src/HOL/SMT_Examples/Boogie_Dijkstra.certs

tuned proofs -- clarified flow of facts wrt. calculation;

5d68fa8702e4a020dc142c33743a5a5445fcba10 6136 0
#2 := false
#53 := 0::Int
decl f30 :: (-> S2 Int)
decl ?v1!7 :: (-> S2 S2)
decl ?v0!20 :: S2
#2123 := ?v0!20
#5431 := (?v1!7 ?v0!20)
#18254 := (f30 #5431)
#1012 := -1::Int
#17799 := (* -1::Int #18254)
decl f15 :: (-> S4 Int)
decl f5 :: (-> S5 S2 S4)
decl f6 :: (-> S6 S2 S5)
decl f7 :: S6
#8 := f7
#5439 := (f6 f7 #5431)
#5440 := (f5 #5439 ?v0!20)
#5441 := (f15 #5440)
#5442 := (* -1::Int #5441)
#18528 := (+ #5442 #17799)
#2126 := (f30 ?v0!20)
#18529 := (+ #2126 #18528)
#15418 := (>= #18529 0::Int)
decl f19 :: (-> S11 S2 Int)
decl f20 :: S11
#109 := f20
#5432 := (f19 f20 #5431)
#5433 := (* -1::Int #5432)
#5443 := (+ #5433 #5442)
#5169 := (f19 f20 ?v0!20)
#5444 := (+ #5169 #5443)
#11830 := (>= #5444 0::Int)
#5445 := (= #5444 0::Int)
#5446 := (not #5445)
decl f1 :: S1
#3 := f1
decl f9 :: (-> S7 S2 S1)
decl f21 :: S7
#115 := f21
#5436 := (f9 f21 #5431)
#5437 := (= #5436 f1)
#5438 := (not #5437)
#5434 := (+ #5169 #5433)
#5435 := (<= #5434 0::Int)
#5447 := (or #5435 #5438 #5446)
#5448 := (not #5447)
#5194 := (* -1::Int #5169)
decl f14 :: Int
#54 := f14
#5429 := (+ f14 #5194)
#5430 := (<= #5429 0::Int)
#17547 := (not #5430)
#5195 := (+ #2126 #5194)
#17503 := (>= #5195 0::Int)
#5176 := (= #2126 #5169)
decl f28 :: S2
#186 := f28
#19609 := (= f28 ?v0!20)
#19613 := (not #19609)
#14451 := (= ?v0!20 f28)
#15274 := (not #14451)
#16593 := (iff #15274 #19613)
#15457 := (iff #14451 #19609)
#14873 := (iff #19609 #14451)
#7691 := [commutativity]: #14873
#16696 := [symm #7691]: #15457
#14829 := [monotonicity #16696]: #16593
#5398 := (f9 f21 ?v0!20)
#5399 := (= #5398 f1)
#14460 := (or #14451 #5399)
#15350 := (not #14460)
decl f10 :: (-> S8 S1 S7)
decl f11 :: (-> S9 S2 S8)
decl f12 :: (-> S10 S7 S9)
decl f13 :: S10
#27 := f13
#196 := (f12 f13 f21)
#197 := (f11 #196 f28)
#198 := (f10 #197 f1)
#14446 := (f9 #198 ?v0!20)
#14450 := (= #14446 f1)
#14478 := (iff #14450 #14460)
#11 := (:var 0 S2)
#42 := (:var 1 S1)
#40 := (:var 2 S2)
#38 := (:var 3 S7)
#39 := (f12 f13 #38)
#41 := (f11 #39 #40)
#43 := (f10 #41 #42)
#44 := (f9 #43 #11)
#3717 := (pattern #44)
#48 := (f9 #38 #11)
#49 := (= #48 f1)
#47 := (= #42 f1)
#46 := (= #11 #40)
#50 := (if #46 #47 #49)
#45 := (= #44 f1)
#51 := (iff #45 #50)
#3718 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1) (?v3 S2)) (:pat #3717) #51)
#52 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1) (?v3 S2)) #51)
#3721 := (iff #52 #3718)
#3719 := (iff #51 #51)
#3720 := [refl]: #3719
#3722 := [quant-intro #3720]: #3721
#1579 := (~ #52 #52)
#1609 := (~ #51 #51)
#1610 := [refl]: #1609
#1580 := [nnf-pos #1610]: #1579
#322 := [asserted]: #52
#1611 := [mp~ #322 #1580]: #52
#3723 := [mp #1611 #3722]: #3718
#7628 := (not #3718)
#15363 := (or #7628 #14478)
#4146 := (= f1 f1)
#14455 := (if #14451 #4146 #5399)
#14456 := (iff #14450 #14455)
#15337 := (or #7628 #14456)
#15318 := (iff #15337 #15363)
#15276 := (iff #15363 #15363)
#15289 := [rewrite]: #15276
#14479 := (iff #14456 #14478)
#14476 := (iff #14455 #14460)
#1 := true
#14457 := (if #14451 true #5399)
#14461 := (iff #14457 #14460)
#14475 := [rewrite]: #14461
#14458 := (iff #14455 #14457)
#4148 := (iff #4146 true)
#4149 := [rewrite]: #4148
#14459 := [monotonicity #4149]: #14458
#14477 := [trans #14459 #14475]: #14476
#14480 := [monotonicity #14477]: #14479
#15256 := [monotonicity #14480]: #15318
#15235 := [trans #15256 #15289]: #15318
#15310 := [quant-inst #115 #186 #3 #2123]: #15337
#15352 := [mp #15310 #15235]: #15363
#16371 := [unit-resolution #15352 #3723]: #14478
#15284 := (not #14450)
decl f29 :: S7
#195 := f29
#4622 := (f9 f29 ?v0!20)
#4623 := (= #4622 f1)
#4630 := (not #4623)
#15122 := (iff #4630 #15284)
#15124 := (iff #4623 #14450)
#16582 := (iff #14450 #4623)
#16482 := (= #14446 #4622)
#9268 := (= #198 f29)
#199 := (= f29 #198)
#91 := (f6 f7 #11)
#3782 := (pattern #91)
#217 := (f9 f29 #11)
#3943 := (pattern #217)
#207 := (f30 #11)
#3918 := (pattern #207)
#2136 := (f5 #91 ?v0!20)
#2137 := (f15 #2136)
#2127 := (* -1::Int #2126)
#2472 := (+ #2127 #2137)
#2473 := (+ #207 #2472)
#2476 := (= #2473 0::Int)
#3030 := (not #2476)
#218 := (= #217 f1)
#225 := (not #218)
#2133 := (+ #207 #2127)
#2134 := (>= #2133 0::Int)
#3031 := (or #2134 #225 #3030)
#3977 := (forall (vars (?v1 S2)) (:pat #3918 #3943 #3782) #3031)
#3982 := (not #3977)
#2128 := (+ f14 #2127)
#2129 := (<= #2128 0::Int)
decl f16 :: S2
#65 := f16
#2124 := (= ?v0!20 f16)
#9 := (:var 1 S2)
#92 := (f5 #91 #9)
#3773 := (pattern #92)
#229 := (f30 #9)
#1275 := (* -1::Int #229)
#1276 := (+ #207 #1275)
#93 := (f15 #92)
#1296 := (+ #93 #1276)
#1294 := (>= #1296 0::Int)
#1027 := (* -1::Int #93)
#1028 := (+ f14 #1027)
#1029 := (<= #1028 0::Int)
#3022 := (or #225 #1029 #1294)
#3969 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3773) #3022)
#3974 := (not #3969)
#3985 := (or #3974 #2124 #2129 #3982)
#3988 := (not #3985)
decl ?v0!19 :: S2
#2092 := ?v0!19
#2105 := (f30 ?v0!19)
#2106 := (* -1::Int #2105)
decl ?v1!18 :: S2
#2091 := ?v1!18
#2104 := (f30 ?v1!18)
#2107 := (+ #2104 #2106)
#2095 := (f6 f7 ?v1!18)
#2096 := (f5 #2095 ?v0!19)
#2097 := (f15 #2096)
#2108 := (+ #2097 #2107)
#2109 := (>= #2108 0::Int)
#2098 := (* -1::Int #2097)
#2099 := (+ f14 #2098)
#2100 := (<= #2099 0::Int)
#2093 := (f9 f29 ?v1!18)
#2094 := (= #2093 f1)
#2985 := (not #2094)
#3000 := (or #2985 #2100 #2109)
#3005 := (not #3000)
#3991 := (or #3005 #3988)
#3994 := (not #3991)
#3960 := (pattern #207 #229)
#1274 := (>= #1276 0::Int)
#226 := (f9 f29 #9)
#227 := (= #226 f1)
#2962 := (not #227)
#2977 := (or #218 #2962 #1274)
#3961 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3960) #2977)
#3966 := (not #3961)
#3997 := (or #3966 #3994)
#4000 := (not #3997)
decl ?v0!17 :: S2
#2065 := ?v0!17
#2074 := (f30 ?v0!17)
#2075 := (* -1::Int #2074)
decl ?v1!16 :: S2
#2064 := ?v1!16
#2073 := (f30 ?v1!16)
#2076 := (+ #2073 #2075)
#2077 := (>= #2076 0::Int)
#2069 := (f9 f29 ?v0!17)
#2070 := (= #2069 f1)
#2939 := (not #2070)
#2066 := (f9 f29 ?v1!16)
#2067 := (= #2066 f1)
#2954 := (or #2067 #2939 #2077)
#2959 := (not #2954)
#4003 := (or #2959 #4000)
#4006 := (not #4003)
#1265 := (>= #207 0::Int)
#3952 := (forall (vars (?v0 S2)) (:pat #3918) #1265)
#3957 := (not #3952)
#4009 := (or #3957 #4006)
#4012 := (not #4009)
decl ?v0!15 :: S2
#2049 := ?v0!15
#2050 := (f30 ?v0!15)
#2051 := (>= #2050 0::Int)
#2052 := (not #2051)
#4015 := (or #2052 #4012)
#4018 := (not #4015)
#221 := (f30 f16)
#222 := (= #221 0::Int)
#713 := (not #222)
#4021 := (or #713 #4018)
#4024 := (not #4021)
#4027 := (or #713 #4024)
#4030 := (not #4027)
#112 := (f19 f20 #11)
#3805 := (pattern #112)
#212 := (= #207 #112)
#603 := (or #225 #212)
#3944 := (forall (vars (?v0 S2)) (:pat #3943 #3918 #3805) #603)
#3949 := (not #3944)
#4033 := (or #3949 #4030)
#4036 := (not #4033)
decl ?v0!14 :: S2
#2024 := ?v0!14
#2029 := (f19 f20 ?v0!14)
#2028 := (f30 ?v0!14)
#2030 := (= #2028 #2029)
#2025 := (f9 f29 ?v0!14)
#2026 := (= #2025 f1)
#2027 := (not #2026)
#2031 := (or #2027 #2030)
#2032 := (not #2031)
#4039 := (or #2032 #4036)
#4042 := (not #4039)
#1255 := (* -1::Int #207)
#1256 := (+ #112 #1255)
#1254 := (>= #1256 0::Int)
#3935 := (forall (vars (?v0 S2)) (:pat #3805 #3918) #1254)
#3940 := (not #3935)
#4045 := (or #3940 #4042)
#4048 := (not #4045)
decl ?v0!13 :: S2
#2006 := ?v0!13
#2008 := (f30 ?v0!13)
#2009 := (* -1::Int #2008)
#2007 := (f19 f20 ?v0!13)
#2010 := (+ #2007 #2009)
#2011 := (>= #2010 0::Int)
#2012 := (not #2011)
#4051 := (or #2012 #4048)
#4054 := (not #4051)
#200 := (f6 f7 f28)
#201 := (f5 #200 #11)
#3917 := (pattern #201)
#202 := (f15 #201)
#1229 := (* -1::Int #202)
#190 := (f19 f20 f28)
#1235 := (* -1::Int #190)
#1236 := (+ #1235 #1229)
#1237 := (+ #112 #1236)
#1238 := (<= #1237 0::Int)
#1230 := (+ f14 #1229)
#1231 := (<= #1230 0::Int)
#2911 := (or #1231 #1238)
#2912 := (not #2911)
#2933 := (or #2912 #212)
#3927 := (forall (vars (?v0 S2)) (:pat #3917 #3805 #3918) #2933)
#3932 := (not #3927)
#1385 := (+ #202 #1255)
#1386 := (+ #190 #1385)
#1383 := (= #1386 0::Int)
#2925 := (or #1231 #1238 #1383)
#3919 := (forall (vars (?v0 S2)) (:pat #3917 #3805 #3918) #2925)
#3924 := (not #3919)
#778 := (not #199)
#116 := (f9 f21 #11)
#3839 := (pattern #116)
#1398 := (+ #112 #1235)
#1397 := (>= #1398 0::Int)
#117 := (= #116 f1)
#1401 := (or #117 #1397)
#3909 := (forall (vars (?v0 S2)) (:pat #3839 #3805) #1401)
#3914 := (not #3909)
#1410 := (+ f14 #1235)
#1411 := (<= #1410 0::Int)
#187 := (f9 f21 f28)
#188 := (= #187 f1)
decl ?v0!12 :: S2
#1961 := ?v0!12
#1965 := (f19 f20 ?v0!12)
#1966 := (* -1::Int #1965)
#1967 := (+ f14 #1966)
#1968 := (<= #1967 0::Int)
#1962 := (f9 f21 ?v0!12)
#1963 := (= #1962 f1)
#4057 := (or #1963 #1968 #188 #1411 #3914 #778 #3924 #3932 #4054)
#4060 := (not #4057)
decl f25 :: S11
#148 := f25
#168 := (f19 f25 f16)
#169 := (= #168 0::Int)
#156 := (f19 f25 #9)
#1149 := (* -1::Int #156)
#153 := (f19 f25 #11)
#1150 := (+ #153 #1149)
#1156 := (+ #93 #1150)
#1179 := (>= #1156 0::Int)
#1136 := (* -1::Int #153)
#1137 := (+ f14 #1136)
#1138 := (<= #1137 0::Int)
#2865 := (or #1138 #1029 #1179)
#3871 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3773) #2865)
#3876 := (not #3871)
#3879 := (or #3876 #169)
#3882 := (not #3879)
decl ?v0!11 :: S2
#1905 := ?v0!11
#1920 := (f19 f25 ?v0!11)
#1921 := (* -1::Int #1920)
decl ?v1!10 :: S2
#1904 := ?v1!10
#1911 := (f6 f7 ?v1!10)
#1912 := (f5 #1911 ?v0!11)
#1913 := (f15 #1912)
#2441 := (+ #1913 #1921)
#1906 := (f19 f25 ?v1!10)
#2442 := (+ #1906 #2441)
#2445 := (>= #2442 0::Int)
#1914 := (* -1::Int #1913)
#1915 := (+ f14 #1914)
#1916 := (<= #1915 0::Int)
#1907 := (* -1::Int #1906)
#1908 := (+ f14 #1907)
#1909 := (<= #1908 0::Int)
#2843 := (or #1909 #1916 #2445)
#2848 := (not #2843)
#3885 := (or #2848 #3882)
#3888 := (not #3885)
#3848 := (pattern #153)
decl ?v1!9 :: (-> S2 S2)
#1880 := (?v1!9 #11)
#1885 := (f6 f7 #1880)
#1886 := (f5 #1885 #11)
#1887 := (f15 #1886)
#2424 := (* -1::Int #1887)
#1881 := (f19 f25 #1880)
#2407 := (* -1::Int #1881)
#2425 := (+ #2407 #2424)
#2426 := (+ #153 #2425)
#2427 := (= #2426 0::Int)
#2813 := (not #2427)
#2408 := (+ #153 #2407)
#2409 := (<= #2408 0::Int)
#2814 := (or #2409 #2813)
#2815 := (not #2814)
#66 := (= #11 f16)
#2821 := (or #66 #1138 #2815)
#3863 := (forall (vars (?v0 S2)) (:pat #3848) #2821)
#3868 := (not #3863)
#3891 := (or #3868 #3888)
#3894 := (not #3891)
decl ?v0!8 :: S2
#1840 := ?v0!8
#1853 := (f5 #91 ?v0!8)
#1854 := (f15 #1853)
#1843 := (f19 f25 ?v0!8)
#1844 := (* -1::Int #1843)
#2377 := (+ #1844 #1854)
#2378 := (+ #153 #2377)
#2381 := (= #2378 0::Int)
#2777 := (not #2381)
#1850 := (+ #153 #1844)
#1851 := (>= #1850 0::Int)
#2778 := (or #1851 #2777)
#3849 := (forall (vars (?v1 S2)) (:pat #3848 #3782) #2778)
#3854 := (not #3849)
#1845 := (+ f14 #1844)
#1846 := (<= #1845 0::Int)
#1841 := (= ?v0!8 f16)
#3857 := (or #1841 #1846 #3854)
#3860 := (not #3857)
#3897 := (or #3860 #3894)
#3900 := (not #3897)
decl f27 :: S11
#151 := f27
decl f26 :: S11
#150 := f26
#152 := (= f26 f27)
#522 := (not #152)
#149 := (= f25 f20)
#531 := (not #149)
decl f24 :: S2
#146 := f24
decl f23 :: S2
#145 := f23
#147 := (= f23 f24)
#540 := (not #147)
decl f22 :: S7
#143 := f22
#144 := (= f22 f21)
#549 := (not #144)
#1091 := (* -1::Int #112)
#1092 := (+ f14 #1091)
#1093 := (<= #1092 0::Int)
#2763 := (or #117 #1093)
#3840 := (forall (vars (?v0 S2)) (:pat #3839 #3805) #2763)
#3845 := (not #3840)
#3903 := (or #3845 #549 #540 #531 #522 #3900)
#3906 := (not #3903)
#4063 := (or #3906 #4060)
#4066 := (not #4063)
#1796 := (?v1!7 #11)
#1803 := (f6 f7 #1796)
#1804 := (f5 #1803 #11)
#1805 := (f15 #1804)
#2350 := (* -1::Int #1805)
#1797 := (f19 f20 #1796)
#2333 := (* -1::Int #1797)
#2351 := (+ #2333 #2350)
#2352 := (+ #112 #2351)
#2353 := (= #2352 0::Int)
#2747 := (not #2353)
#1801 := (f9 f21 #1796)
#1802 := (= #1801 f1)
#2746 := (not #1802)
#2334 := (+ #112 #2333)
#2335 := (<= #2334 0::Int)
#2748 := (or #2335 #2746 #2747)
#2749 := (not #2748)
#2755 := (or #66 #1093 #2749)
#3831 := (forall (vars (?v0 S2)) (:pat #3805) #2755)
#3836 := (not #3831)
#122 := (f19 f20 #9)
#1105 := (* -1::Int #122)
#1106 := (+ #112 #1105)
#1107 := (+ #93 #1106)
#1460 := (>= #1107 0::Int)
#118 := (not #117)
#2727 := (or #118 #1029 #1460)
#3823 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3773) #2727)
#3828 := (not #3823)
#119 := (f9 f21 #9)
#3814 := (pattern #116 #119)
#1109 := (>= #1106 0::Int)
#120 := (= #119 f1)
#2690 := (not #120)
#2705 := (or #117 #2690 #1109)
#3815 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3814) #2705)
#3820 := (not #3815)
#1483 := (>= #112 0::Int)
#3806 := (forall (vars (?v0 S2)) (:pat #3805) #1483)
#3811 := (not #3806)
#110 := (f19 f20 f16)
#111 := (= #110 0::Int)
#878 := (not #111)
decl f17 :: (-> S2 Int)
#67 := (f17 #11)
#3736 := (pattern #67)
decl ?v1!6 :: (-> S2 S2)
#1743 := (?v1!6 #11)
#1750 := (f6 f7 #1743)
#1751 := (f5 #1750 #11)
#1752 := (f15 #1751)
#2308 := (* -1::Int #1752)
#1744 := (f17 #1743)
#2291 := (* -1::Int #1744)
#2309 := (+ #2291 #2308)
#2310 := (+ #67 #2309)
#2311 := (= #2310 0::Int)
#2674 := (not #2311)
decl f18 :: S7
#75 := f18
#1748 := (f9 f18 #1743)
#1749 := (= #1748 f1)
#2673 := (not #1749)
#2292 := (+ #67 #2291)
#2293 := (<= #2292 0::Int)
#2675 := (or #2293 #2673 #2674)
#2676 := (not #2675)
#1053 := (* -1::Int #67)
#1054 := (+ f14 #1053)
#1055 := (<= #1054 0::Int)
#2682 := (or #66 #1055 #2676)
#3797 := (forall (vars (?v0 S2)) (:pat #3736) #2682)
#3802 := (not #3797)
#4069 := (or #3802 #878 #3811 #3820 #3828 #3836 #4066)
#4072 := (not #4069)
#76 := (f9 f18 #11)
#3749 := (pattern #76)
decl ?v0!5 :: S2
#1702 := ?v0!5
#1715 := (f5 #91 ?v0!5)
#1716 := (f15 #1715)
#1705 := (f17 ?v0!5)
#1706 := (* -1::Int #1705)
#1717 := (+ #1706 #1716)
#1718 := (+ #67 #1717)
#1719 := (= #1718 0::Int)
#2637 := (not #1719)
#77 := (= #76 f1)
#78 := (not #77)
#1712 := (+ #67 #1706)
#1713 := (>= #1712 0::Int)
#2638 := (or #1713 #78 #2637)
#3783 := (forall (vars (?v1 S2)) (:pat #3736 #3749 #3782) #2638)
#3788 := (not #3783)
#1707 := (+ f14 #1706)
#1708 := (<= #1707 0::Int)
#1703 := (= ?v0!5 f16)
#3791 := (or #1703 #1708 #3788)
#6181 := (= f14 #1705)
#6178 := (= #1705 f14)
#6207 := (iff #6178 #6181)
#6203 := (iff #6181 #6178)
#6186 := [commutativity]: #6203
#6185 := [symm #6186]: #6207
#1704 := (not #1703)
#3794 := (not #3791)
#6196 := [hypothesis]: #3794
#3351 := (or #3791 #1704)
#3352 := [def-axiom]: #3351
#6201 := [unit-resolution #3352 #6196]: #1704
#72 := (= #67 f14)
#364 := (or #66 #72)
#3743 := (forall (vars (?v0 S2)) (:pat #3736) #364)
#367 := (forall (vars (?v0 S2)) #364)
#3746 := (iff #367 #3743)
#3744 := (iff #364 #364)
#3745 := [refl]: #3744
#3747 := [quant-intro #3745]: #3746
#1589 := (~ #367 #367)
#1619 := (~ #364 #364)
#1620 := [refl]: #1619
#1590 := [nnf-pos #1620]: #1589
#1318 := (= #1296 0::Int)
#1321 := (not #1274)
#1330 := (and #1321 #218 #1318)
#1335 := (exists (vars (?v1 S2)) #1330)
#1307 := (+ f14 #1255)
#1308 := (<= #1307 0::Int)
#1309 := (not #1308)
#71 := (not #66)
#1312 := (and #71 #1309)
#1315 := (not #1312)
#1338 := (or #1315 #1335)
#1341 := (forall (vars (?v0 S2)) #1338)
#1030 := (not #1029)
#1288 := (and #218 #1030)
#1291 := (not #1288)
#1298 := (or #1291 #1294)
#1301 := (forall (vars (?v0 S2) (?v1 S2)) #1298)
#1304 := (not #1301)
#1344 := (or #1304 #1341)
#1347 := (and #1301 #1344)
#228 := (and #225 #227)
#609 := (not #228)
#1279 := (or #609 #1274)
#1282 := (forall (vars (?v0 S2) (?v1 S2)) #1279)
#1285 := (not #1282)
#1350 := (or #1285 #1347)
#1353 := (and #1282 #1350)
#1268 := (forall (vars (?v0 S2)) #1265)
#1271 := (not #1268)
#1356 := (or #1271 #1353)
#1359 := (and #1268 #1356)
#1362 := (or #713 #1359)
#1365 := (and #222 #1362)
#606 := (forall (vars (?v0 S2)) #603)
#736 := (not #606)
#1368 := (or #736 #1365)
#1371 := (and #606 #1368)
#1259 := (forall (vars (?v0 S2)) #1254)
#1262 := (not #1259)
#1374 := (or #1262 #1371)
#1377 := (and #1259 #1374)
#1239 := (not #1238)
#1232 := (not #1231)
#1242 := (and #1232 #1239)
#1245 := (or #1242 #212)
#1248 := (forall (vars (?v0 S2)) #1245)
#1251 := (not #1248)
#1380 := (not #1242)
#1388 := (or #1380 #1383)
#1391 := (forall (vars (?v0 S2)) #1388)
#1394 := (not #1391)
#1404 := (forall (vars (?v0 S2)) #1401)
#1407 := (not #1404)
#1094 := (not #1093)
#1203 := (and #118 #1094)
#1206 := (exists (vars (?v0 S2)) #1203)
#1422 := (not #1206)
#1446 := (or #1422 #188 #1411 #1407 #778 #1394 #1251 #1377)
#1139 := (not #1138)
#1173 := (and #1139 #1030)
#1176 := (not #1173)
#1182 := (or #1176 #1179)
#1185 := (forall (vars (?v0 S2) (?v1 S2)) #1182)
#1188 := (not #1185)
#1191 := (or #1188 #169)
#1194 := (and #1185 #1191)
#1154 := (= #1156 0::Int)
#1148 := (>= #1150 0::Int)
#1151 := (not #1148)
#1158 := (and #1151 #1154)
#1161 := (exists (vars (?v1 S2)) #1158)
#1142 := (and #71 #1139)
#1145 := (not #1142)
#1164 := (or #1145 #1161)
#1167 := (forall (vars (?v0 S2)) #1164)
#1170 := (not #1167)
#1197 := (or #1170 #1194)
#1200 := (and #1167 #1197)
#1224 := (or #1206 #549 #540 #531 #522 #1200)
#1451 := (and #1224 #1446)
#1103 := (= #1107 0::Int)
#1110 := (not #1109)
#1119 := (and #1110 #117 #1103)
#1124 := (exists (vars (?v1 S2)) #1119)
#1097 := (and #71 #1094)
#1100 := (not #1097)
#1127 := (or #1100 #1124)
#1130 := (forall (vars (?v0 S2)) #1127)
#1133 := (not #1130)
#1454 := (and #117 #1030)
#1457 := (not #1454)
#1463 := (or #1457 #1460)
#1466 := (forall (vars (?v0 S2) (?v1 S2)) #1463)
#1469 := (not #1466)
#121 := (and #118 #120)
#391 := (not #121)
#1474 := (or #391 #1109)
#1477 := (forall (vars (?v0 S2) (?v1 S2)) #1474)
#1480 := (not #1477)
#1486 := (forall (vars (?v0 S2)) #1483)
#1489 := (not #1486)
#87 := (f17 #9)
#1015 := (* -1::Int #87)
#1042 := (+ #1015 #93)
#1043 := (+ #67 #1042)
#1065 := (= #1043 0::Int)
#1016 := (+ #67 #1015)
#1014 := (>= #1016 0::Int)
#1068 := (not #1014)
#1077 := (and #1068 #77 #1065)
#1082 := (exists (vars (?v1 S2)) #1077)
#1056 := (not #1055)
#1059 := (and #71 #1056)
#1062 := (not #1059)
#1085 := (or #1062 #1082)
#1088 := (forall (vars (?v0 S2)) #1085)
#1492 := (not #1088)
#1513 := (or #1492 #878 #1489 #1480 #1469 #1133 #1451)
#1518 := (and #1088 #1513)
#1040 := (>= #1043 0::Int)
#1033 := (and #77 #1030)
#1036 := (not #1033)
#1044 := (or #1036 #1040)
#1047 := (forall (vars (?v0 S2) (?v1 S2)) #1044)
#1050 := (not #1047)
#1521 := (or #1050 #1518)
#1524 := (and #1047 #1521)
#84 := (f9 f18 #9)
#85 := (= #84 f1)
#86 := (and #78 #85)
#370 := (not #86)
#1018 := (or #370 #1014)
#1021 := (forall (vars (?v0 S2) (?v1 S2)) #1018)
#1024 := (not #1021)
#1527 := (or #1024 #1524)
#1530 := (and #1021 #1527)
#1005 := (>= #67 0::Int)
#1006 := (forall (vars (?v0 S2)) #1005)
#1009 := (not #1006)
#1533 := (or #1009 #1530)
#1536 := (and #1006 #1533)
#80 := (f17 f16)
#81 := (= #80 0::Int)
#946 := (not #81)
#1539 := (or #946 #1536)
#1542 := (and #81 #1539)
#79 := (forall (vars (?v0 S2)) #78)
#965 := (not #79)
#974 := (not #367)
#68 := (= #67 0::Int)
#358 := (or #71 #68)
#361 := (forall (vars (?v0 S2)) #358)
#983 := (not #361)
#1554 := (or #983 #974 #965 #1542)
#1559 := (not #1554)
#247 := (implies false true)
#234 := (+ #207 #93)
#241 := (= #229 #234)
#242 := (and #218 #241)
#240 := (< #207 #229)
#243 := (and #240 #242)
#244 := (exists (vars (?v1 S2)) #243)
#238 := (< #207 f14)
#239 := (and #71 #238)
#245 := (implies #239 #244)
#246 := (forall (vars (?v0 S2)) #245)
#248 := (implies #246 #247)
#249 := (and #246 #248)
#235 := (<= #229 #234)
#94 := (< #93 f14)
#233 := (and #218 #94)
#236 := (implies #233 #235)
#237 := (forall (vars (?v0 S2) (?v1 S2)) #236)
#250 := (implies #237 #249)
#251 := (and #237 #250)
#230 := (<= #229 #207)
#231 := (implies #228 #230)
#232 := (forall (vars (?v0 S2) (?v1 S2)) #231)
#252 := (implies #232 #251)
#253 := (and #232 #252)
#223 := (<= 0::Int #207)
#224 := (forall (vars (?v0 S2)) #223)
#254 := (implies #224 #253)
#255 := (and #224 #254)
#256 := (implies #222 #255)
#257 := (and #222 #256)
#258 := (implies true #257)
#259 := (implies true #258)
#219 := (implies #218 #212)
#220 := (forall (vars (?v0 S2)) #219)
#260 := (implies #220 #259)
#261 := (and #220 #260)
#215 := (<= #207 #112)
#216 := (forall (vars (?v0 S2)) #215)
#262 := (implies #216 #261)
#263 := (and #216 #262)
#204 := (+ #190 #202)
#205 := (< #204 #112)
#203 := (< #202 f14)
#206 := (and #203 #205)
#211 := (not #206)
#213 := (implies #211 #212)
#214 := (forall (vars (?v0 S2)) #213)
#264 := (implies #214 #263)
#208 := (= #207 #204)
#209 := (implies #206 #208)
#210 := (forall (vars (?v0 S2)) #209)
#265 := (implies #210 #264)
#266 := (implies #199 #265)
#192 := (<= #190 #112)
#193 := (implies #118 #192)
#194 := (forall (vars (?v0 S2)) #193)
#267 := (implies #194 #266)
#191 := (< #190 f14)
#268 := (implies #191 #267)
#189 := (not #188)
#269 := (implies #189 #268)
#131 := (< #112 f14)
