src/HOL/Boogie/Examples/cert/Boogie_Dijkstra.proof

--- a/src/HOL/Boogie/Examples/cert/Boogie_Dijkstra.proof	Wed Dec 23 17:36:26 2009 +0100
+++ b/src/HOL/Boogie/Examples/cert/Boogie_Dijkstra.proof	Wed Dec 23 17:37:42 2009 +0100
@@ -1,6631 +1,6542 @@
 #2 := false
-#52 := 0::int
-decl uf_10 :: (-> T1 int)
+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 ?x71!19 :: T2
-#2002 := ?x71!19
-decl ?x72!18 :: T2
-#2001 := ?x72!18
-#2007 := (uf_1 ?x72!18 ?x71!19)
-#11538 := (uf_3 #2007)
 decl uf_22 :: T2
-#182 := uf_22
-#18065 := (uf_1 uf_22 #11538)
-#18066 := (uf_10 #18065)
-decl uf_24 :: (-> T2 int)
-#18030 := (uf_24 #11538)
-#952 := -1::int
-#18049 := (* -1::int #18030)
-#18091 := (+ #18049 #18066)
-decl uf_4 :: (-> T3 T2 int)
-decl uf_14 :: T3
-#107 := uf_14
-#185 := (uf_4 uf_14 uf_22)
-#18092 := (+ #185 #18091)
-#18113 := (>= #18092 0::int)
-#18070 := (* -1::int #18066)
-decl uf_9 :: int
-#53 := uf_9
-#18074 := (+ uf_9 #18070)
-#18075 := (<= #18074 0::int)
-#17499 := (not #18075)
-#2008 := (uf_10 #2007)
-#2011 := (* -1::int #2008)
-#2012 := (+ uf_9 #2011)
-#2013 := (<= #2012 0::int)
-#2014 := (not #2013)
-#2005 := (uf_24 ?x72!18)
-#2543 := (* -1::int #2005)
-#2544 := (+ #2543 #2011)
-#2003 := (uf_24 ?x71!19)
-#2545 := (+ #2003 #2544)
-#2546 := (<= #2545 0::int)
-decl up_6 :: (-> T4 T2 bool)
-decl uf_23 :: T4
-#190 := uf_23
-#2015 := (up_6 uf_23 ?x72!18)
-#3106 := (not #2015)
-#3121 := (or #2013 #3106 #2546)
-#3126 := (not #3121)
-decl ?x75!20 :: T2
-#2031 := ?x75!20
-#11 := (:var 0 T2)
-#2035 := (uf_1 #11 ?x75!20)
-#4121 := (pattern #2035)
-#199 := (uf_24 #11)
-#4062 := (pattern #199)
-#216 := (up_6 uf_23 #11)
-#4087 := (pattern #216)
-#2036 := (uf_10 #2035)
-#2032 := (uf_24 ?x75!20)
-#2033 := (* -1::int #2032)
-#2581 := (+ #2033 #2036)
-#2582 := (+ #199 #2581)
-#2585 := (= #2582 0::int)
-#3151 := (not #2585)
-#2034 := (+ #199 #2033)
-#2039 := (>= #2034 0::int)
-#223 := (not #216)
-#3152 := (or #223 #2039 #3151)
-#4122 := (forall (vars (?x76 T2)) (:pat #4087 #4062 #4121) #3152)
-#4127 := (not #4122)
-#10 := (:var 1 T2)
-#90 := (uf_1 #11 #10)
-#3916 := (pattern #90)
-#226 := (uf_24 #10)
-#1337 := (* -1::int #226)
-#1338 := (+ #199 #1337)
-#91 := (uf_10 #90)
-#1363 := (+ #91 #1338)
-#1361 := (>= #1363 0::int)
-#967 := (* -1::int #91)
-#968 := (+ uf_9 #967)
-#969 := (<= #968 0::int)
-#3143 := (or #223 #969 #1361)
-#4113 := (forall (vars (?x71 T2) (?x72 T2)) (:pat #3916) #3143)
-#4118 := (not #4113)
-decl uf_11 :: T2
-#64 := uf_11
-#2557 := (= uf_11 ?x75!20)
-#2043 := (+ uf_9 #2033)
-#2044 := (<= #2043 0::int)
-#4130 := (or #2044 #2557 #4118 #4127)
-decl ?x47!7 :: (-> T2 T2)
-#11097 := (?x47!7 ?x75!20)
-decl uf_15 :: T4
-#113 := uf_15
-#11136 := (up_6 uf_15 #11097)
-#11143 := (uf_4 uf_14 #11097)
-#11144 := (* -1::int #11143)
-#10301 := (uf_4 uf_14 ?x75!20)
-#11145 := (+ #10301 #11144)
-#11146 := (<= #11145 0::int)
-#11137 := (not #11136)
-#11147 := (uf_1 #11097 ?x75!20)
-#11148 := (uf_10 #11147)
-#11149 := (* -1::int #11148)
-#11150 := (+ #11144 #11149)
-#11133 := (+ #10301 #11150)
-#11134 := (= #11133 0::int)
-#11135 := (not #11134)
-#11142 := (or #11135 #11137 #11146)
-#11168 := (not #11142)
-#10403 := (* -1::int #10301)
-#11139 := (+ uf_9 #10403)
-#11140 := (<= #11139 0::int)
-#33430 := (not #11140)
-#2045 := (not #2044)
-#4133 := (not #4130)
-#25286 := [hypothesis]: #4133
-#3757 := (or #4130 #2045)
-#3755 := [def-axiom]: #3757
-#25348 := [unit-resolution #3755 #25286]: #2045
-#10404 := (+ #2032 #10403)
-#7777 := (>= #10404 0::int)
-#10311 := (= #2032 #10301)
-#3601 := (or #4130 #4122)
-#3749 := [def-axiom]: #3601
-#25346 := [unit-resolution #3749 #25286]: #4122
-#30592 := (or #10311 #4127)
-#5832 := (uf_1 uf_22 uf_22)
-#6904 := (uf_3 #5832)
-#8027 := (uf_24 #6904)
-#7883 := (* -1::int #8027)
-#10078 := (+ #2032 #7883)
-#10697 := (<= #10078 0::int)
-#30559 := (not #10697)
-#10700 := (uf_1 #6904 ?x75!20)
-#10701 := (uf_10 #10700)
-#30273 := (<= #10701 0::int)
-#30274 := (not #30273)
-#13994 := (= ?x75!20 #6904)
-#30199 := (not #13994)
-#11031 := (up_6 uf_15 ?x75!20)
-#14001 := (or #11031 #13994)
-#30202 := (not #14001)
+#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
-#8048 := (uf_7 uf_15 #6904 uf_8)
-#13996 := (up_6 #8048 ?x75!20)
-#14006 := (iff #13996 #14001)
+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)
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+#914 := (not #437)
+#915 := (or #914 #906)
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+#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)
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+#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)
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+#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)
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+#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)
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+#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)
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+#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
+#1444 := [monotonicity #1441]: #1443
+#1478 := [monotonicity #1444 #1475]: #1477
+#1481 := [monotonicity #1478]: #1480
+#1456 := (iff #834 #1455)
+#1453 := (iff #628 #1452)
+#1450 := (iff #625 #1449)
+#1447 := (iff #179 #1445)
+#1448 := [rewrite]: #1447
+#1451 := [monotonicity #1448]: #1450
+#1454 := [quant-intro #1451]: #1453
+#1457 := [monotonicity #1454]: #1456
+#1484 := [monotonicity #1457 #1481]: #1483
+#1468 := (iff #843 #1459)
+#1460 := (not #1459)
+#1463 := (not #1460)
+#1466 := (iff #1463 #1459)
+#1467 := [rewrite]: #1466
+#1464 := (iff #843 #1463)
+#1461 := (iff #178 #1460)
+#1462 := [rewrite]: #1461
+#1465 := [monotonicity #1462]: #1464
+#1469 := [trans #1465 #1467]: #1468
+#1487 := [monotonicity #1469 #1484]: #1486
+#1490 := [monotonicity #1487]: #1489
+#1471 := (iff #135 #1470)
+#1240 := (iff #134 #1239)
+#1237 := (iff #133 #1236)
+#1121 := (iff #124 #1120)
+#1122 := [rewrite]: #1121
+#1238 := [monotonicity #1122]: #1237
+#1241 := [quant-intro #1238]: #1240
+#1472 := [monotonicity #1241]: #1471
+#1493 := [monotonicity #1472 #1490]: #1492
+#1498 := [trans #1493 #1496]: #1497
+#1260 := (iff #613 #1257)
+#1242 := (or #577 #1233)
+#1245 := (or #586 #1242)
+#1248 := (or #595 #1245)
+#1251 := (or #604 #1248)
+#1254 := (or #1239 #1251)
+#1258 := (iff #1254 #1257)
+#1259 := [rewrite]: #1258
+#1255 := (iff #613 #1254)
+#1252 := (iff #605 #1251)
+#1249 := (iff #596 #1248)
+#1246 := (iff #587 #1245)
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+#1234 := (iff #571 #1233)
+#1231 := (iff #566 #1230)
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+#1225 := (iff #554 #1222)
+#1219 := (or #1214 #162)
+#1223 := (iff #1219 #1222)
+#1224 := [rewrite]: #1223
+#1220 := (iff #554 #1219)
+#1217 := (iff #540 #162)
+#1218 := [rewrite]: #1217
+#1215 := (iff #553 #1214)
+#1212 := (iff #537 #1211)
+#1209 := (iff #532 #1208)
+#1206 := (iff #525 #1205)
+#1207 := [rewrite]: #1206
+#1203 := (iff #531 #1202)
+#1200 := (iff #522 #1199)
+#1166 := (iff #147 #1165)
+#1167 := [rewrite]: #1166
+#1201 := [monotonicity #1058 #1167]: #1200
+#1204 := [monotonicity #1201]: #1203
+#1210 := [monotonicity #1204 #1207]: #1209
+#1213 := [quant-intro #1210]: #1212
+#1216 := [monotonicity #1213]: #1215
+#1221 := [monotonicity #1216 #1218]: #1220
+#1226 := [trans #1221 #1224]: #1225
+#1229 := [monotonicity #1213 #1226]: #1228
+#1197 := (iff #565 #1196)
+#1194 := (iff #519 #1193)
+#1191 := (iff #514 #1190)
+#1188 := (iff #507 #1187)
+#1185 := (iff #504 #1184)
+#1181 := (iff #501 #1180)
+#1183 := [rewrite]: #1181
+#1178 := (iff #150 #1177)
+#1179 := [rewrite]: #1178
+#1186 := [monotonicity #1179 #1183]: #1185
+#1189 := [quant-intro #1186]: #1188
+#1172 := (iff #513 #1171)
+#1169 := (iff #148 #1168)
+#1170 := [monotonicity #1167]: #1169
+#1173 := [monotonicity #1170]: #1172
+#1192 := [monotonicity #1173 #1189]: #1191
+#1195 := [quant-intro #1192]: #1194
+#1198 := [monotonicity #1195]: #1197
+#1232 := [monotonicity #1198 #1229]: #1231
+#1235 := [monotonicity #1195 #1232]: #1234
+#1244 := [monotonicity #1235]: #1243
+#1247 := [monotonicity #1244]: #1246
+#1250 := [monotonicity #1247]: #1249
+#1253 := [monotonicity #1250]: #1252
+#1256 := [monotonicity #1241 #1253]: #1255
+#1261 := [trans #1256 #1259]: #1260
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+#1160 := (iff #878 #1159)
+#1157 := (iff #489 #1156)
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+#1142 := (and #1136 #1139)
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+#1147 := [rewrite]: #1146
+#1143 := (iff #474 #1142)
+#1140 := (iff #471 #1139)
+#1130 := (iff #468 #1129)
+#1134 := [rewrite]: #1130
+#1141 := [monotonicity #1134]: #1140
+#1137 := (iff #126 #1136)
+#1138 := [rewrite]: #1137
+#1144 := [monotonicity #1138 #1141]: #1143
+#1149 := [trans #1144 #1147]: #1148
+#1152 := [quant-intro #1149]: #1151
+#1127 := (iff #483 #1126)
+#1124 := (iff #125 #1123)
+#1125 := [monotonicity #1122]: #1124
+#1128 := [monotonicity #1125]: #1127
+#1155 := [monotonicity #1128 #1152]: #1154
+#1158 := [quant-intro #1155]: #1157
+#1161 := [monotonicity #1158]: #1160
+#1555 := [monotonicity #1161 #1501]: #1554
+#1523 := (iff #887 #1522)
+#1520 := (iff #465 #1519)
+#1517 := (iff #460 #1516)
+#1514 := (iff #453 #1513)
+#1515 := [rewrite]: #1514
+#1511 := (iff #459 #1510)
+#1508 := (iff #447 #1505)
+#1502 := (and #1056 #111)
+#1506 := (iff #1502 #1505)
+#1507 := [rewrite]: #1506
+#1503 := (iff #447 #1502)
+#1504 := [monotonicity #1058]: #1503
+#1509 := [trans #1504 #1507]: #1508
+#1512 := [monotonicity #1509]: #1511
+#1518 := [monotonicity #1512 #1515]: #1517
+#1521 := [quant-intro #1518]: #1520
+#1524 := [monotonicity #1521]: #1523
+#1558 := [monotonicity #1524 #1555]: #1557
+#1534 := (iff #896 #1533)
+#1531 := (iff #444 #1530)
+#1528 := (iff #441 #1527)
+#1525 := (iff #116 #1135)
+#1526 := [rewrite]: #1525
+#1529 := [monotonicity #1526]: #1528
+#1532 := [quant-intro #1529]: #1531
+#1535 := [monotonicity #1532]: #1534
+#1561 := [monotonicity #1535 #1558]: #1560
+#1543 := (iff #905 #1542)
+#1540 := (iff #109 #1539)
+#1537 := (iff #108 #1536)
+#1538 := [rewrite]: #1537
+#1541 := [quant-intro #1538]: #1540
+#1544 := [monotonicity #1541]: #1543
+#1564 := [monotonicity #1544 #1561]: #1563
+#1548 := (iff #914 #1547)
+#1545 := (iff #437 #106)
+#1546 := [rewrite]: #1545
+#1549 := [monotonicity #1546]: #1548
+#1567 := [monotonicity #1549 #1564]: #1566
+#1551 := (iff #930 #1550)
+#1115 := (iff #434 #1114)
+#1112 := (iff #431 #1111)
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+#1106 := (iff #100 #1103)
+#1097 := (and #74 #1091)
+#1100 := (and #1094 #1097)
+#1104 := (iff #1100 #1103)
+#1105 := [rewrite]: #1104
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+#1098 := (iff #99 #1097)
+#1092 := (iff #98 #1091)
+#1093 := [rewrite]: #1092
+#1099 := [monotonicity #1093]: #1098
+#1095 := (iff #97 #1094)
+#1096 := [rewrite]: #1095
+#1102 := [monotonicity #1096 #1099]: #1101
+#1107 := [trans #1102 #1105]: #1106
+#1110 := [quant-intro #1107]: #1109
+#1089 := (iff #430 #1088)
+#1086 := (iff #96 #1085)
+#1083 := (iff #95 #1082)
+#1084 := [rewrite]: #1083
+#1087 := [monotonicity #1084]: #1086
+#1090 := [monotonicity #1087]: #1089
+#1113 := [monotonicity #1090 #1110]: #1112
+#1116 := [quant-intro #1113]: #1115
+#1552 := [monotonicity #1116]: #1551
+#1570 := [monotonicity #1552 #1567]: #1569
+#1575 := [trans #1570 #1573]: #1574
+#1578 := [monotonicity #1116 #1575]: #1577
+#1077 := (iff #942 #1076)
+#1074 := (iff #427 #1073)
+#1071 := (iff #424 #1070)
+#1065 := (iff #92 #1066)
+#1067 := [rewrite]: #1065
+#1063 := (iff #423 #1062)
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+#1061 := [monotonicity #1058]: #1060
+#1064 := [monotonicity #1061]: #1063
+#1072 := [monotonicity #1064 #1067]: #1071
+#1075 := [quant-intro #1072]: #1074
+#1078 := [monotonicity #1075]: #1077
+#1581 := [monotonicity #1078 #1578]: #1580
+#1584 := [monotonicity #1075 #1581]: #1583
+#1051 := (iff #954 #1050)
+#1048 := (iff #420 #1047)
+#1045 := (iff #417 #1044)
+#1039 := (iff #84 #1040)
+#1043 := [rewrite]: #1039
+#1046 := [monotonicity #1043]: #1045
+#1049 := [quant-intro #1046]: #1048
+#1052 := [monotonicity #1049]: #1051
+#1587 := [monotonicity #1052 #1584]: #1586
+#1590 := [monotonicity #1049 #1587]: #1589
+#1036 := (iff #966 #1035)
+#1033 := (iff #80 #1032)
+#1029 := (iff #79 #1031)
+#1030 := [rewrite]: #1029
+#1034 := [quant-intro #1030]: #1033
+#1037 := [monotonicity #1034]: #1036
+#1593 := [monotonicity #1037 #1590]: #1592
+#1596 := [monotonicity #1034 #1593]: #1595
+#1027 := (iff #978 #1026)
+#1024 := (iff #413 #78)
+#1025 := [rewrite]: #1024
+#1028 := [monotonicity #1025]: #1027
+#1599 := [monotonicity #1028 #1596]: #1598
+#1602 := [monotonicity #1025 #1599]: #1601
+#1616 := [monotonicity #1602]: #1615
+#1619 := [monotonicity #1616]: #1618
+#1612 := (iff #1008 #1611)
+#1609 := (iff #396 #1608)
+#1606 := (iff #391 #1605)
+#1603 := (iff #385 #67)
+#1604 := [rewrite]: #1603
+#1607 := [monotonicity #1604]: #1606
+#1610 := [quant-intro #1607]: #1609
+#1613 := [monotonicity #1610]: #1612
+#1622 := [monotonicity #1613 #1619]: #1621
+#1627 := [trans #1622 #1625]: #1626
+#1630 := [monotonicity #1627]: #1629
+#1022 := (iff #271 #1021)
+#1019 := (iff #270 #1009)
+#1014 := (implies true #1009)
+#1017 := (iff #1014 #1009)
+#1018 := [rewrite]: #1017
+#1015 := (iff #270 #1014)
+#1012 := (iff #269 #1009)
+#1005 := (implies #396 #1000)
+#1010 := (iff #1005 #1009)
+#1011 := [rewrite]: #1010
+#1006 := (iff #269 #1005)
+#1003 := (iff #268 #1000)
+#996 := (implies #410 #991)
+#1001 := (iff #996 #1000)
+#1002 := [rewrite]: #1001
+#997 := (iff #268 #996)
+#994 := (iff #267 #991)
+#987 := (implies #76 #984)
+#992 := (iff #987 #991)
+#993 := [rewrite]: #992
+#988 := (iff #267 #987)
+#985 := (iff #266 #984)
+#982 := (iff #265 #979)
+#975 := (implies #413 #972)
+#980 := (iff #975 #979)
+#981 := [rewrite]: #980
+#976 := (iff #265 #975)
+#973 := (iff #264 #972)
+#970 := (iff #263 #967)
+#963 := (implies #80 #960)
+#968 := (iff #963 #967)
+#969 := [rewrite]: #968
+#964 := (iff #263 #963)
+#961 := (iff #262 #960)
+#958 := (iff #261 #955)
+#951 := (implies #420 #948)
+#956 := (iff #951 #955)
+#957 := [rewrite]: #956
+#952 := (iff #261 #951)
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+#678 := (iff #214 #677)
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+#752 := [trans #746 #750]: #751
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+#665 := (iff #202 #662)
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+#663 := (iff #659 #662)
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+#647 := [rewrite]: #646
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+#669 := [quant-intro #666]: #668
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+#788 := [trans #782 #786]: #787
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+#652 := (iff #648 #651)
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+#655 := [trans #650 #653]: #654
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+#806 := [monotonicity #658 #803]: #805
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+#643 := (iff #194 #642)
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+#638 := (iff #634 #637)
+#639 := [rewrite]: #638
+#635 := (iff #193 #634)
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+#644 := [quant-intro #641]: #643
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+#821 := [trans #815 #819]: #820
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+#839 := [trans #833 #837]: #838
+#842 := [monotonicity #839]: #841
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+#533 := (iff #528 #532)
+#534 := [rewrite]: #533
+#529 := (iff #159 #528)
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+#499 := (= #151 #498)
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+#449 := [rewrite]: #448
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+#935 := [trans #929 #933]: #934
+#938 := [monotonicity #436 #935]: #937
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+#947 := [trans #941 #945]: #946
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+#422 := [quant-intro #419]: #421
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+#959 := [trans #953 #957]: #958
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+#965 := [monotonicity #962]: #964
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+#414 := (iff #78 #413)
+#415 := [rewrite]: #414
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+#983 := [trans #977 #981]: #982
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+#989 := [monotonicity #986]: #988
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+#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
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+#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
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+#8156 := [lemma #8153]: #2873
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+#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)
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+#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)
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+#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
+#4363 := [monotonicity #4360]: #4362
+#4130 := (iff #3427 #4129)
+#4127 := (iff #3041 #4124)
+#4125 := (iff #3036 #3036)
+#4126 := [refl]: #4125
+#4128 := [quant-intro #4126]: #4127
+#4131 := [monotonicity #4128]: #4130
+#4122 := (iff #3426 #4121)
+#4119 := (iff #3013 #4116)
+#4117 := (iff #3008 #3008)
+#4118 := [refl]: #4117
+#4120 := [quant-intro #4118]: #4119
+#4123 := [monotonicity #4120]: #4122
+#4114 := (iff #3425 #4113)
+#4111 := (iff #2985 #4108)
+#4109 := (iff #2980 #2980)
+#4110 := [refl]: #4109
+#4112 := [quant-intro #4110]: #4111
+#4115 := [monotonicity #4112]: #4114
+#4105 := (iff #3424 #4104)
+#4102 := (iff #2962 #4099)
+#4100 := (iff #2957 #2957)
+#4101 := [refl]: #4100
+#4103 := [quant-intro #4101]: #4102
+#4106 := [monotonicity #4103]: #4105
+#4097 := (iff #1542 #4096)
+#4094 := (iff #1539 #4091)
+#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
+#4086 := [monotonicity #4083]: #4085
+#4089 := [monotonicity #4086]: #4088
+#4372 := [monotonicity #4089 #4369]: #4371
+#4375 := [monotonicity #4372]: #4374
+#4073 := (iff #3441 #4072)
+#4070 := (iff #2915 #4067)
+#4068 := (iff #2910 #2910)
+#4069 := [refl]: #4068
+#4071 := [quant-intro #4069]: #4070
+#4074 := [monotonicity #4071]: #4073
+#4378 := [monotonicity #4074 #4375]: #4377
+#4381 := [monotonicity #4378]: #4380
+#4384 := [monotonicity #4381]: #4383
+#4387 := [monotonicity #4384]: #4386
+#4064 := (iff #3455 #4063)
+#4061 := (iff #2870 #4058)
+#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
+#4399 := [monotonicity #4396]: #4398
+#4055 := (iff #1035 #4054)
+#4052 := (iff #1032 #4049)
+#4050 := (iff #1031 #1031)
+#4051 := [refl]: #4050
+#4053 := [quant-intro #4051]: #4052
+#4056 := [monotonicity #4053]: #4055
+#4402 := [monotonicity #4056 #4399]: #4401
+#4405 := [monotonicity #4402]: #4404
+#4408 := [monotonicity #4405]: #4407
+#4411 := [monotonicity #4408]: #4410
+#4414 := [monotonicity #4411]: #4413
+#4417 := [monotonicity #4414]: #4416
+#4420 := [monotonicity #4417]: #4419
+#2155 := (not #2154)
+#2752 := (and #201 #2155 #2749)
+#2755 := (not #2752)
+#2758 := (forall (vars (?x76 T2)) #2755)
+#2724 := (not #2721)
+#2160 := (not #2159)
+#2767 := (and #1349 #2160 #2724 #2758)
+#2129 := (not #2128)
+#2694 := (and #2129 #2130)
+#2697 := (not #2694)
+#2715 := (or #2697 #2710)
+#2718 := (not #2715)
+#2772 := (or #2718 #2767)
+#2775 := (and #1325 #2772)
+#2100 := (not #2099)
+#2669 := (and #2098 #2100)
+#2672 := (not #2669)
+#2688 := (or #2672 #2683)
+#2691 := (not #2688)
+#2778 := (or #2691 #2775)
+#2781 := (and #1311 #2778)
+#2784 := (or #2079 #2781)
+#2787 := (and #205 #2784)
+#2790 := (or #1305 #2787)
+#2793 := (and #667 #2790)
+#2796 := (or #2664 #2793)
+#2799 := (and #1297 #2796)
+#2802 := (or #2655 #2799)
+#2018 := (not #2017)
+#2016 := (not #2015)
+#2808 := (and #176 #184 #1286 #1439 #1452 #1460 #2016 #2018 #2802)
+#1961 := (not #1960)
+#1957 := (not #1956)
+#2592 := (and #1957 #1961)
+#2595 := (not #2592)
+#2612 := (or #2595 #2607)
+#2615 := (not #2612)
+#1970 := (not #162)
+#1980 := (and #1970 #1211)
+#2621 := (or #1980 #2615)
+#2565 := (not #2560)
+#2583 := (and #2565 #2578)
+#2586 := (or #1171 #2583)
+#2589 := (forall (vars (?x49 T2)) #2586)
+#2626 := (and #2589 #2621)
+#1890 := (not #1889)
+#2535 := (and #1890 #2532)
+#2538 := (not #2535)
+#2541 := (forall (vars (?x50 T2)) #2538)
+#2507 := (not #2504)
+#1895 := (not #1894)
+#2547 := (and #1895 #2507 #2541)
+#2629 := (or #2547 #2626)
+#1996 := (not #1236)
+#1999 := (forall (vars (?x48 T2)) #1996)
+#2635 := (and #140 #145 #492 #495 #1999 #2629)
+#2813 := (or #2635 #2808)
+#2484 := (not #2479)
+#2487 := (and #1854 #2467 #2484)
+#2490 := (or #1126 #2487)
+#2493 := (forall (vars (?x46 T2)) #2490)
+#2429 := (not #2424)
+#2447 := (and #1828 #2429 #2442)
+#2450 := (or #1088 #2447)
+#2453 := (forall (vars (?x37 T2)) #2450)
+#2819 := (and #106 #1519 #1530 #1539 #2453 #2493 #2813)
+#1784 := (not #1783)
+#2397 := (and #74 #1784 #2394)
+#2400 := (not #2397)
+#2403 := (forall (vars (?x38 T2)) #2400)
+#2369 := (not #2366)
+#1789 := (not #1788)
+#2409 := (and #1789 #2369 #2403)
+#2824 := (or #2409 #2819)
+#2827 := (and #1073 #2824)
+#1757 := (not #1756)
