src/HOL/Boogie/Examples/Boogie_Dijkstra.certs

renamed constant "apply" to "fun_app" (which is closer to the related "fun_upd")

b3c5003cf9ccaad1080e68445c705767d58e45ae 6889 0
#2 := false
decl f11 :: (-> S5 S2 S1)
decl ?v1!7 :: (-> S2 S2)
decl ?v0!20 :: S2
#2295 := ?v0!20
#6027 := (?v1!7 ?v0!20)
decl f20 :: S5
#146 := f20
#12518 := (f11 f20 #6027)
decl 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)
#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)
#4292 := (or #4289 #3330)
#4295 := (not #4292)
#4254 := (pattern #109)
decl ?v1!9 :: (-> S2 S2)
#2065 := (?v1!9 #12)
#2068 := (f5 #2065 #12)
#2069 := (f4 #2068)
#2724 := (* -1::int #2069)
#2066 := (f9 f16 #2065)
#2707 := (* -1::int #2066)
#2725 := (+ #2707 #2724)
#2726 := (+ #109 #2725)
#2727 := (= #2726 0::int)
#3263 := (not #2727)
#2708 := (+ #109 #2707)
#2709 := (<= #2708 0::int)
#3264 := (or #2709 #3263)
#3265 := (not #3264)
#24 := (= #12 f6)
#3271 := (or #24 #1250 #3265)
#4270 := (forall (vars (?v0 S2)) (:pat #4254) #3271)
#4275 := (not #4270)
#4298 := (or #4275 #4295)
#4301 := (not #4298)
decl ?v0!8 :: S2
#2025 := ?v0!8
#2029 := (f5 #12 ?v0!8)
#4255 := (pattern #2029)
#2030 := (f4 #2029)
#2026 := (f9 f16 ?v0!8)
#2027 := (* -1::int #2026)
#2677 := (+ #2027 #2030)
#2678 := (+ #109 #2677)
#2681 := (= #2678 0::int)
#3227 := (not #2681)
#2028 := (+ #109 #2027)
#2033 := (>= #2028 0::int)
#3228 := (or #2033 #3227)
#4256 := (forall (vars (?v1 S2)) (:pat #4254 #4255) #3228)
#4261 := (not #4256)
#2653 := (= f6 ?v0!8)
#2037 := (+ f3 #2027)
#2038 := (<= #2037 0::int)
#4264 := (or #2038 #2653 #4261)
#4267 := (not #4264)
#4304 := (or #4267 #4301)
#4307 := (not #4304)
#1203 := (* -1::int #68)
#1204 := (+ f3 #1203)
#1205 := (<= #1204 0::int)
#3213 := (or #447 #1205)
#4246 := (forall (vars (?v0 S2)) (:pat #4245 #4203) #3213)
#4251 := (not #4246)
#538 := (= f10 f16)
#629 := (not #538)
decl f13 :: S5
#99 := f13
#535 := (= f12 f13)
#647 := (not #535)
decl f18 :: S4
#107 := f18
decl f17 :: S4
#106 := f17
#108 := (= f17 f18)
#620 := (not #108)
decl f15 :: S2
#102 := f15
decl f14 :: S2
#101 := f14
#103 := (= f14 f15)
#638 := (not #103)
#4310 := (or #638 #620 #647 #629 #4251 #4307)
#4313 := (not #4310)
#4471 := (or #4313 #4468)
#4474 := (not #4471)
#1988 := (?v1!7 #12)
#1989 := (f9 f10 #1988)
#2612 := (* -1::int #1989)
#2627 := (+ #68 #2612)
#2628 := (<= #2627 0::int)
#1993 := (f5 #1988 #12)
#1994 := (f4 #1993)
#2613 := (* -1::int #1994)
#2614 := (+ #2612 #2613)
#2615 := (+ #68 #2614)
#2616 := (= #2615 0::int)
#3197 := (not #2616)
#1997 := (f11 f12 #1988)
#1998 := (= f1 #1997)
#3196 := (not #1998)
#3198 := (or #3196 #3197 #2628)
#3199 := (not #3198)
#3205 := (or #24 #1205 #3199)
#4237 := (forall (vars (?v0 S2)) (:pat #4203) #3205)
#4242 := (not #4237)
decl f7 :: (-> S2 int)
#25 := (f7 #12)
#4148 := (pattern #25)
decl ?v1!6 :: (-> S2 S2)
#1960 := (?v1!6 #12)
#1964 := (f7 #1960)
#2571 := (* -1::int #1964)
#1961 := (f5 #1960 #12)
#1962 := (f4 #1961)
#2588 := (* -1::int #1962)
#2589 := (+ #2588 #2571)
#2590 := (+ #25 #2589)
#2591 := (= #2590 0::int)
#3169 := (not #2591)
#2572 := (+ #25 #2571)
#2573 := (<= #2572 0::int)
decl f8 :: (-> S2 S1)
#1970 := (f8 #1960)
#1971 := (= f1 #1970)
#3168 := (not #1971)
#3170 := (or #3168 #2573 #3169)
#3171 := (not #3170)
#1165 := (* -1::int #25)
#1166 := (+ f3 #1165)
#1167 := (<= #1166 0::int)
#3177 := (or #24 #1167 #3171)
#4229 := (forall (vars (?v0 S2)) (:pat #4148) #3177)
#4234 := (not #4229)
#75 := (f11 f12 #11)
#4220 := (pattern #72 #75)
#78 := (f9 f10 #11)
#1217 := (* -1::int #78)
#1218 := (+ #68 #1217)
#1221 := (>= #1218 0::int)
#453 := (= f1 #75)
#3134 := (not #453)
#3149 := (or #447 #3134 #1221)
#4221 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4220) #3149)
#4226 := (not #4221)
#1219 := (+ #49 #1218)
#1614 := (>= #1219 0::int)
#450 := (not #447)
#3126 := (or #450 #1141 #1614)
#4212 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4179) #3126)
#4217 := (not #4212)
#1642 := (>= #68 0::int)
#4204 := (forall (vars (?v0 S2)) (:pat #4203) #1642)
#4209 := (not #4204)
#66 := (f9 f10 f6)
#67 := (= #66 0::int)
#1653 := (not #67)
#4477 := (or #1653 #4209 #4217 #4226 #4234 #4242 #4474)
