int)) (:pat #1481 #1484) #8052)
+#20906 := (iff #8057 #20905)
+#20903 := (iff #8052 #20900)
+#20775 := (or #5040 #6192)
+#20897 := (or #20775 #8034 #20894)
+#20901 := (iff #20897 #20900)
+#20902 := [rewrite]: #20901
+#20898 := (iff #8052 #20897)
+#20895 := (iff #8043 #20894)
+#20896 := [rewrite]: #20895
+#20784 := (iff #7701 #20775)
+#20776 := (not #20775)
+#20779 := (not #20776)
+#20782 := (iff #20779 #20775)
+#20783 := [rewrite]: #20782
+#20780 := (iff #7701 #20779)
+#20777 := (iff #7698 #20776)
+#20778 := [rewrite]: #20777
+#20781 := [monotonicity #20778]: #20780
+#20785 := [trans #20781 #20783]: #20784
+#20899 := [monotonicity #20785 #20896]: #20898
+#20904 := [trans #20899 #20902]: #20903
+#20907 := [quant-intro #20904]: #20906
+#17024 := (~ #8057 #8057)
+#17022 := (~ #8052 #8052)
+#17023 := [refl]: #17022
+#17025 := [nnf-pos #17023]: #17024
+#1497 := (= #1496 f1)
+#1495 := (= #1494 f1)
+#1498 := (and #1495 #1497)
+#1492 := (= #1491 f1)
+#1493 := (not #1492)
+#1499 := (and #1493 #1498)
+#1490 := (= #1489 #1480)
+#1500 := (and #1490 #1499)
+#1380 := (< #168 #255)
+#1381 := (and #293 #1380)
+#1501 := (implies #1381 #1500)
+#1486 := (= #1485 f1)
+#1502 := (implies #1486 #1501)
+#1503 := (forall (vars (?v0 S4) (?v1 int) (?v2 S3) (?v3 int) (?v4 int)) (:pat #1481 #1484) #1502)
+#8060 := (iff #1503 #8057)
+#8014 := (and #8008 #8011)
+#8017 := (and #8005 #8014)
+#8020 := (and #7999 #8017)
+#7665 := (not #1381)
+#8026 := (or #7665 #8020)
+#8035 := (or #8034 #8026)
+#8040 := (forall (vars (?v0 S4) (?v1 int) (?v2 S3) (?v3 int) (?v4 int)) (:pat #1481 #1484) #8035)
+#8058 := (iff #8040 #8057)
+#8055 := (iff #8035 #8052)
+#8046 := (or #7701 #8043)
+#8049 := (or #8034 #8046)
+#8053 := (iff #8049 #8052)
+#8054 := [rewrite]: #8053
+#8050 := (iff #8035 #8049)
+#8047 := (iff #8026 #8046)
+#8044 := (iff #8020 #8043)
+#8045 := [rewrite]: #8044
+#7702 := (iff #7665 #7701)
+#7699 := (iff #1381 #7698)
+#7696 := (iff #1380 #7695)
+#7697 := [rewrite]: #7696
+#7700 := [monotonicity #4117 #7697]: #7699
+#7703 := [monotonicity #7700]: #7702
+#8048 := [monotonicity #7703 #8045]: #8047
+#8051 := [monotonicity #8048]: #8050
+#8056 := [trans #8051 #8054]: #8055
+#8059 := [quant-intro #8056]: #8058
+#8041 := (iff #1503 #8040)
+#8038 := (iff #1502 #8035)
+#8031 := (implies #7996 #8026)
+#8036 := (iff #8031 #8035)
+#8037 := [rewrite]: #8036
+#8032 := (iff #1502 #8031)
+#8029 := (iff #1501 #8026)
+#8023 := (implies #1381 #8020)
+#8027 := (iff #8023 #8026)
+#8028 := [rewrite]: #8027
+#8024 := (iff #1501 #8023)
+#8021 := (iff #1500 #8020)
+#8018 := (iff #1499 #8017)
+#8015 := (iff #1498 #8014)
+#8012 := (iff #1497 #8011)
+#8013 := [rewrite]: #8012
+#8009 := (iff #1495 #8008)
+#8010 := [rewrite]: #8009
+#8016 := [monotonicity #8010 #8013]: #8015
+#8006 := (iff #1493 #8005)
+#8003 := (iff #1492 #8002)
+#8004 := [rewrite]: #8003
+#8007 := [monotonicity #8004]: #8006
+#8019 := [monotonicity #8007 #8016]: #8018
+#8000 := (iff #1490 #7999)
+#8001 := [rewrite]: #8000
+#8022 := [monotonicity #8001 #8019]: #8021
+#8025 := [monotonicity #8022]: #8024
+#8030 := [trans #8025 #8028]: #8029
+#7997 := (iff #1486 #7996)
+#7998 := [rewrite]: #7997
+#8033 := [monotonicity #7998 #8030]: #8032
+#8039 := [trans #8033 #8037]: #8038
+#8042 := [quant-intro #8039]: #8041
+#8061 := [trans #8042 #8059]: #8060
+#7995 := [asserted]: #1503
+#8062 := [mp #7995 #8061]: #8057
+#17026 := [mp~ #8062 #17025]: #8057
+#20908 := [mp #17026 #20907]: #20905
+#27566 := (not #20905)
+#27567 := (or #27566 #27002 #27020 #27028)
+#26998 := (or #26997 #26994 #26992 #26988)
+#26999 := (not #26998)
+#27008 := (or #27007 #27005 #27002 #26999)
+#27568 := (or #27566 #27008)
+#27583 := (iff #27568 #27567)
+#27034 := (or #27002 #27020 #27028)
+#27570 := (or #27566 #27034)
+#27584 := (iff #27570 #27567)
+#27585 := [rewrite]: #27584
+#27575 := (iff #27568 #27570)
+#27037 := (iff #27008 #27034)
+#27031 := (or false #27020 #27002 #27028)
+#27035 := (iff #27031 #27034)
+#27036 := [rewrite]: #27035
+#27032 := (iff #27008 #27031)
+#27029 := (iff #26999 #27028)
+#27026 := (iff #26998 #27025)
+#27027 := [rewrite]: #27026
+#27030 := [monotonicity #27027]: #27029
+#27033 := [monotonicity #27014 #27024 #27030]: #27032
+#27038 := [trans #27033 #27036]: #27037
+#27576 := [monotonicity #27038]: #27575
+#27586 := [trans #27576 #27585]: #27583
+#27569 := [quant-inst]: #27568
+#27587 := [mp #27569 #27586]: #27567
+#28345 := [unit-resolution #27587 #20908 #27050]: #28344
+#28346 := [unit-resolution #28345 #28343]: #27028
+#27610 := (or #27025 #26996)
+#27611 := [def-axiom]: #27610
+#28347 := [unit-resolution #27611 #28346]: #26996
+#28390 := [symm #28347]: #28389
+#28387 := (= #27130 #26995)
+#28385 := (= #26824 #26989)
+#28383 := (= #26989 #26824)
+#28381 := (= #26985 #3063)
+#28371 := (= #26903 #3063)
+#28372 := [symm #28297]: #28371
+#28379 := (= #26985 #26903)
+#28369 := (= #26925 #26903)
+#28370 := [symm #28307]: #28369
+#28377 := (= #26985 #26925)
+#28290 := (= #3007 #26925)
+#28368 := [symm #28313]: #28290
+#28375 := (= #26985 #3007)
+#27157 := (f117 #26021)
+#27171 := (f44 #24835 #27157)
+#28366 := (= #27171 #3007)
+#28358 := (= #27157 f288)
+#28356 := (= #27157 #3008)
+#28354 := (= #24719 #3008)
+#24962 := (= #3008 #24719)
+#24967 := (or #24909 #24962)
+#24968 := [quant-inst]: #24967
+#28348 := [unit-resolution #24968 #23145]: #24962
+#28355 := [symm #28348]: #28354
+#28352 := (= #27157 #24719)
+#28353 := [monotonicity #28351]: #28352
+#28357 := [trans #28353 #28355]: #28356
+#28359 := [trans #28357 #28230]: #28358
+#28367 := [monotonicity #28225 #28359]: #28366
+#28373 := (= #26985 #27171)
+#27153 := (f67 #26021 0::int #24835)
+#27174 := (= #27153 #27171)
+#27177 := (not #27174)
+#27154 := (f139 #27153 #26021)
+#27155 := (= f1 #27154)
+#27156 := (not #27155)
+#27183 := (or #27156 #27177)
+#27188 := (not #27183)
+#28107 := (or #26945 #27188)
+#27158 := (+ #27157 #26908)
+#27159 := (f44 #24835 #27158)
+#27160 := (= #27153 #27159)
+#27161 := (not #27160)
+#27162 := (or #27161 #27156)
+#27163 := (not #27162)
+#28159 := (or #26945 #27163)
+#28161 := (iff #28159 #28107)
+#28165 := (iff #28107 #28107)
+#28170 := [rewrite]: #28165
+#27189 := (iff #27163 #27188)
+#27186 := (iff #27162 #27183)
+#27180 := (or #27177 #27156)
+#27184 := (iff #27180 #27183)
+#27185 := [rewrite]: #27184
+#27181 := (iff #27162 #27180)
+#27178 := (iff #27161 #27177)
+#27175 := (iff #27160 #27174)
+#27172 := (= #27159 #27171)
+#27169 := (= #27158 #27157)
+#27164 := (+ #27157 0::int)
+#27167 := (= #27164 #27157)
+#27168 := [rewrite]: #27167
+#27165 := (= #27158 #27164)
+#27166 := [monotonicity #26917]: #27165
+#27170 := [trans #27166 #27168]: #27169
+#27173 := [monotonicity #27170]: #27172
+#27176 := [monotonicity #27173]: #27175
+#27179 := [monotonicity #27176]: #27178
+#27182 := [monotonicity #27179]: #27181
+#27187 := [trans #27182 #27185]: #27186
+#27190 := [monotonicity #27187]: #27189
+#28164 := [monotonicity #27190]: #28161
+#28201 := [trans #28164 #28170]: #28161
+#28160 := [quant-inst]: #28159
+#28202 := [mp #28160 #28201]: #28107
+#28360 := [unit-resolution #28202 #21124]: #27188
+#28204 := (or #27183 #27174)
+#28200 := [def-axiom]: #28204
+#28361 := [unit-resolution #28200 #28360]: #27174
+#28364 := (= #26985 #27153)
+#28365 := [monotonicity #28363]: #28364
+#28374 := [trans #28365 #28361]: #28373
+#28376 := [trans #28374 #28367]: #28375
+#28378 := [trans #28376 #28368]: #28377
+#28380 := [trans #28378 #28370]: #28379
+#28382 := [trans #28380 #28372]: #28381
+#28384 := [monotonicity #28382]: #28383
+#28386 := [symm #28384]: #28385
+#28388 := [monotonicity #28386]: #28387
+#28392 := [trans #28388 #28390]: #28391
+#28394 := [trans #28392 #28337]: #28393
+#28396 := [monotonicity #28394]: #28395
+#28400 := [trans #28396 #28398]: #28399
+#28402 := [monotonicity #28400]: #28401
+#28404 := [monotonicity #28402]: #28403
+#28406 := [symm #28404]: #28405
+#28408 := [monotonicity #28406]: #28407
+#28409 := [mp #14278 #28408]: #27444
+#28413 := (= #3012 #27133)
+#28410 := (= #27133 #3012)
+#28411 := [monotonicity #28394]: #28410
+#28414 := [symm #28411]: #28413
+#28415 := [trans #14275 #28414]: #27134
+#27395 := (not #27134)
+#27440 := (or #27271 #27395)
+#27441 := [def-axiom]: #27440
+#28416 := [unit-resolution #27441 #28415]: #27271
+#27438 := (or #27291 #27121 #27229 #27250 #27275)
+#27439 := [def-axiom]: #27438
+#28417 := [unit-resolution #27439 #28416 #28409 #28330 #27526 #27248]: false
+#28419 := [lemma #28417]: #28418
+#28684 := [unit-resolution #28419 #28681]: #12098
+#28685 := (or #23420 #18338 #23414)
+#26879 := (= #24835 #26878)
+#26852 := (f49 #3063 #24835)
+#26853 := (= f1 #26852)
+#26881 := (iff #26853 #26879)
+#9136 := (= #241 #1399)
+#11299 := (iff #9136 #11278)
+#23133 := (forall (vars (?v0 S5) (?v1 S3)) (:pat #2695) #11299)
+#11304 := (forall (vars (?v0 S5) (?v1 S3)) #11299)
+#23136 := (iff #11304 #23133)
+#23134 := (iff #11299 #11299)
+#23135 := [refl]: #23134
+#23137 := [quant-intro #23135]: #23136
+#18171 := (~ #11304 #11304)
+#18169 := (~ #11299 #11299)
+#18170 := [refl]: #18169
+#18172 := [nnf-pos #18170]: #18171
+#1905 := (= #1399 #241)
+#2701 := (iff #2696 #1905)
+#2702 := (forall (vars (?v0 S5) (?v1 S3)) #2701)
+#11305 := (iff #2702 #11304)
+#11302 := (iff #2701 #11299)
+#11295 := (iff #11278 #9136)
+#11300 := (iff #11295 #11299)
+#11301 := [rewrite]: #11300
+#11297 := (iff #2701 #11295)
+#9137 := (iff #1905 #9136)
+#9138 := [rewrite]: #9137
+#11298 := [monotonicity #11281 #9138]: #11297
+#11303 := [trans #11298 #11301]: #11302
+#11306 := [quant-intro #11303]: #11305
+#11294 := [asserted]: #2702
+#11309 := [mp #11294 #11306]: #11304
+#18173 := [mp~ #11309 #18172]: #11304
+#23138 := [mp #18173 #23137]: #23133
+#26049 := (not #23133)
+#26872 := (or #26049 #26881)
+#26880 := (iff #26879 #26853)
+#26867 := (or #26049 #26880)
+#26874 := (iff #26867 #26872)
+#26876 := (iff #26872 #26872)
+#26828 := [rewrite]: #26876
+#26882 := (iff #26880 #26881)
+#26883 := [rewrite]: #26882
+#26875 := [monotonicity #26883]: #26874
+#26857 := [trans #26875 #26828]: #26874
+#26873 := [quant-inst]: #26867
+#26827 := [mp #26873 #26857]: #26872
+#26956 := [unit-resolution #26827 #23138]: #26881
+#26860 := (not #26853)
+#26902 := (iff #18329 #26860)
+#26887 := (iff #12089 #26853)
+#26886 := (iff #26853 #12089)
+#26901 := (= #26852 #3064)
+#26885 := [monotonicity #28225]: #26901
+#26884 := [monotonicity #26885]: #26886
+#26888 := [symm #26884]: #26887
+#26889 := [monotonicity #26888]: #26902
+#26951 := [hypothesis]: #18329
+#26890 := [mp #26951 #26889]: #26860
+#26958 := (= #24951 #26878)
+#26959 := [symm #28319]: #26958
+#26957 := (= #24835 #24951)
+#26960 := [trans #28225 #28104]: #26957
+#26947 := [trans #26960 #26959]: #26879
+#26845 := (not #26879)
+#26858 := (not #26881)
+#26843 := (or #26858 #26853 #26845)
+#26844 := [def-axiom]: #26843
+#26948 := [unit-resolution #26844 #26947 #26890 #26956]: false
+#26946 := [lemma #26948]: #12089
+#24648 := (or #23420 #18329 #18338 #23414)
+#24649 := [def-axiom]: #24648
+#28686 := [unit-resolution #24649 #26946]: #28685
+#28687 := [unit-resolution #28686 #28684 #28683]: #23414
+#24626 := (or #23411 #3074)
+#24627 := [def-axiom]: #24626
+#28688 := [unit-resolution #24627 #28687]: #3074
+#24638 := (or #23411 #23405)
+#24639 := [def-axiom]: #24638
+#29126 := [unit-resolution #24639 #28687]: #23405
+#28566 := [hypothesis]: #13381
+#28567 := [th-lemma #14269 #28566]: false
+#28568 := [lemma #28567]: #13378
+#24624 := (or #23408 #13381 #23402)
+#24625 := [def-axiom]: #24624
+#29127 := [unit-resolution #24625 #28568 #29126]: #23402
+#24616 := (or #23399 #23393)
+#24617 := [def-axiom]: #24616
+#29128 := [unit-resolution #24617 #29127]: #23393
+#27454 := (* -1::int #3073)
+#27455 := (+ f296 #27454)
+#27456 := (>= #27455 0::int)
+#28689 := (or #13176 #27456)
+#28690 := [th-lemma]: #28689
+#28691 := [unit-resolution #28690 #28688]: #27456
+#24294 := (not #18370)
+#28692 := [hypothesis]: #22221
+#24295 := (or #22216 #24294)
+#24296 := [def-axiom]: #24295
+#28693 := [unit-resolution #24296 #28692]: #24294
+#28652 := (+ #3073 #18368)
+#28654 := (>= #28652 0::int)
+#28651 := (= #3073 #18367)
+#28700 := (= #18367 #3073)
+#28698 := (= #18366 #3063)
+#28696 := (= ?v0!13 0::int)
+#24297 := (not #18371)
+#24298 := (or #22216 #24297)
+#24299 := [def-axiom]: #24298
+#28694 := [unit-resolution #24299 #28692]: #24297
+#24292 := (or #22216 #18363)
 #24293 := [def-axiom]: #24292
-#29377 := [unit-resolution #24293 #29376]: #13511
-#30318 := (not #29084)
-#30322 := (or #30321 #28220 #30318 #13510)
-#30323 := [th-lemma]: #30322
-#30324 := [unit-resolution #30323 #28214 #29377 #30316]: #30321
-#28963 := (>= #28923 0::int)
-#28964 := (not #28963)
-#29278 := [hypothesis]: #28964
-#24376 := (or #23173 #13743)
-#24377 := [def-axiom]: #24376
-#29279 := [unit-resolution #24377 #29337]: #13743
-#29083 := (<= #29082 0::int)
-#29282 := (or #29281 #29083)
-#29267 := [th-lemma]: #29282
-#29268 := [unit-resolution #29267 #29280]: #29083
-#29269 := [th-lemma #29268 #29279 #29278]: false
-#29270 := [lemma #29269]: #28963
-#30337 := (or #28964 #28974 #28982)
-#28993 := (or #27469 #26943 #28964 #28974 #28982)
-#28959 := (or #28958 #28956 #28953 #28950)
-#28960 := (not #28959)
-#28961 := (+ #28923 #26944)
-#28962 := (>= #28961 0::int)
-#28965 := (or #28964 #28962 #26943 #28960)
-#28994 := (or #27469 #28965)
-#29001 := (iff #28994 #28993)
-#28988 := (or #26943 #28964 #28974 #28982)
-#28996 := (or #27469 #28988)
-#28999 := (iff #28996 #28993)
-#29000 := [rewrite]: #28999
-#28997 := (iff #28994 #28996)
-#28991 := (iff #28965 #28988)
-#28985 := (or #28964 #28974 #26943 #28982)
-#28989 := (iff #28985 #28988)
-#28990 := [rewrite]: #28989
-#28986 := (iff #28965 #28985)
-#28983 := (iff #28960 #28982)
-#28980 := (iff #28959 #28979)
-#28981 := [rewrite]: #28980
-#28984 := [monotonicity #28981]: #28983
-#28977 := (iff #28962 #28974)
-#28966 := (+ #26944 #28923)
-#28969 := (>= #28966 0::int)
-#28975 := (iff #28969 #28974)
-#28976 := [rewrite]: #28975
-#28970 := (iff #28962 #28969)
-#28967 := (= #28961 #28966)
-#28968 := [rewrite]: #28967
-#28971 := [monotonicity #28968]: #28970
-#28978 := [trans #28971 #28976]: #28977
-#28987 := [monotonicity #28978 #28984]: #28986
-#28992 := [trans #28987 #28990]: #28991
-#28998 := [monotonicity #28992]: #28997
-#29002 := [trans #28998 #29000]: #29001
-#28995 := [quant-inst]: #28994
-#29003 := [mp #28995 #29002]: #28993
-#30342 := [unit-resolution #29003 #20706 #28298]: #30337
-#30331 := [unit-resolution #30342 #29270 #30324]: #28982
-#29009 := (or #28979 #28955)
-#29010 := [def-axiom]: #29009
-#30332 := [unit-resolution #29010 #30331]: #28955
-#30385 := [symm #30332]: #30390
-#30388 := (= #29089 #28954)
-#30353 := (= #27629 #28951)
-#30351 := (= #28951 #27629)
-#30349 := (= #28947 #3181)
-#28847 := (uf_116 #3181)
-#28851 := (uf_43 #24643 #28847)
-#30362 := (= #28851 #3181)
-#28852 := (= #3181 #28851)
-#27883 := (uf_48 #3181 #24643)
-#27884 := (= uf_9 #27883)
-#30356 := (= #3182 #27883)
-#28172 := (= #27883 #3182)
-#28173 := [monotonicity #28190]: #28172
-#30335 := [symm #28173]: #30356
-#27886 := (= #24643 #27885)
-#27987 := (* uf_298 #26849)
-#27357 := (uf_116 #26867)
-#27988 := (+ #27357 #27987)
-#27989 := (uf_43 #24643 #27988)
-#28131 := (uf_13 #27989)
-#28268 := (= #28131 #27885)
-#28264 := (= #27885 #28131)
-#28262 := (= #3181 #27989)
-#27983 := (uf_66 #26867 uf_298 #24643)
-#27990 := (= #27983 #27989)
-#27991 := (not #27990)
-#27984 := (uf_138 #27983 #26867)
-#27985 := (= uf_9 #27984)
-#27986 := (not #27985)
-#27994 := (or #27986 #27991)
-#27997 := (not #27994)
-#28002 := (or #26887 #27997)
-#27992 := (or #27991 #27986)
-#27993 := (not #27992)
-#28000 := (or #26887 #27993)
-#28004 := (iff #28000 #28002)
-#28006 := (iff #28002 #28002)
-#28007 := [rewrite]: #28006
-#27998 := (iff #27993 #27997)
-#27995 := (iff #27992 #27994)
-#27996 := [rewrite]: #27995
-#27999 := [monotonicity #27996]: #27998
-#28005 := [monotonicity #27999]: #28004
-#28008 := [trans #28005 #28007]: #28004
-#28003 := [quant-inst]: #28000
-#28078 := [mp #28003 #28008]: #28002
-#28254 := [unit-resolution #28078 #20922]: #27997
-#28081 := (or #27994 #27990)
-#28082 := [def-axiom]: #28081
-#28255 := [unit-resolution #28082 #28254]: #27990
-#28260 := (= #3181 #27983)
-#28258 := (= #27983 #3181)
-#28248 := (= uf_288 #26851)
-#28246 := (= #2980 #26851)
-#28247 := [symm #28245]: #28246
-#28249 := [trans #28193 #28247]: #28248
-#28251 := [monotonicity #28188 #28249]: #28250
-#28253 := [symm #28251]: #28252
-#28259 := [monotonicity #28253 #28190]: #28258
-#28261 := [symm #28259]: #28260
-#28263 := [trans #28261 #28255]: #28262
-#28265 := [monotonicity #28263]: #28264
-#28269 := [symm #28265]: #28268
-#28132 := (= #24643 #28131)
-#28071 := (or #24710 #28132)
-#28072 := [quant-inst]: #28071
-#28240 := [unit-resolution #28072 #22949]: #28132
-#28270 := [trans #28240 #28269]: #27886
-#27765 := (not #27886)
-#27882 := (iff #27884 #27886)
-#27890 := (or #25961 #27882)
-#27887 := (iff #27886 #27884)
-#27891 := (or #25961 #27887)
-#27761 := (iff #27891 #27890)
-#27763 := (iff #27890 #27890)
-#27725 := [rewrite]: #27763
-#27888 := (iff #27887 #27882)
-#27889 := [rewrite]: #27888
-#27762 := [monotonicity #27889]: #27761
-#27726 := [trans #27762 #27725]: #27761
-#27760 := [quant-inst]: #27891
-#27764 := [mp #27760 #27726]: #27890
-#28170 := [unit-resolution #27764 #22936]: #27882
-#27945 := (not #27884)
-#28153 := (iff #18238 #27945)
-#28018 := (iff #12293 #27884)
-#28181 := (iff #27884 #12293)
-#28182 := [monotonicity #28173]: #28181
-#28152 := [symm #28182]: #28018
-#28227 := [monotonicity #28152]: #28153
-#28171 := [hypothesis]: #18238
-#28238 := [mp #28171 #28227]: #27945
-#27759 := (not #27882)
-#27766 := (or #27759 #27884 #27765)
-#27767 := [def-axiom]: #27766
-#28239 := [unit-resolution #27767 #28238 #28170]: #27765
-#28271 := [unit-resolution #28239 #28270]: false
-#28272 := [lemma #28271]: #12293
-#30336 := [trans #28272 #30335]: #27884
-#28860 := (or #27945 #28852)
-#28863 := (or #25945 #27945 #28852)
-#28859 := (or #28852 #27945)
-#28864 := (or #25945 #28859)
-#28871 := (iff #28864 #28863)
-#28866 := (or #25945 #28860)
-#28869 := (iff #28866 #28863)
-#28870 := [rewrite]: #28869
-#28867 := (iff #28864 #28866)
-#28861 := (iff #28859 #28860)
-#28862 := [rewrite]: #28861
-#28868 := [monotonicity #28862]: #28867
-#28872 := [trans #28868 #28870]: #28871
-#28865 := [quant-inst]: #28864
-#28873 := [mp #28865 #28872]: #28863
-#30364 := [unit-resolution #28873 #17966]: #28860
-#30347 := [unit-resolution #30364 #30336]: #28852
-#30363 := [symm #30347]: #30362
-#30346 := (= #28947 #28851)
-#29189 := (* #26849 #28923)
-#29193 := (+ #27108 #29189)
-#29195 := (uf_43 #24643 #29193)
-#30360 := (= #29195 #28851)
-#30340 := (= #29193 #28847)
-#30304 := (= #28847 #29193)
-#30305 := (* -1::int #29193)
-#30306 := (+ #28847 #30305)
-#30307 := (<= #30306 0::int)
-#28720 := (* -1::int #26851)
-#28721 := (+ #24545 #28720)
-#28723 := (>= #28721 0::int)
-#28719 := (= #24545 #26851)
-#30302 := [trans #28310 #28247]: #28719
-#30378 := (not #28719)
-#30355 := (or #30378 #28723)
-#30325 := [th-lemma]: #30355
-#30384 := [unit-resolution #30325 #30302]: #28723
-#29387 := (* -1::int #27108)
-#29388 := (+ #24545 #29387)
-#29389 := (<= #29388 0::int)
-#29386 := (= #24545 #27108)
-#30386 := [symm #28308]: #29386
-#30387 := (not #29386)
-#30405 := (or #30387 #29389)
-#30406 := [th-lemma]: #30405
-#30401 := [unit-resolution #30406 #30386]: #29389
-#28895 := (+ #26851 #27987)
-#28896 := (uf_43 #24643 #28895)
-#29061 := (uf_116 #28896)
-#29065 := (* -1::int #29061)
-#29086 := (+ #28847 #29065)
-#29087 := (<= #29086 0::int)
-#29085 := (= #28847 #29061)
-#30447 := (= #29061 #28847)
-#30411 := (= #28896 #3181)
-#28891 := (uf_66 #24470 uf_298 #24643)
-#30409 := (= #28891 #3181)
-#30410 := [monotonicity #28243 #28190]: #30409
-#30404 := (= #28896 #28891)
-#28897 := (= #28891 #28896)
-#28898 := (not #28897)
-#28892 := (uf_138 #28891 #24470)
-#28893 := (= uf_9 #28892)
-#28894 := (not #28893)
-#28901 := (or #28894 #28898)
-#28904 := (not #28901)
-#28907 := (or #26887 #28904)
-#28899 := (or #28898 #28894)
-#28900 := (not #28899)
-#28908 := (or #26887 #28900)
-#28910 := (iff #28908 #28907)
-#28912 := (iff #28907 #28907)
-#28913 := [rewrite]: #28912
-#28905 := (iff #28900 #28904)
+#28695 := [unit-resolution #24293 #28692]: #18363
+#28697 := [th-lemma #28695 #28694]: #28696
+#28699 := [monotonicity #28697]: #28698
+#28701 := [monotonicity #28699]: #28700
+#28702 := [symm #28701]: #28651
+#28703 := (not #28651)
+#28704 := (or #28703 #28654)
+#28705 := [th-lemma]: #28704
+#28706 := [unit-resolution #28705 #28702]: #28654
+#28707 := [th-lemma #28706 #28693 #28691]: false
+#28708 := [lemma #28707]: #22216
+#24612 := (or #23396 #22221 #23390)
+#24613 := [def-axiom]: #24612
+#29129 := [unit-resolution #24613 #28708 #29128]: #23390
+#24604 := (or #23387 #23381)
+#24605 := [def-axiom]: #24604
+#29130 := [unit-resolution #24605 #29129]: #23381
+#29131 := (or #23384 #13176 #23378)
+#24600 := (or #23384 #13176 #13417 #23378)
+#24601 := [def-axiom]: #24600
+#29132 := [unit-resolution #24601 #14269]: #29131
+#29133 := [unit-resolution #29132 #29130 #28688]: #23378
+#24590 := (or #23375 #23369)
+#24591 := [def-axiom]: #24590
+#29134 := [unit-resolution #24591 #29133]: #23369
+#24588 := (or #23375 #23211)
+#24589 := [def-axiom]: #24588
+#29135 := [unit-resolution #24589 #29133]: #23211
+#24550 := (or #23375 #12159)
+#24551 := [def-axiom]: #24550
+#29136 := [unit-resolution #24551 #29133]: #12159
+#24584 := (or #23375 #15777)
+#24585 := [def-axiom]: #24584
+#29137 := [unit-resolution #24585 #29133]: #15777
+#24574 := (or #23375 #13889)
+#24575 := [def-axiom]: #24574
+#29138 := [unit-resolution #24575 #29133]: #13889
+#27446 := (f14 #26925)
+#27447 := (f67 #26925 f298 #27446)
+#27448 := (f126 #27447 #26925)
+#27529 := (>= #27448 0::int)
+#24570 := (or #23375 #13422)
+#24571 := [def-axiom]: #24570
+#29139 := [unit-resolution #24571 #29133]: #13422
+#27545 := (* -1::int #27448)
+#27618 := (+ f298 #27545)
+#27619 := (<= #27618 0::int)
+#27449 := (= f298 #27448)
+#28734 := (f67 #24672 f298 #26961)
+#28735 := (f126 #28734 #24672)
+#29161 := (= #28735 #27448)
+#29159 := (= #27448 #28735)
+#29140 := (= #26925 #24672)
+#29141 := [trans #28313 #28281]: #29140
+#29156 := (= #27447 #28734)
+#29154 := (= #3117 #28734)
+#29152 := (= #28734 #3117)
+#29144 := (= #26961 f9)
+#29142 := (= #26961 #24951)
+#29143 := [monotonicity #28283]: #29142
+#29145 := [trans #29143 #28321]: #29144
+#29153 := [monotonicity #28283 #29145]: #29152
+#29155 := [symm #29153]: #29154
+#29150 := (= #27447 #3117)
+#29148 := (= #27446 f9)
+#29146 := (= #27446 #24951)
+#29147 := [monotonicity #28313]: #29146
+#29149 := [trans #29147 #28321]: #29148
+#29151 := [monotonicity #28313 #29149]: #29150
+#29157 := [trans #29151 #29155]: #29156
+#29160 := [monotonicity #29157 #29141]: #29159
+#29162 := [symm #29160]: #29161
+#28736 := (= f298 #28735)
+#28739 := (or #26968 #28736)
+#28740 := [quant-inst]: #28739
+#29158 := [unit-resolution #28740 #16991]: #28736
+#29163 := [trans #29158 #29162]: #27449
+#27957 := (not #27449)
+#29164 := (or #27957 #27619)
+#29165 := [th-lemma]: #29164
+#29166 := [unit-resolution #29165 #29163]: #27619
+#29167 := (not #27619)
+#29168 := (or #27529 #22363 #29167)
+#29169 := [th-lemma]: #29168
+#29170 := [unit-resolution #29169 #29166 #29139]: #27529
+#27530 := (not #27529)
+#27982 := (or #23363 #27530 #13888 #22506 #22499 #23216)
+#27827 := (f67 #3007 #27448 f9)
+#27828 := (f111 f287 #27827)
+#27831 := (= f303 #27828)
+#27937 := (= #3118 #27828)
+#27950 := (= #27828 #3118)
+#27944 := (= #27827 #3117)
+#27942 := (= #27448 f298)
+#27452 := (or #26968 #27449)
+#27453 := [quant-inst]: #27452
+#27941 := [unit-resolution #27453 #16991]: #27449
+#27943 := [symm #27941]: #27942
+#27945 := [monotonicity #27943]: #27944
+#27951 := [monotonicity #27945]: #27950
+#27952 := [symm #27951]: #27937
+#27953 := (= f303 #3118)
+#27946 := [hypothesis]: #12159
+#27947 := [hypothesis]: #23366
+#24530 := (or #23363 #12187)
+#24531 := [def-axiom]: #24530
+#27948 := [unit-resolution #24531 #27947]: #12187
+#27949 := [symm #27948]: #3132
+#27954 := [trans #27949 #27946]: #27953
+#27955 := [trans #27954 #27952]: #27831
+#27812 := (<= #27448 4294967295::int)
+#27956 := [hypothesis]: #15777
+#27620 := (>= #27618 0::int)
+#27958 := (or #27957 #27620)
+#27959 := [th-lemma]: #27958
+#27960 := [unit-resolution #27959 #27941]: #27620
+#27961 := (not #27620)
+#27962 := (or #27812 #22506 #27961)
+#27963 := [th-lemma]: #27962
+#27964 := [unit-resolution #27963 #27960 #27956]: #27812
+#27854 := (+ f286 #27545)
+#27855 := (<= #27854 0::int)
+#27966 := (not #27855)
+#27965 := [hypothesis]: #13889
+#27967 := (or #27966 #13888 #27961)
+#27968 := [th-lemma]: #27967
+#27969 := [unit-resolution #27968 #27960 #27965]: #27966
+#27834 := (not #27831)
+#27813 := (not #27812)
+#27979 := (or #27813 #27834 #27855)
+#27970 := [hypothesis]: #27529
+#24538 := (or #23363 #23357)
+#24539 := [def-axiom]: #24538
+#27971 := [unit-resolution #24539 #27947]: #23357
+#27624 := (+ f297 #13750)
+#27627 := (<= #27624 0::int)
+#27972 := (or #12222 #27627)
+#27973 := [th-lemma]: #27972
+#27974 := [unit-resolution #27973 #27948]: #27627
+#27878 := [hypothesis]: #23211
+#24536 := (or #23363 #13710)
+#24537 := [def-axiom]: #24536
+#27975 := [unit-resolution #24537 #27947]: #13710
+#27869 := (not #27627)
+#27884 := (or #22472 #13711 #23216 #27869)
+#27872 := [hypothesis]: #13710
+#27695 := (+ f299 #18960)
+#27696 := (<= #27695 0::int)
+#27707 := (+ f297 #18973)
+#27708 := (>= #27707 0::int)
+#27868 := (not #27708)
+#27862 := [hypothesis]: #27627
+#24513 := (not #18975)
+#27873 := [hypothesis]: #22477
+#24514 := (or #22472 #24513)
+#24515 := [def-axiom]: #24514
+#27874 := [unit-resolution #24515 #27873]: #24513
+#27870 := (or #27868 #18975 #27869)
+#27863 := [hypothesis]: #24513
+#27866 := [hypothesis]: #27708
+#27867 := [th-lemma #27866 #27863 #27862]: false
+#27871 := [lemma #27867]: #27870
+#27875 := [unit-resolution #27871 #27874 #27862]: #27868
+#27879 := (or #27696 #27708)
+#24508 := (or #22472 #18624)
+#24509 := [def-axiom]: #24508
+#27876 := [unit-resolution #24509 #27873]: #18624
+#24506 := (or #22472 #18623)
+#24507 := [def-axiom]: #24506
+#27877 := [unit-resolution #24507 #27873]: #18623
+#27721 := (or #23216 #22456 #22457 #27696 #27708)
+#27684 := (+ #18628 #13915)
+#27685 := (<= #27684 0::int)
+#27686 := (+ ?v0!15 #13446)
+#27687 := (>= #27686 0::int)
+#27688 := (or #22457 #27687 #27685 #22456)
+#27722 := (or #23216 #27688)
+#27729 := (iff #27722 #27721)
+#27716 := (or #22456 #22457 #27696 #27708)
+#27724 := (or #23216 #27716)
+#27727 := (iff #27724 #27721)
+#27728 := [rewrite]: #27727
+#27725 := (iff #27722 #27724)
+#27719 := (iff #27688 #27716)
+#27713 := (or #22457 #27696 #27708 #22456)
+#27717 := (iff #27713 #27716)
+#27718 := [rewrite]: #27717
+#27714 := (iff #27688 #27713)
+#27711 := (iff #27685 #27708)
+#27701 := (+ #13915 #18628)
+#27704 := (<= #27701 0::int)
+#27709 := (iff #27704 #27708)
+#27710 := [rewrite]: #27709
+#27705 := (iff #27685 #27704)
+#27702 := (= #27684 #27701)
+#27703 := [rewrite]: #27702
+#27706 := [monotonicity #27703]: #27705
+#27712 := [trans #27706 #27710]: #27711
+#27699 := (iff #27687 #27696)
+#27689 := (+ #13446 ?v0!15)
+#27692 := (>= #27689 0::int)
+#27697 := (iff #27692 #27696)
+#27698 := [rewrite]: #27697
+#27693 := (iff #27687 #27692)
+#27690 := (= #27686 #27689)
+#27691 := [rewrite]: #27690
+#27694 := [monotonicity #27691]: #27693
+#27700 := [trans #27694 #27698]: #27699
+#27715 := [monotonicity #27700 #27712]: #27714
+#27720 := [trans #27715 #27718]: #27719
+#27726 := [monotonicity #27720]: #27725
+#27730 := [trans #27726 #27728]: #27729
+#27723 := [quant-inst]: #27722
+#27731 := [mp #27723 #27730]: #27721
+#27880 := [unit-resolution #27731 #27878 #27877 #27876]: #27879
+#27881 := [unit-resolution #27880 #27875]: #27696
+#24510 := (not #18962)
+#24511 := (or #22472 #24510)
+#24512 := [def-axiom]: #24511
+#27882 := [unit-resolution #24512 #27873]: #24510
+#27883 := [th-lemma #27882 #27881 #27872]: false
+#27885 := [lemma #27883]: #27884
+#27976 := [unit-resolution #27885 #27975 #27878 #27974]: #22472
+#24522 := (or #23360 #23354 #22477)
+#24523 := [def-axiom]: #24522
+#27977 := [unit-resolution #24523 #27976 #27971]: #23354
+#24502 := (or #23351 #23343)
+#24503 := [def-axiom]: #24502
+#27978 := [unit-resolution #24503 #27977]: #23343
+#27891 := (or #23348 #27530 #27813 #27834 #27855)
+#27818 := (+ #27448 #13351)
+#27819 := (>= #27818 0::int)
+#27826 := (= #27828 f303)
+#27829 := (not #27826)
+#27830 := (or #27829 #27530 #27819 #27813)
+#27892 := (or #23348 #27830)
+#27899 := (iff #27892 #27891)
+#27886 := (or #27530 #27813 #27834 #27855)
+#27894 := (or #23348 #27886)
+#27897 := (iff #27894 #27891)
+#27898 := [rewrite]: #27897
+#27895 := (iff #27892 #27894)
+#27889 := (iff #27830 #27886)
+#27835 := (or #27834 #27530 #27855 #27813)
+#27887 := (iff #27835 #27886)
+#27888 := [rewrite]: #27887
+#27836 := (iff #27830 #27835)
+#27865 := (iff #27819 #27855)
+#27849 := (+ #13351 #27448)
+#27846 := (>= #27849 0::int)
+#27856 := (iff #27846 #27855)
+#27864 := [rewrite]: #27856
+#27852 := (iff #27819 #27846)
+#27850 := (= #27818 #27849)
+#27851 := [rewrite]: #27850
+#27853 := [monotonicity #27851]: #27852
+#27767 := [trans #27853 #27864]: #27865
+#27847 := (iff #27829 #27834)
+#27832 := (iff #27826 #27831)
+#27833 := [rewrite]: #27832
+#27848 := [monotonicity #27833]: #27847
+#27859 := [monotonicity #27848 #27767]: #27836
+#27890 := [trans #27859 #27888]: #27889
+#27896 := [monotonicity #27890]: #27895
+#27900 := [trans #27896 #27898]: #27899
+#27893 := [quant-inst]: #27892
+#27901 := [mp #27893 #27900]: #27891
+#27980 := [unit-resolution #27901 #27978 #27970]: #27979
+#27981 := [unit-resolution #27980 #27969 #27964 #27955]: false
+#27983 := [lemma #27981]: #27982
+#29171 := [unit-resolution #27983 #29170 #29138 #29137 #29136 #29135]: #23363
+#24546 := (or #23372 #23332 #23366)
+#24547 := [def-axiom]: #24546
+#29172 := [unit-resolution #24547 #29171 #29134]: #23332
+#24494 := (or #23329 #13711)
+#24495 := [def-axiom]: #24494
+#29175 := [unit-resolution #24495 #29172]: #13711
+#30109 := (not #29120)
+#30110 := (or #30108 #28255 #30109 #13710)
+#30111 := [th-lemma]: #30110
+#30112 := [unit-resolution #30111 #28249 #29175 #30107]: #30108
+#28999 := (>= #28958 0::int)
+#24572 := (or #23375 #13425)
+#24573 := [def-axiom]: #24572
+#29174 := [unit-resolution #24573 #29133]: #13425
+#29119 := (<= #29118 0::int)
+#29602 := (or #29599 #29119)
+#29603 := [th-lemma]: #29602
+#29604 := [unit-resolution #29603 #29598]: #29119
+#29000 := (not #28999)
+#29605 := [hypothesis]: #29000
+#29606 := [th-lemma #29605 #29604 #29174]: false
+#29607 := [lemma #29606]: #28999
+#30114 := (or #29000 #29010 #29018)
+#29029 := (or #27566 #27002 #29000 #29010 #29018)
+#28995 := (or #28994 #28991 #28989 #28985)
+#28996 := (not #28995)
+#28997 := (+ #28958 #27003)
+#28998 := (>= #28997 0::int)
+#29001 := (or #29000 #28998 #27002 #28996)
+#29030 := (or #27566 #29001)
+#29037 := (iff #29030 #29029)
+#29024 := (or #27002 #29000 #29010 #29018)
+#29032 := (or #27566 #29024)
+#29035 := (iff #29032 #29029)
+#29036 := [rewrite]: #29035
+#29033 := (iff #29030 #29032)
+#29027 := (iff #29001 #29024)
+#29021 := (or #29000 #29010 #27002 #29018)
+#29025 := (iff #29021 #29024)
+#29026 := [rewrite]: #29025
+#29022 := (iff #29001 #29021)
+#29019 := (iff #28996 #29018)
+#29016 := (iff #28995 #29015)
+#29017 := [rewrite]: #29016
+#29020 := [monotonicity #29017]: #29019
+#29013 := (iff #28998 #29010)
+#29002 := (+ #27003 #28958)
+#29005 := (>= #29002 0::int)
+#29011 := (iff #29005 #29010)
+#29012 := [rewrite]: #29011
+#29006 := (iff #28998 #29005)
+#29003 := (= #28997 #29002)
+#29004 := [rewrite]: #29003
+#29007 := [monotonicity #29004]: #29006
+#29014 := [trans #29007 #29012]: #29013
+#29023 := [monotonicity #29014 #29020]: #29022
+#29028 := [trans #29023 #29026]: #29027
+#29034 := [monotonicity #29028]: #29033
+#29038 := [trans #29034 #29036]: #29037
+#29031 := [quant-inst]: #29030
+#29039 := [mp #29031 #29038]: #29029
+#30115 := [unit-resolution #29039 #20908 #28343]: #30114
+#30116 := [unit-resolution #30115 #29607 #30112]: #29018
+#29047 := (or #29015 #28993)
+#29048 := [def-axiom]: #29047
+#30117 := [unit-resolution #29048 #30116]: #28993
+#30148 := [symm #30117]: #30147
+#30145 := (= #29196 #28992)
+#30143 := (= #27673 #28986)
+#30141 := (= #28986 #27673)
+#30139 := (= #28982 #3222)
+#28864 := (f117 #3222)
+#28886 := (f44 #24835 #28864)
+#30133 := (= #28886 #3222)
+#28887 := (= #3222 #28886)
+#27806 := (f49 #3222 #24835)
+#27807 := (= f1 #27806)
+#30119 := (= #3223 #27806)
+#28187 := (= #27806 #3223)
+#28188 := [monotonicity #28225]: #28187
+#30120 := [symm #28188]: #30119
+#27808 := (= #24835 #27769)
+#28021 := (* f299 #26907)
+#27401 := (f117 #26925)
+#28022 := (+ #27401 #28021)
+#28023 := (f44 #24835 #28022)
+#28166 := (f14 #28023)
+#28308 := (= #28166 #27769)
+#28304 := (= #27769 #28166)
+#28302 := (= #3222 #28023)
+#28017 := (f67 #26925 f299 #24835)
+#28024 := (= #28017 #28023)
+#28025 := (not #28024)
+#28018 := (f139 #28017 #26925)
+#28019 := (= f1 #28018)
+#28020 := (not #28019)
+#28028 := (or #28020 #28025)
+#28031 := (not #28028)
+#28040 := (or #26945 #28031)
+#28026 := (or #28025 #28020)
+#28027 := (not #28026)
+#28041 := (or #26945 #28027)
+#28113 := (iff #28041 #28040)
+#28115 := (iff #28040 #28040)
+#28116 := [rewrite]: #28115
+#28032 := (iff #28027 #28031)
+#28029 := (iff #28026 #28028)
+#28030 := [rewrite]: #28029
+#28033 := [monotonicity #28030]: #28032
+#28114 := [monotonicity #28033]: #28113
+#28117 := [trans #28114 #28116]: #28113
+#28042 := [quant-inst]: #28041
+#28118 := [mp #28042 #28117]: #28040
+#28294 := [unit-resolution #28118 #21124]: #28031
+#28121 := (or #28028 #28024)
+#28122 := [def-axiom]: #28121
+#28295 := [unit-resolution #28122 #28294]: #28024
+#28300 := (= #3222 #28017)
+#28298 := (= #28017 #3222)
+#28288 := (= f288 #26909)
+#28286 := (= #3008 #26909)
+#28287 := [symm #28285]: #28286
+#28289 := [trans #28228 #28287]: #28288
+#28291 := [monotonicity #28223 #28289]: #28290
+#28293 := [symm #28291]: #28292
+#28299 := [monotonicity #28293 #28225]: #28298
+#28301 := [symm #28299]: #28300
+#28303 := [trans #28301 #28295]: #28302
+#28305 := [monotonicity #28303]: #28304
+#28309 := [symm #28305]: #28308
+#28167 := (= #24835 #28166)
+#28110 := (or #24903 #28167)
+#28111 := [quant-inst]: #28110
+#28280 := [unit-resolution #28111 #23151]: #28167
+#28310 := [trans #28280 #28309]: #27808
+#27935 := (not #27808)
+#27809 := (iff #27807 #27808)
+#27927 := (or #26049 #27809)
+#27803 := (iff #27808 #27807)
+#27928 := (or #26049 #27803)
+#27760 := (iff #27928 #27927)
+#27770 := (iff #27927 #27927)
+#27804 := [rewrite]: #27770
+#27810 := (iff #27803 #27809)
+#27811 := [rewrite]: #27810
+#27758 := [monotonicity #27811]: #27760
+#27805 := [trans #27758 #27804]: #27760
+#27759 := [quant-inst]: #27928
+#27933 := [mp #27759 #27805]: #27927
+#28217 := [unit-resolution #27933 #23138]: #27809
+#27932 := (not #27807)
+#28276 := (iff #18440 #27932)
+#28274 := (iff #12484 #27807)
+#28262 := (iff #27807 #12484)
+#28273 := [monotonicity #28188]: #28262
+#28275 := [symm #28273]: #28274
+#28277 := [monotonicity #28275]: #28276
+#28052 := [hypothesis]: #18440
+#28278 := [mp #28052 #28277]: #27932
+#27934 := (not #27809)
+#27936 := (or #27934 #27807 #27935)
+#27939 := [def-axiom]: #27936
+#28279 := [unit-resolution #27939 #28278 #28217]: #27935
+#28311 := [unit-resolution #28279 #28310]: false
+#28312 := [lemma #28311]: #12484
+#30121 := [trans #28312 #30120]: #27807
+#28895 := (or #27932 #28887)
+#28898 := (or #26033 #27932 #28887)
+#28894 := (or #28887 #27932)
+#28899 := (or #26033 #28894)
+#28906 := (iff #28899 #28898)
+#28901 := (or #26033 #28895)
+#28904 := (iff #28901 #28898)
+#28905 := [rewrite]: #28904
 #28902 := (iff #28899 #28901)
-#28903 := [rewrite]: #28902
-#28906 := [monotonicity #28903]: #28905
-#28911 := [monotonicity #28906]: #28910
-#28914 := [trans #28911 #28913]: #28910
-#28909 := [quant-inst]: #28908
-#28915 := [mp #28909 #28914]: #28907
-#30402 := [unit-resolution #28915 #20922]: #28904
-#28918 := (or #28901 #28897)
-#28919 := [def-axiom]: #28918
-#30407 := [unit-resolution #28919 #30402]: #28897
-#30408 := [symm #30407]: #30404
-#30421 := [trans #30408 #30410]: #30411
-#30448 := [monotonicity #30421]: #30447
-#30449 := [symm #30448]: #29085
-#30450 := (not #29085)
-#30445 := (or #30450 #29087)
-#30451 := [th-lemma]: #30445
-#30417 := [unit-resolution #30451 #30449]: #29087
-#29066 := (+ #27987 #29065)
-#29067 := (+ #26851 #29066)
-#29081 := (>= #29067 0::int)
-#29068 := (= #29067 0::int)
-#29071 := (or #24716 #29068)
-#29062 := (= #28895 #29061)
-#29072 := (or #24716 #29062)
-#29074 := (iff #29072 #29071)
-#29076 := (iff #29071 #29071)
-#29077 := [rewrite]: #29076
-#29069 := (iff #29062 #29068)
-#29070 := [rewrite]: #29069
-#29075 := [monotonicity #29070]: #29074
-#29078 := [trans #29075 #29077]: #29074
-#29073 := [quant-inst]: #29072
-#29079 := [mp #29073 #29078]: #29071
-#30452 := [unit-resolution #29079 #22943]: #29068
-#30453 := (not #29068)
-#30446 := (or #30453 #29081)
-#30454 := [th-lemma]: #30446
-#30455 := [unit-resolution #30454 #30452]: #29081
-#28726 := (>= #26849 1::int)
-#28724 := (= #26849 1::int)
-#2932 := (uf_139 uf_7)
-#2933 := (= #2932 1::int)
-#11813 := [asserted]: #2933
-#30462 := (= #26849 #2932)
-#30463 := [monotonicity #28190]: #30462
-#30464 := [trans #30463 #11813]: #28724
-#30465 := (not #28724)
-#30466 := (or #30465 #28726)
-#30461 := [th-lemma]: #30466
-#30416 := [unit-resolution #30461 #30464]: #28726
-#28725 := (<= #26849 1::int)
-#30467 := (or #30465 #28725)
-#30422 := [th-lemma]: #30467
-#30468 := [unit-resolution #30422 #30464]: #28725
-#30482 := (not #29389)
-#30487 := (not #29083)
-#30486 := (not #28725)
-#30484 := (not #28726)
-#30471 := (not #28723)
-#30470 := (not #29081)
-#30469 := (not #29087)
-#30483 := (or #30307 #30469 #30470 #30471 #30484 #30486 #30484 #30486 #30487 #30482)
-#30488 := [th-lemma]: #30483
-#30485 := [unit-resolution #30488 #30468 #30416 #30455 #29268 #30417 #30401 #30384]: #30307
-#30317 := (>= #30306 0::int)
-#28722 := (<= #28721 0::int)
-#30489 := (or #30378 #28722)
-#30490 := [th-lemma]: #30489
-#30491 := [unit-resolution #30490 #30302]: #28722
-#29390 := (>= #29388 0::int)
-#30492 := (or #30387 #29390)
-#30493 := [th-lemma]: #30492
-#30494 := [unit-resolution #30493 #30386]: #29390
-#29088 := (>= #29086 0::int)
-#30495 := (or #30450 #29088)
-#30498 := [th-lemma]: #30495
-#30530 := [unit-resolution #30498 #30449]: #29088
-#29080 := (<= #29067 0::int)
-#30531 := (or #30453 #29080)
-#30532 := [th-lemma]: #30531
-#30533 := [unit-resolution #30532 #30452]: #29080
-#30537 := (not #29390)
-#30536 := (not #28722)
-#30535 := (not #29080)
-#30534 := (not #29088)
-#30538 := (or #30317 #30534 #30535 #30536 #30484 #30486 #30484 #30486 #30318 #30537)
-#30539 := [th-lemma]: #30538
-#30540 := [unit-resolution #30539 #30468 #30416 #30533 #30316 #30530 #30494 #30491]: #30317
-#30542 := (not #30317)
-#30541 := (not #30307)
-#30543 := (or #30304 #30541 #30542)
-#30544 := [th-lemma]: #30543
-#30545 := [unit-resolution #30544 #30540 #30485]: #30304
-#29850 := [symm #30545]: #30340
-#29848 := [monotonicity #29850]: #30360
-#30376 := (= #28947 #29195)
-#29247 := (uf_66 #25933 #28923 #24643)
-#29198 := (= #29247 #29195)
-#29266 := (= #29195 #29247)
-#29276 := (not #29266)
-#29248 := (uf_138 #29247 #25933)
-#29249 := (= uf_9 #29248)
-#29182 := (not #29249)
-#29306 := (or #29182 #29276)
-#29310 := (not #29306)
-#29317 := (or #26887 #29310)
-#29183 := (* #28923 #26849)
-#29181 := (+ #27108 #29183)
-#29184 := (uf_43 #24643 #29181)
-#29185 := (= #29247 #29184)
-#29186 := (not #29185)
-#29187 := (or #29186 #29182)
-#29188 := (not #29187)
-#29318 := (or #26887 #29188)
-#29327 := (iff #29318 #29317)
-#29329 := (iff #29317 #29317)
-#29330 := [rewrite]: #29329
-#29311 := (iff #29188 #29310)
-#29308 := (iff #29187 #29306)
-#29303 := (or #29276 #29182)
-#29307 := (iff #29303 #29306)
-#29302 := [rewrite]: #29307
-#29304 := (iff #29187 #29303)
-#29287 := (iff #29186 #29276)
-#29274 := (iff #29185 #29266)
-#29272 := (iff #29198 #29266)
-#29273 := [rewrite]: #29272
-#29199 := (iff #29185 #29198)
-#29196 := (= #29184 #29195)
-#29191 := (= #29181 #29193)
-#29277 := (= #29183 #29189)
-#29192 := [rewrite]: #29277
-#29194 := [monotonicity #29192]: #29191
-#29197 := [monotonicity #29194]: #29196
-#29271 := [monotonicity #29197]: #29199
-#29275 := [trans #29271 #29273]: #29274
-#29288 := [monotonicity #29275]: #29287
-#29305 := [monotonicity #29288]: #29304
-#29309 := [trans #29305 #29302]: #29308
-#29312 := [monotonicity #29309]: #29311
-#29328 := [monotonicity #29312]: #29327
-#29331 := [trans #29328 #29330]: #29327
-#29326 := [quant-inst]: #29318
-#29324 := [mp #29326 #29331]: #29317
-#30334 := [unit-resolution #29324 #20922]: #29310
-#29382 := (or #29306 #29266)
-#29383 := [def-axiom]: #29382
-#30357 := [unit-resolution #29383 #30334]: #29266
-#30359 := [symm #30357]: #29198
-#30333 := (= #28947 #29247)
-#30358 := [monotonicity #28318]: #30333
-#30339 := [trans #30358 #30359]: #30376
-#29851 := [trans #30339 #29848]: #30346
-#29852 := [trans #29851 #30363]: #30349
-#29893 := [monotonicity #29852]: #30351
-#29853 := [symm #29893]: #30353
-#29854 := [monotonicity #29853]: #30388
-#29855 := [trans #29854 #30385]: #30391
-#29856 := [trans #29855 #28292]: #30393
-#29902 := [monotonicity #29856]: #29899
-#29910 := [symm #29902]: #29898
-#29866 := [trans #14075 #29910]: #29093
-#29863 := (not #29093)
-#29864 := (or #29149 #29863)
-#29865 := [def-axiom]: #29864
-#29868 := [unit-resolution #29865 #29866]: #29149
-#29981 := (= #25182 #29107)
-#29939 := (= #29107 #25182)
-#29897 := (= #27885 uf_7)
-#29867 := (= #27885 #24643)
-#28874 := (or #27759 #27945 #27886)
-#28875 := [def-axiom]: #28874
-#29869 := [unit-resolution #28875 #30336 #28170]: #27886
-#29904 := [symm #29869]: #29867
-#29938 := [trans #29904 #28190]: #29897
-#29978 := [monotonicity #29938]: #29939
-#29947 := [symm #29978]: #29981
-#29948 := [trans #27481 #29947]: #29125
-#29688 := (not #29098)
-#29881 := (iff #11878 #29688)
-#29879 := (iff #11875 #29098)
-#29877 := (iff #29098 #11875)
-#29892 := (= #29097 #2990)
-#29889 := (= #29096 #2977)
-#29687 := (= #29096 #24763)
-#29949 := [monotonicity #29856]: #29687
-#29891 := [trans #29949 #28353]: #29889
-#29890 := [monotonicity #29891]: #29892
-#29878 := [monotonicity #29890]: #29877
-#29880 := [symm #29878]: #29879
-#29876 := [monotonicity #29880]: #29881
-#29944 := [mp #14078 #29876]: #29688
-#29015 := (uf_66 #27003 #28923 #24643)
-#29016 := (uf_58 #3150 #29015)
-#29017 := (uf_136 #29016)
-#29018 := (= uf_9 #29017)
-#29050 := (not #29018)
-#30097 := (iff #29050 #29104)
-#30107 := (iff #29018 #29103)
-#30105 := (iff #29103 #29018)
-#29984 := (= #29102 #29017)
-#29995 := (= #27629 #29016)
-#29993 := (= #29016 #27629)
-#29950 := (= #29015 #3181)
-#29983 := (= #28923 uf_298)
-#29952 := [symm #29280]: #29983
-#29951 := [monotonicity #28197 #29952 #28190]: #29950
-#29994 := [monotonicity #29951]: #29993
-#29707 := [symm #29994]: #29995
-#29996 := [monotonicity #29707]: #29984
-#30106 := [monotonicity #29996]: #30105
-#30110 := [symm #30106]: #30107
-#30116 := [monotonicity #30110]: #30097
-#29019 := (uf_24 uf_287 #29015)
-#29020 := (= uf_9 #29019)
-#29021 := (not #29020)
-#29025 := (or #29018 #29021)
-#29028 := (not #29025)
-#29977 := (or #28964 #28974 #29028)
-#29039 := (or #27034 #24483 #27015 #27018 #28964 #28974 #29028)
-#29022 := (or #29021 #29018)
-#29023 := (not #29022)
-#29024 := (or #27018 #28964 #28962 #24483 #27015 #29023)
-#29040 := (or #27034 #29024)
-#29047 := (iff #29040 #29039)
-#29034 := (or #24483 #27015 #27018 #28964 #28974 #29028)
-#29042 := (or #27034 #29034)
-#29045 := (iff #29042 #29039)
-#29046 := [rewrite]: #29045
-#29043 := (iff #29040 #29042)
-#29037 := (iff #29024 #29034)
-#29031 := (or #27018 #28964 #28974 #24483 #27015 #29028)
-#29035 := (iff #29031 #29034)
-#29036 := [rewrite]: #29035
-#29032 := (iff #29024 #29031)
-#29029 := (iff #29023 #29028)
-#29026 := (iff #29022 #29025)
-#29027 := [rewrite]: #29026
-#29030 := [monotonicity #29027]: #29029
-#29033 := [monotonicity #28978 #29030]: #29032
-#29038 := [trans #29033 #29036]: #29037
-#29044 := [monotonicity #29038]: #29043
-#29048 := [trans #29044 #29046]: #29047
-#29041 := [quant-inst]: #29040
-#29049 := [mp #29041 #29048]: #29039
-#29985 := [unit-resolution #29049 #21366 #14064 #28636 #28230]: #29977
-#29986 := [unit-resolution #29985 #29270 #30324]: #29028
-#29051 := (or #29025 #29050)
-#29052 := [def-axiom]: #29051
-#29943 := [unit-resolution #29052 #29986]: #29050
-#30117 := [mp #29943 #30116]: #29104
-#29857 := (or #29143 #29103)
-#29858 := [def-axiom]: #29857
-#30151 := [unit-resolution #29858 #30117]: #29143
-#29678 := (or #29163 #29098 #29140 #29146 #29152)
-#29700 := [def-axiom]: #29678
-#30152 := [unit-resolution #29700 #30151 #29944 #29948 #29868 #29847]: false
-#30153 := [lemma #30152]: #29163
-#29736 := (or #29166 #29158)
-#29737 := [def-axiom]: #29736
-#30575 := [unit-resolution #29737 #30153]: #29166
-#24370 := (or #23173 #13225)
-#24371 := [def-axiom]: #24370
-#29434 := [unit-resolution #24371 #29337]: #13225
-#28236 := (or #12296 #13365 #27015 #13510)
-#28179 := [hypothesis]: #13225
-#28015 := (uf_66 #26867 uf_298 #27402)
-#28016 := (uf_125 #28015 #26867)
-#28046 := (* -1::int #28016)
-#28174 := (+ uf_298 #28046)
-#28175 := (<= #28174 0::int)
-#28017 := (= uf_298 #28016)
-#28020 := (or #26910 #28017)
-#28021 := [quant-inst]: #28020
-#28180 := [unit-resolution #28021 #16791]: #28017
-#28183 := (not #28017)
-#28184 := (or #28183 #28175)
-#28185 := [th-lemma]: #28184
-#28186 := [unit-resolution #28185 #28180]: #28175
-#28037 := (>= #28016 0::int)
-#28038 := (not #28037)
-#28089 := (uf_66 #27003 #28016 #24643)
-#28093 := (uf_24 uf_287 #28089)
-#28094 := (= uf_9 #28093)
-#28095 := (not #28094)
-#28090 := (uf_58 #3150 #28089)
-#28091 := (uf_136 #28090)
-#28092 := (= uf_9 #28091)
-#28099 := (or #28092 #28095)
-#28206 := (iff #18241 #28095)
-#28204 := (iff #12296 #28094)
-#28202 := (iff #28094 #12296)
-#28200 := (= #28093 #3184)
-#28198 := (= #28089 #3181)
-#28191 := (= #28016 uf_298)
-#28192 := [symm #28180]: #28191
-#28199 := [monotonicity #28197 #28192 #28190]: #28198
-#28201 := [monotonicity #28199]: #28200
-#28203 := [monotonicity #28201]: #28202
-#28205 := [symm #28203]: #28204
-#28207 := [monotonicity #28205]: #28206
-#28187 := [hypothesis]: #18241
-#28208 := [mp #28187 #28207]: #28095
-#28127 := (or #28099 #28094)
-#28128 := [def-axiom]: #28127
-#28209 := [unit-resolution #28128 #28208]: #28099
-#28047 := (+ #24645 #28046)
-#28048 := (<= #28047 0::int)
-#28219 := (not #28048)
-#28215 := [hypothesis]: #13511
-#28176 := (>= #28174 0::int)
-#28216 := (or #28183 #28176)
-#28217 := [th-lemma]: #28216
-#28218 := [unit-resolution #28217 #28180]: #28176
-#28221 := (not #28176)
-#28222 := (or #28219 #28220 #28221 #13510)
-#28223 := [th-lemma]: #28222
-#28224 := [unit-resolution #28223 #28218 #28215 #28214]: #28219
-#28102 := (not #28099)
-#28232 := (or #28038 #28048 #28102)
-#28113 := (or #27034 #24483 #27015 #27018 #28038 #28048 #28102)
-#28096 := (or #28095 #28092)
-#28097 := (not #28096)
-#28035 := (+ #28016 #26944)
-#28036 := (>= #28035 0::int)
-#28098 := (or #27018 #28038 #28036 #24483 #27015 #28097)
-#28114 := (or #27034 #28098)
-#28121 := (iff #28114 #28113)
-#28108 := (or #24483 #27015 #27018 #28038 #28048 #28102)
-#28116 := (or #27034 #28108)
-#28119 := (iff #28116 #28113)
-#28120 := [rewrite]: #28119
-#28117 := (iff #28114 #28116)
-#28111 := (iff #28098 #28108)
-#28105 := (or #27018 #28038 #28048 #24483 #27015 #28102)
-#28109 := (iff #28105 #28108)
-#28110 := [rewrite]: #28109
-#28106 := (iff #28098 #28105)
-#28103 := (iff #28097 #28102)
-#28100 := (iff #28096 #28099)
-#28101 := [rewrite]: #28100
-#28104 := [monotonicity #28101]: #28103
-#28051 := (iff #28036 #28048)
-#28040 := (+ #26944 #28016)
-#28043 := (>= #28040 0::int)
-#28049 := (iff #28043 #28048)
-#28050 := [rewrite]: #28049
-#28044 := (iff #28036 #28043)
-#28041 := (= #28035 #28040)
-#28042 := [rewrite]: #28041
-#28045 := [monotonicity #28042]: #28044
-#28052 := [trans #28045 #28050]: #28051
-#28107 := [monotonicity #28052 #28104]: #28106
-#28112 := [trans #28107 #28110]: #28111
-#28118 := [monotonicity #28112]: #28117
-#28122 := [trans #28118 #28120]: #28121
-#28115 := [quant-inst]: #28114
-#28123 := [mp #28115 #28122]: #28113
-#28233 := [unit-resolution #28123 #21366 #14064 #28231 #28230]: #28232
-#28234 := [unit-resolution #28233 #28224 #28209]: #28038
-#28235 := [th-lemma #28234 #28186 #28179]: false
-#28237 := [lemma #28235]: #28236
-#29435 := [unit-resolution #28237 #29377 #28636 #29434]: #12296
-#29885 := (or #29175 #18241 #29169)
-#29886 := [def-axiom]: #29885
-#30576 := [unit-resolution #29886 #29435 #30575]: #29175
-#29751 := (or #29750 #12302 #29172)
-#29749 := [def-axiom]: #29751
-#30581 := [unit-resolution #29749 #30576]: #30580
-#30582 := [unit-resolution #30581 #29980]: #12302
-#30590 := (or #18247 #23106)
-#24294 := (or #23127 #23121)
-#24295 := [def-axiom]: #24294
-#30583 := [unit-resolution #24295 #29376]: #23121
-#30584 := (or #23124 #18241 #23118)
-#24286 := (or #23124 #18238 #18241 #23118)
-#24287 := [def-axiom]: #24286
-#30585 := [unit-resolution #24287 #28272]: #30584
-#30586 := [unit-resolution #30585 #29435 #30583]: #23118
-#24276 := (or #23115 #23109)
-#24277 := [def-axiom]: #24276
-#30587 := [unit-resolution #24277 #30586]: #23109
-#30588 := (or #23112 #18247 #23106)
-#24270 := (or #23112 #18238 #18247 #23106)
-#24271 := [def-axiom]: #24270
-#30589 := [unit-resolution #24271 #28272]: #30588
-#30591 := [unit-resolution #30589 #30587]: #30590
-#30592 := [unit-resolution #30591 #30582]: #23106
-#30593 := (or #23103 #23064)
-#24118 := (not #18612)
-#30252 := (= #3083 #3220)
-#30250 := (= #3220 #3083)
-#30246 := (= #3219 #3082)
-#30243 := [hypothesis]: #23094
-#24232 := (or #23091 #12551)
-#24233 := [def-axiom]: #24232
-#30244 := [unit-resolution #24233 #30243]: #12551
-#30245 := [symm #30244]: #3250
-#30247 := [monotonicity #30245]: #30246
-#30251 := [monotonicity #30247]: #30250
-#30253 := [symm #30251]: #30252
-#30254 := (= uf_304 #3083)
-#24230 := (or #23091 #12548)
-#24231 := [def-axiom]: #24230
-#30248 := [unit-resolution #24231 #30243]: #12548
-#30249 := [symm #30248]: #3249
-#30255 := [trans #30249 #29340]: #30254
-#30256 := [trans #30255 #30253]: #12352
-#24227 := (+ uf_297 #13301)
-#24229 := (>= #24227 0::int)
-#30257 := (or #12557 #24229)
-#30258 := [th-lemma]: #30257
-#30209 := [unit-resolution #30258 #30244]: #24229
-#29871 := (not #24229)
-#29872 := (or #13304 #29871)
-#29900 := [hypothesis]: #24229
-#29901 := [hypothesis]: #13303
-#29870 := [th-lemma #29901 #29900 #29342]: false
-#29873 := [lemma #29870]: #29872
-#30213 := [unit-resolution #29873 #30209]: #13304
-#24106 := (or #22046 #22044 #13303)
-#24107 := [def-axiom]: #24106
-#30214 := [unit-resolution #24107 #30213 #30256]: #22046
-#24108 := (or #23025 #22045)
-#24109 := [def-axiom]: #24108
-#30210 := [unit-resolution #24109 #30214]: #23025
-#24242 := (or #23091 #23055)
-#24243 := [def-axiom]: #24242
-#30215 := [unit-resolution #24243 #30243]: #23055
-#30219 := (or #23058 #23052)
-#15520 := (<= uf_286 4294967295::int)
-#15523 := (iff #13150 #15520)
-#15514 := (+ 4294967295::int #13151)
-#15517 := (>= #15514 0::int)
-#15521 := (iff #15517 #15520)
-#15522 := [rewrite]: #15521
-#15518 := (iff #13150 #15517)
-#15515 := (= #13152 #15514)
-#15516 := [monotonicity #7483]: #15515
-#15519 := [monotonicity #15516]: #15518
-#15524 := [trans #15519 #15522]: #15523
-#14066 := [not-or-elim #14055]: #13155
-#14068 := [and-elim #14066]: #13150
-#15525 := [mp #14068 #15524]: #15520
-#29378 := [hypothesis]: #18279
-#29379 := [th-lemma #29378 #29377 #15525]: false
-#29380 := [lemma #29379]: #15609
-#30216 := (or #13365 #13243)
+#28896 := (iff #28894 #28895)
+#28897 := [rewrite]: #28896
+#28903 := [monotonicity #28897]: #28902
+#28907 := [trans #28903 #28905]: #28906
+#28900 := [quant-inst]: #28899
+#28908 := [mp #28900 #28907]: #28898
+#30122 := [unit-resolution #28908 #18168]: #28895
+#30123 := [unit-resolution #30122 #30121]: #28887
+#30134 := [symm #30123]: #30133
+#30137 := (= #28982 #28886)
+#29347 := (* #26907 #28958)
+#29350 := (+ #27157 #29347)
+#29353 := (f44 #24835 #29350)
+#30131 := (= #29353 #28886)
+#30125 := (= #29350 #28864)
+#30099 := (= #28864 #29350)
+#30100 := (* -1::int #29350)
+#30101 := (+ #28864 #30100)
+#30102 := (<= #30101 0::int)
+#28760 := (* -1::int #26909)
+#28761 := (+ #24719 #28760)
+#28763 := (>= #28761 0::int)
+#28759 := (= #24719 #26909)
+#30090 := [trans #28355 #28287]: #28759
+#30092 := (not #28759)
+#30094 := (or #30092 #28763)
+#30155 := [th-lemma]: #30094
+#30118 := [unit-resolution #30155 #30090]: #28763
+#29472 := (* -1::int #27157)
+#29473 := (+ #24719 #29472)
+#29474 := (<= #29473 0::int)
+#29471 := (= #24719 #27157)
+#30113 := [symm #28353]: #29471
+#30163 := (not #29471)
+#30164 := (or #30163 #29474)
+#30165 := [th-lemma]: #30164
+#30166 := [unit-resolution #30165 #30113]: #29474
+#28930 := (+ #26909 #28021)
+#28931 := (f44 #24835 #28930)
+#29097 := (f117 #28931)
+#29101 := (* -1::int #29097)
+#29122 := (+ #28864 #29101)
+#29123 := (<= #29122 0::int)
+#29121 := (= #28864 #29097)
+#30175 := (= #29097 #28864)
+#30173 := (= #28931 #3222)
+#28926 := (f67 #24672 f299 #24835)
+#30171 := (= #28926 #3222)
+#30172 := [monotonicity #28283 #28225]: #30171
+#30169 := (= #28931 #28926)
+#28932 := (= #28926 #28931)
+#28933 := (not #28932)
+#28927 := (f139 #28926 #24672)
+#28928 := (= f1 #28927)
+#28929 := (not #28928)
+#28936 := (or #28929 #28933)
+#28939 := (not #28936)
+#28942 := (or #26945 #28939)
+#28934 := (or #28933 #28929)
+#28935 := (not #28934)
+#28943 := (or #26945 #28935)
+#28945 := (iff #28943 #28942)
+#28947 := (iff #28942 #28942)
+#28948 := [rewrite]: #28947
+#28940 := (iff #28935 #28939)
+#28937 := (iff #28934 #28936)
+#28938 := [rewrite]: #28937
+#28941 := [monotonicity #28938]: #28940
+#28946 := [monotonicity #28941]: #28945
+#28949 := [trans #28946 #28948]: #28945
+#28944 := [quant-inst]: #28943
+#28950 := [mp #28944 #28949]: #28942
+#30167 := [unit-resolution #28950 #21124]: #28939
+#28953 := (or #28936 #28932)
+#28954 := [def-axiom]: #28953
+#30168 := [unit-resolution #28954 #30167]: #28932
+#30170 := [symm #30168]: #30169
+#30174 := [trans #30170 #30172]: #30173
+#30176 := [monotonicity #30174]: #30175
+#30177 := [symm #30176]: #29121
+#30178 := (not #29121)
+#30179 := (or #30178 #29123)
+#30180 := [th-lemma]: #30179
+#30181 := [unit-resolution #30180 #30177]: #29123
+#29102 := (+ #28021 #29101)
+#29103 := (+ #26909 #29102)
+#29117 := (>= #29103 0::int)
+#29104 := (= #29103 0::int)
+#29107 := (or #24909 #29104)
+#29098 := (= #28930 #29097)
+#29108 := (or #24909 #29098)
+#29110 := (iff #29108 #29107)
+#29112 := (iff #29107 #29107)
+#29113 := [rewrite]: #29112
+#29105 := (iff #29098 #29104)
+#29106 := [rewrite]: #29105
+#29111 := [monotonicity #29106]: #29110
+#29114 := [trans #29111 #29113]: #29110
+#29109 := [quant-inst]: #29108
+#29115 := [mp #29109 #29114]: #29107
+#30182 := [unit-resolution #29115 #23145]: #29104
+#30183 := (not #29104)
+#30184 := (or #30183 #29117)
+#30185 := [th-lemma]: #30184
+#30186 := [unit-resolution #30185 #30182]: #29117
+#28766 := (>= #26907 1::int)
+#28764 := (= #26907 1::int)
+#2963 := (f140 f9)
+#2964 := (= #2963 1::int)
+#11966 := [asserted]: #2964
+#30187 := (= #26907 #2963)
+#30188 := [monotonicity #28225]: #30187
+#30189 := [trans #30188 #11966]: #28764
+#30190 := (not #28764)
+#30191 := (or #30190 #28766)
+#30192 := [th-lemma]: #30191
+#30193 := [unit-resolution #30192 #30189]: #28766
+#28765 := (<= #26907 1::int)
+#30194 := (or #30190 #28765)
+#30195 := [th-lemma]: #30194
+#30196 := [unit-resolution #30195 #30189]: #28765
+#30203 := (not #29119)
+#30202 := (not #29474)
+#30201 := (not #28765)
+#30200 := (not #28766)
+#30199 := (not #28763)
+#30198 := (not #29117)
+#30197 := (not #29123)
+#30204 := (or #30102 #30197 #30198 #30199 #30200 #30201 #30200 #30201 #30202 #30203)
+#30205 := [th-lemma]: #30204
+#30206 := [unit-resolution #30205 #30196 #30193 #30186 #29604 #30181 #30166 #30118]: #30102
+#30103 := (>= #30101 0::int)
+#28762 := (<= #28761 0::int)
+#30207 := (or #30092 #28762)
+#30208 := [th-lemma]: #30207
+#30209 := [unit-resolution #30208 #30090]: #28762
+#29475 := (>= #29473 0::int)
+#30210 := (or #30163 #29475)
+#30211 := [th-lemma]: #30210
+#30212 := [unit-resolution #30211 #30113]: #29475
+#29124 := (>= #29122 0::int)
+#30213 := (or #30178 #29124)
+#30214 := [th-lemma]: #30213
+#30215 := [unit-resolution #30214 #30177]: #29124
+#29116 := (<= #29103 0::int)
+#30216 := (or #30183 #29116)
 #30217 := [th-lemma]: #30216
-#30218 := [unit-resolution #30217 #29434]: #13243
-#24166 := (or #23058 #18276 #18279 #23052)
-#24167 := [def-axiom]: #24166
-#30220 := [unit-resolution #24167 #30218 #29380]: #30219
-#30221 := [unit-resolution #30220 #30215]: #23052
-#24156 := (or #23049 #23043)
-#24157 := [def-axiom]: #24156
-#30223 := [unit-resolution #24157 #30221]: #23043
-#24101 := (>= #13328 -1::int)
-#24152 := (or #23049 #13327)
-#24153 := [def-axiom]: #24152
-#30224 := [unit-resolution #24153 #30221]: #13327
-#30222 := (or #13331 #24101)
-#30225 := [th-lemma]: #30222
-#30226 := [unit-resolution #30225 #30224]: #24101
-#29915 := (not #24101)
-#29916 := (or #13259 #29915)
-#29874 := [hypothesis]: #24101
-#29875 := [hypothesis]: #13264
-#29909 := [th-lemma #29875 #29377 #29874]: false
-#29917 := [lemma #29909]: #29916
-#30227 := [unit-resolution #29917 #30226]: #13259
-#24142 := (or #23046 #13264 #23040)
-#24143 := [def-axiom]: #24142
-#30228 := [unit-resolution #24143 #30227 #30223]: #23040
-#24134 := (or #23037 #23031)
-#24135 := [def-axiom]: #24134
-#30229 := [unit-resolution #24135 #30228]: #23031
-#24130 := (or #23034 #23028 #22098)
-#24131 := [def-axiom]: #24130
-#30230 := [unit-resolution #24131 #30229 #30210]: #22098
-#24119 := (or #22093 #24118)
-#24120 := [def-axiom]: #24119
-#30271 := [unit-resolution #24120 #30230]: #24118
-#30015 := (+ uf_298 #18610)
-#30242 := (>= #30015 0::int)
-#30270 := (not #30242)
-#30496 := (= uf_298 ?x785!14)
-#30527 := (not #30496)
-#24240 := (or #23091 #13417)
-#24241 := [def-axiom]: #24240
-#30232 := [unit-resolution #24241 #30243]: #13417
-#24224 := (+ uf_296 #13279)
-#24225 := (<= #24224 0::int)
-#30234 := (or #12566 #24225)
-#30235 := [th-lemma]: #30234
-#30233 := [unit-resolution #30235 #30248]: #24225
-#24121 := (not #18625)
-#24122 := (or #22093 #24121)
-#24123 := [def-axiom]: #24122
-#30236 := [unit-resolution #24123 #30230]: #24121
-#30514 := (not #24225)
-#30515 := (or #30513 #18625 #30514 #13416)
-#30508 := [hypothesis]: #13417
-#30509 := [hypothesis]: #24225
-#30510 := [hypothesis]: #24121
-#30511 := [hypothesis]: #30503
-#30512 := [th-lemma #30511 #30510 #30509 #30508]: false
-#30516 := [lemma #30512]: #30515
-#30237 := [unit-resolution #30516 #30236 #30233 #30232]: #30513
-#30504 := (or #30502 #30503)
-#30505 := [th-lemma]: #30504
-#30238 := [unit-resolution #30505 #30237]: #30502
-#30528 := (or #30527 #30497)
-#30523 := (= #18302 #3190)
-#30521 := (= #18301 #3181)
-#30519 := (= ?x785!14 uf_298)
-#30518 := [hypothesis]: #30496
-#30520 := [symm #30518]: #30519
-#30522 := [monotonicity #30520]: #30521
+#30218 := [unit-resolution #30217 #30182]: #29116
+#30222 := (not #29475)
+#30221 := (not #28762)
+#30220 := (not #29116)
+#30219 := (not #29124)
+#30223 := (or #30103 #30219 #30220 #30221 #30200 #30201 #30200 #30201 #30222 #30109)
+#30224 := [th-lemma]: #30223
+#30225 := [unit-resolution #30224 #30196 #30193 #30218 #30107 #30215 #30212 #30209]: #30103
+#30227 := (not #30103)
+#30226 := (not #30102)
+#30228 := (or #30099 #30226 #30227)
+#30229 := [th-lemma]: #30228
+#30230 := [unit-resolution #30229 #30225 #30206]: #30099
+#29898 := [symm #30230]: #30125
+#29899 := [monotonicity #29898]: #30131
+#30135 := (= #28982 #29353)
+#29336 := (f67 #26021 #28958 #24835)
+#29356 := (= #29336 #29353)
+#29288 := (not #29356)
+#29337 := (f139 #29336 #26021)
+#29338 := (= f1 #29337)
+#29339 := (not #29338)
+#29296 := (or #29339 #29288)
+#29453 := (not #29296)
+#29456 := (or #26945 #29453)
+#29340 := (* #28958 #26907)
+#29341 := (+ #27157 #29340)
+#29342 := (f44 #24835 #29341)
+#29343 := (= #29336 #29342)
+#29344 := (not #29343)
+#29345 := (or #29344 #29339)
+#29346 := (not #29345)
+#29457 := (or #26945 #29346)
+#29459 := (iff #29457 #29456)
+#29461 := (iff #29456 #29456)
+#29462 := [rewrite]: #29461
+#29454 := (iff #29346 #29453)
+#29451 := (iff #29345 #29296)
+#29293 := (or #29288 #29339)
+#29449 := (iff #29293 #29296)
+#29450 := [rewrite]: #29449
+#29294 := (iff #29345 #29293)
+#29291 := (iff #29344 #29288)
+#29289 := (iff #29343 #29356)
+#29354 := (= #29342 #29353)
+#29351 := (= #29341 #29350)
+#29348 := (= #29340 #29347)
+#29349 := [rewrite]: #29348
+#29352 := [monotonicity #29349]: #29351
+#29355 := [monotonicity #29352]: #29354
+#29290 := [monotonicity #29355]: #29289
+#29292 := [monotonicity #29290]: #29291
+#29295 := [monotonicity #29292]: #29294
+#29452 := [trans #29295 #29450]: #29451
+#29455 := [monotonicity #29452]: #29454
+#29460 := [monotonicity #29455]: #29459
+#29463 := [trans #29460 #29462]: #29459
+#29458 := [quant-inst]: #29457
+#29464 := [mp #29458 #29463]: #29456
+#30127 := [unit-resolution #29464 #21124]: #29453
+#29467 := (or #29296 #29356)
+#29468 := [def-axiom]: #29467
+#30128 := [unit-resolution #29468 #30127]: #29356
+#30129 := (= #28982 #29336)
+#30130 := [monotonicity #28363]: #30129
+#30136 := [trans #30130 #30128]: #30135
+#29900 := [trans #30136 #29899]: #30137
+#29901 := [trans #29900 #30134]: #30139
+#29969 := [monotonicity #29901]: #30141
+#29970 := [symm #29969]: #30143
+#29971 := [monotonicity #29970]: #30145
+#29972 := [trans #29971 #30148]: #30149
+#29973 := [trans #29972 #28337]: #30151
+#29967 := [monotonicity #29973]: #29974
+#29934 := [symm #29967]: #29965
+#29936 := [trans #14275 #29934]: #29200
+#29903 := (not #29200)
+#29904 := (or #29256 #29903)
+#29905 := [def-axiom]: #29904
+#29937 := [unit-resolution #29905 #29936]: #29256
+#29950 := (= #25340 #29214)
+#29941 := (= #29214 #25340)
+#29939 := (= #27769 f9)
+#29932 := (= #27769 #24835)
+#28909 := (or #27934 #27932 #27808)
+#28910 := [def-axiom]: #28909
+#29935 := [unit-resolution #28910 #30121 #28217]: #27808
+#29938 := [symm #29935]: #29932
+#29940 := [trans #29938 #28225]: #29939
+#29942 := [monotonicity #29940]: #29941
+#29951 := [symm #29942]: #29950
+#29949 := [trans #27678 #29951]: #29232
+#29918 := (not #29205)
+#29975 := (iff #12027 #29918)
+#29977 := (iff #12024 #29205)
+#29982 := (iff #29205 #12024)
+#29948 := (= #29204 #3018)
+#29954 := (= #29203 #3005)
+#29952 := (= #29203 #24956)
+#29953 := [monotonicity #29973]: #29952
+#29947 := [trans #29953 #28398]: #29954
+#29956 := [monotonicity #29947]: #29948
+#29976 := [monotonicity #29956]: #29982
+#29966 := [symm #29976]: #29977
+#29985 := [monotonicity #29966]: #29975
+#29980 := [mp #14278 #29985]: #29918
+#29051 := (f67 #27062 #28958 #24835)
+#29052 := (f59 #3185 #29051)
+#29053 := (f137 #29052)
+#29054 := (= f1 #29053)
+#29086 := (not #29054)
+#29994 := (iff #29086 #29211)
+#29992 := (iff #29054 #29210)
+#29990 := (iff #29210 #29054)
+#30005 := (= #29209 #29053)
+#30000 := (= #27673 #29052)
+#29998 := (= #29052 #27673)
+#29996 := (= #29051 #3222)
+#29808 := (= #28958 f299)
+#29822 := [symm #29598]: #29808
+#29997 := [monotonicity #28232 #29822 #28225]: #29996
+#29999 := [monotonicity #29997]: #29998
+#30004 := [symm #29999]: #30000
+#29983 := [monotonicity #30004]: #30005
+#29991 := [monotonicity #29983]: #29990
+#29993 := [symm #29991]: #29992
+#30003 := [monotonicity #29993]: #29994
+#29055 := (f25 f287 #29051)
+#29056 := (= f1 #29055)
+#29057 := (not #29056)
+#29061 := (or #29054 #29057)
+#29064 := (not #29061)
+#29978 := (or #29000 #29010 #29064)
+#29075 := (or #27093 #24685 #27074 #27077 #29000 #29010 #29064)
+#29058 := (or #29057 #29054)
+#29059 := (not #29058)
+#29060 := (or #27077 #29000 #28998 #24685 #27074 #29059)
+#29076 := (or #27093 #29060)
+#29083 := (iff #29076 #29075)
+#29070 := (or #24685 #27074 #27077 #29000 #29010 #29064)
+#29078 := (or #27093 #29070)
+#29081 := (iff #29078 #29075)
+#29082 := [rewrite]: #29081
+#29079 := (iff #29076 #29078)
+#29073 := (iff #29060 #29070)
+#29067 := (or #27077 #29000 #29010 #24685 #27074 #29064)
+#29071 := (iff #29067 #29070)
+#29072 := [rewrite]: #29071
+#29068 := (iff #29060 #29067)
+#29065 := (iff #29059 #29064)
+#29062 := (iff #29058 #29061)
+#29063 := [rewrite]: #29062
+#29066 := [monotonicity #29063]: #29065
+#29069 := [monotonicity #29014 #29066]: #29068
+#29074 := [trans #29069 #29072]: #29073
+#29080 := [monotonicity #29074]: #29079
+#29084 := [trans #29080 #29082]: #29083
+#29077 := [quant-inst]: #29076
+#29085 := [mp #29077 #29084]: #29075
+#29979 := [unit-resolution #29085 #21568 #14260 #28681 #28265]: #29978
+#29986 := [unit-resolution #29979 #29607 #30112]: #29064
+#29087 := (or #29061 #29086)
+#29088 := [def-axiom]: #29087
+#29995 := [unit-resolution #29088 #29986]: #29086
+#29987 := [mp #29995 #30003]: #29211
+#29779 := (or #29250 #29210)
+#29780 := [def-axiom]: #29779
+#30006 := [unit-resolution #29780 #29987]: #29250
+#29820 := (or #29270 #29205 #29247 #29253 #29259)
+#29821 := [def-axiom]: #29820
+#30007 := [unit-resolution #29821 #30006 #29980 #29949 #29937 #29909]: false
+#29988 := [lemma #30007]: #29270
+#29958 := (or #29273 #29265)
+#29959 := [def-axiom]: #29958
+#29912 := [unit-resolution #29959 #29988]: #29273
+#28271 := (or #12487 #13565 #27074 #13710)
+#28214 := [hypothesis]: #13425
+#28049 := (f67 #26925 f299 #27446)
+#28050 := (f126 #28049 #26925)
+#28081 := (* -1::int #28050)
+#28209 := (+ f299 #28081)
+#28210 := (<= #28209 0::int)
+#28051 := (= f299 #28050)
+#28054 := (or #26968 #28051)
+#28055 := [quant-inst]: #28054
+#28215 := [unit-resolution #28055 #16991]: #28051
+#28218 := (not #28051)
+#28219 := (or #28218 #28210)
+#28220 := [th-lemma]: #28219
+#28221 := [unit-resolution #28220 #28215]: #28210
+#28072 := (>= #28050 0::int)
+#28073 := (not #28072)
+#28124 := (f67 #27062 #28050 #24835)
+#28128 := (f25 f287 #28124)
+#28129 := (= f1 #28128)
+#28130 := (not #28129)
+#28125 := (f59 #3185 #28124)
+#28126 := (f137 #28125)
+#28127 := (= f1 #28126)
+#28134 := (or #28127 #28130)
+#28241 := (iff #18443 #28130)
+#28239 := (iff #12487 #28129)
+#28237 := (iff #28129 #12487)
+#28235 := (= #28128 #3225)
+#28233 := (= #28124 #3222)
+#28226 := (= #28050 f299)
+#28227 := [symm #28215]: #28226
+#28234 := [monotonicity #28232 #28227 #28225]: #28233
+#28236 := [monotonicity #28234]: #28235
+#28238 := [monotonicity #28236]: #28237
+#28240 := [symm #28238]: #28239
+#28242 := [monotonicity #28240]: #28241
+#28222 := [hypothesis]: #18443
+#28243 := [mp #28222 #28242]: #28130
+#28162 := (or #28134 #28129)
+#28163 := [def-axiom]: #28162
+#28244 := [unit-resolution #28163 #28243]: #28134
+#28082 := (+ #24837 #28081)
+#28083 := (<= #28082 0::int)
+#28254 := (not #28083)
+#28250 := [hypothesis]: #13711
+#28211 := (>= #28209 0::int)
+#28251 := (or #28218 #28211)
+#28252 := [th-lemma]: #28251
+#28253 := [unit-resolution #28252 #28215]: #28211
+#28256 := (not #28211)
+#28257 := (or #28254 #28255 #28256 #13710)
+#28258 := [th-lemma]: #28257
+#28259 := [unit-resolution #28258 #28253 #28250 #28249]: #28254
+#28137 := (not #28134)
+#28267 := (or #28073 #28083 #28137)
+#28148 := (or #27093 #24685 #27074 #27077 #28073 #28083 #28137)
+#28131 := (or #28130 #28127)
+#28132 := (not #28131)
+#28070 := (+ #28050 #27003)
+#28071 := (>= #28070 0::int)
+#28133 := (or #27077 #28073 #28071 #24685 #27074 #28132)
+#28149 := (or #27093 #28133)
+#28156 := (iff #28149 #28148)
+#28143 := (or #24685 #27074 #27077 #28073 #28083 #28137)
+#28151 := (or #27093 #28143)
+#28154 := (iff #28151 #28148)
+#28155 := [rewrite]: #28154
+#28152 := (iff #28149 #28151)
+#28146 := (iff #28133 #28143)
+#28140 := (or #27077 #28073 #28083 #24685 #27074 #28137)
+#28144 := (iff #28140 #28143)
+#28145 := [rewrite]: #28144
+#28141 := (iff #28133 #28140)
+#28138 := (iff #28132 #28137)
+#28135 := (iff #28131 #28134)
+#28136 := [rewrite]: #28135
+#28139 := [monotonicity #28136]: #28138
+#28086 := (iff #28071 #28083)
+#28075 := (+ #27003 #28050)
+#28078 := (>= #28075 0::int)
+#28084 := (iff #28078 #28083)
+#28085 := [rewrite]: #28084
+#28079 := (iff #28071 #28078)
+#28076 := (= #28070 #28075)
+#28077 := [rewrite]: #28076
+#28080 := [monotonicity #28077]: #28079
+#28087 := [trans #28080 #28085]: #28086
+#28142 := [monotonicity #28087 #28139]: #28141
+#28147 := [trans #28142 #28145]: #28146
+#28153 := [monotonicity #28147]: #28152
+#28157 := [trans #28153 #28155]: #28156
+#28150 := [quant-inst]: #28149
+#28158 := [mp #28150 #28157]: #28148
+#28268 := [unit-resolution #28158 #21568 #14260 #28266 #28265]: #28267
+#28269 := [unit-resolution #28268 #28259 #28244]: #28073
+#28270 := [th-lemma #28269 #28221 #28214]: false
+#28272 := [lemma #28270]: #28271
+#29176 := [unit-resolution #28272 #29175 #28681 #29174]: #12487
+#29910 := (or #29282 #18443 #29276)
+#29911 := [def-axiom]: #29910
+#30002 := [unit-resolution #29911 #29176 #29912]: #29282
+#29866 := (or #29865 #12493 #29279)
+#29864 := [def-axiom]: #29866
+#30009 := [unit-resolution #29864 #30002]: #30008
+#30001 := [unit-resolution #30009 #29946]: #12493
+#30303 := (+ f299 #18812)
+#30496 := (>= #30303 0::int)
+#30578 := (not #30496)
+#30498 := (= f299 ?v0!14)
+#30529 := (not #30498)
+#30497 := [hypothesis]: #23296
+#24442 := (or #23293 #13617)
+#24443 := [def-axiom]: #24442
+#30501 := [unit-resolution #24443 #30497]: #13617
+#24426 := (+ f297 #13479)
+#24427 := (<= #24426 0::int)
+#24432 := (or #23293 #12748)
+#24433 := [def-axiom]: #24432
+#30532 := [unit-resolution #24433 #30497]: #12748
+#30533 := (or #12766 #24427)
+#30534 := [th-lemma]: #30533
+#30535 := [unit-resolution #30534 #30532]: #24427
+#24323 := (not #18827)
+#29968 := [hypothesis]: #23260
+#24444 := (or #23293 #23257)
+#24445 := [def-axiom]: #24444
+#29897 := [unit-resolution #24445 #29968]: #23293
+#24388 := (or #23263 #23257)
+#24389 := [def-axiom]: #24388
+#29984 := [unit-resolution #24389 #29968]: #23263
+#29989 := (or #23272 #18449 #23266)
+#24398 := (or #23272 #18440 #18449 #23266)
+#24399 := [def-axiom]: #24398
+#30012 := [unit-resolution #24399 #28312]: #29989
+#30016 := [unit-resolution #30012 #29984 #30001]: #23272
+#29193 := (or #23269 #23296)
+#29125 := [hypothesis]: #23293
+#24496 := (or #23329 #23323)
+#24497 := [def-axiom]: #24496
+#29173 := [unit-resolution #24497 #29172]: #23323
+#29177 := (or #23326 #18443 #23320)
+#24488 := (or #23326 #18440 #18443 #23320)
+#24489 := [def-axiom]: #24488
+#29178 := [unit-resolution #24489 #28312]: #29177
+#29179 := [unit-resolution #29178 #29176 #29173]: #23320
+#24478 := (or #23317 #23311)
+#24479 := [def-axiom]: #24478
+#29180 := [unit-resolution #24479 #29179]: #23311
+#29181 := [hypothesis]: #23272
+#24394 := (or #23269 #12493)
+#24395 := [def-axiom]: #24394
+#29182 := [unit-resolution #24395 #29181]: #12493
+#29183 := (or #23314 #18449 #23308)
+#24472 := (or #23314 #18440 #18449 #23308)
+#24473 := [def-axiom]: #24472
+#29184 := [unit-resolution #24473 #28312]: #29183
+#29185 := [unit-resolution #29184 #29182 #29180]: #23308
+#24462 := (or #23305 #23299)
+#24463 := [def-axiom]: #24462
+#29186 := [unit-resolution #24463 #29185]: #23299
+#24404 := (or #23275 #23269)
+#24405 := [def-axiom]: #24404
+#29187 := [unit-resolution #24405 #29181]: #23275
+#29188 := (or #23284 #18443 #23278)
+#24414 := (or #23284 #18440 #18443 #23278)
+#24415 := [def-axiom]: #24414
+#29189 := [unit-resolution #24415 #28312]: #29188
+#29190 := [unit-resolution #29189 #29187 #29176]: #23284
+#24422 := (or #23287 #23281)
+#24423 := [def-axiom]: #24422
+#29191 := [unit-resolution #24423 #29190]: #23287
+#24452 := (or #23302 #23290 #23296)
+#24453 := [def-axiom]: #24452
+#29192 := [unit-resolution #24453 #29191 #29186 #29125]: false
+#29194 := [lemma #29192]: #29193
+#30017 := [unit-resolution #29194 #30016 #29897]: false
+#30015 := [lemma #30017]: #23257
+#30484 := (or #23260 #23254)
+#15720 := (<= f286 4294967295::int)
+#15723 := (iff #13350 #15720)
+#15714 := (+ 4294967295::int #13351)
+#15717 := (>= #15714 0::int)
+#15721 := (iff #15717 #15720)
+#15722 := [rewrite]: #15721
+#15718 := (iff #13350 #15717)
+#15715 := (= #13352 #15714)
+#15716 := [monotonicity #7558]: #15715
+#15719 := [monotonicity #15716]: #15718
+#15724 := [trans #15719 #15722]: #15723
+#14266 := [not-or-elim #14255]: #13355
+#14268 := [and-elim #14266]: #13350
+#15725 := [mp #14268 #15724]: #15720
+#29943 := [hypothesis]: #18481
+#29944 := [th-lemma #29175 #29943 #15725]: false
+#29955 := [lemma #29944]: #15809
+#30482 := (or #23260 #18481 #23254)
+#30479 := (or #13565 #13443)
+#30480 := [th-lemma]: #30479
+#30481 := [unit-resolution #30480 #29174]: #13443
+#24368 := (or #23260 #18478 #18481 #23254)
+#24369 := [def-axiom]: #24368
+#30483 := [unit-resolution #24369 #30481]: #30482
+#30485 := [unit-resolution #30483 #29955]: #30484
+#30486 := [unit-resolution #30485 #30015]: #23254
+#24358 := (or #23251 #23245)
+#24359 := [def-axiom]: #24358
+#30536 := [unit-resolution #24359 #30486]: #23245
+#24303 := (>= #13528 -1::int)
+#24354 := (or #23251 #13527)
+#24355 := [def-axiom]: #24354
+#30487 := [unit-resolution #24355 #30486]: #13527
+#30488 := (or #13531 #24303)
+#30489 := [th-lemma]: #30488
+#30490 := [unit-resolution #30489 #30487]: #24303
+#29874 := (not #24303)
+#29875 := (or #29874 #13459)
+#29871 := [hypothesis]: #24303
+#29872 := [hypothesis]: #13464
+#29873 := [th-lemma #29872 #29871 #29175]: false
+#29876 := [lemma #29873]: #29875
+#30537 := [unit-resolution #29876 #30490]: #13459
+#24344 := (or #23248 #13464 #23242)
+#24345 := [def-axiom]: #24344
+#30538 := [unit-resolution #24345 #30537 #30536]: #23242
+#24336 := (or #23239 #23233)
+#24337 := [def-axiom]: #24336
+#30539 := [unit-resolution #24337 #30538]: #23233
+#24429 := (+ f298 #13501)
+#24431 := (>= #24429 0::int)
+#24434 := (or #23293 #12751)
+#24435 := [def-axiom]: #24434
+#30540 := [unit-resolution #24435 #30497]: #12751
+#30541 := (or #12757 #24431)
+#30542 := [th-lemma]: #30541
+#30543 := [unit-resolution #30542 #30540]: #24431
+#30544 := (not #24431)
+#30547 := (or #13504 #30544)
+#30545 := (or #13504 #13888 #30544)
+#30546 := [th-lemma]: #30545
+#30548 := [unit-resolution #30546 #29138]: #30547
+#30549 := [unit-resolution #30548 #30543]: #13504
+#30556 := (= #3118 #3264)
+#30554 := (= #3264 #3118)
+#30551 := (= #3263 #3117)
+#30550 := [symm #30540]: #3294
+#30552 := [monotonicity #30550]: #30551
+#30555 := [monotonicity #30552]: #30554
+#30557 := [symm #30555]: #30556
+#30558 := (= f305 #3118)
+#30553 := [symm #30532]: #3293
+#30559 := [trans #30553 #29136]: #30558
+#30560 := [trans #30559 #30557]: #12552
+#24308 := (or #22248 #22246 #13503)
+#24309 := [def-axiom]: #24308
+#30561 := [unit-resolution #24309 #30560 #30549]: #22248
+#24310 := (or #23227 #22247)
+#24311 := [def-axiom]: #24310
+#30562 := [unit-resolution #24311 #30561]: #23227
+#24332 := (or #23236 #23230 #22300)
+#24333 := [def-axiom]: #24332
+#30563 := [unit-resolution #24333 #30562 #30539]: #22300
+#24324 := (or #22295 #24323)
+#24325 := [def-axiom]: #24324
+#30564 := [unit-resolution #24325 #30563]: #24323
+#30513 := (not #24427)
+#30514 := (or #30512 #18827 #30513 #13616)
+#30507 := [hypothesis]: #13617
+#30508 := [hypothesis]: #24427
+#30509 := [hypothesis]: #24323
+#30510 := [hypothesis]: #30502
+#30511 := [th-lemma #30510 #30509 #30508 #30507]: false
+#30515 := [lemma #30511]: #30514
+#30565 := [unit-resolution #30515 #30564 #30535 #30501]: #30512
+#30506 := (or #30505 #30502)
+#30516 := [th-lemma]: #30506
+#30566 := [unit-resolution #30516 #30565]: #30505
+#30530 := (or #30529 #30499)
+#30525 := (= #18504 #3231)
+#30523 := (= #18503 #3222)
+#30521 := (= ?v0!14 f299)
+#30520 := [hypothesis]: #30498
+#30522 := [symm #30520]: #30521
 #30524 := [monotonicity #30522]: #30523
-#30525 := [symm #30524]: #30497
-#30517 := [hypothesis]: #30502
-#30526 := [unit-resolution #30517 #30525]: false
-#30529 := [lemma #30526]: #30528
-#30239 := [unit-resolution #30529 #30238]: #30527
-#30274 := (or #30496 #30270)
-#30013 := (<= #30015 0::int)
-#30051 := (+ uf_296 #18623)
-#30052 := (>= #30051 0::int)
-#30240 := (not #30052)
-#30241 := (or #30240 #18625 #30514)
-#30283 := [th-lemma]: #30241
-#30284 := [unit-resolution #30283 #30233 #30236]: #30240
-#30286 := (or #30013 #30052)
-#24116 := (or #22093 #18298)
-#24117 := [def-axiom]: #24116
-#30285 := [unit-resolution #24117 #30230]: #18298
-#24114 := (or #22093 #18297)
-#24115 := [def-axiom]: #24114
-#30280 := [unit-resolution #24115 #30230]: #18297
-#30068 := (or #23014 #22077 #22078 #30013 #30052)
-#29997 := (+ #18302 #13715)
-#29992 := (<= #29997 0::int)
-#29998 := (+ ?x785!14 #13246)
-#29999 := (>= #29998 0::int)
-#30001 := (or #22078 #29999 #29992 #22077)
-#30069 := (or #23014 #30001)
-#30076 := (iff #30069 #30068)
-#30063 := (or #22077 #22078 #30013 #30052)
-#30071 := (or #23014 #30063)
-#30074 := (iff #30071 #30068)
-#30075 := [rewrite]: #30074
-#30072 := (iff #30069 #30071)
-#30066 := (iff #30001 #30063)
-#30060 := (or #22078 #30013 #30052 #22077)
-#30064 := (iff #30060 #30063)
-#30065 := [rewrite]: #30064
-#30061 := (iff #30001 #30060)
-#30058 := (iff #29992 #30052)
-#30046 := (+ #13715 #18302)
-#30048 := (<= #30046 0::int)
-#30056 := (iff #30048 #30052)
-#30057 := [rewrite]: #30056
-#30049 := (iff #29992 #30048)
-#30047 := (= #29997 #30046)
-#30042 := [rewrite]: #30047
-#30050 := [monotonicity #30042]: #30049
-#30059 := [trans #30050 #30057]: #30058
-#30030 := (iff #29999 #30013)
-#30002 := (+ #13246 ?x785!14)
-#30012 := (>= #30002 0::int)
-#30016 := (iff #30012 #30013)
-#30017 := [rewrite]: #30016
-#30000 := (iff #29999 #30012)
-#30007 := (= #29998 #30002)
-#30008 := [rewrite]: #30007
-#30014 := [monotonicity #30008]: #30000
-#30031 := [trans #30014 #30017]: #30030
-#30062 := [monotonicity #30031 #30059]: #30061
-#30067 := [trans #30062 #30065]: #30066
-#30073 := [monotonicity #30067]: #30072
-#30077 := [trans #30073 #30075]: #30076
-#30070 := [quant-inst]: #30069
-#30078 := [mp #30070 #30077]: #30068
-#30287 := [unit-resolution #30078 #29339 #30280 #30285]: #30286
-#30288 := [unit-resolution #30287 #30284]: #30013
-#30289 := (not #30013)
-#30299 := (or #30496 #30289 #30270)
-#30273 := [th-lemma]: #30299
-#30269 := [unit-resolution #30273 #30288]: #30274
-#30275 := [unit-resolution #30269 #30239]: #30270
-#30276 := [th-lemma #30275 #30226 #30271]: false
-#30272 := [lemma #30276]: #23091
-#29441 := (or #23103 #23094 #23064)
-#29421 := [hypothesis]: #23061
-#29422 := [hypothesis]: #23106
-#24254 := (or #23103 #12302)
-#24255 := [def-axiom]: #24254
-#29425 := [unit-resolution #24255 #29422]: #12302
-#29426 := (or #23070 #18247 #23064)
-#24196 := (or #23070 #18238 #18247 #23064)
-#24197 := [def-axiom]: #24196
-#29427 := [unit-resolution #24197 #28272]: #29426
-#29428 := [unit-resolution #29427 #29425 #29421]: #23070
-#24202 := (or #23073 #23067)
-#24203 := [def-axiom]: #24202
-#29429 := [unit-resolution #24203 #29428]: #23073
-#29430 := [hypothesis]: #23091
-#24260 := (or #23103 #23097)
-#24261 := [def-axiom]: #24260
-#29431 := [unit-resolution #24261 #29422]: #23097
-#24250 := (or #23100 #23088 #23094)
-#24251 := [def-axiom]: #24250
-#29432 := [unit-resolution #24251 #29431 #29430]: #23088
-#24220 := (or #23085 #23079)
-#24221 := [def-axiom]: #24220
-#29433 := [unit-resolution #24221 #29432]: #23079
-#29438 := (or #23082 #23076)
-#29436 := (or #23082 #18241 #23076)
-#24212 := (or #23082 #18238 #18241 #23076)
-#24213 := [def-axiom]: #24212
-#29437 := [unit-resolution #24213 #28272]: #29436
-#29439 := [unit-resolution #29437 #29435]: #29438
-#29440 := [unit-resolution #29439 #29433 #29429]: false
-#29442 := [lemma #29440]: #29441
-#30594 := [unit-resolution #29442 #30272]: #30593
-#30595 := [unit-resolution #30594 #30592]: #23064
-#24178 := (or #23061 #12313)
-#24179 := [def-axiom]: #24178
-#30596 := [unit-resolution #24179 #30595]: #12313
-#24176 := (or #23061 #12308)
-#24177 := [def-axiom]: #24176
-#30597 := [unit-resolution #24177 #30595]: #12308
-#30598 := [trans #30597 #30596]: #30154
-#30599 := (not #30154)
-#30600 := (or #30599 #30108)
-#30601 := [th-lemma]: #30600
-#30602 := [unit-resolution #30601 #30598]: #30108
-#24186 := (or #23061 #23055)
-#24187 := [def-axiom]: #24186
-#30603 := [unit-resolution #24187 #30595]: #23055
-#30604 := [unit-resolution #30220 #30603]: #23052
-#30605 := [unit-resolution #24157 #30604]: #23043
-#30606 := [unit-resolution #24153 #30604]: #13327
-#30607 := [unit-resolution #30225 #30606]: #24101
-#30608 := [unit-resolution #29917 #30607]: #13259
-#30609 := [unit-resolution #24143 #30608 #30605]: #23040
-#30610 := [unit-resolution #24135 #30609]: #23031
-#30619 := (= #3190 #3220)
-#30615 := (= #3220 #3190)
-#30613 := (= #3219 #3181)
-#24180 := (or #23061 #12316)
-#24181 := [def-axiom]: #24180
-#30611 := [unit-resolution #24181 #30595]: #12316
-#30612 := [symm #30611]: #3200
-#30614 := [monotonicity #30612]: #30613
-#30616 := [monotonicity #30614]: #30615
-#30620 := [symm #30616]: #30619
-#30621 := (= uf_304 #3190)
-#30618 := [symm #30597]: #3193
-#30617 := [symm #30596]: #3198
-#30622 := [trans #30617 #30618]: #30621
-#30623 := [trans #30622 #30620]: #12352
-#29903 := (+ uf_298 #13301)
-#29849 := (>= #29903 0::int)
-#30624 := (or #12440 #29849)
-#30625 := [th-lemma]: #30624
-#30626 := [unit-resolution #30625 #30611]: #29849
-#30627 := (not #29849)
-#30628 := (or #13304 #30627 #13510)
-#30629 := [th-lemma]: #30628
-#30630 := [unit-resolution #30629 #29377 #30626]: #13304
-#30631 := [unit-resolution #24107 #30630 #30623]: #22046
-#30632 := [unit-resolution #24109 #30631]: #23025
-#30633 := [unit-resolution #24131 #30632 #30610]: #22098
-#30634 := [unit-resolution #24123 #30633]: #24121
-#30635 := (not #30108)
-#30636 := (or #30513 #18625 #30635)
-#30637 := [th-lemma]: #30636
-#30638 := [unit-resolution #30637 #30634 #30602]: #30513
-#30639 := [unit-resolution #30505 #30638]: #30502
-#30640 := [unit-resolution #24120 #30633]: #24118
-#30641 := (or #30242 #18612 #29915)
-#30642 := [th-lemma]: #30641
-#30643 := [unit-resolution #30642 #30640 #30607]: #30242
-#30644 := [unit-resolution #24261 #30592]: #23097
-#30645 := (or #23100 #23088)
-#30646 := [unit-resolution #24251 #30272]: #30645
-#30647 := [unit-resolution #30646 #30644]: #23088
-#24218 := (or #23085 #13416)
-#24219 := [def-axiom]: #24218
-#30648 := [unit-resolution #24219 #30647]: #13416
-#30649 := (or #24225 #30635 #13417)
-#30650 := [th-lemma]: #30649
-#30651 := [unit-resolution #30650 #30648 #30602]: #24225
-#30652 := [unit-resolution #30283 #30634 #30651]: #30240
-#30653 := [unit-resolution #24117 #30633]: #18298
-#30654 := [unit-resolution #24115 #30633]: #18297
-#30655 := [unit-resolution #30078 #29339 #30654 #30653 #30652]: #30013
-#30656 := [unit-resolution #30273 #30655 #30643]: #30496
-[unit-resolution #30529 #30656 #30639]: false
+#30526 := [monotonicity #30524]: #30525
+#30527 := [symm #30526]: #30499
+#30519 := [hypothesis]: #30505
+#30528 := [unit-resolution #30519 #30527]: false
+#30531 := [lemma #30528]: #30530
+#30567 := [unit-resolution #30531 #30566]: #30529
+#30581 := (or #30498 #30578)
+#30304 := (<= #30303 0::int)
+#30315 := (+ f297 #18825)
+#30316 := (>= #30315 0::int)
+#30568 := (not #30316)
+#30569 := (or #30568 #18827 #30513)
+#30570 := [th-lemma]: #30569
+#30571 := [unit-resolution #30570 #30535 #30564]: #30568
+#30574 := (or #30304 #30316)
+#24318 := (or #22295 #18500)
+#24319 := [def-axiom]: #24318
+#30572 := [unit-resolution #24319 #30563]: #18500
+#24316 := (or #22295 #18499)
+#24317 := [def-axiom]: #24316
+#30573 := [unit-resolution #24317 #30563]: #18499
+#30329 := (or #23216 #22279 #22280 #30304 #30316)
+#30292 := (+ #18504 #13915)
+#30293 := (<= #30292 0::int)
+#30294 := (+ ?v0!14 #13446)
+#30295 := (>= #30294 0::int)
+#30296 := (or #22280 #30295 #30293 #22279)
+#30330 := (or #23216 #30296)
+#30337 := (iff #30330 #30329)
+#30324 := (or #22279 #22280 #30304 #30316)
+#30332 := (or #23216 #30324)
+#30335 := (iff #30332 #30329)
+#30336 := [rewrite]: #30335
+#30333 := (iff #30330 #30332)
+#30327 := (iff #30296 #30324)
+#30321 := (or #22280 #30304 #30316 #22279)
+#30325 := (iff #30321 #30324)
+#30326 := [rewrite]: #30325
+#30322 := (iff #30296 #30321)
+#30319 := (iff #30293 #30316)
+#30309 := (+ #13915 #18504)
+#30312 := (<= #30309 0::int)
+#30317 := (iff #30312 #30316)
+#30318 := [rewrite]: #30317
+#30313 := (iff #30293 #30312)
+#30310 := (= #30292 #30309)
+#30311 := [rewrite]: #30310
+#30314 := [monotonicity #30311]: #30313
+#30320 := [trans #30314 #30318]: #30319
+#30307 := (iff #30295 #30304)
+#30297 := (+ #13446 ?v0!14)
+#30300 := (>= #30297 0::int)
+#30305 := (iff #30300 #30304)
+#30306 := [rewrite]: #30305
+#30301 := (iff #30295 #30300)
+#30298 := (= #30294 #30297)
+#30299 := [rewrite]: #30298
+#30302 := [monotonicity #30299]: #30301
+#30308 := [trans #30302 #30306]: #30307
+#30323 := [monotonicity #30308 #30320]: #30322
+#30328 := [trans #30323 #30326]: #30327
+#30334 := [monotonicity #30328]: #30333
+#30338 := [trans #30334 #30336]: #30337
+#30331 := [quant-inst]: #30330
+#30339 := [mp #30331 #30338]: #30329
+#30575 := [unit-resolution #30339 #29135 #30573 #30572]: #30574
+#30576 := [unit-resolution #30575 #30571]: #30304
+#30577 := (not #30304)
+#30579 := (or #30498 #30577 #30578)
+#30580 := [th-lemma]: #30579
+#30582 := [unit-resolution #30580 #30576]: #30581
+#30583 := [unit-resolution #30582 #30567]: #30578
+#24320 := (not #18814)
+#24321 := (or #22295 #24320)
+#24322 := [def-axiom]: #24321
+#30584 := [unit-resolution #24322 #30563]: #24320
+#30585 := [th-lemma #30490 #30584 #30583]: false
+#30586 := [lemma #30585]: #23293
+#29632 := [unit-resolution #29194 #30586]: #23269
+#29634 := [unit-resolution #30012 #29632 #30001]: #23266
+#24380 := (or #23263 #12510)
+#24381 := [def-axiom]: #24380
+#30421 := [unit-resolution #24381 #29634]: #12510
+#24374 := (or #23263 #12499)
+#24375 := [def-axiom]: #24374
+#30426 := [unit-resolution #24375 #29634]: #12499
+#30427 := [trans #30426 #30421]: #30077
+#30435 := (not #30077)
+#30436 := (or #30435 #30011)
+#30434 := [th-lemma]: #30436
+#30437 := [unit-resolution #30434 #30427]: #30011
+#30054 := (+ f299 #13501)
+#30072 := (>= #30054 0::int)
+#24382 := (or #23263 #12513)
+#24383 := [def-axiom]: #24382
+#29633 := [unit-resolution #24383 #29634]: #12513
+#29631 := (or #12640 #30072)
+#29635 := [th-lemma]: #29631
+#29636 := [unit-resolution #29635 #29633]: #30072
+#29637 := [hypothesis]: #13503
+#30256 := [th-lemma #29637 #29636 #29175]: false
+#30257 := [lemma #30256]: #13504
+#30461 := (or #22248 #13503)
+#30457 := (= #3231 #3264)
+#30441 := (= #3264 #3231)
+#30439 := (= #3263 #3222)
+#30438 := [symm #29633]: #3243
+#30440 := [monotonicity #30438]: #30439
+#30442 := [monotonicity #30440]: #30441
+#30458 := [symm #30442]: #30457
+#30459 := (= f305 #3231)
+#30456 := [symm #30426]: #3234
+#30455 := [symm #30421]: #3241
+#30454 := [trans #30455 #30456]: #30459
+#30460 := [trans #30454 #30458]: #12552
+#30462 := [unit-resolution #24309 #30460]: #30461
+#30463 := [unit-resolution #30462 #30257]: #22248
+#30464 := [unit-resolution #24311 #30463]: #23227
+#30472 := [unit-resolution #24333 #30539]: #23233
+#30473 := [unit-resolution #30472 #30464]: #22300
+#30375 := [unit-resolution #24325 #30473]: #24323
+#30443 := (not #30011)
+#30444 := (or #30512 #18827 #30443)
+#30495 := [th-lemma]: #30444
+#30587 := [unit-resolution #30495 #30375 #30437]: #30512
+#30588 := [unit-resolution #30516 #30587]: #30505
+#30589 := [unit-resolution #24322 #30473]: #24320
+#30590 := (or #30496 #29874 #18814)
+#30591 := [th-lemma]: #30590
+#30592 := [unit-resolution #30591 #30589 #30490]: #30496
+#30602 := (or #30568 #18827)
+#30593 := (or #18449 #23308)
+#30594 := [unit-resolution #29184 #29180]: #30593
+#30595 := [unit-resolution #30594 #30001]: #23308
+#30596 := [unit-resolution #24463 #30595]: #23299
+#30597 := [unit-resolution #24453 #30586 #30596]: #23290
+#24420 := (or #23287 #13616)
+#24421 := [def-axiom]: #24420
+#30598 := [unit-resolution #24421 #30597]: #13616
+#30599 := (or #24427 #30443 #13617)
+#30600 := [th-lemma]: #30599
+#30601 := [unit-resolution #30600 #30598 #30437]: #24427
+#30603 := [unit-resolution #30570 #30601]: #30602
+#30604 := [unit-resolution #30603 #30375]: #30568
+#30605 := [unit-resolution #24319 #30473]: #18500
+#30606 := [unit-resolution #24317 #30473]: #18499
+#30607 := [unit-resolution #30339 #29135 #30606 #30605 #30604]: #30304
+#30608 := [unit-resolution #30580 #30607 #30592]: #30498
+[unit-resolution #30531 #30608 #30588]: false
 unsat

--- a/src/HOL/IsaMakefile	Wed May 12 23:54:04 2010 +0200
+++ b/src/HOL/IsaMakefile	Wed May 12 23:54:06 2010 +0200
@@ -1099,7 +1099,7 @@
   Multivariate_Analysis/Fashoda.thy			\
   Multivariate_Analysis/Finite_Cartesian_Product.thy	\
   Multivariate_Analysis/Integration.thy			\
-  Multivariate_Analysis/Integration.cert		\
+  Multivariate_Analysis/Integration.certs		\
   Multivariate_Analysis/L2_Norm.thy			\
   Multivariate_Analysis/Multivariate_Analysis.thy	\
   Multivariate_Analysis/Operator_Norm.thy		\

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Multivariate_Analysis/Integration.certs	Wed May 12 23:54:06 2010 +0200
@@ -0,0 +1,4215 @@
+148c2437fb9e64ff4110383f54f5a9a720082439 428 0
+#2 := false
+decl f12 :: S2
+#42 := f12
+decl f5 :: S2
+#25 := f5
+#49 := (= f5 f12)
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+#43 := (f4 f12)
+#593 := (f3 #43)
+#691 := (= #593 f12)
+#594 := (= f12 #593)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#546 := (pattern #9)
+#10 := (f3 #9)
+#98 := (= #8 #10)
+#547 := (forall (vars (?v0 S2)) (:pat #546) #98)
+#101 := (forall (vars (?v0 S2)) #98)
+#550 := (iff #101 #547)
+#548 := (iff #98 #98)
+#549 := [refl]: #548
+#551 := [quant-intro #549]: #550
+#461 := (~ #101 #101)
+#463 := (~ #98 #98)
+#464 := [refl]: #463
+#462 := [nnf-pos #464]: #461
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#102 := (iff #12 #101)
+#99 := (iff #11 #98)
+#100 := [rewrite]: #99
+#103 := [quant-intro #100]: #102
+#97 := [asserted]: #12
+#106 := [mp #97 #103]: #101
+#459 := [mp~ #106 #462]: #101
+#552 := [mp #459 #551]: #547
+#595 := (not #547)
+#600 := (or #595 #594)
+#601 := [quant-inst]: #600
+#685 := [unit-resolution #601 #552]: #594
+#692 := [symm #685]: #691
+#693 := (= f5 #593)
+#26 := (f4 f5)
+#591 := (f3 #26)
+#689 := (= #591 #593)
+#687 := (= #593 #591)
+#683 := (= #43 #26)
+#681 := (= #26 #43)
+#13 := 0::int
+#232 := -1::int
+#235 := (* -1::int #43)
+#236 := (+ #26 #235)
+#301 := (<= #236 0::int)
+#74 := (<= #26 #43)
+#398 := (iff #74 #301)
+#399 := [rewrite]: #398
+#352 := [asserted]: #74
+#400 := [mp #352 #399]: #301
+#234 := (>= #236 0::int)
+decl f6 :: (-> S3 S4 real)
+decl f8 :: (-> S2 S4)
+#29 := (f8 f5)
+decl f9 :: S3
+#31 := f9
+#32 := (f6 f9 #29)
+decl f11 :: S3
+#37 := f11
+#38 := (f6 f11 #29)
+#50 := (f8 f12)
+decl f7 :: S3
+#28 := f7
+#51 := (f6 f7 #50)
+#52 := (ite #49 #51 #38)
+#261 := (ite #234 #52 #32)
+#573 := (= #32 #261)
+#653 := (not #573)
+#199 := 0::real
+#197 := -1::real
+#270 := (* -1::real #261)
+#645 := (+ #32 #270)
+#647 := (>= #645 0::real)
+#650 := (not #647)
+#648 := [hypothesis]: #647
+decl f10 :: S3
+#34 := f10
+#35 := (f6 f10 #29)
+#271 := (+ #35 #270)
+#269 := (>= #271 0::real)
+#272 := (not #269)
+#30 := (f6 f7 #29)
+decl f13 :: S3
+#45 := f13
+#46 := (f6 f13 #29)
+#242 := (ite #234 #46 #30)
+#250 := (* -1::real #242)
+#251 := (+ #35 #250)
+#252 := (<= #251 0::real)
+#253 := (not #252)
+#277 := (and #253 #272)
+#44 := (< #26 #43)
+#53 := (ite #44 #32 #52)
+#54 := (< #35 #53)
+#47 := (ite #44 #30 #46)
+#48 := (< #47 #35)
+#55 := (and #48 #54)
+#278 := (iff #55 #277)
+#275 := (iff #54 #272)
+#266 := (< #35 #261)
+#273 := (iff #266 #272)
+#274 := [rewrite]: #273
+#267 := (iff #54 #266)
+#264 := (= #53 #261)
+#233 := (not #234)
+#258 := (ite #233 #32 #52)
+#262 := (= #258 #261)
+#263 := [rewrite]: #262
+#259 := (= #53 #258)
+#237 := (iff #44 #233)
+#238 := [rewrite]: #237
+#260 := [monotonicity #238]: #259
+#265 := [trans #260 #263]: #264
+#268 := [monotonicity #265]: #267
+#276 := [trans #268 #274]: #275
+#256 := (iff #48 #253)
+#247 := (< #242 #35)
+#254 := (iff #247 #253)
+#255 := [rewrite]: #254
+#248 := (iff #48 #247)
+#245 := (= #47 #242)
+#239 := (ite #233 #30 #46)
+#243 := (= #239 #242)
+#244 := [rewrite]: #243
+#240 := (= #47 #239)
+#241 := [monotonicity #238]: #240
+#246 := [trans #241 #244]: #245
+#249 := [monotonicity #246]: #248
+#257 := [trans #249 #255]: #256
+#279 := [monotonicity #257 #276]: #278
+#183 := [asserted]: #55
+#280 := [mp #183 #279]: #277
+#282 := [and-elim #280]: #272
+#201 := (* -1::real #35)
+#202 := (+ #32 #201)
+#200 := (>= #202 0::real)
+#198 := (not #200)
+#218 := (* -1::real #38)
+#219 := (+ #35 #218)
+#217 := (>= #219 0::real)
+#220 := (not #217)
+#225 := (and #198 #220)
+#27 := (< #26 #26)
+#39 := (ite #27 #32 #38)
+#40 := (< #35 #39)
+#33 := (ite #27 #30 #32)
+#36 := (< #33 #35)
+#41 := (and #36 #40)
+#226 := (iff #41 #225)
+#223 := (iff #40 #220)
+#214 := (< #35 #38)
+#221 := (iff #214 #220)
+#222 := [rewrite]: #221
+#215 := (iff #40 #214)
+#212 := (= #39 #38)
+#207 := (ite false #32 #38)
+#210 := (= #207 #38)
+#211 := [rewrite]: #210
+#208 := (= #39 #207)
+#185 := (iff #27 false)
+#186 := [rewrite]: #185
+#209 := [monotonicity #186]: #208
+#213 := [trans #209 #211]: #212
+#216 := [monotonicity #213]: #215
+#224 := [trans #216 #222]: #223
+#205 := (iff #36 #198)
+#194 := (< #32 #35)
+#203 := (iff #194 #198)
+#204 := [rewrite]: #203
+#195 := (iff #36 #194)
+#192 := (= #33 #32)
+#187 := (ite false #30 #32)
+#190 := (= #187 #32)
+#191 := [rewrite]: #190
+#188 := (= #33 #187)
+#189 := [monotonicity #186]: #188
+#193 := [trans #189 #191]: #192
+#196 := [monotonicity #193]: #195
+#206 := [trans #196 #204]: #205
+#227 := [monotonicity #206 #224]: #226
+#182 := [asserted]: #41
+#228 := [mp #182 #227]: #225
+#229 := [and-elim #228]: #198
+#649 := [th-lemma #229 #282 #648]: false
+#651 := [lemma #649]: #650
+#652 := [hypothesis]: #573
+#654 := (or #653 #647)
+#655 := [th-lemma]: #654
+#656 := [unit-resolution #655 #652 #651]: false
+#657 := [lemma #656]: #653
+#583 := (or #234 #573)
+#584 := [def-axiom]: #583
+#680 := [unit-resolution #584 #657]: #234
+#682 := [th-lemma #680 #400]: #681
+#684 := [symm #682]: #683
+#688 := [monotonicity #684]: #687
+#690 := [symm #688]: #689
+#592 := (= f5 #591)
+#596 := (or #595 #592)
+#597 := [quant-inst]: #596
+#686 := [unit-resolution #597 #552]: #592
+#694 := [trans #686 #690]: #693
+#695 := [trans #694 #692]: #49
+#576 := (not #49)
+#58 := (f6 f13 #50)
+#284 := (ite #49 #32 #58)
+#472 := (* -1::real #284)
+#637 := (+ #32 #472)
+#638 := (<= #637 0::real)
+#585 := (= #32 #284)
+#661 := [hypothesis]: #49
+#587 := (or #576 #585)
+#588 := [def-axiom]: #587
+#662 := [unit-resolution #588 #661]: #585
+#663 := (not #585)
+#664 := (or #663 #638)
+#665 := [th-lemma]: #664
+#666 := [unit-resolution #665 #662]: #638
+#61 := (f6 f10 #50)
+#368 := (* -1::real #61)
+#384 := (+ #51 #368)
+#385 := (<= #384 0::real)
+#386 := (not #385)
+#369 := (+ #58 #368)
+#367 := (>= #369 0::real)
+#366 := (not #367)
+#391 := (and #366 #386)
+#63 := (f6 f9 #50)
+#68 := (< #43 #43)
+#71 := (ite #68 #63 #51)
+#72 := (< #61 #71)
+#69 := (ite #68 #51 #58)
+#70 := (< #69 #61)
+#73 := (and #70 #72)
+#392 := (iff #73 #391)
+#389 := (iff #72 #386)
+#381 := (< #61 #51)
+#387 := (iff #381 #386)
+#388 := [rewrite]: #387
+#382 := (iff #72 #381)
+#379 := (= #71 #51)
+#374 := (ite false #63 #51)
+#377 := (= #374 #51)
+#378 := [rewrite]: #377
+#375 := (= #71 #374)
+#354 := (iff #68 false)
+#355 := [rewrite]: #354
+#376 := [monotonicity #355]: #375
+#380 := [trans #376 #378]: #379
+#383 := [monotonicity #380]: #382
+#390 := [trans #383 #388]: #389
+#372 := (iff #70 #366)
+#363 := (< #58 #61)
+#370 := (iff #363 #366)
+#371 := [rewrite]: #370
+#364 := (iff #70 #363)
+#361 := (= #69 #58)
+#356 := (ite false #51 #58)
+#359 := (= #356 #58)
+#360 := [rewrite]: #359
+#357 := (= #69 #356)
+#358 := [monotonicity #355]: #357
+#362 := [trans #358 #360]: #361
+#365 := [monotonicity #362]: #364
+#373 := [trans #365 #371]: #372
+#393 := [monotonicity #373 #390]: #392
+#351 := [asserted]: #73
+#394 := [mp #351 #393]: #391
+#396 := [and-elim #394]: #386
+#402 := (* -1::real #63)
+#403 := (+ #51 #402)
+#404 := (<= #403 0::real)
+#414 := (* -1::real #58)
+#415 := (+ #51 #414)
+#413 := (>= #415 0::real)
+#64 := (f6 f11 #50)
+#407 := (* -1::real #64)
+#408 := (+ #63 #407)
+#409 := (<= #408 0::real)
+#423 := (and #404 #409 #413)
+#77 := (<= #63 #64)
+#76 := (<= #51 #63)
+#78 := (and #76 #77)
+#75 := (<= #58 #51)
+#79 := (and #75 #78)
+#426 := (iff #79 #423)
+#417 := (and #404 #409)
+#420 := (and #413 #417)
+#424 := (iff #420 #423)
+#425 := [rewrite]: #424
+#421 := (iff #79 #420)
+#418 := (iff #78 #417)
+#410 := (iff #77 #409)
+#411 := [rewrite]: #410
+#405 := (iff #76 #404)
+#406 := [rewrite]: #405
+#419 := [monotonicity #406 #411]: #418
+#412 := (iff #75 #413)
+#416 := [rewrite]: #412
+#422 := [monotonicity #416 #419]: #421
+#427 := [trans #422 #425]: #426
+#353 := [asserted]: #79
+#428 := [mp #353 #427]: #423
+#429 := [and-elim #428]: #404
+#642 := (+ #32 #402)
+#644 := (>= #642 0::real)
+#641 := (= #32 #63)
+#671 := (= #63 #32)
+#669 := (= #50 #29)
+#667 := (= #29 #50)
+#668 := [monotonicity #661]: #667
+#670 := [symm #668]: #669
+#672 := [monotonicity #670]: #671
+#673 := [symm #672]: #641
+#674 := (not #641)
+#675 := (or #674 #644)
+#676 := [th-lemma]: #675
+#677 := [unit-resolution #676 #673]: #644
+#475 := (+ #61 #472)
+#478 := (<= #475 0::real)
+#451 := (not #478)
+#327 := (ite #301 #284 #51)
+#335 := (* -1::real #327)
+#336 := (+ #61 #335)
+#337 := (<= #336 0::real)
+#338 := (not #337)
+#452 := (iff #338 #451)
+#479 := (iff #337 #478)
+#476 := (= #336 #475)
+#473 := (= #335 #472)
+#470 := (= #327 #284)
+#1 := true
+#465 := (ite true #284 #51)
+#468 := (= #465 #284)
+#469 := [rewrite]: #468
+#466 := (= #327 #465)
+#457 := (iff #301 true)
+#458 := [iff-true #400]: #457
+#467 := [monotonicity #458]: #466
+#471 := [trans #467 #469]: #470
+#474 := [monotonicity #471]: #473
+#477 := [monotonicity #474]: #476
+#480 := [monotonicity #477]: #479
+#481 := [monotonicity #480]: #452
+#308 := (ite #301 #64 #63)
+#318 := (* -1::real #308)
+#319 := (+ #61 #318)
+#317 := (>= #319 0::real)
+#316 := (not #317)
+#343 := (and #316 #338)
+#56 := (< #43 #26)
+#65 := (ite #56 #63 #64)
+#66 := (< #61 #65)
+#57 := (= f12 f5)
+#59 := (ite #57 #32 #58)
+#60 := (ite #56 #51 #59)
+#62 := (< #60 #61)
+#67 := (and #62 #66)
+#346 := (iff #67 #343)
+#287 := (ite #56 #51 #284)
+#290 := (< #287 #61)
+#296 := (and #66 #290)
+#344 := (iff #296 #343)
+#341 := (iff #290 #338)
+#332 := (< #327 #61)
+#339 := (iff #332 #338)
+#340 := [rewrite]: #339
+#333 := (iff #290 #332)
+#330 := (= #287 #327)
+#302 := (not #301)
+#324 := (ite #302 #51 #284)
+#328 := (= #324 #327)
+#329 := [rewrite]: #328
+#325 := (= #287 #324)
+#303 := (iff #56 #302)
+#304 := [rewrite]: #303
+#326 := [monotonicity #304]: #325
+#331 := [trans #326 #329]: #330
+#334 := [monotonicity #331]: #333
+#342 := [trans #334 #340]: #341
+#322 := (iff #66 #316)
+#313 := (< #61 #308)
+#320 := (iff #313 #316)
+#321 := [rewrite]: #320
+#314 := (iff #66 #313)
+#311 := (= #65 #308)
+#305 := (ite #302 #63 #64)
+#309 := (= #305 #308)
+#310 := [rewrite]: #309
+#306 := (= #65 #305)
+#307 := [monotonicity #304]: #306
+#312 := [trans #307 #310]: #311
+#315 := [monotonicity #312]: #314
+#323 := [trans #315 #321]: #322
+#345 := [monotonicity #323 #342]: #344
+#299 := (iff #67 #296)
+#293 := (and #290 #66)
+#297 := (iff #293 #296)
+#298 := [rewrite]: #297
+#294 := (iff #67 #293)
+#291 := (iff #62 #290)
+#288 := (= #60 #287)
+#285 := (= #59 #284)
+#231 := (iff #57 #49)
+#283 := [rewrite]: #231
+#286 := [monotonicity #283]: #285
+#289 := [monotonicity #286]: #288
+#292 := [monotonicity #289]: #291
+#295 := [monotonicity #292]: #294
+#300 := [trans #295 #298]: #299
+#347 := [trans #300 #345]: #346
+#184 := [asserted]: #67
+#348 := [mp #184 #347]: #343
+#350 := [and-elim #348]: #338
+#482 := [mp #350 #481]: #451
+#678 := [th-lemma #482 #677 #429 #396 #666]: false
+#679 := [lemma #678]: #576
+[unit-resolution #679 #695]: false
+unsat
+3563da621b35b09e69b7f5fa5fa01c2868364b3e 422 0
+#2 := false
+decl f12 :: S2
+#42 := f12
+decl f5 :: S2
+#25 := f5
+#45 := (= f5 f12)
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+#43 := (f4 f12)
+#598 := (f3 #43)
+#696 := (= #598 f12)
+#599 := (= f12 #598)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#551 := (pattern #9)
+#10 := (f3 #9)
+#98 := (= #8 #10)
+#552 := (forall (vars (?v0 S2)) (:pat #551) #98)
+#101 := (forall (vars (?v0 S2)) #98)
+#555 := (iff #101 #552)
+#553 := (iff #98 #98)
+#554 := [refl]: #553
+#556 := [quant-intro #554]: #555
+#455 := (~ #101 #101)
+#457 := (~ #98 #98)
+#458 := [refl]: #457
+#456 := [nnf-pos #458]: #455
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#102 := (iff #12 #101)
+#99 := (iff #11 #98)
+#100 := [rewrite]: #99
+#103 := [quant-intro #100]: #102
+#97 := [asserted]: #12
+#106 := [mp #97 #103]: #101
+#453 := [mp~ #106 #456]: #101
+#557 := [mp #453 #556]: #552
+#600 := (not #552)
+#605 := (or #600 #599)
+#606 := [quant-inst]: #605
+#690 := [unit-resolution #606 #557]: #599
+#697 := [symm #690]: #696
+#698 := (= f5 #598)
+#26 := (f4 f5)
+#596 := (f3 #26)
+#694 := (= #596 #598)
+#692 := (= #598 #596)
+#688 := (= #43 #26)
+#686 := (= #26 #43)
+#13 := 0::int
+#231 := -1::int
+#234 := (* -1::int #43)
+#235 := (+ #26 #234)
+#295 := (<= #235 0::int)
+#74 := (<= #26 #43)
+#393 := (iff #74 #295)
+#394 := [rewrite]: #393
+#346 := [asserted]: #74
+#395 := [mp #346 #394]: #295
+#233 := (>= #235 0::int)
+decl f6 :: (-> S3 S4 real)
+decl f8 :: (-> S2 S4)
+#29 := (f8 f5)
+decl f7 :: S3
+#28 := f7
+#30 := (f6 f7 #29)
+decl f9 :: S3
+#31 := f9
+#32 := (f6 f9 #29)
+#46 := (f8 f12)
+decl f11 :: S3
+#37 := f11
+#47 := (f6 f11 #46)
+#48 := (ite #45 #47 #32)
+#241 := (ite #233 #48 #30)
+#572 := (= #30 #241)
+#658 := (not #572)
+#199 := 0::real
+#197 := -1::real
+#249 := (* -1::real #241)
+#647 := (+ #30 #249)
+#648 := (<= #647 0::real)
+#652 := (not #648)
+#650 := [hypothesis]: #648
+decl f10 :: S3
+#34 := f10
+#35 := (f6 f10 #29)
+#250 := (+ #35 #249)
+#251 := (<= #250 0::real)
+#252 := (not #251)
+#38 := (f6 f11 #29)
+decl f13 :: S3
+#51 := f13
+#52 := (f6 f13 #29)
+#260 := (ite #233 #52 #38)
+#269 := (* -1::real #260)
+#270 := (+ #35 #269)
+#268 := (>= #270 0::real)
+#271 := (not #268)
+#276 := (and #252 #271)
+#44 := (< #26 #43)
+#53 := (ite #44 #38 #52)
+#54 := (< #35 #53)
+#49 := (ite #44 #30 #48)
+#50 := (< #49 #35)
+#55 := (and #50 #54)
+#277 := (iff #55 #276)
+#274 := (iff #54 #271)
+#265 := (< #35 #260)
+#272 := (iff #265 #271)
+#273 := [rewrite]: #272
+#266 := (iff #54 #265)
+#263 := (= #53 #260)
+#232 := (not #233)
+#257 := (ite #232 #38 #52)
+#261 := (= #257 #260)
+#262 := [rewrite]: #261
+#258 := (= #53 #257)
+#236 := (iff #44 #232)
+#237 := [rewrite]: #236
+#259 := [monotonicity #237]: #258
+#264 := [trans #259 #262]: #263
+#267 := [monotonicity #264]: #266
+#275 := [trans #267 #273]: #274
+#255 := (iff #50 #252)
+#246 := (< #241 #35)
+#253 := (iff #246 #252)
+#254 := [rewrite]: #253
+#247 := (iff #50 #246)
+#244 := (= #49 #241)
+#238 := (ite #232 #30 #48)
+#242 := (= #238 #241)
+#243 := [rewrite]: #242
+#239 := (= #49 #238)
+#240 := [monotonicity #237]: #239
+#245 := [trans #240 #243]: #244
+#248 := [monotonicity #245]: #247
+#256 := [trans #248 #254]: #255
+#278 := [monotonicity #256 #275]: #277
+#183 := [asserted]: #55
+#279 := [mp #183 #278]: #276
+#280 := [and-elim #279]: #252
+#201 := (* -1::real #35)
+#217 := (+ #30 #201)
+#218 := (<= #217 0::real)
+#219 := (not #218)
+#202 := (+ #32 #201)
+#200 := (>= #202 0::real)
+#198 := (not #200)
+#224 := (and #198 #219)
+#27 := (< #26 #26)
+#39 := (ite #27 #38 #30)
+#40 := (< #35 #39)
+#33 := (ite #27 #30 #32)
+#36 := (< #33 #35)
+#41 := (and #36 #40)
+#225 := (iff #41 #224)
+#222 := (iff #40 #219)
+#214 := (< #35 #30)
+#220 := (iff #214 #219)
+#221 := [rewrite]: #220
+#215 := (iff #40 #214)
+#212 := (= #39 #30)
+#207 := (ite false #38 #30)
+#210 := (= #207 #30)
+#211 := [rewrite]: #210
+#208 := (= #39 #207)
+#185 := (iff #27 false)
+#186 := [rewrite]: #185
+#209 := [monotonicity #186]: #208
+#213 := [trans #209 #211]: #212
+#216 := [monotonicity #213]: #215
+#223 := [trans #216 #221]: #222
+#205 := (iff #36 #198)
+#194 := (< #32 #35)
+#203 := (iff #194 #198)
+#204 := [rewrite]: #203
+#195 := (iff #36 #194)
+#192 := (= #33 #32)
+#187 := (ite false #30 #32)
+#190 := (= #187 #32)
+#191 := [rewrite]: #190
+#188 := (= #33 #187)
+#189 := [monotonicity #186]: #188
+#193 := [trans #189 #191]: #192
+#196 := [monotonicity #193]: #195
+#206 := [trans #196 #204]: #205
+#226 := [monotonicity #206 #223]: #225
+#182 := [asserted]: #41
+#227 := [mp #182 #226]: #224
+#229 := [and-elim #227]: #219
+#651 := [th-lemma #229 #280 #650]: false
+#653 := [lemma #651]: #652
+#657 := [hypothesis]: #572
+#659 := (or #658 #648)
+#660 := [th-lemma]: #659
+#661 := [unit-resolution #660 #657 #653]: false
+#662 := [lemma #661]: #658
+#582 := (or #233 #572)
+#583 := [def-axiom]: #582
+#685 := [unit-resolution #583 #662]: #233
+#687 := [th-lemma #685 #395]: #686
+#689 := [symm #687]: #688
+#693 := [monotonicity #689]: #692
+#695 := [symm #693]: #694
+#597 := (= f5 #596)
+#601 := (or #600 #597)
+#602 := [quant-inst]: #601
+#691 := [unit-resolution #602 #557]: #597
+#699 := [trans #691 #695]: #698
+#700 := [trans #699 #697]: #45
+#575 := (not #45)
+#63 := (f6 f13 #46)
+#283 := (ite #45 #30 #63)
+#466 := (* -1::real #283)
+#642 := (+ #30 #466)
+#644 := (>= #642 0::real)
+#590 := (= #30 #283)
+#666 := [hypothesis]: #45
+#592 := (or #575 #590)
+#593 := [def-axiom]: #592
+#667 := [unit-resolution #593 #666]: #590
+#668 := (not #590)
+#669 := (or #668 #644)
+#670 := [th-lemma]: #669
+#671 := [unit-resolution #670 #667]: #644
+#60 := (f6 f10 #46)
+#362 := (* -1::real #60)
+#363 := (+ #47 #362)
+#361 := (>= #363 0::real)
+#360 := (not #361)
+#379 := (* -1::real #63)
+#380 := (+ #60 #379)
+#378 := (>= #380 0::real)
+#381 := (not #378)
+#386 := (and #360 #381)
+#68 := (< #43 #43)
+#71 := (ite #68 #47 #63)
+#72 := (< #60 #71)
+#57 := (f6 f7 #46)
+#69 := (ite #68 #57 #47)
+#70 := (< #69 #60)
+#73 := (and #70 #72)
+#387 := (iff #73 #386)
+#384 := (iff #72 #381)
+#375 := (< #60 #63)
+#382 := (iff #375 #381)
+#383 := [rewrite]: #382
+#376 := (iff #72 #375)
+#373 := (= #71 #63)
+#368 := (ite false #47 #63)
+#371 := (= #368 #63)
+#372 := [rewrite]: #371
+#369 := (= #71 #368)
+#348 := (iff #68 false)
+#349 := [rewrite]: #348
+#370 := [monotonicity #349]: #369
+#374 := [trans #370 #372]: #373
+#377 := [monotonicity #374]: #376
+#385 := [trans #377 #383]: #384
+#366 := (iff #70 #360)
+#357 := (< #47 #60)
+#364 := (iff #357 #360)
+#365 := [rewrite]: #364
+#358 := (iff #70 #357)
+#355 := (= #69 #47)
+#350 := (ite false #57 #47)
+#353 := (= #350 #47)
+#354 := [rewrite]: #353
+#351 := (= #69 #350)
+#352 := [monotonicity #349]: #351
+#356 := [trans #352 #354]: #355
+#359 := [monotonicity #356]: #358
+#367 := [trans #359 #365]: #366
+#388 := [monotonicity #367 #385]: #387
+#345 := [asserted]: #73
+#389 := [mp #345 #388]: #386
+#390 := [and-elim #389]: #360
+#399 := (* -1::real #57)
+#400 := (+ #47 #399)
+#398 := (>= #400 0::real)
+#58 := (f6 f9 #46)
+#407 := (* -1::real #58)
+#408 := (+ #57 #407)
+#406 := (>= #408 0::real)
+#402 := (+ #47 #379)
+#403 := (<= #402 0::real)
+#417 := (and #398 #403 #406)
+#77 := (<= #47 #63)
+#76 := (<= #57 #47)
+#78 := (and #76 #77)
+#75 := (<= #58 #57)
+#79 := (and #75 #78)
+#420 := (iff #79 #417)
+#411 := (and #398 #403)
+#414 := (and #406 #411)
+#418 := (iff #414 #417)
+#419 := [rewrite]: #418
+#415 := (iff #79 #414)
+#412 := (iff #78 #411)
+#404 := (iff #77 #403)
+#405 := [rewrite]: #404
+#397 := (iff #76 #398)
+#401 := [rewrite]: #397
+#413 := [monotonicity #401 #405]: #412
+#409 := (iff #75 #406)
+#410 := [rewrite]: #409
+#416 := [monotonicity #410 #413]: #415
+#421 := [trans #416 #419]: #420
+#347 := [asserted]: #79
+#422 := [mp #347 #421]: #417
+#423 := [and-elim #422]: #398
+#655 := (+ #30 #399)
+#656 := (<= #655 0::real)
+#654 := (= #30 #57)
+#676 := (= #57 #30)
+#674 := (= #46 #29)
+#672 := (= #29 #46)
+#673 := [monotonicity #666]: #672
+#675 := [symm #673]: #674
+#677 := [monotonicity #675]: #676
+#678 := [symm #677]: #654
+#679 := (not #654)
+#680 := (or #679 #656)
+#681 := [th-lemma]: #680
+#682 := [unit-resolution #681 #678]: #656
+#469 := (+ #60 #466)
+#472 := (>= #469 0::real)
+#445 := (not #472)
+#321 := (ite #295 #283 #47)
+#331 := (* -1::real #321)
+#332 := (+ #60 #331)
+#330 := (>= #332 0::real)
+#329 := (not #330)
+#446 := (iff #329 #445)
+#473 := (iff #330 #472)
+#470 := (= #332 #469)
+#467 := (= #331 #466)
+#464 := (= #321 #283)
+#1 := true
+#459 := (ite true #283 #47)
+#462 := (= #459 #283)
+#463 := [rewrite]: #462
+#460 := (= #321 #459)
+#451 := (iff #295 true)
+#452 := [iff-true #395]: #451
+#461 := [monotonicity #452]: #460
+#465 := [trans #461 #463]: #464
+#468 := [monotonicity #465]: #467
+#471 := [monotonicity #468]: #470
+#474 := [monotonicity #471]: #473
+#475 := [monotonicity #474]: #446
+#302 := (ite #295 #58 #57)
+#310 := (* -1::real #302)
+#311 := (+ #60 #310)
+#312 := (<= #311 0::real)
+#313 := (not #312)
+#337 := (and #313 #329)
+#62 := (= f12 f5)
+#64 := (ite #62 #30 #63)
+#56 := (< #43 #26)
+#65 := (ite #56 #47 #64)
+#66 := (< #60 #65)
+#59 := (ite #56 #57 #58)
+#61 := (< #59 #60)
+#67 := (and #61 #66)
+#340 := (iff #67 #337)
+#286 := (ite #56 #47 #283)
+#289 := (< #60 #286)
+#292 := (and #61 #289)
+#338 := (iff #292 #337)
+#335 := (iff #289 #329)
+#326 := (< #60 #321)
+#333 := (iff #326 #329)
+#334 := [rewrite]: #333
+#327 := (iff #289 #326)
+#324 := (= #286 #321)
+#296 := (not #295)
+#318 := (ite #296 #47 #283)
+#322 := (= #318 #321)
+#323 := [rewrite]: #322
+#319 := (= #286 #318)
+#297 := (iff #56 #296)
+#298 := [rewrite]: #297
+#320 := [monotonicity #298]: #319
+#325 := [trans #320 #323]: #324
+#328 := [monotonicity #325]: #327
+#336 := [trans #328 #334]: #335
+#316 := (iff #61 #313)
+#307 := (< #302 #60)
+#314 := (iff #307 #313)
+#315 := [rewrite]: #314
+#308 := (iff #61 #307)
+#305 := (= #59 #302)
+#299 := (ite #296 #57 #58)
+#303 := (= #299 #302)
+#304 := [rewrite]: #303
+#300 := (= #59 #299)
+#301 := [monotonicity #298]: #300
+#306 := [trans #301 #304]: #305
+#309 := [monotonicity #306]: #308
+#317 := [trans #309 #315]: #316
+#339 := [monotonicity #317 #336]: #338
+#293 := (iff #67 #292)
+#290 := (iff #66 #289)
+#287 := (= #65 #286)
+#284 := (= #64 #283)
+#230 := (iff #62 #45)
+#282 := [rewrite]: #230
+#285 := [monotonicity #282]: #284
+#288 := [monotonicity #285]: #287
+#291 := [monotonicity #288]: #290
+#294 := [monotonicity #291]: #293
+#341 := [trans #294 #339]: #340
+#184 := [asserted]: #67
+#342 := [mp #184 #341]: #337
+#344 := [and-elim #342]: #329
+#476 := [mp #344 #475]: #445
+#683 := [th-lemma #476 #682 #423 #390 #671]: false
+#684 := [lemma #683]: #575
+[unit-resolution #684 #700]: false
+unsat
+84444fc7be1372d94ec0514d2ec99e1693c028e3 921 0
+#2 := false
+#58 := 0::int
+decl f5 :: (-> S4 int)
+decl f6 :: (-> S2 S4)
+decl f11 :: (-> S4 S2)
+decl f14 :: S4
+#30 := f14
+#34 := (f11 f14)
+#70 := (f6 #34)
+#605 := (f5 #70)
+#121 := -1::int
+#615 := (* -1::int #605)
+decl f7 :: S4
+#13 := f7
+#14 := (f5 f7)
+#662 := (+ #14 #615)
+#663 := (<= #662 0::int)
+decl f8 :: (-> S5 S2 real)
+decl f19 :: (-> S3 S5)
+decl f15 :: S3
+#40 := f15
+#86 := (f19 f15)
+#650 := (f8 #86 #34)
+decl f10 :: S5
+#19 := f10
+#35 := (f8 f10 #34)
+#651 := (= #35 #650)
+#690 := (not #651)
+decl f13 :: S3
+#28 := f13
+#81 := (f19 f13)
+#749 := (f8 #81 #34)
+#1233 := (= #650 #749)
+#1246 := (not #1233)
+#1335 := (iff #1246 #690)
+#1333 := (iff #1233 #651)
+#1328 := (= #650 #35)
+#1331 := (iff #1328 #651)
+#1332 := [commutativity]: #1331
+#1329 := (iff #1233 #1328)
+#1326 := (= #749 #35)
+#752 := (= #35 #749)
+decl f12 :: S5
+#22 := f12
+#696 := (f8 f12 #34)
+#751 := (= #696 #749)
+#281 := (= f14 #70)
+#755 := (ite #281 #752 #751)
+decl f9 :: S5
+#16 := f9
+#694 := (f8 f9 #34)
+#750 := (= #694 #749)
+#31 := (f5 f14)
+#616 := (+ #31 #615)
+#617 := (<= #616 0::int)
+#758 := (ite #617 #755 #750)
+#9 := (:var 0 S2)
+#17 := (f8 f9 #9)
+#538 := (pattern #17)
+#23 := (f8 f12 #9)
+#537 := (pattern #23)
+#82 := (f8 #81 #9)
+#545 := (pattern #82)
+#11 := (f6 #9)
+#535 := (pattern #11)
+#452 := (= #17 #82)
+#450 := (= #23 #82)
+#449 := (= #35 #82)
+#33 := (= #11 f14)
+#451 := (ite #33 #449 #450)
+#146 := (* -1::int #31)
+#12 := (f5 #11)
+#147 := (+ #12 #146)
+#145 := (>= #147 0::int)
+#453 := (ite #145 #451 #452)
+#546 := (forall (vars (?v0 S2)) (:pat #535 #545 #537 #538) #453)
+#456 := (forall (vars (?v0 S2)) #453)
+#549 := (iff #456 #546)
+#547 := (iff #453 #453)
+#548 := [refl]: #547
+#550 := [quant-intro #548]: #549
+#36 := (ite #33 #35 #23)
+#153 := (ite #145 #36 #17)
+#380 := (= #82 #153)
+#381 := (forall (vars (?v0 S2)) #380)
+#457 := (iff #381 #456)
+#454 := (iff #380 #453)
+#455 := [rewrite]: #454
+#458 := [quant-intro #455]: #457
+#366 := (~ #381 #381)
+#368 := (~ #380 #380)
+#365 := [refl]: #368
+#363 := [nnf-pos #365]: #366
+decl f3 :: (-> S3 S2 real)
+#29 := (f3 f13 #9)
+#158 := (= #29 #153)
+#161 := (forall (vars (?v0 S2)) #158)
+#382 := (iff #161 #381)
+#96 := (:var 1 S3)
+#99 := (f3 #96 #9)
+#97 := (f19 #96)
+#98 := (f8 #97 #9)
+#100 := (= #98 #99)
+#101 := (forall (vars (?v0 S3) (?v1 S2)) #100)
+#298 := [asserted]: #101
+#383 := [rewrite* #298]: #382
+#32 := (< #12 #31)
+#37 := (ite #32 #17 #36)
+#38 := (= #29 #37)
+#39 := (forall (vars (?v0 S2)) #38)
+#162 := (iff #39 #161)
+#159 := (iff #38 #158)
+#156 := (= #37 #153)
+#144 := (not #145)
+#150 := (ite #144 #17 #36)
+#154 := (= #150 #153)
+#155 := [rewrite]: #154
+#151 := (= #37 #150)
+#148 := (iff #32 #144)
+#149 := [rewrite]: #148
+#152 := [monotonicity #149]: #151
+#157 := [trans #152 #155]: #156
+#160 := [monotonicity #157]: #159
+#163 := [quant-intro #160]: #162
+#119 := [asserted]: #39
+#164 := [mp #119 #163]: #161
+#384 := [mp #164 #383]: #381
+#364 := [mp~ #384 #363]: #381
+#459 := [mp #364 #458]: #456
+#551 := [mp #459 #550]: #546
+#761 := (not #546)
+#762 := (or #761 #758)
+#71 := (= #70 f14)
+#753 := (ite #71 #752 #751)
+#606 := (+ #605 #146)
+#607 := (>= #606 0::int)
+#754 := (ite #607 #753 #750)
+#763 := (or #761 #754)
+#765 := (iff #763 #762)
+#767 := (iff #762 #762)
+#768 := [rewrite]: #767
+#759 := (iff #754 #758)
+#756 := (iff #753 #755)
+#282 := (iff #71 #281)
+#283 := [rewrite]: #282
+#757 := [monotonicity #283]: #756
+#620 := (iff #607 #617)
+#609 := (+ #146 #605)
+#612 := (>= #609 0::int)
+#618 := (iff #612 #617)
+#619 := [rewrite]: #618
+#613 := (iff #607 #612)
+#610 := (= #606 #609)
+#611 := [rewrite]: #610
+#614 := [monotonicity #611]: #613
+#621 := [trans #614 #619]: #620
+#760 := [monotonicity #621 #757]: #759
+#766 := [monotonicity #760]: #765
+#769 := [trans #766 #768]: #765
+#764 := [quant-inst]: #763
+#770 := [mp #764 #769]: #762
+#1317 := [unit-resolution #770 #551]: #758
+#981 := (= #31 #605)
+#1295 := (= #605 #31)
+#280 := [asserted]: #71
+#286 := [mp #280 #283]: #281
+#1290 := [symm #286]: #71
+#1296 := [monotonicity #1290]: #1295
+#1297 := [symm #1296]: #981
+#1318 := (not #981)
+#1319 := (or #1318 #617)
+#1320 := [th-lemma]: #1319
+#1321 := [unit-resolution #1320 #1297]: #617
+#639 := (not #617)
+#783 := (not #758)
+#784 := (or #783 #639 #755)
+#785 := [def-axiom]: #784
+#1322 := [unit-resolution #785 #1321 #1317]: #755
+#771 := (not #755)
+#1323 := (or #771 #752)
+#772 := (not #281)
+#773 := (or #771 #772 #752)
+#774 := [def-axiom]: #773
+#1324 := [unit-resolution #774 #286]: #1323
+#1325 := [unit-resolution #1324 #1322]: #752
+#1327 := [symm #1325]: #1326
+#1330 := [monotonicity #1327]: #1329
+#1334 := [trans #1330 #1332]: #1333
+#1336 := [monotonicity #1334]: #1335
+#303 := 0::real
+#301 := -1::real
+#1033 := (* -1::real #749)
+#1234 := (+ #650 #1033)
+#1236 := (>= #1234 0::real)
+#1243 := (not #1236)
+#1237 := [hypothesis]: #1236
+decl f20 :: S5
+#78 := f20
+#1034 := (f8 f20 #34)
+#1037 := (* -1::real #1034)
+#1048 := (+ #749 #1037)
+#1049 := (<= #1048 0::real)
+#1073 := (not #1049)
+decl f17 :: S3
+#48 := f17
+#76 := (f19 f17)
+#601 := (f8 #76 #34)
+#1038 := (+ #601 #1037)
+#1039 := (>= #1038 0::real)
+#1054 := (or #1039 #1049)
+#1057 := (not #1054)
+#79 := (f8 f20 #9)
+#588 := (pattern #79)
+#77 := (f8 #76 #9)
+#561 := (pattern #77)
+#310 := (* -1::real #82)
+#311 := (+ #79 #310)
+#309 := (>= #311 0::real)
+#305 := (* -1::real #79)
+#306 := (+ #77 #305)
+#304 := (>= #306 0::real)
+#422 := (or #304 #309)
+#423 := (not #422)
+#589 := (forall (vars (?v0 S2)) (:pat #561 #588 #545) #423)
+#426 := (forall (vars (?v0 S2)) #423)
+#592 := (iff #426 #589)
+#590 := (iff #423 #423)
+#591 := [refl]: #590
+#593 := [quant-intro #591]: #592
+#312 := (not #309)
+#302 := (not #304)
+#315 := (and #302 #312)
+#318 := (forall (vars (?v0 S2)) #315)
+#427 := (iff #318 #426)
+#424 := (iff #315 #423)
+#425 := [rewrite]: #424
+#428 := [quant-intro #425]: #427
+#414 := (~ #318 #318)
+#412 := (~ #315 #315)
+#413 := [refl]: #412
+#415 := [nnf-pos #413]: #414
+decl f4 :: S3
+#8 := f4
+#89 := (f19 f4)
+#90 := (f8 #89 #9)
+#328 := (* -1::real #90)
+#329 := (+ #79 #328)
+#327 := (>= #329 0::real)
+#330 := (not #327)
+#87 := (f8 #86 #9)
+#321 := (* -1::real #87)
+#322 := (+ #79 #321)
+#323 := (<= #322 0::real)
+#324 := (not #323)
+#333 := (and #324 #330)
+#336 := (forall (vars (?v0 S2)) #333)
+#339 := (and #318 #336)
+#91 := (< #79 #90)
+#88 := (< #87 #79)
+#92 := (and #88 #91)
+#93 := (forall (vars (?v0 S2)) #92)
+#83 := (< #79 #82)
+#80 := (< #77 #79)
+#84 := (and #80 #83)
+#85 := (forall (vars (?v0 S2)) #84)
+#94 := (and #85 #93)
+#340 := (iff #94 #339)
+#337 := (iff #93 #336)
+#334 := (iff #92 #333)
+#331 := (iff #91 #330)
+#332 := [rewrite]: #331
+#325 := (iff #88 #324)
+#326 := [rewrite]: #325
+#335 := [monotonicity #326 #332]: #334
+#338 := [quant-intro #335]: #337
+#319 := (iff #85 #318)
+#316 := (iff #84 #315)
+#313 := (iff #83 #312)
+#314 := [rewrite]: #313
+#307 := (iff #80 #302)
+#308 := [rewrite]: #307
+#317 := [monotonicity #308 #314]: #316
+#320 := [quant-intro #317]: #319
+#341 := [monotonicity #320 #338]: #340
+#297 := [asserted]: #94
+#342 := [mp #297 #341]: #339
+#343 := [and-elim #342]: #318
+#416 := [mp~ #343 #415]: #318
+#429 := [mp #416 #428]: #426
+#594 := [mp #429 #593]: #589
+#1060 := (not #589)
+#1061 := (or #1060 #1057)
+#1035 := (+ #1034 #1033)
+#1036 := (>= #1035 0::real)
+#1040 := (or #1039 #1036)
+#1041 := (not #1040)
+#1062 := (or #1060 #1041)
+#1064 := (iff #1062 #1061)
+#1066 := (iff #1061 #1061)
+#1067 := [rewrite]: #1066
+#1058 := (iff #1041 #1057)
+#1055 := (iff #1040 #1054)
+#1052 := (iff #1036 #1049)
+#1042 := (+ #1033 #1034)
+#1045 := (>= #1042 0::real)
+#1050 := (iff #1045 #1049)
+#1051 := [rewrite]: #1050
+#1046 := (iff #1036 #1045)
+#1043 := (= #1035 #1042)
+#1044 := [rewrite]: #1043
+#1047 := [monotonicity #1044]: #1046
+#1053 := [trans #1047 #1051]: #1052
+#1056 := [monotonicity #1053]: #1055
+#1059 := [monotonicity #1056]: #1058
+#1065 := [monotonicity #1059]: #1064
+#1068 := [trans #1065 #1067]: #1064
+#1063 := [quant-inst]: #1062
+#1069 := [mp #1063 #1068]: #1061
+#1238 := [unit-resolution #1069 #594]: #1057
+#1074 := (or #1054 #1073)
+#1075 := [def-axiom]: #1074
+#1239 := [unit-resolution #1075 #1238]: #1073
+#1150 := (+ #650 #1037)
+#1151 := (>= #1150 0::real)
+#1183 := (not #1151)
+#693 := (f8 #89 #34)
+#1162 := (+ #693 #1037)
+#1163 := (<= #1162 0::real)
+#1168 := (or #1151 #1163)
+#1171 := (not #1168)
+#536 := (pattern #90)
+#553 := (pattern #87)
+#430 := (or #323 #327)
+#431 := (not #430)
+#595 := (forall (vars (?v0 S2)) (:pat #588 #553 #536) #431)
+#434 := (forall (vars (?v0 S2)) #431)
+#598 := (iff #434 #595)
+#596 := (iff #431 #431)
+#597 := [refl]: #596
+#599 := [quant-intro #597]: #598
+#435 := (iff #336 #434)
+#432 := (iff #333 #431)
+#433 := [rewrite]: #432
+#436 := [quant-intro #433]: #435
+#419 := (~ #336 #336)
+#417 := (~ #333 #333)
+#418 := [refl]: #417
+#420 := [nnf-pos #418]: #419
+#344 := [and-elim #342]: #336
+#421 := [mp~ #344 #420]: #336
+#437 := [mp #421 #436]: #434
+#600 := [mp #437 #599]: #595
+#1118 := (not #595)
+#1174 := (or #1118 #1171)
+#1136 := (* -1::real #693)
+#1137 := (+ #1034 #1136)
+#1138 := (>= #1137 0::real)
+#1139 := (* -1::real #650)
+#1140 := (+ #1034 #1139)
+#1141 := (<= #1140 0::real)
+#1142 := (or #1141 #1138)
+#1143 := (not #1142)
+#1175 := (or #1118 #1143)
+#1177 := (iff #1175 #1174)
+#1179 := (iff #1174 #1174)
+#1180 := [rewrite]: #1179
+#1172 := (iff #1143 #1171)
+#1169 := (iff #1142 #1168)
+#1166 := (iff #1138 #1163)
+#1156 := (+ #1136 #1034)
+#1159 := (>= #1156 0::real)
+#1164 := (iff #1159 #1163)
+#1165 := [rewrite]: #1164
+#1160 := (iff #1138 #1159)
+#1157 := (= #1137 #1156)
+#1158 := [rewrite]: #1157
+#1161 := [monotonicity #1158]: #1160
+#1167 := [trans #1161 #1165]: #1166
+#1154 := (iff #1141 #1151)
+#1144 := (+ #1139 #1034)
+#1147 := (<= #1144 0::real)
+#1152 := (iff #1147 #1151)
+#1153 := [rewrite]: #1152
+#1148 := (iff #1141 #1147)
+#1145 := (= #1140 #1144)
+#1146 := [rewrite]: #1145
+#1149 := [monotonicity #1146]: #1148
+#1155 := [trans #1149 #1153]: #1154
+#1170 := [monotonicity #1155 #1167]: #1169
+#1173 := [monotonicity #1170]: #1172
+#1178 := [monotonicity #1173]: #1177
+#1181 := [trans #1178 #1180]: #1177
+#1176 := [quant-inst]: #1175
+#1182 := [mp #1176 #1181]: #1174
+#1240 := [unit-resolution #1182 #600]: #1171
+#1184 := (or #1168 #1183)
+#1185 := [def-axiom]: #1184
+#1241 := [unit-resolution #1185 #1240]: #1183
+#1242 := [th-lemma #1241 #1239 #1237]: false
+#1244 := [lemma #1242]: #1243
+#1247 := (or #1246 #1236)
+#1248 := [th-lemma]: #1247
+#1316 := [unit-resolution #1248 #1244]: #1246
+#1337 := [mp #1316 #1336]: #690
+#1339 := (or #663 #651)
+decl f16 :: S5
+#43 := f16
+#603 := (f8 f16 #34)
+#652 := (= #603 #650)
+#668 := (ite #663 #652 #651)
+#42 := (f8 f10 #9)
+#554 := (pattern #42)
+#44 := (f8 f16 #9)
+#552 := (pattern #44)
+#461 := (= #42 #87)
+#460 := (= #44 #87)
+#124 := (* -1::int #14)
+#125 := (+ #12 #124)
+#123 := (>= #125 0::int)
+#462 := (ite #123 #460 #461)
+#555 := (forall (vars (?v0 S2)) (:pat #535 #552 #553 #554) #462)
+#465 := (forall (vars (?v0 S2)) #462)
+#558 := (iff #465 #555)
+#556 := (iff #462 #462)
+#557 := [refl]: #556
+#559 := [quant-intro #557]: #558
+#169 := (ite #123 #44 #42)
+#385 := (= #87 #169)
+#386 := (forall (vars (?v0 S2)) #385)
+#466 := (iff #386 #465)
+#463 := (iff #385 #462)
+#464 := [rewrite]: #463
+#467 := [quant-intro #464]: #466
+#359 := (~ #386 #386)
+#361 := (~ #385 #385)
+#362 := [refl]: #361
+#360 := [nnf-pos #362]: #359
+#41 := (f3 f15 #9)
+#174 := (= #41 #169)
+#177 := (forall (vars (?v0 S2)) #174)
+#387 := (iff #177 #386)
+#388 := [rewrite* #298]: #387
+#15 := (< #12 #14)
+#45 := (ite #15 #42 #44)
+#46 := (= #41 #45)
+#47 := (forall (vars (?v0 S2)) #46)
+#178 := (iff #47 #177)
+#175 := (iff #46 #174)
+#172 := (= #45 #169)
+#122 := (not #123)
+#166 := (ite #122 #42 #44)
+#170 := (= #166 #169)
+#171 := [rewrite]: #170
+#167 := (= #45 #166)
+#126 := (iff #15 #122)
+#127 := [rewrite]: #126
+#168 := [monotonicity #127]: #167
+#173 := [trans #168 #171]: #172
+#176 := [monotonicity #173]: #175
+#179 := [quant-intro #176]: #178
+#120 := [asserted]: #47
+#180 := [mp #120 #179]: #177
+#389 := [mp #180 #388]: #386
+#357 := [mp~ #389 #360]: #386
+#468 := [mp #357 #467]: #465
+#560 := [mp #468 #559]: #555
+#671 := (not #555)
+#672 := (or #671 #668)
+#653 := (+ #605 #124)
+#654 := (>= #653 0::int)
+#655 := (ite #654 #652 #651)
+#673 := (or #671 #655)
+#675 := (iff #673 #672)
+#677 := (iff #672 #672)
+#678 := [rewrite]: #677
+#669 := (iff #655 #668)
+#666 := (iff #654 #663)
+#656 := (+ #124 #605)
+#659 := (>= #656 0::int)
+#664 := (iff #659 #663)
+#665 := [rewrite]: #664
+#660 := (iff #654 #659)
+#657 := (= #653 #656)
+#658 := [rewrite]: #657
+#661 := [monotonicity #658]: #660
+#667 := [trans #661 #665]: #666
+#670 := [monotonicity #667]: #669
+#676 := [monotonicity #670]: #675
+#679 := [trans #676 #678]: #675
+#674 := [quant-inst]: #673
+#680 := [mp #674 #679]: #672
+#1338 := [unit-resolution #680 #560]: #668
+#681 := (not #668)
+#685 := (or #681 #663 #651)
+#686 := [def-axiom]: #685
+#1340 := [unit-resolution #686 #1338]: #1339
+#1341 := [unit-resolution #1340 #1337]: #663
+#1286 := (+ #14 #146)
+#1287 := (<= #1286 0::int)
+#1376 := (not #1287)
+#1285 := (= #14 #31)
+#1314 := (not #1285)
+#290 := (= f7 f14)
+#702 := (= f7 #70)
+decl f18 :: (-> int S4)
+#985 := (f18 #605)
+#1305 := (= #985 #70)
+#986 := (= #70 #985)
+#53 := (:var 0 S4)
+#54 := (f5 #53)
+#568 := (pattern #54)
+#55 := (f18 #54)
+#181 := (= #53 #55)
+#569 := (forall (vars (?v0 S4)) (:pat #568) #181)
+#199 := (forall (vars (?v0 S4)) #181)
+#572 := (iff #199 #569)
+#570 := (iff #181 #181)
+#571 := [refl]: #570
+#573 := [quant-intro #571]: #572
+#399 := (~ #199 #199)
+#397 := (~ #181 #181)
+#398 := [refl]: #397
+#400 := [nnf-pos #398]: #399
+#56 := (= #55 #53)
+#57 := (forall (vars (?v0 S4)) #56)
+#200 := (iff #57 #199)
+#197 := (iff #56 #181)
+#198 := [rewrite]: #197
+#201 := [quant-intro #198]: #200
+#165 := [asserted]: #57
+#204 := [mp #165 #201]: #199
+#401 := [mp~ #204 #400]: #199
+#574 := [mp #401 #573]: #569
+#989 := (not #569)
+#990 := (or #989 #986)
+#991 := [quant-inst]: #990
+#1289 := [unit-resolution #991 #574]: #986
+#1306 := [symm #1289]: #1305
+#1309 := (= f7 #985)
+#20 := (f11 f7)
+#72 := (f6 #20)
+#797 := (f5 #72)
+#987 := (f18 #797)
+#1303 := (= #987 #985)
+#1300 := (= #797 #605)
+#1298 := (= #797 #31)
+#1291 := [hypothesis]: #1285
+#1293 := (= #797 #14)
+#73 := (= #72 f7)
+#285 := (= f7 #72)
+#287 := (iff #73 #285)
+#288 := [rewrite]: #287
+#284 := [asserted]: #73
+#291 := [mp #284 #288]: #285
+#1292 := [symm #291]: #73
+#1294 := [monotonicity #1292]: #1293
+#1299 := [trans #1294 #1291]: #1298
+#1301 := [trans #1299 #1297]: #1300
+#1304 := [monotonicity #1301]: #1303
+#1307 := (= f7 #987)
+#988 := (= #72 #987)
+#994 := (or #989 #988)
+#995 := [quant-inst]: #994
+#1302 := [unit-resolution #995 #574]: #988
+#1308 := [trans #291 #1302]: #1307
+#1310 := [trans #1308 #1304]: #1309
+#1311 := [trans #1310 #1306]: #702
+#1312 := [trans #1311 #1290]: #290
+#294 := (not #290)
+#74 := (= f14 f7)
+#75 := (not #74)
+#295 := (iff #75 #294)
+#292 := (iff #74 #290)
+#293 := [rewrite]: #292
+#296 := [monotonicity #293]: #295
+#289 := [asserted]: #75
+#299 := [mp #289 #296]: #294
+#1313 := [unit-resolution #299 #1312]: false
+#1315 := [lemma #1313]: #1314
+#1380 := (or #1285 #1376)
+#1288 := (>= #1286 0::int)
+#807 := (* -1::int #797)
+#808 := (+ #31 #807)
+#809 := (<= #808 0::int)
+#793 := (f8 #76 #20)
+#21 := (f8 f10 #20)
+#794 := (= #21 #793)
+#838 := (not #794)
+#883 := (f8 #89 #20)
+#1259 := (= #793 #883)
+#1272 := (not #1259)
+#1362 := (iff #1272 #838)
+#1360 := (iff #1259 #794)
+#1355 := (= #793 #21)
+#1358 := (iff #1355 #794)
+#1359 := [commutativity]: #1358
+#1356 := (iff #1259 #1355)
+#1353 := (= #883 #21)
+#888 := (= #21 #883)
+#886 := (f8 f12 #20)
+#891 := (= #883 #886)
+#894 := (ite #285 #888 #891)
+#884 := (f8 f9 #20)
+#897 := (= #883 #884)
+#853 := (+ #14 #807)
+#854 := (<= #853 0::int)
+#900 := (ite #854 #894 #897)
+#441 := (= #17 #90)
+#439 := (= #23 #90)
+#438 := (= #21 #90)
+#18 := (= #11 f7)
+#440 := (ite #18 #438 #439)
+#442 := (ite #123 #440 #441)
+#539 := (forall (vars (?v0 S2)) (:pat #535 #536 #537 #538) #442)
+#445 := (forall (vars (?v0 S2)) #442)
+#542 := (iff #445 #539)
+#540 := (iff #442 #442)
+#541 := [refl]: #540
+#543 := [quant-intro #541]: #542
+#24 := (ite #18 #21 #23)
+#131 := (ite #123 #24 #17)
+#375 := (= #90 #131)
+#376 := (forall (vars (?v0 S2)) #375)
+#446 := (iff #376 #445)
+#443 := (iff #375 #442)
+#444 := [rewrite]: #443
+#447 := [quant-intro #444]: #446
+#369 := (~ #376 #376)
+#371 := (~ #375 #375)
+#372 := [refl]: #371
+#370 := [nnf-pos #372]: #369
+#10 := (f3 f4 #9)
+#136 := (= #10 #131)
+#139 := (forall (vars (?v0 S2)) #136)
+#377 := (iff #139 #376)
+#378 := [rewrite* #298]: #377
+#25 := (ite #15 #17 #24)
+#26 := (= #10 #25)
+#27 := (forall (vars (?v0 S2)) #26)
+#140 := (iff #27 #139)
+#137 := (iff #26 #136)
+#134 := (= #25 #131)
+#128 := (ite #122 #17 #24)
+#132 := (= #128 #131)
+#133 := [rewrite]: #132
+#129 := (= #25 #128)
+#130 := [monotonicity #127]: #129
+#135 := [trans #130 #133]: #134
+#138 := [monotonicity #135]: #137
+#141 := [quant-intro #138]: #140
+#118 := [asserted]: #27
+#142 := [mp #118 #141]: #139
+#379 := [mp #142 #378]: #376
+#367 := [mp~ #379 #370]: #376
+#448 := [mp #367 #447]: #445
+#544 := [mp #448 #543]: #539
+#717 := (not #539)
+#903 := (or #717 #900)
+#885 := (= #884 #883)
+#887 := (= #886 #883)
+#889 := (ite #73 #888 #887)
+#844 := (+ #797 #124)
+#845 := (>= #844 0::int)
+#890 := (ite #845 #889 #885)
+#904 := (or #717 #890)
+#906 := (iff #904 #903)
+#908 := (iff #903 #903)
+#909 := [rewrite]: #908
+#901 := (iff #890 #900)
+#898 := (iff #885 #897)
+#899 := [rewrite]: #898
+#895 := (iff #889 #894)
+#892 := (iff #887 #891)
+#893 := [rewrite]: #892
+#896 := [monotonicity #288 #893]: #895
+#857 := (iff #845 #854)
+#847 := (+ #124 #797)
+#850 := (>= #847 0::int)
+#855 := (iff #850 #854)
+#856 := [rewrite]: #855
+#851 := (iff #845 #850)
+#848 := (= #844 #847)
+#849 := [rewrite]: #848
+#852 := [monotonicity #849]: #851
+#858 := [trans #852 #856]: #857
+#902 := [monotonicity #858 #896 #899]: #901
+#907 := [monotonicity #902]: #906
+#910 := [trans #907 #909]: #906
+#905 := [quant-inst]: #904
+#911 := [mp #905 #910]: #903
+#1343 := [unit-resolution #911 #544]: #900
+#983 := (= #14 #797)
+#1344 := [symm #1294]: #983
+#1345 := (not #983)
+#1346 := (or #1345 #854)
+#1347 := [th-lemma]: #1346
+#1348 := [unit-resolution #1347 #1344]: #854
+#872 := (not #854)
+#924 := (not #900)
+#925 := (or #924 #872 #894)
+#926 := [def-axiom]: #925
+#1349 := [unit-resolution #926 #1348 #1343]: #894
+#912 := (not #894)
+#1350 := (or #912 #888)
+#913 := (not #285)
+#914 := (or #912 #913 #888)
+#915 := [def-axiom]: #914
+#1351 := [unit-resolution #915 #291]: #1350
+#1352 := [unit-resolution #1351 #1349]: #888
+#1354 := [symm #1352]: #1353
+#1357 := [monotonicity #1354]: #1356
+#1361 := [trans #1357 #1359]: #1360
+#1363 := [monotonicity #1361]: #1362
+#1078 := (* -1::real #883)
+#1260 := (+ #793 #1078)
+#1262 := (>= #1260 0::real)
+#1269 := (not #1262)
+#1263 := [hypothesis]: #1262
+#1079 := (f8 f20 #20)
+#1093 := (* -1::real #1079)
+#1106 := (+ #883 #1093)
+#1107 := (<= #1106 0::real)
+#1131 := (not #1107)
+#841 := (f8 #86 #20)
+#1094 := (+ #841 #1093)
+#1095 := (>= #1094 0::real)
+#1112 := (or #1095 #1107)
+#1115 := (not #1112)
+#1119 := (or #1118 #1115)
+#1080 := (+ #1079 #1078)
+#1081 := (>= #1080 0::real)
+#1082 := (* -1::real #841)
+#1083 := (+ #1079 #1082)
+#1084 := (<= #1083 0::real)
+#1085 := (or #1084 #1081)
+#1086 := (not #1085)
+#1120 := (or #1118 #1086)
+#1122 := (iff #1120 #1119)
+#1124 := (iff #1119 #1119)
+#1125 := [rewrite]: #1124
+#1116 := (iff #1086 #1115)
+#1113 := (iff #1085 #1112)
+#1110 := (iff #1081 #1107)
+#1100 := (+ #1078 #1079)
+#1103 := (>= #1100 0::real)
+#1108 := (iff #1103 #1107)
+#1109 := [rewrite]: #1108
+#1104 := (iff #1081 #1103)
+#1101 := (= #1080 #1100)
+#1102 := [rewrite]: #1101
+#1105 := [monotonicity #1102]: #1104
+#1111 := [trans #1105 #1109]: #1110
+#1098 := (iff #1084 #1095)
+#1087 := (+ #1082 #1079)
+#1090 := (<= #1087 0::real)
+#1096 := (iff #1090 #1095)
+#1097 := [rewrite]: #1096
+#1091 := (iff #1084 #1090)
+#1088 := (= #1083 #1087)
+#1089 := [rewrite]: #1088
+#1092 := [monotonicity #1089]: #1091
+#1099 := [trans #1092 #1097]: #1098
+#1114 := [monotonicity #1099 #1111]: #1113
+#1117 := [monotonicity #1114]: #1116
+#1123 := [monotonicity #1117]: #1122
+#1126 := [trans #1123 #1125]: #1122
+#1121 := [quant-inst]: #1120
+#1127 := [mp #1121 #1126]: #1119
+#1264 := [unit-resolution #1127 #600]: #1115
+#1132 := (or #1112 #1131)
+#1133 := [def-axiom]: #1132
+#1265 := [unit-resolution #1133 #1264]: #1131
+#1194 := (+ #793 #1093)
+#1195 := (>= #1194 0::real)
+#1225 := (not #1195)
+#934 := (f8 #81 #20)
+#1204 := (+ #934 #1093)
+#1205 := (<= #1204 0::real)
+#1210 := (or #1195 #1205)
+#1213 := (not #1210)
+#1216 := (or #1060 #1213)
+#1191 := (* -1::real #934)
+#1192 := (+ #1079 #1191)
+#1193 := (>= #1192 0::real)
+#1196 := (or #1195 #1193)
+#1197 := (not #1196)
+#1217 := (or #1060 #1197)
+#1219 := (iff #1217 #1216)
+#1221 := (iff #1216 #1216)
+#1222 := [rewrite]: #1221
+#1214 := (iff #1197 #1213)
+#1211 := (iff #1196 #1210)
+#1208 := (iff #1193 #1205)
+#1198 := (+ #1191 #1079)
+#1201 := (>= #1198 0::real)
+#1206 := (iff #1201 #1205)
+#1207 := [rewrite]: #1206
+#1202 := (iff #1193 #1201)
+#1199 := (= #1192 #1198)
+#1200 := [rewrite]: #1199
+#1203 := [monotonicity #1200]: #1202
+#1209 := [trans #1203 #1207]: #1208
+#1212 := [monotonicity #1209]: #1211
+#1215 := [monotonicity #1212]: #1214
+#1220 := [monotonicity #1215]: #1219
+#1223 := [trans #1220 #1222]: #1219
+#1218 := [quant-inst]: #1217
+#1224 := [mp #1218 #1223]: #1216
+#1266 := [unit-resolution #1224 #594]: #1213
+#1226 := (or #1210 #1225)
+#1227 := [def-axiom]: #1226
+#1267 := [unit-resolution #1227 #1266]: #1225
+#1268 := [th-lemma #1267 #1265 #1263]: false
+#1270 := [lemma #1268]: #1269
+#1273 := (or #1272 #1262)
+#1274 := [th-lemma]: #1273
+#1342 := [unit-resolution #1274 #1270]: #1272
+#1364 := [mp #1342 #1363]: #838
+#1366 := (or #809 #794)
+#795 := (f8 f16 #20)
+#814 := (= #793 #795)
+#817 := (ite #809 #814 #794)
+#470 := (= #42 #77)
+#469 := (= #44 #77)
+#471 := (ite #145 #469 #470)
+#562 := (forall (vars (?v0 S2)) (:pat #535 #552 #561 #554) #471)
+#474 := (forall (vars (?v0 S2)) #471)
+#565 := (iff #474 #562)
+#563 := (iff #471 #471)
+#564 := [refl]: #563
+#566 := [quant-intro #564]: #565
+#185 := (ite #145 #44 #42)
+#390 := (= #77 #185)
+#391 := (forall (vars (?v0 S2)) #390)
+#475 := (iff #391 #474)
+#472 := (iff #390 #471)
+#473 := [rewrite]: #472
+#476 := [quant-intro #473]: #475
+#348 := (~ #391 #391)
+#358 := (~ #390 #390)
+#347 := [refl]: #358
+#395 := [nnf-pos #347]: #348
+#49 := (f3 f17 #9)
+#190 := (= #49 #185)
+#193 := (forall (vars (?v0 S2)) #190)
+#392 := (iff #193 #391)
+#393 := [rewrite* #298]: #392
+#50 := (ite #32 #42 #44)
+#51 := (= #49 #50)
+#52 := (forall (vars (?v0 S2)) #51)
+#194 := (iff #52 #193)
+#191 := (iff #51 #190)
+#188 := (= #50 #185)
+#182 := (ite #144 #42 #44)
+#186 := (= #182 #185)
+#187 := [rewrite]: #186
+#183 := (= #50 #182)
+#184 := [monotonicity #149]: #183
+#189 := [trans #184 #187]: #188
+#192 := [monotonicity #189]: #191
+#195 := [quant-intro #192]: #194
+#143 := [asserted]: #52
+#196 := [mp #143 #195]: #193
+#394 := [mp #196 #393]: #391
+#396 := [mp~ #394 #395]: #391
+#477 := [mp #396 #476]: #474
+#567 := [mp #477 #566]: #562
+#628 := (not #562)
+#820 := (or #628 #817)
+#796 := (= #795 #793)
+#798 := (+ #797 #146)
+#799 := (>= #798 0::int)
+#800 := (ite #799 #796 #794)
+#821 := (or #628 #800)
+#823 := (iff #821 #820)
+#825 := (iff #820 #820)
+#826 := [rewrite]: #825
+#818 := (iff #800 #817)
+#815 := (iff #796 #814)
+#816 := [rewrite]: #815
+#812 := (iff #799 #809)
+#801 := (+ #146 #797)
+#804 := (>= #801 0::int)
+#810 := (iff #804 #809)
+#811 := [rewrite]: #810
+#805 := (iff #799 #804)
+#802 := (= #798 #801)
+#803 := [rewrite]: #802
+#806 := [monotonicity #803]: #805
+#813 := [trans #806 #811]: #812
+#819 := [monotonicity #813 #816]: #818
+#824 := [monotonicity #819]: #823
+#827 := [trans #824 #826]: #823
+#822 := [quant-inst]: #821
+#828 := [mp #822 #827]: #820
+#1365 := [unit-resolution #828 #567]: #817
+#829 := (not #817)
+#833 := (or #829 #809 #794)
+#834 := [def-axiom]: #833
+#1367 := [unit-resolution #834 #1365]: #1366
+#1368 := [unit-resolution #1367 #1364]: #809
+#984 := (>= #853 0::int)
+#1369 := (or #1345 #984)
+#1370 := [th-lemma]: #1369
+#1371 := [unit-resolution #1370 #1344]: #984
+#830 := (not #809)
+#1372 := (not #984)
+#1373 := (or #1288 #1372 #830)
+#1374 := [th-lemma]: #1373
+#1375 := [unit-resolution #1374 #1371 #1368]: #1288
+#1377 := (not #1288)
+#1378 := (or #1285 #1376 #1377)
+#1379 := [th-lemma]: #1378
+#1381 := [unit-resolution #1379 #1375]: #1380
+#1382 := [unit-resolution #1381 #1315]: #1376
+#982 := (>= #616 0::int)
+#1383 := (or #1318 #982)
+#1384 := [th-lemma]: #1383
+#1385 := [unit-resolution #1384 #1297]: #982
+[th-lemma #1385 #1382 #1341]: false
+unsat
+85264eb8e7f8e85b6d7ee44a562fd15da499cae2 208 0
+#2 := false
+#37 := 0::real
+decl f13 :: (-> S6 S7 real)
+decl f17 :: S7
+#32 := f17
+decl f18 :: S6
+#34 := f18
+#35 := (f13 f18 f17)
+decl f14 :: (-> S8 S9 S6)
+decl f16 :: S9
+#30 := f16
+decl f15 :: (-> S2 S8)
+decl f5 :: S2
+#11 := f5
+#29 := (f15 f5)
+#31 := (f14 #29 f16)
+#33 := (f13 #31 f17)
+#96 := -1::real
+#107 := (* -1::real #33)
+#108 := (+ #107 #35)
+#97 := (* -1::real #35)
+#98 := (+ #33 #97)
+#135 := (>= #98 0::real)
+#142 := (ite #135 #98 #108)
+#150 := (* -1::real #142)
+#383 := (+ #108 #150)
+#384 := (<= #383 0::real)
+#369 := (= #108 #142)
+#136 := (not #135)
+decl f3 :: S2
+#8 := f3
+#47 := (f15 f3)
+#48 := (f14 #47 f16)
+#49 := (f13 #48 f17)
+#172 := (* -1::real #49)
+decl f19 :: S6
+#41 := f19
+#42 := (f13 f19 f17)
+#173 := (+ #42 #172)
+#116 := (* -1::real #42)
+#163 := (+ #116 #49)
+#184 := (<= #173 0::real)
+#191 := (ite #184 #163 #173)
+#199 := (* -1::real #191)
+#382 := (+ #173 #199)
+#385 := (<= #382 0::real)
+#375 := (= #173 #191)
+#185 := (not #184)
+#386 := [hypothesis]: #184
+#394 := (or #136 #185)
+#125 := -1/3::real
+#126 := (* -1/3::real #42)
+#200 := (+ #126 #199)
+#123 := 1/3::real
+#124 := (* 1/3::real #35)
+#201 := (+ #124 #200)
+#202 := (<= #201 0::real)
+#203 := (not #202)
+#44 := 3::real
+#43 := (- #35 #42)
+#45 := (/ #43 3::real)
+#50 := (- #49 #42)
+#52 := (- #50)
+#51 := (< #50 0::real)
+#53 := (ite #51 #52 #50)
+#54 := (< #53 #45)
+#208 := (iff #54 #203)
+#127 := (+ #124 #126)
+#166 := (< #163 0::real)
+#178 := (ite #166 #173 #163)
+#181 := (< #178 #127)
+#206 := (iff #181 #203)
+#196 := (< #191 #127)
+#204 := (iff #196 #203)
+#205 := [rewrite]: #204
+#197 := (iff #181 #196)
+#194 := (= #178 #191)
+#188 := (ite #185 #173 #163)
+#192 := (= #188 #191)
+#193 := [rewrite]: #192
+#189 := (= #178 #188)
+#186 := (iff #166 #185)
+#187 := [rewrite]: #186
+#190 := [monotonicity #187]: #189
+#195 := [trans #190 #193]: #194
+#198 := [monotonicity #195]: #197
+#207 := [trans #198 #205]: #206
+#182 := (iff #54 #181)
+#130 := (= #45 #127)
+#117 := (+ #35 #116)
+#120 := (/ #117 3::real)
+#128 := (= #120 #127)
+#129 := [rewrite]: #128
+#121 := (= #45 #120)
+#118 := (= #43 #117)
+#119 := [rewrite]: #118
+#122 := [monotonicity #119]: #121
+#131 := [trans #122 #129]: #130
+#179 := (= #53 #178)
+#164 := (= #50 #163)
+#165 := [rewrite]: #164
+#176 := (= #52 #173)
+#169 := (- #163)
+#174 := (= #169 #173)
+#175 := [rewrite]: #174
+#170 := (= #52 #169)
+#171 := [monotonicity #165]: #170
+#177 := [trans #171 #175]: #176
+#167 := (iff #51 #166)
+#168 := [monotonicity #165]: #167
+#180 := [monotonicity #168 #177 #165]: #179
+#183 := [monotonicity #180 #131]: #182
+#209 := [trans #183 #207]: #208
+#162 := [asserted]: #54
+#210 := [mp #162 #209]: #203
+#380 := (+ #163 #199)
+#381 := (<= #380 0::real)
+#374 := (= #163 #191)
+#376 := (or #185 #374)
+#377 := [def-axiom]: #376
+#387 := [unit-resolution #377 #386]: #374
+#388 := (not #374)
+#389 := (or #388 #381)
+#390 := [th-lemma]: #389
+#391 := [unit-resolution #390 #387]: #381
+#392 := [hypothesis]: #135
+#214 := (+ #33 #172)
+#215 := (<= #214 0::real)
+#55 := (<= #33 #49)
+#216 := (iff #55 #215)
+#217 := [rewrite]: #216
+#211 := [asserted]: #55
+#218 := [mp #211 #217]: #215
+#393 := [th-lemma #218 #392 #391 #210 #386]: false
+#395 := [lemma #393]: #394
+#396 := [unit-resolution #395 #386]: #136
+#151 := (+ #126 #150)
+#152 := (+ #124 #151)
+#153 := (<= #152 0::real)
+#154 := (not #153)
+#36 := (- #33 #35)
+#39 := (- #36)
+#38 := (< #36 0::real)
+#40 := (ite #38 #39 #36)
+#46 := (< #40 #45)
+#159 := (iff #46 #154)
+#101 := (< #98 0::real)
+#113 := (ite #101 #108 #98)
+#132 := (< #113 #127)
+#157 := (iff #132 #154)
+#147 := (< #142 #127)
+#155 := (iff #147 #154)
+#156 := [rewrite]: #155
+#148 := (iff #132 #147)
+#145 := (= #113 #142)
+#139 := (ite #136 #108 #98)
+#143 := (= #139 #142)
+#144 := [rewrite]: #143
+#140 := (= #113 #139)
+#137 := (iff #101 #136)
+#138 := [rewrite]: #137
+#141 := [monotonicity #138]: #140
+#146 := [trans #141 #144]: #145
+#149 := [monotonicity #146]: #148
+#158 := [trans #149 #156]: #157
+#133 := (iff #46 #132)
+#114 := (= #40 #113)
+#99 := (= #36 #98)
+#100 := [rewrite]: #99
+#111 := (= #39 #108)
+#104 := (- #98)
+#109 := (= #104 #108)
+#110 := [rewrite]: #109
+#105 := (= #39 #104)
+#106 := [monotonicity #100]: #105
+#112 := [trans #106 #110]: #111
+#102 := (iff #38 #101)
+#103 := [monotonicity #100]: #102
+#115 := [monotonicity #103 #112 #100]: #114
+#134 := [monotonicity #115 #131]: #133
+#160 := [trans #134 #158]: #159
+#95 := [asserted]: #46
+#161 := [mp #95 #160]: #154
+#372 := (or #135 #369)
+#373 := [def-axiom]: #372
+#397 := [unit-resolution #373 #396]: #369
+#398 := (not #369)
+#399 := (or #398 #384)
+#400 := [th-lemma]: #399
+#401 := [unit-resolution #400 #397]: #384
+#402 := [th-lemma #401 #161 #391 #210 #218 #396]: false
+#403 := [lemma #402]: #185
+#378 := (or #184 #375)
+#379 := [def-axiom]: #378
+#406 := [unit-resolution #379 #403]: #375
+#407 := (not #375)
+#408 := (or #407 #385)
+#409 := [th-lemma]: #408
+#410 := [unit-resolution #409 #406]: #385
+#412 := (not #215)
+#411 := (not #385)
+#413 := (or #136 #411 #412 #202 #184)
+#414 := [th-lemma]: #413
+#415 := [unit-resolution #414 #403 #210 #218 #410]: #136
+#416 := [unit-resolution #373 #415]: #369
+#417 := [unit-resolution #400 #416]: #384
+[th-lemma #410 #218 #210 #403 #161 #417]: false
+unsat
+93a49e3235fe928f7c40274d2cb077bbf82de367 333 0
+#2 := false
+#11 := 0::real
+decl ?v2!1 :: real
+#225 := ?v2!1
+decl ?v1!2 :: real
+#223 := ?v1!2
+#45 := -1::real
+#238 := (* -1::real ?v1!2)
+#260 := (+ #238 ?v2!1)
+#240 := (* -1::real ?v2!1)
+#266 := (+ ?v1!2 #240)
+#267 := (>= #266 0::real)
+#274 := (ite #267 #266 #260)
+#277 := (* -1::real #274)
+#74 := -1/3::real
+#233 := (* -1/3::real ?v2!1)
+#280 := (+ #233 #277)
+decl ?v3!0 :: real
+#224 := ?v3!0
+#72 := 1/3::real
+#235 := (* 1/3::real ?v3!0)
+#283 := (+ #235 #280)
+#286 := (<= #283 0::real)
+#302 := (not #286)
+decl ?v0!3 :: real
+#221 := ?v0!3
+#248 := (+ ?v0!3 #238)
+#249 := (<= #248 0::real)
+#250 := (not #249)
+#226 := (* -1::real ?v0!3)
+#227 := (+ #226 ?v3!0)
+#228 := (* -1::real ?v3!0)
+#229 := (+ ?v0!3 #228)
+#230 := (>= #229 0::real)
+#231 := (ite #230 #229 #227)
+#232 := (* -1::real #231)
+#234 := (+ #233 #232)
+#236 := (+ #235 #234)
+#237 := (<= #236 0::real)
+#292 := (or #237 #250 #286)
+#297 := (not #292)
+#239 := (+ ?v2!1 #238)
+#241 := (+ #240 ?v1!2)
+#242 := (<= #239 0::real)
+#243 := (ite #242 #241 #239)
+#244 := (* -1::real #243)
+#245 := (+ #233 #244)
+#246 := (+ #235 #245)
+#247 := (<= #246 0::real)
+#251 := (or #250 #247 #237)
+#252 := (not #251)
+#298 := (iff #252 #297)
+#295 := (iff #251 #292)
+#289 := (or #250 #286 #237)
+#293 := (iff #289 #292)
+#294 := [rewrite]: #293
+#290 := (iff #251 #289)
+#287 := (iff #247 #286)
+#284 := (= #246 #283)
+#281 := (= #245 #280)
+#278 := (= #244 #277)
+#275 := (= #243 #274)
+#261 := (= #239 #260)
+#262 := [rewrite]: #261
+#272 := (= #241 #266)
+#273 := [rewrite]: #272
+#270 := (iff #242 #267)
+#263 := (<= #260 0::real)
+#268 := (iff #263 #267)
+#269 := [rewrite]: #268
+#264 := (iff #242 #263)
+#265 := [monotonicity #262]: #264
+#271 := [trans #265 #269]: #270
+#276 := [monotonicity #271 #273 #262]: #275
+#279 := [monotonicity #276]: #278
+#282 := [monotonicity #279]: #281
+#285 := [monotonicity #282]: #284
+#288 := [monotonicity #285]: #287
+#291 := [monotonicity #288]: #290
+#296 := [trans #291 #294]: #295
+#299 := [monotonicity #296]: #298
+#9 := (:var 0 real)
+#8 := (:var 3 real)
+#56 := (* -1::real #8)
+#57 := (+ #56 #9)
+#46 := (* -1::real #9)
+#47 := (+ #8 #46)
+#170 := (>= #47 0::real)
+#177 := (ite #170 #47 #57)
+#185 := (* -1::real #177)
+#15 := (:var 1 real)
+#75 := (* -1/3::real #15)
+#186 := (+ #75 #185)
+#73 := (* 1/3::real #9)
+#187 := (+ #73 #186)
+#188 := (<= #187 0::real)
+#20 := (:var 2 real)
+#93 := (* -1::real #20)
+#94 := (+ #15 #93)
+#65 := (* -1::real #15)
+#84 := (+ #65 #20)
+#139 := (<= #94 0::real)
+#146 := (ite #139 #84 #94)
+#154 := (* -1::real #146)
+#155 := (+ #75 #154)
+#156 := (+ #73 #155)
+#157 := (<= #156 0::real)
+#132 := (+ #8 #93)
+#133 := (<= #132 0::real)
+#136 := (not #133)
+#207 := (or #136 #157 #188)
+#212 := (forall (vars (?v0 real) (?v1 real) (?v2 real) (?v3 real)) #207)
+#215 := (not #212)
+#253 := (~ #215 #252)
+#254 := [sk]: #253
+#26 := (<= #8 #20)
+#27 := (implies #26 false)
+#17 := 3::real
+#16 := (- #9 #15)
+#18 := (/ #16 3::real)
+#21 := (- #20 #15)
+#23 := (- #21)
+#22 := (< #21 0::real)
+#24 := (ite #22 #23 #21)
+#25 := (< #24 #18)
+#28 := (implies #25 #27)
+#10 := (- #8 #9)
+#13 := (- #10)
+#12 := (< #10 0::real)
+#14 := (ite #12 #13 #10)
+#19 := (< #14 #18)
+#29 := (implies #19 #28)
+#30 := (forall (vars (?v0 real) (?v1 real) (?v2 real) (?v3 real)) #29)
+#31 := (not #30)
+#218 := (iff #31 #215)
+#76 := (+ #73 #75)
+#87 := (< #84 0::real)
+#99 := (ite #87 #94 #84)
+#102 := (< #99 #76)
+#111 := (not #102)
+#105 := (not #26)
+#112 := (or #105 #111)
+#50 := (< #47 0::real)
+#62 := (ite #50 #57 #47)
+#81 := (< #62 #76)
+#120 := (not #81)
+#121 := (or #120 #112)
+#126 := (forall (vars (?v0 real) (?v1 real) (?v2 real) (?v3 real)) #121)
+#129 := (not #126)
+#216 := (iff #129 #215)
+#213 := (iff #126 #212)
+#210 := (iff #121 #207)
+#201 := (or #136 #157)
+#204 := (or #188 #201)
+#208 := (iff #204 #207)
+#209 := [rewrite]: #208
+#205 := (iff #121 #204)
+#202 := (iff #112 #201)
+#168 := (iff #111 #157)
+#158 := (not #157)
+#163 := (not #158)
+#166 := (iff #163 #157)
+#167 := [rewrite]: #166
+#164 := (iff #111 #163)
+#161 := (iff #102 #158)
+#151 := (< #146 #76)
+#159 := (iff #151 #158)
+#160 := [rewrite]: #159
+#152 := (iff #102 #151)
+#149 := (= #99 #146)
+#140 := (not #139)
+#143 := (ite #140 #94 #84)
+#147 := (= #143 #146)
+#148 := [rewrite]: #147
+#144 := (= #99 #143)
+#141 := (iff #87 #140)
+#142 := [rewrite]: #141
+#145 := [monotonicity #142]: #144
+#150 := [trans #145 #148]: #149
+#153 := [monotonicity #150]: #152
+#162 := [trans #153 #160]: #161
+#165 := [monotonicity #162]: #164
+#169 := [trans #165 #167]: #168
+#137 := (iff #105 #136)
+#134 := (iff #26 #133)
+#135 := [rewrite]: #134
+#138 := [monotonicity #135]: #137
+#203 := [monotonicity #138 #169]: #202
+#199 := (iff #120 #188)
+#189 := (not #188)
+#194 := (not #189)
+#197 := (iff #194 #188)
+#198 := [rewrite]: #197
+#195 := (iff #120 #194)
+#192 := (iff #81 #189)
+#182 := (< #177 #76)
+#190 := (iff #182 #189)
+#191 := [rewrite]: #190
+#183 := (iff #81 #182)
+#180 := (= #62 #177)
+#171 := (not #170)
+#174 := (ite #171 #57 #47)
+#178 := (= #174 #177)
+#179 := [rewrite]: #178
+#175 := (= #62 #174)
