src/HOL/Boogie/Examples/Boogie_Dijkstra.certs

updated SMT certificates

d29d9bae6b4b919e45b23de87975f8734cce2039 6542 0
#2 := false
decl up_6 :: (-> T4 T2 bool)
decl ?x47!7 :: (-> T2 T2)
decl ?x75!20 :: T2
#2146 := ?x75!20
#5823 := (?x47!7 ?x75!20)
decl uf_23 :: T4
#182 := uf_23
#16800 := (up_6 uf_23 #5823)
decl uf_2 :: (-> T1 T2)
decl uf_1 :: (-> T2 T2 T1)
decl uf_3 :: (-> T1 T2)
decl uf_22 :: T2
#174 := uf_22
#4514 := (uf_1 uf_22 uf_22)
#10482 := (uf_3 #4514)
#15059 := (uf_1 #10482 ?x75!20)
#15842 := (uf_3 #15059)
#16792 := (uf_1 #5823 #15842)
#19843 := (uf_2 #16792)
decl uf_7 :: (-> T4 T2 T5 T4)
decl uf_8 :: T5
#33 := uf_8
decl uf_15 :: T4
#110 := uf_15
#11444 := (uf_7 uf_15 #10482 uf_8)
#27073 := (up_6 #11444 #19843)
#27109 := (not #27073)
#16801 := (not #16800)
#27231 := (iff #16801 #27109)
#27229 := (iff #16800 #27073)
#27227 := (iff #27073 #16800)
#27215 := (= #19843 #5823)
#20888 := (= #5823 #19843)
#11 := (:var 0 T2)
#10 := (:var 1 T2)
#12 := (uf_1 #10 #11)
#3981 := (pattern #12)
#16 := (uf_2 #12)
#303 := (= #10 #16)
#3988 := (forall (vars (?x4 T2) (?x5 T2)) (:pat #3981) #303)
#307 := (forall (vars (?x4 T2) (?x5 T2)) #303)
#3991 := (iff #307 #3988)
#3989 := (iff #303 #303)
#3990 := [refl]: #3989
#3992 := [quant-intro #3990]: #3991
#1642 := (~ #307 #307)
#1676 := (~ #303 #303)
#1677 := [refl]: #1676
#1643 := [nnf-pos #1677]: #1642
#17 := (= #16 #10)
#18 := (forall (vars (?x4 T2) (?x5 T2)) #17)
#308 := (iff #18 #307)
#305 := (iff #17 #303)
#306 := [rewrite]: #305
#309 := [quant-intro #306]: #308
#302 := [asserted]: #18
#312 := [mp #302 #309]: #307
#1678 := [mp~ #312 #1643]: #307
#3993 := [mp #1678 #3992]: #3988
#8415 := (not #3988)
#20865 := (or #8415 #20888)
#20879 := [quant-inst]: #20865
#27214 := [unit-resolution #20879 #3993]: #20888
#27216 := [symm #27214]: #27215
#13523 := (= #11444 uf_23)
#183 := (uf_7 uf_15 uf_22 uf_8)
#7113 := (= #183 uf_23)
#184 := (= uf_23 #183)
#2150 := (uf_1 #11 ?x75!20)
#4271 := (pattern #2150)
decl uf_24 :: (-> T2 int)
#191 := (uf_24 #11)
#4211 := (pattern #191)
#201 := (up_6 uf_23 #11)
#4237 := (pattern #201)
#52 := 0::int
decl uf_10 :: (-> T1 int)
#2151 := (uf_10 #2150)
#2147 := (uf_24 ?x75!20)
#1038 := -1::int
#2148 := (* -1::int #2147)
#2745 := (+ #2148 #2151)
#2746 := (+ #191 #2745)
#2749 := (= #2746 0::int)
#3311 := (not #2749)
#2149 := (+ #191 #2148)
#2154 := (>= #2149 0::int)
#208 := (not #201)
#3312 := (or #208 #2154 #3311)
#4272 := (forall (vars (?x76 T2)) (:pat #4237 #4211 #4271) #3312)
#4277 := (not #4272)
#87 := (uf_1 #11 #10)
#4066 := (pattern #87)
#211 := (uf_24 #10)
#1318 := (* -1::int #211)
#1319 := (+ #191 #1318)
#88 := (uf_10 #87)
#1344 := (+ #88 #1319)
#1342 := (>= #1344 0::int)
#1053 := (* -1::int #88)
decl uf_9 :: int
#53 := uf_9
#1054 := (+ uf_9 #1053)
#1055 := (<= #1054 0::int)
#3303 := (or #208 #1055 #1342)
#4263 := (forall (vars (?x71 T2) (?x72 T2)) (:pat #4066) #3303)
#4268 := (not #4263)
decl uf_11 :: T2
#64 := uf_11
#2721 := (= uf_11 ?x75!20)
#2158 := (+ uf_9 #2148)
#2159 := (<= #2158 0::int)
#4280 := (or #2159 #2721 #4268 #4277)
#4283 := (not #4280)
decl ?x71!19 :: T2
#2117 := ?x71!19
decl ?x72!18 :: T2
#2116 := ?x72!18
#2122 := (uf_1 ?x72!18 ?x71!19)
#2123 := (uf_10 #2122)
#2126 := (* -1::int #2123)
#2120 := (uf_24 ?x72!18)
#2707 := (* -1::int #2120)
#2708 := (+ #2707 #2126)
#2118 := (uf_24 ?x71!19)
#2709 := (+ #2118 #2708)
#2710 := (<= #2709 0::int)
#2130 := (up_6 uf_23 ?x72!18)
#3266 := (not #2130)
#2127 := (+ uf_9 #2126)
#2128 := (<= #2127 0::int)
#3281 := (or #2128 #3266 #2710)
#3286 := (not #3281)
#4286 := (or #3286 #4283)
#4289 := (not #4286)
#4254 := (pattern #191 #211)
#1317 := (>= #1319 0::int)
#209 := (up_6 uf_23 #10)
#3243 := (not #209)
#3258 := (or #201 #3243 #1317)
#4255 := (forall (vars (?x67 T2) (?x68 T2)) (:pat #4254) #3258)
#4260 := (not #4255)
#4292 := (or #4260 #4289)
#4295 := (not #4292)
decl ?x68!16 :: T2
#2091 := ?x68!16
#2095 := (uf_24 ?x68!16)
#2681 := (* -1::int #2095)
decl ?x67!17 :: T2
#2092 := ?x67!17
#2093 := (uf_24 ?x67!17)
#2682 := (+ #2093 #2681)
#2683 := (<= #2682 0::int)
#2099 := (up_6 uf_23 ?x68!16)
#2098 := (up_6 uf_23 ?x67!17)
#3220 := (not #2098)
#3235 := (or #3220 #2099 #2683)
#3240 := (not #3235)
#4298 := (or #3240 #4295)
#4301 := (not #4298)
#1308 := (>= #191 0::int)
#4246 := (forall (vars (?x65 T2)) (:pat #4211) #1308)
#4251 := (not #4246)
#4304 := (or #4251 #4301)
#4307 := (not #4304)
decl ?x65!15 :: T2
#2076 := ?x65!15
#2077 := (uf_24 ?x65!15)
#2078 := (>= #2077 0::int)
#2079 := (not #2078)
#4310 := (or #2079 #4307)
#4313 := (not #4310)
#204 := (uf_24 uf_11)
#205 := (= #204 0::int)
#1305 := (not #205)
#4316 := (or #1305 #4313)
#4319 := (not #4316)
#4322 := (or #1305 #4319)
#4325 := (not #4322)
decl uf_4 :: (-> T3 T2 int)
decl uf_14 :: T3
#104 := uf_14
#107 := (uf_4 uf_14 #11)
#4090 := (pattern #107)
#645 := (= #107 #191)
#662 := (or #208 #645)
#4238 := (forall (vars (?x63 T2)) (:pat #4237 #4090 #4211) #662)
#4243 := (not #4238)
#4328 := (or #4243 #4325)
#4331 := (not #4328)
decl ?x63!14 :: T2
#2052 := ?x63!14
#2054 := (uf_4 uf_14 ?x63!14)
#2053 := (uf_24 ?x63!14)
#2658 := (= #2053 #2054)
#2056 := (up_6 uf_23 ?x63!14)
#2057 := (not #2056)
#2661 := (or #2057 #2658)
#2664 := (not #2661)
#4334 := (or #2664 #4331)
#4337 := (not #4334)
#1293 := (* -1::int #191)
#1294 := (+ #107 #1293)
#1292 := (>= #1294 0::int)
#4229 := (forall (vars (?x61 T2)) (:pat #4090 #4211) #1292)
#4234 := (not #4229)
#4340 := (or #4234 #4337)
#4343 := (not #4340)
decl ?x61!13 :: T2
#2034 := ?x61!13
#2037 := (uf_4 uf_14 ?x61!13)
#2648 := (* -1::int #2037)
#2035 := (uf_24 ?x61!13)
#2649 := (+ #2035 #2648)
#2650 := (<= #2649 0::int)
#2655 := (not #2650)
#4346 := (or #2655 #4343)
#4349 := (not #4346)
#185 := (uf_1 uf_22 #11)
#4212 := (pattern #185)
#186 := (uf_10 #185)
#1431 := (+ #186 #1293)
#177 := (uf_4 uf_14 uf_22)
#1432 := (+ #177 #1431)
#1433 := (= #1432 0::int)
#1262 := (* -1::int #186)
#1268 := (* -1::int #177)
#1269 := (+ #1268 #1262)
#1270 := (+ #107 #1269)
#1271 := (<= #1270 0::int)
#1263 := (+ uf_9 #1262)
#1264 := (<= #1263 0::int)
#3212 := (or #1264 #1271 #1433)
#4221 := (forall (vars (?x59 T2)) (:pat #4212 #4090 #4211) #3212)
#4226 := (not #4221)
#3192 := (or #1264 #1271)
#3193 := (not #3192)
#3196 := (or #645 #3193)
#4213 := (forall (vars (?x60 T2)) (:pat #4090 #4211 #4212) #3196)
#4218 := (not #4213)
decl ?x48!12 :: T2
#2011 := ?x48!12
#2017 := (up_6 uf_15 ?x48!12)
#2012 := (uf_4 uf_14 ?x48!12)
#2013 := (* -1::int #2012)
#2014 := (+ uf_9 #2013)
#2015 := (<= #2014 0::int)
#1458 := (+ uf_9 #1268)
#1459 := (<= #1458 0::int)
#111 := (up_6 uf_15 #11)
#4132 := (pattern #111)
#1446 := (+ #107 #1268)
#1445 := (>= #1446 0::int)
#1449 := (or #111 #1445)
#4203 := (forall (vars (?x58 T2)) (:pat #4132 #4090) #1449)
#4208 := (not #4203)
#825 := (not #184)
#175 := (up_6 uf_15 uf_22)
#4352 := (or #175 #825 #4208 #1459 #2015 #2017 #4218 #4226 #4349)
#4355 := (not #4352)
decl ?x53!11 :: T2
#1945 := ?x53!11
decl ?x54!10 :: T2
#1944 := ?x54!10
#1950 := (uf_1 ?x54!10 ?x53!11)
#1951 := (uf_10 #1950)
#1958 := (* -1::int #1951)
decl uf_19 :: T3
#141 := uf_19
#1948 := (uf_4 uf_19 ?x54!10)
#1954 := (* -1::int #1948)
#2605 := (+ #1954 #1958)
#1946 := (uf_4 uf_19 ?x53!11)
#2606 := (+ #1946 #2605)
#2607 := (<= #2606 0::int)
#1959 := (+ uf_9 #1958)
#1960 := (<= #1959 0::int)
#1955 := (+ uf_9 #1954)
#1956 := (<= #1955 0::int)
#3156 := (or #1956 #1960 #2607)
#3161 := (not #3156)
#149 := (uf_4 uf_19 #10)
#1175 := (* -1::int #149)
#146 := (uf_4 uf_19 #11)
#1176 := (+ #146 #1175)
#1182 := (+ #88 #1176)
#1205 := (>= #1182 0::int)
#1162 := (* -1::int #146)
#1163 := (+ uf_9 #1162)
#1164 := (<= #1163 0::int)
#3124 := (or #1055 #1164 #1205)
#4165 := (forall (vars (?x53 T2) (?x54 T2)) (:pat #4066) #3124)
#4170 := (not #4165)
#161 := (uf_4 uf_19 uf_11)
#162 := (= #161 0::int)
#4173 := (or #162 #4170)
#4176 := (not #4173)
#4179 := (or #4176 #3161)
#4182 := (not #4179)
#4141 := (pattern #146)
decl ?x50!9 :: (-> T2 T2)
#1921 := (?x50!9 #11)
#1924 := (uf_1 #1921 #11)
#1925 := (uf_10 #1924)
#2575 := (* -1::int #1925)
#1922 := (uf_4 uf_19 #1921)
#2558 := (* -1::int #1922)
#2576 := (+ #2558 #2575)
#2577 := (+ #146 #2576)
#2578 := (= #2577 0::int)
#3094 := (not #2578)
#2559 := (+ #146 #2558)
#2560 := (<= #2559 0::int)
#3095 := (or #2560 #3094)
#3096 := (not #3095)
#65 := (= #11 uf_11)
#3102 := (or #65 #1164 #3096)
#4157 := (forall (vars (?x49 T2)) (:pat #4141) #3102)
#4162 := (not #4157)
#4185 := (or #4162 #4182)
#4188 := (not #4185)
decl ?x49!8 :: T2
#1881 := ?x49!8
#1885 := (uf_1 #11 ?x49!8)
#4142 := (pattern #1885)
#1886 := (uf_10 #1885)
#1882 := (uf_4 uf_19 ?x49!8)
#1883 := (* -1::int #1882)
#2528 := (+ #1883 #1886)
#2529 := (+ #146 #2528)
#2532 := (= #2529 0::int)
#3058 := (not #2532)
#1884 := (+ #146 #1883)
#1889 := (>= #1884 0::int)
#3059 := (or #1889 #3058)
#4143 := (forall (vars (?x50 T2)) (:pat #4141 #4142) #3059)
#4148 := (not #4143)
#2504 := (= uf_11 ?x49!8)
#1893 := (+ uf_9 #1883)
#1894 := (<= #1893 0::int)
#4151 := (or #1894 #2504 #4148)
#4154 := (not #4151)
#4191 := (or #4154 #4188)
#4194 := (not #4191)
#1117 := (* -1::int #107)
#1118 := (+ uf_9 #1117)
#1119 := (<= #1118 0::int)
#3044 := (or #111 #1119)
#4133 := (forall (vars (?x48 T2)) (:pat #4132 #4090) #3044)
#4138 := (not #4133)
#495 := (= uf_14 uf_19)
#586 := (not #495)
decl uf_16 :: T4
#136 := uf_16
#492 := (= uf_15 uf_16)
#604 := (not #492)
decl uf_21 :: T3
#144 := uf_21
decl uf_20 :: T3
#143 := uf_20
#145 := (= uf_20 uf_21)
#577 := (not #145)
decl uf_18 :: T2
#139 := uf_18
decl uf_17 :: T2
#138 := uf_17
#140 := (= uf_17 uf_18)
#595 := (not #140)
#4197 := (or #595 #577 #604 #586 #4138 #4194)
#4200 := (not #4197)
#4358 := (or #4200 #4355)
#4361 := (not #4358)
#1845 := (?x47!7 #11)
#1846 := (uf_4 uf_14 #1845)
#2463 := (* -1::int #1846)
#2478 := (+ #107 #2463)
#2479 := (<= #2478 0::int)
#1850 := (uf_1 #1845 #11)
#1851 := (uf_10 #1850)
#2464 := (* -1::int #1851)
#2465 := (+ #2463 #2464)
#2466 := (+ #107 #2465)
#2467 := (= #2466 0::int)
#3028 := (not #2467)
#1854 := (up_6 uf_15 #1845)
#3027 := (not #1854)
#3029 := (or #3027 #3028 #2479)
#3030 := (not #3029)
#3036 := (or #65 #1119 #3030)
#4124 := (forall (vars (?x46 T2)) (:pat #4090) #3036)
#4129 := (not #4124)
decl uf_12 :: (-> T2 int)
#66 := (uf_12 #11)
#4042 := (pattern #66)
decl ?x38!6 :: (-> T2 T2)
#1818 := (?x38!6 #11)
#1822 := (uf_12 #1818)
#2422 := (* -1::int #1822)
#1819 := (uf_1 #1818 #11)
#1820 := (uf_10 #1819)
#2439 := (* -1::int #1820)
#2440 := (+ #2439 #2422)
#2441 := (+ #66 #2440)
#2442 := (= #2441 0::int)
#3000 := (not #2442)
#2423 := (+ #66 #2422)
#2424 := (<= #2423 0::int)
decl up_13 :: (-> T2 bool)
#1828 := (up_13 #1818)
#2999 := (not #1828)
#3001 := (or #2999 #2424 #3000)
#3002 := (not #3001)
#1079 := (* -1::int #66)
#1080 := (+ uf_9 #1079)
#1081 := (<= #1080 0::int)
#3008 := (or #65 #1081 #3002)
#4116 := (forall (vars (?x37 T2)) (:pat #4042) #3008)
#4121 := (not #4116)
#113 := (up_6 uf_15 #10)
#4107 := (pattern #111 #113)
#115 := (uf_4 uf_14 #10)
#1131 := (* -1::int #115)
#1132 := (+ #107 #1131)
#1135 := (>= #1132 0::int)
#2965 := (not #113)
#2980 := (or #111 #2965 #1135)
#4108 := (forall (vars (?x42 T2) (?x43 T2)) (:pat #4107) #2980)
#4113 := (not #4108)
#1133 := (+ #88 #1132)
#1513 := (>= #1133 0::int)
#112 := (not #111)
#2957 := (or #112 #1055 #1513)
#4099 := (forall (vars (?x44 T2) (?x45 T2)) (:pat #4066) #2957)
#4104 := (not #4099)
#1536 := (>= #107 0::int)
#4091 := (forall (vars (?x41 T2)) (:pat #4090) #1536)
#4096 := (not #4091)
#105 := (uf_4 uf_14 uf_11)
#106 := (= #105 0::int)
#1547 := (not #106)
#4364 := (or #1547 #4096 #4104 #4113 #4121 #4129 #4361)
#4367 := (not #4364)
decl ?x37!5 :: T2
#1774 := ?x37!5
#1775 := (uf_1 #11 ?x37!5)
#4075 := (pattern #1775)
#74 := (up_13 #11)
#4035 := (pattern #74)
#1777 := (uf_12 ?x37!5)
#1778 := (* -1::int #1777)
#1776 := (uf_10 #1775)
#2390 := (+ #1776 #1778)
#2391 := (+ #66 #2390)
#2394 := (= #2391 0::int)
#2918 := (not #2394)
#1782 := (+ #66 #1778)
#1783 := (>= #1782 0::int)
#75 := (not #74)
#2919 := (or #75 #1783 #2918)
#4076 := (forall (vars (?x38 T2)) (:pat #4035 #4042 #4075) #2919)
#4081 := (not #4076)
#2366 := (= uf_11 ?x37!5)
#1787 := (+ uf_9 #1778)
#1788 := (<= #1787 0::int)
#4084 := (or #1788 #2366 #4081)
#4087 := (not #4084)
#4370 := (or #4087 #4367)
#4373 := (not #4370)
#83 := (uf_12 #10)
#1041 := (* -1::int #83)
#1068 := (+ #1041 #88)
#1069 := (+ #66 #1068)
#1066 := (>= #1069 0::int)
#2910 := (or #75 #1055 #1066)
#4067 := (forall (vars (?x33 T2) (?x34 T2)) (:pat #4066) #2910)
#4072 := (not #4067)
#4376 := (or #4072 #4373)
#4379 := (not #4376)
decl ?x34!3 :: T2
#1744 := ?x34!3
#1751 := (uf_12 ?x34!3)
decl ?x33!4 :: T2
#1745 := ?x33!4
#1748 := (uf_12 ?x33!4)
#1749 := (* -1::int #1748)
#2353 := (+ #1749 #1751)
#1746 := (uf_1 ?x34!3 ?x33!4)
#1747 := (uf_10 #1746)
#2354 := (+ #1747 #2353)
#2357 := (>= #2354 0::int)
#1758 := (up_13 ?x34!3)
#2873 := (not #1758)
#1754 := (* -1::int #1747)
#1755 := (+ uf_9 #1754)
#1756 := (<= #1755 0::int)
#2888 := (or #1756 #2873 #2357)
#8152 := [hypothesis]: #1758
#4036 := (forall (vars (?x26 T2)) (:pat #4035) #75)
#76 := (forall (vars (?x26 T2)) #75)
#4039 := (iff #76 #4036)
#4037 := (iff #75 #75)
#4038 := [refl]: #4037
#4040 := [quant-intro #4038]: #4039
#1658 := (~ #76 #76)
#1695 := (~ #75 #75)
#1696 := [refl]: #1695
#1659 := [nnf-pos #1696]: #1658
#67 := (= #66 0::int)
#70 := (not #65)
#1605 := (or #70 #67)
#1608 := (forall (vars (?x24 T2)) #1605)
#1611 := (not #1608)
#1539 := (forall (vars (?x41 T2)) #1536)
#1542 := (not #1539)
#114 := (and #112 #113)
#440 := (not #114)
#1527 := (or #440 #1135)
#1530 := (forall (vars (?x42 T2) (?x43 T2)) #1527)
#1533 := (not #1530)
#1056 := (not #1055)
#1505 := (and #111 #1056)
#1510 := (not #1505)
#1516 := (or #1510 #1513)
#1519 := (forall (vars (?x44 T2) (?x45 T2)) #1516)
#1522 := (not #1519)
#1452 := (forall (vars (?x58 T2)) #1449)
#1455 := (not #1452)
#1272 := (not #1271)
#1265 := (not #1264)
#1275 := (and #1265 #1272)
#1428 := (not #1275)
#1436 := (or #1428 #1433)
#1439 := (forall (vars (?x59 T2)) #1436)
#1442 := (not #1439)
#1366 := (= #1344 0::int)
#1369 := (not #1317)
#1378 := (and #201 #1369 #1366)
#1383 := (exists (vars (?x76 T2)) #1378)
#1355 := (+ uf_9 #1293)
#1356 := (<= #1355 0::int)
#1357 := (not #1356)
#1360 := (and #70 #1357)
#1363 := (not #1360)
#1386 := (or #1363 #1383)
#1389 := (forall (vars (?x75 T2)) #1386)
#1334 := (and #201 #1056)
#1339 := (not #1334)
#1346 := (or #1339 #1342)
#1349 := (forall (vars (?x71 T2) (?x72 T2)) #1346)
#1352 := (not #1349)
#1392 := (or #1352 #1389)
#1395 := (and #1349 #1392)
#210 := (and #208 #209)
#673 := (not #210)
#1322 := (or #673 #1317)
#1325 := (forall (vars (?x67 T2) (?x68 T2)) #1322)
#1328 := (not #1325)
#1398 := (or #1328 #1395)
#1401 := (and #1325 #1398)
#1311 := (forall (vars (?x65 T2)) #1308)
#1314 := (not #1311)
#1404 := (or #1314 #1401)
#1407 := (and #1311 #1404)
#1410 := (or #1305 #1407)
#1413 := (and #205 #1410)
#667 := (forall (vars (?x63 T2)) #662)
#783 := (not #667)
#1416 := (or #783 #1413)
#1419 := (and #667 #1416)
#1297 := (forall (vars (?x61 T2)) #1292)
#1300 := (not #1297)
#1422 := (or #1300 #1419)
#1425 := (and #1297 #1422)
#1281 := (or #645 #1275)
#1286 := (forall (vars (?x60 T2)) #1281)
#1289 := (not #1286)
#1120 := (not #1119)
#1236 := (and #112 #1120)
#1239 := (exists (vars (?x48 T2)) #1236)
#1470 := (not #1239)
#1494 := (or #175 #825 #1470 #1289 #1425 #1442 #1455 #1459)
#1165 := (not #1164)
#1199 := (and #1056 #1165)
#1202 := (not #1199)
#1208 := (or #1202 #1205)
#1211 := (forall (vars (?x53 T2) (?x54 T2)) #1208)
#1214 := (not #1211)
#1222 := (or #162 #1214)
#1227 := (and #1211 #1222)
#1180 := (= #1182 0::int)
#1174 := (>= #1176 0::int)
#1177 := (not #1174)
#1184 := (and #1177 #1180)
#1187 := (exists (vars (?x50 T2)) #1184)
#1168 := (and #70 #1165)
#1171 := (not #1168)
#1190 := (or #1171 #1187)
#1193 := (forall (vars (?x49 T2)) #1190)
#1196 := (not #1193)
#1230 := (or #1196 #1227)
#1233 := (and #1193 #1230)
#1257 := (or #595 #577 #604 #586 #1233 #1239)
#1499 := (and #1257 #1494)
#1136 := (not #1135)
#1129 := (= #1133 0::int)
#1145 := (and #111 #1129 #1136)
#1150 := (exists (vars (?x47 T2)) #1145)
#1123 := (and #70 #1120)
#1126 := (not #1123)
#1153 := (or #1126 #1150)
#1156 := (forall (vars (?x46 T2)) #1153)
#1159 := (not #1156)
#1091 := (= #1069 0::int)
#1042 := (+ #66 #1041)
#1040 := (>= #1042 0::int)
#1094 := (not #1040)
#1103 := (and #74 #1094 #1091)
#1108 := (exists (vars (?x38 T2)) #1103)
#1082 := (not #1081)
#1085 := (and #70 #1082)
#1088 := (not #1085)
#1111 := (or #1088 #1108)
#1114 := (forall (vars (?x37 T2)) #1111)
#1550 := (not #1114)
#1571 := (or #1547 #1550 #1159 #1499 #1522 #1533 #1542)
#1576 := (and #1114 #1571)
#1059 := (and #74 #1056)
#1062 := (not #1059)
#1070 := (or #1062 #1066)
#1073 := (forall (vars (?x33 T2) (?x34 T2)) #1070)
#1076 := (not #1073)
#1579 := (or #1076 #1576)
#1582 := (and #1073 #1579)
#81 := (up_13 #10)
#82 := (and #75 #81)
#416 := (not #82)
#1044 := (or #416 #1040)
#1047 := (forall (vars (?x29 T2) (?x30 T2)) #1044)
#1050 := (not #1047)
#1585 := (or #1050 #1582)
#1588 := (and #1047 #1585)
#1031 := (>= #66 0::int)
#1032 := (forall (vars (?x27 T2)) #1031)
#1035 := (not #1032)
#1591 := (or #1035 #1588)
#1594 := (and #1032 #1591)
#77 := (uf_12 uf_11)
#78 := (= #77 0::int)
#1026 := (not #78)
#1597 := (or #1026 #1594)
#1600 := (and #78 #1597)
#399 := (= uf_9 #66)
#405 := (or #65 #399)
#410 := (forall (vars (?x25 T2)) #405)
#999 := (not #410)
#990 := (not #76)
#1623 := (or #990 #999 #1600 #1611)
#1628 := (not #1623)
#1 := true
#216 := (+ #191 #88)
#223 := (= #211 #216)
#224 := (and #201 #223)
#222 := (< #191 #211)
#225 := (and #222 #224)
#226 := (exists (vars (?x76 T2)) #225)
#220 := (< #191 uf_9)
#221 := (and #70 #220)
#227 := (implies #221 #226)
#228 := (forall (vars (?x75 T2)) #227)
#229 := (and #228 true)
#217 := (<= #211 #216)
#89 := (< #88 uf_9)
#215 := (and #201 #89)
#218 := (implies #215 #217)
#219 := (forall (vars (?x71 T2) (?x72 T2)) #218)
#230 := (implies #219 #229)
#231 := (and #219 #230)
#212 := (<= #211 #191)
#213 := (implies #210 #212)
#214 := (forall (vars (?x67 T2) (?x68 T2)) #213)
#232 := (implies #214 #231)
#233 := (and #214 #232)
#206 := (<= 0::int #191)
#207 := (forall (vars (?x65 T2)) #206)
#234 := (implies #207 #233)
#235 := (and #207 #234)
#236 := (implies #205 #235)
#237 := (and #205 #236)
#196 := (= #191 #107)
#202 := (implies #201 #196)
#203 := (forall (vars (?x63 T2)) #202)
#238 := (implies #203 #237)
#239 := (and #203 #238)
#199 := (<= #191 #107)
#200 := (forall (vars (?x61 T2)) #199)
#240 := (implies #200 #239)
#241 := (and #200 #240)
#188 := (+ #177 #186)
#189 := (< #188 #107)
#187 := (< #186 uf_9)
#190 := (and #187 #189)
#195 := (not #190)
#197 := (implies #195 #196)
#198 := (forall (vars (?x60 T2)) #197)
#242 := (implies #198 #241)
#192 := (= #191 #188)
#193 := (implies #190 #192)
#194 := (forall (vars (?x59 T2)) #193)
#243 := (implies #194 #242)
#244 := (implies #184 #243)
#179 := (<= #177 #107)
#180 := (implies #112 #179)
#181 := (forall (vars (?x58 T2)) #180)
#245 := (implies #181 #244)
#178 := (< #177 uf_9)
#246 := (implies #178 #245)
#176 := (not #175)
#247 := (implies #176 #246)
#124 := (< #107 uf_9)
#133 := (and #112 #124)
#134 := (exists (vars (?x48 T2)) #133)
#248 := (implies #134 #247)
#249 := (implies true #248)
#163 := (and #162 true)
#151 := (+ #146 #88)
#158 := (<= #149 #151)
#147 := (< #146 uf_9)
#157 := (and #147 #89)
#159 := (implies #157 #158)
#160 := (forall (vars (?x53 T2) (?x54 T2)) #159)
#164 := (implies #160 #163)
#165 := (and #160 #164)
#152 := (= #149 #151)
#150 := (< #146 #149)
#153 := (and #150 #152)
#154 := (exists (vars (?x50 T2)) #153)
#148 := (and #70 #147)
#155 := (implies #148 #154)
#156 := (forall (vars (?x49 T2)) #155)
#166 := (implies #156 #165)
#167 := (and #156 #166)
#168 := (implies #145 #167)
#142 := (= uf_19 uf_14)