+#2347 := (and #1757 #1758)
+#2350 := (not #2347)
+#2360 := (or #2350 #2357)
+#2363 := (not #2360)
+#2830 := (or #2363 #2827)
+#2833 := (and #1047 #2830)
+#1728 := (not #1727)
+#2322 := (and #1726 #1728)
+#2325 := (not #2322)
+#2341 := (or #2325 #2336)
+#2344 := (not #2341)
+#2836 := (or #2344 #2833)
+#2839 := (and #1032 #2836)
+#2842 := (or #1707 #2839)
+#2845 := (and #78 #2842)
+#2848 := (or #1026 #2845)
+#3490 := (iff #2848 #3489)
+#3487 := (iff #2845 #3484)
+#3479 := (and #78 #3476)
+#3485 := (iff #3479 #3484)
+#3486 := [rewrite]: #3485
+#3480 := (iff #2845 #3479)
+#3477 := (iff #2842 #3476)
+#3474 := (iff #2839 #3471)
+#3466 := (and #1032 #3463)
+#3472 := (iff #3466 #3471)
+#3473 := [rewrite]: #3472
+#3467 := (iff #2839 #3466)
+#3464 := (iff #2836 #3463)
+#3461 := (iff #2833 #3458)
+#3452 := (and #2870 #3449)
+#3459 := (iff #3452 #3458)
+#3460 := [rewrite]: #3459
+#3453 := (iff #2833 #3452)
+#3450 := (iff #2830 #3449)
+#3447 := (iff #2827 #3444)
+#3438 := (and #2915 #3435)
+#3445 := (iff #3438 #3444)
+#3446 := [rewrite]: #3445
+#3439 := (iff #2827 #3438)
+#3436 := (iff #2824 #3435)
+#3433 := (iff #2819 #3430)
+#3421 := (and #106 #2962 #2985 #1539 #3013 #3041 #3418)
+#3431 := (iff #3421 #3430)
+#3432 := [rewrite]: #3431
+#3422 := (iff #2819 #3421)
+#3419 := (iff #2813 #3418)
+#3416 := (iff #2808 #3413)
+#3406 := (and #176 #184 #3199 #3217 #1452 #1460 #2016 #2018 #3403)
+#3414 := (iff #3406 #3413)
+#3415 := [rewrite]: #3414
+#3407 := (iff #2808 #3406)
+#3404 := (iff #2802 #3403)
+#3401 := (iff #2799 #3398)
+#3393 := (and #1297 #3390)
+#3399 := (iff #3393 #3398)
+#3400 := [rewrite]: #3399
+#3394 := (iff #2799 #3393)
+#3391 := (iff #2796 #3390)
+#3388 := (iff #2793 #3385)
+#3380 := (and #667 #3377)
+#3386 := (iff #3380 #3385)
+#3387 := [rewrite]: #3386
+#3381 := (iff #2793 #3380)
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+#3314 := (iff #2752 #3313)
+#3315 := [rewrite]: #3314
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+#3322 := [trans #3318 #3320]: #3321
+#3325 := [quant-intro #3322]: #3324
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+#3300 := (or #3289 #1342)
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+#3310 := [quant-intro #3307]: #3309
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+#3336 := [trans #3328 #3334]: #3335
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+#3254 := [trans #3250 #3252]: #3253
+#3257 := [monotonicity #3254]: #3256
+#3262 := [trans #3257 #3260]: #3261
+#3265 := [quant-intro #3262]: #3264
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+#3350 := [trans #3342 #3348]: #3349
+#3241 := (iff #2691 #3240)
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+#3221 := (or #3220 #2099)
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+#3223 := (iff #2669 #3222)
+#3224 := [rewrite]: #3223
+#3227 := [monotonicity #3224]: #3226
+#3231 := [trans #3227 #3229]: #3230
+#3234 := [monotonicity #3231]: #3233
+#3239 := [trans #3234 #3237]: #3238
+#3242 := [monotonicity #3239]: #3241
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+#3363 := [trans #3356 #3361]: #3362
+#3366 := [monotonicity #3363]: #3365
+#3369 := [monotonicity #3366]: #3368
+#3376 := [trans #3369 #3374]: #3375
+#3379 := [monotonicity #3376]: #3378
+#3382 := [monotonicity #3379]: #3381
+#3389 := [trans #3382 #3387]: #3388
+#3392 := [monotonicity #3389]: #3391
+#3395 := [monotonicity #3392]: #3394
+#3402 := [trans #3395 #3400]: #3401
+#3405 := [monotonicity #3402]: #3404
+#3218 := (iff #1439 #3217)
+#3215 := (iff #1436 #3212)
+#3209 := (or #3192 #1433)
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+#3204 := [monotonicity #3195]: #3203
+#3208 := [trans #3204 #3206]: #3207
+#3211 := [monotonicity #3208]: #3210
+#3216 := [trans #3211 #3214]: #3215
+#3219 := [quant-intro #3216]: #3218
+#3200 := (iff #1286 #3199)
+#3197 := (iff #1281 #3196)
+#3198 := [monotonicity #3195]: #3197
+#3201 := [quant-intro #3198]: #3200
+#3408 := [monotonicity #3201 #3219 #3405]: #3407
+#3417 := [trans #3408 #3415]: #3416
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+#3181 := (and #140 #145 #492 #495 #3055 #3178)
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+#3144 := (iff #2592 #3143)
+#3145 := [rewrite]: #3144
+#3148 := [monotonicity #3145]: #3147
+#3152 := [trans #3148 #3150]: #3151
+#3155 := [monotonicity #3152]: #3154
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+#3132 := (and #1970 #3129)
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+#3120 := [trans #3116 #3118]: #3119
+#3123 := [monotonicity #3120]: #3122
+#3128 := [trans #3123 #3126]: #3127
+#3131 := [quant-intro #3128]: #3130
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+#3099 := (or #3083 #3096)
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+#3101 := [monotonicity #3093 #3098]: #3100
+#3106 := [trans #3101 #3104]: #3105
+#3109 := [quant-intro #3106]: #3108
+#3169 := [monotonicity #3109 #3166]: #3168
+#3177 := [trans #3169 #3175]: #3176
+#3081 := (iff #2547 #3078)
+#3073 := (and #1895 #2507 #3070)
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+#3062 := [rewrite]: #3061
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+#3069 := [trans #3065 #3067]: #3068
+#3072 := [quant-intro #3069]: #3071
+#3075 := [monotonicity #3072]: #3074
+#3082 := [trans #3075 #3080]: #3081
+#3180 := [monotonicity #3082 #3177]: #3179
+#3056 := (iff #1999 #3055)
+#3053 := (iff #1996 #3044)
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+#3046 := (iff #1236 #3045)
+#3047 := [rewrite]: #3046
+#3050 := [monotonicity #3047]: #3049
+#3054 := [trans #3050 #3052]: #3053
+#3057 := [quant-intro #3054]: #3056
+#3183 := [monotonicity #3057 #3180]: #3182
+#3191 := [trans #3183 #3189]: #3190
+#3420 := [monotonicity #3191 #3417]: #3419
+#3042 := (iff #2493 #3041)
+#3039 := (iff #2490 #3036)
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+#3033 := (or #3016 #3030)
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+#3038 := [rewrite]: #3037
+#3034 := (iff #2490 #3033)
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+#3032 := [rewrite]: #3031
+#3025 := (iff #1126 #3016)
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+#3020 := (not #3017)
+#3023 := (iff #3020 #3016)
+#3024 := [rewrite]: #3023
+#3021 := (iff #1126 #3020)
+#3018 := (iff #1123 #3017)
+#3019 := [rewrite]: #3018
+#3022 := [monotonicity #3019]: #3021
+#3026 := [trans #3022 #3024]: #3025
+#3035 := [monotonicity #3026 #3032]: #3034
+#3040 := [trans #3035 #3038]: #3039
+#3043 := [quant-intro #3040]: #3042
+#3014 := (iff #2453 #3013)
+#3011 := (iff #2450 #3008)
+#2988 := (or #65 #1081)
+#3005 := (or #2988 #3002)
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+#3004 := [rewrite]: #3003
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+#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)
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+#2982 := [rewrite]: #2981
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+#2975 := (iff #440 #2966)
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+#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)
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+#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)
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+#2931 := (iff #2403 #2930)
+#2928 := (iff #2400 #2919)
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+#2923 := (not #2920)
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+#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)
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+#2912 := [rewrite]: #2911
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+#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)
-#3845 := (pattern #32)
+#4001 := (pattern #32)
 #35 := (up_6 #29 #11)
 #34 := (= #30 uf_8)
 #24 := (= #11 #20)
 #36 := (ite #24 #34 #35)
 #37 := (iff #32 #36)
-#3846 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) (:pat #3845) #37)
+#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)
-#3849 := (iff #38 #3846)
-#3847 := (iff #37 #37)
-#3848 := [refl]: #3847
-#3850 := [quant-intro #3848]: #3849
-#1505 := (~ #38 #38)
-#1541 := (~ #37 #37)
-#1542 := [refl]: #1541
-#1506 := [nnf-pos #1542]: #1505
-#309 := [asserted]: #38
-#1543 := [mp~ #309 #1506]: #38
-#3851 := [mp #1543 #3850]: #3846
-#6010 := (not #3846)
-#30184 := (or #6010 #14006)
-#5970 := (= uf_8 uf_8)
-#13995 := (ite #13994 #5970 #11031)
-#13997 := (iff #13996 #13995)
-#30185 := (or #6010 #13997)
-#30191 := (iff #30185 #30184)
-#30193 := (iff #30184 #30184)
-#30194 := [rewrite]: #30193
-#14007 := (iff #13997 #14006)
-#14004 := (iff #13995 #14001)
-#1 := true
-#13998 := (ite #13994 true #11031)
-#14002 := (iff #13998 #14001)
-#14003 := [rewrite]: #14002
-#13999 := (iff #13995 #13998)
-#5975 := (iff #5970 true)
-#5976 := [rewrite]: #5975
-#14000 := [monotonicity #5976]: #13999
-#14005 := [trans #14000 #14003]: #14004
-#14008 := [monotonicity #14005]: #14007
-#30192 := [monotonicity #14008]: #30191
-#30195 := [trans #30192 #30194]: #30191
-#30190 := [quant-inst]: #30185
-#30196 := [mp #30190 #30195]: #30184
-#30517 := [unit-resolution #30196 #3851]: #14006
-#30208 := (not #13996)
-#9424 := (up_6 uf_23 ?x75!20)
-#9640 := (not #9424)
-#30526 := (iff #9640 #30208)
-#30524 := (iff #9424 #13996)
-#30522 := (iff #13996 #9424)
-#8591 := (= #8048 uf_23)
-#191 := (uf_7 uf_15 uf_22 uf_8)
-#7418 := (= #191 uf_23)
-#192 := (= uf_23 #191)
-#4136 := (or #3126 #4133)
-#4139 := (not #4136)
-#4104 := (pattern #199 #226)
-#1336 := (>= #1338 0::int)
-#224 := (up_6 uf_23 #10)
-#3083 := (not #224)
-#3098 := (or #216 #3083 #1336)
-#4105 := (forall (vars (?x67 T2) (?x68 T2)) (:pat #4104) #3098)
-#4110 := (not #4105)
-#4142 := (or #4110 #4139)
-#4145 := (not #4142)
-decl ?x68!16 :: T2
-#1976 := ?x68!16
-#1980 := (uf_24 ?x68!16)
-#2517 := (* -1::int #1980)
-decl ?x67!17 :: T2
-#1977 := ?x67!17
-#1978 := (uf_24 ?x67!17)
-#2518 := (+ #1978 #2517)
-#2519 := (<= #2518 0::int)
-#1984 := (up_6 uf_23 ?x68!16)
-#1983 := (up_6 uf_23 ?x67!17)
-#3060 := (not #1983)
-#3075 := (or #3060 #1984 #2519)
-#3080 := (not #3075)
-#4148 := (or #3080 #4145)
-#4151 := (not #4148)
-#1327 := (>= #199 0::int)
-#4096 := (forall (vars (?x65 T2)) (:pat #4062) #1327)
-#4101 := (not #4096)
-#4154 := (or #4101 #4151)
-#4157 := (not #4154)
-decl ?x65!15 :: T2
-#1961 := ?x65!15
-#1962 := (uf_24 ?x65!15)
-#1963 := (>= #1962 0::int)
-#1964 := (not #1963)
-#4160 := (or #1964 #4157)
-#4163 := (not #4160)
-#219 := (uf_24 uf_11)
-#220 := (= #219 0::int)
-#1324 := (not #220)
-#4166 := (or #1324 #4163)
-#4169 := (not #4166)
-#4172 := (or #1324 #4169)
-#4175 := (not #4172)
-#110 := (uf_4 uf_14 #11)
-#3940 := (pattern #110)
-#658 := (= #110 #199)
-#700 := (or #223 #658)
-#4088 := (forall (vars (?x63 T2)) (:pat #4087 #3940 #4062) #700)
-#4093 := (not #4088)
-#4178 := (or #4093 #4175)
-#4181 := (not #4178)
-decl ?x63!14 :: T2
-#1937 := ?x63!14
-#1939 := (uf_4 uf_14 ?x63!14)
-#1938 := (uf_24 ?x63!14)
-#2494 := (= #1938 #1939)
-#1941 := (up_6 uf_23 ?x63!14)
-#1942 := (not #1941)
-#2497 := (or #1942 #2494)
-#2500 := (not #2497)
-#4184 := (or #2500 #4181)
-#4187 := (not #4184)
-#1248 := (* -1::int #199)
-#1313 := (+ #110 #1248)
-#1312 := (>= #1313 0::int)
-#4079 := (forall (vars (?x61 T2)) (:pat #3940 #4062) #1312)
-#4084 := (not #4079)
-#4190 := (or #4084 #4187)
-#4193 := (not #4190)
-decl ?x61!13 :: T2
-#1919 := ?x61!13
-#1922 := (uf_4 uf_14 ?x61!13)
-#2484 := (* -1::int #1922)
-#1920 := (uf_24 ?x61!13)
-#2485 := (+ #1920 #2484)
-#2486 := (<= #2485 0::int)
-#2491 := (not #2486)
-#4196 := (or #2491 #4193)
-#4199 := (not #4196)
-#193 := (uf_1 uf_22 #11)
-#4061 := (pattern #193)
-#194 := (uf_10 #193)
-#1229 := (* -1::int #194)
-#1235 := (* -1::int #185)
-#1236 := (+ #1235 #1229)
-#1237 := (+ #110 #1236)
-#1238 := (<= #1237 0::int)
-#1230 := (+ uf_9 #1229)
-#1231 := (<= #1230 0::int)
-#3032 := (or #1231 #1238)
-#3033 := (not #3032)
-#3054 := (or #658 #3033)
-#4071 := (forall (vars (?x60 T2)) (:pat #3940 #4062 #4061) #3054)
-#4076 := (not #4071)
-#1249 := (+ #194 #1248)
-#1250 := (+ #185 #1249)
-#1251 := (= #1250 0::int)
-#3046 := (or #1231 #1238 #1251)
-#4063 := (forall (vars (?x59 T2)) (:pat #4061 #3940 #4062) #3046)
-#4068 := (not #4063)
-decl ?x48!12 :: T2
-#1886 := ?x48!12
-#1892 := (up_6 uf_15 ?x48!12)
-#1887 := (uf_4 uf_14 ?x48!12)
-#1888 := (* -1::int #1887)
-#1889 := (+ uf_9 #1888)
-#1890 := (<= #1889 0::int)
-#1281 := (+ uf_9 #1235)
-#1282 := (<= #1281 0::int)
-#114 := (up_6 uf_15 #11)
-#3982 := (pattern #114)
-#1272 := (+ #110 #1235)
-#1271 := (>= #1272 0::int)
-#1275 := (or #114 #1271)
-#4053 := (forall (vars (?x58 T2)) (:pat #3982 #3940) #1275)
-#4058 := (not #4053)
-#3249 := (not #192)
-#183 := (up_6 uf_15 uf_22)
-#4202 := (or #183 #3249 #4058 #1282 #1890 #1892 #4068 #4076 #4199)
-#4205 := (not #4202)
-decl ?x53!11 :: T2
-#1827 := ?x53!11
-decl ?x54!10 :: T2
-#1826 := ?x54!10
-#1832 := (uf_1 ?x54!10 ?x53!11)
-#1833 := (uf_10 #1832)
-#1840 := (* -1::int #1833)
-decl uf_19 :: T3
-#150 := uf_19
-#1830 := (uf_4 uf_19 ?x54!10)
-#1836 := (* -1::int #1830)
-#2443 := (+ #1836 #1840)
-#1828 := (uf_4 uf_19 ?x53!11)
-#2444 := (+ #1828 #2443)
-#2445 := (<= #2444 0::int)
-#1841 := (+ uf_9 #1840)
-#1842 := (<= #1841 0::int)
-#1837 := (+ uf_9 #1836)
-#1838 := (<= #1837 0::int)
-#2992 := (or #1838 #1842 #2445)
-#2997 := (not #2992)
-#163 := (uf_4 uf_19 #10)
-#1165 := (* -1::int #163)
-#160 := (uf_4 uf_19 #11)
-#1166 := (+ #160 #1165)
-#1172 := (+ #91 #1166)
-#1195 := (>= #1172 0::int)
-#1152 := (* -1::int #160)
-#1153 := (+ uf_9 #1152)
-#1154 := (<= #1153 0::int)
-#2960 := (or #969 #1154 #1195)
-#4015 := (forall (vars (?x53 T2) (?x54 T2)) (:pat #3916) #2960)
-#4020 := (not #4015)
-#175 := (uf_4 uf_19 uf_11)
-#176 := (= #175 0::int)
-#4023 := (or #176 #4020)
-#4026 := (not #4023)
-#4029 := (or #4026 #2997)
-#4032 := (not #4029)
-#3991 := (pattern #160)
-decl ?x50!9 :: (-> T2 T2)
-#1803 := (?x50!9 #11)
-#1806 := (uf_1 #1803 #11)
-#1807 := (uf_10 #1806)
-#2413 := (* -1::int #1807)
-#1804 := (uf_4 uf_19 #1803)
-#2396 := (* -1::int #1804)
-#2414 := (+ #2396 #2413)
-#2415 := (+ #160 #2414)
-#2416 := (= #2415 0::int)
-#2930 := (not #2416)
-#2397 := (+ #160 #2396)
-#2398 := (<= #2397 0::int)
-#2931 := (or #2398 #2930)
-#2932 := (not #2931)
-#65 := (= #11 uf_11)
-#2938 := (or #65 #1154 #2932)
-#4007 := (forall (vars (?x49 T2)) (:pat #3991) #2938)
-#4012 := (not #4007)
-#4035 := (or #4012 #4032)
-#4038 := (not #4035)
-decl ?x49!8 :: T2
-#1763 := ?x49!8
-#1767 := (uf_1 #11 ?x49!8)
-#3992 := (pattern #1767)
-#1768 := (uf_10 #1767)
-#1764 := (uf_4 uf_19 ?x49!8)
-#1765 := (* -1::int #1764)
-#2366 := (+ #1765 #1768)
-#2367 := (+ #160 #2366)
-#2370 := (= #2367 0::int)
-#2894 := (not #2370)
-#1766 := (+ #160 #1765)
-#1771 := (>= #1766 0::int)
-#2895 := (or #1771 #2894)
-#3993 := (forall (vars (?x50 T2)) (:pat #3991 #3992) #2895)
-#3998 := (not #3993)
-#2342 := (= uf_11 ?x49!8)
-#1775 := (+ uf_9 #1765)
-#1776 := (<= #1775 0::int)
-#4001 := (or #1776 #2342 #3998)
-#4004 := (not #4001)
-#4041 := (or #4004 #4038)
-#4044 := (not #4041)
-#1054 := (* -1::int #110)
-#1055 := (+ uf_9 #1054)
-#1056 := (<= #1055 0::int)
-#2880 := (or #114 #1056)
-#3983 := (forall (vars (?x48 T2)) (:pat #3982 #3940) #2880)
-#3988 := (not #3983)
-#533 := (= uf_14 uf_19)
-#3023 := (not #533)
-decl uf_16 :: T4
-#145 := uf_16
-#530 := (= uf_15 uf_16)
-#3022 := (not #530)
-decl uf_21 :: T3
-#153 := uf_21
-decl uf_20 :: T3
-#152 := uf_20
-#154 := (= uf_20 uf_21)
-#3021 := (not #154)
-decl uf_18 :: T2
-#148 := uf_18
-decl uf_17 :: T2
-#147 := uf_17
-#149 := (= uf_17 uf_18)
-#3020 := (not #149)
-#4047 := (or #3020 #3021 #3022 #3023 #3988 #4044)
-#4050 := (not #4047)
-#4208 := (or #4050 #4205)
-#4211 := (not #4208)
-#1708 := (?x47!7 #11)
-#1709 := (uf_4 uf_14 #1708)
-#2309 := (* -1::int #1709)
-#2324 := (+ #110 #2309)
-#2325 := (<= #2324 0::int)
-#1713 := (uf_1 #1708 #11)
-#1714 := (uf_10 #1713)
-#2310 := (* -1::int #1714)
-#2311 := (+ #2309 #2310)
-#2312 := (+ #110 #2311)
-#2313 := (= #2312 0::int)
-#2864 := (not #2313)
-#1717 := (up_6 uf_15 #1708)
-#2863 := (not #1717)
-#2865 := (or #2863 #2864 #2325)
-#2866 := (not #2865)
-#2872 := (or #65 #1056 #2866)
-#3974 := (forall (vars (?x46 T2)) (:pat #3940) #2872)
-#3979 := (not #3974)
-decl uf_12 :: (-> T2 int)
-#66 := (uf_12 #11)
-#3886 := (pattern #66)
-decl ?x38!6 :: (-> T2 T2)
-#1680 := (?x38!6 #11)
-#1684 := (uf_12 #1680)
-#2268 := (* -1::int #1684)
-#1681 := (uf_1 #1680 #11)
-#1682 := (uf_10 #1681)
-#2285 := (* -1::int #1682)
-#2286 := (+ #2285 #2268)
-#2287 := (+ #66 #2286)
-#2288 := (= #2287 0::int)
-#2836 := (not #2288)
-#2269 := (+ #66 #2268)
-#2270 := (<= #2269 0::int)
-decl up_13 :: (-> T2 bool)
-#1690 := (up_13 #1680)
-#2835 := (not #1690)
-#2837 := (or #2835 #2270 #2836)
-#2838 := (not #2837)
-#993 := (* -1::int #66)
-#994 := (+ uf_9 #993)
-#995 := (<= #994 0::int)
-#2844 := (or #65 #995 #2838)
-#3966 := (forall (vars (?x37 T2)) (:pat #3886) #2844)
-#3971 := (not #3966)
-#116 := (up_6 uf_15 #10)
-#3957 := (pattern #114 #116)
-#118 := (uf_4 uf_14 #10)
-#1045 := (* -1::int #118)
-#1046 := (+ #110 #1045)
-#1069 := (>= #1046 0::int)
-#2801 := (not #116)
-#2816 := (or #114 #2801 #1069)
-#3958 := (forall (vars (?x42 T2) (?x43 T2)) (:pat #3957) #2816)
-#3963 := (not #3958)
-#1047 := (+ #91 #1046)
-#1043 := (>= #1047 0::int)
-#115 := (not #114)
-#2793 := (or #115 #969 #1043)
-#3949 := (forall (vars (?x44 T2) (?x45 T2)) (:pat #3916) #2793)
-#3954 := (not #3949)
-#1101 := (>= #110 0::int)
-#3941 := (forall (vars (?x41 T2)) (:pat #3940) #1101)
-#3946 := (not #3941)
-#108 := (uf_4 uf_14 uf_11)
-#109 := (= #108 0::int)
-#3266 := (not #109)
-#4214 := (or #3266 #3946 #3954 #3963 #3971 #3979 #4211)
-#4217 := (not #4214)
-decl ?x37!5 :: T2
-#1636 := ?x37!5
-#1637 := (uf_1 #11 ?x37!5)
-#3925 := (pattern #1637)
-#74 := (up_13 #11)
-#3879 := (pattern #74)
-#1639 := (uf_12 ?x37!5)
-#1640 := (* -1::int #1639)
-#1638 := (uf_10 #1637)
-#2238 := (+ #1638 #1640)
-#2239 := (+ #66 #2238)
-#2242 := (= #2239 0::int)
-#2754 := (not #2242)
-#1644 := (+ #66 #1640)
-#1645 := (>= #1644 0::int)
-#75 := (not #74)
-#2755 := (or #75 #1645 #2754)
-#3926 := (forall (vars (?x38 T2)) (:pat #3879 #3886 #3925) #2755)
-#3931 := (not #3926)
-#2214 := (= uf_11 ?x37!5)
-#1649 := (+ uf_9 #1640)
-#1650 := (<= #1649 0::int)
-#3934 := (or #1650 #2214 #3931)
-#3937 := (not #3934)
-#4220 := (or #3937 #4217)
-#4223 := (not #4220)
-#86 := (uf_12 #10)
-#955 := (* -1::int #86)
-#982 := (+ #955 #91)
-#983 := (+ #66 #982)
-#980 := (>= #983 0::int)
-#2746 := (or #75 #969 #980)
-#3917 := (forall (vars (?x33 T2) (?x34 T2)) (:pat #3916) #2746)
-#3922 := (not #3917)
-#4226 := (or #3922 #4223)
-#4229 := (not #4226)
-decl ?x34!3 :: T2
-#1606 := ?x34!3
-#1613 := (uf_12 ?x34!3)
-decl ?x33!4 :: T2
-#1607 := ?x33!4
-#1610 := (uf_12 ?x33!4)
-#1611 := (* -1::int #1610)
-#2201 := (+ #1611 #1613)
-#1608 := (uf_1 ?x34!3 ?x33!4)
-#1609 := (uf_10 #1608)
-#2202 := (+ #1609 #2201)
-#2205 := (>= #2202 0::int)
-#1620 := (up_13 ?x34!3)
-#2709 := (not #1620)
-#1616 := (* -1::int #1609)
-#1617 := (+ uf_9 #1616)
-#1618 := (<= #1617 0::int)
-#2724 := (or #1618 #2709 #2205)
-#2729 := (not #2724)
-#4232 := (or #2729 #4229)
-#4235 := (not #4232)
-#84 := (up_13 #10)
-#3907 := (pattern #74 #84)
-#956 := (+ #66 #955)
-#954 := (>= #956 0::int)
-#1898 := (not #84)
-#2701 := (or #74 #1898 #954)
-#3908 := (forall (vars (?x29 T2) (?x30 T2)) (:pat #3907) #2701)
-#3913 := (not #3908)
-#4238 := (or #3913 #4235)
-#4241 := (not #4238)
-decl ?x30!1 :: T2
-#1581 := ?x30!1
-#1585 := (uf_12 ?x30!1)
-#2182 := (* -1::int #1585)
-decl ?x29!2 :: T2
-#1582 := ?x29!2
-#1583 := (uf_12 ?x29!2)
-#2183 := (+ #1583 #2182)
-#2184 := (<= #2183 0::int)
-#1589 := (up_13 ?x30!1)
-#1588 := (up_13 ?x29!2)
-#1597 := (not #1588)
-#1948 := (or #1597 #1589 #2184)
-#2022 := (not #1948)
-#4244 := (or #2022 #4241)
-#4247 := (not #4244)
-#945 := (>= #66 0::int)
-#3899 := (forall (vars (?x27 T2)) (:pat #3886) #945)
-#3904 := (not #3899)
-#4250 := (or #3904 #4247)
-#4253 := (not #4250)
-decl ?x27!0 :: T2
-#1566 := ?x27!0
-#1567 := (uf_12 ?x27!0)
-#1568 := (>= #1567 0::int)
-#1569 := (not #1568)
-#4256 := (or #1569 #4253)
-#4259 := (not #4256)
-#80 := (uf_12 uf_11)
-#81 := (= #80 0::int)
-#940 := (not #81)
-#4262 := (or #940 #4259)
-#4265 := (not #4262)
-#4992 := [hypothesis]: #940
-#67 := (= #66 0::int)
-#70 := (not #65)
-#921 := (or #70 #67)
-#3893 := (forall (vars (?x24 T2)) (:pat #3886) #921)
-#924 := (forall (vars (?x24 T2)) #921)
-#3896 := (iff #924 #3893)
-#3894 := (iff #921 #921)
-#3895 := [refl]: #3894
-#3897 := [quant-intro #3895]: #3896
-#1521 := (~ #924 #924)
-#1560 := (~ #921 #921)
-#1561 := [refl]: #1560
-#1522 := [nnf-pos #1561]: #1521
-#397 := (= uf_9 #66)
-#403 := (or #65 #397)
-#408 := (forall (vars (?x25 T2)) #403)
-#76 := (forall (vars (?x26 T2)) #75)
-#930 := (and #76 #408 #924)
-#1385 := (= #1363 0::int)
-#1388 := (not #1336)
-#1397 := (and #216 #1388 #1385)
-#1402 := (exists (vars (?x76 T2)) #1397)
-#1374 := (+ uf_9 #1248)
-#1375 := (<= #1374 0::int)
-#1376 := (not #1375)
-#1379 := (and #70 #1376)
-#1382 := (not #1379)
-#1405 := (or #1382 #1402)
-#1408 := (forall (vars (?x75 T2)) #1405)
-#970 := (not #969)
-#1353 := (and #216 #970)
-#1358 := (not #1353)
-#1365 := (or #1358 #1361)
-#1368 := (forall (vars (?x71 T2) (?x72 T2)) #1365)
-#1371 := (not #1368)
-#1411 := (or #1371 #1408)
-#1414 := (and #1368 #1411)
-#225 := (and #223 #224)
-#711 := (not #225)
-#1341 := (or #711 #1336)