#4480 := (not #4477)
decl ?v0!5 :: S2
#1916 := ?v0!5
#1917 := (f5 #12 ?v0!5)
#4188 := (pattern #1917)
#33 := (f8 #12)
#4155 := (pattern #33)
#1919 := (f7 ?v0!5)
#1920 := (* -1::int #1919)
#1918 := (f4 #1917)
#2539 := (+ #1918 #1920)
#2540 := (+ #25 #2539)
#2543 := (= #2540 0::int)
#3087 := (not #2543)
#1924 := (+ #25 #1920)
#1925 := (>= #1924 0::int)
#368 := (= f1 #33)
#371 := (not #368)
#3088 := (or #371 #1925 #3087)
#4189 := (forall (vars (?v1 S2)) (:pat #4155 #4148 #4188) #3088)
#4194 := (not #4189)
#2515 := (= f6 ?v0!5)
#1929 := (+ f3 #1920)
#1930 := (<= #1929 0::int)
#4197 := (or #1930 #2515 #4194)
#4200 := (not #4197)
#4483 := (or #4200 #4480)
#4486 := (not #4483)
#44 := (f7 #11)
#1117 := (* -1::int #44)
#1138 := (+ #1117 #49)
#1139 := (+ #25 #1138)
#1136 := (>= #1139 0::int)
#3079 := (or #371 #1136 #1141)
#4180 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4179) #3079)
#4185 := (not #4180)
#4489 := (or #4185 #4486)
#4492 := (not #4489)
decl ?v1!3 :: S2
#1885 := ?v1!3
#1900 := (f7 ?v1!3)
decl ?v0!4 :: S2
#1886 := ?v0!4
#1897 := (f7 ?v0!4)
#1898 := (* -1::int #1897)
#2496 := (+ #1898 #1900)
#1887 := (f5 ?v1!3 ?v0!4)
#1888 := (f4 #1887)
#2497 := (+ #1888 #2496)
#2500 := (>= #2497 0::int)
#1893 := (f8 ?v1!3)
#1894 := (= f1 #1893)
#3042 := (not #1894)
#1889 := (* -1::int #1888)
#1890 := (+ f3 #1889)
#1891 := (<= #1890 0::int)
#3057 := (or #1891 #3042 #2500)
#3062 := (not #3057)
#4495 := (or #3062 #4492)
#4498 := (not #4495)
#41 := (f8 #11)
#4170 := (pattern #33 #41)
#1118 := (+ #25 #1117)
#1116 := (>= #1118 0::int)
#380 := (= f1 #41)
#3019 := (not #380)
#3034 := (or #368 #3019 #1116)
#4171 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4170) #3034)
#4176 := (not #4171)
#4501 := (or #4176 #4498)
#4504 := (not #4501)
decl ?v1!1 :: S2
#1858 := ?v1!1
#1862 := (f7 ?v1!1)
#2483 := (* -1::int #1862)
decl ?v0!2 :: S2
#1859 := ?v0!2
#1860 := (f7 ?v0!2)
#2484 := (+ #1860 #2483)
#2485 := (<= #2484 0::int)
#1867 := (f8 ?v1!1)
#1868 := (= f1 #1867)
#1865 := (f8 ?v0!2)
#1866 := (= f1 #1865)
#2112 := (not #1866)
#3011 := (or #2112 #1868 #2485)
#3016 := (not #3011)
#4507 := (or #3016 #4504)
#4510 := (not #4507)
#1107 := (>= #25 0::int)
#4162 := (forall (vars (?v0 S2)) (:pat #4148) #1107)
#4167 := (not #4162)
#4513 := (or #4167 #4510)
#4516 := (not #4513)
decl ?v0!0 :: S2
#1843 := ?v0!0
#1844 := (f7 ?v0!0)
#1845 := (>= #1844 0::int)
#1846 := (not #1845)
#4519 := (or #1846 #4516)
#4522 := (not #4519)
#37 := (f7 f6)
#38 := (= #37 0::int)
#1102 := (not #38)
#4525 := (or #1102 #4522)
#4528 := (not #4525)
#26 := (= #25 0::int)
#29 := (not #24)
#1711 := (or #29 #26)
#4535 := (forall (vars (?v0 S2)) (:pat #4148) #1711)
#1714 := (forall (vars (?v0 S2)) #1711)
#4538 := (iff #1714 #4535)
#4536 := (iff #1711 #1711)
#4537 := [refl]: #4536
#4539 := [quant-intro #4537]: #4538
#2167 := (~ #1714 #1714)
#2286 := (~ #1711 #1711)
#2287 := [refl]: #2286
#2168 := [nnf-pos #2287]: #2167
#1717 := (not #1714)
#1645 := (forall (vars (?v0 S2)) #1642)
#1648 := (not #1645)
#456 := (and #450 #453)
#462 := (not #456)
#1631 := (or #462 #1221)
#1636 := (forall (vars (?v0 S2) (?v1 S2)) #1631)
#1639 := (not #1636)
#1142 := (not #1141)
#1606 := (and #447 #1142)
#1611 := (not #1606)
#1617 := (or #1611 #1614)
#1620 := (forall (vars (?v0 S2) (?v1 S2)) #1617)
#1623 := (not #1620)
#1553 := (forall (vars (?v0 S2)) #1548)
#1556 := (not #1553)
#1363 := (not #1362)
#1356 := (not #1355)
#1366 := (and #1356 #1363)
#1524 := (not #1366)
#1532 := (or #1524 #1529)
#1535 := (forall (vars (?v0 S2)) #1532)
#1538 := (not #1535)
#1462 := (= #1440 0::int)
#1465 := (not #1408)
#1474 := (and #713 #1465 #1462)
#1479 := (exists (vars (?v1 S2)) #1474)
#1451 := (+ f3 #1384)
#1452 := (<= #1451 0::int)
#1453 := (not #1452)
#1456 := (and #29 #1453)
#1459 := (not #1456)
#1482 := (or #1459 #1479)
#1485 := (forall (vars (?v0 S2)) #1482)
#1430 := (and #713 #1142)
#1435 := (not #1430)
#1442 := (or #1435 #1438)
#1445 := (forall (vars (?v0 S2) (?v1 S2)) #1442)
#1448 := (not #1445)
#1488 := (or #1448 #1485)
#1491 := (and #1445 #1488)
#736 := (and #719 #733)
#742 := (not #736)
#1416 := (or #742 #1408)