#169 := (implies #142 #168)
#170 := (implies #140 #169)
#137 := (= uf_16 uf_15)
#171 := (implies #137 #170)
#135 := (not #134)
#172 := (implies #135 #171)
#173 := (implies true #172)
#250 := (and #173 #249)
#120 := (+ #107 #88)
#127 := (= #115 #120)
#128 := (and #111 #127)
#126 := (< #107 #115)
#129 := (and #126 #128)
#130 := (exists (vars (?x47 T2)) #129)
#125 := (and #70 #124)
#131 := (implies #125 #130)
#132 := (forall (vars (?x46 T2)) #131)
#251 := (implies #132 #250)
#121 := (<= #115 #120)
#119 := (and #111 #89)
#122 := (implies #119 #121)
#123 := (forall (vars (?x44 T2) (?x45 T2)) #122)
#252 := (implies #123 #251)
#116 := (<= #115 #107)
#117 := (implies #114 #116)
#118 := (forall (vars (?x42 T2) (?x43 T2)) #117)
#253 := (implies #118 #252)
#108 := (<= 0::int #107)
#109 := (forall (vars (?x41 T2)) #108)
#254 := (implies #109 #253)
#255 := (implies #106 #254)
#256 := (implies true #255)
#91 := (+ #66 #88)
#98 := (= #83 #91)
#99 := (and #74 #98)
#97 := (< #66 #83)
#100 := (and #97 #99)
#101 := (exists (vars (?x38 T2)) #100)
#95 := (< #66 uf_9)
#96 := (and #70 #95)
#102 := (implies #96 #101)
#103 := (forall (vars (?x37 T2)) #102)
#257 := (implies #103 #256)
#258 := (and #103 #257)
#92 := (<= #83 #91)
#90 := (and #74 #89)
#93 := (implies #90 #92)
#94 := (forall (vars (?x33 T2) (?x34 T2)) #93)
#259 := (implies #94 #258)
#260 := (and #94 #259)
#84 := (<= #83 #66)
#85 := (implies #82 #84)
#86 := (forall (vars (?x29 T2) (?x30 T2)) #85)
#261 := (implies #86 #260)
#262 := (and #86 #261)
#79 := (<= 0::int #66)
#80 := (forall (vars (?x27 T2)) #79)
#263 := (implies #80 #262)
#264 := (and #80 #263)
#265 := (implies #78 #264)
#266 := (and #78 #265)
#267 := (implies #76 #266)
#71 := (= #66 uf_9)
#72 := (implies #70 #71)
#73 := (forall (vars (?x25 T2)) #72)
#268 := (implies #73 #267)
#68 := (implies #65 #67)
#69 := (forall (vars (?x24 T2)) #68)
#269 := (implies #69 #268)
#270 := (implies true #269)
#271 := (not #270)
#1631 := (iff #271 #1628)
#683 := (+ #88 #191)
#701 := (= #211 #683)
#704 := (and #201 #701)
#707 := (and #222 #704)
#710 := (exists (vars (?x76 T2)) #707)
#716 := (not #221)
#717 := (or #716 #710)
#722 := (forall (vars (?x75 T2)) #717)
#686 := (<= #211 #683)
#680 := (and #89 #201)
#692 := (not #680)
#693 := (or #692 #686)
#698 := (forall (vars (?x71 T2) (?x72 T2)) #693)
#735 := (not #698)
#736 := (or #735 #722)
#741 := (and #698 #736)
#674 := (or #673 #212)
#677 := (forall (vars (?x67 T2) (?x68 T2)) #674)
#747 := (not #677)
#748 := (or #747 #741)
#753 := (and #677 #748)
#759 := (not #207)
#760 := (or #759 #753)
#765 := (and #207 #760)
#670 := (= 0::int #204)
#771 := (not #670)
#772 := (or #771 #765)
#777 := (and #670 #772)
#784 := (or #783 #777)
#789 := (and #667 #784)
#795 := (not #200)
#796 := (or #795 #789)
#801 := (and #200 #796)
#651 := (or #190 #645)
#656 := (forall (vars (?x60 T2)) #651)
#807 := (not #656)
#808 := (or #807 #801)
#631 := (= #188 #191)
#637 := (or #195 #631)
#642 := (forall (vars (?x59 T2)) #637)
#816 := (not #642)
#817 := (or #816 #808)
#826 := (or #825 #817)
#625 := (or #111 #179)
#628 := (forall (vars (?x58 T2)) #625)
#834 := (not #628)
#835 := (or #834 #826)
#843 := (not #178)
#844 := (or #843 #835)
#852 := (or #175 #844)
#860 := (or #135 #852)
#540 := (= 0::int #161)
#498 := (+ #88 #146)
#525 := (<= #149 #498)
#522 := (and #89 #147)
#531 := (not #522)
#532 := (or #531 #525)
#537 := (forall (vars (?x53 T2) (?x54 T2)) #532)
#553 := (not #537)
#554 := (or #553 #540)
#559 := (and #537 #554)
#501 := (= #149 #498)
#504 := (and #150 #501)
#507 := (exists (vars (?x50 T2)) #504)
#513 := (not #148)
#514 := (or #513 #507)
#519 := (forall (vars (?x49 T2)) #514)
#565 := (not #519)
#566 := (or #565 #559)
#571 := (and #519 #566)
#578 := (or #577 #571)
#587 := (or #586 #578)
#596 := (or #595 #587)
#605 := (or #604 #596)
#613 := (or #134 #605)
#872 := (and #613 #860)
#450 := (+ #88 #107)
#468 := (= #115 #450)
#471 := (and #111 #468)
#474 := (and #126 #471)
#477 := (exists (vars (?x47 T2)) #474)
#483 := (not #125)
#484 := (or #483 #477)
#489 := (forall (vars (?x46 T2)) #484)
#878 := (not #489)
#879 := (or #878 #872)
#453 := (<= #115 #450)
#447 := (and #89 #111)
#459 := (not #447)
#460 := (or #459 #453)
#465 := (forall (vars (?x44 T2) (?x45 T2)) #460)
#887 := (not #465)
#888 := (or #887 #879)
#441 := (or #440 #116)
#444 := (forall (vars (?x42 T2) (?x43 T2)) #441)
#896 := (not #444)
#897 := (or #896 #888)
#905 := (not #109)
#906 := (or #905 #897)
#437 := (= 0::int #105)
#914 := (not #437)
#915 := (or #914 #906)
#430 := (not #96)
#431 := (or #430 #101)
#434 := (forall (vars (?x37 T2)) #431)
#930 := (not #434)
#931 := (or #930 #915)
#936 := (and #434 #931)
#423 := (not #90)
#424 := (or #423 #92)
#427 := (forall (vars (?x33 T2) (?x34 T2)) #424)
#942 := (not #427)
#943 := (or #942 #936)
#948 := (and #427 #943)
#417 := (or #416 #84)
#420 := (forall (vars (?x29 T2) (?x30 T2)) #417)
#954 := (not #420)
#955 := (or #954 #948)
#960 := (and #420 #955)
#966 := (not #80)
#967 := (or #966 #960)
#972 := (and #80 #967)
#413 := (= 0::int #77)
#978 := (not #413)
#979 := (or #978 #972)
#984 := (and #413 #979)
#991 := (or #990 #984)
#1000 := (or #999 #991)
#385 := (= 0::int #66)
#391 := (or #70 #385)
#396 := (forall (vars (?x24 T2)) #391)
#1008 := (not #396)
#1009 := (or #1008 #1000)
#1021 := (not #1009)
#1629 := (iff #1021 #1628)
#1626 := (iff #1009 #1623)
#1614 := (or #990 #1600)
#1617 := (or #999 #1614)
#1620 := (or #1611 #1617)
#1624 := (iff #1620 #1623)
#1625 := [rewrite]: #1624
#1621 := (iff #1009 #1620)
#1618 := (iff #1000 #1617)
#1615 := (iff #991 #1614)
#1601 := (iff #984 #1600)
#1598 := (iff #979 #1597)
#1595 := (iff #972 #1594)
#1592 := (iff #967 #1591)
#1589 := (iff #960 #1588)
#1586 := (iff #955 #1585)
#1583 := (iff #948 #1582)
#1580 := (iff #943 #1579)
#1577 := (iff #936 #1576)
#1574 := (iff #931 #1571)
#1553 := (or #1159 #1499)
#1556 := (or #1522 #1553)
#1559 := (or #1533 #1556)
#1562 := (or #1542 #1559)
#1565 := (or #1547 #1562)
#1568 := (or #1550 #1565)
#1572 := (iff #1568 #1571)
#1573 := [rewrite]: #1572
#1569 := (iff #931 #1568)
#1566 := (iff #915 #1565)
#1563 := (iff #906 #1562)
#1560 := (iff #897 #1559)
#1557 := (iff #888 #1556)
#1554 := (iff #879 #1553)
#1500 := (iff #872 #1499)
#1497 := (iff #860 #1494)
#1473 := (or #1289 #1425)
#1476 := (or #1442 #1473)
#1479 := (or #825 #1476)
#1482 := (or #1455 #1479)
#1485 := (or #1459 #1482)
#1488 := (or #175 #1485)
#1491 := (or #1470 #1488)
#1495 := (iff #1491 #1494)
#1496 := [rewrite]: #1495
#1492 := (iff #860 #1491)
#1489 := (iff #852 #1488)
#1486 := (iff #844 #1485)
#1483 := (iff #835 #1482)
#1480 := (iff #826 #1479)
#1477 := (iff #817 #1476)
#1474 := (iff #808 #1473)
#1426 := (iff #801 #1425)
#1423 := (iff #796 #1422)
#1420 := (iff #789 #1419)
#1417 := (iff #784 #1416)
#1414 := (iff #777 #1413)
#1411 := (iff #772 #1410)
#1408 := (iff #765 #1407)
#1405 := (iff #760 #1404)
#1402 := (iff #753 #1401)
#1399 := (iff #748 #1398)
#1396 := (iff #741 #1395)
#1393 := (iff #736 #1392)
#1390 := (iff #722 #1389)
#1387 := (iff #717 #1386)
#1384 := (iff #710 #1383)
#1381 := (iff #707 #1378)
#1372 := (and #201 #1366)
#1375 := (and #1369 #1372)
#1379 := (iff #1375 #1378)
#1380 := [rewrite]: #1379
#1376 := (iff #707 #1375)
#1373 := (iff #704 #1372)
#1367 := (iff #701 #1366)
#1368 := [rewrite]: #1367
#1374 := [monotonicity #1368]: #1373
#1370 := (iff #222 #1369)
#1371 := [rewrite]: #1370
#1377 := [monotonicity #1371 #1374]: #1376
#1382 := [trans #1377 #1380]: #1381
#1385 := [quant-intro #1382]: #1384
#1364 := (iff #716 #1363)
#1361 := (iff #221 #1360)
#1358 := (iff #220 #1357)
#1359 := [rewrite]: #1358
#1362 := [monotonicity #1359]: #1361
#1365 := [monotonicity #1362]: #1364
#1388 := [monotonicity #1365 #1385]: #1387
#1391 := [quant-intro #1388]: #1390
#1353 := (iff #735 #1352)
#1350 := (iff #698 #1349)
#1347 := (iff #693 #1346)
#1343 := (iff #686 #1342)
#1345 := [rewrite]: #1343
#1340 := (iff #692 #1339)
#1337 := (iff #680 #1334)
#1331 := (and #1056 #201)
#1335 := (iff #1331 #1334)
#1336 := [rewrite]: #1335
#1332 := (iff #680 #1331)
#1057 := (iff #89 #1056)
#1058 := [rewrite]: #1057
#1333 := [monotonicity #1058]: #1332
#1338 := [trans #1333 #1336]: #1337
#1341 := [monotonicity #1338]: #1340
#1348 := [monotonicity #1341 #1345]: #1347
#1351 := [quant-intro #1348]: #1350
#1354 := [monotonicity #1351]: #1353
#1394 := [monotonicity #1354 #1391]: #1393
#1397 := [monotonicity #1351 #1394]: #1396
#1329 := (iff #747 #1328)
#1326 := (iff #677 #1325)
#1323 := (iff #674 #1322)
#1320 := (iff #212 #1317)
#1321 := [rewrite]: #1320
#1324 := [monotonicity #1321]: #1323
#1327 := [quant-intro #1324]: #1326
#1330 := [monotonicity #1327]: #1329
#1400 := [monotonicity #1330 #1397]: #1399
#1403 := [monotonicity #1327 #1400]: #1402
#1315 := (iff #759 #1314)
#1312 := (iff #207 #1311)
#1309 := (iff #206 #1308)
#1310 := [rewrite]: #1309
#1313 := [quant-intro #1310]: #1312
#1316 := [monotonicity #1313]: #1315
#1406 := [monotonicity #1316 #1403]: #1405
#1409 := [monotonicity #1313 #1406]: #1408
#1306 := (iff #771 #1305)
#1303 := (iff #670 #205)
#1304 := [rewrite]: #1303
#1307 := [monotonicity #1304]: #1306
#1412 := [monotonicity #1307 #1409]: #1411
#1415 := [monotonicity #1304 #1412]: #1414
#1418 := [monotonicity #1415]: #1417
#1421 := [monotonicity #1418]: #1420
#1301 := (iff #795 #1300)
#1298 := (iff #200 #1297)
#1295 := (iff #199 #1292)
#1296 := [rewrite]: #1295
#1299 := [quant-intro #1296]: #1298
#1302 := [monotonicity #1299]: #1301
#1424 := [monotonicity #1302 #1421]: #1423
#1427 := [monotonicity #1299 #1424]: #1426
#1290 := (iff #807 #1289)
#1287 := (iff #656 #1286)
#1284 := (iff #651 #1281)
#1278 := (or #1275 #645)
#1282 := (iff #1278 #1281)
#1283 := [rewrite]: #1282
#1279 := (iff #651 #1278)
#1276 := (iff #190 #1275)
#1273 := (iff #189 #1272)
#1274 := [rewrite]: #1273
#1266 := (iff #187 #1265)
#1267 := [rewrite]: #1266
#1277 := [monotonicity #1267 #1274]: #1276
#1280 := [monotonicity #1277]: #1279
#1285 := [trans #1280 #1283]: #1284
#1288 := [quant-intro #1285]: #1287
#1291 := [monotonicity #1288]: #1290
#1475 := [monotonicity #1291 #1427]: #1474
#1443 := (iff #816 #1442)
#1440 := (iff #642 #1439)
#1437 := (iff #637 #1436)
#1434 := (iff #631 #1433)
#1435 := [rewrite]: #1434
#1429 := (iff #195 #1428)
#1430 := [monotonicity #1277]: #1429
#1438 := [monotonicity #1430 #1435]: #1437
#1441 := [quant-intro #1438]: #1440
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#1213 := [quant-intro #1210]: #1212
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#1141 := [monotonicity #1134]: #1140
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#1138 := [rewrite]: #1137
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#1537 := (iff #108 #1536)
#1538 := [rewrite]: #1537
#1541 := [quant-intro #1538]: #1540
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#1546 := [rewrite]: #1545
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#1093 := [rewrite]: #1092
#1099 := [monotonicity #1093]: #1098
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#1096 := [rewrite]: #1095
#1102 := [monotonicity #1096 #1099]: #1101
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#1110 := [quant-intro #1107]: #1109
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#1086 := (iff #96 #1085)
#1083 := (iff #95 #1082)
#1084 := [rewrite]: #1083
#1087 := [monotonicity #1084]: #1086
#1090 := [monotonicity #1087]: #1089
#1113 := [monotonicity #1090 #1110]: #1112
#1116 := [quant-intro #1113]: #1115
#1552 := [monotonicity #1116]: #1551
#1570 := [monotonicity #1552 #1567]: #1569
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#1075 := [quant-intro #1072]: #1074
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#1584 := [monotonicity #1075 #1581]: #1583
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#1590 := [monotonicity #1049 #1587]: #1589
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#1029 := (iff #79 #1031)
#1030 := [rewrite]: #1029
#1034 := [quant-intro #1030]: #1033
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#1596 := [monotonicity #1034 #1593]: #1595
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#1024 := (iff #413 #78)
#1025 := [rewrite]: #1024
#1028 := [monotonicity #1025]: #1027
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#1602 := [monotonicity #1025 #1599]: #1601
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#1603 := (iff #385 #67)
#1604 := [rewrite]: #1603
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#1610 := [quant-intro #1607]: #1609
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#1622 := [monotonicity #1613 #1619]: #1621
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#623 := (iff #173 #613)
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#583 := (implies #495 #578)
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#543 := (and #540 true)
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#547 := [rewrite]: #546
#544 := (iff #163 #543)
#541 := (iff #162 #540)
#542 := [rewrite]: #541
#545 := [monotonicity #542]: #544
#549 := [trans #545 #547]: #548
#538 := (iff #160 #537)
#535 := (iff #159 #532)
#528 := (implies #522 #525)
#533 := (iff #528 #532)
#534 := [rewrite]: #533
#529 := (iff #159 #528)
#526 := (iff #158 #525)
#499 := (= #151 #498)
#500 := [rewrite]: #499
#527 := [monotonicity #500]: #526
#523 := (iff #157 #522)
#524 := [rewrite]: #523
#530 := [monotonicity #524 #527]: #529
#536 := [trans #530 #534]: #535
#539 := [quant-intro #536]: #538
#552 := [monotonicity #539 #549]: #551
#558 := [trans #552 #556]: #557
#561 := [monotonicity #539 #558]: #560
#520 := (iff #156 #519)
#517 := (iff #155 #514)
#510 := (implies #148 #507)
#515 := (iff #510 #514)
#516 := [rewrite]: #515
#511 := (iff #155 #510)
#508 := (iff #154 #507)
#505 := (iff #153 #504)
#502 := (iff #152 #501)
#503 := [monotonicity #500]: #502
#506 := [monotonicity #503]: #505
#509 := [quant-intro #506]: #508
#512 := [monotonicity #509]: #511
#518 := [trans #512 #516]: #517
#521 := [quant-intro #518]: #520
#564 := [monotonicity #521 #561]: #563
#570 := [trans #564 #568]: #569
#573 := [monotonicity #521 #570]: #572
#576 := [monotonicity #573]: #575
#582 := [trans #576 #580]: #581
#496 := (iff #142 #495)
#497 := [rewrite]: #496
#585 := [monotonicity #497 #582]: #584
#591 := [trans #585 #589]: #590
#594 := [monotonicity #591]: #593
#600 := [trans #594 #598]: #599
#493 := (iff #137 #492)
#494 := [rewrite]: #493
#603 := [monotonicity #494 #600]: #602
#609 := [trans #603 #607]: #608
#612 := [monotonicity #609]: #611
#617 := [trans #612 #615]: #616
#620 := [monotonicity #617]: #619
#624 := [trans #620 #622]: #623
#874 := [monotonicity #624 #871]: #873
#490 := (iff #132 #489)
#487 := (iff #131 #484)
#480 := (implies #125 #477)
#485 := (iff #480 #484)
#486 := [rewrite]: #485
#481 := (iff #131 #480)
#478 := (iff #130 #477)
#475 := (iff #129 #474)
#472 := (iff #128 #471)
#469 := (iff #127 #468)
#451 := (= #120 #450)
#452 := [rewrite]: #451
#470 := [monotonicity #452]: #469
#473 := [monotonicity #470]: #472
#476 := [monotonicity #473]: #475
#479 := [quant-intro #476]: #478
#482 := [monotonicity #479]: #481
#488 := [trans #482 #486]: #487
#491 := [quant-intro #488]: #490
#877 := [monotonicity #491 #874]: #876
#883 := [trans #877 #881]: #882
#466 := (iff #123 #465)
#463 := (iff #122 #460)
#456 := (implies #447 #453)
#461 := (iff #456 #460)
#462 := [rewrite]: #461
#457 := (iff #122 #456)
#454 := (iff #121 #453)
#455 := [monotonicity #452]: #454
#448 := (iff #119 #447)
#449 := [rewrite]: #448
#458 := [monotonicity #449 #455]: #457
#464 := [trans #458 #462]: #463
#467 := [quant-intro #464]: #466
#886 := [monotonicity #467 #883]: #885
#892 := [trans #886 #890]: #891
#445 := (iff #118 #444)
#442 := (iff #117 #441)
#443 := [rewrite]: #442
#446 := [quant-intro #443]: #445
#895 := [monotonicity #446 #892]: #894
#901 := [trans #895 #899]: #900
#904 := [monotonicity #901]: #903
#910 := [trans #904 #908]: #909
#438 := (iff #106 #437)
#439 := [rewrite]: #438
#913 := [monotonicity #439 #910]: #912
#919 := [trans #913 #917]: #918
#922 := [monotonicity #919]: #921
#926 := [trans #922 #924]: #925
#435 := (iff #103 #434)
#432 := (iff #102 #431)
#433 := [rewrite]: #432
#436 := [quant-intro #433]: #435
#929 := [monotonicity #436 #926]: #928
#935 := [trans #929 #933]: #934
#938 := [monotonicity #436 #935]: #937
#428 := (iff #94 #427)
#425 := (iff #93 #424)
#426 := [rewrite]: #425
#429 := [quant-intro #426]: #428
#941 := [monotonicity #429 #938]: #940
#947 := [trans #941 #945]: #946
#950 := [monotonicity #429 #947]: #949
#421 := (iff #86 #420)
#418 := (iff #85 #417)
#419 := [rewrite]: #418
#422 := [quant-intro #419]: #421
#953 := [monotonicity #422 #950]: #952
#959 := [trans #953 #957]: #958
#962 := [monotonicity #422 #959]: #961
#965 := [monotonicity #962]: #964
#971 := [trans #965 #969]: #970
#974 := [monotonicity #971]: #973
#414 := (iff #78 #413)
#415 := [rewrite]: #414
#977 := [monotonicity #415 #974]: #976
#983 := [trans #977 #981]: #982
#986 := [monotonicity #415 #983]: #985
#989 := [monotonicity #986]: #988
#995 := [trans #989 #993]: #994
#411 := (iff #73 #410)
#408 := (iff #72 #405)
#402 := (implies #70 #399)
#406 := (iff #402 #405)
#407 := [rewrite]: #406
#403 := (iff #72 #402)
#400 := (iff #71 #399)
#401 := [rewrite]: #400
#404 := [monotonicity #401]: #403
#409 := [trans #404 #407]: #408
#412 := [quant-intro #409]: #411
#998 := [monotonicity #412 #995]: #997
#1004 := [trans #998 #1002]: #1003
#397 := (iff #69 #396)
#394 := (iff #68 #391)
#388 := (implies #65 #385)
#392 := (iff #388 #391)
#393 := [rewrite]: #392
#389 := (iff #68 #388)
#386 := (iff #67 #385)
#387 := [rewrite]: #386
#390 := [monotonicity #387]: #389
#395 := [trans #390 #393]: #394
#398 := [quant-intro #395]: #397
#1007 := [monotonicity #398 #1004]: #1006
#1013 := [trans #1007 #1011]: #1012
#1016 := [monotonicity #1013]: #1015
#1020 := [trans #1016 #1018]: #1019
#1023 := [monotonicity #1020]: #1022
#1632 := [trans #1023 #1630]: #1631
#384 := [asserted]: #271
#1633 := [mp #384 #1632]: #1628
#1634 := [not-or-elim #1633]: #76
#1697 := [mp~ #1634 #1659]: #76
#4041 := [mp #1697 #4040]: #4036
#5203 := (not #4036)
#5204 := (or #5203 #2873)
#5205 := [quant-inst]: #5204
#8153 := [unit-resolution #5205 #4041 #8152]: false
#8156 := [lemma #8153]: #2873
#3630 := (or #2888 #1758)
#3965 := [def-axiom]: #3630
#10020 := [unit-resolution #3965 #8156]: #2888
#2893 := (not #2888)
#4382 := (or #2893 #4379)
#4385 := (not #4382)
#4057 := (pattern #74 #81)
#2319 := (not #81)
#2865 := (or #74 #2319 #1040)
#4058 := (forall (vars (?x29 T2) (?x30 T2)) (:pat #4057) #2865)
#4063 := (not #4058)
#4388 := (or #4063 #4385)
#4391 := (not #4388)
decl ?x30!1 :: T2
#1719 := ?x30!1
#1723 := (uf_12 ?x30!1)
#2334 := (* -1::int #1723)
decl ?x29!2 :: T2
#1720 := ?x29!2
#1721 := (uf_12 ?x29!2)
#2335 := (+ #1721 #2334)
#2336 := (<= #2335 0::int)
#1727 := (up_13 ?x30!1)
#1726 := (up_13 ?x29!2)
#1766 := (not #1726)
#1968 := (or #1766 #1727 #2336)
#8727 := [hypothesis]: #1726
#5149 := (or #5203 #1766)
#5178 := [quant-inst]: #5149
#8728 := [unit-resolution #5178 #4041 #8727]: false
#8729 := [lemma #8728]: #1766
#3559 := (or #1968 #1726)
#3644 := [def-axiom]: #3559
#10021 := [unit-resolution #3644 #8729]: #1968
#2108 := (not #1968)
#4394 := (or #2108 #4391)
#4397 := (not #4394)
#4049 := (forall (vars (?x27 T2)) (:pat #4042) #1031)
#4054 := (not #4049)
#4400 := (or #4054 #4397)
#4403 := (not #4400)
decl ?x27!0 :: T2
#1704 := ?x27!0
#1705 := (uf_12 ?x27!0)
#1706 := (>= #1705 0::int)
#1707 := (not #1706)
#4406 := (or #1707 #4403)
#4409 := (not #4406)
#4412 := (or #1026 #4409)
#4415 := (not #4412)
#4422 := (forall (vars (?x24 T2)) (:pat #4042) #1605)
#4425 := (iff #1608 #4422)
#4423 := (iff #1605 #1605)
#4424 := [refl]: #4423
#4426 := [quant-intro #4424]: #4425
#1933 := (~ #1608 #1608)
#2022 := (~ #1605 #1605)
#2023 := [refl]: #2022
#1934 := [nnf-pos #2023]: #1933