#140 := (and #118 #131)
#141 := (exists (vars (?v0 S2)) #140)
#270 := (implies #141 #269)
#271 := (implies true #270)
#272 := (implies true #271)
#170 := (implies #169 true)
#171 := (and #169 #170)
#158 := (+ #153 #93)
#165 := (<= #156 #158)
#154 := (< #153 f14)
#164 := (and #154 #94)
#166 := (implies #164 #165)
#167 := (forall (vars (?v0 S2) (?v1 S2)) #166)
#172 := (implies #167 #171)
#173 := (and #167 #172)
#159 := (= #156 #158)
#157 := (< #153 #156)
#160 := (and #157 #159)
#161 := (exists (vars (?v1 S2)) #160)
#155 := (and #71 #154)
#162 := (implies #155 #161)
#163 := (forall (vars (?v0 S2)) #162)
#174 := (implies #163 #173)
#175 := (and #163 #174)
#176 := (implies true #175)
#177 := (implies #152 #176)
#178 := (implies #149 #177)
#179 := (implies #147 #178)
#180 := (implies #144 #179)
#181 := (implies true #180)
#182 := (implies true #181)
#142 := (not #141)
#183 := (implies #142 #182)
#184 := (implies true #183)
#185 := (implies true #184)
#273 := (and #185 #272)
#274 := (implies true #273)
#127 := (+ #112 #93)
#134 := (= #122 #127)
#135 := (and #117 #134)
#133 := (< #112 #122)
#136 := (and #133 #135)
#137 := (exists (vars (?v1 S2)) #136)
#132 := (and #71 #131)
#138 := (implies #132 #137)
#139 := (forall (vars (?v0 S2)) #138)
#275 := (implies #139 #274)
#128 := (<= #122 #127)
#126 := (and #117 #94)
#129 := (implies #126 #128)
#130 := (forall (vars (?v0 S2) (?v1 S2)) #129)
#276 := (implies #130 #275)
#123 := (<= #122 #112)
#124 := (implies #121 #123)
#125 := (forall (vars (?v0 S2) (?v1 S2)) #124)
#277 := (implies #125 #276)
#113 := (<= 0::Int #112)
#114 := (forall (vars (?v0 S2)) #113)
#278 := (implies #114 #277)
#279 := (implies #111 #278)
#280 := (implies true #279)
#281 := (implies true #280)
#96 := (+ #67 #93)
#103 := (= #87 #96)
#104 := (and #77 #103)
#102 := (< #67 #87)
#105 := (and #102 #104)
#106 := (exists (vars (?v1 S2)) #105)
#100 := (< #67 f14)
#101 := (and #71 #100)
#107 := (implies #101 #106)
#108 := (forall (vars (?v0 S2)) #107)
#282 := (implies #108 #281)
#283 := (and #108 #282)
#97 := (<= #87 #96)
#95 := (and #77 #94)
#98 := (implies #95 #97)
#99 := (forall (vars (?v0 S2) (?v1 S2)) #98)
#284 := (implies #99 #283)
#285 := (and #99 #284)
#88 := (<= #87 #67)
#89 := (implies #86 #88)
#90 := (forall (vars (?v0 S2) (?v1 S2)) #89)
#286 := (implies #90 #285)
#287 := (and #90 #286)
#82 := (<= 0::Int #67)
#83 := (forall (vars (?v0 S2)) #82)
#288 := (implies #83 #287)
#289 := (and #83 #288)
#290 := (implies #81 #289)
#291 := (and #81 #290)
#292 := (implies true #291)
#293 := (implies #79 #292)
#73 := (implies #71 #72)
#74 := (forall (vars (?v0 S2)) #73)
#294 := (implies #74 #293)
#69 := (implies #66 #68)
#70 := (forall (vars (?v0 S2)) #69)
#295 := (implies #70 #294)
#296 := (implies true #295)
#297 := (implies true #296)
#298 := (not #297)
#1562 := (iff #298 #1559)
#616 := (+ #93 #207)
#634 := (= #229 #616)
#637 := (and #218 #634)
#640 := (and #240 #637)
#643 := (exists (vars (?v1 S2)) #640)
#649 := (not #239)
#650 := (or #649 #643)
#655 := (forall (vars (?v0 S2)) #650)
#619 := (<= #229 #616)
#625 := (not #233)
#626 := (or #625 #619)
#631 := (forall (vars (?v0 S2) (?v1 S2)) #626)
#677 := (not #631)
#678 := (or #677 #655)
#683 := (and #631 #678)
#610 := (or #609 #230)
#613 := (forall (vars (?v0 S2) (?v1 S2)) #610)
#689 := (not #613)
#690 := (or #689 #683)
#695 := (and #613 #690)
#701 := (not #224)
#702 := (or #701 #695)
#707 := (and #224 #702)
#714 := (or #713 #707)
#719 := (and #222 #714)
#737 := (or #736 #719)
#742 := (and #606 #737)
#748 := (not #216)
#749 := (or #748 #742)
#754 := (and #216 #749)
#597 := (or #206 #212)
#600 := (forall (vars (?v0 S2)) #597)
#760 := (not #600)
#761 := (or #760 #754)
#591 := (or #211 #208)
#594 := (forall (vars (?v0 S2)) #591)
#769 := (not #594)
#770 := (or #769 #761)
#779 := (or #778 #770)
#585 := (or #117 #192)
#588 := (forall (vars (?v0 S2)) #585)
#787 := (not #588)
#788 := (or #787 #779)
#796 := (not #191)
#797 := (or #796 #788)
#805 := (or #188 #797)
#813 := (or #142 #805)
#440 := (+ #93 #153)
#464 := (<= #156 #440)
#470 := (not #164)
#471 := (or #470 #464)
#476 := (forall (vars (?v0 S2) (?v1 S2)) #471)
#491 := (not #476)
#492 := (or #491 #169)
#497 := (and #476 #492)
#443 := (= #156 #440)
#446 := (and #157 #443)
#449 := (exists (vars (?v1 S2)) #446)
#455 := (not #155)
#456 := (or #455 #449)
#461 := (forall (vars (?v0 S2)) #456)
#503 := (not #461)
#504 := (or #503 #497)
#509 := (and #461 #504)
#523 := (or #522 #509)
#532 := (or #531 #523)
#541 := (or #540 #532)
#550 := (or #549 #541)
#569 := (or #141 #550)
#829 := (and #569 #813)
#398 := (+ #93 #112)
#416 := (= #122 #398)
#419 := (and #117 #416)
#422 := (and #133 #419)
#425 := (exists (vars (?v1 S2)) #422)
#431 := (not #132)
#432 := (or #431 #425)
#437 := (forall (vars (?v0 S2)) #432)
#842 := (not #437)
#843 := (or #842 #829)
#401 := (<= #122 #398)
#407 := (not #126)
#408 := (or #407 #401)
#413 := (forall (vars (?v0 S2) (?v1 S2)) #408)
#851 := (not #413)
#852 := (or #851 #843)
#392 := (or #391 #123)
#395 := (forall (vars (?v0 S2) (?v1 S2)) #392)
#860 := (not #395)
#861 := (or #860 #852)
#869 := (not #114)
#870 := (or #869 #861)
#879 := (or #878 #870)
#384 := (not #101)
#385 := (or #384 #106)
#388 := (forall (vars (?v0 S2)) #385)
#898 := (not #388)
#899 := (or #898 #879)
#904 := (and #388 #899)
#377 := (not #95)
#378 := (or #377 #97)
#381 := (forall (vars (?v0 S2) (?v1 S2)) #378)
#910 := (not #381)
#911 := (or #910 #904)
#916 := (and #381 #911)
#371 := (or #370 #88)
#374 := (forall (vars (?v0 S2) (?v1 S2)) #371)
#922 := (not #374)
#923 := (or #922 #916)
#928 := (and #374 #923)
#934 := (not #83)
#935 := (or #934 #928)
#940 := (and #83 #935)
#947 := (or #946 #940)
#952 := (and #81 #947)
#966 := (or #965 #952)
#975 := (or #974 #966)
#984 := (or #983 #975)
#1000 := (not #984)
#1560 := (iff #1000 #1559)
#1557 := (iff #984 #1554)
#1545 := (or #965 #1542)
#1548 := (or #974 #1545)
#1551 := (or #983 #1548)
#1555 := (iff #1551 #1554)
#1556 := [rewrite]: #1555
#1552 := (iff #984 #1551)
#1549 := (iff #975 #1548)
#1546 := (iff #966 #1545)
#1543 := (iff #952 #1542)
#1540 := (iff #947 #1539)
#1537 := (iff #940 #1536)
#1534 := (iff #935 #1533)
#1531 := (iff #928 #1530)
#1528 := (iff #923 #1527)
#1525 := (iff #916 #1524)
#1522 := (iff #911 #1521)
#1519 := (iff #904 #1518)
#1516 := (iff #899 #1513)
#1495 := (or #1133 #1451)
#1498 := (or #1469 #1495)
#1501 := (or #1480 #1498)
#1504 := (or #1489 #1501)
#1507 := (or #878 #1504)
#1510 := (or #1492 #1507)
#1514 := (iff #1510 #1513)
#1515 := [rewrite]: #1514
#1511 := (iff #899 #1510)
#1508 := (iff #879 #1507)
#1505 := (iff #870 #1504)
#1502 := (iff #861 #1501)
#1499 := (iff #852 #1498)
#1496 := (iff #843 #1495)
#1452 := (iff #829 #1451)
#1449 := (iff #813 #1446)
#1425 := (or #1251 #1377)
#1428 := (or #1394 #1425)
#1431 := (or #778 #1428)
#1434 := (or #1407 #1431)
#1437 := (or #1411 #1434)
#1440 := (or #188 #1437)
#1443 := (or #1422 #1440)
#1447 := (iff #1443 #1446)
#1448 := [rewrite]: #1447
#1444 := (iff #813 #1443)
#1441 := (iff #805 #1440)
#1438 := (iff #797 #1437)
#1435 := (iff #788 #1434)
#1432 := (iff #779 #1431)
#1429 := (iff #770 #1428)
#1426 := (iff #761 #1425)
#1378 := (iff #754 #1377)
#1375 := (iff #749 #1374)
#1372 := (iff #742 #1371)
#1369 := (iff #737 #1368)
#1366 := (iff #719 #1365)
#1363 := (iff #714 #1362)
#1360 := (iff #707 #1359)
#1357 := (iff #702 #1356)
#1354 := (iff #695 #1353)
#1351 := (iff #690 #1350)
#1348 := (iff #683 #1347)
#1345 := (iff #678 #1344)
#1342 := (iff #655 #1341)
#1339 := (iff #650 #1338)
#1336 := (iff #643 #1335)
#1333 := (iff #640 #1330)
#1324 := (and #218 #1318)
#1327 := (and #1321 #1324)
#1331 := (iff #1327 #1330)
#1332 := [rewrite]: #1331
#1328 := (iff #640 #1327)
#1325 := (iff #637 #1324)
#1319 := (iff #634 #1318)
#1320 := [rewrite]: #1319
#1326 := [monotonicity #1320]: #1325
#1322 := (iff #240 #1321)
#1323 := [rewrite]: #1322
#1329 := [monotonicity #1323 #1326]: #1328
#1334 := [trans #1329 #1332]: #1333
#1337 := [quant-intro #1334]: #1336
#1316 := (iff #649 #1315)
#1313 := (iff #239 #1312)
#1310 := (iff #238 #1309)
#1311 := [rewrite]: #1310
#1314 := [monotonicity #1311]: #1313
#1317 := [monotonicity #1314]: #1316
#1340 := [monotonicity #1317 #1337]: #1339
#1343 := [quant-intro #1340]: #1342
#1305 := (iff #677 #1304)
#1302 := (iff #631 #1301)
#1299 := (iff #626 #1298)
#1295 := (iff #619 #1294)
#1297 := [rewrite]: #1295
#1292 := (iff #625 #1291)
#1289 := (iff #233 #1288)
#1031 := (iff #94 #1030)
#1032 := [rewrite]: #1031
#1290 := [monotonicity #1032]: #1289
#1293 := [monotonicity #1290]: #1292
#1300 := [monotonicity #1293 #1297]: #1299
#1303 := [quant-intro #1300]: #1302
#1306 := [monotonicity #1303]: #1305
#1346 := [monotonicity #1306 #1343]: #1345
#1349 := [monotonicity #1303 #1346]: #1348
#1286 := (iff #689 #1285)
#1283 := (iff #613 #1282)
#1280 := (iff #610 #1279)
#1277 := (iff #230 #1274)
#1278 := [rewrite]: #1277
#1281 := [monotonicity #1278]: #1280
#1284 := [quant-intro #1281]: #1283
#1287 := [monotonicity #1284]: #1286
#1352 := [monotonicity #1287 #1349]: #1351
#1355 := [monotonicity #1284 #1352]: #1354
#1272 := (iff #701 #1271)
#1269 := (iff #224 #1268)
#1266 := (iff #223 #1265)
#1267 := [rewrite]: #1266
#1270 := [quant-intro #1267]: #1269
#1273 := [monotonicity #1270]: #1272
#1358 := [monotonicity #1273 #1355]: #1357
#1361 := [monotonicity #1270 #1358]: #1360
#1364 := [monotonicity #1361]: #1363
#1367 := [monotonicity #1364]: #1366
#1370 := [monotonicity #1367]: #1369
#1373 := [monotonicity #1370]: #1372
#1263 := (iff #748 #1262)
#1260 := (iff #216 #1259)
#1257 := (iff #215 #1254)
#1258 := [rewrite]: #1257
#1261 := [quant-intro #1258]: #1260
#1264 := [monotonicity #1261]: #1263
#1376 := [monotonicity #1264 #1373]: #1375
#1379 := [monotonicity #1261 #1376]: #1378
#1252 := (iff #760 #1251)
#1249 := (iff #600 #1248)
#1246 := (iff #597 #1245)
#1243 := (iff #206 #1242)
#1240 := (iff #205 #1239)
#1241 := [rewrite]: #1240
#1233 := (iff #203 #1232)
#1234 := [rewrite]: #1233
#1244 := [monotonicity #1234 #1241]: #1243
#1247 := [monotonicity #1244]: #1246
#1250 := [quant-intro #1247]: #1249
#1253 := [monotonicity #1250]: #1252
#1427 := [monotonicity #1253 #1379]: #1426
#1395 := (iff #769 #1394)
#1392 := (iff #594 #1391)
#1389 := (iff #591 #1388)
#1384 := (iff #208 #1383)
#1387 := [rewrite]: #1384
#1381 := (iff #211 #1380)
#1382 := [monotonicity #1244]: #1381
#1390 := [monotonicity #1382 #1387]: #1389
#1393 := [quant-intro #1390]: #1392
#1396 := [monotonicity #1393]: #1395
#1430 := [monotonicity #1396 #1427]: #1429
#1433 := [monotonicity #1430]: #1432
#1408 := (iff #787 #1407)
#1405 := (iff #588 #1404)
#1402 := (iff #585 #1401)
#1399 := (iff #192 #1397)
#1400 := [rewrite]: #1399
#1403 := [monotonicity #1400]: #1402
#1406 := [quant-intro #1403]: #1405
#1409 := [monotonicity #1406]: #1408
#1436 := [monotonicity #1409 #1433]: #1435
#1420 := (iff #796 #1411)
#1412 := (not #1411)
#1415 := (not #1412)
#1418 := (iff #1415 #1411)
#1419 := [rewrite]: #1418
#1416 := (iff #796 #1415)
#1413 := (iff #191 #1412)
#1414 := [rewrite]: #1413
#1417 := [monotonicity #1414]: #1416
#1421 := [trans #1417 #1419]: #1420
#1439 := [monotonicity #1421 #1436]: #1438
#1442 := [monotonicity #1439]: #1441
#1423 := (iff #142 #1422)
#1207 := (iff #141 #1206)
#1204 := (iff #140 #1203)
#1095 := (iff #131 #1094)
#1096 := [rewrite]: #1095
#1205 := [monotonicity #1096]: #1204
#1208 := [quant-intro #1205]: #1207
#1424 := [monotonicity #1208]: #1423
#1445 := [monotonicity #1424 #1442]: #1444
#1450 := [trans #1445 #1448]: #1449
#1227 := (iff #569 #1224)
#1209 := (or #522 #1200)
#1212 := (or #531 #1209)
#1215 := (or #540 #1212)
#1218 := (or #549 #1215)
#1221 := (or #1206 #1218)
#1225 := (iff #1221 #1224)
#1226 := [rewrite]: #1225
#1222 := (iff #569 #1221)
#1219 := (iff #550 #1218)
#1216 := (iff #541 #1215)
#1213 := (iff #532 #1212)
#1210 := (iff #523 #1209)
#1201 := (iff #509 #1200)
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#1195 := (iff #497 #1194)
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#1189 := (iff #491 #1188)
#1186 := (iff #476 #1185)
#1183 := (iff #471 #1182)
#1180 := (iff #464 #1179)
#1181 := [rewrite]: #1180
#1177 := (iff #470 #1176)
#1174 := (iff #164 #1173)
#1140 := (iff #154 #1139)
#1141 := [rewrite]: #1140
#1175 := [monotonicity #1141 #1032]: #1174
#1178 := [monotonicity #1175]: #1177
#1184 := [monotonicity #1178 #1181]: #1183
#1187 := [quant-intro #1184]: #1186
#1190 := [monotonicity #1187]: #1189
#1193 := [monotonicity #1190]: #1192
#1196 := [monotonicity #1187 #1193]: #1195
#1171 := (iff #503 #1170)
#1168 := (iff #461 #1167)
#1165 := (iff #456 #1164)
#1162 := (iff #449 #1161)
#1159 := (iff #446 #1158)
#1155 := (iff #443 #1154)
#1157 := [rewrite]: #1155
#1152 := (iff #157 #1151)
#1153 := [rewrite]: #1152
#1160 := [monotonicity #1153 #1157]: #1159
#1163 := [quant-intro #1160]: #1162
#1146 := (iff #455 #1145)
#1143 := (iff #155 #1142)
#1144 := [monotonicity #1141]: #1143
#1147 := [monotonicity #1144]: #1146
#1166 := [monotonicity #1147 #1163]: #1165
#1169 := [quant-intro #1166]: #1168
#1172 := [monotonicity #1169]: #1171
#1199 := [monotonicity #1172 #1196]: #1198
#1202 := [monotonicity #1169 #1199]: #1201
#1211 := [monotonicity #1202]: #1210
#1214 := [monotonicity #1211]: #1213
#1217 := [monotonicity #1214]: #1216
#1220 := [monotonicity #1217]: #1219
#1223 := [monotonicity #1208 #1220]: #1222
#1228 := [trans #1223 #1226]: #1227
#1453 := [monotonicity #1228 #1450]: #1452
#1134 := (iff #842 #1133)
#1131 := (iff #437 #1130)
#1128 := (iff #432 #1127)
#1125 := (iff #425 #1124)
#1122 := (iff #422 #1119)
#1113 := (and #117 #1103)
#1116 := (and #1110 #1113)
#1120 := (iff #1116 #1119)
#1121 := [rewrite]: #1120
#1117 := (iff #422 #1116)
#1114 := (iff #419 #1113)
#1104 := (iff #416 #1103)
#1108 := [rewrite]: #1104
#1115 := [monotonicity #1108]: #1114
#1111 := (iff #133 #1110)
#1112 := [rewrite]: #1111
#1118 := [monotonicity #1112 #1115]: #1117
#1123 := [trans #1118 #1121]: #1122
#1126 := [quant-intro #1123]: #1125
#1101 := (iff #431 #1100)
#1098 := (iff #132 #1097)
#1099 := [monotonicity #1096]: #1098
#1102 := [monotonicity #1099]: #1101
#1129 := [monotonicity #1102 #1126]: #1128
#1132 := [quant-intro #1129]: #1131
#1135 := [monotonicity #1132]: #1134
#1497 := [monotonicity #1135 #1453]: #1496
#1470 := (iff #851 #1469)
#1467 := (iff #413 #1466)
#1464 := (iff #408 #1463)
#1461 := (iff #401 #1460)
#1462 := [rewrite]: #1461
#1458 := (iff #407 #1457)
#1455 := (iff #126 #1454)
#1456 := [monotonicity #1032]: #1455
#1459 := [monotonicity #1456]: #1458
#1465 := [monotonicity #1459 #1462]: #1464
#1468 := [quant-intro #1465]: #1467
#1471 := [monotonicity #1468]: #1470
#1500 := [monotonicity #1471 #1497]: #1499
#1481 := (iff #860 #1480)
#1478 := (iff #395 #1477)
#1475 := (iff #392 #1474)
#1472 := (iff #123 #1109)
#1473 := [rewrite]: #1472
#1476 := [monotonicity #1473]: #1475
#1479 := [quant-intro #1476]: #1478
#1482 := [monotonicity #1479]: #1481
#1503 := [monotonicity #1482 #1500]: #1502
#1490 := (iff #869 #1489)
#1487 := (iff #114 #1486)
#1484 := (iff #113 #1483)
#1485 := [rewrite]: #1484
#1488 := [quant-intro #1485]: #1487
#1491 := [monotonicity #1488]: #1490
#1506 := [monotonicity #1491 #1503]: #1505
#1509 := [monotonicity #1506]: #1508
#1493 := (iff #898 #1492)
#1089 := (iff #388 #1088)
#1086 := (iff #385 #1085)
#1083 := (iff #106 #1082)
#1080 := (iff #105 #1077)
#1071 := (and #77 #1065)
#1074 := (and #1068 #1071)
#1078 := (iff #1074 #1077)
#1079 := [rewrite]: #1078
#1075 := (iff #105 #1074)
#1072 := (iff #104 #1071)
#1066 := (iff #103 #1065)
#1067 := [rewrite]: #1066
#1073 := [monotonicity #1067]: #1072
#1069 := (iff #102 #1068)
#1070 := [rewrite]: #1069
#1076 := [monotonicity #1070 #1073]: #1075
#1081 := [trans #1076 #1079]: #1080
#1084 := [quant-intro #1081]: #1083
#1063 := (iff #384 #1062)
#1060 := (iff #101 #1059)
#1057 := (iff #100 #1056)
#1058 := [rewrite]: #1057
#1061 := [monotonicity #1058]: #1060
#1064 := [monotonicity #1061]: #1063
#1087 := [monotonicity #1064 #1084]: #1086
#1090 := [quant-intro #1087]: #1089
#1494 := [monotonicity #1090]: #1493
#1512 := [monotonicity #1494 #1509]: #1511
#1517 := [trans #1512 #1515]: #1516
#1520 := [monotonicity #1090 #1517]: #1519
#1051 := (iff #910 #1050)
#1048 := (iff #381 #1047)
#1045 := (iff #378 #1044)
#1039 := (iff #97 #1040)
#1041 := [rewrite]: #1039
#1037 := (iff #377 #1036)
#1034 := (iff #95 #1033)
#1035 := [monotonicity #1032]: #1034
#1038 := [monotonicity #1035]: #1037
#1046 := [monotonicity #1038 #1041]: #1045
#1049 := [quant-intro #1046]: #1048
#1052 := [monotonicity #1049]: #1051
#1523 := [monotonicity #1052 #1520]: #1522
#1526 := [monotonicity #1049 #1523]: #1525
#1025 := (iff #922 #1024)
#1022 := (iff #374 #1021)
#1019 := (iff #371 #1018)
#1013 := (iff #88 #1014)
#1017 := [rewrite]: #1013
#1020 := [monotonicity #1017]: #1019
#1023 := [quant-intro #1020]: #1022
#1026 := [monotonicity #1023]: #1025
#1529 := [monotonicity #1026 #1526]: #1528
#1532 := [monotonicity #1023 #1529]: #1531
#1010 := (iff #934 #1009)
#1007 := (iff #83 #1006)
#1003 := (iff #82 #1005)
#1004 := [rewrite]: #1003
#1008 := [quant-intro #1004]: #1007
#1011 := [monotonicity #1008]: #1010
#1535 := [monotonicity #1011 #1532]: #1534
#1538 := [monotonicity #1008 #1535]: #1537
#1541 := [monotonicity #1538]: #1540
#1544 := [monotonicity #1541]: #1543
#1547 := [monotonicity #1544]: #1546
#1550 := [monotonicity #1547]: #1549
#1553 := [monotonicity #1550]: #1552
#1558 := [trans #1553 #1556]: #1557
#1561 := [monotonicity #1558]: #1560
#1001 := (iff #298 #1000)
#998 := (iff #297 #984)
#989 := (implies true #984)
#992 := (iff #989 #984)
#993 := [rewrite]: #992
#996 := (iff #297 #989)
#994 := (iff #296 #984)
#990 := (iff #296 #989)
#987 := (iff #295 #984)
#980 := (implies #361 #975)
#985 := (iff #980 #984)
#986 := [rewrite]: #985
#981 := (iff #295 #980)
#978 := (iff #294 #975)
#971 := (implies #367 #966)
#976 := (iff #971 #975)
#977 := [rewrite]: #976
#972 := (iff #294 #971)
#969 := (iff #293 #966)
#962 := (implies #79 #952)
#967 := (iff #962 #966)
#968 := [rewrite]: #967
#963 := (iff #293 #962)
#960 := (iff #292 #952)
#955 := (implies true #952)
#958 := (iff #955 #952)
#959 := [rewrite]: #958
#956 := (iff #292 #955)
#953 := (iff #291 #952)
#950 := (iff #290 #947)
#943 := (implies #81 #940)
#948 := (iff #943 #947)
#949 := [rewrite]: #948
#944 := (iff #290 #943)
#941 := (iff #289 #940)
#938 := (iff #288 #935)
#931 := (implies #83 #928)
#936 := (iff #931 #935)
#937 := [rewrite]: #936
#932 := (iff #288 #931)
#929 := (iff #287 #928)
#926 := (iff #286 #923)
#919 := (implies #374 #916)
#924 := (iff #919 #923)
#925 := [rewrite]: #924
#920 := (iff #286 #919)
#917 := (iff #285 #916)
#914 := (iff #284 #911)
#907 := (implies #381 #904)
#912 := (iff #907 #911)
#913 := [rewrite]: #912
#908 := (iff #284 #907)
#905 := (iff #283 #904)
#902 := (iff #282 #899)
#895 := (implies #388 #879)
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#901 := [rewrite]: #900
#896 := (iff #282 #895)
#893 := (iff #281 #879)
#884 := (implies true #879)
#887 := (iff #884 #879)
#888 := [rewrite]: #887
#891 := (iff #281 #884)
#889 := (iff #280 #879)
#885 := (iff #280 #884)
#882 := (iff #279 #879)
#875 := (implies #111 #870)
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#881 := [rewrite]: #880
#876 := (iff #279 #875)
#873 := (iff #278 #870)
#866 := (implies #114 #861)
#871 := (iff #866 #870)
#872 := [rewrite]: #871
#867 := (iff #278 #866)
#864 := (iff #277 #861)
#857 := (implies #395 #852)
#862 := (iff #857 #861)
#863 := [rewrite]: #862
#858 := (iff #277 #857)
#855 := (iff #276 #852)
#848 := (implies #413 #843)
#853 := (iff #848 #852)
#854 := [rewrite]: #853
#849 := (iff #276 #848)
#846 := (iff #275 #843)
#839 := (implies #437 #829)
#844 := (iff #839 #843)
#845 := [rewrite]: #844
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#837 := (iff #274 #829)
#832 := (implies true #829)
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#836 := [rewrite]: #835
#833 := (iff #274 #832)
#830 := (iff #273 #829)
#827 := (iff #272 #813)
#818 := (implies true #813)
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#822 := [rewrite]: #821
#825 := (iff #272 #818)
#823 := (iff #271 #813)
#819 := (iff #271 #818)
#816 := (iff #270 #813)
#810 := (implies #141 #805)
#814 := (iff #810 #813)
#815 := [rewrite]: #814
#811 := (iff #270 #810)
#808 := (iff #269 #805)
#802 := (implies #189 #797)
#806 := (iff #802 #805)
#807 := [rewrite]: #806
#803 := (iff #269 #802)
#800 := (iff #268 #797)
#793 := (implies #191 #788)
#798 := (iff #793 #797)
#799 := [rewrite]: #798
#794 := (iff #268 #793)
#791 := (iff #267 #788)
#784 := (implies #588 #779)
#789 := (iff #784 #788)
#790 := [rewrite]: #789
#785 := (iff #267 #784)
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#775 := (implies #199 #770)