-#1344 := (forall (vars (?x67 T2) (?x68 T2)) #1341)
-#1347 := (not #1344)
-#1417 := (or #1347 #1414)
-#1420 := (and #1344 #1417)
-#1330 := (forall (vars (?x65 T2)) #1327)
-#1333 := (not #1330)
-#1423 := (or #1333 #1420)
-#1426 := (and #1330 #1423)
-#1429 := (or #1324 #1426)
-#1432 := (and #220 #1429)
-#705 := (forall (vars (?x63 T2)) #700)
-#814 := (not #705)
-#1435 := (or #814 #1432)
-#1438 := (and #705 #1435)
-#1316 := (forall (vars (?x61 T2)) #1312)
-#1319 := (not #1316)
-#1441 := (or #1319 #1438)
-#1444 := (and #1316 #1441)
-#1283 := (not #1282)
-#1278 := (forall (vars (?x58 T2)) #1275)
-#1239 := (not #1238)
-#1232 := (not #1231)
-#1242 := (and #1232 #1239)
-#1263 := (or #658 #1242)
-#1268 := (forall (vars (?x60 T2)) #1263)
-#1245 := (not #1242)
-#1254 := (or #1245 #1251)
-#1257 := (forall (vars (?x59 T2)) #1254)
-#1057 := (not #1056)
-#1132 := (and #115 #1057)
-#1135 := (exists (vars (?x48 T2)) #1132)
-#184 := (not #183)
-#1304 := (and #184 #192 #1135 #1257 #1268 #1278 #1283)
-#1309 := (not #1304)
-#1447 := (or #1309 #1444)
-#1155 := (not #1154)
-#1189 := (and #970 #1155)
-#1192 := (not #1189)
-#1198 := (or #1192 #1195)
-#1201 := (forall (vars (?x53 T2) (?x54 T2)) #1198)
-#1204 := (not #1201)
-#1212 := (or #176 #1204)
-#1217 := (and #1201 #1212)
-#1170 := (= #1172 0::int)
-#1164 := (>= #1166 0::int)
-#1167 := (not #1164)
-#1174 := (and #1167 #1170)
-#1177 := (exists (vars (?x50 T2)) #1174)
-#1158 := (and #70 #1155)
-#1161 := (not #1158)
-#1180 := (or #1161 #1177)
-#1183 := (forall (vars (?x49 T2)) #1180)
-#1186 := (not #1183)
-#1220 := (or #1186 #1217)
-#1223 := (and #1183 #1220)
-#1138 := (not #1135)
-#1144 := (and #149 #154 #530 #533 #1138)
-#1149 := (not #1144)
-#1226 := (or #1149 #1223)
-#1450 := (and #1226 #1447)
-#1104 := (forall (vars (?x41 T2)) #1101)
-#117 := (and #115 #116)
-#456 := (not #117)
-#1095 := (or #456 #1069)
-#1098 := (forall (vars (?x42 T2) (?x43 T2)) #1095)
-#1070 := (not #1069)
-#1066 := (= #1047 0::int)
-#1079 := (and #114 #1066 #1070)
-#1084 := (exists (vars (?x47 T2)) #1079)
-#1060 := (and #70 #1057)
-#1063 := (not #1060)
-#1087 := (or #1063 #1084)
-#1090 := (forall (vars (?x46 T2)) #1087)
-#1034 := (and #114 #970)
-#1039 := (not #1034)
-#1048 := (or #1039 #1043)
-#1051 := (forall (vars (?x44 T2) (?x45 T2)) #1048)
-#1005 := (= #983 0::int)
-#1008 := (not #954)
-#1017 := (and #74 #1008 #1005)
-#1022 := (exists (vars (?x38 T2)) #1017)
-#996 := (not #995)
-#999 := (and #70 #996)
-#1002 := (not #999)
-#1025 := (or #1002 #1022)
-#1028 := (forall (vars (?x37 T2)) #1025)
-#1124 := (and #109 #1028 #1051 #1090 #1098 #1104)
-#1129 := (not #1124)
-#1453 := (or #1129 #1450)
-#1456 := (and #1028 #1453)
-#973 := (and #74 #970)
-#976 := (not #973)
-#984 := (or #976 #980)
-#987 := (forall (vars (?x33 T2) (?x34 T2)) #984)
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-#432 := (not #85)
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-#964 := (not #961)
-#1465 := (or #964 #1462)
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-#946 := (forall (vars (?x27 T2)) #945)
-#949 := (not #946)
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-#1480 := (and #81 #1477)
-#935 := (not #930)
-#1483 := (or #935 #1480)
-#1486 := (not #1483)
-#231 := (+ #199 #91)
-#238 := (= #226 #231)
-#239 := (and #216 #238)
-#237 := (< #199 #226)
-#240 := (and #237 #239)
-#241 := (exists (vars (?x76 T2)) #240)
-#235 := (< #199 uf_9)
-#236 := (and #70 #235)
-#242 := (implies #236 #241)
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-#232 := (<= #226 #231)
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-#230 := (and #216 #92)
-#233 := (implies #230 #232)
-#234 := (forall (vars (?x71 T2) (?x72 T2)) #233)
-#244 := (implies #234 #243)
-#245 := (and #234 #244)
-#227 := (<= #226 #199)
-#228 := (implies #225 #227)
-#229 := (forall (vars (?x67 T2) (?x68 T2)) #228)
-#246 := (implies #229 #245)
-#247 := (and #229 #246)
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-#248 := (implies #222 #247)
-#249 := (and #222 #248)
-#250 := (implies #220 #249)
-#251 := (and #220 #250)
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-#218 := (forall (vars (?x63 T2)) #217)
-#252 := (implies #218 #251)
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-#254 := (implies #215 #253)
-#255 := (and #215 #254)
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-#197 := (< #196 #110)
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-#198 := (and #195 #197)
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-#205 := (implies #203 #204)
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-#201 := (implies #198 #200)
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-#208 := (and #192 #207)
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-#211 := (and #184 #210)
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-#212 := (and #143 #211)
-#213 := (and true #212)
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-#177 := (implies #174 #176)
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-#164 := (< #160 #163)
-#167 := (and #164 #166)
-#168 := (exists (vars (?x50 T2)) #167)
-#162 := (and #70 #161)
-#169 := (implies #162 #168)
-#170 := (forall (vars (?x49 T2)) #169)
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-#180 := (and #170 #179)
-#151 := (= uf_19 uf_14)
-#155 := (and #151 #154)
-#156 := (and #149 #155)
-#146 := (= uf_16 uf_15)
-#157 := (and #146 #156)
-#144 := (not #143)
-#158 := (and #144 #157)
-#159 := (and true #158)
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-#123 := (+ #110 #91)
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-#131 := (and #114 #130)
-#129 := (< #110 #118)
-#132 := (and #129 #131)
-#133 := (exists (vars (?x47 T2)) #132)
-#128 := (and #70 #127)
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-#135 := (forall (vars (?x46 T2)) #134)
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-#122 := (and #114 #92)
-#125 := (implies #122 #124)
-#126 := (forall (vars (?x44 T2) (?x45 T2)) #125)
-#136 := (and #126 #135)
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-#120 := (implies #117 #119)
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-#112 := (forall (vars (?x41 T2)) #111)
-#138 := (and #112 #137)
-#139 := (and #109 #138)
-#140 := (and true #139)
-#94 := (+ #66 #91)
-#101 := (= #86 #94)
-#102 := (and #74 #101)
-#100 := (< #66 #86)
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-#99 := (and #70 #98)
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-#106 := (forall (vars (?x37 T2)) #105)
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-#95 := (<= #86 #94)
-#93 := (and #74 #92)
-#96 := (implies #93 #95)
-#97 := (forall (vars (?x33 T2) (?x34 T2)) #96)
-#260 := (implies #97 #259)
-#261 := (and #97 #260)
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-#88 := (implies #85 #87)
-#89 := (forall (vars (?x29 T2) (?x30 T2)) #88)
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-#77 := (and #73 #76)
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-#78 := (and #69 #77)
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-#718 := (and #92 #216)
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-#767 := (or #766 #760)
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-#779 := (or #778 #772)
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-#791 := (or #790 #784)
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-#708 := (= 0::int #219)
-#802 := (not #708)
-#803 := (or #802 #796)
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-#815 := (or #814 #808)
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-#669 := (forall (vars (?x60 T2)) #664)
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-#672 := (and #655 #669)
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-#687 := (and #143 #684)
-#838 := (not #687)
-#839 := (or #838 #832)
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-#560 := (+ #91 #160)
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-#584 := (and #92 #161)
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-#594 := (or #593 #587)
-#599 := (forall (vars (?x53 T2) (?x54 T2)) #594)
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-#609 := (or #608 #602)
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-#1396 := [monotonicity #1390 #1393]: #1395
-#1401 := [trans #1396 #1399]: #1400
-#1404 := [quant-intro #1401]: #1403
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-#1410 := [quant-intro #1407]: #1409
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-#1346 := [quant-intro #1343]: #1345
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-#1315 := [rewrite]: #1314
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-#1143 := [monotonicity #1140]: #1142
-#1148 := [trans #1143 #1146]: #1147
-#1151 := [monotonicity #1148]: #1150
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-#1452 := [monotonicity #1228 #1449]: #1451
-#1130 := (iff #850 #1129)
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-#1086 := [quant-intro #1083]: #1085
-#1064 := (iff #499 #1063)
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-#1062 := [monotonicity #1059]: #1061
-#1065 := [monotonicity #1062]: #1064
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-#1012 := (iff #102 #1011)
-#1006 := (iff #101 #1005)
-#1007 := [rewrite]: #1006
-#1013 := [monotonicity #1007]: #1012
-#1009 := (iff #100 #1008)
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-#1016 := [monotonicity #1010 #1013]: #1015
-#1021 := [trans #1016 #1019]: #1020
-#1024 := [quant-intro #1021]: #1023
-#1003 := (iff #446 #1002)
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-#997 := (iff #98 #996)
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-#1004 := [monotonicity #1001]: #1003
-#1027 := [monotonicity #1004 #1024]: #1026
-#1030 := [quant-intro #1027]: #1029
-#1123 := [monotonicity #1030 #1120]: #1122
-#1128 := [trans #1123 #1126]: #1127
-#1131 := [monotonicity #1128]: #1130
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-#1458 := [monotonicity #1030 #1455]: #1457
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-#985 := (iff #440 #984)
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-#978 := [monotonicity #975]: #977
-#986 := [monotonicity #978 #981]: #985
-#989 := [quant-intro #986]: #988
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-#1461 := [monotonicity #992 #1458]: #1460
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-#965 := (iff #874 #964)
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-#959 := (iff #433 #958)
-#953 := (iff #87 #954)
-#957 := [rewrite]: #953
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-#942 := [monotonicity #939]: #941
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-#1482 := [monotonicity #939 #1479]: #1481
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-#933 := (iff #419 #930)
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-#920 := [rewrite]: #919
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-#929 := [monotonicity #926]: #928
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-#937 := [monotonicity #934]: #936
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-#914 := (iff #268 #911)
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-#890 := (iff #264 #887)
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-#878 := (iff #262 #875)
-#871 := (implies #436 #868)
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-#872 := (iff #262 #871)
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-#859 := (implies #443 #856)
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-#385 := [rewrite]: #384
-#388 := [monotonicity #385]: #387
-#393 := [trans #388 #391]: #392
-#396 := [quant-intro #393]: #395
-#421 := [monotonicity #396 #418]: #420
-#424 := [monotonicity #421]: #423
-#428 := [trans #424 #426]: #427
-#909 := [monotonicity #428 #906]: #908
-#915 := [trans #909 #913]: #914
-#918 := [monotonicity #915]: #917
-#1490 := [trans #918 #1488]: #1489
-#382 := [asserted]: #269
-#1491 := [mp #382 #1490]: #1486
-#1492 := [not-or-elim #1491]: #930
-#1495 := [and-elim #1492]: #924
-#1562 := [mp~ #1495 #1522]: #924
-#3898 := [mp #1562 #3897]: #3893
-#4872 := (not #3893)
-#4974 := (or #4872 #81)
-#3593 := (= uf_11 uf_11)
-#4532 := (not #3593)
-#4917 := (or #4532 #81)
-#4975 := (or #4872 #4917)
-#4976 := (iff #4975 #4974)
-#4978 := (iff #4974 #4974)
-#4979 := [rewrite]: #4978
-#4972 := (iff #4917 #81)
-#4951 := (or false #81)
-#4969 := (iff #4951 #81)
-#4971 := [rewrite]: #4969
-#4952 := (iff #4917 #4951)
-#4949 := (iff #4532 false)
-#4945 := (not true)
-#4948 := (iff #4945 false)
-#4943 := [rewrite]: #4948
-#4946 := (iff #4532 #4945)
-#4918 := (iff #3593 true)
-#4944 := [rewrite]: #4918
-#4947 := [monotonicity #4944]: #4946
-#4950 := [trans #4947 #4943]: #4949
-#4953 := [monotonicity #4950]: #4952
-#4973 := [trans #4953 #4971]: #4972
-#4977 := [monotonicity #4973]: #4976
-#4980 := [trans #4977 #4979]: #4976
-#4970 := [quant-inst]: #4975
-#4990 := [mp #4970 #4980]: #4974
-#4993 := [unit-resolution #4990 #3898 #4992]: false
-#4994 := [lemma #4993]: #81
-#4268 := (or #940 #4265)
-#3163 := (forall (vars (?x76 T2)) #3152)
-#3170 := (not #3163)
-#3148 := (forall (vars (?x71 T2) (?x72 T2)) #3143)
-#3169 := (not #3148)
-#3171 := (or #2044 #2557 #3169 #3170)
-#3172 := (not #3171)
-#3177 := (or #3126 #3172)
-#3184 := (not #3177)
-#3103 := (forall (vars (?x67 T2) (?x68 T2)) #3098)
-#3183 := (not #3103)
-#3185 := (or #3183 #3184)
-#3186 := (not #3185)
-#3191 := (or #3080 #3186)
-#3197 := (not #3191)
-#3198 := (or #1333 #3197)
-#3199 := (not #3198)
-#3204 := (or #1964 #3199)
-#3210 := (not #3204)
-#3211 := (or #1324 #3210)
-#3212 := (not #3211)
-#3217 := (or #1324 #3212)
-#3223 := (not #3217)
-#3224 := (or #814 #3223)
-#3225 := (not #3224)
-#3230 := (or #2500 #3225)
-#3236 := (not #3230)
-#3237 := (or #1319 #3236)
-#3238 := (not #3237)
-#3243 := (or #2491 #3238)
-#3253 := (not #3243)
-#3057 := (forall (vars (?x60 T2)) #3054)
-#3251 := (not #3057)
-#3051 := (forall (vars (?x59 T2)) #3046)
-#3250 := (not #3051)
-#3252 := (not #1278)
-#3254 := (or #183 #3249 #3252 #1282 #1890 #1892 #3250 #3251 #3253)
-#3255 := (not #3254)
-#2965 := (forall (vars (?x53 T2) (?x54 T2)) #2960)
-#2971 := (not #2965)
-#2972 := (or #176 #2971)
-#2973 := (not #2972)
-#3000 := (or #2973 #2997)
-#3007 := (not #3000)
-#2943 := (forall (vars (?x49 T2)) #2938)
-#3006 := (not #2943)
-#3008 := (or #3006 #3007)
-#3009 := (not #3008)
-#2906 := (forall (vars (?x50 T2)) #2895)
-#2912 := (not #2906)
-#2913 := (or #1776 #2342 #2912)
-#2914 := (not #2913)
-#3014 := (or #2914 #3009)
-#3025 := (not #3014)
-#2891 := (forall (vars (?x48 T2)) #2880)
-#3024 := (not #2891)
-#3026 := (or #3020 #3021 #3022 #3023 #3024 #3025)
-#3027 := (not #3026)
-#3260 := (or #3027 #3255)
-#3272 := (not #3260)
-#2877 := (forall (vars (?x46 T2)) #2872)
-#3271 := (not #2877)
-#2849 := (forall (vars (?x37 T2)) #2844)
-#3270 := (not #2849)
-#2821 := (forall (vars (?x42 T2) (?x43 T2)) #2816)
-#3268 := (not #2821)
-#2798 := (forall (vars (?x44 T2) (?x45 T2)) #2793)
-#3267 := (not #2798)
-#3269 := (not #1104)
-#3273 := (or #3266 #3269 #3267 #3268 #3270 #3271 #3272)
-#3274 := (not #3273)
-#2766 := (forall (vars (?x38 T2)) #2755)
-#2772 := (not #2766)
-#2773 := (or #1650 #2214 #2772)
-#2774 := (not #2773)
-#3279 := (or #2774 #3274)
-#3286 := (not #3279)
-#2751 := (forall (vars (?x33 T2) (?x34 T2)) #2746)
-#3285 := (not #2751)
-#3287 := (or #3285 #3286)
-#3288 := (not #3287)
-#3293 := (or #2729 #3288)
-#3300 := (not #3293)
-#2706 := (forall (vars (?x29 T2) (?x30 T2)) #2701)
-#3299 := (not #2706)
-#3301 := (or #3299 #3300)
-#3302 := (not #3301)
-#3307 := (or #2022 #3302)
-#3313 := (not #3307)
-#3314 := (or #949 #3313)
-#3315 := (not #3314)
-#3320 := (or #1569 #3315)
-#3326 := (not #3320)
-#3327 := (or #940 #3326)
-#3328 := (not #3327)
-#3333 := (or #940 #3328)
-#4269 := (iff #3333 #4268)
-#4266 := (iff #3328 #4265)
-#4263 := (iff #3327 #4262)
-#4260 := (iff #3326 #4259)
-#4257 := (iff #3320 #4256)
-#4254 := (iff #3315 #4253)
-#4251 := (iff #3314 #4250)
-#4248 := (iff #3313 #4247)
-#4245 := (iff #3307 #4244)
-#4242 := (iff #3302 #4241)
-#4239 := (iff #3301 #4238)
-#4236 := (iff #3300 #4235)
-#4233 := (iff #3293 #4232)
-#4230 := (iff #3288 #4229)
-#4227 := (iff #3287 #4226)
-#4224 := (iff #3286 #4223)
-#4221 := (iff #3279 #4220)
-#4218 := (iff #3274 #4217)
-#4215 := (iff #3273 #4214)
-#4212 := (iff #3272 #4211)
-#4209 := (iff #3260 #4208)
-#4206 := (iff #3255 #4205)
-#4203 := (iff #3254 #4202)
-#4200 := (iff #3253 #4199)
-#4197 := (iff #3243 #4196)
-#4194 := (iff #3238 #4193)
-#4191 := (iff #3237 #4190)
-#4188 := (iff #3236 #4187)
-#4185 := (iff #3230 #4184)
-#4182 := (iff #3225 #4181)
-#4179 := (iff #3224 #4178)
-#4176 := (iff #3223 #4175)
-#4173 := (iff #3217 #4172)
-#4170 := (iff #3212 #4169)
-#4167 := (iff #3211 #4166)
-#4164 := (iff #3210 #4163)
-#4161 := (iff #3204 #4160)
-#4158 := (iff #3199 #4157)
-#4155 := (iff #3198 #4154)
-#4152 := (iff #3197 #4151)
-#4149 := (iff #3191 #4148)
-#4146 := (iff #3186 #4145)
-#4143 := (iff #3185 #4142)
-#4140 := (iff #3184 #4139)
-#4137 := (iff #3177 #4136)
-#4134 := (iff #3172 #4133)
-#4131 := (iff #3171 #4130)
-#4128 := (iff #3170 #4127)
-#4125 := (iff #3163 #4122)
-#4123 := (iff #3152 #3152)
-#4124 := [refl]: #4123
-#4126 := [quant-intro #4124]: #4125
-#4129 := [monotonicity #4126]: #4128
-#4119 := (iff #3169 #4118)
-#4116 := (iff #3148 #4113)
-#4114 := (iff #3143 #3143)
-#4115 := [refl]: #4114
-#4117 := [quant-intro #4115]: #4116
-#4120 := [monotonicity #4117]: #4119
-#4132 := [monotonicity #4120 #4129]: #4131
-#4135 := [monotonicity #4132]: #4134
-#4138 := [monotonicity #4135]: #4137
-#4141 := [monotonicity #4138]: #4140
-#4111 := (iff #3183 #4110)
-#4108 := (iff #3103 #4105)
-#4106 := (iff #3098 #3098)
-#4107 := [refl]: #4106
-#4109 := [quant-intro #4107]: #4108
-#4112 := [monotonicity #4109]: #4111
-#4144 := [monotonicity #4112 #4141]: #4143
-#4147 := [monotonicity #4144]: #4146
-#4150 := [monotonicity #4147]: #4149
-#4153 := [monotonicity #4150]: #4152
-#4102 := (iff #1333 #4101)
-#4099 := (iff #1330 #4096)
-#4097 := (iff #1327 #1327)
-#4098 := [refl]: #4097
-#4100 := [quant-intro #4098]: #4099
-#4103 := [monotonicity #4100]: #4102
-#4156 := [monotonicity #4103 #4153]: #4155
-#4159 := [monotonicity #4156]: #4158
-#4162 := [monotonicity #4159]: #4161
-#4165 := [monotonicity #4162]: #4164
-#4168 := [monotonicity #4165]: #4167
-#4171 := [monotonicity #4168]: #4170
-#4174 := [monotonicity #4171]: #4173
-#4177 := [monotonicity #4174]: #4176
-#4094 := (iff #814 #4093)
-#4091 := (iff #705 #4088)
-#4089 := (iff #700 #700)
-#4090 := [refl]: #4089
-#4092 := [quant-intro #4090]: #4091
-#4095 := [monotonicity #4092]: #4094
-#4180 := [monotonicity #4095 #4177]: #4179
-#4183 := [monotonicity #4180]: #4182
-#4186 := [monotonicity #4183]: #4185
-#4189 := [monotonicity #4186]: #4188
-#4085 := (iff #1319 #4084)
-#4082 := (iff #1316 #4079)
-#4080 := (iff #1312 #1312)
-#4081 := [refl]: #4080
-#4083 := [quant-intro #4081]: #4082
-#4086 := [monotonicity #4083]: #4085
-#4192 := [monotonicity #4086 #4189]: #4191
-#4195 := [monotonicity #4192]: #4194
-#4198 := [monotonicity #4195]: #4197
-#4201 := [monotonicity #4198]: #4200
-#4077 := (iff #3251 #4076)
-#4074 := (iff #3057 #4071)
-#4072 := (iff #3054 #3054)
-#4073 := [refl]: #4072
-#4075 := [quant-intro #4073]: #4074
-#4078 := [monotonicity #4075]: #4077
-#4069 := (iff #3250 #4068)
-#4066 := (iff #3051 #4063)
-#4064 := (iff #3046 #3046)
-#4065 := [refl]: #4064
-#4067 := [quant-intro #4065]: #4066
-#4070 := [monotonicity #4067]: #4069
-#4059 := (iff #3252 #4058)
-#4056 := (iff #1278 #4053)
-#4054 := (iff #1275 #1275)
-#4055 := [refl]: #4054
-#4057 := [quant-intro #4055]: #4056
-#4060 := [monotonicity #4057]: #4059
-#4204 := [monotonicity #4060 #4070 #4078 #4201]: #4203
-#4207 := [monotonicity #4204]: #4206
-#4051 := (iff #3027 #4050)
-#4048 := (iff #3026 #4047)
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-#4042 := (iff #3014 #4041)
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-#4033 := (iff #3007 #4032)
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-#4021 := (iff #2971 #4020)
-#4018 := (iff #2965 #4015)
-#4016 := (iff #2960 #2960)
-#4017 := [refl]: #4016
-#4019 := [quant-intro #4017]: #4018
-#4022 := [monotonicity #4019]: #4021
-#4025 := [monotonicity #4022]: #4024
-#4028 := [monotonicity #4025]: #4027
-#4031 := [monotonicity #4028]: #4030
-#4034 := [monotonicity #4031]: #4033
-#4013 := (iff #3006 #4012)
-#4010 := (iff #2943 #4007)
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-#4009 := [refl]: #4008
-#4011 := [quant-intro #4009]: #4010
-#4014 := [monotonicity #4011]: #4013
-#4037 := [monotonicity #4014 #4034]: #4036
-#4040 := [monotonicity #4037]: #4039
-#4005 := (iff #2914 #4004)
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-#3996 := (iff #2906 #3993)
-#3994 := (iff #2895 #2895)
-#3995 := [refl]: #3994
-#3997 := [quant-intro #3995]: #3996
-#4000 := [monotonicity #3997]: #3999
-#4003 := [monotonicity #4000]: #4002
-#4006 := [monotonicity #4003]: #4005
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-#4046 := [monotonicity #4043]: #4045
-#3989 := (iff #3024 #3988)
-#3986 := (iff #2891 #3983)
-#3984 := (iff #2880 #2880)
-#3985 := [refl]: #3984
-#3987 := [quant-intro #3985]: #3986
-#3990 := [monotonicity #3987]: #3989
-#4049 := [monotonicity #3990 #4046]: #4048
-#4052 := [monotonicity #4049]: #4051
-#4210 := [monotonicity #4052 #4207]: #4209
-#4213 := [monotonicity #4210]: #4212
