src/HOL/Boogie/Examples/Boogie_Dijkstra.certs

try to avoid races again (cf. 8c37cb84065f and fd3a36e48b09);

a7dbe4783d45017a8218697dc955b8483ad44034 5937 0
#2 := false
decl f1 :: S1
#3 := f1
decl f11 :: (-> S7 S2 S1)
decl ?v0!20 :: S2
#2034 := ?v0!20
decl f29 :: S7
#190 := f29
#4533 := (f11 f29 ?v0!20)
#4534 := (= #4533 f1)
decl f12 :: (-> S8 S1 S7)
decl f13 :: (-> S9 S2 S8)
decl f28 :: S2
#181 := f28
decl f14 :: (-> S10 S7 S9)
decl f21 :: S7
#115 := f21
decl f15 :: S10
#39 := f15
#191 := (f14 f15 f21)
#192 := (f13 #191 f28)
#193 := (f12 #192 f1)
#11446 := (f11 #193 ?v0!20)
#11447 := (= #11446 f1)
#5309 := (f11 f21 ?v0!20)
#5310 := (= #5309 f1)
#11448 := (= ?v0!20 f28)
#11454 := (or #11448 #5310)
#11459 := (iff #11447 #11454)
#11 := (:var 0 S2)
#54 := (:var 1 S1)
#52 := (:var 2 S2)
#50 := (:var 3 S7)
#51 := (f14 f15 #50)
#53 := (f13 #51 #52)
#55 := (f12 #53 #54)
#56 := (f11 #55 #11)
#3640 := (pattern #56)
#60 := (f11 #50 #11)
#61 := (= #60 f1)
#59 := (= #54 f1)
#58 := (= #11 #52)
#62 := (if #58 #59 #61)
#57 := (= #56 f1)
#63 := (iff #57 #62)
#3641 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1) (?v3 S2)) (:pat #3640) #63)
#64 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1) (?v3 S2)) #63)
#3644 := (iff #64 #3641)
#3642 := (iff #63 #63)
#3643 := [refl]: #3642
#3645 := [quant-intro #3643]: #3644
#1496 := (~ #64 #64)
#1524 := (~ #63 #63)
#1525 := [refl]: #1524
#1497 := [nnf-pos #1525]: #1496
#342 := [asserted]: #64
#1526 := [mp~ #342 #1497]: #64
#3646 := [mp #1526 #3645]: #3641
#7582 := (not #3641)
#10454 := (or #7582 #11459)
#4057 := (= f1 f1)
#11449 := (if #11448 #4057 #5310)
#11450 := (iff #11447 #11449)
#10491 := (or #7582 #11450)
#10475 := (iff #10491 #10454)
#10478 := (iff #10454 #10454)
#10524 := [rewrite]: #10478
#11460 := (iff #11450 #11459)
#11457 := (iff #11449 #11454)
#1 := true
#11451 := (if #11448 true #5310)
#11455 := (iff #11451 #11454)
#11456 := [rewrite]: #11455
#11452 := (iff #11449 #11451)
#4059 := (iff #4057 true)
#4060 := [rewrite]: #4059
#11453 := [monotonicity #4060]: #11452
#11458 := [trans #11453 #11456]: #11457
#11461 := [monotonicity #11458]: #11460
#10477 := [monotonicity #11461]: #10475
#10530 := [trans #10477 #10524]: #10475
#10476 := [quant-inst #115 #181 #3 #2034]: #10491
#10523 := [mp #10476 #10530]: #10454
#13463 := [unit-resolution #10523 #3646]: #11459
#10516 := (not #11459)
#13559 := (or #10516 #11447)
decl f6 :: (-> S5 S2 S4)
decl f7 :: S5
#13 := f7
#91 := (f6 f7 #11)
#3693 := (pattern #91)
#212 := (f11 f29 #11)
#3854 := (pattern #212)
decl f30 :: (-> S2 Int)
#202 := (f30 #11)
#3829 := (pattern #202)
#7 := 0::Int
decl f4 :: (-> S3 Int)
decl f5 :: (-> S4 S2 S3)
#2047 := (f5 #91 ?v0!20)
#2048 := (f4 #2047)
#2037 := (f30 ?v0!20)
#923 := -1::Int
#2038 := (* -1::Int #2037)
#2383 := (+ #2038 #2048)
#2384 := (+ #202 #2383)
#2387 := (= #2384 0::Int)
#2941 := (not #2387)
#213 := (= #212 f1)
#220 := (not #213)
#2044 := (+ #202 #2038)
#2045 := (>= #2044 0::Int)
#2942 := (or #2045 #220 #2941)
#3888 := (forall (vars (?v1 S2)) (:pat #3829 #3854 #3693) #2942)
#3893 := (not #3888)
decl f3 :: Int
#8 := f3
#2039 := (+ f3 #2038)
#2040 := (<= #2039 0::Int)
decl f16 :: S2
#65 := f16
#2035 := (= ?v0!20 f16)
#10 := (:var 1 S2)
#92 := (f5 #91 #10)
#3684 := (pattern #92)
#224 := (f30 #10)
#1186 := (* -1::Int #224)
#1187 := (+ #202 #1186)
#93 := (f4 #92)
#1207 := (+ #93 #1187)
#1205 := (>= #1207 0::Int)
#938 := (* -1::Int #93)
#939 := (+ f3 #938)
#940 := (<= #939 0::Int)
#2933 := (or #220 #940 #1205)
#3880 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3684) #2933)
#3885 := (not #3880)
#3896 := (or #3885 #2035 #2040 #3893)
#3899 := (not #3896)
decl ?v0!19 :: S2
#2003 := ?v0!19
#2016 := (f30 ?v0!19)
#2017 := (* -1::Int #2016)
decl ?v1!18 :: S2
#2002 := ?v1!18
#2015 := (f30 ?v1!18)
#2018 := (+ #2015 #2017)
#2006 := (f6 f7 ?v1!18)
#2007 := (f5 #2006 ?v0!19)
#2008 := (f4 #2007)
#2019 := (+ #2008 #2018)
#2020 := (>= #2019 0::Int)
#2009 := (* -1::Int #2008)
#2010 := (+ f3 #2009)
#2011 := (<= #2010 0::Int)
#2004 := (f11 f29 ?v1!18)
#2005 := (= #2004 f1)
#2896 := (not #2005)
#2911 := (or #2896 #2011 #2020)
#2916 := (not #2911)
#13632 := [hypothesis]: #2916
#2012 := (not #2011)
#3530 := (or #2911 #2012)
#3533 := [def-axiom]: #3530
#10274 := [unit-resolution #3533 #13632]: #2012
#10298 := (or #2911 #2011)
decl f19 :: (-> S11 S2 Int)
decl f20 :: S11
#109 := f20
#112 := (f19 f20 #11)
#3716 := (pattern #112)
#207 := (= #202 #112)
#560 := (or #220 #207)
#3855 := (forall (vars (?v0 S2)) (:pat #3854 #3829 #3716) #560)
#3902 := (or #2916 #3899)
#3905 := (not #3902)
#3871 := (pattern #202 #224)
#1185 := (>= #1187 0::Int)
#221 := (f11 f29 #10)
#222 := (= #221 f1)
#2873 := (not #222)
#2888 := (or #213 #2873 #1185)
#3872 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3871) #2888)
#3877 := (not #3872)
#3908 := (or #3877 #3905)
#3911 := (not #3908)
decl ?v0!17 :: S2
#1976 := ?v0!17
#1985 := (f30 ?v0!17)
#1986 := (* -1::Int #1985)
decl ?v1!16 :: S2
#1975 := ?v1!16
#1984 := (f30 ?v1!16)
#1987 := (+ #1984 #1986)
#1988 := (>= #1987 0::Int)
#1980 := (f11 f29 ?v0!17)
#1981 := (= #1980 f1)
#2850 := (not #1981)
#1977 := (f11 f29 ?v1!16)
#1978 := (= #1977 f1)
#2865 := (or #1978 #2850 #1988)
#2870 := (not #2865)
#3914 := (or #2870 #3911)
#3917 := (not #3914)
#1176 := (>= #202 0::Int)
#3863 := (forall (vars (?v0 S2)) (:pat #3829) #1176)
#3868 := (not #3863)
#3920 := (or #3868 #3917)
#3923 := (not #3920)
decl ?v0!15 :: S2
#1960 := ?v0!15
#1961 := (f30 ?v0!15)
#1962 := (>= #1961 0::Int)
#1963 := (not #1962)
#3926 := (or #1963 #3923)
#3929 := (not #3926)
#216 := (f30 f16)
#217 := (= #216 0::Int)
#661 := (not #217)
#3932 := (or #661 #3929)
#3935 := (not #3932)
#3938 := (or #661 #3935)
#3941 := (not #3938)
#3860 := (not #3855)
#3944 := (or #3860 #3941)
#3947 := (not #3944)
decl ?v0!14 :: S2
#1935 := ?v0!14
#1940 := (f19 f20 ?v0!14)
#1939 := (f30 ?v0!14)
#1941 := (= #1939 #1940)
#1936 := (f11 f29 ?v0!14)
#1937 := (= #1936 f1)
#1938 := (not #1937)
#1942 := (or #1938 #1941)
#195 := (f6 f7 f28)
#196 := (f5 #195 #11)
#3828 := (pattern #196)
#197 := (f4 #196)
#1140 := (* -1::Int #197)
#185 := (f19 f20 f28)
#1146 := (* -1::Int #185)
#1147 := (+ #1146 #1140)
#1148 := (+ #112 #1147)
#1149 := (<= #1148 0::Int)
#1141 := (+ f3 #1140)
#1142 := (<= #1141 0::Int)
#2822 := (or #1142 #1149)
#2823 := (not #2822)
#2844 := (or #2823 #207)
#3838 := (forall (vars (?v0 S2)) (:pat #3828 #3716 #3829) #2844)
#1943 := (not #1942)
#3950 := (or #1943 #3947)
#3953 := (not #3950)
#1166 := (* -1::Int #202)
#1167 := (+ #112 #1166)
#1165 := (>= #1167 0::Int)
#3846 := (forall (vars (?v0 S2)) (:pat #3716 #3829) #1165)
#3851 := (not #3846)
#3956 := (or #3851 #3953)
#3959 := (not #3956)
decl ?v0!13 :: S2
#1917 := ?v0!13
#1919 := (f30 ?v0!13)
#1920 := (* -1::Int #1919)
#1918 := (f19 f20 ?v0!13)
#1921 := (+ #1918 #1920)
#1922 := (>= #1921 0::Int)
#1923 := (not #1922)
#3962 := (or #1923 #3959)
#3965 := (not #3962)
#3843 := (not #3838)
#1296 := (+ #197 #1166)
#1297 := (+ #185 #1296)
#1294 := (= #1297 0::Int)
#2836 := (or #1142 #1149 #1294)
#3830 := (forall (vars (?v0 S2)) (:pat #3828 #3716 #3829) #2836)
#3835 := (not #3830)
#194 := (= f29 #193)
#715 := (not #194)
#116 := (f11 f21 #11)
#3750 := (pattern #116)
#1309 := (+ #112 #1146)
#1308 := (>= #1309 0::Int)
#117 := (= #116 f1)
#1312 := (or #117 #1308)
#3820 := (forall (vars (?v0 S2)) (:pat #3750 #3716) #1312)
#3825 := (not #3820)
#1321 := (+ f3 #1146)
#1322 := (<= #1321 0::Int)
#182 := (f11 f21 f28)
#183 := (= #182 f1)
decl ?v0!12 :: S2
#1872 := ?v0!12
#1876 := (f19 f20 ?v0!12)
#1877 := (* -1::Int #1876)
#1878 := (+ f3 #1877)
#1879 := (<= #1878 0::Int)
#1873 := (f11 f21 ?v0!12)
#1874 := (= #1873 f1)
#3968 := (or #1874 #1879 #183 #1322 #3825 #715 #3835 #3843 #3965)
#3971 := (not #3968)
decl f25 :: S11
#148 := f25
#168 := (f19 f25 f16)
#169 := (= #168 0::Int)
#156 := (f19 f25 #10)
#1060 := (* -1::Int #156)
#153 := (f19 f25 #11)
#1061 := (+ #153 #1060)
#1067 := (+ #93 #1061)
#1090 := (>= #1067 0::Int)
#1047 := (* -1::Int #153)
#1048 := (+ f3 #1047)
#1049 := (<= #1048 0::Int)
#2776 := (or #1049 #940 #1090)
#3782 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3684) #2776)
#3787 := (not #3782)
#3790 := (or #3787 #169)
#3793 := (not #3790)
decl ?v0!11 :: S2
#1816 := ?v0!11
#1831 := (f19 f25 ?v0!11)
#1832 := (* -1::Int #1831)
decl ?v1!10 :: S2
#1815 := ?v1!10
#1822 := (f6 f7 ?v1!10)
#1823 := (f5 #1822 ?v0!11)
#1824 := (f4 #1823)
#2352 := (+ #1824 #1832)
#1817 := (f19 f25 ?v1!10)
#2353 := (+ #1817 #2352)
#2356 := (>= #2353 0::Int)
#1825 := (* -1::Int #1824)
#1826 := (+ f3 #1825)
#1827 := (<= #1826 0::Int)
#1818 := (* -1::Int #1817)
#1819 := (+ f3 #1818)
#1820 := (<= #1819 0::Int)
#2754 := (or #1820 #1827 #2356)
#2759 := (not #2754)
#3796 := (or #2759 #3793)
#3799 := (not #3796)
#3759 := (pattern #153)
decl ?v1!9 :: (-> S2 S2)
#1791 := (?v1!9 #11)
#1796 := (f6 f7 #1791)
#1797 := (f5 #1796 #11)
#1798 := (f4 #1797)
#2335 := (* -1::Int #1798)
#1792 := (f19 f25 #1791)
#2318 := (* -1::Int #1792)
#2336 := (+ #2318 #2335)
#2337 := (+ #153 #2336)
#2338 := (= #2337 0::Int)
#2724 := (not #2338)
#2319 := (+ #153 #2318)
#2320 := (<= #2319 0::Int)
#2725 := (or #2320 #2724)
#2726 := (not #2725)
#66 := (= #11 f16)
#2732 := (or #66 #1049 #2726)
#3774 := (forall (vars (?v0 S2)) (:pat #3759) #2732)
#3779 := (not #3774)
#3802 := (or #3779 #3799)
#3805 := (not #3802)
decl ?v0!8 :: S2
#1751 := ?v0!8
#1764 := (f5 #91 ?v0!8)
#1765 := (f4 #1764)
#1754 := (f19 f25 ?v0!8)
#1755 := (* -1::Int #1754)
#2288 := (+ #1755 #1765)
#2289 := (+ #153 #2288)
#2292 := (= #2289 0::Int)
#2688 := (not #2292)
#1761 := (+ #153 #1755)
#1762 := (>= #1761 0::Int)
#2689 := (or #1762 #2688)
#3760 := (forall (vars (?v1 S2)) (:pat #3759 #3693) #2689)
#3765 := (not #3760)
#1756 := (+ f3 #1755)
#1757 := (<= #1756 0::Int)
#1752 := (= ?v0!8 f16)
#3768 := (or #1752 #1757 #3765)
#3771 := (not #3768)
#3808 := (or #3771 #3805)
#3811 := (not #3808)
decl f27 :: S11
#151 := f27
decl f26 :: S11
#150 := f26
#152 := (= f26 f27)
#494 := (not #152)
#149 := (= f25 f20)
#503 := (not #149)
decl f24 :: S2
#146 := f24
decl f23 :: S2
#145 := f23
#147 := (= f23 f24)
#512 := (not #147)
decl f22 :: S7
#143 := f22
#144 := (= f22 f21)
#521 := (not #144)
#1002 := (* -1::Int #112)
#1003 := (+ f3 #1002)
#1004 := (<= #1003 0::Int)
#2674 := (or #117 #1004)
#3751 := (forall (vars (?v0 S2)) (:pat #3750 #3716) #2674)
#3756 := (not #3751)
#3814 := (or #3756 #521 #512 #503 #494 #3811)
#110 := (f19 f20 f16)
#111 := (= #110 0::Int)
#3817 := (not #3814)
#3974 := (or #3817 #3971)
#3977 := (not #3974)
decl ?v1!7 :: (-> S2 S2)
#1707 := (?v1!7 #11)
#1714 := (f6 f7 #1707)
#1715 := (f5 #1714 #11)
#1716 := (f4 #1715)
#2261 := (* -1::Int #1716)
#1708 := (f19 f20 #1707)
#2244 := (* -1::Int #1708)
#2262 := (+ #2244 #2261)
#2263 := (+ #112 #2262)
#2264 := (= #2263 0::Int)
#2658 := (not #2264)
#1712 := (f11 f21 #1707)
#1713 := (= #1712 f1)
#2657 := (not #1713)
#2245 := (+ #112 #2244)
#2246 := (<= #2245 0::Int)
#2659 := (or #2246 #2657 #2658)
#2660 := (not #2659)
#2666 := (or #66 #1004 #2660)
#3742 := (forall (vars (?v0 S2)) (:pat #3716) #2666)
#3747 := (not #3742)
#122 := (f19 f20 #10)
#1016 := (* -1::Int #122)
#1017 := (+ #112 #1016)
#1018 := (+ #93 #1017)
#1371 := (>= #1018 0::Int)
#118 := (not #117)
#2638 := (or #118 #940 #1371)
#3734 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3684) #2638)
#3739 := (not #3734)
#119 := (f11 f21 #10)
#3725 := (pattern #116 #119)
#1020 := (>= #1017 0::Int)
#120 := (= #119 f1)
#2601 := (not #120)
#2616 := (or #117 #2601 #1020)
#3726 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3725) #2616)
#3731 := (not #3726)
#1394 := (>= #112 0::Int)
#3717 := (forall (vars (?v0 S2)) (:pat #3716) #1394)
#3722 := (not #3717)
#804 := (not #111)
decl f17 :: (-> S2 Int)
#67 := (f17 #11)
#3647 := (pattern #67)
decl ?v1!6 :: (-> S2 S2)
#1654 := (?v1!6 #11)
#1661 := (f6 f7 #1654)
#1662 := (f5 #1661 #11)
#1663 := (f4 #1662)
#2219 := (* -1::Int #1663)
#1655 := (f17 #1654)
#2202 := (* -1::Int #1655)
#2220 := (+ #2202 #2219)
#2221 := (+ #67 #2220)
#2222 := (= #2221 0::Int)
#2585 := (not #2222)
decl f18 :: S7
#75 := f18
#1659 := (f11 f18 #1654)
#1660 := (= #1659 f1)
#2584 := (not #1660)
#2203 := (+ #67 #2202)
#2204 := (<= #2203 0::Int)
#2586 := (or #2204 #2584 #2585)
#2587 := (not #2586)
#964 := (* -1::Int #67)
#965 := (+ f3 #964)
#966 := (<= #965 0::Int)
#2593 := (or #66 #966 #2587)
#3708 := (forall (vars (?v0 S2)) (:pat #3647) #2593)
#3713 := (not #3708)
#3980 := (or #3713 #804 #3722 #3731 #3739 #3747 #3977)
#3983 := (not #3980)
#76 := (f11 f18 #11)
#3660 := (pattern #76)
decl ?v0!5 :: S2
#1613 := ?v0!5
#1626 := (f5 #91 ?v0!5)
#1627 := (f4 #1626)
#1616 := (f17 ?v0!5)
#1617 := (* -1::Int #1616)
#1628 := (+ #1617 #1627)
#1629 := (+ #67 #1628)
#1630 := (= #1629 0::Int)
#2548 := (not #1630)
#77 := (= #76 f1)
#78 := (not #77)
#1623 := (+ #67 #1617)
#1624 := (>= #1623 0::Int)
#2549 := (or #1624 #78 #2548)
#3694 := (forall (vars (?v1 S2)) (:pat #3647 #3660 #3693) #2549)
#3699 := (not #3694)
#1618 := (+ f3 #1617)
#1619 := (<= #1618 0::Int)
#1614 := (= ?v0!5 f16)
#3702 := (or #1614 #1619 #3699)
#6895 := (= f3 #1616)
#6849 := (= #1616 f3)
#6924 := (iff #6849 #6895)
#6925 := (iff #6895 #6849)
#6926 := [commutativity]: #6925
#6927 := [symm #6926]: #6924
#1615 := (not #1614)
#3705 := (not #3702)
#6853 := [hypothesis]: #3705
#3262 := (or #3702 #1615)
#3263 := [def-axiom]: #3262
#6907 := [unit-resolution #3263 #6853]: #1615
#72 := (= #67 f3)
#350 := (or #66 #72)
#3654 := (forall (vars (?v0 S2)) (:pat #3647) #350)
#353 := (forall (vars (?v0 S2)) #350)
#3657 := (iff #353 #3654)
#3655 := (iff #350 #350)
#3656 := [refl]: #3655
#3658 := [quant-intro #3656]: #3657
#1500 := (~ #353 #353)
#1530 := (~ #350 #350)
#1531 := [refl]: #1530
#1501 := [nnf-pos #1531]: #1500
#1229 := (= #1207 0::Int)
#1232 := (not #1185)
#1241 := (and #1232 #213 #1229)
#1246 := (exists (vars (?v1 S2)) #1241)
#1218 := (+ f3 #1166)
#1219 := (<= #1218 0::Int)
#1220 := (not #1219)
#71 := (not #66)
#1223 := (and #71 #1220)
#1226 := (not #1223)
#1249 := (or #1226 #1246)
#1252 := (forall (vars (?v0 S2)) #1249)
#941 := (not #940)
#1199 := (and #213 #941)
#1202 := (not #1199)
#1209 := (or #1202 #1205)
#1212 := (forall (vars (?v0 S2) (?v1 S2)) #1209)
#1215 := (not #1212)
#1255 := (or #1215 #1252)
#1258 := (and #1212 #1255)
#223 := (and #220 #222)
#566 := (not #223)
#1190 := (or #566 #1185)
#1193 := (forall (vars (?v0 S2) (?v1 S2)) #1190)
#1196 := (not #1193)
#1261 := (or #1196 #1258)
#1264 := (and #1193 #1261)
#1179 := (forall (vars (?v0 S2)) #1176)
#1182 := (not #1179)
#1267 := (or #1182 #1264)
#1270 := (and #1179 #1267)
#1273 := (or #661 #1270)
#1276 := (and #217 #1273)
#563 := (forall (vars (?v0 S2)) #560)
#673 := (not #563)
#1279 := (or #673 #1276)
#1282 := (and #563 #1279)
#1170 := (forall (vars (?v0 S2)) #1165)
#1173 := (not #1170)
#1285 := (or #1173 #1282)
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#1143 := (not #1142)
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#1305 := (not #1302)
#1315 := (forall (vars (?v0 S2)) #1312)
#1318 := (not #1315)
#1005 := (not #1004)
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#1333 := (not #1117)
#1357 := (or #1333 #183 #1322 #1318 #715 #1305 #1162 #1288)
#1050 := (not #1049)
#1084 := (and #1050 #941)
#1087 := (not #1084)
#1093 := (or #1087 #1090)
#1096 := (forall (vars (?v0 S2) (?v1 S2)) #1093)
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#1065 := (= #1067 0::Int)
#1059 := (>= #1061 0::Int)
#1062 := (not #1059)
#1069 := (and #1062 #1065)
#1072 := (exists (vars (?v1 S2)) #1069)
#1053 := (and #71 #1050)
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#1075 := (or #1056 #1072)
#1078 := (forall (vars (?v0 S2)) #1075)
#1081 := (not #1078)
#1108 := (or #1081 #1105)
#1111 := (and #1078 #1108)
#1135 := (or #1117 #521 #512 #503 #494 #1111)
#1362 := (and #1135 #1357)
#1014 := (= #1018 0::Int)
#1021 := (not #1020)
#1030 := (and #1021 #117 #1014)
#1035 := (exists (vars (?v1 S2)) #1030)
#1008 := (and #71 #1005)
#1011 := (not #1008)
#1038 := (or #1011 #1035)
#1041 := (forall (vars (?v0 S2)) #1038)
#1044 := (not #1041)
#1365 := (and #117 #941)
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#1374 := (or #1368 #1371)
#1377 := (forall (vars (?v0 S2) (?v1 S2)) #1374)
#1380 := (not #1377)
#121 := (and #118 #120)
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#1385 := (or #377 #1020)
#1388 := (forall (vars (?v0 S2) (?v1 S2)) #1385)
#1391 := (not #1388)
#1397 := (forall (vars (?v0 S2)) #1394)
#1400 := (not #1397)
#87 := (f17 #10)
#926 := (* -1::Int #87)
#953 := (+ #926 #93)
#954 := (+ #67 #953)
#976 := (= #954 0::Int)
#927 := (+ #67 #926)
#925 := (>= #927 0::Int)
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#988 := (and #979 #77 #976)
#993 := (exists (vars (?v1 S2)) #988)
#967 := (not #966)
#970 := (and #71 #967)
#973 := (not #970)
#996 := (or #973 #993)
#999 := (forall (vars (?v0 S2)) #996)
#1403 := (not #999)
#1424 := (or #1403 #804 #1400 #1391 #1380 #1044 #1362)
#1429 := (and #999 #1424)
#951 := (>= #954 0::Int)
#944 := (and #77 #941)
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#955 := (or #947 #951)
#958 := (forall (vars (?v0 S2) (?v1 S2)) #955)
#961 := (not #958)
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#1435 := (and #958 #1432)
#84 := (f11 f18 #10)
#85 := (= #84 f1)
#86 := (and #78 #85)
#356 := (not #86)
#929 := (or #356 #925)
#932 := (forall (vars (?v0 S2) (?v1 S2)) #929)
#935 := (not #932)
#1438 := (or #935 #1435)
#1441 := (and #932 #1438)
#916 := (>= #67 0::Int)
#917 := (forall (vars (?v0 S2)) #916)
#920 := (not #917)
#1444 := (or #920 #1441)
#1447 := (and #917 #1444)
#80 := (f17 f16)
#81 := (= #80 0::Int)
#868 := (not #81)
#1450 := (or #868 #1447)
#1453 := (and #81 #1450)
#79 := (forall (vars (?v0 S2)) #78)
#880 := (not #79)
#889 := (not #353)
#68 := (= #67 0::Int)
#344 := (or #71 #68)
#347 := (forall (vars (?v0 S2)) #344)
#898 := (not #347)
#1465 := (or #898 #889 #880 #1453)
#1470 := (not #1465)
#229 := (+ #202 #93)
#236 := (= #224 #229)
#237 := (and #213 #236)
#235 := (< #202 #224)
#238 := (and #235 #237)
#239 := (exists (vars (?v1 S2)) #238)
#233 := (< #202 f3)
#234 := (and #71 #233)
#240 := (implies #234 #239)
#241 := (forall (vars (?v0 S2)) #240)
#242 := (and #241 true)
#230 := (<= #224 #229)
#94 := (< #93 f3)
#228 := (and #213 #94)
#231 := (implies #228 #230)
#232 := (forall (vars (?v0 S2) (?v1 S2)) #231)
#243 := (implies #232 #242)
#244 := (and #232 #243)
#225 := (<= #224 #202)
#226 := (implies #223 #225)
#227 := (forall (vars (?v0 S2) (?v1 S2)) #226)
#245 := (implies #227 #244)
#246 := (and #227 #245)
#218 := (<= 0::Int #202)
#219 := (forall (vars (?v0 S2)) #218)
#247 := (implies #219 #246)
#248 := (and #219 #247)
#249 := (implies #217 #248)
#250 := (and #217 #249)
#214 := (implies #213 #207)
#215 := (forall (vars (?v0 S2)) #214)
#251 := (implies #215 #250)
#252 := (and #215 #251)
#210 := (<= #202 #112)
#211 := (forall (vars (?v0 S2)) #210)
#253 := (implies #211 #252)
#254 := (and #211 #253)
#199 := (+ #185 #197)
#200 := (< #199 #112)
#198 := (< #197 f3)
#201 := (and #198 #200)
#206 := (not #201)
#208 := (implies #206 #207)
#209 := (forall (vars (?v0 S2)) #208)
#255 := (implies #209 #254)
#203 := (= #202 #199)
#204 := (implies #201 #203)
#205 := (forall (vars (?v0 S2)) #204)
#256 := (implies #205 #255)
#257 := (implies #194 #256)
#187 := (<= #185 #112)
#188 := (implies #118 #187)
#189 := (forall (vars (?v0 S2)) #188)
#258 := (implies #189 #257)
#186 := (< #185 f3)
#259 := (implies #186 #258)
#184 := (not #183)
#260 := (implies #184 #259)
#131 := (< #112 f3)
#140 := (and #118 #131)
#141 := (exists (vars (?v0 S2)) #140)
#261 := (implies #141 #260)
#262 := (implies true #261)
#170 := (and #169 true)
#158 := (+ #153 #93)
#165 := (<= #156 #158)
#154 := (< #153 f3)
#164 := (and #154 #94)
#166 := (implies #164 #165)
#167 := (forall (vars (?v0 S2) (?v1 S2)) #166)
#171 := (implies #167 #170)
#172 := (and #167 #171)
#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)
#173 := (implies #163 #172)
#174 := (and #163 #173)