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#776 := (iff #266 #775)
#773 := (iff #265 #770)
#766 := (implies #594 #761)
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#772 := [rewrite]: #771
#767 := (iff #265 #766)
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#757 := (implies #600 #754)
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#751 := [rewrite]: #750
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#743 := (iff #261 #742)
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#733 := (implies #606 #719)
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#739 := [rewrite]: #738
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#731 := (iff #259 #719)
#722 := (implies true #719)
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#723 := (iff #258 #722)
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#696 := (iff #253 #695)
#693 := (iff #252 #690)
#686 := (implies #613 #683)
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#681 := (iff #250 #678)
#674 := (implies #631 #655)
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#667 := (and #655 true)
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#661 := (iff #248 #660)
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#659 := [rewrite]: #658
#656 := (iff #246 #655)
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#646 := (implies #239 #643)
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#641 := (iff #243 #640)
#638 := (iff #242 #637)
#635 := (iff #241 #634)
#617 := (= #234 #616)
#618 := [rewrite]: #617
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#642 := [monotonicity #639]: #641
#645 := [quant-intro #642]: #644
#648 := [monotonicity #645]: #647
#654 := [trans #648 #652]: #653
#657 := [quant-intro #654]: #656
#662 := [monotonicity #657 #659]: #661
#666 := [trans #662 #664]: #665
#669 := [monotonicity #657 #666]: #668
#673 := [trans #669 #671]: #672
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#629 := (iff #236 #626)
#622 := (implies #233 #619)
#627 := (iff #622 #626)
#628 := [rewrite]: #627
#623 := (iff #236 #622)
#620 := (iff #235 #619)
#621 := [monotonicity #618]: #620
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#630 := [trans #624 #628]: #629
#633 := [quant-intro #630]: #632
#676 := [monotonicity #633 #673]: #675
#682 := [trans #676 #680]: #681
#685 := [monotonicity #633 #682]: #684
#614 := (iff #232 #613)
#611 := (iff #231 #610)
#612 := [rewrite]: #611
#615 := [quant-intro #612]: #614
#688 := [monotonicity #615 #685]: #687
#694 := [trans #688 #692]: #693
#697 := [monotonicity #615 #694]: #696
#700 := [monotonicity #697]: #699
#706 := [trans #700 #704]: #705
#709 := [monotonicity #706]: #708
#712 := [monotonicity #709]: #711
#718 := [trans #712 #716]: #717
#721 := [monotonicity #718]: #720
#724 := [monotonicity #721]: #723
#728 := [trans #724 #726]: #727
#730 := [monotonicity #728]: #729
#732 := [trans #730 #726]: #731
#607 := (iff #220 #606)
#604 := (iff #219 #603)
#605 := [rewrite]: #604
#608 := [quant-intro #605]: #607
#735 := [monotonicity #608 #732]: #734
#741 := [trans #735 #739]: #740
#744 := [monotonicity #608 #741]: #743
#747 := [monotonicity #744]: #746
#753 := [trans #747 #751]: #752
#756 := [monotonicity #753]: #755
#601 := (iff #214 #600)
#598 := (iff #213 #597)
#599 := [rewrite]: #598
#602 := [quant-intro #599]: #601
#759 := [monotonicity #602 #756]: #758
#765 := [trans #759 #763]: #764
#595 := (iff #210 #594)
#592 := (iff #209 #591)
#593 := [rewrite]: #592
#596 := [quant-intro #593]: #595
#768 := [monotonicity #596 #765]: #767
#774 := [trans #768 #772]: #773
#777 := [monotonicity #774]: #776
#783 := [trans #777 #781]: #782
#589 := (iff #194 #588)
#586 := (iff #193 #585)
#587 := [rewrite]: #586
#590 := [quant-intro #587]: #589
#786 := [monotonicity #590 #783]: #785
#792 := [trans #786 #790]: #791
#795 := [monotonicity #792]: #794
#801 := [trans #795 #799]: #800
#804 := [monotonicity #801]: #803
#809 := [trans #804 #807]: #808
#812 := [monotonicity #809]: #811
#817 := [trans #812 #815]: #816
#820 := [monotonicity #817]: #819
#824 := [trans #820 #822]: #823
#826 := [monotonicity #824]: #825
#828 := [trans #826 #822]: #827
#583 := (iff #185 #569)
#574 := (implies true #569)
#577 := (iff #574 #569)
#578 := [rewrite]: #577
#581 := (iff #185 #574)
#579 := (iff #184 #569)
#575 := (iff #184 #574)
#572 := (iff #183 #569)
#566 := (implies #142 #550)
#570 := (iff #566 #569)
#571 := [rewrite]: #570
#567 := (iff #183 #566)
#564 := (iff #182 #550)
#555 := (implies true #550)
#558 := (iff #555 #550)
#559 := [rewrite]: #558
#562 := (iff #182 #555)
#560 := (iff #181 #550)
#556 := (iff #181 #555)
#553 := (iff #180 #550)
#546 := (implies #144 #541)
#551 := (iff #546 #550)
#552 := [rewrite]: #551
#547 := (iff #180 #546)
#544 := (iff #179 #541)
#537 := (implies #147 #532)
#542 := (iff #537 #541)
#543 := [rewrite]: #542
#538 := (iff #179 #537)
#535 := (iff #178 #532)
#528 := (implies #149 #523)
#533 := (iff #528 #532)
#534 := [rewrite]: #533
#529 := (iff #178 #528)
#526 := (iff #177 #523)
#519 := (implies #152 #509)
#524 := (iff #519 #523)
#525 := [rewrite]: #524
#520 := (iff #177 #519)
#517 := (iff #176 #509)
#512 := (implies true #509)
#515 := (iff #512 #509)
#516 := [rewrite]: #515
#513 := (iff #176 #512)
#510 := (iff #175 #509)
#507 := (iff #174 #504)
#500 := (implies #461 #497)
#505 := (iff #500 #504)
#506 := [rewrite]: #505
#501 := (iff #174 #500)
#498 := (iff #173 #497)
#495 := (iff #172 #492)
#488 := (implies #476 #169)
#493 := (iff #488 #492)
#494 := [rewrite]: #493
#489 := (iff #172 #488)
#486 := (iff #171 #169)
#481 := (and #169 true)
#484 := (iff #481 #169)
#485 := [rewrite]: #484
#482 := (iff #171 #481)
#479 := (iff #170 true)
#480 := [rewrite]: #479
#483 := [monotonicity #480]: #482
#487 := [trans #483 #485]: #486
#477 := (iff #167 #476)
#474 := (iff #166 #471)
#467 := (implies #164 #464)
#472 := (iff #467 #471)
#473 := [rewrite]: #472
#468 := (iff #166 #467)
#465 := (iff #165 #464)
#441 := (= #158 #440)
#442 := [rewrite]: #441
#466 := [monotonicity #442]: #465
#469 := [monotonicity #466]: #468
#475 := [trans #469 #473]: #474
#478 := [quant-intro #475]: #477
#490 := [monotonicity #478 #487]: #489
#496 := [trans #490 #494]: #495
#499 := [monotonicity #478 #496]: #498
#462 := (iff #163 #461)
#459 := (iff #162 #456)
#452 := (implies #155 #449)
#457 := (iff #452 #456)
#458 := [rewrite]: #457
#453 := (iff #162 #452)
#450 := (iff #161 #449)
#447 := (iff #160 #446)
#444 := (iff #159 #443)
#445 := [monotonicity #442]: #444
#448 := [monotonicity #445]: #447
#451 := [quant-intro #448]: #450
#454 := [monotonicity #451]: #453
#460 := [trans #454 #458]: #459
#463 := [quant-intro #460]: #462
#502 := [monotonicity #463 #499]: #501
#508 := [trans #502 #506]: #507
#511 := [monotonicity #463 #508]: #510
#514 := [monotonicity #511]: #513
#518 := [trans #514 #516]: #517
#521 := [monotonicity #518]: #520
#527 := [trans #521 #525]: #526
#530 := [monotonicity #527]: #529
#536 := [trans #530 #534]: #535
#539 := [monotonicity #536]: #538
#545 := [trans #539 #543]: #544
#548 := [monotonicity #545]: #547
#554 := [trans #548 #552]: #553
#557 := [monotonicity #554]: #556
#561 := [trans #557 #559]: #560
#563 := [monotonicity #561]: #562
#565 := [trans #563 #559]: #564
#568 := [monotonicity #565]: #567
#573 := [trans #568 #571]: #572
#576 := [monotonicity #573]: #575
#580 := [trans #576 #578]: #579
#582 := [monotonicity #580]: #581
#584 := [trans #582 #578]: #583
#831 := [monotonicity #584 #828]: #830
#834 := [monotonicity #831]: #833
#838 := [trans #834 #836]: #837
#438 := (iff #139 #437)
#435 := (iff #138 #432)
#428 := (implies #132 #425)
#433 := (iff #428 #432)
#434 := [rewrite]: #433
#429 := (iff #138 #428)
#426 := (iff #137 #425)
#423 := (iff #136 #422)
#420 := (iff #135 #419)
#417 := (iff #134 #416)
#399 := (= #127 #398)
#400 := [rewrite]: #399
#418 := [monotonicity #400]: #417
#421 := [monotonicity #418]: #420
#424 := [monotonicity #421]: #423
#427 := [quant-intro #424]: #426
#430 := [monotonicity #427]: #429
#436 := [trans #430 #434]: #435
#439 := [quant-intro #436]: #438
#841 := [monotonicity #439 #838]: #840
#847 := [trans #841 #845]: #846
#414 := (iff #130 #413)
#411 := (iff #129 #408)
#404 := (implies #126 #401)
#409 := (iff #404 #408)
#410 := [rewrite]: #409
#405 := (iff #129 #404)
#402 := (iff #128 #401)
#403 := [monotonicity #400]: #402
#406 := [monotonicity #403]: #405
#412 := [trans #406 #410]: #411
#415 := [quant-intro #412]: #414
#850 := [monotonicity #415 #847]: #849
#856 := [trans #850 #854]: #855
#396 := (iff #125 #395)
#393 := (iff #124 #392)
#394 := [rewrite]: #393
#397 := [quant-intro #394]: #396
#859 := [monotonicity #397 #856]: #858
#865 := [trans #859 #863]: #864
#868 := [monotonicity #865]: #867
#874 := [trans #868 #872]: #873
#877 := [monotonicity #874]: #876
#883 := [trans #877 #881]: #882
#886 := [monotonicity #883]: #885
#890 := [trans #886 #888]: #889
#892 := [monotonicity #890]: #891
#894 := [trans #892 #888]: #893
#389 := (iff #108 #388)
#386 := (iff #107 #385)
#387 := [rewrite]: #386
#390 := [quant-intro #387]: #389
#897 := [monotonicity #390 #894]: #896
#903 := [trans #897 #901]: #902
#906 := [monotonicity #390 #903]: #905
#382 := (iff #99 #381)
#379 := (iff #98 #378)
#380 := [rewrite]: #379
#383 := [quant-intro #380]: #382
#909 := [monotonicity #383 #906]: #908
#915 := [trans #909 #913]: #914
#918 := [monotonicity #383 #915]: #917
#375 := (iff #90 #374)
#372 := (iff #89 #371)
#373 := [rewrite]: #372
#376 := [quant-intro #373]: #375
#921 := [monotonicity #376 #918]: #920
#927 := [trans #921 #925]: #926
#930 := [monotonicity #376 #927]: #929
#933 := [monotonicity #930]: #932
#939 := [trans #933 #937]: #938
#942 := [monotonicity #939]: #941
#945 := [monotonicity #942]: #944
#951 := [trans #945 #949]: #950
#954 := [monotonicity #951]: #953
#957 := [monotonicity #954]: #956
#961 := [trans #957 #959]: #960
#964 := [monotonicity #961]: #963
#970 := [trans #964 #968]: #969
#368 := (iff #74 #367)
#365 := (iff #73 #364)
#366 := [rewrite]: #365
#369 := [quant-intro #366]: #368
#973 := [monotonicity #369 #970]: #972
#979 := [trans #973 #977]: #978
#362 := (iff #70 #361)
#359 := (iff #69 #358)
#360 := [rewrite]: #359
#363 := [quant-intro #360]: #362
#982 := [monotonicity #363 #979]: #981
#988 := [trans #982 #986]: #987
#991 := [monotonicity #988]: #990
#995 := [trans #991 #993]: #994
#997 := [monotonicity #995]: #996
#999 := [trans #997 #993]: #998
#1002 := [monotonicity #999]: #1001
#1563 := [trans #1002 #1561]: #1562
#357 := [asserted]: #298
#1564 := [mp #357 #1563]: #1559
#1566 := [not-or-elim #1564]: #367
#1621 := [mp~ #1566 #1590]: #367
#3748 := [mp #1621 #3747]: #3743
#3348 := (not #3743)
#6198 := (or #3348 #1703 #6178)
#6194 := (or #1703 #6178)
#6199 := (or #3348 #6194)
#6202 := (iff #6199 #6198)
#6174 := [rewrite]: #6202
#6200 := [quant-inst #1702]: #6199
#6180 := [mp #6200 #6174]: #6198
#6206 := [unit-resolution #6180 #3748 #6201]: #6178
#6208 := [mp #6206 #6185]: #6181
#6219 := (not #6181)
#1709 := (not #1708)
#3684 := (or #3791 #1709)
#3685 := [def-axiom]: #3684
#6197 := [unit-resolution #3685 #6196]: #1709
#6214 := (or #6219 #1708)
#6220 := [th-lemma arith triangle-eq]: #6214
#6221 := [unit-resolution #6220 #6197]: #6219
#6209 := [unit-resolution #6221 #6208]: false
#6210 := [lemma #6209]: #3791
#4075 := (or #3794 #4072)
#4078 := (not #4075)
#2629 := (or #78 #1029 #1040)
#3774 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3773) #2629)
#3779 := (not #3774)
#4081 := (or #3779 #4078)
#4084 := (not #4081)
decl ?v0!4 :: S2
#1671 := ?v0!4
#1684 := (f17 ?v0!4)
#1685 := (* -1::Int #1684)
decl ?v1!3 :: S2
#1670 := ?v1!3
#1683 := (f17 ?v1!3)
#2262 := (+ #1683 #1685)
#1674 := (f6 f7 ?v1!3)
#1675 := (f5 #1674 ?v0!4)
#1676 := (f15 #1675)
#2263 := (+ #1676 #2262)
#2266 := (>= #2263 0::Int)
#1677 := (* -1::Int #1676)
#1678 := (+ f14 #1677)
#1679 := (<= #1678 0::Int)
#1672 := (f9 f18 ?v1!3)
#1673 := (= #1672 f1)
#2592 := (not #1673)
#2607 := (or #2592 #1679 #2266)
#2612 := (not #2607)
#4087 := (or #2612 #4084)
#4090 := (not #4087)
#3764 := (pattern #67 #87)
#1760 := (not #85)
#2584 := (or #77 #1760 #1014)
#3765 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3764) #2584)
#3770 := (not #3765)
#4093 := (or #3770 #4090)
#4096 := (not #4093)
decl ?v0!2 :: S2
#1644 := ?v0!2
#1653 := (f17 ?v0!2)
#1654 := (* -1::Int #1653)
decl ?v1!1 :: S2
#1643 := ?v1!1
#1652 := (f17 ?v1!1)
#1655 := (+ #1652 #1654)
#1656 := (>= #1655 0::Int)
#1648 := (f9 f18 ?v0!2)
#1649 := (= #1648 f1)
#2035 := (not #1649)
#1645 := (f9 f18 ?v1!1)
#1646 := (= #1645 f1)
#2083 := (or #1646 #2035 #1656)
#5518 := [hypothesis]: #1649
#3750 := (forall (vars (?v0 S2)) (:pat #3749) #78)
#3753 := (iff #79 #3750)
#3751 := (iff #78 #78)
#3752 := [refl]: #3751
#3754 := [quant-intro #3752]: #3753
#1591 := (~ #79 #79)
#1622 := (~ #78 #78)
#1623 := [refl]: #1622
#1592 := [nnf-pos #1623]: #1591
#1567 := [not-or-elim #1564]: #79
#1624 := [mp~ #1567 #1592]: #79
#3755 := [mp #1624 #3754]: #3750
#7029 := (not #3750)
#4457 := (or #7029 #2035)
#4481 := [quant-inst #1644]: #4457
#5558 := [unit-resolution #4481 #3755 #5518]: false
#6078 := [lemma #5558]: #2035
#3275 := (or #2083 #1649)
#3361 := [def-axiom]: #3275
#7086 := [unit-resolution #3361 #6078]: #2083
#1634 := (not #2083)
#4099 := (or #1634 #4096)
#4102 := (not #4099)
#3756 := (forall (vars (?v0 S2)) (:pat #3736) #1005)
#3761 := (not #3756)
#4105 := (or #3761 #4102)
#4108 := (not #4105)
decl ?v0!0 :: S2
#1628 := ?v0!0
#1629 := (f17 ?v0!0)
#1630 := (>= #1629 0::Int)
#1631 := (not #1630)
#3358 := [hypothesis]: #1631
#3357 := (<= #1629 0::Int)
#4162 := (or #3357 #1630)
#4163 := [th-lemma arith farkas 1 1]: #4162
#4164 := [unit-resolution #4163 #3358]: #3357
#4139 := (not #3357)
#4158 := (or #4139 #1630)
#3325 := (= f14 #1629)
#3384 := (= #1629 f14)
#4135 := (iff #3384 #3325)
#3302 := (iff #3325 #3384)
#4134 := [commutativity]: #3302
#4136 := [symm #4134]: #4135
#3398 := (= ?v0!0 f16)
#3392 := (not #3398)
#3393 := (= #1629 0::Int)
#3356 := (not #3393)
#3312 := (or #3356 #1630)
#3311 := [th-lemma arith triangle-eq]: #3312
#3317 := [unit-resolution #3311 #3358]: #3356
#3737 := (forall (vars (?v0 S2)) (:pat #3736) #358)
#3740 := (iff #361 #3737)
#3738 := (iff #358 #358)
#3739 := [refl]: #3738
#3741 := [quant-intro #3739]: #3740
#1587 := (~ #361 #361)
#1616 := (~ #358 #358)
#1617 := [refl]: #1616
#1588 := [nnf-pos #1617]: #1587
#1565 := [not-or-elim #1564]: #361
#1618 := [mp~ #1565 #1588]: #361
#3742 := [mp #1618 #3741]: #3737
#3375 := (not #3737)
#3379 := (or #3375 #3392 #3393)
#3383 := (or #3392 #3393)
#3370 := (or #3375 #3383)
#3380 := (iff #3370 #3379)
#3347 := [rewrite]: #3380
#3378 := [quant-inst #1628]: #3370
#3349 := [mp #3378 #3347]: #3379
#3292 := [unit-resolution #3349 #3742 #3317]: #3392
#3359 := (or #3348 #3398 #3384)
#3394 := (or #3398 #3384)
#3342 := (or #3348 #3394)
#3335 := (iff #3342 #3359)
#3333 := [rewrite]: #3335
#3334 := [quant-inst #1628]: #3342
#3336 := [mp #3334 #3333]: #3359
#3297 := [unit-resolution #3336 #3748 #3292]: #3384
#4137 := [mp #3297 #4136]: #3325
#3405 := (* -1::Int #1629)
#3337 := (+ f14 #3405)
#3313 := (<= #3337 0::Int)
#4133 := (not #3313)
#326 := (<= f14 0::Int)
#327 := (not #326)
#55 := (< 0::Int f14)
#328 := (iff #55 #327)
#329 := [rewrite]: #328
#323 := [asserted]: #55
#330 := [mp #323 #329]: #327
#4138 := [hypothesis]: #3357
#4140 := (or #4133 #326 #4139)
#4141 := [th-lemma arith assign-bounds 1 1]: #4140
#4142 := [unit-resolution #4141 #4138 #330]: #4133
#4143 := (not #3325)
#4157 := (or #4143 #3313)
#4159 := [th-lemma arith triangle-eq]: #4157
#4160 := [unit-resolution #4159 #4142 #4137]: false
#4161 := [lemma #4160]: #4158
#4165 := [unit-resolution #4161 #4164 #3358]: false
#4166 := [lemma #4165]: #1630
#4111 := (or #1631 #4108)
#4114 := (not #4111)
#4117 := (or #946 #4114)
#4120 := (not #4117)
#4240 := [hypothesis]: #946
#4232 := (or #3375 #81)
#6915 := (= f16 f16)
#6988 := (not #6915)
#4242 := (or #6988 #81)
#4233 := (or #3375 #4242)
#4235 := (iff #4233 #4232)
#4234 := (iff #4232 #4232)
#4237 := [rewrite]: #4234
#4248 := (iff #4242 #81)
#4214 := (or false #81)
#4243 := (iff #4214 #81)
#4247 := [rewrite]: #4243
#4244 := (iff #4242 #4214)
#6996 := (iff #6988 false)
#6991 := (not true)
#6994 := (iff #6991 false)
#6995 := [rewrite]: #6994
#6992 := (iff #6988 #6991)
#6918 := (iff #6915 true)
#6919 := [rewrite]: #6918
#6993 := [monotonicity #6919]: #6992
#6997 := [trans #6993 #6995]: #6996
#4245 := [monotonicity #6997]: #4244
#4246 := [trans #4245 #4247]: #4248
#4236 := [monotonicity #4246]: #4235
#4238 := [trans #4236 #4237]: #4235
#4249 := [quant-inst #65]: #4233
#4231 := [mp #4249 #4238]: #4232
#4241 := [unit-resolution #4231 #3742 #4240]: false
#4239 := [lemma #4241]: #81
#4123 := (or #946 #4120)
#3042 := (forall (vars (?v1 S2)) #3031)
#3049 := (not #3042)
#3027 := (forall (vars (?v0 S2) (?v1 S2)) #3022)
#3048 := (not #3027)
#3050 := (or #3048 #2124 #2129 #3049)
#3051 := (not #3050)
#3056 := (or #3005 #3051)
#3063 := (not #3056)
#2982 := (forall (vars (?v0 S2) (?v1 S2)) #2977)
#3062 := (not #2982)
#3064 := (or #3062 #3063)
#3065 := (not #3064)
#3070 := (or #2959 #3065)
#3076 := (not #3070)
#3077 := (or #1271 #3076)
#3078 := (not #3077)
#3083 := (or #2052 #3078)
#3089 := (not #3083)
#3090 := (or #713 #3089)
#3091 := (not #3090)
#3096 := (or #713 #3091)
#3102 := (not #3096)
#3103 := (or #736 #3102)
#3104 := (not #3103)
#3109 := (or #2032 #3104)
#3115 := (not #3109)
#3116 := (or #1262 #3115)
#3117 := (not #3116)
#3122 := (or #2012 #3117)
#3130 := (not #3122)
#2936 := (forall (vars (?v0 S2)) #2933)
#3129 := (not #2936)
#2930 := (forall (vars (?v0 S2)) #2925)
#3128 := (not #2930)
#3131 := (or #1963 #1968 #188 #1411 #1407 #778 #3128 #3129 #3130)
#3132 := (not #3131)
#2870 := (forall (vars (?v0 S2) (?v1 S2)) #2865)
#2876 := (not #2870)
#2877 := (or #2876 #169)
#2878 := (not #2877)
#2883 := (or #2848 #2878)
#2890 := (not #2883)
#2826 := (forall (vars (?v0 S2)) #2821)
#2889 := (not #2826)
#2891 := (or #2889 #2890)
#2892 := (not #2891)
#2789 := (forall (vars (?v1 S2)) #2778)
#2795 := (not #2789)
#2796 := (or #1841 #1846 #2795)
#2797 := (not #2796)
#2897 := (or #2797 #2892)
#2904 := (not #2897)
#2774 := (forall (vars (?v0 S2)) #2763)
#2903 := (not #2774)
#2905 := (or #2903 #549 #540 #531 #522 #2904)
#2906 := (not #2905)
#3137 := (or #2906 #3132)
#3147 := (not #3137)
#2760 := (forall (vars (?v0 S2)) #2755)
#3146 := (not #2760)
#2732 := (forall (vars (?v0 S2) (?v1 S2)) #2727)
#3145 := (not #2732)
#2710 := (forall (vars (?v0 S2) (?v1 S2)) #2705)
#3144 := (not #2710)
#2687 := (forall (vars (?v0 S2)) #2682)
#3143 := (not #2687)
#3148 := (or #3143 #878 #1489 #3144 #3145 #3146 #3147)
#3149 := (not #3148)
#2649 := (forall (vars (?v1 S2)) #2638)
#2655 := (not #2649)
#2656 := (or #1703 #1708 #2655)
#2657 := (not #2656)
#3154 := (or #2657 #3149)
#3161 := (not #3154)
#2634 := (forall (vars (?v0 S2) (?v1 S2)) #2629)
#3160 := (not #2634)
#3162 := (or #3160 #3161)
#3163 := (not #3162)
#3168 := (or #2612 #3163)
#3175 := (not #3168)
#2589 := (forall (vars (?v0 S2) (?v1 S2)) #2584)
#3174 := (not #2589)
#3176 := (or #3174 #3175)
#3177 := (not #3176)
#3182 := (or #1634 #3177)
#3188 := (not #3182)
#3189 := (or #1009 #3188)
#3190 := (not #3189)
#3195 := (or #1631 #3190)
#3201 := (not #3195)
#3202 := (or #946 #3201)
#3203 := (not #3202)
#3208 := (or #946 #3203)
#4124 := (iff #3208 #4123)
#4121 := (iff #3203 #4120)
#4118 := (iff #3202 #4117)
#4115 := (iff #3201 #4114)
#4112 := (iff #3195 #4111)
#4109 := (iff #3190 #4108)
#4106 := (iff #3189 #4105)
#4103 := (iff #3188 #4102)
#4100 := (iff #3182 #4099)
#4097 := (iff #3177 #4096)
#4094 := (iff #3176 #4093)
#4091 := (iff #3175 #4090)
#4088 := (iff #3168 #4087)
#4085 := (iff #3163 #4084)
#4082 := (iff #3162 #4081)
#4079 := (iff #3161 #4078)
#4076 := (iff #3154 #4075)
#4073 := (iff #3149 #4072)
#4070 := (iff #3148 #4069)
#4067 := (iff #3147 #4066)
#4064 := (iff #3137 #4063)
#4061 := (iff #3132 #4060)
#4058 := (iff #3131 #4057)
#4055 := (iff #3130 #4054)
#4052 := (iff #3122 #4051)
#4049 := (iff #3117 #4048)
#4046 := (iff #3116 #4045)
#4043 := (iff #3115 #4042)
#4040 := (iff #3109 #4039)
#4037 := (iff #3104 #4036)
#4034 := (iff #3103 #4033)
#4031 := (iff #3102 #4030)
#4028 := (iff #3096 #4027)
#4025 := (iff #3091 #4024)
#4022 := (iff #3090 #4021)
#4019 := (iff #3089 #4018)
#4016 := (iff #3083 #4015)
#4013 := (iff #3078 #4012)
#4010 := (iff #3077 #4009)
#4007 := (iff #3076 #4006)
#4004 := (iff #3070 #4003)
#4001 := (iff #3065 #4000)
#3998 := (iff #3064 #3997)
#3995 := (iff #3063 #3994)
#3992 := (iff #3056 #3991)
#3989 := (iff #3051 #3988)
#3986 := (iff #3050 #3985)
#3983 := (iff #3049 #3982)
#3980 := (iff #3042 #3977)
#3978 := (iff #3031 #3031)
#3979 := [refl]: #3978
#3981 := [quant-intro #3979]: #3980
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#3993 := [monotonicity #3990]: #3992