-#3980 := (iff #3271 #3979)
-#3977 := (iff #2877 #3974)
-#3975 := (iff #2872 #2872)
-#3976 := [refl]: #3975
-#3978 := [quant-intro #3976]: #3977
-#3981 := [monotonicity #3978]: #3980
-#3972 := (iff #3270 #3971)
-#3969 := (iff #2849 #3966)
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-#3968 := [refl]: #3967
-#3970 := [quant-intro #3968]: #3969
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-#3959 := (iff #2816 #2816)
-#3960 := [refl]: #3959
-#3962 := [quant-intro #3960]: #3961
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-#3953 := [quant-intro #3951]: #3952
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-#3944 := (iff #1104 #3941)
-#3942 := (iff #1101 #1101)
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-#3945 := [quant-intro #3943]: #3944
-#3948 := [monotonicity #3945]: #3947
-#4216 := [monotonicity #3948 #3956 #3965 #3973 #3981 #4213]: #4215
-#4219 := [monotonicity #4216]: #4218
-#3938 := (iff #2774 #3937)
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-#3929 := (iff #2766 #3926)
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-#3928 := [refl]: #3927
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-#3936 := [monotonicity #3933]: #3935
-#3939 := [monotonicity #3936]: #3938
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-#3919 := [refl]: #3918
-#3921 := [quant-intro #3919]: #3920
-#3924 := [monotonicity #3921]: #3923
-#4228 := [monotonicity #3924 #4225]: #4227
-#4231 := [monotonicity #4228]: #4230
-#4234 := [monotonicity #4231]: #4233
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-#2385 := (and #1777 #2345 #2379)
-#2467 := (or #2385 #2464)
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-#1754 := (forall (vars (?x48 T2)) #1751)
-#2473 := (and #149 #154 #530 #533 #1754 #2467)
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-#2333 := (and #1717 #2313 #2330)
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-#2339 := (forall (vars (?x46 T2)) #2336)
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-#2293 := (and #1690 #2275 #2288)
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-#2299 := (forall (vars (?x37 T2)) #2296)
-#2658 := (and #109 #1051 #1098 #1104 #2299 #2339 #2649)
-#1646 := (not #1645)
-#2245 := (and #74 #1646 #2242)
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-#2663 := (or #2257 #2658)
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-#2684 := (and #81 #2681)
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-#3334 := (iff #2687 #3333)
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-#3325 := [monotonicity #3322]: #3324
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-#2016 := (and #2015 #2014)
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-#2018 := (or #2017 #2010)
-#2019 := (not #2018)
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-#2078 := (and #1344 #2074)
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-#1988 := (or #1987 #1982)
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-#1710 := (+ #1709 #1054)
-#1711 := (>= #1710 0::int)
-#1712 := (not #1711)
-#1715 := (+ #1714 #1710)
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-#1687 := (+ #1684 #993)
-#1688 := (>= #1687 0::int)
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-#1642 := (+ #66 #1641)
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-#2548 := [rewrite]: #2547
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-#2521 := [rewrite]: #2520
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-#2447 := [rewrite]: #2446
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-#2381 := [quant-intro #2378]: #2380
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-#2215 := (iff #1652 #2214)
-#2216 := [rewrite]: #2215
-#2219 := [monotonicity #2216]: #2218
-#2222 := [monotonicity #2219]: #2221
-#2227 := [trans #2222 #2225]: #2226
-#2230 := [monotonicity #2227]: #2229
-#2233 := [monotonicity #2230]: #2232
-#2237 := [trans #2233 #2235]: #2236
-#2256 := [monotonicity #2237 #2253]: #2255
-#2261 := [trans #2256 #2259]: #2260
-#2665 := [monotonicity #2261 #2662]: #2664
-#2668 := [monotonicity #2665]: #2667
-#2212 := (iff #1624 #2211)
-#2209 := (iff #1623 #2208)
-#2206 := (iff #1615 #2205)
-#2203 := (= #1614 #2202)
-#2204 := [rewrite]: #2203
-#2207 := [monotonicity #2204]: #2206
-#2199 := (iff #1622 #2198)
-#2196 := (iff #1621 #2195)
-#2197 := [rewrite]: #2196
-#2200 := [monotonicity #2197]: #2199
-#2210 := [monotonicity #2200 #2207]: #2209
-#2213 := [monotonicity #2210]: #2212
-#2671 := [monotonicity #2213 #2668]: #2670
-#2674 := [monotonicity #2671]: #2673
-#2193 := (iff #1594 #2192)
-#2190 := (iff #1593 #2189)
-#2187 := (iff #1587 #2184)
-#2176 := (+ #1584 #1585)
-#2179 := (>= #2176 0::int)
-#2185 := (iff #2179 #2184)
-#2186 := [rewrite]: #2185
-#2180 := (iff #1587 #2179)
-#2177 := (= #1586 #2176)
-#2178 := [rewrite]: #2177
-#2181 := [monotonicity #2178]: #2180
-#2188 := [trans #2181 #2186]: #2187
-#2174 := (iff #1592 #2173)
-#2171 := (iff #1591 #2170)
-#2172 := [rewrite]: #2171
-#2175 := [monotonicity #2172]: #2174
-#2191 := [monotonicity #2175 #2188]: #2190
-#2194 := [monotonicity #2191]: #2193
-#2677 := [monotonicity #2194 #2674]: #2676
-#2680 := [monotonicity #2677]: #2679
-#2683 := [monotonicity #2680]: #2682
-#2168 := (iff #1523 #81)
-#2169 := [rewrite]: #2168
-#2686 := [monotonicity #2169 #2683]: #2685
-#2689 := [monotonicity #2686]: #2688
-#1496 := (not #1480)
-#2163 := (~ #1496 #2162)
-#2159 := (not #1477)
-#2160 := (~ #2159 #2158)
-#2155 := (not #1474)
-#2156 := (~ #2155 #2154)
-#2151 := (not #1471)
-#2152 := (~ #2151 #2150)
-#2147 := (not #1468)
-#2148 := (~ #2147 #2146)
-#2143 := (not #1465)
-#2144 := (~ #2143 #2142)
-#2139 := (not #1462)
-#2140 := (~ #2139 #2138)
-#2135 := (not #1459)
-#2136 := (~ #2135 #2134)
-#2131 := (not #1456)
-#2132 := (~ #2131 #2130)
-#2127 := (not #1453)
-#2128 := (~ #2127 #2126)
-#2123 := (not #1450)
-#2124 := (~ #2123 #2122)
-#2119 := (not #1447)
-#2120 := (~ #2119 #2118)
-#2115 := (not #1444)
-#2116 := (~ #2115 #2114)
-#2111 := (not #1441)
-#2112 := (~ #2111 #2110)
-#2107 := (not #1438)
-#2108 := (~ #2107 #2106)
-#2103 := (not #1435)
-#2104 := (~ #2103 #2102)
-#2099 := (not #1432)
-#2100 := (~ #2099 #2098)
-#2095 := (not #1429)
-#2096 := (~ #2095 #2094)
-#2091 := (not #1426)
-#2092 := (~ #2091 #2090)
-#2087 := (not #1423)
-#2088 := (~ #2087 #2086)
-#2083 := (not #1420)
-#2084 := (~ #2083 #2082)
-#2079 := (not #1417)
-#2080 := (~ #2079 #2078)
-#2075 := (not #1414)
-#2076 := (~ #2075 #2074)
-#2071 := (not #1411)
-#2072 := (~ #2071 #2070)
-#2052 := (not #1408)
-#2068 := (~ #2052 #2065)
-#2042 := (exists (vars (?x76 T2)) #2041)
-#2050 := (or #2049 #2042)
-#2051 := (not #2050)
-#2066 := (~ #2051 #2065)
-#2062 := (not #2042)
-#2063 := (~ #2062 #2061)
-#2059 := (~ #2058 #2058)
-#2060 := [refl]: #2059
-#2064 := [nnf-neg #2060]: #2063
-#2056 := (~ #2055 #2055)
-#2057 := [refl]: #2056
-#2067 := [nnf-neg #2057 #2064]: #2066
-#2053 := (~ #2052 #2051)
-#2054 := [sk]: #2053
-#2069 := [trans #2054 #2067]: #2068
-#2028 := (not #1371)
-#2029 := (~ #2028 #1368)
-#2026 := (~ #1368 #1368)
-#2024 := (~ #1365 #1365)
-#2025 := [refl]: #2024
-#2027 := [nnf-pos #2025]: #2026
-#2030 := [nnf-neg #2027]: #2029
-#2073 := [nnf-neg #2030 #2069]: #2072
-#2020 := (~ #1371 #2019)
-#2021 := [sk]: #2020
-#2077 := [nnf-neg #2021 #2073]: #2076
-#1998 := (not #1347)
-#1999 := (~ #1998 #1344)
-#1996 := (~ #1344 #1344)
-#1994 := (~ #1341 #1341)
-#1995 := [refl]: #1994
-#1997 := [nnf-pos #1995]: #1996
-#2000 := [nnf-neg #1997]: #1999
-#2081 := [nnf-neg #2000 #2077]: #2080
-#1990 := (~ #1347 #1989)
-#1991 := [sk]: #1990
-#2085 := [nnf-neg #1991 #2081]: #2084
-#1973 := (not #1333)
-#1974 := (~ #1973 #1330)
-#1971 := (~ #1330 #1330)
-#1969 := (~ #1327 #1327)
-#1970 := [refl]: #1969
-#1972 := [nnf-pos #1970]: #1971
-#1975 := [nnf-neg #1972]: #1974
-#2089 := [nnf-neg #1975 #2085]: #2088
-#1965 := (~ #1333 #1964)
-#1966 := [sk]: #1965
-#2093 := [nnf-neg #1966 #2089]: #2092
-#1959 := (~ #1958 #1958)
-#1960 := [refl]: #1959
-#2097 := [nnf-neg #1960 #2093]: #2096
-#1956 := (~ #1324 #1324)
-#1957 := [refl]: #1956
-#2101 := [nnf-neg #1957 #2097]: #2100
-#1953 := (not #814)
-#1954 := (~ #1953 #705)
-#1951 := (~ #705 #705)
-#1949 := (~ #700 #700)
-#1950 := [refl]: #1949
-#1952 := [nnf-pos #1950]: #1951
-#1955 := [nnf-neg #1952]: #1954
-#2105 := [nnf-neg #1955 #2101]: #2104
-#1945 := (~ #814 #1944)
-#1946 := [sk]: #1945
-#2109 := [nnf-neg #1946 #2105]: #2108
-#1934 := (not #1319)
-#1935 := (~ #1934 #1316)
-#1932 := (~ #1316 #1316)
-#1930 := (~ #1312 #1312)
-#1931 := [refl]: #1930
-#1933 := [nnf-pos #1931]: #1932
-#1936 := [nnf-neg #1933]: #1935
-#2113 := [nnf-neg #1936 #2109]: #2112
-#1926 := (~ #1319 #1925)
-#1927 := [sk]: #1926
-#2117 := [nnf-neg #1927 #2113]: #2116
-#1916 := (not #1309)
-#1917 := (~ #1916 #1913)
-#1914 := (~ #1304 #1913)
-#1911 := (~ #1283 #1283)
-#1912 := [refl]: #1911
-#1909 := (~ #1278 #1278)
-#1907 := (~ #1275 #1275)
-#1908 := [refl]: #1907
-#1910 := [nnf-pos #1908]: #1909
-#1905 := (~ #1268 #1268)
-#1903 := (~ #1263 #1263)
-#1904 := [refl]: #1903
-#1906 := [nnf-pos #1904]: #1905
-#1901 := (~ #1257 #1257)
-#1899 := (~ #1254 #1254)
-#1900 := [refl]: #1899
-#1902 := [nnf-pos #1900]: #1901
-#1895 := (~ #1135 #1894)
-#1896 := [sk]: #1895
-#1884 := (~ #192 #192)
-#1885 := [refl]: #1884
-#1882 := (~ #184 #184)
-#1883 := [refl]: #1882
-#1915 := [monotonicity #1883 #1885 #1896 #1902 #1906 #1910 #1912]: #1914
-#1918 := [nnf-neg #1915]: #1917
-#2121 := [nnf-neg #1918 #2117]: #2120
-#1879 := (not #1226)
-#1880 := (~ #1879 #1878)
-#1875 := (not #1223)
-#1876 := (~ #1875 #1874)
-#1871 := (not #1220)
-#1872 := (~ #1871 #1870)
-#1867 := (not #1217)
-#1868 := (~ #1867 #1866)
-#1863 := (not #1212)
-#1864 := (~ #1863 #1862)
-#1859 := (not #1204)
-#1860 := (~ #1859 #1201)
-#1857 := (~ #1201 #1201)
-#1855 := (~ #1198 #1198)
-#1856 := [refl]: #1855
-#1858 := [nnf-pos #1856]: #1857
-#1861 := [nnf-neg #1858]: #1860
-#1853 := (~ #1852 #1852)
-#1854 := [refl]: #1853
-#1865 := [nnf-neg #1854 #1861]: #1864
-#1848 := (~ #1204 #1847)
-#1849 := [sk]: #1848
-#1869 := [nnf-neg #1849 #1865]: #1868
-#1823 := (not #1186)
-#1824 := (~ #1823 #1820)
-#1821 := (~ #1183 #1820)
-#1818 := (~ #1180 #1817)
-#1813 := (~ #1177 #1812)
-#1814 := [sk]: #1813
-#1801 := (~ #1161 #1161)
-#1802 := [refl]: #1801
-#1819 := [monotonicity #1802 #1814]: #1818
-#1822 := [nnf-pos #1819]: #1821
-#1825 := [nnf-neg #1822]: #1824
-#1873 := [nnf-neg #1825 #1869]: #1872
-#1799 := (~ #1186 #1796)
-#1774 := (exists (vars (?x50 T2)) #1773)
-#1782 := (or #1781 #1774)
-#1783 := (not #1782)
-#1797 := (~ #1783 #1796)
-#1793 := (not #1774)
-#1794 := (~ #1793 #1792)
-#1790 := (~ #1789 #1789)
-#1791 := [refl]: #1790
-#1795 := [nnf-neg #1791]: #1794
-#1787 := (~ #1786 #1786)
-#1788 := [refl]: #1787
-#1798 := [nnf-neg #1788 #1795]: #1797
-#1784 := (~ #1186 #1783)
-#1785 := [sk]: #1784
-#1800 := [trans #1785 #1798]: #1799
-#1877 := [nnf-neg #1800 #1873]: #1876
-#1760 := (not #1149)
-#1761 := (~ #1760 #1757)
-#1758 := (~ #1144 #1757)
-#1755 := (~ #1138 #1754)
-#1752 := (~ #1751 #1751)
-#1753 := [refl]: #1752
-#1756 := [nnf-neg #1753]: #1755
-#1749 := (~ #533 #533)
-#1750 := [refl]: #1749
-#1747 := (~ #530 #530)
-#1748 := [refl]: #1747
-#1745 := (~ #154 #154)
-#1746 := [refl]: #1745
-#1743 := (~ #149 #149)
-#1744 := [refl]: #1743
-#1759 := [monotonicity #1744 #1746 #1748 #1750 #1756]: #1758
-#1762 := [nnf-neg #1759]: #1761
-#1881 := [nnf-neg #1762 #1877]: #1880
-#2125 := [nnf-neg #1881 #2121]: #2124
-#1740 := (not #1129)
-#1741 := (~ #1740 #1737)
-#1738 := (~ #1124 #1737)
-#1735 := (~ #1104 #1104)
-#1733 := (~ #1101 #1101)
-#1734 := [refl]: #1733
-#1736 := [nnf-pos #1734]: #1735
-#1731 := (~ #1098 #1098)
-#1729 := (~ #1095 #1095)
-#1730 := [refl]: #1729
-#1732 := [nnf-pos #1730]: #1731
-#1727 := (~ #1090 #1726)
-#1724 := (~ #1087 #1723)
-#1719 := (~ #1084 #1718)
-#1720 := [sk]: #1719
-#1706 := (~ #1063 #1063)
-#1707 := [refl]: #1706
-#1725 := [monotonicity #1707 #1720]: #1724
-#1728 := [nnf-pos #1725]: #1727
-#1704 := (~ #1051 #1051)
-#1702 := (~ #1048 #1048)
-#1703 := [refl]: #1702
-#1705 := [nnf-pos #1703]: #1704
-#1700 := (~ #1028 #1699)
-#1697 := (~ #1025 #1696)
-#1692 := (~ #1022 #1691)
-#1693 := [sk]: #1692
-#1678 := (~ #1002 #1002)
-#1679 := [refl]: #1678
-#1698 := [monotonicity #1679 #1693]: #1697
-#1701 := [nnf-pos #1698]: #1700
-#1676 := (~ #109 #109)
-#1677 := [refl]: #1676
-#1739 := [monotonicity #1677 #1701 #1705 #1728 #1732 #1736]: #1738
-#1742 := [nnf-neg #1739]: #1741
-#2129 := [nnf-neg #1742 #2125]: #2128
-#1658 := (not #1028)
-#1674 := (~ #1658 #1671)
-#1648 := (exists (vars (?x38 T2)) #1647)
-#1656 := (or #1655 #1648)
-#1657 := (not #1656)
-#1672 := (~ #1657 #1671)
-#1668 := (not #1648)
-#1669 := (~ #1668 #1667)
-#1665 := (~ #1664 #1664)
-#1666 := [refl]: #1665
-#1670 := [nnf-neg #1666]: #1669
-#1662 := (~ #1661 #1661)
-#1663 := [refl]: #1662
-#1673 := [nnf-neg #1663 #1670]: #1672
-#1659 := (~ #1658 #1657)
-#1660 := [sk]: #1659
-#1675 := [trans #1660 #1673]: #1674
-#2133 := [nnf-neg #1675 #2129]: #2132
-#1633 := (not #990)
-#1634 := (~ #1633 #987)
-#1631 := (~ #987 #987)
-#1629 := (~ #984 #984)
-#1630 := [refl]: #1629
-#1632 := [nnf-pos #1630]: #1631
-#1635 := [nnf-neg #1632]: #1634
-#2137 := [nnf-neg #1635 #2133]: #2136
-#1625 := (~ #990 #1624)
-#1626 := [sk]: #1625
-#2141 := [nnf-neg #1626 #2137]: #2140
-#1603 := (not #964)
-#1604 := (~ #1603 #961)
-#1601 := (~ #961 #961)
-#1599 := (~ #958 #958)
-#1600 := [refl]: #1599
-#1602 := [nnf-pos #1600]: #1601
-#1605 := [nnf-neg #1602]: #1604
-#2145 := [nnf-neg #1605 #2141]: #2144
-#1595 := (~ #964 #1594)
-#1596 := [sk]: #1595
-#2149 := [nnf-neg #1596 #2145]: #2148
-#1578 := (not #949)
-#1579 := (~ #1578 #946)
-#1576 := (~ #946 #946)
-#1574 := (~ #945 #945)
-#1575 := [refl]: #1574
-#1577 := [nnf-pos #1575]: #1576
-#1580 := [nnf-neg #1577]: #1579
-#2153 := [nnf-neg #1580 #2149]: #2152
-#1570 := (~ #949 #1569)
-#1571 := [sk]: #1570
-#2157 := [nnf-neg #1571 #2153]: #2156
-#1524 := (~ #1523 #1523)
-#1565 := [refl]: #1524
-#2161 := [nnf-neg #1565 #2157]: #2160
-#1563 := (~ #940 #940)
-#1564 := [refl]: #1563
-#2164 := [nnf-neg #1564 #2161]: #2163
-#1497 := [not-or-elim #1491]: #1496
-#2165 := [mp~ #1497 #2164]: #2162
-#2166 := [mp #2165 #2689]: #2687
-#3336 := [mp #2166 #3335]: #3333
-#4271 := [mp #3336 #4270]: #4268
-#6202 := [unit-resolution #4271 #4994]: #4265
-#3591 := (or #4262 #4256)
-#3434 := [def-axiom]: #3591
-#6203 := [unit-resolution #3434 #6202]: #4256
-#6204 := (or #4259 #4253)
-#333 := (<= uf_9 0::int)
-#334 := (not #333)
-#54 := (< 0::int uf_9)
-#335 := (iff #54 #334)
-#336 := [rewrite]: #335
-#329 := [asserted]: #54
-#337 := [mp #329 #336]: #334
-#4524 := (* -1::int #1567)
-#4525 := (+ uf_9 #4524)
-#4534 := (<= #4525 0::int)
-#3581 := (= uf_9 #1567)
-#3568 := (= uf_11 ?x27!0)
-#4428 := (not #3568)
-#4541 := (= #1567 0::int)
-#4864 := (not #4541)
-#4858 := [hypothesis]: #1569
-#4865 := (or #4864 #1568)
-#4866 := [th-lemma]: #4865
-#4867 := [unit-resolution #4866 #4858]: #4864
-#4873 := (or #4872 #4428 #4541)
-#3582 := (= ?x27!0 uf_11)
-#4542 := (not #3582)
-#4427 := (or #4542 #4541)
-#4874 := (or #4872 #4427)
-#4860 := (iff #4874 #4873)
-#4550 := (or #4428 #4541)
-#4876 := (or #4872 #4550)
-#4879 := (iff #4876 #4873)
-#4859 := [rewrite]: #4879
-#4877 := (iff #4874 #4876)
-#4553 := (iff #4427 #4550)
-#4362 := (iff #4542 #4428)
-#3573 := (iff #3582 #3568)
-#3558 := [rewrite]: #3573
-#4538 := [monotonicity #3558]: #4362
-#4871 := [monotonicity #4538]: #4553
-#4878 := [monotonicity #4871]: #4877
-#4861 := [trans #4878 #4859]: #4860
-#4875 := [quant-inst]: #4874
-#4862 := [mp #4875 #4861]: #4873
-#4868 := [unit-resolution #4862 #3898 #4867]: #4428
-#3560 := (or #3568 #3581)
-#3887 := (forall (vars (?x25 T2)) (:pat #3886) #403)
-#3890 := (iff #408 #3887)
-#3888 := (iff #403 #403)
-#3889 := [refl]: #3888
-#3891 := [quant-intro #3889]: #3890
-#1519 := (~ #408 #408)
-#1557 := (~ #403 #403)
-#1558 := [refl]: #1557
-#1520 := [nnf-pos #1558]: #1519
-#1494 := [and-elim #1492]: #408
-#1559 := [mp~ #1494 #1520]: #408
-#3892 := [mp #1559 #3891]: #3887
-#3569 := (not #3887)
-#4289 := (or #3569 #3568 #3581)
-#3578 := (or #3582 #3581)
-#4290 := (or #3569 #3578)
-#4364 := (iff #4290 #4289)
-#4292 := (or #3569 #3560)
-#4308 := (iff #4292 #4289)
-#4363 := [rewrite]: #4308
-#4307 := (iff #4290 #4292)
-#3561 := (iff #3578 #3560)
-#3565 := [monotonicity #3558]: #3561
-#4288 := [monotonicity #3565]: #4307
-#4365 := [trans #4288 #4363]: #4364
-#4291 := [quant-inst]: #4290
-#4366 := [mp #4291 #4365]: #4289
-#4883 := [unit-resolution #4366 #3892]: #3560
-#4884 := [unit-resolution #4883 #4868]: #3581
-#4909 := (not #3581)
-#4910 := (or #4909 #4534)
-#4911 := [th-lemma]: #4910
-#4912 := [unit-resolution #4911 #4884]: #4534
-#4863 := (<= #1567 0::int)
-#4913 := (or #4863 #1568)
-#4908 := [th-lemma]: #4913
-#4914 := [unit-resolution #4908 #4858]: #4863
-#4915 := [th-lemma #4914 #4912 #337]: false
-#4916 := [lemma #4915]: #1568
-#3586 := (or #4259 #1569 #4253)
-#3587 := [def-axiom]: #3586
-#6205 := [unit-resolution #3587 #4916]: #6204
-#6206 := [unit-resolution #6205 #6203]: #4253
-#3610 := (or #4250 #4244)
-#3611 := [def-axiom]: #3610
-#6207 := [unit-resolution #3611 #6206]: #4244
-#5458 := [hypothesis]: #1588
-#3880 := (forall (vars (?x26 T2)) (:pat #3879) #75)
-#3883 := (iff #76 #3880)
-#3881 := (iff #75 #75)
-#3882 := [refl]: #3881
-#3884 := [quant-intro #3882]: #3883
-#1517 := (~ #76 #76)
-#1554 := (~ #75 #75)
-#1555 := [refl]: #1554
-#1518 := [nnf-pos #1555]: #1517
-#1493 := [and-elim #1492]: #76
-#1556 := [mp~ #1493 #1518]: #76
-#3885 := [mp #1556 #3884]: #3880
-#4999 := (not #3880)
-#5000 := (or #4999 #1597)
-#5001 := [quant-inst]: #5000
-#5459 := [unit-resolution #5001 #3885 #5458]: false
-#5460 := [lemma #5459]: #1597
-#3403 := (or #1948 #1588)
-#3488 := [def-axiom]: #3403
-#6208 := [unit-resolution #3488 #5460]: #1948
-#3605 := (or #4247 #2022 #4241)
-#3606 := [def-axiom]: #3605
-#6209 := [unit-resolution #3606 #6208 #6207]: #4241
-#3631 := (or #4238 #4232)
-#3632 := [def-axiom]: #3631
-#6210 := [unit-resolution #3632 #6209]: #4232
-#5548 := [hypothesis]: #1620
-#5094 := (or #4999 #2709)
-#5095 := [quant-inst]: #5094
-#5549 := [unit-resolution #5095 #3885 #5548]: false
-#5553 := [lemma #5549]: #2709
-#3474 := (or #2724 #1620)
-#3809 := [def-axiom]: #3474
-#6211 := [unit-resolution #3809 #5553]: #2724
-#3627 := (or #4235 #2729 #4229)
-#3628 := [def-axiom]: #3627
-#6212 := [unit-resolution #3628 #6211 #6210]: #4229
-#3615 := (or #4226 #4220)
-#3616 := [def-axiom]: #3615
-#6213 := [unit-resolution #3616 #6212]: #4220
-#5484 := (= uf_9 #1639)
-#5561 := (not #5484)
-#5559 := [hypothesis]: #3937
-#3480 := (or #3934 #1651)
-#3812 := [def-axiom]: #3480
-#5560 := [unit-resolution #3812 #5559]: #1651
-#5562 := (or #5561 #1650)
-#5563 := [th-lemma]: #5562
-#5564 := [unit-resolution #5563 #5560]: #5561
-#3813 := (or #3934 #2217)
-#3814 := [def-axiom]: #3813
-#5565 := [unit-resolution #3814 #5559]: #2217
-#5504 := (or #3569 #2214 #5484)
-#5485 := (or #1652 #5484)
-#5505 := (or #3569 #5485)
-#5519 := (iff #5505 #5504)
-#5501 := (or #2214 #5484)
-#5506 := (or #3569 #5501)
-#5509 := (iff #5506 #5504)
-#5510 := [rewrite]: #5509
-#5507 := (iff #5505 #5506)
-#5502 := (iff #5485 #5501)
-#5503 := [monotonicity #2216]: #5502
-#5508 := [monotonicity #5503]: #5507
-#5521 := [trans #5508 #5510]: #5519
-#5500 := [quant-inst]: #5505
-#5522 := [mp #5500 #5521]: #5504
-#5566 := [unit-resolution #5522 #3892 #5565 #5564]: false
-#5567 := [lemma #5566]: #3934
-#3649 := (or #4223 #3937 #4217)
-#3659 := [def-axiom]: #3649
-#6214 := [unit-resolution #3659 #5567 #6213]: #4217
-#5359 := (or #4214 #4205)
-#4367 := (?x47!7 ?x49!8)
-#4714 := (uf_4 uf_19 #4367)
-#4751 := (* -1::int #4714)
-#4368 := (uf_4 uf_14 #4367)
-#5011 := (+ #4368 #4751)
-#5015 := (<= #5011 0::int)
-#5010 := (= #4368 #4714)
-#5211 := (= #4714 #4368)
-#5206 := [hypothesis]: #4202
-#5207 := [hypothesis]: #4217
-#3644 := (or #4214 #4208)
-#3603 := [def-axiom]: #3644
-#5208 := [unit-resolution #3603 #5207]: #4208
-#3678 := (or #4211 #4050 #4205)
-#3679 := [def-axiom]: #3678
-#5209 := [unit-resolution #3679 #5208 #5206]: #4050
-#3496 := (or #4047 #533)
-#3778 := [def-axiom]: #3496
-#5210 := [unit-resolution #3778 #5209]: #533
-#5205 := [symm #5210]: #151
-#5212 := [monotonicity #5205]: #5211
-#5213 := [symm #5212]: #5010
-#5214 := (not #5010)
-#5215 := (or #5214 #5015)
-#5268 := [th-lemma]: #5215
-#5269 := [unit-resolution #5268 #5213]: #5015
-#4369 := (* -1::int #4368)
-#4353 := (uf_1 #4367 ?x49!8)
-#4354 := (uf_10 #4353)
-#4355 := (* -1::int #4354)
-#4432 := (+ #4355 #4369)
-#4301 := (uf_4 uf_14 ?x49!8)
-#4433 := (+ #4301 #4432)
-#4520 := (<= #4433 0::int)
-#4436 := (= #4433 0::int)
-#4418 := (not #4436)
-#4359 := (up_6 uf_15 #4367)
-#4360 := (not #4359)
-#4351 := (+ #4301 #4369)
-#4352 := (<= #4351 0::int)
-#4423 := (or #4352 #4360 #4418)
-#4442 := (not #4423)
-#4302 := (* -1::int #4301)
-#4303 := (+ uf_9 #4302)
-#4283 := (<= #4303 0::int)
-#4675 := (not #4283)
-#3783 := (or #4047 #4041)
-#3772 := [def-axiom]: #3783
-#5270 := [unit-resolution #3772 #5209]: #4041
-#3680 := (or #4214 #109)
-#3676 := [def-axiom]: #3680
-#5271 := [unit-resolution #3676 #5207]: #109
-#5272 := (= #175 #108)
-#5273 := [monotonicity #5205]: #5272
-#5274 := [trans #5273 #5271]: #176
-#3456 := (or #4023 #1852)
-#3457 := [def-axiom]: #3456
-#5275 := [unit-resolution #3457 #5274]: #4023