#175 := (implies #152 #174)
#176 := (implies #149 #175)
#177 := (implies #147 #176)
#178 := (implies #144 #177)
#142 := (not #141)
#179 := (implies #142 #178)
#180 := (implies true #179)
#263 := (and #180 #262)
#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)
#264 := (implies #139 #263)
#128 := (<= #122 #127)
#126 := (and #117 #94)
#129 := (implies #126 #128)
#130 := (forall (vars (?v0 S2) (?v1 S2)) #129)
#265 := (implies #130 #264)
#123 := (<= #122 #112)
#124 := (implies #121 #123)
#125 := (forall (vars (?v0 S2) (?v1 S2)) #124)
#266 := (implies #125 #265)
#113 := (<= 0::Int #112)
#114 := (forall (vars (?v0 S2)) #113)
#267 := (implies #114 #266)
#268 := (implies #111 #267)
#269 := (implies true #268)
#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 f3)
#101 := (and #71 #100)
#107 := (implies #101 #106)
#108 := (forall (vars (?v0 S2)) #107)
#270 := (implies #108 #269)
#271 := (and #108 #270)
#97 := (<= #87 #96)
#95 := (and #77 #94)
#98 := (implies #95 #97)
#99 := (forall (vars (?v0 S2) (?v1 S2)) #98)
#272 := (implies #99 #271)
#273 := (and #99 #272)
#88 := (<= #87 #67)
#89 := (implies #86 #88)
#90 := (forall (vars (?v0 S2) (?v1 S2)) #89)
#274 := (implies #90 #273)
#275 := (and #90 #274)
#82 := (<= 0::Int #67)
#83 := (forall (vars (?v0 S2)) #82)
#276 := (implies #83 #275)
#277 := (and #83 #276)
#278 := (implies #81 #277)
#279 := (and #81 #278)
#280 := (implies #79 #279)
#73 := (implies #71 #72)
#74 := (forall (vars (?v0 S2)) #73)
#281 := (implies #74 #280)
#69 := (implies #66 #68)
#70 := (forall (vars (?v0 S2)) #69)
#282 := (implies #70 #281)
#283 := (implies true #282)
#284 := (not #283)
#1473 := (iff #284 #1470)
#573 := (+ #93 #202)
#591 := (= #224 #573)
#594 := (and #213 #591)
#597 := (and #235 #594)
#600 := (exists (vars (?v1 S2)) #597)
#606 := (not #234)
#607 := (or #606 #600)
#612 := (forall (vars (?v0 S2)) #607)
#576 := (<= #224 #573)
#582 := (not #228)
#583 := (or #582 #576)
#588 := (forall (vars (?v0 S2) (?v1 S2)) #583)
#625 := (not #588)
#626 := (or #625 #612)
#631 := (and #588 #626)
#567 := (or #566 #225)
#570 := (forall (vars (?v0 S2) (?v1 S2)) #567)
#637 := (not #570)
#638 := (or #637 #631)
#643 := (and #570 #638)
#649 := (not #219)
#650 := (or #649 #643)
#655 := (and #219 #650)
#662 := (or #661 #655)
#667 := (and #217 #662)
#674 := (or #673 #667)
#679 := (and #563 #674)
#685 := (not #211)
#686 := (or #685 #679)
#691 := (and #211 #686)
#554 := (or #201 #207)
#557 := (forall (vars (?v0 S2)) #554)
#697 := (not #557)
#698 := (or #697 #691)
#548 := (or #206 #203)
#551 := (forall (vars (?v0 S2)) #548)
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#707 := (or #706 #698)
#716 := (or #715 #707)
#542 := (or #117 #187)
#545 := (forall (vars (?v0 S2)) #542)
#724 := (not #545)
#725 := (or #724 #716)
#733 := (not #186)
#734 := (or #733 #725)
#742 := (or #183 #734)
#750 := (or #142 #742)
#426 := (+ #93 #153)
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#457 := (or #456 #450)
#462 := (forall (vars (?v0 S2) (?v1 S2)) #457)
#470 := (not #462)
#471 := (or #470 #169)
#476 := (and #462 #471)
#429 := (= #156 #426)
#432 := (and #157 #429)
#435 := (exists (vars (?v1 S2)) #432)
#441 := (not #155)
#442 := (or #441 #435)
#447 := (forall (vars (?v0 S2)) #442)
#482 := (not #447)
#483 := (or #482 #476)
#488 := (and #447 #483)
#495 := (or #494 #488)
#504 := (or #503 #495)
#513 := (or #512 #504)
#522 := (or #521 #513)
#530 := (or #141 #522)
#762 := (and #530 #750)
#384 := (+ #93 #112)
#402 := (= #122 #384)
#405 := (and #117 #402)
#408 := (and #133 #405)
#411 := (exists (vars (?v1 S2)) #408)
#417 := (not #132)
#418 := (or #417 #411)
#423 := (forall (vars (?v0 S2)) #418)
#768 := (not #423)
#769 := (or #768 #762)
#387 := (<= #122 #384)
#393 := (not #126)
#394 := (or #393 #387)
#399 := (forall (vars (?v0 S2) (?v1 S2)) #394)
#777 := (not #399)
#778 := (or #777 #769)
#378 := (or #377 #123)
#381 := (forall (vars (?v0 S2) (?v1 S2)) #378)
#786 := (not #381)
#787 := (or #786 #778)
#795 := (not #114)
#796 := (or #795 #787)
#805 := (or #804 #796)
#370 := (not #101)
#371 := (or #370 #106)
#374 := (forall (vars (?v0 S2)) #371)
#820 := (not #374)
#821 := (or #820 #805)
#826 := (and #374 #821)
#363 := (not #95)
#364 := (or #363 #97)
#367 := (forall (vars (?v0 S2) (?v1 S2)) #364)
#832 := (not #367)
#833 := (or #832 #826)
#838 := (and #367 #833)
#357 := (or #356 #88)
#360 := (forall (vars (?v0 S2) (?v1 S2)) #357)
#844 := (not #360)
#845 := (or #844 #838)
#850 := (and #360 #845)
#856 := (not #83)
#857 := (or #856 #850)
#862 := (and #83 #857)
#869 := (or #868 #862)
#874 := (and #81 #869)
#881 := (or #880 #874)
#890 := (or #889 #881)
#899 := (or #898 #890)
#911 := (not #899)
#1471 := (iff #911 #1470)
#1468 := (iff #899 #1465)
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#1459 := (or #889 #1456)
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#1467 := [rewrite]: #1466
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#1460 := (iff #890 #1459)
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#1433 := (iff #833 #1432)
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#1406 := (or #1044 #1362)
#1409 := (or #1380 #1406)
#1412 := (or #1391 #1409)
#1415 := (or #1400 #1412)
#1418 := (or #804 #1415)
#1421 := (or #1403 #1418)
#1425 := (iff #1421 #1424)
#1426 := [rewrite]: #1425
#1422 := (iff #821 #1421)
#1419 := (iff #805 #1418)
#1416 := (iff #796 #1415)
#1413 := (iff #787 #1412)
#1410 := (iff #778 #1409)
#1407 := (iff #769 #1406)
#1363 := (iff #762 #1362)
#1360 := (iff #750 #1357)
#1336 := (or #1162 #1288)
#1339 := (or #1305 #1336)
#1342 := (or #715 #1339)
#1345 := (or #1318 #1342)
#1348 := (or #1322 #1345)
#1351 := (or #183 #1348)
#1354 := (or #1333 #1351)
#1358 := (iff #1354 #1357)
#1359 := [rewrite]: #1358
#1355 := (iff #750 #1354)
#1352 := (iff #742 #1351)
#1349 := (iff #734 #1348)
#1346 := (iff #725 #1345)
#1343 := (iff #716 #1342)
#1340 := (iff #707 #1339)
#1337 := (iff #698 #1336)
#1289 := (iff #691 #1288)
#1286 := (iff #686 #1285)
#1283 := (iff #679 #1282)
#1280 := (iff #674 #1279)
#1277 := (iff #667 #1276)
#1274 := (iff #662 #1273)
#1271 := (iff #655 #1270)
#1268 := (iff #650 #1267)
#1265 := (iff #643 #1264)
#1262 := (iff #638 #1261)
#1259 := (iff #631 #1258)
#1256 := (iff #626 #1255)
#1253 := (iff #612 #1252)
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#1247 := (iff #600 #1246)
#1244 := (iff #597 #1241)
#1235 := (and #213 #1229)
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#1242 := (iff #1238 #1241)
#1243 := [rewrite]: #1242
#1239 := (iff #597 #1238)
#1236 := (iff #594 #1235)
#1230 := (iff #591 #1229)
#1231 := [rewrite]: #1230
#1237 := [monotonicity #1231]: #1236
#1233 := (iff #235 #1232)
#1234 := [rewrite]: #1233
#1240 := [monotonicity #1234 #1237]: #1239
#1245 := [trans #1240 #1243]: #1244
#1248 := [quant-intro #1245]: #1247
#1227 := (iff #606 #1226)
#1224 := (iff #234 #1223)
#1221 := (iff #233 #1220)
#1222 := [rewrite]: #1221
#1225 := [monotonicity #1222]: #1224
#1228 := [monotonicity #1225]: #1227
#1251 := [monotonicity #1228 #1248]: #1250
#1254 := [quant-intro #1251]: #1253
#1216 := (iff #625 #1215)
#1213 := (iff #588 #1212)
#1210 := (iff #583 #1209)
#1206 := (iff #576 #1205)
#1208 := [rewrite]: #1206
#1203 := (iff #582 #1202)
#1200 := (iff #228 #1199)
#942 := (iff #94 #941)
#943 := [rewrite]: #942
#1201 := [monotonicity #943]: #1200
#1204 := [monotonicity #1201]: #1203
#1211 := [monotonicity #1204 #1208]: #1210
#1214 := [quant-intro #1211]: #1213
#1217 := [monotonicity #1214]: #1216
#1257 := [monotonicity #1217 #1254]: #1256
#1260 := [monotonicity #1214 #1257]: #1259
#1197 := (iff #637 #1196)
#1194 := (iff #570 #1193)
#1191 := (iff #567 #1190)
#1188 := (iff #225 #1185)
#1189 := [rewrite]: #1188
#1192 := [monotonicity #1189]: #1191
#1195 := [quant-intro #1192]: #1194
#1198 := [monotonicity #1195]: #1197
#1263 := [monotonicity #1198 #1260]: #1262
#1266 := [monotonicity #1195 #1263]: #1265
#1183 := (iff #649 #1182)
#1180 := (iff #219 #1179)
#1177 := (iff #218 #1176)
#1178 := [rewrite]: #1177
#1181 := [quant-intro #1178]: #1180
#1184 := [monotonicity #1181]: #1183
#1269 := [monotonicity #1184 #1266]: #1268
#1272 := [monotonicity #1181 #1269]: #1271
#1275 := [monotonicity #1272]: #1274
#1278 := [monotonicity #1275]: #1277
#1281 := [monotonicity #1278]: #1280
#1284 := [monotonicity #1281]: #1283
#1174 := (iff #685 #1173)
#1171 := (iff #211 #1170)
#1168 := (iff #210 #1165)
#1169 := [rewrite]: #1168
#1172 := [quant-intro #1169]: #1171
#1175 := [monotonicity #1172]: #1174
#1287 := [monotonicity #1175 #1284]: #1286
#1290 := [monotonicity #1172 #1287]: #1289
#1163 := (iff #697 #1162)
#1160 := (iff #557 #1159)
#1157 := (iff #554 #1156)
#1154 := (iff #201 #1153)
#1151 := (iff #200 #1150)
#1152 := [rewrite]: #1151
#1144 := (iff #198 #1143)
#1145 := [rewrite]: #1144
#1155 := [monotonicity #1145 #1152]: #1154
#1158 := [monotonicity #1155]: #1157
#1161 := [quant-intro #1158]: #1160
#1164 := [monotonicity #1161]: #1163
#1338 := [monotonicity #1164 #1290]: #1337
#1306 := (iff #706 #1305)
#1303 := (iff #551 #1302)
#1300 := (iff #548 #1299)
#1295 := (iff #203 #1294)
#1298 := [rewrite]: #1295
#1292 := (iff #206 #1291)
#1293 := [monotonicity #1155]: #1292
#1301 := [monotonicity #1293 #1298]: #1300
#1304 := [quant-intro #1301]: #1303
#1307 := [monotonicity #1304]: #1306
#1341 := [monotonicity #1307 #1338]: #1340
#1344 := [monotonicity #1341]: #1343
#1319 := (iff #724 #1318)
#1316 := (iff #545 #1315)
#1313 := (iff #542 #1312)
#1310 := (iff #187 #1308)
#1311 := [rewrite]: #1310
#1314 := [monotonicity #1311]: #1313
#1317 := [quant-intro #1314]: #1316
#1320 := [monotonicity #1317]: #1319
#1347 := [monotonicity #1320 #1344]: #1346
#1331 := (iff #733 #1322)
#1323 := (not #1322)
#1326 := (not #1323)
#1329 := (iff #1326 #1322)
#1330 := [rewrite]: #1329
#1327 := (iff #733 #1326)
#1324 := (iff #186 #1323)
#1325 := [rewrite]: #1324
#1328 := [monotonicity #1325]: #1327
#1332 := [trans #1328 #1330]: #1331
#1350 := [monotonicity #1332 #1347]: #1349
#1353 := [monotonicity #1350]: #1352
#1334 := (iff #142 #1333)
#1118 := (iff #141 #1117)
#1115 := (iff #140 #1114)
#1006 := (iff #131 #1005)
#1007 := [rewrite]: #1006
#1116 := [monotonicity #1007]: #1115
#1119 := [quant-intro #1116]: #1118
#1335 := [monotonicity #1119]: #1334
#1356 := [monotonicity #1335 #1353]: #1355
#1361 := [trans #1356 #1359]: #1360
#1138 := (iff #530 #1135)
#1120 := (or #494 #1111)
#1123 := (or #503 #1120)
#1126 := (or #512 #1123)
#1129 := (or #521 #1126)
#1132 := (or #1117 #1129)
#1136 := (iff #1132 #1135)
#1137 := [rewrite]: #1136
#1133 := (iff #530 #1132)
#1130 := (iff #522 #1129)
#1127 := (iff #513 #1126)
#1124 := (iff #504 #1123)
#1121 := (iff #495 #1120)
#1112 := (iff #488 #1111)
#1109 := (iff #483 #1108)
#1106 := (iff #476 #1105)
#1103 := (iff #471 #1102)
#1100 := (iff #470 #1099)
#1097 := (iff #462 #1096)
#1094 := (iff #457 #1093)
#1091 := (iff #450 #1090)
#1092 := [rewrite]: #1091
#1088 := (iff #456 #1087)
#1085 := (iff #164 #1084)
#1051 := (iff #154 #1050)
#1052 := [rewrite]: #1051
#1086 := [monotonicity #1052 #943]: #1085
#1089 := [monotonicity #1086]: #1088
#1095 := [monotonicity #1089 #1092]: #1094
#1098 := [quant-intro #1095]: #1097
#1101 := [monotonicity #1098]: #1100
#1104 := [monotonicity #1101]: #1103
#1107 := [monotonicity #1098 #1104]: #1106
#1082 := (iff #482 #1081)
#1079 := (iff #447 #1078)
#1076 := (iff #442 #1075)
#1073 := (iff #435 #1072)
#1070 := (iff #432 #1069)
#1066 := (iff #429 #1065)
#1068 := [rewrite]: #1066
#1063 := (iff #157 #1062)
#1064 := [rewrite]: #1063
#1071 := [monotonicity #1064 #1068]: #1070
#1074 := [quant-intro #1071]: #1073
#1057 := (iff #441 #1056)
#1054 := (iff #155 #1053)
#1055 := [monotonicity #1052]: #1054
#1058 := [monotonicity #1055]: #1057
#1077 := [monotonicity #1058 #1074]: #1076
#1080 := [quant-intro #1077]: #1079
#1083 := [monotonicity #1080]: #1082
#1110 := [monotonicity #1083 #1107]: #1109
#1113 := [monotonicity #1080 #1110]: #1112
#1122 := [monotonicity #1113]: #1121
#1125 := [monotonicity #1122]: #1124
#1128 := [monotonicity #1125]: #1127
#1131 := [monotonicity #1128]: #1130
#1134 := [monotonicity #1119 #1131]: #1133
#1139 := [trans #1134 #1137]: #1138
#1364 := [monotonicity #1139 #1361]: #1363
#1045 := (iff #768 #1044)
#1042 := (iff #423 #1041)
#1039 := (iff #418 #1038)
#1036 := (iff #411 #1035)
#1033 := (iff #408 #1030)
#1024 := (and #117 #1014)
#1027 := (and #1021 #1024)
#1031 := (iff #1027 #1030)
#1032 := [rewrite]: #1031
#1028 := (iff #408 #1027)
#1025 := (iff #405 #1024)
#1015 := (iff #402 #1014)
#1019 := [rewrite]: #1015
#1026 := [monotonicity #1019]: #1025
#1022 := (iff #133 #1021)
#1023 := [rewrite]: #1022
#1029 := [monotonicity #1023 #1026]: #1028
#1034 := [trans #1029 #1032]: #1033
#1037 := [quant-intro #1034]: #1036
#1012 := (iff #417 #1011)
#1009 := (iff #132 #1008)
#1010 := [monotonicity #1007]: #1009
#1013 := [monotonicity #1010]: #1012
#1040 := [monotonicity #1013 #1037]: #1039
#1043 := [quant-intro #1040]: #1042
#1046 := [monotonicity #1043]: #1045
#1408 := [monotonicity #1046 #1364]: #1407
#1381 := (iff #777 #1380)
#1378 := (iff #399 #1377)
#1375 := (iff #394 #1374)
#1372 := (iff #387 #1371)
#1373 := [rewrite]: #1372
#1369 := (iff #393 #1368)
#1366 := (iff #126 #1365)
#1367 := [monotonicity #943]: #1366
#1370 := [monotonicity #1367]: #1369
#1376 := [monotonicity #1370 #1373]: #1375
#1379 := [quant-intro #1376]: #1378
#1382 := [monotonicity #1379]: #1381
#1411 := [monotonicity #1382 #1408]: #1410
#1392 := (iff #786 #1391)
#1389 := (iff #381 #1388)
#1386 := (iff #378 #1385)
#1383 := (iff #123 #1020)
#1384 := [rewrite]: #1383
#1387 := [monotonicity #1384]: #1386
#1390 := [quant-intro #1387]: #1389
#1393 := [monotonicity #1390]: #1392
#1414 := [monotonicity #1393 #1411]: #1413
#1401 := (iff #795 #1400)
#1398 := (iff #114 #1397)
#1395 := (iff #113 #1394)
#1396 := [rewrite]: #1395
#1399 := [quant-intro #1396]: #1398
#1402 := [monotonicity #1399]: #1401
#1417 := [monotonicity #1402 #1414]: #1416
#1420 := [monotonicity #1417]: #1419
#1404 := (iff #820 #1403)
#1000 := (iff #374 #999)
#997 := (iff #371 #996)
#994 := (iff #106 #993)
#991 := (iff #105 #988)
#982 := (and #77 #976)
#985 := (and #979 #982)
#989 := (iff #985 #988)
#990 := [rewrite]: #989
#986 := (iff #105 #985)
#983 := (iff #104 #982)
#977 := (iff #103 #976)
#978 := [rewrite]: #977
#984 := [monotonicity #978]: #983
#980 := (iff #102 #979)
#981 := [rewrite]: #980
#987 := [monotonicity #981 #984]: #986
#992 := [trans #987 #990]: #991
#995 := [quant-intro #992]: #994
#974 := (iff #370 #973)
#971 := (iff #101 #970)
#968 := (iff #100 #967)
#969 := [rewrite]: #968
#972 := [monotonicity #969]: #971
#975 := [monotonicity #972]: #974
#998 := [monotonicity #975 #995]: #997
#1001 := [quant-intro #998]: #1000
#1405 := [monotonicity #1001]: #1404
#1423 := [monotonicity #1405 #1420]: #1422
#1428 := [trans #1423 #1426]: #1427
#1431 := [monotonicity #1001 #1428]: #1430
#962 := (iff #832 #961)
#959 := (iff #367 #958)
#956 := (iff #364 #955)
#950 := (iff #97 #951)
#952 := [rewrite]: #950
#948 := (iff #363 #947)
#945 := (iff #95 #944)
#946 := [monotonicity #943]: #945
#949 := [monotonicity #946]: #948
#957 := [monotonicity #949 #952]: #956
#960 := [quant-intro #957]: #959
#963 := [monotonicity #960]: #962
#1434 := [monotonicity #963 #1431]: #1433
#1437 := [monotonicity #960 #1434]: #1436
#936 := (iff #844 #935)
#933 := (iff #360 #932)
#930 := (iff #357 #929)
#924 := (iff #88 #925)
#928 := [rewrite]: #924
#931 := [monotonicity #928]: #930
#934 := [quant-intro #931]: #933
#937 := [monotonicity #934]: #936
#1440 := [monotonicity #937 #1437]: #1439
#1443 := [monotonicity #934 #1440]: #1442
#921 := (iff #856 #920)
#918 := (iff #83 #917)
#914 := (iff #82 #916)
#915 := [rewrite]: #914
#919 := [quant-intro #915]: #918
#922 := [monotonicity #919]: #921
#1446 := [monotonicity #922 #1443]: #1445
#1449 := [monotonicity #919 #1446]: #1448
#1452 := [monotonicity #1449]: #1451
#1455 := [monotonicity #1452]: #1454
#1458 := [monotonicity #1455]: #1457
#1461 := [monotonicity #1458]: #1460
#1464 := [monotonicity #1461]: #1463
#1469 := [trans #1464 #1467]: #1468
#1472 := [monotonicity #1469]: #1471
#912 := (iff #284 #911)
#909 := (iff #283 #899)
#904 := (implies true #899)
#907 := (iff #904 #899)
#908 := [rewrite]: #907
#905 := (iff #283 #904)
#902 := (iff #282 #899)
#895 := (implies #347 #890)
#900 := (iff #895 #899)
#901 := [rewrite]: #900
#896 := (iff #282 #895)
#893 := (iff #281 #890)
#886 := (implies #353 #881)
#891 := (iff #886 #890)
#892 := [rewrite]: #891
#887 := (iff #281 #886)
#884 := (iff #280 #881)
#877 := (implies #79 #874)
#882 := (iff #877 #881)
#883 := [rewrite]: #882
#878 := (iff #280 #877)
#875 := (iff #279 #874)
#872 := (iff #278 #869)
#865 := (implies #81 #862)
#870 := (iff #865 #869)
#871 := [rewrite]: #870
#866 := (iff #278 #865)
#863 := (iff #277 #862)
#860 := (iff #276 #857)
#853 := (implies #83 #850)
#858 := (iff #853 #857)
#859 := [rewrite]: #858
#854 := (iff #276 #853)
#851 := (iff #275 #850)
#848 := (iff #274 #845)
#841 := (implies #360 #838)
#846 := (iff #841 #845)
#847 := [rewrite]: #846
#842 := (iff #274 #841)
#839 := (iff #273 #838)
#836 := (iff #272 #833)
#829 := (implies #367 #826)
#834 := (iff #829 #833)
#835 := [rewrite]: #834
#830 := (iff #272 #829)
#827 := (iff #271 #826)
#824 := (iff #270 #821)
#817 := (implies #374 #805)
#822 := (iff #817 #821)
#823 := [rewrite]: #822
#818 := (iff #270 #817)
#815 := (iff #269 #805)
#810 := (implies true #805)
#813 := (iff #810 #805)
#814 := [rewrite]: #813
#811 := (iff #269 #810)
#808 := (iff #268 #805)
#801 := (implies #111 #796)
#806 := (iff #801 #805)
#807 := [rewrite]: #806
#802 := (iff #268 #801)
#799 := (iff #267 #796)
#792 := (implies #114 #787)
#797 := (iff #792 #796)
#798 := [rewrite]: #797
#793 := (iff #267 #792)
#790 := (iff #266 #787)
#783 := (implies #381 #778)
#788 := (iff #783 #787)
#789 := [rewrite]: #788
#784 := (iff #266 #783)
#781 := (iff #265 #778)
#774 := (implies #399 #769)
#779 := (iff #774 #778)
#780 := [rewrite]: #779
#775 := (iff #265 #774)
#772 := (iff #264 #769)
#765 := (implies #423 #762)
#770 := (iff #765 #769)
#771 := [rewrite]: #770
#766 := (iff #264 #765)
#763 := (iff #263 #762)
#760 := (iff #262 #750)
#755 := (implies true #750)
#758 := (iff #755 #750)
#759 := [rewrite]: #758
#756 := (iff #262 #755)
#753 := (iff #261 #750)
#747 := (implies #141 #742)
#751 := (iff #747 #750)
#752 := [rewrite]: #751
#748 := (iff #261 #747)
#745 := (iff #260 #742)
#739 := (implies #184 #734)
#743 := (iff #739 #742)
#744 := [rewrite]: #743
#740 := (iff #260 #739)
#737 := (iff #259 #734)
#730 := (implies #186 #725)
#735 := (iff #730 #734)
#736 := [rewrite]: #735
#731 := (iff #259 #730)
#728 := (iff #258 #725)
#721 := (implies #545 #716)
#726 := (iff #721 #725)
#727 := [rewrite]: #726
#722 := (iff #258 #721)
#719 := (iff #257 #716)
#712 := (implies #194 #707)
#717 := (iff #712 #716)
#718 := [rewrite]: #717
#713 := (iff #257 #712)
#710 := (iff #256 #707)
#703 := (implies #551 #698)
#708 := (iff #703 #707)
#709 := [rewrite]: #708
#704 := (iff #256 #703)
#701 := (iff #255 #698)
#694 := (implies #557 #691)
#699 := (iff #694 #698)
#700 := [rewrite]: #699
#695 := (iff #255 #694)
#692 := (iff #254 #691)
#689 := (iff #253 #686)
#682 := (implies #211 #679)
#687 := (iff #682 #686)
#688 := [rewrite]: #687
#683 := (iff #253 #682)
#680 := (iff #252 #679)
#677 := (iff #251 #674)
#670 := (implies #563 #667)
#675 := (iff #670 #674)
#676 := [rewrite]: #675
#671 := (iff #251 #670)
#668 := (iff #250 #667)
#665 := (iff #249 #662)
#658 := (implies #217 #655)
#663 := (iff #658 #662)
#664 := [rewrite]: #663
#659 := (iff #249 #658)
#656 := (iff #248 #655)
#653 := (iff #247 #650)
#646 := (implies #219 #643)
#651 := (iff #646 #650)
#652 := [rewrite]: #651
#647 := (iff #247 #646)
#644 := (iff #246 #643)
#641 := (iff #245 #638)
#634 := (implies #570 #631)
#639 := (iff #634 #638)
#640 := [rewrite]: #639
#635 := (iff #245 #634)
#632 := (iff #244 #631)
#629 := (iff #243 #626)
#622 := (implies #588 #612)
#627 := (iff #622 #626)
#628 := [rewrite]: #627
#623 := (iff #243 #622)
#620 := (iff #242 #612)
#615 := (and #612 true)