#3996 := [monotonicity #3993]: #3995
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#2868 := (iff #1182 #2865)
#2851 := (or #1138 #1029)
#2862 := (or #2851 #1179)
#2866 := (iff #2862 #2865)
#2867 := [rewrite]: #2866
#2863 := (iff #1182 #2862)
#2860 := (iff #1176 #2851)
#2852 := (not #2851)
#2855 := (not #2852)
#2858 := (iff #2855 #2851)
#2859 := [rewrite]: #2858
#2856 := (iff #1176 #2855)
#2853 := (iff #1173 #2852)
#2854 := [rewrite]: #2853
#2857 := [monotonicity #2854]: #2856
#2861 := [trans #2857 #2859]: #2860
#2864 := [monotonicity #2861]: #2863
#2869 := [trans #2864 #2867]: #2868
#2872 := [quant-intro #2869]: #2871
#2875 := [monotonicity #2872]: #2874
#2882 := [trans #2875 #2880]: #2881
#2849 := (iff #2451 #2848)
#2846 := (iff #2448 #2843)
#2829 := (or #1909 #1916)
#2840 := (or #2829 #2445)
#2844 := (iff #2840 #2843)
#2845 := [rewrite]: #2844
#2841 := (iff #2448 #2840)
#2838 := (iff #1919 #2829)
#2830 := (not #2829)
#2833 := (not #2830)
#2836 := (iff #2833 #2829)
#2837 := [rewrite]: #2836
#2834 := (iff #1919 #2833)
#2831 := (iff #1918 #2830)
#2832 := [rewrite]: #2831
#2835 := [monotonicity #2832]: #2834
#2839 := [trans #2835 #2837]: #2838
#2842 := [monotonicity #2839]: #2841
#2847 := [trans #2842 #2845]: #2846
#2850 := [monotonicity #2847]: #2849
#2885 := [monotonicity #2850 #2882]: #2884
#2827 := (iff #2438 #2826)
#2824 := (iff #2435 #2821)
#2802 := (or #66 #1138)
#2818 := (or #2802 #2815)
#2822 := (iff #2818 #2821)
#2823 := [rewrite]: #2822
#2819 := (iff #2435 #2818)
#2816 := (iff #2432 #2815)
#2817 := [rewrite]: #2816
#2811 := (iff #1145 #2802)
#2803 := (not #2802)
#2806 := (not #2803)
#2809 := (iff #2806 #2802)
#2810 := [rewrite]: #2809
#2807 := (iff #1145 #2806)
#2804 := (iff #1142 #2803)
#2805 := [rewrite]: #2804
#2808 := [monotonicity #2805]: #2807
#2812 := [trans #2808 #2810]: #2811
#2820 := [monotonicity #2812 #2817]: #2819
#2825 := [trans #2820 #2823]: #2824
#2828 := [quant-intro #2825]: #2827
#2888 := [monotonicity #2828 #2885]: #2887
#2896 := [trans #2888 #2894]: #2895
#2800 := (iff #2396 #2797)
#2792 := (and #1842 #1847 #2789)
#2798 := (iff #2792 #2797)
#2799 := [rewrite]: #2798
#2793 := (iff #2396 #2792)
#2790 := (iff #2390 #2789)
#2787 := (iff #2387 #2778)
#2779 := (not #2778)
#2782 := (not #2779)
#2785 := (iff #2782 #2778)
#2786 := [rewrite]: #2785
#2783 := (iff #2387 #2782)
#2780 := (iff #2384 #2779)
#2781 := [rewrite]: #2780
#2784 := [monotonicity #2781]: #2783
#2788 := [trans #2784 #2786]: #2787
#2791 := [quant-intro #2788]: #2790
#2794 := [monotonicity #2791]: #2793
#2801 := [trans #2794 #2799]: #2800
#2899 := [monotonicity #2801 #2896]: #2898
#2775 := (iff #1825 #2774)
#2772 := (iff #1822 #2763)
#2764 := (not #2763)
#2767 := (not #2764)
#2770 := (iff #2767 #2763)
#2771 := [rewrite]: #2770
#2768 := (iff #1822 #2767)
#2765 := (iff #1203 #2764)
#2766 := [rewrite]: #2765
#2769 := [monotonicity #2766]: #2768
#2773 := [trans #2769 #2771]: #2772
#2776 := [quant-intro #2773]: #2775
#2902 := [monotonicity #2776 #2899]: #2901
#2910 := [trans #2902 #2908]: #2909
#3139 := [monotonicity #2910 #3136]: #3138
#2761 := (iff #2364 #2760)
#2758 := (iff #2361 #2755)
#2735 := (or #66 #1093)
#2752 := (or #2735 #2749)
#2756 := (iff #2752 #2755)
#2757 := [rewrite]: #2756
#2753 := (iff #2361 #2752)
#2750 := (iff #2358 #2749)
#2751 := [rewrite]: #2750
#2744 := (iff #1100 #2735)
#2736 := (not #2735)
#2739 := (not #2736)
#2742 := (iff #2739 #2735)
#2743 := [rewrite]: #2742
#2740 := (iff #1100 #2739)
#2737 := (iff #1097 #2736)
#2738 := [rewrite]: #2737
#2741 := [monotonicity #2738]: #2740
#2745 := [trans #2741 #2743]: #2744
#2754 := [monotonicity #2745 #2751]: #2753
#2759 := [trans #2754 #2757]: #2758
#2762 := [quant-intro #2759]: #2761
#2733 := (iff #1466 #2732)
#2730 := (iff #1463 #2727)
#2713 := (or #118 #1029)
#2724 := (or #2713 #1460)
#2728 := (iff #2724 #2727)
#2729 := [rewrite]: #2728
#2725 := (iff #1463 #2724)
#2722 := (iff #1457 #2713)
#2714 := (not #2713)
#2717 := (not #2714)
#2720 := (iff #2717 #2713)
#2721 := [rewrite]: #2720
#2718 := (iff #1457 #2717)
#2715 := (iff #1454 #2714)
#2716 := [rewrite]: #2715
#2719 := [monotonicity #2716]: #2718
#2723 := [trans #2719 #2721]: #2722
#2726 := [monotonicity #2723]: #2725
#2731 := [trans #2726 #2729]: #2730
#2734 := [quant-intro #2731]: #2733
#2711 := (iff #1477 #2710)
#2708 := (iff #1474 #2705)
#2691 := (or #117 #2690)
#2702 := (or #2691 #1109)
#2706 := (iff #2702 #2705)
#2707 := [rewrite]: #2706
#2703 := (iff #1474 #2702)
#2700 := (iff #391 #2691)
#2692 := (not #2691)
#2695 := (not #2692)
#2698 := (iff #2695 #2691)
#2699 := [rewrite]: #2698
#2696 := (iff #391 #2695)
#2693 := (iff #121 #2692)
#2694 := [rewrite]: #2693
#2697 := [monotonicity #2694]: #2696
#2701 := [trans #2697 #2699]: #2700
#2704 := [monotonicity #2701]: #2703
#2709 := [trans #2704 #2707]: #2708
#2712 := [quant-intro #2709]: #2711
#2688 := (iff #2322 #2687)
#2685 := (iff #2319 #2682)
#2662 := (or #66 #1055)
#2679 := (or #2662 #2676)
#2683 := (iff #2679 #2682)
#2684 := [rewrite]: #2683
#2680 := (iff #2319 #2679)
#2677 := (iff #2316 #2676)
#2678 := [rewrite]: #2677
#2671 := (iff #1062 #2662)
#2663 := (not #2662)
#2666 := (not #2663)
#2669 := (iff #2666 #2662)
#2670 := [rewrite]: #2669
#2667 := (iff #1062 #2666)
#2664 := (iff #1059 #2663)
#2665 := [rewrite]: #2664
#2668 := [monotonicity #2665]: #2667
#2672 := [trans #2668 #2670]: #2671
#2681 := [monotonicity #2672 #2678]: #2680
#2686 := [trans #2681 #2684]: #2685
#2689 := [quant-intro #2686]: #2688
#3142 := [monotonicity #2689 #2712 #2734 #2762 #3139]: #3141
#3153 := [trans #3142 #3151]: #3152
#2660 := (iff #2280 #2657)
#2652 := (and #1704 #1709 #2649)
#2658 := (iff #2652 #2657)
#2659 := [rewrite]: #2658
#2653 := (iff #2280 #2652)
#2650 := (iff #1732 #2649)
#2647 := (iff #1729 #2638)
#2639 := (not #2638)
#2642 := (not #2639)
#2645 := (iff #2642 #2638)
#2646 := [rewrite]: #2645
#2643 := (iff #1729 #2642)
#2640 := (iff #1720 #2639)
#2641 := [rewrite]: #2640
#2644 := [monotonicity #2641]: #2643
#2648 := [trans #2644 #2646]: #2647
#2651 := [quant-intro #2648]: #2650
#2654 := [monotonicity #2651]: #2653
#2661 := [trans #2654 #2659]: #2660
#3156 := [monotonicity #2661 #3153]: #3155
#2635 := (iff #1047 #2634)
#2632 := (iff #1044 #2629)
#2615 := (or #78 #1029)
#2626 := (or #2615 #1040)
#2630 := (iff #2626 #2629)
#2631 := [rewrite]: #2630
#2627 := (iff #1044 #2626)
#2624 := (iff #1036 #2615)
#2616 := (not #2615)
#2619 := (not #2616)
#2622 := (iff #2619 #2615)
#2623 := [rewrite]: #2622
#2620 := (iff #1036 #2619)
#2617 := (iff #1033 #2616)
#2618 := [rewrite]: #2617
#2621 := [monotonicity #2618]: #2620
#2625 := [trans #2621 #2623]: #2624
#2628 := [monotonicity #2625]: #2627
#2633 := [trans #2628 #2631]: #2632
#2636 := [quant-intro #2633]: #2635
#3159 := [monotonicity #2636 #3156]: #3158
#3167 := [trans #3159 #3165]: #3166
#2613 := (iff #2272 #2612)
#2610 := (iff #2269 #2607)
#2593 := (or #2592 #1679)
#2604 := (or #2593 #2266)
#2608 := (iff #2604 #2607)
#2609 := [rewrite]: #2608
#2605 := (iff #2269 #2604)
#2602 := (iff #1682 #2593)
#2594 := (not #2593)
#2597 := (not #2594)
#2600 := (iff #2597 #2593)
#2601 := [rewrite]: #2600
#2598 := (iff #1682 #2597)
#2595 := (iff #1681 #2594)
#2596 := [rewrite]: #2595
#2599 := [monotonicity #2596]: #2598
#2603 := [trans #2599 #2601]: #2602
#2606 := [monotonicity #2603]: #2605
#2611 := [trans #2606 #2609]: #2610
#2614 := [monotonicity #2611]: #2613
#3170 := [monotonicity #2614 #3167]: #3169
#2590 := (iff #1021 #2589)
#2587 := (iff #1018 #2584)
#1661 := (or #77 #1760)
#2581 := (or #1661 #1014)
#2585 := (iff #2581 #2584)
#2586 := [rewrite]: #2585
#2582 := (iff #1018 #2581)
#2579 := (iff #370 #1661)
#1662 := (not #1661)
#2574 := (not #1662)
#2577 := (iff #2574 #1661)
#2578 := [rewrite]: #2577
#2575 := (iff #370 #2574)
#2259 := (iff #86 #1662)
#2573 := [rewrite]: #2259
#2576 := [monotonicity #2573]: #2575
#2580 := [trans #2576 #2578]: #2579
#2583 := [monotonicity #2580]: #2582
#2588 := [trans #2583 #2586]: #2587
#2591 := [quant-intro #2588]: #2590
#3173 := [monotonicity #2591 #3170]: #3172
#3181 := [trans #3173 #3179]: #3180
#1635 := (iff #1658 #1634)
#1973 := (iff #1657 #2083)
#2036 := (or #1646 #2035)
#2114 := (or #2036 #1656)
#2015 := (iff #2114 #2083)
#2016 := [rewrite]: #2015
#2115 := (iff #1657 #2114)
#1811 := (iff #1651 #2036)
#1893 := (not #2036)
#1694 := (not #1893)
#1929 := (iff #1694 #2036)
#1930 := [rewrite]: #1929
#2055 := (iff #1651 #1694)
#1894 := (iff #1650 #1893)
#1693 := [rewrite]: #1894
#2056 := [monotonicity #1693]: #2055
#1812 := [trans #2056 #1930]: #1811
#2082 := [monotonicity #1812]: #2115
#1974 := [trans #2082 #2016]: #1973
#1759 := [monotonicity #1974]: #1635
#3184 := [monotonicity #1759 #3181]: #3183
#3187 := [monotonicity #3184]: #3186
#3194 := [trans #3187 #3192]: #3193
#3197 := [monotonicity #3194]: #3196
#3200 := [monotonicity #3197]: #3199
#3207 := [trans #3200 #3205]: #3206
#3210 := [monotonicity #3207]: #3209
#2138 := (+ #2137 #2133)
#2139 := (= #2138 0::Int)
#2140 := (and #2135 #218 #2139)
#2150 := (not #2140)
#2153 := (forall (vars (?v1 S2)) #2150)
#2131 := (and #2125 #2130)
#2132 := (not #2131)
#2147 := (not #2132)
#2157 := (and #2147 #2153)
#2162 := (and #1301 #2157)
#2166 := (or #2111 #2162)
#2170 := (and #1282 #2166)
#2174 := (or #2079 #2170)
#2178 := (and #1268 #2174)
#2182 := (or #2052 #2178)
#2046 := (not #713)
#2186 := (and #2046 #2182)
#2190 := (or #713 #2186)
#2194 := (and #606 #2190)
#2198 := (or #2032 #2194)
#2202 := (and #1259 #2198)
#2206 := (or #2012 #2202)
#1989 := (not #778)
#1970 := (and #1964 #1969)
#2210 := (and #1970 #189 #1412 #1404 #1989 #1391 #1248 #2206)
#1922 := (+ #1906 #1921)
#1923 := (+ #1913 #1922)
#1924 := (>= #1923 0::Int)
#1925 := (or #1919 #1924)
#1926 := (not #1925)
#1945 := (or #1926 #1941)
#1882 := (+ #1881 #1136)
#1888 := (+ #1887 #1882)
#1889 := (= #1888 0::Int)
#1883 := (>= #1882 0::Int)
#1884 := (not #1883)
#1890 := (and #1884 #1889)
#1895 := (or #1145 #1890)
#1898 := (forall (vars (?v0 S2)) #1895)
#1949 := (and #1898 #1945)
#1855 := (+ #1854 #1850)
#1856 := (= #1855 0::Int)
#1857 := (and #1852 #1856)
#1866 := (not #1857)
#1869 := (forall (vars (?v1 S2)) #1866)
#1848 := (and #1842 #1847)
#1849 := (not #1848)
#1863 := (not #1849)
#1873 := (and #1863 #1869)
#1953 := (or #1873 #1949)
#1837 := (not #522)
#1834 := (not #531)
#1831 := (not #540)
#1828 := (not #549)
#1957 := (and #1825 #1828 #1831 #1834 #1837 #1953)
#2214 := (or #1957 #2210)
#1798 := (+ #1797 #1091)
#1806 := (+ #1805 #1798)
#1807 := (= #1806 0::Int)
#1799 := (>= #1798 0::Int)
#1800 := (not #1799)
#1808 := (and #1800 #1802 #1807)
#1813 := (or #1100 #1808)
#1816 := (forall (vars (?v0 S2)) #1813)
#1770 := (not #878)
#1753 := (+ #1053 #1752)
#1754 := (+ #1744 #1753)
#1755 := (= #1754 0::Int)
#1745 := (+ #1744 #1053)
#1746 := (>= #1745 0::Int)
#1747 := (not #1746)
#1756 := (and #1747 #1749 #1755)
#1761 := (or #1062 #1756)
#1764 := (forall (vars (?v0 S2)) #1761)
#2218 := (and #1764 #1770 #1486 #1477 #1466 #1816 #2214)
#1710 := (and #1704 #1709)
#1711 := (not #1710)
#1726 := (not #1711)
#1736 := (and #1726 #1732)
#2222 := (or #1736 #2218)
#2226 := (and #1047 #2222)
#1686 := (+ #1685 #1676)
#1687 := (+ #1683 #1686)
#1688 := (>= #1687 0::Int)
#1689 := (or #1682 #1688)
#1690 := (not #1689)
#2230 := (or #1690 #2226)
#2234 := (and #1021 #2230)
#2238 := (or #1658 #2234)
#2242 := (and #1006 #2238)
#2246 := (or #1631 #2242)
#1593 := (not #946)
#2250 := (and #1593 #2246)
#2254 := (or #946 #2250)
#2571 := (iff #2254 #2570)
#2568 := (iff #2250 #2567)
#2565 := (iff #2246 #2564)
#2562 := (iff #2242 #2561)
#2559 := (iff #2238 #2558)
#2556 := (iff #2234 #2555)
#2553 := (iff #2230 #2552)
#2550 := (iff #2226 #2549)
#2547 := (iff #2222 #2546)
#2544 := (iff #2218 #2543)
#2541 := (iff #2214 #2540)
#2538 := (iff #2210 #2535)
#2532 := (and #1970 #189 #1412 #1404 #199 #1391 #1248 #2529)
#2536 := (iff #2532 #2535)
#2537 := [rewrite]: #2536
#2533 := (iff #2210 #2532)
#2530 := (iff #2206 #2529)
#2527 := (iff #2202 #2526)
#2524 := (iff #2198 #2523)
#2521 := (iff #2194 #2520)
#2518 := (iff #2190 #2517)
#2515 := (iff #2186 #2514)
#2512 := (iff #2182 #2511)
#2509 := (iff #2178 #2508)
#2506 := (iff #2174 #2505)
#2503 := (iff #2170 #2502)
#2500 := (iff #2166 #2499)
#2497 := (iff #2162 #2494)
#2488 := (and #2131 #2485)
#2491 := (and #1301 #2488)
#2495 := (iff #2491 #2494)
#2496 := [rewrite]: #2495
#2492 := (iff #2162 #2491)
#2489 := (iff #2157 #2488)
#2486 := (iff #2153 #2485)
#2483 := (iff #2150 #2482)
#2480 := (iff #2140 #2479)
#2477 := (iff #2139 #2476)
#2474 := (= #2138 #2473)
#2475 := [rewrite]: #2474
#2478 := [monotonicity #2475]: #2477
#2481 := [monotonicity #2478]: #2480
#2484 := [monotonicity #2481]: #2483
#2487 := [quant-intro #2484]: #2486
#2470 := (iff #2147 #2131)
#2471 := [rewrite]: #2470
#2490 := [monotonicity #2471 #2487]: #2489
#2493 := [monotonicity #2490]: #2492
#2498 := [trans #2493 #2496]: #2497
#2501 := [monotonicity #2498]: #2500
#2504 := [monotonicity #2501]: #2503
#2507 := [monotonicity #2504]: #2506
#2510 := [monotonicity #2507]: #2509
#2513 := [monotonicity #2510]: #2512
#2468 := (iff #2046 #222)
#2469 := [rewrite]: #2468
#2516 := [monotonicity #2469 #2513]: #2515
#2519 := [monotonicity #2516]: #2518
#2522 := [monotonicity #2519]: #2521
#2525 := [monotonicity #2522]: #2524
#2528 := [monotonicity #2525]: #2527
#2531 := [monotonicity #2528]: #2530
#2466 := (iff #1989 #199)
#2467 := [rewrite]: #2466
#2534 := [monotonicity #2467 #2531]: #2533
#2539 := [trans #2534 #2537]: #2538
#2464 := (iff #1957 #2463)
#2461 := (iff #1953 #2460)
#2458 := (iff #1949 #2457)
#2455 := (iff #1945 #2454)
#2452 := (iff #1926 #2451)
#2449 := (iff #1925 #2448)
#2446 := (iff #1924 #2445)
#2443 := (= #1923 #2442)
#2444 := [rewrite]: #2443
#2447 := [monotonicity #2444]: #2446
#2450 := [monotonicity #2447]: #2449
#2453 := [monotonicity #2450]: #2452
#2456 := [monotonicity #2453]: #2455
#2439 := (iff #1898 #2438)
#2436 := (iff #1895 #2435)
#2433 := (iff #1890 #2432)
#2430 := (iff #1889 #2427)
#2417 := (+ #1881 #1887)
#2418 := (+ #1136 #2417)
#2421 := (= #2418 0::Int)
#2428 := (iff #2421 #2427)
#2429 := [rewrite]: #2428
#2422 := (iff #1889 #2421)
#2419 := (= #1888 #2418)
#2420 := [rewrite]: #2419
#2423 := [monotonicity #2420]: #2422
#2431 := [trans #2423 #2429]: #2430
#2415 := (iff #1884 #2414)
#2412 := (iff #1883 #2409)
#2401 := (+ #1136 #1881)
#2404 := (>= #2401 0::Int)
#2410 := (iff #2404 #2409)
#2411 := [rewrite]: #2410
#2405 := (iff #1883 #2404)
#2402 := (= #1882 #2401)
#2403 := [rewrite]: #2402
#2406 := [monotonicity #2403]: #2405
#2413 := [trans #2406 #2411]: #2412
#2416 := [monotonicity #2413]: #2415
#2434 := [monotonicity #2416 #2431]: #2433
#2437 := [monotonicity #2434]: #2436
#2440 := [quant-intro #2437]: #2439
#2459 := [monotonicity #2440 #2456]: #2458
#2399 := (iff #1873 #2396)
#2393 := (and #1848 #2390)
#2397 := (iff #2393 #2396)
#2398 := [rewrite]: #2397
#2394 := (iff #1873 #2393)
#2391 := (iff #1869 #2390)
#2388 := (iff #1866 #2387)
#2385 := (iff #1857 #2384)
#2382 := (iff #1856 #2381)
#2379 := (= #1855 #2378)
#2380 := [rewrite]: #2379
#2383 := [monotonicity #2380]: #2382
#2386 := [monotonicity #2383]: #2385
#2389 := [monotonicity #2386]: #2388
#2392 := [quant-intro #2389]: #2391
#2375 := (iff #1863 #1848)
#2376 := [rewrite]: #2375
#2395 := [monotonicity #2376 #2392]: #2394
#2400 := [trans #2395 #2398]: #2399
#2462 := [monotonicity #2400 #2459]: #2461
#2373 := (iff #1837 #152)
#2374 := [rewrite]: #2373
#2371 := (iff #1834 #149)
#2372 := [rewrite]: #2371
#2369 := (iff #1831 #147)
#2370 := [rewrite]: #2369
#2367 := (iff #1828 #144)
#2368 := [rewrite]: #2367
#2465 := [monotonicity #2368 #2370 #2372 #2374 #2462]: #2464
#2542 := [monotonicity #2465 #2539]: #2541
#2365 := (iff #1816 #2364)
#2362 := (iff #1813 #2361)
#2359 := (iff #1808 #2358)
#2356 := (iff #1807 #2353)
#2343 := (+ #1797 #1805)
#2344 := (+ #1091 #2343)
#2347 := (= #2344 0::Int)
#2354 := (iff #2347 #2353)
#2355 := [rewrite]: #2354
#2348 := (iff #1807 #2347)
#2345 := (= #1806 #2344)
#2346 := [rewrite]: #2345
#2349 := [monotonicity #2346]: #2348
#2357 := [trans #2349 #2355]: #2356
#2341 := (iff #1800 #2340)
#2338 := (iff #1799 #2335)
#2327 := (+ #1091 #1797)
#2330 := (>= #2327 0::Int)
#2336 := (iff #2330 #2335)
#2337 := [rewrite]: #2336
#2331 := (iff #1799 #2330)
#2328 := (= #1798 #2327)
#2329 := [rewrite]: #2328
#2332 := [monotonicity #2329]: #2331
#2339 := [trans #2332 #2337]: #2338
#2342 := [monotonicity #2339]: #2341
#2360 := [monotonicity #2342 #2357]: #2359
#2363 := [monotonicity #2360]: #2362
#2366 := [quant-intro #2363]: #2365
#2325 := (iff #1770 #111)
#2326 := [rewrite]: #2325
#2323 := (iff #1764 #2322)
#2320 := (iff #1761 #2319)
#2317 := (iff #1756 #2316)
#2314 := (iff #1755 #2311)
#2301 := (+ #1744 #1752)
#2302 := (+ #1053 #2301)
#2305 := (= #2302 0::Int)
#2312 := (iff #2305 #2311)
#2313 := [rewrite]: #2312
#2306 := (iff #1755 #2305)
#2303 := (= #1754 #2302)
#2304 := [rewrite]: #2303
#2307 := [monotonicity #2304]: #2306
#2315 := [trans #2307 #2313]: #2314
#2299 := (iff #1747 #2298)
#2296 := (iff #1746 #2293)
#2285 := (+ #1053 #1744)
#2288 := (>= #2285 0::Int)
#2294 := (iff #2288 #2293)
#2295 := [rewrite]: #2294
#2289 := (iff #1746 #2288)
#2286 := (= #1745 #2285)
#2287 := [rewrite]: #2286
#2290 := [monotonicity #2287]: #2289
#2297 := [trans #2290 #2295]: #2296
#2300 := [monotonicity #2297]: #2299
#2318 := [monotonicity #2300 #2315]: #2317
#2321 := [monotonicity #2318]: #2320
#2324 := [quant-intro #2321]: #2323
#2545 := [monotonicity #2324 #2326 #2366 #2542]: #2544
#2283 := (iff #1736 #2280)
#2277 := (and #1710 #1732)
#2281 := (iff #2277 #2280)
#2282 := [rewrite]: #2281
#2278 := (iff #1736 #2277)
#2275 := (iff #1726 #1710)
#2276 := [rewrite]: #2275
#2279 := [monotonicity #2276]: #2278
#2284 := [trans #2279 #2282]: #2283
#2548 := [monotonicity #2284 #2545]: #2547
#2551 := [monotonicity #2548]: #2550
#2273 := (iff #1690 #2272)
#2270 := (iff #1689 #2269)
#2267 := (iff #1688 #2266)
#2264 := (= #1687 #2263)
#2265 := [rewrite]: #2264
#2268 := [monotonicity #2265]: #2267
#2271 := [monotonicity #2268]: #2270
#2274 := [monotonicity #2271]: #2273
#2554 := [monotonicity #2274 #2551]: #2553
#2557 := [monotonicity #2554]: #2556
#2560 := [monotonicity #2557]: #2559
#2563 := [monotonicity #2560]: #2562
#2566 := [monotonicity #2563]: #2565
#2260 := (iff #1593 #81)
#2261 := [rewrite]: #2260
#2569 := [monotonicity #2261 #2566]: #2568
#2572 := [monotonicity #2569]: #2571
#1568 := (not #1542)
#2255 := (~ #1568 #2254)
#2251 := (not #1539)
#2252 := (~ #2251 #2250)
#2247 := (not #1536)
#2248 := (~ #2247 #2246)
#2243 := (not #1533)
#2244 := (~ #2243 #2242)
#2239 := (not #1530)
#2240 := (~ #2239 #2238)
#2235 := (not #1527)
#2236 := (~ #2235 #2234)
#2231 := (not #1524)
#2232 := (~ #2231 #2230)
#2227 := (not #1521)
#2228 := (~ #2227 #2226)
#2223 := (not #1518)
#2224 := (~ #2223 #2222)
#2219 := (not #1513)
#2220 := (~ #2219 #2218)
#2215 := (not #1451)
#2216 := (~ #2215 #2214)
#2211 := (not #1446)
#2212 := (~ #2211 #2210)
#2207 := (not #1377)
#2208 := (~ #2207 #2206)
#2203 := (not #1374)
#2204 := (~ #2203 #2202)
#2199 := (not #1371)
#2200 := (~ #2199 #2198)
#2195 := (not #1368)
#2196 := (~ #2195 #2194)
#2191 := (not #1365)
#2192 := (~ #2191 #2190)
#2187 := (not #1362)
#2188 := (~ #2187 #2186)
#2183 := (not #1359)
#2184 := (~ #2183 #2182)
#2179 := (not #1356)
#2180 := (~ #2179 #2178)
#2175 := (not #1353)
#2176 := (~ #2175 #2174)
#2171 := (not #1350)
#2172 := (~ #2171 #2170)
#2167 := (not #1347)
#2168 := (~ #2167 #2166)
#2163 := (not #1344)
#2164 := (~ #2163 #2162)
#2144 := (not #1341)
#2160 := (~ #2144 #2157)
#2141 := (exists (vars (?v1 S2)) #2140)
#2142 := (or #2132 #2141)
#2143 := (not #2142)
#2158 := (~ #2143 #2157)
#2154 := (not #2141)
#2155 := (~ #2154 #2153)
#2151 := (~ #2150 #2150)
#2152 := [refl]: #2151
#2156 := [nnf-neg #2152]: #2155
#2148 := (~ #2147 #2147)
#2149 := [refl]: #2148
#2159 := [nnf-neg #2149 #2156]: #2158
#2145 := (~ #2144 #2143)
#2146 := [sk]: #2145
#2161 := [trans #2146 #2159]: #2160
#2120 := (not #1304)
#2121 := (~ #2120 #1301)
#2118 := (~ #1301 #1301)
#2116 := (~ #1298 #1298)
#2117 := [refl]: #2116
#2119 := [nnf-pos #2117]: #2118
#2122 := [nnf-neg #2119]: #2121
#2165 := [nnf-neg #2122 #2161]: #2164
#2112 := (~ #1304 #2111)
#2113 := [sk]: #2112
#2169 := [nnf-neg #2113 #2165]: #2168
#2088 := (not #1285)
#2089 := (~ #2088 #1282)
#2086 := (~ #1282 #1282)
#2084 := (~ #1279 #1279)
#2085 := [refl]: #2084
#2087 := [nnf-pos #2085]: #2086
#2090 := [nnf-neg #2087]: #2089
#2173 := [nnf-neg #2090 #2169]: #2172
#2080 := (~ #1285 #2079)
#2081 := [sk]: #2080
#2177 := [nnf-neg #2081 #2173]: #2176
#2061 := (not #1271)
#2062 := (~ #2061 #1268)
#2059 := (~ #1268 #1268)
#2057 := (~ #1265 #1265)
#2058 := [refl]: #2057
#2060 := [nnf-pos #2058]: #2059