+#172 := (iff #50 #171)
+#173 := [rewrite]: #172
+#176 := [monotonicity #173]: #175
+#181 := [trans #176 #179]: #180
+#184 := [monotonicity #181]: #183
+#193 := [trans #184 #191]: #192
+#196 := [monotonicity #193]: #195
+#200 := [trans #196 #198]: #199
+#206 := [monotonicity #200 #203]: #205
+#211 := [trans #206 #209]: #210
+#214 := [quant-intro #211]: #213
+#217 := [monotonicity #214]: #216
+#130 := (iff #31 #129)
+#127 := (iff #30 #126)
+#124 := (iff #29 #121)
+#117 := (implies #81 #112)
+#122 := (iff #117 #121)
+#123 := [rewrite]: #122
+#118 := (iff #29 #117)
+#115 := (iff #28 #112)
+#108 := (implies #102 #105)
+#113 := (iff #108 #112)
+#114 := [rewrite]: #113
+#109 := (iff #28 #108)
+#106 := (iff #27 #105)
+#107 := [rewrite]: #106
+#103 := (iff #25 #102)
+#79 := (= #18 #76)
+#66 := (+ #9 #65)
+#69 := (/ #66 3::real)
+#77 := (= #69 #76)
+#78 := [rewrite]: #77
+#70 := (= #18 #69)
+#67 := (= #16 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#80 := [trans #71 #78]: #79
+#100 := (= #24 #99)
+#85 := (= #21 #84)
+#86 := [rewrite]: #85
+#97 := (= #23 #94)
+#90 := (- #84)
+#95 := (= #90 #94)
+#96 := [rewrite]: #95
+#91 := (= #23 #90)
+#92 := [monotonicity #86]: #91
+#98 := [trans #92 #96]: #97
+#88 := (iff #22 #87)
+#89 := [monotonicity #86]: #88
+#101 := [monotonicity #89 #98 #86]: #100
+#104 := [monotonicity #101 #80]: #103
+#110 := [monotonicity #104 #107]: #109
+#116 := [trans #110 #114]: #115
+#82 := (iff #19 #81)
+#63 := (= #14 #62)
+#48 := (= #10 #47)
+#49 := [rewrite]: #48
+#60 := (= #13 #57)
+#53 := (- #47)
+#58 := (= #53 #57)
+#59 := [rewrite]: #58
+#54 := (= #13 #53)
+#55 := [monotonicity #49]: #54
+#61 := [trans #55 #59]: #60
+#51 := (iff #12 #50)
+#52 := [monotonicity #49]: #51
+#64 := [monotonicity #52 #61 #49]: #63
+#83 := [monotonicity #64 #80]: #82
+#119 := [monotonicity #83 #116]: #118
+#125 := [trans #119 #123]: #124
+#128 := [quant-intro #125]: #127
+#131 := [monotonicity #128]: #130
+#219 := [trans #131 #217]: #218
+#44 := [asserted]: #31
+#220 := [mp #44 #219]: #215
+#257 := [mp~ #220 #254]: #252
+#258 := [mp #257 #299]: #297
+#303 := [not-or-elim #258]: #302
+#301 := [not-or-elim #258]: #249
+#259 := (not #237)
+#300 := [not-or-elim #258]: #259
+#376 := (+ #227 #232)
+#377 := (<= #376 0::real)
+#360 := (= #227 #231)
+#361 := (not #230)
+#368 := (not #267)
+#379 := [hypothesis]: #368
+#387 := (or #361 #267)
+#373 := (+ #260 #277)
+#374 := (<= #373 0::real)
+#367 := (= #260 #274)
+#371 := (or #267 #367)
+#372 := [def-axiom]: #371
+#380 := [unit-resolution #372 #379]: #367
+#381 := (not #367)
+#382 := (or #381 #374)
+#383 := [th-lemma]: #382
+#384 := [unit-resolution #383 #380]: #374
+#385 := [hypothesis]: #230
+#386 := [th-lemma #385 #384 #303 #379 #301]: false
+#388 := [lemma #386]: #387
+#389 := [unit-resolution #388 #379]: #361
+#364 := (or #230 #360)
+#365 := [def-axiom]: #364
+#390 := [unit-resolution #365 #389]: #360
+#391 := (not #360)
+#392 := (or #391 #377)
+#393 := [th-lemma]: #392
+#394 := [unit-resolution #393 #390]: #377
+#395 := [th-lemma #384 #303 #379 #394 #300 #301]: false
+#396 := [lemma #395]: #267
+#399 := [hypothesis]: #361
+#400 := [unit-resolution #365 #399]: #360
+#401 := [unit-resolution #393 #400]: #377
+#375 := (+ #266 #277)
+#378 := (<= #375 0::real)
+#366 := (= #266 #274)
+#369 := (or #368 #366)
+#370 := [def-axiom]: #369
+#402 := [unit-resolution #370 #396]: #366
+#403 := (not #366)
+#404 := (or #403 #378)
+#405 := [th-lemma]: #404
+#406 := [unit-resolution #405 #402]: #378
+#407 := [th-lemma #406 #301 #401 #300 #399 #303]: false
+#408 := [lemma #407]: #230
+[th-lemma #406 #301 #408 #396 #303]: false
+unsat
+869cff425b5458015114ab900e59f8623c03a78b 165 0
+#2 := false
+#22 := 0::real
+decl f3 :: (-> S3 S2 real)
+decl ?v0!0 :: S2
+#118 := ?v0!0
+decl f5 :: S3
+#11 := f5
+#119 := (f3 f5 ?v0!0)
+#49 := -1::real
+#117 := (* -1::real #119)
+decl f4 :: S3
+#8 := f4
+#115 := (f3 f4 ?v0!0)
+#120 := (+ #115 #117)
+#121 := (>= #120 0::real)
+decl f6 :: (-> S2 S4 S1)
+decl f7 :: (-> S4 S4 S4)
+decl f9 :: (-> S2 S4 S4)
+decl f11 :: S4
+#17 := f11
+decl f10 :: S2
+#16 := f10
+#18 := (f9 f10 f11)
+decl f8 :: S4
+#15 := f8
+#19 := (f7 f8 #18)
+#123 := (f6 ?v0!0 #19)
+decl f1 :: S1
+#4 := f1
+#124 := (= f1 #123)
+#9 := (:var 0 S2)
+#12 := (f3 f5 #9)
+#81 := (* -1::real #12)
+#10 := (f3 f4 #9)
+#82 := (+ #10 #81)
+#83 := (>= #82 0::real)
+#84 := (not #83)
+#89 := (forall (vars (?v1 S2)) #84)
+#158 := (and #89 #121 #124)
+#122 := (not #121)
+#133 := (not #122)
+#125 := (not #124)
+#130 := (not #125)
+#143 := (and #130 #133 #89)
+#161 := (iff #143 #158)
+#155 := (and #124 #121 #89)
+#159 := (iff #155 #158)
+#160 := [rewrite]: #159
+#156 := (iff #143 #155)
+#153 := (iff #133 #121)
+#154 := [rewrite]: #153
+#151 := (iff #130 #124)
+#152 := [rewrite]: #151
+#157 := [monotonicity #152 #154]: #156
+#162 := [trans #157 #160]: #161
+#92 := (not #89)
+#20 := (f6 #9 #19)
+#46 := (= f1 #20)
+#60 := (not #46)
+#101 := (or #60 #84 #92)
+#106 := (forall (vars (?v0 S2)) #101)
+#109 := (not #106)
+#146 := (~ #109 #143)
+#126 := (or #125 #122 #92)
+#127 := (not #126)
+#144 := (~ #127 #143)
+#140 := (not #92)
+#141 := (~ #140 #89)
+#138 := (~ #89 #89)
+#136 := (~ #84 #84)
+#137 := [refl]: #136
+#139 := [nnf-pos #137]: #138
+#142 := [nnf-neg #139]: #141
+#134 := (~ #133 #133)
+#135 := [refl]: #134
+#131 := (~ #130 #130)
+#132 := [refl]: #131
+#145 := [nnf-neg #132 #135 #142]: #144
+#128 := (~ #109 #127)
+#129 := [sk]: #128
+#147 := [trans #129 #145]: #146
+#23 := (- #12 #10)
+#24 := (< 0::real #23)
+#21 := (= #20 f1)
+#25 := (implies #21 #24)
+#13 := (< #10 #12)
+#14 := (forall (vars (?v1 S2)) #13)
+#26 := (implies #14 #25)
+#27 := (forall (vars (?v0 S2)) #26)
+#28 := (not #27)
+#112 := (iff #28 #109)
+#50 := (* -1::real #10)
+#51 := (+ #50 #12)
+#54 := (< 0::real #51)
+#61 := (or #60 #54)
+#69 := (not #14)
+#70 := (or #69 #61)
+#75 := (forall (vars (?v0 S2)) #70)
+#78 := (not #75)
+#110 := (iff #78 #109)
+#107 := (iff #75 #106)
+#104 := (iff #70 #101)
+#95 := (or #60 #84)
+#98 := (or #92 #95)
+#102 := (iff #98 #101)
+#103 := [rewrite]: #102
+#99 := (iff #70 #98)
+#96 := (iff #61 #95)
+#85 := (iff #54 #84)
+#86 := [rewrite]: #85
+#97 := [monotonicity #86]: #96
+#93 := (iff #69 #92)
+#90 := (iff #14 #89)
+#87 := (iff #13 #84)
+#88 := [rewrite]: #87
+#91 := [quant-intro #88]: #90
+#94 := [monotonicity #91]: #93
+#100 := [monotonicity #94 #97]: #99
+#105 := [trans #100 #103]: #104
+#108 := [quant-intro #105]: #107
+#111 := [monotonicity #108]: #110
+#79 := (iff #28 #78)
+#76 := (iff #27 #75)
+#73 := (iff #26 #70)
+#66 := (implies #14 #61)
+#71 := (iff #66 #70)
+#72 := [rewrite]: #71
+#67 := (iff #26 #66)
+#64 := (iff #25 #61)
+#57 := (implies #46 #54)
+#62 := (iff #57 #61)
+#63 := [rewrite]: #62
+#58 := (iff #25 #57)
+#55 := (iff #24 #54)
+#52 := (= #23 #51)
+#53 := [rewrite]: #52
+#56 := [monotonicity #53]: #55
+#47 := (iff #21 #46)
+#48 := [rewrite]: #47
+#59 := [monotonicity #48 #56]: #58
+#65 := [trans #59 #63]: #64
+#68 := [monotonicity #65]: #67
+#74 := [trans #68 #72]: #73
+#77 := [quant-intro #74]: #76
+#80 := [monotonicity #77]: #79
+#113 := [trans #80 #111]: #112
+#45 := [asserted]: #28
+#114 := [mp #45 #113]: #109
+#148 := [mp~ #114 #147]: #143
+#149 := [mp #148 #162]: #158
+#163 := [and-elim #149]: #121
+#223 := (pattern #12)
+#222 := (pattern #10)
+#224 := (forall (vars (?v1 S2)) (:pat #222 #223) #84)
+#227 := (iff #89 #224)
+#225 := (iff #84 #84)
+#226 := [refl]: #225
+#228 := [quant-intro #226]: #227
+#150 := [and-elim #149]: #89
+#229 := [mp #150 #228]: #224
+#232 := (not #224)
+#233 := (or #232 #122)
+#234 := [quant-inst]: #233
+[unit-resolution #234 #229 #163]: false
+unsat
+2d6fbb869d4e1460704d418830e5da7d2659f315 57 0
+#2 := false
+decl f13 :: (-> S4 S4 S5)
+#44 := (:var 0 S4)
+#43 := (:var 1 S4)
+#45 := (f13 #43 #44)
+#252 := (pattern #45)
+#39 := 0::real
+decl f12 :: (-> S5 real)
+#46 := (f12 #45)
+#133 := (>= #46 0::real)
+#253 := (forall (vars (?v0 S4) (?v1 S4)) (:pat #252) #133)
+#135 := (forall (vars (?v0 S4) (?v1 S4)) #133)
+#256 := (iff #135 #253)
+#254 := (iff #133 #133)
+#255 := [refl]: #254
+#257 := [quant-intro #255]: #256
+#150 := (~ #135 #135)
+#139 := (~ #133 #133)
+#130 := [refl]: #139
+#151 := [nnf-pos #130]: #150
+#47 := (<= 0::real #46)
+#48 := (forall (vars (?v0 S4) (?v1 S4)) #47)
+#136 := (iff #48 #135)
+#132 := (iff #47 #133)
+#134 := [rewrite]: #132
+#137 := [quant-intro #134]: #136
+#129 := [asserted]: #48
+#138 := [mp #129 #137]: #135
+#152 := [mp~ #138 #151]: #135
+#258 := [mp #152 #257]: #253
+decl f14 :: (-> S3 S4)
+decl f4 :: S3
+#8 := f4
+#36 := (f14 f4)
+decl f10 :: S3
+#24 := f10
+#35 := (f14 f10)
+#37 := (f13 #35 #36)
+#38 := (f12 #37)
+#259 := (>= #38 0::real)
+#261 := (not #259)
+#41 := (= #38 0::real)
+#42 := (not #41)
+#128 := [asserted]: #42
+#267 := (or #41 #261)
+#40 := (<= #38 0::real)
+#127 := [asserted]: #40
+#260 := (not #40)
+#265 := (or #41 #260 #261)
+#266 := [th-lemma]: #265
+#268 := [unit-resolution #266 #127]: #267
+#269 := [unit-resolution #268 #128]: #261
+#262 := (not #253)
+#263 := (or #262 #259)
+#264 := [quant-inst]: #263
+[unit-resolution #264 #269 #258]: false
+unsat
+c9590f4753c4b6ca0ef0d09a97231631684bbcc1 91 0
+#2 := false
+#43 := 0::real
+decl f3 :: (-> S2 S3 real)
+decl f5 :: S3
+#9 := f5
+decl f6 :: S2
+#11 := f6
+#12 := (f3 f6 f5)
+#40 := -1::real
+#41 := (* -1::real #12)
+decl f4 :: S2
+#8 := f4
+#10 := (f3 f4 f5)
+#42 := (+ #10 #41)
+#135 := (>= #42 0::real)
+#160 := (not #135)
+#48 := (= #10 #12)
+#60 := (not #48)
+#19 := (= #12 #10)
+#20 := (not #19)
+#61 := (iff #20 #60)
+#58 := (iff #19 #48)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#39 := [asserted]: #20
+#65 := [mp #39 #62]: #60
+#163 := (or #48 #160)
+#44 := (<= #42 0::real)
+#13 := (<= #10 #12)
+#45 := (iff #13 #44)
+#46 := [rewrite]: #45
+#37 := [asserted]: #13
+#47 := [mp #37 #46]: #44
+#159 := (not #44)
+#161 := (or #48 #159 #160)
+#162 := [th-lemma]: #161
+#164 := [unit-resolution #162 #47]: #163
+#165 := [unit-resolution #164 #65]: #160
+#14 := (:var 0 S3)
+#16 := (f3 f4 #14)
+#128 := (pattern #16)
+#15 := (f3 f6 #14)
+#127 := (pattern #15)
+#49 := (* -1::real #16)
+#50 := (+ #15 #49)
+#51 := (<= #50 0::real)
+#129 := (forall (vars (?v0 S3)) (:pat #127 #128) #51)
+#54 := (forall (vars (?v0 S3)) #51)
+#132 := (iff #54 #129)
+#130 := (iff #51 #51)
+#131 := [refl]: #130
+#133 := [quant-intro #131]: #132
+#69 := (~ #54 #54)
+#71 := (~ #51 #51)
+#72 := [refl]: #71
+#70 := [nnf-pos #72]: #69
+#17 := (<= #15 #16)
+#18 := (forall (vars (?v0 S3)) #17)
+#55 := (iff #18 #54)
+#52 := (iff #17 #51)
+#53 := [rewrite]: #52
+#56 := [quant-intro #53]: #55
+#38 := [asserted]: #18
+#57 := [mp #38 #56]: #54
+#67 := [mp~ #57 #70]: #54
+#134 := [mp #67 #133]: #129
+#149 := (not #129)
+#150 := (or #149 #135)
+#136 := (* -1::real #10)
+#137 := (+ #12 #136)
+#138 := (<= #137 0::real)
+#151 := (or #149 #138)
+#153 := (iff #151 #150)
+#155 := (iff #150 #150)
+#156 := [rewrite]: #155
+#147 := (iff #138 #135)
+#139 := (+ #136 #12)
+#142 := (<= #139 0::real)
+#145 := (iff #142 #135)
+#146 := [rewrite]: #145
+#143 := (iff #138 #142)
+#140 := (= #137 #139)
+#141 := [rewrite]: #140
+#144 := [monotonicity #141]: #143
+#148 := [trans #144 #146]: #147
+#154 := [monotonicity #148]: #153
+#157 := [trans #154 #156]: #153
+#152 := [quant-inst]: #151
+#158 := [mp #152 #157]: #150
+[unit-resolution #158 #134 #165]: false
+unsat
+827be21ccd16905d74e993b95541879c4d3dbf92 271 0
+#2 := false
+#8 := 0::real
+decl f4 :: (-> S3 S2 real)
+decl f7 :: S2
+#19 := f7
+decl f5 :: S3
+#11 := f5
+#24 := (f4 f5 f7)
+decl f8 :: S3
+#21 := f8
+#22 := (f4 f8 f7)
+#66 := -1::real
+#87 := (* -1::real #22)
+#88 := (+ #87 #24)
+decl f3 :: real
+#9 := f3
+#148 := (* -1::real #24)
+#149 := (+ #22 #148)
+#150 := (+ f3 #149)
+#151 := (<= #150 0::real)
+#154 := (ite #151 f3 #88)
+#320 := (* -1::real #154)
+#321 := (+ f3 #320)
+#322 := (<= #321 0::real)
+#329 := (not #322)
+#65 := 1/2::real
+#157 := (* 1/2::real #154)
+#289 := (<= #157 0::real)
+#168 := (= #157 0::real)
+#178 := (<= #149 0::real)
+decl f6 :: S3
+#14 := f6
+#20 := (f4 f6 f7)
+#174 := (+ #20 #87)
+#175 := (<= #174 0::real)
+#181 := (and #175 #178)
+#184 := (not #181)
+#171 := (not #168)
+#80 := (* 1/2::real #24)
+#145 := (+ #87 #80)
+#79 := (* 1/2::real #20)
+#146 := (+ #79 #145)
+#143 := (>= #146 0::real)
+#141 := (not #143)
+#193 := (or #141 #171 #184)
+#198 := (not #193)
+#28 := 2::real
+#31 := (- #24 #22)
+#32 := (<= f3 #31)
+#33 := (ite #32 f3 #31)
+#34 := (/ #33 2::real)
+#35 := (+ #22 #34)
+#36 := (= #35 #22)
+#37 := (not #36)
+#27 := (+ #20 #24)
+#29 := (/ #27 2::real)
+#30 := (<= #22 #29)
+#38 := (implies #30 #37)
+#25 := (<= #22 #24)
+#23 := (<= #20 #22)
+#26 := (and #23 #25)
+#39 := (implies #26 #38)
+#40 := (not #39)
+#201 := (iff #40 #198)
+#91 := (<= f3 #88)
+#94 := (ite #91 f3 #88)
+#100 := (* 1/2::real #94)
+#105 := (+ #22 #100)
+#111 := (= #22 #105)
+#116 := (not #111)
+#81 := (+ #79 #80)
+#84 := (<= #22 #81)
+#122 := (not #84)
+#123 := (or #122 #116)
+#131 := (not #26)
+#132 := (or #131 #123)
+#137 := (not #132)
+#199 := (iff #137 #198)
+#196 := (iff #132 #193)
+#187 := (or #141 #171)
+#190 := (or #184 #187)
+#194 := (iff #190 #193)
+#195 := [rewrite]: #194
+#191 := (iff #132 #190)
+#188 := (iff #123 #187)
+#172 := (iff #116 #171)
+#169 := (iff #111 #168)
+#160 := (+ #22 #157)
+#163 := (= #22 #160)
+#166 := (iff #163 #168)
+#167 := [rewrite]: #166
+#164 := (iff #111 #163)
+#161 := (= #105 #160)
+#158 := (= #100 #157)
+#155 := (= #94 #154)
+#152 := (iff #91 #151)
+#153 := [rewrite]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [monotonicity #162]: #164
+#170 := [trans #165 #167]: #169
+#173 := [monotonicity #170]: #172
+#144 := (iff #122 #141)
+#140 := (iff #84 #143)
+#142 := [rewrite]: #140
+#147 := [monotonicity #142]: #144
+#189 := [monotonicity #147 #173]: #188
+#185 := (iff #131 #184)
+#182 := (iff #26 #181)
+#179 := (iff #25 #178)
+#180 := [rewrite]: #179
+#176 := (iff #23 #175)
+#177 := [rewrite]: #176
+#183 := [monotonicity #177 #180]: #182
+#186 := [monotonicity #183]: #185
+#192 := [monotonicity #186 #189]: #191
+#197 := [trans #192 #195]: #196
+#200 := [monotonicity #197]: #199
+#138 := (iff #40 #137)
+#135 := (iff #39 #132)
+#128 := (implies #26 #123)
+#133 := (iff #128 #132)
+#134 := [rewrite]: #133
+#129 := (iff #39 #128)
+#126 := (iff #38 #123)
+#119 := (implies #84 #116)
+#124 := (iff #119 #123)
+#125 := [rewrite]: #124
+#120 := (iff #38 #119)
+#117 := (iff #37 #116)
+#114 := (iff #36 #111)
+#108 := (= #105 #22)
+#112 := (iff #108 #111)
+#113 := [rewrite]: #112
+#109 := (iff #36 #108)
+#106 := (= #35 #105)
+#103 := (= #34 #100)
+#97 := (/ #94 2::real)
+#101 := (= #97 #100)
+#102 := [rewrite]: #101
+#98 := (= #34 #97)
+#95 := (= #33 #94)
+#89 := (= #31 #88)
+#90 := [rewrite]: #89
+#92 := (iff #32 #91)
+#93 := [monotonicity #90]: #92
+#96 := [monotonicity #93 #90]: #95
+#99 := [monotonicity #96]: #98
+#104 := [trans #99 #102]: #103
+#107 := [monotonicity #104]: #106
+#110 := [monotonicity #107]: #109
+#115 := [trans #110 #113]: #114
+#118 := [monotonicity #115]: #117
+#85 := (iff #30 #84)
+#82 := (= #29 #81)
+#83 := [rewrite]: #82
+#86 := [monotonicity #83]: #85
+#121 := [monotonicity #86 #118]: #120
+#127 := [trans #121 #125]: #126
+#130 := [monotonicity #127]: #129
+#136 := [trans #130 #134]: #135
+#139 := [monotonicity #136]: #138
+#202 := [trans #139 #200]: #201
+#59 := [asserted]: #40
+#203 := [mp #59 #202]: #198
+#205 := [not-or-elim #203]: #168
+#324 := (or #171 #289)
+#325 := [th-lemma]: #324
+#326 := [unit-resolution #325 #205]: #289
+#327 := [hypothesis]: #322
+#60 := (<= f3 0::real)
+#61 := (not #60)
+#10 := (< 0::real f3)
+#62 := (iff #10 #61)
+#63 := [rewrite]: #62
+#57 := [asserted]: #10
+#64 := [mp #57 #63]: #61
+#328 := [th-lemma #64 #327 #326]: false
+#330 := [lemma #328]: #329
+#282 := (= f3 #154)
+#283 := (= #88 #154)
+#339 := (not #283)
+#323 := (+ #88 #320)
+#331 := (<= #323 0::real)
+#336 := (not #331)
+#301 := (+ #20 #148)
+#302 := (>= #301 0::real)
+#307 := (not #302)
+#12 := (:var 0 S2)
+#15 := (f4 f6 #12)
+#275 := (pattern #15)
+#13 := (f4 f5 #12)
+#274 := (pattern #13)
+#67 := (* -1::real #15)
+#68 := (+ #13 #67)
+#69 := (<= #68 0::real)
+#218 := (not #69)
+#276 := (forall (vars (?v0 S2)) (:pat #274 #275) #218)
+#223 := (forall (vars (?v0 S2)) #218)
+#279 := (iff #223 #276)
+#277 := (iff #218 #218)
+#278 := [refl]: #277
+#280 := [quant-intro #278]: #279
+#72 := (exists (vars (?v0 S2)) #69)
+#75 := (not #72)
+#220 := (~ #75 #223)
+#219 := (~ #218 #218)
+#222 := [refl]: #219
+#221 := [nnf-neg #222]: #220
+#16 := (<= #13 #15)
+#17 := (exists (vars (?v0 S2)) #16)
+#18 := (not #17)
+#76 := (iff #18 #75)
+#73 := (iff #17 #72)
+#70 := (iff #16 #69)
+#71 := [rewrite]: #70
+#74 := [quant-intro #71]: #73
+#77 := [monotonicity #74]: #76
+#58 := [asserted]: #18
+#78 := [mp #58 #77]: #75
+#216 := [mp~ #78 #221]: #223
+#281 := [mp #216 #280]: #276
+#310 := (not #276)
+#311 := (or #310 #307)
+#291 := (* -1::real #20)
+#292 := (+ #24 #291)
+#293 := (<= #292 0::real)
+#294 := (not #293)
+#312 := (or #310 #294)
+#314 := (iff #312 #311)
+#316 := (iff #311 #311)
+#317 := [rewrite]: #316
+#308 := (iff #294 #307)
+#305 := (iff #293 #302)
+#295 := (+ #291 #24)
+#298 := (<= #295 0::real)
+#303 := (iff #298 #302)
+#304 := [rewrite]: #303
+#299 := (iff #293 #298)
+#296 := (= #292 #295)
+#297 := [rewrite]: #296
+#300 := [monotonicity #297]: #299
+#306 := [trans #300 #304]: #305
+#309 := [monotonicity #306]: #308
+#315 := [monotonicity #309]: #314
+#318 := [trans #315 #317]: #314
+#313 := [quant-inst]: #312
+#319 := [mp #313 #318]: #311
+#333 := [unit-resolution #319 #281]: #307
+#204 := [not-or-elim #203]: #143
+#334 := [hypothesis]: #331
+#335 := [th-lemma #334 #204 #333 #326]: false
+#337 := [lemma #335]: #336
+#338 := [hypothesis]: #283
+#340 := (or #339 #331)
+#341 := [th-lemma]: #340
+#342 := [unit-resolution #341 #338 #337]: false
+#343 := [lemma #342]: #339
+#287 := (or #151 #283)
+#288 := [def-axiom]: #287
+#344 := [unit-resolution #288 #343]: #151
+#284 := (not #151)
+#285 := (or #284 #282)
+#286 := [def-axiom]: #285
+#345 := [unit-resolution #286 #344]: #282
+#346 := (not #282)
+#347 := (or #346 #322)
+#348 := [th-lemma]: #347
+[unit-resolution #348 #345 #330]: false
+unsat
+17761be5b8c4a7d5d589dee9a6fb2f3f1c9050ee 288 0
+#2 := false
+#8 := 0::real
+decl f4 :: (-> S3 S2 real)
+decl f7 :: S2
+#19 := f7
+decl f8 :: S3
+#21 := f8
+#22 := (f4 f8 f7)
+decl f6 :: S3
+#14 := f6
+#20 := (f4 f6 f7)
+#73 := -1::real
+#118 := (* -1::real #20)
+#119 := (+ #118 #22)
+decl f3 :: real
+#9 := f3
+#97 := (* -1::real #22)
+#211 := (+ #20 #97)
+#212 := (+ f3 #211)
+#213 := (<= #212 0::real)
+#216 := (ite #213 f3 #119)
+#397 := (* -1::real #216)
+#398 := (+ f3 #397)
+#399 := (<= #398 0::real)
+#407 := (not #399)
+#72 := 1/2::real
+#287 := (* 1/2::real #216)
+#367 := (<= #287 0::real)
+#288 := (= #287 0::real)
+#139 := -1/2::real
+#219 := (* -1/2::real #216)
+#222 := (+ #22 #219)
+decl f5 :: S3
+#11 := f5
+#24 := (f4 f5 f7)
+#98 := (+ #97 #24)
+#196 := (* -1::real #24)
+#197 := (+ #22 #196)
+#198 := (+ f3 #197)
+#199 := (<= #198 0::real)
+#202 := (ite #199 f3 #98)
+#205 := (* 1/2::real #202)
+#208 := (+ #22 #205)
+#87 := (* 1/2::real #24)
+#185 := (+ #97 #87)
+#86 := (* 1/2::real #20)
+#186 := (+ #86 #185)
+#183 := (>= #186 0::real)
+#225 := (ite #183 #208 #222)
+#228 := (= #22 #225)
+#291 := (iff #228 #288)
+#284 := (= #22 #222)
+#289 := (iff #284 #288)
+#290 := [rewrite]: #289
+#285 := (iff #228 #284)
+#282 := (= #225 #222)
+#277 := (ite false #208 #222)
+#280 := (= #277 #222)
+#281 := [rewrite]: #280
+#278 := (= #225 #277)
+#275 := (iff #183 false)
+#182 := (not #183)
+#237 := (<= #197 0::real)
+#234 := (<= #211 0::real)
+#240 := (and #234 #237)
+#243 := (not #240)
+#231 := (not #228)
+#252 := (or #183 #231 #243)
+#257 := (not #252)
+#28 := 2::real
+#37 := (- #22 #20)
+#38 := (<= f3 #37)
+#39 := (ite #38 f3 #37)
+#40 := (/ #39 2::real)
+#41 := (- #22 #40)
+#32 := (- #24 #22)
+#33 := (<= f3 #32)
+#34 := (ite #33 f3 #32)
+#35 := (/ #34 2::real)
+#36 := (+ #22 #35)
+#27 := (+ #20 #24)
+#29 := (/ #27 2::real)
+#31 := (<= #22 #29)
+#42 := (ite #31 #36 #41)
+#43 := (= #42 #22)
+#44 := (not #43)
+#30 := (< #29 #22)
+#45 := (implies #30 #44)
+#25 := (<= #22 #24)
+#23 := (<= #20 #22)
+#26 := (and #23 #25)
+#46 := (implies #26 #45)
+#47 := (not #46)
+#260 := (iff #47 #257)
+#122 := (<= f3 #119)
+#125 := (ite #122 f3 #119)
+#140 := (* -1/2::real #125)
+#141 := (+ #22 #140)
+#101 := (<= f3 #98)
+#104 := (ite #101 f3 #98)
+#110 := (* 1/2::real #104)
+#115 := (+ #22 #110)
+#88 := (+ #86 #87)
+#94 := (<= #22 #88)
+#146 := (ite #94 #115 #141)
+#152 := (= #22 #146)
+#157 := (not #152)
+#91 := (< #88 #22)
+#163 := (not #91)
+#164 := (or #163 #157)
+#172 := (not #26)
+#173 := (or #172 #164)
+#178 := (not #173)
+#258 := (iff #178 #257)
+#255 := (iff #173 #252)
+#246 := (or #183 #231)
+#249 := (or #243 #246)
+#253 := (iff #249 #252)
+#254 := [rewrite]: #253
+#250 := (iff #173 #249)
+#247 := (iff #164 #246)
+#232 := (iff #157 #231)
+#229 := (iff #152 #228)
+#226 := (= #146 #225)
+#223 := (= #141 #222)
+#220 := (= #140 #219)
+#217 := (= #125 #216)
+#214 := (iff #122 #213)
+#215 := [rewrite]: #214
+#218 := [monotonicity #215]: #217
+#221 := [monotonicity #218]: #220
+#224 := [monotonicity #221]: #223
+#209 := (= #115 #208)
+#206 := (= #110 #205)
+#203 := (= #104 #202)
+#200 := (iff #101 #199)
+#201 := [rewrite]: #200
+#204 := [monotonicity #201]: #203
+#207 := [monotonicity #204]: #206
+#210 := [monotonicity #207]: #209
+#195 := (iff #94 #183)
+#194 := [rewrite]: #195
+#227 := [monotonicity #194 #210 #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#192 := (iff #163 #183)
+#187 := (not #182)
+#190 := (iff #187 #183)
+#191 := [rewrite]: #190
+#188 := (iff #163 #187)
+#181 := (iff #91 #182)
+#184 := [rewrite]: #181
+#189 := [monotonicity #184]: #188
+#193 := [trans #189 #191]: #192
+#248 := [monotonicity #193 #233]: #247
+#244 := (iff #172 #243)
+#241 := (iff #26 #240)
+#238 := (iff #25 #237)
+#239 := [rewrite]: #238
+#235 := (iff #23 #234)
+#236 := [rewrite]: #235
+#242 := [monotonicity #236 #239]: #241
+#245 := [monotonicity #242]: #244
+#251 := [monotonicity #245 #248]: #250
+#256 := [trans #251 #254]: #255
+#259 := [monotonicity #256]: #258
+#179 := (iff #47 #178)
+#176 := (iff #46 #173)
+#169 := (implies #26 #164)
+#174 := (iff #169 #173)
+#175 := [rewrite]: #174
+#170 := (iff #46 #169)
+#167 := (iff #45 #164)
+#160 := (implies #91 #157)
+#165 := (iff #160 #164)
+#166 := [rewrite]: #165
+#161 := (iff #45 #160)
+#158 := (iff #44 #157)
+#155 := (iff #43 #152)
+#149 := (= #146 #22)
+#153 := (iff #149 #152)
+#154 := [rewrite]: #153
+#150 := (iff #43 #149)
+#147 := (= #42 #146)
+#144 := (= #41 #141)
+#131 := (* 1/2::real #125)
+#136 := (- #22 #131)
+#142 := (= #136 #141)
+#143 := [rewrite]: #142
+#137 := (= #41 #136)
+#134 := (= #40 #131)
+#128 := (/ #125 2::real)
+#132 := (= #128 #131)
+#133 := [rewrite]: #132
+#129 := (= #40 #128)
+#126 := (= #39 #125)
+#120 := (= #37 #119)
+#121 := [rewrite]: #120
+#123 := (iff #38 #122)
+#124 := [monotonicity #121]: #123
+#127 := [monotonicity #124 #121]: #126
+#130 := [monotonicity #127]: #129
+#135 := [trans #130 #133]: #134
+#138 := [monotonicity #135]: #137
+#145 := [trans #138 #143]: #144
+#116 := (= #36 #115)
+#113 := (= #35 #110)
+#107 := (/ #104 2::real)
+#111 := (= #107 #110)
+#112 := [rewrite]: #111
+#108 := (= #35 #107)
+#105 := (= #34 #104)
+#99 := (= #32 #98)
+#100 := [rewrite]: #99
+#102 := (iff #33 #101)
+#103 := [monotonicity #100]: #102
+#106 := [monotonicity #103 #100]: #105
+#109 := [monotonicity #106]: #108
+#114 := [trans #109 #112]: #113
+#117 := [monotonicity #114]: #116
+#95 := (iff #31 #94)
+#89 := (= #29 #88)
+#90 := [rewrite]: #89
+#96 := [monotonicity #90]: #95
+#148 := [monotonicity #96 #117 #145]: #147
+#151 := [monotonicity #148]: #150
+#156 := [trans #151 #154]: #155
+#159 := [monotonicity #156]: #158
+#92 := (iff #30 #91)
+#93 := [monotonicity #90]: #92
+#162 := [monotonicity #93 #159]: #161
+#168 := [trans #162 #166]: #167
+#171 := [monotonicity #168]: #170
+#177 := [trans #171 #175]: #176
+#180 := [monotonicity #177]: #179
+#261 := [trans #180 #259]: #260
+#66 := [asserted]: #47
+#262 := [mp #66 #261]: #257
+#263 := [not-or-elim #262]: #182
+#276 := [iff-false #263]: #275
+#279 := [monotonicity #276]: #278
+#283 := [trans #279 #281]: #282
+#286 := [monotonicity #283]: #285
+#292 := [trans #286 #290]: #291
+#264 := [not-or-elim #262]: #228
+#293 := [mp #264 #292]: #288
+#401 := (not #288)
+#402 := (or #401 #367)
+#403 := [th-lemma]: #402
+#404 := [unit-resolution #403 #293]: #367
+#405 := [hypothesis]: #399
+#67 := (<= f3 0::real)
+#68 := (not #67)
+#10 := (< 0::real f3)
+#69 := (iff #10 #68)
+#70 := [rewrite]: #69
+#64 := [asserted]: #10
+#71 := [mp #64 #70]: #68
+#406 := [th-lemma #71 #405 #404]: false
+#408 := [lemma #406]: #407
+#360 := (= f3 #216)
+#361 := (= #119 #216)
+#416 := (not #361)
+#400 := (+ #119 #397)
+#409 := (<= #400 0::real)
+#413 := (not #409)
+#265 := [not-or-elim #262]: #240
+#267 := [and-elim #265]: #237
+#411 := [hypothesis]: #409
+#412 := [th-lemma #411 #267 #263 #404]: false
+#414 := [lemma #412]: #413
+#415 := [hypothesis]: #361
+#417 := (or #416 #409)
+#418 := [th-lemma]: #417
+#419 := [unit-resolution #418 #415 #414]: false
+#420 := [lemma #419]: #416
+#365 := (or #213 #361)
+#366 := [def-axiom]: #365
+#421 := [unit-resolution #366 #420]: #213
+#362 := (not #213)
+#363 := (or #362 #360)
+#364 := [def-axiom]: #363
+#422 := [unit-resolution #364 #421]: #360
+#423 := (not #360)
+#424 := (or #423 #399)
+#425 := [th-lemma]: #424
+[unit-resolution #425 #422 #408]: false
+unsat
+c62e7dbb8c21f248aba4bbd031c4a7dd170e0476 149 0
+#2 := false
+#23 := 0::real
+decl f3 :: (-> S2 S3 real)
+decl f5 :: S3
+#9 := f5
+decl f6 :: S2
+#11 := f6
+#12 := (f3 f6 f5)
+#49 := -1::real
+#161 := (* -1::real #12)
+decl f4 :: S2
+#8 := f4
+#10 := (f3 f4 f5)
+#208 := (+ #10 #161)
+#210 := (>= #208 0::real)
+#13 := (= #10 #12)
+#45 := [asserted]: #13
+#213 := (not #13)
+#214 := (or #213 #210)
+#215 := [th-lemma]: #214
+#216 := [unit-resolution #215 #45]: #210
+decl f7 :: S2
+#16 := f7
+#26 := (f3 f7 f5)
+#165 := (* -1::real #26)
+#166 := (+ #10 #165)
+#212 := (>= #166 0::real)
+#227 := (not #212)
+#211 := (= #10 #26)
+#221 := (not #211)
+#67 := (= #12 #26)
+#75 := (not #67)
+#222 := (iff #75 #221)
+#219 := (iff #67 #211)
+#217 := (iff #211 #67)
+#218 := [monotonicity #45]: #217
+#220 := [symm #218]: #219
+#223 := [monotonicity #220]: #222
+#27 := (= #26 #12)
+#28 := (not #27)
+#76 := (iff #28 #75)
+#73 := (iff #27 #67)
+#74 := [rewrite]: #73
+#77 := [monotonicity #74]: #76
+#48 := [asserted]: #28
+#80 := [mp #48 #77]: #75
+#224 := [mp #80 #223]: #221
+#230 := (or #211 #227)
+#167 := (<= #166 0::real)
+#177 := (+ #12 #165)
+#178 := (>= #177 0::real)
+#183 := (not #178)
+#168 := (not #167)
+#186 := (or #168 #183)
+#189 := (not #186)
+#14 := (:var 0 S3)
+#19 := (f3 f6 #14)
+#154 := (pattern #19)
+#17 := (f3 f7 #14)
+#153 := (pattern #17)
+#15 := (f3 f4 #14)
+#152 := (pattern #15)
+#55 := (* -1::real #19)
+#56 := (+ #17 #55)
+#57 := (<= #56 0::real)
+#82 := (not #57)
+#50 := (* -1::real #17)
+#51 := (+ #15 #50)
+#52 := (<= #51 0::real)
+#85 := (not #52)
+#83 := (or #85 #82)
+#81 := (not #83)
+#155 := (forall (vars (?v0 S3)) (:pat #152 #153 #154) #81)
+#91 := (forall (vars (?v0 S3)) #81)
+#158 := (iff #91 #155)
+#156 := (iff #81 #81)
+#157 := [refl]: #156
+#159 := [quant-intro #157]: #158
+#60 := (and #52 #57)
+#63 := (forall (vars (?v0 S3)) #60)
+#92 := (iff #63 #91)
+#78 := (iff #60 #81)
+#90 := [rewrite]: #78
+#93 := [quant-intro #90]: #92
+#86 := (~ #63 #63)
+#88 := (~ #60 #60)
+#89 := [refl]: #88
+#87 := [nnf-pos #89]: #86
+#20 := (<= #17 #19)
+#18 := (<= #15 #17)
+#21 := (and #18 #20)
+#22 := (forall (vars (?v0 S3)) #21)
+#64 := (iff #22 #63)
+#61 := (iff #21 #60)
+#58 := (iff #20 #57)
+#59 := [rewrite]: #58
+#53 := (iff #18 #52)
+#54 := [rewrite]: #53
+#62 := [monotonicity #54 #59]: #61
+#65 := [quant-intro #62]: #64
+#46 := [asserted]: #22
+#66 := [mp #46 #65]: #63
+#84 := [mp~ #66 #87]: #63
+#94 := [mp #84 #93]: #91
+#160 := [mp #94 #159]: #155
+#192 := (not #155)
+#193 := (or #192 #189)
+#162 := (+ #26 #161)
+#163 := (<= #162 0::real)
+#164 := (not #163)
+#169 := (or #168 #164)
+#170 := (not #169)
+#194 := (or #192 #170)
+#196 := (iff #194 #193)
+#198 := (iff #193 #193)
+#199 := [rewrite]: #198
+#190 := (iff #170 #189)
+#187 := (iff #169 #186)
+#184 := (iff #164 #183)
+#181 := (iff #163 #178)
+#171 := (+ #161 #26)
+#174 := (<= #171 0::real)
+#179 := (iff #174 #178)
+#180 := [rewrite]: #179
+#175 := (iff #163 #174)
+#172 := (= #162 #171)
+#173 := [rewrite]: #172
+#176 := [monotonicity #173]: #175
+#182 := [trans #176 #180]: #181
+#185 := [monotonicity #182]: #184
+#188 := [monotonicity #185]: #187
+#191 := [monotonicity #188]: #190
+#197 := [monotonicity #191]: #196
+#200 := [trans #197 #199]: #196
+#195 := [quant-inst]: #194
+#201 := [mp #195 #200]: #193
+#225 := [unit-resolution #201 #160]: #189
+#202 := (or #186 #167)
+#203 := [def-axiom]: #202
+#226 := [unit-resolution #203 #225]: #167
+#228 := (or #211 #168 #227)
+#229 := [th-lemma]: #228
+#231 := [unit-resolution #229 #226]: #230
+#232 := [unit-resolution #231 #224]: #227
+#204 := (or #186 #178)
+#205 := [def-axiom]: #204
+#233 := [unit-resolution #205 #225]: #178
+[th-lemma #233 #232 #216]: false
+unsat
+f2ad7d91f9a20a669bc2985b9542b252779b00c7 870 0
+#2 := false
+#11 := 0::real
+decl f5 :: real
+#26 := f5
+decl f3 :: real
+#9 := f3
+#76 := -1::real
+#77 := (* -1::real f3)
+#176 := (+ #77 f5)
+#124 := (* -1::real f5)
+#167 := (+ f3 #124)
+#260 := (>= #167 0::real)
+#267 := (ite #260 #167 #176)
+#275 := (* -1::real #267)
+decl f4 :: real
+#15 := f4
+#96 := 1/3::real
+#97 := (* 1/3::real f4)
+#276 := (+ #97 #275)
+#277 := (<= #276 0::real)
+#278 := (not #277)
+decl ?v0!5 :: real
+#448 := ?v0!5
+#459 := (* -1::real ?v0!5)
+#573 := (+ f3 #459)
+#567 := (+ #77 ?v0!5)
+#574 := (<= #573 0::real)
+#581 := (ite #574 #567 #573)
+#584 := (* -1::real #581)
+#587 := (+ #97 #584)
+#590 := (<= #587 0::real)
+#593 := (not #590)
+decl ?v2!3 :: real
+#442 := ?v2!3
+#477 := (* -1::real ?v2!3)
+#544 := (+ f5 #477)
+#538 := (+ #124 ?v2!3)
+#545 := (<= #544 0::real)
+#552 := (ite #545 #538 #544)
+#555 := (* -1::real #552)
+#558 := (+ #97 #555)
+#561 := (<= #558 0::real)
+#564 := (not #561)
+decl ?v4!1 :: real
+#446 := ?v4!1
+#532 := (+ ?v4!1 #459)
+#533 := (>= #532 0::real)
+decl ?v1!4 :: real
+#447 := ?v1!4
+#468 := (* -1::real ?v1!4)
+decl ?v5!0 :: real
+#445 := ?v5!0
+#520 := (+ ?v5!0 #468)
+#521 := (>= #520 0::real)
+#451 := (* -1::real ?v5!0)
+decl ?v3!2 :: real
+#444 := ?v3!2
+#499 := (+ ?v3!2 #451)
+#500 := (>= #499 0::real)
+#449 := (* -1::real ?v4!1)
+#497 := (+ ?v2!3 #449)
+#498 := (>= #497 0::real)
+#486 := (* -1::real ?v3!2)
+#487 := (+ f5 #486)
+#488 := (+ #124 ?v3!2)
+#489 := (<= #487 0::real)
+#490 := (ite #489 #488 #487)
+#491 := (* -1::real #490)
+#492 := (+ #97 #491)
+#493 := (<= #492 0::real)
+#494 := (not #493)
+#469 := (+ f3 #468)
+#470 := (+ #77 ?v1!4)
+#471 := (<= #469 0::real)
+#472 := (ite #471 #470 #469)
+#473 := (* -1::real #472)
+#474 := (+ #97 #473)
+#475 := (<= #474 0::real)
+#476 := (not #475)
+#599 := (and #278 #476 #494 #498 #500 #521 #533 #564 #593)
+#613 := (+ ?v5!0 #449)
+#607 := (+ #451 ?v4!1)
+#614 := (<= #613 0::real)
+#621 := (ite #614 #607 #613)
+#624 := (* -1::real #621)
+#627 := (+ f4 #624)
+#630 := (<= #627 0::real)
+#633 := (not #630)
+#604 := (not #599)
+#636 := (or #604 #633)
+#639 := (not #636)
+#450 := (+ #449 ?v5!0)
+#452 := (+ ?v4!1 #451)
+#453 := (>= #452 0::real)
+#454 := (ite #453 #452 #450)
+#455 := (* -1::real #454)
+#456 := (+ f4 #455)
+#457 := (<= #456 0::real)
+#458 := (not #457)
+#460 := (+ #459 f3)
+#461 := (+ ?v0!5 #77)
+#462 := (>= #461 0::real)
+#463 := (ite #462 #461 #460)
+#464 := (* -1::real #463)
+#465 := (+ #97 #464)
+#466 := (<= #465 0::real)
+#467 := (not #466)
+#478 := (+ #477 f5)
+#479 := (+ ?v2!3 #124)
+#480 := (>= #479 0::real)
+#481 := (ite #480 #479 #478)
+#482 := (* -1::real #481)
+#483 := (+ #97 #482)
+#484 := (<= #483 0::real)
+#485 := (not #484)
+#495 := (+ ?v0!5 #449)
+#496 := (<= #495 0::real)
+#501 := (+ ?v1!4 #451)
+#502 := (<= #501 0::real)
+#503 := (and #502 #500 #498 #496 #278 #494 #485 #476 #467)
+#504 := (not #503)
+#505 := (or #504 #458)
+#506 := (not #505)
+#640 := (iff #506 #639)
+#637 := (iff #505 #636)
+#634 := (iff #458 #633)
+#631 := (iff #457 #630)
+#628 := (= #456 #627)
+#625 := (= #455 #624)
+#622 := (= #454 #621)
+#619 := (= #450 #613)
+#620 := [rewrite]: #619
+#608 := (= #452 #607)
+#609 := [rewrite]: #608
+#617 := (iff #453 #614)
+#610 := (>= #607 0::real)
+#615 := (iff #610 #614)
+#616 := [rewrite]: #615
+#611 := (iff #453 #610)
+#612 := [monotonicity #609]: #611
+#618 := [trans #612 #616]: #617
+#623 := [monotonicity #618 #609 #620]: #622
+#626 := [monotonicity #623]: #625
+#629 := [monotonicity #626]: #628
+#632 := [monotonicity #629]: #631
+#635 := [monotonicity #632]: #634
+#605 := (iff #504 #604)
+#602 := (iff #503 #599)
+#596 := (and #521 #500 #498 #533 #278 #494 #564 #476 #593)
+#600 := (iff #596 #599)
+#601 := [rewrite]: #600
+#597 := (iff #503 #596)
+#594 := (iff #467 #593)
+#591 := (iff #466 #590)
+#588 := (= #465 #587)
+#585 := (= #464 #584)
+#582 := (= #463 #581)
+#579 := (= #460 #573)
+#580 := [rewrite]: #579
+#568 := (= #461 #567)
+#569 := [rewrite]: #568
+#577 := (iff #462 #574)
+#570 := (>= #567 0::real)
+#575 := (iff #570 #574)
+#576 := [rewrite]: #575
+#571 := (iff #462 #570)
+#572 := [monotonicity #569]: #571
+#578 := [trans #572 #576]: #577
+#583 := [monotonicity #578 #569 #580]: #582
+#586 := [monotonicity #583]: #585
+#589 := [monotonicity #586]: #588
+#592 := [monotonicity #589]: #591
+#595 := [monotonicity #592]: #594
+#565 := (iff #485 #564)
+#562 := (iff #484 #561)
+#559 := (= #483 #558)
+#556 := (= #482 #555)
+#553 := (= #481 #552)
+#550 := (= #478 #544)
+#551 := [rewrite]: #550
+#539 := (= #479 #538)
+#540 := [rewrite]: #539
+#548 := (iff #480 #545)
+#541 := (>= #538 0::real)
+#546 := (iff #541 #545)
+#547 := [rewrite]: #546
+#542 := (iff #480 #541)
+#543 := [monotonicity #540]: #542
+#549 := [trans #543 #547]: #548
+#554 := [monotonicity #549 #540 #551]: #553
+#557 := [monotonicity #554]: #556
+#560 := [monotonicity #557]: #559
+#563 := [monotonicity #560]: #562
+#566 := [monotonicity #563]: #565
+#536 := (iff #496 #533)
+#526 := (+ #449 ?v0!5)
+#529 := (<= #526 0::real)
+#534 := (iff #529 #533)
+#535 := [rewrite]: #534
+#530 := (iff #496 #529)
+#527 := (= #495 #526)
+#528 := [rewrite]: #527
+#531 := [monotonicity #528]: #530
+#537 := [trans #531 #535]: #536
+#524 := (iff #502 #521)
+#514 := (+ #451 ?v1!4)
+#517 := (<= #514 0::real)
+#522 := (iff #517 #521)
+#523 := [rewrite]: #522
+#518 := (iff #502 #517)
+#515 := (= #501 #514)
+#516 := [rewrite]: #515
+#519 := [monotonicity #516]: #518
+#525 := [trans #519 #523]: #524
+#598 := [monotonicity #525 #537 #566 #595]: #597
+#603 := [trans #598 #601]: #602
+#606 := [monotonicity #603]: #605
+#638 := [monotonicity #606 #635]: #637
+#641 := [monotonicity #638]: #640
+#46 := (:var 0 real)
+#43 := (:var 1 real)
+#217 := (* -1::real #43)
+#218 := (+ #217 #46)
+#207 := (* -1::real #46)
+#208 := (+ #43 #207)
+#407 := (>= #208 0::real)
+#414 := (ite #407 #208 #218)
+#422 := (* -1::real #414)
+#423 := (+ f4 #422)
+#424 := (<= #423 0::real)
+#425 := (not #424)
+#8 := (:var 5 real)
+#87 := (* -1::real #8)
+#88 := (+ #87 f3)
+#78 := (+ #8 #77)
+#352 := (>= #78 0::real)
+#359 := (ite #352 #78 #88)
+#367 := (* -1::real #359)
+#368 := (+ #97 #367)
+#369 := (<= #368 0::real)
+#370 := (not #369)
+#19 := (:var 4 real)
+#112 := (* -1::real #19)
+#113 := (+ f3 #112)
+#103 := (+ #77 #19)
+#329 := (<= #113 0::real)
+#336 := (ite #329 #103 #113)
+#344 := (* -1::real #336)
+#345 := (+ #97 #344)
+#346 := (<= #345 0::real)
+#347 := (not #346)
+#25 := (:var 3 real)
+#134 := (* -1::real #25)
+#135 := (+ #134 f5)
+#125 := (+ #25 #124)
+#306 := (>= #125 0::real)
+#313 := (ite #306 #125 #135)
+#321 := (* -1::real #313)
+#322 := (+ #97 #321)
+#323 := (<= #322 0::real)
+#324 := (not #323)
+#32 := (:var 2 real)
+#155 := (* -1::real #32)
+#156 := (+ f5 #155)
+#146 := (+ #124 #32)
+#283 := (<= #156 0::real)
+#290 := (ite #283 #146 #156)
+#298 := (* -1::real #290)
+#299 := (+ #97 #298)
+#300 := (<= #299 0::real)
+#301 := (not #300)
+#256 := (+ #8 #217)
+#257 := (<= #256 0::real)
+#253 := (+ #25 #217)
+#252 := (>= #253 0::real)
+#249 := (+ #32 #207)
+#248 := (>= #249 0::real)
+#244 := (+ #19 #207)
+#245 := (<= #244 0::real)
+#399 := (and #245 #248 #252 #257 #278 #301 #324 #347 #370)
+#404 := (not #399)
+#430 := (or #404 #425)
+#433 := (forall (vars (?v0 real) (?v1 real) (?v2 real) (?v3 real) (?v4 real) (?v5 real)) #430)
+#436 := (not #433)
+#507 := (~ #436 #506)
+#508 := [sk]: #507
+#57 := (- #43 #46)
+#59 := (- #57)
+#58 := (< #57 0::real)
+#60 := (ite #58 #59 #57)
+#61 := (< #60 f4)
+#48 := (<= #46 #32)
+#47 := (<= #19 #46)
+#49 := (and #47 #48)
+#45 := (<= #43 #25)
+#50 := (and #45 #49)
+#44 := (<= #8 #43)
+#51 := (and #44 #50)
+#16 := 3::real
+#17 := (/ f4 3::real)
+#38 := (- f3 f5)
+#40 := (- #38)
+#39 := (< #38 0::real)
+#41 := (ite #39 #40 #38)
+#42 := (< #41 #17)
+#52 := (and #42 #51)
+#33 := (- #32 f5)
+#35 := (- #33)
+#34 := (< #33 0::real)
+#36 := (ite #34 #35 #33)
+#37 := (< #36 #17)
+#53 := (and #37 #52)
+#27 := (- #25 f5)
+#29 := (- #27)
+#28 := (< #27 0::real)
+#30 := (ite #28 #29 #27)
+#31 := (< #30 #17)
+#54 := (and #31 #53)
+#20 := (- #19 f3)
+#22 := (- #20)
+#21 := (< #20 0::real)
+#23 := (ite #21 #22 #20)
+#24 := (< #23 #17)
+#55 := (and #24 #54)
+#10 := (- #8 f3)
+#13 := (- #10)
+#12 := (< #10 0::real)
+#14 := (ite #12 #13 #10)
+#18 := (< #14 #17)
+#56 := (and #18 #55)
+#62 := (implies #56 #61)
+#63 := (forall (vars (?v0 real) (?v1 real) (?v2 real) (?v3 real) (?v4 real) (?v5 real)) #62)
+#64 := (not #63)
+#439 := (iff #64 #436)
+#211 := (< #208 0::real)
+#223 := (ite #211 #218 #208)
+#226 := (< #223 f4)
+#170 := (< #167 0::real)
+#181 := (ite #170 #176 #167)
+#184 := (< #181 #97)
+#190 := (and #51 #184)
+#149 := (< #146 0::real)
+#161 := (ite #149 #156 #146)
+#164 := (< #161 #97)
+#195 := (and #164 #190)
+#128 := (< #125 0::real)
+#140 := (ite #128 #135 #125)
+#143 := (< #140 #97)
+#198 := (and #143 #195)
+#106 := (< #103 0::real)
+#118 := (ite #106 #113 #103)
+#121 := (< #118 #97)
+#201 := (and #121 #198)
+#81 := (< #78 0::real)
+#93 := (ite #81 #88 #78)
+#100 := (< #93 #97)
+#204 := (and #100 #201)
+#232 := (not #204)
+#233 := (or #232 #226)
+#238 := (forall (vars (?v0 real) (?v1 real) (?v2 real) (?v3 real) (?v4 real) (?v5 real)) #233)
+#241 := (not #238)
+#437 := (iff #241 #436)
+#434 := (iff #238 #433)
+#431 := (iff #233 #430)
+#428 := (iff #226 #425)
+#419 := (< #414 f4)
+#426 := (iff #419 #425)
+#427 := [rewrite]: #426
+#420 := (iff #226 #419)
+#417 := (= #223 #414)
+#408 := (not #407)
+#411 := (ite #408 #218 #208)
+#415 := (= #411 #414)
+#416 := [rewrite]: #415
+#412 := (= #223 #411)
+#409 := (iff #211 #408)
+#410 := [rewrite]: #409
+#413 := [monotonicity #410]: #412
+#418 := [trans #413 #416]: #417
+#421 := [monotonicity #418]: #420
+#429 := [trans #421 #427]: #428
+#405 := (iff #232 #404)
+#402 := (iff #204 #399)
+#375 := (and #245 #248)
+#378 := (and #252 #375)
+#381 := (and #257 #378)
+#384 := (and #381 #278)
+#387 := (and #301 #384)
+#390 := (and #324 #387)
+#393 := (and #347 #390)
+#396 := (and #370 #393)
+#400 := (iff #396 #399)
+#401 := [rewrite]: #400
+#397 := (iff #204 #396)
+#394 := (iff #201 #393)
+#391 := (iff #198 #390)
+#388 := (iff #195 #387)
+#385 := (iff #190 #384)
+#281 := (iff #184 #278)
+#272 := (< #267 #97)
+#279 := (iff #272 #278)
+#280 := [rewrite]: #279
+#273 := (iff #184 #272)
+#270 := (= #181 #267)
+#261 := (not #260)
+#264 := (ite #261 #176 #167)
+#268 := (= #264 #267)
+#269 := [rewrite]: #268
+#265 := (= #181 #264)
+#262 := (iff #170 #261)
+#263 := [rewrite]: #262
+#266 := [monotonicity #263]: #265
+#271 := [trans #266 #269]: #270
+#274 := [monotonicity #271]: #273
+#282 := [trans #274 #280]: #281
+#382 := (iff #51 #381)
+#379 := (iff #50 #378)
+#376 := (iff #49 #375)
+#250 := (iff #48 #248)
+#251 := [rewrite]: #250
+#246 := (iff #47 #245)
+#247 := [rewrite]: #246
+#377 := [monotonicity #247 #251]: #376
+#254 := (iff #45 #252)
+#255 := [rewrite]: #254
+#380 := [monotonicity #255 #377]: #379
+#258 := (iff #44 #257)
+#259 := [rewrite]: #258
+#383 := [monotonicity #259 #380]: #382
+#386 := [monotonicity #383 #282]: #385
+#304 := (iff #164 #301)
+#295 := (< #290 #97)
+#302 := (iff #295 #301)
+#303 := [rewrite]: #302
+#296 := (iff #164 #295)
+#293 := (= #161 #290)
+#284 := (not #283)
+#287 := (ite #284 #156 #146)
+#291 := (= #287 #290)
+#292 := [rewrite]: #291
+#288 := (= #161 #287)
+#285 := (iff #149 #284)
+#286 := [rewrite]: #285
+#289 := [monotonicity #286]: #288
+#294 := [trans #289 #292]: #293
+#297 := [monotonicity #294]: #296
+#305 := [trans #297 #303]: #304
+#389 := [monotonicity #305 #386]: #388
+#327 := (iff #143 #324)
+#318 := (< #313 #97)
+#325 := (iff #318 #324)
+#326 := [rewrite]: #325
+#319 := (iff #143 #318)
+#316 := (= #140 #313)
+#307 := (not #306)
+#310 := (ite #307 #135 #125)
+#314 := (= #310 #313)
+#315 := [rewrite]: #314
+#311 := (= #140 #310)
+#308 := (iff #128 #307)
+#309 := [rewrite]: #308
+#312 := [monotonicity #309]: #311
+#317 := [trans #312 #315]: #316
+#320 := [monotonicity #317]: #319
+#328 := [trans #320 #326]: #327
+#392 := [monotonicity #328 #389]: #391
+#350 := (iff #121 #347)
+#341 := (< #336 #97)
+#348 := (iff #341 #347)
+#349 := [rewrite]: #348
+#342 := (iff #121 #341)
+#339 := (= #118 #336)
+#330 := (not #329)
+#333 := (ite #330 #113 #103)
+#337 := (= #333 #336)
+#338 := [rewrite]: #337
+#334 := (= #118 #333)
+#331 := (iff #106 #330)
+#332 := [rewrite]: #331
+#335 := [monotonicity #332]: #334
+#340 := [trans #335 #338]: #339
+#343 := [monotonicity #340]: #342
+#351 := [trans #343 #349]: #350
+#395 := [monotonicity #351 #392]: #394
+#373 := (iff #100 #370)
+#364 := (< #359 #97)
+#371 := (iff #364 #370)
+#372 := [rewrite]: #371
+#365 := (iff #100 #364)
+#362 := (= #93 #359)
+#353 := (not #352)
+#356 := (ite #353 #88 #78)
+#360 := (= #356 #359)
+#361 := [rewrite]: #360
+#357 := (= #93 #356)
+#354 := (iff #81 #353)
+#355 := [rewrite]: #354
+#358 := [monotonicity #355]: #357
+#363 := [trans #358 #361]: #362
+#366 := [monotonicity #363]: #365
+#374 := [trans #366 #372]: #373
+#398 := [monotonicity #374 #395]: #397
+#403 := [trans #398 #401]: #402
+#406 := [monotonicity #403]: #405
+#432 := [monotonicity #406 #429]: #431
+#435 := [quant-intro #432]: #434
+#438 := [monotonicity #435]: #437
+#242 := (iff #64 #241)
+#239 := (iff #63 #238)
+#236 := (iff #62 #233)
+#229 := (implies #204 #226)
+#234 := (iff #229 #233)
+#235 := [rewrite]: #234
+#230 := (iff #62 #229)
+#227 := (iff #61 #226)
+#224 := (= #60 #223)
+#209 := (= #57 #208)
+#210 := [rewrite]: #209
+#221 := (= #59 #218)
+#214 := (- #208)
+#219 := (= #214 #218)
+#220 := [rewrite]: #219
+#215 := (= #59 #214)
+#216 := [monotonicity #210]: #215
+#222 := [trans #216 #220]: #221
+#212 := (iff #58 #211)
+#213 := [monotonicity #210]: #212
+#225 := [monotonicity #213 #222 #210]: #224
+#228 := [monotonicity #225]: #227
+#205 := (iff #56 #204)
+#202 := (iff #55 #201)
+#199 := (iff #54 #198)
+#196 := (iff #53 #195)
+#193 := (iff #52 #190)
+#187 := (and #184 #51)
+#191 := (iff #187 #190)
+#192 := [rewrite]: #191
+#188 := (iff #52 #187)
+#185 := (iff #42 #184)
+#98 := (= #17 #97)
+#99 := [rewrite]: #98
+#182 := (= #41 #181)
+#168 := (= #38 #167)
+#169 := [rewrite]: #168
+#179 := (= #40 #176)
+#173 := (- #167)
+#177 := (= #173 #176)
+#178 := [rewrite]: #177
+#174 := (= #40 #173)
+#175 := [monotonicity #169]: #174
+#180 := [trans #175 #178]: #179
+#171 := (iff #39 #170)
+#172 := [monotonicity #169]: #171
+#183 := [monotonicity #172 #180 #169]: #182
+#186 := [monotonicity #183 #99]: #185
+#189 := [monotonicity #186]: #188
+#194 := [trans #189 #192]: #193
+#165 := (iff #37 #164)
+#162 := (= #36 #161)
+#147 := (= #33 #146)
+#148 := [rewrite]: #147
+#159 := (= #35 #156)
+#152 := (- #146)
+#157 := (= #152 #156)
+#158 := [rewrite]: #157
+#153 := (= #35 #152)
+#154 := [monotonicity #148]: #153
+#160 := [trans #154 #158]: #159
+#150 := (iff #34 #149)
+#151 := [monotonicity #148]: #150
+#163 := [monotonicity #151 #160 #148]: #162
+#166 := [monotonicity #163 #99]: #165
+#197 := [monotonicity #166 #194]: #196
+#144 := (iff #31 #143)
+#141 := (= #30 #140)
+#126 := (= #27 #125)
+#127 := [rewrite]: #126
+#138 := (= #29 #135)
+#131 := (- #125)
+#136 := (= #131 #135)
+#137 := [rewrite]: #136
+#132 := (= #29 #131)
+#133 := [monotonicity #127]: #132
+#139 := [trans #133 #137]: #138
+#129 := (iff #28 #128)
+#130 := [monotonicity #127]: #129
+#142 := [monotonicity #130 #139 #127]: #141
+#145 := [monotonicity #142 #99]: #144
+#200 := [monotonicity #145 #197]: #199
+#122 := (iff #24 #121)
+#119 := (= #23 #118)
+#104 := (= #20 #103)
+#105 := [rewrite]: #104
+#116 := (= #22 #113)
+#109 := (- #103)
+#114 := (= #109 #113)
+#115 := [rewrite]: #114
+#110 := (= #22 #109)
+#111 := [monotonicity #105]: #110
+#117 := [trans #111 #115]: #116
+#107 := (iff #21 #106)
+#108 := [monotonicity #105]: #107
+#120 := [monotonicity #108 #117 #105]: #119
+#123 := [monotonicity #120 #99]: #122
+#203 := [monotonicity #123 #200]: #202
+#101 := (iff #18 #100)
+#94 := (= #14 #93)
+#79 := (= #10 #78)
+#80 := [rewrite]: #79
+#91 := (= #13 #88)
+#84 := (- #78)
+#89 := (= #84 #88)
+#90 := [rewrite]: #89
+#85 := (= #13 #84)
+#86 := [monotonicity #80]: #85
+#92 := [trans #86 #90]: #91
+#82 := (iff #12 #81)
+#83 := [monotonicity #80]: #82
+#95 := [monotonicity #83 #92 #80]: #94
+#102 := [monotonicity #95 #99]: #101
+#206 := [monotonicity #102 #203]: #205
+#231 := [monotonicity #206 #228]: #230
+#237 := [trans #231 #235]: #236
+#240 := [quant-intro #237]: #239
+#243 := [monotonicity #240]: #242
+#440 := [trans #243 #438]: #439
+#75 := [asserted]: #64
+#441 := [mp #75 #440]: #436
+#511 := [mp~ #441 #508]: #506
+#512 := [mp #511 #641]: #639
+#513 := [not-or-elim #512]: #599
+#642 := [and-elim #513]: #278
+#644 := [and-elim #513]: #494
+#891 := (+ #488 #491)
+#892 := (<= #891 0::real)
+#720 := (= #488 #490)
+#743 := (not #614)
+#741 := (= #607 #621)
+#884 := (not #741)
+#748 := (+ #607 #624)
+#750 := (>= #748 0::real)
+#778 := (not #750)
+#754 := (+ #538 #555)
+#755 := (<= #754 0::real)
+#777 := (not #755)
+#753 := (+ #573 #584)
+#756 := (<= #753 0::real)
+#735 := (= #573 #581)
+#736 := (not #574)
+#773 := [hypothesis]: #750
+#837 := (or #736 #778)
+#648 := [and-elim #513]: #533
+#645 := [and-elim #513]: #498
+#729 := (not #545)
+#727 := (= #538 #552)
+#814 := (not #727)
+#767 := [hypothesis]: #574
+#802 := (or #777 #778 #736)
+#763 := (+ #176 #275)
+#764 := (<= #763 0::real)
+#708 := (= #176 #267)
+#757 := (+ #469 #473)
+#758 := (<= #757 0::real)
+#714 := (= #469 #472)
+#715 := (not #471)
+#774 := [hypothesis]: #755
+#788 := (or #715 #777 #778 #736)
+#766 := [hypothesis]: #471
+#779 := (or #261 #736 #777 #778 #715)
+#649 := [and-elim #513]: #564
+#650 := [and-elim #513]: #593
+#751 := (+ #567 #584)
+#752 := (<= #751 0::real)
+#734 := (= #567 #581)
+#737 := (or #736 #734)
+#738 := [def-axiom]: #737
+#768 := [unit-resolution #738 #767]: #734
+#769 := (not #734)
+#770 := (or #769 #752)
+#771 := [th-lemma]: #770
+#772 := [unit-resolution #771 #768]: #752
+#651 := [not-or-elim #512]: #630
+#775 := [hypothesis]: #260
+#647 := [and-elim #513]: #521
+#776 := [th-lemma #767 #647 #775 #774 #645 #773 #651 #772 #650 #649 #766]: false
+#780 := [lemma #776]: #779
+#781 := [unit-resolution #780 #766 #774 #773 #767]: #261
+#711 := (or #260 #708)
+#712 := [def-axiom]: #711
+#782 := [unit-resolution #712 #781]: #708
+#783 := (not #708)
+#784 := (or #783 #764)
+#785 := [th-lemma]: #784
+#786 := [unit-resolution #785 #782]: #764
+#787 := [th-lemma #647 #774 #645 #773 #651 #649 #786 #642 #781 #766]: false
+#789 := [lemma #787]: #788
+#761 := [unit-resolution #789 #774 #773 #767]: #715
+#718 := (or #471 #714)
+#719 := [def-axiom]: #718
+#762 := [unit-resolution #719 #761]: #714
+#765 := (not #714)
+#790 := (or #765 #758)
+#791 := [th-lemma]: #790
+#792 := [unit-resolution #791 #762]: #758
+#643 := [and-elim #513]: #476
+#795 := (not #758)
+#794 := (not #498)
+#793 := (not #521)
+#796 := (or #261 #471 #793 #777 #794 #778 #633 #561 #795 #475)
+#797 := [th-lemma]: #796
+#798 := [unit-resolution #797 #761 #643 #645 #647 #649 #651 #773 #774 #792]: #261
+#799 := [unit-resolution #712 #798]: #708
+#800 := [unit-resolution #785 #799]: #764
+#801 := [th-lemma #647 #774 #645 #773 #651 #649 #792 #643 #642 #800]: false
+#803 := [lemma #801]: #802
+#826 := [unit-resolution #803 #767 #773]: #777
+#815 := (or #814 #755)
+#804 := [hypothesis]: #777
+#805 := [hypothesis]: #727
+#816 := [th-lemma]: #815
+#817 := [unit-resolution #816 #805 #804]: false
+#818 := [lemma #817]: #815
+#833 := [unit-resolution #818 #826]: #814
+#730 := (or #729 #727)
+#731 := [def-axiom]: #730
+#834 := [unit-resolution #731 #833]: #729
+#831 := (or #260 #545 #778)
+#806 := [hypothesis]: #261
+#810 := [hypothesis]: #729
+#812 := (or #545 #795 #778 #260)
+#807 := [unit-resolution #712 #806]: #708
+#808 := [unit-resolution #785 #807]: #764
+#809 := [hypothesis]: #758
+#811 := [th-lemma #810 #645 #809 #643 #647 #773 #651 #808 #642 #806]: false
+#813 := [lemma #811]: #812
+#827 := [unit-resolution #813 #806 #773 #810]: #795
+#821 := [hypothesis]: #795
+#822 := [hypothesis]: #714
+#823 := [unit-resolution #791 #822 #821]: false
+#824 := [lemma #823]: #790
+#828 := [unit-resolution #824 #827]: #765
+#829 := [unit-resolution #719 #828]: #471
+#830 := [th-lemma #808 #642 #829 #810 #645 #647 #773 #651 #806]: false
+#832 := [lemma #830]: #831
+#835 := [unit-resolution #832 #834 #773]: #260
+#836 := [th-lemma #767 #835 #834 #645 #648]: false
+#838 := [lemma #836]: #837
+#863 := [unit-resolution #838 #773]: #736
+#739 := (or #574 #735)
+#740 := [def-axiom]: #739
+#864 := [unit-resolution #740 #863]: #735
+#865 := (not #735)
+#866 := (or #865 #756)
+#867 := [th-lemma]: #866
+#868 := [unit-resolution #867 #864]: #756
+#852 := (or #260 #778)
+#845 := [unit-resolution #832 #806 #773]: #545
+#846 := [unit-resolution #731 #845]: #727
+#847 := [unit-resolution #818 #846]: #755
+#840 := (not #764)
+#841 := (or #795 #777 #778 #840)
+#825 := [hypothesis]: #764
+#839 := [th-lemma #774 #645 #647 #773 #651 #809 #643 #825 #642 #649]: false
+#842 := [lemma #839]: #841
+#848 := [unit-resolution #842 #847 #773 #808]: #795
+#849 := [unit-resolution #824 #848]: #765
+#850 := [unit-resolution #719 #849]: #471
+#851 := [th-lemma #847 #649 #645 #647 #773 #651 #808 #850 #806 #642]: false
+#853 := [lemma #851]: #852
+#859 := [unit-resolution #853 #773]: #260
+#870 := (or #471 #778)
+#856 := [hypothesis]: #715
+#857 := [unit-resolution #719 #856]: #714
+#858 := [unit-resolution #824 #857]: #758
+#860 := [unit-resolution #797 #858 #643 #645 #647 #649 #651 #773 #859 #856]: #777
+#861 := [unit-resolution #818 #860]: #814
+#862 := [unit-resolution #731 #861]: #729
+#869 := [th-lemma #643 #650 #863 #868 #859 #862 #645 #647 #773 #651 #858]: false
+#871 := [lemma #869]: #870
+#855 := [unit-resolution #871 #773]: #471
+#872 := (not #756)
+#873 := (or #777 #590 #574 #872 #561 #261 #794 #793 #778 #633 #715)
+#874 := [th-lemma]: #873
+#875 := [unit-resolution #874 #855 #645 #647 #649 #863 #650 #651 #773 #859 #868]: #777
+#876 := (or #545 #261 #794 #793 #778 #633 #715 #590 #574 #872)
+#877 := [th-lemma]: #876
+#878 := [unit-resolution #877 #855 #645 #647 #859 #863 #650 #651 #773 #868]: #545
+#879 := [unit-resolution #731 #878]: #727
+#880 := [unit-resolution #818 #879 #875]: false
+#881 := [lemma #880]: #778
+#883 := [hypothesis]: #741
+#885 := (or #884 #750)
+#886 := [th-lemma]: #885
+#887 := [unit-resolution #886 #883 #881]: false
+#888 := [lemma #887]: #884
+#744 := (or #743 #741)
+#745 := [def-axiom]: #744
+#894 := [unit-resolution #745 #888]: #743
+#930 := [hypothesis]: #736
+#935 := (or #489 #574)
+#931 := [unit-resolution #740 #930]: #735
+#893 := [hypothesis]: #872
+#915 := [hypothesis]: #735
+#916 := [unit-resolution #867 #915 #893]: false
+#917 := [lemma #916]: #866
+#932 := [unit-resolution #917 #931]: #756
+#749 := (+ #613 #624)
+#844 := (>= #749 0::real)
+#742 := (= #613 #621)
+#746 := (or #614 #742)
+#747 := [def-axiom]: #746
+#895 := [unit-resolution #747 #894]: #742
+#896 := (not #742)
+#897 := (or #896 #844)
+#898 := [th-lemma]: #897
+#899 := [unit-resolution #898 #895]: #844
+#913 := (or #872 #260)
+#900 := [hypothesis]: #756
+#646 := [and-elim #513]: #500
+#903 := (not #844)
+#902 := (not #533)
+#901 := (not #500)
+#904 := (or #489 #901 #260 #872 #840 #277 #590 #902 #903 #633)
+#905 := [th-lemma]: #904
+#906 := [unit-resolution #905 #900 #806 #646 #648 #650 #651 #808 #642 #899]: #489
+#722 := (not #489)
+#723 := (or #722 #720)
+#724 := [def-axiom]: #723
+#907 := [unit-resolution #724 #906]: #720
+#908 := (not #720)
+#909 := (or #908 #892)
+#910 := [th-lemma]: #909
+#911 := [unit-resolution #910 #907]: #892
+#912 := [th-lemma #911 #646 #900 #808 #650 #648 #899 #651 #644 #642]: false
+#914 := [lemma #912]: #913
+#890 := [unit-resolution #914 #806]: #872
+#918 := [unit-resolution #917 #890]: #865
+#919 := [unit-resolution #740 #918]: #574
+#920 := (or #489 #901 #260 #902 #903 #633 #840 #277 #736)
+#921 := [th-lemma]: #920
+#922 := [unit-resolution #921 #806 #642 #646 #648 #919 #651 #808 #899]: #489
+#923 := [unit-resolution #724 #922]: #720
+#924 := [unit-resolution #910 #923]: #892
+#925 := [th-lemma #924 #646 #806 #648 #899 #651 #808 #919 #644 #642]: false
+#926 := [lemma #925]: #260
+#933 := [hypothesis]: #722
+#934 := [th-lemma #646 #933 #926 #648 #899 #651 #932 #650 #930]: false
+#936 := [lemma #934]: #935
+#927 := [unit-resolution #936 #930]: #489
+#928 := [unit-resolution #724 #927]: #720
+#929 := [unit-resolution #910 #928]: #892
+#937 := [th-lemma #929 #644 #926 #932 #650 #646 #648 #899 #651 #927]: false
+#938 := [lemma #937]: #574
+#940 := (or #489 #261 #614 #901 #902 #736)
+#941 := [th-lemma]: #940
+#942 := [unit-resolution #941 #926 #646 #648 #938 #894]: #489
+#943 := [unit-resolution #724 #942]: #720
+#944 := [unit-resolution #910 #943]: #892
+#760 := (+ #167 #275)
+#819 := (<= #760 0::real)
+#707 := (= #167 #267)
+#709 := (or #261 #707)
+#710 := [def-axiom]: #709
+#945 := [unit-resolution #710 #926]: #707
+#946 := (not #707)
+#947 := (or #946 #819)
+#948 := [th-lemma]: #947
+#949 := [unit-resolution #948 #945]: #819
+[th-lemma #926 #949 #646 #648 #899 #651 #938 #944 #644 #642]: false
+unsat

--- a/src/HOL/SMT_Examples/ROOT.ML	Wed May 12 23:54:04 2010 +0200
+++ b/src/HOL/SMT_Examples/ROOT.ML	Wed May 12 23:54:06 2010 +0200
@@ -1,1 +1,2 @@
+quick_and_dirty := true;
 use_thys ["SMT_Tests", "SMT_Examples", "SMT_Word_Examples"];

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT_Examples/SMT_Examples.certs	Wed May 12 23:54:06 2010 +0200
@@ -0,0 +1,13275 @@
+d296070a9a1ad4678f3ec56cd19a634e50fd638a 8 0
+#2 := false
+#1 := true
+#8 := (not true)
+#26 := (iff #8 false)
+#27 := [rewrite]: #26
+#25 := [asserted]: #8
+[mp #25 #27]: false
+unsat
+32bb24b231f8ef17d3b0def6817d84cc062a6d75 33 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#10 := (not #9)
+#11 := (or #9 #10)
+#12 := (not #11)
+#48 := (iff #12 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (iff #11 true)
+#30 := (= f1 f3)
+#33 := (not #30)
+#36 := (or #30 #33)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #11 #36)
+#34 := (iff #10 #33)
+#31 := (iff #9 #30)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#38 := [monotonicity #32 #35]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#29 := [asserted]: #12
+[mp #29 #49]: false
+unsat
+574c632d113dfa2ca17f7e2ecc357ab25fbced89 37 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#1 := true
+#10 := (and #9 true)
+#11 := (iff #10 #9)
+#12 := (not #11)
+#52 := (iff #12 false)
+#47 := (not true)
+#50 := (iff #47 false)
+#51 := [rewrite]: #50
+#48 := (iff #12 #47)
+#45 := (iff #11 true)
+#30 := (= f1 f3)
+#40 := (iff #30 #30)
+#43 := (iff #40 true)
+#44 := [rewrite]: #43
+#41 := (iff #11 #40)
+#31 := (iff #9 #30)
+#32 := [rewrite]: #31
+#38 := (iff #10 #30)
+#33 := (and #30 true)
+#36 := (iff #33 #30)
+#37 := [rewrite]: #36
+#34 := (iff #10 #33)
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39 #32]: #41
+#46 := [trans #42 #44]: #45
+#49 := [monotonicity #46]: #48
+#53 := [trans #49 #51]: #52
+#29 := [asserted]: #12
+[mp #29 #53]: false
+unsat
+8ef67dc17184cdb997c34c282ec976aab91f0c9d 66 0
+#2 := false
+decl f4 :: S1
+#10 := f4
+decl f1 :: S1
+#4 := f1
+#37 := (= f1 f4)
+decl f3 :: S1
+#8 := f3
+#34 := (= f1 f3)
+#40 := (or #34 #37)
+#84 := (iff #40 false)
+#79 := (or false false)
+#82 := (iff #79 false)
+#83 := [rewrite]: #82
+#80 := (iff #40 #79)
+#75 := (iff #37 false)
+#66 := (not #37)
+#43 := (not #34)
+#49 := (and #43 #40)
+#57 := (not #49)
+#58 := (or #37 #57)
+#63 := (not #58)
+#11 := (= f4 f1)
+#9 := (= f3 f1)
+#13 := (not #9)
+#12 := (or #9 #11)
+#14 := (and #12 #13)
+#15 := (implies #14 #11)
+#16 := (not #15)
+#64 := (iff #16 #63)
+#61 := (iff #15 #58)
+#54 := (implies #49 #37)
+#59 := (iff #54 #58)
+#60 := [rewrite]: #59
+#55 := (iff #15 #54)
+#38 := (iff #11 #37)
+#39 := [rewrite]: #38
+#52 := (iff #14 #49)
+#46 := (and #40 #43)
+#50 := (iff #46 #49)
+#51 := [rewrite]: #50
+#47 := (iff #14 #46)
+#44 := (iff #13 #43)
+#35 := (iff #9 #34)
+#36 := [rewrite]: #35
+#45 := [monotonicity #36]: #44
+#41 := (iff #12 #40)
+#42 := [monotonicity #36 #39]: #41
+#48 := [monotonicity #42 #45]: #47
+#53 := [trans #48 #51]: #52
+#56 := [monotonicity #53 #39]: #55
+#62 := [trans #56 #60]: #61
+#65 := [monotonicity #62]: #64
+#33 := [asserted]: #16
+#68 := [mp #33 #65]: #63
+#67 := [not-or-elim #68]: #66
+#76 := [iff-false #67]: #75
+#77 := (iff #34 false)
+#69 := [not-or-elim #68]: #49
+#70 := [and-elim #69]: #43
+#78 := [iff-false #70]: #77
+#81 := [monotonicity #78 #76]: #80
+#85 := [trans #81 #83]: #84
+#71 := [and-elim #69]: #40
+[mp #71 #85]: false
+unsat
+ceadbcd40be3b7ac62a2203b95e7db34fb2bec42 1 0
+unsat
+d20c57e06043d23215073c59e7d2eb20f25833ac 94 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+decl f5 :: S1
+#13 := f5
+#14 := (= f5 f1)
+#17 := (and #9 #14)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#16 := (and #14 #11)
+#18 := (or #16 #17)
+#19 := (implies #9 #18)
+#20 := (or #19 #9)
+#12 := (and #9 #11)
+#15 := (or #12 #14)
+#21 := (implies #15 #20)
+#22 := (not #21)
+#107 := (iff #22 false)
+#49 := (= f1 f5)
+#40 := (= f1 f3)
+#63 := (and #40 #49)
+#43 := (= f1 f4)
+#58 := (and #43 #49)
+#66 := (or #58 #63)
+#72 := (not #40)
+#73 := (or #72 #66)
+#81 := (or #40 #73)
+#46 := (and #40 #43)
+#52 := (or #46 #49)
+#89 := (not #52)
+#90 := (or #89 #81)
+#95 := (not #90)
+#105 := (iff #95 false)
+#1 := true
+#100 := (not true)
+#103 := (iff #100 false)
+#104 := [rewrite]: #103
+#101 := (iff #95 #100)
+#98 := (iff #90 true)
+#99 := [rewrite]: #98
+#102 := [monotonicity #99]: #101
+#106 := [trans #102 #104]: #105
+#96 := (iff #22 #95)
+#93 := (iff #21 #90)
+#86 := (implies #52 #81)
+#91 := (iff #86 #90)
+#92 := [rewrite]: #91
+#87 := (iff #21 #86)
+#84 := (iff #20 #81)
+#78 := (or #73 #40)
+#82 := (iff #78 #81)
+#83 := [rewrite]: #82
+#79 := (iff #20 #78)
+#41 := (iff #9 #40)
+#42 := [rewrite]: #41
+#76 := (iff #19 #73)
+#69 := (implies #40 #66)
+#74 := (iff #69 #73)
+#75 := [rewrite]: #74
+#70 := (iff #19 #69)
+#67 := (iff #18 #66)
+#64 := (iff #17 #63)
+#50 := (iff #14 #49)
+#51 := [rewrite]: #50
+#65 := [monotonicity #42 #51]: #64
+#61 := (iff #16 #58)
+#55 := (and #49 #43)
+#59 := (iff #55 #58)
+#60 := [rewrite]: #59
+#56 := (iff #16 #55)
+#44 := (iff #11 #43)
+#45 := [rewrite]: #44
+#57 := [monotonicity #51 #45]: #56
+#62 := [trans #57 #60]: #61
+#68 := [monotonicity #62 #65]: #67
+#71 := [monotonicity #42 #68]: #70
+#77 := [trans #71 #75]: #76
+#80 := [monotonicity #77 #42]: #79
+#85 := [trans #80 #83]: #84
+#53 := (iff #15 #52)
+#47 := (iff #12 #46)
+#48 := [monotonicity #42 #45]: #47
+#54 := [monotonicity #48 #51]: #53
+#88 := [monotonicity #54 #85]: #87
+#94 := [trans #88 #92]: #93
+#97 := [monotonicity #94]: #96
+#108 := [trans #97 #106]: #107
+#39 := [asserted]: #22
+[mp #39 #108]: false
+unsat
+72c3865e0e36884211edef00a7d296b6225c2e7f 72 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#10 := (iff #9 #9)
+#11 := (iff #10 #9)
+#12 := (iff #11 #9)
+#13 := (iff #12 #9)
+#14 := (iff #13 #9)
+#15 := (iff #14 #9)
+#16 := (iff #15 #9)
+#17 := (iff #16 #9)
+#18 := (iff #17 #9)
+#19 := (not #18)
+#87 := (iff #19 false)
+#1 := true
+#82 := (not true)
+#85 := (iff #82 false)
+#86 := [rewrite]: #85
+#83 := (iff #19 #82)
+#80 := (iff #18 true)
+#37 := (= f1 f3)
+#40 := (iff #37 #37)
+#43 := (iff #40 true)
+#44 := [rewrite]: #43
+#78 := (iff #18 #40)
+#38 := (iff #9 #37)
+#39 := [rewrite]: #38
+#76 := (iff #17 #37)
+#47 := (iff true #37)
+#50 := (iff #47 #37)
+#51 := [rewrite]: #50
+#74 := (iff #17 #47)
+#72 := (iff #16 true)
+#70 := (iff #16 #40)
+#68 := (iff #15 #37)
+#66 := (iff #15 #47)
+#64 := (iff #14 true)
+#62 := (iff #14 #40)
+#60 := (iff #13 #37)
+#58 := (iff #13 #47)
+#56 := (iff #12 true)
+#54 := (iff #12 #40)
+#52 := (iff #11 #37)
+#48 := (iff #11 #47)
+#45 := (iff #10 true)
+#41 := (iff #10 #40)
+#42 := [monotonicity #39 #39]: #41
+#46 := [trans #42 #44]: #45
+#49 := [monotonicity #46 #39]: #48
+#53 := [trans #49 #51]: #52
+#55 := [monotonicity #53 #39]: #54
+#57 := [trans #55 #44]: #56
+#59 := [monotonicity #57 #39]: #58
+#61 := [trans #59 #51]: #60
+#63 := [monotonicity #61 #39]: #62
+#65 := [trans #63 #44]: #64
+#67 := [monotonicity #65 #39]: #66
+#69 := [trans #67 #51]: #68
+#71 := [monotonicity #69 #39]: #70
+#73 := [trans #71 #44]: #72
+#75 := [monotonicity #73 #39]: #74
+#77 := [trans #75 #51]: #76
+#79 := [monotonicity #77 #39]: #78
+#81 := [trans #79 #44]: #80
+#84 := [monotonicity #81]: #83
+#88 := [trans #84 #86]: #87
+#36 := [asserted]: #19
+[mp #36 #88]: false
+unsat
+79de3dae14f97a3a364a771776e83f08947fcde3 234 0
+#2 := false
+decl f6 :: S1
+#14 := f6
+decl f1 :: S1
+#4 := f1
+#79 := (= f1 f6)
+decl f5 :: S1
+#12 := f5
+#76 := (= f1 f5)
+decl f4 :: S1
+#10 := f4
+#73 := (= f1 f4)
+decl f3 :: S1
+#8 := f3
+#70 := (= f1 f3)
+#91 := (or #70 #73 #76 #79)
+#298 := (iff #91 false)
+#293 := (or false false false false)
+#296 := (iff #293 false)
+#297 := [rewrite]: #296
+#294 := (iff #91 #293)
+#250 := (iff #79 false)
+#180 := (not #79)
+#186 := (or #76 #180)
+#258 := (iff #186 #180)
+#253 := (or false #180)
+#256 := (iff #253 #180)
+#257 := [rewrite]: #256
+#254 := (iff #186 #253)
+#251 := (iff #76 false)
+#120 := (not #76)
+decl f11 :: S1
+#44 := f11
+#45 := (= f11 f1)
+#46 := (not #45)
+#47 := (and #45 #46)
+decl f10 :: S1
+#41 := f10
+#42 := (= f10 f1)
+#48 := (or #42 #47)
+#43 := (not #42)
+#49 := (and #43 #48)
+#13 := (= f5 f1)
+#50 := (or #13 #49)
+#51 := (not #50)
+#233 := (iff #51 #120)
+#231 := (iff #50 #76)
+#226 := (or #76 false)
+#229 := (iff #226 #76)
+#230 := [rewrite]: #229
+#227 := (iff #50 #226)
+#224 := (iff #49 false)
+#192 := (= f1 f10)
+#196 := (not #192)
+#219 := (and #196 #192)
+#222 := (iff #219 false)
+#223 := [rewrite]: #222
+#220 := (iff #49 #219)
+#217 := (iff #48 #192)
+#212 := (or #192 false)
+#215 := (iff #212 #192)
+#216 := [rewrite]: #215
+#213 := (iff #48 #212)
+#210 := (iff #47 false)
+#199 := (= f1 f11)
+#202 := (not #199)
+#205 := (and #199 #202)
+#208 := (iff #205 false)
+#209 := [rewrite]: #208
+#206 := (iff #47 #205)
+#203 := (iff #46 #202)
+#200 := (iff #45 #199)
+#201 := [rewrite]: #200
+#204 := [monotonicity #201]: #203
+#207 := [monotonicity #201 #204]: #206
+#211 := [trans #207 #209]: #210
+#194 := (iff #42 #192)
+#195 := [rewrite]: #194
+#214 := [monotonicity #195 #211]: #213
+#218 := [trans #214 #216]: #217
+#197 := (iff #43 #196)
+#198 := [monotonicity #195]: #197
+#221 := [monotonicity #198 #218]: #220
+#225 := [trans #221 #223]: #224
+#77 := (iff #13 #76)
+#78 := [rewrite]: #77
+#228 := [monotonicity #78 #225]: #227
+#232 := [trans #228 #230]: #231
+#234 := [monotonicity #232]: #233
+#191 := [asserted]: #51
+#237 := [mp #191 #234]: #120
+#252 := [iff-false #237]: #251
+#255 := [monotonicity #252]: #254
+#259 := [trans #255 #257]: #258
+#15 := (= f6 f1)
+#38 := (or #15 false)
+#39 := (not #38)
+#40 := (or #39 #13)
+#189 := (iff #40 #186)
+#183 := (or #180 #76)
+#187 := (iff #183 #186)
+#188 := [rewrite]: #187
+#184 := (iff #40 #183)
+#181 := (iff #39 #180)
+#178 := (iff #38 #79)
+#172 := (or #79 false)
+#176 := (iff #172 #79)
+#177 := [rewrite]: #176
+#174 := (iff #38 #172)
+#80 := (iff #15 #79)
+#81 := [rewrite]: #80
+#175 := [monotonicity #81]: #174
+#179 := [trans #175 #177]: #178
+#182 := [monotonicity #179]: #181
+#185 := [monotonicity #182 #78]: #184
+#190 := [trans #185 #188]: #189
+#171 := [asserted]: #40
+#193 := [mp #171 #190]: #186
+#249 := [mp #193 #259]: #180
+#260 := [iff-false #249]: #250
+#248 := (iff #73 false)
+#165 := (not #73)
+#168 := (or #165 #76)
+#266 := (iff #168 #165)
+#261 := (or #165 false)
+#264 := (iff #261 #165)
+#265 := [rewrite]: #264
+#262 := (iff #168 #261)
+#263 := [monotonicity #252]: #262
+#267 := [trans #263 #265]: #266
+decl f9 :: S1
+#31 := f9
+#32 := (= f9 f1)
+#33 := (not #32)
+#34 := (or #32 #33)
+#11 := (= f4 f1)
+#35 := (and #11 #34)
+#36 := (not #35)
+#37 := (or #36 #13)
+#169 := (iff #37 #168)
+#166 := (iff #36 #165)
+#163 := (iff #35 #73)
+#1 := true
+#158 := (and #73 true)
+#161 := (iff #158 #73)
+#162 := [rewrite]: #161
+#159 := (iff #35 #158)
+#156 := (iff #34 true)
+#144 := (= f1 f9)
+#148 := (not #144)
+#151 := (or #144 #148)
+#154 := (iff #151 true)
+#155 := [rewrite]: #154
+#152 := (iff #34 #151)
+#149 := (iff #33 #148)
+#146 := (iff #32 #144)
+#147 := [rewrite]: #146
+#150 := [monotonicity #147]: #149
+#153 := [monotonicity #147 #150]: #152
+#157 := [trans #153 #155]: #156
+#74 := (iff #11 #73)
+#75 := [rewrite]: #74
+#160 := [monotonicity #75 #157]: #159
+#164 := [trans #160 #162]: #163
+#167 := [monotonicity #164]: #166
+#170 := [monotonicity #167 #78]: #169
+#143 := [asserted]: #37
+#173 := [mp #143 #170]: #168
+#247 := [mp #173 #267]: #165
+#268 := [iff-false #247]: #248
+#246 := (iff #70 false)
+#137 := (not #70)
+#140 := (or #137 #73)
+#274 := (iff #140 #137)
+#269 := (or #137 false)
+#272 := (iff #269 #137)
+#273 := [rewrite]: #272
+#270 := (iff #140 #269)
+#271 := [monotonicity #268]: #270
+#275 := [trans #271 #273]: #274
+#26 := (not #13)
+#27 := (and #13 #26)
+#9 := (= f3 f1)
+#28 := (or #9 #27)
+#29 := (not #28)
+#30 := (or #29 #11)
+#141 := (iff #30 #140)
+#138 := (iff #29 #137)
+#135 := (iff #28 #70)
+#130 := (or #70 false)
+#133 := (iff #130 #70)
+#134 := [rewrite]: #133
+#131 := (iff #28 #130)
+#128 := (iff #27 false)
+#123 := (and #76 #120)
+#126 := (iff #123 false)
+#127 := [rewrite]: #126
+#124 := (iff #27 #123)
+#121 := (iff #26 #120)
+#122 := [monotonicity #78]: #121
+#125 := [monotonicity #78 #122]: #124
+#129 := [trans #125 #127]: #128
+#71 := (iff #9 #70)
+#72 := [rewrite]: #71
+#132 := [monotonicity #72 #129]: #131
+#136 := [trans #132 #134]: #135
+#139 := [monotonicity #136]: #138
+#142 := [monotonicity #139 #75]: #141
+#119 := [asserted]: #30
+#145 := [mp #119 #142]: #140
+#245 := [mp #145 #275]: #137
+#276 := [iff-false #245]: #246
+#295 := [monotonicity #276 #268 #252 #260]: #294
+#299 := [trans #295 #297]: #298
+#16 := (or #13 #15)
+#17 := (or #11 #16)
+#18 := (or #9 #17)
+#94 := (iff #18 #91)
+#82 := (or #76 #79)
+#85 := (or #73 #82)
+#88 := (or #70 #85)
+#92 := (iff #88 #91)
+#93 := [rewrite]: #92
+#89 := (iff #18 #88)
+#86 := (iff #17 #85)
+#83 := (iff #16 #82)
+#84 := [monotonicity #78 #81]: #83
+#87 := [monotonicity #75 #84]: #86
+#90 := [monotonicity #72 #87]: #89
+#95 := [trans #90 #93]: #94
+#69 := [asserted]: #18
+#96 := [mp #69 #95]: #91
+[mp #96 #299]: false
+unsat
+7a59440c66c70049fb2ecd405f9d7f413fe22698 52 0
+#2 := false
+decl f4 :: (-> S2 S2 S2)
+#16 := (:var 1 S2)
+#17 := (:var 0 S2)
+#19 := (f4 #17 #16)
+#535 := (pattern #19)
+#18 := (f4 #16 #17)
+#534 := (pattern #18)
+#20 := (= #18 #19)
+#536 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #534 #535) #20)
+#21 := (forall (vars (?v0 S2) (?v1 S2)) #20)
+#539 := (iff #21 #536)
+#537 := (iff #20 #20)
+#538 := [refl]: #537
+#540 := [quant-intro #538]: #539
+#62 := (~ #21 #21)
+#60 := (~ #20 #20)
+#61 := [refl]: #60
+#63 := [nnf-pos #61]: #62
+#51 := [asserted]: #21
+#56 := [mp~ #51 #63]: #21
+#541 := [mp #56 #540]: #536
+decl f3 :: S2
+#8 := f3
+decl f5 :: S2
+#10 := f5
+#12 := (f4 f5 f3)
+#11 := (f4 f3 f5)
+#13 := (= #11 #12)
+#48 := (not #13)
+#9 := (= f3 f3)
+#14 := (and #9 #13)
+#15 := (not #14)
+#49 := (iff #15 #48)
+#46 := (iff #14 #13)
+#1 := true
+#41 := (and true #13)
+#44 := (iff #41 #13)
+#45 := [rewrite]: #44
+#42 := (iff #14 #41)
+#39 := (iff #9 true)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#50 := [monotonicity #47]: #49
+#38 := [asserted]: #15
+#53 := [mp #38 #50]: #48
+#117 := (not #536)
+#204 := (or #117 #13)
+#118 := [quant-inst]: #204
+[unit-resolution #118 #53 #541]: false
+unsat
+de6b02b2b257f22f19cf83198a5d863ff188f241 2578 0
+#2 := false
+decl f35 :: S1
+#112 := f35
+decl f1 :: S1
+#4 := f1
+#833 := (= f1 f35)
+decl f37 :: S1
+#119 := f37
+#860 := (= f1 f37)
+#1997 := (not #860)
+decl f48 :: S1
+#157 := f48
+#1013 := (= f1 f48)
+decl f57 :: S1
+#188 := f57
+#1139 := (= f1 f57)
+#2552 := (not #1139)
+decl f47 :: S1
+#152 := f47
+#989 := (= f1 f47)
+decl f46 :: S1
+#150 := f46
+#986 := (= f1 f46)
+#2244 := (not #986)
+#3246 := [hypothesis]: #986
+#2332 := (or #1997 #2244)
+#120 := (= f37 f1)
+#314 := (not #120)
+#151 := (= f46 f1)
+#347 := (not #151)
+#358 := (or #347 #314)
+#2335 := (iff #358 #2332)
+#2328 := (or #2244 #1997)
+#2333 := (iff #2328 #2332)
+#2334 := [rewrite]: #2333
+#2330 := (iff #358 #2328)
+#1999 := (iff #314 #1997)
+#861 := (iff #120 #860)
+#862 := [rewrite]: #861
+#2000 := [monotonicity #862]: #1999
+#2246 := (iff #347 #2244)
+#987 := (iff #151 #986)
+#988 := [rewrite]: #987
+#2247 := [monotonicity #988]: #2246
+#2331 := [monotonicity #2247 #2000]: #2330
+#2336 := [trans #2331 #2334]: #2335
+#2327 := [asserted]: #358
+#2339 := [mp #2327 #2336]: #2332
+#3247 := [unit-resolution #2339 #3246]: #1997
+decl f26 :: S1
+#81 := f26
+#707 := (= f1 f26)
+#1689 := (not #707)
+decl f15 :: S1
+#44 := f15
+#562 := (= f1 f15)
+decl f13 :: S1
+#38 := f13
+#538 := (= f1 f13)
+#1370 := (not #538)
+decl f11 :: S1
+#32 := f11
+#514 := (= f1 f11)
+decl f23 :: S1
+#69 := f23
+#656 := (= f1 f23)
+decl f34 :: S1
+#107 := f34
+#809 := (= f1 f34)
+#1879 := (not #809)
+decl f45 :: S1
+#145 := f45
+#962 := (= f1 f45)
+decl f55 :: S1
+#181 := f55
+#1112 := (= f1 f55)
+#2491 := (not #1112)
+#2305 := (not #1013)
+#2312 := (or #2244 #2305)
+#158 := (= f48 f1)
+#355 := (not #158)
+#356 := (or #355 #347)
+#2315 := (iff #356 #2312)
+#2309 := (or #2305 #2244)
+#2313 := (iff #2309 #2312)
+#2314 := [rewrite]: #2313
+#2310 := (iff #356 #2309)
+#2307 := (iff #355 #2305)
+#1014 := (iff #158 #1013)
+#1015 := [rewrite]: #1014
+#2308 := [monotonicity #1015]: #2307
+#2311 := [monotonicity #2308 #2247]: #2310
+#2316 := [trans #2311 #2314]: #2315
+#2304 := [asserted]: #356
+#2319 := [mp #2304 #2316]: #2312
+#3253 := [unit-resolution #2319 #3246]: #2305
+#1169 := (or #1013 #1139)
+decl f6 :: S1
+#17 := f6
+#457 := (= f1 f6)
+#1177 := (or #457 #1013 #1139)
+#2857 := (iff #1177 #1169)
+#2852 := (or false #1013 #1139)
+#2855 := (iff #2852 #1169)
+#2856 := [rewrite]: #2855
+#2853 := (iff #1177 #2852)
+#2776 := (iff #457 false)
+#461 := (not #457)
+#18 := (= f6 f1)
+#19 := (not #18)
+#462 := (iff #19 #461)
+#459 := (iff #18 #457)
+#460 := [rewrite]: #459
+#463 := [monotonicity #460]: #462
+#456 := [asserted]: #19
+#466 := [mp #456 #463]: #461
+#2777 := [iff-false #466]: #2776
+#2854 := [monotonicity #2777]: #2853
+#2858 := [trans #2854 #2856]: #2857
+#189 := (= f57 f1)
+#195 := (or #189 #158)
+#196 := (or #18 #195)
+#1180 := (iff #196 #1177)
+#1174 := (or #457 #1169)
+#1178 := (iff #1174 #1177)
+#1179 := [rewrite]: #1178
+#1175 := (iff #196 #1174)
+#1172 := (iff #195 #1169)
+#1166 := (or #1139 #1013)
+#1170 := (iff #1166 #1169)
+#1171 := [rewrite]: #1170
+#1167 := (iff #195 #1166)
+#1140 := (iff #189 #1139)
+#1141 := [rewrite]: #1140
+#1168 := [monotonicity #1141 #1015]: #1167
+#1173 := [trans #1168 #1171]: #1172
+#1176 := [monotonicity #460 #1173]: #1175
+#1181 := [trans #1176 #1179]: #1180
+#1165 := [asserted]: #196
+#1182 := [mp #1165 #1181]: #1177
+#2859 := [mp #1182 #2858]: #1169
+#3254 := [unit-resolution #2859 #3253]: #1139
+#2567 := (or #2491 #2552)
+#182 := (= f55 f1)
+#380 := (not #182)
+#388 := (not #189)
+#391 := (or #388 #380)
+#2570 := (iff #391 #2567)
+#2563 := (or #2552 #2491)
+#2568 := (iff #2563 #2567)
+#2569 := [rewrite]: #2568
+#2565 := (iff #391 #2563)
+#2493 := (iff #380 #2491)
+#1113 := (iff #182 #1112)
+#1114 := [rewrite]: #1113
+#2494 := [monotonicity #1114]: #2493
+#2554 := (iff #388 #2552)
+#2555 := [monotonicity #1141]: #2554
+#2566 := [monotonicity #2555 #2494]: #2565
+#2571 := [trans #2566 #2569]: #2570
+#2562 := [asserted]: #391
+#2574 := [mp #2562 #2571]: #2567
+#3255 := [unit-resolution #2574 #3254]: #2491
+decl f56 :: S1
+#183 := f56
+#1115 := (= f1 f56)
+#2495 := (not #1115)
+decl f62 :: S1
+#208 := f62
+#1239 := (= f1 f62)
+decl f58 :: S1
+#190 := f58
+#1142 := (= f1 f58)
+#2556 := (not #1142)
+#2559 := (or #2552 #2556)
+#191 := (= f58 f1)
+#389 := (not #191)
+#390 := (or #388 #389)
+#2560 := (iff #390 #2559)
+#2557 := (iff #389 #2556)
+#1143 := (iff #191 #1142)
+#1144 := [rewrite]: #1143
+#2558 := [monotonicity #1144]: #2557
+#2561 := [monotonicity #2555 #2558]: #2560
+#2551 := [asserted]: #390
+#2564 := [mp #2551 #2561]: #2559
+#3594 := [unit-resolution #2564 #3254]: #2556
+#1263 := (or #1142 #1239)
+decl f5 :: S1
+#14 := f5
+#449 := (= f1 f5)
+#1271 := (or #449 #1142 #1239)
+#2875 := (iff #1271 #1263)
+#2870 := (or false #1142 #1239)
+#2873 := (iff #2870 #1263)
+#2874 := [rewrite]: #2873
+#2871 := (iff #1271 #2870)
+#2774 := (iff #449 false)
+#453 := (not #449)
+#15 := (= f5 f1)
+#16 := (not #15)
+#454 := (iff #16 #453)
+#451 := (iff #15 #449)
+#452 := [rewrite]: #451
+#455 := [monotonicity #452]: #454
+#448 := [asserted]: #16
+#458 := [mp #448 #455]: #453
+#2775 := [iff-false #458]: #2774
+#2872 := [monotonicity #2775]: #2871
+#2876 := [trans #2872 #2874]: #2875
+#209 := (= f62 f1)
+#212 := (or #209 #191)
+#213 := (or #15 #212)
+#1274 := (iff #213 #1271)
+#1268 := (or #449 #1263)
+#1272 := (iff #1268 #1271)
+#1273 := [rewrite]: #1272
+#1269 := (iff #213 #1268)
+#1266 := (iff #212 #1263)
+#1260 := (or #1239 #1142)
+#1264 := (iff #1260 #1263)
+#1265 := [rewrite]: #1264
+#1261 := (iff #212 #1260)
+#1240 := (iff #209 #1239)
+#1241 := [rewrite]: #1240
+#1262 := [monotonicity #1241 #1144]: #1261
+#1267 := [trans #1262 #1265]: #1266
+#1270 := [monotonicity #452 #1267]: #1269
+#1275 := [trans #1270 #1273]: #1274
+#1259 := [asserted]: #213
+#1276 := [mp #1259 #1275]: #1271
+#2877 := [mp #1276 #2876]: #1263
+#3595 := [unit-resolution #2877 #3594]: #1239
+#2712 := (not #1239)
+#2729 := (or #2495 #2712)
+#184 := (= f56 f1)
+#381 := (not #184)
+#409 := (not #209)
+#411 := (or #409 #381)
+#2732 := (iff #411 #2729)
+#2725 := (or #2712 #2495)
+#2730 := (iff #2725 #2729)
+#2731 := [rewrite]: #2730
+#2727 := (iff #411 #2725)
+#2496 := (iff #381 #2495)
+#1116 := (iff #184 #1115)
+#1117 := [rewrite]: #1116
+#2497 := [monotonicity #1117]: #2496
+#2714 := (iff #409 #2712)
+#2715 := [monotonicity #1241]: #2714
+#2728 := [monotonicity #2715 #2497]: #2727
+#2733 := [trans #2728 #2731]: #2732
+#2724 := [asserted]: #411
+#2736 := [mp #2724 #2733]: #2729
+#3596 := [unit-resolution #2736 #3595]: #2495
+decl f53 :: S1
+#174 := f53
+#1085 := (= f1 f53)
+#2430 := (not #1085)
+decl f61 :: S1
+#204 := f61
+#1218 := (= f1 f61)
+#2679 := (not #1218)
+#2719 := (or #2679 #2712)
+#205 := (= f61 f1)
+#405 := (not #205)
+#410 := (or #409 #405)
+#2722 := (iff #410 #2719)
+#2716 := (or #2712 #2679)
+#2720 := (iff #2716 #2719)
+#2721 := [rewrite]: #2720
+#2717 := (iff #410 #2716)
+#2681 := (iff #405 #2679)
+#1219 := (iff #205 #1218)
+#1220 := [rewrite]: #1219
+#2682 := [monotonicity #1220]: #2681
+#2718 := [monotonicity #2715 #2682]: #2717
+#2723 := [trans #2718 #2721]: #2722
+#2711 := [asserted]: #410
+#2726 := [mp #2711 #2723]: #2719
+#3597 := [unit-resolution #2726 #3595]: #2679
+#3579 := (or #2430 #1218)
+decl f19 :: S1
+#55 := f19
+#602 := (= f1 f19)
+decl f30 :: S1
+#93 := f30
+#755 := (= f1 f30)
+#1757 := (not #755)
+decl f41 :: S1
+#131 := f41
+#908 := (= f1 f41)
+decl f52 :: S1
+#169 := f52
+#1061 := (= f1 f52)
+#2373 := (not #1061)
+decl f60 :: S1
+#200 := f60
+#1196 := (= f1 f60)
+#3563 := [hypothesis]: #2679
+decl f54 :: S1
+#176 := f54
+#1088 := (= f1 f54)
+#2434 := (not #1088)
+#3175 := [hypothesis]: #1085
+#2437 := (or #2430 #2434)
+#177 := (= f54 f1)
+#373 := (not #177)
+#175 := (= f53 f1)
+#372 := (not #175)
+#374 := (or #372 #373)
+#2438 := (iff #374 #2437)
+#2435 := (iff #373 #2434)
+#1089 := (iff #177 #1088)
+#1090 := [rewrite]: #1089
+#2436 := [monotonicity #1090]: #2435
+#2432 := (iff #372 #2430)
+#1086 := (iff #175 #1085)
+#1087 := [rewrite]: #1086
+#2433 := [monotonicity #1087]: #2432
+#2439 := [monotonicity #2433 #2436]: #2438
+#2429 := [asserted]: #374
+#2442 := [mp #2429 #2439]: #2437
+#3176 := [unit-resolution #2442 #3175]: #2434
+#1232 := (or #1088 #1196 #1218)
+#201 := (= f60 f1)
+#206 := (or #201 #177)
+#207 := (or #205 #206)
+#1235 := (iff #207 #1232)
+#1224 := (or #1088 #1196)
+#1229 := (or #1218 #1224)
+#1233 := (iff #1229 #1232)
+#1234 := [rewrite]: #1233
+#1230 := (iff #207 #1229)
+#1227 := (iff #206 #1224)
+#1221 := (or #1196 #1088)
+#1225 := (iff #1221 #1224)
+#1226 := [rewrite]: #1225
+#1222 := (iff #206 #1221)
+#1198 := (iff #201 #1196)
+#1199 := [rewrite]: #1198
+#1223 := [monotonicity #1199 #1090]: #1222
+#1228 := [trans #1223 #1226]: #1227
+#1231 := [monotonicity #1220 #1228]: #1230
+#1236 := [trans #1231 #1234]: #1235
+#1217 := [asserted]: #207
+#1237 := [mp #1217 #1236]: #1232
+#3564 := [unit-resolution #1237 #3176 #3563]: #1196
+#2646 := (not #1196)
+#2663 := (or #2373 #2646)
+#170 := (= f52 f1)
+#365 := (not #170)
+#401 := (not #201)
+#403 := (or #401 #365)
+#2666 := (iff #403 #2663)
+#2659 := (or #2646 #2373)
+#2664 := (iff #2659 #2663)
+#2665 := [rewrite]: #2664
+#2661 := (iff #403 #2659)
+#2374 := (iff #365 #2373)
+#1062 := (iff #170 #1061)
+#1063 := [rewrite]: #1062
+#2375 := [monotonicity #1063]: #2374
+#2648 := (iff #401 #2646)
+#2649 := [monotonicity #1199]: #2648
+#2662 := [monotonicity #2649 #2375]: #2661
+#2667 := [trans #2662 #2665]: #2666
+#2658 := [asserted]: #403
+#2670 := [mp #2658 #2667]: #2663
+#3565 := [unit-resolution #2670 #3564]: #2373
+decl f51 :: S1
+#167 := f51
+#1058 := (= f1 f51)
+#2369 := (not #1058)
+#2445 := (or #2369 #2430)
+#168 := (= f51 f1)
+#364 := (not #168)
+#375 := (or #372 #364)
+#2448 := (iff #375 #2445)
+#2441 := (or #2430 #2369)
+#2446 := (iff #2441 #2445)
+#2447 := [rewrite]: #2446
+#2443 := (iff #375 #2441)
+#2371 := (iff #364 #2369)
+#1059 := (iff #168 #1058)
+#1060 := [rewrite]: #1059
+#2372 := [monotonicity #1060]: #2371
+#2444 := [monotonicity #2433 #2372]: #2443
+#2449 := [trans #2444 #2447]: #2448
+#2440 := [asserted]: #375
+#2452 := [mp #2440 #2449]: #2445
+#3181 := [unit-resolution #2452 #3175]: #2369
+decl f49 :: S1
+#161 := f49
+#1034 := (= f1 f49)
+#2338 := (not #1034)
+decl f50 :: S1
+#163 := f50
+#1037 := (= f1 f50)
+decl f59 :: S1
+#197 := f59
+#1184 := (= f1 f59)
+#2633 := (not #1184)
+#2653 := (or #2633 #2646)
+#198 := (= f59 f1)
+#399 := (not #198)
+#402 := (or #401 #399)
+#2656 := (iff #402 #2653)
+#2650 := (or #2646 #2633)
+#2654 := (iff #2650 #2653)
+#2655 := [rewrite]: #2654
+#2651 := (iff #402 #2650)
+#2635 := (iff #399 #2633)
+#1185 := (iff #198 #1184)
+#1186 := [rewrite]: #1185
+#2636 := [monotonicity #1186]: #2635
+#2652 := [monotonicity #2649 #2636]: #2651
+#2657 := [trans #2652 #2655]: #2656
+#2645 := [asserted]: #402
+#2660 := [mp #2645 #2657]: #2653
+#3566 := [unit-resolution #2660 #3564]: #2633
+#1190 := (or #1037 #1184)
+#164 := (= f50 f1)
+#199 := (or #198 #164)
+#1193 := (iff #199 #1190)
+#1187 := (or #1184 #1037)
+#1191 := (iff #1187 #1190)
+#1192 := [rewrite]: #1191
+#1188 := (iff #199 #1187)
+#1038 := (iff #164 #1037)
+#1039 := [rewrite]: #1038
+#1189 := [monotonicity #1186 #1039]: #1188
+#1194 := [trans #1189 #1192]: #1193
+#1183 := [asserted]: #199
+#1197 := [mp #1183 #1194]: #1190
+#3567 := [unit-resolution #1197 #3566]: #1037
+#2342 := (not #1037)
+#2345 := (or #2338 #2342)
+#360 := (not #164)
+#162 := (= f49 f1)
+#359 := (not #162)
+#361 := (or #359 #360)
+#2346 := (iff #361 #2345)
+#2343 := (iff #360 #2342)
+#2344 := [monotonicity #1039]: #2343
+#2340 := (iff #359 #2338)
+#1035 := (iff #162 #1034)
+#1036 := [rewrite]: #1035
+#2341 := [monotonicity #1036]: #2340
+#2347 := [monotonicity #2341 #2344]: #2346
+#2337 := [asserted]: #361
+#2350 := [mp #2337 #2347]: #2345
+#3568 := [unit-resolution #2350 #3567]: #2338
+#1078 := (or #908 #1034 #1058 #1061)
+#132 := (= f41 f1)
+#171 := (or #162 #132)
+#172 := (or #170 #171)
+#173 := (or #168 #172)
+#1081 := (iff #173 #1078)
+#1067 := (or #908 #1034)
+#1072 := (or #1061 #1067)
+#1075 := (or #1058 #1072)
+#1079 := (iff #1075 #1078)
+#1080 := [rewrite]: #1079
+#1076 := (iff #173 #1075)
+#1073 := (iff #172 #1072)
+#1070 := (iff #171 #1067)
+#1064 := (or #1034 #908)
+#1068 := (iff #1064 #1067)
+#1069 := [rewrite]: #1068
+#1065 := (iff #171 #1064)
+#909 := (iff #132 #908)
+#910 := [rewrite]: #909
+#1066 := [monotonicity #1036 #910]: #1065
+#1071 := [trans #1066 #1069]: #1070
+#1074 := [monotonicity #1063 #1071]: #1073
+#1077 := [monotonicity #1060 #1074]: #1076
+#1082 := [trans #1077 #1080]: #1081
+#1057 := [asserted]: #173
+#1083 := [mp #1057 #1082]: #1078
+#3569 := [unit-resolution #1083 #3568 #3181 #3565]: #908
+#2065 := (not #908)
+#2106 := (or #1757 #2065)
+#94 := (= f30 f1)
+#283 := (not #94)
+#324 := (not #132)
+#329 := (or #324 #283)
+#2109 := (iff #329 #2106)
+#2102 := (or #2065 #1757)
+#2107 := (iff #2102 #2106)
+#2108 := [rewrite]: #2107
+#2104 := (iff #329 #2102)
+#1758 := (iff #283 #1757)
+#756 := (iff #94 #755)
+#757 := [rewrite]: #756
+#1759 := [monotonicity #757]: #1758
+#2066 := (iff #324 #2065)
+#2067 := [monotonicity #910]: #2066
+#2105 := [monotonicity #2067 #1759]: #2104
+#2110 := [trans #2105 #2108]: #2109
+#2101 := [asserted]: #329
+#2113 := [mp #2101 #2110]: #2106
+#3570 := [unit-resolution #2113 #3569]: #1757
+decl f27 :: S1
+#85 := f27
+#728 := (= f1 f27)
+#1722 := (not #728)
+decl f28 :: S1
+#87 := f28
+#731 := (= f1 f28)
+decl f39 :: S1
+#125 := f39
+#884 := (= f1 f39)
+#2034 := (not #884)
+#2363 := (or #2034 #2342)
+#126 := (= f39 f1)
+#319 := (not #126)
+#363 := (or #360 #319)
+#2366 := (iff #363 #2363)
+#2359 := (or #2342 #2034)
+#2364 := (iff #2359 #2363)
+#2365 := [rewrite]: #2364
+#2361 := (iff #363 #2359)
+#2035 := (iff #319 #2034)
+#885 := (iff #126 #884)
+#886 := [rewrite]: #885
+#2036 := [monotonicity #886]: #2035
+#2362 := [monotonicity #2344 #2036]: #2361
+#2367 := [trans #2362 #2365]: #2366
+#2358 := [asserted]: #363
+#2370 := [mp #2358 #2367]: #2363
+#3571 := [unit-resolution #2370 #3567]: #2034
+decl f38 :: S1
+#123 := f38
+#881 := (= f1 f38)
+#2030 := (not #881)
+#2096 := (or #2030 #2065)
+#124 := (= f38 f1)
+#318 := (not #124)
+#328 := (or #324 #318)
+#2099 := (iff #328 #2096)
+#2092 := (or #2065 #2030)
+#2097 := (iff #2092 #2096)
+#2098 := [rewrite]: #2097
+#2094 := (iff #328 #2092)
+#2032 := (iff #318 #2030)
+#882 := (iff #124 #881)
+#883 := [rewrite]: #882
+#2033 := [monotonicity #883]: #2032
+#2095 := [monotonicity #2067 #2033]: #2094
+#2100 := [trans #2095 #2098]: #2099
+#2091 := [asserted]: #328
+#2103 := [mp #2091 #2100]: #2096
+#3572 := [unit-resolution #2103 #3569]: #2030
+#898 := (or #731 #881 #884)
+#88 := (= f28 f1)
+#127 := (or #126 #88)
+#128 := (or #124 #127)
+#901 := (iff #128 #898)
+#890 := (or #731 #884)
+#895 := (or #881 #890)
+#899 := (iff #895 #898)
+#900 := [rewrite]: #899
+#896 := (iff #128 #895)
+#893 := (iff #127 #890)
+#887 := (or #884 #731)
+#891 := (iff #887 #890)
+#892 := [rewrite]: #891
+#888 := (iff #127 #887)
+#732 := (iff #88 #731)
+#733 := [rewrite]: #732
+#889 := [monotonicity #886 #733]: #888
+#894 := [trans #889 #892]: #893
+#897 := [monotonicity #883 #894]: #896
+#902 := [trans #897 #900]: #901
+#880 := [asserted]: #128
+#903 := [mp #880 #902]: #898
+#3573 := [unit-resolution #903 #3572 #3571]: #731
+#1726 := (not #731)
+#1729 := (or #1722 #1726)
+#278 := (not #88)
+#86 := (= f27 f1)
+#277 := (not #86)
+#279 := (or #277 #278)
+#1730 := (iff #279 #1729)
+#1727 := (iff #278 #1726)
+#1728 := [monotonicity #733]: #1727
+#1724 := (iff #277 #1722)
+#729 := (iff #86 #728)
+#730 := [rewrite]: #729
+#1725 := [monotonicity #730]: #1724
+#1731 := [monotonicity #1725 #1728]: #1730
+#1721 := [asserted]: #279
+#1734 := [mp #1721 #1731]: #1729
+#3574 := [unit-resolution #1734 #3573]: #1722
+#3507 := (or #602 #728 #755)
+decl f29 :: S1
+#91 := f29
+#752 := (= f1 f29)
+#1753 := (not #752)
+decl f32 :: S1
+#100 := f32
+#782 := (= f1 f32)
+#1818 := (not #782)
+#3138 := [hypothesis]: #1818
+decl f42 :: S1
+#136 := f42
+#932 := (= f1 f42)
+#2122 := (not #932)
+decl f44 :: S1
+#143 := f44
+#959 := (= f1 f44)
+#3323 := (or #514 #782)
+decl f8 :: S1
+#22 := f8
+#469 := (= f1 f8)
+decl f7 :: S1
+#20 := f7
+#465 := (= f1 f7)
+#1278 := (not #465)
+decl f9 :: S1
+#26 := f9
+#490 := (= f1 f9)
+#1339 := (not #514)
+#2940 := [hypothesis]: #1339
+decl f12 :: S1
+#34 := f12
+#517 := (= f1 f12)
+#1343 := (not #517)
+decl f22 :: S1
+#67 := f22
+#653 := (= f1 f22)
+#1571 := (not #656)
+#3297 := (or #1571 #782 #514)
+#2248 := (not #989)
+#2923 := [hypothesis]: #656
+#1612 := (or #1343 #1571)
+#35 := (= f12 f1)
+#225 := (not #35)
+#70 := (= f23 f1)
+#258 := (not #70)
+#263 := (or #258 #225)
+#1615 := (iff #263 #1612)
+#1608 := (or #1571 #1343)
+#1613 := (iff #1608 #1612)
+#1614 := [rewrite]: #1613
+#1610 := (iff #263 #1608)
+#1344 := (iff #225 #1343)
+#518 := (iff #35 #517)
+#519 := [rewrite]: #518
+#1345 := [monotonicity #519]: #1344
+#1572 := (iff #258 #1571)
+#657 := (iff #70 #656)
+#658 := [rewrite]: #657
+#1573 := [monotonicity #658]: #1572
+#1611 := [monotonicity #1573 #1345]: #1610
+#1616 := [trans #1611 #1614]: #1615
+#1607 := [asserted]: #263
+#1619 := [mp #1607 #1616]: #1612
+#2918 := [unit-resolution #1619 #2923]: #1343
+#531 := (or #490 #514 #517)
+#27 := (= f9 f1)
+#36 := (or #35 #27)
+#33 := (= f11 f1)
+#37 := (or #33 #36)
+#534 := (iff #37 #531)
+#523 := (or #490 #517)
+#528 := (or #514 #523)
+#532 := (iff #528 #531)
+#533 := [rewrite]: #532
+#529 := (iff #37 #528)
+#526 := (iff #36 #523)
+#520 := (or #517 #490)
+#524 := (iff #520 #523)
+#525 := [rewrite]: #524
+#521 := (iff #36 #520)
+#491 := (iff #27 #490)
+#492 := [rewrite]: #491
+#522 := [monotonicity #519 #492]: #521
+#527 := [trans #522 #525]: #526
+#515 := (iff #33 #514)
+#516 := [rewrite]: #515
+#530 := [monotonicity #516 #527]: #529
+#535 := [trans #530 #533]: #534
+#513 := [asserted]: #37
+#536 := [mp #513 #535]: #531
+#2919 := [unit-resolution #536 #2918 #2940]: #490
+#1308 := (not #490)
+#1323 := (or #1278 #1308)
+#21 := (= f7 f1)
+#214 := (not #21)
+#219 := (not #27)
+#222 := (or #219 #214)
+#1326 := (iff #222 #1323)
+#1319 := (or #1308 #1278)
+#1324 := (iff #1319 #1323)
+#1325 := [rewrite]: #1324
+#1321 := (iff #222 #1319)
+#1279 := (iff #214 #1278)
+#467 := (iff #21 #465)
+#468 := [rewrite]: #467
+#1280 := [monotonicity #468]: #1279
+#1310 := (iff #219 #1308)
+#1311 := [monotonicity #492]: #1310
+#1322 := [monotonicity #1311 #1280]: #1321
+#1327 := [trans #1322 #1325]: #1326
+#1318 := [asserted]: #222
+#1330 := [mp #1318 #1327]: #1323
+#3285 := [unit-resolution #1330 #2919]: #1278
+#2781 := (or #465 #469)
+decl f3 :: S1
+#8 := f3
+#434 := (= f1 f3)
+#483 := (or #434 #465 #469)
+#2784 := (iff #483 #2781)
+#2778 := (or false #465 #469)
+#2782 := (iff #2778 #2781)
+#2783 := [rewrite]: #2782
+#2779 := (iff #483 #2778)
+#2769 := (iff #434 false)
+#437 := (not #434)
+#9 := (= f3 f1)
+#10 := (not #9)
+#438 := (iff #10 #437)
+#435 := (iff #9 #434)
+#436 := [rewrite]: #435
+#439 := [monotonicity #436]: #438
+#433 := [asserted]: #10
+#442 := [mp #433 #439]: #437
+#2771 := [iff-false #442]: #2769
+#2780 := [monotonicity #2771]: #2779
+#2785 := [trans #2780 #2783]: #2784
+#23 := (= f8 f1)
+#24 := (or #23 #9)
+#25 := (or #21 #24)
+#486 := (iff #25 #483)
+#475 := (or #434 #469)
+#480 := (or #465 #475)
+#484 := (iff #480 #483)
+#485 := [rewrite]: #484
+#481 := (iff #25 #480)
+#478 := (iff #24 #475)
+#472 := (or #469 #434)
+#476 := (iff #472 #475)
+#477 := [rewrite]: #476
+#473 := (iff #24 #472)
+#470 := (iff #23 #469)
+#471 := [rewrite]: #470
+#474 := [monotonicity #471 #436]: #473
+#479 := [trans #474 #477]: #478
+#482 := [monotonicity #468 #479]: #481
+#487 := [trans #482 #485]: #486
+#464 := [asserted]: #25
+#488 := [mp #464 #487]: #483
+#2786 := [mp #488 #2785]: #2781
+#3286 := [unit-resolution #2786 #3285]: #469
+decl f21 :: S1
+#62 := f21
+#629 := (= f1 f21)
+decl f18 :: S1
+#53 := f18
+#599 := (= f1 f18)
+#1445 := (not #599)
+#1281 := (not #469)
+#1470 := (or #1281 #1445)
+#215 := (not #23)
+#54 := (= f18 f1)
+#241 := (not #54)
+#245 := (or #241 #215)
+#1473 := (iff #245 #1470)
+#1466 := (or #1445 #1281)
+#1471 := (iff #1466 #1470)
+#1472 := [rewrite]: #1471
+#1468 := (iff #245 #1466)
+#1282 := (iff #215 #1281)
+#1283 := [monotonicity #471]: #1282
+#1447 := (iff #241 #1445)
+#600 := (iff #54 #599)
+#601 := [rewrite]: #600
+#1448 := [monotonicity #601]: #1447
+#1469 := [monotonicity #1448 #1283]: #1468
+#1474 := [trans #1469 #1472]: #1473
+#1465 := [asserted]: #245
+#1477 := [mp #1465 #1474]: #1470
+#3287 := [unit-resolution #1477 #3286]: #1445
+#2917 := (or #1571 #514 #599 #629)
+decl f10 :: S1
+#28 := f10
+#493 := (= f1 f10)
+#1510 := (not #629)
+#2944 := [hypothesis]: #1510
+#3061 := [hypothesis]: #1445
+decl f20 :: S1
+#60 := f20
+#626 := (= f1 f20)
+#1506 := (not #626)
+#1602 := (or #1506 #1571)
+#61 := (= f20 f1)
+#249 := (not #61)
+#262 := (or #258 #249)
+#1605 := (iff #262 #1602)
+#1598 := (or #1571 #1506)
+#1603 := (iff #1598 #1602)
+#1604 := [rewrite]: #1603
+#1600 := (iff #262 #1598)
+#1508 := (iff #249 #1506)
+#627 := (iff #61 #626)
+#628 := [rewrite]: #627
+#1509 := [monotonicity #628]: #1508
+#1601 := [monotonicity #1573 #1509]: #1600
+#1606 := [trans #1601 #1604]: #1605
+#1597 := [asserted]: #262
+#1609 := [mp #1597 #1606]: #1602
+#2920 := [unit-resolution #1609 #2923]: #1506
+#646 := (or #493 #599 #626 #629)
+#29 := (= f10 f1)
+#64 := (or #54 #29)
+#63 := (= f21 f1)
+#65 := (or #63 #64)
+#66 := (or #61 #65)
+#649 := (iff #66 #646)
+#635 := (or #493 #599)
+#640 := (or #629 #635)
+#643 := (or #626 #640)
+#647 := (iff #643 #646)
+#648 := [rewrite]: #647
+#644 := (iff #66 #643)
+#641 := (iff #65 #640)
+#638 := (iff #64 #635)
+#632 := (or #599 #493)
+#636 := (iff #632 #635)
+#637 := [rewrite]: #636
+#633 := (iff #64 #632)
+#494 := (iff #29 #493)
+#495 := [rewrite]: #494
+#634 := [monotonicity #601 #495]: #633
+#639 := [trans #634 #637]: #638
+#630 := (iff #63 #629)
+#631 := [rewrite]: #630
+#642 := [monotonicity #631 #639]: #641
+#645 := [monotonicity #628 #642]: #644
+#650 := [trans #645 #648]: #649
+#625 := [asserted]: #66
+#651 := [mp #625 #650]: #646
+#2921 := [unit-resolution #651 #2920 #3061 #2944]: #493
+#1312 := (not #493)
+#1315 := (or #1308 #1312)
+#220 := (not #29)
+#221 := (or #219 #220)
+#1316 := (iff #221 #1315)
+#1313 := (iff #220 #1312)
+#1314 := [monotonicity #495]: #1313
+#1317 := [monotonicity #1311 #1314]: #1316
+#1307 := [asserted]: #221
+#1320 := [mp #1307 #1317]: #1315
+#2916 := [unit-resolution #1320 #2919 #2921]: false
+#2914 := [lemma #2916]: #2917
+#3288 := [unit-resolution #2914 #3287 #2940 #2923]: #629
+#1869 := (or #1510 #1753)
+#250 := (not #63)
+#92 := (= f29 f1)
+#282 := (not #92)
+#297 := (or #282 #250)
+#1872 := (iff #297 #1869)
+#1865 := (or #1753 #1510)
+#1870 := (iff #1865 #1869)
+#1871 := [rewrite]: #1870
+#1867 := (iff #297 #1865)
+#1511 := (iff #250 #1510)
+#1512 := [monotonicity #631]: #1511
+#1755 := (iff #282 #1753)
+#753 := (iff #92 #752)
+#754 := [rewrite]: #753
+#1756 := [monotonicity #754]: #1755
+#1868 := [monotonicity #1756 #1512]: #1867
+#1873 := [trans #1868 #1871]: #1872
+#1864 := [asserted]: #297
+#1876 := [mp #1864 #1873]: #1869
+#3289 := [unit-resolution #1876 #3288]: #1753
+#2829 := (or #1281 #1112 #782 #752)
+#2880 := (or #2556 #782)
+decl f24 :: S1
+#74 := f24
+#680 := (= f1 f24)
+#1628 := (not #680)
+#2915 := [hypothesis]: #1142
+#2912 := [unit-resolution #2564 #2915]: #2552
+#2913 := [unit-resolution #2859 #2912]: #1013
+#2322 := (or #1997 #2305)
+#357 := (or #355 #314)
+#2325 := (iff #357 #2322)
+#2318 := (or #2305 #1997)
+#2323 := (iff #2318 #2322)
+#2324 := [rewrite]: #2323
+#2320 := (iff #357 #2318)
+#2321 := [monotonicity #2308 #2000]: #2320
+#2326 := [trans #2321 #2324]: #2325
+#2317 := [asserted]: #357
+#2329 := [mp #2317 #2326]: #2322
+#2910 := [unit-resolution #2329 #2913]: #1997
+#1936 := (not #833)
+#2597 := (or #2248 #2556)
+#153 := (= f47 f1)
+#348 := (not #153)
+#394 := (or #389 #348)
+#2600 := (iff #394 #2597)
+#2593 := (or #2556 #2248)
+#2598 := (iff #2593 #2597)
+#2599 := [rewrite]: #2598
+#2595 := (iff #394 #2593)
+#2249 := (iff #348 #2248)
+#990 := (iff #153 #989)
+#991 := [rewrite]: #990
+#2250 := [monotonicity #991]: #2249
+#2596 := [monotonicity #2558 #2250]: #2595
+#2601 := [trans #2596 #2599]: #2600
+#2592 := [asserted]: #394
+#2604 := [mp #2592 #2601]: #2597
+#2911 := [unit-resolution #2604 #2915]: #2248
+#2908 := [unit-resolution #2319 #2913]: #2244
+decl f31 :: S1
+#98 := f31
+#779 := (= f1 f31)
+#1814 := (not #779)
+decl f17 :: S1
+#49 := f17
+#578 := (= f1 f17)
+decl f16 :: S1
+#47 := f16
+#574 := (= f1 f16)
+#1414 := (not #574)
+#2946 := (or #1278 #986 #989 #860 #782)
+#3139 := [hypothesis]: #2248
+#3136 := [hypothesis]: #2244
+decl f36 :: S1
+#114 := f36
+#836 := (= f1 f36)
+#1940 := (not #836)
+decl f25 :: S1
+#76 := f25
+#683 := (= f1 f25)
+#3170 := [hypothesis]: #1997
+#2977 := [hypothesis]: #465
+#2974 := [unit-resolution #1330 #2977]: #1308
+#1333 := (or #1278 #1312)
+#223 := (or #220 #214)
+#1336 := (iff #223 #1333)
+#1329 := (or #1312 #1278)
+#1334 := (iff #1329 #1333)
+#1335 := [rewrite]: #1334
+#1331 := (iff #223 #1329)
+#1332 := [monotonicity #1314 #1280]: #1331
+#1337 := [trans #1332 #1335]: #1336
+#1328 := [asserted]: #223
+#1340 := [mp #1328 #1337]: #1333
+#2975 := [unit-resolution #1340 #2977]: #1312
+#3020 := (or #599 #490 #493 #986 #989 #860)
+#3071 := [hypothesis]: #1308
+decl f33 :: S1
+#105 := f33
+#806 := (= f1 f33)
+#1875 := (not #806)
+#3060 := [hypothesis]: #1312
+#3055 := (or #1689 #986 #989 #599 #493 #490)
+decl f14 :: S1
+#40 := f14
+#541 := (= f1 f14)
+#1374 := (not #541)
+#1401 := (not #562)
+#3074 := [hypothesis]: #707
+#1706 := (or #1401 #1689)
+#45 := (= f15 f1)
+#234 := (not #45)
+#82 := (= f26 f1)
+#273 := (not #82)
+#275 := (or #273 #234)
+#1709 := (iff #275 #1706)
+#1702 := (or #1689 #1401)
+#1707 := (iff #1702 #1706)
+#1708 := [rewrite]: #1707
+#1704 := (iff #275 #1702)
+#1403 := (iff #234 #1401)
+#563 := (iff #45 #562)
+#564 := [rewrite]: #563
+#1404 := [monotonicity #564]: #1403
+#1691 := (iff #273 #1689)
+#708 := (iff #82 #707)
+#709 := [rewrite]: #708
+#1692 := [monotonicity #709]: #1691
+#1705 := [monotonicity #1692 #1404]: #1704
+#1710 := [trans #1705 #1708]: #1709
+#1701 := [asserted]: #275
+#1713 := [mp #1701 #1710]: #1706
+#3075 := [unit-resolution #1713 #3074]: #1401
+#568 := (or #538 #562)
+#39 := (= f13 f1)
+#46 := (or #45 #39)
+#571 := (iff #46 #568)
+#565 := (or #562 #538)
+#569 := (iff #565 #568)
+#570 := [rewrite]: #569
+#566 := (iff #46 #565)
+#539 := (iff #39 #538)
+#540 := [rewrite]: #539
+#567 := [monotonicity #564 #540]: #566
+#572 := [trans #567 #570]: #571
+#561 := [asserted]: #46
+#575 := [mp #561 #572]: #568
+#3072 := [unit-resolution #575 #3075]: #538
+#1377 := (or #1370 #1374)
+#41 := (= f14 f1)
+#230 := (not #41)
+#229 := (not #39)
+#231 := (or #229 #230)
+#1378 := (iff #231 #1377)
+#1375 := (iff #230 #1374)
+#542 := (iff #41 #541)
+#543 := [rewrite]: #542
+#1376 := [monotonicity #543]: #1375
+#1372 := (iff #229 #1370)
+#1373 := [monotonicity #540]: #1372
+#1379 := [monotonicity #1373 #1376]: #1378
+#1369 := [asserted]: #231
+#1382 := [mp #1369 #1379]: #1377
+#3073 := [unit-resolution #1382 #3072]: #1374
+#1696 := (or #1628 #1689)
+#75 := (= f24 f1)
+#265 := (not #75)
+#274 := (or #273 #265)
+#1699 := (iff #274 #1696)
+#1693 := (or #1689 #1628)
+#1697 := (iff #1693 #1696)
+#1698 := [rewrite]: #1697
+#1694 := (iff #274 #1693)
+#1630 := (iff #265 #1628)
+#681 := (iff #75 #680)
+#682 := [rewrite]: #681
+#1631 := [monotonicity #682]: #1630
+#1695 := [monotonicity #1692 #1631]: #1694
+#1700 := [trans #1695 #1698]: #1699
+#1688 := [asserted]: #274
+#1703 := [mp #1688 #1700]: #1696
+#3070 := [unit-resolution #1703 #3074]: #1628
+#1567 := (not #653)
+#1385 := (or #1339 #1370)
+#224 := (not #33)
+#232 := (or #229 #224)
+#1388 := (iff #232 #1385)
+#1381 := (or #1370 #1339)
+#1386 := (iff #1381 #1385)
+#1387 := [rewrite]: #1386
+#1383 := (iff #232 #1381)
+#1341 := (iff #224 #1339)
+#1342 := [monotonicity #516]: #1341
+#1384 := [monotonicity #1373 #1342]: #1383
+#1389 := [trans #1384 #1387]: #1388
+#1380 := [asserted]: #232
+#1392 := [mp #1380 #1389]: #1385
+#3068 := [unit-resolution #1392 #3072]: #1339
+#3069 := [unit-resolution #536 #3068 #3071]: #517
+#1592 := (or #1343 #1567)
+#68 := (= f22 f1)
+#257 := (not #68)
+#261 := (or #257 #225)
+#1595 := (iff #261 #1592)
+#1588 := (or #1567 #1343)
+#1593 := (iff #1588 #1592)
+#1594 := [rewrite]: #1593
+#1590 := (iff #261 #1588)
+#1569 := (iff #257 #1567)
+#654 := (iff #68 #653)
+#655 := [rewrite]: #654
+#1570 := [monotonicity #655]: #1569
+#1591 := [monotonicity #1570 #1345]: #1590
+#1596 := [trans #1591 #1594]: #1595
+#1587 := [asserted]: #261
+#1599 := [mp #1587 #1596]: #1592
+#3066 := [unit-resolution #1599 #3069]: #1567
+#700 := (or #541 #653 #680 #683)
+#78 := (or #68 #41)
+#77 := (= f25 f1)
+#79 := (or #77 #78)
+#80 := (or #75 #79)
+#703 := (iff #80 #700)
+#689 := (or #541 #653)
+#694 := (or #683 #689)
+#697 := (or #680 #694)
+#701 := (iff #697 #700)
+#702 := [rewrite]: #701
+#698 := (iff #80 #697)
+#695 := (iff #79 #694)
+#692 := (iff #78 #689)
+#686 := (or #653 #541)
+#690 := (iff #686 #689)
+#691 := [rewrite]: #690
+#687 := (iff #78 #686)
+#688 := [monotonicity #655 #543]: #687
+#693 := [trans #688 #691]: #692
+#684 := (iff #77 #683)
+#685 := [rewrite]: #684
+#696 := [monotonicity #685 #693]: #695
+#699 := [monotonicity #682 #696]: #698
+#704 := [trans #699 #702]: #703
+#679 := [asserted]: #80
+#705 := [mp #679 #704]: #700
+#3067 := [unit-resolution #705 #3066 #3070 #3073]: #683
+#1632 := (not #683)
+#1981 := (or #1632 #1940)
+#266 := (not #77)
+#115 := (= f36 f1)
+#307 := (not #115)
+#312 := (or #307 #266)
+#1984 := (iff #312 #1981)
+#1977 := (or #1940 #1632)
+#1982 := (iff #1977 #1981)
+#1983 := [rewrite]: #1982
+#1979 := (iff #312 #1977)
+#1633 := (iff #266 #1632)
+#1634 := [monotonicity #685]: #1633
+#1941 := (iff #307 #1940)
+#837 := (iff #115 #836)
+#838 := [rewrite]: #837
+#1942 := [monotonicity #838]: #1941
+#1980 := [monotonicity #1942 #1634]: #1979
+#1985 := [trans #1980 #1983]: #1984
+#1976 := [asserted]: #312
+#1988 := [mp #1976 #1985]: #1981
+#3064 := [unit-resolution #1988 #3067]: #1940
+#1006 := (or #836 #959 #986 #989)
+#144 := (= f44 f1)
+#154 := (or #144 #115)
+#155 := (or #153 #154)
+#156 := (or #151 #155)
+#1009 := (iff #156 #1006)
+#995 := (or #836 #959)
+#1000 := (or #989 #995)
+#1003 := (or #986 #1000)
+#1007 := (iff #1003 #1006)
+#1008 := [rewrite]: #1007
+#1004 := (iff #156 #1003)
+#1001 := (iff #155 #1000)
+#998 := (iff #154 #995)
+#992 := (or #959 #836)
+#996 := (iff #992 #995)
+#997 := [rewrite]: #996
+#993 := (iff #154 #992)
+#960 := (iff #144 #959)
+#961 := [rewrite]: #960
+#994 := [monotonicity #961 #838]: #993
+#999 := [trans #994 #997]: #998
+#1002 := [monotonicity #991 #999]: #1001
+#1005 := [monotonicity #988 #1002]: #1004
+#1010 := [trans #1005 #1008]: #1009
+#985 := [asserted]: #156
+#1011 := [mp #985 #1010]: #1006
+#3065 := [unit-resolution #1011 #3064 #3136 #3139]: #959
+#1991 := (or #1632 #1875)
+#106 := (= f33 f1)
+#298 := (not #106)
+#313 := (or #298 #266)
+#1994 := (iff #313 #1991)
+#1987 := (or #1875 #1632)
+#1992 := (iff #1987 #1991)
+#1993 := [rewrite]: #1992
+#1989 := (iff #313 #1987)
+#1877 := (iff #298 #1875)
+#807 := (iff #106 #806)
+#808 := [rewrite]: #807
+#1878 := [monotonicity #808]: #1877
+#1990 := [monotonicity #1878 #1634]: #1989
+#1995 := [trans #1990 #1993]: #1994
+#1986 := [asserted]: #313
+#1998 := [mp #1986 #1995]: #1991
+#3062 := [unit-resolution #1998 #3067]: #1875
+#3063 := [unit-resolution #1619 #3069]: #1571
+#1622 := (or #1343 #1506)
+#264 := (or #249 #225)
+#1625 := (iff #264 #1622)
+#1618 := (or #1506 #1343)
+#1623 := (iff #1618 #1622)
+#1624 := [rewrite]: #1623
+#1620 := (iff #264 #1618)
+#1621 := [monotonicity #1509 #1345]: #1620
+#1626 := [trans #1621 #1624]: #1625
+#1617 := [asserted]: #264
+#1629 := [mp #1617 #1626]: #1622
+#3058 := [unit-resolution #1629 #3069]: #1506
+#3059 := [unit-resolution #651 #3058 #3061 #3060]: #629
+#1839 := (or #1510 #1814)
+#99 := (= f31 f1)
+#290 := (not #99)
+#294 := (or #290 #250)
+#1842 := (iff #294 #1839)
+#1835 := (or #1814 #1510)
+#1840 := (iff #1835 #1839)
+#1841 := [rewrite]: #1840
+#1837 := (iff #294 #1835)
+#1816 := (iff #290 #1814)
+#780 := (iff #99 #779)
+#781 := [rewrite]: #780
+#1817 := [monotonicity #781]: #1816
+#1838 := [monotonicity #1817 #1512]: #1837
+#1843 := [trans #1838 #1841]: #1842
+#1834 := [asserted]: #294
+#1846 := [mp #1834 #1843]: #1839
+#3056 := [unit-resolution #1846 #3059]: #1814
+#826 := (or #656 #779 #806 #809)
+#109 := (or #99 #70)
+#108 := (= f34 f1)
+#110 := (or #108 #109)
+#111 := (or #106 #110)
+#829 := (iff #111 #826)
+#815 := (or #656 #779)
+#820 := (or #809 #815)
+#823 := (or #806 #820)
+#827 := (iff #823 #826)
+#828 := [rewrite]: #827
+#824 := (iff #111 #823)
+#821 := (iff #110 #820)
+#818 := (iff #109 #815)
+#812 := (or #779 #656)
+#816 := (iff #812 #815)
+#817 := [rewrite]: #816
+#813 := (iff #109 #812)
+#814 := [monotonicity #781 #658]: #813
+#819 := [trans #814 #817]: #818
+#810 := (iff #108 #809)
+#811 := [rewrite]: #810
+#822 := [monotonicity #811 #819]: #821
+#825 := [monotonicity #808 #822]: #824
+#830 := [trans #825 #828]: #829
+#805 := [asserted]: #111
+#831 := [mp #805 #830]: #826
+#3057 := [unit-resolution #831 #3056 #3063 #3062]: #809
+#2183 := (not #959)
+#2208 := (or #1879 #2183)
+#299 := (not #108)
+#339 := (not #144)
+#343 := (or #339 #299)
+#2211 := (iff #343 #2208)
+#2204 := (or #2183 #1879)
+#2209 := (iff #2204 #2208)
+#2210 := [rewrite]: #2209
+#2206 := (iff #343 #2204)
+#1880 := (iff #299 #1879)
+#1881 := [monotonicity #811]: #1880
+#2185 := (iff #339 #2183)
+#2186 := [monotonicity #961]: #2185
+#2207 := [monotonicity #2186 #1881]: #2206
+#2212 := [trans #2207 #2210]: #2211
+#2203 := [asserted]: #343
+#2215 := [mp #2203 #2212]: #2208
+#3054 := [unit-resolution #2215 #3057 #3065]: false
+#3052 := [lemma #3054]: #3055
+#3041 := [unit-resolution #3052 #3061 #3139 #3136 #3060 #3071]: #1689
+#874 := (or #707 #833 #860)
+#113 := (= f35 f1)
+#121 := (or #113 #82)
+#122 := (or #120 #121)
+#877 := (iff #122 #874)
+#866 := (or #707 #833)
+#871 := (or #860 #866)
+#875 := (iff #871 #874)
+#876 := [rewrite]: #875
+#872 := (iff #122 #871)
+#869 := (iff #121 #866)
+#863 := (or #833 #707)
+#867 := (iff #863 #866)
+#868 := [rewrite]: #867
+#864 := (iff #121 #863)
+#834 := (iff #113 #833)
+#835 := [rewrite]: #834
+#865 := [monotonicity #835 #709]: #864
+#870 := [trans #865 #868]: #869
+#873 := [monotonicity #862 #870]: #872
+#878 := [trans #873 #876]: #877
+#859 := [asserted]: #122
+#879 := [mp #859 #878]: #874
+#3038 := [unit-resolution #879 #3041 #3170]: #833
+#1951 := (or #1875 #1936)
+#306 := (not #113)
+#309 := (or #306 #298)
+#1954 := (iff #309 #1951)
+#1947 := (or #1936 #1875)
+#1952 := (iff #1947 #1951)
+#1953 := [rewrite]: #1952
+#1949 := (iff #309 #1947)
+#1938 := (iff #306 #1936)
+#1939 := [monotonicity #835]: #1938
+#1950 := [monotonicity #1939 #1878]: #1949
+#1955 := [trans #1950 #1953]: #1954
+#1946 := [asserted]: #309
+#1958 := [mp #1946 #1955]: #1951
+#3039 := [unit-resolution #1958 #3038]: #1875
+#1943 := (or #1936 #1940)
+#308 := (or #306 #307)
+#1944 := (iff #308 #1943)
+#1945 := [monotonicity #1939 #1942]: #1944
+#1935 := [asserted]: #308
+#1948 := [mp #1935 #1945]: #1943
+#3036 := [unit-resolution #1948 #3038]: #1940
+#3037 := [unit-resolution #1011 #3036 #3136 #3139]: #959
+#3034 := [unit-resolution #2215 #3037]: #1879
+#1961 := (or #1632 #1936)
+#310 := (or #306 #266)
+#1964 := (iff #310 #1961)
+#1957 := (or #1936 #1632)
+#1962 := (iff #1957 #1961)
+#1963 := [rewrite]: #1962
+#1959 := (iff #310 #1957)
+#1960 := [monotonicity #1939 #1634]: #1959
+#1965 := [trans #1960 #1963]: #1964
+#1956 := [asserted]: #310
+#1968 := [mp #1956 #1965]: #1961
+#3035 := [unit-resolution #1968 #3038]: #1632
+#3043 := (or #1506 #683 #490)
+#3053 := [hypothesis]: #626
+#3050 := [unit-resolution #1629 #3053]: #1343
+#3051 := [unit-resolution #536 #3050 #3071]: #514
+#3048 := [unit-resolution #1392 #3051]: #1370
+#3049 := [unit-resolution #575 #3048]: #562
+#1582 := (or #1506 #1567)
+#260 := (or #257 #249)
+#1585 := (iff #260 #1582)
+#1578 := (or #1567 #1506)
+#1583 := (iff #1578 #1582)
+#1584 := [rewrite]: #1583
+#1580 := (iff #260 #1578)
+#1581 := [monotonicity #1570 #1509]: #1580
+#1586 := [trans #1581 #1584]: #1585
+#1577 := [asserted]: #260
+#1589 := [mp #1577 #1586]: #1582
+#3046 := [unit-resolution #1589 #3053]: #1567
+#3047 := [hypothesis]: #1632
+#1395 := (or #1339 #1374)
+#233 := (or #230 #224)
+#1398 := (iff #233 #1395)
+#1391 := (or #1374 #1339)
+#1396 := (iff #1391 #1395)
+#1397 := [rewrite]: #1396
+#1393 := (iff #233 #1391)
+#1394 := [monotonicity #1376 #1342]: #1393
+#1399 := [trans #1394 #1397]: #1398
+#1390 := [asserted]: #233
+#1402 := [mp #1390 #1399]: #1395
+#3044 := [unit-resolution #1402 #3051]: #1374
+#3045 := [unit-resolution #705 #3044 #3047 #3046]: #680
+#1716 := (or #1401 #1628)
+#276 := (or #265 #234)
+#1719 := (iff #276 #1716)
+#1712 := (or #1628 #1401)
+#1717 := (iff #1712 #1716)
+#1718 := [rewrite]: #1717
+#1714 := (iff #276 #1712)
+#1715 := [monotonicity #1631 #1404]: #1714
+#1720 := [trans #1715 #1718]: #1719
+#1711 := [asserted]: #276
+#1723 := [mp #1711 #1720]: #1716
+#3042 := [unit-resolution #1723 #3045 #3049]: false
+#3040 := [lemma #3042]: #3043
+#3032 := [unit-resolution #3040 #3035 #3071]: #1506
+#3033 := [unit-resolution #651 #3032 #3061 #3060]: #629
+#3030 := [unit-resolution #1846 #3033]: #1814
+#3031 := [unit-resolution #831 #3030 #3034 #3039]: #656
+#3028 := [unit-resolution #1619 #3031]: #1343
+#3029 := [unit-resolution #536 #3028 #3071]: #514
+#3026 := [unit-resolution #1392 #3029]: #1370
+#3027 := [unit-resolution #575 #3026]: #562
+#1574 := (or #1567 #1571)
+#259 := (or #257 #258)
+#1575 := (iff #259 #1574)
+#1576 := [monotonicity #1570 #1573]: #1575
+#1566 := [asserted]: #259
+#1579 := [mp #1566 #1576]: #1574
+#3024 := [unit-resolution #1579 #3031]: #1567
+#3025 := [unit-resolution #1402 #3029]: #1374
+#3022 := [unit-resolution #705 #3025 #3035 #3024]: #680
+#3023 := [unit-resolution #1723 #3022 #3027]: false
+#3021 := [lemma #3023]: #3020
+#2972 := [unit-resolution #3021 #2974 #2975 #3136 #3139 #3170]: #599
+#1460 := (or #1414 #1445)
+#48 := (= f16 f1)
+#236 := (not #48)
+#244 := (or #241 #236)
+#1463 := (iff #244 #1460)
+#1456 := (or #1445 #1414)
+#1461 := (iff #1456 #1460)
+#1462 := [rewrite]: #1461
+#1458 := (iff #244 #1456)
+#1416 := (iff #236 #1414)
+#576 := (iff #48 #574)
+#577 := [rewrite]: #576
+#1417 := [monotonicity #577]: #1416
+#1459 := [monotonicity #1448 #1417]: #1458
+#1464 := [trans #1459 #1462]: #1463
+#1455 := [asserted]: #244
+#1467 := [mp #1455 #1464]: #1460
+#2973 := [unit-resolution #1467 #2972]: #1414
+#2800 := (or #574 #578)
+decl f4 :: S1
+#11 := f4
+#441 := (= f1 f4)
+#592 := (or #441 #574 #578)
+#2803 := (iff #592 #2800)
+#2797 := (or false #574 #578)
+#2801 := (iff #2797 #2800)
+#2802 := [rewrite]: #2801
+#2798 := (iff #592 #2797)
+#2772 := (iff #441 false)
+#445 := (not #441)
+#12 := (= f4 f1)
+#13 := (not #12)
+#446 := (iff #13 #445)
+#443 := (iff #12 #441)
+#444 := [rewrite]: #443
+#447 := [monotonicity #444]: #446
+#440 := [asserted]: #13
+#450 := [mp #440 #447]: #445
+#2773 := [iff-false #450]: #2772
+#2799 := [monotonicity #2773]: #2798
+#2804 := [trans #2799 #2802]: #2803
+#50 := (= f17 f1)
+#51 := (or #50 #12)
+#52 := (or #48 #51)
+#595 := (iff #52 #592)
+#584 := (or #441 #578)
+#589 := (or #574 #584)
+#593 := (iff #589 #592)
+#594 := [rewrite]: #593
+#590 := (iff #52 #589)
+#587 := (iff #51 #584)
+#581 := (or #578 #441)
+#585 := (iff #581 #584)
+#586 := [rewrite]: #585
+#582 := (iff #51 #581)
+#579 := (iff #50 #578)
+#580 := [rewrite]: #579
+#583 := [monotonicity #580 #444]: #582
+#588 := [trans #583 #586]: #587
+#591 := [monotonicity #577 #588]: #590
+#596 := [trans #591 #594]: #595
+#573 := [asserted]: #52
+#597 := [mp #573 #596]: #592
+#2805 := [mp #597 #2804]: #2800
+#2970 := [unit-resolution #2805 #2973]: #578
+#1418 := (not #578)
+#1737 := (or #1418 #1722)
+#237 := (not #50)
+#280 := (or #277 #237)
+#1740 := (iff #280 #1737)
+#1733 := (or #1722 #1418)
+#1738 := (iff #1733 #1737)
+#1739 := [rewrite]: #1738
+#1735 := (iff #280 #1733)
+#1419 := (iff #237 #1418)
+#1420 := [monotonicity #580]: #1419
+#1736 := [monotonicity #1725 #1420]: #1735
+#1741 := [trans #1736 #1739]: #1740
+#1732 := [asserted]: #280
+#1744 := [mp #1732 #1741]: #1737
+#2971 := [unit-resolution #1744 #2970]: #1722
+#1449 := (not #602)
+#1452 := (or #1445 #1449)
+#56 := (= f19 f1)
+#242 := (not #56)
+#243 := (or #241 #242)
+#1453 := (iff #243 #1452)
+#1450 := (iff #242 #1449)
+#603 := (iff #56 #602)
+#604 := [rewrite]: #603
+#1451 := [monotonicity #604]: #1450
+#1454 := [monotonicity #1448 #1451]: #1453
+#1444 := [asserted]: #243
+#1457 := [mp #1444 #1454]: #1452
+#2968 := [unit-resolution #1457 #2972]: #1449
+#3076 := (or #2122 #860 #986 #989)
+#3103 := [hypothesis]: #932
+#2198 := (or #2122 #2183)
+#137 := (= f42 f1)
+#331 := (not #137)
+#342 := (or #339 #331)
+#2201 := (iff #342 #2198)
+#2194 := (or #2183 #2122)
+#2199 := (iff #2194 #2198)
+#2200 := [rewrite]: #2199
+#2196 := (iff #342 #2194)
+#2124 := (iff #331 #2122)
+#933 := (iff #137 #932)
+#934 := [rewrite]: #933
+#2125 := [monotonicity #934]: #2124
+#2197 := [monotonicity #2186 #2125]: #2196
+#2202 := [trans #2197 #2200]: #2201
+#2193 := [asserted]: #342
+#2205 := [mp #2193 #2202]: #2198
+#3100 := [unit-resolution #2205 #3103]: #2183
+#3101 := [unit-resolution #1011 #3100 #3136 #3139]: #836
+#3098 := [unit-resolution #1948 #3101]: #1936
+#3099 := [unit-resolution #879 #3098 #3170]: #707
+#3096 := [unit-resolution #1713 #3099]: #1401
+#3097 := [unit-resolution #575 #3096]: #538
+#3094 := [unit-resolution #1392 #3097]: #1339
+#3095 := [unit-resolution #1988 #3101]: #1632
+#3092 := [unit-resolution #1703 #3099]: #1628
+#3093 := [unit-resolution #1382 #3097]: #1374
+#3090 := [unit-resolution #705 #3093 #3092 #3095]: #653
+#3091 := [unit-resolution #1599 #3090]: #1343
+#3088 := [unit-resolution #536 #3091 #3094]: #490
+#3089 := [unit-resolution #1320 #3088]: #1312
+#3086 := [unit-resolution #1589 #3090]: #1506
+#1971 := (or #1875 #1940)
+#311 := (or #307 #298)
+#1974 := (iff #311 #1971)
+#1967 := (or #1940 #1875)
+#1972 := (iff #1967 #1971)
+#1973 := [rewrite]: #1972
+#1969 := (iff #311 #1967)
+#1970 := [monotonicity #1942 #1878]: #1969
+#1975 := [trans #1970 #1973]: #1974
+#1966 := [asserted]: #311
+#1978 := [mp #1966 #1975]: #1971
+#3087 := [unit-resolution #1978 #3101]: #1875
+#2238 := (or #1879 #2122)
+#346 := (or #331 #299)
+#2241 := (iff #346 #2238)
+#2234 := (or #2122 #1879)
+#2239 := (iff #2234 #2238)
+#2240 := [rewrite]: #2239
+#2236 := (iff #346 #2234)
+#2237 := [monotonicity #2125 #1881]: #2236
+#2242 := [trans #2237 #2240]: #2241
+#2233 := [asserted]: #346
+#2245 := [mp #2233 #2242]: #2238
+#3084 := [unit-resolution #2245 #3103]: #1879
+#3085 := [unit-resolution #1579 #3090]: #1571
+#3082 := [unit-resolution #831 #3085 #3084 #3087]: #779
+#3083 := [unit-resolution #1846 #3082]: #1510
+#3080 := [unit-resolution #651 #3083 #3086 #3089]: #599
+#3081 := [unit-resolution #1330 #3088]: #1278
+#3078 := [unit-resolution #2786 #3081]: #469
+#3079 := [unit-resolution #1477 #3078 #3080]: false
+#3077 := [lemma #3079]: #3076
+#2969 := [unit-resolution #3077 #3170 #3136 #3139]: #2122
+#1747 := (or #1418 #1726)
+#281 := (or #278 #237)
+#1750 := (iff #281 #1747)
+#1743 := (or #1726 #1418)
+#1748 := (iff #1743 #1747)
+#1749 := [rewrite]: #1748
+#1745 := (iff #281 #1743)
+#1746 := [monotonicity #1728 #1420]: #1745
+#1751 := [trans #1746 #1749]: #1750
+#1742 := [asserted]: #281
+#1754 := [mp #1742 #1751]: #1747
+#2966 := [unit-resolution #1754 #2970]: #1726
+#3004 := (or #1757 #731 #782 #932)
+#3018 := [hypothesis]: #1726
+#3019 := [hypothesis]: #755
+#2116 := (or #1757 #2030)
+#330 := (or #318 #283)
+#2119 := (iff #330 #2116)
+#2112 := (or #2030 #1757)
+#2117 := (iff #2112 #2116)
+#2118 := [rewrite]: #2117
+#2114 := (iff #330 #2112)
+#2115 := [monotonicity #2033 #1759]: #2114
+#2120 := [trans #2115 #2118]: #2119
+#2111 := [asserted]: #330
+#2123 := [mp #2111 #2120]: #2116
+#3016 := [unit-resolution #2123 #3019]: #2030
+#3017 := [unit-resolution #903 #3016 #3018]: #884
+#2353 := (or #2034 #2338)
+#362 := (or #359 #319)
+#2356 := (iff #362 #2353)
+#2349 := (or #2338 #2034)
+#2354 := (iff #2349 #2353)
+#2355 := [rewrite]: #2354
+#2351 := (iff #362 #2349)
+#2352 := [monotonicity #2341 #2036]: #2351
+#2357 := [trans #2352 #2355]: #2356
+#2348 := [asserted]: #362
+#2360 := [mp #2348 #2357]: #2353
+#3014 := [unit-resolution #2360 #3017]: #2338
+#3015 := [unit-resolution #2113 #3019]: #2065
+decl f43 :: S1
+#138 := f43
+#935 := (= f1 f43)
+#3012 := [hypothesis]: #2122
+decl f40 :: S1
+#129 := f40
+#905 := (= f1 f40)
+#2061 := (not #905)
+#2086 := (or #1757 #2061)
+#130 := (= f40 f1)
+#323 := (not #130)
+#327 := (or #323 #283)
+#2089 := (iff #327 #2086)
+#2082 := (or #2061 #1757)
+#2087 := (iff #2082 #2086)
+#2088 := [rewrite]: #2087
+#2084 := (iff #327 #2082)
+#2063 := (iff #323 #2061)
+#906 := (iff #130 #905)
+#907 := [rewrite]: #906
+#2064 := [monotonicity #907]: #2063
+#2085 := [monotonicity #2064 #1759]: #2084
+#2090 := [trans #2085 #2088]: #2089
+#2081 := [asserted]: #327
+#2093 := [mp #2081 #2090]: #2086
+#3013 := [unit-resolution #2093 #3019]: #2061
+#952 := (or #782 #905 #932 #935)
+#101 := (= f32 f1)
+#140 := (or #130 #101)
+#139 := (= f43 f1)
+#141 := (or #139 #140)
+#142 := (or #137 #141)
+#955 := (iff #142 #952)
+#941 := (or #782 #905)
+#946 := (or #935 #941)
+#949 := (or #932 #946)
+#953 := (iff #949 #952)
+#954 := [rewrite]: #953
+#950 := (iff #142 #949)
+#947 := (iff #141 #946)
+#944 := (iff #140 #941)
+#938 := (or #905 #782)
+#942 := (iff #938 #941)
+#943 := [rewrite]: #942
+#939 := (iff #140 #938)
+#783 := (iff #101 #782)
+#784 := [rewrite]: #783
+#940 := [monotonicity #907 #784]: #939
+#945 := [trans #940 #943]: #944
+#936 := (iff #139 #935)
+#937 := [rewrite]: #936
+#948 := [monotonicity #937 #945]: #947
+#951 := [monotonicity #934 #948]: #950
+#956 := [trans #951 #954]: #955
+#931 := [asserted]: #142
+#957 := [mp #931 #956]: #952
+#3010 := [unit-resolution #957 #3013 #3138 #3012]: #935
+#2126 := (not #935)
+#2485 := (or #2126 #2369)
+#332 := (not #139)
+#379 := (or #364 #332)
+#2488 := (iff #379 #2485)
+#2481 := (or #2369 #2126)
+#2486 := (iff #2481 #2485)
+#2487 := [rewrite]: #2486
+#2483 := (iff #379 #2481)
+#2127 := (iff #332 #2126)
+#2128 := [monotonicity #937]: #2127
+#2484 := [monotonicity #2372 #2128]: #2483
+#2489 := [trans #2484 #2487]: #2488
+#2480 := [asserted]: #379
+#2492 := [mp #2480 #2489]: #2485
+#3011 := [unit-resolution #2492 #3010]: #2369
+#3008 := [unit-resolution #1083 #3011 #3015 #3014]: #1061
+#3009 := [unit-resolution #2370 #3017]: #2342
+#3006 := [unit-resolution #1197 #3009]: #1184
+#2673 := (or #2373 #2633)
+#404 := (or #399 #365)
+#2676 := (iff #404 #2673)
+#2669 := (or #2633 #2373)
+#2674 := (iff #2669 #2673)
+#2675 := [rewrite]: #2674
+#2671 := (iff #404 #2669)
+#2672 := [monotonicity #2636 #2375]: #2671
+#2677 := [trans #2672 #2675]: #2676
+#2668 := [asserted]: #404
+#2680 := [mp #2668 #2677]: #2673
+#3007 := [unit-resolution #2680 #3006 #3008]: false
+#3005 := [lemma #3007]: #3004
+#2967 := [unit-resolution #3005 #2966 #3138 #2969]: #1757
+#772 := (or #602 #728 #752 #755)
+#95 := (or #86 #56)
+#96 := (or #94 #95)
+#97 := (or #92 #96)
+#775 := (iff #97 #772)
+#761 := (or #602 #728)
+#766 := (or #755 #761)
+#769 := (or #752 #766)
+#773 := (iff #769 #772)
+#774 := [rewrite]: #773
+#770 := (iff #97 #769)
+#767 := (iff #96 #766)
+#764 := (iff #95 #761)
+#758 := (or #728 #602)
+#762 := (iff #758 #761)
+#763 := [rewrite]: #762
+#759 := (iff #95 #758)
+#760 := [monotonicity #730 #604]: #759
+#765 := [trans #760 #763]: #764
+#768 := [monotonicity #757 #765]: #767
+#771 := [monotonicity #754 #768]: #770
+#776 := [trans #771 #774]: #775
+#751 := [asserted]: #97
+#777 := [mp #751 #776]: #772
+#2964 := [unit-resolution #777 #2967 #2968 #2971]: #752
+#1829 := (or #1753 #1814)
+#293 := (or #290 #282)
+#1832 := (iff #293 #1829)
+#1825 := (or #1814 #1753)
+#1830 := (iff #1825 #1829)
+#1831 := [rewrite]: #1830
+#1827 := (iff #293 #1825)
+#1828 := [monotonicity #1817 #1756]: #1827
+#1833 := [trans #1828 #1831]: #1832
+#1824 := [asserted]: #293
+#1836 := [mp #1824 #1833]: #1829
+#2965 := [unit-resolution #1836 #2964]: #1814
+#2986 := (or #1339 #779 #986 #989 #860)
+#3002 := [hypothesis]: #514
+#3003 := [unit-resolution #1392 #3002]: #1370
+#3000 := [unit-resolution #575 #3003]: #562
+#3001 := [unit-resolution #1713 #3000]: #1689
+#2998 := [unit-resolution #879 #3001 #3170]: #833
+#2999 := [unit-resolution #1958 #2998]: #1875
+#2996 := [hypothesis]: #1814
+#2997 := [unit-resolution #1948 #2998]: #1940
+#2994 := [unit-resolution #1011 #2997 #3136 #3139]: #959
+#2995 := [unit-resolution #2215 #2994]: #1879
+#2992 := [unit-resolution #1723 #3000]: #1628
+#2993 := [unit-resolution #1402 #3002]: #1374
+#2990 := [unit-resolution #1968 #2998]: #1632
+#2991 := [unit-resolution #705 #2990 #2993 #2992]: #653
+#2988 := [unit-resolution #1579 #2991]: #1571
+#2989 := [unit-resolution #831 #2988 #2995 #2996 #2999]: false
+#2987 := [lemma #2989]: #2986
+#2962 := [unit-resolution #2987 #2965 #3136 #3139 #3170]: #1339
+#2963 := [unit-resolution #536 #2962 #2974]: #517
+#2960 := [unit-resolution #1619 #2963]: #1571
+#2979 := (or #1936 #779 #656 #986 #989)
+#2984 := [hypothesis]: #833
+#2985 := [unit-resolution #1948 #2984]: #1940
+#2982 := [unit-resolution #1011 #2985 #3136 #3139]: #959
+#2983 := [hypothesis]: #1571
+#2980 := [unit-resolution #1958 #2984]: #1875
+#2981 := [unit-resolution #831 #2980 #2996 #2983]: #809
+#2978 := [unit-resolution #2215 #2981 #2982]: false
+#2976 := [lemma #2978]: #2979
+#2961 := [unit-resolution #2976 #2965 #2960 #3136 #3139]: #1936
+#2958 := [unit-resolution #879 #2961 #3170]: #707
+#2959 := [unit-resolution #1703 #2958]: #1628
+#2956 := [unit-resolution #1599 #2963]: #1567
+#2957 := [unit-resolution #1713 #2958]: #1401
+#2954 := [unit-resolution #575 #2957]: #538
+#2955 := [unit-resolution #1382 #2954]: #1374
+#2952 := [unit-resolution #705 #2955 #2956 #2959]: #683
+#2953 := [unit-resolution #1988 #2952]: #1940
+#2950 := [unit-resolution #1011 #2953 #3136 #3139]: #959
+#2951 := [unit-resolution #1998 #2952]: #1875
+#2948 := [unit-resolution #831 #2951 #2965 #2960]: #809
+#2949 := [unit-resolution #2215 #2948 #2950]: false
+#2947 := [lemma #2949]: #2946
+#2909 := [unit-resolution #2947 #2908 #2911 #2910 #3138]: #1278
+#2906 := [unit-resolution #2786 #2909]: #469
+#1500 := (or #1281 #1414)
+#248 := (or #236 #215)
+#1503 := (iff #248 #1500)
+#1496 := (or #1414 #1281)
+#1501 := (iff #1496 #1500)
+#1502 := [rewrite]: #1501
+#1498 := (iff #248 #1496)
+#1499 := [monotonicity #1417 #1283]: #1498
+#1504 := [trans #1499 #1502]: #1503
+#1495 := [asserted]: #248
+#1507 := [mp #1495 #1504]: #1500
+#2907 := [unit-resolution #1507 #2906]: #1414
+#2904 := [unit-resolution #2805 #2907]: #578
+#2905 := [unit-resolution #1744 #2904]: #1722
+#1490 := (or #1281 #1449)
+#247 := (or #242 #215)
+#1493 := (iff #247 #1490)
+#1486 := (or #1449 #1281)
+#1491 := (iff #1486 #1490)
+#1492 := [rewrite]: #1491
+#1488 := (iff #247 #1486)
+#1489 := [monotonicity #1451 #1283]: #1488
+#1494 := [trans #1489 #1492]: #1493
+#1485 := [asserted]: #247
+#1497 := [mp #1485 #1494]: #1490
+#2902 := [unit-resolution #1497 #2906]: #1449
+#2903 := [unit-resolution #3077 #2910 #2908 #2911]: #2122
+#2900 := [unit-resolution #1754 #2904]: #1726
+#2901 := [unit-resolution #3005 #2900 #3138 #2903]: #1757
+#2898 := [unit-resolution #777 #2901 #2902 #2905]: #752
+#2899 := [unit-resolution #1836 #2898]: #1814
+#2896 := [unit-resolution #1876 #2898]: #1510
+#2897 := [unit-resolution #1477 #2906]: #1445
+#2894 := [unit-resolution #2987 #2899 #2908 #2911 #2910]: #1339
+#2895 := [unit-resolution #2914 #2894 #2897 #2896]: #1571
+#2892 := [unit-resolution #2976 #2895 #2899 #2908 #2911]: #1936
+#2893 := [unit-resolution #879 #2892 #2910]: #707
+#2890 := [unit-resolution #1703 #2893]: #1628
+#2936 := (or #1567 #514 #599 #629)
+#2945 := [hypothesis]: #653
+#2942 := [unit-resolution #1589 #2945]: #1506
+#2943 := [unit-resolution #651 #2942 #3061 #2944]: #493
+#2941 := [unit-resolution #1599 #2945]: #1343
+#2938 := [unit-resolution #536 #2941 #2940]: #490
+#2939 := [unit-resolution #1320 #2938 #2943]: false
+#2937 := [lemma #2939]: #2936
+#2891 := [unit-resolution #2937 #2894 #2897 #2896]: #1567
+#2925 := (or #656 #653 #860 #779 #809 #986 #989)
+#2934 := [hypothesis]: #1879
+#2935 := [unit-resolution #831 #2983 #2996 #2934]: #806
+#2932 := [unit-resolution #1998 #2935]: #1632
+#2933 := [hypothesis]: #1567
+#2930 := [unit-resolution #2976 #2983 #2996 #3136 #3139]: #1936
+#2931 := [unit-resolution #879 #2930 #3170]: #707
+#2928 := [unit-resolution #1703 #2931]: #1628
+#2929 := [unit-resolution #705 #2928 #2933 #2932]: #541
+#2926 := [unit-resolution #1713 #2931]: #1401
+#2927 := [unit-resolution #575 #2926]: #538
+#2924 := [unit-resolution #1382 #2927 #2929]: false
+#2922 := [lemma #2924]: #2925
+#2888 := [unit-resolution #2922 #2895 #2910 #2899 #2891 #2908 #2911]: #809
+#2889 := [unit-resolution #2215 #2888]: #2183
+#2886 := [unit-resolution #1011 #2889 #2908 #2911]: #836
+#2887 := [unit-resolution #1988 #2886]: #1632
+#2884 := [unit-resolution #1713 #2893]: #1401
+#2885 := [unit-resolution #575 #2884]: #538
+#2882 := [unit-resolution #1382 #2885]: #1374
+#2883 := [unit-resolution #705 #2882 #2887 #2891 #2890]: false
+#2881 := [lemma #2883]: #2880
+#2851 := [unit-resolution #2881 #3138]: #2556
+#2848 := [unit-resolution #2877 #2851]: #1239
+#2849 := [unit-resolution #2726 #2848]: #2679
+#2846 := [hypothesis]: #2491
+#2847 := [unit-resolution #2736 #2848]: #2495
+#2187 := (not #962)
+#2844 := [hypothesis]: #469
+#2845 := [unit-resolution #1507 #2844]: #1414
+#2842 := [unit-resolution #2805 #2845]: #578
+#2843 := [unit-resolution #1754 #2842]: #1726
+#2840 := [unit-resolution #1497 #2844]: #1449
+#2865 := [hypothesis]: #1753
+#2841 := [unit-resolution #1744 #2842]: #1722
+#2838 := [unit-resolution #777 #2841 #2865 #2840]: #755
+#2839 := [unit-resolution #3005 #2838 #3138 #2843]: #932
+#2218 := (or #2122 #2187)
+#146 := (= f45 f1)
+#340 := (not #146)
+#344 := (or #340 #331)
+#2221 := (iff #344 #2218)
+#2214 := (or #2187 #2122)
+#2219 := (iff #2214 #2218)
+#2220 := [rewrite]: #2219
+#2216 := (iff #344 #2214)
+#2188 := (iff #340 #2187)
+#963 := (iff #146 #962)
+#964 := [rewrite]: #963
+#2189 := [monotonicity #964]: #2188
+#2217 := [monotonicity #2189 #2125]: #2216
+#2222 := [trans #2217 #2220]: #2221
+#2213 := [asserted]: #344
+#2225 := [mp #2213 #2222]: #2218
+#2836 := [unit-resolution #2225 #2839]: #2187
+#1132 := (or #962 #1085 #1112 #1115)
+#185 := (or #175 #146)
+#186 := (or #184 #185)
+#187 := (or #182 #186)
+#1135 := (iff #187 #1132)
+#1121 := (or #962 #1085)
+#1126 := (or #1115 #1121)
+#1129 := (or #1112 #1126)
+#1133 := (iff #1129 #1132)
+#1134 := [rewrite]: #1133
+#1130 := (iff #187 #1129)
+#1127 := (iff #186 #1126)
+#1124 := (iff #185 #1121)
+#1118 := (or #1085 #962)
+#1122 := (iff #1118 #1121)
+#1123 := [rewrite]: #1122
+#1119 := (iff #185 #1118)
+#1120 := [monotonicity #1087 #964]: #1119
+#1125 := [trans #1120 #1123]: #1124
+#1128 := [monotonicity #1117 #1125]: #1127
+#1131 := [monotonicity #1114 #1128]: #1130
+#1136 := [trans #1131 #1134]: #1135
+#1111 := [asserted]: #187
+#1137 := [mp #1111 #1136]: #1132
+#2837 := [unit-resolution #1137 #2836 #2847 #2846]: #1085
+#2834 := [unit-resolution #2442 #2837]: #2434
+#2835 := [unit-resolution #2123 #2838]: #2030
+#2832 := [unit-resolution #903 #2835 #2843]: #884
+#2833 := [unit-resolution #2370 #2832]: #2342
+#2830 := [unit-resolution #1197 #2833]: #1184
+#2831 := [unit-resolution #2660 #2830]: #2646
+#2828 := [unit-resolution #1237 #2831 #2834 #2849]: false
+#2826 := [lemma #2828]: #2829
+#3290 := [unit-resolution #2826 #3289 #3138 #3286]: #1112
+#2607 := (or #2248 #2491)
+#395 := (or #380 #348)
+#2610 := (iff #395 #2607)
+#2603 := (or #2491 #2248)
+#2608 := (iff #2603 #2607)
+#2609 := [rewrite]: #2608
+#2605 := (iff #395 #2603)
+#2606 := [monotonicity #2494 #2250]: #2605
+#2611 := [trans #2606 #2609]: #2610
+#2602 := [asserted]: #395
+#2614 := [mp #2602 #2611]: #2607
+#3291 := [unit-resolution #2614 #3290]: #2248
+#3292 := [unit-resolution #2574 #3290]: #2552
+#3293 := [unit-resolution #2859 #3292]: #1013
+#3294 := [unit-resolution #2319 #3293]: #2244
+#3295 := [unit-resolution #2329 #3293]: #1997
+#2861 := (or #989 #782 #752 #860 #986)
+#2878 := [unit-resolution #3077 #3139 #3170 #3136]: #2122
+#2879 := [unit-resolution #2947 #3139 #3136 #3170 #3138]: #1278
+#2868 := [unit-resolution #2786 #2879]: #469
+#2869 := [unit-resolution #1507 #2868]: #1414
+#2866 := [unit-resolution #2805 #2869]: #578
+#2867 := [unit-resolution #1754 #2866]: #1726
+#2864 := [unit-resolution #1497 #2868]: #1449
+#2862 := [unit-resolution #1744 #2866]: #1722
+#2863 := [unit-resolution #777 #2862 #2865 #2864]: #755
+#2860 := [unit-resolution #3005 #2863 #2867 #3138 #2878]: false
+#2850 := [lemma #2860]: #2861
+#3296 := [unit-resolution #2850 #3295 #3294 #3289 #3291 #3138]: false
+#3298 := [lemma #3296]: #3297
+#3299 := [unit-resolution #3298 #2940 #3138]: #1571
+#3283 := (or #656 #514 #782 #653)
+#3275 := (or #707 #782 #656 #514)
+#3213 := [hypothesis]: #1689
+#3259 := (or #2244 #782 #656 #707 #514)
+#3173 := (or #1814 #860 #782 #514)
+#2791 := [hypothesis]: #779
+#2792 := [unit-resolution #1846 #2791]: #1510
+#2789 := [unit-resolution #1836 #2791]: #1753
+#2793 := (or #1112 #782 #752 #629 #514)
+#2827 := [unit-resolution #2826 #2846 #3138 #2865]: #1281
+#2824 := [unit-resolution #2786 #2827]: #465
+#2825 := [unit-resolution #1340 #2824]: #1312
+#2822 := [unit-resolution #1330 #2824]: #1308
+#2823 := [unit-resolution #536 #2822 #2940]: #517
+#2820 := [unit-resolution #1629 #2823]: #1506
+#2821 := [unit-resolution #651 #2820 #2825 #2944]: #599
+#2818 := [unit-resolution #1467 #2821]: #1414
+#2819 := [unit-resolution #2805 #2818]: #578
+#2816 := [unit-resolution #1754 #2819]: #1726
+#2817 := [unit-resolution #1457 #2821]: #1449
+#2814 := [unit-resolution #1744 #2819]: #1722
+#2815 := [unit-resolution #777 #2814 #2865 #2817]: #755
+#2812 := [unit-resolution #3005 #2815 #3138 #2816]: #932
+#2813 := [unit-resolution #2225 #2812]: #2187
+#2810 := [unit-resolution #1137 #2813 #2847 #2846]: #1085
+#2811 := [unit-resolution #2442 #2810]: #2434
+#2808 := [unit-resolution #2123 #2815]: #2030
+#2809 := [unit-resolution #903 #2808 #2816]: #884
+#2806 := [unit-resolution #2370 #2809]: #2342
+#2807 := [unit-resolution #1197 #2806]: #1184
+#2795 := [unit-resolution #2660 #2807]: #2646
+#2796 := [unit-resolution #1237 #2795 #2811 #2849]: false
+#2794 := [lemma #2796]: #2793
+#2790 := [unit-resolution #2794 #2789 #3138 #2792 #2940]: #1112
+#2787 := [unit-resolution #2574 #2790]: #2552
+#2788 := [unit-resolution #2859 #2787]: #1013
+#2768 := [unit-resolution #2614 #2790]: #2248
+#2764 := [unit-resolution #2850 #2768 #2789 #3170 #3138]: #986
+#3172 := [unit-resolution #2319 #2764 #2788]: false
+#3174 := [lemma #3172]: #3173
+#3248 := [unit-resolution #3174 #3247 #3138 #2940]: #1814
+#3249 := [unit-resolution #879 #3247 #3213]: #833
+#3250 := [unit-resolution #1958 #3249]: #1875
+#3251 := [unit-resolution #831 #3250 #3248 #2983]: #809
+#3252 := [unit-resolution #2245 #3251]: #2122
+#2228 := (or #1879 #2187)
+#345 := (or #340 #299)
+#2231 := (iff #345 #2228)
+#2224 := (or #2187 #1879)
+#2229 := (iff #2224 #2228)
+#2230 := [rewrite]: #2229
+#2226 := (iff #345 #2224)
+#2227 := [monotonicity #2189 #1881]: #2226
+#2232 := [trans #2227 #2230]: #2231
+#2223 := [asserted]: #345
+#2235 := [mp #2223 #2232]: #2228
+#3256 := [unit-resolution #2235 #3251]: #2187
+#3257 := [unit-resolution #1137 #3256 #2847 #3255]: #1085
+#3187 := (or #2430 #782 #932)
+#3177 := [unit-resolution #1237 #3176 #2849]: #1196
+#3178 := [unit-resolution #2660 #3177]: #2633
+#3179 := [unit-resolution #1197 #3178]: #1037
+#3180 := [unit-resolution #2670 #3177]: #2373
+#2455 := (or #2126 #2430)
+#376 := (or #372 #332)
+#2458 := (iff #376 #2455)
+#2451 := (or #2430 #2126)
+#2456 := (iff #2451 #2455)
+#2457 := [rewrite]: #2456
+#2453 := (iff #376 #2451)
+#2454 := [monotonicity #2433 #2128]: #2453
+#2459 := [trans #2454 #2457]: #2458
+#2450 := [asserted]: #376
+#2462 := [mp #2450 #2459]: #2455
+#3182 := [unit-resolution #2462 #3175]: #2126
+#3183 := [unit-resolution #957 #3182 #3138 #3012]: #905
+#2068 := (or #2061 #2065)
+#325 := (or #323 #324)
+#2069 := (iff #325 #2068)
+#2070 := [monotonicity #2064 #2067]: #2069
+#2060 := [asserted]: #325
+#2073 := [mp #2060 #2070]: #2068
+#3184 := [unit-resolution #2073 #3183]: #2065
+#3185 := [unit-resolution #1083 #3184 #3181 #3180]: #1034
+#3186 := [unit-resolution #2350 #3185 #3179]: false
+#3188 := [lemma #3186]: #3187
+#3258 := [unit-resolution #3188 #3257 #3252 #3138]: false
+#3260 := [lemma #3258]: #3259
+#3261 := [unit-resolution #3260 #3213 #2983 #3138 #2940]: #2244
+#3244 := (or #986 #782 #514 #989 #656 #707)
+#3216 := (or #860 #656 #986 #989 #707 #782 #514)
+#3212 := [unit-resolution #3174 #3170 #3138 #2940]: #1814
+#3214 := [unit-resolution #879 #3170 #3213]: #833
+#3215 := [unit-resolution #2976 #3214 #3212 #2983 #3136 #3139]: false
+#3217 := [lemma #3215]: #3216
+#3236 := [unit-resolution #3217 #3136 #2983 #3139 #3213 #3138 #2940]: #860
+#3237 := [unit-resolution #2329 #3236]: #2305
+#3238 := [unit-resolution #2859 #3237]: #1139
+#3239 := [unit-resolution #2574 #3238]: #2491
+#3234 := (or #779 #656 #989 #986 #782 #1112)
+#3224 := (or #2187 #779 #656 #989 #986)
+#3218 := [hypothesis]: #962
+#2190 := (or #2183 #2187)
+#341 := (or #339 #340)
+#2191 := (iff #341 #2190)
+#2192 := [monotonicity #2186 #2189]: #2191
+#2182 := [asserted]: #341
+#2195 := [mp #2182 #2192]: #2190
+#3219 := [unit-resolution #2195 #3218]: #2183
+#3220 := [unit-resolution #1011 #3219 #3139 #3136]: #836
+#3221 := [unit-resolution #2235 #3218]: #1879
+#3222 := [unit-resolution #831 #3221 #2996 #2983]: #806
+#3223 := [unit-resolution #1978 #3222 #3220]: false
+#3225 := [lemma #3223]: #3224
+#3226 := [unit-resolution #3225 #2996 #2983 #3139 #3136]: #2187
+#3227 := [unit-resolution #1137 #3226 #2847 #2846]: #1085
+#3228 := [unit-resolution #3188 #3227 #3138]: #932
+#3229 := [unit-resolution #2205 #3228]: #2183
+#3230 := [unit-resolution #1011 #3229 #3139 #3136]: #836
+#3231 := [unit-resolution #2245 #3228]: #1879
+#3232 := [unit-resolution #831 #3231 #2996 #2983]: #806
+#3233 := [unit-resolution #1978 #3232 #3230]: false
+#3235 := [lemma #3233]: #3234
+#3240 := [unit-resolution #3235 #3136 #3139 #2983 #3138 #3239]: #779
+#3241 := [unit-resolution #1836 #3240]: #1753
+#3242 := [unit-resolution #1846 #3240]: #1510
+#3243 := [unit-resolution #2794 #3242 #3241 #3138 #3239 #2940]: false
+#3245 := [lemma #3243]: #3244
+#3262 := [unit-resolution #3245 #3261 #2940 #3138 #2983 #3213]: #989
+#2577 := (or #2248 #2552)
+#392 := (or #388 #348)
+#2580 := (iff #392 #2577)
+#2573 := (or #2552 #2248)
+#2578 := (iff #2573 #2577)
+#2579 := [rewrite]: #2578
+#2575 := (iff #392 #2573)
+#2576 := [monotonicity #2555 #2250]: #2575
+#2581 := [trans #2576 #2579]: #2580
+#2572 := [asserted]: #392
+#2584 := [mp #2572 #2581]: #2577
+#3263 := [unit-resolution #2584 #3262]: #2552
+#3264 := [unit-resolution #2859 #3263]: #1013
+#3265 := [unit-resolution #2329 #3264]: #1997
+#3266 := [unit-resolution #3174 #3265 #3138 #2940]: #1814
+#3267 := [unit-resolution #879 #3265 #3213]: #833
+#3268 := [unit-resolution #1958 #3267]: #1875
+#3269 := [unit-resolution #831 #3268 #3266 #2983]: #809
+#3270 := [unit-resolution #2245 #3269]: #2122
+#3271 := [unit-resolution #2614 #3262]: #2491
+#3272 := [unit-resolution #2235 #3269]: #2187
+#3273 := [unit-resolution #1137 #3272 #2847 #3271]: #1085
+#3274 := [unit-resolution #3188 #3273 #3270 #3138]: false
+#3276 := [lemma #3274]: #3275
+#3277 := [unit-resolution #3276 #2983 #3138 #2940]: #707
+#3278 := [unit-resolution #1703 #3277]: #1628
+#3210 := (or #541 #782 #656 #514 #680 #653)
+#3189 := [hypothesis]: #1628
+#3190 := [hypothesis]: #1374
+#3191 := [unit-resolution #705 #3190 #2933 #3189]: #683
+#3192 := [unit-resolution #1998 #3191]: #1875
+#555 := (or #514 #538 #541)
+#42 := (or #41 #33)
+#43 := (or #39 #42)
+#558 := (iff #43 #555)
+#547 := (or #514 #541)
+#552 := (or #538 #547)
+#556 := (iff #552 #555)
+#557 := [rewrite]: #556
+#553 := (iff #43 #552)
+#550 := (iff #42 #547)
+#544 := (or #541 #514)
+#548 := (iff #544 #547)
+#549 := [rewrite]: #548
+#545 := (iff #42 #544)
+#546 := [monotonicity #543 #516]: #545
+#551 := [trans #546 #549]: #550
+#554 := [monotonicity #540 #551]: #553
+#559 := [trans #554 #557]: #558
+#537 := [asserted]: #43
+#560 := [mp #537 #559]: #555
+#3193 := [unit-resolution #560 #3190 #2940]: #538
+#1408 := (or #1370 #1401)
+#235 := (or #234 #229)
+#1411 := (iff #235 #1408)
+#1405 := (or #1401 #1370)
+#1409 := (iff #1405 #1408)
+#1410 := [rewrite]: #1409
+#1406 := (iff #235 #1405)
+#1407 := [monotonicity #1404 #1373]: #1406
+#1412 := [trans #1407 #1410]: #1411
+#1400 := [asserted]: #235
+#1415 := [mp #1400 #1412]: #1408
+#3194 := [unit-resolution #1415 #3193]: #1401
+#721 := (or #562 #680 #707)
+#83 := (or #75 #45)
+#84 := (or #82 #83)
+#724 := (iff #84 #721)
+#713 := (or #562 #680)
+#718 := (or #707 #713)
+#722 := (iff #718 #721)
+#723 := [rewrite]: #722
+#719 := (iff #84 #718)
+#716 := (iff #83 #713)
+#710 := (or #680 #562)
+#714 := (iff #710 #713)
+#715 := [rewrite]: #714
+#711 := (iff #83 #710)
+#712 := [monotonicity #682 #564]: #711
+#717 := [trans #712 #715]: #716
+#720 := [monotonicity #709 #717]: #719
+#725 := [trans #720 #723]: #724
+#706 := [asserted]: #84
+#726 := [mp #706 #725]: #721
+#3195 := [unit-resolution #726 #3194 #3189]: #707
+#2014 := (or #1689 #1997)
+#316 := (or #314 #273)
+#2017 := (iff #316 #2014)
+#2010 := (or #1997 #1689)
+#2015 := (iff #2010 #2014)
+#2016 := [rewrite]: #2015
+#2012 := (iff #316 #2010)
+#2013 := [monotonicity #2000 #1692]: #2012
+#2018 := [trans #2013 #2016]: #2017
+#2009 := [asserted]: #316
+#2021 := [mp #2009 #2018]: #2014
+#3196 := [unit-resolution #2021 #3195]: #1997
+#3197 := [unit-resolution #3174 #3196 #3138 #2940]: #1814
+#3198 := [unit-resolution #831 #3197 #3192 #2983]: #809
+#3199 := [unit-resolution #2235 #3198]: #2187
+#3200 := [unit-resolution #2245 #3198]: #2122
+#3201 := [unit-resolution #3188 #3200 #3138]: #2430
+#3202 := [unit-resolution #1137 #3201 #2847 #3199]: #1112
+#3203 := [unit-resolution #2574 #3202]: #2552
+#3204 := [unit-resolution #2859 #3203]: #1013
+#3205 := [unit-resolution #2215 #3198]: #2183
+#3206 := [unit-resolution #1988 #3191]: #1940
+#3207 := [unit-resolution #2614 #3202]: #2248
+#3208 := [unit-resolution #1011 #3207 #3206 #3205]: #986
+#3209 := [unit-resolution #2319 #3208 #3204]: false
+#3211 := [lemma #3209]: #3210
+#3279 := [unit-resolution #3211 #3278 #2983 #2940 #3138 #2933]: #541
+#3280 := [unit-resolution #1713 #3277]: #1401
+#3281 := [unit-resolution #575 #3280]: #538
+#3282 := [unit-resolution #1382 #3281 #3279]: false
+#3284 := [lemma #3282]: #3283
+#3300 := [unit-resolution #3284 #3299 #3138 #2940]: #653
+#3301 := [unit-resolution #1599 #3300]: #1343
+#3302 := [unit-resolution #536 #3301 #2940]: #490
+#3303 := [unit-resolution #1330 #3302]: #1278
+#3304 := [unit-resolution #2786 #3303]: #469
+#3305 := [unit-resolution #1477 #3304]: #1445
+#3306 := [unit-resolution #2937 #3305 #2940 #3300]: #629
+#3307 := [unit-resolution #1876 #3306]: #1753
+#3308 := [unit-resolution #2826 #3307 #3138 #3304]: #1112
+#3309 := [unit-resolution #2574 #3308]: #2552
+#3310 := [unit-resolution #2859 #3309]: #1013
+#3311 := [unit-resolution #1507 #3304]: #1414
+#3312 := [unit-resolution #2805 #3311]: #578
+#3313 := [unit-resolution #1754 #3312]: #1726
+#3314 := [unit-resolution #1497 #3304]: #1449
+#3315 := [unit-resolution #1744 #3312]: #1722
+#3316 := [unit-resolution #777 #3315 #3307 #3314]: #755
+#3317 := [unit-resolution #3005 #3316 #3138 #3313]: #932
+#3318 := [unit-resolution #3276 #3299 #3138 #2940]: #707
+#3319 := [unit-resolution #2021 #3318]: #1997
+#3320 := [unit-resolution #2614 #3308]: #2248
+#3321 := [unit-resolution #3077 #3320 #3319 #3317]: #986
+#3322 := [unit-resolution #2319 #3321 #3310]: false
+#3324 := [lemma #3322]: #3323
+#3326 := [unit-resolution #3324 #3138]: #514
+#3394 := [unit-resolution #1392 #3326]: #1370
+#3395 := [unit-resolution #575 #3394]: #562
+#3396 := [unit-resolution #1713 #3395]: #1689
+#3466 := [unit-resolution #1723 #3395]: #1628
+#3467 := [unit-resolution #1402 #3326]: #1374
+#3464 := (or #656 #782)
+#3428 := (or #2248 #782 #656)
+#3392 := [hypothesis]: #989
+#3393 := [unit-resolution #2614 #3392]: #2491
+#3397 := [unit-resolution #2584 #3392]: #2552
+#3398 := [unit-resolution #2859 #3397]: #1013
+#3399 := [unit-resolution #2329 #3398]: #1997
+#3400 := [unit-resolution #879 #3399 #3396]: #833
+#3401 := [unit-resolution #1958 #3400]: #1875
+#3390 := (or #1879 #782 #1112)
+#3385 := [hypothesis]: #809
+#3386 := [unit-resolution #2245 #3385]: #2122
+#3387 := [unit-resolution #2235 #3385]: #2187
+#3388 := [unit-resolution #1137 #3387 #2847 #2846]: #1085
+#3389 := [unit-resolution #3188 #3388 #3386 #3138]: false
+#3391 := [lemma #3389]: #3390
+#3402 := [unit-resolution #3391 #3393 #3138]: #1879
+#3403 := [unit-resolution #831 #3402 #2983 #3401]: #779
+#3404 := [unit-resolution #1846 #3403]: #1510
+#1354 := (or #1308 #1339)
+#227 := (or #224 #219)
+#1357 := (iff #227 #1354)
+#1350 := (or #1339 #1308)
+#1355 := (iff #1350 #1354)
+#1356 := [rewrite]: #1355
+#1352 := (iff #227 #1350)
+#1353 := [monotonicity #1342 #1311]: #1352
+#1358 := [trans #1353 #1356]: #1357
+#1349 := [asserted]: #227
+#1361 := [mp #1349 #1358]: #1354
+#3338 := [unit-resolution #1361 #3326]: #1308
+#3405 := [unit-resolution #1968 #3400]: #1632
+#3406 := [unit-resolution #3040 #3405 #3338]: #1506
+#3407 := [unit-resolution #1836 #3403]: #1753
+#3408 := [unit-resolution #2826 #3407 #3138 #3393]: #1281
+#3409 := [unit-resolution #2786 #3408]: #465
+#3410 := [unit-resolution #1340 #3409]: #1312
+#3411 := [unit-resolution #651 #3410 #3406 #3404]: #599
+#3412 := [unit-resolution #1467 #3411]: #1414
+#3413 := [unit-resolution #2805 #3412]: #578
+#3414 := [unit-resolution #1754 #3413]: #1726
+#3415 := [unit-resolution #1457 #3411]: #1449
+#3416 := [unit-resolution #1744 #3413]: #1722
+#3417 := [unit-resolution #777 #3416 #3407 #3415]: #755
+#3418 := [unit-resolution #3005 #3417 #3138 #3414]: #932
+#3419 := [unit-resolution #2225 #3418]: #2187
+#3420 := [unit-resolution #1137 #3419 #2847 #3393]: #1085
+#3421 := [unit-resolution #2442 #3420]: #2434
+#3422 := [unit-resolution #2123 #3417]: #2030
+#3423 := [unit-resolution #903 #3422 #3414]: #884
+#3424 := [unit-resolution #2370 #3423]: #2342
+#3425 := [unit-resolution #1197 #3424]: #1184
+#3426 := [unit-resolution #2660 #3425]: #2646
+#3427 := [unit-resolution #1237 #3426 #3421 #2849]: false
+#3429 := [lemma #3427]: #3428
+#3430 := [unit-resolution #3429 #2983 #3138]: #2248
+#3383 := (or #989 #986 #782 #656)
+#3329 := (or #860 #986 #989 #782)
+#3325 := [unit-resolution #2850 #3170 #3136 #3139 #3138]: #752
+#3327 := [unit-resolution #2987 #3170 #3326 #3136 #3139]: #779
+#3328 := [unit-resolution #1836 #3327 #3325]: false
+#3330 := [lemma #3328]: #3329
+#3331 := [unit-resolution #3330 #3139 #3136 #3138]: #860
+#3332 := [unit-resolution #2329 #3331]: #2305
+#3333 := [unit-resolution #2859 #3332]: #1139
+#3334 := [unit-resolution #2574 #3333]: #2491
+#3355 := [unit-resolution #3235 #3334 #2983 #3136 #3138 #3139]: #779
+#3356 := [unit-resolution #1846 #3355]: #1510
+#3357 := [unit-resolution #1836 #3355]: #1753
+#3353 := (or #932 #782 #752 #629 #986 #989)
+#3335 := [unit-resolution #2826 #2865 #3138 #3334]: #1281
+#3336 := [unit-resolution #2786 #3335]: #465
+#3337 := [unit-resolution #1340 #3336]: #1312
+#3339 := [unit-resolution #3188 #3012 #3138]: #2430
+#3340 := [unit-resolution #1137 #3339 #2847 #3334]: #962
+#3341 := [unit-resolution #2195 #3340]: #2183
+#3342 := [unit-resolution #1011 #3341 #3136 #3139]: #836
+#3343 := [unit-resolution #1988 #3342]: #1632
+#3344 := [unit-resolution #3040 #3343 #3338]: #1506
+#3345 := [unit-resolution #651 #3344 #2944 #3337]: #599
+#3346 := [unit-resolution #1467 #3345]: #1414
+#3347 := [unit-resolution #2805 #3346]: #578
+#3348 := [unit-resolution #1754 #3347]: #1726
+#3349 := [unit-resolution #1457 #3345]: #1449
+#3350 := [unit-resolution #1744 #3347]: #1722
+#3351 := [unit-resolution #777 #3350 #2865 #3349]: #755
+#3352 := [unit-resolution #3005 #3351 #3348 #3138 #3012]: false
+#3354 := [lemma #3352]: #3353
+#3358 := [unit-resolution #3354 #3357 #3138 #3356 #3136 #3139]: #932
+#3359 := [unit-resolution #2225 #3358]: #2187
+#3360 := [unit-resolution #1137 #3359 #2847 #3334]: #1085
+#3361 := [unit-resolution #2442 #3360]: #2434
+#3362 := [unit-resolution #1237 #3361 #2849]: #1196
+#3363 := [unit-resolution #2670 #3362]: #2373
+#3364 := [unit-resolution #2452 #3360]: #2369
+#3365 := [unit-resolution #2660 #3362]: #2633
+#3366 := [unit-resolution #1197 #3365]: #1037
+#3367 := [unit-resolution #2350 #3366]: #2338
+#3368 := [unit-resolution #1083 #3367 #3364 #3363]: #908
+#3369 := [unit-resolution #2826 #3357 #3138 #3334]: #1281
+#3370 := [unit-resolution #2786 #3369]: #465
+#3371 := [unit-resolution #1340 #3370]: #1312
+#3372 := [unit-resolution #2205 #3358]: #2183
+#3373 := [unit-resolution #1011 #3372 #3136 #3139]: #836
+#3374 := [unit-resolution #1988 #3373]: #1632
+#3375 := [unit-resolution #3040 #3374 #3338]: #1506
+#3376 := [unit-resolution #651 #3375 #3356 #3371]: #599
+#3377 := [unit-resolution #1467 #3376]: #1414
+#3378 := [unit-resolution #2805 #3377]: #578
+#3379 := [unit-resolution #1754 #3378]: #1726
+#3380 := [unit-resolution #2370 #3366]: #2034
+#3381 := [unit-resolution #903 #3380 #3379]: #881
+#3382 := [unit-resolution #2103 #3381 #3368]: false
+#3384 := [lemma #3382]: #3383
+#3431 := [unit-resolution #3384 #3430 #3138 #2983]: #986
+#3432 := [unit-resolution #2319 #3431]: #2305
+#3433 := [unit-resolution #2859 #3432]: #1139
+#3434 := [unit-resolution #2574 #3433]: #2491
+#3435 := [unit-resolution #2339 #3431]: #1997
+#3436 := [unit-resolution #879 #3435 #3396]: #833
+#3437 := [unit-resolution #1958 #3436]: #1875
+#3438 := [unit-resolution #3391 #3434 #3138]: #1879
+#3439 := [unit-resolution #831 #3438 #2983 #3437]: #779
+#3440 := [unit-resolution #1846 #3439]: #1510
+#3441 := [unit-resolution #1968 #3436]: #1632
+#3442 := [unit-resolution #3040 #3441 #3338]: #1506
+#3443 := [unit-resolution #1836 #3439]: #1753
+#3444 := [unit-resolution #2826 #3443 #3138 #3434]: #1281
+#3445 := [unit-resolution #2786 #3444]: #465
+#3446 := [unit-resolution #1340 #3445]: #1312
+#3447 := [unit-resolution #651 #3446 #3442 #3440]: #599
+#3448 := [unit-resolution #1467 #3447]: #1414
+#3449 := [unit-resolution #2805 #3448]: #578
+#3450 := [unit-resolution #1754 #3449]: #1726
+#3451 := [unit-resolution #1457 #3447]: #1449
+#3452 := [unit-resolution #1744 #3449]: #1722
+#3453 := [unit-resolution #777 #3452 #3443 #3451]: #755
+#3454 := [unit-resolution #3005 #3453 #3138 #3450]: #932
+#3455 := [unit-resolution #2225 #3454]: #2187
+#3456 := [unit-resolution #1137 #3455 #2847 #3434]: #1085
+#3457 := [unit-resolution #2442 #3456]: #2434
+#3458 := [unit-resolution #2123 #3453]: #2030
+#3459 := [unit-resolution #903 #3458 #3450]: #884
+#3460 := [unit-resolution #2370 #3459]: #2342
+#3461 := [unit-resolution #1197 #3460]: #1184
+#3462 := [unit-resolution #2660 #3461]: #2646
+#3463 := [unit-resolution #1237 #3462 #3457 #2849]: false
+#3465 := [lemma #3463]: #3464
+#3468 := [unit-resolution #3465 #3138]: #656
+#3469 := [unit-resolution #1579 #3468]: #1567
+#3470 := [unit-resolution #705 #3469 #3467 #3466]: #683
+#3471 := [unit-resolution #1968 #3470]: #1936
+#3472 := [unit-resolution #879 #3471 #3396]: #860
+#3473 := [unit-resolution #2339 #3472]: #2244
+#3474 := [unit-resolution #1988 #3470]: #1940
+#3475 := [unit-resolution #2329 #3472]: #2305
+#3476 := [unit-resolution #2859 #3475]: #1139
+#3477 := [unit-resolution #2584 #3476]: #2248
+#3478 := [unit-resolution #1011 #3477 #3474 #3473]: #959
+#3479 := [unit-resolution #2205 #3478]: #2122
+#3480 := [unit-resolution #2574 #3476]: #2491
+#3481 := [unit-resolution #2195 #3478]: #2187
+#3482 := [unit-resolution #1137 #3481 #2847 #3480]: #1085
+#3483 := [unit-resolution #3188 #3482 #3479 #3138]: false
+#3484 := [lemma #3483]: #782
+#1849 := (or #1753 #1818)
+#291 := (not #101)
+#295 := (or #291 #282)
+#1852 := (iff #295 #1849)
+#1845 := (or #1818 #1753)
+#1850 := (iff #1845 #1849)
+#1851 := [rewrite]: #1850
+#1847 := (iff #295 #1845)
+#1819 := (iff #291 #1818)
+#1820 := [monotonicity #784]: #1819
+#1848 := [monotonicity #1820 #1756]: #1847
+#1853 := [trans #1848 #1851]: #1852
+#1844 := [asserted]: #295
+#1856 := [mp #1844 #1853]: #1849
+#3506 := [unit-resolution #1856 #3484]: #1753
+#3508 := [unit-resolution #777 #3506]: #3507
+#3575 := [unit-resolution #3508 #3574 #3570]: #602
+#3576 := [unit-resolution #1754 #3573]: #1418
+#3577 := [unit-resolution #2805 #3576]: #574
+#1480 := (or #1414 #1449)
+#246 := (or #242 #236)
+#1483 := (iff #246 #1480)
+#1476 := (or #1449 #1414)
+#1481 := (iff #1476 #1480)
+#1482 := [rewrite]: #1481
+#1478 := (iff #246 #1476)
+#1479 := [monotonicity #1451 #1417]: #1478
+#1484 := [trans #1479 #1482]: #1483
+#1475 := [asserted]: #246
+#1487 := [mp #1475 #1484]: #1480
+#3578 := [unit-resolution #1487 #3577 #3575]: false
+#3580 := [lemma #3578]: #3579
+#3598 := [unit-resolution #3580 #3597]: #2430
+#3599 := [unit-resolution #1137 #3598 #3596 #3255]: #962
+#3600 := [unit-resolution #2235 #3599]: #1879
+#3592 := (or #1875 #860)
+#3581 := [hypothesis]: #806
+#3582 := [unit-resolution #1958 #3581]: #1936
+#3583 := [unit-resolution #879 #3582 #3170]: #707
+#3584 := [unit-resolution #1713 #3583]: #1401
+#3585 := [unit-resolution #575 #3584]: #538
+#3586 := [unit-resolution #1392 #3585]: #1339