#618 := (iff #615 #612)
#619 := [rewrite]: #618
#616 := (iff #242 #615)
#613 := (iff #241 #612)
#610 := (iff #240 #607)
#603 := (implies #234 #600)
#608 := (iff #603 #607)
#609 := [rewrite]: #608
#604 := (iff #240 #603)
#601 := (iff #239 #600)
#598 := (iff #238 #597)
#595 := (iff #237 #594)
#592 := (iff #236 #591)
#574 := (= #229 #573)
#575 := [rewrite]: #574
#593 := [monotonicity #575]: #592
#596 := [monotonicity #593]: #595
#599 := [monotonicity #596]: #598
#602 := [quant-intro #599]: #601
#605 := [monotonicity #602]: #604
#611 := [trans #605 #609]: #610
#614 := [quant-intro #611]: #613
#617 := [monotonicity #614]: #616
#621 := [trans #617 #619]: #620
#589 := (iff #232 #588)
#586 := (iff #231 #583)
#579 := (implies #228 #576)
#584 := (iff #579 #583)
#585 := [rewrite]: #584
#580 := (iff #231 #579)
#577 := (iff #230 #576)
#578 := [monotonicity #575]: #577
#581 := [monotonicity #578]: #580
#587 := [trans #581 #585]: #586
#590 := [quant-intro #587]: #589
#624 := [monotonicity #590 #621]: #623
#630 := [trans #624 #628]: #629
#633 := [monotonicity #590 #630]: #632
#571 := (iff #227 #570)
#568 := (iff #226 #567)
#569 := [rewrite]: #568
#572 := [quant-intro #569]: #571
#636 := [monotonicity #572 #633]: #635
#642 := [trans #636 #640]: #641
#645 := [monotonicity #572 #642]: #644
#648 := [monotonicity #645]: #647
#654 := [trans #648 #652]: #653
#657 := [monotonicity #654]: #656
#660 := [monotonicity #657]: #659
#666 := [trans #660 #664]: #665
#669 := [monotonicity #666]: #668
#564 := (iff #215 #563)
#561 := (iff #214 #560)
#562 := [rewrite]: #561
#565 := [quant-intro #562]: #564
#672 := [monotonicity #565 #669]: #671
#678 := [trans #672 #676]: #677
#681 := [monotonicity #565 #678]: #680
#684 := [monotonicity #681]: #683
#690 := [trans #684 #688]: #689
#693 := [monotonicity #690]: #692
#558 := (iff #209 #557)
#555 := (iff #208 #554)
#556 := [rewrite]: #555
#559 := [quant-intro #556]: #558
#696 := [monotonicity #559 #693]: #695
#702 := [trans #696 #700]: #701
#552 := (iff #205 #551)
#549 := (iff #204 #548)
#550 := [rewrite]: #549
#553 := [quant-intro #550]: #552
#705 := [monotonicity #553 #702]: #704
#711 := [trans #705 #709]: #710
#714 := [monotonicity #711]: #713
#720 := [trans #714 #718]: #719
#546 := (iff #189 #545)
#543 := (iff #188 #542)
#544 := [rewrite]: #543
#547 := [quant-intro #544]: #546
#723 := [monotonicity #547 #720]: #722
#729 := [trans #723 #727]: #728
#732 := [monotonicity #729]: #731
#738 := [trans #732 #736]: #737
#741 := [monotonicity #738]: #740
#746 := [trans #741 #744]: #745
#749 := [monotonicity #746]: #748
#754 := [trans #749 #752]: #753
#757 := [monotonicity #754]: #756
#761 := [trans #757 #759]: #760
#540 := (iff #180 #530)
#535 := (implies true #530)
#538 := (iff #535 #530)
#539 := [rewrite]: #538
#536 := (iff #180 #535)
#533 := (iff #179 #530)
#527 := (implies #142 #522)
#531 := (iff #527 #530)
#532 := [rewrite]: #531
#528 := (iff #179 #527)
#525 := (iff #178 #522)
#518 := (implies #144 #513)
#523 := (iff #518 #522)
#524 := [rewrite]: #523
#519 := (iff #178 #518)
#516 := (iff #177 #513)
#509 := (implies #147 #504)
#514 := (iff #509 #513)
#515 := [rewrite]: #514
#510 := (iff #177 #509)
#507 := (iff #176 #504)
#500 := (implies #149 #495)
#505 := (iff #500 #504)
#506 := [rewrite]: #505
#501 := (iff #176 #500)
#498 := (iff #175 #495)
#491 := (implies #152 #488)
#496 := (iff #491 #495)
#497 := [rewrite]: #496
#492 := (iff #175 #491)
#489 := (iff #174 #488)
#486 := (iff #173 #483)
#479 := (implies #447 #476)
#484 := (iff #479 #483)
#485 := [rewrite]: #484
#480 := (iff #173 #479)
#477 := (iff #172 #476)
#474 := (iff #171 #471)
#467 := (implies #462 #169)
#472 := (iff #467 #471)
#473 := [rewrite]: #472
#468 := (iff #171 #467)
#465 := (iff #170 #169)
#466 := [rewrite]: #465
#463 := (iff #167 #462)
#460 := (iff #166 #457)
#453 := (implies #164 #450)
#458 := (iff #453 #457)
#459 := [rewrite]: #458
#454 := (iff #166 #453)
#451 := (iff #165 #450)
#427 := (= #158 #426)
#428 := [rewrite]: #427
#452 := [monotonicity #428]: #451
#455 := [monotonicity #452]: #454
#461 := [trans #455 #459]: #460
#464 := [quant-intro #461]: #463
#469 := [monotonicity #464 #466]: #468
#475 := [trans #469 #473]: #474
#478 := [monotonicity #464 #475]: #477
#448 := (iff #163 #447)
#445 := (iff #162 #442)
#438 := (implies #155 #435)
#443 := (iff #438 #442)
#444 := [rewrite]: #443
#439 := (iff #162 #438)
#436 := (iff #161 #435)
#433 := (iff #160 #432)
#430 := (iff #159 #429)
#431 := [monotonicity #428]: #430
#434 := [monotonicity #431]: #433
#437 := [quant-intro #434]: #436
#440 := [monotonicity #437]: #439
#446 := [trans #440 #444]: #445
#449 := [quant-intro #446]: #448
#481 := [monotonicity #449 #478]: #480
#487 := [trans #481 #485]: #486
#490 := [monotonicity #449 #487]: #489
#493 := [monotonicity #490]: #492
#499 := [trans #493 #497]: #498
#502 := [monotonicity #499]: #501
#508 := [trans #502 #506]: #507
#511 := [monotonicity #508]: #510
#517 := [trans #511 #515]: #516
#520 := [monotonicity #517]: #519
#526 := [trans #520 #524]: #525
#529 := [monotonicity #526]: #528
#534 := [trans #529 #532]: #533
#537 := [monotonicity #534]: #536
#541 := [trans #537 #539]: #540
#764 := [monotonicity #541 #761]: #763
#424 := (iff #139 #423)
#421 := (iff #138 #418)
#414 := (implies #132 #411)
#419 := (iff #414 #418)
#420 := [rewrite]: #419
#415 := (iff #138 #414)
#412 := (iff #137 #411)
#409 := (iff #136 #408)
#406 := (iff #135 #405)
#403 := (iff #134 #402)
#385 := (= #127 #384)
#386 := [rewrite]: #385
#404 := [monotonicity #386]: #403
#407 := [monotonicity #404]: #406
#410 := [monotonicity #407]: #409
#413 := [quant-intro #410]: #412
#416 := [monotonicity #413]: #415
#422 := [trans #416 #420]: #421
#425 := [quant-intro #422]: #424
#767 := [monotonicity #425 #764]: #766
#773 := [trans #767 #771]: #772
#400 := (iff #130 #399)
#397 := (iff #129 #394)
#390 := (implies #126 #387)
#395 := (iff #390 #394)
#396 := [rewrite]: #395
#391 := (iff #129 #390)
#388 := (iff #128 #387)
#389 := [monotonicity #386]: #388
#392 := [monotonicity #389]: #391
#398 := [trans #392 #396]: #397
#401 := [quant-intro #398]: #400
#776 := [monotonicity #401 #773]: #775
#782 := [trans #776 #780]: #781
#382 := (iff #125 #381)
#379 := (iff #124 #378)
#380 := [rewrite]: #379
#383 := [quant-intro #380]: #382
#785 := [monotonicity #383 #782]: #784
#791 := [trans #785 #789]: #790
#794 := [monotonicity #791]: #793
#800 := [trans #794 #798]: #799
#803 := [monotonicity #800]: #802
#809 := [trans #803 #807]: #808
#812 := [monotonicity #809]: #811
#816 := [trans #812 #814]: #815
#375 := (iff #108 #374)
#372 := (iff #107 #371)
#373 := [rewrite]: #372
#376 := [quant-intro #373]: #375
#819 := [monotonicity #376 #816]: #818
#825 := [trans #819 #823]: #824
#828 := [monotonicity #376 #825]: #827
#368 := (iff #99 #367)
#365 := (iff #98 #364)
#366 := [rewrite]: #365
#369 := [quant-intro #366]: #368
#831 := [monotonicity #369 #828]: #830
#837 := [trans #831 #835]: #836
#840 := [monotonicity #369 #837]: #839
#361 := (iff #90 #360)
#358 := (iff #89 #357)
#359 := [rewrite]: #358
#362 := [quant-intro #359]: #361
#843 := [monotonicity #362 #840]: #842
#849 := [trans #843 #847]: #848
#852 := [monotonicity #362 #849]: #851
#855 := [monotonicity #852]: #854
#861 := [trans #855 #859]: #860
#864 := [monotonicity #861]: #863
#867 := [monotonicity #864]: #866
#873 := [trans #867 #871]: #872
#876 := [monotonicity #873]: #875
#879 := [monotonicity #876]: #878
#885 := [trans #879 #883]: #884
#354 := (iff #74 #353)
#351 := (iff #73 #350)
#352 := [rewrite]: #351
#355 := [quant-intro #352]: #354
#888 := [monotonicity #355 #885]: #887
#894 := [trans #888 #892]: #893
#348 := (iff #70 #347)
#345 := (iff #69 #344)
#346 := [rewrite]: #345
#349 := [quant-intro #346]: #348
#897 := [monotonicity #349 #894]: #896
#903 := [trans #897 #901]: #902
#906 := [monotonicity #903]: #905
#910 := [trans #906 #908]: #909
#913 := [monotonicity #910]: #912
#1474 := [trans #913 #1472]: #1473
#343 := [asserted]: #284
#1475 := [mp #343 #1474]: #1470
#1477 := [not-or-elim #1475]: #353
#1532 := [mp~ #1477 #1501]: #353
#3659 := [mp #1532 #3658]: #3654
#3289 := (not #3654)
#6890 := (or #3289 #1614 #6849)
#6850 := (or #1614 #6849)
#6891 := (or #3289 #6850)
#6893 := (iff #6891 #6890)
#6888 := [rewrite]: #6893
#6892 := [quant-inst #1613]: #6891
#6894 := [mp #6892 #6888]: #6890
#6908 := [unit-resolution #6894 #3659 #6907]: #6849
#6928 := [mp #6908 #6927]: #6895
#6897 := (not #6895)
#1620 := (not #1619)
#3595 := (or #3702 #1620)
#3596 := [def-axiom]: #3595
#6889 := [unit-resolution #3596 #6853]: #1620
#6898 := (or #6897 #1619)
#6903 := [th-lemma arith triangle-eq]: #6898
#6904 := [unit-resolution #6903 #6889]: #6897
#6929 := [unit-resolution #6904 #6928]: false
#6930 := [lemma #6929]: #3702
#3986 := (or #3705 #3983)
#3989 := (not #3986)
#2540 := (or #78 #940 #951)
#3685 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3684) #2540)
#3690 := (not #3685)
#3992 := (or #3690 #3989)
#3995 := (not #3992)
decl ?v0!4 :: S2
#1582 := ?v0!4
#1595 := (f17 ?v0!4)
#1596 := (* -1::Int #1595)
decl ?v1!3 :: S2
#1581 := ?v1!3
#1594 := (f17 ?v1!3)
#2173 := (+ #1594 #1596)
#1585 := (f6 f7 ?v1!3)
#1586 := (f5 #1585 ?v0!4)
#1587 := (f4 #1586)
#2174 := (+ #1587 #2173)
#2177 := (>= #2174 0::Int)
#1588 := (* -1::Int #1587)
#1589 := (+ f3 #1588)
#1590 := (<= #1589 0::Int)
#1583 := (f11 f18 ?v1!3)
#1584 := (= #1583 f1)
#2503 := (not #1584)
#2518 := (or #2503 #1590 #2177)
#2523 := (not #2518)
#3998 := (or #2523 #3995)
#4001 := (not #3998)
#3675 := (pattern #67 #87)
#1605 := (not #85)
#2495 := (or #77 #1605 #925)
#3676 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3675) #2495)
#3681 := (not #3676)
#4004 := (or #3681 #4001)
#4007 := (not #4004)
decl ?v0!2 :: S2
#1555 := ?v0!2
#1564 := (f17 ?v0!2)
#1565 := (* -1::Int #1564)
decl ?v1!1 :: S2
#1554 := ?v1!1
#1563 := (f17 ?v1!1)
#1566 := (+ #1563 #1565)
#1567 := (>= #1566 0::Int)
#1559 := (f11 f18 ?v0!2)
#1560 := (= #1559 f1)
#1884 := (not #1560)
#1556 := (f11 f18 ?v1!1)
#1557 := (= #1556 f1)
#1841 := (or #1557 #1884 #1567)
#1946 := (not #1841)
#4010 := (or #1946 #4007)
#4013 := (not #4010)
#3667 := (forall (vars (?v0 S2)) (:pat #3647) #916)
#3672 := (not #3667)
#4016 := (or #3672 #4013)
#4019 := (not #4016)
decl ?v0!0 :: S2
#1539 := ?v0!0
#1540 := (f17 ?v0!0)
#1541 := (>= #1540 0::Int)
#3259 := (= f3 #1540)
#3321 := (= #1540 f3)
#3223 := (iff #3321 #3259)
#3224 := (iff #3259 #3321)
#3227 := [commutativity]: #3224
#3222 := [symm #3227]: #3223
#3345 := (= ?v0!0 f16)
#3353 := (not #3345)
#3306 := (= #1540 0::Int)
#3281 := (not #3306)
#1542 := (not #1541)
#3290 := [hypothesis]: #1542
#3246 := (or #3281 #1541)
#3244 := [th-lemma arith triangle-eq]: #3246
#3247 := [unit-resolution #3244 #3290]: #3281
#3648 := (forall (vars (?v0 S2)) (:pat #3647) #344)
#3651 := (iff #347 #3648)
#3649 := (iff #344 #344)
#3650 := [refl]: #3649
#3652 := [quant-intro #3650]: #3651
#1498 := (~ #347 #347)
#1527 := (~ #344 #344)
#1528 := [refl]: #1527
#1499 := [nnf-pos #1528]: #1498
#1476 := [not-or-elim #1475]: #347
#1529 := [mp~ #1476 #1499]: #347
#3653 := [mp #1529 #3652]: #3648
#3310 := (not #3648)
#3309 := (or #3310 #3353 #3306)
#3307 := (or #3353 #3306)
#3303 := (or #3310 #3307)
#3294 := (iff #3303 #3309)
#3295 := [rewrite]: #3294
#3304 := [quant-inst #1539]: #3303
#3305 := [mp #3304 #3295]: #3309
#3236 := [unit-resolution #3305 #3653 #3247]: #3353
#3291 := (or #3289 #3345 #3321)
#3308 := (or #3345 #3321)
#3258 := (or #3289 #3308)
#3268 := (iff #3258 #3291)
#3269 := [rewrite]: #3268
#3260 := [quant-inst #1539]: #3258
#3267 := [mp #3260 #3269]: #3291
#3248 := [unit-resolution #3267 #3659 #3236]: #3321
#3228 := [mp #3248 #3222]: #3259
#3316 := (* -1::Int #1540)
#3270 := (+ f3 #3316)
#3253 := (<= #3270 0::Int)
#4045 := (not #3253)
#307 := (<= f3 0::Int)
#308 := (not #307)
#9 := (< 0::Int f3)
#309 := (iff #9 #308)
#310 := [rewrite]: #309
#304 := [asserted]: #9
#311 := [mp #304 #310]: #308
#3286 := (<= #1540 0::Int)
#3203 := (or #3286 #1541)
#3208 := [th-lemma arith farkas 1 1]: #3203
#3213 := [unit-resolution #3208 #3290]: #3286
#4046 := (not #3286)
#4047 := (or #4045 #307 #4046)
#4048 := [th-lemma arith assign-bounds 1 1]: #4047
#4049 := [unit-resolution #4048 #3213 #311]: #4045
#4044 := (not #3259)
#4050 := (or #4044 #3253)
#4051 := [th-lemma arith triangle-eq]: #4050
#4052 := [unit-resolution #4051 #4049 #3228]: false
#4053 := [lemma #4052]: #1541
#4022 := (or #1542 #4019)
#4025 := (not #4022)
#4028 := (or #868 #4025)
#4031 := (not #4028)
#4121 := [hypothesis]: #868
#4075 := (or #3310 #81)
#6826 := (= f16 f16)
#6905 := (not #6826)
#4054 := (or #6905 #81)
#4076 := (or #3310 #4054)
#4084 := (iff #4076 #4075)
#4117 := (iff #4075 #4075)
#4118 := [rewrite]: #4117
#4073 := (iff #4054 #81)
#4068 := (or false #81)
#4069 := (iff #4068 #81)
#4072 := [rewrite]: #4069
#4070 := (iff #4054 #4068)
#6915 := (iff #6905 false)
#6910 := (not true)
#6913 := (iff #6910 false)
#6914 := [rewrite]: #6913
#6911 := (iff #6905 #6910)
#6829 := (iff #6826 true)
#6830 := [rewrite]: #6829
#6912 := [monotonicity #6830]: #6911
#6916 := [trans #6912 #6914]: #6915
#4071 := [monotonicity #6916]: #4070
#4074 := [trans #4071 #4072]: #4073
#4085 := [monotonicity #4074]: #4084
#4119 := [trans #4085 #4118]: #4084
#4077 := [quant-inst #65]: #4076
#4120 := [mp #4077 #4119]: #4075
#4116 := [unit-resolution #4120 #3653 #4121]: false
#4122 := [lemma #4116]: #81
#4034 := (or #868 #4031)
#2953 := (forall (vars (?v1 S2)) #2942)
#2960 := (not #2953)
#2938 := (forall (vars (?v0 S2) (?v1 S2)) #2933)
#2959 := (not #2938)
#2961 := (or #2959 #2035 #2040 #2960)
#2962 := (not #2961)
#2967 := (or #2916 #2962)
#2974 := (not #2967)
#2893 := (forall (vars (?v0 S2) (?v1 S2)) #2888)
#2973 := (not #2893)
#2975 := (or #2973 #2974)
#2976 := (not #2975)
#2981 := (or #2870 #2976)
#2987 := (not #2981)
#2988 := (or #1182 #2987)
#2989 := (not #2988)
#2994 := (or #1963 #2989)
#3000 := (not #2994)
#3001 := (or #661 #3000)
#3002 := (not #3001)
#3007 := (or #661 #3002)
#3013 := (not #3007)
#3014 := (or #673 #3013)
#3015 := (not #3014)
#3020 := (or #1943 #3015)
#3026 := (not #3020)
#3027 := (or #1173 #3026)
#3028 := (not #3027)
#3033 := (or #1923 #3028)
#3041 := (not #3033)
#2847 := (forall (vars (?v0 S2)) #2844)
#3040 := (not #2847)
#2841 := (forall (vars (?v0 S2)) #2836)
#3039 := (not #2841)
#3042 := (or #1874 #1879 #183 #1322 #1318 #715 #3039 #3040 #3041)
#3043 := (not #3042)
#2781 := (forall (vars (?v0 S2) (?v1 S2)) #2776)
#2787 := (not #2781)
#2788 := (or #2787 #169)
#2789 := (not #2788)
#2794 := (or #2759 #2789)
#2801 := (not #2794)
#2737 := (forall (vars (?v0 S2)) #2732)
#2800 := (not #2737)
#2802 := (or #2800 #2801)
#2803 := (not #2802)
#2700 := (forall (vars (?v1 S2)) #2689)
#2706 := (not #2700)
#2707 := (or #1752 #1757 #2706)
#2708 := (not #2707)
#2808 := (or #2708 #2803)
#2815 := (not #2808)
#2685 := (forall (vars (?v0 S2)) #2674)
#2814 := (not #2685)
#2816 := (or #2814 #521 #512 #503 #494 #2815)
#2817 := (not #2816)
#3048 := (or #2817 #3043)
#3058 := (not #3048)
#2671 := (forall (vars (?v0 S2)) #2666)
#3057 := (not #2671)
#2643 := (forall (vars (?v0 S2) (?v1 S2)) #2638)
#3056 := (not #2643)
#2621 := (forall (vars (?v0 S2) (?v1 S2)) #2616)
#3055 := (not #2621)
#2598 := (forall (vars (?v0 S2)) #2593)
#3054 := (not #2598)
#3059 := (or #3054 #804 #1400 #3055 #3056 #3057 #3058)
#3060 := (not #3059)
#2560 := (forall (vars (?v1 S2)) #2549)
#2566 := (not #2560)
#2567 := (or #1614 #1619 #2566)
#2568 := (not #2567)
#3065 := (or #2568 #3060)
#3072 := (not #3065)
#2545 := (forall (vars (?v0 S2) (?v1 S2)) #2540)
#3071 := (not #2545)
#3073 := (or #3071 #3072)
#3074 := (not #3073)
#3079 := (or #2523 #3074)
#3086 := (not #3079)
#2500 := (forall (vars (?v0 S2) (?v1 S2)) #2495)
#3085 := (not #2500)
#3087 := (or #3085 #3086)
#3088 := (not #3087)
#3093 := (or #1946 #3088)
#3099 := (not #3093)
#3100 := (or #920 #3099)
#3101 := (not #3100)
#3106 := (or #1542 #3101)
#3112 := (not #3106)
#3113 := (or #868 #3112)
#3114 := (not #3113)
#3119 := (or #868 #3114)
#4035 := (iff #3119 #4034)
#4032 := (iff #3114 #4031)
#4029 := (iff #3113 #4028)
#4026 := (iff #3112 #4025)
#4023 := (iff #3106 #4022)
#4020 := (iff #3101 #4019)
#4017 := (iff #3100 #4016)
#4014 := (iff #3099 #4013)
#4011 := (iff #3093 #4010)
#4008 := (iff #3088 #4007)
#4005 := (iff #3087 #4004)
#4002 := (iff #3086 #4001)
#3999 := (iff #3079 #3998)
#3996 := (iff #3074 #3995)
#3993 := (iff #3073 #3992)
#3990 := (iff #3072 #3989)
#3987 := (iff #3065 #3986)
#3984 := (iff #3060 #3983)
#3981 := (iff #3059 #3980)
#3978 := (iff #3058 #3977)
#3975 := (iff #3048 #3974)
#3972 := (iff #3043 #3971)
#3969 := (iff #3042 #3968)
#3966 := (iff #3041 #3965)
#3963 := (iff #3033 #3962)
#3960 := (iff #3028 #3959)
#3957 := (iff #3027 #3956)
#3954 := (iff #3026 #3953)
#3951 := (iff #3020 #3950)
#3948 := (iff #3015 #3947)
#3945 := (iff #3014 #3944)
#3942 := (iff #3013 #3941)
#3939 := (iff #3007 #3938)
#3936 := (iff #3002 #3935)
#3933 := (iff #3001 #3932)
#3930 := (iff #3000 #3929)
#3927 := (iff #2994 #3926)
#3924 := (iff #2989 #3923)
#3921 := (iff #2988 #3920)
#3918 := (iff #2987 #3917)
#3915 := (iff #2981 #3914)
#3912 := (iff #2976 #3911)
#3909 := (iff #2975 #3908)
#3906 := (iff #2974 #3905)
#3903 := (iff #2967 #3902)
#3900 := (iff #2962 #3899)
#3897 := (iff #2961 #3896)
#3894 := (iff #2960 #3893)
#3891 := (iff #2953 #3888)
#3889 := (iff #2942 #2942)
#3890 := [refl]: #3889
#3892 := [quant-intro #3890]: #3891
#3895 := [monotonicity #3892]: #3894
#3886 := (iff #2959 #3885)
#3883 := (iff #2938 #3880)
#3881 := (iff #2933 #2933)
#3882 := [refl]: #3881
#3884 := [quant-intro #3882]: #3883
#3887 := [monotonicity #3884]: #3886
#3898 := [monotonicity #3887 #3895]: #3897
#3901 := [monotonicity #3898]: #3900
#3904 := [monotonicity #3901]: #3903
#3907 := [monotonicity #3904]: #3906
#3878 := (iff #2973 #3877)
#3875 := (iff #2893 #3872)
#3873 := (iff #2888 #2888)
#3874 := [refl]: #3873
#3876 := [quant-intro #3874]: #3875
#3879 := [monotonicity #3876]: #3878
#3910 := [monotonicity #3879 #3907]: #3909
#3913 := [monotonicity #3910]: #3912
#3916 := [monotonicity #3913]: #3915
#3919 := [monotonicity #3916]: #3918
#3869 := (iff #1182 #3868)
#3866 := (iff #1179 #3863)
#3864 := (iff #1176 #1176)
#3865 := [refl]: #3864
#3867 := [quant-intro #3865]: #3866
#3870 := [monotonicity #3867]: #3869
#3922 := [monotonicity #3870 #3919]: #3921
#3925 := [monotonicity #3922]: #3924
#3928 := [monotonicity #3925]: #3927
#3931 := [monotonicity #3928]: #3930
#3934 := [monotonicity #3931]: #3933
#3937 := [monotonicity #3934]: #3936
#3940 := [monotonicity #3937]: #3939
#3943 := [monotonicity #3940]: #3942
#3861 := (iff #673 #3860)
#3858 := (iff #563 #3855)
#3856 := (iff #560 #560)
#3857 := [refl]: #3856
#3859 := [quant-intro #3857]: #3858
#3862 := [monotonicity #3859]: #3861
#3946 := [monotonicity #3862 #3943]: #3945
#3949 := [monotonicity #3946]: #3948
#3952 := [monotonicity #3949]: #3951
#3955 := [monotonicity #3952]: #3954
#3852 := (iff #1173 #3851)
#3849 := (iff #1170 #3846)
#3847 := (iff #1165 #1165)
#3848 := [refl]: #3847
#3850 := [quant-intro #3848]: #3849
#3853 := [monotonicity #3850]: #3852
#3958 := [monotonicity #3853 #3955]: #3957
#3961 := [monotonicity #3958]: #3960
#3964 := [monotonicity #3961]: #3963
#3967 := [monotonicity #3964]: #3966
#3844 := (iff #3040 #3843)
#3841 := (iff #2847 #3838)
#3839 := (iff #2844 #2844)
#3840 := [refl]: #3839
#3842 := [quant-intro #3840]: #3841
#3845 := [monotonicity #3842]: #3844
#3836 := (iff #3039 #3835)
#3833 := (iff #2841 #3830)
#3831 := (iff #2836 #2836)
#3832 := [refl]: #3831
#3834 := [quant-intro #3832]: #3833
#3837 := [monotonicity #3834]: #3836
#3826 := (iff #1318 #3825)
#3823 := (iff #1315 #3820)
#3821 := (iff #1312 #1312)
#3822 := [refl]: #3821
#3824 := [quant-intro #3822]: #3823
#3827 := [monotonicity #3824]: #3826
#3970 := [monotonicity #3827 #3837 #3845 #3967]: #3969
#3973 := [monotonicity #3970]: #3972
#3818 := (iff #2817 #3817)
#3815 := (iff #2816 #3814)
#3812 := (iff #2815 #3811)
#3809 := (iff #2808 #3808)
#3806 := (iff #2803 #3805)
#3803 := (iff #2802 #3802)
#3800 := (iff #2801 #3799)