#1421 := (forall (vars (?v0 S2) (?v1 S2)) #1416)
#1424 := (not #1421)
#1494 := (or #1424 #1491)
#1497 := (and #1421 #1494)
#1402 := (forall (vars (?v0 S2)) #1399)
#1405 := (not #1402)
#1500 := (or #1405 #1497)
#1503 := (and #1402 #1500)
#1506 := (or #1396 #1503)
#1509 := (and #170 #1506)
#725 := (forall (vars (?v0 S2)) #720)
#859 := (not #725)
#1512 := (or #859 #1509)
#1515 := (and #725 #1512)
#1388 := (forall (vars (?v0 S2)) #1383)
#1391 := (not #1388)
#1518 := (or #1391 #1515)
#1521 := (and #1388 #1518)
#1372 := (or #699 #1366)
#1377 := (forall (vars (?v0 S2)) #1372)
#1380 := (not #1377)
#1206 := (not #1205)
#1325 := (and #450 #1206)
#1330 := (exists (vars (?v0 S2)) #1325)
#1571 := (not #1330)
#1595 := (or #901 #668 #1571 #1380 #1521 #1538 #1556 #1560)
#1251 := (not #1250)
#1285 := (and #1142 #1251)
#1288 := (not #1285)
#1294 := (or #1288 #1291)
#1297 := (forall (vars (?v0 S2) (?v1 S2)) #1294)
#1300 := (not #1297)
#1308 := (or #125 #1300)
#1313 := (and #1297 #1308)
#1266 := (= #1268 0::int)
#1260 := (>= #1262 0::int)
#1263 := (not #1260)
#1270 := (and #1263 #1266)
#1273 := (exists (vars (?v1 S2)) #1270)
#1254 := (and #29 #1251)
#1257 := (not #1254)
#1276 := (or #1257 #1273)
#1279 := (forall (vars (?v0 S2)) #1276)
#1282 := (not #1279)
#1316 := (or #1282 #1313)
#1319 := (and #1279 #1316)
#1348 := (or #638 #620 #647 #629 #1319 #1330)
#1600 := (and #1348 #1595)
#1222 := (not #1221)
#1215 := (= #1219 0::int)
#1231 := (and #447 #1215 #1222)
#1236 := (exists (vars (?v1 S2)) #1231)
#1209 := (and #29 #1206)
#1212 := (not #1209)
#1239 := (or #1212 #1236)
#1242 := (forall (vars (?v0 S2)) #1239)
#1245 := (not #1242)
#1177 := (= #1139 0::int)
#1180 := (not #1116)
#1189 := (and #368 #1180 #1177)
#1194 := (exists (vars (?v1 S2)) #1189)
#1168 := (not #1167)
#1171 := (and #29 #1168)
#1174 := (not #1171)
#1197 := (or #1174 #1194)
#1200 := (forall (vars (?v0 S2)) #1197)
#1656 := (not #1200)
#1677 := (or #1653 #1656 #1245 #1600 #1623 #1639 #1648)
#1682 := (and #1200 #1677)
#1148 := (and #368 #1142)
#1153 := (not #1148)
#1156 := (or #1136 #1153)
#1159 := (forall (vars (?v0 S2) (?v1 S2)) #1156)
#1162 := (not #1159)
#1685 := (or #1162 #1682)
#1688 := (and #1159 #1685)
#383 := (and #371 #380)
#389 := (not #383)
#1123 := (or #389 #1116)
#1128 := (forall (vars (?v0 S2) (?v1 S2)) #1123)
#1131 := (not #1128)
#1691 := (or #1131 #1688)
#1694 := (and #1128 #1691)
#1108 := (forall (vars (?v0 S2)) #1107)
#1111 := (not #1108)
#1697 := (or #1111 #1694)
#1700 := (and #1108 #1697)
#1703 := (or #1102 #1700)
#1706 := (and #38 #1703)
#374 := (forall (vars (?v0 S2)) #371)
#1066 := (not #374)
#354 := (= f3 #25)
#360 := (or #24 #354)
#365 := (forall (vars (?v0 S2)) #360)
#1075 := (not #365)
#1729 := (or #1075 #1066 #1706 #1717)
#1734 := (not #1729)
#182 := (+ #155 #49)
#189 := (= #177 #182)
#166 := (= #165 f1)
#190 := (and #166 #189)
#188 := (< #155 #177)
#191 := (and #188 #190)
#192 := (exists (vars (?v1 S2)) #191)
#186 := (< #155 f3)
#187 := (and #29 #186)
#193 := (implies #187 #192)
#194 := (forall (vars (?v0 S2)) #193)
#195 := (and #194 true)
#183 := (<= #177 #182)
#50 := (< #49 f3)
#181 := (and #166 #50)
#184 := (implies #181 #183)
#185 := (forall (vars (?v0 S2) (?v1 S2)) #184)
#196 := (implies #185 #195)
#197 := (and #185 #196)
#178 := (<= #177 #155)
#175 := (= #174 f1)
#173 := (not #166)
#176 := (and #173 #175)
#179 := (implies #176 #178)
#180 := (forall (vars (?v0 S2) (?v1 S2)) #179)
#198 := (implies #180 #197)
#199 := (and #180 #198)
#171 := (<= 0::int #155)
#172 := (forall (vars (?v0 S2)) #171)
#200 := (implies #172 #199)
#201 := (and #172 #200)
#202 := (implies #170 #201)
#203 := (and #170 #202)
#160 := (= #155 #68)
#167 := (implies #166 #160)
#168 := (forall (vars (?v0 S2)) #167)
#204 := (implies #168 #203)
#205 := (and #168 #204)
#163 := (<= #155 #68)
#164 := (forall (vars (?v0 S2)) #163)
#206 := (implies #164 #205)
#207 := (and #164 #206)
#152 := (+ #141 #150)
#153 := (< #152 #68)
#151 := (< #150 f3)
#154 := (and #151 #153)
#159 := (not #154)
#161 := (implies #159 #160)
#162 := (forall (vars (?v0 S2)) #161)
#208 := (implies #162 #207)
#156 := (= #155 #152)
#157 := (implies #154 #156)