+#3587 := [unit-resolution #1703 #3583]: #1628
+#3588 := [unit-resolution #1998 #3581]: #1632
+#3589 := [unit-resolution #1382 #3585]: #1374
+#3590 := [unit-resolution #705 #3589 #3588 #3587]: #653
+#3129 := (or #1567 #514)
+#3134 := (or #1567 #514 #599)
+#1859 := (or #1510 #1818)
+#296 := (or #291 #250)
+#1862 := (iff #296 #1859)
+#1855 := (or #1818 #1510)
+#1860 := (iff #1855 #1859)
+#1861 := [rewrite]: #1860
+#1857 := (iff #296 #1855)
+#1858 := [monotonicity #1820 #1512]: #1857
+#1863 := [trans #1858 #1861]: #1862
+#1854 := [asserted]: #296
+#1866 := [mp #1854 #1863]: #1859
+#3137 := [unit-resolution #1866 #3484]: #1510
+#3135 := [unit-resolution #2937 #3137]: #3134
+#3141 := [unit-resolution #3135 #2945 #2940]: #599
+#3132 := [unit-resolution #1477 #3141]: #1281
+#3133 := [unit-resolution #1330 #2938]: #1278
+#3130 := [unit-resolution #2786 #3133 #3132]: false
+#3126 := [lemma #3130]: #3129
+#3591 := [unit-resolution #3126 #3590 #3586]: false
+#3593 := [lemma #3591]: #3592
+#3601 := [unit-resolution #3593 #3247]: #1875
+#3602 := (or #656 #806 #809)
+#1821 := (or #1814 #1818)
+#292 := (or #290 #291)
+#1822 := (iff #292 #1821)
+#1823 := [monotonicity #1817 #1820]: #1822
+#1813 := [asserted]: #292
+#1826 := [mp #1813 #1823]: #1821
+#3127 := [unit-resolution #1826 #3484]: #1814
+#3603 := [unit-resolution #831 #3127]: #3602
+#3604 := [unit-resolution #3603 #3601 #3600]: #656
+#3522 := (or #514 #1571)
+#3515 := (or #1571 #514 #599)
+#3516 := [unit-resolution #2914 #3137]: #3515
+#3517 := [unit-resolution #3516 #2940 #2923]: #599
+#3518 := [unit-resolution #1477 #3517]: #1281
+#3519 := [unit-resolution #536 #2940 #2918]: #490
+#3520 := [unit-resolution #1330 #3519]: #1278
+#3521 := [unit-resolution #2786 #3520 #3518]: false
+#3523 := [lemma #3521]: #3522
+#3605 := [unit-resolution #3523 #3604]: #514
+#3606 := [unit-resolution #1392 #3605]: #1370
+#3607 := [unit-resolution #575 #3606]: #562
+#3608 := [unit-resolution #1713 #3607]: #1689
+#3609 := [unit-resolution #879 #3608 #3247]: #833
+#3610 := [unit-resolution #1402 #3605]: #1374
+#3611 := [unit-resolution #1579 #3604]: #1567
+#3612 := [unit-resolution #1723 #3607]: #1628
+#3613 := [unit-resolution #705 #3612 #3611 #3610]: #683
+#3614 := [unit-resolution #1968 #3613 #3609]: false
+#3615 := [lemma #3614]: #2244
+#3561 := (or #986 #989)
+#3513 := (or #656 #986 #989)
+#3107 := (or #860 #989 #986 #656)
+#3128 := (or #1936 #656 #986 #989)
+#3131 := [unit-resolution #2976 #3127]: #3128
+#3124 := [unit-resolution #3131 #2983 #3139 #3136]: #1936
+#3119 := [unit-resolution #879 #3170 #3124]: #707
+#3118 := [unit-resolution #1703 #3119]: #1628
+#3123 := [unit-resolution #1713 #3119]: #1401
+#3120 := [unit-resolution #575 #3123]: #538
+#3121 := [unit-resolution #1382 #3120]: #1374
+#3116 := (or #1339 #986 #989 #860)
+#3108 := [unit-resolution #2987 #3127]: #3116
+#3111 := [unit-resolution #3108 #3170 #3139 #3136]: #1339
+#3109 := [unit-resolution #3126 #3111]: #1567
+#3106 := [unit-resolution #705 #3109 #3121 #3118]: #683
+#3110 := [unit-resolution #1988 #3106]: #1940
+#3117 := (or #656 #653 #860 #809 #986 #989)
+#3122 := [unit-resolution #2922 #3127]: #3117
+#3125 := [unit-resolution #3122 #3109 #3136 #3139 #2983 #3170]: #809
+#3114 := [unit-resolution #2215 #3125]: #2183
+#3113 := [unit-resolution #1011 #3114 #3110 #3139 #3136]: false
+#3115 := [lemma #3113]: #3107
+#3112 := [unit-resolution #3115 #2983 #3136 #3139]: #860
+#3104 := [unit-resolution #2329 #3112]: #2305
+#3105 := [unit-resolution #2859 #3104]: #1139
+#3102 := [unit-resolution #2564 #3105]: #2556
+#3485 := [unit-resolution #2877 #3102]: #1239
+#3486 := [unit-resolution #2726 #3485]: #2679
+#3487 := [unit-resolution #2574 #3105]: #2491
+#3488 := (or #2187 #656 #989 #986)
+#3489 := [unit-resolution #3225 #3127]: #3488
+#3490 := [unit-resolution #3489 #2983 #3136 #3139]: #2187
+#3491 := [unit-resolution #2736 #3485]: #2495
+#3492 := [unit-resolution #1137 #3491 #3490 #3487]: #1085
+#3493 := [unit-resolution #2442 #3492]: #2434
+#3494 := [unit-resolution #1237 #3493 #3486]: #1196
+#3495 := [unit-resolution #2670 #3494]: #2373
+#3496 := [unit-resolution #2452 #3492]: #2369
+#3497 := [unit-resolution #2660 #3494]: #2633
+#3498 := [unit-resolution #1197 #3497]: #1037
+#3499 := [unit-resolution #2350 #3498]: #2338
+#3500 := [unit-resolution #1083 #3499 #3496 #3495]: #908
+#3501 := [unit-resolution #2113 #3500]: #1757
+#3502 := [unit-resolution #2370 #3498]: #2034
+#3503 := [unit-resolution #2103 #3500]: #2030
+#3504 := [unit-resolution #903 #3503 #3502]: #731
+#3505 := [unit-resolution #1734 #3504]: #1722
+#3509 := [unit-resolution #3508 #3505 #3501]: #602
+#3510 := [unit-resolution #1754 #3504]: #1418
+#3511 := [unit-resolution #2805 #3510]: #574
+#3512 := [unit-resolution #1487 #3511 #3509]: false
+#3514 := [lemma #3512]: #3513
+#3524 := [unit-resolution #3514 #3136 #3139]: #656
+#3525 := [unit-resolution #3523 #3524]: #514
+#3526 := [unit-resolution #3108 #3525 #3139 #3136]: #860
+#3527 := [unit-resolution #2329 #3526]: #2305
+#3528 := [unit-resolution #2859 #3527]: #1139
+#3529 := [unit-resolution #2564 #3528]: #2556
+#3530 := [unit-resolution #2877 #3529]: #1239
+#3531 := [unit-resolution #2726 #3530]: #2679
+#3532 := [unit-resolution #2574 #3528]: #2491
+#3533 := [unit-resolution #1402 #3525]: #1374
+#3534 := [unit-resolution #1579 #3524]: #1567
+#3535 := [unit-resolution #1392 #3525]: #1370
+#3536 := [unit-resolution #575 #3535]: #562
+#3537 := [unit-resolution #1723 #3536]: #1628
+#3538 := [unit-resolution #705 #3537 #3534 #3533]: #683
+#3539 := [unit-resolution #1988 #3538]: #1940
+#3540 := [unit-resolution #1011 #3539 #3139 #3136]: #959
+#3541 := [unit-resolution #2195 #3540]: #2187
+#3542 := [unit-resolution #2736 #3530]: #2495
+#3543 := [unit-resolution #1137 #3542 #3541 #3532]: #1085
+#3544 := [unit-resolution #2442 #3543]: #2434
+#3545 := [unit-resolution #1237 #3544 #3531]: #1196
+#3546 := [unit-resolution #2670 #3545]: #2373
+#3547 := [unit-resolution #2452 #3543]: #2369
+#3548 := [unit-resolution #2660 #3545]: #2633
+#3549 := [unit-resolution #1197 #3548]: #1037
+#3550 := [unit-resolution #2350 #3549]: #2338
+#3551 := [unit-resolution #1083 #3550 #3547 #3546]: #908
+#3552 := [unit-resolution #2113 #3551]: #1757
+#3553 := [unit-resolution #2370 #3549]: #2034
+#3554 := [unit-resolution #2103 #3551]: #2030
+#3555 := [unit-resolution #903 #3554 #3553]: #731
+#3556 := [unit-resolution #1734 #3555]: #1722
+#3557 := [unit-resolution #3508 #3556 #3552]: #602
+#3558 := [unit-resolution #1754 #3555]: #1418
+#3559 := [unit-resolution #2805 #3558]: #574
+#3560 := [unit-resolution #1487 #3559 #3557]: false
+#3562 := [lemma #3560]: #3561
+#3616 := [unit-resolution #3562 #3615]: #989
+#3617 := [unit-resolution #2584 #3616]: #2552
+#3618 := [unit-resolution #2859 #3617]: #1013
+#3619 := [unit-resolution #2329 #3618]: #1997
+#3620 := [unit-resolution #3593 #3619]: #1875
+#3621 := [unit-resolution #2614 #3616]: #2491
+#3622 := [unit-resolution #2604 #3616]: #2556
+#3623 := [unit-resolution #2877 #3622]: #1239
+#3624 := [unit-resolution #2736 #3623]: #2495
+#3625 := [unit-resolution #2726 #3623]: #2679
+#3626 := [unit-resolution #3580 #3625]: #2430
+#3627 := [unit-resolution #1137 #3626 #3624 #3621]: #962
+#3628 := [unit-resolution #2235 #3627]: #1879
+#3629 := [unit-resolution #3603 #3628 #3620]: #656
+#3630 := [unit-resolution #3523 #3629]: #514
+#3631 := [unit-resolution #1392 #3630]: #1370
+#3632 := [unit-resolution #575 #3631]: #562
+#3633 := [unit-resolution #1713 #3632]: #1689
+#3634 := [unit-resolution #879 #3633 #3619]: #833
+#3635 := [unit-resolution #1402 #3630]: #1374
+#3636 := [unit-resolution #1579 #3629]: #1567
+#3637 := [unit-resolution #1723 #3632]: #1628
+#3638 := [unit-resolution #705 #3637 #3636 #3635]: #683
+[unit-resolution #1968 #3638 #3634]: false
+unsat
+963adaec295f3cad11b90a8d9b0f3f328fee4eb9 95 0
+#2 := false
+decl f3 :: (-> int S1)
+decl ?v0!0 :: int
+#74 := ?v0!0
+#75 := (f3 ?v0!0)
+decl f1 :: S1
+#4 := f1
+#76 := (= f1 #75)
+#68 := (not #76)
+decl ?v1!1 :: int
+#85 := ?v1!1
+#86 := (f3 ?v1!1)
+#87 := (= f1 #86)
+#105 := (or #76 #87)
+#108 := (not #105)
+#111 := (and #76 #108)
+#88 := (or #87 #76)
+#89 := (not #88)
+#82 := (not #68)
+#95 := (and #82 #89)
+#112 := (iff #95 #111)
+#109 := (iff #89 #108)
+#106 := (iff #88 #105)
+#107 := [rewrite]: #106
+#110 := [monotonicity #107]: #109
+#103 := (iff #82 #76)
+#104 := [rewrite]: #103
+#113 := [monotonicity #104 #110]: #112
+#11 := (:var 1 int)
+#12 := (f3 #11)
+#39 := (= f1 #12)
+#8 := (:var 0 int)
+#9 := (f3 #8)
+#36 := (= f1 #9)
+#45 := (or #36 #39)
+#50 := (forall (vars (?v1 int)) #45)
+#56 := (not #36)
+#57 := (or #56 #50)
+#62 := (forall (vars (?v0 int)) #57)
+#65 := (not #62)
+#98 := (~ #65 #95)
+#77 := (or #36 #76)
+#71 := (forall (vars (?v1 int)) #77)
+#78 := (or #68 #71)
+#79 := (not #78)
+#96 := (~ #79 #95)
+#90 := (not #71)
+#91 := (~ #90 #89)
+#92 := [sk]: #91
+#83 := (~ #82 #82)
+#84 := [refl]: #83
+#97 := [nnf-neg #84 #92]: #96
+#80 := (~ #65 #79)
+#81 := [sk]: #80
+#99 := [trans #81 #97]: #98
+#10 := (= #9 f1)
+#13 := (= #12 f1)
+#14 := (or #13 #10)
+#15 := (forall (vars (?v1 int)) #14)
+#16 := (implies #10 #15)
+#17 := (forall (vars (?v0 int)) #16)
+#18 := (not #17)
+#66 := (iff #18 #65)
+#63 := (iff #17 #62)
+#60 := (iff #16 #57)
+#53 := (implies #36 #50)
+#58 := (iff #53 #57)
+#59 := [rewrite]: #58
+#54 := (iff #16 #53)
+#51 := (iff #15 #50)
+#48 := (iff #14 #45)
+#42 := (or #39 #36)
+#46 := (iff #42 #45)
+#47 := [rewrite]: #46
+#43 := (iff #14 #42)
+#37 := (iff #10 #36)
+#38 := [rewrite]: #37
+#40 := (iff #13 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41 #38]: #43
+#49 := [trans #44 #47]: #48
+#52 := [quant-intro #49]: #51
+#55 := [monotonicity #38 #52]: #54
+#61 := [trans #55 #59]: #60
+#64 := [quant-intro #61]: #63
+#67 := [monotonicity #64]: #66
+#35 := [asserted]: #18
+#70 := [mp #35 #67]: #65
+#100 := [mp~ #70 #99]: #95
+#101 := [mp #100 #113]: #111
+#114 := [and-elim #101]: #108
+#115 := [not-or-elim #114]: #68
+#102 := [and-elim #101]: #76
+[unit-resolution #102 #115]: false
+unsat
+02303e47876761c1d2ed5df38d9bde0c05751a27 146 0
+#2 := false
+decl f3 :: (-> S1 S2 S1)
+#9 := (:var 0 S2)
+decl f4 :: S1
+#15 := f4
+#16 := (f3 f4 #9)
+#614 := (pattern #16)
+decl f1 :: S1
+#4 := f1
+#54 := (= f1 #16)
+#95 := (not #54)
+#615 := (forall (vars (?v0 S2)) (:pat #614) #95)
+decl f5 :: S2
+#19 := f5
+#20 := (f3 f4 f5)
+#61 := (= f1 #20)
+#192 := (= f1 f4)
+#193 := (iff #61 #192)
+#8 := (:var 1 S1)
+#10 := (f3 #8 #9)
+#607 := (pattern #10)
+#44 := (= f1 #8)
+#41 := (= f1 #10)
+#47 := (iff #41 #44)
+#608 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #607) #47)
+#50 := (forall (vars (?v0 S1) (?v1 S2)) #47)
+#611 := (iff #50 #608)
+#609 := (iff #47 #47)
+#610 := [refl]: #609
+#612 := [quant-intro #610]: #611
+#86 := (~ #50 #50)
+#84 := (~ #47 #47)
+#85 := [refl]: #84
+#87 := [nnf-pos #85]: #86
+#12 := (= #8 f1)
+#11 := (= #10 f1)
+#13 := (iff #11 #12)
+#14 := (forall (vars (?v0 S1) (?v1 S2)) #13)
+#51 := (iff #14 #50)
+#48 := (iff #13 #47)
+#45 := (iff #12 #44)
+#46 := [rewrite]: #45
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#49 := [monotonicity #43 #46]: #48
+#52 := [quant-intro #49]: #51
+#40 := [asserted]: #14
+#55 := [mp #40 #52]: #50
+#79 := [mp~ #55 #87]: #50
+#613 := [mp #79 #612]: #608
+#194 := (not #608)
+#270 := (or #194 #193)
+#602 := [quant-inst]: #270
+#279 := [unit-resolution #602 #613]: #193
+decl ?v0!0 :: S2
+#76 := ?v0!0
+#88 := (f3 f4 ?v0!0)
+#80 := (= f1 #88)
+#278 := (iff #80 #192)
+#280 := (or #194 #278)
+#271 := [quant-inst]: #280
+#269 := [unit-resolution #271 #613]: #278
+#282 := (not #278)
+#241 := (or #282 #192)
+#101 := (not #61)
+#257 := [hypothesis]: #101
+#106 := (or #61 #80)
+#98 := (forall (vars (?v0 S2)) #95)
+#107 := (or #101 #98)
+#114 := (and #106 #107)
+#108 := (and #107 #106)
+#115 := (iff #108 #114)
+#116 := [rewrite]: #115
+#58 := (exists (vars (?v0 S2)) #54)
+#70 := (not #58)
+#71 := (iff #61 #70)
+#109 := (~ #71 #108)
+#99 := (~ #70 #98)
+#96 := (~ #95 #95)
+#97 := [refl]: #96
+#100 := [nnf-neg #97]: #99
+#92 := (not #70)
+#93 := (~ #92 #80)
+#81 := (~ #58 #80)
+#89 := [sk]: #81
+#94 := [nnf-neg #89]: #93
+#104 := (~ #61 #61)
+#105 := [refl]: #104
+#102 := (~ #101 #101)
+#103 := [refl]: #102
+#110 := [nnf-pos #103 #105 #94 #100]: #109
+#21 := (= #20 f1)
+#17 := (= #16 f1)
+#18 := (exists (vars (?v0 S2)) #17)
+#22 := (iff #18 #21)
+#23 := (not #22)
+#74 := (iff #23 #71)
+#64 := (iff #58 #61)
+#67 := (not #64)
+#72 := (iff #67 #71)
+#73 := [rewrite]: #72
+#68 := (iff #23 #67)
+#65 := (iff #22 #64)
+#62 := (iff #21 #61)
+#63 := [rewrite]: #62
+#59 := (iff #18 #58)
+#56 := (iff #17 #54)
+#57 := [rewrite]: #56
+#60 := [quant-intro #57]: #59
+#66 := [monotonicity #60 #63]: #65
+#69 := [monotonicity #66]: #68
+#75 := [trans #69 #73]: #74
+#53 := [asserted]: #23
+#78 := [mp #53 #75]: #71
+#111 := [mp~ #78 #110]: #108
+#112 := [mp #111 #116]: #114
+#113 := [and-elim #112]: #106
+#598 := [unit-resolution #113 #257]: #80
+#285 := (not #80)
+#264 := (or #282 #285 #192)
+#599 := [def-axiom]: #264
+#582 := [unit-resolution #599 #598]: #241
+#245 := [unit-resolution #582 #269]: #192
+#283 := (not #192)
+#603 := (not #193)
+#246 := (or #603 #283)
+#604 := (or #603 #61 #283)
+#605 := [def-axiom]: #604
+#247 := [unit-resolution #605 #257]: #246
+#248 := [unit-resolution #247 #245 #279]: false
+#584 := [lemma #248]: #61
+#620 := (or #101 #615)
+#621 := (iff #107 #620)
+#618 := (iff #98 #615)
+#616 := (iff #95 #95)
+#617 := [refl]: #616
+#619 := [quant-intro #617]: #618
+#622 := [monotonicity #619]: #621
+#117 := [and-elim #112]: #107
+#623 := [mp #117 #622]: #620
+#284 := [unit-resolution #623 #584]: #615
+#596 := (not #615)
+#256 := (or #596 #101)
+#261 := [quant-inst]: #256
+[unit-resolution #261 #584 #284]: false
+unsat
+b2decb74065cb968996625139aa422ae59e9e137 146 2
+#2 := false
+decl f3 :: (-> S1 S2 S1)
+#9 := (:var 0 S2)
+decl f5 :: S1
+#23 := f5
+#24 := (f3 f5 #9)
+#693 := (pattern #24)
+decl f1 :: S1
+#4 := f1
+#78 := (= f1 #24)
+#174 := (not #78)
+#694 := (forall (vars (?v0 S2)) (:pat #693) #174)
+decl f4 :: S2
+#18 := f4
+#27 := (f3 f5 f4)
+#85 := (= f1 #27)
+#252 := (= f1 f5)
+#253 := (iff #85 #252)
+#8 := (:var 1 S1)
+#10 := (f3 #8 #9)
+#670 := (pattern #10)
+#51 := (= f1 #8)
+#48 := (= f1 #10)
+#54 := (iff #48 #51)
+#671 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #670) #54)
+#57 := (forall (vars (?v0 S1) (?v1 S2)) #54)
+#674 := (iff #57 #671)
+#672 := (iff #54 #54)
+#673 := [refl]: #672
+#675 := [quant-intro #673]: #674
+#112 := (~ #57 #57)
+#110 := (~ #54 #54)
+#111 := [refl]: #110
+#113 := [nnf-pos #111]: #112
+#12 := (= #8 f1)
+#11 := (= #10 f1)
+#13 := (iff #11 #12)
+#14 := (forall (vars (?v0 S1) (?v1 S2)) #13)
+#58 := (iff #14 #57)
+#55 := (iff #13 #54)
+#52 := (iff #12 #51)
+#53 := [rewrite]: #52
+#49 := (iff #11 #48)
+#50 := [rewrite]: #49
+#56 := [monotonicity #50 #53]: #55
+#59 := [quant-intro #56]: #58
+#47 := [asserted]: #14
+#62 := [mp #47 #59]: #57
+#103 := [mp~ #62 #113]: #57
+#676 := [mp #103 #675]: #671
+#254 := (not #671)
+#330 := (or #254 #253)
+#331 := [quant-inst]: #330
+#340 := [unit-resolution #331 #676]: #253
+decl ?v0!3 :: S2
+#145 := ?v0!3
+#146 := (f3 f5 ?v0!3)
+#118 := (= f1 #146)
+#339 := (iff #118 #252)
+#341 := (or #254 #339)
+#332 := [quant-inst]: #341
+#658 := [unit-resolution #332 #676]: #339
+#343 := (not #339)
+#661 := (or #343 #252)
+#180 := (not #85)
+#660 := [hypothesis]: #180
+#185 := (or #85 #118)
+#177 := (forall (vars (?v0 S2)) #174)
+#186 := (or #180 #177)
+#193 := (and #185 #186)
+#187 := (and #186 #185)
+#194 := (iff #187 #193)
+#195 := [rewrite]: #194
+#82 := (exists (vars (?v0 S2)) #78)
+#94 := (not #82)
+#95 := (iff #85 #94)
+#188 := (~ #95 #187)
+#178 := (~ #94 #177)
+#175 := (~ #174 #174)
+#176 := [refl]: #175
+#179 := [nnf-neg #176]: #178
+#171 := (not #94)
+#172 := (~ #171 #118)
+#119 := (~ #82 #118)
+#168 := [sk]: #119
+#173 := [nnf-neg #168]: #172
+#183 := (~ #85 #85)
+#184 := [refl]: #183
+#181 := (~ #180 #180)
+#182 := [refl]: #181
+#189 := [nnf-pos #182 #184 #173 #179]: #188
+#28 := (= #27 f1)
+#25 := (= #24 f1)
+#26 := (exists (vars (?v0 S2)) #25)
+#29 := (iff #26 #28)
+#30 := (not #29)
+#98 := (iff #30 #95)
+#88 := (iff #82 #85)
+#91 := (not #88)
+#96 := (iff #91 #95)
+#97 := [rewrite]: #96
+#92 := (iff #30 #91)
+#89 := (iff #29 #88)
+#86 := (iff #28 #85)
+#87 := [rewrite]: #86
+#83 := (iff #26 #82)
+#80 := (iff #25 #78)
+#81 := [rewrite]: #80
+#84 := [quant-intro #81]: #83
+#90 := [monotonicity #84 #87]: #89
+#93 := [monotonicity #90]: #92
+#99 := [trans #93 #97]: #98
+#77 := [asserted]: #30
+#102 := [mp #77 #99]: #95
+#190 := [mp~ #102 #189]: #187
+#191 := [mp #190 #195]: #193
+#192 := [and-elim #191]: #185
+#318 := [unit-resolution #192 #660]: #118
+#342 := (not #118)
+#346 := (or #343 #342 #252)
+#325 := [def-axiom]: #346
+#302 := [unit-resolution #325 #318]: #661
+#645 := [unit-resolution #302 #658]: #252
+#344 := (not #252)
+#665 := (not #253)
+#306 := (or #665 #344)
+#666 := (or #665 #85 #344)
+#667 := [def-axiom]: #666
+#307 := [unit-resolution #667 #660]: #306
+#308 := [unit-resolution #307 #645 #340]: false
+#309 := [lemma #308]: #85
+#699 := (or #180 #694)
+#700 := (iff #186 #699)
+#697 := (iff #177 #694)
+#695 := (iff #174 #174)
+#696 := [refl]: #695
+#698 := [quant-intro #696]: #697
+#701 := [monotonicity #698]: #700
+#196 := [and-elim #191]: #186
+#702 := [mp #196 #701]: #699
+#272 := [unit-resolution #702 #309]: #694
+#669 := (not #694)
+#659 := (or #669 #180)
+#317 := [quant-inst]: #659
+[unit-resolution #317 #309 #272]: false
+unsat
+WARNING: failed to find a pattern for quantifier (quantifier id: k!13)
+
+2ac0be1d14d2be0e9bbc5f93b96f7b41fb69108e 91 0
+#2 := false
+decl f3 :: (-> S2 S1)
+decl f4 :: S2
+#8 := f4
+#9 := (f3 f4)
+decl f1 :: S1
+#4 := f1
+#41 := (= f1 #9)
+decl f5 :: S2
+#19 := f5
+#20 := (f3 f5)
+#63 := (= f1 #20)
+#70 := (not #41)
+#71 := (or #70 #63)
+#76 := (not #71)
+#21 := (= #20 f1)
+#10 := (= #9 f1)
+#22 := (implies #10 #21)
+#23 := (not #22)
+#77 := (iff #23 #76)
+#74 := (iff #22 #71)
+#67 := (implies #41 #63)
+#72 := (iff #67 #71)
+#73 := [rewrite]: #72
+#68 := (iff #22 #67)
+#65 := (iff #21 #63)
+#66 := [rewrite]: #65
+#42 := (iff #10 #41)
+#43 := [rewrite]: #42
+#69 := [monotonicity #43 #66]: #68
+#75 := [trans #69 #73]: #74
+#78 := [monotonicity #75]: #77
+#62 := [asserted]: #23
+#81 := [mp #62 #78]: #76
+#79 := [not-or-elim #81]: #41
+#11 := (:var 0 S2)
+#12 := (f3 #11)
+#576 := (pattern #12)
+#44 := (= f1 #12)
+#53 := (not #44)
+#577 := (forall (vars (?v0 S2)) (:pat #576) #53)
+#56 := (forall (vars (?v0 S2)) #53)
+#580 := (iff #56 #577)
+#578 := (iff #53 #53)
+#579 := [refl]: #578
+#581 := [quant-intro #579]: #580
+#47 := (exists (vars (?v0 S2)) #44)
+#50 := (not #47)
+#87 := (~ #50 #56)
+#90 := (~ #53 #53)
+#91 := [refl]: #90
+#99 := [nnf-neg #91]: #87
+#59 := (ite #41 #50 #56)
+#97 := (iff #59 #50)
+#1 := true
+#92 := (ite true #50 #56)
+#95 := (iff #92 #50)
+#96 := [rewrite]: #95
+#93 := (iff #59 #92)
+#88 := (iff #41 true)
+#89 := [iff-true #79]: #88
+#94 := [monotonicity #89]: #93
+#98 := [trans #94 #96]: #97
+#13 := (= #12 f1)
+#16 := (not #13)
+#17 := (forall (vars (?v0 S2)) #16)
+#14 := (exists (vars (?v0 S2)) #13)
+#15 := (not #14)
+#18 := (ite #10 #15 #17)
+#60 := (iff #18 #59)
+#57 := (iff #17 #56)
+#54 := (iff #16 #53)
+#45 := (iff #13 #44)
+#46 := [rewrite]: #45
+#55 := [monotonicity #46]: #54
+#58 := [quant-intro #55]: #57
+#51 := (iff #15 #50)
+#48 := (iff #14 #47)
+#49 := [quant-intro #46]: #48
+#52 := [monotonicity #49]: #51
+#61 := [monotonicity #43 #52 #58]: #60
+#40 := [asserted]: #18
+#64 := [mp #40 #61]: #59
+#86 := [mp #64 #98]: #50
+#85 := [mp~ #86 #99]: #56
+#582 := [mp #85 #581]: #577
+#161 := (not #577)
+#248 := (or #161 #70)
+#162 := [quant-inst]: #248
+[unit-resolution #162 #582 #79]: false
+unsat
[phone]d25438c6ae5473fad2de32b7d8 17 0
+#2 := false
+#8 := 3::int
+#9 := (= 3::int 3::int)
+#10 := (not #9)
+#35 := (iff #10 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #10 #30)
+#28 := (iff #9 true)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#27 := [asserted]: #10
+[mp #27 #36]: false
+unsat
+b2020b3a3ba93004ca7a53417cddc32dc8d008ca 17 0
+#2 := false
+#8 := 3::real
+#9 := (= 3::real 3::real)
+#10 := (not #9)
+#35 := (iff #10 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #10 #30)
+#28 := (iff #9 true)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#27 := [asserted]: #10
+[mp #27 #36]: false
+unsat
+be5a225497850b7db6ae5b15ea7142081ca2d5a8 26 0
+#2 := false
+#11 := 4::int
+#9 := 1::int
+#8 := 3::int
+#10 := (+ 3::int 1::int)
+#12 := (= #10 4::int)
+#13 := (not #12)
+#44 := (iff #13 false)
+#1 := true
+#39 := (not true)
+#42 := (iff #39 false)
+#43 := [rewrite]: #42
+#40 := (iff #13 #39)
+#37 := (iff #12 true)
+#32 := (= 4::int 4::int)
+#35 := (iff #32 true)
+#36 := [rewrite]: #35
+#33 := (iff #12 #32)
+#31 := [rewrite]: #12
+#34 := [monotonicity #31]: #33
+#38 := [trans #34 #36]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#30 := [asserted]: #13
+[mp #30 #45]: false
+unsat
+27da8eb82d7b78036f585d0fe4fd9359af185902 41 0
+#2 := false
+decl f3 :: int
+#8 := f3
+decl f5 :: int
+#10 := f5
+#13 := (+ f5 f3)
+decl f4 :: int
+#9 := f4
+#14 := (+ f4 #13)
+#11 := (+ f4 f5)
+#12 := (+ f3 #11)
+#15 := (= #12 #14)
+#16 := (not #15)
+#56 := (iff #16 false)
+#1 := true
+#51 := (not true)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #16 #51)
+#49 := (iff #15 true)
+#44 := (= #12 #12)
+#47 := (iff #44 true)
+#48 := [rewrite]: #47
+#45 := (iff #15 #44)
+#42 := (= #14 #12)
+#34 := (+ f3 f5)
+#37 := (+ f4 #34)
+#40 := (= #37 #12)
+#41 := [rewrite]: #40
+#38 := (= #14 #37)
+#35 := (= #13 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#33 := [asserted]: #16
+[mp #33 #57]: false
+unsat
+91ecdcadc7bcd881c06aad90ddc50bfc34a0d967 35 0
+#2 := false
+#9 := 3::int
+#10 := 8::int
+#11 := (<= 3::int 8::int)
+#12 := (ite #11 8::int 3::int)
+#8 := 5::int
+#13 := (< 5::int #12)
+#14 := (not #13)
+#55 := (iff #14 false)
+#1 := true
+#50 := (not true)
+#53 := (iff #50 false)
+#54 := [rewrite]: #53
+#51 := (iff #14 #50)
+#48 := (iff #13 true)
+#43 := (< 5::int 8::int)
+#46 := (iff #43 true)
+#47 := [rewrite]: #46
+#44 := (iff #13 #43)
+#41 := (= #12 8::int)
+#36 := (ite true 8::int 3::int)
+#39 := (= #36 8::int)
+#40 := [rewrite]: #39
+#37 := (= #12 #36)
+#34 := (iff #11 true)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#52 := [monotonicity #49]: #51
+#56 := [trans #52 #54]: #55
+#31 := [asserted]: #14
+[mp #31 #56]: false
+unsat
+f7013e025d7ca304e0eee556d2e11dcb683e132a 209 0
+#2 := false
+#11 := 0::real
+decl f4 :: real
+#9 := f4
+#41 := -1::real
+#43 := (* -1::real f4)
+#93 := (>= f4 0::real)
+#100 := (ite #93 f4 #43)
+#112 := (* -1::real #100)
+#149 := (+ f4 #112)
+#150 := (<= #149 0::real)
+#139 := (= f4 #100)
+#151 := (+ #43 #112)
+#154 := (<= #151 0::real)
+#140 := (= #43 #100)
+#94 := (not #93)
+#223 := [hypothesis]: #94
+#143 := (or #93 #140)
+#144 := [def-axiom]: #143
+#224 := [unit-resolution #144 #223]: #140
+#197 := (not #140)
+#198 := (or #197 #154)
+#199 := [th-lemma]: #198
+#225 := [unit-resolution #199 #224]: #154
+decl f3 :: real
+#8 := f3
+#42 := (* -1::real f3)
+#81 := (>= f3 0::real)
+#88 := (ite #81 f3 #42)
+#111 := (* -1::real #88)
+#179 := (+ f3 #111)
+#180 := (<= #179 0::real)
+#128 := (= f3 #88)
+#10 := (+ f3 f4)
+#69 := (>= #10 0::real)
+#152 := (+ #42 #111)
+#153 := (<= #152 0::real)
+#126 := (= #42 #88)
+#82 := (not #81)
+#44 := (+ #42 #43)
+#76 := (ite #69 #10 #44)
+#145 := (* -1::real #76)
+#146 := (+ #44 #145)
+#148 := (>= #146 0::real)
+#132 := (= #44 #76)
+#70 := (not #69)
+#161 := [hypothesis]: #70
+#129 := (or #69 #132)
+#130 := [def-axiom]: #129
+#170 := [unit-resolution #130 #161]: #132
+#171 := (not #132)
+#172 := (or #171 #148)
+#173 := [th-lemma]: #172
+#174 := [unit-resolution #173 #170]: #148
+#176 := (or #94 #69)
+#155 := [hypothesis]: #93
+#141 := (or #94 #139)
+#142 := [def-axiom]: #141
+#156 := [unit-resolution #142 #155]: #139
+#157 := (not #139)
+#158 := (or #157 #150)
+#159 := [th-lemma]: #158
+#160 := [unit-resolution #159 #156]: #150
+#162 := (or #82 #94 #69)
+#163 := [th-lemma]: #162
+#164 := [unit-resolution #163 #155 #161]: #82
+#137 := (or #81 #126)
+#138 := [def-axiom]: #137
+#165 := [unit-resolution #138 #164]: #126
+#166 := (not #126)
+#167 := (or #166 #153)
+#168 := [th-lemma]: #167
+#169 := [unit-resolution #168 #165]: #153
+#113 := (+ #111 #112)
+#114 := (+ #76 #113)
+#115 := (<= #114 0::real)
+#120 := (not #115)
+#19 := (- f4)
+#18 := (< f4 0::real)
+#20 := (ite #18 #19 f4)
+#16 := (- f3)
+#15 := (< f3 0::real)
+#17 := (ite #15 #16 f3)
+#21 := (+ #17 #20)
+#13 := (- #10)
+#12 := (< #10 0::real)
+#14 := (ite #12 #13 #10)
+#22 := (<= #14 #21)
+#23 := (not #22)
+#123 := (iff #23 #120)
+#57 := (ite #18 #43 f4)
+#52 := (ite #15 #42 f3)
+#60 := (+ #52 #57)
+#47 := (ite #12 #44 #10)
+#63 := (<= #47 #60)
+#66 := (not #63)
+#121 := (iff #66 #120)
+#118 := (iff #63 #115)
+#105 := (+ #88 #100)
+#108 := (<= #76 #105)
+#116 := (iff #108 #115)
+#117 := [rewrite]: #116
+#109 := (iff #63 #108)
+#106 := (= #60 #105)
+#103 := (= #57 #100)
+#97 := (ite #94 #43 f4)
+#101 := (= #97 #100)
+#102 := [rewrite]: #101
+#98 := (= #57 #97)
+#95 := (iff #18 #94)
+#96 := [rewrite]: #95
+#99 := [monotonicity #96]: #98
+#104 := [trans #99 #102]: #103
+#91 := (= #52 #88)
+#85 := (ite #82 #42 f3)
+#89 := (= #85 #88)
+#90 := [rewrite]: #89
+#86 := (= #52 #85)
+#83 := (iff #15 #82)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84]: #86
+#92 := [trans #87 #90]: #91
+#107 := [monotonicity #92 #104]: #106
+#79 := (= #47 #76)
+#73 := (ite #70 #44 #10)
+#77 := (= #73 #76)
+#78 := [rewrite]: #77
+#74 := (= #47 #73)
+#71 := (iff #12 #70)
+#72 := [rewrite]: #71
+#75 := [monotonicity #72]: #74
+#80 := [trans #75 #78]: #79
+#110 := [monotonicity #80 #107]: #109
+#119 := [trans #110 #117]: #118
+#122 := [monotonicity #119]: #121
+#67 := (iff #23 #66)
+#64 := (iff #22 #63)
+#61 := (= #21 #60)
+#58 := (= #20 #57)
+#55 := (= #19 #43)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#53 := (= #17 #52)
+#50 := (= #16 #42)
+#51 := [rewrite]: #50
+#54 := [monotonicity #51]: #53
+#62 := [monotonicity #54 #59]: #61
+#48 := (= #14 #47)
+#45 := (= #13 #44)
+#46 := [rewrite]: #45
+#49 := [monotonicity #46]: #48
+#65 := [monotonicity #49 #62]: #64
+#68 := [monotonicity #65]: #67
+#124 := [trans #68 #122]: #123
+#40 := [asserted]: #23
+#125 := [mp #40 #124]: #120
+#175 := [th-lemma #125 #174 #155 #169 #160]: false
+#177 := [lemma #175]: #176
+#195 := [unit-resolution #177 #161]: #94
+#196 := [unit-resolution #144 #195]: #140
+#200 := [unit-resolution #199 #196]: #154
+#192 := (not #148)
+#191 := (not #154)
+#193 := (or #82 #191 #192)
+#182 := [hypothesis]: #81
+#183 := [hypothesis]: #148
+#184 := [hypothesis]: #154
+#135 := (or #82 #128)
+#136 := [def-axiom]: #135
+#185 := [unit-resolution #136 #182]: #128
+#186 := (not #128)
+#187 := (or #186 #180)
+#188 := [th-lemma]: #187
+#189 := [unit-resolution #188 #185]: #180
+#190 := [th-lemma #189 #184 #125 #183 #182]: false
+#194 := [lemma #190]: #193
+#201 := [unit-resolution #194 #200 #174]: #82
+#202 := [unit-resolution #138 #201]: #126
+#203 := [unit-resolution #168 #202]: #153
+#204 := [th-lemma #200 #125 #174 #203]: false
+#205 := [lemma #204]: #69
+#208 := [hypothesis]: #82
+#209 := (or #93 #81 #70)
+#210 := [th-lemma]: #209
+#211 := [unit-resolution #210 #208 #205]: #93
+#212 := [unit-resolution #142 #211]: #139
+#213 := [unit-resolution #159 #212]: #150
+#214 := [unit-resolution #138 #208]: #126
+#215 := [unit-resolution #168 #214]: #153
+#147 := (+ #10 #145)
+#181 := (>= #147 0::real)
+#131 := (= #10 #76)
+#133 := (or #70 #131)
+#134 := [def-axiom]: #133
+#216 := [unit-resolution #134 #205]: #131
+#217 := (not #131)
+#218 := (or #217 #181)
+#219 := [th-lemma]: #218
+#220 := [unit-resolution #219 #216]: #181
+#221 := [th-lemma #208 #125 #220 #215 #213]: false
+#222 := [lemma #221]: #81
+#226 := [unit-resolution #136 #222]: #128
+#227 := [unit-resolution #188 #226]: #180
+#228 := [th-lemma #125 #220 #227 #223 #225]: false
+#229 := [lemma #228]: #93
+#230 := [unit-resolution #142 #229]: #139
+#231 := [unit-resolution #159 #230]: #150
+[th-lemma #125 #220 #227 #231]: false
+unsat
+f7520b53fa3979c118a10ff2625efed570862fcf 42 0
+#2 := false
+decl f3 :: (-> S1 S2)
+decl f1 :: S1
+#4 := f1
+#13 := (f3 f1)
+decl f2 :: S1
+#5 := f2
+#9 := 3::int
+#8 := 2::int
+#10 := (< 2::int 3::int)
+#11 := (ite #10 f1 f2)
+#12 := (f3 #11)
+#14 := (= #12 #13)
+#15 := (not #14)
+#57 := (iff #15 false)
+#1 := true
+#52 := (not true)
+#55 := (iff #52 false)
+#56 := [rewrite]: #55
+#53 := (iff #15 #52)
+#50 := (iff #14 true)
+#45 := (= #13 #13)
+#48 := (iff #45 true)
+#49 := [rewrite]: #48
+#46 := (iff #14 #45)
+#42 := (= #11 f1)
+#37 := (ite true f1 f2)
+#40 := (= #37 f1)
+#41 := [rewrite]: #40
+#38 := (= #11 #37)
+#35 := (iff #10 true)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#43 := [trans #39 #41]: #42
+#44 := [monotonicity #43]: #14
+#47 := [monotonicity #44]: #46
+#51 := [trans #47 #49]: #50
+#54 := [monotonicity #51]: #53
+#58 := [trans #54 #56]: #57
+#32 := [asserted]: #15
+[mp #32 #58]: false
+unsat
+12074cc6dbadf6cb8cee50c8e211c3bd46e830d4 54 0
+#2 := false
+#13 := 1::int
+decl f3 :: int
+#9 := f3
+#14 := (< f3 1::int)
+#10 := 3::int
+#11 := (+ f3 3::int)
+#8 := 4::int
+#12 := (<= 4::int #11)
+#15 := (or #12 #14)
+#16 := (not #15)
+#71 := (iff #16 false)
+#34 := (+ 3::int f3)
+#37 := (<= 4::int #34)
+#43 := (or #14 #37)
+#48 := (not #43)
+#69 := (iff #48 false)
+#1 := true
+#64 := (not true)
+#67 := (iff #64 false)
+#68 := [rewrite]: #67
+#65 := (iff #48 #64)
+#62 := (iff #43 true)
+#53 := (>= f3 1::int)
+#51 := (not #53)
+#57 := (or #51 #53)
+#60 := (iff #57 true)
+#61 := [rewrite]: #60
+#58 := (iff #43 #57)
+#55 := (iff #37 #53)
+#56 := [rewrite]: #55
+#52 := (iff #14 #51)
+#54 := [rewrite]: #52
+#59 := [monotonicity #54 #56]: #58
+#63 := [trans #59 #61]: #62
+#66 := [monotonicity #63]: #65
+#70 := [trans #66 #68]: #69
+#49 := (iff #16 #48)
+#46 := (iff #15 #43)
+#40 := (or #37 #14)
+#44 := (iff #40 #43)
+#45 := [rewrite]: #44
+#41 := (iff #15 #40)
+#38 := (iff #12 #37)
+#35 := (= #11 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#42 := [monotonicity #39]: #41
+#47 := [trans #42 #45]: #46
+#50 := [monotonicity #47]: #49
+#72 := [trans #50 #70]: #71
+#33 := [asserted]: #16
+[mp #33 #72]: false
+unsat
+930a6e842e3c7e28c99fd492d2b79f72c8a8f5d4 63 0
+#2 := false
+#15 := 0::int
+decl f4 :: int
+#11 := f4
+#47 := -1::int
+#50 := (* -1::int f4)
+decl f3 :: int
+#9 := f3
+#51 := (+ f3 #50)
+#68 := (>= #51 0::int)
+#92 := (iff #68 false)
+#49 := -4::int
+#85 := (>= -4::int 0::int)
+#82 := (iff #85 false)
+#91 := [rewrite]: #82
+#86 := (iff #68 #85)
+#52 := (= #51 -4::int)
+#12 := 4::int
+#13 := (+ f3 4::int)
+#14 := (= f4 #13)
+#54 := (iff #14 #52)
+#37 := (+ 4::int f3)
+#44 := (= f4 #37)
+#48 := (iff #44 #52)
+#53 := [rewrite]: #48
+#45 := (iff #14 #44)
+#42 := (= #13 #37)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#55 := [trans #46 #53]: #54
+#36 := [asserted]: #14
+#56 := [mp #36 #55]: #52
+#84 := [monotonicity #56]: #86
+#93 := [trans #84 #91]: #92
+#16 := (- f4 f3)
+#17 := (< 0::int #16)
+#18 := (not #17)
+#79 := (iff #18 #68)
+#58 := (* -1::int f3)
+#59 := (+ #58 f4)
+#62 := (< 0::int #59)
+#65 := (not #62)
+#77 := (iff #65 #68)
+#69 := (not #68)
+#72 := (not #69)
+#75 := (iff #72 #68)
+#76 := [rewrite]: #75
+#73 := (iff #65 #72)
+#70 := (iff #62 #69)
+#71 := [rewrite]: #70
+#74 := [monotonicity #71]: #73
+#78 := [trans #74 #76]: #77
+#66 := (iff #18 #65)
+#63 := (iff #17 #62)
+#60 := (= #16 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#67 := [monotonicity #64]: #66
+#80 := [trans #67 #78]: #79
+#57 := [asserted]: #18
+#81 := [mp #57 #80]: #68
+[mp #81 #93]: false
+unsat
+2d540daa9a5982f146f06d4f791270060139fb82 35 0
+#2 := false
+#10 := 5::int
+#8 := 2::int
+#9 := (+ 2::int 2::int)
+#11 := (= #9 5::int)
+#12 := (not #11)
+#13 := (not #12)
+#53 := (iff #13 false)
+#1 := true
+#48 := (not true)
+#51 := (iff #48 false)
+#52 := [rewrite]: #51
+#49 := (iff #13 #48)
+#46 := (iff #12 true)
+#41 := (not false)
+#44 := (iff #41 true)
+#45 := [rewrite]: #44
+#42 := (iff #12 #41)
+#39 := (iff #11 false)
+#31 := 4::int
+#34 := (= 4::int 5::int)
+#37 := (iff #34 false)
+#38 := [rewrite]: #37
+#35 := (iff #11 #34)
+#32 := (= #9 4::int)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#40 := [trans #36 #38]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#50 := [monotonicity #47]: #49
+#54 := [trans #50 #52]: #53
+#30 := [asserted]: #13
+[mp #30 #54]: false
+unsat
+1ca8ec8a16bb6be2b4bc945c32b7811d276383ea 45 0
+#2 := false
+#15 := 4::real
+decl f4 :: real
+#12 := f4
+#11 := 7::real
+#13 := (* 7::real f4)
+decl f3 :: real
+#9 := f3
+#8 := 3::real
+#10 := (* 3::real f3)
+#14 := (+ #10 #13)
+#46 := (>= #14 4::real)
+#44 := (not #46)
+#16 := (< #14 4::real)
+#45 := (iff #16 #44)
+#42 := [rewrite]: #45
+#39 := [asserted]: #16
+#43 := [mp #39 #42]: #44
+#17 := 2::real
+#18 := (* 2::real f3)
+#48 := (<= #18 3::real)
+#49 := (not #48)
+#19 := (< 3::real #18)
+#50 := (iff #19 #49)
+#51 := [rewrite]: #50
+#40 := [asserted]: #19
+#52 := [mp #40 #51]: #49
+#20 := 0::real
+#56 := (>= f4 0::real)
+#21 := (< f4 0::real)
+#22 := (not #21)
+#63 := (iff #22 #56)
+#54 := (not #56)
+#58 := (not #54)
+#61 := (iff #58 #56)
+#62 := [rewrite]: #61
+#59 := (iff #22 #58)
+#55 := (iff #21 #54)
+#57 := [rewrite]: #55
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#41 := [asserted]: #22
+#65 := [mp #41 #64]: #56
+[th-lemma #65 #52 #43]: false
+unsat
+19eb85476104d695f3fb1ddc54ee1117bc5c649b 59 0
+#2 := false
+#20 := (not false)
+decl f4 :: int
+#12 := f4
+#8 := 0::int
+#16 := (<= 0::int f4)
+#17 := (not #16)
+#18 := (or #17 #16)
+#10 := 1::int
+#11 := (- 1::int)
+#13 := (* #11 f4)
+decl f3 :: int
+#9 := f3
+#14 := (+ f3 #13)
+#15 := (<= 0::int #14)
+#19 := (or #15 #18)
+#21 := (iff #19 #20)
+#22 := (not #21)
+#75 := (iff #22 false)
+#1 := true
+#70 := (not true)
+#73 := (iff #70 false)
+#74 := [rewrite]: #73
+#71 := (iff #22 #70)
+#68 := (iff #21 true)
+#63 := (iff true true)
+#66 := (iff #63 true)
+#67 := [rewrite]: #66
+#64 := (iff #21 #63)
+#61 := (iff #20 true)
+#62 := [rewrite]: #61
+#59 := (iff #19 true)
+#40 := -1::int
+#43 := (* -1::int f4)
+#46 := (+ f3 #43)
+#49 := (<= 0::int #46)
+#54 := (or #49 true)
+#57 := (iff #54 true)
+#58 := [rewrite]: #57
+#55 := (iff #19 #54)
+#52 := (iff #18 true)
+#53 := [rewrite]: #52
+#50 := (iff #15 #49)
+#47 := (= #14 #46)
+#44 := (= #13 #43)
+#41 := (= #11 -1::int)
+#42 := [rewrite]: #41
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#51 := [monotonicity #48]: #50
+#56 := [monotonicity #51 #53]: #55
+#60 := [trans #56 #58]: #59
+#65 := [monotonicity #60 #62]: #64
+#69 := [trans #65 #67]: #68
+#72 := [monotonicity #69]: #71
+#76 := [trans #72 #74]: #75
+#39 := [asserted]: #22
+[mp #39 #76]: false
+unsat
+fd37cd3a37260b090398813729fb9f9e3e6ede0b 43 0
+#2 := false
+decl f3 :: int
+#8 := f3
+#9 := 3::int
+#11 := (<= 3::int f3)
+#10 := (< f3 3::int)
+#12 := (iff #10 #11)
+#13 := (not #12)
+#14 := (not #13)
+#61 := (iff #14 false)
+#59 := (iff #12 false)
+#50 := (>= f3 3::int)
+#48 := (not #50)
+#54 := (iff #48 #50)
+#57 := (iff #54 false)
+#58 := [rewrite]: #57
+#55 := (iff #12 #54)
+#52 := (iff #11 #50)
+#53 := [rewrite]: #52
+#49 := (iff #10 #48)
+#51 := [rewrite]: #49
+#56 := [monotonicity #51 #53]: #55
+#60 := [trans #56 #58]: #59
+#46 := (iff #14 #12)
+#40 := (iff #11 #10)
+#44 := (iff #40 #12)
+#45 := [rewrite]: #44
+#42 := (iff #14 #40)
+#32 := (not #10)
+#33 := (iff #11 #32)
+#36 := (not #33)
+#39 := (iff #36 #40)
+#41 := [rewrite]: #39
+#37 := (iff #14 #36)
+#34 := (iff #13 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#43 := [trans #38 #41]: #42
+#47 := [trans #43 #45]: #46
+#62 := [trans #47 #60]: #61
+#31 := [asserted]: #14
+[mp #31 #62]: false
+unsat
+d8e619656134946c37ccb9d50a3aa7bd99ca40e4 86 0
+#2 := false
+decl f3 :: int
+#9 := f3
+#11 := 2::int
+#34 := (* 2::int f3)
+#8 := 0::int
+#65 := (= 0::int #34)
+#66 := (not #65)
+#55 := (= #34 0::int)
+#109 := (not #55)
+#115 := (iff #109 #66)
+#113 := (iff #55 #65)
+#114 := [commutativity]: #113
+#116 := [monotonicity #114]: #115
+#67 := (<= #34 0::int)
+#105 := (not #67)
+#35 := (<= f3 0::int)
+#36 := (not #35)
+#10 := (< 0::int f3)
+#37 := (iff #10 #36)
+#38 := [rewrite]: #37
+#32 := [asserted]: #10
+#39 := [mp #32 #38]: #36
+#106 := (or #105 #35)
+#107 := [th-lemma]: #106
+#108 := [unit-resolution #107 #39]: #105
+#110 := (or #109 #67)
+#111 := [th-lemma]: #110
+#112 := [unit-resolution #111 #108]: #109
+#117 := [mp #112 #116]: #66
+#61 := (= f3 #34)
+#62 := (not #61)
+#63 := (= 0::int f3)
+#64 := (not #63)
+#59 := (and #64 #66 #62)
+#74 := (not #59)
+#47 := (distinct 0::int f3 #34)
+#52 := (not #47)
+#13 := (- f3 f3)
+#12 := (* f3 2::int)
+#14 := (distinct f3 #12 #13)
+#15 := (not #14)
+#53 := (iff #15 #52)
+#50 := (iff #14 #47)
+#44 := (distinct f3 #34 0::int)
+#48 := (iff #44 #47)
+#49 := [rewrite]: #48
+#45 := (iff #14 #44)
+#42 := (= #13 0::int)
+#43 := [rewrite]: #42
+#40 := (= #12 #34)
+#41 := [rewrite]: #40
+#46 := [monotonicity #41 #43]: #45
+#51 := [trans #46 #49]: #50
+#54 := [monotonicity #51]: #53
+#33 := [asserted]: #15
+#57 := [mp #33 #54]: #52
+#85 := (or #47 #74)
+#86 := [def-axiom]: #85
+#87 := [unit-resolution #86 #57]: #74
+#60 := (= f3 0::int)
+#88 := (not #60)
+#94 := (iff #88 #64)
+#92 := (iff #60 #63)
+#93 := [commutativity]: #92
+#95 := [monotonicity #93]: #94
+#89 := (or #88 #35)
+#90 := [th-lemma]: #89
+#91 := [unit-resolution #90 #39]: #88
+#96 := [mp #91 #95]: #64
+#69 := -1::int
+#70 := (* -1::int #34)
+#71 := (+ f3 #70)
+#73 := (>= #71 0::int)
+#97 := (not #73)
+#98 := (or #97 #35)
+#99 := [th-lemma]: #98
+#100 := [unit-resolution #99 #39]: #97
+#101 := (or #62 #73)
+#102 := [th-lemma]: #101
+#103 := [unit-resolution #102 #100]: #62
+#81 := (or #59 #63 #65 #61)
+#82 := [def-axiom]: #81
+#104 := [unit-resolution #82 #103 #96 #87]: #65
+[unit-resolution #104 #117]: false
+unsat
+6a9b967b365ad3d87acfc367c5cffe6fea3ab37a 551 0
+#2 := false
+#174 := 0::int
+decl f4 :: int
+#9 := f4
+#171 := -1::int
+#207 := (* -1::int f4)
+decl f3 :: int
+#8 := f3
+#208 := (+ f3 #207)
+#223 := (>= #208 0::int)
+decl f5 :: int
+#11 := f5
+#14 := (= f4 f5)
+#172 := (* -1::int f5)
+#196 := (+ f4 #172)
+#242 := (<= #196 0::int)
+#173 := (+ f3 #172)
+#175 := (<= #173 0::int)
+#176 := (not #175)
+#19 := (= f3 f5)
+#436 := (not #19)
+#243 := (not #242)
+#594 := [hypothesis]: #243
+#533 := (or #436 #242)
+#273 := (and #19 #243)
+#377 := (not #273)
+#542 := (iff #377 #533)
+#534 := (not #533)
+#537 := (not #534)
+#540 := (iff #537 #533)
+#541 := [rewrite]: #540
+#538 := (iff #377 #537)
+#535 := (iff #273 #534)
+#536 := [rewrite]: #535
+#539 := [monotonicity #536]: #538
+#543 := [trans #539 #541]: #542
+#222 := (not #223)
+#195 := (>= #196 0::int)
+#194 := (not #195)
+#292 := (and #194 #222)
+#284 := (and #14 #222)
+#183 := (>= #173 0::int)
+#182 := (not #183)
+#278 := (and #182 #243)
+#21 := (= f3 f4)
+#265 := (and #21 #194)
+#209 := (<= #208 0::int)
+#210 := (not #209)
+#257 := (and #210 #243)
+#249 := (and #21 #243)
+#237 := (and #176 #222)
+#229 := (and #19 #222)
+#219 := (and #14 #210)
+#216 := (and #182 #210)
+#213 := (and #19 #210)
+#202 := (and #176 #194)
+#189 := (and #21 #182)
+#179 := (and #14 #176)
+#120 := (and #14 #21)
+#342 := (or #120 #179 #189 #202 #213 #216 #219 #229 #237 #249 #257 #265 #273 #278 #284 #292)
+#347 := (not #342)
+#25 := (= f4 f3)
+#31 := (= f5 f4)
+#38 := (and #31 #25)
+#27 := (< f5 f3)
+#37 := (and #14 #27)
+#39 := (or #37 #38)
+#16 := (< f3 f5)
+#36 := (and #25 #16)
+#40 := (or #36 #39)
+#12 := (< f4 f5)
+#35 := (and #12 #27)
+#41 := (or #35 #40)
+#29 := (= f5 f3)
+#23 := (< f4 f3)
+#34 := (and #23 #29)
+#42 := (or #34 #41)
+#33 := (and #23 #16)
+#43 := (or #33 #42)
+#32 := (and #31 #23)
+#44 := (or #32 #43)
+#10 := (< f3 f4)
+#30 := (and #29 #10)
+#45 := (or #30 #44)
+#28 := (and #27 #10)
+#46 := (or #28 #45)
+#17 := (< f5 f4)
+#26 := (and #17 #25)
+#47 := (or #26 #46)
+#24 := (and #17 #23)
+#48 := (or #24 #47)
+#22 := (and #21 #12)
+#49 := (or #22 #48)
+#20 := (and #19 #17)
+#50 := (or #20 #49)
+#18 := (and #16 #17)
+#51 := (or #18 #50)
+#15 := (and #10 #14)
+#52 := (or #15 #51)
+#13 := (and #10 #12)
+#53 := (or #13 #52)
+#54 := (not #53)
+#350 := (iff #54 #347)
+#123 := (or #37 #120)
+#115 := (and #16 #21)
+#126 := (or #115 #123)
+#129 := (or #35 #126)
+#107 := (and #19 #23)
+#132 := (or #107 #129)
+#101 := (and #16 #23)
+#135 := (or #101 #132)
+#98 := (and #14 #23)
+#138 := (or #98 #135)
+#91 := (and #10 #19)
+#141 := (or #91 #138)
+#83 := (and #10 #27)
+#144 := (or #83 #141)
+#80 := (and #17 #21)
+#147 := (or #80 #144)
+#150 := (or #24 #147)
+#75 := (and #12 #21)
+#153 := (or #75 #150)
+#72 := (and #17 #19)
+#156 := (or #72 #153)
+#159 := (or #18 #156)
+#162 := (or #15 #159)
+#165 := (or #13 #162)
+#168 := (not #165)
+#348 := (iff #168 #347)
+#345 := (iff #165 #342)
+#297 := (or #179 #120)
+#300 := (or #189 #297)
+#303 := (or #202 #300)
+#306 := (or #213 #303)
+#309 := (or #216 #306)
+#312 := (or #219 #309)
+#315 := (or #229 #312)
+#318 := (or #237 #315)
+#321 := (or #249 #318)
+#324 := (or #257 #321)
+#327 := (or #265 #324)
+#330 := (or #273 #327)
+#333 := (or #278 #330)
+#336 := (or #284 #333)
+#339 := (or #292 #336)
+#343 := (iff #339 #342)
+#344 := [rewrite]: #343
+#340 := (iff #165 #339)
+#337 := (iff #162 #336)
+#334 := (iff #159 #333)
+#331 := (iff #156 #330)
+#328 := (iff #153 #327)
+#325 := (iff #150 #324)
+#322 := (iff #147 #321)
+#319 := (iff #144 #318)
+#316 := (iff #141 #315)
+#313 := (iff #138 #312)
+#310 := (iff #135 #309)
+#307 := (iff #132 #306)
+#304 := (iff #129 #303)
+#301 := (iff #126 #300)
+#298 := (iff #123 #297)
+#180 := (iff #37 #179)
+#177 := (iff #27 #176)
+#178 := [rewrite]: #177
+#181 := [monotonicity #178]: #180
+#299 := [monotonicity #181]: #298
+#192 := (iff #115 #189)
+#186 := (and #182 #21)
+#190 := (iff #186 #189)
+#191 := [rewrite]: #190
+#187 := (iff #115 #186)
+#184 := (iff #16 #182)
+#185 := [rewrite]: #184
+#188 := [monotonicity #185]: #187
+#193 := [trans #188 #191]: #192
+#302 := [monotonicity #193 #299]: #301
+#205 := (iff #35 #202)
+#199 := (and #194 #176)
+#203 := (iff #199 #202)
+#204 := [rewrite]: #203
+#200 := (iff #35 #199)
+#197 := (iff #12 #194)
+#198 := [rewrite]: #197
+#201 := [monotonicity #198 #178]: #200
+#206 := [trans #201 #204]: #205
+#305 := [monotonicity #206 #302]: #304
+#214 := (iff #107 #213)
+#211 := (iff #23 #210)
+#212 := [rewrite]: #211
+#215 := [monotonicity #212]: #214
+#308 := [monotonicity #215 #305]: #307
+#217 := (iff #101 #216)
+#218 := [monotonicity #185 #212]: #217
+#311 := [monotonicity #218 #308]: #310
+#220 := (iff #98 #219)
+#221 := [monotonicity #212]: #220
+#314 := [monotonicity #221 #311]: #313
+#232 := (iff #91 #229)
+#226 := (and #222 #19)
+#230 := (iff #226 #229)
+#231 := [rewrite]: #230
+#227 := (iff #91 #226)
+#224 := (iff #10 #222)
+#225 := [rewrite]: #224
+#228 := [monotonicity #225]: #227
+#233 := [trans #228 #231]: #232
+#317 := [monotonicity #233 #314]: #316
+#240 := (iff #83 #237)
+#234 := (and #222 #176)
+#238 := (iff #234 #237)
+#239 := [rewrite]: #238
+#235 := (iff #83 #234)
+#236 := [monotonicity #225 #178]: #235
+#241 := [trans #236 #239]: #240
+#320 := [monotonicity #241 #317]: #319
+#252 := (iff #80 #249)
+#246 := (and #243 #21)
+#250 := (iff #246 #249)
+#251 := [rewrite]: #250
+#247 := (iff #80 #246)
+#244 := (iff #17 #243)
+#245 := [rewrite]: #244
+#248 := [monotonicity #245]: #247
+#253 := [trans #248 #251]: #252
+#323 := [monotonicity #253 #320]: #322
+#260 := (iff #24 #257)
+#254 := (and #243 #210)
+#258 := (iff #254 #257)
+#259 := [rewrite]: #258
+#255 := (iff #24 #254)
+#256 := [monotonicity #245 #212]: #255
+#261 := [trans #256 #259]: #260
+#326 := [monotonicity #261 #323]: #325
+#268 := (iff #75 #265)
+#262 := (and #194 #21)
+#266 := (iff #262 #265)
+#267 := [rewrite]: #266
+#263 := (iff #75 #262)
+#264 := [monotonicity #198]: #263
+#269 := [trans #264 #267]: #268
+#329 := [monotonicity #269 #326]: #328
+#276 := (iff #72 #273)
+#270 := (and #243 #19)
+#274 := (iff #270 #273)
+#275 := [rewrite]: #274
+#271 := (iff #72 #270)
+#272 := [monotonicity #245]: #271
+#277 := [trans #272 #275]: #276
+#332 := [monotonicity #277 #329]: #331
+#279 := (iff #18 #278)
+#280 := [monotonicity #185 #245]: #279
+#335 := [monotonicity #280 #332]: #334
+#287 := (iff #15 #284)
+#281 := (and #222 #14)
+#285 := (iff #281 #284)
+#286 := [rewrite]: #285
+#282 := (iff #15 #281)
+#283 := [monotonicity #225]: #282
+#288 := [trans #283 #286]: #287
+#338 := [monotonicity #288 #335]: #337
+#295 := (iff #13 #292)
+#289 := (and #222 #194)
+#293 := (iff #289 #292)
+#294 := [rewrite]: #293
+#290 := (iff #13 #289)
+#291 := [monotonicity #225 #198]: #290
+#296 := [trans #291 #294]: #295
+#341 := [monotonicity #296 #338]: #340
+#346 := [trans #341 #344]: #345
+#349 := [monotonicity #346]: #348
+#169 := (iff #54 #168)
+#166 := (iff #53 #165)
+#163 := (iff #52 #162)
+#160 := (iff #51 #159)
+#157 := (iff #50 #156)
+#154 := (iff #49 #153)
+#151 := (iff #48 #150)
+#148 := (iff #47 #147)
+#145 := (iff #46 #144)
+#142 := (iff #45 #141)
+#139 := (iff #44 #138)
+#136 := (iff #43 #135)
+#133 := (iff #42 #132)
+#130 := (iff #41 #129)
+#127 := (iff #40 #126)
+#124 := (iff #39 #123)
+#121 := (iff #38 #120)
+#78 := (iff #25 #21)
+#79 := [rewrite]: #78
+#96 := (iff #31 #14)
+#97 := [rewrite]: #96
+#122 := [monotonicity #97 #79]: #121
+#125 := [monotonicity #122]: #124
+#118 := (iff #36 #115)
+#112 := (and #21 #16)
+#116 := (iff #112 #115)
+#117 := [rewrite]: #116
+#113 := (iff #36 #112)
+#114 := [monotonicity #79]: #113
+#119 := [trans #114 #117]: #118
+#128 := [monotonicity #119 #125]: #127
+#131 := [monotonicity #128]: #130
+#110 := (iff #34 #107)
+#104 := (and #23 #19)
+#108 := (iff #104 #107)
+#109 := [rewrite]: #108
+#105 := (iff #34 #104)
+#86 := (iff #29 #19)
+#87 := [rewrite]: #86
+#106 := [monotonicity #87]: #105
+#111 := [trans #106 #109]: #110
+#134 := [monotonicity #111 #131]: #133
+#102 := (iff #33 #101)
+#103 := [rewrite]: #102
+#137 := [monotonicity #103 #134]: #136
+#99 := (iff #32 #98)
+#100 := [monotonicity #97]: #99
+#140 := [monotonicity #100 #137]: #139
+#94 := (iff #30 #91)
+#88 := (and #19 #10)
+#92 := (iff #88 #91)
+#93 := [rewrite]: #92
+#89 := (iff #30 #88)
+#90 := [monotonicity #87]: #89
+#95 := [trans #90 #93]: #94
+#143 := [monotonicity #95 #140]: #142
+#84 := (iff #28 #83)
+#85 := [rewrite]: #84
+#146 := [monotonicity #85 #143]: #145
+#81 := (iff #26 #80)
+#82 := [monotonicity #79]: #81
+#149 := [monotonicity #82 #146]: #148
+#152 := [monotonicity #149]: #151
+#76 := (iff #22 #75)
+#77 := [rewrite]: #76
+#155 := [monotonicity #77 #152]: #154
+#73 := (iff #20 #72)
+#74 := [rewrite]: #73
+#158 := [monotonicity #74 #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [monotonicity #164]: #166
+#170 := [monotonicity #167]: #169
+#351 := [trans #170 #349]: #350
+#71 := [asserted]: #54
+#352 := [mp #71 #351]: #347
+#378 := [not-or-elim #352]: #377
+#544 := [mp #378 #543]: #533
+#595 := [unit-resolution #544 #594]: #436
+#545 := (or #183 #242)
+#379 := (not #278)
+#554 := (iff #379 #545)
+#546 := (not #545)
+#549 := (not #546)
+#552 := (iff #549 #545)
+#553 := [rewrite]: #552
+#550 := (iff #379 #549)
+#547 := (iff #278 #546)
+#548 := [rewrite]: #547
+#551 := [monotonicity #548]: #550
+#555 := [trans #551 #553]: #554
+#380 := [not-or-elim #352]: #379
+#556 := [mp #380 #555]: #545
+#596 := [unit-resolution #556 #594]: #183
+#585 := (or #19 #176 #182)
+#586 := [th-lemma]: #585
+#597 := [unit-resolution #586 #596 #595]: #176
+#485 := (or #175 #223)
+#369 := (not #237)
+#494 := (iff #369 #485)
+#486 := (not #485)
+#489 := (not #486)
+#492 := (iff #489 #485)
+#493 := [rewrite]: #492
+#490 := (iff #369 #489)
+#487 := (iff #237 #486)
+#488 := [rewrite]: #487
+#491 := [monotonicity #488]: #490
+#495 := [trans #491 #493]: #494
+#370 := [not-or-elim #352]: #369
+#496 := [mp #370 #495]: #485
+#598 := [unit-resolution #496 #597]: #223
+#581 := [hypothesis]: #210
+#509 := (or #209 #242)
+#373 := (not #257)
+#518 := (iff #373 #509)
+#510 := (not #509)
+#513 := (not #510)
+#516 := (iff #513 #509)
+#517 := [rewrite]: #516
+#514 := (iff #373 #513)
+#511 := (iff #257 #510)
+#512 := [rewrite]: #511
+#515 := [monotonicity #512]: #514
+#519 := [trans #515 #517]: #518
+#374 := [not-or-elim #352]: #373
+#520 := [mp #374 #519]: #509
+#582 := [unit-resolution #520 #581]: #242
+#437 := (or #436 #209)
+#361 := (not #213)
+#446 := (iff #361 #437)
+#438 := (not #437)
+#441 := (not #438)
+#444 := (iff #441 #437)
+#445 := [rewrite]: #444
+#442 := (iff #361 #441)
+#439 := (iff #213 #438)
+#440 := [rewrite]: #439
+#443 := [monotonicity #440]: #442
+#447 := [trans #443 #445]: #446
+#362 := [not-or-elim #352]: #361
+#448 := [mp #362 #447]: #437
+#583 := [unit-resolution #448 #581]: #436
+#449 := (or #183 #209)
+#363 := (not #216)
+#458 := (iff #363 #449)
+#450 := (not #449)
+#453 := (not #450)
+#456 := (iff #453 #449)
+#457 := [rewrite]: #456
+#454 := (iff #363 #453)
+#451 := (iff #216 #450)
+#452 := [rewrite]: #451
+#455 := [monotonicity #452]: #454
+#459 := [trans #455 #457]: #458
+#364 := [not-or-elim #352]: #363
+#460 := [mp #364 #459]: #449
+#584 := [unit-resolution #460 #581]: #183
+#587 := [unit-resolution #586 #584 #583]: #176
+#424 := (or #175 #195)
+#359 := (not #202)
+#433 := (iff #359 #424)
+#425 := (not #424)
+#428 := (not #425)
+#431 := (iff #428 #424)
+#432 := [rewrite]: #431
+#429 := (iff #359 #428)
+#426 := (iff #202 #425)
+#427 := [rewrite]: #426
+#430 := [monotonicity #427]: #429
+#434 := [trans #430 #432]: #433
+#360 := [not-or-elim #352]: #359
+#435 := [mp #360 #434]: #424
+#588 := [unit-resolution #435 #587]: #195
+#420 := (not #14)
+#461 := (or #420 #209)
+#365 := (not #219)
+#470 := (iff #365 #461)
+#462 := (not #461)
+#465 := (not #462)
+#468 := (iff #465 #461)
+#469 := [rewrite]: #468
+#466 := (iff #365 #465)
+#463 := (iff #219 #462)
+#464 := [rewrite]: #463
+#467 := [monotonicity #464]: #466
+#471 := [trans #467 #469]: #470
+#366 := [not-or-elim #352]: #365
+#472 := [mp #366 #471]: #461
+#589 := [unit-resolution #472 #581]: #420
+#590 := (or #14 #243 #194)
+#591 := [th-lemma]: #590
+#592 := [unit-resolution #591 #589 #588 #582]: false
+#593 := [lemma #592]: #209
+#421 := (not #21)
+#497 := (or #421 #242)
+#371 := (not #249)
+#506 := (iff #371 #497)
+#498 := (not #497)
+#501 := (not #498)
+#504 := (iff #501 #497)
+#505 := [rewrite]: #504
+#502 := (iff #371 #501)
+#499 := (iff #249 #498)
+#500 := [rewrite]: #499
+#503 := [monotonicity #500]: #502
+#507 := [trans #503 #505]: #506
+#372 := [not-or-elim #352]: #371
+#508 := [mp #372 #507]: #497
+#599 := [unit-resolution #508 #594]: #421
+#600 := (or #21 #210 #222)
+#601 := [th-lemma]: #600
+#602 := [unit-resolution #601 #599 #593 #598]: false
+#603 := [lemma #602]: #242
+#609 := [hypothesis]: #194
+#569 := (or #195 #223)
+#383 := (not #292)
+#578 := (iff #383 #569)
+#570 := (not #569)
+#573 := (not #570)
+#576 := (iff #573 #569)
+#577 := [rewrite]: #576
+#574 := (iff #383 #573)
+#571 := (iff #292 #570)
+#572 := [rewrite]: #571
+#575 := [monotonicity #572]: #574
+#579 := [trans #575 #577]: #578
+#384 := [not-or-elim #352]: #383
+#580 := [mp #384 #579]: #569
+#610 := [unit-resolution #580 #609]: #223
+#521 := (or #421 #195)
+#375 := (not #265)
+#530 := (iff #375 #521)
+#522 := (not #521)
+#525 := (not #522)
+#528 := (iff #525 #521)
+#529 := [rewrite]: #528
+#526 := (iff #375 #525)
+#523 := (iff #265 #522)
+#524 := [rewrite]: #523
+#527 := [monotonicity #524]: #526
+#531 := [trans #527 #529]: #530
+#376 := [not-or-elim #352]: #375
+#532 := [mp #376 #531]: #521
+#611 := [unit-resolution #532 #609]: #421
+#612 := [unit-resolution #601 #611 #593 #610]: false
+#613 := [lemma #612]: #195
+#614 := [th-lemma #613 #603]: #14
+#557 := (or #420 #223)
+#381 := (not #284)
+#566 := (iff #381 #557)
+#558 := (not #557)
+#561 := (not #558)
+#564 := (iff #561 #557)
+#565 := [rewrite]: #564
+#562 := (iff #381 #561)
+#559 := (iff #284 #558)
+#560 := [rewrite]: #559
+#563 := [monotonicity #560]: #562
+#567 := [trans #563 #565]: #566
+#382 := [not-or-elim #352]: #381
+#568 := [mp #382 #567]: #557
+#616 := [unit-resolution #568 #614]: #223
+#422 := (or #420 #421)
+#353 := (not #120)
+#413 := (iff #353 #422)
+#423 := (not #422)
+#416 := (not #423)
+#415 := (iff #416 #422)
+#412 := [rewrite]: #415
+#417 := (iff #353 #416)
+#418 := (iff #120 #423)
+#419 := [rewrite]: #418
+#414 := [monotonicity #419]: #417
+#410 := [trans #414 #412]: #413
+#354 := [not-or-elim #352]: #353
+#411 := [mp #354 #410]: #422
+#617 := [unit-resolution #411 #614]: #421
+[unit-resolution #601 #617 #593 #616]: false
+unsat
+3472db0bdce7435abc0f58525f23f29f3d75b8fe 2109 0
+#2 := false
+#10 := 0::int
+decl f3 :: int
+#8 := f3
+#95 := -1::int
+#114 := (* -1::int f3)
+#537 := (>= f3 0::int)
+#544 := (ite #537 f3 #114)
+#555 := (* -1::int #544)
+#744 := (+ f3 #555)
+#745 := (<= #744 0::int)
+#715 := (= f3 #544)
+decl f6 :: int
+#17 := f6
+#131 := (* -1::int f6)
+#508 := (>= f6 0::int)
+#515 := (ite #508 f6 #131)
+#526 := (* -1::int #515)
+#749 := (+ f6 #526)
+#752 := (<= #749 0::int)
+#707 := (= f6 #515)
+decl f13 :: int
+#59 := f13
+#734 := (* -1::int f13)
+decl f4 :: int
+#9 := f4
+#735 := (+ f4 #734)
+#737 := (>= #735 0::int)
+#988 := (+ #131 #526)
+#1057 := (<= #988 0::int)
+#708 := (= #131 #515)
+#509 := (not #508)
+#1129 := [hypothesis]: #509
+#711 := (or #508 #708)
+#712 := [def-axiom]: #711
+#1130 := [unit-resolution #712 #1129]: #708
+#1131 := (not #708)
+#1132 := (or #1131 #1057)
+#1133 := [th-lemma]: #1132
+#1134 := [unit-resolution #1133 #1130]: #1057
+decl f12 :: int
+#53 := f12
+#233 := (* -1::int f12)
+#334 := (>= f12 0::int)
+#341 := (ite #334 f12 #233)
+#352 := (* -1::int #341)
+#864 := (+ f12 #352)
+#901 := (>= #864 0::int)
+#655 := (= f12 #341)
+decl f8 :: int
+#29 := f8
+#165 := (* -1::int f8)
+#450 := (>= f8 0::int)
+#457 := (ite #450 f8 #165)
+#468 := (* -1::int #457)
+#750 := (+ f8 #468)
+#903 := (>= #750 0::int)
+#736 := (<= #735 0::int)
+#967 := (not #736)
+#66 := (= f4 f13)
+#648 := (not #66)
+decl f5 :: int
+#14 := f5
+#65 := (= f5 f12)
+#731 := (+ f5 #233)
+#732 := (<= #731 0::int)
+#987 := (>= #744 0::int)
+#451 := (not #450)
+#691 := (= f8 #457)
+#769 := (not #691)
+#1246 := (not #903)
+#1580 := [hypothesis]: #1246
+#1040 := (or #769 #903)
+#1581 := [hypothesis]: #691
+#1041 := [th-lemma]: #1040
+#1582 := [unit-resolution #1041 #1581 #1580]: false
+#1583 := [lemma #1582]: #1040
+#1834 := [unit-resolution #1583 #1580]: #769
+#693 := (or #451 #691)
+#694 := [def-axiom]: #693
+#1835 := [unit-resolution #694 #1834]: #451
+#1343 := (or #450 #508)
+decl f7 :: int
+#23 := f7
+#148 := (* -1::int f7)
+#479 := (>= f7 0::int)
+#486 := (ite #479 f7 #148)
+#497 := (* -1::int #486)
+#1334 := (+ f7 #497)
+#1335 := (<= #1334 0::int)
+#699 := (= f7 #486)
+decl f9 :: int
+#35 := f9
+#182 := (* -1::int f9)
+#421 := (>= f9 0::int)
+#428 := (ite #421 f9 #182)
+#439 := (* -1::int #428)
+#753 := (+ f9 #439)
+#986 := (>= #753 0::int)
+#683 := (= f9 #428)
+#480 := (not #479)
+#810 := [hypothesis]: #480
+#1193 := (or #450 #479)
+#733 := (>= #731 0::int)
+#1141 := (or #537 #479)
+#538 := (not #537)
+#907 := [hypothesis]: #538
+#1136 := (or #508 #537 #479)
+#527 := (+ f7 #526)
+#528 := (+ f3 #527)
+#714 := (>= #528 0::int)
+#529 := (= #528 0::int)
+#96 := (* -1::int f4)
+#566 := (>= f4 0::int)
+#573 := (ite #566 f4 #96)
+#584 := (* -1::int #573)
+#585 := (+ f5 #584)
+#586 := (+ f3 #585)
+#587 := (= #586 0::int)
+#592 := (not #587)
+#556 := (+ f6 #555)
+#557 := (+ f4 #556)
+#558 := (= #557 0::int)
+#563 := (not #558)
+#534 := (not #529)
+#498 := (+ f8 #497)
+#499 := (+ f6 #498)
+#500 := (= #499 0::int)
+#505 := (not #500)
+#469 := (+ f9 #468)
+#470 := (+ f7 #469)
+#471 := (= #470 0::int)
+#476 := (not #471)
+decl f10 :: int
+#41 := f10
+#440 := (+ f10 #439)
+#441 := (+ f8 #440)
+#442 := (= #441 0::int)
+#447 := (not #442)
+#199 := (* -1::int f10)
+#392 := (>= f10 0::int)
+#399 := (ite #392 f10 #199)
+#410 := (* -1::int #399)
+decl f11 :: int
+#47 := f11
+#411 := (+ f11 #410)
+#412 := (+ f9 #411)
+#413 := (= #412 0::int)
+#418 := (not #413)
+#216 := (* -1::int f11)
+#363 := (>= f11 0::int)
+#370 := (ite #363 f11 #216)
+#381 := (* -1::int #370)
+#382 := (+ f12 #381)
+#383 := (+ f10 #382)
+#384 := (= #383 0::int)
+#389 := (not #384)
+#353 := (+ f13 #352)
+#354 := (+ f11 #353)
+#355 := (= #354 0::int)
+#360 := (not #355)
+#67 := (and #65 #66)
+#622 := (or #67 #360 #389 #418 #447 #476 #505 #534 #563 #592)
+#627 := (not #622)
+#61 := (- f12)
+#60 := (< f12 0::int)
+#62 := (ite #60 #61 f12)
+#63 := (- #62 f11)
+#64 := (= f13 #63)
+#68 := (implies #64 #67)
+#55 := (- f11)
+#54 := (< f11 0::int)
+#56 := (ite #54 #55 f11)
+#57 := (- #56 f10)
+#58 := (= f12 #57)
+#69 := (implies #58 #68)
+#49 := (- f10)
+#48 := (< f10 0::int)
+#50 := (ite #48 #49 f10)
+#51 := (- #50 f9)
+#52 := (= f11 #51)
+#70 := (implies #52 #69)
+#43 := (- f9)
+#42 := (< f9 0::int)
+#44 := (ite #42 #43 f9)
+#45 := (- #44 f8)
+#46 := (= f10 #45)
+#71 := (implies #46 #70)
+#37 := (- f8)
+#36 := (< f8 0::int)
+#38 := (ite #36 #37 f8)
+#39 := (- #38 f7)
+#40 := (= f9 #39)
+#72 := (implies #40 #71)
+#31 := (- f7)
+#30 := (< f7 0::int)
+#32 := (ite #30 #31 f7)
+#33 := (- #32 f6)
+#34 := (= f8 #33)
+#73 := (implies #34 #72)
+#25 := (- f6)
+#24 := (< f6 0::int)
+#26 := (ite #24 #25 f6)
+#27 := (- #26 f3)
+#28 := (= f7 #27)
+#74 := (implies #28 #73)
+#19 := (- f3)
+#18 := (< f3 0::int)
+#20 := (ite #18 #19 f3)
+#21 := (- #20 f4)
+#22 := (= f6 #21)
+#75 := (implies #22 #74)
+#12 := (- f4)
+#11 := (< f4 0::int)
+#13 := (ite #11 #12 f4)
+#15 := (- #13 f5)
+#16 := (= f3 #15)
+#76 := (implies #16 #75)
+#77 := (not #76)
+#630 := (iff #77 #627)
+#236 := (ite #60 #233 f12)
+#242 := (+ #216 #236)
+#247 := (= f13 #242)
+#253 := (not #247)
+#254 := (or #67 #253)
+#219 := (ite #54 #216 f11)
+#225 := (+ #199 #219)
+#230 := (= f12 #225)
+#262 := (not #230)
+#263 := (or #262 #254)
+#202 := (ite #48 #199 f10)
+#208 := (+ #182 #202)
+#213 := (= f11 #208)
+#271 := (not #213)
+#272 := (or #271 #263)
+#185 := (ite #42 #182 f9)
+#191 := (+ #165 #185)
+#196 := (= f10 #191)
+#280 := (not #196)
+#281 := (or #280 #272)
+#168 := (ite #36 #165 f8)
+#174 := (+ #148 #168)
+#179 := (= f9 #174)
+#289 := (not #179)
+#290 := (or #289 #281)
+#151 := (ite #30 #148 f7)
+#157 := (+ #131 #151)
+#162 := (= f8 #157)
+#298 := (not #162)
+#299 := (or #298 #290)
+#134 := (ite #24 #131 f6)
+#140 := (+ #114 #134)
+#145 := (= f7 #140)
+#307 := (not #145)
+#308 := (or #307 #299)
+#117 := (ite #18 #114 f3)
+#123 := (+ #96 #117)
+#128 := (= f6 #123)
+#316 := (not #128)
+#317 := (or #316 #308)
+#99 := (ite #11 #96 f4)
+#105 := (* -1::int f5)
+#106 := (+ #105 #99)
+#111 := (= f3 #106)
+#325 := (not #111)
+#326 := (or #325 #317)
+#331 := (not #326)
+#628 := (iff #331 #627)
+#625 := (iff #326 #622)
+#595 := (or #67 #360)
+#598 := (or #389 #595)
+#601 := (or #418 #598)
+#604 := (or #447 #601)
+#607 := (or #476 #604)
+#610 := (or #505 #607)
+#613 := (or #534 #610)
+#616 := (or #563 #613)
+#619 := (or #592 #616)
+#623 := (iff #619 #622)
+#624 := [rewrite]: #623
+#620 := (iff #326 #619)
+#617 := (iff #317 #616)
+#614 := (iff #308 #613)
+#611 := (iff #299 #610)
+#608 := (iff #290 #607)
+#605 := (iff #281 #604)
+#602 := (iff #272 #601)
+#599 := (iff #263 #598)
+#596 := (iff #254 #595)
+#361 := (iff #253 #360)
+#358 := (iff #247 #355)
+#346 := (+ #216 #341)
+#349 := (= f13 #346)
+#356 := (iff #349 #355)
+#357 := [rewrite]: #356
+#350 := (iff #247 #349)
+#347 := (= #242 #346)
+#344 := (= #236 #341)
+#335 := (not #334)
+#338 := (ite #335 #233 f12)
+#342 := (= #338 #341)
+#343 := [rewrite]: #342
+#339 := (= #236 #338)
+#336 := (iff #60 #335)
+#337 := [rewrite]: #336
+#340 := [monotonicity #337]: #339
+#345 := [trans #340 #343]: #344
+#348 := [monotonicity #345]: #347
+#351 := [monotonicity #348]: #350
+#359 := [trans #351 #357]: #358
+#362 := [monotonicity #359]: #361
+#597 := [monotonicity #362]: #596
+#390 := (iff #262 #389)
+#387 := (iff #230 #384)
+#375 := (+ #199 #370)
+#378 := (= f12 #375)
+#385 := (iff #378 #384)
+#386 := [rewrite]: #385
+#379 := (iff #230 #378)
+#376 := (= #225 #375)
+#373 := (= #219 #370)
+#364 := (not #363)
+#367 := (ite #364 #216 f11)
+#371 := (= #367 #370)
+#372 := [rewrite]: #371
+#368 := (= #219 #367)
+#365 := (iff #54 #364)
+#366 := [rewrite]: #365
+#369 := [monotonicity #366]: #368
+#374 := [trans #369 #372]: #373
+#377 := [monotonicity #374]: #376
+#380 := [monotonicity #377]: #379
+#388 := [trans #380 #386]: #387
+#391 := [monotonicity #388]: #390
+#600 := [monotonicity #391 #597]: #599
+#419 := (iff #271 #418)
+#416 := (iff #213 #413)
+#404 := (+ #182 #399)
+#407 := (= f11 #404)
+#414 := (iff #407 #413)
+#415 := [rewrite]: #414
+#408 := (iff #213 #407)
+#405 := (= #208 #404)
+#402 := (= #202 #399)
+#393 := (not #392)
+#396 := (ite #393 #199 f10)
+#400 := (= #396 #399)
+#401 := [rewrite]: #400
+#397 := (= #202 #396)
+#394 := (iff #48 #393)
+#395 := [rewrite]: #394
+#398 := [monotonicity #395]: #397
+#403 := [trans #398 #401]: #402
+#406 := [monotonicity #403]: #405
+#409 := [monotonicity #406]: #408
+#417 := [trans #409 #415]: #416
+#420 := [monotonicity #417]: #419
+#603 := [monotonicity #420 #600]: #602
+#448 := (iff #280 #447)
+#445 := (iff #196 #442)
+#433 := (+ #165 #428)
+#436 := (= f10 #433)
+#443 := (iff #436 #442)
+#444 := [rewrite]: #443
+#437 := (iff #196 #436)
+#434 := (= #191 #433)
+#431 := (= #185 #428)
+#422 := (not #421)
+#425 := (ite #422 #182 f9)
+#429 := (= #425 #428)
+#430 := [rewrite]: #429
+#426 := (= #185 #425)
+#423 := (iff #42 #422)
+#424 := [rewrite]: #423
+#427 := [monotonicity #424]: #426
+#432 := [trans #427 #430]: #431
+#435 := [monotonicity #432]: #434
+#438 := [monotonicity #435]: #437
+#446 := [trans #438 #444]: #445
+#449 := [monotonicity #446]: #448
+#606 := [monotonicity #449 #603]: #605
+#477 := (iff #289 #476)
+#474 := (iff #179 #471)
+#462 := (+ #148 #457)
+#465 := (= f9 #462)
+#472 := (iff #465 #471)
+#473 := [rewrite]: #472
+#466 := (iff #179 #465)
+#463 := (= #174 #462)
+#460 := (= #168 #457)
+#454 := (ite #451 #165 f8)
+#458 := (= #454 #457)
+#459 := [rewrite]: #458
+#455 := (= #168 #454)
+#452 := (iff #36 #451)
+#453 := [rewrite]: #452
+#456 := [monotonicity #453]: #455
+#461 := [trans #456 #459]: #460
+#464 := [monotonicity #461]: #463
+#467 := [monotonicity #464]: #466
+#475 := [trans #467 #473]: #474
+#478 := [monotonicity #475]: #477
+#609 := [monotonicity #478 #606]: #608
+#506 := (iff #298 #505)
+#503 := (iff #162 #500)
+#491 := (+ #131 #486)
+#494 := (= f8 #491)
+#501 := (iff #494 #500)
+#502 := [rewrite]: #501
+#495 := (iff #162 #494)
+#492 := (= #157 #491)
+#489 := (= #151 #486)
+#483 := (ite #480 #148 f7)
+#487 := (= #483 #486)
+#488 := [rewrite]: #487
+#484 := (= #151 #483)
+#481 := (iff #30 #480)
+#482 := [rewrite]: #481
+#485 := [monotonicity #482]: #484
+#490 := [trans #485 #488]: #489
+#493 := [monotonicity #490]: #492
+#496 := [monotonicity #493]: #495
+#504 := [trans #496 #502]: #503
+#507 := [monotonicity #504]: #506
+#612 := [monotonicity #507 #609]: #611
+#535 := (iff #307 #534)
+#532 := (iff #145 #529)
+#520 := (+ #114 #515)
+#523 := (= f7 #520)
+#530 := (iff #523 #529)
+#531 := [rewrite]: #530
+#524 := (iff #145 #523)
+#521 := (= #140 #520)
+#518 := (= #134 #515)
+#512 := (ite #509 #131 f6)
+#516 := (= #512 #515)
+#517 := [rewrite]: #516
+#513 := (= #134 #512)
+#510 := (iff #24 #509)
+#511 := [rewrite]: #510
+#514 := [monotonicity #511]: #513
+#519 := [trans #514 #517]: #518
+#522 := [monotonicity #519]: #521
+#525 := [monotonicity #522]: #524
+#533 := [trans #525 #531]: #532
+#536 := [monotonicity #533]: #535
+#615 := [monotonicity #536 #612]: #614
+#564 := (iff #316 #563)
+#561 := (iff #128 #558)
+#549 := (+ #96 #544)
+#552 := (= f6 #549)
+#559 := (iff #552 #558)
+#560 := [rewrite]: #559
+#553 := (iff #128 #552)
+#550 := (= #123 #549)
+#547 := (= #117 #544)
+#541 := (ite #538 #114 f3)
+#545 := (= #541 #544)
+#546 := [rewrite]: #545
+#542 := (= #117 #541)
+#539 := (iff #18 #538)
+#540 := [rewrite]: #539
+#543 := [monotonicity #540]: #542
+#548 := [trans #543 #546]: #547
+#551 := [monotonicity #548]: #550
+#554 := [monotonicity #551]: #553
+#562 := [trans #554 #560]: #561
+#565 := [monotonicity #562]: #564
+#618 := [monotonicity #565 #615]: #617
+#593 := (iff #325 #592)
+#590 := (iff #111 #587)
+#578 := (+ #105 #573)
+#581 := (= f3 #578)
+#588 := (iff #581 #587)
+#589 := [rewrite]: #588
+#582 := (iff #111 #581)
+#579 := (= #106 #578)
+#576 := (= #99 #573)
+#567 := (not #566)
+#570 := (ite #567 #96 f4)
+#574 := (= #570 #573)
+#575 := [rewrite]: #574
+#571 := (= #99 #570)
+#568 := (iff #11 #567)
+#569 := [rewrite]: #568
+#572 := [monotonicity #569]: #571
+#577 := [trans #572 #575]: #576
+#580 := [monotonicity #577]: #579
+#583 := [monotonicity #580]: #582
+#591 := [trans #583 #589]: #590
+#594 := [monotonicity #591]: #593
+#621 := [monotonicity #594 #618]: #620
+#626 := [trans #621 #624]: #625
+#629 := [monotonicity #626]: #628
+#332 := (iff #77 #331)
+#329 := (iff #76 #326)
+#322 := (implies #111 #317)
+#327 := (iff #322 #326)
+#328 := [rewrite]: #327
+#323 := (iff #76 #322)
+#320 := (iff #75 #317)
+#313 := (implies #128 #308)
+#318 := (iff #313 #317)
+#319 := [rewrite]: #318
+#314 := (iff #75 #313)
+#311 := (iff #74 #308)
+#304 := (implies #145 #299)
+#309 := (iff #304 #308)
+#310 := [rewrite]: #309
+#305 := (iff #74 #304)
+#302 := (iff #73 #299)
+#295 := (implies #162 #290)
+#300 := (iff #295 #299)
+#301 := [rewrite]: #300
+#296 := (iff #73 #295)
+#293 := (iff #72 #290)
+#286 := (implies #179 #281)
+#291 := (iff #286 #290)
+#292 := [rewrite]: #291
+#287 := (iff #72 #286)
+#284 := (iff #71 #281)
+#277 := (implies #196 #272)
+#282 := (iff #277 #281)
+#283 := [rewrite]: #282
+#278 := (iff #71 #277)
+#275 := (iff #70 #272)
+#268 := (implies #213 #263)
+#273 := (iff #268 #272)
+#274 := [rewrite]: #273
+#269 := (iff #70 #268)
+#266 := (iff #69 #263)
+#259 := (implies #230 #254)
+#264 := (iff #259 #263)
+#265 := [rewrite]: #264
+#260 := (iff #69 #259)
+#257 := (iff #68 #254)
+#250 := (implies #247 #67)
+#255 := (iff #250 #254)
+#256 := [rewrite]: #255
+#251 := (iff #68 #250)
+#248 := (iff #64 #247)
+#245 := (= #63 #242)
+#239 := (- #236 f11)
+#243 := (= #239 #242)
+#244 := [rewrite]: #243
+#240 := (= #63 #239)
+#237 := (= #62 #236)
+#234 := (= #61 #233)
+#235 := [rewrite]: #234
+#238 := [monotonicity #235]: #237
+#241 := [monotonicity #238]: #240
+#246 := [trans #241 #244]: #245
+#249 := [monotonicity #246]: #248
+#252 := [monotonicity #249]: #251
+#258 := [trans #252 #256]: #257
+#231 := (iff #58 #230)
+#228 := (= #57 #225)
+#222 := (- #219 f10)
+#226 := (= #222 #225)
+#227 := [rewrite]: #226
+#223 := (= #57 #222)
+#220 := (= #56 #219)
+#217 := (= #55 #216)
+#218 := [rewrite]: #217
+#221 := [monotonicity #218]: #220
+#224 := [monotonicity #221]: #223
+#229 := [trans #224 #227]: #228
+#232 := [monotonicity #229]: #231
+#261 := [monotonicity #232 #258]: #260
+#267 := [trans #261 #265]: #266
+#214 := (iff #52 #213)
+#211 := (= #51 #208)
+#205 := (- #202 f9)
+#209 := (= #205 #208)
+#210 := [rewrite]: #209
+#206 := (= #51 #205)
+#203 := (= #50 #202)
+#200 := (= #49 #199)
+#201 := [rewrite]: #200
+#204 := [monotonicity #201]: #203
+#207 := [monotonicity #204]: #206
+#212 := [trans #207 #210]: #211
+#215 := [monotonicity #212]: #214
+#270 := [monotonicity #215 #267]: #269
+#276 := [trans #270 #274]: #275
+#197 := (iff #46 #196)
+#194 := (= #45 #191)
+#188 := (- #185 f8)
+#192 := (= #188 #191)
+#193 := [rewrite]: #192
+#189 := (= #45 #188)
+#186 := (= #44 #185)
+#183 := (= #43 #182)
+#184 := [rewrite]: #183
+#187 := [monotonicity #184]: #186
+#190 := [monotonicity #187]: #189
+#195 := [trans #190 #193]: #194
+#198 := [monotonicity #195]: #197
+#279 := [monotonicity #198 #276]: #278
+#285 := [trans #279 #283]: #284
+#180 := (iff #40 #179)
+#177 := (= #39 #174)
+#171 := (- #168 f7)
+#175 := (= #171 #174)
+#176 := [rewrite]: #175
+#172 := (= #39 #171)
+#169 := (= #38 #168)
+#166 := (= #37 #165)
+#167 := [rewrite]: #166
+#170 := [monotonicity #167]: #169
+#173 := [monotonicity #170]: #172
+#178 := [trans #173 #176]: #177
+#181 := [monotonicity #178]: #180
+#288 := [monotonicity #181 #285]: #287
+#294 := [trans #288 #292]: #293
+#163 := (iff #34 #162)
+#160 := (= #33 #157)
+#154 := (- #151 f6)
+#158 := (= #154 #157)
+#159 := [rewrite]: #158
+#155 := (= #33 #154)
+#152 := (= #32 #151)
+#149 := (= #31 #148)
+#150 := [rewrite]: #149
+#153 := [monotonicity #150]: #152
+#156 := [monotonicity #153]: #155
+#161 := [trans #156 #159]: #160
+#164 := [monotonicity #161]: #163
+#297 := [monotonicity #164 #294]: #296
+#303 := [trans #297 #301]: #302
+#146 := (iff #28 #145)
+#143 := (= #27 #140)
+#137 := (- #134 f3)
+#141 := (= #137 #140)
+#142 := [rewrite]: #141
+#138 := (= #27 #137)
+#135 := (= #26 #134)
+#132 := (= #25 #131)
+#133 := [rewrite]: #132
+#136 := [monotonicity #133]: #135
+#139 := [monotonicity #136]: #138
+#144 := [trans #139 #142]: #143
+#147 := [monotonicity #144]: #146
+#306 := [monotonicity #147 #303]: #305
+#312 := [trans #306 #310]: #311
+#129 := (iff #22 #128)
+#126 := (= #21 #123)
+#120 := (- #117 f4)
+#124 := (= #120 #123)
+#125 := [rewrite]: #124
+#121 := (= #21 #120)
+#118 := (= #20 #117)
+#115 := (= #19 #114)
+#116 := [rewrite]: #115
+#119 := [monotonicity #116]: #118
+#122 := [monotonicity #119]: #121
+#127 := [trans #122 #125]: #126
+#130 := [monotonicity #127]: #129
+#315 := [monotonicity #130 #312]: #314
+#321 := [trans #315 #319]: #320
+#112 := (iff #16 #111)
+#109 := (= #15 #106)
+#102 := (- #99 f5)
+#107 := (= #102 #106)
+#108 := [rewrite]: #107
+#103 := (= #15 #102)
+#100 := (= #13 #99)
+#97 := (= #12 #96)
+#98 := [rewrite]: #97
+#101 := [monotonicity #98]: #100
+#104 := [monotonicity #101]: #103
+#110 := [trans #104 #108]: #109
+#113 := [monotonicity #110]: #112
+#324 := [monotonicity #113 #321]: #323
+#330 := [trans #324 #328]: #329
+#333 := [monotonicity #330]: #332
+#631 := [trans #333 #629]: #630
+#94 := [asserted]: #77
+#632 := [mp #94 #631]: #627
+#641 := [not-or-elim #632]: #529
+#908 := (or #534 #714)
+#909 := [th-lemma]: #908
+#910 := [unit-resolution #909 #641]: #714
+#1135 := [th-lemma #910 #907 #1129 #810 #1134]: false
+#1137 := [lemma #1135]: #1136
+#1128 := [unit-resolution #1137 #907 #810]: #508
+#709 := (or #509 #707)
+#710 := [def-axiom]: #709
+#1138 := [unit-resolution #710 #1128]: #707
+#926 := (not #707)
+#927 := (or #926 #752)
+#928 := [th-lemma]: #927
+#1139 := [unit-resolution #928 #1138]: #752
+#1140 := [th-lemma #910 #907 #1128 #810 #1139]: false
+#1142 := [lemma #1140]: #1141
+#1144 := [unit-resolution #1142 #810]: #537
+#717 := (or #538 #715)
+#718 := [def-axiom]: #717
+#1145 := [unit-resolution #718 #1144]: #715
+#895 := (not #715)
+#896 := (or #895 #745)
+#797 := (not #745)
+#893 := [hypothesis]: #797
+#894 := [hypothesis]: #715
+#897 := [th-lemma]: #896
+#898 := [unit-resolution #897 #894 #893]: false
+#899 := [lemma #898]: #896
+#1146 := [unit-resolution #899 #1145]: #745
+#741 := (+ f4 #584)
+#742 := (<= #741 0::int)
+#723 := (= f4 #573)
+#722 := (>= #557 0::int)
+#642 := [not-or-elim #632]: #558
+#782 := (or #563 #722)
+#783 := [th-lemma]: #782
+#784 := [unit-resolution #783 #642]: #722
+#738 := (+ #148 #497)
+#739 := (<= #738 0::int)
+#700 := (= #148 #486)
+#703 := (or #479 #700)
+#704 := [def-axiom]: #703
+#811 := [unit-resolution #704 #810]: #700
+#812 := (not #700)
+#904 := (or #812 #739)
+#905 := [th-lemma]: #904
+#906 := [unit-resolution #905 #811]: #739
+#706 := (>= #499 0::int)
+#640 := [not-or-elim #632]: #500
+#911 := (or #505 #706)
+#912 := [th-lemma]: #911
+#913 := [unit-resolution #912 #640]: #706
+#914 := [hypothesis]: #451
+#917 := (not #739)
+#916 := (not #706)
+#922 := (or #508 #479 #916 #917 #450)
+#923 := [th-lemma]: #922
+#924 := [unit-resolution #923 #914 #913 #810 #906]: #508
+#925 := [unit-resolution #710 #924]: #707
+#1072 := [unit-resolution #928 #925]: #752
+#918 := (not #714)
+#915 := (not #752)
+#996 := (not #722)
+#1076 := (or #566 #797 #479 #996 #915 #918)
+#1077 := [th-lemma]: #1076
+#1147 := [unit-resolution #1077 #1072 #784 #1146 #910 #810]: #566
+#725 := (or #567 #723)
+#726 := [def-axiom]: #725
+#1148 := [unit-resolution #726 #1147]: #723
+#934 := (not #723)
+#935 := (or #934 #742)
+#936 := [th-lemma]: #935
+#1149 := [unit-resolution #936 #1148]: #742
+#798 := (not #742)
+#891 := (or #797 #798 #733 #479)
+#747 := (+ #165 #468)
+#748 := (<= #747 0::int)
+#692 := (= #165 #457)
+#762 := (not #733)
+#763 := [hypothesis]: #762
+#780 := [hypothesis]: #742
+#781 := [hypothesis]: #745
+#856 := (or #451 #479 #798 #733 #797)
+#754 := (<= #753 0::int)
+#820 := (not #754)
+#764 := [hypothesis]: #450
+#847 := (or #820 #797 #798 #733 #451 #479)
+#760 := (+ #216 #381)
+#809 := (>= #760 0::int)
+#668 := (= #216 #370)
+#667 := (= f11 #370)
+#803 := (not #667)
+#759 := (+ f11 #381)
+#761 := (>= #759 0::int)
+#794 := (not #761)
+#740 := (>= #738 0::int)
+#813 := (or #812 #740)
+#814 := [th-lemma]: #813
+#815 := [unit-resolution #814 #811]: #740
+#756 := (+ f10 #410)
+#758 := (>= #756 0::int)
+#675 := (= f10 #399)
+#690 := (>= #441 0::int)
+#638 := [not-or-elim #632]: #442
+#816 := (or #447 #690)
+#817 := [th-lemma]: #816
+#818 := [unit-resolution #817 #638]: #690
+#751 := (<= #750 0::int)
+#768 := [unit-resolution #694 #764]: #691
+#770 := (or #769 #751)
+#771 := [th-lemma]: #770
+#772 := [unit-resolution #771 #768]: #751
+#698 := (>= #470 0::int)
+#639 := [not-or-elim #632]: #471
+#765 := (or #476 #698)
+#766 := [th-lemma]: #765
+#767 := [unit-resolution #766 #639]: #698
+#819 := [hypothesis]: #754
+#823 := (not #690)
+#822 := (not #698)
+#821 := (not #751)
+#824 := (or #392 #820 #821 #479 #822 #823)
+#825 := [th-lemma]: #824
+#826 := [unit-resolution #825 #819 #767 #810 #772 #818]: #392
+#677 := (or #393 #675)
+#678 := [def-axiom]: #677
+#827 := [unit-resolution #678 #826]: #675
+#828 := (not #675)
+#829 := (or #828 #758)
+#830 := [th-lemma]: #829
+#831 := [unit-resolution #830 #827]: #758
+#796 := (not #740)
+#795 := (not #758)
+#799 := (or #794 #795 #796 #797 #798 #451 #733)
+#673 := (<= #383 0::int)
+#636 := [not-or-elim #632]: #384
+#773 := (or #389 #673)
+#774 := [th-lemma]: #773
+#775 := [unit-resolution #774 #636]: #673
+#776 := [hypothesis]: #761
+#730 := (>= #586 0::int)
+#643 := [not-or-elim #632]: #587
+#777 := (or #592 #730)
+#778 := [th-lemma]: #777
+#779 := [unit-resolution #778 #643]: #730
+#785 := [hypothesis]: #740
+#705 := (<= #499 0::int)
+#786 := (or #505 #705)
+#787 := [th-lemma]: #786
+#788 := [unit-resolution #787 #640]: #705
+#681 := (<= #412 0::int)
+#637 := [not-or-elim #632]: #413
+#789 := (or #418 #681)
+#790 := [th-lemma]: #789
+#791 := [unit-resolution #790 #637]: #681
+#792 := [hypothesis]: #758
+#793 := [th-lemma #792 #791 #788 #785 #784 #781 #780 #779 #776 #775 #772 #767 #764 #763]: false
+#800 := [lemma #793]: #799
+#832 := [unit-resolution #800 #831 #815 #781 #780 #764 #763]: #794
+#804 := (or #803 #761)
+#801 := [hypothesis]: #794
+#802 := [hypothesis]: #667
+#805 := [th-lemma]: #804
+#806 := [unit-resolution #805 #802 #801]: false
+#807 := [lemma #806]: #804
+#833 := [unit-resolution #807 #832]: #803
+#669 := (or #364 #667)
+#670 := [def-axiom]: #669
+#834 := [unit-resolution #670 #833]: #364
+#671 := (or #363 #668)
+#672 := [def-axiom]: #671
+#835 := [unit-resolution #672 #834]: #668
+#836 := (not #668)
+#837 := (or #836 #809)
+#838 := [th-lemma]: #837
+#839 := [unit-resolution #838 #835]: #809
+#682 := (>= #412 0::int)
+#840 := (or #418 #682)
+#841 := [th-lemma]: #840
+#842 := [unit-resolution #841 #637]: #682
+#757 := (<= #756 0::int)
+#843 := (or #828 #757)
+#844 := [th-lemma]: #843
+#845 := [unit-resolution #844 #827]: #757
+#846 := [th-lemma #819 #818 #845 #842 #788 #815 #784 #781 #780 #779 #763 #775 #772 #767 #839]: false
+#848 := [lemma #846]: #847
+#849 := [unit-resolution #848 #764 #780 #763 #781 #810]: #820
+#859 := (or #421 #479 #451)
+#857 := [hypothesis]: #422
+#858 := [th-lemma #810 #857 #772 #767 #764]: false
+#860 := [lemma #858]: #859
+#850 := [unit-resolution #860 #764 #810]: #421
+#685 := (or #422 #683)
+#686 := [def-axiom]: #685
+#851 := [unit-resolution #686 #850]: #683
+#852 := (not #683)
+#853 := (or #852 #754)
+#854 := [th-lemma]: #853
+#855 := [unit-resolution #854 #851 #849]: false
+#861 := [lemma #855]: #856
+#865 := [unit-resolution #861 #781 #780 #763 #810]: #451
+#695 := (or #450 #692)
+#696 := [def-axiom]: #695
+#866 := [unit-resolution #696 #865]: #692
+#867 := (not #692)
+#868 := (or #867 #748)
+#869 := [th-lemma]: #868
+#870 := [unit-resolution #869 #866]: #748
+#871 := (not #748)
+#872 := (or #421 #871 #479 #822 #450)
+#873 := [th-lemma]: #872
+#874 := [unit-resolution #873 #865 #767 #810 #870]: #421
+#875 := [unit-resolution #686 #874]: #683
+#876 := [unit-resolution #854 #875]: #754
+#877 := (or #392 #422 #820 #823 #450)
+#878 := [th-lemma]: #877
+#879 := [unit-resolution #878 #874 #818 #865 #876]: #392
+#880 := [unit-resolution #678 #879]: #675
+#881 := [unit-resolution #830 #880]: #758
+#882 := [unit-resolution #844 #880]: #757
+#884 := (not #682)
+#883 := (not #757)
+#885 := (or #363 #883 #884 #820 #823 #450)
+#886 := [th-lemma]: #885
+#887 := [unit-resolution #886 #865 #818 #842 #876 #882]: #363
+#888 := [unit-resolution #670 #887]: #667
+#889 := [unit-resolution #807 #888]: #761
+#890 := [th-lemma #767 #889 #784 #781 #780 #779 #763 #775 #788 #815 #881 #791 #870]: false
+#892 := [lemma #890]: #891
+#1150 := [unit-resolution #892 #1149 #1146 #810]: #733
+#1056 := (+ #233 #352)
+#1143 := (<= #1056 0::int)
+#656 := (= #233 #341)
+#1084 := (or #895 #987)
+#1085 := [th-lemma]: #1084
+#1151 := [unit-resolution #1085 #1145]: #987
+#729 := (<= #586 0::int)
+#1098 := (or #592 #729)
+#1099 := [th-lemma]: #1098
+#1100 := [unit-resolution #1099 #643]: #729
+#721 := (<= #557 0::int)
+#1032 := (or #563 #721)
+#1033 := [th-lemma]: #1032
+#1034 := [unit-resolution #1033 #642]: #721
+#1055 := (>= #741 0::int)
+#1081 := (or #934 #1055)
+#1082 := [th-lemma]: #1081
+#1152 := [unit-resolution #1082 #1148]: #1055
+#1108 := (not #721)
+#1107 := (not #987)
+#1106 := (not #729)
+#1105 := (not #1055)
+#1116 := (or #335 #762 #1105 #1106 #1107 #479 #916 #917 #1108 #450)
+#1117 := [th-lemma]: #1116
+#1153 := [unit-resolution #1117 #1152 #810 #913 #1034 #1100 #1150 #906 #1151 #914]: #335
+#651 := (or #334 #656)
+#652 := [def-axiom]: #651
+#1154 := [unit-resolution #652 #1153]: #656
+#1120 := (not #656)
+#1155 := (or #1120 #1143)
+#1156 := [th-lemma]: #1155
+#1157 := [unit-resolution #1156 #1154]: #1143
+#1127 := (>= #749 0::int)
+#1158 := (or #926 #1127)
+#1159 := [th-lemma]: #1158
+#1160 := [unit-resolution #1159 #925]: #1127
+#1061 := [unit-resolution #696 #914]: #692
+#1062 := [unit-resolution #869 #1061]: #748
+#1063 := [unit-resolution #873 #1062 #767 #810 #914]: #421
+#1064 := [unit-resolution #686 #1063]: #683
+#1046 := (or #852 #986)
+#1047 := [th-lemma]: #1046
+#1161 := [unit-resolution #1047 #1064]: #986
+#1066 := (or #751 #450 #871)
+#1067 := [th-lemma]: #1066
+#1162 := [unit-resolution #1067 #1062 #914]: #751
+#1065 := [unit-resolution #854 #1064]: #754
+#1163 := [unit-resolution #825 #1065 #767 #810 #1162 #818]: #392
+#1164 := [unit-resolution #678 #1163]: #675
+#1165 := [unit-resolution #830 #1164]: #758
+#650 := (>= #354 0::int)
+#635 := [not-or-elim #632]: #355
+#1166 := (or #360 #650)
+#1167 := [th-lemma]: #1166
+#1168 := [unit-resolution #1167 #635]: #650
+#713 := (<= #528 0::int)
+#1169 := (or #534 #713)
+#1170 := [th-lemma]: #1169
+#1171 := [unit-resolution #1170 #641]: #713
+#689 := (<= #441 0::int)
+#1049 := (or #447 #689)
+#1050 := [th-lemma]: #1049
+#1051 := [unit-resolution #1050 #638]: #689
+#1125 := (or #450 #737 #479)
+#1059 := (not #737)
+#1060 := [hypothesis]: #1059
+#1068 := [unit-resolution #1067 #914 #1062]: #751
+#1069 := [unit-resolution #825 #1065 #767 #810 #1068 #818]: #392
+#1070 := [unit-resolution #678 #1069]: #675
+#1071 := [unit-resolution #844 #1070]: #757
+#649 := (<= #354 0::int)
+#954 := (or #360 #649)
+#955 := [th-lemma]: #954
+#956 := [unit-resolution #955 #635]: #649
+#930 := (or #450 #537 #479)
+#919 := (or #537 #450 #915 #479 #916 #917 #918)
+#920 := [th-lemma]: #919
+#921 := [unit-resolution #920 #914 #913 #910 #907 #906 #810]: #915
+#929 := [unit-resolution #928 #925 #921]: false
+#931 := [lemma #929]: #930
+#1073 := [unit-resolution #931 #914 #810]: #537
+#1074 := [unit-resolution #718 #1073]: #715
+#1075 := [unit-resolution #899 #1074]: #745
+#1078 := [unit-resolution #1077 #1075 #784 #810 #910 #1072]: #566
+#1079 := [unit-resolution #726 #1078]: #723
+#1080 := [unit-resolution #936 #1079]: #742
+#1083 := [unit-resolution #1082 #1079]: #1055
+#1086 := [unit-resolution #1085 #1074]: #987
+#900 := (>= #747 0::int)
+#1087 := (or #867 #900)
+#1088 := [th-lemma]: #1087
+#1089 := [unit-resolution #1088 #1061]: #900
+#863 := (<= #759 0::int)
+#1090 := [unit-resolution #886 #1071 #818 #914 #1065 #842]: #363
+#1091 := [unit-resolution #670 #1090]: #667
+#1092 := (or #803 #863)
+#1093 := [th-lemma]: #1092
+#1094 := [unit-resolution #1093 #1091]: #863
+#674 := (>= #383 0::int)
+#1095 := (or #389 #674)
+#1096 := [th-lemma]: #1095
+#1097 := [unit-resolution #1096 #636]: #674
+#697 := (<= #470 0::int)
+#1043 := (or #476 #697)
+#1044 := [th-lemma]: #1043
+#1045 := [unit-resolution #1044 #639]: #697
+#1104 := (not #697)
+#1103 := (not #900)
+#1102 := (not #674)
+#1101 := (not #863)
+#1109 := (or #732 #1101 #1102 #1103 #1104 #883 #884 #1105 #1106 #1107 #916 #917 #1108)
+#1110 := [th-lemma]: #1109
+#1111 := [unit-resolution #1110 #1071 #1045 #913 #1034 #1100 #1097 #906 #842 #1094 #1089 #1086 #1083]: #732
+#1058 := (>= #1056 0::int)
+#1112 := (or #737 #736)
+#1113 := [th-lemma]: #1112
+#1114 := [unit-resolution #1113 #1060]: #736
+#1053 := (or #733 #479 #967)
+#743 := (+ #96 #584)
+#862 := (<= #743 0::int)
+#724 := (= #96 #573)
+#963 := [hypothesis]: #736
+#984 := (or #567 #479 #967 #733)
+#932 := [hypothesis]: #566
+#933 := [unit-resolution #726 #932]: #723
+#937 := [unit-resolution #936 #933]: #742
+#938 := (or #733 #732)
+#939 := [th-lemma]: #938
+#940 := [unit-resolution #939 #763]: #732
+#941 := [unit-resolution #892 #937 #763 #810]: #797
+#942 := [unit-resolution #899 #941]: #895
+#943 := [unit-resolution #718 #942]: #538
+#945 := (not #732)
+#944 := (not #730)
+#946 := (or #334 #537 #567 #798 #944 #945)
+#947 := [th-lemma]: #946
+#948 := [unit-resolution #947 #943 #932 #779 #940 #937]: #334
+#653 := (or #335 #655)
+#654 := [def-axiom]: #653
+#949 := [unit-resolution #654 #948]: #655
+#950 := (not #655)
+#951 := (or #950 #901)
+#952 := [th-lemma]: #951
+#953 := [unit-resolution #952 #949]: #901
+#957 := [unit-resolution #931 #943 #810]: #450
+#958 := [unit-resolution #860 #957 #810]: #421
+#959 := [unit-resolution #686 #958]: #683
+#960 := [unit-resolution #854 #959]: #754
+#961 := [unit-resolution #694 #957]: #691
+#962 := [unit-resolution #771 #961]: #751
+#966 := (not #649)
+#965 := (not #901)
+#964 := (not #673)
+#968 := (or #794 #964 #823 #479 #965 #966 #967 #820 #821 #822 #567)
+#969 := [th-lemma]: #968
+#970 := [unit-resolution #969 #932 #818 #767 #810 #775 #963 #962 #960 #956 #953]: #794
+#971 := [unit-resolution #807 #970]: #803
+#972 := [unit-resolution #670 #971]: #364
+#973 := [unit-resolution #672 #972]: #668
+#974 := [unit-resolution #838 #973]: #809
+#746 := (+ #114 #555)
+#808 := (<= #746 0::int)
+#716 := (= #114 #544)
+#719 := (or #537 #716)
+#720 := [def-axiom]: #719
+#975 := [unit-resolution #720 #943]: #716
+#976 := (not #716)
+#977 := (or #976 #808)
+#978 := [th-lemma]: #977
+#979 := [unit-resolution #978 #975]: #808
+#980 := [unit-resolution #825 #962 #767 #810 #960 #818]: #392
+#981 := [unit-resolution #678 #980]: #675
+#982 := [unit-resolution #844 #981]: #757
+#983 := [th-lemma #943 #937 #779 #940 #775 #818 #960 #962 #767 #982 #842 #979 #788 #815 #784 #974]: false
+#985 := [lemma #983]: #984
+#1007 := [unit-resolution #985 #763 #963 #810]: #567
+#727 := (or #566 #724)
+#728 := [def-axiom]: #727
+#1008 := [unit-resolution #728 #1007]: #724
+#1009 := (not #724)
+#1010 := (or #1009 #862)
+#1011 := [th-lemma]: #1010
+#1012 := [unit-resolution #1011 #1008]: #862
+#1013 := (not #862)
+#1014 := (or #742 #566 #1013)
+#1015 := [th-lemma]: #1014
+#1016 := [unit-resolution #1015 #1007 #1012]: #742
+#1017 := [unit-resolution #892 #1016 #763 #810]: #797
+#1018 := [unit-resolution #899 #1017]: #895
+#1019 := [unit-resolution #718 #1018]: #538
+#1020 := [unit-resolution #931 #1019 #810]: #450
+#1021 := [unit-resolution #694 #1020]: #691
+#1022 := [unit-resolution #771 #1021]: #751
+#1023 := [unit-resolution #860 #1020 #810]: #421
+#1024 := [unit-resolution #686 #1023]: #683
+#1025 := [unit-resolution #854 #1024]: #754
+#1026 := [unit-resolution #825 #1025 #767 #810 #1022 #818]: #392
+#1027 := [unit-resolution #678 #1026]: #675
+#1028 := [unit-resolution #844 #1027]: #757
+#1005 := (or #363 #537 #566 #796 #820 #883)
+#989 := [unit-resolution #720 #907]: #716
+#990 := [unit-resolution #978 #989]: #808
+#991 := [hypothesis]: #757
+#992 := [hypothesis]: #567
+#993 := [hypothesis]: #364
+#995 := (not #808)
+#994 := (not #705)
+#997 := (or #915 #918 #537 #883 #823 #994 #796 #884 #363 #820 #995 #996 #566)
+#998 := [th-lemma]: #997
+#999 := [unit-resolution #998 #993 #818 #788 #910 #907 #784 #992 #785 #819 #991 #842 #990]: #915
+#1000 := (or #508 #995 #537 #996 #566)
+#1001 := [th-lemma]: #1000
+#1002 := [unit-resolution #1001 #907 #784 #992 #990]: #508
+#1003 := [unit-resolution #710 #1002]: #707
+#1004 := [unit-resolution #928 #1003 #999]: false
+#1006 := [lemma #1004]: #1005
+#1029 := [unit-resolution #1006 #1019 #1007 #815 #1025 #1028]: #363
+#1030 := [unit-resolution #670 #1029]: #667
+#1031 := [unit-resolution #807 #1030]: #761
+#1035 := [unit-resolution #830 #1027]: #758
+#902 := (>= #746 0::int)
+#1036 := [unit-resolution #720 #1019]: #716
+#1037 := (or #976 #902)
+#1038 := [th-lemma]: #1037
+#1039 := [unit-resolution #1038 #1036]: #902
+#1042 := [unit-resolution #1041 #1021]: #903
+#1048 := [unit-resolution #1047 #1024]: #986
+#1052 := [th-lemma #1051 #1048 #1045 #1042 #1039 #1035 #913 #906 #1034 #791 #1031 #763 #775 #1012 #779 #1026]: false
+#1054 := [lemma #1052]: #1053
+#1115 := [unit-resolution #1054 #1114 #810]: #733
+#1118 := [unit-resolution #1117 #914 #810 #913 #1034 #1100 #1115 #906 #1086 #1083]: #335
+#1119 := [unit-resolution #652 #1118]: #656
+#1121 := (or #1120 #1058)
+#1122 := [th-lemma]: #1121
+#1123 := [unit-resolution #1122 #1119]: #1058
+#1124 := [th-lemma #1123 #1111 #1080 #779 #1075 #788 #815 #784 #956 #1072 #910 #1071 #818 #842 #1065 #1060]: false
+#1126 := [lemma #1124]: #1125
+#1172 := [unit-resolution #1126 #914 #810]: #737
+#1179 := (not #689)
+#1178 := (not #986)
+#1177 := (not #713)
+#1176 := (not #1127)
+#1175 := (not #681)
+#1174 := (not #650)
+#1173 := (not #1143)
+#1180 := (or #732 #1173 #1105 #1106 #916 #917 #1107 #1108 #795 #1174 #1059 #1175 #1176 #1177 #1178 #1179)
+#1181 := [th-lemma]: #1180
+#1182 := [unit-resolution #1181 #1172 #1051 #913 #1171 #1034 #1100 #1168 #791 #906 #1165 #1151 #1152 #1161 #1160 #1157]: #732
+#1183 := (or #65 #945 #762)
+#1184 := [th-lemma]: #1183
+#1185 := [unit-resolution #1184 #1182 #1150]: #65
+#1186 := (or #736 #1173 #762 #1105 #1106 #916 #917 #1107 #1108 #795 #1174 #1175 #1176 #1177 #1178 #1179)
+#1187 := [th-lemma]: #1186
+#1188 := [unit-resolution #1187 #1150 #1051 #913 #1171 #1034 #1100 #791 #1168 #906 #1165 #1151 #1152 #1161 #1160 #1157]: #736
+#1189 := (or #66 #967 #1059)
+#1190 := [th-lemma]: #1189
+#1191 := [unit-resolution #1190 #1188 #1172]: #66
+#647 := (not #65)
+#646 := (or #647 #648)
+#633 := (not #67)
+#660 := (iff #633 #646)
+#644 := (not #646)
+#663 := (not #644)
+#662 := (iff #663 #646)
+#659 := [rewrite]: #662
+#664 := (iff #633 #663)
+#665 := (iff #67 #644)
+#666 := [rewrite]: #665
+#661 := [monotonicity #666]: #664
+#657 := [trans #661 #659]: #660
+#634 := [not-or-elim #632]: #633
+#658 := [mp #634 #657]: #646
+#1192 := [unit-resolution #658 #1191 #1185]: false
+#1194 := [lemma #1192]: #1193
+#1217 := [unit-resolution #1194 #810]: #450
+#1221 := [unit-resolution #860 #1217 #810]: #421
+#1222 := [unit-resolution #686 #1221]: #683
+#1223 := [unit-resolution #1047 #1222]: #986
+#1224 := [unit-resolution #694 #1217]: #691
+#1225 := [unit-resolution #1041 #1224]: #903
+#1214 := (or #566 #479)
+#1206 := (or #566 #797 #479 #915)
+#1207 := [unit-resolution #1077 #784 #910]: #1206
+#1208 := [unit-resolution #1207 #992 #810 #1146]: #915
+#1209 := (or #508 #538 #797 #996 #566)
+#1210 := [th-lemma]: #1209
+#1211 := [unit-resolution #1210 #992 #784 #1144 #1146]: #508
+#1212 := [unit-resolution #710 #1211]: #707
+#1213 := [unit-resolution #928 #1212 #1208]: false
+#1215 := [lemma #1213]: #1214
+#1226 := [unit-resolution #1215 #810]: #566
+#1227 := [unit-resolution #726 #1226]: #723
+#1228 := [unit-resolution #1082 #1227]: #1055
+#755 := (<= #760 0::int)
+#1245 := (not #755)
+#1312 := [hypothesis]: #1245
+#1242 := (or #836 #755)
+#1313 := [hypothesis]: #668
+#1243 := [th-lemma]: #1242
+#1314 := [unit-resolution #1243 #1313 #1312]: false
+#1315 := [lemma #1314]: #1242
+#1316 := [unit-resolution #1315 #1312]: #836
+#1317 := [unit-resolution #672 #1316]: #363
+#1318 := (or #755 #364 #1101)
+#1319 := [th-lemma]: #1318
+#1320 := [unit-resolution #1319 #1317 #1312]: #1101
+#1321 := [unit-resolution #670 #1317]: #667
+#1322 := [unit-resolution #1093 #1321 #1320]: false
+#1323 := [lemma #1322]: #755
+#1229 := [unit-resolution #771 #1224]: #751
+#1230 := [unit-resolution #854 #1222]: #754
+#1231 := (or #392 #820 #821 #479)
+#1232 := [unit-resolution #825 #767 #818]: #1231
+#1233 := [unit-resolution #1232 #1230 #810 #1229]: #392
+#1234 := [unit-resolution #678 #1233]: #675
+#1235 := [unit-resolution #830 #1234]: #758
+#1276 := (or #508 #479)
+#1218 := (or #451 #479 #733 #797)
+#1196 := [hypothesis]: #798
+#1197 := [hypothesis]: #723
+#1198 := [unit-resolution #936 #1197 #1196]: false
+#1199 := [lemma #1198]: #935
+#1200 := [unit-resolution #1199 #1196]: #934
+#1201 := [unit-resolution #726 #1200]: #567
+#1202 := [unit-resolution #1015 #1201 #1196]: #1013
+#1203 := [unit-resolution #728 #1201]: #724
+#1204 := [unit-resolution #1011 #1203 #1202]: false
+#1205 := [lemma #1204]: #742
+#1219 := [unit-resolution #861 #1205]: #1218
+#1220 := [unit-resolution #1219 #1146 #1217 #810]: #733
+#1238 := (or #364 #795 #1178 #508 #479 #917)
+#1236 := (or #364 #795 #1175 #1178 #1179 #508 #479 #916 #917)
+#1237 := [th-lemma]: #1236
+#1239 := [unit-resolution #1237 #1051 #913 #791]: #1238
+#1240 := [unit-resolution #1239 #1129 #810 #1223 #906 #1235]: #364
+#1241 := [unit-resolution #672 #1240]: #668
+#1244 := [unit-resolution #1243 #1241]: #755
+#1247 := (or #732 #1245 #1102 #795 #1175 #1246 #1179 #1104 #917 #916 #1107 #1108 #1178 #1105 #1106)
+#1248 := [th-lemma]: #1247
+#1249 := [unit-resolution #1248 #1244 #1051 #1045 #913 #1034 #1100 #1097 #1235 #791 #906 #1151 #1228 #1225 #1223]: #732
+#1250 := [unit-resolution #1184 #1249 #1220]: #65
+#1251 := [unit-resolution #658 #1250]: #648
+#1252 := [unit-resolution #844 #1234]: #757
+#1255 := (or #334 #1245 #1246 #1178 #508 #917 #795)
+#1253 := (or #334 #1245 #1102 #1104 #1246 #1179 #1178 #508 #916 #917 #795 #1175)
+#1254 := [th-lemma]: #1253
+#1256 := [unit-resolution #1254 #791 #1051 #1045 #913 #1097]: #1255
+#1257 := [unit-resolution #1256 #1244 #1223 #906 #1235 #1129 #1225]: #334
+#1258 := [unit-resolution #654 #1257]: #655
+#1259 := [unit-resolution #952 #1258]: #901
+#1260 := (not #1057)
+#1261 := (or #737 #883 #966 #884 #823 #796 #994 #820 #1260 #918 #965 #762 #1105 #1106)
+#1262 := [th-lemma]: #1261
+#1263 := [unit-resolution #1262 #1259 #818 #788 #910 #1100 #1220 #956 #1230 #815 #1252 #842 #1228 #1134]: #737
+#1216 := (<= #864 0::int)
+#1264 := (or #950 #1216)
+#1265 := [th-lemma]: #1264
+#1266 := [unit-resolution #1265 #1258]: #1216
+#1195 := (>= #988 0::int)
+#1267 := (or #1131 #1195)
+#1268 := [th-lemma]: #1267
+#1269 := [unit-resolution #1268 #1130]: #1195
+#1271 := (not #1216)
+#1270 := (not #1195)
+#1272 := (or #736 #795 #1174 #1175 #1179 #917 #916 #1178 #1270 #1177 #1271 #945 #798 #944)
+#1273 := [th-lemma]: #1272
+#1274 := [unit-resolution #1273 #1249 #1051 #913 #1171 #779 #791 #1168 #1235 #1205 #906 #1223 #1269 #1266]: #736
+#1275 := [unit-resolution #1190 #1274 #1263 #1251]: false
+#1277 := [lemma #1275]: #1276
+#1324 := [unit-resolution #1277 #810]: #508
+#1325 := [unit-resolution #710 #1324]: #707
+#1326 := [unit-resolution #928 #1325]: #752
+#1327 := [unit-resolution #1159 #1325]: #1127
+#1328 := (or #1057 #915 #509)
+#1329 := [th-lemma]: #1328
+#1330 := [unit-resolution #1329 #1326 #1324]: #1057
+#1310 := (or #945 #795 #917 #1178 #762 #820 #796 #883 #1105 #1260 #1107 #1176 #915 #797)
+#1282 := [hypothesis]: #733
+#1281 := [hypothesis]: #732
+#1283 := [unit-resolution #1184 #1281 #1282]: #65
+#1284 := [unit-resolution #658 #1283]: #648
+#1298 := [hypothesis]: #1057
+#1286 := [hypothesis]: #1055
+#1285 := [hypothesis]: #986
+#1287 := [hypothesis]: #987
+#1288 := [hypothesis]: #739
+#1289 := [hypothesis]: #1127
+#1280 := [hypothesis]: #752
+#1296 := (or #1120 #883 #796 #820 #945 #915 #797 #762 #1176 #917 #795 #1107 #1105 #1178)
+#1278 := [hypothesis]: #656
+#1279 := [unit-resolution #1122 #1278]: #1058
+#1290 := [unit-resolution #1156 #1278]: #1143
+#1291 := (or #736 #1173 #762 #1105 #917 #1107 #795 #1176 #1178)
+#1292 := [unit-resolution #1187 #1051 #913 #1171 #1034 #1100 #791 #1168]: #1291
+#1293 := [unit-resolution #1292 #1290 #1282 #1289 #1288 #792 #1287 #1286 #1285]: #736
+#1294 := [unit-resolution #1190 #1293 #1284]: #1059
+#1295 := [th-lemma #991 #956 #1294 #842 #818 #785 #788 #819 #910 #1281 #1205 #779 #1280 #781 #784 #1279]: false
+#1297 := [lemma #1295]: #1296
+#1299 := [unit-resolution #1297 #1281 #785 #819 #991 #1280 #781 #1282 #1289 #1288 #792 #1287 #1286 #1285]: #1120
+#1300 := [unit-resolution #652 #1299]: #334
+#1301 := [unit-resolution #654 #1300]: #655
+#1302 := [unit-resolution #952 #1301]: #901
+#1303 := [unit-resolution #1262 #1302 #818 #788 #910 #1100 #1282 #956 #819 #785 #991 #842 #1286 #1298]: #737
+#1304 := [unit-resolution #1265 #1301]: #1216
+#1305 := (or #1195 #1176 #335 #762 #1105 #1106 #1107 #1108)
+#1306 := [th-lemma]: #1305
+#1307 := [unit-resolution #1306 #1300 #1100 #1282 #1287 #1286 #1289 #1034]: #1195
+#1308 := [unit-resolution #1273 #1307 #1051 #913 #1171 #779 #1281 #1304 #792 #1205 #1288 #1285 #791 #1168]: #736
+#1309 := [unit-resolution #1190 #1308 #1303 #1284]: false
+#1311 := [lemma #1309]: #1310
+#1331 := [unit-resolution #1311 #1235 #906 #1223 #1220 #1230 #815 #1252 #1228 #1330 #1151 #1327 #1326 #1146]: #945
+#1332 := [unit-resolution #1248 #1331 #1235 #1051 #1045 #913 #1034 #1100 #1097 #1323 #791 #906 #1151 #1228 #1225 #1223]: false
+#1333 := [lemma #1332]: #479
+#701 := (or #480 #699)
+#702 := [def-axiom]: #701
+#1337 := [unit-resolution #702 #1333]: #699
+#1338 := (not #699)
+#1339 := (or #1338 #1335)
+#1340 := [th-lemma]: #1339
+#1341 := [unit-resolution #1340 #1337]: #1335
+#1342 := [th-lemma #1333 #914 #913 #1129 #1341]: false
+#1344 := [lemma #1342]: #1343
+#1992 := [unit-resolution #1344 #1835]: #508
+#1993 := [unit-resolution #710 #1992]: #707
+#1994 := [unit-resolution #928 #1993]: #752
+#1828 := (or #903 #751)
+#1829 := [th-lemma]: #1828
+#1830 := [unit-resolution #1829 #1580]: #751
+#1836 := [unit-resolution #696 #1835]: #692
+#1849 := [unit-resolution #1088 #1836]: #900
+#1997 := (or #1103 #821 #915 #537)
+#1351 := (not #1335)
+#1995 := (or #1103 #821 #915 #1351 #916 #918 #537)
+#1996 := [th-lemma]: #1995
+#1998 := [unit-resolution #1996 #910 #913 #1341]: #1997
+#1999 := [unit-resolution #1998 #1849 #1830 #1994]: #537
+#2000 := [unit-resolution #718 #1999]: #715
+#2001 := [unit-resolution #1085 #2000]: #987
+#1578 := (or #450 #363)
+#1563 := (or #392 #363 #450)
+#1547 := [hypothesis]: #393
+#1345 := (+ #199 #410)
+#1346 := (<= #1345 0::int)
+#676 := (= #199 #399)
+#679 := (or #392 #676)
+#680 := [def-axiom]: #679
+#1548 := [unit-resolution #680 #1547]: #676
+#1362 := (not #676)
+#1363 := (or #1362 #1346)
+#1370 := (not #1346)
+#1390 := [hypothesis]: #1370
+#1391 := [hypothesis]: #676
+#1364 := [th-lemma]: #1363
+#1392 := [unit-resolution #1364 #1391 #1390]: false
+#1393 := [lemma #1392]: #1363
+#1549 := [unit-resolution #1393 #1548]: #1346
+#1550 := (or #757 #1370 #392)
+#1551 := [th-lemma]: #1550
+#1552 := [unit-resolution #1551 #1549 #1547]: #757
+#1553 := (or #363 #883 #820 #450)
+#1554 := [unit-resolution #886 #818 #842]: #1553
+#1555 := [unit-resolution #1554 #1552 #993 #914]: #820
+#684 := (= #182 #428)
+#1466 := (not #684)
+#1451 := (+ #182 #439)
+#1452 := (<= #1451 0::int)
+#1461 := (not #1452)
+#1556 := (or #1461 #1104 #823 #480 #1103 #392)
+#1557 := [th-lemma]: #1556
+#1558 := [unit-resolution #1557 #1547 #1045 #1333 #1089 #818]: #1461
+#1467 := (or #1466 #1452)
+#1464 := [hypothesis]: #1461
+#1465 := [hypothesis]: #684
+#1468 := [th-lemma]: #1467
+#1469 := [unit-resolution #1468 #1465 #1464]: false
+#1470 := [lemma #1469]: #1467
+#1559 := [unit-resolution #1470 #1558]: #1466
+#687 := (or #421 #684)
+#688 := [def-axiom]: #687
+#1560 := [unit-resolution #688 #1559]: #421
+#1561 := [unit-resolution #686 #1560]: #683
+#1562 := [unit-resolution #854 #1561 #1555]: false
+#1564 := [lemma #1562]: #1563
+#1571 := [unit-resolution #1564 #914 #993]: #392
+#1572 := [unit-resolution #678 #1571]: #675
+#1573 := [unit-resolution #844 #1572]: #757
+#1574 := [unit-resolution #1554 #1573 #993 #914]: #820
+#1569 := (or #421 #393 #363)
+#1565 := [hypothesis]: #392
+#1566 := [unit-resolution #678 #1565]: #675
+#1567 := [unit-resolution #844 #1566]: #757
+#1568 := [th-lemma #1565 #993 #842 #857 #1567]: false
+#1570 := [lemma #1568]: #1569
+#1575 := [unit-resolution #1570 #1571 #993]: #421
+#1576 := [unit-resolution #686 #1575]: #683
+#1577 := [unit-resolution #854 #1576 #1574]: false
+#1579 := [lemma #1577]: #1578
+#2002 := [unit-resolution #1579 #1835]: #363
+#2003 := [unit-resolution #670 #2002]: #667
+#2004 := [unit-resolution #1093 #2003]: #863
+#2005 := [unit-resolution #899 #2000]: #745
+#1968 := (or #732 #797 #915 #1101 #1103 #1107)
+#1722 := [hypothesis]: #863
+#1950 := [hypothesis]: #900
+#1749 := [hypothesis]: #945
+#1958 := (or #732 #1101 #1103 #1105 #1107)
+#1720 := (or #421 #392)
+#1588 := (or #392 #450)
+#1584 := (or #392 #422 #820 #450)
+#1585 := [unit-resolution #878 #818]: #1584
+#1586 := [unit-resolution #1585 #1560 #914 #1547]: #820
+#1587 := [unit-resolution #854 #1561 #1586]: false
+#1589 := [lemma #1587]: #1588
+#1626 := [unit-resolution #1589 #1547]: #450
+#1627 := [unit-resolution #694 #1626]: #691
+#1649 := [unit-resolution #771 #1627]: #751
+#1675 := (or #421 #821 #508)
+#1352 := (or #421 #821 #822 #508 #1351 #916)
+#1353 := [th-lemma]: #1352
+#1676 := [unit-resolution #1353 #913 #767 #1341]: #1675
+#1677 := [unit-resolution #1676 #857 #1649]: #508
+#1678 := [unit-resolution #710 #1677]: #707
+#1679 := [unit-resolution #1159 #1678]: #1127
+#1628 := [unit-resolution #1583 #1627]: #903
+#1680 := [unit-resolution #688 #857]: #684
+#1681 := [unit-resolution #1470 #1680]: #1452
+#1336 := (>= #1334 0::int)
+#1366 := (or #1338 #1336)
+#1367 := [th-lemma]: #1366
+#1368 := [unit-resolution #1367 #1337]: #1336
+#1369 := (not #1336)
+#1682 := (or #538 #1369 #994 #1177 #823 #421 #392 #1176 #1461)
+#1683 := [th-lemma]: #1682
+#1684 := [unit-resolution #1683 #857 #818 #788 #1171 #1547 #1679 #1368 #1681]: #538
+#1685 := [unit-resolution #720 #1684]: #716
+#1686 := [unit-resolution #978 #1685]: #808
+#1689 := (or #566 #995 #1246 #392 #1176 #1461)
+#1687 := (or #566 #996 #995 #1369 #994 #1246 #1104 #823 #392 #1176 #1177 #1461)
+#1688 := [th-lemma]: #1687
+#1690 := [unit-resolution #1688 #1045 #788 #1171 #784 #1368 #818]: #1689
+#1691 := [unit-resolution #1690 #1686 #1547 #1681 #1628 #1679]: #566
+#1692 := [unit-resolution #726 #1691]: #723
+#1693 := [unit-resolution #1082 #1692]: #1055
+#1673 := (or #363 #392)
+#1387 := (not #809)
+#1545 := (or #537 #733)
+#1509 := [unit-resolution #1038 #989]: #902
+#1446 := (or #508 #733)
+#1381 := (or #537 #733 #508)
+#1348 := [unit-resolution #1344 #1129]: #450
+#1349 := [unit-resolution #694 #1348]: #691
+#1350 := [unit-resolution #771 #1349]: #751
+#1354 := [unit-resolution #1353 #1129 #913 #767 #1350 #1341]: #421
+#1355 := [unit-resolution #686 #1354]: #683
+#1356 := [unit-resolution #1047 #1355]: #986
+#1357 := [unit-resolution #1041 #1349]: #903
+#1358 := (or #393 #1246 #1179 #1104 #1178 #918 #537 #508 #1260)
+#1359 := [th-lemma]: #1358
+#1360 := [unit-resolution #1359 #907 #1045 #1129 #910 #1051 #1357 #1356 #1134]: #393
+#1361 := [unit-resolution #680 #1360]: #676
+#1365 := [unit-resolution #1364 #1361]: #1346
+#1371 := (or #363 #1179 #1178 #884 #1369 #994 #918 #537 #1260 #1370 #1246 #1104)
+#1372 := [th-lemma]: #1371
+#1373 := [unit-resolution #1372 #907 #1051 #1045 #788 #910 #842 #1357 #1356 #1134 #1368 #1365]: #363
+#1374 := [unit-resolution #854 #1355]: #754
+#1347 := (>= #1345 0::int)
+#1375 := (or #1362 #1347)
+#1376 := [th-lemma]: #1375
+#1377 := [unit-resolution #1376 #1361]: #1347
+#1378 := [th-lemma #775 #763 #791 #1350 #767 #784 #1205 #779 #1341 #913 #990 #1377 #818 #1374 #1171 #1269]: #794
+#1379 := [unit-resolution #807 #1378]: #803
+#1380 := [unit-resolution #670 #1379 #1373]: false
+#1382 := [lemma #1380]: #1381
+#1418 := [unit-resolution #1382 #1129 #763]: #537
+#1419 := [unit-resolution #718 #1418]: #715
+#1420 := [unit-resolution #899 #1419]: #745
+#1400 := (or #1387 #733 #1246 #797)
+#1383 := [hypothesis]: #809
+#1385 := [hypothesis]: #903
+#1388 := (or #1370 #733 #1246 #797 #1387)
+#1384 := [hypothesis]: #1346
+#1386 := [th-lemma #775 #763 #1385 #1045 #784 #1205 #779 #1384 #842 #1368 #788 #781 #1383]: false
+#1389 := [lemma #1386]: #1388
+#1394 := [unit-resolution #1389 #1383 #1385 #781 #763]: #1370
+#1395 := [unit-resolution #1393 #1394]: #1362
+#1396 := [unit-resolution #680 #1395]: #392
+#1397 := [unit-resolution #678 #1396]: #675
+#1398 := [unit-resolution #844 #1397]: #757
+#1399 := [th-lemma #775 #763 #1385 #1045 #784 #1205 #779 #842 #1368 #788 #781 #1398 #1396 #1383]: false
+#1401 := [lemma #1399]: #1400
+#1421 := [unit-resolution #1401 #1357 #763 #1420]: #1387
+#1402 := [hypothesis]: #1387
+#1403 := [unit-resolution #838 #1313 #1402]: false
+#1404 := [lemma #1403]: #837
+#1422 := [unit-resolution #1404 #1421]: #836
+#1423 := [unit-resolution #672 #1422]: #363
+#1424 := [unit-resolution #670 #1423]: #667
+#1425 := [unit-resolution #807 #1424]: #761
+#1426 := (or #795 #794 #964 #945 #821 #822 #996 #798 #944 #1175 #1351 #916 #797 #508)
+#1427 := [th-lemma]: #1426
+#1428 := [unit-resolution #1427 #1129 #767 #913 #791 #784 #779 #940 #1350 #1425 #775 #1420 #1205 #1341]: #795
+#1414 := (not #1347)
+#1429 := (or #752 #1260 #508)
+#1430 := [th-lemma]: #1429
+#1431 := [unit-resolution #1430 #1134 #1129]: #752
+#1432 := (or #1270 #915 #334 #945 #798 #944 #797 #996)
+#1433 := [th-lemma]: #1432
+#1434 := [unit-resolution #1433 #1420 #779 #940 #1269 #1205 #1431 #784]: #334
+#1435 := [unit-resolution #654 #1434]: #655
+#1436 := [unit-resolution #1265 #1435]: #1216
+#1437 := [unit-resolution #952 #1435]: #901
+#1412 := (or #737 #821 #820 #1270 #965 #794 #538)
+#1405 := [hypothesis]: #537
+#1406 := [unit-resolution #718 #1405]: #715
+#1407 := [unit-resolution #899 #1406]: #745
+#1408 := [hypothesis]: #901
+#1409 := [hypothesis]: #1195
+#1410 := [hypothesis]: #751
+#1411 := [th-lemma #1410 #818 #767 #819 #1171 #1409 #956 #1060 #1408 #776 #775 #784 #1407 #1405]: false
+#1413 := [lemma #1411]: #1412
+#1438 := [unit-resolution #1413 #1350 #1374 #1269 #1437 #1425 #1418]: #737
+#1439 := (or #1059 #1174 #1175 #823 #820 #1271 #733 #798 #944 #1351 #916 #1177 #1270 #1414 #821 #822)
+#1440 := [th-lemma]: #1439
+#1441 := [unit-resolution #1440 #1438 #818 #767 #913 #1171 #779 #763 #1436 #1350 #1374 #1205 #791 #1269 #1341 #1168]: #1414
+#1415 := [hypothesis]: #1414
+#1416 := [unit-resolution #1376 #1391 #1415]: false
+#1417 := [lemma #1416]: #1375
+#1442 := [unit-resolution #1417 #1441]: #1362
+#1443 := [unit-resolution #680 #1442]: #392
+#1444 := [unit-resolution #678 #1443]: #675
+#1445 := [unit-resolution #830 #1444 #1428]: false
+#1447 := [lemma #1445]: #1446
+#1455 := [unit-resolution #1447 #763]: #508
+#1456 := [unit-resolution #710 #1455]: #707
+#1453 := [unit-resolution #928 #1456]: #752
+#1449 := (or #450 #537 #915)
+#1448 := [th-lemma #914 #1341 #913 #910 #907 #1280]: false
+#1450 := [lemma #1448]: #1449
+#1525 := [unit-resolution #1450 #907 #1453]: #450
+#1526 := [unit-resolution #694 #1525]: #691
+#1527 := [unit-resolution #771 #1526]: #751
+#1528 := (or #745 #537 #995)
+#1529 := [th-lemma]: #1528
+#1530 := [unit-resolution #1529 #990 #907]: #745
+#1531 := [unit-resolution #1041 #1526]: #903
+#1532 := [unit-resolution #1401 #1531 #763 #1530]: #1387
+#1533 := [unit-resolution #1404 #1532]: #836
+#1534 := [unit-resolution #672 #1533]: #363
+#1535 := [unit-resolution #670 #1534]: #667
+#1536 := [unit-resolution #807 #1535]: #761
+#1513 := (not #902)
+#1537 := (or #1513 #821 #733 #794 #795)
+#1516 := [hypothesis]: #1013
+#1519 := (or #862 #567)
+#1517 := (or #862 #567 #798)
+#1518 := [th-lemma]: #1517
+#1520 := [unit-resolution #1518 #1205]: #1519
+#1521 := [unit-resolution #1520 #1516]: #567
+#1522 := [unit-resolution #728 #1521]: #724
+#1523 := [unit-resolution #1011 #1522 #1516]: false
+#1524 := [lemma #1523]: #862
+#1514 := (or #1013 #1513 #821 #733 #794 #795)
+#1510 := [hypothesis]: #862
+#1511 := [hypothesis]: #902
+#1512 := [th-lemma #1034 #1511 #1341 #913 #1410 #767 #763 #779 #791 #776 #775 #792 #1510]: false
+#1515 := [lemma #1512]: #1514
+#1538 := [unit-resolution #1515 #1524]: #1537
+#1539 := [unit-resolution #1538 #1536 #763 #1527 #1509]: #795
+#1490 := (or #1414 #995 #1246 #733 #821 #797)
+#1457 := [unit-resolution #1159 #1456]: #1127
+#1458 := [hypothesis]: #808
+#1471 := [unit-resolution #1401 #1385 #763 #781]: #1387
+#1472 := [unit-resolution #1404 #1471]: #836
+#1473 := [unit-resolution #672 #1472]: #363
+#1474 := [unit-resolution #670 #1473]: #667
+#1475 := [unit-resolution #807 #1474]: #761
+#1459 := [hypothesis]: #1347
+#1462 := (or #1461 #1414 #1246 #733 #794 #995)
+#1454 := [hypothesis]: #1452
+#1460 := [th-lemma #1459 #1385 #818 #1045 #763 #779 #791 #776 #775 #784 #1458 #1368 #788 #1457 #1171 #1454 #1205]: false
+#1463 := [lemma #1460]: #1462
+#1476 := [unit-resolution #1463 #1459 #1385 #763 #1475 #1458]: #1461
+#1477 := [unit-resolution #1470 #1476]: #1466
+#1478 := [unit-resolution #688 #1477]: #421
+#1479 := (or #1195 #1369 #994 #422 #1246 #1104 #1176)
+#1480 := [th-lemma]: #1479
+#1481 := [unit-resolution #1480 #1478 #788 #1385 #1457 #1045 #1368]: #1195
+#1482 := [unit-resolution #1433 #1481 #779 #940 #781 #1205 #1453 #784]: #334
+#1483 := [unit-resolution #654 #1482]: #655
+#1484 := [unit-resolution #952 #1483]: #901
+#1485 := [unit-resolution #686 #1478]: #683
+#1486 := [unit-resolution #854 #1485]: #754
+#1487 := [unit-resolution #1265 #1483]: #1216
+#1488 := [unit-resolution #1440 #1487 #818 #767 #913 #1171 #779 #763 #1459 #1410 #1486 #1205 #1481 #791 #1341 #1168]: #1059
+#1489 := [th-lemma #818 #956 #1488 #1475 #775 #784 #1458 #1368 #788 #1457 #1171 #1385 #1045 #1486 #1478 #1484]: false
+#1491 := [lemma #1489]: #1490
+#1540 := [unit-resolution #1491 #1530 #1531 #763 #1527 #990]: #1414
+#1541 := [unit-resolution #1417 #1540]: #1362
+#1542 := [unit-resolution #680 #1541]: #392
+#1543 := [unit-resolution #678 #1542]: #675
+#1544 := [unit-resolution #830 #1543 #1539]: false
+#1546 := [lemma #1544]: #1545
+#1597 := [unit-resolution #1546 #763]: #537
+#1598 := [unit-resolution #718 #1597]: #715
+#1590 := [unit-resolution #899 #1598]: #745
+#1601 := (or #450 #733)
+#1591 := [unit-resolution #1579 #914]: #363
+#1592 := [unit-resolution #670 #1591]: #667
+#1593 := [unit-resolution #807 #1592]: #761
+#1594 := [unit-resolution #1589 #914]: #392
+#1595 := [unit-resolution #678 #1594]: #675
+#1596 := [unit-resolution #830 #1595]: #758
+#1599 := [unit-resolution #1085 #1598]: #987
+#1600 := [th-lemma #1034 #1368 #788 #763 #779 #775 #1599 #1457 #1171 #767 #1062 #791 #1596 #1593 #1524]: false
+#1602 := [lemma #1600]: #1601
+#1603 := [unit-resolution #1602 #763]: #450
+#1604 := [unit-resolution #694 #1603]: #691
+#1605 := [unit-resolution #1583 #1604]: #903
+#1606 := [unit-resolution #1401 #1605 #763 #1590]: #1387
+#1607 := [unit-resolution #1404 #1606]: #836
+#1608 := [unit-resolution #672 #1607]: #363
+#1609 := [unit-resolution #670 #1608]: #667
+#1610 := [unit-resolution #807 #1609]: #761
+#1611 := [unit-resolution #771 #1604]: #751
+#1612 := (or #902 #1107 #451 #1176 #1369 #994 #1177)
+#1613 := [th-lemma]: #1612
+#1614 := [unit-resolution #1613 #1599 #1171 #788 #1457 #1368 #1603]: #902
+#1615 := [unit-resolution #1538 #1614 #763 #1611 #1610]: #795
+#1616 := (or #808 #538 #797)
+#1617 := [th-lemma]: #1616
+#1618 := [unit-resolution #1617 #1590 #1597]: #808
+#1619 := [unit-resolution #1491 #1611 #1590 #763 #1605 #1618]: #1414
+#1620 := [unit-resolution #1417 #1619]: #1362
+#1621 := [unit-resolution #680 #1620]: #392
+#1622 := [unit-resolution #678 #1621]: #675
+#1623 := [unit-resolution #830 #1622 #1615]: false
+#1624 := [lemma #1623]: #733
+#1625 := [unit-resolution #1417 #1548]: #1347
+#1629 := (or #509 #1369 #994 #1246 #1104 #363 #884 #392 #1370)
+#1630 := [th-lemma]: #1629
+#1631 := [unit-resolution #1630 #993 #842 #1045 #788 #1547 #1628 #1368 #1549]: #509
+#1632 := [unit-resolution #712 #1631]: #708
+#1633 := [unit-resolution #1133 #1632]: #1057
+#1634 := (or #421 #363 #884 #392 #1370)
+#1635 := [th-lemma]: #1634
+#1636 := [unit-resolution #1635 #993 #842 #1547 #1549]: #421
+#1637 := [unit-resolution #686 #1636]: #683
+#1638 := [unit-resolution #1047 #1637]: #986
+#1639 := (or #363 #1178 #537 #1260 #1370 #1246)
+#1640 := [unit-resolution #1372 #1051 #1045 #788 #910 #1368 #842]: #1639
+#1641 := [unit-resolution #1640 #1638 #1549 #1628 #993 #1633]: #537
+#1642 := [unit-resolution #718 #1641]: #715
+#1643 := [unit-resolution #899 #1642]: #745
+#1644 := (or #508 #538 #797 #566)
+#1645 := [unit-resolution #1210 #784]: #1644
+#1646 := [unit-resolution #1645 #1643 #1631 #1641]: #566
+#1647 := [unit-resolution #726 #1646]: #723
+#1648 := [unit-resolution #1082 #1647]: #1055
+#1650 := [unit-resolution #1085 #1642]: #987
+#1651 := (or #732 #1105 #1106 #1102 #1108 #1351 #916 #1107 #821 #822 #1175 #1414 #1245)
+#1652 := [th-lemma]: #1651
+#1653 := [unit-resolution #1652 #1650 #767 #913 #1034 #1100 #1097 #1649 #1323 #791 #1648 #1341 #1625]: #732
+#1654 := [unit-resolution #1184 #1653 #1624]: #65
+#1655 := [unit-resolution #854 #1637]: #754
+#1656 := [unit-resolution #1268 #1632]: #1195
+#1661 := (or #334 #363 #392)
+#1659 := (or #334 #363 #1245 #392)
+#1657 := (or #334 #363 #1245 #1102 #392)
+#1658 := [th-lemma]: #1657
+#1660 := [unit-resolution #1658 #1097]: #1659
+#1662 := [unit-resolution #1660 #1323]: #1661
+#1663 := [unit-resolution #1662 #993 #1547]: #334
+#1664 := [unit-resolution #654 #1663]: #655
+#1665 := [unit-resolution #1265 #1664]: #1216
+#1666 := [th-lemma #1168 #1665 #1097 #1034 #1650 #1323 #1341 #913 #1649 #767 #791 #1625 #1656 #1171 #1655 #818]: #736
+#1667 := [unit-resolution #672 #993]: #668
+#1668 := [unit-resolution #1404 #1667]: #809
+#1669 := [unit-resolution #952 #1664]: #901
+#1670 := [th-lemma #956 #1669 #775 #784 #1643 #1668 #1368 #788 #1628 #1045 #842 #1549 #1633 #910 #1638 #1051]: #737
+#1671 := [unit-resolution #1190 #1670 #1666]: #66
+#1672 := [unit-resolution #658 #1671 #1654]: false
+#1674 := [lemma #1672]: #1673
+#1694 := [unit-resolution #1674 #1547]: #363
+#1695 := [unit-resolution #670 #1694]: #667
+#1696 := [unit-resolution #1093 #1695]: #863
+#1697 := (or #334 #1102 #884 #883 #421 #1101)
+#1698 := [th-lemma]: #1697
+#1699 := [unit-resolution #1698 #857 #842 #1097 #1552 #1696]: #334
+#1700 := [unit-resolution #654 #1699]: #655
+#1701 := [unit-resolution #952 #1700]: #901
+#1702 := [unit-resolution #1265 #1700]: #1216
+#1703 := [unit-resolution #928 #1678]: #752
+#1492 := (>= #1451 0::int)
+#1704 := (or #1466 #1492)
+#1705 := [th-lemma]: #1704
+#1706 := [unit-resolution #1705 #1680]: #1492
+#1707 := [unit-resolution #1038 #1685]: #902
+#1708 := (not #1492)
+#1711 := (or #736 #1708 #915 #1271 #1101 #1513 #821)
+#1709 := (or #736 #1708 #1179 #915 #1351 #916 #918 #1174 #1271 #1101 #1102 #1108 #1513 #821 #822)
+#1710 := [th-lemma]: #1709
+#1712 := [unit-resolution #1710 #1051 #767 #913 #910 #1034 #1341 #1097 #1168]: #1711
+#1713 := [unit-resolution #1712 #1707 #1706 #1649 #1703 #1696 #1702]: #736
+#1714 := [unit-resolution #807 #1695]: #761
+#1507 := (or #737 #1176 #965 #794 #995 #1246 #1461)
+#1493 := [th-lemma #818 #1289 #1368 #788 #1171 #956 #1060 #1408 #776 #775 #784 #1458 #1385 #1045 #1454]: false
+#1508 := [lemma #1493]: #1507
+#1715 := [unit-resolution #1508 #1686 #1628 #1714 #1681 #1701 #1679]: #737
+#1716 := [unit-resolution #1190 #1715 #1713]: #66
+#1717 := [unit-resolution #658 #1716]: #647
+#1718 := [unit-resolution #1184 #1717 #1624]: #945
+#1719 := [th-lemma #1718 #1100 #1341 #913 #842 #1549 #910 #1051 #1703 #1706 #956 #1713 #1701 #1693]: false
+#1721 := [lemma #1719]: #1720
+#1753 := [unit-resolution #1721 #1547]: #421
+#1803 := (or #508 #392)
+#1779 := (or #537 #392)
+#1754 := [unit-resolution #686 #1753]: #683
+#1755 := [unit-resolution #1047 #1754]: #986
+#1756 := [unit-resolution #854 #1754]: #754
+#1757 := (or #1452 #820 #422)
+#1758 := [th-lemma]: #1757
+#1759 := [unit-resolution #1758 #1756 #1753]: #1452
+#1744 := (or #508 #794 #820 #821 #1414 #537 #1101 #1246 #1178 #1370)
+#1723 := (or #508 #995 #537 #566)
+#1724 := [unit-resolution #1001 #784]: #1723
+#1725 := [unit-resolution #1724 #1129 #990 #907]: #566
+#1726 := [unit-resolution #726 #1725]: #723
+#1727 := [unit-resolution #1082 #1726]: #1055
+#1728 := [th-lemma #1727 #1100 #1368 #788 #842 #1384 #910 #1385 #1045 #1285 #1051 #1509 #1034 #1722 #1097 #1134]: #732
+#1729 := [unit-resolution #1184 #1728 #1624]: #65
+#1730 := [unit-resolution #658 #1729]: #648
+#1731 := (or #334 #1101 #884 #1370 #1102 #508 #1369 #994 #1246 #1104 #918 #537 #1178 #1179 #1260)
+#1732 := [th-lemma]: #1731
+#1733 := [unit-resolution #1732 #1129 #842 #1051 #1045 #788 #1097 #910 #907 #1722 #1385 #1285 #1134 #1368 #1384]: #334
+#1734 := [unit-resolution #654 #1733]: #655
+#1735 := [unit-resolution #1265 #1734]: #1216
+#1738 := (or #736 #820 #1271 #945 #1270 #1414 #821)
+#1736 := (or #736 #1174 #1175 #823 #820 #1271 #945 #798 #944 #1351 #916 #1177 #1270 #1414 #821 #822)
+#1737 := [th-lemma]: #1736
+#1739 := [unit-resolution #1737 #818 #767 #913 #1171 #779 #1205 #791 #1341 #1168]: #1738
+#1740 := [unit-resolution #1739 #1735 #1459 #1269 #1410 #819 #1728]: #736
+#1741 := [unit-resolution #1190 #1740 #1730]: #1059
+#1742 := [unit-resolution #952 #1734]: #901
+#1743 := [th-lemma #990 #1171 #784 #956 #1742 #776 #775 #819 #1410 #767 #818 #1269 #1741]: false
+#1745 := [lemma #1743]: #1744
+#1760 := [unit-resolution #1745 #907 #1756 #1649 #1625 #1714 #1696 #1628 #1755 #1549]: #508
+#1761 := [unit-resolution #710 #1760]: #707
+#1762 := [unit-resolution #1159 #1761]: #1127
+#1763 := [unit-resolution #1690 #1762 #1547 #1759 #1628 #990]: #566
+#1764 := [unit-resolution #726 #1763]: #723
+#1765 := [unit-resolution #1082 #1764]: #1055
+#1751 := (or #732 #509 #1105 #1370 #1246 #1178 #1513 #1101)
+#1746 := [hypothesis]: #508
+#1747 := [unit-resolution #710 #1746]: #707
+#1748 := [unit-resolution #928 #1747]: #752
+#1750 := [th-lemma #1746 #1749 #1286 #1100 #1368 #788 #842 #1384 #910 #1385 #1045 #1285 #1051 #1511 #1034 #1722 #1097 #1748]: false
+#1752 := [lemma #1750]: #1751
+#1766 := [unit-resolution #1752 #1760 #1765 #1549 #1628 #1755 #1509 #1696]: #732
+#1767 := [unit-resolution #1184 #1766 #1624]: #65
+#1768 := [unit-resolution #658 #1767]: #648
+#1769 := (or #1195 #422 #1246 #1176)
+#1770 := [unit-resolution #1480 #788 #1045 #1368]: #1769
+#1771 := [unit-resolution #1770 #1762 #1628 #1753]: #1195
+#1505 := (or #334 #945 #537)
+#1494 := [hypothesis]: #335
+#1495 := (or #334 #537 #567 #945)
+#1496 := [unit-resolution #947 #1205 #779]: #1495
+#1497 := [unit-resolution #1496 #1494 #907 #1281]: #567
+#1500 := (or #334 #945 #566 #1013 #537)
+#1498 := (or #334 #945 #566 #1013 #537 #944)
+#1499 := [th-lemma]: #1498
+#1501 := [unit-resolution #1499 #779]: #1500
+#1502 := [unit-resolution #1501 #1497 #1281 #1494 #907]: #1013
+#1503 := [unit-resolution #728 #1497]: #724
+#1504 := [unit-resolution #1011 #1503 #1502]: false
+#1506 := [lemma #1504]: #1505
+#1772 := [unit-resolution #1506 #1766 #907]: #334
+#1773 := [unit-resolution #654 #1772]: #655
+#1774 := [unit-resolution #1265 #1773]: #1216
+#1775 := [unit-resolution #1739 #1774 #1625 #1771 #1649 #1756 #1766]: #736
+#1776 := [unit-resolution #952 #1773]: #901
+#1777 := [unit-resolution #1508 #1776 #1628 #1714 #1759 #990 #1762]: #737
+#1778 := [unit-resolution #1190 #1777 #1775 #1768]: false
+#1780 := [lemma #1778]: #1779
+#1781 := [unit-resolution #1780 #1547]: #537
+#1782 := [unit-resolution #718 #1781]: #715
+#1783 := [unit-resolution #1085 #1782]: #987
+#1784 := [unit-resolution #899 #1782]: #745
+#1785 := [unit-resolution #1645 #1129 #1784 #1781]: #566
+#1786 := [unit-resolution #726 #1785]: #723
+#1787 := [unit-resolution #1082 #1786]: #1055
+#1788 := [unit-resolution #1652 #1787 #767 #913 #1034 #1100 #1097 #1649 #1323 #791 #1783 #1341 #1625]: #732
+#1789 := [unit-resolution #1184 #1788 #1624]: #65
+#1790 := [unit-resolution #658 #1789]: #648
+#1791 := (or #752 #508 #1177 #821 #822 #820 #823 #538 #392)
+#1792 := [th-lemma]: #1791
+#1793 := [unit-resolution #1792 #1129 #767 #818 #1171 #1781 #1649 #1756 #1547]: #752
+#1794 := (or #1270 #915 #334 #945 #797)
+#1795 := [unit-resolution #1433 #779 #1205 #784]: #1794
+#1796 := [unit-resolution #1795 #1788 #1269 #1784 #1793]: #334
+#1797 := [unit-resolution #654 #1796]: #655
+#1798 := [unit-resolution #1265 #1797]: #1216
+#1799 := [unit-resolution #1739 #1798 #1625 #1269 #1649 #1756 #1788]: #736
+#1800 := [unit-resolution #952 #1797]: #901
+#1801 := [unit-resolution #1413 #1800 #1714 #1649 #1756 #1781 #1269]: #737
+#1802 := [unit-resolution #1190 #1801 #1799 #1790]: false
+#1804 := [lemma #1802]: #1803
+#1805 := [unit-resolution #1804 #1547]: #508
+#1806 := [unit-resolution #710 #1805]: #707
+#1807 := [unit-resolution #1159 #1806]: #1127
+#1808 := (or #1270 #1177 #821 #822 #820 #823 #538 #509 #392)
+#1809 := [th-lemma]: #1808
+#1810 := [unit-resolution #1809 #1805 #767 #818 #1171 #1781 #1649 #1756 #1547]: #1270
+#1811 := [unit-resolution #1770 #1810 #1807 #1628 #1753]: false
+#1812 := [lemma #1811]: #392
+#1850 := [unit-resolution #678 #1812]: #675
+#1851 := [unit-resolution #844 #1850]: #757
+#1956 := (or #732 #1101 #1103 #883 #1105 #1107)
+#1951 := (or #739 #480 #1351)
+#1952 := [th-lemma]: #1951
+#1953 := [unit-resolution #1952 #1333 #1341]: #739
+#1954 := (or #732 #1101 #1103 #883 #1105 #1107 #917)
+#1955 := [unit-resolution #1110 #1045 #913 #1034 #1100 #842 #1097]: #1954
+#1957 := [unit-resolution #1955 #1953]: #1956
+#1959 := [unit-resolution #1957 #1851]: #1958
+#1960 := [unit-resolution #1959 #1749 #1950 #1722 #1287]: #1105
+#1827 := (>= #743 0::int)
+#1888 := (not #1827)
+#1961 := (or #1888 #732 #1106 #1101 #1102 #996 #883 #884 #1351 #916 #1103 #1104 #797 #915 #918)
+#1962 := [th-lemma]: #1961
+#1963 := [unit-resolution #1962 #1749 #1045 #913 #910 #784 #1100 #842 #781 #1851 #1280 #1722 #1950 #1341 #1097]: #1888
+#1846 := (or #1009 #1827)
+#1891 := [hypothesis]: #1888
+#1892 := [hypothesis]: #724
+#1847 := [th-lemma]: #1846
+#1893 := [unit-resolution #1847 #1892 #1891]: false
+#1894 := [lemma #1893]: #1846
+#1964 := [unit-resolution #1894 #1963]: #1009
+#1965 := [unit-resolution #728 #1964]: #566
+#1966 := [unit-resolution #726 #1965]: #723
+#1967 := [unit-resolution #1082 #1966 #1960]: false
+#1969 := [lemma #1967]: #1968
+#2006 := [unit-resolution #1969 #2005 #1994 #2004 #1849 #2001]: #732
+#2007 := (or #65 #945)
+#2008 := [unit-resolution #1184 #1624]: #2007
+#2009 := [unit-resolution #2008 #2006]: #65
+#2010 := [unit-resolution #658 #2009]: #648
+#2011 := [unit-resolution #807 #2003]: #761
+#1987 := (or #737 #1103 #915 #797 #1101 #794)
+#1979 := (or #737 #965 #797 #794 #915 #1103)
+#1819 := [hypothesis]: #820
+#1820 := (or #986 #754)
+#1821 := [th-lemma]: #1820
+#1822 := [unit-resolution #1821 #1819]: #986
+#1817 := (or #421 #1178)
+#1813 := (or #1178 #421 #1461)
+#1814 := [th-lemma]: #1813
+#1815 := [unit-resolution #1814 #857 #1285]: #1461
+#1816 := [unit-resolution #1470 #1815 #1680]: false
+#1818 := [lemma #1816]: #1817
+#1823 := [unit-resolution #1818 #1822]: #421
+#1824 := [unit-resolution #686 #1823]: #683
+#1825 := [unit-resolution #854 #1824 #1819]: false
+#1826 := [lemma #1825]: #754
+#1871 := (or #903 #421)
+#1831 := [unit-resolution #1676 #1830 #857]: #508
+#1832 := [unit-resolution #710 #1831]: #707
+#1833 := [unit-resolution #1159 #1832]: #1127
+#1837 := [unit-resolution #869 #1836]: #748
+#1838 := [unit-resolution #928 #1832]: #752
+#1839 := [unit-resolution #1450 #1838 #1835]: #537
+#1840 := [unit-resolution #718 #1839]: #715
+#1841 := [unit-resolution #1085 #1840]: #987
+#1842 := (or #567 #1176 #1177 #1108 #1107 #822 #421 #450 #871)
+#1843 := [th-lemma]: #1842
+#1844 := [unit-resolution #1843 #1841 #767 #1171 #1034 #857 #1835 #1837 #1833]: #567
+#1845 := [unit-resolution #728 #1844]: #724
+#1848 := [unit-resolution #1847 #1845]: #1827
+#1852 := [unit-resolution #899 #1840]: #745
+#1853 := [unit-resolution #1570 #857 #1812]: #363
+#1854 := [unit-resolution #670 #1853]: #667
+#1855 := [unit-resolution #1093 #1854]: #863
+#1856 := [unit-resolution #1698 #1855 #842 #1097 #1851 #857]: #334
+#1857 := [unit-resolution #654 #1856]: #655
+#1858 := [unit-resolution #952 #1857]: #901
+#1859 := [unit-resolution #807 #1854]: #761
+#1860 := (or #737 #966 #965 #797 #996 #794 #964 #915 #918 #1461 #823 #1104 #1103)
+#1861 := [th-lemma]: #1860
+#1862 := [unit-resolution #1861 #1852 #818 #1045 #910 #784 #956 #1859 #775 #1838 #1858 #1849 #1681]: #737
+#1863 := [unit-resolution #1265 #1857]: #1216
+#1864 := (or #736 #1174 #1271 #1107 #1108 #1101 #1102 #1176 #1177 #1708 #1179 #822 #871)
+#1865 := [th-lemma]: #1864
+#1866 := [unit-resolution #1865 #1837 #1051 #767 #1171 #1034 #1168 #1097 #1855 #1841 #1833 #1863 #1706]: #736
+#1867 := [unit-resolution #1190 #1866 #1862]: #66
+#1868 := [unit-resolution #658 #1867]: #647
+#1869 := [unit-resolution #1184 #1868 #1624]: #945
+#1870 := [th-lemma #1869 #1100 #1341 #913 #1855 #1097 #1852 #784 #1851 #842 #1838 #910 #1045 #1849 #1848]: false
+#1872 := [lemma #1870]: #1871
+#1916 := [unit-resolution #1872 #857]: #903
+#1875 := (or #508 #421)
+#1873 := [unit-resolution #1676 #1129 #857]: #821
+#1874 := [unit-resolution #771 #1349 #1873]: false
+#1876 := [lemma #1874]: #1875
+#1917 := [unit-resolution #1876 #857]: #508
+#1918 := [unit-resolution #710 #1917]: #707
+#1919 := [unit-resolution #1159 #1918]: #1127
+#1920 := [unit-resolution #928 #1918]: #752
+#1914 := (or #976 #1708 #915 #1101 #1246 #1271 #794 #1461 #1176 #965)
+#1895 := [hypothesis]: #716
+#1896 := [unit-resolution #978 #1895]: #808
+#1897 := [unit-resolution #1508 #1896 #1385 #776 #1454 #1289 #1408]: #737
+#1898 := [hypothesis]: #1492
+#1884 := (or #450 #1246)
+#1880 := (or #1246 #450 #871)
+#1881 := [th-lemma]: #1880
+#1882 := [unit-resolution #1881 #914 #1385]: #871
+#1883 := [unit-resolution #869 #1061 #1882]: false
+#1885 := [lemma #1883]: #1884
+#1899 := [unit-resolution #1885 #1385]: #450
+#1900 := [unit-resolution #694 #1899]: #691
+#1877 := [hypothesis]: #821
+#1878 := [unit-resolution #771 #1581 #1877]: false
+#1879 := [lemma #1878]: #770
+#1901 := [unit-resolution #1879 #1900]: #751
+#1902 := [hypothesis]: #1216
+#1903 := [unit-resolution #1038 #1895]: #902
+#1904 := [unit-resolution #1712 #1903 #1902 #1901 #1280 #1722 #1898]: #736
+#1905 := [unit-resolution #1190 #1904 #1897]: #66
+#1906 := [unit-resolution #658 #1905]: #647
+#1907 := [unit-resolution #1184 #1906 #1624]: #945
+#1889 := (or #1888 #732 #1101 #995 #1246)
+#1886 := [hypothesis]: #1827
+#1887 := [th-lemma #1749 #1100 #1722 #1097 #784 #1851 #842 #1458 #1385 #1368 #788 #1045 #1886]: false
+#1890 := [lemma #1887]: #1889
+#1908 := [unit-resolution #1890 #1907 #1722 #1896 #1385]: #1888
+#1909 := [unit-resolution #1894 #1908]: #1009
+#1910 := [unit-resolution #728 #1909]: #566
+#1911 := [unit-resolution #726 #1910]: #723
+#1912 := [unit-resolution #1082 #1911]: #1055
+#1913 := [th-lemma #1898 #1051 #1280 #910 #1341 #913 #1034 #1903 #1901 #767 #1907 #1912 #1100 #1722 #1097 #1851 #842 #1812]: false
+#1915 := [lemma #1913]: #1914
+#1921 := [unit-resolution #1915 #1706 #1920 #1855 #1916 #1863 #1859 #1681 #1919 #1858]: #976
+#1922 := [unit-resolution #720 #1921]: #537
+#1923 := [unit-resolution #718 #1922]: #715
+#1924 := [unit-resolution #899 #1923]: #745
+#1925 := [unit-resolution #1617 #1924 #1922]: #808
+#1926 := [unit-resolution #1885 #1916]: #450
+#1927 := [unit-resolution #1085 #1923]: #987
+#1928 := [unit-resolution #1613 #1927 #1171 #788 #1919 #1368 #1926]: #902
+#1929 := [unit-resolution #830 #1850]: #758
+#1930 := [unit-resolution #694 #1926]: #691
+#1931 := [unit-resolution #1879 #1930]: #751
+#1932 := (or #1414 #1461 #823 #1176 #1177 #1369 #994 #538 #421 #883)
+#1933 := [th-lemma]: #1932
+#1934 := [unit-resolution #1933 #1922 #788 #1171 #818 #1851 #1919 #1368 #857 #1681]: #1414
+#1935 := (or #1347 #795 #1708 #1179 #915 #918 #1351 #916 #567 #1108 #1513 #821 #822)
+#1936 := [th-lemma]: #1935
+#1937 := [unit-resolution #1936 #1934 #913 #910 #1034 #767 #1931 #1929 #1920 #1341 #1051 #1928 #1706]: #567
+#1938 := [unit-resolution #728 #1937]: #724
+#1939 := [unit-resolution #1894 #1938]: #1827
+#1940 := [unit-resolution #1508 #1925 #1916 #1859 #1681 #1919 #1858]: #737
+#1941 := (or #748 #451 #821)
+#1942 := [th-lemma]: #1941
+#1943 := [unit-resolution #1942 #1931 #1926]: #748
+#1944 := [unit-resolution #1865 #1927 #1051 #767 #1171 #1034 #1168 #1097 #1855 #1943 #1919 #1863 #1706]: #736
+#1945 := [unit-resolution #1190 #1944 #1940]: #66
+#1946 := [unit-resolution #658 #1945]: #647
+#1947 := [unit-resolution #1184 #1946 #1624]: #945
+#1948 := [unit-resolution #1890 #1947 #1939 #1855 #1925 #1916]: false
+#1949 := [lemma #1948]: #421
+#1978 := [unit-resolution #1758 #1949 #1826]: #1452
+#1980 := [unit-resolution #1861 #818 #1045 #910 #784 #956 #775 #1978]: #1979
+#1981 := [unit-resolution #1980 #1060 #776 #1280 #1950 #781]: #965
+#1972 := (not #1058)
+#1973 := (or #1972 #737 #1103 #915 #797 #1101)
+#1970 := [hypothesis]: #1058
+#1971 := [th-lemma #956 #1060 #1826 #1851 #842 #818 #784 #1950 #1045 #1280 #910 #781 #1722 #1097 #1970]: false
+#1974 := [lemma #1971]: #1973
+#1982 := [unit-resolution #1974 #1060 #1950 #1280 #781 #1722]: #1972
+#1975 := [hypothesis]: #1972
+#1976 := [unit-resolution #1122 #1278 #1975]: false
+#1977 := [lemma #1976]: #1121
+#1983 := [unit-resolution #1977 #1982]: #1120
+#1984 := [unit-resolution #652 #1983]: #334
+#1985 := [unit-resolution #654 #1984]: #655
+#1986 := [unit-resolution #952 #1985 #1981]: false
+#1988 := [lemma #1986]: #1987
+#2012 := [unit-resolution #1988 #1849 #1994 #2005 #2004 #2011]: #737
+#2013 := [unit-resolution #1190 #2012 #2010]: #967
+#2014 := [unit-resolution #1159 #1993]: #1127
+#2015 := [unit-resolution #686 #1949]: #683
+#2016 := [unit-resolution #1047 #2015]: #986
+#2017 := (or #1173 #1174 #736 #1178 #795 #1175 #1179 #1108 #871 #822 #1176 #1177 #1107 #794 #964)
+#2018 := [th-lemma]: #2017
+#2019 := [unit-resolution #2018 #2013 #791 #1051 #767 #1171 #1034 #775 #2011 #1929 #1837 #2001 #2016 #2014 #1168]: #1173
+#1989 := [hypothesis]: #1173
+#1990 := [unit-resolution #1156 #1278 #1989]: false
+#1991 := [lemma #1990]: #1155
+#2020 := [unit-resolution #1991 #2019]: #1120
+#2021 := [unit-resolution #652 #2020]: #334
+#2022 := [unit-resolution #654 #2021]: #655
+#2023 := [unit-resolution #1265 #2022]: #1216
+#2024 := (or #1492 #335 #794 #964 #1178 #795 #1175)
+#2025 := [th-lemma]: #2024
+#2026 := [unit-resolution #2025 #2011 #791 #775 #1929 #2016 #2021]: #1492
+#2027 := (or #736 #1271 #1107 #1101 #1176 #1708 #871)
+#2028 := [unit-resolution #1865 #1051 #767 #1171 #1034 #1168 #1097]: #2027
+#2029 := [unit-resolution #2028 #2026 #2023 #2004 #1837 #2014 #2001 #2013]: false
+#2030 := [lemma #2029]: #903
+#2045 := (or #334 #1246 #508)
+#2043 := (or #334 #1246 #1178 #508 #795)
+#2044 := [unit-resolution #1256 #1953 #1323]: #2043
+#2046 := [unit-resolution #2044 #1929 #2016]: #2045
+#2047 := [unit-resolution #2046 #1129 #2030]: #334
+#2048 := [unit-resolution #654 #2047]: #655
+#2049 := [unit-resolution #952 #2048]: #901
+#2054 := (or #740 #1246)
+#2052 := (or #740 #1246 #1178 #393)
+#2050 := (or #740 #1369 #1246 #1179 #1104 #1178 #393)
+#2051 := [th-lemma]: #2050
+#2053 := [unit-resolution #2051 #1045 #1051 #1368]: #2052
+#2055 := [unit-resolution #2053 #1812 #2016]: #2054
+#2056 := [unit-resolution #2055 #2030]: #740
+#2064 := (or #1246 #537 #508 #1260)
+#2057 := (or #1346 #883 #393)
+#2058 := [th-lemma]: #2057
+#2059 := [unit-resolution #2058 #1851 #1812]: #1346
+#2062 := (or #795 #1370 #1246 #1178 #537 #508 #1260)
+#2060 := (or #795 #1370 #1246 #1179 #1104 #1178 #918 #537 #508 #1260)
+#2061 := [th-lemma]: #2060
+#2063 := [unit-resolution #2061 #910 #1045 #1051]: #2062
+#2065 := [unit-resolution #2063 #2059 #1929 #2016]: #2064
+#2066 := [unit-resolution #2065 #1134 #2030 #1129]: #537
+#2067 := [unit-resolution #718 #2066]: #715
+#2068 := [unit-resolution #899 #2067]: #745
+#2069 := (or #796 #1351 #996 #566 #915 #918 #797)
+#2070 := [th-lemma]: #2069
+#2071 := [unit-resolution #2070 #2068 #784 #910 #2056 #1431 #1341]: #566
+#2072 := [unit-resolution #726 #2071]: #723
+#2073 := [unit-resolution #1082 #2072]: #1055
+#2076 := (or #737 #796 #1260 #965 #1105)
+#2074 := (or #737 #883 #796 #820 #1260 #965 #762 #1105)
+#2075 := [unit-resolution #1262 #818 #788 #910 #1100 #956 #842]: #2074
+#2077 := [unit-resolution #2075 #1624 #1826 #1851]: #2076
+#2078 := [unit-resolution #2077 #2073 #2056 #2049 #1134]: #737
+#2079 := [unit-resolution #1265 #2048]: #1216
+#2080 := [unit-resolution #1085 #2067]: #987
+#2083 := (or #732 #1246 #1107 #1105)
+#2081 := (or #732 #795 #1246 #1107 #1178 #1105)
+#2082 := [unit-resolution #1248 #1051 #1045 #913 #1034 #1100 #1097 #1323 #791 #1953]: #2081
+#2084 := [unit-resolution #2082 #1929 #2016]: #2083
+#2085 := [unit-resolution #2084 #2073 #2080 #2030]: #732
+#2088 := (or #736 #1270 #1271 #945)
+#2086 := (or #736 #795 #1178 #1270 #1271 #945)
+#2087 := [unit-resolution #1273 #1051 #913 #1171 #779 #1205 #1953 #791 #1168]: #2086
+#2089 := [unit-resolution #2087 #1929 #2016]: #2088
+#2090 := [unit-resolution #2089 #2085 #1269 #2079]: #736
+#2091 := [unit-resolution #2008 #2085]: #65
+#2092 := [unit-resolution #658 #2091]: #648
+#2093 := [unit-resolution #1190 #2092 #2090 #2078]: false
+#2094 := [lemma #2093]: #508
+#2095 := [unit-resolution #710 #2094]: #707
+#2096 := [unit-resolution #928 #2095]: #752
+#2097 := [unit-resolution #1885 #2030]: #450
+#2098 := [unit-resolution #694 #2097]: #691
+#2099 := [unit-resolution #1879 #2098]: #751
+#2100 := (or #509 #1369 #994 #1246 #1104 #883 #884 #393 #363)
+#2101 := [th-lemma]: #2100
+#2102 := [unit-resolution #2101 #2094 #842 #1045 #788 #1812 #1851 #2030 #1368]: #363
+#2103 := (or #900 #1246 #1178 #795 #1175 #364 #1179)
+#2104 := [th-lemma]: #2103
+#2105 := [unit-resolution #2104 #791 #1051 #1929 #2102 #2030 #2016]: #900
+#2106 := [unit-resolution #1998 #2105 #2099 #2096]: #537
+#2107 := [unit-resolution #718 #2106]: #715
+#2108 := [unit-resolution #899 #2107]: #745
+#2031 := [hypothesis]: #1101
+#2032 := (or #863 #761)
+#2033 := [th-lemma]: #2032
+#2034 := [unit-resolution #2033 #2031]: #761
+#2037 := (or #794 #363)
+#2035 := (or #794 #1245 #363)
+#2036 := [th-lemma]: #2035
+#2038 := [unit-resolution #2036 #1323]: #2037
+#2039 := [unit-resolution #2038 #2034]: #363
+#2040 := [unit-resolution #670 #2039]: #667
+#2041 := [unit-resolution #1093 #2040 #2031]: false
+#2042 := [lemma #2041]: #863
+#2109 := [unit-resolution #1085 #2107]: #987
+#2110 := [unit-resolution #2070 #2108 #784 #910 #2056 #2096 #1341]: #566
+#2111 := [unit-resolution #726 #2110]: #723
+#2112 := [unit-resolution #1082 #2111]: #1055
+#2113 := [unit-resolution #1159 #2095]: #1127
+#2114 := [unit-resolution #1329 #2096 #2094]: #1057
+#2117 := (or #945 #796 #1105 #1260 #1107 #1176 #915 #797)
+#2115 := (or #945 #795 #1178 #762 #820 #796 #883 #1105 #1260 #1107 #1176 #915 #797)
+#2116 := [unit-resolution #1311 #1953]: #2115
+#2118 := [unit-resolution #2116 #1624 #1929 #1826 #2016 #1851]: #2117
+#2119 := [unit-resolution #2118 #2109 #2056 #2114 #2113 #2112 #2096 #2108]: #945
+[unit-resolution #1969 #2119 #2109 #2096 #2042 #2105 #2108]: false
+unsat
+a7454ef6a585851531e583bdd8d90b81666edf52 52 0
+#2 := false
+#12 := 1::real
+decl f3 :: real
+#8 := f3
+#10 := 2::real
+#11 := (* 2::real f3)
+#13 := (+ #11 1::real)
+#9 := (+ f3 f3)
+#14 := (< #9 #13)
+#15 := (or false #14)
+#16 := (or #14 #15)
+#17 := (not #16)
+#69 := (iff #17 false)
+#37 := (+ 1::real #11)
+#40 := (< #11 #37)
+#57 := (not #40)
+#67 := (iff #57 false)
+#1 := true
+#62 := (not true)
+#65 := (iff #62 false)
+#66 := [rewrite]: #65
+#63 := (iff #57 #62)
+#60 := (iff #40 true)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#68 := [trans #64 #66]: #67
+#58 := (iff #17 #57)
+#55 := (iff #16 #40)
+#50 := (or #40 #40)
+#53 := (iff #50 #40)
+#54 := [rewrite]: #53
+#51 := (iff #16 #50)
+#48 := (iff #15 #40)
+#43 := (or false #40)
+#46 := (iff #43 #40)
+#47 := [rewrite]: #46
+#44 := (iff #15 #43)
+#41 := (iff #14 #40)
+#38 := (= #13 #37)
+#39 := [rewrite]: #38
+#35 := (= #9 #11)
+#36 := [rewrite]: #35
+#42 := [monotonicity #36 #39]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#52 := [monotonicity #42 #49]: #51
+#56 := [trans #52 #54]: #55
+#59 := [monotonicity #56]: #58
+#70 := [trans #59 #68]: #69
+#34 := [asserted]: #17
+[mp #34 #70]: false
+unsat
+5499526a7594537bc3adeae435f91fadfa11a18c 101 0
+#2 := false
+#9 := 0::real
+decl f3 :: real
+#8 := f3
+#10 := (= f3 0::real)
+#11 := (not #10)
+#43 := [asserted]: #11
+#99 := (<= f3 0::real)
+#21 := 2::real
+#45 := (* 2::real f3)
+#100 := (<= #45 0::real)
+#93 := (= #45 0::real)
+#20 := 4::real
+#15 := (- f3)
+#14 := (< f3 0::real)
+#16 := (ite #14 #15 f3)
+#13 := 1::real
+#17 := (< 1::real #16)
+#18 := (not #17)
+#19 := (or #17 #18)
+#22 := (ite #19 4::real 2::real)
+#23 := (* #22 f3)
+#12 := (+ f3 f3)
+#24 := (= #12 #23)
+#25 := (not #24)
+#26 := (not #25)
+#94 := (iff #26 #93)
+#75 := (* 4::real f3)
+#78 := (= #45 #75)
+#91 := (iff #78 #93)
+#92 := [rewrite]: #91
+#89 := (iff #26 #78)
+#81 := (not #78)
+#84 := (not #81)
+#87 := (iff #84 #78)
+#88 := [rewrite]: #87
+#85 := (iff #26 #84)
+#82 := (iff #25 #81)
+#79 := (iff #24 #78)
+#76 := (= #23 #75)
+#73 := (= #22 4::real)
+#1 := true
+#68 := (ite true 4::real 2::real)
+#71 := (= #68 4::real)
+#72 := [rewrite]: #71
+#69 := (= #22 #68)
+#66 := (iff #19 true)
+#48 := -1::real
+#49 := (* -1::real f3)
+#52 := (ite #14 #49 f3)
+#55 := (< 1::real #52)
+#58 := (not #55)
+#61 := (or #55 #58)
+#64 := (iff #61 true)
+#65 := [rewrite]: #64
+#62 := (iff #19 #61)
+#59 := (iff #18 #58)
+#56 := (iff #17 #55)
+#53 := (= #16 #52)
+#50 := (= #15 #49)
+#51 := [rewrite]: #50
+#54 := [monotonicity #51]: #53
+#57 := [monotonicity #54]: #56
+#60 := [monotonicity #57]: #59
+#63 := [monotonicity #57 #60]: #62
+#67 := [trans #63 #65]: #66
+#70 := [monotonicity #67]: #69
+#74 := [trans #70 #72]: #73
+#77 := [monotonicity #74]: #76
+#46 := (= #12 #45)
+#47 := [rewrite]: #46
+#80 := [monotonicity #47 #77]: #79
+#83 := [monotonicity #80]: #82
+#86 := [monotonicity #83]: #85
+#90 := [trans #86 #88]: #89
+#95 := [trans #90 #92]: #94
+#44 := [asserted]: #26
+#96 := [mp #44 #95]: #93
+#102 := (not #93)
+#103 := (or #102 #100)
+#104 := [th-lemma]: #103
+#105 := [unit-resolution #104 #96]: #100
+#106 := (not #100)
+#107 := (or #99 #106)
+#108 := [th-lemma]: #107
+#109 := [unit-resolution #108 #105]: #99
+#97 := (>= f3 0::real)
+#101 := (>= #45 0::real)
+#110 := (or #102 #101)
+#111 := [th-lemma]: #110
+#112 := [unit-resolution #111 #96]: #101
+#113 := (not #101)
+#114 := (or #97 #113)
+#115 := [th-lemma]: #114
+#116 := [unit-resolution #115 #112]: #97
+#118 := (not #97)
+#117 := (not #99)
+#119 := (or #10 #117 #118)
+#120 := [th-lemma]: #119
+[unit-resolution #120 #116 #109 #43]: false
+unsat
+512a24457d1008a070152357a3d1ca6519a3110c 24 0
+#2 := false
+#8 := (exists (vars (?v0 int)) false)
+#9 := (not #8)
+#10 := (not #9)
+#42 := (iff #10 false)
+#1 := true
+#37 := (not true)
+#40 := (iff #37 false)
+#41 := [rewrite]: #40
+#38 := (iff #10 #37)
+#35 := (iff #9 true)
+#30 := (not false)
+#33 := (iff #30 true)
+#34 := [rewrite]: #33
+#31 := (iff #9 #30)
+#28 := (iff #8 false)
+#29 := [elim-unused]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#39 := [monotonicity #36]: #38
+#43 := [trans #39 #41]: #42
+#27 := [asserted]: #10
+[mp #27 #43]: false
+unsat
+2bd6ac566d6a147b46ecb8caed0a511ca55b141c 24 0
+#2 := false
+#8 := (exists (vars (?v0 real)) false)
+#9 := (not #8)
+#10 := (not #9)
+#42 := (iff #10 false)
+#1 := true
+#37 := (not true)
+#40 := (iff #37 false)
+#41 := [rewrite]: #40
+#38 := (iff #10 #37)
+#35 := (iff #9 true)
+#30 := (not false)
+#33 := (iff #30 true)
+#34 := [rewrite]: #33
+#31 := (iff #9 #30)
+#28 := (iff #8 false)
+#29 := [elim-unused]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#39 := [monotonicity #36]: #38
+#43 := [trans #39 #41]: #42
+#27 := [asserted]: #10
+[mp #27 #43]: false
+unsat
+e7e0dc21cd513d4b03eef3800b25925d59d2e3f6 1 0
+unsat
+be601e3d8f8e3cc99db3c33b213c810d4f870e66 1 0
+unsat
+2b5ea80215a4775a67f2e4685d423c2766fd2643 1 0
+unsat
+4bfc5cfdb12b8b5a08a33f5540fcd9843079b67a 67 0
+#2 := false
+#9 := 0::int
+#12 := 1::int
+#142 := (= 1::int 0::int)
+#144 := (iff #142 false)
+#145 := [rewrite]: #144
+decl ?v0!1 :: int
+#54 := ?v0!1
+#47 := (= ?v0!1 0::int)
+decl ?v1!0 :: int
+#53 := ?v1!0
+#50 := (= ?v1!0 1::int)
+#57 := (and #47 #50)
+#68 := (= ?v1!0 ?v0!1)
+#71 := (not #68)
+#58 := (not #57)
+#74 := (or #58 #71)
+#77 := (not #74)
+#55 := (= ?v0!1 ?v1!0)
+#56 := (not #55)
+#59 := (or #58 #56)
+#60 := (not #59)
+#78 := (iff #60 #77)
+#75 := (iff #59 #74)
+#72 := (iff #56 #71)
+#69 := (iff #55 #68)
+#70 := [rewrite]: #69
+#73 := [monotonicity #70]: #72
+#76 := [monotonicity #73]: #75
+#79 := [monotonicity #76]: #78
+#11 := (:var 0 int)
+#8 := (:var 1 int)
+#15 := (= #8 #11)
+#16 := (not #15)
+#13 := (= #11 1::int)
+#10 := (= #8 0::int)
+#14 := (and #10 #13)
+#37 := (not #14)
+#38 := (or #37 #16)
+#41 := (forall (vars (?v0 int) (?v1 int)) #38)
+#44 := (not #41)
+#61 := (~ #44 #60)
+#62 := [sk]: #61
+#17 := (implies #14 #16)
+#18 := (forall (vars (?v0 int) (?v1 int)) #17)
+#19 := (not #18)
+#45 := (iff #19 #44)
+#42 := (iff #18 #41)
+#39 := (iff #17 #38)
+#40 := [rewrite]: #39
+#43 := [quant-intro #40]: #42
+#46 := [monotonicity #43]: #45
+#36 := [asserted]: #19
+#49 := [mp #36 #46]: #44
+#65 := [mp~ #49 #62]: #60
+#66 := [mp #65 #79]: #77
+#67 := [not-or-elim #66]: #57
+#80 := [and-elim #67]: #47
+#140 := (= 1::int ?v0!1)
+#82 := [not-or-elim #66]: #68
+#138 := (= 1::int ?v1!0)
+#81 := [and-elim #67]: #50
+#139 := [symm #81]: #138
+#141 := [trans #139 #82]: #140
+#143 := [trans #141 #80]: #142
+[mp #143 #145]: false
+unsat
+c365a72d1de4853f4116b170892fc897015e6fe6 82 0
+#2 := false
+#9 := (:var 0 int)
+#11 := 0::int
+#13 := (<= 0::int #9)
+#12 := (< #9 0::int)
+#14 := (or #12 #13)
+#8 := (:var 1 int)
+#10 := (< #8 #9)
+#15 := (implies #10 #14)
+#16 := (forall (vars (?v1 int)) #15)
+#17 := (exists (vars (?v0 int)) #16)
+#18 := (not #17)
+#100 := (iff #18 false)
+#36 := (not #10)
+#37 := (or #36 #14)
+#40 := (forall (vars (?v1 int)) #37)
+#43 := (exists (vars (?v0 int)) #40)
+#46 := (not #43)
+#98 := (iff #46 false)
+#1 := true
+#93 := (not true)
+#96 := (iff #93 false)
+#97 := [rewrite]: #96
+#94 := (iff #46 #93)
+#91 := (iff #43 true)
+#86 := (exists (vars (?v0 int)) true)
+#89 := (iff #86 true)
+#90 := [elim-unused]: #89
+#87 := (iff #43 #86)
+#84 := (iff #40 true)
+#79 := (forall (vars (?v1 int)) true)
+#82 := (iff #79 true)
+#83 := [elim-unused]: #82
+#80 := (iff #40 #79)
+#77 := (iff #37 true)
+#51 := (>= #9 0::int)
+#49 := (not #51)
+#69 := (or #49 #51)
+#55 := -1::int
+#58 := (* -1::int #9)
+#59 := (+ #8 #58)
+#57 := (>= #59 0::int)
+#72 := (or #57 #69)
+#75 := (iff #72 true)
+#76 := [rewrite]: #75
+#73 := (iff #37 #72)
+#70 := (iff #14 #69)
+#53 := (iff #13 #51)
+#54 := [rewrite]: #53
+#50 := (iff #12 #49)
+#52 := [rewrite]: #50
+#71 := [monotonicity #52 #54]: #70
+#67 := (iff #36 #57)
+#56 := (not #57)
+#62 := (not #56)
+#65 := (iff #62 #57)
+#66 := [rewrite]: #65
+#63 := (iff #36 #62)
+#60 := (iff #10 #56)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#68 := [trans #64 #66]: #67
+#74 := [monotonicity #68 #71]: #73
+#78 := [trans #74 #76]: #77
+#81 := [quant-intro #78]: #80
+#85 := [trans #81 #83]: #84
+#88 := [quant-intro #85]: #87
+#92 := [trans #88 #90]: #91
+#95 := [monotonicity #92]: #94
+#99 := [trans #95 #97]: #98
+#47 := (iff #18 #46)
+#44 := (iff #17 #43)
+#41 := (iff #16 #40)
+#38 := (iff #15 #37)
+#39 := [rewrite]: #38
+#42 := [quant-intro #39]: #41
+#45 := [quant-intro #42]: #44
+#48 := [monotonicity #45]: #47
+#101 := [trans #48 #99]: #100
+#35 := [asserted]: #18
+[mp #35 #101]: false
+unsat
+3c9d3e136c0159be65ffdd67f8135bbff5309982 78 0
+#2 := false
+#9 := (:var 0 int)
+#11 := 2::int
+#15 := (* 2::int #9)
+#13 := 1::int
+#8 := (:var 1 int)
+#12 := (* 2::int #8)
+#14 := (+ #12 1::int)
+#16 := (< #14 #15)
+#10 := (< #8 #9)
+#17 := (implies #10 #16)
+#18 := (forall (vars (?v0 int) (?v1 int)) #17)
+#19 := (not #18)
+#96 := (iff #19 false)
+#37 := (+ 1::int #12)
+#40 := (< #37 #15)
+#46 := (not #10)
+#47 := (or #46 #40)
+#52 := (forall (vars (?v0 int) (?v1 int)) #47)
+#55 := (not #52)
+#94 := (iff #55 false)
+#1 := true
+#89 := (not true)
+#92 := (iff #89 false)
+#93 := [rewrite]: #92
+#90 := (iff #55 #89)
+#87 := (iff #52 true)
+#82 := (forall (vars (?v0 int) (?v1 int)) true)
+#85 := (iff #82 true)
+#86 := [elim-unused]: #85
+#83 := (iff #52 #82)
+#80 := (iff #47 true)
+#60 := 0::int
+#58 := -1::int
+#62 := (* -1::int #9)
+#63 := (+ #8 #62)
+#61 := (>= #63 0::int)
+#59 := (not #61)
+#74 := (or #61 #59)
+#78 := (iff #74 true)
+#79 := [rewrite]: #78
+#76 := (iff #47 #74)
+#75 := (iff #40 #59)
+#73 := [rewrite]: #75
+#71 := (iff #46 #61)
+#66 := (not #59)
+#69 := (iff #66 #61)
+#70 := [rewrite]: #69
+#67 := (iff #46 #66)
+#64 := (iff #10 #59)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#72 := [trans #68 #70]: #71
+#77 := [monotonicity #72 #73]: #76
+#81 := [trans #77 #79]: #80
+#84 := [quant-intro #81]: #83
+#88 := [trans #84 #86]: #87
+#91 := [monotonicity #88]: #90
+#95 := [trans #91 #93]: #94
+#56 := (iff #19 #55)
+#53 := (iff #18 #52)
+#50 := (iff #17 #47)
+#43 := (implies #10 #40)
+#48 := (iff #43 #47)
+#49 := [rewrite]: #48
+#44 := (iff #17 #43)
+#41 := (iff #16 #40)
+#38 := (= #14 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#51 := [trans #45 #49]: #50
+#54 := [quant-intro #51]: #53
+#57 := [monotonicity #54]: #56
+#97 := [trans #57 #95]: #96
+#36 := [asserted]: #19
+[mp #36 #97]: false
+unsat
+96e0c09363319f1eb7b1466a9c40cafcf229e29a 61 0
+#2 := false
+#13 := (:var 0 int)
+#8 := 2::int
+#14 := (* 2::int #13)
+#11 := 1::int
+#9 := (:var 1 int)
+#10 := (* 2::int #9)
+#12 := (+ #10 1::int)
+#15 := (= #12 #14)
+#16 := (not #15)
+#17 := (forall (vars (?v0 int) (?v1 int)) #16)
+#18 := (not #17)
+#79 := (iff #18 false)
+#36 := (+ 1::int #10)
+#42 := (= #14 #36)
+#47 := (not #42)
+#50 := (forall (vars (?v0 int) (?v1 int)) #47)
+#53 := (not #50)
+#77 := (iff #53 false)
+#1 := true
+#72 := (not true)
+#75 := (iff #72 false)
+#76 := [rewrite]: #75
+#73 := (iff #53 #72)
+#70 := (iff #50 true)
+#65 := (forall (vars (?v0 int) (?v1 int)) true)
+#68 := (iff #65 true)
+#69 := [elim-unused]: #68
+#66 := (iff #50 #65)
+#63 := (iff #47 true)
+#56 := (not false)
+#61 := (iff #56 true)
+#62 := [rewrite]: #61
+#57 := (iff #47 #56)
+#58 := (iff #42 false)
+#59 := [rewrite]: #58
+#60 := [monotonicity #59]: #57
+#64 := [trans #60 #62]: #63
+#67 := [quant-intro #64]: #66
+#71 := [trans #67 #69]: #70
+#74 := [monotonicity #71]: #73
+#78 := [trans #74 #76]: #77
+#54 := (iff #18 #53)
+#51 := (iff #17 #50)
+#48 := (iff #16 #47)
+#45 := (iff #15 #42)
+#39 := (= #36 #14)
+#43 := (iff #39 #42)
+#44 := [rewrite]: #43
+#40 := (iff #15 #39)
+#37 := (= #12 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#46 := [trans #41 #44]: #45
+#49 := [monotonicity #46]: #48
+#52 := [quant-intro #49]: #51
+#55 := [monotonicity #52]: #54
+#80 := [trans #55 #78]: #79
+#35 := [asserted]: #18
+[mp #35 #80]: false
+unsat
+3990cca690691d622e503f7585b9ff729a5d9f50 111 0
+#2 := false
+#8 := 2::int
+decl ?v0!1 :: int
+#92 := ?v0!1
+decl ?v1!0 :: int
+#91 := ?v1!0
+#106 := (+ ?v1!0 ?v0!1)
+#112 := (>= #106 2::int)
+#118 := (<= #106 2::int)
+#121 := (not #118)
+#115 := (not #112)
+#109 := (= #106 2::int)
+#124 := (or #109 #115 #121)
+#127 := (not #124)
+#93 := (+ ?v0!1 ?v1!0)
+#94 := (<= #93 2::int)
+#88 := (not #94)
+#86 := (>= #93 2::int)
+#95 := (not #86)
+#96 := (= #93 2::int)
+#97 := (or #96 #95 #88)
+#98 := (not #97)
+#128 := (iff #98 #127)
+#125 := (iff #97 #124)
+#122 := (iff #88 #121)
+#119 := (iff #94 #118)
+#107 := (= #93 #106)
+#108 := [rewrite]: #107
+#120 := [monotonicity #108]: #119
+#123 := [monotonicity #120]: #122
+#116 := (iff #95 #115)
+#113 := (iff #86 #112)
+#114 := [monotonicity #108]: #113
+#117 := [monotonicity #114]: #116
+#110 := (iff #96 #109)
+#111 := [monotonicity #108]: #110
+#126 := [monotonicity #111 #117 #123]: #125
+#129 := [monotonicity #126]: #128
+#10 := (:var 0 int)
+#9 := (:var 1 int)
+#11 := (+ #9 #10)
+#61 := (<= #11 2::int)
+#63 := (not #61)
+#59 := (>= #11 2::int)
+#56 := (not #59)
+#13 := (= #11 2::int)
+#72 := (or #13 #56 #63)
+#77 := (forall (vars (?v0 int) (?v1 int)) #72)
+#80 := (not #77)
+#99 := (~ #80 #98)
+#100 := [sk]: #99
+#14 := (< #11 2::int)
+#15 := (or #13 #14)
+#12 := (< 2::int #11)
+#16 := (or #12 #15)
+#17 := (forall (vars (?v0 int) (?v1 int)) #16)
+#18 := (not #17)
+#83 := (iff #18 #80)
+#36 := (= 2::int #11)
+#42 := (or #14 #36)
+#47 := (or #12 #42)
+#50 := (forall (vars (?v0 int) (?v1 int)) #47)
+#53 := (not #50)
+#81 := (iff #53 #80)
+#78 := (iff #50 #77)
+#75 := (iff #47 #72)
+#66 := (or #56 #13)
+#69 := (or #63 #66)
+#73 := (iff #69 #72)
+#74 := [rewrite]: #73
+#70 := (iff #47 #69)
+#67 := (iff #42 #66)
+#60 := (iff #36 #13)
+#62 := [rewrite]: #60
+#58 := (iff #14 #56)
+#57 := [rewrite]: #58
+#68 := [monotonicity #57 #62]: #67
+#64 := (iff #12 #63)
+#65 := [rewrite]: #64
+#71 := [monotonicity #65 #68]: #70
+#76 := [trans #71 #74]: #75
+#79 := [quant-intro #76]: #78
+#82 := [monotonicity #79]: #81
+#54 := (iff #18 #53)
+#51 := (iff #17 #50)
+#48 := (iff #16 #47)
+#45 := (iff #15 #42)
+#39 := (or #36 #14)
+#43 := (iff #39 #42)
+#44 := [rewrite]: #43
+#40 := (iff #15 #39)
+#37 := (iff #13 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#46 := [trans #41 #44]: #45