#3797 := (iff #2794 #3796)
#3794 := (iff #2789 #3793)
#3791 := (iff #2788 #3790)
#3788 := (iff #2787 #3787)
#3785 := (iff #2781 #3782)
#3783 := (iff #2776 #2776)
#3784 := [refl]: #3783
#3786 := [quant-intro #3784]: #3785
#3789 := [monotonicity #3786]: #3788
#3792 := [monotonicity #3789]: #3791
#3795 := [monotonicity #3792]: #3794
#3798 := [monotonicity #3795]: #3797
#3801 := [monotonicity #3798]: #3800
#3780 := (iff #2800 #3779)
#3777 := (iff #2737 #3774)
#3775 := (iff #2732 #2732)
#3776 := [refl]: #3775
#3778 := [quant-intro #3776]: #3777
#3781 := [monotonicity #3778]: #3780
#3804 := [monotonicity #3781 #3801]: #3803
#3807 := [monotonicity #3804]: #3806
#3772 := (iff #2708 #3771)
#3769 := (iff #2707 #3768)
#3766 := (iff #2706 #3765)
#3763 := (iff #2700 #3760)
#3761 := (iff #2689 #2689)
#3762 := [refl]: #3761
#3764 := [quant-intro #3762]: #3763
#3767 := [monotonicity #3764]: #3766
#3770 := [monotonicity #3767]: #3769
#3773 := [monotonicity #3770]: #3772
#3810 := [monotonicity #3773 #3807]: #3809
#3813 := [monotonicity #3810]: #3812
#3757 := (iff #2814 #3756)
#3754 := (iff #2685 #3751)
#3752 := (iff #2674 #2674)
#3753 := [refl]: #3752
#3755 := [quant-intro #3753]: #3754
#3758 := [monotonicity #3755]: #3757
#3816 := [monotonicity #3758 #3813]: #3815
#3819 := [monotonicity #3816]: #3818
#3976 := [monotonicity #3819 #3973]: #3975
#3979 := [monotonicity #3976]: #3978
#3748 := (iff #3057 #3747)
#3745 := (iff #2671 #3742)
#3743 := (iff #2666 #2666)
#3744 := [refl]: #3743
#3746 := [quant-intro #3744]: #3745
#3749 := [monotonicity #3746]: #3748
#3740 := (iff #3056 #3739)
#3737 := (iff #2643 #3734)
#3735 := (iff #2638 #2638)
#3736 := [refl]: #3735
#3738 := [quant-intro #3736]: #3737
#3741 := [monotonicity #3738]: #3740
#3732 := (iff #3055 #3731)
#3729 := (iff #2621 #3726)
#3727 := (iff #2616 #2616)
#3728 := [refl]: #3727
#3730 := [quant-intro #3728]: #3729
#3733 := [monotonicity #3730]: #3732
#3723 := (iff #1400 #3722)
#3720 := (iff #1397 #3717)
#3718 := (iff #1394 #1394)
#3719 := [refl]: #3718
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#2612 := [trans #2608 #2610]: #2611
#2615 := [monotonicity #2612]: #2614
#2620 := [trans #2615 #2618]: #2619
#2623 := [quant-intro #2620]: #2622
#2599 := (iff #2233 #2598)
#2596 := (iff #2230 #2593)
#2573 := (or #66 #966)
#2590 := (or #2573 #2587)
#2594 := (iff #2590 #2593)
#2595 := [rewrite]: #2594
#2591 := (iff #2230 #2590)
#2588 := (iff #2227 #2587)
#2589 := [rewrite]: #2588
#2582 := (iff #973 #2573)
#2574 := (not #2573)
#2577 := (not #2574)
#2580 := (iff #2577 #2573)
#2581 := [rewrite]: #2580
#2578 := (iff #973 #2577)
#2575 := (iff #970 #2574)
#2576 := [rewrite]: #2575
#2579 := [monotonicity #2576]: #2578
#2583 := [trans #2579 #2581]: #2582
#2592 := [monotonicity #2583 #2589]: #2591
#2597 := [trans #2592 #2595]: #2596
#2600 := [quant-intro #2597]: #2599
#3053 := [monotonicity #2600 #2623 #2645 #2673 #3050]: #3052
#3064 := [trans #3053 #3062]: #3063
#2571 := (iff #2191 #2568)
#2563 := (and #1615 #1620 #2560)
#2569 := (iff #2563 #2568)
#2570 := [rewrite]: #2569
#2564 := (iff #2191 #2563)
#2561 := (iff #1643 #2560)
#2558 := (iff #1640 #2549)
#2550 := (not #2549)
#2553 := (not #2550)
#2556 := (iff #2553 #2549)
#2557 := [rewrite]: #2556
#2554 := (iff #1640 #2553)
#2551 := (iff #1631 #2550)
#2552 := [rewrite]: #2551
#2555 := [monotonicity #2552]: #2554
#2559 := [trans #2555 #2557]: #2558
#2562 := [quant-intro #2559]: #2561
#2565 := [monotonicity #2562]: #2564
#2572 := [trans #2565 #2570]: #2571
#3067 := [monotonicity #2572 #3064]: #3066
#2546 := (iff #958 #2545)
#2543 := (iff #955 #2540)
#2526 := (or #78 #940)
#2537 := (or #2526 #951)
#2541 := (iff #2537 #2540)
#2542 := [rewrite]: #2541
#2538 := (iff #955 #2537)
#2535 := (iff #947 #2526)
#2527 := (not #2526)
#2530 := (not #2527)
#2533 := (iff #2530 #2526)
#2534 := [rewrite]: #2533
#2531 := (iff #947 #2530)
#2528 := (iff #944 #2527)
#2529 := [rewrite]: #2528
#2532 := [monotonicity #2529]: #2531
#2536 := [trans #2532 #2534]: #2535
#2539 := [monotonicity #2536]: #2538
#2544 := [trans #2539 #2542]: #2543
#2547 := [quant-intro #2544]: #2546
#3070 := [monotonicity #2547 #3067]: #3069
#3078 := [trans #3070 #3076]: #3077
#2524 := (iff #2183 #2523)
#2521 := (iff #2180 #2518)
#2504 := (or #2503 #1590)
#2515 := (or #2504 #2177)
#2519 := (iff #2515 #2518)
#2520 := [rewrite]: #2519
#2516 := (iff #2180 #2515)
#2513 := (iff #1593 #2504)
#2505 := (not #2504)
#2508 := (not #2505)
#2511 := (iff #2508 #2504)
#2512 := [rewrite]: #2511
#2509 := (iff #1593 #2508)
#2506 := (iff #1592 #2505)
#2507 := [rewrite]: #2506
#2510 := [monotonicity #2507]: #2509
#2514 := [trans #2510 #2512]: #2513
#2517 := [monotonicity #2514]: #2516
#2522 := [trans #2517 #2520]: #2521
#2525 := [monotonicity #2522]: #2524
#3081 := [monotonicity #2525 #3078]: #3080
#2501 := (iff #932 #2500)
#2498 := (iff #929 #2495)
#1670 := (or #77 #1605)
#2492 := (or #1670 #925)
#2496 := (iff #2492 #2495)
#2497 := [rewrite]: #2496
#2493 := (iff #929 #2492)
#2490 := (iff #356 #1670)
#1671 := (not #1670)
#2485 := (not #1671)
#2488 := (iff #2485 #1670)
#2489 := [rewrite]: #2488
#2486 := (iff #356 #2485)
#2170 := (iff #86 #1671)
#2484 := [rewrite]: #2170
#2487 := [monotonicity #2484]: #2486
#2491 := [trans #2487 #2489]: #2490
#2494 := [monotonicity #2491]: #2493
#2499 := [trans #2494 #2497]: #2498
#2502 := [quant-intro #2499]: #2501
#3084 := [monotonicity #2502 #3081]: #3083
#3092 := [trans #3084 #3090]: #3091
#1947 := (iff #1569 #1946)
#1966 := (iff #1568 #1841)
#1885 := (or #1557 #1884)
#1545 := (or #1885 #1567)
#1926 := (iff #1545 #1841)
#1927 := [rewrite]: #1926
#1546 := (iff #1568 #1545)
#1572 := (iff #1562 #1885)
#1804 := (not #1885)
#2026 := (not #1804)
#1993 := (iff #2026 #1885)
#1994 := [rewrite]: #1993
#1722 := (iff #1562 #2026)
#1805 := (iff #1561 #1804)
#2025 := [rewrite]: #1805
#1723 := [monotonicity #2025]: #1722
#1573 := [trans #1723 #1994]: #1572
#1840 := [monotonicity #1573]: #1546
#1967 := [trans #1840 #1927]: #1966
#1604 := [monotonicity #1967]: #1947
#3095 := [monotonicity #1604 #3092]: #3094
#3098 := [monotonicity #3095]: #3097
#3105 := [trans #3098 #3103]: #3104
#3108 := [monotonicity #3105]: #3107
#3111 := [monotonicity #3108]: #3110
#3118 := [trans #3111 #3116]: #3117
#3121 := [monotonicity #3118]: #3120
#2049 := (+ #2048 #2044)
#2050 := (= #2049 0::Int)
#2051 := (and #2046 #213 #2050)
#2061 := (not #2051)
#2064 := (forall (vars (?v1 S2)) #2061)
#2042 := (and #2036 #2041)
#2043 := (not #2042)
#2058 := (not #2043)
#2068 := (and #2058 #2064)
#2073 := (and #1212 #2068)
#2077 := (or #2022 #2073)
#2081 := (and #1193 #2077)
#2085 := (or #1990 #2081)
#2089 := (and #1179 #2085)
#2093 := (or #1963 #2089)
#1957 := (not #661)
#2097 := (and #1957 #2093)
#2101 := (or #661 #2097)
#2105 := (and #563 #2101)
#2109 := (or #1943 #2105)
#2113 := (and #1170 #2109)
#2117 := (or #1923 #2113)
#1900 := (not #715)
#1881 := (and #1875 #1880)
#2121 := (and #1881 #184 #1323 #1315 #1900 #1302 #1159 #2117)
#1833 := (+ #1817 #1832)
#1834 := (+ #1824 #1833)
#1835 := (>= #1834 0::Int)
#1836 := (or #1830 #1835)
#1837 := (not #1836)
#1856 := (or #1837 #1852)
#1793 := (+ #1792 #1047)
#1799 := (+ #1798 #1793)
#1800 := (= #1799 0::Int)
#1794 := (>= #1793 0::Int)
#1795 := (not #1794)
#1801 := (and #1795 #1800)
#1806 := (or #1056 #1801)
#1809 := (forall (vars (?v0 S2)) #1806)
#1860 := (and #1809 #1856)
#1766 := (+ #1765 #1761)
#1767 := (= #1766 0::Int)
#1768 := (and #1763 #1767)
#1777 := (not #1768)
#1780 := (forall (vars (?v1 S2)) #1777)
#1759 := (and #1753 #1758)
#1760 := (not #1759)
#1774 := (not #1760)
#1784 := (and #1774 #1780)
#1864 := (or #1784 #1860)
#1748 := (not #494)
#1745 := (not #503)
#1742 := (not #512)
#1739 := (not #521)
#1868 := (and #1736 #1739 #1742 #1745 #1748 #1864)
#2125 := (or #1868 #2121)
#1709 := (+ #1708 #1002)
#1717 := (+ #1716 #1709)
#1718 := (= #1717 0::Int)
#1710 := (>= #1709 0::Int)
#1711 := (not #1710)
#1719 := (and #1711 #1713 #1718)
#1724 := (or #1011 #1719)
#1727 := (forall (vars (?v0 S2)) #1724)
#1681 := (not #804)
#1664 := (+ #964 #1663)
#1665 := (+ #1655 #1664)
#1666 := (= #1665 0::Int)
#1656 := (+ #1655 #964)
#1657 := (>= #1656 0::Int)
#1658 := (not #1657)
#1667 := (and #1658 #1660 #1666)
#1672 := (or #973 #1667)
#1675 := (forall (vars (?v0 S2)) #1672)
#2129 := (and #1675 #1681 #1397 #1388 #1377 #1727 #2125)
#1621 := (and #1615 #1620)
#1622 := (not #1621)
#1637 := (not #1622)
#1647 := (and #1637 #1643)
#2133 := (or #1647 #2129)
#2137 := (and #958 #2133)
#1597 := (+ #1596 #1587)
#1598 := (+ #1594 #1597)
#1599 := (>= #1598 0::Int)
#1600 := (or #1593 #1599)
#1601 := (not #1600)
#2141 := (or #1601 #2137)
#2145 := (and #932 #2141)
#2149 := (or #1569 #2145)
#2153 := (and #917 #2149)
#2157 := (or #1542 #2153)
#1504 := (not #868)
#2161 := (and #1504 #2157)
#2165 := (or #868 #2161)
#2482 := (iff #2165 #2481)
#2479 := (iff #2161 #2478)
#2476 := (iff #2157 #2475)
#2473 := (iff #2153 #2472)
#2470 := (iff #2149 #2469)
#2467 := (iff #2145 #2466)
#2464 := (iff #2141 #2463)
#2461 := (iff #2137 #2460)
#2458 := (iff #2133 #2457)
#2455 := (iff #2129 #2454)
#2452 := (iff #2125 #2451)
#2449 := (iff #2121 #2446)
#2443 := (and #1881 #184 #1323 #1315 #194 #1302 #1159 #2440)
#2447 := (iff #2443 #2446)
#2448 := [rewrite]: #2447
#2444 := (iff #2121 #2443)
#2441 := (iff #2117 #2440)
#2438 := (iff #2113 #2437)
#2435 := (iff #2109 #2434)
#2432 := (iff #2105 #2431)
#2429 := (iff #2101 #2428)
#2426 := (iff #2097 #2425)
#2423 := (iff #2093 #2422)
#2420 := (iff #2089 #2419)
#2417 := (iff #2085 #2416)
#2414 := (iff #2081 #2413)
#2411 := (iff #2077 #2410)
#2408 := (iff #2073 #2405)
#2399 := (and #2042 #2396)
#2402 := (and #1212 #2399)
#2406 := (iff #2402 #2405)
#2407 := [rewrite]: #2406
#2403 := (iff #2073 #2402)
#2400 := (iff #2068 #2399)
#2397 := (iff #2064 #2396)
#2394 := (iff #2061 #2393)
#2391 := (iff #2051 #2390)
#2388 := (iff #2050 #2387)
#2385 := (= #2049 #2384)
#2386 := [rewrite]: #2385
#2389 := [monotonicity #2386]: #2388
#2392 := [monotonicity #2389]: #2391
#2395 := [monotonicity #2392]: #2394
#2398 := [quant-intro #2395]: #2397
#2381 := (iff #2058 #2042)
#2382 := [rewrite]: #2381
#2401 := [monotonicity #2382 #2398]: #2400
#2404 := [monotonicity #2401]: #2403
#2409 := [trans #2404 #2407]: #2408
#2412 := [monotonicity #2409]: #2411
#2415 := [monotonicity #2412]: #2414
#2418 := [monotonicity #2415]: #2417
#2421 := [monotonicity #2418]: #2420
#2424 := [monotonicity #2421]: #2423
#2379 := (iff #1957 #217)
#2380 := [rewrite]: #2379
#2427 := [monotonicity #2380 #2424]: #2426
#2430 := [monotonicity #2427]: #2429
#2433 := [monotonicity #2430]: #2432
#2436 := [monotonicity #2433]: #2435
#2439 := [monotonicity #2436]: #2438
#2442 := [monotonicity #2439]: #2441
#2377 := (iff #1900 #194)
#2378 := [rewrite]: #2377
#2445 := [monotonicity #2378 #2442]: #2444
#2450 := [trans #2445 #2448]: #2449
#2375 := (iff #1868 #2374)
#2372 := (iff #1864 #2371)
#2369 := (iff #1860 #2368)
#2366 := (iff #1856 #2365)
#2363 := (iff #1837 #2362)
#2360 := (iff #1836 #2359)
#2357 := (iff #1835 #2356)
#2354 := (= #1834 #2353)
#2355 := [rewrite]: #2354
#2358 := [monotonicity #2355]: #2357
#2361 := [monotonicity #2358]: #2360
#2364 := [monotonicity #2361]: #2363
#2367 := [monotonicity #2364]: #2366
#2350 := (iff #1809 #2349)
#2347 := (iff #1806 #2346)
#2344 := (iff #1801 #2343)
#2341 := (iff #1800 #2338)
#2328 := (+ #1792 #1798)
#2329 := (+ #1047 #2328)
#2332 := (= #2329 0::Int)
#2339 := (iff #2332 #2338)
#2340 := [rewrite]: #2339
#2333 := (iff #1800 #2332)
#2330 := (= #1799 #2329)
#2331 := [rewrite]: #2330
#2334 := [monotonicity #2331]: #2333
#2342 := [trans #2334 #2340]: #2341
#2326 := (iff #1795 #2325)
#2323 := (iff #1794 #2320)
#2312 := (+ #1047 #1792)
#2315 := (>= #2312 0::Int)
#2321 := (iff #2315 #2320)
#2322 := [rewrite]: #2321
#2316 := (iff #1794 #2315)
#2313 := (= #1793 #2312)
#2314 := [rewrite]: #2313
#2317 := [monotonicity #2314]: #2316
#2324 := [trans #2317 #2322]: #2323
#2327 := [monotonicity #2324]: #2326
#2345 := [monotonicity #2327 #2342]: #2344
#2348 := [monotonicity #2345]: #2347
#2351 := [quant-intro #2348]: #2350
#2370 := [monotonicity #2351 #2367]: #2369
#2310 := (iff #1784 #2307)
#2304 := (and #1759 #2301)
#2308 := (iff #2304 #2307)
#2309 := [rewrite]: #2308
#2305 := (iff #1784 #2304)
#2302 := (iff #1780 #2301)
#2299 := (iff #1777 #2298)
#2296 := (iff #1768 #2295)
#2293 := (iff #1767 #2292)
#2290 := (= #1766 #2289)
#2291 := [rewrite]: #2290
#2294 := [monotonicity #2291]: #2293
#2297 := [monotonicity #2294]: #2296
#2300 := [monotonicity #2297]: #2299
#2303 := [quant-intro #2300]: #2302
#2286 := (iff #1774 #1759)
#2287 := [rewrite]: #2286
#2306 := [monotonicity #2287 #2303]: #2305
#2311 := [trans #2306 #2309]: #2310
#2373 := [monotonicity #2311 #2370]: #2372
#2284 := (iff #1748 #152)
#2285 := [rewrite]: #2284
#2282 := (iff #1745 #149)
#2283 := [rewrite]: #2282
#2280 := (iff #1742 #147)
#2281 := [rewrite]: #2280
#2278 := (iff #1739 #144)
#2279 := [rewrite]: #2278
#2376 := [monotonicity #2279 #2281 #2283 #2285 #2373]: #2375
#2453 := [monotonicity #2376 #2450]: #2452
#2276 := (iff #1727 #2275)
#2273 := (iff #1724 #2272)
#2270 := (iff #1719 #2269)
#2267 := (iff #1718 #2264)
#2254 := (+ #1708 #1716)
#2255 := (+ #1002 #2254)
#2258 := (= #2255 0::Int)
#2265 := (iff #2258 #2264)
#2266 := [rewrite]: #2265
#2259 := (iff #1718 #2258)
#2256 := (= #1717 #2255)
#2257 := [rewrite]: #2256
#2260 := [monotonicity #2257]: #2259
#2268 := [trans #2260 #2266]: #2267
#2252 := (iff #1711 #2251)
#2249 := (iff #1710 #2246)
#2238 := (+ #1002 #1708)
#2241 := (>= #2238 0::Int)
#2247 := (iff #2241 #2246)
#2248 := [rewrite]: #2247
#2242 := (iff #1710 #2241)
#2239 := (= #1709 #2238)
#2240 := [rewrite]: #2239
#2243 := [monotonicity #2240]: #2242
#2250 := [trans #2243 #2248]: #2249
#2253 := [monotonicity #2250]: #2252
#2271 := [monotonicity #2253 #2268]: #2270
#2274 := [monotonicity #2271]: #2273
#2277 := [quant-intro #2274]: #2276
#2236 := (iff #1681 #111)
#2237 := [rewrite]: #2236
#2234 := (iff #1675 #2233)
#2231 := (iff #1672 #2230)
#2228 := (iff #1667 #2227)
#2225 := (iff #1666 #2222)
#2212 := (+ #1655 #1663)
#2213 := (+ #964 #2212)
#2216 := (= #2213 0::Int)
#2223 := (iff #2216 #2222)
#2224 := [rewrite]: #2223
#2217 := (iff #1666 #2216)
#2214 := (= #1665 #2213)
#2215 := [rewrite]: #2214
#2218 := [monotonicity #2215]: #2217
#2226 := [trans #2218 #2224]: #2225
#2210 := (iff #1658 #2209)
#2207 := (iff #1657 #2204)
#2196 := (+ #964 #1655)
#2199 := (>= #2196 0::Int)
#2205 := (iff #2199 #2204)
#2206 := [rewrite]: #2205
#2200 := (iff #1657 #2199)
#2197 := (= #1656 #2196)
#2198 := [rewrite]: #2197
#2201 := [monotonicity #2198]: #2200
#2208 := [trans #2201 #2206]: #2207
#2211 := [monotonicity #2208]: #2210
#2229 := [monotonicity #2211 #2226]: #2228
#2232 := [monotonicity #2229]: #2231
#2235 := [quant-intro #2232]: #2234
#2456 := [monotonicity #2235 #2237 #2277 #2453]: #2455
#2194 := (iff #1647 #2191)
#2188 := (and #1621 #1643)
#2192 := (iff #2188 #2191)
#2193 := [rewrite]: #2192
#2189 := (iff #1647 #2188)
#2186 := (iff #1637 #1621)
#2187 := [rewrite]: #2186
#2190 := [monotonicity #2187]: #2189
#2195 := [trans #2190 #2193]: #2194
#2459 := [monotonicity #2195 #2456]: #2458
#2462 := [monotonicity #2459]: #2461
#2184 := (iff #1601 #2183)
#2181 := (iff #1600 #2180)
#2178 := (iff #1599 #2177)
#2175 := (= #1598 #2174)
#2176 := [rewrite]: #2175
#2179 := [monotonicity #2176]: #2178
#2182 := [monotonicity #2179]: #2181
#2185 := [monotonicity #2182]: #2184
#2465 := [monotonicity #2185 #2462]: #2464
#2468 := [monotonicity #2465]: #2467
#2471 := [monotonicity #2468]: #2470
#2474 := [monotonicity #2471]: #2473
#2477 := [monotonicity #2474]: #2476
#2171 := (iff #1504 #81)
#2172 := [rewrite]: #2171
#2480 := [monotonicity #2172 #2477]: #2479
#2483 := [monotonicity #2480]: #2482
#1479 := (not #1453)
#2166 := (~ #1479 #2165)
#2162 := (not #1450)
#2163 := (~ #2162 #2161)
#2158 := (not #1447)
#2159 := (~ #2158 #2157)
#2154 := (not #1444)
#2155 := (~ #2154 #2153)
#2150 := (not #1441)
#2151 := (~ #2150 #2149)
#2146 := (not #1438)
#2147 := (~ #2146 #2145)
#2142 := (not #1435)
#2143 := (~ #2142 #2141)
#2138 := (not #1432)
#2139 := (~ #2138 #2137)
#2134 := (not #1429)
#2135 := (~ #2134 #2133)
#2130 := (not #1424)
#2131 := (~ #2130 #2129)
#2126 := (not #1362)
#2127 := (~ #2126 #2125)
#2122 := (not #1357)
#2123 := (~ #2122 #2121)
#2118 := (not #1288)
#2119 := (~ #2118 #2117)
#2114 := (not #1285)
#2115 := (~ #2114 #2113)
#2110 := (not #1282)
#2111 := (~ #2110 #2109)
#2106 := (not #1279)
#2107 := (~ #2106 #2105)
#2102 := (not #1276)
#2103 := (~ #2102 #2101)
#2098 := (not #1273)
#2099 := (~ #2098 #2097)
#2094 := (not #1270)
#2095 := (~ #2094 #2093)
#2090 := (not #1267)
#2091 := (~ #2090 #2089)
#2086 := (not #1264)
#2087 := (~ #2086 #2085)
#2082 := (not #1261)
#2083 := (~ #2082 #2081)
#2078 := (not #1258)
#2079 := (~ #2078 #2077)
#2074 := (not #1255)
#2075 := (~ #2074 #2073)
#2055 := (not #1252)
#2071 := (~ #2055 #2068)
#2052 := (exists (vars (?v1 S2)) #2051)
#2053 := (or #2043 #2052)
#2054 := (not #2053)
#2069 := (~ #2054 #2068)
#2065 := (not #2052)
#2066 := (~ #2065 #2064)
#2062 := (~ #2061 #2061)
#2063 := [refl]: #2062
#2067 := [nnf-neg #2063]: #2066
#2059 := (~ #2058 #2058)
#2060 := [refl]: #2059
#2070 := [nnf-neg #2060 #2067]: #2069
#2056 := (~ #2055 #2054)
#2057 := [sk]: #2056
#2072 := [trans #2057 #2070]: #2071
#2031 := (not #1215)
#2032 := (~ #2031 #1212)
#2029 := (~ #1212 #1212)
#2027 := (~ #1209 #1209)
#2028 := [refl]: #2027
#2030 := [nnf-pos #2028]: #2029
#2033 := [nnf-neg #2030]: #2032
#2076 := [nnf-neg #2033 #2072]: #2075
#2023 := (~ #1215 #2022)
#2024 := [sk]: #2023
#2080 := [nnf-neg #2024 #2076]: #2079
#1999 := (not #1196)
#2000 := (~ #1999 #1193)
#1997 := (~ #1193 #1193)
#1995 := (~ #1190 #1190)
#1996 := [refl]: #1995
#1998 := [nnf-pos #1996]: #1997
#2001 := [nnf-neg #1998]: #2000
#2084 := [nnf-neg #2001 #2080]: #2083
#1991 := (~ #1196 #1990)
#1992 := [sk]: #1991
#2088 := [nnf-neg #1992 #2084]: #2087
#1972 := (not #1182)
#1973 := (~ #1972 #1179)
#1970 := (~ #1179 #1179)
#1968 := (~ #1176 #1176)
#1969 := [refl]: #1968
#1971 := [nnf-pos #1969]: #1970
#1974 := [nnf-neg #1971]: #1973
#2092 := [nnf-neg #1974 #2088]: #2091
#1964 := (~ #1182 #1963)
#1965 := [sk]: #1964
#2096 := [nnf-neg #1965 #2092]: #2095
#1958 := (~ #1957 #1957)
#1959 := [refl]: #1958
#2100 := [nnf-neg #1959 #2096]: #2099
#1955 := (~ #661 #661)
#1956 := [refl]: #1955
#2104 := [nnf-neg #1956 #2100]: #2103
#1952 := (not #673)
#1953 := (~ #1952 #563)
#1950 := (~ #563 #563)
#1948 := (~ #560 #560)
#1949 := [refl]: #1948
#1951 := [nnf-pos #1949]: #1950
#1954 := [nnf-neg #1951]: #1953
#2108 := [nnf-neg #1954 #2104]: #2107
#1944 := (~ #673 #1943)
#1945 := [sk]: #1944
#2112 := [nnf-neg #1945 #2108]: #2111
#1932 := (not #1173)
#1933 := (~ #1932 #1170)
#1930 := (~ #1170 #1170)
#1928 := (~ #1165 #1165)
#1929 := [refl]: #1928
#1931 := [nnf-pos #1929]: #1930
#1934 := [nnf-neg #1931]: #1933
#2116 := [nnf-neg #1934 #2112]: #2115
#1924 := (~ #1173 #1923)
#1925 := [sk]: #1924
#2120 := [nnf-neg #1925 #2116]: #2119
#1914 := (not #1162)
#1915 := (~ #1914 #1159)
#1912 := (~ #1159 #1159)
#1910 := (~ #1156 #1156)
#1911 := [refl]: #1910
#1913 := [nnf-pos #1911]: #1912
#1916 := [nnf-neg #1913]: #1915
#1907 := (not #1305)
#1908 := (~ #1907 #1302)
#1905 := (~ #1302 #1302)
#1903 := (~ #1299 #1299)
#1904 := [refl]: #1903
#1906 := [nnf-pos #1904]: #1905
#1909 := [nnf-neg #1906]: #1908
#1901 := (~ #1900 #1900)
#1902 := [refl]: #1901
#1897 := (not #1318)
#1898 := (~ #1897 #1315)
#1895 := (~ #1315 #1315)
#1893 := (~ #1312 #1312)
#1894 := [refl]: #1893
#1896 := [nnf-pos #1894]: #1895
#1899 := [nnf-neg #1896]: #1898
#1891 := (~ #1323 #1323)
#1892 := [refl]: #1891
#1889 := (~ #184 #184)
#1890 := [refl]: #1889
#1886 := (not #1333)
#1887 := (~ #1886 #1881)
#1882 := (~ #1117 #1881)
#1883 := [sk]: #1882
#1888 := [nnf-neg #1883]: #1887
#2124 := [nnf-neg #1888 #1890 #1892 #1899 #1902 #1909 #1916 #2120]: #2123
#1869 := (not #1135)
#1870 := (~ #1869 #1868)
#1865 := (not #1111)
#1866 := (~ #1865 #1864)
#1861 := (not #1108)
#1862 := (~ #1861 #1860)