#158 := (forall (vars (?v0 S2)) #157)
#209 := (implies #158 #208)
#210 := (implies #148 #209)
#143 := (<= #141 #68)
#73 := (= #72 f1)
#74 := (not #73)
#144 := (implies #74 #143)
#145 := (forall (vars (?v0 S2)) #144)
#211 := (implies #145 #210)
#142 := (< #141 f3)
#212 := (implies #142 #211)
#139 := (= #138 f1)
#140 := (not #139)
#213 := (implies #140 #212)
#87 := (< #68 f3)
#96 := (and #74 #87)
#97 := (exists (vars (?v0 S2)) #96)
#214 := (implies #97 #213)
#215 := (implies true #214)
#126 := (and #125 true)
#114 := (+ #109 #49)
#121 := (<= #112 #114)
#110 := (< #109 f3)
#120 := (and #110 #50)
#122 := (implies #120 #121)
#123 := (forall (vars (?v0 S2) (?v1 S2)) #122)
#127 := (implies #123 #126)
#128 := (and #123 #127)
#115 := (= #112 #114)
#113 := (< #109 #112)
#116 := (and #113 #115)
#117 := (exists (vars (?v1 S2)) #116)
#111 := (and #29 #110)
#118 := (implies #111 #117)
#119 := (forall (vars (?v0 S2)) #118)
#129 := (implies #119 #128)
#130 := (and #119 #129)
#131 := (implies #108 #130)
#105 := (= f16 f10)
#132 := (implies #105 #131)
#133 := (implies #103 #132)
#100 := (= f13 f12)
#134 := (implies #100 #133)
#98 := (not #97)
#135 := (implies #98 #134)
#136 := (implies true #135)
#216 := (and #136 #215)
#83 := (+ #68 #49)
#90 := (= #78 #83)
#91 := (and #73 #90)
#89 := (< #68 #78)
#92 := (and #89 #91)
#93 := (exists (vars (?v1 S2)) #92)
#88 := (and #29 #87)
#94 := (implies #88 #93)
#95 := (forall (vars (?v0 S2)) #94)
#217 := (implies #95 #216)
#84 := (<= #78 #83)
#82 := (and #73 #50)
#85 := (implies #82 #84)
#86 := (forall (vars (?v0 S2) (?v1 S2)) #85)
#218 := (implies #86 #217)
#79 := (<= #78 #68)
#76 := (= #75 f1)
#77 := (and #74 #76)
#80 := (implies #77 #79)
#81 := (forall (vars (?v0 S2) (?v1 S2)) #80)
#219 := (implies #81 #218)
#69 := (<= 0::int #68)
#70 := (forall (vars (?v0 S2)) #69)
#220 := (implies #70 #219)
#221 := (implies #67 #220)
#222 := (implies true #221)
#52 := (+ #25 #49)
#59 := (= #44 #52)
#34 := (= #33 f1)
#60 := (and #34 #59)
#58 := (< #25 #44)
#61 := (and #58 #60)
#62 := (exists (vars (?v1 S2)) #61)
#56 := (< #25 f3)
#57 := (and #29 #56)
#63 := (implies #57 #62)
#64 := (forall (vars (?v0 S2)) #63)
#223 := (implies #64 #222)
#224 := (and #64 #223)
#53 := (<= #44 #52)
#51 := (and #34 #50)
#54 := (implies #51 #53)
#55 := (forall (vars (?v0 S2) (?v1 S2)) #54)
#225 := (implies #55 #224)
#226 := (and #55 #225)
#45 := (<= #44 #25)
#42 := (= #41 f1)
#35 := (not #34)
#43 := (and #35 #42)
#46 := (implies #43 #45)
#47 := (forall (vars (?v0 S2) (?v1 S2)) #46)
#227 := (implies #47 #226)
#228 := (and #47 #227)
#39 := (<= 0::int #25)
#40 := (forall (vars (?v0 S2)) #39)
#229 := (implies #40 #228)
#230 := (and #40 #229)
#231 := (implies #38 #230)
#232 := (and #38 #231)
#36 := (forall (vars (?v0 S2)) #35)
#233 := (implies #36 #232)
#30 := (= #25 f3)
#31 := (implies #29 #30)
#32 := (forall (vars (?v0 S2)) #31)
#234 := (implies #32 #233)
#27 := (implies #24 #26)
#28 := (forall (vars (?v0 S2)) #27)
#235 := (implies #28 #234)
#236 := (implies true #235)
#237 := (not #236)
#1737 := (iff #237 #1734)
#759 := (+ #49 #155)
#777 := (= #177 #759)
#780 := (and #713 #777)
#783 := (and #188 #780)
#786 := (exists (vars (?v1 S2)) #783)
#792 := (not #187)
#793 := (or #792 #786)
#798 := (forall (vars (?v0 S2)) #793)
#762 := (<= #177 #759)
#754 := (and #50 #713)
#768 := (not #754)
#769 := (or #768 #762)
#774 := (forall (vars (?v0 S2) (?v1 S2)) #769)
#811 := (not #774)
#812 := (or #811 #798)
#817 := (and #774 #812)
#743 := (or #178 #742)
#748 := (forall (vars (?v0 S2) (?v1 S2)) #743)
#823 := (not #748)
#824 := (or #823 #817)
#829 := (and #748 #824)
#835 := (not #172)
#836 := (or #835 #829)
#841 := (and #172 #836)
#728 := (= 0::int #169)
#847 := (not #728)
#848 := (or #847 #841)
#853 := (and #728 #848)
#860 := (or #859 #853)
#865 := (and #725 #860)
#871 := (not #164)
#872 := (or #871 #865)
#877 := (and #164 #872)
#705 := (or #154 #699)
#710 := (forall (vars (?v0 S2)) #705)
#883 := (not #710)
#884 := (or #883 #877)
#685 := (= #152 #155)
#691 := (or #159 #685)
#696 := (forall (vars (?v0 S2)) #691)
#892 := (not #696)
#893 := (or #892 #884)
#902 := (or #901 #893)