+#49 := [monotonicity #46]: #48
+#52 := [quant-intro #49]: #51
+#55 := [monotonicity #52]: #54
+#84 := [trans #55 #82]: #83
+#35 := [asserted]: #18
+#85 := [mp #35 #84]: #80
+#103 := [mp~ #85 #100]: #98
+#104 := [mp #103 #129]: #127
+#131 := [not-or-elim #104]: #112
+#105 := (not #109)
+#130 := [not-or-elim #104]: #105
+#132 := [not-or-elim #104]: #118
+#188 := (or #109 #121 #115)
+#189 := [th-lemma]: #188
+[unit-resolution #189 #132 #130 #131]: false
+unsat
+64bba02f58cf5d8a89cc3d6fd23df0f74a6646a6 89 0
+#2 := false
+#8 := 0::int
+decl ?v0!0 :: int
+#85 := ?v0!0
+#80 := (<= ?v0!0 0::int)
+#151 := (not #80)
+#160 := [hypothesis]: #151
+#54 := -1::int
+#86 := (<= ?v0!0 -1::int)
+#87 := (not #86)
+#161 := (or #87 #80)
+#162 := [th-lemma]: #161
+#163 := [unit-resolution #162 #160]: #87
+#164 := (or #80 #86)
+#11 := 1::int
+#88 := (>= ?v0!0 1::int)
+#82 := (not #88)
+#89 := (ite #80 #82 #87)
+#90 := (not #89)
+#9 := (:var 0 int)
+#55 := (<= #9 -1::int)
+#56 := (not #55)
+#60 := (>= #9 1::int)
+#59 := (not #60)
+#50 := (<= #9 0::int)
+#66 := (ite #50 #59 #56)
+#71 := (forall (vars (?v0 int)) #66)
+#74 := (not #71)
+#91 := (~ #74 #90)
+#92 := [sk]: #91
+#14 := (< #9 1::int)
+#12 := (+ #9 1::int)
+#13 := (< 0::int #12)
+#10 := (< 0::int #9)
+#15 := (ite #10 #13 #14)
+#16 := (forall (vars (?v0 int)) #15)
+#17 := (not #16)
+#77 := (iff #17 #74)
+#35 := (+ 1::int #9)
+#38 := (< 0::int #35)
+#41 := (ite #10 #38 #14)
+#44 := (forall (vars (?v0 int)) #41)
+#47 := (not #44)
+#75 := (iff #47 #74)
+#72 := (iff #44 #71)
+#69 := (iff #41 #66)
+#51 := (not #50)
+#63 := (ite #51 #56 #59)
+#67 := (iff #63 #66)
+#68 := [rewrite]: #67
+#64 := (iff #41 #63)
+#61 := (iff #14 #59)
+#62 := [rewrite]: #61
+#57 := (iff #38 #56)
+#58 := [rewrite]: #57
+#52 := (iff #10 #51)
+#53 := [rewrite]: #52
+#65 := [monotonicity #53 #58 #62]: #64
+#70 := [trans #65 #68]: #69
+#73 := [quant-intro #70]: #72
+#76 := [monotonicity #73]: #75
+#48 := (iff #17 #47)
+#45 := (iff #16 #44)
+#42 := (iff #15 #41)
+#39 := (iff #13 #38)
+#36 := (= #12 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#46 := [quant-intro #43]: #45
+#49 := [monotonicity #46]: #48
+#78 := [trans #49 #76]: #77
+#34 := [asserted]: #17
+#79 := [mp #34 #78]: #74
+#95 := [mp~ #79 #92]: #90
+#158 := (or #89 #80 #86)
+#159 := [def-axiom]: #158
+#165 := [unit-resolution #159 #95]: #164
+#166 := [unit-resolution #165 #163 #160]: false
+#167 := [lemma #166]: #80
+#168 := (or #82 #151)
+#169 := [th-lemma]: #168
+#170 := [unit-resolution #169 #167]: #82
+#171 := (or #151 #88)
+#156 := (or #89 #151 #88)
+#157 := [def-axiom]: #156
+#172 := [unit-resolution #157 #95]: #171
+[unit-resolution #172 #170 #167]: false
+unsat
+d2bfc1de87fbaa5e6bd6599d098877a198138706 83 2
+#2 := false
+#9 := 0::int
+#8 := (:var 0 int)
+#47 := (<= #8 0::int)
+#48 := (not #47)
+#45 := (>= #8 0::int)
+#43 := (not #45)
+#51 := (or #43 #48)
+#54 := (forall (vars (?v0 int)) #51)
+#187 := (not #54)
+#123 := (<= 0::int 0::int)
+#209 := (not #123)
+#124 := (>= 0::int 0::int)
+#210 := (not #124)
+#211 := (or #210 #209)
+#192 := (or #187 #211)
+#177 := (iff #192 #187)
+#188 := (or #187 false)
+#514 := (iff #188 #187)
+#176 := [rewrite]: #514
+#530 := (iff #192 #188)
+#538 := (iff #211 false)
+#534 := (or false false)
+#537 := (iff #534 false)
+#532 := [rewrite]: #537
+#535 := (iff #211 #534)
+#200 := (iff #209 false)
+#1 := true
+#214 := (not true)
+#212 := (iff #214 false)
+#216 := [rewrite]: #212
+#320 := (iff #209 #214)
+#533 := (iff #123 true)
+#189 := [rewrite]: #533
+#527 := [monotonicity #189]: #320
+#201 := [trans #527 #216]: #200
+#195 := (iff #210 false)
+#142 := (iff #210 #214)
+#202 := (iff #124 true)
+#213 := [rewrite]: #202
+#215 := [monotonicity #213]: #142
+#531 := [trans #215 #216]: #195
+#536 := [monotonicity #531 #201]: #535
+#528 := [trans #536 #532]: #538
+#172 := [monotonicity #528]: #530
+#178 := [trans #172 #176]: #177
+#529 := [quant-inst]: #192
+#179 := [mp #529 #178]: #187
+#67 := (~ #54 #54)
+#65 := (~ #51 #51)
+#66 := [refl]: #65
+#68 := [nnf-pos #66]: #67
+#11 := (< 0::int #8)
+#10 := (< #8 0::int)
+#12 := (or #10 #11)
+#13 := (forall (vars (?v0 int)) #12)
+#14 := (ite #13 false true)
+#15 := (not #14)
+#57 := (iff #15 #54)
+#55 := (iff #13 #54)
+#52 := (iff #12 #51)
+#49 := (iff #11 #48)
+#50 := [rewrite]: #49
+#44 := (iff #10 #43)
+#46 := [rewrite]: #44
+#53 := [monotonicity #46 #50]: #52
+#56 := [quant-intro #53]: #55
+#41 := (iff #15 #13)
+#33 := (not #13)
+#36 := (not #33)
+#39 := (iff #36 #13)
+#40 := [rewrite]: #39
+#37 := (iff #15 #36)
+#34 := (iff #14 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#42 := [trans #38 #40]: #41
+#58 := [trans #42 #56]: #57
+#32 := [asserted]: #15
+#59 := [mp #32 #58]: #54
+#62 := [mp~ #59 #68]: #54
+[unit-resolution #62 #179]: false
+unsat
+WARNING: failed to find a pattern for quantifier (quantifier id: k!9)
+
+d085c245b7da6740b8f1ddee257b026bd0bf4583 180 2
+#2 := false
+#16 := 3::int
+#37 := -1::int
+decl z3name!0 :: bool
+#90 := z3name!0
+#97 := (ite z3name!0 -1::int 3::int)
+#613 := (>= #97 3::int)
+#315 := (not #613)
+#8 := 0::int
+#100 := (<= #97 0::int)
+#9 := (:var 0 int)
+#53 := (<= #9 0::int)
+#54 := (not #53)
+#50 := (>= #9 0::int)
+#49 := (not #50)
+#57 := (or #49 #54)
+#60 := (forall (vars (?v0 int)) #57)
+#63 := (ite #60 -1::int 3::int)
+#69 := (<= #63 0::int)
+#101 := (~ #69 #100)
+#98 := (= #63 #97)
+#95 := (~ #60 z3name!0)
+#93 := (not #60)
+#87 := (or z3name!0 #93)
+#91 := (not z3name!0)
+#92 := (or #91 #60)
+#85 := (and #92 #87)
+#94 := [intro-def]: #85
+#96 := [apply-def #94]: #95
+#99 := [monotonicity #96]: #98
+#102 := [monotonicity #99]: #101
+#14 := 1::int
+#15 := (- 1::int)
+#11 := (< 0::int #9)
+#10 := (< #9 0::int)
+#12 := (or #10 #11)
+#13 := (forall (vars (?v0 int)) #12)
+#17 := (ite #13 #15 3::int)
+#18 := (< 0::int #17)
+#19 := (not #18)
+#82 := (iff #19 #69)
+#40 := (ite #13 -1::int 3::int)
+#43 := (< 0::int #40)
+#46 := (not #43)
+#80 := (iff #46 #69)
+#70 := (not #69)
+#75 := (not #70)
+#78 := (iff #75 #69)
+#79 := [rewrite]: #78
+#76 := (iff #46 #75)
+#73 := (iff #43 #70)
+#66 := (< 0::int #63)
+#71 := (iff #66 #70)
+#72 := [rewrite]: #71
+#67 := (iff #43 #66)
+#64 := (= #40 #63)
+#61 := (iff #13 #60)
+#58 := (iff #12 #57)
+#55 := (iff #11 #54)
+#56 := [rewrite]: #55
+#51 := (iff #10 #49)
+#52 := [rewrite]: #51
+#59 := [monotonicity #52 #56]: #58
+#62 := [quant-intro #59]: #61
+#65 := [monotonicity #62]: #64
+#68 := [monotonicity #65]: #67
+#74 := [trans #68 #72]: #73
+#77 := [monotonicity #74]: #76
+#81 := [trans #77 #79]: #80
+#47 := (iff #19 #46)
+#44 := (iff #18 #43)
+#41 := (= #17 #40)
+#38 := (= #15 -1::int)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#83 := [trans #48 #81]: #82
+#36 := [asserted]: #19
+#84 := [mp #36 #83]: #69
+#131 := [mp~ #84 #102]: #100
+#316 := (not #100)
+#317 := (or #315 #316)
+#318 := [th-lemma]: #317
+#212 := [unit-resolution #318 #131]: #315
+#295 := (= #97 3::int)
+#270 := (<= 0::int 0::int)
+#400 := (not #270)
+#607 := (>= 0::int 0::int)
+#281 := (not #607)
+#282 := (or #281 #400)
+#600 := (or #93 #282)
+#245 := (iff #600 #93)
+#601 := (or #93 false)
+#604 := (iff #601 #93)
+#244 := [rewrite]: #604
+#239 := (iff #600 #601)
+#598 := (iff #282 false)
+#258 := (or false false)
+#596 := (iff #258 false)
+#597 := [rewrite]: #596
+#259 := (iff #282 #258)
+#594 := (iff #400 false)
+#1 := true
+#616 := (not true)
+#618 := (iff #616 false)
+#608 := [rewrite]: #618
+#610 := (iff #400 #616)
+#609 := (iff #270 true)
+#269 := [rewrite]: #609
+#253 := [monotonicity #269]: #610
+#257 := [trans #253 #608]: #594
+#268 := (iff #281 false)
+#617 := (iff #281 #616)
+#614 := (iff #607 true)
+#615 := [rewrite]: #614
+#612 := [monotonicity #615]: #617
+#273 := [trans #612 #608]: #268
+#260 := [monotonicity #273 #257]: #259
+#599 := [trans #260 #597]: #598
+#602 := [monotonicity #599]: #239
+#605 := [trans #602 #244]: #245
+#595 := [quant-inst]: #600
+#603 := [mp #595 #605]: #93
+#606 := [hypothesis]: #60
+#592 := [unit-resolution #606 #603]: false
+#593 := [lemma #592]: #93
+#134 := (or #60 #91)
+decl ?v0!1 :: int
+#113 := ?v0!1
+#116 := (>= ?v0!1 0::int)
+#117 := (not #116)
+#114 := (<= ?v0!1 0::int)
+#115 := (not #114)
+#137 := (or #115 #117)
+#140 := (not #137)
+#143 := (or z3name!0 #140)
+#146 := (and #134 #143)
+#118 := (or #117 #115)
+#119 := (not #118)
+#124 := (or z3name!0 #119)
+#127 := (and #92 #124)
+#147 := (iff #127 #146)
+#144 := (iff #124 #143)
+#141 := (iff #119 #140)
+#138 := (iff #118 #137)
+#139 := [rewrite]: #138
+#142 := [monotonicity #139]: #141
+#145 := [monotonicity #142]: #144
+#135 := (iff #92 #134)
+#136 := [rewrite]: #135
+#148 := [monotonicity #136 #145]: #147
+#128 := (~ #85 #127)
+#125 := (~ #87 #124)
+#120 := (~ #93 #119)
+#121 := [sk]: #120
+#111 := (~ z3name!0 z3name!0)
+#112 := [refl]: #111
+#126 := [monotonicity #112 #121]: #125
+#109 := (~ #92 #92)
+#107 := (~ #60 #60)
+#105 := (~ #57 #57)
+#106 := [refl]: #105
+#108 := [nnf-pos #106]: #107
+#103 := (~ #91 #91)
+#104 := [refl]: #103
+#110 := [monotonicity #104 #108]: #109
+#129 := [monotonicity #110 #126]: #128
+#130 := [mp~ #94 #129]: #127
+#132 := [mp #130 #148]: #146
+#133 := [and-elim #132]: #134
+#588 := [unit-resolution #133 #593]: #91
+#297 := (or z3name!0 #295)
+#276 := [def-axiom]: #297
+#589 := [unit-resolution #276 #588]: #295
+#311 := (not #295)
+#312 := (or #311 #613)
+#586 := [th-lemma]: #312
+[unit-resolution #586 #589 #212]: false
+unsat
+WARNING: failed to find a pattern for quantifier (quantifier id: k!9)
+
+5cfbea22b49c2358c1e253cb2085b4c25ec3e266 68 0
+#2 := false
+#16 := 1::int
+#13 := (:var 1 int)
+#11 := 6::int
+#12 := (- 6::int)
+#14 := (* #12 #13)
+#9 := (:var 2 int)
+#8 := 4::int
+#10 := (* 4::int #9)
+#15 := (+ #10 #14)
+#17 := (= #15 1::int)
+#18 := (exists (vars (?v0 int) (?v1 int) (?v2 int)) #17)
+#19 := (not #18)
+#20 := (not #19)
+#87 := (iff #20 false)
+#58 := (:var 0 int)
+#38 := -6::int
+#59 := (* -6::int #58)
+#60 := (* 4::int #13)
+#61 := (+ #60 #59)
+#62 := (= 1::int #61)
+#63 := (exists (vars (?v0 int) (?v1 int)) #62)
+#85 := (iff #63 false)
+#81 := (exists (vars (?v0 int) (?v1 int)) false)
+#83 := (iff #81 false)
+#84 := [elim-unused]: #83
+#82 := (iff #63 #81)
+#78 := (iff #62 false)
+#79 := [rewrite]: #78
+#80 := [quant-intro #79]: #82
+#86 := [trans #80 #84]: #85
+#76 := (iff #20 #63)
+#68 := (not #63)
+#71 := (not #68)
+#74 := (iff #71 #63)
+#75 := [rewrite]: #74
+#72 := (iff #20 #71)
+#69 := (iff #19 #68)
+#66 := (iff #18 #63)
+#41 := (* -6::int #13)
+#44 := (+ #10 #41)
+#50 := (= 1::int #44)
+#55 := (exists (vars (?v0 int) (?v1 int) (?v2 int)) #50)
+#64 := (iff #55 #63)
+#65 := [elim-unused]: #64
+#56 := (iff #18 #55)
+#53 := (iff #17 #50)
+#47 := (= #44 1::int)
+#51 := (iff #47 #50)
+#52 := [rewrite]: #51
+#48 := (iff #17 #47)
+#45 := (= #15 #44)
+#42 := (= #14 #41)
+#39 := (= #12 -6::int)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#46 := [monotonicity #43]: #45
+#49 := [monotonicity #46]: #48
+#54 := [trans #49 #52]: #53
+#57 := [quant-intro #54]: #56
+#67 := [trans #57 #65]: #66
+#70 := [monotonicity #67]: #69
+#73 := [monotonicity #70]: #72
+#77 := [trans #73 #75]: #76
+#88 := [trans #77 #86]: #87
+#37 := [asserted]: #20
+[mp #37 #88]: false
+unsat
+00ea1ec7da3d2196f1891a60aeb0912f7ce4a20d 107 0
+#2 := false
+#8 := 0::int
+decl ?v1!1 :: int
+#90 := ?v1!1
+decl ?v2!0 :: int
+#89 := ?v2!0
+#113 := (+ ?v2!0 ?v1!1)
+#116 := (<= #113 0::int)
+#119 := (not #116)
+#94 := (<= ?v1!1 0::int)
+#95 := (not #94)
+#84 := (<= ?v2!0 0::int)
+#93 := (not #84)
+#107 := (and #93 #95)
+#110 := (not #107)
+#122 := (or #110 #119)
+#125 := (not #122)
+#91 := (+ ?v1!1 ?v2!0)
+#92 := (<= #91 0::int)
+#86 := (not #92)
+#96 := (and #95 #93)
+#97 := (not #96)
+#98 := (or #97 #86)
+#99 := (not #98)
+#126 := (iff #99 #125)
+#123 := (iff #98 #122)
+#120 := (iff #86 #119)
+#117 := (iff #92 #116)
+#114 := (= #91 #113)
+#115 := [rewrite]: #114
+#118 := [monotonicity #115]: #117
+#121 := [monotonicity #118]: #120
+#111 := (iff #97 #110)
+#108 := (iff #96 #107)
+#109 := [rewrite]: #108
+#112 := [monotonicity #109]: #111
+#124 := [monotonicity #112 #121]: #123
+#127 := [monotonicity #124]: #126
+#11 := (:var 0 int)
+#9 := (:var 1 int)
+#14 := (+ #9 #11)
+#68 := (<= #14 0::int)
+#69 := (not #68)
+#58 := (<= #11 0::int)
+#59 := (not #58)
+#54 := (<= #9 0::int)
+#55 := (not #54)
+#62 := (and #55 #59)
+#65 := (not #62)
+#72 := (or #65 #69)
+#75 := (forall (vars (?v1 int) (?v2 int)) #72)
+#78 := (not #75)
+#100 := (~ #78 #99)
+#101 := [sk]: #100
+#15 := (< 0::int #14)
+#12 := (< 0::int #11)
+#10 := (< 0::int #9)
+#13 := (and #10 #12)
+#16 := (implies #13 #15)
+#17 := (forall (vars (?v1 int) (?v2 int)) #16)
+#18 := (exists (vars (?v0 int)) #17)
+#19 := (not #18)
+#81 := (iff #19 #78)
+#37 := (not #13)
+#38 := (or #37 #15)
+#41 := (forall (vars (?v1 int) (?v2 int)) #38)
+#51 := (not #41)
+#79 := (iff #51 #78)
+#76 := (iff #41 #75)
+#73 := (iff #38 #72)
+#70 := (iff #15 #69)
+#71 := [rewrite]: #70
+#66 := (iff #37 #65)
+#63 := (iff #13 #62)
+#60 := (iff #12 #59)
+#61 := [rewrite]: #60
+#56 := (iff #10 #55)
+#57 := [rewrite]: #56
+#64 := [monotonicity #57 #61]: #63
+#67 := [monotonicity #64]: #66
+#74 := [monotonicity #67 #71]: #73
+#77 := [quant-intro #74]: #76
+#80 := [monotonicity #77]: #79
+#52 := (iff #19 #51)
+#49 := (iff #18 #41)
+#44 := (exists (vars (?v0 int)) #41)
+#47 := (iff #44 #41)
+#48 := [elim-unused]: #47
+#45 := (iff #18 #44)
+#42 := (iff #17 #41)
+#39 := (iff #16 #38)
+#40 := [rewrite]: #39
+#43 := [quant-intro #40]: #42
+#46 := [quant-intro #43]: #45
+#50 := [trans #46 #48]: #49
+#53 := [monotonicity #50]: #52
+#82 := [trans #53 #80]: #81
+#36 := [asserted]: #19
+#83 := [mp #36 #82]: #78
+#104 := [mp~ #83 #101]: #99
+#105 := [mp #104 #127]: #125
+#130 := [not-or-elim #105]: #116
+#106 := [not-or-elim #105]: #107
+#129 := [and-elim #106]: #95
+#128 := [and-elim #106]: #93
+[th-lemma #128 #129 #130]: false
+unsat
+b9445a31d58a20efa0cc799b1255d3623574803a 117 0
+#2 := false
+#8 := 0::int
+decl ?v1!1 :: int
+#100 := ?v1!1
+#103 := (<= ?v1!1 0::int)
+#104 := (not #103)
+#11 := 0::real
+decl ?v2!0 :: real
+#99 := ?v2!0
+#101 := (<= ?v2!0 0::real)
+#102 := (not #101)
+#116 := (and #102 #104)
+#119 := (not #116)
+#38 := -1::int
+#98 := (<= ?v1!1 -1::int)
+#96 := (not #98)
+#125 := (or #96 #119)
+#130 := (not #125)
+#105 := (and #104 #102)
+#106 := (not #105)
+#107 := (or #106 #96)
+#108 := (not #107)
+#131 := (iff #108 #130)
+#128 := (iff #107 #125)
+#122 := (or #119 #96)
+#126 := (iff #122 #125)
+#127 := [rewrite]: #126
+#123 := (iff #107 #122)
+#120 := (iff #106 #119)
+#117 := (iff #105 #116)
+#118 := [rewrite]: #117
+#121 := [monotonicity #118]: #120
+#124 := [monotonicity #121]: #123
+#129 := [trans #124 #127]: #128
+#132 := [monotonicity #129]: #131
+#9 := (:var 1 int)
+#80 := (<= #9 -1::int)
+#81 := (not #80)
+#12 := (:var 0 real)
+#70 := (<= #12 0::real)
+#71 := (not #70)
+#66 := (<= #9 0::int)
+#67 := (not #66)
+#74 := (and #67 #71)
+#77 := (not #74)
+#84 := (or #77 #81)
+#87 := (forall (vars (?v1 int) (?v2 real)) #84)
+#90 := (not #87)
+#109 := (~ #90 #108)
+#110 := [sk]: #109
+#15 := 1::int
+#16 := (- 1::int)
+#17 := (< #16 #9)
+#13 := (< 0::real #12)
+#10 := (< 0::int #9)
+#14 := (and #10 #13)
+#18 := (implies #14 #17)
+#19 := (forall (vars (?v1 int) (?v2 real)) #18)
+#20 := (exists (vars (?v0 int)) #19)
+#21 := (not #20)
+#93 := (iff #21 #90)
+#41 := (< -1::int #9)
+#47 := (not #14)
+#48 := (or #47 #41)
+#53 := (forall (vars (?v1 int) (?v2 real)) #48)
+#63 := (not #53)
+#91 := (iff #63 #90)
+#88 := (iff #53 #87)
+#85 := (iff #48 #84)
+#82 := (iff #41 #81)
+#83 := [rewrite]: #82
+#78 := (iff #47 #77)
+#75 := (iff #14 #74)
+#72 := (iff #13 #71)
+#73 := [rewrite]: #72
+#68 := (iff #10 #67)
+#69 := [rewrite]: #68
+#76 := [monotonicity #69 #73]: #75
+#79 := [monotonicity #76]: #78
+#86 := [monotonicity #79 #83]: #85
+#89 := [quant-intro #86]: #88
+#92 := [monotonicity #89]: #91
+#64 := (iff #21 #63)
+#61 := (iff #20 #53)
+#56 := (exists (vars (?v0 int)) #53)
+#59 := (iff #56 #53)
+#60 := [elim-unused]: #59
+#57 := (iff #20 #56)
+#54 := (iff #19 #53)
+#51 := (iff #18 #48)
+#44 := (implies #14 #41)
+#49 := (iff #44 #48)
+#50 := [rewrite]: #49
+#45 := (iff #18 #44)
+#42 := (iff #17 #41)
+#39 := (= #16 -1::int)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#46 := [monotonicity #43]: #45
+#52 := [trans #46 #50]: #51
+#55 := [quant-intro #52]: #54
+#58 := [quant-intro #55]: #57
+#62 := [trans #58 #60]: #61
+#65 := [monotonicity #62]: #64
+#94 := [trans #65 #92]: #93
+#37 := [asserted]: #21
+#95 := [mp #37 #94]: #90
+#113 := [mp~ #95 #110]: #108
+#114 := [mp #113 #132]: #130
+#133 := [not-or-elim #114]: #116
+#135 := [and-elim #133]: #104
+#115 := [not-or-elim #114]: #98
+#191 := (or #96 #103)
+#192 := [th-lemma]: #191
+#193 := [unit-resolution #192 #115]: #103
+[unit-resolution #193 #135]: false
+unsat
+672f871feb35cc0fe285fb265c3124eed8d40fd4 148 0
+#2 := false
+#149 := (not false)
+#11 := 0::int
+#9 := (:var 0 int)
+#57 := (<= #9 0::int)
+#58 := (not #57)
+#152 := (or #58 #149)
+#155 := (not #152)
+#158 := (forall (vars (?v0 int)) #155)
+#185 := (iff #158 false)
+#180 := (forall (vars (?v0 int)) false)
+#183 := (iff #180 false)
+#184 := [elim-unused]: #183
+#181 := (iff #158 #180)
+#178 := (iff #155 false)
+#1 := true
+#173 := (not true)
+#176 := (iff #173 false)
+#177 := [rewrite]: #176
+#174 := (iff #155 #173)
+#171 := (iff #152 true)
+#166 := (or #58 true)
+#169 := (iff #166 true)
+#170 := [rewrite]: #169
+#167 := (iff #152 #166)
+#164 := (iff #149 true)
+#165 := [rewrite]: #164
+#168 := [monotonicity #165]: #167
+#172 := [trans #168 #170]: #171
+#175 := [monotonicity #172]: #174
+#179 := [trans #175 #177]: #178
+#182 := [quant-intro #179]: #181
+#186 := [trans #182 #184]: #185
+#61 := -1::int
+#62 := (* -1::int #9)
+#8 := (:var 1 int)
+#63 := (+ #8 #62)
+#64 := (<= #63 0::int)
+#67 := (not #64)
+#73 := (or #58 #67)
+#78 := (forall (vars (?v1 int)) #73)
+#81 := (not #78)
+#84 := (or #58 #81)
+#110 := (not #84)
+#128 := (forall (vars (?v0 int)) #110)
+#161 := (iff #128 #158)
+#132 := (forall (vars (?v1 int)) #58)
+#135 := (not #132)
+#138 := (or #58 #135)
+#141 := (not #138)
+#144 := (forall (vars (?v0 int)) #141)
+#159 := (iff #144 #158)
+#160 := [rewrite]: #159
+#145 := (iff #128 #144)
+#146 := [rewrite]: #145
+#162 := [trans #146 #160]: #161
+#121 := (and #57 #78)
+#124 := (forall (vars (?v0 int)) #121)
+#129 := (iff #124 #128)
+#118 := (iff #121 #110)
+#127 := [rewrite]: #118
+#130 := [quant-intro #127]: #129
+#101 := (not #58)
+#109 := (and #101 #78)
+#113 := (forall (vars (?v0 int)) #109)
+#125 := (iff #113 #124)
+#122 := (iff #109 #121)
+#119 := (iff #101 #57)
+#120 := [rewrite]: #119
+#123 := [monotonicity #120]: #122
+#126 := [quant-intro #123]: #125
+#87 := (exists (vars (?v0 int)) #84)
+#90 := (not #87)
+#114 := (~ #90 #113)
+#111 := (~ #110 #109)
+#106 := (not #81)
+#107 := (~ #106 #78)
+#96 := (~ #78 #78)
+#104 := (~ #73 #73)
+#98 := [refl]: #104
+#105 := [nnf-pos #98]: #96
+#108 := [nnf-neg #105]: #107
+#102 := (~ #101 #101)
+#103 := [refl]: #102
+#112 := [nnf-neg #103 #108]: #111
+#115 := [nnf-neg #112]: #114
+#12 := (< 0::int #9)
+#10 := (<= #8 #9)
+#13 := (implies #10 #12)
+#14 := (forall (vars (?v1 int)) #13)
+#15 := (implies #14 #12)
+#16 := (exists (vars (?v0 int)) #15)
+#17 := (not #16)
+#93 := (iff #17 #90)
+#35 := (not #10)
+#36 := (or #35 #12)
+#39 := (forall (vars (?v1 int)) #36)
+#45 := (not #39)
+#46 := (or #12 #45)
+#51 := (exists (vars (?v0 int)) #46)
+#54 := (not #51)
+#91 := (iff #54 #90)
+#88 := (iff #51 #87)
+#85 := (iff #46 #84)
+#82 := (iff #45 #81)
+#79 := (iff #39 #78)
+#76 := (iff #36 #73)
+#70 := (or #67 #58)
+#74 := (iff #70 #73)
+#75 := [rewrite]: #74
+#71 := (iff #36 #70)
+#59 := (iff #12 #58)
+#60 := [rewrite]: #59
+#68 := (iff #35 #67)
+#65 := (iff #10 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#72 := [monotonicity #69 #60]: #71
+#77 := [trans #72 #75]: #76
+#80 := [quant-intro #77]: #79
+#83 := [monotonicity #80]: #82
+#86 := [monotonicity #60 #83]: #85
+#89 := [quant-intro #86]: #88
+#92 := [monotonicity #89]: #91
+#55 := (iff #17 #54)
+#52 := (iff #16 #51)
+#49 := (iff #15 #46)
+#42 := (implies #39 #12)
+#47 := (iff #42 #46)
+#48 := [rewrite]: #47
+#43 := (iff #15 #42)
+#40 := (iff #14 #39)
+#37 := (iff #13 #36)
+#38 := [rewrite]: #37
+#41 := [quant-intro #38]: #40
+#44 := [monotonicity #41]: #43
+#50 := [trans #44 #48]: #49
+#53 := [quant-intro #50]: #52
+#56 := [monotonicity #53]: #55
+#94 := [trans #56 #92]: #93
+#34 := [asserted]: #17
+#95 := [mp #34 #94]: #90
+#116 := [mp~ #95 #115]: #113
+#117 := [mp #116 #126]: #124
+#131 := [mp #117 #130]: #128
+#163 := [mp #131 #162]: #158
+[mp #163 #186]: false
+unsat
+d96de71d370b65dfebac57909ac6156ec810676f 67 0
+#2 := false
+#8 := (:var 0 int)
+#9 := (pattern #8)
+decl f3 :: int
+#10 := f3
+#12 := 2::int
+#14 := (* 2::int f3)
+#13 := (* 2::int #8)
+#15 := (< #13 #14)
+#11 := (< #8 f3)
+#16 := (implies #11 #15)
+#17 := (forall (vars (?v0 int)) (:pat #9) #16)
+#18 := (not #17)
+#84 := (iff #18 false)
+#36 := (not #11)
+#37 := (or #36 #15)
+#40 := (forall (vars (?v0 int)) (:pat #9) #37)
+#43 := (not #40)
+#82 := (iff #43 false)
+#1 := true
+#77 := (not true)
+#80 := (iff #77 false)
+#81 := [rewrite]: #80
+#78 := (iff #43 #77)
+#75 := (iff #40 true)
+#70 := (forall (vars (?v0 int)) (:pat #9) true)
+#73 := (iff #70 true)
+#74 := [elim-unused]: #73
+#71 := (iff #40 #70)
+#68 := (iff #37 true)
+#48 := 0::int
+#46 := -1::int
+#50 := (* -1::int f3)
+#51 := (+ #8 #50)
+#49 := (>= #51 0::int)
+#47 := (not #49)
+#62 := (or #49 #47)
+#66 := (iff #62 true)
+#67 := [rewrite]: #66
+#64 := (iff #37 #62)
+#63 := (iff #15 #47)
+#61 := [rewrite]: #63
+#59 := (iff #36 #49)
+#54 := (not #47)
+#57 := (iff #54 #49)
+#58 := [rewrite]: #57
+#55 := (iff #36 #54)
+#52 := (iff #11 #47)
+#53 := [rewrite]: #52
+#56 := [monotonicity #53]: #55
+#60 := [trans #56 #58]: #59
+#65 := [monotonicity #60 #61]: #64
+#69 := [trans #65 #67]: #68
+#72 := [quant-intro #69]: #71
+#76 := [trans #72 #74]: #75
+#79 := [monotonicity #76]: #78
+#83 := [trans #79 #81]: #82
+#44 := (iff #18 #43)
+#41 := (iff #17 #40)
+#38 := (iff #16 #37)
+#39 := [rewrite]: #38
+#42 := [quant-intro #39]: #41
+#45 := [monotonicity #42]: #44
+#85 := [trans #45 #83]: #84
+#35 := [asserted]: #18
+[mp #35 #85]: false
+unsat
+5642a2762c96b47408c54a74546ed4b1daa4b2f7 1 0
+unsat
+9bc50f45e106d520fb697536efe06c19d8679cb1 75 0
+#2 := false
+#10 := 1::int
+decl f5 :: int
+#12 := f5
+#16 := (+ f5 1::int)
+decl f3 :: int
+#8 := f3
+#17 := (* f3 #16)
+decl f4 :: int
+#9 := f4
+#15 := (* f3 f4)
+#18 := (+ #15 #17)
+#11 := (+ f4 1::int)
+#13 := (+ #11 f5)
+#14 := (* f3 #13)
+#19 := (= #14 #18)
+#20 := (not #19)
+#90 := (iff #20 false)
+#1 := true
+#85 := (not true)
+#88 := (iff #85 false)
+#89 := [rewrite]: #88
+#86 := (iff #20 #85)
+#83 := (iff #19 true)
+#53 := (* f3 f5)
+#54 := (+ #15 #53)
+#55 := (+ f3 #54)
+#78 := (= #55 #55)
+#81 := (iff #78 true)
+#82 := [rewrite]: #81
+#79 := (iff #19 #78)
+#76 := (= #18 #55)
+#66 := (+ f3 #53)
+#71 := (+ #15 #66)
+#74 := (= #71 #55)
+#75 := [rewrite]: #74
+#72 := (= #18 #71)
+#69 := (= #17 #66)
+#60 := (+ 1::int f5)
+#63 := (* f3 #60)
+#67 := (= #63 #66)
+#68 := [rewrite]: #67
+#64 := (= #17 #63)
+#61 := (= #16 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#70 := [trans #65 #68]: #69
+#73 := [monotonicity #70]: #72
+#77 := [trans #73 #75]: #76
+#58 := (= #14 #55)
+#44 := (+ f4 f5)
+#45 := (+ 1::int #44)
+#50 := (* f3 #45)
+#56 := (= #50 #55)
+#57 := [rewrite]: #56
+#51 := (= #14 #50)
+#48 := (= #13 #45)
+#38 := (+ 1::int f4)
+#41 := (+ #38 f5)
+#46 := (= #41 #45)
+#47 := [rewrite]: #46
+#42 := (= #13 #41)
+#39 := (= #11 #38)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#49 := [trans #43 #47]: #48
+#52 := [monotonicity #49]: #51
+#59 := [trans #52 #57]: #58
+#80 := [monotonicity #59 #77]: #79
+#84 := [trans #80 #82]: #83
+#87 := [monotonicity #84]: #86
+#91 := [trans #87 #89]: #90
+#37 := [asserted]: #20
+[mp #37 #91]: false
+unsat
+c3031c5c6adefd1941844fe7f32dc15607540504 62 0
+#2 := false
+decl f4 :: real
+#10 := f4
+decl f3 :: real
+#8 := f3
+#16 := 2::real
+#17 := (* 2::real f3)
+#18 := (* #17 f4)
+#9 := 1::real
+#13 := (- 1::real f4)
+#14 := (* f3 #13)
+#11 := (+ 1::real f4)
+#12 := (* f3 #11)
+#15 := (- #12 #14)
+#19 := (= #15 #18)
+#20 := (not #19)
+#78 := (iff #20 false)
+#1 := true
+#73 := (not true)
+#76 := (iff #73 false)
+#77 := [rewrite]: #76
+#74 := (iff #20 #73)
+#71 := (iff #19 true)
+#38 := (* f3 f4)
+#60 := (* 2::real #38)
+#66 := (= #60 #60)
+#69 := (iff #66 true)
+#70 := [rewrite]: #69
+#67 := (iff #19 #66)
+#64 := (= #18 #60)
+#65 := [rewrite]: #64
+#62 := (= #15 #60)
+#42 := -1::real
+#50 := (* -1::real #38)
+#51 := (+ f3 #50)
+#39 := (+ f3 #38)
+#56 := (- #39 #51)
+#59 := (= #56 #60)
+#61 := [rewrite]: #59
+#57 := (= #15 #56)
+#54 := (= #14 #51)
+#43 := (* -1::real f4)
+#44 := (+ 1::real #43)
+#47 := (* f3 #44)
+#52 := (= #47 #51)
+#53 := [rewrite]: #52
+#48 := (= #14 #47)
+#45 := (= #13 #44)
+#46 := [rewrite]: #45
+#49 := [monotonicity #46]: #48
+#55 := [trans #49 #53]: #54
+#40 := (= #12 #39)
+#41 := [rewrite]: #40
+#58 := [monotonicity #41 #55]: #57
+#63 := [trans #58 #61]: #62
+#68 := [monotonicity #63 #65]: #67
+#72 := [trans #68 #70]: #71
+#75 := [monotonicity #72]: #74
+#79 := [trans #75 #77]: #78
+#37 := [asserted]: #20
+[mp #37 #79]: false
+unsat
+c6ec90450e5ec3b39ae8e9948b0ecc6e4d27e6d7 141 0
+#2 := false
+decl f6 :: int
+#13 := f6
+decl f7 :: int
+#17 := f7
+decl f5 :: int
+#12 := f5
+#28 := (+ f5 f7)
+#29 := (+ #28 f6)
+decl f4 :: int
+#10 := f4
+#9 := 1::int
+#11 := (+ 1::int f4)
+#30 := (* #11 #29)
+#25 := (* f7 f4)
+#23 := (* #11 f7)
+#14 := (+ f5 f6)
+#20 := 2::int
+#21 := (* 2::int #11)
+#22 := (* #21 #14)
+#24 := (+ #22 #23)
+#26 := (+ #24 #25)
+decl f3 :: int
+#8 := f3
+#27 := (+ f3 #26)
+#31 := (- #27 #30)
+#18 := (* f4 f7)
+#15 := (* #11 #14)
+#16 := (+ f3 #15)
+#19 := (+ #16 #18)
+#32 := (= #19 #31)
+#33 := (not #32)
+#154 := (iff #33 false)
+#1 := true
+#149 := (not true)
+#152 := (iff #149 false)
+#153 := [rewrite]: #152
+#150 := (iff #33 #149)
+#147 := (iff #32 true)
+#52 := (* f4 f6)
+#51 := (* f4 f5)
+#53 := (+ #51 #52)
+#64 := (+ #18 #53)
+#65 := (+ f6 #64)
+#66 := (+ f5 #65)
+#67 := (+ f3 #66)
+#141 := (= #67 #67)
+#145 := (iff #141 true)
+#146 := [rewrite]: #145
+#140 := (iff #32 #141)
+#143 := (= #31 #67)
+#128 := (+ f7 #64)
+#129 := (+ f6 #128)
+#130 := (+ f5 #129)
+#82 := (* 2::int #52)
+#80 := (* 2::int #51)
+#83 := (+ #80 #82)
+#109 := (* 2::int #18)
+#110 := (+ #109 #83)
+#111 := (+ f7 #110)
+#81 := (* 2::int f6)
+#112 := (+ #81 #111)
+#79 := (* 2::int f5)
+#113 := (+ #79 #112)
+#118 := (+ f3 #113)
+#135 := (- #118 #130)
+#138 := (= #135 #67)
+#144 := [rewrite]: #138
+#136 := (= #31 #135)
+#133 := (= #30 #130)
+#121 := (+ f6 f7)
+#122 := (+ f5 #121)
+#125 := (* #11 #122)
+#131 := (= #125 #130)
+#132 := [rewrite]: #131
+#126 := (= #30 #125)
+#123 := (= #29 #122)
+#124 := [rewrite]: #123
+#127 := [monotonicity #124]: #126
+#134 := [trans #127 #132]: #133
+#119 := (= #27 #118)
+#116 := (= #26 #113)
+#96 := (+ #18 #83)
+#97 := (+ f7 #96)
+#98 := (+ #81 #97)
+#99 := (+ #79 #98)
+#106 := (+ #99 #18)
+#114 := (= #106 #113)
+#115 := [rewrite]: #114
+#107 := (= #26 #106)
+#104 := (= #25 #18)
+#105 := [rewrite]: #104
+#102 := (= #24 #99)
+#90 := (+ f7 #18)
+#84 := (+ #81 #83)
+#85 := (+ #79 #84)
+#93 := (+ #85 #90)
+#100 := (= #93 #99)
+#101 := [rewrite]: #100
+#94 := (= #24 #93)
+#91 := (= #23 #90)
+#92 := [rewrite]: #91
+#88 := (= #22 #85)
+#72 := (* 2::int f4)
+#73 := (+ 2::int #72)
+#76 := (* #73 #14)
+#86 := (= #76 #85)
+#87 := [rewrite]: #86
+#77 := (= #22 #76)
+#74 := (= #21 #73)
+#75 := [rewrite]: #74
+#78 := [monotonicity #75]: #77
+#89 := [trans #78 #87]: #88
+#95 := [monotonicity #89 #92]: #94
+#103 := [trans #95 #101]: #102
+#108 := [monotonicity #103 #105]: #107
+#117 := [trans #108 #115]: #116
+#120 := [monotonicity #117]: #119
+#137 := [monotonicity #120 #134]: #136
+#142 := [trans #137 #144]: #143
+#70 := (= #19 #67)
+#54 := (+ f6 #53)
+#55 := (+ f5 #54)
+#58 := (+ f3 #55)
+#61 := (+ #58 #18)
+#68 := (= #61 #67)
+#69 := [rewrite]: #68
+#62 := (= #19 #61)
+#59 := (= #16 #58)
+#56 := (= #15 #55)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#63 := [monotonicity #60]: #62
+#71 := [trans #63 #69]: #70
+#139 := [monotonicity #71 #142]: #140
+#148 := [trans #139 #146]: #147
+#151 := [monotonicity #148]: #150
+#155 := [trans #151 #153]: #154
+#50 := [asserted]: #33
+[mp #50 #155]: false
+unsat
+d24efc6c7849616ae702f247385db4189d44ac5a 252 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f3 :: (-> int S2)
+decl f5 :: S2
+#26 := f5
+#27 := (f4 f5)
+#25 := 2::int
+#28 := (* 2::int #27)
+#29 := (f3 #28)
+#298 := (f4 #29)
+#300 := -1::int
+#279 := (* -1::int #298)
+#615 := (+ #28 #279)
+#599 := (<= #615 0::int)
+#617 := (= #615 0::int)
+#611 := (>= #27 0::int)
+#242 := (= #298 0::int)
+#554 := (not #242)
+#593 := (<= #298 0::int)
+#462 := (not #593)
+#30 := 1::int
+#563 := (>= #298 1::int)
+#560 := (= #298 1::int)
+#31 := (f3 1::int)
+#594 := (f4 #31)
+#306 := (= #594 1::int)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#631 := (pattern #16)
+#75 := (>= #14 0::int)
+#76 := (not #75)
+#17 := (f4 #16)
+#57 := (= #14 #17)
+#82 := (or #57 #76)
+#632 := (forall (vars (?v0 int)) (:pat #631) #82)
+#87 := (forall (vars (?v0 int)) #82)
+#635 := (iff #87 #632)
+#633 := (iff #82 #82)
+#634 := [refl]: #633
+#636 := [quant-intro #634]: #635
+#138 := (~ #87 #87)
+#135 := (~ #82 #82)
+#150 := [refl]: #135
+#139 := [nnf-pos #150]: #138
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#90 := (iff #20 #87)
+#64 := (not #15)
+#65 := (or #64 #57)
+#70 := (forall (vars (?v0 int)) #65)
+#88 := (iff #70 #87)
+#85 := (iff #65 #82)
+#79 := (or #76 #57)
+#83 := (iff #79 #82)
+#84 := [rewrite]: #83
+#80 := (iff #65 #79)
+#77 := (iff #64 #76)
+#73 := (iff #15 #75)
+#74 := [rewrite]: #73
+#78 := [monotonicity #74]: #77
+#81 := [monotonicity #78]: #80
+#86 := [trans #81 #84]: #85
+#89 := [quant-intro #86]: #88
+#71 := (iff #20 #70)
+#68 := (iff #19 #65)
+#61 := (implies #15 #57)
+#66 := (iff #61 #65)
+#67 := [rewrite]: #66
+#62 := (iff #19 #61)
+#59 := (iff #18 #57)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#69 := [trans #63 #67]: #68
+#72 := [quant-intro #69]: #71
+#91 := [trans #72 #89]: #90
+#56 := [asserted]: #20
+#92 := [mp #56 #91]: #87
+#151 := [mp~ #92 #139]: #87
+#637 := [mp #151 #636]: #632
+#614 := (not #632)
+#583 := (or #614 #306)
+#316 := (>= 1::int 0::int)
+#590 := (not #316)
+#591 := (= 1::int #594)
+#595 := (or #591 #590)
+#424 := (or #614 #595)
+#426 := (iff #424 #583)
+#569 := (iff #583 #583)
+#570 := [rewrite]: #569
+#582 := (iff #595 #306)
+#579 := (or #306 false)
+#576 := (iff #579 #306)
+#581 := [rewrite]: #576
+#580 := (iff #595 #579)
+#589 := (iff #590 false)
+#1 := true
+#587 := (not true)
+#588 := (iff #587 false)
+#585 := [rewrite]: #588
+#301 := (iff #590 #587)
+#308 := (iff #316 true)
+#586 := [rewrite]: #308
+#584 := [monotonicity #586]: #301
+#578 := [trans #584 #585]: #589
+#305 := (iff #591 #306)
+#307 := [rewrite]: #305
+#575 := [monotonicity #307 #578]: #580
+#577 := [trans #575 #581]: #582
+#568 := [monotonicity #577]: #426
+#571 := [trans #568 #570]: #426
+#425 := [quant-inst]: #424
+#565 := [mp #425 #571]: #583
+#447 := [unit-resolution #565 #637]: #306
+#448 := (= #298 #594)
+#32 := (= #29 #31)
+#134 := [asserted]: #32
+#441 := [monotonicity #134]: #448
+#456 := [trans #441 #447]: #560
+#458 := (not #560)
+#459 := (or #458 #563)
+#452 := [th-lemma]: #459
+#460 := [unit-resolution #452 #456]: #563
+#461 := (not #563)
+#463 := (or #461 #462)
+#464 := [th-lemma]: #463
+#557 := [unit-resolution #464 #460]: #462
+#558 := (or #554 #593)
+#545 := [th-lemma]: #558
+#547 := [unit-resolution #545 #557]: #554
+#608 := (or #242 #611)
+#22 := (= #17 0::int)
+#123 := (or #22 #75)
+#638 := (forall (vars (?v0 int)) (:pat #631) #123)
+#128 := (forall (vars (?v0 int)) #123)
+#641 := (iff #128 #638)
+#639 := (iff #123 #123)
+#640 := [refl]: #639
+#642 := [quant-intro #640]: #641
+#140 := (~ #128 #128)
+#152 := (~ #123 #123)
+#153 := [refl]: #152
+#141 := [nnf-pos #153]: #140
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#131 := (iff #24 #128)
+#94 := (= 0::int #17)
+#100 := (not #21)
+#101 := (or #100 #94)
+#106 := (forall (vars (?v0 int)) #101)
+#129 := (iff #106 #128)
+#126 := (iff #101 #123)
+#120 := (or #75 #22)
+#124 := (iff #120 #123)
+#125 := [rewrite]: #124
+#121 := (iff #101 #120)
+#118 := (iff #94 #22)
+#119 := [rewrite]: #118
+#116 := (iff #100 #75)
+#111 := (not #76)
+#114 := (iff #111 #75)
+#115 := [rewrite]: #114
+#112 := (iff #100 #111)
+#109 := (iff #21 #76)
+#110 := [rewrite]: #109
+#113 := [monotonicity #110]: #112
+#117 := [trans #113 #115]: #116
+#122 := [monotonicity #117 #119]: #121
+#127 := [trans #122 #125]: #126
+#130 := [quant-intro #127]: #129
+#107 := (iff #24 #106)
+#104 := (iff #23 #101)
+#97 := (implies #21 #94)
+#102 := (iff #97 #101)
+#103 := [rewrite]: #102
+#98 := (iff #23 #97)
+#95 := (iff #22 #94)
+#96 := [rewrite]: #95
+#99 := [monotonicity #96]: #98
+#105 := [trans #99 #103]: #104
+#108 := [quant-intro #105]: #107
+#132 := [trans #108 #130]: #131
+#93 := [asserted]: #24
+#133 := [mp #93 #132]: #128
+#154 := [mp~ #133 #141]: #128
+#643 := [mp #154 #642]: #638
+#609 := (not #638)
+#607 := (or #609 #242 #611)
+#209 := (>= #28 0::int)
+#606 := (or #242 #209)
+#610 := (or #609 #606)
+#322 := (iff #610 #607)
+#597 := (or #609 #608)
+#320 := (iff #597 #607)
+#321 := [rewrite]: #320
+#304 := (iff #610 #597)
+#247 := (iff #606 #608)
+#284 := (iff #209 #611)
+#285 := [rewrite]: #284
+#248 := [monotonicity #285]: #247
+#319 := [monotonicity #248]: #304
+#215 := [trans #319 #321]: #322
+#596 := [quant-inst]: #610
+#592 := [mp #596 #215]: #607
+#539 := [unit-resolution #592 #643]: #608
+#536 := [unit-resolution #539 #547]: #611
+#618 := (not #611)
+#612 := (or #618 #617)
+#256 := (or #614 #618 #617)
+#294 := (not #209)
+#299 := (= #28 #298)
+#296 := (or #299 #294)
+#598 := (or #614 #296)
+#602 := (iff #598 #256)
+#261 := (or #614 #612)
+#600 := (iff #261 #256)
+#601 := [rewrite]: #600
+#262 := (iff #598 #261)
+#613 := (iff #296 #612)
+#621 := (or #617 #618)
+#271 := (iff #621 #612)
+#276 := [rewrite]: #271
+#616 := (iff #296 #621)
+#619 := (iff #294 #618)
+#620 := [monotonicity #285]: #619
+#273 := (iff #299 #617)
+#404 := [rewrite]: #273
+#622 := [monotonicity #404 #620]: #616
+#272 := [trans #622 #276]: #613
+#263 := [monotonicity #272]: #262
+#603 := [trans #263 #601]: #602
+#260 := [quant-inst]: #598
+#604 := [mp #260 #603]: #256
+#538 := [unit-resolution #604 #637]: #612
+#548 := [unit-resolution #538 #536]: #617
+#549 := (not #617)
+#550 := (or #549 #599)
+#546 := [th-lemma]: #550
+#551 := [unit-resolution #546 #548]: #599
+#605 := (>= #615 0::int)
+#540 := (or #549 #605)
+#541 := [th-lemma]: #540
+#542 := [unit-resolution #541 #548]: #605
+#562 := (<= #298 1::int)
+#543 := (or #458 #562)
+#537 := [th-lemma]: #543
+#544 := [unit-resolution #537 #456]: #562
+[th-lemma #460 #544 #542 #551]: false
+unsat
+9d1d66e0df5765d961ed3ab158bef74157ce58cb 227 0
+#2 := false
+#27 := 3::int
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#143 := (>= #26 3::int)
+#141 := (not #143)
+#33 := 7::int
+decl f3 :: (-> int S2)
+#29 := 2::int
+#30 := (* 2::int #26)
+#31 := (f3 #30)
+#32 := (f4 #31)
+#147 := (>= #32 7::int)
+#156 := (and #141 #147)
+#34 := (< #32 7::int)
+#35 := (not #34)
+#28 := (< #26 3::int)
+#36 := (and #28 #35)
+#157 := (iff #36 #156)
+#154 := (iff #35 #147)
+#145 := (not #147)
+#149 := (not #145)
+#152 := (iff #149 #147)
+#153 := [rewrite]: #152
+#150 := (iff #35 #149)
+#146 := (iff #34 #145)
+#148 := [rewrite]: #146
+#151 := [monotonicity #148]: #150
+#155 := [trans #151 #153]: #154
+#142 := (iff #28 #141)
+#144 := [rewrite]: #142
+#158 := [monotonicity #144 #155]: #157
+#138 := [asserted]: #36
+#159 := [mp #138 #158]: #156
+#160 := [and-elim #159]: #141
+#13 := 0::int
+#641 := -1::int
+#643 := (* -1::int #32)
+#299 := (+ #30 #643)
+#632 := (>= #299 0::int)
+#430 := (= #299 0::int)
+#311 := (>= #26 0::int)
+#634 := (= #32 0::int)
+#327 := (not #634)
+#331 := (<= #32 0::int)
+#333 := (not #331)
+#161 := [and-elim #159]: #147
+#334 := (or #333 #145)
+#612 := [th-lemma]: #334
+#613 := [unit-resolution #612 #161]: #333
+#610 := (or #327 #331)
+#614 := [th-lemma]: #610
+#611 := [unit-resolution #614 #613]: #327
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#657 := (pattern #16)
+#79 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#127 := (or #22 #79)
+#664 := (forall (vars (?v0 int)) (:pat #657) #127)
+#132 := (forall (vars (?v0 int)) #127)
+#667 := (iff #132 #664)
+#665 := (iff #127 #127)
+#666 := [refl]: #665
+#668 := [quant-intro #666]: #667
+#165 := (~ #132 #132)
+#179 := (~ #127 #127)
+#180 := [refl]: #179
+#166 := [nnf-pos #180]: #165
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#135 := (iff #24 #132)
+#98 := (= 0::int #17)
+#104 := (not #21)
+#105 := (or #104 #98)
+#110 := (forall (vars (?v0 int)) #105)
+#133 := (iff #110 #132)
+#130 := (iff #105 #127)
+#124 := (or #79 #22)
+#128 := (iff #124 #127)
+#129 := [rewrite]: #128
+#125 := (iff #105 #124)
+#122 := (iff #98 #22)
+#123 := [rewrite]: #122
+#120 := (iff #104 #79)
+#80 := (not #79)
+#115 := (not #80)
+#118 := (iff #115 #79)
+#119 := [rewrite]: #118
+#116 := (iff #104 #115)
+#113 := (iff #21 #80)
+#114 := [rewrite]: #113
+#117 := [monotonicity #114]: #116
+#121 := [trans #117 #119]: #120
+#126 := [monotonicity #121 #123]: #125
+#131 := [trans #126 #129]: #130
+#134 := [quant-intro #131]: #133
+#111 := (iff #24 #110)
+#108 := (iff #23 #105)
+#101 := (implies #21 #98)
+#106 := (iff #101 #105)
+#107 := [rewrite]: #106
+#102 := (iff #23 #101)
+#99 := (iff #22 #98)
+#100 := [rewrite]: #99
+#103 := [monotonicity #100]: #102
+#109 := [trans #103 #107]: #108
+#112 := [quant-intro #109]: #111
+#136 := [trans #112 #134]: #135
+#97 := [asserted]: #24
+#137 := [mp #97 #136]: #132
+#181 := [mp~ #137 #166]: #132
+#669 := [mp #181 #668]: #664
+#346 := (not #664)
+#347 := (or #346 #311 #634)
+#324 := (>= #30 0::int)
+#273 := (or #634 #324)
+#348 := (or #346 #273)
+#620 := (iff #348 #347)
+#636 := (or #311 #634)
+#618 := (or #346 #636)
+#342 := (iff #618 #347)
+#616 := [rewrite]: #342
+#619 := (iff #348 #618)
+#330 := (iff #273 #636)
+#274 := (or #634 #311)
+#622 := (iff #274 #636)
+#623 := [rewrite]: #622
+#635 := (iff #273 #274)
+#644 := (iff #324 #311)
+#645 := [rewrite]: #644
+#633 := [monotonicity #645]: #635
+#345 := [trans #633 #623]: #330
+#341 := [monotonicity #345]: #619
+#617 := [trans #341 #616]: #620
+#240 := [quant-inst]: #348
+#621 := [mp #240 #617]: #347
+#615 := [unit-resolution #621 #669 #611]: #311
+#646 := (not #311)
+#302 := (or #646 #430)
+#61 := (= #14 #17)
+#86 := (or #61 #80)
+#658 := (forall (vars (?v0 int)) (:pat #657) #86)
+#91 := (forall (vars (?v0 int)) #86)
+#661 := (iff #91 #658)
+#659 := (iff #86 #86)
+#660 := [refl]: #659
+#662 := [quant-intro #660]: #661
+#163 := (~ #91 #91)
+#139 := (~ #86 #86)
+#177 := [refl]: #139
+#164 := [nnf-pos #177]: #163
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#94 := (iff #20 #91)
+#68 := (not #15)
+#69 := (or #68 #61)
+#74 := (forall (vars (?v0 int)) #69)
+#92 := (iff #74 #91)
+#89 := (iff #69 #86)
+#83 := (or #80 #61)
+#87 := (iff #83 #86)
+#88 := [rewrite]: #87
+#84 := (iff #69 #83)
+#81 := (iff #68 #80)
+#77 := (iff #15 #79)
+#78 := [rewrite]: #77
+#82 := [monotonicity #78]: #81
+#85 := [monotonicity #82]: #84
+#90 := [trans #85 #88]: #89
+#93 := [quant-intro #90]: #92
+#75 := (iff #20 #74)
+#72 := (iff #19 #69)
+#65 := (implies #15 #61)
+#70 := (iff #65 #69)
+#71 := [rewrite]: #70
+#66 := (iff #19 #65)
+#63 := (iff #18 #61)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#73 := [trans #67 #71]: #72
+#76 := [quant-intro #73]: #75
+#95 := [trans #76 #93]: #94
+#60 := [asserted]: #20
+#96 := [mp #60 #95]: #91
+#178 := [mp~ #96 #164]: #91
+#663 := [mp #178 #662]: #658
+#624 := (not #658)
+#286 := (or #624 #646 #430)
+#252 := (not #324)
+#326 := (= #30 #32)
+#305 := (or #326 #252)
+#287 := (or #624 #305)
+#630 := (iff #287 #286)
+#289 := (or #624 #302)
+#628 := (iff #289 #286)
+#629 := [rewrite]: #628
+#626 := (iff #287 #289)
+#640 := (iff #305 #302)
+#648 := (or #430 #646)
+#639 := (iff #648 #302)
+#298 := [rewrite]: #639
+#638 := (iff #305 #648)
+#647 := (iff #252 #646)
+#642 := [monotonicity #645]: #647
+#637 := (iff #326 #430)
+#310 := [rewrite]: #637
+#297 := [monotonicity #310 #642]: #638
+#282 := [trans #297 #298]: #640
+#627 := [monotonicity #282]: #626
+#625 := [trans #627 #629]: #630
+#288 := [quant-inst]: #287
+#631 := [mp #288 #625]: #286
+#604 := [unit-resolution #631 #663]: #302
+#605 := [unit-resolution #604 #615]: #430
+#606 := (not #430)
+#601 := (or #606 #632)
+#602 := [th-lemma]: #601
+#607 := [unit-resolution #602 #605]: #632
+[th-lemma #161 #607 #160]: false
+unsat
[phone]e55d0af271f64ecf734a7a3a67096f 367 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#26 := f5
+#27 := (f4 f5)
+#474 := (= #27 0::int)
+decl f3 :: (-> int S2)
+#256 := (f3 #27)
+#562 := (f4 #256)
+#563 := (= #562 0::int)
+#561 := (>= #27 0::int)
+#482 := (not #561)
+#149 := -1::int
+#353 := (>= #27 -1::int)
+#633 := (not #353)
+#25 := 1::int
+#28 := (+ 1::int #27)
+#29 := (f3 #28)
+#30 := (f4 #29)
+#640 := (* -1::int #30)
+#637 := (+ #27 #640)
+#641 := (= #637 -1::int)
+#476 := (not #641)
+#611 := (<= #637 -1::int)
+#532 := (not #611)
+#150 := (* -1::int #27)
+#151 := (+ #150 #30)
+#154 := (f3 #151)
+#157 := (f4 #154)
+#509 := (+ #640 #157)
+#510 := (+ #27 #509)
+#578 := (>= #510 0::int)
+#507 := (= #510 0::int)
+#600 := (<= #637 0::int)
+#531 := [hypothesis]: #611
+#519 := (or #532 #600)
+#520 := [th-lemma]: #519
+#515 := [unit-resolution #520 #531]: #600
+#593 := (not #600)
+#584 := (or #507 #593)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#677 := (pattern #16)
+#81 := (>= #14 0::int)
+#82 := (not #81)
+#17 := (f4 #16)
+#63 := (= #14 #17)
+#88 := (or #63 #82)
+#678 := (forall (vars (?v0 int)) (:pat #677) #88)
+#93 := (forall (vars (?v0 int)) #88)
+#681 := (iff #93 #678)
+#679 := (iff #88 #88)
+#680 := [refl]: #679
+#682 := [quant-intro #680]: #681
+#185 := (~ #93 #93)
+#182 := (~ #88 #88)
+#197 := [refl]: #182
+#186 := [nnf-pos #197]: #185
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#96 := (iff #20 #93)
+#70 := (not #15)
+#71 := (or #70 #63)
+#76 := (forall (vars (?v0 int)) #71)
+#94 := (iff #76 #93)
+#91 := (iff #71 #88)
+#85 := (or #82 #63)
+#89 := (iff #85 #88)
+#90 := [rewrite]: #89
+#86 := (iff #71 #85)
+#83 := (iff #70 #82)
+#79 := (iff #15 #81)
+#80 := [rewrite]: #79
+#84 := [monotonicity #80]: #83
+#87 := [monotonicity #84]: #86
+#92 := [trans #87 #90]: #91
+#95 := [quant-intro #92]: #94
+#77 := (iff #20 #76)
+#74 := (iff #19 #71)
+#67 := (implies #15 #63)
+#72 := (iff #67 #71)
+#73 := [rewrite]: #72
+#68 := (iff #19 #67)
+#65 := (iff #18 #63)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#75 := [trans #69 #73]: #74
+#78 := [quant-intro #75]: #77
+#97 := [trans #78 #95]: #96
+#62 := [asserted]: #20
+#98 := [mp #62 #97]: #93
+#198 := [mp~ #98 #186]: #93
+#683 := [mp #198 #682]: #678
+#649 := (not #678)
+#596 := (or #649 #507 #593)
+#504 := (>= #151 0::int)
+#505 := (not #504)
+#498 := (= #151 #157)
+#506 := (or #498 #505)
+#592 := (or #649 #506)
+#590 := (iff #592 #596)
+#586 := (or #649 #584)
+#589 := (iff #586 #596)
+#583 := [rewrite]: #589
+#587 := (iff #592 #586)
+#594 := (iff #506 #584)
+#585 := (iff #505 #593)
+#604 := (iff #504 #600)
+#591 := [rewrite]: #604
+#582 := [monotonicity #591]: #585
+#508 := (iff #498 #507)
+#603 := [rewrite]: #508
+#595 := [monotonicity #603 #582]: #594
+#588 := [monotonicity #595]: #587
+#574 := [trans #588 #583]: #590
+#597 := [quant-inst]: #592
+#575 := [mp #597 #574]: #596
+#521 := [unit-resolution #575 #683]: #584
+#489 := [unit-resolution #521 #515]: #507
+#496 := (not #507)
+#455 := (or #496 #578)
+#486 := [th-lemma]: #455
+#488 := [unit-resolution #486 #489]: #578
+#559 := (<= #157 0::int)
+#168 := (* -1::int #157)
+#143 := (f3 0::int)
+#146 := (f4 #143)
+#169 := (+ #146 #168)
+#167 := (>= #169 0::int)
+#34 := (- #30 #27)
+#35 := (f3 #34)
+#36 := (f4 #35)
+#31 := (* 0::int #30)
+#32 := (f3 #31)
+#33 := (f4 #32)
+#37 := (< #33 #36)
+#38 := (not #37)
+#179 := (iff #38 #167)
+#160 := (< #146 #157)
+#163 := (not #160)
+#177 := (iff #163 #167)
+#166 := (not #167)
+#172 := (not #166)
+#175 := (iff #172 #167)
+#176 := [rewrite]: #175
+#173 := (iff #163 #172)
+#170 := (iff #160 #166)
+#171 := [rewrite]: #170
+#174 := [monotonicity #171]: #173
+#178 := [trans #174 #176]: #177
+#164 := (iff #38 #163)
+#161 := (iff #37 #160)
+#158 := (= #36 #157)
+#155 := (= #35 #154)
+#152 := (= #34 #151)
+#153 := [rewrite]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#147 := (= #33 #146)
+#144 := (= #32 #143)
+#141 := (= #31 0::int)
+#142 := [rewrite]: #141
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#162 := [monotonicity #148 #159]: #161
+#165 := [monotonicity #162]: #164
+#180 := [trans #165 #178]: #179
+#140 := [asserted]: #38
+#181 := [mp #140 #180]: #167
+#653 := (<= #146 0::int)
+#667 := (= #146 0::int)
+#650 := (or #649 #667)
+#450 := (>= 0::int 0::int)
+#657 := (not #450)
+#664 := (= 0::int #146)
+#665 := (or #664 #657)
+#645 := (or #649 #665)
+#289 := (iff #645 #650)
+#654 := (iff #650 #650)
+#294 := [rewrite]: #654
+#647 := (iff #665 #667)
+#307 := (or #667 false)
+#310 := (iff #307 #667)
+#646 := [rewrite]: #310
+#308 := (iff #665 #307)
+#303 := (iff #657 false)
+#1 := true
+#318 := (not true)
+#319 := (iff #318 false)
+#660 := [rewrite]: #319
+#323 := (iff #657 #318)
+#668 := (iff #450 true)
+#658 := [rewrite]: #668
+#659 := [monotonicity #658]: #323
+#644 := [trans #659 #660]: #303
+#666 := (iff #664 #667)
+#662 := [rewrite]: #666
+#309 := [monotonicity #662 #644]: #308
+#648 := [trans #309 #646]: #647
+#652 := [monotonicity #648]: #289
+#295 := [trans #652 #294]: #289
+#651 := [quant-inst]: #645
+#655 := [mp #651 #295]: #650
+#490 := [unit-resolution #655 #683]: #667
+#497 := (not #667)
+#499 := (or #497 #653)
+#500 := [th-lemma]: #499
+#501 := [unit-resolution #500 #490]: #653
+#511 := (not #653)
+#491 := (or #559 #511 #166)
+#512 := [th-lemma]: #491
+#467 := [unit-resolution #512 #501 #181]: #559
+#468 := [th-lemma #467 #531 #488]: false
+#473 := [lemma #468]: #532
+#477 := (or #476 #611)
+#478 := [th-lemma]: #477
+#479 := [unit-resolution #478 #473]: #476
+#624 := (or #633 #641)
+#627 := (or #649 #633 #641)
+#639 := (>= #28 0::int)
+#361 := (not #639)
+#362 := (= #28 #30)
+#636 := (or #362 #361)
+#628 := (or #649 #636)
+#615 := (iff #628 #627)
+#629 := (or #649 #624)
+#472 := (iff #629 #627)
+#614 := [rewrite]: #472
+#470 := (iff #628 #629)
+#621 := (iff #636 #624)
+#634 := (or #641 #633)
+#625 := (iff #634 #624)
+#626 := [rewrite]: #625
+#631 := (iff #636 #634)
+#348 := (iff #361 #633)
+#354 := (iff #639 #353)
+#632 := [rewrite]: #354
+#630 := [monotonicity #632]: #348
+#351 := (iff #362 #641)
+#352 := [rewrite]: #351
+#635 := [monotonicity #352 #630]: #631
+#622 := [trans #635 #626]: #621
+#471 := [monotonicity #622]: #470
+#616 := [trans #471 #614]: #615
+#623 := [quant-inst]: #628
+#617 := [mp #623 #616]: #627
+#480 := [unit-resolution #617 #683]: #624
+#481 := [unit-resolution #480 #479]: #633
+#483 := (or #482 #353)
+#484 := [th-lemma]: #483
+#469 := [unit-resolution #484 #481]: #482
+#565 := (or #561 #563)
+#22 := (= #17 0::int)
+#129 := (or #22 #81)
+#684 := (forall (vars (?v0 int)) (:pat #677) #129)
+#134 := (forall (vars (?v0 int)) #129)
+#687 := (iff #134 #684)
+#685 := (iff #129 #129)
+#686 := [refl]: #685
+#688 := [quant-intro #686]: #687
+#187 := (~ #134 #134)
+#199 := (~ #129 #129)
+#200 := [refl]: #199
+#188 := [nnf-pos #200]: #187
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#137 := (iff #24 #134)
+#100 := (= 0::int #17)
+#106 := (not #21)
+#107 := (or #106 #100)
+#112 := (forall (vars (?v0 int)) #107)
+#135 := (iff #112 #134)
+#132 := (iff #107 #129)
+#126 := (or #81 #22)
+#130 := (iff #126 #129)
+#131 := [rewrite]: #130
+#127 := (iff #107 #126)
+#124 := (iff #100 #22)
+#125 := [rewrite]: #124
+#122 := (iff #106 #81)
+#117 := (not #82)
+#120 := (iff #117 #81)
+#121 := [rewrite]: #120
+#118 := (iff #106 #117)
+#115 := (iff #21 #82)
+#116 := [rewrite]: #115
+#119 := [monotonicity #116]: #118
+#123 := [trans #119 #121]: #122
+#128 := [monotonicity #123 #125]: #127
+#133 := [trans #128 #131]: #132
+#136 := [quant-intro #133]: #135
+#113 := (iff #24 #112)
+#110 := (iff #23 #107)
+#103 := (implies #21 #100)
+#108 := (iff #103 #107)
+#109 := [rewrite]: #108
+#104 := (iff #23 #103)
+#101 := (iff #22 #100)
+#102 := [rewrite]: #101
+#105 := [monotonicity #102]: #104
+#111 := [trans #105 #109]: #110
+#114 := [quant-intro #111]: #113
+#138 := [trans #114 #136]: #137
+#99 := [asserted]: #24
+#139 := [mp #99 #138]: #134
+#201 := [mp~ #139 #188]: #134
+#689 := [mp #201 #688]: #684
+#609 := (not #684)
+#544 := (or #609 #561 #563)
+#564 := (or #563 #561)
+#545 := (or #609 #564)
+#552 := (iff #545 #544)
+#548 := (or #609 #565)
+#551 := (iff #548 #544)
+#546 := [rewrite]: #551
+#549 := (iff #545 #548)
+#555 := (iff #564 #565)
+#566 := [rewrite]: #555
+#550 := [monotonicity #566]: #549
+#538 := [trans #550 #546]: #552
+#547 := [quant-inst]: #545
+#534 := [mp #547 #538]: #544
+#485 := [unit-resolution #534 #689]: #565
+#446 := [unit-resolution #485 #469]: #563
+#454 := (= #27 #562)
+#341 := (= f5 #256)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#669 := (pattern #9)
+#10 := (f3 #9)
+#56 := (= #8 #10)
+#670 := (forall (vars (?v0 S2)) (:pat #669) #56)
+#59 := (forall (vars (?v0 S2)) #56)
+#671 := (iff #59 #670)
+#673 := (iff #670 #670)
+#674 := [rewrite]: #673
+#672 := [rewrite]: #671
+#675 := [trans #672 #674]: #671
+#195 := (~ #59 #59)
+#193 := (~ #56 #56)
+#194 := [refl]: #193
+#196 := [nnf-pos #194]: #195
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#60 := (iff #12 #59)
+#57 := (iff #11 #56)
+#58 := [rewrite]: #57
+#61 := [quant-intro #58]: #60
+#55 := [asserted]: #12
+#64 := [mp #55 #61]: #59
+#184 := [mp~ #64 #196]: #59
+#676 := [mp #184 #675]: #670
+#342 := (not #670)
+#343 := (or #342 #341)
+#347 := [quant-inst]: #343
+#447 := [unit-resolution #347 #676]: #341
+#456 := [monotonicity #447]: #454
+#457 := [trans #456 #446]: #474
+#458 := (not #474)
+#460 := (or #458 #561)
+#461 := [th-lemma]: #460
+[unit-resolution #461 #469 #457]: false
+unsat
+2056c3e4e6f79f7bbfaba7f2ae00b9799e9f43ff 299 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f3 :: (-> int S2)
+decl f5 :: S2
+#26 := f5
+#27 := (f4 f5)
+#25 := 1::int
+#28 := (+ 1::int #27)
+#29 := (f3 #28)
+#30 := (f4 #29)
+#140 := -1::int
+#141 := (+ -1::int #30)
+#144 := (f3 #141)
+#291 := (f4 #144)
+#676 := (* -1::int #291)
+#540 := (+ #27 #676)
+#534 := (>= #540 0::int)
+#538 := (= #27 #291)
+#150 := (= f5 #144)
+#169 := (<= #30 0::int)
+#170 := (not #169)
+#176 := (iff #150 #170)
+#191 := (not #176)
+#224 := (iff #191 #150)
+#214 := (not #150)
+#219 := (not #214)
+#222 := (iff #219 #150)
+#223 := [rewrite]: #222
+#220 := (iff #191 #219)
+#217 := (iff #176 #214)
+#211 := (iff #150 false)
+#215 := (iff #211 #214)
+#216 := [rewrite]: #215
+#212 := (iff #176 #211)
+#209 := (iff #170 false)
+#1 := true
+#204 := (not true)
+#207 := (iff #204 false)
+#208 := [rewrite]: #207
+#205 := (iff #170 #204)
+#202 := (iff #169 true)
+#181 := (or #170 #176)
+#184 := (not #181)
+#31 := (< 0::int #30)
+#32 := (- #30 1::int)
+#33 := (f3 #32)
+#34 := (= #33 f5)
+#35 := (iff #31 #34)
+#36 := (or #35 #31)
+#37 := (not #36)
+#187 := (iff #37 #184)
+#155 := (iff #31 #150)
+#161 := (or #31 #155)
+#166 := (not #161)
+#185 := (iff #166 #184)
+#182 := (iff #161 #181)
+#179 := (iff #155 #176)
+#173 := (iff #170 #150)
+#177 := (iff #173 #176)
+#178 := [rewrite]: #177
+#174 := (iff #155 #173)
+#171 := (iff #31 #170)
+#172 := [rewrite]: #171
+#175 := [monotonicity #172]: #174
+#180 := [trans #175 #178]: #179
+#183 := [monotonicity #172 #180]: #182
+#186 := [monotonicity #183]: #185
+#167 := (iff #37 #166)
+#164 := (iff #36 #161)
+#158 := (or #155 #31)
+#162 := (iff #158 #161)
+#163 := [rewrite]: #162
+#159 := (iff #36 #158)
+#156 := (iff #35 #155)
+#153 := (iff #34 #150)
+#147 := (= #144 f5)
+#151 := (iff #147 #150)
+#152 := [rewrite]: #151
+#148 := (iff #34 #147)
+#145 := (= #33 #144)
+#142 := (= #32 #141)
+#143 := [rewrite]: #142
+#146 := [monotonicity #143]: #145
+#149 := [monotonicity #146]: #148
+#154 := [trans #149 #152]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#165 := [trans #160 #163]: #164
+#168 := [monotonicity #165]: #167
+#188 := [trans #168 #186]: #187
+#139 := [asserted]: #37
+#189 := [mp #139 #188]: #184
+#190 := [not-or-elim #189]: #169
+#203 := [iff-true #190]: #202
+#206 := [monotonicity #203]: #205
+#210 := [trans #206 #208]: #209
+#213 := [monotonicity #210]: #212
+#218 := [trans #213 #216]: #217
+#221 := [monotonicity #218]: #220
+#225 := [trans #221 #223]: #224
+#192 := [not-or-elim #189]: #191
+#226 := [mp #192 #225]: #150
+#545 := [monotonicity #226]: #538
+#546 := (not #538)
+#618 := (or #546 #534)
+#620 := [th-lemma]: #618
+#630 := [unit-resolution #620 #545]: #534
+#356 := (* -1::int #30)
+#486 := (+ #27 #356)
+#685 := (<= #486 -1::int)
+#693 := (= #486 -1::int)
+#700 := (>= #27 -1::int)
+#523 := (>= #291 0::int)
+#654 := (= #291 0::int)
+#389 := (>= #30 1::int)
+#669 := (not #389)
+#631 := (or #669 #170)
+#632 := [th-lemma]: #631
+#628 := [unit-resolution #632 #190]: #669
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#713 := (pattern #16)
+#80 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#128 := (or #22 #80)
+#720 := (forall (vars (?v0 int)) (:pat #713) #128)
+#133 := (forall (vars (?v0 int)) #128)
+#723 := (iff #133 #720)
+#721 := (iff #128 #128)
+#722 := [refl]: #721
+#724 := [quant-intro #722]: #723
+#231 := (~ #133 #133)
+#229 := (~ #128 #128)
+#230 := [refl]: #229
+#232 := [nnf-pos #230]: #231
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#136 := (iff #24 #133)
+#99 := (= 0::int #17)
+#105 := (not #21)
+#106 := (or #105 #99)
+#111 := (forall (vars (?v0 int)) #106)
+#134 := (iff #111 #133)
+#131 := (iff #106 #128)
+#125 := (or #80 #22)
+#129 := (iff #125 #128)
+#130 := [rewrite]: #129
+#126 := (iff #106 #125)
+#123 := (iff #99 #22)
+#124 := [rewrite]: #123
+#121 := (iff #105 #80)
+#81 := (not #80)
+#116 := (not #81)
+#119 := (iff #116 #80)
+#120 := [rewrite]: #119
+#117 := (iff #105 #116)
+#114 := (iff #21 #81)
+#115 := [rewrite]: #114
+#118 := [monotonicity #115]: #117
+#122 := [trans #118 #120]: #121
+#127 := [monotonicity #122 #124]: #126
+#132 := [trans #127 #130]: #131
+#135 := [quant-intro #132]: #134
+#112 := (iff #24 #111)
+#109 := (iff #23 #106)
+#102 := (implies #21 #99)
+#107 := (iff #102 #106)
+#108 := [rewrite]: #107
+#103 := (iff #23 #102)
+#100 := (iff #22 #99)
+#101 := [rewrite]: #100
+#104 := [monotonicity #101]: #103
+#110 := [trans #104 #108]: #109
+#113 := [quant-intro #110]: #112
+#137 := [trans #113 #135]: #136
+#98 := [asserted]: #24
+#138 := [mp #98 #137]: #133
+#233 := [mp~ #138 #232]: #133
+#725 := [mp #233 #724]: #720
+#330 := (not #720)
+#645 := (or #330 #389 #654)
+#675 := (>= #141 0::int)
+#655 := (or #654 #675)
+#643 := (or #330 #655)
+#539 := (iff #643 #645)
+#487 := (or #389 #654)
+#528 := (or #330 #487)
+#489 := (iff #528 #645)
+#637 := [rewrite]: #489
+#529 := (iff #643 #528)
+#642 := (iff #655 #487)
+#649 := (or #654 #389)
+#488 := (iff #649 #487)
+#641 := [rewrite]: #488
+#656 := (iff #655 #649)
+#390 := (iff #675 #389)
+#668 := [rewrite]: #390
+#485 := [monotonicity #668]: #656
+#644 := [trans #485 #641]: #642
+#530 := [monotonicity #644]: #529
+#634 := [trans #530 #637]: #539
+#646 := [quant-inst]: #643
+#635 := [mp #646 #634]: #645
+#633 := [unit-resolution #635 #725 #628]: #654
+#622 := (not #654)
+#623 := (or #622 #523)
+#624 := [th-lemma]: #623
+#625 := [unit-resolution #624 #633]: #523
+#626 := (not #534)
+#619 := (not #523)
+#610 := (or #700 #619 #626)
+#611 := [th-lemma]: #610
+#613 := [unit-resolution #611 #625 #630]: #700
+#703 := (not #700)
+#694 := (or #693 #703)
+#62 := (= #14 #17)
+#87 := (or #62 #81)
+#714 := (forall (vars (?v0 int)) (:pat #713) #87)
+#92 := (forall (vars (?v0 int)) #87)
+#717 := (iff #92 #714)
+#715 := (iff #87 #87)
+#716 := [refl]: #715
+#718 := [quant-intro #716]: #717
+#197 := (~ #92 #92)
+#199 := (~ #87 #87)
+#196 := [refl]: #199
+#195 := [nnf-pos #196]: #197
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#95 := (iff #20 #92)
+#69 := (not #15)
+#70 := (or #69 #62)
+#75 := (forall (vars (?v0 int)) #70)
+#93 := (iff #75 #92)
+#90 := (iff #70 #87)
+#84 := (or #81 #62)
+#88 := (iff #84 #87)
+#89 := [rewrite]: #88
+#85 := (iff #70 #84)
+#82 := (iff #69 #81)
+#78 := (iff #15 #80)
+#79 := [rewrite]: #78
+#83 := [monotonicity #79]: #82
+#86 := [monotonicity #83]: #85
+#91 := [trans #86 #89]: #90
+#94 := [quant-intro #91]: #93
+#76 := (iff #20 #75)
+#73 := (iff #19 #70)
+#66 := (implies #15 #62)
+#71 := (iff #66 #70)
+#72 := [rewrite]: #71
+#67 := (iff #19 #66)
+#64 := (iff #18 #62)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#74 := [trans #68 #72]: #73
+#77 := [quant-intro #74]: #76
+#96 := [trans #77 #94]: #95
+#61 := [asserted]: #20
+#97 := [mp #61 #96]: #92
+#193 := [mp~ #97 #195]: #92
+#719 := [mp #193 #718]: #714
+#695 := (not #714)
+#355 := (or #695 #693 #703)
+#382 := (>= #28 0::int)
+#379 := (not #382)
+#697 := (= #28 #30)
+#699 := (or #697 #379)
+#696 := (or #695 #699)
+#682 := (iff #696 #355)
+#680 := (or #695 #694)
+#345 := (iff #680 #355)
+#346 := [rewrite]: #345
+#343 := (iff #696 #680)
+#354 := (iff #699 #694)
+#698 := (iff #379 #703)
+#701 := (iff #382 #700)
+#702 := [rewrite]: #701
+#704 := [monotonicity #702]: #698
+#367 := (iff #697 #693)
+#368 := [rewrite]: #367
+#359 := [monotonicity #368 #704]: #354
+#344 := [monotonicity #359]: #343
+#683 := [trans #344 #346]: #682
+#339 := [quant-inst]: #696
+#684 := [mp #339 #683]: #355
+#614 := [unit-resolution #684 #719]: #694
+#615 := [unit-resolution #614 #613]: #693
+#616 := (not #693)
+#612 := (or #616 #685)
+#617 := [th-lemma]: #612
+#603 := [unit-resolution #617 #615]: #685
+[th-lemma #625 #190 #603 #630]: false
+unsat
+17614b8b1cec9a80dfb452576f370f5b26f06458 458 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f3 :: (-> int S2)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#27 := 1::int
+#143 := (+ 1::int #26)
+#146 := (f3 #143)
+#302 := (f4 #146)
+#362 := (= #302 0::int)
+#171 := (f3 0::int)
+#536 := (f4 #171)
+#542 := (= #536 0::int)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#677 := (pattern #16)
+#83 := (>= #14 0::int)
+#84 := (not #83)
+#17 := (f4 #16)
+#65 := (= #14 #17)
+#90 := (or #65 #84)
+#678 := (forall (vars (?v0 int)) (:pat #677) #90)
+#95 := (forall (vars (?v0 int)) #90)
+#681 := (iff #95 #678)
+#679 := (iff #90 #90)
+#680 := [refl]: #679
+#682 := [quant-intro #680]: #681
+#184 := (~ #95 #95)
+#180 := (~ #90 #90)
+#196 := [refl]: #180
+#185 := [nnf-pos #196]: #184
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#98 := (iff #20 #95)
+#72 := (not #15)
+#73 := (or #72 #65)
+#78 := (forall (vars (?v0 int)) #73)
+#96 := (iff #78 #95)
+#93 := (iff #73 #90)
+#87 := (or #84 #65)
+#91 := (iff #87 #90)
+#92 := [rewrite]: #91
+#88 := (iff #73 #87)
+#85 := (iff #72 #84)
+#81 := (iff #15 #83)
+#82 := [rewrite]: #81
+#86 := [monotonicity #82]: #85
+#89 := [monotonicity #86]: #88
+#94 := [trans #89 #92]: #93
+#97 := [quant-intro #94]: #96
+#79 := (iff #20 #78)
+#76 := (iff #19 #73)
+#69 := (implies #15 #65)
+#74 := (iff #69 #73)
+#75 := [rewrite]: #74
+#70 := (iff #19 #69)
+#67 := (iff #18 #65)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#77 := [trans #71 #75]: #76
+#80 := [quant-intro #77]: #79
+#99 := [trans #80 #97]: #98
+#64 := [asserted]: #20
+#100 := [mp #64 #99]: #95
+#197 := [mp~ #100 #185]: #95
+#683 := [mp #197 #682]: #678
+#655 := (not #678)
+#533 := (or #655 #542)
+#534 := (>= 0::int 0::int)
+#535 := (not #534)
+#539 := (= 0::int #536)
+#540 := (or #539 #535)
+#513 := (or #655 #540)
+#514 := (iff #513 #533)
+#519 := (iff #533 #533)
+#520 := [rewrite]: #519
+#532 := (iff #540 #542)
+#525 := (or #542 false)
+#530 := (iff #525 #542)
+#531 := [rewrite]: #530
+#526 := (iff #540 #525)
+#524 := (iff #535 false)
+#1 := true
+#517 := (not true)
+#522 := (iff #517 false)
+#523 := [rewrite]: #522
+#518 := (iff #535 #517)
+#543 := (iff #534 true)
+#516 := [rewrite]: #543
+#411 := [monotonicity #516]: #518
+#529 := [trans #411 #523]: #524
+#541 := (iff #539 #542)
+#537 := [rewrite]: #541
+#527 := [monotonicity #537 #529]: #526
+#528 := [trans #527 #531]: #532
+#495 := [monotonicity #528]: #514
+#515 := [trans #495 #520]: #514
+#459 := [quant-inst]: #513
+#521 := [mp #459 #515]: #533
+#399 := [unit-resolution #521 #683]: #542
+#360 := (= #302 #536)
+#255 := (= #146 #171)
+#30 := 2::int
+#149 := (* 2::int #26)
+#152 := (f3 #149)
+#155 := (f4 #152)
+#34 := 3::int
+#161 := (+ 3::int #155)
+#166 := (f3 #161)
+#341 := (= #166 #171)
+#332 := (not #341)
+#593 := (f4 #166)
+#560 := (= #593 0::int)
+#403 := (= #593 #536)
+#400 := [hypothesis]: #341
+#392 := [monotonicity #400]: #403
+#404 := [trans #392 #399]: #560
+#395 := (not #560)
+#552 := (<= #593 0::int)
+#408 := (not #552)
+#600 := (>= #155 0::int)
+#307 := -1::int
+#623 := (* -1::int #155)
+#629 := (+ #149 #623)
+#493 := (<= #629 0::int)
+#470 := (= #629 0::int)
+#614 := (>= #26 0::int)
+#447 := (= #26 0::int)
+#665 := (f3 #26)
+#500 := (f4 #665)
+#501 := (= #500 0::int)
+#617 := (not #614)
+#456 := [hypothesis]: #617
+#511 := (or #501 #614)
+#22 := (= #17 0::int)
+#131 := (or #22 #83)
+#684 := (forall (vars (?v0 int)) (:pat #677) #131)
+#136 := (forall (vars (?v0 int)) #131)
+#687 := (iff #136 #684)
+#685 := (iff #131 #131)
+#686 := [refl]: #685
+#688 := [quant-intro #686]: #687
+#186 := (~ #136 #136)
+#198 := (~ #131 #131)
+#199 := [refl]: #198
+#187 := [nnf-pos #199]: #186
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#139 := (iff #24 #136)
+#102 := (= 0::int #17)
+#108 := (not #21)
+#109 := (or #108 #102)
+#114 := (forall (vars (?v0 int)) #109)
+#137 := (iff #114 #136)
+#134 := (iff #109 #131)
+#128 := (or #83 #22)
+#132 := (iff #128 #131)
+#133 := [rewrite]: #132
+#129 := (iff #109 #128)
+#126 := (iff #102 #22)
+#127 := [rewrite]: #126
+#124 := (iff #108 #83)
+#119 := (not #84)
+#122 := (iff #119 #83)
+#123 := [rewrite]: #122
+#120 := (iff #108 #119)
+#117 := (iff #21 #84)
+#118 := [rewrite]: #117
+#121 := [monotonicity #118]: #120
+#125 := [trans #121 #123]: #124
+#130 := [monotonicity #125 #127]: #129
+#135 := [trans #130 #133]: #134
+#138 := [quant-intro #135]: #137
+#115 := (iff #24 #114)
+#112 := (iff #23 #109)
+#105 := (implies #21 #102)
+#110 := (iff #105 #109)
+#111 := [rewrite]: #110
+#106 := (iff #23 #105)
+#103 := (iff #22 #102)
+#104 := [rewrite]: #103
+#107 := [monotonicity #104]: #106
+#113 := [trans #107 #111]: #112
+#116 := [quant-intro #113]: #115
+#140 := [trans #116 #138]: #139
+#101 := [asserted]: #24
+#141 := [mp #101 #140]: #136
+#200 := [mp~ #141 #187]: #136
+#689 := [mp #200 #688]: #684
+#351 := (not #684)
+#467 := (or #351 #501 #614)
+#468 := (or #351 #511)
+#474 := (iff #468 #467)
+#475 := [rewrite]: #474
+#473 := [quant-inst]: #468
+#476 := [mp #473 #475]: #467
+#457 := [unit-resolution #476 #689]: #511
+#458 := [unit-resolution #457 #456]: #501
+#461 := (= #26 #500)
+#666 := (= f5 #665)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#669 := (pattern #9)
+#10 := (f3 #9)
+#58 := (= #8 #10)
+#670 := (forall (vars (?v0 S2)) (:pat #669) #58)
+#61 := (forall (vars (?v0 S2)) #58)
+#671 := (iff #61 #670)
+#673 := (iff #670 #670)
+#674 := [rewrite]: #673
+#672 := [rewrite]: #671
+#675 := [trans #672 #674]: #671
+#194 := (~ #61 #61)
+#192 := (~ #58 #58)
+#193 := [refl]: #192
+#195 := [nnf-pos #193]: #194
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#62 := (iff #12 #61)
+#59 := (iff #11 #58)
+#60 := [rewrite]: #59
+#63 := [quant-intro #60]: #62
+#57 := [asserted]: #12
+#66 := [mp #57 #63]: #61
+#183 := [mp~ #66 #195]: #61
+#676 := [mp #183 #675]: #670
+#668 := (not #670)
+#658 := (or #668 #666)
+#317 := [quant-inst]: #658
+#460 := [unit-resolution #317 #676]: #666
+#462 := [monotonicity #460]: #461
+#463 := [trans #462 #458]: #447
+#464 := (not #447)
+#465 := (or #464 #614)
+#448 := [th-lemma]: #465
+#466 := [unit-resolution #448 #456 #463]: false
+#436 := [lemma #466]: #614
+#618 := (or #470 #617)
+#620 := (or #655 #470 #617)
+#621 := (>= #149 0::int)
+#622 := (not #621)
+#627 := (= #149 #155)
+#628 := (or #627 #622)
+#449 := (or #655 #628)
+#607 := (iff #449 #620)
+#452 := (or #655 #618)
+#608 := (iff #452 #620)
+#609 := [rewrite]: #608
+#605 := (iff #449 #452)
+#619 := (iff #628 #618)
+#611 := (iff #622 #617)
+#615 := (iff #621 #614)
+#616 := [rewrite]: #615
+#612 := [monotonicity #616]: #611
+#471 := (iff #627 #470)
+#472 := [rewrite]: #471
+#613 := [monotonicity #472 #612]: #619
+#606 := [monotonicity #613]: #605
+#610 := [trans #606 #609]: #607
+#451 := [quant-inst]: #449
+#492 := [mp #451 #610]: #620
+#444 := [unit-resolution #492 #683]: #618
+#440 := [unit-resolution #444 #436]: #470
+#445 := (not #470)
+#424 := (or #445 #493)
+#427 := [th-lemma]: #424
+#431 := [unit-resolution #427 #440]: #493
+#435 := (not #493)
+#438 := (or #600 #617 #435)
+#443 := [th-lemma]: #438
+#407 := [unit-resolution #443 #436 #431]: #600
+#595 := -3::int
+#584 := (* -1::int #593)
+#594 := (+ #155 #584)
+#558 := (<= #594 -3::int)
+#596 := (= #594 -3::int)
+#586 := (>= #155 -3::int)
+#649 := (>= #26 -1::int)
+#433 := (or #617 #649)
+#434 := [th-lemma]: #433
+#432 := [unit-resolution #434 #436]: #649
+#651 := (not #649)
+#423 := (or #586 #651 #435)
+#426 := [th-lemma]: #423
+#428 := [unit-resolution #426 #431 #432]: #586
+#589 := (not #586)
+#578 := (or #589 #596)
+#567 := (or #655 #589 #596)
+#604 := (>= #161 0::int)
+#591 := (not #604)
+#585 := (= #161 #593)
+#582 := (or #585 #591)
+#568 := (or #655 #582)
+#554 := (iff #568 #567)
+#571 := (or #655 #578)
+#573 := (iff #571 #567)
+#553 := [rewrite]: #573
+#572 := (iff #568 #571)
+#576 := (iff #582 #578)
+#574 := (or #596 #589)
+#579 := (iff #574 #578)
+#580 := [rewrite]: #579
+#575 := (iff #582 #574)
+#583 := (iff #591 #589)
+#587 := (iff #604 #586)
+#588 := [rewrite]: #587
+#590 := [monotonicity #588]: #583
+#592 := (iff #585 #596)
+#597 := [rewrite]: #592
+#577 := [monotonicity #597 #590]: #575
+#581 := [trans #577 #580]: #576
+#569 := [monotonicity #581]: #572
+#556 := [trans #569 #553]: #554
+#570 := [quant-inst]: #568
+#557 := [mp #570 #556]: #567
+#429 := [unit-resolution #557 #683]: #578
+#425 := [unit-resolution #429 #428]: #596
+#430 := (not #596)
+#420 := (or #430 #558)
+#410 := [th-lemma]: #420
+#412 := [unit-resolution #410 #425]: #558
+#409 := (not #558)
+#406 := (not #600)
+#391 := (or #408 #406 #409)
+#393 := [th-lemma]: #391
+#394 := [unit-resolution #393 #412 #407]: #408
+#396 := (or #395 #552)
+#397 := [th-lemma]: #396
+#398 := [unit-resolution #397 #394]: #395
+#381 := [unit-resolution #398 #404]: false
+#383 := [lemma #381]: #332
+#254 := (= #146 #166)
+#339 := (not #254)
+#401 := (= #302 #593)
+#390 := [hypothesis]: #254
+#375 := [monotonicity #390]: #401
+#385 := (not #401)
+#439 := (+ #302 #584)
+#285 := (>= #439 0::int)
+#419 := (not #285)
+#308 := (* -1::int #302)
+#309 := (+ #26 #308)
+#361 := (>= #309 -1::int)
+#646 := (= #309 -1::int)
+#654 := (or #646 #651)
+#653 := (or #655 #646 #651)
+#322 := (>= #143 0::int)
+#659 := (not #322)
+#644 := (= #143 #302)
+#306 := (or #644 #659)
+#656 := (or #655 #306)
+#368 := (iff #656 #653)
+#643 := (or #655 #654)
+#366 := (iff #643 #653)
+#367 := [rewrite]: #366
+#350 := (iff #656 #643)
+#293 := (iff #306 #654)
+#288 := (iff #659 #651)
+#650 := (iff #322 #649)
+#645 := [rewrite]: #650
+#652 := [monotonicity #645]: #288
+#647 := (iff #644 #646)
+#648 := [rewrite]: #647
+#294 := [monotonicity #648 #652]: #293
+#365 := [monotonicity #294]: #350
+#261 := [trans #365 #367]: #368
+#642 := [quant-inst]: #656
+#638 := [mp #642 #261]: #653
+#413 := [unit-resolution #638 #683]: #654
+#416 := [unit-resolution #413 #432]: #646
+#417 := (not #646)
+#421 := (or #417 #361)
+#414 := [th-lemma]: #421
+#422 := [unit-resolution #414 #416]: #361
+#415 := [hypothesis]: #285
+#418 := [th-lemma #428 #415 #422 #412 #431]: false
+#405 := [lemma #418]: #419
+#386 := (or #385 #285)
+#387 := [th-lemma]: #386
+#382 := [unit-resolution #387 #405]: #385
+#376 := [unit-resolution #382 #375]: false
+#377 := [lemma #376]: #339
+#357 := (or #254 #255 #341)
+#340 := (not #255)
+#343 := (and #339 #340 #332)
+#344 := (not #343)
+#174 := (distinct #146 #166 #171)
+#177 := (not #174)
+#37 := (- #26 #26)
+#38 := (f3 #37)
+#31 := (* #26 2::int)
+#32 := (f3 #31)
+#33 := (f4 #32)
+#35 := (+ #33 3::int)
+#36 := (f3 #35)
+#28 := (+ #26 1::int)
+#29 := (f3 #28)
+#39 := (distinct #29 #36 #38)
+#40 := (not #39)
+#178 := (iff #40 #177)
+#175 := (iff #39 #174)
+#172 := (= #38 #171)
+#169 := (= #37 0::int)
+#170 := [rewrite]: #169
+#173 := [monotonicity #170]: #172
+#167 := (= #36 #166)
+#164 := (= #35 #161)
+#158 := (+ #155 3::int)
+#162 := (= #158 #161)
+#163 := [rewrite]: #162
+#159 := (= #35 #158)
+#156 := (= #33 #155)
+#153 := (= #32 #152)
+#150 := (= #31 #149)
+#151 := [rewrite]: #150
+#154 := [monotonicity #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#165 := [trans #160 #163]: #164
+#168 := [monotonicity #165]: #167
+#147 := (= #29 #146)
+#144 := (= #28 #143)
+#145 := [rewrite]: #144
+#148 := [monotonicity #145]: #147
+#176 := [monotonicity #148 #168 #173]: #175
+#179 := [monotonicity #176]: #178
+#142 := [asserted]: #40
+#182 := [mp #142 #179]: #177
+#331 := (or #174 #344)
+#664 := [def-axiom]: #331
+#356 := [unit-resolution #664 #182]: #344
+#319 := (or #343 #254 #255 #341)
+#450 := [def-axiom]: #319
+#348 := [unit-resolution #450 #356]: #357
+#358 := [unit-resolution #348 #377 #383]: #255
+#326 := [monotonicity #358]: #360
+#328 := [trans #326 #399]: #362
+#373 := (not #362)
+#625 := (<= #302 0::int)
+#369 := (not #625)
+#639 := (<= #309 -1::int)
+#379 := (or #417 #639)
+#378 := [th-lemma]: #379
+#380 := [unit-resolution #378 #416]: #639
+#370 := (not #639)
+#371 := (or #369 #617 #370)
+#363 := [th-lemma]: #371
+#372 := [unit-resolution #363 #380 #436]: #369
+#364 := (or #373 #625)
+#374 := [th-lemma]: #364
+#355 := [unit-resolution #374 #372]: #373
+[unit-resolution #355 #328]: false
+unsat
+c3e137bbf6e1949e43f2587b45392d78547a0ad2 161 0
+#2 := false
+#13 := 0::int
+decl f5 :: int
+#25 := f5
+#135 := -1::int
+#136 := (* -1::int f5)
+#159 := (>= f5 0::int)
+#166 := (ite #159 f5 #136)
+#653 := (* -1::int #166)
+#650 := (+ #136 #653)
+#647 := (<= #650 0::int)
+#345 := (= #136 #166)
+#160 := (not #159)
+#654 := (+ f5 #653)
+#655 := (<= #654 0::int)
+#259 := (= f5 #166)
+#656 := [hypothesis]: #159
+#260 := (or #160 #259)
+#346 := [def-axiom]: #260
+#294 := [unit-resolution #346 #656]: #259
+#657 := (not #259)
+#659 := (or #657 #655)
+#299 := [th-lemma]: #659
+#300 := [unit-resolution #299 #294]: #655
+#278 := (>= #166 0::int)
+#351 := (not #278)
+decl f4 :: (-> S2 int)
+decl f3 :: (-> int S2)
+#171 := (f3 #166)
+#174 := (f4 #171)
+#177 := (= #166 #174)
+#180 := (not #177)
+#27 := (- f5)
+#26 := (< f5 0::int)
+#28 := (ite #26 #27 f5)
+#29 := (f3 #28)
+#30 := (f4 #29)
+#31 := (= #30 #28)
+#32 := (not #31)
+#183 := (iff #32 #180)
+#139 := (ite #26 #136 f5)
+#142 := (f3 #139)
+#145 := (f4 #142)
+#151 := (= #139 #145)
+#156 := (not #151)
+#181 := (iff #156 #180)
+#178 := (iff #151 #177)
+#175 := (= #145 #174)
+#172 := (= #142 #171)
+#169 := (= #139 #166)
+#163 := (ite #160 #136 f5)
+#167 := (= #163 #166)
+#168 := [rewrite]: #167
+#164 := (= #139 #163)
+#161 := (iff #26 #160)
+#162 := [rewrite]: #161
+#165 := [monotonicity #162]: #164
+#170 := [trans #165 #168]: #169
+#173 := [monotonicity #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [monotonicity #170 #176]: #178
+#182 := [monotonicity #179]: #181
+#157 := (iff #32 #156)
+#154 := (iff #31 #151)
+#148 := (= #145 #139)
+#152 := (iff #148 #151)
+#153 := [rewrite]: #152
+#149 := (iff #31 #148)
+#140 := (= #28 #139)
+#137 := (= #27 #136)
+#138 := [rewrite]: #137
+#141 := [monotonicity #138]: #140
+#146 := (= #30 #145)
+#143 := (= #29 #142)
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [monotonicity #147 #141]: #149
+#155 := [trans #150 #153]: #154
+#158 := [monotonicity #155]: #157
+#184 := [trans #158 #182]: #183
+#134 := [asserted]: #32
+#185 := [mp #134 #184]: #180
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#682 := (pattern #16)
+#75 := (>= #14 0::int)
+#76 := (not #75)
+#17 := (f4 #16)
+#57 := (= #14 #17)
+#82 := (or #57 #76)
+#683 := (forall (vars (?v0 int)) (:pat #682) #82)
+#87 := (forall (vars (?v0 int)) #82)
+#686 := (iff #87 #683)
+#684 := (iff #82 #82)
+#685 := [refl]: #684
+#687 := [quant-intro #685]: #686
+#189 := (~ #87 #87)
+#186 := (~ #82 #82)
+#201 := [refl]: #186
+#190 := [nnf-pos #201]: #189
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#90 := (iff #20 #87)
+#64 := (not #15)
+#65 := (or #64 #57)
+#70 := (forall (vars (?v0 int)) #65)
+#88 := (iff #70 #87)
+#85 := (iff #65 #82)
+#79 := (or #76 #57)
+#83 := (iff #79 #82)
+#84 := [rewrite]: #83
+#80 := (iff #65 #79)
+#77 := (iff #64 #76)
+#73 := (iff #15 #75)
+#74 := [rewrite]: #73
+#78 := [monotonicity #74]: #77
+#81 := [monotonicity #78]: #80
+#86 := [trans #81 #84]: #85
+#89 := [quant-intro #86]: #88
+#71 := (iff #20 #70)
+#68 := (iff #19 #65)
+#61 := (implies #15 #57)
+#66 := (iff #61 #65)
+#67 := [rewrite]: #66
+#62 := (iff #19 #61)
+#59 := (iff #18 #57)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#69 := [trans #63 #67]: #68
+#72 := [quant-intro #69]: #71
+#91 := [trans #72 #89]: #90
+#56 := [asserted]: #20
+#92 := [mp #56 #91]: #87
+#202 := [mp~ #92 #190]: #87
+#688 := [mp #202 #687]: #683
+#455 := (not #683)
+#662 := (or #455 #177 #351)
+#666 := (or #177 #351)
+#336 := (or #455 #666)
+#669 := (iff #336 #662)
+#670 := [rewrite]: #669
+#337 := [quant-inst]: #336
+#671 := [mp #337 #670]: #662
+#660 := [unit-resolution #671 #688 #185]: #351
+#658 := [th-lemma #656 #660 #300]: false
+#661 := [lemma #658]: #160
+#347 := (or #159 #345)
+#338 := [def-axiom]: #347
+#370 := [unit-resolution #338 #661]: #345
+#371 := (not #345)
+#372 := (or #371 #647)
+#373 := [th-lemma]: #372
+#266 := [unit-resolution #373 #370]: #647
+#652 := (<= #166 0::int)
+#643 := (or #652 #278)
+#644 := [th-lemma]: #643
+#366 := [unit-resolution #644 #660]: #652
+[th-lemma #661 #366 #266]: false
+unsat
+18766f4ad7b0aacc46a36126374fd797afa1c708 604 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f3 :: (-> int S2)
+decl f7 :: S2
+#42 := f7
+#43 := (f4 f7)
+#41 := 4::int
+#44 := (* 4::int #43)
+#45 := (f3 #44)
+#46 := (f4 #45)
+#612 := (= #46 0::int)
+#991 := (not #612)
+#595 := (<= #46 0::int)
+#986 := (not #595)
+#27 := 1::int
+#206 := (+ 1::int #46)
+#209 := (f3 #206)
+#582 := (f4 #209)
+#518 := (<= #582 1::int)
+#903 := (not #518)
+decl f6 :: (-> S2 S2 S1)
+#8 := (:var 0 S2)
+#519 := (f6 #8 #209)
+#490 := (pattern #519)
+decl f1 :: S1
+#4 := f1
+#530 := (= f1 #519)
+#496 := (not #530)
+#498 := (= #8 #209)
+#32 := (f3 1::int)
+#33 := (= #8 #32)
+#499 := (or #33 #498 #496)
+#503 := (forall (vars (?v1 S2)) (:pat #490) #499)
+#504 := (not #503)
+#494 := (or #504 #518)
+#480 := (not #494)
+decl f5 :: (-> S2 S1)
+#212 := (f5 #209)
+#218 := (= f1 #212)
+#507 := (not #218)
+#483 := (or #507 #480)
+#474 := (not #483)
+decl ?v1!0 :: (-> S2 S2)
+#533 := (?v1!0 #209)
+#534 := (f6 #533 #209)
+#544 := (= f1 #534)
+#525 := (not #544)
+#543 := (= #32 #533)
+#542 := (= #209 #533)
+#469 := (or #542 #543 #525)
+#471 := (not #469)
+#466 := (or #218 #471 #518)
+#453 := (not #466)
+#443 := (or #453 #474)
+#442 := (not #443)
+#9 := (f4 #8)
+#839 := (pattern #9)
+#25 := (f5 #8)
+#887 := (pattern #25)
+#258 := (?v1!0 #8)
+#321 := (= #8 #258)
+#318 := (= #32 #258)
+#276 := (f6 #258 #8)
+#277 := (= f1 #276)
+#278 := (not #277)
+#327 := (or #278 #318 #321)
+#332 := (not #327)
+#183 := (<= #9 1::int)
+#156 := (= f1 #25)
+#341 := (or #156 #183 #332)
+#356 := (not #341)
+#29 := (:var 1 S2)
+#30 := (f6 #8 #29)
+#860 := (pattern #30)
+#159 := (= f1 #30)
+#165 := (not #159)
+#34 := (= #8 #29)
+#187 := (or #33 #34 #165)
+#861 := (forall (vars (?v1 S2)) (:pat #860) #187)
+#866 := (not #861)
+#869 := (or #183 #866)
+#872 := (not #869)
+#300 := (not #156)
+#875 := (or #300 #872)
+#878 := (not #875)
+#881 := (or #878 #356)
+#884 := (not #881)
+#888 := (forall (vars (?v0 S2)) (:pat #887 #839) #884)
+#190 := (forall (vars (?v1 S2)) #187)
+#283 := (not #190)
+#286 := (or #183 #283)
+#287 := (not #286)
+#263 := (or #300 #287)
+#355 := (not #263)
+#357 := (or #355 #356)
+#358 := (not #357)
+#363 := (forall (vars (?v0 S2)) #358)
+#889 := (iff #363 #888)
+#885 := (iff #358 #884)
+#882 := (iff #357 #881)
+#879 := (iff #355 #878)
+#876 := (iff #263 #875)
+#873 := (iff #287 #872)
+#870 := (iff #286 #869)
+#867 := (iff #283 #866)
+#864 := (iff #190 #861)
+#862 := (iff #187 #187)
+#863 := [refl]: #862
+#865 := [quant-intro #863]: #864
+#868 := [monotonicity #865]: #867
+#871 := [monotonicity #868]: #870
+#874 := [monotonicity #871]: #873
+#877 := [monotonicity #874]: #876
+#880 := [monotonicity #877]: #879
+#883 := [monotonicity #880]: #882
+#886 := [monotonicity #883]: #885
+#890 := [quant-intro #886]: #889
+#184 := (not #183)
+#193 := (and #184 #190)
+#306 := (or #300 #193)
+#346 := (and #306 #341)
+#349 := (forall (vars (?v0 S2)) #346)
+#364 := (iff #349 #363)
+#361 := (iff #346 #358)
+#262 := (and #263 #341)
+#359 := (iff #262 #358)
+#360 := [rewrite]: #359
+#353 := (iff #346 #262)
+#264 := (iff #306 #263)
+#315 := (iff #193 #287)
+#352 := [rewrite]: #315
+#261 := [monotonicity #352]: #264
+#354 := [monotonicity #261]: #353
+#362 := [trans #354 #360]: #361
+#365 := [quant-intro #362]: #364
+#279 := (= #258 #8)
+#280 := (= #258 #32)
+#281 := (or #280 #279 #278)
+#282 := (not #281)
+#274 := (not #184)
+#288 := (or #274 #282)
+#305 := (or #156 #288)
+#307 := (and #306 #305)
+#310 := (forall (vars (?v0 S2)) #307)
+#350 := (iff #310 #349)
+#347 := (iff #307 #346)
+#344 := (iff #305 #341)
+#335 := (or #183 #332)
+#338 := (or #156 #335)
+#342 := (iff #338 #341)
+#343 := [rewrite]: #342
+#339 := (iff #305 #338)
+#336 := (iff #288 #335)
+#333 := (iff #282 #332)
+#330 := (iff #281 #327)
+#324 := (or #318 #321 #278)
+#328 := (iff #324 #327)
+#329 := [rewrite]: #328
+#325 := (iff #281 #324)
+#322 := (iff #279 #321)
+#323 := [rewrite]: #322
+#319 := (iff #280 #318)
+#320 := [rewrite]: #319
+#326 := [monotonicity #320 #323]: #325
+#331 := [trans #326 #329]: #330
+#334 := [monotonicity #331]: #333
+#316 := (iff #274 #183)
+#317 := [rewrite]: #316
+#337 := [monotonicity #317 #334]: #336
+#340 := [monotonicity #337]: #339
+#345 := [trans #340 #343]: #344
+#348 := [monotonicity #345]: #347
+#351 := [quant-intro #348]: #350
+#196 := (iff #156 #193)
+#199 := (forall (vars (?v0 S2)) #196)
+#311 := (~ #199 #310)
+#308 := (~ #196 #307)
+#298 := (~ #193 #193)
+#296 := (~ #190 #190)
+#294 := (~ #187 #187)
+#295 := [refl]: #294
+#297 := [nnf-pos #295]: #296
+#292 := (~ #184 #184)
+#293 := [refl]: #292
+#299 := [monotonicity #293 #297]: #298
+#289 := (not #193)
+#290 := (~ #289 #288)
+#284 := (~ #283 #282)
+#285 := [sk]: #284
+#275 := (~ #274 #274)
+#257 := [refl]: #275
+#291 := [nnf-neg #257 #285]: #290
+#303 := (~ #156 #156)
+#304 := [refl]: #303
+#301 := (~ #300 #300)
+#302 := [refl]: #301
+#309 := [nnf-pos #302 #304 #291 #299]: #308
+#312 := [nnf-pos #309]: #311
+#35 := (or #33 #34)
+#31 := (= #30 f1)
+#36 := (implies #31 #35)
+#37 := (forall (vars (?v1 S2)) #36)
+#28 := (< 1::int #9)
+#38 := (and #28 #37)
+#26 := (= #25 f1)
+#39 := (iff #26 #38)
+#40 := (forall (vars (?v0 S2)) #39)
+#202 := (iff #40 #199)
+#166 := (or #35 #165)
+#171 := (forall (vars (?v1 S2)) #166)
+#174 := (and #28 #171)
+#177 := (iff #156 #174)
+#180 := (forall (vars (?v0 S2)) #177)
+#200 := (iff #180 #199)
+#197 := (iff #177 #196)
+#194 := (iff #174 #193)
+#191 := (iff #171 #190)
+#188 := (iff #166 #187)
+#189 := [rewrite]: #188
+#192 := [quant-intro #189]: #191
+#185 := (iff #28 #184)
+#186 := [rewrite]: #185
+#195 := [monotonicity #186 #192]: #194
+#198 := [monotonicity #195]: #197
+#201 := [quant-intro #198]: #200
+#181 := (iff #40 #180)
+#178 := (iff #39 #177)
+#175 := (iff #38 #174)
+#172 := (iff #37 #171)
+#169 := (iff #36 #166)
+#162 := (implies #159 #35)
+#167 := (iff #162 #166)
+#168 := [rewrite]: #167
+#163 := (iff #36 #162)
+#160 := (iff #31 #159)
+#161 := [rewrite]: #160
+#164 := [monotonicity #161]: #163
+#170 := [trans #164 #168]: #169
+#173 := [quant-intro #170]: #172
+#176 := [monotonicity #173]: #175
+#157 := (iff #26 #156)
+#158 := [rewrite]: #157
+#179 := [monotonicity #158 #176]: #178
+#182 := [quant-intro #179]: #181
+#203 := [trans #182 #201]: #202
+#155 := [asserted]: #40
+#204 := [mp #155 #203]: #199
+#313 := [mp~ #204 #312]: #310
+#314 := [mp #313 #351]: #349
+#366 := [mp #314 #365]: #363
+#891 := [mp #366 #890]: #888
+#799 := (not #888)
+#432 := (or #799 #442)
+#526 := (or #525 #543 #542)
+#527 := (not #526)
+#528 := (or #218 #518 #527)
+#529 := (not #528)
+#505 := (or #518 #504)
+#506 := (not #505)
+#497 := (or #507 #506)
+#508 := (not #497)
+#491 := (or #508 #529)
+#493 := (not #491)
+#433 := (or #799 #493)
+#437 := (iff #433 #432)
+#434 := (iff #432 #432)
+#439 := [rewrite]: #434
+#450 := (iff #493 #442)
+#448 := (iff #491 #443)
+#452 := (or #474 #453)
+#444 := (iff #452 #443)
+#447 := [rewrite]: #444
+#457 := (iff #491 #452)
+#454 := (iff #529 #453)
+#446 := (iff #528 #466)
+#462 := (or #218 #518 #471)
+#441 := (iff #462 #466)
+#445 := [rewrite]: #441
+#465 := (iff #528 #462)
+#459 := (iff #527 #471)
+#470 := (iff #526 #469)
+#468 := [rewrite]: #470
+#461 := [monotonicity #468]: #459
+#460 := [monotonicity #461]: #465
+#451 := [trans #460 #445]: #446
+#456 := [monotonicity #451]: #454
+#486 := (iff #508 #474)
+#484 := (iff #497 #483)
+#481 := (iff #506 #480)
+#473 := (iff #505 #494)
+#475 := [rewrite]: #473
+#482 := [monotonicity #475]: #481
+#485 := [monotonicity #482]: #484
+#467 := [monotonicity #485]: #486
+#440 := [monotonicity #467 #456]: #457
+#449 := [trans #440 #447]: #448
+#435 := [monotonicity #449]: #450
+#438 := [monotonicity #435]: #437
+#426 := [trans #438 #439]: #437
+#436 := [quant-inst]: #433
+#428 := [mp #436 #426]: #432
+#962 := [unit-resolution #428 #891]: #442
+#922 := (or #443 #483)
+#923 := [def-axiom]: #922
+#963 := [unit-resolution #923 #962]: #483
+#966 := (or #474 #480)
+#233 := (>= #43 1::int)
+#234 := (not #233)
+#240 := (and #218 #234)
+#51 := (<= 1::int #43)
+#52 := (not #51)
+#47 := (+ #46 1::int)
+#48 := (f3 #47)
+#49 := (f5 #48)
+#50 := (= #49 f1)
+#53 := (and #50 #52)
+#245 := (iff #53 #240)
+#226 := (and #52 #218)
+#243 := (iff #226 #240)
+#237 := (and #234 #218)
+#241 := (iff #237 #240)
+#242 := [rewrite]: #241
+#238 := (iff #226 #237)
+#235 := (iff #52 #234)
+#231 := (iff #51 #233)
+#232 := [rewrite]: #231
+#236 := [monotonicity #232]: #235
+#239 := [monotonicity #236]: #238
+#244 := [trans #239 #242]: #243
+#229 := (iff #53 #226)
+#223 := (and #218 #52)
+#227 := (iff #223 #226)
+#228 := [rewrite]: #227
+#224 := (iff #53 #223)
+#221 := (iff #50 #218)
+#215 := (= #212 f1)
+#219 := (iff #215 #218)
+#220 := [rewrite]: #219
+#216 := (iff #50 #215)
+#213 := (= #49 #212)
+#210 := (= #48 #209)
+#207 := (= #47 #206)
+#208 := [rewrite]: #207
+#211 := [monotonicity #208]: #210
+#214 := [monotonicity #211]: #213
+#217 := [monotonicity #214]: #216
+#222 := [trans #217 #220]: #221
+#225 := [monotonicity #222]: #224
+#230 := [trans #225 #228]: #229
+#246 := [trans #230 #244]: #245
+#205 := [asserted]: #53
+#247 := [mp #205 #246]: #240
+#248 := [and-elim #247]: #218
+#918 := (or #474 #507 #480)
+#919 := [def-axiom]: #918
+#967 := [unit-resolution #919 #248]: #966
+#968 := [unit-resolution #967 #963]: #480
+#910 := (or #494 #903)
+#911 := [def-axiom]: #910
+#969 := [unit-resolution #911 #968]: #903
+#647 := -1::int
+#587 := (* -1::int #582)
+#591 := (+ #46 #587)
+#551 := (>= #591 -1::int)
+#584 := (= #591 -1::int)
+#588 := (>= #46 -1::int)
+#553 := (= #582 0::int)
+#974 := (not #553)
+#540 := (<= #582 0::int)
+#970 := (not #540)
+#971 := (or #970 #518)
+#972 := [th-lemma]: #971
+#973 := [unit-resolution #972 #969]: #970
+#975 := (or #974 #540)
+#976 := [th-lemma]: #975
+#977 := [unit-resolution #976 #973]: #974
+#555 := (or #553 #588)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#847 := (pattern #16)
+#96 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#144 := (or #22 #96)
+#854 := (forall (vars (?v0 int)) (:pat #847) #144)
+#149 := (forall (vars (?v0 int)) #144)
+#857 := (iff #149 #854)
+#855 := (iff #144 #144)
+#856 := [refl]: #855
+#858 := [quant-intro #856]: #857
+#255 := (~ #149 #149)
+#271 := (~ #144 #144)
+#272 := [refl]: #271
+#256 := [nnf-pos #272]: #255
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#152 := (iff #24 #149)
+#115 := (= 0::int #17)
+#121 := (not #21)
+#122 := (or #121 #115)
+#127 := (forall (vars (?v0 int)) #122)
+#150 := (iff #127 #149)
+#147 := (iff #122 #144)
+#141 := (or #96 #22)
+#145 := (iff #141 #144)
+#146 := [rewrite]: #145
+#142 := (iff #122 #141)
+#139 := (iff #115 #22)
+#140 := [rewrite]: #139
+#137 := (iff #121 #96)
+#97 := (not #96)
+#132 := (not #97)
+#135 := (iff #132 #96)
+#136 := [rewrite]: #135
+#133 := (iff #121 #132)
+#130 := (iff #21 #97)
+#131 := [rewrite]: #130
+#134 := [monotonicity #131]: #133
+#138 := [trans #134 #136]: #137
+#143 := [monotonicity #138 #140]: #142
+#148 := [trans #143 #146]: #147
+#151 := [quant-intro #148]: #150
+#128 := (iff #24 #127)
+#125 := (iff #23 #122)
+#118 := (implies #21 #115)
+#123 := (iff #118 #122)
+#124 := [rewrite]: #123
+#119 := (iff #23 #118)
+#116 := (iff #22 #115)
+#117 := [rewrite]: #116
+#120 := [monotonicity #117]: #119
+#126 := [trans #120 #124]: #125
+#129 := [quant-intro #126]: #128
+#153 := [trans #129 #151]: #152
+#114 := [asserted]: #24
+#154 := [mp #114 #153]: #149
+#273 := [mp~ #154 #256]: #149
+#859 := [mp #273 #858]: #854
+#615 := (not #854)
+#558 := (or #615 #553 #588)
+#590 := (>= #206 0::int)
+#554 := (or #553 #590)
+#559 := (or #615 #554)
+#548 := (iff #559 #558)
+#560 := (or #615 #555)
+#547 := (iff #560 #558)
+#549 := [rewrite]: #547
+#545 := (iff #559 #560)
+#556 := (iff #554 #555)
+#589 := (iff #590 #588)
+#575 := [rewrite]: #589
+#557 := [monotonicity #575]: #556
+#546 := [monotonicity #557]: #545
+#550 := [trans #546 #549]: #548
+#552 := [quant-inst]: #559
+#539 := [mp #552 #550]: #558
+#978 := [unit-resolution #539 #859]: #555
+#979 := [unit-resolution #978 #977]: #588
+#577 := (not #588)
+#579 := (or #584 #577)
+#78 := (= #14 #17)
+#103 := (or #78 #97)
+#848 := (forall (vars (?v0 int)) (:pat #847) #103)
+#108 := (forall (vars (?v0 int)) #103)
+#851 := (iff #108 #848)
+#849 := (iff #103 #103)
+#850 := [refl]: #849
+#852 := [quant-intro #850]: #851
+#253 := (~ #108 #108)
+#250 := (~ #103 #103)
+#269 := [refl]: #250
+#254 := [nnf-pos #269]: #253
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#111 := (iff #20 #108)
+#85 := (not #15)
+#86 := (or #85 #78)
+#91 := (forall (vars (?v0 int)) #86)
+#109 := (iff #91 #108)
+#106 := (iff #86 #103)
+#100 := (or #97 #78)
+#104 := (iff #100 #103)
+#105 := [rewrite]: #104
+#101 := (iff #86 #100)
+#98 := (iff #85 #97)
+#94 := (iff #15 #96)
+#95 := [rewrite]: #94
+#99 := [monotonicity #95]: #98
+#102 := [monotonicity #99]: #101
+#107 := [trans #102 #105]: #106
+#110 := [quant-intro #107]: #109
+#92 := (iff #20 #91)
+#89 := (iff #19 #86)
+#82 := (implies #15 #78)
+#87 := (iff #82 #86)
+#88 := [rewrite]: #87
+#83 := (iff #19 #82)
+#80 := (iff #18 #78)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#90 := [trans #84 #88]: #89
+#93 := [quant-intro #90]: #92
+#112 := [trans #93 #110]: #111
+#77 := [asserted]: #20
+#113 := [mp #77 #112]: #108
+#270 := [mp~ #113 #254]: #108
+#853 := [mp #270 #852]: #848
+#628 := (not #848)
+#564 := (or #628 #584 #577)
+#580 := (not #590)
+#583 := (= #206 #582)
+#586 := (or #583 #580)
+#565 := (or #628 #586)
+#572 := (iff #565 #564)
+#567 := (or #628 #579)
+#570 := (iff #567 #564)
+#571 := [rewrite]: #570
+#568 := (iff #565 #567)
+#561 := (iff #586 #579)
+#578 := (iff #580 #577)
+#576 := [monotonicity #575]: #578
+#592 := (iff #583 #584)
+#585 := [rewrite]: #592
+#563 := [monotonicity #585 #576]: #561
+#569 := [monotonicity #563]: #568
+#573 := [trans #569 #571]: #572
+#566 := [quant-inst]: #565
+#562 := [mp #566 #573]: #564
+#980 := [unit-resolution #562 #853]: #579
+#981 := [unit-resolution #980 #979]: #584
+#982 := (not #584)
+#983 := (or #982 #551)
+#984 := [th-lemma]: #983
+#985 := [unit-resolution #984 #981]: #551
+#987 := (not #551)
+#988 := (or #986 #518 #987)
+#989 := [th-lemma]: #988
+#990 := [unit-resolution #989 #985 #969]: #986
+#992 := (or #991 #595)
+#993 := [th-lemma]: #992
+#994 := [unit-resolution #993 #990]: #991
+#653 := (>= #43 0::int)
+#655 := (not #653)
+#648 := (* -1::int #46)
+#649 := (+ #44 #648)
+#650 := (= #649 0::int)
+#999 := (not #650)
+#611 := (>= #649 0::int)
+#995 := (not #611)
+#249 := [and-elim #247]: #234
+#996 := (or #995 #233 #518 #987)
+#997 := [th-lemma]: #996
+#998 := [unit-resolution #997 #249 #985 #969]: #995
+#1000 := (or #999 #611)
+#1001 := [th-lemma]: #1000
+#1002 := [unit-resolution #1001 #998]: #999
+#624 := (or #650 #655)
+#630 := (or #628 #650 #655)
+#643 := (>= #44 0::int)
+#644 := (not #643)
+#645 := (= #44 #46)
+#646 := (or #645 #644)
+#631 := (or #628 #646)
+#606 := (iff #631 #630)
+#633 := (or #628 #624)
+#618 := (iff #633 #630)
+#636 := [rewrite]: #618
+#634 := (iff #631 #633)
+#626 := (iff #646 #624)
+#616 := (iff #644 #655)
+#654 := (iff #643 #653)
+#639 := [rewrite]: #654
+#617 := [monotonicity #639]: #616
+#651 := (iff #645 #650)
+#652 := [rewrite]: #651
+#627 := [monotonicity #652 #617]: #626
+#635 := [monotonicity #627]: #634
+#607 := [trans #635 #636]: #606
+#632 := [quant-inst]: #631
+#608 := [mp #632 #607]: #630
+#1003 := [unit-resolution #608 #853]: #624
+#1004 := [unit-resolution #1003 #1002]: #655
+#455 := (or #612 #653)
+#594 := (or #615 #612 #653)
+#613 := (or #612 #643)
+#597 := (or #615 #613)
+#596 := (iff #597 #594)
+#603 := (or #615 #455)
+#605 := (iff #603 #594)
+#593 := [rewrite]: #605
+#604 := (iff #597 #603)
+#614 := (iff #613 #455)
+#610 := [monotonicity #639]: #614
+#602 := [monotonicity #610]: #604
+#598 := [trans #602 #593]: #596
+#601 := [quant-inst]: #597
+#599 := [mp #601 #598]: #594
+#1005 := [unit-resolution #599 #859]: #455
+[unit-resolution #1005 #1004 #994]: false
+unsat
+c1588b51b288c6a2d08a2016aa66eab50f0a6d1f 61 0
+#2 := false
+decl f7 :: S3
+#12 := f7
+decl f5 :: S3
+#8 := f5
+#14 := (= f5 f7)
+decl f3 :: (-> S2 S3)
+decl f4 :: (-> S3 S4 S2)
+decl f6 :: S4
+#9 := f6
+#10 := (f4 f5 f6)
+#11 := (f3 #10)
+#13 := (= #11 f7)
+#49 := (not #13)
+#50 := (or #49 #14)
+#53 := (not #50)
+#15 := (implies #13 #14)
+#16 := (not #15)
+#54 := (iff #16 #53)
+#51 := (iff #15 #50)
+#52 := [rewrite]: #51
+#55 := [monotonicity #52]: #54
+#48 := [asserted]: #16
+#58 := [mp #48 #55]: #53
+#56 := [not-or-elim #58]: #13
+#157 := (= f5 #11)
+#18 := (:var 0 S4)
+#17 := (:var 1 S3)
+#19 := (f4 #17 #18)
+#575 := (pattern #19)
+#20 := (f3 #19)
+#61 := (= #17 #20)
+#576 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #575) #61)
+#64 := (forall (vars (?v0 S3) (?v1 S4)) #61)
+#579 := (iff #64 #576)
+#577 := (iff #61 #61)
+#578 := [refl]: #577
+#580 := [quant-intro #578]: #579
+#99 := (~ #64 #64)
+#97 := (~ #61 #61)
+#98 := [refl]: #97
+#100 := [nnf-pos #98]: #99
+#21 := (= #20 #17)
+#22 := (forall (vars (?v0 S3) (?v1 S4)) #21)
+#65 := (iff #22 #64)
+#62 := (iff #21 #61)
+#63 := [rewrite]: #62
+#66 := [quant-intro #63]: #65
+#60 := [asserted]: #22
+#69 := [mp #60 #66]: #64
+#89 := [mp~ #69 #100]: #64
+#581 := [mp #89 #580]: #576
+#245 := (not #576)
+#159 := (or #245 #157)
+#246 := [quant-inst]: #159
+#247 := [unit-resolution #246 #581]: #157
+#251 := [trans #247 #56]: #14
+#57 := (not #14)
+#59 := [not-or-elim #58]: #57
+[unit-resolution #59 #251]: false
+unsat
+0c0dd492e144529e5589cd1be0dd8dae2a82d34c 116 0
+#2 := false
+decl f10 :: (-> S5 S3)
+decl f7 :: S5
+#13 := f7
+#18 := (f10 f7)
+decl f9 :: (-> S2 S3)
+decl f3 :: S2
+#8 := f3
+#17 := (f9 f3)
+#19 := (= #17 #18)
+decl f8 :: (-> S4 S3 S5)
+decl f5 :: S3
+#9 := f5
+decl f6 :: S4
+#10 := f6
+#14 := (f8 f6 f5)
+#219 := (f10 #14)
+#275 := (= #219 #18)
+#273 := (= #18 #219)
+#15 := (= f7 #14)
+decl f4 :: (-> S3 S4 S2)
+#11 := (f4 f5 f6)
+#12 := (= f3 #11)
+#16 := (and #12 #15)
+#69 := (not #16)
+#70 := (or #69 #19)
+#73 := (not #70)
+#20 := (implies #16 #19)
+#21 := (not #20)
+#74 := (iff #21 #73)
+#71 := (iff #20 #70)
+#72 := [rewrite]: #71
+#75 := [monotonicity #72]: #74
+#68 := [asserted]: #21
+#78 := [mp #68 #75]: #73
+#76 := [not-or-elim #78]: #16
+#79 := [and-elim #76]: #15
+#274 := [monotonicity #79]: #273
+#613 := [symm #274]: #275
+#616 := (= #17 #219)
+#306 := (= f5 #219)
+#23 := (:var 0 S3)
+#22 := (:var 1 S4)
+#24 := (f8 #22 #23)
+#636 := (pattern #24)
+#34 := (f10 #24)
+#98 := (= #23 #34)
+#650 := (forall (vars (?v0 S4) (?v1 S3)) (:pat #636) #98)
+#102 := (forall (vars (?v0 S4) (?v1 S3)) #98)
+#653 := (iff #102 #650)
+#651 := (iff #98 #98)
+#652 := [refl]: #651
+#654 := [quant-intro #652]: #653
+#141 := (~ #102 #102)
+#133 := (~ #98 #98)
+#134 := [refl]: #133
+#142 := [nnf-pos #134]: #141
+#35 := (= #34 #23)
+#36 := (forall (vars (?v0 S4) (?v1 S3)) #35)
+#103 := (iff #36 #102)
+#100 := (iff #35 #98)
+#101 := [rewrite]: #100
+#104 := [quant-intro #101]: #103
+#97 := [asserted]: #36
+#107 := [mp #97 #104]: #102
+#132 := [mp~ #107 #142]: #102
+#655 := [mp #132 #654]: #650
+#238 := (not #650)
+#311 := (or #238 #306)
+#308 := [quant-inst]: #311
+#625 := [unit-resolution #308 #655]: #306
+#614 := (= #17 f5)
+#309 := (f9 #11)
+#611 := (= #309 f5)
+#310 := (= f5 #309)
+#29 := (:var 0 S4)
+#28 := (:var 1 S3)
+#30 := (f4 #28 #29)
+#643 := (pattern #30)
+#31 := (f9 #30)
+#90 := (= #28 #31)
+#644 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #643) #90)
+#94 := (forall (vars (?v0 S3) (?v1 S4)) #90)
+#647 := (iff #94 #644)
+#645 := (iff #90 #90)
+#646 := [refl]: #645
+#648 := [quant-intro #646]: #647
+#139 := (~ #94 #94)
+#138 := (~ #90 #90)
+#135 := [refl]: #138
+#140 := [nnf-pos #135]: #139
+#32 := (= #31 #28)
+#33 := (forall (vars (?v0 S3) (?v1 S4)) #32)
+#95 := (iff #33 #94)
+#92 := (iff #32 #90)
+#93 := [rewrite]: #92
+#96 := [quant-intro #93]: #95
+#89 := [asserted]: #33
+#99 := [mp #89 #96]: #94
+#136 := [mp~ #99 #140]: #94
+#649 := [mp #136 #648]: #644
+#628 := (not #644)
+#630 := (or #628 #310)
+#285 := [quant-inst]: #630
+#283 := [unit-resolution #285 #649]: #310
+#272 := [symm #283]: #611
+#627 := (= #17 #309)
+#77 := [and-elim #76]: #12
+#268 := [monotonicity #77]: #627
+#615 := [trans #268 #272]: #614
+#617 := [trans #615 #625]: #616
+#612 := [trans #617 #613]: #19
+#80 := (not #19)
+#81 := [not-or-elim #78]: #80
+[unit-resolution #81 #612]: false
+unsat
+aa5b48a48a0873759303c38cf95fb27a82bae860 192 0
+#2 := false
+decl f6 :: (-> S3 S2 S4)
+decl f3 :: S2
+#8 := f3
+decl f8 :: S3
+#16 := f8
+#22 := (f6 f8 f3)
+decl f7 :: (-> S3 S2 S4 S3)
+decl f10 :: S4
+#19 := f10
+decl f5 :: S2
+#12 := f5
+decl f9 :: S4
+#17 := f9
+decl f4 :: S2
+#9 := f4
+#18 := (f7 f8 f4 f9)
+#20 := (f7 #18 f5 f10)
+#21 := (f6 #20 f3)
+#23 := (= #21 #22)
+#173 := (f6 #18 f4)
+#570 := (f7 f8 f4 #173)
+#538 := (f6 #570 f3)
+#539 := (= #538 #22)
+#542 := (= #22 #538)
+#533 := (= #173 #538)
+#10 := (= f3 f4)
+#374 := (ite #10 #533 #542)
+#37 := (:var 0 S2)
+#35 := (:var 1 S4)
+#34 := (:var 2 S2)
+#33 := (:var 3 S3)
+#36 := (f7 #33 #34 #35)
+#38 := (f6 #36 #37)
+#599 := (pattern #38)
+#40 := (f6 #33 #37)
+#100 := (= #38 #40)
+#99 := (= #35 #38)
+#82 := (= #34 #37)
+#107 := (ite #82 #99 #100)
+#600 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) (:pat #599) #107)
+#95 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) #107)
+#603 := (iff #95 #600)
+#601 := (iff #107 #107)
+#602 := [refl]: #601
+#604 := [quant-intro #602]: #603
+#86 := (ite #82 #35 #40)
+#89 := (= #38 #86)
+#92 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) #89)
+#113 := (iff #92 #95)
+#108 := (iff #89 #107)
+#98 := [rewrite]: #108
+#114 := [quant-intro #98]: #113
+#105 := (~ #92 #92)
+#104 := (~ #89 #89)
+#101 := [refl]: #104
+#106 := [nnf-pos #101]: #105
+#39 := (= #37 #34)
+#41 := (ite #39 #35 #40)
+#42 := (= #38 #41)
+#43 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4) (?v3 S2)) #42)
+#93 := (iff #43 #92)
+#90 := (iff #42 #89)
+#87 := (= #41 #86)
+#84 := (iff #39 #82)
+#85 := [rewrite]: #84
+#88 := [monotonicity #85]: #87
+#91 := [monotonicity #88]: #90
+#94 := [quant-intro #91]: #93
+#81 := [asserted]: #43
+#97 := [mp #81 #94]: #92
+#102 := [mp~ #97 #106]: #92
+#115 := [mp #102 #114]: #95
+#605 := [mp #115 #604]: #600
+#251 := (not #600)
+#530 := (or #251 #374)
+#534 := (= f4 f3)
+#540 := (ite #534 #533 #539)
+#531 := (or #251 #540)
+#532 := (iff #531 #530)
+#415 := (iff #530 #530)
+#416 := [rewrite]: #415
+#527 := (iff #540 #374)
+#371 := (iff #539 #542)
+#373 := [rewrite]: #371
+#541 := (iff #534 #10)
+#535 := [rewrite]: #541
+#528 := [monotonicity #535 #373]: #527
+#414 := [monotonicity #528]: #532
+#375 := [trans #414 #416]: #532
+#529 := [quant-inst]: #531
+#523 := [mp #529 #375]: #530
+#526 := [unit-resolution #523 #605]: #374
+#425 := (not #374)
+#513 := (or #425 #542)
+#11 := (not #10)
+#13 := (= f3 f5)
+#14 := (not #13)
+#15 := (and #11 #14)
+#61 := (not #15)
+#62 := (or #61 #23)
+#65 := (not #62)
+#24 := (implies #15 #23)
+#25 := (not #24)
+#66 := (iff #25 #65)
+#63 := (iff #24 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#60 := [asserted]: #25
+#70 := [mp #60 #67]: #65
+#68 := [not-or-elim #70]: #15
+#69 := [and-elim #68]: #11
+#524 := (or #425 #10 #542)
+#409 := [def-axiom]: #524
+#515 := [unit-resolution #409 #69]: #513
+#507 := [unit-resolution #515 #526]: #542
+#509 := [symm #507]: #539
+#510 := (= #21 #538)
+#264 := (f6 #18 f3)
+#519 := (= #264 #538)
+#518 := (= #538 #264)
+#525 := (= #570 #18)
+#431 := (= #173 f9)
+#260 := (= f9 #173)
+#28 := (:var 0 S4)
+#27 := (:var 1 S2)
+#26 := (:var 2 S3)
+#29 := (f7 #26 #27 #28)
+#591 := (pattern #29)
+#30 := (f6 #29 #27)
+#75 := (= #28 #30)
+#593 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) (:pat #591) #75)
+#78 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #75)
+#592 := (iff #78 #593)
+#595 := (iff #593 #593)
+#596 := [rewrite]: #595
+#594 := [rewrite]: #592
+#597 := [trans #594 #596]: #592
+#111 := (~ #78 #78)
+#109 := (~ #75 #75)
+#110 := [refl]: #109
+#112 := [nnf-pos #110]: #111
+#31 := (= #30 #28)
+#32 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #31)
+#79 := (iff #32 #78)
+#76 := (iff #31 #75)
+#77 := [rewrite]: #76
+#80 := [quant-intro #77]: #79
+#74 := [asserted]: #32
+#83 := [mp #74 #80]: #78
+#103 := [mp~ #83 #112]: #78
+#598 := [mp #103 #597]: #593
+#175 := (not #593)
+#262 := (or #175 #260)
+#253 := [quant-inst]: #262
+#430 := [unit-resolution #253 #598]: #260
+#432 := [symm #430]: #431
+#522 := [monotonicity #432]: #525
+#514 := [monotonicity #522]: #518
+#508 := [symm #514]: #519
+#265 := (= #21 #264)
+#263 := (= f10 #21)
+#240 := (ite #13 #263 #265)
+#252 := (or #251 #240)
+#267 := (= f5 f3)
+#246 := (ite #267 #263 #265)
+#586 := (or #251 #246)
+#588 := (iff #586 #252)
+#584 := (iff #252 #252)
+#590 := [rewrite]: #584
+#372 := (iff #246 #240)
+#583 := (iff #267 #13)
+#585 := [rewrite]: #583
+#579 := [monotonicity #585]: #372
+#589 := [monotonicity #579]: #588
+#580 := [trans #589 #590]: #588
+#587 := [quant-inst]: #586
+#238 := [mp #587 #580]: #252
+#504 := [unit-resolution #238 #605]: #240
+#243 := (not #240)
+#506 := (or #243 #265)
+#71 := [and-elim #68]: #14
+#582 := (or #243 #13 #265)
+#223 := [def-axiom]: #582
+#516 := [unit-resolution #223 #71]: #506
+#517 := [unit-resolution #516 #504]: #265
+#511 := [trans #517 #508]: #510
+#505 := [trans #511 #509]: #23
+#72 := (not #23)
+#73 := [not-or-elim #70]: #72
+[unit-resolution #73 #505]: false
+unsat
+e7c21f70fe07677643a624f34aca10d30c0027d1 80 0
+#2 := false
+decl f6 :: (-> S2 S3 S1)
+decl f5 :: S3
+#9 := f5
+decl f4 :: S2
+#8 := f4
+#12 := (f6 f4 f5)
+decl f1 :: S1
+#4 := f1
+#39 := (= f1 #12)
+decl f3 :: (-> S2 S3 S1)
+#10 := (f3 f4 f5)
+#36 := (= f1 #10)
+#49 := (iff #36 #39)
+#74 := (not #49)
+#95 := (iff #74 false)
+#1 := true
+#90 := (not true)
+#93 := (iff #90 false)
+#94 := [rewrite]: #93
+#91 := (iff #74 #90)
+#88 := (iff #49 true)
+#83 := (iff false false)
+#86 := (iff #83 true)
+#87 := [rewrite]: #86
+#84 := (iff #49 #83)
+#81 := (iff #39 false)
+#72 := (not #39)
+#61 := (or #36 #39 #49)
+#64 := (not #61)
+#13 := (= #12 f1)
+#11 := (= #10 f1)
+#16 := (or #11 #13)
+#14 := (and #13 true)
+#15 := (iff #11 #14)
+#17 := (or #15 #16)
+#18 := (not #17)
+#67 := (iff #18 #64)
+#52 := (or #36 #39)
+#55 := (or #49 #52)
+#58 := (not #55)
+#65 := (iff #58 #64)
+#62 := (iff #55 #61)
+#63 := [rewrite]: #62
+#66 := [monotonicity #63]: #65
+#59 := (iff #18 #58)
+#56 := (iff #17 #55)
+#53 := (iff #16 #52)
+#40 := (iff #13 #39)
+#41 := [rewrite]: #40
+#37 := (iff #11 #36)
+#38 := [rewrite]: #37
+#54 := [monotonicity #38 #41]: #53
+#50 := (iff #15 #49)
+#47 := (iff #14 #39)
+#42 := (and #39 true)
+#45 := (iff #42 #39)
+#46 := [rewrite]: #45
+#43 := (iff #14 #42)
+#44 := [monotonicity #41]: #43
+#48 := [trans #44 #46]: #47
+#51 := [monotonicity #38 #48]: #50
+#57 := [monotonicity #51 #54]: #56
+#60 := [monotonicity #57]: #59
+#68 := [trans #60 #66]: #67
+#35 := [asserted]: #18
+#69 := [mp #35 #68]: #64
+#73 := [not-or-elim #69]: #72
+#82 := [iff-false #73]: #81
+#79 := (iff #36 false)
+#70 := (not #36)
+#71 := [not-or-elim #69]: #70
+#80 := [iff-false #71]: #79
+#85 := [monotonicity #80 #82]: #84
+#89 := [trans #85 #87]: #88
+#92 := [monotonicity #89]: #91
+#96 := [trans #92 #94]: #95
+#75 := [not-or-elim #69]: #74
+[mp #75 #96]: false
+unsat
+a8d1804c5819a0c61a2692ceed63656a5bf68bbc 128 0
+#2 := false
+decl f3 :: (-> S2 S2)
+#15 := (:var 0 S2)
+#16 := (f3 #15)
+#577 := (pattern #16)
+#55 := (= #15 #16)
+#578 := (forall (vars (?v0 S2)) (:pat #577) #55)
+#59 := (forall (vars (?v0 S2)) #55)
+#581 := (iff #59 #578)
+#579 := (iff #55 #55)
+#580 := [refl]: #579
+#582 := [quant-intro #580]: #581
+#88 := (~ #59 #59)
+#86 := (~ #55 #55)
+#87 := [refl]: #86
+#89 := [nnf-pos #87]: #88
+#17 := (= #16 #15)
+#18 := (forall (vars (?v0 S2)) #17)
+#60 := (iff #18 #59)
+#57 := (iff #17 #55)
+#58 := [rewrite]: #57
+#61 := [quant-intro #58]: #60
+#54 := [asserted]: #18
+#64 := [mp #54 #61]: #59
+#80 := [mp~ #64 #89]: #59
+#583 := [mp #80 #582]: #578
+decl f4 :: S2
+#8 := f4
+#9 := (f3 f4)
+#42 := (= f4 #9)
+#90 := (not #42)
+decl f5 :: (-> S1 S1)
+decl f1 :: S1
+#4 := f1
+#11 := (f5 f1)
+#45 := (= f1 #11)
+#19 := (:var 0 S1)
+#20 := (f5 #19)
+#584 := (pattern #20)
+#67 := (= f1 #19)
+#63 := (= f1 #20)
+#70 := (iff #63 #67)
+#585 := (forall (vars (?v0 S1)) (:pat #584) #70)
+#73 := (forall (vars (?v0 S1)) #70)
+#588 := (iff #73 #585)
+#586 := (iff #70 #70)
+#587 := [refl]: #586
+#589 := [quant-intro #587]: #588
+#82 := (~ #73 #73)
+#81 := (~ #70 #70)
+#79 := [refl]: #81
+#83 := [nnf-pos #79]: #82
+#22 := (= #19 f1)
+#21 := (= #20 f1)
+#23 := (iff #21 #22)
+#24 := (forall (vars (?v0 S1)) #23)
+#74 := (iff #24 #73)
+#71 := (iff #23 #70)
+#68 := (iff #22 #67)
+#69 := [rewrite]: #68
+#65 := (iff #21 #63)
+#66 := [rewrite]: #65
+#72 := [monotonicity #66 #69]: #71
+#75 := [quant-intro #72]: #74
+#62 := [asserted]: #24
+#78 := [mp #62 #75]: #73
+#76 := [mp~ #78 #83]: #73
+#590 := [mp #76 #589]: #585
+#91 := (not #45)
+#572 := [hypothesis]: #91
+#249 := (not #585)
+#253 := (or #249 #45)
+#159 := (= f1 f1)
+#246 := (iff #45 #159)
+#232 := (or #249 #246)
+#571 := (iff #232 #253)
+#358 := (iff #253 #253)
+#565 := [rewrite]: #358
+#179 := (iff #246 #45)
+#1 := true
+#161 := (iff #45 true)
+#250 := (iff #161 #45)
+#251 := [rewrite]: #250
+#248 := (iff #246 #161)
+#160 := (iff #159 true)
+#247 := [rewrite]: #160
+#239 := [monotonicity #247]: #248
+#252 := [trans #239 #251]: #179
+#226 := [monotonicity #252]: #571
+#237 := [trans #226 #565]: #571
+#569 := [quant-inst]: #232
+#238 := [mp #569 #237]: #253
+#573 := [unit-resolution #238 #572 #590]: false
+#574 := [lemma #573]: #45
+#84 := (or #90 #91)
+#48 := (and #42 #45)
+#51 := (not #48)
+#99 := (iff #51 #84)
+#85 := (not #84)
+#94 := (not #85)
+#97 := (iff #94 #84)
+#98 := [rewrite]: #97
+#95 := (iff #51 #94)
+#92 := (iff #48 #85)
+#93 := [rewrite]: #92
+#96 := [monotonicity #93]: #95
+#100 := [trans #96 #98]: #99
+#12 := (= #11 f1)
+#10 := (= #9 f4)
+#13 := (and #10 #12)
+#14 := (not #13)
+#52 := (iff #14 #51)
+#49 := (iff #13 #48)
+#46 := (iff #12 #45)
+#47 := [rewrite]: #46
+#43 := (iff #10 #42)
+#44 := [rewrite]: #43
+#50 := [monotonicity #44 #47]: #49
+#53 := [monotonicity #50]: #52
+#41 := [asserted]: #14
+#56 := [mp #41 #53]: #51
+#101 := [mp #56 #100]: #84
+#575 := [unit-resolution #101 #574]: #90
+#576 := (not #578)
+#566 := (or #576 #42)
+#224 := [quant-inst]: #566
+[unit-resolution #224 #575 #583]: false
+unsat
+21df96defda428acd4390bdcc6579b5e5c6d79e8 469 0
+#2 := false
+decl f8 :: (-> S2 S4 S4)
+decl f9 :: S4
+#34 := f9
+decl f5 :: (-> int S2)
+#38 := 2::int
+#39 := (f5 2::int)
+#40 := (f8 #39 f9)
+#12 := 1::int
+#33 := (f5 1::int)
+#41 := (f8 #33 #40)
+decl f7 :: (-> S3 S4 S4)
+#35 := (f8 #33 f9)
+#20 := 0::int
+#32 := (f5 0::int)
+#36 := (f8 #32 #35)
+decl f4 :: S3
+#8 := f4
+#37 := (f7 f4 #36)
+#42 := (= #37 #41)
+#519 := (f7 f4 #35)
+decl f3 :: (-> S3 S2 S2)
+#521 := (f3 f4 #32)
+#522 := (f8 #521 #519)
+#812 := (= #522 #41)
+#810 := (= #41 #522)
+#773 := (= #40 #519)
+#598 := (f7 f4 f9)
+#599 := (f3 f4 #33)
+#584 := (f8 #599 #598)
+#771 := (= #584 #519)
+#585 := (= #519 #584)
+#50 := (:var 0 S4)
+#48 := (:var 2 S3)
+#54 := (f7 #48 #50)
+#49 := (:var 1 S2)
+#53 := (f3 #48 #49)
+#55 := (f8 #53 #54)
+#722 := (pattern #55)
+#51 := (f8 #49 #50)
+#52 := (f7 #48 #51)
+#721 := (pattern #52)
+#56 := (= #52 #55)
+#723 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) (:pat #721 #722) #56)
+#57 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #56)
+#726 := (iff #57 #723)
+#724 := (iff #56 #56)
+#725 := [refl]: #724
+#727 := [quant-intro #725]: #726
+#196 := (~ #57 #57)
+#195 := (~ #56 #56)
+#214 := [refl]: #195
+#197 := [nnf-pos #214]: #196
+#181 := [asserted]: #57
+#215 := [mp~ #181 #197]: #57
+#728 := [mp #215 #727]: #723
+#525 := (not #723)
+#589 := (or #525 #585)
+#586 := [quant-inst]: #589
+#731 := [unit-resolution #586 #728]: #585
+#772 := [symm #731]: #771
+#769 := (= #40 #584)
+#397 := (= f9 #598)
+#44 := (:var 0 S3)
+#45 := (f7 #44 f9)
+#714 := (pattern #45)
+#175 := (= f9 #45)
+#715 := (forall (vars (?v0 S3)) (:pat #714) #175)
+#178 := (forall (vars (?v0 S3)) #175)
+#718 := (iff #178 #715)
+#716 := (iff #175 #175)
+#717 := [refl]: #716
+#719 := [quant-intro #717]: #718
+#192 := (~ #178 #178)
+#212 := (~ #175 #175)
+#213 := [refl]: #212
+#193 := [nnf-pos #213]: #192
+#46 := (= #45 f9)
+#47 := (forall (vars (?v0 S3)) #46)
+#179 := (iff #47 #178)
+#176 := (iff #46 #175)
+#177 := [rewrite]: #176
+#180 := [quant-intro #177]: #179
+#174 := [asserted]: #47
+#183 := [mp #174 #180]: #178
+#194 := [mp~ #183 #193]: #178
+#720 := [mp #194 #719]: #715
+#388 := (not #715)
+#380 := (or #388 #397)
+#389 := [quant-inst]: #380
+#732 := [unit-resolution #389 #720]: #397
+#767 := (= #39 #599)
+decl f6 :: (-> S2 int)
+#305 := (f6 #33)
+#617 := (+ 1::int #305)
+#621 := (f5 #617)
+#763 := (= #621 #599)
+#601 := (= #599 #621)
+#9 := (:var 0 S2)
+#11 := (f6 #9)
+#687 := (pattern #11)
+#10 := (f3 f4 #9)
+#686 := (pattern #10)
+#75 := (+ 1::int #11)
+#78 := (f5 #75)
+#81 := (= #10 #78)
+#688 := (forall (vars (?v0 S2)) (:pat #686 #687) #81)
+#84 := (forall (vars (?v0 S2)) #81)
+#691 := (iff #84 #688)
+#689 := (iff #81 #81)
+#690 := [refl]: #689
+#692 := [quant-intro #690]: #691
+#202 := (~ #84 #84)
+#200 := (~ #81 #81)
+#201 := [refl]: #200
+#203 := [nnf-pos #201]: #202
+#13 := (+ #11 1::int)
+#14 := (f5 #13)
+#15 := (= #10 #14)
+#16 := (forall (vars (?v0 S2)) #15)
+#85 := (iff #16 #84)
+#82 := (iff #15 #81)
+#79 := (= #14 #78)
+#76 := (= #13 #75)
+#77 := [rewrite]: #76
+#80 := [monotonicity #77]: #79
+#83 := [monotonicity #80]: #82
+#86 := [quant-intro #83]: #85
+#74 := [asserted]: #16
+#89 := [mp #74 #86]: #84
+#185 := [mp~ #89 #203]: #84
+#693 := [mp #185 #692]: #688
+#608 := (not #688)
+#613 := (or #608 #601)
+#609 := [quant-inst]: #613
+#735 := [unit-resolution #609 #693]: #601
+#764 := [symm #735]: #763
+#765 := (= #39 #621)
+#507 := (f6 #621)
+#313 := (f5 #507)
+#292 := (= #313 #621)
+#17 := (f5 #11)
+#88 := (= #9 #17)
+#694 := (forall (vars (?v0 S2)) (:pat #687) #88)
+#92 := (forall (vars (?v0 S2)) #88)
+#695 := (iff #92 #694)
+#697 := (iff #694 #694)
+#698 := [rewrite]: #697
+#696 := [rewrite]: #695
+#699 := [trans #696 #698]: #695
+#186 := (~ #92 #92)
+#182 := (~ #88 #88)
+#204 := [refl]: #182
+#187 := [nnf-pos #204]: #186
+#18 := (= #17 #9)
+#19 := (forall (vars (?v0 S2)) #18)
+#93 := (iff #19 #92)
+#90 := (iff #18 #88)
+#91 := [rewrite]: #90
+#94 := [quant-intro #91]: #93
+#87 := [asserted]: #19
+#97 := [mp #87 #94]: #92
+#205 := [mp~ #97 #187]: #92
+#700 := [mp #205 #699]: #694
+#354 := (not #694)
+#300 := (or #354 #292)
+#288 := (= #621 #313)
+#301 := (or #354 #288)
+#299 := (iff #301 #300)
+#287 := (iff #300 #300)
+#290 := [rewrite]: #287
+#293 := (iff #288 #292)
+#298 := [rewrite]: #293
+#304 := [monotonicity #298]: #299
+#291 := [trans #304 #290]: #299
+#303 := [quant-inst]: #301
+#294 := [mp #303 #291]: #300
+#736 := [unit-resolution #294 #700]: #292
+#761 := (= #39 #313)
+#759 := (= 2::int #507)
+#757 := (= #507 2::int)
+#579 := -1::int
+#517 := (* -1::int #507)
+#518 := (+ #305 #517)
+#480 := (<= #518 -1::int)
+#528 := (= #518 -1::int)
+#484 := (>= #305 -1::int)
+#570 := (>= #305 1::int)
+#672 := (= #305 1::int)
+#21 := (:var 0 int)
+#23 := (f5 #21)
+#701 := (pattern #23)
+#114 := (>= #21 0::int)
+#115 := (not #114)
+#24 := (f6 #23)
+#96 := (= #21 #24)
+#121 := (or #96 #115)
+#702 := (forall (vars (?v0 int)) (:pat #701) #121)
+#126 := (forall (vars (?v0 int)) #121)
+#705 := (iff #126 #702)
+#703 := (iff #121 #121)
+#704 := [refl]: #703
+#706 := [quant-intro #704]: #705
+#188 := (~ #126 #126)
+#206 := (~ #121 #121)
+#207 := [refl]: #206
+#189 := [nnf-pos #207]: #188
+#25 := (= #24 #21)
+#22 := (<= 0::int #21)
+#26 := (implies #22 #25)
+#27 := (forall (vars (?v0 int)) #26)
+#129 := (iff #27 #126)
+#103 := (not #22)
+#104 := (or #103 #96)
+#109 := (forall (vars (?v0 int)) #104)
+#127 := (iff #109 #126)
+#124 := (iff #104 #121)
+#118 := (or #115 #96)
+#122 := (iff #118 #121)
+#123 := [rewrite]: #122
+#119 := (iff #104 #118)
+#116 := (iff #103 #115)
+#112 := (iff #22 #114)
+#113 := [rewrite]: #112
+#117 := [monotonicity #113]: #116
+#120 := [monotonicity #117]: #119
+#125 := [trans #120 #123]: #124
+#128 := [quant-intro #125]: #127
+#110 := (iff #27 #109)
+#107 := (iff #26 #104)
+#100 := (implies #22 #96)
+#105 := (iff #100 #104)
+#106 := [rewrite]: #105
+#101 := (iff #26 #100)
+#98 := (iff #25 #96)
+#99 := [rewrite]: #98
+#102 := [monotonicity #99]: #101
+#108 := [trans #102 #106]: #107
+#111 := [quant-intro #108]: #110
+#130 := [trans #111 #128]: #129
+#95 := [asserted]: #27
+#131 := [mp #95 #130]: #126
+#208 := [mp~ #131 #189]: #126
+#707 := [mp #208 #706]: #702
+#685 := (not #702)
+#379 := (or #685 #672)
+#662 := (>= 1::int 0::int)
+#668 := (not #662)
+#669 := (= 1::int #305)
+#671 := (or #669 #668)
+#653 := (or #685 #671)
+#654 := (iff #653 #379)
+#368 := (iff #379 #379)
+#369 := [rewrite]: #368
+#656 := (iff #671 #672)
+#383 := (or #672 false)
+#278 := (iff #383 #672)
+#655 := [rewrite]: #278
+#384 := (iff #671 #383)
+#367 := (iff #668 false)
+#1 := true
+#363 := (not true)
+#680 := (iff #363 false)
+#336 := [rewrite]: #680
+#659 := (iff #668 #363)
+#670 := (iff #662 true)
+#673 := [rewrite]: #670
+#660 := [monotonicity #673]: #659
+#382 := [trans #660 #336]: #367
+#310 := (iff #669 #672)
+#311 := [rewrite]: #310
+#385 := [monotonicity #311 #382]: #384
+#378 := [trans #385 #655]: #656
+#658 := [monotonicity #378]: #654
+#370 := [trans #658 #369]: #654
+#657 := [quant-inst]: #653
+#371 := [mp #657 #370]: #379
+#737 := [unit-resolution #371 #707]: #672
+#738 := (not #672)
+#739 := (or #738 #570)
+#740 := [th-lemma]: #739
+#741 := [unit-resolution #740 #737]: #570
+#742 := (not #570)
+#743 := (or #742 #484)
+#744 := [th-lemma]: #743
+#745 := [unit-resolution #744 #741]: #484
+#491 := (not #484)
+#486 := (or #685 #491 #528)
+#503 := (>= #617 0::int)
+#505 := (not #503)
+#514 := (= #617 #507)
+#516 := (or #514 #505)
+#502 := (or #685 #516)
+#477 := (iff #502 #486)
+#497 := (or #491 #528)
+#464 := (or #685 #497)
+#474 := (iff #464 #486)
+#475 := [rewrite]: #474
+#471 := (iff #502 #464)
+#500 := (iff #516 #497)
+#494 := (or #528 #491)
+#498 := (iff #494 #497)
+#499 := [rewrite]: #498
+#495 := (iff #516 #494)
+#492 := (iff #505 #491)
+#485 := (iff #503 #484)
+#490 := [rewrite]: #485
+#493 := [monotonicity #490]: #492
+#508 := (iff #514 #528)
+#529 := [rewrite]: #508
+#496 := [monotonicity #529 #493]: #495
+#501 := [trans #496 #499]: #500
+#473 := [monotonicity #501]: #471
+#478 := [trans #473 #475]: #477
+#463 := [quant-inst]: #502
+#479 := [mp #463 #478]: #486
+#746 := [unit-resolution #479 #707 #745]: #528
+#747 := (not #528)
+#748 := (or #747 #480)
+#749 := [th-lemma]: #748
+#750 := [unit-resolution #749 #746]: #480
+#481 := (>= #518 -1::int)
+#751 := (or #747 #481)
+#752 := [th-lemma]: #751
+#753 := [unit-resolution #752 #746]: #481
+#590 := (<= #305 1::int)
+#754 := (or #738 #590)
+#755 := [th-lemma]: #754
+#756 := [unit-resolution #755 #737]: #590
+#758 := [th-lemma #741 #756 #753 #750]: #757
+#760 := [symm #758]: #759
+#762 := [monotonicity #760]: #761
+#766 := [trans #762 #736]: #765
+#768 := [trans #766 #764]: #767
+#770 := [monotonicity #768 #732]: #769
+#774 := [trans #770 #772]: #773
+#807 := (= #33 #521)
+#272 := (f6 #32)
+#523 := (+ 1::int #272)
+#524 := (f5 #523)
+#803 := (= #524 #521)
+#620 := (= #521 #524)
+#610 := (or #608 #620)
+#602 := [quant-inst]: #610
+#775 := [unit-resolution #602 #693]: #620
+#804 := [symm #775]: #803
+#805 := (= #33 #524)
+#576 := (f6 #524)
+#337 := (f5 #576)
+#351 := (= #337 #524)
+#344 := (or #354 #351)
+#350 := (= #524 #337)
+#355 := (or #354 #350)
+#340 := (iff #355 #344)
+#320 := (iff #344 #344)
+#322 := [rewrite]: #320
+#352 := (iff #350 #351)
+#353 := [rewrite]: #352
+#341 := [monotonicity #353]: #340
+#327 := [trans #341 #322]: #340
+#338 := [quant-inst]: #355
+#328 := [mp #338 #327]: #344
+#776 := [unit-resolution #328 #700]: #351
+#801 := (= #33 #337)
+#799 := (= 1::int #576)
+#797 := (= #576 1::int)
+#580 := (* -1::int #576)
+#581 := (+ #272 #580)
+#541 := (<= #581 -1::int)
+#582 := (= #581 -1::int)
+#561 := (>= #272 -1::int)
+#588 := (>= #272 0::int)
+#361 := (= #272 0::int)
+#675 := (or #685 #361)
+#271 := (>= 0::int 0::int)
+#356 := (not #271)
+#357 := (= 0::int #272)
+#358 := (or #357 #356)
+#334 := (or #685 #358)
+#676 := (iff #334 #675)
+#677 := (iff #675 #675)
+#319 := [rewrite]: #677
+#684 := (iff #358 #361)
+#347 := (or #361 false)
+#682 := (iff #347 #361)
+#683 := [rewrite]: #682
+#348 := (iff #358 #347)
+#467 := (iff #356 false)
+#342 := (iff #356 #363)
+#362 := (iff #271 true)
+#359 := [rewrite]: #362
+#678 := [monotonicity #359]: #342
+#674 := [trans #678 #336]: #467
+#349 := (iff #357 #361)
+#360 := [rewrite]: #349
+#681 := [monotonicity #360 #674]: #348
+#679 := [trans #681 #683]: #684
+#335 := [monotonicity #679]: #676
+#661 := [trans #335 #319]: #676
+#339 := [quant-inst]: #334
+#323 := [mp #339 #661]: #675
+#777 := [unit-resolution #323 #707]: #361
+#778 := (not #361)
+#779 := (or #778 #588)
+#780 := [th-lemma]: #779
+#781 := [unit-resolution #780 #777]: #588
+#782 := (not #588)
+#783 := (or #782 #561)
+#784 := [th-lemma]: #783
+#785 := [unit-resolution #784 #781]: #561
+#565 := (not #561)
+#557 := (or #685 #565 #582)
+#574 := (>= #523 0::int)
+#575 := (not #574)
+#577 := (= #523 #576)
+#578 := (or #577 #575)
+#558 := (or #685 #578)
+#428 := (iff #558 #557)
+#555 := (or #565 #582)
+#554 := (or #685 #555)
+#534 := (iff #554 #557)
+#535 := [rewrite]: #534
+#560 := (iff #558 #554)
+#553 := (iff #578 #555)
+#568 := (or #582 #565)
+#551 := (iff #568 #555)
+#552 := [rewrite]: #551
+#563 := (iff #578 #568)
+#566 := (iff #575 #565)
+#562 := (iff #574 #561)
+#564 := [rewrite]: #562
+#567 := [monotonicity #564]: #566
+#572 := (iff #577 #582)
+#583 := [rewrite]: #572
+#569 := [monotonicity #583 #567]: #563
+#556 := [trans #569 #552]: #553
+#533 := [monotonicity #556]: #560
+#539 := [trans #533 #535]: #428
+#559 := [quant-inst]: #558
+#540 := [mp #559 #539]: #557
+#786 := [unit-resolution #540 #707 #785]: #582
+#787 := (not #582)
+#788 := (or #787 #541)
+#789 := [th-lemma]: #788
+#790 := [unit-resolution #789 #786]: #541
+#546 := (>= #581 -1::int)
+#791 := (or #787 #546)
+#792 := [th-lemma]: #791
+#793 := [unit-resolution #792 #786]: #546
+#587 := (<= #272 0::int)
+#794 := (or #778 #587)
+#795 := [th-lemma]: #794
+#796 := [unit-resolution #795 #777]: #587
+#798 := [th-lemma #781 #796 #793 #790]: #797
+#800 := [symm #798]: #799
+#802 := [monotonicity #800]: #801
+#806 := [trans #802 #776]: #805
+#808 := [trans #806 #804]: #807
+#811 := [monotonicity #808 #774]: #810
+#813 := [symm #811]: #812
+#515 := (= #37 #522)
+#526 := (or #525 #515)
+#527 := [quant-inst]: #526
+#809 := [unit-resolution #527 #728]: #515
+#814 := [trans #809 #813]: #42
+#43 := (not #42)
+#173 := [asserted]: #43
+[unit-resolution #173 #814]: false
+unsat
+aa7b4578015e2de8536adbac81c12fcdd9c70533 38 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S2 S1)
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#10 := (= #9 f1)
+#11 := (forall (vars (?v0 S2)) #10)
+#12 := (not #11)
+#13 := (or #11 #12)
+#14 := (not #13)
+#53 := (iff #14 false)
+#1 := true
+#48 := (not true)
+#51 := (iff #48 false)
+#52 := [rewrite]: #51
+#49 := (iff #14 #48)
+#46 := (iff #13 true)
+#32 := (= f1 #9)
+#35 := (forall (vars (?v0 S2)) #32)
+#38 := (not #35)
+#41 := (or #35 #38)
+#44 := (iff #41 true)
+#45 := [rewrite]: #44
+#42 := (iff #13 #41)
+#39 := (iff #12 #38)
+#36 := (iff #11 #35)
+#33 := (iff #10 #32)
+#34 := [rewrite]: #33
+#37 := [quant-intro #34]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #37 #40]: #42
+#47 := [trans #43 #45]: #46
+#50 := [monotonicity #47]: #49
+#54 := [trans #50 #52]: #53
+#31 := [asserted]: #14
+[mp #31 #54]: false
+unsat
+f2e1a8ca632baec8151f065291059c53754b68ae 366 0
+#2 := false
+decl f3 :: (-> int S2)
+#41 := 6::int
+#42 := (f3 6::int)
+decl f5 :: (-> S2 S2)
+decl f4 :: (-> S2 int)
+#34 := 4::int
+#35 := (f3 4::int)
+#36 := (f5 #35)
+#37 := (f4 #36)
+#38 := (* 4::int #37)
+#39 := (f3 #38)
+#40 := (f5 #39)
+#43 := (= #40 #42)
+#481 := (f5 #42)
+#408 := (= #481 #42)
+#536 := (= #42 #481)
+#625 := (f4 #42)
+#147 := -10::int
+#518 := (+ -10::int #625)
+#477 := (f3 #518)
+#508 := (f5 #477)
+#510 := (= #481 #508)
+#26 := 10::int
+#512 := (>= #625 10::int)
+#519 := (ite #512 #510 #536)
+#8 := (:var 0 S2)
+#25 := (f5 #8)
+#712 := (pattern #25)
+#9 := (f4 #8)
+#691 := (pattern #9)
+#214 := (= #8 #25)
+#148 := (+ -10::int #9)
+#151 := (f3 #148)
+#154 := (f5 #151)
+#213 := (= #25 #154)
+#168 := (>= #9 10::int)
+#197 := (ite #168 #213 #214)
+#713 := (forall (vars (?v0 S2)) (:pat #691 #712) #197)
+#200 := (forall (vars (?v0 S2)) #197)
+#716 := (iff #200 #713)
+#714 := (iff #197 #197)
+#715 := [refl]: #714
+#717 := [quant-intro #715]: #716
+#173 := (ite #168 #154 #8)
+#178 := (= #25 #173)
+#181 := (forall (vars (?v0 S2)) #178)
+#215 := (iff #181 #200)
+#198 := (iff #178 #197)
+#199 := [rewrite]: #198
+#216 := [quant-intro #199]: #215
+#195 := (~ #181 #181)
+#210 := (~ #178 #178)
+#211 := [refl]: #210
+#196 := [nnf-pos #211]: #195
+#28 := (- #9 10::int)
+#29 := (f3 #28)
+#30 := (f5 #29)
+#27 := (< #9 10::int)
+#31 := (ite #27 #8 #30)
+#32 := (= #25 #31)
+#33 := (forall (vars (?v0 S2)) #32)
+#184 := (iff #33 #181)
+#157 := (ite #27 #8 #154)
+#160 := (= #25 #157)
+#163 := (forall (vars (?v0 S2)) #160)
+#182 := (iff #163 #181)
+#179 := (iff #160 #178)
+#176 := (= #157 #173)
+#166 := (not #168)
+#170 := (ite #166 #8 #154)
+#174 := (= #170 #173)
+#175 := [rewrite]: #174
+#171 := (= #157 #170)
+#167 := (iff #27 #166)
+#169 := [rewrite]: #167
+#172 := [monotonicity #169]: #171
+#177 := [trans #172 #175]: #176
+#180 := [monotonicity #177]: #179
+#183 := [quant-intro #180]: #182
+#164 := (iff #33 #163)
+#161 := (iff #32 #160)
+#158 := (= #31 #157)
+#155 := (= #30 #154)
+#152 := (= #29 #151)
+#149 := (= #28 #148)
+#150 := [rewrite]: #149
+#153 := [monotonicity #150]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [quant-intro #162]: #164
+#185 := [trans #165 #183]: #184
+#146 := [asserted]: #33
+#186 := [mp #146 #185]: #181
+#212 := [mp~ #186 #196]: #181
+#217 := [mp #212 #216]: #200
+#718 := [mp #217 #717]: #713
+#341 := (not #713)
+#523 := (or #341 #519)
+#533 := [quant-inst]: #523
+#482 := [unit-resolution #533 #718]: #519
+#534 := (not #512)
+#503 := (<= #625 6::int)
+#615 := (= #625 6::int)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#699 := (pattern #16)
+#13 := 0::int
+#87 := (>= #14 0::int)
+#88 := (not #87)
+#17 := (f4 #16)
+#69 := (= #14 #17)
+#94 := (or #69 #88)
+#700 := (forall (vars (?v0 int)) (:pat #699) #94)
+#99 := (forall (vars (?v0 int)) #94)
+#703 := (iff #99 #700)
+#701 := (iff #94 #94)
+#702 := [refl]: #701
+#704 := [quant-intro #702]: #703
+#191 := (~ #99 #99)
+#188 := (~ #94 #94)
+#205 := [refl]: #188
+#192 := [nnf-pos #205]: #191
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#102 := (iff #20 #99)
+#76 := (not #15)
+#77 := (or #76 #69)
+#82 := (forall (vars (?v0 int)) #77)
+#100 := (iff #82 #99)
+#97 := (iff #77 #94)
+#91 := (or #88 #69)
+#95 := (iff #91 #94)
+#96 := [rewrite]: #95
+#92 := (iff #77 #91)
+#89 := (iff #76 #88)
+#85 := (iff #15 #87)
+#86 := [rewrite]: #85
+#90 := [monotonicity #86]: #89
+#93 := [monotonicity #90]: #92
+#98 := [trans #93 #96]: #97
+#101 := [quant-intro #98]: #100
+#83 := (iff #20 #82)
+#80 := (iff #19 #77)
+#73 := (implies #15 #69)
+#78 := (iff #73 #77)
+#79 := [rewrite]: #78
+#74 := (iff #19 #73)
+#71 := (iff #18 #69)
+#72 := [rewrite]: #71
+#75 := [monotonicity #72]: #74
+#81 := [trans #75 #79]: #80
+#84 := [quant-intro #81]: #83
+#103 := [trans #84 #101]: #102
+#68 := [asserted]: #20
+#104 := [mp #68 #103]: #99
+#206 := [mp~ #104 #192]: #99
+#705 := [mp #206 #704]: #700
+#678 := (not #700)
+#596 := (or #678 #615)
+#531 := (>= 6::int 0::int)
+#532 := (not #531)
+#622 := (= 6::int #625)
+#626 := (or #622 #532)
+#597 := (or #678 #626)
+#600 := (iff #597 #596)
+#602 := (iff #596 #596)
+#598 := [rewrite]: #602
+#605 := (iff #626 #615)
+#619 := (or #615 false)
+#610 := (iff #619 #615)
+#611 := [rewrite]: #610
+#608 := (iff #626 #619)
+#618 := (iff #532 false)
+#1 := true
+#668 := (not true)
+#671 := (iff #668 false)
+#672 := [rewrite]: #671
+#616 := (iff #532 #668)
+#604 := (iff #531 true)
+#606 := [rewrite]: #604
+#617 := [monotonicity #606]: #616
+#614 := [trans #617 #672]: #618
+#613 := (iff #622 #615)
+#607 := [rewrite]: #613
+#609 := [monotonicity #607 #614]: #608
+#612 := [trans #609 #611]: #605
+#601 := [monotonicity #612]: #600
+#603 := [trans #601 #598]: #600
+#599 := [quant-inst]: #597
+#589 := [mp #599 #603]: #596
+#483 := [unit-resolution #589 #705]: #615
+#458 := (not #615)
+#459 := (or #458 #503)
+#460 := [th-lemma]: #459
+#461 := [unit-resolution #460 #483]: #503
+#463 := (not #503)
+#464 := (or #463 #534)
+#465 := [th-lemma]: #464
+#307 := [unit-resolution #465 #461]: #534
+#513 := (not #519)
+#495 := (or #513 #512 #536)
+#496 := [def-axiom]: #495
+#466 := [unit-resolution #496 #307 #482]: #536
+#409 := [symm #466]: #408
+#410 := (= #40 #481)
+#654 := (f4 #39)
+#587 := (+ -10::int #654)
+#558 := (f3 #587)
+#561 := (f5 #558)
+#406 := (= #561 #481)
+#422 := (= #558 #42)
+#420 := (= #587 6::int)
+#340 := (f4 #35)
+#652 := -1::int
+#507 := (* -1::int #340)
+#468 := (+ #37 #507)
+#469 := (<= #468 0::int)
+#491 := (= #37 #340)
+#450 := (= #36 #35)
+#579 := (= #35 #36)
+#580 := (+ -10::int #340)
+#581 := (f3 #580)
+#582 := (f5 #581)
+#583 := (= #36 #582)
+#584 := (>= #340 10::int)
+#585 := (ite #584 #583 #579)
+#577 := (or #341 #585)
+#588 := [quant-inst]: #577
+#462 := [unit-resolution #588 #718]: #585
+#567 := (not #584)
+#559 := (<= #340 4::int)
+#329 := (= #340 4::int)
+#664 := (or #678 #329)
+#683 := (>= 4::int 0::int)
+#685 := (not #683)
+#682 := (= 4::int #340)
+#324 := (or #682 #685)
+#665 := (or #678 #324)
+#387 := (iff #665 #664)
+#389 := (iff #664 #664)
+#390 := [rewrite]: #389
+#677 := (iff #324 #329)
+#310 := (or #329 false)
+#315 := (iff #310 #329)
+#316 := [rewrite]: #315
+#674 := (iff #324 #310)
+#667 := (iff #685 false)
+#669 := (iff #685 #668)
+#330 := (iff #683 true)
+#331 := [rewrite]: #330
+#670 := [monotonicity #331]: #669
+#673 := [trans #670 #672]: #667
+#666 := (iff #682 #329)
+#328 := [rewrite]: #666
+#676 := [monotonicity #328 #673]: #674
+#675 := [trans #676 #316]: #677
+#388 := [monotonicity #675]: #387
+#282 := [trans #388 #390]: #387
+#372 := [quant-inst]: #665
+#660 := [mp #372 #282]: #664
+#467 := [unit-resolution #660 #705]: #329
+#446 := (not #329)
+#449 := (or #446 #559)
+#453 := [th-lemma]: #449
+#455 := [unit-resolution #453 #467]: #559
+#456 := (not #559)
+#454 := (or #456 #567)
+#457 := [th-lemma]: #454
+#445 := [unit-resolution #457 #455]: #567
+#566 := (not #585)
+#571 := (or #566 #584 #579)
+#572 := [def-axiom]: #571
+#448 := [unit-resolution #572 #445 #462]: #579
+#451 := [symm #448]: #450
+#447 := [monotonicity #451]: #491
+#452 := (not #491)
+#442 := (or #452 #469)
+#432 := [th-lemma]: #442
+#434 := [unit-resolution #432 #447]: #469
+#476 := (>= #468 0::int)
+#435 := (or #452 #476)
+#438 := [th-lemma]: #435
+#439 := [unit-resolution #438 #447]: #476
+#565 := (>= #340 4::int)
+#443 := (or #446 #565)
+#436 := [th-lemma]: #443
+#444 := [unit-resolution #436 #467]: #565
+#656 := (* -1::int #654)
+#653 := (+ #38 #656)
+#630 := (<= #653 0::int)
+#657 := (= #653 0::int)
+#648 := (>= #37 0::int)
+#440 := (not #476)
+#437 := (not #565)
+#441 := (or #648 #437 #440)
+#427 := [th-lemma]: #441
+#429 := [unit-resolution #427 #444 #439]: #648
+#649 := (not #648)
+#494 := (or #649 #657)
+#633 := (or #678 #649 #657)
+#375 := (>= #38 0::int)
+#376 := (not #375)
+#655 := (= #38 #654)
+#369 := (or #655 #376)
+#634 := (or #678 #369)
+#474 := (iff #634 #633)
+#641 := (or #678 #494)
+#471 := (iff #641 #633)
+#473 := [rewrite]: #471
+#635 := (iff #634 #641)
+#638 := (iff #369 #494)
+#651 := (or #657 #649)
+#636 := (iff #651 #494)
+#637 := [rewrite]: #636
+#492 := (iff #369 #651)
+#650 := (iff #376 #649)
+#643 := (iff #375 #648)
+#644 := [rewrite]: #643
+#645 := [monotonicity #644]: #650
+#646 := (iff #655 #657)
+#647 := [rewrite]: #646
+#493 := [monotonicity #647 #645]: #492
+#639 := [trans #493 #637]: #638
+#642 := [monotonicity #639]: #635
+#627 := [trans #642 #473]: #474
+#640 := [quant-inst]: #634
+#628 := [mp #640 #627]: #633
+#430 := [unit-resolution #628 #705]: #494
+#428 := [unit-resolution #430 #429]: #657
+#431 := (not #657)
+#413 := (or #431 #630)
+#415 := [th-lemma]: #413
+#416 := [unit-resolution #415 #428]: #630
+#631 := (>= #653 0::int)
+#417 := (or #431 #631)
+#418 := [th-lemma]: #417
+#419 := [unit-resolution #418 #428]: #631
+#421 := [th-lemma #419 #416 #444 #455 #439 #434]: #420
+#423 := [monotonicity #421]: #422
+#407 := [monotonicity #423]: #406
+#562 := (= #40 #561)
+#586 := (= #39 #40)
+#563 := (>= #654 10::int)
+#564 := (ite #563 #562 #586)
+#538 := (or #341 #564)
+#539 := [quant-inst]: #538
+#424 := [unit-resolution #539 #718]: #564
+#425 := (not #630)
+#414 := (or #563 #425 #437 #440)
+#426 := [th-lemma]: #414
+#403 := [unit-resolution #426 #416 #444 #439]: #563
+#433 := (not #563)
+#540 := (not #564)
+#544 := (or #540 #433 #562)
+#545 := [def-axiom]: #544
+#405 := [unit-resolution #545 #403 #424]: #562
+#411 := [trans #405 #407]: #410
+#404 := [trans #411 #409]: #43
+#44 := (not #43)
+#187 := [asserted]: #44
+[unit-resolution #187 #404]: false
+unsat
+b611bff85387673a495359caee35c17082ebae1e 478 0
+#2 := false
+decl f7 :: (-> S4 S2)
+decl f8 :: (-> S1 S4)
+decl f1 :: S1
+#4 := f1
+#28 := (f8 f1)
+#29 := (f7 #28)
+decl f5 :: (-> S3 S2)
+decl f6 :: (-> int S3)
+#25 := 3::int
+#26 := (f6 3::int)
+#27 := (f5 #26)
+#30 := (= #27 #29)
+decl f12 :: (-> S6 S2)
+decl f13 :: (-> S1 S6 S6)
+decl f14 :: S6
+#42 := f14
+#857 := (f13 f1 f14)
+#496 := (f12 #857)
+#602 := (= #496 #29)
+#859 := (= #29 #496)
+#39 := (:var 0 S1)
+#43 := (f13 #39 f14)
+#902 := (pattern #43)
+#40 := (f8 #39)
+#901 := (pattern #40)
+#44 := (f12 #43)
+#41 := (f7 #40)
+#45 := (= #41 #44)
+#903 := (forall (vars (?v0 S1)) (:pat #901 #902) #45)
+#46 := (forall (vars (?v0 S1)) #45)
+#906 := (iff #46 #903)
+#904 := (iff #45 #45)
+#905 := [refl]: #904
+#907 := [quant-intro #905]: #906
+#346 := (~ #46 #46)
+#345 := (~ #45 #45)
+#389 := [refl]: #345
+#347 := [nnf-pos #389]: #346
+#225 := [asserted]: #46
+#390 := [mp~ #225 #347]: #46
+#908 := [mp #390 #907]: #903
+#553 := (not #903)
+#568 := (or #553 #859)
+#569 := [quant-inst]: #568
+#625 := [unit-resolution #569 #908]: #859
+#603 := [symm #625]: #602
+#590 := (= #27 #496)
+decl f18 :: (-> S6 S2)
+#814 := (f18 #857)
+#600 := (= #814 #496)
+#815 := (= #496 #814)
+#62 := (:var 0 S6)
+#64 := (f18 #62)
+#918 := (pattern #64)
+#63 := (f12 #62)
+#917 := (pattern #63)
+#65 := (= #63 #64)
+#919 := (forall (vars (?v0 S6)) (:pat #917 #918) #65)
+#66 := (forall (vars (?v0 S6)) #65)
+#922 := (iff #66 #919)
+#920 := (iff #65 #65)
+#921 := [refl]: #920
+#923 := [quant-intro #921]: #922
+#358 := (~ #66 #66)
+#357 := (~ #65 #65)
+#354 := [refl]: #357
+#359 := [nnf-pos #354]: #358
+#238 := [asserted]: #66
+#355 := [mp~ #238 #359]: #66
+#924 := [mp #355 #923]: #919
+#564 := (not #919)
+#816 := (or #564 #815)
+#823 := [quant-inst]: #816
+#617 := [unit-resolution #823 #924]: #815
+#601 := [symm #617]: #600
+#588 := (= #27 #814)
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+#108 := (f18 f14)
+#821 := (f4 #108)
+#85 := 1::int
+#252 := (f3 1::int)
+#255 := (f4 #252)
+#655 := (+ #255 #821)
+#811 := (f3 #655)
+#697 := (= #811 #814)
+#94 := (:var 1 S1)
+#95 := (f13 #94 #62)
+#960 := (pattern #95)
+#117 := (f4 #64)
+#321 := (+ #117 #255)
+#325 := (f3 #321)
+#116 := (f18 #95)
+#328 := (= #116 #325)
+#961 := (forall (vars (?v0 S1) (?v1 S6)) (:pat #960) #328)
+#331 := (forall (vars (?v0 S1) (?v1 S6)) #328)
+#964 := (iff #331 #961)
+#962 := (iff #328 #328)
+#963 := [refl]: #962
+#965 := [quant-intro #963]: #964
+#374 := (~ #331 #331)
+#373 := (~ #328 #328)
+#370 := [refl]: #373
+#375 := [nnf-pos #370]: #374
+#13 := 0::int
+#86 := (+ 0::int 1::int)
+#87 := (f3 #86)
+#88 := (f4 #87)
+#118 := (+ #117 #88)
+#119 := (f3 #118)
+#120 := (= #116 #119)
+#121 := (forall (vars (?v0 S1) (?v1 S6)) #120)
+#332 := (iff #121 #331)
+#329 := (iff #120 #328)
+#326 := (= #119 #325)
+#323 := (= #118 #321)
+#256 := (= #88 #255)
+#253 := (= #87 #252)
+#249 := (= #86 1::int)
+#251 := [rewrite]: #249
+#254 := [monotonicity #251]: #253
+#257 := [monotonicity #254]: #256
+#324 := [monotonicity #257]: #323
+#327 := [monotonicity #324]: #326
+#330 := [monotonicity #327]: #329
+#333 := [quant-intro #330]: #332
+#320 := [asserted]: #121
+#336 := [mp #320 #333]: #331
+#371 := [mp~ #336 #375]: #331
+#966 := [mp #371 #965]: #961
+#802 := (not #961)
+#805 := (or #802 #697)
+#822 := (+ #821 #255)
+#652 := (f3 #822)
+#654 := (= #814 #652)
+#690 := (or #802 #654)
+#707 := (iff #690 #805)
+#701 := (iff #805 #805)
+#709 := [rewrite]: #701
+#706 := (iff #654 #697)
+#813 := (= #814 #811)
+#656 := (iff #813 #697)
+#804 := [rewrite]: #656
+#695 := (iff #654 #813)
+#812 := (= #652 #811)
+#808 := (= #822 #655)
+#809 := [rewrite]: #808
+#810 := [monotonicity #809]: #812
+#696 := [monotonicity #810]: #695
+#801 := [trans #696 #804]: #706
+#708 := [monotonicity #801]: #707
+#710 := [trans #708 #709]: #707
+#705 := [quant-inst]: #690
+#711 := [mp #705 #710]: #805
+#624 := [unit-resolution #711 #966]: #697
+#586 := (= #27 #811)
+#598 := (= #252 #811)
+#622 := (= #811 #252)
+#619 := (= #655 1::int)
+#807 := (<= #821 0::int)
+#803 := (= #821 0::int)
+#69 := (f3 0::int)
+#543 := (f4 #69)
+#548 := (= #543 0::int)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#880 := (pattern #16)
+#164 := (>= #14 0::int)
+#165 := (not #164)
+#17 := (f4 #16)
+#146 := (= #14 #17)
+#171 := (or #146 #165)
+#881 := (forall (vars (?v0 int)) (:pat #880) #171)
+#176 := (forall (vars (?v0 int)) #171)
+#884 := (iff #176 #881)
+#882 := (iff #171 #171)
+#883 := [refl]: #882
+#885 := [quant-intro #883]: #884
+#338 := (~ #176 #176)
+#334 := (~ #171 #171)
+#382 := [refl]: #334
+#339 := [nnf-pos #382]: #338
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#179 := (iff #20 #176)
+#153 := (not #15)
+#154 := (or #153 #146)
+#159 := (forall (vars (?v0 int)) #154)
+#177 := (iff #159 #176)
+#174 := (iff #154 #171)
+#168 := (or #165 #146)
+#172 := (iff #168 #171)
+#173 := [rewrite]: #172
+#169 := (iff #154 #168)
+#166 := (iff #153 #165)
+#162 := (iff #15 #164)
+#163 := [rewrite]: #162
+#167 := [monotonicity #163]: #166
+#170 := [monotonicity #167]: #169
+#175 := [trans #170 #173]: #174
+#178 := [quant-intro #175]: #177
+#160 := (iff #20 #159)
+#157 := (iff #19 #154)
+#150 := (implies #15 #146)
+#155 := (iff #150 #154)
+#156 := [rewrite]: #155
+#151 := (iff #19 #150)
+#148 := (iff #18 #146)
+#149 := [rewrite]: #148
+#152 := [monotonicity #149]: #151
+#158 := [trans #152 #156]: #157
+#161 := [quant-intro #158]: #160
+#180 := [trans #161 #178]: #179
+#145 := [asserted]: #20
+#181 := [mp #145 #180]: #176
+#383 := [mp~ #181 #339]: #176
+#886 := [mp #383 #885]: #881
+#861 := (not #881)
+#520 := (or #861 #548)
+#458 := (>= 0::int 0::int)
+#542 := (not #458)
+#544 := (= 0::int #543)
+#535 := (or #544 #542)
+#525 := (or #861 #535)
+#521 := (iff #525 #520)
+#505 := (iff #520 #520)
+#847 := [rewrite]: #505
+#865 := (iff #535 #548)
+#534 := (or #548 false)
+#869 := (iff #534 #548)
+#870 := [rewrite]: #869
+#867 := (iff #535 #534)
+#860 := (iff #542 false)
+#1 := true
+#528 := (not true)
+#522 := (iff #528 false)
+#653 := [rewrite]: #522
+#864 := (iff #542 #528)
+#545 := (iff #458 true)
+#549 := [rewrite]: #545
+#866 := [monotonicity #549]: #864
+#533 := [trans #866 #653]: #860
+#546 := (iff #544 #548)
+#547 := [rewrite]: #546
+#868 := [monotonicity #547 #533]: #867
+#871 := [trans #868 #870]: #865
+#863 := [monotonicity #871]: #521
+#509 := [trans #863 #847]: #521
+#862 := [quant-inst]: #525
+#510 := [mp #862 #509]: #520
+#664 := [unit-resolution #510 #886]: #548
+#626 := (= #821 #543)
+#109 := (= #108 #69)
+#302 := (= #69 #108)
+#304 := (iff #109 #302)
+#305 := [rewrite]: #304
+#301 := [asserted]: #109
+#308 := [mp #301 #305]: #302
+#638 := [symm #308]: #109
+#629 := [monotonicity #638]: #626
+#631 := [trans #629 #664]: #803
+#632 := (not #803)
+#628 := (or #632 #807)
+#633 := [th-lemma]: #628
+#623 := [unit-resolution #633 #631]: #807
+#794 := (>= #821 0::int)
+#613 := (or #632 #794)
+#615 := [th-lemma]: #613
+#616 := [unit-resolution #615 #631]: #794
+#726 := (<= #255 1::int)
+#747 := (= #255 1::int)
+#744 := (or #861 #747)
+#756 := (>= 1::int 0::int)
+#757 := (not #756)
+#768 := (= 1::int #255)
+#758 := (or #768 #757)
+#745 := (or #861 #758)
+#746 := (iff #745 #744)
+#720 := (iff #744 #744)
+#721 := [rewrite]: #720
+#742 := (iff #758 #747)
+#755 := (or #747 false)
+#738 := (iff #755 #747)
+#739 := [rewrite]: #738
+#741 := (iff #758 #755)
+#754 := (iff #757 false)
+#752 := (iff #757 #528)
+#750 := (iff #756 true)
+#751 := [rewrite]: #750
+#753 := [monotonicity #751]: #752
+#749 := [trans #753 #653]: #754
+#769 := (iff #768 #747)
+#748 := [rewrite]: #769
+#737 := [monotonicity #748 #749]: #741
+#743 := [trans #737 #739]: #742
+#719 := [monotonicity #743]: #746
+#614 := [trans #719 #721]: #746
+#740 := [quant-inst]: #745
+#725 := [mp #740 #614]: #744
+#645 := [unit-resolution #725 #886]: #747
+#646 := (not #747)
+#488 := (or #646 #726)
+#647 := [th-lemma]: #488
+#643 := [unit-resolution #647 #645]: #726
+#727 := (>= #255 1::int)
+#648 := (or #646 #727)
+#627 := [th-lemma]: #648
+#630 := [unit-resolution #627 #645]: #727
+#620 := [th-lemma #630 #643 #616 #623]: #619
+#608 := [monotonicity #620]: #622
+#599 := [symm #608]: #598
+#607 := (= #27 #252)
+decl f17 :: (-> S5 S2)
+decl f11 :: S5
+#34 := f11
+#106 := (f17 f11)
+#843 := (f4 #106)
+#557 := (+ #255 #843)
+#550 := (f3 #557)
+#596 := (= #550 #252)
+#610 := (= #252 #550)
+#637 := (= 1::int #557)
+#634 := (= #557 1::int)
+#713 := (<= #843 0::int)
+#712 := (= #843 0::int)
+#666 := (= #843 #543)
+#107 := (= #106 #69)
+#297 := (= #69 #106)
+#299 := (iff #107 #297)
+#300 := [rewrite]: #299
+#296 := [asserted]: #107
+#303 := [mp #296 #300]: #297
+#665 := [symm #303]: #107
+#667 := [monotonicity #665]: #666
+#668 := [trans #667 #664]: #712
+#651 := (not #712)
+#669 := (or #651 #713)
+#639 := [th-lemma]: #669
+#640 := [unit-resolution #639 #668]: #713
+#806 := (>= #843 0::int)
+#641 := (or #651 #806)
+#642 := [th-lemma]: #641
+#644 := [unit-resolution #642 #668]: #806
+#636 := [th-lemma #630 #643 #644 #640]: #634
+#635 := [symm #636]: #637
+#611 := [monotonicity #635]: #610
+#597 := [symm #611]: #596
+#606 := (= #27 #550)
+decl f10 :: (-> int S5 S5)
+#854 := (f10 3::int f11)
+#570 := (f17 #854)
+#834 := (= #570 #550)
+#828 := (= #550 #570)
+#57 := (:var 0 S5)
+#77 := (:var 1 int)
+#78 := (f10 #77 #57)
+#953 := (pattern #78)
+#59 := (f17 #57)
+#111 := (f4 #59)
+#307 := (+ #111 #255)
+#311 := (f3 #307)
+#110 := (f17 #78)
+#314 := (= #110 #311)
+#954 := (forall (vars (?v0 int) (?v1 S5)) (:pat #953) #314)
+#317 := (forall (vars (?v0 int) (?v1 S5)) #314)
+#957 := (iff #317 #954)
+#955 := (iff #314 #314)
+#956 := [refl]: #955
+#958 := [quant-intro #956]: #957
+#368 := (~ #317 #317)
+#401 := (~ #314 #314)
+#402 := [refl]: #401
+#369 := [nnf-pos #402]: #368
+#112 := (+ #111 #88)
+#113 := (f3 #112)
+#114 := (= #110 #113)
+#115 := (forall (vars (?v0 int) (?v1 S5)) #114)
+#318 := (iff #115 #317)
+#315 := (iff #114 #314)
+#312 := (= #113 #311)
+#309 := (= #112 #307)
+#310 := [monotonicity #257]: #309
+#313 := [monotonicity #310]: #312
+#316 := [monotonicity #313]: #315
+#319 := [quant-intro #316]: #318
+#306 := [asserted]: #115
+#322 := [mp #306 #319]: #317
+#372 := [mp~ #322 #369]: #317
+#959 := [mp #372 #958]: #954
+#831 := (not #954)
+#826 := (or #831 #828)
+#840 := (+ #843 #255)
+#555 := (f3 #840)
+#556 := (= #570 #555)
+#832 := (or #831 #556)
+#674 := (iff #832 #826)
+#817 := (iff #826 #826)
+#818 := [rewrite]: #817
+#825 := (iff #556 #828)
+#829 := (iff #834 #828)
+#824 := [rewrite]: #829
+#838 := (iff #556 #834)
+#833 := (= #555 #550)
+#835 := (= #840 #557)
+#836 := [rewrite]: #835
+#837 := [monotonicity #836]: #833
+#827 := [monotonicity #837]: #838
+#830 := [trans #827 #824]: #825
+#675 := [monotonicity #830]: #674
+#819 := [trans #675 #818]: #674
+#673 := [quant-inst]: #832
+#820 := [mp #673 #819]: #826
+#659 := [unit-resolution #820 #959]: #828
+#594 := [symm #659]: #834
+#604 := (= #27 #570)
+decl f9 :: (-> S5 S2)
+#491 := (f9 #854)
+#842 := (= #491 #570)
+#910 := (pattern #59)
+#58 := (f9 #57)
+#909 := (pattern #58)
+#60 := (= #58 #59)
+#911 := (forall (vars (?v0 S5)) (:pat #909 #910) #60)
+#61 := (forall (vars (?v0 S5)) #60)
+#914 := (iff #61 #911)
+#912 := (iff #60 #60)
+#913 := [refl]: #912
+#915 := [quant-intro #913]: #914
+#348 := (~ #61 #61)
+#391 := (~ #60 #60)
+#392 := [refl]: #391
+#349 := [nnf-pos #392]: #348
+#237 := [asserted]: #61
+#356 := [mp~ #237 #349]: #61
+#916 := [mp #356 #915]: #911
+#571 := (not #911)
+#844 := (or #571 #842)
+#554 := [quant-inst]: #844
+#657 := [unit-resolution #554 #916]: #842
+#855 := (= #27 #491)
+#35 := (f10 #14 f11)
+#894 := (pattern #35)
+#32 := (f6 #14)
+#893 := (pattern #32)
+#36 := (f9 #35)
+#33 := (f5 #32)
+#37 := (= #33 #36)
+#895 := (forall (vars (?v0 int)) (:pat #893 #894) #37)
+#38 := (forall (vars (?v0 int)) #37)
+#898 := (iff #38 #895)
+#896 := (iff #37 #37)
+#897 := [refl]: #896
+#899 := [quant-intro #897]: #898
+#342 := (~ #38 #38)
+#387 := (~ #37 #37)
+#388 := [refl]: #387
+#343 := [nnf-pos #388]: #342
+#224 := [asserted]: #38
+#344 := [mp~ #224 #343]: #38
+#900 := [mp #344 #899]: #895
+#497 := (not #895)
+#858 := (or #497 #855)
+#856 := [quant-inst]: #858
+#618 := [unit-resolution #856 #900]: #855
+#605 := [trans #618 #657]: #604
+#595 := [trans #605 #594]: #606
+#584 := [trans #595 #597]: #607
+#587 := [trans #584 #599]: #586
+#589 := [trans #587 #624]: #588
+#591 := [trans #589 #601]: #590
+#592 := [trans #591 #603]: #30
+#31 := (not #30)
+#223 := [asserted]: #31
+[unit-resolution #223 #592]: false
+unsat
+1ae66c01a019816f43584ef4a2147068b8c58d05 76 0
+#2 := false
+decl f3 :: (-> int S1)
+#12 := (:var 0 int)
+#13 := (f3 #12)
+#1016 := (pattern #13)
+decl f1 :: S1
+#4 := f1
+#157 := (= f1 #13)
+#1017 := (forall (vars (?v0 int)) (:pat #1016) #157)
+#181 := (forall (vars (?v0 int)) #157)
+#1020 := (iff #181 #1017)
+#1018 := (iff #157 #157)
+#1019 := [refl]: #1018
+#1021 := [quant-intro #1019]: #1020
+#494 := (~ #181 #181)
+#492 := (~ #157 #157)
+#493 := [refl]: #492
+#495 := [nnf-pos #493]: #494
+decl f4 :: (-> S2 S1)
+decl f5 :: (-> int S2 S2)
+decl f6 :: S2
+#15 := f6
+#16 := (f5 #12 f6)
+#17 := (f4 #16)
+#18 := (= #17 f1)
+#19 := (not #18)
+#20 := (or #18 #19)
+#14 := (= #13 f1)
+#21 := (and #14 #20)
+#22 := (forall (vars (?v0 int)) #21)
+#182 := (iff #22 #181)
+#179 := (iff #21 #157)
+#1 := true
+#174 := (and #157 true)
+#177 := (iff #174 #157)
+#178 := [rewrite]: #177
+#175 := (iff #21 #174)
+#172 := (iff #20 true)
+#161 := (= f1 #17)
+#164 := (not #161)
+#167 := (or #161 #164)
+#170 := (iff #167 true)
+#171 := [rewrite]: #170
+#168 := (iff #20 #167)
+#165 := (iff #19 #164)
+#162 := (iff #18 #161)
+#163 := [rewrite]: #162
+#166 := [monotonicity #163]: #165
+#169 := [monotonicity #163 #166]: #168
+#173 := [trans #169 #171]: #172
+#159 := (iff #14 #157)
+#160 := [rewrite]: #159
+#176 := [monotonicity #160 #173]: #175
+#180 := [trans #176 #178]: #179
+#183 := [quant-intro #180]: #182
+#156 := [asserted]: #22
+#186 := [mp #156 #183]: #181
+#468 := [mp~ #186 #495]: #181
+#1022 := [mp #468 #1021]: #1017
+#8 := 1::int
+#9 := (f3 1::int)
+#150 := (= f1 #9)
+#153 := (not #150)
+#10 := (= #9 f1)
+#11 := (not #10)
+#154 := (iff #11 #153)
+#151 := (iff #10 #150)
+#152 := [rewrite]: #151
+#155 := [monotonicity #152]: #154
+#149 := [asserted]: #11
+#158 := [mp #149 #155]: #153
+#603 := (not #1017)
+#688 := (or #603 #150)
+#689 := [quant-inst]: #688
+[unit-resolution #689 #158 #1022]: false
+unsat

--- a/src/HOL/SMT_Examples/SMT_Examples.thy	Wed May 12 23:54:04 2010 +0200
+++ b/src/HOL/SMT_Examples/SMT_Examples.thy	Wed May 12 23:54:06 2010 +0200
@@ -9,7 +9,7 @@
 begin
 
 declare [[smt_solver=z3, z3_proofs=true]]
-declare [[smt_certificates="~~/src/HOL/SMT_Examples/SMT_Basic.certs"]]
+declare [[smt_certificates="~~/src/HOL/SMT_Examples/SMT_Examples.certs"]]
 declare [[smt_fixed=true]]
 
 

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT_Examples/SMT_Tests.certs	Wed May 12 23:54:06 2010 +0200
@@ -0,0 +1,24573 @@
+32bb24b231f8ef17d3b0def6817d84cc062a6d75 33 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#10 := (not #9)
+#11 := (or #9 #10)
+#12 := (not #11)
+#48 := (iff #12 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (iff #11 true)
+#30 := (= f1 f3)
+#33 := (not #30)
+#36 := (or #30 #33)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #11 #36)
+#34 := (iff #10 #33)
+#31 := (iff #9 #30)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#38 := [monotonicity #32 #35]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#29 := [asserted]: #12
+[mp #29 #49]: false
+unsat
+d296070a9a1ad4678f3ec56cd19a634e50fd638a 8 0
+#2 := false
+#1 := true
+#8 := (not true)
+#26 := (iff #8 false)
+#27 := [rewrite]: #26
+#25 := [asserted]: #8
+[mp #25 #27]: false
+unsat
+ae7e7a13c311c9f3e926d7f4a9307c3954711112 41 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#10 := (not #9)
+#11 := (and #9 #10)
+#12 := (not #11)
+#13 := (not #12)
+#56 := (iff #13 false)
+#1 := true
+#51 := (not true)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #13 #51)
+#49 := (iff #12 true)
+#44 := (not false)
+#47 := (iff #44 true)
+#48 := [rewrite]: #47
+#45 := (iff #12 #44)
+#42 := (iff #11 false)
+#31 := (= f1 f3)
+#34 := (not #31)
+#37 := (and #31 #34)
+#40 := (iff #37 false)
+#41 := [rewrite]: #40
+#38 := (iff #11 #37)
+#35 := (iff #10 #34)
+#32 := (iff #9 #31)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#39 := [monotonicity #33 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#30 := [asserted]: #13
+[mp #30 #57]: false
+unsat
+5a2fbe7eaa720a0d1634e4c8ad246283132e9cb9 16 0
+#2 := false
+#8 := (not false)
+#9 := (not #8)
+#34 := (iff #9 false)
+#1 := true
+#29 := (not true)
+#32 := (iff #29 false)
+#33 := [rewrite]: #32
+#30 := (iff #9 #29)
+#27 := (iff #8 true)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#35 := [trans #31 #33]: #34
+#26 := [asserted]: #9
+[mp #26 #35]: false
+unsat
+1818aabb2eeb93cf072a1c54b65c5fbc8da59afb 21 0
+#2 := false
+#1 := true
+#8 := (not true)
+#9 := (not #8)
+#10 := (not #9)
+#39 := (iff #10 false)
+#28 := (iff #8 false)
+#29 := [rewrite]: #28
+#37 := (iff #10 #8)
+#35 := (iff #9 true)
+#30 := (not false)
+#33 := (iff #30 true)
+#34 := [rewrite]: #33
+#31 := (iff #9 #30)
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#38 := [monotonicity #36]: #37
+#40 := [trans #38 #29]: #39
+#27 := [asserted]: #10
+[mp #27 #40]: false
+unsat
+07720e913d13e1bf2c9278ea9348b2924d764925 65 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#12 := (and false #9)
+#13 := (or #12 #9)
+#11 := (not #9)
+#14 := (or #11 #13)
+#1 := true
+#10 := (and true #9)
+#15 := (or #10 #14)
+#16 := (not #15)
+#80 := (iff #16 false)
+#75 := (not true)
+#78 := (iff #75 false)
+#79 := [rewrite]: #78
+#76 := (iff #16 #75)
+#73 := (iff #15 true)
+#34 := (= f1 f3)
+#68 := (or #34 true)
+#71 := (iff #68 true)
+#72 := [rewrite]: #71
+#69 := (iff #15 #68)
+#66 := (iff #14 true)
+#44 := (not #34)
+#61 := (or #44 #34)
+#64 := (iff #61 true)
+#65 := [rewrite]: #64
+#62 := (iff #14 #61)
+#59 := (iff #13 #34)
+#54 := (or false #34)
+#57 := (iff #54 #34)
+#58 := [rewrite]: #57
+#55 := (iff #13 #54)
+#35 := (iff #9 #34)
+#36 := [rewrite]: #35
+#52 := (iff #12 false)
+#47 := (and false #34)
+#50 := (iff #47 false)
+#51 := [rewrite]: #50
+#48 := (iff #12 #47)
+#49 := [monotonicity #36]: #48
+#53 := [trans #49 #51]: #52
+#56 := [monotonicity #53 #36]: #55
+#60 := [trans #56 #58]: #59
+#45 := (iff #11 #44)
+#46 := [monotonicity #36]: #45
+#63 := [monotonicity #46 #60]: #62
+#67 := [trans #63 #65]: #66
+#42 := (iff #10 #34)
+#37 := (and true #34)
+#40 := (iff #37 #34)
+#41 := [rewrite]: #40
+#38 := (iff #10 #37)
+#39 := [monotonicity #36]: #38
+#43 := [trans #39 #41]: #42
+#70 := [monotonicity #43 #67]: #69
+#74 := [trans #70 #72]: #73
+#77 := [monotonicity #74]: #76
+#81 := [trans #77 #79]: #80
+#33 := [asserted]: #16
+[mp #33 #81]: false
+unsat
+d3b6081bc1c34a0421e641acff757eaaefbf5bdf 16 0
+#2 := false
+#1 := true
+#8 := (and true true)
+#9 := (not #8)
+#34 := (iff #9 false)
+#29 := (not true)