#1638 := [not-or-elim #1633]: #1608
#1765 := [mp~ #1638 #1934]: #1608
#4427 := [mp #1765 #4426]: #4422
#4964 := [hypothesis]: #1026
#3570 := (not #4422)
#4986 := (or #3570 #78)
#4909 := (= uf_11 uf_11)
#4907 := (not #4909)
#4899 := (or #4907 #78)
#4987 := (or #3570 #4899)
#4989 := (iff #4987 #4986)
#4980 := (iff #4986 #4986)
#5014 := [rewrite]: #4980
#4981 := (iff #4899 #78)
#4970 := (or false #78)
#4974 := (iff #4970 #78)
#4975 := [rewrite]: #4974
#4973 := (iff #4899 #4970)
#4923 := (iff #4907 false)
#8612 := (not true)
#8647 := (iff #8612 false)
#8648 := [rewrite]: #8647
#4921 := (iff #4907 #8612)
#4919 := (iff #4909 true)
#4920 := [rewrite]: #4919
#4922 := [monotonicity #4920]: #4921
#4972 := [trans #4922 #8648]: #4923
#4963 := [monotonicity #4972]: #4973
#4982 := [trans #4963 #4975]: #4981
#4990 := [monotonicity #4982]: #4989
#5015 := [trans #4990 #5014]: #4989
#4988 := [quant-inst]: #4987
#5016 := [mp #4988 #5015]: #4986
#4971 := [unit-resolution #5016 #4964 #4427]: false
#5020 := [lemma #4971]: #78
#4418 := (or #1026 #4415)
#3323 := (forall (vars (?x76 T2)) #3312)
#3330 := (not #3323)
#3308 := (forall (vars (?x71 T2) (?x72 T2)) #3303)
#3329 := (not #3308)
#3331 := (or #2159 #2721 #3329 #3330)
#3332 := (not #3331)
#3337 := (or #3286 #3332)
#3344 := (not #3337)
#3263 := (forall (vars (?x67 T2) (?x68 T2)) #3258)
#3343 := (not #3263)
#3345 := (or #3343 #3344)
#3346 := (not #3345)
#3351 := (or #3240 #3346)
#3357 := (not #3351)
#3358 := (or #1314 #3357)
#3359 := (not #3358)
#3364 := (or #2079 #3359)
#3370 := (not #3364)
#3371 := (or #1305 #3370)
#3372 := (not #3371)
#3377 := (or #1305 #3372)
#3383 := (not #3377)
#3384 := (or #783 #3383)
#3385 := (not #3384)
#3390 := (or #2664 #3385)
#3396 := (not #3390)
#3397 := (or #1300 #3396)
#3398 := (not #3397)
#3403 := (or #2655 #3398)
#3411 := (not #3403)
#3217 := (forall (vars (?x59 T2)) #3212)
#3410 := (not #3217)
#3199 := (forall (vars (?x60 T2)) #3196)
#3409 := (not #3199)
#3412 := (or #175 #825 #1455 #1459 #2015 #2017 #3409 #3410 #3411)
#3413 := (not #3412)
#3129 := (forall (vars (?x53 T2) (?x54 T2)) #3124)
#3135 := (not #3129)
#3136 := (or #162 #3135)
#3137 := (not #3136)
#3164 := (or #3137 #3161)
#3171 := (not #3164)
#3107 := (forall (vars (?x49 T2)) #3102)
#3170 := (not #3107)
#3172 := (or #3170 #3171)
#3173 := (not #3172)
#3070 := (forall (vars (?x50 T2)) #3059)
#3076 := (not #3070)
#3077 := (or #1894 #2504 #3076)
#3078 := (not #3077)
#3178 := (or #3078 #3173)
#3185 := (not #3178)
#3055 := (forall (vars (?x48 T2)) #3044)
#3184 := (not #3055)
#3186 := (or #595 #577 #604 #586 #3184 #3185)
#3187 := (not #3186)
#3418 := (or #3187 #3413)
#3428 := (not #3418)
#3041 := (forall (vars (?x46 T2)) #3036)
#3427 := (not #3041)
#3013 := (forall (vars (?x37 T2)) #3008)
#3426 := (not #3013)
#2985 := (forall (vars (?x42 T2) (?x43 T2)) #2980)
#3425 := (not #2985)
#2962 := (forall (vars (?x44 T2) (?x45 T2)) #2957)
#3424 := (not #2962)
#3429 := (or #1547 #1542 #3424 #3425 #3426 #3427 #3428)
#3430 := (not #3429)
#2930 := (forall (vars (?x38 T2)) #2919)
#2936 := (not #2930)
#2937 := (or #1788 #2366 #2936)
#2938 := (not #2937)
#3435 := (or #2938 #3430)
#3442 := (not #3435)
#2915 := (forall (vars (?x33 T2) (?x34 T2)) #2910)
#3441 := (not #2915)
#3443 := (or #3441 #3442)
#3444 := (not #3443)
#3449 := (or #2893 #3444)
#3456 := (not #3449)
#2870 := (forall (vars (?x29 T2) (?x30 T2)) #2865)
#3455 := (not #2870)
#3457 := (or #3455 #3456)
#3458 := (not #3457)
#3463 := (or #2108 #3458)
#3469 := (not #3463)
#3470 := (or #1035 #3469)
#3471 := (not #3470)
#3476 := (or #1707 #3471)
#3482 := (not #3476)
#3483 := (or #1026 #3482)
#3484 := (not #3483)
#3489 := (or #1026 #3484)
#4419 := (iff #3489 #4418)
#4416 := (iff #3484 #4415)
#4413 := (iff #3483 #4412)
#4410 := (iff #3482 #4409)
#4407 := (iff #3476 #4406)
#4404 := (iff #3471 #4403)
#4401 := (iff #3470 #4400)
#4398 := (iff #3469 #4397)
#4395 := (iff #3463 #4394)
#4392 := (iff #3458 #4391)
#4389 := (iff #3457 #4388)
#4386 := (iff #3456 #4385)
#4383 := (iff #3449 #4382)
#4380 := (iff #3444 #4379)
#4377 := (iff #3443 #4376)
#4374 := (iff #3442 #4373)
#4371 := (iff #3435 #4370)
#4368 := (iff #3430 #4367)
#4365 := (iff #3429 #4364)
#4362 := (iff #3428 #4361)
#4359 := (iff #3418 #4358)
#4356 := (iff #3413 #4355)
#4353 := (iff #3412 #4352)
#4350 := (iff #3411 #4349)
#4347 := (iff #3403 #4346)
#4344 := (iff #3398 #4343)
#4341 := (iff #3397 #4340)
#4338 := (iff #3396 #4337)
#4335 := (iff #3390 #4334)
#4332 := (iff #3385 #4331)
#4329 := (iff #3384 #4328)
#4326 := (iff #3383 #4325)
#4323 := (iff #3377 #4322)
#4320 := (iff #3372 #4319)
#4317 := (iff #3371 #4316)
#4314 := (iff #3370 #4313)
#4311 := (iff #3364 #4310)
#4308 := (iff #3359 #4307)
#4305 := (iff #3358 #4304)
#4302 := (iff #3357 #4301)
#4299 := (iff #3351 #4298)
#4296 := (iff #3346 #4295)
#4293 := (iff #3345 #4292)
#4290 := (iff #3344 #4289)
#4287 := (iff #3337 #4286)
#4284 := (iff #3332 #4283)
#4281 := (iff #3331 #4280)
#4278 := (iff #3330 #4277)
#4275 := (iff #3323 #4272)
#4273 := (iff #3312 #3312)
#4274 := [refl]: #4273
#4276 := [quant-intro #4274]: #4275
#4279 := [monotonicity #4276]: #4278
#4269 := (iff #3329 #4268)
#4266 := (iff #3308 #4263)
#4264 := (iff #3303 #3303)
#4265 := [refl]: #4264
#4267 := [quant-intro #4265]: #4266
#4270 := [monotonicity #4267]: #4269
#4282 := [monotonicity #4270 #4279]: #4281
#4285 := [monotonicity #4282]: #4284
#4288 := [monotonicity #4285]: #4287
#4291 := [monotonicity #4288]: #4290
#4261 := (iff #3343 #4260)
#4258 := (iff #3263 #4255)
#4256 := (iff #3258 #3258)
#4257 := [refl]: #4256
#4259 := [quant-intro #4257]: #4258
#4262 := [monotonicity #4259]: #4261
#4294 := [monotonicity #4262 #4291]: #4293
#4297 := [monotonicity #4294]: #4296
#4300 := [monotonicity #4297]: #4299
#4303 := [monotonicity #4300]: #4302
#4252 := (iff #1314 #4251)
#4249 := (iff #1311 #4246)
#4247 := (iff #1308 #1308)
#4248 := [refl]: #4247
#4250 := [quant-intro #4248]: #4249
#4253 := [monotonicity #4250]: #4252
#4306 := [monotonicity #4253 #4303]: #4305
#4309 := [monotonicity #4306]: #4308
#4312 := [monotonicity #4309]: #4311
#4315 := [monotonicity #4312]: #4314
#4318 := [monotonicity #4315]: #4317
#4321 := [monotonicity #4318]: #4320
#4324 := [monotonicity #4321]: #4323
#4327 := [monotonicity #4324]: #4326
#4244 := (iff #783 #4243)
#4241 := (iff #667 #4238)
#4239 := (iff #662 #662)
#4240 := [refl]: #4239
#4242 := [quant-intro #4240]: #4241
#4245 := [monotonicity #4242]: #4244
#4330 := [monotonicity #4245 #4327]: #4329
#4333 := [monotonicity #4330]: #4332
#4336 := [monotonicity #4333]: #4335
#4339 := [monotonicity #4336]: #4338
#4235 := (iff #1300 #4234)
#4232 := (iff #1297 #4229)
#4230 := (iff #1292 #1292)
#4231 := [refl]: #4230
#4233 := [quant-intro #4231]: #4232
#4236 := [monotonicity #4233]: #4235
#4342 := [monotonicity #4236 #4339]: #4341
#4345 := [monotonicity #4342]: #4344
#4348 := [monotonicity #4345]: #4347
#4351 := [monotonicity #4348]: #4350
#4227 := (iff #3410 #4226)
#4224 := (iff #3217 #4221)
#4222 := (iff #3212 #3212)
#4223 := [refl]: #4222
#4225 := [quant-intro #4223]: #4224
#4228 := [monotonicity #4225]: #4227
#4219 := (iff #3409 #4218)
#4216 := (iff #3199 #4213)
#4214 := (iff #3196 #3196)
#4215 := [refl]: #4214
#4217 := [quant-intro #4215]: #4216
#4220 := [monotonicity #4217]: #4219
#4209 := (iff #1455 #4208)
#4206 := (iff #1452 #4203)
#4204 := (iff #1449 #1449)
#4205 := [refl]: #4204
#4207 := [quant-intro #4205]: #4206
#4210 := [monotonicity #4207]: #4209
#4354 := [monotonicity #4210 #4220 #4228 #4351]: #4353
#4357 := [monotonicity #4354]: #4356
#4201 := (iff #3187 #4200)
#4198 := (iff #3186 #4197)
#4195 := (iff #3185 #4194)
#4192 := (iff #3178 #4191)
#4189 := (iff #3173 #4188)
#4186 := (iff #3172 #4185)
#4183 := (iff #3171 #4182)
#4180 := (iff #3164 #4179)
#4177 := (iff #3137 #4176)
#4174 := (iff #3136 #4173)
#4171 := (iff #3135 #4170)
#4168 := (iff #3129 #4165)
#4166 := (iff #3124 #3124)
#4167 := [refl]: #4166
#4169 := [quant-intro #4167]: #4168
#4172 := [monotonicity #4169]: #4171
#4175 := [monotonicity #4172]: #4174
#4178 := [monotonicity #4175]: #4177
#4181 := [monotonicity #4178]: #4180
#4184 := [monotonicity #4181]: #4183
#4163 := (iff #3170 #4162)
#4160 := (iff #3107 #4157)
#4158 := (iff #3102 #3102)
#4159 := [refl]: #4158
#4161 := [quant-intro #4159]: #4160
#4164 := [monotonicity #4161]: #4163
#4187 := [monotonicity #4164 #4184]: #4186
#4190 := [monotonicity #4187]: #4189
#4155 := (iff #3078 #4154)
#4152 := (iff #3077 #4151)
#4149 := (iff #3076 #4148)
#4146 := (iff #3070 #4143)
#4144 := (iff #3059 #3059)
#4145 := [refl]: #4144
#4147 := [quant-intro #4145]: #4146
#4150 := [monotonicity #4147]: #4149
#4153 := [monotonicity #4150]: #4152
#4156 := [monotonicity #4153]: #4155
#4193 := [monotonicity #4156 #4190]: #4192
#4196 := [monotonicity #4193]: #4195
#4139 := (iff #3184 #4138)
#4136 := (iff #3055 #4133)
#4134 := (iff #3044 #3044)
#4135 := [refl]: #4134
#4137 := [quant-intro #4135]: #4136
#4140 := [monotonicity #4137]: #4139
#4199 := [monotonicity #4140 #4196]: #4198
#4202 := [monotonicity #4199]: #4201
#4360 := [monotonicity #4202 #4357]: #4359
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#4125 := (iff #3036 #3036)
#4126 := [refl]: #4125
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#4118 := [refl]: #4117
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#4111 := (iff #2985 #4108)
#4109 := (iff #2980 #2980)
#4110 := [refl]: #4109
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#4105 := (iff #3424 #4104)
#4102 := (iff #2962 #4099)
#4100 := (iff #2957 #2957)
#4101 := [refl]: #4100
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#4092 := (iff #1536 #1536)
#4093 := [refl]: #4092
#4095 := [quant-intro #4093]: #4094
#4098 := [monotonicity #4095]: #4097
#4366 := [monotonicity #4098 #4106 #4115 #4123 #4131 #4363]: #4365
#4369 := [monotonicity #4366]: #4368
#4088 := (iff #2938 #4087)
#4085 := (iff #2937 #4084)
#4082 := (iff #2936 #4081)
#4079 := (iff #2930 #4076)
#4077 := (iff #2919 #2919)
#4078 := [refl]: #4077
#4080 := [quant-intro #4078]: #4079
#4083 := [monotonicity #4080]: #4082
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#4375 := [monotonicity #4372]: #4374
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#4069 := [refl]: #4068
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#4074 := [monotonicity #4071]: #4073
#4378 := [monotonicity #4074 #4375]: #4377
#4381 := [monotonicity #4378]: #4380
#4384 := [monotonicity #4381]: #4383
#4387 := [monotonicity #4384]: #4386
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#4059 := (iff #2865 #2865)
#4060 := [refl]: #4059
#4062 := [quant-intro #4060]: #4061
#4065 := [monotonicity #4062]: #4064
#4390 := [monotonicity #4065 #4387]: #4389
#4393 := [monotonicity #4390]: #4392
#4396 := [monotonicity #4393]: #4395
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#4051 := [refl]: #4050
#4053 := [quant-intro #4051]: #4052
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#4402 := [monotonicity #4056 #4399]: #4401
#4405 := [monotonicity #4402]: #4404
#4408 := [monotonicity #4405]: #4407
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#3191 := [trans #3183 #3189]: #3190
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#3031 := (iff #2487 #3030)
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#3018 := (iff #1123 #3017)
#3019 := [rewrite]: #3018
#3022 := [monotonicity #3019]: #3021
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#3043 := [quant-intro #3040]: #3042
#3014 := (iff #2453 #3013)
#3011 := (iff #2450 #3008)
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#3005 := (or #2988 #3002)
#3009 := (iff #3005 #3008)
#3010 := [rewrite]: #3009
#3006 := (iff #2450 #3005)
#3003 := (iff #2447 #3002)
#3004 := [rewrite]: #3003
#2997 := (iff #1088 #2988)
#2989 := (not #2988)
#2992 := (not #2989)
#2995 := (iff #2992 #2988)
#2996 := [rewrite]: #2995
#2993 := (iff #1088 #2992)
#2990 := (iff #1085 #2989)
#2991 := [rewrite]: #2990
#2994 := [monotonicity #2991]: #2993
#2998 := [trans #2994 #2996]: #2997
#3007 := [monotonicity #2998 #3004]: #3006
#3012 := [trans #3007 #3010]: #3011
#3015 := [quant-intro #3012]: #3014
#2986 := (iff #1530 #2985)
#2983 := (iff #1527 #2980)
#2966 := (or #111 #2965)
#2977 := (or #2966 #1135)
#2981 := (iff #2977 #2980)
#2982 := [rewrite]: #2981
#2978 := (iff #1527 #2977)
#2975 := (iff #440 #2966)
#2967 := (not #2966)
#2970 := (not #2967)
#2973 := (iff #2970 #2966)
#2974 := [rewrite]: #2973
#2971 := (iff #440 #2970)
#2968 := (iff #114 #2967)
#2969 := [rewrite]: #2968
#2972 := [monotonicity #2969]: #2971
#2976 := [trans #2972 #2974]: #2975
#2979 := [monotonicity #2976]: #2978
#2984 := [trans #2979 #2982]: #2983
#2987 := [quant-intro #2984]: #2986
#2963 := (iff #1519 #2962)
#2960 := (iff #1516 #2957)
#2943 := (or #112 #1055)
#2954 := (or #2943 #1513)
#2958 := (iff #2954 #2957)
#2959 := [rewrite]: #2958
#2955 := (iff #1516 #2954)
#2952 := (iff #1510 #2943)
#2944 := (not #2943)
#2947 := (not #2944)
#2950 := (iff #2947 #2943)
#2951 := [rewrite]: #2950
#2948 := (iff #1510 #2947)
#2945 := (iff #1505 #2944)
#2946 := [rewrite]: #2945
#2949 := [monotonicity #2946]: #2948
#2953 := [trans #2949 #2951]: #2952
#2956 := [monotonicity #2953]: #2955
#2961 := [trans #2956 #2959]: #2960
#2964 := [quant-intro #2961]: #2963
#3423 := [monotonicity #2964 #2987 #3015 #3043 #3420]: #3422
#3434 := [trans #3423 #3432]: #3433
#2941 := (iff #2409 #2938)
#2933 := (and #1789 #2369 #2930)
#2939 := (iff #2933 #2938)
#2940 := [rewrite]: #2939
#2934 := (iff #2409 #2933)
#2931 := (iff #2403 #2930)
#2928 := (iff #2400 #2919)
#2920 := (not #2919)
#2923 := (not #2920)
#2926 := (iff #2923 #2919)
#2927 := [rewrite]: #2926
#2924 := (iff #2400 #2923)
#2921 := (iff #2397 #2920)
#2922 := [rewrite]: #2921
#2925 := [monotonicity #2922]: #2924
#2929 := [trans #2925 #2927]: #2928
#2932 := [quant-intro #2929]: #2931
#2935 := [monotonicity #2932]: #2934
#2942 := [trans #2935 #2940]: #2941
#3437 := [monotonicity #2942 #3434]: #3436
#2916 := (iff #1073 #2915)
#2913 := (iff #1070 #2910)
#2896 := (or #75 #1055)
#2907 := (or #2896 #1066)
#2911 := (iff #2907 #2910)
#2912 := [rewrite]: #2911
#2908 := (iff #1070 #2907)
#2905 := (iff #1062 #2896)
#2897 := (not #2896)
#2900 := (not #2897)
#2903 := (iff #2900 #2896)
#2904 := [rewrite]: #2903
#2901 := (iff #1062 #2900)
#2898 := (iff #1059 #2897)
#2899 := [rewrite]: #2898
#2902 := [monotonicity #2899]: #2901
#2906 := [trans #2902 #2904]: #2905
#2909 := [monotonicity #2906]: #2908
#2914 := [trans #2909 #2912]: #2913
#2917 := [quant-intro #2914]: #2916
#3440 := [monotonicity #2917 #3437]: #3439
#3448 := [trans #3440 #3446]: #3447
#2894 := (iff #2363 #2893)
#2891 := (iff #2360 #2888)
#2874 := (or #1756 #2873)
#2885 := (or #2874 #2357)
#2889 := (iff #2885 #2888)
#2890 := [rewrite]: #2889
#2886 := (iff #2360 #2885)
#2883 := (iff #2350 #2874)
#2875 := (not #2874)
#2878 := (not #2875)
#2881 := (iff #2878 #2874)
#2882 := [rewrite]: #2881
#2879 := (iff #2350 #2878)
#2876 := (iff #2347 #2875)
#2877 := [rewrite]: #2876
#2880 := [monotonicity #2877]: #2879
#2884 := [trans #2880 #2882]: #2883
#2887 := [monotonicity #2884]: #2886
#2892 := [trans #2887 #2890]: #2891
#2895 := [monotonicity #2892]: #2894
#3451 := [monotonicity #2895 #3448]: #3450
#2871 := (iff #1047 #2870)
#2868 := (iff #1044 #2865)
#2851 := (or #74 #2319)
#2862 := (or #2851 #1040)
#2866 := (iff #2862 #2865)
#2867 := [rewrite]: #2866
#2863 := (iff #1044 #2862)
#2860 := (iff #416 #2851)
#2852 := (not #2851)
#2855 := (not #2852)
#2858 := (iff #2855 #2851)
#2859 := [rewrite]: #2858
#2856 := (iff #416 #2855)
#2853 := (iff #82 #2852)
#2854 := [rewrite]: #2853
#2857 := [monotonicity #2854]: #2856
#2861 := [trans #2857 #2859]: #2860
#2864 := [monotonicity #2861]: #2863
#2869 := [trans #2864 #2867]: #2868
#2872 := [quant-intro #2869]: #2871
#3454 := [monotonicity #2872 #3451]: #3453
#3462 := [trans #3454 #3460]: #3461
#1832 := (iff #2344 #2108)
#1711 := (iff #2341 #1968)
#2062 := (or #1766 #1727)
#1736 := (or #2062 #2336)
#1969 := (iff #1736 #1968)
#1710 := [rewrite]: #1969
#2043 := (iff #2341 #1736)
#2083 := (iff #2325 #2062)
#1666 := (not #2062)
#2137 := (not #1666)
#1859 := (iff #2137 #2062)
#2082 := [rewrite]: #1859
#2138 := (iff #2325 #2137)
#1667 := (iff #2322 #1666)
#2063 := [rewrite]: #1667
#1858 := [monotonicity #2063]: #2138
#1735 := [trans #1858 #2082]: #2083
#2044 := [monotonicity #1735]: #2043
#2107 := [trans #2044 #1710]: #1711
#1833 := [monotonicity #2107]: #1832
#3465 := [monotonicity #1833 #3462]: #3464
#3468 := [monotonicity #3465]: #3467
#3475 := [trans #3468 #3473]: #3474
#3478 := [monotonicity #3475]: #3477
#3481 := [monotonicity #3478]: #3480
#3488 := [trans #3481 #3486]: #3487
#3491 := [monotonicity #3488]: #3490
#2152 := (+ #2151 #2149)
#2153 := (= #2152 0::int)
#2156 := (and #201 #2155 #2153)
#2173 := (not #2156)
#2176 := (forall (vars (?x76 T2)) #2173)
#2161 := (= ?x75!20 uf_11)
#2162 := (not #2161)
#2163 := (and #2162 #2160)
#2164 := (not #2163)
#2170 := (not #2164)
#2180 := (and #2170 #2176)
#2185 := (and #1349 #2180)
#2119 := (* -1::int #2118)
#2121 := (+ #2120 #2119)
#2124 := (+ #2123 #2121)
#2125 := (>= #2124 0::int)
#2131 := (and #2130 #2129)
#2132 := (not #2131)
#2133 := (or #2132 #2125)
#2134 := (not #2133)
#2189 := (or #2134 #2185)
#2193 := (and #1325 #2189)
#2094 := (* -1::int #2093)
#2096 := (+ #2095 #2094)
#2097 := (>= #2096 0::int)
#2101 := (and #2100 #2098)
#2102 := (not #2101)
#2103 := (or #2102 #2097)
#2104 := (not #2103)
#2197 := (or #2104 #2193)
#2201 := (and #1311 #2197)
#2205 := (or #2079 #2201)
#2073 := (not #1305)
#2209 := (and #2073 #2205)
#2213 := (or #1305 #2209)
#2217 := (and #667 #2213)
#2055 := (= #2054 #2053)
#2058 := (or #2057 #2055)
#2059 := (not #2058)
#2221 := (or #2059 #2217)
#2225 := (and #1297 #2221)
#2036 := (* -1::int #2035)
#2038 := (+ #2037 #2036)
#2039 := (>= #2038 0::int)
#2040 := (not #2039)
#2229 := (or #2040 #2225)
#2019 := (and #2018 #2016)
#2008 := (not #825)
#2249 := (and #176 #2008 #2019 #1286 #2229 #1439 #1452 #1460)
#1947 := (* -1::int #1946)
#1949 := (+ #1948 #1947)
#1952 := (+ #1951 #1949)
#1953 := (>= #1952 0::int)
#1962 := (and #1961 #1957)
#1963 := (not #1962)
#1964 := (or #1963 #1953)
#1965 := (not #1964)
#1984 := (or #1965 #1980)
#1923 := (+ #1922 #1162)
#1926 := (+ #1925 #1923)
#1927 := (= #1926 0::int)
#1928 := (>= #1923 0::int)
#1929 := (not #1928)
#1930 := (and #1929 #1927)
#1935 := (or #1171 #1930)
#1938 := (forall (vars (?x49 T2)) #1935)
#1988 := (and #1938 #1984)
#1887 := (+ #1886 #1884)
#1888 := (= #1887 0::int)
#1891 := (and #1890 #1888)
#1907 := (not #1891)
#1910 := (forall (vars (?x50 T2)) #1907)
#1896 := (= ?x49!8 uf_11)
#1897 := (not #1896)
#1898 := (and #1897 #1895)
#1899 := (not #1898)
#1904 := (not #1899)
#1914 := (and #1904 #1910)
#1992 := (or #1914 #1988)
#1878 := (not #586)
#1875 := (not #604)
#1872 := (not #577)
#1869 := (not #595)
#2002 := (and #1869 #1872 #1875 #1878 #1992 #1999)
#2253 := (or #2002 #2249)
#1847 := (+ #1846 #1117)
#1848 := (>= #1847 0::int)
#1849 := (not #1848)
#1852 := (+ #1851 #1847)
#1853 := (= #1852 0::int)
#1855 := (and #1854 #1853 #1849)
#1860 := (or #1126 #1855)
#1863 := (forall (vars (?x46 T2)) #1860)
#1821 := (+ #1079 #1820)
#1823 := (+ #1822 #1821)
#1824 := (= #1823 0::int)
#1825 := (+ #1822 #1079)
#1826 := (>= #1825 0::int)
#1827 := (not #1826)
#1829 := (and #1828 #1827 #1824)
#1834 := (or #1088 #1829)
#1837 := (forall (vars (?x37 T2)) #1834)
#1813 := (not #1547)
#2278 := (and #1813 #1837 #1863 #2253 #1519 #1530 #1539)
#1779 := (+ #1778 #1776)
#1780 := (+ #66 #1779)
#1781 := (= #1780 0::int)
#1785 := (and #74 #1784 #1781)
#1801 := (not #1785)
#1804 := (forall (vars (?x38 T2)) #1801)
#1790 := (= ?x37!5 uf_11)
#1791 := (not #1790)
#1792 := (and #1791 #1789)
#1793 := (not #1792)
#1798 := (not #1793)
#1808 := (and #1798 #1804)
#2282 := (or #1808 #2278)
#2286 := (and #1073 #2282)