#677 := (or #143 #447)
#682 := (forall (vars (?v0 S2)) #677)
#910 := (not #682)
#911 := (or #910 #902)
#919 := (not #142)
#920 := (or #919 #911)
#928 := (or #668 #920)
#524 := (and #87 #450)
#529 := (exists (vars (?v0 S2)) #524)
#532 := (not #529)
#936 := (or #532 #928)
#583 := (= 0::int #124)
#541 := (+ #49 #109)
#568 := (<= #112 #541)
#565 := (and #50 #110)
#574 := (not #565)
#575 := (or #574 #568)
#580 := (forall (vars (?v0 S2) (?v1 S2)) #575)
#596 := (not #580)
#597 := (or #596 #583)
#602 := (and #580 #597)
#544 := (= #112 #541)
#547 := (and #113 #544)
#550 := (exists (vars (?v1 S2)) #547)
#556 := (not #111)
#557 := (or #556 #550)
#562 := (forall (vars (?v0 S2)) #557)
#608 := (not #562)
#609 := (or #608 #602)
#614 := (and #562 #609)
#621 := (or #620 #614)
#630 := (or #629 #621)
#639 := (or #638 #630)
#648 := (or #647 #639)
#656 := (or #529 #648)
#948 := (and #656 #936)
#479 := (+ #49 #68)
#497 := (= #78 #479)
#500 := (and #447 #497)
#503 := (and #89 #500)
#506 := (exists (vars (?v1 S2)) #503)
#512 := (not #88)
#513 := (or #512 #506)
#518 := (forall (vars (?v0 S2)) #513)
#954 := (not #518)
#955 := (or #954 #948)
#482 := (<= #78 #479)
#474 := (and #50 #447)
#488 := (not #474)
#489 := (or #488 #482)
#494 := (forall (vars (?v0 S2) (?v1 S2)) #489)
#963 := (not #494)
#964 := (or #963 #955)
#463 := (or #79 #462)
#468 := (forall (vars (?v0 S2) (?v1 S2)) #463)
#972 := (not #468)
#973 := (or #972 #964)
#981 := (not #70)
#982 := (or #981 #973)
#444 := (= 0::int #66)
#990 := (not #444)
#991 := (or #990 #982)
#421 := (and #59 #368)
#426 := (and #58 #421)
#429 := (exists (vars (?v1 S2)) #426)
#435 := (not #57)
#436 := (or #435 #429)
#441 := (forall (vars (?v0 S2)) #436)
#1006 := (not #441)
#1007 := (or #1006 #991)
#1012 := (and #441 #1007)
#401 := (and #50 #368)
#409 := (not #401)
#410 := (or #53 #409)
#415 := (forall (vars (?v0 S2) (?v1 S2)) #410)
#1018 := (not #415)
#1019 := (or #1018 #1012)
#1024 := (and #415 #1019)
#390 := (or #45 #389)
#395 := (forall (vars (?v0 S2) (?v1 S2)) #390)
#1030 := (not #395)
#1031 := (or #1030 #1024)
#1036 := (and #395 #1031)
#1042 := (not #40)
#1043 := (or #1042 #1036)
#1048 := (and #40 #1043)
#377 := (= 0::int #37)
#1054 := (not #377)
#1055 := (or #1054 #1048)
#1060 := (and #377 #1055)
#1067 := (or #1066 #1060)
#1076 := (or #1075 #1067)
#340 := (= 0::int #25)
#346 := (or #29 #340)
#351 := (forall (vars (?v0 S2)) #346)
#1084 := (not #351)
#1085 := (or #1084 #1076)
#1097 := (not #1085)
#1735 := (iff #1097 #1734)
#1732 := (iff #1085 #1729)
#1720 := (or #1066 #1706)
#1723 := (or #1075 #1720)
#1726 := (or #1717 #1723)
#1730 := (iff #1726 #1729)
#1731 := [rewrite]: #1730
#1727 := (iff #1085 #1726)
#1724 := (iff #1076 #1723)
#1721 := (iff #1067 #1720)
#1707 := (iff #1060 #1706)
#1704 := (iff #1055 #1703)
#1701 := (iff #1048 #1700)
#1698 := (iff #1043 #1697)
#1695 := (iff #1036 #1694)
#1692 := (iff #1031 #1691)
#1689 := (iff #1024 #1688)
#1686 := (iff #1019 #1685)
#1683 := (iff #1012 #1682)
#1680 := (iff #1007 #1677)
#1659 := (or #1245 #1600)
#1662 := (or #1623 #1659)
#1665 := (or #1639 #1662)
#1668 := (or #1648 #1665)
#1671 := (or #1653 #1668)
#1674 := (or #1656 #1671)
#1678 := (iff #1674 #1677)
#1679 := [rewrite]: #1678
#1675 := (iff #1007 #1674)
#1672 := (iff #991 #1671)
#1669 := (iff #982 #1668)
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#1387 := [rewrite]: #1386
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#1365 := [rewrite]: #1364
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#1358 := [rewrite]: #1357
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#1379 := [quant-intro #1376]: #1378
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#1531 := [rewrite]: #1530
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#1544 := [rewrite]: #1543
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#1555 := [quant-intro #1552]: #1554
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#904 := [rewrite]: #903
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#875 := (iff #206 #872)
#868 := (implies #164 #865)
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#826 := [rewrite]: #825