#1857 := (not #1105)
#1858 := (~ #1857 #1856)
#1853 := (not #1102)
#1854 := (~ #1853 #1852)
#1850 := (~ #1849 #1849)
#1851 := [refl]: #1850
#1846 := (not #1099)
#1847 := (~ #1846 #1096)
#1844 := (~ #1096 #1096)
#1842 := (~ #1093 #1093)
#1843 := [refl]: #1842
#1845 := [nnf-pos #1843]: #1844
#1848 := [nnf-neg #1845]: #1847
#1855 := [nnf-neg #1848 #1851]: #1854
#1838 := (~ #1099 #1837)
#1839 := [sk]: #1838
#1859 := [nnf-neg #1839 #1855]: #1858
#1812 := (not #1081)
#1813 := (~ #1812 #1809)
#1810 := (~ #1078 #1809)
#1807 := (~ #1075 #1806)
#1802 := (~ #1072 #1801)
#1803 := [sk]: #1802
#1789 := (~ #1056 #1056)
#1790 := [refl]: #1789
#1808 := [monotonicity #1790 #1803]: #1807
#1811 := [nnf-pos #1808]: #1810
#1814 := [nnf-neg #1811]: #1813
#1863 := [nnf-neg #1814 #1859]: #1862
#1787 := (~ #1081 #1784)
#1769 := (exists (vars (?v1 S2)) #1768)
#1770 := (or #1760 #1769)
#1771 := (not #1770)
#1785 := (~ #1771 #1784)
#1781 := (not #1769)
#1782 := (~ #1781 #1780)
#1778 := (~ #1777 #1777)
#1779 := [refl]: #1778
#1783 := [nnf-neg #1779]: #1782
#1775 := (~ #1774 #1774)
#1776 := [refl]: #1775
#1786 := [nnf-neg #1776 #1783]: #1785
#1772 := (~ #1081 #1771)
#1773 := [sk]: #1772
#1788 := [trans #1773 #1786]: #1787
#1867 := [nnf-neg #1788 #1863]: #1866
#1749 := (~ #1748 #1748)
#1750 := [refl]: #1749
#1746 := (~ #1745 #1745)
#1747 := [refl]: #1746
#1743 := (~ #1742 #1742)
#1744 := [refl]: #1743
#1740 := (~ #1739 #1739)
#1741 := [refl]: #1740
#1737 := (~ #1333 #1736)
#1734 := (~ #1733 #1733)
#1735 := [refl]: #1734
#1738 := [nnf-neg #1735]: #1737
#1871 := [nnf-neg #1738 #1741 #1744 #1747 #1750 #1867]: #1870
#2128 := [nnf-neg #1871 #2124]: #2127
#1730 := (not #1044)
#1731 := (~ #1730 #1727)
#1728 := (~ #1041 #1727)
#1725 := (~ #1038 #1724)
#1720 := (~ #1035 #1719)
#1721 := [sk]: #1720
#1705 := (~ #1011 #1011)
#1706 := [refl]: #1705
#1726 := [monotonicity #1706 #1721]: #1725
#1729 := [nnf-pos #1726]: #1728
#1732 := [nnf-neg #1729]: #1731
#1702 := (not #1380)
#1703 := (~ #1702 #1377)
#1700 := (~ #1377 #1377)
#1698 := (~ #1374 #1374)
#1699 := [refl]: #1698
#1701 := [nnf-pos #1699]: #1700
#1704 := [nnf-neg #1701]: #1703
#1695 := (not #1391)
#1696 := (~ #1695 #1388)
#1693 := (~ #1388 #1388)
#1691 := (~ #1385 #1385)
#1692 := [refl]: #1691
#1694 := [nnf-pos #1692]: #1693
#1697 := [nnf-neg #1694]: #1696
#1688 := (not #1400)
#1689 := (~ #1688 #1397)
#1686 := (~ #1397 #1397)
#1684 := (~ #1394 #1394)
#1685 := [refl]: #1684
#1687 := [nnf-pos #1685]: #1686
#1690 := [nnf-neg #1687]: #1689
#1682 := (~ #1681 #1681)
#1683 := [refl]: #1682
#1678 := (not #1403)
#1679 := (~ #1678 #1675)
#1676 := (~ #999 #1675)
#1673 := (~ #996 #1672)
#1668 := (~ #993 #1667)
#1669 := [sk]: #1668
#1652 := (~ #973 #973)
#1653 := [refl]: #1652
#1674 := [monotonicity #1653 #1669]: #1673
#1677 := [nnf-pos #1674]: #1676
#1680 := [nnf-neg #1677]: #1679
#2132 := [nnf-neg #1680 #1683 #1690 #1697 #1704 #1732 #2128]: #2131
#1650 := (~ #1403 #1647)
#1632 := (exists (vars (?v1 S2)) #1631)
#1633 := (or #1622 #1632)
#1634 := (not #1633)
#1648 := (~ #1634 #1647)
#1644 := (not #1632)
#1645 := (~ #1644 #1643)
#1641 := (~ #1640 #1640)
#1642 := [refl]: #1641
#1646 := [nnf-neg #1642]: #1645
#1638 := (~ #1637 #1637)
#1639 := [refl]: #1638
#1649 := [nnf-neg #1639 #1646]: #1648
#1635 := (~ #1403 #1634)
#1636 := [sk]: #1635
#1651 := [trans #1636 #1649]: #1650
#2136 := [nnf-neg #1651 #2132]: #2135
#1610 := (not #961)
#1611 := (~ #1610 #958)
#1608 := (~ #958 #958)
#1606 := (~ #955 #955)
#1607 := [refl]: #1606
#1609 := [nnf-pos #1607]: #1608
#1612 := [nnf-neg #1609]: #1611
#2140 := [nnf-neg #1612 #2136]: #2139
#1602 := (~ #961 #1601)
#1603 := [sk]: #1602
#2144 := [nnf-neg #1603 #2140]: #2143
#1578 := (not #935)
#1579 := (~ #1578 #932)
#1576 := (~ #932 #932)
#1574 := (~ #929 #929)
#1575 := [refl]: #1574
#1577 := [nnf-pos #1575]: #1576
#1580 := [nnf-neg #1577]: #1579
#2148 := [nnf-neg #1580 #2144]: #2147
#1570 := (~ #935 #1569)
#1571 := [sk]: #1570
#2152 := [nnf-neg #1571 #2148]: #2151
#1551 := (not #920)
#1552 := (~ #1551 #917)
#1549 := (~ #917 #917)
#1547 := (~ #916 #916)
#1548 := [refl]: #1547
#1550 := [nnf-pos #1548]: #1549
#1553 := [nnf-neg #1550]: #1552
#2156 := [nnf-neg #1553 #2152]: #2155
#1543 := (~ #920 #1542)
#1544 := [sk]: #1543
#2160 := [nnf-neg #1544 #2156]: #2159
#1505 := (~ #1504 #1504)
#1538 := [refl]: #1505
#2164 := [nnf-neg #1538 #2160]: #2163
#1536 := (~ #868 #868)
#1537 := [refl]: #1536
#2167 := [nnf-neg #1537 #2164]: #2166
#1480 := [not-or-elim #1475]: #1479
#2168 := [mp~ #1480 #2167]: #2165
#2169 := [mp #2168 #2483]: #2481
#3122 := [mp #2169 #3121]: #3119
#4037 := [mp #3122 #4036]: #4034
#7272 := [unit-resolution #4037 #4122]: #4031
#3361 := (or #4028 #4022)
#3351 := [def-axiom]: #3361
#7273 := [unit-resolution #3351 #7272]: #4022
#3357 := (or #4025 #1542 #4019)
#3359 := [def-axiom]: #3357
#7274 := [unit-resolution #3359 #7273 #4053]: #4019
#3355 := (or #4016 #4010)
#3358 := [def-axiom]: #3355
#7275 := [unit-resolution #3358 #7274]: #4010
#4245 := [hypothesis]: #1560
#3661 := (forall (vars (?v0 S2)) (:pat #3660) #78)
#3664 := (iff #79 #3661)
#3662 := (iff #78 #78)
#3663 := [refl]: #3662
#3665 := [quant-intro #3663]: #3664
#1502 := (~ #79 #79)
#1533 := (~ #78 #78)
#1534 := [refl]: #1533
#1503 := [nnf-pos #1534]: #1502
#1478 := [not-or-elim #1475]: #79
#1535 := [mp~ #1478 #1503]: #79
#3666 := [mp #1535 #3665]: #3661
#6940 := (not #3661)
#4154 := (or #6940 #1884)
#4155 := [quant-inst #1555]: #4154
#4251 := [unit-resolution #4155 #3666 #4245]: false
#4288 := [lemma #4251]: #1884
#3186 := (or #1841 #1560)
#3272 := [def-axiom]: #3186
#7276 := [unit-resolution #3272 #4288]: #1841
#3217 := (or #4013 #1946 #4007)
#3375 := [def-axiom]: #3217
#7277 := [unit-resolution #3375 #7276 #7275]: #4007
#3397 := (or #4004 #3998)
#3367 := [def-axiom]: #3397
#7278 := [unit-resolution #3367 #7277]: #3998
#6766 := [hypothesis]: #1584
#6706 := (or #6940 #2503)
#6719 := [quant-inst #1581]: #6706
#6767 := [unit-resolution #6719 #3666 #6766]: false
#6806 := [lemma #6767]: #2503
#3277 := (or #2518 #1584)
#3274 := [def-axiom]: #3277
#7279 := [unit-resolution #3274 #6806]: #2518
#3394 := (or #4001 #2523 #3995)
#3395 := [def-axiom]: #3394
#7280 := [unit-resolution #3395 #7279 #7278]: #3995
#3378 := (or #3992 #3986)
#3385 := [def-axiom]: #3378
#7281 := [unit-resolution #3385 #7280]: #3986
#3415 := (or #3989 #3705 #3983)
#3400 := [def-axiom]: #3415
#7282 := [unit-resolution #3400 #7281]: #3986
#7283 := [unit-resolution #7282 #6930]: #3983
#3431 := (or #3980 #111)
#3432 := [def-axiom]: #3431
#7286 := [unit-resolution #3432 #7283]: #111
#6676 := (= #168 #110)
#6764 := [hypothesis]: #3817
#3559 := (or #3814 #149)
#3554 := [def-axiom]: #3559
#6807 := [unit-resolution #3554 #6764]: #149
#6734 := [monotonicity #6807]: #6676
#6648 := [trans #6734 #7286]: #169
#3555 := (or #3814 #3751)
#3556 := [def-axiom]: #3555
#6645 := [unit-resolution #3556 #6764]: #3751
#7455 := (or #2754 #3756 #503)
#6650 := (f19 f20 ?v1!10)
#6737 := (* -1::Int #6650)
#6738 := (+ f3 #6737)
#6739 := (<= #6738 0::Int)
#7562 := (not #6739)
#7411 := [hypothesis]: #2759
#3583 := (or #2754 #1821)
#3585 := [def-axiom]: #3583
#7412 := [unit-resolution #3585 #7411]: #1821
#7369 := (+ #1817 #6737)
#7377 := (>= #7369 0::Int)
#7368 := (= #1817 #6650)
#7415 := (= #6650 #1817)
#7413 := (= f20 f25)
#6293 := [hypothesis]: #149
#7414 := [symm #6293]: #7413
#7416 := [monotonicity #7414]: #7415
#7417 := [symm #7416]: #7368
#7404 := (not #7368)
#7405 := (or #7404 #7377)
#7403 := [th-lemma arith triangle-eq]: #7405
#7406 := [unit-resolution #7403 #7417]: #7377
#7563 := (not #7377)
#7564 := (or #7562 #7563 #1820)
#7558 := [hypothesis]: #1821
#7559 := [hypothesis]: #7377
#7560 := [hypothesis]: #6739
#7561 := [th-lemma arith farkas -1 1 1 #7560 #7559 #7558]: false
#7565 := [lemma #7561]: #7564
#7407 := [unit-resolution #7565 #7406 #7412]: #7562
#6285 := (f11 f21 ?v1!10)
#6647 := (= #6285 f1)
#7300 := (not #6647)
#7008 := (f19 f20 ?v0!11)
#7003 := (* -1::Int #7008)
#7301 := (+ #6650 #7003)
#7304 := (+ #1824 #7301)
#7305 := (>= #7304 0::Int)
#7459 := (not #7305)
#7379 := (+ #1831 #7003)
#7380 := (<= #7379 0::Int)
#7378 := (= #1831 #7008)
#7408 := (= #7008 #1831)
#7426 := [monotonicity #7414]: #7408
#7427 := [symm #7426]: #7378
#7425 := (not #7378)
#7428 := (or #7425 #7380)
#7429 := [th-lemma arith triangle-eq]: #7428
#7430 := [unit-resolution #7429 #7427]: #7380
#3586 := (not #2356)
#3584 := (or #2754 #3586)
#3587 := [def-axiom]: #3584
#7458 := [unit-resolution #3587 #7411]: #3586
#7460 := (not #7380)
#7461 := (or #7459 #7460 #2356 #7563)
#7462 := [th-lemma arith assign-bounds -1 -1 1]: #7461
#7463 := [unit-resolution #7462 #7458 #7406 #7430]: #7459
#7466 := (or #7300 #7305)
#3225 := (or #2754 #1828)
#3226 := [def-axiom]: #3225
#7464 := [unit-resolution #3226 #7411]: #1828
#3399 := (or #3980 #3734)
#3404 := [def-axiom]: #3399
#7465 := [unit-resolution #3404 #7283]: #3734
#7309 := (or #3739 #7300 #1827 #7305)
#7306 := (or #7300 #1827 #7305)
#7310 := (or #3739 #7306)
#7312 := (iff #7310 #7309)
#7313 := [rewrite]: #7312
#7311 := [quant-inst #1816 #1815]: #7310
#7314 := [mp #7311 #7313]: #7309
#7451 := [unit-resolution #7314 #7465 #7464]: #7466
#7452 := [unit-resolution #7451 #7463]: #7300
#6728 := (or #6647 #6739)
#7450 := [hypothesis]: #3751
#6799 := (or #3756 #6647 #6739)
#6816 := (or #3756 #6728)
#6846 := (iff #6816 #6799)
#6847 := [rewrite]: #6846
#6817 := [quant-inst #1815]: #6816
#6845 := [mp #6817 #6847]: #6799
#7453 := [unit-resolution #6845 #7450]: #6728
#7454 := [unit-resolution #7453 #7452 #7407]: false
#7468 := [lemma #7454]: #7455
#6971 := [unit-resolution #7468 #6807 #6645]: #2754
#3402 := (or #3814 #3808)
#3403 := [def-axiom]: #3402
#6674 := [unit-resolution #3403 #6764]: #3808
#4377 := (or #3814 #1757)
#4289 := (f19 f20 ?v0!8)
#4618 := (= #1754 #4289)
#6669 := [monotonicity #6807]: #4618
#3405 := (or #3980 #3742)
#3406 := [def-axiom]: #3405
#6675 := [unit-resolution #3406 #7283]: #3742
#4616 := [hypothesis]: #1758
#3298 := (or #3790 #1849)
#3299 := [def-axiom]: #3298
#6729 := [unit-resolution #3299 #6648]: #3790
#6730 := [unit-resolution #7468 #6645 #6807]: #2754
#3571 := (or #3799 #2759 #3793)
#3568 := [def-axiom]: #3571
#6726 := [unit-resolution #3568 #6730 #6729]: #3799
#3283 := (or #3802 #3796)
#3284 := [def-axiom]: #3283
#6731 := [unit-resolution #3284 #6726]: #3802
#3562 := (or #3811 #3771 #3805)
#3566 := [def-axiom]: #3562
#4291 := [unit-resolution #3566 #6731 #6674]: #3771
#3589 := (or #3768 #1753)
#3254 := [def-axiom]: #3589
#4320 := [unit-resolution #3254 #4291]: #1753
#3234 := (or #3768 #3760)
#3575 := [def-axiom]: #3234
#4321 := [unit-resolution #3575 #4291]: #3760
#6324 := (not #4618)
#6580 := (or #6324 #3765 #503 #3747 #1752 #1757)
#4276 := (?v1!7 ?v0!8)
#4648 := (f19 f25 #4276)
#4674 := (* -1::Int #4648)
#4679 := (+ #1754 #4674)
#4680 := (<= #4679 0::Int)
#6358 := (not #4680)
#4271 := (f19 f20 #4276)
#5403 := (+ #4271 #4674)
#5440 := (>= #5403 0::Int)
#5390 := (= #4271 #4648)
#6305 := (= #4648 #4271)
#6306 := [monotonicity #6293]: #6305
#6323 := [symm #6306]: #5390
#6325 := (not #5390)
#6326 := (or #6325 #5440)
#6327 := [th-lemma arith triangle-eq]: #6326
#6322 := [unit-resolution #6327 #6323]: #5440
#4272 := (* -1::Int #4289)
#4349 := (+ #4271 #4272)
#4368 := (>= #4349 0::Int)
#4448 := (not #4368)
#4329 := (f6 f7 #4276)
#4330 := (f5 #4329 ?v0!8)
#4315 := (f4 #4330)
#4366 := (+ #4272 #4315)
#4367 := (+ #4271 #4366)
#4391 := (= #4367 0::Int)
#4390 := (not #4391)
#4326 := (f11 f21 #4276)
#4327 := (= #4326 f1)
#4328 := (not #4327)
#4398 := (or #4368 #4328 #4390)
#4419 := (not #4398)
#4273 := (+ f3 #4272)
#4274 := (<= #4273 0::Int)
#4624 := (not #4274)
#4619 := (+ #1754 #4272)
#4615 := (>= #4619 0::Int)
#6328 := [hypothesis]: #4618
#6329 := (or #6324 #4615)
#6330 := [th-lemma arith triangle-eq]: #6329
#6331 := [unit-resolution #6330 #6328]: #4615
#4625 := (not #4615)
#4646 := (or #4624 #4625 #1757)
#4621 := [hypothesis]: #4274
#4622 := [hypothesis]: #4615
#4623 := [th-lemma arith farkas 1 -1 1 #4622 #4621 #4616]: false
#4647 := [lemma #4623]: #4646
#6332 := [unit-resolution #4647 #6331 #4616]: #4624
#6350 := (or #4274 #4419)
#6351 := [hypothesis]: #1753
#6355 := [hypothesis]: #3742
#4425 := (or #3747 #1752 #4274 #4419)
#4316 := (* -1::Int #4315)
#4323 := (* -1::Int #4271)
#4314 := (+ #4323 #4316)
#4317 := (+ #4289 #4314)
#4318 := (= #4317 0::Int)
#4319 := (not #4318)
#4324 := (+ #4289 #4323)
#4325 := (<= #4324 0::Int)
#4332 := (or #4325 #4328 #4319)
#4333 := (not #4332)
#4337 := (or #1752 #4274 #4333)
#4426 := (or #3747 #4337)
#4439 := (iff #4426 #4425)
#4420 := (or #1752 #4274 #4419)
#4428 := (or #3747 #4420)
#4435 := (iff #4428 #4425)
#4438 := [rewrite]: #4435
#4436 := (iff #4426 #4428)
#4423 := (iff #4337 #4420)
#4421 := (iff #4333 #4419)
#4399 := (iff #4332 #4398)
#4396 := (iff #4319 #4390)
#4394 := (iff #4318 #4391)
#4373 := (+ #4289 #4316)
#4374 := (+ #4323 #4373)
#4364 := (= #4374 0::Int)
#4392 := (iff #4364 #4391)
#4393 := [rewrite]: #4392
#4362 := (iff #4318 #4364)
#4375 := (= #4317 #4374)
#4363 := [rewrite]: #4375
#4365 := [monotonicity #4363]: #4362
#4395 := [trans #4365 #4393]: #4394
#4397 := [monotonicity #4395]: #4396
#4371 := (iff #4325 #4368)
#4338 := (+ #4323 #4289)
#4344 := (<= #4338 0::Int)
#4369 := (iff #4344 #4368)
#4370 := [rewrite]: #4369
#4347 := (iff #4325 #4344)
#4345 := (= #4324 #4338)
#4346 := [rewrite]: #4345
#4348 := [monotonicity #4346]: #4347
#4372 := [trans #4348 #4370]: #4371
#4400 := [monotonicity #4372 #4397]: #4399
#4422 := [monotonicity #4400]: #4421
#4424 := [monotonicity #4422]: #4423
#4437 := [monotonicity #4424]: #4436
#4440 := [trans #4437 #4438]: #4439
#4427 := [quant-inst #1751]: #4426
#4446 := [mp #4427 #4440]: #4425
#6354 := [unit-resolution #4446 #6355 #6351]: #6350
#6356 := [unit-resolution #6354 #6332]: #4419
#4449 := (or #4398 #4448)
#4450 := [def-axiom]: #4449
#6357 := [unit-resolution #4450 #6356]: #4448
#6365 := (not #5440)
#6368 := (or #6358 #4625 #4368 #6365)
#6367 := [th-lemma arith assign-bounds -1 1 -1]: #6368
#6369 := [unit-resolution #6367 #6331 #6357 #6322]: #6358
#4710 := (+ #4316 #4674)
#4711 := (+ #1754 #4710)
#4712 := (= #4711 0::Int)
#4798 := (<= #4711 0::Int)
#5439 := (<= #5403 0::Int)
#6370 := (or #6325 #5439)
#6375 := [th-lemma arith triangle-eq]: #6370
#6378 := [unit-resolution #6375 #6323]: #5439
#4447 := (>= #4367 0::Int)
#4455 := (or #4398 #4391)
#4458 := [def-axiom]: #4455
#6379 := [unit-resolution #4458 #6356]: #4391
#6377 := (or #4390 #4447)
#6383 := [th-lemma arith triangle-eq]: #6377
#6384 := [unit-resolution #6383 #6379]: #4447
#4620 := (<= #4619 0::Int)
#6382 := (or #6324 #4620)
#6386 := [th-lemma arith triangle-eq]: #6382
#6387 := [unit-resolution #6386 #6328]: #4620
#6401 := (not #5439)
#6398 := (not #4447)
#5997 := (not #4620)
#6400 := (or #4798 #5997 #6398 #6401)
#6402 := [th-lemma arith assign-bounds -1 1 -1]: #6400
#6403 := [unit-resolution #6402 #6387 #6384 #6378]: #4798
#4770 := (>= #4711 0::Int)
#4445 := (<= #4367 0::Int)
#6439 := (or #4390 #4445)
#6471 := [th-lemma arith triangle-eq]: #6439
#6466 := [unit-resolution #6471 #6379]: #4445
#6040 := (not #4445)
#6470 := (or #4770 #4625 #6040 #6365)
#6472 := [th-lemma arith assign-bounds -1 1 -1]: #6470
#6473 := [unit-resolution #6472 #6331 #6466 #6322]: #4770
#6475 := (not #4798)
#6474 := (not #4770)
#6476 := (or #4712 #6474 #6475)
#6482 := [th-lemma arith triangle-eq]: #6476
#6571 := [unit-resolution #6482 #6473 #6403]: #4712
#4731 := (not #4712)
#4738 := (or #4680 #4731)
#6577 := [hypothesis]: #3760
#4741 := (or #3765 #4680 #4731)
#4645 := (+ #1755 #4315)
#4650 := (+ #4648 #4645)
#4651 := (= #4650 0::Int)
#4652 := (not #4651)
#4649 := (+ #4648 #1755)
#4644 := (>= #4649 0::Int)
#4653 := (or #4644 #4652)
#4762 := (or #3765 #4653)
#4767 := (iff #4762 #4741)
#4764 := (or #3765 #4738)
#4761 := (iff #4764 #4741)
#4766 := [rewrite]: #4761
#4765 := (iff #4762 #4764)
#4739 := (iff #4653 #4738)
#4732 := (iff #4652 #4731)
#4735 := (iff #4651 #4712)
#4705 := (+ #4315 #4648)
#4706 := (+ #1755 #4705)
#4703 := (= #4706 0::Int)
#4733 := (iff #4703 #4712)
#4734 := [rewrite]: #4733
#4708 := (iff #4651 #4703)
#4707 := (= #4650 #4706)
#4702 := [rewrite]: #4707
#4709 := [monotonicity #4702]: #4708
#4736 := [trans #4709 #4734]: #4735
#4737 := [monotonicity #4736]: #4732
#4683 := (iff #4644 #4680)
#4654 := (+ #1755 #4648)
#4677 := (>= #4654 0::Int)
#4681 := (iff #4677 #4680)
#4682 := [rewrite]: #4681
#4678 := (iff #4644 #4677)
#4675 := (= #4649 #4654)
#4676 := [rewrite]: #4675
#4673 := [monotonicity #4676]: #4678
#4704 := [trans #4673 #4682]: #4683
#4740 := [monotonicity #4704 #4737]: #4739
#4760 := [monotonicity #4740]: #4765
#4768 := [trans #4760 #4766]: #4767
#4763 := [quant-inst #4276]: #4762
#4769 := [mp #4763 #4768]: #4741
#6578 := [unit-resolution #4769 #6577]: #4738
#6579 := [unit-resolution #6578 #6571 #6369]: false
#6581 := [lemma #6579]: #6580
#4376 := [unit-resolution #6581 #4321 #4320 #4616 #6675 #6807 #6669]: false
#4290 := [lemma #4376]: #4377
#6958 := [unit-resolution #4290 #6764]: #1757
#3249 := (or #3768 #1758)
#3591 := [def-axiom]: #3249
#6954 := [unit-resolution #3591 #6958]: #3768
#6959 := [unit-resolution #3566 #6954 #6674]: #3805
#6960 := [unit-resolution #3284 #6959]: #3796
#6961 := [unit-resolution #3568 #6960 #6971]: #3793
#7266 := [unit-resolution #3299 #6961]: #1849
#7267 := [unit-resolution #7266 #6648]: false
#7128 := [lemma #7267]: #3814
#3407 := (or #3980 #3974)
#3408 := [def-axiom]: #3407
#11570 := [unit-resolution #3408 #7283]: #3974
#3419 := (or #3977 #3817 #3971)
#3421 := [def-axiom]: #3419
#12390 := [unit-resolution #3421 #11570]: #3974
#11571 := [unit-resolution #12390 #7128]: #3971
#3445 := (or #3968 #3838)
#3426 := [def-axiom]: #3445
#11843 := [unit-resolution #3426 #11571]: #3838
#3459 := (or #3968 #194)
#3464 := [def-axiom]: #3459
#12662 := [unit-resolution #3464 #11571]: #194
#3456 := (or #3968 #184)
#3457 := [def-axiom]: #3456
#16074 := [unit-resolution #3457 #11571]: #184
#8244 := (or #1942 #183 #715 #3843)
#8160 := (= #185 #1940)
#8155 := (= #1940 #185)
#7789 := (= ?v0!14 f28)
#7634 := (f11 f21 ?v0!14)
#7635 := (= #7634 f1)
#7795 := (or #7789 #7635)
#7768 := (f11 #193 ?v0!14)
#7786 := (= #7768 f1)
#7800 := (iff #7786 #7795)
#7803 := (or #7582 #7800)
#7790 := (if #7789 #4057 #7635)
#7791 := (iff #7786 #7790)
#7804 := (or #7582 #7791)
#7806 := (iff #7804 #7803)
#7808 := (iff #7803 #7803)
#7809 := [rewrite]: #7808
#7801 := (iff #7791 #7800)
#7798 := (iff #7790 #7795)
#7792 := (if #7789 true #7635)
#7796 := (iff #7792 #7795)
#7797 := [rewrite]: #7796
#7793 := (iff #7790 #7792)
#7794 := [monotonicity #4060]: #7793
#7799 := [trans #7794 #7797]: #7798
#7802 := [monotonicity #7799]: #7801
#7807 := [monotonicity #7802]: #7806
#7810 := [trans #7807 #7809]: #7806
#7805 := [quant-inst #115 #181 #3 #1935]: #7804
#7811 := [mp #7805 #7810]: #7803
#7893 := [unit-resolution #7811 #3646]: #7800
#8183 := [hypothesis]: #1943
#3547 := (or #1942 #1937)
#3543 := [def-axiom]: #3547
#8184 := [unit-resolution #3543 #8183]: #1937
#8190 := (= #7768 #1936)
#8191 := (= #193 f29)
#8181 := [hypothesis]: #194
#8195 := [symm #8181]: #8191
#8196 := [monotonicity #8195]: #8190
#8194 := [trans #8196 #8184]: #7786
#7824 := (not #7786)
#7821 := (not #7800)
#7825 := (or #7821 #7824 #7795)
#7826 := [def-axiom]: #7825
#8197 := [unit-resolution #7826 #8194 #7893]: #7795
#7815 := (not #7635)
#8135 := [hypothesis]: #184
#7618 := (* -1::Int #1940)
#7645 := (+ #185 #7618)
#8112 := (>= #7645 0::Int)
#8306 := (not #8112)
#7665 := (f5 #195 ?v0!14)
#7666 := (f4 #7665)
#7684 := (+ #7618 #7666)
#7685 := (+ #185 #7684)
#7686 := (>= #7685 0::Int)
#7740 := (not #7686)
#7667 := (* -1::Int #7666)
#7668 := (+ f3 #7667)
#7669 := (<= #7668 0::Int)
#7717 := (or #7669 #7686)
#7720 := (not #7717)
#3548 := (not #1941)
#3542 := (or #1942 #3548)
#3549 := [def-axiom]: #3542
#8200 := [unit-resolution #3549 #8183]: #3548
#7150 := [hypothesis]: #3838
#7726 := (or #3843 #7720 #1941)
#7670 := (+ #1146 #7667)
#7671 := (+ #1940 #7670)
#7672 := (<= #7671 0::Int)
#7714 := (or #7669 #7672)