#1750 := (+ #1749 #1747)
#1752 := (+ #1751 #1750)
#1753 := (>= #1752 0::int)
#1759 := (and #1758 #1757)
#1760 := (not #1759)
#1761 := (or #1760 #1753)
#1762 := (not #1761)
#2290 := (or #1762 #2286)
#2294 := (and #1047 #2290)
#1722 := (* -1::int #1721)
#1724 := (+ #1723 #1722)
#1725 := (>= #1724 0::int)
#1729 := (and #1728 #1726)
#1730 := (not #1729)
#1731 := (or #1730 #1725)
#1732 := (not #1731)
#2298 := (or #1732 #2294)
#2302 := (and #1032 #2298)
#2306 := (or #1707 #2302)
#1662 := (not #1026)
#2310 := (and #1662 #2306)
#2314 := (or #1026 #2310)
#2849 := (iff #2314 #2848)
#2846 := (iff #2310 #2845)
#2843 := (iff #2306 #2842)
#2840 := (iff #2302 #2839)
#2837 := (iff #2298 #2836)
#2834 := (iff #2294 #2833)
#2831 := (iff #2290 #2830)
#2828 := (iff #2286 #2827)
#2825 := (iff #2282 #2824)
#2822 := (iff #2278 #2819)
#2816 := (and #106 #2453 #2493 #2813 #1519 #1530 #1539)
#2820 := (iff #2816 #2819)
#2821 := [rewrite]: #2820
#2817 := (iff #2278 #2816)
#2814 := (iff #2253 #2813)
#2811 := (iff #2249 #2808)
#2805 := (and #176 #184 #2019 #1286 #2802 #1439 #1452 #1460)
#2809 := (iff #2805 #2808)
#2810 := [rewrite]: #2809
#2806 := (iff #2249 #2805)
#2803 := (iff #2229 #2802)
#2800 := (iff #2225 #2799)
#2797 := (iff #2221 #2796)
#2794 := (iff #2217 #2793)
#2791 := (iff #2213 #2790)
#2788 := (iff #2209 #2787)
#2785 := (iff #2205 #2784)
#2782 := (iff #2201 #2781)
#2779 := (iff #2197 #2778)
#2776 := (iff #2193 #2775)
#2773 := (iff #2189 #2772)
#2770 := (iff #2185 #2767)
#2730 := (and #2160 #2724)
#2761 := (and #2730 #2758)
#2764 := (and #1349 #2761)
#2768 := (iff #2764 #2767)
#2769 := [rewrite]: #2768
#2765 := (iff #2185 #2764)
#2762 := (iff #2180 #2761)
#2759 := (iff #2176 #2758)
#2756 := (iff #2173 #2755)
#2753 := (iff #2156 #2752)
#2750 := (iff #2153 #2749)
#2747 := (= #2152 #2746)
#2748 := [rewrite]: #2747
#2751 := [monotonicity #2748]: #2750
#2754 := [monotonicity #2751]: #2753
#2757 := [monotonicity #2754]: #2756
#2760 := [quant-intro #2757]: #2759
#2743 := (iff #2170 #2730)
#2735 := (not #2730)
#2738 := (not #2735)
#2741 := (iff #2738 #2730)
#2742 := [rewrite]: #2741
#2739 := (iff #2170 #2738)
#2736 := (iff #2164 #2735)
#2733 := (iff #2163 #2730)
#2727 := (and #2724 #2160)
#2731 := (iff #2727 #2730)
#2732 := [rewrite]: #2731
#2728 := (iff #2163 #2727)
#2725 := (iff #2162 #2724)
#2722 := (iff #2161 #2721)
#2723 := [rewrite]: #2722
#2726 := [monotonicity #2723]: #2725
#2729 := [monotonicity #2726]: #2728
#2734 := [trans #2729 #2732]: #2733
#2737 := [monotonicity #2734]: #2736
#2740 := [monotonicity #2737]: #2739
#2744 := [trans #2740 #2742]: #2743
#2763 := [monotonicity #2744 #2760]: #2762
#2766 := [monotonicity #2763]: #2765
#2771 := [trans #2766 #2769]: #2770
#2719 := (iff #2134 #2718)
#2716 := (iff #2133 #2715)
#2713 := (iff #2125 #2710)
#2700 := (+ #2120 #2123)
#2701 := (+ #2119 #2700)
#2704 := (>= #2701 0::int)
#2711 := (iff #2704 #2710)
#2712 := [rewrite]: #2711
#2705 := (iff #2125 #2704)
#2702 := (= #2124 #2701)
#2703 := [rewrite]: #2702
#2706 := [monotonicity #2703]: #2705
#2714 := [trans #2706 #2712]: #2713
#2698 := (iff #2132 #2697)
#2695 := (iff #2131 #2694)
#2696 := [rewrite]: #2695
#2699 := [monotonicity #2696]: #2698
#2717 := [monotonicity #2699 #2714]: #2716
#2720 := [monotonicity #2717]: #2719
#2774 := [monotonicity #2720 #2771]: #2773
#2777 := [monotonicity #2774]: #2776
#2692 := (iff #2104 #2691)
#2689 := (iff #2103 #2688)
#2686 := (iff #2097 #2683)
#2675 := (+ #2094 #2095)
#2678 := (>= #2675 0::int)
#2684 := (iff #2678 #2683)
#2685 := [rewrite]: #2684
#2679 := (iff #2097 #2678)
#2676 := (= #2096 #2675)
#2677 := [rewrite]: #2676
#2680 := [monotonicity #2677]: #2679
#2687 := [trans #2680 #2685]: #2686
#2673 := (iff #2102 #2672)
#2670 := (iff #2101 #2669)
#2671 := [rewrite]: #2670
#2674 := [monotonicity #2671]: #2673
#2690 := [monotonicity #2674 #2687]: #2689
#2693 := [monotonicity #2690]: #2692
#2780 := [monotonicity #2693 #2777]: #2779
#2783 := [monotonicity #2780]: #2782
#2786 := [monotonicity #2783]: #2785
#2667 := (iff #2073 #205)
#2668 := [rewrite]: #2667
#2789 := [monotonicity #2668 #2786]: #2788
#2792 := [monotonicity #2789]: #2791
#2795 := [monotonicity #2792]: #2794
#2665 := (iff #2059 #2664)
#2662 := (iff #2058 #2661)
#2659 := (iff #2055 #2658)
#2660 := [rewrite]: #2659
#2663 := [monotonicity #2660]: #2662
#2666 := [monotonicity #2663]: #2665
#2798 := [monotonicity #2666 #2795]: #2797
#2801 := [monotonicity #2798]: #2800
#2656 := (iff #2040 #2655)
#2653 := (iff #2039 #2650)
#2642 := (+ #2036 #2037)
#2645 := (>= #2642 0::int)
#2651 := (iff #2645 #2650)
#2652 := [rewrite]: #2651
#2646 := (iff #2039 #2645)
#2643 := (= #2038 #2642)
#2644 := [rewrite]: #2643
#2647 := [monotonicity #2644]: #2646
#2654 := [trans #2647 #2652]: #2653
#2657 := [monotonicity #2654]: #2656
#2804 := [monotonicity #2657 #2801]: #2803
#2640 := (iff #2008 #184)
#2641 := [rewrite]: #2640
#2807 := [monotonicity #2641 #2804]: #2806
#2812 := [trans #2807 #2810]: #2811
#2638 := (iff #2002 #2635)
#2632 := (and #140 #145 #492 #495 #2629 #1999)
#2636 := (iff #2632 #2635)
#2637 := [rewrite]: #2636
#2633 := (iff #2002 #2632)
#2630 := (iff #1992 #2629)
#2627 := (iff #1988 #2626)
#2624 := (iff #1984 #2621)
#2618 := (or #2615 #1980)
#2622 := (iff #2618 #2621)
#2623 := [rewrite]: #2622
#2619 := (iff #1984 #2618)
#2616 := (iff #1965 #2615)
#2613 := (iff #1964 #2612)
#2610 := (iff #1953 #2607)
#2598 := (+ #1948 #1951)
#2599 := (+ #1947 #2598)
#2602 := (>= #2599 0::int)
#2608 := (iff #2602 #2607)
#2609 := [rewrite]: #2608
#2603 := (iff #1953 #2602)
#2600 := (= #1952 #2599)
#2601 := [rewrite]: #2600
#2604 := [monotonicity #2601]: #2603
#2611 := [trans #2604 #2609]: #2610
#2596 := (iff #1963 #2595)
#2593 := (iff #1962 #2592)
#2594 := [rewrite]: #2593
#2597 := [monotonicity #2594]: #2596
#2614 := [monotonicity #2597 #2611]: #2613
#2617 := [monotonicity #2614]: #2616
#2620 := [monotonicity #2617]: #2619
#2625 := [trans #2620 #2623]: #2624
#2590 := (iff #1938 #2589)
#2587 := (iff #1935 #2586)
#2584 := (iff #1930 #2583)
#2581 := (iff #1927 #2578)
#2568 := (+ #1922 #1925)
#2569 := (+ #1162 #2568)
#2572 := (= #2569 0::int)
#2579 := (iff #2572 #2578)
#2580 := [rewrite]: #2579
#2573 := (iff #1927 #2572)
#2570 := (= #1926 #2569)
#2571 := [rewrite]: #2570
#2574 := [monotonicity #2571]: #2573
#2582 := [trans #2574 #2580]: #2581
#2566 := (iff #1929 #2565)
#2563 := (iff #1928 #2560)
#2552 := (+ #1162 #1922)
#2555 := (>= #2552 0::int)
#2561 := (iff #2555 #2560)
#2562 := [rewrite]: #2561
#2556 := (iff #1928 #2555)
#2553 := (= #1923 #2552)
#2554 := [rewrite]: #2553
#2557 := [monotonicity #2554]: #2556
#2564 := [trans #2557 #2562]: #2563
#2567 := [monotonicity #2564]: #2566
#2585 := [monotonicity #2567 #2582]: #2584
#2588 := [monotonicity #2585]: #2587
#2591 := [quant-intro #2588]: #2590
#2628 := [monotonicity #2591 #2625]: #2627
#2550 := (iff #1914 #2547)
#2513 := (and #1895 #2507)
#2544 := (and #2513 #2541)
#2548 := (iff #2544 #2547)
#2549 := [rewrite]: #2548
#2545 := (iff #1914 #2544)
#2542 := (iff #1910 #2541)
#2539 := (iff #1907 #2538)
#2536 := (iff #1891 #2535)
#2533 := (iff #1888 #2532)
#2530 := (= #1887 #2529)
#2531 := [rewrite]: #2530
#2534 := [monotonicity #2531]: #2533
#2537 := [monotonicity #2534]: #2536
#2540 := [monotonicity #2537]: #2539
#2543 := [quant-intro #2540]: #2542
#2526 := (iff #1904 #2513)
#2518 := (not #2513)
#2521 := (not #2518)
#2524 := (iff #2521 #2513)
#2525 := [rewrite]: #2524
#2522 := (iff #1904 #2521)
#2519 := (iff #1899 #2518)
#2516 := (iff #1898 #2513)
#2510 := (and #2507 #1895)
#2514 := (iff #2510 #2513)
#2515 := [rewrite]: #2514
#2511 := (iff #1898 #2510)
#2508 := (iff #1897 #2507)
#2505 := (iff #1896 #2504)
#2506 := [rewrite]: #2505
#2509 := [monotonicity #2506]: #2508
#2512 := [monotonicity #2509]: #2511
#2517 := [trans #2512 #2515]: #2516
#2520 := [monotonicity #2517]: #2519
#2523 := [monotonicity #2520]: #2522
#2527 := [trans #2523 #2525]: #2526
#2546 := [monotonicity #2527 #2543]: #2545
#2551 := [trans #2546 #2549]: #2550
#2631 := [monotonicity #2551 #2628]: #2630
#2502 := (iff #1878 #495)
#2503 := [rewrite]: #2502
#2500 := (iff #1875 #492)
#2501 := [rewrite]: #2500
#2498 := (iff #1872 #145)
#2499 := [rewrite]: #2498
#2496 := (iff #1869 #140)
#2497 := [rewrite]: #2496
#2634 := [monotonicity #2497 #2499 #2501 #2503 #2631]: #2633
#2639 := [trans #2634 #2637]: #2638
#2815 := [monotonicity #2639 #2812]: #2814
#2494 := (iff #1863 #2493)
#2491 := (iff #1860 #2490)
#2488 := (iff #1855 #2487)
#2485 := (iff #1849 #2484)
#2482 := (iff #1848 #2479)
#2472 := (+ #1117 #1846)
#2475 := (>= #2472 0::int)
#2480 := (iff #2475 #2479)
#2481 := [rewrite]: #2480
#2476 := (iff #1848 #2475)
#2473 := (= #1847 #2472)
#2474 := [rewrite]: #2473
#2477 := [monotonicity #2474]: #2476
#2483 := [trans #2477 #2481]: #2482
#2486 := [monotonicity #2483]: #2485
#2470 := (iff #1853 #2467)
#2456 := (+ #1846 #1851)
#2457 := (+ #1117 #2456)
#2460 := (= #2457 0::int)
#2468 := (iff #2460 #2467)
#2469 := [rewrite]: #2468
#2461 := (iff #1853 #2460)
#2458 := (= #1852 #2457)
#2459 := [rewrite]: #2458
#2462 := [monotonicity #2459]: #2461
#2471 := [trans #2462 #2469]: #2470
#2489 := [monotonicity #2471 #2486]: #2488
#2492 := [monotonicity #2489]: #2491
#2495 := [quant-intro #2492]: #2494
#2454 := (iff #1837 #2453)
#2451 := (iff #1834 #2450)
#2448 := (iff #1829 #2447)
#2445 := (iff #1824 #2442)
#2432 := (+ #1820 #1822)
#2433 := (+ #1079 #2432)
#2436 := (= #2433 0::int)
#2443 := (iff #2436 #2442)
#2444 := [rewrite]: #2443
#2437 := (iff #1824 #2436)
#2434 := (= #1823 #2433)
#2435 := [rewrite]: #2434
#2438 := [monotonicity #2435]: #2437
#2446 := [trans #2438 #2444]: #2445
#2430 := (iff #1827 #2429)
#2427 := (iff #1826 #2424)
#2416 := (+ #1079 #1822)
#2419 := (>= #2416 0::int)
#2425 := (iff #2419 #2424)
#2426 := [rewrite]: #2425
#2420 := (iff #1826 #2419)
#2417 := (= #1825 #2416)
#2418 := [rewrite]: #2417
#2421 := [monotonicity #2418]: #2420
#2428 := [trans #2421 #2426]: #2427
#2431 := [monotonicity #2428]: #2430
#2449 := [monotonicity #2431 #2446]: #2448
#2452 := [monotonicity #2449]: #2451
#2455 := [quant-intro #2452]: #2454
#2414 := (iff #1813 #106)
#2415 := [rewrite]: #2414
#2818 := [monotonicity #2415 #2455 #2495 #2815]: #2817
#2823 := [trans #2818 #2821]: #2822
#2412 := (iff #1808 #2409)
#2375 := (and #1789 #2369)
#2406 := (and #2375 #2403)
#2410 := (iff #2406 #2409)
#2411 := [rewrite]: #2410
#2407 := (iff #1808 #2406)
#2404 := (iff #1804 #2403)
#2401 := (iff #1801 #2400)
#2398 := (iff #1785 #2397)
#2395 := (iff #1781 #2394)
#2392 := (= #1780 #2391)
#2393 := [rewrite]: #2392
#2396 := [monotonicity #2393]: #2395
#2399 := [monotonicity #2396]: #2398
#2402 := [monotonicity #2399]: #2401
#2405 := [quant-intro #2402]: #2404
#2388 := (iff #1798 #2375)
#2380 := (not #2375)
#2383 := (not #2380)
#2386 := (iff #2383 #2375)
#2387 := [rewrite]: #2386
#2384 := (iff #1798 #2383)
#2381 := (iff #1793 #2380)
#2378 := (iff #1792 #2375)
#2372 := (and #2369 #1789)
#2376 := (iff #2372 #2375)
#2377 := [rewrite]: #2376
#2373 := (iff #1792 #2372)
#2370 := (iff #1791 #2369)
#2367 := (iff #1790 #2366)
#2368 := [rewrite]: #2367
#2371 := [monotonicity #2368]: #2370
#2374 := [monotonicity #2371]: #2373
#2379 := [trans #2374 #2377]: #2378
#2382 := [monotonicity #2379]: #2381
#2385 := [monotonicity #2382]: #2384
#2389 := [trans #2385 #2387]: #2388
#2408 := [monotonicity #2389 #2405]: #2407
#2413 := [trans #2408 #2411]: #2412
#2826 := [monotonicity #2413 #2823]: #2825
#2829 := [monotonicity #2826]: #2828
#2364 := (iff #1762 #2363)
#2361 := (iff #1761 #2360)
#2358 := (iff #1753 #2357)
#2355 := (= #1752 #2354)
#2356 := [rewrite]: #2355
#2359 := [monotonicity #2356]: #2358
#2351 := (iff #1760 #2350)
#2348 := (iff #1759 #2347)
#2349 := [rewrite]: #2348
#2352 := [monotonicity #2349]: #2351
#2362 := [monotonicity #2352 #2359]: #2361
#2365 := [monotonicity #2362]: #2364
#2832 := [monotonicity #2365 #2829]: #2831
#2835 := [monotonicity #2832]: #2834
#2345 := (iff #1732 #2344)
#2342 := (iff #1731 #2341)
#2339 := (iff #1725 #2336)
#2328 := (+ #1722 #1723)
#2331 := (>= #2328 0::int)
#2337 := (iff #2331 #2336)
#2338 := [rewrite]: #2337
#2332 := (iff #1725 #2331)
#2329 := (= #1724 #2328)
#2330 := [rewrite]: #2329
#2333 := [monotonicity #2330]: #2332
#2340 := [trans #2333 #2338]: #2339
#2326 := (iff #1730 #2325)
#2323 := (iff #1729 #2322)
#2324 := [rewrite]: #2323
#2327 := [monotonicity #2324]: #2326
#2343 := [monotonicity #2327 #2340]: #2342
#2346 := [monotonicity #2343]: #2345
#2838 := [monotonicity #2346 #2835]: #2837
#2841 := [monotonicity #2838]: #2840
#2844 := [monotonicity #2841]: #2843
#2320 := (iff #1662 #78)
#2321 := [rewrite]: #2320
#2847 := [monotonicity #2321 #2844]: #2846
#2850 := [monotonicity #2847]: #2849
#1636 := (not #1600)
#2315 := (~ #1636 #2314)
#2311 := (not #1597)
#2312 := (~ #2311 #2310)
#2307 := (not #1594)
#2308 := (~ #2307 #2306)
#2303 := (not #1591)
#2304 := (~ #2303 #2302)
#2299 := (not #1588)
#2300 := (~ #2299 #2298)
#2295 := (not #1585)
#2296 := (~ #2295 #2294)
#2291 := (not #1582)
#2292 := (~ #2291 #2290)
#2287 := (not #1579)
#2288 := (~ #2287 #2286)
#2283 := (not #1576)
#2284 := (~ #2283 #2282)
#2279 := (not #1571)
#2280 := (~ #2279 #2278)
#2275 := (not #1542)
#2276 := (~ #2275 #1539)
#2273 := (~ #1539 #1539)
#2271 := (~ #1536 #1536)
#2272 := [refl]: #2271
#2274 := [nnf-pos #2272]: #2273
#2277 := [nnf-neg #2274]: #2276
#2268 := (not #1533)
#2269 := (~ #2268 #1530)
#2266 := (~ #1530 #1530)
#2264 := (~ #1527 #1527)
#2265 := [refl]: #2264
#2267 := [nnf-pos #2265]: #2266
#2270 := [nnf-neg #2267]: #2269
#2261 := (not #1522)
#2262 := (~ #2261 #1519)
#2259 := (~ #1519 #1519)
#2257 := (~ #1516 #1516)
#2258 := [refl]: #2257
#2260 := [nnf-pos #2258]: #2259
#2263 := [nnf-neg #2260]: #2262
#2254 := (not #1499)
#2255 := (~ #2254 #2253)
#2250 := (not #1494)
#2251 := (~ #2250 #2249)
#2247 := (~ #1460 #1460)
#2248 := [refl]: #2247
#2244 := (not #1455)
#2245 := (~ #2244 #1452)
#2242 := (~ #1452 #1452)
#2240 := (~ #1449 #1449)
#2241 := [refl]: #2240
#2243 := [nnf-pos #2241]: #2242
#2246 := [nnf-neg #2243]: #2245
#2237 := (not #1442)
#2238 := (~ #2237 #1439)
#2235 := (~ #1439 #1439)
#2233 := (~ #1436 #1436)
#2234 := [refl]: #2233
#2236 := [nnf-pos #2234]: #2235
#2239 := [nnf-neg #2236]: #2238
#2230 := (not #1425)
#2231 := (~ #2230 #2229)
#2226 := (not #1422)
#2227 := (~ #2226 #2225)
#2222 := (not #1419)
#2223 := (~ #2222 #2221)
#2218 := (not #1416)
#2219 := (~ #2218 #2217)
#2214 := (not #1413)
#2215 := (~ #2214 #2213)
#2210 := (not #1410)
#2211 := (~ #2210 #2209)
#2206 := (not #1407)
#2207 := (~ #2206 #2205)
#2202 := (not #1404)
#2203 := (~ #2202 #2201)
#2198 := (not #1401)
#2199 := (~ #2198 #2197)
#2194 := (not #1398)
#2195 := (~ #2194 #2193)
#2190 := (not #1395)
#2191 := (~ #2190 #2189)
#2186 := (not #1392)
#2187 := (~ #2186 #2185)
#2167 := (not #1389)
#2183 := (~ #2167 #2180)
#2157 := (exists (vars (?x76 T2)) #2156)
#2165 := (or #2164 #2157)
#2166 := (not #2165)
#2181 := (~ #2166 #2180)
#2177 := (not #2157)
#2178 := (~ #2177 #2176)
#2174 := (~ #2173 #2173)
#2175 := [refl]: #2174
#2179 := [nnf-neg #2175]: #2178
#2171 := (~ #2170 #2170)
#2172 := [refl]: #2171
#2182 := [nnf-neg #2172 #2179]: #2181
#2168 := (~ #2167 #2166)
#2169 := [sk]: #2168
#2184 := [trans #2169 #2182]: #2183
#2143 := (not #1352)
#2144 := (~ #2143 #1349)
#2141 := (~ #1349 #1349)
#2139 := (~ #1346 #1346)
#2140 := [refl]: #2139
#2142 := [nnf-pos #2140]: #2141
#2145 := [nnf-neg #2142]: #2144
#2188 := [nnf-neg #2145 #2184]: #2187
#2135 := (~ #1352 #2134)
#2136 := [sk]: #2135
#2192 := [nnf-neg #2136 #2188]: #2191
#2113 := (not #1328)
#2114 := (~ #2113 #1325)
#2111 := (~ #1325 #1325)
#2109 := (~ #1322 #1322)
#2110 := [refl]: #2109
#2112 := [nnf-pos #2110]: #2111
#2115 := [nnf-neg #2112]: #2114
#2196 := [nnf-neg #2115 #2192]: #2195
#2105 := (~ #1328 #2104)
#2106 := [sk]: #2105
#2200 := [nnf-neg #2106 #2196]: #2199
#2088 := (not #1314)
#2089 := (~ #2088 #1311)
#2086 := (~ #1311 #1311)
#2084 := (~ #1308 #1308)
#2085 := [refl]: #2084
#2087 := [nnf-pos #2085]: #2086
#2090 := [nnf-neg #2087]: #2089
#2204 := [nnf-neg #2090 #2200]: #2203
#2080 := (~ #1314 #2079)
#2081 := [sk]: #2080
#2208 := [nnf-neg #2081 #2204]: #2207
#2074 := (~ #2073 #2073)
#2075 := [refl]: #2074
#2212 := [nnf-neg #2075 #2208]: #2211
#2071 := (~ #1305 #1305)
#2072 := [refl]: #2071
#2216 := [nnf-neg #2072 #2212]: #2215
#2068 := (not #783)
#2069 := (~ #2068 #667)
#2066 := (~ #667 #667)
#2064 := (~ #662 #662)
#2065 := [refl]: #2064
#2067 := [nnf-pos #2065]: #2066
#2070 := [nnf-neg #2067]: #2069
#2220 := [nnf-neg #2070 #2216]: #2219
#2060 := (~ #783 #2059)
#2061 := [sk]: #2060
#2224 := [nnf-neg #2061 #2220]: #2223
#2049 := (not #1300)
#2050 := (~ #2049 #1297)
#2047 := (~ #1297 #1297)
#2045 := (~ #1292 #1292)
#2046 := [refl]: #2045
#2048 := [nnf-pos #2046]: #2047
#2051 := [nnf-neg #2048]: #2050
#2228 := [nnf-neg #2051 #2224]: #2227
#2041 := (~ #1300 #2040)
#2042 := [sk]: #2041
#2232 := [nnf-neg #2042 #2228]: #2231
#2031 := (not #1289)
#2032 := (~ #2031 #1286)
#2029 := (~ #1286 #1286)
#2027 := (~ #1281 #1281)
#2028 := [refl]: #2027
#2030 := [nnf-pos #2028]: #2029
#2033 := [nnf-neg #2030]: #2032
#2024 := (not #1470)
#2025 := (~ #2024 #2019)
#2020 := (~ #1239 #2019)
#2021 := [sk]: #2020
#2026 := [nnf-neg #2021]: #2025
#2009 := (~ #2008 #2008)
#2010 := [refl]: #2009
#2006 := (~ #176 #176)
#2007 := [refl]: #2006
#2252 := [nnf-neg #2007 #2010 #2026 #2033 #2232 #2239 #2246 #2248]: #2251
#2003 := (not #1257)
#2004 := (~ #2003 #2002)
#2000 := (~ #1470 #1999)
#1997 := (~ #1996 #1996)
#1998 := [refl]: #1997
#2001 := [nnf-neg #1998]: #2000
#1993 := (not #1233)
#1994 := (~ #1993 #1992)
#1989 := (not #1230)
#1990 := (~ #1989 #1988)
#1985 := (not #1227)
#1986 := (~ #1985 #1984)
#1981 := (not #1222)
#1982 := (~ #1981 #1980)
#1977 := (not #1214)
#1978 := (~ #1977 #1211)
#1975 := (~ #1211 #1211)
#1973 := (~ #1208 #1208)
#1974 := [refl]: #1973
#1976 := [nnf-pos #1974]: #1975
#1979 := [nnf-neg #1976]: #1978
#1971 := (~ #1970 #1970)
#1972 := [refl]: #1971
#1983 := [nnf-neg #1972 #1979]: #1982
#1966 := (~ #1214 #1965)
#1967 := [sk]: #1966
#1987 := [nnf-neg #1967 #1983]: #1986
#1941 := (not #1196)
#1942 := (~ #1941 #1938)
#1939 := (~ #1193 #1938)
#1936 := (~ #1190 #1935)
#1931 := (~ #1187 #1930)
#1932 := [sk]: #1931
#1919 := (~ #1171 #1171)
#1920 := [refl]: #1919
#1937 := [monotonicity #1920 #1932]: #1936
#1940 := [nnf-pos #1937]: #1939
#1943 := [nnf-neg #1940]: #1942
#1991 := [nnf-neg #1943 #1987]: #1990
#1917 := (~ #1196 #1914)
#1892 := (exists (vars (?x50 T2)) #1891)
#1900 := (or #1899 #1892)
#1901 := (not #1900)
#1915 := (~ #1901 #1914)
#1911 := (not #1892)
#1912 := (~ #1911 #1910)
#1908 := (~ #1907 #1907)
#1909 := [refl]: #1908
#1913 := [nnf-neg #1909]: #1912
#1905 := (~ #1904 #1904)
#1906 := [refl]: #1905
#1916 := [nnf-neg #1906 #1913]: #1915
#1902 := (~ #1196 #1901)
#1903 := [sk]: #1902
#1918 := [trans #1903 #1916]: #1917
#1995 := [nnf-neg #1918 #1991]: #1994
#1879 := (~ #1878 #1878)
#1880 := [refl]: #1879
#1876 := (~ #1875 #1875)
#1877 := [refl]: #1876
#1873 := (~ #1872 #1872)
#1874 := [refl]: #1873
#1870 := (~ #1869 #1869)
#1871 := [refl]: #1870
#2005 := [nnf-neg #1871 #1874 #1877 #1880 #1995 #2001]: #2004
#2256 := [nnf-neg #2005 #2252]: #2255
#1866 := (not #1159)
#1867 := (~ #1866 #1863)
#1864 := (~ #1156 #1863)
#1861 := (~ #1153 #1860)
#1856 := (~ #1150 #1855)
#1857 := [sk]: #1856
#1843 := (~ #1126 #1126)
#1844 := [refl]: #1843
#1862 := [monotonicity #1844 #1857]: #1861
#1865 := [nnf-pos #1862]: #1864
#1868 := [nnf-neg #1865]: #1867
#1840 := (not #1550)
#1841 := (~ #1840 #1837)
#1838 := (~ #1114 #1837)
#1835 := (~ #1111 #1834)
#1830 := (~ #1108 #1829)
#1831 := [sk]: #1830
#1816 := (~ #1088 #1088)
#1817 := [refl]: #1816
#1836 := [monotonicity #1817 #1831]: #1835
#1839 := [nnf-pos #1836]: #1838
#1842 := [nnf-neg #1839]: #1841
#1814 := (~ #1813 #1813)
#1815 := [refl]: #1814