+#32 := (iff #29 false)
+#33 := [rewrite]: #32
+#30 := (iff #9 #29)
+#27 := (iff #8 true)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#35 := [trans #31 #33]: #34
+#26 := [asserted]: #9
+[mp #26 #35]: false
+unsat
+4613b1a9286522197f6752544018c3ecaea8838a 29 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#10 := (implies #9 #9)
+#11 := (not #10)
+#44 := (iff #11 false)
+#1 := true
+#39 := (not true)
+#42 := (iff #39 false)
+#43 := [rewrite]: #42
+#40 := (iff #11 #39)
+#37 := (iff #10 true)
+#29 := (= f1 f3)
+#32 := (implies #29 #29)
+#35 := (iff #32 true)
+#36 := [rewrite]: #35
+#33 := (iff #10 #32)
+#30 := (iff #9 #29)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31 #31]: #33
+#38 := [trans #34 #36]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#28 := [asserted]: #11
+[mp #28 #45]: false
+unsat
+3c555028924c0617a48e7816899f81fd171e8cc6 16 0
+#2 := false
+#1 := true
+#8 := (or true false)
+#9 := (not #8)
+#34 := (iff #9 false)
+#29 := (not true)
+#32 := (iff #29 false)
+#33 := [rewrite]: #32
+#30 := (iff #9 #29)
+#27 := (iff #8 true)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#35 := [trans #31 #33]: #34
+#26 := [asserted]: #9
+[mp #26 #35]: false
+unsat
+280e0943c88a9613c460fbcd9ed182ff9d6c1d83 41 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#10 := (not #9)
+#11 := (and #9 #10)
+#12 := (implies #11 false)
+#13 := (not #12)
+#56 := (iff #13 false)
+#1 := true
+#51 := (not true)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #13 #51)
+#49 := (iff #12 true)
+#44 := (implies false false)
+#47 := (iff #44 true)
+#48 := [rewrite]: #47
+#45 := (iff #12 #44)
+#42 := (iff #11 false)
+#31 := (= f1 f3)
+#34 := (not #31)
+#37 := (and #31 #34)
+#40 := (iff #37 false)
+#41 := [rewrite]: #40
+#38 := (iff #11 #37)
+#35 := (iff #10 #34)
+#32 := (iff #9 #31)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#39 := [monotonicity #33 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#30 := [asserted]: #13
+[mp #30 #57]: false
+unsat
+acdb6c4646d2fb215f71d2ce5c6780077ae4ef74 16 0
+#2 := false
+#1 := true
+#8 := (implies false true)
+#9 := (not #8)
+#34 := (iff #9 false)
+#29 := (not true)
+#32 := (iff #29 false)
+#33 := [rewrite]: #32
+#30 := (iff #9 #29)
+#27 := (iff #8 true)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#35 := [trans #31 #33]: #34
+#26 := [asserted]: #9
+[mp #26 #35]: false
+unsat
+a6b55bc9321a8285602719107ebdeb043021388b 47 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#13 := (and #11 #9)
+#12 := (and #9 #11)
+#14 := (implies #12 #13)
+#15 := (not #14)
+#61 := (iff #15 false)
+#1 := true
+#56 := (not true)
+#59 := (iff #56 false)
+#60 := [rewrite]: #59
+#57 := (iff #15 #56)
+#54 := (iff #14 true)
+#36 := (= f1 f4)
+#33 := (= f1 f3)
+#39 := (and #33 #36)
+#49 := (implies #39 #39)
+#52 := (iff #49 true)
+#53 := [rewrite]: #52
+#50 := (iff #14 #49)
+#47 := (iff #13 #39)
+#42 := (and #36 #33)
+#45 := (iff #42 #39)
+#46 := [rewrite]: #45
+#43 := (iff #13 #42)
+#34 := (iff #9 #33)
+#35 := [rewrite]: #34
+#37 := (iff #11 #36)
+#38 := [rewrite]: #37
+#44 := [monotonicity #38 #35]: #43
+#48 := [trans #44 #46]: #47
+#40 := (iff #12 #39)
+#41 := [monotonicity #35 #38]: #40
+#51 := [monotonicity #41 #48]: #50
+#55 := [trans #51 #53]: #54
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#32 := [asserted]: #15
+[mp #32 #62]: false
+unsat
+09a1c146e8c9fb89362c0920e2565ce27aabf746 47 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#13 := (or #11 #9)
+#12 := (or #9 #11)
+#14 := (implies #12 #13)
+#15 := (not #14)
+#61 := (iff #15 false)
+#1 := true
+#56 := (not true)
+#59 := (iff #56 false)
+#60 := [rewrite]: #59
+#57 := (iff #15 #56)
+#54 := (iff #14 true)
+#36 := (= f1 f4)
+#33 := (= f1 f3)
+#39 := (or #33 #36)
+#49 := (implies #39 #39)
+#52 := (iff #49 true)
+#53 := [rewrite]: #52
+#50 := (iff #14 #49)
+#47 := (iff #13 #39)
+#42 := (or #36 #33)
+#45 := (iff #42 #39)
+#46 := [rewrite]: #45
+#43 := (iff #13 #42)
+#34 := (iff #9 #33)
+#35 := [rewrite]: #34
+#37 := (iff #11 #36)
+#38 := [rewrite]: #37
+#44 := [monotonicity #38 #35]: #43
+#48 := [trans #44 #46]: #47
+#40 := (iff #12 #39)
+#41 := [monotonicity #35 #38]: #40
+#51 := [monotonicity #41 #48]: #50
+#55 := [trans #51 #53]: #54
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#32 := [asserted]: #15
+[mp #32 #62]: false
+unsat
+fdcaeb48c0fe060c788599c1819f3c817e8284ea 55 0
+#2 := false
+decl f3 :: S1
+#8 := f3
+decl f1 :: S1
+#4 := f1
+#33 := (= f1 f3)
+#76 := (iff #33 false)
+#66 := (not #33)
+decl f4 :: S1
+#10 := f4
+#36 := (= f1 f4)
+#39 := (and #33 #36)
+#48 := (not #39)
+#57 := (or #33 #36 #48)
+#60 := (not #57)
+#11 := (= f4 f1)
+#9 := (= f3 f1)
+#13 := (or #9 #11)
+#12 := (and #9 #11)
+#14 := (implies #12 #13)
+#15 := (not #14)
+#63 := (iff #15 #60)
+#42 := (or #33 #36)
+#49 := (or #48 #42)
+#54 := (not #49)
+#61 := (iff #54 #60)
+#58 := (iff #49 #57)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#55 := (iff #15 #54)
+#52 := (iff #14 #49)
+#45 := (implies #39 #42)
+#50 := (iff #45 #49)
+#51 := [rewrite]: #50
+#46 := (iff #14 #45)
+#43 := (iff #13 #42)
+#37 := (iff #11 #36)
+#38 := [rewrite]: #37
+#34 := (iff #9 #33)
+#35 := [rewrite]: #34
+#44 := [monotonicity #35 #38]: #43
+#40 := (iff #12 #39)
+#41 := [monotonicity #35 #38]: #40
+#47 := [monotonicity #41 #44]: #46
+#53 := [trans #47 #51]: #52
+#56 := [monotonicity #53]: #55
+#64 := [trans #56 #62]: #63
+#32 := [asserted]: #15
+#65 := [mp #32 #64]: #60
+#67 := [not-or-elim #65]: #66
+#77 := [iff-false #67]: #76
+#70 := [not-or-elim #65]: #39
+#71 := [and-elim #70]: #33
+[mp #71 #77]: false
+unsat
+c40695de865e974fcc0b75b4d6410d1fe4a01cbd 149 0
+#2 := false
+decl f5 :: S1
+#12 := f5
+decl f1 :: S1
+#4 := f1
+#44 := (= f1 f5)
+decl f4 :: S1
+#10 := f4
+#41 := (= f1 f4)
+decl f3 :: S1
+#8 := f3
+#38 := (= f1 f3)
+#47 := (ite #38 #41 #44)
+#53 := (not #38)
+#54 := (or #53 #41)
+#64 := (or #38 #44)
+#91 := (not #64)
+#90 := (not #54)
+#92 := (or #90 #91)
+#143 := [hypothesis]: #90
+#128 := (or #92 #54)
+#129 := [def-axiom]: #128
+#144 := [unit-resolution #129 #143]: #92
+#78 := (not #47)
+#116 := (or #54 #38)
+#117 := [def-axiom]: #116
+#145 := [unit-resolution #117 #143]: #38
+#110 := (not #41)
+#118 := (or #54 #110)
+#119 := [def-axiom]: #118
+#146 := [unit-resolution #119 #143]: #110
+#106 := (or #78 #53 #41)
+#107 := [def-axiom]: #106
+#147 := [unit-resolution #107 #146 #145]: #78
+#93 := (not #92)
+#137 := (or #47 #93)
+#100 := (iff #47 #92)
+#69 := (and #54 #64)
+#79 := (iff #69 #78)
+#103 := (iff #79 #100)
+#95 := (iff #92 #47)
+#101 := (iff #95 #100)
+#102 := [rewrite]: #101
+#98 := (iff #79 #95)
+#87 := (iff #93 #78)
+#96 := (iff #87 #95)
+#97 := [rewrite]: #96
+#84 := (iff #79 #87)
+#88 := (iff #69 #93)
+#89 := [rewrite]: #88
+#94 := [monotonicity #89]: #84
+#99 := [trans #94 #97]: #98
+#104 := [trans #99 #102]: #103
+#13 := (= f5 f1)
+#9 := (= f3 f1)
+#16 := (not #9)
+#17 := (implies #16 #13)
+#11 := (= f4 f1)
+#15 := (implies #9 #11)
+#18 := (and #15 #17)
+#14 := (ite #9 #11 #13)
+#19 := (iff #14 #18)
+#20 := (not #19)
+#82 := (iff #20 #79)
+#72 := (iff #47 #69)
+#75 := (not #72)
+#80 := (iff #75 #79)
+#81 := [rewrite]: #80
+#76 := (iff #20 #75)
+#73 := (iff #19 #72)
+#70 := (iff #18 #69)
+#67 := (iff #17 #64)
+#61 := (implies #53 #44)
+#65 := (iff #61 #64)
+#66 := [rewrite]: #65
+#62 := (iff #17 #61)
+#45 := (iff #13 #44)
+#46 := [rewrite]: #45
+#59 := (iff #16 #53)
+#39 := (iff #9 #38)
+#40 := [rewrite]: #39
+#60 := [monotonicity #40]: #59
+#63 := [monotonicity #60 #46]: #62
+#68 := [trans #63 #66]: #67
+#57 := (iff #15 #54)
+#50 := (implies #38 #41)
+#55 := (iff #50 #54)
+#56 := [rewrite]: #55
+#51 := (iff #15 #50)
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#52 := [monotonicity #40 #43]: #51
+#58 := [trans #52 #56]: #57
+#71 := [monotonicity #58 #68]: #70
+#48 := (iff #14 #47)
+#49 := [monotonicity #40 #43 #46]: #48
+#74 := [monotonicity #49 #71]: #73
+#77 := [monotonicity #74]: #76
+#83 := [trans #77 #81]: #82
+#37 := [asserted]: #20
+#86 := [mp #37 #83]: #79
+#105 := [mp #86 #104]: #100
+#134 := (not #100)
+#135 := (or #47 #93 #134)
+#136 := [def-axiom]: #135
+#138 := [unit-resolution #136 #105]: #137
+#148 := [unit-resolution #138 #147 #144]: false
+#149 := [lemma #148]: #54
+#150 := [hypothesis]: #78
+#156 := (or #38 #47)
+#151 := [unit-resolution #138 #150]: #93
+#130 := (or #92 #64)
+#131 := [def-axiom]: #130
+#152 := [unit-resolution #131 #151]: #64
+#153 := [hypothesis]: #53
+#113 := (not #44)
+#114 := (or #47 #38 #113)
+#115 := [def-axiom]: #114
+#154 := [unit-resolution #115 #153 #150]: #113
+#126 := (or #91 #38 #44)
+#127 := [def-axiom]: #126
+#155 := [unit-resolution #127 #154 #153 #152]: false
+#157 := [lemma #155]: #156
+#158 := [unit-resolution #157 #150]: #38
+#111 := (or #47 #53 #110)
+#112 := [def-axiom]: #111
+#159 := [unit-resolution #112 #158 #150]: #110
+#120 := (or #90 #53 #41)
+#121 := [def-axiom]: #120
+#160 := [unit-resolution #121 #159 #158 #149]: false
+#161 := [lemma #160]: #47
+#141 := (or #78 #92)
+#139 := (or #78 #92 #134)
+#140 := [def-axiom]: #139
+#142 := [unit-resolution #140 #105]: #141
+#162 := [unit-resolution #142 #161]: #92
+#132 := (or #93 #90 #91)
+#133 := [def-axiom]: #132
+#163 := [unit-resolution #133 #162 #149]: #91
+#122 := (or #64 #53)
+#123 := [def-axiom]: #122
+#164 := [unit-resolution #123 #163]: #53
+#124 := (or #64 #113)
+#125 := [def-axiom]: #124
+#165 := [unit-resolution #125 #163]: #113
+#108 := (or #78 #38 #44)
+#109 := [def-axiom]: #108
+[unit-resolution #109 #165 #164 #161]: false
+unsat
+909eac5ac94649616c92660c5d2f8b06874b48dc 55 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#14 := (not #9)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#12 := (or #9 #11)
+#13 := (not #12)
+#15 := (implies #13 #14)
+#16 := (not #15)
+#69 := (iff #16 false)
+#37 := (= f1 f4)
+#34 := (= f1 f3)
+#40 := (or #34 #37)
+#46 := (not #34)
+#52 := (or #46 #40)
+#57 := (not #52)
+#67 := (iff #57 false)
+#1 := true
+#62 := (not true)
+#65 := (iff #62 false)
+#66 := [rewrite]: #65
+#63 := (iff #57 #62)
+#60 := (iff #52 true)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#68 := [trans #64 #66]: #67
+#58 := (iff #16 #57)
+#55 := (iff #15 #52)
+#43 := (not #40)
+#49 := (implies #43 #46)
+#53 := (iff #49 #52)
+#54 := [rewrite]: #53
+#50 := (iff #15 #49)
+#47 := (iff #14 #46)
+#35 := (iff #9 #34)
+#36 := [rewrite]: #35
+#48 := [monotonicity #36]: #47
+#44 := (iff #13 #43)
+#41 := (iff #12 #40)
+#38 := (iff #11 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #36 #39]: #41
+#45 := [monotonicity #42]: #44
+#51 := [monotonicity #45 #48]: #50
+#56 := [trans #51 #54]: #55
+#59 := [monotonicity #56]: #58
+#70 := [trans #59 #68]: #69
+#33 := [asserted]: #16
+[mp #33 #70]: false
+unsat
+4559f9cf103133ca42ad9e775fb6027fe7dbf044 66 0
+#2 := false
+decl f3 :: S1
+#8 := f3
+decl f1 :: S1
+#4 := f1
+#33 := (= f1 f3)
+#51 := (not #33)
+#87 := [hypothesis]: #33
+decl f4 :: S1
+#10 := f4
+#36 := (= f1 f4)
+#42 := (not #36)
+#43 := (or #33 #42)
+#69 := (or #43 #51)
+#70 := [def-axiom]: #69
+#88 := [unit-resolution #70 #87]: #43
+#67 := (not #43)
+#89 := (or #51 #67)
+#52 := (or #51 #36)
+#57 := (ite #33 #43 #52)
+#60 := (not #57)
+#11 := (= f4 f1)
+#9 := (= f3 f1)
+#13 := (implies #9 #11)
+#12 := (implies #11 #9)
+#14 := (ite #9 #12 #13)
+#15 := (not #14)
+#61 := (iff #15 #60)
+#58 := (iff #14 #57)
+#55 := (iff #13 #52)
+#48 := (implies #33 #36)
+#53 := (iff #48 #52)
+#54 := [rewrite]: #53
+#49 := (iff #13 #48)
+#37 := (iff #11 #36)
+#38 := [rewrite]: #37
+#34 := (iff #9 #33)
+#35 := [rewrite]: #34
+#50 := [monotonicity #35 #38]: #49
+#56 := [trans #50 #54]: #55
+#46 := (iff #12 #43)
+#39 := (implies #36 #33)
+#44 := (iff #39 #43)
+#45 := [rewrite]: #44
+#40 := (iff #12 #39)
+#41 := [monotonicity #38 #35]: #40
+#47 := [trans #41 #45]: #46
+#59 := [monotonicity #35 #47 #56]: #58
+#62 := [monotonicity #59]: #61
+#32 := [asserted]: #15
+#65 := [mp #32 #62]: #60
+#83 := (or #57 #51 #67)
+#84 := [def-axiom]: #83
+#90 := [unit-resolution #84 #65]: #89
+#91 := [unit-resolution #90 #88 #87]: false
+#92 := [lemma #91]: #51
+#63 := (or #52 #33)
+#73 := [def-axiom]: #63
+#93 := [unit-resolution #73 #92]: #52
+#76 := (not #52)
+#94 := (or #33 #76)
+#85 := (or #57 #33 #76)
+#86 := [def-axiom]: #85
+#95 := [unit-resolution #86 #65]: #94
+[unit-resolution #95 #93 #92]: false
+unsat
+70a5da534a7b49a4247fac1cedcc4b2d2d172e2d 55 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#14 := (not #11)
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#12 := (or #9 #11)
+#13 := (not #12)
+#15 := (implies #13 #14)
+#16 := (not #15)
+#69 := (iff #16 false)
+#37 := (= f1 f4)
+#34 := (= f1 f3)
+#40 := (or #34 #37)
+#46 := (not #37)
+#52 := (or #46 #40)
+#57 := (not #52)
+#67 := (iff #57 false)
+#1 := true
+#62 := (not true)
+#65 := (iff #62 false)
+#66 := [rewrite]: #65
+#63 := (iff #57 #62)
+#60 := (iff #52 true)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#68 := [trans #64 #66]: #67
+#58 := (iff #16 #57)
+#55 := (iff #15 #52)
+#43 := (not #40)
+#49 := (implies #43 #46)
+#53 := (iff #49 #52)
+#54 := [rewrite]: #53
+#50 := (iff #15 #49)
+#47 := (iff #14 #46)
+#38 := (iff #11 #37)
+#39 := [rewrite]: #38
+#48 := [monotonicity #39]: #47
+#44 := (iff #13 #43)
+#41 := (iff #12 #40)
+#35 := (iff #9 #34)
+#36 := [rewrite]: #35
+#42 := [monotonicity #36 #39]: #41
+#45 := [monotonicity #42]: #44
+#51 := [monotonicity #45 #48]: #50
+#56 := [trans #51 #54]: #55
+#59 := [monotonicity #56]: #58
+#70 := [trans #59 #68]: #69
+#33 := [asserted]: #16
+[mp #33 #70]: false
+unsat
+453c8097706770edcac8e1bbb9fbf7c33a26c5af 67 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f6 :: S1
+#15 := f6
+#16 := (= f6 f1)
+decl f5 :: S1
+#13 := f5
+#14 := (= f5 f1)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#18 := (ite #11 #14 #16)
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#19 := (ite #9 #14 #18)
+#12 := (or #9 #11)
+#17 := (ite #12 #14 #16)
+#20 := (iff #17 #19)
+#21 := (not #20)
+#79 := (iff #21 false)
+#1 := true
+#74 := (not true)
+#77 := (iff #74 false)
+#78 := [rewrite]: #77
+#75 := (iff #21 #74)
+#72 := (iff #20 true)
+#51 := (= f1 f6)
+#48 := (= f1 f5)
+#42 := (= f1 f4)
+#39 := (= f1 f3)
+#45 := (or #39 #42)
+#54 := (ite #45 #48 #51)
+#67 := (iff #54 #54)
+#70 := (iff #67 true)
+#71 := [rewrite]: #70
+#68 := (iff #20 #67)
+#65 := (iff #19 #54)
+#57 := (ite #42 #48 #51)
+#60 := (ite #39 #48 #57)
+#63 := (iff #60 #54)
+#64 := [rewrite]: #63
+#61 := (iff #19 #60)
+#58 := (iff #18 #57)
+#52 := (iff #16 #51)
+#53 := [rewrite]: #52
+#49 := (iff #14 #48)
+#50 := [rewrite]: #49
+#43 := (iff #11 #42)
+#44 := [rewrite]: #43
+#59 := [monotonicity #44 #50 #53]: #58
+#40 := (iff #9 #39)
+#41 := [rewrite]: #40
+#62 := [monotonicity #41 #50 #59]: #61
+#66 := [trans #62 #64]: #65
+#55 := (iff #17 #54)
+#46 := (iff #12 #45)
+#47 := [monotonicity #41 #44]: #46
+#56 := [monotonicity #47 #50 #53]: #55
+#69 := [monotonicity #56 #66]: #68
+#73 := [trans #69 #71]: #72
+#76 := [monotonicity #73]: #75
+#80 := [trans #76 #78]: #79
+#38 := [asserted]: #21
+[mp #38 #80]: false
+unsat
+66bc415bc7b672ad9bd08a5cad7193639ca92341 49 0
+#2 := false
+decl f3 :: S1
+#8 := f3
+decl f1 :: S1
+#4 := f1
+#34 := (= f1 f3)
+#68 := (iff #34 false)
+#37 := (not #34)
+decl f4 :: S1
+#11 := f4
+#40 := (= f1 f4)
+#43 := (and #34 #40)
+#46 := (not #43)
+#52 := (or #34 #46)
+#57 := (not #52)
+#12 := (= f4 f1)
+#9 := (= f3 f1)
+#13 := (and #9 #12)
+#14 := (not #13)
+#10 := (not #9)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#58 := (iff #16 #57)
+#55 := (iff #15 #52)
+#49 := (implies #37 #46)
+#53 := (iff #49 #52)
+#54 := [rewrite]: #53
+#50 := (iff #15 #49)
+#47 := (iff #14 #46)
+#44 := (iff #13 #43)
+#41 := (iff #12 #40)
+#42 := [rewrite]: #41
+#35 := (iff #9 #34)
+#36 := [rewrite]: #35
+#45 := [monotonicity #36 #42]: #44
+#48 := [monotonicity #45]: #47
+#38 := (iff #10 #37)
+#39 := [monotonicity #36]: #38
+#51 := [monotonicity #39 #48]: #50
+#56 := [trans #51 #54]: #55
+#59 := [monotonicity #56]: #58
+#33 := [asserted]: #16
+#62 := [mp #33 #59]: #57
+#60 := [not-or-elim #62]: #37
+#69 := [iff-false #60]: #68
+#61 := [not-or-elim #62]: #43
+#63 := [and-elim #61]: #34
+[mp #63 #69]: false
+unsat
+a89676df4461617062c6e78fd5ffdff83f5ac142 54 0
+#2 := false
+decl f3 :: S1
+#8 := f3
+decl f1 :: S1
+#4 := f1
+#34 := (= f1 f3)
+#73 := (iff #34 false)
+#37 := (not #34)
+decl f4 :: S1
+#11 := f4
+#40 := (= f1 f4)
+#46 := (and #34 #40)
+#51 := (not #46)
+#57 := (or #34 #51)
+#62 := (not #57)
+#9 := (= f3 f1)
+#12 := (= f4 f1)
+#13 := (and #12 #9)
+#14 := (not #13)
+#10 := (not #9)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#63 := (iff #16 #62)
+#60 := (iff #15 #57)
+#54 := (implies #37 #51)
+#58 := (iff #54 #57)
+#59 := [rewrite]: #58
+#55 := (iff #15 #54)
+#52 := (iff #14 #51)
+#49 := (iff #13 #46)
+#43 := (and #40 #34)
+#47 := (iff #43 #46)
+#48 := [rewrite]: #47
+#44 := (iff #13 #43)
+#35 := (iff #9 #34)
+#36 := [rewrite]: #35
+#41 := (iff #12 #40)
+#42 := [rewrite]: #41
+#45 := [monotonicity #42 #36]: #44
+#50 := [trans #45 #48]: #49
+#53 := [monotonicity #50]: #52
+#38 := (iff #10 #37)
+#39 := [monotonicity #36]: #38
+#56 := [monotonicity #39 #53]: #55
+#61 := [trans #56 #59]: #60
+#64 := [monotonicity #61]: #63
+#33 := [asserted]: #16
+#67 := [mp #33 #64]: #62
+#65 := [not-or-elim #67]: #37
+#74 := [iff-false #65]: #73
+#66 := [not-or-elim #67]: #46
+#68 := [and-elim #66]: #34
+[mp #68 #74]: false
+unsat
+650ce0aefeedeac8455717747dd9f90168da27bb 67 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f6 :: S1
+#15 := f6
+#16 := (= f6 f1)
+decl f5 :: S1
+#13 := f5
+#14 := (= f5 f1)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#18 := (ite #11 #14 #16)
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#19 := (ite #9 #18 #16)
+#12 := (and #9 #11)
+#17 := (ite #12 #14 #16)
+#20 := (iff #17 #19)
+#21 := (not #20)
+#79 := (iff #21 false)
+#1 := true
+#74 := (not true)
+#77 := (iff #74 false)
+#78 := [rewrite]: #77
+#75 := (iff #21 #74)
+#72 := (iff #20 true)
+#51 := (= f1 f6)
+#48 := (= f1 f5)
+#42 := (= f1 f4)
+#39 := (= f1 f3)
+#45 := (and #39 #42)
+#54 := (ite #45 #48 #51)
+#67 := (iff #54 #54)
+#70 := (iff #67 true)
+#71 := [rewrite]: #70
+#68 := (iff #20 #67)
+#65 := (iff #19 #54)
+#57 := (ite #42 #48 #51)
+#60 := (ite #39 #57 #51)
+#63 := (iff #60 #54)
+#64 := [rewrite]: #63
+#61 := (iff #19 #60)
+#52 := (iff #16 #51)
+#53 := [rewrite]: #52
+#58 := (iff #18 #57)
+#49 := (iff #14 #48)
+#50 := [rewrite]: #49
+#43 := (iff #11 #42)
+#44 := [rewrite]: #43
+#59 := [monotonicity #44 #50 #53]: #58
+#40 := (iff #9 #39)
+#41 := [rewrite]: #40
+#62 := [monotonicity #41 #59 #53]: #61
+#66 := [trans #62 #64]: #65
+#55 := (iff #17 #54)
+#46 := (iff #12 #45)
+#47 := [monotonicity #41 #44]: #46
+#56 := [monotonicity #47 #50 #53]: #55
+#69 := [monotonicity #56 #66]: #68
+#73 := [trans #69 #71]: #72
+#76 := [monotonicity #73]: #75
+#80 := [trans #76 #78]: #79
+#38 := [asserted]: #21
+[mp #38 #80]: false
+unsat
+36f523bdbc2a966d0da47f8c8e1a18b288089cd4 60 0
+#2 := false
+decl f4 :: S1
+#10 := f4
+decl f1 :: S1
+#4 := f1
+#39 := (= f1 f4)
+#48 := (not #39)
+decl f3 :: S1
+#8 := f3
+#36 := (= f1 f3)
+#45 := (not #36)
+#51 := (or #45 #48)
+#42 := (and #36 #39)
+#64 := (iff #42 #51)
+#71 := (iff #64 false)
+#54 := (not #51)
+#75 := (iff #54 #51)
+#72 := (iff #75 false)
+#73 := [rewrite]: #72
+#76 := (iff #64 #75)
+#57 := (iff #42 #54)
+#74 := [rewrite]: #57
+#77 := [monotonicity #74]: #76
+#68 := [trans #77 #73]: #71
+#11 := (= f4 f1)
+#14 := (not #11)
+#9 := (= f3 f1)
+#13 := (not #9)
+#15 := (or #13 #14)
+#16 := (not #15)
+#12 := (and #9 #11)
+#17 := (iff #12 #16)
+#18 := (not #17)
+#66 := (iff #18 #64)
+#60 := (not #57)
+#63 := (iff #60 #64)
+#65 := [rewrite]: #63
+#61 := (iff #18 #60)
+#58 := (iff #17 #57)
+#55 := (iff #16 #54)
+#52 := (iff #15 #51)
+#49 := (iff #14 #48)
+#40 := (iff #11 #39)
+#41 := [rewrite]: #40
+#50 := [monotonicity #41]: #49
+#46 := (iff #13 #45)
+#37 := (iff #9 #36)
+#38 := [rewrite]: #37
+#47 := [monotonicity #38]: #46
+#53 := [monotonicity #47 #50]: #52
+#56 := [monotonicity #53]: #55
+#43 := (iff #12 #42)
+#44 := [monotonicity #38 #41]: #43
+#59 := [monotonicity #44 #56]: #58
+#62 := [monotonicity #59]: #61
+#67 := [trans #62 #65]: #66
+#35 := [asserted]: #18
+#70 := [mp #35 #67]: #64
+[mp #70 #68]: false
+unsat
+ee0014e770bb12c9a43047b17bc55a374085eace 186 0
+#2 := false
+decl f5 :: S1
+#12 := f5
+decl f1 :: S1
+#4 := f1
+#47 := (= f1 f5)
+decl f3 :: S1
+#8 := f3
+#41 := (= f1 f3)
+#59 := (not #41)
+#76 := (or #59 #47)
+#119 := (not #76)
+decl f4 :: S1
+#10 := f4
+#44 := (= f1 f4)
+#68 := (or #59 #44)
+decl f6 :: S1
+#14 := f6
+#50 := (= f1 f6)
+#84 := (or #59 #50)
+#89 := (ite #68 #76 #84)
+#130 := (not #89)
+#53 := (ite #44 #47 #50)
+#60 := (or #59 #53)
+#112 := (not #44)
+#165 := [hypothesis]: #112
+#172 := (or #60 #44)
+#98 := (not #60)
+#163 := [hypothesis]: #98
+#148 := (or #60 #41)
+#149 := [def-axiom]: #148
+#164 := [unit-resolution #149 #163]: #41
+#124 := (not #50)
+#139 := (not #53)
+#150 := (or #60 #139)
+#151 := [def-axiom]: #150
+#166 := [unit-resolution #151 #163]: #139
+#146 := (or #53 #44 #124)
+#147 := [def-axiom]: #146
+#167 := [unit-resolution #147 #166 #165]: #124
+#157 := (or #89 #60)
+#99 := (iff #89 #98)
+#15 := (= f6 f1)
+#9 := (= f3 f1)
+#20 := (implies #9 #15)
+#13 := (= f5 f1)
+#19 := (implies #9 #13)
+#11 := (= f4 f1)
+#18 := (implies #9 #11)
+#21 := (ite #18 #19 #20)
+#16 := (ite #11 #13 #15)
+#17 := (implies #9 #16)
+#22 := (iff #17 #21)
+#23 := (not #22)
+#102 := (iff #23 #99)
+#92 := (iff #60 #89)
+#95 := (not #92)
+#100 := (iff #95 #99)
+#101 := [rewrite]: #100
+#96 := (iff #23 #95)
+#93 := (iff #22 #92)
+#90 := (iff #21 #89)
+#87 := (iff #20 #84)
+#81 := (implies #41 #50)
+#85 := (iff #81 #84)
+#86 := [rewrite]: #85
+#82 := (iff #20 #81)
+#51 := (iff #15 #50)
+#52 := [rewrite]: #51
+#42 := (iff #9 #41)
+#43 := [rewrite]: #42
+#83 := [monotonicity #43 #52]: #82
+#88 := [trans #83 #86]: #87
+#79 := (iff #19 #76)
+#73 := (implies #41 #47)
+#77 := (iff #73 #76)
+#78 := [rewrite]: #77
+#74 := (iff #19 #73)
+#48 := (iff #13 #47)
+#49 := [rewrite]: #48
+#75 := [monotonicity #43 #49]: #74
+#80 := [trans #75 #78]: #79
+#71 := (iff #18 #68)
+#65 := (implies #41 #44)
+#69 := (iff #65 #68)
+#70 := [rewrite]: #69
+#66 := (iff #18 #65)
+#45 := (iff #11 #44)
+#46 := [rewrite]: #45
+#67 := [monotonicity #43 #46]: #66
+#72 := [trans #67 #70]: #71
+#91 := [monotonicity #72 #80 #88]: #90
+#63 := (iff #17 #60)
+#56 := (implies #41 #53)
+#61 := (iff #56 #60)
+#62 := [rewrite]: #61
+#57 := (iff #17 #56)
+#54 := (iff #16 #53)
+#55 := [monotonicity #46 #49 #52]: #54
+#58 := [monotonicity #43 #55]: #57
+#64 := [trans #58 #62]: #63
+#94 := [monotonicity #64 #91]: #93
+#97 := [monotonicity #94]: #96
+#103 := [trans #97 #101]: #102
+#40 := [asserted]: #23
+#106 := [mp #40 #103]: #99
+#154 := (not #99)
+#155 := (or #89 #60 #154)
+#156 := [def-axiom]: #155
+#158 := [unit-resolution #156 #106]: #157
+#168 := [unit-resolution #158 #163]: #89
+#109 := (not #68)
+#107 := (or #109 #59 #44)
+#104 := [def-axiom]: #107
+#169 := [unit-resolution #104 #164 #165]: #109
+#133 := (or #130 #68 #84)
+#134 := [def-axiom]: #133
+#170 := [unit-resolution #134 #169 #168]: #84
+#127 := (not #84)
+#128 := (or #127 #59 #50)
+#129 := [def-axiom]: #128
+#171 := [unit-resolution #129 #170 #167 #164]: false
+#173 := [lemma #171]: #172
+#176 := [unit-resolution #173 #165]: #60
+#161 := (or #130 #98)
+#159 := (or #130 #98 #154)
+#160 := [def-axiom]: #159
+#162 := [unit-resolution #160 #106]: #161
+#182 := [unit-resolution #162 #176]: #130
+#180 := (or #84 #44)
+#174 := [hypothesis]: #127
+#125 := (or #84 #124)
+#126 := [def-axiom]: #125
+#175 := [unit-resolution #126 #174]: #124
+#122 := (or #84 #41)
+#123 := [def-axiom]: #122
+#177 := [unit-resolution #123 #174]: #41
+#152 := (or #98 #59 #53)
+#153 := [def-axiom]: #152
+#178 := [unit-resolution #153 #177 #176]: #53
+#142 := (or #139 #44 #50)
+#143 := [def-axiom]: #142
+#179 := [unit-resolution #143 #178 #175 #165]: false
+#181 := [lemma #179]: #180
+#183 := [unit-resolution #181 #165]: #84
+#137 := (or #89 #68 #127)
+#138 := [def-axiom]: #137
+#184 := [unit-resolution #138 #183 #182]: #68
+#135 := (or #89 #109 #119)
+#136 := [def-axiom]: #135
+#185 := [unit-resolution #136 #184 #182]: #119
+#186 := [unit-resolution #104 #184 #165]: #59
+#114 := (or #76 #41)
+#115 := [def-axiom]: #114
+#187 := [unit-resolution #115 #186 #185]: false
+#188 := [lemma #187]: #44
+#113 := (or #68 #112)
+#108 := [def-axiom]: #113
+#191 := [unit-resolution #108 #188]: #68
+#189 := [hypothesis]: #59
+#190 := [unit-resolution #149 #189]: #60
+#192 := [unit-resolution #115 #189]: #76
+#193 := [unit-resolution #136 #192 #191]: #89
+#194 := [unit-resolution #162 #193 #190]: false
+#195 := [lemma #194]: #41
+#116 := (not #47)
+#144 := (or #53 #112 #116)
+#145 := [def-axiom]: #144
+#196 := [unit-resolution #145 #166 #188]: #116
+#131 := (or #130 #109 #76)
+#132 := [def-axiom]: #131
+#197 := [unit-resolution #132 #168 #191]: #76
+#120 := (or #119 #59 #47)
+#121 := [def-axiom]: #120
+#198 := [unit-resolution #121 #197 #196 #195]: false
+#199 := [lemma #198]: #60
+#200 := [unit-resolution #162 #199]: #130
+#201 := [unit-resolution #136 #200 #191]: #119
+#202 := [unit-resolution #153 #199 #195]: #53
+#140 := (or #139 #112 #47)
+#141 := [def-axiom]: #140
+#203 := [unit-resolution #141 #202 #188]: #47
+#117 := (or #76 #116)
+#118 := [def-axiom]: #117
+[unit-resolution #118 #203 #201]: false
+unsat
+39e898ce622db033d98d0949c6c78d8d13333283 79 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f5 :: S1
+#13 := f5
+#14 := (= f5 f1)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#16 := (and #11 #14)
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#17 := (and #9 #16)
+#12 := (and #9 #11)
+#15 := (and #12 #14)
+#18 := (implies #15 #17)
+#19 := (not #18)
+#92 := (iff #19 false)
+#46 := (= f1 f5)
+#40 := (= f1 f4)
+#52 := (and #40 #46)
+#37 := (= f1 f3)
+#55 := (and #37 #52)
+#43 := (and #37 #40)
+#49 := (and #43 #46)
+#61 := (not #49)
+#62 := (or #61 #55)
+#67 := (not #62)
+#90 := (iff #67 false)
+#1 := true
+#85 := (not true)
+#88 := (iff #85 false)
+#89 := [rewrite]: #88
+#86 := (iff #67 #85)
+#83 := (iff #62 true)
+#70 := (and #37 #40 #46)
+#73 := (not #70)
+#78 := (or #73 #70)
+#81 := (iff #78 true)
+#82 := [rewrite]: #81
+#79 := (iff #62 #78)
+#76 := (iff #55 #70)
+#77 := [rewrite]: #76
+#74 := (iff #61 #73)
+#71 := (iff #49 #70)
+#72 := [rewrite]: #71
+#75 := [monotonicity #72]: #74
+#80 := [monotonicity #75 #77]: #79
+#84 := [trans #80 #82]: #83
+#87 := [monotonicity #84]: #86
+#91 := [trans #87 #89]: #90
+#68 := (iff #19 #67)
+#65 := (iff #18 #62)
+#58 := (implies #49 #55)
+#63 := (iff #58 #62)
+#64 := [rewrite]: #63
+#59 := (iff #18 #58)
+#56 := (iff #17 #55)
+#53 := (iff #16 #52)
+#47 := (iff #14 #46)
+#48 := [rewrite]: #47
+#41 := (iff #11 #40)
+#42 := [rewrite]: #41
+#54 := [monotonicity #42 #48]: #53
+#38 := (iff #9 #37)
+#39 := [rewrite]: #38
+#57 := [monotonicity #39 #54]: #56
+#50 := (iff #15 #49)
+#44 := (iff #12 #43)
+#45 := [monotonicity #39 #42]: #44
+#51 := [monotonicity #45 #48]: #50
+#60 := [monotonicity #51 #57]: #59
+#66 := [trans #60 #64]: #65
+#69 := [monotonicity #66]: #68
+#93 := [trans #69 #91]: #92
+#36 := [asserted]: #19
+[mp #36 #93]: false
+unsat
+412649a38963841ee4cc1fd44ea953cb67369cff 33 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#10 := (not #9)
+#11 := (ite #9 #9 #10)
+#12 := (not #11)
+#48 := (iff #12 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (iff #11 true)
+#30 := (= f1 f3)
+#33 := (not #30)
+#36 := (ite #30 #30 #33)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #11 #36)
+#34 := (iff #10 #33)
+#31 := (iff #9 #30)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#38 := [monotonicity #32 #32 #35]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#29 := [asserted]: #12
+[mp #29 #49]: false
+unsat
+3d76513bcca35d0b89ae8be9bed98213f01644cc 94 0
+#2 := false
+decl f5 :: S1
+#13 := f5
+decl f1 :: S1
+#4 := f1
+#46 := (= f1 f5)
+decl f4 :: S1
+#10 := f4
+#40 := (= f1 f4)
+decl f3 :: S1
+#8 := f3
+#37 := (= f1 f3)
+#70 := (or #37 #40 #46)
+#111 := (iff #70 false)
+#106 := (or false false false)
+#109 := (iff #106 false)
+#110 := [rewrite]: #109
+#107 := (iff #70 #106)
+#104 := (iff #46 false)
+#94 := (not #46)
+#73 := (not #70)
+#79 := (or #37 #40 #46 #73)
+#84 := (not #79)
+#14 := (= f5 f1)
+#11 := (= f4 f1)
+#16 := (or #11 #14)
+#9 := (= f3 f1)
+#17 := (or #9 #16)
+#12 := (or #9 #11)
+#15 := (or #12 #14)
+#18 := (implies #15 #17)
+#19 := (not #18)
+#87 := (iff #19 #84)
+#52 := (or #40 #46)
+#55 := (or #37 #52)
+#43 := (or #37 #40)
+#49 := (or #43 #46)
+#61 := (not #49)
+#62 := (or #61 #55)
+#67 := (not #62)
+#85 := (iff #67 #84)
+#82 := (iff #62 #79)
+#76 := (or #73 #55)
+#80 := (iff #76 #79)
+#81 := [rewrite]: #80
+#77 := (iff #62 #76)
+#74 := (iff #61 #73)
+#71 := (iff #49 #70)
+#72 := [rewrite]: #71
+#75 := [monotonicity #72]: #74
+#78 := [monotonicity #75]: #77
+#83 := [trans #78 #81]: #82
+#86 := [monotonicity #83]: #85
+#68 := (iff #19 #67)
+#65 := (iff #18 #62)
+#58 := (implies #49 #55)
+#63 := (iff #58 #62)
+#64 := [rewrite]: #63
+#59 := (iff #18 #58)
+#56 := (iff #17 #55)
+#53 := (iff #16 #52)
+#47 := (iff #14 #46)
+#48 := [rewrite]: #47
+#41 := (iff #11 #40)
+#42 := [rewrite]: #41
+#54 := [monotonicity #42 #48]: #53
+#38 := (iff #9 #37)
+#39 := [rewrite]: #38
+#57 := [monotonicity #39 #54]: #56
+#50 := (iff #15 #49)
+#44 := (iff #12 #43)
+#45 := [monotonicity #39 #42]: #44
+#51 := [monotonicity #45 #48]: #50
+#60 := [monotonicity #51 #57]: #59
+#66 := [trans #60 #64]: #65
+#69 := [monotonicity #66]: #68
+#88 := [trans #69 #86]: #87
+#36 := [asserted]: #19
+#89 := [mp #36 #88]: #84
+#95 := [not-or-elim #89]: #94
+#105 := [iff-false #95]: #104
+#102 := (iff #40 false)
+#92 := (not #40)
+#93 := [not-or-elim #89]: #92
+#103 := [iff-false #93]: #102
+#100 := (iff #37 false)
+#90 := (not #37)
+#91 := [not-or-elim #89]: #90
+#101 := [iff-false #91]: #100
+#108 := [monotonicity #101 #103 #105]: #107
+#112 := [trans #108 #110]: #111
+#96 := [not-or-elim #89]: #70
+[mp #96 #112]: false
+unsat
+cdb5c3594738ea620a30a8c35e72deba5b933ff1 33 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#10 := (not #9)
+#11 := (ite #10 #10 #9)
+#12 := (not #11)
+#48 := (iff #12 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (iff #11 true)
+#30 := (= f1 f3)
+#33 := (not #30)
+#36 := (ite #33 #33 #30)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #11 #36)
+#31 := (iff #9 #30)
+#32 := [rewrite]: #31
+#34 := (iff #10 #33)
+#35 := [monotonicity #32]: #34
+#38 := [monotonicity #35 #35 #32]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#29 := [asserted]: #12
+[mp #29 #49]: false
+unsat
+e872baf26281e471c8aad88c06ade50a163a8bf9 114 0
+#2 := false
+decl f5 :: S1
+#13 := f5
+decl f1 :: S1
+#4 := f1
+#47 := (= f1 f5)
+#116 := (not #47)
+decl f3 :: S1
+#8 := f3
+#38 := (= f1 f3)
+#53 := (or #38 #47)
+#94 := (not #53)
+decl f4 :: S1
+#10 := f4
+#41 := (= f1 f4)
+#56 := (or #41 #47)
+#95 := (not #56)
+#127 := [hypothesis]: #95
+#123 := (or #56 #116)
+#124 := [def-axiom]: #123
+#128 := [unit-resolution #124 #127]: #116
+#86 := (not #41)
+#85 := (not #38)
+#87 := (or #85 #86)
+#121 := (or #56 #86)
+#122 := [def-axiom]: #121
+#129 := [unit-resolution #122 #127]: #86
+#110 := (or #87 #41)
+#111 := [def-axiom]: #110
+#130 := [unit-resolution #111 #129]: #87
+#88 := (not #87)
+#78 := (or #47 #88)
+#44 := (and #38 #41)
+#50 := (or #44 #47)
+#91 := (iff #50 #78)
+#81 := (or #88 #47)
+#89 := (iff #81 #78)
+#90 := [rewrite]: #89
+#82 := (iff #50 #81)
+#83 := (iff #44 #88)
+#84 := [rewrite]: #83
+#80 := [monotonicity #84]: #82
+#92 := [trans #80 #90]: #91
+#59 := (and #53 #56)
+#65 := (not #50)
+#66 := (or #65 #59)
+#71 := (not #66)
+#14 := (= f5 f1)
+#11 := (= f4 f1)
+#17 := (or #11 #14)
+#9 := (= f3 f1)
+#16 := (or #9 #14)
+#18 := (and #16 #17)
+#12 := (and #9 #11)
+#15 := (or #12 #14)
+#19 := (implies #15 #18)
+#20 := (not #19)
+#72 := (iff #20 #71)
+#69 := (iff #19 #66)
+#62 := (implies #50 #59)
+#67 := (iff #62 #66)
+#68 := [rewrite]: #67
+#63 := (iff #19 #62)
+#60 := (iff #18 #59)
+#57 := (iff #17 #56)
+#48 := (iff #14 #47)
+#49 := [rewrite]: #48
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#58 := [monotonicity #43 #49]: #57
+#54 := (iff #16 #53)
+#39 := (iff #9 #38)
+#40 := [rewrite]: #39
+#55 := [monotonicity #40 #49]: #54
+#61 := [monotonicity #55 #58]: #60
+#51 := (iff #15 #50)
+#45 := (iff #12 #44)
+#46 := [monotonicity #40 #43]: #45
+#52 := [monotonicity #46 #49]: #51
+#64 := [monotonicity #52 #61]: #63
+#70 := [trans #64 #68]: #69
+#73 := [monotonicity #70]: #72
+#37 := [asserted]: #20
+#76 := [mp #37 #73]: #71
+#74 := [not-or-elim #76]: #50
+#93 := [mp #74 #92]: #78
+#131 := [unit-resolution #93 #130 #128]: false
+#132 := [lemma #131]: #56
+#96 := (or #94 #95)
+#75 := (not #59)
+#105 := (iff #75 #96)
+#97 := (not #96)
+#100 := (not #97)
+#103 := (iff #100 #96)
+#104 := [rewrite]: #103
+#101 := (iff #75 #100)
+#98 := (iff #59 #97)
+#99 := [rewrite]: #98
+#102 := [monotonicity #99]: #101
+#106 := [trans #102 #104]: #105
+#77 := [not-or-elim #76]: #75
+#107 := [mp #77 #106]: #96
+#133 := [unit-resolution #107 #132]: #94
+#117 := (or #53 #116)
+#118 := [def-axiom]: #117
+#134 := [unit-resolution #118 #133]: #116
+#114 := (or #53 #85)
+#115 := [def-axiom]: #114
+#135 := [unit-resolution #115 #133]: #85
+#108 := (or #87 #38)
+#109 := [def-axiom]: #108
+#136 := [unit-resolution #109 #135]: #87
+[unit-resolution #93 #136 #134]: false
+unsat
+b64bc0bcf45eb1767f3ac5eb748f88080f2b2bee 121 0
+#2 := false
+decl f5 :: S1
+#13 := f5
+decl f1 :: S1
+#4 := f1
+#47 := (= f1 f5)
+decl f3 :: S1
+#8 := f3
+#38 := (= f1 f3)
+#61 := (and #38 #47)
+#98 := (not #61)
+#137 := (iff #98 false)
+#1 := true
+#132 := (not true)
+#135 := (iff #132 false)
+#136 := [rewrite]: #135
+#133 := (iff #98 #132)
+#130 := (iff #61 true)
+#125 := (and true true)
+#128 := (iff #125 true)
+#129 := [rewrite]: #128
+#126 := (iff #61 #125)
+#123 := (iff #47 true)
+decl f4 :: S1
+#10 := f4
+#41 := (= f1 f4)
+#53 := (or #41 #47)
+#120 := (iff #53 #47)
+#115 := (or false #47)
+#118 := (iff #115 #47)
+#119 := [rewrite]: #118
+#116 := (iff #53 #115)
+#103 := (iff #41 false)
+#93 := (not #41)
+#44 := (or #38 #41)
+#58 := (and #44 #53)
+#75 := (not #58)
+#84 := (or #41 #75 #61)
+#87 := (not #84)
+#11 := (= f4 f1)
+#14 := (= f5 f1)
+#9 := (= f3 f1)
+#17 := (and #9 #14)
+#18 := (or #17 #11)
+#15 := (or #14 #11)
+#12 := (or #9 #11)
+#16 := (and #12 #15)
+#19 := (implies #16 #18)
+#20 := (not #19)
+#90 := (iff #20 #87)
+#67 := (or #41 #61)
+#76 := (or #75 #67)
+#81 := (not #76)
+#88 := (iff #81 #87)
+#85 := (iff #76 #84)
+#86 := [rewrite]: #85
+#89 := [monotonicity #86]: #88
+#82 := (iff #20 #81)
+#79 := (iff #19 #76)
+#72 := (implies #58 #67)
+#77 := (iff #72 #76)
+#78 := [rewrite]: #77
+#73 := (iff #19 #72)
+#70 := (iff #18 #67)
+#64 := (or #61 #41)
+#68 := (iff #64 #67)
+#69 := [rewrite]: #68
+#65 := (iff #18 #64)
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#62 := (iff #17 #61)
+#48 := (iff #14 #47)
+#49 := [rewrite]: #48
+#39 := (iff #9 #38)
+#40 := [rewrite]: #39
+#63 := [monotonicity #40 #49]: #62
+#66 := [monotonicity #63 #43]: #65
+#71 := [trans #66 #69]: #70
+#59 := (iff #16 #58)
+#56 := (iff #15 #53)
+#50 := (or #47 #41)
+#54 := (iff #50 #53)
+#55 := [rewrite]: #54
+#51 := (iff #15 #50)
+#52 := [monotonicity #49 #43]: #51
+#57 := [trans #52 #55]: #56
+#45 := (iff #12 #44)
+#46 := [monotonicity #40 #43]: #45
+#60 := [monotonicity #46 #57]: #59
+#74 := [monotonicity #60 #71]: #73
+#80 := [trans #74 #78]: #79
+#83 := [monotonicity #80]: #82
+#91 := [trans #83 #89]: #90
+#37 := [asserted]: #20
+#92 := [mp #37 #91]: #87
+#94 := [not-or-elim #92]: #93
+#104 := [iff-false #94]: #103
+#117 := [monotonicity #104]: #116
+#121 := [trans #117 #119]: #120
+#95 := [not-or-elim #92]: #58
+#97 := [and-elim #95]: #53
+#122 := [mp #97 #121]: #47
+#124 := [iff-true #122]: #123
+#113 := (iff #38 true)
+#110 := (iff #44 #38)
+#105 := (or #38 false)
+#108 := (iff #105 #38)
+#109 := [rewrite]: #108
+#106 := (iff #44 #105)
+#107 := [monotonicity #104]: #106
+#111 := [trans #107 #109]: #110
+#96 := [and-elim #95]: #44
+#112 := [mp #96 #111]: #38
+#114 := [iff-true #112]: #113
+#127 := [monotonicity #114 #124]: #126
+#131 := [trans #127 #129]: #130
+#134 := [monotonicity #131]: #133
+#138 := [trans #134 #136]: #137
+#99 := [not-or-elim #92]: #98
+[mp #99 #138]: false
+unsat
+3fdfe28cd079db59b06011ec3a9e5833720e3939 18 0
+#2 := false
+decl f3 :: S2
+#8 := f3
+#9 := (= f3 f3)
+#10 := (not #9)
+#35 := (iff #10 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #10 #30)
+#28 := (iff #9 true)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#27 := [asserted]: #10
+[mp #27 #36]: false
+unsat
+138a3ace8cb85475ff652dca20ea653b9ddc0574 29 0
+#2 := false
+decl f3 :: S2
+#8 := f3
+decl f4 :: S2
+#9 := f4
+#11 := (= f4 f3)
+#10 := (= f3 f4)
+#12 := (implies #10 #11)
+#13 := (not #12)
+#45 := (iff #13 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #13 #40)
+#38 := (iff #12 true)
+#33 := (implies #10 #10)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #12 #33)
+#31 := (iff #11 #10)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#30 := [asserted]: #13
+[mp #30 #46]: false
+unsat
+c9da60152fdcf3358171ced892606def006be235 110 0
+#2 := false
+decl f4 :: S1
+#10 := f4
+decl f1 :: S1
+#4 := f1
+#41 := (= f1 f4)
+decl f3 :: S1
+#8 := f3
+#38 := (= f1 f3)
+#44 := (or #38 #41)
+#128 := (iff #44 false)
+#123 := (or false false)
+#126 := (iff #123 false)
+#127 := [rewrite]: #126
+#124 := (iff #44 #123)
+#121 := (iff #41 false)
+#117 := (not #41)
+decl f5 :: S1
+#13 := f5
+#47 := (= f1 f5)
+#56 := (and #41 #47)
+#88 := (not #56)
+#118 := (iff #88 #117)
+#115 := (iff #56 #41)
+#1 := true
+#110 := (and #41 true)
+#113 := (iff #110 #41)
+#114 := [rewrite]: #113
+#111 := (iff #56 #110)
+#95 := (iff #47 true)
+#50 := (and #44 #47)
+#53 := (and #38 #47)
+#65 := (not #50)
+#74 := (or #65 #53 #56)
+#77 := (not #74)
+#14 := (= f5 f1)
+#11 := (= f4 f1)
+#17 := (and #11 #14)
+#9 := (= f3 f1)
+#16 := (and #9 #14)
+#18 := (or #16 #17)
+#12 := (or #9 #11)
+#15 := (and #12 #14)
+#19 := (implies #15 #18)
+#20 := (not #19)
+#80 := (iff #20 #77)
+#59 := (or #53 #56)
+#66 := (or #65 #59)
+#71 := (not #66)
+#78 := (iff #71 #77)
+#75 := (iff #66 #74)
+#76 := [rewrite]: #75
+#79 := [monotonicity #76]: #78
+#72 := (iff #20 #71)
+#69 := (iff #19 #66)
+#62 := (implies #50 #59)
+#67 := (iff #62 #66)
+#68 := [rewrite]: #67
+#63 := (iff #19 #62)
+#60 := (iff #18 #59)
+#57 := (iff #17 #56)
+#48 := (iff #14 #47)
+#49 := [rewrite]: #48
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#58 := [monotonicity #43 #49]: #57
+#54 := (iff #16 #53)
+#39 := (iff #9 #38)
+#40 := [rewrite]: #39
+#55 := [monotonicity #40 #49]: #54
+#61 := [monotonicity #55 #58]: #60
+#51 := (iff #15 #50)
+#45 := (iff #12 #44)
+#46 := [monotonicity #40 #43]: #45
+#52 := [monotonicity #46 #49]: #51
+#64 := [monotonicity #52 #61]: #63
+#70 := [trans #64 #68]: #69
+#73 := [monotonicity #70]: #72
+#81 := [trans #73 #79]: #80
+#37 := [asserted]: #20
+#82 := [mp #37 #81]: #77
+#83 := [not-or-elim #82]: #50
+#85 := [and-elim #83]: #47
+#96 := [iff-true #85]: #95
+#112 := [monotonicity #96]: #111
+#116 := [trans #112 #114]: #115
+#119 := [monotonicity #116]: #118
+#89 := [not-or-elim #82]: #88
+#120 := [mp #89 #119]: #117
+#122 := [iff-false #120]: #121
+#108 := (iff #38 false)
+#104 := (not #38)
+#86 := (not #53)
+#105 := (iff #86 #104)
+#102 := (iff #53 #38)
+#97 := (and #38 true)
+#100 := (iff #97 #38)
+#101 := [rewrite]: #100
+#98 := (iff #53 #97)
+#99 := [monotonicity #96]: #98
+#103 := [trans #99 #101]: #102
+#106 := [monotonicity #103]: #105
+#87 := [not-or-elim #82]: #86
+#107 := [mp #87 #106]: #104
+#109 := [iff-false #107]: #108
+#125 := [monotonicity #109 #122]: #124
+#129 := [trans #125 #127]: #128
+#84 := [and-elim #83]: #44
+[mp #84 #129]: false
+unsat
+2aab8007d3f04ab47357a32e4f86dbadd477fa43 34 0
+#2 := false
+decl f5 :: S2
+#11 := f5
+decl f3 :: S2
+#8 := f3
+#14 := (= f3 f5)
+decl f4 :: S2
+#9 := f4
+#12 := (= f4 f5)
+#58 := (iff #12 #14)
+#56 := (iff #14 #12)
+#10 := (= f3 f4)
+#13 := (and #10 #12)
+#34 := (not #13)
+#35 := (or #34 #14)
+#38 := (not #35)
+#15 := (implies #13 #14)
+#16 := (not #15)
+#39 := (iff #16 #38)
+#36 := (iff #15 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#33 := [asserted]: #16
+#43 := [mp #33 #40]: #38
+#41 := [not-or-elim #43]: #13
+#42 := [and-elim #41]: #10
+#57 := [monotonicity #42]: #56
+#59 := [symm #57]: #58
+#44 := [and-elim #41]: #12
+#54 := [mp #44 #59]: #14
+#45 := (not #14)
+#46 := [not-or-elim #43]: #45
+[unit-resolution #46 #54]: false
+unsat
+1f8e71f0583db493868b682b87713e9591cb7a07 127 0
+#2 := false
+decl f5 :: S1
+#13 := f5
+decl f1 :: S1
+#4 := f1
+#47 := (= f1 f5)
+#91 := (not #47)
+decl f4 :: S1
+#10 := f4
+#41 := (= f1 f4)
+#96 := (not #41)
+#92 := (or #96 #91)
+decl f3 :: S1
+#8 := f3
+#38 := (= f1 f3)
+#61 := (or #38 #47)
+#95 := (not #38)
+#97 := (or #95 #96)
+#109 := (not #61)
+#140 := [hypothesis]: #109
+#134 := (or #61 #95)
+#135 := [def-axiom]: #134
+#141 := [unit-resolution #135 #140]: #95
+#128 := (or #97 #38)
+#129 := [def-axiom]: #128
+#142 := [unit-resolution #129 #141]: #97
+#136 := (or #61 #91)
+#137 := [def-axiom]: #136
+#143 := [unit-resolution #137 #140]: #91
+#124 := (or #92 #47)
+#125 := [def-axiom]: #124
+#144 := [unit-resolution #125 #143]: #92
+#98 := (not #97)
+#90 := (not #92)
+#103 := (or #90 #98)
+#53 := (and #41 #47)
+#44 := (and #38 #41)
+#58 := (or #44 #53)
+#106 := (iff #58 #103)
+#100 := (or #98 #90)
+#104 := (iff #100 #103)
+#105 := [rewrite]: #104
+#101 := (iff #58 #100)
+#88 := (iff #53 #90)
+#99 := [rewrite]: #88
+#93 := (iff #44 #98)
+#94 := [rewrite]: #93
+#102 := [monotonicity #94 #99]: #101
+#107 := [trans #102 #105]: #106
+#67 := (and #41 #61)
+#75 := (not #58)
+#76 := (or #75 #67)
+#81 := (not #76)
+#11 := (= f4 f1)
+#14 := (= f5 f1)
+#9 := (= f3 f1)
+#17 := (or #9 #14)
+#18 := (and #17 #11)
+#15 := (and #14 #11)
+#12 := (and #9 #11)
+#16 := (or #12 #15)
+#19 := (implies #16 #18)
+#20 := (not #19)
+#82 := (iff #20 #81)
+#79 := (iff #19 #76)
+#72 := (implies #58 #67)
+#77 := (iff #72 #76)
+#78 := [rewrite]: #77
+#73 := (iff #19 #72)
+#70 := (iff #18 #67)
+#64 := (and #61 #41)
+#68 := (iff #64 #67)
+#69 := [rewrite]: #68
+#65 := (iff #18 #64)
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#62 := (iff #17 #61)
+#48 := (iff #14 #47)
+#49 := [rewrite]: #48
+#39 := (iff #9 #38)
+#40 := [rewrite]: #39
+#63 := [monotonicity #40 #49]: #62
+#66 := [monotonicity #63 #43]: #65
+#71 := [trans #66 #69]: #70
+#59 := (iff #16 #58)
+#56 := (iff #15 #53)
+#50 := (and #47 #41)
+#54 := (iff #50 #53)
+#55 := [rewrite]: #54
+#51 := (iff #15 #50)
+#52 := [monotonicity #49 #43]: #51
+#57 := [trans #52 #55]: #56
+#45 := (iff #12 #44)
+#46 := [monotonicity #40 #43]: #45
+#60 := [monotonicity #46 #57]: #59
+#74 := [monotonicity #60 #71]: #73
+#80 := [trans #74 #78]: #79
+#83 := [monotonicity #80]: #82
+#37 := [asserted]: #20
+#86 := [mp #37 #83]: #81
+#84 := [not-or-elim #86]: #58
+#108 := [mp #84 #107]: #103
+#145 := [unit-resolution #108 #144 #142]: false
+#146 := [lemma #145]: #61
+#110 := (or #96 #109)
+#85 := (not #67)
+#119 := (iff #85 #110)
+#111 := (not #110)
+#114 := (not #111)
+#117 := (iff #114 #110)
+#118 := [rewrite]: #117
+#115 := (iff #85 #114)
+#112 := (iff #67 #111)
+#113 := [rewrite]: #112
+#116 := [monotonicity #113]: #115
+#120 := [trans #116 #118]: #119
+#87 := [not-or-elim #86]: #85
+#121 := [mp #87 #120]: #110
+#147 := [unit-resolution #121 #146]: #96
+#122 := (or #92 #41)
+#123 := [def-axiom]: #122
+#148 := [unit-resolution #123 #147]: #92
+#130 := (or #97 #41)
+#131 := [def-axiom]: #130
+#149 := [unit-resolution #131 #147]: #97
+[unit-resolution #108 #149 #148]: false
+unsat
+5aeacb8767661e0089f1bee00da51c74406606e7 27 0
+#2 := false
+decl f5 :: (-> S2 S2)
+decl f4 :: S2
+#9 := f4
+#12 := (f5 f4)
+decl f3 :: S2
+#8 := f3
+#11 := (f5 f3)
+#13 := (= #11 #12)
+#10 := (= f3 f4)
+#33 := (not #10)
+#34 := (or #33 #13)
+#37 := (not #34)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#38 := (iff #15 #37)
+#35 := (iff #14 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#32 := [asserted]: #15
+#42 := [mp #32 #39]: #37
+#40 := [not-or-elim #42]: #10
+#51 := [monotonicity #40]: #13
+#41 := (not #13)
+#43 := [not-or-elim #42]: #41
+[unit-resolution #43 #51]: false
+unsat
+818dc7a805c1fc0df63db969a20606d71bab3c5a 66 0
+#2 := false
+decl f3 :: S1
+#8 := f3
+decl f1 :: S1
+#4 := f1
+#33 := (= f1 f3)
+decl f4 :: S1
+#10 := f4
+#36 := (= f1 f4)
+#42 := (not #33)
+#43 := (or #42 #36)
+#51 := (not #43)
+#52 := (or #33 #51)
+#82 := (iff #52 #51)
+#77 := (or false #51)
+#80 := (iff #77 #51)
+#81 := [rewrite]: #80
+#78 := (iff #52 #77)
+#75 := (iff #33 false)
+#60 := (not #52)
+#61 := (or #33 #60)
+#66 := (not #61)
+#9 := (= f3 f1)
+#11 := (= f4 f1)
+#12 := (implies #9 #11)
+#13 := (implies #12 #9)
+#14 := (implies #13 #9)
+#15 := (not #14)
+#67 := (iff #15 #66)
+#64 := (iff #14 #61)
+#57 := (implies #52 #33)
+#62 := (iff #57 #61)
+#63 := [rewrite]: #62
+#58 := (iff #14 #57)
+#34 := (iff #9 #33)
+#35 := [rewrite]: #34
+#55 := (iff #13 #52)
+#48 := (implies #43 #33)
+#53 := (iff #48 #52)
+#54 := [rewrite]: #53
+#49 := (iff #13 #48)
+#46 := (iff #12 #43)
+#39 := (implies #33 #36)
+#44 := (iff #39 #43)
+#45 := [rewrite]: #44
+#40 := (iff #12 #39)
+#37 := (iff #11 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #35 #38]: #40
+#47 := [trans #41 #45]: #46
+#50 := [monotonicity #47 #35]: #49
+#56 := [trans #50 #54]: #55
+#59 := [monotonicity #56 #35]: #58
+#65 := [trans #59 #63]: #64
+#68 := [monotonicity #65]: #67
+#32 := [asserted]: #15
+#71 := [mp #32 #68]: #66
+#69 := [not-or-elim #71]: #42
+#76 := [iff-false #69]: #75
+#79 := [monotonicity #76]: #78
+#83 := [trans #79 #81]: #82
+#70 := [not-or-elim #71]: #52
+#84 := [mp #70 #83]: #51
+#74 := [not-or-elim #84]: #33
+[unit-resolution #69 #74]: false
+unsat
+0192b9e7527c6d595018662e41e3d823b138754c 31 0
+#2 := false
+decl f5 :: (-> S2 S2 S3)
+decl f3 :: S2
+#8 := f3
+decl f4 :: S2
+#9 := f4
+#12 := (f5 f4 f3)
+#11 := (f5 f3 f4)
+#13 := (= #11 #12)
+#53 := (= #12 #11)
+#10 := (= f3 f4)
+#33 := (not #10)
+#34 := (or #33 #13)
+#37 := (not #34)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#38 := (iff #15 #37)
+#35 := (iff #14 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#32 := [asserted]: #15
+#42 := [mp #32 #39]: #37
+#40 := [not-or-elim #42]: #10
+#51 := (= f4 f3)
+#52 := [symm #40]: #51
+#54 := [monotonicity #52 #40]: #53
+#49 := [symm #54]: #13
+#41 := (not #13)
+#43 := [not-or-elim #42]: #41
+[unit-resolution #43 #49]: false
+unsat
+46fff20b4c094da53ae081e33798e8a693ab62ec 156 0
+#2 := false
+decl f5 :: S1
+#13 := f5
+decl f1 :: S1
+#4 := f1
+#53 := (= f1 f5)
+#59 := (not #53)
+decl f4 :: S1
+#10 := f4
+#41 := (= f1 f4)
+#60 := (or #41 #59)
+#99 := (not #60)
+decl f3 :: S1
+#8 := f3
+#38 := (= f1 f3)
+#47 := (not #38)
+#48 := (or #47 #41)
+#98 := (not #48)
+#100 := (or #98 #99)
+#68 := (or #38 #53)
+#74 := (not #68)
+#75 := (or #41 #74)
+#122 := (not #75)
+#101 := (not #100)
+#152 := [hypothesis]: #101
+#150 := (or #122 #100)
+#107 := (iff #75 #100)
+#65 := (and #48 #60)
+#86 := (not #65)
+#87 := (iff #75 #86)
+#108 := (iff #87 #107)
+#105 := (iff #86 #100)
+#95 := (not #101)
+#103 := (iff #95 #100)
+#104 := [rewrite]: #103
+#92 := (iff #86 #95)
+#96 := (iff #65 #101)
+#97 := [rewrite]: #96
+#102 := [monotonicity #97]: #92
+#106 := [trans #102 #104]: #105
+#109 := [monotonicity #106]: #108
+#11 := (= f4 f1)
+#14 := (= f5 f1)
+#9 := (= f3 f1)
+#17 := (or #9 #14)
+#18 := (implies #17 #11)
+#15 := (implies #14 #11)
+#12 := (implies #9 #11)
+#16 := (and #12 #15)
+#19 := (iff #16 #18)
+#20 := (not #19)
+#90 := (iff #20 #87)
+#80 := (iff #65 #75)
+#83 := (not #80)
+#88 := (iff #83 #87)
+#89 := [rewrite]: #88
+#84 := (iff #20 #83)
+#81 := (iff #19 #80)
+#78 := (iff #18 #75)
+#71 := (implies #68 #41)
+#76 := (iff #71 #75)
+#77 := [rewrite]: #76
+#72 := (iff #18 #71)
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#69 := (iff #17 #68)
+#54 := (iff #14 #53)
+#55 := [rewrite]: #54
+#39 := (iff #9 #38)
+#40 := [rewrite]: #39
+#70 := [monotonicity #40 #55]: #69
+#73 := [monotonicity #70 #43]: #72
+#79 := [trans #73 #77]: #78
+#66 := (iff #16 #65)
+#63 := (iff #15 #60)
+#56 := (implies #53 #41)
+#61 := (iff #56 #60)
+#62 := [rewrite]: #61
+#57 := (iff #15 #56)
+#58 := [monotonicity #55 #43]: #57
+#64 := [trans #58 #62]: #63
+#51 := (iff #12 #48)
+#44 := (implies #38 #41)
+#49 := (iff #44 #48)
+#50 := [rewrite]: #49
+#45 := (iff #12 #44)
+#46 := [monotonicity #40 #43]: #45
+#52 := [trans #46 #50]: #51
+#67 := [monotonicity #52 #64]: #66
+#82 := [monotonicity #67 #79]: #81
+#85 := [monotonicity #82]: #84
+#91 := [trans #85 #89]: #90
+#37 := [asserted]: #20
+#94 := [mp #37 #91]: #87
+#110 := [mp #94 #109]: #107
+#143 := (not #107)
+#148 := (or #122 #100 #143)
+#149 := [def-axiom]: #148
+#151 := [unit-resolution #149 #110]: #150
+#153 := [unit-resolution #151 #152]: #122
+#120 := (or #75 #68)
+#121 := [def-axiom]: #120
+#154 := [unit-resolution #121 #153]: #68
+#137 := (or #100 #48)
+#138 := [def-axiom]: #137
+#155 := [unit-resolution #138 #152]: #48
+#117 := (not #41)
+#118 := (or #75 #117)
+#119 := [def-axiom]: #118
+#156 := [unit-resolution #119 #153]: #117
+#129 := (or #98 #47 #41)
+#130 := [def-axiom]: #129
+#157 := [unit-resolution #130 #156 #155]: #47
+#139 := (or #100 #60)
+#140 := [def-axiom]: #139
+#158 := [unit-resolution #140 #152]: #60
+#135 := (or #99 #41 #59)
+#136 := [def-axiom]: #135
+#159 := [unit-resolution #136 #156 #158]: #59
+#115 := (or #74 #38 #53)
+#116 := [def-axiom]: #115
+#160 := [unit-resolution #116 #159 #157 #154]: false
+#161 := [lemma #160]: #100
+#146 := (or #75 #101)
+#144 := (or #75 #101 #143)
+#145 := [def-axiom]: #144
+#147 := [unit-resolution #145 #110]: #146
+#162 := [unit-resolution #147 #161]: #75
+#163 := [hypothesis]: #98
+#127 := (or #48 #117)
+#128 := [def-axiom]: #127
+#164 := [unit-resolution #128 #163]: #117
+#125 := (or #48 #38)
+#126 := [def-axiom]: #125
+#165 := [unit-resolution #126 #163]: #38
+#111 := (or #68 #47)
+#112 := [def-axiom]: #111
+#166 := [unit-resolution #112 #165]: #68
+#123 := (or #122 #41 #74)
+#124 := [def-axiom]: #123
+#167 := [unit-resolution #124 #166 #164 #162]: false
+#168 := [lemma #167]: #48
+#141 := (or #101 #98 #99)
+#142 := [def-axiom]: #141
+#169 := [unit-resolution #142 #168 #161]: #99
+#133 := (or #60 #53)
+#134 := [def-axiom]: #133
+#170 := [unit-resolution #134 #169]: #53
+#131 := (or #60 #117)
+#132 := [def-axiom]: #131
+#171 := [unit-resolution #132 #169]: #117
+#172 := [unit-resolution #124 #171 #162]: #74
+#113 := (or #68 #59)
+#114 := [def-axiom]: #113
+[unit-resolution #114 #172 #170]: false
+unsat
+a4fc389fafe13e91a7fdc713fbb6f0ce7029805d 63 0
+#2 := false
+decl f3 :: (-> S2 S2)
+decl f4 :: S2
+#8 := f4
+#9 := (f3 f4)
+#46 := (= f4 #9)
+#10 := (f3 #9)
+#12 := (f3 #10)
+#78 := (= #12 #9)
+#76 := (= #9 #12)
+#37 := (= f4 #10)
+#13 := (f3 #12)
+#14 := (f3 #13)
+#40 := (= f4 #14)
+#43 := (and #37 #40)
+#52 := (not #43)
+#53 := (or #52 #46)
+#58 := (not #53)
+#17 := (= #9 f4)
+#15 := (= #14 f4)
+#11 := (= #10 f4)
+#16 := (and #11 #15)
+#18 := (implies #16 #17)
+#19 := (not #18)
+#59 := (iff #19 #58)
+#56 := (iff #18 #53)
+#49 := (implies #43 #46)
+#54 := (iff #49 #53)
+#55 := [rewrite]: #54
+#50 := (iff #18 #49)
+#47 := (iff #17 #46)
+#48 := [rewrite]: #47
+#44 := (iff #16 #43)
+#41 := (iff #15 #40)
+#42 := [rewrite]: #41
+#38 := (iff #11 #37)
+#39 := [rewrite]: #38
+#45 := [monotonicity #39 #42]: #44
+#51 := [monotonicity #45 #48]: #50
+#57 := [trans #51 #55]: #56
+#60 := [monotonicity #57]: #59
+#36 := [asserted]: #19
+#63 := [mp #36 #60]: #58
+#61 := [not-or-elim #63]: #43
+#62 := [and-elim #61]: #37
+#77 := [monotonicity #62]: #76
+#79 := [symm #77]: #78
+#81 := (= f4 #12)
+#67 := (= #14 #12)
+#70 := (= #12 #14)
+#72 := (= #10 #13)
+#74 := (= #13 #10)
+#75 := [monotonicity #79]: #74
+#73 := [symm #75]: #72
+#71 := [monotonicity #73]: #70
+#80 := [symm #71]: #67
+#64 := [and-elim #61]: #40
+#82 := [trans #64 #80]: #81
+#83 := [trans #82 #79]: #46
+#65 := (not #46)
+#66 := [not-or-elim #63]: #65
+[unit-resolution #66 #83]: false
+unsat
+2f15e9d90b4b089f8a2562ce56366a555231ff22 114 0
+#2 := false
+decl f5 :: S1
+#13 := f5
+decl f1 :: S1
+#4 := f1
+#46 := (= f1 f5)
+decl f4 :: S1
+#10 := f4
+#40 := (= f1 f4)
+#61 := (not #40)
+decl f3 :: S1
+#8 := f3
+#37 := (= f1 f3)
+#70 := (not #37)
+#88 := (or #70 #61 #46)
+#43 := (and #37 #40)
+#52 := (not #43)
+#53 := (or #52 #46)
+#82 := (not #53)
+#94 := (iff #82 #88)
+#129 := (iff #94 false)
+#121 := (not #88)
+#124 := (iff #121 #88)
+#127 := (iff #124 false)
+#128 := [rewrite]: #127
+#125 := (iff #94 #124)
+#122 := (iff #82 #121)
+#119 := (iff #53 #88)
+#107 := (or #70 #61)
+#114 := (or #107 #46)
+#117 := (iff #114 #88)
+#118 := [rewrite]: #117
+#115 := (iff #53 #114)
+#112 := (iff #52 #107)
+#108 := (not #107)
+#105 := (not #108)
+#102 := (iff #105 #107)
+#111 := [rewrite]: #102
+#106 := (iff #52 #105)
+#109 := (iff #43 #108)
+#110 := [rewrite]: #109
+#104 := [monotonicity #110]: #106
+#113 := [trans #104 #111]: #112
+#116 := [monotonicity #113]: #115
+#120 := [trans #116 #118]: #119
+#123 := [monotonicity #120]: #122
+#126 := [monotonicity #123]: #125
+#130 := [trans #126 #128]: #129
+#14 := (= f5 f1)
+#11 := (= f4 f1)
+#16 := (implies #11 #14)
+#9 := (= f3 f1)
+#17 := (implies #9 #16)
+#12 := (and #9 #11)
+#15 := (implies #12 #14)
+#18 := (iff #15 #17)
+#19 := (not #18)
+#99 := (iff #19 #94)
+#62 := (or #61 #46)
+#71 := (or #70 #62)
+#83 := (iff #71 #82)
+#97 := (iff #83 #94)
+#91 := (iff #88 #82)
+#95 := (iff #91 #94)
+#96 := [rewrite]: #95
+#92 := (iff #83 #91)
+#89 := (iff #71 #88)
+#90 := [rewrite]: #89
+#93 := [monotonicity #90]: #92
+#98 := [trans #93 #96]: #97
+#86 := (iff #19 #83)
+#76 := (iff #53 #71)
+#79 := (not #76)
+#84 := (iff #79 #83)
+#85 := [rewrite]: #84
+#80 := (iff #19 #79)
+#77 := (iff #18 #76)
+#74 := (iff #17 #71)
+#67 := (implies #37 #62)
+#72 := (iff #67 #71)
+#73 := [rewrite]: #72
+#68 := (iff #17 #67)
+#65 := (iff #16 #62)
+#58 := (implies #40 #46)
+#63 := (iff #58 #62)
+#64 := [rewrite]: #63
+#59 := (iff #16 #58)
+#47 := (iff #14 #46)
+#48 := [rewrite]: #47
+#41 := (iff #11 #40)
+#42 := [rewrite]: #41
+#60 := [monotonicity #42 #48]: #59
+#66 := [trans #60 #64]: #65
+#38 := (iff #9 #37)
+#39 := [rewrite]: #38
+#69 := [monotonicity #39 #66]: #68
+#75 := [trans #69 #73]: #74
+#56 := (iff #15 #53)
+#49 := (implies #43 #46)
+#54 := (iff #49 #53)
+#55 := [rewrite]: #54
+#50 := (iff #15 #49)
+#44 := (iff #12 #43)
+#45 := [monotonicity #39 #42]: #44
+#51 := [monotonicity #45 #48]: #50
+#57 := [trans #51 #55]: #56
+#78 := [monotonicity #57 #75]: #77
+#81 := [monotonicity #78]: #80
+#87 := [trans #81 #85]: #86
+#100 := [trans #87 #98]: #99
+#36 := [asserted]: #19
+#101 := [mp #36 #100]: #94
+[mp #101 #130]: false
+unsat
+5a01b8711c838d753166b92be13bae6fe9cd2136 195 0
+#2 := false
+decl f6 :: S2
+#13 := f6
+decl f4 :: S2
+#10 := f4
+#15 := (= f4 f6)
+decl f5 :: S2
+#11 := f5
+decl f3 :: S1
+#8 := f3
+decl f1 :: S1
+#4 := f1
+#40 := (= f1 f3)
+#43 := (ite #40 f4 f5)
+#49 := (= f6 #43)
+#200 := (iff #49 #15)
+#198 := (iff #15 #49)
+#46 := (= #43 f6)
+#50 := (iff #46 #49)
+#197 := [commutativity]: #50
+#195 := (iff #15 #46)
+#110 := (= f4 #43)
+#111 := (= f5 #43)
+#57 := (not #40)
+#180 := [hypothesis]: #57
+#114 := (or #40 #111)
+#115 := [def-axiom]: #114
+#184 := [unit-resolution #115 #180]: #111
+#185 := (= f6 f5)
+#18 := (= f5 f6)
+#174 := (iff #110 #15)
+#172 := (iff #15 #110)
+#68 := (or #18 #40)
+#95 := (not #68)
+#58 := (or #15 #57)
+#94 := (not #58)
+#96 := (or #94 #95)
+#123 := (not #18)
+#147 := [hypothesis]: #123
+#157 := (or #96 #18)
+#97 := (not #96)
+#145 := [hypothesis]: #97
+#132 := (or #96 #68)
+#133 := [def-axiom]: #132
+#148 := [unit-resolution #133 #145]: #68
+#128 := (or #95 #18 #40)
+#129 := [def-axiom]: #128
+#149 := [unit-resolution #129 #148 #147]: #40
+#112 := (or #57 #110)
+#113 := [def-axiom]: #112
+#150 := [unit-resolution #113 #149]: #110
+#153 := (= f6 f4)
+#130 := (or #96 #58)
+#131 := [def-axiom]: #130
+#151 := [unit-resolution #131 #145]: #58
+#121 := (or #94 #15 #57)
+#122 := [def-axiom]: #121
+#152 := [unit-resolution #122 #149 #151]: #15
+#154 := [symm #152]: #153
+#155 := [trans #154 #150]: #49
+#82 := (not #49)
+#143 := (or #82 #96)
+#104 := (iff #49 #96)
+#73 := (and #58 #68)
+#83 := (iff #73 #82)
+#107 := (iff #83 #104)
+#99 := (iff #96 #49)
+#105 := (iff #99 #104)
+#106 := [rewrite]: #105
+#102 := (iff #83 #99)
+#91 := (iff #97 #82)
+#100 := (iff #91 #99)
+#101 := [rewrite]: #100
+#88 := (iff #83 #91)
+#92 := (iff #73 #97)
+#93 := [rewrite]: #92
+#98 := [monotonicity #93]: #88
+#103 := [trans #98 #101]: #102
+#108 := [trans #103 #106]: #107
+#9 := (= f3 f1)
+#17 := (not #9)
+#19 := (implies #17 #18)
+#16 := (implies #9 #15)
+#20 := (and #16 #19)
+#12 := (ite #9 f4 f5)
+#14 := (= #12 f6)
+#21 := (iff #14 #20)
+#22 := (not #21)
+#86 := (iff #22 #83)
+#76 := (iff #49 #73)
+#79 := (not #76)
+#84 := (iff #79 #83)
+#85 := [rewrite]: #84
+#80 := (iff #22 #79)
+#77 := (iff #21 #76)
+#74 := (iff #20 #73)
+#71 := (iff #19 #68)
+#65 := (implies #57 #18)
+#69 := (iff #65 #68)
+#70 := [rewrite]: #69
+#66 := (iff #19 #65)
+#63 := (iff #17 #57)
+#41 := (iff #9 #40)
+#42 := [rewrite]: #41
+#64 := [monotonicity #42]: #63
+#67 := [monotonicity #64]: #66
+#72 := [trans #67 #70]: #71
+#61 := (iff #16 #58)
+#54 := (implies #40 #15)
+#59 := (iff #54 #58)
+#60 := [rewrite]: #59
+#55 := (iff #16 #54)
+#56 := [monotonicity #42]: #55
+#62 := [trans #56 #60]: #61
+#75 := [monotonicity #62 #72]: #74
+#52 := (iff #14 #49)
+#51 := [rewrite]: #50
+#47 := (iff #14 #46)
+#44 := (= #12 #43)
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#53 := [trans #48 #51]: #52
+#78 := [monotonicity #53 #75]: #77
+#81 := [monotonicity #78]: #80
+#87 := [trans #81 #85]: #86
+#39 := [asserted]: #22
+#90 := [mp #39 #87]: #83
+#109 := [mp #90 #108]: #104
+#136 := (not #104)
+#141 := (or #82 #96 #136)
+#142 := [def-axiom]: #141
+#144 := [unit-resolution #142 #109]: #143
+#146 := [unit-resolution #144 #145]: #82
+#156 := [unit-resolution #146 #155]: false
+#158 := [lemma #156]: #157
+#159 := [unit-resolution #158 #147]: #96
+#139 := (or #49 #97)
+#137 := (or #49 #97 #136)
+#138 := [def-axiom]: #137
+#140 := [unit-resolution #138 #109]: #139
+#160 := [unit-resolution #140 #159]: #49
+#173 := [monotonicity #160]: #172
+#175 := [symm #173]: #174
+#163 := (not #111)
+#164 := (iff #123 #163)
+#161 := (iff #18 #111)
+#162 := [monotonicity #160]: #161
+#165 := [monotonicity #162]: #164
+#166 := [mp #147 #165]: #163
+#167 := [unit-resolution #115 #166]: #40
+#171 := [unit-resolution #113 #167]: #110
+#176 := [mp #171 #175]: #15
+#116 := (not #15)
+#126 := (or #68 #57)
+#127 := [def-axiom]: #126
+#168 := [unit-resolution #127 #167]: #68
+#134 := (or #97 #94 #95)
+#135 := [def-axiom]: #134
+#169 := [unit-resolution #135 #168 #159]: #94
+#117 := (or #58 #116)
+#118 := [def-axiom]: #117
+#170 := [unit-resolution #118 #169]: #116
+#177 := [unit-resolution #170 #176]: false
+#178 := [lemma #177]: #18
+#186 := [symm #178]: #185
+#187 := [trans #186 #184]: #49
+#124 := (or #68 #123)
+#125 := [def-axiom]: #124
+#179 := [unit-resolution #125 #178]: #68
+#119 := (or #58 #40)
+#120 := [def-axiom]: #119
+#181 := [unit-resolution #120 #180]: #58
+#182 := [unit-resolution #135 #181 #179]: #97
+#183 := [unit-resolution #144 #182]: #82
+#188 := [unit-resolution #183 #187]: false
+#189 := [lemma #188]: #40
+#194 := [unit-resolution #113 #189]: #110
+#196 := [monotonicity #194]: #195
+#199 := [trans #196 #197]: #198
+#201 := [symm #199]: #200
+#202 := (iff #82 #116)
+#203 := [monotonicity #201]: #202
+#190 := [hypothesis]: #82
+#204 := [mp #190 #203]: #116
+#191 := [unit-resolution #140 #190]: #97
+#192 := [unit-resolution #131 #191]: #58
+#193 := [unit-resolution #122 #192 #189]: #15
+#205 := [unit-resolution #193 #204]: false
+#206 := [lemma #205]: #49
+#210 := [mp #206 #201]: #15
+#207 := [unit-resolution #144 #206]: #96
+#208 := [unit-resolution #135 #207 #179]: #94
+#209 := [unit-resolution #118 #208]: #116
+[unit-resolution #209 #210]: false
+unsat
+00473b4aff1959d5177fa5825ae6319bbb679c00 198 0
+#2 := false
+decl f5 :: S1
+#14 := f5
+decl f1 :: S1
+#4 := f1
+#65 := (= f1 f5)
+decl f3 :: S1
+#8 := f3
+#41 := (= f1 f3)
+#86 := (and #41 #65)
+#92 := (not #86)
+decl f4 :: S1
+#10 := f4
+#44 := (= f1 f4)
+#93 := (or #44 #92)
+#214 := (iff #93 false)
+#209 := (or false false)
+#212 := (iff #209 false)
+#213 := [rewrite]: #212
+#210 := (iff #93 #209)
+#207 := (iff #92 false)
+#1 := true
+#202 := (not true)
+#205 := (iff #202 false)
+#206 := [rewrite]: #205
+#203 := (iff #92 #202)
+#200 := (iff #86 true)
+#195 := (and true true)
+#198 := (iff #195 true)
+#199 := [rewrite]: #198
+#196 := (iff #86 #195)
+#193 := (iff #65 true)
+#71 := (not #65)
+#72 := (or #44 #71)
+#80 := (not #72)
+#81 := (or #44 #80)
+#190 := (iff #81 #65)
+#185 := (or false #65)
+#188 := (iff #185 #65)
+#189 := [rewrite]: #188
+#186 := (iff #81 #185)
+#183 := (iff #80 #65)
+#178 := (not #71)
+#181 := (iff #178 #65)
+#182 := [rewrite]: #181
+#179 := (iff #80 #178)
+#176 := (iff #72 #71)
+#171 := (or false #71)
+#174 := (iff #171 #71)
+#175 := [rewrite]: #174
+#172 := (iff #72 #171)
+#145 := (iff #44 false)
+#137 := (not #44)
+#101 := (not #93)
+#110 := (not #81)
+#50 := (not #41)
+#51 := (or #50 #44)
+#59 := (not #51)
+#60 := (or #44 #59)
+#119 := (not #60)
+#128 := (or #44 #119 #110 #101)
+#131 := (not #128)
+#11 := (= f4 f1)
+#15 := (= f5 f1)
+#9 := (= f3 f1)
+#18 := (and #9 #15)
+#19 := (implies #18 #11)
+#20 := (implies #19 #11)
+#16 := (implies #15 #11)
+#17 := (implies #16 #11)
+#21 := (implies #17 #20)
+#12 := (implies #9 #11)
+#13 := (implies #12 #11)
+#22 := (implies #13 #21)
+#23 := (not #22)
+#134 := (iff #23 #131)
+#102 := (or #44 #101)
+#111 := (or #110 #102)
+#120 := (or #119 #111)
+#125 := (not #120)
+#132 := (iff #125 #131)
+#129 := (iff #120 #128)
+#130 := [rewrite]: #129
+#133 := [monotonicity #130]: #132
+#126 := (iff #23 #125)
+#123 := (iff #22 #120)
+#116 := (implies #60 #111)
+#121 := (iff #116 #120)
+#122 := [rewrite]: #121
+#117 := (iff #22 #116)
+#114 := (iff #21 #111)
+#107 := (implies #81 #102)
+#112 := (iff #107 #111)
+#113 := [rewrite]: #112
+#108 := (iff #21 #107)
+#105 := (iff #20 #102)
+#98 := (implies #93 #44)
+#103 := (iff #98 #102)
+#104 := [rewrite]: #103
+#99 := (iff #20 #98)
+#45 := (iff #11 #44)
+#46 := [rewrite]: #45
+#96 := (iff #19 #93)
+#89 := (implies #86 #44)
+#94 := (iff #89 #93)
+#95 := [rewrite]: #94
+#90 := (iff #19 #89)
+#87 := (iff #18 #86)
+#66 := (iff #15 #65)
+#67 := [rewrite]: #66
+#42 := (iff #9 #41)
+#43 := [rewrite]: #42
+#88 := [monotonicity #43 #67]: #87
+#91 := [monotonicity #88 #46]: #90
+#97 := [trans #91 #95]: #96
+#100 := [monotonicity #97 #46]: #99
+#106 := [trans #100 #104]: #105
+#84 := (iff #17 #81)
+#77 := (implies #72 #44)
+#82 := (iff #77 #81)
+#83 := [rewrite]: #82
+#78 := (iff #17 #77)
+#75 := (iff #16 #72)
+#68 := (implies #65 #44)
+#73 := (iff #68 #72)
+#74 := [rewrite]: #73
+#69 := (iff #16 #68)
+#70 := [monotonicity #67 #46]: #69
+#76 := [trans #70 #74]: #75
+#79 := [monotonicity #76 #46]: #78
+#85 := [trans #79 #83]: #84
+#109 := [monotonicity #85 #106]: #108
+#115 := [trans #109 #113]: #114
+#63 := (iff #13 #60)
+#56 := (implies #51 #44)
+#61 := (iff #56 #60)
+#62 := [rewrite]: #61
+#57 := (iff #13 #56)
+#54 := (iff #12 #51)
+#47 := (implies #41 #44)
+#52 := (iff #47 #51)
+#53 := [rewrite]: #52
+#48 := (iff #12 #47)
+#49 := [monotonicity #43 #46]: #48
+#55 := [trans #49 #53]: #54
+#58 := [monotonicity #55 #46]: #57
+#64 := [trans #58 #62]: #63
+#118 := [monotonicity #64 #115]: #117
+#124 := [trans #118 #122]: #123
+#127 := [monotonicity #124]: #126
+#135 := [trans #127 #133]: #134
+#40 := [asserted]: #23
+#136 := [mp #40 #135]: #131
+#138 := [not-or-elim #136]: #137
+#146 := [iff-false #138]: #145
+#173 := [monotonicity #146]: #172
+#177 := [trans #173 #175]: #176
+#180 := [monotonicity #177]: #179
+#184 := [trans #180 #182]: #183
+#187 := [monotonicity #146 #184]: #186
+#191 := [trans #187 #189]: #190
+#140 := [not-or-elim #136]: #81
+#192 := [mp #140 #191]: #65
+#194 := [iff-true #192]: #193
+#169 := (iff #41 true)
+#166 := (iff #60 #41)
+#161 := (or false #41)
+#164 := (iff #161 #41)
+#165 := [rewrite]: #164
+#162 := (iff #60 #161)
+#159 := (iff #59 #41)
+#154 := (not #50)
+#157 := (iff #154 #41)
+#158 := [rewrite]: #157
+#155 := (iff #59 #154)
+#152 := (iff #51 #50)
+#147 := (or #50 false)
+#150 := (iff #147 #50)
+#151 := [rewrite]: #150
+#148 := (iff #51 #147)
+#149 := [monotonicity #146]: #148
+#153 := [trans #149 #151]: #152
+#156 := [monotonicity #153]: #155
+#160 := [trans #156 #158]: #159
+#163 := [monotonicity #146 #160]: #162
+#167 := [trans #163 #165]: #166
+#139 := [not-or-elim #136]: #60
+#168 := [mp #139 #167]: #41
+#170 := [iff-true #168]: #169
+#197 := [monotonicity #170 #194]: #196
+#201 := [trans #197 #199]: #200
+#204 := [monotonicity #201]: #203
+#208 := [trans #204 #206]: #207
+#211 := [monotonicity #146 #208]: #210
+#215 := [trans #211 #213]: #214
+#141 := [not-or-elim #136]: #93
+[mp #141 #215]: false
+unsat
+2cfe9308ab7f394e846bed2379142398e01d0e8d 134 0
+#2 := false
+decl f5 :: S1
+#14 := f5
+decl f1 :: S1
+#4 := f1
+#59 := (= f1 f5)
+decl f3 :: S1
+#8 := f3
+#41 := (= f1 f3)
+#74 := (and #41 #59)
+#80 := (not #74)
+decl f4 :: S1
+#10 := f4
+#44 := (= f1 f4)
+#81 := (or #44 #80)
+#150 := (iff #81 false)
+#145 := (or false false)
+#148 := (iff #145 false)
+#149 := [rewrite]: #148
+#146 := (iff #81 #145)
+#143 := (iff #80 false)
+#1 := true
+#138 := (not true)
+#141 := (iff #138 false)
+#142 := [rewrite]: #141
+#139 := (iff #80 #138)
+#136 := (iff #74 true)
+#131 := (and true true)
+#134 := (iff #131 true)
+#135 := [rewrite]: #134
+#132 := (iff #74 #131)
+#129 := (iff #59 true)
+#86 := (not #81)
+#65 := (not #59)
+#50 := (not #41)
+#108 := (or #50 #44 #65 #86)
+#111 := (not #108)
+#11 := (= f4 f1)
+#15 := (= f5 f1)
+#9 := (= f3 f1)
+#18 := (and #9 #15)
+#19 := (implies #18 #11)
+#20 := (not #19)
+#16 := (implies #15 #11)
+#17 := (not #16)
+#21 := (implies #17 #20)
+#12 := (implies #9 #11)
+#13 := (not #12)
+#22 := (implies #13 #21)
+#23 := (not #22)
+#114 := (iff #23 #111)
+#66 := (or #44 #65)
+#92 := (or #66 #86)
+#51 := (or #50 #44)
+#100 := (or #51 #92)
+#105 := (not #100)
+#112 := (iff #105 #111)
+#109 := (iff #100 #108)
+#110 := [rewrite]: #109
+#113 := [monotonicity #110]: #112
+#106 := (iff #23 #105)
+#103 := (iff #22 #100)
+#56 := (not #51)
+#97 := (implies #56 #92)
+#101 := (iff #97 #100)
+#102 := [rewrite]: #101
+#98 := (iff #22 #97)
+#95 := (iff #21 #92)
+#71 := (not #66)
+#89 := (implies #71 #86)
+#93 := (iff #89 #92)
+#94 := [rewrite]: #93
+#90 := (iff #21 #89)
+#87 := (iff #20 #86)
+#84 := (iff #19 #81)
+#77 := (implies #74 #44)
+#82 := (iff #77 #81)
+#83 := [rewrite]: #82
+#78 := (iff #19 #77)
+#45 := (iff #11 #44)
+#46 := [rewrite]: #45
+#75 := (iff #18 #74)
+#60 := (iff #15 #59)
+#61 := [rewrite]: #60
+#42 := (iff #9 #41)
+#43 := [rewrite]: #42
+#76 := [monotonicity #43 #61]: #75
+#79 := [monotonicity #76 #46]: #78
+#85 := [trans #79 #83]: #84
+#88 := [monotonicity #85]: #87
+#72 := (iff #17 #71)
+#69 := (iff #16 #66)
+#62 := (implies #59 #44)
+#67 := (iff #62 #66)
+#68 := [rewrite]: #67
+#63 := (iff #16 #62)
+#64 := [monotonicity #61 #46]: #63
+#70 := [trans #64 #68]: #69
+#73 := [monotonicity #70]: #72
+#91 := [monotonicity #73 #88]: #90
+#96 := [trans #91 #94]: #95
+#57 := (iff #13 #56)
+#54 := (iff #12 #51)
+#47 := (implies #41 #44)
+#52 := (iff #47 #51)
+#53 := [rewrite]: #52
+#48 := (iff #12 #47)
+#49 := [monotonicity #43 #46]: #48
+#55 := [trans #49 #53]: #54
+#58 := [monotonicity #55]: #57
+#99 := [monotonicity #58 #96]: #98
+#104 := [trans #99 #102]: #103
+#107 := [monotonicity #104]: #106
+#115 := [trans #107 #113]: #114
+#40 := [asserted]: #23
+#116 := [mp #40 #115]: #111
+#120 := [not-or-elim #116]: #59
+#130 := [iff-true #120]: #129
+#125 := (iff #41 true)
+#117 := [not-or-elim #116]: #41
+#126 := [iff-true #117]: #125
+#133 := [monotonicity #126 #130]: #132
+#137 := [trans #133 #135]: #136
+#140 := [monotonicity #137]: #139
+#144 := [trans #140 #142]: #143
+#127 := (iff #44 false)
+#118 := (not #44)
+#119 := [not-or-elim #116]: #118
+#128 := [iff-false #119]: #127
+#147 := [monotonicity #128 #144]: #146
+#151 := [trans #147 #149]: #150
+#121 := [not-or-elim #116]: #81
+[mp #121 #151]: false
+unsat
+ec4d1a12b3f23ddd6f880458ababd57fd69399e9 36 0
+#2 := false
+decl f5 :: S2
+#10 := f5
+decl f3 :: S2
+#8 := f3
+#12 := (= f3 f5)
+#13 := (not #12)
+decl f4 :: S2
+#9 := f4
+#11 := (distinct f3 f4 f5)
+#33 := (not #11)
+#34 := (or #33 #13)
+#37 := (not #34)
+#14 := (implies #11 #13)
+#15 := (not #14)
+#38 := (iff #15 #37)
+#35 := (iff #14 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#32 := [asserted]: #15
+#42 := [mp #32 #39]: #37
+#41 := [not-or-elim #42]: #12
+#52 := (= f4 f5)
+#53 := (not #52)
+#50 := (= f3 f4)
+#51 := (not #50)
+#48 := (and #51 #13 #53)
+#40 := [not-or-elim #42]: #11
+#58 := (or #33 #48)
+#59 := [def-axiom]: #58
+#62 := [unit-resolution #59 #40]: #48
+#49 := (not #48)
+#45 := (or #49 #13)
+#43 := [def-axiom]: #45
+[unit-resolution #43 #62 #41]: false
+unsat
+d49a2aa891a4e97785d87ae0852efd8c830df7dd 162 0
+#2 := false
+decl f5 :: S1
+#12 := f5
+decl f1 :: S1
+#4 := f1
+#44 := (= f1 f5)
+decl f3 :: S1
+#8 := f3
+#38 := (= f1 f3)
+#53 := (not #38)
+#70 := (or #53 #44)
+#97 := (not #70)
+decl f4 :: S1
+#10 := f4
+#41 := (= f1 f4)
+#62 := (or #53 #41)
+#96 := (not #62)
+#98 := (or #96 #97)
+#90 := (not #44)
+#93 := (not #41)
+#100 := (or #93 #90)
+#101 := (not #100)
+#104 := (or #53 #101)
+#107 := (not #104)
+#158 := [hypothesis]: #107
+#145 := (or #104 #100)
+#146 := [def-axiom]: #145
+#159 := [unit-resolution #146 #158]: #100
+#143 := (or #104 #38)
+#144 := [def-axiom]: #143
+#160 := [unit-resolution #144 #158]: #38
+#99 := (not #98)
+#156 := (or #99 #104)
+#113 := (iff #98 #104)
+#47 := (and #41 #44)
+#54 := (or #53 #47)
+#84 := (not #54)
+#75 := (and #62 #70)
+#85 := (iff #75 #84)
+#116 := (iff #85 #113)
+#110 := (iff #99 #107)
+#114 := (iff #110 #113)
+#115 := [rewrite]: #114
+#111 := (iff #85 #110)
+#108 := (iff #84 #107)
+#105 := (iff #54 #104)
+#102 := (iff #47 #101)
+#103 := [rewrite]: #102
+#106 := [monotonicity #103]: #105
+#109 := [monotonicity #106]: #108
+#94 := (iff #75 #99)
+#95 := [rewrite]: #94
+#112 := [monotonicity #95 #109]: #111
+#117 := [trans #112 #115]: #116
+#13 := (= f5 f1)
+#9 := (= f3 f1)
+#17 := (implies #9 #13)
+#11 := (= f4 f1)
+#16 := (implies #9 #11)
+#18 := (and #16 #17)
+#14 := (and #11 #13)
+#15 := (implies #9 #14)
+#19 := (iff #15 #18)
+#20 := (not #19)
+#88 := (iff #20 #85)
+#78 := (iff #54 #75)
+#81 := (not #78)
+#86 := (iff #81 #85)
+#87 := [rewrite]: #86
+#82 := (iff #20 #81)
+#79 := (iff #19 #78)
+#76 := (iff #18 #75)
+#73 := (iff #17 #70)
+#67 := (implies #38 #44)
+#71 := (iff #67 #70)
+#72 := [rewrite]: #71
+#68 := (iff #17 #67)
+#45 := (iff #13 #44)
+#46 := [rewrite]: #45
+#39 := (iff #9 #38)
+#40 := [rewrite]: #39
+#69 := [monotonicity #40 #46]: #68
+#74 := [trans #69 #72]: #73
+#65 := (iff #16 #62)
+#59 := (implies #38 #41)
+#63 := (iff #59 #62)
+#64 := [rewrite]: #63
+#60 := (iff #16 #59)
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#61 := [monotonicity #40 #43]: #60
+#66 := [trans #61 #64]: #65
+#77 := [monotonicity #66 #74]: #76
+#57 := (iff #15 #54)
+#50 := (implies #38 #47)
+#55 := (iff #50 #54)
+#56 := [rewrite]: #55
+#51 := (iff #15 #50)
+#48 := (iff #14 #47)
+#49 := [monotonicity #43 #46]: #48
+#52 := [monotonicity #40 #49]: #51
+#58 := [trans #52 #56]: #57
+#80 := [monotonicity #58 #77]: #79
+#83 := [monotonicity #80]: #82
+#89 := [trans #83 #87]: #88
+#37 := [asserted]: #20
+#92 := [mp #37 #89]: #85
+#118 := [mp #92 #117]: #113
+#149 := (not #113)
+#154 := (or #99 #104 #149)
+#155 := [def-axiom]: #154
+#157 := [unit-resolution #155 #118]: #156
+#161 := [unit-resolution #157 #158]: #99
+#131 := (or #98 #62)
+#132 := [def-axiom]: #131
+#162 := [unit-resolution #132 #161]: #62
+#123 := (or #96 #53 #41)
+#124 := [def-axiom]: #123
+#163 := [unit-resolution #124 #162 #160]: #41
+#133 := (or #98 #70)
+#134 := [def-axiom]: #133
+#164 := [unit-resolution #134 #161]: #70
+#129 := (or #97 #53 #44)
+#130 := [def-axiom]: #129
+#165 := [unit-resolution #130 #164 #160]: #44
+#141 := (or #101 #93 #90)
+#142 := [def-axiom]: #141
+#166 := [unit-resolution #142 #165 #163 #159]: false
+#167 := [lemma #166]: #104
+#152 := (or #98 #107)
+#150 := (or #98 #107 #149)
+#151 := [def-axiom]: #150
+#153 := [unit-resolution #151 #118]: #152
+#168 := [unit-resolution #153 #167]: #98
+#169 := [hypothesis]: #53
+#119 := (or #62 #38)
+#120 := [def-axiom]: #119
+#170 := [unit-resolution #120 #169]: #62
+#125 := (or #70 #38)
+#126 := [def-axiom]: #125
+#171 := [unit-resolution #126 #169]: #70
+#135 := (or #99 #96 #97)
+#136 := [def-axiom]: #135
+#172 := [unit-resolution #136 #171 #170 #168]: false
+#173 := [lemma #172]: #38
+#147 := (or #107 #53 #101)
+#148 := [def-axiom]: #147
+#174 := [unit-resolution #148 #173 #167]: #101
+#137 := (or #100 #41)
+#138 := [def-axiom]: #137
+#175 := [unit-resolution #138 #174]: #41
+#121 := (or #62 #93)
+#122 := [def-axiom]: #121
+#176 := [unit-resolution #122 #175]: #62
+#139 := (or #100 #44)
+#140 := [def-axiom]: #139
+#177 := [unit-resolution #140 #174]: #44
+#127 := (or #70 #90)
+#128 := [def-axiom]: #127
+#178 := [unit-resolution #128 #177]: #70
+[unit-resolution #136 #178 #176 #168]: false
+unsat
+bb1f7f82c156e4b85608a3fcfce6206c30c1bb93 77 0
+#2 := false
+decl f4 :: S2
+#9 := f4
+decl f3 :: S2
+#8 := f3
+#81 := (= f3 f4)
+decl f6 :: S2
+#12 := f6
+#36 := (= f4 f6)
+#100 := (iff #36 #81)
+#98 := (iff #81 #36)
+#13 := (= f6 f4)
+#37 := (iff #13 #36)
+#97 := [commutativity]: #37
+#95 := (iff #81 #13)
+#14 := (= f3 f6)
+#42 := (not #36)
+#15 := (not #14)
+decl f5 :: S2
+#10 := f5
+#11 := (distinct f3 f4 f5)
+#51 := (not #11)
+#60 := (or #51 #15 #42)
+#63 := (not #60)
+#16 := (implies #13 #15)
+#17 := (implies #11 #16)
+#18 := (not #17)
+#66 := (iff #18 #63)
+#43 := (or #15 #42)
+#52 := (or #51 #43)
+#57 := (not #52)
+#64 := (iff #57 #63)
+#61 := (iff #52 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#58 := (iff #18 #57)
+#55 := (iff #17 #52)
+#48 := (implies #11 #43)
+#53 := (iff #48 #52)
+#54 := [rewrite]: #53
+#49 := (iff #17 #48)
+#46 := (iff #16 #43)
+#39 := (implies #36 #15)
+#44 := (iff #39 #43)
+#45 := [rewrite]: #44
+#40 := (iff #16 #39)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#47 := [trans #41 #45]: #46
+#50 := [monotonicity #47]: #49
+#56 := [trans #50 #54]: #55
+#59 := [monotonicity #56]: #58
+#67 := [trans #59 #65]: #66
+#35 := [asserted]: #18
+#68 := [mp #35 #67]: #63
+#70 := [not-or-elim #68]: #14
+#96 := [monotonicity #70]: #95
+#99 := [trans #96 #97]: #98
+#101 := [symm #99]: #100
+#71 := [not-or-elim #68]: #36
+#102 := [mp #71 #101]: #81
+#82 := (not #81)
+#79 := (= f4 f5)
+#80 := (not #79)
+#83 := (= f3 f5)
+#84 := (not #83)
+#77 := (and #82 #84 #80)
+#69 := [not-or-elim #68]: #11
+#89 := (or #51 #77)
+#90 := [def-axiom]: #89
+#93 := [unit-resolution #90 #69]: #77
+#78 := (not #77)
+#75 := (or #78 #82)
+#76 := [def-axiom]: #75
+#94 := [unit-resolution #76 #93]: #82
+[unit-resolution #94 #102]: false
+unsat
+a32448a76e7c2238050b2242f58c388f5af4bb0b 54 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#12 := (implies #11 #9)
+#13 := (implies #9 #12)
+#14 := (not #13)
+#68 := (iff #14 false)
+#35 := (= f1 f4)
+#41 := (not #35)
+#32 := (= f1 f3)
+#42 := (or #32 #41)
+#50 := (not #32)
+#51 := (or #50 #42)
+#56 := (not #51)
+#66 := (iff #56 false)
+#1 := true
+#61 := (not true)
+#64 := (iff #61 false)
+#65 := [rewrite]: #64
+#62 := (iff #56 #61)
+#59 := (iff #51 true)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#67 := [trans #63 #65]: #66
+#57 := (iff #14 #56)
+#54 := (iff #13 #51)
+#47 := (implies #32 #42)
+#52 := (iff #47 #51)
+#53 := [rewrite]: #52
+#48 := (iff #13 #47)
+#45 := (iff #12 #42)
+#38 := (implies #35 #32)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #12 #38)
+#33 := (iff #9 #32)
+#34 := [rewrite]: #33
+#36 := (iff #11 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37 #34]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #34 #46]: #48
+#55 := [trans #49 #53]: #54
+#58 := [monotonicity #55]: #57
+#69 := [trans #58 #67]: #68
+#31 := [asserted]: #14
+[mp #31 #69]: false
+unsat
+f708f93eff4fe8de6618caf7ad2da4c76f2e075e 28 0
+#2 := false
+decl f4 :: S2
+#9 := f4
+decl f3 :: S2
+#8 := f3
+#10 := (distinct f3 f4 f3 f4)
+#11 := (not #10)
+#12 := (not #11)
+#44 := (iff #12 false)
+#1 := true
+#39 := (not true)
+#42 := (iff #39 false)
+#43 := [rewrite]: #42
+#40 := (iff #12 #39)
+#37 := (iff #11 true)
+#32 := (not false)
+#35 := (iff #32 true)
+#36 := [rewrite]: #35
+#33 := (iff #11 #32)
+#30 := (iff #10 false)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31]: #33
+#38 := [trans #34 #36]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#29 := [asserted]: #12
+[mp #29 #45]: false
+unsat
+bdc1bdcbb661b97af9742dbe35f1e882a21fc3b1 30 0
+#2 := false
+decl f4 :: S2
+#9 := f4
+decl f3 :: S2
+#8 := f3
+#10 := (= f3 f4)
+#11 := (not #10)
+#12 := (not #11)
+#13 := (implies #10 #12)
+#14 := (not #13)
+#46 := (iff #14 false)
+#1 := true
+#41 := (not true)
+#44 := (iff #41 false)
+#45 := [rewrite]: #44
+#42 := (iff #14 #41)
+#39 := (iff #13 true)
+#34 := (implies #10 #10)
+#37 := (iff #34 true)
+#38 := [rewrite]: #37
+#35 := (iff #13 #34)
+#32 := (iff #12 #10)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#40 := [trans #36 #38]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#31 := [asserted]: #14
+[mp #31 #47]: false
+unsat
+4beee0db11f1f0218a1c8845ad7dc8b072a3465b 144 0
+#2 := false
+decl f5 :: S1
+#12 := f5
+decl f1 :: S1
+#4 := f1
+#44 := (= f1 f5)
+decl f4 :: S1
+#10 := f4
+#41 := (= f1 f4)
+#50 := (not #41)
+decl f3 :: S1
+#8 := f3
+#38 := (= f1 f3)
+#59 := (not #38)
+#102 := (or #59 #50 #44)
+#160 := (iff #102 false)
+#155 := (or false false false)
+#158 := (iff #155 false)
+#159 := [rewrite]: #158
+#156 := (iff #102 #155)
+#132 := (iff #44 false)
+#123 := (not #44)
+#105 := (not #102)
+#68 := (or #59 #41)
+#84 := (not #68)
+#111 := (or #59 #44 #84 #105)
+#116 := (not #111)
+#13 := (= f5 f1)
+#9 := (= f3 f1)
+#17 := (implies #9 #13)
+#11 := (= f4 f1)
+#16 := (implies #9 #11)
+#18 := (implies #16 #17)
+#14 := (implies #11 #13)
+#15 := (implies #9 #14)
+#19 := (implies #15 #18)
+#20 := (not #19)
+#119 := (iff #20 #116)
+#76 := (or #59 #44)
+#85 := (or #84 #76)
+#51 := (or #50 #44)
+#60 := (or #59 #51)
+#93 := (not #60)
+#94 := (or #93 #85)
+#99 := (not #94)
+#117 := (iff #99 #116)
+#114 := (iff #94 #111)
+#108 := (or #105 #85)
+#112 := (iff #108 #111)
+#113 := [rewrite]: #112
+#109 := (iff #94 #108)
+#106 := (iff #93 #105)
+#103 := (iff #60 #102)
+#104 := [rewrite]: #103
+#107 := [monotonicity #104]: #106
+#110 := [monotonicity #107]: #109
+#115 := [trans #110 #113]: #114
+#118 := [monotonicity #115]: #117
+#100 := (iff #20 #99)
+#97 := (iff #19 #94)
+#90 := (implies #60 #85)
+#95 := (iff #90 #94)
+#96 := [rewrite]: #95
+#91 := (iff #19 #90)
+#88 := (iff #18 #85)
+#81 := (implies #68 #76)
+#86 := (iff #81 #85)
+#87 := [rewrite]: #86
+#82 := (iff #18 #81)
+#79 := (iff #17 #76)
+#73 := (implies #38 #44)
+#77 := (iff #73 #76)
+#78 := [rewrite]: #77
+#74 := (iff #17 #73)
+#45 := (iff #13 #44)
+#46 := [rewrite]: #45
+#39 := (iff #9 #38)
+#40 := [rewrite]: #39
+#75 := [monotonicity #40 #46]: #74
+#80 := [trans #75 #78]: #79
+#71 := (iff #16 #68)
+#65 := (implies #38 #41)
+#69 := (iff #65 #68)
+#70 := [rewrite]: #69
+#66 := (iff #16 #65)
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#67 := [monotonicity #40 #43]: #66
+#72 := [trans #67 #70]: #71
+#83 := [monotonicity #72 #80]: #82
+#89 := [trans #83 #87]: #88
+#63 := (iff #15 #60)
+#56 := (implies #38 #51)
+#61 := (iff #56 #60)
+#62 := [rewrite]: #61
+#57 := (iff #15 #56)
+#54 := (iff #14 #51)
+#47 := (implies #41 #44)
+#52 := (iff #47 #51)
+#53 := [rewrite]: #52
+#48 := (iff #14 #47)
+#49 := [monotonicity #43 #46]: #48
+#55 := [trans #49 #53]: #54
+#58 := [monotonicity #40 #55]: #57
+#64 := [trans #58 #62]: #63
+#92 := [monotonicity #64 #89]: #91
+#98 := [trans #92 #96]: #97
+#101 := [monotonicity #98]: #100
+#120 := [trans #101 #118]: #119
+#37 := [asserted]: #20
+#121 := [mp #37 #120]: #116
+#124 := [not-or-elim #121]: #123
+#133 := [iff-false #124]: #132
+#153 := (iff #50 false)
+#1 := true
+#134 := (not true)
+#137 := (iff #134 false)
+#138 := [rewrite]: #137
+#151 := (iff #50 #134)
+#149 := (iff #41 true)
+#146 := (iff #68 #41)
+#141 := (or false #41)
+#144 := (iff #141 #41)
+#145 := [rewrite]: #144
+#142 := (iff #68 #141)
+#139 := (iff #59 false)
+#135 := (iff #59 #134)
+#130 := (iff #38 true)
+#122 := [not-or-elim #121]: #38
+#131 := [iff-true #122]: #130
+#136 := [monotonicity #131]: #135
+#140 := [trans #136 #138]: #139
+#143 := [monotonicity #140]: #142
+#147 := [trans #143 #145]: #146
+#125 := [not-or-elim #121]: #68
+#148 := [mp #125 #147]: #41
+#150 := [iff-true #148]: #149
+#152 := [monotonicity #150]: #151
+#154 := [trans #152 #138]: #153
+#157 := [monotonicity #140 #154 #133]: #156
+#161 := [trans #157 #159]: #160
+#126 := [not-or-elim #121]: #102
+[mp #126 #161]: false
+unsat
+b39d61834fdb48ccd6c976fd127ad9ad2b57765f 40 0
+#2 := false
+decl f5 :: S2
+#11 := f5
+decl f4 :: S2
+#9 := f4
+decl f3 :: S2
+#8 := f3
+#14 := (distinct f3 f4 f5)
+#15 := (not #14)
+#12 := (= f3 f5)
+#10 := (= f3 f4)
+#13 := (and #10 #12)
+#35 := (not #13)
+#36 := (or #35 #15)
+#39 := (not #36)
+#16 := (implies #13 #15)
+#17 := (not #16)
+#40 := (iff #17 #39)
+#37 := (iff #16 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#34 := [asserted]: #17
+#44 := [mp #34 #41]: #39
+#46 := [not-or-elim #44]: #14
+#58 := (= f4 f5)
+#59 := (not #58)
+#57 := (not #12)
+#56 := (not #10)
+#54 := (and #56 #57 #59)
+#55 := (not #54)
+#42 := [not-or-elim #44]: #13
+#43 := [and-elim #42]: #10
+#52 := (or #55 #56)
+#53 := [def-axiom]: #52
+#66 := [unit-resolution #53 #43]: #55
+#62 := (or #15 #54)
+#63 := [def-axiom]: #62
+#67 := [unit-resolution #63 #66]: #15
+[unit-resolution #67 #46]: false
+unsat
+06703092b87ad607f1fc183aeaf2318c5fc95140 121 0
+#2 := false
+decl f5 :: S1
+#13 := f5
+decl f1 :: S1
+#4 := f1
+#53 := (= f1 f5)
+decl f4 :: S1
+#10 := f4
+#41 := (= f1 f4)
+decl f3 :: S1
+#8 := f3
+#38 := (= f1 f3)
+#47 := (not #38)
+#90 := (or #47 #41 #53)
+#137 := (iff #90 false)
+#132 := (or false false false)
+#135 := (iff #132 false)
+#136 := [rewrite]: #135
+#133 := (iff #90 #132)
+#123 := (iff #53 false)
+#113 := (not #53)
+#93 := (not #90)
+#99 := (or #47 #41 #53 #93)
+#104 := (not #99)
+#14 := (= f5 f1)
+#11 := (= f4 f1)
+#17 := (or #11 #14)
+#9 := (= f3 f1)
+#18 := (implies #9 #17)
+#15 := (implies #9 #14)
+#12 := (implies #9 #11)
+#16 := (or #12 #15)
+#19 := (implies #16 #18)
+#20 := (not #19)
+#107 := (iff #20 #104)
+#67 := (or #41 #53)
+#73 := (or #47 #67)
+#59 := (or #47 #53)
+#48 := (or #47 #41)
+#64 := (or #48 #59)
+#81 := (not #64)
+#82 := (or #81 #73)
+#87 := (not #82)
+#105 := (iff #87 #104)
+#102 := (iff #82 #99)
+#96 := (or #93 #73)
+#100 := (iff #96 #99)
+#101 := [rewrite]: #100
+#97 := (iff #82 #96)
+#94 := (iff #81 #93)
+#91 := (iff #64 #90)
+#92 := [rewrite]: #91
+#95 := [monotonicity #92]: #94
+#98 := [monotonicity #95]: #97
+#103 := [trans #98 #101]: #102
+#106 := [monotonicity #103]: #105
+#88 := (iff #20 #87)
+#85 := (iff #19 #82)
+#78 := (implies #64 #73)
+#83 := (iff #78 #82)
+#84 := [rewrite]: #83
+#79 := (iff #19 #78)
+#76 := (iff #18 #73)
+#70 := (implies #38 #67)
+#74 := (iff #70 #73)
+#75 := [rewrite]: #74
+#71 := (iff #18 #70)
+#68 := (iff #17 #67)
+#54 := (iff #14 #53)
+#55 := [rewrite]: #54
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#69 := [monotonicity #43 #55]: #68
+#39 := (iff #9 #38)
+#40 := [rewrite]: #39
+#72 := [monotonicity #40 #69]: #71
+#77 := [trans #72 #75]: #76
+#65 := (iff #16 #64)
+#62 := (iff #15 #59)
+#56 := (implies #38 #53)
+#60 := (iff #56 #59)
+#61 := [rewrite]: #60
+#57 := (iff #15 #56)
+#58 := [monotonicity #40 #55]: #57
+#63 := [trans #58 #61]: #62
+#51 := (iff #12 #48)
+#44 := (implies #38 #41)
+#49 := (iff #44 #48)
+#50 := [rewrite]: #49
+#45 := (iff #12 #44)
+#46 := [monotonicity #40 #43]: #45
+#52 := [trans #46 #50]: #51
+#66 := [monotonicity #52 #63]: #65
+#80 := [monotonicity #66 #77]: #79
+#86 := [trans #80 #84]: #85
+#89 := [monotonicity #86]: #88
+#108 := [trans #89 #106]: #107
+#37 := [asserted]: #20
+#109 := [mp #37 #108]: #104
+#114 := [not-or-elim #109]: #113
+#124 := [iff-false #114]: #123
+#121 := (iff #41 false)
+#111 := (not #41)
+#112 := [not-or-elim #109]: #111
+#122 := [iff-false #112]: #121
+#130 := (iff #47 false)
+#1 := true
+#125 := (not true)
+#128 := (iff #125 false)
+#129 := [rewrite]: #128
+#126 := (iff #47 #125)
+#119 := (iff #38 true)
+#110 := [not-or-elim #109]: #38
+#120 := [iff-true #110]: #119
+#127 := [monotonicity #120]: #126
+#131 := [trans #127 #129]: #130
+#134 := [monotonicity #131 #122 #124]: #133
+#138 := [trans #134 #136]: #137
+#115 := [not-or-elim #109]: #90
+[mp #115 #138]: false
+unsat
+f12c3118f1895363634ae08d5e1cb8290b015c56 33 0
+#2 := false
+decl f3 :: S2
+#8 := f3
+decl f5 :: S2
+#10 := f5
+decl f4 :: S2
+#9 := f4
+decl f6 :: S2
+#11 := f6
+#13 := (distinct f6 f4 f5 f3)
+#12 := (distinct f3 f4 f5 f6)
+#14 := (implies #12 #13)
+#15 := (not #14)
+#47 := (iff #15 false)
+#1 := true
+#42 := (not true)
+#45 := (iff #42 false)
+#46 := [rewrite]: #45
+#43 := (iff #15 #42)
+#40 := (iff #14 true)
+#35 := (implies #12 #12)
+#38 := (iff #35 true)
+#39 := [rewrite]: #38
+#36 := (iff #14 #35)
+#33 := (iff #13 #12)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#41 := [trans #37 #39]: #40
+#44 := [monotonicity #41]: #43
+#48 := [trans #44 #46]: #47
+#32 := [asserted]: #15
+[mp #32 #48]: false
+unsat
+9a5a01706e8f03de5459124543d7c655f9eae121 123 0
+#2 := false
+decl f4 :: S1
+#10 := f4
+decl f1 :: S1
+#4 := f1
+#38 := (= f1 f4)
+decl f3 :: S1
+#8 := f3
+#35 := (= f1 f3)
+#44 := (not #35)
+#45 := (or #44 #38)
+#53 := (not #45)
+#54 := (or #35 #53)
+#62 := (not #54)
+#63 := (or #35 #62)
+#71 := (not #63)
+#72 := (or #38 #71)
+#140 := (iff #72 false)
+#135 := (or false false)
+#138 := (iff #135 false)
+#139 := [rewrite]: #138
+#136 := (iff #72 #135)
+#133 := (iff #71 false)
+#1 := true
+#128 := (not true)
+#131 := (iff #128 false)
+#132 := [rewrite]: #131
+#129 := (iff #71 #128)
+#126 := (iff #63 true)
+#121 := (or #35 #44)
+#124 := (iff #121 true)
+#125 := [rewrite]: #124
+#122 := (iff #63 #121)
+#119 := (iff #62 #44)
+#117 := (iff #54 #35)
+#112 := (or #35 #35)
+#115 := (iff #112 #35)
+#116 := [rewrite]: #115
+#113 := (iff #54 #112)
+#110 := (iff #53 #35)
+#105 := (not #44)
+#108 := (iff #105 #35)
+#109 := [rewrite]: #108
+#106 := (iff #53 #105)
+#103 := (iff #45 #44)
+#98 := (or #44 false)
+#101 := (iff #98 #44)
+#102 := [rewrite]: #101
+#99 := (iff #45 #98)
+#96 := (iff #38 false)
+#89 := (not #38)
+#80 := (not #72)
+#81 := (or #38 #80)
+#86 := (not #81)
+#11 := (= f4 f1)
+#9 := (= f3 f1)
+#12 := (implies #9 #11)
+#13 := (implies #12 #9)
+#14 := (implies #13 #9)
+#15 := (implies #14 #11)
+#16 := (implies #15 #11)
+#17 := (not #16)
+#87 := (iff #17 #86)
+#84 := (iff #16 #81)
+#77 := (implies #72 #38)
+#82 := (iff #77 #81)
+#83 := [rewrite]: #82
+#78 := (iff #16 #77)
+#39 := (iff #11 #38)
+#40 := [rewrite]: #39
+#75 := (iff #15 #72)
+#68 := (implies #63 #38)
+#73 := (iff #68 #72)
+#74 := [rewrite]: #73
+#69 := (iff #15 #68)
+#66 := (iff #14 #63)
+#59 := (implies #54 #35)
+#64 := (iff #59 #63)
+#65 := [rewrite]: #64
+#60 := (iff #14 #59)
+#36 := (iff #9 #35)
+#37 := [rewrite]: #36
+#57 := (iff #13 #54)
+#50 := (implies #45 #35)
+#55 := (iff #50 #54)
+#56 := [rewrite]: #55
+#51 := (iff #13 #50)
+#48 := (iff #12 #45)
+#41 := (implies #35 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #12 #41)
+#43 := [monotonicity #37 #40]: #42
+#49 := [trans #43 #47]: #48
+#52 := [monotonicity #49 #37]: #51
+#58 := [trans #52 #56]: #57
+#61 := [monotonicity #58 #37]: #60
+#67 := [trans #61 #65]: #66
+#70 := [monotonicity #67 #40]: #69
+#76 := [trans #70 #74]: #75
+#79 := [monotonicity #76 #40]: #78
+#85 := [trans #79 #83]: #84
+#88 := [monotonicity #85]: #87
+#34 := [asserted]: #17
+#91 := [mp #34 #88]: #86
+#90 := [not-or-elim #91]: #89
+#97 := [iff-false #90]: #96
+#100 := [monotonicity #97]: #99
+#104 := [trans #100 #102]: #103
+#107 := [monotonicity #104]: #106
+#111 := [trans #107 #109]: #110
+#114 := [monotonicity #111]: #113
+#118 := [trans #114 #116]: #117
+#120 := [monotonicity #118]: #119
+#123 := [monotonicity #120]: #122
+#127 := [trans #123 #125]: #126
+#130 := [monotonicity #127]: #129
+#134 := [trans #130 #132]: #133
+#137 := [monotonicity #97 #134]: #136
+#141 := [trans #137 #139]: #140
+#92 := [not-or-elim #91]: #72
+[mp #92 #141]: false
+unsat
+224b51e5f287ef2e8191401ac84c3c58a0aead45 91 0
+#2 := false
+decl f5 :: S2
+#10 := f5
+decl f4 :: S2
+#9 := f4
+decl f3 :: S2
+#8 := f3
+#13 := (distinct f3 f4 f5)
+#67 := (= f4 f5)
+#68 := (not #67)
+#63 := (= f3 f5)
+#64 := (not #63)
+#61 := (= f3 f4)
+#62 := (not #61)
+#93 := (and #62 #64 #68)
+decl f6 :: S2
+#11 := f6
+#71 := (= f5 f6)
+#72 := (not #71)
+#69 := (= f4 f6)
+#70 := (not #69)
+#65 := (= f3 f6)
+#66 := (not #65)
+#73 := (and #62 #64 #66 #68 #70 #72)
+#12 := (distinct f3 f4 f5 f6)
+#14 := (distinct f4 f5 f6)
+#15 := (and #13 #14)
+#35 := (not #12)
+#36 := (or #35 #15)
+#39 := (not #36)
+#16 := (implies #12 #15)
+#17 := (not #16)
+#40 := (iff #17 #39)
+#37 := (iff #16 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#34 := [asserted]: #17
+#44 := [mp #34 #41]: #39
+#42 := [not-or-elim #44]: #12
+#89 := (or #35 #73)
+#90 := [def-axiom]: #89
+#121 := [unit-resolution #90 #42]: #73
+#74 := (not #73)
+#75 := (or #74 #62)
+#76 := [def-axiom]: #75
+#122 := [unit-resolution #76 #121]: #62
+#81 := (or #74 #68)
+#82 := [def-axiom]: #81
+#123 := [unit-resolution #82 #121]: #68
+#77 := (or #74 #64)
+#78 := [def-axiom]: #77
+#124 := [unit-resolution #78 #121]: #64
+#101 := (or #93 #61 #63 #67)
+#102 := [def-axiom]: #101
+#125 := [unit-resolution #102 #124 #123 #122]: #93
+#94 := (not #93)
+#105 := (or #13 #94)
+#106 := [def-axiom]: #105
+#126 := [unit-resolution #106 #125]: #13
+#107 := (and #68 #70 #72)
+#85 := (or #74 #72)
+#86 := [def-axiom]: #85
+#127 := [unit-resolution #86 #121]: #72
+#83 := (or #74 #70)
+#84 := [def-axiom]: #83
+#128 := [unit-resolution #84 #121]: #70
+#115 := (or #107 #67 #69 #71)
+#116 := [def-axiom]: #115
+#129 := [unit-resolution #116 #128 #127 #123]: #107
+#108 := (not #107)
+#119 := (or #14 #108)
+#120 := [def-axiom]: #119
+#130 := [unit-resolution #120 #129]: #14
+#54 := (not #14)
+#53 := (not #13)
+#55 := (or #53 #54)
+#43 := (not #15)
+#58 := (iff #43 #55)
+#56 := (not #55)
+#49 := (not #56)
+#46 := (iff #49 #55)
+#57 := [rewrite]: #46
+#50 := (iff #43 #49)
+#51 := (iff #15 #56)
+#52 := [rewrite]: #51
+#48 := [monotonicity #52]: #50
+#59 := [trans #48 #57]: #58
+#45 := [not-or-elim #44]: #43
+#60 := [mp #45 #59]: #55
+[unit-resolution #60 #130 #126]: false
+unsat
+d71c48b66a95c7e63c038fd93ab853e5968a14b6 60 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#14 := (not #9)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#13 := (not #11)
+#15 := (implies #13 #14)
+#12 := (implies #9 #11)
+#16 := (implies #12 #15)
+#17 := (not #16)
+#74 := (iff #17 false)
+#1 := true
+#69 := (not true)
+#72 := (iff #69 false)
+#73 := [rewrite]: #72
+#70 := (iff #17 #69)
+#67 := (iff #16 true)
+#38 := (= f1 f4)
+#35 := (= f1 f3)
+#44 := (not #35)
+#45 := (or #44 #38)
+#62 := (implies #45 #45)
+#65 := (iff #62 true)
+#66 := [rewrite]: #65
+#63 := (iff #16 #62)
+#60 := (iff #15 #45)
+#50 := (not #38)
+#55 := (implies #50 #44)
+#58 := (iff #55 #45)
+#59 := [rewrite]: #58
+#56 := (iff #15 #55)
+#53 := (iff #14 #44)
+#36 := (iff #9 #35)
+#37 := [rewrite]: #36
+#54 := [monotonicity #37]: #53
+#51 := (iff #13 #50)
+#39 := (iff #11 #38)
+#40 := [rewrite]: #39
+#52 := [monotonicity #40]: #51
+#57 := [monotonicity #52 #54]: #56
+#61 := [trans #57 #59]: #60
+#48 := (iff #12 #45)
+#41 := (implies #35 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #12 #41)
+#43 := [monotonicity #37 #40]: #42
+#49 := [trans #43 #47]: #48
+#64 := [monotonicity #49 #61]: #63
+#68 := [trans #64 #66]: #67
+#71 := [monotonicity #68]: #70
+#75 := [trans #71 #73]: #74
+#34 := [asserted]: #17
+[mp #34 #75]: false
+unsat
+af465ab181f70f3a841319fb8648514b03dc0f84 121 0
+#2 := false
+decl f5 :: S1
+#12 := f5
+decl f1 :: S1
+#4 := f1
+#44 := (= f1 f5)
+decl f4 :: S1
+#10 := f4
+#41 := (= f1 f4)
+decl f3 :: S1
+#8 := f3
+#38 := (= f1 f3)
+#53 := (not #38)
+#90 := (or #53 #41 #44)
+#137 := (iff #90 false)
+#132 := (or false false false)
+#135 := (iff #132 false)
+#136 := [rewrite]: #135
+#133 := (iff #90 #132)
+#123 := (iff #44 false)
+#113 := (not #44)
+#93 := (not #90)
+#99 := (or #53 #41 #44 #93)
+#104 := (not #99)
+#13 := (= f5 f1)
+#9 := (= f3 f1)
+#17 := (implies #9 #13)
+#11 := (= f4 f1)
+#16 := (implies #9 #11)
+#18 := (or #16 #17)
+#14 := (or #11 #13)
+#15 := (implies #9 #14)
+#19 := (implies #15 #18)
+#20 := (not #19)
+#107 := (iff #20 #104)
+#70 := (or #53 #44)
+#62 := (or #53 #41)
+#75 := (or #62 #70)
+#47 := (or #41 #44)
+#54 := (or #53 #47)
+#81 := (not #54)
+#82 := (or #81 #75)
+#87 := (not #82)
+#105 := (iff #87 #104)
+#102 := (iff #82 #99)
+#96 := (or #93 #75)
+#100 := (iff #96 #99)
+#101 := [rewrite]: #100
+#97 := (iff #82 #96)
+#94 := (iff #81 #93)
+#91 := (iff #54 #90)
+#92 := [rewrite]: #91
+#95 := [monotonicity #92]: #94
+#98 := [monotonicity #95]: #97
+#103 := [trans #98 #101]: #102
+#106 := [monotonicity #103]: #105
+#88 := (iff #20 #87)
+#85 := (iff #19 #82)
+#78 := (implies #54 #75)
+#83 := (iff #78 #82)
+#84 := [rewrite]: #83
+#79 := (iff #19 #78)
+#76 := (iff #18 #75)
+#73 := (iff #17 #70)
+#67 := (implies #38 #44)
+#71 := (iff #67 #70)
+#72 := [rewrite]: #71
+#68 := (iff #17 #67)
+#45 := (iff #13 #44)
+#46 := [rewrite]: #45
+#39 := (iff #9 #38)
+#40 := [rewrite]: #39
+#69 := [monotonicity #40 #46]: #68
+#74 := [trans #69 #72]: #73
+#65 := (iff #16 #62)
+#59 := (implies #38 #41)
+#63 := (iff #59 #62)
+#64 := [rewrite]: #63
+#60 := (iff #16 #59)
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#61 := [monotonicity #40 #43]: #60
+#66 := [trans #61 #64]: #65
+#77 := [monotonicity #66 #74]: #76
+#57 := (iff #15 #54)
+#50 := (implies #38 #47)
+#55 := (iff #50 #54)
+#56 := [rewrite]: #55
+#51 := (iff #15 #50)
+#48 := (iff #14 #47)
+#49 := [monotonicity #43 #46]: #48
+#52 := [monotonicity #40 #49]: #51
+#58 := [trans #52 #56]: #57
+#80 := [monotonicity #58 #77]: #79
+#86 := [trans #80 #84]: #85
+#89 := [monotonicity #86]: #88
+#108 := [trans #89 #106]: #107
+#37 := [asserted]: #20
+#109 := [mp #37 #108]: #104
+#114 := [not-or-elim #109]: #113
+#124 := [iff-false #114]: #123
+#121 := (iff #41 false)
+#111 := (not #41)
+#112 := [not-or-elim #109]: #111
+#122 := [iff-false #112]: #121
+#130 := (iff #53 false)
+#1 := true
+#125 := (not true)
+#128 := (iff #125 false)
+#129 := [rewrite]: #128
+#126 := (iff #53 #125)
+#119 := (iff #38 true)
+#110 := [not-or-elim #109]: #38
+#120 := [iff-true #110]: #119
+#127 := [monotonicity #120]: #126
+#131 := [trans #127 #129]: #130
+#134 := [monotonicity #131 #122 #124]: #133
+#138 := [trans #134 #136]: #137
+#115 := [not-or-elim #109]: #90
+[mp #115 #138]: false
+unsat
+18979f676bf3221a4e87326c6af281445b312b2a 25 0
+#2 := false
+#8 := (:var 0 S2)
+#9 := (= #8 #8)
+#10 := (forall (vars (?v0 S2)) #9)
+#11 := (not #10)
+#43 := (iff #11 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #11 #38)
+#36 := (iff #10 true)
+#31 := (forall (vars (?v0 S2)) true)
+#34 := (iff #31 true)
+#35 := [elim-unused]: #34
+#32 := (iff #10 #31)
+#29 := (iff #9 true)
+#30 := [rewrite]: #29
+#33 := [quant-intro #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#28 := [asserted]: #11
+[mp #28 #44]: false
+unsat
+e51be74b693abe9c8e61291306ec53588644e492 34 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S2 S1)
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#10 := (= #9 f1)
+#11 := (forall (vars (?v0 S2)) #10)
+#12 := (iff #11 #11)
+#13 := (not #12)
+#49 := (iff #13 false)
+#1 := true
+#44 := (not true)
+#47 := (iff #44 false)
+#48 := [rewrite]: #47
+#45 := (iff #13 #44)
+#42 := (iff #12 true)
+#31 := (= f1 #9)
+#34 := (forall (vars (?v0 S2)) #31)
+#37 := (iff #34 #34)
+#40 := (iff #37 true)
+#41 := [rewrite]: #40
+#38 := (iff #12 #37)
+#35 := (iff #11 #34)
+#32 := (iff #10 #31)
+#33 := [rewrite]: #32
+#36 := [quant-intro #33]: #35
+#39 := [monotonicity #36 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#30 := [asserted]: #13
+[mp #30 #50]: false
+unsat
+4125d60d3582e621620fa3548de9c8eca203e184 84 0
+#2 := false
+decl f4 :: S1
+#10 := f4
+decl f1 :: S1
+#4 := f1
+#38 := (= f1 f4)
+#53 := (not #38)
+#97 := [hypothesis]: #53
+decl f3 :: S1
+#8 := f3
+#35 := (= f1 f3)
+#44 := (not #35)
+#45 := (or #44 #38)
+#54 := (or #35 #53)
+#59 := (and #45 #54)
+#62 := (iff #35 #38)
+#68 := (not #59)
+#69 := (or #68 #62)
+#74 := (not #69)
+#11 := (= f4 f1)
+#9 := (= f3 f1)
+#15 := (iff #9 #11)
+#13 := (implies #11 #9)
+#12 := (implies #9 #11)
+#14 := (and #12 #13)
+#16 := (implies #14 #15)
+#17 := (not #16)
+#75 := (iff #17 #74)
+#72 := (iff #16 #69)
+#65 := (implies #59 #62)
+#70 := (iff #65 #69)
+#71 := [rewrite]: #70
+#66 := (iff #16 #65)
+#63 := (iff #15 #62)
+#39 := (iff #11 #38)
+#40 := [rewrite]: #39
+#36 := (iff #9 #35)
+#37 := [rewrite]: #36
+#64 := [monotonicity #37 #40]: #63
+#60 := (iff #14 #59)
+#57 := (iff #13 #54)
+#50 := (implies #38 #35)
+#55 := (iff #50 #54)
+#56 := [rewrite]: #55
+#51 := (iff #13 #50)
+#52 := [monotonicity #40 #37]: #51
+#58 := [trans #52 #56]: #57
+#48 := (iff #12 #45)
+#41 := (implies #35 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #12 #41)
+#43 := [monotonicity #37 #40]: #42
+#49 := [trans #43 #47]: #48
+#61 := [monotonicity #49 #58]: #60
+#67 := [monotonicity #61 #64]: #66
+#73 := [trans #67 #71]: #72
+#76 := [monotonicity #73]: #75
+#34 := [asserted]: #17
+#79 := [mp #34 #76]: #74
+#77 := [not-or-elim #79]: #59
+#78 := [and-elim #77]: #45
+#98 := [unit-resolution #78 #97]: #44
+#89 := (or #38 #35)
+#90 := (iff #38 #44)
+#81 := (not #62)
+#91 := (iff #81 #90)
+#92 := [rewrite]: #91
+#82 := [not-or-elim #79]: #81
+#93 := [mp #82 #92]: #90
+#94 := (not #90)
+#95 := (or #38 #35 #94)
+#88 := [def-axiom]: #95
+#86 := [unit-resolution #88 #93]: #89
+#99 := [unit-resolution #86 #98 #97]: false
+#100 := [lemma #99]: #38
+#80 := [and-elim #77]: #54
+#101 := [unit-resolution #80 #100]: #35
+#83 := (or #53 #44)
+#87 := (or #53 #44 #94)
+#85 := [def-axiom]: #87
+#96 := [unit-resolution #85 #93]: #83
+[unit-resolution #96 #101 #100]: false
+unsat
+116ce428b94097a0edc4fc87aad57e0632b1fc20 95 0
+#2 := false
+decl f3 :: (-> S2 S1)
+decl ?v0!0 :: S2
+#74 := ?v0!0
+#75 := (f3 ?v0!0)
+decl f1 :: S1
+#4 := f1
+#76 := (= f1 #75)
+#68 := (not #76)
+decl ?v1!1 :: S2
+#85 := ?v1!1
+#86 := (f3 ?v1!1)
+#87 := (= f1 #86)
+#105 := (or #76 #87)
+#108 := (not #105)
+#111 := (and #76 #108)
+#88 := (or #87 #76)
+#89 := (not #88)
+#82 := (not #68)
+#95 := (and #82 #89)
+#112 := (iff #95 #111)
+#109 := (iff #89 #108)
+#106 := (iff #88 #105)
+#107 := [rewrite]: #106
+#110 := [monotonicity #107]: #109
+#103 := (iff #82 #76)
+#104 := [rewrite]: #103
+#113 := [monotonicity #104 #110]: #112
+#11 := (:var 1 S2)
+#12 := (f3 #11)
+#39 := (= f1 #12)
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#36 := (= f1 #9)
+#45 := (or #36 #39)
+#50 := (forall (vars (?v1 S2)) #45)
+#56 := (not #36)
+#57 := (or #56 #50)
+#62 := (forall (vars (?v0 S2)) #57)
+#65 := (not #62)
+#98 := (~ #65 #95)
+#77 := (or #36 #76)
+#71 := (forall (vars (?v1 S2)) #77)
+#78 := (or #68 #71)
+#79 := (not #78)
+#96 := (~ #79 #95)
+#90 := (not #71)
+#91 := (~ #90 #89)
+#92 := [sk]: #91
+#83 := (~ #82 #82)
+#84 := [refl]: #83
+#97 := [nnf-neg #84 #92]: #96
+#80 := (~ #65 #79)
+#81 := [sk]: #80
+#99 := [trans #81 #97]: #98
+#10 := (= #9 f1)
+#13 := (= #12 f1)
+#14 := (or #13 #10)
+#15 := (forall (vars (?v1 S2)) #14)
+#16 := (implies #10 #15)
+#17 := (forall (vars (?v0 S2)) #16)
+#18 := (not #17)
+#66 := (iff #18 #65)
+#63 := (iff #17 #62)
+#60 := (iff #16 #57)
+#53 := (implies #36 #50)
+#58 := (iff #53 #57)
+#59 := [rewrite]: #58
+#54 := (iff #16 #53)
+#51 := (iff #15 #50)
+#48 := (iff #14 #45)
+#42 := (or #39 #36)
+#46 := (iff #42 #45)
+#47 := [rewrite]: #46
+#43 := (iff #14 #42)
+#37 := (iff #10 #36)
+#38 := [rewrite]: #37
+#40 := (iff #13 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41 #38]: #43
+#49 := [trans #44 #47]: #48
+#52 := [quant-intro #49]: #51
+#55 := [monotonicity #38 #52]: #54
+#61 := [trans #55 #59]: #60
+#64 := [quant-intro #61]: #63
+#67 := [monotonicity #64]: #66
+#35 := [asserted]: #18
+#70 := [mp #35 #67]: #65
+#100 := [mp~ #70 #99]: #95
+#101 := [mp #100 #113]: #111
+#114 := [and-elim #101]: #108
+#115 := [not-or-elim #114]: #68
+#102 := [and-elim #101]: #76
+[unit-resolution #102 #115]: false
+unsat
+a2e87bf3803d076628f087b9dbfba9370da7f50c 47 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#13 := (iff #11 #9)
+#12 := (iff #9 #11)
+#14 := (iff #12 #13)
+#15 := (not #14)
+#61 := (iff #15 false)
+#1 := true
+#56 := (not true)
+#59 := (iff #56 false)
+#60 := [rewrite]: #59
+#57 := (iff #15 #56)
+#54 := (iff #14 true)
+#36 := (= f1 f4)
+#33 := (= f1 f3)
+#39 := (iff #33 #36)
+#49 := (iff #39 #39)
+#52 := (iff #49 true)
+#53 := [rewrite]: #52
+#50 := (iff #14 #49)
+#47 := (iff #13 #39)
+#42 := (iff #36 #33)
+#45 := (iff #42 #39)
+#46 := [rewrite]: #45
+#43 := (iff #13 #42)
+#34 := (iff #9 #33)
+#35 := [rewrite]: #34
+#37 := (iff #11 #36)
+#38 := [rewrite]: #37
+#44 := [monotonicity #38 #35]: #43
+#48 := [trans #44 #46]: #47
+#40 := (iff #12 #39)
+#41 := [monotonicity #35 #38]: #40
+#51 := [monotonicity #41 #48]: #50
+#55 := [trans #51 #53]: #54
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#32 := [asserted]: #15
+[mp #32 #62]: false
+unsat
+f55eb15b91cf1e1bc8132b15462149132c31c5f3 41 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#10 := (not #9)
+#11 := (iff #9 #10)
+#12 := (not #11)
+#13 := (not #12)
+#56 := (iff #13 false)
+#1 := true
+#51 := (not true)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #13 #51)
+#49 := (iff #12 true)
+#44 := (not false)
+#47 := (iff #44 true)
+#48 := [rewrite]: #47
+#45 := (iff #12 #44)
+#42 := (iff #11 false)
+#31 := (= f1 f3)
+#34 := (not #31)
+#37 := (iff #31 #34)
+#40 := (iff #37 false)
+#41 := [rewrite]: #40
+#38 := (iff #11 #37)
+#35 := (iff #10 #34)
+#32 := (iff #9 #31)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#39 := [monotonicity #33 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#30 := [asserted]: #13
+[mp #30 #57]: false
+unsat
+f881fcb495cf85502e136be773cb13849da22fee 300 0
+#2 := false
+decl f4 :: (-> S2 S1)
+decl ?v0!1 :: S2
+#92 := ?v0!1
+#610 := (f4 ?v0!1)
+decl f1 :: S1
+#4 := f1
+#611 := (= f1 #610)
+#612 := (not #611)
+decl f3 :: (-> S2 S1)
+#93 := (f3 ?v0!1)
+#94 := (= f1 #93)
+#95 := (not #94)
+#613 := (or #95 #612)
+decl ?v0!0 :: S2
+#81 := ?v0!0
+#82 := (f4 ?v0!0)
+#83 := (= f1 #82)
+#84 := (f3 ?v0!0)
+#85 := (= f1 #84)
+#91 := (not #85)
+#90 := (not #83)
+#99 := (or #90 #91)
+#100 := (not #99)
+#364 := [hypothesis]: #99
+#8 := (:var 0 S2)
+#11 := (f4 #8)
+#666 := (pattern #11)
+#9 := (f3 #8)
+#665 := (pattern #9)
+#40 := (= f1 #11)
+#170 := (not #40)
+#37 := (= f1 #9)
+#169 := (not #37)
+#171 := (or #169 #170)
+#172 := (not #171)
+#667 := (forall (vars (?v0 S2)) (:pat #665 #666) #172)
+#680 := (forall (vars (?v0 S2)) (:pat #666) #40)
+#685 := (not #680)
+#672 := (forall (vars (?v0 S2)) (:pat #665) #37)
+#677 := (not #672)
+#688 := (or #677 #685)
+#691 := (not #688)
+#664 := [hypothesis]: #691
+#249 := (or #688 #672)
+#336 := [def-axiom]: #249
+#654 := [unit-resolution #336 #664]: #672
+decl ?v0!2 :: S2
+#101 := ?v0!2
+#102 := (f4 ?v0!2)
+#103 := (= f1 #102)
+#250 := (or #688 #680)
+#337 := [def-axiom]: #250
+#655 := [unit-resolution #337 #664]: #680
+#339 := (or #103 #685)
+#329 := [hypothesis]: #680
+#104 := (not #103)
+#340 := [hypothesis]: #104
+#341 := (or #685 #103)
+#269 := [quant-inst]: #341
+#342 := [unit-resolution #269 #340 #329]: false
+#343 := [lemma #342]: #339
+#315 := [unit-resolution #343 #655]: #103
+#653 := (or #85 #677)
+#322 := [hypothesis]: #672
+#657 := [hypothesis]: #91
+#659 := (or #677 #85)
+#316 := [quant-inst]: #659
+#446 := [unit-resolution #316 #657 #322]: false
+#327 := [lemma #446]: #653
+#656 := [unit-resolution #327 #654]: #85
+#663 := (or #83 #685)
+#328 := [hypothesis]: #90
+#661 := (or #685 #83)
+#662 := [quant-inst]: #661
+#660 := [unit-resolution #662 #328 #329]: false
+#658 := [lemma #660]: #663
+#299 := [unit-resolution #658 #655]: #83
+#163 := (or #90 #91 #95 #104)
+#132 := (and #83 #85)
+#135 := (not #132)
+#141 := (or #95 #104 #135)
+#166 := (iff #141 #163)
+#160 := (or #95 #104 #99)
+#164 := (iff #160 #163)
+#165 := [rewrite]: #164
+#161 := (iff #141 #160)
+#158 := (iff #135 #99)
+#153 := (not #100)
+#156 := (iff #153 #99)
+#157 := [rewrite]: #156
+#154 := (iff #135 #153)
+#108 := (iff #132 #100)
+#109 := [rewrite]: #108
+#155 := [monotonicity #109]: #154
+#159 := [trans #155 #157]: #158
+#162 := [monotonicity #159]: #161
+#167 := [trans #162 #165]: #166
+#52 := (forall (vars (?v0 S2)) #40)
+#49 := (forall (vars (?v0 S2)) #37)
+#55 := (and #49 #52)
+#43 := (and #37 #40)
+#46 := (forall (vars (?v0 S2)) #43)
+#146 := (or #46 #55)
+#149 := (and #141 #146)
+#124 := (or #55 #46)
+#86 := (and #85 #83)
+#87 := (not #86)
+#110 := (or #95 #104)
+#125 := (or #110 #87)
+#126 := (and #125 #124)
+#150 := (iff #126 #149)
+#147 := (iff #124 #146)
+#148 := [rewrite]: #147
+#144 := (iff #125 #141)
+#138 := (or #110 #135)
+#142 := (iff #138 #141)
+#143 := [rewrite]: #142
+#139 := (iff #125 #138)
+#136 := (iff #87 #135)
+#133 := (iff #86 #132)
+#134 := [rewrite]: #133
+#137 := [monotonicity #134]: #136
+#140 := [monotonicity #137]: #139
+#145 := [trans #140 #143]: #144
+#151 := [monotonicity #145 #148]: #150
+#64 := (not #46)
+#65 := (iff #55 #64)
+#127 := (~ #65 #126)
+#88 := (~ #64 #87)
+#89 := [sk]: #88
+#73 := (not #64)
+#70 := (~ #73 #46)
+#78 := (~ #46 #46)
+#76 := (~ #43 #43)
+#77 := [refl]: #76
+#79 := [nnf-pos #77]: #78
+#80 := [nnf-neg #79]: #70
+#122 := (~ #55 #55)
+#120 := (~ #52 #52)
+#118 := (~ #40 #40)
+#119 := [refl]: #118
+#121 := [nnf-pos #119]: #120
+#116 := (~ #49 #49)
+#114 := (~ #37 #37)
+#115 := [refl]: #114
+#117 := [nnf-pos #115]: #116
+#123 := [monotonicity #117 #121]: #122
+#111 := (not #55)
+#112 := (~ #111 #110)
+#105 := (not #52)
+#106 := (~ #105 #104)
+#107 := [sk]: #106
+#96 := (not #49)
+#97 := (~ #96 #95)
+#98 := [sk]: #97
+#113 := [nnf-neg #98 #107]: #112
+#128 := [nnf-pos #113 #123 #80 #89]: #127
+#12 := (= #11 f1)
+#16 := (forall (vars (?v0 S2)) #12)
+#10 := (= #9 f1)
+#15 := (forall (vars (?v0 S2)) #10)
+#17 := (and #15 #16)
+#13 := (and #10 #12)
+#14 := (forall (vars (?v0 S2)) #13)
+#18 := (iff #14 #17)
+#19 := (not #18)
+#68 := (iff #19 #65)
+#58 := (iff #46 #55)
+#61 := (not #58)
+#66 := (iff #61 #65)
+#67 := [rewrite]: #66
+#62 := (iff #19 #61)
+#59 := (iff #18 #58)
+#56 := (iff #17 #55)
+#53 := (iff #16 #52)
+#41 := (iff #12 #40)
+#42 := [rewrite]: #41
+#54 := [quant-intro #42]: #53
+#50 := (iff #15 #49)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#51 := [quant-intro #39]: #50
+#57 := [monotonicity #51 #54]: #56
+#47 := (iff #14 #46)
+#44 := (iff #13 #43)
+#45 := [monotonicity #39 #42]: #44
+#48 := [quant-intro #45]: #47
+#60 := [monotonicity #48 #57]: #59
+#63 := [monotonicity #60]: #62
+#69 := [trans #63 #67]: #68
+#36 := [asserted]: #19
+#72 := [mp #36 #69]: #65
+#129 := [mp~ #72 #128]: #126
+#130 := [mp #129 #151]: #149
+#131 := [and-elim #130]: #141
+#168 := [mp #131 #167]: #163
+#640 := [unit-resolution #168 #299 #656 #315]: #95
+#314 := (or #677 #94)
+#319 := [quant-inst]: #314
+#303 := [unit-resolution #319 #640 #654]: false
+#304 := [lemma #303]: #688
+#694 := (or #667 #691)
+#178 := (or #96 #105)
+#179 := (not #178)
+#175 := (forall (vars (?v0 S2)) #172)
+#182 := (or #175 #179)
+#695 := (iff #182 #694)
+#692 := (iff #179 #691)
+#689 := (iff #178 #688)
+#686 := (iff #105 #685)
+#683 := (iff #52 #680)
+#681 := (iff #40 #40)
+#682 := [refl]: #681
+#684 := [quant-intro #682]: #683
+#687 := [monotonicity #684]: #686
+#678 := (iff #96 #677)
+#675 := (iff #49 #672)
+#673 := (iff #37 #37)
+#674 := [refl]: #673
+#676 := [quant-intro #674]: #675
+#679 := [monotonicity #676]: #678
+#690 := [monotonicity #679 #687]: #689
+#693 := [monotonicity #690]: #692
+#670 := (iff #175 #667)
+#668 := (iff #172 #172)
+#669 := [refl]: #668
+#671 := [quant-intro #669]: #670
+#696 := [monotonicity #671 #693]: #695
+#183 := (iff #146 #182)
+#180 := (iff #55 #179)
+#181 := [rewrite]: #180
+#176 := (iff #46 #175)
+#173 := (iff #43 #172)
+#174 := [rewrite]: #173
+#177 := [quant-intro #174]: #176
+#184 := [monotonicity #177 #181]: #183
+#152 := [and-elim #130]: #146
+#185 := [mp #152 #184]: #182
+#697 := [mp #185 #696]: #694
+#257 := [unit-resolution #697 #304]: #667
+#646 := (not #667)
+#641 := (or #646 #100)
+#305 := (or #91 #90)
+#306 := (not #305)
+#647 := (or #646 #306)
+#648 := (iff #647 #641)
+#290 := (iff #641 #641)
+#291 := [rewrite]: #290
+#644 := (iff #306 #100)
+#642 := (iff #305 #99)
+#643 := [rewrite]: #642
+#645 := [monotonicity #643]: #644
+#650 := [monotonicity #645]: #648
+#651 := [trans #650 #291]: #648
+#285 := [quant-inst]: #647
+#649 := [mp #285 #651]: #641
+#634 := [unit-resolution #649 #257 #364]: false
+#635 := [lemma #634]: #100
+#652 := (or #99 #83)
+#638 := [def-axiom]: #652
+#608 := [unit-resolution #638 #635]: #83
+#639 := (or #99 #85)
+#361 := [def-axiom]: #639
+#614 := [unit-resolution #361 #635]: #85
+#357 := (f3 ?v0!2)
+#358 := (= f1 #357)
+#632 := (not #358)
+#637 := (or #104 #632)
+#349 := (not #637)
+#466 := [hypothesis]: #637
+#629 := (or #646 #349)
+#636 := (or #632 #104)
+#633 := (not #636)
+#344 := (or #646 #633)
+#630 := (iff #344 #629)
+#631 := (iff #629 #629)
+#620 := [rewrite]: #631
+#350 := (iff #633 #349)
+#347 := (iff #636 #637)
+#348 := [rewrite]: #347
+#628 := [monotonicity #348]: #350
+#627 := [monotonicity #628]: #630
+#621 := [trans #627 #620]: #630
+#626 := [quant-inst]: #344
+#622 := [mp #626 #621]: #629
+#467 := [unit-resolution #622 #257 #466]: false
+#468 := [lemma #467]: #349
+#617 := (or #637 #103)
+#618 := [def-axiom]: #617
+#604 := [unit-resolution #618 #468]: #103
+#605 := [unit-resolution #168 #604 #614 #608]: #95
+#616 := (or #613 #94)
+#445 := [def-axiom]: #616
+#603 := [unit-resolution #445 #605]: #613
+#607 := (not #613)
+#615 := (or #646 #607)
+#609 := [quant-inst]: #615
+[unit-resolution #609 #257 #603]: false
+unsat
+9f209003251b1e93d2b18400dbce611ea9c89175 60 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#14 := (not #9)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#13 := (not #11)
+#15 := (implies #13 #14)
+#12 := (implies #9 #11)
+#16 := (iff #12 #15)
+#17 := (not #16)
+#74 := (iff #17 false)
+#1 := true
+#69 := (not true)
+#72 := (iff #69 false)
+#73 := [rewrite]: #72
+#70 := (iff #17 #69)
+#67 := (iff #16 true)
+#38 := (= f1 f4)
+#35 := (= f1 f3)
+#44 := (not #35)
+#45 := (or #44 #38)
+#62 := (iff #45 #45)
+#65 := (iff #62 true)
+#66 := [rewrite]: #65
+#63 := (iff #16 #62)
+#60 := (iff #15 #45)
+#50 := (not #38)
+#55 := (implies #50 #44)
+#58 := (iff #55 #45)
+#59 := [rewrite]: #58
+#56 := (iff #15 #55)
+#53 := (iff #14 #44)
+#36 := (iff #9 #35)
+#37 := [rewrite]: #36
+#54 := [monotonicity #37]: #53
+#51 := (iff #13 #50)
+#39 := (iff #11 #38)
+#40 := [rewrite]: #39
+#52 := [monotonicity #40]: #51
+#57 := [monotonicity #52 #54]: #56
+#61 := [trans #57 #59]: #60
+#48 := (iff #12 #45)
+#41 := (implies #35 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #12 #41)
+#43 := [monotonicity #37 #40]: #42
+#49 := [trans #43 #47]: #48
+#64 := [monotonicity #49 #61]: #63
+#68 := [trans #64 #66]: #67
+#71 := [monotonicity #68]: #70
+#75 := [trans #71 #73]: #74
+#34 := [asserted]: #17
+[mp #34 #75]: false
+unsat
+233dd705a1a2cd04e17693dd59c653e2f289128d 72 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#10 := (iff #9 #9)
+#11 := (iff #9 #10)
+#12 := (iff #9 #11)
+#13 := (iff #9 #12)
+#14 := (iff #9 #13)
+#15 := (iff #9 #14)
+#16 := (iff #9 #15)
+#17 := (iff #9 #16)
+#18 := (iff #9 #17)
+#19 := (not #18)
+#87 := (iff #19 false)
+#1 := true
+#82 := (not true)
+#85 := (iff #82 false)
+#86 := [rewrite]: #85
+#83 := (iff #19 #82)
+#80 := (iff #18 true)
+#37 := (= f1 f3)
+#40 := (iff #37 #37)
+#43 := (iff #40 true)
+#44 := [rewrite]: #43
+#78 := (iff #18 #40)
+#76 := (iff #17 #37)
+#47 := (iff #37 true)
+#50 := (iff #47 #37)
+#51 := [rewrite]: #50
+#74 := (iff #17 #47)
+#72 := (iff #16 true)
+#70 := (iff #16 #40)
+#68 := (iff #15 #37)
+#66 := (iff #15 #47)
+#64 := (iff #14 true)
+#62 := (iff #14 #40)
+#60 := (iff #13 #37)
+#58 := (iff #13 #47)
+#56 := (iff #12 true)
+#54 := (iff #12 #40)
+#52 := (iff #11 #37)
+#48 := (iff #11 #47)
+#45 := (iff #10 true)
+#41 := (iff #10 #40)
+#38 := (iff #9 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39 #39]: #41
+#46 := [trans #42 #44]: #45
+#49 := [monotonicity #39 #46]: #48
+#53 := [trans #49 #51]: #52
+#55 := [monotonicity #39 #53]: #54
+#57 := [trans #55 #44]: #56
+#59 := [monotonicity #39 #57]: #58
+#61 := [trans #59 #51]: #60
+#63 := [monotonicity #39 #61]: #62
+#65 := [trans #63 #44]: #64
+#67 := [monotonicity #39 #65]: #66
+#69 := [trans #67 #51]: #68
+#71 := [monotonicity #39 #69]: #70
+#73 := [trans #71 #44]: #72
+#75 := [monotonicity #39 #73]: #74
+#77 := [trans #75 #51]: #76
+#79 := [monotonicity #39 #77]: #78
+#81 := [trans #79 #44]: #80
+#84 := [monotonicity #81]: #83
+#88 := [trans #84 #86]: #87
+#36 := [asserted]: #19
+[mp #36 #88]: false
+unsat
+15ca2c1c3840e8c9f4b2011d8b0b39ef04345936 201 0
+#2 := false
+decl f3 :: (-> S2 S1)
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#621 := (pattern #9)
+decl f1 :: S1
+#4 := f1
+#36 := (= f1 #9)
+#622 := (forall (vars (?v0 S2)) (:pat #621) #36)
+decl f4 :: S1
+#12 := f4
+#42 := (= f1 f4)
+#90 := (not #42)
+decl ?v0!0 :: S2
+#81 := ?v0!0
+#82 := (f3 ?v0!0)
+#83 := (= f1 #82)
+#104 := (or #42 #83)
+#105 := (not #104)
+decl ?v0!1 :: S2
+#96 := ?v0!1
+#97 := (f3 ?v0!1)
+#98 := (= f1 #97)
+#118 := (or #42 #98)
+#48 := (or #36 #42)
+#627 := (forall (vars (?v0 S2)) (:pat #621) #48)
+#121 := (not #118)
+#612 := [hypothesis]: #121
+#283 := (or #118 #90)
+#294 := [def-axiom]: #283
+#253 := [unit-resolution #294 #612]: #90
+#615 := (not #622)
+#295 := (not #98)
+#223 := (or #118 #295)
+#296 := [def-axiom]: #223
+#596 := [unit-resolution #296 #612]: #295
+#270 := (or #615 #98)
+#276 := [hypothesis]: #622
+#613 := [hypothesis]: #295
+#402 := [quant-inst]: #270
+#609 := [unit-resolution #402 #613 #276]: false
+#281 := [lemma #609]: #270
+#257 := [unit-resolution #281 #596]: #615
+#632 := (or #622 #42 #627)
+#51 := (forall (vars (?v0 S2)) #48)
+#39 := (forall (vars (?v0 S2)) #36)
+#130 := (or #39 #42 #51)
+#633 := (iff #130 #632)
+#630 := (iff #51 #627)
+#628 := (iff #48 #48)
+#629 := [refl]: #628
+#631 := [quant-intro #629]: #630
+#625 := (iff #39 #622)
+#623 := (iff #36 #36)
+#624 := [refl]: #623
+#626 := [quant-intro #624]: #625
+#634 := [monotonicity #626 #631]: #633
+#84 := (not #83)
+#124 := (and #90 #84)
+#127 := (or #121 #124)
+#133 := (and #127 #130)
+#45 := (or #39 #42)
+#110 := (or #51 #45)
+#93 := (and #84 #90)
+#99 := (or #98 #42)
+#100 := (not #99)
+#111 := (or #100 #93)
+#112 := (and #111 #110)
+#134 := (iff #112 #133)
+#131 := (iff #110 #130)
+#132 := [rewrite]: #131
+#128 := (iff #111 #127)
+#125 := (iff #93 #124)
+#126 := [rewrite]: #125
+#122 := (iff #100 #121)
+#119 := (iff #99 #118)
+#120 := [rewrite]: #119
+#123 := [monotonicity #120]: #122
+#129 := [monotonicity #123 #126]: #128
+#135 := [monotonicity #129 #132]: #134
+#60 := (not #45)
+#61 := (iff #51 #60)
+#113 := (~ #61 #112)
+#94 := (~ #60 #93)
+#91 := (~ #90 #90)
+#92 := [refl]: #91
+#85 := (not #39)
+#86 := (~ #85 #84)
+#87 := [sk]: #86
+#95 := [nnf-neg #87 #92]: #94
+#78 := (not #60)
+#79 := (~ #78 #45)
+#76 := (~ #45 #45)
+#69 := (~ #42 #42)
+#66 := [refl]: #69
+#74 := (~ #39 #39)
+#72 := (~ #36 #36)
+#73 := [refl]: #72
+#75 := [nnf-pos #73]: #74
+#77 := [monotonicity #75 #66]: #76
+#80 := [nnf-neg #77]: #79
+#108 := (~ #51 #51)
+#106 := (~ #48 #48)
+#107 := [refl]: #106
+#109 := [nnf-pos #107]: #108
+#101 := (not #51)
+#102 := (~ #101 #100)
+#103 := [sk]: #102
+#114 := [nnf-pos #103 #109 #80 #95]: #113
+#13 := (= f4 f1)
+#10 := (= #9 f1)
+#15 := (or #10 #13)
+#16 := (forall (vars (?v0 S2)) #15)
+#11 := (forall (vars (?v0 S2)) #10)
+#14 := (or #11 #13)
+#17 := (iff #14 #16)
+#18 := (not #17)
+#64 := (iff #18 #61)
+#54 := (iff #45 #51)
+#57 := (not #54)
+#62 := (iff #57 #61)
+#63 := [rewrite]: #62
+#58 := (iff #18 #57)
+#55 := (iff #17 #54)
+#52 := (iff #16 #51)
+#49 := (iff #15 #48)
+#43 := (iff #13 #42)
+#44 := [rewrite]: #43
+#37 := (iff #10 #36)
+#38 := [rewrite]: #37
+#50 := [monotonicity #38 #44]: #49
+#53 := [quant-intro #50]: #52
+#46 := (iff #14 #45)
+#40 := (iff #11 #39)
+#41 := [quant-intro #38]: #40
+#47 := [monotonicity #41 #44]: #46
+#56 := [monotonicity #47 #53]: #55
+#59 := [monotonicity #56]: #58
+#65 := [trans #59 #63]: #64
+#35 := [asserted]: #18
+#68 := [mp #35 #65]: #61
+#115 := [mp~ #68 #114]: #112
+#116 := [mp #115 #135]: #133
+#136 := [and-elim #116]: #130
+#635 := [mp #136 #634]: #632
+#258 := [unit-resolution #635 #257 #253]: #627
+#282 := (not #627)
+#616 := (or #282 #42 #98)
+#617 := (or #282 #99)
+#273 := (iff #617 #616)
+#619 := (or #282 #118)
+#610 := (iff #619 #616)
+#268 := [rewrite]: #610
+#614 := (iff #617 #619)
+#620 := [monotonicity #120]: #614
+#611 := [trans #620 #268]: #273
+#618 := [quant-inst]: #617
+#269 := [mp #618 #611]: #616
+#259 := [unit-resolution #269 #253 #596 #258]: false
+#260 := [lemma #259]: #118
+#140 := (or #105 #121)
+#143 := (iff #127 #140)
+#137 := (or #121 #105)
+#141 := (iff #137 #140)
+#142 := [rewrite]: #141
+#138 := (iff #127 #137)
+#88 := (iff #124 #105)
+#89 := [rewrite]: #88
+#139 := [monotonicity #89]: #138
+#144 := [trans #139 #142]: #143
+#117 := [and-elim #116]: #127
+#145 := [mp #117 #144]: #140
+#594 := [unit-resolution #145 #260]: #105
+#203 := (or #104 #90)
+#290 := [def-axiom]: #203
+#301 := [unit-resolution #290 #594]: #90
+#608 := [hypothesis]: #627
+#204 := (or #104 #84)
+#291 := [def-axiom]: #204
+#595 := [unit-resolution #291 #594]: #84
+#601 := (or #282 #42 #83)
+#598 := (or #83 #42)
+#602 := (or #282 #598)
+#245 := (iff #602 #601)
+#603 := (or #282 #104)
+#606 := (iff #603 #601)
+#244 := [rewrite]: #606
+#239 := (iff #602 #603)
+#599 := (iff #598 #104)
+#600 := [rewrite]: #599
+#604 := [monotonicity #600]: #239
+#607 := [trans #604 #244]: #245
+#597 := [quant-inst]: #602
+#605 := [mp #597 #607]: #601
+#317 := [unit-resolution #605 #301 #595 #608]: false
+#318 := [lemma #317]: #282
+#319 := [unit-resolution #635 #318 #301]: #622
+#320 := (or #615 #83)
+#211 := [quant-inst]: #320
+[unit-resolution #211 #595 #319]: false
+unsat
+39e227ccd01de1131a3c129a5a992e4af88b7e62 244 0
+#2 := false
+decl f3 :: (-> S2 S1)
+decl ?v0!0 :: S2
+#81 := ?v0!0
+#82 := (f3 ?v0!0)
+decl f1 :: S1
+#4 := f1
+#83 := (= f1 #82)
+#84 := (not #83)
+decl f4 :: S1
+#12 := f4
+#42 := (= f1 f4)
+#90 := (not #42)
+#270 := (or #90 #84)
+decl ?v0!1 :: S2
+#96 := ?v0!1
+#97 := (f3 ?v0!1)
+#98 := (= f1 #97)
+#104 := (not #98)
+#105 := (or #90 #104)
+#88 := (not #105)
+#623 := [hypothesis]: #105
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#647 := (pattern #9)
+#36 := (= f1 #9)
+#160 := (not #36)
+#161 := (or #160 #90)
+#162 := (not #161)
+#662 := (forall (vars (?v0 S2)) (:pat #647) #162)
+#648 := (forall (vars (?v0 S2)) (:pat #647) #36)
+#653 := (not #648)
+#656 := (or #653 #90)
+#659 := (not #656)
+#302 := [hypothesis]: #659
+#229 := (or #656 #648)
+#316 := [def-axiom]: #229
+#639 := [unit-resolution #316 #302]: #648
+#230 := (or #656 #42)
+#317 := [def-axiom]: #230
+#428 := [unit-resolution #317 #302]: #42
+#319 := (or #98 #653)
+#309 := [hypothesis]: #648
+#320 := [hypothesis]: #104
+#321 := (or #653 #98)
+#249 := [quant-inst]: #321
+#322 := [unit-resolution #249 #320 #309]: false
+#323 := [lemma #322]: #319
+#635 := [unit-resolution #323 #639]: #98
+#150 := (or #90 #84 #104)
+#118 := (and #42 #98)
+#121 := (not #118)
+#127 := (or #90 #84 #121)
+#153 := (iff #127 #150)
+#147 := (or #90 #84 #105)
+#151 := (iff #147 #150)
+#152 := [rewrite]: #151
+#148 := (iff #127 #147)
+#145 := (iff #121 #105)
+#140 := (not #88)
+#143 := (iff #140 #105)
+#144 := [rewrite]: #143
+#141 := (iff #121 #140)
+#89 := (iff #118 #88)
+#139 := [rewrite]: #89
+#142 := [monotonicity #139]: #141
+#146 := [trans #142 #144]: #145
+#149 := [monotonicity #146]: #148
+#154 := [trans #149 #152]: #153
+#48 := (and #36 #42)
+#51 := (forall (vars (?v0 S2)) #48)
+#39 := (forall (vars (?v0 S2)) #36)
+#45 := (and #39 #42)
+#132 := (or #45 #51)
+#135 := (and #127 #132)
+#110 := (or #51 #45)
+#93 := (or #84 #90)
+#99 := (and #98 #42)
+#100 := (not #99)
+#111 := (or #100 #93)
+#112 := (and #111 #110)
+#136 := (iff #112 #135)
+#133 := (iff #110 #132)
+#134 := [rewrite]: #133
+#130 := (iff #111 #127)
+#124 := (or #121 #93)
+#128 := (iff #124 #127)
+#129 := [rewrite]: #128
+#125 := (iff #111 #124)
+#122 := (iff #100 #121)
+#119 := (iff #99 #118)
+#120 := [rewrite]: #119
+#123 := [monotonicity #120]: #122
+#126 := [monotonicity #123]: #125
+#131 := [trans #126 #129]: #130
+#137 := [monotonicity #131 #134]: #136
+#60 := (not #45)
+#61 := (iff #51 #60)
+#113 := (~ #61 #112)
+#94 := (~ #60 #93)
+#91 := (~ #90 #90)
+#92 := [refl]: #91
+#85 := (not #39)
+#86 := (~ #85 #84)
+#87 := [sk]: #86
+#95 := [nnf-neg #87 #92]: #94
+#78 := (not #60)
+#79 := (~ #78 #45)
+#76 := (~ #45 #45)
+#69 := (~ #42 #42)
+#66 := [refl]: #69
+#74 := (~ #39 #39)
+#72 := (~ #36 #36)
+#73 := [refl]: #72
+#75 := [nnf-pos #73]: #74
+#77 := [monotonicity #75 #66]: #76
+#80 := [nnf-neg #77]: #79
+#108 := (~ #51 #51)
+#106 := (~ #48 #48)
+#107 := [refl]: #106
+#109 := [nnf-pos #107]: #108
+#101 := (not #51)
+#102 := (~ #101 #100)
+#103 := [sk]: #102
+#114 := [nnf-pos #103 #109 #80 #95]: #113
+#13 := (= f4 f1)
+#10 := (= #9 f1)
+#15 := (and #10 #13)
+#16 := (forall (vars (?v0 S2)) #15)
+#11 := (forall (vars (?v0 S2)) #10)
+#14 := (and #11 #13)
+#17 := (iff #14 #16)
+#18 := (not #17)
+#64 := (iff #18 #61)
+#54 := (iff #45 #51)
+#57 := (not #54)
+#62 := (iff #57 #61)
+#63 := [rewrite]: #62
+#58 := (iff #18 #57)
+#55 := (iff #17 #54)
+#52 := (iff #16 #51)
+#49 := (iff #15 #48)
+#43 := (iff #13 #42)
+#44 := [rewrite]: #43
+#37 := (iff #10 #36)
+#38 := [rewrite]: #37
+#50 := [monotonicity #38 #44]: #49
+#53 := [quant-intro #50]: #52
+#46 := (iff #14 #45)
+#40 := (iff #11 #39)
+#41 := [quant-intro #38]: #40
+#47 := [monotonicity #41 #44]: #46
+#56 := [monotonicity #47 #53]: #55
+#59 := [monotonicity #56]: #58
+#65 := [trans #59 #63]: #64
+#35 := [asserted]: #18
+#68 := [mp #35 #65]: #61
+#115 := [mp~ #68 #114]: #112
+#116 := [mp #115 #137]: #135
+#117 := [and-elim #116]: #127
+#155 := [mp #117 #154]: #150
+#307 := [unit-resolution #155 #635 #428]: #84
+#641 := (or #653 #83)
+#296 := [quant-inst]: #641
+#308 := [unit-resolution #296 #307 #639]: false
+#642 := [lemma #308]: #656
+#667 := (or #659 #662)
+#165 := (forall (vars (?v0 S2)) #162)
+#156 := (or #85 #90)
+#157 := (not #156)
+#168 := (or #157 #165)
+#668 := (iff #168 #667)
+#665 := (iff #165 #662)
+#663 := (iff #162 #162)
+#664 := [refl]: #663
+#666 := [quant-intro #664]: #665
+#660 := (iff #157 #659)
+#657 := (iff #156 #656)
+#654 := (iff #85 #653)
+#651 := (iff #39 #648)
+#649 := (iff #36 #36)
+#650 := [refl]: #649
+#652 := [quant-intro #650]: #651
+#655 := [monotonicity #652]: #654
+#658 := [monotonicity #655]: #657
+#661 := [monotonicity #658]: #660
+#669 := [monotonicity #661 #666]: #668
+#169 := (iff #132 #168)
+#166 := (iff #51 #165)
+#163 := (iff #48 #162)
+#164 := [rewrite]: #163
+#167 := [quant-intro #164]: #166
+#158 := (iff #45 #157)
+#159 := [rewrite]: #158
+#170 := [monotonicity #159 #167]: #169
+#138 := [and-elim #116]: #132
+#171 := [mp #138 #170]: #168
+#670 := [mp #171 #669]: #667
+#629 := [unit-resolution #670 #642]: #662
+#294 := (not #662)
+#299 := (or #294 #88)
+#643 := (or #104 #90)
+#644 := (not #643)
+#637 := (or #294 #644)
+#638 := (iff #637 #299)
+#622 := (iff #299 #299)
+#283 := [rewrite]: #622
+#646 := (iff #644 #88)
+#645 := (iff #643 #105)
+#640 := [rewrite]: #645
+#636 := [monotonicity #640]: #646
+#279 := [monotonicity #636]: #638
+#284 := [trans #279 #283]: #638
+#295 := [quant-inst]: #637
+#285 := [mp #295 #284]: #299
+#265 := [unit-resolution #285 #629 #623]: false
+#630 := [lemma #265]: #88
+#286 := (or #105 #42)
+#624 := [def-axiom]: #286
+#619 := [unit-resolution #624 #630]: #42
+#625 := (or #105 #98)
+#626 := [def-axiom]: #625
+#328 := [unit-resolution #626 #630]: #98
+#329 := [unit-resolution #155 #328 #619]: #84
+#340 := (or #270 #83)
+#614 := [def-axiom]: #340
+#330 := [unit-resolution #614 #329]: #270
+#631 := (not #270)
+#621 := (or #294 #631)
+#632 := (not #93)
+#327 := (or #294 #632)
+#344 := (iff #327 #621)
+#331 := (iff #621 #621)
+#346 := [rewrite]: #331
+#634 := (iff #632 #631)
+#271 := (iff #93 #270)
+#633 := [rewrite]: #271
+#620 := [monotonicity #633]: #634
+#345 := [monotonicity #620]: #344
+#237 := [trans #345 #346]: #344
+#343 := [quant-inst]: #327
+#616 := [mp #343 #237]: #621
+[unit-resolution #616 #629 #330]: false
+unsat
+293275a96c0f9a6369c5c63237687d458f6817d7 25 0
+#2 := false
+#8 := (:var 0 S2)
+#9 := (= #8 #8)
+#10 := (exists (vars (?v0 S2)) #9)
+#11 := (not #10)
+#43 := (iff #11 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #11 #38)
+#36 := (iff #10 true)
+#31 := (exists (vars (?v0 S2)) true)
+#34 := (iff #31 true)
+#35 := [elim-unused]: #34
+#32 := (iff #10 #31)
+#29 := (iff #9 true)
+#30 := [rewrite]: #29
+#33 := [quant-intro #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#28 := [asserted]: #11
+[mp #28 #44]: false
+unsat
+cb32f55c5bc6bd5f823005e6422725f9e998da2f 34 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S2 S1)
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#10 := (= #9 f1)
+#11 := (exists (vars (?v0 S2)) #10)
+#12 := (iff #11 #11)
+#13 := (not #12)
+#49 := (iff #13 false)
+#1 := true
+#44 := (not true)
+#47 := (iff #44 false)
+#48 := [rewrite]: #47
+#45 := (iff #13 #44)
+#42 := (iff #12 true)
+#31 := (= f1 #9)
+#34 := (exists (vars (?v0 S2)) #31)
+#37 := (iff #34 #34)
+#40 := (iff #37 true)
+#41 := [rewrite]: #40
+#38 := (iff #12 #37)
+#35 := (iff #11 #34)
+#32 := (iff #10 #31)
+#33 := [rewrite]: #32
+#36 := [quant-intro #33]: #35
+#39 := [monotonicity #36 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#30 := [asserted]: #13
+[mp #30 #50]: false
+unsat
+01fcfe482cd417aecd358af024dc175a0edc268e 49 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S2 S2 S1)
+#9 := (:var 0 S2)
+#13 := (:var 1 S2)
+#14 := (f3 #13 #9)
+#15 := (= #14 f1)
+#16 := (forall (vars (?v0 S2) (?v1 S2)) #15)
+#8 := (:var 2 S2)
+#10 := (f3 #8 #9)
+#11 := (= #10 f1)
+#12 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #11)
+#17 := (iff #12 #16)
+#18 := (not #17)
+#64 := (iff #18 false)
+#1 := true
+#59 := (not true)
+#62 := (iff #59 false)
+#63 := [rewrite]: #62
+#60 := (iff #18 #59)
+#57 := (iff #17 true)
+#42 := (= f1 #14)
+#43 := (forall (vars (?v0 S2) (?v2 S2)) #42)
+#52 := (iff #43 #43)
+#55 := (iff #52 true)
+#56 := [rewrite]: #55
+#53 := (iff #17 #52)
+#50 := (iff #16 #43)
+#48 := (iff #15 #42)
+#49 := [rewrite]: #48
+#51 := [quant-intro #49]: #50
+#46 := (iff #12 #43)
+#36 := (= f1 #10)
+#39 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #36)
+#44 := (iff #39 #43)
+#45 := [elim-unused]: #44
+#40 := (iff #12 #39)
+#37 := (iff #11 #36)
+#38 := [rewrite]: #37
+#41 := [quant-intro #38]: #40
+#47 := [trans #41 #45]: #46
+#54 := [monotonicity #47 #51]: #53
+#58 := [trans #54 #56]: #57
+#61 := [monotonicity #58]: #60
+#65 := [trans #61 #63]: #64
+#35 := [asserted]: #18
+[mp #35 #65]: false
+unsat
+b43b0d1e4a922ebd6679eaa136d5464c794bec63 258 0
+#2 := false
+decl f4 :: (-> S2 S1)
+decl ?v0!2 :: S2
+#118 := ?v0!2
+#119 := (f4 ?v0!2)
+decl f1 :: S1
+#4 := f1
+#120 := (= f1 #119)
+decl f3 :: (-> S2 S1)
+decl ?v0!1 :: S2
+#111 := ?v0!1
+#112 := (f3 ?v0!1)
+#113 := (= f1 #112)
+#610 := (not #113)
+#308 := [hypothesis]: #113
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#629 := (pattern #9)
+#37 := (= f1 #9)
+#93 := (not #37)
+#636 := (forall (vars (?v0 S2)) (:pat #629) #93)
+#11 := (f4 #8)
+#630 := (pattern #11)
+#40 := (= f1 #11)
+#100 := (not #40)
+#644 := (forall (vars (?v0 S2)) (:pat #630) #100)
+#649 := (not #644)
+#641 := (not #636)
+#652 := (or #641 #649)
+#655 := (not #652)
+#43 := (or #37 #40)
+#87 := (not #43)
+#631 := (forall (vars (?v0 S2)) (:pat #629 #630) #87)
+#280 := (not #631)
+#616 := (f3 ?v0!2)
+#602 := (= f1 #616)
+#326 := (or #120 #602)
+decl ?v0!0 :: S2
+#76 := ?v0!0
+#77 := (f4 ?v0!0)
+#78 := (= f1 #77)
+#626 := (not #78)
+#79 := (f3 ?v0!0)
+#73 := (= f1 #79)
+#70 := (or #73 #78)
+#286 := (not #70)
+#625 := [hypothesis]: #631
+#263 := (or #286 #280)
+#624 := [hypothesis]: #70
+#410 := (or #280 #286)
+#617 := [quant-inst]: #410
+#620 := [unit-resolution #617 #625 #624]: false
+#604 := [lemma #620]: #263
+#584 := [unit-resolution #604 #625]: #286
+#627 := (or #70 #626)
+#622 := [def-axiom]: #627
+#585 := [unit-resolution #622 #584]: #626
+#293 := (not #73)
+#304 := [hypothesis]: #73
+#291 := (or #70 #293)
+#292 := [def-axiom]: #291
+#621 := [unit-resolution #292 #304]: #70
+#233 := (or #641 #293)
+#305 := [hypothesis]: #636
+#306 := [quant-inst]: #233
+#303 := [unit-resolution #306 #305 #304]: false
+#307 := [lemma #303]: #233
+#623 := [unit-resolution #307 #304]: #641
+#213 := (or #652 #636)
+#300 := [def-axiom]: #213
+#628 := [unit-resolution #300 #623]: #652
+#658 := (or #631 #655)
+#103 := (forall (vars (?v0 S2)) #100)
+#117 := (not #103)
+#96 := (forall (vars (?v0 S2)) #93)
+#116 := (not #96)
+#123 := (or #116 #117)
+#124 := (not #123)
+#90 := (forall (vars (?v0 S2)) #87)
+#146 := (or #90 #124)
+#659 := (iff #146 #658)
+#656 := (iff #124 #655)
+#653 := (iff #123 #652)
+#650 := (iff #117 #649)
+#647 := (iff #103 #644)
+#645 := (iff #100 #100)
+#646 := [refl]: #645
+#648 := [quant-intro #646]: #647
+#651 := [monotonicity #648]: #650
+#642 := (iff #116 #641)
+#639 := (iff #96 #636)
+#637 := (iff #93 #93)
+#638 := [refl]: #637
+#640 := [quant-intro #638]: #639
+#643 := [monotonicity #640]: #642
+#654 := [monotonicity #643 #651]: #653
+#657 := [monotonicity #654]: #656
+#634 := (iff #90 #631)
+#632 := (iff #87 #87)
+#633 := [refl]: #632
+#635 := [quant-intro #633]: #634
+#660 := [monotonicity #635 #657]: #659
+#107 := (and #96 #103)
+#136 := (or #90 #107)
+#147 := (iff #136 #146)
+#82 := (iff #107 #124)
+#83 := [rewrite]: #82
+#148 := [monotonicity #83]: #147
+#139 := (or #73 #78 #113 #120)
+#142 := (and #136 #139)
+#125 := (or #113 #120)
+#128 := (or #125 #70)
+#129 := (or #107 #90)
+#130 := (and #129 #128)
+#143 := (iff #130 #142)
+#140 := (iff #128 #139)
+#141 := [rewrite]: #140
+#137 := (iff #129 #136)
+#138 := [rewrite]: #137
+#144 := [monotonicity #138 #141]: #143
+#46 := (exists (vars (?v0 S2)) #43)
+#64 := (not #46)
+#52 := (exists (vars (?v0 S2)) #40)
+#49 := (exists (vars (?v0 S2)) #37)
+#55 := (or #49 #52)
+#65 := (iff #55 #64)
+#131 := (~ #65 #130)
+#91 := (~ #64 #90)
+#88 := (~ #87 #87)
+#89 := [refl]: #88
+#92 := [nnf-neg #89]: #91
+#84 := (not #64)
+#85 := (~ #84 #70)
+#80 := (~ #46 #70)
+#81 := [sk]: #80
+#86 := [nnf-neg #81]: #85
+#126 := (~ #55 #125)
+#121 := (~ #52 #120)
+#122 := [sk]: #121
+#114 := (~ #49 #113)
+#115 := [sk]: #114
+#127 := [monotonicity #115 #122]: #126
+#108 := (not #55)
+#109 := (~ #108 #107)
+#104 := (not #52)
+#105 := (~ #104 #103)
+#101 := (~ #100 #100)
+#102 := [refl]: #101
+#106 := [nnf-neg #102]: #105
+#97 := (not #49)
+#98 := (~ #97 #96)
+#94 := (~ #93 #93)
+#95 := [refl]: #94
+#99 := [nnf-neg #95]: #98
+#110 := [nnf-neg #99 #106]: #109
+#132 := [nnf-pos #110 #127 #86 #92]: #131
+#12 := (= #11 f1)
+#16 := (exists (vars (?v0 S2)) #12)
+#10 := (= #9 f1)
+#15 := (exists (vars (?v0 S2)) #10)
+#17 := (or #15 #16)
+#13 := (or #10 #12)
+#14 := (exists (vars (?v0 S2)) #13)
+#18 := (iff #14 #17)
+#19 := (not #18)
+#68 := (iff #19 #65)
+#58 := (iff #46 #55)
+#61 := (not #58)
+#66 := (iff #61 #65)
+#67 := [rewrite]: #66
+#62 := (iff #19 #61)
+#59 := (iff #18 #58)
+#56 := (iff #17 #55)
+#53 := (iff #16 #52)
+#41 := (iff #12 #40)
+#42 := [rewrite]: #41
+#54 := [quant-intro #42]: #53
+#50 := (iff #15 #49)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#51 := [quant-intro #39]: #50
+#57 := [monotonicity #51 #54]: #56
+#47 := (iff #14 #46)
+#44 := (iff #13 #43)
+#45 := [monotonicity #39 #42]: #44
+#48 := [quant-intro #45]: #47
+#60 := [monotonicity #48 #57]: #59
+#63 := [monotonicity #60]: #62
+#69 := [trans #63 #67]: #68
+#36 := [asserted]: #19
+#72 := [mp #36 #69]: #65
+#133 := [mp~ #72 #132]: #130
+#134 := [mp #133 #144]: #142
+#135 := [and-elim #134]: #136
+#149 := [mp #135 #148]: #146
+#661 := [mp #149 #660]: #658
+#618 := [unit-resolution #661 #628]: #631
+#278 := [unit-resolution #617 #618 #621]: false
+#283 := [lemma #278]: #293
+#267 := (f4 ?v0!1)
+#268 := (= f1 #267)
+#269 := (or #113 #268)
+#270 := (not #269)
+#615 := (or #270 #280)
+#606 := [hypothesis]: #269
+#608 := (or #280 #270)
+#609 := [quant-inst]: #608
+#607 := [unit-resolution #609 #625 #606]: false
+#613 := [lemma #607]: #615
+#586 := [unit-resolution #613 #625]: #270
+#605 := (or #269 #610)
+#611 := [def-axiom]: #605
+#581 := [unit-resolution #611 #586]: #610
+#145 := [and-elim #134]: #139
+#582 := [unit-resolution #145 #581 #283 #585]: #120
+#314 := (not #120)
+#592 := (or #326 #314)
+#593 := [def-axiom]: #592
+#587 := [unit-resolution #593 #582]: #326
+#221 := (not #326)
+#321 := (or #280 #221)
+#603 := (or #602 #120)
+#325 := (not #603)
+#322 := (or #280 #325)
+#600 := (iff #322 #321)
+#601 := (iff #321 #321)
+#311 := [rewrite]: #601
+#598 := (iff #325 #221)
+#327 := (iff #603 #326)
+#328 := [rewrite]: #327
+#599 := [monotonicity #328]: #598
+#597 := [monotonicity #599]: #600
+#312 := [trans #597 #311]: #600
+#596 := [quant-inst]: #322
+#313 := [mp #596 #312]: #321
+#588 := [unit-resolution #313 #625 #587]: false
+#583 := [lemma #588]: #280
+#590 := [unit-resolution #661 #583]: #655
+#595 := [unit-resolution #300 #590]: #636
+#594 := (or #641 #610)
+#591 := [quant-inst]: #594
+#589 := [unit-resolution #591 #595 #308]: false
+#430 := [lemma #589]: #610
+#431 := [hypothesis]: #78
+#214 := (or #652 #644)
+#301 := [def-axiom]: #214
+#432 := [unit-resolution #301 #590]: #644
+#574 := (or #649 #626)
+#575 := [quant-inst]: #574
+#576 := [unit-resolution #575 #432 #431]: false
+#577 := [lemma #576]: #626
+#571 := (or #78 #113 #120)
+#572 := [unit-resolution #145 #283]: #571
+#573 := [unit-resolution #572 #577 #430]: #120
+#578 := (or #649 #314)
+#579 := [quant-inst]: #578
+[unit-resolution #579 #432 #573]: false
+unsat
+157e9ba0de5d7f3b7a1453e2a11927d703beea38 136 0
+#2 := false
+decl f3 :: (-> S2 S2 S1)
+decl f4 :: S2
+#16 := f4
+decl f5 :: S2
+#20 := f5
+#180 := (f3 f5 f4)
+decl f1 :: S1
+#4 := f1
+#267 := (= f1 #180)
+#181 := (not #267)
+#21 := (f3 f4 f5)
+#67 := (= f1 #21)
+#102 := (not #67)
+#9 := (:var 0 S2)
+#17 := (f3 #9 f4)
+#61 := (= f1 #17)
+#64 := (forall (vars (?v0 S2)) #61)
+#73 := (not #64)
+#8 := (:var 1 S2)
+#12 := (f3 #9 #8)
+#46 := (= f1 #12)
+#10 := (f3 #8 #9)
+#43 := (= f1 #10)
+#52 := (not #43)
+#53 := (or #52 #46)
+#58 := (forall (vars (?v0 S2) (?v1 S2)) #53)
+#82 := (not #58)
+#91 := (or #82 #73 #67)
+#94 := (not #91)
+#22 := (= #21 f1)
+#18 := (= #17 f1)
+#19 := (forall (vars (?v0 S2)) #18)
+#23 := (implies #19 #22)
+#13 := (= #12 f1)
+#11 := (= #10 f1)
+#14 := (implies #11 #13)
+#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
+#24 := (implies #15 #23)
+#25 := (not #24)
+#97 := (iff #25 #94)
+#74 := (or #73 #67)
+#83 := (or #82 #74)
+#88 := (not #83)
+#95 := (iff #88 #94)
+#92 := (iff #83 #91)
+#93 := [rewrite]: #92
+#96 := [monotonicity #93]: #95
+#89 := (iff #25 #88)
+#86 := (iff #24 #83)
+#79 := (implies #58 #74)
+#84 := (iff #79 #83)
+#85 := [rewrite]: #84
+#80 := (iff #24 #79)
+#77 := (iff #23 #74)
+#70 := (implies #64 #67)
+#75 := (iff #70 #74)
+#76 := [rewrite]: #75
+#71 := (iff #23 #70)
+#68 := (iff #22 #67)
+#69 := [rewrite]: #68
+#65 := (iff #19 #64)
+#62 := (iff #18 #61)
+#63 := [rewrite]: #62
+#66 := [quant-intro #63]: #65
+#72 := [monotonicity #66 #69]: #71
+#78 := [trans #72 #76]: #77
+#59 := (iff #15 #58)
+#56 := (iff #14 #53)
+#49 := (implies #43 #46)
+#54 := (iff #49 #53)
+#55 := [rewrite]: #54
+#50 := (iff #14 #49)
+#47 := (iff #13 #46)
+#48 := [rewrite]: #47
+#44 := (iff #11 #43)
+#45 := [rewrite]: #44
+#51 := [monotonicity #45 #48]: #50
+#57 := [trans #51 #55]: #56
+#60 := [quant-intro #57]: #59
+#81 := [monotonicity #60 #78]: #80
+#87 := [trans #81 #85]: #86
+#90 := [monotonicity #87]: #89
+#98 := [trans #90 #96]: #97
+#42 := [asserted]: #25
+#99 := [mp #42 #98]: #94
+#103 := [not-or-elim #99]: #102
+#597 := (pattern #12)
+#596 := (pattern #10)
+#598 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #596 #597) #53)
+#601 := (iff #58 #598)
+#599 := (iff #53 #53)
+#600 := [refl]: #599
+#602 := [quant-intro #600]: #601
+#115 := (~ #58 #58)
+#113 := (~ #53 #53)
+#114 := [refl]: #113
+#116 := [nnf-pos #114]: #115
+#100 := [not-or-elim #99]: #58
+#106 := [mp~ #100 #116]: #58
+#603 := [mp #106 #602]: #598
+#271 := (not #598)
+#272 := (or #271 #67 #181)
+#268 := (or #181 #67)
+#200 := (or #271 #268)
+#247 := (iff #200 #272)
+#182 := (or #67 #181)
+#270 := (or #271 #182)
+#588 := (iff #270 #272)
+#590 := [rewrite]: #588
+#274 := (iff #200 #270)
+#269 := (iff #268 #182)
+#260 := [rewrite]: #269
+#253 := [monotonicity #260]: #274
+#377 := [trans #253 #590]: #247
+#273 := [quant-inst]: #200
+#584 := [mp #273 #377]: #272
+#258 := [unit-resolution #584 #603 #103]: #181
+#604 := (pattern #17)
+#605 := (forall (vars (?v0 S2)) (:pat #604) #61)
+#608 := (iff #64 #605)
+#606 := (iff #61 #61)
+#607 := [refl]: #606
+#609 := [quant-intro #607]: #608
+#107 := (~ #64 #64)
+#104 := (~ #61 #61)
+#117 := [refl]: #104
+#108 := [nnf-pos #117]: #107
+#101 := [not-or-elim #99]: #64
+#118 := [mp~ #101 #108]: #64
+#610 := [mp #118 #609]: #605
+#591 := (not #605)
+#592 := (or #591 #267)
+#593 := [quant-inst]: #592
+[unit-resolution #593 #610 #258]: false
+unsat
+b13823d6af0970648680336d47e5ac31c5900b24 124 0
+#2 := false
+decl f3 :: (-> S2 S1)
+decl f4 :: (-> S2 S2)
+decl f5 :: S2
+#16 := f5
+#20 := (f4 f5)
+#21 := (f4 #20)
+#154 := (f3 #21)
+decl f1 :: S1
+#4 := f1
+#241 := (= f1 #154)
+#152 := (f3 #20)
+#239 := (= f1 #152)
+#17 := (f3 f5)
+#62 := (= f1 #17)
+#8 := (:var 0 S2)
+#11 := (f4 #8)
+#12 := (f3 #11)
+#47 := (= f1 #12)
+#9 := (f3 #8)
+#44 := (= f1 #9)
+#53 := (not #44)
+#54 := (or #53 #47)
+#59 := (forall (vars (?v0 S2)) #54)
+#65 := (and #59 #62)
+#22 := (f4 #21)
+#23 := (f3 #22)
+#68 := (= f1 #23)
+#74 := (not #65)
+#75 := (or #74 #68)
+#80 := (not #75)
+#24 := (= #23 f1)
+#18 := (= #17 f1)
+#13 := (= #12 f1)
+#10 := (= #9 f1)
+#14 := (implies #10 #13)
+#15 := (forall (vars (?v0 S2)) #14)
+#19 := (and #15 #18)
+#25 := (implies #19 #24)
+#26 := (not #25)
+#81 := (iff #26 #80)
+#78 := (iff #25 #75)
+#71 := (implies #65 #68)
+#76 := (iff #71 #75)
+#77 := [rewrite]: #76
+#72 := (iff #25 #71)
+#69 := (iff #24 #68)
+#70 := [rewrite]: #69
+#66 := (iff #19 #65)
+#63 := (iff #18 #62)
+#64 := [rewrite]: #63
+#60 := (iff #15 #59)
+#57 := (iff #14 #54)
+#50 := (implies #44 #47)
+#55 := (iff #50 #54)
+#56 := [rewrite]: #55
+#51 := (iff #14 #50)
+#48 := (iff #13 #47)
+#49 := [rewrite]: #48
+#45 := (iff #10 #44)
+#46 := [rewrite]: #45
+#52 := [monotonicity #46 #49]: #51
+#58 := [trans #52 #56]: #57
+#61 := [quant-intro #58]: #60
+#67 := [monotonicity #61 #64]: #66
+#73 := [monotonicity #67 #70]: #72
+#79 := [trans #73 #77]: #78
+#82 := [monotonicity #79]: #81
+#43 := [asserted]: #26
+#85 := [mp #43 #82]: #80
+#83 := [not-or-elim #85]: #65
+#86 := [and-elim #83]: #62
+#570 := (pattern #11)
+#571 := (forall (vars (?v0 S2)) (:pat #570) #54)
+#574 := (iff #59 #571)
+#572 := (iff #54 #54)
+#573 := [refl]: #572
+#575 := [quant-intro #573]: #574
+#100 := (~ #59 #59)
+#98 := (~ #54 #54)
+#99 := [refl]: #98
+#101 := [nnf-pos #99]: #100
+#84 := [and-elim #83]: #59
+#91 := [mp~ #84 #101]: #59
+#576 := [mp #91 #575]: #571
+#153 := (not #62)
+#232 := (not #571)
+#243 := (or #232 #153 #239)
+#240 := (or #153 #239)
+#244 := (or #232 #240)
+#245 := (iff #244 #243)
+#242 := [rewrite]: #245
+#172 := [quant-inst]: #244
+#246 := [mp #172 #242]: #243
+#208 := [unit-resolution #246 #576 #86]: #239
+#225 := (not #239)
+#351 := (or #232 #225 #241)
+#562 := (or #225 #241)
+#558 := (or #232 #562)
+#231 := (iff #558 #351)
+#565 := [rewrite]: #231
+#230 := [quant-inst]: #558
+#566 := [mp #230 #565]: #351
+#209 := [unit-resolution #566 #576 #208]: #241
+#87 := (not #68)
+#88 := [not-or-elim #85]: #87
+#564 := (not #241)
+#569 := (or #232 #68 #564)
+#219 := (or #564 #68)
+#559 := (or #232 #219)
+#545 := (iff #559 #569)
+#567 := (or #68 #564)
+#222 := (or #232 #567)
+#561 := (iff #222 #569)
+#202 := [rewrite]: #561
+#560 := (iff #559 #222)
+#568 := (iff #219 #567)
+#563 := [rewrite]: #568
+#218 := [monotonicity #563]: #560
+#206 := [trans #218 #202]: #545
+#217 := [quant-inst]: #559
+#207 := [mp #217 #206]: #569
+[unit-resolution #207 #576 #88 #209]: false
+unsat
+efa58136de82c8b5811ff6cbc9ea6e3a0dfa88b3 222 0
+#2 := false
+decl f3 :: (-> S2 S1)
+decl ?v0!0 :: S2
+#72 := ?v0!0
+#73 := (f3 ?v0!0)
+decl f1 :: S1
+#4 := f1
+#74 := (= f1 #73)
+#156 := (not #74)
+decl f4 :: S1
+#12 := f4
+#42 := (= f1 f4)
+#92 := (not #42)
+#157 := (or #92 #156)
+#158 := (not #157)
+decl ?v0!1 :: S2
+#105 := ?v0!1
+#106 := (f3 ?v0!1)
+#107 := (= f1 #106)
+#151 := (not #107)
+#152 := (or #92 #151)
+#153 := (not #152)
+#615 := [hypothesis]: #153
+#223 := (or #152 #107)
+#310 := [def-axiom]: #223
+#276 := [unit-resolution #310 #615]: #107
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#640 := (pattern #9)
+#36 := (= f1 #9)
+#85 := (not #36)
+#111 := (or #85 #92)
+#646 := (forall (vars (?v0 S2)) (:pat #640) #111)
+#222 := (or #152 #42)
+#309 := [def-axiom]: #222
+#277 := [unit-resolution #309 #615]: #42
+#641 := (forall (vars (?v0 S2)) (:pat #640) #85)
+#632 := (not #641)
+#634 := (or #632 #151)
+#316 := [hypothesis]: #107
+#295 := [hypothesis]: #641
+#289 := [quant-inst]: #634
+#421 := [unit-resolution #289 #295 #316]: false
+#628 := [lemma #421]: #634
+#278 := [unit-resolution #628 #276]: #632
+#651 := (or #92 #641 #646)
+#144 := (forall (vars (?v0 S2)) #111)
+#88 := (forall (vars (?v0 S2)) #85)
+#147 := (or #92 #88 #144)
+#652 := (iff #147 #651)
+#649 := (iff #144 #646)
+#647 := (iff #111 #111)
+#648 := [refl]: #647
+#650 := [quant-intro #648]: #649
+#644 := (iff #88 #641)
+#642 := (iff #85 #85)
+#643 := [refl]: #642
+#645 := [quant-intro #643]: #644
+#653 := [monotonicity #645 #650]: #652
+#48 := (and #36 #42)
+#98 := (not #48)
+#101 := (forall (vars (?v0 S2)) #98)
+#121 := (or #92 #88 #101)
+#148 := (iff #121 #147)
+#145 := (iff #101 #144)
+#142 := (iff #98 #111)
+#112 := (not #111)
+#137 := (not #112)
+#140 := (iff #137 #111)
+#141 := [rewrite]: #140
+#138 := (iff #98 #137)
+#66 := (iff #48 #112)
+#76 := [rewrite]: #66
+#139 := [monotonicity #76]: #138
+#143 := [trans #139 #141]: #142
+#146 := [quant-intro #143]: #145
+#149 := [monotonicity #146]: #148
+#127 := (and #42 #74)
+#124 := (and #42 #107)
+#130 := (or #124 #127)
+#133 := (and #121 #130)
+#79 := (and #74 #42)
+#108 := (and #107 #42)
+#113 := (or #108 #79)
+#95 := (or #88 #92)
+#114 := (or #101 #95)
+#115 := (and #114 #113)
+#134 := (iff #115 #133)
+#131 := (iff #113 #130)
+#128 := (iff #79 #127)
+#129 := [rewrite]: #128
+#125 := (iff #108 #124)
+#126 := [rewrite]: #125
+#132 := [monotonicity #126 #129]: #131
+#122 := (iff #114 #121)
+#123 := [rewrite]: #122
+#135 := [monotonicity #123 #132]: #134
+#39 := (exists (vars (?v0 S2)) #36)
+#45 := (and #39 #42)
+#60 := (not #45)
+#51 := (exists (vars (?v0 S2)) #48)
+#61 := (iff #51 #60)
+#116 := (~ #61 #115)
+#96 := (~ #60 #95)
+#93 := (~ #92 #92)
+#94 := [refl]: #93
+#89 := (not #39)
+#90 := (~ #89 #88)
+#86 := (~ #85 #85)
+#87 := [refl]: #86
+#91 := [nnf-neg #87]: #90
+#97 := [nnf-neg #91 #94]: #96
+#82 := (not #60)
+#83 := (~ #82 #79)
+#80 := (~ #45 #79)
+#77 := (~ #42 #42)
+#78 := [refl]: #77
+#75 := (~ #39 #74)
+#69 := [sk]: #75
+#81 := [monotonicity #69 #78]: #80
+#84 := [nnf-neg #81]: #83
+#109 := (~ #51 #108)
+#110 := [sk]: #109
+#102 := (not #51)
+#103 := (~ #102 #101)
+#99 := (~ #98 #98)
+#100 := [refl]: #99
+#104 := [nnf-neg #100]: #103
+#117 := [nnf-pos #104 #110 #84 #97]: #116
+#13 := (= f4 f1)
+#10 := (= #9 f1)
+#15 := (and #10 #13)
+#16 := (exists (vars (?v0 S2)) #15)
+#11 := (exists (vars (?v0 S2)) #10)
+#14 := (and #11 #13)
+#17 := (iff #14 #16)
+#18 := (not #17)
+#64 := (iff #18 #61)
+#54 := (iff #45 #51)
+#57 := (not #54)
+#62 := (iff #57 #61)
+#63 := [rewrite]: #62
+#58 := (iff #18 #57)
+#55 := (iff #17 #54)
+#52 := (iff #16 #51)
+#49 := (iff #15 #48)
+#43 := (iff #13 #42)
+#44 := [rewrite]: #43
+#37 := (iff #10 #36)
+#38 := [rewrite]: #37
+#50 := [monotonicity #38 #44]: #49
+#53 := [quant-intro #50]: #52
+#46 := (iff #14 #45)
+#40 := (iff #11 #39)
+#41 := [quant-intro #38]: #40
+#47 := [monotonicity #41 #44]: #46
+#56 := [monotonicity #47 #53]: #55
+#59 := [monotonicity #56]: #58
+#65 := [trans #59 #63]: #64
+#35 := [asserted]: #18
+#68 := [mp #35 #65]: #61
+#118 := [mp~ #68 #117]: #115
+#119 := [mp #118 #135]: #133
+#120 := [and-elim #119]: #121
+#150 := [mp #120 #149]: #147
+#654 := [mp #150 #653]: #651
+#279 := [unit-resolution #654 #278 #277]: #646
+#636 := (not #646)
+#637 := (or #636 #92 #151)
+#300 := (or #151 #92)
+#638 := (or #636 #300)
+#288 := (iff #638 #637)
+#639 := (or #636 #152)
+#292 := (iff #639 #637)
+#630 := [rewrite]: #292
+#629 := (iff #638 #639)
+#301 := (iff #300 #152)
+#635 := [rewrite]: #301
+#287 := [monotonicity #635]: #629
+#631 := [trans #287 #630]: #288
+#633 := [quant-inst]: #638
+#272 := [mp #633 #631]: #637
+#617 := [unit-resolution #272 #277 #279 #276]: false
+#618 := [lemma #617]: #152
+#161 := (or #153 #158)
+#162 := (iff #130 #161)
+#159 := (iff #127 #158)
+#160 := [rewrite]: #159
+#154 := (iff #124 #153)
+#155 := [rewrite]: #154
+#163 := [monotonicity #155 #160]: #162
+#136 := [and-elim #119]: #130
+#164 := [mp #136 #163]: #161
+#614 := [unit-resolution #164 #618]: #158
+#314 := (or #157 #74)
+#242 := [def-axiom]: #314
+#320 := [unit-resolution #242 #614]: #74
+#302 := (or #157 #42)
+#313 := [def-axiom]: #302
+#337 := [unit-resolution #313 #614]: #42
+#336 := [hypothesis]: #646
+#616 := (or #636 #92 #156)
+#619 := (or #156 #92)
+#622 := (or #636 #619)
+#624 := (iff #622 #616)
+#623 := (or #636 #157)
+#264 := (iff #623 #616)
+#626 := [rewrite]: #264
+#625 := (iff #622 #623)
+#620 := (iff #619 #157)
+#621 := [rewrite]: #620
+#263 := [monotonicity #621]: #625