-#3782 := (or #4047 #3983)
-#3779 := [def-axiom]: #3782
-#5276 := [unit-resolution #3779 #5209]: #3983
-#3607 := (or #4214 #3949)
-#3662 := [def-axiom]: #3607
-#5256 := [unit-resolution #3662 #5207]: #3949
-#4685 := (or #2992 #3954 #3988 #3023)
-#4370 := (uf_4 uf_14 ?x54!10)
-#4371 := (* -1::int #4370)
-#4552 := (+ #1830 #4371)
-#4554 := (>= #4552 0::int)
-#4551 := (= #1830 #4370)
-#4633 := (= #4370 #1830)
-#4632 := [hypothesis]: #533
-#4634 := [monotonicity #4632]: #4633
-#4635 := [symm #4634]: #4551
-#4636 := (not #4551)
-#4637 := (or #4636 #4554)
-#4638 := [th-lemma]: #4637
-#4620 := [unit-resolution #4638 #4635]: #4554
-#3503 := (uf_4 uf_14 ?x53!11)
-#3504 := (* -1::int #3503)
-#4545 := (+ #1828 #3504)
-#4549 := (<= #4545 0::int)
-#4544 := (= #1828 #3503)
-#4621 := (= #3503 #1828)
-#4622 := [monotonicity #4632]: #4621
-#4623 := [symm #4622]: #4544
-#4624 := (not #4544)
-#4619 := (or #4624 #4549)
-#4625 := [th-lemma]: #4619
-#4626 := [unit-resolution #4625 #4623]: #4549
-#3437 := (not #2445)
-#4627 := [hypothesis]: #2997
-#3800 := (or #2992 #3437)
-#3802 := [def-axiom]: #3800
-#4628 := [unit-resolution #3802 #4627]: #3437
-#4822 := [hypothesis]: #3983
-#4826 := [hypothesis]: #3949
-#3793 := (or #2992 #1843)
-#3799 := [def-axiom]: #3793
-#4629 := [unit-resolution #3799 #4627]: #1843
-#4372 := (+ uf_9 #4371)
-#4373 := (<= #4372 0::int)
-#4820 := (not #4373)
-#3797 := (or #2992 #1839)
-#3798 := [def-axiom]: #3797
-#4680 := [unit-resolution #3798 #4627]: #1839
-#4816 := (not #4554)
-#4681 := (or #4820 #1838 #4816)
-#4682 := [th-lemma]: #4681
-#4683 := [unit-resolution #4682 #4680 #4620]: #4820
-#4815 := (not #4549)
-#4830 := (or #4373 #3954 #1842 #3988 #2445 #4815 #4816)
-#4446 := (+ #3504 #4370)
-#4447 := (+ #1833 #4446)
-#4450 := (>= #4447 0::int)
-#4814 := (not #4450)
-#4811 := [hypothesis]: #4554
-#4812 := [hypothesis]: #4549
-#4813 := [hypothesis]: #3437
-#4817 := (or #4814 #4815 #2445 #4816)
-#4818 := [th-lemma]: #4817
-#4819 := [unit-resolution #4818 #4813 #4812 #4811]: #4814
-#4374 := (up_6 uf_15 ?x54!10)
-#4821 := [hypothesis]: #4820
-#4376 := (or #4373 #4374)
-#4379 := (or #3988 #4373 #4374)
-#4375 := (or #4374 #4373)
-#4380 := (or #3988 #4375)
-#4387 := (iff #4380 #4379)
-#4382 := (or #3988 #4376)
-#4385 := (iff #4382 #4379)
-#4386 := [rewrite]: #4385
-#4383 := (iff #4380 #4382)
-#4377 := (iff #4375 #4376)
-#4378 := [rewrite]: #4377
-#4384 := [monotonicity #4378]: #4383
-#4388 := [trans #4384 #4386]: #4387
-#4381 := [quant-inst]: #4380
-#4389 := [mp #4381 #4388]: #4379
-#4823 := [unit-resolution #4389 #4822]: #4376
-#4824 := [unit-resolution #4823 #4821]: #4374
-#4444 := (not #4374)
-#4827 := (or #4444 #4450)
-#4825 := [hypothesis]: #1843
-#4461 := (or #3954 #1842 #4444 #4450)
-#4439 := (+ #4370 #3504)
-#4440 := (+ #1833 #4439)
-#4443 := (>= #4440 0::int)
-#4445 := (or #4444 #1842 #4443)
-#4462 := (or #3954 #4445)
-#4469 := (iff #4462 #4461)
-#4456 := (or #1842 #4444 #4450)
-#4464 := (or #3954 #4456)
-#4467 := (iff #4464 #4461)
-#4468 := [rewrite]: #4467
-#4465 := (iff #4462 #4464)
-#4459 := (iff #4445 #4456)
-#4453 := (or #4444 #1842 #4450)
-#4457 := (iff #4453 #4456)
-#4458 := [rewrite]: #4457
-#4454 := (iff #4445 #4453)
-#4451 := (iff #4443 #4450)
-#4448 := (= #4440 #4447)
-#4449 := [rewrite]: #4448
-#4452 := [monotonicity #4449]: #4451
-#4455 := [monotonicity #4452]: #4454
-#4460 := [trans #4455 #4458]: #4459
-#4466 := [monotonicity #4460]: #4465
-#4470 := [trans #4466 #4468]: #4469
-#4463 := [quant-inst]: #4462
-#4471 := [mp #4463 #4470]: #4461
-#4828 := [unit-resolution #4471 #4826 #4825]: #4827
-#4829 := [unit-resolution #4828 #4824 #4819]: false
-#4831 := [lemma #4829]: #4830
-#4684 := [unit-resolution #4831 #4683 #4629 #4826 #4822 #4628 #4626 #4620]: false
-#4686 := [lemma #4684]: #4685
-#5257 := [unit-resolution #4686 #5256 #5276 #5210]: #2992
-#3791 := (or #4032 #4026 #2997)
-#3513 := [def-axiom]: #3791
-#5258 := [unit-resolution #3513 #5257 #5275]: #4032
-#3516 := (or #4035 #4029)
-#3409 := [def-axiom]: #3516
-#5259 := [unit-resolution #3409 #5258]: #4035
-#3785 := (or #4044 #4004 #4038)
-#3789 := [def-axiom]: #3785
-#5260 := [unit-resolution #3789 #5259 #5270]: #4004
-#3466 := (or #4001 #1777)
-#3471 := [def-axiom]: #3466
-#5255 := [unit-resolution #3471 #5260]: #1777
-#4669 := (+ #1764 #4302)
-#4671 := (>= #4669 0::int)
-#4668 := (= #1764 #4301)
-#5261 := (= #4301 #1764)
-#5262 := [monotonicity #5210]: #5261
-#5263 := [symm #5262]: #4668
-#5264 := (not #4668)
-#5265 := (or #5264 #4671)
-#5280 := [th-lemma]: #5265
-#5281 := [unit-resolution #5280 #5263]: #4671
-#4676 := (not #4671)
-#4677 := (or #4675 #4676 #1776)
-#4672 := [hypothesis]: #1777
-#4667 := [hypothesis]: #4283
-#4673 := [hypothesis]: #4671
-#4674 := [th-lemma #4673 #4667 #4672]: false
-#4692 := [lemma #4674]: #4677
-#5302 := [unit-resolution #4692 #5281 #5255]: #4675
-#5305 := (or #4283 #4442)
-#3807 := (or #4001 #2345)
-#3467 := [def-axiom]: #3807
-#5303 := [unit-resolution #3467 #5260]: #2345
-#3669 := (or #4214 #3974)
-#3637 := [def-axiom]: #3669
-#5304 := [unit-resolution #3637 #5207]: #3974
-#4496 := (or #3979 #2342 #4283 #4442)
-#4350 := (+ #4369 #4355)
-#4356 := (+ #4301 #4350)
-#4357 := (= #4356 0::int)
-#4358 := (not #4357)
-#4429 := (or #4360 #4358 #4352)
-#4430 := (not #4429)
-#4431 := (or #1778 #4283 #4430)
-#4502 := (or #3979 #4431)
-#4517 := (iff #4502 #4496)
-#4499 := (or #2342 #4283 #4442)
-#4504 := (or #3979 #4499)
-#4514 := (iff #4504 #4496)
-#4516 := [rewrite]: #4514
-#4505 := (iff #4502 #4504)
-#4500 := (iff #4431 #4499)
-#4497 := (iff #4430 #4442)
-#4426 := (iff #4429 #4423)
-#4421 := (or #4360 #4418 #4352)
-#4424 := (iff #4421 #4423)
-#4425 := [rewrite]: #4424
-#4416 := (iff #4429 #4421)
-#4419 := (iff #4358 #4418)
-#4437 := (iff #4357 #4436)
-#4434 := (= #4356 #4433)
-#4435 := [rewrite]: #4434
-#4417 := [monotonicity #4435]: #4437
-#4420 := [monotonicity #4417]: #4419
-#4422 := [monotonicity #4420]: #4416
-#4441 := [trans #4422 #4425]: #4426
-#4498 := [monotonicity #4441]: #4497
-#4501 := [monotonicity #2344 #4498]: #4500
-#4506 := [monotonicity #4501]: #4505
-#4518 := [trans #4506 #4516]: #4517
-#4503 := [quant-inst]: #4502
-#4519 := [mp #4503 #4518]: #4496
-#5306 := [unit-resolution #4519 #5304 #5303]: #5305
-#5301 := [unit-resolution #5306 #5302]: #4442
-#4531 := (or #4423 #4436)
-#4533 := [def-axiom]: #4531
-#5307 := [unit-resolution #4533 #5301]: #4436
-#5308 := (or #4418 #4520)
-#5309 := [th-lemma]: #5308
-#5310 := [unit-resolution #5309 #5307]: #4520
-#4670 := (<= #4669 0::int)
-#5311 := (or #5264 #4670)
-#5337 := [th-lemma]: #5311
-#5338 := [unit-resolution #5337 #5263]: #4670
-#5016 := (>= #5011 0::int)
-#5339 := (or #5214 #5016)
-#5340 := [th-lemma]: #5339
-#5341 := [unit-resolution #5340 #5213]: #5016
-#4521 := (not #4352)
-#4522 := (or #4423 #4521)
-#4523 := [def-axiom]: #4522
-#5336 := [unit-resolution #4523 #5301]: #4521
-#3808 := (or #4001 #3993)
-#3451 := [def-axiom]: #3808
-#5342 := [unit-resolution #3451 #5260]: #3993
-#4766 := (+ #4355 #4751)
-#4772 := (+ #1764 #4766)
-#4799 := (>= #4772 0::int)
-#4515 := (>= #4433 0::int)
-#5343 := (or #4418 #4515)
-#5344 := [th-lemma]: #5343
-#5345 := [unit-resolution #5344 #5307]: #4515
-#5402 := (not #5016)
-#5346 := (not #4515)
-#5355 := (or #4799 #4676 #5346 #5402)
-#5356 := [th-lemma]: #5355
-#5357 := [unit-resolution #5356 #5281 #5345 #5341]: #4799
-#5412 := (not #5015)
-#5411 := (not #4520)
-#5410 := (not #4670)
-#5417 := (not #4799)
-#5424 := (or #5417 #3998 #4676 #4352 #5402 #5410 #5411 #5412)
-#4752 := (+ #1764 #4751)
-#4753 := (<= #4752 0::int)
-#5401 := (not #4753)
-#5399 := [hypothesis]: #5016
-#5400 := [hypothesis]: #4521
-#5403 := (or #5401 #4676 #4352 #5402)
-#5404 := [th-lemma]: #5403
-#5405 := [unit-resolution #5404 #4673 #5400 #5399]: #5401
-#4773 := (= #4772 0::int)
-#5406 := [hypothesis]: #4799
-#4798 := (<= #4772 0::int)
-#5407 := [hypothesis]: #5015
-#5408 := [hypothesis]: #4520
-#5409 := [hypothesis]: #4670
-#5413 := (or #4798 #5410 #5411 #5412)
-#5414 := [th-lemma]: #5413
-#5415 := [unit-resolution #5414 #5409 #5408 #5407]: #4798
-#5416 := (not #4798)
-#5418 := (or #4773 #5416 #5417)
-#5419 := [th-lemma]: #5418
-#5420 := [unit-resolution #5419 #5415 #5406]: #4773
-#4784 := (not #4773)
-#4786 := (or #4753 #4784)
-#5421 := [hypothesis]: #3993
-#4792 := (or #3998 #4753 #4784)
-#4693 := (+ #1765 #4354)
-#4715 := (+ #4714 #4693)
-#4716 := (= #4715 0::int)
-#4717 := (not #4716)
-#4718 := (+ #4714 #1765)
-#4713 := (>= #4718 0::int)
-#4719 := (or #4713 #4717)
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-#4793 := (iff #4795 #4792)
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-#4769 := (= #4758 0::int)
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-#4775 := [rewrite]: #4774
-#4770 := (iff #4716 #4769)
-#4767 := (= #4715 #4758)
-#4768 := [rewrite]: #4767
-#4771 := [monotonicity #4768]: #4770
-#4783 := [trans #4771 #4775]: #4776
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-#4755 := (iff #4713 #4753)
-#4720 := (+ #1765 #4714)
-#4723 := (>= #4720 0::int)
-#4748 := (iff #4723 #4753)
-#4754 := [rewrite]: #4748
-#4749 := (iff #4713 #4723)
-#4721 := (= #4718 #4720)
-#4722 := [rewrite]: #4721
-#4750 := [monotonicity #4722]: #4749
-#4756 := [trans #4750 #4754]: #4755
-#4791 := [monotonicity #4756 #4785]: #4787
-#4678 := [monotonicity #4791]: #4631
-#4794 := [trans #4678 #4788]: #4793
-#4796 := [quant-inst]: #4795
-#4797 := [mp #4796 #4794]: #4792
-#5422 := [unit-resolution #4797 #5421]: #4786
-#5423 := [unit-resolution #5422 #5420 #5405]: false
-#5425 := [lemma #5423]: #5424
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-#5354 := [lemma #5358]: #5359
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-#8694 := (= #8048 #191)
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-#12 := (uf_1 #10 #11)
-#3825 := (pattern #12)
-#13 := (uf_3 #12)
-#293 := (= #11 #13)
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-#3828 := [refl]: #3827
-#3830 := [quant-intro #3828]: #3829
-#1500 := (~ #297 #297)
-#1532 := (~ #293 #293)
-#1533 := [refl]: #1532
-#1498 := [nnf-pos #1533]: #1500
-#14 := (= #13 #11)
-#15 := (forall (vars (?x2 T2) (?x3 T2)) #14)
-#298 := (iff #15 #297)
-#295 := (iff #14 #293)
-#296 := [rewrite]: #295
-#299 := [quant-intro #296]: #298
-#292 := [asserted]: #15
-#302 := [mp #292 #299]: #297
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-#5007 := (not #3826)
-#6321 := (or #5007 #6905)
-#6319 := [quant-inst]: #6321
-#9756 := [unit-resolution #6319 #3831]: #6905
-#9758 := [symm #9756]: #9757
-#8603 := [monotonicity #9758]: #8694
-#8592 := [trans #8603 #7413]: #8591
-#30523 := [monotonicity #8592]: #30522
-#30525 := [symm #30523]: #30524
-#30527 := [monotonicity #30525]: #30526
-#30518 := (not #10311)
-#30519 := [hypothesis]: #30518
-#10337 := (or #9640 #10311)
-#9157 := (= #185 #1939)
-#9114 := (= #1939 #185)
-#8831 := (= ?x63!14 uf_22)
-#8074 := (= ?x63!14 #6904)
-#8212 := (uf_1 #6904 ?x63!14)
-#8213 := (uf_10 #8212)
-#8269 := (<= #8213 0::int)
-#7863 := (up_6 uf_15 ?x63!14)
-#8055 := (or #7863 #8074)
-#8073 := (up_6 #8048 ?x63!14)
-#8128 := (iff #8055 #8073)
-#8076 := (or #6010 #8128)
-#8075 := (ite #8074 #5970 #7863)
-#8051 := (iff #8073 #8075)
-#8160 := (or #6010 #8051)
-#8176 := (iff #8160 #8076)
-#8178 := (iff #8076 #8076)
-#8204 := [rewrite]: #8178
-#8140 := (iff #8051 #8128)
-#8126 := (iff #8073 #8055)
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-#8139 := [rewrite]: #8138
-#8122 := (iff #8051 #8126)
-#8124 := (iff #8075 #8055)
-#8052 := (ite #8074 true #7863)
-#8123 := (iff #8052 #8055)
-#8118 := [rewrite]: #8123
-#8053 := (iff #8075 #8052)
-#8054 := [monotonicity #5976]: #8053
-#8125 := [trans #8054 #8118]: #8124
-#8127 := [monotonicity #8125]: #8122
-#8158 := [trans #8127 #8139]: #8140
-#8177 := [monotonicity #8158]: #8176
-#8205 := [trans #8177 #8204]: #8176
-#8173 := [quant-inst]: #8160
-#8206 := [mp #8173 #8205]: #8076
-#8606 := [unit-resolution #8206 #3851]: #8128
-#8980 := (iff #1941 #8073)
-#8593 := (iff #8073 #1941)
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-#8453 := [hypothesis]: #2500
-#3769 := (or #2497 #1941)
-#3770 := [def-axiom]: #3769
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-#9018 := [mp #8590 #8983]: #8073
-#8157 := (not #8073)
-#7280 := (not #8128)
-#7285 := (or #7280 #8055 #8157)
-#7639 := [def-axiom]: #7285
-#9019 := [unit-resolution #7639 #9018 #8606]: #8055
-#7891 := (uf_1 uf_22 ?x63!14)
-#7892 := (uf_10 #7891)
-#7831 := (* -1::int #1939)
-#7910 := (+ #7831 #7892)
-#7911 := (+ #185 #7910)
-#7912 := (>= #7911 0::int)
-#7886 := (not #7912)
-#7896 := (* -1::int #7892)
-#7900 := (+ uf_9 #7896)
-#7901 := (<= #7900 0::int)
-#7943 := (or #7901 #7912)
-#7946 := (not #7943)
-#3775 := (not #2494)
-#3776 := (or #2497 #3775)
-#3771 := [def-axiom]: #3776
-#8506 := [unit-resolution #3771 #8453]: #3775
-#3665 := (or #4202 #4071)
-#3666 := [def-axiom]: #3665
-#6216 := [unit-resolution #3666 #6215]: #4071
-#7928 := (or #4076 #2494 #7946)
-#7897 := (+ #1235 #7896)
-#7898 := (+ #1939 #7897)
-#7899 := (<= #7898 0::int)
-#7940 := (or #7901 #7899)
-#7941 := (not #7940)
-#7942 := (or #1940 #7941)
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-#7855 := (iff #7929 #7931)
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-#7947 := (iff #7941 #7946)
-#7944 := (iff #7940 #7943)
-#7915 := (iff #7899 #7912)
-#7903 := (+ #1939 #7896)
-#7904 := (+ #1235 #7903)
-#7907 := (<= #7904 0::int)
-#7913 := (iff #7907 #7912)
-#7914 := [rewrite]: #7913
-#7908 := (iff #7899 #7907)
-#7905 := (= #7898 #7904)
-#7906 := [rewrite]: #7905
-#7909 := [monotonicity #7906]: #7908
-#7916 := [trans #7909 #7914]: #7915
-#7945 := [monotonicity #7916]: #7944
-#7948 := [monotonicity #7945]: #7947
-#7951 := [monotonicity #2496 #7948]: #7950
-#7856 := [monotonicity #7951]: #7855
-#7592 := [trans #7856 #7585]: #7591
-#7930 := [quant-inst]: #7929
-#7582 := [mp #7930 #7592]: #7928
-#9020 := [unit-resolution #7582 #6216 #8506]: #7946
-#7887 := (or #7943 #7886)
-#7888 := [def-axiom]: #7887
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-#6768 := (not #8055)
-#9798 := (or #8269 #7912 #6768)
-#8339 := (uf_3 #8212)
-#9705 := (uf_4 uf_14 #8339)
-#9706 := (* -1::int #9705)
-#8358 := (uf_4 uf_14 #6904)
-#9707 := (+ #8358 #9706)
-#9708 := (>= #9707 0::int)
-#9709 := (up_6 uf_15 #8339)
-#9753 := (iff #7863 #9709)
-#9751 := (iff #9709 #7863)
-#9749 := (= #8339 ?x63!14)
-#8340 := (= ?x63!14 #8339)
-#8389 := (or #5007 #8340)
-#8383 := [quant-inst]: #8389
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-#9750 := [symm #9748]: #9749
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-#9754 := [symm #9752]: #9753
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-#8159 := (not #8074)
-#8299 := (= #8213 0::int)
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-#8270 := (not #8269)
-#9740 := [hypothesis]: #8270
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-#8309 := (or #8159 #8299)
+#4005 := (iff #38 #4002)
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+#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
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+#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)
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+#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
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+#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
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+#5829 := (uf_10 #5828)
+#5830 := (* -1::int #5829)
+#5824 := (uf_4 uf_14 #5823)
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+#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)
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+#3921 := (or #3235 #3920)
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+#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)
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+#6466 := (= #6463 0::int)
+#6403 := (uf_4 uf_14 ?x68!16)
+#6420 := (* -1::int #6403)
+#6455 := (+ #6420 #6437)
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+#6457 := (>= #6456 0::int)
+#6441 := (* -1::int #6437)
+#6445 := (+ uf_9 #6441)
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+#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)
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+#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)
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+#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)
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+#12797 := (iff #12764 #12796)
+#12794 := (iff #12762 #12767)
+#12759 := (ite #12761 true #3749)
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+#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)
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+#13569 := [symm #13567]: #13568
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+#3919 := [def-axiom]: #3918
+#6524 := [unit-resolution #3919 #6522]: #2100
+#13571 := [mp #6524 #13570]: #12866
+#12863 := (not #12796)
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+#13572 := [unit-resolution #12865 #13571 #13565]: #12836
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+#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)
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+#13095 := (iff #13085 #13087)
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+#13084 := (iff #13085 #13091)
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+#6236 := (iff #6252 #6234)
+#6254 := (+ #1268 #6403)
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+#6255 := (= #6251 #6254)
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+#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)
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+#6176 := (uf_4 uf_14 ?x67!17)
+#13287 := (+ #6176 #10842)
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+#13464 := (not #13288)
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+#5358 := (* -1::int #6176)
+#5458 := (+ #2093 #5358)
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+#3847 := (or #4352 #4213)
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+#3821 := (or #4352 #4221)
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+#6754 := [hypothesis]: #4213
+#6603 := (or #4218 #6593 #6598)
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+#6618 := [monotonicity #6602]: #6617
+#6622 := [trans #6618 #6620]: #6621
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+#6623 := [mp #6605 #6622]: #6603
+#6755 := [unit-resolution #6623 #6754 #6748]: #6598
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+#6756 := [unit-resolution #6627 #6755]: #6625
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+#6574 := (or #6548 #6559 #6570)
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+#6576 := (or #4226 #6548 #6559 #6570)
+#6542 := (+ #6484 #2036)
+#6543 := (+ #177 #6542)
+#6541 := (= #6543 0::int)
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+#6566 := (= #6543 #6568)
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+#6573 := [monotonicity #6569]: #6571
+#6575 := [monotonicity #6563 #6573]: #6572
+#6581 := [monotonicity #6575]: #6578
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+#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)
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+#6781 := [unit-resolution #6786 #6783]: #6588
+#6624 := (>= #2649 0::int)
+#6787 := (or #6624 #2650)
+#6788 := [th-lemma]: #6787
+#6789 := [unit-resolution #6788 #6733]: #6624
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+#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)
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+#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
+#6500 := [monotonicity #6491 #6497]: #6499
+#13051 := [monotonicity #6500]: #13050
+#13054 := [trans #13051 #13047]: #13053
+#13048 := [quant-inst]: #13036
+#13055 := [mp #13048 #13054]: #13035
+#13387 := [unit-resolution #13055 #10373]: #6498
+#13388 := [unit-resolution #13387 #13409]: #6495
+#13385 := (or #6492 #6466)
+#13434 := (not #6466)
+#13435 := [hypothesis]: #13434
+#13057 := (not #6446)
+#13439 := [hypothesis]: #6495
+#13077 := (or #6492 #13057)
+#13078 := [def-axiom]: #13077
+#13365 := [unit-resolution #13078 #13439]: #13057
+#13079 := (not #6457)
+#13080 := (or #6492 #13079)
+#13081 := [def-axiom]: #13080
+#13366 := [unit-resolution #13081 #13439]: #13079
+#6469 := (or #6446 #6457 #6466)
+#13012 := (or #4226 #6446 #6457 #6466)
+#6438 := (+ #6437 #2681)
+#6439 := (+ #177 #6438)
+#6440 := (= #6439 0::int)
+#6447 := (or #6446 #6444 #6440)
+#13013 := (or #4226 #6447)
+#13031 := (iff #13013 #13012)
+#13015 := (or #4226 #6469)
+#13029 := (iff #13015 #13012)
+#13030 := [rewrite]: #13029
+#13027 := (iff #13013 #13015)
+#6470 := (iff #6447 #6469)
+#6467 := (iff #6440 #6466)
+#6464 := (= #6439 #6463)
+#6465 := [rewrite]: #6464
+#6468 := [monotonicity #6465]: #6467
+#6471 := [monotonicity #6461 #6468]: #6470
+#13028 := [monotonicity #6471]: #13027
+#13026 := [trans #13028 #13030]: #13031
+#13014 := [quant-inst]: #13013
+#13032 := [mp #13014 #13026]: #13012
+#13367 := [unit-resolution #13032 #10825]: #6469
+#13368 := [unit-resolution #13367 #13366 #13365 #13435]: false
+#13386 := [lemma #13368]: #13385
+#13488 := [unit-resolution #13386 #13388]: #6466
+#13588 := (or #13434 #13033)
+#13589 := [th-lemma]: #13588
+#13590 := [unit-resolution #13589 #13488]: #13033
+#12924 := (uf_1 #10482 ?x68!16)