#7715 := (not #7714)
#7716 := (or #7715 #1941)
#7727 := (or #3843 #7716)
#7734 := (iff #7727 #7726)
#7723 := (or #7720 #1941)
#7729 := (or #3843 #7723)
#7732 := (iff #7729 #7726)
#7733 := [rewrite]: #7732
#7730 := (iff #7727 #7729)
#7724 := (iff #7716 #7723)
#7721 := (iff #7715 #7720)
#7718 := (iff #7714 #7717)
#7689 := (iff #7672 #7686)
#7677 := (+ #1940 #7667)
#7678 := (+ #1146 #7677)
#7681 := (<= #7678 0::Int)
#7687 := (iff #7681 #7686)
#7688 := [rewrite]: #7687
#7682 := (iff #7672 #7681)
#7679 := (= #7671 #7678)
#7680 := [rewrite]: #7679
#7683 := [monotonicity #7680]: #7682
#7690 := [trans #7683 #7688]: #7689
#7719 := [monotonicity #7690]: #7718
#7722 := [monotonicity #7719]: #7721
#7725 := [monotonicity #7722]: #7724
#7731 := [monotonicity #7725]: #7730
#7735 := [trans #7731 #7733]: #7734
#7728 := [quant-inst #1935]: #7727
#7736 := [mp #7728 #7735]: #7726
#8203 := [unit-resolution #7736 #7150 #8200]: #7720
#7741 := (or #7717 #7740)
#7742 := [def-axiom]: #7741
#8251 := [unit-resolution #7742 #8203]: #7740
#8470 := (or #8306 #7686)
#7869 := (= #7666 0::Int)
#8459 := (not #7869)
#7879 := (>= #7666 0::Int)
#8449 := (not #7879)
#8448 := [hypothesis]: #7740
#8280 := [hypothesis]: #8112
#8456 := (or #8449 #7686 #8306)
#8457 := [th-lemma arith assign-bounds -1 1]: #8456
#8458 := [unit-resolution #8457 #8280 #8448]: #8449
#8460 := (or #8459 #7879)
#8461 := [th-lemma arith triangle-eq]: #8460
#8462 := [unit-resolution #8461 #8458]: #8459
#7865 := (= f28 ?v0!14)
#7880 := (<= #7666 0::Int)
#8463 := (or #7880 #7686 #8306)
#8464 := [th-lemma arith assign-bounds 1 1]: #8463
#8465 := [unit-resolution #8464 #8280 #8448]: #7880
#7871 := (not #7880)
#7872 := (or #7865 #7871)
#14 := (f6 f7 #10)
#15 := (f5 #14 #11)
#3600 := (pattern #15)
#16 := (f4 #15)
#325 := (<= #16 0::Int)
#326 := (not #325)
#12 := (= #10 #11)
#329 := (or #12 #326)
#3607 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3600) #329)
#332 := (forall (vars (?v0 S2) (?v1 S2)) #329)
#3610 := (iff #332 #3607)
#3608 := (iff #329 #329)
#3609 := [refl]: #3608
#3611 := [quant-intro #3609]: #3610
#1486 := (~ #332 #332)
#1485 := (~ #329 #329)
#1482 := [refl]: #1485
#1487 := [nnf-pos #1482]: #1486
#21 := (< 0::Int #16)
#20 := (not #12)
#22 := (implies #20 #21)
#23 := (forall (vars (?v0 S2) (?v1 S2)) #22)
#335 := (iff #23 #332)
#318 := (or #12 #21)
#322 := (forall (vars (?v0 S2) (?v1 S2)) #318)
#333 := (iff #322 #332)
#330 := (iff #318 #329)
#327 := (iff #21 #326)
#328 := [rewrite]: #327
#331 := [monotonicity #328]: #330
#334 := [quant-intro #331]: #333
#323 := (iff #23 #322)
#320 := (iff #22 #318)
#321 := [rewrite]: #320
#324 := [quant-intro #321]: #323
#336 := [trans #324 #334]: #335
#317 := [asserted]: #23
#337 := [mp #317 #336]: #332
#1483 := [mp~ #337 #1487]: #332
#3612 := [mp #1483 #3611]: #3607
#7204 := (not #3607)
#7883 := (or #7204 #7865 #7871)
#7884 := (or #7204 #7872)
#7886 := (iff #7884 #7883)
#7887 := [rewrite]: #7886
#7885 := [quant-inst #181 #1935]: #7884
#7888 := [mp #7885 #7887]: #7883
#8466 := [unit-resolution #7888 #3612]: #7872
#8467 := [unit-resolution #8466 #8465]: #7865
#7866 := (not #7865)
#7870 := (or #7866 #7869)
#17 := (= #16 0::Int)
#306 := (or #20 #17)
#3601 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3600) #306)
#314 := (forall (vars (?v0 S2) (?v1 S2)) #306)
#3604 := (iff #314 #3601)
#3602 := (iff #306 #306)
#3603 := [refl]: #3602
#3605 := [quant-intro #3603]: #3604
#1510 := (~ #314 #314)
#1508 := (~ #306 #306)
#1509 := [refl]: #1508
#1511 := [nnf-pos #1509]: #1510
#18 := (implies #12 #17)
#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
#315 := (iff #19 #314)
#312 := (iff #18 #306)
#313 := [rewrite]: #312
#316 := [quant-intro #313]: #315
#305 := [asserted]: #19
#319 := [mp #305 #316]: #314
#1484 := [mp~ #319 #1511]: #314
#3606 := [mp #1484 #3605]: #3601
#7193 := (not #3601)
#7873 := (or #7193 #7866 #7869)
#7874 := (or #7193 #7870)
#7876 := (iff #7874 #7873)
#7877 := [rewrite]: #7876
#7875 := [quant-inst #181 #1935]: #7874
#7878 := [mp #7875 #7877]: #7873
#8468 := [unit-resolution #7878 #3606]: #7870
#8469 := [unit-resolution #8468 #8467 #8462]: false
#8471 := [lemma #8469]: #8470
#8252 := [unit-resolution #8471 #8251]: #8306
#8185 := (or #7815 #183 #8112)
#8103 := [hypothesis]: #8306
#8110 := [hypothesis]: #7635
#3443 := (or #3980 #3726)
#3398 := [def-axiom]: #3443
#8136 := [unit-resolution #3398 #7283]: #3726
#7958 := (or #3731 #183 #7815 #8112)
#8113 := (or #183 #7815 #8112)
#7991 := (or #3731 #8113)
#8023 := (iff #7991 #7958)
#8024 := [rewrite]: #8023
#7992 := [quant-inst #1935 #181]: #7991
#8115 := [mp #7992 #8024]: #7958
#8182 := [unit-resolution #8115 #8136 #8135 #8110 #8103]: false
#8186 := [lemma #8182]: #8185
#8253 := [unit-resolution #8186 #8252 #8135]: #7815
#7818 := (not #7795)
#7819 := (or #7818 #7789 #7635)
#7820 := [def-axiom]: #7819
#8254 := [unit-resolution #7820 #8253 #8197]: #7789
#8255 := [monotonicity #8254]: #8155
#8250 := [symm #8255]: #8160
#8256 := (not #8160)
#8257 := (or #8256 #8112)
#8258 := [th-lemma arith triangle-eq]: #8257
#8243 := [unit-resolution #8258 #8252 #8250]: false
#8281 := [lemma #8243]: #8244
#16076 := [unit-resolution #8281 #16074 #12662 #11843]: #1942
#3450 := (or #3968 #3962)
#3451 := [def-axiom]: #3450
#11686 := [unit-resolution #3451 #11571]: #3962
#3444 := (or #3968 #3830)
#3390 := [def-axiom]: #3444
#12531 := [unit-resolution #3390 #11571]: #3830
#7166 := (or #1922 #3835 #3843)
#7014 := (f5 #195 ?v0!13)
#7015 := (f4 #7014)
#7040 := (+ #1920 #7015)
#7041 := (+ #185 #7040)
#7061 := (>= #7041 0::Int)
#7044 := (= #7041 0::Int)
#7016 := (* -1::Int #7015)
#7017 := (+ f3 #7016)
#7018 := (<= #7017 0::Int)
#7087 := (not #7018)
#6993 := (* -1::Int #1918)
#7033 := (+ #6993 #7015)
#7034 := (+ #185 #7033)
#7035 := (>= #7034 0::Int)
#7067 := (or #7018 #7035)
#7070 := (not #7067)
#7065 := (= #1919 #1918)
#7146 := (not #7065)
#7095 := (= #1918 #1919)
#7138 := (not #7095)
#7147 := (iff #7138 #7146)
#7144 := (iff #7095 #7065)
#7145 := [commutativity]: #7144
#7148 := [monotonicity #7145]: #7147
#7120 := [hypothesis]: #1923
#7141 := (or #7138 #1922)
#7142 := [th-lemma arith triangle-eq]: #7141
#7143 := [unit-resolution #7142 #7120]: #7138
#7149 := [mp #7143 #7148]: #7146
#7073 := (or #7070 #7065)
#7076 := (or #3843 #7070 #7065)
#7019 := (+ #1146 #7016)
#7020 := (+ #1918 #7019)
#7021 := (<= #7020 0::Int)
#7063 := (or #7018 #7021)
#7064 := (not #7063)
#7066 := (or #7064 #7065)
#7077 := (or #3843 #7066)
#7084 := (iff #7077 #7076)
#7079 := (or #3843 #7073)
#7082 := (iff #7079 #7076)
#7083 := [rewrite]: #7082
#7080 := (iff #7077 #7079)
#7074 := (iff #7066 #7073)
#7071 := (iff #7064 #7070)
#7068 := (iff #7063 #7067)
#7038 := (iff #7021 #7035)
#7026 := (+ #1918 #7016)
#7027 := (+ #1146 #7026)
#7030 := (<= #7027 0::Int)
#7036 := (iff #7030 #7035)
#7037 := [rewrite]: #7036
#7031 := (iff #7021 #7030)
#7028 := (= #7020 #7027)
#7029 := [rewrite]: #7028
#7032 := [monotonicity #7029]: #7031
#7039 := [trans #7032 #7037]: #7038
#7069 := [monotonicity #7039]: #7068
#7072 := [monotonicity #7069]: #7071
#7075 := [monotonicity #7072]: #7074
#7081 := [monotonicity #7075]: #7080
#7085 := [trans #7081 #7083]: #7084
#7078 := [quant-inst #1917]: #7077
#7086 := [mp #7078 #7085]: #7076
#7151 := [unit-resolution #7086 #7150]: #7073
#7152 := [unit-resolution #7151 #7149]: #7070
#7088 := (or #7067 #7087)
#7089 := [def-axiom]: #7088
#7153 := [unit-resolution #7089 #7152]: #7087
#7090 := (not #7035)
#7091 := (or #7067 #7090)
#7092 := [def-axiom]: #7091
#7154 := [unit-resolution #7092 #7152]: #7090
#7047 := (or #7018 #7035 #7044)
#7155 := [hypothesis]: #3830
#7050 := (or #3835 #7018 #7035 #7044)
#7022 := (+ #7015 #1920)
#7023 := (+ #185 #7022)
#7024 := (= #7023 0::Int)
#7025 := (or #7018 #7021 #7024)
#7051 := (or #3835 #7025)
#7058 := (iff #7051 #7050)
#7053 := (or #3835 #7047)
#7056 := (iff #7053 #7050)
#7057 := [rewrite]: #7056
#7054 := (iff #7051 #7053)
#7048 := (iff #7025 #7047)
#7045 := (iff #7024 #7044)
#7042 := (= #7023 #7041)
#7043 := [rewrite]: #7042
#7046 := [monotonicity #7043]: #7045
#7049 := [monotonicity #7039 #7046]: #7048
#7055 := [monotonicity #7049]: #7054
#7059 := [trans #7055 #7057]: #7058
#7052 := [quant-inst #1917]: #7051
#7060 := [mp #7052 #7059]: #7050
#7156 := [unit-resolution #7060 #7155]: #7047
#7157 := [unit-resolution #7156 #7154 #7153]: #7044
#7158 := (not #7044)
#7159 := (or #7158 #7061)
#7160 := [th-lemma arith triangle-eq]: #7159
#7161 := [unit-resolution #7160 #7157]: #7061
#7096 := (<= #1921 0::Int)
#7162 := (or #7096 #1922)
#7163 := [th-lemma arith farkas 1 1]: #7162
#7164 := [unit-resolution #7163 #7120]: #7096
#7165 := [th-lemma arith farkas 1 -1 1 #7164 #7154 #7161]: false
#7167 := [lemma #7165]: #7166
#12440 := [unit-resolution #7167 #11843 #12531]: #1922
#3449 := (or #3965 #1923 #3959)
#3342 := [def-axiom]: #3449
#12444 := [unit-resolution #3342 #12440 #11686]: #3959
#3470 := (or #3956 #3950)
#3471 := [def-axiom]: #3470
#16077 := [unit-resolution #3471 #12444]: #3950
#3469 := (or #3953 #1943 #3947)
#3465 := [def-axiom]: #3469
#16078 := [unit-resolution #3465 #16077 #16076]: #3947
#3497 := (or #3944 #3855)
#3475 := [def-axiom]: #3497
#16079 := [unit-resolution #3475 #16078]: #3855
#3466 := (or #3956 #3846)
#3467 := [def-axiom]: #3466
#12445 := [unit-resolution #3467 #12444]: #3846
#3462 := (or #3968 #3820)
#3463 := [def-axiom]: #3462
#16073 := [unit-resolution #3463 #11571]: #3820
#13737 := (or #2911 #3835 #2011 #3825 #715 #3851 #3860)
#6483 := (f5 #195 ?v0!19)
#6481 := (f4 #6483)
#6484 := (* -1::Int #6481)
#6485 := (+ f3 #6484)
#6486 := (<= #6485 0::Int)
#11078 := (not #6486)
#13920 := [hypothesis]: #2012
#11308 := (+ #2008 #6484)
#11417 := (>= #11308 0::Int)
#11979 := (= #2008 #6481)
#13702 := (= #2007 #6483)
#13700 := (= #2006 #195)
#5405 := (= ?v1!18 f28)
#5408 := (f11 f21 ?v1!18)
#5409 := (= #5408 f1)
#6623 := (not #5409)
#6374 := (f19 f20 ?v0!19)
#6445 := (* -1::Int #6374)
#5362 := (f19 f20 ?v1!18)
#6639 := (+ #5362 #6445)
#6640 := (+ #2008 #6639)
#6641 := (>= #6640 0::Int)
#13671 := (not #6641)
#6446 := (+ #2016 #6445)
#6447 := (<= #6446 0::Int)
#9800 := [hypothesis]: #3846
#13118 := (or #3851 #6447)
#6389 := (+ #6374 #2017)
#6399 := (>= #6389 0::Int)
#13113 := (or #3851 #6399)
#13202 := (iff #13113 #13118)
#13233 := (iff #13118 #13118)
#13203 := [rewrite]: #13233
#6468 := (iff #6399 #6447)
#6440 := (+ #2017 #6374)
#6443 := (>= #6440 0::Int)
#6448 := (iff #6443 #6447)
#6467 := [rewrite]: #6448
#6438 := (iff #6399 #6443)
#6441 := (= #6389 #6440)
#6442 := [rewrite]: #6441
#6444 := [monotonicity #6442]: #6438
#6469 := [trans #6444 #6467]: #6468
#13232 := [monotonicity #6469]: #13202
#13234 := [trans #13232 #13203]: #13202
#13204 := [quant-inst #2003]: #13113
#13235 := [mp #13204 #13234]: #13118
#13612 := [unit-resolution #13235 #9800]: #6447
#3418 := (not #2020)
#3433 := (or #2911 #3418)
#3435 := [def-axiom]: #3433
#13665 := [unit-resolution #3435 #13632]: #3418
#5459 := (* -1::Int #5362)
#5460 := (+ #2015 #5459)
#10452 := (>= #5460 0::Int)
#5380 := (= #2015 #5362)
#3434 := (or #2911 #2005)
#3529 := [def-axiom]: #3434
#13666 := [unit-resolution #3529 #13632]: #2005
#8627 := [hypothesis]: #3855
#12607 := (or #3860 #2896 #5380)
#5383 := (or #2896 #5380)
#12544 := (or #3860 #5383)
#12541 := (iff #12544 #12607)
#12546 := [rewrite]: #12541
#12545 := [quant-inst #2002]: #12544
#12601 := [mp #12545 #12546]: #12607
#13667 := [unit-resolution #12601 #8627 #13666]: #5380
#13662 := (not #5380)
#13668 := (or #13662 #10452)
#13669 := [th-lemma arith triangle-eq]: #13668
#13670 := [unit-resolution #13669 #13667]: #10452
#13677 := (not #10452)
#13672 := (not #6447)
#13678 := (or #13671 #13672 #2020 #13677)
#13681 := [th-lemma arith assign-bounds -1 -1 1]: #13678
#13682 := [unit-resolution #13681 #13670 #13665 #13612]: #13671
#13688 := (or #6623 #6641)
#13159 := (or #3739 #6623 #2011 #6641)
#6642 := (or #6623 #2011 #6641)
#13288 := (or #3739 #6642)
#13294 := (iff #13288 #13159)
#13198 := [rewrite]: #13294
#13289 := [quant-inst #2003 #2002]: #13288
#13295 := [mp #13289 #13198]: #13159
#13689 := [unit-resolution #13295 #7465 #13920]: #13688
#13687 := [unit-resolution #13689 #13682]: #6623
#5415 := (or #5405 #5409)
#5397 := (f11 #193 ?v1!18)
#5398 := (= #5397 f1)
#5420 := (iff #5398 #5415)
#12447 := (or #7582 #5420)
#5410 := (if #5405 #4057 #5409)
#5411 := (iff #5398 #5410)
#12452 := (or #7582 #5411)
#12581 := (iff #12452 #12447)
#12632 := (iff #12447 #12447)
#12611 := [rewrite]: #12632
#5421 := (iff #5411 #5420)
#5418 := (iff #5410 #5415)
#5412 := (if #5405 true #5409)
#5416 := (iff #5412 #5415)
#5417 := [rewrite]: #5416
#5413 := (iff #5410 #5412)
#5414 := [monotonicity #4060]: #5413
#5419 := [trans #5414 #5417]: #5418
#5422 := [monotonicity #5419]: #5421
#12631 := [monotonicity #5422]: #12581
#12635 := [trans #12631 #12611]: #12581
#12580 := [quant-inst #115 #181 #3 #2002]: #12452
#12638 := [mp #12580 #12635]: #12447
#13690 := [unit-resolution #12638 #3646]: #5420
#13691 := (= #5397 #2004)
#13692 := [monotonicity #8195]: #13691
#13698 := [trans #13692 #13666]: #5398
#12683 := (not #5398)
#12670 := (not #5420)
#12681 := (or #12670 #12683 #5415)
#12704 := [def-axiom]: #12681
#13699 := [unit-resolution #12704 #13698 #13690]: #5415
#12666 := (not #5415)
#12667 := (or #12666 #5405 #5409)
#12660 := [def-axiom]: #12667
#13697 := [unit-resolution #12660 #13699 #13687]: #5405
#13701 := [monotonicity #13697]: #13700
#13707 := [monotonicity #13701]: #13702
#13708 := [monotonicity #13707]: #11979
#13706 := (not #11979)
#13709 := (or #13706 #11417)
#13710 := [th-lemma arith triangle-eq]: #13709
#13711 := [unit-resolution #13710 #13708]: #11417
#13941 := (not #11417)
#13942 := (or #11078 #13941 #2011)
#13921 := [hypothesis]: #11417
#13939 := [hypothesis]: #6486
#13940 := [th-lemma arith farkas -1 1 1 #13939 #13921 #13920]: false
#13943 := [lemma #13940]: #13942
#13716 := [unit-resolution #13943 #13711 #13920]: #11078
#6511 := (+ #6445 #6481)
#6509 := (+ #185 #6511)
#6512 := (>= #6509 0::Int)
#13270 := (not #6512)
#5484 := (+ #185 #5459)
#5485 := (<= #5484 0::Int)
#9764 := [hypothesis]: #3820
#13305 := (or #3825 #5409 #5485)
#5475 := (+ #5362 #1146)
#5476 := (>= #5475 0::Int)
#5477 := (or #5409 #5476)
#13306 := (or #3825 #5477)
#12884 := (iff #13306 #13305)
#5490 := (or #5409 #5485)
#13352 := (or #3825 #5490)
#13421 := (iff #13352 #13305)
#13422 := [rewrite]: #13421
#13353 := (iff #13306 #13352)
#5491 := (iff #5477 #5490)
#5488 := (iff #5476 #5485)
#5478 := (+ #1146 #5362)
#5481 := (>= #5478 0::Int)
#5486 := (iff #5481 #5485)
#5487 := [rewrite]: #5486
#5482 := (iff #5476 #5481)
#5479 := (= #5475 #5478)
#5480 := [rewrite]: #5479
#5483 := [monotonicity #5480]: #5482
#5489 := [trans #5483 #5487]: #5488
#5492 := [monotonicity #5489]: #5491
#13417 := [monotonicity #5492]: #13353
#13411 := [trans #13417 #13422]: #12884
#13351 := [quant-inst #2002]: #13306
#13416 := [mp #13351 #13411]: #13305
#13717 := [unit-resolution #13416 #9764 #13687]: #5485
#13715 := (not #5485)
#13718 := (or #13270 #13672 #2020 #13941 #13677 #13715)
#13719 := [th-lemma arith assign-bounds -1 -1 1 1 -1]: #13718
#13720 := [unit-resolution #13719 #13612 #13670 #13711 #13665 #13717]: #13270
#6610 := (+ #2017 #6481)
#6611 := (+ #185 #6610)
#6614 := (= #6611 0::Int)
#13728 := (not #6614)
#13284 := (>= #6611 0::Int)
#13725 := (not #13284)
#13726 := (or #13725 #2020 #13941 #13677 #13715)
#13724 := [th-lemma arith assign-bounds -1 1 1 -1]: #13726
#13727 := [unit-resolution #13724 #13670 #13711 #13665 #13717]: #13725
#13729 := (or #13728 #13284)
#13734 := [th-lemma arith triangle-eq]: #13729
#13735 := [unit-resolution #13734 #13727]: #13728
#5073 := (or #6486 #6512 #6614)
#13275 := (or #3835 #6486 #6512 #6614)
#6607 := (+ #6481 #2017)
#6608 := (+ #185 #6607)
#6609 := (= #6608 0::Int)
#6491 := (+ #1146 #6484)
#6492 := (+ #6374 #6491)
#6490 := (<= #6492 0::Int)
#6604 := (or #6486 #6490 #6609)
#13279 := (or #3835 #6604)
#13240 := (iff #13279 #13275)
#13231 := (or #3835 #5073)
#13239 := (iff #13231 #13275)
#13241 := [rewrite]: #13239
#13175 := (iff #13279 #13231)
#5263 := (iff #6604 #5073)
#5033 := (iff #6609 #6614)
#6612 := (= #6608 #6611)
#6613 := [rewrite]: #6612
#5034 := [monotonicity #6613]: #5033
#6529 := (iff #6490 #6512)
#6499 := (+ #6374 #6484)
#6500 := (+ #1146 #6499)
#6502 := (<= #6500 0::Int)
#6513 := (iff #6502 #6512)
#6514 := [rewrite]: #6513
#6503 := (iff #6490 #6502)
#6498 := (= #6492 #6500)
#6501 := [rewrite]: #6498
#6510 := [monotonicity #6501]: #6503
#6530 := [trans #6510 #6514]: #6529
#5264 := [monotonicity #6530 #5034]: #5263
#13238 := [monotonicity #5264]: #13175
#13247 := [trans #13238 #13241]: #13240
#13195 := [quant-inst #2003]: #13279
#13246 := [mp #13195 #13247]: #13275
#13733 := [unit-resolution #13246 #7155]: #5073
#13736 := [unit-resolution #13733 #13735 #13720 #13716]: false
#13738 := [lemma #13736]: #13737
#10281 := [unit-resolution #13738 #12531 #16073 #12662 #12445 #16079]: #10298
#10260 := [unit-resolution #10281 #10274 #13632]: false
#10279 := [lemma #10260]: #2911
#9810 := (or #2865 #3835 #3843 #183 #3825 #715 #3851)
#5727 := (= ?v1!16 f28)
#10217 := (= f28 ?v1!16)
#5888 := (f5 #195 ?v1!16)
#5889 := (f4 #5888)
#10218 := (<= #5889 0::Int)
#4078 := (f30 f28)
#4079 := (* -1::Int #4078)
#4080 := (+ #185 #4079)
#4081 := (>= #4080 0::Int)
#6973 := (or #3851 #4081)
#6974 := [quant-inst #181]: #6973
#9804 := [unit-resolution #6974 #9800]: #4081
#5837 := (+ #1984 #4079)
#5838 := (>= #5837 0::Int)
#9768 := (not #5838)
#5985 := (+ #1985 #4079)
#10128 := (<= #5985 0::Int)
#9482 := (= #1985 #4078)
#5679 := (= ?v0!17 f28)
#5682 := (f11 f21 ?v0!17)
#5683 := (= #5682 f1)
#5689 := (or #5679 #5683)
#5671 := (f11 #193 ?v0!17)
#5672 := (= #5671 f1)
#5694 := (iff #5672 #5689)
#8841 := (or #7582 #5694)
#5684 := (if #5679 #4057 #5683)
#5685 := (iff #5672 #5684)
#8901 := (or #7582 #5685)
#8884 := (iff #8901 #8841)
#8882 := (iff #8841 #8841)
#8885 := [rewrite]: #8882
#5695 := (iff #5685 #5694)
#5692 := (iff #5684 #5689)
#5686 := (if #5679 true #5683)
#5690 := (iff #5686 #5689)
#5691 := [rewrite]: #5690
#5687 := (iff #5684 #5686)
#5688 := [monotonicity #4060]: #5687
#5693 := [trans #5688 #5691]: #5692
#5696 := [monotonicity #5693]: #5695
#8908 := [monotonicity #5696]: #8884
#8886 := [trans #8908 #8885]: #8884
#8883 := [quant-inst #115 #181 #3 #1976]: #8901
#8888 := [mp #8883 #8886]: #8841
#9802 := [unit-resolution #8888 #3646]: #5694
#5971 := [hypothesis]: #2870
#3537 := (or #2865 #1981)
#3540 := [def-axiom]: #3537
#5973 := [unit-resolution #3540 #5971]: #1981
#9805 := (= #5671 #1980)
#9803 := [monotonicity #8195]: #9805
#9712 := [trans #9803 #5973]: #5672
#8941 := (not #5672)
#8928 := (not #5694)
#8937 := (or #8928 #8941 #5689)
#8942 := [def-axiom]: #8937
#9678 := [unit-resolution #8942 #9712 #9802]: #5689
#8913 := (not #5683)
#5652 := (f19 f20 ?v0!17)
#5545 := (* -1::Int #5652)
#5540 := (+ #185 #5545)
#9961 := (>= #5540 0::Int)
#10247 := (not #9961)
#8830 := (not #5727)
#5728 := (f11 f21 ?v1!16)
#5729 := (= #5728 f1)
#5735 := (or #5727 #5729)
#8846 := (not #5735)
#5725 := (f11 #193 ?v1!16)
#5726 := (= #5725 f1)
#5740 := (iff #5726 #5735)
#8823 := (or #7582 #5740)
#5730 := (if #5727 #4057 #5729)
#5731 := (iff #5726 #5730)
#8824 := (or #7582 #5731)
#8825 := (iff #8824 #8823)
#8821 := (iff #8823 #8823)
#8828 := [rewrite]: #8821
#5741 := (iff #5731 #5740)
#5738 := (iff #5730 #5735)
#5732 := (if #5727 true #5729)
#5736 := (iff #5732 #5735)
#5737 := [rewrite]: #5736
#5733 := (iff #5730 #5732)
#5734 := [monotonicity #4060]: #5733
#5739 := [trans #5734 #5737]: #5738
#5742 := [monotonicity #5739]: #5741
#8826 := [monotonicity #5742]: #8825
#8829 := [trans #8826 #8828]: #8825
#8822 := [quant-inst #115 #181 #3 #1975]: #8824
#8827 := [mp #8822 #8829]: #8823
#9713 := [unit-resolution #8827 #3646]: #5740
#8836 := (not #5726)
#9741 := (iff #1979 #8836)
#9711 := (iff #1978 #5726)
#9703 := (iff #5726 #1978)
#9690 := (= #5725 #1977)
#9701 := [monotonicity #8195]: #9690
#9679 := [monotonicity #9701]: #9703
#9734 := [symm #9679]: #9711
#9739 := [monotonicity #9734]: #9741