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#818 := (iff #197 #817)
#815 := (iff #196 #812)
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#813 := (iff #808 #812)
#814 := [rewrite]: #813
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#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
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#787 := (iff #192 #786)
#784 := (iff #191 #783)
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#760 := (= #182 #759)
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#715 := [rewrite]: #714
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#785 := [monotonicity #782]: #784
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#797 := [trans #791 #795]: #796
#800 := [quant-intro #797]: #799
#803 := [monotonicity #800]: #802
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#764 := [monotonicity #761]: #763
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#773 := [trans #767 #771]: #772
#776 := [quant-intro #773]: #775
#810 := [monotonicity #776 #807]: #809
#816 := [trans #810 #814]: #815
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#739 := (implies #736 #178)
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#745 := [rewrite]: #744
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#734 := (iff #175 #733)
#735 := [rewrite]: #734
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#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
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#730 := [rewrite]: #729
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#852 := [trans #846 #850]: #851
#855 := [monotonicity #730 #852]: #854
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#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
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#708 := (iff #161 #705)
#702 := (implies #159 #699)
#706 := (iff #702 #705)
#707 := [rewrite]: #706
#703 := (iff #161 #702)
#704 := [monotonicity #701]: #703
#709 := [trans #704 #707]: #708
#712 := [quant-intro #709]: #711
#882 := [monotonicity #712 #879]: #881
#888 := [trans #882 #886]: #887
#697 := (iff #158 #696)
#694 := (iff #157 #691)
#688 := (implies #154 #685)
#692 := (iff #688 #691)
#693 := [rewrite]: #692
#689 := (iff #157 #688)
#686 := (iff #156 #685)
#687 := [rewrite]: #686
#690 := [monotonicity #687]: #689
#695 := [trans #690 #693]: #694
#698 := [quant-intro #695]: #697
#891 := [monotonicity #698 #888]: #890
#897 := [trans #891 #895]: #896
#900 := [monotonicity #897]: #899
#906 := [trans #900 #904]: #905
#683 := (iff #145 #682)
#680 := (iff #144 #677)
#674 := (implies #450 #143)
#678 := (iff #674 #677)
#679 := [rewrite]: #678
#675 := (iff #144 #674)
#451 := (iff #74 #450)
#448 := (iff #73 #447)
#449 := [rewrite]: #448
#452 := [monotonicity #449]: #451
#676 := [monotonicity #452]: #675
#681 := [trans #676 #679]: #680
#684 := [quant-intro #681]: #683
#909 := [monotonicity #684 #906]: #908
#915 := [trans #909 #913]: #914
#918 := [monotonicity #915]: #917
#924 := [trans #918 #922]: #923
#672 := (iff #140 #671)
#669 := (iff #139 #668)
#670 := [rewrite]: #669
#673 := [monotonicity #670]: #672
#927 := [monotonicity #673 #924]: #926
#932 := [trans #927 #930]: #931
#530 := (iff #97 #529)
#527 := (iff #96 #524)
#521 := (and #450 #87)
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#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
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#661 := (implies true #656)
#664 := (iff #661 #656)
#665 := [rewrite]: #664
#662 := (iff #136 #661)
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#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
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#610 := (iff #605 #609)
#611 := [rewrite]: #610
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#603 := (iff #128 #602)
#600 := (iff #127 #597)
#593 := (implies #580 #583)
#598 := (iff #593 #597)
#599 := [rewrite]: #598
#594 := (iff #127 #593)
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#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
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#576 := (iff #571 #575)
#577 := [rewrite]: #576