#2281 := [nnf-neg #1815 #1842 #1868 #2256 #2263 #2270 #2277]: #2280
#1811 := (~ #1550 #1808)
#1786 := (exists (vars (?x38 T2)) #1785)
#1794 := (or #1793 #1786)
#1795 := (not #1794)
#1809 := (~ #1795 #1808)
#1805 := (not #1786)
#1806 := (~ #1805 #1804)
#1802 := (~ #1801 #1801)
#1803 := [refl]: #1802
#1807 := [nnf-neg #1803]: #1806
#1799 := (~ #1798 #1798)
#1800 := [refl]: #1799
#1810 := [nnf-neg #1800 #1807]: #1809
#1796 := (~ #1550 #1795)
#1797 := [sk]: #1796
#1812 := [trans #1797 #1810]: #1811
#2285 := [nnf-neg #1812 #2281]: #2284
#1771 := (not #1076)
#1772 := (~ #1771 #1073)
#1769 := (~ #1073 #1073)
#1767 := (~ #1070 #1070)
#1768 := [refl]: #1767
#1770 := [nnf-pos #1768]: #1769
#1773 := [nnf-neg #1770]: #1772
#2289 := [nnf-neg #1773 #2285]: #2288
#1763 := (~ #1076 #1762)
#1764 := [sk]: #1763
#2293 := [nnf-neg #1764 #2289]: #2292
#1741 := (not #1050)
#1742 := (~ #1741 #1047)
#1739 := (~ #1047 #1047)
#1737 := (~ #1044 #1044)
#1738 := [refl]: #1737
#1740 := [nnf-pos #1738]: #1739
#1743 := [nnf-neg #1740]: #1742
#2297 := [nnf-neg #1743 #2293]: #2296
#1733 := (~ #1050 #1732)
#1734 := [sk]: #1733
#2301 := [nnf-neg #1734 #2297]: #2300
#1716 := (not #1035)
#1717 := (~ #1716 #1032)
#1714 := (~ #1032 #1032)
#1712 := (~ #1031 #1031)
#1713 := [refl]: #1712
#1715 := [nnf-pos #1713]: #1714
#1718 := [nnf-neg #1715]: #1717
#2305 := [nnf-neg #1718 #2301]: #2304
#1708 := (~ #1035 #1707)
#1709 := [sk]: #1708
#2309 := [nnf-neg #1709 #2305]: #2308
#1663 := (~ #1662 #1662)
#1703 := [refl]: #1663
#2313 := [nnf-neg #1703 #2309]: #2312
#1701 := (~ #1026 #1026)
#1702 := [refl]: #1701
#2316 := [nnf-neg #1702 #2313]: #2315
#1637 := [not-or-elim #1633]: #1636
#2317 := [mp~ #1637 #2316]: #2314
#2318 := [mp #2317 #2850]: #2848
#3492 := [mp #2318 #3491]: #3489
#4421 := [mp #3492 #4420]: #4418
#10019 := [unit-resolution #4421 #5020]: #4415
#3747 := (or #4412 #4406)
#3590 := [def-axiom]: #3747
#10022 := [unit-resolution #3590 #10019]: #4406
#10023 := (or #4409 #4403)
#3664 := (* -1::int #1705)
#3631 := (+ uf_9 #3664)
#3633 := (<= #3631 0::int)
#3738 := (= uf_9 #1705)
#3712 := (= uf_11 ?x27!0)
#3561 := (not #3712)
#3560 := (= #1705 0::int)
#4453 := (not #3560)
#4452 := [hypothesis]: #1707
#4504 := (or #4453 #1706)
#4505 := [th-lemma]: #4504
#4506 := [unit-resolution #4505 #4452]: #4453
#3571 := (or #3570 #3560 #3561)
#3727 := (= ?x27!0 uf_11)
#3562 := (not #3727)
#3563 := (or #3562 #3560)
#3572 := (or #3570 #3563)
#4443 := (iff #3572 #3571)
#3585 := (or #3560 #3561)
#4444 := (or #3570 #3585)
#4447 := (iff #4444 #3571)
#4448 := [rewrite]: #4447
#4445 := (iff #3572 #4444)
#3583 := (iff #3563 #3585)
#4429 := (or #3561 #3560)
#3569 := (iff #4429 #3585)
#3566 := [rewrite]: #3569
#3584 := (iff #3563 #4429)
#3564 := (iff #3562 #3561)
#3710 := (iff #3727 #3712)
#3713 := [rewrite]: #3710
#4428 := [monotonicity #3713]: #3564
#3576 := [monotonicity #4428]: #3584
#3567 := [trans #3576 #3566]: #3583
#4446 := [monotonicity #3567]: #4445
#4449 := [trans #4446 #4448]: #4443
#3568 := [quant-inst]: #3572
#4450 := [mp #3568 #4449]: #3571
#4507 := [unit-resolution #4450 #4427 #4506]: #3561
#3695 := (or #3712 #3738)
#4043 := (forall (vars (?x25 T2)) (:pat #4042) #405)
#4046 := (iff #410 #4043)
#4044 := (iff #405 #405)
#4045 := [refl]: #4044
#4047 := [quant-intro #4045]: #4046
#1660 := (~ #410 #410)
#1698 := (~ #405 #405)
#1699 := [refl]: #1698
#1661 := [nnf-pos #1699]: #1660
#1635 := [not-or-elim #1633]: #410
#1700 := [mp~ #1635 #1661]: #410
#4048 := [mp #1700 #4047]: #4043
#3698 := (not #4043)
#3699 := (or #3698 #3712 #3738)
#3730 := (or #3727 #3738)
#3700 := (or #3698 #3730)
#3662 := (iff #3700 #3699)
#3702 := (or #3698 #3695)
#3653 := (iff #3702 #3699)
#3660 := [rewrite]: #3653
#3659 := (iff #3700 #3702)
#3697 := (iff #3730 #3695)
#3711 := [monotonicity #3713]: #3697
#3661 := [monotonicity #3711]: #3659
#3663 := [trans #3661 #3660]: #3662
#3701 := [quant-inst]: #3700
#3654 := [mp #3701 #3663]: #3699
#4508 := [unit-resolution #3654 #4048]: #3695
#4509 := [unit-resolution #4508 #4507]: #3738
#4510 := (not #3738)
#4511 := (or #4510 #3633)
#4512 := [th-lemma]: #4511
#4492 := [unit-resolution #4512 #4509]: #3633
#4451 := (<= #1705 0::int)
#4493 := (or #4451 #1706)
#4494 := [th-lemma]: #4493
#4495 := [unit-resolution #4494 #4452]: #4451
#335 := (<= uf_9 0::int)
#336 := (not #335)
#54 := (< 0::int uf_9)
#337 := (iff #54 #336)
#338 := [rewrite]: #337
#331 := [asserted]: #54
#339 := [mp #331 #338]: #336
#4496 := [th-lemma #339 #4495 #4492]: false
#4491 := [lemma #4496]: #1706
#3742 := (or #4409 #1707 #4403)
#3743 := [def-axiom]: #3742
#10024 := [unit-resolution #3743 #4491]: #10023
#10025 := [unit-resolution #10024 #10022]: #4403
#3766 := (or #4400 #4394)
#3767 := [def-axiom]: #3766
#10018 := [unit-resolution #3767 #10025]: #4394
#3761 := (or #4397 #2108 #4391)
#3762 := [def-axiom]: #3761
#10026 := [unit-resolution #3762 #10018]: #4394
#10027 := [unit-resolution #10026 #10021]: #4391
#3787 := (or #4388 #4382)
#3788 := [def-axiom]: #3787
#10028 := [unit-resolution #3788 #10027]: #4382
#3783 := (or #4385 #2893 #4379)
#3784 := [def-axiom]: #3783
#10029 := [unit-resolution #3784 #10028 #10020]: #4379
#3771 := (or #4376 #4370)
#3772 := [def-axiom]: #3771
#10030 := [unit-resolution #3772 #10029]: #4370
#10032 := (or #4373 #4367)
#4499 := [hypothesis]: #4087
#3969 := (or #4084 #2369)
#3970 := [def-axiom]: #3969
#4636 := [unit-resolution #3970 #4499]: #2369
#4584 := (= uf_9 #1777)
#4727 := (not #4584)
#3636 := (or #4084 #1789)
#3968 := [def-axiom]: #3636
#4637 := [unit-resolution #3968 #4499]: #1789
#4737 := (or #4727 #1788)
#4738 := [th-lemma]: #4737
#4739 := [unit-resolution #4738 #4637]: #4727
#4758 := (or #4584 #2366)
#4728 := [hypothesis]: #4727
#4729 := [hypothesis]: #2369
#4641 := (or #3698 #2366 #4584)
#4585 := (or #1790 #4584)
#4642 := (or #3698 #4585)
#4628 := (iff #4642 #4641)
#4638 := (or #2366 #4584)
#4644 := (or #3698 #4638)
#4626 := (iff #4644 #4641)
#4627 := [rewrite]: #4626
#4624 := (iff #4642 #4644)
#4639 := (iff #4585 #4638)
#4640 := [monotonicity #2368]: #4639
#4625 := [monotonicity #4640]: #4624
#4623 := [trans #4625 #4627]: #4628
#4643 := [quant-inst]: #4642
#4629 := [mp #4643 #4623]: #4641
#4730 := [unit-resolution #4629 #4048 #4729 #4728]: false
#4760 := [lemma #4730]: #4758
#4740 := [unit-resolution #4760 #4739 #4636]: false
#4741 := [lemma #4740]: #4084
#3805 := (or #4373 #4087 #4367)
#3815 := [def-axiom]: #3805
#10033 := [unit-resolution #3815 #4741]: #10032
#10034 := [unit-resolution #10033 #10030]: #4367
#3800 := (or #4364 #4358)
#3759 := [def-axiom]: #3800
#10246 := [unit-resolution #3759 #10034]: #4358
#3593 := (not #2607)
#3836 := (or #4364 #106)
#3832 := [def-axiom]: #3836
#10035 := [unit-resolution #3832 #10034]: #106
#8124 := (= #161 #105)
#4885 := [hypothesis]: #4200
#3652 := (or #4197 #495)
#3934 := [def-axiom]: #3652
#4886 := [unit-resolution #3934 #4885]: #495
#8139 := [symm #4886]: #142
#7937 := [monotonicity #8139]: #8124
#4736 := [trans #7937 #10035]: #162
#3612 := (or #4173 #1970)
#3613 := [def-axiom]: #3612
#7107 := [unit-resolution #3613 #4736]: #4173
#3939 := (or #4197 #4191)
#3928 := [def-axiom]: #3939
#8726 := [unit-resolution #3928 #4885]: #4191
#10469 := (or #4151 #586)
#8744 := (?x47!7 ?x49!8)
#8817 := (uf_4 uf_19 #8744)
#8836 := (* -1::int #8817)
#8739 := (uf_4 uf_14 #8744)
#9868 := (+ #8739 #8836)
#9874 := (>= #9868 0::int)
#9867 := (= #8739 #8817)
#10418 := (= #8817 #8739)
#6250 := [hypothesis]: #495
#10417 := [symm #6250]: #142
#10419 := [monotonicity #10417]: #10418
#10420 := [symm #10419]: #9867
#10421 := (not #9867)
#10416 := (or #10421 #9874)
#10422 := [th-lemma]: #10416
#10423 := [unit-resolution #10422 #10420]: #9874
#8745 := (* -1::int #8739)
#8586 := (uf_4 uf_14 ?x49!8)
#8746 := (+ #8586 #8745)
#8747 := (<= #8746 0::int)
#8789 := (not #8747)
#8770 := (up_6 uf_15 #8744)
#8771 := (not #8770)
#8748 := (uf_1 #8744 ?x49!8)
#8749 := (uf_10 #8748)
#8765 := (* -1::int #8749)
#8766 := (+ #8745 #8765)
#8767 := (+ #8586 #8766)
#8768 := (= #8767 0::int)
#8769 := (not #8768)
#8754 := (or #8747 #8769 #8771)
#8757 := (not #8754)
#8721 := (* -1::int #8586)
#8734 := (+ uf_9 #8721)
#8722 := (<= #8734 0::int)
#8939 := (not #8722)
#10424 := [hypothesis]: #4154
#3622 := (or #4151 #1895)
#3627 := [def-axiom]: #3622
#10425 := [unit-resolution #3627 #10424]: #1895
#8935 := (+ #1882 #8721)
#8932 := (>= #8935 0::int)
#8934 := (= #1882 #8586)
#10426 := (= #8586 #1882)
#10427 := [monotonicity #6250]: #10426
#10428 := [symm #10427]: #8934
#10429 := (not #8934)
#10430 := (or #10429 #8932)
#10431 := [th-lemma]: #10430
#10432 := [unit-resolution #10431 #10428]: #8932
#8931 := (not #8932)
#8940 := (or #8939 #8931 #1894)
#8936 := [hypothesis]: #1895
#8933 := [hypothesis]: #8722
#8937 := [hypothesis]: #8932
#8938 := [th-lemma #8937 #8933 #8936]: false
#8738 := [lemma #8938]: #8940
#10433 := [unit-resolution #8738 #10432 #10425]: #8939
#10443 := (or #8722 #8757)
#3963 := (or #4151 #2507)
#3623 := [def-axiom]: #3963
#10434 := [unit-resolution #3623 #10424]: #2507
#3825 := (or #4364 #4124)
#3793 := [def-axiom]: #3825
#10442 := [unit-resolution #3793 #10034]: #4124
#8762 := (or #4129 #2504 #8722 #8757)
#8772 := (or #8771 #8769 #8747)
#8773 := (not #8772)
#8753 := (or #1896 #8722 #8773)
#8775 := (or #4129 #8753)
#8781 := (iff #8775 #8762)
#8759 := (or #2504 #8722 #8757)
#8777 := (or #4129 #8759)
#8774 := (iff #8777 #8762)
#8780 := [rewrite]: #8774
#8778 := (iff #8775 #8777)
#8760 := (iff #8753 #8759)
#8752 := (iff #8773 #8757)
#8755 := (iff #8772 #8754)
#8756 := [rewrite]: #8755
#8758 := [monotonicity #8756]: #8752
#8761 := [monotonicity #2506 #8758]: #8760
#8779 := [monotonicity #8761]: #8778
#8782 := [trans #8779 #8780]: #8781
#8776 := [quant-inst]: #8775
#8783 := [mp #8776 #8782]: #8762
#10444 := [unit-resolution #8783 #10442 #10434]: #10443
#10445 := [unit-resolution #10444 #10433]: #8757
#8787 := (or #8754 #8789)
#8790 := [def-axiom]: #8787
#10446 := [unit-resolution #8790 #10445]: #8789
#8831 := (+ #1882 #8836)
#8848 := (<= #8831 0::int)
#8893 := (+ #8765 #8836)
#8894 := (+ #1882 #8893)
#8912 := (= #8894 0::int)
#9084 := (<= #8894 0::int)
#9871 := (<= #9868 0::int)
#10447 := (or #10421 #9871)
#10448 := [th-lemma]: #10447
#10449 := [unit-resolution #10448 #10420]: #9871
#8784 := (<= #8767 0::int)
#8791 := (or #8754 #8768)
#8792 := [def-axiom]: #8791
#10450 := [unit-resolution #8792 #10445]: #8768
#10451 := (or #8769 #8784)
#10452 := [th-lemma]: #10451
#10453 := [unit-resolution #10452 #10450]: #8784
#8930 := (<= #8935 0::int)
#10454 := (or #10429 #8930)
#10455 := [th-lemma]: #10454
#10456 := [unit-resolution #10455 #10428]: #8930
#10096 := (not #9871)
#10098 := (not #8784)
#10097 := (not #8930)
#10099 := (or #9084 #10097 #10098 #10096)
#10059 := [hypothesis]: #9871
#10060 := [hypothesis]: #8784
#10062 := [hypothesis]: #8930
#10063 := (not #9084)
#10064 := [hypothesis]: #10063
#10065 := [th-lemma #10064 #10062 #10060 #10059]: false
#10100 := [lemma #10065]: #10099
#10457 := [unit-resolution #10100 #10456 #10453 #10449]: #9084
#9068 := (>= #8894 0::int)
#8788 := (>= #8767 0::int)
#10458 := (or #8769 #8788)
#10459 := [th-lemma]: #10458
#10460 := [unit-resolution #10459 #10450]: #8788
#10439 := (not #9874)
#10007 := (not #8788)
#10440 := (or #9068 #8931 #10007 #10439)
#10435 := [hypothesis]: #9874
#9938 := [hypothesis]: #8788
#10436 := (not #9068)
#10437 := [hypothesis]: #10436
#10438 := [th-lemma #10437 #8937 #9938 #10435]: false
#10441 := [lemma #10438]: #10440
#10461 := [unit-resolution #10441 #10432 #10460 #10423]: #9068
#10462 := (or #8912 #10063 #10436)
#10463 := [th-lemma]: #10462
#10464 := [unit-resolution #10463 #10461 #10457]: #8912
#8911 := (not #8912)
#8918 := (or #8848 #8911)
#3964 := (or #4151 #4143)
#3607 := [def-axiom]: #3964
#10465 := [unit-resolution #3607 #10424]: #4143
#9022 := (or #4148 #8848 #8911)
#8815 := (+ #1883 #8749)
#8818 := (+ #8817 #8815)
#8819 := (= #8818 0::int)
#8820 := (not #8819)
#8821 := (+ #8817 #1883)
#8825 := (>= #8821 0::int)
#8826 := (or #8825 #8820)
#9031 := (or #4148 #8826)
#9081 := (iff #9031 #9022)
#9078 := (or #4148 #8918)
#9024 := (iff #9078 #9022)
#9080 := [rewrite]: #9024
#9079 := (iff #9031 #9078)
#8919 := (iff #8826 #8918)
#8916 := (iff #8820 #8911)
#8915 := (iff #8819 #8912)
#8886 := (+ #8749 #8817)
#8887 := (+ #1883 #8886)
#8890 := (= #8887 0::int)
#8913 := (iff #8890 #8912)
#8914 := [rewrite]: #8913
#8891 := (iff #8819 #8890)
#8888 := (= #8818 #8887)
#8889 := [rewrite]: #8888
#8892 := [monotonicity #8889]: #8891
#8910 := [trans #8892 #8914]: #8915
#8917 := [monotonicity #8910]: #8916
#8857 := (iff #8825 #8848)
#8827 := (+ #1883 #8817)
#8833 := (>= #8827 0::int)
#8849 := (iff #8833 #8848)
#8856 := [rewrite]: #8849
#8834 := (iff #8825 #8833)
#8829 := (= #8821 #8827)
#8832 := [rewrite]: #8829
#8835 := [monotonicity #8832]: #8834
#8858 := [trans #8835 #8856]: #8857
#8920 := [monotonicity #8858 #8917]: #8919
#9023 := [monotonicity #8920]: #9079
#9082 := [trans #9023 #9080]: #9081
#9032 := [quant-inst]: #9031
#9083 := [mp #9032 #9082]: #9022
#10466 := [unit-resolution #9083 #10465]: #8918
#10467 := [unit-resolution #10466 #10464]: #8848
#10468 := [th-lemma #10432 #10467 #10446 #10423]: false
#10470 := [lemma #10468]: #10469
#8740 := [unit-resolution #10470 #4886]: #4151
#3941 := (or #4194 #4154 #4188)
#3945 := [def-axiom]: #3941
#8741 := [unit-resolution #3945 #8740 #8726]: #4188
#3672 := (or #4185 #4179)
#3565 := [def-axiom]: #3672
#8742 := [unit-resolution #3565 #8741]: #4179
#3947 := (or #4182 #4176 #3161)
#3669 := [def-axiom]: #3947
#8743 := [unit-resolution #3669 #8742 #7107]: #3161
#3956 := (or #3156 #3593)
#3958 := [def-axiom]: #3956
#8786 := [unit-resolution #3958 #8743]: #3593
#3763 := (or #4364 #4099)
#3818 := [def-axiom]: #3763
#10042 := [unit-resolution #3818 #10034]: #4099
#3953 := (or #3156 #1957)
#3954 := [def-axiom]: #3953
#8793 := [unit-resolution #3954 #8743]: #1957
#3949 := (or #3156 #1961)
#3955 := [def-axiom]: #3949
#8794 := [unit-resolution #3955 #8743]: #1961
#4870 := (or #4197 #1956 #4104 #1960 #2607)
#4889 := (uf_4 uf_14 ?x53!11)
#4883 := (= #1946 #4889)
#4887 := (= #4889 #1946)
#4882 := [monotonicity #4886]: #4887
#4888 := [symm #4882]: #4883
#4890 := (* -1::int #4889)
#6163 := (+ #1946 #4890)
#6178 := (<= #6163 0::int)
#6288 := (not #6178)
#6191 := [hypothesis]: #3593
#6244 := [hypothesis]: #1961
#6247 := [hypothesis]: #4099
#6249 := [hypothesis]: #1957
#3938 := (or #4197 #4133)
#3935 := [def-axiom]: #3938
#4841 := [unit-resolution #3935 #4885]: #4133
#6294 := (or #6288 #1956 #4138 #4104 #1960 #2607 #586)
#5206 := (uf_4 uf_14 ?x54!10)
#5207 := (* -1::int #5206)
#5202 := (+ uf_9 #5207)
#5208 := (<= #5202 0::int)
#5209 := (up_6 uf_15 ?x54!10)
#5647 := (not #5209)
#5579 := (+ #4890 #5206)
#5580 := (+ #1951 #5579)
#5572 := (>= #5580 0::int)
#6194 := (not #5572)
#6196 := (+ #1948 #5207)
#6208 := (>= #6196 0::int)
#6195 := (= #1948 #5206)
#6209 := (= #5206 #1948)
#6207 := [monotonicity #6250]: #6209
#6210 := [symm #6207]: #6195
#6211 := (not #6195)
#6212 := (or #6211 #6208)
#6241 := [th-lemma]: #6212
#6242 := [unit-resolution #6241 #6210]: #6208
#6192 := [hypothesis]: #6178
#6289 := (not #6208)
#6290 := (or #6194 #6288 #2607 #6289)
#6190 := [hypothesis]: #6208
#6187 := [hypothesis]: #5572
#6193 := [th-lemma #6187 #6192 #6191 #6190]: false
#6291 := [lemma #6193]: #6290
#6243 := [unit-resolution #6291 #6192 #6191 #6242]: #6194
#6248 := (or #5647 #5572)
#5669 := (or #4104 #1960 #5647 #5572)
#5605 := (+ #5206 #4890)
#5606 := (+ #1951 #5605)
#5646 := (>= #5606 0::int)
#5578 := (or #5647 #1960 #5646)
#5674 := (or #4104 #5578)
#5939 := (iff #5674 #5669)
#5670 := (or #1960 #5647 #5572)
#5676 := (or #4104 #5670)
#5909 := (iff #5676 #5669)
#5910 := [rewrite]: #5909
#5677 := (iff #5674 #5676)
#5673 := (iff #5578 #5670)
#5598 := (or #5647 #1960 #5572)
#5671 := (iff #5598 #5670)
#5672 := [rewrite]: #5671
#5601 := (iff #5578 #5598)
#5599 := (iff #5646 #5572)
#5581 := (= #5606 #5580)
#5582 := [rewrite]: #5581
#5600 := [monotonicity #5582]: #5599
#5602 := [monotonicity #5600]: #5601
#5668 := [trans #5602 #5672]: #5673
#5678 := [monotonicity #5668]: #5677
#5940 := [trans #5678 #5910]: #5939
#5675 := [quant-inst]: #5674
#5941 := [mp #5675 #5940]: #5669
#6177 := [unit-resolution #5941 #6247 #6244]: #6248
#6189 := [unit-resolution #6177 #6243]: #5647
#5211 := (or #5208 #5209)
#6168 := [hypothesis]: #4133
#5237 := (or #4138 #5208 #5209)
#5210 := (or #5209 #5208)
#5238 := (or #4138 #5210)
#5244 := (iff #5238 #5237)
#5240 := (or #4138 #5211)
#5242 := (iff #5240 #5237)
#5243 := [rewrite]: #5242
#5235 := (iff #5238 #5240)
#5212 := (iff #5210 #5211)
#5236 := [rewrite]: #5212
#5241 := [monotonicity #5236]: #5235
#5245 := [trans #5241 #5243]: #5244
#5239 := [quant-inst]: #5238
#5293 := [mp #5239 #5245]: #5237
#6292 := [unit-resolution #5293 #6168]: #5211
#6287 := [unit-resolution #6292 #6189]: #5208
#6293 := [th-lemma #6242 #6287 #6249]: false
#6295 := [lemma #6293]: #6294
#4866 := [unit-resolution #6295 #4841 #6249 #6247 #6244 #6191 #4886]: #6288
#4867 := (not #4883)
#4868 := (or #4867 #6178)
#4869 := [th-lemma]: #4868
#4840 := [unit-resolution #4869 #4866 #4888]: false
#4865 := [lemma #4840]: #4870
#8795 := [unit-resolution #4865 #8794 #8793 #10042 #4885 #8786]: false
#8798 := [lemma #8795]: #4197
#3834 := (or #4361 #4200 #4355)
#3835 := [def-axiom]: #3834
#10367 := [unit-resolution #3835 #8798 #10246]: #4355
#3856 := (or #4352 #184)
#3842 := [def-axiom]: #3856
#10380 := [unit-resolution #3842 #10367]: #184
#10381 := [symm #10380]: #7113
#13521 := (= #11444 #183)
#13346 := (= #10482 uf_22)
#10483 := (= uf_22 #10482)
#13 := (uf_3 #12)
#295 := (= #11 #13)
#3982 := (forall (vars (?x2 T2) (?x3 T2)) (:pat #3981) #295)
#299 := (forall (vars (?x2 T2) (?x3 T2)) #295)
#3985 := (iff #299 #3982)
#3983 := (iff #295 #295)
#3984 := [refl]: #3983
#3986 := [quant-intro #3984]: #3985
#1641 := (~ #299 #299)
#1673 := (~ #295 #295)
#1674 := [refl]: #1673
#1639 := [nnf-pos #1674]: #1641
#14 := (= #13 #11)
#15 := (forall (vars (?x2 T2) (?x3 T2)) #14)
#300 := (iff #15 #299)
#297 := (iff #14 #295)
#298 := [rewrite]: #297
#301 := [quant-intro #298]: #300
#294 := [asserted]: #15
#304 := [mp #294 #301]: #299
#1675 := [mp~ #304 #1639]: #299
#3987 := [mp #1675 #3986]: #3982
#7756 := (not #3982)
#10489 := (or #7756 #10483)
#10490 := [quant-inst]: #10489
#13345 := [unit-resolution #10490 #3987]: #10483
#13347 := [symm #13345]: #13346
#13522 := [monotonicity #13347]: #13521
#13524 := [trans #13522 #10381]: #13523
#27228 := [monotonicity #13524 #27216]: #27227
#27230 := [symm #27228]: #27229
#27232 := [monotonicity #27230]: #27231
#27226 := [hypothesis]: #16801
#27233 := [mp #27226 #27232]: #27109
#27075 := (= #10482 #19843)
#25893 := (up_6 uf_15 #19843)
#27081 := (or #25893 #27075)
#27086 := (iff #27073 #27081)
#30 := (:var 1 T5)
#20 := (:var 2 T2)
#29 := (:var 3 T4)
#31 := (uf_7 #29 #20 #30)
#32 := (up_6 #31 #11)
#4001 := (pattern #32)
#35 := (up_6 #29 #11)
#34 := (= #30 uf_8)
#24 := (= #11 #20)
#36 := (ite #24 #34 #35)
#37 := (iff #32 #36)
#4002 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) (:pat #4001) #37)
#38 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) #37)
#4005 := (iff #38 #4002)
#4003 := (iff #37 #37)
#4004 := [refl]: #4003
#4006 := [quant-intro #4004]: #4005
#1646 := (~ #38 #38)
#1682 := (~ #37 #37)
#1683 := [refl]: #1682
#1647 := [nnf-pos #1683]: #1646
#311 := [asserted]: #38
#1684 := [mp~ #311 #1647]: #38
#4007 := [mp #1684 #4006]: #4002
#6538 := (not #4002)
#27089 := (or #6538 #27086)
#3681 := (= uf_8 uf_8)
#27069 := (= #19843 #10482)
#27070 := (ite #27069 #3681 #25893)
#27074 := (iff #27073 #27070)
#27090 := (or #6538 #27074)
#27092 := (iff #27090 #27089)
#27094 := (iff #27089 #27089)
#27095 := [rewrite]: #27094
#27087 := (iff #27074 #27086)
#27084 := (iff #27070 #27081)
#27078 := (ite #27075 true #25893)