#2063 := [nnf-neg #2060]: #2062
#2181 := [nnf-neg #2063 #2177]: #2180
#2053 := (~ #1271 #2052)
#2054 := [sk]: #2053
#2185 := [nnf-neg #2054 #2181]: #2184
#2047 := (~ #2046 #2046)
#2048 := [refl]: #2047
#2189 := [nnf-neg #2048 #2185]: #2188
#2044 := (~ #713 #713)
#2045 := [refl]: #2044
#2193 := [nnf-neg #2045 #2189]: #2192
#2041 := (not #736)
#2042 := (~ #2041 #606)
#2039 := (~ #606 #606)
#2037 := (~ #603 #603)
#2038 := [refl]: #2037
#2040 := [nnf-pos #2038]: #2039
#2043 := [nnf-neg #2040]: #2042
#2197 := [nnf-neg #2043 #2193]: #2196
#2033 := (~ #736 #2032)
#2034 := [sk]: #2033
#2201 := [nnf-neg #2034 #2197]: #2200
#2021 := (not #1262)
#2022 := (~ #2021 #1259)
#2019 := (~ #1259 #1259)
#2017 := (~ #1254 #1254)
#2018 := [refl]: #2017
#2020 := [nnf-pos #2018]: #2019
#2023 := [nnf-neg #2020]: #2022
#2205 := [nnf-neg #2023 #2201]: #2204
#2013 := (~ #1262 #2012)
#2014 := [sk]: #2013
#2209 := [nnf-neg #2014 #2205]: #2208
#2003 := (not #1251)
#2004 := (~ #2003 #1248)
#2001 := (~ #1248 #1248)
#1999 := (~ #1245 #1245)
#2000 := [refl]: #1999
#2002 := [nnf-pos #2000]: #2001
#2005 := [nnf-neg #2002]: #2004
#1996 := (not #1394)
#1997 := (~ #1996 #1391)
#1994 := (~ #1391 #1391)
#1992 := (~ #1388 #1388)
#1993 := [refl]: #1992
#1995 := [nnf-pos #1993]: #1994
#1998 := [nnf-neg #1995]: #1997
#1990 := (~ #1989 #1989)
#1991 := [refl]: #1990
#1986 := (not #1407)
#1987 := (~ #1986 #1404)
#1984 := (~ #1404 #1404)
#1982 := (~ #1401 #1401)
#1983 := [refl]: #1982
#1985 := [nnf-pos #1983]: #1984
#1988 := [nnf-neg #1985]: #1987
#1980 := (~ #1412 #1412)
#1981 := [refl]: #1980
#1978 := (~ #189 #189)
#1979 := [refl]: #1978
#1975 := (not #1422)
#1976 := (~ #1975 #1970)
#1971 := (~ #1206 #1970)
#1972 := [sk]: #1971
#1977 := [nnf-neg #1972]: #1976
#2213 := [nnf-neg #1977 #1979 #1981 #1988 #1991 #1998 #2005 #2209]: #2212
#1958 := (not #1224)
#1959 := (~ #1958 #1957)
#1954 := (not #1200)
#1955 := (~ #1954 #1953)
#1950 := (not #1197)
#1951 := (~ #1950 #1949)
#1946 := (not #1194)
#1947 := (~ #1946 #1945)
#1942 := (not #1191)
#1943 := (~ #1942 #1941)
#1939 := (~ #1938 #1938)
#1940 := [refl]: #1939
#1935 := (not #1188)
#1936 := (~ #1935 #1185)
#1933 := (~ #1185 #1185)
#1931 := (~ #1182 #1182)
#1932 := [refl]: #1931
#1934 := [nnf-pos #1932]: #1933
#1937 := [nnf-neg #1934]: #1936
#1944 := [nnf-neg #1937 #1940]: #1943
#1927 := (~ #1188 #1926)
#1928 := [sk]: #1927
#1948 := [nnf-neg #1928 #1944]: #1947
#1901 := (not #1170)
#1902 := (~ #1901 #1898)
#1899 := (~ #1167 #1898)
#1896 := (~ #1164 #1895)
#1891 := (~ #1161 #1890)
#1892 := [sk]: #1891
#1878 := (~ #1145 #1145)
#1879 := [refl]: #1878
#1897 := [monotonicity #1879 #1892]: #1896
#1900 := [nnf-pos #1897]: #1899
#1903 := [nnf-neg #1900]: #1902
#1952 := [nnf-neg #1903 #1948]: #1951
#1876 := (~ #1170 #1873)
#1858 := (exists (vars (?v1 S2)) #1857)
#1859 := (or #1849 #1858)
#1860 := (not #1859)
#1874 := (~ #1860 #1873)
#1870 := (not #1858)
#1871 := (~ #1870 #1869)
#1867 := (~ #1866 #1866)
#1868 := [refl]: #1867
#1872 := [nnf-neg #1868]: #1871
#1864 := (~ #1863 #1863)
#1865 := [refl]: #1864
#1875 := [nnf-neg #1865 #1872]: #1874
#1861 := (~ #1170 #1860)
#1862 := [sk]: #1861
#1877 := [trans #1862 #1875]: #1876
#1956 := [nnf-neg #1877 #1952]: #1955
#1838 := (~ #1837 #1837)
#1839 := [refl]: #1838
#1835 := (~ #1834 #1834)
#1836 := [refl]: #1835
#1832 := (~ #1831 #1831)
#1833 := [refl]: #1832
#1829 := (~ #1828 #1828)
#1830 := [refl]: #1829
#1826 := (~ #1422 #1825)
#1823 := (~ #1822 #1822)
#1824 := [refl]: #1823
#1827 := [nnf-neg #1824]: #1826
#1960 := [nnf-neg #1827 #1830 #1833 #1836 #1839 #1956]: #1959
#2217 := [nnf-neg #1960 #2213]: #2216
#1819 := (not #1133)
#1820 := (~ #1819 #1816)
#1817 := (~ #1130 #1816)
#1814 := (~ #1127 #1813)
#1809 := (~ #1124 #1808)
#1810 := [sk]: #1809
#1794 := (~ #1100 #1100)
#1795 := [refl]: #1794
#1815 := [monotonicity #1795 #1810]: #1814
#1818 := [nnf-pos #1815]: #1817
#1821 := [nnf-neg #1818]: #1820
#1791 := (not #1469)
#1792 := (~ #1791 #1466)
#1789 := (~ #1466 #1466)
#1787 := (~ #1463 #1463)
#1788 := [refl]: #1787
#1790 := [nnf-pos #1788]: #1789
#1793 := [nnf-neg #1790]: #1792
#1784 := (not #1480)
#1785 := (~ #1784 #1477)
#1782 := (~ #1477 #1477)
#1780 := (~ #1474 #1474)
#1781 := [refl]: #1780
#1783 := [nnf-pos #1781]: #1782
#1786 := [nnf-neg #1783]: #1785
#1777 := (not #1489)
#1778 := (~ #1777 #1486)
#1775 := (~ #1486 #1486)
#1773 := (~ #1483 #1483)
#1774 := [refl]: #1773
#1776 := [nnf-pos #1774]: #1775
#1779 := [nnf-neg #1776]: #1778
#1771 := (~ #1770 #1770)
#1772 := [refl]: #1771
#1767 := (not #1492)
#1768 := (~ #1767 #1764)
#1765 := (~ #1088 #1764)
#1762 := (~ #1085 #1761)
#1757 := (~ #1082 #1756)
#1758 := [sk]: #1757
#1741 := (~ #1062 #1062)
#1742 := [refl]: #1741
#1763 := [monotonicity #1742 #1758]: #1762
#1766 := [nnf-pos #1763]: #1765
#1769 := [nnf-neg #1766]: #1768
#2221 := [nnf-neg #1769 #1772 #1779 #1786 #1793 #1821 #2217]: #2220
#1739 := (~ #1492 #1736)
#1721 := (exists (vars (?v1 S2)) #1720)
#1722 := (or #1711 #1721)
#1723 := (not #1722)
#1737 := (~ #1723 #1736)
#1733 := (not #1721)
#1734 := (~ #1733 #1732)
#1730 := (~ #1729 #1729)
#1731 := [refl]: #1730
#1735 := [nnf-neg #1731]: #1734
#1727 := (~ #1726 #1726)
#1728 := [refl]: #1727
#1738 := [nnf-neg #1728 #1735]: #1737
#1724 := (~ #1492 #1723)
#1725 := [sk]: #1724
#1740 := [trans #1725 #1738]: #1739
#2225 := [nnf-neg #1740 #2221]: #2224
#1699 := (not #1050)
#1700 := (~ #1699 #1047)
#1697 := (~ #1047 #1047)
#1695 := (~ #1044 #1044)
#1696 := [refl]: #1695
#1698 := [nnf-pos #1696]: #1697
#1701 := [nnf-neg #1698]: #1700
#2229 := [nnf-neg #1701 #2225]: #2228
#1691 := (~ #1050 #1690)
#1692 := [sk]: #1691
#2233 := [nnf-neg #1692 #2229]: #2232
#1667 := (not #1024)
#1668 := (~ #1667 #1021)
#1665 := (~ #1021 #1021)
#1663 := (~ #1018 #1018)
#1664 := [refl]: #1663
#1666 := [nnf-pos #1664]: #1665
#1669 := [nnf-neg #1666]: #1668
#2237 := [nnf-neg #1669 #2233]: #2236
#1659 := (~ #1024 #1658)
#1660 := [sk]: #1659
#2241 := [nnf-neg #1660 #2237]: #2240
#1640 := (not #1009)
#1641 := (~ #1640 #1006)
#1638 := (~ #1006 #1006)
#1636 := (~ #1005 #1005)
#1637 := [refl]: #1636
#1639 := [nnf-pos #1637]: #1638
#1642 := [nnf-neg #1639]: #1641
#2245 := [nnf-neg #1642 #2241]: #2244
#1632 := (~ #1009 #1631)
#1633 := [sk]: #1632
#2249 := [nnf-neg #1633 #2245]: #2248
#1594 := (~ #1593 #1593)
#1627 := [refl]: #1594
#2253 := [nnf-neg #1627 #2249]: #2252
#1625 := (~ #946 #946)
#1626 := [refl]: #1625
#2256 := [nnf-neg #1626 #2253]: #2255
#1569 := [not-or-elim #1564]: #1568
#2257 := [mp~ #1569 #2256]: #2254
#2258 := [mp #2257 #2572]: #2570
#3211 := [mp #2258 #3210]: #3208
#4126 := [mp #3211 #4125]: #4123
#7087 := [unit-resolution #4126 #4239]: #4120
#3450 := (or #4117 #4111)
#3440 := [def-axiom]: #3450
#7088 := [unit-resolution #3440 #7087]: #4111
#3446 := (or #4114 #1631 #4108)
#3448 := [def-axiom]: #3446
#7089 := [unit-resolution #3448 #7088 #4166]: #4108
#3444 := (or #4105 #4099)
#3447 := [def-axiom]: #3444
#7090 := [unit-resolution #3447 #7089]: #4099
#3306 := (or #4102 #1634 #4096)
#3464 := [def-axiom]: #3306
#7091 := [unit-resolution #3464 #7090]: #4099
#7092 := [unit-resolution #7091 #7086]: #4096
#3486 := (or #4093 #4087)
#3456 := [def-axiom]: #3486
#7093 := [unit-resolution #3456 #7092]: #4087
#7095 := (or #4090 #4084)
#6151 := [hypothesis]: #1673
#4285 := (or #7029 #2592)
#4289 := [quant-inst #1670]: #4285
#6152 := [unit-resolution #4289 #3755 #6151]: false
#6170 := [lemma #6152]: #2592
#3366 := (or #2607 #1673)
#3363 := [def-axiom]: #3366
#7094 := [unit-resolution #3363 #6170]: #2607
#3483 := (or #4090 #2612 #4084)
#3484 := [def-axiom]: #3483
#7096 := [unit-resolution #3484 #7094]: #7095
#7097 := [unit-resolution #7096 #7093]: #4084
#3467 := (or #4081 #4075)
#3474 := [def-axiom]: #3467
#7098 := [unit-resolution #3474 #7097]: #4075
#3504 := (or #4078 #3794 #4072)
#3489 := [def-axiom]: #3504
#7099 := [unit-resolution #3489 #7098 #6210]: #4072
#3496 := (or #4069 #4063)
#3497 := [def-axiom]: #3496
#8263 := [unit-resolution #3497 #7099]: #4063
#6420 := (f19 f20 ?v0!8)
#6418 := (* -1::Int #6420)
#6421 := (+ f14 #6418)
#6440 := (<= #6421 0::Int)
#6559 := (?v1!7 ?v0!8)
#6669 := (f6 f7 #6559)
#6677 := (f5 #6669 ?v0!8)
#6678 := (f15 #6677)
#6676 := (* -1::Int #6678)
#6561 := (f19 f20 #6559)
#6563 := (* -1::Int #6561)
#6673 := (+ #6563 #6676)
#6661 := (+ #6420 #6673)
#6662 := (= #6661 0::Int)
#6715 := (not #6662)
#6565 := (f9 f21 #6559)
#6571 := (= #6565 f1)
#6660 := (not #6571)
#6564 := (+ #6420 #6563)
#6562 := (<= #6564 0::Int)
#6716 := (or #6562 #6660 #6715)
#7070 := [hypothesis]: #3906
#3648 := (or #3903 #149)
#3643 := [def-axiom]: #3648
#7106 := [unit-resolution #3643 #7070]: #149
#3491 := (or #3903 #3897)
#3492 := [def-axiom]: #3491
#7107 := [unit-resolution #3492 #7070]: #3897
#3520 := (or #4069 #111)
#3521 := [def-axiom]: #3520
#7324 := [unit-resolution #3521 #7099]: #111
#4279 := (or #531 #169 #878)
#4208 := [hypothesis]: #111
#4276 := (= #168 #110)
#4275 := [hypothesis]: #149
#4274 := [monotonicity #4275]: #4276
#4277 := [trans #4274 #4208]: #169
#4174 := [hypothesis]: #1938
#4278 := [unit-resolution #4174 #4277]: false
#4292 := [lemma #4278]: #4279
#7108 := [unit-resolution #4292 #7106 #7324]: #169
#3387 := (or #3879 #1938)
#3388 := [def-axiom]: #3387
#7066 := [unit-resolution #3388 #7108]: #3879
#3644 := (or #3903 #3840)
#3645 := [def-axiom]: #3644
#7069 := [unit-resolution #3645 #7070]: #3840
#7013 := (or #2843 #3845 #531)
#6412 := (f19 f20 ?v0!11)
#6414 := (* -1::Int #6412)
#6787 := (+ #1920 #6414)
#6788 := (<= #6787 0::Int)
#6785 := (= #1920 #6412)
#6862 := (= #6412 #1920)
#6860 := (= f20 f25)
#6861 := [symm #4275]: #6860
#6895 := [monotonicity #6861]: #6862
#6896 := [symm #6895]: #6785
#6897 := (not #6785)
#6898 := (or #6897 #6788)
#6854 := [th-lemma arith triangle-eq]: #6898
#6855 := [unit-resolution #6854 #6896]: #6788
#6195 := (f19 f20 ?v1!10)
#6193 := (* -1::Int #6195)
#6285 := (+ #1906 #6193)
#6781 := (>= #6285 0::Int)
#6295 := (= #1906 #6195)
#6853 := (= #6195 #1906)
#6856 := [monotonicity #6861]: #6853
#6857 := [symm #6856]: #6295
#6852 := (not #6295)
#4251 := (or #6852 #6781)
#4280 := [th-lemma arith triangle-eq]: #4251
#4281 := [unit-resolution #4280 #6857]: #6781
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#4345 := [hypothesis]: #2848
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#4346 := [unit-resolution #3676 #4345]: #3675
#7082 := [hypothesis]: #3840
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#3315 := [def-axiom]: #3314
#4379 := [unit-resolution #3315 #4345]: #1917
#6179 := (+ f14 #6193)
#6184 := (<= #6179 0::Int)
#7080 := (not #6184)
#3672 := (or #2843 #1910)
#3674 := [def-axiom]: #3672
#4380 := [unit-resolution #3674 #4345]: #1910
#7076 := (not #6781)
#4409 := (or #7080 #1909 #7076)
#4410 := [th-lemma arith assign-bounds -1 -1]: #4409
#7011 := [unit-resolution #4410 #4380 #4281]: #7080
#7075 := (not #6788)
#7104 := (or #6184 #1916 #3845 #2445 #7076 #7075)
#6667 := (+ #6195 #6414)
#6670 := (+ #1913 #6667)
#6694 := (>= #6670 0::Int)
#7074 := (not #6694)
#7071 := [hypothesis]: #6788
#7072 := [hypothesis]: #6781
#7073 := [hypothesis]: #3675
#7077 := (or #7074 #7075 #2445 #7076)
#7078 := [th-lemma arith assign-bounds -1 -1 1]: #7077
#7079 := [unit-resolution #7078 #7073 #7072 #7071]: #7074
#6164 := (f9 f21 ?v1!10)
#4586 := (= #6164 f1)
#7081 := [hypothesis]: #7080
#6183 := (or #4586 #6184)
#6211 := (or #3845 #4586 #6184)
#6212 := (or #3845 #6183)
#6286 := (iff #6212 #6211)
#6287 := [rewrite]: #6286
#6280 := [quant-inst #1904]: #6212
#6288 := [mp #6280 #6287]: #6211
#7083 := [unit-resolution #6288 #7082]: #6183
#7084 := [unit-resolution #7083 #7081]: #4586
#6476 := (not #4586)
#7101 := (or #6476 #6694)
#7085 := [hypothesis]: #1917
#3488 := (or #4069 #3823)
#3493 := [def-axiom]: #3488
#7100 := [unit-resolution #3493 #7099]: #3823
#6719 := (or #3828 #6476 #1916 #6694)
#6695 := (or #6476 #1916 #6694)
#6714 := (or #3828 #6695)
#6721 := (iff #6714 #6719)
#6722 := [rewrite]: #6721
#6720 := [quant-inst #1905 #1904]: #6714
#6723 := [mp #6720 #6722]: #6719
#7102 := [unit-resolution #6723 #7100 #7085]: #7101
#7103 := [unit-resolution #7102 #7084 #7079]: false
#7105 := [lemma #7103]: #7104
#7012 := [unit-resolution #7105 #7011 #4379 #7082 #4346 #4281 #6855]: false
#7019 := [lemma #7012]: #7013
#7109 := [unit-resolution #7019 #7069 #7106]: #2843
#3660 := (or #3888 #2848 #3882)
#3657 := [def-axiom]: #3660
#7110 := [unit-resolution #3657 #7109 #7066]: #3888
#3372 := (or #3891 #3885)
#3373 := [def-axiom]: #3372
#7111 := [unit-resolution #3373 #7110]: #3891
#3651 := (or #3900 #3860 #3894)
#3655 := [def-axiom]: #3651
#7112 := [unit-resolution #3655 #7111 #7107]: #3860
#3323 := (or #3857 #3849)
#3664 := [def-axiom]: #3323
#7113 := [unit-resolution #3664 #7112]: #3849
#7512 := (or #6716 #3854 #531)
#6821 := (f19 f25 #6559)
#7034 := (* -1::Int #6821)
#7035 := (+ #1843 #7034)
#7036 := (<= #7035 0::Int)
#7057 := (+ #6676 #7034)
#7058 := (+ #1843 #7057)
#7059 := (= #7058 0::Int)
#7307 := (+ #6561 #7034)
#7253 := (>= #7307 0::Int)
#7306 := (= #6561 #6821)
#7446 := (= #6821 #6561)
#7447 := [monotonicity #4275]: #7446
#7448 := [symm #7447]: #7306
#7449 := (not #7306)
#7450 := (or #7449 #7253)
#7451 := [th-lemma arith triangle-eq]: #7450
#7452 := [unit-resolution #7451 #7448]: #7253
#6279 := (+ #1843 #6418)
#6798 := (>= #6279 0::Int)
#5095 := (= #1843 #6420)
#7453 := (= #6420 #1843)
#7438 := [monotonicity #6861]: #7453
#7439 := [symm #7438]: #5095
#7437 := (not #5095)
#7440 := (or #7437 #6798)
#7441 := [th-lemma arith triangle-eq]: #7440
#7442 := [unit-resolution #7441 #7439]: #6798
#6767 := (>= #6661 0::Int)
#6490 := (not #6716)
#7455 := [hypothesis]: #6490
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#6113 := [def-axiom]: #6120
#7456 := [unit-resolution #6113 #7455]: #6662
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#7477 := [th-lemma arith triangle-eq]: #7476
#7478 := [unit-resolution #7477 #7456]: #6767
#7252 := (<= #7307 0::Int)
#7479 := (or #7449 #7252)
#7480 := [th-lemma arith triangle-eq]: #7479
#7475 := [unit-resolution #7480 #7448]: #7252
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#7482 := [th-lemma arith triangle-eq]: #7481
#7483 := [unit-resolution #7482 #7439]: #6792
#6766 := (<= #6661 0::Int)
#7484 := (or #6715 #6766)
#7485 := [th-lemma arith triangle-eq]: #7484
#7506 := [unit-resolution #7485 #7456]: #6766
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#7405 := (not #6798)
#7404 := (not #6767)
#7553 := (not #7252)
#7337 := (not #6792)
#7552 := (not #6766)
#7410 := (or #7059 #7552 #7337 #7553 #7404 #7405 #7400)
#7550 := [hypothesis]: #7252
#7330 := [hypothesis]: #6792
#7551 := [hypothesis]: #6766
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#7548 := [hypothesis]: #6858
#7185 := (>= #7058 0::Int)
#7401 := [hypothesis]: #7253
#7402 := [hypothesis]: #6798
#7403 := [hypothesis]: #6767
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#7407 := [th-lemma arith assign-bounds -1 -1 -1]: #7406
#7408 := [unit-resolution #7407 #7403 #7402 #7401]: #7185
#7558 := (not #7185)
#7562 := (or #7558 #7059 #7552 #7337 #7553)
#7549 := [hypothesis]: #7185
#7184 := (<= #7058 0::Int)
#7554 := (or #7184 #7552 #7337 #7553)
#7555 := [th-lemma arith assign-bounds -1 -1 -1]: #7554
#7556 := [unit-resolution #7555 #7551 #7330 #7550]: #7184
#7557 := (not #7184)
#7559 := (or #7059 #7557 #7558)
#7560 := [th-lemma arith triangle-eq]: #7559
#7561 := [unit-resolution #7560 #7556 #7549 #7548]: false
#7563 := [lemma #7561]: #7562
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#7445 := [lemma #7409]: #7410
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#4250 := (or #7036 #6858)
#7508 := [hypothesis]: #3849
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#6893 := (+ #1844 #6678)
#6894 := (+ #6821 #6893)
#6886 := (= #6894 0::Int)
#6904 := (not #6886)
#6822 := (+ #6821 #1844)
#6278 := (>= #6822 0::Int)
#6907 := (or #6278 #6904)
#7149 := (or #3854 #6907)
#7182 := (iff #7149 #7148)
#7158 := (or #3854 #4250)
#7180 := (iff #7158 #7148)
#7181 := [rewrite]: #7180
#7159 := (iff #7149 #7158)
#7060 := (iff #6907 #4250)
#6859 := (iff #6904 #6858)
#7067 := (iff #6886 #7059)
#7045 := (+ #6678 #6821)
#7048 := (+ #1844 #7045)
#7055 := (= #7048 0::Int)
#7063 := (iff #7055 #7059)
#7064 := [rewrite]: #7063
#7056 := (iff #6886 #7055)
#7049 := (= #6894 #7048)
#7050 := [rewrite]: #7049
#7054 := [monotonicity #7050]: #7056
#7068 := [trans #7054 #7064]: #7067
#4217 := [monotonicity #7068]: #6859
#7046 := (iff #6278 #7036)
#7021 := (+ #1844 #6821)
#7026 := (>= #7021 0::Int)
#7037 := (iff #7026 #7036)
#7038 := [rewrite]: #7037
#7033 := (iff #6278 #7026)
#7022 := (= #6822 #7021)
#7025 := [rewrite]: #7022
#6959 := [monotonicity #7025]: #7033
#7047 := [trans #6959 #7038]: #7046
#7065 := [monotonicity #7047 #4217]: #7060
#7179 := [monotonicity #7065]: #7159
#7183 := [trans #7179 #7181]: #7182
#7145 := [quant-inst #6559]: #7149
#7178 := [mp #7145 #7183]: #7148
#7509 := [unit-resolution #7178 #7508]: #4250
#7510 := [unit-resolution #7509 #7507]: #7036
#6768 := (not #6562)
#6392 := (or #6716 #6768)
#6778 := [def-axiom]: #6392
#7505 := [unit-resolution #6778 #7455]: #6768
#7511 := [th-lemma arith farkas -1 -1 -1 1 #7442 #7505 #7452 #7510]: false
#7513 := [lemma #7511]: #7512
#7151 := [unit-resolution #7513 #7113 #7106]: #6716
#7153 := (or #6440 #6490)
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#3494 := (or #4069 #3831)
#3495 := [def-axiom]: #3494
#7150 := [unit-resolution #3495 #7099]: #3831
#6491 := (or #3836 #1841 #6440 #6490)
#6489 := (or #1841 #6440 #6490)
#6492 := (or #3836 #6489)
#6718 := (iff #6492 #6491)
#6381 := [rewrite]: #6718
#6717 := [quant-inst #1840]: #6492
#6724 := [mp #6717 #6381]: #6491
#7154 := [unit-resolution #6724 #7150 #7152]: #7153
#7155 := [unit-resolution #7154 #7151]: #6440
#3338 := (or #3857 #1847)
#3680 := [def-axiom]: #3338
#7156 := [unit-resolution #3680 #7112]: #1847
#7141 := [symm #7106]: #6860
#7142 := [monotonicity #7141]: #7453
#7140 := [symm #7142]: #5095
#7143 := [unit-resolution #7441 #7140]: #6798
#7144 := [th-lemma arith farkas -1 -1 1 #7143 #7156 #7155]: false
#7216 := [lemma #7144]: #3903
#3508 := (or #4066 #3906 #4060)
#3510 := [def-axiom]: #3508
#8264 := [unit-resolution #3510 #7216 #8263]: #4060
#3548 := (or #4057 #199)
#3553 := [def-axiom]: #3548
#9701 := [unit-resolution #3553 #8264]: #199
#9297 := [symm #9701]: #9268
#16690 := [monotonicity #9297]: #16482
#16476 := [monotonicity #16690]: #16582
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#15519 := [hypothesis]: #19098
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#7694 := (f5 #200 ?v0!14)
#7695 := (f15 #7694)
#7647 := (* -1::Int #2029)
#7713 := (+ #7647 #7695)
#7714 := (+ #190 #7713)
#7715 := (>= #7714 0::Int)
#8867 := (not #7715)
#7696 := (* -1::Int #7695)
#7697 := (+ f14 #7696)
#7698 := (<= #7697 0::Int)
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#3637 := (not #2030)
#10219 := [hypothesis]: #2032
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#7911 := [hypothesis]: #7746
#8011 := [hypothesis]: #3637
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#8861 := [unit-resolution #3515 #8264]: #3927
#7814 := (or #3932 #7749 #2030)
#7699 := (+ #1235 #7696)
#7700 := (+ #2029 #7699)
#7701 := (<= #7700 0::Int)
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#7744 := (not #7743)
#7745 := (or #7744 #2030)
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#7842 := (or #3932 #7752)
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#7850 := [rewrite]: #7846
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#7753 := (iff #7745 #7752)
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#7747 := (iff #7743 #7746)
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#7706 := (+ #2029 #7696)
#7707 := (+ #1235 #7706)
#7710 := (<= #7707 0::Int)
#7716 := (iff #7710 #7715)
#7717 := [rewrite]: #7716
#7711 := (iff #7701 #7710)
#7708 := (= #7700 #7707)
#7709 := [rewrite]: #7708
#7712 := [monotonicity #7709]: #7711
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#7754 := [monotonicity #7751]: #7753
#7843 := [monotonicity #7754]: #7813
#7853 := [trans #7843 #7850]: #7852
#7817 := [quant-inst #2024]: #7816
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#7663 := (f9 f21 ?v0!14)
#7664 := (= #7663 f1)
#7818 := (= ?v0!14 f28)
#7841 := (not #7818)
#9402 := (or #7841 #2030)
#8045 := (= #190 #2029)
#8033 := (= #2029 #190)
#8023 := [hypothesis]: #7818
#9294 := [monotonicity #8023]: #8033
#9295 := [symm #9294]: #8045
#8124 := (= #2028 #190)
#4167 := (f30 f28)
#4220 := (= #4167 #190)
#4171 := (f5 #200 f28)
#4172 := (f15 #4171)
#4190 := (>= #4172 0::Int)
#4175 := (* -1::Int #4172)
#4176 := (+ f14 #4175)
#4177 := (<= #4176 0::Int)
#4222 := (or #4177 #4190)
#7990 := (= #4172 0::Int)
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#8752 := [hypothesis]: #8751