#572 := (iff #122 #571)
#569 := (iff #121 #568)
#542 := (= #114 #541)
#543 := [rewrite]: #542
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#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
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#553 := (implies #111 #550)
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#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
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#516 := (iff #94 #513)
#509 := (implies #88 #506)
#514 := (iff #509 #513)
#515 := [rewrite]: #514
#510 := (iff #94 #509)
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#504 := (iff #92 #503)
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#498 := (iff #90 #497)
#480 := (= #83 #479)
#481 := [rewrite]: #480
#499 := [monotonicity #481]: #498
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#505 := [monotonicity #502]: #504
#508 := [quant-intro #505]: #507
#511 := [monotonicity #508]: #510
#517 := [trans #511 #515]: #516
#520 := [quant-intro #517]: #519
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#959 := [trans #953 #957]: #958
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#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
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#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
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#968 := [trans #962 #966]: #967
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#465 := [rewrite]: #464
#460 := (iff #80 #459)
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#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
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#445 := (iff #67 #444)
#446 := [rewrite]: #445
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#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)
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#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)
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#3837 := (or #3836 #38)
#4589 := (or #4588 #3837)
#4591 := (iff #4589 #4586)
#4630 := (iff #4586 #4586)
#4631 := [rewrite]: #4630
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#4585 := [rewrite]: #4577
#3801 := (iff #3837 #3800)
#3796 := (iff #3836 false)
#9474 := (not true)
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#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)
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#2933 := (iff #2346 #2932)
#2930 := (iff #2342 #2929)
#2927 := (iff #2338 #2926)
#2924 := (iff #2334 #2921)
#2884 := (and #2309 #2878)
#2915 := (and #2884 #2912)
#2918 := (and #1445 #2915)
#2922 := (iff #2918 #2921)
#2923 := [rewrite]: #2922
#2919 := (iff #2334 #2918)
#2916 := (iff #2329 #2915)
#2913 := (iff #2325 #2912)
#2910 := (iff #2322 #2909)
#2907 := (iff #2305 #2906)
#2904 := (iff #2302 #2903)
#2901 := (= #2301 #2900)
#2902 := [rewrite]: #2901
#2905 := [monotonicity #2902]: #2904
#2908 := [monotonicity #2905]: #2907
#2911 := [monotonicity #2908]: #2910
#2914 := [quant-intro #2911]: #2913
#2897 := (iff #2319 #2884)
#2889 := (not #2884)
#2892 := (not #2889)
#2895 := (iff #2892 #2884)
#2896 := [rewrite]: #2895
#2893 := (iff #2319 #2892)
#2890 := (iff #2313 #2889)
#2887 := (iff #2312 #2884)
#2881 := (and #2878 #2309)
#2885 := (iff #2881 #2884)
#2886 := [rewrite]: #2885
#2882 := (iff #2312 #2881)
#2879 := (iff #2311 #2878)
#2876 := (iff #2310 #2875)
#2877 := [rewrite]: #2876
#2880 := [monotonicity #2877]: #2879
#2883 := [monotonicity #2880]: #2882
#2888 := [trans #2883 #2886]: #2887
#2891 := [monotonicity #2888]: #2890
#2894 := [monotonicity #2891]: #2893
#2898 := [trans #2894 #2896]: #2897
#2917 := [monotonicity #2898 #2914]: #2916
#2920 := [monotonicity #2917]: #2919
#2925 := [trans #2920 #2923]: #2924
#2873 := (iff #2283 #2872)
#2870 := (iff #2282 #2869)
#2867 := (iff #2273 #2864)
#2854 := (+ #2268 #2271)
#2855 := (+ #2267 #2854)
#2858 := (>= #2855 0::int)
#2865 := (iff #2858 #2864)
#2866 := [rewrite]: #2865
#2859 := (iff #2273 #2858)
#2856 := (= #2272 #2855)
#2857 := [rewrite]: #2856
#2860 := [monotonicity #2857]: #2859
#2868 := [trans #2860 #2866]: #2867