#27082 := (iff #27078 #27081)
#27083 := [rewrite]: #27082
#27079 := (iff #27070 #27078)
#3684 := (iff #3681 true)
#3673 := [rewrite]: #3684
#27076 := (iff #27069 #27075)
#27077 := [rewrite]: #27076
#27080 := [monotonicity #27077 #3673]: #27079
#27085 := [trans #27080 #27083]: #27084
#27088 := [monotonicity #27085]: #27087
#27093 := [monotonicity #27088]: #27092
#27096 := [trans #27093 #27095]: #27092
#27091 := [quant-inst]: #27090
#27097 := [mp #27091 #27096]: #27089
#27196 := [unit-resolution #27097 #4007]: #27086
#27106 := (not #27086)
#27223 := (or #27106 #27073)
#5835 := (up_6 uf_15 #5823)
#27219 := (iff #5835 #25893)
#27217 := (iff #25893 #5835)
#27218 := [monotonicity #27216]: #27217
#27220 := [symm #27218]: #27219
#5836 := (not #5835)
#5828 := (uf_1 #5823 ?x75!20)
#5829 := (uf_10 #5828)
#5830 := (* -1::int #5829)
#5824 := (uf_4 uf_14 #5823)
#5825 := (* -1::int #5824)
#5831 := (+ #5825 #5830)
#5561 := (uf_4 uf_14 ?x75!20)
#5832 := (+ #5561 #5831)
#5833 := (= #5832 0::int)
#5834 := (not #5833)
#5826 := (+ #5561 #5825)
#5827 := (<= #5826 0::int)
#5842 := (or #5827 #5834 #5836)
#5845 := (not #5842)
#5591 := (* -1::int #5561)
#5839 := (+ uf_9 #5591)
#5840 := (<= #5839 0::int)
#22585 := (not #5840)
#6522 := [hypothesis]: #3240
#3920 := (not #2683)
#3921 := (or #3235 #3920)
#3915 := [def-axiom]: #3921
#6523 := [unit-resolution #3915 #6522]: #3920
#13600 := (or #3235 #2683)
#6436 := (uf_1 uf_22 ?x68!16)
#6437 := (uf_10 #6436)
#6462 := (+ #2681 #6437)
#6463 := (+ #177 #6462)
#13033 := (<= #6463 0::int)
#6466 := (= #6463 0::int)
#6403 := (uf_4 uf_14 ?x68!16)
#6420 := (* -1::int #6403)
#6455 := (+ #6420 #6437)
#6456 := (+ #177 #6455)
#6457 := (>= #6456 0::int)
#6441 := (* -1::int #6437)
#6445 := (+ uf_9 #6441)
#6446 := (<= #6445 0::int)
#6492 := (or #6446 #6457)
#6495 := (not #6492)
#6489 := (= #2095 #6403)
#9335 := (not #6489)
#6421 := (+ #2095 #6420)
#13056 := (>= #6421 0::int)
#13361 := (not #13056)
#12929 := (= ?x67!17 #10482)
#6205 := (up_6 uf_15 ?x67!17)
#12936 := (or #6205 #12929)
#12931 := (up_6 #11444 ?x67!17)
#12941 := (iff #12931 #12936)
#12895 := (or #6538 #12941)
#12930 := (ite #12929 #3681 #6205)
#12932 := (iff #12931 #12930)
#12896 := (or #6538 #12932)
#12898 := (iff #12896 #12895)
#12894 := (iff #12895 #12895)
#12900 := [rewrite]: #12894
#12942 := (iff #12932 #12941)
#12939 := (iff #12930 #12936)
#12933 := (ite #12929 true #6205)
#12937 := (iff #12933 #12936)
#12938 := [rewrite]: #12937
#12934 := (iff #12930 #12933)
#12935 := [monotonicity #3673]: #12934
#12940 := [trans #12935 #12938]: #12939
#12943 := [monotonicity #12940]: #12942
#12899 := [monotonicity #12943]: #12898
#12901 := [trans #12899 #12900]: #12898
#12897 := [quant-inst]: #12896
#12902 := [mp #12897 #12901]: #12895
#13389 := [unit-resolution #12902 #4007]: #12941
#11402 := (iff #2098 #12931)
#13390 := (iff #12931 #2098)
#11401 := [monotonicity #13524]: #13390
#13535 := [symm #11401]: #11402
#3775 := (or #3235 #2098)
#3776 := [def-axiom]: #3775
#6525 := [unit-resolution #3776 #6522]: #2098
#13536 := [mp #6525 #13535]: #12931
#12962 := (not #12931)
#12959 := (not #12941)
#12963 := (or #12959 #12962 #12936)
#12964 := [def-axiom]: #12963
#13537 := [unit-resolution #12964 #13536 #13389]: #12936
#10975 := [hypothesis]: #3920
#6233 := (+ #177 #6420)
#6234 := (<= #6233 0::int)
#3749 := (up_6 uf_15 ?x68!16)
#12831 := (not #3749)
#12761 := (= ?x68!16 #10482)
#12767 := (or #3749 #12761)
#12836 := (not #12767)
#12763 := (up_6 #11444 ?x68!16)
#12796 := (iff #12763 #12767)
#12793 := (or #6538 #12796)
#12762 := (ite #12761 #3681 #3749)
#12764 := (iff #12763 #12762)
#12799 := (or #6538 #12764)
#12801 := (iff #12799 #12793)
#12803 := (iff #12793 #12793)
#12828 := [rewrite]: #12803
#12797 := (iff #12764 #12796)
#12794 := (iff #12762 #12767)
#12759 := (ite #12761 true #3749)
#12768 := (iff #12759 #12767)
#12769 := [rewrite]: #12768
#12765 := (iff #12762 #12759)
#12766 := [monotonicity #3673]: #12765
#12795 := [trans #12766 #12769]: #12794
#12798 := [monotonicity #12795]: #12797
#12802 := [monotonicity #12798]: #12801
#12829 := [trans #12802 #12828]: #12801
#12800 := [quant-inst]: #12799
#12830 := [mp #12800 #12829]: #12793
#13565 := [unit-resolution #12830 #4007]: #12796
#12866 := (not #12763)
#13564 := (iff #2100 #12866)
#13568 := (iff #2099 #12763)
#13566 := (iff #12763 #2099)
#13567 := [monotonicity #13524]: #13566
#13569 := [symm #13567]: #13568
#13570 := [monotonicity #13569]: #13564
#3918 := (or #3235 #2100)
#3919 := [def-axiom]: #3918
#6524 := [unit-resolution #3919 #6522]: #2100
#13571 := [mp #6524 #13570]: #12866
#12863 := (not #12796)
#12864 := (or #12863 #12763 #12836)
#12865 := [def-axiom]: #12864
#13572 := [unit-resolution #12865 #13571 #13565]: #12836
#12832 := (or #12767 #12831)
#12827 := [def-axiom]: #12832
#13573 := [unit-resolution #12827 #13572]: #12831
#6238 := (or #3749 #6234)
#3838 := (or #4352 #4203)
#3839 := [def-axiom]: #3838
#10794 := [unit-resolution #3839 #10367]: #4203
#13087 := (or #4208 #3749 #6234)
#6251 := (+ #6403 #1268)
#6252 := (>= #6251 0::int)
#6253 := (or #3749 #6252)
#13085 := (or #4208 #6253)
#13095 := (iff #13085 #13087)
#13091 := (or #4208 #6238)
#13093 := (iff #13091 #13087)
#13094 := [rewrite]: #13093
#13084 := (iff #13085 #13091)
#6239 := (iff #6253 #6238)
#6236 := (iff #6252 #6234)
#6254 := (+ #1268 #6403)
#6257 := (>= #6254 0::int)
#6232 := (iff #6257 #6234)
#6235 := [rewrite]: #6232
#6258 := (iff #6252 #6257)
#6255 := (= #6251 #6254)
#6256 := [rewrite]: #6255
#6259 := [monotonicity #6256]: #6258
#6237 := [trans #6259 #6235]: #6236
#6240 := [monotonicity #6237]: #6239
#13092 := [monotonicity #6240]: #13084
#13096 := [trans #13092 #13094]: #13095
#13090 := [quant-inst]: #13085
#13098 := [mp #13090 #13096]: #13087
#13574 := [unit-resolution #13098 #10794]: #6238
#10559 := [unit-resolution #13574 #13573]: #6234
#12956 := (not #12936)
#13360 := (not #6234)
#13379 := (or #13361 #2683 #13360 #12956)
#4526 := (uf_24 uf_22)
#4567 := (* -1::int #4526)
#6154 := (+ #2093 #4567)
#13335 := (<= #6154 0::int)
#13334 := (= #2093 #4526)
#6206 := (= ?x67!17 uf_22)
#13343 := [hypothesis]: #12936
#10290 := (not #6205)
#10815 := (uf_4 uf_14 #10482)
#10842 := (* -1::int #10815)
#6176 := (uf_4 uf_14 ?x67!17)
#13287 := (+ #6176 #10842)
#13288 := (<= #13287 0::int)
#13464 := (not #13288)
#13357 := [hypothesis]: #6234
#5358 := (* -1::int #6176)
#5458 := (+ #2093 #5358)
#5459 := (<= #5458 0::int)
#3715 := (or #4352 #4346)
#3826 := [def-axiom]: #3715
#10824 := [unit-resolution #3826 #10367]: #4346
#3847 := (or #4352 #4213)
#3820 := [def-axiom]: #3847
#10373 := [unit-resolution #3820 #10367]: #4213
#3821 := (or #4352 #4221)
#3822 := [def-axiom]: #3821
#10825 := [unit-resolution #3822 #10367]: #4221
#6791 := (or #2650 #4226 #4218)
#6483 := (uf_1 uf_22 ?x61!13)
#6484 := (uf_10 #6483)
#6567 := (+ #2036 #6484)
#6568 := (+ #177 #6567)
#6588 := (>= #6568 0::int)
#6570 := (= #6568 0::int)
#6544 := (* -1::int #6484)
#6540 := (+ uf_9 #6544)
#6548 := (<= #6540 0::int)
#6625 := (not #6548)
#6558 := (+ #2648 #6484)
#6553 := (+ #177 #6558)
#6559 := (>= #6553 0::int)
#6596 := (or #6548 #6559)
#6598 := (not #6596)
#6593 := (= #2035 #2037)
#6749 := (not #6593)
#6733 := [hypothesis]: #2655
#6752 := (or #6749 #2650)
#6753 := [th-lemma]: #6752
#6748 := [unit-resolution #6753 #6733]: #6749
#6754 := [hypothesis]: #4213
#6603 := (or #4218 #6593 #6598)
#6545 := (+ #1268 #6544)
#6546 := (+ #2037 #6545)
#6547 := (<= #6546 0::int)
#6589 := (or #6548 #6547)
#6591 := (not #6589)
#6592 := (= #2037 #2035)
#6590 := (or #6592 #6591)
#6604 := (or #4218 #6590)
#6621 := (iff #6604 #6603)
#6601 := (or #6593 #6598)
#6606 := (or #4218 #6601)
#6619 := (iff #6606 #6603)
#6620 := [rewrite]: #6619
#6617 := (iff #6604 #6606)
#6564 := (iff #6590 #6601)
#6599 := (iff #6591 #6598)
#6597 := (iff #6589 #6596)
#6562 := (iff #6547 #6559)
#6550 := (+ #2037 #6544)
#6551 := (+ #1268 #6550)
#6555 := (<= #6551 0::int)
#6560 := (iff #6555 #6559)
#6561 := [rewrite]: #6560
#6556 := (iff #6547 #6555)
#6552 := (= #6546 #6551)
#6554 := [rewrite]: #6552
#6557 := [monotonicity #6554]: #6556
#6563 := [trans #6557 #6561]: #6562
#6565 := [monotonicity #6563]: #6597
#6600 := [monotonicity #6565]: #6599
#6594 := (iff #6592 #6593)
#6595 := [rewrite]: #6594
#6602 := [monotonicity #6595 #6600]: #6564
#6618 := [monotonicity #6602]: #6617
#6622 := [trans #6618 #6620]: #6621
#6605 := [quant-inst]: #6604
#6623 := [mp #6605 #6622]: #6603
#6755 := [unit-resolution #6623 #6754 #6748]: #6598
#6626 := (or #6596 #6625)
#6627 := [def-axiom]: #6626
#6756 := [unit-resolution #6627 #6755]: #6625
#6628 := (not #6559)
#6629 := (or #6596 #6628)
#6630 := [def-axiom]: #6629
#6757 := [unit-resolution #6630 #6755]: #6628
#6574 := (or #6548 #6559 #6570)
#6758 := [hypothesis]: #4221
#6576 := (or #4226 #6548 #6559 #6570)
#6542 := (+ #6484 #2036)
#6543 := (+ #177 #6542)
#6541 := (= #6543 0::int)
#6549 := (or #6548 #6547 #6541)
#6577 := (or #4226 #6549)
#6585 := (iff #6577 #6576)
#6580 := (or #4226 #6574)
#6582 := (iff #6580 #6576)
#6583 := [rewrite]: #6582
#6578 := (iff #6577 #6580)
#6572 := (iff #6549 #6574)
#6571 := (iff #6541 #6570)
#6566 := (= #6543 #6568)
#6569 := [rewrite]: #6566
#6573 := [monotonicity #6569]: #6571
#6575 := [monotonicity #6563 #6573]: #6572
#6581 := [monotonicity #6575]: #6578
#6586 := [trans #6581 #6583]: #6585
#6579 := [quant-inst]: #6577
#6584 := [mp #6579 #6586]: #6576
#6782 := [unit-resolution #6584 #6758]: #6574
#6783 := [unit-resolution #6782 #6757 #6756]: #6570
#6784 := (not #6570)
#6785 := (or #6784 #6588)
#6786 := [th-lemma]: #6785
#6781 := [unit-resolution #6786 #6783]: #6588
#6624 := (>= #2649 0::int)
#6787 := (or #6624 #2650)
#6788 := [th-lemma]: #6787
#6789 := [unit-resolution #6788 #6733]: #6624
#6790 := [th-lemma #6789 #6757 #6781]: false
#6815 := [lemma #6790]: #6791
#10826 := [unit-resolution #6815 #10825 #10373]: #2650
#3853 := (or #4349 #2655 #4343)
#3854 := [def-axiom]: #3853
#10827 := [unit-resolution #3854 #10826 #10824]: #4343
#3866 := (or #4340 #4229)
#3867 := [def-axiom]: #3866
#10835 := [unit-resolution #3867 #10827]: #4229
#10497 := (or #4234 #5459)
#5451 := (+ #6176 #2094)
#5452 := (>= #5451 0::int)
#10498 := (or #4234 #5452)
#10502 := (iff #10498 #10497)
#10504 := (iff #10497 #10497)
#10505 := [rewrite]: #10504
#5485 := (iff #5452 #5459)
#5453 := (+ #2094 #6176)
#5450 := (>= #5453 0::int)
#5460 := (iff #5450 #5459)
#5484 := [rewrite]: #5460
#5456 := (iff #5452 #5450)
#5454 := (= #5451 #5453)
#5455 := [rewrite]: #5454
#5457 := [monotonicity #5455]: #5456
#5486 := [trans #5457 #5484]: #5485
#10503 := [monotonicity #5486]: #10502
#10506 := [trans #10503 #10505]: #10502
#10501 := [quant-inst]: #10498
#10507 := [mp #10501 #10506]: #10497
#11063 := [unit-resolution #10507 #10835]: #5459
#10550 := (+ #177 #10842)
#10551 := (>= #10550 0::int)
#10851 := (= #177 #10815)
#13455 := (= #10815 #177)
#13456 := [monotonicity #13347]: #13455
#13457 := [symm #13456]: #10851
#13458 := (not #10851)
#13459 := (or #13458 #10551)
#13460 := [th-lemma]: #13459
#13461 := [unit-resolution #13460 #13457]: #10551
#13358 := [hypothesis]: #13056
#13331 := (not #10551)
#11754 := (not #5459)
#13362 := (or #13464 #11754 #2683 #13360 #13331 #13361)
#13363 := [th-lemma]: #13362
#13364 := [unit-resolution #13363 #13358 #13461 #11063 #13357 #10975]: #13464
#13586 := (or #10290 #13288)
#13575 := [hypothesis]: #13464
#10840 := (up_6 uf_15 #10482)
#13580 := (not #10840)
#13581 := (iff #176 #13580)
#13578 := (iff #175 #10840)
#13576 := (iff #10840 #175)
#13577 := [monotonicity #13347]: #13576
#13579 := [symm #13577]: #13578
#13582 := [monotonicity #13579]: #13581
#3855 := (or #4352 #176)
#3850 := [def-axiom]: #3855
#10368 := [unit-resolution #3850 #10367]: #176
#13583 := [mp #10368 #13582]: #13580
#13584 := [hypothesis]: #6205
#3799 := (or #4364 #4108)
#3823 := [def-axiom]: #3799
#10473 := [unit-resolution #3823 #10034]: #4108
#13489 := (or #4113 #10290 #10840 #13288)
#13250 := (+ #10815 #5358)
#13251 := (>= #13250 0::int)
#13282 := (or #10840 #10290 #13251)
#13491 := (or #4113 #13282)
#13502 := (iff #13491 #13489)
#13306 := (or #10290 #10840 #13288)
#13497 := (or #4113 #13306)
#13500 := (iff #13497 #13489)
#13501 := [rewrite]: #13500
#13498 := (iff #13491 #13497)
#13319 := (iff #13282 #13306)
#13311 := (or #10840 #10290 #13288)
#13315 := (iff #13311 #13306)
#13318 := [rewrite]: #13315
#13316 := (iff #13282 #13311)
#13309 := (iff #13251 #13288)
#13283 := (+ #5358 #10815)
#13286 := (>= #13283 0::int)
#13289 := (iff #13286 #13288)
#13290 := [rewrite]: #13289
#13280 := (iff #13251 #13286)
#13284 := (= #13250 #13283)
#13285 := [rewrite]: #13284
#13281 := [monotonicity #13285]: #13280
#13310 := [trans #13281 #13290]: #13309
#13317 := [monotonicity #13310]: #13316
#13320 := [trans #13317 #13318]: #13319
#13499 := [monotonicity #13320]: #13498
#13369 := [trans #13499 #13501]: #13502
#13492 := [quant-inst]: #13491
#13383 := [mp #13492 #13369]: #13489
#13585 := [unit-resolution #13383 #10473 #13584 #13583 #13575]: false
#13587 := [lemma #13585]: #13586
#13359 := [unit-resolution #13587 #13364]: #10290
#12957 := (or #12956 #6205 #12929)
#12958 := [def-axiom]: #12957
#13336 := [unit-resolution #12958 #13359 #13343]: #12929
#13380 := [trans #13336 #13347]: #6206
#13381 := [monotonicity #13380]: #13334
#13374 := (not #13334)
#13382 := (or #13374 #13335)
#13438 := [th-lemma]: #13382
#13375 := [unit-resolution #13438 #13381]: #13335
#4768 := (+ #177 #4567)
#4769 := (>= #4768 0::int)
#9856 := (or #4234 #4769)
#9857 := [quant-inst]: #9856
#10836 := [unit-resolution #9857 #10835]: #4769
#13378 := [th-lemma #10975 #13357 #13358 #10836 #13375]: false
#13372 := [lemma #13378]: #13379
#10577 := [unit-resolution #13372 #10559 #10975 #13537]: #13361
#11369 := (or #9335 #13056)
#13408 := [th-lemma]: #11369
#13409 := [unit-resolution #13408 #10577]: #9335
#6498 := (or #6489 #6495)
#13035 := (or #4218 #6489 #6495)
#6442 := (+ #1268 #6441)
#6443 := (+ #6403 #6442)
#6444 := (<= #6443 0::int)
#6485 := (or #6446 #6444)
#6486 := (not #6485)
#6487 := (= #6403 #2095)
#6488 := (or #6487 #6486)
#13036 := (or #4218 #6488)
#13053 := (iff #13036 #13035)
#13049 := (or #4218 #6498)
#13052 := (iff #13049 #13035)
#13047 := [rewrite]: #13052
#13050 := (iff #13036 #13049)
#6499 := (iff #6488 #6498)
#6496 := (iff #6486 #6495)
#6493 := (iff #6485 #6492)
#6460 := (iff #6444 #6457)
#6448 := (+ #6403 #6441)
#6449 := (+ #1268 #6448)
#6452 := (<= #6449 0::int)
#6458 := (iff #6452 #6457)
#6459 := [rewrite]: #6458
#6453 := (iff #6444 #6452)
#6450 := (= #6443 #6449)
#6451 := [rewrite]: #6450
#6454 := [monotonicity #6451]: #6453
#6461 := [trans #6454 #6459]: #6460
#6494 := [monotonicity #6461]: #6493
#6497 := [monotonicity #6494]: #6496
#6490 := (iff #6487 #6489)
#6491 := [rewrite]: #6490
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#13054 := [trans #13051 #13047]: #13053
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#6469 := (or #6446 #6457 #6466)
#13012 := (or #4226 #6446 #6457 #6466)
#6438 := (+ #6437 #2681)
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#13013 := (or #4226 #6447)
#13031 := (iff #13013 #13012)
#13015 := (or #4226 #6469)
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#13030 := [rewrite]: #13029
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#6467 := (iff #6440 #6466)
#6464 := (= #6439 #6463)
#6465 := [rewrite]: #6464
#6468 := [monotonicity #6465]: #6467
#6471 := [monotonicity #6461 #6468]: #6470
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#13014 := [quant-inst]: #13013
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#13367 := [unit-resolution #13032 #10825]: #6469
#13368 := [unit-resolution #13367 #13366 #13365 #13435]: false
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#12925 := (uf_10 #12924)
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#13445 := (= #12925 #6437)
#13443 := (= #12924 #6436)
#13444 := [monotonicity #13347]: #13443
#13446 := [monotonicity #13444]: #13445
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#13448 := (not #13436)
#13449 := (or #13448 #13441)
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#1656 := (~ #378 #378)
#1655 := (~ #375 #375)
#1693 := [refl]: #1655
#1657 := [nnf-pos #1693]: #1656
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#62 := (implies #60 #61)
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#379 := (iff #368 #378)
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#374 := [rewrite]: #373
#377 := [monotonicity #374]: #376
#380 := [quant-intro #377]: #379
#369 := (iff #63 #368)
#366 := (iff #62 #365)
#367 := [rewrite]: #366
#370 := [quant-intro #367]: #369
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#13412 := (= #10482 ?x68!16)
#13413 := (or #13412 #13411)
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#13427 := (iff #13420 #13419)
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#13426 := [rewrite]: #13425
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#13417 := (iff #13413 #13416)
#13414 := (iff #13412 #12761)
#13415 := [rewrite]: #13414
#13418 := [monotonicity #13415]: #13417
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#13428 := [trans #13424 #13426]: #13427
#13421 := [quant-inst]: #13420
#13429 := [mp #13421 #13428]: #13419
#13592 := [unit-resolution #13429 #4034 #13591]: #13411
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#13465 := (or #13463 #2683 #13464 #12761)
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#13453 := [unit-resolution #13429 #4034 #13452]: #13411
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#13593 := [unit-resolution #13466 #13590 #10975 #13591]: #13464
#13594 := [unit-resolution #13587 #13593]: #10290
#13595 := [unit-resolution #12958 #13594 #13537]: #12929
#13596 := [trans #13595 #13347]: #6206
#13597 := [monotonicity #13596]: #13334
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#7663 := [rewrite]: #7662
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#7723 := [monotonicity #7695]: #7704
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#7700 := [quant-inst]: #7694
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#10375 := [unit-resolution #7483 #10373 #10372]: #7631
#7871 := (or #7636 #7832)
#7872 := [def-axiom]: #7871
#10377 := [unit-resolution #7872 #10375]: #7832
#8188 := (= uf_22 ?x63!14)
#8259 := (not #8188)
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#7408 := (+ #177 #6712)
#8885 := (>= #7408 0::int)
#8884 := (= #177 #2054)
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#8129 := (= ?x63!14 uf_22)
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#8985 := (or #8984 #8885)
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#4026 := (iff #358 #4023)
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#4025 := [refl]: #4024
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#1652 := (~ #358 #358)
#1691 := (~ #355 #355)
#1692 := [refl]: #1691
#1653 := [nnf-pos #1692]: #1652
#58 := (implies #55 #57)
#59 := (forall (vars (?x20 T2) (?x21 T2)) #58)
#361 := (iff #59 #358)
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#359 := (iff #350 #358)
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#354 := [rewrite]: #353
#357 := [monotonicity #354]: #356
#360 := [quant-intro #357]: #359
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#342 := (implies #55 #334)
#346 := (iff #342 #345)
#347 := [rewrite]: #346
#343 := (iff #58 #342)
#340 := (iff #57 #334)
#341 := [rewrite]: #340
#344 := [monotonicity #341]: #343
#349 := [trans #344 #347]: #348
#352 := [quant-intro #349]: #351
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#363 := [mp #332 #362]: #358
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#8402 := (or #7068 #8259 #8398)
#8403 := (or #7068 #8399)
#8405 := (iff #8403 #8402)
#8406 := [rewrite]: #8405
#8404 := [quant-inst]: #8403
#8407 := [mp #8404 #8406]: #8402