#3536 := (or #2865 #1979)
#3539 := [def-axiom]: #3536
#5974 := [unit-resolution #3539 #5971]: #1979
#9801 := [mp #5974 #9739]: #8836
#8850 := (not #5740)
#8835 := (or #8850 #5726 #8846)
#8849 := [def-axiom]: #8835
#9795 := [unit-resolution #8849 #9801 #9713]: #8846
#8831 := (or #5735 #8830)
#8842 := [def-axiom]: #8831
#9796 := [unit-resolution #8842 #9795]: #8830
#5855 := (f19 f20 ?v1!16)
#5872 := (* -1::Int #5855)
#4924 := (+ #185 #5872)
#4925 := (<= #4924 0::Int)
#8844 := (not #5729)
#8845 := (or #5735 #8844)
#8843 := [def-axiom]: #8845
#9744 := [unit-resolution #8843 #9795]: #8844
#4948 := (or #5729 #4925)
#9196 := (or #3825 #5729 #4925)
#4892 := (+ #5855 #1146)
#4893 := (>= #4892 0::Int)
#4918 := (or #5729 #4893)
#9197 := (or #3825 #4918)
#9258 := (iff #9197 #9196)
#9254 := (or #3825 #4948)
#9257 := (iff #9254 #9196)
#9252 := [rewrite]: #9257
#9255 := (iff #9197 #9254)
#4949 := (iff #4918 #4948)
#4946 := (iff #4893 #4925)
#4919 := (+ #1146 #5855)
#4922 := (>= #4919 0::Int)
#4926 := (iff #4922 #4925)
#4927 := [rewrite]: #4926
#4917 := (iff #4893 #4922)
#4920 := (= #4892 #4919)
#4921 := [rewrite]: #4920
#4923 := [monotonicity #4921]: #4917
#4947 := [trans #4923 #4927]: #4946
#4950 := [monotonicity #4947]: #4949
#9256 := [monotonicity #4950]: #9255
#9259 := [trans #9256 #9252]: #9258
#9253 := [quant-inst #1975]: #9197
#9260 := [mp #9253 #9259]: #9196
#9738 := [unit-resolution #9260 #9764]: #4948
#9702 := [unit-resolution #9738 #9744]: #4925
#3538 := (not #1988)
#3541 := (or #2865 #3538)
#3425 := [def-axiom]: #3541
#5972 := [unit-resolution #3425 #5971]: #3538
#5605 := (+ #1985 #5545)
#5610 := (<= #5605 0::Int)
#9092 := (or #3851 #5610)
#5582 := (+ #5652 #1986)
#5595 := (>= #5582 0::Int)
#9093 := (or #3851 #5595)
#9104 := (iff #9093 #9092)
#9106 := (iff #9092 #9092)
#9107 := [rewrite]: #9106
#5612 := (iff #5595 #5610)
#5596 := (+ #1986 #5652)
#5600 := (>= #5596 0::Int)
#5611 := (iff #5600 #5610)
#5609 := [rewrite]: #5611
#5603 := (iff #5595 #5600)
#5601 := (= #5582 #5596)
#5602 := [rewrite]: #5601
#5604 := [monotonicity #5602]: #5603
#5613 := [trans #5604 #5609]: #5612
#9105 := [monotonicity #5613]: #9104
#9109 := [trans #9105 #9107]: #9104
#9095 := [quant-inst #1976]: #9093
#9110 := [mp #9095 #9109]: #9092
#9766 := [unit-resolution #9110 #9800]: #5610
#10140 := (not #4925)
#10238 := (not #5610)
#9927 := (or #10247 #3835 #3843 #10238 #1988 #10140 #5727)
#4492 := (* -1::Int #1984)
#5947 := (+ #4492 #5889)
#5948 := (+ #185 #5947)
#5951 := (= #5948 0::Int)
#10144 := (not #5951)
#9091 := (<= #5948 0::Int)
#10246 := (not #9091)
#10223 := [hypothesis]: #8830
#10244 := [hypothesis]: #5610
#10243 := [hypothesis]: #3538
#10222 := [hypothesis]: #9961
#10237 := (or #10246 #10238 #1988 #10247 #5727)
#10201 := (not #10218)
#10234 := (not #10217)
#10235 := (iff #8830 #10234)
#10232 := (iff #5727 #10217)
#10231 := (iff #10217 #5727)
#10226 := [commutativity]: #10231
#10233 := [symm #10226]: #10232
#10236 := [monotonicity #10233]: #10235
#10239 := [mp #10223 #10236]: #10234
#10221 := (or #10217 #10201)
#10224 := (or #7204 #10217 #10201)
#10225 := (or #7204 #10221)
#10228 := (iff #10225 #10224)
#10229 := [rewrite]: #10228
#10227 := [quant-inst #181 #1975]: #10225
#10230 := [mp #10227 #10229]: #10224
#10240 := [unit-resolution #10230 #3612]: #10221
#10242 := [unit-resolution #10240 #10239]: #10201
#10241 := [hypothesis]: #9091
#10245 := [th-lemma arith farkas 1 1 1 1 1 #10244 #10241 #10243 #10242 #10222]: false
#10248 := [lemma #10245]: #10237
#10145 := [unit-resolution #10248 #10222 #10243 #10244 #10223]: #10246
#10146 := (or #10144 #9091)
#9628 := [th-lemma arith triangle-eq]: #10146
#9629 := [unit-resolution #9628 #10145]: #10144
#5890 := (* -1::Int #5889)
#5891 := (+ f3 #5890)
#5892 := (<= #5891 0::Int)
#9034 := (not #5892)
#5907 := (+ #5872 #5889)
#5908 := (+ #185 #5907)
#5909 := (>= #5908 0::Int)
#5914 := (or #5892 #5909)
#5917 := (not #5914)
#5898 := (= #1984 #5855)
#9631 := (not #5898)
#5873 := (+ #1984 #5872)
#9060 := (>= #5873 0::Int)
#10125 := (not #9060)
#10124 := [hypothesis]: #4925
#10137 := (or #10125 #10247 #10238 #1988 #10140)
#10123 := [hypothesis]: #9060
#10122 := [th-lemma arith farkas 1 -1 -1 -1 1 #10222 #10244 #10243 #10124 #10123]: false
#10139 := [lemma #10122]: #10137
#9630 := [unit-resolution #10139 #10222 #10244 #10243 #10124]: #10125
#9632 := (or #9631 #9060)
#9622 := [th-lemma arith triangle-eq]: #9632
#9651 := [unit-resolution #9622 #9630]: #9631
#5920 := (or #5917 #5898)
#8986 := (or #3843 #5917 #5898)
#5893 := (+ #1146 #5890)
#5894 := (+ #5855 #5893)
#5895 := (<= #5894 0::Int)
#5896 := (or #5892 #5895)
#5897 := (not #5896)
#5899 := (or #5897 #5898)
#8987 := (or #3843 #5899)
#9031 := (iff #8987 #8986)
#8999 := (or #3843 #5920)
#9029 := (iff #8999 #8986)
#9030 := [rewrite]: #9029
#8989 := (iff #8987 #8999)
#5921 := (iff #5899 #5920)
#5918 := (iff #5897 #5917)
#5915 := (iff #5896 #5914)
#5912 := (iff #5895 #5909)
#5900 := (+ #5855 #5890)
#5901 := (+ #1146 #5900)
#5904 := (<= #5901 0::Int)
#5910 := (iff #5904 #5909)
#5911 := [rewrite]: #5910
#5905 := (iff #5895 #5904)
#5902 := (= #5894 #5901)
#5903 := [rewrite]: #5902
#5906 := [monotonicity #5903]: #5905
#5913 := [trans #5906 #5911]: #5912
#5916 := [monotonicity #5913]: #5915
#5919 := [monotonicity #5916]: #5918
#5922 := [monotonicity #5919]: #5921
#9028 := [monotonicity #5922]: #8989
#9027 := [trans #9028 #9030]: #9031
#8988 := [quant-inst #1975]: #8987
#9033 := [mp #8988 #9027]: #8986
#9652 := [unit-resolution #9033 #7150]: #5920
#9688 := [unit-resolution #9652 #9651]: #5917
#9035 := (or #5914 #9034)
#9036 := [def-axiom]: #9035
#9689 := [unit-resolution #9036 #9688]: #9034
#9032 := (not #5909)
#9037 := (or #5914 #9032)
#9057 := [def-axiom]: #9037
#9696 := [unit-resolution #9057 #9688]: #9032
#5954 := (or #5892 #5909 #5951)
#9056 := (or #3835 #5892 #5909 #5951)
#5943 := (+ #5889 #4492)
#5944 := (+ #185 #5943)
#5945 := (= #5944 0::Int)
#5946 := (or #5892 #5895 #5945)
#9062 := (or #3835 #5946)
#9087 := (iff #9062 #9056)
#9064 := (or #3835 #5954)
#9066 := (iff #9064 #9056)
#9086 := [rewrite]: #9066
#9065 := (iff #9062 #9064)
#5955 := (iff #5946 #5954)
#5952 := (iff #5945 #5951)
#5949 := (= #5944 #5948)
#5950 := [rewrite]: #5949
#5953 := [monotonicity #5950]: #5952
#5956 := [monotonicity #5913 #5953]: #5955
#9061 := [monotonicity #5956]: #9065
#9088 := [trans #9061 #9086]: #9087
#9063 := [quant-inst #1975]: #9062
#9089 := [mp #9063 #9088]: #9056
#9928 := [unit-resolution #9089 #7155]: #5954
#10012 := [unit-resolution #9928 #9696 #9689 #9629]: false
#10013 := [lemma #10012]: #9927
#9704 := [unit-resolution #10013 #9766 #7150 #7155 #5972 #9702 #9796]: #10247
#9715 := (or #8913 #183 #9961)
#9692 := [hypothesis]: #10247
#9693 := [hypothesis]: #5683
#9660 := (or #3731 #183 #8913 #9961)
#9962 := (or #183 #8913 #9961)
#9687 := (or #3731 #9962)
#9680 := (iff #9687 #9660)
#9681 := [rewrite]: #9680
#9691 := [quant-inst #1976 #181]: #9687
#9682 := [mp #9691 #9681]: #9660
#9714 := [unit-resolution #9682 #8136 #8135 #9693 #9692]: false
#9677 := [lemma #9714]: #9715
#9767 := [unit-resolution #9677 #9704 #8135]: #8913
#8926 := (not #5689)
#8925 := (or #8926 #5679 #5683)
#8927 := [def-axiom]: #8925
#9737 := [unit-resolution #8927 #9767 #9678]: #5679
#8889 := (not #5679)
#10182 := (or #8889 #9482)
#9517 := [hypothesis]: #5679
#10179 := [monotonicity #9517]: #9482
#10138 := (not #9482)
#9568 := [hypothesis]: #10138
#10180 := [unit-resolution #9568 #10179]: false
#10183 := [lemma #10180]: #10182
#9765 := [unit-resolution #10183 #9737]: #9482
#10160 := (or #10138 #10128)
#10174 := [th-lemma arith triangle-eq]: #10160
#9743 := [unit-resolution #10174 #9765]: #10128
#10187 := (not #10128)
#9773 := (or #9768 #10187 #1988)
#9842 := [th-lemma arith assign-bounds -1 -1]: #9773
#9826 := [unit-resolution #9842 #5972 #9743]: #9768
#10190 := (not #4081)
#9659 := (or #10125 #10187 #10190 #1988 #10140)
#10188 := [hypothesis]: #4081
#10185 := [hypothesis]: #10128
#9658 := [th-lemma arith farkas -1 1 -1 1 1 #10123 #10185 #10188 #10243 #10124]: false
#9653 := [lemma #9658]: #9659
#9769 := [unit-resolution #9653 #9743 #9804 #5972 #9702]: #10125
#9841 := [unit-resolution #9622 #9769]: #9631
#9827 := [unit-resolution #9652 #9841]: #5917
#9656 := (or #5914 #5951 #3835)
#9538 := [hypothesis]: #10144
#9541 := [hypothesis]: #5917
#9536 := [unit-resolution #9036 #9541]: #9034
#9599 := [unit-resolution #9057 #9541]: #9032
#9654 := [unit-resolution #9928 #9599 #9536 #9538]: false
#9655 := [lemma #9654]: #9656
#9828 := [unit-resolution #9655 #9827 #7155]: #5951
#9772 := [unit-resolution #9628 #9828]: #9091
#9859 := (or #5838 #10190 #10246 #10218)
#9814 := [th-lemma arith assign-bounds 1 1 1]: #9859
#9837 := [unit-resolution #9814 #9772 #9826 #9804]: #10218
#9763 := [unit-resolution #10230 #3612 #9837]: #10217
#9815 := [symm #9763]: #5727
#9836 := [unit-resolution #9796 #9815]: false
#9843 := [lemma #9836]: #9810
#16075 := [unit-resolution #9843 #12445 #11843 #16074 #16073 #12662 #12531]: #2865
#3458 := (or #3968 #1323)
#3461 := [def-axiom]: #3458
#12443 := [unit-resolution #3461 #11571]: #1323
#8787 := (or #1962 #715 #3835 #3843 #3860 #1322)
#8481 := (= f16 ?v0!15)
#8495 := (not #8481)
#8546 := (= ?v0!15 f16)
#8430 := (not #8546)
#8736 := (iff #8430 #8495)
#8713 := (iff #8546 #8481)
#8711 := (iff #8481 #8546)
#8712 := [commutativity]: #8711
#8714 := [symm #8712]: #8713
#8737 := [monotonicity #8714]: #8736
#8515 := (f11 f21 ?v0!15)
#8516 := (= #8515 f1)
#8392 := (or #8546 #8516)
#8445 := (not #8392)
#6822 := (f13 #191 f16)
#6823 := (f12 #6822 f1)
#8288 := (f11 #6823 ?v0!15)
#8269 := (= #8288 f1)
#8396 := (iff #8269 #8392)
#8419 := (or #7582 #8396)
#8346 := (if #8546 #4057 #8516)
#8341 := (iff #8269 #8346)
#8420 := (or #7582 #8341)
#8421 := (iff #8420 #8419)
#8418 := (iff #8419 #8419)
#8423 := [rewrite]: #8418
#8416 := (iff #8341 #8396)
#8394 := (iff #8346 #8392)
#8362 := (if #8546 true #8516)
#8393 := (iff #8362 #8392)
#8361 := [rewrite]: #8393
#8391 := (iff #8346 #8362)
#8386 := [monotonicity #4060]: #8391
#8395 := [trans #8386 #8361]: #8394
#8417 := [monotonicity #8395]: #8416
#8422 := [monotonicity #8417]: #8421
#8424 := [trans #8422 #8423]: #8421
#8415 := [quant-inst #115 #65 #3 #1960]: #8420
#8425 := [mp #8415 #8424]: #8419
#8638 := [unit-resolution #8425 #3646]: #8396
#8242 := (not #8269)
#4485 := (f11 f29 ?v0!15)
#4486 := (= #4485 f1)
#4487 := (not #4486)
#8707 := (iff #4487 #8242)
#8705 := (iff #4486 #8269)
#8670 := (iff #8269 #4486)
#8666 := (= #8288 #4485)
#8667 := (= #6823 f29)
#8681 := (= #6823 #193)
#8679 := (= #6822 #192)
#7229 := (= f16 f28)
#4163 := (= f28 f16)
#4164 := (?v1!7 f28)
#4172 := (f6 f7 #4164)
#4173 := (f5 #4172 f28)
#4174 := (f4 #4173)
#4175 := (* -1::Int #4174)
#4165 := (f19 f20 #4164)
#4166 := (* -1::Int #4165)
#4176 := (+ #4166 #4175)
#4177 := (+ #185 #4176)
#4178 := (= #4177 0::Int)
#4179 := (not #4178)
#4169 := (f11 f21 #4164)
#4170 := (= #4169 f1)
#4171 := (not #4170)
#4167 := (+ #185 #4166)
#4168 := (<= #4167 0::Int)
#4180 := (or #4168 #4171 #4179)
#7890 := (>= #4167 0::Int)
#9101 := (not #7890)
#6618 := [hypothesis]: #1963
#8892 := (or #1962 #3843 #3835 #9101)
#6496 := (f19 f20 ?v0!15)
#8568 := (>= #6496 0::Int)
#3442 := (or #3980 #3717)
#3422 := [def-axiom]: #3442
#7284 := [unit-resolution #3422 #7283]: #3717
#8851 := (or #3722 #8568)
#8852 := [quant-inst #1960]: #8851
#8854 := [unit-resolution #8852 #7284]: #8568
#6521 := (* -1::Int #6496)
#6522 := (+ #1961 #6521)
#8853 := (>= #6522 0::Int)
#6497 := (= #1961 #6496)
#6537 := (f5 #195 ?v0!15)
#6538 := (f4 #6537)
#6555 := (+ #6521 #6538)
#6556 := (+ #185 #6555)
#6557 := (>= #6556 0::Int)
#6539 := (* -1::Int #6538)
#6540 := (+ f3 #6539)
#6541 := (<= #6540 0::Int)
#6562 := (or #6541 #6557)
#4488 := (* -1::Int #1961)
#6594 := (+ #4488 #6538)
#6595 := (+ #185 #6594)
#6598 := (= #6595 0::Int)
#8864 := (not #6598)
#8820 := (<= #6595 0::Int)
#9100 := (not #8820)
#9097 := [hypothesis]: #7890
#8984 := (or #9100 #1962 #9101)
#8957 := (>= #6538 0::Int)
#8947 := (= #6538 0::Int)
#8943 := (= f28 ?v0!15)
#8958 := (<= #6538 0::Int)
#9098 := [hypothesis]: #8820
#9102 := (or #8958 #1962 #9100 #9101)
#8949 := (not #8958)
#9096 := [hypothesis]: #8949
#8015 := (>= #4165 0::Int)
#8035 := (or #3722 #8015)
#8036 := [quant-inst #4164]: #8035
#8125 := [unit-resolution #8036 #7284]: #8015
#9099 := [th-lemma arith farkas 1 1 1 1 1 #6618 #9098 #8125 #9097 #9096]: false
#9103 := [lemma #9099]: #9102
#9002 := [unit-resolution #9103 #9098 #6618 #9097]: #8958
#8950 := (or #8943 #8949)
#8961 := (or #7204 #8943 #8949)
#8962 := (or #7204 #8950)
#8964 := (iff #8962 #8961)
#8965 := [rewrite]: #8964
#8963 := [quant-inst #181 #1960]: #8962
#8966 := [mp #8963 #8965]: #8961
#9003 := [unit-resolution #8966 #3612]: #8950
#9004 := [unit-resolution #9003 #9002]: #8943
#8944 := (not #8943)
#8948 := (or #8944 #8947)
#8951 := (or #7193 #8944 #8947)
#8952 := (or #7193 #8948)
#8954 := (iff #8952 #8951)
#8955 := [rewrite]: #8954
#8953 := [quant-inst #181 #1960]: #8952
#8956 := [mp #8953 #8955]: #8951
#9005 := [unit-resolution #8956 #3606]: #8948
#9006 := [unit-resolution #9005 #9004]: #8947
#9007 := (not #8947)
#9008 := (or #9007 #8957)
#8982 := [th-lemma arith triangle-eq]: #9008
#8983 := [unit-resolution #8982 #9006]: #8957
#8981 := [th-lemma arith farkas 1 1 1 1 1 #6618 #9098 #8125 #9097 #8983]: false
#8985 := [lemma #8981]: #8984
#8855 := [unit-resolution #8985 #6618 #9097]: #9100
#8856 := (or #8864 #8820)
#8832 := [th-lemma arith triangle-eq]: #8856
#8833 := [unit-resolution #8832 #8855]: #8864
#8898 := (or #6562 #6598 #3835)
#8865 := [hypothesis]: #8864
#8800 := (not #6541)
#6565 := (not #6562)
#8893 := [hypothesis]: #6565
#8801 := (or #6562 #8800)
#8802 := [def-axiom]: #8801
#8894 := [unit-resolution #8802 #8893]: #8800
#8803 := (not #6557)
#8804 := (or #6562 #8803)
#8805 := [def-axiom]: #8804
#8895 := [unit-resolution #8805 #8893]: #8803
#6601 := (or #6541 #6557 #6598)
#8808 := (or #3835 #6541 #6557 #6598)
#6590 := (+ #6538 #4488)
#6591 := (+ #185 #6590)
#6592 := (= #6591 0::Int)
#6542 := (+ #1146 #6539)
#6543 := (+ #6496 #6542)
#6544 := (<= #6543 0::Int)
#6593 := (or #6541 #6544 #6592)
#8809 := (or #3835 #6593)
#8816 := (iff #8809 #8808)
#8811 := (or #3835 #6601)
#8814 := (iff #8811 #8808)
#8815 := [rewrite]: #8814
#8812 := (iff #8809 #8811)
#6602 := (iff #6593 #6601)
#6599 := (iff #6592 #6598)
#6596 := (= #6591 #6595)
#6597 := [rewrite]: #6596
#6600 := [monotonicity #6597]: #6599
#6560 := (iff #6544 #6557)
#6548 := (+ #6496 #6539)
#6549 := (+ #1146 #6548)
#6552 := (<= #6549 0::Int)
#6558 := (iff #6552 #6557)
#6559 := [rewrite]: #6558
#6553 := (iff #6544 #6552)
#6550 := (= #6543 #6549)
#6551 := [rewrite]: #6550
#6554 := [monotonicity #6551]: #6553
#6561 := [trans #6554 #6559]: #6560
#6603 := [monotonicity #6561 #6600]: #6602
#8813 := [monotonicity #6603]: #8812
#8817 := [trans #8813 #8815]: #8816
#8810 := [quant-inst #1960]: #8809
#8818 := [mp #8810 #8817]: #8808
#8896 := [unit-resolution #8818 #7155]: #6601
#8897 := [unit-resolution #8896 #8895 #8894 #8865]: false
#8899 := [lemma #8897]: #8898
#8857 := [unit-resolution #8899 #8833 #7155]: #6562
#6568 := (or #6565 #6497)
#8789 := (or #3843 #6565 #6497)
#6545 := (or #6541 #6544)
#6546 := (not #6545)
#6547 := (or #6546 #6497)
#8790 := (or #3843 #6547)
#8797 := (iff #8790 #8789)
#8792 := (or #3843 #6568)
#8795 := (iff #8792 #8789)
#8796 := [rewrite]: #8795
#8793 := (iff #8790 #8792)
#6569 := (iff #6547 #6568)
#6566 := (iff #6546 #6565)
#6563 := (iff #6545 #6562)
#6564 := [monotonicity #6561]: #6563
#6567 := [monotonicity #6564]: #6566
#6570 := [monotonicity #6567]: #6569
#8794 := [monotonicity #6570]: #8793
#8798 := [trans #8794 #8796]: #8797
#8791 := [quant-inst #1960]: #8790
#8799 := [mp #8791 #8798]: #8789
#8858 := [unit-resolution #8799 #7150]: #6568
#8859 := [unit-resolution #8858 #8857]: #6497
#8860 := (not #6497)
#8861 := (or #8860 #8853)
#8866 := [th-lemma arith triangle-eq]: #8861
#8867 := [unit-resolution #8866 #8859]: #8853
#8891 := [th-lemma arith farkas -1 1 1 #6618 #8867 #8854]: false
#8900 := [lemma #8891]: #8892
#8629 := [unit-resolution #8900 #6618 #7155 #7150]: #9101
#8630 := (or #7890 #4168)
#8631 := [th-lemma arith farkas 1 1]: #8630
#8632 := [unit-resolution #8631 #8629]: #4168
#7337 := (not #4168)
#7338 := (or #4180 #7337)
#7333 := [def-axiom]: #7338
#8633 := [unit-resolution #7333 #8632]: #4180
#4181 := (not #4180)
#8675 := (or #4163 #4181)
#8674 := [hypothesis]: #1323
#7245 := (or #3747 #4163 #1322 #4181)
#4182 := (or #4163 #1322 #4181)
#7243 := (or #3747 #4182)
#7302 := (iff #7243 #7245)
#7303 := [rewrite]: #7302
#7246 := [quant-inst #181]: #7243
#7334 := [mp #7246 #7303]: #7245
#8676 := [unit-resolution #7334 #6675 #8674]: #8675
#8677 := [unit-resolution #8676 #8633]: #4163
#8678 := [symm #8677]: #7229
#8680 := [monotonicity #8678]: #8679
#8682 := [monotonicity #8680]: #8681
#8668 := [trans #8682 #8195]: #8667
#8669 := [monotonicity #8668]: #8666
#8671 := [monotonicity #8669]: #8670
#8706 := [symm #8671]: #8705
#8708 := [monotonicity #8706]: #8707
#8639 := (not #8853)
#8640 := (not #8568)
#8641 := (or #8639 #1962 #8640)
#8514 := [th-lemma arith assign-bounds -1 1]: #8641
#8576 := [unit-resolution #8514 #6618 #8854]: #8639
#8577 := [unit-resolution #8866 #8576]: #8860
#6506 := (or #4487 #6497)
#7822 := (or #3860 #4487 #6497)
#7823 := (or #3860 #6506)
#7827 := (iff #7823 #7822)
#7828 := [rewrite]: #7827
#7817 := [quant-inst #1960]: #7823
#7829 := [mp #7817 #7828]: #7822
#8628 := [unit-resolution #7829 #8627]: #6506
#8513 := [unit-resolution #8628 #8577]: #4487
#8709 := [mp #8513 #8708]: #8242
#8452 := (not #8396)
#8450 := (or #8452 #8269 #8445)
#8453 := [def-axiom]: #8450
#8704 := [unit-resolution #8453 #8709 #8638]: #8445
#8431 := (or #8392 #8430)
#8441 := [def-axiom]: #8431
#8710 := [unit-resolution #8441 #8704]: #8430
#8738 := [mp #8710 #8737]: #8495
#5201 := (f6 f7 f16)
#8435 := (f5 #5201 ?v0!15)
#8487 := (f4 #8435)
#8483 := (<= #8487 0::Int)
#8585 := (* -1::Int #8487)
#8635 := (+ #6538 #8585)
#8637 := (>= #8635 0::Int)
#8573 := (= #6538 #8487)
#8744 := (= #8487 #6538)
#8742 := (= #8435 #6537)
#8735 := (= #5201 #195)
#8739 := (= #195 #5201)
#8740 := [monotonicity #8677]: #8739
#8741 := [symm #8740]: #8735
#8743 := [monotonicity #8741]: #8742
#8745 := [monotonicity #8743]: #8744
#8750 := [symm #8745]: #8573
#8751 := (not #8573)
#8754 := (or #8751 #8637)
#8755 := [th-lemma arith triangle-eq]: #8754
#8761 := [unit-resolution #8755 #8750]: #8637
#4339 := (+ #110 #1146)
#8173 := (<= #4339 0::Int)
#7896 := (= #110 #185)
#8157 := (= #185 #110)
#8762 := [monotonicity #8677]: #8157
#8760 := [symm #8762]: #7896
#8763 := (not #7896)
#8764 := (or #8763 #8173)
#8765 := [th-lemma arith triangle-eq]: #8764
#8771 := [unit-resolution #8765 #8760]: #8173
#3233 := (>= #110 0::Int)
#8772 := (or #804 #3233)
#8770 := [th-lemma arith triangle-eq]: #8772
#8773 := [unit-resolution #8770 #7286]: #3233
#8774 := [unit-resolution #8858 #8577]: #6565
#8775 := [unit-resolution #8899 #8774 #7155]: #6598
#8777 := [unit-resolution #8832 #8775]: #8820
#8769 := (not #8173)
#8781 := (not #3233)
#8778 := (not #8637)
#8782 := (or #8483 #8778 #1962 #9100 #8781 #8769)
#8768 := [th-lemma arith assign-bounds 1 1 1 1 1]: #8782
#8783 := [unit-resolution #8768 #8777 #8773 #8771 #6618 #8761]: #8483
#8489 := (not #8483)
#8570 := (or #8481 #8489)
#8574 := (or #7204 #8481 #8489)
#8575 := (or #7204 #8570)
#8589 := (iff #8575 #8574)
#8600 := [rewrite]: #8589
#8588 := [quant-inst #65 #1960]: #8575
#8634 := [mp #8588 #8600]: #8574
#8784 := [unit-resolution #8634 #3612]: #8570
#8786 := [unit-resolution #8784 #8783 #8738]: false
#8806 := [lemma #8786]: #8787
#16080 := [unit-resolution #8806 #16079 #12531 #11843 #12662 #12443]: #1962
#3476 := (or #3944 #3938)
#3478 := [def-axiom]: #3476
#16081 := [unit-resolution #3478 #16078]: #3938
#4358 := (= #216 #110)
#12868 := (iff #4358 #217)
#12818 := [monotonicity #7286]: #12868
#4342 := (f5 #195 f16)
#4343 := (f4 #4342)
#4350 := (* -1::Int #4343)
#4353 := (+ #1146 #4350)