+#12925 := (uf_10 #12924)
+#13060 := (* -1::int #12925)
+#13437 := (+ #6437 #13060)
+#13441 := (>= #13437 0::int)
+#13436 := (= #6437 #12925)
+#13445 := (= #12925 #6437)
+#13443 := (= #12924 #6436)
+#13444 := [monotonicity #13347]: #13443
+#13446 := [monotonicity #13444]: #13445
+#13447 := [symm #13446]: #13436
+#13448 := (not #13436)
+#13449 := (or #13448 #13441)
+#13450 := [th-lemma]: #13449
+#13451 := [unit-resolution #13450 #13447]: #13441
+#13410 := (<= #12925 0::int)
+#13411 := (not #13410)
+#12833 := (not #12761)
+#12834 := (or #12767 #12833)
+#12835 := [def-axiom]: #12834
+#13591 := [unit-resolution #12835 #13572]: #12833
 #56 := (uf_10 #12)
-#57 := (= #56 0::int)
+#371 := (<= #56 0::int)
+#372 := (not #371)
 #55 := (= #10 #11)
+#375 := (or #55 #372)
+#4029 := (forall (vars (?x22 T2) (?x23 T2)) (:pat #3981) #375)
+#378 := (forall (vars (?x22 T2) (?x23 T2)) #375)
+#4032 := (iff #378 #4029)
+#4030 := (iff #375 #375)
+#4031 := [refl]: #4030
+#4033 := [quant-intro #4031]: #4032
+#1656 := (~ #378 #378)
+#1655 := (~ #375 #375)
+#1693 := [refl]: #1655
+#1657 := [nnf-pos #1693]: #1656
+#61 := (< 0::int #56)
 #60 := (not #55)
-#353 := (or #60 #57)
-#3867 := (forall (vars (?x20 T2) (?x21 T2)) (:pat #3825) #353)
-#356 := (forall (vars (?x20 T2) (?x21 T2)) #353)
-#3870 := (iff #356 #3867)
-#3868 := (iff #353 #353)
-#3869 := [refl]: #3868
-#3871 := [quant-intro #3869]: #3870
-#1511 := (~ #356 #356)
-#1550 := (~ #353 #353)
-#1551 := [refl]: #1550
-#1512 := [nnf-pos #1551]: #1511
+#62 := (implies #60 #61)
+#63 := (forall (vars (?x22 T2) (?x23 T2)) #62)
+#381 := (iff #63 #378)
+#365 := (or #55 #61)
+#368 := (forall (vars (?x22 T2) (?x23 T2)) #365)
+#379 := (iff #368 #378)
+#376 := (iff #365 #375)
+#373 := (iff #61 #372)
+#374 := [rewrite]: #373
+#377 := [monotonicity #374]: #376
+#380 := [quant-intro #377]: #379
+#369 := (iff #63 #368)
+#366 := (iff #62 #365)
+#367 := [rewrite]: #366
+#370 := [quant-intro #367]: #369
+#382 := [trans #370 #380]: #381
+#364 := [asserted]: #63
+#383 := [mp #364 #382]: #378
+#1694 := [mp~ #383 #1657]: #378
+#4034 := [mp #1694 #4033]: #4029
+#7051 := (not #4029)
+#13419 := (or #7051 #12761 #13411)
+#13412 := (= #10482 ?x68!16)
+#13413 := (or #13412 #13411)
+#13420 := (or #7051 #13413)
+#13427 := (iff #13420 #13419)
+#13416 := (or #12761 #13411)
+#13422 := (or #7051 #13416)
+#13425 := (iff #13422 #13419)
+#13426 := [rewrite]: #13425
+#13423 := (iff #13420 #13422)
+#13417 := (iff #13413 #13416)
+#13414 := (iff #13412 #12761)
+#13415 := [rewrite]: #13414
+#13418 := [monotonicity #13415]: #13417
+#13424 := [monotonicity #13418]: #13423
+#13428 := [trans #13424 #13426]: #13427
+#13421 := [quant-inst]: #13420
+#13429 := [mp #13421 #13428]: #13419
+#13592 := [unit-resolution #13429 #4034 #13591]: #13411
+#13463 := (not #13033)
+#13465 := (or #13463 #2683 #13464 #12761)
+#13442 := [hypothesis]: #13288
+#13452 := [hypothesis]: #12833
+#13453 := [unit-resolution #13429 #4034 #13452]: #13411
+#13454 := [hypothesis]: #13033
+#13462 := [th-lemma #13461 #11063 #10975 #13454 #13453 #13451 #13442]: false
+#13466 := [lemma #13462]: #13465
+#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
+#13598 := [unit-resolution #13438 #13597]: #13335
+#13599 := [th-lemma #13598 #10975 #10836 #13592 #13451 #13590]: false
+#13601 := [lemma #13599]: #13600
+#13863 := [unit-resolution #13601 #6523 #6522]: false
+#13851 := [lemma #13863]: #3235
+#7476 := (uf_1 uf_22 ?x63!14)
+#8409 := (uf_2 #7476)
+#8528 := (up_6 uf_15 #8409)
+#8582 := (iff #8528 #175)
+#8563 := (iff #175 #8528)
+#8410 := (= uf_22 #8409)
+#8416 := (or #8415 #8410)
+#8417 := [quant-inst]: #8416
+#8694 := [unit-resolution #8417 #3993]: #8410
+#10477 := [monotonicity #8694]: #8563
+#10478 := [symm #10477]: #8582
+#7477 := (uf_10 #7476)
+#6712 := (* -1::int #2054)
+#7563 := (+ #6712 #7477)
+#7564 := (+ #177 #7563)
+#7637 := (>= #7564 0::int)
+#7832 := (not #7637)
+#7478 := (* -1::int #7477)
+#7480 := (+ uf_9 #7478)
+#7481 := (<= #7480 0::int)
+#7636 := (or #7481 #7637)
+#7631 := (not #7636)
+#3931 := (not #2658)
+#10371 := [hypothesis]: #2664
+#3932 := (or #2661 #3931)
+#3927 := [def-axiom]: #3932
+#10372 := [unit-resolution #3927 #10371]: #3931
+#7698 := (or #4218 #2658 #7631)
+#7472 := (+ #1268 #7478)
+#7479 := (+ #2054 #7472)
+#7474 := (<= #7479 0::int)
+#7482 := (or #7481 #7474)
+#7280 := (not #7482)
+#7373 := (or #2055 #7280)
+#7694 := (or #4218 #7373)
+#6817 := (iff #7694 #7698)
+#7696 := (or #2658 #7631)
+#7699 := (or #4218 #7696)
+#7724 := (iff #7699 #7698)
+#7720 := [rewrite]: #7724
+#7704 := (iff #7694 #7699)
+#7697 := (iff #7373 #7696)
+#7626 := (iff #7280 #7631)
+#7629 := (iff #7482 #7636)
+#7627 := (iff #7474 #7637)
+#7374 := (+ #2054 #7478)
+#7380 := (+ #1268 #7374)
+#7281 := (<= #7380 0::int)
+#7662 := (iff #7281 #7637)
+#7663 := [rewrite]: #7662
+#7369 := (iff #7474 #7281)
+#7381 := (= #7479 #7380)
+#7498 := [rewrite]: #7381
+#7370 := [monotonicity #7498]: #7369
+#7628 := [trans #7370 #7663]: #7627
+#7630 := [monotonicity #7628]: #7629
+#7632 := [monotonicity #7630]: #7626
+#7695 := [monotonicity #2660 #7632]: #7697
+#7723 := [monotonicity #7695]: #7704
+#7303 := [trans #7723 #7720]: #6817
+#7700 := [quant-inst]: #7694
+#7483 := [mp #7700 #7303]: #7698
+#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)
+#9020 := (or #8259 #7637)
+#7408 := (+ #177 #6712)
+#8885 := (>= #7408 0::int)
+#8884 := (= #177 #2054)
+#8950 := (= #2054 #177)
+#8129 := (= ?x63!14 uf_22)
+#8946 := [hypothesis]: #8188
+#8947 := [symm #8946]: #8129
+#8951 := [monotonicity #8947]: #8950
+#8983 := [symm #8951]: #8884
+#8984 := (not #8884)
+#8985 := (or #8984 #8885)
+#8981 := [th-lemma]: #8985
+#8977 := [unit-resolution #8981 #8983]: #8885
+#10121 := [hypothesis]: #7832
+#8408 := (>= #7477 0::int)
+#8398 := (= #7477 0::int)
+#8399 := (or #8259 #8398)
+#57 := (= #56 0::int)
+#355 := (or #60 #57)
+#4023 := (forall (vars (?x20 T2) (?x21 T2)) (:pat #3981) #355)
+#358 := (forall (vars (?x20 T2) (?x21 T2)) #355)
+#4026 := (iff #358 #4023)
+#4024 := (iff #355 #355)
+#4025 := [refl]: #4024
+#4027 := [quant-intro #4025]: #4026
+#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)
-#359 := (iff #59 #356)
-#332 := (= 0::int #56)
-#343 := (or #60 #332)
-#348 := (forall (vars (?x20 T2) (?x21 T2)) #343)
-#357 := (iff #348 #356)
-#354 := (iff #343 #353)
-#351 := (iff #332 #57)
-#352 := [rewrite]: #351
-#355 := [monotonicity #352]: #354
-#358 := [quant-intro #355]: #357
-#349 := (iff #59 #348)
-#346 := (iff #58 #343)
-#340 := (implies #55 #332)
-#344 := (iff #340 #343)
-#345 := [rewrite]: #344
-#341 := (iff #58 #340)
-#338 := (iff #57 #332)
-#339 := [rewrite]: #338
-#342 := [monotonicity #339]: #341
-#347 := [trans #342 #345]: #346
-#350 := [quant-intro #347]: #349
-#360 := [trans #350 #358]: #359
-#330 := [asserted]: #59
-#361 := [mp #330 #360]: #356
-#1513 := [mp~ #361 #1512]: #356
-#3872 := [mp #1513 #3871]: #3867
-#8154 := (not #3867)
-#8319 := (or #8154 #8159 #8299)
-#8250 := (= #6904 ?x63!14)
-#8305 := (not #8250)
-#8306 := (or #8305 #8299)
-#8324 := (or #8154 #8306)
-#8351 := (iff #8324 #8319)
-#8326 := (or #8154 #8309)
-#8342 := (iff #8326 #8319)
-#8343 := [rewrite]: #8342
-#8336 := (iff #8324 #8326)
-#8317 := (iff #8306 #8309)
-#8307 := (iff #8305 #8159)
-#8252 := (iff #8250 #8074)
-#8253 := [rewrite]: #8252
-#8308 := [monotonicity #8253]: #8307
-#8318 := [monotonicity #8308]: #8317
-#8337 := [monotonicity #8318]: #8336
-#8352 := [trans #8337 #8343]: #8351
-#8325 := [quant-inst]: #8324
-#8384 := [mp #8325 #8352]: #8319
-#9745 := [unit-resolution #8384 #3872]: #8309
-#9746 := [unit-resolution #9745 #9744]: #8159
-#6665 := (or #6768 #7863 #8074)
-#6767 := [def-axiom]: #6665
-#9747 := [unit-resolution #6767 #9746 #9739]: #7863
-#9755 := [mp #9747 #9754]: #9709
-#9710 := (not #9709)
-#9767 := (or #9708 #9710)
-#8353 := (up_6 uf_15 #6904)
-#9763 := (not #8353)
-#9764 := (iff #184 #9763)
-#9761 := (iff #183 #8353)
-#9759 := (iff #8353 #183)
-#9760 := [monotonicity #9758]: #9759
-#9762 := [symm #9760]: #9761
-#9765 := [monotonicity #9762]: #9764
-#3699 := (or #4202 #184)
-#3694 := [def-axiom]: #3699
-#7018 := [unit-resolution #3694 #6215]: #184
-#9766 := [mp #7018 #9765]: #9763
-#3643 := (or #4214 #3958)
-#3667 := [def-axiom]: #3643
-#7019 := [unit-resolution #3667 #6214]: #3958
-#9715 := (or #3963 #8353 #9708 #9710)
-#9711 := (or #8353 #9710 #9708)
-#9716 := (or #3963 #9711)
-#9723 := (iff #9716 #9715)
-#9712 := (or #8353 #9708 #9710)
-#9718 := (or #3963 #9712)
-#9721 := (iff #9718 #9715)
-#9722 := [rewrite]: #9721
-#9719 := (iff #9716 #9718)
-#9713 := (iff #9711 #9712)
-#9714 := [rewrite]: #9713
-#9720 := [monotonicity #9714]: #9719
-#9724 := [trans #9720 #9722]: #9723
-#9717 := [quant-inst]: #9716
-#9725 := [mp #9717 #9724]: #9715
-#9768 := [unit-resolution #9725 #7019 #9766]: #9767
-#9769 := [unit-resolution #9768 #9755]: #9708
-#9770 := [hypothesis]: #7886
-#8219 := (* -1::int #8213)
-#8387 := (+ #7892 #8219)
-#8393 := (>= #8387 0::int)
-#8386 := (= #7892 #8213)
-#9773 := (= #8213 #7892)
-#9771 := (= #8212 #7891)
-#9772 := [monotonicity #9758]: #9771
-#9774 := [monotonicity #9772]: #9773
-#9775 := [symm #9774]: #8386
-#9776 := (not #8386)
-#9777 := (or #9776 #8393)
-#9778 := [th-lemma]: #9777
-#9779 := [unit-resolution #9778 #9775]: #8393
-#8385 := (>= #8213 0::int)
-#9780 := (or #8385 #8269)
-#9781 := [th-lemma]: #9780
-#9782 := [unit-resolution #9781 #9740]: #8385
-#9730 := (+ #1939 #9706)
-#9737 := (<= #9730 0::int)
-#9729 := (= #1939 #9705)
-#9783 := (= #9705 #1939)
-#9784 := [monotonicity #9750]: #9783
-#9785 := [symm #9784]: #9729
-#9786 := (not #9729)
-#9787 := (or #9786 #9737)
-#9788 := [th-lemma]: #9787
-#9789 := [unit-resolution #9788 #9785]: #9737
-#8369 := (* -1::int #8358)
-#9504 := (+ #185 #8369)
-#9300 := (>= #9504 0::int)
-#9503 := (= #185 #8358)
-#9790 := (= #8358 #185)
-#9791 := [monotonicity #9758]: #9790
-#9792 := [symm #9791]: #9503
-#9793 := (not #9503)
-#9794 := (or #9793 #9300)
-#9795 := [th-lemma]: #9794
-#9796 := [unit-resolution #9795 #9792]: #9300
-#9797 := [th-lemma #9796 #9789 #9782 #9779 #9770 #9769]: false
-#9799 := [lemma #9797]: #9798
-#9021 := [unit-resolution #9799 #9017 #9019]: #8269
-#8254 := (or #8074 #8270)
-#369 := (<= #56 0::int)
-#370 := (not #369)
-#373 := (or #55 #370)
-#3873 := (forall (vars (?x22 T2) (?x23 T2)) (:pat #3825) #373)
-#376 := (forall (vars (?x22 T2) (?x23 T2)) #373)
-#3876 := (iff #376 #3873)
-#3874 := (iff #373 #373)
-#3875 := [refl]: #3874
-#3877 := [quant-intro #3875]: #3876
-#1515 := (~ #376 #376)
-#1514 := (~ #373 #373)
-#1552 := [refl]: #1514
-#1516 := [nnf-pos #1552]: #1515
-#61 := (< 0::int #56)
-#62 := (implies #60 #61)
-#63 := (forall (vars (?x22 T2) (?x23 T2)) #62)
-#379 := (iff #63 #376)
-#363 := (or #55 #61)
-#366 := (forall (vars (?x22 T2) (?x23 T2)) #363)
-#377 := (iff #366 #376)
-#374 := (iff #363 #373)
-#371 := (iff #61 #370)
-#372 := [rewrite]: #371
-#375 := [monotonicity #372]: #374
-#378 := [quant-intro #375]: #377
-#367 := (iff #63 #366)
-#364 := (iff #62 #363)
-#365 := [rewrite]: #364
-#368 := [quant-intro #365]: #367
-#380 := [trans #368 #378]: #379
-#362 := [asserted]: #63
-#381 := [mp #362 #380]: #376
-#1553 := [mp~ #381 #1516]: #376
-#3878 := [mp #1553 #3877]: #3873
-#7324 := (not #3873)
-#8256 := (or #7324 #8074 #8270)
-#8251 := (or #8250 #8270)
-#8300 := (or #7324 #8251)
-#8316 := (iff #8300 #8256)
-#8302 := (or #7324 #8254)
-#8320 := (iff #8302 #8256)
-#8321 := [rewrite]: #8320
-#8303 := (iff #8300 #8302)
-#8249 := (iff #8251 #8254)
-#8255 := [monotonicity #8253]: #8249
-#8304 := [monotonicity #8255]: #8303
-#8322 := [trans #8304 #8321]: #8316
-#8301 := [quant-inst]: #8300
-#8323 := [mp #8301 #8322]: #8256
-#9022 := [unit-resolution #8323 #3878]: #8254
-#9013 := [unit-resolution #9022 #9021]: #8074
-#8832 := [trans #9013 #9758]: #8831
-#9155 := [monotonicity #8832]: #9114
-#9158 := [symm #9155]: #9157
-#9154 := (= #1938 #185)
-#5830 := (uf_24 uf_22)
-#9156 := (= #5830 #185)
-#5879 := (= #185 #5830)
-#5833 := (uf_10 #5832)
-#5849 := (>= #5833 0::int)
-#5837 := (* -1::int #5833)
-#5841 := (+ uf_9 #5837)
-#5842 := (<= #5841 0::int)
-#5881 := (or #5842 #5849)
-#6879 := (= #5833 0::int)
-decl uf_2 :: (-> T1 T2)
-#5488 := (uf_1 uf_22 uf_11)
-#8349 := (uf_2 #5488)
-#8700 := (uf_1 #8349 #8349)
-#8701 := (uf_10 #8700)
-#9648 := (= #8701 0::int)
-#9665 := (or #8154 #9648)
-#9649 := (= #8349 #8349)
-#9650 := (not #9649)
-#9651 := (or #9650 #9648)
-#9666 := (or #8154 #9651)
-#9668 := (iff #9666 #9665)
-#9670 := (iff #9665 #9665)
-#9671 := [rewrite]: #9670
-#9663 := (iff #9651 #9648)
-#9658 := (or false #9648)
-#9661 := (iff #9658 #9648)
-#9662 := [rewrite]: #9661
-#9659 := (iff #9651 #9658)
-#9656 := (iff #9650 false)
-#9654 := (iff #9650 #4945)
-#9652 := (iff #9649 true)
-#9653 := [rewrite]: #9652
-#9655 := [monotonicity #9653]: #9654
-#9657 := [trans #9655 #4943]: #9656
-#9660 := [monotonicity #9657]: #9659
-#9664 := [trans #9660 #9662]: #9663
-#9669 := [monotonicity #9664]: #9668
-#9672 := [trans #9669 #9671]: #9668
-#9667 := [quant-inst]: #9666
-#9673 := [mp #9667 #9672]: #9665
-#9675 := [unit-resolution #9673 #3872]: #9648
-#9684 := (= #5833 #8701)
-#9682 := (= #5832 #8700)
-#9680 := (= #8700 #5832)
-#9048 := (= #8349 uf_22)
-#8350 := (= uf_22 #8349)
-#16 := (uf_2 #12)
-#301 := (= #10 #16)
-#3832 := (forall (vars (?x4 T2) (?x5 T2)) (:pat #3825) #301)
-#305 := (forall (vars (?x4 T2) (?x5 T2)) #301)
-#3835 := (iff #305 #3832)
-#3833 := (iff #301 #301)
-#3834 := [refl]: #3833
-#3836 := [quant-intro #3834]: #3835
-#1501 := (~ #305 #305)
-#1535 := (~ #301 #301)
-#1536 := [refl]: #1535
-#1502 := [nnf-pos #1536]: #1501
-#17 := (= #16 #10)
-#18 := (forall (vars (?x4 T2) (?x5 T2)) #17)
-#306 := (iff #18 #305)
-#303 := (iff #17 #301)
-#304 := [rewrite]: #303
-#307 := [quant-intro #304]: #306
-#300 := [asserted]: #18
-#310 := [mp #300 #307]: #305
-#1537 := [mp~ #310 #1502]: #305
-#3837 := [mp #1537 #3836]: #3832
-#8156 := (not #3832)
-#8355 := (or #8156 #8350)
-#8356 := [quant-inst]: #8355
-#9047 := [unit-resolution #8356 #3837]: #8350
-#9049 := [symm #9047]: #9048
-#9681 := [monotonicity #9049 #9049]: #9680
-#9683 := [symm #9681]: #9682
-#9685 := [monotonicity #9683]: #9684
-#9686 := [trans #9685 #9675]: #6879
-#5907 := (not #5849)
-#9687 := [hypothesis]: #5907
-#9688 := (not #6879)
-#9689 := (or #9688 #5849)
-#9690 := [th-lemma]: #9689
-#9691 := [unit-resolution #9690 #9687 #9686]: false
-#9692 := [lemma #9691]: #5849
-#5908 := (or #5881 #5907)
-#5909 := [def-axiom]: #5908
-#8604 := [unit-resolution #5909 #9692]: #5881
-#5884 := (not #5881)
-#5887 := (or #5879 #5884)
-#5890 := (or #4076 #5879 #5884)
-#5838 := (+ #1235 #5837)
-#5839 := (+ #185 #5838)
-#5840 := (<= #5839 0::int)
-#5877 := (or #5842 #5840)
-#5878 := (not #5877)
-#5880 := (or #5879 #5878)
-#5891 := (or #4076 #5880)
-#5898 := (iff #5891 #5890)
-#5893 := (or #4076 #5887)
-#5896 := (iff #5893 #5890)
-#5897 := [rewrite]: #5896
-#5894 := (iff #5891 #5893)
-#5888 := (iff #5880 #5887)
-#5885 := (iff #5878 #5884)
-#5882 := (iff #5877 #5881)
-#5852 := (iff #5840 #5849)
-#5846 := (<= #5837 0::int)
-#5850 := (iff #5846 #5849)
-#5851 := [rewrite]: #5850
-#5847 := (iff #5840 #5846)
-#5844 := (= #5839 #5837)
-#5845 := [rewrite]: #5844
-#5848 := [monotonicity #5845]: #5847
-#5853 := [trans #5848 #5851]: #5852
-#5883 := [monotonicity #5853]: #5882
-#5886 := [monotonicity #5883]: #5885
-#5889 := [monotonicity #5886]: #5888
-#5895 := [monotonicity #5889]: #5894
-#5899 := [trans #5895 #5897]: #5898
-#5892 := [quant-inst]: #5891
-#5900 := [mp #5892 #5899]: #5890
-#8599 := [unit-resolution #5900 #6216]: #5887
-#8605 := [unit-resolution #8599 #8604]: #5879
-#9120 := [symm #8605]: #9156
-#9121 := (= #1938 #5830)
-#9149 := [monotonicity #8832]: #9121
-#9182 := [trans #9149 #9120]: #9154
-#9183 := [trans #9182 #9158]: #2494
-#9203 := [unit-resolution #8506 #9183]: false
-#9204 := [lemma #9203]: #2497
-#3559 := (or #4202 #4196)
-#3670 := [def-axiom]: #3559
-#7035 := [unit-resolution #3670 #6215]: #4196
-#6020 := (uf_1 uf_22 ?x61!13)
-#6021 := (uf_10 #6020)
-#6082 := (+ #1921 #6021)
-#6083 := (+ #185 #6082)
-#6104 := (>= #6083 0::int)
-#6086 := (= #6083 0::int)
-#6022 := (* -1::int #6021)
-#6026 := (+ uf_9 #6022)
-#6027 := (<= #6026 0::int)
-#6070 := (not #6027)
-#6042 := (+ #2484 #6021)
-#6043 := (+ #185 #6042)
-#6044 := (>= #6043 0::int)
-#6049 := (or #6027 #6044)
-#6052 := (not #6049)
-#6032 := (= #1920 #1922)
-#6196 := (not #6032)
-#6195 := [hypothesis]: #2491
-#6199 := (or #6196 #2486)
-#6200 := [th-lemma]: #6199
-#6201 := [unit-resolution #6200 #6195]: #6196
-#6058 := (or #4076 #6032 #6052)
-#6023 := (+ #1235 #6022)
-#6024 := (+ #1922 #6023)
-#6025 := (<= #6024 0::int)
-#6028 := (or #6027 #6025)
-#6029 := (not #6028)
-#6030 := (= #1922 #1920)
-#6031 := (or #6030 #6029)
-#6059 := (or #4076 #6031)
-#6066 := (iff #6059 #6058)
-#6055 := (or #6032 #6052)
-#6061 := (or #4076 #6055)
-#6064 := (iff #6061 #6058)
-#6065 := [rewrite]: #6064
-#6062 := (iff #6059 #6061)
-#6056 := (iff #6031 #6055)
-#6053 := (iff #6029 #6052)
-#6050 := (iff #6028 #6049)
-#6047 := (iff #6025 #6044)
-#6035 := (+ #1922 #6022)
-#6036 := (+ #1235 #6035)
-#6039 := (<= #6036 0::int)
-#6045 := (iff #6039 #6044)
-#6046 := [rewrite]: #6045
-#6040 := (iff #6025 #6039)
-#6037 := (= #6024 #6036)
-#6038 := [rewrite]: #6037
-#6041 := [monotonicity #6038]: #6040
-#6048 := [trans #6041 #6046]: #6047
-#6051 := [monotonicity #6048]: #6050
-#6054 := [monotonicity #6051]: #6053
-#6033 := (iff #6030 #6032)
-#6034 := [rewrite]: #6033
-#6057 := [monotonicity #6034 #6054]: #6056
-#6063 := [monotonicity #6057]: #6062
-#6067 := [trans #6063 #6065]: #6066
-#6060 := [quant-inst]: #6059
-#6068 := [mp #6060 #6067]: #6058
-#6217 := [unit-resolution #6068 #6216 #6201]: #6052
-#6071 := (or #6049 #6070)
-#6072 := [def-axiom]: #6071
-#6218 := [unit-resolution #6072 #6217]: #6070
-#6073 := (not #6044)
-#6074 := (or #6049 #6073)
-#6075 := [def-axiom]: #6074
-#6219 := [unit-resolution #6075 #6217]: #6073
-#6089 := (or #6027 #6044 #6086)
-#3691 := (or #4202 #4063)
-#3664 := [def-axiom]: #3691
-#6220 := [unit-resolution #3664 #6215]: #4063
-#6092 := (or #4068 #6027 #6044 #6086)
-#6078 := (+ #6021 #1921)
-#6079 := (+ #185 #6078)
-#6080 := (= #6079 0::int)
-#6081 := (or #6027 #6025 #6080)
-#6093 := (or #4068 #6081)
-#6100 := (iff #6093 #6092)
-#6095 := (or #4068 #6089)
-#6098 := (iff #6095 #6092)
-#6099 := [rewrite]: #6098
-#6096 := (iff #6093 #6095)
-#6090 := (iff #6081 #6089)
-#6087 := (iff #6080 #6086)
-#6084 := (= #6079 #6083)
-#6085 := [rewrite]: #6084
-#6088 := [monotonicity #6085]: #6087
-#6091 := [monotonicity #6048 #6088]: #6090
-#6097 := [monotonicity #6091]: #6096
-#6101 := [trans #6097 #6099]: #6100
-#6094 := [quant-inst]: #6093
-#6102 := [mp #6094 #6101]: #6092
-#6221 := [unit-resolution #6102 #6220]: #6089
-#6222 := [unit-resolution #6221 #6219 #6218]: #6086
-#6223 := (not #6086)
-#6224 := (or #6223 #6104)
-#6225 := [th-lemma]: #6224
-#6226 := [unit-resolution #6225 #6222]: #6104
-#6069 := (>= #2485 0::int)
-#6227 := (or #6069 #2486)
-#6228 := [th-lemma]: #6227
-#6229 := [unit-resolution #6228 #6195]: #6069
-#6230 := [th-lemma #6229 #6219 #6226]: false
-#6231 := [lemma #6230]: #2486
-#3697 := (or #4199 #2491 #4193)
-#3698 := [def-axiom]: #3697
-#7036 := [unit-resolution #3698 #6231 #7035]: #4193
-#3712 := (or #4190 #4184)
-#3713 := [def-axiom]: #3712
-#13484 := [unit-resolution #3713 #7036]: #4184
-#3708 := (or #4187 #2500 #4181)
-#3709 := [def-axiom]: #3708
-#13485 := [unit-resolution #3709 #13484]: #4184
-#13486 := [unit-resolution #13485 #9204]: #4181
-#3719 := (or #4178 #4088)
-#3720 := [def-axiom]: #3719
-#13487 := [unit-resolution #3720 #13486]: #4088
-#21789 := (or #4093 #9640 #10311)
-#10307 := (= #10301 #2032)
-#10310 := (or #9640 #10307)
-#22142 := (or #4093 #10310)
-#16210 := (iff #22142 #21789)
-#22191 := (or #4093 #10337)
-#22697 := (iff #22191 #21789)
-#17223 := [rewrite]: #22697
-#22172 := (iff #22142 #22191)
-#10338 := (iff #10310 #10337)
-#10335 := (iff #10307 #10311)
-#10336 := [rewrite]: #10335
-#10339 := [monotonicity #10336]: #10338
-#22553 := [monotonicity #10339]: #22172
-#20892 := [trans #22553 #17223]: #16210
-#19383 := [quant-inst]: #22142
-#19478 := [mp #19383 #20892]: #21789
-#30520 := [unit-resolution #19478 #13487]: #10337
-#30521 := [unit-resolution #30520 #30519]: #9640
-#30528 := [mp #30521 #30527]: #30208
-#30205 := (not #14006)
-#30206 := (or #30205 #13996 #30202)
-#30207 := [def-axiom]: #30206
-#30529 := [unit-resolution #30207 #30528 #30517]: #30202
-#30200 := (or #14001 #30199)
-#30201 := [def-axiom]: #30200
-#30530 := [unit-resolution #30201 #30529]: #30199
-#30279 := (or #13994 #30274)
-#30282 := (or #7324 #13994 #30274)
-#30275 := (= #6904 ?x75!20)
-#30276 := (or #30275 #30274)
-#30283 := (or #7324 #30276)
-#30290 := (iff #30283 #30282)
-#30285 := (or #7324 #30279)
-#30288 := (iff #30285 #30282)
-#30289 := [rewrite]: #30288
-#30286 := (iff #30283 #30285)
-#30280 := (iff #30276 #30279)
-#30277 := (iff #30275 #13994)
-#30278 := [rewrite]: #30277
-#30281 := [monotonicity #30278]: #30280
-#30287 := [monotonicity #30281]: #30286
-#30291 := [trans #30287 #30289]: #30290
-#30284 := [quant-inst]: #30283
-#30292 := [mp #30284 #30291]: #30282
-#30531 := [unit-resolution #30292 #3878]: #30279
-#30532 := [unit-resolution #30531 #30530]: #30274
-#10732 := (* -1::int #10701)
-#10440 := (uf_1 uf_22 ?x75!20)
-#10441 := (uf_10 #10440)