#8986 := [unit-resolution #8407 #4028]: #8399
#8987 := [unit-resolution #8986 #8946]: #8398
#9015 := (not #8398)
#9016 := (or #9015 #8408)
#8982 := [th-lemma]: #9016
#9017 := [unit-resolution #8982 #8987]: #8408
#9014 := [th-lemma #9017 #10121 #8977]: false
#9021 := [lemma #9014]: #9020
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#7164 := (up_6 uf_15 ?x63!14)
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#8206 := (iff #8173 #8193)
#8209 := (or #6538 #8206)
#8130 := (ite #8129 #3681 #7164)
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#8196 := (iff #8130 #8193)
#8191 := (ite #8188 true #7164)
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#8195 := [rewrite]: #8194
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#8192 := [monotonicity #8190 #3673]: #8186
#8205 := [trans #8192 #8195]: #8196
#8208 := [monotonicity #8205]: #8207
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#8210 := [quant-inst]: #8204
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#8291 := (or #8287 #8290 #8193)
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#10142 := (or #8188 #7637 #4113 #8528 #8262)
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#10112 := (iff #7164 #10074)
#10110 := (iff #10074 #7164)
#10108 := (= #8400 ?x63!14)
#8401 := (= ?x63!14 #8400)
#8411 := (or #7756 #8401)
#8412 := [quant-inst]: #8411
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#10109 := [symm #10107]: #10108
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#10082 := [quant-inst]: #10081
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#10122 := [unit-resolution #8397 #4034]: #8160
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#10095 := (+ #2054 #10071)
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#8816 := (>= #8803 0::int)
#8802 := (= #177 #8525)
#10134 := (= #8525 #177)
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#7330 := (ite #4606 true #4650)
#7334 := (iff #7330 #7333)
#7335 := [rewrite]: #7334
#7331 := (iff #7327 #7330)
#7332 := [monotonicity #3673]: #7331
#7337 := [trans #7332 #7335]: #7336
#7340 := [monotonicity #7337]: #7339
#6820 := [monotonicity #7340]: #6814
#6823 := [trans #6820 #6822]: #6814
#6819 := [quant-inst]: #6818
#6824 := [mp #6819 #6823]: #3737
#7083 := [unit-resolution #6824 #4007]: #7338
#6842 := (not #7328)
#4795 := (up_6 uf_23 uf_11)
#4796 := (not #4795)
#7169 := (iff #4796 #6842)
#7167 := (iff #4795 #7328)
#7115 := (iff #7328 #4795)
#7114 := [symm #7112]: #7113
#7116 := [monotonicity #7114]: #7115
#7168 := [symm #7116]: #7167
#7170 := [monotonicity #7168]: #7169
#7084 := (not #4709)
#7109 := [hypothesis]: #7084
#4798 := (or #4709 #4796)
#7110 := [hypothesis]: #4238
#6714 := (or #4243 #4709 #4796)
#4797 := (or #4796 #4709)
#6729 := (or #4243 #4797)
#6720 := (iff #6729 #6714)
#6728 := (or #4243 #4798)
#6718 := (iff #6728 #6714)
#6719 := [rewrite]: #6718
#6731 := (iff #6729 #6728)
#4799 := (iff #4797 #4798)
#4800 := [rewrite]: #4799
#6717 := [monotonicity #4800]: #6731
#6721 := [trans #6717 #6719]: #6720
#6730 := [quant-inst]: #6729
#6716 := [mp #6730 #6721]: #6714
#7111 := [unit-resolution #6716 #7110]: #4798
#7106 := [unit-resolution #7111 #7109]: #4796
#7171 := [mp #7106 #7170]: #6842
#6840 := (not #7338)
#6841 := (or #6840 #7328 #6837)
#6836 := [def-axiom]: #6841
#7172 := [unit-resolution #6836 #7171 #7083]: #6837
#6829 := (or #7333 #6828)
#6827 := [def-axiom]: #6829
#7173 := [unit-resolution #6827 #7172]: #6828
#6986 := (or #4606 #6984)
#6989 := (or #7051 #4606 #6984)
#4604 := (= uf_22 uf_11)
#6985 := (or #4604 #6984)
#6990 := (or #7051 #6985)
#6978 := (iff #6990 #6989)
#6974 := (or #7051 #6986)
#6977 := (iff #6974 #6989)
#6972 := [rewrite]: #6977
#6975 := (iff #6990 #6974)
#6987 := (iff #6985 #6986)
#4607 := (iff #4604 #4606)
#4608 := [rewrite]: #4607
#6988 := [monotonicity #4608]: #6987
#6976 := [monotonicity #6988]: #6975
#6979 := [trans #6976 #6972]: #6978
#6973 := [quant-inst]: #6990
#6980 := [mp #6973 #6979]: #6989
#7174 := [unit-resolution #6980 #4034]: #6986
#7175 := [unit-resolution #7174 #7173]: #6984
#4672 := (* -1::int #4668)
#4673 := (+ #1268 #4672)
#4674 := (+ #105 #4673)
#4675 := (<= #4674 0::int)
#6530 := (not #4675)
#4676 := (+ uf_9 #4672)
#4677 := (<= #4676 0::int)
#4711 := (or #4675 #4677)
#4714 := (not #4711)
#4717 := (or #4709 #4714)
#6326 := (or #4218 #4709 #4714)
#4707 := (or #4677 #4675)
#4708 := (not #4707)
#4710 := (or #4709 #4708)
#6355 := (or #4218 #4710)
#6360 := (iff #6355 #6326)
#6357 := (or #4218 #4717)
#6354 := (iff #6357 #6326)
#6359 := [rewrite]: #6354
#6352 := (iff #6355 #6357)
#4718 := (iff #4710 #4717)
#4715 := (iff #4708 #4714)
#4712 := (iff #4707 #4711)
#4713 := [rewrite]: #4712
#4716 := [monotonicity #4713]: #4715
#4719 := [monotonicity #4716]: #4718
#6358 := [monotonicity #4719]: #6352
#6361 := [trans #6358 #6359]: #6360
#6356 := [quant-inst]: #6355
#6362 := [mp #6356 #6361]: #6326
#7155 := [unit-resolution #6362 #6754]: #4717
#7156 := [unit-resolution #7155 #7109]: #4714
#6531 := (or #4711 #6530)
#6532 := [def-axiom]: #6531
#7157 := [unit-resolution #6532 #7156]: #6530
#7158 := [hypothesis]: #4645
#7159 := [hypothesis]: #4721
#7154 := [th-lemma #7159 #7158 #7157 #7175]: false
#7163 := [lemma #7154]: #7162
#7744 := [unit-resolution #7163 #7743 #7722 #7112 #7742 #6754]: #4709
#7745 := [mp #7744 #7749]: #205
#3872 := (or #4325 #1305 #4319)
#3874 := [def-axiom]: #3872
#7750 := [unit-resolution #3874 #7745 #7729]: #4319
#3879 := (or #4316 #4310)
#3881 := [def-axiom]: #3879
#7761 := [unit-resolution #3881 #7750]: #4310
#3893 := (or #4313 #2079 #4307)
#3887 := [def-axiom]: #3893
#7762 := [unit-resolution #3887 #7761 #7727]: #2079
#7916 := (not #7489)
#7917 := (or #7878 #2078 #7916)
#7875 := [hypothesis]: #7489
#7876 := [hypothesis]: #7870
#8371 := [hypothesis]: #2079
#7877 := [th-lemma #8371 #7876 #7875]: false
#7918 := [lemma #7877]: #7917
#7763 := [unit-resolution #7918 #7762 #7726]: #7878
#7796 := (or #8359 #7870)
#7792 := [hypothesis]: #7878
#7793 := [hypothesis]: #6838
#7797 := [th-lemma]: #7796
#7798 := [unit-resolution #7797 #7793 #7792]: false
#7799 := [lemma #7798]: #7796
#7790 := [unit-resolution #7799 #7763]: #8359
#7359 := (or #6838 #7356)
#7362 := (or #4218 #6838 #7356)
#7207 := (+ #1268 #7206)
#7208 := (+ #6830 #7207)
#7209 := (<= #7208 0::int)
#7304 := (or #7261 #7209)
#7305 := (not #7304)
#6831 := (= #6830 #2077)
#7306 := (or #6831 #7305)
#7363 := (or #4218 #7306)
#7343 := (iff #7363 #7362)
#7365 := (or #4218 #7359)
#7368 := (iff #7365 #7362)
#7342 := [rewrite]: #7368
#7366 := (iff #7363 #7365)
#7360 := (iff #7306 #7359)
#7357 := (iff #7305 #7356)
#7354 := (iff #7304 #7351)
#7307 := (or #7261 #7251)
#7352 := (iff #7307 #7351)
#7353 := [rewrite]: #7352
#7308 := (iff #7304 #7307)
#7248 := (iff #7209 #7251)
#7263 := (+ #6830 #7206)
#7264 := (+ #1268 #7263)
#7267 := (<= #7264 0::int)
#7252 := (iff #7267 #7251)
#7253 := [rewrite]: #7252
#7268 := (iff #7209 #7267)
#7265 := (= #7208 #7264)
#7266 := [rewrite]: #7265
#7269 := [monotonicity #7266]: #7268
#7254 := [trans #7269 #7253]: #7248
#7350 := [monotonicity #7254]: #7308
#7355 := [trans #7350 #7353]: #7354
#7358 := [monotonicity #7355]: #7357
#6839 := (iff #6831 #6838)
#6843 := [rewrite]: #6839
#7361 := [monotonicity #6843 #7358]: #7360
#7367 := [monotonicity #7361]: #7366
#7341 := [trans #7367 #7342]: #7343
#7364 := [quant-inst]: #7363
#7344 := [mp #7364 #7341]: #7362
#8361 := [unit-resolution #7344 #6754]: #7359
#7794 := [unit-resolution #8361 #7790]: #7356
#7346 := (or #7351 #7345)
#7347 := [def-axiom]: #7346
#7789 := [unit-resolution #7347 #7794]: #7345
#7348 := (not #7261)
#7349 := (or #7351 #7348)
#7411 := [def-axiom]: #7349
#7795 := [unit-resolution #7411 #7794]: #7348
#7313 := (or #7251 #7261 #7273)
#7318 := (or #4226 #7251 #7261 #7273)
#7204 := (+ #7203 #4856)
#7205 := (+ #177 #7204)
#7200 := (= #7205 0::int)
#7262 := (or #7261 #7209 #7200)
#7319 := (or #4226 #7262)
#7326 := (iff #7319 #7318)
#7321 := (or #4226 #7313)
#7324 := (iff #7321 #7318)
#7325 := [rewrite]: #7324
#7322 := (iff #7319 #7321)
#7316 := (iff #7262 #7313)
#7310 := (or #7261 #7251 #7273)
#7314 := (iff #7310 #7313)
#7315 := [rewrite]: #7314
#7311 := (iff #7262 #7310)
#7274 := (iff #7200 #7273)
#7257 := (= #7205 #7256)
#7258 := [rewrite]: #7257
#7309 := [monotonicity #7258]: #7274
#7312 := [monotonicity #7254 #7309]: #7311
#7317 := [trans #7312 #7315]: #7316
#7323 := [monotonicity #7317]: #7322
#7301 := [trans #7323 #7325]: #7326
#7320 := [quant-inst]: #7319
#7302 := [mp #7320 #7301]: #7318
#8365 := [unit-resolution #7302 #6758]: #7313
#7624 := [unit-resolution #8365 #7795 #7789]: #7273
#8367 := (not #7273)
#8368 := (or #8367 #7300)
#8369 := [th-lemma]: #8368
#7625 := [unit-resolution #8369 #7624]: #7300
#7701 := (>= #7203 0::int)
#7612 := (<= #7203 0::int)
#7613 := (not #7612)
#7514 := (= uf_22 ?x65!15)
#7375 := (not #7514)
#7416 := (up_6 uf_15 ?x65!15)
#7539 := (or #7416 #7514)
#4454 := (not #7539)
#7495 := (up_6 #183 ?x65!15)
#7522 := (iff #7495 #7539)
#7523 := (or #6538 #7522)
#7508 := (= ?x65!15 uf_22)
#7509 := (ite #7508 #3681 #7416)
#7510 := (iff #7495 #7509)
#7518 := (or #6538 #7510)
#7525 := (iff #7518 #7523)
#7378 := (iff #7523 #7523)
#7379 := [rewrite]: #7378
#7538 := (iff #7510 #7522)
#7520 := (iff #7509 #7539)
#7517 := (ite #7514 true #7416)
#7519 := (iff #7517 #7539)
#7497 := [rewrite]: #7519
#7513 := (iff #7509 #7517)
#7515 := (iff #7508 #7514)
#7516 := [rewrite]: #7515
#7531 := [monotonicity #7516 #3673]: #7513
#7521 := [trans #7531 #7497]: #7520
#7496 := [monotonicity #7521]: #7538
#7526 := [monotonicity #7496]: #7525
#7371 := [trans #7526 #7379]: #7525
#7524 := [quant-inst]: #7518
#7372 := [mp #7524 #7371]: #7523
#7616 := [unit-resolution #7372 #4007]: #7522
#7486 := (not #7495)
#4859 := (up_6 uf_23 ?x65!15)
#4860 := (not #4859)
#7823 := (iff #4860 #7486)
#7821 := (iff #4859 #7495)
#7819 := (iff #7495 #4859)
#7820 := [monotonicity #7114]: #7819
#7822 := [symm #7820]: #7821
#7818 := [monotonicity #7822]: #7823
#6844 := (or #4860 #6838)
#6854 := (or #4243 #4860 #6838)
#6832 := (or #4860 #6831)
#6855 := (or #4243 #6832)
#6953 := (iff #6855 #6854)
#6950 := (or #4243 #6844)
#6947 := (iff #6950 #6854)
#6948 := [rewrite]: #6947
#6951 := (iff #6855 #6950)
#6845 := (iff #6832 #6844)
#6846 := [monotonicity #6843]: #6845
#6952 := [monotonicity #6846]: #6951
#6954 := [trans #6952 #6948]: #6953
#6949 := [quant-inst]: #6855
#6955 := [mp #6949 #6954]: #6854
#7611 := [unit-resolution #6955 #7743]: #6844
#7791 := [unit-resolution #7611 #7790]: #4860
#7824 := [mp #7791 #7818]: #7486
#7382 := (not #7522)
#7485 := (or #7382 #7495 #4454)
#3736 := [def-axiom]: #7485
#7825 := [unit-resolution #3736 #7824 #7616]: #4454
#7376 := (or #7539 #7375)
#7377 := [def-axiom]: #7376
#7826 := [unit-resolution #7377 #7825]: #7375
#7614 := (or #7514 #7613)
#7661 := (or #7051 #7514 #7613)
#7665 := (or #7051 #7614)
#7668 := (iff #7665 #7661)
#7669 := [rewrite]: #7668
#7667 := [quant-inst]: #7665
#7670 := [mp #7667 #7669]: #7661
#7827 := [unit-resolution #7670 #4034]: #7614
#7828 := [unit-resolution #7827 #7826]: #7613
#7572 := (or #7701 #7612)
#7573 := [th-lemma]: #7572
#7622 := [unit-resolution #7573 #7828]: #7701
#7623 := [th-lemma #7622 #7762 #7625 #7722]: false
#7829 := [lemma #7623]: #7751
#10977 := [unit-resolution #7829 #10825 #10373 #8978 #10380 #10035]: #10976
#10978 := [unit-resolution #10977 #10830]: #4307
#3898 := (or #4304 #4298)
#3899 := [def-axiom]: #3898
#27197 := [unit-resolution #3899 #10978]: #4298
#3897 := (or #4301 #3240 #4295)
#3889 := [def-axiom]: #3897
#27200 := [unit-resolution #3889 #27197]: #4298
#27201 := [unit-resolution #27200 #13851]: #4295
#3811 := (or #4292 #4286)
#3812 := [def-axiom]: #3811
#27202 := [unit-resolution #3812 #27201]: #4286
#27203 := (or #4289 #4283)
#6911 := (uf_1 uf_22 ?x71!19)
#6912 := (uf_10 #6911)
#6865 := (uf_4 uf_14 ?x71!19)
#6895 := (* -1::int #6865)
#6930 := (+ #6895 #6912)
#6931 := (+ #177 #6930)
#6932 := (>= #6931 0::int)
#18852 := (not #6932)
#6916 := (* -1::int #6912)
#19137 := (+ #2123 #6916)
#19141 := (>= #19137 0::int)
#19136 := (= #2123 #6912)
#19003 := (= #2122 #6911)
#5904 := (= ?x72!18 uf_22)
#15400 := (= ?x72!18 #10482)
#5903 := (up_6 uf_15 ?x72!18)
#6616 := (not #5903)
#5874 := (uf_4 uf_14 ?x72!18)
#6991 := (+ #5874 #6895)
#6992 := (+ #2123 #6991)
#6993 := (>= #6992 0::int)
#19560 := (not #6993)
#6896 := (+ #2118 #6895)
#6897 := (<= #6896 0::int)
#18663 := (or #4234 #6897)
#6887 := (+ #6865 #2119)
#6888 := (>= #6887 0::int)
#18661 := (or #4234 #6888)
#18693 := (iff #18661 #18663)
#18718 := (iff #18663 #18663)
#18749 := [rewrite]: #18718
#6900 := (iff #6888 #6897)
#6889 := (+ #2119 #6865)
#6892 := (>= #6889 0::int)
#6898 := (iff #6892 #6897)
#6899 := [rewrite]: #6898
#6893 := (iff #6888 #6892)
#6890 := (= #6887 #6889)
#6891 := [rewrite]: #6890
#6894 := [monotonicity #6891]: #6893
#6901 := [trans #6894 #6899]: #6900
#18748 := [monotonicity #6901]: #18693
#18750 := [trans #18748 #18749]: #18693
#18692 := [quant-inst]: #18661
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#19541 := [unit-resolution #18745 #10835]: #6897
#3755 := (not #2710)
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#19548 := [unit-resolution #3909 #19547]: #3755
#5966 := (* -1::int #5874)
#5967 := (+ #2120 #5966)
#17815 := (>= #5967 0::int)
#5879 := (= #2120 #5874)
#3924 := (or #3281 #2130)
#3753 := [def-axiom]: #3924
#19549 := [unit-resolution #3753 #19547]: #2130
#10831 := [unit-resolution #3876 #10830]: #4238
#16861 := (or #4243 #3266 #5879)
#5875 := (= #5874 #2120)
#5878 := (or #3266 #5875)
#16856 := (or #4243 #5878)
#17034 := (iff #16856 #16861)
#5882 := (or #3266 #5879)
#16863 := (or #4243 #5882)
#16865 := (iff #16863 #16861)
#16726 := [rewrite]: #16865
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#5883 := (iff #5878 #5882)
#5880 := (iff #5875 #5879)
#5881 := [rewrite]: #5880
#5884 := [monotonicity #5881]: #5883
#16860 := [monotonicity #5884]: #16864
#17035 := [trans #16860 #16726]: #17034
#16862 := [quant-inst]: #16856
#17042 := [mp #16862 #17035]: #16861
#19515 := [unit-resolution #17042 #10831 #19549]: #5879
#19551 := (not #5879)
#19558 := (or #19551 #17815)
#19559 := [th-lemma]: #19558
#19557 := [unit-resolution #19559 #19515]: #17815
#19579 := (not #6897)
#19578 := (not #17815)
#19580 := (or #19560 #19578 #19579 #2710)
#19585 := [th-lemma]: #19580
#19586 := [unit-resolution #19585 #19557 #19548 #19541]: #19560
#19584 := (or #6616 #6993)
#3923 := (or #3281 #2129)
#3917 := [def-axiom]: #3923
#19575 := [unit-resolution #3917 #19547]: #2129
#18880 := (or #4104 #2128 #6616 #6993)
#6994 := (or #6616 #2128 #6993)
#18885 := (or #4104 #6994)
#18786 := (iff #18885 #18880)
#6995 := (or #2128 #6616 #6993)
#18887 := (or #4104 #6995)
#18855 := (iff #18887 #18880)
#18785 := [rewrite]: #18855
#18888 := (iff #18885 #18887)
#6996 := (iff #6994 #6995)
#6997 := [rewrite]: #6996
#18854 := [monotonicity #6997]: #18888
#18784 := [trans #18854 #18785]: #18786
#18886 := [quant-inst]: #18885
#18853 := [mp #18886 #18784]: #18880
#18782 := [unit-resolution #18853 #10042 #19575]: #19584
#19562 := [unit-resolution #18782 #19586]: #6616
#15415 := (or #5903 #15400)
#15410 := (up_6 #11444 ?x72!18)
#15420 := (iff #15410 #15415)
#17068 := (or #6538 #15420)
#15401 := (ite #15400 #3681 #5903)
#15411 := (iff #15410 #15401)
#17041 := (or #6538 #15411)
#17071 := (iff #17041 #17068)
#17075 := (iff #17068 #17068)
#17033 := [rewrite]: #17075
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#15418 := (iff #15401 #15415)
#15412 := (ite #15400 true #5903)
#15416 := (iff #15412 #15415)
#15417 := [rewrite]: #15416
#15413 := (iff #15401 #15412)
#15414 := [monotonicity #3673]: #15413
#15419 := [trans #15414 #15417]: #15418
#15422 := [monotonicity #15419]: #15421
#17069 := [monotonicity #15422]: #17071
#17076 := [trans #17069 #17033]: #17071
#17070 := [quant-inst]: #17041
#17077 := [mp #17070 #17076]: #17068
#19567 := [unit-resolution #17077 #4007]: #15420
#19566 := (iff #2130 #15410)
#19561 := (iff #15410 #2130)
#19568 := [monotonicity #13524]: #19561
#19576 := [symm #19568]: #19566
#19577 := [mp #19549 #19576]: #15410
#17132 := (not #15410)
#17134 := (not #15420)
#17137 := (or #17134 #17132 #15415)
#17138 := [def-axiom]: #17137
#19571 := [unit-resolution #17138 #19577 #19567]: #15415
#17112 := (not #15415)
#17133 := (or #17112 #5903 #15400)
#17128 := [def-axiom]: #17133
#19546 := [unit-resolution #17128 #19571 #19562]: #15400
#18949 := [trans #19546 #13347]: #5904
#19152 := [monotonicity #18949]: #19003
#19266 := [monotonicity #19152]: #19136
#19321 := (not #19136)
#18783 := (or #19321 #19141)
#19327 := [th-lemma]: #18783
#19424 := [unit-resolution #19327 #19266]: #19141
#7076 := (uf_2 #2122)
#7082 := (uf_4 uf_14 #7076)
#7096 := (* -1::int #7082)
#7097 := (+ #177 #7096)
#7098 := (<= #7097 0::int)
#19129 := (= #177 #7082)
#19009 := (= #7082 #177)
#19025 := (= #7076 uf_22)
#19026 := (= #7076 #10482)
#19488 := (= #7076 ?x72!18)
#7077 := (= ?x72!18 #7076)
#18938 := (or #8415 #7077)
#18939 := [quant-inst]: #18938
#19425 := [unit-resolution #18939 #3993]: #7077
#19489 := [symm #19425]: #19488
#19027 := [trans #19489 #19546]: #19026
#19116 := [trans #19027 #13347]: #19025
#19117 := [monotonicity #19116]: #19009
#19124 := [symm #19117]: #19129
#19125 := (not #19129)
#19118 := (or #19125 #7098)
#19126 := [th-lemma]: #19118
#19494 := [unit-resolution #19126 #19124]: #7098
#18959 := (+ #5874 #7096)
#18942 := (>= #18959 0::int)
#18958 := (= #5874 #7082)
#19503 := [monotonicity #19425]: #18958
#19714 := (not #18958)
#19715 := (or #19714 #18942)
#19716 := [th-lemma]: #19715
#19717 := [unit-resolution #19716 #19503]: #18942
#19840 := (not #19141)
#19719 := (not #18942)
#19718 := (not #7098)
#19720 := (or #18852 #19579 #2710 #19718 #19719 #19578 #19840)
#19721 := [th-lemma]: #19720
#19722 := [unit-resolution #19721 #19541 #19557 #19548 #19717 #19494 #19424]: #18852
#6920 := (+ uf_9 #6916)
#6921 := (<= #6920 0::int)
#18850 := (not #6921)
#19841 := (or #18850 #19840 #2128)
#19836 := [hypothesis]: #2129
#19837 := [hypothesis]: #6921
#19838 := [hypothesis]: #19141
#19839 := [th-lemma #19838 #19837 #19836]: false
#19842 := [lemma #19839]: #19841
#19748 := [unit-resolution #19842 #19424 #19575]: #18850
#6937 := (+ #2119 #6912)
#6938 := (+ #177 #6937)
#6941 := (= #6938 0::int)
#19752 := (not #6941)
#18700 := (>= #6938 0::int)
#19749 := (not #18700)
#19750 := (or #19749 #2710 #19718 #19719 #19578 #19840)
#19746 := [th-lemma]: #19750
#19747 := [unit-resolution #19746 #19557 #19548 #19717 #19494 #19424]: #19749
#19753 := (or #19752 #18700)
#19754 := [th-lemma]: #19753
#19751 := [unit-resolution #19754 #19747]: #19752
#6944 := (or #6921 #6932 #6941)
#18751 := (or #4226 #6921 #6932 #6941)
#6913 := (+ #6912 #2119)
#6914 := (+ #177 #6913)
#6915 := (= #6914 0::int)
#6917 := (+ #1268 #6916)
#6918 := (+ #6865 #6917)
#6919 := (<= #6918 0::int)
#6922 := (or #6921 #6919 #6915)
#18752 := (or #4226 #6922)
#18697 := (iff #18752 #18751)
#18811 := (or #4226 #6944)
#18691 := (iff #18811 #18751)
#18696 := [rewrite]: #18691
#18695 := (iff #18752 #18811)
#6945 := (iff #6922 #6944)
#6942 := (iff #6915 #6941)
#6939 := (= #6914 #6938)
#6940 := [rewrite]: #6939
#6943 := [monotonicity #6940]: #6942
#6935 := (iff #6919 #6932)
#6923 := (+ #6865 #6916)
#6924 := (+ #1268 #6923)
#6927 := (<= #6924 0::int)
#6933 := (iff #6927 #6932)
#6934 := [rewrite]: #6933
#6928 := (iff #6919 #6927)
#6925 := (= #6918 #6924)
#6926 := [rewrite]: #6925
#6929 := [monotonicity #6926]: #6928
#6936 := [trans #6929 #6934]: #6935
#6946 := [monotonicity #6936 #6943]: #6945
#18690 := [monotonicity #6946]: #18695
#18694 := [trans #18690 #18696]: #18697
#18816 := [quant-inst]: #18752
#18698 := [mp #18816 #18694]: #18751
#19755 := [unit-resolution #18698 #10825]: #6944
#19756 := [unit-resolution #19755 #19751 #19748 #19722]: false