+#627 := [trans #263 #626]: #624
+#258 := [quant-inst]: #622
+#613 := [mp #258 #627]: #616
+#338 := [unit-resolution #613 #337 #336 #320]: false
+#324 := [lemma #338]: #636
+#339 := [unit-resolution #654 #324 #337]: #641
+#609 := (or #632 #156)
+#610 := [quant-inst]: #609
+[unit-resolution #610 #339 #320]: false
+unsat
+27f0d36fd6c0929bba5c83b80c0b177e808eb0e9 64 0
+#2 := false
+decl f3 :: (-> S2 S2 S3)
+decl f4 :: S2
+#14 := f4
+decl f5 :: S2
+#16 := f5
+#18 := (f3 f5 f4)
+#17 := (f3 f4 f5)
+#19 := (= #17 #18)
+#62 := (not #19)
+#8 := (:var 1 S2)
+#9 := (:var 0 S2)
+#11 := (f3 #9 #8)
+#10 := (f3 #8 #9)
+#12 := (= #10 #11)
+#13 := (forall (vars (?v0 S2) (?v1 S2)) #12)
+#52 := (not #13)
+#53 := (or #52 #19)
+#58 := (not #53)
+#15 := (= f4 f4)
+#20 := (and #15 #19)
+#21 := (implies #13 #20)
+#22 := (not #21)
+#59 := (iff #22 #58)
+#56 := (iff #21 #53)
+#49 := (implies #13 #19)
+#54 := (iff #49 #53)
+#55 := [rewrite]: #54
+#50 := (iff #21 #49)
+#47 := (iff #20 #19)
+#1 := true
+#42 := (and true #19)
+#45 := (iff #42 #19)
+#46 := [rewrite]: #45
+#43 := (iff #20 #42)
+#40 := (iff #15 true)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#48 := [trans #44 #46]: #47
+#51 := [monotonicity #48]: #50
+#57 := [trans #51 #55]: #56
+#60 := [monotonicity #57]: #59
+#39 := [asserted]: #22
+#63 := [mp #39 #60]: #58
+#64 := [not-or-elim #63]: #62
+#547 := (pattern #11)
+#546 := (pattern #10)
+#548 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #546 #547) #12)
+#551 := (iff #13 #548)
+#549 := (iff #12 #12)
+#550 := [refl]: #549
+#552 := [quant-intro #550]: #551
+#74 := (~ #13 #13)
+#72 := (~ #12 #12)
+#73 := [refl]: #72
+#75 := [nnf-pos #73]: #74
+#61 := [not-or-elim #63]: #13
+#67 := [mp~ #61 #75]: #13
+#553 := [mp #67 #552]: #548
+#129 := (not #548)
+#216 := (or #129 #19)
+#130 := [quant-inst]: #216
+[unit-resolution #130 #553 #64]: false
+unsat
+ab7c9224394921a685740971ba6d77f051f292c6 49 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S2 S4 S1)
+#9 := (:var 0 S4)
+#13 := (:var 1 S2)
+#14 := (f3 #13 #9)
+#15 := (= #14 f1)
+#16 := (exists (vars (?v0 S2) (?v1 S4)) #15)
+#8 := (:var 2 S2)
+#10 := (f3 #8 #9)
+#11 := (= #10 f1)
+#12 := (exists (vars (?v0 S2) (?v1 S3) (?v2 S4)) #11)
+#17 := (iff #12 #16)
+#18 := (not #17)
+#64 := (iff #18 false)
+#1 := true
+#59 := (not true)
+#62 := (iff #59 false)
+#63 := [rewrite]: #62
+#60 := (iff #18 #59)
+#57 := (iff #17 true)
+#42 := (= f1 #14)
+#43 := (exists (vars (?v0 S2) (?v2 S4)) #42)
+#52 := (iff #43 #43)
+#55 := (iff #52 true)
+#56 := [rewrite]: #55
+#53 := (iff #17 #52)
+#50 := (iff #16 #43)
+#48 := (iff #15 #42)
+#49 := [rewrite]: #48
+#51 := [quant-intro #49]: #50
+#46 := (iff #12 #43)
+#36 := (= f1 #10)
+#39 := (exists (vars (?v0 S2) (?v1 S3) (?v2 S4)) #36)
+#44 := (iff #39 #43)
+#45 := [elim-unused]: #44
+#40 := (iff #12 #39)
+#37 := (iff #11 #36)
+#38 := [rewrite]: #37
+#41 := [quant-intro #38]: #40
+#47 := [trans #41 #45]: #46
+#54 := [monotonicity #47 #51]: #53
+#58 := [trans #54 #56]: #57
+#61 := [monotonicity #58]: #60
+#65 := [trans #61 #63]: #64
+#35 := [asserted]: #18
+[mp #35 #65]: false
+unsat
+a2a7a4fb33d8eca0ac67dbe7e0b63fde0e7908a5 250 0
+#2 := false
+decl f3 :: (-> S2 S1)
+decl f7 :: S2
+#22 := f7
+#25 := (f3 f7)
+decl f1 :: S1
+#4 := f1
+#94 := (= f1 #25)
+#283 := (not #94)
+decl f4 :: (-> S2 S1)
+#8 := (:var 0 S2)
+#11 := (f4 #8)
+#702 := (pattern #11)
+#9 := (f3 #8)
+#701 := (pattern #9)
+#57 := (= f1 #11)
+#54 := (= f1 #9)
+#63 := (not #54)
+#64 := (or #63 #57)
+#703 := (forall (vars (?v0 S2)) (:pat #701 #702) #64)
+#69 := (forall (vars (?v0 S2)) #64)
+#706 := (iff #69 #703)
+#704 := (iff #64 #64)
+#705 := [refl]: #704
+#707 := [quant-intro #705]: #706
+#187 := (~ #69 #69)
+#201 := (~ #64 #64)
+#202 := [refl]: #201
+#188 := [nnf-pos #202]: #187
+decl f6 :: (-> S2 S1)
+#23 := (f6 f7)
+#91 := (= f1 #23)
+#78 := (not #57)
+#86 := (and #63 #78)
+#103 := (not #86)
+#136 := (or #103 #91 #94)
+#139 := (forall (vars (?v0 S2)) #136)
+decl f5 :: S2
+#15 := f5
+#16 := (f4 f5)
+#72 := (= f1 #16)
+#75 := (not #72)
+#148 := (and #69 #75 #139)
+#153 := (not #148)
+#32 := (f4 f7)
+#118 := (= f1 #32)
+#159 := (or #91 #118 #153)
+#164 := (not #159)
+#33 := (= #32 f1)
+#24 := (= #23 f1)
+#34 := (or #24 #33)
+#26 := (= #25 f1)
+#27 := (or #24 #26)
+#10 := (= #9 f1)
+#20 := (not #10)
+#12 := (= #11 f1)
+#19 := (not #12)
+#21 := (and #19 #20)
+#28 := (implies #21 #27)
+#29 := (forall (vars (?v0 S2)) #28)
+#17 := (= #16 f1)
+#18 := (not #17)
+#30 := (and #18 #29)
+#13 := (implies #10 #12)
+#14 := (forall (vars (?v0 S2)) #13)
+#31 := (and #14 #30)
+#35 := (implies #31 #34)
+#36 := (not #35)
+#167 := (iff #36 #164)
+#121 := (or #91 #118)
+#97 := (or #91 #94)
+#104 := (or #103 #97)
+#109 := (forall (vars (?v0 S2)) #104)
+#112 := (and #75 #109)
+#115 := (and #69 #112)
+#127 := (not #115)
+#128 := (or #127 #121)
+#133 := (not #128)
+#165 := (iff #133 #164)
+#162 := (iff #128 #159)
+#156 := (or #153 #121)
+#160 := (iff #156 #159)
+#161 := [rewrite]: #160
+#157 := (iff #128 #156)
+#154 := (iff #127 #153)
+#151 := (iff #115 #148)
+#142 := (and #75 #139)
+#145 := (and #69 #142)
+#149 := (iff #145 #148)
+#150 := [rewrite]: #149
+#146 := (iff #115 #145)
+#143 := (iff #112 #142)
+#140 := (iff #109 #139)
+#137 := (iff #104 #136)
+#138 := [rewrite]: #137
+#141 := [quant-intro #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#152 := [trans #147 #150]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#163 := [trans #158 #161]: #162
+#166 := [monotonicity #163]: #165
+#134 := (iff #36 #133)
+#131 := (iff #35 #128)
+#124 := (implies #115 #121)
+#129 := (iff #124 #128)
+#130 := [rewrite]: #129
+#125 := (iff #35 #124)
+#122 := (iff #34 #121)
+#119 := (iff #33 #118)
+#120 := [rewrite]: #119
+#92 := (iff #24 #91)
+#93 := [rewrite]: #92
+#123 := [monotonicity #93 #120]: #122
+#116 := (iff #31 #115)
+#113 := (iff #30 #112)
+#110 := (iff #29 #109)
+#107 := (iff #28 #104)
+#100 := (implies #86 #97)
+#105 := (iff #100 #104)
+#106 := [rewrite]: #105
+#101 := (iff #28 #100)
+#98 := (iff #27 #97)
+#95 := (iff #26 #94)
+#96 := [rewrite]: #95
+#99 := [monotonicity #93 #96]: #98
+#89 := (iff #21 #86)
+#83 := (and #78 #63)
+#87 := (iff #83 #86)
+#88 := [rewrite]: #87
+#84 := (iff #21 #83)
+#81 := (iff #20 #63)
+#55 := (iff #10 #54)
+#56 := [rewrite]: #55
+#82 := [monotonicity #56]: #81
+#79 := (iff #19 #78)
+#58 := (iff #12 #57)
+#59 := [rewrite]: #58
+#80 := [monotonicity #59]: #79
+#85 := [monotonicity #80 #82]: #84
+#90 := [trans #85 #88]: #89
+#102 := [monotonicity #90 #99]: #101
+#108 := [trans #102 #106]: #107
+#111 := [quant-intro #108]: #110
+#76 := (iff #18 #75)
+#73 := (iff #17 #72)
+#74 := [rewrite]: #73
+#77 := [monotonicity #74]: #76
+#114 := [monotonicity #77 #111]: #113
+#70 := (iff #14 #69)
+#67 := (iff #13 #64)
+#60 := (implies #54 #57)
+#65 := (iff #60 #64)
+#66 := [rewrite]: #65
+#61 := (iff #13 #60)
+#62 := [monotonicity #56 #59]: #61
+#68 := [trans #62 #66]: #67
+#71 := [quant-intro #68]: #70
+#117 := [monotonicity #71 #114]: #116
+#126 := [monotonicity #117 #123]: #125
+#132 := [trans #126 #130]: #131
+#135 := [monotonicity #132]: #134
+#168 := [trans #135 #166]: #167
+#53 := [asserted]: #36
+#169 := [mp #53 #168]: #164
+#174 := [not-or-elim #169]: #148
+#175 := [and-elim #174]: #69
+#185 := [mp~ #175 #188]: #69
+#708 := [mp #185 #707]: #703
+#172 := (not #118)
+#173 := [not-or-elim #169]: #172
+#285 := (not #703)
+#372 := (or #285 #283 #118)
+#370 := (or #283 #118)
+#363 := (or #285 #370)
+#375 := (iff #363 #372)
+#303 := [rewrite]: #375
+#374 := [quant-inst]: #363
+#376 := [mp #374 #303]: #372
+#398 := [unit-resolution #376 #173 #708]: #283
+#217 := (or #54 #57 #94)
+#709 := (forall (vars (?v0 S2)) (:pat #701 #702) #217)
+#222 := (forall (vars (?v0 S2)) #217)
+#712 := (iff #222 #709)
+#710 := (iff #217 #217)
+#711 := [refl]: #710
+#713 := [quant-intro #711]: #712
+#192 := (or #103 #94)
+#197 := (forall (vars (?v0 S2)) #192)
+#223 := (iff #197 #222)
+#220 := (iff #192 #217)
+#203 := (or #54 #57)
+#214 := (or #203 #94)
+#218 := (iff #214 #217)
+#219 := [rewrite]: #218
+#215 := (iff #192 #214)
+#212 := (iff #103 #203)
+#204 := (not #203)
+#207 := (not #204)
+#210 := (iff #207 #203)
+#211 := [rewrite]: #210
+#208 := (iff #103 #207)
+#205 := (iff #86 #204)
+#206 := [rewrite]: #205
+#209 := [monotonicity #206]: #208
+#213 := [trans #209 #211]: #212
+#216 := [monotonicity #213]: #215
+#221 := [trans #216 #219]: #220
+#224 := [quant-intro #221]: #223
+#184 := (~ #197 #197)
+#186 := (~ #192 #192)
+#183 := [refl]: #186
+#180 := [nnf-pos #183]: #184
+#198 := (iff #139 #197)
+#195 := (iff #136 #192)
+#189 := (or #103 false #94)
+#193 := (iff #189 #192)
+#194 := [rewrite]: #193
+#190 := (iff #136 #189)
+#181 := (iff #91 false)
+#170 := (not #91)
+#171 := [not-or-elim #169]: #170
+#182 := [iff-false #171]: #181
+#191 := [monotonicity #182]: #190
+#196 := [trans #191 #194]: #195
+#199 := [quant-intro #196]: #198
+#177 := [and-elim #174]: #139
+#200 := [mp #177 #199]: #197
+#178 := [mp~ #200 #180]: #197
+#225 := [mp #178 #224]: #222
+#714 := [mp #225 #713]: #709
+#356 := (not #709)
+#693 := (or #356 #94 #118)
+#284 := (or #94 #118 #94)
+#695 := (or #356 #284)
+#697 := (iff #695 #693)
+#371 := (or #94 #118)
+#482 := (or #356 #371)
+#362 := (iff #482 #693)
+#696 := [rewrite]: #362
+#689 := (iff #695 #482)
+#373 := (iff #284 #371)
+#377 := [rewrite]: #373
+#361 := [monotonicity #377]: #689
+#698 := [trans #361 #696]: #697
+#350 := [quant-inst]: #695
+#699 := [mp #350 #698]: #693
+[unit-resolution #699 #173 #714 #398]: false
+unsat
+e5bab80a17d61a903fd3b91d7b964fb77f0aeb5f 122 0
+#2 := false
+decl f3 :: (-> S2 S1)
+decl ?v0!1 :: S2
+#122 := ?v0!1
+#125 := (f3 ?v0!1)
+decl f1 :: S1
+#4 := f1
+#126 := (= f1 #125)
+decl f4 :: (-> S2 S1)
+#123 := (f4 ?v0!1)
+#124 := (= f1 #123)
+#135 := (and #124 #126)
+#127 := (and #126 #124)
+#136 := (iff #127 #135)
+#137 := [rewrite]: #136
+#8 := (:var 0 S2)
+#14 := (f4 #8)
+#53 := (= f1 #14)
+#9 := (f3 #8)
+#41 := (= f1 #9)
+#56 := (and #41 #53)
+#59 := (exists (vars (?v0 S2)) #56)
+#128 := (~ #59 #127)
+#129 := [sk]: #128
+#50 := (exists (vars (?v0 S2)) #41)
+#62 := (or #50 #59)
+#110 := (iff #62 #59)
+#105 := (or false #59)
+#108 := (iff #105 #59)
+#109 := [rewrite]: #108
+#106 := (iff #62 #105)
+#103 := (iff #50 false)
+#65 := (not #50)
+#44 := (not #41)
+#47 := (exists (vars (?v0 S2)) #44)
+#89 := (and #47 #65 #62)
+#10 := (= #9 f1)
+#13 := (exists (vars (?v0 S2)) #10)
+#19 := (not #13)
+#15 := (= #14 f1)
+#16 := (and #10 #15)
+#17 := (exists (vars (?v0 S2)) #16)
+#18 := (or #13 #17)
+#20 := (and #18 #19)
+#11 := (not #10)
+#12 := (exists (vars (?v0 S2)) #11)
+#21 := (and #12 #20)
+#22 := (not #21)
+#23 := (not #22)
+#92 := (iff #23 #89)
+#71 := (and #65 #62)
+#76 := (and #47 #71)
+#90 := (iff #76 #89)
+#91 := [rewrite]: #90
+#87 := (iff #23 #76)
+#79 := (not #76)
+#82 := (not #79)
+#85 := (iff #82 #76)
+#86 := [rewrite]: #85
+#83 := (iff #23 #82)
+#80 := (iff #22 #79)
+#77 := (iff #21 #76)
+#74 := (iff #20 #71)
+#68 := (and #62 #65)
+#72 := (iff #68 #71)
+#73 := [rewrite]: #72
+#69 := (iff #20 #68)
+#66 := (iff #19 #65)
+#51 := (iff #13 #50)
+#42 := (iff #10 #41)
+#43 := [rewrite]: #42
+#52 := [quant-intro #43]: #51
+#67 := [monotonicity #52]: #66
+#63 := (iff #18 #62)
+#60 := (iff #17 #59)
+#57 := (iff #16 #56)
+#54 := (iff #15 #53)
+#55 := [rewrite]: #54
+#58 := [monotonicity #43 #55]: #57
+#61 := [quant-intro #58]: #60
+#64 := [monotonicity #52 #61]: #63
+#70 := [monotonicity #64 #67]: #69
+#75 := [trans #70 #73]: #74
+#48 := (iff #12 #47)
+#45 := (iff #11 #44)
+#46 := [monotonicity #43]: #45
+#49 := [quant-intro #46]: #48
+#78 := [monotonicity #49 #75]: #77
+#81 := [monotonicity #78]: #80
+#84 := [monotonicity #81]: #83
+#88 := [trans #84 #86]: #87
+#93 := [trans #88 #91]: #92
+#40 := [asserted]: #23
+#94 := [mp #40 #93]: #89
+#96 := [and-elim #94]: #65
+#104 := [iff-false #96]: #103
+#107 := [monotonicity #104]: #106
+#111 := [trans #107 #109]: #110
+#97 := [and-elim #94]: #62
+#112 := [mp #97 #111]: #59
+#132 := [mp~ #112 #129]: #127
+#133 := [mp #132 #137]: #135
+#138 := [and-elim #133]: #126
+#614 := (pattern #9)
+#615 := (forall (vars (?v0 S2)) (:pat #614) #44)
+#118 := (forall (vars (?v0 S2)) #44)
+#618 := (iff #118 #615)
+#616 := (iff #44 #44)
+#617 := [refl]: #616
+#619 := [quant-intro #617]: #618
+#119 := (~ #65 #118)
+#115 := (~ #44 #44)
+#116 := [refl]: #115
+#120 := [nnf-neg #116]: #119
+#121 := [mp~ #96 #120]: #118
+#620 := [mp #121 #619]: #615
+#198 := (not #126)
+#286 := (not #615)
+#200 := (or #286 #198)
+#287 := [quant-inst]: #200
+[unit-resolution #287 #620 #138]: false
+unsat
+35a55494d50e2bb6e11852505e00f0a8eda3690b 105 0
+#2 := false
+decl f3 :: (-> S1 S1)
+decl ?v0!1 :: S1
+#80 := ?v0!1
+#81 := (f3 ?v0!1)
+decl f1 :: S1
+#4 := f1
+#82 := (= f1 #81)
+decl ?v0!0 :: S1
+#66 := ?v0!0
+#67 := (f3 ?v0!0)
+#68 := (= f1 #67)
+#69 := (not #68)
+#168 := [hypothesis]: #68
+#8 := (:var 0 S1)
+#9 := (f3 #8)
+#584 := (pattern #9)
+#34 := (= f1 #9)
+#43 := (not #34)
+#585 := (forall (vars (?v0 S1)) (:pat #584) #43)
+#46 := (forall (vars (?v0 S1)) #43)
+#588 := (iff #46 #585)
+#586 := (iff #43 #43)
+#587 := [refl]: #586
+#589 := [quant-intro #587]: #588
+#102 := (or #68 #82)
+#107 := (and #46 #102)
+#63 := (not #69)
+#87 := (or #82 #63)
+#88 := (or #46 #46)
+#89 := (and #88 #87)
+#108 := (iff #89 #107)
+#105 := (iff #87 #102)
+#99 := (or #82 #68)
+#103 := (iff #99 #102)
+#104 := [rewrite]: #103
+#100 := (iff #87 #99)
+#97 := (iff #63 #68)
+#98 := [rewrite]: #97
+#101 := [monotonicity #98]: #100
+#106 := [trans #101 #104]: #105
+#95 := (iff #88 #46)
+#96 := [rewrite]: #95
+#109 := [monotonicity #96 #106]: #108
+#37 := (exists (vars (?v0 S1)) #34)
+#55 := (iff #37 #46)
+#90 := (~ #55 #89)
+#76 := (~ #46 #46)
+#74 := (~ #43 #43)
+#75 := [refl]: #74
+#77 := [nnf-pos #75]: #76
+#60 := (not #46)
+#70 := (~ #60 #63)
+#71 := [sk]: #70
+#83 := (~ #37 #82)
+#84 := [sk]: #83
+#40 := (not #37)
+#78 := (~ #40 #46)
+#79 := [nnf-neg #75]: #78
+#91 := [nnf-pos #79 #84 #71 #77]: #90
+#10 := (= #9 f1)
+#13 := (not #10)
+#14 := (forall (vars (?v0 S1)) #13)
+#11 := (exists (vars (?v0 S1)) #10)
+#12 := (not #11)
+#15 := (iff #12 #14)
+#16 := (not #15)
+#58 := (iff #16 #55)
+#49 := (iff #40 #46)
+#52 := (not #49)
+#56 := (iff #52 #55)
+#57 := [rewrite]: #56
+#53 := (iff #16 #52)
+#50 := (iff #15 #49)
+#47 := (iff #14 #46)
+#44 := (iff #13 #43)
+#35 := (iff #10 #34)
+#36 := [rewrite]: #35
+#45 := [monotonicity #36]: #44
+#48 := [quant-intro #45]: #47
+#41 := (iff #12 #40)
+#38 := (iff #11 #37)
+#39 := [quant-intro #36]: #38
+#42 := [monotonicity #39]: #41
+#51 := [monotonicity #42 #48]: #50
+#54 := [monotonicity #51]: #53
+#59 := [trans #54 #57]: #58
+#33 := [asserted]: #16
+#62 := [mp #33 #59]: #55
+#92 := [mp~ #62 #91]: #89
+#93 := [mp #92 #109]: #107
+#94 := [and-elim #93]: #46
+#590 := [mp #94 #589]: #585
+#169 := (not #585)
+#256 := (or #169 #69)
+#170 := [quant-inst]: #256
+#255 := [unit-resolution #170 #590 #168]: false
+#257 := [lemma #255]: #69
+#110 := [and-elim #93]: #102
+#259 := [unit-resolution #110 #257]: #82
+#248 := (not #82)
+#188 := (or #169 #248)
+#261 := [quant-inst]: #188
+[unit-resolution #261 #590 #259]: false
+unsat
+3a3572162e189d1dd3faf86450c29af14c3f5775 1 2
+unsat
+WARNING: failed to find a pattern for quantifier (quantifier id: k!9)
+
+90e400384b7659617fb2ac3414efca4ad4acb82b 230 0
+#2 := false
+decl f3 :: (-> S1 S1)
+decl ?v0!0 :: S1
+#84 := ?v0!0
+#85 := (f3 ?v0!0)
+decl f1 :: S1
+#4 := f1
+#86 := (= f1 #85)
+#87 := (not #86)
+decl ?v0!1 :: S1
+#116 := ?v0!1
+#117 := (f3 ?v0!1)
+#118 := (= f1 #117)
+#119 := (not #118)
+decl f4 :: S1
+#11 := f4
+#39 := (= f1 f4)
+#124 := (or #39 #119)
+#289 := [hypothesis]: #119
+#275 := (or #124 #118)
+#618 := [def-axiom]: #275
+#263 := [unit-resolution #618 #289]: #124
+#8 := (:var 0 S1)
+#9 := (f3 #8)
+#627 := (pattern #9)
+#36 := (= f1 #9)
+#45 := (not #36)
+#46 := (or #45 #39)
+#94 := (not #46)
+#642 := (forall (vars (?v0 S1)) (:pat #627) #94)
+#628 := (forall (vars (?v0 S1)) (:pat #627) #36)
+#633 := (not #628)
+#636 := (or #39 #633)
+#301 := (or #633 #118)
+#300 := [hypothesis]: #628
+#229 := [quant-inst]: #301
+#302 := [unit-resolution #229 #300 #289]: false
+#299 := [lemma #302]: #301
+#264 := [unit-resolution #299 #289]: #633
+#210 := (or #636 #628)
+#297 := [def-axiom]: #210
+#265 := [unit-resolution #297 #264]: #636
+#639 := (not #636)
+#647 := (or #639 #642)
+#97 := (forall (vars (?v0 S1)) #94)
+#54 := (forall (vars (?v0 S1)) #36)
+#60 := (not #54)
+#61 := (or #39 #60)
+#111 := (not #61)
+#146 := (or #111 #97)
+#648 := (iff #146 #647)
+#645 := (iff #97 #642)
+#643 := (iff #94 #94)
+#644 := [refl]: #643
+#646 := [quant-intro #644]: #645
+#640 := (iff #111 #639)
+#637 := (iff #61 #636)
+#634 := (iff #60 #633)
+#631 := (iff #54 #628)
+#629 := (iff #36 #36)
+#630 := [refl]: #629
+#632 := [quant-intro #630]: #631
+#635 := [monotonicity #632]: #634
+#638 := [monotonicity #635]: #637
+#641 := [monotonicity #638]: #640
+#649 := [monotonicity #641 #646]: #648
+#100 := (not #39)
+#110 := (and #100 #54)
+#135 := (or #97 #110)
+#149 := (iff #135 #146)
+#122 := (or #97 #111)
+#147 := (iff #122 #146)
+#148 := [rewrite]: #147
+#123 := (iff #135 #122)
+#89 := (iff #110 #111)
+#90 := [rewrite]: #89
+#145 := [monotonicity #90]: #123
+#150 := [trans #145 #148]: #149
+#138 := (or #39 #87 #119)
+#141 := (and #135 #138)
+#81 := (or #87 #39)
+#127 := (or #124 #81)
+#128 := (or #110 #97)
+#129 := (and #128 #127)
+#142 := (iff #129 #141)
+#139 := (iff #127 #138)
+#140 := [rewrite]: #139
+#136 := (iff #128 #135)
+#137 := [rewrite]: #136
+#143 := [monotonicity #137 #140]: #142
+#51 := (exists (vars (?v0 S1)) #46)
+#72 := (not #51)
+#73 := (iff #61 #72)
+#130 := (~ #73 #129)
+#98 := (~ #72 #97)
+#95 := (~ #94 #94)
+#96 := [refl]: #95
+#99 := [nnf-neg #96]: #98
+#91 := (not #72)
+#92 := (~ #91 #81)
+#78 := (~ #51 #81)
+#88 := [sk]: #78
+#93 := [nnf-neg #88]: #92
+#125 := (~ #61 #124)
+#120 := (~ #60 #119)
+#121 := [sk]: #120
+#114 := (~ #39 #39)
+#115 := [refl]: #114
+#126 := [monotonicity #115 #121]: #125
+#112 := (~ #111 #110)
+#107 := (not #60)
+#108 := (~ #107 #54)
+#105 := (~ #54 #54)
+#103 := (~ #36 #36)
+#104 := [refl]: #103
+#106 := [nnf-pos #104]: #105
+#109 := [nnf-neg #106]: #108
+#101 := (~ #100 #100)
+#102 := [refl]: #101
+#113 := [nnf-neg #102 #109]: #112
+#131 := [nnf-pos #113 #126 #93 #99]: #130
+#12 := (= f4 f1)
+#10 := (= #9 f1)
+#15 := (forall (vars (?v0 S1)) #10)
+#16 := (implies #15 #12)
+#13 := (implies #10 #12)
+#14 := (exists (vars (?v0 S1)) #13)
+#17 := (iff #14 #16)
+#18 := (not #17)
+#76 := (iff #18 #73)
+#66 := (iff #51 #61)
+#69 := (not #66)
+#74 := (iff #69 #73)
+#75 := [rewrite]: #74
+#70 := (iff #18 #69)
+#67 := (iff #17 #66)
+#64 := (iff #16 #61)
+#57 := (implies #54 #39)
+#62 := (iff #57 #61)
+#63 := [rewrite]: #62
+#58 := (iff #16 #57)
+#40 := (iff #12 #39)
+#41 := [rewrite]: #40
+#55 := (iff #15 #54)
+#37 := (iff #10 #36)
+#38 := [rewrite]: #37
+#56 := [quant-intro #38]: #55
+#59 := [monotonicity #56 #41]: #58
+#65 := [trans #59 #63]: #64
+#52 := (iff #14 #51)
+#49 := (iff #13 #46)
+#42 := (implies #36 #39)
+#47 := (iff #42 #46)
+#48 := [rewrite]: #47
+#43 := (iff #13 #42)
+#44 := [monotonicity #38 #41]: #43
+#50 := [trans #44 #48]: #49
+#53 := [quant-intro #50]: #52
+#68 := [monotonicity #53 #65]: #67
+#71 := [monotonicity #68]: #70
+#77 := [trans #71 #75]: #76
+#35 := [asserted]: #18
+#80 := [mp #35 #77]: #73
+#132 := [mp~ #80 #131]: #129
+#133 := [mp #132 #143]: #141
+#134 := [and-elim #133]: #135
+#151 := [mp #134 #150]: #146
+#650 := [mp #151 #649]: #647
+#266 := [unit-resolution #650 #265]: #642
+#276 := (not #124)
+#287 := (not #642)
+#288 := (or #287 #276)
+#303 := (or #119 #39)
+#282 := (not #303)
+#622 := (or #287 #282)
+#624 := (iff #622 #288)
+#620 := (iff #288 #288)
+#626 := [rewrite]: #620
+#408 := (iff #282 #276)
+#619 := (iff #303 #124)
+#621 := [rewrite]: #619
+#615 := [monotonicity #621]: #408
+#625 := [monotonicity #615]: #624
+#616 := [trans #625 #626]: #624
+#623 := [quant-inst]: #622
+#274 := [mp #623 #616]: #288
+#604 := [unit-resolution #274 #266 #263]: false
+#605 := [lemma #604]: #118
+#617 := (or #39 #87)
+#606 := (not #617)
+#597 := [hypothesis]: #606
+#614 := (or #617 #100)
+#600 := [def-axiom]: #614
+#319 := [unit-resolution #600 #597]: #100
+#601 := (or #617 #86)
+#307 := [def-axiom]: #601
+#320 := [unit-resolution #307 #597]: #86
+#144 := [and-elim #133]: #138
+#594 := [unit-resolution #144 #320 #319 #605]: false
+#598 := [lemma #594]: #617
+#217 := (or #606 #287)
+#325 := [hypothesis]: #617
+#311 := [hypothesis]: #642
+#603 := (or #287 #606)
+#279 := (not #81)
+#609 := (or #287 #279)
+#610 := (iff #609 #603)
+#250 := (iff #603 #603)
+#251 := [rewrite]: #250
+#607 := (iff #279 #606)
+#259 := (iff #81 #617)
+#602 := [rewrite]: #259
+#608 := [monotonicity #602]: #607
+#612 := [monotonicity #608]: #610
+#613 := [trans #612 #251]: #610
+#245 := [quant-inst]: #609
+#611 := [mp #245 #613]: #603
+#326 := [unit-resolution #611 #311 #325]: false
+#596 := [lemma #326]: #217
+#595 := [unit-resolution #596 #598]: #287
+#599 := [unit-resolution #650 #595]: #639
+#209 := (or #636 #100)
+#296 := [def-axiom]: #209
+#310 := [unit-resolution #296 #599]: #100
+#312 := [unit-resolution #144 #310 #605]: #87
+#590 := [unit-resolution #297 #599]: #628
+#308 := (or #633 #86)
+#309 := [quant-inst]: #308
+[unit-resolution #309 #590 #312]: false
+unsat
+a110a216a9eb767753bdb8e6565cd9f3828f13c3 1 0
+unsat
+d3e1c4f171290bbc43cf7b8ed3f52dcaba02ad2a 156 0
+#2 := false
+decl f3 :: (-> S1 S2 S1)
+#9 := (:var 0 S2)
+decl f4 :: S1
+#15 := f4
+#16 := (f3 f4 #9)
+#622 := (pattern #16)
+decl f1 :: S1
+#4 := f1
+#54 := (= f1 #16)
+#103 := (not #54)
+#623 := (forall (vars (?v0 S2)) (:pat #622) #103)
+decl f5 :: S2
+#19 := f5
+#20 := (f3 f4 f5)
+#60 := (= f1 #20)
+#200 := (= f1 f4)
+#201 := (iff #60 #200)
+#8 := (:var 1 S1)
+#10 := (f3 #8 #9)
+#615 := (pattern #10)
+#45 := (= f1 #8)
+#42 := (= f1 #10)
+#48 := (iff #42 #45)
+#616 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #615) #48)
+#51 := (forall (vars (?v0 S1) (?v1 S2)) #48)
+#619 := (iff #51 #616)
+#617 := (iff #48 #48)
+#618 := [refl]: #617
+#620 := [quant-intro #618]: #619
+#85 := (~ #51 #51)
+#92 := (~ #48 #48)
+#93 := [refl]: #92
+#86 := [nnf-pos #93]: #85
+#57 := (exists (vars (?v0 S2)) #54)
+#63 := (iff #57 #60)
+#69 := (not #51)
+#70 := (or #69 #63)
+#75 := (not #70)
+#21 := (= #20 f1)
+#17 := (= #16 f1)
+#18 := (exists (vars (?v0 S2)) #17)
+#22 := (iff #18 #21)
+#12 := (= #8 f1)
+#11 := (= #10 f1)
+#13 := (iff #11 #12)
+#14 := (forall (vars (?v0 S1) (?v1 S2)) #13)
+#23 := (implies #14 #22)
+#24 := (not #23)
+#76 := (iff #24 #75)
+#73 := (iff #23 #70)
+#66 := (implies #51 #63)
+#71 := (iff #66 #70)
+#72 := [rewrite]: #71
+#67 := (iff #23 #66)
+#64 := (iff #22 #63)
+#61 := (iff #21 #60)
+#62 := [rewrite]: #61
+#58 := (iff #18 #57)
+#55 := (iff #17 #54)
+#56 := [rewrite]: #55
+#59 := [quant-intro #56]: #58
+#65 := [monotonicity #59 #62]: #64
+#52 := (iff #14 #51)
+#49 := (iff #13 #48)
+#46 := (iff #12 #45)
+#47 := [rewrite]: #46
+#43 := (iff #11 #42)
+#44 := [rewrite]: #43
+#50 := [monotonicity #44 #47]: #49
+#53 := [quant-intro #50]: #52
+#68 := [monotonicity #53 #65]: #67
+#74 := [trans #68 #72]: #73
+#77 := [monotonicity #74]: #76
+#41 := [asserted]: #24
+#80 := [mp #41 #77]: #75
+#78 := [not-or-elim #80]: #51
+#84 := [mp~ #78 #86]: #51
+#621 := [mp #84 #620]: #616
+#202 := (not #616)
+#278 := (or #202 #201)
+#610 := [quant-inst]: #278
+#287 := [unit-resolution #610 #621]: #201
+decl ?v0!0 :: S2
+#82 := ?v0!0
+#94 := (f3 f4 ?v0!0)
+#95 := (= f1 #94)
+#286 := (iff #95 #200)
+#288 := (or #202 #286)
+#279 := [quant-inst]: #288
+#277 := [unit-resolution #279 #621]: #286
+#290 := (not #286)
+#249 := (or #290 #200)
+#109 := (not #60)
+#265 := [hypothesis]: #109
+#114 := (or #60 #95)
+#106 := (forall (vars (?v0 S2)) #103)
+#115 := (or #109 #106)
+#122 := (and #114 #115)
+#116 := (and #115 #114)
+#123 := (iff #116 #122)
+#124 := [rewrite]: #123
+#87 := (not #57)
+#88 := (iff #60 #87)
+#117 := (~ #88 #116)
+#107 := (~ #87 #106)
+#104 := (~ #103 #103)
+#105 := [refl]: #104
+#108 := [nnf-neg #105]: #107
+#100 := (not #87)
+#101 := (~ #100 #95)
+#96 := (~ #57 #95)
+#97 := [sk]: #96
+#102 := [nnf-neg #97]: #101
+#112 := (~ #60 #60)
+#113 := [refl]: #112
+#110 := (~ #109 #109)
+#111 := [refl]: #110
+#118 := [nnf-pos #111 #113 #102 #108]: #117
+#79 := (not #63)
+#89 := (iff #79 #88)
+#90 := [rewrite]: #89
+#81 := [not-or-elim #80]: #79
+#91 := [mp #81 #90]: #88
+#119 := [mp~ #91 #118]: #116
+#120 := [mp #119 #124]: #122
+#121 := [and-elim #120]: #114
+#606 := [unit-resolution #121 #265]: #95
+#293 := (not #95)
+#272 := (or #290 #293 #200)
+#607 := [def-axiom]: #272
+#590 := [unit-resolution #607 #606]: #249
+#253 := [unit-resolution #590 #277]: #200
+#291 := (not #200)
+#611 := (not #201)
+#254 := (or #611 #291)
+#612 := (or #611 #60 #291)
+#613 := [def-axiom]: #612
+#255 := [unit-resolution #613 #265]: #254
+#256 := [unit-resolution #255 #253 #287]: false
+#592 := [lemma #256]: #60
+#628 := (or #109 #623)
+#629 := (iff #115 #628)
+#626 := (iff #106 #623)
+#624 := (iff #103 #103)
+#625 := [refl]: #624
+#627 := [quant-intro #625]: #626
+#630 := [monotonicity #627]: #629
+#125 := [and-elim #120]: #115
+#631 := [mp #125 #630]: #628
+#292 := [unit-resolution #631 #592]: #623
+#604 := (not #623)
+#264 := (or #604 #109)
+#269 := [quant-inst]: #264
+[unit-resolution #269 #592 #292]: false
+unsat
+021e717ac601dc07adaa2b5fdaab95b121236a15 1 0
+unsat
+c6a1ba7fcbcc63d35bcb3c6d55963f5db1b0ec4a 74 0
+#2 := false
+decl f3 :: (-> S2 S3 S4)
+#9 := (:var 0 S3)
+decl ?v0!0 :: S2
+#39 := ?v0!0
+#42 := (f3 ?v0!0 #9)
+#542 := (pattern #42)
+decl f4 :: (-> S2 S3)
+#40 := (f4 ?v0!0)
+#41 := (f3 ?v0!0 #40)
+#57 := (= #41 #42)
+#60 := (not #57)
+#543 := (forall (vars (?v1 S3)) (:pat #542) #60)
+#216 := (not #543)
+#126 := (= #41 #41)
+#213 := (not #126)
+#220 := (or #216 #213)
+#204 := (iff #220 #216)
+#534 := (or #216 false)
+#323 := (iff #534 #216)
+#530 := [rewrite]: #323
+#536 := (iff #220 #534)
+#146 := (iff #213 false)
+#1 := true
+#128 := (not true)
+#217 := (iff #128 false)
+#218 := [rewrite]: #217
+#215 := (iff #213 #128)
+#127 := (iff #126 true)
+#214 := [rewrite]: #127
+#206 := [monotonicity #214]: #215
+#219 := [trans #206 #218]: #146
+#193 := [monotonicity #219]: #536
+#205 := [trans #193 #530]: #204
+#199 := [quant-inst]: #220
+#537 := [mp #199 #205]: #216
+#63 := (forall (vars (?v1 S3)) #60)
+#546 := (iff #63 #543)
+#544 := (iff #60 #60)
+#545 := [refl]: #544
+#547 := [quant-intro #545]: #546
+#36 := (= #42 #41)
+#46 := (not #36)
+#49 := (forall (vars (?v1 S3)) #46)
+#64 := (iff #49 #63)
+#61 := (iff #46 #60)
+#58 := (iff #36 #57)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#65 := [quant-intro #62]: #64
+#8 := (:var 1 S2)
+#11 := (f4 #8)
+#12 := (f3 #8 #11)
+#10 := (f3 #8 #9)
+#13 := (= #10 #12)
+#14 := (exists (vars (?v1 S3)) #13)
+#15 := (forall (vars (?v0 S2)) #14)
+#16 := (not #15)
+#52 := (~ #16 #49)
+#34 := (exists (vars (?v1 S3)) #36)
+#43 := (not #34)
+#50 := (~ #43 #49)
+#47 := (~ #46 #46)
+#48 := [refl]: #47
+#51 := [nnf-neg #48]: #50
+#44 := (~ #16 #43)
+#45 := [sk]: #44
+#53 := [trans #45 #51]: #52
+#33 := [asserted]: #16
+#54 := [mp~ #33 #53]: #49
+#55 := [mp #54 #65]: #63
+#548 := [mp #55 #547]: #543
+[unit-resolution #548 #537]: false
+unsat
+227a4d38b650c5d656f4f2d1c6a5a4b38be4fdb6 1 0
+unsat
+0639f8bc4c0a97519f12b710ca2c55df172f2bff 108 0
+#2 := false
+decl f3 :: (-> S1 S1)
+#11 := (:var 0 S1)
+#12 := (f3 #11)
+#593 := (pattern #12)
+decl f1 :: S1
+#4 := f1
+#45 := (= f1 #12)
+#54 := (not #45)
+#594 := (forall (vars (?v0 S1)) (:pat #593) #54)
+#57 := (forall (vars (?v0 S1)) #54)
+#597 := (iff #57 #594)
+#595 := (iff #54 #54)
+#596 := [refl]: #595
+#598 := [quant-intro #596]: #597
+#48 := (exists (vars (?v0 S1)) #45)
+#51 := (not #48)
+#113 := (~ #51 #57)
+#115 := (~ #54 #54)
+#116 := [refl]: #115
+#114 := [nnf-neg #116]: #113
+decl f4 :: S1
+#8 := f4
+#9 := (f3 f4)
+#42 := (= f1 #9)
+#60 := (ite #42 #51 #57)
+#110 := (iff #60 #51)
+#1 := true
+#105 := (ite true #51 #57)
+#108 := (iff #105 #51)
+#109 := [rewrite]: #108
+#106 := (iff #60 #105)
+#103 := (iff #42 true)
+decl f5 :: S1
+#19 := f5
+#20 := (f3 f5)
+#63 := (= f1 #20)
+#78 := (not #60)
+#69 := (not #42)
+#87 := (or #69 #78 #63)
+#90 := (not #87)
+#21 := (= #20 f1)
+#10 := (= #9 f1)
+#22 := (implies #10 #21)
+#13 := (= #12 f1)
+#16 := (not #13)
+#17 := (forall (vars (?v0 S1)) #16)
+#14 := (exists (vars (?v0 S1)) #13)
+#15 := (not #14)
+#18 := (ite #10 #15 #17)
+#23 := (implies #18 #22)
+#24 := (not #23)
+#93 := (iff #24 #90)
+#70 := (or #69 #63)
+#79 := (or #78 #70)
+#84 := (not #79)
+#91 := (iff #84 #90)
+#88 := (iff #79 #87)
+#89 := [rewrite]: #88
+#92 := [monotonicity #89]: #91
+#85 := (iff #24 #84)
+#82 := (iff #23 #79)
+#75 := (implies #60 #70)
+#80 := (iff #75 #79)
+#81 := [rewrite]: #80
+#76 := (iff #23 #75)
+#73 := (iff #22 #70)
+#66 := (implies #42 #63)
+#71 := (iff #66 #70)
+#72 := [rewrite]: #71
+#67 := (iff #22 #66)
+#64 := (iff #21 #63)
+#65 := [rewrite]: #64
+#43 := (iff #10 #42)
+#44 := [rewrite]: #43
+#68 := [monotonicity #44 #65]: #67
+#74 := [trans #68 #72]: #73
+#61 := (iff #18 #60)
+#58 := (iff #17 #57)
+#55 := (iff #16 #54)
+#46 := (iff #13 #45)
+#47 := [rewrite]: #46
+#56 := [monotonicity #47]: #55
+#59 := [quant-intro #56]: #58
+#52 := (iff #15 #51)
+#49 := (iff #14 #48)
+#50 := [quant-intro #47]: #49
+#53 := [monotonicity #50]: #52
+#62 := [monotonicity #44 #53 #59]: #61
+#77 := [monotonicity #62 #74]: #76
+#83 := [trans #77 #81]: #82
+#86 := [monotonicity #83]: #85
+#94 := [trans #86 #92]: #93
+#41 := [asserted]: #24
+#95 := [mp #41 #94]: #90
+#96 := [not-or-elim #95]: #42
+#104 := [iff-true #96]: #103
+#107 := [monotonicity #104]: #106
+#111 := [trans #107 #109]: #110
+#97 := [not-or-elim #95]: #60
+#112 := [mp #97 #111]: #51
+#102 := [mp~ #112 #114]: #57
+#599 := [mp #102 #598]: #594
+#178 := (not #594)
+#265 := (or #178 #69)
+#179 := [quant-inst]: #265
+[unit-resolution #179 #96 #599]: false
+unsat
+24b3734d5c956814c73081ebdb8796337ed9a903 1 0
+unsat
+44518bbe9d91ef8d978f243d28c5ab98d20e8e24 183 2
+#2 := false
+decl f3 :: (-> S1 S2 S1)
+#9 := (:var 0 S2)
+decl f5 :: S1
+#24 := f5
+#25 := (f3 f5 #9)
+#703 := (pattern #25)
+decl f1 :: S1
+#4 := f1
+#80 := (= f1 #25)
+#184 := (not #80)
+#704 := (forall (vars (?v0 S2)) (:pat #703) #184)
+decl f4 :: S2
+#18 := f4
+#28 := (f3 f5 f4)
+#86 := (= f1 #28)
+#262 := (= f1 f5)
+#263 := (iff #86 #262)
+#8 := (:var 1 S1)
+#10 := (f3 #8 #9)
+#680 := (pattern #10)
+#53 := (= f1 #8)
+#50 := (= f1 #10)
+#56 := (iff #50 #53)
+#681 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #680) #56)
+#59 := (forall (vars (?v0 S1) (?v1 S2)) #56)
+#684 := (iff #59 #681)
+#682 := (iff #56 #56)
+#683 := [refl]: #682
+#685 := [quant-intro #683]: #684
+#115 := (~ #59 #59)
+#122 := (~ #56 #56)
+#123 := [refl]: #122
+#116 := [nnf-pos #123]: #115
+#17 := (:var 0 S1)
+#19 := (f3 #17 f4)
+#68 := (= f1 #19)
+#71 := (forall (vars (?v0 S1)) #68)
+#62 := (exists (vars (?v1 S2)) #50)
+#65 := (forall (vars (?v0 S1)) #62)
+#74 := (iff #65 #71)
+#77 := (and #59 #74)
+#83 := (exists (vars (?v0 S2)) #80)
+#89 := (iff #83 #86)
+#95 := (not #77)
+#96 := (or #95 #89)
+#101 := (not #96)
+#29 := (= #28 f1)
+#26 := (= #25 f1)
+#27 := (exists (vars (?v0 S2)) #26)
+#30 := (iff #27 #29)
+#20 := (= #19 f1)
+#21 := (forall (vars (?v0 S1)) #20)
+#11 := (= #10 f1)
+#15 := (exists (vars (?v1 S2)) #11)
+#16 := (forall (vars (?v0 S1)) #15)
+#22 := (iff #16 #21)
+#12 := (= #8 f1)
+#13 := (iff #11 #12)
+#14 := (forall (vars (?v0 S1) (?v1 S2)) #13)
+#23 := (and #14 #22)
+#31 := (implies #23 #30)
+#32 := (not #31)
+#102 := (iff #32 #101)
+#99 := (iff #31 #96)
+#92 := (implies #77 #89)
+#97 := (iff #92 #96)
+#98 := [rewrite]: #97
+#93 := (iff #31 #92)
+#90 := (iff #30 #89)
+#87 := (iff #29 #86)
+#88 := [rewrite]: #87
+#84 := (iff #27 #83)
+#81 := (iff #26 #80)
+#82 := [rewrite]: #81
+#85 := [quant-intro #82]: #84
+#91 := [monotonicity #85 #88]: #90
+#78 := (iff #23 #77)
+#75 := (iff #22 #74)
+#72 := (iff #21 #71)
+#69 := (iff #20 #68)
+#70 := [rewrite]: #69
+#73 := [quant-intro #70]: #72
+#66 := (iff #16 #65)
+#63 := (iff #15 #62)
+#51 := (iff #11 #50)
+#52 := [rewrite]: #51
+#64 := [quant-intro #52]: #63
+#67 := [quant-intro #64]: #66
+#76 := [monotonicity #67 #73]: #75
+#60 := (iff #14 #59)
+#57 := (iff #13 #56)
+#54 := (iff #12 #53)
+#55 := [rewrite]: #54
+#58 := [monotonicity #52 #55]: #57
+#61 := [quant-intro #58]: #60
+#79 := [monotonicity #61 #76]: #78
+#94 := [monotonicity #79 #91]: #93
+#100 := [trans #94 #98]: #99
+#103 := [monotonicity #100]: #102
+#49 := [asserted]: #32
+#106 := [mp #49 #103]: #101
+#104 := [not-or-elim #106]: #77
+#105 := [and-elim #104]: #59
+#113 := [mp~ #105 #116]: #59
+#686 := [mp #113 #685]: #681
+#264 := (not #681)
+#340 := (or #264 #263)
+#341 := [quant-inst]: #340
+#350 := [unit-resolution #341 #686]: #263
+decl ?v0!3 :: S2
+#155 := ?v0!3
+#156 := (f3 f5 ?v0!3)
+#128 := (= f1 #156)
+#349 := (iff #128 #262)
+#351 := (or #264 #349)
+#342 := [quant-inst]: #351
+#668 := [unit-resolution #342 #686]: #349
+#353 := (not #349)
+#671 := (or #353 #262)
+#190 := (not #86)
+#670 := [hypothesis]: #190
+#195 := (or #86 #128)
+#187 := (forall (vars (?v0 S2)) #184)
+#196 := (or #190 #187)
+#203 := (and #195 #196)
+#197 := (and #196 #195)
+#204 := (iff #197 #203)
+#205 := [rewrite]: #204
+#117 := (not #83)
+#118 := (iff #86 #117)
+#198 := (~ #118 #197)
+#188 := (~ #117 #187)
+#185 := (~ #184 #184)
+#186 := [refl]: #185
+#189 := [nnf-neg #186]: #188
+#181 := (not #117)
+#182 := (~ #181 #128)
+#129 := (~ #83 #128)
+#178 := [sk]: #129
+#183 := [nnf-neg #178]: #182
+#193 := (~ #86 #86)
+#194 := [refl]: #193
+#191 := (~ #190 #190)
+#192 := [refl]: #191
+#199 := [nnf-pos #192 #194 #183 #189]: #198
+#108 := (not #89)
+#119 := (iff #108 #118)
+#120 := [rewrite]: #119
+#109 := [not-or-elim #106]: #108
+#121 := [mp #109 #120]: #118
+#200 := [mp~ #121 #199]: #197
+#201 := [mp #200 #205]: #203
+#202 := [and-elim #201]: #195
+#328 := [unit-resolution #202 #670]: #128
+#352 := (not #128)
+#356 := (or #353 #352 #262)
+#335 := [def-axiom]: #356
+#312 := [unit-resolution #335 #328]: #671
+#655 := [unit-resolution #312 #668]: #262
+#354 := (not #262)
+#675 := (not #263)
+#316 := (or #675 #354)
+#676 := (or #675 #86 #354)
+#677 := [def-axiom]: #676
+#317 := [unit-resolution #677 #670]: #316
+#318 := [unit-resolution #317 #655 #350]: false
+#319 := [lemma #318]: #86
+#709 := (or #190 #704)
+#710 := (iff #196 #709)
+#707 := (iff #187 #704)
+#705 := (iff #184 #184)
+#706 := [refl]: #705
+#708 := [quant-intro #706]: #707
+#711 := [monotonicity #708]: #710
+#206 := [and-elim #201]: #196
+#712 := [mp #206 #711]: #709
+#282 := [unit-resolution #712 #319]: #704
+#679 := (not #704)
+#669 := (or #679 #190)
+#327 := [quant-inst]: #669
+[unit-resolution #327 #319 #282]: false
+unsat
+WARNING: failed to find a pattern for quantifier (quantifier id: k!12)
+
+dda61842424d25cb559a3f8991ef4e1e4903a499 1 0
+unsat
+7f10599800da74136cc3f9154a1eba3209948357 1 0
+unsat
+247ac7268dd0509d03e61fc965462ece3eca85cc 107 0
+#2 := false
+decl f3 :: (-> S2 S1)
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#606 := (pattern #9)
+decl f1 :: S1
+#4 := f1
+#37 := (= f1 #9)
+#43 := (not #37)
+#613 := (forall (vars (?v0 S2)) (:pat #606) #43)
+#115 := (forall (vars (?v0 S2)) #43)
+#616 := (iff #115 #613)
+#614 := (iff #43 #43)
+#615 := [refl]: #614
+#617 := [quant-intro #615]: #616
+#58 := (exists (vars (?v0 S2)) #37)
+#74 := (not #58)
+#116 := (~ #74 #115)
+#113 := (~ #43 #43)
+#114 := [refl]: #113
+#117 := [nnf-neg #114]: #116
+#11 := (:var 1 S2)
+#12 := (= #8 #11)
+#44 := (or #12 #43)
+#49 := (forall (vars (?v1 S2)) #44)
+#52 := (and #37 #49)
+#55 := (exists (vars (?v0 S2)) #52)
+#64 := (not #55)
+#65 := (or #64 #58)
+#70 := (not #65)
+#10 := (= #9 f1)
+#17 := (exists (vars (?v0 S2)) #10)
+#13 := (implies #10 #12)
+#14 := (forall (vars (?v1 S2)) #13)
+#15 := (and #10 #14)
+#16 := (exists (vars (?v0 S2)) #15)
+#18 := (implies #16 #17)
+#19 := (not #18)
+#71 := (iff #19 #70)
+#68 := (iff #18 #65)
+#61 := (implies #55 #58)
+#66 := (iff #61 #65)
+#67 := [rewrite]: #66
+#62 := (iff #18 #61)
+#59 := (iff #17 #58)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#60 := [quant-intro #39]: #59
+#56 := (iff #16 #55)
+#53 := (iff #15 #52)
+#50 := (iff #14 #49)
+#47 := (iff #13 #44)
+#40 := (implies #37 #12)
+#45 := (iff #40 #44)
+#46 := [rewrite]: #45
+#41 := (iff #13 #40)
+#42 := [monotonicity #39]: #41
+#48 := [trans #42 #46]: #47
+#51 := [quant-intro #48]: #50
+#54 := [monotonicity #39 #51]: #53
+#57 := [quant-intro #54]: #56
+#63 := [monotonicity #57 #60]: #62
+#69 := [trans #63 #67]: #68
+#72 := [monotonicity #69]: #71
+#36 := [asserted]: #19
+#75 := [mp #36 #72]: #70
+#76 := [not-or-elim #75]: #74
+#118 := [mp~ #76 #117]: #115
+#618 := [mp #118 #617]: #613
+decl ?v0!0 :: S2
+#84 := ?v0!0
+#79 := (f3 ?v0!0)
+#77 := (= f1 #79)
+#85 := (= #8 ?v0!0)
+#103 := (or #43 #85)
+#106 := (forall (vars (?v1 S2)) #103)
+#109 := (and #77 #106)
+#86 := (or #85 #43)
+#87 := (forall (vars (?v1 S2)) #86)
+#88 := (and #77 #87)
+#110 := (iff #88 #109)
+#107 := (iff #87 #106)
+#104 := (iff #86 #103)
+#105 := [rewrite]: #104
+#108 := [quant-intro #105]: #107
+#111 := [monotonicity #108]: #110
+#89 := (~ #55 #88)
+#97 := (~ #88 #88)
+#95 := (~ #87 #87)
+#93 := (~ #86 #86)
+#94 := [refl]: #93
+#96 := [nnf-pos #94]: #95
+#91 := (~ #77 #77)
+#92 := [refl]: #91
+#98 := [monotonicity #92 #96]: #97
+#90 := [sk]: #89
+#99 := [trans #90 #98]: #89
+#73 := [not-or-elim #75]: #55
+#100 := [mp~ #73 #99]: #88
+#101 := [mp #100 #111]: #109
+#102 := [and-elim #101]: #77
+#191 := (not #77)
+#278 := (not #613)
+#193 := (or #278 #191)
+#279 := [quant-inst]: #193
+[unit-resolution #279 #102 #618]: false
+unsat
+27b043a98368fb44835af50bddf282a2d59b4391 1 2
+unsat
+WARNING: failed to find a pattern for quantifier (quantifier id: k!12)
+
+9fff5372d7dcf3c6868fd1efde54974ccaa78891 1 0
+unsat
+150dd0a5cf6fbd2bec23fe99d00ba9baec864264 75 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S2 S1)
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#10 := (= #9 f1)
+#18 := (not #10)
+#11 := (:var 1 S2)
+#12 := (= #8 #11)
+#17 := (not #12)
+#19 := (implies #17 #18)
+#20 := (forall (vars (?v1 S2)) #19)
+#21 := (and #10 #20)
+#22 := (exists (vars (?v0 S2)) #21)
+#13 := (implies #10 #12)
+#14 := (forall (vars (?v1 S2)) #13)
+#15 := (and #10 #14)
+#16 := (exists (vars (?v0 S2)) #15)
+#23 := (iff #16 #22)
+#24 := (not #23)
+#90 := (iff #24 false)
+#1 := true
+#85 := (not true)
+#88 := (iff #85 false)
+#89 := [rewrite]: #88
+#86 := (iff #24 #85)
+#83 := (iff #23 true)
+#42 := (= f1 #9)
+#48 := (not #42)
+#49 := (or #12 #48)
+#54 := (forall (vars (?v1 S2)) #49)
+#57 := (and #42 #54)
+#60 := (exists (vars (?v0 S2)) #57)
+#78 := (iff #60 #60)
+#81 := (iff #78 true)
+#82 := [rewrite]: #81
+#79 := (iff #23 #78)
+#76 := (iff #22 #60)
+#74 := (iff #21 #57)
+#72 := (iff #20 #54)
+#70 := (iff #19 #49)
+#65 := (implies #17 #48)
+#68 := (iff #65 #49)
+#69 := [rewrite]: #68
+#66 := (iff #19 #65)
+#63 := (iff #18 #48)
+#43 := (iff #10 #42)
+#44 := [rewrite]: #43
+#64 := [monotonicity #44]: #63
+#67 := [monotonicity #64]: #66
+#71 := [trans #67 #69]: #70
+#73 := [quant-intro #71]: #72
+#75 := [monotonicity #44 #73]: #74
+#77 := [quant-intro #75]: #76
+#61 := (iff #16 #60)
+#58 := (iff #15 #57)
+#55 := (iff #14 #54)
+#52 := (iff #13 #49)
+#45 := (implies #42 #12)
+#50 := (iff #45 #49)
+#51 := [rewrite]: #50
+#46 := (iff #13 #45)
+#47 := [monotonicity #44]: #46
+#53 := [trans #47 #51]: #52
+#56 := [quant-intro #53]: #55
+#59 := [monotonicity #44 #56]: #58
+#62 := [quant-intro #59]: #61
+#80 := [monotonicity #62 #77]: #79
+#84 := [trans #80 #82]: #83
+#87 := [monotonicity #84]: #86
+#91 := [trans #87 #89]: #90
+#41 := [asserted]: #24
+[mp #41 #91]: false
+unsat
+23f1460031fa3216d5ae34bab8e296aaa1bb42d0 1 0
+unsat
+060c3042ee22e19c83c26af2e895e991251857c3 207 0
+#2 := false
+decl f3 :: (-> S2 S1)
+decl ?v1!0 :: (-> S2 S2)
+decl f4 :: S2
+#8 := f4
+#221 := (?v1!0 f4)
+#222 := (f3 #221)
+decl f1 :: S1
+#4 := f1
+#309 := (= f1 #222)
+#223 := (not #309)
+#308 := (= f4 #221)
+#313 := (or #308 #223)
+#311 := (not #313)
+#11 := (:var 0 S2)
+#12 := (f3 #11)
+#639 := (pattern #12)
+#120 := (?v1!0 #11)
+#147 := (= #11 #120)
+#121 := (f3 #120)
+#115 := (= f1 #121)
+#128 := (not #115)
+#153 := (or #128 #147)
+#158 := (not #153)
+#46 := (= f1 #12)
+#55 := (not #46)
+#161 := (or #55 #158)
+#646 := (forall (vars (?v0 S2)) (:pat #639) #161)
+#164 := (forall (vars (?v0 S2)) #161)
+#649 := (iff #164 #646)
+#647 := (iff #161 #161)
+#648 := [refl]: #647
+#650 := [quant-intro #648]: #649
+#129 := (= #120 #11)
+#130 := (or #129 #128)
+#131 := (not #130)
+#137 := (or #55 #131)
+#141 := (forall (vars (?v0 S2)) #137)
+#165 := (iff #141 #164)
+#162 := (iff #137 #161)
+#159 := (iff #131 #158)
+#156 := (iff #130 #153)
+#150 := (or #147 #128)
+#154 := (iff #150 #153)
+#155 := [rewrite]: #154
+#151 := (iff #130 #150)
+#148 := (iff #129 #147)
+#149 := [rewrite]: #148
+#152 := [monotonicity #149]: #151
+#157 := [trans #152 #155]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [quant-intro #163]: #165
+#17 := (:var 1 S2)
+#18 := (= #11 #17)
+#67 := (or #18 #55)
+#72 := (forall (vars (?v1 S2)) #67)
+#75 := (and #46 #72)
+#78 := (exists (vars (?v0 S2)) #75)
+#113 := (not #78)
+#142 := (~ #113 #141)
+#138 := (not #75)
+#139 := (~ #138 #137)
+#132 := (not #72)
+#133 := (~ #132 #131)
+#134 := [sk]: #133
+#119 := (~ #55 #55)
+#117 := [refl]: #119
+#140 := [nnf-neg #117 #134]: #139
+#143 := [nnf-neg #140]: #142
+#49 := (= f4 #11)
+#56 := (or #55 #49)
+#61 := (forall (vars (?v0 S2)) #56)
+#84 := (not #61)
+#9 := (f3 f4)
+#43 := (= f1 #9)
+#93 := (not #43)
+#102 := (or #93 #84 #78)
+#105 := (not #102)
+#13 := (= #12 f1)
+#19 := (implies #13 #18)
+#20 := (forall (vars (?v1 S2)) #19)
+#21 := (and #13 #20)
+#22 := (exists (vars (?v0 S2)) #21)
+#14 := (= #11 f4)
+#15 := (implies #13 #14)
+#16 := (forall (vars (?v0 S2)) #15)
+#23 := (implies #16 #22)
+#10 := (= #9 f1)
+#24 := (implies #10 #23)
+#25 := (not #24)
+#108 := (iff #25 #105)
+#85 := (or #84 #78)
+#94 := (or #93 #85)
+#99 := (not #94)
+#106 := (iff #99 #105)
+#103 := (iff #94 #102)
+#104 := [rewrite]: #103
+#107 := [monotonicity #104]: #106
+#100 := (iff #25 #99)
+#97 := (iff #24 #94)
+#90 := (implies #43 #85)
+#95 := (iff #90 #94)
+#96 := [rewrite]: #95
+#91 := (iff #24 #90)
+#88 := (iff #23 #85)
+#81 := (implies #61 #78)
+#86 := (iff #81 #85)
+#87 := [rewrite]: #86
+#82 := (iff #23 #81)
+#79 := (iff #22 #78)
+#76 := (iff #21 #75)
+#73 := (iff #20 #72)
+#70 := (iff #19 #67)
+#64 := (implies #46 #18)
+#68 := (iff #64 #67)
+#69 := [rewrite]: #68
+#65 := (iff #19 #64)
+#47 := (iff #13 #46)
+#48 := [rewrite]: #47
+#66 := [monotonicity #48]: #65
+#71 := [trans #66 #69]: #70
+#74 := [quant-intro #71]: #73
+#77 := [monotonicity #48 #74]: #76
+#80 := [quant-intro #77]: #79
+#62 := (iff #16 #61)
+#59 := (iff #15 #56)
+#52 := (implies #46 #49)
+#57 := (iff #52 #56)
+#58 := [rewrite]: #57
+#53 := (iff #15 #52)
+#50 := (iff #14 #49)
+#51 := [rewrite]: #50
+#54 := [monotonicity #48 #51]: #53
+#60 := [trans #54 #58]: #59
+#63 := [quant-intro #60]: #62
+#83 := [monotonicity #63 #80]: #82
+#89 := [trans #83 #87]: #88
+#44 := (iff #10 #43)
+#45 := [rewrite]: #44
+#92 := [monotonicity #45 #89]: #91
+#98 := [trans #92 #96]: #97
+#101 := [monotonicity #98]: #100
+#109 := [trans #101 #107]: #108
+#42 := [asserted]: #25
+#110 := [mp #42 #109]: #105
+#114 := [not-or-elim #110]: #113
+#144 := [mp~ #114 #143]: #141
+#145 := [mp #144 #166]: #164
+#651 := [mp #145 #650]: #646
+#111 := [not-or-elim #110]: #43
+#420 := (not #646)
+#627 := (or #420 #93 #311)
+#310 := (or #223 #308)
+#301 := (not #310)
+#312 := (or #93 #301)
+#299 := (or #420 #312)
+#638 := (iff #299 #627)
+#631 := (or #93 #311)
+#634 := (or #420 #631)
+#637 := (iff #634 #627)
+#632 := [rewrite]: #637
+#635 := (iff #299 #634)
+#633 := (iff #312 #631)
+#315 := (iff #301 #311)
+#241 := (iff #310 #313)
+#314 := [rewrite]: #241
+#294 := [monotonicity #314]: #315
+#288 := [monotonicity #294]: #633
+#636 := [monotonicity #288]: #635
+#628 := [trans #636 #632]: #638
+#300 := [quant-inst]: #299
+#286 := [mp #300 #628]: #627
+#595 := [unit-resolution #286 #111 #651]: #311
+#630 := (or #313 #309)
+#271 := [def-axiom]: #630
+#596 := [unit-resolution #271 #595]: #309
+#291 := (not #308)
+#629 := (or #313 #291)
+#287 := [def-axiom]: #629
+#591 := [unit-resolution #287 #595]: #291
+#640 := (forall (vars (?v0 S2)) (:pat #639) #56)
+#643 := (iff #61 #640)
+#641 := (iff #56 #56)
+#642 := [refl]: #641
+#644 := [quant-intro #642]: #643
+#126 := (~ #61 #61)
+#124 := (~ #56 #56)
+#125 := [refl]: #124
+#127 := [nnf-pos #125]: #126
+#112 := [not-or-elim #110]: #61
+#118 := [mp~ #112 #127]: #61
+#645 := [mp #118 #644]: #640
+#276 := (not #640)
+#277 := (or #276 #308 #223)
+#278 := (or #276 #310)
+#621 := (iff #278 #277)
+#617 := (or #276 #313)
+#620 := (iff #617 #277)
+#615 := [rewrite]: #620
+#618 := (iff #278 #617)
+#619 := [monotonicity #314]: #618
+#257 := [trans #619 #615]: #621
+#616 := [quant-inst]: #278
+#622 := [mp #616 #257]: #277
+[unit-resolution #622 #645 #591 #596]: false
+unsat
+f2b2af5a9a8fe9ebf2adc96a482b15f0491a9fa9 1 0
+unsat
+7a325dc7f60f1d704b700244e345b2bb3c006973 250 0
+#2 := false
+decl f3 :: (-> S2 S1)
+decl ?v1!1 :: (-> S2 S2)
+decl ?v0!0 :: S2
+#123 := ?v0!0
+#252 := (?v1!1 ?v0!0)
+#253 := (f3 #252)
+decl f1 :: S1
+#4 := f1
+#340 := (= f1 #253)
+#254 := (not #340)
+#339 := (= ?v0!0 #252)
+#272 := (or #339 #254)
+#346 := (not #272)
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#677 := (pattern #9)
+#119 := (?v1!1 #8)
+#154 := (= #8 #119)
+#120 := (f3 #119)
+#134 := (= f1 #120)
+#135 := (not #134)
+#160 := (or #135 #154)
+#165 := (not #160)
+#44 := (= f1 #9)
+#81 := (not #44)
+#168 := (or #81 #165)
+#678 := (forall (vars (?v0 S2)) (:pat #677) #168)
+#171 := (forall (vars (?v0 S2)) #168)
+#681 := (iff #171 #678)
+#679 := (iff #168 #168)
+#680 := [refl]: #679
+#682 := [quant-intro #680]: #681
+#136 := (= #119 #8)
+#137 := (or #136 #135)
+#138 := (not #137)
+#144 := (or #81 #138)
+#148 := (forall (vars (?v0 S2)) #144)
+#172 := (iff #148 #171)
+#169 := (iff #144 #168)
+#166 := (iff #138 #165)
+#163 := (iff #137 #160)
+#157 := (or #154 #135)
+#161 := (iff #157 #160)
+#162 := [rewrite]: #161
+#158 := (iff #137 #157)
+#155 := (iff #136 #154)
+#156 := [rewrite]: #155
+#159 := [monotonicity #156]: #158
+#164 := [trans #159 #162]: #163
+#167 := [monotonicity #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [quant-intro #170]: #172
+#12 := (:var 1 S2)
+#20 := (= #8 #12)
+#82 := (or #20 #81)
+#87 := (forall (vars (?v1 S2)) #82)
+#90 := (and #44 #87)
+#93 := (exists (vars (?v0 S2)) #90)
+#112 := (not #93)
+#149 := (~ #112 #148)
+#145 := (not #90)
+#146 := (~ #145 #144)
+#139 := (not #87)
+#140 := (~ #139 #138)
+#141 := [sk]: #140
+#132 := (~ #81 #81)
+#133 := [refl]: #132
+#147 := [nnf-neg #133 #141]: #146
+#150 := [nnf-neg #147]: #149
+#13 := (f3 #12)
+#50 := (= f1 #13)
+#56 := (and #44 #50)
+#66 := (not #56)
+#67 := (or #20 #66)
+#72 := (forall (vars (?v0 S2) (?v1 S2)) #67)
+#47 := (exists (vars (?v0 S2)) #44)
+#75 := (and #47 #72)
+#99 := (not #75)
+#100 := (or #99 #93)
+#105 := (not #100)
+#10 := (= #9 f1)
+#21 := (implies #10 #20)
+#22 := (forall (vars (?v1 S2)) #21)
+#23 := (and #10 #22)
+#24 := (exists (vars (?v0 S2)) #23)
+#16 := (= #12 #8)
+#14 := (= #13 f1)
+#15 := (and #14 #10)
+#17 := (implies #15 #16)
+#18 := (forall (vars (?v0 S2) (?v1 S2)) #17)
+#11 := (exists (vars (?v0 S2)) #10)
+#19 := (and #11 #18)
+#25 := (implies #19 #24)
+#26 := (not #25)
+#106 := (iff #26 #105)
+#103 := (iff #25 #100)
+#96 := (implies #75 #93)
+#101 := (iff #96 #100)
+#102 := [rewrite]: #101
+#97 := (iff #25 #96)
+#94 := (iff #24 #93)
+#91 := (iff #23 #90)
+#88 := (iff #22 #87)
+#85 := (iff #21 #82)
+#78 := (implies #44 #20)
+#83 := (iff #78 #82)
+#84 := [rewrite]: #83
+#79 := (iff #21 #78)
+#45 := (iff #10 #44)
+#46 := [rewrite]: #45
+#80 := [monotonicity #46]: #79
+#86 := [trans #80 #84]: #85
+#89 := [quant-intro #86]: #88
+#92 := [monotonicity #46 #89]: #91
+#95 := [quant-intro #92]: #94
+#76 := (iff #19 #75)
+#73 := (iff #18 #72)
+#70 := (iff #17 #67)
+#63 := (implies #56 #20)
+#68 := (iff #63 #67)
+#69 := [rewrite]: #68
+#64 := (iff #17 #63)
+#61 := (iff #16 #20)
+#62 := [rewrite]: #61
+#59 := (iff #15 #56)
+#53 := (and #50 #44)
+#57 := (iff #53 #56)
+#58 := [rewrite]: #57
+#54 := (iff #15 #53)
+#51 := (iff #14 #50)
+#52 := [rewrite]: #51
+#55 := [monotonicity #52 #46]: #54
+#60 := [trans #55 #58]: #59
+#65 := [monotonicity #60 #62]: #64
+#71 := [trans #65 #69]: #70
+#74 := [quant-intro #71]: #73
+#48 := (iff #11 #47)
+#49 := [quant-intro #46]: #48
+#77 := [monotonicity #49 #74]: #76
+#98 := [monotonicity #77 #95]: #97
+#104 := [trans #98 #102]: #103
+#107 := [monotonicity #104]: #106
+#43 := [asserted]: #26
+#110 := [mp #43 #107]: #105
+#113 := [not-or-elim #110]: #112
+#151 := [mp~ #113 #150]: #148
+#152 := [mp #151 #173]: #171
+#683 := [mp #152 #682]: #678
+#124 := (f3 ?v0!0)
+#125 := (= f1 #124)
+#126 := (~ #47 #125)
+#116 := [sk]: #126
+#108 := [not-or-elim #110]: #75
+#109 := [and-elim #108]: #47
+#128 := [mp~ #109 #116]: #125
+#343 := (not #125)
+#658 := (not #678)
+#330 := (or #658 #343 #346)
+#341 := (or #254 #339)
+#332 := (not #341)
+#344 := (or #343 #332)
+#331 := (or #658 #344)
+#659 := (iff #331 #330)
+#664 := (or #343 #346)
+#666 := (or #658 #664)
+#663 := (iff #666 #330)
+#669 := [rewrite]: #663
+#667 := (iff #331 #666)
+#319 := (iff #344 #664)
+#325 := (iff #332 #346)
+#345 := (iff #341 #272)
+#342 := [rewrite]: #345
+#662 := [monotonicity #342]: #325
+#451 := [monotonicity #662]: #319
+#668 := [monotonicity #451]: #667
+#317 := [trans #668 #669]: #659
+#665 := [quant-inst]: #331
+#322 := [mp #665 #317]: #330
+#453 := [unit-resolution #322 #128 #683]: #346
+#302 := (or #272 #340)
+#645 := [def-axiom]: #302
+#606 := [unit-resolution #645 #453]: #340
+#660 := (not #339)
+#318 := (or #272 #660)
+#661 := [def-axiom]: #318
+#607 := [unit-resolution #661 #453]: #660
+#670 := (pattern #9 #13)
+#142 := (not #50)
+#186 := (or #20 #81 #142)
+#671 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #670) #186)
+#191 := (forall (vars (?v0 S2) (?v1 S2)) #186)
+#674 := (iff #191 #671)
+#672 := (iff #186 #186)
+#673 := [refl]: #672
+#675 := [quant-intro #673]: #674
+#192 := (iff #72 #191)
+#189 := (iff #67 #186)
+#143 := (or #81 #142)
+#183 := (or #20 #143)
+#187 := (iff #183 #186)
+#188 := [rewrite]: #187
+#184 := (iff #67 #183)
+#181 := (iff #66 #143)
+#153 := (not #143)
+#176 := (not #153)
+#179 := (iff #176 #143)
+#180 := [rewrite]: #179
+#177 := (iff #66 #176)
+#174 := (iff #56 #153)
+#175 := [rewrite]: #174
+#178 := [monotonicity #175]: #177
+#182 := [trans #178 #180]: #181
+#185 := [monotonicity #182]: #184
+#190 := [trans #185 #188]: #189
+#193 := [quant-intro #190]: #192
+#129 := (~ #72 #72)
+#114 := (~ #67 #67)
+#127 := [refl]: #114
+#130 := [nnf-pos #127]: #129
+#111 := [and-elim #108]: #72
+#131 := [mp~ #111 #130]: #72
+#194 := [mp #131 #193]: #191
+#676 := [mp #194 #675]: #671
+#627 := (not #671)
+#622 := (or #627 #343 #339 #254)
+#352 := (= #252 ?v0!0)
+#353 := (or #352 #254 #343)
+#623 := (or #627 #353)
+#473 := (iff #623 #622)
+#635 := (or #343 #339 #254)
+#629 := (or #627 #635)
+#471 := (iff #629 #622)
+#472 := [rewrite]: #471
+#624 := (iff #623 #629)
+#625 := (iff #353 #635)
+#634 := (or #339 #254 #343)
+#632 := (iff #634 #635)
+#636 := [rewrite]: #632
+#347 := (iff #353 #634)
+#355 := (iff #352 #339)
+#633 := [rewrite]: #355
+#631 := [monotonicity #633]: #347
+#626 := [trans #631 #636]: #625
+#630 := [monotonicity #626]: #624
+#615 := [trans #630 #472]: #473
+#628 := [quant-inst]: #623
+#616 := [mp #628 #615]: #622
+[unit-resolution #616 #128 #676 #607 #606]: false
+unsat
+a6ccb14f7a73c3d3f2c9c2bbc93d8537ee62f62b 1 0
+unsat
+0aa1c3973c008a0548a3cef61cdea0cbbc71f686 238 0
+#2 := false
+decl f3 :: (-> S2 S1)
+decl ?v1!1 :: (-> S2 S2)
+decl ?v0!0 :: S2
+#116 := ?v0!0
+#240 := (?v1!1 ?v0!0)
+#241 := (f3 #240)
+decl f1 :: S1
+#4 := f1
+#328 := (= f1 #241)
+#242 := (not #328)
+#327 := (= ?v0!0 #240)
+#260 := (or #327 #242)
+#334 := (not #260)
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#658 := (pattern #9)
+#145 := (?v1!1 #8)
+#166 := (= #8 #145)
+#146 := (f3 #145)
+#147 := (= f1 #146)
+#148 := (not #147)
+#172 := (or #148 #166)
+#177 := (not #172)
+#41 := (= f1 #9)
+#47 := (not #41)
+#180 := (or #47 #177)
+#665 := (forall (vars (?v0 S2)) (:pat #658) #180)
+#183 := (forall (vars (?v0 S2)) #180)
+#668 := (iff #183 #665)
+#666 := (iff #180 #180)
+#667 := [refl]: #666
+#669 := [quant-intro #667]: #668
+#149 := (= #145 #8)
+#150 := (or #149 #148)
+#151 := (not #150)
+#157 := (or #47 #151)
+#160 := (forall (vars (?v0 S2)) #157)
+#184 := (iff #160 #183)
+#181 := (iff #157 #180)
+#178 := (iff #151 #177)
+#175 := (iff #150 #172)
+#169 := (or #166 #148)
+#173 := (iff #169 #172)
+#174 := [rewrite]: #173
+#170 := (iff #150 #169)
+#167 := (iff #149 #166)
+#168 := [rewrite]: #167
+#171 := [monotonicity #168]: #170
+#176 := [trans #171 #174]: #175
+#179 := [monotonicity #176]: #178
+#182 := [monotonicity #179]: #181
+#185 := [quant-intro #182]: #184
+#11 := (:var 1 S2)
+#12 := (= #8 #11)
+#48 := (or #12 #47)
+#53 := (forall (vars (?v1 S2)) #48)
+#56 := (and #41 #53)
+#68 := (not #56)
+#112 := (forall (vars (?v0 S2)) #68)
+#161 := (~ #112 #160)
+#158 := (~ #68 #157)
+#152 := (not #53)
+#153 := (~ #152 #151)
+#154 := [sk]: #153
+#143 := (~ #47 #47)
+#144 := [refl]: #143
+#159 := [nnf-neg #144 #154]: #158
+#162 := [nnf-pos #159]: #161
+decl f4 :: S1
+#17 := f4
+#62 := (= f1 f4)
+#69 := (or #68 #62)
+#74 := (forall (vars (?v0 S2)) #69)
+#113 := (iff #74 #112)
+#110 := (iff #69 #68)
+#105 := (or #68 false)
+#108 := (iff #105 #68)
+#109 := [rewrite]: #108
+#106 := (iff #69 #105)
+#101 := (iff #62 false)
+#92 := (not #62)
+#59 := (exists (vars (?v0 S2)) #56)
+#77 := (and #59 #74)
+#83 := (not #77)
+#84 := (or #62 #83)
+#89 := (not #84)
+#18 := (= f4 f1)
+#10 := (= #9 f1)
+#13 := (implies #10 #12)
+#14 := (forall (vars (?v1 S2)) #13)
+#15 := (and #10 #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 S2)) #19)
+#16 := (exists (vars (?v0 S2)) #15)
+#21 := (and #16 #20)
+#22 := (implies #21 #18)
+#23 := (not #22)
+#90 := (iff #23 #89)
+#87 := (iff #22 #84)
+#80 := (implies #77 #62)
+#85 := (iff #80 #84)
+#86 := [rewrite]: #85
+#81 := (iff #22 #80)
+#63 := (iff #18 #62)
+#64 := [rewrite]: #63
+#78 := (iff #21 #77)
+#75 := (iff #20 #74)
+#72 := (iff #19 #69)
+#65 := (implies #56 #62)
+#70 := (iff #65 #69)
+#71 := [rewrite]: #70
+#66 := (iff #19 #65)
+#57 := (iff #15 #56)
+#54 := (iff #14 #53)
+#51 := (iff #13 #48)
+#44 := (implies #41 #12)
+#49 := (iff #44 #48)
+#50 := [rewrite]: #49
+#45 := (iff #13 #44)
+#42 := (iff #10 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#52 := [trans #46 #50]: #51
+#55 := [quant-intro #52]: #54
+#58 := [monotonicity #43 #55]: #57
+#67 := [monotonicity #58 #64]: #66
+#73 := [trans #67 #71]: #72
+#76 := [quant-intro #73]: #75
+#60 := (iff #16 #59)
+#61 := [quant-intro #58]: #60
+#79 := [monotonicity #61 #76]: #78
+#82 := [monotonicity #79 #64]: #81
+#88 := [trans #82 #86]: #87
+#91 := [monotonicity #88]: #90
+#40 := [asserted]: #23
+#94 := [mp #40 #91]: #89
+#93 := [not-or-elim #94]: #92
+#102 := [iff-false #93]: #101
+#107 := [monotonicity #102]: #106
+#111 := [trans #107 #109]: #110
+#114 := [quant-intro #111]: #113
+#95 := [not-or-elim #94]: #77
+#97 := [and-elim #95]: #74
+#115 := [mp #97 #114]: #112
+#163 := [mp~ #115 #162]: #160
+#164 := [mp #163 #185]: #183
+#670 := [mp #164 #669]: #665
+#100 := (f3 ?v0!0)
+#98 := (= f1 #100)
+#117 := (= #8 ?v0!0)
+#133 := (or #47 #117)
+#136 := (forall (vars (?v1 S2)) #133)
+#139 := (and #98 #136)
+#103 := (or #117 #47)
+#104 := (forall (vars (?v1 S2)) #103)
+#118 := (and #98 #104)
+#140 := (iff #118 #139)
+#137 := (iff #104 #136)
+#134 := (iff #103 #133)
+#135 := [rewrite]: #134
+#138 := [quant-intro #135]: #137
+#141 := [monotonicity #138]: #140
+#119 := (~ #59 #118)
+#127 := (~ #118 #118)
+#125 := (~ #104 #104)
+#123 := (~ #103 #103)
+#124 := [refl]: #123
+#126 := [nnf-pos #124]: #125
+#121 := (~ #98 #98)
+#122 := [refl]: #121
+#128 := [monotonicity #122 #126]: #127
+#120 := [sk]: #119
+#129 := [trans #120 #128]: #119
+#96 := [and-elim #95]: #59
+#130 := [mp~ #96 #129]: #118
+#131 := [mp #130 #141]: #139
+#132 := [and-elim #131]: #98
+#331 := (not #98)
+#646 := (not #665)
+#318 := (or #646 #331 #334)
+#329 := (or #242 #327)
+#320 := (not #329)
+#332 := (or #331 #320)
+#319 := (or #646 #332)
+#647 := (iff #319 #318)
+#652 := (or #331 #334)
+#654 := (or #646 #652)
+#651 := (iff #654 #318)
+#657 := [rewrite]: #651
+#655 := (iff #319 #654)
+#307 := (iff #332 #652)
+#313 := (iff #320 #334)
+#333 := (iff #329 #260)
+#330 := [rewrite]: #333
+#650 := [monotonicity #330]: #313
+#439 := [monotonicity #650]: #307
+#656 := [monotonicity #439]: #655
+#305 := [trans #656 #657]: #647
+#653 := [quant-inst]: #319
+#310 := [mp #653 #305]: #318
+#611 := [unit-resolution #310 #132 #670]: #334
+#290 := (or #260 #328)
+#633 := [def-axiom]: #290
+#616 := [unit-resolution #633 #611]: #328
+#648 := (not #327)
+#306 := (or #260 #648)
+#649 := [def-axiom]: #306
+#617 := [unit-resolution #649 #611]: #648
+#659 := (forall (vars (?v1 S2)) (:pat #658) #133)
+#662 := (iff #136 #659)
+#660 := (iff #133 #133)
+#661 := [refl]: #660
+#663 := [quant-intro #661]: #662
+#142 := [and-elim #131]: #136
+#664 := [mp #142 #663]: #659
+#640 := (not #659)
+#276 := (or #640 #327 #242)
+#296 := (= #240 ?v0!0)
+#297 := (or #242 #296)
+#641 := (or #640 #297)
+#631 := (iff #641 #276)
+#281 := (or #640 #260)
+#642 := (iff #281 #276)
+#645 := [rewrite]: #642
+#282 := (iff #641 #281)
+#639 := (iff #297 #260)
+#637 := (iff #297 #329)
+#635 := (iff #296 #327)
+#636 := [rewrite]: #635
+#638 := [monotonicity #636]: #637
+#634 := [trans #638 #330]: #639
+#644 := [monotonicity #634]: #282
+#632 := [trans #644 #645]: #631
+#643 := [quant-inst]: #641
+#338 := [mp #643 #632]: #276
+[unit-resolution #338 #664 #617 #616]: false
+unsat
+a737d0c51ac36aed8a1a9cd55178cff9a96ed018 1 0
+unsat
+ad3f70e4b510752c5e78466bcf850b69675f0748 43 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#12 := (or #9 #11)
+#13 := (not #12)
+#14 := (or #12 #13)
+#15 := (not #14)
+#57 := (iff #15 false)
+#1 := true
+#52 := (not true)
+#55 := (iff #52 false)
+#56 := [rewrite]: #55
+#53 := (iff #15 #52)
+#50 := (iff #14 true)
+#36 := (= f1 f4)
+#33 := (= f1 f3)
+#39 := (or #33 #36)
+#42 := (not #39)
+#45 := (or #39 #42)
+#48 := (iff #45 true)
+#49 := [rewrite]: #48
+#46 := (iff #14 #45)
+#43 := (iff #13 #42)
+#40 := (iff #12 #39)
+#37 := (iff #11 #36)
+#38 := [rewrite]: #37
+#34 := (iff #9 #33)
+#35 := [rewrite]: #34
+#41 := [monotonicity #35 #38]: #40
+#44 := [monotonicity #41]: #43
+#47 := [monotonicity #41 #44]: #46
+#51 := [trans #47 #49]: #50
+#54 := [monotonicity #51]: #53
+#58 := [trans #54 #56]: #57
+#32 := [asserted]: #15
+[mp #32 #58]: false
+unsat
+da888d49fe89088ba7fe71a85968b4f0e39a7aba 16 0
+#2 := false
+#1 := true
+#8 := (implies true true)
+#9 := (not #8)
+#34 := (iff #9 false)
+#29 := (not true)
+#32 := (iff #29 false)
+#33 := [rewrite]: #32
+#30 := (iff #9 #29)
+#27 := (iff #8 true)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#35 := [trans #31 #33]: #34
+#26 := [asserted]: #9
+[mp #26 #35]: false
+unsat
+7f48a57f233df5237b79dd57ce30e63bdf44eb5b 27 0
+#2 := false
+#1 := true
+#9 := (or false true)
+#8 := (and true false)
+#10 := (implies #8 #9)
+#11 := (not #10)
+#45 := (iff #11 false)
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #11 #40)
+#38 := (iff #10 true)
+#33 := (implies false true)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #10 #33)
+#31 := (iff #9 true)
+#32 := [rewrite]: #31
+#29 := (iff #8 false)
+#30 := [rewrite]: #29
+#35 := [monotonicity #30 #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#28 := [asserted]: #11
+[mp #28 #46]: false
+unsat
+fc8df43e2cfbdb1c49bd1e2ca05690556717ae56 16 0
+#2 := false
+#8 := (implies false false)
+#9 := (not #8)
+#34 := (iff #9 false)
+#1 := true
+#29 := (not true)
+#32 := (iff #29 false)
+#33 := [rewrite]: #32
+#30 := (iff #9 #29)
+#27 := (iff #8 true)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#35 := [trans #31 #33]: #34
+#26 := [asserted]: #9
+[mp #26 #35]: false
+unsat
+4c412f5bcb05790d5fda803ce6123f178d77c3bc 31 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S2 S1)
+decl f4 :: S2
+#8 := f4
+#9 := (f3 f4)
+#10 := (= #9 f1)
+#11 := (iff #10 #10)
+#12 := (not #11)
+#45 := (iff #12 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #12 #40)
+#38 := (iff #11 true)
+#30 := (= f1 #9)
+#33 := (iff #30 #30)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (iff #10 #30)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32 #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#29 := [asserted]: #12
+[mp #29 #46]: false
+unsat
+6c85c042209c5bf364cb8360ac464d560331ff7c 31 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S2 S1)
+decl f4 :: S2
+#8 := f4
+#9 := (f3 f4)
+#10 := (= #9 f1)
+#11 := (implies #10 #10)
+#12 := (not #11)
+#45 := (iff #12 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #12 #40)
+#38 := (iff #11 true)
+#30 := (= f1 #9)
+#33 := (implies #30 #30)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (iff #10 #30)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32 #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#29 := [asserted]: #12
+[mp #29 #46]: false
+unsat
+7f6ad9f295b79d026cc84da045d8a49404f906c2 33 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S2 S3 S1)
+decl f5 :: S3
+#9 := f5
+decl f4 :: S2
+#8 := f4
+#10 := (f3 f4 f5)
+#11 := (= #10 f1)
+#12 := (iff #11 #11)
+#13 := (not #12)
+#46 := (iff #13 false)
+#1 := true
+#41 := (not true)
+#44 := (iff #41 false)
+#45 := [rewrite]: #44
+#42 := (iff #13 #41)
+#39 := (iff #12 true)
+#31 := (= f1 #10)
+#34 := (iff #31 #31)
+#37 := (iff #34 true)
+#38 := [rewrite]: #37
+#35 := (iff #12 #34)
+#32 := (iff #11 #31)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33 #33]: #35
+#40 := [trans #36 #38]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#30 := [asserted]: #13
+[mp #30 #47]: false
+unsat
+7aa85f1d84eee91f0a6d904666dbb90dd37fe476 48 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#12 := (or #9 #11)
+#13 := (implies #9 #12)
+#14 := (not #13)
+#62 := (iff #14 false)
+#35 := (= f1 f4)
+#32 := (= f1 f3)
+#38 := (or #32 #35)
+#44 := (not #32)
+#45 := (or #44 #38)
+#50 := (not #45)
+#60 := (iff #50 false)
+#1 := true
+#55 := (not true)
+#58 := (iff #55 false)
+#59 := [rewrite]: #58
+#56 := (iff #50 #55)
+#53 := (iff #45 true)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#51 := (iff #14 #50)
+#48 := (iff #13 #45)
+#41 := (implies #32 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #13 #41)
+#39 := (iff #12 #38)
+#36 := (iff #11 #35)
+#37 := [rewrite]: #36
+#33 := (iff #9 #32)
+#34 := [rewrite]: #33
+#40 := [monotonicity #34 #37]: #39
+#43 := [monotonicity #34 #40]: #42
+#49 := [trans #43 #47]: #48
+#52 := [monotonicity #49]: #51
+#63 := [trans #52 #61]: #62
+#31 := [asserted]: #14
+[mp #31 #63]: false
+unsat
+058976b8c2e64c1e2ac12f9c692acba51ae0cd04 35 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S2 S1)
+decl f4 :: S2
+#8 := f4
+#9 := (f3 f4)
+#10 := (= #9 f1)
+#11 := (not #10)
+#12 := (ite #10 #10 #11)
+#13 := (not #12)
+#49 := (iff #13 false)
+#1 := true
+#44 := (not true)
+#47 := (iff #44 false)
+#48 := [rewrite]: #47
+#45 := (iff #13 #44)
+#42 := (iff #12 true)
+#31 := (= f1 #9)
+#34 := (not #31)
+#37 := (ite #31 #31 #34)
+#40 := (iff #37 true)
+#41 := [rewrite]: #40
+#38 := (iff #12 #37)
+#35 := (iff #11 #34)
+#32 := (iff #10 #31)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#39 := [monotonicity #33 #33 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#30 := [asserted]: #13
+[mp #30 #50]: false
+unsat
+643e3befcc368aa36d51d58e2d963c26629d80a2 53 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#12 := (or #11 #9)
+#13 := (implies #9 #12)
+#14 := (not #13)
+#67 := (iff #14 false)
+#35 := (= f1 f4)
+#32 := (= f1 f3)
+#41 := (or #32 #35)
+#49 := (not #32)
+#50 := (or #49 #41)
+#55 := (not #50)
+#65 := (iff #55 false)
+#1 := true
+#60 := (not true)
+#63 := (iff #60 false)
+#64 := [rewrite]: #63
+#61 := (iff #55 #60)
+#58 := (iff #50 true)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#66 := [trans #62 #64]: #65
+#56 := (iff #14 #55)
+#53 := (iff #13 #50)
+#46 := (implies #32 #41)
+#51 := (iff #46 #50)
+#52 := [rewrite]: #51
+#47 := (iff #13 #46)
+#44 := (iff #12 #41)
+#38 := (or #35 #32)
+#42 := (iff #38 #41)
+#43 := [rewrite]: #42
+#39 := (iff #12 #38)
+#33 := (iff #9 #32)
+#34 := [rewrite]: #33
+#36 := (iff #11 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37 #34]: #39
+#45 := [trans #40 #43]: #44
+#48 := [monotonicity #34 #45]: #47
+#54 := [trans #48 #52]: #53
+#57 := [monotonicity #54]: #56
+#68 := [trans #57 #66]: #67
+#31 := [asserted]: #14
+[mp #31 #68]: false
+unsat
+afa454836bb1ada63b9eb89ea6c38269311b8712 56 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f4 :: S1
+#11 := f4
+#12 := (= f4 f1)
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#13 := (implies #9 #12)
+#10 := (not #9)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#70 := (iff #15 false)
+#39 := (= f1 f4)
+#33 := (= f1 f3)
+#36 := (not #33)
+#45 := (or #36 #39)
+#53 := (or #33 #45)
+#58 := (not #53)
+#68 := (iff #58 false)
+#1 := true
+#63 := (not true)
+#66 := (iff #63 false)
+#67 := [rewrite]: #66
+#64 := (iff #58 #63)
+#61 := (iff #53 true)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#69 := [trans #65 #67]: #68
+#59 := (iff #15 #58)
+#56 := (iff #14 #53)
+#50 := (implies #36 #45)
+#54 := (iff #50 #53)
+#55 := [rewrite]: #54
+#51 := (iff #14 #50)
+#48 := (iff #13 #45)
+#42 := (implies #33 #39)
+#46 := (iff #42 #45)
+#47 := [rewrite]: #46
+#43 := (iff #13 #42)
+#40 := (iff #12 #39)
+#41 := [rewrite]: #40
+#34 := (iff #9 #33)
+#35 := [rewrite]: #34
+#44 := [monotonicity #35 #41]: #43
+#49 := [trans #44 #47]: #48
+#37 := (iff #10 #36)
+#38 := [monotonicity #35]: #37
+#52 := [monotonicity #38 #49]: #51
+#57 := [trans #52 #55]: #56
+#60 := [monotonicity #57]: #59
+#71 := [trans #60 #69]: #70
+#32 := [asserted]: #15
+[mp #32 #71]: false
+unsat
+a96584af88e2b610042d1242f930cc6c51587530 54 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#12 := (implies #11 #9)
+#13 := (implies #9 #12)
+#14 := (not #13)
+#68 := (iff #14 false)
+#35 := (= f1 f4)
+#41 := (not #35)
+#32 := (= f1 f3)
+#42 := (or #32 #41)
+#50 := (not #32)
+#51 := (or #50 #42)
+#56 := (not #51)
+#66 := (iff #56 false)
+#1 := true
+#61 := (not true)
+#64 := (iff #61 false)
+#65 := [rewrite]: #64
+#62 := (iff #56 #61)
+#59 := (iff #51 true)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#67 := [trans #63 #65]: #66
+#57 := (iff #14 #56)
+#54 := (iff #13 #51)
+#47 := (implies #32 #42)
+#52 := (iff #47 #51)
+#53 := [rewrite]: #52
+#48 := (iff #13 #47)
+#45 := (iff #12 #42)
+#38 := (implies #35 #32)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #12 #38)
+#33 := (iff #9 #32)
+#34 := [rewrite]: #33
+#36 := (iff #11 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37 #34]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #34 #46]: #48
+#55 := [trans #49 #53]: #54
+#58 := [monotonicity #55]: #57
+#69 := [trans #58 #67]: #68
+#31 := [asserted]: #14
+[mp #31 #69]: false
+unsat
+5c717bc0664ca45c994a6287285cf080d3a78d66 3 0
+#2 := false
+[asserted]: false
+unsat
+7a045a1848b4b2a8d896e622d8b797488f2ae65b 89 0
+#2 := false
+decl f4 :: S1
+#10 := f4
+decl f1 :: S1
+#4 := f1
+#38 := (= f1 f4)
+decl f3 :: S1
+#8 := f3
+#35 := (= f1 f3)
+#47 := (not #35)
+#48 := (or #47 #38)
+#106 := (iff #48 false)
+#101 := (or false false)
+#104 := (iff #101 false)
+#105 := [rewrite]: #104
+#102 := (iff #48 #101)
+#92 := (iff #38 false)
+#41 := (not #38)
+#53 := (not #48)
+#75 := (or #47 #38 #53)
+#78 := (not #75)
+#11 := (= f4 f1)
+#9 := (= f3 f1)
+#13 := (implies #9 #11)
+#14 := (not #13)
+#12 := (not #11)
+#15 := (implies #12 #14)
+#16 := (implies #9 #15)
+#17 := (not #16)
+#81 := (iff #17 #78)
+#59 := (or #38 #53)
+#67 := (or #47 #59)
+#72 := (not #67)
+#79 := (iff #72 #78)
+#76 := (iff #67 #75)
+#77 := [rewrite]: #76
+#80 := [monotonicity #77]: #79
+#73 := (iff #17 #72)
+#70 := (iff #16 #67)
+#64 := (implies #35 #59)
+#68 := (iff #64 #67)
+#69 := [rewrite]: #68
+#65 := (iff #16 #64)
+#62 := (iff #15 #59)
+#56 := (implies #41 #53)
+#60 := (iff #56 #59)
+#61 := [rewrite]: #60
+#57 := (iff #15 #56)
+#54 := (iff #14 #53)
+#51 := (iff #13 #48)
+#44 := (implies #35 #38)
+#49 := (iff #44 #48)
+#50 := [rewrite]: #49
+#45 := (iff #13 #44)
+#39 := (iff #11 #38)
+#40 := [rewrite]: #39
+#36 := (iff #9 #35)
+#37 := [rewrite]: #36
+#46 := [monotonicity #37 #40]: #45
+#52 := [trans #46 #50]: #51
+#55 := [monotonicity #52]: #54
+#42 := (iff #12 #41)
+#43 := [monotonicity #40]: #42
+#58 := [monotonicity #43 #55]: #57
+#63 := [trans #58 #61]: #62
+#66 := [monotonicity #37 #63]: #65
+#71 := [trans #66 #69]: #70
+#74 := [monotonicity #71]: #73
+#82 := [trans #74 #80]: #81
+#34 := [asserted]: #17
+#83 := [mp #34 #82]: #78
+#85 := [not-or-elim #83]: #41
+#93 := [iff-false #85]: #92
+#99 := (iff #47 false)
+#1 := true
+#94 := (not true)
+#97 := (iff #94 false)
+#98 := [rewrite]: #97
+#95 := (iff #47 #94)
+#90 := (iff #35 true)
+#84 := [not-or-elim #83]: #35
+#91 := [iff-true #84]: #90
+#96 := [monotonicity #91]: #95
+#100 := [trans #96 #98]: #99
+#103 := [monotonicity #100 #93]: #102
+#107 := [trans #103 #105]: #106
+#86 := [not-or-elim #83]: #48
+[mp #86 #107]: false
+unsat
+053f09fab3ab7dadcbb50216d87e6bbc9c52b970 18 0
+#2 := false
+#9 := 1::int
+#8 := 0::int
+#10 := (< 0::int 1::int)
+#11 := (not #10)
+#38 := (iff #11 false)
+#1 := true
+#33 := (not true)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (iff #10 true)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#28 := [asserted]: #11
+[mp #28 #39]: false
+unsat
+0e7bbb17f9ad81b8c781d5e0b8798e9474d3fd3d 31 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S2 S1)
+decl f4 :: S2
+#8 := f4
+#9 := (f3 f4)
+#10 := (= #9 f1)
+#11 := (iff #10 #10)
+#12 := (not #11)
+#45 := (iff #12 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #12 #40)
+#38 := (iff #11 true)
+#30 := (= f1 #9)
+#33 := (iff #30 #30)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (iff #10 #30)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32 #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#29 := [asserted]: #12
+[mp #29 #46]: false
+unsat
+4c7b1fbd03c5846dd635cd3b84120a6da09efeaf 18 0
+#2 := false
+#9 := 1::int
+#8 := 0::int
+#10 := (<= 0::int 1::int)
+#11 := (not #10)
+#38 := (iff #11 false)
+#1 := true
+#33 := (not true)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (iff #10 true)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#28 := [asserted]: #11
+[mp #28 #39]: false
+unsat
+5ae11eff5645b77b5c2e32c0104eec8daf365335 57 0
+#2 := false
+decl f3 :: (-> S2 S1)
+decl f4 :: S2
+#8 := f4
+#9 := (f3 f4)
+decl f1 :: S1
+#4 := f1
+#33 := (= f1 #9)
+#45 := (not #33)
+decl f5 :: (-> S2 S1)
+#11 := (f5 f4)
+#36 := (= f1 #11)
+#46 := (iff #36 #45)
+#58 := (not #46)
+#73 := (iff #58 false)
+#1 := true
+#68 := (not true)
+#71 := (iff #68 false)
+#72 := [rewrite]: #71
+#69 := (iff #58 #68)
+#66 := (iff #46 true)
+#39 := (iff #33 #36)
+#55 := (not #39)
+#63 := (iff #55 #46)
+#64 := [rewrite]: #63
+#47 := (or #39 #46)
+#52 := (not #47)
+#12 := (= #11 f1)
+#10 := (= #9 f1)
+#13 := (iff #10 #12)
+#14 := (implies #13 #13)
+#15 := (not #14)
+#53 := (iff #15 #52)
+#50 := (iff #14 #47)
+#42 := (implies #39 #39)
+#48 := (iff #42 #47)
+#49 := [rewrite]: #48
+#43 := (iff #14 #42)
+#40 := (iff #13 #39)
+#37 := (iff #12 #36)
+#38 := [rewrite]: #37
+#34 := (iff #10 #33)
+#35 := [rewrite]: #34
+#41 := [monotonicity #35 #38]: #40
+#44 := [monotonicity #41 #41]: #43
+#51 := [trans #44 #49]: #50
+#54 := [monotonicity #51]: #53
+#32 := [asserted]: #15
+#57 := [mp #32 #54]: #52
+#56 := [not-or-elim #57]: #55
+#65 := [mp #56 #64]: #46
+#67 := [iff-true #65]: #66
+#70 := [monotonicity #67]: #69
+#74 := [trans #70 #72]: #73
+#59 := [not-or-elim #57]: #58
+[mp #59 #74]: false
+unsat
+0e8cf46a62144e97d595936465b386e89d7c65da 18 0
+#2 := false
+#9 := 2345678901::int
+#8 := 123456789::int
+#10 := (< 123456789::int 2345678901::int)
+#11 := (not #10)
+#38 := (iff #11 false)
+#1 := true
+#33 := (not true)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (iff #10 true)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#28 := [asserted]: #11
+[mp #28 #39]: false
+unsat
+3dd3fd8b3a088daf54f3fd06483c978f1b0a5c94 50 0
+#2 := false
+decl f5 :: S2
+#11 := f5
+decl f3 :: S2
+#8 := f3
+#13 := (= f3 f5)
+decl f4 :: S2
+#9 := f4
+#12 := (= f4 f5)
+#74 := (iff #12 #13)
+#72 := (iff #13 #12)
+#10 := (= f3 f4)
+#34 := (not #12)
+#41 := (not #10)
+#50 := (or #41 #34 #13)
+#53 := (not #50)
+#14 := (implies #12 #13)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#56 := (iff #16 #53)
+#35 := (or #34 #13)
+#42 := (or #41 #35)
+#47 := (not #42)
+#54 := (iff #47 #53)
+#51 := (iff #42 #50)
+#52 := [rewrite]: #51
+#55 := [monotonicity #52]: #54
+#48 := (iff #16 #47)
+#45 := (iff #15 #42)
+#38 := (implies #10 #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #15 #38)
+#36 := (iff #14 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #46]: #48
+#57 := [trans #49 #55]: #56
+#33 := [asserted]: #16
+#58 := [mp #33 #57]: #53
+#59 := [not-or-elim #58]: #10
+#73 := [monotonicity #59]: #72
+#75 := [symm #73]: #74
+#60 := [not-or-elim #58]: #12
+#70 := [mp #60 #75]: #13
+#61 := (not #13)
+#62 := [not-or-elim #58]: #61
+[unit-resolution #62 #70]: false
+unsat
+def4bedc74a497f81535120f8eb3d73a2126f39d 30 0
+#2 := false
+decl f3 :: (-> int S2)
+#25 := 1::int
+#28 := (f3 1::int)
+#13 := 0::int
+#26 := (+ 0::int 1::int)
+#27 := (f3 #26)
+#29 := (= #27 #28)
+#30 := (not #29)
+#148 := (iff #30 false)
+#1 := true
+#143 := (not true)
+#146 := (iff #143 false)
+#147 := [rewrite]: #146
+#144 := (iff #30 #143)
+#141 := (iff #29 true)
+#136 := (= #28 #28)
+#139 := (iff #136 true)
+#140 := [rewrite]: #139
+#137 := (iff #29 #136)
+#133 := (= #26 1::int)
+#134 := [rewrite]: #133
+#135 := [monotonicity #134]: #29
+#138 := [monotonicity #135]: #137
+#142 := [trans #138 #140]: #141
+#145 := [monotonicity #142]: #144
+#149 := [trans #145 #147]: #148
+#132 := [asserted]: #30
+[mp #132 #149]: false
+unsat
+aff8e33d3cf01d5044aa16af4e5d375f7bc7128f 27 0
+#2 := false
+decl f5 :: (-> S2 S3)
+decl f4 :: S2
+#9 := f4
+#12 := (f5 f4)
+decl f3 :: S2
+#8 := f3
+#11 := (f5 f3)
+#13 := (= #11 #12)
+#10 := (= f3 f4)
+#33 := (not #10)
+#34 := (or #33 #13)
+#37 := (not #34)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#38 := (iff #15 #37)
+#35 := (iff #14 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#32 := [asserted]: #15
+#42 := [mp #32 #39]: #37
+#40 := [not-or-elim #42]: #10
+#51 := [monotonicity #40]: #13
+#41 := (not #13)
+#43 := [not-or-elim #42]: #41
+[unit-resolution #43 #51]: false
+unsat
+a7cad8328ffe36efffb86c5a300175a81ec9473e 225 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f3 :: (-> int S2)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#27 := 1::int
+#135 := (+ 1::int #26)
+#138 := (f3 #135)
+#141 := (f4 #138)
+#150 := -1::int
+#153 := (* -1::int #141)
+#154 := (+ #26 #153)
+#152 := (>= #154 0::int)
+#28 := (+ #26 1::int)
+#29 := (f3 #28)
+#30 := (f4 #29)
+#31 := (< #26 #30)
+#32 := (not #31)
+#164 := (iff #32 #152)
+#144 := (< #26 #141)
+#147 := (not #144)
+#162 := (iff #147 #152)
+#151 := (not #152)
+#157 := (not #151)
+#160 := (iff #157 #152)
+#161 := [rewrite]: #160
+#158 := (iff #147 #157)
+#155 := (iff #144 #151)
+#156 := [rewrite]: #155
+#159 := [monotonicity #156]: #158
+#163 := [trans #159 #161]: #162
+#148 := (iff #32 #147)
+#145 := (iff #31 #144)
+#142 := (= #30 #141)
+#139 := (= #29 #138)
+#136 := (= #28 #135)
+#137 := [rewrite]: #136
+#140 := [monotonicity #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [monotonicity #146]: #148
+#165 := [trans #149 #163]: #164
+#134 := [asserted]: #32
+#166 := [mp #134 #165]: #152
+#347 := (>= #141 0::int)
+#274 := (= #141 0::int)
+#642 := (>= #26 -1::int)
+#649 := (not #642)
+#648 := (= #154 -1::int)
+#336 := (not #648)
+#630 := (<= #154 -1::int)
+#621 := (not #630)
+#625 := (or #621 #151)
+#622 := [th-lemma]: #625
+#626 := [unit-resolution #622 #166]: #621
+#337 := (or #336 #630)
+#338 := [th-lemma]: #337
+#339 := [unit-resolution #338 #626]: #336
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#662 := (pattern #16)
+#75 := (>= #14 0::int)
+#76 := (not #75)
+#17 := (f4 #16)
+#57 := (= #14 #17)
+#82 := (or #57 #76)
+#663 := (forall (vars (?v0 int)) (:pat #662) #82)
+#87 := (forall (vars (?v0 int)) #82)
+#666 := (iff #87 #663)
+#664 := (iff #82 #82)
+#665 := [refl]: #664
+#667 := [quant-intro #665]: #666
+#170 := (~ #87 #87)
+#167 := (~ #82 #82)
+#182 := [refl]: #167
+#171 := [nnf-pos #182]: #170
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#90 := (iff #20 #87)
+#64 := (not #15)
+#65 := (or #64 #57)
+#70 := (forall (vars (?v0 int)) #65)
+#88 := (iff #70 #87)
+#85 := (iff #65 #82)
+#79 := (or #76 #57)
+#83 := (iff #79 #82)
+#84 := [rewrite]: #83
+#80 := (iff #65 #79)
+#77 := (iff #64 #76)
+#73 := (iff #15 #75)
+#74 := [rewrite]: #73
+#78 := [monotonicity #74]: #77
+#81 := [monotonicity #78]: #80
+#86 := [trans #81 #84]: #85
+#89 := [quant-intro #86]: #88
+#71 := (iff #20 #70)
+#68 := (iff #19 #65)
+#61 := (implies #15 #57)
+#66 := (iff #61 #65)
+#67 := [rewrite]: #66
+#62 := (iff #19 #61)
+#59 := (iff #18 #57)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#69 := [trans #63 #67]: #68
+#72 := [quant-intro #69]: #71
+#91 := [trans #72 #89]: #90
+#56 := [asserted]: #20
+#92 := [mp #56 #91]: #87
+#183 := [mp~ #92 #171]: #87
+#668 := [mp #183 #667]: #663
+#645 := (not #663)
+#288 := (or #645 #649 #648)
+#330 := (>= #135 0::int)
+#331 := (not #330)
+#311 := (= #135 #141)
+#646 := (or #311 #331)
+#629 := (or #645 #646)
+#633 := (iff #629 #288)
+#643 := (or #649 #648)
+#293 := (or #645 #643)
+#631 := (iff #293 #288)
+#632 := [rewrite]: #631
+#294 := (iff #629 #293)
+#644 := (iff #646 #643)
+#652 := (or #648 #649)
+#303 := (iff #652 #643)
+#308 := [rewrite]: #303
+#647 := (iff #646 #652)
+#650 := (iff #331 #649)
+#316 := (iff #330 #642)
+#317 := [rewrite]: #316
+#651 := [monotonicity #317]: #650
+#305 := (iff #311 #648)
+#435 := [rewrite]: #305
+#653 := [monotonicity #435 #651]: #647
+#304 := [trans #653 #308]: #644
+#295 := [monotonicity #304]: #294
+#634 := [trans #295 #632]: #633
+#292 := [quant-inst]: #629
+#635 := [mp #292 #634]: #288
+#617 := [unit-resolution #635 #668 #339]: #649
+#22 := (= #17 0::int)
+#123 := (or #22 #75)
+#669 := (forall (vars (?v0 int)) (:pat #662) #123)
+#128 := (forall (vars (?v0 int)) #123)
+#672 := (iff #128 #669)
+#670 := (iff #123 #123)
+#671 := [refl]: #670
+#673 := [quant-intro #671]: #672
+#172 := (~ #128 #128)
+#184 := (~ #123 #123)
+#185 := [refl]: #184
+#173 := [nnf-pos #185]: #172
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#131 := (iff #24 #128)
+#94 := (= 0::int #17)
+#100 := (not #21)
+#101 := (or #100 #94)
+#106 := (forall (vars (?v0 int)) #101)
+#129 := (iff #106 #128)
+#126 := (iff #101 #123)
+#120 := (or #75 #22)
+#124 := (iff #120 #123)
+#125 := [rewrite]: #124
+#121 := (iff #101 #120)
+#118 := (iff #94 #22)
+#119 := [rewrite]: #118
+#116 := (iff #100 #75)
+#111 := (not #76)
+#114 := (iff #111 #75)
+#115 := [rewrite]: #114
+#112 := (iff #100 #111)
+#109 := (iff #21 #76)
+#110 := [rewrite]: #109
+#113 := [monotonicity #110]: #112
+#117 := [trans #113 #115]: #116
+#122 := [monotonicity #117 #119]: #121
+#127 := [trans #122 #125]: #126
+#130 := [quant-intro #127]: #129
+#107 := (iff #24 #106)
+#104 := (iff #23 #101)
+#97 := (implies #21 #94)
+#102 := (iff #97 #101)
+#103 := [rewrite]: #102
+#98 := (iff #23 #97)
+#95 := (iff #22 #94)
+#96 := [rewrite]: #95
+#99 := [monotonicity #96]: #98
+#105 := [trans #99 #103]: #104
+#108 := [quant-intro #105]: #107
+#132 := [trans #108 #130]: #131
+#93 := [asserted]: #24
+#133 := [mp #93 #132]: #128
+#186 := [mp~ #133 #173]: #128
+#674 := [mp #186 #673]: #669
+#640 := (not #669)
+#638 := (or #640 #274 #642)
+#637 := (or #274 #330)
+#641 := (or #640 #637)
+#247 := (iff #641 #638)
+#639 := (or #274 #642)
+#628 := (or #640 #639)
+#352 := (iff #628 #638)
+#353 := [rewrite]: #352
+#350 := (iff #641 #628)
+#279 := (iff #637 #639)
+#280 := [monotonicity #317]: #279
+#351 := [monotonicity #280]: #350
+#623 := [trans #351 #353]: #247
+#627 := [quant-inst]: #641
+#624 := [mp #627 #623]: #638
+#618 := [unit-resolution #624 #674 #617]: #274
+#333 := (not #274)
+#615 := (or #333 #347)
+#619 := [th-lemma]: #615
+#616 := [unit-resolution #619 #618]: #347
+[th-lemma #617 #616 #166]: false
+unsat
+38d6568bcb3518204f41c136744fc9a94ac2289f 73 0
+#2 := false
+decl f3 :: (-> S1 S1)
+decl f4 :: S1
+#12 := f4
+#13 := (f3 f4)
+decl f1 :: S1
+#4 := f1
+#42 := (= f1 #13)
+#73 := (not #42)
+#45 := (= f1 f4)
+#8 := (:var 0 S1)
+#9 := (f3 #8)
+#36 := (= f1 #9)
+#39 := (forall (vars (?v0 S1)) #36)
+#54 := (not #39)
+#63 := (or #54 #42 #45)
+#66 := (not #63)
+#15 := (= f4 f1)
+#14 := (= #13 f1)
+#16 := (or #14 #15)
+#10 := (= #9 f1)
+#11 := (forall (vars (?v0 S1)) #10)
+#17 := (implies #11 #16)
+#18 := (not #17)
+#69 := (iff #18 #66)
+#48 := (or #42 #45)
+#55 := (or #54 #48)
+#60 := (not #55)
+#67 := (iff #60 #66)
+#64 := (iff #55 #63)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#61 := (iff #18 #60)
+#58 := (iff #17 #55)
+#51 := (implies #39 #48)
+#56 := (iff #51 #55)
+#57 := [rewrite]: #56
+#52 := (iff #17 #51)
+#49 := (iff #16 #48)
+#46 := (iff #15 #45)
+#47 := [rewrite]: #46
+#43 := (iff #14 #42)
+#44 := [rewrite]: #43
+#50 := [monotonicity #44 #47]: #49
+#40 := (iff #11 #39)
+#37 := (iff #10 #36)
+#38 := [rewrite]: #37
+#41 := [quant-intro #38]: #40
+#53 := [monotonicity #41 #50]: #52
+#59 := [trans #53 #57]: #58
+#62 := [monotonicity #59]: #61
+#70 := [trans #62 #68]: #69
+#35 := [asserted]: #18
+#71 := [mp #35 #70]: #66
+#74 := [not-or-elim #71]: #73
+#560 := (pattern #9)
+#561 := (forall (vars (?v0 S1)) (:pat #560) #36)
+#564 := (iff #39 #561)
+#562 := (iff #36 #36)
+#563 := [refl]: #562
+#565 := [quant-intro #563]: #564
+#88 := (~ #39 #39)
+#86 := (~ #36 #36)
+#87 := [refl]: #86
+#89 := [nnf-pos #87]: #88
+#72 := [not-or-elim #71]: #39
+#79 := [mp~ #72 #89]: #39
+#566 := [mp #79 #565]: #561
+#145 := (not #561)
+#232 := (or #145 #42)
+#146 := [quant-inst]: #232
+[unit-resolution #146 #566 #74]: false
+unsat
+efee40d670c214f978e2ecbd05f202f54d2c08ae 106 0
+#2 := false
+decl f3 :: (-> S2 S2 S1)
+decl ?v0!0 :: S2
+#72 := ?v0!0
+#83 := (f3 ?v0!0 ?v0!0)
+decl f1 :: S1
+#4 := f1
+#75 := (= f1 #83)
+#76 := (not #75)
+#9 := (:var 0 S2)
+#16 := (f3 #9 #9)
+#50 := (= f1 #16)
+#53 := (forall (vars (?v0 S2)) #50)
+#69 := (not #53)
+#84 := (~ #69 #76)
+#85 := [sk]: #84
+#8 := (:var 1 S2)
+#12 := (f3 #9 #8)
+#41 := (= f1 #12)
+#10 := (f3 #8 #9)
+#38 := (= f1 #10)
+#44 := (and #38 #41)
+#47 := (forall (vars (?v0 S2) (?v1 S2)) #44)
+#59 := (not #47)
+#60 := (or #59 #53)
+#65 := (not #60)
+#17 := (= #16 f1)
+#18 := (forall (vars (?v0 S2)) #17)
+#13 := (= #12 f1)
+#11 := (= #10 f1)
+#14 := (and #11 #13)
+#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
+#19 := (implies #15 #18)
+#20 := (not #19)
+#66 := (iff #20 #65)
+#63 := (iff #19 #60)
+#56 := (implies #47 #53)
+#61 := (iff #56 #60)
+#62 := [rewrite]: #61
+#57 := (iff #19 #56)
+#54 := (iff #18 #53)
+#51 := (iff #17 #50)
+#52 := [rewrite]: #51
+#55 := [quant-intro #52]: #54
+#48 := (iff #15 #47)
+#45 := (iff #14 #44)
+#42 := (iff #13 #41)
+#43 := [rewrite]: #42
+#39 := (iff #11 #38)
+#40 := [rewrite]: #39
+#46 := [monotonicity #40 #43]: #45
+#49 := [quant-intro #46]: #48
+#58 := [monotonicity #49 #55]: #57
+#64 := [trans #58 #62]: #63
+#67 := [monotonicity #64]: #66
+#37 := [asserted]: #20
+#70 := [mp #37 #67]: #65
+#71 := [not-or-elim #70]: #69
+#88 := [mp~ #71 #85]: #76
+#577 := (pattern #12)
+#576 := (pattern #10)
+#87 := (not #41)
+#86 := (not #38)
+#89 := (or #86 #87)
+#90 := (not #89)
+#578 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #576 #577) #90)
+#93 := (forall (vars (?v0 S2) (?v1 S2)) #90)
+#581 := (iff #93 #578)
+#579 := (iff #90 #90)
+#580 := [refl]: #579
+#582 := [quant-intro #580]: #581
+#94 := (iff #47 #93)
+#91 := (iff #44 #90)
+#92 := [rewrite]: #91
+#95 := [quant-intro #92]: #94
+#81 := (~ #47 #47)
+#79 := (~ #44 #44)
+#80 := [refl]: #79
+#82 := [nnf-pos #80]: #81
+#68 := [not-or-elim #70]: #47
+#74 := [mp~ #68 #82]: #47
+#96 := [mp #74 #95]: #93
+#583 := [mp #96 #582]: #578
+#250 := (not #578)
+#254 := (or #250 #75)
+#160 := (or #76 #76)
+#247 := (not #160)
+#233 := (or #250 #247)
+#570 := (iff #233 #254)
+#357 := (iff #254 #254)
+#564 := [rewrite]: #357
+#180 := (iff #247 #75)
+#162 := (not #76)
+#251 := (iff #162 #75)
+#252 := [rewrite]: #251
+#249 := (iff #247 #162)
+#161 := (iff #160 #76)
+#248 := [rewrite]: #161
+#240 := [monotonicity #248]: #249
+#253 := [trans #240 #252]: #180
+#227 := [monotonicity #253]: #570
+#238 := [trans #227 #564]: #570
+#568 := [quant-inst]: #233
+#239 := [mp #568 #238]: #254
+[unit-resolution #239 #583 #88]: false
+unsat
+592c5fbbffdc88780deea852b5e3007b86266cec 428 0
+#2 := false
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#30 := f6
+#31 := (f4 f6)
+#27 := 1::int
+#146 := (+ 1::int #31)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#140 := (+ 1::int #26)
+#443 := (= #140 #146)
+#422 := (not #443)
+decl f3 :: (-> int S2)
+#149 := (f3 #146)
+#143 := (f3 #140)
+#152 := (= #143 #149)
+#419 := [hypothesis]: #443
+#420 := [monotonicity #419]: #152
+#237 := (not #152)
+#35 := (= f5 f6)
+#644 := (f3 #31)
+#463 := (= #644 f6)
+#646 := (= f6 #644)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#652 := (pattern #9)
+#10 := (f3 #9)
+#55 := (= #8 #10)
+#653 := (forall (vars (?v0 S2)) (:pat #652) #55)
+#58 := (forall (vars (?v0 S2)) #55)
+#654 := (iff #58 #653)
+#656 := (iff #653 #653)
+#657 := [rewrite]: #656
+#655 := [rewrite]: #654
+#658 := [trans #655 #657]: #654
+#177 := (~ #58 #58)
+#175 := (~ #55 #55)
+#176 := [refl]: #175
+#178 := [nnf-pos #176]: #177
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#59 := (iff #12 #58)
+#56 := (iff #11 #55)
+#57 := [rewrite]: #56
+#60 := [quant-intro #57]: #59
+#54 := [asserted]: #12
+#63 := [mp #54 #60]: #58
+#166 := [mp~ #63 #178]: #58
+#659 := [mp #166 #658]: #653
+#302 := (not #653)
+#647 := (or #302 #646)
+#648 := [quant-inst]: #647
+#548 := [unit-resolution #648 #659]: #646
+#464 := [symm #548]: #463
+#465 := (= f5 #644)
+#329 := (f3 #26)
+#461 := (= #329 #644)
+#458 := (= #26 #31)
+#651 := -1::int
+#649 := (f4 #143)
+#641 := (* -1::int #649)
+#300 := (+ #26 #641)
+#639 := (<= #300 -1::int)
+#305 := (= #300 -1::int)
+#643 := (>= #26 -1::int)
+#13 := 0::int
+#626 := (= #649 0::int)
+#516 := (not #626)
+#330 := (f4 #149)
+#593 := (= #330 0::int)
+#505 := (not #593)
+#496 := (iff #505 #516)
+#515 := (iff #593 #626)
+#513 := (iff #626 #593)
+#509 := (= #649 #330)
+#36 := (not #35)
+#535 := [hypothesis]: #36
+#328 := (or #35 #152)
+#158 := (iff #36 #152)
+#32 := (+ #31 1::int)
+#33 := (f3 #32)
+#28 := (+ #26 1::int)
+#29 := (f3 #28)
+#34 := (= #29 #33)
+#37 := (iff #34 #36)
+#161 := (iff #37 #158)
+#155 := (iff #152 #36)
+#159 := (iff #155 #158)
+#160 := [rewrite]: #159
+#156 := (iff #37 #155)
+#153 := (iff #34 #152)
+#150 := (= #33 #149)
+#147 := (= #32 #146)
+#148 := [rewrite]: #147
+#151 := [monotonicity #148]: #150
+#144 := (= #29 #143)
+#141 := (= #28 #140)
+#142 := [rewrite]: #141
+#145 := [monotonicity #142]: #144
+#154 := [monotonicity #145 #151]: #153
+#157 := [monotonicity #154]: #156
+#162 := [trans #157 #160]: #161
+#139 := [asserted]: #37
+#165 := [mp #139 #162]: #158
+#322 := (not #158)
+#326 := (or #35 #152 #322)
+#327 := [def-axiom]: #326
+#325 := [unit-resolution #327 #165]: #328
+#508 := [unit-resolution #325 #535]: #152
+#510 := [monotonicity #508]: #509
+#514 := [monotonicity #510]: #513
+#511 := [symm #514]: #515
+#442 := [monotonicity #511]: #496
+#490 := (<= #330 0::int)
+#526 := (not #490)
+#572 := (>= #31 0::int)
+#542 := (= #31 0::int)
+#566 := (f4 #644)
+#573 := (= #566 0::int)
+#544 := (not #572)
+#545 := [hypothesis]: #544
+#558 := (or #572 #573)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#660 := (pattern #16)
+#80 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#128 := (or #22 #80)
+#667 := (forall (vars (?v0 int)) (:pat #660) #128)
+#133 := (forall (vars (?v0 int)) #128)
+#670 := (iff #133 #667)
+#668 := (iff #128 #128)
+#669 := [refl]: #668
+#671 := [quant-intro #669]: #670
+#169 := (~ #133 #133)
+#181 := (~ #128 #128)
+#182 := [refl]: #181
+#170 := [nnf-pos #182]: #169
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#136 := (iff #24 #133)
+#99 := (= 0::int #17)
+#105 := (not #21)
+#106 := (or #105 #99)
+#111 := (forall (vars (?v0 int)) #106)
+#134 := (iff #111 #133)
+#131 := (iff #106 #128)
+#125 := (or #80 #22)
+#129 := (iff #125 #128)
+#130 := [rewrite]: #129
+#126 := (iff #106 #125)
+#123 := (iff #99 #22)
+#124 := [rewrite]: #123
+#121 := (iff #105 #80)
+#81 := (not #80)
+#116 := (not #81)
+#119 := (iff #116 #80)
+#120 := [rewrite]: #119
+#117 := (iff #105 #116)
+#114 := (iff #21 #81)
+#115 := [rewrite]: #114
+#118 := [monotonicity #115]: #117
+#122 := [trans #118 #120]: #121
+#127 := [monotonicity #122 #124]: #126
+#132 := [trans #127 #130]: #131
+#135 := [quant-intro #132]: #134
+#112 := (iff #24 #111)
+#109 := (iff #23 #106)
+#102 := (implies #21 #99)
+#107 := (iff #102 #106)
+#108 := [rewrite]: #107
+#103 := (iff #23 #102)
+#100 := (iff #22 #99)
+#101 := [rewrite]: #100
+#104 := [monotonicity #101]: #103
+#110 := [trans #104 #108]: #109
+#113 := [quant-intro #110]: #112
+#137 := [trans #113 #135]: #136
+#98 := [asserted]: #24
+#138 := [mp #98 #137]: #133
+#183 := [mp~ #138 #170]: #133
+#672 := [mp #183 #671]: #667
+#351 := (not #667)
+#562 := (or #351 #572 #573)
+#557 := (or #573 #572)
+#563 := (or #351 #557)
+#555 := (iff #563 #562)
+#564 := (or #351 #558)
+#553 := (iff #564 #562)
+#554 := [rewrite]: #553
+#550 := (iff #563 #564)
+#560 := (iff #557 #558)
+#561 := [rewrite]: #560
+#551 := [monotonicity #561]: #550
+#552 := [trans #551 #554]: #555
+#559 := [quant-inst]: #563
+#556 := [mp #559 #552]: #562
+#546 := [unit-resolution #556 #672]: #558
+#547 := [unit-resolution #546 #545]: #573
+#538 := (= #31 #566)
+#549 := [monotonicity #548]: #538
+#527 := [trans #549 #547]: #542
+#528 := (not #542)
+#530 := (or #528 #572)
+#531 := [th-lemma]: #530
+#532 := [unit-resolution #531 #545 #527]: false
+#533 := [lemma #532]: #572
+#614 := (* -1::int #330)
+#618 := (+ #31 #614)
+#592 := (<= #618 -1::int)
+#607 := (= #618 -1::int)
+#604 := (>= #31 -1::int)
+#521 := (or #544 #604)
+#517 := [th-lemma]: #521
+#518 := [unit-resolution #517 #533]: #604
+#611 := (not #604)
+#597 := (or #611 #607)
+#62 := (= #14 #17)
+#87 := (or #62 #81)
+#661 := (forall (vars (?v0 int)) (:pat #660) #87)
+#92 := (forall (vars (?v0 int)) #87)
+#664 := (iff #92 #661)
+#662 := (iff #87 #87)
+#663 := [refl]: #662
+#665 := [quant-intro #663]: #664
+#167 := (~ #92 #92)
+#163 := (~ #87 #87)
+#179 := [refl]: #163
+#168 := [nnf-pos #179]: #167
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#95 := (iff #20 #92)
+#69 := (not #15)
+#70 := (or #69 #62)
+#75 := (forall (vars (?v0 int)) #70)
+#93 := (iff #75 #92)
+#90 := (iff #70 #87)
+#84 := (or #81 #62)
+#88 := (iff #84 #87)
+#89 := [rewrite]: #88
+#85 := (iff #70 #84)
+#82 := (iff #69 #81)
+#78 := (iff #15 #80)
+#79 := [rewrite]: #78
+#83 := [monotonicity #79]: #82
+#86 := [monotonicity #83]: #85
+#91 := [trans #86 #89]: #90
+#94 := [quant-intro #91]: #93
+#76 := (iff #20 #75)
+#73 := (iff #19 #70)
+#66 := (implies #15 #62)
+#71 := (iff #66 #70)
+#72 := [rewrite]: #71
+#67 := (iff #19 #66)
+#64 := (iff #18 #62)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#74 := [trans #68 #72]: #73
+#77 := [quant-intro #74]: #76
+#96 := [trans #77 #94]: #95
+#61 := [asserted]: #20
+#97 := [mp #61 #96]: #92
+#180 := [mp~ #97 #168]: #92
+#666 := [mp #180 #665]: #661
+#631 := (not #661)
+#595 := (or #631 #611 #607)
+#615 := (>= #146 0::int)
+#616 := (not #615)
+#613 := (= #146 #330)
+#617 := (or #613 #616)
+#601 := (or #631 #617)
+#588 := (iff #601 #595)
+#596 := (or #631 #597)
+#434 := (iff #596 #595)
+#435 := [rewrite]: #434
+#603 := (iff #601 #596)
+#600 := (iff #617 #597)
+#453 := (or #607 #611)
+#598 := (iff #453 #597)
+#599 := [rewrite]: #598
+#454 := (iff #617 #453)
+#606 := (iff #616 #611)
+#605 := (iff #615 #604)
+#610 := [rewrite]: #605
+#612 := [monotonicity #610]: #606
+#608 := (iff #613 #607)
+#609 := [rewrite]: #608
+#455 := [monotonicity #609 #612]: #454
+#594 := [trans #455 #599]: #600
+#432 := [monotonicity #594]: #603
+#589 := [trans #432 #435]: #588
+#602 := [quant-inst]: #601
+#591 := [mp #602 #589]: #595
+#519 := [unit-resolution #591 #666]: #597
+#522 := [unit-resolution #519 #518]: #607
+#523 := (not #607)
+#524 := (or #523 #592)
+#525 := [th-lemma]: #524
+#520 := [unit-resolution #525 #522]: #592
+#499 := (not #592)
+#500 := (or #526 #544 #499)
+#501 := [th-lemma]: #500
+#394 := [unit-resolution #501 #520 #533]: #526
+#506 := (or #505 #490)
+#507 := [th-lemma]: #506
+#512 := [unit-resolution #507 #394]: #505
+#497 := [mp #512 #442]: #516
+#348 := (or #626 #643)
+#244 := (or #351 #626 #643)
+#313 := (>= #140 0::int)
+#333 := (or #626 #313)
+#621 := (or #351 #333)
+#624 := (iff #621 #244)
+#344 := (or #351 #348)
+#623 := (iff #344 #244)
+#620 := [rewrite]: #623
+#345 := (iff #621 #344)
+#349 := (iff #333 #348)
+#285 := (iff #313 #643)
+#627 := [rewrite]: #285
+#350 := [monotonicity #627]: #349
+#619 := [monotonicity #350]: #345
+#334 := [trans #619 #620]: #624
+#622 := [quant-inst]: #621
+#335 := [mp #622 #334]: #244
+#478 := [unit-resolution #335 #672]: #348
+#502 := [unit-resolution #478 #497]: #643
+#289 := (not #643)
+#292 := (or #305 #289)
+#632 := (or #631 #305 #289)
+#314 := (not #313)
+#650 := (= #140 #649)
+#645 := (or #650 #314)
+#633 := (or #631 #645)
+#277 := (iff #633 #632)
+#634 := (or #631 #292)
+#637 := (iff #634 #632)
+#276 := [rewrite]: #637
+#271 := (iff #633 #634)
+#629 := (iff #645 #292)
+#290 := (iff #314 #289)
+#291 := [monotonicity #627]: #290
+#642 := (iff #650 #305)
+#301 := [rewrite]: #642
+#630 := [monotonicity #301 #291]: #629
+#635 := [monotonicity #630]: #271
+#638 := [trans #635 #276]: #277
+#628 := [quant-inst]: #633
+#636 := [mp #628 #638]: #632
+#503 := [unit-resolution #636 #666]: #292
+#498 := [unit-resolution #503 #502]: #305
+#504 := (not #305)
+#472 := (or #504 #639)
+#479 := [th-lemma]: #472
+#438 := [unit-resolution #479 #498]: #639
+#625 := (>= #300 -1::int)
+#469 := (or #504 #625)
+#471 := [th-lemma]: #469
+#473 := [unit-resolution #471 #498]: #625
+#590 := (>= #618 -1::int)
+#480 := (or #523 #590)
+#482 := [th-lemma]: #480
+#483 := [unit-resolution #482 #522]: #590
+#540 := (+ #330 #641)
+#534 := (<= #540 0::int)
+#539 := (= #330 #649)
+#484 := [symm #510]: #539
+#494 := (not #539)
+#474 := (or #494 #534)
+#495 := [th-lemma]: #474
+#450 := [unit-resolution #495 #484]: #534
+#529 := (>= #540 0::int)
+#451 := (or #494 #529)
+#456 := [th-lemma]: #451
+#457 := [unit-resolution #456 #484]: #529
+#459 := [th-lemma #457 #450 #483 #520 #473 #438]: #458
+#462 := [monotonicity #459]: #461
+#308 := (= f5 #329)
+#433 := (or #302 #308)
+#640 := [quant-inst]: #433
+#460 := [unit-resolution #640 #659]: #308
+#466 := [trans #460 #462]: #465
+#467 := [trans #466 #464]: #35
+#452 := [unit-resolution #535 #467]: false
+#468 := [lemma #452]: #35
+#324 := (or #36 #237)
+#238 := (or #36 #237 #322)
+#323 := [def-axiom]: #238
+#315 := [unit-resolution #323 #165]: #324
+#449 := [unit-resolution #315 #468]: #237
+#421 := [unit-resolution #449 #420]: false
+#424 := [lemma #421]: #422
+#444 := (* -1::int #146)
+#447 := (+ #140 #444)
+#448 := (<= #447 0::int)
+#429 := (* -1::int #31)
+#430 := (+ #26 #429)
+#437 := (<= #430 0::int)
+#425 := [monotonicity #468]: #458
+#426 := (not #458)
+#268 := (or #426 #437)
+#427 := [th-lemma]: #268
+#423 := [unit-resolution #427 #425]: #437
+#428 := (not #437)
+#407 := (or #448 #428)
+#410 := [th-lemma]: #407
+#414 := [unit-resolution #410 #423]: #448
+#431 := (>= #447 0::int)
+#439 := (>= #430 0::int)
+#416 := (or #426 #439)
+#417 := [th-lemma]: #416
+#415 := [unit-resolution #417 #425]: #439
+#418 := (not #439)
+#406 := (or #431 #418)
+#409 := [th-lemma]: #406
+#411 := [unit-resolution #409 #415]: #431
+#408 := (not #431)
+#412 := (not #448)
+#413 := (or #443 #412 #408)
+#403 := [th-lemma]: #413
+#393 := [unit-resolution #403 #411 #414]: #443
+[unit-resolution #393 #424]: false
+unsat
+8ef67dc17184cdb997c34c282ec976aab91f0c9d 66 0
+#2 := false
+decl f4 :: S1
+#10 := f4
+decl f1 :: S1
+#4 := f1
+#37 := (= f1 f4)
+decl f3 :: S1
+#8 := f3
+#34 := (= f1 f3)
+#40 := (or #34 #37)
+#84 := (iff #40 false)
+#79 := (or false false)
+#82 := (iff #79 false)
+#83 := [rewrite]: #82
+#80 := (iff #40 #79)
+#75 := (iff #37 false)
+#66 := (not #37)
+#43 := (not #34)
+#49 := (and #43 #40)
+#57 := (not #49)
+#58 := (or #37 #57)
+#63 := (not #58)
+#11 := (= f4 f1)
+#9 := (= f3 f1)
+#13 := (not #9)
+#12 := (or #9 #11)
+#14 := (and #12 #13)
+#15 := (implies #14 #11)
+#16 := (not #15)
+#64 := (iff #16 #63)
+#61 := (iff #15 #58)
+#54 := (implies #49 #37)
+#59 := (iff #54 #58)
+#60 := [rewrite]: #59
+#55 := (iff #15 #54)
+#38 := (iff #11 #37)
+#39 := [rewrite]: #38
+#52 := (iff #14 #49)
+#46 := (and #40 #43)
+#50 := (iff #46 #49)
+#51 := [rewrite]: #50
+#47 := (iff #14 #46)
+#44 := (iff #13 #43)
+#35 := (iff #9 #34)
+#36 := [rewrite]: #35
+#45 := [monotonicity #36]: #44
+#41 := (iff #12 #40)
+#42 := [monotonicity #36 #39]: #41
+#48 := [monotonicity #42 #45]: #47
+#53 := [trans #48 #51]: #52
+#56 := [monotonicity #53 #39]: #55
+#62 := [trans #56 #60]: #61
+#65 := [monotonicity #62]: #64
+#33 := [asserted]: #16
+#68 := [mp #33 #65]: #63
+#67 := [not-or-elim #68]: #66
+#76 := [iff-false #67]: #75
+#77 := (iff #34 false)
+#69 := [not-or-elim #68]: #49
+#70 := [and-elim #69]: #43
+#78 := [iff-false #70]: #77
+#81 := [monotonicity #78 #76]: #80
+#85 := [trans #81 #83]: #84
+#71 := [and-elim #69]: #40
+[mp #71 #85]: false
+unsat
+850ee68a24d436c0e8f0323d0c7b40aadee077ac 59 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f6 :: S1
+#15 := f6
+#16 := (= f6 f1)
+decl f5 :: S1
+#13 := f5
+#14 := (= f5 f1)
+#17 := (and #14 #16)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#12 := (and #9 #11)
+#18 := (or #12 #17)
+#19 := (implies #18 #18)
+#20 := (not #19)
+#71 := (iff #20 false)
+#1 := true
+#66 := (not true)
+#69 := (iff #66 false)
+#70 := [rewrite]: #69
+#67 := (iff #20 #66)
+#64 := (iff #19 true)
+#50 := (= f1 f6)
+#47 := (= f1 f5)
+#53 := (and #47 #50)
+#41 := (= f1 f4)
+#38 := (= f1 f3)
+#44 := (and #38 #41)
+#56 := (or #44 #53)
+#59 := (implies #56 #56)
+#62 := (iff #59 true)
+#63 := [rewrite]: #62
+#60 := (iff #19 #59)
+#57 := (iff #18 #56)
+#54 := (iff #17 #53)
+#51 := (iff #16 #50)
+#52 := [rewrite]: #51
+#48 := (iff #14 #47)
+#49 := [rewrite]: #48
+#55 := [monotonicity #49 #52]: #54
+#45 := (iff #12 #44)
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#39 := (iff #9 #38)
+#40 := [rewrite]: #39
+#46 := [monotonicity #40 #43]: #45
+#58 := [monotonicity #46 #55]: #57
+#61 := [monotonicity #58 #58]: #60
+#65 := [trans #61 #63]: #64
+#68 := [monotonicity #65]: #67
+#72 := [trans #68 #70]: #71
+#37 := [asserted]: #20
+[mp #37 #72]: false
+unsat
+ed4c7cfe878e23843083428f8a6f715fbfe495d3 409 0
+#2 := false
+#181 := -1::int
+decl f4 :: (-> S2 int)
+decl f3 :: (-> int S2)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#29 := (+ #26 #28)
+#30 := 1::int
+#145 := (+ 1::int #29)
+#148 := (f3 #145)
+#151 := (f4 #148)
+#676 := (* -1::int #151)
+#336 := (+ #28 #676)
+#341 := (+ #26 #336)
+#280 := (>= #341 -1::int)
+#426 := (not #280)
+#163 := (+ 1::int #28)
+#166 := (f3 #163)
+#169 := (f4 #166)
+#185 := (* -1::int #169)
+#602 := (+ #28 #185)
+#574 := (<= #602 -1::int)
+#612 := (= #602 -1::int)
+#610 := (>= #28 -1::int)
+#13 := 0::int
+#554 := (>= #28 0::int)
+#479 := (= #28 0::int)
+#274 := (f3 #28)
+#557 := (f4 #274)
+#535 := (= #557 0::int)
+#462 := (not #554)
+#458 := [hypothesis]: #462
+#536 := (or #535 #554)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#695 := (pattern #16)
+#85 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#133 := (or #22 #85)
+#702 := (forall (vars (?v0 int)) (:pat #695) #133)
+#138 := (forall (vars (?v0 int)) #133)
+#705 := (iff #138 #702)
+#703 := (iff #133 #133)
+#704 := [refl]: #703
+#706 := [quant-intro #704]: #705
+#205 := (~ #138 #138)
+#217 := (~ #133 #133)
+#218 := [refl]: #217
+#206 := [nnf-pos #218]: #205
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#141 := (iff #24 #138)
+#104 := (= 0::int #17)
+#110 := (not #21)
+#111 := (or #110 #104)
+#116 := (forall (vars (?v0 int)) #111)
+#139 := (iff #116 #138)
+#136 := (iff #111 #133)
+#130 := (or #85 #22)
+#134 := (iff #130 #133)
+#135 := [rewrite]: #134
+#131 := (iff #111 #130)
+#128 := (iff #104 #22)
+#129 := [rewrite]: #128
+#126 := (iff #110 #85)
+#86 := (not #85)
+#121 := (not #86)
+#124 := (iff #121 #85)
+#125 := [rewrite]: #124
+#122 := (iff #110 #121)
+#119 := (iff #21 #86)
+#120 := [rewrite]: #119
+#123 := [monotonicity #120]: #122
+#127 := [trans #123 #125]: #126
+#132 := [monotonicity #127 #129]: #131
+#137 := [trans #132 #135]: #136
+#140 := [quant-intro #137]: #139
+#117 := (iff #24 #116)
+#114 := (iff #23 #111)
+#107 := (implies #21 #104)
+#112 := (iff #107 #111)
+#113 := [rewrite]: #112
+#108 := (iff #23 #107)
+#105 := (iff #22 #104)
+#106 := [rewrite]: #105
+#109 := [monotonicity #106]: #108
+#115 := [trans #109 #113]: #114
+#118 := [quant-intro #115]: #117
+#142 := [trans #118 #140]: #141
+#103 := [asserted]: #24
+#143 := [mp #103 #142]: #138
+#219 := [mp~ #143 #206]: #138
+#707 := [mp #219 #706]: #702
+#371 := (not #702)
+#541 := (or #371 #535 #554)
+#542 := (or #371 #536)
+#543 := (iff #542 #541)
+#544 := [rewrite]: #543
+#547 := [quant-inst]: #542
+#545 := [mp #547 #544]: #541
+#463 := [unit-resolution #545 #707]: #536
+#442 := [unit-resolution #463 #458]: #535
+#449 := (= #28 #557)
+#359 := (= f6 #274)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#687 := (pattern #9)
+#10 := (f3 #9)
+#60 := (= #8 #10)
+#688 := (forall (vars (?v0 S2)) (:pat #687) #60)
+#63 := (forall (vars (?v0 S2)) #60)
+#689 := (iff #63 #688)
+#691 := (iff #688 #688)
+#692 := [rewrite]: #691
+#690 := [rewrite]: #689
+#693 := [trans #690 #692]: #689
+#213 := (~ #63 #63)
+#211 := (~ #60 #60)
+#212 := [refl]: #211
+#214 := [nnf-pos #212]: #213
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#64 := (iff #12 #63)
+#61 := (iff #11 #60)
+#62 := [rewrite]: #61
+#65 := [quant-intro #62]: #64
+#59 := [asserted]: #12
+#68 := [mp #59 #65]: #63
+#202 := [mp~ #68 #214]: #63
+#694 := [mp #202 #693]: #688
+#360 := (not #688)
+#361 := (or #360 #359)
+#365 := [quant-inst]: #361
+#445 := [unit-resolution #365 #694]: #359
+#451 := [monotonicity #445]: #449
+#452 := [trans #451 #442]: #479
+#450 := (not #479)
+#453 := (or #450 #554)
+#441 := [th-lemma]: #453
+#444 := [unit-resolution #441 #458 #452]: false
+#446 := [lemma #444]: #554
+#304 := (or #462 #610)
+#447 := [th-lemma]: #304
+#443 := [unit-resolution #447 #446]: #610
+#605 := (not #610)
+#593 := (or #605 #612)
+#67 := (= #14 #17)
+#92 := (or #67 #86)
+#696 := (forall (vars (?v0 int)) (:pat #695) #92)
+#97 := (forall (vars (?v0 int)) #92)
+#699 := (iff #97 #696)
+#697 := (iff #92 #92)
+#698 := [refl]: #697
+#700 := [quant-intro #698]: #699
+#203 := (~ #97 #97)
+#200 := (~ #92 #92)
+#215 := [refl]: #200
+#204 := [nnf-pos #215]: #203
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#100 := (iff #20 #97)
+#74 := (not #15)
+#75 := (or #74 #67)
+#80 := (forall (vars (?v0 int)) #75)
+#98 := (iff #80 #97)
+#95 := (iff #75 #92)
+#89 := (or #86 #67)
+#93 := (iff #89 #92)
+#94 := [rewrite]: #93
+#90 := (iff #75 #89)
+#87 := (iff #74 #86)
+#83 := (iff #15 #85)
+#84 := [rewrite]: #83
+#88 := [monotonicity #84]: #87
+#91 := [monotonicity #88]: #90
+#96 := [trans #91 #94]: #95
+#99 := [quant-intro #96]: #98
+#81 := (iff #20 #80)
+#78 := (iff #19 #75)
+#71 := (implies #15 #67)
+#76 := (iff #71 #75)
+#77 := [rewrite]: #76
+#72 := (iff #19 #71)
+#69 := (iff #18 #67)
+#70 := [rewrite]: #69
+#73 := [monotonicity #70]: #72
+#79 := [trans #73 #77]: #78
+#82 := [quant-intro #79]: #81
+#101 := [trans #82 #99]: #100
+#66 := [asserted]: #20
+#102 := [mp #66 #101]: #97
+#216 := [mp~ #102 #204]: #97
+#701 := [mp #216 #700]: #696
+#670 := (not #696)
+#594 := (or #670 #605 #612)
+#609 := (>= #163 0::int)
+#611 := (not #609)
+#603 := (= #163 #169)
+#600 := (or #603 #611)
+#599 := (or #670 #600)
+#591 := (iff #599 #594)
+#586 := (or #670 #593)
+#590 := (iff #586 #594)
+#587 := [rewrite]: #590
+#588 := (iff #599 #586)
+#597 := (iff #600 #593)
+#601 := (or #612 #605)
+#595 := (iff #601 #593)
+#596 := [rewrite]: #595
+#608 := (iff #600 #601)
+#606 := (iff #611 #605)
+#615 := (iff #609 #610)
+#604 := [rewrite]: #615
+#607 := [monotonicity #604]: #606
+#613 := (iff #603 #612)
+#614 := [rewrite]: #613
+#592 := [monotonicity #614 #607]: #608
+#598 := [trans #592 #596]: #597
+#589 := [monotonicity #598]: #588
+#571 := [trans #589 #587]: #591
+#585 := [quant-inst]: #599
+#572 := [mp #585 #571]: #594
+#448 := [unit-resolution #572 #701]: #593
+#438 := [unit-resolution #448 #443]: #612
+#428 := (not #612)
+#430 := (or #428 #574)
+#431 := [th-lemma]: #430
+#434 := [unit-resolution #431 #438]: #574
+#154 := (+ 1::int #26)
+#157 := (f3 #154)
+#160 := (f4 #157)
+#184 := (* -1::int #160)
+#488 := (+ #26 #184)
+#512 := (<= #488 -1::int)
+#489 := (= #488 -1::int)
+#633 := (>= #26 -1::int)
+#570 := (>= #26 0::int)
+#478 := (= #26 0::int)
+#273 := (f3 #26)
+#556 := (f4 #273)
+#552 := (= #556 0::int)
+#480 := (not #570)
+#481 := [hypothesis]: #480
+#553 := (or #552 #570)
+#558 := (or #371 #552 #570)
+#559 := (or #371 #553)
+#555 := (iff #559 #558)
+#561 := [rewrite]: #555
+#560 := [quant-inst]: #559
+#534 := [mp #560 #561]: #558
+#482 := [unit-resolution #534 #707]: #553
+#483 := [unit-resolution #482 #481]: #552
+#484 := (= #26 #556)
+#358 := (= f5 #273)
+#351 := (or #360 #358)
+#362 := [quant-inst]: #351
+#466 := [unit-resolution #362 #694]: #358
+#454 := [monotonicity #466]: #484
+#455 := [trans #454 #483]: #478
+#456 := (not #478)
+#457 := (or #456 #570)
+#459 := [th-lemma]: #457
+#460 := [unit-resolution #459 #481 #455]: false
+#461 := [lemma #460]: #570
+#435 := (or #480 #633)
+#439 := [th-lemma]: #435
+#432 := [unit-resolution #439 #461]: #633
+#629 := (not #633)
+#637 := (or #489 #629)
+#467 := (or #670 #489 #629)
+#645 := (>= #154 0::int)
+#646 := (not #645)
+#641 := (= #154 #160)
+#647 := (or #641 #646)
+#469 := (or #670 #647)
+#628 := (iff #469 #467)
+#623 := (or #670 #637)
+#627 := (iff #623 #467)
+#625 := [rewrite]: #627
+#624 := (iff #469 #623)
+#631 := (iff #647 #637)
+#630 := (iff #646 #629)
+#634 := (iff #645 #633)
+#635 := [rewrite]: #634
+#636 := [monotonicity #635]: #630
+#490 := (iff #641 #489)
+#632 := [rewrite]: #490
+#638 := [monotonicity #632 #636]: #631
+#626 := [monotonicity #638]: #624
+#510 := [trans #626 #625]: #628
+#470 := [quant-inst]: #469
+#511 := [mp #470 #510]: #467
+#440 := [unit-resolution #511 #701]: #637
+#433 := [unit-resolution #440 #432]: #489
+#436 := (not #489)
+#437 := (or #436 #512)
+#423 := [th-lemma]: #437
+#425 := [unit-resolution #423 #433]: #512
+#186 := (+ #184 #185)
+#187 := (+ #151 #186)
+#183 := (>= #187 0::int)
+#37 := (+ #28 1::int)
+#38 := (f3 #37)
+#39 := (f4 #38)
+#34 := (+ #26 1::int)
+#35 := (f3 #34)
+#36 := (f4 #35)
+#40 := (+ #36 #39)
+#31 := (+ #29 1::int)
+#32 := (f3 #31)
+#33 := (f4 #32)
+#41 := (< #33 #40)
+#42 := (not #41)
+#197 := (iff #42 #183)
+#172 := (+ #160 #169)
+#175 := (< #151 #172)
+#178 := (not #175)
+#195 := (iff #178 #183)
+#182 := (not #183)
+#190 := (not #182)
+#193 := (iff #190 #183)
+#194 := [rewrite]: #193
+#191 := (iff #178 #190)
+#188 := (iff #175 #182)
+#189 := [rewrite]: #188
+#192 := [monotonicity #189]: #191
+#196 := [trans #192 #194]: #195
+#179 := (iff #42 #178)
+#176 := (iff #41 #175)
+#173 := (= #40 #172)
+#170 := (= #39 #169)
+#167 := (= #38 #166)
+#164 := (= #37 #163)
+#165 := [rewrite]: #164
+#168 := [monotonicity #165]: #167
+#171 := [monotonicity #168]: #170
+#161 := (= #36 #160)
+#158 := (= #35 #157)
+#155 := (= #34 #154)
+#156 := [rewrite]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#174 := [monotonicity #162 #171]: #173
+#152 := (= #33 #151)
+#149 := (= #32 #148)
+#146 := (= #31 #145)
+#147 := [rewrite]: #146
+#150 := [monotonicity #147]: #149
+#153 := [monotonicity #150]: #152
+#177 := [monotonicity #153 #174]: #176
+#180 := [monotonicity #177]: #179
+#198 := [trans #180 #196]: #197
+#144 := [asserted]: #42
+#199 := [mp #144 #198]: #183
+#427 := (not #574)
+#424 := (not #512)
+#409 := (or #426 #182 #424 #427)
+#411 := [th-lemma]: #409
+#412 := [unit-resolution #411 #199 #425 #434]: #426
+#677 := (= #341 -1::int)
+#321 := (>= #29 -1::int)
+#413 := (or #321 #629 #462)
+#414 := [th-lemma]: #413
+#415 := [unit-resolution #414 #432 #446]: #321
+#326 := (not #321)
+#667 := (or #326 #677)
+#672 := (or #670 #326 #677)
+#682 := (>= #145 0::int)
+#683 := (not #682)
+#680 := (= #145 #151)
+#686 := (or #680 #683)
+#312 := (or #670 #686)
+#383 := (iff #312 #672)
+#673 := (or #670 #667)
+#660 := (iff #673 #672)
+#661 := [rewrite]: #660
+#671 := (iff #312 #673)
+#669 := (iff #686 #667)
+#664 := (or #677 #326)
+#668 := (iff #664 #667)
+#663 := [rewrite]: #668
+#665 := (iff #686 #664)
+#327 := (iff #683 #326)
+#662 := (iff #682 #321)
+#325 := [rewrite]: #662
+#328 := [monotonicity #325]: #327
+#337 := (iff #680 #677)
+#678 := [rewrite]: #337
+#666 := [monotonicity #678 #328]: #665
+#307 := [trans #666 #663]: #669
+#674 := [monotonicity #307]: #671
+#384 := [trans #674 #661]: #383
+#313 := [quant-inst]: #312
+#385 := [mp #313 #384]: #672
+#416 := [unit-resolution #385 #701]: #667
+#417 := [unit-resolution #416 #415]: #677
+#418 := (not #677)
+#419 := (or #418 #280)
+#420 := [th-lemma]: #419
+[unit-resolution #420 #417 #412]: false
+unsat
+9221620b197e212b4efb9528416b5d35a8c52049 60 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#135 := (f3 #26)
+#141 := (= f5 #135)
+#146 := (not #141)
+#13 := 0::int
+#27 := (+ #26 0::int)
+#28 := (f3 #27)
+#29 := (= #28 f5)
+#30 := (not #29)
+#147 := (iff #30 #146)
+#144 := (iff #29 #141)
+#138 := (= #135 f5)
+#142 := (iff #138 #141)
+#143 := [rewrite]: #142
+#139 := (iff #29 #138)
+#136 := (= #28 #135)
+#133 := (= #27 #26)
+#134 := [rewrite]: #133
+#137 := [monotonicity #134]: #136
+#140 := [monotonicity #137]: #139
+#145 := [trans #140 #143]: #144
+#148 := [monotonicity #145]: #147
+#132 := [asserted]: #30
+#151 := [mp #132 #148]: #146
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#639 := (pattern #9)
+#10 := (f3 #9)
+#48 := (= #8 #10)
+#640 := (forall (vars (?v0 S2)) (:pat #639) #48)
+#51 := (forall (vars (?v0 S2)) #48)
+#641 := (iff #51 #640)
+#643 := (iff #640 #640)
+#644 := [rewrite]: #643
+#642 := [rewrite]: #641
+#645 := [trans #642 #644]: #641
+#163 := (~ #51 #51)
+#161 := (~ #48 #48)
+#162 := [refl]: #161
+#164 := [nnf-pos #162]: #163
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#52 := (iff #12 #51)
+#49 := (iff #11 #48)
+#50 := [rewrite]: #49
+#53 := [quant-intro #50]: #52
+#47 := [asserted]: #12
+#56 := [mp #47 #53]: #51
+#152 := [mp~ #56 #164]: #51
+#646 := [mp #152 #645]: #640
+#224 := (not #640)
+#310 := (or #224 #141)
+#311 := [quant-inst]: #310
+[unit-resolution #311 #646 #151]: false
+unsat
+c3f498b2ca679db6f24e3361991b9cdacf7c1adc 60 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#135 := (f3 #26)
+#141 := (= f5 #135)
+#146 := (not #141)
+#13 := 0::int
+#27 := (+ 0::int #26)
+#28 := (f3 #27)
+#29 := (= #28 f5)
+#30 := (not #29)
+#147 := (iff #30 #146)
+#144 := (iff #29 #141)
+#138 := (= #135 f5)
+#142 := (iff #138 #141)
+#143 := [rewrite]: #142
+#139 := (iff #29 #138)
+#136 := (= #28 #135)
+#133 := (= #27 #26)
+#134 := [rewrite]: #133
+#137 := [monotonicity #134]: #136
+#140 := [monotonicity #137]: #139
+#145 := [trans #140 #143]: #144
+#148 := [monotonicity #145]: #147
+#132 := [asserted]: #30
+#151 := [mp #132 #148]: #146
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#639 := (pattern #9)
+#10 := (f3 #9)
+#48 := (= #8 #10)
+#640 := (forall (vars (?v0 S2)) (:pat #639) #48)
+#51 := (forall (vars (?v0 S2)) #48)
+#641 := (iff #51 #640)
+#643 := (iff #640 #640)
+#644 := [rewrite]: #643
+#642 := [rewrite]: #641
+#645 := [trans #642 #644]: #641
+#163 := (~ #51 #51)
+#161 := (~ #48 #48)
+#162 := [refl]: #161
+#164 := [nnf-pos #162]: #163
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#52 := (iff #12 #51)
+#49 := (iff #11 #48)
+#50 := [rewrite]: #49
+#53 := [quant-intro #50]: #52
+#47 := [asserted]: #12
+#56 := [mp #47 #53]: #51
+#152 := [mp~ #56 #164]: #51
+#646 := [mp #152 #645]: #640
+#224 := (not #640)
+#310 := (or #224 #141)
+#311 := [quant-inst]: #310
+[unit-resolution #311 #646 #151]: false
+unsat
+cbe4e74b79c5e538e779d1562e52667175af768a 37 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#31 := (+ #28 #26)
+#32 := (f3 #31)
+#29 := (+ #26 #28)
+#30 := (f3 #29)
+#33 := (= #30 #32)
+#34 := (not #33)
+#153 := (iff #34 false)
+#1 := true
+#148 := (not true)
+#151 := (iff #148 false)
+#152 := [rewrite]: #151
+#149 := (iff #34 #148)
+#146 := (iff #33 true)
+#141 := (= #30 #30)
+#144 := (iff #141 true)
+#145 := [rewrite]: #144
+#142 := (iff #33 #141)
+#139 := (= #32 #30)
+#137 := (= #31 #29)
+#138 := [rewrite]: #137
+#140 := [monotonicity #138]: #139
+#143 := [monotonicity #140]: #142
+#147 := [trans #143 #145]: #146
+#150 := [monotonicity #147]: #149
+#154 := [trans #150 #152]: #153
+#136 := [asserted]: #34
+[mp #136 #154]: false
+unsat
+8ed55f0689626a8564aca25cbd530e9ad72be6f4 42 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f7 :: S2
+#29 := f7
+#30 := (f4 f7)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#34 := (+ #26 #28)
+#35 := (+ #34 #30)
+#36 := (f3 #35)
+#31 := (+ #28 #30)
+#32 := (+ #26 #31)
+#33 := (f3 #32)
+#37 := (= #33 #36)
+#38 := (not #37)
+#157 := (iff #38 false)
+#1 := true
+#152 := (not true)
+#155 := (iff #152 false)
+#156 := [rewrite]: #155
+#153 := (iff #38 #152)
+#150 := (iff #37 true)
+#145 := (= #33 #33)
+#148 := (iff #145 true)
+#149 := [rewrite]: #148
+#146 := (iff #37 #145)
+#143 := (= #36 #33)
+#141 := (= #35 #32)
+#142 := [rewrite]: #141
+#144 := [monotonicity #142]: #143
+#147 := [monotonicity #144]: #146
+#151 := [trans #147 #149]: #150
+#154 := [monotonicity #151]: #153
+#158 := [trans #154 #156]: #157
+#140 := [asserted]: #38
+[mp #140 #158]: false
+unsat
+e513816199779fdd08259cbaa721d9be6ce61ce8 438 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f3 :: (-> int S2)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#625 := (f3 #26)
+#577 := (f4 #625)
+#575 := (= #577 0::int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#299 := (f3 #28)
+#461 := (f4 #299)
+#570 := (= #461 0::int)
+#576 := (>= #26 0::int)
+#508 := (= #26 0::int)
+#463 := (not #576)
+#424 := [hypothesis]: #463
+#578 := (or #575 #576)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#645 := (pattern #16)
+#80 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#128 := (or #22 #80)
+#652 := (forall (vars (?v0 int)) (:pat #645) #128)
+#133 := (forall (vars (?v0 int)) #128)
+#655 := (iff #133 #652)
+#653 := (iff #128 #128)
+#654 := [refl]: #653
+#656 := [quant-intro #654]: #655
+#153 := (~ #133 #133)
+#165 := (~ #128 #128)
+#166 := [refl]: #165
+#154 := [nnf-pos #166]: #153
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#136 := (iff #24 #133)
+#99 := (= 0::int #17)
+#105 := (not #21)
+#106 := (or #105 #99)
+#111 := (forall (vars (?v0 int)) #106)
+#134 := (iff #111 #133)
+#131 := (iff #106 #128)
+#125 := (or #80 #22)
+#129 := (iff #125 #128)
+#130 := [rewrite]: #129
+#126 := (iff #106 #125)
+#123 := (iff #99 #22)
+#124 := [rewrite]: #123
+#121 := (iff #105 #80)
+#81 := (not #80)
+#116 := (not #81)
+#119 := (iff #116 #80)
+#120 := [rewrite]: #119
+#117 := (iff #105 #116)
+#114 := (iff #21 #81)
+#115 := [rewrite]: #114
+#118 := [monotonicity #115]: #117
+#122 := [trans #118 #120]: #121
+#127 := [monotonicity #122 #124]: #126
+#132 := [trans #127 #130]: #131
+#135 := [quant-intro #132]: #134
+#112 := (iff #24 #111)
+#109 := (iff #23 #106)
+#102 := (implies #21 #99)
+#107 := (iff #102 #106)
+#108 := [rewrite]: #107
+#103 := (iff #23 #102)
+#100 := (iff #22 #99)
+#101 := [rewrite]: #100
+#104 := [monotonicity #101]: #103
+#110 := [trans #104 #108]: #109
+#113 := [quant-intro #110]: #112
+#137 := [trans #113 #135]: #136
+#98 := [asserted]: #24
+#138 := [mp #98 #137]: #133
+#167 := [mp~ #138 #154]: #133
+#657 := [mp #167 #656]: #652
+#336 := (not #652)
+#462 := (or #336 #575 #576)
+#421 := (or #336 #578)
+#471 := (iff #421 #462)
+#566 := [rewrite]: #471
+#569 := [quant-inst]: #421
+#567 := [mp #569 #566]: #462
+#425 := [unit-resolution #567 #657]: #578
+#426 := [unit-resolution #425 #424]: #575
+#504 := (= #26 #577)
+#298 := (= f5 #625)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#637 := (pattern #9)
+#10 := (f3 #9)
+#55 := (= #8 #10)
+#638 := (forall (vars (?v0 S2)) (:pat #637) #55)
+#58 := (forall (vars (?v0 S2)) #55)
+#639 := (iff #58 #638)
+#641 := (iff #638 #638)
+#642 := [rewrite]: #641
+#640 := [rewrite]: #639
+#643 := [trans #640 #642]: #639
+#161 := (~ #58 #58)
+#159 := (~ #55 #55)
+#160 := [refl]: #159
+#162 := [nnf-pos #160]: #161
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#59 := (iff #12 #58)
+#56 := (iff #11 #55)
+#57 := [rewrite]: #56
+#60 := [quant-intro #57]: #59
+#54 := [asserted]: #12
+#63 := [mp #54 #60]: #58
+#150 := [mp~ #63 #162]: #58
+#644 := [mp #150 #643]: #638
+#633 := (not #638)
+#634 := (or #633 #298)
+#635 := [quant-inst]: #634
+#503 := [unit-resolution #635 #644]: #298
+#507 := [monotonicity #503]: #504
+#428 := [trans #507 #426]: #508
+#429 := (not #508)
+#430 := (or #429 #576)
+#431 := [th-lemma]: #430
+#432 := [unit-resolution #431 #424 #428]: false
+#433 := [lemma #432]: #576
+#414 := (or #463 #570)
+#553 := (= #28 0::int)
+#29 := (+ #26 #28)
+#30 := (f3 #29)
+#290 := (f4 #30)
+#628 := -1::int
+#270 := (* -1::int #290)
+#612 := (+ #28 #270)
+#274 := (+ #26 #612)
+#610 := (<= #274 0::int)
+#275 := (= #274 0::int)
+#630 := (>= #29 0::int)
+#460 := (>= #28 0::int)
+#519 := (not #570)
+#483 := [hypothesis]: #519
+#470 := (or #460 #570)
+#466 := (or #336 #460 #570)
+#455 := (or #570 #460)
+#474 := (or #336 #455)
+#572 := (iff #474 #466)
+#476 := (or #336 #470)
+#571 := (iff #476 #466)
+#568 := [rewrite]: #571
+#477 := (iff #474 #476)
+#472 := (iff #455 #470)
+#473 := [rewrite]: #472
+#478 := [monotonicity #473]: #477
+#559 := [trans #478 #568]: #572
+#475 := [quant-inst]: #474
+#561 := [mp #475 #559]: #466
+#489 := [unit-resolution #561 #657]: #470
+#457 := [unit-resolution #489 #483]: #460
+#491 := [hypothesis]: #576
+#464 := (not #460)
+#423 := (or #630 #463 #464)
+#454 := [th-lemma]: #423
+#456 := [unit-resolution #454 #491 #457]: #630
+#636 := (not #630)
+#614 := (or #275 #636)
+#62 := (= #14 #17)
+#87 := (or #62 #81)
+#646 := (forall (vars (?v0 int)) (:pat #645) #87)
+#92 := (forall (vars (?v0 int)) #87)
+#649 := (iff #92 #646)
+#647 := (iff #87 #87)
+#648 := [refl]: #647
+#650 := [quant-intro #648]: #649
+#151 := (~ #92 #92)
+#147 := (~ #87 #87)
+#163 := [refl]: #147
+#152 := [nnf-pos #163]: #151
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#95 := (iff #20 #92)
+#69 := (not #15)
+#70 := (or #69 #62)
+#75 := (forall (vars (?v0 int)) #70)
+#93 := (iff #75 #92)
+#90 := (iff #70 #87)
+#84 := (or #81 #62)
+#88 := (iff #84 #87)
+#89 := [rewrite]: #88
+#85 := (iff #70 #84)
+#82 := (iff #69 #81)
+#78 := (iff #15 #80)
+#79 := [rewrite]: #78
+#83 := [monotonicity #79]: #82
+#86 := [monotonicity #83]: #85
+#91 := [trans #86 #89]: #90
+#94 := [quant-intro #91]: #93
+#76 := (iff #20 #75)
+#73 := (iff #19 #70)
+#66 := (implies #15 #62)
+#71 := (iff #66 #70)
+#72 := [rewrite]: #71
+#67 := (iff #19 #66)
+#64 := (iff #18 #62)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#74 := [trans #68 #72]: #73
+#77 := [quant-intro #74]: #76
+#96 := [trans #77 #94]: #95
+#61 := [asserted]: #20
+#97 := [mp #61 #96]: #92
+#164 := [mp~ #97 #152]: #92
+#651 := [mp #164 #650]: #646
+#617 := (not #646)
+#618 := (or #617 #275 #636)
+#627 := (= #29 #290)
+#286 := (or #627 #636)
+#613 := (or #617 #286)
+#623 := (iff #613 #618)
+#256 := (or #617 #614)
+#261 := (iff #256 #618)
+#262 := [rewrite]: #261
+#620 := (iff #613 #256)
+#615 := (iff #286 #614)
+#276 := (iff #627 #275)
+#277 := [rewrite]: #276
+#616 := [monotonicity #277]: #615
+#622 := [monotonicity #616]: #620
+#621 := [trans #622 #262]: #623
+#619 := [quant-inst]: #613
+#624 := [mp #619 #621]: #618
+#458 := [unit-resolution #624 #651]: #614
+#465 := [unit-resolution #458 #456]: #275
+#467 := (not #275)
+#468 := (or #467 #610)
+#469 := [th-lemma]: #468
+#479 := [unit-resolution #469 #465]: #610
+#611 := (>= #274 0::int)
+#608 := (<= #290 0::int)
+#318 := (= #290 0::int)
+#31 := (f3 0::int)
+#609 := (f4 #31)
+#322 := (= #609 0::int)
+#439 := (or #617 #322)
+#334 := (>= 0::int 0::int)
+#335 := (not #334)
+#319 := (= 0::int #609)
+#320 := (or #319 #335)
+#440 := (or #617 #320)
+#583 := (iff #440 #439)
+#585 := (iff #439 #439)
+#579 := [rewrite]: #585
+#597 := (iff #320 #322)
+#589 := (or #322 false)
+#596 := (iff #589 #322)
+#591 := [rewrite]: #596
+#590 := (iff #320 #589)
+#593 := (iff #335 false)
+#1 := true
+#598 := (not true)
+#603 := (iff #598 false)
+#592 := [rewrite]: #603
+#602 := (iff #335 #598)
+#601 := (iff #334 true)
+#315 := [rewrite]: #601
+#599 := [monotonicity #315]: #602
+#594 := [trans #599 #592]: #593
+#321 := (iff #319 #322)
+#600 := [rewrite]: #321
+#595 := [monotonicity #600 #594]: #590
+#438 := [trans #595 #591]: #597
+#584 := [monotonicity #438]: #583
+#580 := [trans #584 #579]: #583
+#582 := [quant-inst]: #440
+#586 := [mp #582 #580]: #439
+#555 := [unit-resolution #586 #651]: #322
+#495 := (= #290 #609)
+#32 := (= #30 #31)
+#34 := (= f6 #31)
+#35 := (not #34)
+#33 := (= f5 #31)
+#140 := (not #33)
+#141 := (or #140 #35)
+#528 := (= #29 0::int)
+#526 := (= #29 #609)
+#545 := (= #28 #609)
+#309 := (not #141)
+#565 := [hypothesis]: #309
+#222 := (or #141 #34)
+#308 := [def-axiom]: #222
+#556 := [unit-resolution #308 #565]: #34
+#546 := [monotonicity #556]: #545
+#524 := (= #29 #28)
+#552 := (= #26 #28)
+#542 := (= f5 f6)
+#557 := (= #31 f6)
+#551 := [symm #556]: #557
+#221 := (or #141 #33)
+#307 := [def-axiom]: #221
+#558 := [unit-resolution #307 #565]: #33
+#543 := [trans #558 #551]: #542
+#522 := [monotonicity #543]: #552
+#541 := (= #29 #26)
+#540 := (= #26 #29)
+#550 := (<= #28 0::int)
+#547 := [trans #546 #555]: #553
+#548 := (not #553)
+#544 := (or #548 #550)
+#549 := [th-lemma]: #544
+#535 := [unit-resolution #549 #547]: #550
+#536 := (or #548 #460)
+#538 := [th-lemma]: #536
+#539 := [unit-resolution #538 #547]: #460
+#537 := [th-lemma #539 #535]: #540
+#521 := [symm #537]: #541
+#525 := [trans #521 #522]: #524
+#527 := [trans #525 #546]: #526
+#529 := [trans #527 #555]: #528
+#530 := [monotonicity #529]: #32
+#293 := (not #32)
+#287 := (or #293 #141)
+#144 := (iff #32 #141)
+#36 := (implies #33 #35)
+#37 := (iff #32 #36)
+#145 := (iff #37 #144)
+#142 := (iff #36 #141)
+#143 := [rewrite]: #142
+#146 := [monotonicity #143]: #145
+#139 := [asserted]: #37
+#149 := [mp #139 #146]: #144
+#312 := (not #144)
+#629 := (or #293 #141 #312)
+#631 := [def-axiom]: #629
+#418 := [unit-resolution #631 #149]: #287
+#554 := [unit-resolution #418 #565]: #293
+#531 := [unit-resolution #554 #530]: false
+#532 := [lemma #531]: #141
+#310 := (or #32 #309)
+#240 := (or #32 #309 #312)
+#313 := [def-axiom]: #240
+#314 := [unit-resolution #313 #149]: #310
+#494 := [unit-resolution #314 #532]: #32
+#498 := [monotonicity #494]: #495
+#499 := [trans #498 #555]: #318
+#500 := (not #318)
+#496 := (or #500 #608)
+#501 := [th-lemma]: #496
+#481 := [unit-resolution #501 #499]: #608
+#459 := (not #608)
+#480 := (or #611 #463 #464 #459)
+#435 := [th-lemma]: #480
+#436 := [unit-resolution #435 #491 #481 #457]: #611
+#605 := (>= #290 0::int)
+#441 := (or #500 #605)
+#442 := [th-lemma]: #441
+#443 := [unit-resolution #442 #499]: #605
+#562 := (* -1::int #28)
+#563 := (+ #26 #562)
+#490 := (<= #563 0::int)
+#482 := (not #610)
+#444 := (or #490 #464 #459 #482)
+#445 := [th-lemma]: #444
+#446 := [unit-resolution #445 #479 #457 #481]: #490
+#560 := (>= #563 0::int)
+#487 := (or #560 #482 #463)
+#492 := (not #560)
+#497 := [hypothesis]: #492
+#493 := [hypothesis]: #610
+#427 := [th-lemma #481 #493 #497 #491]: false
+#488 := [lemma #427]: #487
+#447 := [unit-resolution #488 #479 #491]: #560
+#448 := [th-lemma #447 #446 #443 #481 #436 #479]: #553
+#451 := (= #461 #28)
+#449 := (= #299 f6)
+#632 := (= f6 #299)
+#626 := (or #633 #632)
+#285 := [quant-inst]: #626
+#523 := [unit-resolution #285 #644]: #632
+#450 := [symm #523]: #449
+#452 := [monotonicity #450]: #451
+#437 := [trans #452 #448]: #570
+#453 := [unit-resolution #483 #437]: false
+#415 := [lemma #453]: #414
+#422 := [unit-resolution #415 #433]: #570
+#391 := (= #577 #461)
+#534 := (= #28 #461)
+#512 := [monotonicity #523]: #534
+#400 := (= #577 #28)
+#405 := [trans #512 #422]: #553
+#406 := [unit-resolution #538 #405]: #460
+#407 := [unit-resolution #454 #406 #433]: #630
+#409 := [unit-resolution #458 #407]: #275
+#410 := [unit-resolution #469 #409]: #610
+#411 := [unit-resolution #445 #410 #406 #481]: #490
+#253 := [unit-resolution #488 #410 #433]: #560
+#412 := (not #490)
+#408 := (or #552 #412 #492)
+#413 := [th-lemma]: #408
+#392 := [unit-resolution #413 #253 #411]: #552
+#401 := (= #577 #26)
+#395 := (= #625 f5)
+#399 := [symm #503]: #395
+#402 := [monotonicity #399]: #401
+#403 := [trans #402 #392]: #400
+#394 := [trans #403 #512]: #391
+#396 := [trans #394 #422]: #575
+#485 := (not #575)
+#514 := (or #519 #34)
+#515 := (= #299 #31)
+#533 := [hypothesis]: #570
+#513 := [trans #512 #533]: #553
+#516 := [monotonicity #513]: #515
+#517 := [trans #523 #516]: #34
+#564 := [hypothesis]: #35
+#518 := [unit-resolution #564 #517]: false
+#520 := [lemma #518]: #514
+#416 := [unit-resolution #520 #422]: #34
+#300 := (or #309 #140 #35)
+#311 := [def-axiom]: #300
+#434 := [unit-resolution #311 #416 #532]: #140
+#486 := (or #485 #33)
+#510 := (= #625 #31)
+#502 := [hypothesis]: #575
+#509 := [trans #507 #502]: #508
+#505 := [monotonicity #509]: #510
+#511 := [trans #503 #505]: #33
+#506 := [hypothesis]: #140
+#484 := [unit-resolution #506 #511]: false
+#379 := [lemma #484]: #486
+#404 := [unit-resolution #379 #434]: #485
+[unit-resolution #404 #396]: false
+unsat
+247007e25d142d8e92de60bbb406994a174b3a43 60 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#135 := (f3 #26)
+#141 := (= f5 #135)
+#146 := (not #141)
+#13 := 0::int
+#27 := (- #26 0::int)
+#28 := (f3 #27)
+#29 := (= #28 f5)
+#30 := (not #29)
+#147 := (iff #30 #146)
+#144 := (iff #29 #141)
+#138 := (= #135 f5)
+#142 := (iff #138 #141)
+#143 := [rewrite]: #142
+#139 := (iff #29 #138)
+#136 := (= #28 #135)
+#133 := (= #27 #26)
+#134 := [rewrite]: #133
+#137 := [monotonicity #134]: #136
+#140 := [monotonicity #137]: #139
+#145 := [trans #140 #143]: #144
+#148 := [monotonicity #145]: #147
+#132 := [asserted]: #30
+#151 := [mp #132 #148]: #146
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#639 := (pattern #9)
+#10 := (f3 #9)
+#48 := (= #8 #10)
+#640 := (forall (vars (?v0 S2)) (:pat #639) #48)
+#51 := (forall (vars (?v0 S2)) #48)
+#641 := (iff #51 #640)
+#643 := (iff #640 #640)
+#644 := [rewrite]: #643
+#642 := [rewrite]: #641
+#645 := [trans #642 #644]: #641
+#163 := (~ #51 #51)
+#161 := (~ #48 #48)
+#162 := [refl]: #161
+#164 := [nnf-pos #162]: #163
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#52 := (iff #12 #51)
+#49 := (iff #11 #48)
+#50 := [rewrite]: #49
+#53 := [quant-intro #50]: #52
+#47 := [asserted]: #12
+#56 := [mp #47 #53]: #51
+#152 := [mp~ #56 #164]: #51
+#646 := [mp #152 #645]: #640
+#224 := (not #640)
+#310 := (or #224 #141)
+#311 := [quant-inst]: #310
+[unit-resolution #311 #646 #151]: false
+unsat
+d93a98dfeff0cecc9d144da28466836fbdae0214 179 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#138 := -1::int
+#139 := (* -1::int #28)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#140 := (+ #26 #139)
+#143 := (f3 #140)
+#13 := 0::int
+#32 := (f3 0::int)
+#149 := (= #32 #143)
+#649 := (f4 #143)
+#597 := (f3 #649)
+#596 := (= #597 #143)
+#499 := (= #143 #597)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#665 := (pattern #9)
+#10 := (f3 #9)
+#53 := (= #8 #10)
+#666 := (forall (vars (?v0 S2)) (:pat #665) #53)
+#56 := (forall (vars (?v0 S2)) #53)
+#667 := (iff #56 #666)
+#669 := (iff #666 #666)
+#670 := [rewrite]: #669
+#668 := [rewrite]: #667
+#671 := [trans #668 #670]: #667
+#192 := (~ #56 #56)
+#190 := (~ #53 #53)
+#191 := [refl]: #190
+#193 := [nnf-pos #191]: #192
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#57 := (iff #12 #56)
+#54 := (iff #11 #53)
+#55 := [rewrite]: #54
+#58 := [quant-intro #55]: #57
+#52 := [asserted]: #12
+#61 := [mp #52 #58]: #56
+#179 := [mp~ #61 #193]: #56
+#672 := [mp #179 #671]: #666
+#338 := (not #666)
+#502 := (or #338 #499)
+#503 := [quant-inst]: #502
+#501 := [unit-resolution #503 #672]: #499
+#600 := [symm #501]: #596
+#506 := (= #32 #597)
+#504 := (= 0::int #649)
+#622 := (= #649 0::int)
+#161 := (>= #140 0::int)
+#160 := (not #161)
+#154 := (not #149)
+#167 := (and #154 #160)
+#30 := (- #26 #28)
+#31 := (f3 #30)
+#33 := (= #31 #32)
+#34 := (not #33)
+#29 := (< #26 #28)
+#35 := (and #29 #34)
+#172 := (iff #35 #167)
+#157 := (and #29 #154)
+#170 := (iff #157 #167)
+#164 := (and #160 #154)
+#168 := (iff #164 #167)
+#169 := [rewrite]: #168
+#165 := (iff #157 #164)
+#162 := (iff #29 #160)
+#163 := [rewrite]: #162
+#166 := [monotonicity #163]: #165
+#171 := [trans #166 #169]: #170
+#158 := (iff #35 #157)
+#155 := (iff #34 #154)
+#152 := (iff #33 #149)
+#146 := (= #143 #32)
+#150 := (iff #146 #149)
+#151 := [rewrite]: #150
+#147 := (iff #33 #146)
+#144 := (= #31 #143)
+#141 := (= #30 #140)
+#142 := [rewrite]: #141
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#153 := [trans #148 #151]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#173 := [trans #159 #171]: #172
+#137 := [asserted]: #35
+#174 := [mp #137 #173]: #167
+#176 := [and-elim #174]: #160
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#673 := (pattern #16)
+#78 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#126 := (or #22 #78)
+#680 := (forall (vars (?v0 int)) (:pat #673) #126)
+#131 := (forall (vars (?v0 int)) #126)
+#683 := (iff #131 #680)
+#681 := (iff #126 #126)
+#682 := [refl]: #681
+#684 := [quant-intro #682]: #683
+#182 := (~ #131 #131)
+#196 := (~ #126 #126)
+#197 := [refl]: #196
+#183 := [nnf-pos #197]: #182
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#134 := (iff #24 #131)
+#97 := (= 0::int #17)
+#103 := (not #21)
+#104 := (or #103 #97)
+#109 := (forall (vars (?v0 int)) #104)
+#132 := (iff #109 #131)
+#129 := (iff #104 #126)
+#123 := (or #78 #22)
+#127 := (iff #123 #126)
+#128 := [rewrite]: #127
+#124 := (iff #104 #123)
+#121 := (iff #97 #22)
+#122 := [rewrite]: #121
+#119 := (iff #103 #78)
+#79 := (not #78)
+#114 := (not #79)
+#117 := (iff #114 #78)
+#118 := [rewrite]: #117
+#115 := (iff #103 #114)
+#112 := (iff #21 #79)
+#113 := [rewrite]: #112
+#116 := [monotonicity #113]: #115
+#120 := [trans #116 #118]: #119
+#125 := [monotonicity #120 #122]: #124
+#130 := [trans #125 #128]: #129
+#133 := [quant-intro #130]: #132
+#110 := (iff #24 #109)
+#107 := (iff #23 #104)
+#100 := (implies #21 #97)
+#105 := (iff #100 #104)
+#106 := [rewrite]: #105
+#101 := (iff #23 #100)
+#98 := (iff #22 #97)
+#99 := [rewrite]: #98
+#102 := [monotonicity #99]: #101
+#108 := [trans #102 #106]: #107
+#111 := [quant-intro #108]: #110
+#135 := [trans #111 #133]: #134
+#96 := [asserted]: #24
+#136 := [mp #96 #135]: #131
+#198 := [mp~ #136 #183]: #131
+#685 := [mp #198 #684]: #680
+#619 := (not #680)
+#625 := (or #619 #161 #622)
+#617 := (or #622 #161)
+#466 := (or #619 #617)
+#607 := (iff #466 #625)
+#618 := (or #161 #622)
+#468 := (or #619 #618)
+#612 := (iff #468 #625)
+#613 := [rewrite]: #612
+#610 := (iff #466 #468)
+#623 := (iff #617 #618)
+#624 := [rewrite]: #623
+#611 := [monotonicity #624]: #610
+#608 := [trans #611 #613]: #607
+#467 := [quant-inst]: #466
+#614 := [mp #467 #608]: #625
+#494 := [unit-resolution #614 #685 #176]: #622
+#505 := [symm #494]: #504
+#599 := [monotonicity #505]: #506
+#587 := [trans #599 #600]: #149
+#175 := [and-elim #174]: #154
+[unit-resolution #175 #587]: false
+unsat
+eee95e43cf8f5bef80fbd286784baba8f5cb9a33 321 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#141 := -1::int
+#142 := (* -1::int #28)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#143 := (+ #26 #142)
+#146 := (f3 #143)
+#13 := 0::int
+#31 := (f3 0::int)
+#152 := (= #31 #146)
+#645 := (f4 #146)
+#547 := (f3 #645)
+#476 := (= #547 #146)
+#548 := (= #146 #547)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#672 := (pattern #9)
+#10 := (f3 #9)
+#56 := (= #8 #10)
+#673 := (forall (vars (?v0 S2)) (:pat #672) #56)
+#59 := (forall (vars (?v0 S2)) #56)
+#674 := (iff #59 #673)
+#676 := (iff #673 #673)
+#677 := [rewrite]: #676
+#675 := [rewrite]: #674
+#678 := [trans #675 #677]: #674
+#199 := (~ #59 #59)
+#197 := (~ #56 #56)
+#198 := [refl]: #197
+#200 := [nnf-pos #198]: #199
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#60 := (iff #12 #59)
+#57 := (iff #11 #56)
+#58 := [rewrite]: #57
+#61 := [quant-intro #58]: #60
+#55 := [asserted]: #12
+#64 := [mp #55 #61]: #59
+#186 := [mp~ #64 #200]: #59
+#679 := [mp #186 #678]: #673
+#345 := (not #673)
+#528 := (or #345 #548)
+#529 := [quant-inst]: #528
+#519 := [unit-resolution #529 #679]: #548
+#477 := [symm #519]: #476
+#470 := (= #31 #547)
+#494 := (= 0::int #645)
+#638 := (= #645 0::int)
+#656 := (>= #143 0::int)
+#659 := (not #656)
+#160 := (* -1::int #26)
+#161 := (+ #160 #28)
+#164 := (f3 #161)
+#617 := (f4 #164)
+#597 := (<= #617 0::int)
+#523 := (not #597)
+#507 := (= #617 0::int)
+#545 := (not #507)
+#170 := (= #31 #164)
+#558 := (f3 #617)
+#539 := (= #558 #164)
+#569 := (= #164 #558)
+#550 := (or #345 #569)
+#551 := [quant-inst]: #550
+#552 := [unit-resolution #551 #679]: #569
+#542 := [symm #552]: #539
+#537 := (= #31 #558)
+#555 := (= 0::int #617)
+#553 := [hypothesis]: #507
+#541 := [symm #553]: #555
+#538 := [monotonicity #541]: #537
+#543 := [trans #538 #542]: #170
+#175 := (not #170)
+#157 := (not #152)
+#178 := (and #157 #175)
+#34 := (- #28 #26)
+#35 := (f3 #34)
+#36 := (= #35 #31)
+#37 := (not #36)
+#29 := (- #26 #28)
+#30 := (f3 #29)
+#32 := (= #30 #31)
+#33 := (not #32)
+#38 := (and #33 #37)
+#179 := (iff #38 #178)
+#176 := (iff #37 #175)
+#173 := (iff #36 #170)
+#167 := (= #164 #31)
+#171 := (iff #167 #170)
+#172 := [rewrite]: #171
+#168 := (iff #36 #167)
+#165 := (= #35 #164)
+#162 := (= #34 #161)
+#163 := [rewrite]: #162
+#166 := [monotonicity #163]: #165
+#169 := [monotonicity #166]: #168
+#174 := [trans #169 #172]: #173
+#177 := [monotonicity #174]: #176
+#158 := (iff #33 #157)
+#155 := (iff #32 #152)
+#149 := (= #146 #31)
+#153 := (iff #149 #152)
+#154 := [rewrite]: #153
+#150 := (iff #32 #149)
+#147 := (= #30 #146)
+#144 := (= #29 #143)
+#145 := [rewrite]: #144
+#148 := [monotonicity #145]: #147
+#151 := [monotonicity #148]: #150
+#156 := [trans #151 #154]: #155
+#159 := [monotonicity #156]: #158
+#180 := [monotonicity #159 #177]: #179
+#140 := [asserted]: #38
+#183 := [mp #140 #180]: #178
+#182 := [and-elim #183]: #175
+#544 := [unit-resolution #182 #543]: false
+#540 := [lemma #544]: #545
+#598 := (>= #617 0::int)
+#621 := (+ #142 #617)
+#622 := (+ #26 #621)
+#505 := (>= #622 0::int)
+#614 := (= #622 0::int)
+#616 := (<= #143 0::int)
+#501 := (or #507 #616)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#680 := (pattern #16)
+#81 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#129 := (or #22 #81)
+#687 := (forall (vars (?v0 int)) (:pat #680) #129)
+#134 := (forall (vars (?v0 int)) #129)
+#690 := (iff #134 #687)
+#688 := (iff #129 #129)
+#689 := [refl]: #688
+#691 := [quant-intro #689]: #690
+#189 := (~ #134 #134)
+#203 := (~ #129 #129)
+#204 := [refl]: #203
+#190 := [nnf-pos #204]: #189
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#137 := (iff #24 #134)
+#100 := (= 0::int #17)
+#106 := (not #21)
+#107 := (or #106 #100)
+#112 := (forall (vars (?v0 int)) #107)
+#135 := (iff #112 #134)
+#132 := (iff #107 #129)
+#126 := (or #81 #22)
+#130 := (iff #126 #129)
+#131 := [rewrite]: #130
+#127 := (iff #107 #126)
+#124 := (iff #100 #22)
+#125 := [rewrite]: #124
+#122 := (iff #106 #81)
+#82 := (not #81)
+#117 := (not #82)
+#120 := (iff #117 #81)
+#121 := [rewrite]: #120
+#118 := (iff #106 #117)
+#115 := (iff #21 #82)
+#116 := [rewrite]: #115
+#119 := [monotonicity #116]: #118
+#123 := [trans #119 #121]: #122
+#128 := [monotonicity #123 #125]: #127
+#133 := [trans #128 #131]: #132
+#136 := [quant-intro #133]: #135
+#113 := (iff #24 #112)
+#110 := (iff #23 #107)
+#103 := (implies #21 #100)
+#108 := (iff #103 #107)
+#109 := [rewrite]: #108
+#104 := (iff #23 #103)
+#101 := (iff #22 #100)
+#102 := [rewrite]: #101
+#105 := [monotonicity #102]: #104
+#111 := [trans #105 #109]: #110
+#114 := [quant-intro #111]: #113
+#138 := [trans #114 #136]: #137
+#99 := [asserted]: #24
+#139 := [mp #99 #138]: #134
+#205 := [mp~ #139 #190]: #134
+#692 := [mp #205 #691]: #687
+#624 := (not #687)
+#511 := (or #624 #507 #616)
+#628 := (>= #161 0::int)
+#508 := (or #507 #628)
+#512 := (or #624 #508)
+#588 := (iff #512 #511)
+#606 := (or #624 #501)
+#594 := (iff #606 #511)
+#596 := [rewrite]: #594
+#603 := (iff #512 #606)
+#509 := (iff #508 #501)
+#623 := (iff #628 #616)
+#452 := [rewrite]: #623
+#510 := [monotonicity #452]: #509
+#607 := [monotonicity #510]: #603
+#585 := [trans #607 #596]: #588
+#513 := [quant-inst]: #512
+#587 := [mp #513 #585]: #511
+#520 := [unit-resolution #587 #692]: #501
+#530 := [unit-resolution #520 #540]: #616
+#454 := (not #616)
+#609 := (or #614 #454)
+#63 := (= #14 #17)
+#88 := (or #63 #82)
+#681 := (forall (vars (?v0 int)) (:pat #680) #88)
+#93 := (forall (vars (?v0 int)) #88)
+#684 := (iff #93 #681)
+#682 := (iff #88 #88)
+#683 := [refl]: #682
+#685 := [quant-intro #683]: #684
+#187 := (~ #93 #93)
+#184 := (~ #88 #88)
+#201 := [refl]: #184
+#188 := [nnf-pos #201]: #187
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#96 := (iff #20 #93)
+#70 := (not #15)
+#71 := (or #70 #63)
+#76 := (forall (vars (?v0 int)) #71)
+#94 := (iff #76 #93)
+#91 := (iff #71 #88)
+#85 := (or #82 #63)
+#89 := (iff #85 #88)
+#90 := [rewrite]: #89
+#86 := (iff #71 #85)
+#83 := (iff #70 #82)
+#79 := (iff #15 #81)
+#80 := [rewrite]: #79
+#84 := [monotonicity #80]: #83
+#87 := [monotonicity #84]: #86
+#92 := [trans #87 #90]: #91
+#95 := [quant-intro #92]: #94
+#77 := (iff #20 #76)
+#74 := (iff #19 #71)
+#67 := (implies #15 #63)
+#72 := (iff #67 #71)
+#73 := [rewrite]: #72
+#68 := (iff #19 #67)
+#65 := (iff #18 #63)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#75 := [trans #69 #73]: #74
+#78 := [quant-intro #75]: #77
+#97 := [trans #78 #95]: #96
+#62 := [asserted]: #20
+#98 := [mp #62 #97]: #93
+#202 := [mp~ #98 #188]: #93
+#686 := [mp #202 #685]: #681
+#647 := (not #681)
+#610 := (or #647 #614 #454)
+#629 := (not #628)
+#618 := (= #161 #617)
+#619 := (or #618 #629)
+#613 := (or #647 #619)
+#601 := (iff #613 #610)
+#496 := (or #647 #609)
+#604 := (iff #496 #610)
+#506 := [rewrite]: #604
+#497 := (iff #613 #496)
+#611 := (iff #619 #609)
+#455 := (iff #629 #454)
+#608 := [monotonicity #452]: #455
+#620 := (iff #618 #614)
+#615 := [rewrite]: #620
+#612 := [monotonicity #615 #608]: #611
+#456 := [monotonicity #612]: #497
+#602 := [trans #456 #506]: #601
+#495 := [quant-inst]: #613
+#605 := [mp #495 #602]: #610
+#533 := [unit-resolution #605 #686]: #609
+#534 := [unit-resolution #533 #530]: #614
+#535 := (not #614)
+#531 := (or #535 #505)
+#536 := [th-lemma]: #531
+#516 := [unit-resolution #536 #534]: #505
+#462 := (not #505)
+#517 := (or #598 #462 #454)
+#498 := [th-lemma]: #517
+#522 := [unit-resolution #498 #530 #516]: #598
+#518 := (not #598)
+#524 := (or #507 #523 #518)
+#492 := [th-lemma]: #524
+#499 := [unit-resolution #492 #522 #540]: #523
+#490 := (<= #622 0::int)
+#458 := (or #535 #490)
+#489 := [th-lemma]: #458
+#491 := [unit-resolution #489 #534]: #490
+#493 := (not #490)
+#500 := (or #659 #597 #493)
+#502 := [th-lemma]: #500
+#503 := [unit-resolution #502 #491 #499]: #659
+#627 := (or #638 #656)
+#625 := (or #624 #638 #656)
+#630 := (or #624 #627)
+#626 := (iff #630 #625)
+#632 := [rewrite]: #626
+#631 := [quant-inst]: #630
+#473 := [mp #631 #632]: #625
+#504 := [unit-resolution #473 #692]: #627
+#514 := [unit-resolution #504 #503]: #638
+#515 := [symm #514]: #494
+#471 := [monotonicity #515]: #470
+#478 := [trans #471 #477]: #152
+#181 := [and-elim #183]: #157
+[unit-resolution #181 #478]: false
+unsat
+206fdc571c96e857b861e47f6915cc8941eb6161 33 0
+#2 := false
+decl f3 :: (-> int S2)
+#13 := 0::int
+#29 := (f3 0::int)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#27 := (* #26 0::int)
+#28 := (f3 #27)
+#30 := (= #28 #29)
+#31 := (not #30)
+#149 := (iff #31 false)
+#1 := true
+#144 := (not true)
+#147 := (iff #144 false)
+#148 := [rewrite]: #147
+#145 := (iff #31 #144)
+#142 := (iff #30 true)
+#137 := (= #29 #29)
+#140 := (iff #137 true)
+#141 := [rewrite]: #140
+#138 := (iff #30 #137)
+#134 := (= #27 0::int)
+#135 := [rewrite]: #134
+#136 := [monotonicity #135]: #30
+#139 := [monotonicity #136]: #138
+#143 := [trans #139 #141]: #142
+#146 := [monotonicity #143]: #145
+#150 := [trans #146 #148]: #149
+#133 := [asserted]: #31
+[mp #133 #150]: false
+unsat
+ee33631d0954fd84f61d52487d899741e6b2c604 33 0
+#2 := false
+decl f3 :: (-> int S2)
+#13 := 0::int
+#29 := (f3 0::int)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#27 := (* 0::int #26)
+#28 := (f3 #27)
+#30 := (= #28 #29)
+#31 := (not #30)
+#149 := (iff #31 false)
+#1 := true
+#144 := (not true)
+#147 := (iff #144 false)
+#148 := [rewrite]: #147
+#145 := (iff #31 #144)
+#142 := (iff #30 true)
+#137 := (= #29 #29)
+#140 := (iff #137 true)
+#141 := [rewrite]: #140
+#138 := (iff #30 #137)
+#134 := (= #27 0::int)
+#135 := [rewrite]: #134
+#136 := [monotonicity #135]: #30
+#139 := [monotonicity #136]: #138
+#143 := [trans #139 #141]: #142
+#146 := [monotonicity #143]: #145
+#150 := [trans #146 #148]: #149
+#133 := [asserted]: #31
+[mp #133 #150]: false
+unsat
+a52f3d3f145bed3b2ad2f7ee15aba0955eef027c 329 0
+#2 := false
+decl f6 :: S2
+#27 := f6
+decl f5 :: S2
+#25 := f5
+#13 := 0::int
+decl f4 :: (-> S2 int)
+#28 := (f4 f6)
+#140 := -1::int
+#141 := (* -1::int #28)
+#26 := (f4 f5)
+#142 := (+ #26 #141)
+#174 := (>= #142 0::int)
+#180 := (ite #174 f5 f6)
+decl f3 :: (-> int S2)
+#145 := (f3 #142)
+#148 := (f4 #145)
+#154 := (+ #28 #148)
+#159 := (f3 #154)
+#188 := (= #159 #180)
+#358 := (= f6 #180)
+#173 := (not #174)
+#272 := (= f5 #180)
+#589 := [hypothesis]: #174
+#273 := (or #173 #272)
+#359 := [def-axiom]: #273
+#590 := [unit-resolution #359 #589]: #272
+#507 := (= #159 f5)
+#291 := (f3 #26)
+#533 := (= #291 f5)
+#364 := (= f5 #291)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#687 := (pattern #9)
+#10 := (f3 #9)
+#55 := (= #8 #10)
+#688 := (forall (vars (?v0 S2)) (:pat #687) #55)
+#58 := (forall (vars (?v0 S2)) #55)
+#689 := (iff #58 #688)
+#691 := (iff #688 #688)
+#692 := [rewrite]: #691
+#690 := [rewrite]: #689
+#693 := [trans #690 #692]: #689
+#212 := (~ #58 #58)
+#210 := (~ #55 #55)
+#211 := [refl]: #210
+#213 := [nnf-pos #211]: #212
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#59 := (iff #12 #58)
+#56 := (iff #11 #55)
+#57 := [rewrite]: #56
+#60 := [quant-intro #57]: #59
+#54 := [asserted]: #12
+#63 := [mp #54 #60]: #58
+#201 := [mp~ #63 #213]: #58
+#694 := [mp #201 #693]: #688
+#361 := (not #688)
+#338 := (or #361 #364)
+#468 := [quant-inst]: #338
+#580 := [unit-resolution #468 #694]: #364
+#539 := [symm #580]: #533
+#532 := (= #159 #291)
+#553 := (= #154 #26)
+#582 := (= #26 #154)
+#683 := (* -1::int #148)
+#684 := (+ #141 #683)
+#685 := (+ #26 #684)
+#672 := (<= #685 0::int)
+#680 := (= #685 0::int)
+#337 := (or #173 #680)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#695 := (pattern #16)
+#80 := (>= #14 0::int)
+#81 := (not #80)
+#17 := (f4 #16)
+#62 := (= #14 #17)
+#87 := (or #62 #81)
+#696 := (forall (vars (?v0 int)) (:pat #695) #87)
+#92 := (forall (vars (?v0 int)) #87)
+#699 := (iff #92 #696)
+#697 := (iff #87 #87)
+#698 := [refl]: #697
+#700 := [quant-intro #698]: #699
+#202 := (~ #92 #92)
+#199 := (~ #87 #87)
+#214 := [refl]: #199
+#203 := [nnf-pos #214]: #202
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#95 := (iff #20 #92)
+#69 := (not #15)
+#70 := (or #69 #62)
+#75 := (forall (vars (?v0 int)) #70)
+#93 := (iff #75 #92)
+#90 := (iff #70 #87)
+#84 := (or #81 #62)
+#88 := (iff #84 #87)
+#89 := [rewrite]: #88
+#85 := (iff #70 #84)
+#82 := (iff #69 #81)
+#78 := (iff #15 #80)
+#79 := [rewrite]: #78
+#83 := [monotonicity #79]: #82
+#86 := [monotonicity #83]: #85
+#91 := [trans #86 #89]: #90
+#94 := [quant-intro #91]: #93
+#76 := (iff #20 #75)
+#73 := (iff #19 #70)
+#66 := (implies #15 #62)
+#71 := (iff #66 #70)
+#72 := [rewrite]: #71
+#67 := (iff #19 #66)
+#64 := (iff #18 #62)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#74 := [trans #68 #72]: #73
+#77 := [quant-intro #74]: #76
+#96 := [trans #77 #94]: #95
+#61 := [asserted]: #20
+#97 := [mp #61 #96]: #92
+#215 := [mp~ #97 #203]: #92
+#701 := [mp #215 #700]: #696
+#326 := (not #696)
+#327 := (or #326 #173 #680)
+#675 := (= #142 #148)
+#349 := (or #675 #173)
+#328 := (or #326 #349)
+#669 := (iff #328 #327)
+#665 := (or #326 #337)
+#668 := (iff #665 #327)
+#663 := [rewrite]: #668
+#666 := (iff #328 #665)
+#662 := (iff #349 #337)
+#336 := (or #680 #173)
+#678 := (iff #336 #337)
+#321 := [rewrite]: #678
+#341 := (iff #349 #336)
+#686 := (iff #675 #680)
+#676 := [rewrite]: #686
+#677 := [monotonicity #676]: #341
+#325 := [trans #677 #321]: #662
+#667 := [monotonicity #325]: #666
+#307 := [trans #667 #663]: #669
+#664 := [quant-inst]: #328
+#670 := [mp #664 #307]: #327
+#547 := [unit-resolution #670 #701]: #337
+#543 := [unit-resolution #547 #589]: #680
+#544 := (not #680)
+#545 := (or #544 #672)
+#548 := [th-lemma]: #545
+#549 := [unit-resolution #548 #543]: #672
+#312 := (>= #685 0::int)
+#550 := (or #544 #312)
+#546 := [th-lemma]: #550
+#551 := [unit-resolution #546 #543]: #312
+#531 := [th-lemma #551 #549]: #582
+#477 := [symm #531]: #553
+#513 := [monotonicity #477]: #532
+#514 := [trans #513 #539]: #507
+#473 := [trans #514 #590]: #188
+#193 := (not #188)
+#34 := (< #26 #28)
+#35 := (ite #34 f6 f5)
+#29 := (- #26 #28)
+#30 := (f3 #29)
+#31 := (f4 #30)
+#32 := (+ #31 #28)
+#33 := (f3 #32)
+#36 := (= #33 #35)
+#37 := (not #36)
+#196 := (iff #37 #193)
+#165 := (= #35 #159)
+#170 := (not #165)
+#194 := (iff #170 #193)
+#191 := (iff #165 #188)
+#185 := (= #180 #159)
+#189 := (iff #185 #188)
+#190 := [rewrite]: #189