#10 := (f6 f7 #9)
#12 := (f5 #10 #11)
#3689 := (pattern #12)
#57 := (f15 #12)
#58 := (= #57 0::Int)
#56 := (= #9 #11)
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#3727 := (iff #333 #3724)
#3725 := (iff #325 #325)
#3726 := [refl]: #3725
#3728 := [quant-intro #3726]: #3727
#1581 := (~ #333 #333)
#1612 := (~ #325 #325)
#1613 := [refl]: #1612
#1582 := [nnf-pos #1613]: #1581
#59 := (implies #56 #58)
#60 := (forall (vars (?v0 S2) (?v1 S2)) #59)
#334 := (iff #60 #333)
#331 := (iff #59 #325)
#332 := [rewrite]: #331
#335 := [quant-intro #332]: #334
#324 := [asserted]: #60
#338 := [mp #324 #335]: #333
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#8741 := (or #6738 #7990)
#4492 := (= f28 f28)
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#8744 := (iff #8742 #8741)
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#8747 := [rewrite]: #8746
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#8005 := (iff #8002 #7990)
#8006 := [rewrite]: #8005
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#8000 := (iff #7989 false)
#7998 := (iff #7989 #6991)
#4495 := (iff #4492 true)
#4496 := [rewrite]: #4495
#7999 := [monotonicity #4496]: #7998
#8001 := [trans #7999 #6995]: #8000
#8004 := [monotonicity #8001]: #8003
#8008 := [trans #8004 #8006]: #8007
#8745 := [monotonicity #8008]: #8744
#8748 := [trans #8745 #8747]: #8744
#8743 := [quant-inst #186 #186]: #8742
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#8758 := [lemma #8757]: #7990
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#4179 := (+ #190 #4178)
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#4223 := (iff #4218 #4222)
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#4187 := (<= #4175 0::Int)
#4191 := (iff #4187 #4190)
#4192 := [rewrite]: #4191
#4188 := (iff #4180 #4187)
#4185 := (= #4179 #4175)
#4186 := [rewrite]: #4185
#4189 := [monotonicity #4186]: #4188
#4194 := [trans #4189 #4192]: #4193
#4224 := [monotonicity #4194]: #4223
#4227 := [monotonicity #4224]: #4226
#4230 := [monotonicity #4227]: #4229
#7238 := [monotonicity #4230]: #7235
#7244 := [trans #7238 #7186]: #7240
#7187 := [quant-inst #186]: #7236
#7245 := [mp #7187 #7244]: #7231
#8876 := [unit-resolution #7245 #8861]: #4228
#9179 := [unit-resolution #8876 #8812]: #4220
#8016 := (= #2028 #4167)
#9174 := [monotonicity #8023]: #8016
#9263 := [trans #9174 #9179]: #8124
#9301 := [trans #9263 #9295]: #2030
#9380 := [unit-resolution #8011 #9301]: false
#9334 := [lemma #9380]: #9402
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#3636 := (or #2031 #2026)
#3632 := [def-axiom]: #3636
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#8848 := (or #2027 #7824)
#7797 := (f9 #198 ?v0!14)
#7815 := (= #7797 f1)
#9264 := [hypothesis]: #2026
#7840 := (= #7797 #2025)
#7882 := [monotonicity #9297]: #7840
#8403 := [trans #7882 #9264]: #7815
#9164 := (not #7815)
#7829 := (iff #7815 #7824)
#8915 := (or #7628 #7829)
#7819 := (if #7818 #4146 #7664)
#7820 := (iff #7815 #7819)
#8856 := (or #7628 #7820)
#9309 := (iff #8856 #8915)
#9313 := (iff #8915 #8915)
#9314 := [rewrite]: #9313
#7830 := (iff #7820 #7829)
#7827 := (iff #7819 #7824)
#7821 := (if #7818 true #7664)
#7825 := (iff #7821 #7824)
#7826 := [rewrite]: #7825
#7822 := (iff #7819 #7821)
#7823 := [monotonicity #4149]: #7822
#7828 := [trans #7823 #7826]: #7827
#7831 := [monotonicity #7828]: #7830
#9244 := [monotonicity #7831]: #9309
#8881 := [trans #9244 #9314]: #9309
#9311 := [quant-inst #115 #186 #3 #2024]: #8856
#8878 := [mp #9311 #8881]: #8915
#9183 := [unit-resolution #8878 #3723]: #7829
#8883 := (not #7829)
#9266 := (or #8883 #9164)
#7847 := (not #7824)
#9239 := [hypothesis]: #7847
#8857 := (or #8883 #9164 #7824)
#8858 := [def-axiom]: #8857
#9241 := [unit-resolution #8858 #9239]: #9266
#9302 := [unit-resolution #9241 #9183]: #9164
#8636 := [unit-resolution #9302 #8403]: false
#8809 := [lemma #8636]: #8848
#10473 := [unit-resolution #8809 #10266]: #7824
#7848 := (or #7847 #7818 #7664)
#7849 := [def-axiom]: #7848
#10408 := [unit-resolution #7849 #10473 #10264]: #7664
#7844 := (not #7664)
#9165 := (or #7844 #7981)
#8853 := [hypothesis]: #7664
#8272 := (not #7981)
#8886 := [hypothesis]: #8272
#3545 := (or #4057 #189)
#3546 := [def-axiom]: #3545
#8131 := [unit-resolution #3546 #8264]: #189
#3532 := (or #4069 #3815)
#3487 := [def-axiom]: #3532
#8132 := [unit-resolution #3487 #7099]: #3815
#7991 := (or #3820 #188 #7844 #7981)
#7982 := (or #188 #7844 #7981)
#7996 := (or #3820 #7982)
#8203 := (iff #7996 #7991)
#8204 := [rewrite]: #8203
#8202 := [quant-inst #2024 #186]: #7996
#8205 := [mp #8202 #8204]: #7991
#8936 := [unit-resolution #8205 #8132 #8131 #8886 #8853]: false
#9170 := [lemma #8936]: #9165
#10474 := [unit-resolution #9170 #10408]: #7981
#10516 := (or #7715 #8272)
#8693 := (>= #7695 0::Int)
#7897 := (= #7695 0::Int)
#9389 := (not #7897)
#9660 := (not #8693)
#9386 := [hypothesis]: #9660
#9403 := (or #9389 #8693)
#9379 := [th-lemma arith triangle-eq]: #9403
#9404 := [unit-resolution #9379 #9386]: #9389
#7892 := (= f28 ?v0!14)
#7893 := (<= #7695 0::Int)
#9385 := (or #8693 #7893)
#9405 := [th-lemma arith farkas 1 1]: #9385
#9406 := [unit-resolution #9405 #9386]: #7893
#7894 := (not #7893)
#7895 := (or #7892 #7894)
#344 := (<= #57 0::Int)
#345 := (not #344)
#348 := (or #56 #345)
#3730 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3689) #348)
#351 := (forall (vars (?v0 S2) (?v1 S2)) #348)
#3733 := (iff #351 #3730)
#3731 := (iff #348 #348)
#3732 := [refl]: #3731
#3734 := [quant-intro #3732]: #3733
#1585 := (~ #351 #351)
#1584 := (~ #348 #348)
#1614 := [refl]: #1584
#1586 := [nnf-pos #1614]: #1585
#62 := (< 0::Int #57)
#63 := (implies #61 #62)
#64 := (forall (vars (?v0 S2) (?v1 S2)) #63)
#354 := (iff #64 #351)
#337 := (or #56 #62)
#341 := (forall (vars (?v0 S2) (?v1 S2)) #337)
#352 := (iff #341 #351)
#349 := (iff #337 #348)
#346 := (iff #62 #345)
#347 := [rewrite]: #346
#350 := [monotonicity #347]: #349
#353 := [quant-intro #350]: #352
#342 := (iff #64 #341)
#339 := (iff #63 #337)
#340 := [rewrite]: #339
#343 := [quant-intro #340]: #342
#355 := [trans #343 #353]: #354
#336 := [asserted]: #64
#356 := [mp #336 #355]: #351
#1615 := [mp~ #356 #1586]: #351
#3735 := [mp #1615 #3734]: #3730
#6342 := (not #3730)
#8933 := (or #6342 #7892 #7894)
#8931 := (or #6342 #7895)
#8940 := (iff #8931 #8933)
#8941 := [rewrite]: #8940
#8926 := [quant-inst #186 #2024]: #8931
#8934 := [mp #8926 #8941]: #8933
#9408 := [unit-resolution #8934 #3735]: #7895
#9410 := [unit-resolution #9408 #9406]: #7892
#7896 := (not #7892)
#7904 := (or #7896 #7897)
#8960 := (or #6738 #7896 #7897)
#8945 := (or #6738 #7904)
#8665 := (iff #8945 #8960)
#8668 := [rewrite]: #8665
#8954 := [quant-inst #186 #2024]: #8945
#8958 := [mp #8954 #8668]: #8960
#9411 := [unit-resolution #8958 #3729]: #7904
#9400 := [unit-resolution #9411 #9410 #9404]: false
#9401 := [lemma #9400]: #8693
#9661 := (or #9660 #7715 #8272)
#8269 := [hypothesis]: #7981
#9623 := [hypothesis]: #8867
#9624 := [hypothesis]: #8693
#9659 := [th-lemma arith farkas 1 -1 1 #9624 #9623 #8269]: false
#9662 := [lemma #9659]: #9661
#10513 := [unit-resolution #9662 #9401]: #10516
#10254 := [unit-resolution #10513 #10474 #10265]: false
#10267 := [lemma #10254]: #2031
#3539 := (or #4057 #4051)
#3540 := [def-axiom]: #3539
#9888 := [unit-resolution #3540 #8264]: #4051
#3533 := (or #4057 #3919)
#3479 := [def-axiom]: #3533
#8832 := [unit-resolution #3479 #8264]: #3919
#4211 := (or #2011 #3932 #3924)
#5422 := [hypothesis]: #3919
#5349 := [hypothesis]: #3927
#5149 := [hypothesis]: #2012
#4951 := (<= #2010 0::Int)
#4210 := (or #4951 #2011)
#4205 := [th-lemma arith farkas 1 1]: #4210
#4212 := [unit-resolution #4205 #5149]: #4951
#5428 := (not #4951)
#5460 := (or #5428 #3924 #3932 #2011)
#4742 := (f5 #200 ?v0!13)
#4743 := (f15 #4742)
#4824 := (+ #2009 #4743)
#4825 := (+ #190 #4824)
#4953 := (>= #4825 0::Int)
#4826 := (= #4825 0::Int)
#4764 := (* -1::Int #4743)
#4765 := (+ f14 #4764)
#4766 := (<= #4765 0::Int)
#4886 := (not #4766)
#4685 := (* -1::Int #2007)
#4797 := (+ #4685 #4743)
#4798 := (+ #190 #4797)
#4799 := (>= #4798 0::Int)
#4959 := (or #4766 #4799)
#4964 := (not #4959)
#4960 := (= #2008 #2007)
#5304 := (not #4960)
#4946 := (= #2007 #2008)
#5150 := (not #4946)
#5348 := (iff #5150 #5304)
#5128 := (iff #4946 #4960)
#5347 := [commutativity]: #5128
#5343 := [monotonicity #5347]: #5348
#5151 := (or #5150 #2011)
#5345 := [th-lemma arith triangle-eq]: #5151
#5346 := [unit-resolution #5345 #5149]: #5150
#5127 := [mp #5346 #5343]: #5304
#4968 := (or #4964 #4960)
#4973 := (or #3932 #4964 #4960)
#4767 := (+ #1235 #4764)
#4762 := (+ #2007 #4767)
#4763 := (<= #4762 0::Int)
#4954 := (or #4766 #4763)
#4955 := (not #4954)
#4961 := (or #4955 #4960)
#4978 := (or #3932 #4961)
#4878 := (iff #4978 #4973)
#4880 := (or #3932 #4968)
#4882 := (iff #4880 #4973)
#4883 := [rewrite]: #4882
#4881 := (iff #4978 #4880)
#4971 := (iff #4961 #4968)
#4969 := (iff #4955 #4964)
#4962 := (iff #4954 #4959)
#4822 := (iff #4763 #4799)
#4772 := (+ #2007 #4764)
#4793 := (+ #1235 #4772)
#4796 := (<= #4793 0::Int)
#4800 := (iff #4796 #4799)
#4801 := [rewrite]: #4800
#4791 := (iff #4763 #4796)
#4794 := (= #4762 #4793)
#4795 := [rewrite]: #4794
#4792 := [monotonicity #4795]: #4791
#4823 := [trans #4792 #4801]: #4822
#4963 := [monotonicity #4823]: #4962
#4970 := [monotonicity #4963]: #4969
#4972 := [monotonicity #4970]: #4971
#4879 := [monotonicity #4972]: #4881
#4884 := [trans #4879 #4883]: #4878
#4979 := [quant-inst #2006]: #4978
#4885 := [mp #4979 #4884]: #4973
#5350 := [unit-resolution #4885 #5349]: #4968
#5351 := [unit-resolution #5350 #5127]: #4964
#4980 := (or #4959 #4886)
#4943 := [def-axiom]: #4980
#5420 := [unit-resolution #4943 #5351]: #4886
#4941 := (not #4799)
#4942 := (or #4959 #4941)
#4944 := [def-axiom]: #4942
#5421 := [unit-resolution #4944 #5351]: #4941
#4829 := (or #4766 #4799 #4826)
#4852 := (or #3924 #4766 #4799 #4826)
#4768 := (+ #4743 #2009)
#4769 := (+ #190 #4768)
#4770 := (= #4769 0::Int)
#4771 := (or #4766 #4763 #4770)
#4853 := (or #3924 #4771)
#4858 := (iff #4853 #4852)
#4849 := (or #3924 #4829)
#4856 := (iff #4849 #4852)
#4857 := [rewrite]: #4856
#4850 := (iff #4853 #4849)
#4830 := (iff #4771 #4829)
#4827 := (iff #4770 #4826)
#4820 := (= #4769 #4825)
#4821 := [rewrite]: #4820
#4828 := [monotonicity #4821]: #4827
#4851 := [monotonicity #4823 #4828]: #4830
#4855 := [monotonicity #4851]: #4850
#4859 := [trans #4855 #4857]: #4858
#4854 := [quant-inst #2006]: #4853
#4887 := [mp #4854 #4859]: #4852
#5423 := [unit-resolution #4887 #5422]: #4829
#5418 := [unit-resolution #5423 #5421 #5420]: #4826
#5424 := (not #4826)
#5395 := (or #5424 #4953)
#5419 := [th-lemma arith triangle-eq]: #5395
#5425 := [unit-resolution #5419 #5418]: #4953
#5426 := [hypothesis]: #4951
#5427 := [th-lemma arith farkas 1 -1 1 #5426 #5421 #5425]: false
#5480 := [lemma #5427]: #5460
#4213 := [unit-resolution #5480 #4212 #5149 #5349 #5422]: false
#4215 := [lemma #4213]: #4211
#9889 := [unit-resolution #4215 #8861 #8832]: #2011
#3538 := (or #4054 #2012 #4048)
#3431 := [def-axiom]: #3538
#9893 := [unit-resolution #3431 #9889 #9888]: #4048
#3559 := (or #4045 #4039)
#3560 := [def-axiom]: #3559
#18769 := [unit-resolution #3560 #9893]: #4039
#3558 := (or #4042 #2032 #4036)
#3554 := [def-axiom]: #3558
#18770 := [unit-resolution #3554 #18769]: #4039
#18771 := [unit-resolution #18770 #10267]: #4036
#3586 := (or #4033 #3944)
#3564 := [def-axiom]: #3586
#18772 := [unit-resolution #3564 #18771]: #3944
#11863 := (or #3949 #4630 #5176)
#11888 := (or #3949 #5179)
#11865 := (iff #11888 #11863)
#11884 := [rewrite]: #11865
#11905 := [quant-inst #2123]: #11888
#11867 := [mp #11905 #11884]: #11863
#10037 := [unit-resolution #11867 #18772]: #5179
#15919 := [unit-resolution #10037 #15519]: #4630
#15588 := [mp #15919 #15539]: #15284
#15473 := (not #14478)
#15461 := (or #15473 #14450 #15350)
#15360 := [def-axiom]: #15461
#15572 := [unit-resolution #15360 #15588 #16371]: #15350
#15307 := (or #14460 #15274)
#15417 := [def-axiom]: #15307
#15639 := [unit-resolution #15417 #15572]: #15274
#15258 := [mp #15639 #14829]: #19613
#5210 := (f5 #200 ?v0!20)
#5211 := (f15 #5210)
#19610 := (<= #5211 0::Int)
#19614 := (= #5211 0::Int)
#5267 := (+ #2127 #5211)
#5268 := (+ #190 #5267)
#14690 := (<= #5268 0::Int)
#5271 := (= #5268 0::Int)
#5228 := (+ #5194 #5211)
#5229 := (+ #190 #5228)
#5230 := (>= #5229 0::Int)
#5212 := (* -1::Int #5211)
#5213 := (+ f14 #5212)
#5214 := (<= #5213 0::Int)
#5235 := (or #5214 #5230)
#5238 := (not #5235)
#5241 := (or #5238 #5176)
#11930 := (or #3932 #5238 #5176)
#5215 := (+ #1235 #5212)
#5216 := (+ #5169 #5215)
#5217 := (<= #5216 0::Int)
#5218 := (or #5214 #5217)
#5219 := (not #5218)
#5220 := (or #5219 #5176)
#11948 := (or #3932 #5220)
#11916 := (iff #11948 #11930)
#11956 := (or #3932 #5241)
#11947 := (iff #11956 #11930)
#11957 := [rewrite]: #11947
#11952 := (iff #11948 #11956)
#5242 := (iff #5220 #5241)
#5239 := (iff #5219 #5238)
#5236 := (iff #5218 #5235)
#5233 := (iff #5217 #5230)
#5221 := (+ #5169 #5212)
#5222 := (+ #1235 #5221)
#5225 := (<= #5222 0::Int)
#5231 := (iff #5225 #5230)
#5232 := [rewrite]: #5231
#5226 := (iff #5217 #5225)
#5223 := (= #5216 #5222)
#5224 := [rewrite]: #5223
#5227 := [monotonicity #5224]: #5226
#5234 := [trans #5227 #5232]: #5233
#5237 := [monotonicity #5234]: #5236
#5240 := [monotonicity #5237]: #5239
#5243 := [monotonicity #5240]: #5242
#11958 := [monotonicity #5243]: #11952
#11917 := [trans #11958 #11957]: #11916
#11951 := [quant-inst #2123]: #11948
#11918 := [mp #11951 #11917]: #11930
#14638 := [unit-resolution #11918 #8861]: #5241
#15554 := [unit-resolution #14638 #15519]: #5238
#19224 := (or #5235 #5271)
#19170 := (not #5271)
#19168 := [hypothesis]: #19170
#11915 := (not #5214)
#19162 := [hypothesis]: #5238
#11961 := (or #5235 #11915)
#11877 := [def-axiom]: #11961
#19173 := [unit-resolution #11877 #19162]: #11915
#11896 := (not #5230)
#11943 := (or #5235 #11896)
#11880 := [def-axiom]: #11943
#19184 := [unit-resolution #11880 #19162]: #11896
#5274 := (or #5214 #5230 #5271)
#11968 := (or #3924 #5214 #5230 #5271)
#5263 := (+ #5211 #2127)
#5264 := (+ #190 #5263)
#5265 := (= #5264 0::Int)
#5266 := (or #5214 #5217 #5265)
#11881 := (or #3924 #5266)
#11987 := (iff #11881 #11968)
#11986 := (or #3924 #5274)
#11985 := (iff #11986 #11968)
#11984 := [rewrite]: #11985
#11929 := (iff #11881 #11986)
#5275 := (iff #5266 #5274)
#5272 := (iff #5265 #5271)
#5269 := (= #5264 #5268)
#5270 := [rewrite]: #5269
#5273 := [monotonicity #5270]: #5272
#5276 := [monotonicity #5234 #5273]: #5275
#11965 := [monotonicity #5276]: #11929
#11971 := [trans #11965 #11984]: #11987
#11962 := [quant-inst #2123]: #11881
#11989 := [mp #11962 #11971]: #11968
#19203 := [unit-resolution #11989 #8832]: #5274
#19204 := [unit-resolution #19203 #19184 #19173 #19168]: false
#19220 := [lemma #19204]: #19224
#15563 := [unit-resolution #19220 #15554]: #5271
#14689 := (or #19170 #14690)
#14714 := [th-lemma arith triangle-eq]: #14689
#15571 := [unit-resolution #14714 #15563]: #14690
#14679 := (>= #5268 0::Int)
#14688 := (or #19170 #14679)
#12799 := [th-lemma arith triangle-eq]: #14688
#15545 := [unit-resolution #12799 #15563]: #14679
#4168 := (* -1::Int #4167)
#4169 := (+ #190 #4168)
#7297 := (<= #4169 0::Int)
#7302 := (= #190 #4167)
#18257 := (iff #4220 #7302)
#18255 := (iff #7302 #4220)
#18256 := [commutativity]: #18255
#18258 := [symm #18256]: #18257
#18259 := [mp #9179 #18258]: #7302
#18260 := (not #7302)
#18261 := (or #18260 #7297)
#18262 := [th-lemma arith triangle-eq]: #18261
#18263 := [unit-resolution #18262 #18259]: #7297
#4170 := (>= #4169 0::Int)
#3555 := (or #4045 #3935)
#3556 := [def-axiom]: #3555
#9894 := [unit-resolution #3556 #9893]: #3935
#7218 := (or #3940 #4170)
#7219 := [quant-inst #186]: #7218
#10752 := [unit-resolution #7219 #9894]: #4170
#5157 := (+ #2126 #4168)
#5318 := (<= #5157 0::Int)
#5330 := (+ #4168 #5212)
#5331 := (+ #2126 #5330)
#5332 := (= #5331 0::Int)
#14652 := (>= #5331 0::Int)
#14681 := (not #14690)
#15108 := (or #14681 #14652)
#10393 := (not #4170)
#15550 := (or #14681 #10393 #14652)
#15472 := [th-lemma arith assign-bounds -1 1]: #15550
#15621 := [unit-resolution #15472 #10752]: #15108
#15637 := [unit-resolution #15621 #15571]: #14652
#14720 := (<= #5331 0::Int)
#12661 := (not #7297)
#14678 := (not #14679)
#15123 := (or #14720 #14678 #12661)
#15620 := [th-lemma arith assign-bounds 1 -1]: #15123
#13505 := [unit-resolution #15620 #15545 #18263]: #14720
#19121 := (not #14652)
#12624 := (not #14720)
#15596 := (or #5332 #12624 #19121)
#15676 := [th-lemma arith triangle-eq]: #15596
#15984 := [unit-resolution #15676 #13505 #15637]: #5332
#5337 := (not #5332)
#15716 := (or #5318 #5337)
#4518 := (f9 f29 f28)
#4519 := (= #4518 f1)
#4144 := (f9 #198 f28)
#4145 := (= #4144 f1)
#31 := (:var 0 S1)
#28 := (:var 2 S7)
#29 := (f12 f13 #28)
#30 := (f11 #29 #9)
#32 := (f10 #30 #31)
#3710 := (pattern #32)
#35 := (= #31 f1)
#33 := (f9 #32 #9)
#34 := (= #33 f1)
#36 := (iff #34 #35)
#3711 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1)) (:pat #3710) #36)
#37 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1)) #36)
#3714 := (iff #37 #3711)
#3712 := (iff #36 #36)
#3713 := [refl]: #3712
#3715 := [quant-intro #3713]: #3714
#1577 := (~ #37 #37)
#1606 := (~ #36 #36)
#1607 := [refl]: #1606
#1578 := [nnf-pos #1607]: #1577
#321 := [asserted]: #37
#1608 := [mp~ #321 #1578]: #37
#3716 := [mp #1608 #3715]: #3711
#6379 := (not #3711)
#6555 := (or #6379 #4145)
#4147 := (iff #4145 #4146)
#6775 := (or #6379 #4147)
#7023 := (iff #6775 #6555)
#7024 := (iff #6555 #6555)
#3437 := [rewrite]: #7024
#4155 := (iff #4147 #4145)
#4150 := (iff #4145 true)
#4153 := (iff #4150 #4145)
#4154 := [rewrite]: #4153
#4151 := (iff #4147 #4150)
#4152 := [monotonicity #4149]: #4151
#4156 := [trans #4152 #4154]: #4155
#7020 := [monotonicity #4156]: #7023
#3310 := [trans #7020 #3437]: #7023
#7010 := [quant-inst #115 #186 #3]: #6775
#6101 := [mp #7010 #3310]: #6555
#12643 := [unit-resolution #6101 #3716]: #4145
#12662 := (= #4518 #4144)
#12669 := [monotonicity #9701]: #12662
#12665 := [trans #12669 #12643]: #4519
#4447 := (= #221 #110)
#8042 := (= #190 #110)
#7927 := (= #110 #190)
#4428 := (+ #110 #1235)
#4429 := (>= #4428 0::Int)
#4424 := (f9 f21 f16)
#4425 := (= #4424 f1)
#7254 := (not #4425)
#4381 := (= ?v0!12 f16)
#4382 := (?v1!7 ?v0!12)
#4390 := (f6 f7 #4382)
#4391 := (f5 #4390 ?v0!12)
#4392 := (f15 #4391)
#4393 := (* -1::Int #4392)
#4383 := (f19 f20 #4382)
#4384 := (* -1::Int #4383)
#4394 := (+ #4384 #4393)
#4395 := (+ #1965 #4394)
#4396 := (= #4395 0::Int)
#4397 := (not #4396)
#4387 := (f9 f21 #4382)
#4388 := (= #4387 f1)
#4389 := (not #4388)
#4385 := (+ #1965 #4384)
#4386 := (<= #4385 0::Int)
#4398 := (or #4386 #4389 #4397)
#4252 := (= f28 f16)
#4431 := (f5 #200 f16)
#4432 := (f15 #4431)
#4439 := (* -1::Int #4432)
#4442 := (+ #1235 #4439)
#4443 := (+ #110 #4442)
#4444 := (<= #4443 0::Int)
#7610 := (not #4444)
#4440 := (+ f14 #4439)
#4441 := (<= #4440 0::Int)
#4445 := (or #4441 #4444)
#4446 := (not #4445)
#9205 := (not #4447)
#5924 := (iff #713 #9205)
#5922 := (iff #222 #4447)
#5921 := (iff #4447 #222)
#5919 := [monotonicity #7324]: #5921
#5923 := [symm #5919]: #5922
#6064 := [monotonicity #5923]: #5924
#5920 := [hypothesis]: #713
#6065 := [mp #5920 #6064]: #9205
#4448 := (or #4446 #4447)
#7601 := (or #3932 #4446 #4447)
#7602 := (or #3932 #4448)
#7604 := (iff #7602 #7601)
#7605 := [rewrite]: #7604
#7603 := [quant-inst #65]: #7602
#7606 := [mp #7603 #7605]: #7601
#6066 := [unit-resolution #7606 #8861]: #4448
#9900 := [unit-resolution #6066 #6065]: #4446
#7611 := (or #4445 #7610)
#7612 := [def-axiom]: #7611
#9807 := [unit-resolution #7612 #9900]: #7610
#8599 := (or #4444 #4252)
#8514 := (<= #4432 0::Int)
#8515 := (not #8514)
#8195 := (not #4252)
#8549 := [hypothesis]: #8195
#8513 := (or #6342 #4252 #8515)
#8516 := (or #4252 #8515)
#8519 := (or #6342 #8516)
#8521 := (iff #8519 #8513)
#8522 := [rewrite]: #8521
#8520 := [quant-inst #186 #65]: #8519
#8523 := [mp #8520 #8522]: #8513
#8552 := [unit-resolution #8523 #3735 #8549]: #8515
#4483 := (<= #110 0::Int)
#7325 := (or #878 #4483)
#7328 := [th-lemma arith triangle-eq]: #7325
#7329 := [unit-resolution #7328 #7324]: #4483
#4253 := (?v1!7 f28)
#4254 := (f19 f20 #4253)
#4255 := (* -1::Int #4254)
#4256 := (+ #190 #4255)
#7963 := (>= #4256 0::Int)
#4257 := (<= #4256 0::Int)
#7326 := (not #4257)
#4261 := (f6 f7 #4253)
#4262 := (f5 #4261 f28)
#4263 := (f15 #4262)
#4264 := (* -1::Int #4263)
#4265 := (+ #4255 #4264)
#4266 := (+ #190 #4265)
#4267 := (= #4266 0::Int)
#4268 := (not #4267)
#4258 := (f9 f21 #4253)
#4259 := (= #4258 f1)
#4260 := (not #4259)
#4269 := (or #4257 #4260 #4268)
#4270 := (not #4269)
#8572 := (or #4252 #4270)
#3547 := (or #4057 #1412)
#3550 := [def-axiom]: #3547