#4354 := (+ #110 #4353)
#4355 := (<= #4354 0::Int)
#4351 := (+ f3 #4350)
#4352 := (<= #4351 0::Int)
#4356 := (or #4352 #4355)
#7200 := (>= #4343 0::Int)
#7186 := (= #4343 0::Int)
#7201 := (<= #4343 0::Int)
#6947 := (not #4355)
#7271 := [hypothesis]: #6947
#7291 := (or #7201 #4355)
#7191 := (not #7201)
#7270 := [hypothesis]: #7191
#4183 := (>= #185 0::Int)
#6896 := (or #3722 #4183)
#6931 := [quant-inst #181]: #6896
#7285 := [unit-resolution #6931 #7284]: #4183
#4595 := (<= #110 0::Int)
#7287 := (or #804 #4595)
#7288 := [th-lemma arith triangle-eq]: #7287
#7289 := [unit-resolution #7288 #7286]: #4595
#7290 := [th-lemma arith farkas 1 1 1 1 #7289 #7285 #7271 #7270]: false
#7292 := [lemma #7290]: #7291
#7227 := [unit-resolution #7292 #7271]: #7201
#7192 := (or #4163 #7191)
#7205 := (or #7204 #4163 #7191)
#7206 := (or #7204 #7192)
#7208 := (iff #7206 #7205)
#7209 := [rewrite]: #7208
#7207 := [quant-inst #181 #65]: #7206
#7210 := [mp #7207 #7209]: #7205
#7228 := [unit-resolution #7210 #3612]: #7192
#7252 := [unit-resolution #7228 #7227]: #4163
#7185 := (not #4163)
#7190 := (or #7185 #7186)
#7194 := (or #7193 #7185 #7186)
#7195 := (or #7193 #7190)
#7197 := (iff #7195 #7194)
#7198 := [rewrite]: #7197
#7196 := [quant-inst #181 #65]: #7195
#7199 := [mp #7196 #7198]: #7194
#7253 := [unit-resolution #7199 #3606]: #7190
#7254 := [unit-resolution #7253 #7252]: #7186
#7255 := (not #7186)
#7256 := (or #7255 #7200)
#7257 := [th-lemma arith triangle-eq]: #7256
#7258 := [unit-resolution #7257 #7254]: #7200
#7259 := [th-lemma arith farkas -1 1 1 1 #7289 #7285 #7271 #7258]: false
#7260 := [lemma #7259]: #4355
#7663 := (or #4356 #6947)
#7661 := [def-axiom]: #7663
#12832 := [unit-resolution #7661 #7260]: #4356
#4357 := (not #4356)
#7631 := (or #3843 #4357 #4358)
#4359 := (or #4357 #4358)
#7632 := (or #3843 #4359)
#7655 := (iff #7632 #7631)
#7656 := [rewrite]: #7655
#7633 := [quant-inst #65]: #7632
#7657 := [mp #7633 #7656]: #7631
#12816 := [unit-resolution #7657 #11843 #12832]: #4358
#16082 := [mp #12816 #12818]: #217
#3496 := (or #3941 #661 #3935)
#3486 := [def-axiom]: #3496
#16083 := [unit-resolution #3486 #16082 #16081]: #3935
#3488 := (or #3932 #3926)
#3489 := [def-axiom]: #3488
#16084 := [unit-resolution #3489 #16083]: #3926
#3504 := (or #3929 #1963 #3923)
#3484 := [def-axiom]: #3504
#16085 := [unit-resolution #3484 #16084 #16080]: #3923
#3507 := (or #3920 #3914)
#3512 := [def-axiom]: #3507
#16086 := [unit-resolution #3512 #16085]: #3914
#3508 := (or #3917 #2870 #3911)
#3509 := [def-axiom]: #3508
#16087 := [unit-resolution #3509 #16086 #16075]: #3911
#3517 := (or #3908 #3902)
#3518 := [def-axiom]: #3517
#11352 := [unit-resolution #3518 #16087]: #3902
#3526 := (or #3905 #2916 #3899)
#3527 := [def-axiom]: #3526
#11376 := [unit-resolution #3527 #11352]: #3902
#11393 := [unit-resolution #11376 #10279]: #3899
#3531 := (or #3896 #3888)
#3535 := [def-axiom]: #3531
#11676 := [unit-resolution #3535 #11393]: #3888
#5121 := (f5 #195 ?v0!20)
#5122 := (f4 #5121)
#5178 := (+ #2038 #5122)
#5179 := (+ #185 #5178)
#5182 := (= #5179 0::Int)
#5080 := (f19 f20 ?v0!20)
#5105 := (* -1::Int #5080)
#5139 := (+ #5105 #5122)
#5140 := (+ #185 #5139)
#5141 := (>= #5140 0::Int)
#5123 := (* -1::Int #5122)
#5124 := (+ f3 #5123)
#5125 := (<= #5124 0::Int)
#5146 := (or #5125 #5141)
#5149 := (not #5146)
#5087 := (= #2037 #5080)
#13314 := (not #5087)
#5106 := (+ #2037 #5105)
#14166 := (>= #5106 0::Int)
#14817 := (not #14166)
#5342 := (?v1!7 ?v0!20)
#14317 := (f30 #5342)
#14337 := (* -1::Int #14317)
#14808 := (+ #2037 #14337)
#14811 := (<= #14808 0::Int)
#11290 := (not #14811)
#14807 := [hypothesis]: #14166
#5343 := (f19 f20 #5342)
#14338 := (+ #5343 #14337)
#14315 := (>= #14338 0::Int)
#10677 := (or #3851 #14315)
#10712 := [quant-inst #5342]: #10677
#11005 := [unit-resolution #10712 #12445]: #14315
#5344 := (* -1::Int #5343)
#5345 := (+ #5080 #5344)
#5346 := (<= #5345 0::Int)
#10400 := (not #5346)
#5350 := (f6 f7 #5342)
#5351 := (f5 #5350 ?v0!20)
#5352 := (f4 #5351)
#5353 := (* -1::Int #5352)
#5354 := (+ #5344 #5353)
#5355 := (+ #5080 #5354)
#5356 := (= #5355 0::Int)
#5357 := (not #5356)
#5347 := (f11 f21 #5342)
#5348 := (= #5347 f1)
#5349 := (not #5348)
#5358 := (or #5346 #5349 #5357)
#5359 := (not #5358)
#5340 := (+ f3 #5105)
#5341 := (<= #5340 0::Int)
#14816 := (not #5341)
#3441 := (or #3896 #2041)
#3534 := [def-axiom]: #3441
#11418 := [unit-resolution #3534 #11393]: #2041
#14818 := (or #14816 #14817 #2040)
#14806 := [hypothesis]: #2041
#14814 := [hypothesis]: #5341
#14815 := [th-lemma arith farkas -1 1 1 #14814 #14807 #14806]: false
#14819 := [lemma #14815]: #14818
#11023 := [unit-resolution #14819 #14807 #11418]: #14816
#11390 := (or #5341 #5359)
#3439 := (or #3896 #2036)
#3440 := [def-axiom]: #3439
#11478 := [unit-resolution #3440 #11393]: #2036
#10408 := (or #3747 #2035 #5341 #5359)
#5360 := (or #2035 #5341 #5359)
#10412 := (or #3747 #5360)
#10411 := (iff #10412 #10408)
#10386 := [rewrite]: #10411
#10414 := [quant-inst #2034]: #10412
#10395 := [mp #10414 #10386]: #10408
#11485 := [unit-resolution #10395 #6675 #11478]: #11390
#11291 := [unit-resolution #11485 #11023]: #5359
#10401 := (or #5358 #10400)
#10402 := [def-axiom]: #10401
#11482 := [unit-resolution #10402 #11291]: #10400
#11483 := (not #14315)
#11288 := (or #11290 #11483 #5346 #14817)
#11531 := [th-lemma arith assign-bounds -1 -1 -1]: #11288
#11296 := [unit-resolution #11531 #11482 #11005 #14807]: #11290
#13958 := (+ #5353 #14337)
#12062 := (+ #2037 #13958)
#14821 := (= #12062 0::Int)
#13983 := (<= #12062 0::Int)
#14568 := (+ f3 #5353)
#14601 := (<= #14568 0::Int)
#11602 := (not #14601)
#12759 := (>= #5355 0::Int)
#10422 := (or #5358 #5356)
#10363 := [def-axiom]: #10422
#11294 := [unit-resolution #10363 #11291]: #5356
#11627 := (or #5357 #12759)
#11292 := [th-lemma arith triangle-eq]: #11627
#11603 := [unit-resolution #11292 #11294]: #12759
#14567 := (>= #5343 0::Int)
#10649 := (or #3722 #14567)
#10651 := [quant-inst #5342]: #10649
#11628 := [unit-resolution #10651 #7284]: #14567
#11599 := (not #14567)
#11625 := (not #12759)
#11629 := (or #11602 #11625 #11599 #2040 #14817)
#11624 := [th-lemma arith assign-bounds -1 -1 -1 -1]: #11629
#11632 := [unit-resolution #11624 #11628 #11418 #11603 #14807]: #11602
#11560 := (or #14601 #13983)
#14300 := (f11 f29 #5342)
#14333 := (= #14300 f1)
#10365 := (or #5358 #5348)
#10415 := [def-axiom]: #10365
#11673 := [unit-resolution #10415 #11291]: #5348
#10266 := (or #14333 #5349)
#15419 := (f11 #193 #5342)
#15442 := (= #15419 f1)
#15453 := (= #5342 f28)
#15432 := (or #15453 #5348)
#15425 := (iff #15442 #15432)
#16310 := (or #7582 #15425)
#15456 := (if #15453 #4057 #5348)
#15457 := (iff #15442 #15456)
#16311 := (or #7582 #15457)
#11286 := (iff #16311 #16310)
#11830 := (iff #16310 #16310)
#12073 := [rewrite]: #11830
#15428 := (iff #15457 #15425)
#15445 := (iff #15456 #15432)
#15460 := (if #15453 true #5348)
#15426 := (iff #15460 #15432)
#15434 := [rewrite]: #15426
#15448 := (iff #15456 #15460)
#15447 := [monotonicity #4060]: #15448
#15427 := [trans #15447 #15434]: #15445
#15429 := [monotonicity #15427]: #15428
#11833 := [monotonicity #15429]: #11286
#12072 := [trans #11833 #12073]: #11286
#11275 := [quant-inst #115 #181 #3 #5342]: #16311
#12074 := [mp #11275 #12072]: #16310
#14187 := [unit-resolution #12074 #3646]: #15425
#13407 := (not #15425)
#14236 := (or #13407 #15442)
#15985 := [hypothesis]: #5348
#12028 := (or #15432 #5349)
#13131 := [def-axiom]: #12028
#14241 := [unit-resolution #13131 #15985]: #15432
#13115 := (not #15432)
#13413 := (or #13407 #15442 #13115)
#10944 := [def-axiom]: #13413
#15276 := [unit-resolution #10944 #14241]: #14236
#15396 := [unit-resolution #15276 #14187]: #15442
#15574 := (= #14300 #15419)
#15601 := [monotonicity #12662]: #15574
#15612 := [trans #15601 #15396]: #14333
#14331 := (not #14333)
#15983 := [hypothesis]: #14331
#9603 := [unit-resolution #15983 #15612]: false
#15650 := [lemma #9603]: #10266
#11630 := [unit-resolution #15650 #11673]: #14333
#3437 := (or #3896 #3880)
#3438 := [def-axiom]: #3437
#11479 := [unit-resolution #3438 #11393]: #3880
#10499 := (or #3885 #14331 #14601 #13983)
#14605 := (+ #14317 #2038)
#12389 := (+ #5352 #14605)
#14602 := (>= #12389 0::Int)
#14600 := (or #14331 #14601 #14602)
#10518 := (or #3885 #14600)
#10536 := (iff #10518 #10499)
#13959 := (or #14331 #14601 #13983)
#10517 := (or #3885 #13959)
#10484 := (iff #10517 #10499)
#10511 := [rewrite]: #10484
#10485 := (iff #10518 #10517)
#14616 := (iff #14600 #13959)
#14615 := (iff #14602 #13983)
#12975 := (+ #5352 #14317)
#13126 := (+ #2038 #12975)
#12668 := (>= #13126 0::Int)
#14613 := (iff #12668 #13983)
#14614 := [rewrite]: #14613
#14298 := (iff #14602 #12668)
#13200 := (= #12389 #13126)
#13162 := [rewrite]: #13200
#14328 := [monotonicity #13162]: #14298
#12036 := [trans #14328 #14614]: #14615
#14617 := [monotonicity #12036]: #14616
#10522 := [monotonicity #14617]: #10485
#10543 := [trans #10522 #10511]: #10536
#10528 := [quant-inst #2034 #5342]: #10518
#10544 := [mp #10528 #10543]: #10499
#11674 := [unit-resolution #10544 #11479 #11630]: #11560
#11672 := [unit-resolution #11674 #11632]: #13983
#10494 := (>= #12062 0::Int)
#11675 := (or #10494 #11625 #11483 #14817)
#11298 := [th-lemma arith assign-bounds -1 -1 -1]: #11675
#11691 := [unit-resolution #11298 #11005 #11603 #14807]: #10494
#11692 := (not #13983)
#11689 := (not #10494)
#11730 := (or #14821 #11689 #11692)
#11758 := [th-lemma arith triangle-eq]: #11730
#11700 := [unit-resolution #11758 #11691 #11672]: #14821
#14826 := (not #14821)
#11282 := (or #14811 #14826)
#10448 := (or #3893 #14811 #14331 #14826)
#14782 := (+ #2038 #5352)
#14792 := (+ #14317 #14782)
#14793 := (= #14792 0::Int)
#14799 := (not #14793)
#14781 := (>= #14605 0::Int)
#14800 := (or #14781 #14331 #14799)
#10450 := (or #3893 #14800)
#10480 := (iff #10450 #10448)
#14829 := (or #14811 #14331 #14826)
#10447 := (or #3893 #14829)
#10416 := (iff #10447 #10448)
#10458 := [rewrite]: #10416
#10443 := (iff #10450 #10447)
#14830 := (iff #14800 #14829)
#14827 := (iff #14799 #14826)
#14824 := (iff #14793 #14821)
#14587 := (= #13126 0::Int)
#14822 := (iff #14587 #14821)
#14823 := [rewrite]: #14822
#14804 := (iff #14793 #14587)
#14310 := (= #14792 #13126)
#14429 := [rewrite]: #14310
#14820 := [monotonicity #14429]: #14804
#14825 := [trans #14820 #14823]: #14824
#14828 := [monotonicity #14825]: #14827
#14204 := (iff #14781 #14811)
#14798 := (+ #2038 #14317)
#14803 := (>= #14798 0::Int)
#14812 := (iff #14803 #14811)
#14813 := [rewrite]: #14812
#14809 := (iff #14781 #14803)
#14801 := (= #14605 #14798)
#14802 := [rewrite]: #14801
#14810 := [monotonicity #14802]: #14809
#14193 := [trans #14810 #14813]: #14204
#14831 := [monotonicity #14193 #14828]: #14830
#10460 := [monotonicity #14831]: #10443
#10495 := [trans #10460 #10458]: #10480
#10455 := [quant-inst #5342]: #10450
#10496 := [mp #10455 #10495]: #10448
#11701 := [unit-resolution #10496 #11676 #11630]: #11282
#11698 := [unit-resolution #11701 #11700 #11296]: false
#11729 := [lemma #11698]: #14817
#13414 := (or #13314 #14166)
#12903 := [th-lemma arith triangle-eq]: #13414
#13464 := [unit-resolution #12903 #11729]: #13314
#5152 := (or #5149 #5087)
#10286 := (or #3843 #5149 #5087)
#5126 := (+ #1146 #5123)
#5127 := (+ #5080 #5126)
#5128 := (<= #5127 0::Int)
#5129 := (or #5125 #5128)
#5130 := (not #5129)
#5131 := (or #5130 #5087)
#10287 := (or #3843 #5131)
#9289 := (iff #10287 #10286)
#6976 := (or #3843 #5152)
#8673 := (iff #6976 #10286)
#8601 := [rewrite]: #8673
#6978 := (iff #10287 #6976)
#5153 := (iff #5131 #5152)
#5150 := (iff #5130 #5149)
#5147 := (iff #5129 #5146)
#5144 := (iff #5128 #5141)
#5132 := (+ #5080 #5123)
#5133 := (+ #1146 #5132)
#5136 := (<= #5133 0::Int)
#5142 := (iff #5136 #5141)
#5143 := [rewrite]: #5142
#5137 := (iff #5128 #5136)
#5134 := (= #5127 #5133)
#5135 := [rewrite]: #5134
#5138 := [monotonicity #5135]: #5137
#5145 := [trans #5138 #5143]: #5144
#5148 := [monotonicity #5145]: #5147
#5151 := [monotonicity #5148]: #5150
#5154 := [monotonicity #5151]: #5153
#9657 := [monotonicity #5154]: #6978
#10282 := [trans #9657 #8601]: #9289
#10280 := [quant-inst #2034]: #10287
#10289 := [mp #10280 #10282]: #10286
#13441 := [unit-resolution #10289 #11843]: #5152
#13534 := [unit-resolution #13441 #13464]: #5149
#12234 := (or #5146 #5182)
#12584 := (not #5182)
#12314 := [hypothesis]: #12584
#10290 := (not #5125)
#12338 := [hypothesis]: #5149
#10299 := (or #5146 #10290)
#10300 := [def-axiom]: #10299
#12289 := [unit-resolution #10300 #12338]: #10290
#10273 := (not #5141)
#10301 := (or #5146 #10273)
#10297 := [def-axiom]: #10301
#12290 := [unit-resolution #10297 #12338]: #10273
#5185 := (or #5125 #5141 #5182)
#10259 := (or #3835 #5125 #5141 #5182)
#5174 := (+ #5122 #2038)
#5175 := (+ #185 #5174)
#5176 := (= #5175 0::Int)
#5177 := (or #5125 #5128 #5176)
#10305 := (or #3835 #5177)
#10308 := (iff #10305 #10259)
#10307 := (or #3835 #5185)
#10311 := (iff #10307 #10259)
#10312 := [rewrite]: #10311
#10303 := (iff #10305 #10307)
#5186 := (iff #5177 #5185)
#5183 := (iff #5176 #5182)
#5180 := (= #5175 #5179)
#5181 := [rewrite]: #5180
#5184 := [monotonicity #5181]: #5183
#5187 := [monotonicity #5145 #5184]: #5186
#10309 := [monotonicity #5187]: #10303
#10313 := [trans #10309 #10312]: #10308
#10306 := [quant-inst #2034]: #10305
#10315 := [mp #10306 #10313]: #10259
#12211 := [unit-resolution #10315 #12531]: #5185
#12231 := [unit-resolution #12211 #12290 #12289 #12314]: false
#12291 := [lemma #12231]: #12234
#13462 := [unit-resolution #12291 #13534]: #5182
#16225 := (or #12584 #11448 #3893)
#12244 := (= f28 ?v0!20)
#12245 := (not #12244)
#15044 := (not #11448)
#16185 := (iff #15044 #12245)
#16160 := (iff #11448 #12244)
#16058 := (iff #12244 #11448)
#16164 := [commutativity]: #16058
#16190 := [symm #16164]: #16160
#16191 := [monotonicity #16190]: #16185
#16121 := [hypothesis]: #15044
#16192 := [mp #16121 #16191]: #12245
#12259 := (<= #5122 0::Int)
#5068 := (+ #2037 #4079)
#5229 := (<= #5068 0::Int)
#5241 := (+ #4079 #5123)
#5242 := (+ #2037 #5241)
#5243 := (= #5242 0::Int)
#11519 := (<= #5242 0::Int)
#7263 := (<= #4080 0::Int)
#7366 := (= #185 #4078)
#4131 := (= #4078 #185)
#16125 := (iff #4131 #7366)
#16136 := (iff #7366 #4131)
#16124 := [commutativity]: #16136
#16126 := [symm #16124]: #16125
#4429 := (f11 f29 f28)
#4430 := (= #4429 f1)
#4055 := (f11 #193 f28)
#4056 := (= #4055 f1)
#43 := (:var 0 S1)
#40 := (:var 2 S7)
#41 := (f14 f15 #40)
#42 := (f13 #41 #10)
#44 := (f12 #42 #43)
#3633 := (pattern #44)
#47 := (= #43 f1)
#45 := (f11 #44 #10)
#46 := (= #45 f1)
#48 := (iff #46 #47)
#3634 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1)) (:pat #3633) #48)
#49 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1)) #48)
#3637 := (iff #49 #3634)
#3635 := (iff #48 #48)
#3636 := [refl]: #3635
#3638 := [quant-intro #3636]: #3637
#1494 := (~ #49 #49)
#1521 := (~ #48 #48)
#1522 := [refl]: #1521
#1495 := [nnf-pos #1522]: #1494
#341 := [asserted]: #49
#1523 := [mp~ #341 #1495]: #49
#3639 := [mp #1523 #3638]: #3634
#7340 := (not #3634)
#7341 := (or #7340 #4056)
#4058 := (iff #4056 #4057)
#7342 := (or #7340 #4058)
#7348 := (iff #7342 #7341)
#7350 := (iff #7341 #7341)
#7244 := [rewrite]: #7350
#4066 := (iff #4058 #4056)
#4061 := (iff #4056 true)
#4064 := (iff #4061 #4056)
#4065 := [rewrite]: #4064
#4062 := (iff #4058 #4061)
#4063 := [monotonicity #4060]: #4062
#4067 := [trans #4063 #4065]: #4066
#7349 := [monotonicity #4067]: #7348
#7353 := [trans #7349 #7244]: #7348
#7343 := [quant-inst #115 #181 #3]: #7342
#7354 := [mp #7343 #7353]: #7341
#12605 := [unit-resolution #7354 #3639]: #4056
#12706 := (= #4429 #4055)
#12710 := [monotonicity #12662]: #12706
#16193 := [trans #12710 #12605]: #4430
#4431 := (not #4430)
#4432 := (or #4431 #4131)
#7269 := (or #3860 #4431 #4131)
#7362 := (or #3860 #4432)
#7363 := (iff #7362 #7269)
#7364 := [rewrite]: #7363
#7360 := [quant-inst #181]: #7362
#7365 := [mp #7360 #7364]: #7269
#16189 := [unit-resolution #7365 #16079]: #4432
#16194 := [unit-resolution #16189 #16193]: #4131
#16138 := [mp #16194 #16126]: #7366
#16186 := (not #7366)
#16135 := (or #16186 #7263)
#16139 := [th-lemma arith triangle-eq]: #16135
#16157 := [unit-resolution #16139 #16138]: #7263
#10310 := (>= #5179 0::Int)
#12437 := [hypothesis]: #5182
#12988 := (or #12584 #10310)
#12982 := [th-lemma arith triangle-eq]: #12988
#12899 := [unit-resolution #12982 #12437]: #10310
#12990 := (not #10310)
#14609 := (not #7263)
#16158 := (or #11519 #14609 #12990)
#16159 := [th-lemma arith assign-bounds -1 1]: #16158
#16228 := [unit-resolution #16159 #12899 #16157]: #11519
#10373 := (>= #5242 0::Int)
#16229 := [unit-resolution #6974 #12445]: #4081
#10316 := (<= #5179 0::Int)
#12603 := (or #12584 #10316)
#11489 := [th-lemma arith triangle-eq]: #12603
#12604 := [unit-resolution #11489 #12437]: #10316
#12705 := (not #10316)
#16235 := (or #10373 #10190 #12705)
#16241 := [th-lemma arith assign-bounds -1 1]: #16235
#16242 := [unit-resolution #16241 #12604 #16229]: #10373
#16244 := (not #11519)
#16243 := (not #10373)
#16245 := (or #5243 #16243 #16244)
#16249 := [th-lemma arith triangle-eq]: #16245
#16215 := [unit-resolution #16249 #16242 #16228]: #5243
#5248 := (not #5243)
#16216 := (or #5229 #5248)
#13006 := [hypothesis]: #3888
#11224 := (or #3893 #5229 #4431 #5248)
#5217 := (+ #4078 #5178)
#5220 := (= #5217 0::Int)
#5221 := (not #5220)
#5209 := (+ #4078 #2038)
#5210 := (>= #5209 0::Int)
#5222 := (or #5210 #4431 #5221)
#10746 := (or #3893 #5222)
#13415 := (iff #10746 #11224)
#5251 := (or #5229 #4431 #5248)
#13664 := (or #3893 #5251)
#11836 := (iff #13664 #11224)
#11867 := [rewrite]: #11836
#12522 := (iff #10746 #13664)
#5252 := (iff #5222 #5251)
#5249 := (iff #5221 #5248)
#5246 := (iff #5220 #5243)
#5234 := (+ #4078 #5122)
#5235 := (+ #2038 #5234)
#5238 := (= #5235 0::Int)
#5244 := (iff #5238 #5243)
#5245 := [rewrite]: #5244
#5239 := (iff #5220 #5238)
#5236 := (= #5217 #5235)
#5237 := [rewrite]: #5236
#5240 := [monotonicity #5237]: #5239
#5247 := [trans #5240 #5245]: #5246
#5250 := [monotonicity #5247]: #5249
#5232 := (iff #5210 #5229)
#5223 := (+ #2038 #4078)
#5226 := (>= #5223 0::Int)
#5230 := (iff #5226 #5229)
#5231 := [rewrite]: #5230
#5227 := (iff #5210 #5226)
#5224 := (= #5209 #5223)
#5225 := [rewrite]: #5224
#5228 := [monotonicity #5225]: #5227
#5233 := [trans #5228 #5231]: #5232
#5253 := [monotonicity #5233 #5250]: #5252
#11978 := [monotonicity #5253]: #12522
#12915 := [trans #11978 #11867]: #13415
#10907 := [quant-inst #181]: #10746
#11685 := [mp #10907 #12915]: #11224
#16217 := [unit-resolution #11685 #13006 #16193]: #16216
#16220 := [unit-resolution #16217 #16215]: #5229
#16221 := (not #5229)
#16195 := (or #12259 #16243 #16221)
#16222 := [th-lemma arith assign-bounds 1 -1]: #16195
#16223 := [unit-resolution #16222 #16242 #16220]: #12259
#12250 := (not #12259)
#12251 := (or #12244 #12250)
#16038 := (or #7204 #12244 #12250)
#16039 := (or #7204 #12251)
#16034 := (iff #16039 #16038)
#16042 := [rewrite]: #16034
#16004 := [quant-inst #181 #2034]: #16039
#16043 := [mp #16004 #16042]: #16038
#16224 := [unit-resolution #16043 #3612]: #12251
#16214 := [unit-resolution #16224 #16223 #16192]: false
#16248 := [lemma #16214]: #16225
#13535 := [unit-resolution #16248 #13462 #11676]: #11448
#10531 := (or #11454 #15044)
#10525 := [def-axiom]: #10531
#13564 := [unit-resolution #10525 #13535]: #11454
#10513 := (not #11454)
#10578 := (or #10516 #11447 #10513)
#10577 := [def-axiom]: #10578
#13561 := [unit-resolution #10577 #13564]: #13559
#13556 := [unit-resolution #13561 #13463]: #11447
#13567 := (= #4533 #11446)
#13557 := [monotonicity #12662]: #13567
#13603 := [trans #13557 #13556]: #4534
#4541 := (not #4534)
#5090 := (or #4541 #5087)
#10267 := (or #3860 #4541 #5087)
#10275 := (or #3860 #5090)
#10272 := (iff #10275 #10267)
#10278 := [rewrite]: #10272
#10276 := [quant-inst #2034]: #10275
#10292 := [mp #10276 #10278]: #10267
#12904 := [unit-resolution #10292 #16079]: #5090
#13444 := [unit-resolution #12904 #13464]: #4541
[unit-resolution #13444 #13603]: false
unsat