#2852 := (iff #2281 #2851)
#2849 := (iff #2280 #2848)
#2850 := [rewrite]: #2849
#2853 := [monotonicity #2850]: #2852
#2871 := [monotonicity #2853 #2868]: #2870
#2874 := [monotonicity #2871]: #2873
#2928 := [monotonicity #2874 #2925]: #2927
#2931 := [monotonicity #2928]: #2930
#2846 := (iff #2252 #2845)
#2843 := (iff #2251 #2842)
#2840 := (iff #2243 #2837)
#2829 := (+ #2240 #2241)
#2832 := (>= #2829 0::int)
#2838 := (iff #2832 #2837)
#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
#2769 := [monotonicity #2766]: #2768
#2774 := [trans #2769 #2772]: #2773
#2739 := (iff #2082 #2738)
#2736 := (iff #2079 #2735)
#2733 := (iff #2074 #2732)
#2730 := (iff #2071 #2727)
#2717 := (+ #2066 #2069)
#2718 := (+ #1248 #2717)
#2721 := (= #2718 0::int)
#2728 := (iff #2721 #2727)
#2729 := [rewrite]: #2728
#2722 := (iff #2071 #2721)
#2719 := (= #2070 #2718)
#2720 := [rewrite]: #2719
#2723 := [monotonicity #2720]: #2722
#2731 := [trans #2723 #2729]: #2730
#2715 := (iff #2073 #2714)
#2712 := (iff #2072 #2709)
#2701 := (+ #1248 #2066)
#2704 := (>= #2701 0::int)
#2710 := (iff #2704 #2709)
#2711 := [rewrite]: #2710
#2705 := (iff #2072 #2704)
#2702 := (= #2067 #2701)
#2703 := [rewrite]: #2702
#2706 := [monotonicity #2703]: #2705
#2713 := [trans #2706 #2711]: #2712
#2716 := [monotonicity #2713]: #2715
#2734 := [monotonicity #2716 #2731]: #2733
#2737 := [monotonicity #2734]: #2736
#2740 := [quant-intro #2737]: #2739
#2777 := [monotonicity #2740 #2774]: #2776
#2699 := (iff #2058 #2696)
#2662 := (and #2039 #2656)
#2693 := (and #2662 #2690)
#2697 := (iff #2693 #2696)
#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
#2649 := (iff #2019 #535)
#2650 := [rewrite]: #2649
#2647 := (iff #2016 #108)
#2648 := [rewrite]: #2647
#2645 := (iff #2013 #103)
#2646 := [rewrite]: #2645
#2783 := [monotonicity #2646 #2648 #2650 #2652 #2780]: #2782
#2788 := [trans #2783 #2786]: #2787
#2969 := [monotonicity #2788 #2966]: #2968
#2643 := (iff #2007 #2642)
#2640 := (iff #2004 #2639)
#2637 := (iff #1999 #2636)
#2634 := (iff #1992 #2633)
#2631 := (iff #1991 #2628)
#2621 := (+ #1203 #1989)
#2624 := (>= #2621 0::int)
#2629 := (iff #2624 #2628)
#2630 := [rewrite]: #2629
#2625 := (iff #1991 #2624)
#2622 := (= #1990 #2621)
#2623 := [rewrite]: #2622
#2626 := [monotonicity #2623]: #2625
#2632 := [trans #2626 #2630]: #2631
#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
#2528 := [trans #2523 #2526]: #2527
#2531 := [monotonicity #2528]: #2530
#2534 := [monotonicity #2531]: #2533
#2538 := [trans #2534 #2536]: #2537
#2557 := [monotonicity #2538 #2554]: #2556
#2562 := [trans #2557 #2560]: #2561
#2980 := [monotonicity #2562 #2977]: #2979
#2983 := [monotonicity #2980]: #2982
#2513 := (iff #1904 #2512)
#2510 := (iff #1903 #2509)
#2507 := (iff #1896 #2506)
#2504 := (iff #1895 #2503)
#2505 := [rewrite]: #2504
#2508 := [monotonicity #2505]: #2507
#2501 := (iff #1902 #2500)
#2498 := (= #1901 #2497)
#2499 := [rewrite]: #2498
#2502 := [monotonicity #2499]: #2501
#2511 := [monotonicity #2502 #2508]: #2510
#2514 := [monotonicity #2511]: #2513
#2986 := [monotonicity #2514 #2983]: #2985
#2989 := [monotonicity #2986]: #2988
#2494 := (iff #1873 #2493)
#2491 := (iff #1872 #2490)
#2488 := (iff #1864 #2485)
#2477 := (+ #1861 #1862)
#2480 := (>= #2477 0::int)
#2486 := (iff #2480 #2485)
#2487 := [rewrite]: #2486
#2481 := (iff #1864 #2480)
#2478 := (= #1863 #2477)
#2479 := [rewrite]: #2478
#2482 := [monotonicity #2479]: #2481
#2489 := [trans #2482 #2487]: #2488
#2475 := (iff #1871 #2474)
#2472 := (iff #1870 #2471)
#2473 := [rewrite]: #2472
#2476 := [monotonicity #2473]: #2475
#2492 := [monotonicity #2476 #2489]: #2491
#2495 := [monotonicity #2492]: #2494
#2992 := [monotonicity #2495 #2989]: #2991
#2995 := [monotonicity #2992]: #2994
#2998 := [monotonicity #2995]: #2997
#2469 := (iff #1814 #38)
#2470 := [rewrite]: #2469
#3001 := [monotonicity #2470 #2998]: #3000
#3004 := [monotonicity #3001]: #3003
#1742 := (not #1706)
#2464 := (~ #1742 #2463)
#2460 := (not #1703)
#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
#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
#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