#8267 := [unit-resolution #3550 #8264]: #1412
#7305 := (or #3836 #4252 #1411 #4270)
#4271 := (or #4252 #1411 #4270)
#7316 := (or #3836 #4271)
#7315 := (iff #7316 #7305)
#7317 := [rewrite]: #7315
#7314 := [quant-inst #186]: #7316
#7318 := [mp #7314 #7317]: #7305
#8573 := [unit-resolution #7318 #7150 #8267]: #8572
#8574 := [unit-resolution #8573 #8549]: #4270
#7322 := (or #4269 #7326)
#7327 := [def-axiom]: #7322
#8575 := [unit-resolution #7327 #8574]: #7326
#8570 := (or #7963 #4257)
#8576 := [th-lemma arith farkas 1 1]: #8570
#8577 := [unit-resolution #8576 #8575]: #7963
#8444 := (>= #4254 0::Int)
#3531 := (or #4069 #3806)
#3511 := [def-axiom]: #3531
#8408 := [unit-resolution #3511 #7099]: #3806
#7889 := (or #3811 #8444)
#7890 := [quant-inst #4253]: #7889
#8578 := [unit-resolution #7890 #8408]: #8444
#8579 := [hypothesis]: #7610
#8580 := [th-lemma arith farkas 1 1 1 1 1 #8579 #8578 #8577 #7329 #8552]: false
#8600 := [lemma #8580]: #8599
#9903 := [unit-resolution #8600 #9807]: #4252
#11140 := (or #4398 #8195)
#4399 := (not #4398)
#11053 := [hypothesis]: #4399
#7585 := (or #4398 #4388)
#7586 := [def-axiom]: #7585
#11054 := [unit-resolution #7586 #11053]: #4388
#11117 := (= #187 #4387)
#8916 := (= f28 #4382)
#10478 := (= f16 #4382)
#8133 := (= #4382 f16)
#8136 := (?v1!7 #4382)
#8144 := (f6 f7 #8136)
#8145 := (f5 #8144 #4382)
#8146 := (f15 #8145)
#8147 := (* -1::Int #8146)
#8137 := (f19 f20 #8136)
#8138 := (* -1::Int #8137)
#8148 := (+ #8138 #8147)
#8149 := (+ #4383 #8148)
#8150 := (= #8149 0::Int)
#8151 := (not #8150)
#8141 := (f9 f21 #8136)
#8142 := (= #8141 f1)
#8143 := (not #8142)
#8139 := (+ #4383 #8138)
#8140 := (<= #8139 0::Int)
#8152 := (or #8140 #8143 #8151)
#9559 := (+ #110 #4384)
#9591 := (>= #9559 0::Int)
#8009 := [hypothesis]: #4252
#8040 := [monotonicity #8009]: #8042
#8044 := [symm #8040]: #7927
#7986 := (not #7927)
#7987 := (or #7986 #4429)
#7985 := [th-lemma arith triangle-eq]: #7987
#8266 := [unit-resolution #7985 #8044]: #4429
#8029 := (+ #190 #4384)
#8030 := (>= #8029 0::Int)
#9838 := (or #3820 #188 #4389 #8030)
#8037 := (or #188 #4389 #8030)
#9839 := (or #3820 #8037)
#9884 := (iff #9839 #9838)
#9885 := [rewrite]: #9884
#9597 := [quant-inst #4382 #186]: #9839
#9897 := [mp #9597 #9885]: #9838
#11049 := [unit-resolution #9897 #8132 #8131 #11054]: #8030
#8411 := (not #4429)
#11055 := (not #8030)
#11056 := (or #9591 #11055 #8411)
#11057 := [th-lemma arith assign-bounds -1 -1]: #11056
#11058 := [unit-resolution #11057 #11049 #8266]: #9591
#10720 := (not #9591)
#11080 := (or #10720 #8140)
#9223 := (>= #8137 0::Int)
#10115 := (not #9223)
#10116 := [hypothesis]: #10115
#10093 := (or #3811 #9223)
#10094 := [quant-inst #8136]: #10093
#10134 := [unit-resolution #10094 #8408 #10116]: false
#10135 := [lemma #10134]: #9223
#7335 := (not #4483)
#11059 := (or #10720 #7335 #10115 #8140)
#11079 := [th-lemma arith assign-bounds -1 1 1]: #11059
#11081 := [unit-resolution #11079 #10135 #7329]: #11080
#11082 := [unit-resolution #11081 #11058]: #8140
#10256 := (not #8140)
#10257 := (or #8152 #10256)
#10263 := [def-axiom]: #10257
#11083 := [unit-resolution #10263 #11082]: #8152
#8153 := (not #8152)
#11107 := (or #8133 #8153)
#8134 := (+ f14 #4384)
#8135 := (<= #8134 0::Int)
#11087 := (not #8135)
#8025 := (>= #4385 0::Int)
#7582 := (not #4386)
#7583 := (or #4398 #7582)
#7584 := [def-axiom]: #7583
#11078 := [unit-resolution #7584 #11053]: #7582
#11084 := (or #8025 #4386)
#11085 := [th-lemma arith farkas 1 1]: #11084
#11086 := [unit-resolution #11085 #11078]: #8025
#11088 := (not #8025)
#11110 := (or #11087 #11088)
#3544 := (or #4057 #1969)
#3549 := [def-axiom]: #3544
#9691 := [unit-resolution #3549 #8264]: #1969
#11108 := (or #11087 #1968 #11088)
#11109 := [th-lemma arith assign-bounds 1 1]: #11108
#11111 := [unit-resolution #11109 #9691]: #11110
#11112 := [unit-resolution #11111 #11086]: #11087
#10255 := (or #3836 #8133 #8135 #8153)
#8154 := (or #8133 #8135 #8153)
#10258 := (or #3836 #8154)
#10260 := (iff #10258 #10255)
#10261 := [rewrite]: #10260
#10259 := [quant-inst #4382]: #10258
#10262 := [mp #10259 #10261]: #10255
#11113 := [unit-resolution #10262 #7150 #11112]: #11107
#11114 := [unit-resolution #11113 #11083]: #8133
#11115 := [symm #11114]: #10478
#11116 := [trans #8009 #11115]: #8916
#11137 := [monotonicity #11116]: #11117
#11138 := [trans #11137 #11054]: #188
#11139 := [unit-resolution #8131 #11138]: false
#11141 := [lemma #11139]: #11140
#9883 := [unit-resolution #11141 #9903]: #4398
#8305 := (or #4381 #4399)
#7574 := (or #3836 #4381 #1968 #4399)
#4400 := (or #4381 #1968 #4399)
#7575 := (or #3836 #4400)
#7577 := (iff #7575 #7574)
#7578 := [rewrite]: #7577
#7576 := [quant-inst #1961]: #7575
#7579 := [mp #7576 #7578]: #7574
#8780 := [unit-resolution #7579 #7150 #9691]: #8305
#18251 := [unit-resolution #8780 #9883]: #4381
#9007 := (not #4381)
#9005 := (or #9007 #7254)
#7350 := [hypothesis]: #4425
#8961 := (= #1962 #4424)
#8959 := [hypothesis]: #4381
#8962 := [monotonicity #8959]: #8961
#9006 := [trans #8962 #7350]: #1963
#3542 := (or #4057 #1964)
#3543 := [def-axiom]: #3542
#8944 := [unit-resolution #3543 #8264]: #1964
#8888 := [unit-resolution #8944 #9006]: false
#9008 := [lemma #8888]: #9005
#9652 := [unit-resolution #9008 #18251]: #7254
#4430 := (or #4425 #4429)
#3551 := (or #4057 #3909)
#3552 := [def-axiom]: #3551
#8603 := [unit-resolution #3552 #8264]: #3909
#7595 := (or #3914 #4425 #4429)
#7596 := (or #3914 #4430)
#7598 := (iff #7596 #7595)
#7599 := [rewrite]: #7598
#7597 := [quant-inst #65]: #7596
#7600 := [mp #7597 #7599]: #7595
#9803 := [unit-resolution #7600 #8603]: #4430
#9901 := [unit-resolution #9803 #9652]: #4429
#9733 := (or #7927 #8411)
#8590 := (<= #4428 0::Int)
#4272 := (>= #190 0::Int)
#7146 := (or #3811 #4272)
#7514 := [quant-inst #186]: #7146
#7845 := [unit-resolution #7514 #8408]: #4272
#8544 := (not #8590)
#7810 := [hypothesis]: #8544
#7888 := [th-lemma arith farkas 1 -1 1 #7810 #7329 #7845]: false
#7759 := [lemma #7888]: #8590
#9935 := (or #7927 #8544 #8411)
#9936 := [th-lemma arith triangle-eq]: #9935
#9606 := [unit-resolution #9936 #7759]: #9733
#9645 := [unit-resolution #9606 #9901]: #7927
#9892 := [symm #9645]: #8042
#9902 := (= #221 #190)
#8871 := (= #221 #4167)
#8010 := (= f16 f28)
#9669 := [symm #9903]: #8010
#9549 := [monotonicity #9669]: #8871
#9612 := [trans #9549 #9179]: #9902
#9668 := [trans #9612 #9892]: #4447
#9570 := [trans #9668 #7324]: #222
#9595 := [unit-resolution #5920 #9570]: false
#9632 := [lemma #9595]: #222
#3565 := (or #4033 #4027)
#3567 := [def-axiom]: #3565
#14028 := [unit-resolution #3567 #18771]: #4027
#3585 := (or #4030 #713 #4024)
#3575 := [def-axiom]: #3585
#14128 := [unit-resolution #3575 #14028]: #4027
#14105 := [unit-resolution #14128 #9632]: #4024
#3577 := (or #4021 #4015)
#3578 := [def-axiom]: #3577
#14080 := [unit-resolution #3578 #14105]: #4015
#14243 := (or #4018 #4012)
#8617 := (or #8544 #2051)
#6626 := (f5 #200 ?v0!15)
#6627 := (f15 #6626)
#9520 := (= #6627 0::Int)
#8602 := (not #9520)
#9750 := (>= #6627 0::Int)
#8541 := (not #9750)
#8393 := [hypothesis]: #8590
#6707 := [hypothesis]: #2052
#3322 := (>= #110 0::Int)
#6072 := (or #3811 #3322)
#6127 := [quant-inst #65]: #6072
#8487 := [unit-resolution #6127 #8408]: #3322
#4577 := (* -1::Int #2050)
#6683 := (+ #4577 #6627)
#6684 := (+ #190 #6683)
#9543 := (<= #6684 0::Int)
#6687 := (= #6684 0::Int)
#6628 := (* -1::Int #6627)
#6629 := (+ f14 #6628)
#6630 := (<= #6629 0::Int)
#9343 := (not #6630)
#6585 := (f19 f20 ?v0!15)
#6610 := (* -1::Int #6585)
#6644 := (+ #6610 #6627)
#6645 := (+ #190 #6644)
#6646 := (>= #6645 0::Int)
#6651 := (or #6630 #6646)
#6654 := (not #6651)
#6586 := (= #2050 #6585)
#9841 := (not #6586)
#6611 := (+ #2050 #6610)
#9310 := (>= #6611 0::Int)
#9745 := (not #9310)
#9746 := (or #9745 #2051)
#9740 := [hypothesis]: #9310
#9233 := (>= #6585 0::Int)
#9593 := (or #3811 #9233)
#9579 := [quant-inst #2049]: #9593
#9741 := [unit-resolution #9579 #8408]: #9233
#9744 := [th-lemma arith farkas -1 1 1 #6707 #9741 #9740]: false
#9747 := [lemma #9744]: #9746
#9587 := [unit-resolution #9747 #6707]: #9745
#9589 := (or #9841 #9310)
#9611 := [th-lemma arith triangle-eq]: #9589
#8492 := [unit-resolution #9611 #9587]: #9841
#9172 := (or #3932 #6654 #6586)
#6631 := (+ #1235 #6628)
#6632 := (+ #6585 #6631)
#6633 := (<= #6632 0::Int)
#6634 := (or #6630 #6633)
#6635 := (not #6634)
#6636 := (or #6635 #6586)
#9240 := (or #3932 #6636)
#9341 := (iff #9240 #9172)
#6657 := (or #6654 #6586)
#8908 := (or #3932 #6657)
#9265 := (iff #8908 #9172)
#9339 := [rewrite]: #9265
#8877 := (iff #9240 #8908)
#6658 := (iff #6636 #6657)
#6655 := (iff #6635 #6654)
#6652 := (iff #6634 #6651)
#6649 := (iff #6633 #6646)
#6637 := (+ #6585 #6628)
#6638 := (+ #1235 #6637)
#6641 := (<= #6638 0::Int)
#6647 := (iff #6641 #6646)
#6648 := [rewrite]: #6647
#6642 := (iff #6633 #6641)
#6639 := (= #6632 #6638)
#6640 := [rewrite]: #6639
#6643 := [monotonicity #6640]: #6642
#6650 := [trans #6643 #6648]: #6649
#6653 := [monotonicity #6650]: #6652
#6656 := [monotonicity #6653]: #6655
#6659 := [monotonicity #6656]: #6658
#8889 := [monotonicity #6659]: #8877
#9337 := [trans #8889 #9339]: #9341
#8828 := [quant-inst #2049]: #9240
#9342 := [mp #8828 #9337]: #9172
#8493 := [unit-resolution #9342 #8861 #8492]: #6654
#9344 := (or #6651 #9343)
#9299 := [def-axiom]: #9344
#8494 := [unit-resolution #9299 #8493]: #9343
#9330 := (not #6646)
#8854 := (or #6651 #9330)
#8855 := [def-axiom]: #8854
#8307 := [unit-resolution #8855 #8493]: #9330
#6690 := (or #6630 #6646 #6687)
#9368 := (or #3924 #6630 #6646 #6687)
#6679 := (+ #6627 #4577)
#6680 := (+ #190 #6679)
#6681 := (= #6680 0::Int)
#6682 := (or #6630 #6633 #6681)
#8704 := (or #3924 #6682)
#9540 := (iff #8704 #9368)
#9390 := (or #3924 #6690)
#9425 := (iff #9390 #9368)
#9539 := [rewrite]: #9425
#9413 := (iff #8704 #9390)
#6691 := (iff #6682 #6690)
#6688 := (iff #6681 #6687)
#6685 := (= #6680 #6684)
#6686 := [rewrite]: #6685
#6689 := [monotonicity #6686]: #6688
#6692 := [monotonicity #6650 #6689]: #6691
#9423 := [monotonicity #6692]: #9413
#9536 := [trans #9423 #9539]: #9540
#9412 := [quant-inst #2049]: #8704
#9541 := [mp #9412 #9536]: #9368
#9868 := [unit-resolution #9541 #8832]: #6690
#8535 := [unit-resolution #9868 #8307 #8494]: #6687
#9870 := (not #6687)
#9871 := (or #9870 #9543)
#9872 := [th-lemma arith triangle-eq]: #9871
#8540 := [unit-resolution #9872 #8535]: #9543
#8548 := (not #3322)
#9874 := (not #9543)
#8539 := (or #8541 #2051 #9874 #8544 #8548)
#8530 := [th-lemma arith assign-bounds -1 -1 -1 1]: #8539
#8601 := [unit-resolution #8530 #8540 #8487 #6707 #8393]: #8541
#8604 := (or #8602 #9750)
#8571 := [th-lemma arith triangle-eq]: #8604
#8605 := [unit-resolution #8571 #8601]: #8602
#9672 := (= f28 ?v0!15)
#9673 := (<= #6627 0::Int)
#8598 := (or #9673 #2051 #9874 #8544 #8548)
#8613 := [th-lemma arith assign-bounds 1 1 1 1]: #8598
#8611 := [unit-resolution #8613 #8540 #8487 #6707 #8393]: #9673
#9674 := (not #9673)
#9609 := (or #6342 #9672 #9674)
#9675 := (or #9672 #9674)
#9610 := (or #6342 #9675)
#9622 := (iff #9610 #9609)
#9618 := [rewrite]: #9622
#9604 := [quant-inst #186 #2049]: #9610
#9619 := [mp #9604 #9618]: #9609
#8607 := [unit-resolution #9619 #3735 #8611]: #9672
#9676 := (not #9672)
#8402 := (or #6738 #9676 #9520)
#9726 := (or #9676 #9520)
#8488 := (or #6738 #9726)
#8484 := (iff #8488 #8402)
#8485 := [rewrite]: #8484
#8489 := [quant-inst #186 #2049]: #8488
#8486 := [mp #8489 #8485]: #8402
#8619 := [unit-resolution #8486 #3729 #8607 #8605]: false
#8618 := [lemma #8619]: #8617
#14242 := [unit-resolution #8618 #7759]: #2051
#3593 := (or #4018 #2052 #4012)
#3573 := [def-axiom]: #3593
#14109 := [unit-resolution #3573 #14242]: #14243
#14124 := [unit-resolution #14109 #14080]: #4012
#3596 := (or #4009 #4003)
#3601 := [def-axiom]: #3596
#14006 := [unit-resolution #3601 #14124]: #4003
#14245 := (or #4006 #4000)
#6060 := [hypothesis]: #2959
#3627 := (not #2077)
#3630 := (or #2954 #3627)
#3514 := [def-axiom]: #3630
#6061 := [unit-resolution #3514 #6060]: #3627
#10344 := (or #2954 #2077)
#5944 := (f19 f20 ?v1!16)
#5961 := (* -1::Int #5944)
#5013 := (+ #190 #5961)
#5014 := (<= #5013 0::Int)
#5817 := (f9 f21 ?v1!16)
#5818 := (= #5817 f1)
#10018 := (not #5818)
#5816 := (= ?v1!16 f28)
#5824 := (or #5816 #5818)
#10022 := (not #5824)
#5814 := (f9 #198 ?v1!16)
#5815 := (= #5814 f1)
#5829 := (iff #5815 #5824)
#9980 := (or #7628 #5829)
#5819 := (if #5816 #4146 #5818)
#5820 := (iff #5815 #5819)
#9981 := (or #7628 #5820)
#10002 := (iff #9981 #9980)
#10009 := (iff #9980 #9980)
#10010 := [rewrite]: #10009
#5830 := (iff #5820 #5829)
#5827 := (iff #5819 #5824)
#5821 := (if #5816 true #5818)
#5825 := (iff #5821 #5824)
#5826 := [rewrite]: #5825
#5822 := (iff #5819 #5821)
#5823 := [monotonicity #4149]: #5822
#5828 := [trans #5823 #5826]: #5827
#5831 := [monotonicity #5828]: #5830
#10008 := [monotonicity #5831]: #10002
#10011 := [trans #10008 #10010]: #10002
#10007 := [quant-inst #115 #186 #3 #2064]: #9981
#10012 := [mp #10007 #10011]: #9980
#10496 := [unit-resolution #10012 #3723]: #5829
#10031 := (not #5815)
#10269 := (iff #2068 #10031)
#10268 := (iff #2067 #5815)
#10548 := (iff #5815 #2067)
#10495 := (= #5814 #2066)
#10497 := [monotonicity #9297]: #10495
#10549 := [monotonicity #10497]: #10548
#10526 := [symm #10549]: #10268
#10270 := [monotonicity #10526]: #10269
#3625 := (or #2954 #2068)
#3628 := [def-axiom]: #3625
#6063 := [unit-resolution #3628 #6060]: #2068
#10271 := [mp #6063 #10270]: #10031
#10024 := (not #5829)
#10025 := (or #10024 #5815 #10022)
#10026 := [def-axiom]: #10025
#10272 := [unit-resolution #10026 #10271 #10496]: #10022
#10019 := (or #5824 #10018)
#10020 := [def-axiom]: #10019
#10273 := [unit-resolution #10020 #10272]: #10018
#5037 := (or #5818 #5014)
#10145 := (or #3914 #5818 #5014)
#4981 := (+ #5944 #1235)
#4982 := (>= #4981 0::Int)
#5007 := (or #5818 #4982)
#10146 := (or #3914 #5007)
#10172 := (iff #10146 #10145)
#10167 := (or #3914 #5037)
#10170 := (iff #10167 #10145)
#10171 := [rewrite]: #10170
#10168 := (iff #10146 #10167)
#5038 := (iff #5007 #5037)
#5035 := (iff #4982 #5014)
#5008 := (+ #1235 #5944)
#5011 := (>= #5008 0::Int)
#5015 := (iff #5011 #5014)
#5016 := [rewrite]: #5015
#5006 := (iff #4982 #5011)
#5009 := (= #4981 #5008)
#5010 := [rewrite]: #5009
#5012 := [monotonicity #5010]: #5006
#5036 := [trans #5012 #5016]: #5035
#5039 := [monotonicity #5036]: #5038
#10169 := [monotonicity #5039]: #10168
#10173 := [trans #10169 #10171]: #10172
#10166 := [quant-inst #2064]: #10146
#10174 := [mp #10166 #10173]: #10145
#10537 := [unit-resolution #10174 #8603]: #5037
#10535 := [unit-resolution #10537 #10273]: #5014
#5741 := (f19 f20 ?v0!17)
#5634 := (* -1::Int #5741)
#5694 := (+ #2074 #5634)
#5699 := (<= #5694 0::Int)
#10122 := (or #3940 #5699)
#5671 := (+ #5741 #2075)
#5684 := (>= #5671 0::Int)
#10124 := (or #3940 #5684)
#10127 := (iff #10124 #10122)
#10130 := (iff #10122 #10122)
#10131 := [rewrite]: #10130
#5701 := (iff #5684 #5699)
#5685 := (+ #2075 #5741)
#5689 := (>= #5685 0::Int)
#5700 := (iff #5689 #5699)
#5698 := [rewrite]: #5700
#5692 := (iff #5684 #5689)
#5690 := (= #5671 #5685)
#5691 := [rewrite]: #5690
#5693 := [monotonicity #5691]: #5692
#5702 := [trans #5693 #5698]: #5701
#10128 := [monotonicity #5702]: #10127
#10132 := [trans #10128 #10131]: #10127
#10126 := [quant-inst #2065]: #10124
#10133 := [mp #10126 #10132]: #10122
#10770 := [unit-resolution #10133 #9894]: #5699
#10716 := [hypothesis]: #3627
#5629 := (+ #190 #5634)
#10727 := (>= #5629 0::Int)
#5771 := (f9 f21 ?v0!17)
#5772 := (= #5771 f1)
#5770 := (= ?v0!17 f28)
#5778 := (or #5770 #5772)
#5760 := (f9 #198 ?v0!17)
#5761 := (= #5760 f1)
#5783 := (iff #5761 #5778)
#10038 := (or #7628 #5783)
#5773 := (if #5770 #4146 #5772)
#5774 := (iff #5761 #5773)
#10036 := (or #7628 #5774)
#10046 := (iff #10036 #10038)
#10028 := (iff #10038 #10038)
#10048 := [rewrite]: #10028
#5784 := (iff #5774 #5783)
#5781 := (iff #5773 #5778)
#5775 := (if #5770 true #5772)
#5779 := (iff #5775 #5778)
#5780 := [rewrite]: #5779
#5776 := (iff #5773 #5775)
#5777 := [monotonicity #4149]: #5776
#5782 := [trans #5777 #5780]: #5781
#5785 := [monotonicity #5782]: #5784
#10047 := [monotonicity #5785]: #10046
#10049 := [trans #10047 #10048]: #10046
#10045 := [quant-inst #115 #186 #3 #2065]: #10036
#10050 := [mp #10045 #10049]: #10038
#10530 := [unit-resolution #10050 #3723]: #5783
#3626 := (or #2954 #2070)
#3629 := [def-axiom]: #3626
#6062 := [unit-resolution #3629 #6060]: #2070
#10538 := (= #5760 #2069)
#10540 := [monotonicity #9297]: #10538
#10544 := [trans #10540 #6062]: #5761
#10058 := (not #5761)
#10073 := (not #5783)
#10059 := (or #10073 #10058 #5778)
#10060 := [def-axiom]: #10059
#10536 := [unit-resolution #10060 #10544 #10530]: #5778
#10051 := (not #5770)
#10683 := (= #2074 #4167)
#10731 := (not #10683)
#6074 := (+ #2074 #4168)
#10684 := (<= #6074 0::Int)
#10570 := (not #10684)
#5977 := (f5 #200 ?v1!16)
#5978 := (f15 #5977)
#10503 := (<= #5978 0::Int)
#10504 := (not #10503)
#10502 := (= f28 ?v1!16)
#10419 := (not #10502)
#10016 := (not #5816)
#10017 := (or #5824 #10016)
#10015 := [def-axiom]: #10017
#10374 := [unit-resolution #10015 #10272]: #10016
#10357 := (or #10419 #5816)
#10399 := [hypothesis]: #10502
#10410 := [symm #10399]: #5816
#10367 := [hypothesis]: #10016
#10417 := [unit-resolution #10367 #10410]: false
#10416 := [lemma #10417]: #10357
#10418 := [unit-resolution #10416 #10374]: #10419
#10343 := (or #10504 #10502)
#10409 := [hypothesis]: #10419
#10318 := [hypothesis]: #10503
#10322 := (or #6342 #10502 #10504)
#10505 := (or #10502 #10504)
#10338 := (or #6342 #10505)
#10339 := (iff #10338 #10322)
#10340 := [rewrite]: #10339
#10295 := [quant-inst #186 #2064]: #10338
#10341 := [mp #10295 #10340]: #10322
#10422 := [unit-resolution #10341 #3735 #10318 #10409]: false
#10472 := [lemma #10422]: #10343
#10405 := [unit-resolution #10472 #10418]: #10504
#10571 := (not #5014)
#10467 := (or #10570 #10503 #2077 #10571)
#4581 := (* -1::Int #2073)
#6036 := (+ #4581 #5978)
#6037 := (+ #190 #6036)
#6040 := (= #6037 0::Int)
#10441 := (not #6040)
#10120 := (<= #6037 0::Int)
#10719 := (not #10120)
#10714 := [hypothesis]: #10504
#10567 := [hypothesis]: #10684
#10406 := (or #10503 #2077 #10719 #10570 #10393)
#10337 := [th-lemma arith assign-bounds 1 1 1 1]: #10406
#10342 := [unit-resolution #10337 #10567 #10714 #10752 #10716]: #10719
#10420 := (or #10441 #10120)
#10421 := [th-lemma arith triangle-eq]: #10420
#10378 := [unit-resolution #10421 #10342]: #10441
#5996 := (+ #5961 #5978)
#5997 := (+ #190 #5996)
#5998 := (>= #5997 0::Int)
#5979 := (* -1::Int #5978)
#5980 := (+ f14 #5979)
#5981 := (<= #5980 0::Int)
#6003 := (or #5981 #5998)
#6006 := (not #6003)
#5987 := (= #2073 #5944)
#10379 := (not #5987)
#5962 := (+ #2073 #5961)
#10107 := (>= #5962 0::Int)
#10569 := (not #10107)
#10566 := [hypothesis]: #5014
#10572 := (or #10569 #2077 #10570 #10571)
#10562 := [hypothesis]: #10107
#10568 := [th-lemma arith farkas -1 1 1 -1 1 #10562 #10716 #10567 #10752 #10566]: false
#10576 := [lemma #10568]: #10572
#10358 := [unit-resolution #10576 #10567 #10716 #10566]: #10569
#10380 := (or #10379 #10107)
#10381 := [th-lemma arith triangle-eq]: #10380
#10359 := [unit-resolution #10381 #10358]: #10379
#6009 := (or #6006 #5987)
#10077 := (or #3932 #6006 #5987)
#5982 := (+ #1235 #5979)
#5983 := (+ #5944 #5982)
#5984 := (<= #5983 0::Int)
#5985 := (or #5981 #5984)
#5986 := (not #5985)
#5988 := (or #5986 #5987)
#10078 := (or #3932 #5988)
#10096 := (iff #10078 #10077)
#10079 := (or #3932 #6009)
#10075 := (iff #10079 #10077)
#10095 := [rewrite]: #10075
#10080 := (iff #10078 #10079)
#6010 := (iff #5988 #6009)
#6007 := (iff #5986 #6006)
#6004 := (iff #5985 #6003)
#6001 := (iff #5984 #5998)
#5989 := (+ #5944 #5979)
#5990 := (+ #1235 #5989)
#5993 := (<= #5990 0::Int)
#5999 := (iff #5993 #5998)
#6000 := [rewrite]: #5999
#5994 := (iff #5984 #5993)
#5991 := (= #5983 #5990)
#5992 := [rewrite]: #5991
#5995 := [monotonicity #5992]: #5994
#6002 := [trans #5995 #6000]: #6001
#6005 := [monotonicity #6002]: #6004
#6008 := [monotonicity #6005]: #6007
#6011 := [monotonicity #6008]: #6010
#10081 := [monotonicity #6011]: #10080
#10097 := [trans #10081 #10095]: #10096
#10076 := [quant-inst #2064]: #10078
#10098 := [mp #10076 #10097]: #10077
#10377 := [unit-resolution #10098 #8861]: #6009
#10383 := [unit-resolution #10377 #10359]: #6006
#10564 := (or #6003 #6040)
#10442 := [hypothesis]: #10441
#10074 := (not #5981)
#10558 := [hypothesis]: #6006
#10099 := (or #6003 #10074)
#10100 := [def-axiom]: #10099
#10559 := [unit-resolution #10100 #10558]: #10074
#10101 := (not #5998)
#10102 := (or #6003 #10101)
#10103 := [def-axiom]: #10102
#10560 := [unit-resolution #10103 #10558]: #10101
#6043 := (or #5981 #5998 #6040)
#10108 := (or #3924 #5981 #5998 #6040)