-#17909 := (+ #10441 #10732)
-#23144 := (>= #17909 0::int)
-#15426 := (= #10441 #10701)
-#30535 := (= #10701 #10441)
-#30533 := (= #10700 #10440)
-#30534 := [monotonicity #9758]: #30533
-#30536 := [monotonicity #30534]: #30535
-#30537 := [symm #30536]: #15426
-#30538 := (not #15426)
-#30539 := (or #30538 #23144)
-#30540 := [th-lemma]: #30539
-#30541 := [unit-resolution #30540 #30537]: #23144
-#5831 := (* -1::int #5830)
-#5854 := (+ #5831 #5833)
-#5855 := (+ #185 #5854)
-#5876 := (>= #5855 0::int)
-#5901 := (+ #185 #5831)
-#5903 := (>= #5901 0::int)
-#3710 := (or #4190 #4079)
-#3711 := [def-axiom]: #3710
-#7037 := [unit-resolution #3711 #7036]: #4079
-#6127 := (or #4084 #5903)
-#6128 := [quant-inst]: #6127
-#6900 := [unit-resolution #6128 #7037]: #5903
-#30542 := (not #5903)
-#30543 := (or #5876 #5907 #30542)
-#30544 := [th-lemma]: #30543
-#30545 := [unit-resolution #30544 #9692 #6900]: #5876
-#6249 := (<= #5833 0::int)
-#6242 := (or #8154 #6879)
-#5994 := (= uf_22 uf_22)
-#6880 := (not #5994)
-#6881 := (or #6880 #6879)
-#6243 := (or #8154 #6881)
-#6245 := (iff #6243 #6242)
-#6241 := (iff #6242 #6242)
-#6246 := [rewrite]: #6241
-#6891 := (iff #6881 #6879)
-#6886 := (or false #6879)
-#6889 := (iff #6886 #6879)
-#6890 := [rewrite]: #6889
-#6887 := (iff #6881 #6886)
-#6884 := (iff #6880 false)
-#6882 := (iff #6880 #4945)
-#5997 := (iff #5994 true)
-#5998 := [rewrite]: #5997
-#6883 := [monotonicity #5998]: #6882
-#6885 := [trans #6883 #4943]: #6884
-#6888 := [monotonicity #6885]: #6887
-#6892 := [trans #6888 #6890]: #6891
-#6240 := [monotonicity #6892]: #6245
-#6247 := [trans #6240 #6246]: #6245
-#6244 := [quant-inst]: #6243
-#6248 := [mp #6244 #6247]: #6242
-#22629 := [unit-resolution #6248 #3872]: #6879
-#22630 := (or #9688 #6249)
-#22631 := [th-lemma]: #22630
-#22632 := [unit-resolution #22631 #22629]: #6249
-#7858 := (+ #5830 #7883)
-#7614 := (>= #7858 0::int)
-#8012 := (= #5830 #8027)
-#23496 := (= #8027 #5830)
-#23497 := [monotonicity #9758]: #23496
-#23498 := [symm #23497]: #8012
-#23499 := (not #8012)
-#30546 := (or #23499 #7614)
-#30547 := [th-lemma]: #30546
-#30548 := [unit-resolution #30547 #23498]: #7614
-#10675 := (+ #2033 #10441)
-#10676 := (+ #185 #10675)
-#22250 := (<= #10676 0::int)
-#10649 := (= #10676 0::int)
-#10442 := (* -1::int #10441)
-#10469 := (+ uf_9 #10442)
-#10470 := (<= #10469 0::int)
-#21628 := (not #10470)
-#10503 := (+ #10403 #10441)
-#10504 := (+ #185 #10503)
-#10499 := (>= #10504 0::int)
-#10509 := (or #10470 #10499)
-#10515 := (not #10509)
-#10520 := (or #10311 #10515)
-#15425 := (or #4076 #10311 #10515)
-#10443 := (+ #1235 #10442)
-#10467 := (+ #10301 #10443)
-#10468 := (<= #10467 0::int)
-#10471 := (or #10470 #10468)
-#10466 := (not #10471)
-#10472 := (or #10307 #10466)
-#22687 := (or #4076 #10472)
-#19499 := (iff #22687 #15425)
-#21215 := (or #4076 #10520)
-#21268 := (iff #21215 #15425)
-#21592 := [rewrite]: #21268
-#21283 := (iff #22687 #21215)
-#10522 := (iff #10472 #10520)
-#10518 := (iff #10466 #10515)
-#10516 := (iff #10471 #10509)
-#10507 := (iff #10468 #10499)
-#10473 := (+ #10301 #10442)
-#10474 := (+ #1235 #10473)
-#10500 := (<= #10474 0::int)
-#10505 := (iff #10500 #10499)
-#10506 := [rewrite]: #10505
-#10501 := (iff #10468 #10500)
-#10475 := (= #10467 #10474)
-#10476 := [rewrite]: #10475
-#10502 := [monotonicity #10476]: #10501
-#10508 := [trans #10502 #10506]: #10507
-#10517 := [monotonicity #10508]: #10516
-#10519 := [monotonicity #10517]: #10518
-#10523 := [monotonicity #10336 #10519]: #10522
-#21447 := [monotonicity #10523]: #21283
-#21457 := [trans #21447 #21592]: #19499
-#20648 := [quant-inst]: #22687
-#21455 := [mp #20648 #21457]: #15425
-#30549 := [unit-resolution #21455 #6216]: #10520
-#30550 := [unit-resolution #30549 #30519]: #10515
-#22684 := (or #10509 #21628)
-#20894 := [def-axiom]: #22684
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-#30560 := (not #22250)
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+#7917 := (or #7878 #2078 #7916)
+#7875 := [hypothesis]: #7489
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+#7763 := [unit-resolution #7918 #7762 #7726]: #7878
+#7796 := (or #8359 #7870)
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+#7793 := [hypothesis]: #6838
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+#7799 := [lemma #7798]: #7796
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+#7362 := (or #4218 #6838 #7356)
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+#6831 := (= #6830 #2077)
+#7306 := (or #6831 #7305)
+#7363 := (or #4218 #7306)
+#7343 := (iff #7363 #7362)
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+#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
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+#7350 := [monotonicity #7254]: #7308
+#7355 := [trans #7350 #7353]: #7354
+#7358 := [monotonicity #7355]: #7357
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+#6843 := [rewrite]: #6839
+#7361 := [monotonicity #6843 #7358]: #7360
+#7367 := [monotonicity #7361]: #7366
+#7341 := [trans #7367 #7342]: #7343
+#7364 := [quant-inst]: #7363
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+#7318 := (or #4226 #7251 #7261 #7273)
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+#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)
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+#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)
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+#7517 := (ite #7514 true #7416)
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+#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
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+#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
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+#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)
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+#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)
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+#18663 := (or #4234 #6897)
+#6887 := (+ #6865 #2119)
+#6888 := (>= #6887 0::int)
+#18661 := (or #4234 #6888)
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+#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
+#18745 := [mp #18692 #18750]: #18663
+#19541 := [unit-resolution #18745 #10835]: #6897
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+#3756 := (or #3281 #3755)
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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)
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+#10831 := [unit-resolution #3876 #10830]: #4238
+#16861 := (or #4243 #3266 #5879)
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+#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
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+#19580 := (or #19560 #19578 #19579 #2710)
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+#18855 := (iff #18887 #18880)
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+#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)
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+#15401 := (ite #15400 #3681 #5903)
+#15411 := (iff #15410 #15401)
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+#17071 := (iff #17041 #17068)
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+#17033 := [rewrite]: #17075
+#15421 := (iff #15411 #15420)
+#15418 := (iff #15401 #15415)
+#15412 := (ite #15400 true #5903)
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+#15417 := [rewrite]: #15416
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+#15414 := [monotonicity #3673]: #15413
+#15419 := [trans #15414 #15417]: #15418
+#15422 := [monotonicity #15419]: #15421
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+#17076 := [trans #17069 #17033]: #17071
+#17070 := [quant-inst]: #17041
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+#19567 := [unit-resolution #17077 #4007]: #15420
+#19566 := (iff #2130 #15410)
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+#19577 := [mp #19549 #19576]: #15410
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+#17134 := (not #15420)
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+#19546 := [unit-resolution #17128 #19571 #19562]: #15400
+#18949 := [trans #19546 #13347]: #5904
+#19152 := [monotonicity #18949]: #19003
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+#19321 := (not #19136)
+#18783 := (or #19321 #19141)
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+#19424 := [unit-resolution #19327 #19266]: #19141
+#7076 := (uf_2 #2122)
+#7082 := (uf_4 uf_14 #7076)
+#7096 := (* -1::int #7082)
+#7097 := (+ #177 #7096)
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+#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
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+#19126 := [th-lemma]: #19118
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+#18959 := (+ #5874 #7096)
+#18942 := (>= #18959 0::int)
+#18958 := (= #5874 #7082)
+#19503 := [monotonicity #19425]: #18958
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+#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)
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+#19722 := [unit-resolution #19721 #19541 #19557 #19548 #19717 #19494 #19424]: #18852
+#6920 := (+ uf_9 #6916)
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+#19841 := (or #18850 #19840 #2128)
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+#19837 := [hypothesis]: #6921
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+#19842 := [lemma #19839]: #19841
+#19748 := [unit-resolution #19842 #19424 #19575]: #18850
+#6937 := (+ #2119 #6912)
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+#19752 := (not #6941)
+#18700 := (>= #6938 0::int)
+#19749 := (not #18700)
+#19750 := (or #19749 #2710 #19718 #19719 #19578 #19840)
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+#19753 := (or #19752 #18700)
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+#6944 := (or #6921 #6932 #6941)
+#18751 := (or #4226 #6921 #6932 #6941)
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+#6915 := (= #6914 0::int)
+#6917 := (+ #1268 #6916)
+#6918 := (+ #6865 #6917)
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+#6922 := (or #6921 #6919 #6915)
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+#18691 := (iff #18811 #18751)
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+#18695 := (iff #18752 #18811)
+#6945 := (iff #6922 #6944)
+#6942 := (iff #6915 #6941)
+#6939 := (= #6914 #6938)
+#6940 := [rewrite]: #6939
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+#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)
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+#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
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+#18570 := (or #5566 #4277)
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+#11725 := (uf_24 #10482)
+#11723 := (* -1::int #11725)
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+#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)
-#3860 := (pattern #47)
-#319 := (= uf_8 #46)
+#4016 := (pattern #47)
+#321 := (= uf_8 #46)
 #48 := (up_6 #47 #10)
-#323 := (iff #48 #319)
-#3861 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) (:pat #3860) #323)
-#326 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) #323)
-#3864 := (iff #326 #3861)
-#3862 := (iff #323 #323)
-#3863 := [refl]: #3862
-#3865 := [quant-intro #3863]: #3864
-#1509 := (~ #326 #326)
-#1547 := (~ #323 #323)
-#1548 := [refl]: #1547
-#1510 := [nnf-pos #1548]: #1509
+#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)
-#327 := (iff #51 #326)
-#324 := (iff #50 #323)
-#321 := (iff #49 #319)
-#322 := [rewrite]: #321
-#325 := [monotonicity #322]: #324
-#328 := [quant-intro #325]: #327
-#318 := [asserted]: #51
-#331 := [mp #318 #328]: #326
-#1549 := [mp~ #331 #1510]: #326
-#3866 := [mp #1549 #3865]: #3861
-#5984 := (not #3861)
-#5985 := (or #5984 #5971)
-#5974 := (iff #5971 #5970)
-#5986 := (or #5984 #5974)
-#5988 := (iff #5986 #5985)
-#5990 := (iff #5985 #5985)
-#5991 := [rewrite]: #5990
-#5982 := (iff #5974 #5971)
-#5977 := (iff #5971 true)
-#5980 := (iff #5977 #5971)
-#5981 := [rewrite]: #5980
-#5978 := (iff #5974 #5977)
-#5979 := [monotonicity #5976]: #5978
-#5983 := [trans #5979 #5981]: #5982
-#5989 := [monotonicity #5983]: #5988
-#5992 := [trans #5989 #5991]: #5988
-#5987 := [quant-inst]: #5986
-#5993 := [mp #5987 #5992]: #5985
-#29383 := [unit-resolution #5993 #3866]: #5971
-#29388 := [mp #29383 #29387]: #8020
-#30588 := [hypothesis]: #4122
-#8023 := (not #8020)
-#23013 := (or #4127 #8023 #10697 #10725)
-#10702 := (+ #2033 #10701)
-#10703 := (+ #8027 #10702)
-#10704 := (= #10703 0::int)
-#10717 := (not #10704)
-#10718 := (+ #8027 #2033)
-#10716 := (>= #10718 0::int)
-#10711 := (or #8023 #10716 #10717)
-#22922 := (or #4127 #10711)
-#22994 := (iff #22922 #23013)
-#10742 := (or #8023 #10697 #10725)
-#22980 := (or #4127 #10742)
-#22955 := (iff #22980 #23013)
-#22999 := [rewrite]: #22955
-#22906 := (iff #22922 #22980)
-#10798 := (iff #10711 #10742)
-#10726 := (iff #10717 #10725)
-#10719 := (iff #10704 #10722)
-#10746 := (+ #8027 #10701)
-#10747 := (+ #2033 #10746)
-#10750 := (= #10747 0::int)
-#10715 := (iff #10750 #10722)
-#10723 := [rewrite]: #10715
-#10730 := (iff #10704 #10750)
-#10748 := (= #10703 #10747)
-#10749 := [rewrite]: #10748
-#10731 := [monotonicity #10749]: #10730
-#10724 := [trans #10731 #10723]: #10719
-#10727 := [monotonicity #10724]: #10726
-#10694 := (iff #10716 #10697)
-#10712 := (+ #2033 #8027)
-#10695 := (>= #10712 0::int)
-#10698 := (iff #10695 #10697)
-#10699 := [rewrite]: #10698
-#10710 := (iff #10716 #10695)
-#10713 := (= #10718 #10712)
-#10714 := [rewrite]: #10713
-#10696 := [monotonicity #10714]: #10710
-#10745 := [trans #10696 #10699]: #10694
-#10796 := [monotonicity #10745 #10727]: #10798
-#21369 := [monotonicity #10796]: #22906
-#17898 := [trans #21369 #22999]: #22994
-#22936 := [quant-inst]: #22922
-#17881 := [mp #22936 #17898]: #23013
-#30590 := [unit-resolution #17881 #30588 #29388]: #30589
-#30591 := [unit-resolution #30590 #30587 #30566]: false
-#30593 := [lemma #30591]: #30592
-#25195 := [unit-resolution #30593 #25346]: #10311
-#35020 := (or #30518 #7777)
-#35021 := [th-lemma]: #35020
-#25253 := [unit-resolution #35021 #25195]: #7777
-#33354 := (not #7777)
-#33351 := (or #33430 #33354 #2044)
-#33352 := [hypothesis]: #11140
-#38137 := [hypothesis]: #2045
-#33346 := [hypothesis]: #7777
-#33353 := [th-lemma #33346 #38137 #33352]: false
-#33355 := [lemma #33353]: #33351
-#25263 := [unit-resolution #33355 #25253 #25348]: #33430
-#25380 := (or #11140 #11168)
-#3758 := (or #4130 #2560)
-#3640 := [def-axiom]: #3758
-#25347 := [unit-resolution #3640 #25286]: #2560
-#10947 := [unit-resolution #3637 #6214]: #3974
-#19098 := (or #3979 #2557 #11140 #11168)
-#11132 := (or #11137 #11135 #11146)
-#11138 := (not #11132)
-#11141 := (or #2046 #11140 #11138)
-#24415 := (or #3979 #11141)
-#24431 := (iff #24415 #19098)
-#11165 := (or #2557 #11140 #11168)
-#24132 := (or #3979 #11165)
-#24604 := (iff #24132 #19098)
-#24448 := [rewrite]: #24604
-#24350 := (iff #24415 #24132)
-#11171 := (iff #11141 #11165)
-#11169 := (iff #11138 #11168)
-#11166 := (iff #11132 #11142)
-#11167 := [rewrite]: #11166
-#11170 := [monotonicity #11167]: #11169
-#11172 := [monotonicity #2559 #11170]: #11171
-#24430 := [monotonicity #11172]: #24350
-#24397 := [trans #24430 #24448]: #24431
-#24390 := [quant-inst]: #24415
-#24306 := [mp #24390 #24397]: #19098
-#25352 := [unit-resolution #24306 #10947 #25347]: #25380
-#25354 := [unit-resolution #25352 #25263]: #11168
-#24534 := (or #11142 #11136)
-#24551 := [def-axiom]: #24534
-#25381 := [unit-resolution #24551 #25354]: #11136
-#31877 := (up_6 uf_23 #11097)
-#31878 := (not #31877)
-#35062 := (or #11142 #31878 #4127)
-#24524 := (not #11146)
-#38825 := [hypothesis]: #11168
-#24595 := (or #11142 #24524)
-#24514 := [def-axiom]: #24595
-#38826 := [unit-resolution #24514 #38825]: #24524
-#31875 := (uf_24 #11097)
-#31894 := (* -1::int #31875)
-#32091 := (+ #2032 #31894)
-#32092 := (<= #32091 0::int)
-#33436 := [hypothesis]: #31877
-#32104 := (+ #11149 #31894)
-#32105 := (+ #2032 #32104)
-#32106 := (= #32105 0::int)
-#35038 := (iff #11134 #32106)
-#35034 := (iff #32106 #11134)
-#35015 := (= #32105 #11133)
-#35029 := (= #11133 #32105)
-#31895 := (+ #11143 #31894)
-#33428 := (<= #31895 0::int)
-#31876 := (= #11143 #31875)
-#31880 := (or #31876 #31878)
-#31423 := (or #4093 #31876 #31878)
-#31879 := (or #31878 #31876)
-#31434 := (or #4093 #31879)
-#31443 := (iff #31434 #31423)
-#31441 := (or #4093 #31880)
-#31431 := (iff #31441 #31423)
-#31440 := [rewrite]: #31431
-#31433 := (iff #31434 #31441)
-#31881 := (iff #31879 #31880)
-#31882 := [rewrite]: #31881
-#31442 := [monotonicity #31882]: #31433
-#31436 := [trans #31442 #31440]: #31443
-#31435 := [quant-inst]: #31434
-#31444 := [mp #31435 #31436]: #31423
-#33899 := [unit-resolution #31444 #13487]: #31880
-#33904 := [unit-resolution #33899 #33436]: #31876
-#23171 := (not #31876)
-#16263 := (or #23171 #33428)
-#31645 := [th-lemma]: #16263
-#31947 := [unit-resolution #31645 #33904]: #33428
-#31896 := (>= #31895 0::int)
-#31469 := (or #4084 #31896)
-#31470 := [quant-inst]: #31469
-#29796 := [unit-resolution #31470 #7037]: #31896
-#10405 := (<= #10404 0::int)
-#25597 := [unit-resolution #30593 #30588]: #10311
-#34536 := (or #30518 #10405)
-#34894 := [th-lemma]: #34536
-#34869 := [unit-resolution #34894 #25597]: #10405
-#35016 := [unit-resolution #35021 #25597]: #7777
-#35035 := [th-lemma #35016 #34869 #29796 #31947]: #35029
-#35036 := [symm #35035]: #35015
-#35037 := [monotonicity #35036]: #35034
-#35039 := [symm #35037]: #35038
-#24631 := (or #11142 #11134)
-#18952 := [def-axiom]: #24631
-#33451 := [unit-resolution #18952 #38825]: #11134
-#35064 := [mp #33451 #35039]: #32106
-#32111 := (not #32106)
-#32114 := (or #31878 #32092 #32111)
-#31607 := (or #4127 #31878 #32092 #32111)
-#32078 := (+ #2033 #11148)
-#32079 := (+ #31875 #32078)
-#32080 := (= #32079 0::int)
-#32081 := (not #32080)
-#32082 := (+ #31875 #2033)
-#32083 := (>= #32082 0::int)
-#32084 := (or #31878 #32083 #32081)
-#31608 := (or #4127 #32084)
-#31636 := (iff #31608 #31607)
-#31565 := (or #4127 #32114)
-#31606 := (iff #31565 #31607)
-#31635 := [rewrite]: #31606
-#31633 := (iff #31608 #31565)
-#32115 := (iff #32084 #32114)
-#32112 := (iff #32081 #32111)
-#32109 := (iff #32080 #32106)
-#32097 := (+ #11148 #31875)
-#32098 := (+ #2033 #32097)
-#32101 := (= #32098 0::int)
-#32107 := (iff #32101 #32106)
-#32108 := [rewrite]: #32107
-#32102 := (iff #32080 #32101)
-#32099 := (= #32079 #32098)
-#32100 := [rewrite]: #32099
-#32103 := [monotonicity #32100]: #32102
-#32110 := [trans #32103 #32108]: #32109
-#32113 := [monotonicity #32110]: #32112
-#32095 := (iff #32083 #32092)
-#32085 := (+ #2033 #31875)
-#32088 := (>= #32085 0::int)
-#32093 := (iff #32088 #32092)
-#32094 := [rewrite]: #32093
-#32089 := (iff #32083 #32088)
-#32086 := (= #32082 #32085)
-#32087 := [rewrite]: #32086
-#32090 := [monotonicity #32087]: #32089
-#32096 := [trans #32090 #32094]: #32095
-#32116 := [monotonicity #32096 #32113]: #32115
-#31634 := [monotonicity #32116]: #31633
-#17991 := [trans #31634 #31635]: #31636
-#31598 := [quant-inst]: #31608
-#23660 := [mp #31598 #17991]: #31607
-#35065 := [unit-resolution #23660 #30588]: #32114
-#35066 := [unit-resolution #35065 #35064 #33436]: #32092
-#35067 := [th-lemma #35016 #29796 #35066 #38826]: false
-#35063 := [lemma #35067]: #35062
-#25287 := [unit-resolution #35063 #25354 #25346]: #31878
-#38842 := (or #31877 #11137)
-#36185 := (up_6 #8048 #11097)
-#38820 := (not #36185)
-#38838 := (iff #31878 #38820)
-#38836 := (iff #31877 #36185)
-#38834 := (iff #36185 #31877)
-#38835 := [monotonicity #8592]: #38834
-#38837 := [symm #38835]: #38836
-#38839 := [monotonicity #38837]: #38838
-#38833 := [hypothesis]: #31878
-#38840 := [mp #38833 #38839]: #38820
-#36187 := (= #6904 #11097)
-#36206 := (or #11136 #36187)
-#36190 := (iff #36185 #36206)
-#38800 := (or #6010 #36190)
-#36182 := (= #11097 #6904)
-#36183 := (ite #36182 #5970 #11136)
-#36186 := (iff #36185 #36183)
-#38801 := (or #6010 #36186)
-#38803 := (iff #38801 #38800)
-#38805 := (iff #38800 #38800)
-#38806 := [rewrite]: #38805
-#36191 := (iff #36186 #36190)
-#36209 := (iff #36183 #36206)
-#36203 := (ite #36187 true #11136)
-#36207 := (iff #36203 #36206)
-#36208 := [rewrite]: #36207
-#36204 := (iff #36183 #36203)
-#36188 := (iff #36182 #36187)
-#36202 := [rewrite]: #36188
-#36205 := [monotonicity #36202 #5976]: #36204
-#36210 := [trans #36205 #36208]: #36209
-#36192 := [monotonicity #36210]: #36191
-#38804 := [monotonicity #36192]: #38803
-#38807 := [trans #38804 #38806]: #38803
-#38802 := [quant-inst]: #38801
-#38808 := [mp #38802 #38807]: #38800
-#38827 := [unit-resolution #38808 #3851]: #36190
-#38817 := (not #36190)
-#38830 := (or #38817 #36185)
-#38828 := [hypothesis]: #11136
-#38809 := (or #36206 #11137)
-#38810 := [def-axiom]: #38809
-#38829 := [unit-resolution #38810 #38828]: #36206
-#38814 := (not #36206)
-#38818 := (or #38817 #36185 #38814)
-#38819 := [def-axiom]: #38818
-#38831 := [unit-resolution #38819 #38829]: #38830
-#38832 := [unit-resolution #38831 #38827]: #36185
-#38841 := [unit-resolution #38832 #38840]: false
-#38843 := [lemma #38841]: #38842
-#25282 := [unit-resolution #38843 #25287 #25381]: false
-#25366 := [lemma #25282]: #4130
-#5604 := (= #108 #219)
-#25448 := (iff #5604 #220)
-#25447 := [commutativity]: #1322