#19782 := [lemma #19756]: #3281
#3808 := (or #4289 #3286 #4283)
#3809 := [def-axiom]: #3808
#27204 := [unit-resolution #3809 #19782]: #27203
#27205 := [unit-resolution #27204 #27202]: #4283
#3913 := (or #4280 #2160)
#3911 := [def-axiom]: #3913
#27206 := [unit-resolution #3911 #27205]: #2160
#5592 := (+ #2147 #5591)
#18461 := (>= #5592 0::int)
#5566 := (= #2147 #5561)
#3757 := (or #4280 #4272)
#3905 := [def-axiom]: #3757
#27207 := [unit-resolution #3905 #27205]: #4272
#18570 := (or #5566 #4277)
#15060 := (uf_10 #15059)
#15086 := (* -1::int #15060)
#11725 := (uf_24 #10482)
#11723 := (* -1::int #11725)
#15087 := (+ #11723 #15086)
#15088 := (+ #2147 #15087)
#15741 := (>= #15088 0::int)
#5607 := (uf_1 uf_22 ?x75!20)
#5608 := (uf_10 #5607)
#15832 := (+ #5608 #15086)
#15834 := (>= #15832 0::int)
#15831 := (= #5608 #15060)
#18427 := (= #15060 #5608)
#18425 := (= #15059 #5607)
#18426 := [monotonicity #13347]: #18425
#18428 := [monotonicity #18426]: #18427
#18429 := [symm #18428]: #15831
#18424 := (not #15831)
#18430 := (or #18424 #15834)
#18431 := [th-lemma]: #18430
#18432 := [unit-resolution #18431 #18429]: #15834
#11677 := (+ #4526 #11723)
#8662 := (>= #11677 0::int)
#8604 := (= #4526 #11725)
#18433 := (= #11725 #4526)
#18434 := [monotonicity #13347]: #18433
#18441 := [symm #18434]: #8604
#18442 := (not #8604)
#18440 := (or #18442 #8662)
#18443 := [th-lemma]: #18440
#18444 := [unit-resolution #18443 #18441]: #8662
#5633 := (+ #2148 #5608)
#5634 := (+ #177 #5633)
#15560 := (<= #5634 0::int)
#5637 := (= #5634 0::int)
#5612 := (* -1::int #5608)
#5616 := (+ uf_9 #5612)
#5617 := (<= #5616 0::int)
#15577 := (not #5617)
#5626 := (+ #5591 #5608)
#5627 := (+ #177 #5626)
#5628 := (>= #5627 0::int)
#5659 := (or #5617 #5628)
#5662 := (not #5659)
#18518 := (not #5566)
#18445 := [hypothesis]: #18518
#5665 := (or #5566 #5662)
#15564 := (or #4218 #5566 #5662)
#5613 := (+ #1268 #5612)
#5614 := (+ #5561 #5613)
#5615 := (<= #5614 0::int)
#5656 := (or #5617 #5615)
#5657 := (not #5656)
#5562 := (= #5561 #2147)
#5658 := (or #5562 #5657)
#15565 := (or #4218 #5658)
#15574 := (iff #15565 #15564)
#15567 := (or #4218 #5665)
#15570 := (iff #15567 #15564)
#15571 := [rewrite]: #15570
#15568 := (iff #15565 #15567)
#5666 := (iff #5658 #5665)
#5663 := (iff #5657 #5662)
#5660 := (iff #5656 #5659)
#5631 := (iff #5615 #5628)
#5619 := (+ #5561 #5612)
#5620 := (+ #1268 #5619)
#5623 := (<= #5620 0::int)
#5629 := (iff #5623 #5628)
#5630 := [rewrite]: #5629
#5624 := (iff #5615 #5623)
#5621 := (= #5614 #5620)
#5622 := [rewrite]: #5621
#5625 := [monotonicity #5622]: #5624
#5632 := [trans #5625 #5630]: #5631
#5661 := [monotonicity #5632]: #5660
#5664 := [monotonicity #5661]: #5663
#5567 := (iff #5562 #5566)
#5568 := [rewrite]: #5567
#5667 := [monotonicity #5568 #5664]: #5666
#15569 := [monotonicity #5667]: #15568
#15575 := [trans #15569 #15571]: #15574
#15566 := [quant-inst]: #15565
#15576 := [mp #15566 #15575]: #15564
#18449 := [unit-resolution #15576 #10373]: #5665
#18450 := [unit-resolution #18449 #18445]: #5662
#15578 := (or #5659 #15577)
#15608 := [def-axiom]: #15578
#18453 := [unit-resolution #15608 #18450]: #15577
#15724 := (not #5628)
#15725 := (or #5659 #15724)
#15726 := [def-axiom]: #15725
#18454 := [unit-resolution #15726 #18450]: #15724
#5640 := (or #5617 #5628 #5637)
#15352 := (or #4226 #5617 #5628 #5637)
#5609 := (+ #5608 #2148)
#5610 := (+ #177 #5609)
#5611 := (= #5610 0::int)
#5618 := (or #5617 #5615 #5611)
#15353 := (or #4226 #5618)
#15526 := (iff #15353 #15352)
#15377 := (or #4226 #5640)
#15505 := (iff #15377 #15352)
#15506 := [rewrite]: #15505
#15408 := (iff #15353 #15377)
#5641 := (iff #5618 #5640)
#5638 := (iff #5611 #5637)
#5635 := (= #5610 #5634)
#5636 := [rewrite]: #5635
#5639 := [monotonicity #5636]: #5638
#5642 := [monotonicity #5632 #5639]: #5641
#15409 := [monotonicity #5642]: #15408
#15549 := [trans #15409 #15506]: #15526
#15376 := [quant-inst]: #15353
#15550 := [mp #15376 #15549]: #15352
#18490 := [unit-resolution #15550 #10825]: #5640
#18491 := [unit-resolution #18490 #18454 #18453]: #5637
#18492 := (not #5637)
#18493 := (or #18492 #15560)
#18494 := [th-lemma]: #18493
#18495 := [unit-resolution #18494 #18491]: #15560
#18499 := (not #15834)
#18498 := (not #4769)
#18497 := (not #8662)
#18496 := (not #15560)
#18500 := (or #15741 #18496 #18497 #18498 #18499)
#18501 := [th-lemma]: #18500
#18502 := [unit-resolution #18501 #18495 #18444 #10836 #18432]: #15741
#15740 := (<= #15088 0::int)
#15833 := (<= #15832 0::int)
#18503 := (or #18424 #15833)
#18504 := [th-lemma]: #18503
#18505 := [unit-resolution #18504 #18429]: #15833
#9287 := (<= #4768 0::int)
#4527 := (= #177 #4526)
#4776 := (up_6 uf_23 uf_22)
#3683 := (up_6 #183 uf_22)
#10821 := (iff #3683 #4776)
#10819 := (iff #4776 #3683)
#10820 := [monotonicity #10380]: #10819
#10822 := [symm #10820]: #10821
#46 := (:var 0 T5)
#45 := (:var 2 T4)
#47 := (uf_7 #45 #10 #46)
#4016 := (pattern #47)
#321 := (= uf_8 #46)
#48 := (up_6 #47 #10)
#325 := (iff #48 #321)
#4017 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) (:pat #4016) #325)
#328 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) #325)
#4020 := (iff #328 #4017)
#4018 := (iff #325 #325)
#4019 := [refl]: #4018
#4021 := [quant-intro #4019]: #4020
#1650 := (~ #328 #328)
#1688 := (~ #325 #325)
#1689 := [refl]: #1688
#1651 := [nnf-pos #1689]: #1650
#49 := (= #46 uf_8)
#50 := (iff #48 #49)
#51 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) #50)
#329 := (iff #51 #328)
#326 := (iff #50 #325)
#323 := (iff #49 #321)
#324 := [rewrite]: #323
#327 := [monotonicity #324]: #326
#330 := [quant-intro #327]: #329
#320 := [asserted]: #51
#333 := [mp #320 #330]: #328
#1690 := [mp~ #333 #1651]: #328
#4022 := [mp #1690 #4021]: #4017
#8841 := (not #4017)
#8843 := (or #8841 #3683)
#3682 := (iff #3683 #3681)
#8837 := (or #8841 #3682)
#8844 := (iff #8837 #8843)
#8846 := (iff #8843 #8843)
#8847 := [rewrite]: #8846
#3668 := (iff #3682 #3683)
#3674 := (iff #3683 true)
#3676 := (iff #3674 #3683)
#3677 := [rewrite]: #3676
#3675 := (iff #3682 #3674)
#3667 := [monotonicity #3673]: #3675
#3678 := [trans #3667 #3677]: #3668
#8845 := [monotonicity #3678]: #8844
#8842 := [trans #8845 #8847]: #8844
#8838 := [quant-inst]: #8837
#9410 := [mp #8838 #8842]: #8843
#10818 := [unit-resolution #9410 #4022]: #3683
#10823 := [mp #10818 #10822]: #4776
#4777 := (not #4776)
#4781 := (or #4527 #4777)
#10191 := (or #4243 #4527 #4777)
#4780 := (or #4777 #4527)
#10192 := (or #4243 #4780)
#10250 := (iff #10192 #10191)
#10193 := (or #4243 #4781)
#10248 := (iff #10193 #10191)
#10249 := [rewrite]: #10248
#10194 := (iff #10192 #10193)
#4782 := (iff #4780 #4781)
#4783 := [rewrite]: #4782
#10247 := [monotonicity #4783]: #10194
#10252 := [trans #10247 #10249]: #10250
#10190 := [quant-inst]: #10192
#10253 := [mp #10190 #10252]: #10191
#10832 := [unit-resolution #10253 #10831]: #4781
#10833 := [unit-resolution #10832 #10823]: #4527
#9343 := (not #4527)
#9344 := (or #9343 #9287)
#9345 := [th-lemma]: #9344
#10834 := [unit-resolution #9345 #10833]: #9287
#11672 := (<= #11677 0::int)
#18506 := (or #18442 #11672)
#18507 := [th-lemma]: #18506
#18508 := [unit-resolution #18507 #18441]: #11672
#15561 := (>= #5634 0::int)
#18482 := (or #18492 #15561)
#18483 := [th-lemma]: #18482
#18481 := [unit-resolution #18483 #18491]: #15561
#18487 := (not #15833)
#18486 := (not #9287)
#18485 := (not #11672)
#18484 := (not #15561)
#18488 := (or #15740 #18484 #18485 #18486 #18487)
#18489 := [th-lemma]: #18488
#17776 := [unit-resolution #18489 #18481 #18508 #10834 #18505]: #15740
#15089 := (= #15088 0::int)
#15094 := (not #15089)
#14996 := (+ #2147 #11723)
#15074 := (<= #14996 0::int)
#18551 := (not #15074)
#17160 := (uf_3 #5828)
#17947 := (uf_1 #10482 #17160)
#17948 := (uf_10 #17947)
#17950 := (* -1::int #17948)
#18119 := (+ #5608 #17950)
#18161 := (>= #18119 0::int)
#18116 := (= #5608 #17948)
#17971 := (= #17948 #5608)
#17965 := (= #17947 #5607)
#17826 := (= #17160 ?x75!20)
#17161 := (= ?x75!20 #17160)
#17164 := (or #7756 #17161)
#17165 := [quant-inst]: #17164
#17777 := [unit-resolution #17165 #3987]: #17161
#17827 := [symm #17777]: #17826
#17970 := [monotonicity #13347 #17827]: #17965
#17974 := [monotonicity #17970]: #17971
#17975 := [symm #17974]: #18116
#17976 := (not #18116)
#17979 := (or #17976 #18161)
#18037 := [th-lemma]: #17979
#18038 := [unit-resolution #18037 #17975]: #18161
#18048 := (<= #17948 0::int)
#18049 := (not #18048)
#18467 := (= #10482 #17160)
#17898 := (not #18467)
#18462 := (up_6 uf_15 #17160)
#18473 := (or #18462 #18467)
#17926 := (not #18473)
#18465 := (up_6 #11444 #17160)
#18478 := (iff #18465 #18473)
#17873 := (or #6538 #18478)
#18463 := (= #17160 #10482)
#18464 := (ite #18463 #3681 #18462)
#18466 := (iff #18465 #18464)
#17874 := (or #6538 #18466)
#17876 := (iff #17874 #17873)
#17892 := (iff #17873 #17873)
#17893 := [rewrite]: #17892
#18479 := (iff #18466 #18478)
#18476 := (iff #18464 #18473)
#18470 := (ite #18467 true #18462)
#18474 := (iff #18470 #18473)
#18475 := [rewrite]: #18474
#18471 := (iff #18464 #18470)
#18468 := (iff #18463 #18467)
#18469 := [rewrite]: #18468
#18472 := [monotonicity #18469 #3673]: #18471
#18477 := [trans #18472 #18475]: #18476
#18480 := [monotonicity #18477]: #18479
#17891 := [monotonicity #18480]: #17876
#17894 := [trans #17891 #17893]: #17876
#17875 := [quant-inst]: #17874
#17895 := [mp #17875 #17894]: #17873
#18337 := [unit-resolution #17895 #4007]: #18478
#17931 := (not #18465)
#4948 := (up_6 uf_23 ?x75!20)
#4949 := (not #4948)
#18452 := (iff #4949 #17931)
#18352 := (iff #4948 #18465)
#18341 := (iff #18465 #4948)
#18342 := [monotonicity #13524 #17827]: #18341
#18451 := [symm #18342]: #18352
#18455 := [monotonicity #18451]: #18452
#5569 := (or #4949 #5566)
#14917 := (or #4243 #4949 #5566)
#5565 := (or #4949 #5562)
#14918 := (or #4243 #5565)
#15338 := (iff #14918 #14917)
#15153 := (or #4243 #5569)
#15201 := (iff #15153 #14917)
#15202 := [rewrite]: #15201
#15162 := (iff #14918 #15153)
#5570 := (iff #5565 #5569)
#5571 := [monotonicity #5568]: #5570
#15163 := [monotonicity #5571]: #15162
#15339 := [trans #15163 #15202]: #15338
#15152 := [quant-inst]: #14918
#15340 := [mp #15152 #15339]: #14917
#18516 := [unit-resolution #15340 #10831]: #5569
#18338 := [unit-resolution #18516 #18445]: #4949
#18456 := [mp #18338 #18455]: #17931
#17929 := (not #18478)
#17930 := (or #17929 #18465 #17926)
#17925 := [def-axiom]: #17930
#18457 := [unit-resolution #17925 #18456 #18337]: #17926
#17899 := (or #18473 #17898)
#17900 := [def-axiom]: #17899
#18460 := [unit-resolution #17900 #18457]: #17898
#18064 := (or #18049 #18467)
#18066 := (or #7051 #18049 #18467)
#18063 := (or #18467 #18049)
#18067 := (or #7051 #18063)
#18081 := (iff #18067 #18066)
#18073 := (or #7051 #18064)
#18075 := (iff #18073 #18066)
#18076 := [rewrite]: #18075
#18071 := (iff #18067 #18073)
#18062 := (iff #18063 #18064)
#18065 := [rewrite]: #18062
#18074 := [monotonicity #18065]: #18071
#18082 := [trans #18074 #18076]: #18081
#18072 := [quant-inst]: #18067
#18080 := [mp #18072 #18082]: #18066
#18549 := [unit-resolution #18080 #4034]: #18064
#18550 := [unit-resolution #18549 #18460]: #18049
#18552 := (not #18161)
#18553 := (or #18551 #18496 #18497 #18498 #18048 #18552)
#18554 := [th-lemma]: #18553
#18555 := [unit-resolution #18554 #18495 #18444 #10836 #18550 #18038]: #18551
#18562 := (or #15074 #15094)
#11728 := (up_6 uf_23 #10482)
#18558 := (iff #3683 #11728)
#18556 := (iff #11728 #3683)
#18557 := [monotonicity #10380 #13347]: #18556
#18559 := [symm #18557]: #18558
#18560 := [mp #10818 #18559]: #11728
#18561 := [hypothesis]: #4272
#11732 := (not #11728)
#15729 := (or #4277 #11732 #15074 #15094)
#15061 := (+ #2148 #15060)
#15062 := (+ #11725 #15061)
#15063 := (= #15062 0::int)
#15064 := (not #15063)
#15065 := (+ #11725 #2148)
#15066 := (>= #15065 0::int)
#15067 := (or #11732 #15066 #15064)
#15730 := (or #4277 #15067)
#15737 := (iff #15730 #15729)
#15097 := (or #11732 #15074 #15094)
#15732 := (or #4277 #15097)
#15735 := (iff #15732 #15729)
#15736 := [rewrite]: #15735
#15733 := (iff #15730 #15732)
#15098 := (iff #15067 #15097)
#15095 := (iff #15064 #15094)
#15092 := (iff #15063 #15089)
#15079 := (+ #11725 #15060)
#15080 := (+ #2148 #15079)
#15083 := (= #15080 0::int)
#15090 := (iff #15083 #15089)
#15091 := [rewrite]: #15090
#15084 := (iff #15063 #15083)
#15081 := (= #15062 #15080)
#15082 := [rewrite]: #15081
#15085 := [monotonicity #15082]: #15084
#15093 := [trans #15085 #15091]: #15092
#15096 := [monotonicity #15093]: #15095
#15077 := (iff #15066 #15074)
#15068 := (+ #2148 #11725)
#15071 := (>= #15068 0::int)
#15075 := (iff #15071 #15074)
#15076 := [rewrite]: #15075
#15072 := (iff #15066 #15071)
#15069 := (= #15065 #15068)
#15070 := [rewrite]: #15069
#15073 := [monotonicity #15070]: #15072
#15078 := [trans #15073 #15076]: #15077
#15099 := [monotonicity #15078 #15096]: #15098
#15734 := [monotonicity #15099]: #15733
#15738 := [trans #15734 #15736]: #15737
#15731 := [quant-inst]: #15730
#15739 := [mp #15731 #15738]: #15729
#18563 := [unit-resolution #15739 #18561 #18560]: #18562
#18564 := [unit-resolution #18563 #18555]: #15094
#18566 := (not #15741)
#18565 := (not #15740)
#18567 := (or #15089 #18565 #18566)
#18568 := [th-lemma]: #18567
#18569 := [unit-resolution #18568 #18564 #17776 #18502]: false
#18571 := [lemma #18569]: #18570
#27208 := [unit-resolution #18571 #27207]: #5566
#18519 := (or #18518 #18461)
#18520 := [th-lemma]: #18519
#27209 := [unit-resolution #18520 #27208]: #18461
#22580 := (not #18461)
#22586 := (or #22585 #22580 #2159)
#22581 := [hypothesis]: #2160
#22582 := [hypothesis]: #18461
#22583 := [hypothesis]: #5840
#22584 := [th-lemma #22583 #22582 #22581]: false
#22587 := [lemma #22584]: #22586
#27210 := [unit-resolution #22587 #27209 #27206]: #22585
#3914 := (or #4280 #2724)
#3796 := [def-axiom]: #3914
#27211 := [unit-resolution #3796 #27205]: #2724
#16286 := (or #4129 #2721 #5840 #5845)
#5837 := (or #5836 #5834 #5827)
#5838 := (not #5837)
#5841 := (or #2161 #5840 #5838)
#16309 := (or #4129 #5841)
#16464 := (iff #16309 #16286)
#5848 := (or #2721 #5840 #5845)
#16025 := (or #4129 #5848)
#16414 := (iff #16025 #16286)
#16302 := [rewrite]: #16414
#16445 := (iff #16309 #16025)
#5849 := (iff #5841 #5848)
#5846 := (iff #5838 #5845)
#5843 := (iff #5837 #5842)
#5844 := [rewrite]: #5843
#5847 := [monotonicity #5844]: #5846
#5850 := [monotonicity #2723 #5847]: #5849
#16461 := [monotonicity #5850]: #16445
#16413 := [trans #16461 #16302]: #16464
#16307 := [quant-inst]: #16309
#16444 := [mp #16307 #16413]: #16286
#27212 := [unit-resolution #16444 #10442 #27211 #27210]: #5845
#16693 := (or #5842 #5835)
#16554 := [def-axiom]: #16693
#27213 := [unit-resolution #16554 #27212]: #5835
#27221 := [mp #27213 #27220]: #25893
#25894 := (not #25893)
#27098 := (or #27081 #25894)
#27099 := [def-axiom]: #27098
#27222 := [unit-resolution #27099 #27221]: #27081
#27103 := (not #27081)
#27107 := (or #27106 #27073 #27103)
#27108 := [def-axiom]: #27107
#27224 := [unit-resolution #27108 #27222]: #27223
#27225 := [unit-resolution #27224 #27196]: #27073
#27234 := [unit-resolution #27225 #27233]: false
#27235 := [lemma #27234]: #16800
#16798 := (uf_24 #5823)
#16817 := (* -1::int #16798)
#17010 := (+ #2147 #16817)
#17011 := (<= #17010 0::int)
#22559 := (not #17011)
#15902 := (not #5827)
#16589 := (or #5842 #15902)
#16412 := [def-axiom]: #16589
#22552 := [unit-resolution #16412 #27212]: #15902
#16818 := (+ #5824 #16817)
#16819 := (>= #16818 0::int)
#16900 := (or #4234 #16819)
#15938 := [quant-inst]: #16900
#22558 := [unit-resolution #15938 #10835]: #16819
#22544 := (not #16819)
#23021 := (or #22559 #5827 #22580 #22544)
#22554 := [th-lemma]: #23021
#18055 := [unit-resolution #22554 #27209 #22558 #22552]: #22559
#16977 := (+ #5830 #16817)
#16978 := (+ #2147 #16977)
#17021 := (= #16978 0::int)
#19944 := (>= #16978 0::int)
#9360 := (>= #5832 0::int)
#16497 := (or #5842 #5833)
#16618 := [def-axiom]: #16497
#16042 := [unit-resolution #16618 #27212]: #5833
#21361 := (or #5834 #9360)
#21365 := [th-lemma]: #21361
#22952 := [unit-resolution #21365 #16042]: #9360
#22974 := (not #9360)
#23033 := (or #19944 #22974 #22580 #22544)
#22976 := [th-lemma]: #23033
#22955 := [unit-resolution #22976 #22952 #22558 #27209]: #19944
#16979 := (<= #16978 0::int)
#22549 := (<= #16818 0::int)
#16799 := (= #5824 #16798)
#16803 := (or #16799 #16801)
#17738 := (or #4243 #16799 #16801)
#16802 := (or #16801 #16799)
#18032 := (or #4243 #16802)
#15937 := (iff #18032 #17738)
#18787 := (or #4243 #16803)
#18974 := (iff #18787 #17738)
#19070 := [rewrite]: #18974
#19064 := (iff #18032 #18787)
#16804 := (iff #16802 #16803)
#16805 := [rewrite]: #16804
#17444 := [monotonicity #16805]: #19064
#19082 := [trans #17444 #19070]: #15937
#19040 := [quant-inst]: #18032
#17767 := [mp #19040 #19082]: #17738
#18817 := [unit-resolution #17767 #10831]: #16803
#23050 := [unit-resolution #18817 #27235]: #16799
#23024 := (not #16799)
#23019 := (or #23024 #22549)
#23047 := [th-lemma]: #23019
#23015 := [unit-resolution #23047 #23050]: #22549
#5593 := (<= #5592 0::int)
#20441 := (not #5593)
#20442 := [hypothesis]: #20441
#20353 := (or #4234 #5593)
#5583 := (+ #5561 #2148)
#5584 := (>= #5583 0::int)
#20370 := (or #4234 #5584)
#20377 := (iff #20370 #20353)
#20384 := (iff #20353 #20353)
#20387 := [rewrite]: #20384
#5596 := (iff #5584 #5593)
#5585 := (+ #2148 #5561)
#5588 := (>= #5585 0::int)
#5594 := (iff #5588 #5593)
#5595 := [rewrite]: #5594
#5589 := (iff #5584 #5588)
#5586 := (= #5583 #5585)
#5587 := [rewrite]: #5586
#5590 := [monotonicity #5587]: #5589
#5597 := [trans #5590 #5595]: #5596
#20383 := [monotonicity #5597]: #20377
#20388 := [trans #20383 #20387]: #20377
#20376 := [quant-inst]: #20370
#20438 := [mp #20376 #20388]: #20353
#20437 := [unit-resolution #20438 #10835 #20442]: false
#20443 := [lemma #20437]: #5593
#15900 := (<= #5832 0::int)
#23077 := (or #5834 #15900)
#23040 := [th-lemma]: #23077
#23022 := [unit-resolution #23040 #16042]: #15900
#23053 := (not #22549)
#22936 := (not #15900)
#23179 := (or #16979 #22936 #20441 #23053)
#23061 := [th-lemma]: #23179
#23075 := [unit-resolution #23061 #23022 #20443 #23015]: #16979
#23181 := (not #19944)
#23180 := (not #16979)
#23059 := (or #17021 #23180 #23181)
#23057 := [th-lemma]: #23059
#23182 := [unit-resolution #23057 #23075 #22955]: #17021
#17026 := (not #17021)
#17029 := (or #16801 #17011 #17026)
#19879 := (or #4277 #16801 #17011 #17026)
#16998 := (+ #2148 #5829)
#16999 := (+ #16798 #16998)
#17000 := (= #16999 0::int)
#17001 := (not #17000)
#16962 := (+ #16798 #2148)
#17002 := (>= #16962 0::int)
#17003 := (or #16801 #17002 #17001)
#19880 := (or #4277 #17003)
#19850 := (iff #19880 #19879)
#19873 := (or #4277 #17029)
#19915 := (iff #19873 #19879)
#19874 := [rewrite]: #19915
#20138 := (iff #19880 #19873)
#17030 := (iff #17003 #17029)
#17027 := (iff #17001 #17026)
#17024 := (iff #17000 #17021)
#16970 := (+ #5829 #16798)
#16971 := (+ #2148 #16970)
#17018 := (= #16971 0::int)
#17022 := (iff #17018 #17021)
#17023 := [rewrite]: #17022
#17019 := (iff #17000 #17018)
#17016 := (= #16999 #16971)
#17017 := [rewrite]: #17016
#17020 := [monotonicity #17017]: #17019
#17025 := [trans #17020 #17023]: #17024
#17028 := [monotonicity #17025]: #17027
#17014 := (iff #17002 #17011)
#17004 := (+ #2148 #16798)
#17007 := (>= #17004 0::int)
#17012 := (iff #17007 #17011)
#17013 := [rewrite]: #17012
#17008 := (iff #17002 #17007)
#17005 := (= #16962 #17004)
#17006 := [rewrite]: #17005
#17009 := [monotonicity #17006]: #17008
#17015 := [trans #17009 #17013]: #17014
#17031 := [monotonicity #17015 #17028]: #17030
#20025 := [monotonicity #17031]: #20138
#20123 := [trans #20025 #19874]: #19850
#19878 := [quant-inst]: #19880
#19916 := [mp #19878 #20123]: #19879
#23081 := [unit-resolution #19916 #27207]: #17029
[unit-resolution #23081 #23182 #18055 #27235]: false
unsat