#6032 := (+ #5978 #4581)
#6033 := (+ #190 #6032)
#6034 := (= #6033 0::Int)
#6035 := (or #5981 #5984 #6034)
#10109 := (or #3924 #6035)
#10118 := (iff #10109 #10108)
#10110 := (or #3924 #6043)
#10113 := (iff #10110 #10108)
#10114 := [rewrite]: #10113
#10111 := (iff #10109 #10110)
#6044 := (iff #6035 #6043)
#6041 := (iff #6034 #6040)
#6038 := (= #6033 #6037)
#6039 := [rewrite]: #6038
#6042 := [monotonicity #6039]: #6041
#6045 := [monotonicity #6002 #6042]: #6044
#10112 := [monotonicity #6045]: #10111
#10119 := [trans #10112 #10114]: #10118
#10104 := [quant-inst #2064]: #10109
#10117 := [mp #10104 #10119]: #10108
#10561 := [unit-resolution #10117 #8832]: #6043
#10563 := [unit-resolution #10561 #10560 #10559 #10442]: false
#10565 := [lemma #10563]: #10564
#10382 := [unit-resolution #10565 #10383 #10378]: false
#10471 := [lemma #10382]: #10467
#10423 := [unit-resolution #10471 #10405 #10716 #10535]: #10570
#10738 := (or #10731 #10684)
#10737 := [th-lemma arith triangle-eq]: #10738
#10531 := [unit-resolution #10737 #10423]: #10731
#10368 := (or #10051 #10683)
#10401 := [hypothesis]: #5770
#10400 := [monotonicity #10401]: #10683
#10370 := [hypothesis]: #10731
#10402 := [unit-resolution #10370 #10400]: false
#10369 := [lemma #10402]: #10368
#10426 := [unit-resolution #10369 #10531]: #10051
#10070 := (not #5778)
#10071 := (or #10070 #5770 #5772)
#10072 := [def-axiom]: #10071
#10427 := [unit-resolution #10072 #10426 #10536]: #5772
#10067 := (not #5772)
#10803 := (or #10067 #10727)
#10782 := (not #10727)
#10800 := [hypothesis]: #10782
#10801 := [hypothesis]: #5772
#10785 := (or #3820 #188 #10067 #10727)
#10728 := (or #188 #10067 #10727)
#10786 := (or #3820 #10728)
#10788 := (iff #10786 #10785)
#10789 := [rewrite]: #10788
#10787 := [quant-inst #2065 #186]: #10786
#10790 := [mp #10787 #10789]: #10785
#10802 := [unit-resolution #10790 #8132 #8131 #10801 #10800]: false
#10804 := [lemma #10802]: #10803
#10428 := [unit-resolution #10804 #10427]: #10727
#10429 := (not #5699)
#10276 := (or #10782 #2077 #10719 #10503 #10429)
#10278 := [th-lemma arith assign-bounds 1 1 1 1]: #10276
#10279 := [unit-resolution #10278 #10428 #10770 #10405 #10716]: #10719
#10280 := [unit-resolution #10421 #10279]: #10441
#10275 := [unit-resolution #10565 #10280]: #6003
#10281 := [unit-resolution #10377 #10275]: #5987
#10277 := [unit-resolution #10381 #10281]: #10107
#10282 := [th-lemma arith farkas -1 -1 1 1 1 #10277 #10428 #10716 #10770 #10535]: false
#10345 := [lemma #10282]: #10344
#11340 := [unit-resolution #10345 #6061 #6060]: false
#11363 := [lemma #11340]: #2954
#3597 := (or #4006 #2959 #4000)
#3598 := [def-axiom]: #3597
#14089 := [unit-resolution #3598 #11363]: #14245
#14298 := [unit-resolution #14089 #14006]: #4000
#3606 := (or #3997 #3991)
#3607 := [def-axiom]: #3606
#17543 := [unit-resolution #3607 #14298]: #3991
#16954 := [hypothesis]: #3005
#3619 := (or #3000 #2101)
#3622 := [def-axiom]: #3619
#16970 := [unit-resolution #3622 #16954]: #2101
#6572 := (f5 #200 ?v0!19)
#6570 := (f15 #6572)
#6573 := (* -1::Int #6570)
#16948 := (+ #2097 #6573)
#16952 := (>= #16948 0::Int)
#16938 := (= #2097 #6570)
#17002 := (= #2096 #6572)
#16996 := (= #2095 #200)
#5496 := (= ?v1!18 f28)
#5497 := (f9 f21 ?v1!18)
#5498 := (= #5497 f1)
#6712 := (not #5498)
#6463 := (f19 f20 ?v0!19)
#6534 := (* -1::Int #6463)
#5451 := (f19 f20 ?v1!18)
#6728 := (+ #5451 #6534)
#6729 := (+ #2097 #6728)
#6730 := (>= #6729 0::Int)
#16957 := (not #6730)
#3507 := (not #2109)
#3522 := (or #3000 #3507)
#3524 := [def-axiom]: #3522
#16955 := [unit-resolution #3524 #16954]: #3507
#5548 := (* -1::Int #5451)
#5549 := (+ #2104 #5548)
#12637 := (>= #5549 0::Int)
#5469 := (= #2104 #5451)
#3523 := (or #3000 #2094)
#3618 := [def-axiom]: #3523
#16956 := [unit-resolution #3618 #16954]: #2094
#16334 := (or #3949 #2985 #5469)
#5472 := (or #2985 #5469)
#16340 := (or #3949 #5472)
#16341 := (iff #16340 #16334)
#16068 := [rewrite]: #16341
#16335 := [quant-inst #2091]: #16340
#16150 := [mp #16335 #16068]: #16334
#16959 := [unit-resolution #16150 #18772 #16956]: #5469
#16963 := (not #5469)
#16964 := (or #16963 #12637)
#16966 := [th-lemma arith triangle-eq]: #16964
#16967 := [unit-resolution #16966 #16959]: #12637
#16961 := (not #12637)
#12548 := (or #16957 #16961 #2109)
#6535 := (+ #2105 #6534)
#6536 := (<= #6535 0::Int)
#18328 := (not #6536)
#18338 := [hypothesis]: #18328
#17088 := (or #3940 #6536)
#6478 := (+ #6463 #2106)
#6488 := (>= #6478 0::Int)
#17089 := (or #3940 #6488)
#18276 := (iff #17089 #17088)
#18278 := (iff #17088 #17088)
#18289 := [rewrite]: #18278
#6557 := (iff #6488 #6536)
#6529 := (+ #2106 #6463)
#6532 := (>= #6529 0::Int)
#6537 := (iff #6532 #6536)
#6556 := [rewrite]: #6537
#6527 := (iff #6488 #6532)
#6530 := (= #6478 #6529)
#6531 := [rewrite]: #6530
#6533 := [monotonicity #6531]: #6527
#6558 := [trans #6533 #6556]: #6557
#18277 := [monotonicity #6558]: #18276
#18290 := [trans #18277 #18289]: #18276
#18275 := [quant-inst #2092]: #17089
#18291 := [mp #18275 #18290]: #17088
#18339 := [unit-resolution #18291 #9894 #18338]: false
#18340 := [lemma #18339]: #6536
#16962 := (or #16957 #16961 #18328 #2109)
#16968 := [th-lemma arith assign-bounds 1 -1 -1]: #16962
#12549 := [unit-resolution #16968 #18340]: #12548
#12627 := [unit-resolution #12549 #16967 #16955]: #16957
#16932 := (or #6712 #6730)
#16777 := (or #3828 #6712 #2100 #6730)
#6731 := (or #6712 #2100 #6730)
#16782 := (or #3828 #6731)
#16783 := (iff #16782 #16777)
#16775 := [rewrite]: #16783
#16780 := [quant-inst #2092 #2091]: #16782
#16784 := [mp #16780 #16775]: #16777
#16975 := [unit-resolution #16784 #7100 #16970]: #16932
#12604 := [unit-resolution #16975 #12627]: #6712
#5504 := (or #5496 #5498)
#5486 := (f9 #198 ?v1!18)
#5487 := (= #5486 f1)
#5509 := (iff #5487 #5504)
#16182 := (or #7628 #5509)
#5499 := (if #5496 #4146 #5498)
#5500 := (iff #5487 #5499)
#16247 := (or #7628 #5500)
#16275 := (iff #16247 #16182)
#16296 := (iff #16182 #16182)
#15136 := [rewrite]: #16296
#5510 := (iff #5500 #5509)
#5507 := (iff #5499 #5504)
#5501 := (if #5496 true #5498)
#5505 := (iff #5501 #5504)
#5506 := [rewrite]: #5505
#5502 := (iff #5499 #5501)
#5503 := [monotonicity #4149]: #5502
#5508 := [trans #5503 #5506]: #5507
#5511 := [monotonicity #5508]: #5510
#15135 := [monotonicity #5511]: #16275
#15137 := [trans #15135 #15136]: #16275
#16092 := [quant-inst #115 #186 #3 #2091]: #16247
#16292 := [mp #16092 #15137]: #16182
#16991 := [unit-resolution #16292 #3723]: #5509
#16993 := (= #5486 #2093)
#16994 := [monotonicity #9297]: #16993
#16974 := [trans #16994 #16956]: #5487
#16337 := (not #5487)
#15281 := (not #5509)
#16421 := (or #15281 #16337 #5504)
#16336 := [def-axiom]: #16421
#16992 := [unit-resolution #16336 #16974 #16991]: #5504
#16342 := (not #5504)
#16264 := (or #16342 #5496 #5498)
#15134 := [def-axiom]: #16264
#12567 := [unit-resolution #15134 #16992 #12604]: #5496
#12652 := [monotonicity #12567]: #16996
#12545 := [monotonicity #12652]: #17002
#12613 := [monotonicity #12545]: #16938
#16983 := (not #16938)
#16973 := (or #16983 #16952)
#16987 := [th-lemma arith triangle-eq]: #16973
#12610 := [unit-resolution #16987 #12613]: #16952
#6574 := (+ f14 #6573)
#6575 := (<= #6574 0::Int)
#6600 := (+ #6534 #6570)
#6598 := (+ #190 #6600)
#6601 := (>= #6598 0::Int)
#12029 := (not #6601)
#6452 := (+ #2104 #4168)
#6453 := (>= #6452 0::Int)
#5573 := (+ #190 #5548)
#5574 := (<= #5573 0::Int)
#16786 := (or #3914 #5498 #5574)
#5564 := (+ #5451 #1235)
#5565 := (>= #5564 0::Int)
#5566 := (or #5498 #5565)
#16796 := (or #3914 #5566)
#16822 := (iff #16796 #16786)
#5579 := (or #5498 #5574)
#16815 := (or #3914 #5579)
#16827 := (iff #16815 #16786)
#16821 := [rewrite]: #16827
#16825 := (iff #16796 #16815)
#5580 := (iff #5566 #5579)
#5577 := (iff #5565 #5574)
#5567 := (+ #1235 #5451)
#5570 := (>= #5567 0::Int)
#5575 := (iff #5570 #5574)
#5576 := [rewrite]: #5575
#5571 := (iff #5565 #5570)
#5568 := (= #5564 #5567)
#5569 := [rewrite]: #5568
#5572 := [monotonicity #5569]: #5571
#5578 := [trans #5572 #5576]: #5577
#5581 := [monotonicity #5578]: #5580
#16826 := [monotonicity #5581]: #16825
#16820 := [trans #16826 #16821]: #16822
#16817 := [quant-inst #2091]: #16796
#16823 := [mp #16817 #16820]: #16786
#12620 := [unit-resolution #16823 #8603 #12604]: #5574
#16986 := (not #5574)
#12638 := (or #6453 #16986 #16961)
#16989 := (or #6453 #16986 #16961 #10393)
#16990 := [th-lemma arith assign-bounds 1 -1 -1]: #16989
#12605 := [unit-resolution #16990 #10752]: #12638
#12619 := [unit-resolution #12605 #12620 #16967]: #6453
#12634 := (not #16952)
#12636 := (not #6453)
#12622 := (or #12029 #18328 #2109 #12636 #12661 #12634)
#12656 := [th-lemma arith assign-bounds -1 -1 1 -1 1]: #12622
#12623 := [unit-resolution #12656 #12619 #18340 #18263 #16955 #12610]: #12029
#6617 := (or #6575 #6601)
#6699 := (+ #2106 #6570)
#6700 := (+ #190 #6699)
#6703 := (= #6700 0::Int)
#11657 := (not #6703)
#12480 := (>= #6700 0::Int)
#17015 := (not #12480)
#17017 := (or #3000 #17015)
#16969 := [unit-resolution #16968 #16967 #18340 #16955]: #16957
#16976 := [unit-resolution #16975 #16969]: #6712
#16995 := [unit-resolution #15134 #16992 #16976]: #5496
#16997 := [monotonicity #16995]: #16996
#16981 := [monotonicity #16997]: #17002
#16982 := [monotonicity #16981]: #16938
#16980 := [unit-resolution #16987 #16982]: #16952
#16988 := [unit-resolution #16823 #8603 #16976]: #5574
#17010 := [unit-resolution #16990 #16967 #10752 #16988]: #6453
#17013 := [hypothesis]: #12480
#17014 := [th-lemma arith farkas 1 -1 1 -1 1 #17013 #16955 #17010 #18263 #16980]: false
#17018 := [lemma #17014]: #17017
#12641 := [unit-resolution #17018 #16954]: #17015
#11714 := (or #11657 #12480)
#12635 := [th-lemma arith triangle-eq]: #11714
#12017 := [unit-resolution #12635 #12641]: #11657
#12092 := (or #3924 #6575 #6601 #6703)
#6696 := (+ #6570 #2106)
#6697 := (+ #190 #6696)
#6698 := (= #6697 0::Int)
#6580 := (+ #1235 #6573)
#6581 := (+ #6463 #6580)
#6579 := (<= #6581 0::Int)
#6693 := (or #6575 #6579 #6698)
#12098 := (or #3924 #6693)
#12143 := (iff #12098 #12092)
#5162 := (or #6575 #6601 #6703)
#12058 := (or #3924 #5162)
#12141 := (iff #12058 #12092)
#12147 := [rewrite]: #12141
#12060 := (iff #12098 #12058)
#5352 := (iff #6693 #5162)
#5122 := (iff #6698 #6703)
#6701 := (= #6697 #6700)
#6702 := [rewrite]: #6701
#5123 := [monotonicity #6702]: #5122
#6618 := (iff #6579 #6601)
#6588 := (+ #6463 #6573)
#6589 := (+ #1235 #6588)
#6591 := (<= #6589 0::Int)
#6602 := (iff #6591 #6601)
#6603 := [rewrite]: #6602
#6592 := (iff #6579 #6591)
#6587 := (= #6581 #6589)
#6590 := [rewrite]: #6587
#6599 := [monotonicity #6590]: #6592
#6619 := [trans #6599 #6603]: #6618
#5353 := [monotonicity #6619 #5123]: #5352
#12148 := [monotonicity #5353]: #12060
#12142 := [trans #12148 #12147]: #12143
#12130 := [quant-inst #2092]: #12098
#12144 := [mp #12130 #12142]: #12092
#12644 := [unit-resolution #12144 #8832 #12017]: #6617
#11750 := [unit-resolution #12644 #12623]: #6575
#12020 := [th-lemma arith farkas -1 1 1 #11750 #12610 #16970]: false
#12047 := [lemma #12020]: #3000
#3615 := (or #3994 #3005 #3988)
#3616 := [def-axiom]: #3615
#17550 := [unit-resolution #3616 #12047 #17543]: #3988
#3620 := (or #3985 #3977)
#3624 := [def-axiom]: #3620
#14729 := [unit-resolution #3624 #17550]: #3977
#4520 := (not #4519)
#9879 := (or #3982 #5318 #4520 #5337)
#5308 := (+ #4167 #5267)
#5309 := (= #5308 0::Int)
#5310 := (not #5309)
#5298 := (+ #4167 #2127)
#5299 := (>= #5298 0::Int)
#5311 := (or #5299 #4520 #5310)
#9846 := (or #3982 #5311)
#3396 := (iff #9846 #9879)
#5340 := (or #5318 #4520 #5337)
#9859 := (or #3982 #5340)
#8772 := (iff #9859 #9879)
#8417 := [rewrite]: #8772
#7921 := (iff #9846 #9859)
#5341 := (iff #5311 #5340)
#5338 := (iff #5310 #5337)
#5335 := (iff #5309 #5332)
#5323 := (+ #4167 #5211)
#5324 := (+ #2127 #5323)
#5327 := (= #5324 0::Int)
#5333 := (iff #5327 #5332)
#5334 := [rewrite]: #5333
#5328 := (iff #5309 #5327)
#5325 := (= #5308 #5324)
#5326 := [rewrite]: #5325
#5329 := [monotonicity #5326]: #5328
#5336 := [trans #5329 #5334]: #5335
#5339 := [monotonicity #5336]: #5338
#5321 := (iff #5299 #5318)
#5312 := (+ #2127 #4167)
#5315 := (>= #5312 0::Int)
#5319 := (iff #5315 #5318)
#5320 := [rewrite]: #5319
#5316 := (iff #5299 #5315)
#5313 := (= #5298 #5312)
#5314 := [rewrite]: #5313
#5317 := [monotonicity #5314]: #5316
#5322 := [trans #5317 #5320]: #5321
#5342 := [monotonicity #5322 #5339]: #5341
#7809 := [monotonicity #5342]: #7921
#9848 := [trans #7809 #8417]: #3396
#9851 := [quant-inst #186]: #9846
#9882 := [mp #9851 #9848]: #9879
#14657 := [unit-resolution #9882 #14729 #12665]: #15716
#13744 := [unit-resolution #14657 #15984]: #5318
#5158 := (>= #5157 0::Int)
#15624 := (or #4623 #5158)
#3612 := (or #3997 #3961)
#3617 := [def-axiom]: #3612
#14246 := [unit-resolution #3617 #14298]: #3961
#11761 := (or #3966 #4623 #4520 #5158)
#5159 := (or #4623 #4520 #5158)
#10607 := (or #3966 #5159)
#11378 := (iff #10607 #11761)
#11392 := [rewrite]: #11378
#10887 := [quant-inst #186 #2123]: #10607
#11762 := [mp #10887 #11392]: #11761
#15544 := [unit-resolution #11762 #14246 #12665]: #15624
#13741 := [unit-resolution #15544 #15919]: #5158
#13599 := [th-lemma arith eq-propagate 1 1 -1 -1 1 1 #13741 #13744 #10752 #18263 #15545 #15571]: #19614
#13366 := (not #19614)
#15910 := (or #13366 #19610)
#15852 := [th-lemma arith triangle-eq]: #15910
#12478 := [unit-resolution #15852 #13599]: #19610
#19611 := (not #19610)
#19612 := (or #19609 #19611)
#12798 := (or #6342 #19609 #19611)
#14603 := (or #6342 #19612)
#14654 := (iff #14603 #12798)
#14656 := [rewrite]: #14654
#14666 := [quant-inst #186 #2123]: #14603
#14616 := [mp #14666 #14656]: #12798
#13305 := [unit-resolution #14616 #3735]: #19612
#16503 := [unit-resolution #13305 #12478]: #19609
#15534 := [unit-resolution #16503 #15258]: false
#16669 := [lemma #15534]: #5176
#19122 := (or #19098 #17503)
#17519 := (not #17503)
#19187 := [hypothesis]: #17519
#19192 := [hypothesis]: #5176
#19097 := [th-lemma arith triangle-eq]: #19122
#19172 := [unit-resolution #19097 #19192 #19187]: false
#19096 := [lemma #19172]: #19122
#24633 := [unit-resolution #19096 #16669]: #17503
#17541 := (or #17547 #17519)
#3530 := (or #3985 #2130)
#3623 := [def-axiom]: #3530
#17522 := [unit-resolution #3623 #17550]: #2130
#17561 := [hypothesis]: #17503
#17545 := [hypothesis]: #5430
#17548 := [th-lemma arith farkas -1 1 1 #17545 #17561 #17522]: false
#17521 := [lemma #17548]: #17541
#24634 := [unit-resolution #17521 #24633]: #17547
#21003 := (or #5430 #5448)
#3528 := (or #3985 #2125)
#3529 := [def-axiom]: #3528
#21002 := [unit-resolution #3529 #17550]: #2125
#11823 := (or #3836 #2124 #5430 #5448)
#5449 := (or #2124 #5430 #5448)
#11543 := (or #3836 #5449)
#11822 := (iff #11543 #11823)
#11793 := [rewrite]: #11822
#11827 := [quant-inst #2123]: #11543
#11829 := [mp #11827 #11793]: #11823
#21004 := [unit-resolution #11829 #7150 #21002]: #21003
#24635 := [unit-resolution #21004 #24634]: #5448
#10444 := (or #5447 #5445)
#11271 := [def-axiom]: #10444
#20098 := [unit-resolution #11271 #24635]: #5445
#20099 := (or #5446 #11830)
#20097 := [th-lemma arith triangle-eq]: #20099
#20088 := [unit-resolution #20097 #20098]: #11830
#18274 := (+ #5432 #17799)
#18321 := (>= #18274 0::Int)
#15420 := (or #3940 #18321)
#15369 := [quant-inst #5431]: #15420
#19872 := [unit-resolution #15369 #9894]: #18321
#20100 := (not #18321)
#19873 := (not #11830)
#20101 := (or #15418 #19873 #17519 #20100)
#20102 := [th-lemma arith assign-bounds -1 -1 -1]: #20101
#20082 := [unit-resolution #20102 #24633 #19872 #20088]: #15418
#18473 := (<= #18529 0::Int)
#18450 := (+ f14 #5442)
#18526 := (<= #18450 0::Int)
#19955 := (not #18526)
#18451 := (>= #5432 0::Int)
#15358 := (or #3811 #18451)
#15465 := [quant-inst #5431]: #15358
#21016 := [unit-resolution #15465 #8408]: #18451
#21023 := (not #18451)
#19947 := (or #19955 #2129 #17519 #21023 #19873)
#19948 := [th-lemma arith assign-bounds -1 -1 -1 -1]: #19947
#19989 := [unit-resolution #19948 #21016 #24633 #20088 #17522]: #19955
#18253 := (f9 f29 #5431)
#17861 := (= #18253 f1)
#24578 := (f9 #198 #5431)
#24579 := (= #24578 f1)
#24590 := (= #5431 f28)
#24596 := (or #24590 #5437)
#24601 := (iff #24579 #24596)
#24604 := (or #7628 #24601)
#24591 := (if #24590 #4146 #5437)
#24592 := (iff #24579 #24591)
#24605 := (or #7628 #24592)
#24607 := (iff #24605 #24604)
#24609 := (iff #24604 #24604)
#24610 := [rewrite]: #24609
#24602 := (iff #24592 #24601)
#24599 := (iff #24591 #24596)
#24593 := (if #24590 true #5437)
#24597 := (iff #24593 #24596)
#24598 := [rewrite]: #24597
#24594 := (iff #24591 #24593)
#24595 := [monotonicity #4149]: #24594
#24600 := [trans #24595 #24598]: #24599
#24603 := [monotonicity #24600]: #24602
#24608 := [monotonicity #24603]: #24607
#24611 := [trans #24608 #24610]: #24607
#24606 := [quant-inst #115 #186 #3 #5431]: #24605
#24612 := [mp #24606 #24611]: #24604
#24632 := [unit-resolution #24612 #3723]: #24601
#24621 := (not #24601)
#24638 := (or #24621 #24579)
#12006 := (or #5447 #5437)
#12000 := [def-axiom]: #12006
#24636 := [unit-resolution #12000 #24635]: #5437
#24616 := (or #24596 #5438)
#24617 := [def-axiom]: #24616
#24637 := [unit-resolution #24617 #24636]: #24596
#24618 := (not #24596)
#24622 := (or #24621 #24579 #24618)
#24623 := [def-axiom]: #24622
#24639 := [unit-resolution #24623 #24637]: #24638
#24640 := [unit-resolution #24639 #24632]: #24579
#24641 := (= #18253 #24578)
#24642 := [monotonicity #9701]: #24641
#24643 := [trans #24642 #24640]: #17861
#17862 := (not #17861)
#24631 := [hypothesis]: #17862
#24644 := [unit-resolution #24631 #24643]: false
#24645 := [lemma #24644]: #17861
#12615 := (or #17862 #18526 #18473)
#3526 := (or #3985 #3969)
#3527 := [def-axiom]: #3526
#22006 := [unit-resolution #3527 #17550]: #3969
#16736 := (or #3974 #17862 #18526 #18473)
#18522 := (+ #18254 #2127)
#18507 := (+ #5441 #18522)
#18515 := (>= #18507 0::Int)
#18516 := (or #17862 #18526 #18515)
#16729 := (or #3974 #18516)
#15322 := (iff #16729 #16736)
#16781 := (or #3974 #12615)
#16766 := (iff #16781 #16736)
#16787 := [rewrite]: #16766
#16771 := (iff #16729 #16781)
#13633 := (iff #18516 #12615)
#14647 := (iff #18515 #18473)
#18513 := (+ #5441 #18254)
#18523 := (+ #2127 #18513)
#18470 := (>= #18523 0::Int)
#18472 := (iff #18470 #18473)
#18530 := [rewrite]: #18472
#18514 := (iff #18515 #18470)
#18525 := (= #18507 #18523)
#18520 := [rewrite]: #18525
#18527 := [monotonicity #18520]: #18514
#12281 := [trans #18527 #18530]: #14647
#14300 := [monotonicity #12281]: #13633
#15106 := [monotonicity #14300]: #16771
#16805 := [trans #15106 #16787]: #15322
#16779 := [quant-inst #2123 #5431]: #16729
#15127 := [mp #16779 #16805]: #16736
#20083 := [unit-resolution #15127 #22006]: #12615
#19946 := [unit-resolution #20083 #24645 #19989]: #18473
#18690 := (= #18529 0::Int)
#18704 := (not #18690)
#18651 := (+ #2126 #17799)
#18655 := (<= #18651 0::Int)
#18872 := (not #18655)
#11828 := (not #5435)
#11949 := (or #5447 #11828)
#11796 := [def-axiom]: #11949
#19950 := [unit-resolution #11796 #24635]: #11828
#18977 := (or #18872 #5435 #17519 #20100)
#18978 := [th-lemma arith assign-bounds -1 -1 -1]: #18977
#18953 := [unit-resolution #18978 #24633 #19872 #19950]: #18872
#18707 := (or #18655 #17862 #18704)
#16901 := (or #3982 #18655 #17862 #18704)
#18650 := (+ #2127 #5441)
#18592 := (+ #18254 #18650)
#18638 := (= #18592 0::Int)
#18644 := (not #18638)
#18662 := (>= #18522 0::Int)
#18615 := (or #18662 #17862 #18644)
#16863 := (or #3982 #18615)
#12904 := (iff #16863 #16901)
#16890 := (or #3982 #18707)
#16885 := (iff #16890 #16901)
#15516 := [rewrite]: #16885
#15161 := (iff #16863 #16890)
#18708 := (iff #18615 #18707)
#18692 := (iff #18644 #18704)
#18691 := (iff #18638 #18690)
#18658 := (= #18523 0::Int)
#18654 := (iff #18658 #18690)
#18693 := [rewrite]: #18654
#18673 := (iff #18638 #18658)
#18649 := (= #18592 #18523)
#18653 := [rewrite]: #18649
#18674 := [monotonicity #18653]: #18673
#18694 := [trans #18674 #18693]: #18691
#18689 := [monotonicity #18694]: #18692
#18659 := (iff #18662 #18655)
#18581 := (+ #2127 #18254)
#18641 := (>= #18581 0::Int)
#18666 := (iff #18641 #18655)
#18665 := [rewrite]: #18666
#18646 := (iff #18662 #18641)
#18645 := (= #18522 #18581)
#18596 := [rewrite]: #18645
#18647 := [monotonicity #18596]: #18646
#18664 := [trans #18647 #18665]: #18659
#18709 := [monotonicity #18664 #18689]: #18708
#15308 := [monotonicity #18709]: #15161
#16914 := [trans #15308 #15516]: #12904
#16811 := [quant-inst #5431]: #16863
#15485 := [mp #16811 #16914]: #16901
#19077 := [unit-resolution #15485 #14729]: #18707
#19169 := [unit-resolution #19077 #24645 #18953]: #18704
#19090 := (not #15418)
#19243 := (not #18473)
#19996 := (or #18690 #19243 #19090)
#19953 := [th-lemma arith triangle-eq]: #19996
[unit-resolution #19953 #19169 #19946 #20082]: false
unsat