-#25445 := (iff #5604 #708)
-#6918 := [unit-resolution #3676 #6214]: #109
-#25446 := [monotonicity #6918]: #25445
-#25449 := [trans #25446 #25447]: #25448
-#5555 := (uf_10 #5488)
-#5558 := (* -1::int #5555)
-#5571 := (+ uf_9 #5558)
-#5572 := (<= #5571 0::int)
-#5568 := (+ #1235 #5558)
-#5569 := (+ #108 #5568)
-#5570 := (<= #5569 0::int)
-#5606 := (or #5570 #5572)
-#5486 := (+ #108 #1235)
-#7088 := (<= #5486 0::int)
-#3577 := (<= #108 0::int)
-#6919 := (or #3266 #3577)
-#6920 := [th-lemma]: #6919
-#6921 := [unit-resolution #6920 #6918]: #3577
-#5969 := (>= #185 0::int)
-#3681 := (or #4214 #3941)
-#3661 := [def-axiom]: #3681
-#7734 := [unit-resolution #3661 #6214]: #3941
-#5972 := (or #3946 #5969)
-#5973 := [quant-inst]: #5972
-#7735 := [unit-resolution #5973 #7734]: #5969
-#5140 := (not #3577)
-#25432 := (not #5969)
-#25433 := (or #7088 #25432 #5140)
-#25434 := [th-lemma]: #25433
-#25435 := [unit-resolution #25434 #7735 #6921]: #7088
-#8448 := (+ #5555 #5837)
-#8450 := (>= #8448 0::int)
-#8695 := (uf_1 #6904 uf_11)
-#8696 := (uf_10 #8695)
-#9032 := (= #8696 0::int)
-#22996 := (not #9032)
-#15055 := (>= #8696 0::int)
-#22691 := (not #15055)
-#10009 := (not #8450)
-#23412 := [hypothesis]: #10009
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-#8632 := (* -1::int #8696)
-#15323 := (+ #5555 #8632)
-#15325 := (>= #15323 0::int)
-#9629 := (= #5555 #8696)
-#23372 := (= #8696 #5555)
-#23413 := (= #8695 #5488)
-#23441 := [monotonicity #9758]: #23413
-#23440 := [monotonicity #23441]: #23372
-#23446 := [symm #23440]: #9629
-#23447 := (not #9629)
-#23449 := (or #23447 #15325)
-#23379 := [th-lemma]: #23449
-#22669 := [unit-resolution #23379 #23446]: #15325
-#22695 := (not #15325)
-#23448 := (or #8450 #23491 #22691 #22695)
-#22698 := [th-lemma]: #23448
-#22700 := [unit-resolution #22698 #22669 #22632]: #22699
-#22883 := [unit-resolution #22700 #23412]: #22691
-#23043 := (or #22996 #15055)
-#23450 := [th-lemma]: #23043
-#23034 := [unit-resolution #23450 #22883]: #22996
-#8929 := (= uf_11 #6904)
-#8788 := (<= #8696 0::int)
-#8449 := (<= #8448 0::int)
-#10435 := (or #8450 #8449)
-#10434 := [th-lemma]: #10435
-#23407 := [unit-resolution #10434 #23412]: #8449
-#10438 := (not #8449)
-#23443 := (or #10438 #8788)
-#22944 := (or #10438 #23491 #8788 #22695)
-#23411 := [th-lemma]: #22944
-#23409 := [unit-resolution #23411 #22669 #22632]: #23443
-#23442 := [unit-resolution #23409 #23407]: #8788
-#8794 := (not #8788)
-#8933 := (or #8794 #8929)
-#12371 := (or #7324 #8794 #8929)
-#8795 := (= #6904 uf_11)
-#8796 := (or #8795 #8794)
-#12524 := (or #7324 #8796)
-#13058 := (iff #12524 #12371)
-#12579 := (or #7324 #8933)
-#13029 := (iff #12579 #12371)
-#13057 := [rewrite]: #13029
-#12620 := (iff #12524 #12579)
-#8965 := (iff #8796 #8933)
-#8931 := (or #8929 #8794)
-#8934 := (iff #8931 #8933)
-#8964 := [rewrite]: #8934
-#8932 := (iff #8796 #8931)
-#8924 := (iff #8795 #8929)
-#8930 := [rewrite]: #8924
-#8928 := [monotonicity #8930]: #8932
-#8966 := [trans #8928 #8964]: #8965
-#12543 := [monotonicity #8966]: #12620
-#13028 := [trans #12543 #13057]: #13058
-#12621 := [quant-inst]: #12524
-#13055 := [mp #12621 #13028]: #12371
-#23444 := [unit-resolution #13055 #3878]: #8933
-#20374 := [unit-resolution #23444 #23442]: #8929
-#9008 := (not #8929)
-#9009 := (or #9008 #9032)
-#12859 := (or #8154 #9008 #9032)
-#9033 := (not #8795)
-#9007 := (or #9033 #9032)
-#13122 := (or #8154 #9007)
-#13134 := (iff #13122 #12859)
-#12878 := (or #8154 #9009)
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-#13150 := [rewrite]: #13147
-#13131 := (iff #13122 #12878)
-#9010 := (iff #9007 #9009)
-#9006 := (iff #9033 #9008)
-#9031 := [monotonicity #8930]: #9006
-#9011 := [monotonicity #9031]: #9010
-#13120 := [monotonicity #9011]: #13131
-#13149 := [trans #13120 #13150]: #13134
-#13056 := [quant-inst]: #13122
-#13151 := [mp #13056 #13149]: #12859
-#23445 := [unit-resolution #13151 #3872]: #9009
-#11092 := [unit-resolution #23445 #20374 #23034]: false
-#17852 := [lemma #11092]: #8450
-#25436 := (not #7088)
-#25439 := (or #5570 #10009 #25436)
-#25437 := (or #5570 #5907 #10009 #25436)
-#25438 := [th-lemma]: #25437
-#25440 := [unit-resolution #25438 #9692]: #25439
-#25441 := [unit-resolution #25440 #17852 #25435]: #5570
-#5629 := (not #5570)
-#5630 := (or #5606 #5629)
-#5631 := [def-axiom]: #5630
-#25442 := [unit-resolution #5631 #25441]: #5606
-#5609 := (not #5606)
-#5612 := (or #5604 #5609)
-#5615 := (or #4076 #5604 #5609)
-#5602 := (or #5572 #5570)
-#5603 := (not #5602)
-#5605 := (or #5604 #5603)
-#5616 := (or #4076 #5605)
-#5623 := (iff #5616 #5615)
-#5618 := (or #4076 #5612)
-#5621 := (iff #5618 #5615)
-#5622 := [rewrite]: #5621
-#5619 := (iff #5616 #5618)
-#5613 := (iff #5605 #5612)
-#5610 := (iff #5603 #5609)
-#5607 := (iff #5602 #5606)
-#5608 := [rewrite]: #5607
-#5611 := [monotonicity #5608]: #5610
-#5614 := [monotonicity #5611]: #5613
-#5620 := [monotonicity #5614]: #5619
-#5624 := [trans #5620 #5622]: #5623
-#5617 := [quant-inst]: #5616
-#5625 := [mp #5617 #5624]: #5615
-#25443 := [unit-resolution #5625 #6216]: #5612
-#25444 := [unit-resolution #25443 #25442]: #5604
-#25450 := [mp #25444 #25449]: #220
-#3717 := (or #4178 #4172)
-#3721 := [def-axiom]: #3717
-#13489 := [unit-resolution #3721 #13486]: #4172
-#3716 := (or #4175 #1324 #4169)
-#3718 := [def-axiom]: #3716
-#25451 := [unit-resolution #3718 #13489]: #4172
-#25452 := [unit-resolution #25451 #25450]: #4169
-#3723 := (or #4166 #4160)
-#3725 := [def-axiom]: #3723
-#25453 := [unit-resolution #3725 #25452]: #4160
-#25454 := (or #4163 #4157)
-#8769 := (or #4093 #1963)
-#8407 := (uf_4 uf_14 ?x65!15)
-#8699 := (>= #8407 0::int)
-#8702 := (or #3946 #8699)
-#8703 := [quant-inst]: #8702
-#8764 := [unit-resolution #8703 #7734]: #8699
-#9046 := [hypothesis]: #1964
-#8438 := (* -1::int #8407)
-#8439 := (+ #1962 #8438)
-#8763 := (>= #8439 0::int)
-#8412 := (= #1962 #8407)
-#9060 := [hypothesis]: #4088
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-#8454 := (uf_1 uf_22 ?x65!15)
-#8455 := (uf_10 #8454)
-#8429 := (* -1::int #1962)
-#8511 := (+ #8429 #8455)
-#8512 := (+ #185 #8511)
-#8532 := (<= #8512 0::int)
-#8515 := (= #8512 0::int)
-#8456 := (* -1::int #8455)
-#8460 := (+ uf_9 #8456)
-#8461 := (<= #8460 0::int)
-#8499 := (not #8461)
-#8472 := (+ #8438 #8455)
-#8473 := (+ #185 #8472)
-#8474 := (>= #8473 0::int)
-#8479 := (or #8461 #8474)
-#8482 := (not #8479)
-#9034 := (not #8412)
-#9035 := [hypothesis]: #9034
-#8485 := (or #8412 #8482)
-#8488 := (or #4076 #8412 #8482)
-#8457 := (+ #1235 #8456)
-#8458 := (+ #8407 #8457)
-#8459 := (<= #8458 0::int)
-#8462 := (or #8461 #8459)
-#8463 := (not #8462)
-#8408 := (= #8407 #1962)
-#8464 := (or #8408 #8463)
-#8489 := (or #4076 #8464)
-#8496 := (iff #8489 #8488)
-#8491 := (or #4076 #8485)
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-#8495 := [rewrite]: #8494
-#8492 := (iff #8489 #8491)
-#8486 := (iff #8464 #8485)
-#8483 := (iff #8463 #8482)
-#8480 := (iff #8462 #8479)
-#8477 := (iff #8459 #8474)
-#8465 := (+ #8407 #8456)
-#8466 := (+ #1235 #8465)
-#8469 := (<= #8466 0::int)
-#8475 := (iff #8469 #8474)
-#8476 := [rewrite]: #8475
-#8470 := (iff #8459 #8469)
-#8467 := (= #8458 #8466)
-#8468 := [rewrite]: #8467
-#8471 := [monotonicity #8468]: #8470
-#8478 := [trans #8471 #8476]: #8477
-#8481 := [monotonicity #8478]: #8480
-#8484 := [monotonicity #8481]: #8483
-#8413 := (iff #8408 #8412)
-#8414 := [rewrite]: #8413
-#8487 := [monotonicity #8414 #8484]: #8486
-#8493 := [monotonicity #8487]: #8492
-#8497 := [trans #8493 #8495]: #8496
-#8490 := [quant-inst]: #8489
-#8498 := [mp #8490 #8497]: #8488
-#9036 := [unit-resolution #8498 #6216]: #8485
-#9037 := [unit-resolution #9036 #9035]: #8482
-#8500 := (or #8479 #8499)
-#8501 := [def-axiom]: #8500
-#9038 := [unit-resolution #8501 #9037]: #8499
-#8502 := (not #8474)
-#8503 := (or #8479 #8502)
-#8504 := [def-axiom]: #8503
-#9039 := [unit-resolution #8504 #9037]: #8502
-#8518 := (or #8461 #8474 #8515)
-#8521 := (or #4068 #8461 #8474 #8515)
-#8507 := (+ #8455 #8429)
-#8508 := (+ #185 #8507)
-#8509 := (= #8508 0::int)
-#8510 := (or #8461 #8459 #8509)
-#8522 := (or #4068 #8510)
-#8529 := (iff #8522 #8521)
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-#8527 := (iff #8524 #8521)
-#8528 := [rewrite]: #8527
-#8525 := (iff #8522 #8524)
-#8519 := (iff #8510 #8518)
-#8516 := (iff #8509 #8515)
-#8513 := (= #8508 #8512)
-#8514 := [rewrite]: #8513
-#8517 := [monotonicity #8514]: #8516
-#8520 := [monotonicity #8478 #8517]: #8519
-#8526 := [monotonicity #8520]: #8525
-#8530 := [trans #8526 #8528]: #8529
-#8523 := [quant-inst]: #8522
-#8531 := [mp #8523 #8530]: #8521
-#9040 := [unit-resolution #8531 #6220]: #8518
-#9041 := [unit-resolution #9040 #9039 #9038]: #8515
-#9042 := (not #8515)
-#9043 := (or #9042 #8532)
-#9044 := [th-lemma]: #9043
-#9045 := [unit-resolution #9044 #9041]: #8532
-#8903 := (uf_1 #8349 ?x65!15)
-#8904 := (uf_10 #8903)
-#8910 := (* -1::int #8904)
-#8982 := (+ #8455 #8910)
-#8986 := (>= #8982 0::int)
-#8981 := (= #8455 #8904)
-#9052 := (= #8904 #8455)
-#9050 := (= #8903 #8454)
-#9051 := [monotonicity #9049]: #9050
-#9053 := [monotonicity #9051]: #9052
-#9054 := [symm #9053]: #8981
-#9055 := (not #8981)
-#9056 := (or #9055 #8986)
-#9057 := [th-lemma]: #9056
-#9058 := [unit-resolution #9057 #9054]: #8986
-#8974 := (>= #8904 0::int)
-#8935 := (<= #8904 0::int)
-#8936 := (not #8935)
-#8859 := (= ?x65!15 #8349)
-#8887 := (not #8859)
-#8612 := (up_6 uf_15 ?x65!15)
-#8867 := (or #8612 #8859)
-#8890 := (not #8867)
-#8861 := (uf_7 uf_15 #8349 uf_8)
-#8862 := (up_6 #8861 ?x65!15)
-#8872 := (iff #8862 #8867)
-#8875 := (or #6010 #8872)
-#8860 := (ite #8859 #5970 #8612)
-#8863 := (iff #8862 #8860)
-#8876 := (or #6010 #8863)
-#8878 := (iff #8876 #8875)
-#8880 := (iff #8875 #8875)
-#8881 := [rewrite]: #8880
-#8873 := (iff #8863 #8872)
-#8870 := (iff #8860 #8867)
-#8864 := (ite #8859 true #8612)
-#8868 := (iff #8864 #8867)
-#8869 := [rewrite]: #8868
-#8865 := (iff #8860 #8864)
-#8866 := [monotonicity #5976]: #8865
-#8871 := [trans #8866 #8869]: #8870
-#8874 := [monotonicity #8871]: #8873
-#8879 := [monotonicity #8874]: #8878
-#8882 := [trans #8879 #8881]: #8878
-#8877 := [quant-inst]: #8876
-#8883 := [mp #8877 #8882]: #8875
-#9059 := [unit-resolution #8883 #3851]: #8872
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-#8409 := (up_6 uf_23 ?x65!15)
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-#9067 := (iff #8862 #8409)
-#9065 := (= #8861 uf_23)
-#9063 := (= #8861 #191)
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-#9066 := [trans #9064 #7413]: #9065
-#9068 := [monotonicity #9066]: #9067
-#9070 := [symm #9068]: #9069
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-#8411 := (or #8410 #8408)
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-#8425 := [rewrite]: #8424
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-#8423 := [monotonicity #8417]: #8422
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-#8420 := [quant-inst]: #8419
-#8428 := [mp #8420 #8427]: #8418
-#9061 := [unit-resolution #8428 #9060]: #8415
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-#9073 := [mp #9062 #9072]: #8896
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-#8894 := (or #8893 #8862 #8890)
-#8895 := [def-axiom]: #8894
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-#8888 := (or #8867 #8887)
-#8889 := [def-axiom]: #8888
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-#8941 := (or #8859 #8936)
-#8944 := (or #7324 #8859 #8936)
-#8937 := (= #8349 ?x65!15)
-#8938 := (or #8937 #8936)
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-#8939 := (iff #8937 #8859)
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-#8953 := [trans #8949 #8951]: #8952
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-#8954 := [mp #8946 #8953]: #8944
-#9076 := [unit-resolution #8954 #3878]: #8941
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-#9078 := (or #8974 #8935)
-#9079 := [th-lemma]: #9078
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-#9083 := [lemma #9081]: #9082
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-#8766 := (or #9034 #8763)
-#8767 := [th-lemma]: #8766
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-#8770 := [lemma #8768]: #8769
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-#25456 := [unit-resolution #25455 #25453]: #4157
-#3742 := (or #4154 #4148)
-#3743 := [def-axiom]: #3742
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-#6820 := (+ #1978 #5831)
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-#6819 := (= #1978 #5830)
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-#6353 := [rewrite]: #6352
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-#6336 := (ite #6333 true #6328)
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-#6335 := [rewrite]: #6334
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-#6343 := [trans #6338 #6341]: #6342
-#6346 := [monotonicity #6343]: #6345
-#6351 := [monotonicity #6346]: #6350
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-#6282 := [quant-inst]: #6281
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-#7493 := [mp #7458 #7492]: #6301
-#6298 := (not #6277)
-#6299 := (or #6298 #6264 #6295)
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-#6483 := (uf_4 uf_14 ?x68!16)
-#6494 := (* -1::int #6483)
-#6696 := (+ #185 #6494)
-#6697 := (<= #6696 0::int)
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-#6290 := (or #6272 #6289)
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-#7496 := [unit-resolution #6291 #7494]: #6289
-#6702 := (or #6257 #6697)
-#3682 := (or #4202 #4053)
-#3683 := [def-axiom]: #3682
-#7497 := [unit-resolution #3683 #6215]: #4053
-#6705 := (or #4058 #6257 #6697)
-#6685 := (+ #6483 #1235)
-#6686 := (>= #6685 0::int)
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-#6708 := (or #4058 #6702)
-#6711 := (iff #6708 #6705)
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-#11555 := (+ #11552 #1235)
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-#11558 := (or #11557 #11556)
-#24959 := (or #4058 #11558)
-#26166 := (iff #24959 #26052)
-#24944 := (or #4058 #11572)
-#26155 := (iff #24944 #26052)
-#24069 := [rewrite]: #26155
-#24260 := (iff #24959 #24944)
-#11573 := (iff #11558 #11572)
-#11570 := (iff #11556 #11567)
-#11559 := (+ #1235 #11552)
-#11562 := (>= #11559 0::int)
-#11568 := (iff #11562 #11567)
-#11569 := [rewrite]: #11568
-#11563 := (iff #11556 #11562)
-#11560 := (= #11555 #11559)
-#11561 := [rewrite]: #11560
-#11564 := [monotonicity #11561]: #11563
-#11571 := [trans #11564 #11569]: #11570
-#11574 := [monotonicity #11571]: #11573
-#24990 := [monotonicity #11574]: #24260
-#24992 := [trans #24990 #24069]: #26166
-#24970 := [quant-inst]: #24959
-#26321 := [mp #24970 #24992]: #26052
-#30243 := [unit-resolution #26321 #7497]: #11572
-#30133 := [unit-resolution #30243 #30237]: #11567
-#22774 := (not #11567)
-#22822 := (or #15413 #2546 #22878 #22774 #22794)
-#22808 := [hypothesis]: #11404
-#22807 := [hypothesis]: #22657
-#17228 := (+ #10897 #11565)
-#17121 := (>= #17228 0::int)
-#17229 := (= #10897 #11552)
-#22789 := [monotonicity #22805]: #17229
-#22790 := (not #17229)
-#22787 := (or #22790 #17121)
-#22771 := [th-lemma]: #22787
-#22781 := [unit-resolution #22771 #22789]: #17121
-#22802 := [hypothesis]: #11567
-#22779 := [hypothesis]: #3599
-#22829 := [unit-resolution #15163 #7037]: #11370
-#18268 := (+ #11385 #18070)
-#18269 := (<= #18268 0::int)
-#17117 := (= #11385 #18066)
-#22830 := (= #11384 #18065)
-#22818 := [monotonicity #22732]: #22830
-#22816 := [monotonicity #22818]: #17117
-#22804 := (not #17117)
-#22797 := (or #22804 #18269)
-#22821 := [th-lemma]: #22797
-#22813 := [unit-resolution #22821 #22816]: #18269
-#22819 := [th-lemma #22813 #22829 #22779 #22810 #22802 #22781 #22807 #22808]: false
-#18715 := [lemma #22819]: #22822
-#30242 := [unit-resolution #18715 #30210 #30138 #30133 #30156]: #15413
-#30247 := (or #17430 #11404)
-#18270 := (>= #18268 0::int)
-#22014 := (uf_1 #6904 ?x72!18)
-#23089 := (uf_3 #22014)
-#25777 := (uf_1 #23089 ?x71!19)
-#25872 := (uf_3 #25777)
-#27572 := (= #25872 #11538)
-#26806 := (= #11538 #25872)
-#26804 := (= #2007 #25777)
-#23115 := (= ?x72!18 #23089)
-#17768 := (or #5007 #23115)
-#17877 := [quant-inst]: #17768
-#26799 := [unit-resolution #17877 #3831]: #23115
-#27568 := [monotonicity #26799]: #26804
-#27571 := [monotonicity #27568]: #26806
-#27573 := [symm #27571]: #27572
-#25873 := (= ?x71!19 #25872)
-#26816 := (not #25873)
-#27263 := [hypothesis]: #26816
-#27265 := (or #5007 #25873)
-#27266 := [quant-inst]: #27265
-#27264 := [unit-resolution #27266 #3831 #27263]: false
-#27269 := [lemma #27264]: #25873
-#27574 := [trans #27269 #27573]: #11539
-#28371 := [monotonicity #27574]: #22830
-#28372 := [monotonicity #28371]: #17117
-#28370 := [hypothesis]: #22804
-#28373 := [unit-resolution #28370 #28372]: false
-#28374 := [lemma #28373]: #17117
-#20936 := (or #22804 #18270)
-#20938 := [th-lemma]: #20936
-#30213 := [unit-resolution #20938 #28374]: #18270
-#21441 := (not #18270)
-#30244 := (or #17430 #11404 #21441)
-#18023 := (+ #11332 #11659)
-#18024 := (<= #18023 0::int)
-#17225 := (= #11332 #11646)
-#26817 := (or #26816 #17225)
-#26812 := (= #11646 #11332)
-#26810 := (= #11538 ?x71!19)
-#26808 := (= #25872 ?x71!19)
-#26794 := [hypothesis]: #25873
-#26809 := [symm #26794]: #26808
-#26802 := (= #25777 #2007)
-#26800 := (= #23089 ?x72!18)
-#26801 := [symm #26799]: #26800
-#26803 := [monotonicity #26801]: #26802
-#26805 := [symm #26803]: #26804
-#26807 := [monotonicity #26805]: #26806
-#26811 := [trans #26807 #26809]: #26810
-#26813 := [monotonicity #26811]: #26812
-#26814 := [symm #26813]: #17225
-#21448 := (not #17225)
-#26793 := [hypothesis]: #21448
-#26815 := [unit-resolution #26793 #26814]: false
-#26818 := [lemma #26815]: #26817
-#30239 := [unit-resolution #26818 #27269]: #17225
-#21454 := (or #21448 #18024)
-#20933 := [th-lemma]: #21454
-#30238 := [unit-resolution #20933 #30239]: #18024
-#22247 := (not #18024)
-#22226 := (or #17430 #22247 #11404 #21441)
-#22243 := [th-lemma]: #22226
-#30246 := [unit-resolution #22243 #30238]: #30244
-#30265 := [unit-resolution #30246 #30213]: #30247
-#30266 := [unit-resolution #30265 #30242]: #17430
-#25738 := (or #18075 #18086 #18113)
-#26503 := [hypothesis]: #17430
-#26498 := [hypothesis]: #17499
-#18095 := (= #18092 0::int)
-#22231 := (not #18095)
-#25748 := (not #18113)
-#25749 := [hypothesis]: #25748
-#22367 := (or #22231 #18113)
-#22447 := [th-lemma]: #22367
-#25750 := [unit-resolution #22447 #25749]: #22231
-#26505 := (or #18095 #18086 #18075)
-#26497 := [hypothesis]: #22231
-#17115 := (or #4068 #18075 #18086 #18095)
-#18067 := (+ #18066 #18049)
-#18068 := (+ #185 #18067)
-#18069 := (= #18068 0::int)
-#18071 := (+ #1235 #18070)
-#18072 := (+ #11646 #18071)
-#18073 := (<= #18072 0::int)
-#18076 := (or #18075 #18073 #18069)
-#17396 := (or #4068 #18076)
-#17345 := (iff #17396 #17115)
-#18098 := (or #18075 #18086 #18095)
-#17361 := (or #4068 #18098)
-#17360 := (iff #17361 #17115)
-#17359 := [rewrite]: #17360
-#17363 := (iff #17396 #17361)
-#18099 := (iff #18076 #18098)
-#18096 := (iff #18069 #18095)
-#18093 := (= #18068 #18092)
-#18094 := [rewrite]: #18093
-#18097 := [monotonicity #18094]: #18096
-#18089 := (iff #18073 #18086)
-#18077 := (+ #11646 #18070)
-#18078 := (+ #1235 #18077)
-#18081 := (<= #18078 0::int)
-#18087 := (iff #18081 #18086)
-#18088 := [rewrite]: #18087
-#18082 := (iff #18073 #18081)
-#18079 := (= #18072 #18078)
-#18080 := [rewrite]: #18079
-#18083 := [monotonicity #18080]: #18082
-#18090 := [trans #18083 #18088]: #18089
-#18100 := [monotonicity #18090 #18097]: #18099
-#17346 := [monotonicity #18100]: #17363
-#17364 := [trans #17346 #17359]: #17345
-#17381 := [quant-inst]: #17396
-#17317 := [mp #17381 #17364]: #17115
-#26504 := [unit-resolution #17317 #6220 #26503 #26498 #26497]: false
-#26506 := [lemma #26504]: #26505
-#25751 := [unit-resolution #26506 #25750 #26498 #26503]: false
-#25739 := [lemma #25751]: #25738
-#30267 := [unit-resolution #25739 #30266 #30169]: #18113
-#25874 := (uf_2 #25777)
-#25875 := (= #23089 #25874)
-#28275 := (not #25875)
-#28360 := [hypothesis]: #28275
-#28362 := (or #8156 #25875)
-#28363 := [quant-inst]: #28362
-#28361 := [unit-resolution #28363 #3837 #28360]: false
-#28364 := [lemma #28361]: #25875
-#28276 := (or #28275 #17229)
-#28264 := (= #11552 #10897)
-#28260 := (= #11547 #23089)
-#28258 := (= #25874 #23089)
-#28251 := [hypothesis]: #25875
-#28259 := [symm #28251]: #28258
-#28256 := (= #11547 #25874)
-#28257 := [monotonicity #27568]: #28256
-#28261 := [trans #28257 #28259]: #28260
-#28263 := [trans #28261 #26801]: #28262
-#28265 := [monotonicity #28263]: #28264
-#28273 := [symm #28265]: #17229
-#28210 := [hypothesis]: #22790
-#28274 := [unit-resolution #28210 #28273]: false
-#28277 := [lemma #28274]: #28276
-#26555 := [unit-resolution #28277 #28364]: #17229
-#30245 := [unit-resolution #22771 #26555]: #17121
-#18258 := (+ #2003 #18049)
-#18261 := (<= #18258 0::int)
-#17226 := (= #2003 #18030)
-#27788 := [monotonicity #27574]: #17226
-#21452 := (not #17226)
-#27567 := [hypothesis]: #21452
-#27789 := [unit-resolution #27567 #27788]: false
-#27872 := [lemma #27789]: #17226
-#22901 := (or #21452 #18261)
-#22182 := [th-lemma]: #22901
-#30269 := [unit-resolution #22182 #27872]: #18261
-[th-lemma #30269 #30245 #30138 #30133 #30156 #30210 #30267]: false
+#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