+#186 := (iff #165 #185)
+#183 := (= #35 #180)
+#177 := (ite #173 f6 f5)
+#181 := (= #177 #180)
+#182 := [rewrite]: #181
+#178 := (= #35 #177)
+#175 := (iff #34 #173)
+#176 := [rewrite]: #175
+#179 := [monotonicity #176]: #178
+#184 := [trans #179 #182]: #183
+#187 := [monotonicity #184]: #186
+#192 := [trans #187 #190]: #191
+#195 := [monotonicity #192]: #194
+#171 := (iff #37 #170)
+#168 := (iff #36 #165)
+#162 := (= #159 #35)
+#166 := (iff #162 #165)
+#167 := [rewrite]: #166
+#163 := (iff #36 #162)
+#160 := (= #33 #159)
+#157 := (= #32 #154)
+#151 := (+ #148 #28)
+#155 := (= #151 #154)
+#156 := [rewrite]: #155
+#152 := (= #32 #151)
+#149 := (= #31 #148)
+#146 := (= #30 #145)
+#143 := (= #29 #142)
+#144 := [rewrite]: #143
+#147 := [monotonicity #144]: #146
+#150 := [monotonicity #147]: #149
+#153 := [monotonicity #150]: #152
+#158 := [trans #153 #156]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#169 := [trans #164 #167]: #168
+#172 := [monotonicity #169]: #171
+#197 := [trans #172 #195]: #196
+#139 := [asserted]: #37
+#198 := [mp #139 #197]: #193
+#504 := [unit-resolution #198 #473]: false
+#506 := [lemma #504]: #173
+#360 := (or #174 #358)
+#351 := [def-axiom]: #360
+#542 := [unit-resolution #351 #506]: #358
+#498 := (= #159 f6)
+#362 := (f3 #28)
+#496 := (= #362 f6)
+#363 := (= f6 #362)
+#365 := (or #361 #363)
+#344 := [quant-inst]: #365
+#541 := [unit-resolution #344 #694]: #363
+#497 := [symm #541]: #496
+#492 := (= #159 #362)
+#486 := (= #154 #28)
+#530 := (= #28 #154)
+#655 := (<= #148 0::int)
+#313 := (= #148 0::int)
+#671 := (or #174 #313)
+#22 := (= #17 0::int)
+#128 := (or #22 #80)
+#702 := (forall (vars (?v0 int)) (:pat #695) #128)
+#133 := (forall (vars (?v0 int)) #128)
+#705 := (iff #133 #702)
+#703 := (iff #128 #128)
+#704 := [refl]: #703
+#706 := [quant-intro #704]: #705
+#204 := (~ #133 #133)
+#216 := (~ #128 #128)
+#217 := [refl]: #216
+#205 := [nnf-pos #217]: #204
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#136 := (iff #24 #133)
+#99 := (= 0::int #17)
+#105 := (not #21)
+#106 := (or #105 #99)
+#111 := (forall (vars (?v0 int)) #106)
+#134 := (iff #111 #133)
+#131 := (iff #106 #128)
+#125 := (or #80 #22)
+#129 := (iff #125 #128)
+#130 := [rewrite]: #129
+#126 := (iff #106 #125)
+#123 := (iff #99 #22)
+#124 := [rewrite]: #123
+#121 := (iff #105 #80)
+#116 := (not #81)
+#119 := (iff #116 #80)
+#120 := [rewrite]: #119
+#117 := (iff #105 #116)
+#114 := (iff #21 #81)
+#115 := [rewrite]: #114
+#118 := [monotonicity #115]: #117
+#122 := [trans #118 #120]: #121
+#127 := [monotonicity #122 #124]: #126
+#132 := [trans #127 #130]: #131
+#135 := [quant-intro #132]: #134
+#112 := (iff #24 #111)
+#109 := (iff #23 #106)
+#102 := (implies #21 #99)
+#107 := (iff #102 #106)
+#108 := [rewrite]: #107
+#103 := (iff #23 #102)
+#100 := (iff #22 #99)
+#101 := [rewrite]: #100
+#104 := [monotonicity #101]: #103
+#110 := [trans #104 #108]: #109
+#113 := [quant-intro #110]: #112
+#137 := [trans #113 #135]: #136
+#98 := [asserted]: #24
+#138 := [mp #98 #137]: #133
+#218 := [mp~ #138 #205]: #133
+#707 := [mp #218 #706]: #702
+#661 := (not #702)
+#383 := (or #661 #174 #313)
+#673 := (or #313 #174)
+#384 := (or #661 #673)
+#380 := (iff #384 #383)
+#386 := (or #661 #671)
+#657 := (iff #386 #383)
+#379 := [rewrite]: #657
+#279 := (iff #384 #386)
+#674 := (iff #673 #671)
+#660 := [rewrite]: #674
+#656 := [monotonicity #660]: #279
+#654 := [trans #656 #379]: #380
+#385 := [quant-inst]: #384
+#658 := [mp #385 #654]: #383
+#537 := [unit-resolution #658 #707]: #671
+#538 := [unit-resolution #537 #506]: #313
+#508 := (not #313)
+#515 := (or #508 #655)
+#517 := [th-lemma]: #515
+#518 := [unit-resolution #517 #538]: #655
+#659 := (>= #148 0::int)
+#519 := (or #508 #659)
+#529 := [th-lemma]: #519
+#509 := [unit-resolution #529 #538]: #659
+#485 := [th-lemma #509 #518]: #530
+#491 := [symm #485]: #486
+#493 := [monotonicity #491]: #492
+#499 := [trans #493 #497]: #498
+#500 := [trans #499 #542]: #188
+[unit-resolution #198 #500]: false
+unsat
+71a8731b24573e8c3f19635efbc778a168d7006c 60 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#136 := (f3 #26)
+#142 := (= f5 #136)
+#147 := (not #142)
+#27 := 1::int
+#28 := (* #26 1::int)
+#29 := (f3 #28)
+#30 := (= #29 f5)
+#31 := (not #30)
+#148 := (iff #31 #147)
+#145 := (iff #30 #142)
+#139 := (= #136 f5)
+#143 := (iff #139 #142)
+#144 := [rewrite]: #143
+#140 := (iff #30 #139)
+#137 := (= #29 #136)
+#134 := (= #28 #26)
+#135 := [rewrite]: #134
+#138 := [monotonicity #135]: #137
+#141 := [monotonicity #138]: #140
+#146 := [trans #141 #144]: #145
+#149 := [monotonicity #146]: #148
+#133 := [asserted]: #31
+#152 := [mp #133 #149]: #147
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#639 := (pattern #9)
+#10 := (f3 #9)
+#49 := (= #8 #10)
+#640 := (forall (vars (?v0 S2)) (:pat #639) #49)
+#52 := (forall (vars (?v0 S2)) #49)
+#641 := (iff #52 #640)
+#643 := (iff #640 #640)
+#644 := [rewrite]: #643
+#642 := [rewrite]: #641
+#645 := [trans #642 #644]: #641
+#164 := (~ #52 #52)
+#162 := (~ #49 #49)
+#163 := [refl]: #162
+#165 := [nnf-pos #163]: #164
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#53 := (iff #12 #52)
+#50 := (iff #11 #49)
+#51 := [rewrite]: #50
+#54 := [quant-intro #51]: #53
+#48 := [asserted]: #12
+#57 := [mp #48 #54]: #52
+#153 := [mp~ #57 #165]: #52
+#646 := [mp #153 #645]: #640
+#225 := (not #640)
+#310 := (or #225 #142)
+#311 := [quant-inst]: #310
+[unit-resolution #311 #646 #152]: false
+unsat
+be5efb86f9b9b267348d77366692337b5c5df35f 517 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f3 :: (-> int S2)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#143 := -1::int
+#144 := (* -1::int #28)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#145 := (+ #26 #144)
+#148 := (f3 #145)
+#151 := (f4 #148)
+#664 := (* -1::int #151)
+#665 := (+ #144 #664)
+#666 := (+ #26 #665)
+#661 := (= #666 0::int)
+#422 := (not #661)
+#293 := (>= #666 0::int)
+#314 := (not #293)
+decl f7 :: S2
+#32 := f7
+#33 := (f4 f7)
+#157 := (* -1::int #33)
+#166 := (+ #144 #157)
+#167 := (+ #26 #166)
+#503 := (>= #167 0::int)
+#504 := (not #503)
+#170 := (f3 #167)
+#158 := (+ #157 #151)
+#163 := (f3 #158)
+#173 := (= #163 #170)
+#497 := (f4 #170)
+#490 := (f3 #497)
+#447 := (= #490 #170)
+#511 := (= #170 #490)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#668 := (pattern #9)
+#10 := (f3 #9)
+#58 := (= #8 #10)
+#669 := (forall (vars (?v0 S2)) (:pat #668) #58)
+#61 := (forall (vars (?v0 S2)) #58)
+#670 := (iff #61 #669)
+#672 := (iff #669 #669)
+#673 := [rewrite]: #672
+#671 := [rewrite]: #670
+#674 := [trans #671 #673]: #670
+#193 := (~ #61 #61)
+#191 := (~ #58 #58)
+#192 := [refl]: #191
+#194 := [nnf-pos #192]: #193
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#62 := (iff #12 #61)
+#59 := (iff #11 #58)
+#60 := [rewrite]: #59
+#63 := [quant-intro #60]: #62
+#57 := [asserted]: #12
+#66 := [mp #57 #63]: #61
+#182 := [mp~ #66 #194]: #61
+#675 := [mp #182 #674]: #669
+#341 := (not #669)
+#445 := (or #341 #511)
+#446 := [quant-inst]: #445
+#459 := [unit-resolution #446 #675]: #511
+#465 := [symm #459]: #447
+#435 := (= #163 #490)
+#360 := (f4 #163)
+#495 := (f3 #360)
+#463 := (= #495 #490)
+#327 := (= #360 #497)
+#507 := (* -1::int #497)
+#508 := (+ #157 #507)
+#509 := (+ #144 #508)
+#602 := (+ #26 #509)
+#578 := (<= #602 0::int)
+#599 := (= #602 0::int)
+#400 := [hypothesis]: #503
+#583 := (or #504 #599)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#676 := (pattern #16)
+#83 := (>= #14 0::int)
+#84 := (not #83)
+#17 := (f4 #16)
+#65 := (= #14 #17)
+#90 := (or #65 #84)
+#677 := (forall (vars (?v0 int)) (:pat #676) #90)
+#95 := (forall (vars (?v0 int)) #90)
+#680 := (iff #95 #677)
+#678 := (iff #90 #90)
+#679 := [refl]: #678
+#681 := [quant-intro #679]: #680
+#183 := (~ #95 #95)
+#179 := (~ #90 #90)
+#195 := [refl]: #179
+#184 := [nnf-pos #195]: #183
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#98 := (iff #20 #95)
+#72 := (not #15)
+#73 := (or #72 #65)
+#78 := (forall (vars (?v0 int)) #73)
+#96 := (iff #78 #95)
+#93 := (iff #73 #90)
+#87 := (or #84 #65)
+#91 := (iff #87 #90)
+#92 := [rewrite]: #91
+#88 := (iff #73 #87)
+#85 := (iff #72 #84)
+#81 := (iff #15 #83)
+#82 := [rewrite]: #81
+#86 := [monotonicity #82]: #85
+#89 := [monotonicity #86]: #88
+#94 := [trans #89 #92]: #93
+#97 := [quant-intro #94]: #96
+#79 := (iff #20 #78)
+#76 := (iff #19 #73)
+#69 := (implies #15 #65)
+#74 := (iff #69 #73)
+#75 := [rewrite]: #74
+#70 := (iff #19 #69)
+#67 := (iff #18 #65)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#77 := [trans #71 #75]: #76
+#80 := [quant-intro #77]: #79
+#99 := [trans #80 #97]: #98
+#64 := [asserted]: #20
+#100 := [mp #64 #99]: #95
+#196 := [mp~ #100 #184]: #95
+#682 := [mp #196 #681]: #677
+#307 := (not #677)
+#596 := (or #307 #504 #599)
+#505 := (= #167 #497)
+#506 := (or #505 #504)
+#585 := (or #307 #506)
+#574 := (iff #585 #596)
+#587 := (or #307 #583)
+#589 := (iff #587 #596)
+#573 := [rewrite]: #589
+#588 := (iff #585 #587)
+#595 := (iff #506 #583)
+#592 := (or #599 #504)
+#593 := (iff #592 #583)
+#594 := [rewrite]: #593
+#584 := (iff #506 #592)
+#603 := (iff #505 #599)
+#590 := [rewrite]: #603
+#581 := [monotonicity #590]: #584
+#591 := [trans #581 #594]: #595
+#582 := [monotonicity #591]: #588
+#576 := [trans #582 #573]: #574
+#586 := [quant-inst]: #585
+#577 := [mp #586 #576]: #596
+#401 := [unit-resolution #577 #682]: #583
+#399 := [unit-resolution #401 #400]: #599
+#402 := (not #599)
+#391 := (or #402 #578)
+#403 := [th-lemma]: #391
+#398 := [unit-resolution #403 #399]: #578
+#579 := (>= #602 0::int)
+#378 := (or #402 #579)
+#377 := [th-lemma]: #378
+#379 := [unit-resolution #377 #399]: #579
+#653 := (<= #666 0::int)
+#319 := (>= #145 0::int)
+#561 := (>= #497 0::int)
+#368 := (not #578)
+#369 := (or #561 #368 #504)
+#370 := [th-lemma]: #369
+#362 := [unit-resolution #370 #398 #400]: #561
+#372 := (not #579)
+#371 := (not #561)
+#354 := (or #319 #371 #372)
+#562 := (>= #33 0::int)
+#397 := (= #33 0::int)
+#253 := (f3 #33)
+#563 := (f4 #253)
+#564 := (= #563 0::int)
+#380 := (not #562)
+#382 := [hypothesis]: #380
+#565 := (or #562 #564)
+#22 := (= #17 0::int)
+#131 := (or #22 #83)
+#683 := (forall (vars (?v0 int)) (:pat #676) #131)
+#136 := (forall (vars (?v0 int)) #131)
+#686 := (iff #136 #683)
+#684 := (iff #131 #131)
+#685 := [refl]: #684
+#687 := [quant-intro #685]: #686
+#185 := (~ #136 #136)
+#197 := (~ #131 #131)
+#198 := [refl]: #197
+#186 := [nnf-pos #198]: #185
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#139 := (iff #24 #136)
+#102 := (= 0::int #17)
+#108 := (not #21)
+#109 := (or #108 #102)
+#114 := (forall (vars (?v0 int)) #109)
+#137 := (iff #114 #136)
+#134 := (iff #109 #131)
+#128 := (or #83 #22)
+#132 := (iff #128 #131)
+#133 := [rewrite]: #132
+#129 := (iff #109 #128)
+#126 := (iff #102 #22)
+#127 := [rewrite]: #126
+#124 := (iff #108 #83)
+#119 := (not #84)
+#122 := (iff #119 #83)
+#123 := [rewrite]: #122
+#120 := (iff #108 #119)
+#117 := (iff #21 #84)
+#118 := [rewrite]: #117
+#121 := [monotonicity #118]: #120
+#125 := [trans #121 #123]: #124
+#130 := [monotonicity #125 #127]: #129
+#135 := [trans #130 #133]: #134
+#138 := [quant-intro #135]: #137
+#115 := (iff #24 #114)
+#112 := (iff #23 #109)
+#105 := (implies #21 #102)
+#110 := (iff #105 #109)
+#111 := [rewrite]: #110
+#106 := (iff #23 #105)
+#103 := (iff #22 #102)
+#104 := [rewrite]: #103
+#107 := [monotonicity #104]: #106
+#113 := [trans #107 #111]: #112
+#116 := [quant-intro #113]: #115
+#140 := [trans #116 #138]: #139
+#101 := [asserted]: #24
+#141 := [mp #101 #140]: #136
+#199 := [mp~ #141 #186]: #136
+#688 := [mp #199 #687]: #683
+#641 := (not #683)
+#546 := (or #641 #562 #564)
+#554 := (or #564 #562)
+#547 := (or #641 #554)
+#533 := (iff #547 #546)
+#549 := (or #641 #565)
+#551 := (iff #549 #546)
+#537 := [rewrite]: #551
+#550 := (iff #547 #549)
+#543 := (iff #554 #565)
+#544 := [rewrite]: #543
+#545 := [monotonicity #544]: #550
+#534 := [trans #545 #537]: #533
+#548 := [quant-inst]: #547
+#535 := [mp #548 #534]: #546
+#383 := [unit-resolution #535 #688]: #565
+#384 := [unit-resolution #383 #382]: #564
+#386 := (= #33 #563)
+#339 := (= f7 #253)
+#332 := (or #341 #339)
+#343 := [quant-inst]: #332
+#385 := [unit-resolution #343 #675]: #339
+#387 := [monotonicity #385]: #386
+#388 := [trans #387 #384]: #397
+#381 := (not #397)
+#389 := (or #381 #562)
+#374 := [th-lemma]: #389
+#375 := [unit-resolution #374 #382 #388]: false
+#376 := [lemma #375]: #562
+#363 := (or #380 #319 #371 #372)
+#373 := [th-lemma]: #363
+#355 := [unit-resolution #373 #376]: #354
+#356 := [unit-resolution #355 #362 #379]: #319
+#449 := (not #319)
+#318 := (or #449 #661)
+#308 := (or #307 #449 #661)
+#331 := (= #145 #151)
+#663 := (or #331 #449)
+#309 := (or #307 #663)
+#650 := (iff #309 #308)
+#646 := (or #307 #318)
+#649 := (iff #646 #308)
+#644 := [rewrite]: #649
+#647 := (iff #309 #646)
+#643 := (iff #663 #318)
+#317 := (or #661 #449)
+#659 := (iff #317 #318)
+#302 := [rewrite]: #659
+#322 := (iff #663 #317)
+#667 := (iff #331 #661)
+#657 := [rewrite]: #667
+#658 := [monotonicity #657]: #322
+#306 := [trans #658 #302]: #643
+#648 := [monotonicity #306]: #647
+#288 := [trans #648 #644]: #650
+#645 := [quant-inst]: #309
+#651 := [mp #645 #288]: #308
+#424 := [unit-resolution #651 #682]: #318
+#348 := [unit-resolution #424 #356]: #661
+#425 := (or #422 #653)
+#427 := [th-lemma]: #425
+#357 := [unit-resolution #427 #348]: #653
+#358 := (or #422 #293)
+#349 := [th-lemma]: #358
+#359 := [unit-resolution #349 #348]: #293
+#350 := (+ #664 #360)
+#351 := (+ #33 #350)
+#611 := (<= #351 0::int)
+#636 := (= #351 0::int)
+#352 := (+ #33 #664)
+#353 := (<= #352 0::int)
+#294 := (= #151 0::int)
+#432 := (not #653)
+#575 := (= #497 0::int)
+#440 := (not #575)
+#618 := (= #360 0::int)
+#347 := (not #353)
+#443 := [hypothesis]: #347
+#451 := (or #353 #618)
+#606 := (or #641 #353 #618)
+#652 := (>= #158 0::int)
+#612 := (or #618 #652)
+#609 := (or #641 #612)
+#597 := (iff #609 #606)
+#492 := (or #641 #451)
+#600 := (iff #492 #606)
+#502 := [rewrite]: #600
+#493 := (iff #609 #492)
+#607 := (iff #612 #451)
+#619 := (or #618 #353)
+#604 := (iff #619 #451)
+#605 := [rewrite]: #604
+#448 := (iff #612 #619)
+#631 := (iff #652 #353)
+#632 := [rewrite]: #631
+#450 := [monotonicity #632]: #448
+#608 := [trans #450 #605]: #607
+#452 := [monotonicity #608]: #493
+#598 := [trans #452 #502]: #597
+#491 := [quant-inst]: #609
+#601 := [mp #491 #598]: #606
+#439 := [unit-resolution #601 #688]: #451
+#444 := [unit-resolution #439 #443]: #618
+#441 := (not #618)
+#442 := (or #440 #441)
+#461 := (= #490 #495)
+#456 := (= #497 #360)
+#453 := (= 0::int #360)
+#468 := [hypothesis]: #618
+#455 := [symm #468]: #453
+#484 := [hypothesis]: #575
+#457 := [trans #484 #455]: #456
+#462 := [monotonicity #457]: #461
+#464 := [symm #462]: #463
+#454 := (= #163 #495)
+#510 := (or #341 #454)
+#483 := [quant-inst]: #510
+#460 := [unit-resolution #483 #675]: #454
+#436 := [trans #460 #464]: #435
+#437 := [trans #436 #465]: #173
+#176 := (not #173)
+#36 := (+ #28 #33)
+#37 := (- #26 #36)
+#38 := (f3 #37)
+#29 := (- #26 #28)
+#30 := (f3 #29)
+#31 := (f4 #30)
+#34 := (- #31 #33)
+#35 := (f3 #34)
+#39 := (= #35 #38)
+#40 := (not #39)
+#177 := (iff #40 #176)
+#174 := (iff #39 #173)
+#171 := (= #38 #170)
+#168 := (= #37 #167)
+#169 := [rewrite]: #168
+#172 := [monotonicity #169]: #171
+#164 := (= #35 #163)
+#161 := (= #34 #158)
+#154 := (- #151 #33)
+#159 := (= #154 #158)
+#160 := [rewrite]: #159
+#155 := (= #34 #154)
+#152 := (= #31 #151)
+#149 := (= #30 #148)
+#146 := (= #29 #145)
+#147 := [rewrite]: #146
+#150 := [monotonicity #147]: #149
+#153 := [monotonicity #150]: #152
+#156 := [monotonicity #153]: #155
+#162 := [trans #156 #160]: #161
+#165 := [monotonicity #162]: #164
+#175 := [monotonicity #165 #172]: #174
+#178 := [monotonicity #175]: #177
+#142 := [asserted]: #40
+#181 := [mp #142 #178]: #176
+#438 := [unit-resolution #181 #437]: false
+#285 := [lemma #438]: #442
+#423 := [unit-resolution #285 #444]: #440
+#566 := (or #503 #575)
+#570 := (or #641 #503 #575)
+#580 := (or #575 #503)
+#571 := (or #641 #580)
+#557 := (iff #571 #570)
+#572 := (or #641 #566)
+#555 := (iff #572 #570)
+#556 := [rewrite]: #555
+#552 := (iff #571 #572)
+#567 := (iff #580 #566)
+#569 := [rewrite]: #567
+#553 := [monotonicity #569]: #552
+#558 := [trans #553 #556]: #557
+#568 := [quant-inst]: #571
+#559 := [mp #568 #558]: #570
+#426 := [unit-resolution #559 #688]: #566
+#430 := [unit-resolution #426 #423]: #503
+#433 := (or #432 #504 #353)
+#431 := [th-lemma]: #433
+#434 := [unit-resolution #431 #443 #430]: #432
+#428 := [unit-resolution #427 #434]: #422
+#429 := [unit-resolution #424 #428]: #449
+#654 := (or #294 #319)
+#642 := (or #641 #294 #319)
+#364 := (or #641 #654)
+#366 := (iff #364 #642)
+#367 := [rewrite]: #366
+#365 := [quant-inst]: #364
+#260 := [mp #365 #367]: #642
+#419 := [unit-resolution #260 #688]: #654
+#409 := [unit-resolution #419 #429]: #294
+#638 := (>= #151 0::int)
+#411 := (not #638)
+#412 := (or #504 #319 #411 #353)
+#415 := [th-lemma]: #412
+#416 := [unit-resolution #415 #429 #443 #430]: #411
+#420 := (not #294)
+#413 := (or #420 #638)
+#421 := [th-lemma]: #413
+#414 := [unit-resolution #421 #416 #409]: false
+#417 := [lemma #414]: #353
+#624 := (or #347 #636)
+#627 := (or #307 #347 #636)
+#655 := (not #652)
+#361 := (= #158 #360)
+#635 := (or #361 #655)
+#622 := (or #307 #635)
+#615 := (iff #622 #627)
+#469 := (or #307 #624)
+#613 := (iff #469 #627)
+#614 := [rewrite]: #613
+#470 := (iff #622 #469)
+#621 := (iff #635 #624)
+#630 := (or #636 #347)
+#625 := (iff #630 #624)
+#620 := [rewrite]: #625
+#634 := (iff #635 #630)
+#629 := (iff #655 #347)
+#633 := [monotonicity #632]: #629
+#639 := (iff #361 #636)
+#640 := [rewrite]: #639
+#623 := [monotonicity #640 #633]: #634
+#626 := [trans #623 #620]: #621
+#471 := [monotonicity #626]: #470
+#616 := [trans #471 #614]: #615
+#628 := [quant-inst]: #622
+#610 := [mp #628 #616]: #627
+#326 := [unit-resolution #610 #682]: #624
+#328 := [unit-resolution #326 #417]: #636
+#329 := (not #636)
+#320 := (or #329 #611)
+#333 := [th-lemma]: #320
+#334 := [unit-resolution #333 #328]: #611
+#617 := (>= #351 0::int)
+#335 := (or #329 #617)
+#336 := [th-lemma]: #335
+#337 := [unit-resolution #336 #328]: #617
+#338 := [th-lemma #337 #334 #359 #357 #379 #398]: #327
+#321 := [monotonicity #338]: #463
+#323 := [trans #460 #321]: #435
+#324 := [trans #323 #465]: #173
+#303 := [unit-resolution #181 #324]: false
+#305 := [lemma #303]: #504
+#501 := (>= #360 0::int)
+#310 := (not #617)
+#311 := (or #501 #310 #347)
+#312 := [th-lemma]: #311
+#313 := [unit-resolution #312 #337 #417]: #501
+#304 := (not #611)
+#315 := (not #501)
+#316 := (or #314 #503 #315 #304)
+#297 := [th-lemma]: #316
+#299 := [unit-resolution #297 #334 #313 #305]: #314
+#300 := [unit-resolution #349 #299]: #422
+#637 := (<= #151 0::int)
+#270 := (not #637)
+#486 := (<= #360 0::int)
+#289 := (not #486)
+#298 := [unit-resolution #426 #305]: #575
+#301 := [unit-resolution #285 #298]: #441
+#295 := (or #618 #289)
+#291 := (or #618 #289 #315)
+#292 := [th-lemma]: #291
+#290 := [unit-resolution #292 #313]: #295
+#296 := [unit-resolution #290 #301]: #289
+#275 := (or #270 #380 #486 #304)
+#276 := [th-lemma]: #275
+#281 := [unit-resolution #276 #334 #296 #376]: #270
+#283 := (or #420 #637)
+#284 := [th-lemma]: #283
+#286 := [unit-resolution #284 #281]: #420
+#282 := [unit-resolution #419 #286]: #319
+[unit-resolution #424 #282 #300]: false
+unsat
+32c022ad17c4cf631a4452767891ed2e2599b6b6 60 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#26 := f5
+#27 := (f4 f5)
+#136 := (f3 #27)
+#142 := (= f5 #136)
+#147 := (not #142)
+#25 := 1::int
+#28 := (* 1::int #27)
+#29 := (f3 #28)
+#30 := (= #29 f5)
+#31 := (not #30)
+#148 := (iff #31 #147)
+#145 := (iff #30 #142)
+#139 := (= #136 f5)
+#143 := (iff #139 #142)
+#144 := [rewrite]: #143
+#140 := (iff #30 #139)
+#137 := (= #29 #136)
+#134 := (= #28 #27)
+#135 := [rewrite]: #134
+#138 := [monotonicity #135]: #137
+#141 := [monotonicity #138]: #140
+#146 := [trans #141 #144]: #145
+#149 := [monotonicity #146]: #148
+#133 := [asserted]: #31
+#152 := [mp #133 #149]: #147
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#639 := (pattern #9)
+#10 := (f3 #9)
+#49 := (= #8 #10)
+#640 := (forall (vars (?v0 S2)) (:pat #639) #49)
+#52 := (forall (vars (?v0 S2)) #49)
+#641 := (iff #52 #640)
+#643 := (iff #640 #640)
+#644 := [rewrite]: #643
+#642 := [rewrite]: #641
+#645 := [trans #642 #644]: #641
+#164 := (~ #52 #52)
+#162 := (~ #49 #49)
+#163 := [refl]: #162
+#165 := [nnf-pos #163]: #164
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#53 := (iff #12 #52)
+#50 := (iff #11 #49)
+#51 := [rewrite]: #50
+#54 := [quant-intro #51]: #53
+#48 := [asserted]: #12
+#57 := [mp #48 #54]: #52
+#153 := [mp~ #57 #165]: #52
+#646 := [mp #153 #645]: #640
+#225 := (not #640)
+#310 := (or #225 #142)
+#311 := [quant-inst]: #310
+[unit-resolution #311 #646 #152]: false
+unsat
+2ac54103a8769196595536554467f2a8a0f9df5d 35 0
+#2 := false
+decl f3 :: (-> int S2)
+#25 := 3::int
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#26 := f5
+#27 := (f4 f5)
+#30 := (* #27 3::int)
+#31 := (f3 #30)
+#28 := (* 3::int #27)
+#29 := (f3 #28)
+#32 := (= #29 #31)
+#33 := (not #32)
+#152 := (iff #33 false)
+#1 := true
+#147 := (not true)
+#150 := (iff #147 false)
+#151 := [rewrite]: #150
+#148 := (iff #33 #147)
+#145 := (iff #32 true)
+#140 := (= #29 #29)
+#143 := (iff #140 true)
+#144 := [rewrite]: #143
+#141 := (iff #32 #140)
+#138 := (= #31 #29)
+#136 := (= #30 #28)
+#137 := [rewrite]: #136
+#139 := [monotonicity #137]: #138
+#142 := [monotonicity #139]: #141
+#146 := [trans #142 #144]: #145
+#149 := [monotonicity #146]: #148
+#153 := [trans #149 #151]: #152
+#135 := [asserted]: #33
+[mp #135 #153]: false
+unsat
+9f38d775fa2d48952160d8de09d7750a63b8d751 60 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#137 := -1::int
+#138 := (* -1::int #28)
+#139 := (+ #26 #138)
+#140 := (<= #139 0::int)
+#143 := (ite #140 #26 #28)
+#151 := (* -1::int #143)
+#637 := (+ #28 #151)
+#266 := (>= #637 0::int)
+#317 := (= #28 #143)
+#232 := (not #140)
+#231 := (= #26 #143)
+#624 := (not #231)
+#152 := (+ #26 #151)
+#150 := (>= #152 0::int)
+#156 := (not #150)
+#29 := (<= #26 #28)
+#30 := (ite #29 #26 #28)
+#31 := (<= #30 #26)
+#32 := (not #31)
+#157 := (iff #32 #156)
+#154 := (iff #31 #150)
+#146 := (<= #143 #26)
+#149 := (iff #146 #150)
+#153 := [rewrite]: #149
+#147 := (iff #31 #146)
+#144 := (= #30 #143)
+#141 := (iff #29 #140)
+#142 := [rewrite]: #141
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#155 := [trans #148 #153]: #154
+#158 := [monotonicity #155]: #157
+#134 := [asserted]: #32
+#159 := [mp #134 #158]: #156
+#280 := [hypothesis]: #231
+#625 := (or #624 #150)
+#626 := [th-lemma]: #625
+#627 := [unit-resolution #626 #280 #159]: false
+#622 := [lemma #627]: #624
+#318 := (or #232 #231)
+#319 := [def-axiom]: #318
+#629 := [unit-resolution #319 #622]: #232
+#310 := (or #140 #317)
+#321 := [def-axiom]: #310
+#631 := [unit-resolution #321 #629]: #317
+#271 := (not #317)
+#272 := (or #271 #266)
+#632 := [th-lemma]: #272
+#630 := [unit-resolution #632 #631]: #266
+[th-lemma #159 #629 #630]: false
+unsat
+4a98bcbed5ad69511a5cad5cf29dba7132d6fdfc 60 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#137 := -1::int
+#138 := (* -1::int #28)
+#139 := (+ #26 #138)
+#140 := (<= #139 0::int)
+#143 := (ite #140 #26 #28)
+#150 := (* -1::int #143)
+#151 := (+ #28 #150)
+#149 := (>= #151 0::int)
+#156 := (not #149)
+#29 := (<= #26 #28)
+#30 := (ite #29 #26 #28)
+#31 := (<= #30 #28)
+#32 := (not #31)
+#157 := (iff #32 #156)
+#154 := (iff #31 #149)
+#146 := (<= #143 #28)
+#152 := (iff #146 #149)
+#153 := [rewrite]: #152
+#147 := (iff #31 #146)
+#144 := (= #30 #143)
+#141 := (iff #29 #140)
+#142 := [rewrite]: #141
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#155 := [trans #148 #153]: #154
+#158 := [monotonicity #155]: #157
+#134 := [asserted]: #32
+#159 := [mp #134 #158]: #156
+#317 := (= #28 #143)
+#232 := (not #140)
+#625 := [hypothesis]: #140
+#637 := (+ #26 #150)
+#624 := (>= #637 0::int)
+#231 := (= #26 #143)
+#318 := (or #232 #231)
+#319 := [def-axiom]: #318
+#626 := [unit-resolution #319 #625]: #231
+#627 := (not #231)
+#622 := (or #627 #624)
+#628 := [th-lemma]: #622
+#266 := [unit-resolution #628 #626]: #624
+#629 := [th-lemma #266 #159 #625]: false
+#631 := [lemma #629]: #232
+#310 := (or #140 #317)
+#321 := [def-axiom]: #310
+#271 := [unit-resolution #321 #631]: #317
+#272 := (not #317)
+#632 := (or #272 #149)
+#630 := [th-lemma]: #632
+[unit-resolution #630 #271 #159]: false
+unsat
+d8f08e2943c080c0d03c02c5a3f03bf5fa773cee 253 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#138 := -1::int
+#139 := (* -1::int #28)
+#140 := (+ #26 #139)
+#141 := (<= #140 0::int)
+#144 := (ite #141 #26 #28)
+#153 := (* -1::int #144)
+#639 := (+ #26 #153)
+#626 := (>= #639 0::int)
+#274 := (not #626)
+#643 := (>= #28 0::int)
+#333 := (= #28 0::int)
+decl f3 :: (-> int S2)
+#325 := (f3 #28)
+#644 := (f4 #325)
+#638 := (= #644 0::int)
+#340 := (not #643)
+#580 := [hypothesis]: #340
+#298 := (or #638 #643)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#656 := (pattern #16)
+#76 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#124 := (or #22 #76)
+#663 := (forall (vars (?v0 int)) (:pat #656) #124)
+#129 := (forall (vars (?v0 int)) #124)
+#666 := (iff #129 #663)
+#664 := (iff #124 #124)
+#665 := [refl]: #664
+#667 := [quant-intro #665]: #666
+#165 := (~ #129 #129)
+#177 := (~ #124 #124)
+#178 := [refl]: #177
+#166 := [nnf-pos #178]: #165
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#132 := (iff #24 #129)
+#95 := (= 0::int #17)
+#101 := (not #21)
+#102 := (or #101 #95)
+#107 := (forall (vars (?v0 int)) #102)
+#130 := (iff #107 #129)
+#127 := (iff #102 #124)
+#121 := (or #76 #22)
+#125 := (iff #121 #124)
+#126 := [rewrite]: #125
+#122 := (iff #102 #121)
+#119 := (iff #95 #22)
+#120 := [rewrite]: #119
+#117 := (iff #101 #76)
+#77 := (not #76)
+#112 := (not #77)
+#115 := (iff #112 #76)
+#116 := [rewrite]: #115
+#113 := (iff #101 #112)
+#110 := (iff #21 #77)
+#111 := [rewrite]: #110
+#114 := [monotonicity #111]: #113
+#118 := [trans #114 #116]: #117
+#123 := [monotonicity #118 #120]: #122
+#128 := [trans #123 #126]: #127
+#131 := [quant-intro #128]: #130
+#108 := (iff #24 #107)
+#105 := (iff #23 #102)
+#98 := (implies #21 #95)
+#103 := (iff #98 #102)
+#104 := [rewrite]: #103
+#99 := (iff #23 #98)
+#96 := (iff #22 #95)
+#97 := [rewrite]: #96
+#100 := [monotonicity #97]: #99
+#106 := [trans #100 #104]: #105
+#109 := [quant-intro #106]: #108
+#133 := [trans #109 #131]: #132
+#94 := [asserted]: #24
+#134 := [mp #94 #133]: #129
+#179 := [mp~ #134 #166]: #129
+#668 := [mp #179 #667]: #663
+#645 := (not #663)
+#623 := (or #645 #638 #643)
+#286 := (or #645 #298)
+#288 := (iff #286 #623)
+#289 := [rewrite]: #288
+#287 := [quant-inst]: #286
+#625 := [mp #287 #289]: #623
+#616 := [unit-resolution #625 #668]: #298
+#482 := [unit-resolution #616 #580]: #638
+#331 := (= #28 #644)
+#322 := (= f6 #325)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#648 := (pattern #9)
+#10 := (f3 #9)
+#51 := (= #8 #10)
+#649 := (forall (vars (?v0 S2)) (:pat #648) #51)
+#54 := (forall (vars (?v0 S2)) #51)
+#650 := (iff #54 #649)
+#652 := (iff #649 #649)
+#653 := [rewrite]: #652
+#651 := [rewrite]: #650
+#654 := [trans #651 #653]: #650
+#173 := (~ #54 #54)
+#171 := (~ #51 #51)
+#172 := [refl]: #171
+#174 := [nnf-pos #172]: #173
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#55 := (iff #12 #54)
+#52 := (iff #11 #51)
+#53 := [rewrite]: #52
+#56 := [quant-intro #53]: #55
+#50 := [asserted]: #12
+#59 := [mp #50 #56]: #54
+#162 := [mp~ #59 #174]: #54
+#655 := [mp #162 #654]: #649
+#326 := (not #649)
+#429 := (or #326 #322)
+#636 := [quant-inst]: #429
+#330 := [unit-resolution #636 #655]: #322
+#332 := [monotonicity #330]: #331
+#577 := [trans #332 #482]: #333
+#578 := (not #333)
+#581 := (or #578 #643)
+#466 := [th-lemma]: #581
+#481 := [unit-resolution #466 #580 #577]: false
+#483 := [lemma #481]: #643
+#485 := (or #340 #274)
+#154 := (+ #28 #153)
+#155 := (+ #26 #154)
+#151 := (>= #155 0::int)
+#158 := (not #151)
+#31 := (+ #26 #28)
+#29 := (<= #26 #28)
+#30 := (ite #29 #26 #28)
+#32 := (<= #30 #31)
+#33 := (not #32)
+#159 := (iff #33 #158)
+#156 := (iff #32 #151)
+#147 := (<= #144 #31)
+#150 := (iff #147 #151)
+#152 := [rewrite]: #150
+#148 := (iff #32 #147)
+#145 := (= #30 #144)
+#142 := (iff #29 #141)
+#143 := [rewrite]: #142
+#146 := [monotonicity #143]: #145
+#149 := [monotonicity #146]: #148
+#157 := [trans #149 #152]: #156
+#160 := [monotonicity #157]: #159
+#135 := [asserted]: #33
+#161 := [mp #135 #160]: #158
+#341 := (or #340 #274 #151)
+#615 := [th-lemma]: #341
+#486 := [unit-resolution #615 #161]: #485
+#487 := [unit-resolution #486 #483]: #274
+#233 := (= #26 #144)
+#324 := (f3 #26)
+#299 := (f4 #324)
+#310 := (= #299 0::int)
+#586 := (iff #310 #233)
+#587 := (iff #233 #310)
+#584 := (= #144 0::int)
+#607 := (>= #154 0::int)
+#319 := (= #28 #144)
+#604 := (iff #310 #319)
+#614 := (iff #319 #310)
+#612 := (= 0::int #299)
+#613 := (iff #612 #310)
+#610 := [commutativity]: #613
+#327 := (iff #319 #612)
+#617 := (= #144 #299)
+#347 := (= #26 #299)
+#252 := (= f5 #324)
+#305 := (or #326 #252)
+#640 := [quant-inst]: #305
+#344 := [unit-resolution #640 #655]: #252
+#240 := [monotonicity #344]: #347
+#345 := (= #144 #26)
+#627 := (not #319)
+#628 := [hypothesis]: #627
+#312 := (or #141 #319)
+#323 := [def-axiom]: #312
+#629 := [unit-resolution #323 #628]: #141
+#234 := (not #141)
+#320 := (or #234 #233)
+#321 := [def-axiom]: #320
+#624 := [unit-resolution #321 #629]: #233
+#346 := [symm #624]: #345
+#618 := [trans #346 #240]: #617
+#630 := (not #233)
+#268 := (or #630 #626)
+#631 := [th-lemma]: #268
+#633 := [unit-resolution #631 #624]: #626
+#619 := [unit-resolution #615 #633 #161]: #340
+#620 := [unit-resolution #616 #619]: #638
+#611 := [trans #332 #620]: #333
+#609 := [monotonicity #611 #618]: #327
+#603 := [trans #609 #610]: #614
+#605 := [symm #603]: #604
+#642 := (>= #26 0::int)
+#273 := (not #642)
+#634 := (or #273 #234 #274 #151)
+#632 := [th-lemma]: #634
+#635 := [unit-resolution #632 #629 #161 #633]: #273
+#311 := (or #310 #642)
+#646 := (or #645 #310 #642)
+#641 := (or #645 #311)
+#637 := (iff #641 #646)
+#297 := [rewrite]: #637
+#647 := [quant-inst]: #641
+#302 := [mp #647 #297]: #646
+#621 := [unit-resolution #302 #668]: #311
+#622 := [unit-resolution #621 #635]: #310
+#600 := [mp #622 #605]: #319
+#601 := [unit-resolution #628 #600]: false
+#606 := [lemma #601]: #319
+#608 := (or #627 #607)
+#449 := [th-lemma]: #608
+#450 := [unit-resolution #449 #606]: #607
+#602 := [hypothesis]: #630
+#590 := [unit-resolution #321 #602]: #234
+#451 := (not #607)
+#591 := (or #340 #451 #141 #151)
+#597 := [th-lemma]: #591
+#598 := [unit-resolution #597 #590 #161 #450]: #340
+#592 := [unit-resolution #616 #598]: #638
+#430 := (= #144 #644)
+#599 := (= #144 #28)
+#428 := [symm #606]: #599
+#431 := [trans #428 #332]: #430
+#585 := [trans #431 #592]: #584
+#588 := [monotonicity #240 #585]: #587
+#589 := [symm #588]: #586
+#593 := (or #273 #451 #151)
+#594 := [th-lemma]: #593
+#595 := [unit-resolution #594 #450 #161]: #273
+#596 := [unit-resolution #621 #595]: #310
+#471 := [mp #596 #589]: #233
+#472 := [unit-resolution #602 #471]: false
+#473 := [lemma #472]: #233
+[unit-resolution #631 #473 #487]: false
+unsat
+9645c7f91c8b74fcb674b8c2a12640172b195c7f 103 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f7 :: S2
+#30 := f7
+#31 := (f4 f7)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#143 := -1::int
+#146 := (* -1::int #31)
+#150 := (+ #28 #146)
+#151 := (<= #150 0::int)
+#154 := (ite #151 #28 #31)
+#162 := (* -1::int #154)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#163 := (+ #26 #162)
+#161 := (>= #163 0::int)
+#177 := (* -1::int #28)
+#178 := (+ #26 #177)
+#176 := (>= #178 0::int)
+#175 := (not #176)
+#147 := (+ #26 #146)
+#145 := (>= #147 0::int)
+#144 := (not #145)
+#187 := (and #144 #161 #175)
+#33 := (<= #28 #31)
+#34 := (ite #33 #28 #31)
+#35 := (< #26 #34)
+#36 := (not #35)
+#32 := (< #26 #31)
+#37 := (and #32 #36)
+#29 := (< #26 #28)
+#38 := (and #29 #37)
+#190 := (iff #38 #187)
+#181 := (and #144 #161)
+#184 := (and #175 #181)
+#188 := (iff #184 #187)
+#189 := [rewrite]: #188
+#185 := (iff #38 #184)
+#182 := (iff #37 #181)
+#173 := (iff #36 #161)
+#160 := (not #161)
+#168 := (not #160)
+#171 := (iff #168 #161)
+#172 := [rewrite]: #171
+#169 := (iff #36 #168)
+#166 := (iff #35 #160)
+#157 := (< #26 #154)
+#164 := (iff #157 #160)
+#165 := [rewrite]: #164
+#158 := (iff #35 #157)
+#155 := (= #34 #154)
+#152 := (iff #33 #151)
+#153 := [rewrite]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#167 := [trans #159 #165]: #166
+#170 := [monotonicity #167]: #169
+#174 := [trans #170 #172]: #173
+#148 := (iff #32 #144)
+#149 := [rewrite]: #148
+#183 := [monotonicity #149 #174]: #182
+#179 := (iff #29 #175)
+#180 := [rewrite]: #179
+#186 := [monotonicity #180 #183]: #185
+#191 := [trans #186 #189]: #190
+#140 := [asserted]: #38
+#192 := [mp #140 #191]: #187
+#194 := [and-elim #192]: #161
+#193 := [and-elim #192]: #144
+#365 := (+ #31 #162)
+#638 := (<= #365 0::int)
+#353 := (= #31 #154)
+#268 := (not #151)
+#267 := (= #28 #154)
+#643 := (not #267)
+#652 := (+ #28 #162)
+#374 := (<= #652 0::int)
+#645 := (not #374)
+#195 := [and-elim #192]: #175
+#366 := [hypothesis]: #374
+#367 := [th-lemma #366 #195 #194]: false
+#646 := [lemma #367]: #645
+#361 := [hypothesis]: #267
+#647 := (or #643 #374)
+#644 := [th-lemma]: #647
+#648 := [unit-resolution #644 #361 #646]: false
+#637 := [lemma #648]: #643
+#354 := (or #268 #267)
+#355 := [def-axiom]: #354
+#634 := [unit-resolution #355 #637]: #268
+#346 := (or #151 #353)
+#357 := [def-axiom]: #346
+#635 := [unit-resolution #357 #634]: #353
+#640 := (not #353)
+#641 := (or #640 #638)
+#636 := [th-lemma]: #641
+#642 := [unit-resolution #636 #635]: #638
+[th-lemma #642 #193 #194]: false
+unsat
+fa8e0a2694e045a39788da23e6dc3bda6b4f57dc 117 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#13 := 0::int
+#141 := -1::int
+#142 := (* -1::int #28)
+#143 := (+ #26 #142)
+#154 := (>= #143 0::int)
+#156 := (ite #154 #28 #26)
+#159 := (f3 #156)
+#144 := (<= #143 0::int)
+#147 := (ite #144 #26 #28)
+#150 := (f3 #147)
+#162 := (= #150 #159)
+#649 := (f3 #26)
+#558 := (= #649 #159)
+#556 := (= #159 #649)
+#564 := (= #156 #26)
+#259 := (= #26 #156)
+#436 := (f3 #28)
+#577 := (= #436 #159)
+#586 := (= #159 #436)
+#479 := (= #156 #28)
+#331 := (= #28 #156)
+#489 := (not #259)
+#584 := [hypothesis]: #489
+#312 := (or #154 #259)
+#647 := [def-axiom]: #312
+#588 := [unit-resolution #647 #584]: #154
+#332 := (not #154)
+#329 := (or #332 #331)
+#333 := [def-axiom]: #329
+#490 := [unit-resolution #333 #588]: #331
+#480 := [symm #490]: #479
+#590 := [monotonicity #480]: #586
+#579 := [symm #590]: #577
+#491 := (= #150 #436)
+#492 := (= #147 #28)
+#326 := (= #28 #147)
+#241 := (not #144)
+#496 := (or #241 #259)
+#473 := (= #26 #28)
+#585 := [hypothesis]: #144
+#488 := [th-lemma #588 #585]: #473
+#494 := [trans #488 #490]: #259
+#495 := [unit-resolution #584 #494]: false
+#589 := [lemma #495]: #496
+#439 := [unit-resolution #589 #584]: #241
+#319 := (or #144 #326)
+#330 := [def-axiom]: #319
+#587 := [unit-resolution #330 #439]: #326
+#493 := [symm #587]: #492
+#484 := [monotonicity #493]: #491
+#571 := [trans #484 #579]: #162
+#165 := (not #162)
+#32 := (<= #28 #26)
+#33 := (ite #32 #28 #26)
+#34 := (f3 #33)
+#29 := (<= #26 #28)
+#30 := (ite #29 #26 #28)
+#31 := (f3 #30)
+#35 := (= #31 #34)
+#36 := (not #35)
+#166 := (iff #36 #165)
+#163 := (iff #35 #162)
+#160 := (= #34 #159)
+#157 := (= #33 #156)
+#153 := (iff #32 #154)
+#155 := [rewrite]: #153
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#151 := (= #31 #150)
+#148 := (= #30 #147)
+#145 := (iff #29 #144)
+#146 := [rewrite]: #145
+#149 := [monotonicity #146]: #148
+#152 := [monotonicity #149]: #151
+#164 := [monotonicity #152 #161]: #163
+#167 := [monotonicity #164]: #166
+#138 := [asserted]: #36
+#168 := [mp #138 #167]: #165
+#568 := [unit-resolution #168 #571]: false
+#570 := [lemma #568]: #259
+#565 := [symm #570]: #564
+#557 := [monotonicity #565]: #556
+#555 := [symm #557]: #558
+#553 := (= #150 #649)
+#562 := (= #147 #26)
+#240 := (= #26 #147)
+#435 := [hypothesis]: #241
+#437 := (or #154 #144)
+#596 := [th-lemma]: #437
+#478 := [unit-resolution #596 #435]: #154
+#580 := [unit-resolution #333 #478]: #331
+#581 := [symm #580]: #479
+#572 := [monotonicity #581]: #586
+#573 := [symm #572]: #577
+#582 := [unit-resolution #330 #435]: #326
+#578 := [symm #582]: #492
+#583 := [monotonicity #578]: #491
+#574 := [trans #583 #573]: #162
+#575 := [unit-resolution #168 #574]: false
+#569 := [lemma #575]: #144
+#327 := (or #241 #240)
+#328 := [def-axiom]: #327
+#566 := [unit-resolution #328 #569]: #240
+#567 := [symm #566]: #562
+#554 := [monotonicity #567]: #553
+#559 := [trans #554 #555]: #162
+[unit-resolution #168 #559]: false
+unsat
+da2ff9ef6139e0a66caeccee0485bd5a70c1edcc 156 0
+#2 := false
+decl f3 :: (-> int S2)
+#13 := 0::int
+#30 := (f3 0::int)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#27 := (<= #26 0::int)
+#28 := (ite #27 #26 0::int)
+#29 := (f3 #28)
+#31 := (= #29 #30)
+#294 := (= #28 0::int)
+#299 := (f3 #26)
+#576 := (f4 #299)
+#577 := (= #576 0::int)
+#442 := (= #26 0::int)
+#567 := (not #294)
+#573 := [hypothesis]: #567
+#287 := (or #27 #294)
+#298 := [def-axiom]: #287
+#404 := [unit-resolution #298 #573]: #27
+#581 := (>= #26 0::int)
+#408 := (not #577)
+#556 := (iff #567 #408)
+#448 := (iff #294 #577)
+#565 := (= #28 #576)
+#564 := (= #26 #576)
+#561 := (= #576 #26)
+#568 := (= #299 f5)
+#227 := (= f5 #299)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#624 := (pattern #9)
+#10 := (f3 #9)
+#50 := (= #8 #10)
+#625 := (forall (vars (?v0 S2)) (:pat #624) #50)
+#53 := (forall (vars (?v0 S2)) #50)
+#626 := (iff #53 #625)
+#628 := (iff #625 #625)
+#629 := [rewrite]: #628
+#627 := [rewrite]: #626
+#630 := [trans #627 #629]: #626
+#148 := (~ #53 #53)
+#146 := (~ #50 #50)
+#147 := [refl]: #146
+#149 := [nnf-pos #147]: #148
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#54 := (iff #12 #53)
+#51 := (iff #11 #50)
+#52 := [rewrite]: #51
+#55 := [quant-intro #52]: #54
+#49 := [asserted]: #12
+#58 := [mp #49 #55]: #53
+#137 := [mp~ #58 #149]: #53
+#631 := [mp #137 #630]: #625
+#301 := (not #625)
+#280 := (or #301 #227)
+#616 := [quant-inst]: #280
+#574 := [unit-resolution #616 #631]: #227
+#575 := [symm #574]: #568
+#563 := [monotonicity #575]: #561
+#562 := [symm #563]: #564
+#407 := (= #28 #26)
+#208 := (= #26 #28)
+#209 := (not #27)
+#295 := (or #209 #208)
+#296 := [def-axiom]: #295
+#406 := [unit-resolution #296 #404]: #208
+#560 := [symm #406]: #407
+#447 := [trans #560 #562]: #565
+#449 := [monotonicity #447]: #448
+#458 := [monotonicity #449]: #556
+#553 := [mp #573 #458]: #408
+#582 := (or #577 #581)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#632 := (pattern #16)
+#75 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#123 := (or #22 #75)
+#639 := (forall (vars (?v0 int)) (:pat #632) #123)
+#128 := (forall (vars (?v0 int)) #123)
+#642 := (iff #128 #639)
+#640 := (iff #123 #123)
+#641 := [refl]: #640
+#643 := [quant-intro #641]: #642
+#140 := (~ #128 #128)
+#152 := (~ #123 #123)
+#153 := [refl]: #152
+#141 := [nnf-pos #153]: #140
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#131 := (iff #24 #128)
+#94 := (= 0::int #17)
+#100 := (not #21)
+#101 := (or #100 #94)
+#106 := (forall (vars (?v0 int)) #101)
+#129 := (iff #106 #128)
+#126 := (iff #101 #123)
+#120 := (or #75 #22)
+#124 := (iff #120 #123)
+#125 := [rewrite]: #124
+#121 := (iff #101 #120)
+#118 := (iff #94 #22)
+#119 := [rewrite]: #118
+#116 := (iff #100 #75)
+#76 := (not #75)
+#111 := (not #76)
+#114 := (iff #111 #75)
+#115 := [rewrite]: #114
+#112 := (iff #100 #111)
+#109 := (iff #21 #76)
+#110 := [rewrite]: #109
+#113 := [monotonicity #110]: #112
+#117 := [trans #113 #115]: #116
+#122 := [monotonicity #117 #119]: #121
+#127 := [trans #122 #125]: #126
+#130 := [quant-intro #127]: #129
+#107 := (iff #24 #106)
+#104 := (iff #23 #101)
+#97 := (implies #21 #94)
+#102 := (iff #97 #101)
+#103 := [rewrite]: #102
+#98 := (iff #23 #97)
+#95 := (iff #22 #94)
+#96 := [rewrite]: #95
+#99 := [monotonicity #96]: #98
+#105 := [trans #99 #103]: #104
+#108 := [quant-intro #105]: #107
+#132 := [trans #108 #130]: #131
+#93 := [asserted]: #24
+#133 := [mp #93 #132]: #128
+#154 := [mp~ #133 #141]: #128
+#644 := [mp #154 #643]: #639
+#614 := (not #639)
+#584 := (or #614 #577 #581)
+#425 := (or #614 #582)
+#427 := (iff #425 #584)
+#569 := [rewrite]: #427
+#426 := [quant-inst]: #425
+#570 := [mp #426 #569]: #584
+#554 := [unit-resolution #570 #644]: #582
+#557 := [unit-resolution #554 #553]: #581
+#457 := [th-lemma #557 #404]: #442
+#459 := [trans #563 #457]: #577
+#460 := [unit-resolution #553 #459]: false
+#453 := [lemma #460]: #294
+#583 := [monotonicity #453]: #31
+#32 := (not #31)
+#134 := [asserted]: #32
+[unit-resolution #134 #583]: false
+unsat
+88cc1cfdc9ecc3f2138c9180ec327ce09b9116c5 60 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#137 := -1::int
+#138 := (* -1::int #28)
+#139 := (+ #26 #138)
+#140 := (<= #139 0::int)
+#143 := (ite #140 #28 #26)
+#149 := (* -1::int #143)
+#150 := (+ #26 #149)
+#151 := (<= #150 0::int)
+#156 := (not #151)
+#29 := (<= #26 #28)
+#30 := (ite #29 #28 #26)
+#31 := (<= #26 #30)
+#32 := (not #31)
+#157 := (iff #32 #156)
+#154 := (iff #31 #151)
+#146 := (<= #26 #143)
+#152 := (iff #146 #151)
+#153 := [rewrite]: #152
+#147 := (iff #31 #146)
+#144 := (= #30 #143)
+#141 := (iff #29 #140)
+#142 := [rewrite]: #141
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#155 := [trans #148 #153]: #154
+#158 := [monotonicity #155]: #157
+#134 := [asserted]: #32
+#159 := [mp #134 #158]: #156
+#317 := (= #26 #143)
+#232 := (not #140)
+#625 := [hypothesis]: #140
+#637 := (+ #28 #149)
+#280 := (<= #637 0::int)
+#231 := (= #28 #143)
+#318 := (or #232 #231)
+#319 := [def-axiom]: #318
+#626 := [unit-resolution #319 #625]: #231
+#627 := (not #231)
+#622 := (or #627 #280)
+#628 := [th-lemma]: #622
+#266 := [unit-resolution #628 #626]: #280
+#629 := [th-lemma #266 #159 #625]: false
+#631 := [lemma #629]: #232
+#310 := (or #140 #317)
+#321 := [def-axiom]: #310
+#271 := [unit-resolution #321 #631]: #317
+#272 := (not #317)
+#632 := (or #272 #151)
+#630 := [th-lemma]: #632
+[unit-resolution #630 #271 #159]: false
+unsat
+0122efc10e38b5cd510be1952412037a9414e10c 60 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#137 := -1::int
+#140 := (* -1::int #28)
+#141 := (+ #26 #140)
+#139 := (>= #141 0::int)
+#143 := (ite #139 #26 #28)
+#149 := (* -1::int #143)
+#637 := (+ #28 #149)
+#628 := (<= #637 0::int)
+#317 := (= #28 #143)
+#232 := (not #139)
+#231 := (= #26 #143)
+#624 := (not #231)
+#150 := (+ #26 #149)
+#151 := (<= #150 0::int)
+#156 := (not #151)
+#29 := (<= #28 #26)
+#30 := (ite #29 #26 #28)
+#31 := (<= #26 #30)
+#32 := (not #31)
+#157 := (iff #32 #156)
+#154 := (iff #31 #151)
+#146 := (<= #26 #143)
+#152 := (iff #146 #151)
+#153 := [rewrite]: #152
+#147 := (iff #31 #146)
+#144 := (= #30 #143)
+#138 := (iff #29 #139)
+#142 := [rewrite]: #138
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#155 := [trans #148 #153]: #154
+#158 := [monotonicity #155]: #157
+#134 := [asserted]: #32
+#159 := [mp #134 #158]: #156
+#280 := [hypothesis]: #231
+#625 := (or #624 #151)
+#626 := [th-lemma]: #625
+#627 := [unit-resolution #626 #280 #159]: false
+#622 := [lemma #627]: #624
+#318 := (or #232 #231)
+#319 := [def-axiom]: #318
+#629 := [unit-resolution #319 #622]: #232
+#310 := (or #139 #317)
+#321 := [def-axiom]: #310
+#631 := [unit-resolution #321 #629]: #317
+#271 := (not #317)
+#272 := (or #271 #628)
+#632 := [th-lemma]: #272
+#630 := [unit-resolution #632 #631]: #628
+[th-lemma #159 #629 #630]: false
+unsat
+7c9e3abcd68f2ba67093ec54bd9616e29dfd7553 437 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#142 := -1::int
+#143 := (* -1::int #28)
+#144 := (+ #26 #143)
+#172 := (<= #144 0::int)
+#175 := (ite #172 #28 #26)
+#181 := (* -1::int #175)
+#565 := (+ #26 #181)
+#496 := (<= #565 0::int)
+#354 := (= #26 #175)
+#269 := (not #172)
+#566 := [hypothesis]: #172
+decl f3 :: (-> int S2)
+#147 := (f3 #144)
+#150 := (f4 #147)
+#375 := (<= #150 0::int)
+#504 := (not #375)
+#153 := (* -1::int #26)
+#154 := (+ #153 #28)
+#157 := (f3 #154)
+#160 := (f4 #157)
+#182 := (+ #160 #181)
+#183 := (+ #150 #182)
+#184 := (<= #183 0::int)
+#189 := (not #184)
+#36 := (<= #26 #28)
+#37 := (ite #36 #28 #26)
+#32 := (- #28 #26)
+#33 := (f3 #32)
+#34 := (f4 #33)
+#29 := (- #26 #28)
+#30 := (f3 #29)
+#31 := (f4 #30)
+#35 := (+ #31 #34)
+#38 := (<= #35 #37)
+#39 := (not #38)
+#192 := (iff #39 #189)
+#163 := (+ #150 #160)
+#166 := (<= #163 #37)
+#169 := (not #166)
+#190 := (iff #169 #189)
+#187 := (iff #166 #184)
+#178 := (<= #163 #175)
+#185 := (iff #178 #184)
+#186 := [rewrite]: #185
+#179 := (iff #166 #178)
+#176 := (= #37 #175)
+#173 := (iff #36 #172)
+#174 := [rewrite]: #173
+#177 := [monotonicity #174]: #176
+#180 := [monotonicity #177]: #179
+#188 := [trans #180 #186]: #187
+#191 := [monotonicity #188]: #190
+#170 := (iff #39 #169)
+#167 := (iff #38 #166)
+#164 := (= #35 #163)
+#161 := (= #34 #160)
+#158 := (= #33 #157)
+#155 := (= #32 #154)
+#156 := [rewrite]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#151 := (= #31 #150)
+#148 := (= #30 #147)
+#145 := (= #29 #144)
+#146 := [rewrite]: #145
+#149 := [monotonicity #146]: #148
+#152 := [monotonicity #149]: #151
+#165 := [monotonicity #152 #162]: #164
+#168 := [monotonicity #165]: #167
+#171 := [monotonicity #168]: #170
+#193 := [trans #171 #191]: #192
+#141 := [asserted]: #39
+#194 := [mp #141 #193]: #189
+#366 := (+ #143 #160)
+#367 := (+ #26 #366)
+#631 := (<= #367 0::int)
+#655 := (= #367 0::int)
+#649 := (or #269 #655)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#691 := (pattern #16)
+#82 := (>= #14 0::int)
+#83 := (not #82)
+#17 := (f4 #16)
+#64 := (= #14 #17)
+#89 := (or #64 #83)
+#692 := (forall (vars (?v0 int)) (:pat #691) #89)
+#94 := (forall (vars (?v0 int)) #89)
+#695 := (iff #94 #692)
+#693 := (iff #89 #89)
+#694 := [refl]: #693
+#696 := [quant-intro #694]: #695
+#198 := (~ #94 #94)
+#195 := (~ #89 #89)
+#210 := [refl]: #195
+#199 := [nnf-pos #210]: #198
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#97 := (iff #20 #94)
+#71 := (not #15)
+#72 := (or #71 #64)
+#77 := (forall (vars (?v0 int)) #72)
+#95 := (iff #77 #94)
+#92 := (iff #72 #89)
+#86 := (or #83 #64)
+#90 := (iff #86 #89)
+#91 := [rewrite]: #90
+#87 := (iff #72 #86)
+#84 := (iff #71 #83)
+#80 := (iff #15 #82)
+#81 := [rewrite]: #80
+#85 := [monotonicity #81]: #84
+#88 := [monotonicity #85]: #87
+#93 := [trans #88 #91]: #92
+#96 := [quant-intro #93]: #95
+#78 := (iff #20 #77)
+#75 := (iff #19 #72)
+#68 := (implies #15 #64)
+#73 := (iff #68 #72)
+#74 := [rewrite]: #73
+#69 := (iff #19 #68)
+#66 := (iff #18 #64)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#76 := [trans #70 #74]: #75
+#79 := [quant-intro #76]: #78
+#98 := [trans #79 #96]: #97
+#63 := [asserted]: #20
+#99 := [mp #63 #98]: #94
+#211 := [mp~ #99 #199]: #94
+#697 := [mp #211 #696]: #692
+#324 := (not #692)
+#636 := (or #324 #269 #655)
+#656 := (>= #154 0::int)
+#657 := (not #656)
+#650 := (= #154 #160)
+#654 := (or #650 #657)
+#641 := (or #324 #654)
+#628 := (iff #641 #636)
+#637 := (or #324 #649)
+#485 := (iff #637 #636)
+#486 := [rewrite]: #485
+#643 := (iff #641 #637)
+#640 := (iff #654 #649)
+#644 := (or #655 #269)
+#638 := (iff #644 #649)
+#639 := [rewrite]: #638
+#648 := (iff #654 #644)
+#647 := (iff #657 #269)
+#368 := (iff #656 #172)
+#646 := [rewrite]: #368
+#362 := [monotonicity #646]: #647
+#651 := (iff #650 #655)
+#365 := [rewrite]: #651
+#645 := [monotonicity #365 #362]: #648
+#635 := [trans #645 #639]: #640
+#484 := [monotonicity #635]: #643
+#629 := [trans #484 #486]: #628
+#642 := [quant-inst]: #641
+#630 := [mp #642 #629]: #636
+#425 := [unit-resolution #630 #697]: #649
+#537 := [unit-resolution #425 #566]: #655
+#509 := (not #655)
+#533 := (or #509 #631)
+#534 := [th-lemma]: #533
+#529 := [unit-resolution #534 #537]: #631
+#501 := (>= #26 0::int)
+#560 := (= #26 0::int)
+#359 := (f3 #26)
+#516 := (f4 #359)
+#518 := (= #516 0::int)
+#552 := (not #501)
+#548 := [hypothesis]: #552
+#512 := (or #501 #518)
+#22 := (= #17 0::int)
+#130 := (or #22 #82)
+#698 := (forall (vars (?v0 int)) (:pat #691) #130)
+#135 := (forall (vars (?v0 int)) #130)
+#701 := (iff #135 #698)
+#699 := (iff #130 #130)
+#700 := [refl]: #699
+#702 := [quant-intro #700]: #701
+#200 := (~ #135 #135)
+#212 := (~ #130 #130)
+#213 := [refl]: #212
+#201 := [nnf-pos #213]: #200
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#138 := (iff #24 #135)
+#101 := (= 0::int #17)
+#107 := (not #21)
+#108 := (or #107 #101)
+#113 := (forall (vars (?v0 int)) #108)
+#136 := (iff #113 #135)
+#133 := (iff #108 #130)
+#127 := (or #82 #22)
+#131 := (iff #127 #130)
+#132 := [rewrite]: #131
+#128 := (iff #108 #127)
+#125 := (iff #101 #22)
+#126 := [rewrite]: #125
+#123 := (iff #107 #82)
+#118 := (not #83)
+#121 := (iff #118 #82)
+#122 := [rewrite]: #121
+#119 := (iff #107 #118)
+#116 := (iff #21 #83)
+#117 := [rewrite]: #116
+#120 := [monotonicity #117]: #119
+#124 := [trans #120 #122]: #123
+#129 := [monotonicity #124 #126]: #128
+#134 := [trans #129 #132]: #133
+#137 := [quant-intro #134]: #136
+#114 := (iff #24 #113)
+#111 := (iff #23 #108)
+#104 := (implies #21 #101)
+#109 := (iff #104 #108)
+#110 := [rewrite]: #109
+#105 := (iff #23 #104)
+#102 := (iff #22 #101)
+#103 := [rewrite]: #102
+#106 := [monotonicity #103]: #105
+#112 := [trans #106 #110]: #111
+#115 := [quant-intro #112]: #114
+#139 := [trans #115 #137]: #138
+#100 := [asserted]: #24
+#140 := [mp #100 #139]: #135
+#214 := [mp~ #140 #201]: #135
+#703 := [mp #214 #702]: #698
+#379 := (not #698)
+#522 := (or #379 #501 #518)
+#519 := (or #518 #501)
+#523 := (or #379 #519)
+#599 := (iff #523 #522)
+#617 := (or #379 #512)
+#605 := (iff #617 #522)
+#607 := [rewrite]: #605
+#614 := (iff #523 #617)
+#520 := (iff #519 #512)
+#521 := [rewrite]: #520
+#618 := [monotonicity #521]: #614
+#596 := [trans #618 #607]: #599
+#524 := [quant-inst]: #523
+#598 := [mp #524 #596]: #522
+#549 := [unit-resolution #598 #703]: #512
+#550 := [unit-resolution #549 #548]: #518
+#554 := (= #26 #516)
+#287 := (= f5 #359)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#683 := (pattern #9)
+#10 := (f3 #9)
+#57 := (= #8 #10)
+#684 := (forall (vars (?v0 S2)) (:pat #683) #57)
+#60 := (forall (vars (?v0 S2)) #57)
+#685 := (iff #60 #684)
+#687 := (iff #684 #684)
+#688 := [rewrite]: #687
+#686 := [rewrite]: #685
+#689 := [trans #686 #688]: #685
+#208 := (~ #60 #60)
+#206 := (~ #57 #57)
+#207 := [refl]: #206
+#209 := [nnf-pos #207]: #208
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#61 := (iff #12 #60)
+#58 := (iff #11 #57)
+#59 := [rewrite]: #58
+#62 := [quant-intro #59]: #61
+#56 := [asserted]: #12
+#65 := [mp #56 #62]: #60
+#197 := [mp~ #65 #209]: #60
+#690 := [mp #197 #689]: #684
+#361 := (not #684)
+#340 := (or #361 #287)
+#675 := [quant-inst]: #340
+#553 := [unit-resolution #675 #690]: #287
+#555 := [monotonicity #553]: #554
+#556 := [trans #555 #550]: #560
+#551 := (not #560)
+#557 := (or #551 #501)
+#530 := [th-lemma]: #557
+#531 := [unit-resolution #530 #548 #556]: false
+#532 := [lemma #531]: #501
+#569 := (+ #28 #181)
+#580 := (<= #569 0::int)
+#268 := (= #28 #175)
+#355 := (or #269 #268)
+#356 := [def-axiom]: #355
+#535 := [unit-resolution #356 #566]: #268
+#503 := (not #268)
+#510 := (or #503 #580)
+#469 := [th-lemma]: #510
+#500 := [unit-resolution #469 #535]: #580
+#511 := (not #631)
+#502 := (not #580)
+#513 := (or #552 #502 #504 #184 #511)
+#514 := [th-lemma]: #513
+#515 := [unit-resolution #514 #500 #532 #529 #194]: #504
+#337 := (* -1::int #150)
+#673 := (+ #143 #337)
+#333 := (+ #26 #673)
+#669 := (>= #333 0::int)
+#674 := (= #333 0::int)
+#680 := (>= #144 0::int)
+#667 := (= #150 0::int)
+#525 := (not #667)
+#505 := (or #525 #375)
+#526 := [th-lemma]: #505
+#481 := [unit-resolution #526 #515]: #525
+#670 := (or #667 #680)
+#380 := (or #379 #667 #680)
+#381 := (or #379 #670)
+#275 := (iff #381 #380)
+#652 := [rewrite]: #275
+#382 := [quant-inst]: #381
+#653 := [mp #382 #652]: #380
+#482 := [unit-resolution #653 #703]: #670
+#487 := [unit-resolution #482 #481]: #680
+#681 := (not #680)
+#321 := (or #674 #681)
+#660 := (or #324 #674 #681)
+#672 := (= #144 #150)
+#332 := (or #672 #681)
+#661 := (or #324 #332)
+#666 := (iff #661 #660)
+#663 := (or #324 #321)
+#665 := (iff #663 #660)
+#303 := [rewrite]: #665
+#664 := (iff #661 #663)
+#322 := (iff #332 #321)
+#317 := (iff #672 #674)
+#658 := [rewrite]: #317
+#323 := [monotonicity #658]: #322
+#659 := [monotonicity #323]: #664
+#668 := [trans #659 #303]: #666
+#662 := [quant-inst]: #661
+#308 := [mp #662 #668]: #660
+#488 := [unit-resolution #308 #697]: #321
+#489 := [unit-resolution #488 #487]: #674
+#490 := (not #674)
+#491 := (or #490 #669)
+#492 := [th-lemma]: #491
+#493 := [unit-resolution #492 #489]: #669
+#494 := [th-lemma #493 #515 #566]: false
+#495 := [lemma #494]: #269
+#347 := (or #172 #354)
+#358 := [def-axiom]: #347
+#498 := [unit-resolution #358 #495]: #354
+#483 := (not #354)
+#499 := (or #483 #496)
+#460 := [th-lemma]: #499
+#461 := [unit-resolution #460 #498]: #496
+#613 := (<= #160 0::int)
+#626 := (= #160 0::int)
+#463 := (or #172 #626)
+#622 := (or #379 #172 #626)
+#632 := (or #626 #656)
+#623 := (or #379 #632)
+#615 := (iff #623 #622)
+#624 := (or #379 #463)
+#508 := (iff #624 #622)
+#467 := [rewrite]: #508
+#506 := (iff #623 #624)
+#619 := (iff #632 #463)
+#633 := (or #626 #172)
+#465 := (iff #633 #463)
+#466 := [rewrite]: #465
+#627 := (iff #632 #633)
+#634 := [monotonicity #646]: #627
+#620 := [trans #634 #466]: #619
+#507 := [monotonicity #620]: #506
+#517 := [trans #507 #467]: #615
+#621 := [quant-inst]: #623
+#612 := [mp #621 #517]: #622
+#468 := [unit-resolution #612 #703]: #463
+#470 := [unit-resolution #468 #495]: #626
+#471 := (not #626)
+#472 := (or #471 #613)
+#474 := [th-lemma]: #472
+#475 := [unit-resolution #474 #470]: #613
+#608 := (>= #28 0::int)
+#536 := (= #28 0::int)
+#360 := (f3 #28)
+#609 := (f4 #360)
+#610 := (= #609 0::int)
+#538 := (not #608)
+#543 := [hypothesis]: #538
+#611 := (or #608 #610)
+#602 := (or #379 #608 #610)
+#606 := (or #610 #608)
+#603 := (or #379 #606)
+#593 := (iff #603 #602)
+#604 := (or #379 #611)
+#591 := (iff #604 #602)
+#592 := [rewrite]: #591
+#588 := (iff #603 #604)
+#600 := (iff #606 #611)
+#601 := [rewrite]: #600
+#589 := [monotonicity #601]: #588
+#594 := [trans #589 #592]: #593
+#597 := [quant-inst]: #603
+#590 := [mp #597 #594]: #602
+#539 := [unit-resolution #590 #703]: #611
+#540 := [unit-resolution #539 #543]: #610
+#544 := (= #28 #609)
+#357 := (= f6 #360)
+#464 := (or #361 #357)
+#671 := [quant-inst]: #464
+#541 := [unit-resolution #671 #690]: #357
+#545 := [monotonicity #541]: #544
+#546 := [trans #545 #540]: #536
+#542 := (not #536)
+#547 := (or #542 #608)
+#527 := [th-lemma]: #547
+#473 := [unit-resolution #527 #543 #546]: false
+#528 := [lemma #473]: #608
+#476 := (or #680 #172)
+#477 := [th-lemma]: #476
+#478 := [unit-resolution #477 #495]: #680
+#479 := [unit-resolution #488 #478]: #674
+#462 := [unit-resolution #492 #479]: #669
+[th-lemma #462 #528 #194 #475 #461]: false
+unsat
+76ee9f1370ee47b53f6c11c1682ef1e7a8911478 103 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+decl f7 :: S2
+#30 := f7
+#31 := (f4 f7)
+#143 := -1::int
+#144 := (* -1::int #31)
+#150 := (+ #26 #144)
+#151 := (<= #150 0::int)
+#154 := (ite #151 #31 #26)
+#160 := (* -1::int #154)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#161 := (+ #28 #160)
+#162 := (<= #161 0::int)
+#177 := (* -1::int #28)
+#178 := (+ #26 #177)
+#176 := (>= #178 0::int)
+#175 := (not #176)
+#145 := (+ #28 #144)
+#146 := (<= #145 0::int)
+#147 := (not #146)
+#187 := (and #147 #162 #175)
+#33 := (<= #26 #31)
+#34 := (ite #33 #31 #26)
+#35 := (< #34 #28)
+#36 := (not #35)
+#32 := (< #31 #28)
+#37 := (and #32 #36)
+#29 := (< #26 #28)
+#38 := (and #29 #37)
+#190 := (iff #38 #187)
+#181 := (and #147 #162)
+#184 := (and #175 #181)
+#188 := (iff #184 #187)
+#189 := [rewrite]: #188
+#185 := (iff #38 #184)
+#182 := (iff #37 #181)
+#173 := (iff #36 #162)
+#163 := (not #162)
+#168 := (not #163)
+#171 := (iff #168 #162)
+#172 := [rewrite]: #171
+#169 := (iff #36 #168)
+#166 := (iff #35 #163)
+#157 := (< #154 #28)
+#164 := (iff #157 #163)
+#165 := [rewrite]: #164
+#158 := (iff #35 #157)
+#155 := (= #34 #154)
+#152 := (iff #33 #151)
+#153 := [rewrite]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#167 := [trans #159 #165]: #166
+#170 := [monotonicity #167]: #169
+#174 := [trans #170 #172]: #173
+#148 := (iff #32 #147)
+#149 := [rewrite]: #148
+#183 := [monotonicity #149 #174]: #182
+#179 := (iff #29 #175)
+#180 := [rewrite]: #179
+#186 := [monotonicity #180 #183]: #185
+#191 := [trans #186 #189]: #190
+#140 := [asserted]: #38
+#192 := [mp #140 #191]: #187
+#194 := [and-elim #192]: #162
+#195 := [and-elim #192]: #175
+#374 := (+ #26 #160)
+#639 := (>= #374 0::int)
+#353 := (= #26 #154)
+#268 := (not #151)
+#267 := (= #31 #154)
+#643 := (not #267)
+#652 := (+ #31 #160)
+#365 := (>= #652 0::int)
+#645 := (not #365)
+#193 := [and-elim #192]: #147
+#366 := [hypothesis]: #365
+#367 := [th-lemma #366 #193 #194]: false
+#646 := [lemma #367]: #645
+#361 := [hypothesis]: #267
+#647 := (or #643 #365)
+#644 := [th-lemma]: #647
+#648 := [unit-resolution #644 #361 #646]: false
+#637 := [lemma #648]: #643
+#354 := (or #268 #267)
+#355 := [def-axiom]: #354
+#634 := [unit-resolution #355 #637]: #268
+#346 := (or #151 #353)
+#357 := [def-axiom]: #346
+#635 := [unit-resolution #357 #634]: #353
+#640 := (not #353)
+#641 := (or #640 #639)
+#636 := [th-lemma]: #641
+#642 := [unit-resolution #636 #635]: #639
+[th-lemma #642 #195 #194]: false
+unsat
+18b47c81a9d452efdc99018694a5a7712659d793 119 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#13 := 0::int
+#141 := -1::int
+#142 := (* -1::int #28)
+#143 := (+ #26 #142)
+#154 := (>= #143 0::int)
+#156 := (ite #154 #26 #28)
+#159 := (f3 #156)
+#144 := (<= #143 0::int)
+#147 := (ite #144 #28 #26)
+#150 := (f3 #147)
+#162 := (= #150 #159)
+#436 := (f3 #28)
+#559 := (= #436 #159)
+#558 := (= #159 #436)
+#566 := (= #156 #28)
+#259 := (= #28 #156)
+#649 := (f3 #26)
+#571 := (= #649 #159)
+#577 := (= #159 #649)
+#479 := (= #156 #26)
+#331 := (= #26 #156)
+#489 := (not #259)
+#584 := [hypothesis]: #489
+#312 := (or #154 #259)
+#647 := [def-axiom]: #312
+#585 := [unit-resolution #647 #584]: #154
+#332 := (not #154)
+#329 := (or #332 #331)
+#333 := [def-axiom]: #329
+#588 := [unit-resolution #333 #585]: #331
+#480 := [symm #588]: #479
+#579 := [monotonicity #480]: #577
+#568 := [symm #579]: #571
+#586 := (= #150 #649)
+#492 := (= #147 #26)
+#326 := (= #26 #147)
+#241 := (not #144)
+#496 := (or #241 #259)
+#491 := (= #28 #26)
+#488 := (= #26 #28)
+#473 := [hypothesis]: #144
+#490 := [th-lemma #585 #473]: #488
+#484 := [symm #490]: #491
+#494 := [trans #484 #588]: #259
+#495 := [unit-resolution #584 #494]: false
+#589 := [lemma #495]: #496
+#439 := [unit-resolution #589 #584]: #241
+#319 := (or #144 #326)
+#330 := [def-axiom]: #319
+#587 := [unit-resolution #330 #439]: #326
+#493 := [symm #587]: #492
+#590 := [monotonicity #493]: #586
+#570 := [trans #590 #568]: #162
+#165 := (not #162)
+#32 := (<= #28 #26)
+#33 := (ite #32 #26 #28)
+#34 := (f3 #33)
+#29 := (<= #26 #28)
+#30 := (ite #29 #28 #26)
+#31 := (f3 #30)
+#35 := (= #31 #34)
+#36 := (not #35)
+#166 := (iff #36 #165)
+#163 := (iff #35 #162)
+#160 := (= #34 #159)
+#157 := (= #33 #156)
+#153 := (iff #32 #154)
+#155 := [rewrite]: #153
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#151 := (= #31 #150)
+#148 := (= #30 #147)
+#145 := (iff #29 #144)
+#146 := [rewrite]: #145
+#149 := [monotonicity #146]: #148
+#152 := [monotonicity #149]: #151
+#164 := [monotonicity #152 #161]: #163
+#167 := [monotonicity #164]: #166
+#138 := [asserted]: #36
+#168 := [mp #138 #167]: #165
+#580 := [unit-resolution #168 #570]: false
+#581 := [lemma #580]: #259
+#562 := [symm #581]: #566
+#555 := [monotonicity #562]: #558
+#539 := [symm #555]: #559
+#556 := (= #150 #436)
+#553 := (= #147 #28)
+#240 := (= #28 #147)
+#435 := [hypothesis]: #241
+#437 := (or #154 #144)
+#596 := [th-lemma]: #437
+#478 := [unit-resolution #596 #435]: #154
+#582 := [unit-resolution #333 #478]: #331
+#578 := [symm #582]: #479
+#574 := [monotonicity #578]: #577
+#575 := [symm #574]: #571
+#583 := [unit-resolution #330 #435]: #326
+#572 := [symm #583]: #492
+#573 := [monotonicity #572]: #586
+#569 := [trans #573 #575]: #162
+#576 := [unit-resolution #168 #569]: false
+#560 := [lemma #576]: #144
+#327 := (or #241 #240)
+#328 := [def-axiom]: #327
+#567 := [unit-resolution #328 #560]: #240
+#554 := [symm #567]: #553
+#557 := [monotonicity #554]: #556
+#540 := [trans #557 #539]: #162
+[unit-resolution #168 #540]: false
+unsat
+aeb27ae732eb5ade79f0b082530ea53b942db1bc 164 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#13 := 0::int
+#27 := (<= #26 0::int)
+#28 := (ite #27 0::int #26)
+#29 := (f3 #28)
+#134 := (= f5 #29)
+#305 := (f3 #26)
+#596 := (= #305 #29)
+#595 := (= #29 #305)
+#249 := (= #28 #26)
+#300 := (= #26 #28)
+#611 := (f4 #305)
+#606 := (= #611 0::int)
+#314 := (= #26 0::int)
+#613 := (not #300)
+#603 := [hypothesis]: #613
+#293 := (or #27 #300)
+#304 := [def-axiom]: #293
+#604 := [unit-resolution #304 #603]: #27
+#610 := (>= #26 0::int)
+#597 := (not #606)
+#601 := (iff #613 #597)
+#322 := (iff #300 #606)
+#214 := (= #28 0::int)
+#215 := (not #27)
+#301 := (or #215 #214)
+#302 := [def-axiom]: #301
+#311 := [unit-resolution #302 #604]: #214
+#599 := (= #26 #611)
+#329 := (= #611 #26)
+#327 := (= #305 f5)
+#233 := (= f5 #305)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#630 := (pattern #9)
+#10 := (f3 #9)
+#49 := (= #8 #10)
+#631 := (forall (vars (?v0 S2)) (:pat #630) #49)
+#52 := (forall (vars (?v0 S2)) #49)
+#632 := (iff #52 #631)
+#634 := (iff #631 #631)
+#635 := [rewrite]: #634
+#633 := [rewrite]: #632
+#636 := [trans #633 #635]: #632
+#154 := (~ #52 #52)
+#152 := (~ #49 #49)
+#153 := [refl]: #152
+#155 := [nnf-pos #153]: #154
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#53 := (iff #12 #52)
+#50 := (iff #11 #49)
+#51 := [rewrite]: #50
+#54 := [quant-intro #51]: #53
+#48 := [asserted]: #12
+#57 := [mp #48 #54]: #52
+#143 := [mp~ #57 #155]: #52
+#637 := [mp #143 #636]: #631
+#307 := (not #631)
+#286 := (or #307 #233)
+#622 := [quant-inst]: #286
+#326 := [unit-resolution #622 #637]: #233
+#328 := [symm #326]: #327
+#221 := [monotonicity #328]: #329
+#600 := [symm #221]: #599
+#323 := [monotonicity #600 #311]: #322
+#598 := [monotonicity #323]: #601
+#602 := [mp #603 #598]: #597
+#612 := (or #606 #610)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#638 := (pattern #16)
+#74 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#122 := (or #22 #74)
+#645 := (forall (vars (?v0 int)) (:pat #638) #122)
+#127 := (forall (vars (?v0 int)) #122)
+#648 := (iff #127 #645)
+#646 := (iff #122 #122)
+#647 := [refl]: #646
+#649 := [quant-intro #647]: #648
+#146 := (~ #127 #127)
+#158 := (~ #122 #122)
+#159 := [refl]: #158
+#147 := [nnf-pos #159]: #146
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#130 := (iff #24 #127)
+#93 := (= 0::int #17)
+#99 := (not #21)
+#100 := (or #99 #93)
+#105 := (forall (vars (?v0 int)) #100)
+#128 := (iff #105 #127)
+#125 := (iff #100 #122)
+#119 := (or #74 #22)
+#123 := (iff #119 #122)
+#124 := [rewrite]: #123
+#120 := (iff #100 #119)
+#117 := (iff #93 #22)
+#118 := [rewrite]: #117
+#115 := (iff #99 #74)
+#75 := (not #74)
+#110 := (not #75)
+#113 := (iff #110 #74)
+#114 := [rewrite]: #113
+#111 := (iff #99 #110)
+#108 := (iff #21 #75)
+#109 := [rewrite]: #108
+#112 := [monotonicity #109]: #111
+#116 := [trans #112 #114]: #115
+#121 := [monotonicity #116 #118]: #120
+#126 := [trans #121 #124]: #125
+#129 := [quant-intro #126]: #128
+#106 := (iff #24 #105)
+#103 := (iff #23 #100)
+#96 := (implies #21 #93)
+#101 := (iff #96 #100)
+#102 := [rewrite]: #101
+#97 := (iff #23 #96)
+#94 := (iff #22 #93)
+#95 := [rewrite]: #94
+#98 := [monotonicity #95]: #97
+#104 := [trans #98 #102]: #103
+#107 := [quant-intro #104]: #106
+#131 := [trans #107 #129]: #130
+#92 := [asserted]: #24
+#132 := [mp #92 #131]: #127
+#160 := [mp~ #132 #147]: #127
+#650 := [mp #160 #649]: #645
+#620 := (not #645)
+#615 := (or #620 #606 #610)
+#254 := (or #620 #612)
+#616 := (iff #254 #615)
+#614 := [rewrite]: #616
+#255 := [quant-inst]: #254
+#617 := [mp #255 #614]: #615
+#312 := [unit-resolution #617 #650]: #612
+#313 := [unit-resolution #312 #602]: #610
+#315 := [th-lemma #313 #604]: #314
+#593 := [trans #221 #315]: #606
+#594 := [unit-resolution #602 #593]: false
+#308 := [lemma #594]: #300
+#591 := [symm #308]: #249
+#592 := [monotonicity #591]: #595
+#585 := [symm #592]: #596
+#586 := [trans #326 #585]: #134
+#137 := (not #134)
+#30 := (= #29 f5)
+#31 := (not #30)
+#138 := (iff #31 #137)
+#135 := (iff #30 #134)
+#136 := [rewrite]: #135
+#139 := [monotonicity #136]: #138
+#133 := [asserted]: #31
+#142 := [mp #133 #139]: #137
+[unit-resolution #142 #586]: false
+unsat
+32b7349c65f2a98027993cfc5b819fa9c76f7f70 139 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#625 := (= #26 0::int)
+decl f3 :: (-> int S2)
+#211 := (f3 #26)
+#212 := (f4 #211)
+#298 := (= #212 0::int)
+#135 := (>= #26 0::int)
+#136 := (not #135)
+#27 := (<= 0::int #26)
+#28 := (not #27)
+#137 := (iff #28 #136)
+#133 := (iff #27 #135)
+#134 := [rewrite]: #133
+#138 := [monotonicity #134]: #137
+#130 := [asserted]: #28
+#139 := [mp #130 #138]: #136
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#635 := (pattern #16)
+#71 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#119 := (or #22 #71)
+#642 := (forall (vars (?v0 int)) (:pat #635) #119)
+#124 := (forall (vars (?v0 int)) #119)
+#645 := (iff #124 #642)
+#643 := (iff #119 #119)
+#644 := [refl]: #643
+#646 := [quant-intro #644]: #645
+#143 := (~ #124 #124)
+#155 := (~ #119 #119)
+#156 := [refl]: #155
+#144 := [nnf-pos #156]: #143
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#127 := (iff #24 #124)
+#90 := (= 0::int #17)
+#96 := (not #21)
+#97 := (or #96 #90)
+#102 := (forall (vars (?v0 int)) #97)
+#125 := (iff #102 #124)
+#122 := (iff #97 #119)
+#116 := (or #71 #22)
+#120 := (iff #116 #119)
+#121 := [rewrite]: #120
+#117 := (iff #97 #116)
+#114 := (iff #90 #22)
+#115 := [rewrite]: #114
+#112 := (iff #96 #71)
+#72 := (not #71)
+#107 := (not #72)
+#110 := (iff #107 #71)
+#111 := [rewrite]: #110
+#108 := (iff #96 #107)
+#105 := (iff #21 #72)
+#106 := [rewrite]: #105
+#109 := [monotonicity #106]: #108
+#113 := [trans #109 #111]: #112
+#118 := [monotonicity #113 #115]: #117
+#123 := [trans #118 #121]: #122
+#126 := [quant-intro #123]: #125
+#103 := (iff #24 #102)
+#100 := (iff #23 #97)
+#93 := (implies #21 #90)
+#98 := (iff #93 #97)
+#99 := [rewrite]: #98
+#94 := (iff #23 #93)
+#91 := (iff #22 #90)
+#92 := [rewrite]: #91
+#95 := [monotonicity #92]: #94
+#101 := [trans #95 #99]: #100
+#104 := [quant-intro #101]: #103
+#128 := [trans #104 #126]: #127
+#89 := [asserted]: #24
+#129 := [mp #89 #128]: #124
+#157 := [mp~ #129 #144]: #124
+#647 := [mp #157 #646]: #642
+#304 := (not #642)
+#283 := (or #304 #135 #298)
+#302 := (or #298 #135)
+#619 := (or #304 #302)
+#622 := (iff #619 #283)
+#230 := (or #135 #298)
+#277 := (or #304 #230)
+#288 := (iff #277 #283)
+#289 := [rewrite]: #288
+#408 := (iff #619 #277)
+#303 := (iff #302 #230)
+#300 := [rewrite]: #303
+#615 := [monotonicity #300]: #408
+#623 := [trans #615 #289]: #622
+#621 := [quant-inst]: #619
+#624 := [mp #621 #623]: #283
+#626 := [unit-resolution #624 #647 #139]: #298
+#275 := (= #26 #212)
+#297 := (= f5 #211)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#627 := (pattern #9)
+#10 := (f3 #9)
+#46 := (= #8 #10)
+#628 := (forall (vars (?v0 S2)) (:pat #627) #46)
+#49 := (forall (vars (?v0 S2)) #46)
+#629 := (iff #49 #628)
+#631 := (iff #628 #628)
+#632 := [rewrite]: #631
+#630 := [rewrite]: #629
+#633 := [trans #630 #632]: #629
+#151 := (~ #49 #49)
+#149 := (~ #46 #46)
+#150 := [refl]: #149
+#152 := [nnf-pos #150]: #151
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#50 := (iff #12 #49)
+#47 := (iff #11 #46)
+#48 := [rewrite]: #47
+#51 := [quant-intro #48]: #50
+#45 := [asserted]: #12
+#54 := [mp #45 #51]: #49
+#140 := [mp~ #54 #152]: #49
+#634 := [mp #140 #633]: #628
+#299 := (not #628)
+#290 := (or #299 #297)
+#301 := [quant-inst]: #290
+#616 := [unit-resolution #301 #634]: #297
+#280 := [monotonicity #616]: #275
+#617 := [trans #280 #626]: #625
+#276 := (not #625)
+#618 := (or #276 #135)
+#260 := [th-lemma]: #618
+[unit-resolution #260 #139 #617]: false
+unsat
+cd6e6ee8cf8b75d0011d82bd241ec9736c128fa6 75 0
+#2 := false
+decl f3 :: (-> int S2)
+#28 := 1::int
+#30 := (f3 1::int)
+decl f5 :: S2
+#25 := f5
+#31 := (= f5 #30)
+decl f4 :: (-> S2 int)
+#26 := (f4 f5)
+#226 := (f3 #26)
+#337 := (= #226 #30)
+#615 := (= #30 #226)
+#625 := (= 1::int #26)
+#266 := (= #26 1::int)
+#29 := (<= #26 1::int)
+#13 := 0::int
+#139 := (<= #26 0::int)
+#140 := (not #139)
+#32 := (not #31)
+#146 := (and #29 #32 #140)
+#33 := (and #29 #32)
+#27 := (< 0::int #26)
+#34 := (and #27 #33)
+#149 := (iff #34 #146)
+#143 := (and #140 #33)
+#147 := (iff #143 #146)
+#148 := [rewrite]: #147
+#144 := (iff #34 #143)
+#141 := (iff #27 #140)
+#142 := [rewrite]: #141
+#145 := [monotonicity #142]: #144
+#150 := [trans #145 #148]: #149
+#136 := [asserted]: #34
+#151 := [mp #136 #150]: #146
+#152 := [and-elim #151]: #29
+#154 := [and-elim #151]: #140
+#627 := [th-lemma #154 #152]: #266
+#628 := [symm #627]: #625
+#322 := [monotonicity #628]: #615
+#338 := [symm #322]: #337
+#311 := (= f5 #226)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#641 := (pattern #9)
+#10 := (f3 #9)
+#52 := (= #8 #10)
+#642 := (forall (vars (?v0 S2)) (:pat #641) #52)
+#55 := (forall (vars (?v0 S2)) #52)
+#643 := (iff #55 #642)
+#645 := (iff #642 #642)
+#646 := [rewrite]: #645
+#644 := [rewrite]: #643
+#647 := [trans #644 #646]: #643
+#170 := (~ #55 #55)
+#168 := (~ #52 #52)
+#169 := [refl]: #168
+#171 := [nnf-pos #169]: #170
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#56 := (iff #12 #55)
+#53 := (iff #11 #52)
+#54 := [rewrite]: #53
+#57 := [quant-intro #54]: #56
+#51 := [asserted]: #12
+#60 := [mp #51 #57]: #55
+#155 := [mp~ #60 #171]: #55
+#648 := [mp #155 #647]: #642
+#313 := (not #642)
+#304 := (or #313 #311)
+#315 := [quant-inst]: #304
+#614 := [unit-resolution #315 #648]: #311
+#339 := [trans #614 #338]: #31
+#153 := [and-elim #151]: #32
+[unit-resolution #153 #339]: false
+unsat
+000880aa19ed4a1843957e82181d2a42342f1991 20 0
+#2 := false
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#27 := (<= #26 #26)
+#28 := (not #27)
+#140 := (iff #28 false)
+#1 := true
+#135 := (not true)
+#138 := (iff #135 false)
+#139 := [rewrite]: #138
+#136 := (iff #28 #135)
+#133 := (iff #27 true)
+#134 := [rewrite]: #133
+#137 := [monotonicity #134]: #136
+#141 := [trans #137 #139]: #140
+#130 := [asserted]: #28
+[mp #130 #141]: false
+unsat
+88eeafff0d413fa89914541cc48ed55eef3db1b1 319 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#144 := -1::int
+#145 := (* -1::int #28)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#146 := (+ #26 #145)
+#147 := (<= #146 0::int)
+decl f3 :: (-> int S2)
+#30 := 3::int
+#34 := (* 3::int #28)
+#35 := (f3 #34)
+#36 := (f4 #35)
+#150 := (* -1::int #36)
+#31 := (* 3::int #26)
+#32 := (f3 #31)
+#33 := (f4 #32)
+#151 := (+ #33 #150)
+#152 := (<= #151 0::int)
+#155 := (not #152)
+#158 := (and #147 #155)
+#37 := (<= #33 #36)
+#38 := (not #37)
+#29 := (<= #26 #28)
+#39 := (and #29 #38)
+#159 := (iff #39 #158)
+#156 := (iff #38 #155)
+#153 := (iff #37 #152)
+#154 := [rewrite]: #153
+#157 := [monotonicity #154]: #156
+#148 := (iff #29 #147)
+#149 := [rewrite]: #148
+#160 := [monotonicity #149 #157]: #159
+#141 := [asserted]: #39
+#161 := [mp #141 #160]: #158
+#162 := [and-elim #161]: #147
+#163 := [and-elim #161]: #155
+#612 := (+ #34 #150)
+#589 := (<= #612 0::int)
+#616 := (= #612 0::int)
+#607 := (>= #28 0::int)
+#542 := (= #28 0::int)
+#236 := (f3 #28)
+#584 := (f4 #236)
+#581 := (= #584 0::int)
+#608 := (not #607)
+#544 := [hypothesis]: #608
+#575 := (or #581 #607)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#658 := (pattern #16)
+#82 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#130 := (or #22 #82)
+#665 := (forall (vars (?v0 int)) (:pat #658) #130)
+#135 := (forall (vars (?v0 int)) #130)
+#668 := (iff #135 #665)
+#666 := (iff #130 #130)
+#667 := [refl]: #666
+#669 := [quant-intro #667]: #668
+#167 := (~ #135 #135)
+#181 := (~ #130 #130)
+#182 := [refl]: #181
+#168 := [nnf-pos #182]: #167
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#138 := (iff #24 #135)
+#101 := (= 0::int #17)
+#107 := (not #21)
+#108 := (or #107 #101)
+#113 := (forall (vars (?v0 int)) #108)
+#136 := (iff #113 #135)
+#133 := (iff #108 #130)
+#127 := (or #82 #22)
+#131 := (iff #127 #130)
+#132 := [rewrite]: #131
+#128 := (iff #108 #127)
+#125 := (iff #101 #22)
+#126 := [rewrite]: #125
+#123 := (iff #107 #82)
+#83 := (not #82)
+#118 := (not #83)
+#121 := (iff #118 #82)
+#122 := [rewrite]: #121
+#119 := (iff #107 #118)
+#116 := (iff #21 #83)
+#117 := [rewrite]: #116
+#120 := [monotonicity #117]: #119
+#124 := [trans #120 #122]: #123
+#129 := [monotonicity #124 #126]: #128
+#134 := [trans #129 #132]: #133
+#137 := [quant-intro #134]: #136
+#114 := (iff #24 #113)
+#111 := (iff #23 #108)
+#104 := (implies #21 #101)
+#109 := (iff #104 #108)
+#110 := [rewrite]: #109
+#105 := (iff #23 #104)
+#102 := (iff #22 #101)
+#103 := [rewrite]: #102
+#106 := [monotonicity #103]: #105
+#112 := [trans #106 #110]: #111
+#115 := [quant-intro #112]: #114
+#139 := [trans #115 #137]: #138
+#100 := [asserted]: #24
+#140 := [mp #100 #139]: #135
+#183 := [mp~ #140 #168]: #135
+#670 := [mp #183 #669]: #665
+#242 := (not #665)
+#573 := (or #242 #581 #607)
+#578 := (or #242 #575)
+#568 := (iff #578 #573)
+#569 := [rewrite]: #568
+#567 := [quant-inst]: #578
+#570 := [mp #567 #569]: #573
+#545 := [unit-resolution #570 #670]: #575
+#546 := [unit-resolution #545 #544]: #581
+#547 := (= #28 #584)
+#322 := (= f6 #236)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#650 := (pattern #9)
+#10 := (f3 #9)
+#57 := (= #8 #10)
+#651 := (forall (vars (?v0 S2)) (:pat #650) #57)
+#60 := (forall (vars (?v0 S2)) #57)
+#652 := (iff #60 #651)
+#654 := (iff #651 #651)
+#655 := [rewrite]: #654
+#653 := [rewrite]: #652
+#656 := [trans #653 #655]: #652
+#177 := (~ #60 #60)
+#175 := (~ #57 #57)
+#176 := [refl]: #175
+#178 := [nnf-pos #176]: #177
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#61 := (iff #12 #60)
+#58 := (iff #11 #57)
+#59 := [rewrite]: #58
+#62 := [quant-intro #59]: #61
+#56 := [asserted]: #12
+#65 := [mp #56 #62]: #60
+#164 := [mp~ #65 #178]: #60
+#657 := [mp #164 #656]: #651
+#323 := (not #651)
+#327 := (or #323 #322)
+#324 := [quant-inst]: #327
+#536 := [unit-resolution #324 #657]: #322
+#525 := [monotonicity #536]: #547
+#526 := [trans #525 #546]: #542
+#528 := (not #542)
+#529 := (or #528 #607)
+#530 := [th-lemma]: #529
+#531 := [unit-resolution #530 #544 #526]: false
+#532 := [lemma #531]: #607
+#453 := (or #608 #616)
+#64 := (= #14 #17)
+#89 := (or #64 #83)
+#659 := (forall (vars (?v0 int)) (:pat #658) #89)
+#94 := (forall (vars (?v0 int)) #89)
+#662 := (iff #94 #659)
+#660 := (iff #89 #89)
+#661 := [refl]: #660
+#663 := [quant-intro #661]: #662
+#165 := (~ #94 #94)
+#142 := (~ #89 #89)
+#179 := [refl]: #142
+#166 := [nnf-pos #179]: #165
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#97 := (iff #20 #94)
+#71 := (not #15)
+#72 := (or #71 #64)
+#77 := (forall (vars (?v0 int)) #72)
+#95 := (iff #77 #94)
+#92 := (iff #72 #89)
+#86 := (or #83 #64)
+#90 := (iff #86 #89)
+#91 := [rewrite]: #90
+#87 := (iff #72 #86)
+#84 := (iff #71 #83)
+#80 := (iff #15 #82)
+#81 := [rewrite]: #80
+#85 := [monotonicity #81]: #84
+#88 := [monotonicity #85]: #87
+#93 := [trans #88 #91]: #92
+#96 := [quant-intro #93]: #95
+#78 := (iff #20 #77)
+#75 := (iff #19 #72)
+#68 := (implies #15 #64)
+#73 := (iff #68 #72)
+#74 := [rewrite]: #73
+#69 := (iff #19 #68)
+#66 := (iff #18 #64)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#76 := [trans #70 #74]: #75
+#79 := [quant-intro #76]: #78
+#98 := [trans #79 #96]: #97
+#63 := [asserted]: #20
+#99 := [mp #63 #98]: #94
+#180 := [mp~ #99 #166]: #94
+#664 := [mp #180 #663]: #659
+#629 := (not #659)
+#592 := (or #629 #608 #616)
+#614 := (>= #34 0::int)
+#329 := (not #614)
+#611 := (= #34 #36)
+#615 := (or #611 #329)
+#593 := (or #629 #615)
+#433 := (iff #593 #592)
+#600 := (or #629 #453)
+#430 := (iff #600 #592)
+#432 := [rewrite]: #430
+#594 := (iff #593 #600)
+#597 := (iff #615 #453)
+#610 := (or #616 #608)
+#595 := (iff #610 #453)
+#596 := [rewrite]: #595
+#451 := (iff #615 #610)
+#609 := (iff #329 #608)
+#602 := (iff #614 #607)
+#603 := [rewrite]: #602
+#604 := [monotonicity #603]: #609
+#605 := (iff #611 #616)
+#606 := [rewrite]: #605
+#452 := [monotonicity #606 #604]: #451
+#598 := [trans #452 #596]: #597
+#601 := [monotonicity #598]: #594
+#586 := [trans #601 #432]: #433
+#599 := [quant-inst]: #593
+#587 := [mp #599 #586]: #592
+#543 := [unit-resolution #587 #664]: #453
+#527 := [unit-resolution #543 #532]: #616
+#533 := (not #616)
+#519 := (or #533 #589)
+#515 := [th-lemma]: #519
+#516 := [unit-resolution #515 #527]: #589
+#646 := (* -1::int #33)
+#647 := (+ #31 #646)
+#623 := (>= #647 0::int)
+#648 := (= #647 0::int)
+#639 := (>= #26 0::int)
+#624 := (= #33 0::int)
+#518 := (not #624)
+#335 := (<= #33 0::int)
+#517 := (not #335)
+#520 := (not #589)
+#521 := (or #517 #608 #520 #152)
+#522 := [th-lemma]: #521
+#523 := [unit-resolution #522 #163 #532 #516]: #517
+#524 := (or #518 #335)
+#497 := [th-lemma]: #524
+#498 := [unit-resolution #497 #523]: #518
+#347 := (or #624 #639)
+#619 := (or #242 #624 #639)
+#301 := (>= #31 0::int)
+#346 := (or #624 #301)
+#620 := (or #242 #346)
+#332 := (iff #620 #619)
+#343 := (or #242 #347)
+#618 := (iff #343 #619)
+#622 := [rewrite]: #618
+#617 := (iff #620 #343)
+#348 := (iff #346 #347)
+#299 := (iff #301 #639)
+#304 := [rewrite]: #299
+#349 := [monotonicity #304]: #348
+#621 := [monotonicity #349]: #617
+#333 := [trans #621 #622]: #332
+#342 := [quant-inst]: #620
+#334 := [mp #342 #333]: #619
+#499 := [unit-resolution #334 #670]: #347
+#392 := [unit-resolution #499 #498]: #639
+#640 := (not #639)
+#289 := (or #640 #648)
+#630 := (or #629 #640 #648)
+#431 := (not #301)
+#313 := (= #31 #33)
+#645 := (or #313 #431)
+#631 := (or #629 #645)
+#276 := (iff #631 #630)
+#632 := (or #629 #289)
+#635 := (iff #632 #630)
+#275 := [rewrite]: #635
+#270 := (iff #631 #632)
+#627 := (iff #645 #289)
+#284 := (or #648 #640)
+#290 := (iff #284 #289)
+#291 := [rewrite]: #290
+#625 := (iff #645 #284)
+#300 := (iff #431 #640)
+#641 := [monotonicity #304]: #300
+#643 := (iff #313 #648)
+#649 := [rewrite]: #643
+#288 := [monotonicity #649 #641]: #625
+#628 := [trans #288 #291]: #627
+#633 := [monotonicity #628]: #270
+#636 := [trans #633 #275]: #276
+#626 := [quant-inst]: #631
+#634 := [mp #626 #636]: #630
+#503 := [unit-resolution #634 #664]: #289
+#504 := [unit-resolution #503 #392]: #648
+#505 := (not #648)
+#510 := (or #505 #623)
+#506 := [th-lemma]: #510
+#507 := [unit-resolution #506 #504]: #623
+[th-lemma #507 #516 #163 #162]: false
+unsat
+b07d26f06f2f8e3a614ec9af094d242833240836 325 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#549 := (= #26 0::int)
+decl f3 :: (-> int S2)
+#241 := (f3 #26)
+#495 := (f4 #241)
+#496 := (= #495 0::int)
+#645 := (>= #26 0::int)
+#646 := (not #645)
+#30 := 3::int
+#31 := (* 3::int #26)
+#32 := (f3 #31)
+#33 := (f4 #32)
+#144 := -1::int
+#652 := (* -1::int #33)
+#653 := (+ #31 #652)
+#654 := (= #653 0::int)
+#503 := (not #654)
+#629 := (>= #653 0::int)
+#527 := (not #629)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#34 := (* 3::int #28)
+#35 := (f3 #34)
+#36 := (f4 #35)
+#153 := (* -1::int #36)
+#618 := (+ #34 #153)
+#595 := (<= #618 0::int)
+#622 := (= #618 0::int)
+#613 := (>= #28 0::int)
+#548 := (= #28 0::int)
+#242 := (f3 #28)
+#590 := (f4 #242)
+#587 := (= #590 0::int)
+#614 := (not #613)
+#550 := [hypothesis]: #614
+#581 := (or #587 #613)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#664 := (pattern #16)
+#82 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#130 := (or #22 #82)
+#671 := (forall (vars (?v0 int)) (:pat #664) #130)
+#135 := (forall (vars (?v0 int)) #130)
+#674 := (iff #135 #671)
+#672 := (iff #130 #130)
+#673 := [refl]: #672
+#675 := [quant-intro #673]: #674
+#173 := (~ #135 #135)
+#187 := (~ #130 #130)
+#188 := [refl]: #187
+#174 := [nnf-pos #188]: #173
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#138 := (iff #24 #135)
+#101 := (= 0::int #17)
+#107 := (not #21)
+#108 := (or #107 #101)
+#113 := (forall (vars (?v0 int)) #108)
+#136 := (iff #113 #135)
+#133 := (iff #108 #130)
+#127 := (or #82 #22)
+#131 := (iff #127 #130)
+#132 := [rewrite]: #131
+#128 := (iff #108 #127)
+#125 := (iff #101 #22)
+#126 := [rewrite]: #125
+#123 := (iff #107 #82)
+#83 := (not #82)
+#118 := (not #83)
+#121 := (iff #118 #82)
+#122 := [rewrite]: #121
+#119 := (iff #107 #118)
+#116 := (iff #21 #83)
+#117 := [rewrite]: #116
+#120 := [monotonicity #117]: #119
+#124 := [trans #120 #122]: #123
+#129 := [monotonicity #124 #126]: #128
+#134 := [trans #129 #132]: #133
+#137 := [quant-intro #134]: #136
+#114 := (iff #24 #113)
+#111 := (iff #23 #108)
+#104 := (implies #21 #101)
+#109 := (iff #104 #108)
+#110 := [rewrite]: #109
+#105 := (iff #23 #104)
+#102 := (iff #22 #101)
+#103 := [rewrite]: #102
+#106 := [monotonicity #103]: #105
+#112 := [trans #106 #110]: #111
+#115 := [quant-intro #112]: #114
+#139 := [trans #115 #137]: #138
+#100 := [asserted]: #24
+#140 := [mp #100 #139]: #135
+#189 := [mp~ #140 #174]: #135
+#676 := [mp #189 #675]: #671
+#248 := (not #671)
+#579 := (or #248 #587 #613)
+#584 := (or #248 #581)
+#574 := (iff #584 #579)
+#575 := [rewrite]: #574
+#573 := [quant-inst]: #584
+#576 := [mp #573 #575]: #579
+#551 := [unit-resolution #576 #676]: #581
+#552 := [unit-resolution #551 #550]: #587
+#553 := (= #28 #590)
+#328 := (= f6 #242)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#656 := (pattern #9)
+#10 := (f3 #9)
+#57 := (= #8 #10)
+#657 := (forall (vars (?v0 S2)) (:pat #656) #57)
+#60 := (forall (vars (?v0 S2)) #57)
+#658 := (iff #60 #657)
+#660 := (iff #657 #657)
+#661 := [rewrite]: #660
+#659 := [rewrite]: #658
+#662 := [trans #659 #661]: #658
+#183 := (~ #60 #60)
+#181 := (~ #57 #57)
+#182 := [refl]: #181
+#184 := [nnf-pos #182]: #183
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#61 := (iff #12 #60)
+#58 := (iff #11 #57)
+#59 := [rewrite]: #58
+#62 := [quant-intro #59]: #61
+#56 := [asserted]: #12
+#65 := [mp #56 #62]: #60
+#170 := [mp~ #65 #184]: #60
+#663 := [mp #170 #662]: #657
+#329 := (not #657)
+#333 := (or #329 #328)
+#330 := [quant-inst]: #333
+#542 := [unit-resolution #330 #663]: #328
+#531 := [monotonicity #542]: #553
+#532 := [trans #531 #552]: #548
+#534 := (not #548)
+#535 := (or #534 #613)
+#536 := [th-lemma]: #535
+#537 := [unit-resolution #536 #550 #532]: false
+#538 := [lemma #537]: #613
+#459 := (or #614 #622)
+#64 := (= #14 #17)
+#89 := (or #64 #83)
+#665 := (forall (vars (?v0 int)) (:pat #664) #89)
+#94 := (forall (vars (?v0 int)) #89)
+#668 := (iff #94 #665)
+#666 := (iff #89 #89)
+#667 := [refl]: #666
+#669 := [quant-intro #667]: #668
+#171 := (~ #94 #94)
+#142 := (~ #89 #89)
+#185 := [refl]: #142
+#172 := [nnf-pos #185]: #171
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#97 := (iff #20 #94)
+#71 := (not #15)
+#72 := (or #71 #64)
+#77 := (forall (vars (?v0 int)) #72)
+#95 := (iff #77 #94)
+#92 := (iff #72 #89)
+#86 := (or #83 #64)
+#90 := (iff #86 #89)
+#91 := [rewrite]: #90
+#87 := (iff #72 #86)
+#84 := (iff #71 #83)
+#80 := (iff #15 #82)
+#81 := [rewrite]: #80
+#85 := [monotonicity #81]: #84
+#88 := [monotonicity #85]: #87
+#93 := [trans #88 #91]: #92
+#96 := [quant-intro #93]: #95
+#78 := (iff #20 #77)
+#75 := (iff #19 #72)
+#68 := (implies #15 #64)
+#73 := (iff #68 #72)
+#74 := [rewrite]: #73
+#69 := (iff #19 #68)
+#66 := (iff #18 #64)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#76 := [trans #70 #74]: #75
+#79 := [quant-intro #76]: #78
+#98 := [trans #79 #96]: #97
+#63 := [asserted]: #20
+#99 := [mp #63 #98]: #94
+#186 := [mp~ #99 #172]: #94
+#670 := [mp #186 #669]: #665
+#635 := (not #665)
+#598 := (or #635 #614 #622)
+#620 := (>= #34 0::int)
+#335 := (not #620)
+#617 := (= #34 #36)
+#621 := (or #617 #335)
+#599 := (or #635 #621)
+#439 := (iff #599 #598)
+#606 := (or #635 #459)
+#436 := (iff #606 #598)
+#438 := [rewrite]: #436
+#600 := (iff #599 #606)
+#603 := (iff #621 #459)
+#616 := (or #622 #614)
+#601 := (iff #616 #459)
+#602 := [rewrite]: #601
+#457 := (iff #621 #616)
+#615 := (iff #335 #614)
+#608 := (iff #620 #613)
+#609 := [rewrite]: #608
+#610 := [monotonicity #609]: #615
+#611 := (iff #617 #622)
+#612 := [rewrite]: #611
+#458 := [monotonicity #612 #610]: #457
+#604 := [trans #458 #602]: #603
+#607 := [monotonicity #604]: #600
+#592 := [trans #607 #438]: #439
+#605 := [quant-inst]: #599
+#593 := [mp #605 #592]: #598
+#539 := [unit-resolution #593 #670]: #459
+#525 := [unit-resolution #539 #538]: #622
+#521 := (not #622)
+#522 := (or #521 #595)
+#523 := [th-lemma]: #522
+#526 := [unit-resolution #523 #525]: #595
+#147 := (* -1::int #28)
+#148 := (+ #26 #147)
+#146 := (>= #148 0::int)
+#145 := (not #146)
+#154 := (+ #33 #153)
+#152 := (>= #154 0::int)
+#164 := (and #145 #152)
+#37 := (< #33 #36)
+#38 := (not #37)
+#29 := (< #26 #28)
+#39 := (and #29 #38)
+#165 := (iff #39 #164)
+#162 := (iff #38 #152)
+#151 := (not #152)
+#157 := (not #151)
+#160 := (iff #157 #152)
+#161 := [rewrite]: #160
+#158 := (iff #38 #157)
+#155 := (iff #37 #151)
+#156 := [rewrite]: #155
+#159 := [monotonicity #156]: #158
+#163 := [trans #159 #161]: #162
+#149 := (iff #29 #145)
+#150 := [rewrite]: #149
+#166 := [monotonicity #150 #163]: #165
+#141 := [asserted]: #39
+#167 := [mp #141 #166]: #164
+#168 := [and-elim #167]: #145
+#169 := [and-elim #167]: #152
+#528 := (not #595)
+#529 := (or #527 #151 #528 #146)
+#524 := [th-lemma]: #529
+#530 := [unit-resolution #524 #169 #168 #526]: #527
+#504 := (or #503 #629)
+#505 := [th-lemma]: #504
+#398 := [unit-resolution #505 #530]: #503
+#295 := (or #646 #654)
+#636 := (or #635 #646 #654)
+#307 := (>= #31 0::int)
+#437 := (not #307)
+#319 := (= #31 #33)
+#651 := (or #319 #437)
+#637 := (or #635 #651)
+#282 := (iff #637 #636)
+#638 := (or #635 #295)
+#641 := (iff #638 #636)
+#281 := [rewrite]: #641
+#276 := (iff #637 #638)
+#633 := (iff #651 #295)
+#290 := (or #654 #646)
+#296 := (iff #290 #295)
+#297 := [rewrite]: #296
+#631 := (iff #651 #290)
+#306 := (iff #437 #646)
+#305 := (iff #307 #645)
+#310 := [rewrite]: #305
+#647 := [monotonicity #310]: #306
+#649 := (iff #319 #654)
+#655 := [rewrite]: #649
+#294 := [monotonicity #655 #647]: #631
+#634 := [trans #294 #297]: #633
+#639 := [monotonicity #634]: #276
+#642 := [trans #639 #281]: #282
+#632 := [quant-inst]: #637
+#640 := [mp #632 #642]: #636
+#509 := [unit-resolution #640 #670]: #295
+#510 := [unit-resolution #509 #398]: #646
+#497 := (or #496 #645)
+#591 := (or #248 #496 #645)
+#578 := (or #248 #497)
+#572 := (iff #578 #591)
+#569 := [rewrite]: #572
+#580 := [quant-inst]: #578
+#571 := [mp #580 #569]: #591
+#511 := [unit-resolution #571 #676]: #497
+#516 := [unit-resolution #511 #510]: #496
+#513 := (= #26 #495)
+#327 := (= f5 #241)
+#320 := (or #329 #327)
+#331 := [quant-inst]: #320
+#512 := [unit-resolution #331 #663]: #327
+#514 := [monotonicity #512]: #513
+#517 := [trans #514 #516]: #549
+#518 := (not #549)
+#519 := (or #518 #645)
+#515 := [th-lemma]: #519
+[unit-resolution #515 #510 #517]: false
+unsat
+11038cb4c13dcad01559beed85cfa0b91db3362e 38 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#137 := -1::int
+#140 := (* -1::int #28)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#141 := (+ #26 #140)
+#144 := (<= #141 0::int)
+#147 := (not #144)
+#139 := (>= #141 0::int)
+#138 := (not #139)
+#150 := (and #138 #147)
+#30 := (<= #26 #28)
+#31 := (not #30)
+#29 := (< #26 #28)
+#32 := (and #29 #31)
+#151 := (iff #32 #150)
+#148 := (iff #31 #147)
+#145 := (iff #30 #144)
+#146 := [rewrite]: #145
+#149 := [monotonicity #146]: #148
+#142 := (iff #29 #138)
+#143 := [rewrite]: #142
+#152 := [monotonicity #143 #149]: #151
+#134 := [asserted]: #32
+#153 := [mp #134 #152]: #150
+#155 := [and-elim #153]: #147
+#154 := [and-elim #153]: #138
+#227 := (or #144 #139)
+#313 := [th-lemma]: #227
+#228 := [unit-resolution #313 #154]: #144
+[unit-resolution #228 #155]: false
+unsat
+837c405f2b45308cfbf3a46d2a4facdbd42feddf 292 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f3 :: (-> int S2)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#30 := 1::int
+#139 := (+ 1::int #26)
+#142 := (f3 #139)
+#145 := (f4 #142)
+#157 := -1::int
+#165 := (* -1::int #145)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#166 := (+ #28 #165)
+#164 := (>= #166 0::int)
+#160 := (* -1::int #28)
+#161 := (+ #26 #160)
+#159 := (>= #161 0::int)
+#319 := (+ #26 #165)
+#643 := (>= #319 -1::int)
+#324 := (= #319 -1::int)
+#661 := (>= #26 -1::int)
+#634 := (>= #26 0::int)
+#613 := (= #26 0::int)
+#344 := (f3 #26)
+#349 := (f4 #344)
+#631 := (= #349 0::int)
+#606 := (not #634)
+#607 := [hypothesis]: #606
+#635 := (or #631 #634)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#678 := (pattern #16)
+#79 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#127 := (or #22 #79)
+#685 := (forall (vars (?v0 int)) (:pat #678) #127)
+#132 := (forall (vars (?v0 int)) #127)
+#688 := (iff #132 #685)
+#686 := (iff #127 #127)
+#687 := [refl]: #686
+#689 := [quant-intro #687]: #688
+#188 := (~ #132 #132)
+#200 := (~ #127 #127)
+#201 := [refl]: #200
+#189 := [nnf-pos #201]: #188
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#135 := (iff #24 #132)
+#98 := (= 0::int #17)
+#104 := (not #21)
+#105 := (or #104 #98)
+#110 := (forall (vars (?v0 int)) #105)
+#133 := (iff #110 #132)
+#130 := (iff #105 #127)
+#124 := (or #79 #22)
+#128 := (iff #124 #127)
+#129 := [rewrite]: #128
+#125 := (iff #105 #124)
+#122 := (iff #98 #22)
+#123 := [rewrite]: #122
+#120 := (iff #104 #79)
+#80 := (not #79)
+#115 := (not #80)
+#118 := (iff #115 #79)
+#119 := [rewrite]: #118
+#116 := (iff #104 #115)
+#113 := (iff #21 #80)
+#114 := [rewrite]: #113
+#117 := [monotonicity #114]: #116
+#121 := [trans #117 #119]: #120
+#126 := [monotonicity #121 #123]: #125
+#131 := [trans #126 #129]: #130
+#134 := [quant-intro #131]: #133
+#111 := (iff #24 #110)
+#108 := (iff #23 #105)
+#101 := (implies #21 #98)
+#106 := (iff #101 #105)
+#107 := [rewrite]: #106
+#102 := (iff #23 #101)
+#99 := (iff #22 #98)
+#100 := [rewrite]: #99
+#103 := [monotonicity #100]: #102
+#109 := [trans #103 #107]: #108
+#112 := [quant-intro #109]: #111
+#136 := [trans #112 #134]: #135
+#97 := [asserted]: #24
+#137 := [mp #97 #136]: #132
+#202 := [mp~ #137 #189]: #132
+#690 := [mp #202 #689]: #685
+#263 := (not #685)
+#625 := (or #263 #631 #634)
+#626 := (or #263 #635)
+#622 := (iff #626 #625)
+#623 := [rewrite]: #622
+#627 := [quant-inst]: #626
+#628 := [mp #627 #623]: #625
+#609 := [unit-resolution #628 #690]: #635
+#610 := [unit-resolution #609 #607]: #631
+#611 := (= #26 #349)
+#348 := (= f5 #344)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#670 := (pattern #9)
+#10 := (f3 #9)
+#54 := (= #8 #10)
+#671 := (forall (vars (?v0 S2)) (:pat #670) #54)
+#57 := (forall (vars (?v0 S2)) #54)
+#672 := (iff #57 #671)
+#674 := (iff #671 #671)
+#675 := [rewrite]: #674
+#673 := [rewrite]: #672
+#676 := [trans #673 #675]: #672
+#196 := (~ #57 #57)
+#194 := (~ #54 #54)
+#195 := [refl]: #194
+#197 := [nnf-pos #195]: #196
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#58 := (iff #12 #57)
+#55 := (iff #11 #54)
+#56 := [rewrite]: #55
+#59 := [quant-intro #56]: #58
+#53 := [asserted]: #12
+#62 := [mp #53 #59]: #57
+#185 := [mp~ #62 #197]: #57
+#677 := [mp #185 #676]: #671
+#664 := (not #671)
+#321 := (or #664 #348)
+#451 := [quant-inst]: #321
+#608 := [unit-resolution #451 #677]: #348
+#493 := [monotonicity #608]: #611
+#494 := [trans #493 #610]: #613
+#495 := (not #613)
+#454 := (or #495 #634)
+#602 := [th-lemma]: #454
+#504 := [unit-resolution #602 #607 #494]: false
+#599 := [lemma #504]: #634
+#619 := (or #606 #661)
+#600 := [th-lemma]: #619
+#603 := [unit-resolution #600 #599]: #661
+#308 := (not #661)
+#311 := (or #324 #308)
+#61 := (= #14 #17)
+#86 := (or #61 #80)
+#679 := (forall (vars (?v0 int)) (:pat #678) #86)
+#91 := (forall (vars (?v0 int)) #86)
+#682 := (iff #91 #679)
+#680 := (iff #86 #86)
+#681 := [refl]: #680
+#683 := [quant-intro #681]: #682
+#186 := (~ #91 #91)
+#183 := (~ #86 #86)
+#198 := [refl]: #183
+#187 := [nnf-pos #198]: #186
+#18 := (= #17 #14)
+#15 := (<= 0::int #14)
+#19 := (implies #15 #18)
+#20 := (forall (vars (?v0 int)) #19)
+#94 := (iff #20 #91)
+#68 := (not #15)
+#69 := (or #68 #61)
+#74 := (forall (vars (?v0 int)) #69)
+#92 := (iff #74 #91)
+#89 := (iff #69 #86)
+#83 := (or #80 #61)
+#87 := (iff #83 #86)
+#88 := [rewrite]: #87
+#84 := (iff #69 #83)
+#81 := (iff #68 #80)
+#77 := (iff #15 #79)
+#78 := [rewrite]: #77
+#82 := [monotonicity #78]: #81
+#85 := [monotonicity #82]: #84
+#90 := [trans #85 #88]: #89
+#93 := [quant-intro #90]: #92
+#75 := (iff #20 #74)
+#72 := (iff #19 #69)
+#65 := (implies #15 #61)
+#70 := (iff #65 #69)
+#71 := [rewrite]: #70
+#66 := (iff #19 #65)
+#63 := (iff #18 #61)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#73 := [trans #67 #71]: #72
+#76 := [quant-intro #73]: #75
+#95 := [trans #76 #93]: #94
+#60 := [asserted]: #20
+#96 := [mp #60 #95]: #91
+#199 := [mp~ #96 #187]: #91
+#684 := [mp #199 #683]: #679
+#649 := (not #679)
+#650 := (or #649 #324 #308)
+#666 := (>= #139 0::int)
+#667 := (not #666)
+#669 := (= #139 #145)
+#659 := (or #669 #667)
+#651 := (or #649 #659)
+#296 := (iff #651 #650)
+#652 := (or #649 #311)
+#655 := (iff #652 #650)
+#295 := [rewrite]: #655
+#290 := (iff #651 #652)
+#647 := (iff #659 #311)
+#309 := (iff #667 #308)
+#304 := (iff #666 #661)
+#645 := [rewrite]: #304
+#310 := [monotonicity #645]: #309
+#660 := (iff #669 #324)
+#320 := [rewrite]: #660
+#648 := [monotonicity #320 #310]: #647
+#653 := [monotonicity #648]: #290
+#656 := [trans #653 #295]: #296
+#646 := [quant-inst]: #651
+#654 := [mp #646 #656]: #650
+#488 := [unit-resolution #654 #684]: #311
+#503 := [unit-resolution #488 #603]: #324
+#505 := (not #324)
+#506 := (or #505 #643)
+#499 := [th-lemma]: #506
+#507 := [unit-resolution #499 #503]: #643
+#158 := (not #159)
+#508 := [hypothesis]: #158
+#169 := (not #164)
+#342 := (or #159 #169)
+#175 := (iff #159 #164)
+#31 := (+ #26 1::int)
+#32 := (f3 #31)
+#33 := (f4 #32)
+#34 := (<= #33 #28)
+#35 := (not #34)
+#29 := (< #26 #28)
+#36 := (iff #29 #35)
+#180 := (iff #36 #175)
+#148 := (<= #145 #28)
+#151 := (not #148)
+#154 := (iff #29 #151)
+#178 := (iff #154 #175)
+#172 := (iff #158 #169)
+#176 := (iff #172 #175)
+#177 := [rewrite]: #176
+#173 := (iff #154 #172)
+#170 := (iff #151 #169)
+#167 := (iff #148 #164)
+#168 := [rewrite]: #167
+#171 := [monotonicity #168]: #170
+#162 := (iff #29 #158)
+#163 := [rewrite]: #162
+#174 := [monotonicity #163 #171]: #173
+#179 := [trans #174 #177]: #178
+#155 := (iff #36 #154)
+#152 := (iff #35 #151)
+#149 := (iff #34 #148)
+#146 := (= #33 #145)
+#143 := (= #32 #142)
+#140 := (= #31 #139)
+#141 := [rewrite]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [monotonicity #147]: #149
+#153 := [monotonicity #150]: #152
+#156 := [monotonicity #153]: #155
+#181 := [trans #156 #179]: #180
+#138 := [asserted]: #36
+#182 := [mp #138 #181]: #175
+#256 := (not #175)
+#341 := (or #159 #169 #256)
+#257 := [def-axiom]: #341
+#343 := [unit-resolution #257 #182]: #342
+#509 := [unit-resolution #343 #508]: #169
+#510 := (not #643)
+#511 := (or #510 #159 #164)
+#604 := [th-lemma]: #511
+#601 := [unit-resolution #604 #509 #508 #507]: false
+#605 := [lemma #601]: #159
+#346 := (or #158 #164)
+#334 := (or #158 #164 #256)
+#345 := [def-axiom]: #334
+#347 := [unit-resolution #345 #182]: #346
+#592 := [unit-resolution #347 #605]: #164
+#657 := (<= #319 -1::int)
+#594 := (or #505 #657)
+#586 := [th-lemma]: #594
+#583 := [unit-resolution #586 #503]: #657
+[th-lemma #583 #605 #592]: false
+unsat
+75870ee37db906045eff49499698b090187a95a8 11 0
+#2 := false
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#27 := (< #26 #26)
+#132 := (iff #27 false)
+#133 := [rewrite]: #132
+#129 := [asserted]: #27
+[mp #129 #133]: false
+unsat
+65a9b991d68316f9955463b295888cc0b941d7e9 54 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#141 := -1::int
+#154 := (* -1::int #28)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#155 := (+ #26 #154)
+#156 := (<= #155 0::int)
+decl f7 :: S2
+#30 := f7
+#31 := (f4 f7)
+#142 := (* -1::int #31)
+#147 := (+ #26 #142)
+#148 := (<= #147 0::int)
+#151 := (not #148)
+#143 := (+ #28 #142)
+#144 := (<= #143 0::int)
+#165 := (and #144 #151 #156)
+#33 := (<= #26 #31)
+#34 := (not #33)
+#32 := (<= #28 #31)
+#35 := (and #32 #34)
+#29 := (<= #26 #28)
+#36 := (and #29 #35)
+#168 := (iff #36 #165)
+#159 := (and #144 #151)
+#162 := (and #156 #159)
+#166 := (iff #162 #165)
+#167 := [rewrite]: #166
+#163 := (iff #36 #162)
+#160 := (iff #35 #159)
+#152 := (iff #34 #151)
+#149 := (iff #33 #148)
+#150 := [rewrite]: #149
+#153 := [monotonicity #150]: #152
+#145 := (iff #32 #144)
+#146 := [rewrite]: #145
+#161 := [monotonicity #146 #153]: #160
+#157 := (iff #29 #156)
+#158 := [rewrite]: #157
+#164 := [monotonicity #158 #161]: #163
+#169 := [trans #164 #167]: #168
+#138 := [asserted]: #36
+#170 := [mp #138 #169]: #165
+#173 := [and-elim #170]: #156
+#172 := [and-elim #170]: #151
+#171 := [and-elim #170]: #144
+[th-lemma #171 #172 #173]: false
+unsat
+949587f0e75e73196b0b151bf0911a3bb0f90ff6 55 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#141 := -1::int
+#156 := (* -1::int #28)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#157 := (+ #26 #156)
+#155 := (>= #157 0::int)
+#154 := (not #155)
+decl f7 :: S2
+#30 := f7
+#31 := (f4 f7)
+#142 := (* -1::int #31)
+#147 := (+ #26 #142)
+#148 := (<= #147 0::int)
+#151 := (not #148)
+#143 := (+ #28 #142)
+#144 := (<= #143 0::int)
+#166 := (and #144 #151 #154)
+#33 := (<= #26 #31)
+#34 := (not #33)
+#32 := (<= #28 #31)
+#35 := (and #32 #34)
+#29 := (< #26 #28)
+#36 := (and #29 #35)
+#169 := (iff #36 #166)
+#160 := (and #144 #151)
+#163 := (and #154 #160)
+#167 := (iff #163 #166)
+#168 := [rewrite]: #167
+#164 := (iff #36 #163)
+#161 := (iff #35 #160)
+#152 := (iff #34 #151)
+#149 := (iff #33 #148)
+#150 := [rewrite]: #149
+#153 := [monotonicity #150]: #152
+#145 := (iff #32 #144)
+#146 := [rewrite]: #145
+#162 := [monotonicity #146 #153]: #161
+#158 := (iff #29 #154)
+#159 := [rewrite]: #158
+#165 := [monotonicity #159 #162]: #164
+#170 := [trans #165 #168]: #169
+#138 := [asserted]: #36
+#171 := [mp #138 #170]: #166
+#174 := [and-elim #171]: #154
+#173 := [and-elim #171]: #151
+#172 := [and-elim #171]: #144
+[th-lemma #172 #173 #174]: false
+unsat
+e0147cb04fc2e3bc1038fd5f0ee658954044a8ae 55 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#141 := -1::int
+#155 := (* -1::int #28)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#156 := (+ #26 #155)
+#157 := (<= #156 0::int)
+decl f7 :: S2
+#30 := f7
+#31 := (f4 f7)
+#144 := (* -1::int #31)
+#148 := (+ #26 #144)
+#149 := (<= #148 0::int)
+#152 := (not #149)
+#145 := (+ #28 #144)
+#143 := (>= #145 0::int)
+#142 := (not #143)
+#166 := (and #142 #152 #157)
+#33 := (<= #26 #31)
+#34 := (not #33)
+#32 := (< #28 #31)
+#35 := (and #32 #34)
+#29 := (<= #26 #28)
+#36 := (and #29 #35)
+#169 := (iff #36 #166)
+#160 := (and #142 #152)
+#163 := (and #157 #160)
+#167 := (iff #163 #166)
+#168 := [rewrite]: #167
+#164 := (iff #36 #163)
+#161 := (iff #35 #160)
+#153 := (iff #34 #152)
+#150 := (iff #33 #149)
+#151 := [rewrite]: #150
+#154 := [monotonicity #151]: #153
+#146 := (iff #32 #142)
+#147 := [rewrite]: #146
+#162 := [monotonicity #147 #154]: #161
+#158 := (iff #29 #157)
+#159 := [rewrite]: #158
+#165 := [monotonicity #159 #162]: #164
+#170 := [trans #165 #168]: #169
+#138 := [asserted]: #36
+#171 := [mp #138 #170]: #166
+#174 := [and-elim #171]: #157
+#172 := [and-elim #171]: #142
+#173 := [and-elim #171]: #152
+[th-lemma #173 #172 #174]: false
+unsat
+7f2af445a3047b7cf9ba6ecc7dbf1305f9ebc50e 61 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#141 := -1::int
+#162 := (* -1::int #28)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#163 := (+ #26 #162)
+#161 := (>= #163 0::int)
+#160 := (not #161)
+decl f7 :: S2
+#30 := f7
+#31 := (f4 f7)
+#144 := (* -1::int #31)
+#150 := (+ #26 #144)
+#149 := (>= #150 0::int)
+#145 := (+ #28 #144)
+#143 := (>= #145 0::int)
+#142 := (not #143)
+#172 := (and #142 #149 #160)
+#33 := (< #26 #31)
+#34 := (not #33)
+#32 := (< #28 #31)
+#35 := (and #32 #34)
+#29 := (< #26 #28)
+#36 := (and #29 #35)
+#175 := (iff #36 #172)
+#166 := (and #142 #149)
+#169 := (and #160 #166)
+#173 := (iff #169 #172)
+#174 := [rewrite]: #173
+#170 := (iff #36 #169)
+#167 := (iff #35 #166)
+#158 := (iff #34 #149)
+#148 := (not #149)
+#153 := (not #148)
+#156 := (iff #153 #149)
+#157 := [rewrite]: #156
+#154 := (iff #34 #153)
+#151 := (iff #33 #148)
+#152 := [rewrite]: #151
+#155 := [monotonicity #152]: #154
+#159 := [trans #155 #157]: #158
+#146 := (iff #32 #142)
+#147 := [rewrite]: #146
+#168 := [monotonicity #147 #159]: #167
+#164 := (iff #29 #160)
+#165 := [rewrite]: #164
+#171 := [monotonicity #165 #168]: #170
+#176 := [trans #171 #174]: #175
+#138 := [asserted]: #36
+#177 := [mp #138 #176]: #172
+#180 := [and-elim #177]: #160
+#178 := [and-elim #177]: #142
+#179 := [and-elim #177]: #149
+[th-lemma #179 #178 #180]: false
+unsat
+482ecd4de600d63ba37499412aa93699dc969167 53 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#140 := -1::int
+#154 := (* -1::int #28)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#155 := (+ #26 #154)
+#153 := (>= #155 0::int)
+#152 := (not #153)
+decl f7 :: S2
+#30 := f7
+#31 := (f4 f7)
+#143 := (* -1::int #31)
+#147 := (+ #26 #143)
+#148 := (<= #147 0::int)
+#149 := (not #148)
+#144 := (+ #28 #143)
+#142 := (>= #144 0::int)
+#141 := (not #142)
+#164 := (and #141 #149 #152)
+#33 := (< #31 #26)
+#32 := (< #28 #31)
+#34 := (and #32 #33)
+#29 := (< #26 #28)
+#35 := (and #29 #34)
+#167 := (iff #35 #164)
+#158 := (and #141 #149)
+#161 := (and #152 #158)
+#165 := (iff #161 #164)
+#166 := [rewrite]: #165
+#162 := (iff #35 #161)
+#159 := (iff #34 #158)
+#150 := (iff #33 #149)
+#151 := [rewrite]: #150
+#145 := (iff #32 #141)
+#146 := [rewrite]: #145
+#160 := [monotonicity #146 #151]: #159
+#156 := (iff #29 #152)
+#157 := [rewrite]: #156
+#163 := [monotonicity #157 #160]: #162
+#168 := [trans #163 #166]: #167
+#137 := [asserted]: #35
+#169 := [mp #137 #168]: #164
+#172 := [and-elim #169]: #152
+#170 := [and-elim #169]: #141
+#171 := [and-elim #169]: #149
+[th-lemma #171 #170 #172]: false
+unsat
+ed434a8d852f3ef0c4b2a01de695370158eb1708 17 0
+#2 := false
+#8 := 0::int
+#9 := (= 0::int 0::int)
+#10 := (not #9)
+#35 := (iff #10 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #10 #30)
+#28 := (iff #9 true)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#27 := [asserted]: #10
+[mp #27 #36]: false
+unsat
+338357cf4196be773c72026276e98bed42563d5e 25 0
+#2 := false
+#8 := 0::int
+#9 := (- 0::int)
+#10 := (= 0::int #9)
+#11 := (not #10)
+#43 := (iff #11 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #11 #38)
+#36 := (iff #10 true)
+#31 := (= 0::int 0::int)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #10 #31)
+#29 := (= #9 0::int)
+#30 := [rewrite]: #29
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#28 := [asserted]: #11
+[mp #28 #44]: false
+unsat
+867d1fafdaadf30f7a059d5589fdb8c2bf408653 17 0
+#2 := false
+#8 := 1::int
+#9 := (= 1::int 1::int)
+#10 := (not #9)
+#35 := (iff #10 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #10 #30)
+#28 := (iff #9 true)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#27 := [asserted]: #10
+[mp #27 #36]: false
+unsat
+5943aea69963bbcc197c3d50093a07c2985107c2 34 0
+#2 := false
+#8 := 1::int
+#9 := (- 1::int)
+#10 := (= #9 1::int)
+#11 := (not #10)
+#12 := (not #11)
+#52 := (iff #12 false)
+#1 := true
+#47 := (not true)
+#50 := (iff #47 false)
+#51 := [rewrite]: #50
+#48 := (iff #12 #47)
+#45 := (iff #11 true)
+#40 := (not false)
+#43 := (iff #40 true)
+#44 := [rewrite]: #43
+#41 := (iff #11 #40)
+#38 := (iff #10 false)
+#30 := -1::int
+#33 := (= -1::int 1::int)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #10 #33)
+#31 := (= #9 -1::int)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#49 := [monotonicity #46]: #48
+#53 := [trans #49 #51]: #52
+#29 := [asserted]: #12
+[mp #29 #53]: false
+unsat
+8e1bb3306a0749f86b5eb9ba42882d9894f78d3d 26 0
+#2 := false
+decl f3 :: int
+#8 := f3
+#9 := 0::int
+#10 := (+ f3 0::int)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+715dc24e87073f9f3b4eba5f97976011aef52fdb 40 0
+#2 := false
+#12 := 567::int
+#10 := 345::int
+#8 := 123::int
+#9 := (- 123::int)
+#11 := (+ #9 345::int)
+#13 := (< #11 567::int)
+#14 := (not #13)
+#58 := (iff #14 false)
+#38 := 222::int
+#43 := (< 222::int 567::int)
+#46 := (not #43)
+#56 := (iff #46 false)
+#1 := true
+#51 := (not true)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #46 #51)
+#49 := (iff #43 true)
+#50 := [rewrite]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#47 := (iff #14 #46)
+#44 := (iff #13 #43)
+#41 := (= #11 222::int)
+#32 := -123::int
+#35 := (+ -123::int 345::int)
+#39 := (= #35 222::int)
+#40 := [rewrite]: #39
+#36 := (= #11 #35)
+#33 := (= #9 -123::int)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#42 := [trans #37 #40]: #41
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#59 := [trans #48 #57]: #58
+#31 := [asserted]: #14
+[mp #31 #59]: false
+unsat
+d639d04a056e1fcc050de165453e89b0bfe78d22 26 0
+#2 := false
+decl f3 :: int
+#9 := f3
+#8 := 0::int
+#10 := (+ 0::int f3)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+bb65114f0b3cbddac138f9f5170c5cee40e42881 30 0
+#2 := false
+#10 := 2345678901::int
+#8 := 123456789::int
+#9 := (- 123456789::int)
+#11 := (< #9 2345678901::int)
+#12 := (not #11)
+#48 := (iff #12 false)
+#30 := -123456789::int
+#33 := (< -123456789::int 2345678901::int)
+#36 := (not #33)
+#46 := (iff #36 false)
+#1 := true
+#41 := (not true)
+#44 := (iff #41 false)
+#45 := [rewrite]: #44
+#42 := (iff #36 #41)
+#39 := (iff #33 true)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#37 := (iff #12 #36)
+#34 := (iff #11 #33)
+#31 := (= #9 -123456789::int)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#38 := [monotonicity #35]: #37
+#49 := [trans #38 #47]: #48
+#29 := [asserted]: #12
+[mp #29 #49]: false
+unsat
+3b63f6086e2140e850f10e8d6167751f9a080815 29 0
+#2 := false
+decl f3 :: int
+#8 := f3
+decl f4 :: int
+#9 := f4
+#11 := (+ f4 f3)
+#10 := (+ f3 f4)
+#12 := (= #10 #11)
+#13 := (not #12)
+#45 := (iff #13 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #13 #40)
+#38 := (iff #12 true)
+#33 := (= #10 #10)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #12 #33)
+#31 := (= #11 #10)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#30 := [asserted]: #13
+[mp #30 #46]: false
+unsat
+1ce9f759ae49f3864320a9981e66669d7d207503 33 0
+#2 := false
+decl f5 :: int
+#10 := f5
+decl f4 :: int
+#9 := f4
+decl f3 :: int
+#8 := f3
+#13 := (+ f3 f4)
+#14 := (+ #13 f5)
+#11 := (+ f4 f5)
+#12 := (+ f3 #11)
+#15 := (= #12 #14)
+#16 := (not #15)
+#48 := (iff #16 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #16 #43)
+#41 := (iff #15 true)
+#36 := (= #12 #12)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #15 #36)
+#34 := (= #14 #12)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#33 := [asserted]: #16
+[mp #33 #49]: false
+unsat
+64c69e25d3a0449c698081f4cb9242fb6934e70f 26 0
+#2 := false
+#8 := 1::int
+#9 := (- 1::int)
+#10 := (= #9 #9)
+#11 := (not #10)
+#44 := (iff #11 false)
+#1 := true
+#39 := (not true)
+#42 := (iff #39 false)
+#43 := [rewrite]: #42
+#40 := (iff #11 #39)
+#37 := (iff #10 true)
+#29 := -1::int
+#32 := (= -1::int -1::int)
+#35 := (iff #32 true)
+#36 := [rewrite]: #35
+#33 := (iff #10 #32)
+#30 := (= #9 -1::int)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31 #31]: #33
+#38 := [trans #34 #36]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#28 := [asserted]: #11
+[mp #28 #45]: false
+unsat
+874be756bcaf30e65c16d8e08cb52dff2d8a608c 45 0
+#2 := false
+decl f4 :: int
+#9 := f4
+#13 := (- f4)
+decl f3 :: int
+#8 := f3
+#14 := (= f3 #13)
+#11 := 0::int
+#10 := (+ f3 f4)
+#12 := (= #10 0::int)
+#15 := (iff #12 #14)
+#16 := (not #15)
+#62 := (iff #16 false)
+#47 := (not #12)
+#34 := -1::int
+#35 := (* -1::int f4)
+#38 := (= f3 #35)
+#48 := (iff #38 #47)
+#60 := (iff #48 false)
+#55 := (iff #12 #47)
+#58 := (iff #55 false)
+#59 := [rewrite]: #58
+#56 := (iff #48 #55)
+#53 := (iff #38 #12)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#51 := (iff #16 #48)
+#41 := (iff #12 #38)
+#44 := (not #41)
+#49 := (iff #44 #48)
+#50 := [rewrite]: #49
+#45 := (iff #16 #44)
+#42 := (iff #15 #41)
+#39 := (iff #14 #38)
+#36 := (= #13 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#46 := [monotonicity #43]: #45
+#52 := [trans #46 #50]: #51
+#63 := [trans #52 #61]: #62
+#33 := [asserted]: #16
+[mp #33 #63]: false
+unsat
+47f2b1fe93be442ab0a662dee31bf529fde2944c 26 0
+#2 := false
+#8 := 3::int
+#9 := (- 3::int)
+#10 := (= #9 #9)
+#11 := (not #10)
+#44 := (iff #11 false)
+#1 := true
+#39 := (not true)
+#42 := (iff #39 false)
+#43 := [rewrite]: #42
+#40 := (iff #11 #39)
+#37 := (iff #10 true)
+#29 := -3::int
+#32 := (= -3::int -3::int)
+#35 := (iff #32 true)
+#36 := [rewrite]: #35
+#33 := (iff #10 #32)
+#30 := (= #9 -3::int)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31 #31]: #33
+#38 := [trans #34 #36]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#28 := [asserted]: #11
+[mp #28 #45]: false
+unsat
+2482501dff9d1180d8ed87b147225f74cf2613dc 58 0
+#2 := false
+decl f3 :: int
+#8 := f3
+#10 := 0::int
+#12 := (< 0::int f3)
+#9 := (- f3)
+#11 := (< #9 0::int)
+#13 := (iff #11 #12)
+#14 := (not #13)
+#76 := (iff #14 false)
+#50 := (not #12)
+#32 := -1::int
+#33 := (* -1::int f3)
+#36 := (< #33 0::int)
+#51 := (iff #36 #50)
+#74 := (iff #51 false)
+#56 := (<= f3 0::int)
+#57 := (not #56)
+#69 := (iff #57 #56)
+#72 := (iff #69 false)
+#73 := [rewrite]: #72
+#70 := (iff #51 #69)
+#67 := (iff #50 #56)
+#62 := (not #57)
+#65 := (iff #62 #56)
+#66 := [rewrite]: #65
+#63 := (iff #50 #62)
+#60 := (iff #12 #57)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#68 := [trans #64 #66]: #67
+#58 := (iff #36 #57)
+#59 := [rewrite]: #58
+#71 := [monotonicity #59 #68]: #70
+#75 := [trans #71 #73]: #74
+#54 := (iff #14 #51)
+#42 := (iff #12 #36)
+#47 := (not #42)
+#52 := (iff #47 #51)
+#53 := [rewrite]: #52
+#48 := (iff #14 #47)
+#45 := (iff #13 #42)
+#39 := (iff #36 #12)
+#43 := (iff #39 #42)
+#44 := [rewrite]: #43
+#40 := (iff #13 #39)
+#37 := (iff #11 #36)
+#34 := (= #9 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#46 := [trans #41 #44]: #45
+#49 := [monotonicity #46]: #48
+#55 := [trans #49 #53]: #54
+#77 := [trans #55 #75]: #76
+#31 := [asserted]: #14
+[mp #31 #77]: false
+unsat
+8ec4c3ebc255a7267982d00d4ae0cabf0d20510a 61 0
+#2 := false
+#8 := 0::int
+decl f3 :: int
+#9 := f3
+#11 := (- f3)
+#12 := (< #11 0::int)
+#10 := (< 0::int f3)
+#13 := (implies #10 #12)
+#14 := (not #13)
+#78 := (iff #14 false)
+#32 := -1::int
+#33 := (* -1::int f3)
+#36 := (< #33 0::int)
+#42 := (not #10)
+#43 := (or #42 #36)
+#48 := (not #43)
+#76 := (iff #48 false)
+#1 := true
+#71 := (not true)
+#74 := (iff #71 false)
+#75 := [rewrite]: #74
+#72 := (iff #48 #71)
+#69 := (iff #43 true)
+#51 := (<= f3 0::int)
+#52 := (not #51)
+#64 := (or #51 #52)
+#67 := (iff #64 true)
+#68 := [rewrite]: #67
+#65 := (iff #43 #64)
+#62 := (iff #36 #52)
+#63 := [rewrite]: #62
+#60 := (iff #42 #51)
+#55 := (not #52)
+#58 := (iff #55 #51)
+#59 := [rewrite]: #58
+#56 := (iff #42 #55)
+#53 := (iff #10 #52)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#66 := [monotonicity #61 #63]: #65
+#70 := [trans #66 #68]: #69
+#73 := [monotonicity #70]: #72
+#77 := [trans #73 #75]: #76
+#49 := (iff #14 #48)
+#46 := (iff #13 #43)
+#39 := (implies #10 #36)
+#44 := (iff #39 #43)
+#45 := [rewrite]: #44
+#40 := (iff #13 #39)
+#37 := (iff #12 #36)
+#34 := (= #11 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#47 := [trans #41 #45]: #46
+#50 := [monotonicity #47]: #49
+#79 := [trans #50 #77]: #78
+#31 := [asserted]: #14
+[mp #31 #79]: false
+unsat
[phone]e2fa11bd81435e99b55b58ebfafb1e77 26 0
+#2 := false
+decl f3 :: int
+#8 := f3
+#9 := 0::int
+#10 := (- f3 0::int)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+668c2d2887e11c00b7ba359c2de9bccabf20f1e2 61 0
+#2 := false
+decl f3 :: int
+#8 := f3
+#11 := (- f3)
+#9 := 0::int
+#12 := (< 0::int #11)
+#10 := (< f3 0::int)
+#13 := (implies #10 #12)
+#14 := (not #13)
+#78 := (iff #14 false)
+#32 := -1::int
+#33 := (* -1::int f3)
+#36 := (< 0::int #33)
+#42 := (not #10)
+#43 := (or #42 #36)
+#48 := (not #43)
+#76 := (iff #48 false)
+#1 := true
+#71 := (not true)
+#74 := (iff #71 false)
+#75 := [rewrite]: #74
+#72 := (iff #48 #71)
+#69 := (iff #43 true)
+#51 := (>= f3 0::int)
+#52 := (not #51)
+#64 := (or #51 #52)
+#67 := (iff #64 true)
+#68 := [rewrite]: #67
+#65 := (iff #43 #64)
+#62 := (iff #36 #52)
+#63 := [rewrite]: #62
+#60 := (iff #42 #51)
+#55 := (not #52)
+#58 := (iff #55 #51)
+#59 := [rewrite]: #58
+#56 := (iff #42 #55)
+#53 := (iff #10 #52)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#66 := [monotonicity #61 #63]: #65
+#70 := [trans #66 #68]: #69
+#73 := [monotonicity #70]: #72
+#77 := [trans #73 #75]: #76
+#49 := (iff #14 #48)
+#46 := (iff #13 #43)
+#39 := (implies #10 #36)
+#44 := (iff #39 #43)
+#45 := [rewrite]: #44
+#40 := (iff #13 #39)
+#37 := (iff #12 #36)
+#34 := (= #11 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#47 := [trans #41 #45]: #46
+#50 := [monotonicity #47]: #49
+#79 := [trans #50 #77]: #78
+#31 := [asserted]: #14
+[mp #31 #79]: false
+unsat
+4c9b1171e8f5ec24906ea56a788bc2e3bdd3eeca 32 0
+#2 := false
+decl f3 :: int
+#9 := f3
+#11 := (- f3)
+#8 := 0::int
+#10 := (- 0::int f3)
+#12 := (= #10 #11)
+#13 := (not #12)
+#49 := (iff #13 false)
+#1 := true
+#44 := (not true)
+#47 := (iff #44 false)
+#48 := [rewrite]: #47
+#45 := (iff #13 #44)
+#42 := (iff #12 true)
+#31 := -1::int
+#32 := (* -1::int f3)
+#37 := (= #32 #32)
+#40 := (iff #37 true)
+#41 := [rewrite]: #40
+#38 := (iff #12 #37)
+#35 := (= #11 #32)
+#36 := [rewrite]: #35
+#33 := (= #10 #32)
+#34 := [rewrite]: #33
+#39 := [monotonicity #34 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#30 := [asserted]: #13
+[mp #30 #50]: false
+unsat
+d57becfa9f4b7e88a7dcbf91788610a6cb73b146 64 0
+#2 := false
+#12 := 0::int
+decl f4 :: int
+#9 := f4
+decl f3 :: int
+#8 := f3
+#11 := (- f3 f4)
+#13 := (< #11 0::int)
+#10 := (< f3 f4)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#80 := (iff #15 false)
+#33 := -1::int
+#34 := (* -1::int f4)
+#35 := (+ f3 #34)
+#38 := (< #35 0::int)
+#44 := (not #10)
+#45 := (or #44 #38)
+#50 := (not #45)
+#78 := (iff #50 false)
+#1 := true
+#73 := (not true)
+#76 := (iff #73 false)
+#77 := [rewrite]: #76
+#74 := (iff #50 #73)
+#71 := (iff #45 true)
+#54 := (>= #35 0::int)
+#53 := (not #54)
+#66 := (or #54 #53)
+#69 := (iff #66 true)
+#70 := [rewrite]: #69
+#67 := (iff #45 #66)
+#64 := (iff #38 #53)
+#65 := [rewrite]: #64
+#62 := (iff #44 #54)
+#57 := (not #53)
+#60 := (iff #57 #54)
+#61 := [rewrite]: #60
+#58 := (iff #44 #57)
+#55 := (iff #10 #53)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#63 := [trans #59 #61]: #62
+#68 := [monotonicity #63 #65]: #67
+#72 := [trans #68 #70]: #71
+#75 := [monotonicity #72]: #74
+#79 := [trans #75 #77]: #78
+#51 := (iff #15 #50)
+#48 := (iff #14 #45)
+#41 := (implies #10 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #14 #41)
+#39 := (iff #13 #38)
+#36 := (= #11 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#49 := [trans #43 #47]: #48
+#52 := [monotonicity #49]: #51
+#81 := [trans #52 #79]: #80
+#32 := [asserted]: #15
+[mp #32 #81]: false
+unsat
+c1b0e98ca220494689565415ab1dcebe6fa0d444 26 0
+#2 := false
+#9 := 0::int
+decl f3 :: int
+#8 := f3
+#10 := (* f3 0::int)
+#11 := (= #10 0::int)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= 0::int 0::int)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
[phone]c5abeeb69b9185128b009b95b5f 44 0
+#2 := false
+decl f3 :: int
+#8 := f3
+decl f4 :: int
+#9 := f4
+#11 := (- f4 f3)
+#12 := (- #11)
+#10 := (- f3 f4)
+#13 := (= #10 #12)
+#14 := (not #13)
+#60 := (iff #14 false)
+#1 := true
+#55 := (not true)
+#58 := (iff #55 false)
+#59 := [rewrite]: #58
+#56 := (iff #14 #55)
+#53 := (iff #13 true)
+#32 := -1::int
+#33 := (* -1::int f4)
+#34 := (+ f3 #33)
+#48 := (= #34 #34)
+#51 := (iff #48 true)
+#52 := [rewrite]: #51
+#49 := (iff #13 #48)
+#46 := (= #12 #34)
+#37 := (* -1::int f3)
+#38 := (+ #37 f4)
+#41 := (- #38)
+#44 := (= #41 #34)
+#45 := [rewrite]: #44
+#42 := (= #12 #41)
+#39 := (= #11 #38)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#35 := (= #10 #34)
+#36 := [rewrite]: #35
+#50 := [monotonicity #36 #47]: #49
+#54 := [trans #50 #52]: #53
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#31 := [asserted]: #14
+[mp #31 #61]: false
+unsat
+dece965f3c6151f83b0de59bbe4f0ba10e7e97f9 26 0
+#2 := false
+#8 := 0::int
+decl f3 :: int
+#9 := f3
+#10 := (* 0::int f3)
+#11 := (= #10 0::int)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= 0::int 0::int)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+054a96393770a76ee29957e3d16bb134c9dadb35 42 0
+#2 := false
+decl f3 :: int
+#8 := f3
+decl f4 :: int
+#9 := f4
+#11 := (- f4)
+#12 := (+ #11 f3)
+#10 := (- f3 f4)
+#13 := (= #10 #12)
+#14 := (not #13)
+#58 := (iff #14 false)
+#1 := true
+#53 := (not true)
+#56 := (iff #53 false)
+#57 := [rewrite]: #56
+#54 := (iff #14 #53)
+#51 := (iff #13 true)
+#32 := -1::int
+#33 := (* -1::int f4)
+#34 := (+ f3 #33)
+#46 := (= #34 #34)
+#49 := (iff #46 true)
+#50 := [rewrite]: #49
+#47 := (iff #13 #46)
+#44 := (= #12 #34)
+#39 := (+ #33 f3)
+#42 := (= #39 #34)
+#43 := [rewrite]: #42
+#40 := (= #12 #39)
+#37 := (= #11 #33)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#35 := (= #10 #34)
+#36 := [rewrite]: #35
+#48 := [monotonicity #36 #45]: #47
+#52 := [trans #48 #50]: #51
+#55 := [monotonicity #52]: #54
+#59 := [trans #55 #57]: #58
+#31 := [asserted]: #14
+[mp #31 #59]: false
+unsat
+461fdb6982dad0d1b399fb5db09287115e6b6cc3 26 0
+#2 := false
+decl f3 :: int
+#8 := f3
+#9 := 1::int
+#10 := (* f3 1::int)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+ad203296ea503ecdd81c71c4ae272e08de16a654 48 0
+#2 := false
+decl f5 :: int
+#11 := f5
+decl f4 :: int
+#9 := f4
+#13 := (+ f4 f5)
+decl f3 :: int
+#8 := f3
+#14 := (- f3 #13)
+#10 := (- f3 f4)
+#12 := (- #10 f5)
+#15 := (= #12 #14)
+#16 := (not #15)
+#63 := (iff #16 false)
+#1 := true
+#58 := (not true)
+#61 := (iff #58 false)
+#62 := [rewrite]: #61
+#59 := (iff #16 #58)
+#56 := (iff #15 true)
+#34 := -1::int
+#42 := (* -1::int f5)
+#35 := (* -1::int f4)
+#43 := (+ #35 #42)
+#44 := (+ f3 #43)
+#51 := (= #44 #44)
+#54 := (iff #51 true)
+#55 := [rewrite]: #54
+#52 := (iff #15 #51)
+#49 := (= #14 #44)
+#50 := [rewrite]: #49
+#47 := (= #12 #44)
+#36 := (+ f3 #35)
+#39 := (- #36 f5)
+#45 := (= #39 #44)
+#46 := [rewrite]: #45
+#40 := (= #12 #39)
+#37 := (= #10 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#48 := [trans #41 #46]: #47
+#53 := [monotonicity #48 #50]: #52
+#57 := [trans #53 #55]: #56
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#33 := [asserted]: #16
+[mp #33 #64]: false
+unsat
+0b54863485aa10cf645d5bc7b322d1ba8118b0d8 26 0
+#2 := false
+decl f3 :: int
+#9 := f3
+#8 := 1::int
+#10 := (* 1::int f3)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+00cbc9bbde1a21b4ec41867ca29cd9a793c98e95 40 0
+#2 := false
+decl f3 :: int
+#8 := f3
+#12 := (- f3)
+#9 := 1::int
+#10 := (- 1::int)
+#11 := (* f3 #10)
+#13 := (= #11 #12)
+#14 := (not #13)
+#57 := (iff #14 false)
+#1 := true
+#52 := (not true)
+#55 := (iff #52 false)
+#56 := [rewrite]: #55
+#53 := (iff #14 #52)
+#50 := (iff #13 true)
+#32 := -1::int
+#38 := (* -1::int f3)
+#45 := (= #38 #38)
+#48 := (iff #45 true)
+#49 := [rewrite]: #48
+#46 := (iff #13 #45)
+#43 := (= #12 #38)
+#44 := [rewrite]: #43
+#41 := (= #11 #38)
+#35 := (* f3 -1::int)
+#39 := (= #35 #38)
+#40 := [rewrite]: #39
+#36 := (= #11 #35)
+#33 := (= #10 -1::int)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#42 := [trans #37 #40]: #41
+#47 := [monotonicity #42 #44]: #46
+#51 := [trans #47 #49]: #50
+#54 := [monotonicity #51]: #53
+#58 := [trans #54 #56]: #57
+#31 := [asserted]: #14
+[mp #31 #58]: false
+unsat
+98af8ac1621f25bec4b921bca3d925b1b20ce7aa 75 0
+#2 := false
+#8 := 0::int
+decl f3 :: int
+#9 := f3
+#32 := -1::int
+#33 := (* -1::int f3)
+#45 := (>= f3 0::int)
+#52 := (ite #45 f3 #33)
+#73 := (* -1::int #52)
+#81 := (+ f3 #73)
+#90 := (<= #81 0::int)
+#76 := (= f3 #52)
+#71 := (+ #33 #73)
+#80 := (<= #71 0::int)
+#77 := (= #33 #52)
+#46 := (not #45)
+#82 := [hypothesis]: #46
+#74 := (or #45 #77)
+#75 := [def-axiom]: #74
+#83 := [unit-resolution #75 #82]: #77
+#84 := (not #77)
+#85 := (or #84 #80)
+#86 := [th-lemma]: #85
+#87 := [unit-resolution #86 #83]: #80
+#61 := (>= #52 0::int)
+#65 := (not #61)
+#11 := (- f3)
+#10 := (< f3 0::int)
+#12 := (ite #10 #11 f3)
+#13 := (<= 0::int #12)
+#14 := (not #13)
+#68 := (iff #14 #65)
+#36 := (ite #10 #33 f3)
+#39 := (<= 0::int #36)
+#42 := (not #39)
+#66 := (iff #42 #65)
+#63 := (iff #39 #61)
+#57 := (<= 0::int #52)
+#60 := (iff #57 #61)
+#62 := [rewrite]: #60
+#58 := (iff #39 #57)
+#55 := (= #36 #52)
+#49 := (ite #46 #33 f3)
+#53 := (= #49 #52)
+#54 := [rewrite]: #53
+#50 := (= #36 #49)
+#47 := (iff #10 #46)
+#48 := [rewrite]: #47
+#51 := [monotonicity #48]: #50
+#56 := [trans #51 #54]: #55
+#59 := [monotonicity #56]: #58
+#64 := [trans #59 #62]: #63
+#67 := [monotonicity #64]: #66
+#43 := (iff #14 #42)
+#40 := (iff #13 #39)
+#37 := (= #12 #36)
+#34 := (= #11 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#44 := [monotonicity #41]: #43
+#69 := [trans #44 #67]: #68
+#31 := [asserted]: #14
+#70 := [mp #31 #69]: #65
+#88 := [th-lemma #82 #70 #87]: false
+#89 := [lemma #88]: #45
+#78 := (or #46 #76)
+#79 := [def-axiom]: #78
+#92 := [unit-resolution #79 #89]: #76
+#93 := (not #76)
+#94 := (or #93 #90)
+#95 := [th-lemma]: #94
+#96 := [unit-resolution #95 #92]: #90
+[th-lemma #89 #70 #96]: false
+unsat
+372ec6980c70cef9ac29be50305f6f70f148ceb4 35 0
+#2 := false
+decl f3 :: int
+#10 := f3
+#12 := (- f3)
+#8 := 1::int
+#9 := (- 1::int)
+#11 := (* #9 f3)
+#13 := (= #11 #12)
+#14 := (not #13)
+#52 := (iff #14 false)
+#1 := true
+#47 := (not true)
+#50 := (iff #47 false)
+#51 := [rewrite]: #50
+#48 := (iff #14 #47)
+#45 := (iff #13 true)
+#32 := -1::int
+#35 := (* -1::int f3)
+#40 := (= #35 #35)
+#43 := (iff #40 true)
+#44 := [rewrite]: #43
+#41 := (iff #13 #40)
+#38 := (= #12 #35)
+#39 := [rewrite]: #38
+#36 := (= #11 #35)
+#33 := (= #9 -1::int)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#42 := [monotonicity #37 #39]: #41
+#46 := [trans #42 #44]: #45
+#49 := [monotonicity #46]: #48
+#53 := [trans #49 #51]: #52
+#31 := [asserted]: #14
+[mp #31 #53]: false
+unsat
+85ed4b98db23623099a1ab59de709435336b46b9 132 0
+#2 := false
+#9 := 0::int
+decl f3 :: int
+#8 := f3
+#66 := (>= f3 0::int)
+#67 := (not #66)
+#34 := -1::int
+#35 := (* -1::int f3)
+#73 := (ite #66 f3 #35)
+#102 := (= f3 #73)
+#130 := (not #102)
+#14 := (= f3 0::int)
+#82 := (= #73 0::int)
+#124 := (iff #82 #14)
+#122 := (iff #14 #82)
+#121 := [hypothesis]: #102
+#123 := [monotonicity #121]: #122
+#125 := [symm #123]: #124
+#131 := (or #82 #130)
+#60 := (not #14)
+#99 := (not #82)
+#126 := (iff #99 #60)
+#127 := [monotonicity #125]: #126
+#119 := [hypothesis]: #99
+#128 := [mp #119 #127]: #60
+#112 := (or #14 #82)
+#89 := (iff #60 #82)
+#11 := (- f3)
+#10 := (< f3 0::int)
+#12 := (ite #10 #11 f3)
+#13 := (= #12 0::int)
+#15 := (iff #13 #14)
+#16 := (not #15)
+#94 := (iff #16 #89)
+#38 := (ite #10 #35 f3)
+#44 := (= 0::int #38)
+#61 := (iff #44 #60)
+#92 := (iff #61 #89)
+#86 := (iff #82 #60)
+#90 := (iff #86 #89)
+#91 := [rewrite]: #90
+#87 := (iff #61 #86)
+#84 := (iff #44 #82)
+#78 := (= 0::int #73)
+#81 := (iff #78 #82)
+#83 := [rewrite]: #81
+#79 := (iff #44 #78)
+#76 := (= #38 #73)
+#70 := (ite #67 #35 f3)
+#74 := (= #70 #73)
+#75 := [rewrite]: #74
+#71 := (= #38 #70)
+#68 := (iff #10 #67)
+#69 := [rewrite]: #68
+#72 := [monotonicity #69]: #71
+#77 := [trans #72 #75]: #76
+#80 := [monotonicity #77]: #79
+#85 := [trans #80 #83]: #84
+#88 := [monotonicity #85]: #87
+#93 := [trans #88 #91]: #92
+#64 := (iff #16 #61)
+#52 := (iff #14 #44)
+#57 := (not #52)
+#62 := (iff #57 #61)
+#63 := [rewrite]: #62
+#58 := (iff #16 #57)
+#55 := (iff #15 #52)
+#49 := (iff #44 #14)
+#53 := (iff #49 #52)
+#54 := [rewrite]: #53
+#50 := (iff #15 #49)
+#47 := (iff #13 #44)
+#41 := (= #38 0::int)
+#45 := (iff #41 #44)
+#46 := [rewrite]: #45
+#42 := (iff #13 #41)
+#39 := (= #12 #38)
+#36 := (= #11 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#48 := [trans #43 #46]: #47
+#51 := [monotonicity #48]: #50
+#56 := [trans #51 #54]: #55
+#59 := [monotonicity #56]: #58
+#65 := [trans #59 #63]: #64
+#95 := [trans #65 #93]: #94
+#33 := [asserted]: #16
+#96 := [mp #33 #95]: #89
+#97 := (not #89)
+#110 := (or #14 #82 #97)
+#111 := [def-axiom]: #110
+#113 := [unit-resolution #111 #96]: #112
+#120 := [unit-resolution #113 #119]: #14
+#129 := [unit-resolution #120 #128]: false
+#132 := [lemma #129]: #131
+#133 := [unit-resolution #132 #121]: #82
+#135 := [mp #133 #125]: #14
+#108 := (or #60 #99)
+#106 := (or #60 #99 #97)
+#107 := [def-axiom]: #106
+#109 := [unit-resolution #107 #96]: #108
+#134 := [unit-resolution #109 #133]: #60
+#136 := [unit-resolution #134 #135]: false
+#137 := [lemma #136]: #130
+#104 := (or #67 #102)
+#105 := [def-axiom]: #104
+#143 := [unit-resolution #105 #137]: #67
+#138 := (= #35 0::int)
+#147 := (not #138)
+#157 := (iff #147 #99)
+#155 := (iff #138 #82)
+#103 := (= #35 #73)
+#100 := (or #66 #103)
+#101 := [def-axiom]: #100
+#154 := [unit-resolution #101 #143]: #103
+#156 := [monotonicity #154]: #155
+#158 := [monotonicity #156]: #157
+#139 := (<= #35 0::int)
+#145 := (not #139)
+#142 := [hypothesis]: #139
+#144 := [th-lemma #143 #142]: false
+#146 := [lemma #144]: #145
+#148 := (or #147 #139)
+#149 := [th-lemma]: #148
+#153 := [unit-resolution #149 #146]: #147
+#159 := [mp #153 #158]: #99
+#160 := [unit-resolution #113 #159]: #14
+#161 := (or #60 #66)
+#162 := [th-lemma]: #161
+[unit-resolution #162 #160 #143]: false
+unsat
+92c9831074e5b2d154f59e6c16ca64cf6c2306e5 28 0
+#2 := false
+#8 := 3::int
+decl f3 :: int
+#9 := f3
+#11 := (* f3 3::int)
+#10 := (* 3::int f3)
+#12 := (= #10 #11)
+#13 := (not #12)
+#45 := (iff #13 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #13 #40)
+#38 := (iff #12 true)
+#33 := (= #10 #10)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #12 #33)
+#31 := (= #11 #10)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#30 := [asserted]: #13
+[mp #30 #46]: false
+unsat
+63bab884626cc49af1ccdd9b8ddfe0dc08303f89 103 0
+#2 := false
+#8 := 0::int
+decl f3 :: int
+#9 := f3
+#34 := -1::int
+#35 := (* -1::int f3)
+#112 := (* -1::int #35)
+#113 := (+ f3 #112)
+#115 := (>= #113 0::int)
+#111 := (= f3 #35)
+#61 := (>= f3 0::int)
+#68 := (ite #61 f3 #35)
+#118 := (= #68 #35)
+#96 := (= #35 #68)
+#62 := (not #61)
+#107 := [hypothesis]: #61
+#73 := (= f3 #68)
+#97 := (or #62 #73)
+#98 := [def-axiom]: #97
+#108 := [unit-resolution #98 #107]: #73
+#95 := (not #73)
+#101 := (or #62 #95)
+#83 := (iff #62 #73)
+#12 := (- f3)
+#11 := (< f3 0::int)
+#13 := (ite #11 #12 f3)
+#14 := (= #13 f3)
+#10 := (<= 0::int f3)
+#15 := (iff #10 #14)
+#16 := (not #15)
+#88 := (iff #16 #83)
+#55 := (not #10)
+#38 := (ite #11 #35 f3)
+#44 := (= f3 #38)
+#56 := (iff #44 #55)
+#86 := (iff #56 #83)
+#80 := (iff #73 #62)
+#84 := (iff #80 #83)
+#85 := [rewrite]: #84
+#81 := (iff #56 #80)
+#78 := (iff #55 #62)
+#76 := (iff #10 #61)
+#77 := [rewrite]: #76
+#79 := [monotonicity #77]: #78
+#74 := (iff #44 #73)
+#71 := (= #38 #68)
+#65 := (ite #62 #35 f3)
+#69 := (= #65 #68)
+#70 := [rewrite]: #69
+#66 := (= #38 #65)
+#63 := (iff #11 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#72 := [trans #67 #70]: #71
+#75 := [monotonicity #72]: #74
+#82 := [monotonicity #75 #79]: #81
+#87 := [trans #82 #85]: #86
+#59 := (iff #16 #56)
+#49 := (iff #10 #44)
+#52 := (not #49)
+#57 := (iff #52 #56)
+#58 := [rewrite]: #57
+#53 := (iff #16 #52)
+#50 := (iff #15 #49)
+#47 := (iff #14 #44)
+#41 := (= #38 f3)
+#45 := (iff #41 #44)
+#46 := [rewrite]: #45
+#42 := (iff #14 #41)
+#39 := (= #13 #38)
+#36 := (= #12 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#48 := [trans #43 #46]: #47
+#51 := [monotonicity #48]: #50
+#54 := [monotonicity #51]: #53
+#60 := [trans #54 #58]: #59
+#89 := [trans #60 #87]: #88
+#33 := [asserted]: #16
+#90 := [mp #33 #89]: #83
+#93 := (not #83)
+#91 := (or #62 #95 #93)
+#100 := [def-axiom]: #91
+#102 := [unit-resolution #100 #90]: #101
+#109 := [unit-resolution #102 #108 #107]: false
+#110 := [lemma #109]: #62
+#99 := (or #61 #96)
+#94 := [def-axiom]: #99
+#116 := [unit-resolution #94 #110]: #96
+#119 := [symm #116]: #118
+#105 := (or #61 #73)
+#103 := (or #61 #73 #93)
+#104 := [def-axiom]: #103
+#106 := [unit-resolution #104 #90]: #105
+#117 := [unit-resolution #106 #110]: #73
+#120 := [trans #117 #119]: #111
+#121 := (not #111)
+#122 := (or #121 #115)
+#123 := [th-lemma]: #122
+#124 := [unit-resolution #123 #120]: #115
+[th-lemma #110 #124]: false
+unsat
+1d80fb1bb6a7cd91244703f8571db834177b7724 149 0
+#2 := false
+#9 := 0::int
+decl f3 :: int
+#8 := f3
+#34 := -1::int
+#35 := (* -1::int f3)
+#61 := (>= f3 0::int)
+#68 := (ite #61 f3 #35)
+#111 := (* -1::int #68)
+#156 := (+ f3 #111)
+#157 := (<= #156 0::int)
+#98 := (= f3 #68)
+#10 := (<= f3 0::int)
+#55 := (not #10)
+#78 := (+ f3 #68)
+#77 := (= #78 0::int)
+#93 := (not #77)
+#115 := [hypothesis]: #93
+#95 := (>= #78 0::int)
+#112 := (+ #35 #111)
+#113 := (<= #112 0::int)
+#73 := (= #35 #68)
+#62 := (not #61)
+#131 := (or #62 #77)
+#118 := (= f3 0::int)
+#109 := (or #10 #77)
+#85 := (iff #55 #77)
+#12 := (- f3)
+#11 := (< f3 0::int)
+#13 := (ite #11 #12 f3)
+#14 := (= #13 #12)
+#15 := (iff #10 #14)
+#16 := (not #15)
+#90 := (iff #16 #85)
+#38 := (ite #11 #35 f3)
+#44 := (= #35 #38)
+#56 := (iff #44 #55)
+#88 := (iff #56 #85)
+#82 := (iff #77 #55)
+#86 := (iff #82 #85)
+#87 := [rewrite]: #86
+#83 := (iff #56 #82)
+#80 := (iff #44 #77)
+#76 := (iff #73 #77)
+#79 := [rewrite]: #76
+#74 := (iff #44 #73)
+#71 := (= #38 #68)
+#65 := (ite #62 #35 f3)
+#69 := (= #65 #68)
+#70 := [rewrite]: #69
+#66 := (= #38 #65)
+#63 := (iff #11 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#72 := [trans #67 #70]: #71
+#75 := [monotonicity #72]: #74
+#81 := [trans #75 #79]: #80
+#84 := [monotonicity #81]: #83
+#89 := [trans #84 #87]: #88
+#59 := (iff #16 #56)
+#49 := (iff #10 #44)
+#52 := (not #49)
+#57 := (iff #52 #56)
+#58 := [rewrite]: #57
+#53 := (iff #16 #52)
+#50 := (iff #15 #49)
+#47 := (iff #14 #44)
+#41 := (= #38 #35)
+#45 := (iff #41 #44)
+#46 := [rewrite]: #45
+#42 := (iff #14 #41)
+#36 := (= #12 #35)
+#37 := [rewrite]: #36
+#39 := (= #13 #38)
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40 #37]: #42
+#48 := [trans #43 #46]: #47
+#51 := [monotonicity #48]: #50
+#54 := [monotonicity #51]: #53
+#60 := [trans #54 #58]: #59
+#91 := [trans #60 #89]: #90
+#33 := [asserted]: #16
+#92 := [mp #33 #91]: #85
+#102 := (not #85)
+#107 := (or #10 #77 #102)
+#108 := [def-axiom]: #107
+#110 := [unit-resolution #108 #92]: #109
+#116 := [unit-resolution #110 #115]: #10
+#117 := [hypothesis]: #61
+#119 := [th-lemma #117 #116]: #118
+#127 := (= #78 f3)
+#125 := (= #68 f3)
+#99 := (or #62 #98)
+#100 := [def-axiom]: #99
+#120 := [unit-resolution #100 #117]: #98
+#126 := [symm #120]: #125
+#123 := (= #78 #68)
+#121 := (= #68 #78)
+#122 := [th-lemma #117 #116]: #121
+#124 := [symm #122]: #123
+#128 := [trans #124 #126]: #127
+#129 := [trans #128 #119]: #77
+#130 := [unit-resolution #115 #129]: false
+#132 := [lemma #130]: #131
+#133 := [unit-resolution #132 #115]: #62
+#101 := (or #61 #73)
+#96 := [def-axiom]: #101
+#134 := [unit-resolution #96 #133]: #73
+#135 := (not #73)
+#136 := (or #135 #113)
+#137 := [th-lemma]: #136
+#138 := [unit-resolution #137 #134]: #113
+#139 := (not #113)
+#140 := (or #95 #139)
+#141 := [th-lemma]: #140
+#142 := [unit-resolution #141 #138]: #95
+#97 := (<= #78 0::int)
+#114 := (>= #112 0::int)
+#143 := (or #135 #114)
+#144 := [th-lemma]: #143
+#145 := [unit-resolution #144 #134]: #114
+#146 := (not #114)
+#147 := (or #97 #146)
+#148 := [th-lemma]: #147
+#149 := [unit-resolution #148 #145]: #97
+#151 := (not #95)
+#150 := (not #97)
+#152 := (or #77 #150 #151)
+#153 := [th-lemma]: #152
+#154 := [unit-resolution #153 #149 #142 #115]: false
+#155 := [lemma #154]: #77
+#105 := (or #55 #93)
+#103 := (or #55 #93 #102)
+#104 := [def-axiom]: #103
+#106 := [unit-resolution #104 #92]: #105
+#159 := [unit-resolution #106 #155]: #55
+#160 := (or #61 #10)
+#161 := [th-lemma]: #160
+#162 := [unit-resolution #161 #159]: #61
+#163 := [unit-resolution #100 #162]: #98
+#164 := (not #98)
+#165 := (or #164 #157)
+#166 := [th-lemma]: #165
+#167 := [unit-resolution #166 #163]: #157
+#168 := (or #93 #97)
+#169 := [th-lemma]: #168
+#170 := [unit-resolution #169 #155]: #97
+[th-lemma #159 #170 #167]: false
+unsat
+d757d2450917b1126e9b960ef50b94860dff541d 114 0
+#2 := false
+#9 := 0::int
+decl f3 :: int
+#8 := f3
+#35 := -1::int
+#36 := (* -1::int f3)
+#67 := (>= f3 0::int)
+#74 := (ite #67 f3 #36)
+#88 := (* -1::int #74)
+#127 := (+ #36 #88)
+#137 := (<= #127 0::int)
+#114 := (= #36 #74)
+#68 := (not #67)
+#125 := (+ f3 #88)
+#126 := (<= #125 0::int)
+#113 := (= f3 #74)
+#128 := [hypothesis]: #67
+#115 := (or #68 #113)
+#116 := [def-axiom]: #115
+#129 := [unit-resolution #116 #128]: #113
+#130 := (not #113)
+#131 := (or #130 #126)
+#132 := [th-lemma]: #131
+#133 := [unit-resolution #132 #129]: #126
+#83 := (>= #74 0::int)
+#82 := (not #83)
+#94 := (ite #83 #74 #88)
+#99 := (= #74 #94)
+#102 := (not #99)
+#11 := (- f3)
+#10 := (< f3 0::int)
+#12 := (ite #10 #11 f3)
+#14 := (- #12)
+#13 := (< #12 0::int)
+#15 := (ite #13 #14 #12)
+#16 := (= #15 #12)
+#17 := (not #16)
+#105 := (iff #17 #102)
+#39 := (ite #10 #36 f3)
+#48 := (* -1::int #39)
+#42 := (< #39 0::int)
+#53 := (ite #42 #48 #39)
+#59 := (= #39 #53)
+#64 := (not #59)
+#103 := (iff #64 #102)
+#100 := (iff #59 #99)
+#97 := (= #53 #94)
+#91 := (ite #82 #88 #74)
+#95 := (= #91 #94)
+#96 := [rewrite]: #95
+#92 := (= #53 #91)
+#77 := (= #39 #74)
+#71 := (ite #68 #36 f3)
+#75 := (= #71 #74)
+#76 := [rewrite]: #75
+#72 := (= #39 #71)
+#69 := (iff #10 #68)
+#70 := [rewrite]: #69
+#73 := [monotonicity #70]: #72
+#78 := [trans #73 #76]: #77
+#89 := (= #48 #88)
+#90 := [monotonicity #78]: #89
+#86 := (iff #42 #82)
+#79 := (< #74 0::int)
+#84 := (iff #79 #82)
+#85 := [rewrite]: #84
+#80 := (iff #42 #79)
+#81 := [monotonicity #78]: #80
+#87 := [trans #81 #85]: #86
+#93 := [monotonicity #87 #90 #78]: #92
+#98 := [trans #93 #96]: #97
+#101 := [monotonicity #78 #98]: #100
+#104 := [monotonicity #101]: #103
+#65 := (iff #17 #64)
+#62 := (iff #16 #59)
+#56 := (= #53 #39)
+#60 := (iff #56 #59)
+#61 := [rewrite]: #60
+#57 := (iff #16 #56)
+#40 := (= #12 #39)
+#37 := (= #11 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#54 := (= #15 #53)
+#51 := (= #14 #48)
+#45 := (- #39)
+#49 := (= #45 #48)
+#50 := [rewrite]: #49
+#46 := (= #14 #45)
+#47 := [monotonicity #41]: #46
+#52 := [trans #47 #50]: #51
+#43 := (iff #13 #42)
+#44 := [monotonicity #41]: #43
+#55 := [monotonicity #44 #52 #41]: #54
+#58 := [monotonicity #55 #41]: #57
+#63 := [trans #58 #61]: #62
+#66 := [monotonicity #63]: #65
+#106 := [trans #66 #104]: #105
+#34 := [asserted]: #17
+#107 := [mp #34 #106]: #102
+#108 := (or #82 #99)
+#117 := [def-axiom]: #108
+#134 := [unit-resolution #117 #107]: #82
+#135 := [th-lemma #128 #134 #133]: false
+#136 := [lemma #135]: #68
+#111 := (or #67 #114)
+#112 := [def-axiom]: #111
+#139 := [unit-resolution #112 #136]: #114
+#140 := (not #114)
+#141 := (or #140 #137)
+#142 := [th-lemma]: #141
+#143 := [unit-resolution #142 #139]: #137
+[th-lemma #136 #134 #143]: false
+unsat
+5c7cb1cc77a21c05a0f34b1d636fd78635d99286 57 0
+#2 := false
+#36 := 0::int
+decl f4 :: int
+#9 := f4
+decl f3 :: int
+#8 := f3
+#33 := -1::int
+#34 := (* -1::int f4)
+#35 := (+ f3 #34)
+#37 := (<= #35 0::int)
+#40 := (ite #37 f3 f4)
+#48 := (* -1::int #40)
+#49 := (+ f3 #48)
+#47 := (>= #49 0::int)
+#53 := (not #47)
+#10 := (<= f3 f4)
+#11 := (ite #10 f3 f4)
+#12 := (<= #11 f3)
+#13 := (not #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #47)
+#43 := (<= #40 f3)
+#46 := (iff #43 #47)
+#50 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#52 := [trans #45 #50]: #51
+#55 := [monotonicity #52]: #54
+#30 := [asserted]: #13
+#56 := [mp #30 #55]: #53
+#60 := (= f3 #40)
+#31 := (+ f4 #48)
+#65 := (>= #31 0::int)
+#61 := (= f4 #40)
+#62 := (not #37)
+#66 := [hypothesis]: #62
+#59 := (or #37 #61)
+#57 := [def-axiom]: #59
+#67 := [unit-resolution #57 #66]: #61
+#68 := (not #61)
+#69 := (or #68 #65)
+#70 := [th-lemma]: #69
+#71 := [unit-resolution #70 #67]: #65
+#72 := [th-lemma #56 #66 #71]: false
+#73 := [lemma #72]: #37
+#63 := (or #62 #60)
+#58 := [def-axiom]: #63
+#74 := [unit-resolution #58 #73]: #60
+#75 := (not #60)
+#76 := (or #75 #47)
+#77 := [th-lemma]: #76
+[unit-resolution #77 #74 #56]: false
+unsat
+10e42ba36f16f5b77635ba4696f9e210ae8fff63 57 0
+#2 := false
+#36 := 0::int
+decl f4 :: int
+#9 := f4
+#33 := -1::int
+#34 := (* -1::int f4)
+decl f3 :: int
+#8 := f3
+#35 := (+ f3 #34)
+#37 := (<= #35 0::int)
+#40 := (ite #37 f3 f4)
+#61 := (= f4 #40)
+#65 := (not #61)
+#47 := (* -1::int #40)
+#48 := (+ f4 #47)
+#46 := (>= #48 0::int)
+#53 := (not #46)
+#10 := (<= f3 f4)
+#11 := (ite #10 f3 f4)
+#12 := (<= #11 f4)
+#13 := (not #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #46)
+#43 := (<= #40 f4)
+#49 := (iff #43 #46)
+#50 := [rewrite]: #49
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#52 := [trans #45 #50]: #51
+#55 := [monotonicity #52]: #54
+#30 := [asserted]: #13
+#56 := [mp #30 #55]: #53
+#64 := [hypothesis]: #61
+#66 := (or #65 #46)
+#67 := [th-lemma]: #66
+#68 := [unit-resolution #67 #64 #56]: false
+#69 := [lemma #68]: #65
+#59 := (or #37 #61)
+#57 := [def-axiom]: #59
+#72 := [unit-resolution #57 #69]: #37
+#31 := (+ f3 #47)
+#71 := (>= #31 0::int)
+#60 := (= f3 #40)
+#62 := (not #37)
+#63 := (or #62 #60)
+#58 := [def-axiom]: #63
+#73 := [unit-resolution #58 #72]: #60
+#74 := (not #60)
+#75 := (or #74 #71)
+#76 := [th-lemma]: #75
+#77 := [unit-resolution #76 #73]: #71
+[th-lemma #77 #56 #72]: false
+unsat
+91d7fdd486bebfbe440c8a2d28eb4c92f78f7bd1 103 0
+#2 := false
+#45 := 0::int
+decl f5 :: int
+#11 := f5
+decl f4 :: int
+#9 := f4
+#43 := -1::int
+#53 := (* -1::int f5)
+#63 := (+ f4 #53)
+#64 := (<= #63 0::int)
+#67 := (ite #64 f4 f5)
+#75 := (* -1::int #67)
+decl f3 :: int
+#8 := f3
+#76 := (+ f3 #75)
+#74 := (>= #76 0::int)
+#73 := (not #74)
+#54 := (+ f3 #53)
+#52 := (>= #54 0::int)
+#51 := (not #52)
+#47 := (* -1::int f4)
+#48 := (+ f3 #47)
+#46 := (>= #48 0::int)
+#44 := (not #46)
+#57 := (and #44 #51)
+#60 := (not #57)
+#81 := (or #60 #73)
+#84 := (not #81)
+#14 := (<= f4 f5)
+#15 := (ite #14 f4 f5)
+#16 := (< f3 #15)
+#12 := (< f3 f5)
+#10 := (< f3 f4)
+#13 := (and #10 #12)
+#17 := (implies #13 #16)
+#18 := (not #17)
+#87 := (iff #18 #84)
+#36 := (not #13)
+#37 := (or #36 #16)
+#40 := (not #37)
+#85 := (iff #40 #84)
+#82 := (iff #37 #81)
+#79 := (iff #16 #73)
+#70 := (< f3 #67)
+#77 := (iff #70 #73)
+#78 := [rewrite]: #77
+#71 := (iff #16 #70)
+#68 := (= #15 #67)
+#65 := (iff #14 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#72 := [monotonicity #69]: #71
+#80 := [trans #72 #78]: #79
+#61 := (iff #36 #60)
+#58 := (iff #13 #57)
+#55 := (iff #12 #51)
+#56 := [rewrite]: #55
+#49 := (iff #10 #44)
+#50 := [rewrite]: #49
+#59 := [monotonicity #50 #56]: #58
+#62 := [monotonicity #59]: #61
+#83 := [monotonicity #62 #80]: #82
+#86 := [monotonicity #83]: #85
+#41 := (iff #18 #40)
+#38 := (iff #17 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#88 := [trans #42 #86]: #87
+#35 := [asserted]: #18
+#89 := [mp #35 #88]: #84
+#93 := [not-or-elim #89]: #74
+#90 := [not-or-elim #89]: #57
+#92 := [and-elim #90]: #51
+#98 := (+ f5 #75)
+#115 := (<= #98 0::int)
+#104 := (= f5 #67)
+#105 := (not #64)
+#103 := (= f4 #67)
+#110 := (not #103)
+#100 := (+ f4 #75)
+#97 := (<= #100 0::int)
+#107 := (not #97)
+#91 := [and-elim #90]: #44
+#96 := [hypothesis]: #97
+#94 := [th-lemma #96 #91 #93]: false
+#108 := [lemma #94]: #107
+#109 := [hypothesis]: #103
+#111 := (or #110 #97)
+#112 := [th-lemma]: #111
+#113 := [unit-resolution #112 #109 #108]: false
+#114 := [lemma #113]: #110
+#106 := (or #105 #103)
+#101 := [def-axiom]: #106
+#117 := [unit-resolution #101 #114]: #105
+#102 := (or #64 #104)
+#99 := [def-axiom]: #102
+#118 := [unit-resolution #99 #117]: #104
+#119 := (not #104)
+#120 := (or #119 #115)
+#121 := [th-lemma]: #120
+#122 := [unit-resolution #121 #118]: #115
+[th-lemma #122 #92 #93]: false
+unsat
+3d8b7b7060fb0e75fadc99b439fcfbd64f5e5bd8 57 0
+#2 := false
+#36 := 0::int
+decl f4 :: int
+#9 := f4
+#33 := -1::int
+#34 := (* -1::int f4)
+decl f3 :: int
+#8 := f3
+#35 := (+ f3 #34)
+#37 := (<= #35 0::int)
+#40 := (ite #37 f4 f3)
+#61 := (= f3 #40)
+#65 := (not #61)
+#46 := (* -1::int #40)
+#47 := (+ f3 #46)
+#48 := (<= #47 0::int)
+#53 := (not #48)
+#10 := (<= f3 f4)
+#11 := (ite #10 f4 f3)
+#12 := (<= f3 #11)
+#13 := (not #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #48)
+#43 := (<= f3 #40)
+#49 := (iff #43 #48)
+#50 := [rewrite]: #49
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#52 := [trans #45 #50]: #51
+#55 := [monotonicity #52]: #54
+#30 := [asserted]: #13
+#56 := [mp #30 #55]: #53
+#64 := [hypothesis]: #61
+#66 := (or #65 #48)
+#67 := [th-lemma]: #66
+#68 := [unit-resolution #67 #64 #56]: false
+#69 := [lemma #68]: #65
+#59 := (or #37 #61)
+#57 := [def-axiom]: #59
+#72 := [unit-resolution #57 #69]: #37
+#31 := (+ f4 #46)
+#70 := (<= #31 0::int)
+#60 := (= f4 #40)
+#62 := (not #37)
+#63 := (or #62 #60)
+#58 := [def-axiom]: #63
+#73 := [unit-resolution #58 #72]: #60
+#74 := (not #60)
+#75 := (or #74 #70)
+#76 := [th-lemma]: #75
+#77 := [unit-resolution #76 #73]: #70
+[th-lemma #77 #56 #72]: false
+unsat
+11fa6e1b37f0031ac059637e25afb0cf1222dc3f 86 0
+#2 := false
+decl f3 :: int
+#8 := f3
+decl f4 :: int
+#9 := f4
+#38 := 0::int
+#35 := -1::int
+#36 := (* -1::int f4)
+#37 := (+ f3 #36)
+#46 := (>= #37 0::int)
+#48 := (ite #46 f4 f3)
+#39 := (<= #37 0::int)
+#42 := (ite #39 f3 f4)
+#51 := (= #42 #48)
+#33 := (= f4 #48)
+#65 := (= f3 #48)
+#66 := (not #46)
+#71 := [hypothesis]: #66
+#69 := (or #46 #65)
+#70 := [def-axiom]: #69
+#72 := [unit-resolution #70 #71]: #65
+#77 := (= #42 f3)
+#61 := (= f3 #42)
+#73 := (or #46 #39)
+#74 := [th-lemma]: #73
+#75 := [unit-resolution #74 #71]: #39
+#63 := (not #39)
+#64 := (or #63 #61)
+#59 := [def-axiom]: #64
+#76 := [unit-resolution #59 #75]: #61
+#78 := [symm #76]: #77
+#79 := [trans #78 #72]: #51
+#54 := (not #51)
+#12 := (<= f4 f3)
+#13 := (ite #12 f4 f3)
+#10 := (<= f3 f4)
+#11 := (ite #10 f3 f4)
+#14 := (= #11 #13)
+#15 := (not #14)
+#55 := (iff #15 #54)
+#52 := (iff #14 #51)
+#49 := (= #13 #48)
+#45 := (iff #12 #46)
+#47 := [rewrite]: #45
+#50 := [monotonicity #47]: #49
+#43 := (= #11 #42)
+#40 := (iff #10 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#53 := [monotonicity #44 #50]: #52
+#56 := [monotonicity #53]: #55
+#32 := [asserted]: #15
+#57 := [mp #32 #56]: #54
+#80 := [unit-resolution #57 #79]: false
+#81 := [lemma #80]: #46
+#67 := (or #66 #33)
+#68 := [def-axiom]: #67
+#83 := [unit-resolution #68 #81]: #33
+#103 := (= #42 f4)
+#82 := (= f3 f4)
+#62 := (= f4 #42)
+#93 := (not #62)
+#94 := (iff #54 #93)
+#91 := (iff #51 #62)
+#89 := (iff #62 #51)
+#84 := (= #48 #42)
+#87 := (iff #84 #51)
+#88 := [commutativity]: #87
+#85 := (iff #62 #84)
+#86 := [monotonicity #83]: #85
+#90 := [trans #86 #88]: #89
+#92 := [symm #90]: #91
+#95 := [monotonicity #92]: #94
+#96 := [mp #57 #95]: #93
+#60 := (or #39 #62)
+#58 := [def-axiom]: #60
+#97 := [unit-resolution #58 #96]: #39
+#98 := (or #82 #63 #66)
+#99 := [th-lemma]: #98
+#100 := [unit-resolution #99 #97 #81]: #82
+#101 := [unit-resolution #59 #97]: #61
+#102 := [symm #101]: #77
+#104 := [trans #102 #100]: #103
+#105 := [trans #104 #83]: #51
+[unit-resolution #57 #105]: false
+unsat
+d9ad9cbc455d3076d4a7e86bc3367086cdbf80aa 57 0
+#2 := false
+#35 := 0::int
+decl f4 :: int
+#9 := f4
+decl f3 :: int
+#8 := f3
+#33 := -1::int
+#37 := (* -1::int f4)
+#38 := (+ f3 #37)
+#36 := (>= #38 0::int)
+#40 := (ite #36 f3 f4)
+#46 := (* -1::int #40)
+#47 := (+ f3 #46)
+#48 := (<= #47 0::int)
+#53 := (not #48)
+#10 := (<= f4 f3)
+#11 := (ite #10 f3 f4)
+#12 := (<= f3 #11)
+#13 := (not #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #48)
+#43 := (<= f3 #40)
+#49 := (iff #43 #48)
+#50 := [rewrite]: #49
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#34 := (iff #10 #36)
+#39 := [rewrite]: #34
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#52 := [trans #45 #50]: #51
+#55 := [monotonicity #52]: #54
+#30 := [asserted]: #13
+#56 := [mp #30 #55]: #53
+#60 := (= f3 #40)
+#31 := (+ f4 #46)
+#64 := (<= #31 0::int)
+#61 := (= f4 #40)
+#62 := (not #36)
+#66 := [hypothesis]: #62
+#59 := (or #36 #61)
+#57 := [def-axiom]: #59
+#67 := [unit-resolution #57 #66]: #61
+#68 := (not #61)
+#69 := (or #68 #64)
+#70 := [th-lemma]: #69
+#71 := [unit-resolution #70 #67]: #64
+#72 := [th-lemma #56 #66 #71]: false
+#73 := [lemma #72]: #36
+#63 := (or #62 #60)
+#58 := [def-axiom]: #63
+#74 := [unit-resolution #58 #73]: #60
+#75 := (not #60)
+#76 := (or #75 #48)
+#77 := [th-lemma]: #76
+[unit-resolution #77 #74 #56]: false
+unsat
+57fed093c0e757f5135ad67112d460f34a931a41 68 0
+#2 := false
+#8 := 0::int
+decl f3 :: int
+#9 := f3
+#11 := (<= f3 0::int)
+#12 := (ite #11 f3 0::int)
+#13 := (= #12 0::int)
+#76 := (= f3 0::int)
+#50 := (>= f3 0::int)
+#51 := (not #50)
+#59 := (or #13 #51)
+#64 := (not #59)
+#10 := (<= 0::int f3)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#67 := (iff #15 #64)
+#33 := (= 0::int #12)
+#39 := (not #10)
+#40 := (or #39 #33)
+#45 := (not #40)
+#65 := (iff #45 #64)
+#62 := (iff #40 #59)
+#56 := (or #51 #13)
+#60 := (iff #56 #59)
+#61 := [rewrite]: #60
+#57 := (iff #40 #56)
+#54 := (iff #33 #13)
+#55 := [rewrite]: #54
+#52 := (iff #39 #51)
+#48 := (iff #10 #50)
+#49 := [rewrite]: #48
+#53 := [monotonicity #49]: #52
+#58 := [monotonicity #53 #55]: #57
+#63 := [trans #58 #61]: #62
+#66 := [monotonicity #63]: #65
+#46 := (iff #15 #45)
+#43 := (iff #14 #40)
+#36 := (implies #10 #33)
+#41 := (iff #36 #40)
+#42 := [rewrite]: #41
+#37 := (iff #14 #36)
+#34 := (iff #13 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#44 := [trans #38 #42]: #43
+#47 := [monotonicity #44]: #46
+#68 := [trans #47 #66]: #67
+#32 := [asserted]: #15
+#69 := [mp #32 #68]: #64
+#72 := [not-or-elim #69]: #50
+#70 := (not #13)
+#71 := [not-or-elim #69]: #70
+#78 := (or #11 #13)
+#79 := [def-axiom]: #78
+#77 := [unit-resolution #79 #71]: #11
+#81 := (not #11)
+#75 := (or #76 #81 #51)
+#73 := [th-lemma]: #75
+#84 := [unit-resolution #73 #77 #72]: #76
+#86 := (= #12 f3)
+#80 := (= f3 #12)
+#82 := (or #81 #80)
+#83 := [def-axiom]: #82
+#85 := [unit-resolution #83 #77]: #80
+#87 := [symm #85]: #86
+#88 := [trans #87 #84]: #13
+[unit-resolution #71 #88]: false
+unsat
+512e03c208778cc0f727c8eba68f23d12462f16f 103 0
+#2 := false
+#45 := 0::int
+decl f3 :: int
+#8 := f3
+decl f5 :: int
+#11 := f5
+#43 := -1::int
+#51 := (* -1::int f5)
+#63 := (+ f3 #51)
+#64 := (<= #63 0::int)
+#67 := (ite #64 f5 f3)
+#73 := (* -1::int #67)
+decl f4 :: int
+#9 := f4
+#74 := (+ f4 #73)
+#75 := (<= #74 0::int)
+#76 := (not #75)
+#52 := (+ f4 #51)
+#53 := (<= #52 0::int)
+#54 := (not #53)
+#47 := (* -1::int f4)
+#48 := (+ f3 #47)
+#46 := (>= #48 0::int)
+#44 := (not #46)
+#57 := (and #44 #54)
+#60 := (not #57)
+#81 := (or #60 #76)
+#84 := (not #81)
+#14 := (<= f3 f5)
+#15 := (ite #14 f5 f3)
+#16 := (< #15 f4)
+#12 := (< f5 f4)
+#10 := (< f3 f4)
+#13 := (and #10 #12)
+#17 := (implies #13 #16)
+#18 := (not #17)
+#87 := (iff #18 #84)
+#36 := (not #13)
+#37 := (or #36 #16)
+#40 := (not #37)
+#85 := (iff #40 #84)
+#82 := (iff #37 #81)
+#79 := (iff #16 #76)
+#70 := (< #67 f4)
+#77 := (iff #70 #76)
+#78 := [rewrite]: #77
+#71 := (iff #16 #70)
+#68 := (= #15 #67)
+#65 := (iff #14 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#72 := [monotonicity #69]: #71
+#80 := [trans #72 #78]: #79
+#61 := (iff #36 #60)
+#58 := (iff #13 #57)
+#55 := (iff #12 #54)
+#56 := [rewrite]: #55
+#49 := (iff #10 #44)
+#50 := [rewrite]: #49
+#59 := [monotonicity #50 #56]: #58
+#62 := [monotonicity #59]: #61
+#83 := [monotonicity #62 #80]: #82
+#86 := [monotonicity #83]: #85
+#41 := (iff #18 #40)
+#38 := (iff #17 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#88 := [trans #42 #86]: #87
+#35 := [asserted]: #18
+#89 := [mp #35 #88]: #84
+#93 := [not-or-elim #89]: #75
+#90 := [not-or-elim #89]: #57
+#91 := [and-elim #90]: #44
+#97 := (+ f3 #73)
+#116 := (>= #97 0::int)
+#104 := (= f3 #67)
+#105 := (not #64)
+#103 := (= f5 #67)
+#110 := (not #103)
+#100 := (+ f5 #73)
+#98 := (>= #100 0::int)
+#107 := (not #98)
+#92 := [and-elim #90]: #54
+#96 := [hypothesis]: #98
+#94 := [th-lemma #96 #92 #93]: false
+#108 := [lemma #94]: #107
+#109 := [hypothesis]: #103
+#111 := (or #110 #98)
+#112 := [th-lemma]: #111
+#113 := [unit-resolution #112 #109 #108]: false
+#114 := [lemma #113]: #110
+#106 := (or #105 #103)
+#101 := [def-axiom]: #106
+#117 := [unit-resolution #101 #114]: #105
+#102 := (or #64 #104)
+#99 := [def-axiom]: #102
+#118 := [unit-resolution #99 #117]: #104
+#119 := (not #104)
+#120 := (or #119 #116)
+#121 := [th-lemma]: #120
+#122 := [unit-resolution #121 #118]: #116
+[th-lemma #122 #91 #93]: false
+unsat
+db9aca2dd61369561517d2cc1ec903d7f769a531 124 0
+#2 := false
+#13 := 0::int
+decl f4 :: int
+#9 := f4
+decl f3 :: int
+#8 := f3
+#36 := -1::int
+#38 := (* -1::int f4)
+#51 := (+ f3 #38)
+#52 := (<= #51 0::int)
+#55 := (ite #52 f3 f4)
+#103 := (* -1::int #55)
+#104 := (+ f3 #103)
+#106 := (>= #104 0::int)
+#91 := (= f3 #55)
+#105 := (+ f4 #103)
+#123 := (>= #105 0::int)
+#92 := (= f4 #55)
+#93 := (not #52)
+#134 := [hypothesis]: #93
+#90 := (or #52 #92)
+#88 := [def-axiom]: #90
+#135 := [unit-resolution #88 #134]: #92
+#126 := (not #92)
+#127 := (or #126 #123)
+#128 := [th-lemma]: #127
+#136 := [unit-resolution #128 #135]: #123
+#37 := (* -1::int f3)
+#39 := (+ #37 #38)
+#12 := (+ f3 f4)
+#58 := (>= #12 0::int)
+#65 := (ite #58 #12 #39)
+#73 := (* -1::int #65)
+#74 := (+ #55 #73)
+#75 := (<= #74 0::int)
+#80 := (not #75)
+#15 := (- #12)
+#14 := (< #12 0::int)
+#16 := (ite #14 #15 #12)
+#10 := (<= f3 f4)
+#11 := (ite #10 f3 f4)
+#17 := (<= #11 #16)
+#18 := (not #17)
+#83 := (iff #18 #80)
+#42 := (ite #14 #39 #12)
+#45 := (<= #11 #42)
+#48 := (not #45)
+#81 := (iff #48 #80)
+#78 := (iff #45 #75)
+#70 := (<= #55 #65)
+#76 := (iff #70 #75)
+#77 := [rewrite]: #76
+#71 := (iff #45 #70)
+#68 := (= #42 #65)
+#59 := (not #58)
+#62 := (ite #59 #39 #12)
+#66 := (= #62 #65)
+#67 := [rewrite]: #66
+#63 := (= #42 #62)
+#60 := (iff #14 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#69 := [trans #64 #67]: #68
+#56 := (= #11 #55)
+#53 := (iff #10 #52)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#72 := [monotonicity #57 #69]: #71
+#79 := [trans #72 #77]: #78
+#82 := [monotonicity #79]: #81
+#49 := (iff #18 #48)
+#46 := (iff #17 #45)
+#43 := (= #16 #42)
+#40 := (= #15 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#47 := [monotonicity #44]: #46
+#50 := [monotonicity #47]: #49
+#84 := [trans #50 #82]: #83
+#35 := [asserted]: #18
+#85 := [mp #35 #84]: #80
+#102 := (+ #12 #73)
+#122 := (<= #102 0::int)
+#86 := (= #12 #65)
+#108 := [hypothesis]: #59
+#120 := (or #93 #58)
+#107 := [hypothesis]: #52
+#100 := (+ #39 #73)
+#101 := (<= #100 0::int)
+#95 := (= #39 #65)
+#98 := (or #58 #95)
+#99 := [def-axiom]: #98
+#109 := [unit-resolution #99 #108]: #95
+#110 := (not #95)
+#111 := (or #110 #101)
+#112 := [th-lemma]: #111
+#113 := [unit-resolution #112 #109]: #101
+#94 := (or #93 #91)
+#89 := [def-axiom]: #94
+#114 := [unit-resolution #89 #107]: #91
+#115 := (not #91)
+#116 := (or #115 #106)
+#117 := [th-lemma]: #116
+#118 := [unit-resolution #117 #114]: #106
+#119 := [th-lemma #108 #118 #113 #85 #107]: false
+#121 := [lemma #119]: #120
+#124 := [unit-resolution #121 #108]: #93
+#125 := [unit-resolution #88 #124]: #92
+#129 := [unit-resolution #128 #125]: #123
+#130 := [th-lemma #113 #85 #108 #124 #129]: false
+#131 := [lemma #130]: #58
+#96 := (or #59 #86)
+#97 := [def-axiom]: #96
+#137 := [unit-resolution #97 #131]: #86
+#138 := (not #86)
+#139 := (or #138 #122)
+#140 := [th-lemma]: #139
+#141 := [unit-resolution #140 #137]: #122
+#142 := [th-lemma #134 #131 #141 #85 #136]: false
+#143 := [lemma #142]: #52
+#144 := [unit-resolution #89 #143]: #91
+#145 := [unit-resolution #117 #144]: #106
+[th-lemma #131 #143 #141 #85 #145]: false
+unsat
+aa80380d55249b8c8a3b69b0ba102b48ab444bd4 88 0
+#2 := false
+decl f4 :: int
+#9 := f4
+decl f3 :: int
+#8 := f3
+#38 := 0::int
+#35 := -1::int
+#36 := (* -1::int f4)
+#37 := (+ f3 #36)
+#46 := (>= #37 0::int)
+#48 := (ite #46 f3 f4)
+#39 := (<= #37 0::int)
+#42 := (ite #39 f4 f3)
+#51 := (= #42 #48)
+#33 := (= f3 #48)
+#65 := (= f4 #48)
+#66 := (not #46)
+#71 := [hypothesis]: #66
+#69 := (or #46 #65)
+#70 := [def-axiom]: #69
+#72 := [unit-resolution #70 #71]: #65
+#77 := (= #42 f4)
+#61 := (= f4 #42)
+#73 := (or #46 #39)
+#74 := [th-lemma]: #73
+#75 := [unit-resolution #74 #71]: #39
+#63 := (not #39)
+#64 := (or #63 #61)
+#59 := [def-axiom]: #64
+#76 := [unit-resolution #59 #75]: #61
+#78 := [symm #76]: #77
+#79 := [trans #78 #72]: #51
+#54 := (not #51)
+#12 := (<= f4 f3)
+#13 := (ite #12 f3 f4)
+#10 := (<= f3 f4)
+#11 := (ite #10 f4 f3)
+#14 := (= #11 #13)
+#15 := (not #14)
+#55 := (iff #15 #54)
+#52 := (iff #14 #51)
+#49 := (= #13 #48)
+#45 := (iff #12 #46)
+#47 := [rewrite]: #45
+#50 := [monotonicity #47]: #49
+#43 := (= #11 #42)
+#40 := (iff #10 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#53 := [monotonicity #44 #50]: #52
+#56 := [monotonicity #53]: #55
+#32 := [asserted]: #15
+#57 := [mp #32 #56]: #54
+#80 := [unit-resolution #57 #79]: false
+#81 := [lemma #80]: #46
+#67 := (or #66 #33)
+#68 := [def-axiom]: #67
+#83 := [unit-resolution #68 #81]: #33
+#107 := (= #42 f3)
+#105 := (= f4 f3)
+#82 := (= f3 f4)
+#62 := (= f3 #42)
+#95 := (not #62)
+#96 := (iff #54 #95)
+#93 := (iff #51 #62)
+#91 := (iff #62 #51)
+#86 := (= #48 #42)
+#89 := (iff #86 #51)
+#90 := [commutativity]: #89
+#87 := (iff #62 #86)
+#88 := [monotonicity #83]: #87
+#92 := [trans #88 #90]: #91
+#94 := [symm #92]: #93
+#97 := [monotonicity #94]: #96
+#98 := [mp #57 #97]: #95
+#60 := (or #39 #62)
+#58 := [def-axiom]: #60
+#99 := [unit-resolution #58 #98]: #39
+#101 := (or #82 #63 #66)
+#102 := [th-lemma]: #101
+#103 := [unit-resolution #102 #99 #81]: #82
+#106 := [symm #103]: #105
+#100 := [unit-resolution #59 #99]: #61
+#104 := [symm #100]: #77
+#108 := [trans #104 #106]: #107
+#109 := [trans #108 #83]: #51
+[unit-resolution #57 #109]: false
+unsat
+f6b25b18b1ebd8ef0f2fc91bf2f3835c988c562e 66 0
+#2 := false
+decl f3 :: int
+#9 := f3
+#8 := 0::int
+#11 := (<= f3 0::int)
+#12 := (ite #11 0::int f3)
+#33 := (= f3 #12)
+#84 := (= 0::int #12)
+#78 := (= #12 0::int)
+#68 := (not #33)
+#50 := (>= f3 0::int)
+#51 := (not #50)
+#57 := (or #33 #51)
+#62 := (not #57)
+#13 := (= #12 f3)
+#10 := (<= 0::int f3)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#65 := (iff #15 #62)
+#39 := (not #10)
+#40 := (or #39 #33)
+#45 := (not #40)
+#63 := (iff #45 #62)
+#60 := (iff #40 #57)
+#54 := (or #51 #33)
+#58 := (iff #54 #57)
+#59 := [rewrite]: #58
+#55 := (iff #40 #54)
+#52 := (iff #39 #51)
+#48 := (iff #10 #50)
+#49 := [rewrite]: #48
+#53 := [monotonicity #49]: #52
+#56 := [monotonicity #53]: #55
+#61 := [trans #56 #59]: #60
+#64 := [monotonicity #61]: #63
+#46 := (iff #15 #45)
+#43 := (iff #14 #40)
+#36 := (implies #10 #33)
+#41 := (iff #36 #40)
+#42 := [rewrite]: #41
+#37 := (iff #14 #36)
+#34 := (iff #13 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#44 := [trans #38 #42]: #43
+#47 := [monotonicity #44]: #46
+#66 := [trans #47 #64]: #65
+#32 := [asserted]: #15
+#67 := [mp #32 #66]: #62
+#69 := [not-or-elim #67]: #68
+#76 := (or #11 #33)
+#77 := [def-axiom]: #76
+#75 := [unit-resolution #77 #69]: #11
+#79 := (not #11)
+#80 := (or #79 #78)
+#81 := [def-axiom]: #80
+#73 := [unit-resolution #81 #75]: #78
+#85 := [symm #73]: #84
+#74 := (= f3 0::int)
+#70 := [not-or-elim #67]: #50
+#71 := (or #74 #79 #51)
+#82 := [th-lemma]: #71
+#83 := [unit-resolution #82 #75 #70]: #74
+#86 := [trans #83 #85]: #33
+[unit-resolution #69 #86]: false
+unsat
+7f59060b40cd618dd873f83da89208e01474e50b 228 0
+#2 := false
+#9 := 0::int
+decl f4 :: int
+#14 := f4
+#40 := -1::int
+#55 := (* -1::int f4)
+#91 := (>= f4 0::int)
+#98 := (ite #91 f4 #55)
+#103 := (* -1::int #98)
+#159 := (+ f4 #103)
+#160 := (<= #159 0::int)
+#134 := (= f4 #98)
+decl f3 :: int
+#8 := f3
+#109 := (+ f3 #55)
+#110 := (<= #109 0::int)
+#113 := (ite #110 f4 f3)
+#155 := (* -1::int #113)
+#180 := (+ f3 #155)
+#190 := (<= #180 0::int)
+#146 := (= f3 #113)
+#147 := (not #110)
+#76 := (>= f3 0::int)
+#161 := (+ #55 #103)
+#179 := (<= #161 0::int)
+#200 := (not #179)
+#77 := (not #76)
+#168 := [hypothesis]: #77
+#145 := (= f4 #113)
+#205 := (not #145)
+#156 := (+ f4 #155)
+#157 := (<= #156 0::int)
+#176 := (not #157)
+#188 := (or #176 #76)
+#132 := (= #55 #98)
+#92 := (not #91)
+#174 := [hypothesis]: #157
+#177 := (or #92 #176 #76)
+#162 := [hypothesis]: #91
+#141 := (or #92 #134)
+#142 := [def-axiom]: #141
+#163 := [unit-resolution #142 #162]: #134
+#164 := (not #134)
+#165 := (or #164 #160)
+#166 := [th-lemma]: #165
+#167 := [unit-resolution #166 #163]: #160
+#41 := (* -1::int f3)
+#83 := (ite #76 f3 #41)
+#88 := (* -1::int #83)
+#152 := (+ #41 #88)
+#153 := (<= #152 0::int)
+#138 := (= #41 #83)
+#135 := (or #76 #138)
+#136 := [def-axiom]: #135
+#169 := [unit-resolution #136 #168]: #138
+#170 := (not #138)
+#171 := (or #170 #153)
+#172 := [th-lemma]: #171
+#173 := [unit-resolution #172 #169]: #153
+#122 := (+ #98 #113)
+#123 := (+ #83 #122)
+#120 := (>= #123 0::int)
+#126 := (not #120)
+#19 := (<= f3 f4)
+#20 := (ite #19 f4 f3)
+#16 := (- f4)
+#15 := (< f4 0::int)
+#17 := (ite #15 #16 f4)
+#11 := (- f3)
+#10 := (< f3 0::int)
+#12 := (ite #10 #11 f3)
+#13 := (- #12)
+#18 := (- #13 #17)
+#21 := (<= #18 #20)
+#22 := (not #21)
+#129 := (iff #22 #126)
+#58 := (ite #15 #55 f4)
+#64 := (* -1::int #58)
+#44 := (ite #10 #41 f3)
+#50 := (* -1::int #44)
+#65 := (+ #50 #64)
+#70 := (<= #65 #20)
+#73 := (not #70)
+#127 := (iff #73 #126)
+#124 := (iff #70 #120)
+#106 := (+ #88 #103)
+#116 := (<= #106 #113)
+#119 := (iff #116 #120)
+#121 := [rewrite]: #119
+#117 := (iff #70 #116)
+#114 := (= #20 #113)
+#111 := (iff #19 #110)
+#112 := [rewrite]: #111
+#115 := [monotonicity #112]: #114
+#107 := (= #65 #106)
+#104 := (= #64 #103)
+#101 := (= #58 #98)
+#95 := (ite #92 #55 f4)
+#99 := (= #95 #98)
+#100 := [rewrite]: #99
+#96 := (= #58 #95)
+#93 := (iff #15 #92)
+#94 := [rewrite]: #93
+#97 := [monotonicity #94]: #96
+#102 := [trans #97 #100]: #101
+#105 := [monotonicity #102]: #104
+#89 := (= #50 #88)
+#86 := (= #44 #83)
+#80 := (ite #77 #41 f3)
+#84 := (= #80 #83)
+#85 := [rewrite]: #84
+#81 := (= #44 #80)
+#78 := (iff #10 #77)
+#79 := [rewrite]: #78
+#82 := [monotonicity #79]: #81
+#87 := [trans #82 #85]: #86
+#90 := [monotonicity #87]: #89
+#108 := [monotonicity #90 #105]: #107
+#118 := [monotonicity #108 #115]: #117
+#125 := [trans #118 #121]: #124
+#128 := [monotonicity #125]: #127
+#74 := (iff #22 #73)
+#71 := (iff #21 #70)
+#68 := (= #18 #65)
+#61 := (- #50 #58)
+#66 := (= #61 #65)
+#67 := [rewrite]: #66
+#62 := (= #18 #61)
+#59 := (= #17 #58)
+#56 := (= #16 #55)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#53 := (= #13 #50)
+#47 := (- #44)
+#51 := (= #47 #50)
+#52 := [rewrite]: #51
+#48 := (= #13 #47)
+#45 := (= #12 #44)
+#42 := (= #11 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#49 := [monotonicity #46]: #48
+#54 := [trans #49 #52]: #53
+#63 := [monotonicity #54 #60]: #62
+#69 := [trans #63 #67]: #68
+#72 := [monotonicity #69]: #71
+#75 := [monotonicity #72]: #74
+#130 := [trans #75 #128]: #129
+#39 := [asserted]: #22
+#131 := [mp #39 #130]: #126
+#175 := [th-lemma #162 #174 #131 #168 #173 #167]: false
+#178 := [lemma #175]: #177
+#181 := [unit-resolution #178 #174 #168]: #92
+#143 := (or #91 #132)
+#144 := [def-axiom]: #143
+#182 := [unit-resolution #144 #181]: #132
+#183 := (not #132)
+#184 := (or #183 #179)
+#185 := [th-lemma]: #184
+#186 := [unit-resolution #185 #182]: #179
+#187 := [th-lemma #174 #131 #168 #173 #186]: false
+#189 := [lemma #187]: #188
+#210 := [unit-resolution #189 #168]: #176
+#206 := (or #205 #157)
+#203 := [hypothesis]: #176
+#204 := [hypothesis]: #145
+#207 := [th-lemma]: #206
+#208 := [unit-resolution #207 #204 #203]: false
+#209 := [lemma #208]: #206
+#211 := [unit-resolution #209 #210]: #205
+#148 := (or #147 #145)
+#149 := [def-axiom]: #148
+#212 := [unit-resolution #149 #211]: #147
+#201 := (or #110 #200 #76)
+#192 := [hypothesis]: #147
+#150 := (or #110 #146)
+#151 := [def-axiom]: #150
+#193 := [unit-resolution #151 #192]: #146
+#194 := (not #146)
+#195 := (or #194 #190)
+#196 := [th-lemma]: #195
+#197 := [unit-resolution #196 #193]: #190
+#198 := [hypothesis]: #179
+#199 := [th-lemma #131 #173 #198 #168 #192 #197]: false
+#202 := [lemma #199]: #201
+#213 := [unit-resolution #202 #212 #168]: #200
+#214 := (or #92 #76 #110)
+#215 := [th-lemma]: #214
+#216 := [unit-resolution #215 #168 #212]: #92
+#217 := [unit-resolution #144 #216]: #132
+#218 := [unit-resolution #185 #217 #213]: false
+#219 := [lemma #218]: #76
+#222 := [hypothesis]: #92
+#223 := (or #147 #77 #91)
+#224 := [th-lemma]: #223
+#225 := [unit-resolution #224 #222 #219]: #147
+#226 := [unit-resolution #151 #225]: #146
+#227 := [unit-resolution #196 #226]: #190
+#228 := [unit-resolution #144 #222]: #132
+#229 := [unit-resolution #185 #228]: #179
+#154 := (+ f3 #88)
+#158 := (<= #154 0::int)
+#137 := (= f3 #83)
+#139 := (or #77 #137)
+#140 := [def-axiom]: #139
+#230 := [unit-resolution #140 #219]: #137
+#231 := (not #137)
+#232 := (or #231 #158)
+#233 := [th-lemma]: #232
+#234 := [unit-resolution #233 #230]: #158
+#235 := [th-lemma #219 #131 #234 #229 #225 #227]: false
+#236 := [lemma #235]: #91
+#237 := [unit-resolution #142 #236]: #134
+#238 := [unit-resolution #166 #237]: #160
+#239 := (not #160)
+#240 := (or #179 #239 #92)
+#241 := [th-lemma]: #240
+#242 := [unit-resolution #241 #236 #238]: #179
+#243 := (not #158)
+#244 := (or #176 #77 #120 #243 #200)
+#245 := [th-lemma]: #244
+#246 := [unit-resolution #245 #242 #219 #131 #234]: #176
+#247 := [unit-resolution #209 #246]: #205
+#248 := [unit-resolution #149 #247]: #147
+#249 := [unit-resolution #151 #248]: #146
+#250 := [unit-resolution #196 #249]: #190
+[th-lemma #236 #250 #131 #234 #248 #238]: false
+unsat
+eb26b9eee04f34772db75112e08806ee4a73deb5 56 0
+#2 := false
+#11 := 1::int
+decl f3 :: int
+#9 := f3
+#14 := (= f3 1::int)
+#12 := (<= f3 1::int)
+#8 := 0::int
+#41 := (<= f3 0::int)
+#42 := (not #41)
+#48 := (and #12 #42)
+#53 := (not #48)
+#59 := (or #14 #53)
+#64 := (not #59)
+#10 := (< 0::int f3)
+#13 := (and #10 #12)
+#15 := (implies #13 #14)
+#16 := (not #15)
+#67 := (iff #16 #64)
+#34 := (not #13)
+#35 := (or #34 #14)
+#38 := (not #35)
+#65 := (iff #38 #64)
+#62 := (iff #35 #59)
+#56 := (or #53 #14)
+#60 := (iff #56 #59)
+#61 := [rewrite]: #60
+#57 := (iff #35 #56)
+#54 := (iff #34 #53)
+#51 := (iff #13 #48)
+#45 := (and #42 #12)
+#49 := (iff #45 #48)
+#50 := [rewrite]: #49
+#46 := (iff #13 #45)
+#43 := (iff #10 #42)
+#44 := [rewrite]: #43
+#47 := [monotonicity #44]: #46
+#52 := [trans #47 #50]: #51
+#55 := [monotonicity #52]: #54
+#58 := [monotonicity #55]: #57
+#63 := [trans #58 #61]: #62
+#66 := [monotonicity #63]: #65
+#39 := (iff #16 #38)
+#36 := (iff #15 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#68 := [trans #40 #66]: #67
+#33 := [asserted]: #16
+#69 := [mp #33 #68]: #64
+#72 := [not-or-elim #69]: #48
+#73 := [and-elim #72]: #12
+#74 := [and-elim #72]: #42
+#85 := [th-lemma #74 #73]: #14
+#70 := (not #14)
+#71 := [not-or-elim #69]: #70
+[unit-resolution #71 #85]: false
+unsat
+f0448e2303985e4b308e27be63206293bdf9a306 18 0
+#2 := false
+decl f3 :: int
+#8 := f3
+#9 := (<= f3 f3)
+#10 := (not #9)
+#37 := (iff #10 false)
+#1 := true
+#32 := (not true)
+#35 := (iff #32 false)
+#36 := [rewrite]: #35
+#33 := (iff #10 #32)
+#30 := (iff #9 true)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31]: #33
+#38 := [trans #34 #36]: #37
+#27 := [asserted]: #10
+[mp #27 #38]: false
+unsat
+7f4a9fec0a381e3d10ca9892d4357ad593dddf34 51 0
+#2 := false
+decl f4 :: int
+#9 := f4
+#11 := 3::int
+#13 := (* 3::int f4)
+decl f3 :: int
+#8 := f3
+#12 := (* 3::int f3)
+#14 := (<= #12 #13)
+#10 := (<= f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#67 := (iff #16 false)
+#34 := (not #10)
+#35 := (or #34 #14)
+#38 := (not #35)
+#65 := (iff #38 false)
+#1 := true
+#60 := (not true)
+#63 := (iff #60 false)
+#64 := [rewrite]: #63
+#61 := (iff #38 #60)
+#58 := (iff #35 true)
+#44 := 0::int
+#41 := -1::int
+#42 := (* -1::int f4)
+#43 := (+ f3 #42)
+#45 := (<= #43 0::int)
+#48 := (not #45)
+#53 := (or #48 #45)
+#56 := (iff #53 true)
+#57 := [rewrite]: #56
+#54 := (iff #35 #53)
+#51 := (iff #14 #45)
+#52 := [rewrite]: #51
+#49 := (iff #34 #48)
+#46 := (iff #10 #45)
+#47 := [rewrite]: #46
+#50 := [monotonicity #47]: #49
+#55 := [monotonicity #50 #52]: #54
+#59 := [trans #55 #57]: #58
+#62 := [monotonicity #59]: #61
+#66 := [trans #62 #64]: #65
+#39 := (iff #16 #38)
+#36 := (iff #15 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#68 := [trans #40 #66]: #67
+#33 := [asserted]: #16
+[mp #33 #68]: false
+unsat
+3680b6c490cc91b12df65cc99434d497190dfa9a 17 0
+#2 := false
+#8 := 0::real
+#9 := (= 0::real 0::real)
+#10 := (not #9)
+#35 := (iff #10 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #10 #30)
+#28 := (iff #9 true)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#27 := [asserted]: #10
+[mp #27 #36]: false
+unsat
+ec737777e677e7c45520e1db9e539dd2412843f6 25 0
+#2 := false
+#8 := 0::real
+#9 := (- 0::real)
+#10 := (= 0::real #9)
+#11 := (not #10)
+#43 := (iff #11 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #11 #38)
+#36 := (iff #10 true)
+#31 := (= 0::real 0::real)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #10 #31)
+#29 := (= #9 0::real)
+#30 := [rewrite]: #29
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#28 := [asserted]: #11
+[mp #28 #44]: false
+unsat
+dbe1e0599b3d29d7583fb07a395943a3aea1f4e4 56 0
+#2 := false
+decl f4 :: int
+#9 := f4
+#11 := 3::int
+#13 := (* 3::int f4)
+decl f3 :: int
+#8 := f3
+#12 := (* 3::int f3)
+#14 := (< #12 #13)
+#10 := (< f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#72 := (iff #16 false)
+#34 := (not #10)
+#35 := (or #34 #14)
+#38 := (not #35)
+#70 := (iff #38 false)
+#1 := true
+#65 := (not true)
+#68 := (iff #65 false)
+#69 := [rewrite]: #68
+#66 := (iff #38 #65)
+#63 := (iff #35 true)
+#43 := 0::int
+#41 := -1::int
+#45 := (* -1::int f4)
+#46 := (+ f3 #45)
+#44 := (>= #46 0::int)
+#42 := (not #44)
+#57 := (or #44 #42)
+#61 := (iff #57 true)
+#62 := [rewrite]: #61
+#59 := (iff #35 #57)
+#58 := (iff #14 #42)
+#56 := [rewrite]: #58
+#54 := (iff #34 #44)
+#49 := (not #42)
+#52 := (iff #49 #44)
+#53 := [rewrite]: #52
+#50 := (iff #34 #49)
+#47 := (iff #10 #42)
+#48 := [rewrite]: #47
+#51 := [monotonicity #48]: #50
+#55 := [trans #51 #53]: #54
+#60 := [monotonicity #55 #56]: #59
+#64 := [trans #60 #62]: #63
+#67 := [monotonicity #64]: #66
+#71 := [trans #67 #69]: #70
+#39 := (iff #16 #38)
+#36 := (iff #15 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#73 := [trans #40 #71]: #72
+#33 := [asserted]: #16
+[mp #33 #73]: false
+unsat
+200cec1612f3827738af83efa5baf8bfcd74c7e6 17 0
+#2 := false
+#8 := 1::real
+#9 := (= 1::real 1::real)
+#10 := (not #9)
+#35 := (iff #10 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #10 #30)
+#28 := (iff #9 true)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#27 := [asserted]: #10
+[mp #27 #36]: false
+unsat
+9e881bb7df2f7ec1f6b2377876015489227bbe22 52 0
+#2 := false
+#40 := 0::int
+decl f4 :: int
+#9 := f4
+#38 := -1::int
+#42 := (* -1::int f4)
+decl f3 :: int
+#8 := f3
+#43 := (+ f3 #42)
+#53 := (<= #43 0::int)
+#66 := (not #53)
+#41 := (>= #43 0::int)
+#56 := (or #41 #53)
+#59 := (not #56)
+#11 := (<= f3 f4)
+#10 := (< f3 f4)
+#12 := (implies #10 #11)
+#13 := (not #12)
+#62 := (iff #13 #59)
+#31 := (not #10)
+#32 := (or #31 #11)
+#35 := (not #32)
+#60 := (iff #35 #59)
+#57 := (iff #32 #56)
+#54 := (iff #11 #53)
+#55 := [rewrite]: #54
+#51 := (iff #31 #41)
+#39 := (not #41)
+#46 := (not #39)
+#49 := (iff #46 #41)
+#50 := [rewrite]: #49
+#47 := (iff #31 #46)
+#44 := (iff #10 #39)
+#45 := [rewrite]: #44
+#48 := [monotonicity #45]: #47
+#52 := [trans #48 #50]: #51
+#58 := [monotonicity #52 #55]: #57
+#61 := [monotonicity #58]: #60
+#36 := (iff #13 #35)
+#33 := (iff #12 #32)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#63 := [trans #37 #61]: #62
+#30 := [asserted]: #13
+#64 := [mp #30 #63]: #59
+#67 := [not-or-elim #64]: #66
+#65 := [not-or-elim #64]: #39
+#75 := (or #53 #41)
+#76 := [th-lemma]: #75
+#77 := [unit-resolution #76 #65]: #53
+[unit-resolution #77 #67]: false
+unsat
+d3fb8e790d00a83a7b4b9342eef24670066914ba 34 0
+#2 := false
+#8 := 1::real
+#9 := (- 1::real)
+#10 := (= #9 1::real)
+#11 := (not #10)
+#12 := (not #11)
+#52 := (iff #12 false)
+#1 := true
+#47 := (not true)
+#50 := (iff #47 false)
+#51 := [rewrite]: #50
+#48 := (iff #12 #47)
+#45 := (iff #11 true)
+#40 := (not false)
+#43 := (iff #40 true)
+#44 := [rewrite]: #43
+#41 := (iff #11 #40)
+#38 := (iff #10 false)
+#30 := -1::real
+#33 := (= -1::real 1::real)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #10 #33)
+#31 := (= #9 -1::real)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#49 := [monotonicity #46]: #48
+#53 := [trans #49 #51]: #52
+#29 := [asserted]: #12
+[mp #29 #53]: false
+unsat
+51bf0a9abf1819d8ded3eaa12d8b05e8c0179093 73 0
+#2 := false
+#58 := 0::int
+decl f4 :: int
+#9 := f4
+#51 := -1::int
+#52 := (* -1::int f4)
+decl f3 :: int
+#8 := f3
+#53 := (+ f3 #52)
+#59 := (>= #53 0::int)
+#54 := (<= #53 -1::int)
+#79 := (not #54)
+#57 := (not #59)
+#86 := [hypothesis]: #57
+#84 := (or #79 #59)
+#69 := (iff #54 #59)
+#11 := 1::int
+#12 := (+ f3 1::int)
+#13 := (<= #12 f4)
+#10 := (< f3 f4)
+#14 := (iff #10 #13)
+#15 := (not #14)
+#72 := (iff #15 #69)
+#45 := (not #10)
+#33 := (+ 1::int f3)
+#36 := (<= #33 f4)
+#46 := (iff #36 #45)
+#70 := (iff #46 #69)
+#67 := (iff #45 #59)
+#62 := (not #57)
+#65 := (iff #62 #59)
+#66 := [rewrite]: #65
+#63 := (iff #45 #62)
+#60 := (iff #10 #57)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#68 := [trans #64 #66]: #67
+#55 := (iff #36 #54)
+#56 := [rewrite]: #55
+#71 := [monotonicity #56 #68]: #70
+#49 := (iff #15 #46)
+#39 := (iff #10 #36)
+#42 := (not #39)
+#47 := (iff #42 #46)
+#48 := [rewrite]: #47
+#43 := (iff #15 #42)
+#40 := (iff #14 #39)
+#37 := (iff #13 #36)
+#34 := (= #12 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#44 := [monotonicity #41]: #43
+#50 := [trans #44 #48]: #49
+#73 := [trans #50 #71]: #72
+#32 := [asserted]: #15
+#74 := [mp #32 #73]: #69
+#80 := (not #69)
+#77 := (or #79 #59 #80)
+#75 := [def-axiom]: #77
+#85 := [unit-resolution #75 #74]: #84
+#87 := [unit-resolution #85 #86]: #79
+#88 := [th-lemma #86 #87]: false
+#89 := [lemma #88]: #59
+#90 := (or #57 #79)
+#91 := [th-lemma]: #90
+#92 := [unit-resolution #91 #89]: #79
+#83 := (or #54 #57)
+#81 := (or #54 #57 #80)
+#82 := [def-axiom]: #81
+#78 := [unit-resolution #82 #74]: #83
+[unit-resolution #78 #92 #89]: false
+unsat
+71a16b5f7cfa5ed20839063a47fff437d61d2c53 18 0
+#2 := false
+#9 := 1::real
+#8 := 0::real
+#10 := (< 0::real 1::real)
+#11 := (not #10)
+#38 := (iff #11 false)
+#1 := true
+#33 := (not true)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (iff #10 true)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#28 := [asserted]: #11
+[mp #28 #39]: false
+unsat
+2428cde9ba944e6b67ba948c2db63ec99833c830 18 0
+#2 := false
+#9 := 1::real
+#8 := 0::real
+#10 := (<= 0::real 1::real)
+#11 := (not #10)
+#38 := (iff #11 false)
+#1 := true
+#33 := (not true)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (iff #10 true)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#28 := [asserted]: #11
+[mp #28 #39]: false
+unsat
+a680c2822602cd080d52600c3f371f228a52ab07 15 0
+#2 := false
+decl f3 :: int
+#8 := f3
+#9 := (< f3 f3)
+#10 := (not #9)
+#11 := (not #10)
+#33 := (iff #11 false)
+#31 := (iff #9 false)
+#32 := [rewrite]: #31
+#29 := (iff #11 #9)
+#30 := [rewrite]: #29
+#34 := [trans #30 #32]: #33
+#28 := [asserted]: #11
+[mp #28 #34]: false
+unsat
+3d517e934dda3c9e791e45743b6060cbe359a1b0 40 0
+#2 := false
+#12 := 567::real
+#10 := 345::real
+#8 := 123::real
+#9 := (- 123::real)
+#11 := (+ #9 345::real)
+#13 := (< #11 567::real)
+#14 := (not #13)
+#58 := (iff #14 false)
+#38 := 222::real
+#43 := (< 222::real 567::real)
+#46 := (not #43)
+#56 := (iff #46 false)
+#1 := true
+#51 := (not true)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #46 #51)
+#49 := (iff #43 true)
+#50 := [rewrite]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#47 := (iff #14 #46)
+#44 := (iff #13 #43)
+#41 := (= #11 222::real)
+#32 := -123::real
+#35 := (+ -123::real 345::real)
+#39 := (= #35 222::real)
+#40 := [rewrite]: #39
+#36 := (= #11 #35)
+#33 := (= #9 -123::real)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#42 := [trans #37 #40]: #41
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#59 := [trans #48 #57]: #58
+#31 := [asserted]: #14
+[mp #31 #59]: false
+unsat
+3ca9f6025aa0aae7c19eaaf9e7bcf7496930f051 75 0
+#2 := false
+#53 := 0::int
+decl f4 :: int
+#9 := f4
+#50 := -1::int
+#64 := (* -1::int f4)
+decl f3 :: int
+#8 := f3
+#65 := (+ f3 #64)
+#66 := (<= #65 0::int)
+#69 := (not #66)
+decl f5 :: int
+#11 := f5
+#51 := (* -1::int f5)
+#60 := (+ f3 #51)
+#61 := (<= #60 0::int)
+#52 := (+ f4 #51)
+#54 := (<= #52 0::int)
+#57 := (not #54)
+#78 := (or #57 #61 #69)
+#83 := (not #78)
+#13 := (<= f3 f5)
+#12 := (<= f4 f5)
+#14 := (implies #12 #13)
+#10 := (<= f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#86 := (iff #16 #83)
+#34 := (not #12)
+#35 := (or #34 #13)
+#41 := (not #10)
+#42 := (or #41 #35)
+#47 := (not #42)
+#84 := (iff #47 #83)
+#81 := (iff #42 #78)
+#72 := (or #57 #61)
+#75 := (or #69 #72)
+#79 := (iff #75 #78)
+#80 := [rewrite]: #79
+#76 := (iff #42 #75)
+#73 := (iff #35 #72)
+#62 := (iff #13 #61)
+#63 := [rewrite]: #62
+#58 := (iff #34 #57)
+#55 := (iff #12 #54)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#74 := [monotonicity #59 #63]: #73
+#70 := (iff #41 #69)
+#67 := (iff #10 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#77 := [monotonicity #71 #74]: #76
+#82 := [trans #77 #80]: #81
+#85 := [monotonicity #82]: #84
+#48 := (iff #16 #47)
+#45 := (iff #15 #42)
+#38 := (implies #10 #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #15 #38)
+#36 := (iff #14 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #46]: #48
+#87 := [trans #49 #85]: #86
+#33 := [asserted]: #16
+#88 := [mp #33 #87]: #83
+#92 := [not-or-elim #88]: #66
+#90 := (not #61)
+#91 := [not-or-elim #88]: #90
+#89 := [not-or-elim #88]: #54
+[th-lemma #89 #91 #92]: false
+unsat
+7ea96733c54b74118ac502b44b56589cca23bf91 18 0
+#2 := false
+#9 := 2345678901::real
+#8 := 123456789::real
+#10 := (< 123456789::real 2345678901::real)
+#11 := (not #10)
+#38 := (iff #11 false)
+#1 := true
+#33 := (not true)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (iff #10 true)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#28 := [asserted]: #11
+[mp #28 #39]: false
+unsat
+35d0ec85b1b4756984ec0a2aa12570b74d8f6576 80 0
+#2 := false
+#53 := 0::int
+decl f4 :: int
+#9 := f4
+#50 := -1::int
+#66 := (* -1::int f4)
+decl f3 :: int
+#8 := f3
+#67 := (+ f3 #66)
+#65 := (>= #67 0::int)
+#64 := (not #65)
+decl f5 :: int
+#11 := f5
+#51 := (* -1::int f5)
+#60 := (+ f3 #51)
+#61 := (<= #60 0::int)
+#52 := (+ f4 #51)
+#54 := (<= #52 0::int)
+#57 := (not #54)
+#83 := (or #57 #61 #65)
+#88 := (not #83)
+#13 := (<= f3 f5)
+#12 := (<= f4 f5)
+#14 := (implies #12 #13)
+#10 := (< f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#91 := (iff #16 #88)
+#34 := (not #12)
+#35 := (or #34 #13)
+#41 := (not #10)
+#42 := (or #41 #35)
+#47 := (not #42)
+#89 := (iff #47 #88)
+#86 := (iff #42 #83)
+#77 := (or #57 #61)
+#80 := (or #65 #77)
+#84 := (iff #80 #83)
+#85 := [rewrite]: #84
+#81 := (iff #42 #80)
+#78 := (iff #35 #77)
+#62 := (iff #13 #61)
+#63 := [rewrite]: #62
+#58 := (iff #34 #57)
+#55 := (iff #12 #54)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#79 := [monotonicity #59 #63]: #78
+#75 := (iff #41 #65)
+#70 := (not #64)
+#73 := (iff #70 #65)
+#74 := [rewrite]: #73
+#71 := (iff #41 #70)
+#68 := (iff #10 #64)
+#69 := [rewrite]: #68
+#72 := [monotonicity #69]: #71
+#76 := [trans #72 #74]: #75
+#82 := [monotonicity #76 #79]: #81
+#87 := [trans #82 #85]: #86
+#90 := [monotonicity #87]: #89
+#48 := (iff #16 #47)
+#45 := (iff #15 #42)
+#38 := (implies #10 #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #15 #38)
+#36 := (iff #14 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #46]: #48
+#92 := [trans #49 #90]: #91
+#33 := [asserted]: #16
+#93 := [mp #33 #92]: #88
+#97 := [not-or-elim #93]: #64
+#95 := (not #61)
+#96 := [not-or-elim #93]: #95
+#94 := [not-or-elim #93]: #54
+[th-lemma #94 #96 #97]: false
+unsat
+dadd2b3f64435d0fb7af768c594e06ecb347e621 30 0
+#2 := false
+#10 := 2345678901::real
+#8 := 123456789::real
+#9 := (- 123456789::real)
+#11 := (< #9 2345678901::real)
+#12 := (not #11)
+#48 := (iff #12 false)
+#30 := -123456789::real
+#33 := (< -123456789::real 2345678901::real)
+#36 := (not #33)
+#46 := (iff #36 false)
+#1 := true
+#41 := (not true)
+#44 := (iff #41 false)
+#45 := [rewrite]: #44
+#42 := (iff #36 #41)
+#39 := (iff #33 true)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#37 := (iff #12 #36)
+#34 := (iff #11 #33)
+#31 := (= #9 -123456789::real)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#38 := [monotonicity #35]: #37
+#49 := [trans #38 #47]: #48
+#29 := [asserted]: #12
+[mp #29 #49]: false
+unsat
+31af85823bea7952455c5b8289eec98083c10812 80 0
+#2 := false
+#52 := 0::int
+decl f4 :: int
+#9 := f4
+#50 := -1::int
+#69 := (* -1::int f4)
+decl f3 :: int
+#8 := f3
+#70 := (+ f3 #69)
+#71 := (<= #70 0::int)
+#74 := (not #71)
+decl f5 :: int
+#11 := f5
+#54 := (* -1::int f5)
+#65 := (+ f3 #54)
+#66 := (<= #65 0::int)
+#55 := (+ f4 #54)
+#53 := (>= #55 0::int)
+#83 := (or #53 #66 #74)
+#88 := (not #83)
+#13 := (<= f3 f5)
+#12 := (< f4 f5)
+#14 := (implies #12 #13)
+#10 := (<= f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#91 := (iff #16 #88)
+#34 := (not #12)
+#35 := (or #34 #13)
+#41 := (not #10)
+#42 := (or #41 #35)
+#47 := (not #42)
+#89 := (iff #47 #88)
+#86 := (iff #42 #83)
+#77 := (or #53 #66)
+#80 := (or #74 #77)
+#84 := (iff #80 #83)
+#85 := [rewrite]: #84
+#81 := (iff #42 #80)
+#78 := (iff #35 #77)
+#67 := (iff #13 #66)
+#68 := [rewrite]: #67
+#63 := (iff #34 #53)
+#51 := (not #53)
+#58 := (not #51)
+#61 := (iff #58 #53)
+#62 := [rewrite]: #61
+#59 := (iff #34 #58)
+#56 := (iff #12 #51)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#79 := [monotonicity #64 #68]: #78
+#75 := (iff #41 #74)
+#72 := (iff #10 #71)
+#73 := [rewrite]: #72
+#76 := [monotonicity #73]: #75
+#82 := [monotonicity #76 #79]: #81
+#87 := [trans #82 #85]: #86
+#90 := [monotonicity #87]: #89
+#48 := (iff #16 #47)
+#45 := (iff #15 #42)
+#38 := (implies #10 #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #15 #38)
+#36 := (iff #14 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #46]: #48
+#92 := [trans #49 #90]: #91
+#33 := [asserted]: #16
+#93 := [mp #33 #92]: #88
+#97 := [not-or-elim #93]: #71
+#94 := [not-or-elim #93]: #51
+#95 := (not #66)
+#96 := [not-or-elim #93]: #95
+[th-lemma #96 #94 #97]: false
+unsat
+70e88c864c6db4b847a2f7eb6c64b44c8f1c8124 26 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := 0::real
+#10 := (+ f3 0::real)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+e48677f09b08fd6733ef8c5373faf8e64833ab2c 85 0
+#2 := false
+#52 := 0::int
+decl f4 :: int
+#9 := f4
+#50 := -1::int
+#72 := (* -1::int f4)
+decl f3 :: int
+#8 := f3
+#73 := (+ f3 #72)
+#71 := (>= #73 0::int)
+#70 := (not #71)
+decl f5 :: int
+#11 := f5
+#54 := (* -1::int f5)
+#67 := (+ f3 #54)
+#66 := (>= #67 0::int)
+#65 := (not #66)
+#55 := (+ f4 #54)
+#53 := (>= #55 0::int)
+#89 := (or #53 #65 #71)
+#94 := (not #89)
+#13 := (< f3 f5)
+#12 := (< f4 f5)
+#14 := (implies #12 #13)
+#10 := (< f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#97 := (iff #16 #94)
+#34 := (not #12)
+#35 := (or #34 #13)
+#41 := (not #10)
+#42 := (or #41 #35)
+#47 := (not #42)
+#95 := (iff #47 #94)
+#92 := (iff #42 #89)
+#83 := (or #53 #65)
+#86 := (or #71 #83)
+#90 := (iff #86 #89)
+#91 := [rewrite]: #90
+#87 := (iff #42 #86)
+#84 := (iff #35 #83)
+#68 := (iff #13 #65)
+#69 := [rewrite]: #68
+#63 := (iff #34 #53)
+#51 := (not #53)
+#58 := (not #51)
+#61 := (iff #58 #53)
+#62 := [rewrite]: #61
+#59 := (iff #34 #58)
+#56 := (iff #12 #51)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#85 := [monotonicity #64 #69]: #84
+#81 := (iff #41 #71)
+#76 := (not #70)
+#79 := (iff #76 #71)
+#80 := [rewrite]: #79
+#77 := (iff #41 #76)
+#74 := (iff #10 #70)
+#75 := [rewrite]: #74
+#78 := [monotonicity #75]: #77
+#82 := [trans #78 #80]: #81
+#88 := [monotonicity #82 #85]: #87
+#93 := [trans #88 #91]: #92
+#96 := [monotonicity #93]: #95
+#48 := (iff #16 #47)
+#45 := (iff #15 #42)
+#38 := (implies #10 #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #15 #38)
+#36 := (iff #14 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #46]: #48
+#98 := [trans #49 #96]: #97
+#33 := [asserted]: #16
+#99 := [mp #33 #98]: #94
+#102 := [not-or-elim #99]: #70
+#100 := [not-or-elim #99]: #51
+#101 := [not-or-elim #99]: #66
+[th-lemma #101 #100 #102]: false
+unsat
+1750fe3e6afdf716eeb70c933529e67e9b6803c7 26 0
+#2 := false
+decl f3 :: real
+#9 := f3
+#8 := 0::real
+#10 := (+ 0::real f3)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+69d20d63c84007048141281611e49dadf61146c1 29 0
+#2 := false
+decl f3 :: real
+#8 := f3
+decl f4 :: real
+#9 := f4
+#11 := (+ f4 f3)
+#10 := (+ f3 f4)
+#12 := (= #10 #11)
+#13 := (not #12)
+#45 := (iff #13 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #13 #40)
+#38 := (iff #12 true)
+#33 := (= #10 #10)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #12 #33)
+#31 := (= #11 #10)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#30 := [asserted]: #13
+[mp #30 #46]: false
+unsat
+4ae7128a23bf2930a8498c167f5a28b2e14524e3 69 0
+#2 := false
+#44 := 0::int
+decl f5 :: int
+#11 := f5
+#42 := -1::int
+#51 := (* -1::int f5)
+decl f3 :: int
+#8 := f3
+#62 := (+ f3 #51)
+#63 := (<= #62 0::int)
+#64 := (not #63)
+decl f4 :: int
+#9 := f4
+#52 := (+ f4 #51)
+#50 := (>= #52 0::int)
+#53 := (not #50)
+#46 := (* -1::int f4)
+#47 := (+ f3 #46)
+#45 := (>= #47 0::int)
+#43 := (not #45)
+#56 := (and #43 #53)
+#59 := (not #56)
+#74 := (or #59 #63)
+#77 := (not #74)
+#14 := (< f5 f3)
+#15 := (not #14)
+#12 := (< f4 f5)
+#10 := (< f3 f4)
+#13 := (and #10 #12)
+#16 := (implies #13 #15)
+#17 := (not #16)
+#80 := (iff #17 #77)
+#35 := (not #13)
+#36 := (or #35 #15)
+#39 := (not #36)
+#78 := (iff #39 #77)
+#75 := (iff #36 #74)
+#72 := (iff #15 #63)
+#67 := (not #64)
+#70 := (iff #67 #63)
+#71 := [rewrite]: #70
+#68 := (iff #15 #67)
+#65 := (iff #14 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#73 := [trans #69 #71]: #72
+#60 := (iff #35 #59)
+#57 := (iff #13 #56)
+#54 := (iff #12 #53)
+#55 := [rewrite]: #54
+#48 := (iff #10 #43)
+#49 := [rewrite]: #48
+#58 := [monotonicity #49 #55]: #57
+#61 := [monotonicity #58]: #60
+#76 := [monotonicity #61 #73]: #75
+#79 := [monotonicity #76]: #78
+#40 := (iff #17 #39)
+#37 := (iff #16 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#81 := [trans #41 #79]: #80
+#34 := [asserted]: #17
+#82 := [mp #34 #81]: #77
+#86 := [not-or-elim #82]: #64
+#83 := [not-or-elim #82]: #56
+#84 := [and-elim #83]: #43
+#85 := [and-elim #83]: #53
+[th-lemma #85 #84 #86]: false
+unsat
+1a0a736d3a32332defd35838ed3918f39ef91381 33 0
+#2 := false
+decl f5 :: real
+#10 := f5
+decl f4 :: real
+#9 := f4
+decl f3 :: real
+#8 := f3
+#13 := (+ f3 f4)
+#14 := (+ #13 f5)
+#11 := (+ f4 f5)
+#12 := (+ f3 #11)
+#15 := (= #12 #14)
+#16 := (not #15)
+#48 := (iff #16 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #16 #43)
+#41 := (iff #15 true)
+#36 := (= #12 #12)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #15 #36)
+#34 := (= #14 #12)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#33 := [asserted]: #16
+[mp #33 #49]: false
+unsat
+d40ed0654760a137f6aba17a9e5eb1b632371b23 45 0
+#2 := false
+decl f4 :: real
+#9 := f4
+#13 := (- f4)
+decl f3 :: real
+#8 := f3
+#14 := (= f3 #13)
+#11 := 0::real
+#10 := (+ f3 f4)
+#12 := (= #10 0::real)
+#15 := (iff #12 #14)
+#16 := (not #15)
+#62 := (iff #16 false)
+#47 := (not #12)
+#34 := -1::real
+#35 := (* -1::real f4)
+#38 := (= f3 #35)
+#48 := (iff #38 #47)
+#60 := (iff #48 false)
+#55 := (iff #12 #47)
+#58 := (iff #55 false)
+#59 := [rewrite]: #58
+#56 := (iff #48 #55)
+#53 := (iff #38 #12)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#51 := (iff #16 #48)
+#41 := (iff #12 #38)
+#44 := (not #41)
+#49 := (iff #44 #48)
+#50 := [rewrite]: #49
+#45 := (iff #16 #44)
+#42 := (iff #15 #41)
+#39 := (iff #14 #38)
+#36 := (= #13 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#46 := [monotonicity #43]: #45
+#52 := [trans #46 #50]: #51
+#63 := [trans #52 #61]: #62
+#33 := [asserted]: #16
+[mp #33 #63]: false
+unsat
+2e5f7999cc8eb3b8360ba5eefe8486091d5b23e0 58 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#10 := 0::real
+#12 := (< 0::real f3)
+#9 := (- f3)
+#11 := (< #9 0::real)
+#13 := (iff #11 #12)
+#14 := (not #13)
+#76 := (iff #14 false)
+#50 := (not #12)
+#32 := -1::real
+#33 := (* -1::real f3)
+#36 := (< #33 0::real)
+#51 := (iff #36 #50)
+#74 := (iff #51 false)
+#56 := (<= f3 0::real)
+#57 := (not #56)
+#69 := (iff #57 #56)
+#72 := (iff #69 false)
+#73 := [rewrite]: #72
+#70 := (iff #51 #69)
+#67 := (iff #50 #56)
+#62 := (not #57)
+#65 := (iff #62 #56)
+#66 := [rewrite]: #65
+#63 := (iff #50 #62)
+#60 := (iff #12 #57)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#68 := [trans #64 #66]: #67
+#58 := (iff #36 #57)
+#59 := [rewrite]: #58
+#71 := [monotonicity #59 #68]: #70
+#75 := [trans #71 #73]: #74
+#54 := (iff #14 #51)
+#42 := (iff #12 #36)
+#47 := (not #42)
+#52 := (iff #47 #51)
+#53 := [rewrite]: #52
+#48 := (iff #14 #47)
+#45 := (iff #13 #42)
+#39 := (iff #36 #12)
+#43 := (iff #39 #42)
+#44 := [rewrite]: #43
+#40 := (iff #13 #39)
+#37 := (iff #11 #36)
+#34 := (= #9 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#46 := [trans #41 #44]: #45
+#49 := [monotonicity #46]: #48
+#55 := [trans #49 #53]: #54
+#77 := [trans #55 #75]: #76
+#31 := [asserted]: #14
+[mp #31 #77]: false
+unsat
+50c9906c7d751f92217d01455225257cf462c453 26 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := 0::real
+#10 := (- f3 0::real)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+e9e8aa80c40e8ef0e6e99e4aa18d0a13b21b0376 61 0
+#2 := false
+#8 := 0::real
+decl f3 :: real
+#9 := f3
+#11 := (- f3)
+#12 := (< #11 0::real)
+#10 := (< 0::real f3)
+#13 := (implies #10 #12)
+#14 := (not #13)
+#78 := (iff #14 false)
+#32 := -1::real
+#33 := (* -1::real f3)
+#36 := (< #33 0::real)
+#42 := (not #10)
+#43 := (or #42 #36)
+#48 := (not #43)
+#76 := (iff #48 false)
+#1 := true
+#71 := (not true)
+#74 := (iff #71 false)
+#75 := [rewrite]: #74
+#72 := (iff #48 #71)
+#69 := (iff #43 true)
+#51 := (<= f3 0::real)
+#52 := (not #51)
+#64 := (or #51 #52)
+#67 := (iff #64 true)
+#68 := [rewrite]: #67
+#65 := (iff #43 #64)
+#62 := (iff #36 #52)
+#63 := [rewrite]: #62
+#60 := (iff #42 #51)
+#55 := (not #52)
+#58 := (iff #55 #51)
+#59 := [rewrite]: #58
+#56 := (iff #42 #55)
+#53 := (iff #10 #52)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#66 := [monotonicity #61 #63]: #65
+#70 := [trans #66 #68]: #69
+#73 := [monotonicity #70]: #72
+#77 := [trans #73 #75]: #76
+#49 := (iff #14 #48)
+#46 := (iff #13 #43)
+#39 := (implies #10 #36)
+#44 := (iff #39 #43)
+#45 := [rewrite]: #44
+#40 := (iff #13 #39)
+#37 := (iff #12 #36)
+#34 := (= #11 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#47 := [trans #41 #45]: #46
+#50 := [monotonicity #47]: #49
+#79 := [trans #50 #77]: #78
+#31 := [asserted]: #14
+[mp #31 #79]: false
+unsat
+acca7aae09e2e9a49a4d632200e33dc782e588aa 32 0
+#2 := false
+decl f3 :: real
+#9 := f3
+#11 := (- f3)
+#8 := 0::real
+#10 := (- 0::real f3)
+#12 := (= #10 #11)
+#13 := (not #12)
+#49 := (iff #13 false)
+#1 := true
+#44 := (not true)
+#47 := (iff #44 false)
+#48 := [rewrite]: #47
+#45 := (iff #13 #44)
+#42 := (iff #12 true)
+#31 := -1::real
+#32 := (* -1::real f3)
+#37 := (= #32 #32)
+#40 := (iff #37 true)
+#41 := [rewrite]: #40
+#38 := (iff #12 #37)
+#35 := (= #11 #32)
+#36 := [rewrite]: #35
+#33 := (= #10 #32)
+#34 := [rewrite]: #33
+#39 := [monotonicity #34 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#30 := [asserted]: #13
+[mp #30 #50]: false
+unsat
+0ace06c6b03ac83c82084015bdca2809234a4101 61 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#11 := (- f3)
+#9 := 0::real
+#12 := (< 0::real #11)
+#10 := (< f3 0::real)
+#13 := (implies #10 #12)
+#14 := (not #13)
+#78 := (iff #14 false)
+#32 := -1::real
+#33 := (* -1::real f3)
+#36 := (< 0::real #33)
+#42 := (not #10)
+#43 := (or #42 #36)
+#48 := (not #43)
+#76 := (iff #48 false)
+#1 := true
+#71 := (not true)
+#74 := (iff #71 false)
+#75 := [rewrite]: #74
+#72 := (iff #48 #71)
+#69 := (iff #43 true)
+#51 := (>= f3 0::real)
+#52 := (not #51)
+#64 := (or #51 #52)
+#67 := (iff #64 true)
+#68 := [rewrite]: #67
+#65 := (iff #43 #64)
+#62 := (iff #36 #52)
+#63 := [rewrite]: #62
+#60 := (iff #42 #51)
+#55 := (not #52)
+#58 := (iff #55 #51)
+#59 := [rewrite]: #58
+#56 := (iff #42 #55)
+#53 := (iff #10 #52)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#66 := [monotonicity #61 #63]: #65
+#70 := [trans #66 #68]: #69
+#73 := [monotonicity #70]: #72
+#77 := [trans #73 #75]: #76
+#49 := (iff #14 #48)
+#46 := (iff #13 #43)
+#39 := (implies #10 #36)
+#44 := (iff #39 #43)
+#45 := [rewrite]: #44
+#40 := (iff #13 #39)
+#37 := (iff #12 #36)
+#34 := (= #11 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#47 := [trans #41 #45]: #46
+#50 := [monotonicity #47]: #49
+#79 := [trans #50 #77]: #78
+#31 := [asserted]: #14
+[mp #31 #79]: false
+unsat
+7e2acc6f3578e9594f16685aec01d464f0afcefe 64 0
+#2 := false
+#12 := 0::real
+decl f4 :: real
+#9 := f4
+decl f3 :: real
+#8 := f3
+#11 := (- f3 f4)
+#13 := (< #11 0::real)
+#10 := (< f3 f4)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#80 := (iff #15 false)
+#33 := -1::real
+#34 := (* -1::real f4)
+#35 := (+ f3 #34)
+#38 := (< #35 0::real)
+#44 := (not #10)
+#45 := (or #44 #38)
+#50 := (not #45)
+#78 := (iff #50 false)
+#1 := true
+#73 := (not true)
+#76 := (iff #73 false)
+#77 := [rewrite]: #76
+#74 := (iff #50 #73)
+#71 := (iff #45 true)
+#54 := (>= #35 0::real)
+#53 := (not #54)
+#66 := (or #54 #53)
+#69 := (iff #66 true)
+#70 := [rewrite]: #69
+#67 := (iff #45 #66)
+#64 := (iff #38 #53)
+#65 := [rewrite]: #64
+#62 := (iff #44 #54)
+#57 := (not #53)
+#60 := (iff #57 #54)
+#61 := [rewrite]: #60
+#58 := (iff #44 #57)
+#55 := (iff #10 #53)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#63 := [trans #59 #61]: #62
+#68 := [monotonicity #63 #65]: #67
+#72 := [trans #68 #70]: #71
+#75 := [monotonicity #72]: #74
+#79 := [trans #75 #77]: #78
+#51 := (iff #15 #50)
+#48 := (iff #14 #45)
+#41 := (implies #10 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #14 #41)
+#39 := (iff #13 #38)
+#36 := (= #11 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#49 := [trans #43 #47]: #48
+#52 := [monotonicity #49]: #51
+#81 := [trans #52 #79]: #80
+#32 := [asserted]: #15
+[mp #32 #81]: false
+unsat
+b9bc7b6c72b913aad9adac918987becb58cf13fa 44 0
+#2 := false
+decl f3 :: real
+#8 := f3
+decl f4 :: real
+#9 := f4
+#11 := (- f4 f3)
+#12 := (- #11)
+#10 := (- f3 f4)
+#13 := (= #10 #12)
+#14 := (not #13)
+#60 := (iff #14 false)
+#1 := true
+#55 := (not true)
+#58 := (iff #55 false)
+#59 := [rewrite]: #58
+#56 := (iff #14 #55)
+#53 := (iff #13 true)
+#32 := -1::real
+#33 := (* -1::real f4)
+#34 := (+ f3 #33)
+#48 := (= #34 #34)
+#51 := (iff #48 true)
+#52 := [rewrite]: #51
+#49 := (iff #13 #48)
+#46 := (= #12 #34)
+#37 := (* -1::real f3)
+#38 := (+ #37 f4)
+#41 := (- #38)
+#44 := (= #41 #34)
+#45 := [rewrite]: #44
+#42 := (= #12 #41)
+#39 := (= #11 #38)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#35 := (= #10 #34)
+#36 := [rewrite]: #35
+#50 := [monotonicity #36 #47]: #49
+#54 := [trans #50 #52]: #53
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#31 := [asserted]: #14
+[mp #31 #61]: false
+unsat
+73bf4a32a24c07787655407ab8d48c7e68594bd3 42 0
+#2 := false
+decl f3 :: real
+#8 := f3
+decl f4 :: real
+#9 := f4
+#11 := (- f4)
+#12 := (+ #11 f3)
+#10 := (- f3 f4)
+#13 := (= #10 #12)
+#14 := (not #13)
+#58 := (iff #14 false)
+#1 := true
+#53 := (not true)
+#56 := (iff #53 false)
+#57 := [rewrite]: #56
+#54 := (iff #14 #53)
+#51 := (iff #13 true)
+#32 := -1::real
+#33 := (* -1::real f4)
+#34 := (+ f3 #33)
+#46 := (= #34 #34)
+#49 := (iff #46 true)
+#50 := [rewrite]: #49
+#47 := (iff #13 #46)
+#44 := (= #12 #34)
+#39 := (+ #33 f3)
+#42 := (= #39 #34)
+#43 := [rewrite]: #42
+#40 := (= #12 #39)
+#37 := (= #11 #33)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#35 := (= #10 #34)
+#36 := [rewrite]: #35
+#48 := [monotonicity #36 #45]: #47
+#52 := [trans #48 #50]: #51
+#55 := [monotonicity #52]: #54
+#59 := [trans #55 #57]: #58
+#31 := [asserted]: #14
+[mp #31 #59]: false
+unsat
+9bd93d3b0ddd945e550dcfe8a6ffb45c7f693fe1 30 0
+#2 := false
+#8 := 1::real
+#9 := 2::real
+#10 := (/ 1::real 2::real)
+#11 := (< #10 1::real)
+#12 := (not #11)
+#48 := (iff #12 false)
+#30 := 1/2::real
+#33 := (< 1/2::real 1::real)
+#36 := (not #33)
+#46 := (iff #36 false)
+#1 := true
+#41 := (not true)
+#44 := (iff #41 false)
+#45 := [rewrite]: #44
+#42 := (iff #36 #41)
+#39 := (iff #33 true)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#37 := (iff #12 #36)
+#34 := (iff #11 #33)
+#31 := (= #10 1/2::real)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#38 := [monotonicity #35]: #37
+#49 := [trans #38 #47]: #48
+#29 := [asserted]: #12
+[mp #29 #49]: false
+unsat
+00dd8ae97a6500a3bdd8c17f92b12c5c85a7310b 48 0
+#2 := false
+decl f5 :: real
+#11 := f5
+decl f4 :: real
+#9 := f4
+#13 := (+ f4 f5)
+decl f3 :: real
+#8 := f3
+#14 := (- f3 #13)
+#10 := (- f3 f4)
+#12 := (- #10 f5)
+#15 := (= #12 #14)
+#16 := (not #15)
+#63 := (iff #16 false)
+#1 := true
+#58 := (not true)
+#61 := (iff #58 false)
+#62 := [rewrite]: #61
+#59 := (iff #16 #58)
+#56 := (iff #15 true)
+#34 := -1::real
+#42 := (* -1::real f5)
+#35 := (* -1::real f4)
+#43 := (+ #35 #42)
+#44 := (+ f3 #43)
+#51 := (= #44 #44)
+#54 := (iff #51 true)
+#55 := [rewrite]: #54
+#52 := (iff #15 #51)
+#49 := (= #14 #44)
+#50 := [rewrite]: #49
+#47 := (= #12 #44)
+#36 := (+ f3 #35)
+#39 := (- #36 f5)
+#45 := (= #39 #44)
+#46 := [rewrite]: #45
+#40 := (= #12 #39)
+#37 := (= #10 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#48 := [trans #41 #46]: #47
+#53 := [monotonicity #48 #50]: #52
+#57 := [trans #53 #55]: #56
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#33 := [asserted]: #16
+[mp #33 #64]: false
+unsat
+8df4cccdaeae7b8dba6943e970d61ef9c5d5c03a 27 0
+#2 := false
+#9 := 3::real
+#8 := 1::real
+#10 := (/ 1::real 3::real)
+#11 := (= #10 #10)
+#12 := (not #11)
+#45 := (iff #12 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #12 #40)
+#38 := (iff #11 true)
+#30 := 1/3::real
+#33 := (= 1/3::real 1/3::real)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (= #10 1/3::real)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32 #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#29 := [asserted]: #12
+[mp #29 #46]: false
+unsat
+3d1c0db1afc349d77cdcd71f7e3bab1aba5dbe51 48 0
+#2 := false
+#9 := 3::real
+#8 := 1::real
+#12 := (- 1::real)
+#13 := (/ #12 3::real)
+#10 := (- 3::real)
+#11 := (/ 1::real #10)
+#14 := (= #11 #13)
+#15 := (not #14)
+#66 := (iff #15 false)
+#1 := true
+#61 := (not true)
+#64 := (iff #61 false)
+#65 := [rewrite]: #64
+#62 := (iff #15 #61)
+#59 := (iff #14 true)
+#39 := -1/3::real
+#54 := (= -1/3::real -1/3::real)
+#57 := (iff #54 true)
+#58 := [rewrite]: #57
+#55 := (iff #14 #54)
+#52 := (= #13 -1/3::real)
+#44 := -1::real
+#47 := (/ -1::real 3::real)
+#50 := (= #47 -1/3::real)
+#51 := [rewrite]: #50
+#48 := (= #13 #47)
+#45 := (= #12 -1::real)
+#46 := [rewrite]: #45
+#49 := [monotonicity #46]: #48
+#53 := [trans #49 #51]: #52
+#42 := (= #11 -1/3::real)
+#33 := -3::real
+#36 := (/ 1::real -3::real)
+#40 := (= #36 -1/3::real)
+#41 := [rewrite]: #40
+#37 := (= #11 #36)
+#34 := (= #10 -3::real)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#43 := [trans #38 #41]: #42
+#56 := [monotonicity #43 #53]: #55
+#60 := [trans #56 #58]: #59
+#63 := [monotonicity #60]: #62
+#67 := [trans #63 #65]: #66
+#32 := [asserted]: #15
+[mp #32 #67]: false
+unsat
+87b5c605d55a2e66da4dfd975d21b4153bb5414e 36 0
+#2 := false
+#10 := 3::real
+#8 := 1::real
+#9 := (- 1::real)
+#11 := (/ #9 3::real)
+#12 := (= #11 #11)
+#13 := (not #12)
+#54 := (iff #13 false)
+#1 := true
+#49 := (not true)
+#52 := (iff #49 false)
+#53 := [rewrite]: #52
+#50 := (iff #13 #49)
+#47 := (iff #12 true)
+#37 := -1/3::real
+#42 := (= -1/3::real -1/3::real)
+#45 := (iff #42 true)
+#46 := [rewrite]: #45
+#43 := (iff #12 #42)
+#40 := (= #11 -1/3::real)
+#31 := -1::real
+#34 := (/ -1::real 3::real)
+#38 := (= #34 -1/3::real)
+#39 := [rewrite]: #38
+#35 := (= #11 #34)
+#32 := (= #9 -1::real)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#41 := [trans #36 #39]: #40
+#44 := [monotonicity #41 #41]: #43
+#48 := [trans #44 #46]: #47
+#51 := [monotonicity #48]: #50
+#55 := [trans #51 #53]: #54
+#30 := [asserted]: #13
+[mp #30 #55]: false
+unsat
+69f379b62648823dab96490b884403f1a100b051 36 0
+#2 := false
+decl f3 :: real
+#9 := f3
+#8 := 3::real
+#10 := (/ f3 3::real)
+#11 := (* 3::real #10)
+#12 := (= #11 f3)
+#13 := (not #12)
+#53 := (iff #13 false)
+#1 := true
+#48 := (not true)
+#51 := (iff #48 false)
+#52 := [rewrite]: #51
+#49 := (iff #13 #48)
+#46 := (iff #12 true)
+#41 := (= f3 f3)
+#44 := (iff #41 true)
+#45 := [rewrite]: #44
+#42 := (iff #12 #41)
+#31 := 1/3::real
+#32 := (* 1/3::real f3)
+#35 := (* 3::real #32)
+#38 := (= #35 f3)
+#39 := [rewrite]: #38
+#36 := (= #11 #35)
+#33 := (= #10 #32)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#40 := [trans #37 #39]: #12
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#50 := [monotonicity #47]: #49
+#54 := [trans #50 #52]: #53
+#30 := [asserted]: #13
+[mp #30 #54]: false
+unsat
+c568dbbce6e2e01b901ce930d7e767e667036eac 43 0
+#2 := false
+#10 := 3::real
+#8 := 1::real
+#13 := (/ 1::real 3::real)
+#11 := (- 3::real)
+#9 := (- 1::real)
+#12 := (/ #9 #11)
+#14 := (= #12 #13)
+#15 := (not #14)
+#61 := (iff #15 false)
+#1 := true
+#56 := (not true)
+#59 := (iff #56 false)
+#60 := [rewrite]: #59
+#57 := (iff #15 #56)
+#54 := (iff #14 true)
+#42 := 1/3::real
+#49 := (= 1/3::real 1/3::real)
+#52 := (iff #49 true)
+#53 := [rewrite]: #52
+#50 := (iff #14 #49)
+#47 := (= #13 1/3::real)
+#48 := [rewrite]: #47
+#45 := (= #12 1/3::real)
+#36 := -3::real
+#33 := -1::real
+#39 := (/ -1::real -3::real)
+#43 := (= #39 1/3::real)
+#44 := [rewrite]: #43
+#40 := (= #12 #39)
+#37 := (= #11 -3::real)
+#38 := [rewrite]: #37
+#34 := (= #9 -1::real)
+#35 := [rewrite]: #34
+#41 := [monotonicity #35 #38]: #40
+#46 := [trans #41 #44]: #45
+#51 := [monotonicity #46 #48]: #50
+#55 := [trans #51 #53]: #54
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#32 := [asserted]: #15
+[mp #32 #62]: false
+unsat
[phone]d5a7d77b2ca31653ed08be03e48773 35 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := 3::real
+#10 := (* f3 3::real)
+#11 := (/ #10 3::real)
+#12 := (= #11 f3)
+#13 := (not #12)
+#52 := (iff #13 false)
+#1 := true
+#47 := (not true)
+#50 := (iff #47 false)
+#51 := [rewrite]: #50
+#48 := (iff #13 #47)
+#45 := (iff #12 true)
+#40 := (= f3 f3)
+#43 := (iff #40 true)
+#44 := [rewrite]: #43
+#41 := (iff #12 #40)
+#31 := (* 3::real f3)
+#34 := (/ #31 3::real)
+#37 := (= #34 f3)
+#38 := [rewrite]: #37
+#35 := (= #11 #34)
+#32 := (= #10 #31)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#39 := [trans #36 #38]: #12
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#49 := [monotonicity #46]: #48
+#53 := [trans #49 #51]: #52
+#30 := [asserted]: #13
+[mp #30 #53]: false
+unsat
+b263639810279d9b6652040b63841cf9ecc49673 26 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := 1::real
+#10 := (/ f3 1::real)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+a4bc584e73aac52f28ef031b730a576d8872cda7 62 0
+#2 := false
+#8 := 0::real
+decl f3 :: real
+#9 := f3
+#67 := 1/3::real
+#68 := (* 1/3::real f3)
+#69 := (<= #68 0::real)
+#65 := (not #69)
+#54 := (<= f3 0::real)
+#71 := (or #54 #65)
+#74 := (not #71)
+#13 := 3::real
+#11 := 2::real
+#12 := (* 2::real f3)
+#14 := (/ #12 3::real)
+#15 := (< #14 f3)
+#10 := (< 0::real f3)
+#16 := (implies #10 #15)
+#17 := (not #16)
+#77 := (iff #17 #74)
+#36 := 2/3::real
+#37 := (* 2/3::real f3)
+#39 := (< #37 f3)
+#45 := (not #10)
+#46 := (or #45 #39)
+#51 := (not #46)
+#75 := (iff #51 #74)
+#72 := (iff #46 #71)
+#66 := (iff #39 #65)
+#70 := [rewrite]: #66
+#63 := (iff #45 #54)
+#55 := (not #54)
+#58 := (not #55)
+#61 := (iff #58 #54)
+#62 := [rewrite]: #61
+#59 := (iff #45 #58)
+#56 := (iff #10 #55)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#73 := [monotonicity #64 #70]: #72
+#76 := [monotonicity #73]: #75
+#52 := (iff #17 #51)
+#49 := (iff #16 #46)
+#42 := (implies #10 #39)
+#47 := (iff #42 #46)
+#48 := [rewrite]: #47
+#43 := (iff #16 #42)
+#40 := (iff #15 #39)
+#35 := (= #14 #37)
+#38 := [rewrite]: #35
+#41 := [monotonicity #38]: #40
+#44 := [monotonicity #41]: #43
+#50 := [trans #44 #48]: #49
+#53 := [monotonicity #50]: #52
+#78 := [trans #53 #76]: #77
+#34 := [asserted]: #17
+#79 := [mp #34 #78]: #74
+#81 := [not-or-elim #79]: #69
+#80 := [not-or-elim #79]: #55
+[th-lemma #80 #81]: false
+unsat
+7d08518b217d1a1becfa0af110d54307de30c5dc 60 0
+#2 := false
+#8 := 0::real
+decl f3 :: real
+#9 := f3
+#65 := 2/3::real
+#66 := (* 2/3::real f3)
+#67 := (<= #66 0::real)
+#63 := (not #67)
+#52 := (<= f3 0::real)
+#69 := (or #52 #63)
+#72 := (not #69)
+#11 := 3::real
+#12 := (/ f3 3::real)
+#13 := (< #12 f3)
+#10 := (< 0::real f3)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#75 := (iff #15 #72)
+#33 := 1/3::real
+#34 := (* 1/3::real f3)
+#37 := (< #34 f3)
+#43 := (not #10)
+#44 := (or #43 #37)
+#49 := (not #44)
+#73 := (iff #49 #72)
+#70 := (iff #44 #69)
+#64 := (iff #37 #63)
+#68 := [rewrite]: #64
+#61 := (iff #43 #52)
+#53 := (not #52)
+#56 := (not #53)
+#59 := (iff #56 #52)
+#60 := [rewrite]: #59
+#57 := (iff #43 #56)
+#54 := (iff #10 #53)
+#55 := [rewrite]: #54
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#71 := [monotonicity #62 #68]: #70
+#74 := [monotonicity #71]: #73
+#50 := (iff #15 #49)
+#47 := (iff #14 #44)
+#40 := (implies #10 #37)
+#45 := (iff #40 #44)
+#46 := [rewrite]: #45
+#41 := (iff #14 #40)
+#38 := (iff #13 #37)
+#35 := (= #12 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#42 := [monotonicity #39]: #41
+#48 := [trans #42 #46]: #47
+#51 := [monotonicity #48]: #50
+#76 := [trans #51 #74]: #75
+#32 := [asserted]: #15
+#77 := [mp #32 #76]: #72
+#79 := [not-or-elim #77]: #67
+#78 := [not-or-elim #77]: #53
+[th-lemma #78 #79]: false
+unsat
+3264c4e64061840798cc6aff819c1a9ea6efdf83 62 0
+#2 := false
+#9 := 0::real
+decl f3 :: real
+#8 := f3
+#69 := 1/3::real
+#70 := (* 1/3::real f3)
+#67 := (>= #70 0::real)
+#65 := (not #67)
+#56 := (>= f3 0::real)
+#71 := (or #56 #65)
+#74 := (not #71)
+#13 := 3::real
+#11 := 2::real
+#12 := (* 2::real f3)
+#14 := (/ #12 3::real)
+#15 := (< f3 #14)
+#10 := (< f3 0::real)
+#16 := (implies #10 #15)
+#17 := (not #16)
+#77 := (iff #17 #74)
+#36 := 2/3::real
+#37 := (* 2/3::real f3)
+#39 := (< f3 #37)
+#45 := (not #10)
+#46 := (or #45 #39)
+#51 := (not #46)
+#75 := (iff #51 #74)
+#72 := (iff #46 #71)
+#66 := (iff #39 #65)
+#68 := [rewrite]: #66
+#63 := (iff #45 #56)
+#54 := (not #56)
+#58 := (not #54)
+#61 := (iff #58 #56)
+#62 := [rewrite]: #61
+#59 := (iff #45 #58)
+#55 := (iff #10 #54)
+#57 := [rewrite]: #55
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#73 := [monotonicity #64 #68]: #72
+#76 := [monotonicity #73]: #75
+#52 := (iff #17 #51)
+#49 := (iff #16 #46)
+#42 := (implies #10 #39)
+#47 := (iff #42 #46)
+#48 := [rewrite]: #47
+#43 := (iff #16 #42)
+#40 := (iff #15 #39)
+#35 := (= #14 #37)
+#38 := [rewrite]: #35
+#41 := [monotonicity #38]: #40
+#44 := [monotonicity #41]: #43
+#50 := [trans #44 #48]: #49
+#53 := [monotonicity #50]: #52
+#78 := [trans #53 #76]: #77
+#34 := [asserted]: #17
+#79 := [mp #34 #78]: #74
+#81 := [not-or-elim #79]: #67
+#80 := [not-or-elim #79]: #54
+[th-lemma #80 #81]: false
+unsat
+6c2103bd90ca9e5c8cf0a5b4be8090b54399dce8 60 0
+#2 := false
+#9 := 0::real
+decl f3 :: real
+#8 := f3
+#67 := 2/3::real
+#68 := (* 2/3::real f3)
+#65 := (>= #68 0::real)
+#63 := (not #65)
+#54 := (>= f3 0::real)
+#69 := (or #54 #63)
+#72 := (not #69)
+#11 := 3::real
+#12 := (/ f3 3::real)
+#13 := (< f3 #12)
+#10 := (< f3 0::real)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#75 := (iff #15 #72)
+#33 := 1/3::real
+#34 := (* 1/3::real f3)
+#37 := (< f3 #34)
+#43 := (not #10)
+#44 := (or #43 #37)
+#49 := (not #44)
+#73 := (iff #49 #72)
+#70 := (iff #44 #69)
+#64 := (iff #37 #63)
+#66 := [rewrite]: #64
+#61 := (iff #43 #54)
+#52 := (not #54)
+#56 := (not #52)
+#59 := (iff #56 #54)
+#60 := [rewrite]: #59
+#57 := (iff #43 #56)
+#53 := (iff #10 #52)
+#55 := [rewrite]: #53
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#71 := [monotonicity #62 #66]: #70
+#74 := [monotonicity #71]: #73
+#50 := (iff #15 #49)
+#47 := (iff #14 #44)
+#40 := (implies #10 #37)
+#45 := (iff #40 #44)
+#46 := [rewrite]: #45
+#41 := (iff #14 #40)
+#38 := (iff #13 #37)
+#35 := (= #12 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#42 := [monotonicity #39]: #41
+#48 := [trans #42 #46]: #47
+#51 := [monotonicity #48]: #50
+#76 := [trans #51 #74]: #75
+#32 := [asserted]: #15
+#77 := [mp #32 #76]: #72
+#79 := [not-or-elim #77]: #65
+#78 := [not-or-elim #77]: #52
+[th-lemma #78 #79]: false
+unsat
+38c4aea1d2d6bacd07395ef4b2393dfbcb439bc0 75 0
+#2 := false
+#8 := 0::real
+decl f3 :: real
+#9 := f3
+#32 := -1::real
+#33 := (* -1::real f3)
+#45 := (>= f3 0::real)
+#52 := (ite #45 f3 #33)
+#73 := (* -1::real #52)
+#81 := (+ f3 #73)
+#90 := (<= #81 0::real)
+#76 := (= f3 #52)
+#71 := (+ #33 #73)
+#80 := (<= #71 0::real)
+#77 := (= #33 #52)
+#46 := (not #45)
+#82 := [hypothesis]: #46
+#74 := (or #45 #77)
+#75 := [def-axiom]: #74
+#83 := [unit-resolution #75 #82]: #77
+#84 := (not #77)
+#85 := (or #84 #80)
+#86 := [th-lemma]: #85
+#87 := [unit-resolution #86 #83]: #80
+#61 := (>= #52 0::real)
+#65 := (not #61)
+#11 := (- f3)
+#10 := (< f3 0::real)
+#12 := (ite #10 #11 f3)
+#13 := (<= 0::real #12)
+#14 := (not #13)
+#68 := (iff #14 #65)
+#36 := (ite #10 #33 f3)
+#39 := (<= 0::real #36)
+#42 := (not #39)
+#66 := (iff #42 #65)
+#63 := (iff #39 #61)
+#57 := (<= 0::real #52)
+#60 := (iff #57 #61)
+#62 := [rewrite]: #60
+#58 := (iff #39 #57)
+#55 := (= #36 #52)
+#49 := (ite #46 #33 f3)
+#53 := (= #49 #52)
+#54 := [rewrite]: #53
+#50 := (= #36 #49)
+#47 := (iff #10 #46)
+#48 := [rewrite]: #47
+#51 := [monotonicity #48]: #50
+#56 := [trans #51 #54]: #55
+#59 := [monotonicity #56]: #58
+#64 := [trans #59 #62]: #63
+#67 := [monotonicity #64]: #66
+#43 := (iff #14 #42)
+#40 := (iff #13 #39)
+#37 := (= #12 #36)
+#34 := (= #11 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#44 := [monotonicity #41]: #43
+#69 := [trans #44 #67]: #68
+#31 := [asserted]: #14
+#70 := [mp #31 #69]: #65
+#88 := [th-lemma #82 #70 #87]: false
+#89 := [lemma #88]: #45
+#78 := (or #46 #76)
+#79 := [def-axiom]: #78
+#92 := [unit-resolution #79 #89]: #76
+#93 := (not #76)
+#94 := (or #93 #90)
+#95 := [th-lemma]: #94
+#96 := [unit-resolution #95 #92]: #90
+[th-lemma #89 #70 #96]: false
+unsat
+4d115301f8b89c507668ca5b7281bced36458867 57 0
+#2 := false
+#36 := 0::real
+decl f4 :: real
+#9 := f4
+decl f3 :: real
+#8 := f3
+#33 := -1::real
+#34 := (* -1::real f4)
+#35 := (+ f3 #34)
+#37 := (<= #35 0::real)
+#40 := (ite #37 f3 f4)
+#48 := (* -1::real #40)
+#49 := (+ f3 #48)
+#47 := (>= #49 0::real)
+#53 := (not #47)
+#10 := (<= f3 f4)
+#11 := (ite #10 f3 f4)
+#12 := (<= #11 f3)
+#13 := (not #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #47)
+#43 := (<= #40 f3)
+#46 := (iff #43 #47)
+#50 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#52 := [trans #45 #50]: #51
+#55 := [monotonicity #52]: #54
+#30 := [asserted]: #13
+#56 := [mp #30 #55]: #53
+#60 := (= f3 #40)
+#31 := (+ f4 #48)
+#65 := (>= #31 0::real)
+#61 := (= f4 #40)
+#62 := (not #37)
+#66 := [hypothesis]: #62
+#59 := (or #37 #61)
+#57 := [def-axiom]: #59
+#67 := [unit-resolution #57 #66]: #61
+#68 := (not #61)
+#69 := (or #68 #65)
+#70 := [th-lemma]: #69
+#71 := [unit-resolution #70 #67]: #65
+#72 := [th-lemma #56 #66 #71]: false
+#73 := [lemma #72]: #37
+#63 := (or #62 #60)
+#58 := [def-axiom]: #63
+#74 := [unit-resolution #58 #73]: #60
+#75 := (not #60)
+#76 := (or #75 #47)
+#77 := [th-lemma]: #76
+[unit-resolution #77 #74 #56]: false
+unsat
+dfa0c0d7e307b713d1c0a6fb4345c0cb4048e97d 132 0
+#2 := false
+#9 := 0::real
+decl f3 :: real
+#8 := f3
+#66 := (>= f3 0::real)
+#67 := (not #66)
+#34 := -1::real
+#35 := (* -1::real f3)
+#73 := (ite #66 f3 #35)
+#102 := (= f3 #73)
+#130 := (not #102)
+#14 := (= f3 0::real)
+#82 := (= #73 0::real)
+#124 := (iff #82 #14)
+#122 := (iff #14 #82)
+#121 := [hypothesis]: #102
+#123 := [monotonicity #121]: #122
+#125 := [symm #123]: #124
+#131 := (or #82 #130)
+#60 := (not #14)
+#99 := (not #82)
+#126 := (iff #99 #60)
+#127 := [monotonicity #125]: #126
+#119 := [hypothesis]: #99
+#128 := [mp #119 #127]: #60
+#112 := (or #14 #82)
+#89 := (iff #60 #82)
+#11 := (- f3)
+#10 := (< f3 0::real)
+#12 := (ite #10 #11 f3)
+#13 := (= #12 0::real)
+#15 := (iff #13 #14)
+#16 := (not #15)
+#94 := (iff #16 #89)
+#38 := (ite #10 #35 f3)
+#44 := (= 0::real #38)
+#61 := (iff #44 #60)
+#92 := (iff #61 #89)
+#86 := (iff #82 #60)
+#90 := (iff #86 #89)
+#91 := [rewrite]: #90
+#87 := (iff #61 #86)
+#84 := (iff #44 #82)
+#78 := (= 0::real #73)
+#81 := (iff #78 #82)
+#83 := [rewrite]: #81
+#79 := (iff #44 #78)
+#76 := (= #38 #73)
+#70 := (ite #67 #35 f3)
+#74 := (= #70 #73)
+#75 := [rewrite]: #74
+#71 := (= #38 #70)
+#68 := (iff #10 #67)
+#69 := [rewrite]: #68
+#72 := [monotonicity #69]: #71
+#77 := [trans #72 #75]: #76
+#80 := [monotonicity #77]: #79
+#85 := [trans #80 #83]: #84
+#88 := [monotonicity #85]: #87
+#93 := [trans #88 #91]: #92
+#64 := (iff #16 #61)
+#52 := (iff #14 #44)
+#57 := (not #52)
+#62 := (iff #57 #61)
+#63 := [rewrite]: #62
+#58 := (iff #16 #57)
+#55 := (iff #15 #52)
+#49 := (iff #44 #14)
+#53 := (iff #49 #52)
+#54 := [rewrite]: #53
+#50 := (iff #15 #49)
+#47 := (iff #13 #44)
+#41 := (= #38 0::real)
+#45 := (iff #41 #44)
+#46 := [rewrite]: #45
+#42 := (iff #13 #41)
+#39 := (= #12 #38)
+#36 := (= #11 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#48 := [trans #43 #46]: #47
+#51 := [monotonicity #48]: #50
+#56 := [trans #51 #54]: #55
+#59 := [monotonicity #56]: #58
+#65 := [trans #59 #63]: #64
+#95 := [trans #65 #93]: #94
+#33 := [asserted]: #16
+#96 := [mp #33 #95]: #89
+#97 := (not #89)
+#110 := (or #14 #82 #97)
+#111 := [def-axiom]: #110
+#113 := [unit-resolution #111 #96]: #112
+#120 := [unit-resolution #113 #119]: #14
+#129 := [unit-resolution #120 #128]: false
+#132 := [lemma #129]: #131
+#133 := [unit-resolution #132 #121]: #82
+#135 := [mp #133 #125]: #14
+#108 := (or #60 #99)
+#106 := (or #60 #99 #97)
+#107 := [def-axiom]: #106
+#109 := [unit-resolution #107 #96]: #108
+#134 := [unit-resolution #109 #133]: #60
+#136 := [unit-resolution #134 #135]: false
+#137 := [lemma #136]: #130
+#104 := (or #67 #102)
+#105 := [def-axiom]: #104
+#143 := [unit-resolution #105 #137]: #67
+#138 := (= #35 0::real)
+#147 := (not #138)
+#157 := (iff #147 #99)
+#155 := (iff #138 #82)
+#103 := (= #35 #73)
+#100 := (or #66 #103)
+#101 := [def-axiom]: #100
+#154 := [unit-resolution #101 #143]: #103
+#156 := [monotonicity #154]: #155
+#158 := [monotonicity #156]: #157
+#139 := (<= #35 0::real)
+#145 := (not #139)
+#142 := [hypothesis]: #139
+#144 := [th-lemma #143 #142]: false
+#146 := [lemma #144]: #145
+#148 := (or #147 #139)
+#149 := [th-lemma]: #148
+#153 := [unit-resolution #149 #146]: #147
+#159 := [mp #153 #158]: #99
+#160 := [unit-resolution #113 #159]: #14
+#161 := (or #60 #66)
+#162 := [th-lemma]: #161
+[unit-resolution #162 #160 #143]: false
+unsat
+6655ab648d12420f565ba36d5ae332d6fbbff845 57 0
+#2 := false
+#36 := 0::real
+decl f4 :: real
+#9 := f4
+#33 := -1::real
+#34 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#35 := (+ f3 #34)
+#37 := (<= #35 0::real)
+#40 := (ite #37 f3 f4)
+#61 := (= f4 #40)
+#65 := (not #61)
+#47 := (* -1::real #40)
+#48 := (+ f4 #47)
+#46 := (>= #48 0::real)
+#53 := (not #46)
+#10 := (<= f3 f4)
+#11 := (ite #10 f3 f4)
+#12 := (<= #11 f4)
+#13 := (not #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #46)
+#43 := (<= #40 f4)
+#49 := (iff #43 #46)
+#50 := [rewrite]: #49
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#52 := [trans #45 #50]: #51
+#55 := [monotonicity #52]: #54
+#30 := [asserted]: #13
+#56 := [mp #30 #55]: #53
+#64 := [hypothesis]: #61
+#66 := (or #65 #46)
+#67 := [th-lemma]: #66
+#68 := [unit-resolution #67 #64 #56]: false
+#69 := [lemma #68]: #65
+#59 := (or #37 #61)
+#57 := [def-axiom]: #59
+#72 := [unit-resolution #57 #69]: #37
+#31 := (+ f3 #47)
+#71 := (>= #31 0::real)
+#60 := (= f3 #40)
+#62 := (not #37)
+#63 := (or #62 #60)
+#58 := [def-axiom]: #63
+#73 := [unit-resolution #58 #72]: #60
+#74 := (not #60)
+#75 := (or #74 #71)
+#76 := [th-lemma]: #75
+#77 := [unit-resolution #76 #73]: #71
+[th-lemma #77 #56 #72]: false
+unsat
+9adcfa237e60c42bd298fd44b174819c2b7e48c6 103 0
+#2 := false
+#8 := 0::real
+decl f3 :: real
+#9 := f3
+#34 := -1::real
+#35 := (* -1::real f3)
+#112 := (* -1::real #35)
+#113 := (+ f3 #112)
+#115 := (>= #113 0::real)
+#111 := (= f3 #35)
+#61 := (>= f3 0::real)
+#68 := (ite #61 f3 #35)
+#118 := (= #68 #35)
+#96 := (= #35 #68)
+#62 := (not #61)
+#107 := [hypothesis]: #61
+#73 := (= f3 #68)
+#97 := (or #62 #73)
+#98 := [def-axiom]: #97
+#108 := [unit-resolution #98 #107]: #73
+#95 := (not #73)
+#101 := (or #62 #95)
+#83 := (iff #62 #73)
+#12 := (- f3)
+#11 := (< f3 0::real)
+#13 := (ite #11 #12 f3)
+#14 := (= #13 f3)
+#10 := (<= 0::real f3)
+#15 := (iff #10 #14)
+#16 := (not #15)
+#88 := (iff #16 #83)
+#55 := (not #10)
+#38 := (ite #11 #35 f3)
+#44 := (= f3 #38)
+#56 := (iff #44 #55)
+#86 := (iff #56 #83)
+#80 := (iff #73 #62)
+#84 := (iff #80 #83)
+#85 := [rewrite]: #84
+#81 := (iff #56 #80)
+#78 := (iff #55 #62)
+#76 := (iff #10 #61)
+#77 := [rewrite]: #76
+#79 := [monotonicity #77]: #78
+#74 := (iff #44 #73)
+#71 := (= #38 #68)
+#65 := (ite #62 #35 f3)
+#69 := (= #65 #68)
+#70 := [rewrite]: #69
+#66 := (= #38 #65)
+#63 := (iff #11 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#72 := [trans #67 #70]: #71
+#75 := [monotonicity #72]: #74
+#82 := [monotonicity #75 #79]: #81
+#87 := [trans #82 #85]: #86
+#59 := (iff #16 #56)
+#49 := (iff #10 #44)
+#52 := (not #49)
+#57 := (iff #52 #56)
+#58 := [rewrite]: #57
+#53 := (iff #16 #52)
+#50 := (iff #15 #49)
+#47 := (iff #14 #44)
+#41 := (= #38 f3)
+#45 := (iff #41 #44)
+#46 := [rewrite]: #45
+#42 := (iff #14 #41)
+#39 := (= #13 #38)
+#36 := (= #12 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#48 := [trans #43 #46]: #47
+#51 := [monotonicity #48]: #50
+#54 := [monotonicity #51]: #53
+#60 := [trans #54 #58]: #59
+#89 := [trans #60 #87]: #88
+#33 := [asserted]: #16
+#90 := [mp #33 #89]: #83
+#93 := (not #83)
+#91 := (or #62 #95 #93)
+#100 := [def-axiom]: #91
+#102 := [unit-resolution #100 #90]: #101
+#109 := [unit-resolution #102 #108 #107]: false
+#110 := [lemma #109]: #62
+#99 := (or #61 #96)
+#94 := [def-axiom]: #99
+#116 := [unit-resolution #94 #110]: #96
+#119 := [symm #116]: #118
+#105 := (or #61 #73)
+#103 := (or #61 #73 #93)
+#104 := [def-axiom]: #103
+#106 := [unit-resolution #104 #90]: #105
+#117 := [unit-resolution #106 #110]: #73
+#120 := [trans #117 #119]: #111
+#121 := (not #111)
+#122 := (or #121 #115)
+#123 := [th-lemma]: #122
+#124 := [unit-resolution #123 #120]: #115
+[th-lemma #110 #124]: false
+unsat
+ee668ce9e0fa0c7fac3c07515b5e406674a29e92 103 0
+#2 := false
+#45 := 0::real
+decl f5 :: real
+#11 := f5
+decl f4 :: real
+#9 := f4
+#43 := -1::real
+#53 := (* -1::real f5)
+#63 := (+ f4 #53)
+#64 := (<= #63 0::real)
+#67 := (ite #64 f4 f5)
+#75 := (* -1::real #67)
+decl f3 :: real
+#8 := f3
+#76 := (+ f3 #75)
+#74 := (>= #76 0::real)
+#73 := (not #74)
+#54 := (+ f3 #53)
+#52 := (>= #54 0::real)
+#51 := (not #52)
+#47 := (* -1::real f4)
+#48 := (+ f3 #47)
+#46 := (>= #48 0::real)
+#44 := (not #46)
+#57 := (and #44 #51)
+#60 := (not #57)
+#81 := (or #60 #73)
+#84 := (not #81)
+#14 := (<= f4 f5)
+#15 := (ite #14 f4 f5)
+#16 := (< f3 #15)
+#12 := (< f3 f5)
+#10 := (< f3 f4)
+#13 := (and #10 #12)
+#17 := (implies #13 #16)
+#18 := (not #17)
+#87 := (iff #18 #84)
+#36 := (not #13)
+#37 := (or #36 #16)
+#40 := (not #37)
+#85 := (iff #40 #84)
+#82 := (iff #37 #81)
+#79 := (iff #16 #73)
+#70 := (< f3 #67)
+#77 := (iff #70 #73)
+#78 := [rewrite]: #77
+#71 := (iff #16 #70)
+#68 := (= #15 #67)
+#65 := (iff #14 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#72 := [monotonicity #69]: #71
+#80 := [trans #72 #78]: #79
+#61 := (iff #36 #60)
+#58 := (iff #13 #57)
+#55 := (iff #12 #51)
+#56 := [rewrite]: #55
+#49 := (iff #10 #44)
+#50 := [rewrite]: #49
+#59 := [monotonicity #50 #56]: #58
+#62 := [monotonicity #59]: #61
+#83 := [monotonicity #62 #80]: #82
+#86 := [monotonicity #83]: #85
+#41 := (iff #18 #40)
+#38 := (iff #17 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#88 := [trans #42 #86]: #87
+#35 := [asserted]: #18
+#89 := [mp #35 #88]: #84
+#93 := [not-or-elim #89]: #74
+#90 := [not-or-elim #89]: #57
+#92 := [and-elim #90]: #51
+#98 := (+ f5 #75)
+#115 := (<= #98 0::real)
+#104 := (= f5 #67)
+#105 := (not #64)
+#103 := (= f4 #67)
+#110 := (not #103)
+#100 := (+ f4 #75)
+#97 := (<= #100 0::real)
+#107 := (not #97)
+#91 := [and-elim #90]: #44
+#96 := [hypothesis]: #97
+#94 := [th-lemma #96 #91 #93]: false
+#108 := [lemma #94]: #107
+#109 := [hypothesis]: #103
+#111 := (or #110 #97)
+#112 := [th-lemma]: #111
+#113 := [unit-resolution #112 #109 #108]: false
+#114 := [lemma #113]: #110
+#106 := (or #105 #103)
+#101 := [def-axiom]: #106
+#117 := [unit-resolution #101 #114]: #105
+#102 := (or #64 #104)
+#99 := [def-axiom]: #102
+#118 := [unit-resolution #99 #117]: #104
+#119 := (not #104)
+#120 := (or #119 #115)
+#121 := [th-lemma]: #120
+#122 := [unit-resolution #121 #118]: #115
+[th-lemma #122 #92 #93]: false
+unsat
+c4a9e24c8934134e79e09f07b7517e3fb630224e 149 0
+#2 := false
+#9 := 0::real
+decl f3 :: real
+#8 := f3
+#34 := -1::real
+#35 := (* -1::real f3)
+#61 := (>= f3 0::real)
+#68 := (ite #61 f3 #35)
+#111 := (* -1::real #68)
+#156 := (+ f3 #111)
+#157 := (<= #156 0::real)
+#98 := (= f3 #68)
+#10 := (<= f3 0::real)
+#55 := (not #10)
+#78 := (+ f3 #68)
+#77 := (= #78 0::real)
+#93 := (not #77)
+#115 := [hypothesis]: #93
+#95 := (>= #78 0::real)
+#112 := (+ #35 #111)
+#113 := (<= #112 0::real)
+#73 := (= #35 #68)
+#62 := (not #61)
+#131 := (or #62 #77)
+#118 := (= f3 0::real)
+#109 := (or #10 #77)
+#85 := (iff #55 #77)
+#12 := (- f3)
+#11 := (< f3 0::real)
+#13 := (ite #11 #12 f3)
+#14 := (= #13 #12)
+#15 := (iff #10 #14)
+#16 := (not #15)
+#90 := (iff #16 #85)
+#38 := (ite #11 #35 f3)
+#44 := (= #35 #38)
+#56 := (iff #44 #55)
+#88 := (iff #56 #85)
+#82 := (iff #77 #55)
+#86 := (iff #82 #85)
+#87 := [rewrite]: #86
+#83 := (iff #56 #82)
+#80 := (iff #44 #77)
+#76 := (iff #73 #77)
+#79 := [rewrite]: #76
+#74 := (iff #44 #73)
+#71 := (= #38 #68)
+#65 := (ite #62 #35 f3)
+#69 := (= #65 #68)
+#70 := [rewrite]: #69
+#66 := (= #38 #65)
+#63 := (iff #11 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#72 := [trans #67 #70]: #71
+#75 := [monotonicity #72]: #74
+#81 := [trans #75 #79]: #80
+#84 := [monotonicity #81]: #83
+#89 := [trans #84 #87]: #88
+#59 := (iff #16 #56)
+#49 := (iff #10 #44)
+#52 := (not #49)
+#57 := (iff #52 #56)
+#58 := [rewrite]: #57
+#53 := (iff #16 #52)
+#50 := (iff #15 #49)
+#47 := (iff #14 #44)
+#41 := (= #38 #35)
+#45 := (iff #41 #44)
+#46 := [rewrite]: #45
+#42 := (iff #14 #41)
+#36 := (= #12 #35)
+#37 := [rewrite]: #36
+#39 := (= #13 #38)
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40 #37]: #42
+#48 := [trans #43 #46]: #47
+#51 := [monotonicity #48]: #50
+#54 := [monotonicity #51]: #53
+#60 := [trans #54 #58]: #59
+#91 := [trans #60 #89]: #90
+#33 := [asserted]: #16
+#92 := [mp #33 #91]: #85
+#102 := (not #85)
+#107 := (or #10 #77 #102)
+#108 := [def-axiom]: #107
+#110 := [unit-resolution #108 #92]: #109
+#116 := [unit-resolution #110 #115]: #10
+#117 := [hypothesis]: #61
+#119 := [th-lemma #117 #116]: #118
+#127 := (= #78 f3)
+#125 := (= #68 f3)
+#99 := (or #62 #98)
+#100 := [def-axiom]: #99
+#120 := [unit-resolution #100 #117]: #98
+#126 := [symm #120]: #125
+#123 := (= #78 #68)
+#121 := (= #68 #78)
+#122 := [th-lemma #117 #116]: #121
+#124 := [symm #122]: #123
+#128 := [trans #124 #126]: #127
+#129 := [trans #128 #119]: #77
+#130 := [unit-resolution #115 #129]: false
+#132 := [lemma #130]: #131
+#133 := [unit-resolution #132 #115]: #62
+#101 := (or #61 #73)
+#96 := [def-axiom]: #101
+#134 := [unit-resolution #96 #133]: #73
+#135 := (not #73)
+#136 := (or #135 #113)
+#137 := [th-lemma]: #136
+#138 := [unit-resolution #137 #134]: #113
+#139 := (not #113)
+#140 := (or #95 #139)
+#141 := [th-lemma]: #140
+#142 := [unit-resolution #141 #138]: #95
+#97 := (<= #78 0::real)
+#114 := (>= #112 0::real)
+#143 := (or #135 #114)
+#144 := [th-lemma]: #143
+#145 := [unit-resolution #144 #134]: #114
+#146 := (not #114)
+#147 := (or #97 #146)
+#148 := [th-lemma]: #147
+#149 := [unit-resolution #148 #145]: #97
+#151 := (not #95)
+#150 := (not #97)
+#152 := (or #77 #150 #151)
+#153 := [th-lemma]: #152
+#154 := [unit-resolution #153 #149 #142 #115]: false
+#155 := [lemma #154]: #77
+#105 := (or #55 #93)
+#103 := (or #55 #93 #102)
+#104 := [def-axiom]: #103
+#106 := [unit-resolution #104 #92]: #105
+#159 := [unit-resolution #106 #155]: #55
+#160 := (or #61 #10)
+#161 := [th-lemma]: #160
+#162 := [unit-resolution #161 #159]: #61
+#163 := [unit-resolution #100 #162]: #98
+#164 := (not #98)
+#165 := (or #164 #157)
+#166 := [th-lemma]: #165
+#167 := [unit-resolution #166 #163]: #157
+#168 := (or #93 #97)
+#169 := [th-lemma]: #168
+#170 := [unit-resolution #169 #155]: #97
+[th-lemma #159 #170 #167]: false
+unsat
+6621a3ffc07b1d1f7378f6c00c067bb0ce9ac306 86 0
+#2 := false
+decl f3 :: real
+#8 := f3
+decl f4 :: real
+#9 := f4
+#38 := 0::real
+#35 := -1::real
+#36 := (* -1::real f4)
+#37 := (+ f3 #36)
+#46 := (>= #37 0::real)
+#48 := (ite #46 f4 f3)
+#39 := (<= #37 0::real)
+#42 := (ite #39 f3 f4)
+#51 := (= #42 #48)
+#33 := (= f4 #48)
+#65 := (= f3 #48)
+#66 := (not #46)
+#71 := [hypothesis]: #66
+#69 := (or #46 #65)
+#70 := [def-axiom]: #69
+#72 := [unit-resolution #70 #71]: #65
+#77 := (= #42 f3)
+#61 := (= f3 #42)
+#73 := (or #46 #39)
+#74 := [th-lemma]: #73
+#75 := [unit-resolution #74 #71]: #39
+#63 := (not #39)
+#64 := (or #63 #61)
+#59 := [def-axiom]: #64
+#76 := [unit-resolution #59 #75]: #61
+#78 := [symm #76]: #77
+#79 := [trans #78 #72]: #51
+#54 := (not #51)
+#12 := (<= f4 f3)
+#13 := (ite #12 f4 f3)
+#10 := (<= f3 f4)
+#11 := (ite #10 f3 f4)
+#14 := (= #11 #13)
+#15 := (not #14)
+#55 := (iff #15 #54)
+#52 := (iff #14 #51)
+#49 := (= #13 #48)
+#45 := (iff #12 #46)
+#47 := [rewrite]: #45
+#50 := [monotonicity #47]: #49
+#43 := (= #11 #42)
+#40 := (iff #10 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#53 := [monotonicity #44 #50]: #52
+#56 := [monotonicity #53]: #55
+#32 := [asserted]: #15
+#57 := [mp #32 #56]: #54
+#80 := [unit-resolution #57 #79]: false
+#81 := [lemma #80]: #46
+#67 := (or #66 #33)
+#68 := [def-axiom]: #67
+#83 := [unit-resolution #68 #81]: #33
+#103 := (= #42 f4)
+#82 := (= f3 f4)
+#62 := (= f4 #42)
+#93 := (not #62)
+#94 := (iff #54 #93)
+#91 := (iff #51 #62)
+#89 := (iff #62 #51)
+#84 := (= #48 #42)
+#87 := (iff #84 #51)
+#88 := [commutativity]: #87
+#85 := (iff #62 #84)
+#86 := [monotonicity #83]: #85
+#90 := [trans #86 #88]: #89
+#92 := [symm #90]: #91
+#95 := [monotonicity #92]: #94
+#96 := [mp #57 #95]: #93
+#60 := (or #39 #62)
+#58 := [def-axiom]: #60
+#97 := [unit-resolution #58 #96]: #39
+#98 := (or #82 #63 #66)
+#99 := [th-lemma]: #98
+#100 := [unit-resolution #99 #97 #81]: #82
+#101 := [unit-resolution #59 #97]: #61
+#102 := [symm #101]: #77
+#104 := [trans #102 #100]: #103
+#105 := [trans #104 #83]: #51
+[unit-resolution #57 #105]: false
+unsat
+46bd95326d38ccebb90178efd68b73f641b282a9 68 0
+#2 := false
+#8 := 0::real
+decl f3 :: real
+#9 := f3
+#11 := (<= f3 0::real)
+#12 := (ite #11 f3 0::real)
+#13 := (= #12 0::real)
+#76 := (= f3 0::real)
+#50 := (>= f3 0::real)
+#51 := (not #50)
+#59 := (or #13 #51)
+#64 := (not #59)
+#10 := (<= 0::real f3)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#67 := (iff #15 #64)
+#33 := (= 0::real #12)
+#39 := (not #10)
+#40 := (or #39 #33)
+#45 := (not #40)
+#65 := (iff #45 #64)
+#62 := (iff #40 #59)
+#56 := (or #51 #13)
+#60 := (iff #56 #59)
+#61 := [rewrite]: #60
+#57 := (iff #40 #56)
+#54 := (iff #33 #13)
+#55 := [rewrite]: #54
+#52 := (iff #39 #51)
+#48 := (iff #10 #50)
+#49 := [rewrite]: #48
+#53 := [monotonicity #49]: #52
+#58 := [monotonicity #53 #55]: #57
+#63 := [trans #58 #61]: #62
+#66 := [monotonicity #63]: #65
+#46 := (iff #15 #45)
+#43 := (iff #14 #40)
+#36 := (implies #10 #33)
+#41 := (iff #36 #40)
+#42 := [rewrite]: #41
+#37 := (iff #14 #36)
+#34 := (iff #13 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#44 := [trans #38 #42]: #43
+#47 := [monotonicity #44]: #46
+#68 := [trans #47 #66]: #67
+#32 := [asserted]: #15
+#69 := [mp #32 #68]: #64
+#72 := [not-or-elim #69]: #50
+#70 := (not #13)
+#71 := [not-or-elim #69]: #70
+#78 := (or #11 #13)
+#79 := [def-axiom]: #78
+#77 := [unit-resolution #79 #71]: #11
+#81 := (not #11)
+#75 := (or #76 #81 #51)
+#73 := [th-lemma]: #75
+#84 := [unit-resolution #73 #77 #72]: #76
+#86 := (= #12 f3)
+#80 := (= f3 #12)
+#82 := (or #81 #80)
+#83 := [def-axiom]: #82
+#85 := [unit-resolution #83 #77]: #80
+#87 := [symm #85]: #86
+#88 := [trans #87 #84]: #13
+[unit-resolution #71 #88]: false
+unsat
+fe8f01cf58e022d252300f3afc6a7b8ad4a81839 114 0
+#2 := false
+#9 := 0::real
+decl f3 :: real
+#8 := f3
+#35 := -1::real
+#36 := (* -1::real f3)
+#67 := (>= f3 0::real)
+#74 := (ite #67 f3 #36)
+#88 := (* -1::real #74)
+#127 := (+ #36 #88)
+#137 := (<= #127 0::real)
+#114 := (= #36 #74)
+#68 := (not #67)
+#125 := (+ f3 #88)
+#126 := (<= #125 0::real)
+#113 := (= f3 #74)
+#128 := [hypothesis]: #67
+#115 := (or #68 #113)
+#116 := [def-axiom]: #115
+#129 := [unit-resolution #116 #128]: #113
+#130 := (not #113)
+#131 := (or #130 #126)
+#132 := [th-lemma]: #131
+#133 := [unit-resolution #132 #129]: #126
+#83 := (>= #74 0::real)
+#82 := (not #83)
+#94 := (ite #83 #74 #88)
+#99 := (= #74 #94)
+#102 := (not #99)
+#11 := (- f3)
+#10 := (< f3 0::real)
+#12 := (ite #10 #11 f3)
+#14 := (- #12)
+#13 := (< #12 0::real)
+#15 := (ite #13 #14 #12)
+#16 := (= #15 #12)
+#17 := (not #16)
+#105 := (iff #17 #102)
+#39 := (ite #10 #36 f3)
+#48 := (* -1::real #39)
+#42 := (< #39 0::real)
+#53 := (ite #42 #48 #39)
+#59 := (= #39 #53)
+#64 := (not #59)
+#103 := (iff #64 #102)
+#100 := (iff #59 #99)
+#97 := (= #53 #94)
+#91 := (ite #82 #88 #74)
+#95 := (= #91 #94)
+#96 := [rewrite]: #95
+#92 := (= #53 #91)
+#77 := (= #39 #74)
+#71 := (ite #68 #36 f3)
+#75 := (= #71 #74)
+#76 := [rewrite]: #75
+#72 := (= #39 #71)
+#69 := (iff #10 #68)
+#70 := [rewrite]: #69
+#73 := [monotonicity #70]: #72
+#78 := [trans #73 #76]: #77
+#89 := (= #48 #88)
+#90 := [monotonicity #78]: #89
+#86 := (iff #42 #82)
+#79 := (< #74 0::real)
+#84 := (iff #79 #82)
+#85 := [rewrite]: #84
+#80 := (iff #42 #79)
+#81 := [monotonicity #78]: #80
+#87 := [trans #81 #85]: #86
+#93 := [monotonicity #87 #90 #78]: #92
+#98 := [trans #93 #96]: #97
+#101 := [monotonicity #78 #98]: #100
+#104 := [monotonicity #101]: #103
+#65 := (iff #17 #64)
+#62 := (iff #16 #59)
+#56 := (= #53 #39)
+#60 := (iff #56 #59)
+#61 := [rewrite]: #60
+#57 := (iff #16 #56)
+#40 := (= #12 #39)
+#37 := (= #11 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#54 := (= #15 #53)
+#51 := (= #14 #48)
+#45 := (- #39)
+#49 := (= #45 #48)
+#50 := [rewrite]: #49
+#46 := (= #14 #45)
+#47 := [monotonicity #41]: #46
+#52 := [trans #47 #50]: #51
+#43 := (iff #13 #42)
+#44 := [monotonicity #41]: #43
+#55 := [monotonicity #44 #52 #41]: #54
+#58 := [monotonicity #55 #41]: #57
+#63 := [trans #58 #61]: #62
+#66 := [monotonicity #63]: #65
+#106 := [trans #66 #104]: #105
+#34 := [asserted]: #17
+#107 := [mp #34 #106]: #102
+#108 := (or #82 #99)
+#117 := [def-axiom]: #108
+#134 := [unit-resolution #117 #107]: #82
+#135 := [th-lemma #128 #134 #133]: false
+#136 := [lemma #135]: #68
+#111 := (or #67 #114)
+#112 := [def-axiom]: #111
+#139 := [unit-resolution #112 #136]: #114
+#140 := (not #114)
+#141 := (or #140 #137)
+#142 := [th-lemma]: #141
+#143 := [unit-resolution #142 #139]: #137
+[th-lemma #136 #134 #143]: false
+unsat
+0bc87aa75b23fa78f642cf1f3aa485350d8be4f2 124 0
+#2 := false
+#13 := 0::real
+decl f4 :: real
+#9 := f4
+decl f3 :: real
+#8 := f3
+#36 := -1::real
+#38 := (* -1::real f4)
+#51 := (+ f3 #38)
+#52 := (<= #51 0::real)
+#55 := (ite #52 f3 f4)
+#103 := (* -1::real #55)
+#104 := (+ f3 #103)
+#106 := (>= #104 0::real)
+#91 := (= f3 #55)
+#105 := (+ f4 #103)
+#123 := (>= #105 0::real)
+#92 := (= f4 #55)
+#93 := (not #52)
+#134 := [hypothesis]: #93
+#90 := (or #52 #92)
+#88 := [def-axiom]: #90
+#135 := [unit-resolution #88 #134]: #92
+#126 := (not #92)
+#127 := (or #126 #123)
+#128 := [th-lemma]: #127
+#136 := [unit-resolution #128 #135]: #123
+#37 := (* -1::real f3)
+#39 := (+ #37 #38)
+#12 := (+ f3 f4)
+#58 := (>= #12 0::real)
+#65 := (ite #58 #12 #39)
+#73 := (* -1::real #65)
+#74 := (+ #55 #73)
+#75 := (<= #74 0::real)
+#80 := (not #75)
+#15 := (- #12)
+#14 := (< #12 0::real)
+#16 := (ite #14 #15 #12)
+#10 := (<= f3 f4)
+#11 := (ite #10 f3 f4)
+#17 := (<= #11 #16)
+#18 := (not #17)
+#83 := (iff #18 #80)
+#42 := (ite #14 #39 #12)
+#45 := (<= #11 #42)
+#48 := (not #45)
+#81 := (iff #48 #80)
+#78 := (iff #45 #75)
+#70 := (<= #55 #65)
+#76 := (iff #70 #75)
+#77 := [rewrite]: #76
+#71 := (iff #45 #70)
+#68 := (= #42 #65)
+#59 := (not #58)
+#62 := (ite #59 #39 #12)
+#66 := (= #62 #65)
+#67 := [rewrite]: #66
+#63 := (= #42 #62)
+#60 := (iff #14 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#69 := [trans #64 #67]: #68
+#56 := (= #11 #55)
+#53 := (iff #10 #52)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#72 := [monotonicity #57 #69]: #71
+#79 := [trans #72 #77]: #78
+#82 := [monotonicity #79]: #81
+#49 := (iff #18 #48)
+#46 := (iff #17 #45)
+#43 := (= #16 #42)
+#40 := (= #15 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#47 := [monotonicity #44]: #46
+#50 := [monotonicity #47]: #49
+#84 := [trans #50 #82]: #83
+#35 := [asserted]: #18
+#85 := [mp #35 #84]: #80
+#102 := (+ #12 #73)
+#122 := (<= #102 0::real)
+#86 := (= #12 #65)
+#108 := [hypothesis]: #59
+#120 := (or #93 #58)
+#107 := [hypothesis]: #52
+#100 := (+ #39 #73)
+#101 := (<= #100 0::real)
+#95 := (= #39 #65)
+#98 := (or #58 #95)
+#99 := [def-axiom]: #98
+#109 := [unit-resolution #99 #108]: #95
+#110 := (not #95)
+#111 := (or #110 #101)
+#112 := [th-lemma]: #111
+#113 := [unit-resolution #112 #109]: #101
+#94 := (or #93 #91)
+#89 := [def-axiom]: #94
+#114 := [unit-resolution #89 #107]: #91
+#115 := (not #91)
+#116 := (or #115 #106)
+#117 := [th-lemma]: #116
+#118 := [unit-resolution #117 #114]: #106
+#119 := [th-lemma #108 #118 #113 #85 #107]: false
+#121 := [lemma #119]: #120
+#124 := [unit-resolution #121 #108]: #93
+#125 := [unit-resolution #88 #124]: #92
+#129 := [unit-resolution #128 #125]: #123
+#130 := [th-lemma #113 #85 #108 #124 #129]: false
+#131 := [lemma #130]: #58
+#96 := (or #59 #86)
+#97 := [def-axiom]: #96
+#137 := [unit-resolution #97 #131]: #86
+#138 := (not #86)
+#139 := (or #138 #122)
+#140 := [th-lemma]: #139
+#141 := [unit-resolution #140 #137]: #122
+#142 := [th-lemma #134 #131 #141 #85 #136]: false
+#143 := [lemma #142]: #52
+#144 := [unit-resolution #89 #143]: #91
+#145 := [unit-resolution #117 #144]: #106
+[th-lemma #131 #143 #141 #85 #145]: false
+unsat
+80cd3c3fe766c682a1b2d6b1e7013b88feafd6ca 57 0
+#2 := false
+#36 := 0::real
+decl f4 :: real
+#9 := f4
+#33 := -1::real
+#34 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#35 := (+ f3 #34)
+#37 := (<= #35 0::real)
+#40 := (ite #37 f4 f3)
+#61 := (= f3 #40)
+#65 := (not #61)
+#46 := (* -1::real #40)
+#47 := (+ f3 #46)
+#48 := (<= #47 0::real)
+#53 := (not #48)
+#10 := (<= f3 f4)
+#11 := (ite #10 f4 f3)
+#12 := (<= f3 #11)
+#13 := (not #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #48)
+#43 := (<= f3 #40)
+#49 := (iff #43 #48)
+#50 := [rewrite]: #49
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#52 := [trans #45 #50]: #51
+#55 := [monotonicity #52]: #54
+#30 := [asserted]: #13
+#56 := [mp #30 #55]: #53
+#64 := [hypothesis]: #61
+#66 := (or #65 #48)
+#67 := [th-lemma]: #66
+#68 := [unit-resolution #67 #64 #56]: false
+#69 := [lemma #68]: #65
+#59 := (or #37 #61)
+#57 := [def-axiom]: #59
+#72 := [unit-resolution #57 #69]: #37
+#31 := (+ f4 #46)
+#70 := (<= #31 0::real)
+#60 := (= f4 #40)
+#62 := (not #37)
+#63 := (or #62 #60)
+#58 := [def-axiom]: #63
+#73 := [unit-resolution #58 #72]: #60
+#74 := (not #60)
+#75 := (or #74 #70)
+#76 := [th-lemma]: #75
+#77 := [unit-resolution #76 #73]: #70
+[th-lemma #77 #56 #72]: false
+unsat
+6eb0fb73353335cf541aa0794ee6ca4d2c180864 57 0
+#2 := false
+#35 := 0::real
+decl f4 :: real
+#9 := f4
+decl f3 :: real
+#8 := f3
+#33 := -1::real
+#37 := (* -1::real f4)
+#38 := (+ f3 #37)
+#36 := (>= #38 0::real)
+#40 := (ite #36 f3 f4)
+#46 := (* -1::real #40)
+#47 := (+ f3 #46)
+#48 := (<= #47 0::real)
+#53 := (not #48)
+#10 := (<= f4 f3)
+#11 := (ite #10 f3 f4)
+#12 := (<= f3 #11)
+#13 := (not #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #48)
+#43 := (<= f3 #40)
+#49 := (iff #43 #48)
+#50 := [rewrite]: #49
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#34 := (iff #10 #36)
+#39 := [rewrite]: #34
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#52 := [trans #45 #50]: #51
+#55 := [monotonicity #52]: #54
+#30 := [asserted]: #13
+#56 := [mp #30 #55]: #53
+#60 := (= f3 #40)
+#31 := (+ f4 #46)
+#64 := (<= #31 0::real)
+#61 := (= f4 #40)
+#62 := (not #36)
+#66 := [hypothesis]: #62
+#59 := (or #36 #61)
+#57 := [def-axiom]: #59
+#67 := [unit-resolution #57 #66]: #61
+#68 := (not #61)
+#69 := (or #68 #64)
+#70 := [th-lemma]: #69
+#71 := [unit-resolution #70 #67]: #64
+#72 := [th-lemma #56 #66 #71]: false
+#73 := [lemma #72]: #36
+#63 := (or #62 #60)
+#58 := [def-axiom]: #63
+#74 := [unit-resolution #58 #73]: #60
+#75 := (not #60)
+#76 := (or #75 #48)
+#77 := [th-lemma]: #76
+[unit-resolution #77 #74 #56]: false
+unsat
+20f752e2f472eccd72355373443410a7257bcab2 18 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := (<= f3 f3)
+#10 := (not #9)
+#37 := (iff #10 false)
+#1 := true
+#32 := (not true)
+#35 := (iff #32 false)
+#36 := [rewrite]: #35
+#33 := (iff #10 #32)
+#30 := (iff #9 true)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31]: #33
+#38 := [trans #34 #36]: #37
+#27 := [asserted]: #10
+[mp #27 #38]: false
+unsat
+7294c1769d42d53cd19fbaf8cd8b1759222d3816 103 0
+#2 := false
+#45 := 0::real
+decl f3 :: real
+#8 := f3
+decl f5 :: real
+#11 := f5
+#43 := -1::real
+#51 := (* -1::real f5)
+#63 := (+ f3 #51)
+#64 := (<= #63 0::real)
+#67 := (ite #64 f5 f3)
+#73 := (* -1::real #67)
+decl f4 :: real
+#9 := f4
+#74 := (+ f4 #73)
+#75 := (<= #74 0::real)
+#76 := (not #75)
+#52 := (+ f4 #51)
+#53 := (<= #52 0::real)
+#54 := (not #53)
+#47 := (* -1::real f4)
+#48 := (+ f3 #47)
+#46 := (>= #48 0::real)
+#44 := (not #46)
+#57 := (and #44 #54)
+#60 := (not #57)
+#81 := (or #60 #76)
+#84 := (not #81)
+#14 := (<= f3 f5)
+#15 := (ite #14 f5 f3)
+#16 := (< #15 f4)
+#12 := (< f5 f4)
+#10 := (< f3 f4)
+#13 := (and #10 #12)
+#17 := (implies #13 #16)
+#18 := (not #17)
+#87 := (iff #18 #84)
+#36 := (not #13)
+#37 := (or #36 #16)
+#40 := (not #37)
+#85 := (iff #40 #84)
+#82 := (iff #37 #81)
+#79 := (iff #16 #76)
+#70 := (< #67 f4)
+#77 := (iff #70 #76)
+#78 := [rewrite]: #77
+#71 := (iff #16 #70)
+#68 := (= #15 #67)
+#65 := (iff #14 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#72 := [monotonicity #69]: #71
+#80 := [trans #72 #78]: #79
+#61 := (iff #36 #60)
+#58 := (iff #13 #57)
+#55 := (iff #12 #54)
+#56 := [rewrite]: #55
+#49 := (iff #10 #44)
+#50 := [rewrite]: #49
+#59 := [monotonicity #50 #56]: #58
+#62 := [monotonicity #59]: #61
+#83 := [monotonicity #62 #80]: #82
+#86 := [monotonicity #83]: #85
+#41 := (iff #18 #40)
+#38 := (iff #17 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#88 := [trans #42 #86]: #87
+#35 := [asserted]: #18
+#89 := [mp #35 #88]: #84
+#93 := [not-or-elim #89]: #75
+#90 := [not-or-elim #89]: #57
+#91 := [and-elim #90]: #44
+#97 := (+ f3 #73)
+#116 := (>= #97 0::real)
+#104 := (= f3 #67)
+#105 := (not #64)
+#103 := (= f5 #67)
+#110 := (not #103)
+#100 := (+ f5 #73)
+#98 := (>= #100 0::real)
+#107 := (not #98)
+#92 := [and-elim #90]: #54
+#96 := [hypothesis]: #98
+#94 := [th-lemma #96 #92 #93]: false
+#108 := [lemma #94]: #107
+#109 := [hypothesis]: #103
+#111 := (or #110 #98)
+#112 := [th-lemma]: #111
+#113 := [unit-resolution #112 #109 #108]: false
+#114 := [lemma #113]: #110
+#106 := (or #105 #103)
+#101 := [def-axiom]: #106
+#117 := [unit-resolution #101 #114]: #105
+#102 := (or #64 #104)
+#99 := [def-axiom]: #102
+#118 := [unit-resolution #99 #117]: #104
+#119 := (not #104)
+#120 := (or #119 #116)
+#121 := [th-lemma]: #120
+#122 := [unit-resolution #121 #118]: #116
+[th-lemma #122 #91 #93]: false
+unsat
+de5d01d854b7029d707ff72bb7662d8b73532863 50 0
+#2 := false
+#44 := 0::real
+decl f4 :: real
+#9 := f4
+#41 := -1::real
+#42 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#43 := (+ f3 #42)
+#45 := (<= #43 0::real)
+#51 := -3::real
+#52 := (* -3::real f4)
+#11 := 3::real
+#12 := (* 3::real f3)
+#53 := (+ #12 #52)
+#54 := (<= #53 0::real)
+#48 := (not #45)
+#57 := (or #48 #54)
+#60 := (not #57)
+#13 := (* 3::real f4)
+#14 := (<= #12 #13)
+#10 := (<= f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#63 := (iff #16 #60)
+#34 := (not #10)
+#35 := (or #34 #14)
+#38 := (not #35)
+#61 := (iff #38 #60)
+#58 := (iff #35 #57)
+#55 := (iff #14 #54)
+#56 := [rewrite]: #55
+#49 := (iff #34 #48)
+#46 := (iff #10 #45)
+#47 := [rewrite]: #46
+#50 := [monotonicity #47]: #49
+#59 := [monotonicity #50 #56]: #58
+#62 := [monotonicity #59]: #61
+#39 := (iff #16 #38)
+#36 := (iff #15 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#64 := [trans #40 #62]: #63
+#33 := [asserted]: #16
+#65 := [mp #33 #64]: #60
+#66 := [not-or-elim #65]: #45
+#67 := (not #54)
+#68 := [not-or-elim #65]: #67
+[th-lemma #68 #66]: false
+unsat
+aa7d3312f6710561997326a18f2cc9732070e79e 88 0
+#2 := false
+decl f4 :: real
+#9 := f4
+decl f3 :: real
+#8 := f3
+#38 := 0::real
+#35 := -1::real
+#36 := (* -1::real f4)
+#37 := (+ f3 #36)
+#46 := (>= #37 0::real)
+#48 := (ite #46 f3 f4)
+#39 := (<= #37 0::real)
+#42 := (ite #39 f4 f3)
+#51 := (= #42 #48)
+#33 := (= f3 #48)
+#65 := (= f4 #48)
+#66 := (not #46)
+#71 := [hypothesis]: #66
+#69 := (or #46 #65)
+#70 := [def-axiom]: #69
+#72 := [unit-resolution #70 #71]: #65
+#77 := (= #42 f4)
+#61 := (= f4 #42)
+#73 := (or #46 #39)
+#74 := [th-lemma]: #73
+#75 := [unit-resolution #74 #71]: #39
+#63 := (not #39)
+#64 := (or #63 #61)
+#59 := [def-axiom]: #64
+#76 := [unit-resolution #59 #75]: #61
+#78 := [symm #76]: #77
+#79 := [trans #78 #72]: #51
+#54 := (not #51)
+#12 := (<= f4 f3)
+#13 := (ite #12 f3 f4)
+#10 := (<= f3 f4)
+#11 := (ite #10 f4 f3)
+#14 := (= #11 #13)
+#15 := (not #14)
+#55 := (iff #15 #54)
+#52 := (iff #14 #51)
+#49 := (= #13 #48)
+#45 := (iff #12 #46)
+#47 := [rewrite]: #45
+#50 := [monotonicity #47]: #49
+#43 := (= #11 #42)
+#40 := (iff #10 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#53 := [monotonicity #44 #50]: #52
+#56 := [monotonicity #53]: #55
+#32 := [asserted]: #15
+#57 := [mp #32 #56]: #54
+#80 := [unit-resolution #57 #79]: false
+#81 := [lemma #80]: #46
+#67 := (or #66 #33)
+#68 := [def-axiom]: #67
+#83 := [unit-resolution #68 #81]: #33
+#107 := (= #42 f3)
+#105 := (= f4 f3)
+#82 := (= f3 f4)
+#62 := (= f3 #42)
+#95 := (not #62)
+#96 := (iff #54 #95)
+#93 := (iff #51 #62)
+#91 := (iff #62 #51)
+#86 := (= #48 #42)
+#89 := (iff #86 #51)
+#90 := [commutativity]: #89
+#87 := (iff #62 #86)
+#88 := [monotonicity #83]: #87
+#92 := [trans #88 #90]: #91
+#94 := [symm #92]: #93
+#97 := [monotonicity #94]: #96
+#98 := [mp #57 #97]: #95
+#60 := (or #39 #62)
+#58 := [def-axiom]: #60
+#99 := [unit-resolution #58 #98]: #39
+#101 := (or #82 #63 #66)
+#102 := [th-lemma]: #101
+#103 := [unit-resolution #102 #99 #81]: #82
+#106 := [symm #103]: #105
+#100 := [unit-resolution #59 #99]: #61
+#104 := [symm #100]: #77
+#108 := [trans #104 #106]: #107
+#109 := [trans #108 #83]: #51
+[unit-resolution #57 #109]: false
+unsat
+78432a7ec8ec5313cf1224b5d36cefc0e44a3f9a 55 0
+#2 := false
+#43 := 0::real
+decl f4 :: real
+#9 := f4
+#56 := -3::real
+#59 := (* -3::real f4)
+decl f3 :: real
+#8 := f3
+#11 := 3::real
+#12 := (* 3::real f3)
+#60 := (+ #12 #59)
+#58 := (>= #60 0::real)
+#57 := (not #58)
+#41 := -1::real
+#45 := (* -1::real f4)
+#46 := (+ f3 #45)
+#44 := (>= #46 0::real)
+#63 := (or #44 #57)
+#66 := (not #63)
+#13 := (* 3::real f4)
+#14 := (< #12 #13)
+#10 := (< f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#69 := (iff #16 #66)
+#34 := (not #10)
+#35 := (or #34 #14)
+#38 := (not #35)
+#67 := (iff #38 #66)
+#64 := (iff #35 #63)
+#61 := (iff #14 #57)
+#62 := [rewrite]: #61
+#54 := (iff #34 #44)
+#42 := (not #44)
+#49 := (not #42)
+#52 := (iff #49 #44)
+#53 := [rewrite]: #52
+#50 := (iff #34 #49)
+#47 := (iff #10 #42)
+#48 := [rewrite]: #47
+#51 := [monotonicity #48]: #50
+#55 := [trans #51 #53]: #54
+#65 := [monotonicity #55 #62]: #64
+#68 := [monotonicity #65]: #67
+#39 := (iff #16 #38)
+#36 := (iff #15 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#70 := [trans #40 #68]: #69
+#33 := [asserted]: #16
+#71 := [mp #33 #70]: #66
+#73 := [not-or-elim #71]: #58
+#72 := [not-or-elim #71]: #42
+[th-lemma #72 #73]: false
+unsat
+16abee9f0675672a15a1cf601bbd7cd463542971 66 0
+#2 := false
+decl f3 :: real
+#9 := f3
+#8 := 0::real
+#11 := (<= f3 0::real)
+#12 := (ite #11 0::real f3)
+#33 := (= f3 #12)
+#84 := (= 0::real #12)
+#78 := (= #12 0::real)
+#68 := (not #33)
+#50 := (>= f3 0::real)
+#51 := (not #50)
+#57 := (or #33 #51)
+#62 := (not #57)
+#13 := (= #12 f3)
+#10 := (<= 0::real f3)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#65 := (iff #15 #62)
+#39 := (not #10)
+#40 := (or #39 #33)
+#45 := (not #40)
+#63 := (iff #45 #62)
+#60 := (iff #40 #57)
+#54 := (or #51 #33)
+#58 := (iff #54 #57)
+#59 := [rewrite]: #58
+#55 := (iff #40 #54)
+#52 := (iff #39 #51)
+#48 := (iff #10 #50)
+#49 := [rewrite]: #48
+#53 := [monotonicity #49]: #52
+#56 := [monotonicity #53]: #55
+#61 := [trans #56 #59]: #60
+#64 := [monotonicity #61]: #63
+#46 := (iff #15 #45)
+#43 := (iff #14 #40)
+#36 := (implies #10 #33)
+#41 := (iff #36 #40)
+#42 := [rewrite]: #41
+#37 := (iff #14 #36)
+#34 := (iff #13 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#44 := [trans #38 #42]: #43
+#47 := [monotonicity #44]: #46
+#66 := [trans #47 #64]: #65
+#32 := [asserted]: #15
+#67 := [mp #32 #66]: #62
+#69 := [not-or-elim #67]: #68
+#76 := (or #11 #33)
+#77 := [def-axiom]: #76
+#75 := [unit-resolution #77 #69]: #11
+#79 := (not #11)
+#80 := (or #79 #78)
+#81 := [def-axiom]: #80
+#73 := [unit-resolution #81 #75]: #78
+#85 := [symm #73]: #84
+#74 := (= f3 0::real)
+#70 := [not-or-elim #67]: #50
+#71 := (or #74 #79 #51)
+#82 := [th-lemma]: #71
+#83 := [unit-resolution #82 #75 #70]: #74
+#86 := [trans #83 #85]: #33
+[unit-resolution #69 #86]: false
+unsat
+6b577a8e26cad5ef5e776e0c3cf6f19a5beeec9c 52 0
+#2 := false
+#40 := 0::real
+decl f4 :: real
+#9 := f4
+#38 := -1::real
+#42 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#43 := (+ f3 #42)
+#53 := (<= #43 0::real)
+#66 := (not #53)
+#41 := (>= #43 0::real)
+#56 := (or #41 #53)
+#59 := (not #56)
+#11 := (<= f3 f4)
+#10 := (< f3 f4)
+#12 := (implies #10 #11)
+#13 := (not #12)
+#62 := (iff #13 #59)
+#31 := (not #10)
+#32 := (or #31 #11)
+#35 := (not #32)
+#60 := (iff #35 #59)
+#57 := (iff #32 #56)
+#54 := (iff #11 #53)
+#55 := [rewrite]: #54
+#51 := (iff #31 #41)
+#39 := (not #41)
+#46 := (not #39)
+#49 := (iff #46 #41)
+#50 := [rewrite]: #49
+#47 := (iff #31 #46)
+#44 := (iff #10 #39)
+#45 := [rewrite]: #44
+#48 := [monotonicity #45]: #47
+#52 := [trans #48 #50]: #51
+#58 := [monotonicity #52 #55]: #57
+#61 := [monotonicity #58]: #60
+#36 := (iff #13 #35)
+#33 := (iff #12 #32)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#63 := [trans #37 #61]: #62
+#30 := [asserted]: #13
+#64 := [mp #30 #63]: #59
+#67 := [not-or-elim #64]: #66
+#65 := [not-or-elim #64]: #39
+#75 := (or #53 #41)
+#76 := [th-lemma]: #75
+#77 := [unit-resolution #76 #65]: #53
+[unit-resolution #77 #67]: false
+unsat
+69ba0c9fc19b8d967fe68219b563ee3645949198 228 0
+#2 := false
+#9 := 0::real
+decl f4 :: real
+#14 := f4
+#40 := -1::real
+#55 := (* -1::real f4)
+#91 := (>= f4 0::real)
+#98 := (ite #91 f4 #55)
+#103 := (* -1::real #98)
+#159 := (+ f4 #103)
+#160 := (<= #159 0::real)
+#134 := (= f4 #98)
+decl f3 :: real
+#8 := f3
+#109 := (+ f3 #55)
+#110 := (<= #109 0::real)
+#113 := (ite #110 f4 f3)
+#155 := (* -1::real #113)
+#180 := (+ f3 #155)
+#190 := (<= #180 0::real)
+#146 := (= f3 #113)
+#147 := (not #110)
+#76 := (>= f3 0::real)
+#161 := (+ #55 #103)
+#179 := (<= #161 0::real)
+#200 := (not #179)
+#77 := (not #76)
+#168 := [hypothesis]: #77
+#145 := (= f4 #113)
+#205 := (not #145)
+#156 := (+ f4 #155)
+#157 := (<= #156 0::real)
+#176 := (not #157)
+#188 := (or #176 #76)
+#132 := (= #55 #98)
+#92 := (not #91)
+#174 := [hypothesis]: #157
+#177 := (or #92 #176 #76)
+#162 := [hypothesis]: #91
+#141 := (or #92 #134)
+#142 := [def-axiom]: #141
+#163 := [unit-resolution #142 #162]: #134
+#164 := (not #134)
+#165 := (or #164 #160)
+#166 := [th-lemma]: #165
+#167 := [unit-resolution #166 #163]: #160
+#41 := (* -1::real f3)
+#83 := (ite #76 f3 #41)
+#88 := (* -1::real #83)
+#152 := (+ #41 #88)
+#153 := (<= #152 0::real)
+#138 := (= #41 #83)
+#135 := (or #76 #138)
+#136 := [def-axiom]: #135
+#169 := [unit-resolution #136 #168]: #138
+#170 := (not #138)
+#171 := (or #170 #153)
+#172 := [th-lemma]: #171
+#173 := [unit-resolution #172 #169]: #153
+#122 := (+ #98 #113)
+#123 := (+ #83 #122)
+#120 := (>= #123 0::real)
+#126 := (not #120)
+#19 := (<= f3 f4)
+#20 := (ite #19 f4 f3)
+#16 := (- f4)
+#15 := (< f4 0::real)
+#17 := (ite #15 #16 f4)
+#11 := (- f3)
+#10 := (< f3 0::real)
+#12 := (ite #10 #11 f3)
+#13 := (- #12)
+#18 := (- #13 #17)
+#21 := (<= #18 #20)
+#22 := (not #21)
+#129 := (iff #22 #126)
+#58 := (ite #15 #55 f4)
+#64 := (* -1::real #58)
+#44 := (ite #10 #41 f3)
+#50 := (* -1::real #44)
+#65 := (+ #50 #64)
+#70 := (<= #65 #20)
+#73 := (not #70)
+#127 := (iff #73 #126)
+#124 := (iff #70 #120)
+#106 := (+ #88 #103)
+#116 := (<= #106 #113)
+#119 := (iff #116 #120)
+#121 := [rewrite]: #119
+#117 := (iff #70 #116)
+#114 := (= #20 #113)
+#111 := (iff #19 #110)
+#112 := [rewrite]: #111
+#115 := [monotonicity #112]: #114
+#107 := (= #65 #106)
+#104 := (= #64 #103)
+#101 := (= #58 #98)
+#95 := (ite #92 #55 f4)
+#99 := (= #95 #98)
+#100 := [rewrite]: #99
+#96 := (= #58 #95)
+#93 := (iff #15 #92)
+#94 := [rewrite]: #93
+#97 := [monotonicity #94]: #96
+#102 := [trans #97 #100]: #101
+#105 := [monotonicity #102]: #104
+#89 := (= #50 #88)
+#86 := (= #44 #83)
+#80 := (ite #77 #41 f3)
+#84 := (= #80 #83)
+#85 := [rewrite]: #84
+#81 := (= #44 #80)
+#78 := (iff #10 #77)
+#79 := [rewrite]: #78
+#82 := [monotonicity #79]: #81
+#87 := [trans #82 #85]: #86
+#90 := [monotonicity #87]: #89
+#108 := [monotonicity #90 #105]: #107
+#118 := [monotonicity #108 #115]: #117
+#125 := [trans #118 #121]: #124
+#128 := [monotonicity #125]: #127
+#74 := (iff #22 #73)
+#71 := (iff #21 #70)
+#68 := (= #18 #65)
+#61 := (- #50 #58)
+#66 := (= #61 #65)
+#67 := [rewrite]: #66
+#62 := (= #18 #61)
+#59 := (= #17 #58)
+#56 := (= #16 #55)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#53 := (= #13 #50)
+#47 := (- #44)
+#51 := (= #47 #50)
+#52 := [rewrite]: #51
+#48 := (= #13 #47)
+#45 := (= #12 #44)
+#42 := (= #11 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#49 := [monotonicity #46]: #48
+#54 := [trans #49 #52]: #53
+#63 := [monotonicity #54 #60]: #62
+#69 := [trans #63 #67]: #68
+#72 := [monotonicity #69]: #71
+#75 := [monotonicity #72]: #74
+#130 := [trans #75 #128]: #129
+#39 := [asserted]: #22
+#131 := [mp #39 #130]: #126
+#175 := [th-lemma #162 #174 #131 #168 #173 #167]: false
+#178 := [lemma #175]: #177
+#181 := [unit-resolution #178 #174 #168]: #92
+#143 := (or #91 #132)
+#144 := [def-axiom]: #143
+#182 := [unit-resolution #144 #181]: #132
+#183 := (not #132)
+#184 := (or #183 #179)
+#185 := [th-lemma]: #184
+#186 := [unit-resolution #185 #182]: #179
+#187 := [th-lemma #174 #131 #168 #173 #186]: false
+#189 := [lemma #187]: #188
+#210 := [unit-resolution #189 #168]: #176
+#206 := (or #205 #157)
+#203 := [hypothesis]: #176
+#204 := [hypothesis]: #145
+#207 := [th-lemma]: #206
+#208 := [unit-resolution #207 #204 #203]: false
+#209 := [lemma #208]: #206
+#211 := [unit-resolution #209 #210]: #205
+#148 := (or #147 #145)
+#149 := [def-axiom]: #148
+#212 := [unit-resolution #149 #211]: #147
+#201 := (or #110 #200 #76)
+#192 := [hypothesis]: #147
+#150 := (or #110 #146)
+#151 := [def-axiom]: #150
+#193 := [unit-resolution #151 #192]: #146
+#194 := (not #146)
+#195 := (or #194 #190)
+#196 := [th-lemma]: #195
+#197 := [unit-resolution #196 #193]: #190
+#198 := [hypothesis]: #179
+#199 := [th-lemma #131 #173 #198 #168 #192 #197]: false
+#202 := [lemma #199]: #201
+#213 := [unit-resolution #202 #212 #168]: #200
+#214 := (or #92 #76 #110)
+#215 := [th-lemma]: #214
+#216 := [unit-resolution #215 #168 #212]: #92
+#217 := [unit-resolution #144 #216]: #132
+#218 := [unit-resolution #185 #217 #213]: false
+#219 := [lemma #218]: #76
+#222 := [hypothesis]: #92
+#223 := (or #147 #77 #91)
+#224 := [th-lemma]: #223
+#225 := [unit-resolution #224 #222 #219]: #147
+#226 := [unit-resolution #151 #225]: #146
+#227 := [unit-resolution #196 #226]: #190
+#228 := [unit-resolution #144 #222]: #132
+#229 := [unit-resolution #185 #228]: #179
+#154 := (+ f3 #88)
+#158 := (<= #154 0::real)
+#137 := (= f3 #83)
+#139 := (or #77 #137)
+#140 := [def-axiom]: #139
+#230 := [unit-resolution #140 #219]: #137
+#231 := (not #137)
+#232 := (or #231 #158)
+#233 := [th-lemma]: #232
+#234 := [unit-resolution #233 #230]: #158
+#235 := [th-lemma #219 #131 #234 #229 #225 #227]: false
+#236 := [lemma #235]: #91
+#237 := [unit-resolution #142 #236]: #134
+#238 := [unit-resolution #166 #237]: #160
+#239 := (not #160)
+#240 := (or #179 #239 #92)
+#241 := [th-lemma]: #240
+#242 := [unit-resolution #241 #236 #238]: #179
+#243 := (not #158)
+#244 := (or #176 #77 #120 #243 #200)
+#245 := [th-lemma]: #244
+#246 := [unit-resolution #245 #242 #219 #131 #234]: #176
+#247 := [unit-resolution #209 #246]: #205
+#248 := [unit-resolution #149 #247]: #147
+#249 := [unit-resolution #151 #248]: #146
+#250 := [unit-resolution #196 #249]: #190
+[th-lemma #236 #250 #131 #234 #248 #238]: false
+unsat
[phone]d0feefc7d25de982e0418835e698 15 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := (< f3 f3)
+#10 := (not #9)
+#11 := (not #10)
+#33 := (iff #11 false)
+#31 := (iff #9 false)
+#32 := [rewrite]: #31
+#29 := (iff #11 #9)
+#30 := [rewrite]: #29
+#34 := [trans #30 #32]: #33
+#28 := [asserted]: #11
+[mp #28 #34]: false
+unsat
[phone]b86f3e786793e2f93fd5e340a23eb081 75 0
+#2 := false
+#53 := 0::real
+decl f4 :: real
+#9 := f4
+#50 := -1::real
+#64 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#65 := (+ f3 #64)
+#66 := (<= #65 0::real)
+#69 := (not #66)
+decl f5 :: real
+#11 := f5
+#51 := (* -1::real f5)
+#60 := (+ f3 #51)
+#61 := (<= #60 0::real)
+#52 := (+ f4 #51)
+#54 := (<= #52 0::real)
+#57 := (not #54)
+#78 := (or #57 #61 #69)
+#83 := (not #78)
+#13 := (<= f3 f5)
+#12 := (<= f4 f5)
+#14 := (implies #12 #13)
+#10 := (<= f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#86 := (iff #16 #83)
+#34 := (not #12)
+#35 := (or #34 #13)
+#41 := (not #10)
+#42 := (or #41 #35)
+#47 := (not #42)
+#84 := (iff #47 #83)
+#81 := (iff #42 #78)
+#72 := (or #57 #61)
+#75 := (or #69 #72)
+#79 := (iff #75 #78)
+#80 := [rewrite]: #79
+#76 := (iff #42 #75)
+#73 := (iff #35 #72)
+#62 := (iff #13 #61)
+#63 := [rewrite]: #62
+#58 := (iff #34 #57)
+#55 := (iff #12 #54)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#74 := [monotonicity #59 #63]: #73
+#70 := (iff #41 #69)
+#67 := (iff #10 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#77 := [monotonicity #71 #74]: #76
+#82 := [trans #77 #80]: #81
+#85 := [monotonicity #82]: #84
+#48 := (iff #16 #47)
+#45 := (iff #15 #42)
+#38 := (implies #10 #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #15 #38)
+#36 := (iff #14 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #46]: #48
+#87 := [trans #49 #85]: #86
+#33 := [asserted]: #16
+#88 := [mp #33 #87]: #83
+#92 := [not-or-elim #88]: #66
+#90 := (not #61)
+#91 := [not-or-elim #88]: #90
+#89 := [not-or-elim #88]: #54
+[th-lemma #89 #91 #92]: false
+unsat
+0af1c435b2c76daa9283b9e1b16e38657d180db7 80 0
+#2 := false
+#53 := 0::real
+decl f4 :: real
+#9 := f4
+#50 := -1::real
+#66 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#67 := (+ f3 #66)
+#65 := (>= #67 0::real)
+#64 := (not #65)
+decl f5 :: real
+#11 := f5
+#51 := (* -1::real f5)
+#60 := (+ f3 #51)
+#61 := (<= #60 0::real)
+#52 := (+ f4 #51)
+#54 := (<= #52 0::real)
+#57 := (not #54)
+#83 := (or #57 #61 #65)
+#88 := (not #83)
+#13 := (<= f3 f5)
+#12 := (<= f4 f5)
+#14 := (implies #12 #13)
+#10 := (< f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#91 := (iff #16 #88)
+#34 := (not #12)
+#35 := (or #34 #13)
+#41 := (not #10)
+#42 := (or #41 #35)
+#47 := (not #42)
+#89 := (iff #47 #88)
+#86 := (iff #42 #83)
+#77 := (or #57 #61)
+#80 := (or #65 #77)
+#84 := (iff #80 #83)
+#85 := [rewrite]: #84
+#81 := (iff #42 #80)
+#78 := (iff #35 #77)
+#62 := (iff #13 #61)
+#63 := [rewrite]: #62
+#58 := (iff #34 #57)
+#55 := (iff #12 #54)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#79 := [monotonicity #59 #63]: #78
+#75 := (iff #41 #65)
+#70 := (not #64)
+#73 := (iff #70 #65)
+#74 := [rewrite]: #73
+#71 := (iff #41 #70)
+#68 := (iff #10 #64)
+#69 := [rewrite]: #68
+#72 := [monotonicity #69]: #71
+#76 := [trans #72 #74]: #75
+#82 := [monotonicity #76 #79]: #81
+#87 := [trans #82 #85]: #86
+#90 := [monotonicity #87]: #89
+#48 := (iff #16 #47)
+#45 := (iff #15 #42)
+#38 := (implies #10 #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #15 #38)
+#36 := (iff #14 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #46]: #48
+#92 := [trans #49 #90]: #91
+#33 := [asserted]: #16
+#93 := [mp #33 #92]: #88
+#97 := [not-or-elim #93]: #64
+#95 := (not #61)
+#96 := [not-or-elim #93]: #95
+#94 := [not-or-elim #93]: #54
+[th-lemma #94 #96 #97]: false
+unsat
+bc24b7127bf1ebd5e05fa62d67103e609bbd595b 80 0
+#2 := false
+#52 := 0::real
+decl f4 :: real
+#9 := f4
+#50 := -1::real
+#69 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#70 := (+ f3 #69)
+#71 := (<= #70 0::real)
+#74 := (not #71)
+decl f5 :: real
+#11 := f5
+#54 := (* -1::real f5)
+#65 := (+ f3 #54)
+#66 := (<= #65 0::real)
+#55 := (+ f4 #54)
+#53 := (>= #55 0::real)
+#83 := (or #53 #66 #74)
+#88 := (not #83)
+#13 := (<= f3 f5)
+#12 := (< f4 f5)
+#14 := (implies #12 #13)
+#10 := (<= f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#91 := (iff #16 #88)
+#34 := (not #12)
+#35 := (or #34 #13)
+#41 := (not #10)
+#42 := (or #41 #35)
+#47 := (not #42)
+#89 := (iff #47 #88)
+#86 := (iff #42 #83)
+#77 := (or #53 #66)
+#80 := (or #74 #77)
+#84 := (iff #80 #83)
+#85 := [rewrite]: #84
+#81 := (iff #42 #80)
+#78 := (iff #35 #77)
+#67 := (iff #13 #66)
+#68 := [rewrite]: #67
+#63 := (iff #34 #53)
+#51 := (not #53)
+#58 := (not #51)
+#61 := (iff #58 #53)
+#62 := [rewrite]: #61
+#59 := (iff #34 #58)
+#56 := (iff #12 #51)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#79 := [monotonicity #64 #68]: #78
+#75 := (iff #41 #74)
+#72 := (iff #10 #71)
+#73 := [rewrite]: #72
+#76 := [monotonicity #73]: #75
+#82 := [monotonicity #76 #79]: #81
+#87 := [trans #82 #85]: #86
+#90 := [monotonicity #87]: #89
+#48 := (iff #16 #47)
+#45 := (iff #15 #42)
+#38 := (implies #10 #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #15 #38)
+#36 := (iff #14 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #46]: #48
+#92 := [trans #49 #90]: #91
+#33 := [asserted]: #16
+#93 := [mp #33 #92]: #88
+#97 := [not-or-elim #93]: #71
+#94 := [not-or-elim #93]: #51
+#95 := (not #66)
+#96 := [not-or-elim #93]: #95
+[th-lemma #96 #94 #97]: false
+unsat
+3aeb9c9a0e29e2bb76776c94f5a20ea84ac742ba 43 0
+#2 := false
+decl f5 :: (-> S2 S2 S3)
+#15 := (:var 0 S2)
+#14 := (:var 1 S2)
+#16 := (f5 #14 #15)
+#561 := (pattern #16)
+decl f4 :: (-> S3 S2)
+#17 := (f4 #16)
+#47 := (= #14 #17)
+#562 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #561) #47)
+#50 := (forall (vars (?v0 S2) (?v1 S2)) #47)
+#565 := (iff #50 #562)
+#563 := (iff #47 #47)
+#564 := [refl]: #563
+#566 := [quant-intro #564]: #565
+#83 := (~ #50 #50)
+#81 := (~ #47 #47)
+#82 := [refl]: #81
+#84 := [nnf-pos #82]: #83
+#18 := (= #17 #14)
+#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
+#51 := (iff #19 #50)
+#48 := (iff #18 #47)
+#49 := [rewrite]: #48
+#52 := [quant-intro #49]: #51
+#46 := [asserted]: #19
+#55 := [mp #46 #52]: #50
+#73 := [mp~ #55 #84]: #50
+#567 := [mp #73 #566]: #562
+decl f6 :: S2
+#9 := f6
+decl f3 :: S2
+#8 := f3
+#10 := (f5 f3 f6)
+#11 := (f4 #10)
+#12 := (= f3 #11)
+#13 := (not #12)
+#45 := [asserted]: #13
+#144 := (not #562)
+#231 := (or #144 #12)
+#145 := [quant-inst]: #231
+[unit-resolution #145 #45 #567]: false
+unsat
+3ea988e6f95dbd7bd08d11a287c40acf0b4bd08d 85 0
+#2 := false
+#52 := 0::real
+decl f4 :: real
+#9 := f4
+#50 := -1::real
+#72 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#73 := (+ f3 #72)
+#71 := (>= #73 0::real)
+#70 := (not #71)
+decl f5 :: real
+#11 := f5
+#54 := (* -1::real f5)
+#67 := (+ f3 #54)
+#66 := (>= #67 0::real)
+#65 := (not #66)
+#55 := (+ f4 #54)
+#53 := (>= #55 0::real)
+#89 := (or #53 #65 #71)
+#94 := (not #89)
+#13 := (< f3 f5)
+#12 := (< f4 f5)
+#14 := (implies #12 #13)
+#10 := (< f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#97 := (iff #16 #94)
+#34 := (not #12)
+#35 := (or #34 #13)
+#41 := (not #10)
+#42 := (or #41 #35)
+#47 := (not #42)
+#95 := (iff #47 #94)
+#92 := (iff #42 #89)
+#83 := (or #53 #65)
+#86 := (or #71 #83)
+#90 := (iff #86 #89)
+#91 := [rewrite]: #90
+#87 := (iff #42 #86)
+#84 := (iff #35 #83)
+#68 := (iff #13 #65)
+#69 := [rewrite]: #68
+#63 := (iff #34 #53)
+#51 := (not #53)
+#58 := (not #51)
+#61 := (iff #58 #53)
+#62 := [rewrite]: #61
+#59 := (iff #34 #58)
+#56 := (iff #12 #51)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#85 := [monotonicity #64 #69]: #84
+#81 := (iff #41 #71)
+#76 := (not #70)
+#79 := (iff #76 #71)
+#80 := [rewrite]: #79
+#77 := (iff #41 #76)
+#74 := (iff #10 #70)
+#75 := [rewrite]: #74
+#78 := [monotonicity #75]: #77
+#82 := [trans #78 #80]: #81
+#88 := [monotonicity #82 #85]: #87
+#93 := [trans #88 #91]: #92
+#96 := [monotonicity #93]: #95
+#48 := (iff #16 #47)
+#45 := (iff #15 #42)
+#38 := (implies #10 #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #15 #38)
+#36 := (iff #14 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #46]: #48
+#98 := [trans #49 #96]: #97
+#33 := [asserted]: #16
+#99 := [mp #33 #98]: #94
+#102 := [not-or-elim #99]: #70
+#100 := [not-or-elim #99]: #51
+#101 := [not-or-elim #99]: #66
+[th-lemma #101 #100 #102]: false
+unsat
+833f5435eb8a2a79499caa251090162736238118 43 0
+#2 := false
+decl f5 :: (-> S2 S2 S3)
+#15 := (:var 0 S2)
+#14 := (:var 1 S2)
+#16 := (f5 #14 #15)
+#561 := (pattern #16)
+decl f4 :: (-> S3 S2)
+#20 := (f4 #16)
+#54 := (= #15 #20)
+#568 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #561) #54)
+#58 := (forall (vars (?v0 S2) (?v1 S2)) #54)
+#571 := (iff #58 #568)
+#569 := (iff #54 #54)
+#570 := [refl]: #569
+#572 := [quant-intro #570]: #571
+#75 := (~ #58 #58)
+#74 := (~ #54 #54)
+#72 := [refl]: #74
+#76 := [nnf-pos #72]: #75
+#21 := (= #20 #15)
+#22 := (forall (vars (?v0 S2) (?v1 S2)) #21)
+#59 := (iff #22 #58)
+#56 := (iff #21 #54)
+#57 := [rewrite]: #56
+#60 := [quant-intro #57]: #59
+#53 := [asserted]: #22
+#63 := [mp #53 #60]: #58
+#69 := [mp~ #63 #76]: #58
+#573 := [mp #69 #572]: #568
+decl f3 :: S2
+#8 := f3
+decl f6 :: S2
+#9 := f6
+#10 := (f5 f6 f3)
+#11 := (f4 #10)
+#12 := (= f3 #11)
+#13 := (not #12)
+#45 := [asserted]: #13
+#234 := (not #568)
+#235 := (or #234 #12)
+#163 := [quant-inst]: #235
+[unit-resolution #163 #45 #573]: false
+unsat
+fa7bd11236791d7e4e69f14295f0dacac77cd667 69 0
+#2 := false
+#44 := 0::real
+decl f5 :: real
+#11 := f5
+#42 := -1::real
+#51 := (* -1::real f5)
+decl f3 :: real
+#8 := f3
+#62 := (+ f3 #51)
+#63 := (<= #62 0::real)
+#64 := (not #63)
+decl f4 :: real
+#9 := f4
+#52 := (+ f4 #51)
+#50 := (>= #52 0::real)
+#53 := (not #50)
+#46 := (* -1::real f4)
+#47 := (+ f3 #46)
+#45 := (>= #47 0::real)
+#43 := (not #45)
+#56 := (and #43 #53)
+#59 := (not #56)
+#74 := (or #59 #63)
+#77 := (not #74)
+#14 := (< f5 f3)
+#15 := (not #14)
+#12 := (< f4 f5)
+#10 := (< f3 f4)
+#13 := (and #10 #12)
+#16 := (implies #13 #15)
+#17 := (not #16)
+#80 := (iff #17 #77)
+#35 := (not #13)
+#36 := (or #35 #15)
+#39 := (not #36)
+#78 := (iff #39 #77)
+#75 := (iff #36 #74)
+#72 := (iff #15 #63)
+#67 := (not #64)
+#70 := (iff #67 #63)
+#71 := [rewrite]: #70
+#68 := (iff #15 #67)
+#65 := (iff #14 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#73 := [trans #69 #71]: #72
+#60 := (iff #35 #59)
+#57 := (iff #13 #56)
+#54 := (iff #12 #53)
+#55 := [rewrite]: #54
+#48 := (iff #10 #43)
+#49 := [rewrite]: #48
+#58 := [monotonicity #49 #55]: #57
+#61 := [monotonicity #58]: #60
+#76 := [monotonicity #61 #73]: #75
+#79 := [monotonicity #76]: #78
+#40 := (iff #17 #39)
+#37 := (iff #16 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#81 := [trans #41 #79]: #80
+#34 := [asserted]: #17
+#82 := [mp #34 #81]: #77
+#86 := [not-or-elim #82]: #64
+#83 := [not-or-elim #82]: #56
+#84 := [and-elim #83]: #43
+#85 := [and-elim #83]: #53
+[th-lemma #85 #84 #86]: false
+unsat
+8b890c6b59495e349b21aa4197ae112481a22f92 85 0
+#2 := false
+decl f5 :: S2
+#9 := f5
+decl f4 :: S2
+#8 := f4
+#13 := (= f4 f5)
+decl f6 :: (-> S3 S2)
+decl f3 :: (-> S2 S2 S3)
+#11 := (f3 f5 f4)
+#349 := (f6 #11)
+#548 := (= #349 f5)
+#556 := (= f5 #349)
+#17 := (:var 0 S2)
+#16 := (:var 1 S2)
+#18 := (f3 #16 #17)
+#568 := (pattern #18)
+#19 := (f6 #18)
+#53 := (= #16 #19)
+#569 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #568) #53)
+#57 := (forall (vars (?v0 S2) (?v1 S2)) #53)
+#572 := (iff #57 #569)
+#570 := (iff #53 #53)
+#571 := [refl]: #570
+#573 := [quant-intro #571]: #572
+#90 := (~ #57 #57)
+#88 := (~ #53 #53)
+#89 := [refl]: #88
+#91 := [nnf-pos #89]: #90
+#20 := (= #19 #16)
+#21 := (forall (vars (?v0 S2) (?v1 S2)) #20)
+#58 := (iff #21 #57)
+#55 := (iff #20 #53)
+#56 := [rewrite]: #55
+#59 := [quant-intro #56]: #58
+#52 := [asserted]: #21
+#62 := [mp #52 #59]: #57
+#80 := [mp~ #62 #91]: #57
+#574 := [mp #80 #573]: #569
+#560 := (not #569)
+#566 := (or #560 #556)
+#561 := [quant-inst]: #566
+#207 := [unit-resolution #561 #574]: #556
+#549 := [symm #207]: #548
+#544 := (= f4 #349)
+#10 := (f3 f4 f5)
+#243 := (f6 #10)
+#546 := (= #243 #349)
+#12 := (= #10 #11)
+#559 := (= #11 #10)
+#48 := (not #12)
+#567 := [hypothesis]: #48
+#238 := (or #13 #12)
+#49 := (iff #13 #48)
+#14 := (iff #12 #13)
+#15 := (not #14)
+#50 := (iff #15 #49)
+#51 := [rewrite]: #50
+#47 := [asserted]: #15
+#54 := [mp #47 #51]: #49
+#150 := (not #49)
+#237 := (or #13 #12 #150)
+#151 := [def-axiom]: #237
+#152 := [unit-resolution #151 #54]: #238
+#557 := [unit-resolution #152 #567]: #13
+#558 := (= f5 f4)
+#216 := [symm #557]: #558
+#200 := [monotonicity #216 #557]: #559
+#543 := [symm #200]: #12
+#204 := [unit-resolution #567 #543]: false
+#205 := [lemma #204]: #12
+#547 := [monotonicity #205]: #546
+#240 := (= f4 #243)
+#562 := (or #560 #240)
+#217 := [quant-inst]: #562
+#545 := [unit-resolution #217 #574]: #240
+#550 := [trans #545 #547]: #544
+#186 := [trans #550 #549]: #13
+#239 := (not #13)
+#242 := (or #239 #48)
+#230 := (or #239 #48 #150)
+#241 := [def-axiom]: #230
+#170 := [unit-resolution #241 #54]: #242
+#206 := [unit-resolution #170 #205]: #239
+[unit-resolution #206 #186]: false
+unsat
+21d7570da3e83b6c75740a6708991286b46b2be1 155 0
+#2 := false
+decl f7 :: S2
+#12 := f7
+decl f5 :: S2
+#9 := f5
+#16 := (= f5 f7)
+#100 := (not #16)
+decl f6 :: S2
+#11 := f6
+decl f4 :: S2
+#8 := f4
+#15 := (= f4 f6)
+#99 := (not #15)
+#90 := (or #99 #100)
+decl f3 :: (-> S2 S2 S3)
+#13 := (f3 f6 f7)
+#10 := (f3 f4 f5)
+#14 := (= #10 #13)
+#91 := (not #90)
+#240 := [hypothesis]: #91
+#175 := (or #90 #16)
+#262 := [def-axiom]: #175
+#228 := [unit-resolution #262 #240]: #16
+#174 := (or #90 #15)
+#261 := [def-axiom]: #174
+#229 := [unit-resolution #261 #240]: #15
+#230 := [monotonicity #229 #228]: #14
+#52 := (not #14)
+#247 := (or #52 #90)
+#111 := (iff #14 #90)
+#17 := (and #15 #16)
+#53 := (iff #17 #52)
+#114 := (iff #53 #111)
+#106 := (iff #90 #14)
+#112 := (iff #106 #111)
+#113 := [rewrite]: #112
+#109 := (iff #53 #106)
+#103 := (iff #91 #52)
+#107 := (iff #103 #106)
+#108 := [rewrite]: #107
+#104 := (iff #53 #103)
+#101 := (iff #17 #91)
+#102 := [rewrite]: #101
+#105 := [monotonicity #102]: #104
+#110 := [trans #105 #108]: #109
+#115 := [trans #110 #113]: #114
+#18 := (iff #14 #17)
+#19 := (not #18)
+#54 := (iff #19 #53)
+#55 := [rewrite]: #54
+#51 := [asserted]: #19
+#58 := [mp #51 #55]: #53
+#116 := [mp #58 #115]: #111
+#254 := (not #111)
+#264 := (or #52 #90 #254)
+#268 := [def-axiom]: #264
+#584 := [unit-resolution #268 #116]: #247
+#583 := [unit-resolution #584 #240]: #52
+#231 := [unit-resolution #583 #230]: false
+#569 := [lemma #231]: #90
+decl f8 :: (-> S3 S2)
+#588 := (f8 #13)
+#574 := (= #588 f6)
+#589 := (= f6 #588)
+#21 := (:var 0 S2)
+#20 := (:var 1 S2)
+#22 := (f3 #20 #21)
+#592 := (pattern #22)
+#23 := (f8 #22)
+#57 := (= #20 #23)
+#593 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #592) #57)
+#61 := (forall (vars (?v0 S2) (?v1 S2)) #57)
+#596 := (iff #61 #593)
+#594 := (iff #57 #57)
+#595 := [refl]: #594
+#597 := [quant-intro #595]: #596
+#94 := (~ #61 #61)
+#92 := (~ #57 #57)
+#93 := [refl]: #92
+#95 := [nnf-pos #93]: #94
+#24 := (= #23 #20)
+#25 := (forall (vars (?v0 S2) (?v1 S2)) #24)
+#62 := (iff #25 #61)
+#59 := (iff #24 #57)
+#60 := [rewrite]: #59
+#63 := [quant-intro #60]: #62
+#56 := [asserted]: #25
+#66 := [mp #56 #63]: #61
+#84 := [mp~ #66 #95]: #61
+#598 := [mp #84 #597]: #593
+#252 := (not #593)
+#244 := (or #252 #589)
+#582 := [quant-inst]: #244
+#570 := [unit-resolution #582 #598]: #589
+#210 := [symm #570]: #574
+#575 := (= f4 #588)
+#586 := (f8 #10)
+#573 := (= #586 #588)
+#194 := (or #14 #91)
+#265 := (or #14 #91 #254)
+#266 := [def-axiom]: #265
+#267 := [unit-resolution #266 #116]: #194
+#571 := [unit-resolution #267 #569]: #14
+#568 := [monotonicity #571]: #573
+#241 := (= f4 #586)
+#253 := (or #252 #241)
+#587 := [quant-inst]: #253
+#572 := [unit-resolution #587 #598]: #241
+#577 := [trans #572 #568]: #575
+#215 := [trans #577 #210]: #15
+decl f9 :: (-> S3 S2)
+#581 := (f9 #13)
+#565 := (= #581 f7)
+#239 := (= f7 #581)
+#26 := (f9 #22)
+#65 := (= #21 #26)
+#599 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #592) #65)
+#69 := (forall (vars (?v0 S2) (?v1 S2)) #65)
+#602 := (iff #69 #599)
+#600 := (iff #65 #65)
+#601 := [refl]: #600
+#603 := [quant-intro #601]: #602
+#86 := (~ #69 #69)
+#85 := (~ #65 #65)
+#83 := [refl]: #85
+#87 := [nnf-pos #83]: #86
+#27 := (= #26 #21)
+#28 := (forall (vars (?v0 S2) (?v1 S2)) #27)
+#70 := (iff #28 #69)
+#67 := (iff #27 #65)
+#68 := [rewrite]: #67
+#71 := [quant-intro #68]: #70
+#64 := [asserted]: #28
+#74 := [mp #64 #71]: #69
+#80 := [mp~ #74 #87]: #69
+#604 := [mp #80 #603]: #599
+#590 := (not #599)
+#224 := (or #590 #239)
+#567 := [quant-inst]: #224
+#216 := [unit-resolution #567 #604]: #239
+#566 := [symm #216]: #565
+#272 := (= f5 #581)
+#373 := (f9 #10)
+#576 := (= #373 #581)
+#579 := [monotonicity #571]: #576
+#580 := (= f5 #373)
+#585 := (or #590 #580)
+#591 := [quant-inst]: #585
+#578 := [unit-resolution #591 #604]: #580
+#288 := [trans #578 #579]: #272
+#289 := [trans #288 #566]: #16
+#176 := (or #91 #99 #100)
+#263 := [def-axiom]: #176
+[unit-resolution #263 #289 #215 #569]: false
+unsat
+3a10723d79463b83d231ba1fcb5ffec2e0721a2e 91 0
+#2 := false
+decl f9 :: S3
+#14 := f9
+decl f5 :: S3
+#8 := f5
+#21 := (= f5 f9)
+decl f3 :: (-> S2 S3)
+decl f4 :: (-> S3 S4 S2)
+decl f6 :: (-> S3 S5 S4)
+decl f11 :: S5
+#16 := f11
+decl f10 :: S3
+#15 := f10
+#17 := (f6 f10 f11)
+#18 := (f4 f9 #17)
+#19 := (f3 #18)
+decl f8 :: S5
+#10 := f8
+decl f7 :: S3
+#9 := f7
+#11 := (f6 f7 f8)
+#12 := (f4 f5 #11)
+#13 := (f3 #12)
+#20 := (= #13 #19)
+#22 := (iff #20 #21)
+#324 := (iff #21 #20)
+#603 := (= f9 #19)
+#30 := (:var 0 S4)
+#24 := (:var 1 S3)
+#31 := (f4 #24 #30)
+#635 := (pattern #31)
+#32 := (f3 #31)
+#82 := (= #24 #32)
+#636 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #635) #82)
+#86 := (forall (vars (?v0 S3) (?v1 S4)) #82)
+#639 := (iff #86 #636)
+#637 := (iff #82 #82)
+#638 := [refl]: #637
+#640 := [quant-intro #638]: #639
+#127 := (~ #86 #86)
+#126 := (~ #82 #82)
+#124 := [refl]: #126
+#128 := [nnf-pos #124]: #127
+#33 := (= #32 #24)
+#34 := (forall (vars (?v0 S3) (?v1 S4)) #33)
+#87 := (iff #34 #86)
+#84 := (iff #33 #82)
+#85 := [rewrite]: #84
+#88 := [quant-intro #85]: #87
+#81 := [asserted]: #34
+#91 := [mp #81 #88]: #86
+#121 := [mp~ #91 #128]: #86
+#641 := [mp #121 #640]: #636
+#276 := (not #636)
+#606 := (or #276 #603)
+#607 := [quant-inst]: #606
+#602 := [unit-resolution #607 #641]: #603
+#627 := (= f5 #13)
+#619 := (or #276 #627)
+#260 := [quant-inst]: #619
+#308 := [unit-resolution #260 #641]: #627
+#325 := [monotonicity #308 #602]: #324
+#326 := [symm #325]: #22
+#299 := (not #21)
+#69 := (not #20)
+#312 := (iff #69 #299)
+#327 := [monotonicity #326]: #312
+#614 := [hypothesis]: #69
+#218 := [mp #614 #327]: #299
+#298 := (or #21 #20)
+#70 := (iff #21 #69)
+#23 := (not #22)
+#71 := (iff #23 #70)
+#72 := [rewrite]: #71
+#68 := [asserted]: #23
+#75 := [mp #68 #72]: #70
+#210 := (not #70)
+#297 := (or #21 #20 #210)
+#211 := [def-axiom]: #297
+#212 := [unit-resolution #211 #75]: #298
+#612 := [unit-resolution #212 #614]: #21
+#597 := [unit-resolution #612 #218]: false
+#598 := [lemma #597]: #20
+#321 := [mp #598 #326]: #21
+#302 := (or #299 #69)
+#290 := (or #299 #69 #210)
+#301 := [def-axiom]: #290
+#230 := [unit-resolution #301 #75]: #302
+#320 := [unit-resolution #230 #598]: #299
+[unit-resolution #320 #321]: false
+unsat
+41219eaede1dcbc709d171a52e3a33f173c7cf67 210 0
+#2 := false
+decl f11 :: S5
+#16 := f11
+decl f8 :: S5
+#10 := f8
+#22 := (= f8 f11)
+#158 := (not #22)
+decl f10 :: S4
+#15 := f10
+decl f7 :: S4
+#9 := f7
+#21 := (= f7 f10)
+#157 := (not #21)
+#139 := (or #157 #158)
+decl f3 :: (-> S2 S3)
+decl f4 :: (-> S4 S3 S2)
+decl f6 :: (-> S4 S5 S3)
+#17 := (f6 f10 f11)
+decl f9 :: S4
+#14 := f9
+#18 := (f4 f9 #17)
+#19 := (f3 #18)
+#11 := (f6 f7 f8)
+decl f5 :: S4
+#8 := f5
+#12 := (f4 f5 #11)
+#13 := (f3 #12)
+#20 := (= #13 #19)
+#626 := (= #17 #19)
+#32 := (:var 0 S3)
+#26 := (:var 1 S4)
+#33 := (f4 #26 #32)
+#657 := (pattern #33)
+#40 := (f3 #33)
+#100 := (= #32 #40)
+#670 := (forall (vars (?v0 S4) (?v1 S3)) (:pat #657) #100)
+#104 := (forall (vars (?v0 S4) (?v1 S3)) #100)
+#673 := (iff #104 #670)
+#671 := (iff #100 #100)
+#672 := [refl]: #671
+#674 := [quant-intro #672]: #673
+#133 := (~ #104 #104)
+#148 := (~ #100 #100)
+#149 := [refl]: #148
+#134 := [nnf-pos #149]: #133
+#41 := (= #40 #32)
+#42 := (forall (vars (?v0 S4) (?v1 S3)) #41)
+#105 := (iff #42 #104)
+#102 := (iff #41 #100)
+#103 := [rewrite]: #102
+#106 := [quant-intro #103]: #105
+#99 := [asserted]: #42
+#109 := [mp #99 #106]: #104
+#150 := [mp~ #109 #134]: #104
+#675 := [mp #150 #674]: #670
+#629 := (not #670)
+#273 := (or #629 #626)
+#274 := [quant-inst]: #273
+#334 := [unit-resolution #274 #675]: #626
+#621 := (= #13 #17)
+#343 := (= #11 #17)
+#140 := (not #139)
+#330 := [hypothesis]: #140
+#233 := (or #139 #22)
+#320 := [def-axiom]: #233
+#349 := [unit-resolution #320 #330]: #22
+#232 := (or #139 #21)
+#319 := [def-axiom]: #232
+#240 := [unit-resolution #319 #330]: #21
+#617 := [monotonicity #240 #349]: #343
+#620 := (= #13 #11)
+#286 := (= #11 #13)
+#630 := (or #629 #286)
+#631 := [quant-inst]: #630
+#619 := [unit-resolution #631 #675]: #286
+#342 := [symm #619]: #620
+#618 := [trans #342 #617]: #621
+#622 := [trans #618 #334]: #20
+#71 := (not #20)
+#305 := (or #71 #139)
+#169 := (iff #20 #139)
+#23 := (and #21 #22)
+#72 := (iff #23 #71)
+#172 := (iff #72 #169)
+#164 := (iff #139 #20)
+#170 := (iff #164 #169)
+#171 := [rewrite]: #170
+#167 := (iff #72 #164)
+#161 := (iff #140 #71)
+#165 := (iff #161 #164)
+#166 := [rewrite]: #165
+#162 := (iff #72 #161)
+#159 := (iff #23 #140)
+#160 := [rewrite]: #159
+#163 := [monotonicity #160]: #162
+#168 := [trans #163 #166]: #167
+#173 := [trans #168 #171]: #172
+#24 := (iff #20 #23)
+#25 := (not #24)
+#73 := (iff #25 #72)
+#74 := [rewrite]: #73
+#70 := [asserted]: #25
+#77 := [mp #70 #74]: #72
+#174 := [mp #77 #173]: #169
+#312 := (not #169)
+#322 := (or #71 #139 #312)
+#326 := [def-axiom]: #322
+#642 := [unit-resolution #326 #174]: #305
+#346 := [unit-resolution #642 #330]: #71
+#331 := [unit-resolution #346 #622]: false
+#332 := [lemma #331]: #139
+decl f12 :: (-> S3 S4)
+#646 := (f12 #17)
+#606 := (= #646 f10)
+#647 := (= f10 #646)
+#27 := (:var 0 S5)
+#28 := (f6 #26 #27)
+#650 := (pattern #28)
+#29 := (f12 #28)
+#76 := (= #26 #29)
+#651 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #650) #76)
+#80 := (forall (vars (?v0 S4) (?v1 S5)) #76)
+#654 := (iff #80 #651)
+#652 := (iff #76 #76)
+#653 := [refl]: #652
+#655 := [quant-intro #653]: #654
+#143 := (~ #80 #80)
+#141 := (~ #76 #76)
+#142 := [refl]: #141
+#144 := [nnf-pos #142]: #143
+#30 := (= #29 #26)
+#31 := (forall (vars (?v0 S4) (?v1 S5)) #30)
+#81 := (iff #31 #80)
+#78 := (iff #30 #76)
+#79 := [rewrite]: #78
+#82 := [quant-intro #79]: #81
+#75 := [asserted]: #31
+#85 := [mp #75 #82]: #80
+#127 := [mp~ #85 #144]: #80
+#656 := [mp #127 #655]: #651
+#310 := (not #651)
+#302 := (or #310 #647)
+#640 := [quant-inst]: #302
+#333 := [unit-resolution #640 #656]: #647
+#607 := [symm #333]: #606
+#602 := (= f7 #646)
+#644 := (f12 #11)
+#616 := (= #644 #646)
+#613 := (= #19 #17)
+#614 := [symm #334]: #613
+#327 := (= #11 #19)
+#252 := (or #20 #140)
+#323 := (or #20 #140 #312)
+#324 := [def-axiom]: #323
+#325 := [unit-resolution #324 #174]: #252
+#335 := [unit-resolution #325 #332]: #20
+#611 := [trans #619 #335]: #327
+#615 := [trans #611 #614]: #343
+#605 := [monotonicity #615]: #616
+#299 := (= f7 #644)
+#311 := (or #310 #299)
+#645 := [quant-inst]: #311
+#612 := [unit-resolution #645 #656]: #299
+#603 := [trans #612 #605]: #602
+#608 := [trans #603 #607]: #21
+decl f14 :: (-> S3 S5)
+#639 := (f14 #17)
+#452 := (= #639 f11)
+#297 := (= f11 #639)
+#37 := (f14 #28)
+#92 := (= #27 #37)
+#664 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #650) #92)
+#96 := (forall (vars (?v0 S4) (?v1 S5)) #92)
+#667 := (iff #96 #664)
+#665 := (iff #92 #92)
+#666 := [refl]: #665
+#668 := [quant-intro #666]: #667
+#131 := (~ #96 #96)
+#145 := (~ #92 #92)
+#146 := [refl]: #145
+#132 := [nnf-pos #146]: #131
+#38 := (= #37 #27)
+#39 := (forall (vars (?v0 S4) (?v1 S5)) #38)
+#97 := (iff #39 #96)
+#94 := (iff #38 #92)
+#95 := [rewrite]: #94
+#98 := [quant-intro #95]: #97
+#91 := [asserted]: #39
+#101 := [mp #91 #98]: #96
+#147 := [mp~ #101 #132]: #96
+#669 := [mp #147 #668]: #664
+#648 := (not #664)
+#282 := (or #648 #297)
+#625 := [quant-inst]: #282
+#609 := [unit-resolution #625 #669]: #297
+#453 := [symm #609]: #452
+#595 := (= f8 #639)
+#431 := (f14 #11)
+#610 := (= #431 #639)
+#451 := [monotonicity #615]: #610
+#638 := (= f8 #431)
+#643 := (or #648 #638)
+#649 := [quant-inst]: #643
+#604 := [unit-resolution #649 #669]: #638
+#596 := [trans #604 #451]: #595
+#597 := [trans #596 #453]: #22
+#234 := (or #140 #157 #158)
+#321 := [def-axiom]: #234
+[unit-resolution #321 #597 #608 #332]: false
+unsat
+e7d7ee57f96345ce1235238d825e8494a21738fc 144 0
+#2 := false
+decl f11 :: S3
+#16 := f11
+decl f8 :: S3
+#9 := f8
+#23 := (= f8 f11)
+decl f3 :: (-> S2 S3)
+decl f4 :: (-> S4 S2)
+decl f5 :: (-> S3 S2 S4)
+decl f7 :: (-> S3 S5 S2)
+decl f12 :: S5
+#17 := f12
+#18 := (f7 f11 f12)
+decl f10 :: S3
+#15 := f10
+#19 := (f5 f10 #18)
+#20 := (f4 #19)
+#21 := (f3 #20)
+decl f9 :: S5
+#10 := f9
+#11 := (f7 f8 f9)
+decl f6 :: S3
+#8 := f6
+#12 := (f5 f6 #11)
+#13 := (f4 #12)
+#14 := (f3 #13)
+#22 := (= #14 #21)
+#24 := (iff #22 #23)
+#315 := (= #21 f11)
+#411 := (f3 #18)
+#312 := (= #411 f11)
+#618 := (= f11 #411)
+#27 := (:var 0 S5)
+#26 := (:var 1 S3)
+#28 := (f7 #26 #27)
+#630 := (pattern #28)
+#29 := (f3 #28)
+#76 := (= #26 #29)
+#631 := (forall (vars (?v0 S3) (?v1 S5)) (:pat #630) #76)
+#80 := (forall (vars (?v0 S3) (?v1 S5)) #76)
+#634 := (iff #80 #631)
+#632 := (iff #76 #76)
+#633 := [refl]: #632
+#635 := [quant-intro #633]: #634
+#143 := (~ #80 #80)
+#141 := (~ #76 #76)
+#142 := [refl]: #141
+#144 := [nnf-pos #142]: #143
+#30 := (= #29 #26)
+#31 := (forall (vars (?v0 S3) (?v1 S5)) #30)
+#81 := (iff #31 #80)
+#78 := (iff #30 #76)
+#79 := [rewrite]: #78
+#82 := [quant-intro #79]: #81
+#75 := [asserted]: #31
+#85 := [mp #75 #82]: #80
+#127 := [mp~ #85 #144]: #80
+#636 := [mp #127 #635]: #631
+#622 := (not #631)
+#628 := (or #622 #618)
+#623 := [quant-inst]: #628
+#323 := [unit-resolution #623 #636]: #618
+#313 := [symm #323]: #312
+#602 := (= #21 #411)
+#601 := (= #20 #18)
+#607 := (= #18 #20)
+#32 := (:var 0 S2)
+#33 := (f5 #26 #32)
+#637 := (pattern #33)
+#40 := (f4 #33)
+#100 := (= #32 #40)
+#650 := (forall (vars (?v0 S3) (?v1 S2)) (:pat #637) #100)
+#104 := (forall (vars (?v0 S3) (?v1 S2)) #100)
+#653 := (iff #104 #650)
+#651 := (iff #100 #100)
+#652 := [refl]: #651
+#654 := [quant-intro #652]: #653
+#133 := (~ #104 #104)
+#148 := (~ #100 #100)
+#149 := [refl]: #148
+#134 := [nnf-pos #149]: #133
+#41 := (= #40 #32)
+#42 := (forall (vars (?v0 S3) (?v1 S2)) #41)
+#105 := (iff #42 #104)
+#102 := (iff #41 #100)
+#103 := [rewrite]: #102
+#106 := [quant-intro #103]: #105
+#99 := [asserted]: #42
+#109 := [mp #99 #106]: #104
+#150 := [mp~ #109 #134]: #104
+#655 := [mp #150 #654]: #650
+#267 := (not #650)
+#606 := (or #267 #607)
+#612 := [quant-inst]: #606
+#597 := [unit-resolution #612 #655]: #607
+#598 := [symm #597]: #601
+#311 := [monotonicity #598]: #602
+#593 := [trans #311 #313]: #315
+#587 := (= #14 f8)
+#305 := (f3 #11)
+#585 := (= #305 f8)
+#302 := (= f8 #305)
+#624 := (or #622 #302)
+#279 := [quant-inst]: #624
+#594 := [unit-resolution #279 #636]: #302
+#586 := [symm #594]: #585
+#592 := (= #14 #305)
+#591 := (= #13 #11)
+#620 := (= #11 #13)
+#268 := (or #267 #620)
+#269 := [quant-inst]: #268
+#307 := [unit-resolution #269 #655]: #620
+#595 := [symm #307]: #591
+#596 := [monotonicity #595]: #592
+#582 := [trans #596 #586]: #587
+#583 := [monotonicity #582 #593]: #24
+#301 := (not #23)
+#71 := (not #22)
+#588 := (iff #71 #301)
+#589 := [monotonicity #583]: #588
+#220 := [hypothesis]: #71
+#584 := [mp #220 #589]: #301
+#300 := (or #23 #22)
+#72 := (iff #23 #71)
+#25 := (not #24)
+#73 := (iff #25 #72)
+#74 := [rewrite]: #73
+#70 := [asserted]: #25
+#77 := [mp #70 #74]: #72
+#212 := (not #72)
+#299 := (or #23 #22 #212)
+#213 := [def-axiom]: #299
+#214 := [unit-resolution #213 #77]: #300
+#599 := [unit-resolution #214 #220]: #23
+#590 := [unit-resolution #599 #584]: false
+#431 := [lemma #590]: #22
+#433 := [mp #431 #583]: #23
+#304 := (or #301 #71)
+#292 := (or #301 #71 #212)
+#303 := [def-axiom]: #292
+#232 := [unit-resolution #303 #77]: #304
+#432 := [unit-resolution #232 #431]: #301
+[unit-resolution #432 #433]: false
+unsat
+05084d48ca9cf46fab3aa08abec156f92f6b3e83 144 0
+#2 := false
+decl f12 :: S3
+#17 := f12
+decl f9 :: S3
+#10 := f9
+#23 := (= f9 f12)
+decl f3 :: (-> S2 S3)
+decl f4 :: (-> S4 S2)
+decl f5 :: (-> S5 S2 S4)
+decl f7 :: (-> S5 S3 S2)
+decl f11 :: S5
+#16 := f11
+#18 := (f7 f11 f12)
+decl f10 :: S5
+#15 := f10
+#19 := (f5 f10 #18)
+#20 := (f4 #19)
+#21 := (f3 #20)
+decl f8 :: S5
+#9 := f8
+#11 := (f7 f8 f9)
+decl f6 :: S5
+#8 := f6
+#12 := (f5 f6 #11)
+#13 := (f4 #12)
+#14 := (f3 #13)
+#22 := (= #14 #21)
+#24 := (iff #22 #23)
+#315 := (= #21 f12)
+#626 := (f3 #18)
+#312 := (= #626 f12)
+#627 := (= f12 #626)
+#27 := (:var 0 S3)
+#26 := (:var 1 S5)
+#28 := (f7 #26 #27)
+#630 := (pattern #28)
+#37 := (f3 #28)
+#92 := (= #27 #37)
+#644 := (forall (vars (?v0 S5) (?v1 S3)) (:pat #630) #92)
+#96 := (forall (vars (?v0 S5) (?v1 S3)) #92)
+#647 := (iff #96 #644)
+#645 := (iff #92 #92)
+#646 := [refl]: #645
+#648 := [quant-intro #646]: #647
+#131 := (~ #96 #96)
+#145 := (~ #92 #92)
+#146 := [refl]: #145
+#132 := [nnf-pos #146]: #131
+#38 := (= #37 #27)
+#39 := (forall (vars (?v0 S5) (?v1 S3)) #38)
+#97 := (iff #39 #96)
+#94 := (iff #38 #92)
+#95 := [rewrite]: #94
+#98 := [quant-intro #95]: #97
+#91 := [asserted]: #39
+#101 := [mp #91 #98]: #96
+#147 := [mp~ #101 #132]: #96
+#649 := [mp #147 #648]: #644
+#290 := (not #644)
+#277 := (or #290 #627)
+#282 := [quant-inst]: #277
+#323 := [unit-resolution #282 #649]: #627
+#313 := [symm #323]: #312
+#602 := (= #21 #626)
+#601 := (= #20 #18)
+#607 := (= #18 #20)
+#32 := (:var 0 S2)
+#33 := (f5 #26 #32)
+#637 := (pattern #33)
+#40 := (f4 #33)
+#100 := (= #32 #40)
+#650 := (forall (vars (?v0 S5) (?v1 S2)) (:pat #637) #100)
+#104 := (forall (vars (?v0 S5) (?v1 S2)) #100)
+#653 := (iff #104 #650)
+#651 := (iff #100 #100)
+#652 := [refl]: #651
+#654 := [quant-intro #652]: #653
+#133 := (~ #104 #104)
+#148 := (~ #100 #100)
+#149 := [refl]: #148
+#134 := [nnf-pos #149]: #133
+#41 := (= #40 #32)
+#42 := (forall (vars (?v0 S5) (?v1 S2)) #41)
+#105 := (iff #42 #104)
+#102 := (iff #41 #100)
+#103 := [rewrite]: #102
+#106 := [quant-intro #103]: #105
+#99 := [asserted]: #42
+#109 := [mp #99 #106]: #104
+#150 := [mp~ #109 #134]: #104
+#655 := [mp #150 #654]: #650
+#267 := (not #650)
+#606 := (or #267 #607)
+#612 := [quant-inst]: #606
+#597 := [unit-resolution #612 #655]: #607
+#598 := [symm #597]: #601
+#311 := [monotonicity #598]: #602
+#593 := [trans #311 #313]: #315
+#587 := (= #14 f9)
+#306 := (f3 #11)
+#585 := (= #306 f9)
+#285 := (= f9 #306)
+#291 := (or #290 #285)
+#625 := [quant-inst]: #291
+#594 := [unit-resolution #625 #649]: #285
+#586 := [symm #594]: #585
+#592 := (= #14 #306)
+#591 := (= #13 #11)
+#620 := (= #11 #13)
+#268 := (or #267 #620)
+#269 := [quant-inst]: #268
+#307 := [unit-resolution #269 #655]: #620
+#595 := [symm #307]: #591
+#596 := [monotonicity #595]: #592
+#582 := [trans #596 #586]: #587
+#583 := [monotonicity #582 #593]: #24
+#301 := (not #23)
+#71 := (not #22)
+#588 := (iff #71 #301)
+#589 := [monotonicity #583]: #588
+#220 := [hypothesis]: #71
+#584 := [mp #220 #589]: #301
+#300 := (or #23 #22)
+#72 := (iff #23 #71)
+#25 := (not #24)
+#73 := (iff #25 #72)
+#74 := [rewrite]: #73
+#70 := [asserted]: #25
+#77 := [mp #70 #74]: #72
+#212 := (not #72)
+#299 := (or #23 #22 #212)
+#213 := [def-axiom]: #299
+#214 := [unit-resolution #213 #77]: #300
+#599 := [unit-resolution #214 #220]: #23
+#590 := [unit-resolution #599 #584]: false
+#431 := [lemma #590]: #22
+#433 := [mp #431 #583]: #23
+#304 := (or #301 #71)
+#292 := (or #301 #71 #212)
+#303 := [def-axiom]: #292
+#232 := [unit-resolution #303 #77]: #304
+#432 := [unit-resolution #232 #431]: #301
+[unit-resolution #432 #433]: false
+unsat
+b9b01af627407ae858abb87a30d0e6558ef2eead 103 0
+#2 := false
+decl f6 :: S3
+#9 := f6
+decl f5 :: S3
+#8 := f5
+#14 := (= f5 f6)
+decl f7 :: (-> S2 S3)
+decl f4 :: (-> S3 S3 S2)
+#10 := (f4 f5 f6)
+#12 := (f7 #10)
+decl f3 :: (-> S2 S3)
+#11 := (f3 #10)
+#13 := (= #11 #12)
+#15 := (iff #13 #14)
+#558 := (iff #14 #13)
+#241 := (= f6 #12)
+#18 := (:var 0 S3)
+#17 := (:var 1 S3)
+#19 := (f4 #17 #18)
+#569 := (pattern #19)
+#23 := (f7 #19)
+#62 := (= #18 #23)
+#576 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #569) #62)
+#66 := (forall (vars (?v0 S3) (?v1 S3)) #62)
+#579 := (iff #66 #576)
+#577 := (iff #62 #62)
+#578 := [refl]: #577
+#580 := [quant-intro #578]: #579
+#83 := (~ #66 #66)
+#82 := (~ #62 #62)
+#80 := [refl]: #82
+#84 := [nnf-pos #80]: #83
+#24 := (= #23 #18)
+#25 := (forall (vars (?v0 S3) (?v1 S3)) #24)
+#67 := (iff #25 #66)
+#64 := (iff #24 #62)
+#65 := [rewrite]: #64
+#68 := [quant-intro #65]: #67
+#61 := [asserted]: #25
+#71 := [mp #61 #68]: #66
+#77 := [mp~ #71 #84]: #66
+#581 := [mp #77 #580]: #576
+#350 := (not #576)
+#557 := (or #350 #241)
+#229 := [quant-inst]: #557
+#562 := [unit-resolution #229 #581]: #241
+#244 := (= f5 #11)
+#20 := (f3 #19)
+#54 := (= #17 #20)
+#570 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #569) #54)
+#58 := (forall (vars (?v0 S3) (?v1 S3)) #54)
+#573 := (iff #58 #570)
+#571 := (iff #54 #54)
+#572 := [refl]: #571
+#574 := [quant-intro #572]: #573
+#91 := (~ #58 #58)
+#89 := (~ #54 #54)
+#90 := [refl]: #89
+#92 := [nnf-pos #90]: #91
+#21 := (= #20 #17)
+#22 := (forall (vars (?v0 S3) (?v1 S3)) #21)
+#59 := (iff #22 #58)
+#56 := (iff #21 #54)
+#57 := [rewrite]: #56
+#60 := [quant-intro #57]: #59
+#53 := [asserted]: #22
+#63 := [mp #53 #60]: #58
+#81 := [mp~ #63 #92]: #58
+#575 := [mp #81 #574]: #570
+#224 := (not #570)
+#561 := (or #224 #244)
+#563 := [quant-inst]: #561
+#568 := [unit-resolution #563 #575]: #244
+#216 := [monotonicity #568 #562]: #558
+#221 := [symm #216]: #15
+#240 := (not #14)
+#49 := (not #13)
+#559 := (iff #49 #240)
+#217 := [monotonicity #221]: #559
+#230 := [hypothesis]: #49
+#560 := [mp #230 #217]: #240
+#239 := (or #14 #13)
+#50 := (iff #14 #49)
+#16 := (not #15)
+#51 := (iff #16 #50)
+#52 := [rewrite]: #51
+#48 := [asserted]: #16
+#55 := [mp #48 #52]: #50
+#151 := (not #50)
+#238 := (or #14 #13 #151)
+#152 := [def-axiom]: #238
+#153 := [unit-resolution #152 #55]: #239
+#564 := [unit-resolution #153 #230]: #14
+#201 := [unit-resolution #564 #560]: false
+#544 := [lemma #201]: #13
+#206 := [mp #544 #221]: #14
+#243 := (or #240 #49)
+#231 := (or #240 #49 #151)
+#242 := [def-axiom]: #231
+#171 := [unit-resolution #242 #55]: #243
+#205 := [unit-resolution #171 #544]: #240
+[unit-resolution #205 #206]: false
+unsat
+27f36608f534be1341919c1ca51bc62461483549 111 0
+#2 := false
+decl f9 :: (-> S2 S3)
+decl f7 :: S2
+#13 := f7
+#18 := (f9 f7)
+decl f8 :: (-> S2 S3)
+decl f3 :: S2
+#8 := f3
+#17 := (f8 f3)
+#19 := (= #17 #18)
+decl f4 :: (-> S3 S3 S2)
+decl f5 :: S3
+#9 := f5
+decl f6 :: S3
+#10 := f6
+#14 := (f4 f6 f5)
+#258 := (f9 #14)
+#220 := (= #258 #18)
+#230 := (= #18 #258)
+#15 := (= f7 #14)
+#11 := (f4 f5 f6)
+#12 := (= f3 #11)
+#16 := (and #12 #15)
+#54 := (not #16)
+#55 := (or #54 #19)
+#58 := (not #55)
+#20 := (implies #16 #19)
+#21 := (not #20)
+#59 := (iff #21 #58)
+#56 := (iff #20 #55)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#53 := [asserted]: #21
+#63 := [mp #53 #60]: #58
+#61 := [not-or-elim #63]: #16
+#64 := [and-elim #61]: #15
+#573 := [monotonicity #64]: #230
+#221 := [symm #573]: #220
+#561 := (= #17 #258)
+#237 := (= f5 #258)
+#23 := (:var 0 S3)
+#22 := (:var 1 S3)
+#24 := (f4 #22 #23)
+#582 := (pattern #24)
+#28 := (f9 #24)
+#75 := (= #23 #28)
+#589 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #582) #75)
+#79 := (forall (vars (?v0 S3) (?v1 S3)) #75)
+#592 := (iff #79 #589)
+#590 := (iff #75 #75)
+#591 := [refl]: #590
+#593 := [quant-intro #591]: #592
+#100 := (~ #79 #79)
+#99 := (~ #75 #75)
+#96 := [refl]: #99
+#101 := [nnf-pos #96]: #100
+#29 := (= #28 #23)
+#30 := (forall (vars (?v0 S3) (?v1 S3)) #29)
+#80 := (iff #30 #79)
+#77 := (iff #29 #75)
+#78 := [rewrite]: #77
+#81 := [quant-intro #78]: #80
+#74 := [asserted]: #30
+#84 := [mp #74 #81]: #79
+#97 := [mp~ #84 #101]: #79
+#594 := [mp #97 #593]: #589
+#184 := (not #589)
+#570 := (or #184 #237)
+#242 := [quant-inst]: #570
+#581 := [unit-resolution #242 #594]: #237
+#559 := (= #17 f5)
+#164 := (f8 #11)
+#218 := (= #164 f5)
+#251 := (= f5 #164)
+#25 := (f8 #24)
+#68 := (= #22 #25)
+#583 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #582) #68)
+#71 := (forall (vars (?v0 S3) (?v1 S3)) #68)
+#586 := (iff #71 #583)
+#584 := (iff #68 #68)
+#585 := [refl]: #584
+#587 := [quant-intro #585]: #586
+#108 := (~ #71 #71)
+#106 := (~ #68 #68)
+#107 := [refl]: #106
+#109 := [nnf-pos #107]: #108
+#26 := (= #25 #22)
+#27 := (forall (vars (?v0 S3) (?v1 S3)) #26)
+#72 := (iff #27 #71)
+#69 := (iff #26 #68)
+#70 := [rewrite]: #69
+#73 := [quant-intro #70]: #72
+#67 := [asserted]: #27
+#76 := [mp #67 #73]: #71
+#98 := [mp~ #76 #109]: #71
+#588 := [mp #98 #587]: #583
+#166 := (not #583)
+#253 := (or #166 #251)
+#244 := [quant-inst]: #253
+#575 := [unit-resolution #244 #588]: #251
+#219 := [symm #575]: #218
+#234 := (= #17 #164)
+#62 := [and-elim #61]: #12
+#572 := [monotonicity #62]: #234
+#560 := [trans #572 #219]: #559
+#562 := [trans #560 #581]: #561
+#563 := [trans #562 #221]: #19
+#65 := (not #19)
+#66 := [not-or-elim #63]: #65
+[unit-resolution #66 #563]: false
+unsat
+37ed3b448ab9c39e3b6673cc263e2847f1d1a0a1 117 0
+#2 := false
+decl f6 :: (-> S3 S3 S2)
+decl f3 :: (-> S2 S3)
+decl f4 :: S2
+#8 := f4
+#9 := (f3 f4)
+decl f5 :: (-> S2 S3)
+#10 := (f5 f4)
+#12 := (f6 #10 #9)
+#13 := (= f4 #12)
+#349 := (f6 #9 #10)
+#550 := (= #349 #12)
+#549 := (= #12 #349)
+#11 := (= #9 #10)
+#243 := (f3 #12)
+#543 := (= #243 #10)
+#240 := (= #10 #243)
+#17 := (:var 0 S3)
+#16 := (:var 1 S3)
+#18 := (f6 #16 #17)
+#568 := (pattern #18)
+#19 := (f3 #18)
+#53 := (= #16 #19)
+#569 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #568) #53)
+#57 := (forall (vars (?v0 S3) (?v1 S3)) #53)
+#572 := (iff #57 #569)
+#570 := (iff #53 #53)
+#571 := [refl]: #570
+#573 := [quant-intro #571]: #572
+#90 := (~ #57 #57)
+#88 := (~ #53 #53)
+#89 := [refl]: #88
+#91 := [nnf-pos #89]: #90
+#20 := (= #19 #16)
+#21 := (forall (vars (?v0 S3) (?v1 S3)) #20)
+#58 := (iff #21 #57)
+#55 := (iff #20 #53)
+#56 := [rewrite]: #55
+#59 := [quant-intro #56]: #58
+#52 := [asserted]: #21
+#62 := [mp #52 #59]: #57
+#80 := [mp~ #62 #91]: #57
+#574 := [mp #80 #573]: #569
+#560 := (not #569)
+#562 := (or #560 #240)
+#217 := [quant-inst]: #562
+#220 := [unit-resolution #217 #574]: #240
+#204 := [symm #220]: #543
+#559 := (= #9 #243)
+#558 := (= #243 #9)
+#557 := (= #12 f4)
+#48 := (not #11)
+#564 := [hypothesis]: #48
+#238 := (or #13 #11)
+#49 := (iff #13 #48)
+#14 := (iff #11 #13)
+#15 := (not #14)
+#50 := (iff #15 #49)
+#51 := [rewrite]: #50
+#47 := [asserted]: #15
+#54 := [mp #47 #51]: #49
+#150 := (not #49)
+#237 := (or #13 #11 #150)
+#151 := [def-axiom]: #237
+#152 := [unit-resolution #151 #54]: #238
+#565 := [unit-resolution #152 #564]: #13
+#215 := [symm #565]: #557
+#216 := [monotonicity #215]: #558
+#200 := [symm #216]: #559
+#205 := [trans #200 #204]: #11
+#206 := [unit-resolution #564 #205]: false
+#207 := [lemma #206]: #11
+#546 := (= #10 #9)
+#547 := [symm #207]: #546
+#544 := [monotonicity #547 #207]: #549
+#186 := [symm #544]: #550
+#556 := (= f4 #349)
+#25 := (:var 0 S2)
+#27 := (f5 #25)
+#582 := (pattern #27)
+#26 := (f3 #25)
+#581 := (pattern #26)
+#28 := (f6 #26 #27)
+#69 := (= #25 #28)
+#583 := (forall (vars (?v0 S2)) (:pat #581 #582) #69)
+#73 := (forall (vars (?v0 S2)) #69)
+#586 := (iff #73 #583)
+#584 := (iff #69 #69)
+#585 := [refl]: #584
+#587 := [quant-intro #585]: #586
+#84 := (~ #73 #73)
+#92 := (~ #69 #69)
+#93 := [refl]: #92
+#85 := [nnf-pos #93]: #84
+#29 := (= #28 #25)
+#30 := (forall (vars (?v0 S2)) #29)
+#74 := (iff #30 #73)
+#71 := (iff #29 #69)
+#72 := [rewrite]: #71
+#75 := [quant-intro #72]: #74
+#68 := [asserted]: #30
+#78 := [mp #68 #75]: #73
+#94 := [mp~ #78 #85]: #73
+#588 := [mp #94 #587]: #583
+#566 := (not #583)
+#561 := (or #566 #556)
+#567 := [quant-inst]: #561
+#548 := [unit-resolution #567 #588]: #556
+#551 := [trans #548 #186]: #13
+#239 := (not #13)
+#242 := (or #239 #48)
+#230 := (or #239 #48 #150)
+#241 := [def-axiom]: #230
+#170 := [unit-resolution #241 #54]: #242
+#545 := [unit-resolution #170 #207]: #239
+[unit-resolution #545 #551]: false
+unsat

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT_Examples/SMT_Word_Examples.certs	Wed May 12 23:54:06 2010 +0200
@@ -0,0 +1,50 @@
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